LMFDB - Embedded newform 4019.2.a.b.1.16

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:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-2.43886 q^{2} -0.628245 q^{3} +3.94805 q^{4} +3.87591 q^{5} +1.53220 q^{6} -4.09962 q^{7} -4.75103 q^{8} -2.60531 q^{9} +O(q^{10})$	\(q-2.43886 q^{2} -0.628245 q^{3} +3.94805 q^{4} +3.87591 q^{5} +1.53220 q^{6} -4.09962 q^{7} -4.75103 q^{8} -2.60531 q^{9} -9.45281 q^{10} -2.21292 q^{11} -2.48034 q^{12} +1.62769 q^{13} +9.99840 q^{14} -2.43502 q^{15} +3.69100 q^{16} +6.22231 q^{17} +6.35399 q^{18} +2.20181 q^{19} +15.3023 q^{20} +2.57556 q^{21} +5.39702 q^{22} +3.51792 q^{23} +2.98481 q^{24} +10.0227 q^{25} -3.96970 q^{26} +3.52150 q^{27} -16.1855 q^{28} -1.15470 q^{29} +5.93868 q^{30} +5.67640 q^{31} +0.500206 q^{32} +1.39026 q^{33} -15.1754 q^{34} -15.8897 q^{35} -10.2859 q^{36} -11.2931 q^{37} -5.36992 q^{38} -1.02259 q^{39} -18.4146 q^{40} +6.68311 q^{41} -6.28144 q^{42} -4.36322 q^{43} -8.73674 q^{44} -10.0979 q^{45} -8.57973 q^{46} -5.80689 q^{47} -2.31885 q^{48} +9.80686 q^{49} -24.4439 q^{50} -3.90913 q^{51} +6.42619 q^{52} +8.19329 q^{53} -8.58847 q^{54} -8.57709 q^{55} +19.4774 q^{56} -1.38328 q^{57} +2.81617 q^{58} +2.69786 q^{59} -9.61358 q^{60} -9.72805 q^{61} -13.8440 q^{62} +10.6808 q^{63} -8.60194 q^{64} +6.30877 q^{65} -3.39065 q^{66} -8.40586 q^{67} +24.5660 q^{68} -2.21012 q^{69} +38.7529 q^{70} -15.5834 q^{71} +12.3779 q^{72} +11.0703 q^{73} +27.5424 q^{74} -6.29669 q^{75} +8.69287 q^{76} +9.07214 q^{77} +2.49394 q^{78} -5.03435 q^{79} +14.3060 q^{80} +5.60356 q^{81} -16.2992 q^{82} -9.40283 q^{83} +10.1685 q^{84} +24.1171 q^{85} +10.6413 q^{86} +0.725437 q^{87} +10.5137 q^{88} +11.8335 q^{89} +24.6275 q^{90} -6.67289 q^{91} +13.8889 q^{92} -3.56617 q^{93} +14.1622 q^{94} +8.53402 q^{95} -0.314252 q^{96} -6.70100 q^{97} -23.9176 q^{98} +5.76535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.43886	−1.72454	−0.862268	−	0.506452i	$-0.830957\pi$
$2$	−2.43886	−1.72454	−0.862268	+	0.506452i	$0.830957\pi$
$3$	−0.628245	−0.362717	−0.181359	−	0.983417i	$-0.558049\pi$
$3$	−0.628245	−0.362717	−0.181359	+	0.983417i	$0.558049\pi$
$4$	3.94805	1.97403
$5$	3.87591	1.73336	0.866680	−	0.498865i	$-0.166250\pi$
$5$	3.87591	1.73336	0.866680	+	0.498865i	$0.166250\pi$
$6$	1.53220	0.625519
$7$	−4.09962	−1.54951	−0.774755	−	0.632262i	$-0.782127\pi$
$7$	−4.09962	−1.54951	−0.774755	+	0.632262i	$0.782127\pi$
$8$	−4.75103	−1.67974
$9$	−2.60531	−0.868436
$10$	−9.45281	−2.98924
$11$	−2.21292	−0.667222	−0.333611	−	0.942711i	$-0.608267\pi$
$11$	−2.21292	−0.667222	−0.333611	+	0.942711i	$0.608267\pi$
$12$	−2.48034	−0.716013
$13$	1.62769	0.451439	0.225720	−	0.974192i	$-0.427527\pi$
$13$	1.62769	0.451439	0.225720	+	0.974192i	$0.427527\pi$
$14$	9.99840	2.67219
$15$	−2.43502	−0.628719
$16$	3.69100	0.922751
$17$	6.22231	1.50913	0.754566	−	0.656224i	$-0.227847\pi$
$17$	6.22231	1.50913	0.754566	+	0.656224i	$0.227847\pi$
$18$	6.35399	1.49765
$19$	2.20181	0.505130	0.252565	−	0.967580i	$-0.418726\pi$
$19$	2.20181	0.505130	0.252565	+	0.967580i	$0.418726\pi$
$20$	15.3023	3.42170
$21$	2.57556	0.562034
$22$	5.39702	1.15065
$23$	3.51792	0.733537	0.366769	−	0.930312i	$-0.380464\pi$
$23$	3.51792	0.733537	0.366769	+	0.930312i	$0.380464\pi$
$24$	2.98481	0.609271
$25$	10.0227	2.00453
$26$	−3.96970	−0.778523
$27$	3.52150	0.677714
$28$	−16.1855	−3.05877
$29$	−1.15470	−0.214423	−0.107212	−	0.994236i	$-0.534192\pi$
$29$	−1.15470	−0.214423	−0.107212	+	0.994236i	$0.534192\pi$
$30$	5.93868	1.08425
$31$	5.67640	1.01951	0.509756	−	0.860319i	$-0.329736\pi$
$31$	5.67640	1.01951	0.509756	+	0.860319i	$0.329736\pi$
$32$	0.500206	0.0884247
$33$	1.39026	0.242013
$34$	−15.1754	−2.60255
$35$	−15.8897	−2.68586
$36$	−10.2859	−1.71432
$37$	−11.2931	−1.85658	−0.928291	−	0.371855i	$-0.878722\pi$
$37$	−11.2931	−1.85658	−0.928291	+	0.371855i	$0.878722\pi$
$38$	−5.36992	−0.871116
$39$	−1.02259	−0.163745
$40$	−18.4146	−2.91160
$41$	6.68311	1.04373	0.521863	−	0.853029i	$-0.325237\pi$
$41$	6.68311	1.04373	0.521863	+	0.853029i	$0.325237\pi$
$42$	−6.28144	−0.969248
$43$	−4.36322	−0.665385	−0.332693	−	0.943035i	$-0.607957\pi$
$43$	−4.36322	−0.665385	−0.332693	+	0.943035i	$0.607957\pi$
$44$	−8.73674	−1.31711
$45$	−10.0979	−1.50531
$46$	−8.57973	−1.26501
$47$	−5.80689	−0.847021	−0.423511	−	0.905891i	$-0.639202\pi$
$47$	−5.80689	−0.847021	−0.423511	+	0.905891i	$0.639202\pi$
$48$	−2.31885	−0.334698
$49$	9.80686	1.40098
$50$	−24.4439	−3.45689
$51$	−3.90913	−0.547388
$52$	6.42619	0.891152
$53$	8.19329	1.12543	0.562717	−	0.826649i	$-0.309756\pi$
$53$	8.19329	1.12543	0.562717	+	0.826649i	$0.309756\pi$
$54$	−8.58847	−1.16874
$55$	−8.57709	−1.15654
$56$	19.4774	2.60278
$57$	−1.38328	−0.183219
$58$	2.81617	0.369781
$59$	2.69786	0.351232	0.175616	−	0.984459i	$-0.443808\pi$
$59$	2.69786	0.351232	0.175616	+	0.984459i	$0.443808\pi$
$60$	−9.61358	−1.24111
$61$	−9.72805	−1.24555	−0.622775	−	0.782401i	$-0.713995\pi$
$61$	−9.72805	−1.24555	−0.622775	+	0.782401i	$0.713995\pi$
$62$	−13.8440	−1.75818
$63$	10.6808	1.34565
$64$	−8.60194	−1.07524
$65$	6.30877	0.782506
$66$	−3.39065	−0.417360
$67$	−8.40586	−1.02694	−0.513470	−	0.858108i	$-0.671640\pi$
$67$	−8.40586	−1.02694	−0.513470	+	0.858108i	$0.671640\pi$
$68$	24.5660	2.97907
$69$	−2.21012	−0.266067
$70$	38.7529	4.63186
$71$	−15.5834	−1.84941	−0.924705	−	0.380684i	$-0.875689\pi$
$71$	−15.5834	−1.84941	−0.924705	+	0.380684i	$0.875689\pi$
$72$	12.3779	1.45875
$73$	11.0703	1.29568	0.647839	−	0.761777i	$-0.275673\pi$
$73$	11.0703	1.29568	0.647839	+	0.761777i	$0.275673\pi$
$74$	27.5424	3.20174
$75$	−6.29669	−0.727079
$76$	8.69287	0.997140
$77$	9.07214	1.03387
$78$	2.49394	0.282384
$79$	−5.03435	−0.566409	−0.283204	−	0.959060i	$-0.591398\pi$
$79$	−5.03435	−0.566409	−0.283204	+	0.959060i	$0.591398\pi$
$80$	14.3060	1.59946
$81$	5.60356	0.622618
$82$	−16.2992	−1.79994
$83$	−9.40283	−1.03209	−0.516047	−	0.856560i	$-0.672597\pi$
$83$	−9.40283	−1.03209	−0.516047	+	0.856560i	$0.672597\pi$
$84$	10.1685	1.10947
$85$	24.1171	2.61587
$86$	10.6413	1.14748
$87$	0.725437	0.0777750
$88$	10.5137	1.12076
$89$	11.8335	1.25435	0.627174	−	0.778879i	$-0.284212\pi$
$89$	11.8335	1.25435	0.627174	+	0.778879i	$0.284212\pi$
$90$	24.6275	2.59597
$91$	−6.67289	−0.699509
$92$	13.8889	1.44802
$93$	−3.56617	−0.369794
$94$	14.1622	1.46072
$95$	8.53402	0.875572
$96$	−0.314252	−0.0320732
$97$	−6.70100	−0.680383	−0.340192	−	0.940356i	$-0.610492\pi$
$97$	−6.70100	−0.680383	−0.340192	+	0.940356i	$0.610492\pi$
$98$	−23.9176	−2.41604
$99$	5.76535	0.579440
$100$	39.5700	3.95700
$101$	13.5965	1.35290	0.676450	−	0.736489i	$-0.263518\pi$
$101$	13.5965	1.35290	0.676450	+	0.736489i	$0.263518\pi$
$102$	9.53384	0.943991
$103$	1.60985	0.158624	0.0793119	−	0.996850i	$-0.474728\pi$
$103$	1.60985	0.158624	0.0793119	+	0.996850i	$0.474728\pi$
$104$	−7.73319	−0.758301
$105$	9.98264	0.974206
$106$	−19.9823	−1.94085
$107$	0.759987	0.0734708	0.0367354	−	0.999325i	$-0.488304\pi$
$107$	0.759987	0.0734708	0.0367354	+	0.999325i	$0.488304\pi$
$108$	13.9031	1.33782
$109$	13.3165	1.27549	0.637744	−	0.770248i	$-0.279868\pi$
$109$	13.3165	1.27549	0.637744	+	0.770248i	$0.279868\pi$
$110$	20.9184	1.99449
$111$	7.09486	0.673414
$112$	−15.1317	−1.42981
$113$	−8.56360	−0.805596	−0.402798	−	0.915289i	$-0.631962\pi$
$113$	−8.56360	−0.805596	−0.402798	+	0.915289i	$0.631962\pi$
$114$	3.37362	0.315969
$115$	13.6351	1.27148
$116$	−4.55883	−0.423277
$117$	−4.24063	−0.392046
$118$	−6.57971	−0.605712
$119$	−25.5091	−2.33842
$120$	11.5688	1.05609
$121$	−6.10297	−0.554815
$122$	23.7254	2.14799
$123$	−4.19863	−0.378578
$124$	22.4107	2.01254
$125$	19.4674	1.74122
$126$	−26.0489	−2.32062
$127$	−20.8677	−1.85171	−0.925854	−	0.377882i	$-0.876652\pi$
$127$	−20.8677	−1.85171	−0.925854	+	0.377882i	$0.876652\pi$
$128$	19.9785	1.76587
$129$	2.74117	0.241347
$130$	−15.3862	−1.34946
$131$	10.0230	0.875715	0.437857	−	0.899044i	$-0.355737\pi$
$131$	10.0230	0.875715	0.437857	+	0.899044i	$0.355737\pi$
$132$	5.48881	0.477739
$133$	−9.02659	−0.782704
$134$	20.5007	1.77099
$135$	13.6490	1.17472
$136$	−29.5624	−2.53495
$137$	−3.80142	−0.324777	−0.162389	−	0.986727i	$-0.551920\pi$
$137$	−3.80142	−0.324777	−0.162389	+	0.986727i	$0.551920\pi$
$138$	5.39017	0.458842
$139$	5.68409	0.482119	0.241059	−	0.970510i	$-0.422505\pi$
$139$	5.68409	0.482119	0.241059	+	0.970510i	$0.422505\pi$
$140$	−62.7335	−5.30195
$141$	3.64814	0.307229
$142$	38.0058	3.18938
$143$	−3.60195	−0.301210
$144$	−9.61620	−0.801350
$145$	−4.47553	−0.371673
$146$	−26.9989	−2.23444
$147$	−6.16111	−0.508160
$148$	−44.5859	−3.66494
$149$	−9.66764	−0.792004	−0.396002	−	0.918250i	$-0.629603\pi$
$149$	−9.66764	−0.792004	−0.396002	+	0.918250i	$0.629603\pi$
$150$	15.3568	1.25387
$151$	19.4769	1.58500	0.792502	−	0.609869i	$-0.208778\pi$
$151$	19.4769	1.58500	0.792502	+	0.609869i	$0.208778\pi$
$152$	−10.4609	−0.848489
$153$	−16.2110	−1.31059
$154$	−22.1257	−1.78294
$155$	22.0012	1.76718
$156$	−4.03722	−0.323236
$157$	1.76005	0.140467	0.0702334	−	0.997531i	$-0.477626\pi$
$157$	1.76005	0.140467	0.0702334	+	0.997531i	$0.477626\pi$
$158$	12.2781	0.976793
$159$	−5.14739	−0.408215
$160$	1.93875	0.153272
$161$	−14.4221	−1.13662
$162$	−13.6663	−1.07373
$163$	8.12353	0.636284	0.318142	−	0.948043i	$-0.396941\pi$
$163$	8.12353	0.636284	0.318142	+	0.948043i	$0.396941\pi$
$164$	26.3853	2.06034
$165$	5.38851	0.419495
$166$	22.9322	1.77988
$167$	22.1876	1.71693	0.858464	−	0.512873i	$-0.171419\pi$
$167$	22.1876	1.71693	0.858464	+	0.512873i	$0.171419\pi$
$168$	−12.2366	−0.944072
$169$	−10.3506	−0.796203
$170$	−58.8183	−4.51116
$171$	−5.73640	−0.438673
$172$	−17.2262	−1.31349
$173$	−9.30584	−0.707510	−0.353755	−	0.935338i	$-0.615095\pi$
$173$	−9.30584	−0.707510	−0.353755	+	0.935338i	$0.615095\pi$
$174$	−1.76924	−0.134126
$175$	−41.0891	−3.10605
$176$	−8.16791	−0.615680
$177$	−1.69492	−0.127398
$178$	−28.8603	−2.16317
$179$	1.19714	0.0894786	0.0447393	−	0.998999i	$-0.485754\pi$
$179$	1.19714	0.0894786	0.0447393	+	0.998999i	$0.485754\pi$
$180$	−39.8672	−2.97152
$181$	20.4926	1.52321	0.761603	−	0.648044i	$-0.224413\pi$
$181$	20.4926	1.52321	0.761603	+	0.648044i	$0.224413\pi$
$182$	16.2743	1.20633
$183$	6.11159	0.451782
$184$	−16.7137	−1.23215
$185$	−43.7712	−3.21812
$186$	8.69739	0.637723
$187$	−13.7695	−1.00693
$188$	−22.9259	−1.67204
$189$	−14.4368	−1.05012
$190$	−20.8133	−1.50996
$191$	11.0771	0.801509	0.400754	−	0.916186i	$-0.368748\pi$
$191$	11.0771	0.801509	0.400754	+	0.916186i	$0.368748\pi$
$192$	5.40412	0.390009
$193$	19.4580	1.40061	0.700307	−	0.713841i	$-0.253046\pi$
$193$	19.4580	1.40061	0.700307	+	0.713841i	$0.253046\pi$
$194$	16.3428	1.17335
$195$	−3.96345	−0.283828
$196$	38.7180	2.76557
$197$	11.4181	0.813503	0.406752	−	0.913539i	$-0.366661\pi$
$197$	11.4181	0.813503	0.406752	+	0.913539i	$0.366661\pi$
$198$	−14.0609	−0.999265
$199$	20.0999	1.42485	0.712423	−	0.701751i	$-0.247598\pi$
$199$	20.0999	1.42485	0.712423	+	0.701751i	$0.247598\pi$
$200$	−47.6180	−3.36710
$201$	5.28094	0.372489
$202$	−33.1599	−2.33312
$203$	4.73385	0.332251
$204$	−15.4335	−1.08056
$205$	25.9031	1.80915
$206$	−3.92621	−0.273552
$207$	−9.16527	−0.637031
$208$	6.00780	0.416566
$209$	−4.87244	−0.337034
$210$	−24.3463	−1.68005
$211$	21.0824	1.45137	0.725685	−	0.688027i	$-0.241523\pi$
$211$	21.0824	1.45137	0.725685	+	0.688027i	$0.241523\pi$
$212$	32.3475	2.22164
$213$	9.79019	0.670813
$214$	−1.85350	−0.126703
$215$	−16.9115	−1.15335
$216$	−16.7308	−1.13838
$217$	−23.2711	−1.57974
$218$	−32.4771	−2.19963
$219$	−6.95484	−0.469965
$220$	−33.8628	−2.28303
$221$	10.1280	0.681281
$222$	−17.3034	−1.16133
$223$	12.6501	0.847111	0.423555	−	0.905870i	$-0.360782\pi$
$223$	12.6501	0.847111	0.423555	+	0.905870i	$0.360782\pi$
$224$	−2.05065	−0.137015
$225$	−26.1122	−1.74081
$226$	20.8855	1.38928
$227$	0.455889	0.0302584	0.0151292	−	0.999886i	$-0.495184\pi$
$227$	0.455889	0.0302584	0.0151292	+	0.999886i	$0.495184\pi$
$228$	−5.46125	−0.361680
$229$	4.05325	0.267846	0.133923	−	0.990992i	$-0.457242\pi$
$229$	4.05325	0.267846	0.133923	+	0.990992i	$0.457242\pi$
$230$	−33.2542	−2.19272
$231$	−5.69952	−0.375001
$232$	5.48604	0.360176
$233$	2.02974	0.132973	0.0664865	−	0.997787i	$-0.478821\pi$
$233$	2.02974	0.132973	0.0664865	+	0.997787i	$0.478821\pi$
$234$	10.3423	0.676098
$235$	−22.5070	−1.46819
$236$	10.6513	0.693340
$237$	3.16280	0.205446
$238$	62.2132	4.03268
$239$	−2.94077	−0.190223	−0.0951114	−	0.995467i	$-0.530321\pi$
$239$	−2.94077	−0.190223	−0.0951114	+	0.995467i	$0.530321\pi$
$240$	−8.98766	−0.580151
$241$	−1.99108	−0.128257	−0.0641285	−	0.997942i	$-0.520427\pi$
$241$	−1.99108	−0.128257	−0.0641285	+	0.997942i	$0.520427\pi$
$242$	14.8843	0.956799
$243$	−14.0849	−0.903548
$244$	−38.4068	−2.45875
$245$	38.0105	2.42840
$246$	10.2399	0.652871
$247$	3.58386	0.228036
$248$	−26.9687	−1.71252
$249$	5.90728	0.374358
$250$	−47.4784	−3.00280
$251$	22.2070	1.40170	0.700848	−	0.713311i	$-0.252805\pi$
$251$	22.2070	1.40170	0.700848	+	0.713311i	$0.252805\pi$
$252$	42.1682	2.65635
$253$	−7.78490	−0.489432
$254$	50.8934	3.19334
$255$	−15.1514	−0.948821
$256$	−31.5210	−1.97006
$257$	−10.2911	−0.641943	−0.320971	−	0.947089i	$-0.604009\pi$
$257$	−10.2911	−0.641943	−0.320971	+	0.947089i	$0.604009\pi$
$258$	−6.68534	−0.416211
$259$	46.2976	2.87679
$260$	24.9073	1.54469
$261$	3.00836	0.186213
$262$	−24.4448	−1.51020
$263$	−11.3371	−0.699076	−0.349538	−	0.936922i	$-0.613661\pi$
$263$	−11.3371	−0.699076	−0.349538	+	0.936922i	$0.613661\pi$
$264$	−6.60515	−0.406519
$265$	31.7564	1.95078
$266$	22.0146	1.34980
$267$	−7.43432	−0.454973
$268$	−33.1868	−2.02720
$269$	−18.4372	−1.12414	−0.562068	−	0.827091i	$-0.689994\pi$
$269$	−18.4372	−1.12414	−0.562068	+	0.827091i	$0.689994\pi$
$270$	−33.2881	−2.02585
$271$	28.4641	1.72907	0.864534	−	0.502574i	$-0.167614\pi$
$271$	28.4641	1.72907	0.864534	+	0.502574i	$0.167614\pi$
$272$	22.9666	1.39255
$273$	4.19221	0.253724
$274$	9.27115	0.560090
$275$	−22.1794	−1.33747
$276$	−8.72565	−0.525222
$277$	1.83137	0.110036	0.0550182	−	0.998485i	$-0.482478\pi$
$277$	1.83137	0.110036	0.0550182	+	0.998485i	$0.482478\pi$
$278$	−13.8627	−0.831431
$279$	−14.7888	−0.885380
$280$	75.4926	4.51155
$281$	5.63789	0.336328	0.168164	−	0.985759i	$-0.446216\pi$
$281$	5.63789	0.336328	0.168164	+	0.985759i	$0.446216\pi$
$282$	−8.89732	−0.529828
$283$	12.8735	0.765248	0.382624	−	0.923904i	$-0.375020\pi$
$283$	12.8735	0.765248	0.382624	+	0.923904i	$0.375020\pi$
$284$	−61.5241	−3.65078
$285$	−5.36145	−0.317585
$286$	8.78466	0.519448
$287$	−27.3982	−1.61726
$288$	−1.30319	−0.0767912
$289$	21.7172	1.27748
$290$	10.9152	0.640963
$291$	4.20986	0.246787
$292$	43.7060	2.55770
$293$	14.1162	0.824679	0.412340	−	0.911030i	$-0.364712\pi$
$293$	14.1162	0.824679	0.412340	+	0.911030i	$0.364712\pi$
$294$	15.0261	0.876340
$295$	10.4567	0.608810
$296$	53.6541	3.11858
$297$	−7.79282	−0.452185
$298$	23.5780	1.36584
$299$	5.72607	0.331147
$300$	−24.8596	−1.43527
$301$	17.8875	1.03102
$302$	−47.5014	−2.73340
$303$	−8.54191	−0.490720
$304$	8.12690	0.466109
$305$	−37.7050	−2.15898
$306$	39.5365	2.26015
$307$	−21.9501	−1.25276	−0.626380	−	0.779517i	$-0.715464\pi$
$307$	−21.9501	−1.25276	−0.626380	+	0.779517i	$0.715464\pi$
$308$	35.8173	2.04088
$309$	−1.01138	−0.0575355
$310$	−53.6579	−3.04756
$311$	−25.2490	−1.43174	−0.715871	−	0.698233i	$-0.753970\pi$
$311$	−25.2490	−1.43174	−0.715871	+	0.698233i	$0.753970\pi$
$312$	4.85833	0.275049
$313$	8.19362	0.463131	0.231565	−	0.972819i	$-0.425615\pi$
$313$	8.19362	0.463131	0.231565	+	0.972819i	$0.425615\pi$
$314$	−4.29251	−0.242240
$315$	41.3977	2.33250
$316$	−19.8759	−1.11811
$317$	31.9121	1.79236	0.896180	−	0.443691i	$-0.146331\pi$
$317$	31.9121	1.79236	0.896180	+	0.443691i	$0.146331\pi$
$318$	12.5538	0.703981
$319$	2.55527	0.143068
$320$	−33.3403	−1.86378
$321$	−0.477458	−0.0266491
$322$	35.1736	1.96015
$323$	13.7004	0.762309
$324$	22.1231	1.22906
$325$	16.3138	0.904925
$326$	−19.8122	−1.09729
$327$	−8.36602	−0.462642
$328$	−31.7517	−1.75319
$329$	23.8060	1.31247
$330$	−13.1418	−0.723435
$331$	11.6244	0.638933	0.319466	−	0.947598i	$-0.396496\pi$
$331$	11.6244	0.638933	0.319466	+	0.947598i	$0.396496\pi$
$332$	−37.1228	−2.03738
$333$	29.4221	1.61232
$334$	−54.1125	−2.96091
$335$	−32.5804	−1.78005
$336$	9.50641	0.518617
$337$	−27.7217	−1.51010	−0.755049	−	0.655668i	$-0.772387\pi$
$337$	−27.7217	−1.51010	−0.755049	+	0.655668i	$0.772387\pi$
$338$	25.2438	1.37308
$339$	5.38004	0.292203
$340$	95.2156	5.16379
$341$	−12.5614	−0.680240
$342$	13.9903	0.756508
$343$	−11.5071	−0.621323
$344$	20.7298	1.11768
$345$	−8.56621	−0.461189
$346$	22.6957	1.22013
$347$	−26.5737	−1.42655	−0.713276	−	0.700883i	$-0.752789\pi$
$347$	−26.5737	−1.42655	−0.713276	+	0.700883i	$0.752789\pi$
$348$	2.86406	0.153530
$349$	17.4443	0.933772	0.466886	−	0.884317i	$-0.345376\pi$
$349$	17.4443	0.933772	0.466886	+	0.884317i	$0.345376\pi$
$350$	100.211	5.35649
$351$	5.73191	0.305947
$352$	−1.10692	−0.0589989
$353$	30.8824	1.64371	0.821853	−	0.569699i	$-0.192940\pi$
$353$	30.8824	1.64371	0.821853	+	0.569699i	$0.192940\pi$
$354$	4.13367	0.219702
$355$	−60.3999	−3.20569
$356$	46.7192	2.47611
$357$	16.0260	0.848183
$358$	−2.91967	−0.154309
$359$	23.4050	1.23527	0.617633	−	0.786466i	$-0.288092\pi$
$359$	23.4050	1.23527	0.617633	+	0.786466i	$0.288092\pi$
$360$	47.9756	2.52854
$361$	−14.1520	−0.744843
$362$	−49.9787	−2.62682
$363$	3.83415	0.201241
$364$	−26.3449	−1.38085
$365$	42.9074	2.24588
$366$	−14.9053	−0.779114
$367$	28.3927	1.48209	0.741043	−	0.671458i	$-0.234332\pi$
$367$	28.3927	1.48209	0.741043	+	0.671458i	$0.234332\pi$
$368$	12.9847	0.676872
$369$	−17.4116	−0.906410
$370$	106.752	5.54977
$371$	−33.5894	−1.74387
$372$	−14.0794	−0.729983
$373$	13.6212	0.705281	0.352640	−	0.935759i	$-0.385284\pi$
$373$	13.6212	0.705281	0.352640	+	0.935759i	$0.385284\pi$
$374$	33.5819	1.73648
$375$	−12.2303	−0.631570
$376$	27.5887	1.42278
$377$	−1.87950	−0.0967991
$378$	35.2094	1.81098
$379$	−3.96826	−0.203836	−0.101918	−	0.994793i	$-0.532498\pi$
$379$	−3.96826	−0.203836	−0.101918	+	0.994793i	$0.532498\pi$
$380$	33.6928	1.72840
$381$	13.1100	0.671646
$382$	−27.0155	−1.38223
$383$	2.84868	0.145561	0.0727804	−	0.997348i	$-0.476813\pi$
$383$	2.84868	0.145561	0.0727804	+	0.997348i	$0.476813\pi$
$384$	−12.5514	−0.640511
$385$	35.1628	1.79206
$386$	−47.4553	−2.41541
$387$	11.3675	0.577845
$388$	−26.4559	−1.34309
$389$	0.863906	0.0438018	0.0219009	−	0.999760i	$-0.493028\pi$
$389$	0.863906	0.0438018	0.0219009	+	0.999760i	$0.493028\pi$
$390$	9.66630	0.489472
$391$	21.8896	1.10701
$392$	−46.5927	−2.35329
$393$	−6.29690	−0.317637
$394$	−27.8471	−1.40292
$395$	−19.5127	−0.981790
$396$	22.7619	1.14383
$397$	14.8634	0.745973	0.372986	−	0.927837i	$-0.378334\pi$
$397$	14.8634	0.745973	0.372986	+	0.927837i	$0.378334\pi$
$398$	−49.0209	−2.45720
$399$	5.67090	0.283900
$400$	36.9937	1.84969
$401$	28.9868	1.44753	0.723767	−	0.690045i	$-0.242409\pi$
$401$	28.9868	1.44753	0.723767	+	0.690045i	$0.242409\pi$
$402$	−12.8795	−0.642370
$403$	9.23940	0.460247
$404$	53.6796	2.67066
$405$	21.7189	1.07922
$406$	−11.5452	−0.572979
$407$	24.9909	1.23875
$408$	18.5724	0.919471
$409$	33.9530	1.67887	0.839434	−	0.543462i	$-0.182887\pi$
$409$	33.9530	1.67887	0.839434	+	0.543462i	$0.182887\pi$
$410$	−63.1742	−3.11995
$411$	2.38822	0.117802
$412$	6.35579	0.313127
$413$	−11.0602	−0.544237
$414$	22.3528	1.09858
$415$	−36.4445	−1.78899
$416$	0.814178	0.0399184
$417$	−3.57100	−0.174873
$418$	11.8832	0.581227
$419$	−2.04520	−0.0999148	−0.0499574	−	0.998751i	$-0.515909\pi$
$419$	−2.04520	−0.0999148	−0.0499574	+	0.998751i	$0.515909\pi$
$420$	39.4120	1.92311
$421$	16.2367	0.791329	0.395665	−	0.918395i	$-0.370514\pi$
$421$	16.2367	0.791329	0.395665	+	0.918395i	$0.370514\pi$
$422$	−51.4170	−2.50294
$423$	15.1287	0.735584
$424$	−38.9266	−1.89044
$425$	62.3642	3.02511
$426$	−23.8769	−1.15684
$427$	39.8813	1.92999
$428$	3.00047	0.145033
$429$	2.26290	0.109254
$430$	41.2447	1.98900
$431$	8.97949	0.432527	0.216263	−	0.976335i	$-0.430613\pi$
$431$	8.97949	0.432527	0.216263	+	0.976335i	$0.430613\pi$
$432$	12.9979	0.625361
$433$	−9.54993	−0.458940	−0.229470	−	0.973316i	$-0.573699\pi$
$433$	−9.54993	−0.458940	−0.229470	+	0.973316i	$0.573699\pi$
$434$	56.7549	2.72432
$435$	2.81173	0.134812
$436$	52.5742	2.51785
$437$	7.74580	0.370532
$438$	16.9619	0.810471
$439$	35.2852	1.68407	0.842036	−	0.539422i	$-0.181357\pi$
$439$	35.2852	1.68407	0.842036	+	0.539422i	$0.181357\pi$
$440$	40.7500	1.94268
$441$	−25.5499	−1.21666
$442$	−24.7007	−1.17489
$443$	−11.0824	−0.526542	−0.263271	−	0.964722i	$-0.584801\pi$
$443$	−11.0824	−0.526542	−0.263271	+	0.964722i	$0.584801\pi$
$444$	28.0109	1.32934
$445$	45.8655	2.17423
$446$	−30.8518	−1.46087
$447$	6.07364	0.287273
$448$	35.2647	1.66610
$449$	0.709031	0.0334613	0.0167306	−	0.999860i	$-0.494674\pi$
$449$	0.709031	0.0334613	0.0167306	+	0.999860i	$0.494674\pi$
$450$	63.6840	3.00209
$451$	−14.7892	−0.696397
$452$	−33.8095	−1.59027
$453$	−12.2362	−0.574908
$454$	−1.11185	−0.0521817
$455$	−25.8635	−1.21250
$456$	6.57198	0.307761
$457$	−27.5148	−1.28709	−0.643545	−	0.765408i	$-0.722537\pi$
$457$	−27.5148	−1.28709	−0.643545	+	0.765408i	$0.722537\pi$
$458$	−9.88532	−0.461911
$459$	21.9119	1.02276
$460$	53.8322	2.50994
$461$	4.35888	0.203013	0.101507	−	0.994835i	$-0.467634\pi$
$461$	4.35888	0.203013	0.101507	+	0.994835i	$0.467634\pi$
$462$	13.9004	0.646703
$463$	2.30016	0.106898	0.0534488	−	0.998571i	$-0.482979\pi$
$463$	2.30016	0.106898	0.0534488	+	0.998571i	$0.482979\pi$
$464$	−4.26202	−0.197859
$465$	−13.8221	−0.640986
$466$	−4.95027	−0.229317
$467$	−0.847476	−0.0392165	−0.0196083	−	0.999808i	$-0.506242\pi$
$467$	−0.847476	−0.0392165	−0.0196083	+	0.999808i	$0.506242\pi$
$468$	−16.7422	−0.773909
$469$	34.4608	1.59125
$470$	54.8914	2.53195
$471$	−1.10574	−0.0509497
$472$	−12.8176	−0.589978
$473$	9.65548	0.443960
$474$	−7.71365	−0.354299
$475$	22.0680	1.01255
$476$	−100.711	−4.61609
$477$	−21.3461	−0.977369
$478$	7.17214	0.328046
$479$	−34.9972	−1.59906	−0.799530	−	0.600626i	$-0.794918\pi$
$479$	−34.9972	−1.59906	−0.799530	+	0.600626i	$0.794918\pi$
$480$	−1.21801	−0.0555943
$481$	−18.3817	−0.838134
$482$	4.85598	0.221184
$483$	9.06063	0.412273
$484$	−24.0948	−1.09522
$485$	−25.9725	−1.17935
$486$	34.3512	1.55820
$487$	−42.1102	−1.90819	−0.954097	−	0.299498i	$-0.903181\pi$
$487$	−42.1102	−1.90819	−0.954097	+	0.299498i	$0.903181\pi$
$488$	46.2182	2.09220
$489$	−5.10356	−0.230791
$490$	−92.7024	−4.18787
$491$	−34.7830	−1.56973	−0.784866	−	0.619665i	$-0.787268\pi$
$491$	−34.7830	−1.56973	−0.784866	+	0.619665i	$0.787268\pi$
$492$	−16.5764	−0.747322
$493$	−7.18494	−0.323593
$494$	−8.74054	−0.393256
$495$	22.3460	1.00438
$496$	20.9516	0.940755
$497$	63.8860	2.86568
$498$	−14.4070	−0.645595
$499$	13.9032	0.622391	0.311195	−	0.950346i	$-0.399271\pi$
$499$	13.9032	0.622391	0.311195	+	0.950346i	$0.399271\pi$
$500$	76.8584	3.43721
$501$	−13.9392	−0.622759
$502$	−54.1599	−2.41728
$503$	−21.4824	−0.957855	−0.478927	−	0.877855i	$-0.658974\pi$
$503$	−21.4824	−0.957855	−0.478927	+	0.877855i	$0.658974\pi$
$504$	−50.7446	−2.26035
$505$	52.6987	2.34506
$506$	18.9863	0.844044
$507$	6.50273	0.288796
$508$	−82.3867	−3.65532
$509$	−38.1621	−1.69151	−0.845753	−	0.533574i	$-0.820848\pi$
$509$	−38.1621	−1.69151	−0.845753	+	0.533574i	$0.820848\pi$
$510$	36.9523	1.63628
$511$	−45.3839	−2.00767
$512$	36.9184	1.63158
$513$	7.75369	0.342334
$514$	25.0986	1.10705
$515$	6.23965	0.274952
$516$	10.8223	0.476424
$517$	12.8502	0.565151
$518$	−112.913	−4.96113
$519$	5.84634	0.256626
$520$	−29.9731	−1.31441
$521$	−30.1596	−1.32132	−0.660658	−	0.750687i	$-0.729723\pi$
$521$	−30.1596	−1.32132	−0.660658	+	0.750687i	$0.729723\pi$
$522$	−7.33698	−0.321131
$523$	30.6838	1.34171	0.670854	−	0.741589i	$-0.265928\pi$
$523$	30.6838	1.34171	0.670854	+	0.741589i	$0.265928\pi$
$524$	39.5714	1.72868
$525$	25.8140	1.12662
$526$	27.6496	1.20558
$527$	35.3203	1.53858
$528$	5.13145	0.223318
$529$	−10.6242	−0.461923
$530$	−77.4496	−3.36420
$531$	−7.02876	−0.305022
$532$	−35.6374	−1.54508
$533$	10.8780	0.471179
$534$	18.1313	0.784618
$535$	2.94564	0.127351
$536$	39.9365	1.72499
$537$	−0.752098	−0.0324554
$538$	44.9658	1.93861
$539$	−21.7018	−0.934765
$540$	53.8871	2.31893
$541$	37.6465	1.61855	0.809275	−	0.587430i	$-0.199860\pi$
$541$	37.6465	1.61855	0.809275	+	0.587430i	$0.199860\pi$
$542$	−69.4199	−2.98184
$543$	−12.8744	−0.552493
$544$	3.11244	0.133445
$545$	51.6135	2.21088
$546$	−10.2242	−0.437556
$547$	17.9264	0.766477	0.383238	−	0.923650i	$-0.374809\pi$
$547$	17.9264	0.766477	0.383238	+	0.923650i	$0.374809\pi$
$548$	−15.0082	−0.641119
$549$	25.3446	1.08168
$550$	54.0925	2.30651
$551$	−2.54244	−0.108312
$552$	10.5003	0.446923
$553$	20.6389	0.877656
$554$	−4.46646	−0.189762
$555$	27.4990	1.16727
$556$	22.4411	0.951714
$557$	−5.15105	−0.218257	−0.109128	−	0.994028i	$-0.534806\pi$
$557$	−5.15105	−0.218257	−0.109128	+	0.994028i	$0.534806\pi$
$558$	36.0678	1.52687
$559$	−7.10196	−0.300381
$560$	−58.6491	−2.47838
$561$	8.65062	0.365229
$562$	−13.7500	−0.580010
$563$	8.56675	0.361045	0.180523	−	0.983571i	$-0.442221\pi$
$563$	8.56675	0.361045	0.180523	+	0.983571i	$0.442221\pi$
$564$	14.4031	0.606478
$565$	−33.1917	−1.39639
$566$	−31.3966	−1.31970
$567$	−22.9725	−0.964752
$568$	74.0372	3.10653
$569$	26.3362	1.10407	0.552036	−	0.833820i	$-0.313851\pi$
$569$	26.3362	1.10407	0.552036	+	0.833820i	$0.313851\pi$
$570$	13.0758	0.547687
$571$	34.1341	1.42847	0.714233	−	0.699908i	$-0.246776\pi$
$571$	34.1341	1.42847	0.714233	+	0.699908i	$0.246776\pi$
$572$	−14.2207	−0.594596
$573$	−6.95911	−0.290721
$574$	66.8204	2.78903
$575$	35.2590	1.47040
$576$	22.4107	0.933780
$577$	−17.0854	−0.711276	−0.355638	−	0.934624i	$-0.615736\pi$
$577$	−17.0854	−0.711276	−0.355638	+	0.934624i	$0.615736\pi$
$578$	−52.9652	−2.20306
$579$	−12.2244	−0.508027
$580$	−17.6696	−0.733691
$581$	38.5480	1.59924
$582$	−10.2673	−0.425592
$583$	−18.1311	−0.750915
$584$	−52.5952	−2.17641
$585$	−16.4363	−0.679557
$586$	−34.4276	−1.42219
$587$	26.8654	1.10886	0.554428	−	0.832232i	$-0.312937\pi$
$587$	26.8654	1.10886	0.554428	+	0.832232i	$0.312937\pi$
$588$	−24.3244	−1.00312
$589$	12.4984	0.514986
$590$	−25.5024	−1.04992
$591$	−7.17334	−0.295072
$592$	−41.6830	−1.71316
$593$	−3.42519	−0.140656	−0.0703278	−	0.997524i	$-0.522405\pi$
$593$	−3.42519	−0.140656	−0.0703278	+	0.997524i	$0.522405\pi$
$594$	19.0056	0.779810
$595$	−98.8710	−4.05331
$596$	−38.1683	−1.56344
$597$	−12.6277	−0.516816
$598$	−13.9651	−0.571076
$599$	2.91800	0.119226	0.0596131	−	0.998222i	$-0.481013\pi$
$599$	2.91800	0.119226	0.0596131	+	0.998222i	$0.481013\pi$
$600$	29.9157	1.22131
$601$	4.93129	0.201152	0.100576	−	0.994929i	$-0.467931\pi$
$601$	4.93129	0.201152	0.100576	+	0.994929i	$0.467931\pi$
$602$	−43.6253	−1.77803
$603$	21.8999	0.891831
$604$	76.8956	3.12884
$605$	−23.6545	−0.961694
$606$	20.8325	0.846264
$607$	11.4106	0.463144	0.231572	−	0.972818i	$-0.425613\pi$
$607$	11.4106	0.463144	0.231572	+	0.972818i	$0.425613\pi$
$608$	1.10136	0.0446660
$609$	−2.97401	−0.120513
$610$	91.9574	3.72325
$611$	−9.45179	−0.382379
$612$	−64.0020	−2.58713
$613$	−46.8967	−1.89414	−0.947070	−	0.321026i	$-0.895972\pi$
$613$	−46.8967	−1.89414	−0.947070	+	0.321026i	$0.895972\pi$
$614$	53.5334	2.16043
$615$	−16.2735	−0.656211
$616$	−43.1020	−1.73663
$617$	−38.5838	−1.55332	−0.776662	−	0.629917i	$-0.783089\pi$
$617$	−38.5838	−1.55332	−0.776662	+	0.629917i	$0.783089\pi$
$618$	2.46662	0.0992221
$619$	8.36777	0.336329	0.168165	−	0.985759i	$-0.446216\pi$
$619$	8.36777	0.336329	0.168165	+	0.985759i	$0.446216\pi$
$620$	86.8619	3.48846
$621$	12.3884	0.497128
$622$	61.5790	2.46909
$623$	−48.5128	−1.94362
$624$	−3.77437	−0.151096
$625$	25.3406	1.01362
$626$	−19.9831	−0.798686
$627$	3.06109	0.122248
$628$	6.94875	0.277285
$629$	−70.2695	−2.80183
$630$	−100.963	−4.02247
$631$	36.2698	1.44388	0.721939	−	0.691957i	$-0.243251\pi$
$631$	36.2698	1.44388	0.721939	+	0.691957i	$0.243251\pi$
$632$	23.9184	0.951421
$633$	−13.2449	−0.526437
$634$	−77.8291	−3.09099
$635$	−80.8812	−3.20967
$636$	−20.3222	−0.805826
$637$	15.9625	0.632457
$638$	−6.23196	−0.246726
$639$	40.5996	1.60610
$640$	77.4350	3.06089
$641$	−27.1168	−1.07105	−0.535525	−	0.844520i	$-0.679886\pi$
$641$	−27.1168	−1.07105	−0.535525	+	0.844520i	$0.679886\pi$
$642$	1.16445	0.0459573
$643$	−28.3221	−1.11691	−0.558457	−	0.829534i	$-0.688606\pi$
$643$	−28.3221	−1.11691	−0.558457	+	0.829534i	$0.688606\pi$
$644$	−56.9393	−2.24372
$645$	10.6245	0.418341
$646$	−33.4133	−1.31463
$647$	−2.15649	−0.0847804	−0.0423902	−	0.999101i	$-0.513497\pi$
$647$	−2.15649	−0.0847804	−0.0423902	+	0.999101i	$0.513497\pi$
$648$	−26.6227	−1.04584
$649$	−5.97016	−0.234349
$650$	−39.7870	−1.56058
$651$	14.6199	0.573000
$652$	32.0721	1.25604
$653$	6.52339	0.255280	0.127640	−	0.991821i	$-0.459260\pi$
$653$	6.52339	0.255280	0.127640	+	0.991821i	$0.459260\pi$
$654$	20.4036	0.797842
$655$	38.8483	1.51793
$656$	24.6674	0.963100
$657$	−28.8415	−1.12521
$658$	−58.0596	−2.26340
$659$	−16.7915	−0.654105	−0.327052	−	0.945006i	$-0.606055\pi$
$659$	−16.7915	−0.654105	−0.327052	+	0.945006i	$0.606055\pi$
$660$	21.2741	0.828094
$661$	−20.6732	−0.804093	−0.402047	−	0.915619i	$-0.631701\pi$
$661$	−20.6732	−0.804093	−0.402047	+	0.915619i	$0.631701\pi$
$662$	−28.3502	−1.10186
$663$	−6.36285	−0.247112
$664$	44.6731	1.73365
$665$	−34.9862	−1.35671
$666$	−71.7565	−2.78051
$667$	−4.06216	−0.157288
$668$	87.5978	3.38926
$669$	−7.94733	−0.307262
$670$	79.4590	3.06977
$671$	21.5274	0.831058
$672$	1.28831	0.0496977
$673$	−20.3307	−0.783691	−0.391846	−	0.920031i	$-0.628163\pi$
$673$	−20.3307	−0.783691	−0.391846	+	0.920031i	$0.628163\pi$
$674$	67.6095	2.60422
$675$	35.2949	1.35850
$676$	−40.8648	−1.57172
$677$	−29.8163	−1.14593	−0.572967	−	0.819578i	$-0.694208\pi$
$677$	−29.8163	−1.14593	−0.572967	+	0.819578i	$0.694208\pi$
$678$	−13.1212	−0.503915
$679$	27.4715	1.05426
$680$	−114.581	−4.39399
$681$	−0.286410	−0.0109752
$682$	30.6356	1.17310
$683$	−2.96283	−0.113369	−0.0566847	−	0.998392i	$-0.518053\pi$
$683$	−2.96283	−0.113369	−0.0566847	+	0.998392i	$0.518053\pi$
$684$	−22.6476	−0.865953
$685$	−14.7340	−0.562956
$686$	28.0641	1.07149
$687$	−2.54643	−0.0971525
$688$	−16.1047	−0.613985
$689$	13.3361	0.508065
$690$	20.8918	0.795337
$691$	−1.29240	−0.0491651	−0.0245825	−	0.999698i	$-0.507826\pi$
$691$	−1.29240	−0.0491651	−0.0245825	+	0.999698i	$0.507826\pi$
$692$	−36.7399	−1.39664
$693$	−23.6357	−0.897847
$694$	64.8097	2.46014
$695$	22.0310	0.835685
$696$	−3.44657	−0.130642
$697$	41.5844	1.57512
$698$	−42.5443	−1.61032
$699$	−1.27518	−0.0482316
$700$	−162.222	−6.13141
$701$	40.9042	1.54493	0.772464	−	0.635058i	$-0.219024\pi$
$701$	40.9042	1.54493	0.772464	+	0.635058i	$0.219024\pi$
$702$	−13.9793	−0.527616
$703$	−24.8654	−0.937816
$704$	19.0354	0.717425
$705$	14.1399	0.532539
$706$	−75.3180	−2.83463
$707$	−55.7403	−2.09633
$708$	−6.69162	−0.251486
$709$	−12.9779	−0.487396	−0.243698	−	0.969851i	$-0.578361\pi$
$709$	−12.9779	−0.487396	−0.243698	+	0.969851i	$0.578361\pi$
$710$	147.307	5.52833
$711$	13.1160	0.491890
$712$	−56.2212	−2.10698
$713$	19.9691	0.747850
$714$	−39.0851	−1.46272
$715$	−13.9608	−0.522105
$716$	4.72638	0.176633
$717$	1.84752	0.0689971
$718$	−57.0815	−2.13026
$719$	−39.4615	−1.47166	−0.735832	−	0.677164i	$-0.763209\pi$
$719$	−39.4615	−1.47166	−0.735832	+	0.677164i	$0.763209\pi$
$720$	−37.2715	−1.38903
$721$	−6.59979	−0.245789
$722$	34.5148	1.28451
$723$	1.25089	0.0465210
$724$	80.9059	3.00685
$725$	−11.5732	−0.429819
$726$	−9.35098	−0.347047
$727$	−14.2405	−0.528151	−0.264075	−	0.964502i	$-0.585067\pi$
$727$	−14.2405	−0.528151	−0.264075	+	0.964502i	$0.585067\pi$
$728$	31.7031	1.17500
$729$	−7.96191	−0.294885
$730$	−104.645	−3.87309
$731$	−27.1493	−1.00415
$732$	24.1289	0.891829
$733$	23.5915	0.871374	0.435687	−	0.900098i	$-0.356506\pi$
$733$	23.5915	0.871374	0.435687	+	0.900098i	$0.356506\pi$
$734$	−69.2458	−2.55591
$735$	−23.8799	−0.880823
$736$	1.75969	0.0648629
$737$	18.6015	0.685196
$738$	42.4644	1.56314
$739$	25.2279	0.928025	0.464013	−	0.885829i	$-0.346409\pi$
$739$	25.2279	0.928025	0.464013	+	0.885829i	$0.346409\pi$
$740$	−172.811	−6.35266
$741$	−2.25154	−0.0827124
$742$	81.9198	3.00737
$743$	21.3735	0.784117	0.392059	−	0.919940i	$-0.371763\pi$
$743$	21.3735	0.784117	0.392059	+	0.919940i	$0.371763\pi$
$744$	16.9430	0.621159
$745$	−37.4709	−1.37283
$746$	−33.2203	−1.21628
$747$	24.4973	0.896308
$748$	−54.3627	−1.98770
$749$	−3.11566	−0.113844
$750$	29.8280	1.08917
$751$	−14.4616	−0.527713	−0.263856	−	0.964562i	$-0.584994\pi$
$751$	−14.4616	−0.527713	−0.263856	+	0.964562i	$0.584994\pi$
$752$	−21.4332	−0.781590
$753$	−13.9514	−0.508419
$754$	4.58384	0.166933
$755$	75.4905	2.74738
$756$	−56.9973	−2.07297
$757$	6.16797	0.224179	0.112089	−	0.993698i	$-0.464246\pi$
$757$	6.16797	0.224179	0.112089	+	0.993698i	$0.464246\pi$
$758$	9.67803	0.351522
$759$	4.89082	0.177525
$760$	−40.5454	−1.47074
$761$	17.5936	0.637768	0.318884	−	0.947794i	$-0.396692\pi$
$761$	17.5936	0.637768	0.318884	+	0.947794i	$0.396692\pi$
$762$	−31.9735	−1.15828
$763$	−54.5925	−1.97638
$764$	43.7328	1.58220
$765$	−62.8325	−2.27172
$766$	−6.94754	−0.251025
$767$	4.39127	0.158560
$768$	19.8029	0.714576
$769$	33.4473	1.20614	0.603070	−	0.797689i	$-0.293944\pi$
$769$	33.4473	1.20614	0.603070	+	0.797689i	$0.293944\pi$
$770$	−85.7572	−3.09048
$771$	6.46535	0.232844
$772$	76.8210	2.76485
$773$	−2.14793	−0.0772557	−0.0386279	−	0.999254i	$-0.512299\pi$
$773$	−2.14793	−0.0772557	−0.0386279	+	0.999254i	$0.512299\pi$
$774$	−27.7239	−0.996514
$775$	56.8927	2.04364
$776$	31.8366	1.14287
$777$	−29.0862	−1.04346
$778$	−2.10695	−0.0755377
$779$	14.7150	0.527218
$780$	−15.6479	−0.560284
$781$	34.4849	1.23397
$782$	−53.3858	−1.90907
$783$	−4.06630	−0.145318
$784$	36.1972	1.29276
$785$	6.82177	0.243480
$786$	15.3573	0.547776
$787$	−28.2561	−1.00722	−0.503611	−	0.863931i	$-0.667995\pi$
$787$	−28.2561	−1.00722	−0.503611	+	0.863931i	$0.667995\pi$
$788$	45.0791	1.60588
$789$	7.12247	0.253567
$790$	47.5888	1.69313
$791$	35.1075	1.24828
$792$	−27.3913	−0.973309
$793$	−15.8342	−0.562290
$794$	−36.2498	−1.28646
$795$	−19.9508	−0.707582
$796$	79.3555	2.81268
$797$	49.1722	1.74177	0.870885	−	0.491487i	$-0.163547\pi$
$797$	49.1722	1.74177	0.870885	+	0.491487i	$0.163547\pi$
$798$	−13.8306	−0.489596
$799$	−36.1323	−1.27827
$800$	5.01340	0.177250
$801$	−30.8299	−1.08932
$802$	−70.6949	−2.49632
$803$	−24.4977	−0.864505
$804$	20.8494	0.735302
$805$	−55.8989	−1.97018
$806$	−22.5336	−0.793713
$807$	11.5831	0.407744
$808$	−64.5972	−2.27252
$809$	48.3023	1.69822	0.849109	−	0.528217i	$-0.177139\pi$
$809$	48.3023	1.69822	0.849109	+	0.528217i	$0.177139\pi$
$810$	−52.9694	−1.86115
$811$	−23.2458	−0.816271	−0.408135	−	0.912921i	$-0.633821\pi$
$811$	−23.2458	−0.816271	−0.408135	+	0.912921i	$0.633821\pi$
$812$	18.6895	0.655872
$813$	−17.8824	−0.627163
$814$	−60.9493	−2.13627
$815$	31.4861	1.10291
$816$	−14.4286	−0.505103
$817$	−9.60700	−0.336106
$818$	−82.8067	−2.89527
$819$	17.3849	0.607479
$820$	102.267	3.57131
$821$	41.4282	1.44586	0.722928	−	0.690923i	$-0.242796\pi$
$821$	41.4282	1.44586	0.722928	+	0.690923i	$0.242796\pi$
$822$	−5.82455	−0.203154
$823$	13.4994	0.470560	0.235280	−	0.971928i	$-0.424399\pi$
$823$	13.4994	0.470560	0.235280	+	0.971928i	$0.424399\pi$
$824$	−7.64847	−0.266447
$825$	13.9341	0.485123
$826$	26.9743	0.938556
$827$	−12.3354	−0.428943	−0.214471	−	0.976730i	$-0.568803\pi$
$827$	−12.3354	−0.428943	−0.214471	+	0.976730i	$0.568803\pi$
$828$	−36.1850	−1.25751
$829$	32.9824	1.14553	0.572764	−	0.819720i	$-0.305871\pi$
$829$	32.9824	1.14553	0.572764	+	0.819720i	$0.305871\pi$
$830$	88.8831	3.08518
$831$	−1.15055	−0.0399121
$832$	−14.0013	−0.485407
$833$	61.0214	2.11427
$834$	8.70918	0.301574
$835$	85.9971	2.97605
$836$	−19.2367	−0.665314
$837$	19.9895	0.690937
$838$	4.98797	0.172307
$839$	37.3200	1.28843	0.644214	−	0.764845i	$-0.277184\pi$
$839$	37.3200	1.28843	0.644214	+	0.764845i	$0.277184\pi$
$840$	−47.4278	−1.63642
$841$	−27.6667	−0.954023
$842$	−39.5991	−1.36468
$843$	−3.54197	−0.121992
$844$	83.2342	2.86504
$845$	−40.1181	−1.38011
$846$	−36.8969	−1.26854
$847$	25.0198	0.859691
$848$	30.2415	1.03850
$849$	−8.08769	−0.277569
$850$	−152.098	−5.21691
$851$	−39.7284	−1.36187
$852$	38.6522	1.32420
$853$	37.3887	1.28017	0.640083	−	0.768306i	$-0.278900\pi$
$853$	37.3887	1.28017	0.640083	+	0.768306i	$0.278900\pi$
$854$	−97.2650	−3.32834
$855$	−22.2338	−0.760379
$856$	−3.61072	−0.123412
$857$	40.6864	1.38982	0.694911	−	0.719095i	$-0.255444\pi$
$857$	40.6864	1.38982	0.694911	+	0.719095i	$0.255444\pi$
$858$	−5.51891	−0.188413
$859$	16.1103	0.549676	0.274838	−	0.961491i	$-0.411376\pi$
$859$	16.1103	0.549676	0.274838	+	0.961491i	$0.411376\pi$
$860$	−66.7673	−2.27675
$861$	17.2128	0.586610
$862$	−21.8997	−0.745908
$863$	−37.9883	−1.29314	−0.646569	−	0.762855i	$-0.723797\pi$
$863$	−37.9883	−1.29314	−0.646569	+	0.762855i	$0.723797\pi$
$864$	1.76148	0.0599267
$865$	−36.0686	−1.22637
$866$	23.2910	0.791459
$867$	−13.6437	−0.463364
$868$	−91.8753	−3.11845
$869$	11.1406	0.377920
$870$	−6.85742	−0.232488
$871$	−13.6821	−0.463601
$872$	−63.2670	−2.14249
$873$	17.4582	0.590869
$874$	−18.8909	−0.638996
$875$	−79.8090	−2.69804
$876$	−27.4581	−0.927722
$877$	−3.73410	−0.126092	−0.0630458	−	0.998011i	$-0.520081\pi$
$877$	−3.73410	−0.126092	−0.0630458	+	0.998011i	$0.520081\pi$
$878$	−86.0558	−2.90424
$879$	−8.86845	−0.299125
$880$	−31.6581	−1.06719
$881$	0.934871	0.0314966	0.0157483	−	0.999876i	$-0.494987\pi$
$881$	0.934871	0.0314966	0.0157483	+	0.999876i	$0.494987\pi$
$882$	62.3127	2.09818
$883$	19.9915	0.672768	0.336384	−	0.941725i	$-0.390796\pi$
$883$	19.9915	0.672768	0.336384	+	0.941725i	$0.390796\pi$
$884$	39.9858	1.34487
$885$	−6.56934	−0.220826
$886$	27.0285	0.908041
$887$	7.01024	0.235381	0.117690	−	0.993050i	$-0.462451\pi$
$887$	7.01024	0.235381	0.117690	+	0.993050i	$0.462451\pi$
$888$	−33.7079	−1.13116
$889$	85.5495	2.86924
$890$	−111.860	−3.74955
$891$	−12.4003	−0.415424
$892$	49.9431	1.67222
$893$	−12.7857	−0.427856
$894$	−14.8128	−0.495413
$895$	4.64001	0.155099
$896$	−81.9044	−2.73623
$897$	−3.59738	−0.120113
$898$	−1.72923	−0.0577051
$899$	−6.55456	−0.218607
$900$	−103.092	−3.43640
$901$	50.9812	1.69843
$902$	36.0689	1.20096
$903$	−11.2378	−0.373969
$904$	40.6859	1.35319
$905$	79.4276	2.64026
$906$	29.8425	0.991450
$907$	43.6889	1.45066	0.725332	−	0.688399i	$-0.241686\pi$
$907$	43.6889	1.45066	0.725332	+	0.688399i	$0.241686\pi$
$908$	1.79987	0.0597308
$909$	−35.4230	−1.17491
$910$	63.0776	2.09100
$911$	−36.8510	−1.22093	−0.610464	−	0.792044i	$-0.709017\pi$
$911$	−36.8510	−1.22093	−0.610464	+	0.792044i	$0.709017\pi$
$912$	−5.10568	−0.169066
$913$	20.8077	0.688636
$914$	67.1049	2.21963
$915$	23.6880	0.783101
$916$	16.0024	0.528736
$917$	−41.0905	−1.35693
$918$	−53.4401	−1.76379
$919$	35.8749	1.18340	0.591702	−	0.806157i	$-0.298456\pi$
$919$	35.8749	1.18340	0.591702	+	0.806157i	$0.298456\pi$
$920$	−64.7810	−2.13577
$921$	13.7901	0.454398
$922$	−10.6307	−0.350103
$923$	−25.3649	−0.834896
$924$	−22.5020	−0.740262
$925$	−113.188	−3.72158
$926$	−5.60978	−0.184349
$927$	−4.19417	−0.137755
$928$	−0.577590	−0.0189603
$929$	19.9934	0.655961	0.327980	−	0.944685i	$-0.393632\pi$
$929$	19.9934	0.655961	0.327980	+	0.944685i	$0.393632\pi$
$930$	33.7103	1.10540
$931$	21.5929	0.707678
$932$	8.01354	0.262492
$933$	15.8626	0.519317
$934$	2.06688	0.0676303
$935$	−53.3694	−1.74536
$936$	20.1473	0.658536
$937$	−2.82509	−0.0922918	−0.0461459	−	0.998935i	$-0.514694\pi$
$937$	−2.82509	−0.0922918	−0.0461459	+	0.998935i	$0.514694\pi$
$938$	−84.0452	−2.74417
$939$	−5.14760	−0.167985
$940$	−88.8586	−2.89825
$941$	5.68873	0.185447	0.0927236	−	0.995692i	$-0.470443\pi$
$941$	5.68873	0.185447	0.0927236	+	0.995692i	$0.470443\pi$
$942$	2.69674	0.0878647
$943$	23.5107	0.765613
$944$	9.95781	0.324099
$945$	−55.9558	−1.82024
$946$	−23.5484	−0.765625
$947$	−41.8313	−1.35933	−0.679667	−	0.733521i	$-0.737876\pi$
$947$	−41.8313	−1.35933	−0.679667	+	0.733521i	$0.737876\pi$
$948$	12.4869	0.405556
$949$	18.0189	0.584920
$950$	−53.8209	−1.74618
$951$	−20.0486	−0.650119
$952$	121.194	3.92794
$953$	57.6205	1.86651	0.933256	−	0.359211i	$-0.116954\pi$
$953$	57.6205	1.86651	0.933256	+	0.359211i	$0.116954\pi$
$954$	52.0601	1.68551
$955$	42.9337	1.38930
$956$	−11.6103	−0.375505
$957$	−1.60534	−0.0518932
$958$	85.3533	2.75764
$959$	15.5844	0.503246
$960$	20.9459	0.676026
$961$	1.22149	0.0394028
$962$	44.8305	1.44539
$963$	−1.98000	−0.0638047
$964$	−7.86090	−0.253182
$965$	75.4173	2.42777
$966$	−22.0976	−0.710979
$967$	30.5409	0.982128	0.491064	−	0.871124i	$-0.336608\pi$
$967$	30.5409	0.982128	0.491064	+	0.871124i	$0.336608\pi$
$968$	28.9954	0.931946
$969$	−8.60718	−0.276502
$970$	63.3432	2.03383
$971$	−22.4503	−0.720465	−0.360233	−	0.932863i	$-0.617303\pi$
$971$	−22.4503	−0.720465	−0.360233	+	0.932863i	$0.617303\pi$
$972$	−55.6080	−1.78363
$973$	−23.3026	−0.747047
$974$	102.701	3.29075
$975$	−10.2490	−0.328232
$976$	−35.9063	−1.14933
$977$	−1.42834	−0.0456966	−0.0228483	−	0.999739i	$-0.507273\pi$
$977$	−1.42834	−0.0456966	−0.0228483	+	0.999739i	$0.507273\pi$
$978$	12.4469	0.398008
$979$	−26.1866	−0.836928
$980$	150.067	4.79373
$981$	−34.6936	−1.10768
$982$	84.8309	2.70706
$983$	−42.0376	−1.34079	−0.670396	−	0.742004i	$-0.733876\pi$
$983$	−42.0376	−1.34079	−0.670396	+	0.742004i	$0.733876\pi$
$984$	19.9478	0.635913
$985$	44.2554	1.41009
$986$	17.5231	0.558048
$987$	−14.9560	−0.476055
$988$	14.1493	0.450148
$989$	−15.3495	−0.488085
$990$	−54.4988	−1.73208
$991$	−28.6001	−0.908513	−0.454257	−	0.890871i	$-0.650095\pi$
$991$	−28.6001	−0.908513	−0.454257	+	0.890871i	$0.650095\pi$
$992$	2.83937	0.0901500
$993$	−7.30294	−0.231752
$994$	−155.809	−4.94197
$995$	77.9055	2.46977
$996$	23.3222	0.738993
$997$	−1.34132	−0.0424802	−0.0212401	−	0.999774i	$-0.506761\pi$
$997$	−1.34132	−0.0424802	−0.0212401	+	0.999774i	$0.506761\pi$
$998$	−33.9079	−1.07334
$999$	−39.7689	−1.25823

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.16	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.16	✓	186	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)

\(f(q)\)	\(=\)	\(q-2.43886 q^{2} -0.628245 q^{3} +3.94805 q^{4} +3.87591 q^{5} +1.53220 q^{6} -4.09962 q^{7} -4.75103 q^{8} -2.60531 q^{9} +O(q^{10})\)	\(q-2.43886 q^{2} -0.628245 q^{3} +3.94805 q^{4} +3.87591 q^{5} +1.53220 q^{6} -4.09962 q^{7} -4.75103 q^{8} -2.60531 q^{9} -9.45281 q^{10} -2.21292 q^{11} -2.48034 q^{12} +1.62769 q^{13} +9.99840 q^{14} -2.43502 q^{15} +3.69100 q^{16} +6.22231 q^{17} +6.35399 q^{18} +2.20181 q^{19} +15.3023 q^{20} +2.57556 q^{21} +5.39702 q^{22} +3.51792 q^{23} +2.98481 q^{24} +10.0227 q^{25} -3.96970 q^{26} +3.52150 q^{27} -16.1855 q^{28} -1.15470 q^{29} +5.93868 q^{30} +5.67640 q^{31} +0.500206 q^{32} +1.39026 q^{33} -15.1754 q^{34} -15.8897 q^{35} -10.2859 q^{36} -11.2931 q^{37} -5.36992 q^{38} -1.02259 q^{39} -18.4146 q^{40} +6.68311 q^{41} -6.28144 q^{42} -4.36322 q^{43} -8.73674 q^{44} -10.0979 q^{45} -8.57973 q^{46} -5.80689 q^{47} -2.31885 q^{48} +9.80686 q^{49} -24.4439 q^{50} -3.90913 q^{51} +6.42619 q^{52} +8.19329 q^{53} -8.58847 q^{54} -8.57709 q^{55} +19.4774 q^{56} -1.38328 q^{57} +2.81617 q^{58} +2.69786 q^{59} -9.61358 q^{60} -9.72805 q^{61} -13.8440 q^{62} +10.6808 q^{63} -8.60194 q^{64} +6.30877 q^{65} -3.39065 q^{66} -8.40586 q^{67} +24.5660 q^{68} -2.21012 q^{69} +38.7529 q^{70} -15.5834 q^{71} +12.3779 q^{72} +11.0703 q^{73} +27.5424 q^{74} -6.29669 q^{75} +8.69287 q^{76} +9.07214 q^{77} +2.49394 q^{78} -5.03435 q^{79} +14.3060 q^{80} +5.60356 q^{81} -16.2992 q^{82} -9.40283 q^{83} +10.1685 q^{84} +24.1171 q^{85} +10.6413 q^{86} +0.725437 q^{87} +10.5137 q^{88} +11.8335 q^{89} +24.6275 q^{90} -6.67289 q^{91} +13.8889 q^{92} -3.56617 q^{93} +14.1622 q^{94} +8.53402 q^{95} -0.314252 q^{96} -6.70100 q^{97} -23.9176 q^{98} +5.76535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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