LMFDB - Embedded newform 717.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,2,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, 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("717.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	717.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:	$5.72527382493$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.2585660609.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 4x^{6} + 15x^{5} + x^{4} - 19x^{3} + 6x^{2} + 3x - 1 $ x^8 - 3x^7 - 4x^6 + 15x^5 + x^4 - 19x^3 + 6x^2 + 3x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.74142$ of defining polynomial
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37665 q^{2} +1.00000 q^{3} +3.64845 q^{4} +0.0257644 q^{5} -2.37665 q^{6} +0.278803 q^{7} -3.91777 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.37665 q^{2} +1.00000 q^{3} +3.64845 q^{4} +0.0257644 q^{5} -2.37665 q^{6} +0.278803 q^{7} -3.91777 q^{8} +1.00000 q^{9} -0.0612329 q^{10} -2.03679 q^{11} +3.64845 q^{12} -5.15341 q^{13} -0.662616 q^{14} +0.0257644 q^{15} +2.01427 q^{16} -6.10504 q^{17} -2.37665 q^{18} +7.62467 q^{19} +0.0940000 q^{20} +0.278803 q^{21} +4.84073 q^{22} -9.14155 q^{23} -3.91777 q^{24} -4.99934 q^{25} +12.2478 q^{26} +1.00000 q^{27} +1.01720 q^{28} -2.35001 q^{29} -0.0612329 q^{30} +2.04609 q^{31} +3.04835 q^{32} -2.03679 q^{33} +14.5095 q^{34} +0.00718319 q^{35} +3.64845 q^{36} -1.68276 q^{37} -18.1211 q^{38} -5.15341 q^{39} -0.100939 q^{40} -5.01835 q^{41} -0.662616 q^{42} +6.43995 q^{43} -7.43111 q^{44} +0.0257644 q^{45} +21.7262 q^{46} +6.24342 q^{47} +2.01427 q^{48} -6.92227 q^{49} +11.8817 q^{50} -6.10504 q^{51} -18.8019 q^{52} +7.02807 q^{53} -2.37665 q^{54} -0.0524766 q^{55} -1.09229 q^{56} +7.62467 q^{57} +5.58513 q^{58} +0.590925 q^{59} +0.0940000 q^{60} +12.7963 q^{61} -4.86283 q^{62} +0.278803 q^{63} -11.2734 q^{64} -0.132774 q^{65} +4.84073 q^{66} -13.7116 q^{67} -22.2739 q^{68} -9.14155 q^{69} -0.0170719 q^{70} -13.1943 q^{71} -3.91777 q^{72} -15.7242 q^{73} +3.99933 q^{74} -4.99934 q^{75} +27.8182 q^{76} -0.567863 q^{77} +12.2478 q^{78} -0.773284 q^{79} +0.0518964 q^{80} +1.00000 q^{81} +11.9268 q^{82} -0.895907 q^{83} +1.01720 q^{84} -0.157293 q^{85} -15.3055 q^{86} -2.35001 q^{87} +7.97967 q^{88} -11.3261 q^{89} -0.0612329 q^{90} -1.43679 q^{91} -33.3524 q^{92} +2.04609 q^{93} -14.8384 q^{94} +0.196445 q^{95} +3.04835 q^{96} -7.22776 q^{97} +16.4518 q^{98} -2.03679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 5 q^{2} + 8 q^{3} + 7 q^{4} - 13 q^{5} - 5 q^{6} - 7 q^{7} - 15 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 5 * q^2 + 8 * q^3 + 7 * q^4 - 13 * q^5 - 5 * q^6 - 7 * q^7 - 15 * q^8 + 8 * q^9	\( 8 q - 5 q^{2} + 8 q^{3} + 7 q^{4} - 13 q^{5} - 5 q^{6} - 7 q^{7} - 15 q^{8} + 8 q^{9} + 4 q^{10} - 19 q^{11} + 7 q^{12} - 3 q^{13} - 8 q^{14} - 13 q^{15} + 9 q^{16} - 13 q^{17} - 5 q^{18} - 6 q^{19} - 18 q^{20} - 7 q^{21} + 3 q^{22} - 18 q^{23} - 15 q^{24} + 7 q^{25} + 8 q^{27} - 2 q^{28} - 10 q^{29} + 4 q^{30} - 2 q^{31} - 20 q^{32} - 19 q^{33} - 4 q^{34} - 7 q^{35} + 7 q^{36} - 8 q^{37} + 9 q^{38} - 3 q^{39} + 29 q^{40} - 22 q^{41} - 8 q^{42} - 24 q^{43} - 7 q^{44} - 13 q^{45} + 30 q^{46} - 17 q^{47} + 9 q^{48} + 15 q^{49} + 24 q^{50} - 13 q^{51} + 22 q^{52} - 5 q^{54} + 32 q^{55} + 19 q^{56} - 6 q^{57} + 18 q^{58} - 24 q^{59} - 18 q^{60} + 10 q^{61} + 30 q^{62} - 7 q^{63} + 33 q^{64} - 17 q^{65} + 3 q^{66} - 48 q^{67} - 21 q^{68} - 18 q^{69} + 31 q^{70} - 17 q^{71} - 15 q^{72} + 2 q^{73} + 9 q^{74} + 7 q^{75} + 10 q^{76} + 10 q^{77} + 17 q^{79} + 8 q^{80} + 8 q^{81} - 17 q^{82} - 37 q^{83} - 2 q^{84} + 28 q^{85} - q^{86} - 10 q^{87} + 15 q^{88} - 41 q^{89} + 4 q^{90} - 39 q^{91} - 38 q^{92} - 2 q^{93} + 2 q^{94} + 16 q^{95} - 20 q^{96} - 20 q^{97} + 46 q^{98} - 19 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 8 * q^3 + 7 * q^4 - 13 * q^5 - 5 * q^6 - 7 * q^7 - 15 * q^8 + 8 * q^9 + 4 * q^10 - 19 * q^11 + 7 * q^12 - 3 * q^13 - 8 * q^14 - 13 * q^15 + 9 * q^16 - 13 * q^17 - 5 * q^18 - 6 * q^19 - 18 * q^20 - 7 * q^21 + 3 * q^22 - 18 * q^23 - 15 * q^24 + 7 * q^25 + 8 * q^27 - 2 * q^28 - 10 * q^29 + 4 * q^30 - 2 * q^31 - 20 * q^32 - 19 * q^33 - 4 * q^34 - 7 * q^35 + 7 * q^36 - 8 * q^37 + 9 * q^38 - 3 * q^39 + 29 * q^40 - 22 * q^41 - 8 * q^42 - 24 * q^43 - 7 * q^44 - 13 * q^45 + 30 * q^46 - 17 * q^47 + 9 * q^48 + 15 * q^49 + 24 * q^50 - 13 * q^51 + 22 * q^52 - 5 * q^54 + 32 * q^55 + 19 * q^56 - 6 * q^57 + 18 * q^58 - 24 * q^59 - 18 * q^60 + 10 * q^61 + 30 * q^62 - 7 * q^63 + 33 * q^64 - 17 * q^65 + 3 * q^66 - 48 * q^67 - 21 * q^68 - 18 * q^69 + 31 * q^70 - 17 * q^71 - 15 * q^72 + 2 * q^73 + 9 * q^74 + 7 * q^75 + 10 * q^76 + 10 * q^77 + 17 * q^79 + 8 * q^80 + 8 * q^81 - 17 * q^82 - 37 * q^83 - 2 * q^84 + 28 * q^85 - q^86 - 10 * q^87 + 15 * q^88 - 41 * q^89 + 4 * q^90 - 39 * q^91 - 38 * q^92 - 2 * q^93 + 2 * q^94 + 16 * q^95 - 20 * q^96 - 20 * q^97 + 46 * q^98 - 19 * 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 $

$2$	−2.37665	−1.68054	−0.840271	−	0.542166i	$-0.817604\pi$
$2$	−2.37665	−1.68054	−0.840271	+	0.542166i	$0.817604\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.64845	1.82422
$5$	0.0257644	0.0115222	0.00576110	−	0.999983i	$-0.498166\pi$
$5$	0.0257644	0.0115222	0.00576110	+	0.999983i	$0.498166\pi$
$6$	−2.37665	−0.970262
$7$	0.278803	0.105378	0.0526888	−	0.998611i	$-0.483221\pi$
$7$	0.278803	0.105378	0.0526888	+	0.998611i	$0.483221\pi$
$8$	−3.91777	−1.38514
$9$	1.00000	0.333333
$10$	−0.0612329	−0.0193635
$11$	−2.03679	−0.614115	−0.307057	−	0.951691i	$-0.599344\pi$
$11$	−2.03679	−0.614115	−0.307057	+	0.951691i	$0.599344\pi$
$12$	3.64845	1.05322
$13$	−5.15341	−1.42930	−0.714649	−	0.699483i	$-0.753414\pi$
$13$	−5.15341	−1.42930	−0.714649	+	0.699483i	$0.753414\pi$
$14$	−0.662616	−0.177092
$15$	0.0257644	0.00665234
$16$	2.01427	0.503567
$17$	−6.10504	−1.48069	−0.740345	−	0.672227i	$-0.765338\pi$
$17$	−6.10504	−1.48069	−0.740345	+	0.672227i	$0.765338\pi$
$18$	−2.37665	−0.560181
$19$	7.62467	1.74922	0.874610	−	0.484828i	$-0.161118\pi$
$19$	7.62467	1.74922	0.874610	+	0.484828i	$0.161118\pi$
$20$	0.0940000	0.0210190
$21$	0.278803	0.0608398
$22$	4.84073	1.03205
$23$	−9.14155	−1.90614	−0.953072	−	0.302744i	$-0.902097\pi$
$23$	−9.14155	−1.90614	−0.953072	+	0.302744i	$0.902097\pi$
$24$	−3.91777	−0.799712
$25$	−4.99934	−0.999867
$26$	12.2478	2.40200
$27$	1.00000	0.192450
$28$	1.01720	0.192232
$29$	−2.35001	−0.436385	−0.218193	−	0.975906i	$-0.570016\pi$
$29$	−2.35001	−0.436385	−0.218193	+	0.975906i	$0.570016\pi$
$30$	−0.0612329	−0.0111795
$31$	2.04609	0.367488	0.183744	−	0.982974i	$-0.441178\pi$
$31$	2.04609	0.367488	0.183744	+	0.982974i	$0.441178\pi$
$32$	3.04835	0.538877
$33$	−2.03679	−0.354559
$34$	14.5095	2.48836
$35$	0.00718319	0.00121418
$36$	3.64845	0.608074
$37$	−1.68276	−0.276644	−0.138322	−	0.990387i	$-0.544171\pi$
$37$	−1.68276	−0.276644	−0.138322	+	0.990387i	$0.544171\pi$
$38$	−18.1211	−2.93964
$39$	−5.15341	−0.825206
$40$	−0.100939	−0.0159599
$41$	−5.01835	−0.783735	−0.391867	−	0.920022i	$-0.628171\pi$
$41$	−5.01835	−0.783735	−0.391867	+	0.920022i	$0.628171\pi$
$42$	−0.662616	−0.102244
$43$	6.43995	0.982083	0.491041	−	0.871136i	$-0.336616\pi$
$43$	6.43995	0.982083	0.491041	+	0.871136i	$0.336616\pi$
$44$	−7.43111	−1.12028
$45$	0.0257644	0.00384073
$46$	21.7262	3.20336
$47$	6.24342	0.910697	0.455348	−	0.890313i	$-0.349515\pi$
$47$	6.24342	0.910697	0.455348	+	0.890313i	$0.349515\pi$
$48$	2.01427	0.290734
$49$	−6.92227	−0.988896
$50$	11.8817	1.68032
$51$	−6.10504	−0.854877
$52$	−18.8019	−2.60736
$53$	7.02807	0.965380	0.482690	−	0.875791i	$-0.339660\pi$
$53$	7.02807	0.965380	0.482690	+	0.875791i	$0.339660\pi$
$54$	−2.37665	−0.323421
$55$	−0.0524766	−0.00707595
$56$	−1.09229	−0.145963
$57$	7.62467	1.00991
$58$	5.58513	0.733364
$59$	0.590925	0.0769319	0.0384659	−	0.999260i	$-0.487753\pi$
$59$	0.590925	0.0769319	0.0384659	+	0.999260i	$0.487753\pi$
$60$	0.0940000	0.0121354
$61$	12.7963	1.63840	0.819199	−	0.573509i	$-0.194418\pi$
$61$	12.7963	1.63840	0.819199	+	0.573509i	$0.194418\pi$
$62$	−4.86283	−0.617580
$63$	0.278803	0.0351259
$64$	−11.2734	−1.40917
$65$	−0.132774	−0.0164686
$66$	4.84073	0.595852
$67$	−13.7116	−1.67514	−0.837568	−	0.546333i	$-0.816023\pi$
$67$	−13.7116	−1.67514	−0.837568	+	0.546333i	$0.816023\pi$
$68$	−22.2739	−2.70111
$69$	−9.14155	−1.10051
$70$	−0.0170719	−0.00204048
$71$	−13.1943	−1.56588	−0.782938	−	0.622099i	$-0.786280\pi$
$71$	−13.1943	−1.56588	−0.782938	+	0.622099i	$0.786280\pi$
$72$	−3.91777	−0.461714
$73$	−15.7242	−1.84038	−0.920190	−	0.391473i	$-0.871966\pi$
$73$	−15.7242	−1.84038	−0.920190	+	0.391473i	$0.871966\pi$
$74$	3.99933	0.464912
$75$	−4.99934	−0.577274
$76$	27.8182	3.19097
$77$	−0.567863	−0.0647139
$78$	12.2478	1.38679
$79$	−0.773284	−0.0870013	−0.0435006	−	0.999053i	$-0.513851\pi$
$79$	−0.773284	−0.0870013	−0.0435006	+	0.999053i	$0.513851\pi$
$80$	0.0518964	0.00580219
$81$	1.00000	0.111111
$82$	11.9268	1.31710
$83$	−0.895907	−0.0983386	−0.0491693	−	0.998790i	$-0.515657\pi$
$83$	−0.895907	−0.0983386	−0.0491693	+	0.998790i	$0.515657\pi$
$84$	1.01720	0.110985
$85$	−0.157293	−0.0170608
$86$	−15.3055	−1.65043
$87$	−2.35001	−0.251947
$88$	7.97967	0.850636
$89$	−11.3261	−1.20056	−0.600282	−	0.799789i	$-0.704945\pi$
$89$	−11.3261	−1.20056	−0.600282	+	0.799789i	$0.704945\pi$
$90$	−0.0612329	−0.00645451
$91$	−1.43679	−0.150616
$92$	−33.3524	−3.47723
$93$	2.04609	0.212169
$94$	−14.8384	−1.53046
$95$	0.196445	0.0201548
$96$	3.04835	0.311121
$97$	−7.22776	−0.733868	−0.366934	−	0.930247i	$-0.619593\pi$
$97$	−7.22776	−0.733868	−0.366934	+	0.930247i	$0.619593\pi$
$98$	16.4518	1.66188
$99$	−2.03679	−0.204705
$100$	−18.2398	−1.82398
$101$	16.8027	1.67194	0.835968	−	0.548779i	$-0.184907\pi$
$101$	16.8027	1.67194	0.835968	+	0.548779i	$0.184907\pi$
$102$	14.5095	1.43666
$103$	−19.3974	−1.91128	−0.955639	−	0.294539i	$-0.904834\pi$
$103$	−19.3974	−1.91128	−0.955639	+	0.294539i	$0.904834\pi$
$104$	20.1899	1.97978
$105$	0.00718319	0.000701008 0
$106$	−16.7032	−1.62236
$107$	6.11779	0.591429	0.295715	−	0.955276i	$-0.404442\pi$
$107$	6.11779	0.591429	0.295715	+	0.955276i	$0.404442\pi$
$108$	3.64845	0.351072
$109$	−7.56214	−0.724322	−0.362161	−	0.932116i	$-0.617961\pi$
$109$	−7.56214	−0.724322	−0.362161	+	0.932116i	$0.617961\pi$
$110$	0.124718	0.0118914
$111$	−1.68276	−0.159721
$112$	0.561584	0.0530647
$113$	15.2645	1.43596	0.717982	−	0.696061i	$-0.245066\pi$
$113$	15.2645	1.43596	0.717982	+	0.696061i	$0.245066\pi$
$114$	−18.1211	−1.69720
$115$	−0.235526	−0.0219630
$116$	−8.57387	−0.796064
$117$	−5.15341	−0.476433
$118$	−1.40442	−0.129287
$119$	−1.70210	−0.156032
$120$	−0.100939	−0.00921444
$121$	−6.85149	−0.622863
$122$	−30.4123	−2.75340
$123$	−5.01835	−0.452489
$124$	7.46504	0.670381
$125$	−0.257627	−0.0230429
$126$	−0.662616	−0.0590305
$127$	12.1796	1.08076	0.540382	−	0.841420i	$-0.318280\pi$
$127$	12.1796	1.08076	0.540382	+	0.841420i	$0.318280\pi$
$128$	20.6961	1.82930
$129$	6.43995	0.567006
$130$	0.315558	0.0276763
$131$	−19.1767	−1.67548	−0.837740	−	0.546069i	$-0.816124\pi$
$131$	−19.1767	−1.67548	−0.837740	+	0.546069i	$0.816124\pi$
$132$	−7.43111	−0.646795
$133$	2.12578	0.184329
$134$	32.5876	2.81514
$135$	0.0257644	0.00221745
$136$	23.9182	2.05097
$137$	13.4380	1.14809	0.574043	−	0.818825i	$-0.305374\pi$
$137$	13.4380	1.14809	0.574043	+	0.818825i	$0.305374\pi$
$138$	21.7262	1.84946
$139$	0.557919	0.0473221	0.0236611	−	0.999720i	$-0.492468\pi$
$139$	0.557919	0.0473221	0.0236611	+	0.999720i	$0.492468\pi$
$140$	0.0262075	0.00221494
$141$	6.24342	0.525791
$142$	31.3582	2.63152
$143$	10.4964	0.877753
$144$	2.01427	0.167856
$145$	−0.0605465	−0.00502811
$146$	37.3709	3.09284
$147$	−6.92227	−0.570939
$148$	−6.13946	−0.504661
$149$	12.3376	1.01074	0.505369	−	0.862903i	$-0.331356\pi$
$149$	12.3376	1.01074	0.505369	+	0.862903i	$0.331356\pi$
$150$	11.8817	0.970133
$151$	21.2706	1.73098	0.865490	−	0.500926i	$-0.167007\pi$
$151$	21.2706	1.73098	0.865490	+	0.500926i	$0.167007\pi$
$152$	−29.8717	−2.42292
$153$	−6.10504	−0.493563
$154$	1.34961	0.108755
$155$	0.0527162	0.00423427
$156$	−18.8019	−1.50536
$157$	5.45605	0.435440	0.217720	−	0.976011i	$-0.430138\pi$
$157$	5.45605	0.435440	0.217720	+	0.976011i	$0.430138\pi$
$158$	1.83782	0.146209
$159$	7.02807	0.557362
$160$	0.0785388	0.00620904
$161$	−2.54869	−0.200865
$162$	−2.37665	−0.186727
$163$	−14.4183	−1.12933	−0.564664	−	0.825321i	$-0.690994\pi$
$163$	−14.4183	−1.12933	−0.564664	+	0.825321i	$0.690994\pi$
$164$	−18.3092	−1.42971
$165$	−0.0524766	−0.00408530
$166$	2.12925	0.165262
$167$	−7.79493	−0.603190	−0.301595	−	0.953436i	$-0.597519\pi$
$167$	−7.79493	−0.603190	−0.301595	+	0.953436i	$0.597519\pi$
$168$	−1.09229	−0.0842717
$169$	13.5576	1.04289
$170$	0.373829	0.0286714
$171$	7.62467	0.583073
$172$	23.4958	1.79154
$173$	−6.30699	−0.479512	−0.239756	−	0.970833i	$-0.577067\pi$
$173$	−6.30699	−0.479512	−0.239756	+	0.970833i	$0.577067\pi$
$174$	5.58513	0.423408
$175$	−1.39383	−0.105364
$176$	−4.10264	−0.309248
$177$	0.590925	0.0444166
$178$	26.9181	2.01760
$179$	4.21211	0.314828	0.157414	−	0.987533i	$-0.449684\pi$
$179$	4.21211	0.314828	0.157414	+	0.987533i	$0.449684\pi$
$180$	0.0940000	0.00700635
$181$	3.08536	0.229333	0.114666	−	0.993404i	$-0.463420\pi$
$181$	3.08536	0.229333	0.114666	+	0.993404i	$0.463420\pi$
$182$	3.41473	0.253117
$183$	12.7963	0.945930
$184$	35.8145	2.64028
$185$	−0.0433553	−0.00318755
$186$	−4.86283	−0.356560
$187$	12.4347	0.909314
$188$	22.7788	1.66131
$189$	0.278803	0.0202799
$190$	−0.466880	−0.0338711
$191$	15.4370	1.11698	0.558491	−	0.829510i	$-0.311380\pi$
$191$	15.4370	1.11698	0.558491	+	0.829510i	$0.311380\pi$
$192$	−11.2734	−0.813586
$193$	22.0775	1.58917	0.794585	−	0.607153i	$-0.207688\pi$
$193$	22.0775	1.58917	0.794585	+	0.607153i	$0.207688\pi$
$194$	17.1778	1.23330
$195$	−0.132774	−0.00950818
$196$	−25.2555	−1.80397
$197$	−15.3584	−1.09424	−0.547120	−	0.837055i	$-0.684276\pi$
$197$	−15.3584	−1.09424	−0.547120	+	0.837055i	$0.684276\pi$
$198$	4.84073	0.344015
$199$	15.0703	1.06830	0.534152	−	0.845388i	$-0.320631\pi$
$199$	15.0703	1.06830	0.534152	+	0.845388i	$0.320631\pi$
$200$	19.5863	1.38496
$201$	−13.7116	−0.967140
$202$	−39.9342	−2.80976
$203$	−0.655189	−0.0459852
$204$	−22.2739	−1.55949
$205$	−0.129295	−0.00903034
$206$	46.1007	3.21199
$207$	−9.14155	−0.635381
$208$	−10.3803	−0.719747
$209$	−15.5298	−1.07422
$210$	−0.0170719	−0.00117807
$211$	−10.7626	−0.740929	−0.370465	−	0.928847i	$-0.620802\pi$
$211$	−10.7626	−0.740929	−0.370465	+	0.928847i	$0.620802\pi$
$212$	25.6415	1.76107
$213$	−13.1943	−0.904059
$214$	−14.5398	−0.993922
$215$	0.165921	0.0113157
$216$	−3.91777	−0.266571
$217$	0.570455	0.0387250
$218$	17.9725	1.21725
$219$	−15.7242	−1.06254
$220$	−0.191458	−0.0129081
$221$	31.4618	2.11635
$222$	3.99933	0.268417
$223$	−14.1459	−0.947278	−0.473639	−	0.880719i	$-0.657060\pi$
$223$	−14.1459	−0.947278	−0.473639	+	0.880719i	$0.657060\pi$
$224$	0.849888	0.0567855
$225$	−4.99934	−0.333289
$226$	−36.2783	−2.41320
$227$	−12.9750	−0.861179	−0.430590	−	0.902548i	$-0.641694\pi$
$227$	−12.9750	−0.861179	−0.430590	+	0.902548i	$0.641694\pi$
$228$	27.8182	1.84231
$229$	−6.75261	−0.446225	−0.223112	−	0.974793i	$-0.571622\pi$
$229$	−6.75261	−0.446225	−0.223112	+	0.974793i	$0.571622\pi$
$230$	0.559763	0.0369097
$231$	−0.567863	−0.0373626
$232$	9.20679	0.604455
$233$	6.46492	0.423531	0.211766	−	0.977320i	$-0.432079\pi$
$233$	6.46492	0.423531	0.211766	+	0.977320i	$0.432079\pi$
$234$	12.2478	0.800665
$235$	0.160858	0.0104932
$236$	2.15596	0.140341
$237$	−0.773284	−0.0502302
$238$	4.04530	0.262218
$239$	1.00000	0.0646846
$239$	1.00000	0.0646846
$240$	0.0518964	0.00334990
$241$	7.00103	0.450976	0.225488	−	0.974246i	$-0.427602\pi$
$241$	7.00103	0.450976	0.225488	+	0.974246i	$0.427602\pi$
$242$	16.2836	1.04675
$243$	1.00000	0.0641500
$244$	46.6866	2.98880
$245$	−0.178348	−0.0113942
$246$	11.9268	0.760428
$247$	−39.2930	−2.50016
$248$	−8.01611	−0.509023
$249$	−0.895907	−0.0567758
$250$	0.612288	0.0387245
$251$	−6.65566	−0.420102	−0.210051	−	0.977690i	$-0.567363\pi$
$251$	−6.65566	−0.420102	−0.210051	+	0.977690i	$0.567363\pi$
$252$	1.01720	0.0640774
$253$	18.6194	1.17059
$254$	−28.9466	−1.81627
$255$	−0.157293	−0.00985005
$256$	−26.6406	−1.66504
$257$	−29.2010	−1.82151	−0.910754	−	0.412950i	$-0.864498\pi$
$257$	−29.2010	−1.82151	−0.910754	+	0.412950i	$0.864498\pi$
$258$	−15.3055	−0.952877
$259$	−0.469159	−0.0291521
$260$	−0.484420	−0.0300425
$261$	−2.35001	−0.145462
$262$	45.5763	2.81572
$263$	8.29069	0.511226	0.255613	−	0.966779i	$-0.417723\pi$
$263$	8.29069	0.511226	0.255613	+	0.966779i	$0.417723\pi$
$264$	7.97967	0.491115
$265$	0.181074	0.0111233
$266$	−5.05223	−0.309772
$267$	−11.3261	−0.693145
$268$	−50.0260	−3.05582
$269$	10.3283	0.629728	0.314864	−	0.949137i	$-0.398041\pi$
$269$	10.3283	0.629728	0.314864	+	0.949137i	$0.398041\pi$
$270$	−0.0612329	−0.00372651
$271$	−3.51373	−0.213444	−0.106722	−	0.994289i	$-0.534035\pi$
$271$	−3.51373	−0.213444	−0.106722	+	0.994289i	$0.534035\pi$
$272$	−12.2972	−0.745626
$273$	−1.43679	−0.0869582
$274$	−31.9374	−1.92941
$275$	10.1826	0.614033
$276$	−33.3524	−2.00758
$277$	−2.30574	−0.138539	−0.0692693	−	0.997598i	$-0.522067\pi$
$277$	−2.30574	−0.138539	−0.0692693	+	0.997598i	$0.522067\pi$
$278$	−1.32598	−0.0795268
$279$	2.04609	0.122496
$280$	−0.0281421	−0.00168181
$281$	2.37399	0.141621	0.0708103	−	0.997490i	$-0.477442\pi$
$281$	2.37399	0.141621	0.0708103	+	0.997490i	$0.477442\pi$
$282$	−14.8384	−0.883614
$283$	7.74423	0.460347	0.230173	−	0.973150i	$-0.426071\pi$
$283$	7.74423	0.460347	0.230173	+	0.973150i	$0.426071\pi$
$284$	−48.1387	−2.85651
$285$	0.196445	0.0116364
$286$	−24.9462	−1.47510
$287$	−1.39913	−0.0825881
$288$	3.04835	0.179626
$289$	20.2715	1.19244
$290$	0.143898	0.00844996
$291$	−7.22776	−0.423699
$292$	−57.3689	−3.35726
$293$	21.6810	1.26662	0.633308	−	0.773900i	$-0.281697\pi$
$293$	21.6810	1.26662	0.633308	+	0.773900i	$0.281697\pi$
$294$	16.4518	0.959487
$295$	0.0152248	0.000886424 0
$296$	6.59268	0.383192
$297$	−2.03679	−0.118186
$298$	−29.3222	−1.69859
$299$	47.1101	2.72445
$300$	−18.2398	−1.05308
$301$	1.79548	0.103490
$302$	−50.5528	−2.90899
$303$	16.8027	0.965292
$304$	15.3581	0.880849
$305$	0.329689	0.0188779
$306$	14.5095	0.829454
$307$	7.75733	0.442734	0.221367	−	0.975191i	$-0.428948\pi$
$307$	7.75733	0.442734	0.221367	+	0.975191i	$0.428948\pi$
$308$	−2.07182	−0.118053
$309$	−19.3974	−1.10348
$310$	−0.125288	−0.00711587
$311$	21.5541	1.22222	0.611111	−	0.791545i	$-0.290723\pi$
$311$	21.5541	1.22222	0.611111	+	0.791545i	$0.290723\pi$
$312$	20.1899	1.14303
$313$	6.85326	0.387369	0.193685	−	0.981064i	$-0.437956\pi$
$313$	6.85326	0.387369	0.193685	+	0.981064i	$0.437956\pi$
$314$	−12.9671	−0.731776
$315$	0.00718319	0.000404727 0
$316$	−2.82129	−0.158710
$317$	−12.3935	−0.696089	−0.348044	−	0.937478i	$-0.613154\pi$
$317$	−12.3935	−0.696089	−0.348044	+	0.937478i	$0.613154\pi$
$318$	−16.7032	−0.936671
$319$	4.78646	0.267991
$320$	−0.290452	−0.0162367
$321$	6.11779	0.341462
$322$	6.05733	0.337562
$323$	−46.5489	−2.59005
$324$	3.64845	0.202691
$325$	25.7636	1.42911
$326$	34.2672	1.89788
$327$	−7.56214	−0.418187
$328$	19.6608	1.08558
$329$	1.74068	0.0959671
$330$	0.124718	0.00686552
$331$	−24.9260	−1.37006	−0.685029	−	0.728516i	$-0.740210\pi$
$331$	−24.9260	−1.37006	−0.685029	+	0.728516i	$0.740210\pi$
$332$	−3.26867	−0.179392
$333$	−1.68276	−0.0922147
$334$	18.5258	1.01369
$335$	−0.353271	−0.0193012
$336$	0.561584	0.0306369
$337$	4.98114	0.271340	0.135670	−	0.990754i	$-0.456681\pi$
$337$	4.98114	0.271340	0.135670	+	0.990754i	$0.456681\pi$
$338$	−32.2216	−1.75263
$339$	15.2645	0.829055
$340$	−0.573874	−0.0311227
$341$	−4.16745	−0.225680
$342$	−18.1211	−0.979879
$343$	−3.88157	−0.209585
$344$	−25.2303	−1.36032
$345$	−0.235526	−0.0126803
$346$	14.9895	0.805840
$347$	4.09751	0.219966	0.109983	−	0.993933i	$-0.464920\pi$
$347$	4.09751	0.219966	0.109983	+	0.993933i	$0.464920\pi$
$348$	−8.57387	−0.459608
$349$	−28.1421	−1.50641	−0.753207	−	0.657784i	$-0.771494\pi$
$349$	−28.1421	−1.50641	−0.753207	+	0.657784i	$0.771494\pi$
$350$	3.31264	0.177068
$351$	−5.15341	−0.275069
$352$	−6.20884	−0.330932
$353$	0.0904223	0.00481269	0.00240635	−	0.999997i	$-0.499234\pi$
$353$	0.0904223	0.00481269	0.00240635	+	0.999997i	$0.499234\pi$
$354$	−1.40442	−0.0746441
$355$	−0.339944	−0.0180423
$356$	−41.3226	−2.19009
$357$	−1.70210	−0.0900849
$358$	−10.0107	−0.529081
$359$	24.8752	1.31286	0.656432	−	0.754385i	$-0.272065\pi$
$359$	24.8752	1.31286	0.656432	+	0.754385i	$0.272065\pi$
$360$	−0.100939	−0.00531996
$361$	39.1356	2.05977
$362$	−7.33280	−0.385403
$363$	−6.85149	−0.359610
$364$	−5.24203	−0.274757
$365$	−0.405125	−0.0212052
$366$	−30.4123	−1.58967
$367$	−29.7572	−1.55331	−0.776657	−	0.629923i	$-0.783086\pi$
$367$	−29.7572	−1.55331	−0.776657	+	0.629923i	$0.783086\pi$
$368$	−18.4135	−0.959871
$369$	−5.01835	−0.261245
$370$	0.103040	0.00535681
$371$	1.95945	0.101729
$372$	7.46504	0.387044
$373$	−30.5940	−1.58410	−0.792049	−	0.610458i	$-0.790986\pi$
$373$	−30.5940	−1.58410	−0.792049	+	0.610458i	$0.790986\pi$
$374$	−29.5528	−1.52814
$375$	−0.257627	−0.0133038
$376$	−24.4603	−1.26144
$377$	12.1105	0.623724
$378$	−0.662616	−0.0340813
$379$	18.8693	0.969249	0.484625	−	0.874722i	$-0.338956\pi$
$379$	18.8693	0.969249	0.484625	+	0.874722i	$0.338956\pi$
$380$	0.716719	0.0367669
$381$	12.1796	0.623979
$382$	−36.6883	−1.87714
$383$	20.1842	1.03136	0.515682	−	0.856780i	$-0.327539\pi$
$383$	20.1842	1.03136	0.515682	+	0.856780i	$0.327539\pi$
$384$	20.6961	1.05614
$385$	−0.0146306	−0.000745647 0
$386$	−52.4703	−2.67067
$387$	6.43995	0.327361
$388$	−26.3701	−1.33874
$389$	15.0307	0.762086	0.381043	−	0.924557i	$-0.375565\pi$
$389$	15.0307	0.762086	0.381043	+	0.924557i	$0.375565\pi$
$390$	0.315558	0.0159789
$391$	55.8095	2.82241
$392$	27.1199	1.36976
$393$	−19.1767	−0.967339
$394$	36.5014	1.83892
$395$	−0.0199232	−0.00100245
$396$	−7.43111	−0.373427
$397$	−5.10447	−0.256186	−0.128093	−	0.991762i	$-0.540886\pi$
$397$	−5.10447	−0.256186	−0.128093	+	0.991762i	$0.540886\pi$
$398$	−35.8168	−1.79533
$399$	2.12578	0.106422
$400$	−10.0700	−0.503500
$401$	−5.43949	−0.271635	−0.135818	−	0.990734i	$-0.543366\pi$
$401$	−5.43949	−0.271635	−0.135818	+	0.990734i	$0.543366\pi$
$402$	32.5876	1.62532
$403$	−10.5443	−0.525250
$404$	61.3039	3.04998
$405$	0.0257644	0.00128024
$406$	1.55715	0.0772801
$407$	3.42743	0.169891
$408$	23.9182	1.18413
$409$	24.8260	1.22757	0.613784	−	0.789474i	$-0.289647\pi$
$409$	24.8260	1.22757	0.613784	+	0.789474i	$0.289647\pi$
$410$	0.307288	0.0151759
$411$	13.4380	0.662848
$412$	−70.7702	−3.48660
$413$	0.164752	0.00810690
$414$	21.7262	1.06779
$415$	−0.0230825	−0.00113308
$416$	−15.7094	−0.770215
$417$	0.557919	0.0273214
$418$	36.9089	1.80527
$419$	−8.01165	−0.391395	−0.195697	−	0.980664i	$-0.562697\pi$
$419$	−8.01165	−0.391395	−0.195697	+	0.980664i	$0.562697\pi$
$420$	0.0262075	0.00127879
$421$	−18.8614	−0.919250	−0.459625	−	0.888113i	$-0.652016\pi$
$421$	−18.8614	−0.919250	−0.459625	+	0.888113i	$0.652016\pi$
$422$	25.5789	1.24516
$423$	6.24342	0.303566
$424$	−27.5344	−1.33719
$425$	30.5211	1.48049
$426$	31.3582	1.51931
$427$	3.56765	0.172650
$428$	22.3204	1.07890
$429$	10.4964	0.506771
$430$	−0.394336	−0.0190166
$431$	−9.12088	−0.439337	−0.219669	−	0.975575i	$-0.570498\pi$
$431$	−9.12088	−0.439337	−0.219669	+	0.975575i	$0.570498\pi$
$432$	2.01427	0.0969115
$433$	19.7465	0.948957	0.474478	−	0.880267i	$-0.342637\pi$
$433$	19.7465	0.948957	0.474478	+	0.880267i	$0.342637\pi$
$434$	−1.35577	−0.0650791
$435$	−0.0605465	−0.00290298
$436$	−27.5901	−1.32132
$437$	−69.7013	−3.33426
$438$	37.3709	1.78565
$439$	20.6064	0.983489	0.491744	−	0.870740i	$-0.336359\pi$
$439$	20.6064	0.983489	0.491744	+	0.870740i	$0.336359\pi$
$440$	0.205592	0.00980119
$441$	−6.92227	−0.329632
$442$	−74.7735	−3.55661
$443$	28.8343	1.36996	0.684980	−	0.728562i	$-0.259811\pi$
$443$	28.8343	1.36996	0.684980	+	0.728562i	$0.259811\pi$
$444$	−6.13946	−0.291366
$445$	−0.291810	−0.0138331
$446$	33.6197	1.59194
$447$	12.3376	0.583550
$448$	−3.14305	−0.148495
$449$	−3.94322	−0.186092	−0.0930461	−	0.995662i	$-0.529660\pi$
$449$	−3.94322	−0.186092	−0.0930461	+	0.995662i	$0.529660\pi$
$450$	11.8817	0.560106
$451$	10.2213	0.481303
$452$	55.6918	2.61952
$453$	21.2706	0.999382
$454$	30.8369	1.44725
$455$	−0.0370179	−0.00173543
$456$	−29.8717	−1.39887
$457$	2.01811	0.0944032	0.0472016	−	0.998885i	$-0.484970\pi$
$457$	2.01811	0.0944032	0.0472016	+	0.998885i	$0.484970\pi$
$458$	16.0486	0.749900
$459$	−6.10504	−0.284959
$460$	−0.859306	−0.0400653
$461$	−6.74171	−0.313993	−0.156996	−	0.987599i	$-0.550181\pi$
$461$	−6.74171	−0.313993	−0.156996	+	0.987599i	$0.550181\pi$
$462$	1.34961	0.0627895
$463$	−1.18406	−0.0550281	−0.0275141	−	0.999621i	$-0.508759\pi$
$463$	−1.18406	−0.0550281	−0.0275141	+	0.999621i	$0.508759\pi$
$464$	−4.73354	−0.219749
$465$	0.0527162	0.00244466
$466$	−15.3648	−0.711762
$467$	−19.3721	−0.896435	−0.448217	−	0.893925i	$-0.647941\pi$
$467$	−19.3721	−0.896435	−0.448217	+	0.893925i	$0.647941\pi$
$468$	−18.8019	−0.869119
$469$	−3.82283	−0.176522
$470$	−0.382303	−0.0176343
$471$	5.45605	0.251402
$472$	−2.31511	−0.106562
$473$	−13.1168	−0.603112
$474$	1.83782	0.0844140
$475$	−38.1183	−1.74899
$476$	−6.21003	−0.284636
$477$	7.02807	0.321793
$478$	−2.37665	−0.108705
$479$	−18.4331	−0.842229	−0.421114	−	0.907008i	$-0.638361\pi$
$479$	−18.4331	−0.842229	−0.421114	+	0.907008i	$0.638361\pi$
$480$	0.0785388	0.00358479
$481$	8.67195	0.395407
$482$	−16.6390	−0.757884
$483$	−2.54869	−0.115969
$484$	−24.9973	−1.13624
$485$	−0.186219	−0.00845577
$486$	−2.37665	−0.107807
$487$	−18.0119	−0.816196	−0.408098	−	0.912938i	$-0.633808\pi$
$487$	−18.0119	−0.816196	−0.408098	+	0.912938i	$0.633808\pi$
$488$	−50.1330	−2.26941
$489$	−14.4183	−0.652018
$490$	0.423870	0.0191485
$491$	−24.4196	−1.10204	−0.551022	−	0.834491i	$-0.685762\pi$
$491$	−24.4196	−1.10204	−0.551022	+	0.834491i	$0.685762\pi$
$492$	−18.3092	−0.825442
$493$	14.3469	0.646151
$494$	93.3856	4.20162
$495$	−0.0524766	−0.00235865
$496$	4.12137	0.185055
$497$	−3.67861	−0.165008
$498$	2.12925	0.0954142
$499$	−41.9920	−1.87982	−0.939909	−	0.341424i	$-0.889091\pi$
$499$	−41.9920	−1.87982	−0.939909	+	0.341424i	$0.889091\pi$
$500$	−0.939938	−0.0420353
$501$	−7.79493	−0.348252
$502$	15.8182	0.705999
$503$	−20.7828	−0.926660	−0.463330	−	0.886186i	$-0.653346\pi$
$503$	−20.7828	−0.926660	−0.463330	+	0.886186i	$0.653346\pi$
$504$	−1.09229	−0.0486543
$505$	0.432913	0.0192644
$506$	−44.2517	−1.96723
$507$	13.5576	0.602114
$508$	44.4366	1.97155
$509$	5.99687	0.265807	0.132903	−	0.991129i	$-0.457570\pi$
$509$	5.99687	0.265807	0.132903	+	0.991129i	$0.457570\pi$
$510$	0.373829	0.0165534
$511$	−4.38396	−0.193935
$512$	21.9231	0.968872
$513$	7.62467	0.336637
$514$	69.4004	3.06112
$515$	−0.499761	−0.0220221
$516$	23.4958	1.03435
$517$	−12.7165	−0.559273
$518$	1.11502	0.0489914
$519$	−6.30699	−0.276846
$520$	0.520180	0.0228114
$521$	16.5355	0.724434	0.362217	−	0.932094i	$-0.382020\pi$
$521$	16.5355	0.724434	0.362217	+	0.932094i	$0.382020\pi$
$522$	5.58513	0.244455
$523$	32.1156	1.40432	0.702159	−	0.712021i	$-0.252220\pi$
$523$	32.1156	1.40432	0.702159	+	0.712021i	$0.252220\pi$
$524$	−69.9653	−3.05645
$525$	−1.39383	−0.0608317
$526$	−19.7040	−0.859137
$527$	−12.4915	−0.544136
$528$	−4.10264	−0.178544
$529$	60.5679	2.63338
$530$	−0.430349	−0.0186932
$531$	0.590925	0.0256440
$532$	7.75579	0.336256
$533$	25.8616	1.12019
$534$	26.9181	1.16486
$535$	0.157621	0.00681456
$536$	53.7189	2.32030
$537$	4.21211	0.181766
$538$	−24.5467	−1.05828
$539$	14.0992	0.607295
$540$	0.0940000	0.00404512
$541$	5.54845	0.238547	0.119273	−	0.992861i	$-0.461944\pi$
$541$	5.54845	0.238547	0.119273	+	0.992861i	$0.461944\pi$
$542$	8.35089	0.358702
$543$	3.08536	0.132405
$544$	−18.6103	−0.797909
$545$	−0.194834	−0.00834578
$546$	3.41473	0.146137
$547$	−15.5519	−0.664950	−0.332475	−	0.943112i	$-0.607884\pi$
$547$	−15.5519	−0.664950	−0.332475	+	0.943112i	$0.607884\pi$
$548$	49.0278	2.09437
$549$	12.7963	0.546133
$550$	−24.2004	−1.03191
$551$	−17.9180	−0.763333
$552$	35.8145	1.52437
$553$	−0.215594	−0.00916798
$554$	5.47993	0.232820
$555$	−0.0433553	−0.00184033
$556$	2.03554	0.0863261
$557$	−8.63893	−0.366043	−0.183022	−	0.983109i	$-0.558588\pi$
$557$	−8.63893	−0.366043	−0.183022	+	0.983109i	$0.558588\pi$
$558$	−4.86283	−0.205860
$559$	−33.1877	−1.40369
$560$	0.0144689	0.000611421 0
$561$	12.4347	0.524992
$562$	−5.64214	−0.237999
$563$	−0.842054	−0.0354883	−0.0177442	−	0.999843i	$-0.505648\pi$
$563$	−0.842054	−0.0354883	−0.0177442	+	0.999843i	$0.505648\pi$
$564$	22.7788	0.959160
$565$	0.393281	0.0165455
$566$	−18.4053	−0.773632
$567$	0.278803	0.0117086
$568$	51.6923	2.16896
$569$	−21.8149	−0.914529	−0.457264	−	0.889331i	$-0.651171\pi$
$569$	−21.8149	−0.914529	−0.457264	+	0.889331i	$0.651171\pi$
$570$	−0.466880	−0.0195555
$571$	−42.4539	−1.77664	−0.888320	−	0.459225i	$-0.848127\pi$
$571$	−42.4539	−1.77664	−0.888320	+	0.459225i	$0.848127\pi$
$572$	38.2956	1.60122
$573$	15.4370	0.644890
$574$	3.32524	0.138793
$575$	45.7017	1.90589
$576$	−11.2734	−0.469724
$577$	−7.68299	−0.319847	−0.159924	−	0.987129i	$-0.551125\pi$
$577$	−7.68299	−0.319847	−0.159924	+	0.987129i	$0.551125\pi$
$578$	−48.1782	−2.00395
$579$	22.0775	0.917508
$580$	−0.220901	−0.00917240
$581$	−0.249782	−0.0103627
$582$	17.1778	0.712044
$583$	−14.3147	−0.592854
$584$	61.6039	2.54919
$585$	−0.132774	−0.00548955
$586$	−51.5280	−2.12860
$587$	−27.4112	−1.13138	−0.565691	−	0.824617i	$-0.691391\pi$
$587$	−27.4112	−1.13138	−0.565691	+	0.824617i	$0.691391\pi$
$588$	−25.2555	−1.04152
$589$	15.6007	0.642818
$590$	−0.0361840	−0.00148967
$591$	−15.3584	−0.631759
$592$	−3.38953	−0.139309
$593$	11.8026	0.484676	0.242338	−	0.970192i	$-0.422086\pi$
$593$	11.8026	0.484676	0.242338	+	0.970192i	$0.422086\pi$
$594$	4.84073	0.198617
$595$	−0.0438537	−0.00179783
$596$	45.0132	1.84381
$597$	15.0703	0.616786
$598$	−111.964	−4.57855
$599$	40.5909	1.65850	0.829250	−	0.558878i	$-0.188768\pi$
$599$	40.5909	1.65850	0.829250	+	0.558878i	$0.188768\pi$
$600$	19.5863	0.799606
$601$	26.1587	1.06704	0.533518	−	0.845789i	$-0.320870\pi$
$601$	26.1587	1.06704	0.533518	+	0.845789i	$0.320870\pi$
$602$	−4.26721	−0.173919
$603$	−13.7116	−0.558379
$604$	77.6048	3.15769
$605$	−0.176525	−0.00717675
$606$	−39.9342	−1.62221
$607$	9.11023	0.369773	0.184886	−	0.982760i	$-0.440808\pi$
$607$	9.11023	0.369773	0.184886	+	0.982760i	$0.440808\pi$
$608$	23.2426	0.942613
$609$	−0.655189	−0.0265496
$610$	−0.783554	−0.0317252
$611$	−32.1749	−1.30166
$612$	−22.2739	−0.900369
$613$	32.7264	1.32181	0.660903	−	0.750471i	$-0.270174\pi$
$613$	32.7264	1.32181	0.660903	+	0.750471i	$0.270174\pi$
$614$	−18.4364	−0.744034
$615$	−0.129295	−0.00521367
$616$	2.22476	0.0896380
$617$	10.9150	0.439420	0.219710	−	0.975565i	$-0.429489\pi$
$617$	10.9150	0.439420	0.219710	+	0.975565i	$0.429489\pi$
$618$	46.1007	1.85444
$619$	13.3610	0.537023	0.268512	−	0.963276i	$-0.413468\pi$
$619$	13.3610	0.537023	0.268512	+	0.963276i	$0.413468\pi$
$620$	0.192332	0.00772425
$621$	−9.14155	−0.366838
$622$	−51.2265	−2.05400
$623$	−3.15775	−0.126512
$624$	−10.3803	−0.415546
$625$	24.9900	0.999602
$626$	−16.2878	−0.650990
$627$	−15.5298	−0.620202
$628$	19.9061	0.794340
$629$	10.2733	0.409624
$630$	−0.0170719	−0.000680161 0
$631$	6.65225	0.264822	0.132411	−	0.991195i	$-0.457728\pi$
$631$	6.65225	0.264822	0.132411	+	0.991195i	$0.457728\pi$
$632$	3.02955	0.120509
$633$	−10.7626	−0.427776
$634$	29.4550	1.16981
$635$	0.313800	0.0124528
$636$	25.6415	1.01675
$637$	35.6733	1.41343
$638$	−11.3757	−0.450370
$639$	−13.1943	−0.521959
$640$	0.533223	0.0210775
$641$	−15.5217	−0.613072	−0.306536	−	0.951859i	$-0.599170\pi$
$641$	−15.5217	−0.613072	−0.306536	+	0.951859i	$0.599170\pi$
$642$	−14.5398	−0.573841
$643$	11.0238	0.434736	0.217368	−	0.976090i	$-0.430253\pi$
$643$	11.0238	0.434736	0.217368	+	0.976090i	$0.430253\pi$
$644$	−9.29876	−0.366422
$645$	0.165921	0.00653315
$646$	110.630	4.35269
$647$	−3.72529	−0.146456	−0.0732281	−	0.997315i	$-0.523330\pi$
$647$	−3.72529	−0.146456	−0.0732281	+	0.997315i	$0.523330\pi$
$648$	−3.91777	−0.153905
$649$	−1.20359	−0.0472450
$650$	−61.2310	−2.40168
$651$	0.570455	0.0223579
$652$	−52.6044	−2.06015
$653$	24.7641	0.969094	0.484547	−	0.874765i	$-0.338984\pi$
$653$	24.7641	0.969094	0.484547	+	0.874765i	$0.338984\pi$
$654$	17.9725	0.702782
$655$	−0.494077	−0.0193052
$656$	−10.1083	−0.394663
$657$	−15.7242	−0.613460
$658$	−4.13699	−0.161277
$659$	−18.3793	−0.715955	−0.357978	−	0.933730i	$-0.616534\pi$
$659$	−18.3793	−0.715955	−0.357978	+	0.933730i	$0.616534\pi$
$660$	−0.191458	−0.00745250
$661$	9.04414	0.351776	0.175888	−	0.984410i	$-0.443720\pi$
$661$	9.04414	0.351776	0.175888	+	0.984410i	$0.443720\pi$
$662$	59.2403	2.30244
$663$	31.4618	1.22187
$664$	3.50996	0.136213
$665$	0.0547695	0.00212387
$666$	3.99933	0.154971
$667$	21.4827	0.831813
$668$	−28.4394	−1.10035
$669$	−14.1459	−0.546911
$670$	0.839599	0.0324366
$671$	−26.0634	−1.00616
$672$	0.849888	0.0327851
$673$	−8.58994	−0.331118	−0.165559	−	0.986200i	$-0.552943\pi$
$673$	−8.58994	−0.331118	−0.165559	+	0.986200i	$0.552943\pi$
$674$	−11.8384	−0.455998
$675$	−4.99934	−0.192425
$676$	49.4642	1.90247
$677$	25.4361	0.977589	0.488795	−	0.872399i	$-0.337437\pi$
$677$	25.4361	0.977589	0.488795	+	0.872399i	$0.337437\pi$
$678$	−36.2783	−1.39326
$679$	−2.01512	−0.0773333
$680$	0.616237	0.0236316
$681$	−12.9750	−0.497202
$682$	9.90455	0.379265
$683$	−19.5583	−0.748379	−0.374189	−	0.927352i	$-0.622079\pi$
$683$	−19.5583	−0.748379	−0.374189	+	0.927352i	$0.622079\pi$
$684$	27.8182	1.06366
$685$	0.346222	0.0132285
$686$	9.22512	0.352217
$687$	−6.75261	−0.257628
$688$	12.9718	0.494544
$689$	−36.2185	−1.37982
$690$	0.559763	0.0213098
$691$	0.645673	0.0245626	0.0122813	−	0.999925i	$-0.496091\pi$
$691$	0.645673	0.0245626	0.0122813	+	0.999925i	$0.496091\pi$
$692$	−23.0107	−0.874736
$693$	−0.567863	−0.0215713
$694$	−9.73833	−0.369662
$695$	0.0143745	0.000545254 0
$696$	9.20679	0.348982
$697$	30.6372	1.16047
$698$	66.8839	2.53159
$699$	6.46492	0.244526
$700$	−5.08531	−0.192207
$701$	10.2299	0.386378	0.193189	−	0.981162i	$-0.438117\pi$
$701$	10.2299	0.386378	0.193189	+	0.981162i	$0.438117\pi$
$702$	12.2478	0.462264
$703$	−12.8305	−0.483911
$704$	22.9615	0.865393
$705$	0.160858	0.00605827
$706$	−0.214902	−0.00808794
$707$	4.68465	0.176185
$708$	2.15596	0.0810259
$709$	−24.7768	−0.930512	−0.465256	−	0.885176i	$-0.654038\pi$
$709$	−24.7768	−0.930512	−0.465256	+	0.885176i	$0.654038\pi$
$710$	0.807926	0.0303209
$711$	−0.773284	−0.0290004
$712$	44.3730	1.66295
$713$	−18.7044	−0.700486
$714$	4.04530	0.151391
$715$	0.270433	0.0101136
$716$	15.3676	0.574316
$717$	1.00000	0.0373457
$718$	−59.1196	−2.20632
$719$	−33.8314	−1.26170	−0.630849	−	0.775906i	$-0.717293\pi$
$719$	−33.8314	−1.26170	−0.630849	+	0.775906i	$0.717293\pi$
$720$	0.0518964	0.00193406
$721$	−5.40804	−0.201406
$722$	−93.0114	−3.46153
$723$	7.00103	0.260371
$724$	11.2568	0.418354
$725$	11.7485	0.436327
$726$	16.2836	0.604340
$727$	16.1218	0.597926	0.298963	−	0.954265i	$-0.403359\pi$
$727$	16.1218	0.597926	0.298963	+	0.954265i	$0.403359\pi$
$728$	5.62900	0.208625
$729$	1.00000	0.0370370
$730$	0.962838	0.0356362
$731$	−39.3161	−1.45416
$732$	46.6866	1.72559
$733$	35.9947	1.32949	0.664746	−	0.747069i	$-0.268540\pi$
$733$	35.9947	1.32949	0.664746	+	0.747069i	$0.268540\pi$
$734$	70.7224	2.61041
$735$	−0.178348	−0.00657847
$736$	−27.8666	−1.02718
$737$	27.9276	1.02873
$738$	11.9268	0.439033
$739$	−17.9466	−0.660177	−0.330089	−	0.943950i	$-0.607079\pi$
$739$	−17.9466	−0.660177	−0.330089	+	0.943950i	$0.607079\pi$
$740$	−0.158180	−0.00581480
$741$	−39.2930	−1.44347
$742$	−4.65691	−0.170961
$743$	−16.8853	−0.619461	−0.309730	−	0.950824i	$-0.600239\pi$
$743$	−16.8853	−0.619461	−0.309730	+	0.950824i	$0.600239\pi$
$744$	−8.01611	−0.293885
$745$	0.317872	0.0116459
$746$	72.7111	2.66214
$747$	−0.895907	−0.0327795
$748$	45.3672	1.65879
$749$	1.70566	0.0623234
$750$	0.612288	0.0223576
$751$	0.315906	0.0115276	0.00576379	−	0.999983i	$-0.498165\pi$
$751$	0.315906	0.0115276	0.00576379	+	0.999983i	$0.498165\pi$
$752$	12.5759	0.458597
$753$	−6.65566	−0.242546
$754$	−28.7825	−1.04820
$755$	0.548026	0.0199447
$756$	1.01720	0.0369951
$757$	−15.5642	−0.565691	−0.282846	−	0.959165i	$-0.591278\pi$
$757$	−15.5642	−0.565691	−0.282846	+	0.959165i	$0.591278\pi$
$758$	−44.8456	−1.62886
$759$	18.6194	0.675841
$760$	−0.769627	−0.0279173
$761$	−40.5084	−1.46843	−0.734214	−	0.678918i	$-0.762449\pi$
$761$	−40.5084	−1.46843	−0.734214	+	0.678918i	$0.762449\pi$
$762$	−28.9466	−1.04862
$763$	−2.10835	−0.0763273
$764$	56.3211	2.03763
$765$	−0.157293	−0.00568693
$766$	−47.9707	−1.73325
$767$	−3.04528	−0.109959
$768$	−26.6406	−0.961310
$769$	−10.1080	−0.364502	−0.182251	−	0.983252i	$-0.558338\pi$
$769$	−10.1080	−0.364502	−0.182251	+	0.983252i	$0.558338\pi$
$770$	0.0347719	0.00125309
$771$	−29.2010	−1.05165
$772$	80.5484	2.89900
$773$	11.7846	0.423862	0.211931	−	0.977285i	$-0.432025\pi$
$773$	11.7846	0.423862	0.211931	+	0.977285i	$0.432025\pi$
$774$	−15.3055	−0.550144
$775$	−10.2291	−0.367439
$776$	28.3167	1.01651
$777$	−0.469159	−0.0168310
$778$	−35.7226	−1.28072
$779$	−38.2633	−1.37092
$780$	−0.484420	−0.0173450
$781$	26.8740	0.961628
$782$	−132.639	−4.74318
$783$	−2.35001	−0.0839824
$784$	−13.9433	−0.497975
$785$	0.140572	0.00501723
$786$	45.5763	1.62565
$787$	−21.4867	−0.765919	−0.382959	−	0.923765i	$-0.625095\pi$
$787$	−21.4867	−0.765919	−0.382959	+	0.923765i	$0.625095\pi$
$788$	−56.0342	−1.99614
$789$	8.29069	0.295156
$790$	0.0473504	0.00168465
$791$	4.25579	0.151319
$792$	7.97967	0.283545
$793$	−65.9445	−2.34176
$794$	12.1315	0.430531
$795$	0.181074	0.00642203
$796$	54.9832	1.94883
$797$	3.12085	0.110546	0.0552731	−	0.998471i	$-0.482397\pi$
$797$	3.12085	0.110546	0.0552731	+	0.998471i	$0.482397\pi$
$798$	−5.05223	−0.178847
$799$	−38.1164	−1.34846
$800$	−15.2397	−0.538805
$801$	−11.3261	−0.400188
$802$	12.9277	0.456494
$803$	32.0269	1.13020
$804$	−50.0260	−1.76428
$805$	−0.0656655	−0.00231440
$806$	25.0601	0.882705
$807$	10.3283	0.363574
$808$	−65.8293	−2.31587
$809$	−56.3119	−1.97982	−0.989911	−	0.141692i	$-0.954746\pi$
$809$	−56.3119	−1.97982	−0.989911	+	0.141692i	$0.954746\pi$
$810$	−0.0612329	−0.00215150
$811$	53.6605	1.88427	0.942137	−	0.335228i	$-0.108813\pi$
$811$	53.6605	1.88427	0.942137	+	0.335228i	$0.108813\pi$
$812$	−2.39042	−0.0838873
$813$	−3.51373	−0.123232
$814$	−8.14578	−0.285510
$815$	−0.371479	−0.0130123
$816$	−12.2972	−0.430487
$817$	49.1025	1.71788
$818$	−59.0027	−2.06298
$819$	−1.43679	−0.0502053
$820$	−0.471725	−0.0164734
$821$	−18.4668	−0.644496	−0.322248	−	0.946655i	$-0.604438\pi$
$821$	−18.4668	−0.644496	−0.322248	+	0.946655i	$0.604438\pi$
$822$	−31.9374	−1.11394
$823$	−17.7034	−0.617103	−0.308551	−	0.951208i	$-0.599844\pi$
$823$	−17.7034	−0.617103	−0.308551	+	0.951208i	$0.599844\pi$
$824$	75.9945	2.64739
$825$	10.1826	0.354512
$826$	−0.391556	−0.0136240
$827$	−0.788450	−0.0274171	−0.0137085	−	0.999906i	$-0.504364\pi$
$827$	−0.788450	−0.0274171	−0.0137085	+	0.999906i	$0.504364\pi$
$828$	−33.3524	−1.15908
$829$	29.0143	1.00771	0.503854	−	0.863789i	$-0.331915\pi$
$829$	29.0143	1.00771	0.503854	+	0.863789i	$0.331915\pi$
$830$	0.0548590	0.00190418
$831$	−2.30574	−0.0799853
$832$	58.0963	2.01413
$833$	42.2607	1.46425
$834$	−1.32598	−0.0459148
$835$	−0.200832	−0.00695007
$836$	−56.6598	−1.95962
$837$	2.04609	0.0707231
$838$	19.0409	0.657755
$839$	−4.66991	−0.161223	−0.0806115	−	0.996746i	$-0.525687\pi$
$839$	−4.66991	−0.161223	−0.0806115	+	0.996746i	$0.525687\pi$
$840$	−0.0281421	−0.000970995 0
$841$	−23.4775	−0.809568
$842$	44.8269	1.54484
$843$	2.37399	0.0817647
$844$	−39.2668	−1.35162
$845$	0.349304	0.0120164
$846$	−14.8384	−0.510155
$847$	−1.91022	−0.0656358
$848$	14.1564	0.486133
$849$	7.74423	0.265781
$850$	−72.5380	−2.48803
$851$	15.3830	0.527324
$852$	−48.1387	−1.64921
$853$	−16.7142	−0.572285	−0.286142	−	0.958187i	$-0.592373\pi$
$853$	−16.7142	−0.572285	−0.286142	+	0.958187i	$0.592373\pi$
$854$	−8.47903	−0.290146
$855$	0.196445	0.00671828
$856$	−23.9681	−0.819213
$857$	0.927876	0.0316956	0.0158478	−	0.999874i	$-0.494955\pi$
$857$	0.927876	0.0316956	0.0158478	+	0.999874i	$0.494955\pi$
$858$	−24.9462	−0.851650
$859$	−47.4067	−1.61749	−0.808747	−	0.588156i	$-0.799854\pi$
$859$	−47.4067	−1.61749	−0.808747	+	0.588156i	$0.799854\pi$
$860$	0.605355	0.0206424
$861$	−1.39913	−0.0476823
$862$	21.6771	0.738325
$863$	−42.6921	−1.45326	−0.726628	−	0.687031i	$-0.758914\pi$
$863$	−42.6921	−1.45326	−0.726628	+	0.687031i	$0.758914\pi$
$864$	3.04835	0.103707
$865$	−0.162496	−0.00552503
$866$	−46.9305	−1.59476
$867$	20.2715	0.688457
$868$	2.08128	0.0706431
$869$	1.57502	0.0534288
$870$	0.143898	0.00487859
$871$	70.6614	2.39427
$872$	29.6268	1.00329
$873$	−7.22776	−0.244623
$874$	165.655	5.60337
$875$	−0.0718271	−0.00242820
$876$	−57.3689	−1.93832
$877$	26.8609	0.907029	0.453515	−	0.891249i	$-0.350170\pi$
$877$	26.8609	0.907029	0.453515	+	0.891249i	$0.350170\pi$
$878$	−48.9741	−1.65279
$879$	21.6810	0.731281
$880$	−0.105702	−0.00356321
$881$	−8.49551	−0.286221	−0.143111	−	0.989707i	$-0.545710\pi$
$881$	−8.49551	−0.286221	−0.143111	+	0.989707i	$0.545710\pi$
$882$	16.4518	0.553960
$883$	−14.3664	−0.483466	−0.241733	−	0.970343i	$-0.577716\pi$
$883$	−14.3664	−0.483466	−0.241733	+	0.970343i	$0.577716\pi$
$884$	114.787	3.86069
$885$	0.0152248	0.000511777 0
$886$	−68.5290	−2.30228
$887$	−33.4301	−1.12247	−0.561237	−	0.827655i	$-0.689674\pi$
$887$	−33.4301	−1.12247	−0.561237	+	0.827655i	$0.689674\pi$
$888$	6.59268	0.221236
$889$	3.39571	0.113888
$890$	0.693529	0.0232471
$891$	−2.03679	−0.0682350
$892$	−51.6105	−1.72805
$893$	47.6040	1.59301
$894$	−29.3222	−0.980681
$895$	0.108522	0.00362751
$896$	5.77014	0.192767
$897$	47.1101	1.57296
$898$	9.37165	0.312736
$899$	−4.80832	−0.160366
$900$	−18.2398	−0.607994
$901$	−42.9066	−1.42943
$902$	−24.2925	−0.808850
$903$	1.79548	0.0597497
$904$	−59.8029	−1.98902
$905$	0.0794923	0.00264241
$906$	−50.5528	−1.67950
$907$	35.8979	1.19197	0.595985	−	0.802995i	$-0.296762\pi$
$907$	35.8979	1.19197	0.595985	+	0.802995i	$0.296762\pi$
$908$	−47.3385	−1.57098
$909$	16.8027	0.557312
$910$	0.0879785	0.00291646
$911$	−7.57044	−0.250820	−0.125410	−	0.992105i	$-0.540025\pi$
$911$	−7.57044	−0.250820	−0.125410	+	0.992105i	$0.540025\pi$
$912$	15.3581	0.508558
$913$	1.82477	0.0603912
$914$	−4.79633	−0.158649
$915$	0.329689	0.0108992
$916$	−24.6365	−0.814014
$917$	−5.34653	−0.176558
$918$	14.5095	0.478886
$919$	−54.7630	−1.80647	−0.903233	−	0.429151i	$-0.858813\pi$
$919$	−54.7630	−1.80647	−0.903233	+	0.429151i	$0.858813\pi$
$920$	0.922739	0.0304218
$921$	7.75733	0.255613
$922$	16.0227	0.527678
$923$	67.9957	2.23810
$924$	−2.07182	−0.0681577
$925$	8.41269	0.276608
$926$	2.81410	0.0924771
$927$	−19.3974	−0.637093
$928$	−7.16363	−0.235158
$929$	−24.6234	−0.807868	−0.403934	−	0.914788i	$-0.632358\pi$
$929$	−24.6234	−0.807868	−0.403934	+	0.914788i	$0.632358\pi$
$930$	−0.125288	−0.00410835
$931$	−52.7800	−1.72980
$932$	23.5869	0.772615
$933$	21.5541	0.705650
$934$	46.0407	1.50650
$935$	0.320372	0.0104773
$936$	20.1899	0.659927
$937$	50.6151	1.65352	0.826762	−	0.562552i	$-0.190180\pi$
$937$	50.6151	1.65352	0.826762	+	0.562552i	$0.190180\pi$
$938$	9.08551	0.296652
$939$	6.85326	0.223648
$940$	0.586882	0.0191420
$941$	45.9093	1.49660	0.748299	−	0.663361i	$-0.230871\pi$
$941$	45.9093	1.49660	0.748299	+	0.663361i	$0.230871\pi$
$942$	−12.9671	−0.422491
$943$	45.8755	1.49391
$944$	1.19028	0.0387403
$945$	0.00718319	0.000233669 0
$946$	31.1740	1.01355
$947$	−59.4856	−1.93302	−0.966511	−	0.256624i	$-0.917390\pi$
$947$	−59.4856	−1.93302	−0.966511	+	0.256624i	$0.917390\pi$
$948$	−2.82129	−0.0916311
$949$	81.0333	2.63045
$950$	90.5937	2.93925
$951$	−12.3935	−0.401887
$952$	6.66845	0.216126
$953$	−17.3642	−0.562482	−0.281241	−	0.959637i	$-0.590746\pi$
$953$	−17.3642	−0.562482	−0.281241	+	0.959637i	$0.590746\pi$
$954$	−16.7032	−0.540787
$955$	0.397725	0.0128701
$956$	3.64845	0.117999
$957$	4.78646	0.154724
$958$	43.8089	1.41540
$959$	3.74656	0.120983
$960$	−0.290452	−0.00937429
$961$	−26.8135	−0.864952
$962$	−20.6102	−0.664498
$963$	6.11779	0.197143
$964$	25.5429	0.822680
$965$	0.568812	0.0183107
$966$	6.05733	0.194891
$967$	−23.7018	−0.762198	−0.381099	−	0.924534i	$-0.624454\pi$
$967$	−23.7018	−0.762198	−0.381099	+	0.924534i	$0.624454\pi$
$968$	26.8426	0.862754
$969$	−46.5489	−1.49537
$970$	0.442577	0.0142103
$971$	49.1695	1.57792	0.788961	−	0.614443i	$-0.210619\pi$
$971$	49.1695	1.57792	0.788961	+	0.614443i	$0.210619\pi$
$972$	3.64845	0.117024
$973$	0.155550	0.00498669
$974$	42.8079	1.37165
$975$	25.7636	0.825096
$976$	25.7752	0.825043
$977$	−13.2514	−0.423950	−0.211975	−	0.977275i	$-0.567990\pi$
$977$	−13.2514	−0.423950	−0.211975	+	0.977275i	$0.567990\pi$
$978$	34.2672	1.09574
$979$	23.0688	0.737284
$980$	−0.650694	−0.0207856
$981$	−7.56214	−0.241441
$982$	58.0369	1.85203
$983$	37.4907	1.19577	0.597884	−	0.801582i	$-0.296008\pi$
$983$	37.4907	1.19577	0.597884	+	0.801582i	$0.296008\pi$
$984$	19.6608	0.626762
$985$	−0.395699	−0.0126080
$986$	−34.0975	−1.08588
$987$	1.74068	0.0554066
$988$	−143.358	−4.56084
$989$	−58.8711	−1.87199
$990$	0.124718	0.00396381
$991$	−2.23181	−0.0708957	−0.0354479	−	0.999372i	$-0.511286\pi$
$991$	−2.23181	−0.0708957	−0.0354479	+	0.999372i	$0.511286\pi$
$992$	6.23718	0.198031
$993$	−24.9260	−0.791003
$994$	8.74276	0.277304
$995$	0.388277	0.0123092
$996$	−3.26867	−0.103572
$997$	−39.8110	−1.26083	−0.630414	−	0.776259i	$-0.717115\pi$
$997$	−39.8110	−1.26083	−0.630414	+	0.776259i	$0.717115\pi$
$998$	99.8001	3.15912
$999$	−1.68276	−0.0532402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.f.1.2	✓	8
3.2	odd	2		2151.2.a.g.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.f.1.2	✓	8	1.1	even	1	trivial
2151.2.a.g.1.7		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37665 q^{2} +1.00000 q^{3} +3.64845 q^{4} +0.0257644 q^{5} -2.37665 q^{6} +0.278803 q^{7} -3.91777 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.37665 q^{2} +1.00000 q^{3} +3.64845 q^{4} +0.0257644 q^{5} -2.37665 q^{6} +0.278803 q^{7} -3.91777 q^{8} +1.00000 q^{9} -0.0612329 q^{10} -2.03679 q^{11} +3.64845 q^{12} -5.15341 q^{13} -0.662616 q^{14} +0.0257644 q^{15} +2.01427 q^{16} -6.10504 q^{17} -2.37665 q^{18} +7.62467 q^{19} +0.0940000 q^{20} +0.278803 q^{21} +4.84073 q^{22} -9.14155 q^{23} -3.91777 q^{24} -4.99934 q^{25} +12.2478 q^{26} +1.00000 q^{27} +1.01720 q^{28} -2.35001 q^{29} -0.0612329 q^{30} +2.04609 q^{31} +3.04835 q^{32} -2.03679 q^{33} +14.5095 q^{34} +0.00718319 q^{35} +3.64845 q^{36} -1.68276 q^{37} -18.1211 q^{38} -5.15341 q^{39} -0.100939 q^{40} -5.01835 q^{41} -0.662616 q^{42} +6.43995 q^{43} -7.43111 q^{44} +0.0257644 q^{45} +21.7262 q^{46} +6.24342 q^{47} +2.01427 q^{48} -6.92227 q^{49} +11.8817 q^{50} -6.10504 q^{51} -18.8019 q^{52} +7.02807 q^{53} -2.37665 q^{54} -0.0524766 q^{55} -1.09229 q^{56} +7.62467 q^{57} +5.58513 q^{58} +0.590925 q^{59} +0.0940000 q^{60} +12.7963 q^{61} -4.86283 q^{62} +0.278803 q^{63} -11.2734 q^{64} -0.132774 q^{65} +4.84073 q^{66} -13.7116 q^{67} -22.2739 q^{68} -9.14155 q^{69} -0.0170719 q^{70} -13.1943 q^{71} -3.91777 q^{72} -15.7242 q^{73} +3.99933 q^{74} -4.99934 q^{75} +27.8182 q^{76} -0.567863 q^{77} +12.2478 q^{78} -0.773284 q^{79} +0.0518964 q^{80} +1.00000 q^{81} +11.9268 q^{82} -0.895907 q^{83} +1.01720 q^{84} -0.157293 q^{85} -15.3055 q^{86} -2.35001 q^{87} +7.97967 q^{88} -11.3261 q^{89} -0.0612329 q^{90} -1.43679 q^{91} -33.3524 q^{92} +2.04609 q^{93} -14.8384 q^{94} +0.196445 q^{95} +3.04835 q^{96} -7.22776 q^{97} +16.4518 q^{98} -2.03679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 5 q^{2} + 8 q^{3} + 7 q^{4} - 13 q^{5} - 5 q^{6} - 7 q^{7} - 15 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 5 * q^2 + 8 * q^3 + 7 * q^4 - 13 * q^5 - 5 * q^6 - 7 * q^7 - 15 * q^8 + 8 * q^9	\( 8 q - 5 q^{2} + 8 q^{3} + 7 q^{4} - 13 q^{5} - 5 q^{6} - 7 q^{7} - 15 q^{8} + 8 q^{9} + 4 q^{10} - 19 q^{11} + 7 q^{12} - 3 q^{13} - 8 q^{14} - 13 q^{15} + 9 q^{16} - 13 q^{17} - 5 q^{18} - 6 q^{19} - 18 q^{20} - 7 q^{21} + 3 q^{22} - 18 q^{23} - 15 q^{24} + 7 q^{25} + 8 q^{27} - 2 q^{28} - 10 q^{29} + 4 q^{30} - 2 q^{31} - 20 q^{32} - 19 q^{33} - 4 q^{34} - 7 q^{35} + 7 q^{36} - 8 q^{37} + 9 q^{38} - 3 q^{39} + 29 q^{40} - 22 q^{41} - 8 q^{42} - 24 q^{43} - 7 q^{44} - 13 q^{45} + 30 q^{46} - 17 q^{47} + 9 q^{48} + 15 q^{49} + 24 q^{50} - 13 q^{51} + 22 q^{52} - 5 q^{54} + 32 q^{55} + 19 q^{56} - 6 q^{57} + 18 q^{58} - 24 q^{59} - 18 q^{60} + 10 q^{61} + 30 q^{62} - 7 q^{63} + 33 q^{64} - 17 q^{65} + 3 q^{66} - 48 q^{67} - 21 q^{68} - 18 q^{69} + 31 q^{70} - 17 q^{71} - 15 q^{72} + 2 q^{73} + 9 q^{74} + 7 q^{75} + 10 q^{76} + 10 q^{77} + 17 q^{79} + 8 q^{80} + 8 q^{81} - 17 q^{82} - 37 q^{83} - 2 q^{84} + 28 q^{85} - q^{86} - 10 q^{87} + 15 q^{88} - 41 q^{89} + 4 q^{90} - 39 q^{91} - 38 q^{92} - 2 q^{93} + 2 q^{94} + 16 q^{95} - 20 q^{96} - 20 q^{97} + 46 q^{98} - 19 q^{99}+O(q^{100}) \) 8 * q - 5 * q^2 + 8 * q^3 + 7 * q^4 - 13 * q^5 - 5 * q^6 - 7 * q^7 - 15 * q^8 + 8 * q^9 + 4 * q^10 - 19 * q^11 + 7 * q^12 - 3 * q^13 - 8 * q^14 - 13 * q^15 + 9 * q^16 - 13 * q^17 - 5 * q^18 - 6 * q^19 - 18 * q^20 - 7 * q^21 + 3 * q^22 - 18 * q^23 - 15 * q^24 + 7 * q^25 + 8 * q^27 - 2 * q^28 - 10 * q^29 + 4 * q^30 - 2 * q^31 - 20 * q^32 - 19 * q^33 - 4 * q^34 - 7 * q^35 + 7 * q^36 - 8 * q^37 + 9 * q^38 - 3 * q^39 + 29 * q^40 - 22 * q^41 - 8 * q^42 - 24 * q^43 - 7 * q^44 - 13 * q^45 + 30 * q^46 - 17 * q^47 + 9 * q^48 + 15 * q^49 + 24 * q^50 - 13 * q^51 + 22 * q^52 - 5 * q^54 + 32 * q^55 + 19 * q^56 - 6 * q^57 + 18 * q^58 - 24 * q^59 - 18 * q^60 + 10 * q^61 + 30 * q^62 - 7 * q^63 + 33 * q^64 - 17 * q^65 + 3 * q^66 - 48 * q^67 - 21 * q^68 - 18 * q^69 + 31 * q^70 - 17 * q^71 - 15 * q^72 + 2 * q^73 + 9 * q^74 + 7 * q^75 + 10 * q^76 + 10 * q^77 + 17 * q^79 + 8 * q^80 + 8 * q^81 - 17 * q^82 - 37 * q^83 - 2 * q^84 + 28 * q^85 - q^86 - 10 * q^87 + 15 * q^88 - 41 * q^89 + 4 * q^90 - 39 * q^91 - 38 * q^92 - 2 * q^93 + 2 * q^94 + 16 * q^95 - 20 * q^96 - 20 * q^97 + 46 * q^98 - 19 * q^99

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