LMFDB - Embedded newform 6018.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.46673$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.37322 q^{5} -1.00000 q^{6} +3.14256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.37322 q^{5} -1.00000 q^{6} +3.14256 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.37322 q^{10} +2.46673 q^{11} -1.00000 q^{12} -5.85410 q^{13} +3.14256 q^{14} +3.37322 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.93346 q^{19} -3.37322 q^{20} -3.14256 q^{21} +2.46673 q^{22} -6.50785 q^{23} -1.00000 q^{24} +6.37863 q^{25} -5.85410 q^{26} -1.00000 q^{27} +3.14256 q^{28} +0.329578 q^{29} +3.37322 q^{30} +5.56024 q^{31} +1.00000 q^{32} -2.46673 q^{33} +1.00000 q^{34} -10.6005 q^{35} +1.00000 q^{36} -6.52993 q^{37} +1.93346 q^{38} +5.85410 q^{39} -3.37322 q^{40} -1.38737 q^{41} -3.14256 q^{42} -11.8312 q^{43} +2.46673 q^{44} -3.37322 q^{45} -6.50785 q^{46} +13.3033 q^{47} -1.00000 q^{48} +2.87567 q^{49} +6.37863 q^{50} -1.00000 q^{51} -5.85410 q^{52} +2.03490 q^{53} -1.00000 q^{54} -8.32083 q^{55} +3.14256 q^{56} -1.93346 q^{57} +0.329578 q^{58} -1.00000 q^{59} +3.37322 q^{60} -5.22274 q^{61} +5.56024 q^{62} +3.14256 q^{63} +1.00000 q^{64} +19.7472 q^{65} -2.46673 q^{66} -11.6632 q^{67} +1.00000 q^{68} +6.50785 q^{69} -10.6005 q^{70} +9.28461 q^{71} +1.00000 q^{72} +5.39530 q^{73} -6.52993 q^{74} -6.37863 q^{75} +1.93346 q^{76} +7.75185 q^{77} +5.85410 q^{78} -2.16463 q^{79} -3.37322 q^{80} +1.00000 q^{81} -1.38737 q^{82} -2.50163 q^{83} -3.14256 q^{84} -3.37322 q^{85} -11.8312 q^{86} -0.329578 q^{87} +2.46673 q^{88} +10.4048 q^{89} -3.37322 q^{90} -18.3969 q^{91} -6.50785 q^{92} -5.56024 q^{93} +13.3033 q^{94} -6.52200 q^{95} -1.00000 q^{96} +7.09017 q^{97} +2.87567 q^{98} +2.46673 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} - 10 q^{13} + q^{14} + 3 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 8 q^{19} - 3 q^{20} - q^{21} + 2 q^{22} - 10 q^{23} - 4 q^{24} + 5 q^{25} - 10 q^{26} - 4 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} + 17 q^{31} + 4 q^{32} - 2 q^{33} + 4 q^{34} - 8 q^{35} + 4 q^{36} - 9 q^{37} - 8 q^{38} + 10 q^{39} - 3 q^{40} - q^{42} - 14 q^{43} + 2 q^{44} - 3 q^{45} - 10 q^{46} + 2 q^{47} - 4 q^{48} - 5 q^{49} + 5 q^{50} - 4 q^{51} - 10 q^{52} - 11 q^{53} - 4 q^{54} - 12 q^{55} + q^{56} + 8 q^{57} - 5 q^{58} - 4 q^{59} + 3 q^{60} - 28 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{66} - q^{67} + 4 q^{68} + 10 q^{69} - 8 q^{70} + 12 q^{71} + 4 q^{72} + 10 q^{73} - 9 q^{74} - 5 q^{75} - 8 q^{76} + 10 q^{78} + 4 q^{79} - 3 q^{80} + 4 q^{81} + 17 q^{83} - q^{84} - 3 q^{85} - 14 q^{86} + 5 q^{87} + 2 q^{88} - 13 q^{89} - 3 q^{90} - 25 q^{91} - 10 q^{92} - 17 q^{93} + 2 q^{94} - 15 q^{95} - 4 q^{96} + 6 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 - 10 * q^13 + q^14 + 3 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 8 * q^19 - 3 * q^20 - q^21 + 2 * q^22 - 10 * q^23 - 4 * q^24 + 5 * q^25 - 10 * q^26 - 4 * q^27 + q^28 - 5 * q^29 + 3 * q^30 + 17 * q^31 + 4 * q^32 - 2 * q^33 + 4 * q^34 - 8 * q^35 + 4 * q^36 - 9 * q^37 - 8 * q^38 + 10 * q^39 - 3 * q^40 - q^42 - 14 * q^43 + 2 * q^44 - 3 * q^45 - 10 * q^46 + 2 * q^47 - 4 * q^48 - 5 * q^49 + 5 * q^50 - 4 * q^51 - 10 * q^52 - 11 * q^53 - 4 * q^54 - 12 * q^55 + q^56 + 8 * q^57 - 5 * q^58 - 4 * q^59 + 3 * q^60 - 28 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^66 - q^67 + 4 * q^68 + 10 * q^69 - 8 * q^70 + 12 * q^71 + 4 * q^72 + 10 * q^73 - 9 * q^74 - 5 * q^75 - 8 * q^76 + 10 * q^78 + 4 * q^79 - 3 * q^80 + 4 * q^81 + 17 * q^83 - q^84 - 3 * q^85 - 14 * q^86 + 5 * q^87 + 2 * q^88 - 13 * q^89 - 3 * q^90 - 25 * q^91 - 10 * q^92 - 17 * q^93 + 2 * q^94 - 15 * q^95 - 4 * q^96 + 6 * q^97 - 5 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.37322	−1.50855	−0.754275	−	0.656558i	$-0.772012\pi$
$5$	−3.37322	−1.50855	−0.754275	+	0.656558i	$0.772012\pi$
$6$	−1.00000	−0.408248
$7$	3.14256	1.18778	0.593888	−	0.804548i	$-0.297592\pi$
$7$	3.14256	1.18778	0.593888	+	0.804548i	$0.297592\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.37322	−1.06671
$11$	2.46673	0.743748	0.371874	−	0.928283i	$-0.378715\pi$
$11$	2.46673	0.743748	0.371874	+	0.928283i	$0.378715\pi$
$12$	−1.00000	−0.288675
$13$	−5.85410	−1.62364	−0.811818	−	0.583911i	$-0.801522\pi$
$13$	−5.85410	−1.62364	−0.811818	+	0.583911i	$0.801522\pi$
$14$	3.14256	0.839884
$15$	3.37322	0.870962
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	1.93346	0.443567	0.221783	−	0.975096i	$-0.428812\pi$
$19$	1.93346	0.443567	0.221783	+	0.975096i	$0.428812\pi$
$20$	−3.37322	−0.754275
$21$	−3.14256	−0.685762
$22$	2.46673	0.525909
$23$	−6.50785	−1.35698	−0.678491	−	0.734609i	$-0.737366\pi$
$23$	−6.50785	−1.35698	−0.678491	+	0.734609i	$0.737366\pi$
$24$	−1.00000	−0.204124
$25$	6.37863	1.27573
$26$	−5.85410	−1.14808
$27$	−1.00000	−0.192450
$28$	3.14256	0.593888
$29$	0.329578	0.0612011	0.0306005	−	0.999532i	$-0.490258\pi$
$29$	0.329578	0.0612011	0.0306005	+	0.999532i	$0.490258\pi$
$30$	3.37322	0.615863
$31$	5.56024	0.998649	0.499324	−	0.866415i	$-0.333582\pi$
$31$	5.56024	0.998649	0.499324	+	0.866415i	$0.333582\pi$
$32$	1.00000	0.176777
$33$	−2.46673	−0.429403
$34$	1.00000	0.171499
$35$	−10.6005	−1.79182
$36$	1.00000	0.166667
$37$	−6.52993	−1.07351	−0.536757	−	0.843737i	$-0.680351\pi$
$37$	−6.52993	−1.07351	−0.536757	+	0.843737i	$0.680351\pi$
$38$	1.93346	0.313649
$39$	5.85410	0.937407
$40$	−3.37322	−0.533353
$41$	−1.38737	−0.216671	−0.108335	−	0.994114i	$-0.534552\pi$
$41$	−1.38737	−0.216671	−0.108335	+	0.994114i	$0.534552\pi$
$42$	−3.14256	−0.484907
$43$	−11.8312	−1.80424	−0.902121	−	0.431483i	$-0.857991\pi$
$43$	−11.8312	−1.80424	−0.902121	+	0.431483i	$0.857991\pi$
$44$	2.46673	0.371874
$45$	−3.37322	−0.502850
$46$	−6.50785	−0.959531
$47$	13.3033	1.94049	0.970246	−	0.242120i	$-0.0778429\pi$
$47$	13.3033	1.94049	0.970246	+	0.242120i	$0.0778429\pi$
$48$	−1.00000	−0.144338
$49$	2.87567	0.410810
$50$	6.37863	0.902074
$51$	−1.00000	−0.140028
$52$	−5.85410	−0.811818
$53$	2.03490	0.279515	0.139758	−	0.990186i	$-0.455368\pi$
$53$	2.03490	0.279515	0.139758	+	0.990186i	$0.455368\pi$
$54$	−1.00000	−0.136083
$55$	−8.32083	−1.12198
$56$	3.14256	0.419942
$57$	−1.93346	−0.256094
$58$	0.329578	0.0432757
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.37322	0.435481
$61$	−5.22274	−0.668703	−0.334351	−	0.942448i	$-0.608517\pi$
$61$	−5.22274	−0.668703	−0.334351	+	0.942448i	$0.608517\pi$
$62$	5.56024	0.706151
$63$	3.14256	0.395925
$64$	1.00000	0.125000
$65$	19.7472	2.44934
$66$	−2.46673	−0.303634
$67$	−11.6632	−1.42489	−0.712446	−	0.701727i	$-0.752412\pi$
$67$	−11.6632	−1.42489	−0.712446	+	0.701727i	$0.752412\pi$
$68$	1.00000	0.121268
$69$	6.50785	0.783454
$70$	−10.6005	−1.26701
$71$	9.28461	1.10188	0.550940	−	0.834545i	$-0.314269\pi$
$71$	9.28461	1.10188	0.550940	+	0.834545i	$0.314269\pi$
$72$	1.00000	0.117851
$73$	5.39530	0.631472	0.315736	−	0.948847i	$-0.397749\pi$
$73$	5.39530	0.631472	0.315736	+	0.948847i	$0.397749\pi$
$74$	−6.52993	−0.759089
$75$	−6.37863	−0.736540
$76$	1.93346	0.221783
$77$	7.75185	0.883405
$78$	5.85410	0.662847
$79$	−2.16463	−0.243540	−0.121770	−	0.992558i	$-0.538857\pi$
$79$	−2.16463	−0.243540	−0.121770	+	0.992558i	$0.538857\pi$
$80$	−3.37322	−0.377138
$81$	1.00000	0.111111
$82$	−1.38737	−0.153209
$83$	−2.50163	−0.274590	−0.137295	−	0.990530i	$-0.543841\pi$
$83$	−2.50163	−0.274590	−0.137295	+	0.990530i	$0.543841\pi$
$84$	−3.14256	−0.342881
$85$	−3.37322	−0.365877
$86$	−11.8312	−1.27579
$87$	−0.329578	−0.0353345
$88$	2.46673	0.262954
$89$	10.4048	1.10290	0.551452	−	0.834206i	$-0.314074\pi$
$89$	10.4048	1.10290	0.551452	+	0.834206i	$0.314074\pi$
$90$	−3.37322	−0.355569
$91$	−18.3969	−1.92851
$92$	−6.50785	−0.678491
$93$	−5.56024	−0.576570
$94$	13.3033	1.37214
$95$	−6.52200	−0.669143
$96$	−1.00000	−0.102062
$97$	7.09017	0.719898	0.359949	−	0.932972i	$-0.382794\pi$
$97$	7.09017	0.719898	0.359949	+	0.932972i	$0.382794\pi$
$98$	2.87567	0.290487
$99$	2.46673	0.247916
$100$	6.37863	0.637863
$101$	2.68123	0.266792	0.133396	−	0.991063i	$-0.457412\pi$
$101$	2.68123	0.266792	0.133396	+	0.991063i	$0.457412\pi$
$102$	−1.00000	−0.0990148
$103$	−5.26304	−0.518583	−0.259291	−	0.965799i	$-0.583489\pi$
$103$	−5.26304	−0.518583	−0.259291	+	0.965799i	$0.583489\pi$
$104$	−5.85410	−0.574042
$105$	10.6005	1.03451
$106$	2.03490	0.197647
$107$	3.46880	0.335341	0.167671	−	0.985843i	$-0.446376\pi$
$107$	3.46880	0.335341	0.167671	+	0.985843i	$0.446376\pi$
$108$	−1.00000	−0.0962250
$109$	−9.99044	−0.956910	−0.478455	−	0.878112i	$-0.658803\pi$
$109$	−9.99044	−0.956910	−0.478455	+	0.878112i	$0.658803\pi$
$110$	−8.32083	−0.793360
$111$	6.52993	0.619793
$112$	3.14256	0.296944
$113$	−8.88648	−0.835970	−0.417985	−	0.908454i	$-0.637263\pi$
$113$	−8.88648	−0.835970	−0.417985	+	0.908454i	$0.637263\pi$
$114$	−1.93346	−0.181085
$115$	21.9524	2.04708
$116$	0.329578	0.0306005
$117$	−5.85410	−0.541212
$118$	−1.00000	−0.0920575
$119$	3.14256	0.288078
$120$	3.37322	0.307932
$121$	−4.91523	−0.446839
$122$	−5.22274	−0.472844
$123$	1.38737	0.125095
$124$	5.56024	0.499324
$125$	−4.65041	−0.415945
$126$	3.14256	0.279961
$127$	−7.56276	−0.671087	−0.335543	−	0.942025i	$-0.608920\pi$
$127$	−7.56276	−0.671087	−0.335543	+	0.942025i	$0.608920\pi$
$128$	1.00000	0.0883883
$129$	11.8312	1.04168
$130$	19.7472	1.73194
$131$	−5.92856	−0.517981	−0.258991	−	0.965880i	$-0.583390\pi$
$131$	−5.92856	−0.517981	−0.258991	+	0.965880i	$0.583390\pi$
$132$	−2.46673	−0.214701
$133$	6.07602	0.526858
$134$	−11.6632	−1.00755
$135$	3.37322	0.290321
$136$	1.00000	0.0857493
$137$	−18.8312	−1.60886	−0.804429	−	0.594048i	$-0.797529\pi$
$137$	−18.8312	−1.60886	−0.804429	+	0.594048i	$0.797529\pi$
$138$	6.50785	0.553985
$139$	−15.9704	−1.35459	−0.677297	−	0.735710i	$-0.736849\pi$
$139$	−15.9704	−1.35459	−0.677297	+	0.735710i	$0.736849\pi$
$140$	−10.6005	−0.895910
$141$	−13.3033	−1.12034
$142$	9.28461	0.779147
$143$	−14.4405	−1.20758
$144$	1.00000	0.0833333
$145$	−1.11174	−0.0923249
$146$	5.39530	0.446518
$147$	−2.87567	−0.237181
$148$	−6.52993	−0.536757
$149$	−1.04158	−0.0853295	−0.0426648	−	0.999089i	$-0.513585\pi$
$149$	−1.04158	−0.0853295	−0.0426648	+	0.999089i	$0.513585\pi$
$150$	−6.37863	−0.520813
$151$	−16.3852	−1.33341	−0.666706	−	0.745321i	$-0.732296\pi$
$151$	−16.3852	−1.33341	−0.666706	+	0.745321i	$0.732296\pi$
$152$	1.93346	0.156825
$153$	1.00000	0.0808452
$154$	7.75185	0.624662
$155$	−18.7559	−1.50651
$156$	5.85410	0.468703
$157$	−15.0267	−1.19926	−0.599629	−	0.800278i	$-0.704685\pi$
$157$	−15.0267	−1.19926	−0.599629	+	0.800278i	$0.704685\pi$
$158$	−2.16463	−0.172209
$159$	−2.03490	−0.161378
$160$	−3.37322	−0.266677
$161$	−20.4513	−1.61179
$162$	1.00000	0.0785674
$163$	−14.9571	−1.17153	−0.585765	−	0.810481i	$-0.699206\pi$
$163$	−14.9571	−1.17153	−0.585765	+	0.810481i	$0.699206\pi$
$164$	−1.38737	−0.108335
$165$	8.32083	0.647776
$166$	−2.50163	−0.194164
$167$	−18.5880	−1.43838	−0.719190	−	0.694814i	$-0.755487\pi$
$167$	−18.5880	−1.43838	−0.719190	+	0.694814i	$0.755487\pi$
$168$	−3.14256	−0.242454
$169$	21.2705	1.63619
$170$	−3.37322	−0.258714
$171$	1.93346	0.147856
$172$	−11.8312	−0.902121
$173$	20.2946	1.54297	0.771485	−	0.636248i	$-0.219514\pi$
$173$	20.2946	1.54297	0.771485	+	0.636248i	$0.219514\pi$
$174$	−0.329578	−0.0249852
$175$	20.0452	1.51527
$176$	2.46673	0.185937
$177$	1.00000	0.0751646
$178$	10.4048	0.779871
$179$	−3.15048	−0.235478	−0.117739	−	0.993045i	$-0.537565\pi$
$179$	−3.15048	−0.235478	−0.117739	+	0.993045i	$0.537565\pi$
$180$	−3.37322	−0.251425
$181$	22.7182	1.68863	0.844315	−	0.535847i	$-0.180008\pi$
$181$	22.7182	1.68863	0.844315	+	0.535847i	$0.180008\pi$
$182$	−18.3969	−1.36367
$183$	5.22274	0.386076
$184$	−6.50785	−0.479765
$185$	22.0269	1.61945
$186$	−5.56024	−0.407697
$187$	2.46673	0.180385
$188$	13.3033	0.970246
$189$	−3.14256	−0.228587
$190$	−6.52200	−0.473156
$191$	−5.28543	−0.382440	−0.191220	−	0.981547i	$-0.561244\pi$
$191$	−5.28543	−0.382440	−0.191220	+	0.981547i	$0.561244\pi$
$192$	−1.00000	−0.0721688
$193$	−1.37248	−0.0987933	−0.0493967	−	0.998779i	$-0.515730\pi$
$193$	−1.37248	−0.0987933	−0.0493967	+	0.998779i	$0.515730\pi$
$194$	7.09017	0.509045
$195$	−19.7472	−1.41413
$196$	2.87567	0.205405
$197$	−9.45881	−0.673912	−0.336956	−	0.941520i	$-0.609397\pi$
$197$	−9.45881	−0.673912	−0.336956	+	0.941520i	$0.609397\pi$
$198$	2.46673	0.175303
$199$	−1.57691	−0.111784	−0.0558922	−	0.998437i	$-0.517800\pi$
$199$	−1.57691	−0.111784	−0.0558922	+	0.998437i	$0.517800\pi$
$200$	6.37863	0.451037
$201$	11.6632	0.822661
$202$	2.68123	0.188651
$203$	1.03572	0.0726931
$204$	−1.00000	−0.0700140
$205$	4.67991	0.326859
$206$	−5.26304	−0.366693
$207$	−6.50785	−0.452327
$208$	−5.85410	−0.405909
$209$	4.76934	0.329902
$210$	10.6005	0.731507
$211$	−2.69790	−0.185731	−0.0928656	−	0.995679i	$-0.529603\pi$
$211$	−2.69790	−0.185731	−0.0928656	+	0.995679i	$0.529603\pi$
$212$	2.03490	0.139758
$213$	−9.28461	−0.636171
$214$	3.46880	0.237122
$215$	39.9093	2.72179
$216$	−1.00000	−0.0680414
$217$	17.4734	1.18617
$218$	−9.99044	−0.676638
$219$	−5.39530	−0.364580
$220$	−8.32083	−0.560990
$221$	−5.85410	−0.393790
$222$	6.52993	0.438260
$223$	−0.501126	−0.0335579	−0.0167790	−	0.999859i	$-0.505341\pi$
$223$	−0.501126	−0.0335579	−0.0167790	+	0.999859i	$0.505341\pi$
$224$	3.14256	0.209971
$225$	6.37863	0.425242
$226$	−8.88648	−0.591120
$227$	−24.9724	−1.65748	−0.828740	−	0.559634i	$-0.810942\pi$
$227$	−24.9724	−1.65748	−0.828740	+	0.559634i	$0.810942\pi$
$228$	−1.93346	−0.128047
$229$	−8.61803	−0.569496	−0.284748	−	0.958602i	$-0.591910\pi$
$229$	−8.61803	−0.569496	−0.284748	+	0.958602i	$0.591910\pi$
$230$	21.9524	1.44750
$231$	−7.75185	−0.510034
$232$	0.329578	0.0216378
$233$	−15.4803	−1.01415	−0.507074	−	0.861903i	$-0.669273\pi$
$233$	−15.4803	−1.01415	−0.507074	+	0.861903i	$0.669273\pi$
$234$	−5.85410	−0.382695
$235$	−44.8751	−2.92733
$236$	−1.00000	−0.0650945
$237$	2.16463	0.140608
$238$	3.14256	0.203702
$239$	16.9846	1.09864	0.549320	−	0.835612i	$-0.314887\pi$
$239$	16.9846	1.09864	0.549320	+	0.835612i	$0.314887\pi$
$240$	3.37322	0.217741
$241$	−15.2710	−0.983690	−0.491845	−	0.870683i	$-0.663677\pi$
$241$	−15.2710	−0.983690	−0.491845	+	0.870683i	$0.663677\pi$
$242$	−4.91523	−0.315963
$243$	−1.00000	−0.0641500
$244$	−5.22274	−0.334351
$245$	−9.70028	−0.619728
$246$	1.38737	0.0884555
$247$	−11.3187	−0.720191
$248$	5.56024	0.353076
$249$	2.50163	0.158534
$250$	−4.65041	−0.294118
$251$	−15.3524	−0.969035	−0.484517	−	0.874782i	$-0.661005\pi$
$251$	−15.3524	−0.969035	−0.484517	+	0.874782i	$0.661005\pi$
$252$	3.14256	0.197963
$253$	−16.0531	−1.00925
$254$	−7.56276	−0.474530
$255$	3.37322	0.211239
$256$	1.00000	0.0625000
$257$	−18.8503	−1.17585	−0.587923	−	0.808917i	$-0.700054\pi$
$257$	−18.8503	−1.17585	−0.587923	+	0.808917i	$0.700054\pi$
$258$	11.8312	0.736579
$259$	−20.5207	−1.27509
$260$	19.7472	1.22467
$261$	0.329578	0.0204004
$262$	−5.92856	−0.366268
$263$	10.9699	0.676434	0.338217	−	0.941068i	$-0.390176\pi$
$263$	10.9699	0.676434	0.338217	+	0.941068i	$0.390176\pi$
$264$	−2.46673	−0.151817
$265$	−6.86417	−0.421663
$266$	6.07602	0.372545
$267$	−10.4048	−0.636762
$268$	−11.6632	−0.712446
$269$	26.9034	1.64033	0.820164	−	0.572128i	$-0.193882\pi$
$269$	26.9034	1.64033	0.820164	+	0.572128i	$0.193882\pi$
$270$	3.37322	0.205288
$271$	−12.5353	−0.761467	−0.380734	−	0.924685i	$-0.624329\pi$
$271$	−12.5353	−0.761467	−0.380734	+	0.924685i	$0.624329\pi$
$272$	1.00000	0.0606339
$273$	18.3969	1.11343
$274$	−18.8312	−1.13763
$275$	15.7344	0.948818
$276$	6.50785	0.391727
$277$	−8.23991	−0.495088	−0.247544	−	0.968877i	$-0.579624\pi$
$277$	−8.23991	−0.495088	−0.247544	+	0.968877i	$0.579624\pi$
$278$	−15.9704	−0.957843
$279$	5.56024	0.332883
$280$	−10.6005	−0.633504
$281$	13.1412	0.783940	0.391970	−	0.919978i	$-0.371794\pi$
$281$	13.1412	0.783940	0.391970	+	0.919978i	$0.371794\pi$
$282$	−13.3033	−0.792203
$283$	12.3462	0.733904	0.366952	−	0.930240i	$-0.380401\pi$
$283$	12.3462	0.733904	0.366952	+	0.930240i	$0.380401\pi$
$284$	9.28461	0.550940
$285$	6.52200	0.386330
$286$	−14.4405	−0.853885
$287$	−4.35989	−0.257356
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−1.11174	−0.0652836
$291$	−7.09017	−0.415633
$292$	5.39530	0.315736
$293$	−26.1217	−1.52605	−0.763024	−	0.646370i	$-0.776286\pi$
$293$	−26.1217	−1.52605	−0.763024	+	0.646370i	$0.776286\pi$
$294$	−2.87567	−0.167713
$295$	3.37322	0.196397
$296$	−6.52993	−0.379544
$297$	−2.46673	−0.143134
$298$	−1.04158	−0.0603371
$299$	38.0976	2.20324
$300$	−6.37863	−0.368270
$301$	−37.1803	−2.14303
$302$	−16.3852	−0.942864
$303$	−2.68123	−0.154033
$304$	1.93346	0.110892
$305$	17.6175	1.00877
$306$	1.00000	0.0571662
$307$	0.874854	0.0499305	0.0249653	−	0.999688i	$-0.492052\pi$
$307$	0.874854	0.0499305	0.0249653	+	0.999688i	$0.492052\pi$
$308$	7.75185	0.441703
$309$	5.26304	0.299404
$310$	−18.7559	−1.06527
$311$	−23.2733	−1.31971	−0.659853	−	0.751395i	$-0.729381\pi$
$311$	−23.2733	−1.31971	−0.659853	+	0.751395i	$0.729381\pi$
$312$	5.85410	0.331423
$313$	17.2410	0.974517	0.487259	−	0.873258i	$-0.337997\pi$
$313$	17.2410	0.974517	0.487259	+	0.873258i	$0.337997\pi$
$314$	−15.0267	−0.848004
$315$	−10.6005	−0.597273
$316$	−2.16463	−0.121770
$317$	26.7315	1.50139	0.750696	−	0.660648i	$-0.229718\pi$
$317$	26.7315	1.50139	0.750696	+	0.660648i	$0.229718\pi$
$318$	−2.03490	−0.114112
$319$	0.812980	0.0455182
$320$	−3.37322	−0.188569
$321$	−3.46880	−0.193609
$322$	−20.4513	−1.13971
$323$	1.93346	0.107581
$324$	1.00000	0.0555556
$325$	−37.3411	−2.07131
$326$	−14.9571	−0.828397
$327$	9.99044	0.552472
$328$	−1.38737	−0.0766047
$329$	41.8065	2.30487
$330$	8.32083	0.458047
$331$	−3.56743	−0.196084	−0.0980418	−	0.995182i	$-0.531258\pi$
$331$	−3.56743	−0.196084	−0.0980418	+	0.995182i	$0.531258\pi$
$332$	−2.50163	−0.137295
$333$	−6.52993	−0.357838
$334$	−18.5880	−1.01709
$335$	39.3427	2.14952
$336$	−3.14256	−0.171441
$337$	−5.28814	−0.288064	−0.144032	−	0.989573i	$-0.546007\pi$
$337$	−5.28814	−0.288064	−0.144032	+	0.989573i	$0.546007\pi$
$338$	21.2705	1.15696
$339$	8.88648	0.482647
$340$	−3.37322	−0.182939
$341$	13.7156	0.742743
$342$	1.93346	0.104550
$343$	−12.9609	−0.699825
$344$	−11.8312	−0.637896
$345$	−21.9524	−1.18188
$346$	20.2946	1.09104
$347$	−13.9472	−0.748722	−0.374361	−	0.927283i	$-0.622138\pi$
$347$	−13.9472	−0.748722	−0.374361	+	0.927283i	$0.622138\pi$
$348$	−0.329578	−0.0176672
$349$	−6.54038	−0.350098	−0.175049	−	0.984560i	$-0.556008\pi$
$349$	−6.54038	−0.350098	−0.175049	+	0.984560i	$0.556008\pi$
$350$	20.0452	1.07146
$351$	5.85410	0.312469
$352$	2.46673	0.131477
$353$	−18.8813	−1.00495	−0.502475	−	0.864592i	$-0.667577\pi$
$353$	−18.8813	−1.00495	−0.502475	+	0.864592i	$0.667577\pi$
$354$	1.00000	0.0531494
$355$	−31.3191	−1.66224
$356$	10.4048	0.551452
$357$	−3.14256	−0.166322
$358$	−3.15048	−0.166508
$359$	11.8225	0.623966	0.311983	−	0.950088i	$-0.399007\pi$
$359$	11.8225	0.623966	0.311983	+	0.950088i	$0.399007\pi$
$360$	−3.37322	−0.177784
$361$	−15.2617	−0.803248
$362$	22.7182	1.19404
$363$	4.91523	0.257983
$364$	−18.3969	−0.964257
$365$	−18.1995	−0.952607
$366$	5.22274	0.272997
$367$	14.1474	0.738487	0.369244	−	0.929333i	$-0.379617\pi$
$367$	14.1474	0.738487	0.369244	+	0.929333i	$0.379617\pi$
$368$	−6.50785	−0.339245
$369$	−1.38737	−0.0722236
$370$	22.0269	1.14512
$371$	6.39479	0.332001
$372$	−5.56024	−0.288285
$373$	−12.9429	−0.670160	−0.335080	−	0.942190i	$-0.608763\pi$
$373$	−12.9429	−0.670160	−0.335080	+	0.942190i	$0.608763\pi$
$374$	2.46673	0.127552
$375$	4.65041	0.240146
$376$	13.3033	0.686068
$377$	−1.92938	−0.0993683
$378$	−3.14256	−0.161636
$379$	17.9900	0.924083	0.462042	−	0.886858i	$-0.347117\pi$
$379$	17.9900	0.924083	0.462042	+	0.886858i	$0.347117\pi$
$380$	−6.52200	−0.334572
$381$	7.56276	0.387452
$382$	−5.28543	−0.270426
$383$	−18.0693	−0.923300	−0.461650	−	0.887062i	$-0.652742\pi$
$383$	−18.0693	−0.923300	−0.461650	+	0.887062i	$0.652742\pi$
$384$	−1.00000	−0.0510310
$385$	−26.1487	−1.33266
$386$	−1.37248	−0.0698574
$387$	−11.8312	−0.601414
$388$	7.09017	0.359949
$389$	2.03416	0.103136	0.0515680	−	0.998669i	$-0.483578\pi$
$389$	2.03416	0.103136	0.0515680	+	0.998669i	$0.483578\pi$
$390$	−19.7472	−0.999938
$391$	−6.50785	−0.329116
$392$	2.87567	0.145243
$393$	5.92856	0.299057
$394$	−9.45881	−0.476528
$395$	7.30179	0.367393
$396$	2.46673	0.123958
$397$	22.6213	1.13533	0.567665	−	0.823260i	$-0.307847\pi$
$397$	22.6213	1.13533	0.567665	+	0.823260i	$0.307847\pi$
$398$	−1.57691	−0.0790435
$399$	−6.07602	−0.304182
$400$	6.37863	0.318931
$401$	1.63004	0.0814004	0.0407002	−	0.999171i	$-0.487041\pi$
$401$	1.63004	0.0814004	0.0407002	+	0.999171i	$0.487041\pi$
$402$	11.6632	0.581709
$403$	−32.5502	−1.62144
$404$	2.68123	0.133396
$405$	−3.37322	−0.167617
$406$	1.03572	0.0514018
$407$	−16.1076	−0.798423
$408$	−1.00000	−0.0495074
$409$	−9.28951	−0.459337	−0.229668	−	0.973269i	$-0.573764\pi$
$409$	−9.28951	−0.459337	−0.229668	+	0.973269i	$0.573764\pi$
$410$	4.67991	0.231124
$411$	18.8312	0.928875
$412$	−5.26304	−0.259291
$413$	−3.14256	−0.154635
$414$	−6.50785	−0.319844
$415$	8.43856	0.414233
$416$	−5.85410	−0.287021
$417$	15.9704	0.782075
$418$	4.76934	0.233276
$419$	18.9655	0.926527	0.463263	−	0.886221i	$-0.346678\pi$
$419$	18.9655	0.926527	0.463263	+	0.886221i	$0.346678\pi$
$420$	10.6005	0.517254
$421$	0.579289	0.0282328	0.0141164	−	0.999900i	$-0.495506\pi$
$421$	0.579289	0.0282328	0.0141164	+	0.999900i	$0.495506\pi$
$422$	−2.69790	−0.131332
$423$	13.3033	0.646831
$424$	2.03490	0.0988235
$425$	6.37863	0.309409
$426$	−9.28461	−0.449841
$427$	−16.4128	−0.794269
$428$	3.46880	0.167671
$429$	14.4405	0.697194
$430$	39.9093	1.92460
$431$	0.546170	0.0263081	0.0131540	−	0.999913i	$-0.495813\pi$
$431$	0.546170	0.0263081	0.0131540	+	0.999913i	$0.495813\pi$
$432$	−1.00000	−0.0481125
$433$	21.7182	1.04371	0.521855	−	0.853034i	$-0.325240\pi$
$433$	21.7182	1.04371	0.521855	+	0.853034i	$0.325240\pi$
$434$	17.4734	0.838749
$435$	1.11174	0.0533038
$436$	−9.99044	−0.478455
$437$	−12.5827	−0.601912
$438$	−5.39530	−0.257797
$439$	−14.4683	−0.690534	−0.345267	−	0.938505i	$-0.612212\pi$
$439$	−14.4683	−0.690534	−0.345267	+	0.938505i	$0.612212\pi$
$440$	−8.32083	−0.396680
$441$	2.87567	0.136937
$442$	−5.85410	−0.278451
$443$	26.5833	1.26301	0.631505	−	0.775372i	$-0.282437\pi$
$443$	26.5833	1.26301	0.631505	+	0.775372i	$0.282437\pi$
$444$	6.52993	0.309897
$445$	−35.0976	−1.66379
$446$	−0.501126	−0.0237290
$447$	1.04158	0.0492650
$448$	3.14256	0.148472
$449$	−30.2045	−1.42544	−0.712719	−	0.701450i	$-0.752536\pi$
$449$	−30.2045	−1.42544	−0.712719	+	0.701450i	$0.752536\pi$
$450$	6.37863	0.300691
$451$	−3.42227	−0.161148
$452$	−8.88648	−0.417985
$453$	16.3852	0.769845
$454$	−24.9724	−1.17201
$455$	62.0567	2.90926
$456$	−1.93346	−0.0905427
$457$	−22.2522	−1.04092	−0.520458	−	0.853887i	$-0.674239\pi$
$457$	−22.2522	−1.04092	−0.520458	+	0.853887i	$0.674239\pi$
$458$	−8.61803	−0.402694
$459$	−1.00000	−0.0466760
$460$	21.9524	1.02354
$461$	20.0675	0.934637	0.467319	−	0.884089i	$-0.345220\pi$
$461$	20.0675	0.934637	0.467319	+	0.884089i	$0.345220\pi$
$462$	−7.75185	−0.360649
$463$	12.2854	0.570952	0.285476	−	0.958386i	$-0.407848\pi$
$463$	12.2854	0.570952	0.285476	+	0.958386i	$0.407848\pi$
$464$	0.329578	0.0153003
$465$	18.7559	0.869785
$466$	−15.4803	−0.717111
$467$	−41.5877	−1.92445	−0.962224	−	0.272258i	$-0.912230\pi$
$467$	−41.5877	−1.92445	−0.962224	+	0.272258i	$0.912230\pi$
$468$	−5.85410	−0.270606
$469$	−36.6524	−1.69245
$470$	−44.8751	−2.06994
$471$	15.0267	0.692392
$472$	−1.00000	−0.0460287
$473$	−29.1844	−1.34190
$474$	2.16463	0.0994249
$475$	12.3328	0.565870
$476$	3.14256	0.144039
$477$	2.03490	0.0931717
$478$	16.9846	0.776856
$479$	37.0756	1.69403	0.847013	−	0.531572i	$-0.178399\pi$
$479$	37.0756	1.69403	0.847013	+	0.531572i	$0.178399\pi$
$480$	3.37322	0.153966
$481$	38.2269	1.74300
$482$	−15.2710	−0.695574
$483$	20.4513	0.930567
$484$	−4.91523	−0.223420
$485$	−23.9167	−1.08600
$486$	−1.00000	−0.0453609
$487$	−33.0265	−1.49657	−0.748287	−	0.663375i	$-0.769123\pi$
$487$	−33.0265	−1.49657	−0.748287	+	0.663375i	$0.769123\pi$
$488$	−5.22274	−0.236422
$489$	14.9571	0.676383
$490$	−9.70028	−0.438214
$491$	−30.5190	−1.37731	−0.688653	−	0.725091i	$-0.741797\pi$
$491$	−30.5190	−1.37731	−0.688653	+	0.725091i	$0.741797\pi$
$492$	1.38737	0.0625475
$493$	0.329578	0.0148434
$494$	−11.3187	−0.509252
$495$	−8.32083	−0.373994
$496$	5.56024	0.249662
$497$	29.1774	1.30879
$498$	2.50163	0.112101
$499$	25.5419	1.14341	0.571707	−	0.820458i	$-0.306281\pi$
$499$	25.5419	1.14341	0.571707	+	0.820458i	$0.306281\pi$
$500$	−4.65041	−0.207973
$501$	18.5880	0.830449
$502$	−15.3524	−0.685211
$503$	−17.3205	−0.772284	−0.386142	−	0.922439i	$-0.626193\pi$
$503$	−17.3205	−0.772284	−0.386142	+	0.922439i	$0.626193\pi$
$504$	3.14256	0.139981
$505$	−9.04439	−0.402470
$506$	−16.0531	−0.713649
$507$	−21.2705	−0.944657
$508$	−7.56276	−0.335543
$509$	−2.14380	−0.0950225	−0.0475112	−	0.998871i	$-0.515129\pi$
$509$	−2.14380	−0.0950225	−0.0475112	+	0.998871i	$0.515129\pi$
$510$	3.37322	0.149369
$511$	16.9550	0.750046
$512$	1.00000	0.0441942
$513$	−1.93346	−0.0853645
$514$	−18.8503	−0.831449
$515$	17.7534	0.782309
$516$	11.8312	0.520840
$517$	32.8158	1.44324
$518$	−20.5207	−0.901627
$519$	−20.2946	−0.890834
$520$	19.7472	0.865971
$521$	36.5419	1.60093	0.800466	−	0.599379i	$-0.204586\pi$
$521$	36.5419	1.60093	0.800466	+	0.599379i	$0.204586\pi$
$522$	0.329578	0.0144252
$523$	−17.5677	−0.768182	−0.384091	−	0.923295i	$-0.625485\pi$
$523$	−17.5677	−0.768182	−0.384091	+	0.923295i	$0.625485\pi$
$524$	−5.92856	−0.258991
$525$	−20.0452	−0.874844
$526$	10.9699	0.478311
$527$	5.56024	0.242208
$528$	−2.46673	−0.107351
$529$	19.3522	0.841398
$530$	−6.86417	−0.298160
$531$	−1.00000	−0.0433963
$532$	6.07602	0.263429
$533$	8.12181	0.351794
$534$	−10.4048	−0.450259
$535$	−11.7010	−0.505879
$536$	−11.6632	−0.503775
$537$	3.15048	0.135953
$538$	26.9034	1.15989
$539$	7.09351	0.305539
$540$	3.37322	0.145160
$541$	29.8415	1.28299	0.641493	−	0.767129i	$-0.278315\pi$
$541$	29.8415	1.28299	0.641493	+	0.767129i	$0.278315\pi$
$542$	−12.5353	−0.538439
$543$	−22.7182	−0.974931
$544$	1.00000	0.0428746
$545$	33.7000	1.44355
$546$	18.3969	0.787313
$547$	−1.92710	−0.0823967	−0.0411983	−	0.999151i	$-0.513118\pi$
$547$	−1.92710	−0.0823967	−0.0411983	+	0.999151i	$0.513118\pi$
$548$	−18.8312	−0.804429
$549$	−5.22274	−0.222901
$550$	15.7344	0.670915
$551$	0.637227	0.0271468
$552$	6.50785	0.276993
$553$	−6.80248	−0.289271
$554$	−8.23991	−0.350080
$555$	−22.0269	−0.934990
$556$	−15.9704	−0.677297
$557$	−19.1683	−0.812185	−0.406093	−	0.913832i	$-0.633109\pi$
$557$	−19.1683	−0.812185	−0.406093	+	0.913832i	$0.633109\pi$
$558$	5.56024	0.235384
$559$	69.2611	2.92943
$560$	−10.6005	−0.447955
$561$	−2.46673	−0.104145
$562$	13.1412	0.554330
$563$	12.7827	0.538727	0.269363	−	0.963039i	$-0.413187\pi$
$563$	12.7827	0.538727	0.269363	+	0.963039i	$0.413187\pi$
$564$	−13.3033	−0.560172
$565$	29.9761	1.26110
$566$	12.3462	0.518948
$567$	3.14256	0.131975
$568$	9.28461	0.389574
$569$	−6.45842	−0.270751	−0.135375	−	0.990794i	$-0.543224\pi$
$569$	−6.45842	−0.270751	−0.135375	+	0.990794i	$0.543224\pi$
$570$	6.52200	0.273177
$571$	−23.0688	−0.965401	−0.482700	−	0.875786i	$-0.660344\pi$
$571$	−23.0688	−0.965401	−0.482700	+	0.875786i	$0.660344\pi$
$572$	−14.4405	−0.603788
$573$	5.28543	0.220802
$574$	−4.35989	−0.181978
$575$	−41.5112	−1.73114
$576$	1.00000	0.0416667
$577$	−14.8856	−0.619696	−0.309848	−	0.950786i	$-0.600278\pi$
$577$	−14.8856	−0.619696	−0.309848	+	0.950786i	$0.600278\pi$
$578$	1.00000	0.0415945
$579$	1.37248	0.0570384
$580$	−1.11174	−0.0461625
$581$	−7.86152	−0.326151
$582$	−7.09017	−0.293897
$583$	5.01955	0.207889
$584$	5.39530	0.223259
$585$	19.7472	0.816446
$586$	−26.1217	−1.07908
$587$	5.52572	0.228071	0.114036	−	0.993477i	$-0.463622\pi$
$587$	5.52572	0.228071	0.114036	+	0.993477i	$0.463622\pi$
$588$	−2.87567	−0.118591
$589$	10.7505	0.442968
$590$	3.37322	0.138873
$591$	9.45881	0.389083
$592$	−6.52993	−0.268378
$593$	−35.2040	−1.44565	−0.722827	−	0.691029i	$-0.757158\pi$
$593$	−35.2040	−1.44565	−0.722827	+	0.691029i	$0.757158\pi$
$594$	−2.46673	−0.101211
$595$	−10.6005	−0.434580
$596$	−1.04158	−0.0426648
$597$	1.57691	0.0645387
$598$	38.0976	1.55793
$599$	−28.4553	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$599$	−28.4553	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$600$	−6.37863	−0.260406
$601$	20.1770	0.823037	0.411518	−	0.911401i	$-0.364999\pi$
$601$	20.1770	0.823037	0.411518	+	0.911401i	$0.364999\pi$
$602$	−37.1803	−1.51535
$603$	−11.6632	−0.474964
$604$	−16.3852	−0.666706
$605$	16.5802	0.674080
$606$	−2.68123	−0.108918
$607$	12.8181	0.520269	0.260135	−	0.965572i	$-0.416233\pi$
$607$	12.8181	0.520269	0.260135	+	0.965572i	$0.416233\pi$
$608$	1.93346	0.0784123
$609$	−1.03572	−0.0419694
$610$	17.6175	0.713310
$611$	−77.8791	−3.15065
$612$	1.00000	0.0404226
$613$	0.0415506	0.00167821	0.000839107	−	1.00000i	$-0.499733\pi$
$613$	0.0415506	0.00167821	0.000839107		1.00000i	$0.499733\pi$
$614$	0.874854	0.0353062
$615$	−4.67991	−0.188712
$616$	7.75185	0.312331
$617$	26.8541	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$617$	26.8541	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$618$	5.26304	0.211711
$619$	−0.863587	−0.0347105	−0.0173553	−	0.999849i	$-0.505525\pi$
$619$	−0.863587	−0.0347105	−0.0173553	+	0.999849i	$0.505525\pi$
$620$	−18.7559	−0.753256
$621$	6.50785	0.261151
$622$	−23.2733	−0.933173
$623$	32.6976	1.31000
$624$	5.85410	0.234352
$625$	−16.2063	−0.648250
$626$	17.2410	0.689088
$627$	−4.76934	−0.190469
$628$	−15.0267	−0.599629
$629$	−6.52993	−0.260365
$630$	−10.6005	−0.422336
$631$	−44.0164	−1.75226	−0.876132	−	0.482071i	$-0.839885\pi$
$631$	−44.0164	−1.75226	−0.876132	+	0.482071i	$0.839885\pi$
$632$	−2.16463	−0.0861045
$633$	2.69790	0.107232
$634$	26.7315	1.06164
$635$	25.5109	1.01237
$636$	−2.03490	−0.0806890
$637$	−16.8345	−0.667006
$638$	0.812980	0.0321862
$639$	9.28461	0.367294
$640$	−3.37322	−0.133338
$641$	−37.3558	−1.47546	−0.737732	−	0.675093i	$-0.764103\pi$
$641$	−37.3558	−1.47546	−0.737732	+	0.675093i	$0.764103\pi$
$642$	−3.46880	−0.136902
$643$	40.4210	1.59405	0.797024	−	0.603947i	$-0.206406\pi$
$643$	40.4210	1.59405	0.797024	+	0.603947i	$0.206406\pi$
$644$	−20.4513	−0.805894
$645$	−39.9093	−1.57143
$646$	1.93346	0.0760711
$647$	25.5839	1.00581	0.502903	−	0.864343i	$-0.332265\pi$
$647$	25.5839	1.00581	0.502903	+	0.864343i	$0.332265\pi$
$648$	1.00000	0.0392837
$649$	−2.46673	−0.0968277
$650$	−37.3411	−1.46464
$651$	−17.4734	−0.684836
$652$	−14.9571	−0.585765
$653$	47.9178	1.87517	0.937585	−	0.347757i	$-0.113057\pi$
$653$	47.9178	1.87517	0.937585	+	0.347757i	$0.113057\pi$
$654$	9.99044	0.390657
$655$	19.9984	0.781401
$656$	−1.38737	−0.0541677
$657$	5.39530	0.210491
$658$	41.8065	1.62979
$659$	24.2943	0.946371	0.473186	−	0.880963i	$-0.343104\pi$
$659$	24.2943	0.946371	0.473186	+	0.880963i	$0.343104\pi$
$660$	8.32083	0.323888
$661$	0.808630	0.0314520	0.0157260	−	0.999876i	$-0.494994\pi$
$661$	0.808630	0.0314520	0.0157260	+	0.999876i	$0.494994\pi$
$662$	−3.56743	−0.138652
$663$	5.85410	0.227354
$664$	−2.50163	−0.0970821
$665$	−20.4958	−0.794792
$666$	−6.52993	−0.253030
$667$	−2.14484	−0.0830487
$668$	−18.5880	−0.719190
$669$	0.501126	0.0193747
$670$	39.3427	1.51994
$671$	−12.8831	−0.497346
$672$	−3.14256	−0.121227
$673$	−25.0857	−0.966984	−0.483492	−	0.875349i	$-0.660632\pi$
$673$	−25.0857	−0.966984	−0.483492	+	0.875349i	$0.660632\pi$
$674$	−5.28814	−0.203692
$675$	−6.37863	−0.245513
$676$	21.2705	0.818097
$677$	6.43109	0.247167	0.123583	−	0.992334i	$-0.460561\pi$
$677$	6.43109	0.247167	0.123583	+	0.992334i	$0.460561\pi$
$678$	8.88648	0.341283
$679$	22.2813	0.855077
$680$	−3.37322	−0.129357
$681$	24.9724	0.956946
$682$	13.7156	0.525198
$683$	35.4215	1.35536	0.677682	−	0.735355i	$-0.262985\pi$
$683$	35.4215	1.35536	0.677682	+	0.735355i	$0.262985\pi$
$684$	1.93346	0.0739278
$685$	63.5218	2.42705
$686$	−12.9609	−0.494851
$687$	8.61803	0.328799
$688$	−11.8312	−0.451061
$689$	−11.9125	−0.453831
$690$	−21.9524	−0.835715
$691$	0.0103794	0.000394852 0	0.000197426	−	1.00000i	$-0.499937\pi$
$691$	0.0103794	0.000394852 0	0.000197426		1.00000i	$0.499937\pi$
$692$	20.2946	0.771485
$693$	7.75185	0.294468
$694$	−13.9472	−0.529427
$695$	53.8718	2.04347
$696$	−0.329578	−0.0124926
$697$	−1.38737	−0.0525504
$698$	−6.54038	−0.247557
$699$	15.4803	0.585519
$700$	20.0452	0.757637
$701$	30.2867	1.14391	0.571956	−	0.820284i	$-0.306185\pi$
$701$	30.2867	1.14391	0.571956	+	0.820284i	$0.306185\pi$
$702$	5.85410	0.220949
$703$	−12.6254	−0.476175
$704$	2.46673	0.0929685
$705$	44.8751	1.69010
$706$	−18.8813	−0.710608
$707$	8.42592	0.316889
$708$	1.00000	0.0375823
$709$	39.6421	1.48879	0.744395	−	0.667739i	$-0.232738\pi$
$709$	39.6421	1.48879	0.744395	+	0.667739i	$0.232738\pi$
$710$	−31.3191	−1.17538
$711$	−2.16463	−0.0811801
$712$	10.4048	0.389936
$713$	−36.1852	−1.35515
$714$	−3.14256	−0.117607
$715$	48.7110	1.82169
$716$	−3.15048	−0.117739
$717$	−16.9846	−0.634301
$718$	11.8225	0.441210
$719$	16.7736	0.625550	0.312775	−	0.949827i	$-0.398741\pi$
$719$	16.7736	0.625550	0.312775	+	0.949827i	$0.398741\pi$
$720$	−3.37322	−0.125713
$721$	−16.5394	−0.615960
$722$	−15.2617	−0.567982
$723$	15.2710	0.567933
$724$	22.7182	0.844315
$725$	2.10225	0.0780758
$726$	4.91523	0.182421
$727$	23.7502	0.880847	0.440423	−	0.897790i	$-0.354828\pi$
$727$	23.7502	0.880847	0.440423	+	0.897790i	$0.354828\pi$
$728$	−18.3969	−0.681833
$729$	1.00000	0.0370370
$730$	−18.1995	−0.673595
$731$	−11.8312	−0.437593
$732$	5.22274	0.193038
$733$	31.7446	1.17251	0.586257	−	0.810125i	$-0.300601\pi$
$733$	31.7446	1.17251	0.586257	+	0.810125i	$0.300601\pi$
$734$	14.1474	0.522189
$735$	9.70028	0.357800
$736$	−6.50785	−0.239883
$737$	−28.7701	−1.05976
$738$	−1.38737	−0.0510698
$739$	21.9576	0.807725	0.403863	−	0.914820i	$-0.367667\pi$
$739$	21.9576	0.807725	0.403863	+	0.914820i	$0.367667\pi$
$740$	22.0269	0.809725
$741$	11.3187	0.415803
$742$	6.39479	0.234760
$743$	−42.4081	−1.55580	−0.777902	−	0.628386i	$-0.783716\pi$
$743$	−42.4081	−1.55580	−0.777902	+	0.628386i	$0.783716\pi$
$744$	−5.56024	−0.203848
$745$	3.51348	0.128724
$746$	−12.9429	−0.473875
$747$	−2.50163	−0.0915299
$748$	2.46673	0.0901926
$749$	10.9009	0.398310
$750$	4.65041	0.169809
$751$	33.0969	1.20772	0.603861	−	0.797090i	$-0.293628\pi$
$751$	33.0969	1.20772	0.603861	+	0.797090i	$0.293628\pi$
$752$	13.3033	0.485123
$753$	15.3524	0.559472
$754$	−1.92938	−0.0702640
$755$	55.2710	2.01152
$756$	−3.14256	−0.114294
$757$	7.27400	0.264378	0.132189	−	0.991225i	$-0.457799\pi$
$757$	7.27400	0.264378	0.132189	+	0.991225i	$0.457799\pi$
$758$	17.9900	0.653426
$759$	16.0531	0.582692
$760$	−6.52200	−0.236578
$761$	−44.7377	−1.62174	−0.810870	−	0.585227i	$-0.801005\pi$
$761$	−44.7377	−1.62174	−0.810870	+	0.585227i	$0.801005\pi$
$762$	7.56276	0.273970
$763$	−31.3955	−1.13659
$764$	−5.28543	−0.191220
$765$	−3.37322	−0.121959
$766$	−18.0693	−0.652872
$767$	5.85410	0.211379
$768$	−1.00000	−0.0360844
$769$	37.5111	1.35268	0.676342	−	0.736588i	$-0.263564\pi$
$769$	37.5111	1.35268	0.676342	+	0.736588i	$0.263564\pi$
$770$	−26.1487	−0.942334
$771$	18.8503	0.678875
$772$	−1.37248	−0.0493967
$773$	20.0639	0.721647	0.360823	−	0.932634i	$-0.382496\pi$
$773$	20.0639	0.721647	0.360823	+	0.932634i	$0.382496\pi$
$774$	−11.8312	−0.425264
$775$	35.4667	1.27400
$776$	7.09017	0.254522
$777$	20.5207	0.736175
$778$	2.03416	0.0729281
$779$	−2.68243	−0.0961080
$780$	−19.7472	−0.707063
$781$	22.9026	0.819521
$782$	−6.50785	−0.232720
$783$	−0.329578	−0.0117782
$784$	2.87567	0.102703
$785$	50.6883	1.80914
$786$	5.92856	0.211465
$787$	20.8849	0.744466	0.372233	−	0.928139i	$-0.378592\pi$
$787$	20.8849	0.744466	0.372233	+	0.928139i	$0.378592\pi$
$788$	−9.45881	−0.336956
$789$	−10.9699	−0.390540
$790$	7.30179	0.259786
$791$	−27.9263	−0.992944
$792$	2.46673	0.0876515
$793$	30.5744	1.08573
$794$	22.6213	0.802800
$795$	6.86417	0.243447
$796$	−1.57691	−0.0558922
$797$	35.3972	1.25383	0.626917	−	0.779086i	$-0.284317\pi$
$797$	35.3972	1.25383	0.626917	+	0.779086i	$0.284317\pi$
$798$	−6.07602	−0.215089
$799$	13.3033	0.470639
$800$	6.37863	0.225518
$801$	10.4048	0.367635
$802$	1.63004	0.0575588
$803$	13.3087	0.469656
$804$	11.6632	0.411331
$805$	68.9868	2.43147
$806$	−32.5502	−1.14653
$807$	−26.9034	−0.947044
$808$	2.68123	0.0943254
$809$	−49.4493	−1.73854	−0.869272	−	0.494335i	$-0.835412\pi$
$809$	−49.4493	−1.73854	−0.869272	+	0.494335i	$0.835412\pi$
$810$	−3.37322	−0.118523
$811$	−45.2206	−1.58791	−0.793955	−	0.607977i	$-0.791981\pi$
$811$	−45.2206	−1.58791	−0.793955	+	0.607977i	$0.791981\pi$
$812$	1.03572	0.0363466
$813$	12.5353	0.439633
$814$	−16.1076	−0.564570
$815$	50.4536	1.76731
$816$	−1.00000	−0.0350070
$817$	−22.8752	−0.800302
$818$	−9.28951	−0.324800
$819$	−18.3969	−0.642838
$820$	4.67991	0.163429
$821$	23.0885	0.805793	0.402896	−	0.915246i	$-0.368003\pi$
$821$	23.0885	0.805793	0.402896	+	0.915246i	$0.368003\pi$
$822$	18.8312	0.656814
$823$	41.9773	1.46324	0.731619	−	0.681714i	$-0.238765\pi$
$823$	41.9773	1.46324	0.731619	+	0.681714i	$0.238765\pi$
$824$	−5.26304	−0.183347
$825$	−15.7344	−0.547800
$826$	−3.14256	−0.109344
$827$	48.8393	1.69831	0.849155	−	0.528143i	$-0.177112\pi$
$827$	48.8393	1.69831	0.849155	+	0.528143i	$0.177112\pi$
$828$	−6.50785	−0.226164
$829$	−23.8739	−0.829176	−0.414588	−	0.910009i	$-0.636074\pi$
$829$	−23.8739	−0.829176	−0.414588	+	0.910009i	$0.636074\pi$
$830$	8.43856	0.292907
$831$	8.23991	0.285839
$832$	−5.85410	−0.202954
$833$	2.87567	0.0996361
$834$	15.9704	0.553011
$835$	62.7013	2.16987
$836$	4.76934	0.164951
$837$	−5.56024	−0.192190
$838$	18.9655	0.655153
$839$	28.4762	0.983108	0.491554	−	0.870847i	$-0.336429\pi$
$839$	28.4762	0.983108	0.491554	+	0.870847i	$0.336429\pi$
$840$	10.6005	0.365754
$841$	−28.8914	−0.996254
$842$	0.579289	0.0199636
$843$	−13.1412	−0.452608
$844$	−2.69790	−0.0928656
$845$	−71.7501	−2.46828
$846$	13.3033	0.457378
$847$	−15.4464	−0.530745
$848$	2.03490	0.0698788
$849$	−12.3462	−0.423720
$850$	6.37863	0.218785
$851$	42.4958	1.45674
$852$	−9.28461	−0.318086
$853$	−44.3809	−1.51957	−0.759786	−	0.650173i	$-0.774697\pi$
$853$	−44.3809	−1.51957	−0.759786	+	0.650173i	$0.774697\pi$
$854$	−16.4128	−0.561633
$855$	−6.52200	−0.223048
$856$	3.46880	0.118561
$857$	−24.3431	−0.831543	−0.415772	−	0.909469i	$-0.636488\pi$
$857$	−24.3431	−0.831543	−0.415772	+	0.909469i	$0.636488\pi$
$858$	14.4405	0.492991
$859$	21.5013	0.733616	0.366808	−	0.930297i	$-0.380451\pi$
$859$	21.5013	0.733616	0.366808	+	0.930297i	$0.380451\pi$
$860$	39.9093	1.36090
$861$	4.35989	0.148585
$862$	0.546170	0.0186026
$863$	43.3549	1.47582	0.737909	−	0.674900i	$-0.235813\pi$
$863$	43.3549	1.47582	0.737909	+	0.674900i	$0.235813\pi$
$864$	−1.00000	−0.0340207
$865$	−68.4582	−2.32765
$866$	21.7182	0.738014
$867$	−1.00000	−0.0339618
$868$	17.4734	0.593085
$869$	−5.33957	−0.181132
$870$	1.11174	0.0376915
$871$	68.2778	2.31350
$872$	−9.99044	−0.338319
$873$	7.09017	0.239966
$874$	−12.5827	−0.425616
$875$	−14.6142	−0.494050
$876$	−5.39530	−0.182290
$877$	−39.1162	−1.32086	−0.660431	−	0.750887i	$-0.729626\pi$
$877$	−39.1162	−1.32086	−0.660431	+	0.750887i	$0.729626\pi$
$878$	−14.4683	−0.488281
$879$	26.1217	0.881064
$880$	−8.32083	−0.280495
$881$	10.3853	0.349889	0.174944	−	0.984578i	$-0.444025\pi$
$881$	10.3853	0.349889	0.174944	+	0.984578i	$0.444025\pi$
$882$	2.87567	0.0968289
$883$	37.4487	1.26025	0.630125	−	0.776494i	$-0.283004\pi$
$883$	37.4487	1.26025	0.630125	+	0.776494i	$0.283004\pi$
$884$	−5.85410	−0.196895
$885$	−3.37322	−0.113390
$886$	26.5833	0.893083
$887$	−3.14287	−0.105527	−0.0527636	−	0.998607i	$-0.516803\pi$
$887$	−3.14287	−0.105527	−0.0527636	+	0.998607i	$0.516803\pi$
$888$	6.52993	0.219130
$889$	−23.7664	−0.797100
$890$	−35.0976	−1.17648
$891$	2.46673	0.0826386
$892$	−0.501126	−0.0167790
$893$	25.7215	0.860738
$894$	1.04158	0.0348356
$895$	10.6273	0.355231
$896$	3.14256	0.104985
$897$	−38.0976	−1.27204
$898$	−30.2045	−1.00794
$899$	1.83253	0.0611184
$900$	6.37863	0.212621
$901$	2.03490	0.0677923
$902$	−3.42227	−0.113949
$903$	37.1803	1.23728
$904$	−8.88648	−0.295560
$905$	−76.6335	−2.54738
$906$	16.3852	0.544363
$907$	16.2442	0.539379	0.269690	−	0.962947i	$-0.413079\pi$
$907$	16.2442	0.539379	0.269690	+	0.962947i	$0.413079\pi$
$908$	−24.9724	−0.828740
$909$	2.68123	0.0889308
$910$	62.0567	2.05716
$911$	38.3617	1.27098	0.635490	−	0.772109i	$-0.280798\pi$
$911$	38.3617	1.27098	0.635490	+	0.772109i	$0.280798\pi$
$912$	−1.93346	−0.0640234
$913$	−6.17085	−0.204225
$914$	−22.2522	−0.736038
$915$	−17.6175	−0.582415
$916$	−8.61803	−0.284748
$917$	−18.6309	−0.615245
$918$	−1.00000	−0.0330049
$919$	50.9624	1.68110	0.840548	−	0.541738i	$-0.182233\pi$
$919$	50.9624	1.68110	0.840548	+	0.541738i	$0.182233\pi$
$920$	21.9524	0.723750
$921$	−0.874854	−0.0288274
$922$	20.0675	0.660888
$923$	−54.3531	−1.78905
$924$	−7.75185	−0.255017
$925$	−41.6520	−1.36951
$926$	12.2854	0.403724
$927$	−5.26304	−0.172861
$928$	0.329578	0.0108189
$929$	23.6447	0.775757	0.387879	−	0.921710i	$-0.373208\pi$
$929$	23.6447	0.775757	0.387879	+	0.921710i	$0.373208\pi$
$930$	18.7559	0.615031
$931$	5.56001	0.182222
$932$	−15.4803	−0.507074
$933$	23.2733	0.761933
$934$	−41.5877	−1.36079
$935$	−8.32083	−0.272120
$936$	−5.85410	−0.191347
$937$	−51.0925	−1.66912	−0.834559	−	0.550918i	$-0.814278\pi$
$937$	−51.0925	−1.66912	−0.834559	+	0.550918i	$0.814278\pi$
$938$	−36.6524	−1.19674
$939$	−17.2410	−0.562638
$940$	−44.8751	−1.46367
$941$	40.9985	1.33651	0.668256	−	0.743932i	$-0.267041\pi$
$941$	40.9985	1.33651	0.668256	+	0.743932i	$0.267041\pi$
$942$	15.0267	0.489595
$943$	9.02880	0.294018
$944$	−1.00000	−0.0325472
$945$	10.6005	0.344836
$946$	−29.1844	−0.948867
$947$	−45.1259	−1.46639	−0.733197	−	0.680017i	$-0.761973\pi$
$947$	−45.1259	−1.46639	−0.733197	+	0.680017i	$0.761973\pi$
$948$	2.16463	0.0703040
$949$	−31.5846	−1.02528
$950$	12.3328	0.400130
$951$	−26.7315	−0.866829
$952$	3.14256	0.101851
$953$	19.5650	0.633773	0.316887	−	0.948463i	$-0.397363\pi$
$953$	19.5650	0.633773	0.316887	+	0.948463i	$0.397363\pi$
$954$	2.03490	0.0658823
$955$	17.8289	0.576930
$956$	16.9846	0.549320
$957$	−0.812980	−0.0262799
$958$	37.0756	1.19786
$959$	−59.1782	−1.91096
$960$	3.37322	0.108870
$961$	−0.0837123	−0.00270040
$962$	38.2269	1.23248
$963$	3.46880	0.111780
$964$	−15.2710	−0.491845
$965$	4.62968	0.149035
$966$	20.4513	0.658010
$967$	56.3942	1.81351	0.906757	−	0.421653i	$-0.138550\pi$
$967$	56.3942	1.81351	0.906757	+	0.421653i	$0.138550\pi$
$968$	−4.91523	−0.157982
$969$	−1.93346	−0.0621118
$970$	−23.9167	−0.767919
$971$	8.85254	0.284092	0.142046	−	0.989860i	$-0.454632\pi$
$971$	8.85254	0.284092	0.142046	+	0.989860i	$0.454632\pi$
$972$	−1.00000	−0.0320750
$973$	−50.1880	−1.60895
$974$	−33.0265	−1.05824
$975$	37.3411	1.19587
$976$	−5.22274	−0.167176
$977$	24.8394	0.794682	0.397341	−	0.917671i	$-0.369933\pi$
$977$	24.8394	0.794682	0.397341	+	0.917671i	$0.369933\pi$
$978$	14.9571	0.478275
$979$	25.6658	0.820283
$980$	−9.70028	−0.309864
$981$	−9.99044	−0.318970
$982$	−30.5190	−0.973902
$983$	−23.8922	−0.762043	−0.381022	−	0.924566i	$-0.624428\pi$
$983$	−23.8922	−0.762043	−0.381022	+	0.924566i	$0.624428\pi$
$984$	1.38737	0.0442277
$985$	31.9066	1.01663
$986$	0.329578	0.0104959
$987$	−41.8065	−1.33072
$988$	−11.3187	−0.360096
$989$	76.9958	2.44832
$990$	−8.32083	−0.264453
$991$	−42.2005	−1.34054	−0.670271	−	0.742116i	$-0.733822\pi$
$991$	−42.2005	−1.34054	−0.670271	+	0.742116i	$0.733822\pi$
$992$	5.56024	0.176538
$993$	3.56743	0.113209
$994$	29.1774	0.925452
$995$	5.31927	0.168632
$996$	2.50163	0.0792672
$997$	26.4101	0.836417	0.418208	−	0.908351i	$-0.362658\pi$
$997$	26.4101	0.836417	0.418208	+	0.908351i	$0.362658\pi$
$998$	25.5419	0.808516
$999$	6.52993	0.206598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.n.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.n.1.1	✓	4	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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.37322 q^{5} -1.00000 q^{6} +3.14256 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.37322 q^{5} -1.00000 q^{6} +3.14256 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.37322 q^{10} +2.46673 q^{11} -1.00000 q^{12} -5.85410 q^{13} +3.14256 q^{14} +3.37322 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +1.93346 q^{19} -3.37322 q^{20} -3.14256 q^{21} +2.46673 q^{22} -6.50785 q^{23} -1.00000 q^{24} +6.37863 q^{25} -5.85410 q^{26} -1.00000 q^{27} +3.14256 q^{28} +0.329578 q^{29} +3.37322 q^{30} +5.56024 q^{31} +1.00000 q^{32} -2.46673 q^{33} +1.00000 q^{34} -10.6005 q^{35} +1.00000 q^{36} -6.52993 q^{37} +1.93346 q^{38} +5.85410 q^{39} -3.37322 q^{40} -1.38737 q^{41} -3.14256 q^{42} -11.8312 q^{43} +2.46673 q^{44} -3.37322 q^{45} -6.50785 q^{46} +13.3033 q^{47} -1.00000 q^{48} +2.87567 q^{49} +6.37863 q^{50} -1.00000 q^{51} -5.85410 q^{52} +2.03490 q^{53} -1.00000 q^{54} -8.32083 q^{55} +3.14256 q^{56} -1.93346 q^{57} +0.329578 q^{58} -1.00000 q^{59} +3.37322 q^{60} -5.22274 q^{61} +5.56024 q^{62} +3.14256 q^{63} +1.00000 q^{64} +19.7472 q^{65} -2.46673 q^{66} -11.6632 q^{67} +1.00000 q^{68} +6.50785 q^{69} -10.6005 q^{70} +9.28461 q^{71} +1.00000 q^{72} +5.39530 q^{73} -6.52993 q^{74} -6.37863 q^{75} +1.93346 q^{76} +7.75185 q^{77} +5.85410 q^{78} -2.16463 q^{79} -3.37322 q^{80} +1.00000 q^{81} -1.38737 q^{82} -2.50163 q^{83} -3.14256 q^{84} -3.37322 q^{85} -11.8312 q^{86} -0.329578 q^{87} +2.46673 q^{88} +10.4048 q^{89} -3.37322 q^{90} -18.3969 q^{91} -6.50785 q^{92} -5.56024 q^{93} +13.3033 q^{94} -6.52200 q^{95} -1.00000 q^{96} +7.09017 q^{97} +2.87567 q^{98} +2.46673 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 3 q^{5} - 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 3 q^{10} + 2 q^{11} - 4 q^{12} - 10 q^{13} + q^{14} + 3 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} - 8 q^{19} - 3 q^{20} - q^{21} + 2 q^{22} - 10 q^{23} - 4 q^{24} + 5 q^{25} - 10 q^{26} - 4 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} + 17 q^{31} + 4 q^{32} - 2 q^{33} + 4 q^{34} - 8 q^{35} + 4 q^{36} - 9 q^{37} - 8 q^{38} + 10 q^{39} - 3 q^{40} - q^{42} - 14 q^{43} + 2 q^{44} - 3 q^{45} - 10 q^{46} + 2 q^{47} - 4 q^{48} - 5 q^{49} + 5 q^{50} - 4 q^{51} - 10 q^{52} - 11 q^{53} - 4 q^{54} - 12 q^{55} + q^{56} + 8 q^{57} - 5 q^{58} - 4 q^{59} + 3 q^{60} - 28 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{66} - q^{67} + 4 q^{68} + 10 q^{69} - 8 q^{70} + 12 q^{71} + 4 q^{72} + 10 q^{73} - 9 q^{74} - 5 q^{75} - 8 q^{76} + 10 q^{78} + 4 q^{79} - 3 q^{80} + 4 q^{81} + 17 q^{83} - q^{84} - 3 q^{85} - 14 q^{86} + 5 q^{87} + 2 q^{88} - 13 q^{89} - 3 q^{90} - 25 q^{91} - 10 q^{92} - 17 q^{93} + 2 q^{94} - 15 q^{95} - 4 q^{96} + 6 q^{97} - 5 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 3 * q^5 - 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 3 * q^10 + 2 * q^11 - 4 * q^12 - 10 * q^13 + q^14 + 3 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 - 8 * q^19 - 3 * q^20 - q^21 + 2 * q^22 - 10 * q^23 - 4 * q^24 + 5 * q^25 - 10 * q^26 - 4 * q^27 + q^28 - 5 * q^29 + 3 * q^30 + 17 * q^31 + 4 * q^32 - 2 * q^33 + 4 * q^34 - 8 * q^35 + 4 * q^36 - 9 * q^37 - 8 * q^38 + 10 * q^39 - 3 * q^40 - q^42 - 14 * q^43 + 2 * q^44 - 3 * q^45 - 10 * q^46 + 2 * q^47 - 4 * q^48 - 5 * q^49 + 5 * q^50 - 4 * q^51 - 10 * q^52 - 11 * q^53 - 4 * q^54 - 12 * q^55 + q^56 + 8 * q^57 - 5 * q^58 - 4 * q^59 + 3 * q^60 - 28 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^66 - q^67 + 4 * q^68 + 10 * q^69 - 8 * q^70 + 12 * q^71 + 4 * q^72 + 10 * q^73 - 9 * q^74 - 5 * q^75 - 8 * q^76 + 10 * q^78 + 4 * q^79 - 3 * q^80 + 4 * q^81 + 17 * q^83 - q^84 - 3 * q^85 - 14 * q^86 + 5 * q^87 + 2 * q^88 - 13 * q^89 - 3 * q^90 - 25 * q^91 - 10 * q^92 - 17 * q^93 + 2 * q^94 - 15 * q^95 - 4 * q^96 + 6 * q^97 - 5 * q^98 + 2 * q^99

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