LMFDB - Embedded newform 8027.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} +O(q^{10})$	\(q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} -10.2085 q^{10} -5.27584 q^{11} -13.1950 q^{12} -1.39263 q^{13} +0.217280 q^{14} -9.89583 q^{15} +11.8609 q^{16} +5.32569 q^{17} -9.80360 q^{18} -6.49744 q^{19} +19.5542 q^{20} +0.210626 q^{21} +14.0640 q^{22} +1.00000 q^{23} +21.3973 q^{24} +9.66503 q^{25} +3.71240 q^{26} -1.75104 q^{27} -0.416197 q^{28} +7.22284 q^{29} +26.3798 q^{30} +7.84095 q^{31} -15.0574 q^{32} +13.6333 q^{33} -14.1969 q^{34} -0.312135 q^{35} +18.7787 q^{36} +4.66717 q^{37} +17.3205 q^{38} +3.59871 q^{39} -31.7095 q^{40} -2.06103 q^{41} -0.561476 q^{42} +0.0993810 q^{43} -26.9395 q^{44} +14.0834 q^{45} -2.66575 q^{46} +0.534447 q^{47} -30.6498 q^{48} -6.99336 q^{49} -25.7645 q^{50} -13.7622 q^{51} -7.11106 q^{52} +0.809749 q^{53} +4.66784 q^{54} -20.2038 q^{55} +0.674916 q^{56} +16.7901 q^{57} -19.2543 q^{58} +11.8358 q^{59} -50.5301 q^{60} +5.44642 q^{61} -20.9020 q^{62} -0.299756 q^{63} +16.4175 q^{64} -5.33308 q^{65} -36.3430 q^{66} -1.74709 q^{67} +27.1940 q^{68} -2.58411 q^{69} +0.832073 q^{70} +8.14606 q^{71} -30.4519 q^{72} -1.58643 q^{73} -12.4415 q^{74} -24.9755 q^{75} -33.1772 q^{76} +0.430024 q^{77} -9.59326 q^{78} -8.81922 q^{79} +45.4212 q^{80} -6.50797 q^{81} +5.49418 q^{82} +3.59595 q^{83} +1.07550 q^{84} +20.3947 q^{85} -0.264924 q^{86} -18.6646 q^{87} +43.6857 q^{88} -6.68289 q^{89} -37.5428 q^{90} +0.113511 q^{91} +5.10620 q^{92} -20.2619 q^{93} -1.42470 q^{94} -24.8819 q^{95} +38.9100 q^{96} +6.48504 q^{97} +18.6425 q^{98} -19.4025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.66575	−1.88497	−0.942483	−	0.334253i	$-0.891516\pi$
$2$	−2.66575	−1.88497	−0.942483	+	0.334253i	$0.891516\pi$
$3$	−2.58411	−1.49194	−0.745968	−	0.665982i	$-0.768013\pi$
$3$	−2.58411	−1.49194	−0.745968	+	0.665982i	$0.768013\pi$
$4$	5.10620	2.55310
$5$	3.82950	1.71260	0.856301	−	0.516477i	$-0.172757\pi$
$5$	3.82950	1.71260	0.856301	+	0.516477i	$0.172757\pi$
$6$	6.88858	2.81225
$7$	−0.0815082	−0.0308072	−0.0154036	−	0.999881i	$-0.504903\pi$
$7$	−0.0815082	−0.0308072	−0.0154036	+	0.999881i	$0.504903\pi$
$8$	−8.28034	−2.92754
$9$	3.67762	1.22587
$10$	−10.2085	−3.22820
$11$	−5.27584	−1.59073	−0.795363	−	0.606134i	$-0.792720\pi$
$11$	−5.27584	−1.59073	−0.795363	+	0.606134i	$0.792720\pi$
$12$	−13.1950	−3.80906
$13$	−1.39263	−0.386247	−0.193123	−	0.981174i	$-0.561862\pi$
$13$	−1.39263	−0.386247	−0.193123	+	0.981174i	$0.561862\pi$
$14$	0.217280	0.0580706
$15$	−9.89583	−2.55509
$16$	11.8609	2.96522
$17$	5.32569	1.29167	0.645835	−	0.763477i	$-0.276509\pi$
$17$	5.32569	1.29167	0.645835	+	0.763477i	$0.276509\pi$
$18$	−9.80360	−2.31073
$19$	−6.49744	−1.49061	−0.745307	−	0.666721i	$-0.767697\pi$
$19$	−6.49744	−1.49061	−0.745307	+	0.666721i	$0.767697\pi$
$20$	19.5542	4.37245
$21$	0.210626	0.0459624
$22$	14.0640	2.99846
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	21.3973	4.36771
$25$	9.66503	1.93301
$26$	3.71240	0.728062
$27$	−1.75104	−0.336989
$28$	−0.416197	−0.0786539
$29$	7.22284	1.34125	0.670624	−	0.741798i	$-0.266026\pi$
$29$	7.22284	1.34125	0.670624	+	0.741798i	$0.266026\pi$
$30$	26.3798	4.81627
$31$	7.84095	1.40828	0.704138	−	0.710063i	$-0.251333\pi$
$31$	7.84095	1.40828	0.704138	+	0.710063i	$0.251333\pi$
$32$	−15.0574	−2.66180
$33$	13.6333	2.37326
$34$	−14.1969	−2.43475
$35$	−0.312135	−0.0527605
$36$	18.7787	3.12978
$37$	4.66717	0.767279	0.383639	−	0.923483i	$-0.374671\pi$
$37$	4.66717	0.767279	0.383639	+	0.923483i	$0.374671\pi$
$38$	17.3205	2.80976
$39$	3.59871	0.576256
$40$	−31.7095	−5.01372
$41$	−2.06103	−0.321879	−0.160939	−	0.986964i	$-0.551452\pi$
$41$	−2.06103	−0.321879	−0.160939	+	0.986964i	$0.551452\pi$
$42$	−0.561476	−0.0866376
$43$	0.0993810	0.0151555	0.00757773	−	0.999971i	$-0.497588\pi$
$43$	0.0993810	0.0151555	0.00757773	+	0.999971i	$0.497588\pi$
$44$	−26.9395	−4.06128
$45$	14.0834	2.09943
$46$	−2.66575	−0.393043
$47$	0.534447	0.0779571	0.0389786	−	0.999240i	$-0.487590\pi$
$47$	0.534447	0.0779571	0.0389786	+	0.999240i	$0.487590\pi$
$48$	−30.6498	−4.42392
$49$	−6.99336	−0.999051
$50$	−25.7645	−3.64365
$51$	−13.7622	−1.92709
$52$	−7.11106	−0.986127
$53$	0.809749	0.111228	0.0556138	−	0.998452i	$-0.482288\pi$
$53$	0.809749	0.111228	0.0556138	+	0.998452i	$0.482288\pi$
$54$	4.66784	0.635212
$55$	−20.2038	−2.72428
$56$	0.674916	0.0901894
$57$	16.7901	2.22390
$58$	−19.2543	−2.52821
$59$	11.8358	1.54089	0.770443	−	0.637509i	$-0.220035\pi$
$59$	11.8358	1.54089	0.770443	+	0.637509i	$0.220035\pi$
$60$	−50.5301	−6.52341
$61$	5.44642	0.697342	0.348671	−	0.937245i	$-0.386633\pi$
$61$	5.44642	0.697342	0.348671	+	0.937245i	$0.386633\pi$
$62$	−20.9020	−2.65456
$63$	−0.299756	−0.0377657
$64$	16.4175	2.05218
$65$	−5.33308	−0.661487
$66$	−36.3430	−4.47352
$67$	−1.74709	−0.213441	−0.106720	−	0.994289i	$-0.534035\pi$
$67$	−1.74709	−0.213441	−0.106720	+	0.994289i	$0.534035\pi$
$68$	27.1940	3.29776
$69$	−2.58411	−0.311090
$70$	0.832073	0.0994518
$71$	8.14606	0.966760	0.483380	−	0.875411i	$-0.339409\pi$
$71$	8.14606	0.966760	0.483380	+	0.875411i	$0.339409\pi$
$72$	−30.4519	−3.58880
$73$	−1.58643	−0.185677	−0.0928386	−	0.995681i	$-0.529594\pi$
$73$	−1.58643	−0.185677	−0.0928386	+	0.995681i	$0.529594\pi$
$74$	−12.4415	−1.44629
$75$	−24.9755	−2.88392
$76$	−33.1772	−3.80569
$77$	0.430024	0.0490058
$78$	−9.59326	−1.08622
$79$	−8.81922	−0.992240	−0.496120	−	0.868254i	$-0.665242\pi$
$79$	−8.81922	−0.992240	−0.496120	+	0.868254i	$0.665242\pi$
$80$	45.4212	5.07824
$81$	−6.50797	−0.723108
$82$	5.49418	0.606731
$83$	3.59595	0.394707	0.197353	−	0.980332i	$-0.436765\pi$
$83$	3.59595	0.394707	0.197353	+	0.980332i	$0.436765\pi$
$84$	1.07550	0.117347
$85$	20.3947	2.21212
$86$	−0.264924	−0.0285675
$87$	−18.6646	−2.00106
$88$	43.6857	4.65692
$89$	−6.68289	−0.708385	−0.354192	−	0.935173i	$-0.615244\pi$
$89$	−6.68289	−0.708385	−0.354192	+	0.935173i	$0.615244\pi$
$90$	−37.5428	−3.95736
$91$	0.113511	0.0118992
$92$	5.10620	0.532358
$93$	−20.2619	−2.10106
$94$	−1.42470	−0.146947
$95$	−24.8819	−2.55283
$96$	38.9100	3.97123
$97$	6.48504	0.658456	0.329228	−	0.944250i	$-0.393212\pi$
$97$	6.48504	0.658456	0.329228	+	0.944250i	$0.393212\pi$
$98$	18.6425	1.88318
$99$	−19.4025	−1.95003
$100$	49.3516	4.93516
$101$	−8.54543	−0.850302	−0.425151	−	0.905122i	$-0.639779\pi$
$101$	−8.54543	−0.850302	−0.425151	+	0.905122i	$0.639779\pi$
$102$	36.6864	3.63250
$103$	8.41543	0.829197	0.414599	−	0.910004i	$-0.363922\pi$
$103$	8.41543	0.829197	0.414599	+	0.910004i	$0.363922\pi$
$104$	11.5315	1.13075
$105$	0.806592	0.0787153
$106$	−2.15858	−0.209660
$107$	−5.20146	−0.502844	−0.251422	−	0.967878i	$-0.580898\pi$
$107$	−5.20146	−0.502844	−0.251422	+	0.967878i	$0.580898\pi$
$108$	−8.94118	−0.860365
$109$	0.741143	0.0709886	0.0354943	−	0.999370i	$-0.488699\pi$
$109$	0.741143	0.0709886	0.0354943	+	0.999370i	$0.488699\pi$
$110$	53.8582	5.13518
$111$	−12.0605	−1.14473
$112$	−0.966759	−0.0913501
$113$	−20.9429	−1.97015	−0.985073	−	0.172139i	$-0.944932\pi$
$113$	−20.9429	−1.97015	−0.985073	+	0.172139i	$0.944932\pi$
$114$	−44.7581	−4.19198
$115$	3.82950	0.357102
$116$	36.8813	3.42434
$117$	−5.12157	−0.473490
$118$	−31.5512	−2.90452
$119$	−0.434088	−0.0397927
$120$	81.9409	7.48014
$121$	16.8345	1.53041
$122$	−14.5188	−1.31447
$123$	5.32593	0.480223
$124$	40.0375	3.59547
$125$	17.8647	1.59787
$126$	0.799074	0.0711872
$127$	14.5128	1.28780	0.643900	−	0.765109i	$-0.277315\pi$
$127$	14.5128	1.28780	0.643900	+	0.765109i	$0.277315\pi$
$128$	−13.6500	−1.20650
$129$	−0.256811	−0.0226110
$130$	14.2166	1.24688
$131$	−18.2729	−1.59651	−0.798254	−	0.602321i	$-0.794243\pi$
$131$	−18.2729	−1.59651	−0.798254	+	0.602321i	$0.794243\pi$
$132$	69.6146	6.05917
$133$	0.529595	0.0459217
$134$	4.65730	0.402329
$135$	−6.70561	−0.577127
$136$	−44.0985	−3.78142
$137$	−3.15018	−0.269138	−0.134569	−	0.990904i	$-0.542965\pi$
$137$	−3.15018	−0.269138	−0.134569	+	0.990904i	$0.542965\pi$
$138$	6.88858	0.586395
$139$	0.471167	0.0399639	0.0199819	−	0.999800i	$-0.493639\pi$
$139$	0.471167	0.0399639	0.0199819	+	0.999800i	$0.493639\pi$
$140$	−1.59383	−0.134703
$141$	−1.38107	−0.116307
$142$	−21.7153	−1.82231
$143$	7.34731	0.614413
$144$	43.6198	3.63498
$145$	27.6598	2.29702
$146$	4.22901	0.349995
$147$	18.0716	1.49052
$148$	23.8315	1.95894
$149$	−20.5405	−1.68275	−0.841374	−	0.540454i	$-0.818253\pi$
$149$	−20.5405	−1.68275	−0.841374	+	0.540454i	$0.818253\pi$
$150$	66.5783	5.43610
$151$	11.1393	0.906500	0.453250	−	0.891383i	$-0.350264\pi$
$151$	11.1393	0.906500	0.453250	+	0.891383i	$0.350264\pi$
$152$	53.8010	4.36384
$153$	19.5859	1.58342
$154$	−1.14634	−0.0923743
$155$	30.0269	2.41182
$156$	18.3758	1.47124
$157$	14.9918	1.19648	0.598238	−	0.801318i	$-0.295868\pi$
$157$	14.9918	1.19648	0.598238	+	0.801318i	$0.295868\pi$
$158$	23.5098	1.87034
$159$	−2.09248	−0.165944
$160$	−57.6623	−4.55860
$161$	−0.0815082	−0.00642375
$162$	17.3486	1.36303
$163$	17.8388	1.39724	0.698622	−	0.715490i	$-0.253797\pi$
$163$	17.8388	1.39724	0.698622	+	0.715490i	$0.253797\pi$
$164$	−10.5240	−0.821789
$165$	52.2088	4.06445
$166$	−9.58589	−0.744010
$167$	8.80636	0.681457	0.340728	−	0.940162i	$-0.389326\pi$
$167$	8.80636	0.681457	0.340728	+	0.940162i	$0.389326\pi$
$168$	−1.74406	−0.134557
$169$	−11.0606	−0.850813
$170$	−54.3671	−4.16977
$171$	−23.8951	−1.82730
$172$	0.507459	0.0386934
$173$	12.1499	0.923741	0.461870	−	0.886947i	$-0.347179\pi$
$173$	12.1499	0.923741	0.461870	+	0.886947i	$0.347179\pi$
$174$	49.7551	3.77192
$175$	−0.787780	−0.0595505
$176$	−62.5761	−4.71685
$177$	−30.5849	−2.29890
$178$	17.8149	1.33528
$179$	−16.8562	−1.25989	−0.629946	−	0.776639i	$-0.716923\pi$
$179$	−16.8562	−1.25989	−0.629946	+	0.776639i	$0.716923\pi$
$180$	71.9128	5.36006
$181$	19.3918	1.44138	0.720692	−	0.693256i	$-0.243824\pi$
$181$	19.3918	1.44138	0.720692	+	0.693256i	$0.243824\pi$
$182$	−0.302591	−0.0224296
$183$	−14.0741	−1.04039
$184$	−8.28034	−0.610435
$185$	17.8729	1.31404
$186$	54.0130	3.96043
$187$	−28.0975	−2.05469
$188$	2.72899	0.199032
$189$	0.142724	0.0103817
$190$	66.3288	4.81200
$191$	−14.9036	−1.07839	−0.539193	−	0.842182i	$-0.681271\pi$
$191$	−14.9036	−1.07839	−0.539193	+	0.842182i	$0.681271\pi$
$192$	−42.4245	−3.06173
$193$	−10.5594	−0.760084	−0.380042	−	0.924969i	$-0.624090\pi$
$193$	−10.5594	−0.760084	−0.380042	+	0.924969i	$0.624090\pi$
$194$	−17.2875	−1.24117
$195$	13.7813	0.986897
$196$	−35.7095	−2.55068
$197$	12.4171	0.884683	0.442342	−	0.896847i	$-0.354148\pi$
$197$	12.4171	0.884683	0.442342	+	0.896847i	$0.354148\pi$
$198$	51.7222	3.67574
$199$	−13.7366	−0.973765	−0.486882	−	0.873467i	$-0.661866\pi$
$199$	−13.7366	−0.973765	−0.486882	+	0.873467i	$0.661866\pi$
$200$	−80.0298	−5.65896
$201$	4.51467	0.318440
$202$	22.7799	1.60279
$203$	−0.588721	−0.0413201
$204$	−70.2724	−4.92005
$205$	−7.89271	−0.551251
$206$	−22.4334	−1.56301
$207$	3.67762	0.255612
$208$	−16.5178	−1.14531
$209$	34.2794	2.37116
$210$	−2.15017	−0.148376
$211$	−23.0962	−1.59001	−0.795003	−	0.606606i	$-0.792531\pi$
$211$	−23.0962	−1.59001	−0.795003	+	0.606606i	$0.792531\pi$
$212$	4.13474	0.283975
$213$	−21.0503	−1.44234
$214$	13.8658	0.947845
$215$	0.380579	0.0259553
$216$	14.4992	0.986548
$217$	−0.639102	−0.0433851
$218$	−1.97570	−0.133811
$219$	4.09950	0.277018
$220$	−103.165	−6.95536
$221$	−7.41673	−0.498903
$222$	32.1502	2.15778
$223$	−25.5626	−1.71180	−0.855900	−	0.517141i	$-0.826996\pi$
$223$	−25.5626	−1.71180	−0.855900	+	0.517141i	$0.826996\pi$
$224$	1.22730	0.0820026
$225$	35.5443	2.36962
$226$	55.8285	3.71366
$227$	−8.14130	−0.540357	−0.270179	−	0.962810i	$-0.587083\pi$
$227$	−8.14130	−0.540357	−0.270179	+	0.962810i	$0.587083\pi$
$228$	85.7335	5.67784
$229$	11.9423	0.789168	0.394584	−	0.918860i	$-0.370889\pi$
$229$	11.9423	0.789168	0.394584	+	0.918860i	$0.370889\pi$
$230$	−10.2085	−0.673126
$231$	−1.11123	−0.0731135
$232$	−59.8076	−3.92656
$233$	3.34280	0.218994	0.109497	−	0.993987i	$-0.465076\pi$
$233$	3.34280	0.218994	0.109497	+	0.993987i	$0.465076\pi$
$234$	13.6528	0.892512
$235$	2.04666	0.133510
$236$	60.4358	3.93404
$237$	22.7898	1.48036
$238$	1.15717	0.0750080
$239$	−21.4295	−1.38616	−0.693079	−	0.720861i	$-0.743747\pi$
$239$	−21.4295	−1.38616	−0.693079	+	0.720861i	$0.743747\pi$
$240$	−117.373	−7.57641
$241$	15.4937	0.998040	0.499020	−	0.866591i	$-0.333693\pi$
$241$	15.4937	0.998040	0.499020	+	0.866591i	$0.333693\pi$
$242$	−44.8764	−2.88477
$243$	22.0704	1.41582
$244$	27.8105	1.78038
$245$	−26.7810	−1.71098
$246$	−14.1976	−0.905204
$247$	9.04854	0.575745
$248$	−64.9258	−4.12279
$249$	−9.29233	−0.588878
$250$	−47.6228	−3.01193
$251$	10.8668	0.685904	0.342952	−	0.939353i	$-0.388573\pi$
$251$	10.8668	0.685904	0.342952	+	0.939353i	$0.388573\pi$
$252$	−1.53062	−0.0964197
$253$	−5.27584	−0.331689
$254$	−38.6874	−2.42746
$255$	−52.7022	−3.30034
$256$	3.55241	0.222025
$257$	−19.5127	−1.21717	−0.608584	−	0.793489i	$-0.708262\pi$
$257$	−19.5127	−1.21717	−0.608584	+	0.793489i	$0.708262\pi$
$258$	0.684594	0.0426209
$259$	−0.380413	−0.0236377
$260$	−27.2318	−1.68884
$261$	26.5629	1.64420
$262$	48.7108	3.00937
$263$	−13.6333	−0.840665	−0.420333	−	0.907370i	$-0.638087\pi$
$263$	−13.6333	−0.840665	−0.420333	+	0.907370i	$0.638087\pi$
$264$	−112.889	−6.94782
$265$	3.10093	0.190489
$266$	−1.41176	−0.0865608
$267$	17.2693	1.05687
$268$	−8.92099	−0.544936
$269$	24.2554	1.47888	0.739440	−	0.673223i	$-0.235090\pi$
$269$	24.2554	1.47888	0.739440	+	0.673223i	$0.235090\pi$
$270$	17.8755	1.08787
$271$	−15.1768	−0.921923	−0.460962	−	0.887420i	$-0.652495\pi$
$271$	−15.1768	−0.921923	−0.460962	+	0.887420i	$0.652495\pi$
$272$	63.1674	3.83008
$273$	−0.293325	−0.0177528
$274$	8.39758	0.507316
$275$	−50.9912	−3.07488
$276$	−13.1950	−0.794244
$277$	−5.34590	−0.321204	−0.160602	−	0.987019i	$-0.551344\pi$
$277$	−5.34590	−0.321204	−0.160602	+	0.987019i	$0.551344\pi$
$278$	−1.25601	−0.0753306
$279$	28.8360	1.72637
$280$	2.58459	0.154459
$281$	31.1392	1.85761	0.928806	−	0.370567i	$-0.120837\pi$
$281$	31.1392	1.85761	0.928806	+	0.370567i	$0.120837\pi$
$282$	3.68158	0.219235
$283$	4.75351	0.282567	0.141284	−	0.989969i	$-0.454877\pi$
$283$	4.75351	0.282567	0.141284	+	0.989969i	$0.454877\pi$
$284$	41.5954	2.46823
$285$	64.2976	3.80866
$286$	−19.5860	−1.15815
$287$	0.167991	0.00991619
$288$	−55.3754	−3.26303
$289$	11.3630	0.668411
$290$	−73.7341	−4.32981
$291$	−16.7580	−0.982374
$292$	−8.10061	−0.474052
$293$	17.1833	1.00386	0.501931	−	0.864908i	$-0.332623\pi$
$293$	17.1833	1.00386	0.501931	+	0.864908i	$0.332623\pi$
$294$	−48.1743	−2.80958
$295$	45.3250	2.63893
$296$	−38.6458	−2.24624
$297$	9.23822	0.536056
$298$	54.7559	3.17192
$299$	−1.39263	−0.0805380
$300$	−127.530	−7.36294
$301$	−0.00810037	−0.000466897 0
$302$	−29.6944	−1.70872
$303$	22.0823	1.26860
$304$	−77.0653	−4.42000
$305$	20.8570	1.19427
$306$	−52.2109	−2.98470
$307$	5.60189	0.319717	0.159858	−	0.987140i	$-0.448896\pi$
$307$	5.60189	0.319717	0.159858	+	0.987140i	$0.448896\pi$
$308$	2.19579	0.125117
$309$	−21.7464	−1.23711
$310$	−80.0441	−4.54620
$311$	12.0853	0.685292	0.342646	−	0.939465i	$-0.388677\pi$
$311$	12.0853	0.685292	0.342646	+	0.939465i	$0.388677\pi$
$312$	−29.7986	−1.68701
$313$	18.4171	1.04099	0.520497	−	0.853864i	$-0.325747\pi$
$313$	18.4171	1.04099	0.520497	+	0.853864i	$0.325747\pi$
$314$	−39.9644	−2.25532
$315$	−1.14792	−0.0646777
$316$	−45.0327	−2.53329
$317$	2.65768	0.149270	0.0746352	−	0.997211i	$-0.476221\pi$
$317$	2.65768	0.149270	0.0746352	+	0.997211i	$0.476221\pi$
$318$	5.57802	0.312800
$319$	−38.1065	−2.13356
$320$	62.8706	3.51457
$321$	13.4411	0.750211
$322$	0.217280	0.0121086
$323$	−34.6033	−1.92538
$324$	−33.2310	−1.84617
$325$	−13.4598	−0.746618
$326$	−47.5538	−2.63376
$327$	−1.91519	−0.105910
$328$	17.0660	0.942314
$329$	−0.0435618	−0.00240164
$330$	−139.175	−7.66136
$331$	3.65090	0.200672	0.100336	−	0.994954i	$-0.468008\pi$
$331$	3.65090	0.200672	0.100336	+	0.994954i	$0.468008\pi$
$332$	18.3616	1.00773
$333$	17.1641	0.940586
$334$	−23.4755	−1.28452
$335$	−6.69047	−0.365539
$336$	2.49821	0.136289
$337$	21.9355	1.19490	0.597450	−	0.801906i	$-0.296180\pi$
$337$	21.9355	1.19490	0.597450	+	0.801906i	$0.296180\pi$
$338$	29.4847	1.60376
$339$	54.1188	2.93933
$340$	104.139	5.64776
$341$	−41.3676	−2.24018
$342$	63.6983	3.44441
$343$	1.14057	0.0615852
$344$	−0.822908	−0.0443682
$345$	−9.89583	−0.532774
$346$	−32.3886	−1.74122
$347$	−1.93887	−0.104084	−0.0520420	−	0.998645i	$-0.516573\pi$
$347$	−1.93887	−0.104084	−0.0520420	+	0.998645i	$0.516573\pi$
$348$	−95.3052	−5.10890
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	2.10002	0.112251
$351$	2.43856	0.130161
$352$	79.4405	4.23419
$353$	14.3814	0.765444	0.382722	−	0.923864i	$-0.374987\pi$
$353$	14.3814	0.765444	0.382722	+	0.923864i	$0.374987\pi$
$354$	81.5316	4.33336
$355$	31.1953	1.65568
$356$	−34.1242	−1.80858
$357$	1.12173	0.0593682
$358$	44.9343	2.37485
$359$	−9.04464	−0.477358	−0.238679	−	0.971099i	$-0.576714\pi$
$359$	−9.04464	−0.477358	−0.238679	+	0.971099i	$0.576714\pi$
$360$	−116.616	−6.14618
$361$	23.2167	1.22193
$362$	−51.6937	−2.71696
$363$	−43.5021	−2.28327
$364$	0.579610	0.0303798
$365$	−6.07521	−0.317991
$366$	37.5181	1.96110
$367$	−4.46087	−0.232855	−0.116428	−	0.993199i	$-0.537144\pi$
$367$	−4.46087	−0.232855	−0.116428	+	0.993199i	$0.537144\pi$
$368$	11.8609	0.618291
$369$	−7.57969	−0.394583
$370$	−47.6447	−2.47693
$371$	−0.0660012	−0.00342661
$372$	−103.461	−5.36421
$373$	30.2512	1.56635	0.783175	−	0.621801i	$-0.213599\pi$
$373$	30.2512	1.56635	0.783175	+	0.621801i	$0.213599\pi$
$374$	74.9008	3.87303
$375$	−46.1644	−2.38392
$376$	−4.42540	−0.228223
$377$	−10.0588	−0.518053
$378$	−0.380467	−0.0195691
$379$	−24.9774	−1.28300	−0.641501	−	0.767122i	$-0.721688\pi$
$379$	−24.9774	−1.28300	−0.641501	+	0.767122i	$0.721688\pi$
$380$	−127.052	−6.51763
$381$	−37.5026	−1.92132
$382$	39.7292	2.03272
$383$	33.1013	1.69140	0.845700	−	0.533659i	$-0.179183\pi$
$383$	33.1013	1.69140	0.845700	+	0.533659i	$0.179183\pi$
$384$	35.2730	1.80002
$385$	1.64678	0.0839275
$386$	28.1487	1.43273
$387$	0.365485	0.0185787
$388$	33.1139	1.68110
$389$	−15.0250	−0.761799	−0.380900	−	0.924616i	$-0.624386\pi$
$389$	−15.0250	−0.761799	−0.380900	+	0.924616i	$0.624386\pi$
$390$	−36.7373	−1.86027
$391$	5.32569	0.269332
$392$	57.9074	2.92476
$393$	47.2191	2.38189
$394$	−33.1009	−1.66760
$395$	−33.7732	−1.69931
$396$	−99.0732	−4.97862
$397$	1.40240	0.0703846	0.0351923	−	0.999381i	$-0.488796\pi$
$397$	1.40240	0.0703846	0.0351923	+	0.999381i	$0.488796\pi$
$398$	36.6184	1.83551
$399$	−1.36853	−0.0685122
$400$	114.636	5.73179
$401$	13.5860	0.678450	0.339225	−	0.940705i	$-0.389835\pi$
$401$	13.5860	0.678450	0.339225	+	0.940705i	$0.389835\pi$
$402$	−12.0350	−0.600249
$403$	−10.9196	−0.543942
$404$	−43.6347	−2.17091
$405$	−24.9222	−1.23840
$406$	1.56938	0.0778870
$407$	−24.6233	−1.22053
$408$	113.955	5.64163
$409$	−25.0607	−1.23917	−0.619587	−	0.784928i	$-0.712700\pi$
$409$	−25.0607	−1.23917	−0.619587	+	0.784928i	$0.712700\pi$
$410$	21.0400	1.03909
$411$	8.14041	0.401537
$412$	42.9709	2.11702
$413$	−0.964713	−0.0474704
$414$	−9.80360	−0.481821
$415$	13.7707	0.675976
$416$	20.9694	1.02811
$417$	−1.21755	−0.0596235
$418$	−91.3803	−4.46955
$419$	2.43725	0.119068	0.0595338	−	0.998226i	$-0.481039\pi$
$419$	2.43725	0.119068	0.0595338	+	0.998226i	$0.481039\pi$
$420$	4.11862	0.200968
$421$	32.1163	1.56525	0.782625	−	0.622493i	$-0.213880\pi$
$421$	32.1163	1.56525	0.782625	+	0.622493i	$0.213880\pi$
$422$	61.5685	2.99711
$423$	1.96549	0.0955656
$424$	−6.70499	−0.325623
$425$	51.4730	2.49681
$426$	56.1148	2.71877
$427$	−0.443928	−0.0214832
$428$	−26.5597	−1.28381
$429$	−18.9862	−0.916664
$430$	−1.01453	−0.0489248
$431$	19.0155	0.915943	0.457971	−	0.888967i	$-0.348576\pi$
$431$	19.0155	0.915943	0.457971	+	0.888967i	$0.348576\pi$
$432$	−20.7689	−0.999245
$433$	23.3980	1.12444	0.562218	−	0.826989i	$-0.309948\pi$
$433$	23.3980	1.12444	0.562218	+	0.826989i	$0.309948\pi$
$434$	1.70368	0.0817794
$435$	−71.4760	−3.42701
$436$	3.78442	0.181241
$437$	−6.49744	−0.310815
$438$	−10.9282	−0.522171
$439$	−9.87946	−0.471521	−0.235760	−	0.971811i	$-0.575758\pi$
$439$	−9.87946	−0.471521	−0.235760	+	0.971811i	$0.575758\pi$
$440$	167.294	7.97544
$441$	−25.7189	−1.22471
$442$	19.7711	0.940416
$443$	30.0851	1.42938	0.714692	−	0.699439i	$-0.246567\pi$
$443$	30.0851	1.42938	0.714692	+	0.699439i	$0.246567\pi$
$444$	−61.5833	−2.92261
$445$	−25.5921	−1.21318
$446$	68.1435	3.22669
$447$	53.0790	2.51055
$448$	−1.33816	−0.0632220
$449$	−40.7064	−1.92105	−0.960526	−	0.278190i	$-0.910265\pi$
$449$	−40.7064	−1.92105	−0.960526	+	0.278190i	$0.910265\pi$
$450$	−94.7521	−4.46666
$451$	10.8737	0.512021
$452$	−106.939	−5.02998
$453$	−28.7851	−1.35244
$454$	21.7026	1.01856
$455$	0.434690	0.0203786
$456$	−139.028	−6.51057
$457$	1.61931	0.0757479	0.0378740	−	0.999283i	$-0.487941\pi$
$457$	1.61931	0.0757479	0.0378740	+	0.999283i	$0.487941\pi$
$458$	−31.8351	−1.48756
$459$	−9.32552	−0.435278
$460$	19.5542	0.911718
$461$	−21.2793	−0.991077	−0.495539	−	0.868586i	$-0.665029\pi$
$461$	−21.2793	−0.991077	−0.495539	+	0.868586i	$0.665029\pi$
$462$	2.96226	0.137817
$463$	−7.43494	−0.345531	−0.172766	−	0.984963i	$-0.555270\pi$
$463$	−7.43494	−0.345531	−0.172766	+	0.984963i	$0.555270\pi$
$464$	85.6692	3.97709
$465$	−77.5928	−3.59828
$466$	−8.91105	−0.412797
$467$	−4.86079	−0.224930	−0.112465	−	0.993656i	$-0.535875\pi$
$467$	−4.86079	−0.224930	−0.112465	+	0.993656i	$0.535875\pi$
$468$	−26.1518	−1.20887
$469$	0.142402	0.00657552
$470$	−5.45588	−0.251661
$471$	−38.7405	−1.78507
$472$	−98.0042	−4.51101
$473$	−0.524318	−0.0241082
$474$	−60.7519	−2.79043
$475$	−62.7980	−2.88137
$476$	−2.21654	−0.101595
$477$	2.97795	0.136351
$478$	57.1256	2.61286
$479$	−20.9271	−0.956185	−0.478092	−	0.878310i	$-0.658672\pi$
$479$	−20.9271	−0.956185	−0.478092	+	0.878310i	$0.658672\pi$
$480$	149.006	6.80114
$481$	−6.49966	−0.296359
$482$	−41.3024	−1.88127
$483$	0.210626	0.00958382
$484$	85.9602	3.90728
$485$	24.8344	1.12767
$486$	−58.8342	−2.66877
$487$	34.1201	1.54613	0.773064	−	0.634327i	$-0.218723\pi$
$487$	34.1201	1.54613	0.773064	+	0.634327i	$0.218723\pi$
$488$	−45.0982	−2.04150
$489$	−46.0975	−2.08460
$490$	71.3914	3.22513
$491$	−30.3656	−1.37038	−0.685191	−	0.728363i	$-0.740281\pi$
$491$	−30.3656	−1.37038	−0.685191	+	0.728363i	$0.740281\pi$
$492$	27.1953	1.22606
$493$	38.4666	1.73245
$494$	−24.1211	−1.08526
$495$	−74.3019	−3.33962
$496$	93.0006	4.17585
$497$	−0.663971	−0.0297832
$498$	24.7710	1.11001
$499$	29.8874	1.33794	0.668972	−	0.743288i	$-0.266735\pi$
$499$	29.8874	1.33794	0.668972	+	0.743288i	$0.266735\pi$
$500$	91.2209	4.07952
$501$	−22.7566	−1.01669
$502$	−28.9680	−1.29291
$503$	5.00538	0.223179	0.111589	−	0.993754i	$-0.464406\pi$
$503$	5.00538	0.223179	0.111589	+	0.993754i	$0.464406\pi$
$504$	2.48208	0.110561
$505$	−32.7247	−1.45623
$506$	14.0640	0.625223
$507$	28.5817	1.26936
$508$	74.1051	3.28788
$509$	−15.1497	−0.671500	−0.335750	−	0.941951i	$-0.608990\pi$
$509$	−15.1497	−0.671500	−0.335750	+	0.941951i	$0.608990\pi$
$510$	140.491	6.22103
$511$	0.129307	0.00572019
$512$	17.8301	0.787987
$513$	11.3773	0.502320
$514$	52.0159	2.29432
$515$	32.2269	1.42009
$516$	−1.31133	−0.0577281
$517$	−2.81966	−0.124008
$518$	1.01408	0.0445563
$519$	−31.3967	−1.37816
$520$	44.1597	1.93653
$521$	−6.42035	−0.281280	−0.140640	−	0.990061i	$-0.544916\pi$
$521$	−6.42035	−0.281280	−0.140640	+	0.990061i	$0.544916\pi$
$522$	−70.8098	−3.09926
$523$	10.8136	0.472844	0.236422	−	0.971650i	$-0.424025\pi$
$523$	10.8136	0.472844	0.236422	+	0.971650i	$0.424025\pi$
$524$	−93.3050	−4.07605
$525$	2.03571	0.0888456
$526$	36.3429	1.58463
$527$	41.7585	1.81903
$528$	161.703	7.03724
$529$	1.00000	0.0434783
$530$	−8.26629	−0.359065
$531$	43.5275	1.88893
$532$	2.70422	0.117243
$533$	2.87026	0.124325
$534$	−46.0356	−1.99216
$535$	−19.9190	−0.861172
$536$	14.4665	0.624857
$537$	43.5583	1.87968
$538$	−64.6588	−2.78764
$539$	36.8958	1.58922
$540$	−34.2402	−1.47346
$541$	40.6434	1.74740	0.873698	−	0.486468i	$-0.161715\pi$
$541$	40.6434	1.74740	0.873698	+	0.486468i	$0.161715\pi$
$542$	40.4574	1.73780
$543$	−50.1106	−2.15045
$544$	−80.1911	−3.43817
$545$	2.83820	0.121575
$546$	0.781929	0.0334635
$547$	−20.8107	−0.889803	−0.444902	−	0.895580i	$-0.646761\pi$
$547$	−20.8107	−0.889803	−0.444902	+	0.895580i	$0.646761\pi$
$548$	−16.0854	−0.687136
$549$	20.0298	0.854853
$550$	135.929	5.79605
$551$	−46.9300	−1.99928
$552$	21.3973	0.910730
$553$	0.718839	0.0305682
$554$	14.2508	0.605459
$555$	−46.1856	−1.96047
$556$	2.40587	0.102032
$557$	−1.62632	−0.0689095	−0.0344548	−	0.999406i	$-0.510969\pi$
$557$	−1.62632	−0.0689095	−0.0344548	+	0.999406i	$0.510969\pi$
$558$	−76.8696	−3.25415
$559$	−0.138401	−0.00585375
$560$	−3.70220	−0.156446
$561$	72.6070	3.06547
$562$	−83.0093	−3.50154
$563$	28.8410	1.21550	0.607751	−	0.794127i	$-0.292072\pi$
$563$	28.8410	1.21550	0.607751	+	0.794127i	$0.292072\pi$
$564$	−7.05202	−0.296944
$565$	−80.2009	−3.37408
$566$	−12.6717	−0.532629
$567$	0.530453	0.0222769
$568$	−67.4522	−2.83023
$569$	4.55057	0.190770	0.0953850	−	0.995440i	$-0.469592\pi$
$569$	4.55057	0.190770	0.0953850	+	0.995440i	$0.469592\pi$
$570$	−171.401	−7.17920
$571$	25.7621	1.07811	0.539054	−	0.842271i	$-0.318782\pi$
$571$	25.7621	1.07811	0.539054	+	0.842271i	$0.318782\pi$
$572$	37.5168	1.56866
$573$	38.5125	1.60888
$574$	−0.447821	−0.0186917
$575$	9.66503	0.403060
$576$	60.3772	2.51572
$577$	6.44218	0.268192	0.134096	−	0.990968i	$-0.457187\pi$
$577$	6.44218	0.268192	0.134096	+	0.990968i	$0.457187\pi$
$578$	−30.2908	−1.25993
$579$	27.2867	1.13400
$580$	141.237	5.86453
$581$	−0.293100	−0.0121598
$582$	44.6727	1.85174
$583$	−4.27210	−0.176932
$584$	13.1361	0.543578
$585$	−19.6130	−0.810899
$586$	−45.8064	−1.89225
$587$	36.4265	1.50348	0.751741	−	0.659458i	$-0.229214\pi$
$587$	36.4265	1.50348	0.751741	+	0.659458i	$0.229214\pi$
$588$	92.2772	3.80545
$589$	−50.9461	−2.09920
$590$	−120.825	−4.97429
$591$	−32.0872	−1.31989
$592$	55.3568	2.27515
$593$	−45.2862	−1.85968	−0.929841	−	0.367961i	$-0.880056\pi$
$593$	−45.2862	−1.85968	−0.929841	+	0.367961i	$0.880056\pi$
$594$	−24.6268	−1.01045
$595$	−1.66234	−0.0681491
$596$	−104.884	−4.29622
$597$	35.4970	1.45280
$598$	3.71240	0.151812
$599$	20.4669	0.836253	0.418127	−	0.908389i	$-0.362687\pi$
$599$	20.4669	0.836253	0.418127	+	0.908389i	$0.362687\pi$
$600$	206.806	8.44281
$601$	15.1597	0.618377	0.309188	−	0.951001i	$-0.399943\pi$
$601$	15.1597	0.618377	0.309188	+	0.951001i	$0.399943\pi$
$602$	0.0215935	0.000880086 0
$603$	−6.42513	−0.261652
$604$	56.8793	2.31439
$605$	64.4676	2.62098
$606$	−58.8659	−2.39126
$607$	−11.2314	−0.455869	−0.227934	−	0.973677i	$-0.573197\pi$
$607$	−11.2314	−0.455869	−0.227934	+	0.973677i	$0.573197\pi$
$608$	97.8346	3.96772
$609$	1.52132	0.0616469
$610$	−55.5995	−2.25116
$611$	−0.744289	−0.0301107
$612$	100.009	4.04264
$613$	41.0310	1.65723	0.828613	−	0.559822i	$-0.189131\pi$
$613$	41.0310	1.65723	0.828613	+	0.559822i	$0.189131\pi$
$614$	−14.9332	−0.602656
$615$	20.3956	0.822431
$616$	−3.56075	−0.143467
$617$	−25.4016	−1.02263	−0.511314	−	0.859394i	$-0.670841\pi$
$617$	−25.4016	−1.02263	−0.511314	+	0.859394i	$0.670841\pi$
$618$	57.9704	2.33191
$619$	−38.2963	−1.53926	−0.769629	−	0.638491i	$-0.779559\pi$
$619$	−38.2963	−1.53926	−0.769629	+	0.638491i	$0.779559\pi$
$620$	153.323	6.15761
$621$	−1.75104	−0.0702670
$622$	−32.2162	−1.29175
$623$	0.544710	0.0218234
$624$	42.6839	1.70872
$625$	20.0877	0.803509
$626$	−49.0952	−1.96224
$627$	−88.5818	−3.53762
$628$	76.5512	3.05473
$629$	24.8559	0.991071
$630$	3.06005	0.121915
$631$	13.9775	0.556436	0.278218	−	0.960518i	$-0.410256\pi$
$631$	13.9775	0.556436	0.278218	+	0.960518i	$0.410256\pi$
$632$	73.0262	2.90483
$633$	59.6830	2.37219
$634$	−7.08471	−0.281370
$635$	55.5766	2.20549
$636$	−10.6846	−0.423673
$637$	9.73918	0.385880
$638$	101.582	4.02168
$639$	29.9581	1.18513
$640$	−52.2725	−2.06625
$641$	−32.2541	−1.27396	−0.636979	−	0.770881i	$-0.719816\pi$
$641$	−32.2541	−1.27396	−0.636979	+	0.770881i	$0.719816\pi$
$642$	−35.8307	−1.41412
$643$	−14.3131	−0.564452	−0.282226	−	0.959348i	$-0.591073\pi$
$643$	−14.3131	−0.564452	−0.282226	+	0.959348i	$0.591073\pi$
$644$	−0.416197	−0.0164005
$645$	−0.983458	−0.0387236
$646$	92.2437	3.62928
$647$	13.9962	0.550246	0.275123	−	0.961409i	$-0.411281\pi$
$647$	13.9962	0.550246	0.275123	+	0.961409i	$0.411281\pi$
$648$	53.8882	2.11693
$649$	−62.4436	−2.45113
$650$	35.8805	1.40735
$651$	1.65151	0.0647278
$652$	91.0886	3.56731
$653$	16.8225	0.658316	0.329158	−	0.944275i	$-0.393235\pi$
$653$	16.8225	0.658316	0.329158	+	0.944275i	$0.393235\pi$
$654$	5.10542	0.199638
$655$	−69.9759	−2.73418
$656$	−24.4456	−0.954442
$657$	−5.83427	−0.227617
$658$	0.116125	0.00452702
$659$	3.48427	0.135728	0.0678640	−	0.997695i	$-0.478382\pi$
$659$	3.48427	0.135728	0.0678640	+	0.997695i	$0.478382\pi$
$660$	266.589	10.3770
$661$	44.8868	1.74589	0.872947	−	0.487815i	$-0.162206\pi$
$661$	44.8868	1.74589	0.872947	+	0.487815i	$0.162206\pi$
$662$	−9.73237	−0.378259
$663$	19.1656	0.744332
$664$	−29.7757	−1.15552
$665$	2.02808	0.0786456
$666$	−45.7551	−1.77297
$667$	7.22284	0.279669
$668$	44.9671	1.73983
$669$	66.0566	2.55390
$670$	17.8351	0.689030
$671$	−28.7344	−1.10928
$672$	−3.17148	−0.122343
$673$	27.0875	1.04415	0.522073	−	0.852901i	$-0.325159\pi$
$673$	27.0875	1.04415	0.522073	+	0.852901i	$0.325159\pi$
$674$	−58.4744	−2.25235
$675$	−16.9239	−0.651401
$676$	−56.4775	−2.17221
$677$	−24.1492	−0.928129	−0.464064	−	0.885802i	$-0.653609\pi$
$677$	−24.1492	−0.928129	−0.464064	+	0.885802i	$0.653609\pi$
$678$	−144.267	−5.54054
$679$	−0.528584	−0.0202852
$680$	−168.875	−6.47606
$681$	21.0380	0.806178
$682$	110.276	4.22267
$683$	34.9350	1.33675	0.668376	−	0.743824i	$-0.266990\pi$
$683$	34.9350	1.33675	0.668376	+	0.743824i	$0.266990\pi$
$684$	−122.013	−4.66529
$685$	−12.0636	−0.460926
$686$	−3.04048	−0.116086
$687$	−30.8602	−1.17739
$688$	1.17875	0.0449393
$689$	−1.12768	−0.0429613
$690$	26.3798	1.00426
$691$	18.3266	0.697178	0.348589	−	0.937276i	$-0.386661\pi$
$691$	18.3266	0.697178	0.348589	+	0.937276i	$0.386661\pi$
$692$	62.0399	2.35840
$693$	1.58147	0.0600749
$694$	5.16854	0.196195
$695$	1.80433	0.0684422
$696$	154.549	5.85818
$697$	−10.9764	−0.415761
$698$	2.66575	0.100900
$699$	−8.63816	−0.326725
$700$	−4.02256	−0.152039
$701$	33.1286	1.25125	0.625626	−	0.780123i	$-0.284844\pi$
$701$	33.1286	1.25125	0.625626	+	0.780123i	$0.284844\pi$
$702$	−6.50058	−0.245349
$703$	−30.3247	−1.14372
$704$	−86.6159	−3.26446
$705$	−5.28880	−0.199188
$706$	−38.3371	−1.44284
$707$	0.696523	0.0261954
$708$	−156.173	−5.86933
$709$	26.3230	0.988580	0.494290	−	0.869297i	$-0.335428\pi$
$709$	26.3230	0.988580	0.494290	+	0.869297i	$0.335428\pi$
$710$	−83.1588	−3.12089
$711$	−32.4338	−1.21636
$712$	55.3366	2.07383
$713$	7.84095	0.293646
$714$	−2.99025	−0.111907
$715$	28.1365	1.05224
$716$	−86.0711	−3.21663
$717$	55.3762	2.06806
$718$	24.1107	0.899804
$719$	47.8069	1.78290	0.891448	−	0.453123i	$-0.149690\pi$
$719$	47.8069	1.78290	0.891448	+	0.453123i	$0.149690\pi$
$720$	167.042	6.22528
$721$	−0.685927	−0.0255453
$722$	−61.8898	−2.30330
$723$	−40.0375	−1.48901
$724$	99.0185	3.68000
$725$	69.8090	2.59264
$726$	115.966	4.30389
$727$	−42.4811	−1.57554	−0.787769	−	0.615971i	$-0.788764\pi$
$727$	−42.4811	−1.57554	−0.787769	+	0.615971i	$0.788764\pi$
$728$	−0.939910	−0.0348354
$729$	−37.5085	−1.38920
$730$	16.1950	0.599403
$731$	0.529272	0.0195758
$732$	−71.8653	−2.65622
$733$	33.4133	1.23415	0.617075	−	0.786905i	$-0.288318\pi$
$733$	33.4133	1.23415	0.617075	+	0.786905i	$0.288318\pi$
$734$	11.8915	0.438925
$735$	69.2051	2.55267
$736$	−15.0574	−0.555023
$737$	9.21736	0.339526
$738$	20.2055	0.743776
$739$	48.5329	1.78531	0.892656	−	0.450738i	$-0.148839\pi$
$739$	48.5329	1.78531	0.892656	+	0.450738i	$0.148839\pi$
$740$	91.2627	3.35488
$741$	−23.3824	−0.858975
$742$	0.175942	0.00645905
$743$	−17.3928	−0.638081	−0.319040	−	0.947741i	$-0.603361\pi$
$743$	−17.3928	−0.638081	−0.319040	+	0.947741i	$0.603361\pi$
$744$	167.775	6.15094
$745$	−78.6599	−2.88188
$746$	−80.6421	−2.95252
$747$	13.2245	0.483861
$748$	−143.471	−5.24583
$749$	0.423962	0.0154912
$750$	123.063	4.49361
$751$	4.51639	0.164805	0.0824027	−	0.996599i	$-0.473741\pi$
$751$	4.51639	0.164805	0.0824027	+	0.996599i	$0.473741\pi$
$752$	6.33901	0.231160
$753$	−28.0809	−1.02332
$754$	26.8141	0.976512
$755$	42.6577	1.55247
$756$	0.728780	0.0265055
$757$	−6.38700	−0.232139	−0.116070	−	0.993241i	$-0.537030\pi$
$757$	−6.38700	−0.232139	−0.116070	+	0.993241i	$0.537030\pi$
$758$	66.5833	2.41842
$759$	13.6333	0.494859
$760$	206.031	7.47352
$761$	−35.0503	−1.27057	−0.635286	−	0.772277i	$-0.719118\pi$
$761$	−35.0503	−1.27057	−0.635286	+	0.772277i	$0.719118\pi$
$762$	99.9724	3.62162
$763$	−0.0604092	−0.00218696
$764$	−76.1007	−2.75323
$765$	75.0040	2.71177
$766$	−88.2398	−3.18823
$767$	−16.4829	−0.595162
$768$	−9.17980	−0.331248
$769$	−5.95980	−0.214916	−0.107458	−	0.994210i	$-0.534271\pi$
$769$	−5.95980	−0.214916	−0.107458	+	0.994210i	$0.534271\pi$
$770$	−4.38989	−0.158200
$771$	50.4230	1.81594
$772$	−53.9185	−1.94057
$773$	−0.385305	−0.0138584	−0.00692922	−	0.999976i	$-0.502206\pi$
$773$	−0.385305	−0.0138584	−0.00692922	+	0.999976i	$0.502206\pi$
$774$	−0.974291	−0.0350202
$775$	75.7831	2.72221
$776$	−53.6983	−1.92766
$777$	0.983029	0.0352660
$778$	40.0529	1.43597
$779$	13.3914	0.479797
$780$	70.3699	2.51965
$781$	−42.9773	−1.53785
$782$	−14.1969	−0.507681
$783$	−12.6475	−0.451985
$784$	−82.9474	−2.96241
$785$	57.4111	2.04909
$786$	−125.874	−4.48978
$787$	−7.84030	−0.279476	−0.139738	−	0.990188i	$-0.544626\pi$
$787$	−7.84030	−0.279476	−0.139738	+	0.990188i	$0.544626\pi$
$788$	63.4043	2.25868
$789$	35.2299	1.25422
$790$	90.0307	3.20315
$791$	1.70702	0.0606947
$792$	160.660	5.70879
$793$	−7.58486	−0.269346
$794$	−3.73845	−0.132673
$795$	−8.01314	−0.284197
$796$	−70.1421	−2.48612
$797$	−44.1213	−1.56286	−0.781428	−	0.623995i	$-0.785508\pi$
$797$	−44.1213	−1.56286	−0.781428	+	0.623995i	$0.785508\pi$
$798$	3.64815	0.129143
$799$	2.84630	0.100695
$800$	−145.530	−5.14528
$801$	−24.5771	−0.868390
$802$	−36.2167	−1.27886
$803$	8.36973	0.295361
$804$	23.0528	0.813010
$805$	−0.312135	−0.0110013
$806$	29.1088	1.02531
$807$	−62.6787	−2.20639
$808$	70.7591	2.48929
$809$	41.5418	1.46053	0.730266	−	0.683163i	$-0.239396\pi$
$809$	41.5418	1.46053	0.730266	+	0.683163i	$0.239396\pi$
$810$	66.4364	2.33434
$811$	−54.3388	−1.90809	−0.954047	−	0.299659i	$-0.903127\pi$
$811$	−54.3388	−1.90809	−0.954047	+	0.299659i	$0.903127\pi$
$812$	−3.00613	−0.105494
$813$	39.2184	1.37545
$814$	65.6393	2.30066
$815$	68.3137	2.39293
$816$	−163.231	−5.71424
$817$	−0.645722	−0.0225909
$818$	66.8055	2.33580
$819$	0.417450	0.0145869
$820$	−40.3017	−1.40740
$821$	−12.1937	−0.425563	−0.212782	−	0.977100i	$-0.568252\pi$
$821$	−12.1937	−0.425563	−0.212782	+	0.977100i	$0.568252\pi$
$822$	−21.7003	−0.756883
$823$	6.13549	0.213870	0.106935	−	0.994266i	$-0.465896\pi$
$823$	6.13549	0.213870	0.106935	+	0.994266i	$0.465896\pi$
$824$	−69.6827	−2.42751
$825$	131.767	4.58753
$826$	2.57168	0.0894801
$827$	−29.8981	−1.03966	−0.519830	−	0.854270i	$-0.674005\pi$
$827$	−29.8981	−1.03966	−0.519830	+	0.854270i	$0.674005\pi$
$828$	18.7787	0.652604
$829$	31.8990	1.10790	0.553948	−	0.832551i	$-0.313121\pi$
$829$	31.8990	1.10790	0.553948	+	0.832551i	$0.313121\pi$
$830$	−36.7091	−1.27419
$831$	13.8144	0.479216
$832$	−22.8635	−0.792649
$833$	−37.2445	−1.29044
$834$	3.24567	0.112388
$835$	33.7239	1.16706
$836$	175.038	6.05380
$837$	−13.7299	−0.474573
$838$	−6.49710	−0.224439
$839$	18.8566	0.651001	0.325500	−	0.945542i	$-0.394467\pi$
$839$	18.8566	0.651001	0.325500	+	0.945542i	$0.394467\pi$
$840$	−6.67885	−0.230442
$841$	23.1694	0.798946
$842$	−85.6138	−2.95045
$843$	−80.4672	−2.77144
$844$	−117.934	−4.05944
$845$	−42.3564	−1.45711
$846$	−5.23951	−0.180138
$847$	−1.37215	−0.0471476
$848$	9.60433	0.329814
$849$	−12.2836	−0.421572
$850$	−137.214	−4.70640
$851$	4.66717	0.159989
$852$	−107.487	−3.68245
$853$	−0.158682	−0.00543318	−0.00271659	−	0.999996i	$-0.500865\pi$
$853$	−0.158682	−0.00543318	−0.00271659	+	0.999996i	$0.500865\pi$
$854$	1.18340	0.0404950
$855$	−91.5062	−3.12945
$856$	43.0699	1.47210
$857$	−36.3170	−1.24057	−0.620283	−	0.784378i	$-0.712982\pi$
$857$	−36.3170	−1.24057	−0.620283	+	0.784378i	$0.712982\pi$
$858$	50.6125	1.72788
$859$	39.8576	1.35992	0.679962	−	0.733247i	$-0.261996\pi$
$859$	39.8576	1.35992	0.679962	+	0.733247i	$0.261996\pi$
$860$	1.94331	0.0662664
$861$	−0.434107	−0.0147943
$862$	−50.6904	−1.72652
$863$	−19.2445	−0.655091	−0.327546	−	0.944835i	$-0.606221\pi$
$863$	−19.2445	−0.655091	−0.327546	+	0.944835i	$0.606221\pi$
$864$	26.3662	0.896996
$865$	46.5280	1.58200
$866$	−62.3732	−2.11953
$867$	−29.3632	−0.997226
$868$	−3.26338	−0.110766
$869$	46.5288	1.57838
$870$	190.537	6.45981
$871$	2.43305	0.0824409
$872$	−6.13692	−0.207822
$873$	23.8495	0.807183
$874$	17.3205	0.585875
$875$	−1.45612	−0.0492259
$876$	20.9329	0.707256
$877$	−30.0245	−1.01386	−0.506928	−	0.861988i	$-0.669219\pi$
$877$	−30.0245	−1.01386	−0.506928	+	0.861988i	$0.669219\pi$
$878$	26.3361	0.888801
$879$	−44.4036	−1.49770
$880$	−239.635	−8.07809
$881$	−40.5363	−1.36570	−0.682852	−	0.730557i	$-0.739261\pi$
$881$	−40.5363	−1.36570	−0.682852	+	0.730557i	$0.739261\pi$
$882$	68.5601	2.30854
$883$	−8.47099	−0.285071	−0.142536	−	0.989790i	$-0.545526\pi$
$883$	−8.47099	−0.285071	−0.142536	+	0.989790i	$0.545526\pi$
$884$	−37.8713	−1.27375
$885$	−117.125	−3.93711
$886$	−80.1991	−2.69434
$887$	−1.67384	−0.0562020	−0.0281010	−	0.999605i	$-0.508946\pi$
$887$	−1.67384	−0.0562020	−0.0281010	+	0.999605i	$0.508946\pi$
$888$	99.8649	3.35125
$889$	−1.18291	−0.0396735
$890$	68.2220	2.28681
$891$	34.3350	1.15027
$892$	−130.528	−4.37040
$893$	−3.47254	−0.116204
$894$	−141.495	−4.73231
$895$	−64.5507	−2.15769
$896$	1.11258	0.0371688
$897$	3.59871	0.120158
$898$	108.513	3.62112
$899$	56.6340	1.88885
$900$	181.496	6.04988
$901$	4.31247	0.143669
$902$	−28.9864	−0.965143
$903$	0.0209322	0.000696581 0
$904$	173.415	5.76768
$905$	74.2609	2.46852
$906$	76.7337	2.54931
$907$	10.9074	0.362175	0.181087	−	0.983467i	$-0.442038\pi$
$907$	10.9074	0.362175	0.181087	+	0.983467i	$0.442038\pi$
$908$	−41.5711	−1.37959
$909$	−31.4268	−1.04236
$910$	−1.15877	−0.0384129
$911$	−23.0359	−0.763213	−0.381606	−	0.924325i	$-0.624629\pi$
$911$	−23.0359	−0.763213	−0.381606	+	0.924325i	$0.624629\pi$
$912$	199.145	6.59436
$913$	−18.9717	−0.627870
$914$	−4.31666	−0.142782
$915$	−53.8968	−1.78177
$916$	60.9797	2.01483
$917$	1.48939	0.0491840
$918$	24.8595	0.820484
$919$	−24.5438	−0.809627	−0.404813	−	0.914399i	$-0.632663\pi$
$919$	−24.5438	−0.809627	−0.404813	+	0.914399i	$0.632663\pi$
$920$	−31.7095	−1.04543
$921$	−14.4759	−0.476997
$922$	56.7253	1.86815
$923$	−11.3445	−0.373408
$924$	−5.67416	−0.186666
$925$	45.1084	1.48316
$926$	19.8197	0.651315
$927$	30.9488	1.01649
$928$	−108.757	−3.57013
$929$	−58.7238	−1.92667	−0.963333	−	0.268308i	$-0.913535\pi$
$929$	−58.7238	−1.92667	−0.963333	+	0.268308i	$0.913535\pi$
$930$	206.843	6.78264
$931$	45.4389	1.48920
$932$	17.0690	0.559114
$933$	−31.2296	−1.02241
$934$	12.9576	0.423986
$935$	−107.599	−3.51887
$936$	42.4084	1.38616
$937$	43.3543	1.41632	0.708162	−	0.706050i	$-0.249525\pi$
$937$	43.3543	1.41632	0.708162	+	0.706050i	$0.249525\pi$
$938$	−0.379608	−0.0123946
$939$	−47.5917	−1.55310
$940$	10.4507	0.340863
$941$	30.3458	0.989244	0.494622	−	0.869108i	$-0.335307\pi$
$941$	30.3458	0.989244	0.494622	+	0.869108i	$0.335307\pi$
$942$	103.272	3.36479
$943$	−2.06103	−0.0671164
$944$	140.383	4.56907
$945$	0.546563	0.0177797
$946$	1.39770	0.0454431
$947$	21.5319	0.699693	0.349846	−	0.936807i	$-0.386234\pi$
$947$	21.5319	0.699693	0.349846	+	0.936807i	$0.386234\pi$
$948$	116.369	3.77950
$949$	2.20931	0.0717172
$950$	167.403	5.43128
$951$	−6.86774	−0.222702
$952$	3.59439	0.116495
$953$	−16.1237	−0.522298	−0.261149	−	0.965298i	$-0.584101\pi$
$953$	−16.1237	−0.522298	−0.261149	+	0.965298i	$0.584101\pi$
$954$	−7.93845	−0.257017
$955$	−57.0732	−1.84685
$956$	−109.423	−3.53900
$957$	98.4715	3.18313
$958$	55.7864	1.80238
$959$	0.256765	0.00829139
$960$	−162.464	−5.24352
$961$	30.4805	0.983243
$962$	17.3264	0.558627
$963$	−19.1290	−0.616423
$964$	79.1142	2.54810
$965$	−40.4373	−1.30172
$966$	−0.561476	−0.0180652
$967$	−18.5513	−0.596571	−0.298285	−	0.954477i	$-0.596415\pi$
$967$	−18.5513	−0.596571	−0.298285	+	0.954477i	$0.596415\pi$
$968$	−139.395	−4.48033
$969$	89.4188	2.87255
$970$	−66.2023	−2.12563
$971$	54.4186	1.74638	0.873188	−	0.487384i	$-0.162049\pi$
$971$	54.4186	1.74638	0.873188	+	0.487384i	$0.162049\pi$
$972$	112.696	3.61473
$973$	−0.0384040	−0.00123117
$974$	−90.9555	−2.91440
$975$	34.7817	1.11391
$976$	64.5993	2.06777
$977$	−46.5569	−1.48949	−0.744744	−	0.667351i	$-0.767428\pi$
$977$	−46.5569	−1.48949	−0.744744	+	0.667351i	$0.767428\pi$
$978$	122.884	3.92940
$979$	35.2579	1.12685
$980$	−136.749	−4.36830
$981$	2.72564	0.0870231
$982$	80.9471	2.58312
$983$	47.6652	1.52028	0.760142	−	0.649757i	$-0.225130\pi$
$983$	47.6652	1.52028	0.760142	+	0.649757i	$0.225130\pi$
$984$	−44.1005	−1.40587
$985$	47.5513	1.51511
$986$	−102.542	−3.26561
$987$	0.112569	0.00358310
$988$	46.2037	1.46993
$989$	0.0993810	0.00316013
$990$	198.070	6.29508
$991$	1.49095	0.0473614	0.0236807	−	0.999720i	$-0.492461\pi$
$991$	1.49095	0.0473614	0.0236807	+	0.999720i	$0.492461\pi$
$992$	−118.064	−3.74855
$993$	−9.43432	−0.299389
$994$	1.76998	0.0561403
$995$	−52.6044	−1.66767
$996$	−47.4485	−1.50346
$997$	−15.9636	−0.505573	−0.252786	−	0.967522i	$-0.581347\pi$
$997$	−15.9636	−0.505573	−0.252786	+	0.967522i	$0.581347\pi$
$998$	−79.6722	−2.52198
$999$	−8.17243	−0.258564

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.6	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.6	✓	176	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} +O(q^{10})\)	\(q-2.66575 q^{2} -2.58411 q^{3} +5.10620 q^{4} +3.82950 q^{5} +6.88858 q^{6} -0.0815082 q^{7} -8.28034 q^{8} +3.67762 q^{9} -10.2085 q^{10} -5.27584 q^{11} -13.1950 q^{12} -1.39263 q^{13} +0.217280 q^{14} -9.89583 q^{15} +11.8609 q^{16} +5.32569 q^{17} -9.80360 q^{18} -6.49744 q^{19} +19.5542 q^{20} +0.210626 q^{21} +14.0640 q^{22} +1.00000 q^{23} +21.3973 q^{24} +9.66503 q^{25} +3.71240 q^{26} -1.75104 q^{27} -0.416197 q^{28} +7.22284 q^{29} +26.3798 q^{30} +7.84095 q^{31} -15.0574 q^{32} +13.6333 q^{33} -14.1969 q^{34} -0.312135 q^{35} +18.7787 q^{36} +4.66717 q^{37} +17.3205 q^{38} +3.59871 q^{39} -31.7095 q^{40} -2.06103 q^{41} -0.561476 q^{42} +0.0993810 q^{43} -26.9395 q^{44} +14.0834 q^{45} -2.66575 q^{46} +0.534447 q^{47} -30.6498 q^{48} -6.99336 q^{49} -25.7645 q^{50} -13.7622 q^{51} -7.11106 q^{52} +0.809749 q^{53} +4.66784 q^{54} -20.2038 q^{55} +0.674916 q^{56} +16.7901 q^{57} -19.2543 q^{58} +11.8358 q^{59} -50.5301 q^{60} +5.44642 q^{61} -20.9020 q^{62} -0.299756 q^{63} +16.4175 q^{64} -5.33308 q^{65} -36.3430 q^{66} -1.74709 q^{67} +27.1940 q^{68} -2.58411 q^{69} +0.832073 q^{70} +8.14606 q^{71} -30.4519 q^{72} -1.58643 q^{73} -12.4415 q^{74} -24.9755 q^{75} -33.1772 q^{76} +0.430024 q^{77} -9.59326 q^{78} -8.81922 q^{79} +45.4212 q^{80} -6.50797 q^{81} +5.49418 q^{82} +3.59595 q^{83} +1.07550 q^{84} +20.3947 q^{85} -0.264924 q^{86} -18.6646 q^{87} +43.6857 q^{88} -6.68289 q^{89} -37.5428 q^{90} +0.113511 q^{91} +5.10620 q^{92} -20.2619 q^{93} -1.42470 q^{94} -24.8819 q^{95} +38.9100 q^{96} +6.48504 q^{97} +18.6425 q^{98} -19.4025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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