LMFDB - Embedded newform 6046.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.25917 q^{3} +1.00000 q^{4} -0.219000 q^{5} -3.25917 q^{6} -4.63324 q^{7} +1.00000 q^{8} +7.62218 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.25917 q^{3} +1.00000 q^{4} -0.219000 q^{5} -3.25917 q^{6} -4.63324 q^{7} +1.00000 q^{8} +7.62218 q^{9} -0.219000 q^{10} -4.69643 q^{11} -3.25917 q^{12} +2.92319 q^{13} -4.63324 q^{14} +0.713757 q^{15} +1.00000 q^{16} +3.44502 q^{17} +7.62218 q^{18} +1.26840 q^{19} -0.219000 q^{20} +15.1005 q^{21} -4.69643 q^{22} -0.315650 q^{23} -3.25917 q^{24} -4.95204 q^{25} +2.92319 q^{26} -15.0645 q^{27} -4.63324 q^{28} +4.23556 q^{29} +0.713757 q^{30} -3.63613 q^{31} +1.00000 q^{32} +15.3065 q^{33} +3.44502 q^{34} +1.01468 q^{35} +7.62218 q^{36} +4.00271 q^{37} +1.26840 q^{38} -9.52718 q^{39} -0.219000 q^{40} -8.57705 q^{41} +15.1005 q^{42} -1.81994 q^{43} -4.69643 q^{44} -1.66925 q^{45} -0.315650 q^{46} +13.1366 q^{47} -3.25917 q^{48} +14.4670 q^{49} -4.95204 q^{50} -11.2279 q^{51} +2.92319 q^{52} +8.95021 q^{53} -15.0645 q^{54} +1.02852 q^{55} -4.63324 q^{56} -4.13392 q^{57} +4.23556 q^{58} +2.97365 q^{59} +0.713757 q^{60} +9.25255 q^{61} -3.63613 q^{62} -35.3154 q^{63} +1.00000 q^{64} -0.640179 q^{65} +15.3065 q^{66} -10.0090 q^{67} +3.44502 q^{68} +1.02876 q^{69} +1.01468 q^{70} +9.54186 q^{71} +7.62218 q^{72} +0.550206 q^{73} +4.00271 q^{74} +16.1395 q^{75} +1.26840 q^{76} +21.7597 q^{77} -9.52718 q^{78} +1.94506 q^{79} -0.219000 q^{80} +26.2311 q^{81} -8.57705 q^{82} +11.8317 q^{83} +15.1005 q^{84} -0.754459 q^{85} -1.81994 q^{86} -13.8044 q^{87} -4.69643 q^{88} -1.91852 q^{89} -1.66925 q^{90} -13.5439 q^{91} -0.315650 q^{92} +11.8507 q^{93} +13.1366 q^{94} -0.277778 q^{95} -3.25917 q^{96} -13.8663 q^{97} +14.4670 q^{98} -35.7970 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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
$3$	−3.25917	−1.88168	−0.940841	−	0.338849i	$-0.889963\pi$
$3$	−3.25917	−1.88168	−0.940841	+	0.338849i	$0.889963\pi$
$4$	1.00000	0.500000
$5$	−0.219000	−0.0979396	−0.0489698	−	0.998800i	$-0.515594\pi$
$5$	−0.219000	−0.0979396	−0.0489698	+	0.998800i	$0.515594\pi$
$6$	−3.25917	−1.33055
$7$	−4.63324	−1.75120	−0.875601	−	0.483035i	$-0.839534\pi$
$7$	−4.63324	−1.75120	−0.875601	+	0.483035i	$0.839534\pi$
$8$	1.00000	0.353553
$9$	7.62218	2.54073
$10$	−0.219000	−0.0692538
$11$	−4.69643	−1.41603	−0.708014	−	0.706199i	$-0.750408\pi$
$11$	−4.69643	−1.41603	−0.708014	+	0.706199i	$0.750408\pi$
$12$	−3.25917	−0.940841
$13$	2.92319	0.810748	0.405374	−	0.914151i	$-0.367141\pi$
$13$	2.92319	0.810748	0.405374	+	0.914151i	$0.367141\pi$
$14$	−4.63324	−1.23829
$15$	0.713757	0.184291
$16$	1.00000	0.250000
$17$	3.44502	0.835541	0.417771	−	0.908553i	$-0.362812\pi$
$17$	3.44502	0.835541	0.417771	+	0.908553i	$0.362812\pi$
$18$	7.62218	1.79656
$19$	1.26840	0.290990	0.145495	−	0.989359i	$-0.453523\pi$
$19$	1.26840	0.290990	0.145495	+	0.989359i	$0.453523\pi$
$20$	−0.219000	−0.0489698
$21$	15.1005	3.29520
$22$	−4.69643	−1.00128
$23$	−0.315650	−0.0658176	−0.0329088	−	0.999458i	$-0.510477\pi$
$23$	−0.315650	−0.0658176	−0.0329088	+	0.999458i	$0.510477\pi$
$24$	−3.25917	−0.665275
$25$	−4.95204	−0.990408
$26$	2.92319	0.573286
$27$	−15.0645	−2.89916
$28$	−4.63324	−0.875601
$29$	4.23556	0.786525	0.393262	−	0.919426i	$-0.371346\pi$
$29$	4.23556	0.786525	0.393262	+	0.919426i	$0.371346\pi$
$30$	0.713757	0.130314
$31$	−3.63613	−0.653068	−0.326534	−	0.945186i	$-0.605881\pi$
$31$	−3.63613	−0.653068	−0.326534	+	0.945186i	$0.605881\pi$
$32$	1.00000	0.176777
$33$	15.3065	2.66451
$34$	3.44502	0.590817
$35$	1.01468	0.171512
$36$	7.62218	1.27036
$37$	4.00271	0.658041	0.329020	−	0.944323i	$-0.393282\pi$
$37$	4.00271	0.658041	0.329020	+	0.944323i	$0.393282\pi$
$38$	1.26840	0.205761
$39$	−9.52718	−1.52557
$40$	−0.219000	−0.0346269
$41$	−8.57705	−1.33951	−0.669755	−	0.742582i	$-0.733601\pi$
$41$	−8.57705	−1.33951	−0.669755	+	0.742582i	$0.733601\pi$
$42$	15.1005	2.33006
$43$	−1.81994	−0.277538	−0.138769	−	0.990325i	$-0.544315\pi$
$43$	−1.81994	−0.277538	−0.138769	+	0.990325i	$0.544315\pi$
$44$	−4.69643	−0.708014
$45$	−1.66925	−0.248838
$46$	−0.315650	−0.0465401
$47$	13.1366	1.91617	0.958083	−	0.286491i	$-0.0924889\pi$
$47$	13.1366	1.91617	0.958083	+	0.286491i	$0.0924889\pi$
$48$	−3.25917	−0.470420
$49$	14.4670	2.06671
$50$	−4.95204	−0.700324
$51$	−11.2279	−1.57222
$52$	2.92319	0.405374
$53$	8.95021	1.22941	0.614703	−	0.788758i	$-0.289276\pi$
$53$	8.95021	1.22941	0.614703	+	0.788758i	$0.289276\pi$
$54$	−15.0645	−2.05001
$55$	1.02852	0.138685
$56$	−4.63324	−0.619143
$57$	−4.13392	−0.547551
$58$	4.23556	0.556157
$59$	2.97365	0.387137	0.193568	−	0.981087i	$-0.437994\pi$
$59$	2.97365	0.387137	0.193568	+	0.981087i	$0.437994\pi$
$60$	0.713757	0.0921456
$61$	9.25255	1.18467	0.592334	−	0.805693i	$-0.298207\pi$
$61$	9.25255	1.18467	0.592334	+	0.805693i	$0.298207\pi$
$62$	−3.63613	−0.461789
$63$	−35.3154	−4.44932
$64$	1.00000	0.125000
$65$	−0.640179	−0.0794044
$66$	15.3065	1.88409
$67$	−10.0090	−1.22279	−0.611396	−	0.791325i	$-0.709392\pi$
$67$	−10.0090	−1.22279	−0.611396	+	0.791325i	$0.709392\pi$
$68$	3.44502	0.417771
$69$	1.02876	0.123848
$70$	1.01468	0.121277
$71$	9.54186	1.13241	0.566205	−	0.824264i	$-0.308411\pi$
$71$	9.54186	1.13241	0.566205	+	0.824264i	$0.308411\pi$
$72$	7.62218	0.898282
$73$	0.550206	0.0643967	0.0321983	−	0.999481i	$-0.489749\pi$
$73$	0.550206	0.0643967	0.0321983	+	0.999481i	$0.489749\pi$
$74$	4.00271	0.465305
$75$	16.1395	1.86363
$76$	1.26840	0.145495
$77$	21.7597	2.47975
$78$	−9.52718	−1.07874
$79$	1.94506	0.218836	0.109418	−	0.993996i	$-0.465101\pi$
$79$	1.94506	0.218836	0.109418	+	0.993996i	$0.465101\pi$
$80$	−0.219000	−0.0244849
$81$	26.2311	2.91456
$82$	−8.57705	−0.947177
$83$	11.8317	1.29870	0.649349	−	0.760491i	$-0.275041\pi$
$83$	11.8317	1.29870	0.649349	+	0.760491i	$0.275041\pi$
$84$	15.1005	1.64760
$85$	−0.754459	−0.0818326
$86$	−1.81994	−0.196249
$87$	−13.8044	−1.47999
$88$	−4.69643	−0.500641
$89$	−1.91852	−0.203363	−0.101682	−	0.994817i	$-0.532422\pi$
$89$	−1.91852	−0.203363	−0.101682	+	0.994817i	$0.532422\pi$
$90$	−1.66925	−0.175955
$91$	−13.5439	−1.41978
$92$	−0.315650	−0.0329088
$93$	11.8507	1.22887
$94$	13.1366	1.35493
$95$	−0.277778	−0.0284995
$96$	−3.25917	−0.332637
$97$	−13.8663	−1.40791	−0.703956	−	0.710244i	$-0.748585\pi$
$97$	−13.8663	−1.40791	−0.703956	+	0.710244i	$0.748585\pi$
$98$	14.4670	1.46138
$99$	−35.7970	−3.59774
$100$	−4.95204	−0.495204
$101$	−16.5696	−1.64874	−0.824370	−	0.566052i	$-0.808470\pi$
$101$	−16.5696	−1.64874	−0.824370	+	0.566052i	$0.808470\pi$
$102$	−11.2279	−1.11173
$103$	−10.5046	−1.03504	−0.517522	−	0.855670i	$-0.673146\pi$
$103$	−10.5046	−1.03504	−0.517522	+	0.855670i	$0.673146\pi$
$104$	2.92319	0.286643
$105$	−3.30701	−0.322731
$106$	8.95021	0.869322
$107$	9.10822	0.880525	0.440262	−	0.897869i	$-0.354885\pi$
$107$	9.10822	0.880525	0.440262	+	0.897869i	$0.354885\pi$
$108$	−15.0645	−1.44958
$109$	7.16315	0.686105	0.343053	−	0.939316i	$-0.388539\pi$
$109$	7.16315	0.686105	0.343053	+	0.939316i	$0.388539\pi$
$110$	1.02852	0.0980652
$111$	−13.0455	−1.23822
$112$	−4.63324	−0.437800
$113$	−18.7808	−1.76675	−0.883375	−	0.468667i	$-0.844734\pi$
$113$	−18.7808	−1.76675	−0.883375	+	0.468667i	$0.844734\pi$
$114$	−4.13392	−0.387177
$115$	0.0691273	0.00644615
$116$	4.23556	0.393262
$117$	22.2811	2.05989
$118$	2.97365	0.273747
$119$	−15.9616	−1.46320
$120$	0.713757	0.0651568
$121$	11.0565	1.00513
$122$	9.25255	0.837686
$123$	27.9540	2.52053
$124$	−3.63613	−0.326534
$125$	2.17949	0.194940
$126$	−35.3154	−3.14615
$127$	15.2480	1.35304	0.676521	−	0.736423i	$-0.263487\pi$
$127$	15.2480	1.35304	0.676521	+	0.736423i	$0.263487\pi$
$128$	1.00000	0.0883883
$129$	5.93148	0.522238
$130$	−0.640179	−0.0561474
$131$	−16.3267	−1.42647	−0.713236	−	0.700924i	$-0.752771\pi$
$131$	−16.3267	−1.42647	−0.713236	+	0.700924i	$0.752771\pi$
$132$	15.3065	1.33226
$133$	−5.87679	−0.509582
$134$	−10.0090	−0.864644
$135$	3.29911	0.283942
$136$	3.44502	0.295408
$137$	−0.0553162	−0.00472598	−0.00236299	−	0.999997i	$-0.500752\pi$
$137$	−0.0553162	−0.00472598	−0.00236299	+	0.999997i	$0.500752\pi$
$138$	1.02876	0.0875736
$139$	−0.894814	−0.0758971	−0.0379486	−	0.999280i	$-0.512082\pi$
$139$	−0.894814	−0.0758971	−0.0379486	+	0.999280i	$0.512082\pi$
$140$	1.01468	0.0857560
$141$	−42.8143	−3.60561
$142$	9.54186	0.800735
$143$	−13.7286	−1.14804
$144$	7.62218	0.635182
$145$	−0.927587	−0.0770319
$146$	0.550206	0.0455353
$147$	−47.1502	−3.88889
$148$	4.00271	0.329020
$149$	−0.607971	−0.0498069	−0.0249034	−	0.999690i	$-0.507928\pi$
$149$	−0.607971	−0.0498069	−0.0249034	+	0.999690i	$0.507928\pi$
$150$	16.1395	1.31779
$151$	2.55669	0.208060	0.104030	−	0.994574i	$-0.466826\pi$
$151$	2.55669	0.208060	0.104030	+	0.994574i	$0.466826\pi$
$152$	1.26840	0.102881
$153$	26.2586	2.12288
$154$	21.7597	1.75345
$155$	0.796311	0.0639612
$156$	−9.52718	−0.762785
$157$	3.71559	0.296537	0.148268	−	0.988947i	$-0.452630\pi$
$157$	3.71559	0.296537	0.148268	+	0.988947i	$0.452630\pi$
$158$	1.94506	0.154741
$159$	−29.1703	−2.31335
$160$	−0.219000	−0.0173134
$161$	1.46248	0.115260
$162$	26.2311	2.06091
$163$	−12.8769	−1.00860	−0.504299	−	0.863529i	$-0.668249\pi$
$163$	−12.8769	−1.00860	−0.504299	+	0.863529i	$0.668249\pi$
$164$	−8.57705	−0.669755
$165$	−3.35211	−0.260961
$166$	11.8317	0.918318
$167$	22.3108	1.72646	0.863231	−	0.504809i	$-0.168437\pi$
$167$	22.3108	1.72646	0.863231	+	0.504809i	$0.168437\pi$
$168$	15.1005	1.16503
$169$	−4.45493	−0.342687
$170$	−0.754459	−0.0578644
$171$	9.66794	0.739326
$172$	−1.81994	−0.138769
$173$	−2.34241	−0.178090	−0.0890452	−	0.996028i	$-0.528382\pi$
$173$	−2.34241	−0.178090	−0.0890452	+	0.996028i	$0.528382\pi$
$174$	−13.8044	−1.04651
$175$	22.9440	1.73440
$176$	−4.69643	−0.354007
$177$	−9.69164	−0.728468
$178$	−1.91852	−0.143799
$179$	1.10851	0.0828537	0.0414268	−	0.999142i	$-0.486810\pi$
$179$	1.10851	0.0828537	0.0414268	+	0.999142i	$0.486810\pi$
$180$	−1.66925	−0.124419
$181$	−24.5000	−1.82107	−0.910536	−	0.413430i	$-0.864331\pi$
$181$	−24.5000	−1.82107	−0.910536	+	0.413430i	$0.864331\pi$
$182$	−13.5439	−1.00394
$183$	−30.1556	−2.22917
$184$	−0.315650	−0.0232700
$185$	−0.876591	−0.0644483
$186$	11.8507	0.868939
$187$	−16.1793	−1.18315
$188$	13.1366	0.958083
$189$	69.7973	5.07701
$190$	−0.277778	−0.0201522
$191$	−15.9876	−1.15682	−0.578412	−	0.815745i	$-0.696327\pi$
$191$	−15.9876	−1.15682	−0.578412	+	0.815745i	$0.696327\pi$
$192$	−3.25917	−0.235210
$193$	−25.9328	−1.86668	−0.933342	−	0.358989i	$-0.883122\pi$
$193$	−25.9328	−1.86668	−0.933342	+	0.358989i	$0.883122\pi$
$194$	−13.8663	−0.995544
$195$	2.08645	0.149414
$196$	14.4670	1.03335
$197$	−14.3873	−1.02505	−0.512525	−	0.858672i	$-0.671290\pi$
$197$	−14.3873	−1.02505	−0.512525	+	0.858672i	$0.671290\pi$
$198$	−35.7970	−2.54398
$199$	17.3626	1.23080	0.615402	−	0.788213i	$-0.288994\pi$
$199$	17.3626	1.23080	0.615402	+	0.788213i	$0.288994\pi$
$200$	−4.95204	−0.350162
$201$	32.6209	2.30090
$202$	−16.5696	−1.16583
$203$	−19.6244	−1.37736
$204$	−11.2279	−0.786111
$205$	1.87837	0.131191
$206$	−10.5046	−0.731887
$207$	−2.40594	−0.167225
$208$	2.92319	0.202687
$209$	−5.95693	−0.412050
$210$	−3.30701	−0.228205
$211$	−15.8567	−1.09162	−0.545809	−	0.837910i	$-0.683777\pi$
$211$	−15.8567	−1.09162	−0.545809	+	0.837910i	$0.683777\pi$
$212$	8.95021	0.614703
$213$	−31.0985	−2.13084
$214$	9.10822	0.622625
$215$	0.398566	0.0271820
$216$	−15.0645	−1.02501
$217$	16.8471	1.14365
$218$	7.16315	0.485150
$219$	−1.79321	−0.121174
$220$	1.02852	0.0693426
$221$	10.0705	0.677414
$222$	−13.0455	−0.875556
$223$	11.9536	0.800471	0.400235	−	0.916412i	$-0.368928\pi$
$223$	11.9536	0.800471	0.400235	+	0.916412i	$0.368928\pi$
$224$	−4.63324	−0.309572
$225$	−37.7453	−2.51636
$226$	−18.7808	−1.24928
$227$	1.70658	0.113269	0.0566347	−	0.998395i	$-0.481963\pi$
$227$	1.70658	0.113269	0.0566347	+	0.998395i	$0.481963\pi$
$228$	−4.13392	−0.273775
$229$	−11.5112	−0.760683	−0.380341	−	0.924846i	$-0.624194\pi$
$229$	−11.5112	−0.760683	−0.380341	+	0.924846i	$0.624194\pi$
$230$	0.0691273	0.00455812
$231$	−70.9186	−4.66610
$232$	4.23556	0.278078
$233$	−13.5233	−0.885943	−0.442972	−	0.896536i	$-0.646076\pi$
$233$	−13.5233	−0.885943	−0.442972	+	0.896536i	$0.646076\pi$
$234$	22.2811	1.45656
$235$	−2.87690	−0.187669
$236$	2.97365	0.193568
$237$	−6.33927	−0.411780
$238$	−15.9616	−1.03464
$239$	−2.19934	−0.142263	−0.0711317	−	0.997467i	$-0.522661\pi$
$239$	−2.19934	−0.142263	−0.0711317	+	0.997467i	$0.522661\pi$
$240$	0.713757	0.0460728
$241$	9.88392	0.636679	0.318340	−	0.947977i	$-0.396875\pi$
$241$	9.88392	0.636679	0.318340	+	0.947977i	$0.396875\pi$
$242$	11.0565	0.710736
$243$	−40.2981	−2.58512
$244$	9.25255	0.592334
$245$	−3.16826	−0.202413
$246$	27.9540	1.78228
$247$	3.70777	0.235920
$248$	−3.63613	−0.230894
$249$	−38.5615	−2.44374
$250$	2.17949	0.137843
$251$	−15.5193	−0.979572	−0.489786	−	0.871843i	$-0.662925\pi$
$251$	−15.5193	−0.979572	−0.489786	+	0.871843i	$0.662925\pi$
$252$	−35.3154	−2.22466
$253$	1.48243	0.0931995
$254$	15.2480	0.956745
$255$	2.45891	0.153983
$256$	1.00000	0.0625000
$257$	−3.88023	−0.242042	−0.121021	−	0.992650i	$-0.538617\pi$
$257$	−3.88023	−0.242042	−0.121021	+	0.992650i	$0.538617\pi$
$258$	5.93148	0.369278
$259$	−18.5455	−1.15236
$260$	−0.640179	−0.0397022
$261$	32.2842	1.99834
$262$	−16.3267	−1.00867
$263$	5.62661	0.346952	0.173476	−	0.984838i	$-0.444500\pi$
$263$	5.62661	0.346952	0.173476	+	0.984838i	$0.444500\pi$
$264$	15.3065	0.942047
$265$	−1.96009	−0.120408
$266$	−5.87679	−0.360329
$267$	6.25279	0.382665
$268$	−10.0090	−0.611396
$269$	−2.01274	−0.122719	−0.0613595	−	0.998116i	$-0.519544\pi$
$269$	−2.01274	−0.122719	−0.0613595	+	0.998116i	$0.519544\pi$
$270$	3.29911	0.200778
$271$	−8.30889	−0.504729	−0.252365	−	0.967632i	$-0.581208\pi$
$271$	−8.30889	−0.504729	−0.252365	+	0.967632i	$0.581208\pi$
$272$	3.44502	0.208885
$273$	44.1418	2.67158
$274$	−0.0553162	−0.00334177
$275$	23.2569	1.40244
$276$	1.02876	0.0619239
$277$	5.81221	0.349222	0.174611	−	0.984638i	$-0.444133\pi$
$277$	5.81221	0.349222	0.174611	+	0.984638i	$0.444133\pi$
$278$	−0.894814	−0.0536674
$279$	−27.7152	−1.65927
$280$	1.01468	0.0606387
$281$	−15.7687	−0.940679	−0.470340	−	0.882486i	$-0.655869\pi$
$281$	−15.7687	−0.940679	−0.470340	+	0.882486i	$0.655869\pi$
$282$	−42.8143	−2.54955
$283$	0.454614	0.0270240	0.0135120	−	0.999909i	$-0.495699\pi$
$283$	0.454614	0.0270240	0.0135120	+	0.999909i	$0.495699\pi$
$284$	9.54186	0.566205
$285$	0.905326	0.0536269
$286$	−13.7286	−0.811788
$287$	39.7396	2.34575
$288$	7.62218	0.449141
$289$	−5.13180	−0.301871
$290$	−0.927587	−0.0544698
$291$	45.1927	2.64924
$292$	0.550206	0.0321983
$293$	−23.7064	−1.38494	−0.692470	−	0.721446i	$-0.743478\pi$
$293$	−23.7064	−1.38494	−0.692470	+	0.721446i	$0.743478\pi$
$294$	−47.1502	−2.74986
$295$	−0.651229	−0.0379160
$296$	4.00271	0.232653
$297$	70.7492	4.10528
$298$	−0.607971	−0.0352188
$299$	−0.922707	−0.0533615
$300$	16.1395	0.931816
$301$	8.43222	0.486025
$302$	2.55669	0.147121
$303$	54.0032	3.10240
$304$	1.26840	0.0727475
$305$	−2.02630	−0.116026
$306$	26.2586	1.50110
$307$	−11.7783	−0.672224	−0.336112	−	0.941822i	$-0.609112\pi$
$307$	−11.7783	−0.672224	−0.336112	+	0.941822i	$0.609112\pi$
$308$	21.7597	1.23987
$309$	34.2361	1.94762
$310$	0.796311	0.0452274
$311$	10.9272	0.619625	0.309813	−	0.950798i	$-0.399734\pi$
$311$	10.9272	0.619625	0.309813	+	0.950798i	$0.399734\pi$
$312$	−9.52718	−0.539371
$313$	28.0738	1.58683	0.793414	−	0.608683i	$-0.208302\pi$
$313$	28.0738	1.58683	0.793414	+	0.608683i	$0.208302\pi$
$314$	3.71559	0.209683
$315$	7.73406	0.435765
$316$	1.94506	0.109418
$317$	29.0069	1.62919	0.814596	−	0.580029i	$-0.196959\pi$
$317$	29.0069	1.62919	0.814596	+	0.580029i	$0.196959\pi$
$318$	−29.1703	−1.63579
$319$	−19.8920	−1.11374
$320$	−0.219000	−0.0122425
$321$	−29.6852	−1.65687
$322$	1.46248	0.0815011
$323$	4.36966	0.243134
$324$	26.2311	1.45728
$325$	−14.4758	−0.802972
$326$	−12.8769	−0.713187
$327$	−23.3459	−1.29103
$328$	−8.57705	−0.473588
$329$	−60.8649	−3.35559
$330$	−3.35211	−0.184528
$331$	−25.8814	−1.42257	−0.711284	−	0.702905i	$-0.751886\pi$
$331$	−25.8814	−1.42257	−0.711284	+	0.702905i	$0.751886\pi$
$332$	11.8317	0.649349
$333$	30.5093	1.67190
$334$	22.3108	1.22079
$335$	2.19196	0.119760
$336$	15.1005	0.823801
$337$	22.9756	1.25156	0.625779	−	0.780000i	$-0.284781\pi$
$337$	22.9756	1.25156	0.625779	+	0.780000i	$0.284781\pi$
$338$	−4.45493	−0.242316
$339$	61.2098	3.32446
$340$	−0.754459	−0.0409163
$341$	17.0768	0.924762
$342$	9.66794	0.522782
$343$	−34.5962	−1.86802
$344$	−1.81994	−0.0981245
$345$	−0.225297	−0.0121296
$346$	−2.34241	−0.125929
$347$	−23.8772	−1.28179	−0.640897	−	0.767627i	$-0.721437\pi$
$347$	−23.8772	−1.28179	−0.640897	+	0.767627i	$0.721437\pi$
$348$	−13.8044	−0.739994
$349$	21.0683	1.12776	0.563880	−	0.825857i	$-0.309308\pi$
$349$	21.0683	1.12776	0.563880	+	0.825857i	$0.309308\pi$
$350$	22.9440	1.22641
$351$	−44.0363	−2.35049
$352$	−4.69643	−0.250321
$353$	24.9410	1.32748	0.663738	−	0.747965i	$-0.268969\pi$
$353$	24.9410	1.32748	0.663738	+	0.747965i	$0.268969\pi$
$354$	−9.69164	−0.515105
$355$	−2.08967	−0.110908
$356$	−1.91852	−0.101682
$357$	52.0217	2.75328
$358$	1.10851	0.0585864
$359$	10.1829	0.537434	0.268717	−	0.963219i	$-0.413400\pi$
$359$	10.1829	0.537434	0.268717	+	0.963219i	$0.413400\pi$
$360$	−1.66925	−0.0879774
$361$	−17.3912	−0.915325
$362$	−24.5000	−1.28769
$363$	−36.0349	−1.89134
$364$	−13.5439	−0.709892
$365$	−0.120495	−0.00630699
$366$	−30.1556	−1.57626
$367$	31.4049	1.63932	0.819661	−	0.572849i	$-0.194162\pi$
$367$	31.4049	1.63932	0.819661	+	0.572849i	$0.194162\pi$
$368$	−0.315650	−0.0164544
$369$	−65.3758	−3.40333
$370$	−0.876591	−0.0455718
$371$	−41.4685	−2.15294
$372$	11.8507	0.614433
$373$	−20.6661	−1.07005	−0.535025	−	0.844836i	$-0.679698\pi$
$373$	−20.6661	−1.07005	−0.535025	+	0.844836i	$0.679698\pi$
$374$	−16.1793	−0.836613
$375$	−7.10334	−0.366815
$376$	13.1366	0.677467
$377$	12.3814	0.637674
$378$	69.7973	3.58999
$379$	0.347879	0.0178693	0.00893467	−	0.999960i	$-0.497156\pi$
$379$	0.347879	0.0178693	0.00893467	+	0.999960i	$0.497156\pi$
$380$	−0.277778	−0.0142497
$381$	−49.6958	−2.54599
$382$	−15.9876	−0.817998
$383$	−30.0943	−1.53775	−0.768875	−	0.639400i	$-0.779183\pi$
$383$	−30.0943	−1.53775	−0.768875	+	0.639400i	$0.779183\pi$
$384$	−3.25917	−0.166319
$385$	−4.76537	−0.242866
$386$	−25.9328	−1.31994
$387$	−13.8719	−0.705148
$388$	−13.8663	−0.703956
$389$	−6.76066	−0.342779	−0.171390	−	0.985203i	$-0.554826\pi$
$389$	−6.76066	−0.342779	−0.171390	+	0.985203i	$0.554826\pi$
$390$	2.08645	0.105652
$391$	−1.08742	−0.0549933
$392$	14.4670	0.730692
$393$	53.2116	2.68417
$394$	−14.3873	−0.724819
$395$	−0.425967	−0.0214327
$396$	−35.7970	−1.79887
$397$	−25.2886	−1.26920	−0.634598	−	0.772842i	$-0.718834\pi$
$397$	−25.2886	−1.26920	−0.634598	+	0.772842i	$0.718834\pi$
$398$	17.3626	0.870310
$399$	19.1534	0.958872
$400$	−4.95204	−0.247602
$401$	−13.3757	−0.667953	−0.333976	−	0.942581i	$-0.608391\pi$
$401$	−13.3757	−0.667953	−0.333976	+	0.942581i	$0.608391\pi$
$402$	32.6209	1.62698
$403$	−10.6291	−0.529474
$404$	−16.5696	−0.824370
$405$	−5.74460	−0.285451
$406$	−19.6244	−0.973943
$407$	−18.7984	−0.931804
$408$	−11.2279	−0.555865
$409$	19.0345	0.941197	0.470598	−	0.882348i	$-0.344038\pi$
$409$	19.0345	0.941197	0.470598	+	0.882348i	$0.344038\pi$
$410$	1.87837	0.0927661
$411$	0.180285	0.00889280
$412$	−10.5046	−0.517522
$413$	−13.7777	−0.677955
$414$	−2.40594	−0.118246
$415$	−2.59114	−0.127194
$416$	2.92319	0.143321
$417$	2.91635	0.142814
$418$	−5.95693	−0.291363
$419$	13.8007	0.674210	0.337105	−	0.941467i	$-0.390552\pi$
$419$	13.8007	0.674210	0.337105	+	0.941467i	$0.390552\pi$
$420$	−3.30701	−0.161366
$421$	−33.9603	−1.65512	−0.827562	−	0.561374i	$-0.810273\pi$
$421$	−33.9603	−1.65512	−0.827562	+	0.561374i	$0.810273\pi$
$422$	−15.8567	−0.771890
$423$	100.129	4.86845
$424$	8.95021	0.434661
$425$	−17.0599	−0.827527
$426$	−31.0985	−1.50673
$427$	−42.8693	−2.07459
$428$	9.10822	0.440262
$429$	44.7438	2.16025
$430$	0.398566	0.0192205
$431$	0.434391	0.0209239	0.0104619	−	0.999945i	$-0.496670\pi$
$431$	0.434391	0.0209239	0.0104619	+	0.999945i	$0.496670\pi$
$432$	−15.0645	−0.724789
$433$	−29.6018	−1.42257	−0.711285	−	0.702904i	$-0.751886\pi$
$433$	−29.6018	−1.42257	−0.711285	+	0.702904i	$0.751886\pi$
$434$	16.8471	0.808685
$435$	3.02316	0.144950
$436$	7.16315	0.343053
$437$	−0.400369	−0.0191523
$438$	−1.79321	−0.0856830
$439$	14.4309	0.688751	0.344375	−	0.938832i	$-0.388091\pi$
$439$	14.4309	0.688751	0.344375	+	0.938832i	$0.388091\pi$
$440$	1.02852	0.0490326
$441$	110.270	5.25094
$442$	10.0705	0.479004
$443$	6.73463	0.319972	0.159986	−	0.987119i	$-0.448855\pi$
$443$	6.73463	0.319972	0.159986	+	0.987119i	$0.448855\pi$
$444$	−13.0455	−0.619112
$445$	0.420156	0.0199173
$446$	11.9536	0.566018
$447$	1.98148	0.0937207
$448$	−4.63324	−0.218900
$449$	−34.2569	−1.61668	−0.808341	−	0.588714i	$-0.799634\pi$
$449$	−34.2569	−1.61668	−0.808341	+	0.588714i	$0.799634\pi$
$450$	−37.7453	−1.77933
$451$	40.2815	1.89678
$452$	−18.7808	−0.883375
$453$	−8.33268	−0.391503
$454$	1.70658	0.0800936
$455$	2.96610	0.139053
$456$	−4.13392	−0.193588
$457$	20.9807	0.981434	0.490717	−	0.871319i	$-0.336735\pi$
$457$	20.9807	0.981434	0.490717	+	0.871319i	$0.336735\pi$
$458$	−11.5112	−0.537884
$459$	−51.8974	−2.42236
$460$	0.0691273	0.00322308
$461$	−3.41725	−0.159157	−0.0795787	−	0.996829i	$-0.525357\pi$
$461$	−3.41725	−0.159157	−0.0795787	+	0.996829i	$0.525357\pi$
$462$	−70.9186	−3.29943
$463$	−9.67057	−0.449429	−0.224715	−	0.974425i	$-0.572145\pi$
$463$	−9.67057	−0.449429	−0.224715	+	0.974425i	$0.572145\pi$
$464$	4.23556	0.196631
$465$	−2.59531	−0.120355
$466$	−13.5233	−0.626457
$467$	9.81103	0.454001	0.227000	−	0.973895i	$-0.427108\pi$
$467$	9.81103	0.454001	0.227000	+	0.973895i	$0.427108\pi$
$468$	22.2811	1.02994
$469$	46.3740	2.14135
$470$	−2.87690	−0.132702
$471$	−12.1097	−0.557987
$472$	2.97365	0.136874
$473$	8.54721	0.393001
$474$	−6.33927	−0.291173
$475$	−6.28115	−0.288199
$476$	−15.9616	−0.731601
$477$	68.2201	3.12359
$478$	−2.19934	−0.100595
$479$	12.1499	0.555144	0.277572	−	0.960705i	$-0.410470\pi$
$479$	12.1499	0.555144	0.277572	+	0.960705i	$0.410470\pi$
$480$	0.713757	0.0325784
$481$	11.7007	0.533505
$482$	9.88392	0.450200
$483$	−4.76648	−0.216882
$484$	11.0565	0.502566
$485$	3.03672	0.137890
$486$	−40.2981	−1.82796
$487$	13.5521	0.614103	0.307051	−	0.951693i	$-0.400658\pi$
$487$	13.5521	0.614103	0.307051	+	0.951693i	$0.400658\pi$
$488$	9.25255	0.418843
$489$	41.9680	1.89786
$490$	−3.16826	−0.143127
$491$	−32.0625	−1.44696	−0.723480	−	0.690345i	$-0.757459\pi$
$491$	−32.0625	−1.44696	−0.723480	+	0.690345i	$0.757459\pi$
$492$	27.9540	1.26027
$493$	14.5916	0.657174
$494$	3.70777	0.166820
$495$	7.83954	0.352361
$496$	−3.63613	−0.163267
$497$	−44.2098	−1.98308
$498$	−38.5615	−1.72798
$499$	10.7313	0.480400	0.240200	−	0.970723i	$-0.422787\pi$
$499$	10.7313	0.480400	0.240200	+	0.970723i	$0.422787\pi$
$500$	2.17949	0.0974699
$501$	−72.7147	−3.24865
$502$	−15.5193	−0.692662
$503$	−25.4925	−1.13665	−0.568327	−	0.822803i	$-0.692409\pi$
$503$	−25.4925	−1.13665	−0.568327	+	0.822803i	$0.692409\pi$
$504$	−35.3154	−1.57307
$505$	3.62874	0.161477
$506$	1.48243	0.0659020
$507$	14.5194	0.644828
$508$	15.2480	0.676521
$509$	16.5946	0.735541	0.367771	−	0.929917i	$-0.380121\pi$
$509$	16.5946	0.735541	0.367771	+	0.929917i	$0.380121\pi$
$510$	2.45891	0.108882
$511$	−2.54924	−0.112772
$512$	1.00000	0.0441942
$513$	−19.1077	−0.843626
$514$	−3.88023	−0.171150
$515$	2.30049	0.101372
$516$	5.93148	0.261119
$517$	−61.6950	−2.71334
$518$	−18.5455	−0.814843
$519$	7.63432	0.335110
$520$	−0.640179	−0.0280737
$521$	−2.73822	−0.119964	−0.0599818	−	0.998199i	$-0.519104\pi$
$521$	−2.73822	−0.119964	−0.0599818	+	0.998199i	$0.519104\pi$
$522$	32.2842	1.41304
$523$	−1.48245	−0.0648230	−0.0324115	−	0.999475i	$-0.510319\pi$
$523$	−1.48245	−0.0648230	−0.0324115	+	0.999475i	$0.510319\pi$
$524$	−16.3267	−0.713236
$525$	−74.7784	−3.26360
$526$	5.62661	0.245332
$527$	−12.5265	−0.545665
$528$	15.3065	0.666128
$529$	−22.9004	−0.995668
$530$	−1.96009	−0.0851410
$531$	22.6657	0.983608
$532$	−5.87679	−0.254791
$533$	−25.0724	−1.08601
$534$	6.25279	0.270585
$535$	−1.99470	−0.0862383
$536$	−10.0090	−0.432322
$537$	−3.61281	−0.155904
$538$	−2.01274	−0.0867754
$539$	−67.9431	−2.92651
$540$	3.29911	0.141971
$541$	−38.3725	−1.64976	−0.824880	−	0.565308i	$-0.808758\pi$
$541$	−38.3725	−1.64976	−0.824880	+	0.565308i	$0.808758\pi$
$542$	−8.30889	−0.356898
$543$	79.8497	3.42668
$544$	3.44502	0.147704
$545$	−1.56873	−0.0671969
$546$	44.1418	1.88909
$547$	−7.08255	−0.302828	−0.151414	−	0.988470i	$-0.548383\pi$
$547$	−7.08255	−0.302828	−0.151414	+	0.988470i	$0.548383\pi$
$548$	−0.0553162	−0.00236299
$549$	70.5246	3.00992
$550$	23.2569	0.991678
$551$	5.37237	0.228871
$552$	1.02876	0.0437868
$553$	−9.01193	−0.383226
$554$	5.81221	0.246937
$555$	2.85696	0.121271
$556$	−0.894814	−0.0379486
$557$	−12.0848	−0.512048	−0.256024	−	0.966670i	$-0.582413\pi$
$557$	−12.0848	−0.512048	−0.256024	+	0.966670i	$0.582413\pi$
$558$	−27.7152	−1.17328
$559$	−5.32003	−0.225013
$560$	1.01468	0.0428780
$561$	52.7311	2.22631
$562$	−15.7687	−0.665161
$563$	−21.0807	−0.888446	−0.444223	−	0.895916i	$-0.646520\pi$
$563$	−21.0807	−0.888446	−0.444223	+	0.895916i	$0.646520\pi$
$564$	−42.8143	−1.80281
$565$	4.11299	0.173035
$566$	0.454614	0.0191088
$567$	−121.535	−5.10399
$568$	9.54186	0.400368
$569$	−35.8643	−1.50351	−0.751755	−	0.659443i	$-0.770792\pi$
$569$	−35.8643	−1.50351	−0.751755	+	0.659443i	$0.770792\pi$
$570$	0.905326	0.0379199
$571$	−4.48386	−0.187644	−0.0938219	−	0.995589i	$-0.529908\pi$
$571$	−4.48386	−0.187644	−0.0938219	+	0.995589i	$0.529908\pi$
$572$	−13.7286	−0.574021
$573$	52.1064	2.17677
$574$	39.7396	1.65870
$575$	1.56311	0.0651863
$576$	7.62218	0.317591
$577$	25.7779	1.07315	0.536573	−	0.843854i	$-0.319719\pi$
$577$	25.7779	1.07315	0.536573	+	0.843854i	$0.319719\pi$
$578$	−5.13180	−0.213455
$579$	84.5194	3.51251
$580$	−0.927587	−0.0385160
$581$	−54.8192	−2.27428
$582$	45.1927	1.87330
$583$	−42.0341	−1.74087
$584$	0.550206	0.0227677
$585$	−4.87956	−0.201745
$586$	−23.7064	−0.979301
$587$	0.858958	0.0354530	0.0177265	−	0.999843i	$-0.494357\pi$
$587$	0.858958	0.0354530	0.0177265	+	0.999843i	$0.494357\pi$
$588$	−47.1502	−1.94444
$589$	−4.61205	−0.190036
$590$	−0.651229	−0.0268107
$591$	46.8905	1.92882
$592$	4.00271	0.164510
$593$	31.2223	1.28215	0.641073	−	0.767480i	$-0.278490\pi$
$593$	31.2223	1.28215	0.641073	+	0.767480i	$0.278490\pi$
$594$	70.7492	2.90287
$595$	3.49559	0.143305
$596$	−0.607971	−0.0249034
$597$	−56.5878	−2.31598
$598$	−0.922707	−0.0377323
$599$	46.0732	1.88250	0.941249	−	0.337713i	$-0.109653\pi$
$599$	46.0732	1.88250	0.941249	+	0.337713i	$0.109653\pi$
$600$	16.1395	0.658894
$601$	−19.7661	−0.806278	−0.403139	−	0.915139i	$-0.632081\pi$
$601$	−19.7661	−0.806278	−0.403139	+	0.915139i	$0.632081\pi$
$602$	8.43222	0.343671
$603$	−76.2902	−3.10678
$604$	2.55669	0.104030
$605$	−2.42136	−0.0984423
$606$	54.0032	2.19373
$607$	14.8855	0.604182	0.302091	−	0.953279i	$-0.402315\pi$
$607$	14.8855	0.604182	0.302091	+	0.953279i	$0.402315\pi$
$608$	1.26840	0.0514403
$609$	63.9592	2.59176
$610$	−2.02630	−0.0820427
$611$	38.4008	1.55353
$612$	26.2586	1.06144
$613$	7.91356	0.319626	0.159813	−	0.987147i	$-0.448911\pi$
$613$	7.91356	0.319626	0.159813	+	0.987147i	$0.448911\pi$
$614$	−11.7783	−0.475334
$615$	−6.12193	−0.246860
$616$	21.7597	0.876724
$617$	−4.81741	−0.193942	−0.0969708	−	0.995287i	$-0.530915\pi$
$617$	−4.81741	−0.193942	−0.0969708	+	0.995287i	$0.530915\pi$
$618$	34.2361	1.37718
$619$	−22.0551	−0.886471	−0.443235	−	0.896405i	$-0.646169\pi$
$619$	−22.0551	−0.886471	−0.443235	+	0.896405i	$0.646169\pi$
$620$	0.796311	0.0319806
$621$	4.75510	0.190816
$622$	10.9272	0.438141
$623$	8.88899	0.356130
$624$	−9.52718	−0.381393
$625$	24.2829	0.971316
$626$	28.0738	1.12206
$627$	19.4147	0.775347
$628$	3.71559	0.148268
$629$	13.7894	0.549820
$630$	7.73406	0.308133
$631$	15.4532	0.615183	0.307592	−	0.951518i	$-0.400477\pi$
$631$	15.4532	0.615183	0.307592	+	0.951518i	$0.400477\pi$
$632$	1.94506	0.0773703
$633$	51.6795	2.05408
$634$	29.0069	1.15201
$635$	−3.33931	−0.132516
$636$	−29.1703	−1.15668
$637$	42.2897	1.67558
$638$	−19.8920	−0.787533
$639$	72.7298	2.87715
$640$	−0.219000	−0.00865672
$641$	−16.4612	−0.650178	−0.325089	−	0.945683i	$-0.605394\pi$
$641$	−16.4612	−0.650178	−0.325089	+	0.945683i	$0.605394\pi$
$642$	−29.6852	−1.17158
$643$	0.807624	0.0318496	0.0159248	−	0.999873i	$-0.494931\pi$
$643$	0.807624	0.0318496	0.0159248	+	0.999873i	$0.494931\pi$
$644$	1.46248	0.0576300
$645$	−1.29899	−0.0511478
$646$	4.36966	0.171922
$647$	9.80496	0.385473	0.192736	−	0.981251i	$-0.438264\pi$
$647$	9.80496	0.385473	0.192736	+	0.981251i	$0.438264\pi$
$648$	26.2311	1.03045
$649$	−13.9656	−0.548196
$650$	−14.4758	−0.567787
$651$	−54.9074	−2.15199
$652$	−12.8769	−0.504299
$653$	−9.30476	−0.364124	−0.182062	−	0.983287i	$-0.558277\pi$
$653$	−9.30476	−0.364124	−0.182062	+	0.983287i	$0.558277\pi$
$654$	−23.3459	−0.912897
$655$	3.57555	0.139708
$656$	−8.57705	−0.334877
$657$	4.19376	0.163614
$658$	−60.8649	−2.37276
$659$	−43.6895	−1.70190	−0.850950	−	0.525247i	$-0.823973\pi$
$659$	−43.6895	−1.70190	−0.850950	+	0.525247i	$0.823973\pi$
$660$	−3.35211	−0.130481
$661$	11.9525	0.464900	0.232450	−	0.972608i	$-0.425326\pi$
$661$	11.9525	0.464900	0.232450	+	0.972608i	$0.425326\pi$
$662$	−25.8814	−1.00591
$663$	−32.8214	−1.27468
$664$	11.8317	0.459159
$665$	1.28701	0.0499083
$666$	30.5093	1.18221
$667$	−1.33696	−0.0517672
$668$	22.3108	0.863231
$669$	−38.9587	−1.50623
$670$	2.19196	0.0846829
$671$	−43.4539	−1.67752
$672$	15.1005	0.582515
$673$	7.72537	0.297791	0.148896	−	0.988853i	$-0.452428\pi$
$673$	7.72537	0.297791	0.148896	+	0.988853i	$0.452428\pi$
$674$	22.9756	0.884985
$675$	74.5998	2.87135
$676$	−4.45493	−0.171344
$677$	−28.4838	−1.09472	−0.547361	−	0.836897i	$-0.684367\pi$
$677$	−28.4838	−1.09472	−0.547361	+	0.836897i	$0.684367\pi$
$678$	61.2098	2.35075
$679$	64.2461	2.46554
$680$	−0.754459	−0.0289322
$681$	−5.56202	−0.213137
$682$	17.0768	0.653905
$683$	24.1859	0.925449	0.462725	−	0.886502i	$-0.346872\pi$
$683$	24.1859	0.925449	0.462725	+	0.886502i	$0.346872\pi$
$684$	9.66794	0.369663
$685$	0.0121142	0.000462861 0
$686$	−34.5962	−1.32089
$687$	37.5170	1.43136
$688$	−1.81994	−0.0693845
$689$	26.1632	0.996739
$690$	−0.225297	−0.00857693
$691$	3.21778	0.122410	0.0612050	−	0.998125i	$-0.480506\pi$
$691$	3.21778	0.122410	0.0612050	+	0.998125i	$0.480506\pi$
$692$	−2.34241	−0.0890452
$693$	165.856	6.30036
$694$	−23.8772	−0.906365
$695$	0.195964	0.00743334
$696$	−13.8044	−0.523255
$697$	−29.5481	−1.11922
$698$	21.0683	0.797446
$699$	44.0748	1.66706
$700$	22.9440	0.867202
$701$	25.1960	0.951640	0.475820	−	0.879543i	$-0.342151\pi$
$701$	25.1960	0.951640	0.475820	+	0.879543i	$0.342151\pi$
$702$	−44.0363	−1.66204
$703$	5.07702	0.191483
$704$	−4.69643	−0.177003
$705$	9.37632	0.353133
$706$	24.9410	0.938667
$707$	76.7711	2.88728
$708$	−9.69164	−0.364234
$709$	47.6771	1.79055	0.895276	−	0.445511i	$-0.146978\pi$
$709$	47.6771	1.79055	0.895276	+	0.445511i	$0.146978\pi$
$710$	−2.08967	−0.0784237
$711$	14.8256	0.556003
$712$	−1.91852	−0.0718997
$713$	1.14774	0.0429833
$714$	52.0217	1.94686
$715$	3.00655	0.112439
$716$	1.10851	0.0414268
$717$	7.16802	0.267695
$718$	10.1829	0.380023
$719$	2.50465	0.0934076	0.0467038	−	0.998909i	$-0.485128\pi$
$719$	2.50465	0.0934076	0.0467038	+	0.998909i	$0.485128\pi$
$720$	−1.66925	−0.0622094
$721$	48.6702	1.81257
$722$	−17.3912	−0.647232
$723$	−32.2134	−1.19803
$724$	−24.5000	−0.910536
$725$	−20.9747	−0.778980
$726$	−36.0349	−1.33738
$727$	16.6047	0.615833	0.307917	−	0.951413i	$-0.400368\pi$
$727$	16.6047	0.615833	0.307917	+	0.951413i	$0.400368\pi$
$728$	−13.5439	−0.501969
$729$	52.6451	1.94982
$730$	−0.120495	−0.00445971
$731$	−6.26973	−0.231894
$732$	−30.1556	−1.11458
$733$	−5.84399	−0.215853	−0.107926	−	0.994159i	$-0.534421\pi$
$733$	−5.84399	−0.215853	−0.107926	+	0.994159i	$0.534421\pi$
$734$	31.4049	1.15918
$735$	10.3259	0.380876
$736$	−0.315650	−0.0116350
$737$	47.0065	1.73151
$738$	−65.3758	−2.40652
$739$	−36.5716	−1.34531	−0.672653	−	0.739958i	$-0.734845\pi$
$739$	−36.5716	−1.34531	−0.672653	+	0.739958i	$0.734845\pi$
$740$	−0.876591	−0.0322241
$741$	−12.0842	−0.443926
$742$	−41.4685	−1.52236
$743$	46.6699	1.71215	0.856076	−	0.516850i	$-0.172895\pi$
$743$	46.6699	1.71215	0.856076	+	0.516850i	$0.172895\pi$
$744$	11.8507	0.434470
$745$	0.133145	0.00487807
$746$	−20.6661	−0.756640
$747$	90.1833	3.29964
$748$	−16.1793	−0.591575
$749$	−42.2006	−1.54198
$750$	−7.10334	−0.259377
$751$	5.61681	0.204960	0.102480	−	0.994735i	$-0.467322\pi$
$751$	5.61681	0.204960	0.102480	+	0.994735i	$0.467322\pi$
$752$	13.1366	0.479041
$753$	50.5802	1.84324
$754$	12.3814	0.450903
$755$	−0.559914	−0.0203773
$756$	69.7973	2.53850
$757$	42.0305	1.52762	0.763811	−	0.645439i	$-0.223326\pi$
$757$	42.0305	1.52762	0.763811	+	0.645439i	$0.223326\pi$
$758$	0.347879	0.0126355
$759$	−4.83149	−0.175372
$760$	−0.277778	−0.0100761
$761$	4.06500	0.147356	0.0736780	−	0.997282i	$-0.476526\pi$
$761$	4.06500	0.147356	0.0736780	+	0.997282i	$0.476526\pi$
$762$	−49.6958	−1.80029
$763$	−33.1886	−1.20151
$764$	−15.9876	−0.578412
$765$	−5.75062	−0.207914
$766$	−30.0943	−1.08735
$767$	8.69257	0.313870
$768$	−3.25917	−0.117605
$769$	36.8617	1.32927	0.664633	−	0.747170i	$-0.268588\pi$
$769$	36.8617	1.32927	0.664633	+	0.747170i	$0.268588\pi$
$770$	−4.76537	−0.171732
$771$	12.6463	0.455447
$772$	−25.9328	−0.933342
$773$	29.2465	1.05192	0.525962	−	0.850508i	$-0.323705\pi$
$773$	29.2465	1.05192	0.525962	+	0.850508i	$0.323705\pi$
$774$	−13.8719	−0.498615
$775$	18.0062	0.646803
$776$	−13.8663	−0.497772
$777$	60.4430	2.16838
$778$	−6.76066	−0.242381
$779$	−10.8791	−0.389784
$780$	2.08645	0.0747069
$781$	−44.8127	−1.60352
$782$	−1.08742	−0.0388862
$783$	−63.8065	−2.28026
$784$	14.4670	0.516677
$785$	−0.813713	−0.0290427
$786$	53.2116	1.89799
$787$	−7.89941	−0.281584	−0.140792	−	0.990039i	$-0.544965\pi$
$787$	−7.89941	−0.281584	−0.140792	+	0.990039i	$0.544965\pi$
$788$	−14.3873	−0.512525
$789$	−18.3381	−0.652852
$790$	−0.425967	−0.0151552
$791$	87.0161	3.09393
$792$	−35.7970	−1.27199
$793$	27.0470	0.960467
$794$	−25.2886	−0.897457
$795$	6.38828	0.226569
$796$	17.3626	0.615402
$797$	54.3636	1.92566	0.962828	−	0.270114i	$-0.0870615\pi$
$797$	54.3636	1.92566	0.962828	+	0.270114i	$0.0870615\pi$
$798$	19.1534	0.678025
$799$	45.2558	1.60104
$800$	−4.95204	−0.175081
$801$	−14.6233	−0.516690
$802$	−13.3757	−0.472314
$803$	−2.58400	−0.0911875
$804$	32.6209	1.15045
$805$	−0.320284	−0.0112885
$806$	−10.6291	−0.374394
$807$	6.55986	0.230918
$808$	−16.5696	−0.582917
$809$	−47.1569	−1.65795	−0.828975	−	0.559286i	$-0.811075\pi$
$809$	−47.1569	−1.65795	−0.828975	+	0.559286i	$0.811075\pi$
$810$	−5.74460	−0.201845
$811$	−29.0537	−1.02021	−0.510107	−	0.860111i	$-0.670394\pi$
$811$	−29.0537	−1.02021	−0.510107	+	0.860111i	$0.670394\pi$
$812$	−19.6244	−0.688682
$813$	27.0801	0.949740
$814$	−18.7984	−0.658885
$815$	2.82004	0.0987817
$816$	−11.2279	−0.393056
$817$	−2.30840	−0.0807608
$818$	19.0345	0.665527
$819$	−103.234	−3.60728
$820$	1.87837	0.0655955
$821$	−33.7800	−1.17893	−0.589465	−	0.807794i	$-0.700661\pi$
$821$	−33.7800	−1.17893	−0.589465	+	0.807794i	$0.700661\pi$
$822$	0.180285	0.00628816
$823$	−17.8009	−0.620502	−0.310251	−	0.950655i	$-0.600413\pi$
$823$	−17.8009	−0.620502	−0.310251	+	0.950655i	$0.600413\pi$
$824$	−10.5046	−0.365944
$825$	−75.7982	−2.63895
$826$	−13.7777	−0.479386
$827$	5.68181	0.197576	0.0987879	−	0.995109i	$-0.468503\pi$
$827$	5.68181	0.197576	0.0987879	+	0.995109i	$0.468503\pi$
$828$	−2.40594	−0.0836123
$829$	−12.8737	−0.447123	−0.223561	−	0.974690i	$-0.571768\pi$
$829$	−12.8737	−0.447123	−0.223561	+	0.974690i	$0.571768\pi$
$830$	−2.59114	−0.0899397
$831$	−18.9430	−0.657124
$832$	2.92319	0.101344
$833$	49.8390	1.72682
$834$	2.91635	0.100985
$835$	−4.88606	−0.169089
$836$	−5.95693	−0.206025
$837$	54.7763	1.89335
$838$	13.8007	0.476738
$839$	−54.9763	−1.89799	−0.948996	−	0.315289i	$-0.897898\pi$
$839$	−54.9763	−1.89799	−0.948996	+	0.315289i	$0.897898\pi$
$840$	−3.30701	−0.114103
$841$	−11.0600	−0.381379
$842$	−33.9603	−1.17035
$843$	51.3927	1.77006
$844$	−15.8567	−0.545809
$845$	0.975629	0.0335626
$846$	100.129	3.44252
$847$	−51.2273	−1.76019
$848$	8.95021	0.307352
$849$	−1.48166	−0.0508506
$850$	−17.0599	−0.585150
$851$	−1.26345	−0.0433107
$852$	−31.0985	−1.06542
$853$	20.0797	0.687516	0.343758	−	0.939058i	$-0.388300\pi$
$853$	20.0797	0.687516	0.343758	+	0.939058i	$0.388300\pi$
$854$	−42.8693	−1.46696
$855$	−2.11728	−0.0724093
$856$	9.10822	0.311312
$857$	−4.84298	−0.165433	−0.0827165	−	0.996573i	$-0.526360\pi$
$857$	−4.84298	−0.165433	−0.0827165	+	0.996573i	$0.526360\pi$
$858$	44.7438	1.52753
$859$	−17.6828	−0.603331	−0.301665	−	0.953414i	$-0.597543\pi$
$859$	−17.6828	−0.603331	−0.301665	+	0.953414i	$0.597543\pi$
$860$	0.398566	0.0135910
$861$	−129.518	−4.41396
$862$	0.434391	0.0147954
$863$	−2.94277	−0.100173	−0.0500866	−	0.998745i	$-0.515950\pi$
$863$	−2.94277	−0.100173	−0.0500866	+	0.998745i	$0.515950\pi$
$864$	−15.0645	−0.512503
$865$	0.512988	0.0174421
$866$	−29.6018	−1.00591
$867$	16.7254	0.568025
$868$	16.8471	0.571827
$869$	−9.13483	−0.309878
$870$	3.02316	0.102495
$871$	−29.2582	−0.991376
$872$	7.16315	0.242575
$873$	−105.692	−3.57712
$874$	−0.400369	−0.0135427
$875$	−10.0981	−0.341379
$876$	−1.79321	−0.0605870
$877$	−40.1447	−1.35559	−0.677795	−	0.735251i	$-0.737064\pi$
$877$	−40.1447	−1.35559	−0.677795	+	0.735251i	$0.737064\pi$
$878$	14.4309	0.487020
$879$	77.2630	2.60602
$880$	1.02852	0.0346713
$881$	45.8585	1.54501	0.772505	−	0.635008i	$-0.219003\pi$
$881$	45.8585	1.54501	0.772505	+	0.635008i	$0.219003\pi$
$882$	110.270	3.71297
$883$	−25.2798	−0.850734	−0.425367	−	0.905021i	$-0.639855\pi$
$883$	−25.2798	−0.850734	−0.425367	+	0.905021i	$0.639855\pi$
$884$	10.0705	0.338707
$885$	2.12247	0.0713459
$886$	6.73463	0.226254
$887$	0.865869	0.0290730	0.0145365	−	0.999894i	$-0.495373\pi$
$887$	0.865869	0.0290730	0.0145365	+	0.999894i	$0.495373\pi$
$888$	−13.0455	−0.437778
$889$	−70.6478	−2.36945
$890$	0.420156	0.0140837
$891$	−123.192	−4.12710
$892$	11.9536	0.400235
$893$	16.6624	0.557585
$894$	1.98148	0.0662705
$895$	−0.242763	−0.00811466
$896$	−4.63324	−0.154786
$897$	3.00726	0.100409
$898$	−34.2569	−1.14317
$899$	−15.4011	−0.513654
$900$	−37.7453	−1.25818
$901$	30.8337	1.02722
$902$	40.2815	1.34123
$903$	−27.4820	−0.914544
$904$	−18.7808	−0.624640
$905$	5.36549	0.178355
$906$	−8.33268	−0.276835
$907$	10.4968	0.348540	0.174270	−	0.984698i	$-0.444243\pi$
$907$	10.4968	0.348540	0.174270	+	0.984698i	$0.444243\pi$
$908$	1.70658	0.0566347
$909$	−126.297	−4.18900
$910$	2.96610	0.0983254
$911$	−31.0794	−1.02971	−0.514853	−	0.857278i	$-0.672154\pi$
$911$	−31.0794	−1.02971	−0.514853	+	0.857278i	$0.672154\pi$
$912$	−4.13392	−0.136888
$913$	−55.5668	−1.83899
$914$	20.9807	0.693979
$915$	6.60407	0.218324
$916$	−11.5112	−0.380341
$917$	75.6457	2.49804
$918$	−51.8974	−1.71287
$919$	−23.5595	−0.777155	−0.388578	−	0.921416i	$-0.627033\pi$
$919$	−23.5595	−0.777155	−0.388578	+	0.921416i	$0.627033\pi$
$920$	0.0691273	0.00227906
$921$	38.3875	1.26491
$922$	−3.41725	−0.112541
$923$	27.8927	0.918100
$924$	−70.9186	−2.33305
$925$	−19.8216	−0.651729
$926$	−9.67057	−0.317795
$927$	−80.0676	−2.62977
$928$	4.23556	0.139039
$929$	56.7939	1.86335	0.931674	−	0.363295i	$-0.118348\pi$
$929$	56.7939	1.86335	0.931674	+	0.363295i	$0.118348\pi$
$930$	−2.59531	−0.0851036
$931$	18.3498	0.601391
$932$	−13.5233	−0.442972
$933$	−35.6136	−1.16594
$934$	9.81103	0.321027
$935$	3.54327	0.115877
$936$	22.2811	0.728281
$937$	10.1578	0.331840	0.165920	−	0.986139i	$-0.446941\pi$
$937$	10.1578	0.331840	0.165920	+	0.986139i	$0.446941\pi$
$938$	46.3740	1.51417
$939$	−91.4974	−2.98590
$940$	−2.87690	−0.0938343
$941$	−17.6787	−0.576308	−0.288154	−	0.957584i	$-0.593042\pi$
$941$	−17.6787	−0.576308	−0.288154	+	0.957584i	$0.593042\pi$
$942$	−12.1097	−0.394557
$943$	2.70735	0.0881633
$944$	2.97365	0.0967842
$945$	−15.2856	−0.497240
$946$	8.54721	0.277894
$947$	59.8389	1.94450	0.972251	−	0.233940i	$-0.0751620\pi$
$947$	59.8389	1.94450	0.972251	+	0.233940i	$0.0751620\pi$
$948$	−6.33927	−0.205890
$949$	1.60836	0.0522095
$950$	−6.28115	−0.203787
$951$	−94.5385	−3.06562
$952$	−15.9616	−0.517320
$953$	−13.4604	−0.436025	−0.218013	−	0.975946i	$-0.569957\pi$
$953$	−13.4604	−0.436025	−0.218013	+	0.975946i	$0.569957\pi$
$954$	68.2201	2.20871
$955$	3.50128	0.113299
$956$	−2.19934	−0.0711317
$957$	64.8315	2.09570
$958$	12.1499	0.392546
$959$	0.256294	0.00827615
$960$	0.713757	0.0230364
$961$	−17.7786	−0.573503
$962$	11.7007	0.377245
$963$	69.4245	2.23717
$964$	9.88392	0.318340
$965$	5.67927	0.182822
$966$	−4.76648	−0.153359
$967$	−52.1945	−1.67846	−0.839230	−	0.543776i	$-0.816994\pi$
$967$	−52.1945	−1.67846	−0.839230	+	0.543776i	$0.816994\pi$
$968$	11.0565	0.355368
$969$	−14.2414	−0.457501
$970$	3.03672	0.0975032
$971$	27.1812	0.872285	0.436142	−	0.899878i	$-0.356344\pi$
$971$	27.1812	0.872285	0.436142	+	0.899878i	$0.356344\pi$
$972$	−40.2981	−1.29256
$973$	4.14589	0.132911
$974$	13.5521	0.434236
$975$	47.1790	1.51094
$976$	9.25255	0.296167
$977$	−58.0411	−1.85690	−0.928449	−	0.371460i	$-0.878857\pi$
$977$	−58.0411	−1.85690	−0.928449	+	0.371460i	$0.878857\pi$
$978$	41.9680	1.34199
$979$	9.01022	0.287968
$980$	−3.16826	−0.101206
$981$	54.5988	1.74321
$982$	−32.0625	−1.02316
$983$	37.9897	1.21168	0.605842	−	0.795585i	$-0.292836\pi$
$983$	37.9897	1.21168	0.605842	+	0.795585i	$0.292836\pi$
$984$	27.9540	0.891142
$985$	3.15080	0.100393
$986$	14.5916	0.464692
$987$	198.369	6.31416
$988$	3.70777	0.117960
$989$	0.574464	0.0182669
$990$	7.83954	0.249157
$991$	−25.0013	−0.794193	−0.397096	−	0.917777i	$-0.629982\pi$
$991$	−25.0013	−0.794193	−0.397096	+	0.917777i	$0.629982\pi$
$992$	−3.63613	−0.115447
$993$	84.3517	2.67682
$994$	−44.2098	−1.40225
$995$	−3.80241	−0.120545
$996$	−38.5615	−1.22187
$997$	−37.7535	−1.19567	−0.597833	−	0.801620i	$-0.703972\pi$
$997$	−37.7535	−1.19567	−0.597833	+	0.801620i	$0.703972\pi$
$998$	10.7313	0.339694
$999$	−60.2986	−1.90776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.3	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.3	✓	56	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.25917 q^{3} +1.00000 q^{4} -0.219000 q^{5} -3.25917 q^{6} -4.63324 q^{7} +1.00000 q^{8} +7.62218 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.25917 q^{3} +1.00000 q^{4} -0.219000 q^{5} -3.25917 q^{6} -4.63324 q^{7} +1.00000 q^{8} +7.62218 q^{9} -0.219000 q^{10} -4.69643 q^{11} -3.25917 q^{12} +2.92319 q^{13} -4.63324 q^{14} +0.713757 q^{15} +1.00000 q^{16} +3.44502 q^{17} +7.62218 q^{18} +1.26840 q^{19} -0.219000 q^{20} +15.1005 q^{21} -4.69643 q^{22} -0.315650 q^{23} -3.25917 q^{24} -4.95204 q^{25} +2.92319 q^{26} -15.0645 q^{27} -4.63324 q^{28} +4.23556 q^{29} +0.713757 q^{30} -3.63613 q^{31} +1.00000 q^{32} +15.3065 q^{33} +3.44502 q^{34} +1.01468 q^{35} +7.62218 q^{36} +4.00271 q^{37} +1.26840 q^{38} -9.52718 q^{39} -0.219000 q^{40} -8.57705 q^{41} +15.1005 q^{42} -1.81994 q^{43} -4.69643 q^{44} -1.66925 q^{45} -0.315650 q^{46} +13.1366 q^{47} -3.25917 q^{48} +14.4670 q^{49} -4.95204 q^{50} -11.2279 q^{51} +2.92319 q^{52} +8.95021 q^{53} -15.0645 q^{54} +1.02852 q^{55} -4.63324 q^{56} -4.13392 q^{57} +4.23556 q^{58} +2.97365 q^{59} +0.713757 q^{60} +9.25255 q^{61} -3.63613 q^{62} -35.3154 q^{63} +1.00000 q^{64} -0.640179 q^{65} +15.3065 q^{66} -10.0090 q^{67} +3.44502 q^{68} +1.02876 q^{69} +1.01468 q^{70} +9.54186 q^{71} +7.62218 q^{72} +0.550206 q^{73} +4.00271 q^{74} +16.1395 q^{75} +1.26840 q^{76} +21.7597 q^{77} -9.52718 q^{78} +1.94506 q^{79} -0.219000 q^{80} +26.2311 q^{81} -8.57705 q^{82} +11.8317 q^{83} +15.1005 q^{84} -0.754459 q^{85} -1.81994 q^{86} -13.8044 q^{87} -4.69643 q^{88} -1.91852 q^{89} -1.66925 q^{90} -13.5439 q^{91} -0.315650 q^{92} +11.8507 q^{93} +13.1366 q^{94} -0.277778 q^{95} -3.25917 q^{96} -13.8663 q^{97} +14.4670 q^{98} -35.7970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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