LMFDB - Embedded newform 4019.2.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.80607 q^{2} -1.31751 q^{3} +5.87400 q^{4} -0.399238 q^{5} +3.69703 q^{6} -2.36747 q^{7} -10.8707 q^{8} -1.26416 q^{9} +O(q^{10})$	\(q-2.80607 q^{2} -1.31751 q^{3} +5.87400 q^{4} -0.399238 q^{5} +3.69703 q^{6} -2.36747 q^{7} -10.8707 q^{8} -1.26416 q^{9} +1.12029 q^{10} +2.46090 q^{11} -7.73907 q^{12} -3.67009 q^{13} +6.64328 q^{14} +0.526001 q^{15} +18.7559 q^{16} +0.403400 q^{17} +3.54731 q^{18} -3.40499 q^{19} -2.34512 q^{20} +3.11918 q^{21} -6.90544 q^{22} -1.68571 q^{23} +14.3223 q^{24} -4.84061 q^{25} +10.2985 q^{26} +5.61809 q^{27} -13.9065 q^{28} +4.26751 q^{29} -1.47599 q^{30} +7.68319 q^{31} -30.8888 q^{32} -3.24227 q^{33} -1.13197 q^{34} +0.945184 q^{35} -7.42567 q^{36} -4.32879 q^{37} +9.55462 q^{38} +4.83540 q^{39} +4.33999 q^{40} -9.31616 q^{41} -8.75261 q^{42} +5.43144 q^{43} +14.4553 q^{44} +0.504700 q^{45} +4.73023 q^{46} -10.1972 q^{47} -24.7111 q^{48} -1.39507 q^{49} +13.5831 q^{50} -0.531485 q^{51} -21.5581 q^{52} -11.7397 q^{53} -15.7647 q^{54} -0.982484 q^{55} +25.7361 q^{56} +4.48612 q^{57} -11.9749 q^{58} -12.9488 q^{59} +3.08973 q^{60} -9.90635 q^{61} -21.5595 q^{62} +2.99286 q^{63} +49.1643 q^{64} +1.46524 q^{65} +9.09801 q^{66} +11.3238 q^{67} +2.36957 q^{68} +2.22095 q^{69} -2.65225 q^{70} -5.90895 q^{71} +13.7423 q^{72} +12.9985 q^{73} +12.1469 q^{74} +6.37757 q^{75} -20.0009 q^{76} -5.82611 q^{77} -13.5684 q^{78} +1.30020 q^{79} -7.48806 q^{80} -3.60943 q^{81} +26.1417 q^{82} +1.89580 q^{83} +18.3220 q^{84} -0.161053 q^{85} -15.2410 q^{86} -5.62250 q^{87} -26.7517 q^{88} +7.84277 q^{89} -1.41622 q^{90} +8.68885 q^{91} -9.90189 q^{92} -10.1227 q^{93} +28.6139 q^{94} +1.35940 q^{95} +40.6965 q^{96} -13.3027 q^{97} +3.91467 q^{98} -3.11097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.80607	−1.98419	−0.992094	−	0.125498i	$-0.959947\pi$
$2$	−2.80607	−1.98419	−0.992094	+	0.125498i	$0.959947\pi$
$3$	−1.31751	−0.760667	−0.380333	−	0.924849i	$-0.624191\pi$
$3$	−1.31751	−0.760667	−0.380333	+	0.924849i	$0.624191\pi$
$4$	5.87400	2.93700
$5$	−0.399238	−0.178545	−0.0892723	−	0.996007i	$-0.528454\pi$
$5$	−0.399238	−0.178545	−0.0892723	+	0.996007i	$0.528454\pi$
$6$	3.69703	1.50931
$7$	−2.36747	−0.894820	−0.447410	−	0.894329i	$-0.647654\pi$
$7$	−2.36747	−0.894820	−0.447410	+	0.894329i	$0.647654\pi$
$8$	−10.8707	−3.84337
$9$	−1.26416	−0.421386
$10$	1.12029	0.354266
$11$	2.46090	0.741989	0.370995	−	0.928635i	$-0.379017\pi$
$11$	2.46090	0.741989	0.370995	+	0.928635i	$0.379017\pi$
$12$	−7.73907	−2.23408
$13$	−3.67009	−1.01790	−0.508951	−	0.860796i	$-0.669966\pi$
$13$	−3.67009	−1.01790	−0.508951	+	0.860796i	$0.669966\pi$
$14$	6.64328	1.77549
$15$	0.526001	0.135813
$16$	18.7559	4.68897
$17$	0.403400	0.0978389	0.0489195	−	0.998803i	$-0.484422\pi$
$17$	0.403400	0.0978389	0.0489195	+	0.998803i	$0.484422\pi$
$18$	3.54731	0.836109
$19$	−3.40499	−0.781158	−0.390579	−	0.920569i	$-0.627725\pi$
$19$	−3.40499	−0.781158	−0.390579	+	0.920569i	$0.627725\pi$
$20$	−2.34512	−0.524385
$21$	3.11918	0.680660
$22$	−6.90544	−1.47225
$23$	−1.68571	−0.351496	−0.175748	−	0.984435i	$-0.556234\pi$
$23$	−1.68571	−0.351496	−0.175748	+	0.984435i	$0.556234\pi$
$24$	14.3223	2.92353
$25$	−4.84061	−0.968122
$26$	10.2985	2.01971
$27$	5.61809	1.08120
$28$	−13.9065	−2.62809
$29$	4.26751	0.792457	0.396228	−	0.918152i	$-0.370319\pi$
$29$	4.26751	0.792457	0.396228	+	0.918152i	$0.370319\pi$
$30$	−1.47599	−0.269478
$31$	7.68319	1.37994	0.689971	−	0.723837i	$-0.257623\pi$
$31$	7.68319	1.37994	0.689971	+	0.723837i	$0.257623\pi$
$32$	−30.8888	−5.46043
$33$	−3.24227	−0.564406
$34$	−1.13197	−0.194131
$35$	0.945184	0.159765
$36$	−7.42567	−1.23761
$37$	−4.32879	−0.711648	−0.355824	−	0.934553i	$-0.615800\pi$
$37$	−4.32879	−0.711648	−0.355824	+	0.934553i	$0.615800\pi$
$38$	9.55462	1.54996
$39$	4.83540	0.774283
$40$	4.33999	0.686213
$41$	−9.31616	−1.45494	−0.727470	−	0.686140i	$-0.759304\pi$
$41$	−9.31616	−1.45494	−0.727470	+	0.686140i	$0.759304\pi$
$42$	−8.75261	−1.35056
$43$	5.43144	0.828287	0.414143	−	0.910212i	$-0.364081\pi$
$43$	5.43144	0.828287	0.414143	+	0.910212i	$0.364081\pi$
$44$	14.4553	2.17922
$45$	0.504700	0.0752362
$46$	4.73023	0.697434
$47$	−10.1972	−1.48741	−0.743705	−	0.668508i	$-0.766933\pi$
$47$	−10.1972	−1.48741	−0.743705	+	0.668508i	$0.766933\pi$
$48$	−24.7111	−3.56674
$49$	−1.39507	−0.199296
$50$	13.5831	1.92094
$51$	−0.531485	−0.0744228
$52$	−21.5581	−2.98958
$53$	−11.7397	−1.61257	−0.806286	−	0.591525i	$-0.798526\pi$
$53$	−11.7397	−1.61257	−0.806286	+	0.591525i	$0.798526\pi$
$54$	−15.7647	−2.14531
$55$	−0.982484	−0.132478
$56$	25.7361	3.43913
$57$	4.48612	0.594201
$58$	−11.9749	−1.57238
$59$	−12.9488	−1.68579	−0.842897	−	0.538075i	$-0.819152\pi$
$59$	−12.9488	−1.68579	−0.842897	+	0.538075i	$0.819152\pi$
$60$	3.08973	0.398883
$61$	−9.90635	−1.26838	−0.634189	−	0.773178i	$-0.718666\pi$
$61$	−9.90635	−1.26838	−0.634189	+	0.773178i	$0.718666\pi$
$62$	−21.5595	−2.73806
$63$	2.99286	0.377065
$64$	49.1643	6.14554
$65$	1.46524	0.181741
$66$	9.09801	1.11989
$67$	11.3238	1.38342	0.691711	−	0.722174i	$-0.256857\pi$
$67$	11.3238	1.38342	0.691711	+	0.722174i	$0.256857\pi$
$68$	2.36957	0.287353
$69$	2.22095	0.267371
$70$	−2.65225	−0.317004
$71$	−5.90895	−0.701263	−0.350631	−	0.936514i	$-0.614033\pi$
$71$	−5.90895	−0.701263	−0.350631	+	0.936514i	$0.614033\pi$
$72$	13.7423	1.61954
$73$	12.9985	1.52136	0.760678	−	0.649130i	$-0.224867\pi$
$73$	12.9985	1.52136	0.760678	+	0.649130i	$0.224867\pi$
$74$	12.1469	1.41204
$75$	6.37757	0.736418
$76$	−20.0009	−2.29426
$77$	−5.82611	−0.663947
$78$	−13.5684	−1.53632
$79$	1.30020	0.146284	0.0731421	−	0.997322i	$-0.476697\pi$
$79$	1.30020	0.146284	0.0731421	+	0.997322i	$0.476697\pi$
$80$	−7.48806	−0.837190
$81$	−3.60943	−0.401047
$82$	26.1417	2.88687
$83$	1.89580	0.208091	0.104045	−	0.994573i	$-0.466821\pi$
$83$	1.89580	0.208091	0.104045	+	0.994573i	$0.466821\pi$
$84$	18.3220	1.99910
$85$	−0.161053	−0.0174686
$86$	−15.2410	−1.64348
$87$	−5.62250	−0.602795
$88$	−26.7517	−2.85174
$89$	7.84277	0.831332	0.415666	−	0.909517i	$-0.363549\pi$
$89$	7.84277	0.831332	0.415666	+	0.909517i	$0.363549\pi$
$90$	−1.41622	−0.149283
$91$	8.68885	0.910839
$92$	−9.90189	−1.03234
$93$	−10.1227	−1.04968
$94$	28.6139	2.95130
$95$	1.35940	0.139472
$96$	40.6965	4.15357
$97$	−13.3027	−1.35068	−0.675342	−	0.737505i	$-0.736004\pi$
$97$	−13.3027	−1.35068	−0.675342	+	0.737505i	$0.736004\pi$
$98$	3.91467	0.395441
$99$	−3.11097	−0.312664
$100$	−28.4337	−2.84337
$101$	−2.98936	−0.297452	−0.148726	−	0.988878i	$-0.547517\pi$
$101$	−2.98936	−0.297452	−0.148726	+	0.988878i	$0.547517\pi$
$102$	1.49138	0.147669
$103$	−3.38243	−0.333281	−0.166640	−	0.986018i	$-0.553292\pi$
$103$	−3.38243	−0.333281	−0.166640	+	0.986018i	$0.553292\pi$
$104$	39.8965	3.91217
$105$	−1.24529	−0.121528
$106$	32.9424	3.19965
$107$	−7.50356	−0.725396	−0.362698	−	0.931907i	$-0.618144\pi$
$107$	−7.50356	−0.725396	−0.362698	+	0.931907i	$0.618144\pi$
$108$	33.0006	3.17549
$109$	9.15852	0.877227	0.438613	−	0.898676i	$-0.355470\pi$
$109$	9.15852	0.877227	0.438613	+	0.898676i	$0.355470\pi$
$110$	2.75691	0.262861
$111$	5.70324	0.541327
$112$	−44.4041	−4.19579
$113$	−5.10977	−0.480687	−0.240343	−	0.970688i	$-0.577260\pi$
$113$	−5.10977	−0.480687	−0.240343	+	0.970688i	$0.577260\pi$
$114$	−12.5883	−1.17901
$115$	0.673001	0.0627577
$116$	25.0674	2.32745
$117$	4.63958	0.428930
$118$	36.3353	3.34493
$119$	−0.955039	−0.0875483
$120$	−5.71800	−0.521980
$121$	−4.94397	−0.449452
$122$	27.7979	2.51670
$123$	12.2742	1.10672
$124$	45.1311	4.05289
$125$	3.92874	0.351397
$126$	−8.39816	−0.748168
$127$	−7.98790	−0.708812	−0.354406	−	0.935092i	$-0.615317\pi$
$127$	−7.98790	−0.708812	−0.354406	+	0.935092i	$0.615317\pi$
$128$	−76.1806	−6.73348
$129$	−7.15599	−0.630050
$130$	−4.11156	−0.360608
$131$	−5.30698	−0.463673	−0.231837	−	0.972755i	$-0.574473\pi$
$131$	−5.30698	−0.463673	−0.231837	+	0.972755i	$0.574473\pi$
$132$	−19.0451	−1.65766
$133$	8.06122	0.698996
$134$	−31.7753	−2.74497
$135$	−2.24295	−0.193043
$136$	−4.38524	−0.376031
$137$	3.17044	0.270869	0.135435	−	0.990786i	$-0.456757\pi$
$137$	3.17044	0.270869	0.135435	+	0.990786i	$0.456757\pi$
$138$	−6.23214	−0.530515
$139$	11.9222	1.01123	0.505616	−	0.862759i	$-0.331265\pi$
$139$	11.9222	1.01123	0.505616	+	0.862759i	$0.331265\pi$
$140$	5.55201	0.469231
$141$	13.4349	1.13142
$142$	16.5809	1.39144
$143$	−9.03173	−0.755272
$144$	−23.7104	−1.97587
$145$	−1.70375	−0.141489
$146$	−36.4745	−3.01865
$147$	1.83803	0.151598
$148$	−25.4273	−2.09011
$149$	19.0771	1.56285	0.781427	−	0.623997i	$-0.214492\pi$
$149$	19.0771	1.56285	0.781427	+	0.623997i	$0.214492\pi$
$150$	−17.8959	−1.46119
$151$	9.04612	0.736163	0.368081	−	0.929794i	$-0.380015\pi$
$151$	9.04612	0.736163	0.368081	+	0.929794i	$0.380015\pi$
$152$	37.0146	3.00228
$153$	−0.509962	−0.0412280
$154$	16.3484	1.31740
$155$	−3.06742	−0.246381
$156$	28.4031	2.27407
$157$	−11.2720	−0.899600	−0.449800	−	0.893129i	$-0.648505\pi$
$157$	−11.2720	−0.899600	−0.449800	+	0.893129i	$0.648505\pi$
$158$	−3.64846	−0.290255
$159$	15.4672	1.22663
$160$	12.3320	0.974930
$161$	3.99088	0.314526
$162$	10.1283	0.795753
$163$	−12.8532	−1.00674	−0.503369	−	0.864071i	$-0.667906\pi$
$163$	−12.8532	−1.00674	−0.503369	+	0.864071i	$0.667906\pi$
$164$	−54.7231	−4.27316
$165$	1.29444	0.100772
$166$	−5.31973	−0.412891
$167$	16.3194	1.26283	0.631416	−	0.775444i	$-0.282474\pi$
$167$	16.3194	1.26283	0.631416	+	0.775444i	$0.282474\pi$
$168$	−33.9076	−2.61603
$169$	0.469596	0.0361227
$170$	0.451924	0.0346610
$171$	4.30445	0.329169
$172$	31.9043	2.43268
$173$	−21.8224	−1.65913	−0.829564	−	0.558411i	$-0.811411\pi$
$173$	−21.8224	−1.65913	−0.829564	+	0.558411i	$0.811411\pi$
$174$	15.7771	1.19606
$175$	11.4600	0.866295
$176$	46.1564	3.47917
$177$	17.0603	1.28233
$178$	−22.0073	−1.64952
$179$	−22.2411	−1.66238	−0.831190	−	0.555989i	$-0.812340\pi$
$179$	−22.2411	−1.66238	−0.831190	+	0.555989i	$0.812340\pi$
$180$	2.96461	0.220969
$181$	12.6304	0.938811	0.469405	−	0.882983i	$-0.344468\pi$
$181$	12.6304	0.938811	0.469405	+	0.882983i	$0.344468\pi$
$182$	−24.3815	−1.80728
$183$	13.0517	0.964813
$184$	18.3249	1.35093
$185$	1.72822	0.127061
$186$	28.4050	2.08275
$187$	0.992727	0.0725954
$188$	−59.8982	−4.36853
$189$	−13.3007	−0.967481
$190$	−3.81457	−0.276738
$191$	−20.9551	−1.51626	−0.758130	−	0.652104i	$-0.773887\pi$
$191$	−20.9551	−1.51626	−0.758130	+	0.652104i	$0.773887\pi$
$192$	−64.7747	−4.67471
$193$	4.98417	0.358768	0.179384	−	0.983779i	$-0.442590\pi$
$193$	4.98417	0.358768	0.179384	+	0.983779i	$0.442590\pi$
$194$	37.3282	2.68001
$195$	−1.93047	−0.138244
$196$	−8.19467	−0.585333
$197$	−14.2455	−1.01495	−0.507475	−	0.861667i	$-0.669421\pi$
$197$	−14.2455	−1.01495	−0.507475	+	0.861667i	$0.669421\pi$
$198$	8.72958	0.620384
$199$	5.18056	0.367240	0.183620	−	0.982997i	$-0.441218\pi$
$199$	5.18056	0.367240	0.183620	+	0.982997i	$0.441218\pi$
$200$	52.6208	3.72085
$201$	−14.9193	−1.05232
$202$	8.38833	0.590201
$203$	−10.1032	−0.709106
$204$	−3.12194	−0.218580
$205$	3.71936	0.259772
$206$	9.49132	0.661292
$207$	2.13101	0.148116
$208$	−68.8359	−4.77291
$209$	−8.37933	−0.579611
$210$	3.49437	0.241135
$211$	−20.9880	−1.44487	−0.722437	−	0.691437i	$-0.756978\pi$
$211$	−20.9880	−1.44487	−0.722437	+	0.691437i	$0.756978\pi$
$212$	−68.9590	−4.73613
$213$	7.78512	0.533427
$214$	21.0555	1.43932
$215$	−2.16844	−0.147886
$216$	−61.0725	−4.15546
$217$	−18.1897	−1.23480
$218$	−25.6994	−1.74058
$219$	−17.1256	−1.15724
$220$	−5.77111	−0.389088
$221$	−1.48052	−0.0995903
$222$	−16.0037	−1.07409
$223$	1.97301	0.132122	0.0660612	−	0.997816i	$-0.478957\pi$
$223$	1.97301	0.132122	0.0660612	+	0.997816i	$0.478957\pi$
$224$	73.1285	4.88610
$225$	6.11930	0.407953
$226$	14.3383	0.953773
$227$	−23.8469	−1.58278	−0.791388	−	0.611314i	$-0.790641\pi$
$227$	−23.8469	−1.58278	−0.791388	+	0.611314i	$0.790641\pi$
$228$	26.3515	1.74517
$229$	4.30631	0.284569	0.142285	−	0.989826i	$-0.454555\pi$
$229$	4.30631	0.284569	0.142285	+	0.989826i	$0.454555\pi$
$230$	−1.88848	−0.124523
$231$	7.67598	0.505042
$232$	−46.3908	−3.04571
$233$	−2.52111	−0.165163	−0.0825817	−	0.996584i	$-0.526317\pi$
$233$	−2.52111	−0.165163	−0.0825817	+	0.996584i	$0.526317\pi$
$234$	−13.0190	−0.851077
$235$	4.07110	0.265569
$236$	−76.0614	−4.95118
$237$	−1.71304	−0.111274
$238$	2.67990	0.173712
$239$	7.26385	0.469860	0.234930	−	0.972012i	$-0.424514\pi$
$239$	7.26385	0.469860	0.234930	+	0.972012i	$0.424514\pi$
$240$	9.86562	0.636823
$241$	13.9609	0.899299	0.449649	−	0.893205i	$-0.351549\pi$
$241$	13.9609	0.899299	0.449649	+	0.893205i	$0.351549\pi$
$242$	13.8731	0.891797
$243$	−12.0988	−0.776138
$244$	−58.1899	−3.72523
$245$	0.556966	0.0355833
$246$	−34.4421	−2.19595
$247$	12.4966	0.795142
$248$	−83.5216	−5.30363
$249$	−2.49774	−0.158288
$250$	−11.0243	−0.697238
$251$	−17.8133	−1.12437	−0.562183	−	0.827013i	$-0.690038\pi$
$251$	−17.8133	−1.12437	−0.562183	+	0.827013i	$0.690038\pi$
$252$	17.5801	1.10744
$253$	−4.14837	−0.260806
$254$	22.4146	1.40642
$255$	0.212189	0.0132878
$256$	115.439	7.21495
$257$	12.3465	0.770152	0.385076	−	0.922885i	$-0.374175\pi$
$257$	12.3465	0.770152	0.385076	+	0.922885i	$0.374175\pi$
$258$	20.0802	1.25014
$259$	10.2483	0.636798
$260$	8.60682	0.533773
$261$	−5.39481	−0.333930
$262$	14.8917	0.920015
$263$	−1.84256	−0.113617	−0.0568086	−	0.998385i	$-0.518092\pi$
$263$	−1.84256	−0.113617	−0.0568086	+	0.998385i	$0.518092\pi$
$264$	35.2457	2.16922
$265$	4.68693	0.287916
$266$	−22.6203	−1.38694
$267$	−10.3329	−0.632366
$268$	66.5160	4.06311
$269$	22.7172	1.38509	0.692545	−	0.721375i	$-0.256490\pi$
$269$	22.7172	1.38509	0.692545	+	0.721375i	$0.256490\pi$
$270$	6.29387	0.383033
$271$	5.56723	0.338185	0.169093	−	0.985600i	$-0.445916\pi$
$271$	5.56723	0.338185	0.169093	+	0.985600i	$0.445916\pi$
$272$	7.56613	0.458764
$273$	−11.4477	−0.692845
$274$	−8.89647	−0.537455
$275$	−11.9123	−0.718336
$276$	13.0459	0.785269
$277$	15.3698	0.923479	0.461739	−	0.887016i	$-0.347225\pi$
$277$	15.3698	0.923479	0.461739	+	0.887016i	$0.347225\pi$
$278$	−33.4546	−2.00647
$279$	−9.71277	−0.581488
$280$	−10.2748	−0.614038
$281$	19.6602	1.17283	0.586414	−	0.810012i	$-0.300539\pi$
$281$	19.6602	1.17283	0.586414	+	0.810012i	$0.300539\pi$
$282$	−37.6992	−2.24496
$283$	−1.06753	−0.0634583	−0.0317292	−	0.999497i	$-0.510101\pi$
$283$	−1.06753	−0.0634583	−0.0317292	+	0.999497i	$0.510101\pi$
$284$	−34.7092	−2.05961
$285$	−1.79103	−0.106091
$286$	25.3436	1.49860
$287$	22.0558	1.30191
$288$	39.0484	2.30095
$289$	−16.8373	−0.990428
$290$	4.78084	0.280740
$291$	17.5265	1.02742
$292$	76.3530	4.46822
$293$	18.8943	1.10381	0.551907	−	0.833905i	$-0.313900\pi$
$293$	18.8943	1.10381	0.551907	+	0.833905i	$0.313900\pi$
$294$	−5.15763	−0.300799
$295$	5.16966	0.300989
$296$	47.0570	2.73513
$297$	13.8255	0.802239
$298$	−53.5315	−3.10099
$299$	6.18673	0.357788
$300$	37.4618	2.16286
$301$	−12.8588	−0.741168
$302$	−25.3840	−1.46069
$303$	3.93852	0.226262
$304$	−63.8636	−3.66283
$305$	3.95499	0.226462
$306$	1.43099	0.0818040
$307$	24.6949	1.40941	0.704706	−	0.709499i	$-0.251079\pi$
$307$	24.6949	1.40941	0.704706	+	0.709499i	$0.251079\pi$
$308$	−34.2226	−1.95001
$309$	4.45640	0.253516
$310$	8.60738	0.488866
$311$	25.1873	1.42824	0.714121	−	0.700022i	$-0.246827\pi$
$311$	25.1873	1.42824	0.714121	+	0.700022i	$0.246827\pi$
$312$	−52.5642	−2.97586
$313$	20.9808	1.18591	0.592954	−	0.805236i	$-0.297962\pi$
$313$	20.9808	1.18591	0.592954	+	0.805236i	$0.297962\pi$
$314$	31.6299	1.78498
$315$	−1.19486	−0.0673229
$316$	7.63740	0.429637
$317$	−13.4668	−0.756372	−0.378186	−	0.925730i	$-0.623452\pi$
$317$	−13.4668	−0.756372	−0.378186	+	0.925730i	$0.623452\pi$
$318$	−43.4020	−2.43386
$319$	10.5019	0.587994
$320$	−19.6283	−1.09725
$321$	9.88604	0.551785
$322$	−11.1987	−0.624078
$323$	−1.37357	−0.0764276
$324$	−21.2018	−1.17788
$325$	17.7655	0.985452
$326$	36.0668	1.99756
$327$	−12.0665	−0.667277
$328$	101.273	5.59188
$329$	24.1415	1.33097
$330$	−3.63227	−0.199950
$331$	−8.42310	−0.462976	−0.231488	−	0.972838i	$-0.574359\pi$
$331$	−8.42310	−0.462976	−0.231488	+	0.972838i	$0.574359\pi$
$332$	11.1359	0.611163
$333$	5.47228	0.299879
$334$	−45.7932	−2.50569
$335$	−4.52089	−0.247003
$336$	58.5029	3.19160
$337$	1.41767	0.0772253	0.0386127	−	0.999254i	$-0.487706\pi$
$337$	1.41767	0.0772253	0.0386127	+	0.999254i	$0.487706\pi$
$338$	−1.31772	−0.0716743
$339$	6.73219	0.365642
$340$	−0.946023	−0.0513053
$341$	18.9076	1.02390
$342$	−12.0786	−0.653134
$343$	19.8751	1.07315
$344$	−59.0436	−3.18342
$345$	−0.886688	−0.0477377
$346$	61.2352	3.29202
$347$	20.9307	1.12362	0.561809	−	0.827267i	$-0.310105\pi$
$347$	20.9307	1.12362	0.561809	+	0.827267i	$0.310105\pi$
$348$	−33.0266	−1.77041
$349$	28.3384	1.51692	0.758459	−	0.651721i	$-0.225953\pi$
$349$	28.3384	1.51692	0.758459	+	0.651721i	$0.225953\pi$
$350$	−32.1575	−1.71889
$351$	−20.6189	−1.10056
$352$	−76.0143	−4.05158
$353$	−16.6230	−0.884755	−0.442377	−	0.896829i	$-0.645865\pi$
$353$	−16.6230	−0.884755	−0.442377	+	0.896829i	$0.645865\pi$
$354$	−47.8722	−2.54438
$355$	2.35907	0.125207
$356$	46.0684	2.44162
$357$	1.25828	0.0665950
$358$	62.4100	3.29847
$359$	−10.8523	−0.572765	−0.286382	−	0.958115i	$-0.592453\pi$
$359$	−10.8523	−0.572765	−0.286382	+	0.958115i	$0.592453\pi$
$360$	−5.48644	−0.289161
$361$	−7.40605	−0.389792
$362$	−35.4417	−1.86278
$363$	6.51375	0.341883
$364$	51.0383	2.67513
$365$	−5.18948	−0.271630
$366$	−36.6240	−1.91437
$367$	30.3976	1.58674	0.793372	−	0.608737i	$-0.208324\pi$
$367$	30.3976	1.58674	0.793372	+	0.608737i	$0.208324\pi$
$368$	−31.6171	−1.64815
$369$	11.7771	0.613092
$370$	−4.84949	−0.252113
$371$	27.7934	1.44296
$372$	−59.4608	−3.08290
$373$	6.35223	0.328906	0.164453	−	0.986385i	$-0.447414\pi$
$373$	6.35223	0.328906	0.164453	+	0.986385i	$0.447414\pi$
$374$	−2.78566	−0.144043
$375$	−5.17617	−0.267296
$376$	110.850	5.71667
$377$	−15.6622	−0.806643
$378$	37.3225	1.91966
$379$	−6.10324	−0.313503	−0.156751	−	0.987638i	$-0.550102\pi$
$379$	−6.10324	−0.313503	−0.156751	+	0.987638i	$0.550102\pi$
$380$	7.98512	0.409628
$381$	10.5242	0.539169
$382$	58.8014	3.00854
$383$	−23.8827	−1.22035	−0.610173	−	0.792268i	$-0.708900\pi$
$383$	−23.8827	−1.22035	−0.610173	+	0.792268i	$0.708900\pi$
$384$	100.369	5.12193
$385$	2.32600	0.118544
$386$	−13.9859	−0.711863
$387$	−6.86620	−0.349029
$388$	−78.1400	−3.96696
$389$	0.968740	0.0491171	0.0245585	−	0.999698i	$-0.492182\pi$
$389$	0.968740	0.0491171	0.0245585	+	0.999698i	$0.492182\pi$
$390$	5.41703	0.274302
$391$	−0.680018	−0.0343900
$392$	15.1654	0.765970
$393$	6.99202	0.352701
$394$	39.9738	2.01385
$395$	−0.519090	−0.0261183
$396$	−18.2738	−0.918294
$397$	15.7193	0.788931	0.394466	−	0.918911i	$-0.370930\pi$
$397$	15.7193	0.788931	0.394466	+	0.918911i	$0.370930\pi$
$398$	−14.5370	−0.728673
$399$	−10.6208	−0.531703
$400$	−90.7899	−4.53950
$401$	−4.41247	−0.220348	−0.110174	−	0.993912i	$-0.535141\pi$
$401$	−4.41247	−0.220348	−0.110174	+	0.993912i	$0.535141\pi$
$402$	41.8644	2.08801
$403$	−28.1980	−1.40464
$404$	−17.5595	−0.873617
$405$	1.44102	0.0716048
$406$	28.3503	1.40700
$407$	−10.6527	−0.528035
$408$	5.77761	0.286035
$409$	14.6260	0.723211	0.361606	−	0.932331i	$-0.382229\pi$
$409$	14.6260	0.723211	0.361606	+	0.932331i	$0.382229\pi$
$410$	−10.4368	−0.515435
$411$	−4.17710	−0.206041
$412$	−19.8684	−0.978846
$413$	30.6560	1.50848
$414$	−5.97976	−0.293889
$415$	−0.756874	−0.0371535
$416$	113.365	5.55818
$417$	−15.7077	−0.769210
$418$	23.5130	1.15006
$419$	−25.2896	−1.23548	−0.617738	−	0.786384i	$-0.711951\pi$
$419$	−25.2896	−1.23548	−0.617738	+	0.786384i	$0.711951\pi$
$420$	−7.31485	−0.356928
$421$	−29.4671	−1.43614	−0.718068	−	0.695972i	$-0.754974\pi$
$421$	−29.4671	−1.43614	−0.718068	+	0.695972i	$0.754974\pi$
$422$	58.8937	2.86690
$423$	12.8908	0.626774
$424$	127.619	6.19772
$425$	−1.95270	−0.0947200
$426$	−21.8455	−1.05842
$427$	23.4530	1.13497
$428$	−44.0759	−2.13049
$429$	11.8994	0.574510
$430$	6.08477	0.293434
$431$	−18.0201	−0.867998	−0.433999	−	0.900913i	$-0.642898\pi$
$431$	−18.0201	−0.867998	−0.433999	+	0.900913i	$0.642898\pi$
$432$	105.372	5.06972
$433$	10.1534	0.487942	0.243971	−	0.969783i	$-0.421550\pi$
$433$	10.1534	0.487942	0.243971	+	0.969783i	$0.421550\pi$
$434$	51.0416	2.45007
$435$	2.24471	0.107626
$436$	53.7971	2.57642
$437$	5.73984	0.274574
$438$	48.0557	2.29619
$439$	−21.1296	−1.00846	−0.504231	−	0.863569i	$-0.668224\pi$
$439$	−21.1296	−1.00846	−0.504231	+	0.863569i	$0.668224\pi$
$440$	10.6803	0.509163
$441$	1.76360	0.0839807
$442$	4.15443	0.197606
$443$	27.6393	1.31318	0.656590	−	0.754247i	$-0.271998\pi$
$443$	27.6393	1.31318	0.656590	+	0.754247i	$0.271998\pi$
$444$	33.5008	1.58988
$445$	−3.13113	−0.148430
$446$	−5.53639	−0.262156
$447$	−25.1343	−1.18881
$448$	−116.395	−5.49916
$449$	15.6488	0.738513	0.369257	−	0.929327i	$-0.379612\pi$
$449$	15.6488	0.738513	0.369257	+	0.929327i	$0.379612\pi$
$450$	−17.1712	−0.809456
$451$	−22.9261	−1.07955
$452$	−30.0148	−1.41178
$453$	−11.9184	−0.559975
$454$	66.9160	3.14052
$455$	−3.46892	−0.162625
$456$	−48.7672	−2.28374
$457$	28.5797	1.33690	0.668452	−	0.743756i	$-0.266957\pi$
$457$	28.5797	1.33690	0.668452	+	0.743756i	$0.266957\pi$
$458$	−12.0838	−0.564639
$459$	2.26634	0.105784
$460$	3.95321	0.184319
$461$	11.8062	0.549869	0.274934	−	0.961463i	$-0.411344\pi$
$461$	11.8062	0.549869	0.274934	+	0.961463i	$0.411344\pi$
$462$	−21.5393	−1.00210
$463$	−21.2583	−0.987956	−0.493978	−	0.869474i	$-0.664458\pi$
$463$	−21.2583	−0.987956	−0.493978	+	0.869474i	$0.664458\pi$
$464$	80.0409	3.71581
$465$	4.04136	0.187414
$466$	7.07440	0.327715
$467$	25.9948	1.20289	0.601447	−	0.798912i	$-0.294591\pi$
$467$	25.9948	1.20289	0.601447	+	0.798912i	$0.294591\pi$
$468$	27.2529	1.25977
$469$	−26.8088	−1.23791
$470$	−11.4238	−0.526939
$471$	14.8510	0.684296
$472$	140.763	6.47913
$473$	13.3662	0.614580
$474$	4.80689	0.220788
$475$	16.4822	0.756256
$476$	−5.60990	−0.257129
$477$	14.8409	0.679516
$478$	−20.3828	−0.932290
$479$	35.6872	1.63059	0.815294	−	0.579047i	$-0.196575\pi$
$479$	35.6872	1.63059	0.815294	+	0.579047i	$0.196575\pi$
$480$	−16.2476	−0.741596
$481$	15.8871	0.724388
$482$	−39.1751	−1.78438
$483$	−5.25804	−0.239249
$484$	−29.0409	−1.32004
$485$	5.31094	0.241157
$486$	33.9500	1.54000
$487$	25.0893	1.13690	0.568452	−	0.822717i	$-0.307543\pi$
$487$	25.0893	1.13690	0.568452	+	0.822717i	$0.307543\pi$
$488$	107.689	4.87485
$489$	16.9342	0.765792
$490$	−1.56288	−0.0706039
$491$	−8.52607	−0.384776	−0.192388	−	0.981319i	$-0.561623\pi$
$491$	−8.52607	−0.384776	−0.192388	+	0.981319i	$0.561623\pi$
$492$	72.0984	3.25045
$493$	1.72151	0.0775331
$494$	−35.0664	−1.57771
$495$	1.24202	0.0558245
$496$	144.105	6.47051
$497$	13.9893	0.627504
$498$	7.00881	0.314072
$499$	−14.6142	−0.654223	−0.327112	−	0.944986i	$-0.606075\pi$
$499$	−14.6142	−0.654223	−0.327112	+	0.944986i	$0.606075\pi$
$500$	23.0774	1.03205
$501$	−21.5010	−0.960594
$502$	49.9853	2.23095
$503$	22.2387	0.991575	0.495787	−	0.868444i	$-0.334880\pi$
$503$	22.2387	0.991575	0.495787	+	0.868444i	$0.334880\pi$
$504$	−32.5345	−1.44920
$505$	1.19346	0.0531085
$506$	11.6406	0.517488
$507$	−0.618698	−0.0274774
$508$	−46.9210	−2.08178
$509$	4.78603	0.212137	0.106069	−	0.994359i	$-0.466174\pi$
$509$	4.78603	0.212137	0.106069	+	0.994359i	$0.466174\pi$
$510$	−0.595416	−0.0263655
$511$	−30.7735	−1.36134
$512$	−171.568	−7.58233
$513$	−19.1295	−0.844589
$514$	−34.6450	−1.52813
$515$	1.35039	0.0595055
$516$	−42.0343	−1.85046
$517$	−25.0942	−1.10364
$518$	−28.7574	−1.26353
$519$	28.7513	1.26204
$520$	−15.9282	−0.698497
$521$	33.4542	1.46566	0.732828	−	0.680414i	$-0.238200\pi$
$521$	33.4542	1.46566	0.732828	+	0.680414i	$0.238200\pi$
$522$	15.1382	0.662580
$523$	−34.4130	−1.50478	−0.752388	−	0.658720i	$-0.771098\pi$
$523$	−34.4130	−1.50478	−0.752388	+	0.658720i	$0.771098\pi$
$524$	−31.1732	−1.36181
$525$	−15.0987	−0.658962
$526$	5.17035	0.225438
$527$	3.09940	0.135012
$528$	−60.8116	−2.64649
$529$	−20.1584	−0.876451
$530$	−13.1518	−0.571279
$531$	16.3694	0.710370
$532$	47.3516	2.05295
$533$	34.1912	1.48098
$534$	28.9949	1.25473
$535$	2.99570	0.129516
$536$	−123.098	−5.31701
$537$	29.3030	1.26452
$538$	−63.7458	−2.74828
$539$	−3.43314	−0.147876
$540$	−13.1751	−0.566966
$541$	−39.5432	−1.70010	−0.850048	−	0.526705i	$-0.823427\pi$
$541$	−39.5432	−1.70010	−0.850048	+	0.526705i	$0.823427\pi$
$542$	−15.6220	−0.671023
$543$	−16.6407	−0.714122
$544$	−12.4606	−0.534242
$545$	−3.65643	−0.156624
$546$	32.1229	1.37473
$547$	16.5009	0.705526	0.352763	−	0.935713i	$-0.385242\pi$
$547$	16.5009	0.705526	0.352763	+	0.935713i	$0.385242\pi$
$548$	18.6232	0.795543
$549$	12.5232	0.534477
$550$	33.4266	1.42531
$551$	−14.5308	−0.619034
$552$	−24.1433	−1.02761
$553$	−3.07820	−0.130898
$554$	−43.1285	−1.83236
$555$	−2.27695	−0.0966510
$556$	70.0313	2.96999
$557$	38.7550	1.64210	0.821051	−	0.570855i	$-0.193388\pi$
$557$	38.7550	1.64210	0.821051	+	0.570855i	$0.193388\pi$
$558$	27.2547	1.15378
$559$	−19.9339	−0.843114
$560$	17.7278	0.749135
$561$	−1.30793	−0.0552209
$562$	−55.1677	−2.32711
$563$	17.9462	0.756343	0.378172	−	0.925736i	$-0.376553\pi$
$563$	17.9462	0.756343	0.378172	+	0.925736i	$0.376553\pi$
$564$	78.9167	3.32299
$565$	2.04001	0.0858240
$566$	2.99557	0.125913
$567$	8.54522	0.358865
$568$	64.2344	2.69522
$569$	11.7737	0.493581	0.246790	−	0.969069i	$-0.420624\pi$
$569$	11.7737	0.493581	0.246790	+	0.969069i	$0.420624\pi$
$570$	5.02574	0.210505
$571$	−23.8001	−0.996001	−0.498001	−	0.867177i	$-0.665932\pi$
$571$	−23.8001	−0.996001	−0.498001	+	0.867177i	$0.665932\pi$
$572$	−53.0524	−2.21823
$573$	27.6086	1.15337
$574$	−61.8899	−2.58323
$575$	8.15989	0.340291
$576$	−62.1515	−2.58965
$577$	−27.1677	−1.13101	−0.565504	−	0.824746i	$-0.691318\pi$
$577$	−27.1677	−1.13101	−0.565504	+	0.824746i	$0.691318\pi$
$578$	47.2465	1.96519
$579$	−6.56670	−0.272903
$580$	−10.0078	−0.415553
$581$	−4.48825	−0.186204
$582$	−49.1804	−2.03859
$583$	−28.8902	−1.19651
$584$	−141.302	−5.84714
$585$	−1.85230	−0.0765830
$586$	−53.0185	−2.19018
$587$	39.6797	1.63776	0.818879	−	0.573967i	$-0.194596\pi$
$587$	39.6797	1.63776	0.818879	+	0.573967i	$0.194596\pi$
$588$	10.7966	0.445244
$589$	−26.1612	−1.07795
$590$	−14.5064	−0.597219
$591$	18.7686	0.772038
$592$	−81.1903	−3.33690
$593$	−19.3762	−0.795687	−0.397843	−	0.917453i	$-0.630241\pi$
$593$	−19.3762	−0.795687	−0.397843	+	0.917453i	$0.630241\pi$
$594$	−38.7954	−1.59179
$595$	0.381288	0.0156313
$596$	112.059	4.59010
$597$	−6.82545	−0.279347
$598$	−17.3604	−0.709919
$599$	4.16481	0.170170	0.0850848	−	0.996374i	$-0.472884\pi$
$599$	4.16481	0.170170	0.0850848	+	0.996374i	$0.472884\pi$
$600$	−69.3286	−2.83033
$601$	−5.17857	−0.211238	−0.105619	−	0.994407i	$-0.533682\pi$
$601$	−5.17857	−0.211238	−0.105619	+	0.994407i	$0.533682\pi$
$602$	36.0826	1.47062
$603$	−14.3151	−0.582955
$604$	53.1369	2.16211
$605$	1.97382	0.0802472
$606$	−11.0517	−0.448946
$607$	−2.00292	−0.0812961	−0.0406481	−	0.999174i	$-0.512942\pi$
$607$	−2.00292	−0.0812961	−0.0406481	+	0.999174i	$0.512942\pi$
$608$	105.176	4.26546
$609$	13.3111	0.539394
$610$	−11.0980	−0.449343
$611$	37.4246	1.51404
$612$	−2.99552	−0.121087
$613$	31.0873	1.25560	0.627802	−	0.778373i	$-0.283955\pi$
$613$	31.0873	1.25560	0.627802	+	0.778373i	$0.283955\pi$
$614$	−69.2955	−2.79654
$615$	−4.90031	−0.197600
$616$	63.3339	2.55180
$617$	9.41782	0.379147	0.189574	−	0.981867i	$-0.439289\pi$
$617$	9.41782	0.379147	0.189574	+	0.981867i	$0.439289\pi$
$618$	−12.5049	−0.503023
$619$	36.0298	1.44816	0.724081	−	0.689715i	$-0.242264\pi$
$619$	36.0298	1.44816	0.724081	+	0.689715i	$0.242264\pi$
$620$	−18.0180	−0.723621
$621$	−9.47049	−0.380038
$622$	−70.6773	−2.83390
$623$	−18.5675	−0.743892
$624$	90.6922	3.63059
$625$	22.6345	0.905382
$626$	−58.8736	−2.35306
$627$	11.0399	0.440891
$628$	−66.2115	−2.64213
$629$	−1.74623	−0.0696269
$630$	3.35286	0.133581
$631$	−41.5836	−1.65542	−0.827709	−	0.561157i	$-0.810356\pi$
$631$	−41.5836	−1.65542	−0.827709	+	0.561157i	$0.810356\pi$
$632$	−14.1341	−0.562225
$633$	27.6520	1.09907
$634$	37.7888	1.50078
$635$	3.18907	0.126554
$636$	90.8545	3.60261
$637$	5.12005	0.202864
$638$	−29.4690	−1.16669
$639$	7.46985	0.295503
$640$	30.4142	1.20223
$641$	−21.4278	−0.846346	−0.423173	−	0.906049i	$-0.639084\pi$
$641$	−21.4278	−0.846346	−0.423173	+	0.906049i	$0.639084\pi$
$642$	−27.7409	−1.09484
$643$	7.60432	0.299885	0.149942	−	0.988695i	$-0.452091\pi$
$643$	7.60432	0.299885	0.149942	+	0.988695i	$0.452091\pi$
$644$	23.4425	0.923762
$645$	2.85694	0.112492
$646$	3.85434	0.151647
$647$	−49.7215	−1.95475	−0.977377	−	0.211504i	$-0.932164\pi$
$647$	−49.7215	−1.95475	−0.977377	+	0.211504i	$0.932164\pi$
$648$	39.2370	1.54137
$649$	−31.8658	−1.25084
$650$	−49.8511	−1.95532
$651$	23.9652	0.939271
$652$	−75.4996	−2.95679
$653$	−29.0775	−1.13789	−0.568946	−	0.822375i	$-0.692649\pi$
$653$	−29.0775	−1.13789	−0.568946	+	0.822375i	$0.692649\pi$
$654$	33.8593	1.32400
$655$	2.11875	0.0827863
$656$	−174.733	−6.82217
$657$	−16.4321	−0.641078
$658$	−67.7427	−2.64089
$659$	−28.2122	−1.09899	−0.549497	−	0.835496i	$-0.685180\pi$
$659$	−28.2122	−1.09899	−0.549497	+	0.835496i	$0.685180\pi$
$660$	7.60352	0.295966
$661$	41.4779	1.61330	0.806652	−	0.591026i	$-0.201277\pi$
$661$	41.4779	1.61330	0.806652	+	0.591026i	$0.201277\pi$
$662$	23.6358	0.918630
$663$	1.95060	0.0757550
$664$	−20.6086	−0.799770
$665$	−3.21834	−0.124802
$666$	−15.3556	−0.595016
$667$	−7.19380	−0.278545
$668$	95.8601	3.70894
$669$	−2.59947	−0.100501
$670$	12.6859	0.490099
$671$	−24.3785	−0.941123
$672$	−96.3478	−3.71670
$673$	1.75176	0.0675254	0.0337627	−	0.999430i	$-0.489251\pi$
$673$	1.75176	0.0675254	0.0337627	+	0.999430i	$0.489251\pi$
$674$	−3.97807	−0.153230
$675$	−27.1950	−1.04673
$676$	2.75840	0.106092
$677$	−20.9541	−0.805332	−0.402666	−	0.915347i	$-0.631916\pi$
$677$	−20.9541	−0.805332	−0.402666	+	0.915347i	$0.631916\pi$
$678$	−18.8910	−0.725503
$679$	31.4938	1.20862
$680$	1.75075	0.0671384
$681$	31.4186	1.20396
$682$	−53.0558	−2.03161
$683$	39.7883	1.52246	0.761228	−	0.648484i	$-0.224597\pi$
$683$	39.7883	1.52246	0.761228	+	0.648484i	$0.224597\pi$
$684$	25.2843	0.966770
$685$	−1.26576	−0.0483622
$686$	−55.7708	−2.12934
$687$	−5.67362	−0.216462
$688$	101.871	3.88381
$689$	43.0858	1.64144
$690$	2.48810	0.0947205
$691$	28.6274	1.08904	0.544519	−	0.838749i	$-0.316712\pi$
$691$	28.6274	1.08904	0.544519	+	0.838749i	$0.316712\pi$
$692$	−128.185	−4.87286
$693$	7.36513	0.279778
$694$	−58.7329	−2.22947
$695$	−4.75981	−0.180550
$696$	61.1205	2.31677
$697$	−3.75814	−0.142350
$698$	−79.5193	−3.00985
$699$	3.32160	0.125634
$700$	67.3161	2.54431
$701$	49.1549	1.85656	0.928278	−	0.371887i	$-0.121289\pi$
$701$	49.1549	1.85656	0.928278	+	0.371887i	$0.121289\pi$
$702$	57.8580	2.18371
$703$	14.7395	0.555910
$704$	120.988	4.55992
$705$	−5.36372	−0.202010
$706$	46.6453	1.75552
$707$	7.07722	0.266166
$708$	100.212	3.76620
$709$	21.7657	0.817428	0.408714	−	0.912663i	$-0.365977\pi$
$709$	21.7657	0.817428	0.408714	+	0.912663i	$0.365977\pi$
$710$	−6.61972	−0.248434
$711$	−1.64366	−0.0616422
$712$	−85.2564	−3.19512
$713$	−12.9517	−0.485044
$714$	−3.53080	−0.132137
$715$	3.60581	0.134850
$716$	−130.644	−4.88241
$717$	−9.57022	−0.357407
$718$	30.4524	1.13647
$719$	−15.7889	−0.588825	−0.294412	−	0.955678i	$-0.595124\pi$
$719$	−15.7889	−0.588825	−0.294412	+	0.955678i	$0.595124\pi$
$720$	9.46610	0.352781
$721$	8.00781	0.298227
$722$	20.7819	0.773421
$723$	−18.3936	−0.684067
$724$	74.1910	2.75729
$725$	−20.6573	−0.767195
$726$	−18.2780	−0.678361
$727$	−0.553168	−0.0205159	−0.0102579	−	0.999947i	$-0.503265\pi$
$727$	−0.553168	−0.0205159	−0.0102579	+	0.999947i	$0.503265\pi$
$728$	−94.4539	−3.50069
$729$	26.7686	0.991429
$730$	14.5620	0.538964
$731$	2.19104	0.0810387
$732$	76.6660	2.83366
$733$	19.8051	0.731519	0.365759	−	0.930709i	$-0.380809\pi$
$733$	19.8051	0.731519	0.365759	+	0.930709i	$0.380809\pi$
$734$	−85.2978	−3.14840
$735$	−0.733810	−0.0270670
$736$	52.0698	1.91932
$737$	27.8667	1.02648
$738$	−33.0473	−1.21649
$739$	50.9179	1.87304	0.936522	−	0.350608i	$-0.114025\pi$
$739$	50.9179	1.87304	0.936522	+	0.350608i	$0.114025\pi$
$740$	10.1515	0.373178
$741$	−16.4645	−0.604838
$742$	−77.9902	−2.86311
$743$	27.2844	1.00097	0.500484	−	0.865746i	$-0.333155\pi$
$743$	27.2844	1.00097	0.500484	+	0.865746i	$0.333155\pi$
$744$	110.041	4.03429
$745$	−7.61628	−0.279039
$746$	−17.8248	−0.652611
$747$	−2.39659	−0.0876866
$748$	5.83128	0.213213
$749$	17.7645	0.649099
$750$	14.5247	0.530366
$751$	−8.03394	−0.293163	−0.146581	−	0.989199i	$-0.546827\pi$
$751$	−8.03394	−0.293163	−0.146581	+	0.989199i	$0.546827\pi$
$752$	−191.257	−6.97443
$753$	23.4693	0.855267
$754$	43.9491	1.60053
$755$	−3.61155	−0.131438
$756$	−78.1281	−2.84149
$757$	−30.9725	−1.12571	−0.562857	−	0.826554i	$-0.690298\pi$
$757$	−30.9725	−1.12571	−0.562857	+	0.826554i	$0.690298\pi$
$758$	17.1261	0.622048
$759$	5.46554	0.198386
$760$	−14.7776	−0.536041
$761$	−0.0524583	−0.00190161	−0.000950805	−	1.00000i	$-0.500303\pi$
$761$	−0.0524583	−0.00190161	−0.000950805		1.00000i	$0.500303\pi$
$762$	−29.5315	−1.06981
$763$	−21.6825	−0.784960
$764$	−123.090	−4.45325
$765$	0.203596	0.00736103
$766$	67.0163	2.42140
$767$	47.5234	1.71597
$768$	−152.093	−5.48817
$769$	11.9028	0.429228	0.214614	−	0.976699i	$-0.431151\pi$
$769$	11.9028	0.429228	0.214614	+	0.976699i	$0.431151\pi$
$770$	−6.52692	−0.235214
$771$	−16.2666	−0.585829
$772$	29.2770	1.05370
$773$	43.8129	1.57584	0.787920	−	0.615777i	$-0.211158\pi$
$773$	43.8129	1.57584	0.787920	+	0.615777i	$0.211158\pi$
$774$	19.2670	0.692538
$775$	−37.1913	−1.33595
$776$	144.610	5.19118
$777$	−13.5023	−0.484391
$778$	−2.71835	−0.0974575
$779$	31.7214	1.13654
$780$	−11.3396	−0.406023
$781$	−14.5413	−0.520329
$782$	1.90817	0.0682362
$783$	23.9752	0.856805
$784$	−26.1659	−0.934495
$785$	4.50019	0.160619
$786$	−19.6201	−0.699824
$787$	0.0755029	0.00269139	0.00134569	−	0.999999i	$-0.499572\pi$
$787$	0.0755029	0.00269139	0.00134569	+	0.999999i	$0.499572\pi$
$788$	−83.6781	−2.98091
$789$	2.42760	0.0864248
$790$	1.45660	0.0518235
$791$	12.0972	0.430128
$792$	33.8184	1.20168
$793$	36.3572	1.29108
$794$	−44.1095	−1.56539
$795$	−6.17510	−0.219008
$796$	30.4306	1.07858
$797$	33.1161	1.17303	0.586515	−	0.809938i	$-0.300499\pi$
$797$	33.1161	1.17303	0.586515	+	0.809938i	$0.300499\pi$
$798$	29.8025	1.05500
$799$	−4.11354	−0.145527
$800$	149.521	5.28636
$801$	−9.91450	−0.350312
$802$	12.3817	0.437212
$803$	31.9879	1.12883
$804$	−87.6357	−3.09067
$805$	−1.59331	−0.0561568
$806$	79.1255	2.78708
$807$	−29.9301	−1.05359
$808$	32.4964	1.14322
$809$	−26.5369	−0.932989	−0.466494	−	0.884524i	$-0.654483\pi$
$809$	−26.5369	−0.932989	−0.466494	+	0.884524i	$0.654483\pi$
$810$	−4.04359	−0.142077
$811$	−31.2586	−1.09764	−0.548819	−	0.835941i	$-0.684922\pi$
$811$	−31.2586	−1.09764	−0.548819	+	0.835941i	$0.684922\pi$
$812$	−59.3463	−2.08265
$813$	−7.33490	−0.257246
$814$	29.8922	1.04772
$815$	5.13147	0.179748
$816$	−9.96847	−0.348966
$817$	−18.4940	−0.647023
$818$	−41.0416	−1.43499
$819$	−10.9841	−0.383815
$820$	21.8475	0.762949
$821$	31.5580	1.10138	0.550691	−	0.834709i	$-0.314364\pi$
$821$	31.5580	1.10138	0.550691	+	0.834709i	$0.314364\pi$
$822$	11.7212	0.408824
$823$	−20.4068	−0.711336	−0.355668	−	0.934612i	$-0.615747\pi$
$823$	−20.4068	−0.711336	−0.355668	+	0.934612i	$0.615747\pi$
$824$	36.7694	1.28092
$825$	15.6946	0.546414
$826$	−86.0227	−2.99311
$827$	26.3798	0.917315	0.458657	−	0.888613i	$-0.348331\pi$
$827$	26.3798	0.917315	0.458657	+	0.888613i	$0.348331\pi$
$828$	12.5176	0.435015
$829$	−10.2061	−0.354471	−0.177236	−	0.984168i	$-0.556715\pi$
$829$	−10.2061	−0.354471	−0.177236	+	0.984168i	$0.556715\pi$
$830$	2.12384	0.0737195
$831$	−20.2499	−0.702460
$832$	−180.438	−6.25555
$833$	−0.562773	−0.0194989
$834$	44.0769	1.52626
$835$	−6.51531	−0.225472
$836$	−49.2202	−1.70232
$837$	43.1648	1.49199
$838$	70.9641	2.45142
$839$	−28.6044	−0.987532	−0.493766	−	0.869595i	$-0.664380\pi$
$839$	−28.6044	−0.987532	−0.493766	+	0.869595i	$0.664380\pi$
$840$	13.5372	0.467078
$841$	−10.7884	−0.372012
$842$	82.6865	2.84957
$843$	−25.9025	−0.892131
$844$	−123.284	−4.24360
$845$	−0.187480	−0.00644952
$846$	−36.1726	−1.24364
$847$	11.7047	0.402179
$848$	−220.189	−7.56131
$849$	1.40649	0.0482706
$850$	5.47941	0.187942
$851$	7.29710	0.250141
$852$	45.7298	1.56668
$853$	−17.5726	−0.601674	−0.300837	−	0.953676i	$-0.597266\pi$
$853$	−17.5726	−0.601674	−0.300837	+	0.953676i	$0.597266\pi$
$854$	−65.8107	−2.25199
$855$	−1.71850	−0.0587714
$856$	81.5689	2.78797
$857$	5.70620	0.194920	0.0974600	−	0.995239i	$-0.468928\pi$
$857$	5.70620	0.194920	0.0974600	+	0.995239i	$0.468928\pi$
$858$	−33.3906	−1.13994
$859$	−12.3043	−0.419818	−0.209909	−	0.977721i	$-0.567317\pi$
$859$	−12.3043	−0.419818	−0.209909	+	0.977721i	$0.567317\pi$
$860$	−12.7374	−0.434342
$861$	−29.0587	−0.990319
$862$	50.5656	1.72227
$863$	50.5428	1.72050	0.860248	−	0.509876i	$-0.170309\pi$
$863$	50.5428	1.72050	0.860248	+	0.509876i	$0.170309\pi$
$864$	−173.536	−5.90382
$865$	8.71234	0.296228
$866$	−28.4911	−0.968168
$867$	22.1833	0.753385
$868$	−106.847	−3.62661
$869$	3.19967	0.108541
$870$	−6.29881	−0.213550
$871$	−41.5594	−1.40819
$872$	−99.5595	−3.37151
$873$	16.8167	0.569160
$874$	−16.1064	−0.544806
$875$	−9.30119	−0.314438
$876$	−100.596	−3.39883
$877$	−8.79695	−0.297052	−0.148526	−	0.988909i	$-0.547453\pi$
$877$	−8.79695	−0.297052	−0.148526	+	0.988909i	$0.547453\pi$
$878$	59.2912	2.00098
$879$	−24.8934	−0.839635
$880$	−18.4274	−0.621186
$881$	35.7142	1.20324	0.601622	−	0.798781i	$-0.294521\pi$
$881$	35.7142	1.20324	0.601622	+	0.798781i	$0.294521\pi$
$882$	−4.94876	−0.166634
$883$	−7.70825	−0.259403	−0.129702	−	0.991553i	$-0.541402\pi$
$883$	−7.70825	−0.259403	−0.129702	+	0.991553i	$0.541402\pi$
$884$	−8.69656	−0.292497
$885$	−6.81110	−0.228953
$886$	−77.5576	−2.60560
$887$	14.8810	0.499654	0.249827	−	0.968290i	$-0.419626\pi$
$887$	14.8810	0.499654	0.249827	+	0.968290i	$0.419626\pi$
$888$	−61.9982	−2.08052
$889$	18.9111	0.634259
$890$	8.78615	0.294512
$891$	−8.88243	−0.297573
$892$	11.5895	0.388044
$893$	34.7213	1.16190
$894$	70.5284	2.35882
$895$	8.87949	0.296809
$896$	180.356	6.02526
$897$	−8.15110	−0.272157
$898$	−43.9116	−1.46535
$899$	32.7881	1.09354
$900$	35.9448	1.19816
$901$	−4.73580	−0.157772
$902$	64.3322	2.14203
$903$	16.9416	0.563782
$904$	55.5468	1.84746
$905$	−5.04254	−0.167620
$906$	33.4438	1.11109
$907$	17.2269	0.572009	0.286004	−	0.958228i	$-0.407673\pi$
$907$	17.2269	0.572009	0.286004	+	0.958228i	$0.407673\pi$
$908$	−140.077	−4.64861
$909$	3.77902	0.125342
$910$	9.73401	0.322679
$911$	−17.4688	−0.578767	−0.289383	−	0.957213i	$-0.593450\pi$
$911$	−17.4688	−0.578767	−0.289383	+	0.957213i	$0.593450\pi$
$912$	84.1411	2.78619
$913$	4.66537	0.154401
$914$	−80.1966	−2.65267
$915$	−5.21075	−0.172262
$916$	25.2953	0.835780
$917$	12.5641	0.414904
$918$	−6.35949	−0.209894
$919$	54.3755	1.79368	0.896842	−	0.442352i	$-0.145856\pi$
$919$	54.3755	1.79368	0.896842	+	0.442352i	$0.145856\pi$
$920$	−7.31599	−0.241201
$921$	−32.5359	−1.07209
$922$	−33.1289	−1.09104
$923$	21.6864	0.713816
$924$	45.0887	1.48331
$925$	20.9540	0.688962
$926$	59.6521	1.96029
$927$	4.27593	0.140440
$928$	−131.818	−4.32715
$929$	−23.6979	−0.777504	−0.388752	−	0.921342i	$-0.627094\pi$
$929$	−23.6979	−0.777504	−0.388752	+	0.921342i	$0.627094\pi$
$930$	−11.3403	−0.371864
$931$	4.75021	0.155682
$932$	−14.8090	−0.485085
$933$	−33.1846	−1.08642
$934$	−72.9430	−2.38677
$935$	−0.396334	−0.0129615
$936$	−50.4355	−1.64854
$937$	−14.7042	−0.480367	−0.240183	−	0.970728i	$-0.577208\pi$
$937$	−14.7042	−0.480367	−0.240183	+	0.970728i	$0.577208\pi$
$938$	75.2272	2.45626
$939$	−27.6425	−0.902080
$940$	23.9136	0.779977
$941$	−43.7463	−1.42609	−0.713045	−	0.701119i	$-0.752684\pi$
$941$	−43.7463	−1.42609	−0.713045	+	0.701119i	$0.752684\pi$
$942$	−41.6728	−1.35777
$943$	15.7044	0.511405
$944$	−242.867	−7.90464
$945$	5.31013	0.172738
$946$	−37.5065	−1.21944
$947$	−39.4897	−1.28324	−0.641622	−	0.767021i	$-0.721738\pi$
$947$	−39.4897	−1.28324	−0.641622	+	0.767021i	$0.721738\pi$
$948$	−10.0624	−0.326811
$949$	−47.7056	−1.54859
$950$	−46.2502	−1.50055
$951$	17.7427	0.575347
$952$	10.3819	0.336481
$953$	−9.82067	−0.318123	−0.159061	−	0.987269i	$-0.550847\pi$
$953$	−9.82067	−0.318123	−0.159061	+	0.987269i	$0.550847\pi$
$954$	−41.6444	−1.34829
$955$	8.36608	0.270720
$956$	42.6679	1.37998
$957$	−13.8364	−0.447268
$958$	−100.140	−3.23539
$959$	−7.50594	−0.242379
$960$	25.8605	0.834644
$961$	28.0314	0.904238
$962$	−44.5801	−1.43732
$963$	9.48569	0.305672
$964$	82.0062	2.64124
$965$	−1.98987	−0.0640561
$966$	14.7544	0.474715
$967$	49.6628	1.59705	0.798524	−	0.601963i	$-0.205614\pi$
$967$	49.6628	1.59705	0.798524	+	0.601963i	$0.205614\pi$
$968$	53.7445	1.72741
$969$	1.80970	0.0581360
$970$	−14.9028	−0.478501
$971$	11.7140	0.375919	0.187960	−	0.982177i	$-0.439813\pi$
$971$	11.7140	0.375919	0.187960	+	0.982177i	$0.439813\pi$
$972$	−71.0683	−2.27952
$973$	−28.2256	−0.904871
$974$	−70.4021	−2.25583
$975$	−23.4063	−0.749601
$976$	−185.802	−5.94739
$977$	6.49146	0.207680	0.103840	−	0.994594i	$-0.466887\pi$
$977$	6.49146	0.207680	0.103840	+	0.994594i	$0.466887\pi$
$978$	−47.5185	−1.51948
$979$	19.3003	0.616839
$980$	3.27162	0.104508
$981$	−11.5778	−0.369651
$982$	23.9247	0.763468
$983$	9.42429	0.300588	0.150294	−	0.988641i	$-0.451978\pi$
$983$	9.42429	0.300588	0.150294	+	0.988641i	$0.451978\pi$
$984$	−133.429	−4.25355
$985$	5.68734	0.181214
$986$	−4.83068	−0.153840
$987$	−31.8068	−1.01242
$988$	73.4052	2.33533
$989$	−9.15586	−0.291139
$990$	−3.48518	−0.110766
$991$	−14.7314	−0.467959	−0.233980	−	0.972241i	$-0.575175\pi$
$991$	−14.7314	−0.467959	−0.233980	+	0.972241i	$0.575175\pi$
$992$	−237.325	−7.53507
$993$	11.0975	0.352170
$994$	−39.2548	−1.24509
$995$	−2.06827	−0.0655687
$996$	−14.6717	−0.464891
$997$	16.7151	0.529371	0.264686	−	0.964335i	$-0.414732\pi$
$997$	16.7151	0.529371	0.264686	+	0.964335i	$0.414732\pi$
$998$	41.0085	1.29810
$999$	−24.3195	−0.769435

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.80607 q^{2} -1.31751 q^{3} +5.87400 q^{4} -0.399238 q^{5} +3.69703 q^{6} -2.36747 q^{7} -10.8707 q^{8} -1.26416 q^{9} +O(q^{10})\)	\(q-2.80607 q^{2} -1.31751 q^{3} +5.87400 q^{4} -0.399238 q^{5} +3.69703 q^{6} -2.36747 q^{7} -10.8707 q^{8} -1.26416 q^{9} +1.12029 q^{10} +2.46090 q^{11} -7.73907 q^{12} -3.67009 q^{13} +6.64328 q^{14} +0.526001 q^{15} +18.7559 q^{16} +0.403400 q^{17} +3.54731 q^{18} -3.40499 q^{19} -2.34512 q^{20} +3.11918 q^{21} -6.90544 q^{22} -1.68571 q^{23} +14.3223 q^{24} -4.84061 q^{25} +10.2985 q^{26} +5.61809 q^{27} -13.9065 q^{28} +4.26751 q^{29} -1.47599 q^{30} +7.68319 q^{31} -30.8888 q^{32} -3.24227 q^{33} -1.13197 q^{34} +0.945184 q^{35} -7.42567 q^{36} -4.32879 q^{37} +9.55462 q^{38} +4.83540 q^{39} +4.33999 q^{40} -9.31616 q^{41} -8.75261 q^{42} +5.43144 q^{43} +14.4553 q^{44} +0.504700 q^{45} +4.73023 q^{46} -10.1972 q^{47} -24.7111 q^{48} -1.39507 q^{49} +13.5831 q^{50} -0.531485 q^{51} -21.5581 q^{52} -11.7397 q^{53} -15.7647 q^{54} -0.982484 q^{55} +25.7361 q^{56} +4.48612 q^{57} -11.9749 q^{58} -12.9488 q^{59} +3.08973 q^{60} -9.90635 q^{61} -21.5595 q^{62} +2.99286 q^{63} +49.1643 q^{64} +1.46524 q^{65} +9.09801 q^{66} +11.3238 q^{67} +2.36957 q^{68} +2.22095 q^{69} -2.65225 q^{70} -5.90895 q^{71} +13.7423 q^{72} +12.9985 q^{73} +12.1469 q^{74} +6.37757 q^{75} -20.0009 q^{76} -5.82611 q^{77} -13.5684 q^{78} +1.30020 q^{79} -7.48806 q^{80} -3.60943 q^{81} +26.1417 q^{82} +1.89580 q^{83} +18.3220 q^{84} -0.161053 q^{85} -15.2410 q^{86} -5.62250 q^{87} -26.7517 q^{88} +7.84277 q^{89} -1.41622 q^{90} +8.68885 q^{91} -9.90189 q^{92} -10.1227 q^{93} +28.6139 q^{94} +1.35940 q^{95} +40.6965 q^{96} -13.3027 q^{97} +3.91467 q^{98} -3.11097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 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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