LMFDB - Embedded newform 8018.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.15270 q^{3} +1.00000 q^{4} -2.25930 q^{5} +3.15270 q^{6} -1.49908 q^{7} -1.00000 q^{8} +6.93949 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.15270 q^{3} +1.00000 q^{4} -2.25930 q^{5} +3.15270 q^{6} -1.49908 q^{7} -1.00000 q^{8} +6.93949 q^{9} +2.25930 q^{10} -3.03780 q^{11} -3.15270 q^{12} +3.87845 q^{13} +1.49908 q^{14} +7.12289 q^{15} +1.00000 q^{16} -3.17671 q^{17} -6.93949 q^{18} -1.00000 q^{19} -2.25930 q^{20} +4.72616 q^{21} +3.03780 q^{22} +3.24887 q^{23} +3.15270 q^{24} +0.104448 q^{25} -3.87845 q^{26} -12.4200 q^{27} -1.49908 q^{28} +1.46754 q^{29} -7.12289 q^{30} -10.7748 q^{31} -1.00000 q^{32} +9.57725 q^{33} +3.17671 q^{34} +3.38689 q^{35} +6.93949 q^{36} +3.23320 q^{37} +1.00000 q^{38} -12.2276 q^{39} +2.25930 q^{40} +3.81474 q^{41} -4.72616 q^{42} +1.14203 q^{43} -3.03780 q^{44} -15.6784 q^{45} -3.24887 q^{46} -0.559156 q^{47} -3.15270 q^{48} -4.75275 q^{49} -0.104448 q^{50} +10.0152 q^{51} +3.87845 q^{52} -1.40524 q^{53} +12.4200 q^{54} +6.86330 q^{55} +1.49908 q^{56} +3.15270 q^{57} -1.46754 q^{58} -0.460242 q^{59} +7.12289 q^{60} -2.40804 q^{61} +10.7748 q^{62} -10.4029 q^{63} +1.00000 q^{64} -8.76260 q^{65} -9.57725 q^{66} -9.34516 q^{67} -3.17671 q^{68} -10.2427 q^{69} -3.38689 q^{70} +4.71211 q^{71} -6.93949 q^{72} -8.63876 q^{73} -3.23320 q^{74} -0.329294 q^{75} -1.00000 q^{76} +4.55392 q^{77} +12.2276 q^{78} +6.74778 q^{79} -2.25930 q^{80} +18.3380 q^{81} -3.81474 q^{82} +2.80787 q^{83} +4.72616 q^{84} +7.17716 q^{85} -1.14203 q^{86} -4.62671 q^{87} +3.03780 q^{88} +16.9928 q^{89} +15.6784 q^{90} -5.81413 q^{91} +3.24887 q^{92} +33.9698 q^{93} +0.559156 q^{94} +2.25930 q^{95} +3.15270 q^{96} +7.51517 q^{97} +4.75275 q^{98} -21.0808 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.15270	−1.82021	−0.910105	−	0.414378i	$-0.863999\pi$
$3$	−3.15270	−1.82021	−0.910105	+	0.414378i	$0.863999\pi$
$4$	1.00000	0.500000
$5$	−2.25930	−1.01039	−0.505195	−	0.863005i	$-0.668580\pi$
$5$	−2.25930	−1.01039	−0.505195	+	0.863005i	$0.668580\pi$
$6$	3.15270	1.28708
$7$	−1.49908	−0.566601	−0.283300	−	0.959031i	$-0.591429\pi$
$7$	−1.49908	−0.566601	−0.283300	+	0.959031i	$0.591429\pi$
$8$	−1.00000	−0.353553
$9$	6.93949	2.31316
$10$	2.25930	0.714454
$11$	−3.03780	−0.915930	−0.457965	−	0.888970i	$-0.651422\pi$
$11$	−3.03780	−0.915930	−0.457965	+	0.888970i	$0.651422\pi$
$12$	−3.15270	−0.910105
$13$	3.87845	1.07569	0.537844	−	0.843044i	$-0.319239\pi$
$13$	3.87845	1.07569	0.537844	+	0.843044i	$0.319239\pi$
$14$	1.49908	0.400647
$15$	7.12289	1.83912
$16$	1.00000	0.250000
$17$	−3.17671	−0.770466	−0.385233	−	0.922819i	$-0.625879\pi$
$17$	−3.17671	−0.770466	−0.385233	+	0.922819i	$0.625879\pi$
$18$	−6.93949	−1.63565
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.25930	−0.505195
$21$	4.72616	1.03133
$22$	3.03780	0.647661
$23$	3.24887	0.677437	0.338719	−	0.940888i	$-0.390007\pi$
$23$	3.24887	0.677437	0.338719	+	0.940888i	$0.390007\pi$
$24$	3.15270	0.643541
$25$	0.104448	0.0208897
$26$	−3.87845	−0.760627
$27$	−12.4200	−2.39023
$28$	−1.49908	−0.283300
$29$	1.46754	0.272516	0.136258	−	0.990673i	$-0.456492\pi$
$29$	1.46754	0.272516	0.136258	+	0.990673i	$0.456492\pi$
$30$	−7.12289	−1.30046
$31$	−10.7748	−1.93522	−0.967608	−	0.252456i	$-0.918762\pi$
$31$	−10.7748	−1.93522	−0.967608	+	0.252456i	$0.918762\pi$
$32$	−1.00000	−0.176777
$33$	9.57725	1.66719
$34$	3.17671	0.544802
$35$	3.38689	0.572488
$36$	6.93949	1.15658
$37$	3.23320	0.531536	0.265768	−	0.964037i	$-0.414375\pi$
$37$	3.23320	0.531536	0.265768	+	0.964037i	$0.414375\pi$
$38$	1.00000	0.162221
$39$	−12.2276	−1.95798
$40$	2.25930	0.357227
$41$	3.81474	0.595763	0.297881	−	0.954603i	$-0.403720\pi$
$41$	3.81474	0.595763	0.297881	+	0.954603i	$0.403720\pi$
$42$	−4.72616	−0.729262
$43$	1.14203	0.174158	0.0870792	−	0.996201i	$-0.472247\pi$
$43$	1.14203	0.174158	0.0870792	+	0.996201i	$0.472247\pi$
$44$	−3.03780	−0.457965
$45$	−15.6784	−2.33720
$46$	−3.24887	−0.479020
$47$	−0.559156	−0.0815613	−0.0407807	−	0.999168i	$-0.512984\pi$
$47$	−0.559156	−0.0815613	−0.0407807	+	0.999168i	$0.512984\pi$
$48$	−3.15270	−0.455052
$49$	−4.75275	−0.678964
$50$	−0.104448	−0.0147712
$51$	10.0152	1.40241
$52$	3.87845	0.537844
$53$	−1.40524	−0.193024	−0.0965120	−	0.995332i	$-0.530769\pi$
$53$	−1.40524	−0.193024	−0.0965120	+	0.995332i	$0.530769\pi$
$54$	12.4200	1.69015
$55$	6.86330	0.925448
$56$	1.49908	0.200324
$57$	3.15270	0.417585
$58$	−1.46754	−0.192698
$59$	−0.460242	−0.0599184	−0.0299592	−	0.999551i	$-0.509538\pi$
$59$	−0.460242	−0.0599184	−0.0299592	+	0.999551i	$0.509538\pi$
$60$	7.12289	0.919561
$61$	−2.40804	−0.308319	−0.154159	−	0.988046i	$-0.549267\pi$
$61$	−2.40804	−0.308319	−0.154159	+	0.988046i	$0.549267\pi$
$62$	10.7748	1.36840
$63$	−10.4029	−1.31064
$64$	1.00000	0.125000
$65$	−8.76260	−1.08687
$66$	−9.57725	−1.17888
$67$	−9.34516	−1.14169	−0.570847	−	0.821057i	$-0.693385\pi$
$67$	−9.34516	−1.14169	−0.570847	+	0.821057i	$0.693385\pi$
$68$	−3.17671	−0.385233
$69$	−10.2427	−1.23308
$70$	−3.38689	−0.404810
$71$	4.71211	0.559225	0.279612	−	0.960113i	$-0.409794\pi$
$71$	4.71211	0.559225	0.279612	+	0.960113i	$0.409794\pi$
$72$	−6.93949	−0.817826
$73$	−8.63876	−1.01109	−0.505545	−	0.862800i	$-0.668709\pi$
$73$	−8.63876	−1.01109	−0.505545	+	0.862800i	$0.668709\pi$
$74$	−3.23320	−0.375852
$75$	−0.329294	−0.0380236
$76$	−1.00000	−0.114708
$77$	4.55392	0.518967
$78$	12.2276	1.38450
$79$	6.74778	0.759184	0.379592	−	0.925154i	$-0.376064\pi$
$79$	6.74778	0.759184	0.379592	+	0.925154i	$0.376064\pi$
$80$	−2.25930	−0.252598
$81$	18.3380	2.03756
$82$	−3.81474	−0.421268
$83$	2.80787	0.308203	0.154102	−	0.988055i	$-0.450752\pi$
$83$	2.80787	0.308203	0.154102	+	0.988055i	$0.450752\pi$
$84$	4.72616	0.515666
$85$	7.17716	0.778472
$86$	−1.14203	−0.123149
$87$	−4.62671	−0.496035
$88$	3.03780	0.323830
$89$	16.9928	1.80123	0.900615	−	0.434617i	$-0.143116\pi$
$89$	16.9928	1.80123	0.900615	+	0.434617i	$0.143116\pi$
$90$	15.6784	1.65265
$91$	−5.81413	−0.609486
$92$	3.24887	0.338719
$93$	33.9698	3.52250
$94$	0.559156	0.0576726
$95$	2.25930	0.231800
$96$	3.15270	0.321771
$97$	7.51517	0.763049	0.381525	−	0.924359i	$-0.375399\pi$
$97$	7.51517	0.763049	0.381525	+	0.924359i	$0.375399\pi$
$98$	4.75275	0.480100
$99$	−21.0808	−2.11870
$100$	0.104448	0.0104448
$101$	16.6574	1.65748	0.828738	−	0.559637i	$-0.189059\pi$
$101$	16.6574	1.65748	0.828738	+	0.559637i	$0.189059\pi$
$102$	−10.0152	−0.991654
$103$	−0.337757	−0.0332801	−0.0166401	−	0.999862i	$-0.505297\pi$
$103$	−0.337757	−0.0332801	−0.0166401	+	0.999862i	$0.505297\pi$
$104$	−3.87845	−0.380313
$105$	−10.6778	−1.04205
$106$	1.40524	0.136489
$107$	−10.1160	−0.977954	−0.488977	−	0.872297i	$-0.662630\pi$
$107$	−10.1160	−0.977954	−0.488977	+	0.872297i	$0.662630\pi$
$108$	−12.4200	−1.19512
$109$	−6.73026	−0.644642	−0.322321	−	0.946630i	$-0.604463\pi$
$109$	−6.73026	−0.644642	−0.322321	+	0.946630i	$0.604463\pi$
$110$	−6.86330	−0.654390
$111$	−10.1933	−0.967506
$112$	−1.49908	−0.141650
$113$	−2.15323	−0.202559	−0.101279	−	0.994858i	$-0.532294\pi$
$113$	−2.15323	−0.202559	−0.101279	+	0.994858i	$0.532294\pi$
$114$	−3.15270	−0.295277
$115$	−7.34019	−0.684476
$116$	1.46754	0.136258
$117$	26.9145	2.48824
$118$	0.460242	0.0423687
$119$	4.76216	0.436547
$120$	−7.12289	−0.650228
$121$	−1.77179	−0.161071
$122$	2.40804	0.218014
$123$	−12.0267	−1.08441
$124$	−10.7748	−0.967608
$125$	11.0605	0.989284
$126$	10.4029	0.926762
$127$	−10.6611	−0.946022	−0.473011	−	0.881057i	$-0.656833\pi$
$127$	−10.6611	−0.946022	−0.473011	+	0.881057i	$0.656833\pi$
$128$	−1.00000	−0.0883883
$129$	−3.60048	−0.317005
$130$	8.76260	0.768530
$131$	11.7544	1.02699	0.513495	−	0.858093i	$-0.328351\pi$
$131$	11.7544	1.02699	0.513495	+	0.858093i	$0.328351\pi$
$132$	9.57725	0.833593
$133$	1.49908	0.129987
$134$	9.34516	0.807299
$135$	28.0605	2.41507
$136$	3.17671	0.272401
$137$	2.68977	0.229803	0.114901	−	0.993377i	$-0.463345\pi$
$137$	2.68977	0.229803	0.114901	+	0.993377i	$0.463345\pi$
$138$	10.2427	0.871917
$139$	8.43676	0.715596	0.357798	−	0.933799i	$-0.383528\pi$
$139$	8.43676	0.715596	0.357798	+	0.933799i	$0.383528\pi$
$140$	3.38689	0.286244
$141$	1.76285	0.148459
$142$	−4.71211	−0.395432
$143$	−11.7820	−0.985256
$144$	6.93949	0.578291
$145$	−3.31562	−0.275347
$146$	8.63876	0.714949
$147$	14.9840	1.23586
$148$	3.23320	0.265768
$149$	10.2635	0.840817	0.420409	−	0.907335i	$-0.361887\pi$
$149$	10.2635	0.840817	0.420409	+	0.907335i	$0.361887\pi$
$150$	0.329294	0.0268867
$151$	15.1541	1.23323	0.616613	−	0.787267i	$-0.288504\pi$
$151$	15.1541	1.23323	0.616613	+	0.787267i	$0.288504\pi$
$152$	1.00000	0.0811107
$153$	−22.0448	−1.78221
$154$	−4.55392	−0.366965
$155$	24.3436	1.95533
$156$	−12.2276	−0.978990
$157$	6.87183	0.548432	0.274216	−	0.961668i	$-0.411582\pi$
$157$	6.87183	0.548432	0.274216	+	0.961668i	$0.411582\pi$
$158$	−6.74778	−0.536824
$159$	4.43028	0.351344
$160$	2.25930	0.178614
$161$	−4.87034	−0.383836
$162$	−18.3380	−1.44077
$163$	−14.3771	−1.12611	−0.563053	−	0.826421i	$-0.690373\pi$
$163$	−14.3771	−1.12611	−0.563053	+	0.826421i	$0.690373\pi$
$164$	3.81474	0.297881
$165$	−21.6379	−1.68451
$166$	−2.80787	−0.217933
$167$	21.1353	1.63550	0.817749	−	0.575575i	$-0.195222\pi$
$167$	21.1353	1.63550	0.817749	+	0.575575i	$0.195222\pi$
$168$	−4.72616	−0.364631
$169$	2.04239	0.157107
$170$	−7.17716	−0.550463
$171$	−6.93949	−0.530676
$172$	1.14203	0.0870792
$173$	16.6634	1.26689	0.633447	−	0.773786i	$-0.281640\pi$
$173$	16.6634	1.26689	0.633447	+	0.773786i	$0.281640\pi$
$174$	4.62671	0.350750
$175$	−0.156577	−0.0118361
$176$	−3.03780	−0.228983
$177$	1.45100	0.109064
$178$	−16.9928	−1.27366
$179$	−1.54908	−0.115784	−0.0578918	−	0.998323i	$-0.518438\pi$
$179$	−1.54908	−0.115784	−0.0578918	+	0.998323i	$0.518438\pi$
$180$	−15.6784	−1.16860
$181$	11.7252	0.871525	0.435762	−	0.900062i	$-0.356479\pi$
$181$	11.7252	0.871525	0.435762	+	0.900062i	$0.356479\pi$
$182$	5.81413	0.430972
$183$	7.59183	0.561204
$184$	−3.24887	−0.239510
$185$	−7.30479	−0.537059
$186$	−33.9698	−2.49078
$187$	9.65021	0.705694
$188$	−0.559156	−0.0407807
$189$	18.6186	1.35431
$190$	−2.25930	−0.163907
$191$	10.5849	0.765900	0.382950	−	0.923769i	$-0.374908\pi$
$191$	10.5849	0.765900	0.382950	+	0.923769i	$0.374908\pi$
$192$	−3.15270	−0.227526
$193$	−23.4035	−1.68462	−0.842311	−	0.538991i	$-0.818806\pi$
$193$	−23.4035	−1.68462	−0.842311	+	0.538991i	$0.818806\pi$
$194$	−7.51517	−0.539557
$195$	27.6258	1.97832
$196$	−4.75275	−0.339482
$197$	25.3147	1.80360	0.901800	−	0.432153i	$-0.142246\pi$
$197$	25.3147	1.80360	0.901800	+	0.432153i	$0.142246\pi$
$198$	21.0808	1.49814
$199$	−7.13772	−0.505979	−0.252990	−	0.967469i	$-0.581414\pi$
$199$	−7.13772	−0.505979	−0.252990	+	0.967469i	$0.581414\pi$
$200$	−0.104448	−0.00738562
$201$	29.4625	2.07812
$202$	−16.6574	−1.17201
$203$	−2.19997	−0.154408
$204$	10.0152	0.701205
$205$	−8.61866	−0.601953
$206$	0.337757	0.0235326
$207$	22.5455	1.56702
$208$	3.87845	0.268922
$209$	3.03780	0.210129
$210$	10.6778	0.736839
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−1.40524	−0.0965120
$213$	−14.8559	−1.01791
$214$	10.1160	0.691518
$215$	−2.58020	−0.175968
$216$	12.4200	0.845074
$217$	16.1524	1.09650
$218$	6.73026	0.455831
$219$	27.2354	1.84040
$220$	6.86330	0.462724
$221$	−12.3207	−0.828782
$222$	10.1933	0.684130
$223$	8.20659	0.549554	0.274777	−	0.961508i	$-0.411396\pi$
$223$	8.20659	0.549554	0.274777	+	0.961508i	$0.411396\pi$
$224$	1.49908	0.100162
$225$	0.724818	0.0483212
$226$	2.15323	0.143231
$227$	−9.18561	−0.609671	−0.304835	−	0.952405i	$-0.598601\pi$
$227$	−9.18561	−0.609671	−0.304835	+	0.952405i	$0.598601\pi$
$228$	3.15270	0.208792
$229$	16.8078	1.11069	0.555345	−	0.831620i	$-0.312586\pi$
$229$	16.8078	1.11069	0.555345	+	0.831620i	$0.312586\pi$
$230$	7.34019	0.483998
$231$	−14.3571	−0.944628
$232$	−1.46754	−0.0963488
$233$	−26.7715	−1.75386	−0.876929	−	0.480620i	$-0.840411\pi$
$233$	−26.7715	−1.75386	−0.876929	+	0.480620i	$0.840411\pi$
$234$	−26.9145	−1.75945
$235$	1.26330	0.0824088
$236$	−0.460242	−0.0299592
$237$	−21.2737	−1.38187
$238$	−4.76216	−0.308685
$239$	8.00344	0.517700	0.258850	−	0.965918i	$-0.416657\pi$
$239$	8.00344	0.517700	0.258850	+	0.965918i	$0.416657\pi$
$240$	7.12289	0.459781
$241$	2.93960	0.189356	0.0946781	−	0.995508i	$-0.469818\pi$
$241$	2.93960	0.189356	0.0946781	+	0.995508i	$0.469818\pi$
$242$	1.77179	0.113895
$243$	−20.5542	−1.31855
$244$	−2.40804	−0.154159
$245$	10.7379	0.686019
$246$	12.0267	0.766796
$247$	−3.87845	−0.246780
$248$	10.7748	0.684202
$249$	−8.85234	−0.560995
$250$	−11.0605	−0.699530
$251$	4.64008	0.292879	0.146440	−	0.989220i	$-0.453219\pi$
$251$	4.64008	0.292879	0.146440	+	0.989220i	$0.453219\pi$
$252$	−10.4029	−0.655320
$253$	−9.86942	−0.620485
$254$	10.6611	0.668938
$255$	−22.6274	−1.41698
$256$	1.00000	0.0625000
$257$	22.2718	1.38928	0.694639	−	0.719358i	$-0.255564\pi$
$257$	22.2718	1.38928	0.694639	+	0.719358i	$0.255564\pi$
$258$	3.60048	0.224156
$259$	−4.84685	−0.301168
$260$	−8.76260	−0.543433
$261$	10.1840	0.630373
$262$	−11.7544	−0.726191
$263$	−31.1446	−1.92046	−0.960228	−	0.279217i	$-0.909925\pi$
$263$	−31.1446	−1.92046	−0.960228	+	0.279217i	$0.909925\pi$
$264$	−9.57725	−0.589439
$265$	3.17485	0.195030
$266$	−1.49908	−0.0919148
$267$	−53.5730	−3.27862
$268$	−9.34516	−0.570847
$269$	16.5378	1.00833	0.504164	−	0.863608i	$-0.331801\pi$
$269$	16.5378	1.00833	0.504164	+	0.863608i	$0.331801\pi$
$270$	−28.0605	−1.70771
$271$	−2.78737	−0.169321	−0.0846604	−	0.996410i	$-0.526981\pi$
$271$	−2.78737	−0.169321	−0.0846604	+	0.996410i	$0.526981\pi$
$272$	−3.17671	−0.192617
$273$	18.3302	1.10939
$274$	−2.68977	−0.162495
$275$	−0.317293	−0.0191335
$276$	−10.2427	−0.616539
$277$	−6.01882	−0.361636	−0.180818	−	0.983517i	$-0.557874\pi$
$277$	−6.01882	−0.361636	−0.180818	+	0.983517i	$0.557874\pi$
$278$	−8.43676	−0.506003
$279$	−74.7718	−4.47647
$280$	−3.38689	−0.202405
$281$	22.4994	1.34220	0.671102	−	0.741365i	$-0.265821\pi$
$281$	22.4994	1.34220	0.671102	+	0.741365i	$0.265821\pi$
$282$	−1.76285	−0.104976
$283$	24.3138	1.44531	0.722654	−	0.691210i	$-0.242922\pi$
$283$	24.3138	1.44531	0.722654	+	0.691210i	$0.242922\pi$
$284$	4.71211	0.279612
$285$	−7.12289	−0.421924
$286$	11.7820	0.696681
$287$	−5.71862	−0.337560
$288$	−6.93949	−0.408913
$289$	−6.90849	−0.406382
$290$	3.31562	0.194700
$291$	−23.6930	−1.38891
$292$	−8.63876	−0.505545
$293$	−7.79302	−0.455273	−0.227636	−	0.973746i	$-0.573100\pi$
$293$	−7.79302	−0.455273	−0.227636	+	0.973746i	$0.573100\pi$
$294$	−14.9840	−0.873882
$295$	1.03983	0.0605410
$296$	−3.23320	−0.187926
$297$	37.7295	2.18928
$298$	−10.2635	−0.594548
$299$	12.6006	0.728712
$300$	−0.329294	−0.0190118
$301$	−1.71200	−0.0986782
$302$	−15.1541	−0.872022
$303$	−52.5158	−3.01695
$304$	−1.00000	−0.0573539
$305$	5.44050	0.311522
$306$	22.0448	1.26022
$307$	9.44315	0.538949	0.269475	−	0.963008i	$-0.413150\pi$
$307$	9.44315	0.538949	0.269475	+	0.963008i	$0.413150\pi$
$308$	4.55392	0.259483
$309$	1.06484	0.0605768
$310$	−24.3436	−1.38262
$311$	−25.0081	−1.41808	−0.709040	−	0.705168i	$-0.750871\pi$
$311$	−25.0081	−1.41808	−0.709040	+	0.705168i	$0.750871\pi$
$312$	12.2276	0.692250
$313$	−5.70980	−0.322737	−0.161368	−	0.986894i	$-0.551591\pi$
$313$	−5.70980	−0.322737	−0.161368	+	0.986894i	$0.551591\pi$
$314$	−6.87183	−0.387800
$315$	23.5032	1.32426
$316$	6.74778	0.379592
$317$	−23.9285	−1.34396	−0.671979	−	0.740570i	$-0.734555\pi$
$317$	−23.9285	−1.34396	−0.671979	+	0.740570i	$0.734555\pi$
$318$	−4.43028	−0.248438
$319$	−4.45809	−0.249605
$320$	−2.25930	−0.126299
$321$	31.8928	1.78008
$322$	4.87034	0.271413
$323$	3.17671	0.176757
$324$	18.3380	1.01878
$325$	0.405098	0.0224708
$326$	14.3771	0.796277
$327$	21.2185	1.17338
$328$	−3.81474	−0.210634
$329$	0.838223	0.0462127
$330$	21.6379	1.19113
$331$	−8.34775	−0.458834	−0.229417	−	0.973328i	$-0.573682\pi$
$331$	−8.34775	−0.458834	−0.229417	+	0.973328i	$0.573682\pi$
$332$	2.80787	0.154102
$333$	22.4368	1.22953
$334$	−21.1353	−1.15647
$335$	21.1136	1.15356
$336$	4.72616	0.257833
$337$	−1.60844	−0.0876174	−0.0438087	−	0.999040i	$-0.513949\pi$
$337$	−1.60844	−0.0876174	−0.0438087	+	0.999040i	$0.513949\pi$
$338$	−2.04239	−0.111091
$339$	6.78848	0.368699
$340$	7.17716	0.389236
$341$	32.7318	1.77252
$342$	6.93949	0.375244
$343$	17.6184	0.951302
$344$	−1.14203	−0.0615743
$345$	23.1414	1.24589
$346$	−16.6634	−0.895829
$347$	−10.7805	−0.578727	−0.289364	−	0.957219i	$-0.593444\pi$
$347$	−10.7805	−0.578727	−0.289364	+	0.957219i	$0.593444\pi$
$348$	−4.62671	−0.248018
$349$	17.7810	0.951796	0.475898	−	0.879501i	$-0.342123\pi$
$349$	17.7810	0.951796	0.475898	+	0.879501i	$0.342123\pi$
$350$	0.156577	0.00836939
$351$	−48.1704	−2.57114
$352$	3.03780	0.161915
$353$	13.5785	0.722713	0.361357	−	0.932428i	$-0.382314\pi$
$353$	13.5785	0.722713	0.361357	+	0.932428i	$0.382314\pi$
$354$	−1.45100	−0.0771199
$355$	−10.6461	−0.565036
$356$	16.9928	0.900615
$357$	−15.0136	−0.794607
$358$	1.54908	0.0818714
$359$	5.04359	0.266190	0.133095	−	0.991103i	$-0.457508\pi$
$359$	5.04359	0.266190	0.133095	+	0.991103i	$0.457508\pi$
$360$	15.6784	0.826324
$361$	1.00000	0.0526316
$362$	−11.7252	−0.616261
$363$	5.58590	0.293184
$364$	−5.81413	−0.304743
$365$	19.5176	1.02160
$366$	−7.59183	−0.396831
$367$	2.74679	0.143381	0.0716907	−	0.997427i	$-0.477161\pi$
$367$	2.74679	0.143381	0.0716907	+	0.997427i	$0.477161\pi$
$368$	3.24887	0.169359
$369$	26.4724	1.37810
$370$	7.30479	0.379758
$371$	2.10657	0.109368
$372$	33.9698	1.76125
$373$	10.2367	0.530037	0.265018	−	0.964243i	$-0.414622\pi$
$373$	10.2367	0.530037	0.265018	+	0.964243i	$0.414622\pi$
$374$	−9.65021	−0.499001
$375$	−34.8705	−1.80070
$376$	0.559156	0.0288363
$377$	5.69179	0.293142
$378$	−18.6186	−0.957639
$379$	3.38717	0.173987	0.0869937	−	0.996209i	$-0.472274\pi$
$379$	3.38717	0.173987	0.0869937	+	0.996209i	$0.472274\pi$
$380$	2.25930	0.115900
$381$	33.6113	1.72196
$382$	−10.5849	−0.541573
$383$	−8.12315	−0.415074	−0.207537	−	0.978227i	$-0.566545\pi$
$383$	−8.12315	−0.415074	−0.207537	+	0.978227i	$0.566545\pi$
$384$	3.15270	0.160885
$385$	−10.2887	−0.524359
$386$	23.4035	1.19121
$387$	7.92512	0.402856
$388$	7.51517	0.381525
$389$	10.6628	0.540626	0.270313	−	0.962772i	$-0.412873\pi$
$389$	10.6628	0.540626	0.270313	+	0.962772i	$0.412873\pi$
$390$	−27.6258	−1.39889
$391$	−10.3207	−0.521942
$392$	4.75275	0.240050
$393$	−37.0581	−1.86934
$394$	−25.3147	−1.27534
$395$	−15.2453	−0.767073
$396$	−21.0808	−1.05935
$397$	1.32452	0.0664760	0.0332380	−	0.999447i	$-0.489418\pi$
$397$	1.32452	0.0664760	0.0332380	+	0.999447i	$0.489418\pi$
$398$	7.13772	0.357781
$399$	−4.72616	−0.236604
$400$	0.104448	0.00522242
$401$	−17.3827	−0.868053	−0.434026	−	0.900900i	$-0.642908\pi$
$401$	−17.3827	−0.868053	−0.434026	+	0.900900i	$0.642908\pi$
$402$	−29.4625	−1.46945
$403$	−41.7897	−2.08169
$404$	16.6574	0.828738
$405$	−41.4311	−2.05873
$406$	2.19997	0.109183
$407$	−9.82182	−0.486850
$408$	−10.0152	−0.495827
$409$	12.0300	0.594844	0.297422	−	0.954746i	$-0.403873\pi$
$409$	12.0300	0.594844	0.297422	+	0.954746i	$0.403873\pi$
$410$	8.61866	0.425645
$411$	−8.48003	−0.418289
$412$	−0.337757	−0.0166401
$413$	0.689941	0.0339498
$414$	−22.5455	−1.10805
$415$	−6.34382	−0.311406
$416$	−3.87845	−0.190157
$417$	−26.5985	−1.30254
$418$	−3.03780	−0.148584
$419$	9.89216	0.483264	0.241632	−	0.970368i	$-0.422317\pi$
$419$	9.89216	0.483264	0.241632	+	0.970368i	$0.422317\pi$
$420$	−10.6778	−0.521024
$421$	−28.3477	−1.38158	−0.690792	−	0.723053i	$-0.742738\pi$
$421$	−28.3477	−1.38158	−0.690792	+	0.723053i	$0.742738\pi$
$422$	1.00000	0.0486792
$423$	−3.88026	−0.188665
$424$	1.40524	0.0682443
$425$	−0.331803	−0.0160948
$426$	14.8559	0.719769
$427$	3.60986	0.174694
$428$	−10.1160	−0.488977
$429$	37.1449	1.79337
$430$	2.58020	0.124428
$431$	0.658752	0.0317310	0.0158655	−	0.999874i	$-0.494950\pi$
$431$	0.658752	0.0317310	0.0158655	+	0.999874i	$0.494950\pi$
$432$	−12.4200	−0.597558
$433$	6.23777	0.299768	0.149884	−	0.988704i	$-0.452110\pi$
$433$	6.23777	0.299768	0.149884	+	0.988704i	$0.452110\pi$
$434$	−16.1524	−0.775339
$435$	10.4531	0.501190
$436$	−6.73026	−0.322321
$437$	−3.24887	−0.155415
$438$	−27.2354	−1.30136
$439$	−40.6260	−1.93897	−0.969487	−	0.245141i	$-0.921166\pi$
$439$	−40.6260	−1.93897	−0.969487	+	0.245141i	$0.921166\pi$
$440$	−6.86330	−0.327195
$441$	−32.9816	−1.57055
$442$	12.3207	0.586037
$443$	10.7549	0.510979	0.255489	−	0.966812i	$-0.417763\pi$
$443$	10.7549	0.510979	0.255489	+	0.966812i	$0.417763\pi$
$444$	−10.1933	−0.483753
$445$	−38.3918	−1.81995
$446$	−8.20659	−0.388593
$447$	−32.3576	−1.53046
$448$	−1.49908	−0.0708251
$449$	−37.2453	−1.75771	−0.878857	−	0.477085i	$-0.841693\pi$
$449$	−37.2453	−1.75771	−0.878857	+	0.477085i	$0.841693\pi$
$450$	−0.724818	−0.0341683
$451$	−11.5884	−0.545677
$452$	−2.15323	−0.101279
$453$	−47.7764	−2.24473
$454$	9.18561	0.431102
$455$	13.1359	0.615819
$456$	−3.15270	−0.147638
$457$	−17.6885	−0.827432	−0.413716	−	0.910406i	$-0.635769\pi$
$457$	−17.6885	−0.827432	−0.413716	+	0.910406i	$0.635769\pi$
$458$	−16.8078	−0.785377
$459$	39.4548	1.84159
$460$	−7.34019	−0.342238
$461$	−0.994485	−0.0463178	−0.0231589	−	0.999732i	$-0.507372\pi$
$461$	−0.994485	−0.0463178	−0.0231589	+	0.999732i	$0.507372\pi$
$462$	14.3571	0.667953
$463$	−5.07023	−0.235634	−0.117817	−	0.993035i	$-0.537590\pi$
$463$	−5.07023	−0.235634	−0.117817	+	0.993035i	$0.537590\pi$
$464$	1.46754	0.0681289
$465$	−76.7480	−3.55910
$466$	26.7715	1.24016
$467$	−6.05126	−0.280019	−0.140009	−	0.990150i	$-0.544713\pi$
$467$	−6.05126	−0.280019	−0.140009	+	0.990150i	$0.544713\pi$
$468$	26.9145	1.24412
$469$	14.0092	0.646884
$470$	−1.26330	−0.0582718
$471$	−21.6648	−0.998260
$472$	0.460242	0.0211843
$473$	−3.46926	−0.159517
$474$	21.2737	0.977133
$475$	−0.104448	−0.00479242
$476$	4.76216	0.218273
$477$	−9.75162	−0.446496
$478$	−8.00344	−0.366069
$479$	17.5383	0.801346	0.400673	−	0.916221i	$-0.368776\pi$
$479$	17.5383	0.801346	0.400673	+	0.916221i	$0.368776\pi$
$480$	−7.12289	−0.325114
$481$	12.5398	0.571767
$482$	−2.93960	−0.133895
$483$	15.3547	0.698663
$484$	−1.77179	−0.0805357
$485$	−16.9790	−0.770978
$486$	20.5542	0.932356
$487$	16.2677	0.737162	0.368581	−	0.929596i	$-0.379844\pi$
$487$	16.2677	0.737162	0.368581	+	0.929596i	$0.379844\pi$
$488$	2.40804	0.109007
$489$	45.3268	2.04975
$490$	−10.7379	−0.485088
$491$	26.8743	1.21282	0.606410	−	0.795152i	$-0.292609\pi$
$491$	26.8743	1.21282	0.606410	+	0.795152i	$0.292609\pi$
$492$	−12.0267	−0.542207
$493$	−4.66196	−0.209964
$494$	3.87845	0.174500
$495$	47.6278	2.14071
$496$	−10.7748	−0.483804
$497$	−7.06386	−0.316857
$498$	8.85234	0.396683
$499$	27.3801	1.22570	0.612850	−	0.790199i	$-0.290023\pi$
$499$	27.3801	1.22570	0.612850	+	0.790199i	$0.290023\pi$
$500$	11.0605	0.494642
$501$	−66.6331	−2.97695
$502$	−4.64008	−0.207097
$503$	−30.1377	−1.34377	−0.671887	−	0.740654i	$-0.734516\pi$
$503$	−30.1377	−1.34377	−0.671887	+	0.740654i	$0.734516\pi$
$504$	10.4029	0.463381
$505$	−37.6342	−1.67470
$506$	9.86942	0.438749
$507$	−6.43902	−0.285967
$508$	−10.6611	−0.473011
$509$	3.93003	0.174196	0.0870978	−	0.996200i	$-0.472241\pi$
$509$	3.93003	0.174196	0.0870978	+	0.996200i	$0.472241\pi$
$510$	22.6274	1.00196
$511$	12.9502	0.572884
$512$	−1.00000	−0.0441942
$513$	12.4200	0.548356
$514$	−22.2718	−0.982369
$515$	0.763094	0.0336260
$516$	−3.60048	−0.158502
$517$	1.69860	0.0747045
$518$	4.84685	0.212958
$519$	−52.5346	−2.30601
$520$	8.76260	0.384265
$521$	23.3312	1.02216	0.511079	−	0.859534i	$-0.329246\pi$
$521$	23.3312	1.02216	0.511079	+	0.859534i	$0.329246\pi$
$522$	−10.1840	−0.445741
$523$	−25.0647	−1.09600	−0.548002	−	0.836477i	$-0.684611\pi$
$523$	−25.0647	−1.09600	−0.548002	+	0.836477i	$0.684611\pi$
$524$	11.7544	0.513495
$525$	0.493639	0.0215442
$526$	31.1446	1.35797
$527$	34.2286	1.49102
$528$	9.57725	0.416796
$529$	−12.4448	−0.541079
$530$	−3.17485	−0.137907
$531$	−3.19384	−0.138601
$532$	1.49908	0.0649936
$533$	14.7953	0.640856
$534$	53.5730	2.31833
$535$	22.8552	0.988116
$536$	9.34516	0.403650
$537$	4.88378	0.210750
$538$	−16.5378	−0.712995
$539$	14.4379	0.621883
$540$	28.0605	1.20753
$541$	11.5126	0.494966	0.247483	−	0.968892i	$-0.420397\pi$
$541$	11.5126	0.494966	0.247483	+	0.968892i	$0.420397\pi$
$542$	2.78737	0.119728
$543$	−36.9659	−1.58636
$544$	3.17671	0.136200
$545$	15.2057	0.651341
$546$	−18.3302	−0.784459
$547$	−16.0788	−0.687480	−0.343740	−	0.939065i	$-0.611694\pi$
$547$	−16.0788	−0.687480	−0.343740	+	0.939065i	$0.611694\pi$
$548$	2.68977	0.114901
$549$	−16.7106	−0.713191
$550$	0.317293	0.0135294
$551$	−1.46754	−0.0625194
$552$	10.2427	0.435959
$553$	−10.1155	−0.430154
$554$	6.01882	0.255715
$555$	23.0298	0.977559
$556$	8.43676	0.357798
$557$	17.7042	0.750153	0.375077	−	0.926994i	$-0.377616\pi$
$557$	17.7042	0.750153	0.375077	+	0.926994i	$0.377616\pi$
$558$	74.7718	3.16534
$559$	4.42932	0.187340
$560$	3.38689	0.143122
$561$	−30.4242	−1.28451
$562$	−22.4994	−0.949081
$563$	−38.4061	−1.61862	−0.809311	−	0.587380i	$-0.800159\pi$
$563$	−38.4061	−1.61862	−0.809311	+	0.587380i	$0.800159\pi$
$564$	1.76285	0.0742294
$565$	4.86480	0.204664
$566$	−24.3138	−1.02199
$567$	−27.4902	−1.15448
$568$	−4.71211	−0.197716
$569$	27.1065	1.13636	0.568182	−	0.822903i	$-0.307647\pi$
$569$	27.1065	1.13636	0.568182	+	0.822903i	$0.307647\pi$
$570$	7.12289	0.298345
$571$	19.5831	0.819527	0.409764	−	0.912192i	$-0.365611\pi$
$571$	19.5831	0.819527	0.409764	+	0.912192i	$0.365611\pi$
$572$	−11.7820	−0.492628
$573$	−33.3711	−1.39410
$574$	5.71862	0.238691
$575$	0.339340	0.0141514
$576$	6.93949	0.289145
$577$	22.4007	0.932553	0.466277	−	0.884639i	$-0.345595\pi$
$577$	22.4007	0.932553	0.466277	+	0.884639i	$0.345595\pi$
$578$	6.90849	0.287355
$579$	73.7842	3.06637
$580$	−3.31562	−0.137674
$581$	−4.20923	−0.174628
$582$	23.6930	0.982108
$583$	4.26882	0.176797
$584$	8.63876	0.357474
$585$	−60.8079	−2.51410
$586$	7.79302	0.321927
$587$	9.08578	0.375010	0.187505	−	0.982264i	$-0.439960\pi$
$587$	9.08578	0.375010	0.187505	+	0.982264i	$0.439960\pi$
$588$	14.9840	0.617928
$589$	10.7748	0.443969
$590$	−1.03983	−0.0428089
$591$	−79.8096	−3.28293
$592$	3.23320	0.132884
$593$	−11.6694	−0.479205	−0.239603	−	0.970871i	$-0.577017\pi$
$593$	−11.6694	−0.479205	−0.239603	+	0.970871i	$0.577017\pi$
$594$	−37.7295	−1.54806
$595$	−10.7592	−0.441083
$596$	10.2635	0.420409
$597$	22.5030	0.920988
$598$	−12.6006	−0.515277
$599$	7.53912	0.308040	0.154020	−	0.988068i	$-0.450778\pi$
$599$	7.53912	0.308040	0.154020	+	0.988068i	$0.450778\pi$
$600$	0.329294	0.0134434
$601$	−18.0846	−0.737687	−0.368843	−	0.929492i	$-0.620246\pi$
$601$	−18.0846	−0.737687	−0.368843	+	0.929492i	$0.620246\pi$
$602$	1.71200	0.0697760
$603$	−64.8506	−2.64092
$604$	15.1541	0.616613
$605$	4.00300	0.162745
$606$	52.5158	2.13331
$607$	−40.6126	−1.64841	−0.824207	−	0.566289i	$-0.808379\pi$
$607$	−40.6126	−1.64841	−0.824207	+	0.566289i	$0.808379\pi$
$608$	1.00000	0.0405554
$609$	6.93583	0.281054
$610$	−5.44050	−0.220279
$611$	−2.16866	−0.0877346
$612$	−22.0448	−0.891107
$613$	−6.59984	−0.266565	−0.133283	−	0.991078i	$-0.542552\pi$
$613$	−6.59984	−0.266565	−0.133283	+	0.991078i	$0.542552\pi$
$614$	−9.44315	−0.381095
$615$	27.1720	1.09568
$616$	−4.55392	−0.183482
$617$	−14.7725	−0.594718	−0.297359	−	0.954766i	$-0.596106\pi$
$617$	−14.7725	−0.594718	−0.297359	+	0.954766i	$0.596106\pi$
$618$	−1.06484	−0.0428343
$619$	29.9294	1.20297	0.601483	−	0.798886i	$-0.294577\pi$
$619$	29.9294	1.20297	0.601483	+	0.798886i	$0.294577\pi$
$620$	24.3436	0.977663
$621$	−40.3510	−1.61923
$622$	25.0081	1.00273
$623$	−25.4736	−1.02058
$624$	−12.2276	−0.489495
$625$	−25.5113	−1.02045
$626$	5.70980	0.228209
$627$	−9.57725	−0.382479
$628$	6.87183	0.274216
$629$	−10.2710	−0.409530
$630$	−23.5032	−0.936392
$631$	21.0636	0.838529	0.419264	−	0.907864i	$-0.362288\pi$
$631$	21.0636	0.838529	0.419264	+	0.907864i	$0.362288\pi$
$632$	−6.74778	−0.268412
$633$	3.15270	0.125308
$634$	23.9285	0.950322
$635$	24.0867	0.955852
$636$	4.43028	0.175672
$637$	−18.4333	−0.730354
$638$	4.45809	0.176498
$639$	32.6996	1.29358
$640$	2.25930	0.0893068
$641$	−26.4473	−1.04461	−0.522303	−	0.852760i	$-0.674927\pi$
$641$	−26.4473	−1.04461	−0.522303	+	0.852760i	$0.674927\pi$
$642$	−31.8928	−1.25871
$643$	20.1647	0.795218	0.397609	−	0.917555i	$-0.369840\pi$
$643$	20.1647	0.795218	0.397609	+	0.917555i	$0.369840\pi$
$644$	−4.87034	−0.191918
$645$	8.13457	0.320299
$646$	−3.17671	−0.124986
$647$	0.169917	0.00668012	0.00334006	−	0.999994i	$-0.498937\pi$
$647$	0.169917	0.00668012	0.00334006	+	0.999994i	$0.498937\pi$
$648$	−18.3380	−0.720385
$649$	1.39812	0.0548811
$650$	−0.405098	−0.0158892
$651$	−50.9235	−1.99585
$652$	−14.3771	−0.563053
$653$	−16.4578	−0.644045	−0.322023	−	0.946732i	$-0.604363\pi$
$653$	−16.4578	−0.644045	−0.322023	+	0.946732i	$0.604363\pi$
$654$	−21.2185	−0.829708
$655$	−26.5568	−1.03766
$656$	3.81474	0.148941
$657$	−59.9486	−2.33882
$658$	−0.838223	−0.0326773
$659$	−49.0828	−1.91199	−0.955997	−	0.293377i	$-0.905221\pi$
$659$	−49.0828	−1.91199	−0.955997	+	0.293377i	$0.905221\pi$
$660$	−21.6379	−0.842254
$661$	−39.6746	−1.54316	−0.771581	−	0.636131i	$-0.780534\pi$
$661$	−39.6746	−1.54316	−0.771581	+	0.636131i	$0.780534\pi$
$662$	8.34775	0.324444
$663$	38.8435	1.50856
$664$	−2.80787	−0.108966
$665$	−3.38689	−0.131338
$666$	−22.4368	−0.869408
$667$	4.76786	0.184612
$668$	21.1353	0.817749
$669$	−25.8729	−1.00030
$670$	−21.1136	−0.815688
$671$	7.31515	0.282398
$672$	−4.72616	−0.182315
$673$	−26.3186	−1.01451	−0.507253	−	0.861797i	$-0.669339\pi$
$673$	−26.3186	−1.01451	−0.507253	+	0.861797i	$0.669339\pi$
$674$	1.60844	0.0619549
$675$	−1.29725	−0.0499311
$676$	2.04239	0.0785533
$677$	−35.5174	−1.36505	−0.682523	−	0.730864i	$-0.739117\pi$
$677$	−35.5174	−1.36505	−0.682523	+	0.730864i	$0.739117\pi$
$678$	−6.78848	−0.260710
$679$	−11.2659	−0.432344
$680$	−7.17716	−0.275231
$681$	28.9594	1.10973
$682$	−32.7318	−1.25336
$683$	−8.86575	−0.339238	−0.169619	−	0.985510i	$-0.554254\pi$
$683$	−8.86575	−0.339238	−0.169619	+	0.985510i	$0.554254\pi$
$684$	−6.93949	−0.265338
$685$	−6.07701	−0.232191
$686$	−17.6184	−0.672672
$687$	−52.9899	−2.02169
$688$	1.14203	0.0435396
$689$	−5.45014	−0.207634
$690$	−23.1414	−0.880977
$691$	−31.5448	−1.20002	−0.600010	−	0.799992i	$-0.704837\pi$
$691$	−31.5448	−1.20002	−0.600010	+	0.799992i	$0.704837\pi$
$692$	16.6634	0.633447
$693$	31.6018	1.20045
$694$	10.7805	0.409222
$695$	−19.0612	−0.723032
$696$	4.62671	0.175375
$697$	−12.1184	−0.459015
$698$	−17.7810	−0.673021
$699$	84.4023	3.19239
$700$	−0.156577	−0.00591805
$701$	21.4138	0.808789	0.404394	−	0.914585i	$-0.367482\pi$
$701$	21.4138	0.808789	0.404394	+	0.914585i	$0.367482\pi$
$702$	48.1704	1.81807
$703$	−3.23320	−0.121943
$704$	−3.03780	−0.114491
$705$	−3.98281	−0.150001
$706$	−13.5785	−0.511035
$707$	−24.9709	−0.939127
$708$	1.45100	0.0545320
$709$	−33.0551	−1.24141	−0.620704	−	0.784045i	$-0.713153\pi$
$709$	−33.0551	−1.24141	−0.620704	+	0.784045i	$0.713153\pi$
$710$	10.6461	0.399541
$711$	46.8261	1.75612
$712$	−16.9928	−0.636831
$713$	−35.0061	−1.31099
$714$	15.0136	0.561872
$715$	26.6190	0.995494
$716$	−1.54908	−0.0578918
$717$	−25.2324	−0.942322
$718$	−5.04359	−0.188225
$719$	−24.0967	−0.898656	−0.449328	−	0.893367i	$-0.648336\pi$
$719$	−24.0967	−0.898656	−0.449328	+	0.893367i	$0.648336\pi$
$720$	−15.6784	−0.584300
$721$	0.506326	0.0188566
$722$	−1.00000	−0.0372161
$723$	−9.26765	−0.344668
$724$	11.7252	0.435762
$725$	0.153282	0.00569276
$726$	−5.58590	−0.207312
$727$	31.5674	1.17077	0.585385	−	0.810755i	$-0.300943\pi$
$727$	31.5674	1.17077	0.585385	+	0.810755i	$0.300943\pi$
$728$	5.81413	0.215486
$729$	9.78700	0.362482
$730$	−19.5176	−0.722378
$731$	−3.62791	−0.134183
$732$	7.59183	0.280602
$733$	4.64204	0.171458	0.0857289	−	0.996319i	$-0.472678\pi$
$733$	4.64204	0.171458	0.0857289	+	0.996319i	$0.472678\pi$
$734$	−2.74679	−0.101386
$735$	−33.8533	−1.24870
$736$	−3.24887	−0.119755
$737$	28.3887	1.04571
$738$	−26.4724	−0.974461
$739$	8.89853	0.327338	0.163669	−	0.986515i	$-0.447667\pi$
$739$	8.89853	0.327338	0.163669	+	0.986515i	$0.447667\pi$
$740$	−7.30479	−0.268529
$741$	12.2276	0.449191
$742$	−2.10657	−0.0773345
$743$	−24.1062	−0.884369	−0.442185	−	0.896924i	$-0.645796\pi$
$743$	−24.1062	−0.884369	−0.442185	+	0.896924i	$0.645796\pi$
$744$	−33.9698	−1.24539
$745$	−23.1883	−0.849554
$746$	−10.2367	−0.374792
$747$	19.4851	0.712924
$748$	9.65021	0.352847
$749$	15.1648	0.554109
$750$	34.8705	1.27329
$751$	20.2780	0.739954	0.369977	−	0.929041i	$-0.379366\pi$
$751$	20.2780	0.739954	0.369977	+	0.929041i	$0.379366\pi$
$752$	−0.559156	−0.0203903
$753$	−14.6288	−0.533102
$754$	−5.69179	−0.207283
$755$	−34.2378	−1.24604
$756$	18.6186	0.677153
$757$	−1.50610	−0.0547403	−0.0273701	−	0.999625i	$-0.508713\pi$
$757$	−1.50610	−0.0547403	−0.0273701	+	0.999625i	$0.508713\pi$
$758$	−3.38717	−0.123028
$759$	31.1153	1.12941
$760$	−2.25930	−0.0819535
$761$	−4.24719	−0.153961	−0.0769803	−	0.997033i	$-0.524528\pi$
$761$	−4.24719	−0.153961	−0.0769803	+	0.997033i	$0.524528\pi$
$762$	−33.6113	−1.21761
$763$	10.0892	0.365255
$764$	10.5849	0.382950
$765$	49.8058	1.80073
$766$	8.12315	0.293501
$767$	−1.78503	−0.0644535
$768$	−3.15270	−0.113763
$769$	−23.5607	−0.849621	−0.424811	−	0.905282i	$-0.639659\pi$
$769$	−23.5607	−0.849621	−0.424811	+	0.905282i	$0.639659\pi$
$770$	10.2887	0.370778
$771$	−70.2163	−2.52878
$772$	−23.4035	−0.842311
$773$	25.7501	0.926166	0.463083	−	0.886315i	$-0.346743\pi$
$773$	25.7501	0.926166	0.463083	+	0.886315i	$0.346743\pi$
$774$	−7.92512	−0.284863
$775$	−1.12541	−0.0404260
$776$	−7.51517	−0.269779
$777$	15.2806	0.548190
$778$	−10.6628	−0.382281
$779$	−3.81474	−0.136677
$780$	27.6258	0.989162
$781$	−14.3144	−0.512211
$782$	10.3207	0.369069
$783$	−18.2269	−0.651375
$784$	−4.75275	−0.169741
$785$	−15.5255	−0.554130
$786$	37.0581	1.32182
$787$	−11.0332	−0.393293	−0.196646	−	0.980474i	$-0.563005\pi$
$787$	−11.0332	−0.393293	−0.196646	+	0.980474i	$0.563005\pi$
$788$	25.3147	0.901800
$789$	98.1893	3.49563
$790$	15.2453	0.542402
$791$	3.22787	0.114770
$792$	21.0808	0.749072
$793$	−9.33948	−0.331655
$794$	−1.32452	−0.0470056
$795$	−10.0093	−0.354995
$796$	−7.13772	−0.252990
$797$	0.460893	0.0163257	0.00816284	−	0.999967i	$-0.497402\pi$
$797$	0.460893	0.0163257	0.00816284	+	0.999967i	$0.497402\pi$
$798$	4.72616	0.167304
$799$	1.77628	0.0628403
$800$	−0.104448	−0.00369281
$801$	117.921	4.16654
$802$	17.3827	0.613806
$803$	26.2428	0.926088
$804$	29.4625	1.03906
$805$	11.0036	0.387825
$806$	41.7897	1.47198
$807$	−52.1386	−1.83537
$808$	−16.6574	−0.586006
$809$	−7.17518	−0.252266	−0.126133	−	0.992013i	$-0.540257\pi$
$809$	−7.17518	−0.252266	−0.126133	+	0.992013i	$0.540257\pi$
$810$	41.4311	1.45574
$811$	−17.1640	−0.602708	−0.301354	−	0.953512i	$-0.597439\pi$
$811$	−17.1640	−0.602708	−0.301354	+	0.953512i	$0.597439\pi$
$812$	−2.19997	−0.0772038
$813$	8.78773	0.308199
$814$	9.82182	0.344255
$815$	32.4823	1.13781
$816$	10.0152	0.350603
$817$	−1.14203	−0.0399547
$818$	−12.0300	−0.420618
$819$	−40.3471	−1.40984
$820$	−8.61866	−0.300977
$821$	19.2335	0.671254	0.335627	−	0.941995i	$-0.391052\pi$
$821$	19.2335	0.671254	0.335627	+	0.941995i	$0.391052\pi$
$822$	8.48003	0.295775
$823$	4.57979	0.159642	0.0798208	−	0.996809i	$-0.474565\pi$
$823$	4.57979	0.159642	0.0798208	+	0.996809i	$0.474565\pi$
$824$	0.337757	0.0117663
$825$	1.00033	0.0348270
$826$	−0.689941	−0.0240061
$827$	−6.43071	−0.223618	−0.111809	−	0.993730i	$-0.535664\pi$
$827$	−6.43071	−0.223618	−0.111809	+	0.993730i	$0.535664\pi$
$828$	22.5455	0.783511
$829$	−14.4554	−0.502057	−0.251028	−	0.967980i	$-0.580769\pi$
$829$	−14.4554	−0.502057	−0.251028	+	0.967980i	$0.580769\pi$
$830$	6.34382	0.220197
$831$	18.9755	0.658253
$832$	3.87845	0.134461
$833$	15.0981	0.523119
$834$	26.5985	0.921032
$835$	−47.7510	−1.65249
$836$	3.03780	0.105064
$837$	133.823	4.62561
$838$	−9.89216	−0.341719
$839$	−42.9259	−1.48197	−0.740983	−	0.671524i	$-0.765640\pi$
$839$	−42.9259	−1.48197	−0.740983	+	0.671524i	$0.765640\pi$
$840$	10.6778	0.368420
$841$	−26.8463	−0.925735
$842$	28.3477	0.976928
$843$	−70.9338	−2.44309
$844$	−1.00000	−0.0344214
$845$	−4.61437	−0.158739
$846$	3.88026	0.133406
$847$	2.65606	0.0912632
$848$	−1.40524	−0.0482560
$849$	−76.6541	−2.63076
$850$	0.331803	0.0113807
$851$	10.5043	0.360082
$852$	−14.8559	−0.508953
$853$	28.5584	0.977821	0.488910	−	0.872334i	$-0.337395\pi$
$853$	28.5584	0.977821	0.488910	+	0.872334i	$0.337395\pi$
$854$	−3.60986	−0.123527
$855$	15.6784	0.536190
$856$	10.1160	0.345759
$857$	24.1466	0.824832	0.412416	−	0.910996i	$-0.364685\pi$
$857$	24.1466	0.824832	0.412416	+	0.910996i	$0.364685\pi$
$858$	−37.1449	−1.26811
$859$	25.3168	0.863799	0.431900	−	0.901922i	$-0.357843\pi$
$859$	25.3168	0.863799	0.431900	+	0.901922i	$0.357843\pi$
$860$	−2.58020	−0.0879840
$861$	18.0291	0.614429
$862$	−0.658752	−0.0224372
$863$	−13.1854	−0.448837	−0.224418	−	0.974493i	$-0.572048\pi$
$863$	−13.1854	−0.448837	−0.224418	+	0.974493i	$0.572048\pi$
$864$	12.4200	0.422537
$865$	−37.6476	−1.28006
$866$	−6.23777	−0.211968
$867$	21.7804	0.739700
$868$	16.1524	0.548248
$869$	−20.4984	−0.695360
$870$	−10.4531	−0.354395
$871$	−36.2448	−1.22811
$872$	6.73026	0.227915
$873$	52.1514	1.76506
$874$	3.24887	0.109895
$875$	−16.5807	−0.560529
$876$	27.2354	0.920198
$877$	32.5095	1.09777	0.548885	−	0.835898i	$-0.315053\pi$
$877$	32.5095	1.09777	0.548885	+	0.835898i	$0.315053\pi$
$878$	40.6260	1.37106
$879$	24.5690	0.828692
$880$	6.86330	0.231362
$881$	32.6841	1.10115	0.550577	−	0.834784i	$-0.314408\pi$
$881$	32.6841	1.10115	0.550577	+	0.834784i	$0.314408\pi$
$882$	32.9816	1.11055
$883$	−10.3084	−0.346905	−0.173453	−	0.984842i	$-0.555492\pi$
$883$	−10.3084	−0.346905	−0.173453	+	0.984842i	$0.555492\pi$
$884$	−12.3207	−0.414391
$885$	−3.27825	−0.110197
$886$	−10.7549	−0.361317
$887$	−44.9688	−1.50990	−0.754952	−	0.655780i	$-0.772340\pi$
$887$	−44.9688	−1.50990	−0.754952	+	0.655780i	$0.772340\pi$
$888$	10.1933	0.342065
$889$	15.9819	0.536017
$890$	38.3918	1.28690
$891$	−55.7072	−1.86626
$892$	8.20659	0.274777
$893$	0.559156	0.0187115
$894$	32.3576	1.08220
$895$	3.49984	0.116987
$896$	1.49908	0.0500809
$897$	−39.7259	−1.32641
$898$	37.2453	1.24289
$899$	−15.8125	−0.527377
$900$	0.724818	0.0241606
$901$	4.46403	0.148718
$902$	11.5884	0.385852
$903$	5.39742	0.179615
$904$	2.15323	0.0716154
$905$	−26.4907	−0.880581
$906$	47.7764	1.58726
$907$	−37.9192	−1.25908	−0.629542	−	0.776966i	$-0.716758\pi$
$907$	−37.9192	−1.25908	−0.629542	+	0.776966i	$0.716758\pi$
$908$	−9.18561	−0.304835
$909$	115.594	3.83401
$910$	−13.1359	−0.435450
$911$	18.4120	0.610018	0.305009	−	0.952350i	$-0.401341\pi$
$911$	18.4120	0.610018	0.305009	+	0.952350i	$0.401341\pi$
$912$	3.15270	0.104396
$913$	−8.52973	−0.282293
$914$	17.6885	0.585083
$915$	−17.1522	−0.567036
$916$	16.8078	0.555345
$917$	−17.6209	−0.581893
$918$	−39.4548	−1.30220
$919$	55.5232	1.83154	0.915771	−	0.401701i	$-0.131581\pi$
$919$	55.5232	1.83154	0.915771	+	0.401701i	$0.131581\pi$
$920$	7.34019	0.241999
$921$	−29.7714	−0.981000
$922$	0.994485	0.0327516
$923$	18.2757	0.601552
$924$	−14.3571	−0.472314
$925$	0.337703	0.0111036
$926$	5.07023	0.166618
$927$	−2.34386	−0.0769824
$928$	−1.46754	−0.0481744
$929$	20.5845	0.675355	0.337677	−	0.941262i	$-0.390359\pi$
$929$	20.5845	0.675355	0.337677	+	0.941262i	$0.390359\pi$
$930$	76.7480	2.51666
$931$	4.75275	0.155765
$932$	−26.7715	−0.876929
$933$	78.8429	2.58120
$934$	6.05126	0.198003
$935$	−21.8028	−0.713026
$936$	−26.9145	−0.879727
$937$	22.4599	0.733732	0.366866	−	0.930274i	$-0.380431\pi$
$937$	22.4599	0.733732	0.366866	+	0.930274i	$0.380431\pi$
$938$	−14.0092	−0.457416
$939$	18.0013	0.587449
$940$	1.26330	0.0412044
$941$	−22.4106	−0.730565	−0.365282	−	0.930897i	$-0.619028\pi$
$941$	−22.4106	−0.730565	−0.365282	+	0.930897i	$0.619028\pi$
$942$	21.6648	0.705877
$943$	12.3936	0.403592
$944$	−0.460242	−0.0149796
$945$	−42.0651	−1.36838
$946$	3.46926	0.112795
$947$	−16.5309	−0.537184	−0.268592	−	0.963254i	$-0.586558\pi$
$947$	−16.5309	−0.537184	−0.268592	+	0.963254i	$0.586558\pi$
$948$	−21.2737	−0.690937
$949$	−33.5050	−1.08762
$950$	0.104448	0.00338875
$951$	75.4392	2.44628
$952$	−4.76216	−0.154343
$953$	−57.4110	−1.85972	−0.929862	−	0.367908i	$-0.880074\pi$
$953$	−57.4110	−1.85972	−0.929862	+	0.367908i	$0.880074\pi$
$954$	9.75162	0.315720
$955$	−23.9146	−0.773858
$956$	8.00344	0.258850
$957$	14.0550	0.454334
$958$	−17.5383	−0.566637
$959$	−4.03220	−0.130206
$960$	7.12289	0.229890
$961$	85.0970	2.74506
$962$	−12.5398	−0.404300
$963$	−70.2001	−2.26217
$964$	2.93960	0.0946781
$965$	52.8757	1.70213
$966$	−15.3547	−0.494029
$967$	−4.38110	−0.140887	−0.0704434	−	0.997516i	$-0.522441\pi$
$967$	−4.38110	−0.140887	−0.0704434	+	0.997516i	$0.522441\pi$
$968$	1.77179	0.0569473
$969$	−10.0152	−0.321735
$970$	16.9790	0.545164
$971$	−23.2502	−0.746136	−0.373068	−	0.927804i	$-0.621694\pi$
$971$	−23.2502	−0.746136	−0.373068	+	0.927804i	$0.621694\pi$
$972$	−20.5542	−0.659276
$973$	−12.6474	−0.405457
$974$	−16.2677	−0.521252
$975$	−1.27715	−0.0409015
$976$	−2.40804	−0.0770796
$977$	−28.6740	−0.917361	−0.458681	−	0.888601i	$-0.651678\pi$
$977$	−28.6740	−0.917361	−0.458681	+	0.888601i	$0.651678\pi$
$978$	−45.3268	−1.44939
$979$	−51.6206	−1.64980
$980$	10.7379	0.343009
$981$	−46.7046	−1.49116
$982$	−26.8743	−0.857593
$983$	−6.82114	−0.217561	−0.108780	−	0.994066i	$-0.534694\pi$
$983$	−6.82114	−0.217561	−0.108780	+	0.994066i	$0.534694\pi$
$984$	12.0267	0.383398
$985$	−57.1936	−1.82234
$986$	4.66196	0.148467
$987$	−2.64266	−0.0841168
$988$	−3.87845	−0.123390
$989$	3.71032	0.117981
$990$	−47.6278	−1.51371
$991$	15.7644	0.500773	0.250386	−	0.968146i	$-0.419442\pi$
$991$	15.7644	0.500773	0.250386	+	0.968146i	$0.419442\pi$
$992$	10.7748	0.342101
$993$	26.3179	0.835173
$994$	7.06386	0.224052
$995$	16.1263	0.511237
$996$	−8.85234	−0.280497
$997$	18.7961	0.595278	0.297639	−	0.954678i	$-0.403801\pi$
$997$	18.7961	0.595278	0.297639	+	0.954678i	$0.403801\pi$
$998$	−27.3801	−0.866701
$999$	−40.1564	−1.27049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.3	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.3	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.15270 q^{3} +1.00000 q^{4} -2.25930 q^{5} +3.15270 q^{6} -1.49908 q^{7} -1.00000 q^{8} +6.93949 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.15270 q^{3} +1.00000 q^{4} -2.25930 q^{5} +3.15270 q^{6} -1.49908 q^{7} -1.00000 q^{8} +6.93949 q^{9} +2.25930 q^{10} -3.03780 q^{11} -3.15270 q^{12} +3.87845 q^{13} +1.49908 q^{14} +7.12289 q^{15} +1.00000 q^{16} -3.17671 q^{17} -6.93949 q^{18} -1.00000 q^{19} -2.25930 q^{20} +4.72616 q^{21} +3.03780 q^{22} +3.24887 q^{23} +3.15270 q^{24} +0.104448 q^{25} -3.87845 q^{26} -12.4200 q^{27} -1.49908 q^{28} +1.46754 q^{29} -7.12289 q^{30} -10.7748 q^{31} -1.00000 q^{32} +9.57725 q^{33} +3.17671 q^{34} +3.38689 q^{35} +6.93949 q^{36} +3.23320 q^{37} +1.00000 q^{38} -12.2276 q^{39} +2.25930 q^{40} +3.81474 q^{41} -4.72616 q^{42} +1.14203 q^{43} -3.03780 q^{44} -15.6784 q^{45} -3.24887 q^{46} -0.559156 q^{47} -3.15270 q^{48} -4.75275 q^{49} -0.104448 q^{50} +10.0152 q^{51} +3.87845 q^{52} -1.40524 q^{53} +12.4200 q^{54} +6.86330 q^{55} +1.49908 q^{56} +3.15270 q^{57} -1.46754 q^{58} -0.460242 q^{59} +7.12289 q^{60} -2.40804 q^{61} +10.7748 q^{62} -10.4029 q^{63} +1.00000 q^{64} -8.76260 q^{65} -9.57725 q^{66} -9.34516 q^{67} -3.17671 q^{68} -10.2427 q^{69} -3.38689 q^{70} +4.71211 q^{71} -6.93949 q^{72} -8.63876 q^{73} -3.23320 q^{74} -0.329294 q^{75} -1.00000 q^{76} +4.55392 q^{77} +12.2276 q^{78} +6.74778 q^{79} -2.25930 q^{80} +18.3380 q^{81} -3.81474 q^{82} +2.80787 q^{83} +4.72616 q^{84} +7.17716 q^{85} -1.14203 q^{86} -4.62671 q^{87} +3.03780 q^{88} +16.9928 q^{89} +15.6784 q^{90} -5.81413 q^{91} +3.24887 q^{92} +33.9698 q^{93} +0.559156 q^{94} +2.25930 q^{95} +3.15270 q^{96} +7.51517 q^{97} +4.75275 q^{98} -21.0808 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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