LMFDB - Embedded newform 4019.2.a.a.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.68954 q^{2} +1.48905 q^{3} +5.23361 q^{4} +2.84645 q^{5} -4.00487 q^{6} -1.97182 q^{7} -8.69693 q^{8} -0.782716 q^{9} +O(q^{10})$	\(q-2.68954 q^{2} +1.48905 q^{3} +5.23361 q^{4} +2.84645 q^{5} -4.00487 q^{6} -1.97182 q^{7} -8.69693 q^{8} -0.782716 q^{9} -7.65564 q^{10} +0.969092 q^{11} +7.79314 q^{12} +0.141478 q^{13} +5.30329 q^{14} +4.23852 q^{15} +12.9235 q^{16} +2.63561 q^{17} +2.10514 q^{18} -6.42189 q^{19} +14.8972 q^{20} -2.93615 q^{21} -2.60641 q^{22} -4.17326 q^{23} -12.9502 q^{24} +3.10229 q^{25} -0.380512 q^{26} -5.63267 q^{27} -10.3197 q^{28} -6.47609 q^{29} -11.3997 q^{30} +5.48936 q^{31} -17.3644 q^{32} +1.44303 q^{33} -7.08858 q^{34} -5.61270 q^{35} -4.09643 q^{36} +7.27495 q^{37} +17.2719 q^{38} +0.210669 q^{39} -24.7554 q^{40} -9.16295 q^{41} +7.89689 q^{42} -3.14839 q^{43} +5.07185 q^{44} -2.22796 q^{45} +11.2241 q^{46} +7.22524 q^{47} +19.2438 q^{48} -3.11192 q^{49} -8.34374 q^{50} +3.92457 q^{51} +0.740443 q^{52} -0.976175 q^{53} +15.1493 q^{54} +2.75848 q^{55} +17.1488 q^{56} -9.56255 q^{57} +17.4177 q^{58} +7.43638 q^{59} +22.1828 q^{60} +7.32616 q^{61} -14.7638 q^{62} +1.54338 q^{63} +20.8551 q^{64} +0.402712 q^{65} -3.88109 q^{66} +3.10669 q^{67} +13.7938 q^{68} -6.21422 q^{69} +15.0956 q^{70} -6.27268 q^{71} +6.80722 q^{72} -15.0594 q^{73} -19.5662 q^{74} +4.61949 q^{75} -33.6097 q^{76} -1.91088 q^{77} -0.566603 q^{78} -5.62324 q^{79} +36.7861 q^{80} -6.03921 q^{81} +24.6441 q^{82} +0.130762 q^{83} -15.3667 q^{84} +7.50215 q^{85} +8.46771 q^{86} -9.64326 q^{87} -8.42812 q^{88} -2.11617 q^{89} +5.99219 q^{90} -0.278970 q^{91} -21.8412 q^{92} +8.17396 q^{93} -19.4326 q^{94} -18.2796 q^{95} -25.8565 q^{96} -8.57706 q^{97} +8.36963 q^{98} -0.758524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68954	−1.90179	−0.950895	−	0.309513i	$-0.899834\pi$
$2$	−2.68954	−1.90179	−0.950895	+	0.309513i	$0.899834\pi$
$3$	1.48905	0.859706	0.429853	−	0.902899i	$-0.358565\pi$
$3$	1.48905	0.859706	0.429853	+	0.902899i	$0.358565\pi$
$4$	5.23361	2.61681
$5$	2.84645	1.27297	0.636486	−	0.771288i	$-0.280387\pi$
$5$	2.84645	1.27297	0.636486	+	0.771288i	$0.280387\pi$
$6$	−4.00487	−1.63498
$7$	−1.97182	−0.745278	−0.372639	−	0.927976i	$-0.621547\pi$
$7$	−1.97182	−0.745278	−0.372639	+	0.927976i	$0.621547\pi$
$8$	−8.69693	−3.07483
$9$	−0.782716	−0.260905
$10$	−7.65564	−2.42093
$11$	0.969092	0.292192	0.146096	−	0.989270i	$-0.453329\pi$
$11$	0.969092	0.292192	0.146096	+	0.989270i	$0.453329\pi$
$12$	7.79314	2.24969
$13$	0.141478	0.0392391	0.0196195	−	0.999808i	$-0.493755\pi$
$13$	0.141478	0.0392391	0.0196195	+	0.999808i	$0.493755\pi$
$14$	5.30329	1.41736
$15$	4.23852	1.09438
$16$	12.9235	3.23087
$17$	2.63561	0.639230	0.319615	−	0.947547i	$-0.396446\pi$
$17$	2.63561	0.639230	0.319615	+	0.947547i	$0.396446\pi$
$18$	2.10514	0.496187
$19$	−6.42189	−1.47328	−0.736642	−	0.676283i	$-0.763590\pi$
$19$	−6.42189	−1.47328	−0.736642	+	0.676283i	$0.763590\pi$
$20$	14.8972	3.33112
$21$	−2.93615	−0.640720
$22$	−2.60641	−0.555688
$23$	−4.17326	−0.870185	−0.435093	−	0.900386i	$-0.643284\pi$
$23$	−4.17326	−0.870185	−0.435093	+	0.900386i	$0.643284\pi$
$24$	−12.9502	−2.64345
$25$	3.10229	0.620459
$26$	−0.380512	−0.0746245
$27$	−5.63267	−1.08401
$28$	−10.3197	−1.95025
$29$	−6.47609	−1.20258	−0.601290	−	0.799031i	$-0.705346\pi$
$29$	−6.47609	−1.20258	−0.601290	+	0.799031i	$0.705346\pi$
$30$	−11.3997	−2.08129
$31$	5.48936	0.985919	0.492959	−	0.870052i	$-0.335915\pi$
$31$	5.48936	0.985919	0.492959	+	0.870052i	$0.335915\pi$
$32$	−17.3644	−3.06961
$33$	1.44303	0.251199
$34$	−7.08858	−1.21568
$35$	−5.61270	−0.948719
$36$	−4.09643	−0.682739
$37$	7.27495	1.19599	0.597997	−	0.801498i	$-0.295963\pi$
$37$	7.27495	1.19599	0.597997	+	0.801498i	$0.295963\pi$
$38$	17.2719	2.80188
$39$	0.210669	0.0337341
$40$	−24.7554	−3.91417
$41$	−9.16295	−1.43101	−0.715506	−	0.698606i	$-0.753804\pi$
$41$	−9.16295	−1.43101	−0.715506	+	0.698606i	$0.753804\pi$
$42$	7.89689	1.21852
$43$	−3.14839	−0.480125	−0.240062	−	0.970757i	$-0.577168\pi$
$43$	−3.14839	−0.480125	−0.240062	+	0.970757i	$0.577168\pi$
$44$	5.07185	0.764611
$45$	−2.22796	−0.332125
$46$	11.2241	1.65491
$47$	7.22524	1.05391	0.526955	−	0.849893i	$-0.323334\pi$
$47$	7.22524	1.05391	0.526955	+	0.849893i	$0.323334\pi$
$48$	19.2438	2.77760
$49$	−3.11192	−0.444560
$50$	−8.34374	−1.17998
$51$	3.92457	0.549550
$52$	0.740443	0.102681
$53$	−0.976175	−0.134088	−0.0670440	−	0.997750i	$-0.521357\pi$
$53$	−0.976175	−0.134088	−0.0670440	+	0.997750i	$0.521357\pi$
$54$	15.1493	2.06156
$55$	2.75848	0.371953
$56$	17.1488	2.29160
$57$	−9.56255	−1.26659
$58$	17.4177	2.28706
$59$	7.43638	0.968135	0.484067	−	0.875031i	$-0.339159\pi$
$59$	7.43638	0.968135	0.484067	+	0.875031i	$0.339159\pi$
$60$	22.1828	2.86379
$61$	7.32616	0.938018	0.469009	−	0.883193i	$-0.344611\pi$
$61$	7.32616	0.938018	0.469009	+	0.883193i	$0.344611\pi$
$62$	−14.7638	−1.87501
$63$	1.54338	0.194447
$64$	20.8551	2.60689
$65$	0.402712	0.0499502
$66$	−3.88109	−0.477729
$67$	3.10669	0.379543	0.189771	−	0.981828i	$-0.439225\pi$
$67$	3.10669	0.379543	0.189771	+	0.981828i	$0.439225\pi$
$68$	13.7938	1.67274
$69$	−6.21422	−0.748104
$70$	15.0956	1.80426
$71$	−6.27268	−0.744430	−0.372215	−	0.928146i	$-0.621402\pi$
$71$	−6.27268	−0.744430	−0.372215	+	0.928146i	$0.621402\pi$
$72$	6.80722	0.802239
$73$	−15.0594	−1.76257	−0.881285	−	0.472586i	$-0.843321\pi$
$73$	−15.0594	−1.76257	−0.881285	+	0.472586i	$0.843321\pi$
$74$	−19.5662	−2.27453
$75$	4.61949	0.533412
$76$	−33.6097	−3.85530
$77$	−1.91088	−0.217765
$78$	−0.566603	−0.0641551
$79$	−5.62324	−0.632664	−0.316332	−	0.948648i	$-0.602451\pi$
$79$	−5.62324	−0.632664	−0.316332	+	0.948648i	$0.602451\pi$
$80$	36.7861	4.11281
$81$	−6.03921	−0.671023
$82$	24.6441	2.72149
$83$	0.130762	0.0143530	0.00717652	−	0.999974i	$-0.497716\pi$
$83$	0.130762	0.0143530	0.00717652	+	0.999974i	$0.497716\pi$
$84$	−15.3667	−1.67664
$85$	7.50215	0.813722
$86$	8.46771	0.913097
$87$	−9.64326	−1.03387
$88$	−8.42812	−0.898441
$89$	−2.11617	−0.224314	−0.112157	−	0.993691i	$-0.535776\pi$
$89$	−2.11617	−0.224314	−0.112157	+	0.993691i	$0.535776\pi$
$90$	5.99219	0.631633
$91$	−0.278970	−0.0292440
$92$	−21.8412	−2.27711
$93$	8.17396	0.847600
$94$	−19.4326	−2.00431
$95$	−18.2796	−1.87545
$96$	−25.8565	−2.63896
$97$	−8.57706	−0.870868	−0.435434	−	0.900221i	$-0.643405\pi$
$97$	−8.57706	−0.870868	−0.435434	+	0.900221i	$0.643405\pi$
$98$	8.36963	0.845460
$99$	−0.758524	−0.0762345
$100$	16.2362	1.62362
$101$	11.2784	1.12224	0.561121	−	0.827734i	$-0.310370\pi$
$101$	11.2784	1.12224	0.561121	+	0.827734i	$0.310370\pi$
$102$	−10.5553	−1.04513
$103$	−6.61551	−0.651846	−0.325923	−	0.945396i	$-0.605675\pi$
$103$	−6.61551	−0.651846	−0.325923	+	0.945396i	$0.605675\pi$
$104$	−1.23043	−0.120653
$105$	−8.35761	−0.815619
$106$	2.62546	0.255007
$107$	−5.26944	−0.509416	−0.254708	−	0.967018i	$-0.581979\pi$
$107$	−5.26944	−0.509416	−0.254708	+	0.967018i	$0.581979\pi$
$108$	−29.4792	−2.83664
$109$	3.16119	0.302787	0.151393	−	0.988474i	$-0.451624\pi$
$109$	3.16119	0.302787	0.151393	+	0.988474i	$0.451624\pi$
$110$	−7.41902	−0.707376
$111$	10.8328	1.02820
$112$	−25.4828	−2.40790
$113$	−4.09685	−0.385399	−0.192699	−	0.981258i	$-0.561724\pi$
$113$	−4.09685	−0.385399	−0.192699	+	0.981258i	$0.561724\pi$
$114$	25.7188	2.40879
$115$	−11.8790	−1.10772
$116$	−33.8934	−3.14692
$117$	−0.110737	−0.0102377
$118$	−20.0004	−1.84119
$119$	−5.19696	−0.476404
$120$	−36.8621	−3.36504
$121$	−10.0609	−0.914624
$122$	−19.7040	−1.78391
$123$	−13.6441	−1.23025
$124$	28.7292	2.57996
$125$	−5.40173	−0.483145
$126$	−4.15097	−0.369798
$127$	−11.0972	−0.984717	−0.492359	−	0.870392i	$-0.663865\pi$
$127$	−11.0972	−0.984717	−0.492359	+	0.870392i	$0.663865\pi$
$128$	−21.3619	−1.88814
$129$	−4.68812	−0.412766
$130$	−1.08311	−0.0949949
$131$	−2.29027	−0.200102	−0.100051	−	0.994982i	$-0.531901\pi$
$131$	−2.29027	−0.200102	−0.100051	+	0.994982i	$0.531901\pi$
$132$	7.55227	0.657341
$133$	12.6628	1.09801
$134$	−8.35556	−0.721811
$135$	−16.0331	−1.37991
$136$	−22.9217	−1.96552
$137$	−9.16110	−0.782685	−0.391343	−	0.920245i	$-0.627989\pi$
$137$	−9.16110	−0.782685	−0.391343	+	0.920245i	$0.627989\pi$
$138$	16.7134	1.42274
$139$	−5.16851	−0.438387	−0.219194	−	0.975681i	$-0.570343\pi$
$139$	−5.16851	−0.438387	−0.219194	+	0.975681i	$0.570343\pi$
$140$	−29.3747	−2.48261
$141$	10.7588	0.906052
$142$	16.8706	1.41575
$143$	0.137106	0.0114653
$144$	−10.1154	−0.842952
$145$	−18.4339	−1.53085
$146$	40.5028	3.35204
$147$	−4.63382	−0.382191
$148$	38.0743	3.12969
$149$	−22.2384	−1.82184	−0.910920	−	0.412583i	$-0.864627\pi$
$149$	−22.2384	−1.82184	−0.910920	+	0.412583i	$0.864627\pi$
$150$	−12.4243	−1.01444
$151$	8.29780	0.675266	0.337633	−	0.941278i	$-0.390374\pi$
$151$	8.29780	0.675266	0.337633	+	0.941278i	$0.390374\pi$
$152$	55.8507	4.53009
$153$	−2.06294	−0.166778
$154$	5.13937	0.414143
$155$	15.6252	1.25505
$156$	1.10256	0.0882755
$157$	−8.76374	−0.699423	−0.349711	−	0.936858i	$-0.613720\pi$
$157$	−8.76374	−0.699423	−0.349711	+	0.936858i	$0.613720\pi$
$158$	15.1239	1.20319
$159$	−1.45358	−0.115276
$160$	−49.4268	−3.90753
$161$	8.22893	0.648530
$162$	16.2427	1.27615
$163$	−4.80034	−0.375992	−0.187996	−	0.982170i	$-0.560199\pi$
$163$	−4.80034	−0.375992	−0.187996	+	0.982170i	$0.560199\pi$
$164$	−47.9553	−3.74468
$165$	4.10752	0.319770
$166$	−0.351690	−0.0272965
$167$	6.33321	0.490079	0.245039	−	0.969513i	$-0.421199\pi$
$167$	6.33321	0.490079	0.245039	+	0.969513i	$0.421199\pi$
$168$	25.5355	1.97010
$169$	−12.9800	−0.998460
$170$	−20.1773	−1.54753
$171$	5.02652	0.384387
$172$	−16.4774	−1.25639
$173$	24.0518	1.82863	0.914314	−	0.405007i	$-0.132731\pi$
$173$	24.0518	1.82863	0.914314	+	0.405007i	$0.132731\pi$
$174$	25.9359	1.96620
$175$	−6.11717	−0.462415
$176$	12.5240	0.944036
$177$	11.0732	0.832311
$178$	5.69152	0.426598
$179$	13.5172	1.01032	0.505160	−	0.863026i	$-0.331433\pi$
$179$	13.5172	1.01032	0.505160	+	0.863026i	$0.331433\pi$
$180$	−11.6603	−0.869108
$181$	−21.5354	−1.60071	−0.800357	−	0.599524i	$-0.795357\pi$
$181$	−21.5354	−1.60071	−0.800357	+	0.599524i	$0.795357\pi$
$182$	0.750301	0.0556160
$183$	10.9091	0.806420
$184$	36.2946	2.67567
$185$	20.7078	1.52247
$186$	−21.9842	−1.61196
$187$	2.55415	0.186778
$188$	37.8141	2.75788
$189$	11.1066	0.807888
$190$	49.1637	3.56671
$191$	19.1929	1.38875	0.694376	−	0.719612i	$-0.255680\pi$
$191$	19.1929	1.38875	0.694376	+	0.719612i	$0.255680\pi$
$192$	31.0544	2.24116
$193$	−16.9350	−1.21901	−0.609503	−	0.792784i	$-0.708631\pi$
$193$	−16.9350	−1.21901	−0.609503	+	0.792784i	$0.708631\pi$
$194$	23.0683	1.65621
$195$	0.599660	0.0429425
$196$	−16.2866	−1.16333
$197$	6.70301	0.477570	0.238785	−	0.971072i	$-0.423251\pi$
$197$	6.70301	0.477570	0.238785	+	0.971072i	$0.423251\pi$
$198$	2.04008	0.144982
$199$	8.64761	0.613013	0.306507	−	0.951869i	$-0.400840\pi$
$199$	8.64761	0.613013	0.306507	+	0.951869i	$0.400840\pi$
$200$	−26.9804	−1.90780
$201$	4.62603	0.326295
$202$	−30.3337	−2.13427
$203$	12.7697	0.896257
$204$	20.5397	1.43807
$205$	−26.0819	−1.82164
$206$	17.7927	1.23967
$207$	3.26648	0.227036
$208$	1.82839	0.126776
$209$	−6.22341	−0.430482
$210$	22.4781	1.55114
$211$	−26.3564	−1.81445	−0.907225	−	0.420646i	$-0.861804\pi$
$211$	−26.3564	−1.81445	−0.907225	+	0.420646i	$0.861804\pi$
$212$	−5.10892	−0.350882
$213$	−9.34037	−0.639991
$214$	14.1724	0.968802
$215$	−8.96174	−0.611186
$216$	48.9869	3.33314
$217$	−10.8240	−0.734784
$218$	−8.50213	−0.575837
$219$	−22.4243	−1.51529
$220$	14.4368	0.973328
$221$	0.372882	0.0250828
$222$	−29.1352	−1.95543
$223$	−2.48378	−0.166326	−0.0831631	−	0.996536i	$-0.526502\pi$
$223$	−2.48378	−0.166326	−0.0831631	+	0.996536i	$0.526502\pi$
$224$	34.2394	2.28772
$225$	−2.42822	−0.161881
$226$	11.0186	0.732948
$227$	29.3579	1.94855	0.974275	−	0.225363i	$-0.0723568\pi$
$227$	29.3579	1.94855	0.974275	+	0.225363i	$0.0723568\pi$
$228$	−50.0467	−3.31442
$229$	−2.90630	−0.192053	−0.0960267	−	0.995379i	$-0.530613\pi$
$229$	−2.90630	−0.192053	−0.0960267	+	0.995379i	$0.530613\pi$
$230$	31.9490	2.10666
$231$	−2.84540	−0.187214
$232$	56.3221	3.69773
$233$	−4.16719	−0.273001	−0.136501	−	0.990640i	$-0.543586\pi$
$233$	−4.16719	−0.273001	−0.136501	+	0.990640i	$0.543586\pi$
$234$	0.297832	0.0194699
$235$	20.5663	1.34160
$236$	38.9192	2.53342
$237$	−8.37332	−0.543905
$238$	13.9774	0.906021
$239$	10.6447	0.688545	0.344273	−	0.938870i	$-0.388126\pi$
$239$	10.6447	0.688545	0.344273	+	0.938870i	$0.388126\pi$
$240$	54.7765	3.53581
$241$	−18.5123	−1.19248	−0.596242	−	0.802805i	$-0.703340\pi$
$241$	−18.5123	−1.19248	−0.596242	+	0.802805i	$0.703340\pi$
$242$	27.0591	1.73942
$243$	7.90530	0.507125
$244$	38.3423	2.45461
$245$	−8.85794	−0.565913
$246$	36.6964	2.33968
$247$	−0.908559	−0.0578103
$248$	−47.7406	−3.03153
$249$	0.194712	0.0123394
$250$	14.5282	0.918841
$251$	−19.5901	−1.23651	−0.618257	−	0.785976i	$-0.712161\pi$
$251$	−19.5901	−1.23651	−0.618257	+	0.785976i	$0.712161\pi$
$252$	8.07743	0.508830
$253$	−4.04428	−0.254261
$254$	29.8463	1.87273
$255$	11.1711	0.699562
$256$	15.7434	0.983964
$257$	12.8840	0.803681	0.401841	−	0.915710i	$-0.368371\pi$
$257$	12.8840	0.803681	0.401841	+	0.915710i	$0.368371\pi$
$258$	12.6089	0.784995
$259$	−14.3449	−0.891348
$260$	2.10764	0.130710
$261$	5.06894	0.313760
$262$	6.15977	0.380552
$263$	3.91410	0.241354	0.120677	−	0.992692i	$-0.461494\pi$
$263$	3.91410	0.241354	0.120677	+	0.992692i	$0.461494\pi$
$264$	−12.5499	−0.772395
$265$	−2.77864	−0.170690
$266$	−34.0571	−2.08818
$267$	−3.15109	−0.192844
$268$	16.2592	0.993190
$269$	21.7074	1.32352	0.661762	−	0.749714i	$-0.269809\pi$
$269$	21.7074	1.32352	0.661762	+	0.749714i	$0.269809\pi$
$270$	43.1217	2.62430
$271$	−8.44795	−0.513176	−0.256588	−	0.966521i	$-0.582598\pi$
$271$	−8.44795	−0.513176	−0.256588	+	0.966521i	$0.582598\pi$
$272$	34.0613	2.06527
$273$	−0.415402	−0.0251413
$274$	24.6391	1.48850
$275$	3.00641	0.181293
$276$	−32.5228	−1.95764
$277$	3.10322	0.186455	0.0932274	−	0.995645i	$-0.470282\pi$
$277$	3.10322	0.186455	0.0932274	+	0.995645i	$0.470282\pi$
$278$	13.9009	0.833721
$279$	−4.29661	−0.257231
$280$	48.8132	2.91715
$281$	−23.1583	−1.38151	−0.690753	−	0.723091i	$-0.742721\pi$
$281$	−23.1583	−1.38151	−0.690753	+	0.723091i	$0.742721\pi$
$282$	−28.9361	−1.72312
$283$	18.8153	1.11845	0.559226	−	0.829015i	$-0.311098\pi$
$283$	18.8153	1.11845	0.559226	+	0.829015i	$0.311098\pi$
$284$	−32.8288	−1.94803
$285$	−27.2194	−1.61234
$286$	−0.368751	−0.0218047
$287$	18.0677	1.06650
$288$	13.5914	0.800878
$289$	−10.0535	−0.591385
$290$	49.5786	2.91136
$291$	−12.7717	−0.748691
$292$	−78.8151	−4.61230
$293$	−11.3737	−0.664461	−0.332231	−	0.943198i	$-0.607801\pi$
$293$	−11.3737	−0.664461	−0.332231	+	0.943198i	$0.607801\pi$
$294$	12.4628	0.726848
$295$	21.1673	1.23241
$296$	−63.2697	−3.67748
$297$	−5.45858	−0.316739
$298$	59.8110	3.46476
$299$	−0.590427	−0.0341453
$300$	24.1766	1.39584
$301$	6.20806	0.357827
$302$	−22.3173	−1.28421
$303$	16.7941	0.964799
$304$	−82.9933	−4.75999
$305$	20.8536	1.19407
$306$	5.54834	0.317178
$307$	11.3818	0.649591	0.324796	−	0.945784i	$-0.394704\pi$
$307$	11.3818	0.649591	0.324796	+	0.945784i	$0.394704\pi$
$308$	−10.0008	−0.569848
$309$	−9.85086	−0.560396
$310$	−42.0246	−2.38684
$311$	−32.6052	−1.84887	−0.924434	−	0.381341i	$-0.875462\pi$
$311$	−32.6052	−1.84887	−0.924434	+	0.381341i	$0.875462\pi$
$312$	−1.83217	−0.103726
$313$	−8.15024	−0.460679	−0.230339	−	0.973110i	$-0.573984\pi$
$313$	−8.15024	−0.460679	−0.230339	+	0.973110i	$0.573984\pi$
$314$	23.5704	1.33016
$315$	4.39315	0.247526
$316$	−29.4299	−1.65556
$317$	−7.94241	−0.446090	−0.223045	−	0.974808i	$-0.571600\pi$
$317$	−7.94241	−0.446090	−0.223045	+	0.974808i	$0.571600\pi$
$318$	3.90945	0.219231
$319$	−6.27593	−0.351385
$320$	59.3631	3.31850
$321$	−7.84648	−0.437948
$322$	−22.1320	−1.23337
$323$	−16.9256	−0.941767
$324$	−31.6069	−1.75594
$325$	0.438908	0.0243462
$326$	12.9107	0.715057
$327$	4.70718	0.260308
$328$	79.6895	4.40012
$329$	−14.2469	−0.785456
$330$	−11.0473	−0.608136
$331$	−4.53620	−0.249332	−0.124666	−	0.992199i	$-0.539786\pi$
$331$	−4.53620	−0.249332	−0.124666	+	0.992199i	$0.539786\pi$
$332$	0.684360	0.0375591
$333$	−5.69422	−0.312041
$334$	−17.0334	−0.932027
$335$	8.84305	0.483148
$336$	−37.9453	−2.07009
$337$	23.8272	1.29795	0.648975	−	0.760810i	$-0.275198\pi$
$337$	23.8272	1.29795	0.648975	+	0.760810i	$0.275198\pi$
$338$	34.9102	1.89886
$339$	−6.10043	−0.331330
$340$	39.2633	2.12935
$341$	5.31970	0.288078
$342$	−13.5190	−0.731024
$343$	19.9389	1.07660
$344$	27.3813	1.47630
$345$	−17.6885	−0.952315
$346$	−64.6883	−3.47767
$347$	28.3865	1.52387	0.761933	−	0.647656i	$-0.224251\pi$
$347$	28.3865	1.52387	0.761933	+	0.647656i	$0.224251\pi$
$348$	−50.4691	−2.70543
$349$	−22.2622	−1.19167	−0.595834	−	0.803107i	$-0.703179\pi$
$349$	−22.2622	−1.19167	−0.595834	+	0.803107i	$0.703179\pi$
$350$	16.4524	0.879416
$351$	−0.796901	−0.0425355
$352$	−16.8277	−0.896917
$353$	12.3431	0.656957	0.328479	−	0.944511i	$-0.393464\pi$
$353$	12.3431	0.656957	0.328479	+	0.944511i	$0.393464\pi$
$354$	−29.7817	−1.58288
$355$	−17.8549	−0.947639
$356$	−11.0752	−0.586986
$357$	−7.73855	−0.409568
$358$	−36.3549	−1.92142
$359$	−15.3169	−0.808397	−0.404198	−	0.914671i	$-0.632449\pi$
$359$	−15.3169	−0.808397	−0.404198	+	0.914671i	$0.632449\pi$
$360$	19.3764	1.02123
$361$	22.2407	1.17056
$362$	57.9203	3.04422
$363$	−14.9812	−0.786308
$364$	−1.46002	−0.0765259
$365$	−42.8659	−2.24370
$366$	−29.3403	−1.53364
$367$	27.2799	1.42400	0.711998	−	0.702181i	$-0.247790\pi$
$367$	27.2799	1.42400	0.711998	+	0.702181i	$0.247790\pi$
$368$	−53.9331	−2.81146
$369$	7.17199	0.373359
$370$	−55.6944	−2.89541
$371$	1.92484	0.0999328
$372$	42.7794	2.21801
$373$	33.7013	1.74499	0.872495	−	0.488623i	$-0.162501\pi$
$373$	33.7013	1.74499	0.872495	+	0.488623i	$0.162501\pi$
$374$	−6.86949	−0.355213
$375$	−8.04347	−0.415363
$376$	−62.8374	−3.24059
$377$	−0.916227	−0.0471881
$378$	−29.8717	−1.53643
$379$	4.21012	0.216259	0.108130	−	0.994137i	$-0.465514\pi$
$379$	4.21012	0.216259	0.108130	+	0.994137i	$0.465514\pi$
$380$	−95.6685	−4.90769
$381$	−16.5243	−0.846568
$382$	−51.6201	−2.64112
$383$	5.47474	0.279746	0.139873	−	0.990169i	$-0.455331\pi$
$383$	5.47474	0.279746	0.139873	+	0.990169i	$0.455331\pi$
$384$	−31.8090	−1.62325
$385$	−5.43922	−0.277208
$386$	45.5473	2.31829
$387$	2.46429	0.125267
$388$	−44.8890	−2.27889
$389$	1.41870	0.0719308	0.0359654	−	0.999353i	$-0.488549\pi$
$389$	1.41870	0.0719308	0.0359654	+	0.999353i	$0.488549\pi$
$390$	−1.61281	−0.0816677
$391$	−10.9991	−0.556249
$392$	27.0642	1.36695
$393$	−3.41034	−0.172029
$394$	−18.0280	−0.908238
$395$	−16.0063	−0.805364
$396$	−3.96982	−0.199491
$397$	−12.4690	−0.625799	−0.312900	−	0.949786i	$-0.601300\pi$
$397$	−12.4690	−0.625799	−0.312900	+	0.949786i	$0.601300\pi$
$398$	−23.2581	−1.16582
$399$	18.8556	0.943963
$400$	40.0925	2.00462
$401$	−6.89936	−0.344537	−0.172269	−	0.985050i	$-0.555110\pi$
$401$	−6.89936	−0.344537	−0.172269	+	0.985050i	$0.555110\pi$
$402$	−12.4419	−0.620545
$403$	0.776626	0.0386865
$404$	59.0268	2.93669
$405$	−17.1903	−0.854194
$406$	−34.3446	−1.70449
$407$	7.05009	0.349460
$408$	−34.1317	−1.68977
$409$	−2.33801	−0.115607	−0.0578037	−	0.998328i	$-0.518410\pi$
$409$	−2.33801	−0.115607	−0.0578037	+	0.998328i	$0.518410\pi$
$410$	70.1483	3.46438
$411$	−13.6414	−0.672879
$412$	−34.6230	−1.70575
$413$	−14.6632	−0.721530
$414$	−8.78532	−0.431775
$415$	0.372209	0.0182710
$416$	−2.45668	−0.120449
$417$	−7.69620	−0.376884
$418$	16.7381	0.818687
$419$	14.9386	0.729798	0.364899	−	0.931047i	$-0.381103\pi$
$419$	14.9386	0.729798	0.364899	+	0.931047i	$0.381103\pi$
$420$	−43.7405	−2.13432
$421$	−6.28634	−0.306378	−0.153189	−	0.988197i	$-0.548954\pi$
$421$	−6.28634	−0.306378	−0.153189	+	0.988197i	$0.548954\pi$
$422$	70.8866	3.45070
$423$	−5.65531	−0.274971
$424$	8.48972	0.412297
$425$	8.17645	0.396616
$426$	25.1213	1.21713
$427$	−14.4459	−0.699085
$428$	−27.5782	−1.33304
$429$	0.204158	0.00985683
$430$	24.1029	1.16235
$431$	−16.3816	−0.789076	−0.394538	−	0.918880i	$-0.629095\pi$
$431$	−16.3816	−0.789076	−0.394538	+	0.918880i	$0.629095\pi$
$432$	−72.7937	−3.50229
$433$	5.11242	0.245687	0.122844	−	0.992426i	$-0.460799\pi$
$433$	5.11242	0.245687	0.122844	+	0.992426i	$0.460799\pi$
$434$	29.1117	1.39740
$435$	−27.4491	−1.31608
$436$	16.5444	0.792335
$437$	26.8002	1.28203
$438$	60.3109	2.88177
$439$	36.9558	1.76381	0.881903	−	0.471431i	$-0.156262\pi$
$439$	36.9558	1.76381	0.881903	+	0.471431i	$0.156262\pi$
$440$	−23.9903	−1.14369
$441$	2.43575	0.115988
$442$	−1.00288	−0.0477022
$443$	−18.2296	−0.866112	−0.433056	−	0.901367i	$-0.642565\pi$
$443$	−18.2296	−0.866112	−0.433056	+	0.901367i	$0.642565\pi$
$444$	56.6947	2.69061
$445$	−6.02358	−0.285545
$446$	6.68022	0.316318
$447$	−33.1142	−1.56625
$448$	−41.1225	−1.94286
$449$	23.0667	1.08859	0.544293	−	0.838895i	$-0.316798\pi$
$449$	23.0667	1.08859	0.544293	+	0.838895i	$0.316798\pi$
$450$	6.53078	0.307864
$451$	−8.87974	−0.418131
$452$	−21.4413	−1.00851
$453$	12.3559	0.580530
$454$	−78.9591	−3.70573
$455$	−0.794075	−0.0372268
$456$	83.1648	3.89455
$457$	−36.6949	−1.71652	−0.858258	−	0.513219i	$-0.828453\pi$
$457$	−36.6949	−1.71652	−0.858258	+	0.513219i	$0.828453\pi$
$458$	7.81659	0.365245
$459$	−14.8455	−0.692930
$460$	−62.1701	−2.89869
$461$	7.97235	0.371309	0.185655	−	0.982615i	$-0.440559\pi$
$461$	7.97235	0.371309	0.185655	+	0.982615i	$0.440559\pi$
$462$	7.65281	0.356041
$463$	−40.1567	−1.86624	−0.933120	−	0.359565i	$-0.882925\pi$
$463$	−40.1567	−1.86624	−0.933120	+	0.359565i	$0.882925\pi$
$464$	−83.6937	−3.88538
$465$	23.2668	1.07897
$466$	11.2078	0.519191
$467$	23.5227	1.08850	0.544251	−	0.838923i	$-0.316814\pi$
$467$	23.5227	1.08850	0.544251	+	0.838923i	$0.316814\pi$
$468$	−0.579557	−0.0267900
$469$	−6.12584	−0.282865
$470$	−55.3138	−2.55144
$471$	−13.0497	−0.601298
$472$	−64.6737	−2.97685
$473$	−3.05108	−0.140289
$474$	22.5204	1.03439
$475$	−19.9226	−0.914112
$476$	−27.1989	−1.24666
$477$	0.764068	0.0349843
$478$	−28.6292	−1.30947
$479$	−2.08633	−0.0953266	−0.0476633	−	0.998863i	$-0.515177\pi$
$479$	−2.08633	−0.0953266	−0.0476633	+	0.998863i	$0.515177\pi$
$480$	−73.5992	−3.35933
$481$	1.02925	0.0469297
$482$	49.7896	2.26785
$483$	12.2533	0.557546
$484$	−52.6547	−2.39339
$485$	−24.4142	−1.10859
$486$	−21.2616	−0.964446
$487$	14.3532	0.650403	0.325202	−	0.945645i	$-0.394568\pi$
$487$	14.3532	0.650403	0.325202	+	0.945645i	$0.394568\pi$
$488$	−63.7151	−2.88425
$489$	−7.14797	−0.323242
$490$	23.8238	1.07625
$491$	22.8477	1.03110	0.515552	−	0.856858i	$-0.327587\pi$
$491$	22.8477	1.03110	0.515552	+	0.856858i	$0.327587\pi$
$492$	−71.4081	−3.21933
$493$	−17.0685	−0.768725
$494$	2.44360	0.109943
$495$	−2.15910	−0.0970444
$496$	70.9417	3.18538
$497$	12.3686	0.554808
$498$	−0.523686	−0.0234669
$499$	−36.2329	−1.62201	−0.811003	−	0.585043i	$-0.801078\pi$
$499$	−36.2329	−1.62201	−0.811003	+	0.585043i	$0.801078\pi$
$500$	−28.2706	−1.26430
$501$	9.43050	0.421324
$502$	52.6882	2.35159
$503$	−0.228293	−0.0101791	−0.00508955	−	0.999987i	$-0.501620\pi$
$503$	−0.228293	−0.0101791	−0.00508955	+	0.999987i	$0.501620\pi$
$504$	−13.4226	−0.597891
$505$	32.1034	1.42858
$506$	10.8772	0.483552
$507$	−19.3279	−0.858382
$508$	−58.0785	−2.57682
$509$	2.53941	0.112557	0.0562787	−	0.998415i	$-0.482076\pi$
$509$	2.53941	0.112557	0.0562787	+	0.998415i	$0.482076\pi$
$510$	−30.0451	−1.33042
$511$	29.6944	1.31360
$512$	0.381276	0.0168502
$513$	36.1724	1.59705
$514$	−34.6520	−1.52843
$515$	−18.8307	−0.829782
$516$	−24.5358	−1.08013
$517$	7.00192	0.307944
$518$	38.5811	1.69516
$519$	35.8145	1.57208
$520$	−3.50235	−0.153588
$521$	1.16670	0.0511139	0.0255570	−	0.999673i	$-0.491864\pi$
$521$	1.16670	0.0511139	0.0255570	+	0.999673i	$0.491864\pi$
$522$	−13.6331	−0.596705
$523$	24.3062	1.06284	0.531419	−	0.847109i	$-0.321659\pi$
$523$	24.3062	1.06284	0.531419	+	0.847109i	$0.321659\pi$
$524$	−11.9864	−0.523628
$525$	−9.10880	−0.397541
$526$	−10.5271	−0.459004
$527$	14.4678	0.630229
$528$	18.6490	0.811593
$529$	−5.58388	−0.242777
$530$	7.47325	0.324617
$531$	−5.82058	−0.252592
$532$	66.2723	2.87327
$533$	−1.29636	−0.0561516
$534$	8.47499	0.366749
$535$	−14.9992	−0.648472
$536$	−27.0187	−1.16703
$537$	20.1278	0.868579
$538$	−58.3829	−2.51706
$539$	−3.01574	−0.129897
$540$	−83.9112	−3.61096
$541$	9.64344	0.414604	0.207302	−	0.978277i	$-0.433532\pi$
$541$	9.64344	0.414604	0.207302	+	0.978277i	$0.433532\pi$
$542$	22.7211	0.975954
$543$	−32.0674	−1.37614
$544$	−45.7657	−1.96219
$545$	8.99817	0.385439
$546$	1.11724	0.0478134
$547$	−23.3633	−0.998941	−0.499470	−	0.866331i	$-0.666472\pi$
$547$	−23.3633	−0.998941	−0.499470	+	0.866331i	$0.666472\pi$
$548$	−47.9456	−2.04814
$549$	−5.73430	−0.244734
$550$	−8.08585	−0.344782
$551$	41.5888	1.77174
$552$	54.0446	2.30029
$553$	11.0880	0.471511
$554$	−8.34624	−0.354598
$555$	30.8350	1.30887
$556$	−27.0500	−1.14718
$557$	1.05234	0.0445891	0.0222945	−	0.999751i	$-0.492903\pi$
$557$	1.05234	0.0445891	0.0222945	+	0.999751i	$0.492903\pi$
$558$	11.5559	0.489200
$559$	−0.445429	−0.0188396
$560$	−72.5356	−3.06519
$561$	3.80327	0.160574
$562$	62.2850	2.62734
$563$	−12.6829	−0.534520	−0.267260	−	0.963624i	$-0.586118\pi$
$563$	−12.6829	−0.534520	−0.267260	+	0.963624i	$0.586118\pi$
$564$	56.3073	2.37096
$565$	−11.6615	−0.490602
$566$	−50.6044	−2.12706
$567$	11.9082	0.500099
$568$	54.5530	2.28900
$569$	31.2132	1.30853	0.654263	−	0.756267i	$-0.272979\pi$
$569$	31.2132	1.30853	0.654263	+	0.756267i	$0.272979\pi$
$570$	73.2075	3.06632
$571$	−1.15665	−0.0484043	−0.0242022	−	0.999707i	$-0.507705\pi$
$571$	−1.15665	−0.0484043	−0.0242022	+	0.999707i	$0.507705\pi$
$572$	0.717558	0.0300026
$573$	28.5793	1.19392
$574$	−48.5938	−2.02826
$575$	−12.9467	−0.539914
$576$	−16.3236	−0.680151
$577$	16.2396	0.676062	0.338031	−	0.941135i	$-0.390239\pi$
$577$	16.2396	0.676062	0.338031	+	0.941135i	$0.390239\pi$
$578$	27.0394	1.12469
$579$	−25.2171	−1.04799
$580$	−96.4759	−4.00594
$581$	−0.257840	−0.0106970
$582$	34.3500	1.42385
$583$	−0.946003	−0.0391795
$584$	130.970	5.41960
$585$	−0.315209	−0.0130323
$586$	30.5901	1.26367
$587$	3.64583	0.150479	0.0752397	−	0.997165i	$-0.476028\pi$
$587$	3.64583	0.150479	0.0752397	+	0.997165i	$0.476028\pi$
$588$	−24.2516	−1.00012
$589$	−35.2521	−1.45254
$590$	−56.9303	−2.34378
$591$	9.98116	0.410570
$592$	94.0177	3.86410
$593$	−16.9578	−0.696375	−0.348187	−	0.937425i	$-0.613203\pi$
$593$	−16.9578	−0.696375	−0.348187	+	0.937425i	$0.613203\pi$
$594$	14.6811	0.602371
$595$	−14.7929	−0.606449
$596$	−116.387	−4.76740
$597$	12.8768	0.527011
$598$	1.58797	0.0649371
$599$	−35.2928	−1.44203	−0.721013	−	0.692922i	$-0.756323\pi$
$599$	−35.2928	−1.44203	−0.721013	+	0.692922i	$0.756323\pi$
$600$	−40.1753	−1.64015
$601$	−10.0824	−0.411271	−0.205636	−	0.978629i	$-0.565926\pi$
$601$	−10.0824	−0.411271	−0.205636	+	0.978629i	$0.565926\pi$
$602$	−16.6968	−0.680511
$603$	−2.43166	−0.0990247
$604$	43.4275	1.76704
$605$	−28.6378	−1.16429
$606$	−45.1685	−1.83484
$607$	37.6275	1.52725	0.763626	−	0.645659i	$-0.223417\pi$
$607$	37.6275	1.52725	0.763626	+	0.645659i	$0.223417\pi$
$608$	111.512	4.52241
$609$	19.0148	0.770518
$610$	−56.0865	−2.27087
$611$	1.02222	0.0413544
$612$	−10.7966	−0.436427
$613$	45.0843	1.82094	0.910469	−	0.413577i	$-0.135721\pi$
$613$	45.0843	1.82094	0.910469	+	0.413577i	$0.135721\pi$
$614$	−30.6117	−1.23539
$615$	−38.8374	−1.56607
$616$	16.6188	0.669589
$617$	19.2196	0.773753	0.386877	−	0.922131i	$-0.373554\pi$
$617$	19.2196	0.773753	0.386877	+	0.922131i	$0.373554\pi$
$618$	26.4943	1.06576
$619$	−9.79054	−0.393515	−0.196758	−	0.980452i	$-0.563041\pi$
$619$	−9.79054	−0.393515	−0.196758	+	0.980452i	$0.563041\pi$
$620$	81.7763	3.28422
$621$	23.5066	0.943288
$622$	87.6928	3.51616
$623$	4.17271	0.167176
$624$	2.72258	0.108990
$625$	−30.8872	−1.23549
$626$	21.9204	0.876115
$627$	−9.26699	−0.370088
$628$	−45.8660	−1.83025
$629$	19.1739	0.764515
$630$	−11.8155	−0.470742
$631$	−7.65006	−0.304544	−0.152272	−	0.988339i	$-0.548659\pi$
$631$	−7.65006	−0.304544	−0.152272	+	0.988339i	$0.548659\pi$
$632$	48.9049	1.94533
$633$	−39.2461	−1.55989
$634$	21.3614	0.848370
$635$	−31.5877	−1.25352
$636$	−7.60746	−0.301656
$637$	−0.440270	−0.0174441
$638$	16.8794	0.668260
$639$	4.90973	0.194226
$640$	−60.8056	−2.40355
$641$	9.95088	0.393036	0.196518	−	0.980500i	$-0.437037\pi$
$641$	9.95088	0.393036	0.196518	+	0.980500i	$0.437037\pi$
$642$	21.1034	0.832885
$643$	20.2349	0.797985	0.398992	−	0.916954i	$-0.369360\pi$
$643$	20.2349	0.797985	0.398992	+	0.916954i	$0.369360\pi$
$644$	43.0670	1.69708
$645$	−13.3445	−0.525440
$646$	45.5221	1.79104
$647$	−16.5408	−0.650287	−0.325144	−	0.945665i	$-0.605413\pi$
$647$	−16.5408	−0.650287	−0.325144	+	0.945665i	$0.605413\pi$
$648$	52.5225	2.06328
$649$	7.20654	0.282882
$650$	−1.18046	−0.0463014
$651$	−16.1176	−0.631698
$652$	−25.1231	−0.983898
$653$	8.82825	0.345476	0.172738	−	0.984968i	$-0.444739\pi$
$653$	8.82825	0.345476	0.172738	+	0.984968i	$0.444739\pi$
$654$	−12.6601	−0.495051
$655$	−6.51915	−0.254724
$656$	−118.417	−4.62342
$657$	11.7872	0.459864
$658$	38.3175	1.49377
$659$	−18.0942	−0.704850	−0.352425	−	0.935840i	$-0.614643\pi$
$659$	−18.0942	−0.704850	−0.352425	+	0.935840i	$0.614643\pi$
$660$	21.4972	0.836776
$661$	−37.3285	−1.45191	−0.725955	−	0.687742i	$-0.758602\pi$
$661$	−37.3285	−1.45191	−0.725955	+	0.687742i	$0.758602\pi$
$662$	12.2003	0.474178
$663$	0.555242	0.0215638
$664$	−1.13723	−0.0441331
$665$	36.0441	1.39773
$666$	15.3148	0.593437
$667$	27.0264	1.04647
$668$	33.1456	1.28244
$669$	−3.69848	−0.142992
$670$	−23.7837	−0.918845
$671$	7.09972	0.274082
$672$	50.9843	1.96676
$673$	−43.4055	−1.67316	−0.836579	−	0.547847i	$-0.815448\pi$
$673$	−43.4055	−1.67316	−0.836579	+	0.547847i	$0.815448\pi$
$674$	−64.0841	−2.46843
$675$	−17.4742	−0.672583
$676$	−67.9322	−2.61278
$677$	−41.7076	−1.60295	−0.801476	−	0.598027i	$-0.795952\pi$
$677$	−41.7076	−1.60295	−0.801476	+	0.598027i	$0.795952\pi$
$678$	16.4073	0.630120
$679$	16.9124	0.649039
$680$	−65.2456	−2.50206
$681$	43.7155	1.67518
$682$	−14.3075	−0.547864
$683$	25.8138	0.987739	0.493869	−	0.869536i	$-0.335582\pi$
$683$	25.8138	0.987739	0.493869	+	0.869536i	$0.335582\pi$
$684$	26.3069	1.00587
$685$	−26.0766	−0.996337
$686$	−53.6264	−2.04747
$687$	−4.32763	−0.165110
$688$	−40.6882	−1.55122
$689$	−0.138108	−0.00526148
$690$	47.5738	1.81110
$691$	40.5448	1.54240	0.771198	−	0.636595i	$-0.219658\pi$
$691$	40.5448	1.54240	0.771198	+	0.636595i	$0.219658\pi$
$692$	125.878	4.78516
$693$	1.49567	0.0568159
$694$	−76.3465	−2.89807
$695$	−14.7119	−0.558055
$696$	83.8667	3.17896
$697$	−24.1500	−0.914746
$698$	59.8751	2.26630
$699$	−6.20517	−0.234701
$700$	−32.0149	−1.21005
$701$	−8.78844	−0.331935	−0.165967	−	0.986131i	$-0.553075\pi$
$701$	−8.78844	−0.331935	−0.165967	+	0.986131i	$0.553075\pi$
$702$	2.14330	0.0808935
$703$	−46.7189	−1.76204
$704$	20.2105	0.761713
$705$	30.6244	1.15338
$706$	−33.1973	−1.24940
$707$	−22.2390	−0.836383
$708$	57.9528	2.17800
$709$	0.298517	0.0112110	0.00560552	−	0.999984i	$-0.498216\pi$
$709$	0.298517	0.0112110	0.00560552	+	0.999984i	$0.498216\pi$
$710$	48.0214	1.80221
$711$	4.40140	0.165065
$712$	18.4042	0.689726
$713$	−22.9085	−0.857932
$714$	20.8131	0.778912
$715$	0.390265	0.0145951
$716$	70.7436	2.64381
$717$	15.8505	0.591947
$718$	41.1955	1.53740
$719$	−16.0622	−0.599020	−0.299510	−	0.954093i	$-0.596823\pi$
$719$	−16.0622	−0.599020	−0.299510	+	0.954093i	$0.596823\pi$
$720$	−28.7931	−1.07305
$721$	13.0446	0.485806
$722$	−59.8173	−2.22617
$723$	−27.5659	−1.02519
$724$	−112.708	−4.18876
$725$	−20.0907	−0.746152
$726$	40.2924	1.49539
$727$	12.6602	0.469539	0.234770	−	0.972051i	$-0.424566\pi$
$727$	12.6602	0.469539	0.234770	+	0.972051i	$0.424566\pi$
$728$	2.42618	0.0899203
$729$	29.8891	1.10700
$730$	115.289	4.26705
$731$	−8.29793	−0.306910
$732$	57.0938	2.11025
$733$	8.68099	0.320640	0.160320	−	0.987065i	$-0.448747\pi$
$733$	8.68099	0.320640	0.160320	+	0.987065i	$0.448747\pi$
$734$	−73.3702	−2.70814
$735$	−13.1900	−0.486519
$736$	72.4660	2.67113
$737$	3.01067	0.110899
$738$	−19.2893	−0.710050
$739$	−4.76806	−0.175396	−0.0876980	−	0.996147i	$-0.527951\pi$
$739$	−4.76806	−0.175396	−0.0876980	+	0.996147i	$0.527951\pi$
$740$	108.377	3.98400
$741$	−1.35289	−0.0496998
$742$	−5.17694	−0.190051
$743$	−16.1270	−0.591644	−0.295822	−	0.955243i	$-0.595593\pi$
$743$	−16.1270	−0.591644	−0.295822	+	0.955243i	$0.595593\pi$
$744$	−71.0883	−2.60622
$745$	−63.3005	−2.31915
$746$	−90.6410	−3.31860
$747$	−0.102350	−0.00374478
$748$	13.3674	0.488762
$749$	10.3904	0.379657
$750$	21.6332	0.789933
$751$	8.51332	0.310656	0.155328	−	0.987863i	$-0.450357\pi$
$751$	8.51332	0.310656	0.155328	+	0.987863i	$0.450357\pi$
$752$	93.3753	3.40505
$753$	−29.1707	−1.06304
$754$	2.46423	0.0897419
$755$	23.6193	0.859595
$756$	58.1278	2.11409
$757$	2.22024	0.0806961	0.0403481	−	0.999186i	$-0.487153\pi$
$757$	2.22024	0.0806961	0.0403481	+	0.999186i	$0.487153\pi$
$758$	−11.3233	−0.411280
$759$	−6.02215	−0.218590
$760$	158.977	5.76668
$761$	4.16054	0.150819	0.0754096	−	0.997153i	$-0.475974\pi$
$761$	4.16054	0.150819	0.0754096	+	0.997153i	$0.475974\pi$
$762$	44.4428	1.60999
$763$	−6.23330	−0.225660
$764$	100.448	3.63410
$765$	−5.87205	−0.212304
$766$	−14.7245	−0.532018
$767$	1.05209	0.0379887
$768$	23.4428	0.845920
$769$	−28.0164	−1.01030	−0.505148	−	0.863033i	$-0.668562\pi$
$769$	−28.0164	−1.01030	−0.505148	+	0.863033i	$0.668562\pi$
$770$	14.6290	0.527192
$771$	19.1850	0.690930
$772$	−88.6311	−3.18990
$773$	−18.7859	−0.675684	−0.337842	−	0.941203i	$-0.609697\pi$
$773$	−18.7859	−0.675684	−0.337842	+	0.941203i	$0.609697\pi$
$774$	−6.62781	−0.238232
$775$	17.0296	0.611722
$776$	74.5940	2.67777
$777$	−21.3603	−0.766298
$778$	−3.81564	−0.136797
$779$	58.8435	2.10829
$780$	3.13839	0.112372
$781$	−6.07881	−0.217517
$782$	29.5825	1.05787
$783$	36.4777	1.30361
$784$	−40.2169	−1.43632
$785$	−24.9456	−0.890346
$786$	9.17224	0.327163
$787$	7.67685	0.273650	0.136825	−	0.990595i	$-0.456310\pi$
$787$	7.67685	0.273650	0.136825	+	0.990595i	$0.456310\pi$
$788$	35.0810	1.24971
$789$	5.82831	0.207493
$790$	43.0495	1.53163
$791$	8.07825	0.287229
$792$	6.59683	0.234408
$793$	1.03649	0.0368070
$794$	33.5358	1.19014
$795$	−4.13754	−0.146743
$796$	45.2583	1.60414
$797$	21.0434	0.745395	0.372697	−	0.927953i	$-0.378433\pi$
$797$	21.0434	0.745395	0.372697	+	0.927953i	$0.378433\pi$
$798$	−50.7130	−1.79522
$799$	19.0429	0.673690
$800$	−53.8693	−1.90457
$801$	1.65636	0.0585246
$802$	18.5561	0.655238
$803$	−14.5939	−0.515009
$804$	24.2109	0.853852
$805$	23.4233	0.825561
$806$	−2.08877	−0.0735736
$807$	32.3235	1.13784
$808$	−98.0874	−3.45070
$809$	21.5585	0.757958	0.378979	−	0.925405i	$-0.376275\pi$
$809$	21.5585	0.757958	0.378979	+	0.925405i	$0.376275\pi$
$810$	46.2340	1.62450
$811$	−3.86806	−0.135826	−0.0679129	−	0.997691i	$-0.521634\pi$
$811$	−3.86806	−0.135826	−0.0679129	+	0.997691i	$0.521634\pi$
$812$	66.8317	2.34533
$813$	−12.5795	−0.441181
$814$	−18.9615	−0.664600
$815$	−13.6639	−0.478627
$816$	50.7191	1.77553
$817$	20.2186	0.707360
$818$	6.28818	0.219861
$819$	0.218354	0.00762992
$820$	−136.503	−4.76688
$821$	5.46599	0.190765	0.0953823	−	0.995441i	$-0.469593\pi$
$821$	5.46599	0.190765	0.0953823	+	0.995441i	$0.469593\pi$
$822$	36.6890	1.27968
$823$	26.9437	0.939198	0.469599	−	0.882880i	$-0.344399\pi$
$823$	26.9437	0.939198	0.469599	+	0.882880i	$0.344399\pi$
$824$	57.5346	2.00431
$825$	4.47671	0.155859
$826$	39.4373	1.37220
$827$	−47.2681	−1.64367	−0.821836	−	0.569724i	$-0.807050\pi$
$827$	−47.2681	−1.64367	−0.821836	+	0.569724i	$0.807050\pi$
$828$	17.0955	0.594109
$829$	−34.1786	−1.18707	−0.593536	−	0.804808i	$-0.702268\pi$
$829$	−34.1786	−1.18707	−0.593536	+	0.804808i	$0.702268\pi$
$830$	−1.00107	−0.0347476
$831$	4.62087	0.160296
$832$	2.95055	0.102292
$833$	−8.20182	−0.284176
$834$	20.6992	0.716755
$835$	18.0272	0.623857
$836$	−32.5709	−1.12649
$837$	−30.9198	−1.06874
$838$	−40.1779	−1.38792
$839$	−23.4868	−0.810853	−0.405427	−	0.914128i	$-0.632877\pi$
$839$	−23.4868	−0.810853	−0.405427	+	0.914128i	$0.632877\pi$
$840$	72.6855	2.50789
$841$	12.9398	0.446199
$842$	16.9074	0.582666
$843$	−34.4839	−1.18769
$844$	−137.939	−4.74806
$845$	−36.9469	−1.27101
$846$	15.2102	0.522936
$847$	19.8382	0.681649
$848$	−12.6156	−0.433221
$849$	28.0170	0.961540
$850$	−21.9909	−0.754280
$851$	−30.3603	−1.04074
$852$	−48.8839	−1.67473
$853$	−36.7476	−1.25821	−0.629107	−	0.777318i	$-0.716579\pi$
$853$	−36.7476	−1.25821	−0.629107	+	0.777318i	$0.716579\pi$
$854$	38.8527	1.32951
$855$	14.3077	0.489315
$856$	45.8279	1.56637
$857$	4.44054	0.151686	0.0758430	−	0.997120i	$-0.475835\pi$
$857$	4.44054	0.151686	0.0758430	+	0.997120i	$0.475835\pi$
$858$	−0.549090	−0.0187456
$859$	−37.8683	−1.29205	−0.646026	−	0.763316i	$-0.723570\pi$
$859$	−37.8683	−1.29205	−0.646026	+	0.763316i	$0.723570\pi$
$860$	−46.9023	−1.59935
$861$	26.9038	0.916879
$862$	44.0590	1.50066
$863$	−24.1185	−0.821004	−0.410502	−	0.911860i	$-0.634647\pi$
$863$	−24.1185	−0.821004	−0.410502	+	0.911860i	$0.634647\pi$
$864$	97.8077	3.32748
$865$	68.4624	2.32779
$866$	−13.7500	−0.467246
$867$	−14.9703	−0.508417
$868$	−56.6488	−1.92279
$869$	−5.44944	−0.184860
$870$	73.8253	2.50291
$871$	0.439530	0.0148929
$872$	−27.4926	−0.931017
$873$	6.71340	0.227214
$874$	−72.0803	−2.43815
$875$	10.6512	0.360078
$876$	−117.360	−3.96523
$877$	−13.6507	−0.460950	−0.230475	−	0.973078i	$-0.574028\pi$
$877$	−13.6507	−0.460950	−0.230475	+	0.973078i	$0.574028\pi$
$878$	−99.3941	−3.35439
$879$	−16.9361	−0.571241
$880$	35.6491	1.20173
$881$	24.7124	0.832581	0.416291	−	0.909232i	$-0.363330\pi$
$881$	24.7124	0.832581	0.416291	+	0.909232i	$0.363330\pi$
$882$	−6.55104	−0.220585
$883$	20.3510	0.684864	0.342432	−	0.939543i	$-0.388749\pi$
$883$	20.3510	0.684864	0.342432	+	0.939543i	$0.388749\pi$
$884$	1.95152	0.0656368
$885$	31.5193	1.05951
$886$	49.0291	1.64716
$887$	22.5525	0.757239	0.378620	−	0.925552i	$-0.376399\pi$
$887$	22.5525	0.757239	0.378620	+	0.925552i	$0.376399\pi$
$888$	−94.2120	−3.16155
$889$	21.8817	0.733889
$890$	16.2006	0.543047
$891$	−5.85255	−0.196068
$892$	−12.9991	−0.435243
$893$	−46.3997	−1.55271
$894$	89.0619	2.97867
$895$	38.4760	1.28611
$896$	42.1218	1.40719
$897$	−0.879178	−0.0293549
$898$	−62.0388	−2.07026
$899$	−35.5496	−1.18565
$900$	−12.7083	−0.423611
$901$	−2.57282	−0.0857130
$902$	23.8824	0.795197
$903$	9.24414	0.307626
$904$	35.6300	1.18504
$905$	−61.2995	−2.03766
$906$	−33.2316	−1.10405
$907$	5.47335	0.181740	0.0908699	−	0.995863i	$-0.471035\pi$
$907$	5.47335	0.181740	0.0908699	+	0.995863i	$0.471035\pi$
$908$	153.648	5.09898
$909$	−8.82778	−0.292799
$910$	2.13570	0.0707976
$911$	54.6493	1.81061	0.905306	−	0.424760i	$-0.139642\pi$
$911$	54.6493	1.81061	0.905306	+	0.424760i	$0.139642\pi$
$912$	−123.581	−4.09219
$913$	0.126721	0.00419385
$914$	98.6923	3.26445
$915$	31.0521	1.02655
$916$	−15.2104	−0.502567
$917$	4.51601	0.149132
$918$	39.9276	1.31781
$919$	−46.6089	−1.53749	−0.768744	−	0.639557i	$-0.779118\pi$
$919$	−46.6089	−1.53749	−0.768744	+	0.639557i	$0.779118\pi$
$920$	103.311	3.40605
$921$	16.9481	0.558458
$922$	−21.4419	−0.706152
$923$	−0.887449	−0.0292107
$924$	−14.8917	−0.489902
$925$	22.5690	0.742065
$926$	108.003	3.54920
$927$	5.17807	0.170070
$928$	112.453	3.69145
$929$	−42.9668	−1.40970	−0.704848	−	0.709358i	$-0.748985\pi$
$929$	−42.9668	−1.40970	−0.704848	+	0.709358i	$0.748985\pi$
$930$	−62.5769	−2.05198
$931$	19.9844	0.654963
$932$	−21.8094	−0.714392
$933$	−48.5509	−1.58948
$934$	−63.2652	−2.07010
$935$	7.27027	0.237763
$936$	0.963075	0.0314791
$937$	−20.0212	−0.654065	−0.327032	−	0.945013i	$-0.606049\pi$
$937$	−20.0212	−0.654065	−0.327032	+	0.945013i	$0.606049\pi$
$938$	16.4757	0.537950
$939$	−12.1362	−0.396048
$940$	107.636	3.51070
$941$	−12.1715	−0.396779	−0.198390	−	0.980123i	$-0.563571\pi$
$941$	−12.1715	−0.396779	−0.198390	+	0.980123i	$0.563571\pi$
$942$	35.0976	1.14354
$943$	38.2394	1.24525
$944$	96.1040	3.12792
$945$	31.6145	1.02842
$946$	8.20599	0.266800
$947$	−19.5101	−0.633993	−0.316996	−	0.948427i	$-0.602674\pi$
$947$	−19.5101	−0.633993	−0.316996	+	0.948427i	$0.602674\pi$
$948$	−43.8227	−1.42330
$949$	−2.13058	−0.0691615
$950$	53.5826	1.73845
$951$	−11.8267	−0.383506
$952$	45.1976	1.46486
$953$	−28.6937	−0.929480	−0.464740	−	0.885447i	$-0.653852\pi$
$953$	−28.6937	−0.929480	−0.464740	+	0.885447i	$0.653852\pi$
$954$	−2.05499	−0.0665327
$955$	54.6318	1.76784
$956$	55.7100	1.80179
$957$	−9.34520	−0.302088
$958$	5.61125	0.181291
$959$	18.0640	0.583318
$960$	88.3949	2.85293
$961$	−0.866905	−0.0279647
$962$	−2.76820	−0.0892504
$963$	4.12447	0.132909
$964$	−96.8864	−3.12050
$965$	−48.2046	−1.55176
$966$	−32.9558	−1.06033
$967$	−38.7028	−1.24460	−0.622299	−	0.782779i	$-0.713801\pi$
$967$	−38.7028	−1.24460	−0.622299	+	0.782779i	$0.713801\pi$
$968$	87.4986	2.81231
$969$	−25.2032	−0.809643
$970$	65.6629	2.10831
$971$	51.9398	1.66683	0.833414	−	0.552649i	$-0.186383\pi$
$971$	51.9398	1.66683	0.833414	+	0.552649i	$0.186383\pi$
$972$	41.3733	1.32705
$973$	10.1914	0.326721
$974$	−38.6034	−1.23693
$975$	0.653558	0.0209306
$976$	94.6795	3.03062
$977$	38.2392	1.22338	0.611690	−	0.791098i	$-0.290490\pi$
$977$	38.2392	1.22338	0.611690	+	0.791098i	$0.290490\pi$
$978$	19.2247	0.614739
$979$	−2.05076	−0.0655427
$980$	−46.3590	−1.48088
$981$	−2.47431	−0.0789987
$982$	−61.4499	−1.96094
$983$	−0.225406	−0.00718932	−0.00359466	−	0.999994i	$-0.501144\pi$
$983$	−0.225406	−0.00718932	−0.00359466	+	0.999994i	$0.501144\pi$
$984$	118.662	3.78281
$985$	19.0798	0.607933
$986$	45.9063	1.46195
$987$	−21.2144	−0.675261
$988$	−4.75505	−0.151278
$989$	13.1391	0.417798
$990$	5.80699	0.184558
$991$	−4.77500	−0.151683	−0.0758415	−	0.997120i	$-0.524164\pi$
$991$	−4.77500	−0.151683	−0.0758415	+	0.997120i	$0.524164\pi$
$992$	−95.3192	−3.02639
$993$	−6.75465	−0.214352
$994$	−33.2658	−1.05513
$995$	24.6150	0.780349
$996$	1.01905	0.0322898
$997$	27.1906	0.861136	0.430568	−	0.902558i	$-0.358313\pi$
$997$	27.1906	0.861136	0.430568	+	0.902558i	$0.358313\pi$
$998$	97.4496	3.08471
$999$	−40.9774	−1.29647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.4	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.68954 q^{2} +1.48905 q^{3} +5.23361 q^{4} +2.84645 q^{5} -4.00487 q^{6} -1.97182 q^{7} -8.69693 q^{8} -0.782716 q^{9} +O(q^{10})\)	\(q-2.68954 q^{2} +1.48905 q^{3} +5.23361 q^{4} +2.84645 q^{5} -4.00487 q^{6} -1.97182 q^{7} -8.69693 q^{8} -0.782716 q^{9} -7.65564 q^{10} +0.969092 q^{11} +7.79314 q^{12} +0.141478 q^{13} +5.30329 q^{14} +4.23852 q^{15} +12.9235 q^{16} +2.63561 q^{17} +2.10514 q^{18} -6.42189 q^{19} +14.8972 q^{20} -2.93615 q^{21} -2.60641 q^{22} -4.17326 q^{23} -12.9502 q^{24} +3.10229 q^{25} -0.380512 q^{26} -5.63267 q^{27} -10.3197 q^{28} -6.47609 q^{29} -11.3997 q^{30} +5.48936 q^{31} -17.3644 q^{32} +1.44303 q^{33} -7.08858 q^{34} -5.61270 q^{35} -4.09643 q^{36} +7.27495 q^{37} +17.2719 q^{38} +0.210669 q^{39} -24.7554 q^{40} -9.16295 q^{41} +7.89689 q^{42} -3.14839 q^{43} +5.07185 q^{44} -2.22796 q^{45} +11.2241 q^{46} +7.22524 q^{47} +19.2438 q^{48} -3.11192 q^{49} -8.34374 q^{50} +3.92457 q^{51} +0.740443 q^{52} -0.976175 q^{53} +15.1493 q^{54} +2.75848 q^{55} +17.1488 q^{56} -9.56255 q^{57} +17.4177 q^{58} +7.43638 q^{59} +22.1828 q^{60} +7.32616 q^{61} -14.7638 q^{62} +1.54338 q^{63} +20.8551 q^{64} +0.402712 q^{65} -3.88109 q^{66} +3.10669 q^{67} +13.7938 q^{68} -6.21422 q^{69} +15.0956 q^{70} -6.27268 q^{71} +6.80722 q^{72} -15.0594 q^{73} -19.5662 q^{74} +4.61949 q^{75} -33.6097 q^{76} -1.91088 q^{77} -0.566603 q^{78} -5.62324 q^{79} +36.7861 q^{80} -6.03921 q^{81} +24.6441 q^{82} +0.130762 q^{83} -15.3667 q^{84} +7.50215 q^{85} +8.46771 q^{86} -9.64326 q^{87} -8.42812 q^{88} -2.11617 q^{89} +5.99219 q^{90} -0.278970 q^{91} -21.8412 q^{92} +8.17396 q^{93} -19.4326 q^{94} -18.2796 q^{95} -25.8565 q^{96} -8.57706 q^{97} +8.36963 q^{98} -0.758524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 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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