LMFDB - Embedded newform 8030.2.a.v.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.216637.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 4x^{3} + 7x^{2} + x - 2 $ x^5 - 2x^4 - 4x^3 + 7*x^2 + x - 2
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			$0.581553$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.38979 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38979 q^{6} +1.27596 q^{7} +1.00000 q^{8} +8.49065 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.38979 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38979 q^{6} +1.27596 q^{7} +1.00000 q^{8} +8.49065 q^{9} +1.00000 q^{10} +1.00000 q^{11} -3.38979 q^{12} -6.37288 q^{13} +1.27596 q^{14} -3.38979 q^{15} +1.00000 q^{16} -4.31350 q^{17} +8.49065 q^{18} +2.03588 q^{19} +1.00000 q^{20} -4.32525 q^{21} +1.00000 q^{22} +5.87814 q^{23} -3.38979 q^{24} +1.00000 q^{25} -6.37288 q^{26} -18.6121 q^{27} +1.27596 q^{28} -1.36916 q^{29} -3.38979 q^{30} +8.83773 q^{31} +1.00000 q^{32} -3.38979 q^{33} -4.31350 q^{34} +1.27596 q^{35} +8.49065 q^{36} -1.21239 q^{37} +2.03588 q^{38} +21.6027 q^{39} +1.00000 q^{40} +3.71434 q^{41} -4.32525 q^{42} -6.71830 q^{43} +1.00000 q^{44} +8.49065 q^{45} +5.87814 q^{46} -10.0246 q^{47} -3.38979 q^{48} -5.37191 q^{49} +1.00000 q^{50} +14.6218 q^{51} -6.37288 q^{52} -8.27201 q^{53} -18.6121 q^{54} +1.00000 q^{55} +1.27596 q^{56} -6.90119 q^{57} -1.36916 q^{58} -13.9774 q^{59} -3.38979 q^{60} -0.979378 q^{61} +8.83773 q^{62} +10.8338 q^{63} +1.00000 q^{64} -6.37288 q^{65} -3.38979 q^{66} +0.367267 q^{67} -4.31350 q^{68} -19.9256 q^{69} +1.27596 q^{70} -4.19342 q^{71} +8.49065 q^{72} +1.00000 q^{73} -1.21239 q^{74} -3.38979 q^{75} +2.03588 q^{76} +1.27596 q^{77} +21.6027 q^{78} -7.97460 q^{79} +1.00000 q^{80} +37.6192 q^{81} +3.71434 q^{82} -9.52819 q^{83} -4.32525 q^{84} -4.31350 q^{85} -6.71830 q^{86} +4.64117 q^{87} +1.00000 q^{88} +18.4531 q^{89} +8.49065 q^{90} -8.13157 q^{91} +5.87814 q^{92} -29.9580 q^{93} -10.0246 q^{94} +2.03588 q^{95} -3.38979 q^{96} +15.7497 q^{97} -5.37191 q^{98} +8.49065 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - 7 q^{13} - 8 q^{14} - 5 q^{15} + 5 q^{16} - 3 q^{17} + 4 q^{18} + 4 q^{19} + 5 q^{20} - 3 q^{21} + 5 q^{22} - 3 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} - 11 q^{27} - 8 q^{28} - 12 q^{29} - 5 q^{30} - q^{31} + 5 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 4 q^{36} + 4 q^{38} + 8 q^{39} + 5 q^{40} + q^{41} - 3 q^{42} + 5 q^{44} + 4 q^{45} - 3 q^{46} - 17 q^{47} - 5 q^{48} + 13 q^{49} + 5 q^{50} + 23 q^{51} - 7 q^{52} - 43 q^{53} - 11 q^{54} + 5 q^{55} - 8 q^{56} - 29 q^{57} - 12 q^{58} - 9 q^{59} - 5 q^{60} - 22 q^{61} - q^{62} + 25 q^{63} + 5 q^{64} - 7 q^{65} - 5 q^{66} - 9 q^{67} - 3 q^{68} + q^{69} - 8 q^{70} - 34 q^{71} + 4 q^{72} + 5 q^{73} - 5 q^{75} + 4 q^{76} - 8 q^{77} + 8 q^{78} - 24 q^{79} + 5 q^{80} + 25 q^{81} + q^{82} - 5 q^{83} - 3 q^{84} - 3 q^{85} + 30 q^{87} + 5 q^{88} + 58 q^{89} + 4 q^{90} - 9 q^{91} - 3 q^{92} - 32 q^{93} - 17 q^{94} + 4 q^{95} - 5 q^{96} + 13 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - 7 * q^13 - 8 * q^14 - 5 * q^15 + 5 * q^16 - 3 * q^17 + 4 * q^18 + 4 * q^19 + 5 * q^20 - 3 * q^21 + 5 * q^22 - 3 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 - 11 * q^27 - 8 * q^28 - 12 * q^29 - 5 * q^30 - q^31 + 5 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 4 * q^36 + 4 * q^38 + 8 * q^39 + 5 * q^40 + q^41 - 3 * q^42 + 5 * q^44 + 4 * q^45 - 3 * q^46 - 17 * q^47 - 5 * q^48 + 13 * q^49 + 5 * q^50 + 23 * q^51 - 7 * q^52 - 43 * q^53 - 11 * q^54 + 5 * q^55 - 8 * q^56 - 29 * q^57 - 12 * q^58 - 9 * q^59 - 5 * q^60 - 22 * q^61 - q^62 + 25 * q^63 + 5 * q^64 - 7 * q^65 - 5 * q^66 - 9 * q^67 - 3 * q^68 + q^69 - 8 * q^70 - 34 * q^71 + 4 * q^72 + 5 * q^73 - 5 * q^75 + 4 * q^76 - 8 * q^77 + 8 * q^78 - 24 * q^79 + 5 * q^80 + 25 * q^81 + q^82 - 5 * q^83 - 3 * q^84 - 3 * q^85 + 30 * q^87 + 5 * q^88 + 58 * q^89 + 4 * q^90 - 9 * q^91 - 3 * q^92 - 32 * q^93 - 17 * q^94 + 4 * q^95 - 5 * q^96 + 13 * q^97 + 13 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.38979	−1.95709	−0.978547	−	0.206023i	$-0.933948\pi$
$3$	−3.38979	−1.95709	−0.978547	+	0.206023i	$0.933948\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.38979	−1.38387
$7$	1.27596	0.482269	0.241135	−	0.970492i	$-0.422480\pi$
$7$	1.27596	0.482269	0.241135	+	0.970492i	$0.422480\pi$
$8$	1.00000	0.353553
$9$	8.49065	2.83022
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.38979	−0.978547
$13$	−6.37288	−1.76752	−0.883759	−	0.467942i	$-0.844995\pi$
$13$	−6.37288	−1.76752	−0.883759	+	0.467942i	$0.844995\pi$
$14$	1.27596	0.341016
$15$	−3.38979	−0.875239
$16$	1.00000	0.250000
$17$	−4.31350	−1.04618	−0.523088	−	0.852278i	$-0.675220\pi$
$17$	−4.31350	−1.04618	−0.523088	+	0.852278i	$0.675220\pi$
$18$	8.49065	2.00127
$19$	2.03588	0.467062	0.233531	−	0.972349i	$-0.424972\pi$
$19$	2.03588	0.467062	0.233531	+	0.972349i	$0.424972\pi$
$20$	1.00000	0.223607
$21$	−4.32525	−0.943846
$22$	1.00000	0.213201
$23$	5.87814	1.22568	0.612838	−	0.790208i	$-0.290028\pi$
$23$	5.87814	1.22568	0.612838	+	0.790208i	$0.290028\pi$
$24$	−3.38979	−0.691937
$25$	1.00000	0.200000
$26$	−6.37288	−1.24982
$27$	−18.6121	−3.58191
$28$	1.27596	0.241135
$29$	−1.36916	−0.254247	−0.127124	−	0.991887i	$-0.540575\pi$
$29$	−1.36916	−0.254247	−0.127124	+	0.991887i	$0.540575\pi$
$30$	−3.38979	−0.618888
$31$	8.83773	1.58730	0.793651	−	0.608373i	$-0.208177\pi$
$31$	8.83773	1.58730	0.793651	+	0.608373i	$0.208177\pi$
$32$	1.00000	0.176777
$33$	−3.38979	−0.590086
$34$	−4.31350	−0.739759
$35$	1.27596	0.215677
$36$	8.49065	1.41511
$37$	−1.21239	−0.199315	−0.0996577	−	0.995022i	$-0.531775\pi$
$37$	−1.21239	−0.199315	−0.0996577	+	0.995022i	$0.531775\pi$
$38$	2.03588	0.330263
$39$	21.6027	3.45920
$40$	1.00000	0.158114
$41$	3.71434	0.580083	0.290041	−	0.957014i	$-0.406331\pi$
$41$	3.71434	0.580083	0.290041	+	0.957014i	$0.406331\pi$
$42$	−4.32525	−0.667400
$43$	−6.71830	−1.02453	−0.512265	−	0.858827i	$-0.671194\pi$
$43$	−6.71830	−1.02453	−0.512265	+	0.858827i	$0.671194\pi$
$44$	1.00000	0.150756
$45$	8.49065	1.26571
$46$	5.87814	0.866684
$47$	−10.0246	−1.46223	−0.731117	−	0.682252i	$-0.761001\pi$
$47$	−10.0246	−1.46223	−0.731117	+	0.682252i	$0.761001\pi$
$48$	−3.38979	−0.489274
$49$	−5.37191	−0.767416
$50$	1.00000	0.141421
$51$	14.6218	2.04747
$52$	−6.37288	−0.883759
$53$	−8.27201	−1.13625	−0.568124	−	0.822943i	$-0.692331\pi$
$53$	−8.27201	−1.13625	−0.568124	+	0.822943i	$0.692331\pi$
$54$	−18.6121	−2.53279
$55$	1.00000	0.134840
$56$	1.27596	0.170508
$57$	−6.90119	−0.914085
$58$	−1.36916	−0.179780
$59$	−13.9774	−1.81970	−0.909848	−	0.414942i	$-0.863802\pi$
$59$	−13.9774	−1.81970	−0.909848	+	0.414942i	$0.863802\pi$
$60$	−3.38979	−0.437620
$61$	−0.979378	−0.125396	−0.0626982	−	0.998033i	$-0.519971\pi$
$61$	−0.979378	−0.125396	−0.0626982	+	0.998033i	$0.519971\pi$
$62$	8.83773	1.12239
$63$	10.8338	1.36493
$64$	1.00000	0.125000
$65$	−6.37288	−0.790458
$66$	−3.38979	−0.417254
$67$	0.367267	0.0448688	0.0224344	−	0.999748i	$-0.492858\pi$
$67$	0.367267	0.0448688	0.0224344	+	0.999748i	$0.492858\pi$
$68$	−4.31350	−0.523088
$69$	−19.9256	−2.39877
$70$	1.27596	0.152507
$71$	−4.19342	−0.497667	−0.248834	−	0.968546i	$-0.580047\pi$
$71$	−4.19342	−0.497667	−0.248834	+	0.968546i	$0.580047\pi$
$72$	8.49065	1.00063
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−1.21239	−0.140937
$75$	−3.38979	−0.391419
$76$	2.03588	0.233531
$77$	1.27596	0.145410
$78$	21.6027	2.44602
$79$	−7.97460	−0.897213	−0.448606	−	0.893729i	$-0.648079\pi$
$79$	−7.97460	−0.897213	−0.448606	+	0.893729i	$0.648079\pi$
$80$	1.00000	0.111803
$81$	37.6192	4.17991
$82$	3.71434	0.410180
$83$	−9.52819	−1.04585	−0.522927	−	0.852377i	$-0.675160\pi$
$83$	−9.52819	−1.04585	−0.522927	+	0.852377i	$0.675160\pi$
$84$	−4.32525	−0.471923
$85$	−4.31350	−0.467864
$86$	−6.71830	−0.724453
$87$	4.64117	0.497586
$88$	1.00000	0.106600
$89$	18.4531	1.95603	0.978013	−	0.208542i	$-0.0668718\pi$
$89$	18.4531	1.95603	0.978013	+	0.208542i	$0.0668718\pi$
$90$	8.49065	0.894993
$91$	−8.13157	−0.852420
$92$	5.87814	0.612838
$93$	−29.9580	−3.10650
$94$	−10.0246	−1.03396
$95$	2.03588	0.208877
$96$	−3.38979	−0.345969
$97$	15.7497	1.59914	0.799570	−	0.600573i	$-0.205061\pi$
$97$	15.7497	1.59914	0.799570	+	0.600573i	$0.205061\pi$
$98$	−5.37191	−0.542645
$99$	8.49065	0.853343
$100$	1.00000	0.100000
$101$	13.7088	1.36408	0.682041	−	0.731314i	$-0.261093\pi$
$101$	13.7088	1.36408	0.682041	+	0.731314i	$0.261093\pi$
$102$	14.6218	1.44778
$103$	−9.11681	−0.898306	−0.449153	−	0.893455i	$-0.648274\pi$
$103$	−9.11681	−0.898306	−0.449153	+	0.893455i	$0.648274\pi$
$104$	−6.37288	−0.624912
$105$	−4.32525	−0.422101
$106$	−8.27201	−0.803449
$107$	14.3074	1.38315	0.691573	−	0.722306i	$-0.256918\pi$
$107$	14.3074	1.38315	0.691573	+	0.722306i	$0.256918\pi$
$108$	−18.6121	−1.79095
$109$	−0.438667	−0.0420167	−0.0210083	−	0.999779i	$-0.506688\pi$
$109$	−0.438667	−0.0420167	−0.0210083	+	0.999779i	$0.506688\pi$
$110$	1.00000	0.0953463
$111$	4.10974	0.390079
$112$	1.27596	0.120567
$113$	16.5312	1.55512	0.777561	−	0.628807i	$-0.216457\pi$
$113$	16.5312	1.55512	0.777561	+	0.628807i	$0.216457\pi$
$114$	−6.90119	−0.646356
$115$	5.87814	0.548139
$116$	−1.36916	−0.127124
$117$	−54.1099	−5.00246
$118$	−13.9774	−1.28672
$119$	−5.50387	−0.504539
$120$	−3.38979	−0.309444
$121$	1.00000	0.0909091
$122$	−0.979378	−0.0886687
$123$	−12.5908	−1.13528
$124$	8.83773	0.793651
$125$	1.00000	0.0894427
$126$	10.8338	0.965149
$127$	4.98622	0.442456	0.221228	−	0.975222i	$-0.428994\pi$
$127$	4.98622	0.442456	0.221228	+	0.975222i	$0.428994\pi$
$128$	1.00000	0.0883883
$129$	22.7736	2.00510
$130$	−6.37288	−0.558938
$131$	−3.68306	−0.321791	−0.160895	−	0.986971i	$-0.551438\pi$
$131$	−3.68306	−0.321791	−0.160895	+	0.986971i	$0.551438\pi$
$132$	−3.38979	−0.295043
$133$	2.59771	0.225250
$134$	0.367267	0.0317270
$135$	−18.6121	−1.60188
$136$	−4.31350	−0.369879
$137$	−11.4421	−0.977564	−0.488782	−	0.872406i	$-0.662559\pi$
$137$	−11.4421	−0.977564	−0.488782	+	0.872406i	$0.662559\pi$
$138$	−19.9256	−1.69618
$139$	−9.29033	−0.787996	−0.393998	−	0.919111i	$-0.628908\pi$
$139$	−9.29033	−0.787996	−0.393998	+	0.919111i	$0.628908\pi$
$140$	1.27596	0.107839
$141$	33.9812	2.86173
$142$	−4.19342	−0.351904
$143$	−6.37288	−0.532927
$144$	8.49065	0.707554
$145$	−1.36916	−0.113703
$146$	1.00000	0.0827606
$147$	18.2096	1.50191
$148$	−1.21239	−0.0996577
$149$	−8.20032	−0.671796	−0.335898	−	0.941898i	$-0.609040\pi$
$149$	−8.20032	−0.671796	−0.335898	+	0.941898i	$0.609040\pi$
$150$	−3.38979	−0.276775
$151$	−19.4245	−1.58074	−0.790370	−	0.612630i	$-0.790112\pi$
$151$	−19.4245	−1.58074	−0.790370	+	0.612630i	$0.790112\pi$
$152$	2.03588	0.165131
$153$	−36.6244	−2.96091
$154$	1.27596	0.102820
$155$	8.83773	0.709863
$156$	21.6027	1.72960
$157$	−19.3921	−1.54766	−0.773828	−	0.633395i	$-0.781661\pi$
$157$	−19.3921	−1.54766	−0.773828	+	0.633395i	$0.781661\pi$
$158$	−7.97460	−0.634425
$159$	28.0403	2.22374
$160$	1.00000	0.0790569
$161$	7.50030	0.591106
$162$	37.6192	2.95565
$163$	−6.99055	−0.547542	−0.273771	−	0.961795i	$-0.588271\pi$
$163$	−6.99055	−0.547542	−0.273771	+	0.961795i	$0.588271\pi$
$164$	3.71434	0.290041
$165$	−3.38979	−0.263895
$166$	−9.52819	−0.739531
$167$	10.9337	0.846073	0.423037	−	0.906113i	$-0.360964\pi$
$167$	10.9337	0.846073	0.423037	+	0.906113i	$0.360964\pi$
$168$	−4.32525	−0.333700
$169$	27.6136	2.12412
$170$	−4.31350	−0.330830
$171$	17.2859	1.32189
$172$	−6.71830	−0.512265
$173$	−14.2779	−1.08553	−0.542764	−	0.839885i	$-0.682622\pi$
$173$	−14.2779	−1.08553	−0.542764	+	0.839885i	$0.682622\pi$
$174$	4.64117	0.351847
$175$	1.27596	0.0964539
$176$	1.00000	0.0753778
$177$	47.3802	3.56132
$178$	18.4531	1.38312
$179$	−11.7461	−0.877947	−0.438974	−	0.898500i	$-0.644658\pi$
$179$	−11.7461	−0.877947	−0.438974	+	0.898500i	$0.644658\pi$
$180$	8.49065	0.632856
$181$	4.67451	0.347454	0.173727	−	0.984794i	$-0.444419\pi$
$181$	4.67451	0.347454	0.173727	+	0.984794i	$0.444419\pi$
$182$	−8.13157	−0.602752
$183$	3.31988	0.245413
$184$	5.87814	0.433342
$185$	−1.21239	−0.0891366
$186$	−29.9580	−2.19663
$187$	−4.31350	−0.315434
$188$	−10.0246	−0.731117
$189$	−23.7484	−1.72744
$190$	2.03588	0.147698
$191$	8.41189	0.608663	0.304331	−	0.952566i	$-0.401567\pi$
$191$	8.41189	0.608663	0.304331	+	0.952566i	$0.401567\pi$
$192$	−3.38979	−0.244637
$193$	−3.85445	−0.277449	−0.138725	−	0.990331i	$-0.544300\pi$
$193$	−3.85445	−0.277449	−0.138725	+	0.990331i	$0.544300\pi$
$194$	15.7497	1.13076
$195$	21.6027	1.54700
$196$	−5.37191	−0.383708
$197$	4.87162	0.347088	0.173544	−	0.984826i	$-0.444478\pi$
$197$	4.87162	0.347088	0.173544	+	0.984826i	$0.444478\pi$
$198$	8.49065	0.603404
$199$	−17.6913	−1.25410	−0.627051	−	0.778978i	$-0.715738\pi$
$199$	−17.6913	−1.25410	−0.627051	+	0.778978i	$0.715738\pi$
$200$	1.00000	0.0707107
$201$	−1.24496	−0.0878125
$202$	13.7088	0.964551
$203$	−1.74701	−0.122616
$204$	14.6218	1.02373
$205$	3.71434	0.259421
$206$	−9.11681	−0.635199
$207$	49.9092	3.46893
$208$	−6.37288	−0.441879
$209$	2.03588	0.140825
$210$	−4.32525	−0.298470
$211$	20.6081	1.41872	0.709360	−	0.704846i	$-0.248984\pi$
$211$	20.6081	1.41872	0.709360	+	0.704846i	$0.248984\pi$
$212$	−8.27201	−0.568124
$213$	14.2148	0.973982
$214$	14.3074	0.978032
$215$	−6.71830	−0.458184
$216$	−18.6121	−1.26640
$217$	11.2766	0.765507
$218$	−0.438667	−0.0297103
$219$	−3.38979	−0.229061
$220$	1.00000	0.0674200
$221$	27.4894	1.84914
$222$	4.10974	0.275828
$223$	17.7959	1.19170	0.595850	−	0.803096i	$-0.296815\pi$
$223$	17.7959	1.19170	0.595850	+	0.803096i	$0.296815\pi$
$224$	1.27596	0.0852540
$225$	8.49065	0.566044
$226$	16.5312	1.09964
$227$	24.0405	1.59563	0.797813	−	0.602905i	$-0.205990\pi$
$227$	24.0405	1.59563	0.797813	+	0.602905i	$0.205990\pi$
$228$	−6.90119	−0.457043
$229$	−10.3646	−0.684910	−0.342455	−	0.939534i	$-0.611259\pi$
$229$	−10.3646	−0.684910	−0.342455	+	0.939534i	$0.611259\pi$
$230$	5.87814	0.387593
$231$	−4.32525	−0.284580
$232$	−1.36916	−0.0898900
$233$	9.05203	0.593018	0.296509	−	0.955030i	$-0.404177\pi$
$233$	9.05203	0.593018	0.296509	+	0.955030i	$0.404177\pi$
$234$	−54.1099	−3.53727
$235$	−10.0246	−0.653931
$236$	−13.9774	−0.909848
$237$	27.0322	1.75593
$238$	−5.50387	−0.356763
$239$	−10.4398	−0.675294	−0.337647	−	0.941273i	$-0.609631\pi$
$239$	−10.4398	−0.675294	−0.337647	+	0.941273i	$0.609631\pi$
$240$	−3.38979	−0.218810
$241$	−20.1320	−1.29682	−0.648409	−	0.761293i	$-0.724565\pi$
$241$	−20.1320	−1.29682	−0.648409	+	0.761293i	$0.724565\pi$
$242$	1.00000	0.0642824
$243$	−71.6847	−4.59858
$244$	−0.979378	−0.0626982
$245$	−5.37191	−0.343199
$246$	−12.5908	−0.802762
$247$	−12.9744	−0.825541
$248$	8.83773	0.561196
$249$	32.2985	2.04684
$250$	1.00000	0.0632456
$251$	−8.61093	−0.543517	−0.271759	−	0.962365i	$-0.587605\pi$
$251$	−8.61093	−0.543517	−0.271759	+	0.962365i	$0.587605\pi$
$252$	10.8338	0.682464
$253$	5.87814	0.369555
$254$	4.98622	0.312863
$255$	14.6218	0.915655
$256$	1.00000	0.0625000
$257$	−20.2178	−1.26115	−0.630577	−	0.776127i	$-0.717182\pi$
$257$	−20.2178	−1.26115	−0.630577	+	0.776127i	$0.717182\pi$
$258$	22.7736	1.41782
$259$	−1.54696	−0.0961237
$260$	−6.37288	−0.395229
$261$	−11.6251	−0.719575
$262$	−3.68306	−0.227540
$263$	−16.3950	−1.01096	−0.505478	−	0.862839i	$-0.668684\pi$
$263$	−16.3950	−1.01096	−0.505478	+	0.862839i	$0.668684\pi$
$264$	−3.38979	−0.208627
$265$	−8.27201	−0.508146
$266$	2.59771	0.159276
$267$	−62.5521	−3.82813
$268$	0.367267	0.0224344
$269$	2.88126	0.175674	0.0878368	−	0.996135i	$-0.472005\pi$
$269$	2.88126	0.175674	0.0878368	+	0.996135i	$0.472005\pi$
$270$	−18.6121	−1.13270
$271$	−25.8594	−1.57084	−0.785422	−	0.618960i	$-0.787554\pi$
$271$	−25.8594	−1.57084	−0.785422	+	0.618960i	$0.787554\pi$
$272$	−4.31350	−0.261544
$273$	27.5643	1.66827
$274$	−11.4421	−0.691242
$275$	1.00000	0.0603023
$276$	−19.9256	−1.19938
$277$	11.5823	0.695914	0.347957	−	0.937511i	$-0.386876\pi$
$277$	11.5823	0.695914	0.347957	+	0.937511i	$0.386876\pi$
$278$	−9.29033	−0.557197
$279$	75.0381	4.49241
$280$	1.27596	0.0762535
$281$	−7.14607	−0.426299	−0.213149	−	0.977020i	$-0.568372\pi$
$281$	−7.14607	−0.426299	−0.213149	+	0.977020i	$0.568372\pi$
$282$	33.9812	2.02355
$283$	27.5523	1.63781	0.818906	−	0.573927i	$-0.194581\pi$
$283$	27.5523	1.63781	0.818906	+	0.573927i	$0.194581\pi$
$284$	−4.19342	−0.248834
$285$	−6.90119	−0.408791
$286$	−6.37288	−0.376836
$287$	4.73937	0.279756
$288$	8.49065	0.500317
$289$	1.60626	0.0944858
$290$	−1.36916	−0.0804001
$291$	−53.3881	−3.12967
$292$	1.00000	0.0585206
$293$	−16.0728	−0.938984	−0.469492	−	0.882937i	$-0.655563\pi$
$293$	−16.0728	−0.938984	−0.469492	+	0.882937i	$0.655563\pi$
$294$	18.2096	1.06201
$295$	−13.9774	−0.813793
$296$	−1.21239	−0.0704686
$297$	−18.6121	−1.07999
$298$	−8.20032	−0.475032
$299$	−37.4607	−2.16641
$300$	−3.38979	−0.195709
$301$	−8.57231	−0.494100
$302$	−19.4245	−1.11775
$303$	−46.4701	−2.66964
$304$	2.03588	0.116766
$305$	−0.979378	−0.0560790
$306$	−36.6244	−2.09368
$307$	7.46421	0.426005	0.213002	−	0.977052i	$-0.431676\pi$
$307$	7.46421	0.426005	0.213002	+	0.977052i	$0.431676\pi$
$308$	1.27596	0.0727048
$309$	30.9041	1.75807
$310$	8.83773	0.501949
$311$	−33.0919	−1.87647	−0.938236	−	0.345997i	$-0.887541\pi$
$311$	−33.0919	−1.87647	−0.938236	+	0.345997i	$0.887541\pi$
$312$	21.6027	1.22301
$313$	10.5337	0.595403	0.297701	−	0.954659i	$-0.403780\pi$
$313$	10.5337	0.595403	0.297701	+	0.954659i	$0.403780\pi$
$314$	−19.3921	−1.09436
$315$	10.8338	0.610414
$316$	−7.97460	−0.448606
$317$	−24.9034	−1.39872	−0.699358	−	0.714771i	$-0.746531\pi$
$317$	−24.9034	−1.39872	−0.699358	+	0.714771i	$0.746531\pi$
$318$	28.0403	1.57242
$319$	−1.36916	−0.0766585
$320$	1.00000	0.0559017
$321$	−48.4989	−2.70695
$322$	7.50030	0.417975
$323$	−8.78175	−0.488630
$324$	37.6192	2.08996
$325$	−6.37288	−0.353504
$326$	−6.99055	−0.387171
$327$	1.48699	0.0822306
$328$	3.71434	0.205090
$329$	−12.7910	−0.705191
$330$	−3.38979	−0.186602
$331$	−20.7557	−1.14083	−0.570417	−	0.821355i	$-0.693218\pi$
$331$	−20.7557	−1.14083	−0.570417	+	0.821355i	$0.693218\pi$
$332$	−9.52819	−0.522927
$333$	−10.2940	−0.564106
$334$	10.9337	0.598264
$335$	0.367267	0.0200659
$336$	−4.32525	−0.235962
$337$	20.6643	1.12566	0.562828	−	0.826574i	$-0.309713\pi$
$337$	20.6643	1.12566	0.562828	+	0.826574i	$0.309713\pi$
$338$	27.6136	1.50198
$339$	−56.0372	−3.04352
$340$	−4.31350	−0.233932
$341$	8.83773	0.478590
$342$	17.2859	0.934716
$343$	−15.7861	−0.852371
$344$	−6.71830	−0.362226
$345$	−19.9256	−1.07276
$346$	−14.2779	−0.767584
$347$	−6.77594	−0.363751	−0.181876	−	0.983322i	$-0.558217\pi$
$347$	−6.77594	−0.363751	−0.181876	+	0.983322i	$0.558217\pi$
$348$	4.64117	0.248793
$349$	8.50296	0.455153	0.227577	−	0.973760i	$-0.426920\pi$
$349$	8.50296	0.455153	0.227577	+	0.973760i	$0.426920\pi$
$350$	1.27596	0.0682032
$351$	118.613	6.33109
$352$	1.00000	0.0533002
$353$	−31.1164	−1.65616	−0.828081	−	0.560609i	$-0.810567\pi$
$353$	−31.1164	−1.65616	−0.828081	+	0.560609i	$0.810567\pi$
$354$	47.3802	2.51823
$355$	−4.19342	−0.222564
$356$	18.4531	0.978013
$357$	18.6569	0.987430
$358$	−11.7461	−0.620803
$359$	26.0884	1.37689	0.688446	−	0.725288i	$-0.258293\pi$
$359$	26.0884	1.37689	0.688446	+	0.725288i	$0.258293\pi$
$360$	8.49065	0.447497
$361$	−14.8552	−0.781853
$362$	4.67451	0.245687
$363$	−3.38979	−0.177918
$364$	−8.13157	−0.426210
$365$	1.00000	0.0523424
$366$	3.31988	0.173533
$367$	−21.7528	−1.13549	−0.567744	−	0.823205i	$-0.692184\pi$
$367$	−21.7528	−1.13549	−0.567744	+	0.823205i	$0.692184\pi$
$368$	5.87814	0.306419
$369$	31.5372	1.64176
$370$	−1.21239	−0.0630291
$371$	−10.5548	−0.547978
$372$	−29.9580	−1.55325
$373$	29.9923	1.55294	0.776471	−	0.630153i	$-0.217008\pi$
$373$	29.9923	1.55294	0.776471	+	0.630153i	$0.217008\pi$
$374$	−4.31350	−0.223046
$375$	−3.38979	−0.175048
$376$	−10.0246	−0.516978
$377$	8.72551	0.449387
$378$	−23.7484	−1.22149
$379$	−17.9651	−0.922807	−0.461404	−	0.887190i	$-0.652654\pi$
$379$	−17.9651	−0.922807	−0.461404	+	0.887190i	$0.652654\pi$
$380$	2.03588	0.104438
$381$	−16.9022	−0.865928
$382$	8.41189	0.430390
$383$	−28.3772	−1.45001	−0.725004	−	0.688745i	$-0.758162\pi$
$383$	−28.3772	−1.45001	−0.725004	+	0.688745i	$0.758162\pi$
$384$	−3.38979	−0.172984
$385$	1.27596	0.0650292
$386$	−3.85445	−0.196186
$387$	−57.0427	−2.89964
$388$	15.7497	0.799570
$389$	−4.69308	−0.237949	−0.118974	−	0.992897i	$-0.537961\pi$
$389$	−4.69308	−0.237949	−0.118974	+	0.992897i	$0.537961\pi$
$390$	21.6027	1.09389
$391$	−25.3553	−1.28227
$392$	−5.37191	−0.271323
$393$	12.4848	0.629775
$394$	4.87162	0.245428
$395$	−7.97460	−0.401246
$396$	8.49065	0.426671
$397$	−5.85893	−0.294051	−0.147026	−	0.989133i	$-0.546970\pi$
$397$	−5.85893	−0.294051	−0.147026	+	0.989133i	$0.546970\pi$
$398$	−17.6913	−0.886784
$399$	−8.80568	−0.440835
$400$	1.00000	0.0500000
$401$	23.4591	1.17149	0.585745	−	0.810495i	$-0.300802\pi$
$401$	23.4591	1.17149	0.585745	+	0.810495i	$0.300802\pi$
$402$	−1.24496	−0.0620928
$403$	−56.3218	−2.80559
$404$	13.7088	0.682041
$405$	37.6192	1.86931
$406$	−1.74701	−0.0867024
$407$	−1.21239	−0.0600959
$408$	14.6218	0.723889
$409$	−8.00003	−0.395576	−0.197788	−	0.980245i	$-0.563376\pi$
$409$	−8.00003	−0.395576	−0.197788	+	0.980245i	$0.563376\pi$
$410$	3.71434	0.183438
$411$	38.7862	1.91318
$412$	−9.11681	−0.449153
$413$	−17.8346	−0.877584
$414$	49.9092	2.45291
$415$	−9.52819	−0.467720
$416$	−6.37288	−0.312456
$417$	31.4922	1.54218
$418$	2.03588	0.0995780
$419$	−38.0151	−1.85716	−0.928579	−	0.371136i	$-0.878969\pi$
$419$	−38.0151	−1.85716	−0.928579	+	0.371136i	$0.878969\pi$
$420$	−4.32525	−0.211050
$421$	20.9173	1.01945	0.509724	−	0.860338i	$-0.329748\pi$
$421$	20.9173	1.01945	0.509724	+	0.860338i	$0.329748\pi$
$422$	20.6081	1.00319
$423$	−85.1152	−4.13844
$424$	−8.27201	−0.401724
$425$	−4.31350	−0.209235
$426$	14.2148	0.688709
$427$	−1.24965	−0.0604749
$428$	14.3074	0.691573
$429$	21.6027	1.04299
$430$	−6.71830	−0.323985
$431$	18.8663	0.908758	0.454379	−	0.890808i	$-0.349861\pi$
$431$	18.8663	0.908758	0.454379	+	0.890808i	$0.349861\pi$
$432$	−18.6121	−0.895477
$433$	11.4356	0.549561	0.274781	−	0.961507i	$-0.411395\pi$
$433$	11.4356	0.549561	0.274781	+	0.961507i	$0.411395\pi$
$434$	11.2766	0.541296
$435$	4.64117	0.222527
$436$	−0.438667	−0.0210083
$437$	11.9672	0.572468
$438$	−3.38979	−0.161970
$439$	−10.7841	−0.514697	−0.257348	−	0.966319i	$-0.582849\pi$
$439$	−10.7841	−0.514697	−0.257348	+	0.966319i	$0.582849\pi$
$440$	1.00000	0.0476731
$441$	−45.6111	−2.17196
$442$	27.4894	1.30754
$443$	8.47840	0.402821	0.201410	−	0.979507i	$-0.435448\pi$
$443$	8.47840	0.402821	0.201410	+	0.979507i	$0.435448\pi$
$444$	4.10974	0.195040
$445$	18.4531	0.874762
$446$	17.7959	0.842659
$447$	27.7973	1.31477
$448$	1.27596	0.0602837
$449$	0.252706	0.0119259	0.00596296	−	0.999982i	$-0.498102\pi$
$449$	0.252706	0.0119259	0.00596296	+	0.999982i	$0.498102\pi$
$450$	8.49065	0.400253
$451$	3.71434	0.174902
$452$	16.5312	0.777561
$453$	65.8448	3.09366
$454$	24.0405	1.12828
$455$	−8.13157	−0.381214
$456$	−6.90119	−0.323178
$457$	−25.2732	−1.18223	−0.591116	−	0.806587i	$-0.701312\pi$
$457$	−25.2732	−1.18223	−0.591116	+	0.806587i	$0.701312\pi$
$458$	−10.3646	−0.484305
$459$	80.2834	3.74731
$460$	5.87814	0.274070
$461$	−5.64748	−0.263029	−0.131515	−	0.991314i	$-0.541984\pi$
$461$	−5.64748	−0.263029	−0.131515	+	0.991314i	$0.541984\pi$
$462$	−4.32525	−0.201229
$463$	−21.8640	−1.01611	−0.508053	−	0.861326i	$-0.669635\pi$
$463$	−21.8640	−1.01611	−0.508053	+	0.861326i	$0.669635\pi$
$464$	−1.36916	−0.0635618
$465$	−29.9580	−1.38927
$466$	9.05203	0.419327
$467$	−21.0845	−0.975674	−0.487837	−	0.872935i	$-0.662214\pi$
$467$	−21.0845	−0.975674	−0.487837	+	0.872935i	$0.662214\pi$
$468$	−54.1099	−2.50123
$469$	0.468620	0.0216388
$470$	−10.0246	−0.462399
$471$	65.7350	3.02891
$472$	−13.9774	−0.643360
$473$	−6.71830	−0.308908
$474$	27.0322	1.24163
$475$	2.03588	0.0934125
$476$	−5.50387	−0.252269
$477$	−70.2348	−3.21583
$478$	−10.4398	−0.477505
$479$	−21.3653	−0.976207	−0.488103	−	0.872786i	$-0.662311\pi$
$479$	−21.3653	−0.976207	−0.488103	+	0.872786i	$0.662311\pi$
$480$	−3.38979	−0.154722
$481$	7.72640	0.352294
$482$	−20.1320	−0.916988
$483$	−25.4244	−1.15685
$484$	1.00000	0.0454545
$485$	15.7497	0.715157
$486$	−71.6847	−3.25169
$487$	0.110895	0.00502515	0.00251258	−	0.999997i	$-0.499200\pi$
$487$	0.110895	0.00502515	0.00251258	+	0.999997i	$0.499200\pi$
$488$	−0.979378	−0.0443343
$489$	23.6965	1.07159
$490$	−5.37191	−0.242678
$491$	17.4258	0.786415	0.393208	−	0.919450i	$-0.371365\pi$
$491$	17.4258	0.786415	0.393208	+	0.919450i	$0.371365\pi$
$492$	−12.5908	−0.567638
$493$	5.90589	0.265988
$494$	−12.9744	−0.583746
$495$	8.49065	0.381626
$496$	8.83773	0.396826
$497$	−5.35066	−0.240010
$498$	32.2985	1.44733
$499$	9.08271	0.406598	0.203299	−	0.979117i	$-0.434834\pi$
$499$	9.08271	0.406598	0.203299	+	0.979117i	$0.434834\pi$
$500$	1.00000	0.0447214
$501$	−37.0628	−1.65585
$502$	−8.61093	−0.384325
$503$	−11.2180	−0.500186	−0.250093	−	0.968222i	$-0.580461\pi$
$503$	−11.2180	−0.500186	−0.250093	+	0.968222i	$0.580461\pi$
$504$	10.8338	0.482575
$505$	13.7088	0.610036
$506$	5.87814	0.261315
$507$	−93.6041	−4.15710
$508$	4.98622	0.221228
$509$	−17.4712	−0.774395	−0.387198	−	0.921997i	$-0.626557\pi$
$509$	−17.4712	−0.774395	−0.387198	+	0.921997i	$0.626557\pi$
$510$	14.6218	0.647466
$511$	1.27596	0.0564454
$512$	1.00000	0.0441942
$513$	−37.8920	−1.67297
$514$	−20.2178	−0.891771
$515$	−9.11681	−0.401735
$516$	22.7736	1.00255
$517$	−10.0246	−0.440880
$518$	−1.54696	−0.0679697
$519$	48.3990	2.12448
$520$	−6.37288	−0.279469
$521$	−10.5796	−0.463500	−0.231750	−	0.972775i	$-0.574445\pi$
$521$	−10.5796	−0.463500	−0.231750	+	0.972775i	$0.574445\pi$
$522$	−11.6251	−0.508817
$523$	−26.3499	−1.15220	−0.576099	−	0.817380i	$-0.695426\pi$
$523$	−26.3499	−1.15220	−0.576099	+	0.817380i	$0.695426\pi$
$524$	−3.68306	−0.160895
$525$	−4.32525	−0.188769
$526$	−16.3950	−0.714854
$527$	−38.1215	−1.66060
$528$	−3.38979	−0.147522
$529$	11.5525	0.502284
$530$	−8.27201	−0.359313
$531$	−118.677	−5.15014
$532$	2.59771	0.112625
$533$	−23.6710	−1.02531
$534$	−62.5521	−2.70690
$535$	14.3074	0.618562
$536$	0.367267	0.0158635
$537$	39.8169	1.71823
$538$	2.88126	0.124220
$539$	−5.37191	−0.231385
$540$	−18.6121	−0.800939
$541$	−16.0995	−0.692173	−0.346087	−	0.938203i	$-0.612490\pi$
$541$	−16.0995	−0.692173	−0.346087	+	0.938203i	$0.612490\pi$
$542$	−25.8594	−1.11076
$543$	−15.8456	−0.679999
$544$	−4.31350	−0.184940
$545$	−0.438667	−0.0187904
$546$	27.5643	1.17964
$547$	−13.2619	−0.567039	−0.283520	−	0.958966i	$-0.591502\pi$
$547$	−13.2619	−0.567039	−0.283520	+	0.958966i	$0.591502\pi$
$548$	−11.4421	−0.488782
$549$	−8.31555	−0.354899
$550$	1.00000	0.0426401
$551$	−2.78745	−0.118749
$552$	−19.9256	−0.848092
$553$	−10.1753	−0.432698
$554$	11.5823	0.492085
$555$	4.10974	0.174449
$556$	−9.29033	−0.393998
$557$	41.2407	1.74743	0.873713	−	0.486442i	$-0.161706\pi$
$557$	41.2407	1.74743	0.873713	+	0.486442i	$0.161706\pi$
$558$	75.0381	3.17662
$559$	42.8149	1.81088
$560$	1.27596	0.0539193
$561$	14.6218	0.617334
$562$	−7.14607	−0.301439
$563$	−23.0088	−0.969707	−0.484853	−	0.874595i	$-0.661127\pi$
$563$	−23.0088	−0.969707	−0.484853	+	0.874595i	$0.661127\pi$
$564$	33.9812	1.43087
$565$	16.5312	0.695472
$566$	27.5523	1.15811
$567$	48.0008	2.01584
$568$	−4.19342	−0.175952
$569$	1.16222	0.0487227	0.0243614	−	0.999703i	$-0.492245\pi$
$569$	1.16222	0.0487227	0.0243614	+	0.999703i	$0.492245\pi$
$570$	−6.90119	−0.289059
$571$	−24.0024	−1.00447	−0.502234	−	0.864732i	$-0.667488\pi$
$571$	−24.0024	−1.00447	−0.502234	+	0.864732i	$0.667488\pi$
$572$	−6.37288	−0.266463
$573$	−28.5145	−1.19121
$574$	4.73937	0.197817
$575$	5.87814	0.245135
$576$	8.49065	0.353777
$577$	2.81263	0.117092	0.0585458	−	0.998285i	$-0.481354\pi$
$577$	2.81263	0.117092	0.0585458	+	0.998285i	$0.481354\pi$
$578$	1.60626	0.0668116
$579$	13.0658	0.542995
$580$	−1.36916	−0.0568514
$581$	−12.1576	−0.504383
$582$	−53.3881	−2.21301
$583$	−8.27201	−0.342592
$584$	1.00000	0.0413803
$585$	−54.1099	−2.23717
$586$	−16.0728	−0.663962
$587$	41.0009	1.69229	0.846144	−	0.532954i	$-0.178918\pi$
$587$	41.0009	1.69229	0.846144	+	0.532954i	$0.178918\pi$
$588$	18.2096	0.750953
$589$	17.9925	0.741369
$590$	−13.9774	−0.575438
$591$	−16.5137	−0.679284
$592$	−1.21239	−0.0498289
$593$	−11.5317	−0.473549	−0.236775	−	0.971565i	$-0.576090\pi$
$593$	−11.5317	−0.473549	−0.236775	+	0.971565i	$0.576090\pi$
$594$	−18.6121	−0.763665
$595$	−5.50387	−0.225637
$596$	−8.20032	−0.335898
$597$	59.9697	2.45440
$598$	−37.4607	−1.53188
$599$	−46.0055	−1.87974	−0.939868	−	0.341539i	$-0.889052\pi$
$599$	−46.0055	−1.87974	−0.939868	+	0.341539i	$0.889052\pi$
$600$	−3.38979	−0.138387
$601$	−25.2379	−1.02947	−0.514737	−	0.857348i	$-0.672110\pi$
$601$	−25.2379	−1.02947	−0.514737	+	0.857348i	$0.672110\pi$
$602$	−8.57231	−0.349381
$603$	3.11834	0.126988
$604$	−19.4245	−0.790370
$605$	1.00000	0.0406558
$606$	−46.4701	−1.88772
$607$	36.6941	1.48937	0.744684	−	0.667417i	$-0.232600\pi$
$607$	36.6941	1.48937	0.744684	+	0.667417i	$0.232600\pi$
$608$	2.03588	0.0825657
$609$	5.92197	0.239971
$610$	−0.979378	−0.0396538
$611$	63.8854	2.58453
$612$	−36.6244	−1.48045
$613$	−2.42111	−0.0977878	−0.0488939	−	0.998804i	$-0.515570\pi$
$613$	−2.42111	−0.0977878	−0.0488939	+	0.998804i	$0.515570\pi$
$614$	7.46421	0.301231
$615$	−12.5908	−0.507711
$616$	1.27596	0.0514101
$617$	−16.2627	−0.654710	−0.327355	−	0.944901i	$-0.606157\pi$
$617$	−16.2627	−0.654710	−0.327355	+	0.944901i	$0.606157\pi$
$618$	30.9041	1.24314
$619$	−39.7723	−1.59858	−0.799292	−	0.600943i	$-0.794792\pi$
$619$	−39.7723	−1.59858	−0.799292	+	0.600943i	$0.794792\pi$
$620$	8.83773	0.354932
$621$	−109.405	−4.39026
$622$	−33.0919	−1.32687
$623$	23.5455	0.943332
$624$	21.6027	0.864800
$625$	1.00000	0.0400000
$626$	10.5337	0.421013
$627$	−6.90119	−0.275607
$628$	−19.3921	−0.773828
$629$	5.22963	0.208519
$630$	10.8338	0.431628
$631$	27.8864	1.11014	0.555070	−	0.831804i	$-0.312691\pi$
$631$	27.8864	1.11014	0.555070	+	0.831804i	$0.312691\pi$
$632$	−7.97460	−0.317213
$633$	−69.8571	−2.77657
$634$	−24.9034	−0.989042
$635$	4.98622	0.197872
$636$	28.0403	1.11187
$637$	34.2345	1.35642
$638$	−1.36916	−0.0542057
$639$	−35.6049	−1.40851
$640$	1.00000	0.0395285
$641$	21.0769	0.832486	0.416243	−	0.909253i	$-0.363347\pi$
$641$	21.0769	0.832486	0.416243	+	0.909253i	$0.363347\pi$
$642$	−48.4989	−1.91410
$643$	3.03460	0.119673	0.0598364	−	0.998208i	$-0.480942\pi$
$643$	3.03460	0.119673	0.0598364	+	0.998208i	$0.480942\pi$
$644$	7.50030	0.295553
$645$	22.7736	0.896709
$646$	−8.78175	−0.345513
$647$	1.92977	0.0758671	0.0379336	−	0.999280i	$-0.487922\pi$
$647$	1.92977	0.0758671	0.0379336	+	0.999280i	$0.487922\pi$
$648$	37.6192	1.47782
$649$	−13.9774	−0.548659
$650$	−6.37288	−0.249965
$651$	−38.2254	−1.49817
$652$	−6.99055	−0.273771
$653$	−40.7993	−1.59660	−0.798300	−	0.602261i	$-0.794267\pi$
$653$	−40.7993	−1.59660	−0.798300	+	0.602261i	$0.794267\pi$
$654$	1.48699	0.0581458
$655$	−3.68306	−0.143909
$656$	3.71434	0.145021
$657$	8.49065	0.331252
$658$	−12.7910	−0.498645
$659$	29.0631	1.13214	0.566068	−	0.824359i	$-0.308464\pi$
$659$	29.0631	1.13214	0.566068	+	0.824359i	$0.308464\pi$
$660$	−3.38979	−0.131947
$661$	17.2958	0.672728	0.336364	−	0.941732i	$-0.390803\pi$
$661$	17.2958	0.672728	0.336364	+	0.941732i	$0.390803\pi$
$662$	−20.7557	−0.806691
$663$	−93.1831	−3.61893
$664$	−9.52819	−0.369765
$665$	2.59771	0.100735
$666$	−10.2940	−0.398883
$667$	−8.04814	−0.311625
$668$	10.9337	0.423037
$669$	−60.3242	−2.33227
$670$	0.367267	0.0141888
$671$	−0.979378	−0.0378085
$672$	−4.32525	−0.166850
$673$	30.3727	1.17078	0.585391	−	0.810751i	$-0.300941\pi$
$673$	30.3727	1.17078	0.585391	+	0.810751i	$0.300941\pi$
$674$	20.6643	0.795959
$675$	−18.6121	−0.716382
$676$	27.6136	1.06206
$677$	47.9364	1.84234	0.921172	−	0.389156i	$-0.127233\pi$
$677$	47.9364	1.84234	0.921172	+	0.389156i	$0.127233\pi$
$678$	−56.0372	−2.15209
$679$	20.0961	0.771216
$680$	−4.31350	−0.165415
$681$	−81.4923	−3.12279
$682$	8.83773	0.338414
$683$	−28.9872	−1.10916	−0.554581	−	0.832129i	$-0.687122\pi$
$683$	−28.9872	−1.10916	−0.554581	+	0.832129i	$0.687122\pi$
$684$	17.2859	0.660944
$685$	−11.4421	−0.437180
$686$	−15.7861	−0.602717
$687$	35.1337	1.34043
$688$	−6.71830	−0.256133
$689$	52.7165	2.00834
$690$	−19.9256	−0.758556
$691$	22.9624	0.873531	0.436766	−	0.899575i	$-0.356124\pi$
$691$	22.9624	0.873531	0.436766	+	0.899575i	$0.356124\pi$
$692$	−14.2779	−0.542764
$693$	10.8338	0.411541
$694$	−6.77594	−0.257211
$695$	−9.29033	−0.352402
$696$	4.64117	0.175923
$697$	−16.0218	−0.606869
$698$	8.50296	0.321842
$699$	−30.6845	−1.16059
$700$	1.27596	0.0482269
$701$	−8.23029	−0.310854	−0.155427	−	0.987847i	$-0.549675\pi$
$701$	−8.23029	−0.310854	−0.155427	+	0.987847i	$0.549675\pi$
$702$	118.613	4.47675
$703$	−2.46827	−0.0930927
$704$	1.00000	0.0376889
$705$	33.9812	1.27981
$706$	−31.1164	−1.17108
$707$	17.4920	0.657854
$708$	47.3802	1.78066
$709$	19.3126	0.725299	0.362649	−	0.931926i	$-0.381872\pi$
$709$	19.3126	0.725299	0.362649	+	0.931926i	$0.381872\pi$
$710$	−4.19342	−0.157376
$711$	−67.7096	−2.53931
$712$	18.4531	0.691560
$713$	51.9494	1.94552
$714$	18.6569	0.698219
$715$	−6.37288	−0.238332
$716$	−11.7461	−0.438974
$717$	35.3887	1.32161
$718$	26.0884	0.973609
$719$	−26.3634	−0.983189	−0.491594	−	0.870824i	$-0.663586\pi$
$719$	−26.3634	−0.983189	−0.491594	+	0.870824i	$0.663586\pi$
$720$	8.49065	0.316428
$721$	−11.6327	−0.433226
$722$	−14.8552	−0.552853
$723$	68.2432	2.53799
$724$	4.67451	0.173727
$725$	−1.36916	−0.0508495
$726$	−3.38979	−0.125807
$727$	−13.4850	−0.500130	−0.250065	−	0.968229i	$-0.580452\pi$
$727$	−13.4850	−0.500130	−0.250065	+	0.968229i	$0.580452\pi$
$728$	−8.13157	−0.301376
$729$	130.138	4.81994
$730$	1.00000	0.0370117
$731$	28.9794	1.07184
$732$	3.31988	0.122706
$733$	−9.52840	−0.351939	−0.175970	−	0.984396i	$-0.556306\pi$
$733$	−9.52840	−0.351939	−0.175970	+	0.984396i	$0.556306\pi$
$734$	−21.7528	−0.802912
$735$	18.2096	0.671673
$736$	5.87814	0.216671
$737$	0.367267	0.0135285
$738$	31.5372	1.16090
$739$	−20.6913	−0.761143	−0.380571	−	0.924752i	$-0.624273\pi$
$739$	−20.6913	−0.761143	−0.380571	+	0.924752i	$0.624273\pi$
$740$	−1.21239	−0.0445683
$741$	43.9804	1.61566
$742$	−10.5548	−0.387479
$743$	4.55144	0.166976	0.0834882	−	0.996509i	$-0.473394\pi$
$743$	4.55144	0.166976	0.0834882	+	0.996509i	$0.473394\pi$
$744$	−29.9580	−1.09831
$745$	−8.20032	−0.300436
$746$	29.9923	1.09810
$747$	−80.9005	−2.96000
$748$	−4.31350	−0.157717
$749$	18.2557	0.667049
$750$	−3.38979	−0.123778
$751$	−24.0964	−0.879290	−0.439645	−	0.898172i	$-0.644896\pi$
$751$	−24.0964	−0.879290	−0.439645	+	0.898172i	$0.644896\pi$
$752$	−10.0246	−0.365559
$753$	29.1892	1.06371
$754$	8.72551	0.317764
$755$	−19.4245	−0.706928
$756$	−23.7484	−0.863722
$757$	1.78991	0.0650554	0.0325277	−	0.999471i	$-0.489644\pi$
$757$	1.78991	0.0650554	0.0325277	+	0.999471i	$0.489644\pi$
$758$	−17.9651	−0.652523
$759$	−19.9256	−0.723255
$760$	2.03588	0.0738490
$761$	23.6257	0.856430	0.428215	−	0.903677i	$-0.359143\pi$
$761$	23.6257	0.856430	0.428215	+	0.903677i	$0.359143\pi$
$762$	−16.9022	−0.612303
$763$	−0.559724	−0.0202634
$764$	8.41189	0.304331
$765$	−36.6244	−1.32416
$766$	−28.3772	−1.02531
$767$	89.0759	3.21635
$768$	−3.38979	−0.122318
$769$	19.4885	0.702772	0.351386	−	0.936231i	$-0.385710\pi$
$769$	19.4885	0.702772	0.351386	+	0.936231i	$0.385710\pi$
$770$	1.27596	0.0459826
$771$	68.5342	2.46820
$772$	−3.85445	−0.138725
$773$	−1.46336	−0.0526333	−0.0263167	−	0.999654i	$-0.508378\pi$
$773$	−1.46336	−0.0526333	−0.0263167	+	0.999654i	$0.508378\pi$
$774$	−57.0427	−2.05036
$775$	8.83773	0.317461
$776$	15.7497	0.565382
$777$	5.24388	0.188123
$778$	−4.69308	−0.168255
$779$	7.56195	0.270935
$780$	21.6027	0.773500
$781$	−4.19342	−0.150052
$782$	−25.3553	−0.906705
$783$	25.4831	0.910691
$784$	−5.37191	−0.191854
$785$	−19.3921	−0.692133
$786$	12.4848	0.445318
$787$	30.4362	1.08493	0.542466	−	0.840078i	$-0.317491\pi$
$787$	30.4362	1.08493	0.542466	+	0.840078i	$0.317491\pi$
$788$	4.87162	0.173544
$789$	55.5754	1.97854
$790$	−7.97460	−0.283724
$791$	21.0932	0.749988
$792$	8.49065	0.301702
$793$	6.24145	0.221640
$794$	−5.85893	−0.207926
$795$	28.0403	0.994489
$796$	−17.6913	−0.627051
$797$	−32.4395	−1.14906	−0.574532	−	0.818482i	$-0.694816\pi$
$797$	−32.4395	−1.14906	−0.574532	+	0.818482i	$0.694816\pi$
$798$	−8.80568	−0.311718
$799$	43.2410	1.52976
$800$	1.00000	0.0353553
$801$	156.679	5.53598
$802$	23.4591	0.828369
$803$	1.00000	0.0352892
$804$	−1.24496	−0.0439062
$805$	7.50030	0.264351
$806$	−56.3218	−1.98385
$807$	−9.76686	−0.343810
$808$	13.7088	0.482276
$809$	18.6206	0.654666	0.327333	−	0.944909i	$-0.393850\pi$
$809$	18.6206	0.654666	0.327333	+	0.944909i	$0.393850\pi$
$810$	37.6192	1.32181
$811$	7.42173	0.260612	0.130306	−	0.991474i	$-0.458404\pi$
$811$	7.42173	0.260612	0.130306	+	0.991474i	$0.458404\pi$
$812$	−1.74701	−0.0613079
$813$	87.6577	3.07429
$814$	−1.21239	−0.0424942
$815$	−6.99055	−0.244868
$816$	14.6218	0.511867
$817$	−13.6776	−0.478520
$818$	−8.00003	−0.279714
$819$	−69.0423	−2.41253
$820$	3.71434	0.129710
$821$	19.6264	0.684964	0.342482	−	0.939524i	$-0.388732\pi$
$821$	19.6264	0.684964	0.342482	+	0.939524i	$0.388732\pi$
$822$	38.7862	1.35283
$823$	16.9073	0.589353	0.294676	−	0.955597i	$-0.404788\pi$
$823$	16.9073	0.589353	0.294676	+	0.955597i	$0.404788\pi$
$824$	−9.11681	−0.317599
$825$	−3.38979	−0.118017
$826$	−17.8346	−0.620545
$827$	40.0169	1.39152	0.695762	−	0.718273i	$-0.255067\pi$
$827$	40.0169	1.39152	0.695762	+	0.718273i	$0.255067\pi$
$828$	49.9092	1.73447
$829$	2.53035	0.0878828	0.0439414	−	0.999034i	$-0.486009\pi$
$829$	2.53035	0.0878828	0.0439414	+	0.999034i	$0.486009\pi$
$830$	−9.52819	−0.330728
$831$	−39.2616	−1.36197
$832$	−6.37288	−0.220940
$833$	23.1717	0.802853
$834$	31.4922	1.09049
$835$	10.9337	0.378376
$836$	2.03588	0.0704123
$837$	−164.489	−5.68557
$838$	−38.0151	−1.31321
$839$	−0.203583	−0.00702845	−0.00351423	−	0.999994i	$-0.501119\pi$
$839$	−0.203583	−0.00702845	−0.00351423	+	0.999994i	$0.501119\pi$
$840$	−4.32525	−0.149235
$841$	−27.1254	−0.935358
$842$	20.9173	0.720858
$843$	24.2236	0.834306
$844$	20.6081	0.709360
$845$	27.6136	0.949935
$846$	−85.1152	−2.92632
$847$	1.27596	0.0438427
$848$	−8.27201	−0.284062
$849$	−93.3963	−3.20535
$850$	−4.31350	−0.147952
$851$	−7.12659	−0.244296
$852$	14.2148	0.486991
$853$	48.7852	1.67037	0.835187	−	0.549966i	$-0.185359\pi$
$853$	48.7852	1.67037	0.835187	+	0.549966i	$0.185359\pi$
$854$	−1.24965	−0.0427622
$855$	17.2859	0.591166
$856$	14.3074	0.489016
$857$	−26.7364	−0.913299	−0.456650	−	0.889647i	$-0.650951\pi$
$857$	−26.7364	−0.913299	−0.456650	+	0.889647i	$0.650951\pi$
$858$	21.6027	0.737504
$859$	26.7839	0.913855	0.456928	−	0.889504i	$-0.348950\pi$
$859$	26.7839	0.913855	0.456928	+	0.889504i	$0.348950\pi$
$860$	−6.71830	−0.229092
$861$	−16.0655	−0.547509
$862$	18.8663	0.642589
$863$	−27.7878	−0.945907	−0.472954	−	0.881087i	$-0.656812\pi$
$863$	−27.7878	−0.945907	−0.472954	+	0.881087i	$0.656812\pi$
$864$	−18.6121	−0.633198
$865$	−14.2779	−0.485463
$866$	11.4356	0.388599
$867$	−5.44487	−0.184918
$868$	11.2766	0.382754
$869$	−7.97460	−0.270520
$870$	4.64117	0.157351
$871$	−2.34055	−0.0793064
$872$	−0.438667	−0.0148551
$873$	133.725	4.52592
$874$	11.9672	0.404796
$875$	1.27596	0.0431355
$876$	−3.38979	−0.114530
$877$	27.7794	0.938043	0.469021	−	0.883187i	$-0.344607\pi$
$877$	27.7794	0.938043	0.469021	+	0.883187i	$0.344607\pi$
$878$	−10.7841	−0.363946
$879$	54.4834	1.83768
$880$	1.00000	0.0337100
$881$	−10.1732	−0.342744	−0.171372	−	0.985206i	$-0.554820\pi$
$881$	−10.1732	−0.342744	−0.171372	+	0.985206i	$0.554820\pi$
$882$	−45.6111	−1.53580
$883$	13.6724	0.460112	0.230056	−	0.973177i	$-0.426109\pi$
$883$	13.6724	0.460112	0.230056	+	0.973177i	$0.426109\pi$
$884$	27.4894	0.924568
$885$	47.3802	1.59267
$886$	8.47840	0.284837
$887$	−47.6510	−1.59996	−0.799982	−	0.600024i	$-0.795158\pi$
$887$	−47.6510	−1.59996	−0.799982	+	0.600024i	$0.795158\pi$
$888$	4.10974	0.137914
$889$	6.36224	0.213383
$890$	18.4531	0.618550
$891$	37.6192	1.26029
$892$	17.7959	0.595850
$893$	−20.4088	−0.682955
$894$	27.7973	0.929682
$895$	−11.7461	−0.392630
$896$	1.27596	0.0426270
$897$	126.984	4.23986
$898$	0.252706	0.00843289
$899$	−12.1003	−0.403568
$900$	8.49065	0.283022
$901$	35.6813	1.18872
$902$	3.71434	0.123674
$903$	29.0583	0.967000
$904$	16.5312	0.549819
$905$	4.67451	0.155386
$906$	65.8448	2.18755
$907$	−10.5984	−0.351914	−0.175957	−	0.984398i	$-0.556302\pi$
$907$	−10.5984	−0.351914	−0.175957	+	0.984398i	$0.556302\pi$
$908$	24.0405	0.797813
$909$	116.397	3.86065
$910$	−8.13157	−0.269559
$911$	21.3971	0.708918	0.354459	−	0.935072i	$-0.384665\pi$
$911$	21.3971	0.708918	0.354459	+	0.935072i	$0.384665\pi$
$912$	−6.90119	−0.228521
$913$	−9.52819	−0.315337
$914$	−25.2732	−0.835964
$915$	3.31988	0.109752
$916$	−10.3646	−0.342455
$917$	−4.69946	−0.155190
$918$	80.2834	2.64975
$919$	26.2661	0.866439	0.433220	−	0.901288i	$-0.357377\pi$
$919$	26.2661	0.866439	0.433220	+	0.901288i	$0.357377\pi$
$920$	5.87814	0.193797
$921$	−25.3021	−0.833731
$922$	−5.64748	−0.185990
$923$	26.7242	0.879636
$924$	−4.32525	−0.142290
$925$	−1.21239	−0.0398631
$926$	−21.8640	−0.718496
$927$	−77.4077	−2.54240
$928$	−1.36916	−0.0449450
$929$	−29.8500	−0.979347	−0.489673	−	0.871906i	$-0.662884\pi$
$929$	−29.8500	−0.979347	−0.489673	+	0.871906i	$0.662884\pi$
$930$	−29.9580	−0.982362
$931$	−10.9366	−0.358431
$932$	9.05203	0.296509
$933$	112.175	3.67243
$934$	−21.0845	−0.689906
$935$	−4.31350	−0.141066
$936$	−54.1099	−1.76864
$937$	31.8793	1.04145	0.520726	−	0.853724i	$-0.325661\pi$
$937$	31.8793	1.04145	0.520726	+	0.853724i	$0.325661\pi$
$938$	0.468620	0.0153010
$939$	−35.7072	−1.16526
$940$	−10.0246	−0.326966
$941$	−40.1454	−1.30870	−0.654352	−	0.756190i	$-0.727058\pi$
$941$	−40.1454	−1.30870	−0.654352	+	0.756190i	$0.727058\pi$
$942$	65.7350	2.14176
$943$	21.8334	0.710994
$944$	−13.9774	−0.454924
$945$	−23.7484	−0.772537
$946$	−6.71830	−0.218431
$947$	22.4925	0.730909	0.365454	−	0.930829i	$-0.380914\pi$
$947$	22.4925	0.730909	0.365454	+	0.930829i	$0.380914\pi$
$948$	27.0322	0.877965
$949$	−6.37288	−0.206872
$950$	2.03588	0.0660526
$951$	84.4173	2.73742
$952$	−5.50387	−0.178381
$953$	8.80007	0.285062	0.142531	−	0.989790i	$-0.454476\pi$
$953$	8.80007	0.285062	0.142531	+	0.989790i	$0.454476\pi$
$954$	−70.2348	−2.27393
$955$	8.41189	0.272202
$956$	−10.4398	−0.337647
$957$	4.64117	0.150028
$958$	−21.3653	−0.690282
$959$	−14.5997	−0.471449
$960$	−3.38979	−0.109405
$961$	47.1054	1.51953
$962$	7.72640	0.249109
$963$	121.479	3.91460
$964$	−20.1320	−0.648409
$965$	−3.85445	−0.124079
$966$	−25.4244	−0.818017
$967$	−23.4336	−0.753574	−0.376787	−	0.926300i	$-0.622971\pi$
$967$	−23.4336	−0.753574	−0.376787	+	0.926300i	$0.622971\pi$
$968$	1.00000	0.0321412
$969$	29.7683	0.956295
$970$	15.7497	0.505693
$971$	−0.800642	−0.0256938	−0.0128469	−	0.999917i	$-0.504089\pi$
$971$	−0.800642	−0.0256938	−0.0128469	+	0.999917i	$0.504089\pi$
$972$	−71.6847	−2.29929
$973$	−11.8541	−0.380026
$974$	0.110895	0.00355332
$975$	21.6027	0.691840
$976$	−0.979378	−0.0313491
$977$	−4.12175	−0.131867	−0.0659333	−	0.997824i	$-0.521002\pi$
$977$	−4.12175	−0.131867	−0.0659333	+	0.997824i	$0.521002\pi$
$978$	23.6965	0.757730
$979$	18.4531	0.589764
$980$	−5.37191	−0.171600
$981$	−3.72457	−0.118916
$982$	17.4258	0.556080
$983$	−38.1352	−1.21632	−0.608162	−	0.793813i	$-0.708093\pi$
$983$	−38.1352	−1.21632	−0.608162	+	0.793813i	$0.708093\pi$
$984$	−12.5908	−0.401381
$985$	4.87162	0.155223
$986$	5.90589	0.188082
$987$	43.3588	1.38013
$988$	−12.9744	−0.412771
$989$	−39.4911	−1.25574
$990$	8.49065	0.269851
$991$	−5.10825	−0.162269	−0.0811344	−	0.996703i	$-0.525854\pi$
$991$	−5.10825	−0.162269	−0.0811344	+	0.996703i	$0.525854\pi$
$992$	8.83773	0.280598
$993$	70.3572	2.23272
$994$	−5.35066	−0.169713
$995$	−17.6913	−0.560852
$996$	32.2985	1.02342
$997$	29.8704	0.946005	0.473003	−	0.881061i	$-0.343170\pi$
$997$	29.8704	0.946005	0.473003	+	0.881061i	$0.343170\pi$
$998$	9.08271	0.287508
$999$	22.5651	0.713930

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.v.1.1	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.v.1.1	✓	5	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.38979 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38979 q^{6} +1.27596 q^{7} +1.00000 q^{8} +8.49065 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.38979 q^{3} +1.00000 q^{4} +1.00000 q^{5} -3.38979 q^{6} +1.27596 q^{7} +1.00000 q^{8} +8.49065 q^{9} +1.00000 q^{10} +1.00000 q^{11} -3.38979 q^{12} -6.37288 q^{13} +1.27596 q^{14} -3.38979 q^{15} +1.00000 q^{16} -4.31350 q^{17} +8.49065 q^{18} +2.03588 q^{19} +1.00000 q^{20} -4.32525 q^{21} +1.00000 q^{22} +5.87814 q^{23} -3.38979 q^{24} +1.00000 q^{25} -6.37288 q^{26} -18.6121 q^{27} +1.27596 q^{28} -1.36916 q^{29} -3.38979 q^{30} +8.83773 q^{31} +1.00000 q^{32} -3.38979 q^{33} -4.31350 q^{34} +1.27596 q^{35} +8.49065 q^{36} -1.21239 q^{37} +2.03588 q^{38} +21.6027 q^{39} +1.00000 q^{40} +3.71434 q^{41} -4.32525 q^{42} -6.71830 q^{43} +1.00000 q^{44} +8.49065 q^{45} +5.87814 q^{46} -10.0246 q^{47} -3.38979 q^{48} -5.37191 q^{49} +1.00000 q^{50} +14.6218 q^{51} -6.37288 q^{52} -8.27201 q^{53} -18.6121 q^{54} +1.00000 q^{55} +1.27596 q^{56} -6.90119 q^{57} -1.36916 q^{58} -13.9774 q^{59} -3.38979 q^{60} -0.979378 q^{61} +8.83773 q^{62} +10.8338 q^{63} +1.00000 q^{64} -6.37288 q^{65} -3.38979 q^{66} +0.367267 q^{67} -4.31350 q^{68} -19.9256 q^{69} +1.27596 q^{70} -4.19342 q^{71} +8.49065 q^{72} +1.00000 q^{73} -1.21239 q^{74} -3.38979 q^{75} +2.03588 q^{76} +1.27596 q^{77} +21.6027 q^{78} -7.97460 q^{79} +1.00000 q^{80} +37.6192 q^{81} +3.71434 q^{82} -9.52819 q^{83} -4.32525 q^{84} -4.31350 q^{85} -6.71830 q^{86} +4.64117 q^{87} +1.00000 q^{88} +18.4531 q^{89} +8.49065 q^{90} -8.13157 q^{91} +5.87814 q^{92} -29.9580 q^{93} -10.0246 q^{94} +2.03588 q^{95} -3.38979 q^{96} +15.7497 q^{97} -5.37191 q^{98} +8.49065 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 5 q^{5} - 5 q^{6} - 8 q^{7} + 5 q^{8} + 4 q^{9} + 5 q^{10} + 5 q^{11} - 5 q^{12} - 7 q^{13} - 8 q^{14} - 5 q^{15} + 5 q^{16} - 3 q^{17} + 4 q^{18} + 4 q^{19} + 5 q^{20} - 3 q^{21} + 5 q^{22} - 3 q^{23} - 5 q^{24} + 5 q^{25} - 7 q^{26} - 11 q^{27} - 8 q^{28} - 12 q^{29} - 5 q^{30} - q^{31} + 5 q^{32} - 5 q^{33} - 3 q^{34} - 8 q^{35} + 4 q^{36} + 4 q^{38} + 8 q^{39} + 5 q^{40} + q^{41} - 3 q^{42} + 5 q^{44} + 4 q^{45} - 3 q^{46} - 17 q^{47} - 5 q^{48} + 13 q^{49} + 5 q^{50} + 23 q^{51} - 7 q^{52} - 43 q^{53} - 11 q^{54} + 5 q^{55} - 8 q^{56} - 29 q^{57} - 12 q^{58} - 9 q^{59} - 5 q^{60} - 22 q^{61} - q^{62} + 25 q^{63} + 5 q^{64} - 7 q^{65} - 5 q^{66} - 9 q^{67} - 3 q^{68} + q^{69} - 8 q^{70} - 34 q^{71} + 4 q^{72} + 5 q^{73} - 5 q^{75} + 4 q^{76} - 8 q^{77} + 8 q^{78} - 24 q^{79} + 5 q^{80} + 25 q^{81} + q^{82} - 5 q^{83} - 3 q^{84} - 3 q^{85} + 30 q^{87} + 5 q^{88} + 58 q^{89} + 4 q^{90} - 9 q^{91} - 3 q^{92} - 32 q^{93} - 17 q^{94} + 4 q^{95} - 5 q^{96} + 13 q^{97} + 13 q^{98} + 4 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 5 * q^5 - 5 * q^6 - 8 * q^7 + 5 * q^8 + 4 * q^9 + 5 * q^10 + 5 * q^11 - 5 * q^12 - 7 * q^13 - 8 * q^14 - 5 * q^15 + 5 * q^16 - 3 * q^17 + 4 * q^18 + 4 * q^19 + 5 * q^20 - 3 * q^21 + 5 * q^22 - 3 * q^23 - 5 * q^24 + 5 * q^25 - 7 * q^26 - 11 * q^27 - 8 * q^28 - 12 * q^29 - 5 * q^30 - q^31 + 5 * q^32 - 5 * q^33 - 3 * q^34 - 8 * q^35 + 4 * q^36 + 4 * q^38 + 8 * q^39 + 5 * q^40 + q^41 - 3 * q^42 + 5 * q^44 + 4 * q^45 - 3 * q^46 - 17 * q^47 - 5 * q^48 + 13 * q^49 + 5 * q^50 + 23 * q^51 - 7 * q^52 - 43 * q^53 - 11 * q^54 + 5 * q^55 - 8 * q^56 - 29 * q^57 - 12 * q^58 - 9 * q^59 - 5 * q^60 - 22 * q^61 - q^62 + 25 * q^63 + 5 * q^64 - 7 * q^65 - 5 * q^66 - 9 * q^67 - 3 * q^68 + q^69 - 8 * q^70 - 34 * q^71 + 4 * q^72 + 5 * q^73 - 5 * q^75 + 4 * q^76 - 8 * q^77 + 8 * q^78 - 24 * q^79 + 5 * q^80 + 25 * q^81 + q^82 - 5 * q^83 - 3 * q^84 - 3 * q^85 + 30 * q^87 + 5 * q^88 + 58 * q^89 + 4 * q^90 - 9 * q^91 - 3 * q^92 - 32 * q^93 - 17 * q^94 + 4 * q^95 - 5 * q^96 + 13 * q^97 + 13 * q^98 + 4 * q^99

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