LMFDB - Embedded newform 4019.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27033 q^{2} +2.56855 q^{3} +3.15439 q^{4} -3.84625 q^{5} -5.83145 q^{6} +2.23399 q^{7} -2.62085 q^{8} +3.59745 q^{9} +O(q^{10})$	\(q-2.27033 q^{2} +2.56855 q^{3} +3.15439 q^{4} -3.84625 q^{5} -5.83145 q^{6} +2.23399 q^{7} -2.62085 q^{8} +3.59745 q^{9} +8.73225 q^{10} +5.55771 q^{11} +8.10221 q^{12} -1.81200 q^{13} -5.07190 q^{14} -9.87928 q^{15} -0.358595 q^{16} +6.38063 q^{17} -8.16739 q^{18} -4.73218 q^{19} -12.1326 q^{20} +5.73813 q^{21} -12.6178 q^{22} -7.52305 q^{23} -6.73178 q^{24} +9.79363 q^{25} +4.11383 q^{26} +1.53457 q^{27} +7.04689 q^{28} -6.13482 q^{29} +22.4292 q^{30} -8.28838 q^{31} +6.05583 q^{32} +14.2752 q^{33} -14.4861 q^{34} -8.59250 q^{35} +11.3478 q^{36} -4.94682 q^{37} +10.7436 q^{38} -4.65420 q^{39} +10.0804 q^{40} -1.16600 q^{41} -13.0274 q^{42} -8.18381 q^{43} +17.5312 q^{44} -13.8367 q^{45} +17.0798 q^{46} +2.07973 q^{47} -0.921069 q^{48} -2.00927 q^{49} -22.2348 q^{50} +16.3890 q^{51} -5.71575 q^{52} -4.08713 q^{53} -3.48399 q^{54} -21.3763 q^{55} -5.85496 q^{56} -12.1548 q^{57} +13.9281 q^{58} -7.66081 q^{59} -31.1631 q^{60} -3.88618 q^{61} +18.8174 q^{62} +8.03668 q^{63} -13.0315 q^{64} +6.96939 q^{65} -32.4095 q^{66} -3.34197 q^{67} +20.1270 q^{68} -19.3233 q^{69} +19.5078 q^{70} +8.28628 q^{71} -9.42837 q^{72} -2.74452 q^{73} +11.2309 q^{74} +25.1554 q^{75} -14.9271 q^{76} +12.4159 q^{77} +10.5666 q^{78} +13.5107 q^{79} +1.37925 q^{80} -6.85071 q^{81} +2.64721 q^{82} +13.5659 q^{83} +18.1003 q^{84} -24.5415 q^{85} +18.5799 q^{86} -15.7576 q^{87} -14.5659 q^{88} +11.2464 q^{89} +31.4138 q^{90} -4.04799 q^{91} -23.7307 q^{92} -21.2891 q^{93} -4.72167 q^{94} +18.2011 q^{95} +15.5547 q^{96} -13.8861 q^{97} +4.56170 q^{98} +19.9936 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * 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 $

$2$	−2.27033	−1.60536	−0.802682	−	0.596407i	$-0.796595\pi$
$2$	−2.27033	−1.60536	−0.802682	+	0.596407i	$0.796595\pi$
$3$	2.56855	1.48295	0.741476	−	0.670979i	$-0.234126\pi$
$3$	2.56855	1.48295	0.741476	+	0.670979i	$0.234126\pi$
$4$	3.15439	1.57720
$5$	−3.84625	−1.72009	−0.860047	−	0.510214i	$-0.829566\pi$
$5$	−3.84625	−1.72009	−0.860047	+	0.510214i	$0.829566\pi$
$6$	−5.83145	−2.38068
$7$	2.23399	0.844371	0.422185	−	0.906510i	$-0.361263\pi$
$7$	2.23399	0.844371	0.422185	+	0.906510i	$0.361263\pi$
$8$	−2.62085	−0.926610
$9$	3.59745	1.19915
$10$	8.73225	2.76138
$11$	5.55771	1.67571	0.837856	−	0.545891i	$-0.183809\pi$
$11$	5.55771	1.67571	0.837856	+	0.545891i	$0.183809\pi$
$12$	8.10221	2.33891
$13$	−1.81200	−0.502558	−0.251279	−	0.967915i	$-0.580851\pi$
$13$	−1.81200	−0.502558	−0.251279	+	0.967915i	$0.580851\pi$
$14$	−5.07190	−1.35552
$15$	−9.87928	−2.55082
$16$	−0.358595	−0.0896487
$17$	6.38063	1.54753	0.773765	−	0.633473i	$-0.218371\pi$
$17$	6.38063	1.54753	0.773765	+	0.633473i	$0.218371\pi$
$18$	−8.16739	−1.92507
$19$	−4.73218	−1.08564	−0.542818	−	0.839850i	$-0.682643\pi$
$19$	−4.73218	−1.08564	−0.542818	+	0.839850i	$0.682643\pi$
$20$	−12.1326	−2.71293
$21$	5.73813	1.25216
$22$	−12.6178	−2.69013
$23$	−7.52305	−1.56867	−0.784333	−	0.620341i	$-0.786994\pi$
$23$	−7.52305	−1.56867	−0.784333	+	0.620341i	$0.786994\pi$
$24$	−6.73178	−1.37412
$25$	9.79363	1.95873
$26$	4.11383	0.806788
$27$	1.53457	0.295329
$28$	7.04689	1.33174
$29$	−6.13482	−1.13921	−0.569604	−	0.821920i	$-0.692903\pi$
$29$	−6.13482	−1.13921	−0.569604	+	0.821920i	$0.692903\pi$
$30$	22.4292	4.09500
$31$	−8.28838	−1.48864	−0.744319	−	0.667824i	$-0.767226\pi$
$31$	−8.28838	−1.48864	−0.744319	+	0.667824i	$0.767226\pi$
$32$	6.05583	1.07053
$33$	14.2752	2.48500
$34$	−14.4861	−2.48435
$35$	−8.59250	−1.45240
$36$	11.3478	1.89129
$37$	−4.94682	−0.813253	−0.406626	−	0.913594i	$-0.633295\pi$
$37$	−4.94682	−0.813253	−0.406626	+	0.913594i	$0.633295\pi$
$38$	10.7436	1.74284
$39$	−4.65420	−0.745269
$40$	10.0804	1.59386
$41$	−1.16600	−0.182099	−0.0910496	−	0.995846i	$-0.529022\pi$
$41$	−1.16600	−0.182099	−0.0910496	+	0.995846i	$0.529022\pi$
$42$	−13.0274	−2.01018
$43$	−8.18381	−1.24802	−0.624010	−	0.781416i	$-0.714498\pi$
$43$	−8.18381	−1.24802	−0.624010	+	0.781416i	$0.714498\pi$
$44$	17.5312	2.64293
$45$	−13.8367	−2.06265
$46$	17.0798	2.51828
$47$	2.07973	0.303360	0.151680	−	0.988430i	$-0.451532\pi$
$47$	2.07973	0.303360	0.151680	+	0.988430i	$0.451532\pi$
$48$	−0.921069	−0.132945
$49$	−2.00927	−0.287038
$50$	−22.2348	−3.14447
$51$	16.3890	2.29491
$52$	−5.71575	−0.792632
$53$	−4.08713	−0.561410	−0.280705	−	0.959794i	$-0.590568\pi$
$53$	−4.08713	−0.561410	−0.280705	+	0.959794i	$0.590568\pi$
$54$	−3.48399	−0.474110
$55$	−21.3763	−2.88238
$56$	−5.85496	−0.782402
$57$	−12.1548	−1.60995
$58$	13.9281	1.82884
$59$	−7.66081	−0.997352	−0.498676	−	0.866788i	$-0.666180\pi$
$59$	−7.66081	−0.997352	−0.498676	+	0.866788i	$0.666180\pi$
$60$	−31.1631	−4.02314
$61$	−3.88618	−0.497574	−0.248787	−	0.968558i	$-0.580032\pi$
$61$	−3.88618	−0.497574	−0.248787	+	0.968558i	$0.580032\pi$
$62$	18.8174	2.38981
$63$	8.03668	1.01253
$64$	−13.0315	−1.62894
$65$	6.96939	0.864447
$66$	−32.4095	−3.98933
$67$	−3.34197	−0.408287	−0.204143	−	0.978941i	$-0.565441\pi$
$67$	−3.34197	−0.408287	−0.204143	+	0.978941i	$0.565441\pi$
$68$	20.1270	2.44076
$69$	−19.3233	−2.32626
$70$	19.5078	2.33163
$71$	8.28628	0.983401	0.491701	−	0.870764i	$-0.336375\pi$
$71$	8.28628	0.983401	0.491701	+	0.870764i	$0.336375\pi$
$72$	−9.42837	−1.11114
$73$	−2.74452	−0.321221	−0.160611	−	0.987018i	$-0.551346\pi$
$73$	−2.74452	−0.321221	−0.160611	+	0.987018i	$0.551346\pi$
$74$	11.2309	1.30557
$75$	25.1554	2.90470
$76$	−14.9271	−1.71226
$77$	12.4159	1.41492
$78$	10.5666	1.19643
$79$	13.5107	1.52008	0.760039	−	0.649878i	$-0.225180\pi$
$79$	13.5107	1.52008	0.760039	+	0.649878i	$0.225180\pi$
$80$	1.37925	0.154204
$81$	−6.85071	−0.761191
$82$	2.64721	0.292336
$83$	13.5659	1.48905	0.744523	−	0.667597i	$-0.232677\pi$
$83$	13.5659	1.48905	0.744523	+	0.667597i	$0.232677\pi$
$84$	18.1003	1.97490
$85$	−24.5415	−2.66190
$86$	18.5799	2.00353
$87$	−15.7576	−1.68939
$88$	−14.5659	−1.55273
$89$	11.2464	1.19211	0.596056	−	0.802943i	$-0.296734\pi$
$89$	11.2464	1.19211	0.596056	+	0.802943i	$0.296734\pi$
$90$	31.4138	3.31131
$91$	−4.04799	−0.424345
$92$	−23.7307	−2.47409
$93$	−21.2891	−2.20758
$94$	−4.72167	−0.487003
$95$	18.2011	1.86740
$96$	15.5547	1.58754
$97$	−13.8861	−1.40992	−0.704962	−	0.709245i	$-0.749036\pi$
$97$	−13.8861	−1.40992	−0.704962	+	0.709245i	$0.749036\pi$
$98$	4.56170	0.460801
$99$	19.9936	2.00943
$100$	30.8930	3.08930
$101$	18.7561	1.86630	0.933149	−	0.359490i	$-0.117049\pi$
$101$	18.7561	1.86630	0.933149	+	0.359490i	$0.117049\pi$
$102$	−37.2083	−3.68417
$103$	11.3382	1.11718	0.558592	−	0.829443i	$-0.311342\pi$
$103$	11.3382	1.11718	0.558592	+	0.829443i	$0.311342\pi$
$104$	4.74897	0.465675
$105$	−22.0703	−2.15384
$106$	9.27913	0.901268
$107$	−9.47885	−0.916355	−0.458178	−	0.888861i	$-0.651498\pi$
$107$	−9.47885	−0.916355	−0.458178	+	0.888861i	$0.651498\pi$
$108$	4.84064	0.465791
$109$	−5.00923	−0.479797	−0.239898	−	0.970798i	$-0.577114\pi$
$109$	−5.00923	−0.479797	−0.239898	+	0.970798i	$0.577114\pi$
$110$	48.5313	4.62728
$111$	−12.7062	−1.20602
$112$	−0.801099	−0.0756968
$113$	3.43407	0.323050	0.161525	−	0.986869i	$-0.448359\pi$
$113$	3.43407	0.323050	0.161525	+	0.986869i	$0.448359\pi$
$114$	27.5955	2.58455
$115$	28.9355	2.69825
$116$	−19.3516	−1.79675
$117$	−6.51856	−0.602641
$118$	17.3926	1.60111
$119$	14.2543	1.30669
$120$	25.8921	2.36362
$121$	19.8881	1.80801
$122$	8.82290	0.798787
$123$	−2.99494	−0.270044
$124$	−26.1448	−2.34787
$125$	−18.4375	−1.64910
$126$	−18.2459	−1.62547
$127$	−1.28093	−0.113665	−0.0568323	−	0.998384i	$-0.518100\pi$
$127$	−1.28093	−0.113665	−0.0568323	+	0.998384i	$0.518100\pi$
$128$	17.4742	1.54452
$129$	−21.0205	−1.85075
$130$	−15.8228	−1.38775
$131$	1.62959	0.142378	0.0711889	−	0.997463i	$-0.477321\pi$
$131$	1.62959	0.142378	0.0711889	+	0.997463i	$0.477321\pi$
$132$	45.0297	3.91934
$133$	−10.5717	−0.916679
$134$	7.58737	0.655449
$135$	−5.90235	−0.507993
$136$	−16.7227	−1.43396
$137$	−9.94269	−0.849462	−0.424731	−	0.905320i	$-0.639631\pi$
$137$	−9.94269	−0.849462	−0.424731	+	0.905320i	$0.639631\pi$
$138$	43.8703	3.73449
$139$	−1.71348	−0.145336	−0.0726678	−	0.997356i	$-0.523151\pi$
$139$	−1.71348	−0.145336	−0.0726678	+	0.997356i	$0.523151\pi$
$140$	−27.1041	−2.29072
$141$	5.34189	0.449868
$142$	−18.8126	−1.57872
$143$	−10.0706	−0.842142
$144$	−1.29003	−0.107502
$145$	23.5960	1.95954
$146$	6.23096	0.515678
$147$	−5.16090	−0.425664
$148$	−15.6042	−1.28266
$149$	−10.2621	−0.840706	−0.420353	−	0.907361i	$-0.638094\pi$
$149$	−10.2621	−0.840706	−0.420353	+	0.907361i	$0.638094\pi$
$150$	−57.1111	−4.66310
$151$	−1.97974	−0.161109	−0.0805545	−	0.996750i	$-0.525669\pi$
$151$	−1.97974	−0.161109	−0.0805545	+	0.996750i	$0.525669\pi$
$152$	12.4023	1.00596
$153$	22.9540	1.85572
$154$	−28.1882	−2.27147
$155$	31.8792	2.56060
$156$	−14.6812	−1.17544
$157$	−5.38169	−0.429506	−0.214753	−	0.976668i	$-0.568895\pi$
$157$	−5.38169	−0.429506	−0.214753	+	0.976668i	$0.568895\pi$
$158$	−30.6738	−2.44028
$159$	−10.4980	−0.832545
$160$	−23.2922	−1.84141
$161$	−16.8065	−1.32453
$162$	15.5534	1.22199
$163$	−24.7688	−1.94004	−0.970019	−	0.243028i	$-0.921859\pi$
$163$	−24.7688	−1.94004	−0.970019	+	0.243028i	$0.921859\pi$
$164$	−3.67803	−0.287206
$165$	−54.9062	−4.27444
$166$	−30.7989	−2.39046
$167$	−5.66512	−0.438380	−0.219190	−	0.975682i	$-0.570342\pi$
$167$	−5.66512	−0.438380	−0.219190	+	0.975682i	$0.570342\pi$
$168$	−15.0388	−1.16027
$169$	−9.71667	−0.747436
$170$	55.7173	4.27332
$171$	−17.0238	−1.30184
$172$	−25.8150	−1.96837
$173$	−14.7769	−1.12347	−0.561733	−	0.827319i	$-0.689865\pi$
$173$	−14.7769	−1.12347	−0.561733	+	0.827319i	$0.689865\pi$
$174$	35.7749	2.71209
$175$	21.8789	1.65389
$176$	−1.99297	−0.150225
$177$	−19.6772	−1.47903
$178$	−25.5329	−1.91377
$179$	−17.0927	−1.27757	−0.638785	−	0.769385i	$-0.720563\pi$
$179$	−17.0927	−1.27757	−0.638785	+	0.769385i	$0.720563\pi$
$180$	−43.6463	−3.25320
$181$	7.09110	0.527077	0.263539	−	0.964649i	$-0.415110\pi$
$181$	7.09110	0.527077	0.263539	+	0.964649i	$0.415110\pi$
$182$	9.19027	0.681228
$183$	−9.98184	−0.737879
$184$	19.7168	1.45354
$185$	19.0267	1.39887
$186$	48.3333	3.54397
$187$	35.4617	2.59322
$188$	6.56028	0.478457
$189$	3.42823	0.249367
$190$	−41.3225	−2.99785
$191$	−13.6519	−0.987814	−0.493907	−	0.869515i	$-0.664432\pi$
$191$	−13.6519	−0.987814	−0.493907	+	0.869515i	$0.664432\pi$
$192$	−33.4721	−2.41564
$193$	1.58570	0.114141	0.0570706	−	0.998370i	$-0.481824\pi$
$193$	1.58570	0.114141	0.0570706	+	0.998370i	$0.481824\pi$
$194$	31.5261	2.26344
$195$	17.9012	1.28193
$196$	−6.33802	−0.452716
$197$	−18.5550	−1.32199	−0.660996	−	0.750390i	$-0.729866\pi$
$197$	−18.5550	−1.32199	−0.660996	+	0.750390i	$0.729866\pi$
$198$	−45.3920	−3.22587
$199$	2.11660	0.150042	0.0750208	−	0.997182i	$-0.476098\pi$
$199$	2.11660	0.150042	0.0750208	+	0.997182i	$0.476098\pi$
$200$	−25.6676	−1.81498
$201$	−8.58402	−0.605470
$202$	−42.5824	−2.99609
$203$	−13.7052	−0.961913
$204$	51.6972	3.61953
$205$	4.48474	0.313228
$206$	−25.7414	−1.79349
$207$	−27.0638	−1.88106
$208$	0.649773	0.0450537
$209$	−26.3001	−1.81921
$210$	50.1067	3.45769
$211$	26.9004	1.85190	0.925951	−	0.377643i	$-0.123265\pi$
$211$	26.9004	1.85190	0.925951	+	0.377643i	$0.123265\pi$
$212$	−12.8924	−0.885454
$213$	21.2837	1.45834
$214$	21.5201	1.47108
$215$	31.4770	2.14671
$216$	−4.02188	−0.273655
$217$	−18.5162	−1.25696
$218$	11.3726	0.770249
$219$	−7.04943	−0.476356
$220$	−67.4293	−4.54608
$221$	−11.5617	−0.777723
$222$	28.8472	1.93610
$223$	1.58231	0.105959	0.0529797	−	0.998596i	$-0.483128\pi$
$223$	1.58231	0.105959	0.0529797	+	0.998596i	$0.483128\pi$
$224$	13.5287	0.903923
$225$	35.2321	2.34880
$226$	−7.79648	−0.518614
$227$	14.7145	0.976636	0.488318	−	0.872666i	$-0.337611\pi$
$227$	14.7145	0.976636	0.488318	+	0.872666i	$0.337611\pi$
$228$	−38.3411	−2.53920
$229$	−17.2207	−1.13797	−0.568986	−	0.822347i	$-0.692664\pi$
$229$	−17.2207	−1.13797	−0.568986	+	0.822347i	$0.692664\pi$
$230$	−65.6932	−4.33168
$231$	31.8908	2.09826
$232$	16.0784	1.05560
$233$	18.1270	1.18754	0.593771	−	0.804634i	$-0.297638\pi$
$233$	18.1270	1.18754	0.593771	+	0.804634i	$0.297638\pi$
$234$	14.7993	0.967459
$235$	−7.99915	−0.521807
$236$	−24.1652	−1.57302
$237$	34.7030	2.25420
$238$	−32.3619	−2.09771
$239$	−5.09077	−0.329295	−0.164647	−	0.986353i	$-0.552649\pi$
$239$	−5.09077	−0.329295	−0.164647	+	0.986353i	$0.552649\pi$
$240$	3.54266	0.228678
$241$	−16.7294	−1.07763	−0.538817	−	0.842423i	$-0.681129\pi$
$241$	−16.7294	−1.07763	−0.538817	+	0.842423i	$0.681129\pi$
$242$	−45.1526	−2.90252
$243$	−22.2001	−1.42414
$244$	−12.2585	−0.784771
$245$	7.72814	0.493733
$246$	6.79949	0.433520
$247$	8.57469	0.545594
$248$	21.7226	1.37939
$249$	34.8446	2.20818
$250$	41.8592	2.64741
$251$	−15.4303	−0.973952	−0.486976	−	0.873415i	$-0.661900\pi$
$251$	−15.4303	−0.973952	−0.486976	+	0.873415i	$0.661900\pi$
$252$	25.3508	1.59695
$253$	−41.8109	−2.62863
$254$	2.90814	0.182473
$255$	−63.0360	−3.94747
$256$	−13.6091	−0.850569
$257$	16.9890	1.05974	0.529872	−	0.848078i	$-0.322240\pi$
$257$	16.9890	1.05974	0.529872	+	0.848078i	$0.322240\pi$
$258$	47.7235	2.97114
$259$	−11.0512	−0.686687
$260$	21.9842	1.36340
$261$	−22.0697	−1.36608
$262$	−3.69970	−0.228568
$263$	8.03751	0.495614	0.247807	−	0.968809i	$-0.420290\pi$
$263$	8.03751	0.495614	0.247807	+	0.968809i	$0.420290\pi$
$264$	−37.4133	−2.30263
$265$	15.7201	0.965679
$266$	24.0011	1.47160
$267$	28.8868	1.76785
$268$	−10.5419	−0.643948
$269$	1.59105	0.0970077	0.0485039	−	0.998823i	$-0.484555\pi$
$269$	1.59105	0.0970077	0.0485039	+	0.998823i	$0.484555\pi$
$270$	13.4003	0.815515
$271$	−18.8708	−1.14632	−0.573159	−	0.819444i	$-0.694282\pi$
$271$	−18.8708	−1.14632	−0.573159	+	0.819444i	$0.694282\pi$
$272$	−2.28806	−0.138734
$273$	−10.3975	−0.629283
$274$	22.5732	1.36370
$275$	54.4301	3.28226
$276$	−60.9534	−3.66896
$277$	8.08553	0.485812	0.242906	−	0.970050i	$-0.421899\pi$
$277$	8.08553	0.485812	0.242906	+	0.970050i	$0.421899\pi$
$278$	3.89016	0.233317
$279$	−29.8170	−1.78510
$280$	22.5196	1.34581
$281$	−28.0223	−1.67167	−0.835835	−	0.548980i	$-0.815016\pi$
$281$	−28.0223	−1.67167	−0.835835	+	0.548980i	$0.815016\pi$
$282$	−12.1278	−0.722202
$283$	−12.9713	−0.771063	−0.385531	−	0.922695i	$-0.625982\pi$
$283$	−12.9713	−0.771063	−0.385531	+	0.922695i	$0.625982\pi$
$284$	26.1382	1.55102
$285$	46.7505	2.76926
$286$	22.8635	1.35194
$287$	−2.60485	−0.153759
$288$	21.7855	1.28372
$289$	23.7124	1.39485
$290$	−53.5708	−3.14578
$291$	−35.6672	−2.09085
$292$	−8.65728	−0.506629
$293$	12.7056	0.742268	0.371134	−	0.928579i	$-0.378969\pi$
$293$	12.7056	0.742268	0.371134	+	0.928579i	$0.378969\pi$
$294$	11.7169	0.683346
$295$	29.4654	1.71554
$296$	12.9649	0.753568
$297$	8.52871	0.494886
$298$	23.2984	1.34964
$299$	13.6318	0.788345
$300$	79.3501	4.58128
$301$	−18.2826	−1.05379
$302$	4.49466	0.258639
$303$	48.1759	2.76763
$304$	1.69693	0.0973259
$305$	14.9472	0.855874
$306$	−52.1131	−2.97911
$307$	17.9463	1.02425	0.512125	−	0.858911i	$-0.328858\pi$
$307$	17.9463	1.02425	0.512125	+	0.858911i	$0.328858\pi$
$308$	39.1646	2.23161
$309$	29.1227	1.65673
$310$	−72.3762	−4.11069
$311$	−0.210574	−0.0119405	−0.00597027	−	0.999982i	$-0.501900\pi$
$311$	−0.210574	−0.0119405	−0.00597027	+	0.999982i	$0.501900\pi$
$312$	12.1980	0.690574
$313$	24.2054	1.36817	0.684085	−	0.729403i	$-0.260202\pi$
$313$	24.2054	1.36817	0.684085	+	0.729403i	$0.260202\pi$
$314$	12.2182	0.689513
$315$	−30.9111	−1.74164
$316$	42.6182	2.39746
$317$	−26.6942	−1.49930	−0.749648	−	0.661836i	$-0.769777\pi$
$317$	−26.6942	−1.49930	−0.749648	+	0.661836i	$0.769777\pi$
$318$	23.8339	1.33654
$319$	−34.0955	−1.90898
$320$	50.1225	2.80193
$321$	−24.3469	−1.35891
$322$	38.1562	2.12636
$323$	−30.1943	−1.68005
$324$	−21.6098	−1.20055
$325$	−17.7460	−0.984373
$326$	56.2332	3.11447
$327$	−12.8664	−0.711516
$328$	3.05592	0.168735
$329$	4.64610	0.256148
$330$	124.655	6.86203
$331$	−8.19228	−0.450288	−0.225144	−	0.974325i	$-0.572285\pi$
$331$	−8.19228	−0.450288	−0.225144	+	0.974325i	$0.572285\pi$
$332$	42.7920	2.34852
$333$	−17.7959	−0.975212
$334$	12.8617	0.703760
$335$	12.8541	0.702292
$336$	−2.05766	−0.112255
$337$	21.2070	1.15522	0.577609	−	0.816314i	$-0.303986\pi$
$337$	21.2070	1.15522	0.577609	+	0.816314i	$0.303986\pi$
$338$	22.0600	1.19991
$339$	8.82059	0.479069
$340$	−77.4135	−4.19834
$341$	−46.0644	−2.49453
$342$	38.6495	2.08993
$343$	−20.1267	−1.08674
$344$	21.4485	1.15643
$345$	74.3224	4.00138
$346$	33.5484	1.80357
$347$	35.9548	1.93015	0.965077	−	0.261968i	$-0.0843713\pi$
$347$	35.9548	1.93015	0.965077	+	0.261968i	$0.0843713\pi$
$348$	−49.7056	−2.66450
$349$	10.5131	0.562751	0.281376	−	0.959598i	$-0.409209\pi$
$349$	10.5131	0.562751	0.281376	+	0.959598i	$0.409209\pi$
$350$	−49.6723	−2.65510
$351$	−2.78064	−0.148420
$352$	33.6565	1.79390
$353$	13.7533	0.732013	0.366006	−	0.930612i	$-0.380725\pi$
$353$	13.7533	0.732013	0.366006	+	0.930612i	$0.380725\pi$
$354$	44.6736	2.37438
$355$	−31.8711	−1.69154
$356$	35.4754	1.88019
$357$	36.6129	1.93776
$358$	38.8061	2.05097
$359$	−16.5022	−0.870954	−0.435477	−	0.900200i	$-0.643420\pi$
$359$	−16.5022	−0.870954	−0.435477	+	0.900200i	$0.643420\pi$
$360$	36.2638	1.91127
$361$	3.39349	0.178605
$362$	−16.0991	−0.846151
$363$	51.0836	2.68120
$364$	−12.7690	−0.669275
$365$	10.5561	0.552531
$366$	22.6620	1.18456
$367$	−6.74324	−0.351994	−0.175997	−	0.984391i	$-0.556315\pi$
$367$	−6.74324	−0.351994	−0.175997	+	0.984391i	$0.556315\pi$
$368$	2.69773	0.140629
$369$	−4.19464	−0.218364
$370$	−43.1969	−2.24570
$371$	−9.13062	−0.474038
$372$	−67.1543	−3.48179
$373$	−1.97547	−0.102286	−0.0511429	−	0.998691i	$-0.516286\pi$
$373$	−1.97547	−0.102286	−0.0511429	+	0.998691i	$0.516286\pi$
$374$	−80.5097	−4.16306
$375$	−47.3576	−2.44554
$376$	−5.45065	−0.281096
$377$	11.1163	0.572517
$378$	−7.78320	−0.400325
$379$	4.36681	0.224308	0.112154	−	0.993691i	$-0.464225\pi$
$379$	4.36681	0.224308	0.112154	+	0.993691i	$0.464225\pi$
$380$	57.4135	2.94525
$381$	−3.29014	−0.168559
$382$	30.9942	1.58580
$383$	−35.1012	−1.79359	−0.896793	−	0.442451i	$-0.854109\pi$
$383$	−35.1012	−1.79359	−0.896793	+	0.442451i	$0.854109\pi$
$384$	44.8833	2.29044
$385$	−47.7546	−2.43380
$386$	−3.60006	−0.183238
$387$	−29.4408	−1.49656
$388$	−43.8023	−2.22373
$389$	−9.47091	−0.480194	−0.240097	−	0.970749i	$-0.577179\pi$
$389$	−9.47091	−0.480194	−0.240097	+	0.970749i	$0.577179\pi$
$390$	−40.6417	−2.05797
$391$	−48.0018	−2.42756
$392$	5.26599	0.265973
$393$	4.18568	0.211140
$394$	42.1260	2.12228
$395$	−51.9657	−2.61468
$396$	63.0675	3.16926
$397$	−24.4676	−1.22799	−0.613996	−	0.789309i	$-0.710439\pi$
$397$	−24.4676	−1.22799	−0.613996	+	0.789309i	$0.710439\pi$
$398$	−4.80537	−0.240872
$399$	−27.1538	−1.35939
$400$	−3.51195	−0.175597
$401$	34.6947	1.73257	0.866286	−	0.499549i	$-0.166501\pi$
$401$	34.6947	1.73257	0.866286	+	0.499549i	$0.166501\pi$
$402$	19.4885	0.972000
$403$	15.0185	0.748126
$404$	59.1640	2.94352
$405$	26.3496	1.30932
$406$	31.1152	1.54422
$407$	−27.4930	−1.36278
$408$	−42.9530	−2.12649
$409$	2.50548	0.123888	0.0619441	−	0.998080i	$-0.480270\pi$
$409$	2.50548	0.123888	0.0619441	+	0.998080i	$0.480270\pi$
$410$	−10.1818	−0.502845
$411$	−25.5383	−1.25971
$412$	35.7651	1.76202
$413$	−17.1142	−0.842135
$414$	61.4437	3.01979
$415$	−52.1776	−2.56130
$416$	−10.9731	−0.538002
$417$	−4.40116	−0.215526
$418$	59.7098	2.92050
$419$	−3.62336	−0.177013	−0.0885064	−	0.996076i	$-0.528209\pi$
$419$	−3.62336	−0.177013	−0.0885064	+	0.996076i	$0.528209\pi$
$420$	−69.6183	−3.39702
$421$	−22.5157	−1.09735	−0.548673	−	0.836037i	$-0.684867\pi$
$421$	−22.5157	−1.09735	−0.548673	+	0.836037i	$0.684867\pi$
$422$	−61.0728	−2.97298
$423$	7.48171	0.363773
$424$	10.7117	0.520209
$425$	62.4895	3.03119
$426$	−48.3211	−2.34116
$427$	−8.68170	−0.420137
$428$	−29.9000	−1.44527
$429$	−25.8667	−1.24886
$430$	−71.4631	−3.44626
$431$	35.7270	1.72091	0.860456	−	0.509525i	$-0.170179\pi$
$431$	35.7270	1.72091	0.860456	+	0.509525i	$0.170179\pi$
$432$	−0.550290	−0.0264758
$433$	−6.21874	−0.298854	−0.149427	−	0.988773i	$-0.547743\pi$
$433$	−6.21874	−0.298854	−0.149427	+	0.988773i	$0.547743\pi$
$434$	42.0379	2.01788
$435$	60.6076	2.90591
$436$	−15.8011	−0.756734
$437$	35.6004	1.70300
$438$	16.0045	0.764726
$439$	−31.7342	−1.51459	−0.757295	−	0.653073i	$-0.773480\pi$
$439$	−31.7342	−1.51459	−0.757295	+	0.653073i	$0.773480\pi$
$440$	56.0241	2.67085
$441$	−7.22824	−0.344202
$442$	26.2488	1.24853
$443$	13.6556	0.648798	0.324399	−	0.945920i	$-0.394838\pi$
$443$	13.6556	0.648798	0.324399	+	0.945920i	$0.394838\pi$
$444$	−40.0802	−1.90212
$445$	−43.2563	−2.05054
$446$	−3.59237	−0.170104
$447$	−26.3588	−1.24673
$448$	−29.1124	−1.37543
$449$	6.59485	0.311230	0.155615	−	0.987818i	$-0.450264\pi$
$449$	6.59485	0.311230	0.155615	+	0.987818i	$0.450264\pi$
$450$	−79.9884	−3.77069
$451$	−6.48031	−0.305146
$452$	10.8324	0.509514
$453$	−5.08506	−0.238917
$454$	−33.4068	−1.56786
$455$	15.5696	0.729913
$456$	31.8560	1.49179
$457$	35.8175	1.67547	0.837737	−	0.546074i	$-0.183878\pi$
$457$	35.8175	1.67547	0.837737	+	0.546074i	$0.183878\pi$
$458$	39.0965	1.82686
$459$	9.79154	0.457030
$460$	91.2740	4.25567
$461$	40.0180	1.86382	0.931911	−	0.362686i	$-0.118140\pi$
$461$	40.0180	1.86382	0.931911	+	0.362686i	$0.118140\pi$
$462$	−72.4027	−3.36848
$463$	−10.8530	−0.504382	−0.252191	−	0.967678i	$-0.581151\pi$
$463$	−10.8530	−0.504382	−0.252191	+	0.967678i	$0.581151\pi$
$464$	2.19992	0.102128
$465$	81.8833	3.79725
$466$	−41.1543	−1.90644
$467$	−19.3463	−0.895239	−0.447620	−	0.894224i	$-0.647728\pi$
$467$	−19.3463	−0.895239	−0.447620	+	0.894224i	$0.647728\pi$
$468$	−20.5621	−0.950484
$469$	−7.46595	−0.344745
$470$	18.1607	0.837691
$471$	−13.8231	−0.636937
$472$	20.0778	0.924157
$473$	−45.4833	−2.09132
$474$	−78.7872	−3.61882
$475$	−46.3452	−2.12646
$476$	44.9636	2.06090
$477$	−14.7032	−0.673215
$478$	11.5577	0.528638
$479$	40.4170	1.84670	0.923349	−	0.383962i	$-0.125441\pi$
$479$	40.4170	1.84670	0.923349	+	0.383962i	$0.125441\pi$
$480$	−59.8272	−2.73073
$481$	8.96363	0.408706
$482$	37.9812	1.73000
$483$	−43.1682	−1.96422
$484$	62.7349	2.85159
$485$	53.4095	2.42520
$486$	50.4016	2.28626
$487$	8.72990	0.395590	0.197795	−	0.980243i	$-0.436622\pi$
$487$	8.72990	0.395590	0.197795	+	0.980243i	$0.436622\pi$
$488$	10.1851	0.461057
$489$	−63.6198	−2.87699
$490$	−17.5454	−0.792622
$491$	−15.0355	−0.678543	−0.339272	−	0.940688i	$-0.610181\pi$
$491$	−15.0355	−0.678543	−0.339272	+	0.940688i	$0.610181\pi$
$492$	−9.44721	−0.425913
$493$	−39.1440	−1.76296
$494$	−19.4674	−0.875878
$495$	−76.9002	−3.45641
$496$	2.97217	0.133455
$497$	18.5115	0.830355
$498$	−79.1086	−3.54494
$499$	−3.09287	−0.138456	−0.0692279	−	0.997601i	$-0.522054\pi$
$499$	−3.09287	−0.138456	−0.0692279	+	0.997601i	$0.522054\pi$
$500$	−58.1591	−2.60095
$501$	−14.5511	−0.650097
$502$	35.0319	1.56355
$503$	−3.78401	−0.168721	−0.0843604	−	0.996435i	$-0.526885\pi$
$503$	−3.78401	−0.168721	−0.0843604	+	0.996435i	$0.526885\pi$
$504$	−21.0629	−0.938217
$505$	−72.1405	−3.21021
$506$	94.9246	4.21991
$507$	−24.9577	−1.10841
$508$	−4.04057	−0.179271
$509$	14.9105	0.660894	0.330447	−	0.943825i	$-0.392800\pi$
$509$	14.9105	0.660894	0.330447	+	0.943825i	$0.392800\pi$
$510$	143.113	6.33713
$511$	−6.13124	−0.271230
$512$	−4.05124	−0.179041
$513$	−7.26187	−0.320619
$514$	−38.5706	−1.70128
$515$	−43.6095	−1.92166
$516$	−66.3070	−2.91900
$517$	11.5585	0.508343
$518$	25.0898	1.10238
$519$	−37.9552	−1.66605
$520$	−18.2657	−0.801005
$521$	17.6835	0.774727	0.387363	−	0.921927i	$-0.373386\pi$
$521$	17.6835	0.774727	0.387363	+	0.921927i	$0.373386\pi$
$522$	50.1054	2.19306
$523$	−15.3764	−0.672364	−0.336182	−	0.941797i	$-0.609136\pi$
$523$	−15.3764	−0.672364	−0.336182	+	0.941797i	$0.609136\pi$
$524$	5.14036	0.224558
$525$	56.1971	2.45264
$526$	−18.2478	−0.795642
$527$	−52.8851	−2.30371
$528$	−5.11903	−0.222777
$529$	33.5963	1.46071
$530$	−35.6898	−1.55027
$531$	−27.5594	−1.19597
$532$	−33.3471	−1.44578
$533$	2.11280	0.0915153
$534$	−65.5826	−2.83804
$535$	36.4580	1.57622
$536$	8.75880	0.378323
$537$	−43.9035	−1.89458
$538$	−3.61220	−0.155733
$539$	−11.1669	−0.480994
$540$	−18.6183	−0.801205
$541$	6.86967	0.295350	0.147675	−	0.989036i	$-0.452821\pi$
$541$	6.86967	0.295350	0.147675	+	0.989036i	$0.452821\pi$
$542$	42.8429	1.84026
$543$	18.2138	0.781631
$544$	38.6400	1.65668
$545$	19.2667	0.825296
$546$	23.6057	1.01023
$547$	25.4993	1.09027	0.545136	−	0.838348i	$-0.316478\pi$
$547$	25.4993	1.09027	0.545136	+	0.838348i	$0.316478\pi$
$548$	−31.3631	−1.33977
$549$	−13.9803	−0.596665
$550$	−123.574	−5.26923
$551$	29.0310	1.23676
$552$	50.6436	2.15553
$553$	30.1829	1.28351
$554$	−18.3568	−0.779906
$555$	48.8711	2.07446
$556$	−5.40499	−0.229223
$557$	−33.8576	−1.43459	−0.717297	−	0.696767i	$-0.754621\pi$
$557$	−33.8576	−1.43459	−0.717297	+	0.696767i	$0.754621\pi$
$558$	67.6944	2.86573
$559$	14.8290	0.627202
$560$	3.08123	0.130206
$561$	91.0851	3.84562
$562$	63.6199	2.68364
$563$	−0.242530	−0.0102214	−0.00511071	−	0.999987i	$-0.501627\pi$
$563$	−0.242530	−0.0102214	−0.00511071	+	0.999987i	$0.501627\pi$
$564$	16.8504	0.709530
$565$	−13.2083	−0.555677
$566$	29.4491	1.23784
$567$	−15.3045	−0.642727
$568$	−21.7171	−0.911229
$569$	14.9904	0.628428	0.314214	−	0.949352i	$-0.398259\pi$
$569$	14.9904	0.628428	0.314214	+	0.949352i	$0.398259\pi$
$570$	−106.139	−4.44567
$571$	8.86566	0.371016	0.185508	−	0.982643i	$-0.440607\pi$
$571$	8.86566	0.371016	0.185508	+	0.982643i	$0.440607\pi$
$572$	−31.7665	−1.32822
$573$	−35.0655	−1.46488
$574$	5.91386	0.246840
$575$	−73.6780	−3.07259
$576$	−46.8802	−1.95334
$577$	−0.0495283	−0.00206189	−0.00103094	−	0.999999i	$-0.500328\pi$
$577$	−0.0495283	−0.00206189	−0.00103094	+	0.999999i	$0.500328\pi$
$578$	−53.8351	−2.23924
$579$	4.07295	0.169266
$580$	74.4312	3.09059
$581$	30.3060	1.25731
$582$	80.9763	3.35658
$583$	−22.7151	−0.940762
$584$	7.19297	0.297647
$585$	25.0720	1.03660
$586$	−28.8459	−1.19161
$587$	21.5217	0.888294	0.444147	−	0.895954i	$-0.353507\pi$
$587$	21.5217	0.888294	0.444147	+	0.895954i	$0.353507\pi$
$588$	−16.2795	−0.671356
$589$	39.2221	1.61612
$590$	−66.8961	−2.75407
$591$	−47.6595	−1.96045
$592$	1.77391	0.0729071
$593$	−37.6113	−1.54451	−0.772256	−	0.635311i	$-0.780872\pi$
$593$	−37.6113	−1.54451	−0.772256	+	0.635311i	$0.780872\pi$
$594$	−19.3630	−0.794472
$595$	−54.8256	−2.24763
$596$	−32.3708	−1.32596
$597$	5.43659	0.222505
$598$	−30.9486	−1.26558
$599$	−2.80798	−0.114731	−0.0573654	−	0.998353i	$-0.518270\pi$
$599$	−2.80798	−0.114731	−0.0573654	+	0.998353i	$0.518270\pi$
$600$	−65.9286	−2.69152
$601$	4.56714	0.186298	0.0931488	−	0.995652i	$-0.470307\pi$
$601$	4.56714	0.186298	0.0931488	+	0.995652i	$0.470307\pi$
$602$	41.5075	1.69172
$603$	−12.0226	−0.489597
$604$	−6.24488	−0.254100
$605$	−76.4947	−3.10995
$606$	−109.375	−4.44306
$607$	24.6421	1.00019	0.500095	−	0.865970i	$-0.333298\pi$
$607$	24.6421	1.00019	0.500095	+	0.865970i	$0.333298\pi$
$608$	−28.6572	−1.16220
$609$	−35.2024	−1.42647
$610$	−33.9351	−1.37399
$611$	−3.76846	−0.152456
$612$	72.4059	2.92683
$613$	−11.8843	−0.480000	−0.240000	−	0.970773i	$-0.577148\pi$
$613$	−11.8843	−0.480000	−0.240000	+	0.970773i	$0.577148\pi$
$614$	−40.7440	−1.64429
$615$	11.5193	0.464502
$616$	−32.5402	−1.31108
$617$	−46.7220	−1.88096	−0.940479	−	0.339851i	$-0.889623\pi$
$617$	−46.7220	−1.88096	−0.940479	+	0.339851i	$0.889623\pi$
$618$	−66.1180	−2.65966
$619$	2.84489	0.114346	0.0571729	−	0.998364i	$-0.481791\pi$
$619$	2.84489	0.114346	0.0571729	+	0.998364i	$0.481791\pi$
$620$	100.559	4.03857
$621$	−11.5447	−0.463272
$622$	0.478072	0.0191689
$623$	25.1243	1.00658
$624$	1.66897	0.0668124
$625$	21.9471	0.877882
$626$	−54.9542	−2.19641
$627$	−67.5530	−2.69781
$628$	−16.9760	−0.677415
$629$	−31.5639	−1.25853
$630$	70.1783	2.79597
$631$	40.9656	1.63082	0.815408	−	0.578887i	$-0.196513\pi$
$631$	40.9656	1.63082	0.815408	+	0.578887i	$0.196513\pi$
$632$	−35.4096	−1.40852
$633$	69.0951	2.74628
$634$	60.6047	2.40692
$635$	4.92679	0.195514
$636$	−33.1148	−1.31309
$637$	3.64079	0.144253
$638$	77.4081	3.06461
$639$	29.8095	1.17924
$640$	−67.2101	−2.65671
$641$	26.3723	1.04164	0.520822	−	0.853665i	$-0.325626\pi$
$641$	26.3723	1.04164	0.520822	+	0.853665i	$0.325626\pi$
$642$	55.2755	2.18155
$643$	−21.7714	−0.858581	−0.429290	−	0.903166i	$-0.641236\pi$
$643$	−21.7714	−0.858581	−0.429290	+	0.903166i	$0.641236\pi$
$644$	−53.0142	−2.08905
$645$	80.8502	3.18347
$646$	68.5509	2.69710
$647$	21.8978	0.860892	0.430446	−	0.902616i	$-0.358356\pi$
$647$	21.8978	0.860892	0.430446	+	0.902616i	$0.358356\pi$
$648$	17.9547	0.705327
$649$	−42.5765	−1.67128
$650$	40.2893	1.58028
$651$	−47.5598	−1.86402
$652$	−78.1304	−3.05982
$653$	7.39587	0.289423	0.144711	−	0.989474i	$-0.453775\pi$
$653$	7.39587	0.289423	0.144711	+	0.989474i	$0.453775\pi$
$654$	29.2111	1.14224
$655$	−6.26780	−0.244903
$656$	0.418123	0.0163250
$657$	−9.87326	−0.385192
$658$	−10.5482	−0.411211
$659$	−42.0498	−1.63803	−0.819013	−	0.573775i	$-0.805479\pi$
$659$	−42.0498	−1.63803	−0.819013	+	0.573775i	$0.805479\pi$
$660$	−173.196	−6.74163
$661$	−46.0429	−1.79086	−0.895431	−	0.445201i	$-0.853132\pi$
$661$	−46.0429	−1.79086	−0.895431	+	0.445201i	$0.853132\pi$
$662$	18.5992	0.722877
$663$	−29.6968	−1.15333
$664$	−35.5541	−1.37976
$665$	40.6612	1.57677
$666$	40.4026	1.56557
$667$	46.1526	1.78703
$668$	−17.8700	−0.691412
$669$	4.06425	0.157133
$670$	−29.1829	−1.12744
$671$	−21.5982	−0.833790
$672$	34.7491	1.34048
$673$	6.58495	0.253831	0.126916	−	0.991914i	$-0.459492\pi$
$673$	6.58495	0.253831	0.126916	+	0.991914i	$0.459492\pi$
$674$	−48.1468	−1.85455
$675$	15.0290	0.578468
$676$	−30.6502	−1.17885
$677$	0.912294	0.0350623	0.0175312	−	0.999846i	$-0.494419\pi$
$677$	0.912294	0.0350623	0.0175312	+	0.999846i	$0.494419\pi$
$678$	−20.0256	−0.769080
$679$	−31.0216	−1.19050
$680$	64.3196	2.46654
$681$	37.7949	1.44831
$682$	104.581	4.00463
$683$	19.3088	0.738831	0.369416	−	0.929264i	$-0.379558\pi$
$683$	19.3088	0.738831	0.369416	+	0.929264i	$0.379558\pi$
$684$	−53.6996	−2.05326
$685$	38.2421	1.46115
$686$	45.6941	1.74461
$687$	−44.2321	−1.68756
$688$	2.93467	0.111883
$689$	7.40587	0.282141
$690$	−168.736	−6.42368
$691$	51.2370	1.94915	0.974574	−	0.224065i	$-0.0719327\pi$
$691$	51.2370	1.94915	0.974574	+	0.224065i	$0.0719327\pi$
$692$	−46.6121	−1.77193
$693$	44.6655	1.69670
$694$	−81.6292	−3.09860
$695$	6.59047	0.249991
$696$	41.2983	1.56541
$697$	−7.43984	−0.281804
$698$	−23.8681	−0.903421
$699$	46.5602	1.76107
$700$	69.0147	2.60851
$701$	−9.12396	−0.344607	−0.172304	−	0.985044i	$-0.555121\pi$
$701$	−9.12396	−0.344607	−0.172304	+	0.985044i	$0.555121\pi$
$702$	6.31297	0.238268
$703$	23.4092	0.882896
$704$	−72.4254	−2.72964
$705$	−20.5462	−0.773816
$706$	−31.2244	−1.17515
$707$	41.9009	1.57585
$708$	−62.0695	−2.33271
$709$	38.2691	1.43723	0.718613	−	0.695411i	$-0.244777\pi$
$709$	38.2691	1.43723	0.718613	+	0.695411i	$0.244777\pi$
$710$	72.3579	2.71554
$711$	48.6042	1.82280
$712$	−29.4750	−1.10462
$713$	62.3540	2.33517
$714$	−83.1232	−3.11081
$715$	38.7338	1.44856
$716$	−53.9172	−2.01498
$717$	−13.0759	−0.488328
$718$	37.4655	1.39820
$719$	−10.8281	−0.403820	−0.201910	−	0.979404i	$-0.564715\pi$
$719$	−10.8281	−0.403820	−0.201910	+	0.979404i	$0.564715\pi$
$720$	4.96176	0.184914
$721$	25.3294	0.943317
$722$	−7.70435	−0.286726
$723$	−42.9702	−1.59808
$724$	22.3681	0.831304
$725$	−60.0822	−2.23140
$726$	−115.977	−4.30430
$727$	−19.0617	−0.706958	−0.353479	−	0.935443i	$-0.615001\pi$
$727$	−19.0617	−0.706958	−0.353479	+	0.935443i	$0.615001\pi$
$728$	10.6092	0.393202
$729$	−36.4700	−1.35074
$730$	−23.9658	−0.887014
$731$	−52.2179	−1.93135
$732$	−31.4866	−1.16378
$733$	−11.0491	−0.408108	−0.204054	−	0.978960i	$-0.565412\pi$
$733$	−11.0491	−0.408108	−0.204054	+	0.978960i	$0.565412\pi$
$734$	15.3094	0.565079
$735$	19.8501	0.732183
$736$	−45.5583	−1.67930
$737$	−18.5737	−0.684171
$738$	9.52320	0.350554
$739$	−28.6146	−1.05261	−0.526303	−	0.850297i	$-0.676422\pi$
$739$	−28.6146	−1.05261	−0.526303	+	0.850297i	$0.676422\pi$
$740$	60.0177	2.20630
$741$	22.0245	0.809091
$742$	20.7295	0.761005
$743$	2.67288	0.0980583	0.0490292	−	0.998797i	$-0.484387\pi$
$743$	2.67288	0.0980583	0.0490292	+	0.998797i	$0.484387\pi$
$744$	55.7956	2.04557
$745$	39.4707	1.44609
$746$	4.48496	0.164206
$747$	48.8024	1.78559
$748$	111.860	4.09001
$749$	−21.1757	−0.773743
$750$	107.517	3.92598
$751$	19.1414	0.698480	0.349240	−	0.937033i	$-0.386440\pi$
$751$	19.1414	0.698480	0.349240	+	0.937033i	$0.386440\pi$
$752$	−0.745780	−0.0271958
$753$	−39.6335	−1.44433
$754$	−25.2376	−0.919099
$755$	7.61457	0.277123
$756$	10.8140	0.393300
$757$	12.9082	0.469155	0.234577	−	0.972097i	$-0.424629\pi$
$757$	12.9082	0.469155	0.234577	+	0.972097i	$0.424629\pi$
$758$	−9.91410	−0.360096
$759$	−107.393	−3.89814
$760$	−47.7024	−1.73035
$761$	−33.9667	−1.23129	−0.615646	−	0.788022i	$-0.711105\pi$
$761$	−33.9667	−1.23129	−0.615646	+	0.788022i	$0.711105\pi$
$762$	7.46971	0.270599
$763$	−11.1906	−0.405126
$764$	−43.0633	−1.55798
$765$	−88.2867	−3.19201
$766$	79.6912	2.87936
$767$	13.8814	0.501227
$768$	−34.9557	−1.26135
$769$	−16.9456	−0.611074	−0.305537	−	0.952180i	$-0.598836\pi$
$769$	−16.9456	−0.611074	−0.305537	+	0.952180i	$0.598836\pi$
$770$	108.419	3.90714
$771$	43.6371	1.57155
$772$	5.00192	0.180023
$773$	−35.5432	−1.27840	−0.639200	−	0.769040i	$-0.720735\pi$
$773$	−35.5432	−1.27840	−0.639200	+	0.769040i	$0.720735\pi$
$774$	66.8404	2.40253
$775$	−81.1734	−2.91583
$776$	36.3935	1.30645
$777$	−28.3855	−1.01832
$778$	21.5021	0.770887
$779$	5.51773	0.197693
$780$	56.4675	2.02186
$781$	46.0528	1.64790
$782$	108.980	3.89711
$783$	−9.41433	−0.336441
$784$	0.720513	0.0257326
$785$	20.6993	0.738791
$786$	−9.50287	−0.338956
$787$	22.9887	0.819458	0.409729	−	0.912207i	$-0.365623\pi$
$787$	22.9887	0.819458	0.409729	+	0.912207i	$0.365623\pi$
$788$	−58.5299	−2.08504
$789$	20.6448	0.734973
$790$	117.979	4.19751
$791$	7.67170	0.272774
$792$	−52.4001	−1.86196
$793$	7.04174	0.250059
$794$	55.5494	1.97138
$795$	40.3779	1.43206
$796$	6.67658	0.236645
$797$	10.5915	0.375170	0.187585	−	0.982248i	$-0.439934\pi$
$797$	10.5915	0.375170	0.187585	+	0.982248i	$0.439934\pi$
$798$	61.6481	2.18232
$799$	13.2700	0.469458
$800$	59.3085	2.09687
$801$	40.4582	1.42952
$802$	−78.7684	−2.78141
$803$	−15.2532	−0.538275
$804$	−27.0774	−0.954945
$805$	64.6418	2.27833
$806$	−34.0970	−1.20102
$807$	4.08668	0.143858
$808$	−49.1568	−1.72933
$809$	−21.2773	−0.748072	−0.374036	−	0.927414i	$-0.622026\pi$
$809$	−21.2773	−0.748072	−0.374036	+	0.927414i	$0.622026\pi$
$810$	−59.8221	−2.10194
$811$	−55.7911	−1.95909	−0.979545	−	0.201224i	$-0.935508\pi$
$811$	−55.7911	−1.95909	−0.979545	+	0.201224i	$0.935508\pi$
$812$	−43.2314	−1.51713
$813$	−48.4706	−1.69994
$814$	62.4182	2.18776
$815$	95.2668	3.33705
$816$	−5.87700	−0.205736
$817$	38.7273	1.35490
$818$	−5.68827	−0.198886
$819$	−14.5624	−0.508853
$820$	14.1466	0.494022
$821$	−31.9290	−1.11433	−0.557165	−	0.830402i	$-0.688111\pi$
$821$	−31.9290	−1.11433	−0.557165	+	0.830402i	$0.688111\pi$
$822$	57.9803	2.02230
$823$	−13.1916	−0.459831	−0.229915	−	0.973211i	$-0.573845\pi$
$823$	−13.1916	−0.459831	−0.229915	+	0.973211i	$0.573845\pi$
$824$	−29.7157	−1.03519
$825$	139.807	4.86744
$826$	38.8549	1.35193
$827$	34.4944	1.19949	0.599744	−	0.800192i	$-0.295269\pi$
$827$	34.4944	1.19949	0.599744	+	0.800192i	$0.295269\pi$
$828$	−85.3698	−2.96681
$829$	22.5511	0.783232	0.391616	−	0.920129i	$-0.371916\pi$
$829$	22.5511	0.783232	0.391616	+	0.920129i	$0.371916\pi$
$830$	118.460	4.11182
$831$	20.7681	0.720437
$832$	23.6131	0.818637
$833$	−12.8204	−0.444200
$834$	9.99208	0.345997
$835$	21.7895	0.754056
$836$	−82.9607	−2.86926
$837$	−12.7191	−0.439637
$838$	8.22623	0.284170
$839$	−47.6739	−1.64589	−0.822944	−	0.568123i	$-0.807670\pi$
$839$	−47.6739	−1.64589	−0.822944	+	0.568123i	$0.807670\pi$
$840$	57.8428	1.99577
$841$	8.63600	0.297793
$842$	51.1180	1.76164
$843$	−71.9767	−2.47901
$844$	84.8545	2.92081
$845$	37.3727	1.28566
$846$	−16.9859	−0.583989
$847$	44.4300	1.52663
$848$	1.46562	0.0503297
$849$	−33.3174	−1.14345
$850$	−141.872	−4.86616
$851$	37.2152	1.27572
$852$	67.1372	2.30008
$853$	−26.7100	−0.914534	−0.457267	−	0.889330i	$-0.651172\pi$
$853$	−26.7100	−0.914534	−0.457267	+	0.889330i	$0.651172\pi$
$854$	19.7103	0.674473
$855$	65.4776	2.23929
$856$	24.8426	0.849104
$857$	18.0824	0.617684	0.308842	−	0.951113i	$-0.400059\pi$
$857$	18.0824	0.617684	0.308842	+	0.951113i	$0.400059\pi$
$858$	58.7259	2.00487
$859$	−33.0324	−1.12705	−0.563525	−	0.826099i	$-0.690555\pi$
$859$	−33.0324	−1.12705	−0.563525	+	0.826099i	$0.690555\pi$
$860$	99.2908	3.38579
$861$	−6.69068	−0.228018
$862$	−81.1121	−2.76269
$863$	16.0710	0.547064	0.273532	−	0.961863i	$-0.411808\pi$
$863$	16.0710	0.547064	0.273532	+	0.961863i	$0.411808\pi$
$864$	9.29311	0.316158
$865$	56.8356	1.93247
$866$	14.1186	0.479769
$867$	60.9066	2.06850
$868$	−58.4074	−1.98248
$869$	75.0888	2.54721
$870$	−137.599	−4.66505
$871$	6.05564	0.205188
$872$	13.1284	0.444585
$873$	−49.9546	−1.69071
$874$	−80.8246	−2.73393
$875$	−41.1893	−1.39245
$876$	−22.2367	−0.751307
$877$	−6.58507	−0.222362	−0.111181	−	0.993800i	$-0.535463\pi$
$877$	−6.58507	−0.222362	−0.111181	+	0.993800i	$0.535463\pi$
$878$	72.0471	2.43147
$879$	32.6349	1.10075
$880$	7.66544	0.258402
$881$	4.37013	0.147233	0.0736166	−	0.997287i	$-0.476546\pi$
$881$	4.37013	0.147233	0.0736166	+	0.997287i	$0.476546\pi$
$882$	16.4105	0.552569
$883$	46.5428	1.56629	0.783145	−	0.621839i	$-0.213614\pi$
$883$	46.5428	1.56629	0.783145	+	0.621839i	$0.213614\pi$
$884$	−36.4701	−1.22662
$885$	75.6833	2.54407
$886$	−31.0028	−1.04156
$887$	−21.7092	−0.728922	−0.364461	−	0.931219i	$-0.618747\pi$
$887$	−21.7092	−0.728922	−0.364461	+	0.931219i	$0.618747\pi$
$888$	33.3009	1.11751
$889$	−2.86160	−0.0959750
$890$	98.2060	3.29187
$891$	−38.0743	−1.27554
$892$	4.99123	0.167119
$893$	−9.84164	−0.329338
$894$	59.8431	2.00145
$895$	65.7429	2.19754
$896$	39.0373	1.30414
$897$	35.0138	1.16908
$898$	−14.9725	−0.499638
$899$	50.8477	1.69587
$900$	111.136	3.70453
$901$	−26.0785	−0.868799
$902$	14.7124	0.489870
$903$	−46.9598	−1.56272
$904$	−9.00019	−0.299342
$905$	−27.2741	−0.906623
$906$	11.5448	0.383549
$907$	32.8950	1.09226	0.546130	−	0.837700i	$-0.316100\pi$
$907$	32.8950	1.09226	0.546130	+	0.837700i	$0.316100\pi$
$908$	46.4153	1.54035
$909$	67.4739	2.23797
$910$	−35.3481	−1.17178
$911$	53.0502	1.75763	0.878816	−	0.477161i	$-0.158334\pi$
$911$	53.0502	1.75763	0.878816	+	0.477161i	$0.158334\pi$
$912$	4.35866	0.144330
$913$	75.3950	2.49521
$914$	−81.3176	−2.68975
$915$	38.3926	1.26922
$916$	−54.3207	−1.79481
$917$	3.64049	0.120220
$918$	−22.2300	−0.733700
$919$	18.0592	0.595719	0.297859	−	0.954610i	$-0.403727\pi$
$919$	18.0592	0.595719	0.297859	+	0.954610i	$0.403727\pi$
$920$	−75.8357	−2.50023
$921$	46.0960	1.51891
$922$	−90.8539	−2.99212
$923$	−15.0147	−0.494216
$924$	100.596	3.30937
$925$	−48.4474	−1.59294
$926$	24.6399	0.809716
$927$	40.7885	1.33967
$928$	−37.1514	−1.21955
$929$	−21.9974	−0.721711	−0.360855	−	0.932622i	$-0.617515\pi$
$929$	−21.9974	−0.721711	−0.360855	+	0.932622i	$0.617515\pi$
$930$	−185.902	−6.09597
$931$	9.50821	0.311619
$932$	57.1798	1.87299
$933$	−0.540869	−0.0177073
$934$	43.9224	1.43719
$935$	−136.394	−4.46058
$936$	17.0842	0.558414
$937$	14.5182	0.474288	0.237144	−	0.971474i	$-0.423789\pi$
$937$	14.5182	0.474288	0.237144	+	0.971474i	$0.423789\pi$
$938$	16.9502	0.553442
$939$	62.1727	2.02893
$940$	−25.2325	−0.822992
$941$	36.3792	1.18593	0.592965	−	0.805228i	$-0.297957\pi$
$941$	36.3792	1.18593	0.592965	+	0.805228i	$0.297957\pi$
$942$	31.3831	1.02252
$943$	8.77191	0.285653
$944$	2.74713	0.0894114
$945$	−13.1858	−0.428935
$946$	103.262	3.35733
$947$	−29.0149	−0.942858	−0.471429	−	0.881904i	$-0.656262\pi$
$947$	−29.0149	−0.942858	−0.471429	+	0.881904i	$0.656262\pi$
$948$	109.467	3.55532
$949$	4.97306	0.161432
$950$	105.219	3.41375
$951$	−68.5654	−2.22339
$952$	−37.3584	−1.21079
$953$	7.46111	0.241689	0.120844	−	0.992671i	$-0.461440\pi$
$953$	7.46111	0.241689	0.120844	+	0.992671i	$0.461440\pi$
$954$	33.3812	1.08076
$955$	52.5085	1.69913
$956$	−16.0583	−0.519362
$957$	−87.5761	−2.83093
$958$	−91.7598	−2.96462
$959$	−22.2119	−0.717260
$960$	128.742	4.15513
$961$	37.6973	1.21604
$962$	−20.3504	−0.656123
$963$	−34.0997	−1.09885
$964$	−52.7710	−1.69964
$965$	−6.09900	−0.196334
$966$	98.0061	3.15329
$967$	−45.2259	−1.45437	−0.727184	−	0.686443i	$-0.759171\pi$
$967$	−45.2259	−1.45437	−0.727184	+	0.686443i	$0.759171\pi$
$968$	−52.1238	−1.67532
$969$	−77.5555	−2.49144
$970$	−121.257	−3.89333
$971$	−52.1270	−1.67284	−0.836418	−	0.548092i	$-0.815354\pi$
$971$	−52.1270	−1.67284	−0.836418	+	0.548092i	$0.815354\pi$
$972$	−70.0279	−2.24615
$973$	−3.82791	−0.122717
$974$	−19.8197	−0.635065
$975$	−45.5816	−1.45978
$976$	1.39356	0.0446069
$977$	12.6096	0.403416	0.201708	−	0.979446i	$-0.435351\pi$
$977$	12.6096	0.403416	0.201708	+	0.979446i	$0.435351\pi$
$978$	144.438	4.61861
$979$	62.5040	1.99764
$980$	24.3776	0.778714
$981$	−18.0204	−0.575348
$982$	34.1356	1.08931
$983$	−25.5607	−0.815260	−0.407630	−	0.913147i	$-0.633645\pi$
$983$	−25.5607	−0.815260	−0.407630	+	0.913147i	$0.633645\pi$
$984$	7.84928	0.250226
$985$	71.3673	2.27395
$986$	88.8698	2.83019
$987$	11.9337	0.379855
$988$	27.0479	0.860509
$989$	61.5673	1.95773
$990$	174.589	5.54880
$991$	−34.5071	−1.09615	−0.548077	−	0.836428i	$-0.684640\pi$
$991$	−34.5071	−1.09615	−0.548077	+	0.836428i	$0.684640\pi$
$992$	−50.1930	−1.59363
$993$	−21.0423	−0.667756
$994$	−42.0272	−1.33302
$995$	−8.14096	−0.258086
$996$	109.913	3.48274
$997$	−46.4270	−1.47036	−0.735178	−	0.677874i	$-0.762902\pi$
$997$	−46.4270	−1.47036	−0.735178	+	0.677874i	$0.762902\pi$
$998$	7.02183	0.222272
$999$	−7.59126	−0.240177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.18	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.18	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27033 q^{2} +2.56855 q^{3} +3.15439 q^{4} -3.84625 q^{5} -5.83145 q^{6} +2.23399 q^{7} -2.62085 q^{8} +3.59745 q^{9} +O(q^{10})\)	\(q-2.27033 q^{2} +2.56855 q^{3} +3.15439 q^{4} -3.84625 q^{5} -5.83145 q^{6} +2.23399 q^{7} -2.62085 q^{8} +3.59745 q^{9} +8.73225 q^{10} +5.55771 q^{11} +8.10221 q^{12} -1.81200 q^{13} -5.07190 q^{14} -9.87928 q^{15} -0.358595 q^{16} +6.38063 q^{17} -8.16739 q^{18} -4.73218 q^{19} -12.1326 q^{20} +5.73813 q^{21} -12.6178 q^{22} -7.52305 q^{23} -6.73178 q^{24} +9.79363 q^{25} +4.11383 q^{26} +1.53457 q^{27} +7.04689 q^{28} -6.13482 q^{29} +22.4292 q^{30} -8.28838 q^{31} +6.05583 q^{32} +14.2752 q^{33} -14.4861 q^{34} -8.59250 q^{35} +11.3478 q^{36} -4.94682 q^{37} +10.7436 q^{38} -4.65420 q^{39} +10.0804 q^{40} -1.16600 q^{41} -13.0274 q^{42} -8.18381 q^{43} +17.5312 q^{44} -13.8367 q^{45} +17.0798 q^{46} +2.07973 q^{47} -0.921069 q^{48} -2.00927 q^{49} -22.2348 q^{50} +16.3890 q^{51} -5.71575 q^{52} -4.08713 q^{53} -3.48399 q^{54} -21.3763 q^{55} -5.85496 q^{56} -12.1548 q^{57} +13.9281 q^{58} -7.66081 q^{59} -31.1631 q^{60} -3.88618 q^{61} +18.8174 q^{62} +8.03668 q^{63} -13.0315 q^{64} +6.96939 q^{65} -32.4095 q^{66} -3.34197 q^{67} +20.1270 q^{68} -19.3233 q^{69} +19.5078 q^{70} +8.28628 q^{71} -9.42837 q^{72} -2.74452 q^{73} +11.2309 q^{74} +25.1554 q^{75} -14.9271 q^{76} +12.4159 q^{77} +10.5666 q^{78} +13.5107 q^{79} +1.37925 q^{80} -6.85071 q^{81} +2.64721 q^{82} +13.5659 q^{83} +18.1003 q^{84} -24.5415 q^{85} +18.5799 q^{86} -15.7576 q^{87} -14.5659 q^{88} +11.2464 q^{89} +31.4138 q^{90} -4.04799 q^{91} -23.7307 q^{92} -21.2891 q^{93} -4.72167 q^{94} +18.2011 q^{95} +15.5547 q^{96} -13.8861 q^{97} +4.56170 q^{98} +19.9936 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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