LMFDB - Embedded newform 8014.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$91$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.25449 q^{3} +1.00000 q^{4} +0.777840 q^{5} +2.25449 q^{6} +1.47835 q^{7} -1.00000 q^{8} +2.08272 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.25449 q^{3} +1.00000 q^{4} +0.777840 q^{5} +2.25449 q^{6} +1.47835 q^{7} -1.00000 q^{8} +2.08272 q^{9} -0.777840 q^{10} -5.33841 q^{11} -2.25449 q^{12} +4.84063 q^{13} -1.47835 q^{14} -1.75363 q^{15} +1.00000 q^{16} +3.30651 q^{17} -2.08272 q^{18} -5.21391 q^{19} +0.777840 q^{20} -3.33293 q^{21} +5.33841 q^{22} -6.51821 q^{23} +2.25449 q^{24} -4.39497 q^{25} -4.84063 q^{26} +2.06801 q^{27} +1.47835 q^{28} +7.15345 q^{29} +1.75363 q^{30} -8.77657 q^{31} -1.00000 q^{32} +12.0354 q^{33} -3.30651 q^{34} +1.14992 q^{35} +2.08272 q^{36} -0.774253 q^{37} +5.21391 q^{38} -10.9131 q^{39} -0.777840 q^{40} -4.49253 q^{41} +3.33293 q^{42} +6.52052 q^{43} -5.33841 q^{44} +1.62002 q^{45} +6.51821 q^{46} +3.38927 q^{47} -2.25449 q^{48} -4.81447 q^{49} +4.39497 q^{50} -7.45448 q^{51} +4.84063 q^{52} +6.53388 q^{53} -2.06801 q^{54} -4.15243 q^{55} -1.47835 q^{56} +11.7547 q^{57} -7.15345 q^{58} -9.45851 q^{59} -1.75363 q^{60} -7.74630 q^{61} +8.77657 q^{62} +3.07899 q^{63} +1.00000 q^{64} +3.76523 q^{65} -12.0354 q^{66} +7.46740 q^{67} +3.30651 q^{68} +14.6952 q^{69} -1.14992 q^{70} +6.86424 q^{71} -2.08272 q^{72} +0.792125 q^{73} +0.774253 q^{74} +9.90840 q^{75} -5.21391 q^{76} -7.89206 q^{77} +10.9131 q^{78} -14.4377 q^{79} +0.777840 q^{80} -10.9104 q^{81} +4.49253 q^{82} +5.53303 q^{83} -3.33293 q^{84} +2.57193 q^{85} -6.52052 q^{86} -16.1274 q^{87} +5.33841 q^{88} +17.6800 q^{89} -1.62002 q^{90} +7.15616 q^{91} -6.51821 q^{92} +19.7867 q^{93} -3.38927 q^{94} -4.05558 q^{95} +2.25449 q^{96} +14.7843 q^{97} +4.81447 q^{98} -11.1184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) $ 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * 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
$3$	−2.25449	−1.30163	−0.650815	−	0.759237i	$-0.725572\pi$
$3$	−2.25449	−1.30163	−0.650815	+	0.759237i	$0.725572\pi$
$4$	1.00000	0.500000
$5$	0.777840	0.347861	0.173930	−	0.984758i	$-0.444353\pi$
$5$	0.777840	0.347861	0.173930	+	0.984758i	$0.444353\pi$
$6$	2.25449	0.920391
$7$	1.47835	0.558765	0.279383	−	0.960180i	$-0.409870\pi$
$7$	1.47835	0.558765	0.279383	+	0.960180i	$0.409870\pi$
$8$	−1.00000	−0.353553
$9$	2.08272	0.694239
$10$	−0.777840	−0.245975
$11$	−5.33841	−1.60959	−0.804796	−	0.593552i	$-0.797725\pi$
$11$	−5.33841	−1.60959	−0.804796	+	0.593552i	$0.797725\pi$
$12$	−2.25449	−0.650815
$13$	4.84063	1.34255	0.671274	−	0.741209i	$-0.265747\pi$
$13$	4.84063	1.34255	0.671274	+	0.741209i	$0.265747\pi$
$14$	−1.47835	−0.395107
$15$	−1.75363	−0.452785
$16$	1.00000	0.250000
$17$	3.30651	0.801946	0.400973	−	0.916090i	$-0.368672\pi$
$17$	3.30651	0.801946	0.400973	+	0.916090i	$0.368672\pi$
$18$	−2.08272	−0.490901
$19$	−5.21391	−1.19615	−0.598076	−	0.801439i	$-0.704068\pi$
$19$	−5.21391	−1.19615	−0.598076	+	0.801439i	$0.704068\pi$
$20$	0.777840	0.173930
$21$	−3.33293	−0.727305
$22$	5.33841	1.13815
$23$	−6.51821	−1.35914	−0.679570	−	0.733611i	$-0.737834\pi$
$23$	−6.51821	−1.35914	−0.679570	+	0.733611i	$0.737834\pi$
$24$	2.25449	0.460195
$25$	−4.39497	−0.878993
$26$	−4.84063	−0.949325
$27$	2.06801	0.397988
$28$	1.47835	0.279383
$29$	7.15345	1.32836	0.664181	−	0.747572i	$-0.268780\pi$
$29$	7.15345	1.32836	0.664181	+	0.747572i	$0.268780\pi$
$30$	1.75363	0.320168
$31$	−8.77657	−1.57632	−0.788159	−	0.615471i	$-0.788966\pi$
$31$	−8.77657	−1.57632	−0.788159	+	0.615471i	$0.788966\pi$
$32$	−1.00000	−0.176777
$33$	12.0354	2.09509
$34$	−3.30651	−0.567062
$35$	1.14992	0.194372
$36$	2.08272	0.347119
$37$	−0.774253	−0.127286	−0.0636432	−	0.997973i	$-0.520272\pi$
$37$	−0.774253	−0.127286	−0.0636432	+	0.997973i	$0.520272\pi$
$38$	5.21391	0.845807
$39$	−10.9131	−1.74750
$40$	−0.777840	−0.122987
$41$	−4.49253	−0.701615	−0.350807	−	0.936448i	$-0.614093\pi$
$41$	−4.49253	−0.701615	−0.350807	+	0.936448i	$0.614093\pi$
$42$	3.33293	0.514282
$43$	6.52052	0.994370	0.497185	−	0.867645i	$-0.334367\pi$
$43$	6.52052	0.994370	0.497185	+	0.867645i	$0.334367\pi$
$44$	−5.33841	−0.804796
$45$	1.62002	0.241498
$46$	6.51821	0.961057
$47$	3.38927	0.494376	0.247188	−	0.968968i	$-0.420494\pi$
$47$	3.38927	0.494376	0.247188	+	0.968968i	$0.420494\pi$
$48$	−2.25449	−0.325407
$49$	−4.81447	−0.687781
$50$	4.39497	0.621542
$51$	−7.45448	−1.04384
$52$	4.84063	0.671274
$53$	6.53388	0.897498	0.448749	−	0.893658i	$-0.351870\pi$
$53$	6.53388	0.897498	0.448749	+	0.893658i	$0.351870\pi$
$54$	−2.06801	−0.281420
$55$	−4.15243	−0.559914
$56$	−1.47835	−0.197553
$57$	11.7547	1.55695
$58$	−7.15345	−0.939294
$59$	−9.45851	−1.23139	−0.615697	−	0.787983i	$-0.711125\pi$
$59$	−9.45851	−1.23139	−0.615697	+	0.787983i	$0.711125\pi$
$60$	−1.75363	−0.226393
$61$	−7.74630	−0.991812	−0.495906	−	0.868376i	$-0.665164\pi$
$61$	−7.74630	−0.991812	−0.495906	+	0.868376i	$0.665164\pi$
$62$	8.77657	1.11463
$63$	3.07899	0.387916
$64$	1.00000	0.125000
$65$	3.76523	0.467020
$66$	−12.0354	−1.48145
$67$	7.46740	0.912288	0.456144	−	0.889906i	$-0.349230\pi$
$67$	7.46740	0.912288	0.456144	+	0.889906i	$0.349230\pi$
$68$	3.30651	0.400973
$69$	14.6952	1.76910
$70$	−1.14992	−0.137442
$71$	6.86424	0.814635	0.407318	−	0.913287i	$-0.366464\pi$
$71$	6.86424	0.814635	0.407318	+	0.913287i	$0.366464\pi$
$72$	−2.08272	−0.245450
$73$	0.792125	0.0927113	0.0463556	−	0.998925i	$-0.485239\pi$
$73$	0.792125	0.0927113	0.0463556	+	0.998925i	$0.485239\pi$
$74$	0.774253	0.0900051
$75$	9.90840	1.14412
$76$	−5.21391	−0.598076
$77$	−7.89206	−0.899384
$78$	10.9131	1.23567
$79$	−14.4377	−1.62437	−0.812184	−	0.583401i	$-0.801722\pi$
$79$	−14.4377	−1.62437	−0.812184	+	0.583401i	$0.801722\pi$
$80$	0.777840	0.0869651
$81$	−10.9104	−1.21227
$82$	4.49253	0.496117
$83$	5.53303	0.607329	0.303665	−	0.952779i	$-0.401790\pi$
$83$	5.53303	0.607329	0.303665	+	0.952779i	$0.401790\pi$
$84$	−3.33293	−0.363653
$85$	2.57193	0.278965
$86$	−6.52052	−0.703125
$87$	−16.1274	−1.72903
$88$	5.33841	0.569077
$89$	17.6800	1.87408	0.937039	−	0.349224i	$-0.113555\pi$
$89$	17.6800	1.87408	0.937039	+	0.349224i	$0.113555\pi$
$90$	−1.62002	−0.170765
$91$	7.15616	0.750170
$92$	−6.51821	−0.679570
$93$	19.7867	2.05178
$94$	−3.38927	−0.349576
$95$	−4.05558	−0.416094
$96$	2.25449	0.230098
$97$	14.7843	1.50112	0.750560	−	0.660802i	$-0.229784\pi$
$97$	14.7843	1.50112	0.750560	+	0.660802i	$0.229784\pi$
$98$	4.81447	0.486335
$99$	−11.1184	−1.11744
$100$	−4.39497	−0.439497
$101$	−11.6712	−1.16133	−0.580664	−	0.814143i	$-0.697207\pi$
$101$	−11.6712	−1.16133	−0.580664	+	0.814143i	$0.697207\pi$
$102$	7.45448	0.738104
$103$	−1.47057	−0.144900	−0.0724499	−	0.997372i	$-0.523082\pi$
$103$	−1.47057	−0.144900	−0.0724499	+	0.997372i	$0.523082\pi$
$104$	−4.84063	−0.474663
$105$	−2.59249	−0.253001
$106$	−6.53388	−0.634627
$107$	−15.7898	−1.52646	−0.763230	−	0.646126i	$-0.776388\pi$
$107$	−15.7898	−1.52646	−0.763230	+	0.646126i	$0.776388\pi$
$108$	2.06801	0.198994
$109$	1.77419	0.169937	0.0849683	−	0.996384i	$-0.472921\pi$
$109$	1.77419	0.169937	0.0849683	+	0.996384i	$0.472921\pi$
$110$	4.15243	0.395919
$111$	1.74554	0.165680
$112$	1.47835	0.139691
$113$	13.3015	1.25130	0.625652	−	0.780102i	$-0.284833\pi$
$113$	13.3015	1.25130	0.625652	+	0.780102i	$0.284833\pi$
$114$	−11.7547	−1.10093
$115$	−5.07012	−0.472791
$116$	7.15345	0.664181
$117$	10.0817	0.932049
$118$	9.45851	0.870727
$119$	4.88819	0.448100
$120$	1.75363	0.160084
$121$	17.4986	1.59079
$122$	7.74630	0.701317
$123$	10.1283	0.913242
$124$	−8.77657	−0.788159
$125$	−7.30778	−0.653628
$126$	−3.07899	−0.274298
$127$	3.11538	0.276445	0.138223	−	0.990401i	$-0.455861\pi$
$127$	3.11538	0.276445	0.138223	+	0.990401i	$0.455861\pi$
$128$	−1.00000	−0.0883883
$129$	−14.7004	−1.29430
$130$	−3.76523	−0.330233
$131$	15.2576	1.33306	0.666530	−	0.745478i	$-0.267779\pi$
$131$	15.2576	1.33306	0.666530	+	0.745478i	$0.267779\pi$
$132$	12.0354	1.04755
$133$	−7.70800	−0.668368
$134$	−7.46740	−0.645085
$135$	1.60858	0.138444
$136$	−3.30651	−0.283531
$137$	14.2062	1.21371	0.606857	−	0.794811i	$-0.292430\pi$
$137$	14.2062	1.21371	0.606857	+	0.794811i	$0.292430\pi$
$138$	−14.6952	−1.25094
$139$	8.12815	0.689420	0.344710	−	0.938709i	$-0.387977\pi$
$139$	8.12815	0.689420	0.344710	+	0.938709i	$0.387977\pi$
$140$	1.14992	0.0971862
$141$	−7.64106	−0.643494
$142$	−6.86424	−0.576034
$143$	−25.8413	−2.16096
$144$	2.08272	0.173560
$145$	5.56424	0.462085
$146$	−0.792125	−0.0655568
$147$	10.8542	0.895236
$148$	−0.774253	−0.0636432
$149$	4.77744	0.391384	0.195692	−	0.980665i	$-0.437305\pi$
$149$	4.77744	0.391384	0.195692	+	0.980665i	$0.437305\pi$
$150$	−9.90840	−0.809017
$151$	−13.8230	−1.12490	−0.562450	−	0.826831i	$-0.690141\pi$
$151$	−13.8230	−1.12490	−0.562450	+	0.826831i	$0.690141\pi$
$152$	5.21391	0.422904
$153$	6.88652	0.556742
$154$	7.89206	0.635961
$155$	−6.82677	−0.548339
$156$	−10.9131	−0.873750
$157$	−19.3001	−1.54032	−0.770158	−	0.637853i	$-0.779823\pi$
$157$	−19.3001	−1.54032	−0.770158	+	0.637853i	$0.779823\pi$
$158$	14.4377	1.14860
$159$	−14.7306	−1.16821
$160$	−0.777840	−0.0614936
$161$	−9.63622	−0.759440
$162$	10.9104	0.857205
$163$	4.30572	0.337250	0.168625	−	0.985680i	$-0.446067\pi$
$163$	4.30572	0.337250	0.168625	+	0.985680i	$0.446067\pi$
$164$	−4.49253	−0.350807
$165$	9.36160	0.728800
$166$	−5.53303	−0.429446
$167$	−7.92378	−0.613161	−0.306580	−	0.951845i	$-0.599185\pi$
$167$	−7.92378	−0.613161	−0.306580	+	0.951845i	$0.599185\pi$
$168$	3.33293	0.257141
$169$	10.4317	0.802438
$170$	−2.57193	−0.197258
$171$	−10.8591	−0.830415
$172$	6.52052	0.497185
$173$	12.3479	0.938790	0.469395	−	0.882988i	$-0.344472\pi$
$173$	12.3479	0.938790	0.469395	+	0.882988i	$0.344472\pi$
$174$	16.1274	1.22261
$175$	−6.49731	−0.491151
$176$	−5.33841	−0.402398
$177$	21.3241	1.60282
$178$	−17.6800	−1.32517
$179$	11.1405	0.832681	0.416341	−	0.909209i	$-0.363312\pi$
$179$	11.1405	0.832681	0.416341	+	0.909209i	$0.363312\pi$
$180$	1.62002	0.120749
$181$	−7.83919	−0.582683	−0.291341	−	0.956619i	$-0.594102\pi$
$181$	−7.83919	−0.582683	−0.291341	+	0.956619i	$0.594102\pi$
$182$	−7.15616	−0.530450
$183$	17.4639	1.29097
$184$	6.51821	0.480529
$185$	−0.602245	−0.0442779
$186$	−19.7867	−1.45083
$187$	−17.6515	−1.29081
$188$	3.38927	0.247188
$189$	3.05724	0.222382
$190$	4.05558	0.294223
$191$	15.4705	1.11941	0.559704	−	0.828693i	$-0.310915\pi$
$191$	15.4705	1.11941	0.559704	+	0.828693i	$0.310915\pi$
$192$	−2.25449	−0.162704
$193$	−1.85244	−0.133341	−0.0666706	−	0.997775i	$-0.521238\pi$
$193$	−1.85244	−0.133341	−0.0666706	+	0.997775i	$0.521238\pi$
$194$	−14.7843	−1.06145
$195$	−8.48868	−0.607887
$196$	−4.81447	−0.343891
$197$	−8.61476	−0.613776	−0.306888	−	0.951746i	$-0.599288\pi$
$197$	−8.61476	−0.613776	−0.306888	+	0.951746i	$0.599288\pi$
$198$	11.1184	0.790150
$199$	3.39984	0.241009	0.120504	−	0.992713i	$-0.461549\pi$
$199$	3.39984	0.241009	0.120504	+	0.992713i	$0.461549\pi$
$200$	4.39497	0.310771
$201$	−16.8352	−1.18746
$202$	11.6712	0.821183
$203$	10.5753	0.742242
$204$	−7.45448	−0.521918
$205$	−3.49447	−0.244064
$206$	1.47057	0.102460
$207$	−13.5756	−0.943568
$208$	4.84063	0.335637
$209$	27.8340	1.92532
$210$	2.59249	0.178899
$211$	−20.4374	−1.40697	−0.703485	−	0.710710i	$-0.748374\pi$
$211$	−20.4374	−1.40697	−0.703485	+	0.710710i	$0.748374\pi$
$212$	6.53388	0.448749
$213$	−15.4753	−1.06035
$214$	15.7898	1.07937
$215$	5.07192	0.345902
$216$	−2.06801	−0.140710
$217$	−12.9749	−0.880792
$218$	−1.77419	−0.120163
$219$	−1.78584	−0.120676
$220$	−4.15243	−0.279957
$221$	16.0056	1.07665
$222$	−1.74554	−0.117153
$223$	−24.8822	−1.66623	−0.833117	−	0.553097i	$-0.813446\pi$
$223$	−24.8822	−1.66623	−0.833117	+	0.553097i	$0.813446\pi$
$224$	−1.47835	−0.0987767
$225$	−9.15346	−0.610231
$226$	−13.3015	−0.884805
$227$	8.65724	0.574601	0.287301	−	0.957840i	$-0.407242\pi$
$227$	8.65724	0.574601	0.287301	+	0.957840i	$0.407242\pi$
$228$	11.7547	0.778473
$229$	0.669525	0.0442435	0.0221217	−	0.999755i	$-0.492958\pi$
$229$	0.669525	0.0442435	0.0221217	+	0.999755i	$0.492958\pi$
$230$	5.07012	0.334314
$231$	17.7926	1.17066
$232$	−7.15345	−0.469647
$233$	−5.74535	−0.376390	−0.188195	−	0.982132i	$-0.560264\pi$
$233$	−5.74535	−0.376390	−0.188195	+	0.982132i	$0.560264\pi$
$234$	−10.0817	−0.659058
$235$	2.63631	0.171974
$236$	−9.45851	−0.615697
$237$	32.5496	2.11433
$238$	−4.88819	−0.316854
$239$	−13.7133	−0.887038	−0.443519	−	0.896265i	$-0.646270\pi$
$239$	−13.7133	−0.887038	−0.443519	+	0.896265i	$0.646270\pi$
$240$	−1.75363	−0.113196
$241$	−6.26556	−0.403600	−0.201800	−	0.979427i	$-0.564679\pi$
$241$	−6.26556	−0.403600	−0.201800	+	0.979427i	$0.564679\pi$
$242$	−17.4986	−1.12486
$243$	18.3934	1.17994
$244$	−7.74630	−0.495906
$245$	−3.74489	−0.239252
$246$	−10.1283	−0.645760
$247$	−25.2386	−1.60589
$248$	8.77657	0.557313
$249$	−12.4742	−0.790517
$250$	7.30778	0.462184
$251$	−0.218375	−0.0137837	−0.00689187	−	0.999976i	$-0.502194\pi$
$251$	−0.218375	−0.0137837	−0.00689187	+	0.999976i	$0.502194\pi$
$252$	3.07899	0.193958
$253$	34.7969	2.18766
$254$	−3.11538	−0.195476
$255$	−5.79840	−0.363110
$256$	1.00000	0.0625000
$257$	−17.6166	−1.09889	−0.549446	−	0.835529i	$-0.685161\pi$
$257$	−17.6166	−1.09889	−0.549446	+	0.835529i	$0.685161\pi$
$258$	14.7004	0.915209
$259$	−1.14462	−0.0711232
$260$	3.76523	0.233510
$261$	14.8986	0.922200
$262$	−15.2576	−0.942616
$263$	−7.24915	−0.447001	−0.223501	−	0.974704i	$-0.571749\pi$
$263$	−7.24915	−0.447001	−0.223501	+	0.974704i	$0.571749\pi$
$264$	−12.0354	−0.740727
$265$	5.08231	0.312204
$266$	7.70800	0.472608
$267$	−39.8594	−2.43936
$268$	7.46740	0.456144
$269$	−28.4928	−1.73724	−0.868619	−	0.495480i	$-0.834992\pi$
$269$	−28.4928	−1.73724	−0.868619	+	0.495480i	$0.834992\pi$
$270$	−1.60858	−0.0978949
$271$	19.4963	1.18432	0.592159	−	0.805821i	$-0.298276\pi$
$271$	19.4963	1.18432	0.592159	+	0.805821i	$0.298276\pi$
$272$	3.30651	0.200487
$273$	−16.1335	−0.976443
$274$	−14.2062	−0.858226
$275$	23.4621	1.41482
$276$	14.6952	0.884548
$277$	−25.8260	−1.55173	−0.775867	−	0.630896i	$-0.782687\pi$
$277$	−25.8260	−1.55173	−0.775867	+	0.630896i	$0.782687\pi$
$278$	−8.12815	−0.487494
$279$	−18.2791	−1.09434
$280$	−1.14992	−0.0687210
$281$	19.1945	1.14505	0.572525	−	0.819887i	$-0.305964\pi$
$281$	19.1945	1.14505	0.572525	+	0.819887i	$0.305964\pi$
$282$	7.64106	0.455019
$283$	14.1252	0.839658	0.419829	−	0.907603i	$-0.362090\pi$
$283$	14.1252	0.839658	0.419829	+	0.907603i	$0.362090\pi$
$284$	6.86424	0.407318
$285$	9.14326	0.541600
$286$	25.8413	1.52803
$287$	−6.64154	−0.392038
$288$	−2.08272	−0.122725
$289$	−6.06700	−0.356882
$290$	−5.56424	−0.326743
$291$	−33.3311	−1.95390
$292$	0.792125	0.0463556
$293$	23.8530	1.39351	0.696754	−	0.717310i	$-0.254627\pi$
$293$	23.8530	1.39351	0.696754	+	0.717310i	$0.254627\pi$
$294$	−10.8542	−0.633028
$295$	−7.35721	−0.428353
$296$	0.774253	0.0450025
$297$	−11.0399	−0.640598
$298$	−4.77744	−0.276750
$299$	−31.5522	−1.82471
$300$	9.90840	0.572062
$301$	9.63963	0.555619
$302$	13.8230	0.795425
$303$	26.3126	1.51162
$304$	−5.21391	−0.299038
$305$	−6.02538	−0.345012
$306$	−6.88652	−0.393676
$307$	12.3779	0.706445	0.353222	−	0.935539i	$-0.385086\pi$
$307$	12.3779	0.706445	0.353222	+	0.935539i	$0.385086\pi$
$308$	−7.89206	−0.449692
$309$	3.31539	0.188606
$310$	6.82677	0.387734
$311$	18.1601	1.02977	0.514883	−	0.857261i	$-0.327835\pi$
$311$	18.1601	1.02977	0.514883	+	0.857261i	$0.327835\pi$
$312$	10.9131	0.617835
$313$	12.9301	0.730852	0.365426	−	0.930840i	$-0.380923\pi$
$313$	12.9301	0.730852	0.365426	+	0.930840i	$0.380923\pi$
$314$	19.3001	1.08917
$315$	2.39496	0.134941
$316$	−14.4377	−0.812184
$317$	28.5114	1.60136	0.800679	−	0.599094i	$-0.204473\pi$
$317$	28.5114	1.60136	0.800679	+	0.599094i	$0.204473\pi$
$318$	14.7306	0.826049
$319$	−38.1881	−2.13812
$320$	0.777840	0.0434826
$321$	35.5980	1.98689
$322$	9.63622	0.537005
$323$	−17.2398	−0.959249
$324$	−10.9104	−0.606136
$325$	−21.2744	−1.18009
$326$	−4.30572	−0.238472
$327$	−3.99989	−0.221194
$328$	4.49253	0.248058
$329$	5.01054	0.276240
$330$	−9.36160	−0.515339
$331$	17.4272	0.957885	0.478942	−	0.877846i	$-0.341020\pi$
$331$	17.4272	0.957885	0.478942	+	0.877846i	$0.341020\pi$
$332$	5.53303	0.303665
$333$	−1.61255	−0.0883671
$334$	7.92378	0.433570
$335$	5.80844	0.317349
$336$	−3.33293	−0.181826
$337$	15.5818	0.848792	0.424396	−	0.905477i	$-0.360486\pi$
$337$	15.5818	0.848792	0.424396	+	0.905477i	$0.360486\pi$
$338$	−10.4317	−0.567409
$339$	−29.9882	−1.62873
$340$	2.57193	0.139483
$341$	46.8529	2.53723
$342$	10.8591	0.587192
$343$	−17.4660	−0.943074
$344$	−6.52052	−0.351563
$345$	11.4305	0.615399
$346$	−12.3479	−0.663825
$347$	14.8899	0.799331	0.399665	−	0.916661i	$-0.369126\pi$
$347$	14.8899	0.799331	0.399665	+	0.916661i	$0.369126\pi$
$348$	−16.1274	−0.864517
$349$	−34.7848	−1.86199	−0.930995	−	0.365032i	$-0.881058\pi$
$349$	−34.7848	−1.86199	−0.930995	+	0.365032i	$0.881058\pi$
$350$	6.49731	0.347296
$351$	10.0105	0.534318
$352$	5.33841	0.284538
$353$	−7.02922	−0.374127	−0.187064	−	0.982348i	$-0.559897\pi$
$353$	−7.02922	−0.374127	−0.187064	+	0.982348i	$0.559897\pi$
$354$	−21.3241	−1.13336
$355$	5.33928	0.283380
$356$	17.6800	0.937039
$357$	−11.0204	−0.583260
$358$	−11.1405	−0.588795
$359$	22.0463	1.16356	0.581779	−	0.813347i	$-0.302357\pi$
$359$	22.0463	1.16356	0.581779	+	0.813347i	$0.302357\pi$
$360$	−1.62002	−0.0853825
$361$	8.18481	0.430779
$362$	7.83919	0.412019
$363$	−39.4505	−2.07061
$364$	7.15616	0.375085
$365$	0.616147	0.0322506
$366$	−17.4639	−0.912855
$367$	29.0871	1.51834	0.759168	−	0.650895i	$-0.225606\pi$
$367$	29.0871	1.51834	0.759168	+	0.650895i	$0.225606\pi$
$368$	−6.51821	−0.339785
$369$	−9.35666	−0.487088
$370$	0.602245	0.0313092
$371$	9.65939	0.501491
$372$	19.7867	1.02589
$373$	−2.52708	−0.130847	−0.0654236	−	0.997858i	$-0.520840\pi$
$373$	−2.52708	−0.130847	−0.0654236	+	0.997858i	$0.520840\pi$
$374$	17.6515	0.912738
$375$	16.4753	0.850781
$376$	−3.38927	−0.174788
$377$	34.6272	1.78339
$378$	−3.05724	−0.157248
$379$	21.7026	1.11479	0.557394	−	0.830248i	$-0.311801\pi$
$379$	21.7026	1.11479	0.557394	+	0.830248i	$0.311801\pi$
$380$	−4.05558	−0.208047
$381$	−7.02359	−0.359829
$382$	−15.4705	−0.791541
$383$	35.0201	1.78944	0.894722	−	0.446623i	$-0.147373\pi$
$383$	35.0201	1.78944	0.894722	+	0.446623i	$0.147373\pi$
$384$	2.25449	0.115049
$385$	−6.13876	−0.312860
$386$	1.85244	0.0942865
$387$	13.5804	0.690330
$388$	14.7843	0.750560
$389$	−1.09380	−0.0554579	−0.0277290	−	0.999615i	$-0.508828\pi$
$389$	−1.09380	−0.0554579	−0.0277290	+	0.999615i	$0.508828\pi$
$390$	8.48868	0.429841
$391$	−21.5525	−1.08996
$392$	4.81447	0.243167
$393$	−34.3980	−1.73515
$394$	8.61476	0.434006
$395$	−11.2302	−0.565054
$396$	−11.1184	−0.558720
$397$	−14.9741	−0.751527	−0.375763	−	0.926716i	$-0.622619\pi$
$397$	−14.9741	−0.751527	−0.375763	+	0.926716i	$0.622619\pi$
$398$	−3.39984	−0.170419
$399$	17.3776	0.869967
$400$	−4.39497	−0.219748
$401$	9.06110	0.452490	0.226245	−	0.974070i	$-0.427355\pi$
$401$	9.06110	0.452490	0.226245	+	0.974070i	$0.427355\pi$
$402$	16.8352	0.839662
$403$	−42.4841	−2.11628
$404$	−11.6712	−0.580664
$405$	−8.48658	−0.421701
$406$	−10.5753	−0.524845
$407$	4.13328	0.204879
$408$	7.45448	0.369052
$409$	8.39066	0.414892	0.207446	−	0.978247i	$-0.433485\pi$
$409$	8.39066	0.414892	0.207446	+	0.978247i	$0.433485\pi$
$410$	3.49447	0.172579
$411$	−32.0276	−1.57981
$412$	−1.47057	−0.0724499
$413$	−13.9830	−0.688060
$414$	13.5756	0.667203
$415$	4.30381	0.211266
$416$	−4.84063	−0.237331
$417$	−18.3248	−0.897370
$418$	−27.8340	−1.36140
$419$	−6.41372	−0.313331	−0.156665	−	0.987652i	$-0.550074\pi$
$419$	−6.41372	−0.313331	−0.156665	+	0.987652i	$0.550074\pi$
$420$	−2.59249	−0.126500
$421$	−29.3983	−1.43279	−0.716394	−	0.697696i	$-0.754209\pi$
$421$	−29.3983	−1.43279	−0.716394	+	0.697696i	$0.754209\pi$
$422$	20.4374	0.994878
$423$	7.05888	0.343215
$424$	−6.53388	−0.317313
$425$	−14.5320	−0.704905
$426$	15.4753	0.749783
$427$	−11.4518	−0.554190
$428$	−15.7898	−0.763230
$429$	58.2588	2.81276
$430$	−5.07192	−0.244590
$431$	−15.6998	−0.756235	−0.378117	−	0.925758i	$-0.623428\pi$
$431$	−15.6998	−0.756235	−0.378117	+	0.925758i	$0.623428\pi$
$432$	2.06801	0.0994970
$433$	1.05930	0.0509065	0.0254533	−	0.999676i	$-0.491897\pi$
$433$	1.05930	0.0509065	0.0254533	+	0.999676i	$0.491897\pi$
$434$	12.9749	0.622814
$435$	−12.5445	−0.601463
$436$	1.77419	0.0849683
$437$	33.9853	1.62574
$438$	1.78584	0.0853306
$439$	12.8161	0.611678	0.305839	−	0.952083i	$-0.401063\pi$
$439$	12.8161	0.611678	0.305839	+	0.952083i	$0.401063\pi$
$440$	4.15243	0.197959
$441$	−10.0272	−0.477484
$442$	−16.0056	−0.761308
$443$	−17.2957	−0.821744	−0.410872	−	0.911693i	$-0.634776\pi$
$443$	−17.2957	−0.821744	−0.410872	+	0.911693i	$0.634776\pi$
$444$	1.74554	0.0828398
$445$	13.7522	0.651918
$446$	24.8822	1.17821
$447$	−10.7707	−0.509436
$448$	1.47835	0.0698457
$449$	23.6905	1.11802	0.559012	−	0.829159i	$-0.311180\pi$
$449$	23.6905	1.11802	0.559012	+	0.829159i	$0.311180\pi$
$450$	9.15346	0.431498
$451$	23.9830	1.12931
$452$	13.3015	0.625652
$453$	31.1638	1.46420
$454$	−8.65724	−0.406304
$455$	5.56635	0.260954
$456$	−11.7547	−0.550464
$457$	−24.3387	−1.13852	−0.569259	−	0.822158i	$-0.692770\pi$
$457$	−24.3387	−1.13852	−0.569259	+	0.822158i	$0.692770\pi$
$458$	−0.669525	−0.0312849
$459$	6.83788	0.319165
$460$	−5.07012	−0.236396
$461$	−10.3623	−0.482620	−0.241310	−	0.970448i	$-0.577577\pi$
$461$	−10.3623	−0.482620	−0.241310	+	0.970448i	$0.577577\pi$
$462$	−17.7926	−0.827785
$463$	−15.0933	−0.701445	−0.350723	−	0.936479i	$-0.614064\pi$
$463$	−15.0933	−0.701445	−0.350723	+	0.936479i	$0.614064\pi$
$464$	7.15345	0.332090
$465$	15.3909	0.713734
$466$	5.74535	0.266148
$467$	−3.09640	−0.143284	−0.0716421	−	0.997430i	$-0.522824\pi$
$467$	−3.09640	−0.143284	−0.0716421	+	0.997430i	$0.522824\pi$
$468$	10.0817	0.466025
$469$	11.0395	0.509755
$470$	−2.63631	−0.121604
$471$	43.5119	2.00492
$472$	9.45851	0.435363
$473$	−34.8092	−1.60053
$474$	−32.5496	−1.49505
$475$	22.9149	1.05141
$476$	4.88819	0.224050
$477$	13.6082	0.623078
$478$	13.7133	0.627231
$479$	−3.93727	−0.179899	−0.0899493	−	0.995946i	$-0.528670\pi$
$479$	−3.93727	−0.179899	−0.0899493	+	0.995946i	$0.528670\pi$
$480$	1.75363	0.0800419
$481$	−3.74787	−0.170888
$482$	6.26556	0.285389
$483$	21.7247	0.988510
$484$	17.4986	0.795393
$485$	11.4998	0.522181
$486$	−18.3934	−0.834343
$487$	−5.14467	−0.233127	−0.116564	−	0.993183i	$-0.537188\pi$
$487$	−5.14467	−0.233127	−0.116564	+	0.993183i	$0.537188\pi$
$488$	7.74630	0.350658
$489$	−9.70718	−0.438974
$490$	3.74489	0.169177
$491$	−16.2144	−0.731747	−0.365873	−	0.930665i	$-0.619230\pi$
$491$	−16.2144	−0.731747	−0.365873	+	0.930665i	$0.619230\pi$
$492$	10.1283	0.456621
$493$	23.6529	1.06527
$494$	25.2386	1.13554
$495$	−8.64833	−0.388714
$496$	−8.77657	−0.394080
$497$	10.1478	0.455190
$498$	12.4742	0.558980
$499$	−5.99196	−0.268237	−0.134118	−	0.990965i	$-0.542820\pi$
$499$	−5.99196	−0.268237	−0.134118	+	0.990965i	$0.542820\pi$
$500$	−7.30778	−0.326814
$501$	17.8641	0.798108
$502$	0.218375	0.00974657
$503$	28.6666	1.27818	0.639089	−	0.769133i	$-0.279311\pi$
$503$	28.6666	1.27818	0.639089	+	0.769133i	$0.279311\pi$
$504$	−3.07899	−0.137149
$505$	−9.07832	−0.403980
$506$	−34.7969	−1.54691
$507$	−23.5181	−1.04448
$508$	3.11538	0.138223
$509$	29.1652	1.29273	0.646363	−	0.763030i	$-0.276289\pi$
$509$	29.1652	1.29273	0.646363	+	0.763030i	$0.276289\pi$
$510$	5.79840	0.256757
$511$	1.17104	0.0518038
$512$	−1.00000	−0.0441942
$513$	−10.7824	−0.476054
$514$	17.6166	0.777035
$515$	−1.14387	−0.0504049
$516$	−14.7004	−0.647150
$517$	−18.0933	−0.795743
$518$	1.14462	0.0502917
$519$	−27.8381	−1.22196
$520$	−3.76523	−0.165116
$521$	−14.3527	−0.628804	−0.314402	−	0.949290i	$-0.601804\pi$
$521$	−14.3527	−0.628804	−0.314402	+	0.949290i	$0.601804\pi$
$522$	−14.8986	−0.652094
$523$	34.9419	1.52790	0.763951	−	0.645274i	$-0.223257\pi$
$523$	34.9419	1.52790	0.763951	+	0.645274i	$0.223257\pi$
$524$	15.2576	0.666530
$525$	14.6481	0.639296
$526$	7.24915	0.316078
$527$	−29.0198	−1.26412
$528$	12.0354	0.523773
$529$	19.4870	0.847262
$530$	−5.08231	−0.220762
$531$	−19.6994	−0.854881
$532$	−7.70800	−0.334184
$533$	−21.7467	−0.941952
$534$	39.8594	1.72488
$535$	−12.2820	−0.530995
$536$	−7.46740	−0.322543
$537$	−25.1162	−1.08384
$538$	28.4928	1.22841
$539$	25.7016	1.10705
$540$	1.60858	0.0692222
$541$	2.72468	0.117143	0.0585715	−	0.998283i	$-0.481345\pi$
$541$	2.72468	0.117143	0.0585715	+	0.998283i	$0.481345\pi$
$542$	−19.4963	−0.837439
$543$	17.6734	0.758437
$544$	−3.30651	−0.141765
$545$	1.38004	0.0591142
$546$	16.1335	0.690449
$547$	29.7380	1.27151	0.635753	−	0.771892i	$-0.280690\pi$
$547$	29.7380	1.27151	0.635753	+	0.771892i	$0.280690\pi$
$548$	14.2062	0.606857
$549$	−16.1333	−0.688554
$550$	−23.4621	−1.00043
$551$	−37.2974	−1.58892
$552$	−14.6952	−0.625470
$553$	−21.3440	−0.907641
$554$	25.8260	1.09724
$555$	1.35775	0.0576334
$556$	8.12815	0.344710
$557$	−40.3627	−1.71022	−0.855111	−	0.518445i	$-0.826511\pi$
$557$	−40.3627	−1.71022	−0.855111	+	0.518445i	$0.826511\pi$
$558$	18.2791	0.773816
$559$	31.5634	1.33499
$560$	1.14992	0.0485931
$561$	39.7951	1.68015
$562$	−19.1945	−0.809672
$563$	42.3614	1.78532	0.892659	−	0.450732i	$-0.148837\pi$
$563$	42.3614	1.78532	0.892659	+	0.450732i	$0.148837\pi$
$564$	−7.64106	−0.321747
$565$	10.3465	0.435279
$566$	−14.1252	−0.593728
$567$	−16.1295	−0.677375
$568$	−6.86424	−0.288017
$569$	−11.2951	−0.473517	−0.236759	−	0.971569i	$-0.576085\pi$
$569$	−11.2951	−0.473517	−0.236759	+	0.971569i	$0.576085\pi$
$570$	−9.14326	−0.382969
$571$	44.8768	1.87804	0.939018	−	0.343867i	$-0.111737\pi$
$571$	44.8768	1.87804	0.939018	+	0.343867i	$0.111737\pi$
$572$	−25.8413	−1.08048
$573$	−34.8781	−1.45705
$574$	6.64154	0.277213
$575$	28.6473	1.19467
$576$	2.08272	0.0867798
$577$	−22.2527	−0.926393	−0.463197	−	0.886256i	$-0.653298\pi$
$577$	−22.2527	−0.926393	−0.463197	+	0.886256i	$0.653298\pi$
$578$	6.06700	0.252354
$579$	4.17629	0.173561
$580$	5.56424	0.231042
$581$	8.17978	0.339354
$582$	33.3311	1.38162
$583$	−34.8806	−1.44461
$584$	−0.792125	−0.0327784
$585$	7.84191	0.324223
$586$	−23.8530	−0.985360
$587$	−40.7959	−1.68383	−0.841913	−	0.539614i	$-0.818570\pi$
$587$	−40.7959	−1.68383	−0.841913	+	0.539614i	$0.818570\pi$
$588$	10.8542	0.447618
$589$	45.7602	1.88552
$590$	7.35721	0.302891
$591$	19.4219	0.798909
$592$	−0.774253	−0.0318216
$593$	11.1759	0.458940	0.229470	−	0.973316i	$-0.426301\pi$
$593$	11.1759	0.458940	0.229470	+	0.973316i	$0.426301\pi$
$594$	11.0399	0.452971
$595$	3.80223	0.155876
$596$	4.77744	0.195692
$597$	−7.66491	−0.313704
$598$	31.5522	1.29027
$599$	25.3906	1.03743	0.518716	−	0.854946i	$-0.326410\pi$
$599$	25.3906	1.03743	0.518716	+	0.854946i	$0.326410\pi$
$600$	−9.90840	−0.404509
$601$	40.3938	1.64770	0.823850	−	0.566808i	$-0.191822\pi$
$601$	40.3938	1.64770	0.823850	+	0.566808i	$0.191822\pi$
$602$	−9.63963	−0.392882
$603$	15.5525	0.633346
$604$	−13.8230	−0.562450
$605$	13.6111	0.553372
$606$	−26.3126	−1.06888
$607$	35.4331	1.43819	0.719093	−	0.694914i	$-0.244557\pi$
$607$	35.4331	1.43819	0.719093	+	0.694914i	$0.244557\pi$
$608$	5.21391	0.211452
$609$	−23.8419	−0.966125
$610$	6.02538	0.243960
$611$	16.4062	0.663723
$612$	6.88652	0.278371
$613$	−35.0150	−1.41424	−0.707121	−	0.707092i	$-0.750006\pi$
$613$	−35.0150	−1.41424	−0.707121	+	0.707092i	$0.750006\pi$
$614$	−12.3779	−0.499532
$615$	7.87823	0.317681
$616$	7.89206	0.317980
$617$	38.4328	1.54725	0.773623	−	0.633647i	$-0.218443\pi$
$617$	38.4328	1.54725	0.773623	+	0.633647i	$0.218443\pi$
$618$	−3.31539	−0.133364
$619$	39.5548	1.58984	0.794922	−	0.606712i	$-0.207512\pi$
$619$	39.5548	1.58984	0.794922	+	0.606712i	$0.207512\pi$
$620$	−6.82677	−0.274169
$621$	−13.4797	−0.540921
$622$	−18.1601	−0.728154
$623$	26.1373	1.04717
$624$	−10.9131	−0.436875
$625$	16.2905	0.651622
$626$	−12.9301	−0.516791
$627$	−62.7514	−2.50605
$628$	−19.3001	−0.770158
$629$	−2.56007	−0.102077
$630$	−2.39496	−0.0954176
$631$	−26.8885	−1.07041	−0.535207	−	0.844721i	$-0.679766\pi$
$631$	−26.8885	−1.07041	−0.535207	+	0.844721i	$0.679766\pi$
$632$	14.4377	0.574301
$633$	46.0759	1.83135
$634$	−28.5114	−1.13233
$635$	2.42327	0.0961644
$636$	−14.7306	−0.584105
$637$	−23.3051	−0.923380
$638$	38.1881	1.51188
$639$	14.2963	0.565551
$640$	−0.777840	−0.0307468
$641$	1.23339	0.0487161	0.0243580	−	0.999703i	$-0.492246\pi$
$641$	1.23339	0.0487161	0.0243580	+	0.999703i	$0.492246\pi$
$642$	−35.5980	−1.40494
$643$	5.50219	0.216985	0.108493	−	0.994097i	$-0.465398\pi$
$643$	5.50219	0.216985	0.108493	+	0.994097i	$0.465398\pi$
$644$	−9.63622	−0.379720
$645$	−11.4346	−0.450236
$646$	17.2398	0.678292
$647$	47.7387	1.87680	0.938401	−	0.345547i	$-0.112307\pi$
$647$	47.7387	1.87680	0.938401	+	0.345547i	$0.112307\pi$
$648$	10.9104	0.428603
$649$	50.4934	1.98204
$650$	21.2744	0.834450
$651$	29.2517	1.14646
$652$	4.30572	0.168625
$653$	−5.25511	−0.205649	−0.102824	−	0.994700i	$-0.532788\pi$
$653$	−5.25511	−0.205649	−0.102824	+	0.994700i	$0.532788\pi$
$654$	3.99989	0.156408
$655$	11.8679	0.463719
$656$	−4.49253	−0.175404
$657$	1.64977	0.0643637
$658$	−5.01054	−0.195331
$659$	−49.6663	−1.93472	−0.967362	−	0.253400i	$-0.918451\pi$
$659$	−49.6663	−1.93472	−0.967362	+	0.253400i	$0.918451\pi$
$660$	9.36160	0.364400
$661$	29.7082	1.15552	0.577758	−	0.816208i	$-0.303928\pi$
$661$	29.7082	1.15552	0.577758	+	0.816208i	$0.303928\pi$
$662$	−17.4272	−0.677327
$663$	−36.0844	−1.40140
$664$	−5.53303	−0.214723
$665$	−5.99559	−0.232499
$666$	1.61255	0.0624850
$667$	−46.6277	−1.80543
$668$	−7.92378	−0.306580
$669$	56.0966	2.16882
$670$	−5.80844	−0.224400
$671$	41.3529	1.59641
$672$	3.33293	0.128571
$673$	35.6575	1.37450	0.687249	−	0.726422i	$-0.258818\pi$
$673$	35.6575	1.37450	0.687249	+	0.726422i	$0.258818\pi$
$674$	−15.5818	−0.600187
$675$	−9.08881	−0.349829
$676$	10.4317	0.401219
$677$	51.2020	1.96785	0.983926	−	0.178578i	$-0.0571498\pi$
$677$	51.2020	1.96785	0.983926	+	0.178578i	$0.0571498\pi$
$678$	29.9882	1.15169
$679$	21.8565	0.838774
$680$	−2.57193	−0.0986292
$681$	−19.5176	−0.747918
$682$	−46.8529	−1.79409
$683$	38.6445	1.47869	0.739345	−	0.673327i	$-0.235135\pi$
$683$	38.6445	1.47869	0.739345	+	0.673327i	$0.235135\pi$
$684$	−10.8591	−0.415207
$685$	11.0501	0.422203
$686$	17.4660	0.666854
$687$	−1.50944	−0.0575886
$688$	6.52052	0.248592
$689$	31.6281	1.20493
$690$	−11.4305	−0.435153
$691$	37.2369	1.41656	0.708279	−	0.705932i	$-0.249472\pi$
$691$	37.2369	1.41656	0.708279	+	0.705932i	$0.249472\pi$
$692$	12.3479	0.469395
$693$	−16.4369	−0.624387
$694$	−14.8899	−0.565212
$695$	6.32240	0.239822
$696$	16.1274	0.611306
$697$	−14.8546	−0.562657
$698$	34.7848	1.31663
$699$	12.9528	0.489920
$700$	−6.49731	−0.245575
$701$	19.4801	0.735752	0.367876	−	0.929875i	$-0.380085\pi$
$701$	19.4801	0.735752	0.367876	+	0.929875i	$0.380085\pi$
$702$	−10.0105	−0.377820
$703$	4.03688	0.152254
$704$	−5.33841	−0.201199
$705$	−5.94352	−0.223846
$706$	7.02922	0.264548
$707$	−17.2542	−0.648910
$708$	21.3241	0.801409
$709$	36.0241	1.35291	0.676457	−	0.736483i	$-0.263515\pi$
$709$	36.0241	1.35291	0.676457	+	0.736483i	$0.263515\pi$
$710$	−5.33928	−0.200380
$711$	−30.0696	−1.12770
$712$	−17.6800	−0.662587
$713$	57.2075	2.14244
$714$	11.0204	0.412427
$715$	−20.1004	−0.751711
$716$	11.1405	0.416341
$717$	30.9164	1.15459
$718$	−22.0463	−0.822760
$719$	−34.7209	−1.29487	−0.647436	−	0.762120i	$-0.724159\pi$
$719$	−34.7209	−1.29487	−0.647436	+	0.762120i	$0.724159\pi$
$720$	1.62002	0.0603746
$721$	−2.17403	−0.0809650
$722$	−8.18481	−0.304607
$723$	14.1256	0.525338
$724$	−7.83919	−0.291341
$725$	−31.4392	−1.16762
$726$	39.4505	1.46415
$727$	42.0814	1.56071	0.780357	−	0.625334i	$-0.215037\pi$
$727$	42.0814	1.56071	0.780357	+	0.625334i	$0.215037\pi$
$728$	−7.15616	−0.265225
$729$	−8.73647	−0.323573
$730$	−0.616147	−0.0228046
$731$	21.5601	0.797431
$732$	17.4639	0.645486
$733$	−6.43479	−0.237674	−0.118837	−	0.992914i	$-0.537917\pi$
$733$	−6.43479	−0.237674	−0.118837	+	0.992914i	$0.537917\pi$
$734$	−29.0871	−1.07363
$735$	8.44280	0.311417
$736$	6.51821	0.240264
$737$	−39.8641	−1.46841
$738$	9.35666	0.344423
$739$	−26.0392	−0.957867	−0.478934	−	0.877851i	$-0.658977\pi$
$739$	−26.0392	−0.957867	−0.478934	+	0.877851i	$0.658977\pi$
$740$	−0.602245	−0.0221390
$741$	56.9001	2.09028
$742$	−9.65939	−0.354607
$743$	22.1534	0.812728	0.406364	−	0.913711i	$-0.366797\pi$
$743$	22.1534	0.812728	0.406364	+	0.913711i	$0.366797\pi$
$744$	−19.7867	−0.725414
$745$	3.71609	0.136147
$746$	2.52708	0.0925230
$747$	11.5237	0.421631
$748$	−17.6515	−0.645403
$749$	−23.3430	−0.852933
$750$	−16.4753	−0.601593
$751$	7.25459	0.264724	0.132362	−	0.991201i	$-0.457744\pi$
$751$	7.25459	0.264724	0.132362	+	0.991201i	$0.457744\pi$
$752$	3.38927	0.123594
$753$	0.492325	0.0179413
$754$	−34.6272	−1.26105
$755$	−10.7521	−0.391309
$756$	3.05724	0.111191
$757$	11.4281	0.415361	0.207680	−	0.978197i	$-0.433409\pi$
$757$	11.4281	0.415361	0.207680	+	0.978197i	$0.433409\pi$
$758$	−21.7026	−0.788274
$759$	−78.4491	−2.84752
$760$	4.05558	0.147111
$761$	2.13822	0.0775105	0.0387553	−	0.999249i	$-0.487661\pi$
$761$	2.13822	0.0775105	0.0387553	+	0.999249i	$0.487661\pi$
$762$	7.02359	0.254438
$763$	2.62288	0.0949547
$764$	15.4705	0.559704
$765$	5.35661	0.193669
$766$	−35.0201	−1.26533
$767$	−45.7851	−1.65321
$768$	−2.25449	−0.0813518
$769$	14.6157	0.527054	0.263527	−	0.964652i	$-0.415114\pi$
$769$	14.6157	0.527054	0.263527	+	0.964652i	$0.415114\pi$
$770$	6.13876	0.221226
$771$	39.7164	1.43035
$772$	−1.85244	−0.0666706
$773$	42.4471	1.52672	0.763358	−	0.645975i	$-0.223549\pi$
$773$	42.4471	1.52672	0.763358	+	0.645975i	$0.223549\pi$
$774$	−13.5804	−0.488137
$775$	38.5727	1.38557
$776$	−14.7843	−0.530726
$777$	2.58053	0.0925761
$778$	1.09380	0.0392147
$779$	23.4236	0.839238
$780$	−8.48868	−0.303943
$781$	−36.6441	−1.31123
$782$	21.5525	0.770716
$783$	14.7934	0.528672
$784$	−4.81447	−0.171945
$785$	−15.0124	−0.535815
$786$	34.3980	1.22694
$787$	30.8805	1.10077	0.550385	−	0.834911i	$-0.314481\pi$
$787$	30.8805	1.10077	0.550385	+	0.834911i	$0.314481\pi$
$788$	−8.61476	−0.306888
$789$	16.3431	0.581830
$790$	11.2302	0.399553
$791$	19.6644	0.699185
$792$	11.1184	0.395075
$793$	−37.4970	−1.33156
$794$	14.9741	0.531410
$795$	−11.4580	−0.406374
$796$	3.39984	0.120504
$797$	−49.3338	−1.74749	−0.873746	−	0.486382i	$-0.838316\pi$
$797$	−49.3338	−1.74749	−0.873746	+	0.486382i	$0.838316\pi$
$798$	−17.3776	−0.615160
$799$	11.2066	0.396463
$800$	4.39497	0.155385
$801$	36.8225	1.30106
$802$	−9.06110	−0.319959
$803$	−4.22869	−0.149227
$804$	−16.8352	−0.593731
$805$	−7.49543	−0.264179
$806$	42.4841	1.49644
$807$	64.2367	2.26124
$808$	11.6712	0.410591
$809$	39.7258	1.39668	0.698342	−	0.715765i	$-0.253922\pi$
$809$	39.7258	1.39668	0.698342	+	0.715765i	$0.253922\pi$
$810$	8.48658	0.298188
$811$	43.5275	1.52846	0.764229	−	0.644945i	$-0.223120\pi$
$811$	43.5275	1.52846	0.764229	+	0.644945i	$0.223120\pi$
$812$	10.5753	0.371121
$813$	−43.9542	−1.54154
$814$	−4.13328	−0.144871
$815$	3.34916	0.117316
$816$	−7.45448	−0.260959
$817$	−33.9974	−1.18942
$818$	−8.39066	−0.293373
$819$	14.9043	0.520797
$820$	−3.49447	−0.122032
$821$	8.44763	0.294824	0.147412	−	0.989075i	$-0.452906\pi$
$821$	8.44763	0.294824	0.147412	+	0.989075i	$0.452906\pi$
$822$	32.0276	1.11709
$823$	17.8825	0.623345	0.311672	−	0.950190i	$-0.399111\pi$
$823$	17.8825	0.623345	0.311672	+	0.950190i	$0.399111\pi$
$824$	1.47057	0.0512298
$825$	−52.8951	−1.84157
$826$	13.9830	0.486532
$827$	−12.1374	−0.422060	−0.211030	−	0.977480i	$-0.567682\pi$
$827$	−12.1374	−0.422060	−0.211030	+	0.977480i	$0.567682\pi$
$828$	−13.5756	−0.471784
$829$	−7.89742	−0.274289	−0.137144	−	0.990551i	$-0.543792\pi$
$829$	−7.89742	−0.274289	−0.137144	+	0.990551i	$0.543792\pi$
$830$	−4.30381	−0.149387
$831$	58.2244	2.01978
$832$	4.84063	0.167819
$833$	−15.9191	−0.551564
$834$	18.3248	0.634536
$835$	−6.16344	−0.213294
$836$	27.8340	0.962658
$837$	−18.1500	−0.627356
$838$	6.41372	0.221558
$839$	29.5347	1.01965	0.509826	−	0.860278i	$-0.329710\pi$
$839$	29.5347	1.01965	0.509826	+	0.860278i	$0.329710\pi$
$840$	2.59249	0.0894493
$841$	22.1718	0.764545
$842$	29.3983	1.01313
$843$	−43.2738	−1.49043
$844$	−20.4374	−0.703485
$845$	8.11419	0.279136
$846$	−7.05888	−0.242689
$847$	25.8692	0.888876
$848$	6.53388	0.224374
$849$	−31.8452	−1.09292
$850$	14.5320	0.498443
$851$	5.04674	0.173000
$852$	−15.4753	−0.530177
$853$	12.4535	0.426400	0.213200	−	0.977009i	$-0.431611\pi$
$853$	12.4535	0.426400	0.213200	+	0.977009i	$0.431611\pi$
$854$	11.4518	0.391872
$855$	−8.44663	−0.288869
$856$	15.7898	0.539685
$857$	24.4254	0.834357	0.417178	−	0.908825i	$-0.363019\pi$
$857$	24.4254	0.834357	0.417178	+	0.908825i	$0.363019\pi$
$858$	−58.2588	−1.98892
$859$	−13.1205	−0.447665	−0.223833	−	0.974628i	$-0.571857\pi$
$859$	−13.1205	−0.447665	−0.223833	+	0.974628i	$0.571857\pi$
$860$	5.07192	0.172951
$861$	14.9733	0.510288
$862$	15.6998	0.534739
$863$	20.0576	0.682770	0.341385	−	0.939924i	$-0.389104\pi$
$863$	20.0576	0.682770	0.341385	+	0.939924i	$0.389104\pi$
$864$	−2.06801	−0.0703550
$865$	9.60466	0.326568
$866$	−1.05930	−0.0359964
$867$	13.6780	0.464528
$868$	−12.9749	−0.440396
$869$	77.0744	2.61457
$870$	12.5445	0.425299
$871$	36.1469	1.22479
$872$	−1.77419	−0.0600817
$873$	30.7915	1.04214
$874$	−33.9853	−1.14957
$875$	−10.8035	−0.365224
$876$	−1.78584	−0.0603378
$877$	−2.22645	−0.0751820	−0.0375910	−	0.999293i	$-0.511968\pi$
$877$	−2.22645	−0.0751820	−0.0375910	+	0.999293i	$0.511968\pi$
$878$	−12.8161	−0.432522
$879$	−53.7764	−1.81383
$880$	−4.15243	−0.139978
$881$	−10.2720	−0.346073	−0.173037	−	0.984915i	$-0.555358\pi$
$881$	−10.2720	−0.346073	−0.173037	+	0.984915i	$0.555358\pi$
$882$	10.0272	0.337632
$883$	23.8093	0.801247	0.400624	−	0.916243i	$-0.368794\pi$
$883$	23.8093	0.801247	0.400624	+	0.916243i	$0.368794\pi$
$884$	16.0056	0.538326
$885$	16.5867	0.557557
$886$	17.2957	0.581061
$887$	−10.0920	−0.338857	−0.169429	−	0.985542i	$-0.554192\pi$
$887$	−10.0920	−0.338857	−0.169429	+	0.985542i	$0.554192\pi$
$888$	−1.74554	−0.0585766
$889$	4.60564	0.154468
$890$	−13.7522	−0.460976
$891$	58.2444	1.95126
$892$	−24.8822	−0.833117
$893$	−17.6713	−0.591348
$894$	10.7707	0.360226
$895$	8.66554	0.289657
$896$	−1.47835	−0.0493883
$897$	71.1341	2.37510
$898$	−23.6905	−0.790563
$899$	−62.7827	−2.09392
$900$	−9.15346	−0.305115
$901$	21.6043	0.719745
$902$	−23.9830	−0.798545
$903$	−21.7324	−0.723210
$904$	−13.3015	−0.442403
$905$	−6.09764	−0.202692
$906$	−31.1638	−1.03535
$907$	−18.8697	−0.626558	−0.313279	−	0.949661i	$-0.601428\pi$
$907$	−18.8697	−0.626558	−0.313279	+	0.949661i	$0.601428\pi$
$908$	8.65724	0.287301
$909$	−24.3078	−0.806238
$910$	−5.56635	−0.184523
$911$	−44.2219	−1.46514	−0.732569	−	0.680693i	$-0.761679\pi$
$911$	−44.2219	−1.46514	−0.732569	+	0.680693i	$0.761679\pi$
$912$	11.7547	0.389237
$913$	−29.5376	−0.977552
$914$	24.3387	0.805054
$915$	13.5841	0.449078
$916$	0.669525	0.0221217
$917$	22.5561	0.744868
$918$	−6.83788	−0.225684
$919$	21.0238	0.693510	0.346755	−	0.937956i	$-0.387284\pi$
$919$	21.0238	0.693510	0.346755	+	0.937956i	$0.387284\pi$
$920$	5.07012	0.167157
$921$	−27.9059	−0.919529
$922$	10.3623	0.341264
$923$	33.2272	1.09369
$924$	17.7926	0.585332
$925$	3.40281	0.111884
$926$	15.0933	0.495997
$927$	−3.06278	−0.100595
$928$	−7.15345	−0.234823
$929$	56.4325	1.85149	0.925745	−	0.378149i	$-0.123439\pi$
$929$	56.4325	1.85149	0.925745	+	0.378149i	$0.123439\pi$
$930$	−15.3909	−0.504686
$931$	25.1022	0.822691
$932$	−5.74535	−0.188195
$933$	−40.9418	−1.34037
$934$	3.09640	0.101317
$935$	−13.7300	−0.449021
$936$	−10.0817	−0.329529
$937$	26.9087	0.879070	0.439535	−	0.898226i	$-0.355143\pi$
$937$	26.9087	0.879070	0.439535	+	0.898226i	$0.355143\pi$
$938$	−11.0395	−0.360451
$939$	−29.1507	−0.951299
$940$	2.63631	0.0859869
$941$	−37.0133	−1.20660	−0.603299	−	0.797515i	$-0.706148\pi$
$941$	−37.0133	−1.20660	−0.603299	+	0.797515i	$0.706148\pi$
$942$	−43.5119	−1.41769
$943$	29.2832	0.953593
$944$	−9.45851	−0.307848
$945$	2.37805	0.0773579
$946$	34.8092	1.13175
$947$	−25.5800	−0.831240	−0.415620	−	0.909538i	$-0.636435\pi$
$947$	−25.5800	−0.831240	−0.415620	+	0.909538i	$0.636435\pi$
$948$	32.5496	1.05716
$949$	3.83439	0.124469
$950$	−22.9149	−0.743459
$951$	−64.2785	−2.08437
$952$	−4.88819	−0.158427
$953$	50.2201	1.62679	0.813394	−	0.581713i	$-0.197617\pi$
$953$	50.2201	1.62679	0.813394	+	0.581713i	$0.197617\pi$
$954$	−13.6082	−0.440582
$955$	12.0336	0.389398
$956$	−13.7133	−0.443519
$957$	86.0945	2.78304
$958$	3.93727	0.127208
$959$	21.0017	0.678182
$960$	−1.75363	−0.0565982
$961$	46.0282	1.48478
$962$	3.74787	0.120836
$963$	−32.8857	−1.05973
$964$	−6.26556	−0.201800
$965$	−1.44090	−0.0463841
$966$	−21.7247	−0.698982
$967$	−39.9531	−1.28481	−0.642403	−	0.766367i	$-0.722062\pi$
$967$	−39.9531	−1.28481	−0.642403	+	0.766367i	$0.722062\pi$
$968$	−17.4986	−0.562428
$969$	38.8670	1.24859
$970$	−11.4998	−0.369237
$971$	−18.3367	−0.588453	−0.294227	−	0.955736i	$-0.595062\pi$
$971$	−18.3367	−0.588453	−0.294227	+	0.955736i	$0.595062\pi$
$972$	18.3934	0.589970
$973$	12.0163	0.385224
$974$	5.14467	0.164846
$975$	47.9629	1.53604
$976$	−7.74630	−0.247953
$977$	37.2253	1.19094	0.595471	−	0.803377i	$-0.296965\pi$
$977$	37.2253	1.19094	0.595471	+	0.803377i	$0.296965\pi$
$978$	9.70718	0.310402
$979$	−94.3832	−3.01650
$980$	−3.74489	−0.119626
$981$	3.69513	0.117977
$982$	16.2144	0.517423
$983$	−0.682045	−0.0217539	−0.0108769	−	0.999941i	$-0.503462\pi$
$983$	−0.682045	−0.0217539	−0.0108769	+	0.999941i	$0.503462\pi$
$984$	−10.1283	−0.322880
$985$	−6.70091	−0.213509
$986$	−23.6529	−0.753263
$987$	−11.2962	−0.359562
$988$	−25.2386	−0.802946
$989$	−42.5021	−1.35149
$990$	8.64833	0.274862
$991$	24.3986	0.775046	0.387523	−	0.921860i	$-0.373331\pi$
$991$	24.3986	0.775046	0.387523	+	0.921860i	$0.373331\pi$
$992$	8.77657	0.278656
$993$	−39.2894	−1.24681
$994$	−10.1478	−0.321868
$995$	2.64453	0.0838374
$996$	−12.4742	−0.395259
$997$	−21.4518	−0.679385	−0.339693	−	0.940536i	$-0.610323\pi$
$997$	−21.4518	−0.679385	−0.339693	+	0.940536i	$0.610323\pi$
$998$	5.99196	0.189672
$999$	−1.60116	−0.0506584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.e.1.18	✓	91

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.e.1.18	✓	91	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.25449 q^{3} +1.00000 q^{4} +0.777840 q^{5} +2.25449 q^{6} +1.47835 q^{7} -1.00000 q^{8} +2.08272 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.25449 q^{3} +1.00000 q^{4} +0.777840 q^{5} +2.25449 q^{6} +1.47835 q^{7} -1.00000 q^{8} +2.08272 q^{9} -0.777840 q^{10} -5.33841 q^{11} -2.25449 q^{12} +4.84063 q^{13} -1.47835 q^{14} -1.75363 q^{15} +1.00000 q^{16} +3.30651 q^{17} -2.08272 q^{18} -5.21391 q^{19} +0.777840 q^{20} -3.33293 q^{21} +5.33841 q^{22} -6.51821 q^{23} +2.25449 q^{24} -4.39497 q^{25} -4.84063 q^{26} +2.06801 q^{27} +1.47835 q^{28} +7.15345 q^{29} +1.75363 q^{30} -8.77657 q^{31} -1.00000 q^{32} +12.0354 q^{33} -3.30651 q^{34} +1.14992 q^{35} +2.08272 q^{36} -0.774253 q^{37} +5.21391 q^{38} -10.9131 q^{39} -0.777840 q^{40} -4.49253 q^{41} +3.33293 q^{42} +6.52052 q^{43} -5.33841 q^{44} +1.62002 q^{45} +6.51821 q^{46} +3.38927 q^{47} -2.25449 q^{48} -4.81447 q^{49} +4.39497 q^{50} -7.45448 q^{51} +4.84063 q^{52} +6.53388 q^{53} -2.06801 q^{54} -4.15243 q^{55} -1.47835 q^{56} +11.7547 q^{57} -7.15345 q^{58} -9.45851 q^{59} -1.75363 q^{60} -7.74630 q^{61} +8.77657 q^{62} +3.07899 q^{63} +1.00000 q^{64} +3.76523 q^{65} -12.0354 q^{66} +7.46740 q^{67} +3.30651 q^{68} +14.6952 q^{69} -1.14992 q^{70} +6.86424 q^{71} -2.08272 q^{72} +0.792125 q^{73} +0.774253 q^{74} +9.90840 q^{75} -5.21391 q^{76} -7.89206 q^{77} +10.9131 q^{78} -14.4377 q^{79} +0.777840 q^{80} -10.9104 q^{81} +4.49253 q^{82} +5.53303 q^{83} -3.33293 q^{84} +2.57193 q^{85} -6.52052 q^{86} -16.1274 q^{87} +5.33841 q^{88} +17.6800 q^{89} -1.62002 q^{90} +7.15616 q^{91} -6.51821 q^{92} +19.7867 q^{93} -3.38927 q^{94} -4.05558 q^{95} +2.25449 q^{96} +14.7843 q^{97} +4.81447 q^{98} -11.1184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9}+O(q^{10}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9	\( 91 q - 91 q^{2} - 2 q^{3} + 91 q^{4} + 22 q^{5} + 2 q^{6} - 14 q^{7} - 91 q^{8} + 123 q^{9} - 22 q^{10} + 59 q^{11} - 2 q^{12} - 15 q^{13} + 14 q^{14} + 23 q^{15} + 91 q^{16} + 25 q^{17} - 123 q^{18} + 2 q^{19} + 22 q^{20} + 20 q^{21} - 59 q^{22} + 36 q^{23} + 2 q^{24} + 121 q^{25} + 15 q^{26} - 8 q^{27} - 14 q^{28} + 71 q^{29} - 23 q^{30} + 13 q^{31} - 91 q^{32} + 24 q^{33} - 25 q^{34} + 27 q^{35} + 123 q^{36} + 5 q^{37} - 2 q^{38} + 48 q^{39} - 22 q^{40} + 77 q^{41} - 20 q^{42} - 36 q^{43} + 59 q^{44} + 62 q^{45} - 36 q^{46} + 41 q^{47} - 2 q^{48} + 137 q^{49} - 121 q^{50} + 13 q^{51} - 15 q^{52} + 33 q^{53} + 8 q^{54} + 12 q^{55} + 14 q^{56} + 52 q^{57} - 71 q^{58} + 76 q^{59} + 23 q^{60} + 18 q^{61} - 13 q^{62} - 18 q^{63} + 91 q^{64} + 84 q^{65} - 24 q^{66} - 59 q^{67} + 25 q^{68} + 64 q^{69} - 27 q^{70} + 124 q^{71} - 123 q^{72} + 43 q^{73} - 5 q^{74} + 9 q^{75} + 2 q^{76} + 50 q^{77} - 48 q^{78} - 20 q^{79} + 22 q^{80} + 227 q^{81} - 77 q^{82} + 29 q^{83} + 20 q^{84} + 3 q^{85} + 36 q^{86} - 25 q^{87} - 59 q^{88} + 148 q^{89} - 62 q^{90} + 27 q^{91} + 36 q^{92} + 65 q^{93} - 41 q^{94} + 54 q^{95} + 2 q^{96} + 38 q^{97} - 137 q^{98} + 157 q^{99}+O(q^{100}) \) 91 * q - 91 * q^2 - 2 * q^3 + 91 * q^4 + 22 * q^5 + 2 * q^6 - 14 * q^7 - 91 * q^8 + 123 * q^9 - 22 * q^10 + 59 * q^11 - 2 * q^12 - 15 * q^13 + 14 * q^14 + 23 * q^15 + 91 * q^16 + 25 * q^17 - 123 * q^18 + 2 * q^19 + 22 * q^20 + 20 * q^21 - 59 * q^22 + 36 * q^23 + 2 * q^24 + 121 * q^25 + 15 * q^26 - 8 * q^27 - 14 * q^28 + 71 * q^29 - 23 * q^30 + 13 * q^31 - 91 * q^32 + 24 * q^33 - 25 * q^34 + 27 * q^35 + 123 * q^36 + 5 * q^37 - 2 * q^38 + 48 * q^39 - 22 * q^40 + 77 * q^41 - 20 * q^42 - 36 * q^43 + 59 * q^44 + 62 * q^45 - 36 * q^46 + 41 * q^47 - 2 * q^48 + 137 * q^49 - 121 * q^50 + 13 * q^51 - 15 * q^52 + 33 * q^53 + 8 * q^54 + 12 * q^55 + 14 * q^56 + 52 * q^57 - 71 * q^58 + 76 * q^59 + 23 * q^60 + 18 * q^61 - 13 * q^62 - 18 * q^63 + 91 * q^64 + 84 * q^65 - 24 * q^66 - 59 * q^67 + 25 * q^68 + 64 * q^69 - 27 * q^70 + 124 * q^71 - 123 * q^72 + 43 * q^73 - 5 * q^74 + 9 * q^75 + 2 * q^76 + 50 * q^77 - 48 * q^78 - 20 * q^79 + 22 * q^80 + 227 * q^81 - 77 * q^82 + 29 * q^83 + 20 * q^84 + 3 * q^85 + 36 * q^86 - 25 * q^87 - 59 * q^88 + 148 * q^89 - 62 * q^90 + 27 * q^91 + 36 * q^92 + 65 * q^93 - 41 * q^94 + 54 * q^95 + 2 * q^96 + 38 * q^97 - 137 * q^98 + 157 * q^99

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