LMFDB - Embedded newform 6014.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.71746 q^{3} +1.00000 q^{4} -1.04814 q^{5} +1.71746 q^{6} +0.0655046 q^{7} -1.00000 q^{8} -0.0503220 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.71746 q^{3} +1.00000 q^{4} -1.04814 q^{5} +1.71746 q^{6} +0.0655046 q^{7} -1.00000 q^{8} -0.0503220 q^{9} +1.04814 q^{10} +4.27038 q^{11} -1.71746 q^{12} -6.72429 q^{13} -0.0655046 q^{14} +1.80014 q^{15} +1.00000 q^{16} +2.76604 q^{17} +0.0503220 q^{18} -6.40806 q^{19} -1.04814 q^{20} -0.112502 q^{21} -4.27038 q^{22} +2.26983 q^{23} +1.71746 q^{24} -3.90140 q^{25} +6.72429 q^{26} +5.23881 q^{27} +0.0655046 q^{28} -7.79205 q^{29} -1.80014 q^{30} +1.00000 q^{31} -1.00000 q^{32} -7.33422 q^{33} -2.76604 q^{34} -0.0686581 q^{35} -0.0503220 q^{36} -9.59673 q^{37} +6.40806 q^{38} +11.5487 q^{39} +1.04814 q^{40} +7.28706 q^{41} +0.112502 q^{42} +5.53633 q^{43} +4.27038 q^{44} +0.0527446 q^{45} -2.26983 q^{46} +4.91622 q^{47} -1.71746 q^{48} -6.99571 q^{49} +3.90140 q^{50} -4.75057 q^{51} -6.72429 q^{52} -4.08882 q^{53} -5.23881 q^{54} -4.47597 q^{55} -0.0655046 q^{56} +11.0056 q^{57} +7.79205 q^{58} +2.36749 q^{59} +1.80014 q^{60} -6.56713 q^{61} -1.00000 q^{62} -0.00329633 q^{63} +1.00000 q^{64} +7.04801 q^{65} +7.33422 q^{66} -6.50724 q^{67} +2.76604 q^{68} -3.89834 q^{69} +0.0686581 q^{70} +13.9515 q^{71} +0.0503220 q^{72} -0.131825 q^{73} +9.59673 q^{74} +6.70051 q^{75} -6.40806 q^{76} +0.279730 q^{77} -11.5487 q^{78} +2.29366 q^{79} -1.04814 q^{80} -8.84650 q^{81} -7.28706 q^{82} -15.3117 q^{83} -0.112502 q^{84} -2.89920 q^{85} -5.53633 q^{86} +13.3826 q^{87} -4.27038 q^{88} +3.01300 q^{89} -0.0527446 q^{90} -0.440472 q^{91} +2.26983 q^{92} -1.71746 q^{93} -4.91622 q^{94} +6.71655 q^{95} +1.71746 q^{96} -1.00000 q^{97} +6.99571 q^{98} -0.214894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) $ 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * 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
$3$	−1.71746	−0.991578	−0.495789	−	0.868443i	$-0.665121\pi$
$3$	−1.71746	−0.991578	−0.495789	+	0.868443i	$0.665121\pi$
$4$	1.00000	0.500000
$5$	−1.04814	−0.468743	−0.234372	−	0.972147i	$-0.575303\pi$
$5$	−1.04814	−0.468743	−0.234372	+	0.972147i	$0.575303\pi$
$6$	1.71746	0.701151
$7$	0.0655046	0.0247584	0.0123792	−	0.999923i	$-0.496059\pi$
$7$	0.0655046	0.0247584	0.0123792	+	0.999923i	$0.496059\pi$
$8$	−1.00000	−0.353553
$9$	−0.0503220	−0.0167740
$10$	1.04814	0.331451
$11$	4.27038	1.28757	0.643784	−	0.765207i	$-0.277363\pi$
$11$	4.27038	1.28757	0.643784	+	0.765207i	$0.277363\pi$
$12$	−1.71746	−0.495789
$13$	−6.72429	−1.86498	−0.932492	−	0.361191i	$-0.882370\pi$
$13$	−6.72429	−1.86498	−0.932492	+	0.361191i	$0.882370\pi$
$14$	−0.0655046	−0.0175068
$15$	1.80014	0.464795
$16$	1.00000	0.250000
$17$	2.76604	0.670863	0.335432	−	0.942065i	$-0.391118\pi$
$17$	2.76604	0.670863	0.335432	+	0.942065i	$0.391118\pi$
$18$	0.0503220	0.0118610
$19$	−6.40806	−1.47011	−0.735055	−	0.678008i	$-0.762844\pi$
$19$	−6.40806	−1.47011	−0.735055	+	0.678008i	$0.762844\pi$
$20$	−1.04814	−0.234372
$21$	−0.112502	−0.0245499
$22$	−4.27038	−0.910449
$23$	2.26983	0.473291	0.236646	−	0.971596i	$-0.423952\pi$
$23$	2.26983	0.473291	0.236646	+	0.971596i	$0.423952\pi$
$24$	1.71746	0.350576
$25$	−3.90140	−0.780280
$26$	6.72429	1.31874
$27$	5.23881	1.00821
$28$	0.0655046	0.0123792
$29$	−7.79205	−1.44695	−0.723474	−	0.690352i	$-0.757456\pi$
$29$	−7.79205	−1.44695	−0.723474	+	0.690352i	$0.757456\pi$
$30$	−1.80014	−0.328660
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−7.33422	−1.27672
$34$	−2.76604	−0.474372
$35$	−0.0686581	−0.0116053
$36$	−0.0503220	−0.00838701
$37$	−9.59673	−1.57769	−0.788847	−	0.614590i	$-0.789321\pi$
$37$	−9.59673	−1.57769	−0.788847	+	0.614590i	$0.789321\pi$
$38$	6.40806	1.03952
$39$	11.5487	1.84928
$40$	1.04814	0.165726
$41$	7.28706	1.13805	0.569024	−	0.822321i	$-0.307321\pi$
$41$	7.28706	1.13805	0.569024	+	0.822321i	$0.307321\pi$
$42$	0.112502	0.0173594
$43$	5.53633	0.844283	0.422141	−	0.906530i	$-0.361279\pi$
$43$	5.53633	0.844283	0.422141	+	0.906530i	$0.361279\pi$
$44$	4.27038	0.643784
$45$	0.0527446	0.00786270
$46$	−2.26983	−0.334668
$47$	4.91622	0.717104	0.358552	−	0.933510i	$-0.383270\pi$
$47$	4.91622	0.717104	0.358552	+	0.933510i	$0.383270\pi$
$48$	−1.71746	−0.247894
$49$	−6.99571	−0.999387
$50$	3.90140	0.551741
$51$	−4.75057	−0.665213
$52$	−6.72429	−0.932492
$53$	−4.08882	−0.561642	−0.280821	−	0.959760i	$-0.590607\pi$
$53$	−4.08882	−0.561642	−0.280821	+	0.959760i	$0.590607\pi$
$54$	−5.23881	−0.712912
$55$	−4.47597	−0.603539
$56$	−0.0655046	−0.00875342
$57$	11.0056	1.45773
$58$	7.79205	1.02315
$59$	2.36749	0.308220	0.154110	−	0.988054i	$-0.450749\pi$
$59$	2.36749	0.308220	0.154110	+	0.988054i	$0.450749\pi$
$60$	1.80014	0.232398
$61$	−6.56713	−0.840835	−0.420418	−	0.907331i	$-0.638116\pi$
$61$	−6.56713	−0.840835	−0.420418	+	0.907331i	$0.638116\pi$
$62$	−1.00000	−0.127000
$63$	−0.00329633	−0.000415298 0
$64$	1.00000	0.125000
$65$	7.04801	0.874198
$66$	7.33422	0.902780
$67$	−6.50724	−0.794986	−0.397493	−	0.917605i	$-0.630120\pi$
$67$	−6.50724	−0.794986	−0.397493	+	0.917605i	$0.630120\pi$
$68$	2.76604	0.335432
$69$	−3.89834	−0.469305
$70$	0.0686581	0.00820621
$71$	13.9515	1.65574	0.827872	−	0.560917i	$-0.189551\pi$
$71$	13.9515	1.65574	0.827872	+	0.560917i	$0.189551\pi$
$72$	0.0503220	0.00593051
$73$	−0.131825	−0.0154290	−0.00771449	−	0.999970i	$-0.502456\pi$
$73$	−0.131825	−0.0154290	−0.00771449	+	0.999970i	$0.502456\pi$
$74$	9.59673	1.11560
$75$	6.70051	0.773708
$76$	−6.40806	−0.735055
$77$	0.279730	0.0318782
$78$	−11.5487	−1.30764
$79$	2.29366	0.258057	0.129029	−	0.991641i	$-0.458814\pi$
$79$	2.29366	0.258057	0.129029	+	0.991641i	$0.458814\pi$
$80$	−1.04814	−0.117186
$81$	−8.84650	−0.982945
$82$	−7.28706	−0.804722
$83$	−15.3117	−1.68068	−0.840340	−	0.542060i	$-0.817644\pi$
$83$	−15.3117	−1.68068	−0.840340	+	0.542060i	$0.817644\pi$
$84$	−0.112502	−0.0122749
$85$	−2.89920	−0.314463
$86$	−5.53633	−0.596998
$87$	13.3826	1.43476
$88$	−4.27038	−0.455224
$89$	3.01300	0.319377	0.159689	−	0.987167i	$-0.448951\pi$
$89$	3.01300	0.319377	0.159689	+	0.987167i	$0.448951\pi$
$90$	−0.0527446	−0.00555977
$91$	−0.440472	−0.0461740
$92$	2.26983	0.236646
$93$	−1.71746	−0.178093
$94$	−4.91622	−0.507069
$95$	6.71655	0.689104
$96$	1.71746	0.175288
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	6.99571	0.706673
$99$	−0.214894	−0.0215977
$100$	−3.90140	−0.390140
$101$	−7.71289	−0.767461	−0.383731	−	0.923445i	$-0.625361\pi$
$101$	−7.71289	−0.767461	−0.383731	+	0.923445i	$0.625361\pi$
$102$	4.75057	0.470377
$103$	13.8985	1.36946	0.684731	−	0.728796i	$-0.259920\pi$
$103$	13.8985	1.36946	0.684731	+	0.728796i	$0.259920\pi$
$104$	6.72429	0.659371
$105$	0.117918	0.0115076
$106$	4.08882	0.397141
$107$	−11.9126	−1.15164	−0.575819	−	0.817577i	$-0.695317\pi$
$107$	−11.9126	−1.15164	−0.575819	+	0.817577i	$0.695317\pi$
$108$	5.23881	0.504105
$109$	−2.80160	−0.268345	−0.134172	−	0.990958i	$-0.542838\pi$
$109$	−2.80160	−0.268345	−0.134172	+	0.990958i	$0.542838\pi$
$110$	4.47597	0.426767
$111$	16.4820	1.56441
$112$	0.0655046	0.00618960
$113$	−10.6947	−1.00608	−0.503039	−	0.864264i	$-0.667785\pi$
$113$	−10.6947	−1.00608	−0.503039	+	0.864264i	$0.667785\pi$
$114$	−11.0056	−1.03077
$115$	−2.37910	−0.221852
$116$	−7.79205	−0.723474
$117$	0.338380	0.0312833
$118$	−2.36749	−0.217945
$119$	0.181188	0.0166095
$120$	−1.80014	−0.164330
$121$	7.23617	0.657833
$122$	6.56713	0.594560
$123$	−12.5153	−1.12846
$124$	1.00000	0.0898027
$125$	9.32993	0.834494
$126$	0.00329633	0.000293660 0
$127$	2.72548	0.241847	0.120923	−	0.992662i	$-0.461414\pi$
$127$	2.72548	0.241847	0.120923	+	0.992662i	$0.461414\pi$
$128$	−1.00000	−0.0883883
$129$	−9.50844	−0.837172
$130$	−7.04801	−0.618152
$131$	0.970001	0.0847494	0.0423747	−	0.999102i	$-0.486508\pi$
$131$	0.970001	0.0847494	0.0423747	+	0.999102i	$0.486508\pi$
$132$	−7.33422	−0.638362
$133$	−0.419757	−0.0363976
$134$	6.50724	0.562140
$135$	−5.49102	−0.472592
$136$	−2.76604	−0.237186
$137$	3.08939	0.263945	0.131972	−	0.991253i	$-0.457869\pi$
$137$	3.08939	0.263945	0.131972	+	0.991253i	$0.457869\pi$
$138$	3.89834	0.331849
$139$	−6.56870	−0.557150	−0.278575	−	0.960414i	$-0.589862\pi$
$139$	−6.56870	−0.557150	−0.278575	+	0.960414i	$0.589862\pi$
$140$	−0.0686581	−0.00580267
$141$	−8.44343	−0.711065
$142$	−13.9515	−1.17079
$143$	−28.7153	−2.40129
$144$	−0.0503220	−0.00419350
$145$	8.16717	0.678247
$146$	0.131825	0.0109099
$147$	12.0149	0.990970
$148$	−9.59673	−0.788847
$149$	−10.6338	−0.871154	−0.435577	−	0.900151i	$-0.643456\pi$
$149$	−10.6338	−0.871154	−0.435577	+	0.900151i	$0.643456\pi$
$150$	−6.70051	−0.547094
$151$	5.97199	0.485994	0.242997	−	0.970027i	$-0.421869\pi$
$151$	5.97199	0.485994	0.242997	+	0.970027i	$0.421869\pi$
$152$	6.40806	0.519762
$153$	−0.139193	−0.0112531
$154$	−0.279730	−0.0225413
$155$	−1.04814	−0.0841888
$156$	11.5487	0.924638
$157$	2.77937	0.221818	0.110909	−	0.993831i	$-0.464624\pi$
$157$	2.77937	0.221818	0.110909	+	0.993831i	$0.464624\pi$
$158$	−2.29366	−0.182474
$159$	7.02239	0.556912
$160$	1.04814	0.0828629
$161$	0.148684	0.0117179
$162$	8.84650	0.695047
$163$	−4.52860	−0.354707	−0.177354	−	0.984147i	$-0.556754\pi$
$163$	−4.52860	−0.354707	−0.177354	+	0.984147i	$0.556754\pi$
$164$	7.28706	0.569024
$165$	7.68730	0.598456
$166$	15.3117	1.18842
$167$	−24.1836	−1.87138	−0.935690	−	0.352824i	$-0.885221\pi$
$167$	−24.1836	−1.87138	−0.935690	+	0.352824i	$0.885221\pi$
$168$	0.112502	0.00867970
$169$	32.2161	2.47816
$170$	2.89920	0.222359
$171$	0.322467	0.0246596
$172$	5.53633	0.422141
$173$	11.0683	0.841506	0.420753	−	0.907175i	$-0.361766\pi$
$173$	11.0683	0.841506	0.420753	+	0.907175i	$0.361766\pi$
$174$	−13.3826	−1.01453
$175$	−0.255560	−0.0193185
$176$	4.27038	0.321892
$177$	−4.06607	−0.305624
$178$	−3.01300	−0.225834
$179$	−7.01638	−0.524429	−0.262214	−	0.965010i	$-0.584453\pi$
$179$	−7.01638	−0.524429	−0.262214	+	0.965010i	$0.584453\pi$
$180$	0.0527446	0.00393135
$181$	6.98324	0.519060	0.259530	−	0.965735i	$-0.416432\pi$
$181$	6.98324	0.519060	0.259530	+	0.965735i	$0.416432\pi$
$182$	0.440472	0.0326500
$183$	11.2788	0.833753
$184$	−2.26983	−0.167334
$185$	10.0587	0.739533
$186$	1.71746	0.125930
$187$	11.8121	0.863783
$188$	4.91622	0.358552
$189$	0.343166	0.0249617
$190$	−6.71655	−0.487270
$191$	10.3209	0.746797	0.373399	−	0.927671i	$-0.378192\pi$
$191$	10.3209	0.746797	0.373399	+	0.927671i	$0.378192\pi$
$192$	−1.71746	−0.123947
$193$	−3.76122	−0.270739	−0.135369	−	0.990795i	$-0.543222\pi$
$193$	−3.76122	−0.270739	−0.135369	+	0.990795i	$0.543222\pi$
$194$	1.00000	0.0717958
$195$	−12.1047	−0.866836
$196$	−6.99571	−0.499694
$197$	−3.11239	−0.221748	−0.110874	−	0.993834i	$-0.535365\pi$
$197$	−3.11239	−0.221748	−0.110874	+	0.993834i	$0.535365\pi$
$198$	0.214894	0.0152719
$199$	8.71917	0.618086	0.309043	−	0.951048i	$-0.399991\pi$
$199$	8.71917	0.618086	0.309043	+	0.951048i	$0.399991\pi$
$200$	3.90140	0.275871
$201$	11.1759	0.788291
$202$	7.71289	0.542677
$203$	−0.510415	−0.0358241
$204$	−4.75057	−0.332607
$205$	−7.63787	−0.533452
$206$	−13.8985	−0.968355
$207$	−0.114222	−0.00793900
$208$	−6.72429	−0.466246
$209$	−27.3649	−1.89287
$210$	−0.117918	−0.00813710
$211$	−22.1419	−1.52431	−0.762155	−	0.647395i	$-0.775858\pi$
$211$	−22.1419	−1.52431	−0.762155	+	0.647395i	$0.775858\pi$
$212$	−4.08882	−0.280821
$213$	−23.9613	−1.64180
$214$	11.9126	0.814331
$215$	−5.80286	−0.395752
$216$	−5.23881	−0.356456
$217$	0.0655046	0.00444674
$218$	2.80160	0.189748
$219$	0.226405	0.0152990
$220$	−4.47597	−0.301770
$221$	−18.5997	−1.25115
$222$	−16.4820	−1.10620
$223$	−26.5414	−1.77734	−0.888671	−	0.458546i	$-0.848371\pi$
$223$	−26.5414	−1.77734	−0.888671	+	0.458546i	$0.848371\pi$
$224$	−0.0655046	−0.00437671
$225$	0.196326	0.0130884
$226$	10.6947	0.711404
$227$	14.2717	0.947245	0.473623	−	0.880728i	$-0.342946\pi$
$227$	14.2717	0.947245	0.473623	+	0.880728i	$0.342946\pi$
$228$	11.0056	0.728864
$229$	23.8092	1.57336	0.786678	−	0.617364i	$-0.211799\pi$
$229$	23.8092	1.57336	0.786678	+	0.617364i	$0.211799\pi$
$230$	2.37910	0.156873
$231$	−0.480425	−0.0316097
$232$	7.79205	0.511573
$233$	−1.23640	−0.0809994	−0.0404997	−	0.999180i	$-0.512895\pi$
$233$	−1.23640	−0.0809994	−0.0404997	+	0.999180i	$0.512895\pi$
$234$	−0.338380	−0.0221206
$235$	−5.15290	−0.336138
$236$	2.36749	0.154110
$237$	−3.93928	−0.255884
$238$	−0.181188	−0.0117447
$239$	−0.818860	−0.0529676	−0.0264838	−	0.999649i	$-0.508431\pi$
$239$	−0.818860	−0.0529676	−0.0264838	+	0.999649i	$0.508431\pi$
$240$	1.80014	0.116199
$241$	29.1996	1.88091	0.940455	−	0.339917i	$-0.110399\pi$
$241$	29.1996	1.88091	0.940455	+	0.339917i	$0.110399\pi$
$242$	−7.23617	−0.465158
$243$	−0.522906	−0.0335445
$244$	−6.56713	−0.420418
$245$	7.33249	0.468456
$246$	12.5153	0.797944
$247$	43.0897	2.74173
$248$	−1.00000	−0.0635001
$249$	26.2973	1.66652
$250$	−9.32993	−0.590076
$251$	29.3440	1.85218	0.926088	−	0.377308i	$-0.123150\pi$
$251$	29.3440	1.85218	0.926088	+	0.377308i	$0.123150\pi$
$252$	−0.00329633	−0.000207649 0
$253$	9.69302	0.609395
$254$	−2.72548	−0.171012
$255$	4.97927	0.311814
$256$	1.00000	0.0625000
$257$	−5.51970	−0.344310	−0.172155	−	0.985070i	$-0.555073\pi$
$257$	−5.51970	−0.344310	−0.172155	+	0.985070i	$0.555073\pi$
$258$	9.50844	0.591970
$259$	−0.628630	−0.0390612
$260$	7.04801	0.437099
$261$	0.392112	0.0242711
$262$	−0.970001	−0.0599269
$263$	13.5189	0.833610	0.416805	−	0.908996i	$-0.363150\pi$
$263$	13.5189	0.833610	0.416805	+	0.908996i	$0.363150\pi$
$264$	7.33422	0.451390
$265$	4.28566	0.263266
$266$	0.419757	0.0257370
$267$	−5.17471	−0.316687
$268$	−6.50724	−0.397493
$269$	12.6825	0.773265	0.386633	−	0.922234i	$-0.373638\pi$
$269$	12.6825	0.773265	0.386633	+	0.922234i	$0.373638\pi$
$270$	5.49102	0.334173
$271$	−17.1439	−1.04142	−0.520708	−	0.853735i	$-0.674332\pi$
$271$	−17.1439	−1.04142	−0.520708	+	0.853735i	$0.674332\pi$
$272$	2.76604	0.167716
$273$	0.756495	0.0457851
$274$	−3.08939	−0.186637
$275$	−16.6605	−1.00466
$276$	−3.89834	−0.234653
$277$	−18.5653	−1.11548	−0.557739	−	0.830016i	$-0.688331\pi$
$277$	−18.5653	−1.11548	−0.557739	+	0.830016i	$0.688331\pi$
$278$	6.56870	0.393965
$279$	−0.0503220	−0.00301270
$280$	0.0686581	0.00410311
$281$	−23.8248	−1.42127	−0.710634	−	0.703562i	$-0.751592\pi$
$281$	−23.8248	−1.42127	−0.710634	+	0.703562i	$0.751592\pi$
$282$	8.44343	0.502799
$283$	13.4102	0.797155	0.398578	−	0.917135i	$-0.369504\pi$
$283$	13.4102	0.797155	0.398578	+	0.917135i	$0.369504\pi$
$284$	13.9515	0.827872
$285$	−11.5354	−0.683300
$286$	28.7153	1.69797
$287$	0.477336	0.0281763
$288$	0.0503220	0.00296525
$289$	−9.34902	−0.549942
$290$	−8.16717	−0.479593
$291$	1.71746	0.100679
$292$	−0.131825	−0.00771449
$293$	−25.5839	−1.49463	−0.747313	−	0.664472i	$-0.768656\pi$
$293$	−25.5839	−1.49463	−0.747313	+	0.664472i	$0.768656\pi$
$294$	−12.0149	−0.700721
$295$	−2.48146	−0.144476
$296$	9.59673	0.557799
$297$	22.3717	1.29814
$298$	10.6338	0.615999
$299$	−15.2630	−0.882681
$300$	6.70051	0.386854
$301$	0.362655	0.0209031
$302$	−5.97199	−0.343650
$303$	13.2466	0.760997
$304$	−6.40806	−0.367527
$305$	6.88329	0.394136
$306$	0.139193	0.00795712
$307$	13.9207	0.794496	0.397248	−	0.917711i	$-0.369965\pi$
$307$	13.9207	0.794496	0.397248	+	0.917711i	$0.369965\pi$
$308$	0.279730	0.0159391
$309$	−23.8702	−1.35793
$310$	1.04814	0.0595304
$311$	−11.2392	−0.637316	−0.318658	−	0.947870i	$-0.603232\pi$
$311$	−11.2392	−0.637316	−0.318658	+	0.947870i	$0.603232\pi$
$312$	−11.5487	−0.653818
$313$	2.85879	0.161588	0.0807941	−	0.996731i	$-0.474254\pi$
$313$	2.85879	0.161588	0.0807941	+	0.996731i	$0.474254\pi$
$314$	−2.77937	−0.156849
$315$	0.00345502	0.000194668 0
$316$	2.29366	0.129029
$317$	4.49489	0.252458	0.126229	−	0.992001i	$-0.459713\pi$
$317$	4.49489	0.252458	0.126229	+	0.992001i	$0.459713\pi$
$318$	−7.02239	−0.393796
$319$	−33.2750	−1.86304
$320$	−1.04814	−0.0585929
$321$	20.4595	1.14194
$322$	−0.148684	−0.00828584
$323$	−17.7249	−0.986242
$324$	−8.84650	−0.491472
$325$	26.2342	1.45521
$326$	4.52860	0.250816
$327$	4.81165	0.266085
$328$	−7.28706	−0.402361
$329$	0.322035	0.0177544
$330$	−7.68730	−0.423172
$331$	18.7040	1.02807	0.514033	−	0.857771i	$-0.328151\pi$
$331$	18.7040	1.02807	0.514033	+	0.857771i	$0.328151\pi$
$332$	−15.3117	−0.840340
$333$	0.482927	0.0264642
$334$	24.1836	1.32327
$335$	6.82051	0.372644
$336$	−0.112502	−0.00613747
$337$	20.4851	1.11590	0.557948	−	0.829876i	$-0.311589\pi$
$337$	20.4851	1.11590	0.557948	+	0.829876i	$0.311589\pi$
$338$	−32.2161	−1.75233
$339$	18.3678	0.997604
$340$	−2.89920	−0.157231
$341$	4.27038	0.231254
$342$	−0.322467	−0.0174370
$343$	−0.916783	−0.0495017
$344$	−5.53633	−0.298499
$345$	4.08601	0.219984
$346$	−11.0683	−0.595034
$347$	32.2077	1.72900	0.864499	−	0.502635i	$-0.167636\pi$
$347$	32.2077	1.72900	0.864499	+	0.502635i	$0.167636\pi$
$348$	13.3826	0.717380
$349$	−2.84685	−0.152388	−0.0761941	−	0.997093i	$-0.524277\pi$
$349$	−2.84685	−0.152388	−0.0761941	+	0.997093i	$0.524277\pi$
$350$	0.255560	0.0136602
$351$	−35.2273	−1.88030
$352$	−4.27038	−0.227612
$353$	1.95813	0.104221	0.0521103	−	0.998641i	$-0.483405\pi$
$353$	1.95813	0.104221	0.0521103	+	0.998641i	$0.483405\pi$
$354$	4.06607	0.216109
$355$	−14.6232	−0.776119
$356$	3.01300	0.159689
$357$	−0.311184	−0.0164696
$358$	7.01638	0.370827
$359$	30.7013	1.62035	0.810175	−	0.586188i	$-0.199372\pi$
$359$	30.7013	1.62035	0.810175	+	0.586188i	$0.199372\pi$
$360$	−0.0527446	−0.00277989
$361$	22.0632	1.16122
$362$	−6.98324	−0.367031
$363$	−12.4278	−0.652293
$364$	−0.440472	−0.0230870
$365$	0.138172	0.00723223
$366$	−11.2788	−0.589553
$367$	0.461234	0.0240762	0.0120381	−	0.999928i	$-0.496168\pi$
$367$	0.461234	0.0240762	0.0120381	+	0.999928i	$0.496168\pi$
$368$	2.26983	0.118323
$369$	−0.366700	−0.0190896
$370$	−10.0587	−0.522929
$371$	−0.267836	−0.0139054
$372$	−1.71746	−0.0890463
$373$	18.7708	0.971915	0.485958	−	0.873982i	$-0.338471\pi$
$373$	18.7708	0.971915	0.485958	+	0.873982i	$0.338471\pi$
$374$	−11.8121	−0.610787
$375$	−16.0238	−0.827465
$376$	−4.91622	−0.253535
$377$	52.3961	2.69853
$378$	−0.343166	−0.0176506
$379$	7.12034	0.365747	0.182874	−	0.983136i	$-0.441460\pi$
$379$	7.12034	0.365747	0.182874	+	0.983136i	$0.441460\pi$
$380$	6.71655	0.344552
$381$	−4.68090	−0.239810
$382$	−10.3209	−0.528065
$383$	−10.8692	−0.555391	−0.277695	−	0.960669i	$-0.589571\pi$
$383$	−10.8692	−0.555391	−0.277695	+	0.960669i	$0.589571\pi$
$384$	1.71746	0.0876439
$385$	−0.293196	−0.0149427
$386$	3.76122	0.191441
$387$	−0.278599	−0.0141620
$388$	−1.00000	−0.0507673
$389$	−4.43195	−0.224709	−0.112354	−	0.993668i	$-0.535839\pi$
$389$	−4.43195	−0.224709	−0.112354	+	0.993668i	$0.535839\pi$
$390$	12.1047	0.612945
$391$	6.27843	0.317514
$392$	6.99571	0.353337
$393$	−1.66594	−0.0840356
$394$	3.11239	0.156800
$395$	−2.40408	−0.120963
$396$	−0.214894	−0.0107988
$397$	5.04042	0.252972	0.126486	−	0.991968i	$-0.459630\pi$
$397$	5.04042	0.252972	0.126486	+	0.991968i	$0.459630\pi$
$398$	−8.71917	−0.437053
$399$	0.720918	0.0360910
$400$	−3.90140	−0.195070
$401$	30.3774	1.51698	0.758489	−	0.651686i	$-0.225938\pi$
$401$	30.3774	1.51698	0.758489	+	0.651686i	$0.225938\pi$
$402$	−11.1759	−0.557406
$403$	−6.72429	−0.334961
$404$	−7.71289	−0.383731
$405$	9.27239	0.460749
$406$	0.510415	0.0253315
$407$	−40.9817	−2.03139
$408$	4.75057	0.235188
$409$	0.914105	0.0451996	0.0225998	−	0.999745i	$-0.492806\pi$
$409$	0.914105	0.0451996	0.0225998	+	0.999745i	$0.492806\pi$
$410$	7.63787	0.377208
$411$	−5.30592	−0.261722
$412$	13.8985	0.684731
$413$	0.155081	0.00763105
$414$	0.114222	0.00561372
$415$	16.0488	0.787807
$416$	6.72429	0.329686
$417$	11.2815	0.552457
$418$	27.3649	1.33846
$419$	35.3377	1.72636	0.863180	−	0.504897i	$-0.168470\pi$
$419$	35.3377	1.72636	0.863180	+	0.504897i	$0.168470\pi$
$420$	0.117918	0.00575380
$421$	22.0025	1.07234	0.536168	−	0.844111i	$-0.319871\pi$
$421$	22.0025	1.07234	0.536168	+	0.844111i	$0.319871\pi$
$422$	22.1419	1.07785
$423$	−0.247394	−0.0120287
$424$	4.08882	0.198570
$425$	−10.7914	−0.523461
$426$	23.9613	1.16093
$427$	−0.430178	−0.0208177
$428$	−11.9126	−0.575819
$429$	49.3175	2.38107
$430$	5.80286	0.279839
$431$	18.5454	0.893299	0.446649	−	0.894709i	$-0.352617\pi$
$431$	18.5454	0.893299	0.446649	+	0.894709i	$0.352617\pi$
$432$	5.23881	0.252053
$433$	−14.7431	−0.708509	−0.354255	−	0.935149i	$-0.615265\pi$
$433$	−14.7431	−0.708509	−0.354255	+	0.935149i	$0.615265\pi$
$434$	−0.0655046	−0.00314432
$435$	−14.0268	−0.672534
$436$	−2.80160	−0.134172
$437$	−14.5452	−0.695790
$438$	−0.226405	−0.0108180
$439$	10.0529	0.479800	0.239900	−	0.970798i	$-0.422885\pi$
$439$	10.0529	0.479800	0.239900	+	0.970798i	$0.422885\pi$
$440$	4.47597	0.213383
$441$	0.352038	0.0167637
$442$	18.5997	0.884696
$443$	5.82953	0.276970	0.138485	−	0.990365i	$-0.455777\pi$
$443$	5.82953	0.276970	0.138485	+	0.990365i	$0.455777\pi$
$444$	16.4820	0.782203
$445$	−3.15805	−0.149706
$446$	26.5414	1.25677
$447$	18.2631	0.863817
$448$	0.0655046	0.00309480
$449$	11.1519	0.526292	0.263146	−	0.964756i	$-0.415240\pi$
$449$	11.1519	0.526292	0.263146	+	0.964756i	$0.415240\pi$
$450$	−0.196326	−0.00925491
$451$	31.1186	1.46532
$452$	−10.6947	−0.503039
$453$	−10.2567	−0.481901
$454$	−14.2717	−0.669804
$455$	0.461677	0.0216438
$456$	−11.0056	−0.515384
$457$	15.3851	0.719684	0.359842	−	0.933013i	$-0.382831\pi$
$457$	15.3851	0.719684	0.359842	+	0.933013i	$0.382831\pi$
$458$	−23.8092	−1.11253
$459$	14.4908	0.676371
$460$	−2.37910	−0.110926
$461$	28.2554	1.31599	0.657993	−	0.753024i	$-0.271406\pi$
$461$	28.2554	1.31599	0.657993	+	0.753024i	$0.271406\pi$
$462$	0.480425	0.0223514
$463$	−22.7878	−1.05904	−0.529519	−	0.848298i	$-0.677627\pi$
$463$	−22.7878	−1.05904	−0.529519	+	0.848298i	$0.677627\pi$
$464$	−7.79205	−0.361737
$465$	1.80014	0.0834797
$466$	1.23640	0.0572752
$467$	−30.8800	−1.42895	−0.714477	−	0.699659i	$-0.753335\pi$
$467$	−30.8800	−1.42895	−0.714477	+	0.699659i	$0.753335\pi$
$468$	0.338380	0.0156416
$469$	−0.426255	−0.0196826
$470$	5.15290	0.237685
$471$	−4.77347	−0.219950
$472$	−2.36749	−0.108972
$473$	23.6423	1.08707
$474$	3.93928	0.180937
$475$	25.0004	1.14710
$476$	0.181188	0.00830476
$477$	0.205758	0.00942099
$478$	0.818860	0.0374538
$479$	4.30168	0.196549	0.0982744	−	0.995159i	$-0.468668\pi$
$479$	4.30168	0.196549	0.0982744	+	0.995159i	$0.468668\pi$
$480$	−1.80014	−0.0821650
$481$	64.5313	2.94237
$482$	−29.1996	−1.33000
$483$	−0.255359	−0.0116193
$484$	7.23617	0.328917
$485$	1.04814	0.0475937
$486$	0.522906	0.0237195
$487$	7.06998	0.320371	0.160186	−	0.987087i	$-0.448791\pi$
$487$	7.06998	0.320371	0.160186	+	0.987087i	$0.448791\pi$
$488$	6.56713	0.297280
$489$	7.77770	0.351720
$490$	−7.33249	−0.331248
$491$	11.2002	0.505458	0.252729	−	0.967537i	$-0.418672\pi$
$491$	11.2002	0.505458	0.252729	+	0.967537i	$0.418672\pi$
$492$	−12.5153	−0.564232
$493$	−21.5531	−0.970704
$494$	−43.0897	−1.93870
$495$	0.225240	0.0101238
$496$	1.00000	0.0449013
$497$	0.913891	0.0409936
$498$	−26.2973	−1.17841
$499$	11.4082	0.510700	0.255350	−	0.966849i	$-0.417809\pi$
$499$	11.4082	0.510700	0.255350	+	0.966849i	$0.417809\pi$
$500$	9.32993	0.417247
$501$	41.5343	1.85562
$502$	−29.3440	−1.30969
$503$	−1.89063	−0.0842992	−0.0421496	−	0.999111i	$-0.513421\pi$
$503$	−1.89063	−0.0842992	−0.0421496	+	0.999111i	$0.513421\pi$
$504$	0.00329633	0.000146830 0
$505$	8.08420	0.359742
$506$	−9.69302	−0.430907
$507$	−55.3300	−2.45729
$508$	2.72548	0.120923
$509$	6.79733	0.301286	0.150643	−	0.988588i	$-0.451866\pi$
$509$	6.79733	0.301286	0.150643	+	0.988588i	$0.451866\pi$
$510$	−4.97927	−0.220486
$511$	−0.00863516	−0.000381997 0
$512$	−1.00000	−0.0441942
$513$	−33.5706	−1.48218
$514$	5.51970	0.243464
$515$	−14.5676	−0.641926
$516$	−9.50844	−0.418586
$517$	20.9941	0.923321
$518$	0.628630	0.0276204
$519$	−19.0094	−0.834418
$520$	−7.04801	−0.309076
$521$	−11.8742	−0.520220	−0.260110	−	0.965579i	$-0.583759\pi$
$521$	−11.8742	−0.520220	−0.260110	+	0.965579i	$0.583759\pi$
$522$	−0.392112	−0.0171623
$523$	21.2543	0.929386	0.464693	−	0.885472i	$-0.346165\pi$
$523$	21.2543	0.929386	0.464693	+	0.885472i	$0.346165\pi$
$524$	0.970001	0.0423747
$525$	0.438914	0.0191558
$526$	−13.5189	−0.589451
$527$	2.76604	0.120491
$528$	−7.33422	−0.319181
$529$	−17.8479	−0.775995
$530$	−4.28566	−0.186157
$531$	−0.119137	−0.00517009
$532$	−0.419757	−0.0181988
$533$	−49.0004	−2.12244
$534$	5.17471	0.223932
$535$	12.4861	0.539822
$536$	6.50724	0.281070
$537$	12.0504	0.520012
$538$	−12.6825	−0.546781
$539$	−29.8744	−1.28678
$540$	−5.49102	−0.236296
$541$	38.0780	1.63710	0.818550	−	0.574435i	$-0.194778\pi$
$541$	38.0780	1.63710	0.818550	+	0.574435i	$0.194778\pi$
$542$	17.1439	0.736392
$543$	−11.9935	−0.514689
$544$	−2.76604	−0.118593
$545$	2.93648	0.125785
$546$	−0.756495	−0.0323750
$547$	−7.68946	−0.328777	−0.164389	−	0.986396i	$-0.552565\pi$
$547$	−7.68946	−0.328777	−0.164389	+	0.986396i	$0.552565\pi$
$548$	3.08939	0.131972
$549$	0.330472	0.0141042
$550$	16.6605	0.710405
$551$	49.9319	2.12717
$552$	3.89834	0.165924
$553$	0.150245	0.00638909
$554$	18.5653	0.788762
$555$	−17.2755	−0.733304
$556$	−6.56870	−0.278575
$557$	−22.4354	−0.950617	−0.475308	−	0.879819i	$-0.657663\pi$
$557$	−22.4354	−0.950617	−0.475308	+	0.879819i	$0.657663\pi$
$558$	0.0503220	0.00213030
$559$	−37.2279	−1.57457
$560$	−0.0686581	−0.00290133
$561$	−20.2868	−0.856507
$562$	23.8248	1.00499
$563$	−4.60113	−0.193914	−0.0969572	−	0.995289i	$-0.530911\pi$
$563$	−4.60113	−0.193914	−0.0969572	+	0.995289i	$0.530911\pi$
$564$	−8.44343	−0.355532
$565$	11.2096	0.471592
$566$	−13.4102	−0.563674
$567$	−0.579487	−0.0243362
$568$	−13.9515	−0.585394
$569$	20.4688	0.858095	0.429047	−	0.903282i	$-0.358849\pi$
$569$	20.4688	0.858095	0.429047	+	0.903282i	$0.358849\pi$
$570$	11.5354	0.483166
$571$	40.0567	1.67632	0.838160	−	0.545424i	$-0.183631\pi$
$571$	40.0567	1.67632	0.838160	+	0.545424i	$0.183631\pi$
$572$	−28.7153	−1.20065
$573$	−17.7258	−0.740507
$574$	−0.477336	−0.0199236
$575$	−8.85550	−0.369300
$576$	−0.0503220	−0.00209675
$577$	−16.8840	−0.702888	−0.351444	−	0.936209i	$-0.614309\pi$
$577$	−16.8840	−0.702888	−0.351444	+	0.936209i	$0.614309\pi$
$578$	9.34902	0.388868
$579$	6.45976	0.268459
$580$	8.16717	0.339123
$581$	−1.00299	−0.0416110
$582$	−1.71746	−0.0711911
$583$	−17.4608	−0.723153
$584$	0.131825	0.00545497
$585$	−0.354670	−0.0146638
$586$	25.5839	1.05686
$587$	19.3646	0.799261	0.399631	−	0.916676i	$-0.369138\pi$
$587$	19.3646	0.799261	0.399631	+	0.916676i	$0.369138\pi$
$588$	12.0149	0.495485
$589$	−6.40806	−0.264039
$590$	2.48146	0.102160
$591$	5.34541	0.219881
$592$	−9.59673	−0.394423
$593$	−34.8026	−1.42917	−0.714586	−	0.699548i	$-0.753385\pi$
$593$	−34.8026	−1.42917	−0.714586	+	0.699548i	$0.753385\pi$
$594$	−22.3717	−0.917924
$595$	−0.189911	−0.00778560
$596$	−10.6338	−0.435577
$597$	−14.9749	−0.612880
$598$	15.2630	0.624150
$599$	−41.9324	−1.71331	−0.856656	−	0.515888i	$-0.827462\pi$
$599$	−41.9324	−1.71331	−0.856656	+	0.515888i	$0.827462\pi$
$600$	−6.70051	−0.273547
$601$	−34.3467	−1.40103	−0.700516	−	0.713636i	$-0.747047\pi$
$601$	−34.3467	−1.40103	−0.700516	+	0.713636i	$0.747047\pi$
$602$	−0.362655	−0.0147807
$603$	0.327458	0.0133351
$604$	5.97199	0.242997
$605$	−7.58453	−0.308355
$606$	−13.2466	−0.538106
$607$	19.2781	0.782475	0.391237	−	0.920290i	$-0.372047\pi$
$607$	19.2781	0.782475	0.391237	+	0.920290i	$0.372047\pi$
$608$	6.40806	0.259881
$609$	0.876619	0.0355224
$610$	−6.88329	−0.278696
$611$	−33.0581	−1.33739
$612$	−0.139193	−0.00562654
$613$	−31.9618	−1.29093	−0.645463	−	0.763791i	$-0.723336\pi$
$613$	−31.9618	−1.29093	−0.645463	+	0.763791i	$0.723336\pi$
$614$	−13.9207	−0.561793
$615$	13.1178	0.528959
$616$	−0.279730	−0.0112706
$617$	−25.0274	−1.00757	−0.503783	−	0.863830i	$-0.668059\pi$
$617$	−25.0274	−1.00757	−0.503783	+	0.863830i	$0.668059\pi$
$618$	23.8702	0.960199
$619$	8.41225	0.338117	0.169058	−	0.985606i	$-0.445927\pi$
$619$	8.41225	0.338117	0.169058	+	0.985606i	$0.445927\pi$
$620$	−1.04814	−0.0420944
$621$	11.8912	0.477177
$622$	11.2392	0.450650
$623$	0.197365	0.00790727
$624$	11.5487	0.462319
$625$	9.72791	0.389116
$626$	−2.85879	−0.114260
$627$	46.9981	1.87692
$628$	2.77937	0.110909
$629$	−26.5450	−1.05842
$630$	−0.00345502	−0.000137651 0
$631$	−14.6240	−0.582171	−0.291085	−	0.956697i	$-0.594016\pi$
$631$	−14.6240	−0.582171	−0.291085	+	0.956697i	$0.594016\pi$
$632$	−2.29366	−0.0912370
$633$	38.0278	1.51147
$634$	−4.49489	−0.178515
$635$	−2.85668	−0.113364
$636$	7.02239	0.278456
$637$	47.0412	1.86384
$638$	33.2750	1.31737
$639$	−0.702070	−0.0277735
$640$	1.04814	0.0414314
$641$	46.5063	1.83689	0.918443	−	0.395553i	$-0.129447\pi$
$641$	46.5063	1.83689	0.918443	+	0.395553i	$0.129447\pi$
$642$	−20.4595	−0.807472
$643$	5.64455	0.222600	0.111300	−	0.993787i	$-0.464499\pi$
$643$	5.64455	0.222600	0.111300	+	0.993787i	$0.464499\pi$
$644$	0.148684	0.00585897
$645$	9.96619	0.392419
$646$	17.7249	0.697379
$647$	48.0054	1.88729	0.943644	−	0.330961i	$-0.107373\pi$
$647$	48.0054	1.88729	0.943644	+	0.330961i	$0.107373\pi$
$648$	8.84650	0.347523
$649$	10.1101	0.396855
$650$	−26.2342	−1.02899
$651$	−0.112502	−0.00440929
$652$	−4.52860	−0.177354
$653$	41.5444	1.62576	0.812878	−	0.582434i	$-0.197899\pi$
$653$	41.5444	1.62576	0.812878	+	0.582434i	$0.197899\pi$
$654$	−4.81165	−0.188150
$655$	−1.01670	−0.0397257
$656$	7.28706	0.284512
$657$	0.00663372	0.000258806 0
$658$	−0.322035	−0.0125542
$659$	34.1283	1.32945	0.664726	−	0.747088i	$-0.268548\pi$
$659$	34.1283	1.32945	0.664726	+	0.747088i	$0.268548\pi$
$660$	7.68730	0.299228
$661$	15.5430	0.604555	0.302277	−	0.953220i	$-0.402253\pi$
$661$	15.5430	0.604555	0.302277	+	0.953220i	$0.402253\pi$
$662$	−18.7040	−0.726952
$663$	31.9442	1.24061
$664$	15.3117	0.594210
$665$	0.439965	0.0170611
$666$	−0.482927	−0.0187130
$667$	−17.6866	−0.684828
$668$	−24.1836	−0.935690
$669$	45.5838	1.76237
$670$	−6.82051	−0.263499
$671$	−28.0442	−1.08263
$672$	0.112502	0.00433985
$673$	17.3461	0.668643	0.334321	−	0.942459i	$-0.391493\pi$
$673$	17.3461	0.668643	0.334321	+	0.942459i	$0.391493\pi$
$674$	−20.4851	−0.789058
$675$	−20.4387	−0.786686
$676$	32.2161	1.23908
$677$	16.3499	0.628379	0.314189	−	0.949360i	$-0.398267\pi$
$677$	16.3499	0.628379	0.314189	+	0.949360i	$0.398267\pi$
$678$	−18.3678	−0.705412
$679$	−0.0655046	−0.00251384
$680$	2.89920	0.111179
$681$	−24.5111	−0.939267
$682$	−4.27038	−0.163521
$683$	49.6517	1.89987	0.949935	−	0.312447i	$-0.101149\pi$
$683$	49.6517	1.89987	0.949935	+	0.312447i	$0.101149\pi$
$684$	0.322467	0.0123298
$685$	−3.23812	−0.123722
$686$	0.916783	0.0350030
$687$	−40.8914	−1.56010
$688$	5.53633	0.211071
$689$	27.4944	1.04745
$690$	−4.08601	−0.155552
$691$	41.7534	1.58837	0.794187	−	0.607673i	$-0.207897\pi$
$691$	41.7534	1.58837	0.794187	+	0.607673i	$0.207897\pi$
$692$	11.0683	0.420753
$693$	−0.0140766	−0.000534725 0
$694$	−32.2077	−1.22259
$695$	6.88493	0.261160
$696$	−13.3826	−0.507265
$697$	20.1563	0.763475
$698$	2.84685	0.107755
$699$	2.12347	0.0803171
$700$	−0.255560	−0.00965925
$701$	−51.2123	−1.93426	−0.967130	−	0.254281i	$-0.918161\pi$
$701$	−51.2123	−1.93426	−0.967130	+	0.254281i	$0.918161\pi$
$702$	35.2273	1.32957
$703$	61.4964	2.31938
$704$	4.27038	0.160946
$705$	8.84991	0.333307
$706$	−1.95813	−0.0736951
$707$	−0.505230	−0.0190011
$708$	−4.06607	−0.152812
$709$	−17.5539	−0.659251	−0.329625	−	0.944112i	$-0.606922\pi$
$709$	−17.5539	−0.659251	−0.329625	+	0.944112i	$0.606922\pi$
$710$	14.6232	0.548799
$711$	−0.115422	−0.00432866
$712$	−3.01300	−0.112917
$713$	2.26983	0.0850056
$714$	0.311184	0.0116458
$715$	30.0977	1.12559
$716$	−7.01638	−0.262214
$717$	1.40636	0.0525215
$718$	−30.7013	−1.14576
$719$	49.7415	1.85505	0.927523	−	0.373767i	$-0.121934\pi$
$719$	49.7415	1.85505	0.927523	+	0.373767i	$0.121934\pi$
$720$	0.0527446	0.00196568
$721$	0.910417	0.0339057
$722$	−22.0632	−0.821107
$723$	−50.1492	−1.86507
$724$	6.98324	0.259530
$725$	30.3999	1.12902
$726$	12.4278	0.461241
$727$	26.3614	0.977691	0.488845	−	0.872370i	$-0.337418\pi$
$727$	26.3614	0.977691	0.488845	+	0.872370i	$0.337418\pi$
$728$	0.440472	0.0163250
$729$	27.4376	1.01621
$730$	−0.138172	−0.00511396
$731$	15.3137	0.566398
$732$	11.2788	0.416877
$733$	29.5089	1.08993	0.544967	−	0.838457i	$-0.316542\pi$
$733$	29.5089	1.08993	0.544967	+	0.838457i	$0.316542\pi$
$734$	−0.461234	−0.0170245
$735$	−12.5933	−0.464510
$736$	−2.26983	−0.0836669
$737$	−27.7884	−1.02360
$738$	0.366700	0.0134984
$739$	−27.2280	−1.00160	−0.500799	−	0.865564i	$-0.666960\pi$
$739$	−27.2280	−1.00160	−0.500799	+	0.865564i	$0.666960\pi$
$740$	10.0587	0.369766
$741$	−74.0049	−2.71864
$742$	0.267836	0.00983258
$743$	−48.4244	−1.77652	−0.888259	−	0.459342i	$-0.848085\pi$
$743$	−48.4244	−1.77652	−0.888259	+	0.459342i	$0.848085\pi$
$744$	1.71746	0.0629652
$745$	11.1457	0.408348
$746$	−18.7708	−0.687248
$747$	0.770517	0.0281917
$748$	11.8121	0.431891
$749$	−0.780332	−0.0285127
$750$	16.0238	0.585106
$751$	45.8837	1.67432	0.837160	−	0.546958i	$-0.184214\pi$
$751$	45.8837	1.67432	0.837160	+	0.546958i	$0.184214\pi$
$752$	4.91622	0.179276
$753$	−50.3972	−1.83658
$754$	−52.3961	−1.90815
$755$	−6.25950	−0.227806
$756$	0.343166	0.0124808
$757$	−28.7160	−1.04370	−0.521851	−	0.853037i	$-0.674758\pi$
$757$	−28.7160	−1.04370	−0.521851	+	0.853037i	$0.674758\pi$
$758$	−7.12034	−0.258622
$759$	−16.6474	−0.604263
$760$	−6.71655	−0.243635
$761$	−8.92731	−0.323615	−0.161807	−	0.986822i	$-0.551732\pi$
$761$	−8.92731	−0.323615	−0.161807	+	0.986822i	$0.551732\pi$
$762$	4.68090	0.169571
$763$	−0.183518	−0.00664379
$764$	10.3209	0.373399
$765$	0.145894	0.00527480
$766$	10.8692	0.392721
$767$	−15.9197	−0.574826
$768$	−1.71746	−0.0619736
$769$	22.8911	0.825473	0.412736	−	0.910851i	$-0.364573\pi$
$769$	22.8911	0.825473	0.412736	+	0.910851i	$0.364573\pi$
$770$	0.293196	0.0105661
$771$	9.47988	0.341410
$772$	−3.76122	−0.135369
$773$	−17.5847	−0.632479	−0.316239	−	0.948679i	$-0.602420\pi$
$773$	−17.5847	−0.632479	−0.316239	+	0.948679i	$0.602420\pi$
$774$	0.278599	0.0100141
$775$	−3.90140	−0.140142
$776$	1.00000	0.0358979
$777$	1.07965	0.0387322
$778$	4.43195	0.158893
$779$	−46.6959	−1.67306
$780$	−12.1047	−0.433418
$781$	59.5784	2.13188
$782$	−6.27843	−0.224516
$783$	−40.8211	−1.45883
$784$	−6.99571	−0.249847
$785$	−2.91318	−0.103976
$786$	1.66594	0.0594221
$787$	27.7928	0.990705	0.495353	−	0.868692i	$-0.335039\pi$
$787$	27.7928	0.990705	0.495353	+	0.868692i	$0.335039\pi$
$788$	−3.11239	−0.110874
$789$	−23.2182	−0.826589
$790$	2.40408	0.0855334
$791$	−0.700555	−0.0249089
$792$	0.214894	0.00763594
$793$	44.1593	1.56814
$794$	−5.04042	−0.178878
$795$	−7.36046	−0.261049
$796$	8.71917	0.309043
$797$	2.45541	0.0869749	0.0434875	−	0.999054i	$-0.486153\pi$
$797$	2.45541	0.0869749	0.0434875	+	0.999054i	$0.486153\pi$
$798$	−0.720918	−0.0255202
$799$	13.5985	0.481079
$800$	3.90140	0.137935
$801$	−0.151620	−0.00535724
$802$	−30.3774	−1.07266
$803$	−0.562944	−0.0198659
$804$	11.1759	0.394145
$805$	−0.155842	−0.00549271
$806$	6.72429	0.236853
$807$	−21.7817	−0.766753
$808$	7.71289	0.271338
$809$	−20.0289	−0.704178	−0.352089	−	0.935967i	$-0.614528\pi$
$809$	−20.0289	−0.704178	−0.352089	+	0.935967i	$0.614528\pi$
$810$	−9.27239	−0.325798
$811$	4.63896	0.162896	0.0814479	−	0.996678i	$-0.474046\pi$
$811$	4.63896	0.162896	0.0814479	+	0.996678i	$0.474046\pi$
$812$	−0.510415	−0.0179121
$813$	29.4440	1.03264
$814$	40.9817	1.43641
$815$	4.74662	0.166267
$816$	−4.75057	−0.166303
$817$	−35.4771	−1.24119
$818$	−0.914105	−0.0319609
$819$	0.0221655	0.000774524 0
$820$	−7.63787	−0.266726
$821$	12.0840	0.421733	0.210867	−	0.977515i	$-0.432371\pi$
$821$	12.0840	0.421733	0.210867	+	0.977515i	$0.432371\pi$
$822$	5.30592	0.185065
$823$	1.52027	0.0529932	0.0264966	−	0.999649i	$-0.491565\pi$
$823$	1.52027	0.0529932	0.0264966	+	0.999649i	$0.491565\pi$
$824$	−13.8985	−0.484178
$825$	28.6137	0.996202
$826$	−0.155081	−0.00539597
$827$	36.1741	1.25790	0.628949	−	0.777447i	$-0.283486\pi$
$827$	36.1741	1.25790	0.628949	+	0.777447i	$0.283486\pi$
$828$	−0.114222	−0.00396950
$829$	−30.2611	−1.05101	−0.525506	−	0.850790i	$-0.676124\pi$
$829$	−30.2611	−1.05101	−0.525506	+	0.850790i	$0.676124\pi$
$830$	−16.0488	−0.557064
$831$	31.8851	1.10608
$832$	−6.72429	−0.233123
$833$	−19.3504	−0.670452
$834$	−11.2815	−0.390646
$835$	25.3478	0.877196
$836$	−27.3649	−0.946433
$837$	5.23881	0.181080
$838$	−35.3377	−1.22072
$839$	−28.0958	−0.969976	−0.484988	−	0.874521i	$-0.661176\pi$
$839$	−28.0958	−0.969976	−0.484988	+	0.874521i	$0.661176\pi$
$840$	−0.117918	−0.00406855
$841$	31.7161	1.09366
$842$	−22.0025	−0.758256
$843$	40.9182	1.40930
$844$	−22.1419	−0.762155
$845$	−33.7671	−1.16162
$846$	0.247394	0.00850559
$847$	0.474002	0.0162869
$848$	−4.08882	−0.140411
$849$	−23.0316	−0.790441
$850$	10.7914	0.370143
$851$	−21.7829	−0.746709
$852$	−23.9613	−0.820899
$853$	13.5927	0.465406	0.232703	−	0.972548i	$-0.425243\pi$
$853$	13.5927	0.465406	0.232703	+	0.972548i	$0.425243\pi$
$854$	0.430178	0.0147204
$855$	−0.337991	−0.0115590
$856$	11.9126	0.407165
$857$	48.3279	1.65085	0.825424	−	0.564513i	$-0.190936\pi$
$857$	48.3279	1.65085	0.825424	+	0.564513i	$0.190936\pi$
$858$	−49.3175	−1.68367
$859$	−13.1470	−0.448569	−0.224285	−	0.974524i	$-0.572005\pi$
$859$	−13.1470	−0.448569	−0.224285	+	0.974524i	$0.572005\pi$
$860$	−5.80286	−0.197876
$861$	−0.819807	−0.0279390
$862$	−18.5454	−0.631658
$863$	−33.8712	−1.15299	−0.576494	−	0.817101i	$-0.695580\pi$
$863$	−33.8712	−1.15299	−0.576494	+	0.817101i	$0.695580\pi$
$864$	−5.23881	−0.178228
$865$	−11.6011	−0.394450
$866$	14.7431	0.500992
$867$	16.0566	0.545310
$868$	0.0655046	0.00222337
$869$	9.79482	0.332266
$870$	14.0268	0.475554
$871$	43.7566	1.48264
$872$	2.80160	0.0948742
$873$	0.0503220	0.00170314
$874$	14.5452	0.491998
$875$	0.611153	0.0206607
$876$	0.226405	0.00764951
$877$	−48.6254	−1.64196	−0.820982	−	0.570955i	$-0.806573\pi$
$877$	−48.6254	−1.64196	−0.820982	+	0.570955i	$0.806573\pi$
$878$	−10.0529	−0.339270
$879$	43.9394	1.48204
$880$	−4.47597	−0.150885
$881$	20.3800	0.686620	0.343310	−	0.939222i	$-0.388452\pi$
$881$	20.3800	0.686620	0.343310	+	0.939222i	$0.388452\pi$
$882$	−0.352038	−0.0118537
$883$	7.00770	0.235828	0.117914	−	0.993024i	$-0.462379\pi$
$883$	7.00770	0.235828	0.117914	+	0.993024i	$0.462379\pi$
$884$	−18.5997	−0.625575
$885$	4.26182	0.143259
$886$	−5.82953	−0.195847
$887$	−25.1536	−0.844576	−0.422288	−	0.906462i	$-0.638773\pi$
$887$	−25.1536	−0.844576	−0.422288	+	0.906462i	$0.638773\pi$
$888$	−16.4820	−0.553101
$889$	0.178531	0.00598775
$890$	3.15805	0.105858
$891$	−37.7779	−1.26561
$892$	−26.5414	−0.888671
$893$	−31.5034	−1.05422
$894$	−18.2631	−0.610811
$895$	7.35416	0.245822
$896$	−0.0655046	−0.00218836
$897$	26.2136	0.875246
$898$	−11.1519	−0.372145
$899$	−7.79205	−0.259879
$900$	0.196326	0.00654421
$901$	−11.3098	−0.376785
$902$	−31.1186	−1.03613
$903$	−0.622847	−0.0207270
$904$	10.6947	0.355702
$905$	−7.31943	−0.243306
$906$	10.2567	0.340755
$907$	−50.3282	−1.67112	−0.835560	−	0.549400i	$-0.814856\pi$
$907$	−50.3282	−1.67112	−0.835560	+	0.549400i	$0.814856\pi$
$908$	14.2717	0.473623
$909$	0.388128	0.0128734
$910$	−0.461677	−0.0153045
$911$	−32.5848	−1.07958	−0.539791	−	0.841799i	$-0.681497\pi$
$911$	−32.5848	−1.07958	−0.539791	+	0.841799i	$0.681497\pi$
$912$	11.0056	0.364432
$913$	−65.3869	−2.16399
$914$	−15.3851	−0.508894
$915$	−11.8218	−0.390816
$916$	23.8092	0.786678
$917$	0.0635395	0.00209826
$918$	−14.4908	−0.478267
$919$	−51.8620	−1.71077	−0.855384	−	0.517994i	$-0.826679\pi$
$919$	−51.8620	−1.71077	−0.855384	+	0.517994i	$0.826679\pi$
$920$	2.37910	0.0784366
$921$	−23.9083	−0.787804
$922$	−28.2554	−0.930543
$923$	−93.8143	−3.08794
$924$	−0.480425	−0.0158048
$925$	37.4407	1.23104
$926$	22.7878	0.748853
$927$	−0.699402	−0.0229714
$928$	7.79205	0.255787
$929$	42.2645	1.38665	0.693327	−	0.720623i	$-0.256144\pi$
$929$	42.2645	1.38665	0.693327	+	0.720623i	$0.256144\pi$
$930$	−1.80014	−0.0590290
$931$	44.8289	1.46921
$932$	−1.23640	−0.0404997
$933$	19.3029	0.631948
$934$	30.8800	1.01042
$935$	−12.3807	−0.404892
$936$	−0.338380	−0.0110603
$937$	15.3189	0.500448	0.250224	−	0.968188i	$-0.419496\pi$
$937$	15.3189	0.500448	0.250224	+	0.968188i	$0.419496\pi$
$938$	0.426255	0.0139177
$939$	−4.90986	−0.160227
$940$	−5.15290	−0.168069
$941$	19.7515	0.643880	0.321940	−	0.946760i	$-0.395665\pi$
$941$	19.7515	0.643880	0.321940	+	0.946760i	$0.395665\pi$
$942$	4.77347	0.155528
$943$	16.5404	0.538628
$944$	2.36749	0.0770551
$945$	−0.359687	−0.0117006
$946$	−23.6423	−0.768676
$947$	−31.3243	−1.01790	−0.508951	−	0.860795i	$-0.669967\pi$
$947$	−31.3243	−1.01790	−0.508951	+	0.860795i	$0.669967\pi$
$948$	−3.93928	−0.127942
$949$	0.886432	0.0287748
$950$	−25.0004	−0.811120
$951$	−7.71980	−0.250332
$952$	−0.181188	−0.00587235
$953$	−49.3437	−1.59840	−0.799199	−	0.601066i	$-0.794743\pi$
$953$	−49.3437	−1.59840	−0.799199	+	0.601066i	$0.794743\pi$
$954$	−0.205758	−0.00666165
$955$	−10.8178	−0.350056
$956$	−0.818860	−0.0264838
$957$	57.1486	1.84735
$958$	−4.30168	−0.138981
$959$	0.202370	0.00653486
$960$	1.80014	0.0580994
$961$	1.00000	0.0322581
$962$	−64.5313	−2.08057
$963$	0.599468	0.0193176
$964$	29.1996	0.940455
$965$	3.94230	0.126907
$966$	0.255359	0.00821605
$967$	1.48449	0.0477380	0.0238690	−	0.999715i	$-0.492402\pi$
$967$	1.48449	0.0477380	0.0238690	+	0.999715i	$0.492402\pi$
$968$	−7.23617	−0.232579
$969$	30.4419	0.977936
$970$	−1.04814	−0.0336538
$971$	−26.5288	−0.851350	−0.425675	−	0.904876i	$-0.639963\pi$
$971$	−26.5288	−0.851350	−0.425675	+	0.904876i	$0.639963\pi$
$972$	−0.522906	−0.0167722
$973$	−0.430280	−0.0137942
$974$	−7.06998	−0.226537
$975$	−45.0562	−1.44295
$976$	−6.56713	−0.210209
$977$	16.8399	0.538756	0.269378	−	0.963034i	$-0.413182\pi$
$977$	16.8399	0.538756	0.269378	+	0.963034i	$0.413182\pi$
$978$	−7.77770	−0.248704
$979$	12.8667	0.411220
$980$	7.33249	0.234228
$981$	0.140982	0.00450122
$982$	−11.2002	−0.357413
$983$	2.10862	0.0672545	0.0336272	−	0.999434i	$-0.489294\pi$
$983$	2.10862	0.0672545	0.0336272	+	0.999434i	$0.489294\pi$
$984$	12.5153	0.398972
$985$	3.26222	0.103943
$986$	21.5531	0.686391
$987$	−0.553083	−0.0176048
$988$	43.0897	1.37087
$989$	12.5665	0.399592
$990$	−0.225240	−0.00715859
$991$	1.41639	0.0449930	0.0224965	−	0.999747i	$-0.492839\pi$
$991$	1.41639	0.0449930	0.0224965	+	0.999747i	$0.492839\pi$
$992$	−1.00000	−0.0317500
$993$	−32.1234	−1.01941
$994$	−0.913891	−0.0289869
$995$	−9.13893	−0.289723
$996$	26.2973	0.833262
$997$	−24.6531	−0.780773	−0.390386	−	0.920651i	$-0.627659\pi$
$997$	−24.6531	−0.780773	−0.390386	+	0.920651i	$0.627659\pi$
$998$	−11.4082	−0.361120
$999$	−50.2755	−1.59065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.l.1.11	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.l.1.11	✓	38	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.71746 q^{3} +1.00000 q^{4} -1.04814 q^{5} +1.71746 q^{6} +0.0655046 q^{7} -1.00000 q^{8} -0.0503220 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.71746 q^{3} +1.00000 q^{4} -1.04814 q^{5} +1.71746 q^{6} +0.0655046 q^{7} -1.00000 q^{8} -0.0503220 q^{9} +1.04814 q^{10} +4.27038 q^{11} -1.71746 q^{12} -6.72429 q^{13} -0.0655046 q^{14} +1.80014 q^{15} +1.00000 q^{16} +2.76604 q^{17} +0.0503220 q^{18} -6.40806 q^{19} -1.04814 q^{20} -0.112502 q^{21} -4.27038 q^{22} +2.26983 q^{23} +1.71746 q^{24} -3.90140 q^{25} +6.72429 q^{26} +5.23881 q^{27} +0.0655046 q^{28} -7.79205 q^{29} -1.80014 q^{30} +1.00000 q^{31} -1.00000 q^{32} -7.33422 q^{33} -2.76604 q^{34} -0.0686581 q^{35} -0.0503220 q^{36} -9.59673 q^{37} +6.40806 q^{38} +11.5487 q^{39} +1.04814 q^{40} +7.28706 q^{41} +0.112502 q^{42} +5.53633 q^{43} +4.27038 q^{44} +0.0527446 q^{45} -2.26983 q^{46} +4.91622 q^{47} -1.71746 q^{48} -6.99571 q^{49} +3.90140 q^{50} -4.75057 q^{51} -6.72429 q^{52} -4.08882 q^{53} -5.23881 q^{54} -4.47597 q^{55} -0.0655046 q^{56} +11.0056 q^{57} +7.79205 q^{58} +2.36749 q^{59} +1.80014 q^{60} -6.56713 q^{61} -1.00000 q^{62} -0.00329633 q^{63} +1.00000 q^{64} +7.04801 q^{65} +7.33422 q^{66} -6.50724 q^{67} +2.76604 q^{68} -3.89834 q^{69} +0.0686581 q^{70} +13.9515 q^{71} +0.0503220 q^{72} -0.131825 q^{73} +9.59673 q^{74} +6.70051 q^{75} -6.40806 q^{76} +0.279730 q^{77} -11.5487 q^{78} +2.29366 q^{79} -1.04814 q^{80} -8.84650 q^{81} -7.28706 q^{82} -15.3117 q^{83} -0.112502 q^{84} -2.89920 q^{85} -5.53633 q^{86} +13.3826 q^{87} -4.27038 q^{88} +3.01300 q^{89} -0.0527446 q^{90} -0.440472 q^{91} +2.26983 q^{92} -1.71746 q^{93} -4.91622 q^{94} +6.71655 q^{95} +1.71746 q^{96} -1.00000 q^{97} +6.99571 q^{98} -0.214894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9	\( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 38 * q - 38 * q^2 - 2 * q^3 + 38 * q^4 + 2 * q^5 + 2 * q^6 + 3 * q^7 - 38 * q^8 + 54 * q^9 - 2 * q^10 + 6 * q^11 - 2 * q^12 + 12 * q^13 - 3 * q^14 + 19 * q^15 + 38 * q^16 + 16 * q^17 - 54 * q^18 + 37 * q^19 + 2 * q^20 + 8 * q^21 - 6 * q^22 - 12 * q^23 + 2 * q^24 + 66 * q^25 - 12 * q^26 - 5 * q^27 + 3 * q^28 + 3 * q^29 - 19 * q^30 + 38 * q^31 - 38 * q^32 + 12 * q^33 - 16 * q^34 - 16 * q^35 + 54 * q^36 + 5 * q^37 - 37 * q^38 + 36 * q^39 - 2 * q^40 + 7 * q^41 - 8 * q^42 + 7 * q^43 + 6 * q^44 + 45 * q^45 + 12 * q^46 - 10 * q^47 - 2 * q^48 + 111 * q^49 - 66 * q^50 - 13 * q^51 + 12 * q^52 + 5 * q^53 + 5 * q^54 + 56 * q^55 - 3 * q^56 - 5 * q^57 - 3 * q^58 + 14 * q^59 + 19 * q^60 + 54 * q^61 - 38 * q^62 - 3 * q^63 + 38 * q^64 + 8 * q^65 - 12 * q^66 - 9 * q^67 + 16 * q^68 + 45 * q^69 + 16 * q^70 + 13 * q^71 - 54 * q^72 + 65 * q^73 - 5 * q^74 - 14 * q^75 + 37 * q^76 - 22 * q^77 - 36 * q^78 - 11 * q^79 + 2 * q^80 + 46 * q^81 - 7 * q^82 - 42 * q^83 + 8 * q^84 + 18 * q^85 - 7 * q^86 - 19 * q^87 - 6 * q^88 + 74 * q^89 - 45 * q^90 + 14 * q^91 - 12 * q^92 - 2 * q^93 + 10 * q^94 - 10 * q^95 + 2 * q^96 - 38 * q^97 - 111 * q^98 + 15 * q^99

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