LMFDB - Embedded newform 4013.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.76303 q^{2} -0.741544 q^{3} +5.63435 q^{4} +1.49530 q^{5} +2.04891 q^{6} +0.791604 q^{7} -10.0418 q^{8} -2.45011 q^{9} +O(q^{10})$	\(q-2.76303 q^{2} -0.741544 q^{3} +5.63435 q^{4} +1.49530 q^{5} +2.04891 q^{6} +0.791604 q^{7} -10.0418 q^{8} -2.45011 q^{9} -4.13156 q^{10} -4.54540 q^{11} -4.17811 q^{12} +1.47647 q^{13} -2.18723 q^{14} -1.10883 q^{15} +16.4772 q^{16} -3.75689 q^{17} +6.76974 q^{18} -1.69556 q^{19} +8.42504 q^{20} -0.587009 q^{21} +12.5591 q^{22} -4.62469 q^{23} +7.44644 q^{24} -2.76408 q^{25} -4.07955 q^{26} +4.04150 q^{27} +4.46017 q^{28} -10.5881 q^{29} +3.06373 q^{30} +5.58446 q^{31} -25.4433 q^{32} +3.37061 q^{33} +10.3804 q^{34} +1.18369 q^{35} -13.8048 q^{36} -4.37625 q^{37} +4.68488 q^{38} -1.09487 q^{39} -15.0155 q^{40} -3.56906 q^{41} +1.62192 q^{42} +6.70865 q^{43} -25.6103 q^{44} -3.66366 q^{45} +12.7782 q^{46} -11.0634 q^{47} -12.2185 q^{48} -6.37336 q^{49} +7.63723 q^{50} +2.78590 q^{51} +8.31897 q^{52} +8.01148 q^{53} -11.1668 q^{54} -6.79673 q^{55} -7.94914 q^{56} +1.25733 q^{57} +29.2553 q^{58} +1.14706 q^{59} -6.24754 q^{60} +7.60807 q^{61} -15.4300 q^{62} -1.93952 q^{63} +37.3463 q^{64} +2.20777 q^{65} -9.31310 q^{66} -15.0773 q^{67} -21.1676 q^{68} +3.42941 q^{69} -3.27056 q^{70} +8.91325 q^{71} +24.6036 q^{72} +10.7102 q^{73} +12.0917 q^{74} +2.04968 q^{75} -9.55336 q^{76} -3.59815 q^{77} +3.02516 q^{78} -9.34204 q^{79} +24.6383 q^{80} +4.35339 q^{81} +9.86142 q^{82} +17.6410 q^{83} -3.30741 q^{84} -5.61768 q^{85} -18.5362 q^{86} +7.85155 q^{87} +45.6440 q^{88} +10.1264 q^{89} +10.1228 q^{90} +1.16878 q^{91} -26.0571 q^{92} -4.14112 q^{93} +30.5686 q^{94} -2.53537 q^{95} +18.8673 q^{96} +6.03117 q^{97} +17.6098 q^{98} +11.1367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) $ 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * 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 $

$2$	−2.76303	−1.95376	−0.976879	−	0.213791i	$-0.931419\pi$
$2$	−2.76303	−1.95376	−0.976879	+	0.213791i	$0.931419\pi$
$3$	−0.741544	−0.428130	−0.214065	−	0.976819i	$-0.568670\pi$
$3$	−0.741544	−0.428130	−0.214065	+	0.976819i	$0.568670\pi$
$4$	5.63435	2.81717
$5$	1.49530	0.668719	0.334359	−	0.942446i	$-0.391480\pi$
$5$	1.49530	0.668719	0.334359	+	0.942446i	$0.391480\pi$
$6$	2.04891	0.836463
$7$	0.791604	0.299198	0.149599	−	0.988747i	$-0.452202\pi$
$7$	0.791604	0.299198	0.149599	+	0.988747i	$0.452202\pi$
$8$	−10.0418	−3.55032
$9$	−2.45011	−0.816704
$10$	−4.13156	−1.30652
$11$	−4.54540	−1.37049	−0.685244	−	0.728313i	$-0.740304\pi$
$11$	−4.54540	−1.37049	−0.685244	+	0.728313i	$0.740304\pi$
$12$	−4.17811	−1.20612
$13$	1.47647	0.409500	0.204750	−	0.978814i	$-0.434362\pi$
$13$	1.47647	0.409500	0.204750	+	0.978814i	$0.434362\pi$
$14$	−2.18723	−0.584561
$15$	−1.10883	−0.286299
$16$	16.4772	4.11929
$17$	−3.75689	−0.911180	−0.455590	−	0.890190i	$-0.650572\pi$
$17$	−3.75689	−0.911180	−0.455590	+	0.890190i	$0.650572\pi$
$18$	6.76974	1.59564
$19$	−1.69556	−0.388988	−0.194494	−	0.980904i	$-0.562306\pi$
$19$	−1.69556	−0.388988	−0.194494	+	0.980904i	$0.562306\pi$
$20$	8.42504	1.88390
$21$	−0.587009	−0.128096
$22$	12.5591	2.67760
$23$	−4.62469	−0.964315	−0.482158	−	0.876085i	$-0.660147\pi$
$23$	−4.62469	−0.964315	−0.482158	+	0.876085i	$0.660147\pi$
$24$	7.44644	1.52000
$25$	−2.76408	−0.552815
$26$	−4.07955	−0.800065
$27$	4.04150	0.777786
$28$	4.46017	0.842893
$29$	−10.5881	−1.96616	−0.983082	−	0.183164i	$-0.941366\pi$
$29$	−10.5881	−1.96616	−0.983082	+	0.183164i	$0.941366\pi$
$30$	3.06373	0.559359
$31$	5.58446	1.00300	0.501499	−	0.865158i	$-0.332782\pi$
$31$	5.58446	1.00300	0.501499	+	0.865158i	$0.332782\pi$
$32$	−25.4433	−4.49778
$33$	3.37061	0.586748
$34$	10.3804	1.78023
$35$	1.18369	0.200079
$36$	−13.8048	−2.30080
$37$	−4.37625	−0.719451	−0.359726	−	0.933058i	$-0.617130\pi$
$37$	−4.37625	−0.719451	−0.359726	+	0.933058i	$0.617130\pi$
$38$	4.68488	0.759988
$39$	−1.09487	−0.175320
$40$	−15.0155	−2.37416
$41$	−3.56906	−0.557393	−0.278696	−	0.960379i	$-0.589902\pi$
$41$	−3.56906	−0.557393	−0.278696	+	0.960379i	$0.589902\pi$
$42$	1.62192	0.250268
$43$	6.70865	1.02306	0.511530	−	0.859266i	$-0.329079\pi$
$43$	6.70865	1.02306	0.511530	+	0.859266i	$0.329079\pi$
$44$	−25.6103	−3.86090
$45$	−3.66366	−0.546146
$46$	12.7782	1.88404
$47$	−11.0634	−1.61376	−0.806882	−	0.590712i	$-0.798847\pi$
$47$	−11.0634	−1.61376	−0.806882	+	0.590712i	$0.798847\pi$
$48$	−12.2185	−1.76359
$49$	−6.37336	−0.910480
$50$	7.63723	1.08007
$51$	2.78590	0.390104
$52$	8.31897	1.15363
$53$	8.01148	1.10046	0.550230	−	0.835013i	$-0.314540\pi$
$53$	8.01148	1.10046	0.550230	+	0.835013i	$0.314540\pi$
$54$	−11.1668	−1.51961
$55$	−6.79673	−0.916471
$56$	−7.94914	−1.06225
$57$	1.25733	0.166537
$58$	29.2553	3.84141
$59$	1.14706	0.149334	0.0746671	−	0.997209i	$-0.476211\pi$
$59$	1.14706	0.149334	0.0746671	+	0.997209i	$0.476211\pi$
$60$	−6.24754	−0.806553
$61$	7.60807	0.974114	0.487057	−	0.873370i	$-0.338070\pi$
$61$	7.60807	0.974114	0.487057	+	0.873370i	$0.338070\pi$
$62$	−15.4300	−1.95962
$63$	−1.93952	−0.244357
$64$	37.3463	4.66829
$65$	2.20777	0.273841
$66$	−9.31310	−1.14636
$67$	−15.0773	−1.84199	−0.920995	−	0.389574i	$-0.872622\pi$
$67$	−15.0773	−1.84199	−0.920995	+	0.389574i	$0.872622\pi$
$68$	−21.1676	−2.56695
$69$	3.42941	0.412853
$70$	−3.27056	−0.390907
$71$	8.91325	1.05781	0.528904	−	0.848682i	$-0.322603\pi$
$71$	8.91325	1.05781	0.528904	+	0.848682i	$0.322603\pi$
$72$	24.6036	2.89956
$73$	10.7102	1.25353	0.626767	−	0.779207i	$-0.284378\pi$
$73$	10.7102	1.25353	0.626767	+	0.779207i	$0.284378\pi$
$74$	12.0917	1.40563
$75$	2.04968	0.236677
$76$	−9.55336	−1.09585
$77$	−3.59815	−0.410048
$78$	3.02516	0.342532
$79$	−9.34204	−1.05106	−0.525531	−	0.850775i	$-0.676133\pi$
$79$	−9.34204	−1.05106	−0.525531	+	0.850775i	$0.676133\pi$
$80$	24.6383	2.75465
$81$	4.35339	0.483710
$82$	9.86142	1.08901
$83$	17.6410	1.93635	0.968176	−	0.250269i	$-0.0805190\pi$
$83$	17.6410	1.93635	0.968176	+	0.250269i	$0.0805190\pi$
$84$	−3.30741	−0.360868
$85$	−5.61768	−0.609323
$86$	−18.5362	−1.99881
$87$	7.85155	0.841775
$88$	45.6440	4.86567
$89$	10.1264	1.07340	0.536700	−	0.843773i	$-0.319671\pi$
$89$	10.1264	1.07340	0.536700	+	0.843773i	$0.319671\pi$
$90$	10.1228	1.06704
$91$	1.16878	0.122522
$92$	−26.0571	−2.71664
$93$	−4.14112	−0.429414
$94$	30.5686	3.15291
$95$	−2.53537	−0.260123
$96$	18.8673	1.92564
$97$	6.03117	0.612373	0.306186	−	0.951972i	$-0.400947\pi$
$97$	6.03117	0.612373	0.306186	+	0.951972i	$0.400947\pi$
$98$	17.6098	1.77886
$99$	11.1367	1.11928
$100$	−15.5738	−1.55738
$101$	13.4082	1.33416	0.667081	−	0.744986i	$-0.267544\pi$
$101$	13.4082	1.33416	0.667081	+	0.744986i	$0.267544\pi$
$102$	−7.69753	−0.762169
$103$	−6.62535	−0.652816	−0.326408	−	0.945229i	$-0.605838\pi$
$103$	−6.62535	−0.652816	−0.326408	+	0.945229i	$0.605838\pi$
$104$	−14.8265	−1.45386
$105$	−0.877755	−0.0856601
$106$	−22.1360	−2.15004
$107$	6.54216	0.632455	0.316227	−	0.948683i	$-0.397584\pi$
$107$	6.54216	0.632455	0.316227	+	0.948683i	$0.397584\pi$
$108$	22.7712	2.19116
$109$	0.783325	0.0750290	0.0375145	−	0.999296i	$-0.488056\pi$
$109$	0.783325	0.0750290	0.0375145	+	0.999296i	$0.488056\pi$
$110$	18.7796	1.79056
$111$	3.24518	0.308019
$112$	13.0434	1.23248
$113$	17.5337	1.64943	0.824714	−	0.565550i	$-0.191336\pi$
$113$	17.5337	1.64943	0.824714	+	0.565550i	$0.191336\pi$
$114$	−3.47404	−0.325374
$115$	−6.91531	−0.644856
$116$	−59.6571	−5.53903
$117$	−3.61753	−0.334441
$118$	−3.16936	−0.291763
$119$	−2.97397	−0.272623
$120$	11.1347	1.01645
$121$	9.66062	0.878238
$122$	−21.0213	−1.90318
$123$	2.64661	0.238637
$124$	31.4648	2.82562
$125$	−11.6096	−1.03840
$126$	5.35895	0.477414
$127$	11.7816	1.04545	0.522724	−	0.852502i	$-0.324916\pi$
$127$	11.7816	1.04545	0.522724	+	0.852502i	$0.324916\pi$
$128$	−52.3025	−4.62293
$129$	−4.97476	−0.438003
$130$	−6.10015	−0.535018
$131$	14.1101	1.23280	0.616401	−	0.787432i	$-0.288590\pi$
$131$	14.1101	1.23280	0.616401	+	0.787432i	$0.288590\pi$
$132$	18.9912	1.65297
$133$	−1.34221	−0.116384
$134$	41.6592	3.59880
$135$	6.04325	0.520120
$136$	37.7260	3.23498
$137$	20.0438	1.71246	0.856230	−	0.516595i	$-0.172801\pi$
$137$	20.0438	1.71246	0.856230	+	0.516595i	$0.172801\pi$
$138$	−9.47557	−0.806614
$139$	−1.74770	−0.148238	−0.0741192	−	0.997249i	$-0.523615\pi$
$139$	−1.74770	−0.148238	−0.0741192	+	0.997249i	$0.523615\pi$
$140$	6.66930	0.563659
$141$	8.20400	0.690902
$142$	−24.6276	−2.06670
$143$	−6.71116	−0.561215
$144$	−40.3709	−3.36424
$145$	−15.8324	−1.31481
$146$	−29.5926	−2.44910
$147$	4.72613	0.389804
$148$	−24.6573	−2.02682
$149$	−9.94228	−0.814504	−0.407252	−	0.913316i	$-0.633513\pi$
$149$	−9.94228	−0.814504	−0.407252	+	0.913316i	$0.633513\pi$
$150$	−5.66334	−0.462410
$151$	−12.4403	−1.01238	−0.506189	−	0.862422i	$-0.668946\pi$
$151$	−12.4403	−1.01238	−0.506189	+	0.862422i	$0.668946\pi$
$152$	17.0265	1.38103
$153$	9.20481	0.744165
$154$	9.94181	0.801134
$155$	8.35044	0.670724
$156$	−6.16888	−0.493905
$157$	−0.131606	−0.0105033	−0.00525165	−	0.999986i	$-0.501672\pi$
$157$	−0.131606	−0.0105033	−0.00525165	+	0.999986i	$0.501672\pi$
$158$	25.8124	2.05352
$159$	−5.94086	−0.471141
$160$	−38.0454	−3.00775
$161$	−3.66093	−0.288521
$162$	−12.0286	−0.945053
$163$	0.985623	0.0771999	0.0386000	−	0.999255i	$-0.487710\pi$
$163$	0.985623	0.0771999	0.0386000	+	0.999255i	$0.487710\pi$
$164$	−20.1093	−1.57027
$165$	5.04007	0.392369
$166$	−48.7427	−3.78317
$167$	−11.7854	−0.911982	−0.455991	−	0.889984i	$-0.650715\pi$
$167$	−11.7854	−0.911982	−0.455991	+	0.889984i	$0.650715\pi$
$168$	5.89464	0.454781
$169$	−10.8200	−0.832310
$170$	15.5218	1.19047
$171$	4.15431	0.317688
$172$	37.7989	2.88214
$173$	2.96528	0.225446	0.112723	−	0.993626i	$-0.464043\pi$
$173$	2.96528	0.225446	0.112723	+	0.993626i	$0.464043\pi$
$174$	−21.6941	−1.64463
$175$	−2.18805	−0.165401
$176$	−74.8952	−5.64544
$177$	−0.850594	−0.0639345
$178$	−27.9797	−2.09717
$179$	−1.64176	−0.122711	−0.0613556	−	0.998116i	$-0.519542\pi$
$179$	−1.64176	−0.122711	−0.0613556	+	0.998116i	$0.519542\pi$
$180$	−20.6423	−1.53859
$181$	−15.2539	−1.13381	−0.566907	−	0.823782i	$-0.691860\pi$
$181$	−15.2539	−1.13381	−0.566907	+	0.823782i	$0.691860\pi$
$182$	−3.22939	−0.239378
$183$	−5.64172	−0.417048
$184$	46.4403	3.42363
$185$	−6.54381	−0.481111
$186$	11.4420	0.838971
$187$	17.0766	1.24876
$188$	−62.3351	−4.54625
$189$	3.19927	0.232712
$190$	7.00531	0.508218
$191$	−6.33740	−0.458558	−0.229279	−	0.973361i	$-0.573637\pi$
$191$	−6.33740	−0.458558	−0.229279	+	0.973361i	$0.573637\pi$
$192$	−27.6939	−1.99864
$193$	25.8923	1.86377	0.931884	−	0.362756i	$-0.118164\pi$
$193$	25.8923	1.86377	0.931884	+	0.362756i	$0.118164\pi$
$194$	−16.6643	−1.19643
$195$	−1.63716	−0.117239
$196$	−35.9097	−2.56498
$197$	−3.96918	−0.282792	−0.141396	−	0.989953i	$-0.545159\pi$
$197$	−3.96918	−0.282792	−0.141396	+	0.989953i	$0.545159\pi$
$198$	−30.7711	−2.18681
$199$	20.0750	1.42308	0.711539	−	0.702647i	$-0.247999\pi$
$199$	20.0750	1.42308	0.711539	+	0.702647i	$0.247999\pi$
$200$	27.7563	1.96267
$201$	11.1805	0.788612
$202$	−37.0472	−2.60663
$203$	−8.38160	−0.588273
$204$	15.6967	1.09899
$205$	−5.33681	−0.372739
$206$	18.3061	1.27544
$207$	11.3310	0.787560
$208$	24.3281	1.68685
$209$	7.70698	0.533103
$210$	2.42526	0.167359
$211$	−17.8312	−1.22755	−0.613775	−	0.789481i	$-0.710350\pi$
$211$	−17.8312	−1.22755	−0.613775	+	0.789481i	$0.710350\pi$
$212$	45.1394	3.10019
$213$	−6.60956	−0.452880
$214$	−18.0762	−1.23566
$215$	10.0315	0.684139
$216$	−40.5840	−2.76139
$217$	4.42068	0.300095
$218$	−2.16435	−0.146588
$219$	−7.94207	−0.536676
$220$	−38.2951	−2.58186
$221$	−5.54695	−0.373128
$222$	−8.96654	−0.601795
$223$	14.1680	0.948761	0.474380	−	0.880320i	$-0.342672\pi$
$223$	14.1680	0.948761	0.474380	+	0.880320i	$0.342672\pi$
$224$	−20.1410	−1.34573
$225$	6.77230	0.451487
$226$	−48.4461	−3.22258
$227$	−21.0096	−1.39445	−0.697227	−	0.716850i	$-0.745583\pi$
$227$	−21.0096	−1.39445	−0.697227	+	0.716850i	$0.745583\pi$
$228$	7.08423	0.469165
$229$	−21.3576	−1.41135	−0.705673	−	0.708537i	$-0.749355\pi$
$229$	−21.3576	−1.41135	−0.705673	+	0.708537i	$0.749355\pi$
$230$	19.1072	1.25989
$231$	2.66819	0.175554
$232$	106.324	6.98051
$233$	−0.0127939	−0.000838157 0	−0.000419078	−	1.00000i	$-0.500133\pi$
$233$	−0.0127939	−0.000838157 0	−0.000419078		1.00000i	$0.500133\pi$
$234$	9.99535	0.653416
$235$	−16.5431	−1.07915
$236$	6.46292	0.420700
$237$	6.92753	0.449992
$238$	8.21718	0.532640
$239$	−1.28351	−0.0830231	−0.0415115	−	0.999138i	$-0.513217\pi$
$239$	−1.28351	−0.0830231	−0.0415115	+	0.999138i	$0.513217\pi$
$240$	−18.2704	−1.17935
$241$	1.41120	0.0909033	0.0454516	−	0.998967i	$-0.485527\pi$
$241$	1.41120	0.0909033	0.0454516	+	0.998967i	$0.485527\pi$
$242$	−26.6926	−1.71586
$243$	−15.3527	−0.984877
$244$	42.8665	2.74425
$245$	−9.53009	−0.608855
$246$	−7.31267	−0.466239
$247$	−2.50345	−0.159291
$248$	−56.0781	−3.56096
$249$	−13.0816	−0.829011
$250$	32.0778	2.02878
$251$	9.63953	0.608442	0.304221	−	0.952602i	$-0.401604\pi$
$251$	9.63953	0.608442	0.304221	+	0.952602i	$0.401604\pi$
$252$	−10.9279	−0.688395
$253$	21.0211	1.32158
$254$	−32.5530	−2.04255
$255$	4.16576	0.260870
$256$	69.8209	4.36381
$257$	−3.94673	−0.246190	−0.123095	−	0.992395i	$-0.539282\pi$
$257$	−3.94673	−0.246190	−0.123095	+	0.992395i	$0.539282\pi$
$258$	13.7454	0.855752
$259$	−3.46426	−0.215259
$260$	12.4394	0.771456
$261$	25.9421	1.60578
$262$	−38.9866	−2.40860
$263$	18.0329	1.11196	0.555978	−	0.831197i	$-0.312344\pi$
$263$	18.0329	1.11196	0.555978	+	0.831197i	$0.312344\pi$
$264$	−33.8470	−2.08314
$265$	11.9796	0.735899
$266$	3.70857	0.227387
$267$	−7.50920	−0.459555
$268$	−84.9510	−5.18921
$269$	−26.2197	−1.59864	−0.799322	−	0.600902i	$-0.794808\pi$
$269$	−26.2197	−1.59864	−0.799322	+	0.600902i	$0.794808\pi$
$270$	−16.6977	−1.01619
$271$	21.8046	1.32453	0.662267	−	0.749268i	$-0.269594\pi$
$271$	21.8046	1.32453	0.662267	+	0.749268i	$0.269594\pi$
$272$	−61.9029	−3.75342
$273$	−0.866704	−0.0524553
$274$	−55.3818	−3.34573
$275$	12.5638	0.757627
$276$	19.3225	1.16308
$277$	−10.5886	−0.636209	−0.318104	−	0.948056i	$-0.603046\pi$
$277$	−10.5886	−0.636209	−0.318104	+	0.948056i	$0.603046\pi$
$278$	4.82896	0.289622
$279$	−13.6825	−0.819153
$280$	−11.8864	−0.710346
$281$	0.0611906	0.00365033	0.00182516	−	0.999998i	$-0.499419\pi$
$281$	0.0611906	0.00365033	0.00182516	+	0.999998i	$0.499419\pi$
$282$	−22.6679	−1.34986
$283$	28.6724	1.70440	0.852198	−	0.523219i	$-0.175269\pi$
$283$	28.6724	1.70440	0.852198	+	0.523219i	$0.175269\pi$
$284$	50.2203	2.98003
$285$	1.88009	0.111367
$286$	18.5431	1.09648
$287$	−2.82528	−0.166771
$288$	62.3390	3.67336
$289$	−2.88577	−0.169751
$290$	43.7455	2.56882
$291$	−4.47238	−0.262175
$292$	60.3449	3.53142
$293$	14.8283	0.866277	0.433138	−	0.901327i	$-0.357406\pi$
$293$	14.8283	0.866277	0.433138	+	0.901327i	$0.357406\pi$
$294$	−13.0584	−0.761584
$295$	1.71520	0.0998626
$296$	43.9455	2.55428
$297$	−18.3702	−1.06595
$298$	27.4708	1.59134
$299$	−6.82824	−0.394887
$300$	11.5486	0.666760
$301$	5.31060	0.306098
$302$	34.3730	1.97794
$303$	−9.94273	−0.571195
$304$	−27.9380	−1.60235
$305$	11.3764	0.651408
$306$	−25.4332	−1.45392
$307$	24.2257	1.38263	0.691317	−	0.722551i	$-0.257031\pi$
$307$	24.2257	1.38263	0.691317	+	0.722551i	$0.257031\pi$
$308$	−20.2732	−1.15518
$309$	4.91299	0.279490
$310$	−23.0725	−1.31043
$311$	−7.99318	−0.453252	−0.226626	−	0.973982i	$-0.572769\pi$
$311$	−7.99318	−0.453252	−0.226626	+	0.973982i	$0.572769\pi$
$312$	10.9945	0.622440
$313$	−10.7564	−0.607987	−0.303993	−	0.952674i	$-0.598320\pi$
$313$	−10.7564	−0.607987	−0.303993	+	0.952674i	$0.598320\pi$
$314$	0.363632	0.0205209
$315$	−2.90016	−0.163406
$316$	−52.6363	−2.96102
$317$	7.23490	0.406352	0.203176	−	0.979142i	$-0.434874\pi$
$317$	7.23490	0.406352	0.203176	+	0.979142i	$0.434874\pi$
$318$	16.4148	0.920495
$319$	48.1272	2.69461
$320$	55.8440	3.12178
$321$	−4.85130	−0.270773
$322$	10.1153	0.563701
$323$	6.37003	0.354438
$324$	24.5285	1.36270
$325$	−4.08109	−0.226378
$326$	−2.72331	−0.150830
$327$	−0.580870	−0.0321222
$328$	35.8398	1.97892
$329$	−8.75784	−0.482836
$330$	−13.9259	−0.766595
$331$	−4.89424	−0.269012	−0.134506	−	0.990913i	$-0.542945\pi$
$331$	−4.89424	−0.269012	−0.134506	+	0.990913i	$0.542945\pi$
$332$	99.3956	5.45504
$333$	10.7223	0.587579
$334$	32.5634	1.78179
$335$	−22.5452	−1.23177
$336$	−9.67224	−0.527664
$337$	27.9553	1.52282	0.761411	−	0.648269i	$-0.224507\pi$
$337$	27.9553	1.52282	0.761411	+	0.648269i	$0.224507\pi$
$338$	29.8961	1.62613
$339$	−13.0020	−0.706170
$340$	−31.6520	−1.71657
$341$	−25.3836	−1.37460
$342$	−11.4785	−0.620686
$343$	−10.5864	−0.571612
$344$	−67.3670	−3.63219
$345$	5.12800	0.276082
$346$	−8.19317	−0.440467
$347$	−7.95586	−0.427093	−0.213546	−	0.976933i	$-0.568501\pi$
$347$	−7.95586	−0.427093	−0.213546	+	0.976933i	$0.568501\pi$
$348$	44.2384	2.37143
$349$	−4.92054	−0.263390	−0.131695	−	0.991290i	$-0.542042\pi$
$349$	−4.92054	−0.263390	−0.131695	+	0.991290i	$0.542042\pi$
$350$	6.04566	0.323154
$351$	5.96717	0.318504
$352$	115.650	6.16416
$353$	−29.0355	−1.54540	−0.772702	−	0.634769i	$-0.781095\pi$
$353$	−29.0355	−1.54540	−0.772702	+	0.634769i	$0.781095\pi$
$354$	2.35022	0.124913
$355$	13.3280	0.707376
$356$	57.0559	3.02395
$357$	2.20533	0.116718
$358$	4.53625	0.239748
$359$	26.9431	1.42200	0.711000	−	0.703192i	$-0.248242\pi$
$359$	26.9431	1.42200	0.711000	+	0.703192i	$0.248242\pi$
$360$	36.7898	1.93899
$361$	−16.1251	−0.848689
$362$	42.1470	2.21520
$363$	−7.16377	−0.376000
$364$	6.58533	0.345165
$365$	16.0150	0.838261
$366$	15.5882	0.814810
$367$	−4.16088	−0.217196	−0.108598	−	0.994086i	$-0.534636\pi$
$367$	−4.16088	−0.217196	−0.108598	+	0.994086i	$0.534636\pi$
$368$	−76.2018	−3.97229
$369$	8.74459	0.455225
$370$	18.0808	0.939974
$371$	6.34192	0.329256
$372$	−23.3325	−1.20973
$373$	−9.23283	−0.478058	−0.239029	−	0.971012i	$-0.576829\pi$
$373$	−9.23283	−0.478058	−0.239029	+	0.971012i	$0.576829\pi$
$374$	−47.1831	−2.43978
$375$	8.60904	0.444569
$376$	111.097	5.72938
$377$	−15.6331	−0.805145
$378$	−8.83967	−0.454664
$379$	29.8834	1.53501	0.767504	−	0.641044i	$-0.221499\pi$
$379$	29.8834	1.53501	0.767504	+	0.641044i	$0.221499\pi$
$380$	−14.2851	−0.732813
$381$	−8.73657	−0.447588
$382$	17.5104	0.895912
$383$	32.4959	1.66046	0.830231	−	0.557420i	$-0.188209\pi$
$383$	32.4959	1.66046	0.830231	+	0.557420i	$0.188209\pi$
$384$	38.7846	1.97922
$385$	−5.38032	−0.274207
$386$	−71.5412	−3.64135
$387$	−16.4370	−0.835537
$388$	33.9817	1.72516
$389$	−19.0280	−0.964758	−0.482379	−	0.875963i	$-0.660227\pi$
$389$	−19.0280	−0.964758	−0.482379	+	0.875963i	$0.660227\pi$
$390$	4.52352	0.229058
$391$	17.3745	0.878665
$392$	64.0001	3.23249
$393$	−10.4632	−0.527800
$394$	10.9670	0.552508
$395$	−13.9692	−0.702865
$396$	62.7482	3.15322
$397$	−3.93635	−0.197560	−0.0987799	−	0.995109i	$-0.531494\pi$
$397$	−3.93635	−0.197560	−0.0987799	+	0.995109i	$0.531494\pi$
$398$	−55.4678	−2.78035
$399$	0.995308	0.0498277
$400$	−45.5441	−2.27721
$401$	18.3749	0.917599	0.458800	−	0.888540i	$-0.348280\pi$
$401$	18.3749	0.917599	0.458800	+	0.888540i	$0.348280\pi$
$402$	−30.8921	−1.54076
$403$	8.24530	0.410728
$404$	75.5462	3.75856
$405$	6.50963	0.323466
$406$	23.1586	1.14934
$407$	19.8918	0.985999
$408$	−27.9755	−1.38499
$409$	−9.00621	−0.445329	−0.222664	−	0.974895i	$-0.571475\pi$
$409$	−9.00621	−0.445329	−0.222664	+	0.974895i	$0.571475\pi$
$410$	14.7458	0.728242
$411$	−14.8634	−0.733156
$412$	−37.3295	−1.83909
$413$	0.908016	0.0446805
$414$	−31.3080	−1.53870
$415$	26.3786	1.29488
$416$	−37.5664	−1.84184
$417$	1.29600	0.0634654
$418$	−21.2946	−1.04155
$419$	13.3691	0.653125	0.326563	−	0.945176i	$-0.394110\pi$
$419$	13.3691	0.653125	0.326563	+	0.945176i	$0.394110\pi$
$420$	−4.94557	−0.241319
$421$	21.8121	1.06306	0.531529	−	0.847040i	$-0.321618\pi$
$421$	21.8121	1.06306	0.531529	+	0.847040i	$0.321618\pi$
$422$	49.2681	2.39833
$423$	27.1066	1.31797
$424$	−80.4498	−3.90699
$425$	10.3843	0.503714
$426$	18.2624	0.884818
$427$	6.02258	0.291453
$428$	36.8608	1.78173
$429$	4.97662	0.240273
$430$	−27.7172	−1.33664
$431$	−4.38198	−0.211073	−0.105536	−	0.994415i	$-0.533656\pi$
$431$	−4.38198	−0.211073	−0.105536	+	0.994415i	$0.533656\pi$
$432$	66.5924	3.20393
$433$	−37.9739	−1.82491	−0.912455	−	0.409178i	$-0.865815\pi$
$433$	−37.9739	−1.82491	−0.912455	+	0.409178i	$0.865815\pi$
$434$	−12.2145	−0.586314
$435$	11.7404	0.562911
$436$	4.41353	0.211370
$437$	7.84144	0.375107
$438$	21.9442	1.04853
$439$	20.8390	0.994592	0.497296	−	0.867581i	$-0.334326\pi$
$439$	20.8390	0.994592	0.497296	+	0.867581i	$0.334326\pi$
$440$	68.2515	3.25376
$441$	15.6155	0.743593
$442$	15.3264	0.729003
$443$	22.3398	1.06140	0.530698	−	0.847561i	$-0.321930\pi$
$443$	22.3398	1.06140	0.530698	+	0.847561i	$0.321930\pi$
$444$	18.2845	0.867743
$445$	15.1421	0.717803
$446$	−39.1467	−1.85365
$447$	7.37264	0.348714
$448$	29.5635	1.39674
$449$	−35.4774	−1.67428	−0.837142	−	0.546986i	$-0.815775\pi$
$449$	−35.4774	−1.67428	−0.837142	+	0.546986i	$0.815775\pi$
$450$	−18.7121	−0.882096
$451$	16.2228	0.763900
$452$	98.7907	4.64672
$453$	9.22503	0.433430
$454$	58.0502	2.72443
$455$	1.74768	0.0819326
$456$	−12.6259	−0.591261
$457$	3.35799	0.157080	0.0785401	−	0.996911i	$-0.474974\pi$
$457$	3.35799	0.157080	0.0785401	+	0.996911i	$0.474974\pi$
$458$	59.0116	2.75743
$459$	−15.1835	−0.708703
$460$	−38.9632	−1.81667
$461$	−26.4549	−1.23213	−0.616063	−	0.787697i	$-0.711273\pi$
$461$	−26.4549	−1.23213	−0.616063	+	0.787697i	$0.711273\pi$
$462$	−7.37229	−0.342990
$463$	−42.3126	−1.96643	−0.983216	−	0.182444i	$-0.941599\pi$
$463$	−42.3126	−1.96643	−0.983216	+	0.182444i	$0.941599\pi$
$464$	−174.462	−8.09921
$465$	−6.19222	−0.287157
$466$	0.0353500	0.00163756
$467$	16.4481	0.761128	0.380564	−	0.924755i	$-0.375730\pi$
$467$	16.4481	0.761128	0.380564	+	0.924755i	$0.375730\pi$
$468$	−20.3824	−0.942177
$469$	−11.9353	−0.551120
$470$	45.7092	2.10841
$471$	0.0975916	0.00449678
$472$	−11.5185	−0.530184
$473$	−30.4935	−1.40209
$474$	−19.1410	−0.879175
$475$	4.68665	0.215038
$476$	−16.7564	−0.768028
$477$	−19.6290	−0.898751
$478$	3.54637	0.162207
$479$	−23.0187	−1.05175	−0.525875	−	0.850562i	$-0.676262\pi$
$479$	−23.0187	−1.05175	−0.525875	+	0.850562i	$0.676262\pi$
$480$	28.2123	1.28771
$481$	−6.46142	−0.294615
$482$	−3.89919	−0.177603
$483$	2.71474	0.123525
$484$	54.4313	2.47415
$485$	9.01841	0.409505
$486$	42.4201	1.92421
$487$	18.2131	0.825313	0.412656	−	0.910887i	$-0.364601\pi$
$487$	18.2131	0.825313	0.412656	+	0.910887i	$0.364601\pi$
$488$	−76.3988	−3.45841
$489$	−0.730882	−0.0330516
$490$	26.3320	1.18956
$491$	−37.2365	−1.68046	−0.840231	−	0.542229i	$-0.817581\pi$
$491$	−37.2365	−1.68046	−0.840231	+	0.542229i	$0.817581\pi$
$492$	14.9119	0.672281
$493$	39.7784	1.79153
$494$	6.91711	0.311215
$495$	16.6528	0.748486
$496$	92.0160	4.13164
$497$	7.05576	0.316494
$498$	36.1448	1.61969
$499$	−29.0431	−1.30015	−0.650074	−	0.759871i	$-0.725262\pi$
$499$	−29.0431	−1.30015	−0.650074	+	0.759871i	$0.725262\pi$
$500$	−65.4127	−2.92534
$501$	8.73939	0.390447
$502$	−26.6343	−1.18875
$503$	4.26158	0.190014	0.0950072	−	0.995477i	$-0.469713\pi$
$503$	4.26158	0.190014	0.0950072	+	0.995477i	$0.469713\pi$
$504$	19.4763	0.867543
$505$	20.0492	0.892179
$506$	−58.0819	−2.58205
$507$	8.02352	0.356337
$508$	66.3816	2.94521
$509$	−30.8315	−1.36658	−0.683291	−	0.730146i	$-0.739452\pi$
$509$	−30.8315	−1.36658	−0.683291	+	0.730146i	$0.739452\pi$
$510$	−11.5101	−0.509677
$511$	8.47823	0.375055
$512$	−88.3123	−3.90289
$513$	−6.85259	−0.302549
$514$	10.9049	0.480997
$515$	−9.90690	−0.436550
$516$	−28.0295	−1.23393
$517$	50.2876	2.21165
$518$	9.57186	0.420563
$519$	−2.19889	−0.0965204
$520$	−22.1700	−0.972221
$521$	−20.9688	−0.918659	−0.459330	−	0.888266i	$-0.651910\pi$
$521$	−20.9688	−0.918659	−0.459330	+	0.888266i	$0.651910\pi$
$522$	−71.6788	−3.13730
$523$	5.19413	0.227123	0.113562	−	0.993531i	$-0.463774\pi$
$523$	5.19413	0.227123	0.113562	+	0.993531i	$0.463774\pi$
$524$	79.5010	3.47302
$525$	1.62254	0.0708133
$526$	−49.8255	−2.17249
$527$	−20.9802	−0.913912
$528$	55.5381	2.41698
$529$	−1.61222	−0.0700964
$530$	−33.0999	−1.43777
$531$	−2.81042	−0.121962
$532$	−7.56248	−0.327875
$533$	−5.26962	−0.228253
$534$	20.7481	0.897860
$535$	9.78250	0.422934
$536$	151.404	6.53965
$537$	1.21744	0.0525364
$538$	72.4459	3.12337
$539$	28.9695	1.24780
$540$	34.0498	1.46527
$541$	−34.2179	−1.47114	−0.735572	−	0.677447i	$-0.763086\pi$
$541$	−34.2179	−1.47114	−0.735572	+	0.677447i	$0.763086\pi$
$542$	−60.2468	−2.58782
$543$	11.3114	0.485420
$544$	95.5878	4.09829
$545$	1.17131	0.0501733
$546$	2.39473	0.102485
$547$	30.7407	1.31438	0.657189	−	0.753726i	$-0.271745\pi$
$547$	30.7407	1.31438	0.657189	+	0.753726i	$0.271745\pi$
$548$	112.934	4.82430
$549$	−18.6406	−0.795563
$550$	−34.7142	−1.48022
$551$	17.9528	0.764814
$552$	−34.4375	−1.46576
$553$	−7.39520	−0.314476
$554$	29.2567	1.24300
$555$	4.85252	0.205978
$556$	−9.84717	−0.417613
$557$	6.01329	0.254791	0.127396	−	0.991852i	$-0.459338\pi$
$557$	6.01329	0.254791	0.127396	+	0.991852i	$0.459338\pi$
$558$	37.8053	1.60043
$559$	9.90515	0.418943
$560$	19.5038	0.824186
$561$	−12.6630	−0.534633
$562$	−0.169072	−0.00713186
$563$	37.1248	1.56462	0.782312	−	0.622887i	$-0.214041\pi$
$563$	37.1248	1.56462	0.782312	+	0.622887i	$0.214041\pi$
$564$	46.2242	1.94639
$565$	26.2181	1.10300
$566$	−79.2227	−3.32998
$567$	3.44616	0.144725
$568$	−89.5052	−3.75555
$569$	−1.10748	−0.0464281	−0.0232141	−	0.999731i	$-0.507390\pi$
$569$	−1.10748	−0.0464281	−0.0232141	+	0.999731i	$0.507390\pi$
$570$	−5.19474	−0.217584
$571$	−15.3862	−0.643891	−0.321945	−	0.946758i	$-0.604337\pi$
$571$	−15.3862	−0.643891	−0.321945	+	0.946758i	$0.604337\pi$
$572$	−37.8130	−1.58104
$573$	4.69946	0.196323
$574$	7.80634	0.325830
$575$	12.7830	0.533088
$576$	−91.5028	−3.81262
$577$	−21.2693	−0.885452	−0.442726	−	0.896657i	$-0.645989\pi$
$577$	−21.2693	−0.885452	−0.442726	+	0.896657i	$0.645989\pi$
$578$	7.97346	0.331652
$579$	−19.2003	−0.797936
$580$	−89.2054	−3.70405
$581$	13.9647	0.579353
$582$	12.3573	0.512227
$583$	−36.4153	−1.50817
$584$	−107.550	−4.45044
$585$	−5.40929	−0.223647
$586$	−40.9710	−1.69250
$587$	0.628355	0.0259350	0.0129675	−	0.999916i	$-0.495872\pi$
$587$	0.628355	0.0259350	0.0129675	+	0.999916i	$0.495872\pi$
$588$	26.6286	1.09815
$589$	−9.46877	−0.390154
$590$	−4.73914	−0.195107
$591$	2.94332	0.121072
$592$	−72.1082	−2.96363
$593$	−12.7267	−0.522621	−0.261311	−	0.965255i	$-0.584155\pi$
$593$	−12.7267	−0.522621	−0.261311	+	0.965255i	$0.584155\pi$
$594$	50.7574	2.08260
$595$	−4.44698	−0.182308
$596$	−56.0183	−2.29460
$597$	−14.8865	−0.609263
$598$	18.8666	0.771514
$599$	36.1455	1.47686	0.738432	−	0.674328i	$-0.235567\pi$
$599$	36.1455	1.47686	0.738432	+	0.674328i	$0.235567\pi$
$600$	−20.5825	−0.840279
$601$	−29.6753	−1.21048	−0.605241	−	0.796042i	$-0.706923\pi$
$601$	−29.6753	−1.21048	−0.605241	+	0.796042i	$0.706923\pi$
$602$	−14.6733	−0.598041
$603$	36.9412	1.50436
$604$	−70.0930	−2.85205
$605$	14.4455	0.587294
$606$	27.4721	1.11598
$607$	11.1887	0.454134	0.227067	−	0.973879i	$-0.427086\pi$
$607$	11.1887	0.454134	0.227067	+	0.973879i	$0.427086\pi$
$608$	43.1406	1.74958
$609$	6.21532	0.251858
$610$	−31.4332	−1.27269
$611$	−16.3348	−0.660837
$612$	51.8631	2.09644
$613$	41.5884	1.67974	0.839871	−	0.542787i	$-0.182631\pi$
$613$	41.5884	1.67974	0.839871	+	0.542787i	$0.182631\pi$
$614$	−66.9364	−2.70133
$615$	3.95748	0.159581
$616$	36.1320	1.45580
$617$	45.3086	1.82405	0.912027	−	0.410130i	$-0.134517\pi$
$617$	45.3086	1.82405	0.912027	+	0.410130i	$0.134517\pi$
$618$	−13.5747	−0.546056
$619$	6.24301	0.250928	0.125464	−	0.992098i	$-0.459958\pi$
$619$	6.24301	0.250928	0.125464	+	0.992098i	$0.459958\pi$
$620$	47.0493	1.88954
$621$	−18.6907	−0.750031
$622$	22.0854	0.885544
$623$	8.01613	0.321160
$624$	−18.0404	−0.722192
$625$	−3.53950	−0.141580
$626$	29.7202	1.18786
$627$	−5.71506	−0.228238
$628$	−0.741514	−0.0295896
$629$	16.4411	0.655550
$630$	8.01325	0.319255
$631$	24.1763	0.962445	0.481223	−	0.876598i	$-0.340193\pi$
$631$	24.1763	0.962445	0.481223	+	0.876598i	$0.340193\pi$
$632$	93.8111	3.73160
$633$	13.2226	0.525551
$634$	−19.9903	−0.793915
$635$	17.6170	0.699111
$636$	−33.4729	−1.32729
$637$	−9.41011	−0.372842
$638$	−132.977	−5.26461
$639$	−21.8385	−0.863916
$640$	−78.2080	−3.09144
$641$	46.8041	1.84865	0.924325	−	0.381607i	$-0.124629\pi$
$641$	46.8041	1.84865	0.924325	+	0.381607i	$0.124629\pi$
$642$	13.4043	0.529025
$643$	−6.23773	−0.245992	−0.122996	−	0.992407i	$-0.539250\pi$
$643$	−6.23773	−0.245992	−0.122996	+	0.992407i	$0.539250\pi$
$644$	−20.6269	−0.812815
$645$	−7.43876	−0.292901
$646$	−17.6006	−0.692486
$647$	2.34797	0.0923082	0.0461541	−	0.998934i	$-0.485303\pi$
$647$	2.34797	0.0923082	0.0461541	+	0.998934i	$0.485303\pi$
$648$	−43.7160	−1.71733
$649$	−5.21383	−0.204661
$650$	11.2762	0.442288
$651$	−3.27813	−0.128480
$652$	5.55334	0.217486
$653$	−6.03809	−0.236289	−0.118144	−	0.992996i	$-0.537695\pi$
$653$	−6.03809	−0.236289	−0.118144	+	0.992996i	$0.537695\pi$
$654$	1.60496	0.0627590
$655$	21.0988	0.824398
$656$	−58.8079	−2.29606
$657$	−26.2412	−1.02377
$658$	24.1982	0.943344
$659$	14.5848	0.568145	0.284072	−	0.958803i	$-0.408314\pi$
$659$	14.5848	0.568145	0.284072	+	0.958803i	$0.408314\pi$
$660$	28.3975	1.10537
$661$	−2.99975	−0.116677	−0.0583384	−	0.998297i	$-0.518580\pi$
$661$	−2.99975	−0.116677	−0.0583384	+	0.998297i	$0.518580\pi$
$662$	13.5229	0.525584
$663$	4.11331	0.159748
$664$	−177.148	−6.87467
$665$	−2.00701	−0.0778285
$666$	−29.6261	−1.14799
$667$	48.9668	1.89600
$668$	−66.4030	−2.56921
$669$	−10.5062	−0.406193
$670$	62.2930	2.40659
$671$	−34.5817	−1.33501
$672$	14.9354	0.576147
$673$	−49.9218	−1.92434	−0.962172	−	0.272442i	$-0.912169\pi$
$673$	−49.9218	−1.92434	−0.962172	+	0.272442i	$0.912169\pi$
$674$	−77.2414	−2.97523
$675$	−11.1710	−0.429972
$676$	−60.9638	−2.34476
$677$	−4.37552	−0.168165	−0.0840825	−	0.996459i	$-0.526796\pi$
$677$	−4.37552	−0.168165	−0.0840825	+	0.996459i	$0.526796\pi$
$678$	35.9249	1.37969
$679$	4.77430	0.183221
$680$	56.4117	2.16329
$681$	15.5795	0.597009
$682$	70.1356	2.68563
$683$	21.1782	0.810360	0.405180	−	0.914237i	$-0.367209\pi$
$683$	21.1782	0.810360	0.405180	+	0.914237i	$0.367209\pi$
$684$	23.4068	0.894982
$685$	29.9716	1.14515
$686$	29.2506	1.11679
$687$	15.8376	0.604240
$688$	110.540	4.21428
$689$	11.8287	0.450639
$690$	−14.1688	−0.539398
$691$	17.1152	0.651094	0.325547	−	0.945526i	$-0.394452\pi$
$691$	17.1152	0.651094	0.325547	+	0.945526i	$0.394452\pi$
$692$	16.7074	0.635121
$693$	8.81588	0.334888
$694$	21.9823	0.834436
$695$	−2.61334	−0.0991298
$696$	−78.8439	−2.98857
$697$	13.4086	0.507885
$698$	13.5956	0.514601
$699$	0.00948724	0.000358840 0
$700$	−12.3283	−0.465964
$701$	−9.13005	−0.344837	−0.172419	−	0.985024i	$-0.555158\pi$
$701$	−9.13005	−0.344837	−0.172419	+	0.985024i	$0.555158\pi$
$702$	−16.4875	−0.622279
$703$	7.42019	0.279858
$704$	−169.754	−6.39784
$705$	12.2675	0.462019
$706$	80.2261	3.01935
$707$	10.6140	0.399179
$708$	−4.79254	−0.180115
$709$	18.4119	0.691473	0.345736	−	0.938332i	$-0.387629\pi$
$709$	18.4119	0.691473	0.345736	+	0.938332i	$0.387629\pi$
$710$	−36.8257	−1.38204
$711$	22.8891	0.858407
$712$	−101.688	−3.81091
$713$	−25.8264	−0.967206
$714$	−6.09339	−0.228040
$715$	−10.0352	−0.375295
$716$	−9.25027	−0.345699
$717$	0.951776	0.0355447
$718$	−74.4445	−2.77825
$719$	28.4010	1.05918	0.529589	−	0.848255i	$-0.322346\pi$
$719$	28.4010	1.05918	0.529589	+	0.848255i	$0.322346\pi$
$720$	−60.3667	−2.24973
$721$	−5.24466	−0.195321
$722$	44.5541	1.65813
$723$	−1.04646	−0.0389184
$724$	−85.9458	−3.19415
$725$	29.2664	1.08693
$726$	19.7937	0.734614
$727$	−36.4501	−1.35186	−0.675929	−	0.736967i	$-0.736257\pi$
$727$	−36.4501	−1.35186	−0.675929	+	0.736967i	$0.736257\pi$
$728$	−11.7367	−0.434991
$729$	−1.67547	−0.0620544
$730$	−44.2498	−1.63776
$731$	−25.2037	−0.932192
$732$	−31.7874	−1.17490
$733$	−10.5286	−0.388884	−0.194442	−	0.980914i	$-0.562290\pi$
$733$	−10.5286	−0.388884	−0.194442	+	0.980914i	$0.562290\pi$
$734$	11.4967	0.424349
$735$	7.06698	0.260669
$736$	117.667	4.33728
$737$	68.5325	2.52443
$738$	−24.1616	−0.889400
$739$	26.5167	0.975433	0.487717	−	0.873002i	$-0.337830\pi$
$739$	26.5167	0.975433	0.487717	+	0.873002i	$0.337830\pi$
$740$	−36.8701	−1.35537
$741$	1.85642	0.0681971
$742$	−17.5229	−0.643287
$743$	21.1740	0.776799	0.388399	−	0.921491i	$-0.373028\pi$
$743$	21.1740	0.776799	0.388399	+	0.921491i	$0.373028\pi$
$744$	41.5843	1.52456
$745$	−14.8667	−0.544674
$746$	25.5106	0.934010
$747$	−43.2225	−1.58143
$748$	96.2152	3.51798
$749$	5.17880	0.189229
$750$	−23.7871	−0.868581
$751$	−3.42631	−0.125028	−0.0625139	−	0.998044i	$-0.519912\pi$
$751$	−3.42631	−0.125028	−0.0625139	+	0.998044i	$0.519912\pi$
$752$	−182.294	−6.64757
$753$	−7.14813	−0.260492
$754$	43.1947	1.57306
$755$	−18.6020	−0.676996
$756$	18.0258	0.655591
$757$	37.2666	1.35448	0.677239	−	0.735763i	$-0.263176\pi$
$757$	37.2666	1.35448	0.677239	+	0.735763i	$0.263176\pi$
$758$	−82.5688	−2.99903
$759$	−15.5880	−0.565810
$760$	25.4597	0.923521
$761$	43.9879	1.59456	0.797281	−	0.603608i	$-0.206271\pi$
$761$	43.9879	1.59456	0.797281	+	0.603608i	$0.206271\pi$
$762$	24.1394	0.874479
$763$	0.620084	0.0224485
$764$	−35.7071	−1.29184
$765$	13.7640	0.497637
$766$	−89.7871	−3.24414
$767$	1.69360	0.0611524
$768$	−51.7752	−1.86828
$769$	−10.4991	−0.378607	−0.189303	−	0.981919i	$-0.560623\pi$
$769$	−10.4991	−0.378607	−0.189303	+	0.981919i	$0.560623\pi$
$770$	14.8660	0.535733
$771$	2.92667	0.105402
$772$	145.886	5.25056
$773$	−45.2200	−1.62645	−0.813225	−	0.581949i	$-0.802290\pi$
$773$	−45.2200	−1.62645	−0.813225	+	0.581949i	$0.802290\pi$
$774$	45.4158	1.63244
$775$	−15.4359	−0.554472
$776$	−60.5639	−2.17412
$777$	2.56890	0.0921587
$778$	52.5750	1.88490
$779$	6.05154	0.216819
$780$	−9.22432	−0.330284
$781$	−40.5142	−1.44971
$782$	−48.0062	−1.71670
$783$	−42.7919	−1.52926
$784$	−105.015	−3.75053
$785$	−0.196791	−0.00702376
$786$	28.9102	1.03119
$787$	5.35085	0.190737	0.0953685	−	0.995442i	$-0.469597\pi$
$787$	5.35085	0.190737	0.0953685	+	0.995442i	$0.469597\pi$
$788$	−22.3637	−0.796675
$789$	−13.3722	−0.476062
$790$	38.5972	1.37323
$791$	13.8797	0.493506
$792$	−111.833	−3.97381
$793$	11.2331	0.398900
$794$	10.8763	0.385984
$795$	−8.88337	−0.315061
$796$	113.109	4.00906
$797$	49.0032	1.73578	0.867892	−	0.496753i	$-0.165475\pi$
$797$	49.0032	1.73578	0.867892	+	0.496753i	$0.165475\pi$
$798$	−2.75007	−0.0973513
$799$	41.5640	1.47043
$800$	70.3272	2.48644
$801$	−24.8109	−0.876651
$802$	−50.7705	−1.79277
$803$	−48.6821	−1.71795
$804$	62.9948	2.22166
$805$	−5.47418	−0.192940
$806$	−22.7820	−0.802463
$807$	19.4431	0.684428
$808$	−134.642	−4.73670
$809$	−0.822929	−0.0289326	−0.0144663	−	0.999895i	$-0.504605\pi$
$809$	−0.822929	−0.0289326	−0.0144663	+	0.999895i	$0.504605\pi$
$810$	−17.9863	−0.631975
$811$	51.7928	1.81869	0.909345	−	0.416042i	$-0.136583\pi$
$811$	51.7928	1.81869	0.909345	+	0.416042i	$0.136583\pi$
$812$	−47.2248	−1.65727
$813$	−16.1691	−0.567073
$814$	−54.9617	−1.92641
$815$	1.47380	0.0516250
$816$	45.9037	1.60695
$817$	−11.3749	−0.397958
$818$	24.8845	0.870065
$819$	−2.86365	−0.100064
$820$	−30.0694	−1.05007
$821$	−3.31842	−0.115814	−0.0579068	−	0.998322i	$-0.518443\pi$
$821$	−3.31842	−0.115814	−0.0579068	+	0.998322i	$0.518443\pi$
$822$	41.0680	1.43241
$823$	−7.42091	−0.258677	−0.129338	−	0.991601i	$-0.541285\pi$
$823$	−7.42091	−0.258677	−0.129338	+	0.991601i	$0.541285\pi$
$824$	66.5306	2.31770
$825$	−9.31662	−0.324363
$826$	−2.50888	−0.0872950
$827$	5.43011	0.188823	0.0944117	−	0.995533i	$-0.469903\pi$
$827$	5.43011	0.188823	0.0944117	+	0.995533i	$0.469903\pi$
$828$	63.8429	2.21869
$829$	48.8926	1.69811	0.849055	−	0.528305i	$-0.177172\pi$
$829$	48.8926	1.69811	0.849055	+	0.528305i	$0.177172\pi$
$830$	−72.8850	−2.52987
$831$	7.85193	0.272380
$832$	55.1409	1.91167
$833$	23.9440	0.829612
$834$	−3.58089	−0.123996
$835$	−17.6227	−0.609859
$836$	43.4238	1.50184
$837$	22.5696	0.780118
$838$	−36.9394	−1.27605
$839$	−11.1829	−0.386078	−0.193039	−	0.981191i	$-0.561834\pi$
$839$	−11.1829	−0.386078	−0.193039	+	0.981191i	$0.561834\pi$
$840$	8.81425	0.304121
$841$	83.1083	2.86580
$842$	−60.2676	−2.07696
$843$	−0.0453755	−0.00156282
$844$	−100.467	−3.45822
$845$	−16.1792	−0.556581
$846$	−74.8964	−2.57499
$847$	7.64738	0.262767
$848$	132.006	4.53312
$849$	−21.2618	−0.729704
$850$	−28.6922	−0.984136
$851$	20.2388	0.693778
$852$	−37.2406	−1.27584
$853$	22.5491	0.772066	0.386033	−	0.922485i	$-0.373845\pi$
$853$	22.5491	0.772066	0.386033	+	0.922485i	$0.373845\pi$
$854$	−16.6406	−0.569429
$855$	6.21194	0.212444
$856$	−65.6952	−2.24542
$857$	−1.51916	−0.0518934	−0.0259467	−	0.999663i	$-0.508260\pi$
$857$	−1.51916	−0.0518934	−0.0259467	+	0.999663i	$0.508260\pi$
$858$	−13.7506	−0.469436
$859$	53.4199	1.82266	0.911332	−	0.411671i	$-0.135055\pi$
$859$	53.4199	1.82266	0.911332	+	0.411671i	$0.135055\pi$
$860$	56.5207	1.92734
$861$	2.09507	0.0713997
$862$	12.1076	0.412385
$863$	13.9996	0.476551	0.238276	−	0.971198i	$-0.423418\pi$
$863$	13.9996	0.476551	0.238276	+	0.971198i	$0.423418\pi$
$864$	−102.829	−3.49831
$865$	4.43399	0.150760
$866$	104.923	3.56543
$867$	2.13992	0.0726755
$868$	24.9076	0.845420
$869$	42.4633	1.44047
$870$	−32.4392	−1.09979
$871$	−22.2613	−0.754296
$872$	−7.86601	−0.266377
$873$	−14.7771	−0.500127
$874$	−21.6661	−0.732868
$875$	−9.19023	−0.310686
$876$	−44.7484	−1.51191
$877$	0.749647	0.0253138	0.0126569	−	0.999920i	$-0.495971\pi$
$877$	0.749647	0.0253138	0.0126569	+	0.999920i	$0.495971\pi$
$878$	−57.5789	−1.94319
$879$	−10.9958	−0.370879
$880$	−111.991	−3.77521
$881$	−22.5396	−0.759378	−0.379689	−	0.925114i	$-0.623969\pi$
$881$	−22.5396	−0.759378	−0.379689	+	0.925114i	$0.623969\pi$
$882$	−43.1460	−1.45280
$883$	−7.49186	−0.252121	−0.126061	−	0.992023i	$-0.540233\pi$
$883$	−7.49186	−0.252121	−0.126061	+	0.992023i	$0.540233\pi$
$884$	−31.2535	−1.05117
$885$	−1.27189	−0.0427542
$886$	−61.7256	−2.07371
$887$	28.7077	0.963909	0.481955	−	0.876196i	$-0.339927\pi$
$887$	28.7077	0.963909	0.481955	+	0.876196i	$0.339927\pi$
$888$	−32.5875	−1.09357
$889$	9.32637	0.312796
$890$	−41.8380	−1.40241
$891$	−19.7879	−0.662919
$892$	79.8275	2.67282
$893$	18.7587	0.627735
$894$	−20.3708	−0.681302
$895$	−2.45493	−0.0820593
$896$	−41.4029	−1.38317
$897$	5.06344	0.169063
$898$	98.0253	3.27115
$899$	−59.1289	−1.97206
$900$	38.1575	1.27192
$901$	−30.0982	−1.00272
$902$	−44.8240	−1.49248
$903$	−3.93804	−0.131050
$904$	−176.070	−5.85599
$905$	−22.8092	−0.758202
$906$	−25.4891	−0.846818
$907$	−46.2859	−1.53690	−0.768449	−	0.639911i	$-0.778971\pi$
$907$	−46.2859	−1.53690	−0.768449	+	0.639911i	$0.778971\pi$
$908$	−118.375	−3.92842
$909$	−32.8515	−1.08962
$910$	−4.82890	−0.160077
$911$	−0.775371	−0.0256892	−0.0128446	−	0.999918i	$-0.504089\pi$
$911$	−0.775371	−0.0256892	−0.0128446	+	0.999918i	$0.504089\pi$
$912$	20.7172	0.686016
$913$	−80.1854	−2.65375
$914$	−9.27824	−0.306897
$915$	−8.43606	−0.278888
$916$	−120.336	−3.97601
$917$	11.1696	0.368852
$918$	41.9524	1.38464
$919$	−28.2861	−0.933073	−0.466537	−	0.884502i	$-0.654498\pi$
$919$	−28.2861	−0.933073	−0.466537	+	0.884502i	$0.654498\pi$
$920$	69.4422	2.28944
$921$	−17.9644	−0.591948
$922$	73.0956	2.40728
$923$	13.1602	0.433173
$924$	15.0335	0.494566
$925$	12.0963	0.397724
$926$	116.911	3.84193
$927$	16.2329	0.533157
$928$	269.397	8.84338
$929$	−25.1339	−0.824618	−0.412309	−	0.911044i	$-0.635278\pi$
$929$	−25.1339	−0.824618	−0.412309	+	0.911044i	$0.635278\pi$
$930$	17.1093	0.561036
$931$	10.8064	0.354166
$932$	−0.0720853	−0.00236123
$933$	5.92729	0.194051
$934$	−45.4467	−1.48706
$935$	25.5346	0.835070
$936$	36.3266	1.18737
$937$	−45.7130	−1.49338	−0.746689	−	0.665174i	$-0.768358\pi$
$937$	−45.7130	−1.49338	−0.746689	+	0.665174i	$0.768358\pi$
$938$	32.9776	1.07676
$939$	7.97633	0.260298
$940$	−93.2097	−3.04017
$941$	−4.17560	−0.136121	−0.0680604	−	0.997681i	$-0.521681\pi$
$941$	−4.17560	−0.136121	−0.0680604	+	0.997681i	$0.521681\pi$
$942$	−0.269649	−0.00878563
$943$	16.5058	0.537502
$944$	18.9003	0.615151
$945$	4.78386	0.155619
$946$	84.2544	2.73935
$947$	−45.8879	−1.49115	−0.745577	−	0.666419i	$-0.767826\pi$
$947$	−45.8879	−1.49115	−0.745577	+	0.666419i	$0.767826\pi$
$948$	39.0321	1.26770
$949$	15.8133	0.513322
$950$	−12.9494	−0.420133
$951$	−5.36499	−0.173972
$952$	29.8641	0.967900
$953$	−0.897710	−0.0290797	−0.0145398	−	0.999894i	$-0.504628\pi$
$953$	−0.897710	−0.0290797	−0.0145398	+	0.999894i	$0.504628\pi$
$954$	54.2356	1.75594
$955$	−9.47632	−0.306647
$956$	−7.23172	−0.233890
$957$	−35.6884	−1.15364
$958$	63.6014	2.05487
$959$	15.8668	0.512365
$960$	−41.4108	−1.33653
$961$	0.186147	0.00600473
$962$	17.8531	0.575608
$963$	−16.0290	−0.516529
$964$	7.95118	0.256090
$965$	38.7168	1.24634
$966$	−7.50090	−0.241338
$967$	−26.5900	−0.855077	−0.427539	−	0.903997i	$-0.640619\pi$
$967$	−26.5900	−0.855077	−0.427539	+	0.903997i	$0.640619\pi$
$968$	−97.0101	−3.11802
$969$	−4.72365	−0.151746
$970$	−24.9182	−0.800074
$971$	31.8160	1.02103	0.510513	−	0.859870i	$-0.329456\pi$
$971$	31.8160	1.02103	0.510513	+	0.859870i	$0.329456\pi$
$972$	−86.5025	−2.77457
$973$	−1.38349	−0.0443527
$974$	−50.3233	−1.61246
$975$	3.02630	0.0969193
$976$	125.359	4.01266
$977$	28.6949	0.918031	0.459015	−	0.888428i	$-0.348202\pi$
$977$	28.6949	0.918031	0.459015	+	0.888428i	$0.348202\pi$
$978$	2.01945	0.0645749
$979$	−46.0287	−1.47108
$980$	−53.6958	−1.71525
$981$	−1.91924	−0.0612765
$982$	102.886	3.28322
$983$	−39.8875	−1.27221	−0.636107	−	0.771601i	$-0.719456\pi$
$983$	−39.8875	−1.27221	−0.636107	+	0.771601i	$0.719456\pi$
$984$	−26.5768	−0.847237
$985$	−5.93512	−0.189109
$986$	−109.909	−3.50022
$987$	6.49432	0.206717
$988$	−14.1053	−0.448749
$989$	−31.0254	−0.986552
$990$	−46.0121	−1.46236
$991$	18.7079	0.594277	0.297138	−	0.954834i	$-0.403968\pi$
$991$	18.7079	0.594277	0.297138	+	0.954834i	$0.403968\pi$
$992$	−142.087	−4.51127
$993$	3.62929	0.115172
$994$	−19.4953	−0.618353
$995$	30.0181	0.951639
$996$	−73.7062	−2.33547
$997$	47.2768	1.49727	0.748636	−	0.662981i	$-0.230709\pi$
$997$	47.2768	1.49727	0.748636	+	0.662981i	$0.230709\pi$
$998$	80.2470	2.54018
$999$	−17.6866	−0.559579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.c.1.2	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.c.1.2	✓	176	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.76303 q^{2} -0.741544 q^{3} +5.63435 q^{4} +1.49530 q^{5} +2.04891 q^{6} +0.791604 q^{7} -10.0418 q^{8} -2.45011 q^{9} +O(q^{10})\)	\(q-2.76303 q^{2} -0.741544 q^{3} +5.63435 q^{4} +1.49530 q^{5} +2.04891 q^{6} +0.791604 q^{7} -10.0418 q^{8} -2.45011 q^{9} -4.13156 q^{10} -4.54540 q^{11} -4.17811 q^{12} +1.47647 q^{13} -2.18723 q^{14} -1.10883 q^{15} +16.4772 q^{16} -3.75689 q^{17} +6.76974 q^{18} -1.69556 q^{19} +8.42504 q^{20} -0.587009 q^{21} +12.5591 q^{22} -4.62469 q^{23} +7.44644 q^{24} -2.76408 q^{25} -4.07955 q^{26} +4.04150 q^{27} +4.46017 q^{28} -10.5881 q^{29} +3.06373 q^{30} +5.58446 q^{31} -25.4433 q^{32} +3.37061 q^{33} +10.3804 q^{34} +1.18369 q^{35} -13.8048 q^{36} -4.37625 q^{37} +4.68488 q^{38} -1.09487 q^{39} -15.0155 q^{40} -3.56906 q^{41} +1.62192 q^{42} +6.70865 q^{43} -25.6103 q^{44} -3.66366 q^{45} +12.7782 q^{46} -11.0634 q^{47} -12.2185 q^{48} -6.37336 q^{49} +7.63723 q^{50} +2.78590 q^{51} +8.31897 q^{52} +8.01148 q^{53} -11.1668 q^{54} -6.79673 q^{55} -7.94914 q^{56} +1.25733 q^{57} +29.2553 q^{58} +1.14706 q^{59} -6.24754 q^{60} +7.60807 q^{61} -15.4300 q^{62} -1.93952 q^{63} +37.3463 q^{64} +2.20777 q^{65} -9.31310 q^{66} -15.0773 q^{67} -21.1676 q^{68} +3.42941 q^{69} -3.27056 q^{70} +8.91325 q^{71} +24.6036 q^{72} +10.7102 q^{73} +12.0917 q^{74} +2.04968 q^{75} -9.55336 q^{76} -3.59815 q^{77} +3.02516 q^{78} -9.34204 q^{79} +24.6383 q^{80} +4.35339 q^{81} +9.86142 q^{82} +17.6410 q^{83} -3.30741 q^{84} -5.61768 q^{85} -18.5362 q^{86} +7.85155 q^{87} +45.6440 q^{88} +10.1264 q^{89} +10.1228 q^{90} +1.16878 q^{91} -26.0571 q^{92} -4.14112 q^{93} +30.5686 q^{94} -2.53537 q^{95} +18.8673 q^{96} +6.03117 q^{97} +17.6098 q^{98} +11.1367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9}+O(q^{10}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9	\( 176 q + 11 q^{2} + 53 q^{3} + 191 q^{4} + 5 q^{5} + 19 q^{6} + 46 q^{7} + 36 q^{8} + 193 q^{9} + 43 q^{10} + 18 q^{11} + 95 q^{12} + 95 q^{13} + 2 q^{14} + 36 q^{15} + 225 q^{16} + 35 q^{17} + 46 q^{18} + 127 q^{19} + 4 q^{20} + 32 q^{21} + 60 q^{22} + 35 q^{23} + 26 q^{24} + 207 q^{25} + 19 q^{26} + 191 q^{27} + 87 q^{28} + 16 q^{29} + 28 q^{30} + 93 q^{31} + 73 q^{32} + 70 q^{33} + 45 q^{34} + 73 q^{35} + 206 q^{36} + 64 q^{37} + 35 q^{38} + 72 q^{39} + 139 q^{40} + 19 q^{41} + 35 q^{42} + 261 q^{43} + 11 q^{44} + 12 q^{45} + 58 q^{46} + 40 q^{47} + 130 q^{48} + 234 q^{49} - 14 q^{50} + 76 q^{51} + 263 q^{52} + 17 q^{53} + 28 q^{54} + 170 q^{55} - 10 q^{56} + 60 q^{57} + 52 q^{58} + 69 q^{59} + 37 q^{60} + 110 q^{61} + 71 q^{62} + 101 q^{63} + 250 q^{64} - q^{65} + 43 q^{66} + 190 q^{67} + 48 q^{68} + 45 q^{69} + 14 q^{70} + 9 q^{71} + 98 q^{72} + 182 q^{73} - 23 q^{74} + 219 q^{75} + 197 q^{76} + 25 q^{77} - 26 q^{78} + 105 q^{79} + 20 q^{80} + 236 q^{81} + 107 q^{82} + 130 q^{83} + 38 q^{84} + 73 q^{85} - 24 q^{86} + 171 q^{87} + 165 q^{88} + 40 q^{89} + 45 q^{90} + 182 q^{91} - 4 q^{92} + 23 q^{93} + 98 q^{94} + 30 q^{95} - 2 q^{96} + 168 q^{97} + 82 q^{98} + 50 q^{99}+O(q^{100}) \) 176 * q + 11 * q^2 + 53 * q^3 + 191 * q^4 + 5 * q^5 + 19 * q^6 + 46 * q^7 + 36 * q^8 + 193 * q^9 + 43 * q^10 + 18 * q^11 + 95 * q^12 + 95 * q^13 + 2 * q^14 + 36 * q^15 + 225 * q^16 + 35 * q^17 + 46 * q^18 + 127 * q^19 + 4 * q^20 + 32 * q^21 + 60 * q^22 + 35 * q^23 + 26 * q^24 + 207 * q^25 + 19 * q^26 + 191 * q^27 + 87 * q^28 + 16 * q^29 + 28 * q^30 + 93 * q^31 + 73 * q^32 + 70 * q^33 + 45 * q^34 + 73 * q^35 + 206 * q^36 + 64 * q^37 + 35 * q^38 + 72 * q^39 + 139 * q^40 + 19 * q^41 + 35 * q^42 + 261 * q^43 + 11 * q^44 + 12 * q^45 + 58 * q^46 + 40 * q^47 + 130 * q^48 + 234 * q^49 - 14 * q^50 + 76 * q^51 + 263 * q^52 + 17 * q^53 + 28 * q^54 + 170 * q^55 - 10 * q^56 + 60 * q^57 + 52 * q^58 + 69 * q^59 + 37 * q^60 + 110 * q^61 + 71 * q^62 + 101 * q^63 + 250 * q^64 - q^65 + 43 * q^66 + 190 * q^67 + 48 * q^68 + 45 * q^69 + 14 * q^70 + 9 * q^71 + 98 * q^72 + 182 * q^73 - 23 * q^74 + 219 * q^75 + 197 * q^76 + 25 * q^77 - 26 * q^78 + 105 * q^79 + 20 * q^80 + 236 * q^81 + 107 * q^82 + 130 * q^83 + 38 * q^84 + 73 * q^85 - 24 * q^86 + 171 * q^87 + 165 * q^88 + 40 * q^89 + 45 * q^90 + 182 * q^91 - 4 * q^92 + 23 * q^93 + 98 * q^94 + 30 * q^95 - 2 * q^96 + 168 * q^97 + 82 * q^98 + 50 * q^99

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