LMFDB - Embedded newform 418.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(1,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, 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("418.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.469.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 5x + 4 $ x^3 - x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.16425$ of defining polynomial
Character	$\chi$	$=$	418.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.16425 q^{3} +1.00000 q^{4} +4.16425 q^{5} -2.16425 q^{6} -0.683969 q^{7} +1.00000 q^{8} +1.68397 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.16425 q^{3} +1.00000 q^{4} +4.16425 q^{5} -2.16425 q^{6} -0.683969 q^{7} +1.00000 q^{8} +1.68397 q^{9} +4.16425 q^{10} -1.00000 q^{11} -2.16425 q^{12} +2.68397 q^{13} -0.683969 q^{14} -9.01247 q^{15} +1.00000 q^{16} +3.36794 q^{17} +1.68397 q^{18} -1.00000 q^{19} +4.16425 q^{20} +1.48028 q^{21} -1.00000 q^{22} -1.36794 q^{23} -2.16425 q^{24} +12.3410 q^{25} +2.68397 q^{26} +2.84822 q^{27} -0.683969 q^{28} +2.79631 q^{29} -9.01247 q^{30} +5.01247 q^{31} +1.00000 q^{32} +2.16425 q^{33} +3.36794 q^{34} -2.84822 q^{35} +1.68397 q^{36} -11.6964 q^{37} -1.00000 q^{38} -5.80877 q^{39} +4.16425 q^{40} -7.01247 q^{41} +1.48028 q^{42} +7.86068 q^{43} -1.00000 q^{44} +7.01247 q^{45} -1.36794 q^{46} +2.96056 q^{47} -2.16425 q^{48} -6.53219 q^{49} +12.3410 q^{50} -7.28905 q^{51} +2.68397 q^{52} -10.3285 q^{53} +2.84822 q^{54} -4.16425 q^{55} -0.683969 q^{56} +2.16425 q^{57} +2.79631 q^{58} -9.92112 q^{59} -9.01247 q^{60} +2.00000 q^{61} +5.01247 q^{62} -1.15178 q^{63} +1.00000 q^{64} +11.1767 q^{65} +2.16425 q^{66} -0.683969 q^{67} +3.36794 q^{68} +2.96056 q^{69} -2.84822 q^{70} +3.53219 q^{71} +1.68397 q^{72} +0.407381 q^{73} -11.6964 q^{74} -26.7089 q^{75} -1.00000 q^{76} +0.683969 q^{77} -5.80877 q^{78} -7.28905 q^{79} +4.16425 q^{80} -11.2162 q^{81} -7.01247 q^{82} -12.1892 q^{83} +1.48028 q^{84} +14.0249 q^{85} +7.86068 q^{86} -6.05191 q^{87} -1.00000 q^{88} -16.6819 q^{89} +7.01247 q^{90} -1.83575 q^{91} -1.36794 q^{92} -10.8482 q^{93} +2.96056 q^{94} -4.16425 q^{95} -2.16425 q^{96} -11.6964 q^{97} -6.53219 q^{98} -1.68397 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + q^6 + q^7 + 3 * q^8 + 2 * q^9	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} + 3 q^{8} + 2 q^{9} + 5 q^{10} - 3 q^{11} + q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 3 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 5 q^{20} - 3 q^{22} + 2 q^{23} + q^{24} + 4 q^{25} + 5 q^{26} - 2 q^{27} + q^{28} + 7 q^{29} - 9 q^{30} - 3 q^{31} + 3 q^{32} - q^{33} + 4 q^{34} + 2 q^{35} + 2 q^{36} - 14 q^{37} - 3 q^{38} + 2 q^{39} + 5 q^{40} - 3 q^{41} - 5 q^{43} - 3 q^{44} + 3 q^{45} + 2 q^{46} + q^{48} - 6 q^{49} + 4 q^{50} + 2 q^{51} + 5 q^{52} - 16 q^{53} - 2 q^{54} - 5 q^{55} + q^{56} - q^{57} + 7 q^{58} - 12 q^{59} - 9 q^{60} + 6 q^{61} - 3 q^{62} - 14 q^{63} + 3 q^{64} + 8 q^{65} - q^{66} + q^{67} + 4 q^{68} + 2 q^{70} - 3 q^{71} + 2 q^{72} + 4 q^{73} - 14 q^{74} - 41 q^{75} - 3 q^{76} - q^{77} + 2 q^{78} + 2 q^{79} + 5 q^{80} - 17 q^{81} - 3 q^{82} + 7 q^{83} + 6 q^{85} - 5 q^{86} - 9 q^{87} - 3 q^{88} + 16 q^{89} + 3 q^{90} - 13 q^{91} + 2 q^{92} - 22 q^{93} - 5 q^{95} + q^{96} - 14 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + q^6 + q^7 + 3 * q^8 + 2 * q^9 + 5 * q^10 - 3 * q^11 + q^12 + 5 * q^13 + q^14 - 9 * q^15 + 3 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 5 * q^20 - 3 * q^22 + 2 * q^23 + q^24 + 4 * q^25 + 5 * q^26 - 2 * q^27 + q^28 + 7 * q^29 - 9 * q^30 - 3 * q^31 + 3 * q^32 - q^33 + 4 * q^34 + 2 * q^35 + 2 * q^36 - 14 * q^37 - 3 * q^38 + 2 * q^39 + 5 * q^40 - 3 * q^41 - 5 * q^43 - 3 * q^44 + 3 * q^45 + 2 * q^46 + q^48 - 6 * q^49 + 4 * q^50 + 2 * q^51 + 5 * q^52 - 16 * q^53 - 2 * q^54 - 5 * q^55 + q^56 - q^57 + 7 * q^58 - 12 * q^59 - 9 * q^60 + 6 * q^61 - 3 * q^62 - 14 * q^63 + 3 * q^64 + 8 * q^65 - q^66 + q^67 + 4 * q^68 + 2 * q^70 - 3 * q^71 + 2 * q^72 + 4 * q^73 - 14 * q^74 - 41 * q^75 - 3 * q^76 - q^77 + 2 * q^78 + 2 * q^79 + 5 * q^80 - 17 * q^81 - 3 * q^82 + 7 * q^83 + 6 * q^85 - 5 * q^86 - 9 * q^87 - 3 * q^88 + 16 * q^89 + 3 * q^90 - 13 * q^91 + 2 * q^92 - 22 * q^93 - 5 * q^95 + q^96 - 14 * q^97 - 6 * q^98 - 2 * 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
$3$	−2.16425	−1.24953	−0.624765	−	0.780813i	$-0.714805\pi$
$3$	−2.16425	−1.24953	−0.624765	+	0.780813i	$0.714805\pi$
$4$	1.00000	0.500000
$5$	4.16425	1.86231	0.931154	−	0.364626i	$-0.118803\pi$
$5$	4.16425	1.86231	0.931154	+	0.364626i	$0.118803\pi$
$6$	−2.16425	−0.883551
$7$	−0.683969	−0.258516	−0.129258	−	0.991611i	$-0.541260\pi$
$7$	−0.683969	−0.258516	−0.129258	+	0.991611i	$0.541260\pi$
$8$	1.00000	0.353553
$9$	1.68397	0.561323
$10$	4.16425	1.31685
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.16425	−0.624765
$13$	2.68397	0.744399	0.372200	−	0.928153i	$-0.378604\pi$
$13$	2.68397	0.744399	0.372200	+	0.928153i	$0.378604\pi$
$14$	−0.683969	−0.182798
$15$	−9.01247	−2.32701
$16$	1.00000	0.250000
$17$	3.36794	0.816845	0.408423	−	0.912793i	$-0.366079\pi$
$17$	3.36794	0.816845	0.408423	+	0.912793i	$0.366079\pi$
$18$	1.68397	0.396915
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.16425	0.931154
$21$	1.48028	0.323023
$22$	−1.00000	−0.213201
$23$	−1.36794	−0.285235	−0.142617	−	0.989778i	$-0.545552\pi$
$23$	−1.36794	−0.285235	−0.142617	+	0.989778i	$0.545552\pi$
$24$	−2.16425	−0.441775
$25$	12.3410	2.46819
$26$	2.68397	0.526370
$27$	2.84822	0.548140
$28$	−0.683969	−0.129258
$29$	2.79631	0.519262	0.259631	−	0.965708i	$-0.416399\pi$
$29$	2.79631	0.519262	0.259631	+	0.965708i	$0.416399\pi$
$30$	−9.01247	−1.64544
$31$	5.01247	0.900265	0.450133	−	0.892962i	$-0.351377\pi$
$31$	5.01247	0.900265	0.450133	+	0.892962i	$0.351377\pi$
$32$	1.00000	0.176777
$33$	2.16425	0.376747
$34$	3.36794	0.577597
$35$	−2.84822	−0.481437
$36$	1.68397	0.280662
$37$	−11.6964	−1.92288	−0.961441	−	0.275011i	$-0.911318\pi$
$37$	−11.6964	−1.92288	−0.961441	+	0.275011i	$0.911318\pi$
$38$	−1.00000	−0.162221
$39$	−5.80877	−0.930148
$40$	4.16425	0.658425
$41$	−7.01247	−1.09516	−0.547582	−	0.836752i	$-0.684451\pi$
$41$	−7.01247	−1.09516	−0.547582	+	0.836752i	$0.684451\pi$
$42$	1.48028	0.228412
$43$	7.86068	1.19874	0.599371	−	0.800471i	$-0.295417\pi$
$43$	7.86068	1.19874	0.599371	+	0.800471i	$0.295417\pi$
$44$	−1.00000	−0.150756
$45$	7.01247	1.04536
$46$	−1.36794	−0.201691
$47$	2.96056	0.431842	0.215921	−	0.976411i	$-0.430725\pi$
$47$	2.96056	0.431842	0.215921	+	0.976411i	$0.430725\pi$
$48$	−2.16425	−0.312382
$49$	−6.53219	−0.933169
$50$	12.3410	1.74528
$51$	−7.28905	−1.02067
$52$	2.68397	0.372200
$53$	−10.3285	−1.41873	−0.709364	−	0.704842i	$-0.751018\pi$
$53$	−10.3285	−1.41873	−0.709364	+	0.704842i	$0.751018\pi$
$54$	2.84822	0.387593
$55$	−4.16425	−0.561507
$56$	−0.683969	−0.0913992
$57$	2.16425	0.286662
$58$	2.79631	0.367173
$59$	−9.92112	−1.29162	−0.645810	−	0.763499i	$-0.723480\pi$
$59$	−9.92112	−1.29162	−0.645810	+	0.763499i	$0.723480\pi$
$60$	−9.01247	−1.16350
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	5.01247	0.636584
$63$	−1.15178	−0.145111
$64$	1.00000	0.125000
$65$	11.1767	1.38630
$66$	2.16425	0.266401
$67$	−0.683969	−0.0835601	−0.0417801	−	0.999127i	$-0.513303\pi$
$67$	−0.683969	−0.0835601	−0.0417801	+	0.999127i	$0.513303\pi$
$68$	3.36794	0.408423
$69$	2.96056	0.356409
$70$	−2.84822	−0.340427
$71$	3.53219	0.419193	0.209597	−	0.977788i	$-0.432785\pi$
$71$	3.53219	0.419193	0.209597	+	0.977788i	$0.432785\pi$
$72$	1.68397	0.198458
$73$	0.407381	0.0476803	0.0238402	−	0.999716i	$-0.492411\pi$
$73$	0.407381	0.0476803	0.0238402	+	0.999716i	$0.492411\pi$
$74$	−11.6964	−1.35968
$75$	−26.7089	−3.08408
$76$	−1.00000	−0.114708
$77$	0.683969	0.0779455
$78$	−5.80877	−0.657714
$79$	−7.28905	−0.820083	−0.410041	−	0.912067i	$-0.634486\pi$
$79$	−7.28905	−0.820083	−0.410041	+	0.912067i	$0.634486\pi$
$80$	4.16425	0.465577
$81$	−11.2162	−1.24624
$82$	−7.01247	−0.774397
$83$	−12.1892	−1.33794	−0.668968	−	0.743291i	$-0.733264\pi$
$83$	−12.1892	−1.33794	−0.668968	+	0.743291i	$0.733264\pi$
$84$	1.48028	0.161512
$85$	14.0249	1.52122
$86$	7.86068	0.847639
$87$	−6.05191	−0.648833
$88$	−1.00000	−0.106600
$89$	−16.6819	−1.76828	−0.884140	−	0.467222i	$-0.845255\pi$
$89$	−16.6819	−1.76828	−0.884140	+	0.467222i	$0.845255\pi$
$90$	7.01247	0.739179
$91$	−1.83575	−0.192439
$92$	−1.36794	−0.142617
$93$	−10.8482	−1.12491
$94$	2.96056	0.305358
$95$	−4.16425	−0.427243
$96$	−2.16425	−0.220888
$97$	−11.6964	−1.18759	−0.593796	−	0.804615i	$-0.702372\pi$
$97$	−11.6964	−1.18759	−0.593796	+	0.804615i	$0.702372\pi$
$98$	−6.53219	−0.659850
$99$	−1.68397	−0.169245
$100$	12.3410	1.23410
$101$	3.59262	0.357479	0.178739	−	0.983896i	$-0.442798\pi$
$101$	3.59262	0.357479	0.178739	+	0.983896i	$0.442798\pi$
$102$	−7.28905	−0.721724
$103$	−4.46781	−0.440227	−0.220113	−	0.975474i	$-0.570643\pi$
$103$	−4.46781	−0.440227	−0.220113	+	0.975474i	$0.570643\pi$
$104$	2.68397	0.263185
$105$	6.16425	0.601569
$106$	−10.3285	−1.00319
$107$	9.69643	0.937390	0.468695	−	0.883360i	$-0.344724\pi$
$107$	9.69643	0.937390	0.468695	+	0.883360i	$0.344724\pi$
$108$	2.84822	0.274070
$109$	6.00000	0.574696	0.287348	−	0.957826i	$-0.407226\pi$
$109$	6.00000	0.574696	0.287348	+	0.957826i	$0.407226\pi$
$110$	−4.16425	−0.397045
$111$	25.3140	2.40270
$112$	−0.683969	−0.0646290
$113$	10.4323	0.981389	0.490695	−	0.871332i	$-0.336743\pi$
$113$	10.4323	0.981389	0.490695	+	0.871332i	$0.336743\pi$
$114$	2.16425	0.202700
$115$	−5.69643	−0.531195
$116$	2.79631	0.259631
$117$	4.51972	0.417848
$118$	−9.92112	−0.913313
$119$	−2.30357	−0.211168
$120$	−9.01247	−0.822722
$121$	1.00000	0.0909091
$122$	2.00000	0.181071
$123$	15.1767	1.36844
$124$	5.01247	0.450133
$125$	30.5696	2.73423
$126$	−1.15178	−0.102609
$127$	15.2891	1.35668	0.678342	−	0.734746i	$-0.262699\pi$
$127$	15.2891	1.35668	0.678342	+	0.734746i	$0.262699\pi$
$128$	1.00000	0.0883883
$129$	−17.0125	−1.49786
$130$	11.1767	0.980263
$131$	3.64453	0.318424	0.159212	−	0.987244i	$-0.449105\pi$
$131$	3.64453	0.318424	0.159212	+	0.987244i	$0.449105\pi$
$132$	2.16425	0.188374
$133$	0.683969	0.0593076
$134$	−0.683969	−0.0590859
$135$	11.8607	1.02080
$136$	3.36794	0.288798
$137$	14.6840	1.25454	0.627268	−	0.778803i	$-0.284173\pi$
$137$	14.6840	1.25454	0.627268	+	0.778803i	$0.284173\pi$
$138$	2.96056	0.252019
$139$	−18.5966	−1.57734	−0.788670	−	0.614817i	$-0.789230\pi$
$139$	−18.5966	−1.57734	−0.788670	+	0.614817i	$0.789230\pi$
$140$	−2.84822	−0.240718
$141$	−6.40738	−0.539599
$142$	3.53219	0.296414
$143$	−2.68397	−0.224445
$144$	1.68397	0.140331
$145$	11.6445	0.967025
$146$	0.407381	0.0337151
$147$	14.1373	1.16602
$148$	−11.6964	−0.961441
$149$	4.30357	0.352562	0.176281	−	0.984340i	$-0.443593\pi$
$149$	4.30357	0.352562	0.176281	+	0.984340i	$0.443593\pi$
$150$	−26.7089	−2.18077
$151$	−21.6964	−1.76563	−0.882815	−	0.469720i	$-0.844355\pi$
$151$	−21.6964	−1.76563	−0.882815	+	0.469720i	$0.844355\pi$
$152$	−1.00000	−0.0811107
$153$	5.67150	0.458514
$154$	0.683969	0.0551158
$155$	20.8731	1.67657
$156$	−5.80877	−0.465074
$157$	−10.9001	−0.869925	−0.434962	−	0.900449i	$-0.643238\pi$
$157$	−10.9001	−0.869925	−0.434962	+	0.900449i	$0.643238\pi$
$158$	−7.28905	−0.579886
$159$	22.3534	1.77274
$160$	4.16425	0.329213
$161$	0.935628	0.0737378
$162$	−11.2162	−0.881224
$163$	19.7214	1.54470	0.772348	−	0.635199i	$-0.219082\pi$
$163$	19.7214	1.54470	0.772348	+	0.635199i	$0.219082\pi$
$164$	−7.01247	−0.547582
$165$	9.01247	0.701619
$166$	−12.1892	−0.946064
$167$	7.77532	0.601672	0.300836	−	0.953676i	$-0.402734\pi$
$167$	7.77532	0.601672	0.300836	+	0.953676i	$0.402734\pi$
$168$	1.48028	0.114206
$169$	−5.79631	−0.445870
$170$	14.0249	1.07566
$171$	−1.68397	−0.128776
$172$	7.86068	0.599371
$173$	15.7818	1.19987	0.599934	−	0.800050i	$-0.295194\pi$
$173$	15.7818	1.19987	0.599934	+	0.800050i	$0.295194\pi$
$174$	−6.05191	−0.458794
$175$	−8.44084	−0.638067
$176$	−1.00000	−0.0753778
$177$	21.4718	1.61392
$178$	−16.6819	−1.25036
$179$	−7.97302	−0.595932	−0.297966	−	0.954577i	$-0.596308\pi$
$179$	−7.97302	−0.595932	−0.297966	+	0.954577i	$0.596308\pi$
$180$	7.01247	0.522678
$181$	−2.55318	−0.189776	−0.0948881	−	0.995488i	$-0.530249\pi$
$181$	−2.55318	−0.189776	−0.0948881	+	0.995488i	$0.530249\pi$
$182$	−1.83575	−0.136075
$183$	−4.32850	−0.319972
$184$	−1.36794	−0.100846
$185$	−48.7069	−3.58100
$186$	−10.8482	−0.795430
$187$	−3.36794	−0.246288
$188$	2.96056	0.215921
$189$	−1.94809	−0.141703
$190$	−4.16425	−0.302106
$191$	8.22468	0.595117	0.297559	−	0.954704i	$-0.403828\pi$
$191$	8.22468	0.595117	0.297559	+	0.954704i	$0.403828\pi$
$192$	−2.16425	−0.156191
$193$	−24.2141	−1.74297	−0.871485	−	0.490422i	$-0.836842\pi$
$193$	−24.2141	−1.74297	−0.871485	+	0.490422i	$0.836842\pi$
$194$	−11.6964	−0.839755
$195$	−24.1892	−1.73222
$196$	−6.53219	−0.466585
$197$	26.6570	1.89923	0.949616	−	0.313416i	$-0.101473\pi$
$197$	26.6570	1.89923	0.949616	+	0.313416i	$0.101473\pi$
$198$	−1.68397	−0.119674
$199$	−7.06437	−0.500780	−0.250390	−	0.968145i	$-0.580559\pi$
$199$	−7.06437	−0.500780	−0.250390	+	0.968145i	$0.580559\pi$
$200$	12.3410	0.872638
$201$	1.48028	0.104411
$202$	3.59262	0.252776
$203$	−1.91259	−0.134237
$204$	−7.28905	−0.510336
$205$	−29.2016	−2.03953
$206$	−4.46781	−0.311287
$207$	−2.30357	−0.160109
$208$	2.68397	0.186100
$209$	1.00000	0.0691714
$210$	6.16425	0.425374
$211$	−11.0644	−0.761703	−0.380851	−	0.924636i	$-0.624369\pi$
$211$	−11.0644	−0.761703	−0.380851	+	0.924636i	$0.624369\pi$
$212$	−10.3285	−0.709364
$213$	−7.64453	−0.523794
$214$	9.69643	0.662835
$215$	32.7338	2.23243
$216$	2.84822	0.193797
$217$	−3.42837	−0.232733
$218$	6.00000	0.406371
$219$	−0.881673	−0.0595779
$220$	−4.16425	−0.280754
$221$	9.03944	0.608059
$222$	25.3140	1.69896
$223$	−14.7359	−0.986787	−0.493394	−	0.869806i	$-0.664244\pi$
$223$	−14.7359	−0.986787	−0.493394	+	0.869806i	$0.664244\pi$
$224$	−0.683969	−0.0456996
$225$	20.7818	1.38545
$226$	10.4323	0.693947
$227$	21.8002	1.44693	0.723467	−	0.690359i	$-0.242548\pi$
$227$	21.8002	1.44693	0.723467	+	0.690359i	$0.242548\pi$
$228$	2.16425	0.143331
$229$	17.7483	1.17284	0.586422	−	0.810006i	$-0.300536\pi$
$229$	17.7483	1.17284	0.586422	+	0.810006i	$0.300536\pi$
$230$	−5.69643	−0.375612
$231$	−1.48028	−0.0973952
$232$	2.79631	0.183587
$233$	−20.3534	−1.33340	−0.666699	−	0.745327i	$-0.732293\pi$
$233$	−20.3534	−1.33340	−0.666699	+	0.745327i	$0.732293\pi$
$234$	4.51972	0.295463
$235$	12.3285	0.804222
$236$	−9.92112	−0.645810
$237$	15.7753	1.02472
$238$	−2.30357	−0.149318
$239$	3.75687	0.243012	0.121506	−	0.992591i	$-0.461228\pi$
$239$	3.75687	0.243012	0.121506	+	0.992591i	$0.461228\pi$
$240$	−9.01247	−0.581752
$241$	−9.14974	−0.589386	−0.294693	−	0.955592i	$-0.595217\pi$
$241$	−9.14974	−0.589386	−0.294693	+	0.955592i	$0.595217\pi$
$242$	1.00000	0.0642824
$243$	15.7299	1.00907
$244$	2.00000	0.128037
$245$	−27.2016	−1.73785
$246$	15.1767	0.967632
$247$	−2.68397	−0.170777
$248$	5.01247	0.318292
$249$	26.3804	1.67179
$250$	30.5696	1.93339
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	−1.15178	−0.0725555
$253$	1.36794	0.0860015
$254$	15.2891	0.959321
$255$	−30.3534	−1.90081
$256$	1.00000	0.0625000
$257$	23.2102	1.44781	0.723905	−	0.689899i	$-0.242345\pi$
$257$	23.2102	1.44781	0.723905	+	0.689899i	$0.242345\pi$
$258$	−17.0125	−1.05915
$259$	8.00000	0.497096
$260$	11.1767	0.693150
$261$	4.70890	0.291474
$262$	3.64453	0.225160
$263$	−22.2141	−1.36978	−0.684890	−	0.728646i	$-0.740150\pi$
$263$	−22.2141	−1.36978	−0.684890	+	0.728646i	$0.740150\pi$
$264$	2.16425	0.133200
$265$	−43.0104	−2.64211
$266$	0.683969	0.0419368
$267$	36.1038	2.20952
$268$	−0.683969	−0.0417801
$269$	−18.9855	−1.15757	−0.578783	−	0.815482i	$-0.696472\pi$
$269$	−18.9855	−1.15757	−0.578783	+	0.815482i	$0.696472\pi$
$270$	11.8607	0.721818
$271$	20.7338	1.25949	0.629745	−	0.776802i	$-0.283159\pi$
$271$	20.7338	1.25949	0.629745	+	0.776802i	$0.283159\pi$
$272$	3.36794	0.204211
$273$	3.97302	0.240458
$274$	14.6840	0.887091
$275$	−12.3410	−0.744188
$276$	2.96056	0.178205
$277$	21.8422	1.31237	0.656186	−	0.754599i	$-0.272169\pi$
$277$	21.8422	1.31237	0.656186	+	0.754599i	$0.272169\pi$
$278$	−18.5966	−1.11535
$279$	8.44084	0.505340
$280$	−2.84822	−0.170214
$281$	0.164248	0.00979821	0.00489911	−	0.999988i	$-0.498441\pi$
$281$	0.164248	0.00979821	0.00489911	+	0.999988i	$0.498441\pi$
$282$	−6.40738	−0.381554
$283$	4.30152	0.255699	0.127849	−	0.991794i	$-0.459193\pi$
$283$	4.30152	0.255699	0.127849	+	0.991794i	$0.459193\pi$
$284$	3.53219	0.209597
$285$	9.01247	0.533852
$286$	−2.68397	−0.158706
$287$	4.79631	0.283117
$288$	1.68397	0.0992288
$289$	−5.65699	−0.332764
$290$	11.6445	0.683790
$291$	25.3140	1.48393
$292$	0.407381	0.0238402
$293$	32.5511	1.90166	0.950829	−	0.309717i	$-0.100234\pi$
$293$	32.5511	1.90166	0.950829	+	0.309717i	$0.100234\pi$
$294$	14.1373	0.824502
$295$	−41.3140	−2.40539
$296$	−11.6964	−0.679841
$297$	−2.84822	−0.165270
$298$	4.30357	0.249299
$299$	−3.67150	−0.212329
$300$	−26.7089	−1.54204
$301$	−5.37646	−0.309894
$302$	−21.6964	−1.24849
$303$	−7.77532	−0.446680
$304$	−1.00000	−0.0573539
$305$	8.32850	0.476888
$306$	5.67150	0.324218
$307$	22.2496	1.26985	0.634926	−	0.772573i	$-0.281030\pi$
$307$	22.2496	1.26985	0.634926	+	0.772573i	$0.281030\pi$
$308$	0.683969	0.0389728
$309$	9.66946	0.550076
$310$	20.8731	1.18552
$311$	−20.9855	−1.18998	−0.594989	−	0.803734i	$-0.702844\pi$
$311$	−20.9855	−1.18998	−0.594989	+	0.803734i	$0.702844\pi$
$312$	−5.80877	−0.328857
$313$	−11.4533	−0.647379	−0.323689	−	0.946163i	$-0.604923\pi$
$313$	−11.4533	−0.647379	−0.323689	+	0.946163i	$0.604923\pi$
$314$	−10.9001	−0.615130
$315$	−4.79631	−0.270241
$316$	−7.28905	−0.410041
$317$	10.7109	0.601587	0.300793	−	0.953689i	$-0.402749\pi$
$317$	10.7109	0.601587	0.300793	+	0.953689i	$0.402749\pi$
$318$	22.3534	1.25352
$319$	−2.79631	−0.156563
$320$	4.16425	0.232789
$321$	−20.9855	−1.17130
$322$	0.935628	0.0521405
$323$	−3.36794	−0.187397
$324$	−11.2162	−0.623120
$325$	33.1228	1.83732
$326$	19.7214	1.09227
$327$	−12.9855	−0.718099
$328$	−7.01247	−0.387199
$329$	−2.02493	−0.111638
$330$	9.01247	0.496120
$331$	−6.77138	−0.372189	−0.186094	−	0.982532i	$-0.559583\pi$
$331$	−6.77138	−0.372189	−0.186094	+	0.982532i	$0.559583\pi$
$332$	−12.1892	−0.668968
$333$	−19.6964	−1.07936
$334$	7.77532	0.425447
$335$	−2.84822	−0.155615
$336$	1.48028	0.0807558
$337$	21.0374	1.14598	0.572990	−	0.819562i	$-0.305783\pi$
$337$	21.0374	1.14598	0.572990	+	0.819562i	$0.305783\pi$
$338$	−5.79631	−0.315278
$339$	−22.5781	−1.22627
$340$	14.0249	0.760609
$341$	−5.01247	−0.271440
$342$	−1.68397	−0.0910586
$343$	9.25560	0.499755
$344$	7.86068	0.423820
$345$	12.3285	0.663744
$346$	15.7818	0.848435
$347$	−29.9710	−1.60893	−0.804463	−	0.594003i	$-0.797547\pi$
$347$	−29.9710	−1.60893	−0.804463	+	0.594003i	$0.797547\pi$
$348$	−6.05191	−0.324416
$349$	−22.6570	−1.21280	−0.606400	−	0.795159i	$-0.707387\pi$
$349$	−22.6570	−1.21280	−0.606400	+	0.795159i	$0.707387\pi$
$350$	−8.44084	−0.451182
$351$	7.64453	0.408035
$352$	−1.00000	−0.0533002
$353$	−1.18524	−0.0630839	−0.0315419	−	0.999502i	$-0.510042\pi$
$353$	−1.18524	−0.0630839	−0.0315419	+	0.999502i	$0.510042\pi$
$354$	21.4718	1.14121
$355$	14.7089	0.780667
$356$	−16.6819	−0.884140
$357$	4.98549	0.263860
$358$	−7.97302	−0.421387
$359$	19.3659	1.02209	0.511046	−	0.859553i	$-0.329258\pi$
$359$	19.3659	1.02209	0.511046	+	0.859553i	$0.329258\pi$
$360$	7.01247	0.369589
$361$	1.00000	0.0526316
$362$	−2.55318	−0.134192
$363$	−2.16425	−0.113594
$364$	−1.83575	−0.0962196
$365$	1.69643	0.0887954
$366$	−4.32850	−0.226254
$367$	−18.3036	−0.955438	−0.477719	−	0.878513i	$-0.658536\pi$
$367$	−18.3036	−0.955438	−0.477719	+	0.878513i	$0.658536\pi$
$368$	−1.36794	−0.0713087
$369$	−11.8088	−0.614740
$370$	−48.7069	−2.53215
$371$	7.06437	0.366764
$372$	−10.8482	−0.562454
$373$	6.46781	0.334891	0.167445	−	0.985881i	$-0.446448\pi$
$373$	6.46781	0.334891	0.167445	+	0.985881i	$0.446448\pi$
$374$	−3.36794	−0.174152
$375$	−66.1602	−3.41650
$376$	2.96056	0.152679
$377$	7.50521	0.386538
$378$	−1.94809	−0.100199
$379$	31.9191	1.63957	0.819786	−	0.572670i	$-0.194092\pi$
$379$	31.9191	1.63957	0.819786	+	0.572670i	$0.194092\pi$
$380$	−4.16425	−0.213621
$381$	−33.0893	−1.69522
$382$	8.22468	0.420811
$383$	5.66946	0.289696	0.144848	−	0.989454i	$-0.453731\pi$
$383$	5.66946	0.289696	0.144848	+	0.989454i	$0.453731\pi$
$384$	−2.16425	−0.110444
$385$	2.84822	0.145159
$386$	−24.2141	−1.23247
$387$	13.2371	0.672882
$388$	−11.6964	−0.593796
$389$	20.1642	1.02237	0.511184	−	0.859471i	$-0.329207\pi$
$389$	20.1642	1.02237	0.511184	+	0.859471i	$0.329207\pi$
$390$	−24.1892	−1.22487
$391$	−4.60713	−0.232993
$392$	−6.53219	−0.329925
$393$	−7.88766	−0.397880
$394$	26.6570	1.34296
$395$	−30.3534	−1.52725
$396$	−1.68397	−0.0846226
$397$	−15.8272	−0.794346	−0.397173	−	0.917744i	$-0.630009\pi$
$397$	−15.8272	−0.794346	−0.397173	+	0.917744i	$0.630009\pi$
$398$	−7.06437	−0.354105
$399$	−1.48028	−0.0741066
$400$	12.3410	0.617048
$401$	9.06437	0.452653	0.226327	−	0.974051i	$-0.427328\pi$
$401$	9.06437	0.452653	0.226327	+	0.974051i	$0.427328\pi$
$402$	1.48028	0.0738296
$403$	13.4533	0.670157
$404$	3.59262	0.178739
$405$	−46.7069	−2.32088
$406$	−1.91259	−0.0949202
$407$	11.6964	0.579771
$408$	−7.28905	−0.360862
$409$	2.90012	0.143402	0.0717010	−	0.997426i	$-0.477157\pi$
$409$	2.90012	0.143402	0.0717010	+	0.997426i	$0.477157\pi$
$410$	−29.2016	−1.44217
$411$	−31.7797	−1.56758
$412$	−4.46781	−0.220113
$413$	6.78574	0.333904
$414$	−2.30357	−0.113214
$415$	−50.7588	−2.49165
$416$	2.68397	0.131592
$417$	40.2476	1.97093
$418$	1.00000	0.0489116
$419$	19.7753	0.966088	0.483044	−	0.875596i	$-0.339531\pi$
$419$	19.7753	0.966088	0.483044	+	0.875596i	$0.339531\pi$
$420$	6.16425	0.300785
$421$	14.9855	0.730348	0.365174	−	0.930939i	$-0.381009\pi$
$421$	14.9855	0.730348	0.365174	+	0.930939i	$0.381009\pi$
$422$	−11.0644	−0.538605
$423$	4.98549	0.242403
$424$	−10.3285	−0.501596
$425$	41.5636	2.01613
$426$	−7.64453	−0.370379
$427$	−1.36794	−0.0661992
$428$	9.69643	0.468695
$429$	5.80877	0.280450
$430$	32.7338	1.57857
$431$	39.4427	1.89989	0.949945	−	0.312418i	$-0.101139\pi$
$431$	39.4427	1.89989	0.949945	+	0.312418i	$0.101139\pi$
$432$	2.84822	0.137035
$433$	−1.23919	−0.0595518	−0.0297759	−	0.999557i	$-0.509479\pi$
$433$	−1.23919	−0.0595518	−0.0297759	+	0.999557i	$0.509479\pi$
$434$	−3.42837	−0.164567
$435$	−25.2016	−1.20833
$436$	6.00000	0.287348
$437$	1.36794	0.0654374
$438$	−0.881673	−0.0421280
$439$	−11.1852	−0.533842	−0.266921	−	0.963718i	$-0.586006\pi$
$439$	−11.1852	−0.533842	−0.266921	+	0.963718i	$0.586006\pi$
$440$	−4.16425	−0.198523
$441$	−11.0000	−0.523810
$442$	9.03944	0.429962
$443$	23.8422	1.13278	0.566389	−	0.824138i	$-0.308340\pi$
$443$	23.8422	1.13278	0.566389	+	0.824138i	$0.308340\pi$
$444$	25.3140	1.20135
$445$	−69.4677	−3.29308
$446$	−14.7359	−0.697764
$447$	−9.31398	−0.440536
$448$	−0.683969	−0.0323145
$449$	20.9066	0.986644	0.493322	−	0.869847i	$-0.335783\pi$
$449$	20.9066	0.986644	0.493322	+	0.869847i	$0.335783\pi$
$450$	20.7818	0.979663
$451$	7.01247	0.330204
$452$	10.4323	0.490695
$453$	46.9565	2.20621
$454$	21.8002	1.02314
$455$	−7.64453	−0.358381
$456$	2.16425	0.101350
$457$	−4.18270	−0.195658	−0.0978292	−	0.995203i	$-0.531190\pi$
$457$	−4.18270	−0.195658	−0.0978292	+	0.995203i	$0.531190\pi$
$458$	17.7483	0.829326
$459$	9.59262	0.447745
$460$	−5.69643	−0.265598
$461$	−31.5387	−1.46890	−0.734451	−	0.678662i	$-0.762560\pi$
$461$	−31.5387	−1.46890	−0.734451	+	0.678662i	$0.762560\pi$
$462$	−1.48028	−0.0688688
$463$	−4.60713	−0.214112	−0.107056	−	0.994253i	$-0.534142\pi$
$463$	−4.60713	−0.214112	−0.107056	+	0.994253i	$0.534142\pi$
$464$	2.79631	0.129815
$465$	−45.1747	−2.09492
$466$	−20.3534	−0.942854
$467$	−3.94605	−0.182601	−0.0913006	−	0.995823i	$-0.529102\pi$
$467$	−3.94605	−0.182601	−0.0913006	+	0.995823i	$0.529102\pi$
$468$	4.51972	0.208924
$469$	0.467814	0.0216016
$470$	12.3285	0.568671
$471$	23.5906	1.08700
$472$	−9.92112	−0.456656
$473$	−7.86068	−0.361435
$474$	15.7753	0.724584
$475$	−12.3410	−0.566242
$476$	−2.30357	−0.105584
$477$	−17.3929	−0.796365
$478$	3.75687	0.171835
$479$	−16.6840	−0.762310	−0.381155	−	0.924511i	$-0.624474\pi$
$479$	−16.6840	−0.762310	−0.381155	+	0.924511i	$0.624474\pi$
$480$	−9.01247	−0.411361
$481$	−31.3929	−1.43139
$482$	−9.14974	−0.416759
$483$	−2.02493	−0.0921375
$484$	1.00000	0.0454545
$485$	−48.7069	−2.21166
$486$	15.7299	0.713522
$487$	−14.4388	−0.654284	−0.327142	−	0.944975i	$-0.606086\pi$
$487$	−14.4388	−0.654284	−0.327142	+	0.944975i	$0.606086\pi$
$488$	2.00000	0.0905357
$489$	−42.6819	−1.93014
$490$	−27.2016	−1.22884
$491$	6.38040	0.287944	0.143972	−	0.989582i	$-0.454013\pi$
$491$	6.38040	0.287944	0.143972	+	0.989582i	$0.454013\pi$
$492$	15.1767	0.684219
$493$	9.41780	0.424156
$494$	−2.68397	−0.120757
$495$	−7.01247	−0.315187
$496$	5.01247	0.225066
$497$	−2.41591	−0.108368
$498$	26.3804	1.18213
$499$	−31.8252	−1.42469	−0.712345	−	0.701829i	$-0.752367\pi$
$499$	−31.8252	−1.42469	−0.712345	+	0.701829i	$0.752367\pi$
$500$	30.5696	1.36711
$501$	−16.8277	−0.751807
$502$	−12.0000	−0.535586
$503$	24.5716	1.09559	0.547797	−	0.836611i	$-0.315466\pi$
$503$	24.5716	1.09559	0.547797	+	0.836611i	$0.315466\pi$
$504$	−1.15178	−0.0513045
$505$	14.9606	0.665736
$506$	1.36794	0.0608123
$507$	12.5447	0.557128
$508$	15.2891	0.678342
$509$	−5.56769	−0.246783	−0.123392	−	0.992358i	$-0.539377\pi$
$509$	−5.56769	−0.246783	−0.123392	+	0.992358i	$0.539377\pi$
$510$	−30.3534	−1.34407
$511$	−0.278636	−0.0123261
$512$	1.00000	0.0441942
$513$	−2.84822	−0.125752
$514$	23.2102	1.02376
$515$	−18.6051	−0.819838
$516$	−17.0125	−0.748932
$517$	−2.96056	−0.130205
$518$	8.00000	0.351500
$519$	−34.1557	−1.49927
$520$	11.1767	0.490131
$521$	−10.8148	−0.473803	−0.236902	−	0.971534i	$-0.576132\pi$
$521$	−10.8148	−0.473803	−0.236902	+	0.971534i	$0.576132\pi$
$522$	4.70890	0.206103
$523$	−18.4074	−0.804899	−0.402449	−	0.915442i	$-0.631841\pi$
$523$	−18.4074	−0.804899	−0.402449	+	0.915442i	$0.631841\pi$
$524$	3.64453	0.159212
$525$	18.2681	0.797284
$526$	−22.2141	−0.968581
$527$	16.8817	0.735377
$528$	2.16425	0.0941868
$529$	−21.1287	−0.918641
$530$	−43.0104	−1.86825
$531$	−16.7069	−0.725016
$532$	0.683969	0.0296538
$533$	−18.8212	−0.815238
$534$	36.1038	1.56236
$535$	40.3784	1.74571
$536$	−0.683969	−0.0295430
$537$	17.2556	0.744634
$538$	−18.9855	−0.818522
$539$	6.53219	0.281361
$540$	11.8607	0.510402
$541$	33.0644	1.42155	0.710774	−	0.703420i	$-0.248345\pi$
$541$	33.0644	1.42155	0.710774	+	0.703420i	$0.248345\pi$
$542$	20.7338	0.890594
$543$	5.52571	0.237131
$544$	3.36794	0.144399
$545$	24.9855	1.07026
$546$	3.97302	0.170030
$547$	34.1287	1.45924	0.729620	−	0.683853i	$-0.239697\pi$
$547$	34.1287	1.45924	0.729620	+	0.683853i	$0.239697\pi$
$548$	14.6840	0.627268
$549$	3.36794	0.143740
$550$	−12.3410	−0.526220
$551$	−2.79631	−0.119127
$552$	2.96056	0.126010
$553$	4.98549	0.212004
$554$	21.8422	0.927987
$555$	105.414	4.47456
$556$	−18.5966	−0.788670
$557$	20.5112	0.869087	0.434544	−	0.900651i	$-0.356910\pi$
$557$	20.5112	0.869087	0.434544	+	0.900651i	$0.356910\pi$
$558$	8.44084	0.357329
$559$	21.0978	0.892343
$560$	−2.84822	−0.120359
$561$	7.28905	0.307744
$562$	0.164248	0.00692838
$563$	−27.0104	−1.13835	−0.569177	−	0.822215i	$-0.692738\pi$
$563$	−27.0104	−1.13835	−0.569177	+	0.822215i	$0.692738\pi$
$564$	−6.40738	−0.269799
$565$	43.4427	1.82765
$566$	4.30152	0.180806
$567$	7.67150	0.322173
$568$	3.53219	0.148207
$569$	7.56564	0.317168	0.158584	−	0.987345i	$-0.449307\pi$
$569$	7.56564	0.317168	0.158584	+	0.987345i	$0.449307\pi$
$570$	9.01247	0.377491
$571$	42.2226	1.76696	0.883481	−	0.468467i	$-0.155193\pi$
$571$	42.2226	1.76696	0.883481	+	0.468467i	$0.155193\pi$
$572$	−2.68397	−0.112222
$573$	−17.8002	−0.743616
$574$	4.79631	0.200194
$575$	−16.8817	−0.704014
$576$	1.68397	0.0701654
$577$	−25.9191	−1.07902	−0.539512	−	0.841978i	$-0.681391\pi$
$577$	−25.9191	−1.07902	−0.539512	+	0.841978i	$0.681391\pi$
$578$	−5.65699	−0.235300
$579$	52.4053	2.17789
$580$	11.6445	0.483513
$581$	8.33702	0.345878
$582$	25.3140	1.04930
$583$	10.3285	0.427763
$584$	0.407381	0.0168575
$585$	18.8212	0.778162
$586$	32.5511	1.34467
$587$	20.6570	0.852605	0.426303	−	0.904581i	$-0.359816\pi$
$587$	20.6570	0.852605	0.426303	+	0.904581i	$0.359816\pi$
$588$	14.1373	0.583011
$589$	−5.01247	−0.206535
$590$	−41.3140	−1.70087
$591$	−57.6923	−2.37315
$592$	−11.6964	−0.480720
$593$	−28.1287	−1.15511	−0.577555	−	0.816352i	$-0.695993\pi$
$593$	−28.1287	−1.15511	−0.577555	+	0.816352i	$0.695993\pi$
$594$	−2.84822	−0.116864
$595$	−9.59262	−0.393259
$596$	4.30357	0.176281
$597$	15.2891	0.625739
$598$	−3.67150	−0.150139
$599$	−26.3179	−1.07532	−0.537661	−	0.843161i	$-0.680692\pi$
$599$	−26.3179	−1.07532	−0.537661	+	0.843161i	$0.680692\pi$
$600$	−26.7089	−1.09039
$601$	38.4053	1.56659	0.783293	−	0.621653i	$-0.213538\pi$
$601$	38.4053	1.56659	0.783293	+	0.621653i	$0.213538\pi$
$602$	−5.37646	−0.219128
$603$	−1.15178	−0.0469042
$604$	−21.6964	−0.882815
$605$	4.16425	0.169301
$606$	−7.77532	−0.315851
$607$	−33.2600	−1.34998	−0.674991	−	0.737826i	$-0.735853\pi$
$607$	−33.2600	−1.34998	−0.674991	+	0.737826i	$0.735853\pi$
$608$	−1.00000	−0.0405554
$609$	4.13932	0.167734
$610$	8.32850	0.337211
$611$	7.94605	0.321463
$612$	5.67150	0.229257
$613$	17.5506	0.708864	0.354432	−	0.935082i	$-0.384674\pi$
$613$	17.5506	0.708864	0.354432	+	0.935082i	$0.384674\pi$
$614$	22.2496	0.897921
$615$	63.1996	2.54845
$616$	0.683969	0.0275579
$617$	14.6840	0.591154	0.295577	−	0.955319i	$-0.404488\pi$
$617$	14.6840	0.591154	0.295577	+	0.955319i	$0.404488\pi$
$618$	9.66946	0.388963
$619$	11.1183	0.446883	0.223442	−	0.974717i	$-0.428271\pi$
$619$	11.1183	0.446883	0.223442	+	0.974717i	$0.428271\pi$
$620$	20.8731	0.838286
$621$	−3.89619	−0.156349
$622$	−20.9855	−0.841441
$623$	11.4099	0.457129
$624$	−5.80877	−0.232537
$625$	65.5945	2.62378
$626$	−11.4533	−0.457766
$627$	−2.16425	−0.0864317
$628$	−10.9001	−0.434962
$629$	−39.3929	−1.57070
$630$	−4.79631	−0.191090
$631$	−46.0748	−1.83421	−0.917104	−	0.398648i	$-0.869480\pi$
$631$	−46.0748	−1.83421	−0.917104	+	0.398648i	$0.869480\pi$
$632$	−7.28905	−0.289943
$633$	23.9460	0.951770
$634$	10.7109	0.425386
$635$	63.6674	2.52656
$636$	22.3534	0.886371
$637$	−17.5322	−0.694651
$638$	−2.79631	−0.110707
$639$	5.94809	0.235303
$640$	4.16425	0.164606
$641$	−11.3181	−0.447037	−0.223519	−	0.974700i	$-0.571754\pi$
$641$	−11.3181	−0.447037	−0.223519	+	0.974700i	$0.571754\pi$
$642$	−20.9855	−0.828231
$643$	−30.6280	−1.20785	−0.603925	−	0.797041i	$-0.706397\pi$
$643$	−30.6280	−1.20785	−0.603925	+	0.797041i	$0.706397\pi$
$644$	0.935628	0.0368689
$645$	−70.8441	−2.78948
$646$	−3.36794	−0.132510
$647$	−31.2720	−1.22943	−0.614715	−	0.788750i	$-0.710729\pi$
$647$	−31.2720	−1.22943	−0.614715	+	0.788750i	$0.710729\pi$
$648$	−11.2162	−0.440612
$649$	9.92112	0.389438
$650$	33.1228	1.29918
$651$	7.41985	0.290807
$652$	19.7214	0.772348
$653$	−2.09389	−0.0819402	−0.0409701	−	0.999160i	$-0.513045\pi$
$653$	−2.09389	−0.0819402	−0.0409701	+	0.999160i	$0.513045\pi$
$654$	−12.9855	−0.507773
$655$	15.1767	0.593003
$656$	−7.01247	−0.273791
$657$	0.686016	0.0267641
$658$	−2.02493	−0.0789400
$659$	24.7608	0.964544	0.482272	−	0.876022i	$-0.339812\pi$
$659$	24.7608	0.964544	0.482272	+	0.876022i	$0.339812\pi$
$660$	9.01247	0.350810
$661$	36.4033	1.41592	0.707962	−	0.706251i	$-0.249615\pi$
$661$	36.4033	1.41592	0.707962	+	0.706251i	$0.249615\pi$
$662$	−6.77138	−0.263177
$663$	−19.5636	−0.759787
$664$	−12.1892	−0.473032
$665$	2.84822	0.110449
$666$	−19.6964	−0.763221
$667$	−3.82518	−0.148112
$668$	7.77532	0.300836
$669$	31.8921	1.23302
$670$	−2.84822	−0.110036
$671$	−2.00000	−0.0772091
$672$	1.48028	0.0571030
$673$	−16.1728	−0.623415	−0.311707	−	0.950178i	$-0.600901\pi$
$673$	−16.1728	−0.623415	−0.311707	+	0.950178i	$0.600901\pi$
$674$	21.0374	0.810330
$675$	35.1497	1.35291
$676$	−5.79631	−0.222935
$677$	5.32456	0.204639	0.102320	−	0.994752i	$-0.467374\pi$
$677$	5.32456	0.204639	0.102320	+	0.994752i	$0.467374\pi$
$678$	−22.5781	−0.867107
$679$	8.00000	0.307012
$680$	14.0249	0.537832
$681$	−47.1811	−1.80799
$682$	−5.01247	−0.191937
$683$	49.1562	1.88091	0.940455	−	0.339918i	$-0.110399\pi$
$683$	49.1562	1.88091	0.940455	+	0.339918i	$0.110399\pi$
$684$	−1.68397	−0.0643882
$685$	61.1477	2.33633
$686$	9.25560	0.353380
$687$	−38.4118	−1.46550
$688$	7.86068	0.299686
$689$	−27.7214	−1.05610
$690$	12.3285	0.469338
$691$	−6.51120	−0.247698	−0.123849	−	0.992301i	$-0.539524\pi$
$691$	−6.51120	−0.247698	−0.123849	+	0.992301i	$0.539524\pi$
$692$	15.7818	0.599934
$693$	1.15178	0.0437526
$694$	−29.9710	−1.13768
$695$	−77.4407	−2.93749
$696$	−6.05191	−0.229397
$697$	−23.6175	−0.894578
$698$	−22.6570	−0.857580
$699$	44.0499	1.66612
$700$	−8.44084	−0.319034
$701$	−5.77532	−0.218131	−0.109065	−	0.994035i	$-0.534786\pi$
$701$	−5.77532	−0.218131	−0.109065	+	0.994035i	$0.534786\pi$
$702$	7.64453	0.288524
$703$	11.6964	0.441139
$704$	−1.00000	−0.0376889
$705$	−26.6819	−1.00490
$706$	−1.18524	−0.0446070
$707$	−2.45724	−0.0924140
$708$	21.4718	0.806958
$709$	−35.6155	−1.33757	−0.668784	−	0.743457i	$-0.733185\pi$
$709$	−35.6155	−1.33757	−0.668784	+	0.743457i	$0.733185\pi$
$710$	14.7089	0.552015
$711$	−12.2745	−0.460331
$712$	−16.6819	−0.625181
$713$	−6.85674	−0.256787
$714$	4.98549	0.186577
$715$	−11.1767	−0.417985
$716$	−7.97302	−0.297966
$717$	−8.13079	−0.303650
$718$	19.3659	0.722729
$719$	−8.93563	−0.333243	−0.166621	−	0.986021i	$-0.553286\pi$
$719$	−8.93563	−0.333243	−0.166621	+	0.986021i	$0.553286\pi$
$720$	7.01247	0.261339
$721$	3.05585	0.113806
$722$	1.00000	0.0372161
$723$	19.8023	0.736455
$724$	−2.55318	−0.0948881
$725$	34.5091	1.28164
$726$	−2.16425	−0.0803228
$727$	−1.42189	−0.0527351	−0.0263675	−	0.999652i	$-0.508394\pi$
$727$	−1.42189	−0.0527351	−0.0263675	+	0.999652i	$0.508394\pi$
$728$	−1.83575	−0.0680375
$729$	−0.394916	−0.0146265
$730$	1.69643	0.0627878
$731$	26.4743	0.979187
$732$	−4.32850	−0.159986
$733$	−46.7567	−1.72700	−0.863499	−	0.504350i	$-0.831732\pi$
$733$	−46.7567	−1.72700	−0.863499	+	0.504350i	$0.831732\pi$
$734$	−18.3036	−0.675597
$735$	58.8711	2.17149
$736$	−1.36794	−0.0504229
$737$	0.683969	0.0251943
$738$	−11.8088	−0.434687
$739$	−34.4886	−1.26869	−0.634343	−	0.773052i	$-0.718729\pi$
$739$	−34.4886	−1.26869	−0.634343	+	0.773052i	$0.718729\pi$
$740$	−48.7069	−1.79050
$741$	5.80877	0.213391
$742$	7.06437	0.259341
$743$	−10.9606	−0.402104	−0.201052	−	0.979581i	$-0.564436\pi$
$743$	−10.9606	−0.402104	−0.201052	+	0.979581i	$0.564436\pi$
$744$	−10.8482	−0.397715
$745$	17.9211	0.656579
$746$	6.46781	0.236803
$747$	−20.5262	−0.751014
$748$	−3.36794	−0.123144
$749$	−6.63206	−0.242330
$750$	−66.1602	−2.41583
$751$	13.3140	0.485834	0.242917	−	0.970047i	$-0.421896\pi$
$751$	13.3140	0.485834	0.242917	+	0.970047i	$0.421896\pi$
$752$	2.96056	0.107960
$753$	25.9710	0.946435
$754$	7.50521	0.273324
$755$	−90.3493	−3.28815
$756$	−1.94809	−0.0708514
$757$	−8.54260	−0.310486	−0.155243	−	0.987876i	$-0.549616\pi$
$757$	−8.54260	−0.310486	−0.155243	+	0.987876i	$0.549616\pi$
$758$	31.9191	1.15935
$759$	−2.96056	−0.107461
$760$	−4.16425	−0.151053
$761$	32.7318	1.18653	0.593263	−	0.805009i	$-0.297839\pi$
$761$	32.7318	1.18653	0.593263	+	0.805009i	$0.297839\pi$
$762$	−33.0893	−1.19870
$763$	−4.10381	−0.148568
$764$	8.22468	0.297559
$765$	23.6175	0.853894
$766$	5.66946	0.204846
$767$	−26.6280	−0.961480
$768$	−2.16425	−0.0780956
$769$	50.5491	1.82285	0.911423	−	0.411470i	$-0.134985\pi$
$769$	50.5491	1.82285	0.911423	+	0.411470i	$0.134985\pi$
$770$	2.84822	0.102643
$771$	−50.2326	−1.80908
$772$	−24.2141	−0.871485
$773$	−40.7359	−1.46517	−0.732584	−	0.680677i	$-0.761686\pi$
$773$	−40.7359	−1.46517	−0.732584	+	0.680677i	$0.761686\pi$
$774$	13.2371	0.475799
$775$	61.8586	2.22203
$776$	−11.6964	−0.419878
$777$	−17.3140	−0.621136
$778$	20.1642	0.722923
$779$	7.01247	0.251248
$780$	−24.1892	−0.866112
$781$	−3.53219	−0.126392
$782$	−4.60713	−0.164751
$783$	7.96450	0.284628
$784$	−6.53219	−0.233292
$785$	−45.3908	−1.62007
$786$	−7.88766	−0.281343
$787$	8.53613	0.304280	0.152140	−	0.988359i	$-0.451384\pi$
$787$	8.53613	0.304280	0.152140	+	0.988359i	$0.451384\pi$
$788$	26.6570	0.949616
$789$	48.0768	1.71158
$790$	−30.3534	−1.07993
$791$	−7.13538	−0.253705
$792$	−1.68397	−0.0598372
$793$	5.36794	0.190621
$794$	−15.8272	−0.561687
$795$	93.0852	3.30139
$796$	−7.06437	−0.250390
$797$	−16.0249	−0.567632	−0.283816	−	0.958879i	$-0.591601\pi$
$797$	−16.0249	−0.567632	−0.283816	+	0.958879i	$0.591601\pi$
$798$	−1.48028	−0.0524013
$799$	9.97098	0.352748
$800$	12.3410	0.436319
$801$	−28.0918	−0.992576
$802$	9.06437	0.320074
$803$	−0.407381	−0.0143762
$804$	1.48028	0.0522054
$805$	3.89619	0.137322
$806$	13.4533	0.473872
$807$	41.0893	1.44641
$808$	3.59262	0.126388
$809$	−20.1458	−0.708288	−0.354144	−	0.935191i	$-0.615228\pi$
$809$	−20.1458	−0.708288	−0.354144	+	0.935191i	$0.615228\pi$
$810$	−46.7069	−1.64111
$811$	8.27454	0.290558	0.145279	−	0.989391i	$-0.453592\pi$
$811$	8.27454	0.290558	0.145279	+	0.989391i	$0.453592\pi$
$812$	−1.91259	−0.0671187
$813$	−44.8731	−1.57377
$814$	11.6964	0.409960
$815$	82.1247	2.87670
$816$	−7.28905	−0.255168
$817$	−7.86068	−0.275010
$818$	2.90012	0.101400
$819$	−3.09135	−0.108021
$820$	−29.2016	−1.01977
$821$	−21.5137	−0.750835	−0.375417	−	0.926856i	$-0.622501\pi$
$821$	−21.5137	−0.750835	−0.375417	+	0.926856i	$0.622501\pi$
$822$	−31.7797	−1.10845
$823$	−5.26412	−0.183496	−0.0917479	−	0.995782i	$-0.529245\pi$
$823$	−5.26412	−0.183496	−0.0917479	+	0.995782i	$0.529245\pi$
$824$	−4.46781	−0.155644
$825$	26.7089	0.929885
$826$	6.78574	0.236106
$827$	16.7069	0.580954	0.290477	−	0.956882i	$-0.406186\pi$
$827$	16.7069	0.580954	0.290477	+	0.956882i	$0.406186\pi$
$828$	−2.30357	−0.0800544
$829$	−5.55064	−0.192782	−0.0963908	−	0.995344i	$-0.530730\pi$
$829$	−5.55064	−0.192782	−0.0963908	+	0.995344i	$0.530730\pi$
$830$	−50.7588	−1.76186
$831$	−47.2720	−1.63985
$832$	2.68397	0.0930499
$833$	−22.0000	−0.762255
$834$	40.2476	1.39366
$835$	32.3784	1.12050
$836$	1.00000	0.0345857
$837$	14.2766	0.493471
$838$	19.7753	0.683127
$839$	15.3744	0.530784	0.265392	−	0.964141i	$-0.414499\pi$
$839$	15.3744	0.530784	0.265392	+	0.964141i	$0.414499\pi$
$840$	6.16425	0.212687
$841$	−21.1807	−0.730367
$842$	14.9855	0.516434
$843$	−0.355473	−0.0122431
$844$	−11.0644	−0.380851
$845$	−24.1373	−0.830347
$846$	4.98549	0.171405
$847$	−0.683969	−0.0235015
$848$	−10.3285	−0.354682
$849$	−9.30955	−0.319503
$850$	41.5636	1.42562
$851$	16.0000	0.548473
$852$	−7.64453	−0.261897
$853$	24.8028	0.849231	0.424616	−	0.905374i	$-0.360409\pi$
$853$	24.8028	0.849231	0.424616	+	0.905374i	$0.360409\pi$
$854$	−1.36794	−0.0468099
$855$	−7.01247	−0.239821
$856$	9.69643	0.331417
$857$	−45.6445	−1.55919	−0.779594	−	0.626286i	$-0.784574\pi$
$857$	−45.6445	−1.55919	−0.779594	+	0.626286i	$0.784574\pi$
$858$	5.80877	0.198308
$859$	54.8356	1.87097	0.935483	−	0.353371i	$-0.114965\pi$
$859$	54.8356	1.87097	0.935483	+	0.353371i	$0.114965\pi$
$860$	32.7338	1.11621
$861$	−10.3804	−0.353763
$862$	39.4427	1.34342
$863$	45.8771	1.56167	0.780837	−	0.624735i	$-0.214793\pi$
$863$	45.8771	1.56167	0.780837	+	0.624735i	$0.214793\pi$
$864$	2.84822	0.0968983
$865$	65.7193	2.23452
$866$	−1.23919	−0.0421095
$867$	12.2431	0.415799
$868$	−3.42837	−0.116367
$869$	7.28905	0.247264
$870$	−25.2016	−0.854416
$871$	−1.83575	−0.0622021
$872$	6.00000	0.203186
$873$	−19.6964	−0.666623
$874$	1.36794	0.0462712
$875$	−20.9087	−0.706841
$876$	−0.881673	−0.0297890
$877$	−15.6609	−0.528832	−0.264416	−	0.964409i	$-0.585179\pi$
$877$	−15.6609	−0.528832	−0.264416	+	0.964409i	$0.585179\pi$
$878$	−11.1852	−0.377484
$879$	−70.4487	−2.37618
$880$	−4.16425	−0.140377
$881$	−3.39492	−0.114378	−0.0571888	−	0.998363i	$-0.518214\pi$
$881$	−3.39492	−0.114378	−0.0571888	+	0.998363i	$0.518214\pi$
$882$	−11.0000	−0.370389
$883$	−33.6425	−1.13216	−0.566080	−	0.824350i	$-0.691541\pi$
$883$	−33.6425	−1.13216	−0.566080	+	0.824350i	$0.691541\pi$
$884$	9.03944	0.304029
$885$	89.4137	3.00561
$886$	23.8422	0.800995
$887$	−22.1287	−0.743011	−0.371505	−	0.928431i	$-0.621158\pi$
$887$	−22.1287	−0.743011	−0.371505	+	0.928431i	$0.621158\pi$
$888$	25.3140	0.849482
$889$	−10.4572	−0.350725
$890$	−69.4677	−2.32856
$891$	11.2162	0.375755
$892$	−14.7359	−0.493394
$893$	−2.96056	−0.0990713
$894$	−9.31398	−0.311506
$895$	−33.2016	−1.10981
$896$	−0.683969	−0.0228498
$897$	7.94605	0.265311
$898$	20.9066	0.697662
$899$	14.0164	0.467473
$900$	20.7818	0.692727
$901$	−34.7857	−1.15888
$902$	7.01247	0.233490
$903$	11.6360	0.387222
$904$	10.4323	0.346973
$905$	−10.6321	−0.353422
$906$	46.9565	1.56002
$907$	−21.7633	−0.722640	−0.361320	−	0.932442i	$-0.617674\pi$
$907$	−21.7633	−0.722640	−0.361320	+	0.932442i	$0.617674\pi$
$908$	21.8002	0.723467
$909$	6.04986	0.200661
$910$	−7.64453	−0.253414
$911$	46.8356	1.55173	0.775866	−	0.630897i	$-0.217313\pi$
$911$	46.8356	1.55173	0.775866	+	0.630897i	$0.217313\pi$
$912$	2.16425	0.0716654
$913$	12.1892	0.403403
$914$	−4.18270	−0.138351
$915$	−18.0249	−0.595886
$916$	17.7483	0.586422
$917$	−2.49274	−0.0823177
$918$	9.59262	0.316604
$919$	−42.0563	−1.38731	−0.693655	−	0.720307i	$-0.744001\pi$
$919$	−42.0563	−1.38731	−0.693655	+	0.720307i	$0.744001\pi$
$920$	−5.69643	−0.187806
$921$	−48.1537	−1.58672
$922$	−31.5387	−1.03867
$923$	9.48028	0.312047
$924$	−1.48028	−0.0486976
$925$	−144.345	−4.74604
$926$	−4.60713	−0.151400
$927$	−7.52366	−0.247109
$928$	2.79631	0.0917934
$929$	36.1018	1.18446	0.592230	−	0.805769i	$-0.298248\pi$
$929$	36.1018	1.18446	0.592230	+	0.805769i	$0.298248\pi$
$930$	−45.1747	−1.48134
$931$	6.53219	0.214084
$932$	−20.3534	−0.666699
$933$	45.4178	1.48691
$934$	−3.94605	−0.129119
$935$	−14.0249	−0.458664
$936$	4.51972	0.147732
$937$	47.3638	1.54731	0.773655	−	0.633607i	$-0.218427\pi$
$937$	47.3638	1.54731	0.773655	+	0.633607i	$0.218427\pi$
$938$	0.467814	0.0152747
$939$	24.7878	0.808919
$940$	12.3285	0.402111
$941$	−9.34301	−0.304573	−0.152287	−	0.988336i	$-0.548664\pi$
$941$	−9.34301	−0.304573	−0.152287	+	0.988336i	$0.548664\pi$
$942$	23.5906	0.768622
$943$	9.59262	0.312379
$944$	−9.92112	−0.322905
$945$	−8.11234	−0.263894
$946$	−7.86068	−0.255573
$947$	22.2496	0.723015	0.361508	−	0.932369i	$-0.382262\pi$
$947$	22.2496	0.723015	0.361508	+	0.932369i	$0.382262\pi$
$948$	15.7753	0.512359
$949$	1.09340	0.0354932
$950$	−12.3410	−0.400394
$951$	−23.1811	−0.751700
$952$	−2.30357	−0.0746590
$953$	−31.9710	−1.03564	−0.517821	−	0.855489i	$-0.673257\pi$
$953$	−31.9710	−1.03564	−0.517821	+	0.855489i	$0.673257\pi$
$954$	−17.3929	−0.563115
$955$	34.2496	1.10829
$956$	3.75687	0.121506
$957$	6.05191	0.195630
$958$	−16.6840	−0.539035
$959$	−10.0434	−0.324318
$960$	−9.01247	−0.290876
$961$	−5.87519	−0.189522
$962$	−31.3929	−1.01215
$963$	16.3285	0.526178
$964$	−9.14974	−0.294693
$965$	−100.834	−3.24595
$966$	−2.02493	−0.0651511
$967$	5.97098	0.192014	0.0960068	−	0.995381i	$-0.469393\pi$
$967$	5.97098	0.192014	0.0960068	+	0.995381i	$0.469393\pi$
$968$	1.00000	0.0321412
$969$	7.28905	0.234158
$970$	−48.7069	−1.56388
$971$	−19.0999	−0.612944	−0.306472	−	0.951880i	$-0.599149\pi$
$971$	−19.0999	−0.612944	−0.306472	+	0.951880i	$0.599149\pi$
$972$	15.7299	0.504536
$973$	12.7195	0.407768
$974$	−14.4388	−0.462649
$975$	−71.6859	−2.29578
$976$	2.00000	0.0640184
$977$	−10.2745	−0.328712	−0.164356	−	0.986401i	$-0.552555\pi$
$977$	−10.2745	−0.328712	−0.164356	+	0.986401i	$0.552555\pi$
$978$	−42.6819	−1.36482
$979$	16.6819	0.533157
$980$	−27.2016	−0.868925
$981$	10.1038	0.322590
$982$	6.38040	0.203607
$983$	33.0084	1.05280	0.526402	−	0.850236i	$-0.323541\pi$
$983$	33.0084	1.05280	0.526402	+	0.850236i	$0.323541\pi$
$984$	15.1767	0.483816
$985$	111.006	3.53696
$986$	9.41780	0.299924
$987$	4.38245	0.139495
$988$	−2.68397	−0.0853884
$989$	−10.7529	−0.341923
$990$	−7.01247	−0.222871
$991$	1.56564	0.0497343	0.0248671	−	0.999691i	$-0.492084\pi$
$991$	1.56564	0.0497343	0.0248671	+	0.999691i	$0.492084\pi$
$992$	5.01247	0.159146
$993$	14.6549	0.465061
$994$	−2.41591	−0.0766279
$995$	−29.4178	−0.932607
$996$	26.3804	0.835895
$997$	46.5361	1.47381	0.736907	−	0.675994i	$-0.236286\pi$
$997$	46.5361	1.47381	0.736907	+	0.675994i	$0.236286\pi$
$998$	−31.8252	−1.00741
$999$	−33.3140	−1.05401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.a.h.1.1	✓	3
3.2	odd	2		3762.2.a.bd.1.1		3
4.3	odd	2		3344.2.a.p.1.3		3
11.10	odd	2		4598.2.a.bm.1.1		3
19.18	odd	2		7942.2.a.bc.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.h.1.1	✓	3	1.1	even	1	trivial
3344.2.a.p.1.3		3	4.3	odd	2
3762.2.a.bd.1.1		3	3.2	odd	2
4598.2.a.bm.1.1		3	11.10	odd	2
7942.2.a.bc.1.3		3	19.18	odd	2

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.16425 q^{3} +1.00000 q^{4} +4.16425 q^{5} -2.16425 q^{6} -0.683969 q^{7} +1.00000 q^{8} +1.68397 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.16425 q^{3} +1.00000 q^{4} +4.16425 q^{5} -2.16425 q^{6} -0.683969 q^{7} +1.00000 q^{8} +1.68397 q^{9} +4.16425 q^{10} -1.00000 q^{11} -2.16425 q^{12} +2.68397 q^{13} -0.683969 q^{14} -9.01247 q^{15} +1.00000 q^{16} +3.36794 q^{17} +1.68397 q^{18} -1.00000 q^{19} +4.16425 q^{20} +1.48028 q^{21} -1.00000 q^{22} -1.36794 q^{23} -2.16425 q^{24} +12.3410 q^{25} +2.68397 q^{26} +2.84822 q^{27} -0.683969 q^{28} +2.79631 q^{29} -9.01247 q^{30} +5.01247 q^{31} +1.00000 q^{32} +2.16425 q^{33} +3.36794 q^{34} -2.84822 q^{35} +1.68397 q^{36} -11.6964 q^{37} -1.00000 q^{38} -5.80877 q^{39} +4.16425 q^{40} -7.01247 q^{41} +1.48028 q^{42} +7.86068 q^{43} -1.00000 q^{44} +7.01247 q^{45} -1.36794 q^{46} +2.96056 q^{47} -2.16425 q^{48} -6.53219 q^{49} +12.3410 q^{50} -7.28905 q^{51} +2.68397 q^{52} -10.3285 q^{53} +2.84822 q^{54} -4.16425 q^{55} -0.683969 q^{56} +2.16425 q^{57} +2.79631 q^{58} -9.92112 q^{59} -9.01247 q^{60} +2.00000 q^{61} +5.01247 q^{62} -1.15178 q^{63} +1.00000 q^{64} +11.1767 q^{65} +2.16425 q^{66} -0.683969 q^{67} +3.36794 q^{68} +2.96056 q^{69} -2.84822 q^{70} +3.53219 q^{71} +1.68397 q^{72} +0.407381 q^{73} -11.6964 q^{74} -26.7089 q^{75} -1.00000 q^{76} +0.683969 q^{77} -5.80877 q^{78} -7.28905 q^{79} +4.16425 q^{80} -11.2162 q^{81} -7.01247 q^{82} -12.1892 q^{83} +1.48028 q^{84} +14.0249 q^{85} +7.86068 q^{86} -6.05191 q^{87} -1.00000 q^{88} -16.6819 q^{89} +7.01247 q^{90} -1.83575 q^{91} -1.36794 q^{92} -10.8482 q^{93} +2.96056 q^{94} -4.16425 q^{95} -2.16425 q^{96} -11.6964 q^{97} -6.53219 q^{98} -1.68397 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + q^6 + q^7 + 3 * q^8 + 2 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} + 5 q^{5} + q^{6} + q^{7} + 3 q^{8} + 2 q^{9} + 5 q^{10} - 3 q^{11} + q^{12} + 5 q^{13} + q^{14} - 9 q^{15} + 3 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 5 q^{20} - 3 q^{22} + 2 q^{23} + q^{24} + 4 q^{25} + 5 q^{26} - 2 q^{27} + q^{28} + 7 q^{29} - 9 q^{30} - 3 q^{31} + 3 q^{32} - q^{33} + 4 q^{34} + 2 q^{35} + 2 q^{36} - 14 q^{37} - 3 q^{38} + 2 q^{39} + 5 q^{40} - 3 q^{41} - 5 q^{43} - 3 q^{44} + 3 q^{45} + 2 q^{46} + q^{48} - 6 q^{49} + 4 q^{50} + 2 q^{51} + 5 q^{52} - 16 q^{53} - 2 q^{54} - 5 q^{55} + q^{56} - q^{57} + 7 q^{58} - 12 q^{59} - 9 q^{60} + 6 q^{61} - 3 q^{62} - 14 q^{63} + 3 q^{64} + 8 q^{65} - q^{66} + q^{67} + 4 q^{68} + 2 q^{70} - 3 q^{71} + 2 q^{72} + 4 q^{73} - 14 q^{74} - 41 q^{75} - 3 q^{76} - q^{77} + 2 q^{78} + 2 q^{79} + 5 q^{80} - 17 q^{81} - 3 q^{82} + 7 q^{83} + 6 q^{85} - 5 q^{86} - 9 q^{87} - 3 q^{88} + 16 q^{89} + 3 q^{90} - 13 q^{91} + 2 q^{92} - 22 q^{93} - 5 q^{95} + q^{96} - 14 q^{97} - 6 q^{98} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 + 5 * q^5 + q^6 + q^7 + 3 * q^8 + 2 * q^9 + 5 * q^10 - 3 * q^11 + q^12 + 5 * q^13 + q^14 - 9 * q^15 + 3 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 5 * q^20 - 3 * q^22 + 2 * q^23 + q^24 + 4 * q^25 + 5 * q^26 - 2 * q^27 + q^28 + 7 * q^29 - 9 * q^30 - 3 * q^31 + 3 * q^32 - q^33 + 4 * q^34 + 2 * q^35 + 2 * q^36 - 14 * q^37 - 3 * q^38 + 2 * q^39 + 5 * q^40 - 3 * q^41 - 5 * q^43 - 3 * q^44 + 3 * q^45 + 2 * q^46 + q^48 - 6 * q^49 + 4 * q^50 + 2 * q^51 + 5 * q^52 - 16 * q^53 - 2 * q^54 - 5 * q^55 + q^56 - q^57 + 7 * q^58 - 12 * q^59 - 9 * q^60 + 6 * q^61 - 3 * q^62 - 14 * q^63 + 3 * q^64 + 8 * q^65 - q^66 + q^67 + 4 * q^68 + 2 * q^70 - 3 * q^71 + 2 * q^72 + 4 * q^73 - 14 * q^74 - 41 * q^75 - 3 * q^76 - q^77 + 2 * q^78 + 2 * q^79 + 5 * q^80 - 17 * q^81 - 3 * q^82 + 7 * q^83 + 6 * q^85 - 5 * q^86 - 9 * q^87 - 3 * q^88 + 16 * q^89 + 3 * q^90 - 13 * q^91 + 2 * q^92 - 22 * q^93 - 5 * q^95 + q^96 - 14 * q^97 - 6 * q^98 - 2 * q^99

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