LMFDB - Embedded newform 6034.2.a.p.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.679472 q^{3} +1.00000 q^{4} -2.19065 q^{5} +0.679472 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.53832 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.679472 q^{3} +1.00000 q^{4} -2.19065 q^{5} +0.679472 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.53832 q^{9} +2.19065 q^{10} +2.71532 q^{11} -0.679472 q^{12} -4.48649 q^{13} -1.00000 q^{14} +1.48849 q^{15} +1.00000 q^{16} -5.92751 q^{17} +2.53832 q^{18} -5.99392 q^{19} -2.19065 q^{20} -0.679472 q^{21} -2.71532 q^{22} -7.05883 q^{23} +0.679472 q^{24} -0.201031 q^{25} +4.48649 q^{26} +3.76313 q^{27} +1.00000 q^{28} -6.68395 q^{29} -1.48849 q^{30} -9.81858 q^{31} -1.00000 q^{32} -1.84498 q^{33} +5.92751 q^{34} -2.19065 q^{35} -2.53832 q^{36} -9.60094 q^{37} +5.99392 q^{38} +3.04844 q^{39} +2.19065 q^{40} +6.31918 q^{41} +0.679472 q^{42} +10.0137 q^{43} +2.71532 q^{44} +5.56058 q^{45} +7.05883 q^{46} +2.70994 q^{47} -0.679472 q^{48} +1.00000 q^{49} +0.201031 q^{50} +4.02758 q^{51} -4.48649 q^{52} +2.75447 q^{53} -3.76313 q^{54} -5.94832 q^{55} -1.00000 q^{56} +4.07270 q^{57} +6.68395 q^{58} -6.34452 q^{59} +1.48849 q^{60} +9.89818 q^{61} +9.81858 q^{62} -2.53832 q^{63} +1.00000 q^{64} +9.82834 q^{65} +1.84498 q^{66} +5.96185 q^{67} -5.92751 q^{68} +4.79628 q^{69} +2.19065 q^{70} +11.1085 q^{71} +2.53832 q^{72} -13.1219 q^{73} +9.60094 q^{74} +0.136595 q^{75} -5.99392 q^{76} +2.71532 q^{77} -3.04844 q^{78} -11.8567 q^{79} -2.19065 q^{80} +5.05801 q^{81} -6.31918 q^{82} -16.1176 q^{83} -0.679472 q^{84} +12.9851 q^{85} -10.0137 q^{86} +4.54156 q^{87} -2.71532 q^{88} +5.57448 q^{89} -5.56058 q^{90} -4.48649 q^{91} -7.05883 q^{92} +6.67145 q^{93} -2.70994 q^{94} +13.1306 q^{95} +0.679472 q^{96} +6.69656 q^{97} -1.00000 q^{98} -6.89233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−0.679472	−0.392293	−0.196147	−	0.980575i	$-0.562843\pi$
$3$	−0.679472	−0.392293	−0.196147	+	0.980575i	$0.562843\pi$
$4$	1.00000	0.500000
$5$	−2.19065	−0.979691	−0.489845	−	0.871809i	$-0.662947\pi$
$5$	−2.19065	−0.979691	−0.489845	+	0.871809i	$0.662947\pi$
$6$	0.679472	0.277393
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.53832	−0.846106
$10$	2.19065	0.692746
$11$	2.71532	0.818698	0.409349	−	0.912378i	$-0.365756\pi$
$11$	2.71532	0.818698	0.409349	+	0.912378i	$0.365756\pi$
$12$	−0.679472	−0.196147
$13$	−4.48649	−1.24433	−0.622164	−	0.782887i	$-0.713746\pi$
$13$	−4.48649	−1.24433	−0.622164	+	0.782887i	$0.713746\pi$
$14$	−1.00000	−0.267261
$15$	1.48849	0.384326
$16$	1.00000	0.250000
$17$	−5.92751	−1.43763	−0.718816	−	0.695200i	$-0.755316\pi$
$17$	−5.92751	−1.43763	−0.718816	+	0.695200i	$0.755316\pi$
$18$	2.53832	0.598287
$19$	−5.99392	−1.37510	−0.687549	−	0.726138i	$-0.741313\pi$
$19$	−5.99392	−1.37510	−0.687549	+	0.726138i	$0.741313\pi$
$20$	−2.19065	−0.489845
$21$	−0.679472	−0.148273
$22$	−2.71532	−0.578907
$23$	−7.05883	−1.47187	−0.735934	−	0.677054i	$-0.763256\pi$
$23$	−7.05883	−1.47187	−0.735934	+	0.677054i	$0.763256\pi$
$24$	0.679472	0.138697
$25$	−0.201031	−0.0402063
$26$	4.48649	0.879872
$27$	3.76313	0.724215
$28$	1.00000	0.188982
$29$	−6.68395	−1.24118	−0.620589	−	0.784136i	$-0.713106\pi$
$29$	−6.68395	−1.24118	−0.620589	+	0.784136i	$0.713106\pi$
$30$	−1.48849	−0.271760
$31$	−9.81858	−1.76347	−0.881734	−	0.471746i	$-0.843624\pi$
$31$	−9.81858	−1.76347	−0.881734	+	0.471746i	$0.843624\pi$
$32$	−1.00000	−0.176777
$33$	−1.84498	−0.321170
$34$	5.92751	1.01656
$35$	−2.19065	−0.370288
$36$	−2.53832	−0.423053
$37$	−9.60094	−1.57839	−0.789193	−	0.614146i	$-0.789501\pi$
$37$	−9.60094	−1.57839	−0.789193	+	0.614146i	$0.789501\pi$
$38$	5.99392	0.972341
$39$	3.04844	0.488141
$40$	2.19065	0.346373
$41$	6.31918	0.986889	0.493445	−	0.869777i	$-0.335738\pi$
$41$	6.31918	0.986889	0.493445	+	0.869777i	$0.335738\pi$
$42$	0.679472	0.104845
$43$	10.0137	1.52708	0.763540	−	0.645761i	$-0.223460\pi$
$43$	10.0137	1.52708	0.763540	+	0.645761i	$0.223460\pi$
$44$	2.71532	0.409349
$45$	5.56058	0.828922
$46$	7.05883	1.04077
$47$	2.70994	0.395286	0.197643	−	0.980274i	$-0.436671\pi$
$47$	2.70994	0.395286	0.197643	+	0.980274i	$0.436671\pi$
$48$	−0.679472	−0.0980734
$49$	1.00000	0.142857
$50$	0.201031	0.0284301
$51$	4.02758	0.563974
$52$	−4.48649	−0.622164
$53$	2.75447	0.378355	0.189178	−	0.981943i	$-0.439418\pi$
$53$	2.75447	0.378355	0.189178	+	0.981943i	$0.439418\pi$
$54$	−3.76313	−0.512097
$55$	−5.94832	−0.802071
$56$	−1.00000	−0.133631
$57$	4.07270	0.539442
$58$	6.68395	0.877645
$59$	−6.34452	−0.825986	−0.412993	−	0.910734i	$-0.635517\pi$
$59$	−6.34452	−0.825986	−0.412993	+	0.910734i	$0.635517\pi$
$60$	1.48849	0.192163
$61$	9.89818	1.26733	0.633666	−	0.773607i	$-0.281549\pi$
$61$	9.89818	1.26733	0.633666	+	0.773607i	$0.281549\pi$
$62$	9.81858	1.24696
$63$	−2.53832	−0.319798
$64$	1.00000	0.125000
$65$	9.82834	1.21906
$66$	1.84498	0.227101
$67$	5.96185	0.728356	0.364178	−	0.931329i	$-0.381350\pi$
$67$	5.96185	0.728356	0.364178	+	0.931329i	$0.381350\pi$
$68$	−5.92751	−0.718816
$69$	4.79628	0.577404
$70$	2.19065	0.261833
$71$	11.1085	1.31833	0.659166	−	0.751997i	$-0.270909\pi$
$71$	11.1085	1.31833	0.659166	+	0.751997i	$0.270909\pi$
$72$	2.53832	0.299144
$73$	−13.1219	−1.53581	−0.767903	−	0.640567i	$-0.778700\pi$
$73$	−13.1219	−1.53581	−0.767903	+	0.640567i	$0.778700\pi$
$74$	9.60094	1.11609
$75$	0.136595	0.0157727
$76$	−5.99392	−0.687549
$77$	2.71532	0.309439
$78$	−3.04844	−0.345168
$79$	−11.8567	−1.33398	−0.666991	−	0.745066i	$-0.732418\pi$
$79$	−11.8567	−1.33398	−0.666991	+	0.745066i	$0.732418\pi$
$80$	−2.19065	−0.244923
$81$	5.05801	0.562001
$82$	−6.31918	−0.697836
$83$	−16.1176	−1.76913	−0.884566	−	0.466415i	$-0.845545\pi$
$83$	−16.1176	−1.76913	−0.884566	+	0.466415i	$0.845545\pi$
$84$	−0.679472	−0.0741365
$85$	12.9851	1.40844
$86$	−10.0137	−1.07981
$87$	4.54156	0.486906
$88$	−2.71532	−0.289454
$89$	5.57448	0.590893	0.295447	−	0.955359i	$-0.404532\pi$
$89$	5.57448	0.590893	0.295447	+	0.955359i	$0.404532\pi$
$90$	−5.56058	−0.586136
$91$	−4.48649	−0.470311
$92$	−7.05883	−0.735934
$93$	6.67145	0.691797
$94$	−2.70994	−0.279509
$95$	13.1306	1.34717
$96$	0.679472	0.0693483
$97$	6.69656	0.679933	0.339966	−	0.940438i	$-0.389584\pi$
$97$	6.69656	0.679933	0.339966	+	0.940438i	$0.389584\pi$
$98$	−1.00000	−0.101015
$99$	−6.89233	−0.692706
$100$	−0.201031	−0.0201031
$101$	1.49436	0.148695	0.0743473	−	0.997232i	$-0.476313\pi$
$101$	1.49436	0.148695	0.0743473	+	0.997232i	$0.476313\pi$
$102$	−4.02758	−0.398790
$103$	−18.8377	−1.85613	−0.928067	−	0.372414i	$-0.878530\pi$
$103$	−18.8377	−1.85613	−0.928067	+	0.372414i	$0.878530\pi$
$104$	4.48649	0.439936
$105$	1.48849	0.145262
$106$	−2.75447	−0.267538
$107$	−6.35888	−0.614737	−0.307368	−	0.951591i	$-0.599448\pi$
$107$	−6.35888	−0.614737	−0.307368	+	0.951591i	$0.599448\pi$
$108$	3.76313	0.362108
$109$	0.646636	0.0619365	0.0309682	−	0.999520i	$-0.490141\pi$
$109$	0.646636	0.0619365	0.0309682	+	0.999520i	$0.490141\pi$
$110$	5.94832	0.567150
$111$	6.52357	0.619190
$112$	1.00000	0.0944911
$113$	−0.291308	−0.0274039	−0.0137020	−	0.999906i	$-0.504362\pi$
$113$	−0.291308	−0.0274039	−0.0137020	+	0.999906i	$0.504362\pi$
$114$	−4.07270	−0.381443
$115$	15.4635	1.44197
$116$	−6.68395	−0.620589
$117$	11.3881	1.05283
$118$	6.34452	0.584060
$119$	−5.92751	−0.543374
$120$	−1.48849	−0.135880
$121$	−3.62706	−0.329733
$122$	−9.89818	−0.896139
$123$	−4.29370	−0.387150
$124$	−9.81858	−0.881734
$125$	11.3937	1.01908
$126$	2.53832	0.226131
$127$	7.24048	0.642489	0.321244	−	0.946996i	$-0.395899\pi$
$127$	7.24048	0.642489	0.321244	+	0.946996i	$0.395899\pi$
$128$	−1.00000	−0.0883883
$129$	−6.80405	−0.599063
$130$	−9.82834	−0.862003
$131$	−21.7018	−1.89610	−0.948048	−	0.318128i	$-0.896946\pi$
$131$	−21.7018	−1.89610	−0.948048	+	0.318128i	$0.896946\pi$
$132$	−1.84498	−0.160585
$133$	−5.99392	−0.519738
$134$	−5.96185	−0.515025
$135$	−8.24372	−0.709507
$136$	5.92751	0.508280
$137$	−14.5537	−1.24341	−0.621703	−	0.783253i	$-0.713559\pi$
$137$	−14.5537	−1.24341	−0.621703	+	0.783253i	$0.713559\pi$
$138$	−4.79628	−0.408286
$139$	−2.23338	−0.189433	−0.0947164	−	0.995504i	$-0.530194\pi$
$139$	−2.23338	−0.189433	−0.0947164	+	0.995504i	$0.530194\pi$
$140$	−2.19065	−0.185144
$141$	−1.84133	−0.155068
$142$	−11.1085	−0.932202
$143$	−12.1822	−1.01873
$144$	−2.53832	−0.211526
$145$	14.6422	1.21597
$146$	13.1219	1.08598
$147$	−0.679472	−0.0560419
$148$	−9.60094	−0.789193
$149$	1.64757	0.134974	0.0674872	−	0.997720i	$-0.478502\pi$
$149$	1.64757	0.134974	0.0674872	+	0.997720i	$0.478502\pi$
$150$	−0.136595	−0.0111530
$151$	−14.8306	−1.20690	−0.603450	−	0.797401i	$-0.706208\pi$
$151$	−14.8306	−1.20690	−0.603450	+	0.797401i	$0.706208\pi$
$152$	5.99392	0.486171
$153$	15.0459	1.21639
$154$	−2.71532	−0.218806
$155$	21.5091	1.72765
$156$	3.04844	0.244071
$157$	14.2020	1.13344	0.566722	−	0.823909i	$-0.308211\pi$
$157$	14.2020	1.13344	0.566722	+	0.823909i	$0.308211\pi$
$158$	11.8567	0.943267
$159$	−1.87158	−0.148426
$160$	2.19065	0.173186
$161$	−7.05883	−0.556313
$162$	−5.05801	−0.397395
$163$	−10.5061	−0.822901	−0.411451	−	0.911432i	$-0.634978\pi$
$163$	−10.5061	−0.822901	−0.411451	+	0.911432i	$0.634978\pi$
$164$	6.31918	0.493445
$165$	4.04172	0.314647
$166$	16.1176	1.25097
$167$	16.6938	1.29180	0.645901	−	0.763421i	$-0.276482\pi$
$167$	16.6938	1.29180	0.645901	+	0.763421i	$0.276482\pi$
$168$	0.679472	0.0524224
$169$	7.12855	0.548350
$170$	−12.9851	−0.995914
$171$	15.2145	1.16348
$172$	10.0137	0.763540
$173$	0.879132	0.0668392	0.0334196	−	0.999441i	$-0.489360\pi$
$173$	0.879132	0.0668392	0.0334196	+	0.999441i	$0.489360\pi$
$174$	−4.54156	−0.344294
$175$	−0.201031	−0.0151965
$176$	2.71532	0.204675
$177$	4.31092	0.324029
$178$	−5.57448	−0.417825
$179$	13.5587	1.01343	0.506714	−	0.862114i	$-0.330860\pi$
$179$	13.5587	1.01343	0.506714	+	0.862114i	$0.330860\pi$
$180$	5.56058	0.414461
$181$	−19.4859	−1.44838	−0.724188	−	0.689603i	$-0.757785\pi$
$181$	−19.4859	−1.44838	−0.724188	+	0.689603i	$0.757785\pi$
$182$	4.48649	0.332560
$183$	−6.72554	−0.497166
$184$	7.05883	0.520384
$185$	21.0323	1.54633
$186$	−6.67145	−0.489174
$187$	−16.0951	−1.17699
$188$	2.70994	0.197643
$189$	3.76313	0.273728
$190$	−13.1306	−0.952594
$191$	9.78825	0.708253	0.354127	−	0.935198i	$-0.384778\pi$
$191$	9.78825	0.708253	0.354127	+	0.935198i	$0.384778\pi$
$192$	−0.679472	−0.0490367
$193$	−9.75313	−0.702046	−0.351023	−	0.936367i	$-0.614166\pi$
$193$	−9.75313	−0.702046	−0.351023	+	0.936367i	$0.614166\pi$
$194$	−6.69656	−0.480785
$195$	−6.67808	−0.478228
$196$	1.00000	0.0714286
$197$	16.0227	1.14157	0.570785	−	0.821099i	$-0.306639\pi$
$197$	16.0227	1.14157	0.570785	+	0.821099i	$0.306639\pi$
$198$	6.89233	0.489817
$199$	2.22908	0.158016	0.0790078	−	0.996874i	$-0.474825\pi$
$199$	2.22908	0.158016	0.0790078	+	0.996874i	$0.474825\pi$
$200$	0.201031	0.0142151
$201$	−4.05091	−0.285729
$202$	−1.49436	−0.105143
$203$	−6.68395	−0.469121
$204$	4.02758	0.281987
$205$	−13.8431	−0.966846
$206$	18.8377	1.31248
$207$	17.9175	1.24536
$208$	−4.48649	−0.311082
$209$	−16.2754	−1.12579
$210$	−1.48849	−0.102715
$211$	−1.42265	−0.0979395	−0.0489698	−	0.998800i	$-0.515594\pi$
$211$	−1.42265	−0.0979395	−0.0489698	+	0.998800i	$0.515594\pi$
$212$	2.75447	0.189178
$213$	−7.54789	−0.517173
$214$	6.35888	0.434684
$215$	−21.9366	−1.49607
$216$	−3.76313	−0.256049
$217$	−9.81858	−0.666529
$218$	−0.646636	−0.0437957
$219$	8.91598	0.602486
$220$	−5.94832	−0.401036
$221$	26.5937	1.78889
$222$	−6.52357	−0.437833
$223$	6.37638	0.426994	0.213497	−	0.976944i	$-0.431515\pi$
$223$	6.37638	0.426994	0.213497	+	0.976944i	$0.431515\pi$
$224$	−1.00000	−0.0668153
$225$	0.510281	0.0340188
$226$	0.291308	0.0193775
$227$	−27.0438	−1.79496	−0.897480	−	0.441055i	$-0.854604\pi$
$227$	−27.0438	−1.79496	−0.897480	+	0.441055i	$0.854604\pi$
$228$	4.07270	0.269721
$229$	17.8018	1.17638	0.588189	−	0.808724i	$-0.299841\pi$
$229$	17.8018	1.17638	0.588189	+	0.808724i	$0.299841\pi$
$230$	−15.4635	−1.01963
$231$	−1.84498	−0.121391
$232$	6.68395	0.438823
$233$	−3.54534	−0.232263	−0.116131	−	0.993234i	$-0.537049\pi$
$233$	−3.54534	−0.232263	−0.116131	+	0.993234i	$0.537049\pi$
$234$	−11.3881	−0.744465
$235$	−5.93655	−0.387258
$236$	−6.34452	−0.412993
$237$	8.05629	0.523312
$238$	5.92751	0.384223
$239$	30.5676	1.97725	0.988625	−	0.150399i	$-0.0480559\pi$
$239$	30.5676	1.97725	0.988625	+	0.150399i	$0.0480559\pi$
$240$	1.48849	0.0960815
$241$	−11.1391	−0.717531	−0.358765	−	0.933428i	$-0.616802\pi$
$241$	−11.1391	−0.717531	−0.358765	+	0.933428i	$0.616802\pi$
$242$	3.62706	0.233156
$243$	−14.7262	−0.944684
$244$	9.89818	0.633666
$245$	−2.19065	−0.139956
$246$	4.29370	0.273757
$247$	26.8916	1.71107
$248$	9.81858	0.623480
$249$	10.9514	0.694019
$250$	−11.3937	−0.720599
$251$	10.5826	0.667971	0.333985	−	0.942578i	$-0.391606\pi$
$251$	10.5826	0.667971	0.333985	+	0.942578i	$0.391606\pi$
$252$	−2.53832	−0.159899
$253$	−19.1669	−1.20502
$254$	−7.24048	−0.454308
$255$	−8.82303	−0.552520
$256$	1.00000	0.0625000
$257$	15.1181	0.943039	0.471519	−	0.881856i	$-0.343706\pi$
$257$	15.1181	0.943039	0.471519	+	0.881856i	$0.343706\pi$
$258$	6.80405	0.423602
$259$	−9.60094	−0.596573
$260$	9.82834	0.609528
$261$	16.9660	1.05017
$262$	21.7018	1.34074
$263$	5.13332	0.316534	0.158267	−	0.987396i	$-0.449409\pi$
$263$	5.13332	0.316534	0.158267	+	0.987396i	$0.449409\pi$
$264$	1.84498	0.113551
$265$	−6.03409	−0.370671
$266$	5.99392	0.367511
$267$	−3.78770	−0.231804
$268$	5.96185	0.364178
$269$	0.331293	0.0201993	0.0100997	−	0.999949i	$-0.496785\pi$
$269$	0.331293	0.0201993	0.0100997	+	0.999949i	$0.496785\pi$
$270$	8.24372	0.501697
$271$	−4.97207	−0.302032	−0.151016	−	0.988531i	$-0.548254\pi$
$271$	−4.97207	−0.302032	−0.151016	+	0.988531i	$0.548254\pi$
$272$	−5.92751	−0.359408
$273$	3.04844	0.184500
$274$	14.5537	0.879221
$275$	−0.545864	−0.0329168
$276$	4.79628	0.288702
$277$	−17.2644	−1.03732	−0.518659	−	0.854981i	$-0.673568\pi$
$277$	−17.2644	−1.03732	−0.518659	+	0.854981i	$0.673568\pi$
$278$	2.23338	0.133949
$279$	24.9227	1.49208
$280$	2.19065	0.130917
$281$	−0.625631	−0.0373220	−0.0186610	−	0.999826i	$-0.505940\pi$
$281$	−0.625631	−0.0373220	−0.0186610	+	0.999826i	$0.505940\pi$
$282$	1.84133	0.109650
$283$	−13.1040	−0.778953	−0.389476	−	0.921036i	$-0.627344\pi$
$283$	−13.1040	−0.778953	−0.389476	+	0.921036i	$0.627344\pi$
$284$	11.1085	0.659166
$285$	−8.92188	−0.528486
$286$	12.1822	0.720350
$287$	6.31918	0.373009
$288$	2.53832	0.149572
$289$	18.1354	1.06679
$290$	−14.6422	−0.859821
$291$	−4.55013	−0.266733
$292$	−13.1219	−0.767903
$293$	14.0307	0.819682	0.409841	−	0.912157i	$-0.365584\pi$
$293$	14.0307	0.819682	0.409841	+	0.912157i	$0.365584\pi$
$294$	0.679472	0.0396276
$295$	13.8986	0.809211
$296$	9.60094	0.558043
$297$	10.2181	0.592914
$298$	−1.64757	−0.0954414
$299$	31.6693	1.83148
$300$	0.136595	0.00788633
$301$	10.0137	0.577182
$302$	14.8306	0.853407
$303$	−1.01538	−0.0583319
$304$	−5.99392	−0.343775
$305$	−21.6835	−1.24159
$306$	−15.0459	−0.860117
$307$	−16.4353	−0.938013	−0.469006	−	0.883195i	$-0.655388\pi$
$307$	−16.4353	−0.938013	−0.469006	+	0.883195i	$0.655388\pi$
$308$	2.71532	0.154719
$309$	12.7997	0.728149
$310$	−21.5091	−1.22164
$311$	−33.8949	−1.92200	−0.961001	−	0.276545i	$-0.910811\pi$
$311$	−33.8949	−1.92200	−0.961001	+	0.276545i	$0.910811\pi$
$312$	−3.04844	−0.172584
$313$	−26.5620	−1.50137	−0.750687	−	0.660659i	$-0.770277\pi$
$313$	−26.5620	−1.50137	−0.750687	+	0.660659i	$0.770277\pi$
$314$	−14.2020	−0.801466
$315$	5.56058	0.313303
$316$	−11.8567	−0.666991
$317$	−1.60376	−0.0900761	−0.0450380	−	0.998985i	$-0.514341\pi$
$317$	−1.60376	−0.0900761	−0.0450380	+	0.998985i	$0.514341\pi$
$318$	1.87158	0.104953
$319$	−18.1490	−1.01615
$320$	−2.19065	−0.122461
$321$	4.32068	0.241157
$322$	7.05883	0.393373
$323$	35.5290	1.97689
$324$	5.05801	0.281001
$325$	0.901924	0.0500298
$326$	10.5061	0.581879
$327$	−0.439371	−0.0242973
$328$	−6.31918	−0.348918
$329$	2.70994	0.149404
$330$	−4.04172	−0.222489
$331$	19.7401	1.08501	0.542506	−	0.840052i	$-0.317476\pi$
$331$	19.7401	1.08501	0.542506	+	0.840052i	$0.317476\pi$
$332$	−16.1176	−0.884566
$333$	24.3702	1.33548
$334$	−16.6938	−0.913442
$335$	−13.0604	−0.713564
$336$	−0.679472	−0.0370682
$337$	9.65069	0.525707	0.262853	−	0.964836i	$-0.415336\pi$
$337$	9.65069	0.525707	0.262853	+	0.964836i	$0.415336\pi$
$338$	−7.12855	−0.387742
$339$	0.197935	0.0107504
$340$	12.9851	0.704218
$341$	−26.6605	−1.44375
$342$	−15.2145	−0.822704
$343$	1.00000	0.0539949
$344$	−10.0137	−0.539904
$345$	−10.5070	−0.565677
$346$	−0.879132	−0.0472624
$347$	24.2750	1.30315	0.651574	−	0.758585i	$-0.274109\pi$
$347$	24.2750	1.30315	0.651574	+	0.758585i	$0.274109\pi$
$348$	4.54156	0.243453
$349$	7.68778	0.411518	0.205759	−	0.978603i	$-0.434034\pi$
$349$	7.68778	0.411518	0.205759	+	0.978603i	$0.434034\pi$
$350$	0.201031	0.0107456
$351$	−16.8832	−0.901161
$352$	−2.71532	−0.144727
$353$	−27.2183	−1.44869	−0.724343	−	0.689440i	$-0.757857\pi$
$353$	−27.2183	−1.44869	−0.724343	+	0.689440i	$0.757857\pi$
$354$	−4.31092	−0.229123
$355$	−24.3348	−1.29156
$356$	5.57448	0.295447
$357$	4.02758	0.213162
$358$	−13.5587	−0.716602
$359$	23.9197	1.26243	0.631217	−	0.775607i	$-0.282556\pi$
$359$	23.9197	1.26243	0.631217	+	0.775607i	$0.282556\pi$
$360$	−5.56058	−0.293068
$361$	16.9270	0.890896
$362$	19.4859	1.02416
$363$	2.46449	0.129352
$364$	−4.48649	−0.235156
$365$	28.7456	1.50461
$366$	6.72554	0.351549
$367$	30.5336	1.59384	0.796921	−	0.604084i	$-0.206461\pi$
$367$	30.5336	1.59384	0.796921	+	0.604084i	$0.206461\pi$
$368$	−7.05883	−0.367967
$369$	−16.0401	−0.835013
$370$	−21.0323	−1.09342
$371$	2.75447	0.143005
$372$	6.67145	0.345899
$373$	20.1616	1.04393	0.521965	−	0.852967i	$-0.325199\pi$
$373$	20.1616	1.04393	0.521965	+	0.852967i	$0.325199\pi$
$374$	16.0951	0.832256
$375$	−7.74168	−0.399778
$376$	−2.70994	−0.139755
$377$	29.9874	1.54443
$378$	−3.76313	−0.193555
$379$	−18.4682	−0.948648	−0.474324	−	0.880350i	$-0.657307\pi$
$379$	−18.4682	−0.948648	−0.474324	+	0.880350i	$0.657307\pi$
$380$	13.1306	0.673586
$381$	−4.91970	−0.252044
$382$	−9.78825	−0.500811
$383$	1.59606	0.0815548	0.0407774	−	0.999168i	$-0.487017\pi$
$383$	1.59606	0.0815548	0.0407774	+	0.999168i	$0.487017\pi$
$384$	0.679472	0.0346742
$385$	−5.94832	−0.303154
$386$	9.75313	0.496421
$387$	−25.4180	−1.29207
$388$	6.69656	0.339966
$389$	11.4075	0.578381	0.289191	−	0.957272i	$-0.406614\pi$
$389$	11.4075	0.578381	0.289191	+	0.957272i	$0.406614\pi$
$390$	6.67808	0.338158
$391$	41.8413	2.11600
$392$	−1.00000	−0.0505076
$393$	14.7458	0.743826
$394$	−16.0227	−0.807212
$395$	25.9739	1.30689
$396$	−6.89233	−0.346353
$397$	−0.595360	−0.0298803	−0.0149401	−	0.999888i	$-0.504756\pi$
$397$	−0.595360	−0.0298803	−0.0149401	+	0.999888i	$0.504756\pi$
$398$	−2.22908	−0.111734
$399$	4.07270	0.203890
$400$	−0.201031	−0.0100516
$401$	27.5055	1.37356	0.686779	−	0.726866i	$-0.259024\pi$
$401$	27.5055	1.37356	0.686779	+	0.726866i	$0.259024\pi$
$402$	4.05091	0.202041
$403$	44.0509	2.19433
$404$	1.49436	0.0743473
$405$	−11.0804	−0.550587
$406$	6.68395	0.331719
$407$	−26.0696	−1.29222
$408$	−4.02758	−0.199395
$409$	17.7786	0.879094	0.439547	−	0.898220i	$-0.355139\pi$
$409$	17.7786	0.879094	0.439547	+	0.898220i	$0.355139\pi$
$410$	13.8431	0.683664
$411$	9.88883	0.487780
$412$	−18.8377	−0.928067
$413$	−6.34452	−0.312193
$414$	−17.9175	−0.880599
$415$	35.3080	1.73320
$416$	4.48649	0.219968
$417$	1.51752	0.0743133
$418$	16.2754	0.796054
$419$	−11.1387	−0.544163	−0.272082	−	0.962274i	$-0.587712\pi$
$419$	−11.1387	−0.544163	−0.272082	+	0.962274i	$0.587712\pi$
$420$	1.48849	0.0726308
$421$	−1.85644	−0.0904773	−0.0452386	−	0.998976i	$-0.514405\pi$
$421$	−1.85644	−0.0904773	−0.0452386	+	0.998976i	$0.514405\pi$
$422$	1.42265	0.0692537
$423$	−6.87869	−0.334453
$424$	−2.75447	−0.133769
$425$	1.19162	0.0578018
$426$	7.54789	0.365697
$427$	9.89818	0.479006
$428$	−6.35888	−0.307368
$429$	8.27748	0.399641
$430$	21.9366	1.05788
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	3.76313	0.181054
$433$	−29.7915	−1.43169	−0.715845	−	0.698260i	$-0.753958\pi$
$433$	−29.7915	−1.43169	−0.715845	+	0.698260i	$0.753958\pi$
$434$	9.81858	0.471307
$435$	−9.94898	−0.477017
$436$	0.646636	0.0309682
$437$	42.3100	2.02396
$438$	−8.91598	−0.426022
$439$	27.3122	1.30354	0.651770	−	0.758417i	$-0.274027\pi$
$439$	27.3122	1.30354	0.651770	+	0.758417i	$0.274027\pi$
$440$	5.94832	0.283575
$441$	−2.53832	−0.120872
$442$	−26.5937	−1.26493
$443$	−40.5681	−1.92745	−0.963725	−	0.266898i	$-0.914001\pi$
$443$	−40.5681	−1.92745	−0.963725	+	0.266898i	$0.914001\pi$
$444$	6.52357	0.309595
$445$	−12.2118	−0.578893
$446$	−6.37638	−0.301930
$447$	−1.11948	−0.0529496
$448$	1.00000	0.0472456
$449$	11.4949	0.542478	0.271239	−	0.962512i	$-0.412567\pi$
$449$	11.4949	0.542478	0.271239	+	0.962512i	$0.412567\pi$
$450$	−0.510281	−0.0240549
$451$	17.1586	0.807965
$452$	−0.291308	−0.0137020
$453$	10.0770	0.473459
$454$	27.0438	1.26923
$455$	9.82834	0.460760
$456$	−4.07270	−0.190722
$457$	−14.4229	−0.674676	−0.337338	−	0.941384i	$-0.609526\pi$
$457$	−14.4229	−0.674676	−0.337338	+	0.941384i	$0.609526\pi$
$458$	−17.8018	−0.831825
$459$	−22.3060	−1.04116
$460$	15.4635	0.720987
$461$	−28.4124	−1.32330	−0.661648	−	0.749815i	$-0.730143\pi$
$461$	−28.4124	−1.32330	−0.661648	+	0.749815i	$0.730143\pi$
$462$	1.84498	0.0858363
$463$	−1.30246	−0.0605303	−0.0302652	−	0.999542i	$-0.509635\pi$
$463$	−1.30246	−0.0605303	−0.0302652	+	0.999542i	$0.509635\pi$
$464$	−6.68395	−0.310294
$465$	−14.6148	−0.677747
$466$	3.54534	0.164235
$467$	−16.4985	−0.763458	−0.381729	−	0.924274i	$-0.624671\pi$
$467$	−16.4985	−0.763458	−0.381729	+	0.924274i	$0.624671\pi$
$468$	11.3881	0.526416
$469$	5.96185	0.275293
$470$	5.93655	0.273832
$471$	−9.64987	−0.444643
$472$	6.34452	0.292030
$473$	27.1904	1.25022
$474$	−8.05629	−0.370038
$475$	1.20496	0.0552876
$476$	−5.92751	−0.271687
$477$	−6.99172	−0.320129
$478$	−30.5676	−1.39813
$479$	7.30310	0.333687	0.166844	−	0.985983i	$-0.446642\pi$
$479$	7.30310	0.333687	0.166844	+	0.985983i	$0.446642\pi$
$480$	−1.48849	−0.0679399
$481$	43.0745	1.96403
$482$	11.1391	0.507371
$483$	4.79628	0.218238
$484$	−3.62706	−0.164866
$485$	−14.6699	−0.666124
$486$	14.7262	0.667993
$487$	−10.9237	−0.495001	−0.247500	−	0.968888i	$-0.579609\pi$
$487$	−10.9237	−0.495001	−0.247500	+	0.968888i	$0.579609\pi$
$488$	−9.89818	−0.448070
$489$	7.13860	0.322819
$490$	2.19065	0.0989637
$491$	−7.14218	−0.322322	−0.161161	−	0.986928i	$-0.551524\pi$
$491$	−7.14218	−0.322322	−0.161161	+	0.986928i	$0.551524\pi$
$492$	−4.29370	−0.193575
$493$	39.6192	1.78436
$494$	−26.8916	−1.20991
$495$	15.0987	0.678637
$496$	−9.81858	−0.440867
$497$	11.1085	0.498283
$498$	−10.9514	−0.490745
$499$	−22.7232	−1.01723	−0.508615	−	0.860994i	$-0.669842\pi$
$499$	−22.7232	−1.01723	−0.508615	+	0.860994i	$0.669842\pi$
$500$	11.3937	0.509540
$501$	−11.3429	−0.506765
$502$	−10.5826	−0.472327
$503$	−31.2928	−1.39528	−0.697639	−	0.716450i	$-0.745766\pi$
$503$	−31.2928	−1.39528	−0.697639	+	0.716450i	$0.745766\pi$
$504$	2.53832	0.113066
$505$	−3.27363	−0.145675
$506$	19.1669	0.852074
$507$	−4.84365	−0.215114
$508$	7.24048	0.321244
$509$	−31.8529	−1.41186	−0.705928	−	0.708283i	$-0.749470\pi$
$509$	−31.8529	−1.41186	−0.705928	+	0.708283i	$0.749470\pi$
$510$	8.82303	0.390691
$511$	−13.1219	−0.580480
$512$	−1.00000	−0.0441942
$513$	−22.5559	−0.995867
$514$	−15.1181	−0.666829
$515$	41.2669	1.81844
$516$	−6.80405	−0.299532
$517$	7.35835	0.323620
$518$	9.60094	0.421841
$519$	−0.597346	−0.0262206
$520$	−9.82834	−0.431001
$521$	10.4032	0.455772	0.227886	−	0.973688i	$-0.426819\pi$
$521$	10.4032	0.455772	0.227886	+	0.973688i	$0.426819\pi$
$522$	−16.9660	−0.742581
$523$	−18.0305	−0.788420	−0.394210	−	0.919020i	$-0.628982\pi$
$523$	−18.0305	−0.788420	−0.394210	+	0.919020i	$0.628982\pi$
$524$	−21.7018	−0.948048
$525$	0.136595	0.00596150
$526$	−5.13332	−0.223823
$527$	58.1997	2.53522
$528$	−1.84498	−0.0802925
$529$	26.8270	1.16639
$530$	6.03409	0.262104
$531$	16.1044	0.698872
$532$	−5.99392	−0.259869
$533$	−28.3509	−1.22801
$534$	3.78770	0.163910
$535$	13.9301	0.602252
$536$	−5.96185	−0.257513
$537$	−9.21278	−0.397561
$538$	−0.331293	−0.0142831
$539$	2.71532	0.116957
$540$	−8.24372	−0.354753
$541$	−38.4671	−1.65383	−0.826914	−	0.562328i	$-0.809906\pi$
$541$	−38.4671	−1.65383	−0.826914	+	0.562328i	$0.809906\pi$
$542$	4.97207	0.213569
$543$	13.2401	0.568188
$544$	5.92751	0.254140
$545$	−1.41656	−0.0606786
$546$	−3.04844	−0.130461
$547$	−18.6630	−0.797974	−0.398987	−	0.916957i	$-0.630638\pi$
$547$	−18.6630	−0.797974	−0.398987	+	0.916957i	$0.630638\pi$
$548$	−14.5537	−0.621703
$549$	−25.1247	−1.07230
$550$	0.545864	0.0232757
$551$	40.0630	1.70674
$552$	−4.79628	−0.204143
$553$	−11.8567	−0.504198
$554$	17.2644	0.733494
$555$	−14.2909	−0.606615
$556$	−2.23338	−0.0947164
$557$	4.42976	0.187695	0.0938475	−	0.995587i	$-0.470083\pi$
$557$	4.42976	0.187695	0.0938475	+	0.995587i	$0.470083\pi$
$558$	−24.9227	−1.05506
$559$	−44.9264	−1.90019
$560$	−2.19065	−0.0925721
$561$	10.9361	0.461724
$562$	0.625631	0.0263906
$563$	9.03846	0.380926	0.190463	−	0.981694i	$-0.439001\pi$
$563$	9.03846	0.380926	0.190463	+	0.981694i	$0.439001\pi$
$564$	−1.84133	−0.0775340
$565$	0.638155	0.0268474
$566$	13.1040	0.550803
$567$	5.05801	0.212416
$568$	−11.1085	−0.466101
$569$	6.56697	0.275302	0.137651	−	0.990481i	$-0.456045\pi$
$569$	6.56697	0.275302	0.137651	+	0.990481i	$0.456045\pi$
$570$	8.92188	0.373696
$571$	−4.55395	−0.190577	−0.0952884	−	0.995450i	$-0.530377\pi$
$571$	−4.55395	−0.190577	−0.0952884	+	0.995450i	$0.530377\pi$
$572$	−12.1822	−0.509364
$573$	−6.65084	−0.277843
$574$	−6.31918	−0.263757
$575$	1.41905	0.0591783
$576$	−2.53832	−0.105763
$577$	−26.5920	−1.10704	−0.553519	−	0.832836i	$-0.686715\pi$
$577$	−26.5920	−1.10704	−0.553519	+	0.832836i	$0.686715\pi$
$578$	−18.1354	−0.754333
$579$	6.62698	0.275408
$580$	14.6422	0.607985
$581$	−16.1176	−0.668669
$582$	4.55013	0.188609
$583$	7.47925	0.309759
$584$	13.1219	0.542989
$585$	−24.9475	−1.03145
$586$	−14.0307	−0.579603
$587$	25.2112	1.04058	0.520289	−	0.853990i	$-0.325824\pi$
$587$	25.2112	1.04058	0.520289	+	0.853990i	$0.325824\pi$
$588$	−0.679472	−0.0280210
$589$	58.8517	2.42494
$590$	−13.8986	−0.572198
$591$	−10.8870	−0.447830
$592$	−9.60094	−0.394596
$593$	9.81026	0.402859	0.201430	−	0.979503i	$-0.435441\pi$
$593$	9.81026	0.402859	0.201430	+	0.979503i	$0.435441\pi$
$594$	−10.2181	−0.419253
$595$	12.9851	0.532338
$596$	1.64757	0.0674872
$597$	−1.51460	−0.0619885
$598$	−31.6693	−1.29506
$599$	−7.01113	−0.286467	−0.143234	−	0.989689i	$-0.545750\pi$
$599$	−7.01113	−0.286467	−0.143234	+	0.989689i	$0.545750\pi$
$600$	−0.136595	−0.00557648
$601$	−35.9194	−1.46518	−0.732591	−	0.680669i	$-0.761689\pi$
$601$	−35.9194	−1.46518	−0.732591	+	0.680669i	$0.761689\pi$
$602$	−10.0137	−0.408129
$603$	−15.1331	−0.616266
$604$	−14.8306	−0.603450
$605$	7.94564	0.323036
$606$	1.01538	0.0412469
$607$	−1.19475	−0.0484935	−0.0242467	−	0.999706i	$-0.507719\pi$
$607$	−1.19475	−0.0484935	−0.0242467	+	0.999706i	$0.507719\pi$
$608$	5.99392	0.243085
$609$	4.54156	0.184033
$610$	21.6835	0.877939
$611$	−12.1581	−0.491865
$612$	15.0459	0.608195
$613$	6.93541	0.280119	0.140059	−	0.990143i	$-0.455271\pi$
$613$	6.93541	0.280119	0.140059	+	0.990143i	$0.455271\pi$
$614$	16.4353	0.663275
$615$	9.40602	0.379287
$616$	−2.71532	−0.109403
$617$	−5.21360	−0.209892	−0.104946	−	0.994478i	$-0.533467\pi$
$617$	−5.21360	−0.209892	−0.104946	+	0.994478i	$0.533467\pi$
$618$	−12.7997	−0.514879
$619$	−43.7721	−1.75935	−0.879674	−	0.475577i	$-0.842239\pi$
$619$	−43.7721	−1.75935	−0.879674	+	0.475577i	$0.842239\pi$
$620$	21.5091	0.863827
$621$	−26.5633	−1.06595
$622$	33.8949	1.35906
$623$	5.57448	0.223337
$624$	3.04844	0.122035
$625$	−23.9544	−0.958177
$626$	26.5620	1.06163
$627$	11.0587	0.441640
$628$	14.2020	0.566722
$629$	56.9097	2.26914
$630$	−5.56058	−0.221539
$631$	−23.9756	−0.954452	−0.477226	−	0.878781i	$-0.658358\pi$
$631$	−23.9756	−0.954452	−0.477226	+	0.878781i	$0.658358\pi$
$632$	11.8567	0.471634
$633$	0.966654	0.0384210
$634$	1.60376	0.0636934
$635$	−15.8614	−0.629440
$636$	−1.87158	−0.0742132
$637$	−4.48649	−0.177761
$638$	18.1490	0.718527
$639$	−28.1968	−1.11545
$640$	2.19065	0.0865932
$641$	27.3905	1.08186	0.540929	−	0.841068i	$-0.318073\pi$
$641$	27.3905	1.08186	0.540929	+	0.841068i	$0.318073\pi$
$642$	−4.32068	−0.170524
$643$	−49.8261	−1.96495	−0.982474	−	0.186398i	$-0.940319\pi$
$643$	−49.8261	−1.96495	−0.982474	+	0.186398i	$0.940319\pi$
$644$	−7.05883	−0.278157
$645$	14.9053	0.586896
$646$	−35.5290	−1.39787
$647$	26.8735	1.05651	0.528253	−	0.849087i	$-0.322847\pi$
$647$	26.8735	1.05651	0.528253	+	0.849087i	$0.322847\pi$
$648$	−5.05801	−0.198697
$649$	−17.2274	−0.676233
$650$	−0.901924	−0.0353764
$651$	6.67145	0.261475
$652$	−10.5061	−0.411451
$653$	25.7988	1.00958	0.504792	−	0.863241i	$-0.331569\pi$
$653$	25.7988	1.00958	0.504792	+	0.863241i	$0.331569\pi$
$654$	0.439371	0.0171808
$655$	47.5412	1.85759
$656$	6.31918	0.246722
$657$	33.3076	1.29945
$658$	−2.70994	−0.105645
$659$	37.8273	1.47354	0.736771	−	0.676142i	$-0.236350\pi$
$659$	37.8273	1.47354	0.736771	+	0.676142i	$0.236350\pi$
$660$	4.04172	0.157324
$661$	50.6473	1.96995	0.984977	−	0.172687i	$-0.0552449\pi$
$661$	50.6473	1.96995	0.984977	+	0.172687i	$0.0552449\pi$
$662$	−19.7401	−0.767219
$663$	−18.0697	−0.701768
$664$	16.1176	0.625483
$665$	13.1306	0.509183
$666$	−24.3702	−0.944328
$667$	47.1808	1.82685
$668$	16.6938	0.645901
$669$	−4.33257	−0.167507
$670$	13.0604	0.504566
$671$	26.8767	1.03756
$672$	0.679472	0.0262112
$673$	−0.865647	−0.0333682	−0.0166841	−	0.999861i	$-0.505311\pi$
$673$	−0.865647	−0.0333682	−0.0166841	+	0.999861i	$0.505311\pi$
$674$	−9.65069	−0.371731
$675$	−0.756508	−0.0291180
$676$	7.12855	0.274175
$677$	−10.8904	−0.418553	−0.209276	−	0.977857i	$-0.567111\pi$
$677$	−10.8904	−0.418553	−0.209276	+	0.977857i	$0.567111\pi$
$678$	−0.197935	−0.00760167
$679$	6.69656	0.256990
$680$	−12.9851	−0.497957
$681$	18.3755	0.704151
$682$	26.6605	1.02088
$683$	48.2438	1.84600	0.923000	−	0.384801i	$-0.125730\pi$
$683$	48.2438	1.84600	0.923000	+	0.384801i	$0.125730\pi$
$684$	15.2145	0.581739
$685$	31.8821	1.21815
$686$	−1.00000	−0.0381802
$687$	−12.0958	−0.461485
$688$	10.0137	0.381770
$689$	−12.3579	−0.470798
$690$	10.5070	0.399994
$691$	30.0736	1.14405	0.572026	−	0.820236i	$-0.306158\pi$
$691$	30.0736	1.14405	0.572026	+	0.820236i	$0.306158\pi$
$692$	0.879132	0.0334196
$693$	−6.89233	−0.261818
$694$	−24.2750	−0.921465
$695$	4.89257	0.185586
$696$	−4.54156	−0.172147
$697$	−37.4570	−1.41878
$698$	−7.68778	−0.290987
$699$	2.40896	0.0911152
$700$	−0.201031	−0.00759827
$701$	−4.23829	−0.160078	−0.0800390	−	0.996792i	$-0.525504\pi$
$701$	−4.23829	−0.160078	−0.0800390	+	0.996792i	$0.525504\pi$
$702$	16.8832	0.637217
$703$	57.5472	2.17043
$704$	2.71532	0.102337
$705$	4.03372	0.151919
$706$	27.2183	1.02438
$707$	1.49436	0.0562012
$708$	4.31092	0.162014
$709$	−1.42802	−0.0536304	−0.0268152	−	0.999640i	$-0.508537\pi$
$709$	−1.42802	−0.0536304	−0.0268152	+	0.999640i	$0.508537\pi$
$710$	24.3348	0.913270
$711$	30.0960	1.12869
$712$	−5.57448	−0.208912
$713$	69.3076	2.59559
$714$	−4.02758	−0.150728
$715$	26.6870	0.998039
$716$	13.5587	0.506714
$717$	−20.7698	−0.775662
$718$	−23.9197	−0.892675
$719$	−9.62680	−0.359019	−0.179510	−	0.983756i	$-0.557451\pi$
$719$	−9.62680	−0.359019	−0.179510	+	0.983756i	$0.557451\pi$
$720$	5.56058	0.207231
$721$	−18.8377	−0.701553
$722$	−16.9270	−0.629959
$723$	7.56869	0.281483
$724$	−19.4859	−0.724188
$725$	1.34368	0.0499031
$726$	−2.46449	−0.0914657
$727$	19.9891	0.741355	0.370678	−	0.928762i	$-0.379125\pi$
$727$	19.9891	0.741355	0.370678	+	0.928762i	$0.379125\pi$
$728$	4.48649	0.166280
$729$	−5.16800	−0.191408
$730$	−28.7456	−1.06392
$731$	−59.3565	−2.19538
$732$	−6.72554	−0.248583
$733$	26.9709	0.996192	0.498096	−	0.867122i	$-0.334033\pi$
$733$	26.9709	0.996192	0.498096	+	0.867122i	$0.334033\pi$
$734$	−30.5336	−1.12702
$735$	1.48849	0.0549037
$736$	7.05883	0.260192
$737$	16.1883	0.596304
$738$	16.0401	0.590443
$739$	−18.8026	−0.691667	−0.345833	−	0.938296i	$-0.612404\pi$
$739$	−18.8026	−0.691667	−0.345833	+	0.938296i	$0.612404\pi$
$740$	21.0323	0.773165
$741$	−18.2721	−0.671242
$742$	−2.75447	−0.101120
$743$	−14.0393	−0.515054	−0.257527	−	0.966271i	$-0.582908\pi$
$743$	−14.0393	−0.515054	−0.257527	+	0.966271i	$0.582908\pi$
$744$	−6.67145	−0.244587
$745$	−3.60926	−0.132233
$746$	−20.1616	−0.738169
$747$	40.9115	1.49687
$748$	−16.0951	−0.588494
$749$	−6.35888	−0.232349
$750$	7.74168	0.282686
$751$	18.1443	0.662093	0.331047	−	0.943614i	$-0.392598\pi$
$751$	18.1443	0.662093	0.331047	+	0.943614i	$0.392598\pi$
$752$	2.70994	0.0988214
$753$	−7.19061	−0.262040
$754$	−29.9874	−1.09208
$755$	32.4888	1.18239
$756$	3.76313	0.136864
$757$	−48.9292	−1.77836	−0.889182	−	0.457554i	$-0.848726\pi$
$757$	−48.9292	−1.77836	−0.889182	+	0.457554i	$0.848726\pi$
$758$	18.4682	0.670795
$759$	13.0234	0.472720
$760$	−13.1306	−0.476297
$761$	51.1699	1.85491	0.927454	−	0.373937i	$-0.121992\pi$
$761$	51.1699	1.85491	0.927454	+	0.373937i	$0.121992\pi$
$762$	4.91970	0.178222
$763$	0.646636	0.0234098
$764$	9.78825	0.354127
$765$	−32.9604	−1.19169
$766$	−1.59606	−0.0576679
$767$	28.4646	1.02780
$768$	−0.679472	−0.0245183
$769$	−4.79077	−0.172760	−0.0863798	−	0.996262i	$-0.527530\pi$
$769$	−4.79077	−0.172760	−0.0863798	+	0.996262i	$0.527530\pi$
$770$	5.94832	0.214363
$771$	−10.2723	−0.369948
$772$	−9.75313	−0.351023
$773$	7.96327	0.286419	0.143210	−	0.989692i	$-0.454258\pi$
$773$	7.96327	0.286419	0.143210	+	0.989692i	$0.454258\pi$
$774$	25.4180	0.913632
$775$	1.97384	0.0709025
$776$	−6.69656	−0.240393
$777$	6.52357	0.234032
$778$	−11.4075	−0.408977
$779$	−37.8766	−1.35707
$780$	−6.67808	−0.239114
$781$	30.1630	1.07932
$782$	−41.8413	−1.49624
$783$	−25.1526	−0.898880
$784$	1.00000	0.0357143
$785$	−31.1117	−1.11042
$786$	−14.7458	−0.525964
$787$	−33.6381	−1.19907	−0.599535	−	0.800349i	$-0.704648\pi$
$787$	−33.6381	−1.19907	−0.599535	+	0.800349i	$0.704648\pi$
$788$	16.0227	0.570785
$789$	−3.48795	−0.124174
$790$	−25.9739	−0.924110
$791$	−0.291308	−0.0103577
$792$	6.89233	0.244908
$793$	−44.4080	−1.57698
$794$	0.595360	0.0211285
$795$	4.10000	0.145412
$796$	2.22908	0.0790078
$797$	−9.48729	−0.336057	−0.168029	−	0.985782i	$-0.553740\pi$
$797$	−9.48729	−0.336057	−0.168029	+	0.985782i	$0.553740\pi$
$798$	−4.07270	−0.144172
$799$	−16.0632	−0.568275
$800$	0.201031	0.00710753
$801$	−14.1498	−0.499958
$802$	−27.5055	−0.971253
$803$	−35.6302	−1.25736
$804$	−4.05091	−0.142865
$805$	15.4635	0.545015
$806$	−44.0509	−1.55163
$807$	−0.225105	−0.00792406
$808$	−1.49436	−0.0525715
$809$	15.7399	0.553387	0.276693	−	0.960958i	$-0.410761\pi$
$809$	15.7399	0.553387	0.276693	+	0.960958i	$0.410761\pi$
$810$	11.0804	0.389324
$811$	26.7880	0.940653	0.470326	−	0.882492i	$-0.344136\pi$
$811$	26.7880	0.940653	0.470326	+	0.882492i	$0.344136\pi$
$812$	−6.68395	−0.234561
$813$	3.37839	0.118485
$814$	26.0696	0.913738
$815$	23.0152	0.806189
$816$	4.02758	0.140993
$817$	−60.0214	−2.09988
$818$	−17.7786	−0.621613
$819$	11.3881	0.397933
$820$	−13.8431	−0.483423
$821$	−2.36996	−0.0827123	−0.0413561	−	0.999144i	$-0.513168\pi$
$821$	−2.36996	−0.0827123	−0.0413561	+	0.999144i	$0.513168\pi$
$822$	−9.88883	−0.344912
$823$	37.6663	1.31297	0.656483	−	0.754341i	$-0.272043\pi$
$823$	37.6663	1.31297	0.656483	+	0.754341i	$0.272043\pi$
$824$	18.8377	0.656242
$825$	0.370899	0.0129130
$826$	6.34452	0.220754
$827$	11.5307	0.400963	0.200482	−	0.979697i	$-0.435749\pi$
$827$	11.5307	0.400963	0.200482	+	0.979697i	$0.435749\pi$
$828$	17.9175	0.622678
$829$	33.8885	1.17700	0.588498	−	0.808499i	$-0.299719\pi$
$829$	33.8885	1.17700	0.588498	+	0.808499i	$0.299719\pi$
$830$	−35.3080	−1.22556
$831$	11.7307	0.406933
$832$	−4.48649	−0.155541
$833$	−5.92751	−0.205376
$834$	−1.51752	−0.0525474
$835$	−36.5703	−1.26557
$836$	−16.2754	−0.562895
$837$	−36.9486	−1.27713
$838$	11.1387	0.384782
$839$	−49.7828	−1.71869	−0.859347	−	0.511392i	$-0.829130\pi$
$839$	−49.7828	−1.71869	−0.859347	+	0.511392i	$0.829130\pi$
$840$	−1.48849	−0.0513577
$841$	15.6752	0.540523
$842$	1.85644	0.0639771
$843$	0.425098	0.0146412
$844$	−1.42265	−0.0489698
$845$	−15.6162	−0.537214
$846$	6.87869	0.236494
$847$	−3.62706	−0.124627
$848$	2.75447	0.0945889
$849$	8.90381	0.305578
$850$	−1.19162	−0.0408721
$851$	67.7714	2.32317
$852$	−7.54789	−0.258587
$853$	−15.3657	−0.526113	−0.263056	−	0.964780i	$-0.584731\pi$
$853$	−15.3657	−0.526113	−0.263056	+	0.964780i	$0.584731\pi$
$854$	−9.89818	−0.338709
$855$	−33.3296	−1.13985
$856$	6.35888	0.217342
$857$	−35.6836	−1.21893	−0.609465	−	0.792813i	$-0.708616\pi$
$857$	−35.6836	−1.21893	−0.609465	+	0.792813i	$0.708616\pi$
$858$	−8.27748	−0.282589
$859$	52.4399	1.78923	0.894614	−	0.446840i	$-0.147451\pi$
$859$	52.4399	1.78923	0.894614	+	0.446840i	$0.147451\pi$
$860$	−21.9366	−0.748033
$861$	−4.29370	−0.146329
$862$	1.00000	0.0340601
$863$	−30.6153	−1.04216	−0.521079	−	0.853509i	$-0.674470\pi$
$863$	−30.6153	−1.04216	−0.521079	+	0.853509i	$0.674470\pi$
$864$	−3.76313	−0.128024
$865$	−1.92588	−0.0654817
$866$	29.7915	1.01236
$867$	−12.3225	−0.418494
$868$	−9.81858	−0.333264
$869$	−32.1946	−1.09213
$870$	9.94898	0.337302
$871$	−26.7478	−0.906313
$872$	−0.646636	−0.0218979
$873$	−16.9980	−0.575295
$874$	−42.3100	−1.43116
$875$	11.3937	0.385176
$876$	8.91598	0.301243
$877$	−49.8301	−1.68264	−0.841321	−	0.540536i	$-0.818221\pi$
$877$	−49.8301	−1.68264	−0.841321	+	0.540536i	$0.818221\pi$
$878$	−27.3122	−0.921742
$879$	−9.53347	−0.321556
$880$	−5.94832	−0.200518
$881$	38.1566	1.28553	0.642765	−	0.766064i	$-0.277787\pi$
$881$	38.1566	1.28553	0.642765	+	0.766064i	$0.277787\pi$
$882$	2.53832	0.0854696
$883$	0.745753	0.0250966	0.0125483	−	0.999921i	$-0.496006\pi$
$883$	0.745753	0.0250966	0.0125483	+	0.999921i	$0.496006\pi$
$884$	26.5937	0.894443
$885$	−9.44375	−0.317448
$886$	40.5681	1.36291
$887$	13.2023	0.443291	0.221646	−	0.975127i	$-0.428857\pi$
$887$	13.2023	0.443291	0.221646	+	0.975127i	$0.428857\pi$
$888$	−6.52357	−0.218917
$889$	7.24048	0.242838
$890$	12.2118	0.409339
$891$	13.7341	0.460109
$892$	6.37638	0.213497
$893$	−16.2432	−0.543557
$894$	1.11948	0.0374410
$895$	−29.7025	−0.992846
$896$	−1.00000	−0.0334077
$897$	−21.5184	−0.718479
$898$	−11.4949	−0.383590
$899$	65.6269	2.18878
$900$	0.510281	0.0170094
$901$	−16.3271	−0.543936
$902$	−17.1586	−0.571317
$903$	−6.80405	−0.226425
$904$	0.291308	0.00968875
$905$	42.6869	1.41896
$906$	−10.0770	−0.334786
$907$	6.21787	0.206461	0.103230	−	0.994657i	$-0.467082\pi$
$907$	6.21787	0.206461	0.103230	+	0.994657i	$0.467082\pi$
$908$	−27.0438	−0.897480
$909$	−3.79316	−0.125811
$910$	−9.82834	−0.325806
$911$	9.82573	0.325541	0.162770	−	0.986664i	$-0.447957\pi$
$911$	9.82573	0.325541	0.162770	+	0.986664i	$0.447957\pi$
$912$	4.07270	0.134861
$913$	−43.7643	−1.44839
$914$	14.4229	0.477068
$915$	14.7333	0.487069
$916$	17.8018	0.588189
$917$	−21.7018	−0.716657
$918$	22.3060	0.736208
$919$	−13.8723	−0.457606	−0.228803	−	0.973473i	$-0.573481\pi$
$919$	−13.8723	−0.457606	−0.228803	+	0.973473i	$0.573481\pi$
$920$	−15.4635	−0.509815
$921$	11.1673	0.367976
$922$	28.4124	0.935711
$923$	−49.8380	−1.64044
$924$	−1.84498	−0.0606954
$925$	1.93009	0.0634610
$926$	1.30246	0.0428014
$927$	47.8161	1.57049
$928$	6.68395	0.219411
$929$	−56.2826	−1.84657	−0.923286	−	0.384114i	$-0.874507\pi$
$929$	−56.2826	−1.84657	−0.923286	+	0.384114i	$0.874507\pi$
$930$	14.6148	0.479240
$931$	−5.99392	−0.196443
$932$	−3.54534	−0.116131
$933$	23.0306	0.753989
$934$	16.4985	0.539847
$935$	35.2587	1.15308
$936$	−11.3881	−0.372233
$937$	55.5421	1.81448	0.907240	−	0.420613i	$-0.138185\pi$
$937$	55.5421	1.81448	0.907240	+	0.420613i	$0.138185\pi$
$938$	−5.96185	−0.194661
$939$	18.0481	0.588979
$940$	−5.93655	−0.193629
$941$	10.3795	0.338361	0.169180	−	0.985585i	$-0.445888\pi$
$941$	10.3795	0.338361	0.169180	+	0.985585i	$0.445888\pi$
$942$	9.64987	0.314410
$943$	−44.6060	−1.45257
$944$	−6.34452	−0.206496
$945$	−8.24372	−0.268168
$946$	−27.1904	−0.884037
$947$	−0.992120	−0.0322396	−0.0161198	−	0.999870i	$-0.505131\pi$
$947$	−0.992120	−0.0322396	−0.0161198	+	0.999870i	$0.505131\pi$
$948$	8.05629	0.261656
$949$	58.8713	1.91104
$950$	−1.20496	−0.0390942
$951$	1.08971	0.0353363
$952$	5.92751	0.192112
$953$	−45.6025	−1.47721	−0.738605	−	0.674139i	$-0.764515\pi$
$953$	−45.6025	−1.47721	−0.738605	+	0.674139i	$0.764515\pi$
$954$	6.99172	0.226365
$955$	−21.4427	−0.693869
$956$	30.5676	0.988625
$957$	12.3318	0.398629
$958$	−7.30310	−0.235953
$959$	−14.5537	−0.469963
$960$	1.48849	0.0480408
$961$	65.4045	2.10982
$962$	−43.0745	−1.38878
$963$	16.1409	0.520132
$964$	−11.1391	−0.358765
$965$	21.3657	0.687788
$966$	−4.79628	−0.154318
$967$	−31.7156	−1.01990	−0.509952	−	0.860203i	$-0.670337\pi$
$967$	−31.7156	−1.01990	−0.509952	+	0.860203i	$0.670337\pi$
$968$	3.62706	0.116578
$969$	−24.1410	−0.775520
$970$	14.6699	0.471021
$971$	33.0664	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$971$	33.0664	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$972$	−14.7262	−0.472342
$973$	−2.23338	−0.0715989
$974$	10.9237	0.350018
$975$	−0.612832	−0.0196263
$976$	9.89818	0.316833
$977$	26.3651	0.843494	0.421747	−	0.906713i	$-0.361417\pi$
$977$	26.3651	0.843494	0.421747	+	0.906713i	$0.361417\pi$
$978$	−7.13860	−0.228267
$979$	15.1365	0.483763
$980$	−2.19065	−0.0699779
$981$	−1.64137	−0.0524048
$982$	7.14218	0.227916
$983$	47.5224	1.51573	0.757864	−	0.652413i	$-0.226243\pi$
$983$	47.5224	1.51573	0.757864	+	0.652413i	$0.226243\pi$
$984$	4.29370	0.136878
$985$	−35.1002	−1.11839
$986$	−39.6192	−1.26173
$987$	−1.84133	−0.0586102
$988$	26.8916	0.855536
$989$	−70.6852	−2.24766
$990$	−15.0987	−0.479869
$991$	0.880115	0.0279578	0.0139789	−	0.999902i	$-0.495550\pi$
$991$	0.880115	0.0279578	0.0139789	+	0.999902i	$0.495550\pi$
$992$	9.81858	0.311740
$993$	−13.4128	−0.425643
$994$	−11.1085	−0.352339
$995$	−4.88315	−0.154806
$996$	10.9514	0.347009
$997$	−24.3181	−0.770162	−0.385081	−	0.922883i	$-0.625827\pi$
$997$	−24.3181	−0.770162	−0.385081	+	0.922883i	$0.625827\pi$
$998$	22.7232	0.719291
$999$	−36.1296	−1.14309

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.10	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.10	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.679472 q^{3} +1.00000 q^{4} -2.19065 q^{5} +0.679472 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.53832 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.679472 q^{3} +1.00000 q^{4} -2.19065 q^{5} +0.679472 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.53832 q^{9} +2.19065 q^{10} +2.71532 q^{11} -0.679472 q^{12} -4.48649 q^{13} -1.00000 q^{14} +1.48849 q^{15} +1.00000 q^{16} -5.92751 q^{17} +2.53832 q^{18} -5.99392 q^{19} -2.19065 q^{20} -0.679472 q^{21} -2.71532 q^{22} -7.05883 q^{23} +0.679472 q^{24} -0.201031 q^{25} +4.48649 q^{26} +3.76313 q^{27} +1.00000 q^{28} -6.68395 q^{29} -1.48849 q^{30} -9.81858 q^{31} -1.00000 q^{32} -1.84498 q^{33} +5.92751 q^{34} -2.19065 q^{35} -2.53832 q^{36} -9.60094 q^{37} +5.99392 q^{38} +3.04844 q^{39} +2.19065 q^{40} +6.31918 q^{41} +0.679472 q^{42} +10.0137 q^{43} +2.71532 q^{44} +5.56058 q^{45} +7.05883 q^{46} +2.70994 q^{47} -0.679472 q^{48} +1.00000 q^{49} +0.201031 q^{50} +4.02758 q^{51} -4.48649 q^{52} +2.75447 q^{53} -3.76313 q^{54} -5.94832 q^{55} -1.00000 q^{56} +4.07270 q^{57} +6.68395 q^{58} -6.34452 q^{59} +1.48849 q^{60} +9.89818 q^{61} +9.81858 q^{62} -2.53832 q^{63} +1.00000 q^{64} +9.82834 q^{65} +1.84498 q^{66} +5.96185 q^{67} -5.92751 q^{68} +4.79628 q^{69} +2.19065 q^{70} +11.1085 q^{71} +2.53832 q^{72} -13.1219 q^{73} +9.60094 q^{74} +0.136595 q^{75} -5.99392 q^{76} +2.71532 q^{77} -3.04844 q^{78} -11.8567 q^{79} -2.19065 q^{80} +5.05801 q^{81} -6.31918 q^{82} -16.1176 q^{83} -0.679472 q^{84} +12.9851 q^{85} -10.0137 q^{86} +4.54156 q^{87} -2.71532 q^{88} +5.57448 q^{89} -5.56058 q^{90} -4.48649 q^{91} -7.05883 q^{92} +6.67145 q^{93} -2.70994 q^{94} +13.1306 q^{95} +0.679472 q^{96} +6.69656 q^{97} -1.00000 q^{98} -6.89233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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