LMFDB - Embedded newform 95.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,2,Mod(1,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, 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("95.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	95.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:	$0.758578819202$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	95.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009 q^{2} -1.70928 q^{3} +2.70928 q^{4} +1.00000 q^{5} -3.70928 q^{6} +1.07838 q^{7} +1.53919 q^{8} -0.0783777 q^{9} +O(q^{10})$	\(q+2.17009 q^{2} -1.70928 q^{3} +2.70928 q^{4} +1.00000 q^{5} -3.70928 q^{6} +1.07838 q^{7} +1.53919 q^{8} -0.0783777 q^{9} +2.17009 q^{10} -6.34017 q^{11} -4.63090 q^{12} +1.36910 q^{13} +2.34017 q^{14} -1.70928 q^{15} -2.07838 q^{16} +3.26180 q^{17} -0.170086 q^{18} -1.00000 q^{19} +2.70928 q^{20} -1.84324 q^{21} -13.7587 q^{22} +2.34017 q^{23} -2.63090 q^{24} +1.00000 q^{25} +2.97107 q^{26} +5.26180 q^{27} +2.92162 q^{28} +1.41855 q^{29} -3.70928 q^{30} +8.68035 q^{31} -7.58864 q^{32} +10.8371 q^{33} +7.07838 q^{34} +1.07838 q^{35} -0.212347 q^{36} +5.36910 q^{37} -2.17009 q^{38} -2.34017 q^{39} +1.53919 q^{40} -3.26180 q^{41} -4.00000 q^{42} -11.9155 q^{43} -17.1773 q^{44} -0.0783777 q^{45} +5.07838 q^{46} +1.07838 q^{47} +3.55252 q^{48} -5.83710 q^{49} +2.17009 q^{50} -5.57531 q^{51} +3.70928 q^{52} +6.63090 q^{53} +11.4186 q^{54} -6.34017 q^{55} +1.65983 q^{56} +1.70928 q^{57} +3.07838 q^{58} -11.4186 q^{59} -4.63090 q^{60} +5.60197 q^{61} +18.8371 q^{62} -0.0845208 q^{63} -12.3112 q^{64} +1.36910 q^{65} +23.5174 q^{66} +10.3896 q^{67} +8.83710 q^{68} -4.00000 q^{69} +2.34017 q^{70} -10.8371 q^{71} -0.120638 q^{72} +5.41855 q^{73} +11.6514 q^{74} -1.70928 q^{75} -2.70928 q^{76} -6.83710 q^{77} -5.07838 q^{78} +14.2557 q^{79} -2.07838 q^{80} -8.75872 q^{81} -7.07838 q^{82} -14.3402 q^{83} -4.99386 q^{84} +3.26180 q^{85} -25.8576 q^{86} -2.42469 q^{87} -9.75872 q^{88} +7.57531 q^{89} -0.170086 q^{90} +1.47641 q^{91} +6.34017 q^{92} -14.8371 q^{93} +2.34017 q^{94} -1.00000 q^{95} +12.9711 q^{96} -8.88655 q^{97} -12.6670 q^{98} +0.496928 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 2 * q^3 + q^4 + 3 * q^5 - 4 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 3 q^{8} + 3 q^{9} + q^{10} - 8 q^{11} - 10 q^{12} + 8 q^{13} - 4 q^{14} + 2 q^{15} - 3 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} + q^{20} - 12 q^{21} - 16 q^{22} - 4 q^{23} - 4 q^{24} + 3 q^{25} - 6 q^{26} + 8 q^{27} + 12 q^{28} - 10 q^{29} - 4 q^{30} + 4 q^{31} - 3 q^{32} + 4 q^{33} + 18 q^{34} - 11 q^{36} + 20 q^{37} - q^{38} + 4 q^{39} + 3 q^{40} - 2 q^{41} - 12 q^{42} - 4 q^{43} - 12 q^{44} + 3 q^{45} + 12 q^{46} + 10 q^{48} + 11 q^{49} + q^{50} + 4 q^{51} + 4 q^{52} + 16 q^{53} + 20 q^{54} - 8 q^{55} + 16 q^{56} - 2 q^{57} + 6 q^{58} - 20 q^{59} - 10 q^{60} - 2 q^{61} + 28 q^{62} - 32 q^{63} - 11 q^{64} + 8 q^{65} + 20 q^{66} + 2 q^{67} - 2 q^{68} - 12 q^{69} - 4 q^{70} - 4 q^{71} - 13 q^{72} + 2 q^{73} - 2 q^{74} + 2 q^{75} - q^{76} + 8 q^{77} - 12 q^{78} - 3 q^{80} - q^{81} - 18 q^{82} - 32 q^{83} + 20 q^{84} + 2 q^{85} - 16 q^{86} - 28 q^{87} - 4 q^{88} + 2 q^{89} + 5 q^{90} + 20 q^{91} + 8 q^{92} - 16 q^{93} - 4 q^{94} - 3 q^{95} + 24 q^{96} + 20 q^{97} - 15 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + q^2 + 2 * q^3 + q^4 + 3 * q^5 - 4 * q^6 + 3 * q^8 + 3 * q^9 + q^10 - 8 * q^11 - 10 * q^12 + 8 * q^13 - 4 * q^14 + 2 * q^15 - 3 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 + q^20 - 12 * q^21 - 16 * q^22 - 4 * q^23 - 4 * q^24 + 3 * q^25 - 6 * q^26 + 8 * q^27 + 12 * q^28 - 10 * q^29 - 4 * q^30 + 4 * q^31 - 3 * q^32 + 4 * q^33 + 18 * q^34 - 11 * q^36 + 20 * q^37 - q^38 + 4 * q^39 + 3 * q^40 - 2 * q^41 - 12 * q^42 - 4 * q^43 - 12 * q^44 + 3 * q^45 + 12 * q^46 + 10 * q^48 + 11 * q^49 + q^50 + 4 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 - 8 * q^55 + 16 * q^56 - 2 * q^57 + 6 * q^58 - 20 * q^59 - 10 * q^60 - 2 * q^61 + 28 * q^62 - 32 * q^63 - 11 * q^64 + 8 * q^65 + 20 * q^66 + 2 * q^67 - 2 * q^68 - 12 * q^69 - 4 * q^70 - 4 * q^71 - 13 * q^72 + 2 * q^73 - 2 * q^74 + 2 * q^75 - q^76 + 8 * q^77 - 12 * q^78 - 3 * q^80 - q^81 - 18 * q^82 - 32 * q^83 + 20 * q^84 + 2 * q^85 - 16 * q^86 - 28 * q^87 - 4 * q^88 + 2 * q^89 + 5 * q^90 + 20 * q^91 + 8 * q^92 - 16 * q^93 - 4 * q^94 - 3 * q^95 + 24 * q^96 + 20 * q^97 - 15 * q^98 - 16 * 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 $

$2$	2.17009	1.53448	0.767241	−	0.641358i	$-0.221629\pi$
$2$	2.17009	1.53448	0.767241	+	0.641358i	$0.221629\pi$
$3$	−1.70928	−0.986851	−0.493425	−	0.869788i	$-0.664255\pi$
$3$	−1.70928	−0.986851	−0.493425	+	0.869788i	$0.664255\pi$
$4$	2.70928	1.35464
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.70928	−1.51431
$7$	1.07838	0.407588	0.203794	−	0.979014i	$-0.434673\pi$
$7$	1.07838	0.407588	0.203794	+	0.979014i	$0.434673\pi$
$8$	1.53919	0.544185
$9$	−0.0783777	−0.0261259
$10$	2.17009	0.686242
$11$	−6.34017	−1.91163	−0.955817	−	0.293962i	$-0.905026\pi$
$11$	−6.34017	−1.91163	−0.955817	+	0.293962i	$0.905026\pi$
$12$	−4.63090	−1.33682
$13$	1.36910	0.379721	0.189860	−	0.981811i	$-0.439196\pi$
$13$	1.36910	0.379721	0.189860	+	0.981811i	$0.439196\pi$
$14$	2.34017	0.625438
$15$	−1.70928	−0.441333
$16$	−2.07838	−0.519594
$17$	3.26180	0.791102	0.395551	−	0.918444i	$-0.370554\pi$
$17$	3.26180	0.791102	0.395551	+	0.918444i	$0.370554\pi$
$18$	−0.170086	−0.0400898
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.70928	0.605812
$21$	−1.84324	−0.402229
$22$	−13.7587	−2.93337
$23$	2.34017	0.487960	0.243980	−	0.969780i	$-0.421547\pi$
$23$	2.34017	0.487960	0.243980	+	0.969780i	$0.421547\pi$
$24$	−2.63090	−0.537030
$25$	1.00000	0.200000
$26$	2.97107	0.582675
$27$	5.26180	1.01263
$28$	2.92162	0.552135
$29$	1.41855	0.263418	0.131709	−	0.991288i	$-0.457954\pi$
$29$	1.41855	0.263418	0.131709	+	0.991288i	$0.457954\pi$
$30$	−3.70928	−0.677218
$31$	8.68035	1.55904	0.779518	−	0.626380i	$-0.215464\pi$
$31$	8.68035	1.55904	0.779518	+	0.626380i	$0.215464\pi$
$32$	−7.58864	−1.34149
$33$	10.8371	1.88650
$34$	7.07838	1.21393
$35$	1.07838	0.182279
$36$	−0.212347	−0.0353911
$37$	5.36910	0.882675	0.441337	−	0.897341i	$-0.354504\pi$
$37$	5.36910	0.882675	0.441337	+	0.897341i	$0.354504\pi$
$38$	−2.17009	−0.352035
$39$	−2.34017	−0.374728
$40$	1.53919	0.243367
$41$	−3.26180	−0.509407	−0.254703	−	0.967019i	$-0.581978\pi$
$41$	−3.26180	−0.509407	−0.254703	+	0.967019i	$0.581978\pi$
$42$	−4.00000	−0.617213
$43$	−11.9155	−1.81709	−0.908547	−	0.417783i	$-0.862807\pi$
$43$	−11.9155	−1.81709	−0.908547	+	0.417783i	$0.862807\pi$
$44$	−17.1773	−2.58957
$45$	−0.0783777	−0.0116839
$46$	5.07838	0.748766
$47$	1.07838	0.157298	0.0786488	−	0.996902i	$-0.474939\pi$
$47$	1.07838	0.157298	0.0786488	+	0.996902i	$0.474939\pi$
$48$	3.55252	0.512762
$49$	−5.83710	−0.833872
$50$	2.17009	0.306897
$51$	−5.57531	−0.780699
$52$	3.70928	0.514384
$53$	6.63090	0.910824	0.455412	−	0.890281i	$-0.349492\pi$
$53$	6.63090	0.910824	0.455412	+	0.890281i	$0.349492\pi$
$54$	11.4186	1.55387
$55$	−6.34017	−0.854909
$56$	1.65983	0.221804
$57$	1.70928	0.226399
$58$	3.07838	0.404211
$59$	−11.4186	−1.48657	−0.743284	−	0.668976i	$-0.766733\pi$
$59$	−11.4186	−1.48657	−0.743284	+	0.668976i	$0.766733\pi$
$60$	−4.63090	−0.597846
$61$	5.60197	0.717259	0.358629	−	0.933480i	$-0.383244\pi$
$61$	5.60197	0.717259	0.358629	+	0.933480i	$0.383244\pi$
$62$	18.8371	2.39231
$63$	−0.0845208	−0.0106486
$64$	−12.3112	−1.53891
$65$	1.36910	0.169816
$66$	23.5174	2.89480
$67$	10.3896	1.26929	0.634647	−	0.772802i	$-0.281145\pi$
$67$	10.3896	1.26929	0.634647	+	0.772802i	$0.281145\pi$
$68$	8.83710	1.07166
$69$	−4.00000	−0.481543
$70$	2.34017	0.279704
$71$	−10.8371	−1.28613	−0.643064	−	0.765813i	$-0.722337\pi$
$71$	−10.8371	−1.28613	−0.643064	+	0.765813i	$0.722337\pi$
$72$	−0.120638	−0.0142173
$73$	5.41855	0.634193	0.317097	−	0.948393i	$-0.397292\pi$
$73$	5.41855	0.634193	0.317097	+	0.948393i	$0.397292\pi$
$74$	11.6514	1.35445
$75$	−1.70928	−0.197370
$76$	−2.70928	−0.310775
$77$	−6.83710	−0.779160
$78$	−5.07838	−0.575013
$79$	14.2557	1.60389	0.801943	−	0.597400i	$-0.203800\pi$
$79$	14.2557	1.60389	0.801943	+	0.597400i	$0.203800\pi$
$80$	−2.07838	−0.232370
$81$	−8.75872	−0.973192
$82$	−7.07838	−0.781676
$83$	−14.3402	−1.57404	−0.787019	−	0.616928i	$-0.788377\pi$
$83$	−14.3402	−1.57404	−0.787019	+	0.616928i	$0.788377\pi$
$84$	−4.99386	−0.544874
$85$	3.26180	0.353791
$86$	−25.8576	−2.78830
$87$	−2.42469	−0.259954
$88$	−9.75872	−1.04028
$89$	7.57531	0.802981	0.401490	−	0.915863i	$-0.368492\pi$
$89$	7.57531	0.802981	0.401490	+	0.915863i	$0.368492\pi$
$90$	−0.170086	−0.0179287
$91$	1.47641	0.154770
$92$	6.34017	0.661009
$93$	−14.8371	−1.53854
$94$	2.34017	0.241370
$95$	−1.00000	−0.102598
$96$	12.9711	1.32385
$97$	−8.88655	−0.902292	−0.451146	−	0.892450i	$-0.648985\pi$
$97$	−8.88655	−0.902292	−0.451146	+	0.892450i	$0.648985\pi$
$98$	−12.6670	−1.27956
$99$	0.496928	0.0499432
$100$	2.70928	0.270928
$101$	−4.92162	−0.489720	−0.244860	−	0.969558i	$-0.578742\pi$
$101$	−4.92162	−0.489720	−0.244860	+	0.969558i	$0.578742\pi$
$102$	−12.0989	−1.19797
$103$	6.38962	0.629588	0.314794	−	0.949160i	$-0.398065\pi$
$103$	6.38962	0.629588	0.314794	+	0.949160i	$0.398065\pi$
$104$	2.10731	0.206638
$105$	−1.84324	−0.179882
$106$	14.3896	1.39764
$107$	2.29072	0.221453	0.110726	−	0.993851i	$-0.464682\pi$
$107$	2.29072	0.221453	0.110726	+	0.993851i	$0.464682\pi$
$108$	14.2557	1.37175
$109$	−12.8371	−1.22957	−0.614786	−	0.788694i	$-0.710757\pi$
$109$	−12.8371	−1.22957	−0.614786	+	0.788694i	$0.710757\pi$
$110$	−13.7587	−1.31184
$111$	−9.17727	−0.871068
$112$	−2.24128	−0.211781
$113$	−12.8865	−1.21226	−0.606132	−	0.795364i	$-0.707280\pi$
$113$	−12.8865	−1.21226	−0.606132	+	0.795364i	$0.707280\pi$
$114$	3.70928	0.347405
$115$	2.34017	0.218222
$116$	3.84324	0.356836
$117$	−0.107307	−0.00992055
$118$	−24.7792	−2.28111
$119$	3.51745	0.322444
$120$	−2.63090	−0.240167
$121$	29.1978	2.65434
$122$	12.1568	1.10062
$123$	5.57531	0.502708
$124$	23.5174	2.11193
$125$	1.00000	0.0894427
$126$	−0.183417	−0.0163401
$127$	−8.23287	−0.730549	−0.365274	−	0.930900i	$-0.619025\pi$
$127$	−8.23287	−0.730549	−0.365274	+	0.930900i	$0.619025\pi$
$128$	−11.5392	−1.01993
$129$	20.3668	1.79320
$130$	2.97107	0.260580
$131$	1.47641	0.128995	0.0644973	−	0.997918i	$-0.479456\pi$
$131$	1.47641	0.128995	0.0644973	+	0.997918i	$0.479456\pi$
$132$	29.3607	2.55552
$133$	−1.07838	−0.0935072
$134$	22.5464	1.94771
$135$	5.26180	0.452863
$136$	5.02052	0.430506
$137$	−3.94214	−0.336800	−0.168400	−	0.985719i	$-0.553860\pi$
$137$	−3.94214	−0.336800	−0.168400	+	0.985719i	$0.553860\pi$
$138$	−8.68035	−0.738920
$139$	8.86376	0.751815	0.375907	−	0.926657i	$-0.377331\pi$
$139$	8.86376	0.751815	0.375907	+	0.926657i	$0.377331\pi$
$140$	2.92162	0.246922
$141$	−1.84324	−0.155229
$142$	−23.5174	−1.97354
$143$	−8.68035	−0.725887
$144$	0.162899	0.0135749
$145$	1.41855	0.117804
$146$	11.7587	0.973159
$147$	9.97721	0.822907
$148$	14.5464	1.19570
$149$	−19.7587	−1.61870	−0.809349	−	0.587328i	$-0.800180\pi$
$149$	−19.7587	−1.61870	−0.809349	+	0.587328i	$0.800180\pi$
$150$	−3.70928	−0.302861
$151$	3.41855	0.278198	0.139099	−	0.990279i	$-0.455579\pi$
$151$	3.41855	0.278198	0.139099	+	0.990279i	$0.455579\pi$
$152$	−1.53919	−0.124845
$153$	−0.255652	−0.0206683
$154$	−14.8371	−1.19561
$155$	8.68035	0.697222
$156$	−6.34017	−0.507620
$157$	9.41855	0.751682	0.375841	−	0.926684i	$-0.377354\pi$
$157$	9.41855	0.751682	0.375841	+	0.926684i	$0.377354\pi$
$158$	30.9360	2.46114
$159$	−11.3340	−0.898847
$160$	−7.58864	−0.599934
$161$	2.52359	0.198887
$162$	−19.0072	−1.49335
$163$	−2.92162	−0.228839	−0.114420	−	0.993433i	$-0.536501\pi$
$163$	−2.92162	−0.228839	−0.114420	+	0.993433i	$0.536501\pi$
$164$	−8.83710	−0.690062
$165$	10.8371	0.843667
$166$	−31.1194	−2.41534
$167$	20.9132	1.61831	0.809156	−	0.587593i	$-0.199924\pi$
$167$	20.9132	1.61831	0.809156	+	0.587593i	$0.199924\pi$
$168$	−2.83710	−0.218887
$169$	−11.1256	−0.855812
$170$	7.07838	0.542887
$171$	0.0783777	0.00599370
$172$	−32.2823	−2.46150
$173$	−1.05559	−0.0802551	−0.0401276	−	0.999195i	$-0.512776\pi$
$173$	−1.05559	−0.0802551	−0.0401276	+	0.999195i	$0.512776\pi$
$174$	−5.26180	−0.398896
$175$	1.07838	0.0815177
$176$	13.1773	0.993274
$177$	19.5174	1.46702
$178$	16.4391	1.23216
$179$	0.894960	0.0668925	0.0334462	−	0.999441i	$-0.489352\pi$
$179$	0.894960	0.0668925	0.0334462	+	0.999441i	$0.489352\pi$
$180$	−0.212347	−0.0158274
$181$	−0.837101	−0.0622213	−0.0311106	−	0.999516i	$-0.509904\pi$
$181$	−0.837101	−0.0622213	−0.0311106	+	0.999516i	$0.509904\pi$
$182$	3.20394	0.237492
$183$	−9.57531	−0.707827
$184$	3.60197	0.265541
$185$	5.36910	0.394744
$186$	−32.1978	−2.36086
$187$	−20.6803	−1.51230
$188$	2.92162	0.213081
$189$	5.67420	0.412738
$190$	−2.17009	−0.157435
$191$	22.0410	1.59483	0.797417	−	0.603429i	$-0.206199\pi$
$191$	22.0410	1.59483	0.797417	+	0.603429i	$0.206199\pi$
$192$	21.0433	1.51867
$193$	12.7877	0.920475	0.460238	−	0.887796i	$-0.347764\pi$
$193$	12.7877	0.920475	0.460238	+	0.887796i	$0.347764\pi$
$194$	−19.2846	−1.38455
$195$	−2.34017	−0.167583
$196$	−15.8143	−1.12959
$197$	−9.20394	−0.655753	−0.327877	−	0.944721i	$-0.606333\pi$
$197$	−9.20394	−0.655753	−0.327877	+	0.944721i	$0.606333\pi$
$198$	1.07838	0.0766370
$199$	−16.1978	−1.14823	−0.574116	−	0.818774i	$-0.694654\pi$
$199$	−16.1978	−1.14823	−0.574116	+	0.818774i	$0.694654\pi$
$200$	1.53919	0.108837
$201$	−17.7587	−1.25260
$202$	−10.6803	−0.751467
$203$	1.52973	0.107366
$204$	−15.1050	−1.05756
$205$	−3.26180	−0.227814
$206$	13.8660	0.966092
$207$	−0.183417	−0.0127484
$208$	−2.84551	−0.197301
$209$	6.34017	0.438559
$210$	−4.00000	−0.276026
$211$	7.78539	0.535968	0.267984	−	0.963423i	$-0.413643\pi$
$211$	7.78539	0.535968	0.267984	+	0.963423i	$0.413643\pi$
$212$	17.9649	1.23384
$213$	18.5236	1.26922
$214$	4.97107	0.339815
$215$	−11.9155	−0.812629
$216$	8.09890	0.551060
$217$	9.36069	0.635445
$218$	−27.8576	−1.88676
$219$	−9.26180	−0.625854
$220$	−17.1773	−1.15809
$221$	4.46573	0.300398
$222$	−19.9155	−1.33664
$223$	12.5464	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$223$	12.5464	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$224$	−8.18342	−0.546778
$225$	−0.0783777	−0.00522518
$226$	−27.9649	−1.86020
$227$	2.29072	0.152041	0.0760204	−	0.997106i	$-0.475779\pi$
$227$	2.29072	0.152041	0.0760204	+	0.997106i	$0.475779\pi$
$228$	4.63090	0.306689
$229$	−5.91548	−0.390906	−0.195453	−	0.980713i	$-0.562618\pi$
$229$	−5.91548	−0.390906	−0.195453	+	0.980713i	$0.562618\pi$
$230$	5.07838	0.334858
$231$	11.6865	0.768915
$232$	2.18342	0.143348
$233$	13.5174	0.885557	0.442779	−	0.896631i	$-0.353993\pi$
$233$	13.5174	0.885557	0.442779	+	0.896631i	$0.353993\pi$
$234$	−0.232866	−0.0152229
$235$	1.07838	0.0703456
$236$	−30.9360	−2.01376
$237$	−24.3668	−1.58280
$238$	7.63317	0.494785
$239$	13.8432	0.895445	0.447723	−	0.894173i	$-0.352235\pi$
$239$	13.8432	0.895445	0.447723	+	0.894173i	$0.352235\pi$
$240$	3.55252	0.229314
$241$	7.26180	0.467773	0.233887	−	0.972264i	$-0.424856\pi$
$241$	7.26180	0.467773	0.233887	+	0.972264i	$0.424856\pi$
$242$	63.3617	4.07305
$243$	−0.814315	−0.0522383
$244$	15.1773	0.971625
$245$	−5.83710	−0.372919
$246$	12.0989	0.771397
$247$	−1.36910	−0.0871139
$248$	13.3607	0.848405
$249$	24.5113	1.55334
$250$	2.17009	0.137248
$251$	10.4703	0.660877	0.330439	−	0.943827i	$-0.392803\pi$
$251$	10.4703	0.660877	0.330439	+	0.943827i	$0.392803\pi$
$252$	−0.228990	−0.0144250
$253$	−14.8371	−0.932801
$254$	−17.8660	−1.12101
$255$	−5.57531	−0.349139
$256$	−0.418551	−0.0261594
$257$	−23.6248	−1.47367	−0.736836	−	0.676072i	$-0.763681\pi$
$257$	−23.6248	−1.47367	−0.736836	+	0.676072i	$0.763681\pi$
$258$	44.1978	2.75163
$259$	5.78992	0.359768
$260$	3.70928	0.230039
$261$	−0.111183	−0.00688204
$262$	3.20394	0.197940
$263$	5.65983	0.349000	0.174500	−	0.984657i	$-0.444169\pi$
$263$	5.65983	0.349000	0.174500	+	0.984657i	$0.444169\pi$
$264$	16.6803	1.02660
$265$	6.63090	0.407333
$266$	−2.34017	−0.143485
$267$	−12.9483	−0.792422
$268$	28.1483	1.71943
$269$	−2.31351	−0.141057	−0.0705286	−	0.997510i	$-0.522469\pi$
$269$	−2.31351	−0.141057	−0.0705286	+	0.997510i	$0.522469\pi$
$270$	11.4186	0.694911
$271$	−19.7009	−1.19674	−0.598371	−	0.801219i	$-0.704185\pi$
$271$	−19.7009	−1.19674	−0.598371	+	0.801219i	$0.704185\pi$
$272$	−6.77924	−0.411052
$273$	−2.52359	−0.152735
$274$	−8.55479	−0.516814
$275$	−6.34017	−0.382327
$276$	−10.8371	−0.652317
$277$	−25.7321	−1.54609	−0.773045	−	0.634351i	$-0.781267\pi$
$277$	−25.7321	−1.54609	−0.773045	+	0.634351i	$0.781267\pi$
$278$	19.2351	1.15365
$279$	−0.680346	−0.0407312
$280$	1.65983	0.0991936
$281$	−6.58145	−0.392616	−0.196308	−	0.980542i	$-0.562895\pi$
$281$	−6.58145	−0.392616	−0.196308	+	0.980542i	$0.562895\pi$
$282$	−4.00000	−0.238197
$283$	−0.496928	−0.0295393	−0.0147697	−	0.999891i	$-0.504702\pi$
$283$	−0.496928	−0.0295393	−0.0147697	+	0.999891i	$0.504702\pi$
$284$	−29.3607	−1.74224
$285$	1.70928	0.101249
$286$	−18.8371	−1.11386
$287$	−3.51745	−0.207628
$288$	0.594780	0.0350478
$289$	−6.36069	−0.374158
$290$	3.07838	0.180769
$291$	15.1896	0.890428
$292$	14.6803	0.859102
$293$	6.63090	0.387381	0.193691	−	0.981063i	$-0.437954\pi$
$293$	6.63090	0.387381	0.193691	+	0.981063i	$0.437954\pi$
$294$	21.6514	1.26274
$295$	−11.4186	−0.664814
$296$	8.26406	0.480339
$297$	−33.3607	−1.93578
$298$	−42.8781	−2.48386
$299$	3.20394	0.185288
$300$	−4.63090	−0.267365
$301$	−12.8494	−0.740626
$302$	7.41855	0.426890
$303$	8.41241	0.483280
$304$	2.07838	0.119203
$305$	5.60197	0.320768
$306$	−0.554787	−0.0317151
$307$	14.6042	0.833508	0.416754	−	0.909019i	$-0.363168\pi$
$307$	14.6042	0.833508	0.416754	+	0.909019i	$0.363168\pi$
$308$	−18.5236	−1.05548
$309$	−10.9216	−0.621309
$310$	18.8371	1.06988
$311$	19.3340	1.09633	0.548166	−	0.836369i	$-0.315326\pi$
$311$	19.3340	1.09633	0.548166	+	0.836369i	$0.315326\pi$
$312$	−3.60197	−0.203921
$313$	30.6803	1.73416	0.867078	−	0.498173i	$-0.165995\pi$
$313$	30.6803	1.73416	0.867078	+	0.498173i	$0.165995\pi$
$314$	20.4391	1.15344
$315$	−0.0845208	−0.00476221
$316$	38.6225	2.17268
$317$	18.7298	1.05197	0.525985	−	0.850494i	$-0.323697\pi$
$317$	18.7298	1.05197	0.525985	+	0.850494i	$0.323697\pi$
$318$	−24.5958	−1.37927
$319$	−8.99386	−0.503559
$320$	−12.3112	−0.688219
$321$	−3.91548	−0.218541
$322$	5.47641	0.305188
$323$	−3.26180	−0.181491
$324$	−23.7298	−1.31832
$325$	1.36910	0.0759441
$326$	−6.34017	−0.351150
$327$	21.9421	1.21340
$328$	−5.02052	−0.277212
$329$	1.16290	0.0641127
$330$	23.5174	1.29459
$331$	−2.73820	−0.150505	−0.0752527	−	0.997164i	$-0.523976\pi$
$331$	−2.73820	−0.150505	−0.0752527	+	0.997164i	$0.523976\pi$
$332$	−38.8515	−2.13225
$333$	−0.420818	−0.0230607
$334$	45.3835	2.48327
$335$	10.3896	0.567646
$336$	3.83096	0.208996
$337$	−6.04945	−0.329534	−0.164767	−	0.986332i	$-0.552687\pi$
$337$	−6.04945	−0.329534	−0.164767	+	0.986332i	$0.552687\pi$
$338$	−24.1434	−1.31323
$339$	22.0267	1.19632
$340$	8.83710	0.479259
$341$	−55.0349	−2.98031
$342$	0.170086	0.00919722
$343$	−13.8432	−0.747465
$344$	−18.3402	−0.988836
$345$	−4.00000	−0.215353
$346$	−2.29072	−0.123150
$347$	−5.97334	−0.320666	−0.160333	−	0.987063i	$-0.551257\pi$
$347$	−5.97334	−0.320666	−0.160333	+	0.987063i	$0.551257\pi$
$348$	−6.56916	−0.352144
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	2.34017	0.125088
$351$	7.20394	0.384518
$352$	48.1133	2.56445
$353$	−14.0989	−0.750409	−0.375204	−	0.926942i	$-0.622427\pi$
$353$	−14.0989	−0.750409	−0.375204	+	0.926942i	$0.622427\pi$
$354$	42.3545	2.25112
$355$	−10.8371	−0.575174
$356$	20.5236	1.08775
$357$	−6.01229	−0.318204
$358$	1.94214	0.102645
$359$	6.02666	0.318075	0.159038	−	0.987273i	$-0.449161\pi$
$359$	6.02666	0.318075	0.159038	+	0.987273i	$0.449161\pi$
$360$	−0.120638	−0.00635819
$361$	1.00000	0.0526316
$362$	−1.81658	−0.0954775
$363$	−49.9071	−2.61944
$364$	4.00000	0.209657
$365$	5.41855	0.283620
$366$	−20.7792	−1.08615
$367$	1.07838	0.0562909	0.0281454	−	0.999604i	$-0.491040\pi$
$367$	1.07838	0.0562909	0.0281454	+	0.999604i	$0.491040\pi$
$368$	−4.86376	−0.253541
$369$	0.255652	0.0133087
$370$	11.6514	0.605728
$371$	7.15061	0.371241
$372$	−40.1978	−2.08416
$373$	12.3051	0.637134	0.318567	−	0.947900i	$-0.396798\pi$
$373$	12.3051	0.637134	0.318567	+	0.947900i	$0.396798\pi$
$374$	−44.8781	−2.32059
$375$	−1.70928	−0.0882666
$376$	1.65983	0.0855990
$377$	1.94214	0.100025
$378$	12.3135	0.633339
$379$	1.04718	0.0537901	0.0268950	−	0.999638i	$-0.491438\pi$
$379$	1.04718	0.0537901	0.0268950	+	0.999638i	$0.491438\pi$
$380$	−2.70928	−0.138983
$381$	14.0722	0.720942
$382$	47.8310	2.44724
$383$	0.0806452	0.00412078	0.00206039	−	0.999998i	$-0.499344\pi$
$383$	0.0806452	0.00412078	0.00206039	+	0.999998i	$0.499344\pi$
$384$	19.7237	1.00652
$385$	−6.83710	−0.348451
$386$	27.7503	1.41245
$387$	0.933908	0.0474732
$388$	−24.0761	−1.22228
$389$	−20.5236	−1.04059	−0.520294	−	0.853987i	$-0.674178\pi$
$389$	−20.5236	−1.04059	−0.520294	+	0.853987i	$0.674178\pi$
$390$	−5.07838	−0.257154
$391$	7.63317	0.386026
$392$	−8.98440	−0.453781
$393$	−2.52359	−0.127298
$394$	−19.9733	−1.00624
$395$	14.2557	0.717280
$396$	1.34632	0.0676549
$397$	39.4596	1.98042	0.990210	−	0.139586i	$-0.0445771\pi$
$397$	39.4596	1.98042	0.990210	+	0.139586i	$0.0445771\pi$
$398$	−35.1506	−1.76194
$399$	1.84324	0.0922776
$400$	−2.07838	−0.103919
$401$	0.470266	0.0234840	0.0117420	−	0.999931i	$-0.496262\pi$
$401$	0.470266	0.0234840	0.0117420	+	0.999931i	$0.496262\pi$
$402$	−38.5380	−1.92210
$403$	11.8843	0.591998
$404$	−13.3340	−0.663393
$405$	−8.75872	−0.435224
$406$	3.31965	0.164752
$407$	−34.0410	−1.68735
$408$	−8.58145	−0.424845
$409$	10.4826	0.518329	0.259164	−	0.965833i	$-0.416553\pi$
$409$	10.4826	0.518329	0.259164	+	0.965833i	$0.416553\pi$
$410$	−7.07838	−0.349576
$411$	6.73820	0.332371
$412$	17.3112	0.852864
$413$	−12.3135	−0.605908
$414$	−0.398032	−0.0195622
$415$	−14.3402	−0.703931
$416$	−10.3896	−0.509393
$417$	−15.1506	−0.741929
$418$	13.7587	0.672961
$419$	34.6681	1.69365	0.846823	−	0.531875i	$-0.178512\pi$
$419$	34.6681	1.69365	0.846823	+	0.531875i	$0.178512\pi$
$420$	−4.99386	−0.243675
$421$	−34.6102	−1.68680	−0.843399	−	0.537288i	$-0.819449\pi$
$421$	−34.6102	−1.68680	−0.843399	+	0.537288i	$0.819449\pi$
$422$	16.8950	0.822434
$423$	−0.0845208	−0.00410954
$424$	10.2062	0.495657
$425$	3.26180	0.158220
$426$	40.1978	1.94759
$427$	6.04104	0.292346
$428$	6.20620	0.299988
$429$	14.8371	0.716342
$430$	−25.8576	−1.24697
$431$	6.73820	0.324568	0.162284	−	0.986744i	$-0.448114\pi$
$431$	6.73820	0.324568	0.162284	+	0.986744i	$0.448114\pi$
$432$	−10.9360	−0.526158
$433$	20.4741	0.983924	0.491962	−	0.870617i	$-0.336280\pi$
$433$	20.4741	0.983924	0.491962	+	0.870617i	$0.336280\pi$
$434$	20.3135	0.975080
$435$	−2.42469	−0.116255
$436$	−34.7792	−1.66562
$437$	−2.34017	−0.111946
$438$	−20.0989	−0.960362
$439$	−21.4596	−1.02421	−0.512105	−	0.858923i	$-0.671134\pi$
$439$	−21.4596	−1.02421	−0.512105	+	0.858923i	$0.671134\pi$
$440$	−9.75872	−0.465229
$441$	0.457499	0.0217857
$442$	9.69102	0.460955
$443$	−21.5441	−1.02359	−0.511796	−	0.859107i	$-0.671020\pi$
$443$	−21.5441	−1.02359	−0.511796	+	0.859107i	$0.671020\pi$
$444$	−24.8638	−1.17998
$445$	7.57531	0.359104
$446$	27.2267	1.28922
$447$	33.7731	1.59741
$448$	−13.2762	−0.627240
$449$	−8.47027	−0.399737	−0.199868	−	0.979823i	$-0.564051\pi$
$449$	−8.47027	−0.399737	−0.199868	+	0.979823i	$0.564051\pi$
$450$	−0.170086	−0.00801795
$451$	20.6803	0.973799
$452$	−34.9132	−1.64218
$453$	−5.84324	−0.274540
$454$	4.97107	0.233304
$455$	1.47641	0.0692151
$456$	2.63090	0.123203
$457$	11.3607	0.531431	0.265715	−	0.964052i	$-0.414392\pi$
$457$	11.3607	0.531431	0.265715	+	0.964052i	$0.414392\pi$
$458$	−12.8371	−0.599838
$459$	17.1629	0.801096
$460$	6.34017	0.295612
$461$	3.04718	0.141921	0.0709607	−	0.997479i	$-0.477394\pi$
$461$	3.04718	0.141921	0.0709607	+	0.997479i	$0.477394\pi$
$462$	25.3607	1.17989
$463$	−9.97334	−0.463500	−0.231750	−	0.972775i	$-0.574445\pi$
$463$	−9.97334	−0.463500	−0.231750	+	0.972775i	$0.574445\pi$
$464$	−2.94828	−0.136871
$465$	−14.8371	−0.688054
$466$	29.3340	1.35887
$467$	1.49079	0.0689853	0.0344927	−	0.999405i	$-0.489018\pi$
$467$	1.49079	0.0689853	0.0344927	+	0.999405i	$0.489018\pi$
$468$	−0.290725	−0.0134388
$469$	11.2039	0.517350
$470$	2.34017	0.107944
$471$	−16.0989	−0.741798
$472$	−17.5753	−0.808969
$473$	75.5462	3.47362
$474$	−52.8781	−2.42877
$475$	−1.00000	−0.0458831
$476$	9.52973	0.436795
$477$	−0.519715	−0.0237961
$478$	30.0410	1.37405
$479$	−10.1711	−0.464731	−0.232365	−	0.972629i	$-0.574647\pi$
$479$	−10.1711	−0.464731	−0.232365	+	0.972629i	$0.574647\pi$
$480$	12.9711	0.592046
$481$	7.35085	0.335170
$482$	15.7587	0.717790
$483$	−4.31351	−0.196272
$484$	79.1049	3.59568
$485$	−8.88655	−0.403517
$486$	−1.76713	−0.0801588
$487$	−24.2784	−1.10016	−0.550081	−	0.835112i	$-0.685403\pi$
$487$	−24.2784	−1.10016	−0.550081	+	0.835112i	$0.685403\pi$
$488$	8.62249	0.390322
$489$	4.99386	0.225830
$490$	−12.6670	−0.572237
$491$	19.2039	0.866662	0.433331	−	0.901235i	$-0.357338\pi$
$491$	19.2039	0.866662	0.433331	+	0.901235i	$0.357338\pi$
$492$	15.1050	0.680988
$493$	4.62702	0.208391
$494$	−2.97107	−0.133675
$495$	0.496928	0.0223353
$496$	−18.0410	−0.810067
$497$	−11.6865	−0.524211
$498$	53.1917	2.38357
$499$	7.33403	0.328316	0.164158	−	0.986434i	$-0.447509\pi$
$499$	7.33403	0.328316	0.164158	+	0.986434i	$0.447509\pi$
$500$	2.70928	0.121162
$501$	−35.7464	−1.59703
$502$	22.7214	1.01410
$503$	29.0616	1.29579	0.647895	−	0.761729i	$-0.275649\pi$
$503$	29.0616	1.29579	0.647895	+	0.761729i	$0.275649\pi$
$504$	−0.130094	−0.00579483
$505$	−4.92162	−0.219009
$506$	−32.1978	−1.43137
$507$	19.0166	0.844559
$508$	−22.3051	−0.989629
$509$	26.0456	1.15445	0.577225	−	0.816585i	$-0.304136\pi$
$509$	26.0456	1.15445	0.577225	+	0.816585i	$0.304136\pi$
$510$	−12.0989	−0.535748
$511$	5.84324	0.258490
$512$	22.1701	0.979789
$513$	−5.26180	−0.232314
$514$	−51.2678	−2.26132
$515$	6.38962	0.281560
$516$	55.1794	2.42914
$517$	−6.83710	−0.300695
$518$	12.5646	0.552058
$519$	1.80430	0.0791998
$520$	2.10731	0.0924115
$521$	−38.8248	−1.70095	−0.850473	−	0.526019i	$-0.823684\pi$
$521$	−38.8248	−1.70095	−0.850473	+	0.526019i	$0.823684\pi$
$522$	−0.241276	−0.0105604
$523$	4.59970	0.201131	0.100565	−	0.994930i	$-0.467935\pi$
$523$	4.59970	0.201131	0.100565	+	0.994930i	$0.467935\pi$
$524$	4.00000	0.174741
$525$	−1.84324	−0.0804458
$526$	12.2823	0.535534
$527$	28.3135	1.23336
$528$	−22.5236	−0.980213
$529$	−17.5236	−0.761895
$530$	14.3896	0.625045
$531$	0.894960	0.0388380
$532$	−2.92162	−0.126668
$533$	−4.46573	−0.193432
$534$	−28.0989	−1.21596
$535$	2.29072	0.0990367
$536$	15.9916	0.690731
$537$	−1.52973	−0.0660129
$538$	−5.02052	−0.216450
$539$	37.0082	1.59406
$540$	14.2557	0.613466
$541$	−12.1256	−0.521318	−0.260659	−	0.965431i	$-0.583940\pi$
$541$	−12.1256	−0.521318	−0.260659	+	0.965431i	$0.583940\pi$
$542$	−42.7526	−1.83638
$543$	1.43084	0.0614031
$544$	−24.7526	−1.06126
$545$	−12.8371	−0.549881
$546$	−5.47641	−0.234369
$547$	−9.54023	−0.407911	−0.203955	−	0.978980i	$-0.565380\pi$
$547$	−9.54023	−0.407911	−0.203955	+	0.978980i	$0.565380\pi$
$548$	−10.6803	−0.456242
$549$	−0.439070	−0.0187390
$550$	−13.7587	−0.586674
$551$	−1.41855	−0.0604323
$552$	−6.15676	−0.262049
$553$	15.3730	0.653726
$554$	−55.8408	−2.37245
$555$	−9.17727	−0.389554
$556$	24.0144	1.01844
$557$	19.9421	0.844976	0.422488	−	0.906369i	$-0.361157\pi$
$557$	19.9421	0.844976	0.422488	+	0.906369i	$0.361157\pi$
$558$	−1.47641	−0.0625014
$559$	−16.3135	−0.689988
$560$	−2.24128	−0.0947112
$561$	35.3484	1.49241
$562$	−14.2823	−0.602463
$563$	23.5525	0.992620	0.496310	−	0.868145i	$-0.334688\pi$
$563$	23.5525	0.992620	0.496310	+	0.868145i	$0.334688\pi$
$564$	−4.99386	−0.210279
$565$	−12.8865	−0.542141
$566$	−1.07838	−0.0453276
$567$	−9.44521	−0.396662
$568$	−16.6803	−0.699892
$569$	−10.0000	−0.419222	−0.209611	−	0.977785i	$-0.567220\pi$
$569$	−10.0000	−0.419222	−0.209611	+	0.977785i	$0.567220\pi$
$570$	3.70928	0.155364
$571$	−23.5031	−0.983573	−0.491786	−	0.870716i	$-0.663656\pi$
$571$	−23.5031	−0.983573	−0.491786	+	0.870716i	$0.663656\pi$
$572$	−23.5174	−0.983314
$573$	−37.6742	−1.57386
$574$	−7.63317	−0.318602
$575$	2.34017	0.0975920
$576$	0.964928	0.0402053
$577$	16.4703	0.685666	0.342833	−	0.939396i	$-0.388613\pi$
$577$	16.4703	0.685666	0.342833	+	0.939396i	$0.388613\pi$
$578$	−13.8033	−0.574140
$579$	−21.8576	−0.908372
$580$	3.84324	0.159582
$581$	−15.4641	−0.641560
$582$	32.9627	1.36635
$583$	−42.0410	−1.74116
$584$	8.34017	0.345119
$585$	−0.107307	−0.00443660
$586$	14.3896	0.594430
$587$	−28.8104	−1.18913	−0.594567	−	0.804046i	$-0.702677\pi$
$587$	−28.8104	−1.18913	−0.594567	+	0.804046i	$0.702677\pi$
$588$	27.0310	1.11474
$589$	−8.68035	−0.357667
$590$	−24.7792	−1.02015
$591$	15.7321	0.647131
$592$	−11.1590	−0.458633
$593$	−43.2450	−1.77586	−0.887929	−	0.459980i	$-0.847856\pi$
$593$	−43.2450	−1.77586	−0.887929	+	0.459980i	$0.847856\pi$
$594$	−72.3956	−2.97043
$595$	3.51745	0.144201
$596$	−53.5318	−2.19275
$597$	27.6865	1.13313
$598$	6.95282	0.284322
$599$	−44.2967	−1.80991	−0.904957	−	0.425503i	$-0.860097\pi$
$599$	−44.2967	−1.80991	−0.904957	+	0.425503i	$0.860097\pi$
$600$	−2.63090	−0.107406
$601$	−24.3090	−0.991584	−0.495792	−	0.868441i	$-0.665122\pi$
$601$	−24.3090	−0.991584	−0.495792	+	0.868441i	$0.665122\pi$
$602$	−27.8843	−1.13648
$603$	−0.814315	−0.0331615
$604$	9.26180	0.376857
$605$	29.1978	1.18706
$606$	18.2557	0.741585
$607$	−6.29072	−0.255333	−0.127666	−	0.991817i	$-0.540749\pi$
$607$	−6.29072	−0.255333	−0.127666	+	0.991817i	$0.540749\pi$
$608$	7.58864	0.307760
$609$	−2.61474	−0.105954
$610$	12.1568	0.492213
$611$	1.47641	0.0597291
$612$	−0.692632	−0.0279980
$613$	−12.7915	−0.516645	−0.258322	−	0.966059i	$-0.583170\pi$
$613$	−12.7915	−0.516645	−0.258322	+	0.966059i	$0.583170\pi$
$614$	31.6925	1.27900
$615$	5.57531	0.224818
$616$	−10.5236	−0.424008
$617$	17.9299	0.721829	0.360914	−	0.932599i	$-0.382465\pi$
$617$	17.9299	0.721829	0.360914	+	0.932599i	$0.382465\pi$
$618$	−23.7009	−0.953389
$619$	26.8515	1.07925	0.539626	−	0.841905i	$-0.318566\pi$
$619$	26.8515	1.07925	0.539626	+	0.841905i	$0.318566\pi$
$620$	23.5174	0.944483
$621$	12.3135	0.494124
$622$	41.9565	1.68230
$623$	8.16904	0.327286
$624$	4.86376	0.194706
$625$	1.00000	0.0400000
$626$	66.5790	2.66103
$627$	−10.8371	−0.432792
$628$	25.5174	1.01826
$629$	17.5129	0.698286
$630$	−0.183417	−0.00730753
$631$	35.5318	1.41450	0.707250	−	0.706964i	$-0.249936\pi$
$631$	35.5318	1.41450	0.707250	+	0.706964i	$0.249936\pi$
$632$	21.9421	0.872812
$633$	−13.3074	−0.528920
$634$	40.6453	1.61423
$635$	−8.23287	−0.326711
$636$	−30.7070	−1.21761
$637$	−7.99159	−0.316638
$638$	−19.5174	−0.772703
$639$	0.849388	0.0336013
$640$	−11.5392	−0.456126
$641$	12.9360	0.510941	0.255471	−	0.966817i	$-0.417770\pi$
$641$	12.9360	0.510941	0.255471	+	0.966817i	$0.417770\pi$
$642$	−8.49693	−0.335347
$643$	8.49693	0.335086	0.167543	−	0.985865i	$-0.446417\pi$
$643$	8.49693	0.335086	0.167543	+	0.985865i	$0.446417\pi$
$644$	6.83710	0.269420
$645$	20.3668	0.801943
$646$	−7.07838	−0.278495
$647$	−45.4908	−1.78843	−0.894214	−	0.447640i	$-0.852264\pi$
$647$	−45.4908	−1.78843	−0.894214	+	0.447640i	$0.852264\pi$
$648$	−13.4813	−0.529597
$649$	72.3956	2.84178
$650$	2.97107	0.116535
$651$	−16.0000	−0.627089
$652$	−7.91548	−0.309994
$653$	35.9421	1.40652	0.703262	−	0.710930i	$-0.251726\pi$
$653$	35.9421	1.40652	0.703262	+	0.710930i	$0.251726\pi$
$654$	47.6163	1.86195
$655$	1.47641	0.0576881
$656$	6.77924	0.264685
$657$	−0.424694	−0.0165689
$658$	2.52359	0.0983798
$659$	30.9360	1.20510	0.602548	−	0.798083i	$-0.294152\pi$
$659$	30.9360	1.20510	0.602548	+	0.798083i	$0.294152\pi$
$660$	29.3607	1.14286
$661$	10.0989	0.392802	0.196401	−	0.980524i	$-0.437075\pi$
$661$	10.0989	0.392802	0.196401	+	0.980524i	$0.437075\pi$
$662$	−5.94214	−0.230948
$663$	−7.63317	−0.296448
$664$	−22.0722	−0.856569
$665$	−1.07838	−0.0418177
$666$	−0.913212	−0.0353862
$667$	3.31965	0.128538
$668$	56.6596	2.19223
$669$	−21.4452	−0.829120
$670$	22.5464	0.871043
$671$	−35.5174	−1.37114
$672$	13.9877	0.539588
$673$	−8.67194	−0.334279	−0.167139	−	0.985933i	$-0.553453\pi$
$673$	−8.67194	−0.334279	−0.167139	+	0.985933i	$0.553453\pi$
$674$	−13.1278	−0.505665
$675$	5.26180	0.202527
$676$	−30.1422	−1.15932
$677$	41.9793	1.61340	0.806698	−	0.590964i	$-0.201253\pi$
$677$	41.9793	1.61340	0.806698	+	0.590964i	$0.201253\pi$
$678$	47.7998	1.83574
$679$	−9.58306	−0.367764
$680$	5.02052	0.192528
$681$	−3.91548	−0.150041
$682$	−119.430	−4.57323
$683$	46.3896	1.77505	0.887525	−	0.460760i	$-0.152423\pi$
$683$	46.3896	1.77505	0.887525	+	0.460760i	$0.152423\pi$
$684$	0.212347	0.00811929
$685$	−3.94214	−0.150621
$686$	−30.0410	−1.14697
$687$	10.1112	0.385766
$688$	24.7649	0.944152
$689$	9.07838	0.345859
$690$	−8.68035	−0.330455
$691$	−34.8515	−1.32581	−0.662906	−	0.748702i	$-0.730677\pi$
$691$	−34.8515	−1.32581	−0.662906	+	0.748702i	$0.730677\pi$
$692$	−2.85989	−0.108717
$693$	0.535877	0.0203563
$694$	−12.9627	−0.492056
$695$	8.86376	0.336222
$696$	−3.73206	−0.141463
$697$	−10.6393	−0.402993
$698$	−21.7009	−0.821390
$699$	−23.1050	−0.873913
$700$	2.92162	0.110427
$701$	35.6430	1.34622	0.673109	−	0.739543i	$-0.264959\pi$
$701$	35.6430	1.34622	0.673109	+	0.739543i	$0.264959\pi$
$702$	15.6332	0.590036
$703$	−5.36910	−0.202500
$704$	78.0554	2.94182
$705$	−1.84324	−0.0694206
$706$	−30.5958	−1.15149
$707$	−5.30737	−0.199604
$708$	52.8781	1.98728
$709$	16.7214	0.627985	0.313992	−	0.949426i	$-0.398333\pi$
$709$	16.7214	0.627985	0.313992	+	0.949426i	$0.398333\pi$
$710$	−23.5174	−0.882594
$711$	−1.11733	−0.0419030
$712$	11.6598	0.436970
$713$	20.3135	0.760747
$714$	−13.0472	−0.488278
$715$	−8.68035	−0.324627
$716$	2.42469	0.0906151
$717$	−23.6619	−0.883670
$718$	13.0784	0.488081
$719$	−6.85148	−0.255517	−0.127758	−	0.991805i	$-0.540778\pi$
$719$	−6.85148	−0.255517	−0.127758	+	0.991805i	$0.540778\pi$
$720$	0.162899	0.00607087
$721$	6.89043	0.256613
$722$	2.17009	0.0807623
$723$	−12.4124	−0.461622
$724$	−2.26794	−0.0842873
$725$	1.41855	0.0526837
$726$	−108.303	−4.01949
$727$	34.4391	1.27727	0.638637	−	0.769508i	$-0.279498\pi$
$727$	34.4391	1.27727	0.638637	+	0.769508i	$0.279498\pi$
$728$	2.27247	0.0842235
$729$	27.6681	1.02474
$730$	11.7587	0.435210
$731$	−38.8659	−1.43751
$732$	−25.9421	−0.958849
$733$	−19.3607	−0.715103	−0.357552	−	0.933893i	$-0.616388\pi$
$733$	−19.3607	−0.715103	−0.357552	+	0.933893i	$0.616388\pi$
$734$	2.34017	0.0863774
$735$	9.97721	0.368015
$736$	−17.7587	−0.654595
$737$	−65.8720	−2.42643
$738$	0.554787	0.0204220
$739$	−20.0000	−0.735712	−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000	−0.735712	−0.367856	+	0.929883i	$0.619908\pi$
$740$	14.5464	0.534735
$741$	2.34017	0.0859684
$742$	15.5174	0.569663
$743$	−12.7154	−0.466483	−0.233242	−	0.972419i	$-0.574933\pi$
$743$	−12.7154	−0.466483	−0.233242	+	0.972419i	$0.574933\pi$
$744$	−22.8371	−0.837249
$745$	−19.7587	−0.723904
$746$	26.7031	0.977671
$747$	1.12395	0.0411232
$748$	−56.0288	−2.04861
$749$	2.47027	0.0902616
$750$	−3.70928	−0.135444
$751$	3.15836	0.115250	0.0576252	−	0.998338i	$-0.481647\pi$
$751$	3.15836	0.115250	0.0576252	+	0.998338i	$0.481647\pi$
$752$	−2.24128	−0.0817309
$753$	−17.8966	−0.652187
$754$	4.21461	0.153487
$755$	3.41855	0.124414
$756$	15.3730	0.559110
$757$	28.0410	1.01917	0.509584	−	0.860421i	$-0.329799\pi$
$757$	28.0410	1.01917	0.509584	+	0.860421i	$0.329799\pi$
$758$	2.27247	0.0825399
$759$	25.3607	0.920535
$760$	−1.53919	−0.0558322
$761$	−16.4924	−0.597849	−0.298924	−	0.954277i	$-0.596628\pi$
$761$	−16.4924	−0.597849	−0.298924	+	0.954277i	$0.596628\pi$
$762$	30.5380	1.10627
$763$	−13.8432	−0.501159
$764$	59.7152	2.16042
$765$	−0.255652	−0.00924312
$766$	0.175007	0.00632326
$767$	−15.6332	−0.564481
$768$	0.715418	0.0258154
$769$	26.9627	0.972298	0.486149	−	0.873876i	$-0.338401\pi$
$769$	26.9627	0.972298	0.486149	+	0.873876i	$0.338401\pi$
$770$	−14.8371	−0.534692
$771$	40.3812	1.45429
$772$	34.6453	1.24691
$773$	42.1939	1.51761	0.758805	−	0.651318i	$-0.225784\pi$
$773$	42.1939	1.51761	0.758805	+	0.651318i	$0.225784\pi$
$774$	2.02666	0.0728469
$775$	8.68035	0.311807
$776$	−13.6781	−0.491014
$777$	−9.89657	−0.355037
$778$	−44.5380	−1.59676
$779$	3.26180	0.116866
$780$	−6.34017	−0.227015
$781$	68.7091	2.45860
$782$	16.5646	0.592350
$783$	7.46412	0.266746
$784$	12.1317	0.433275
$785$	9.41855	0.336162
$786$	−5.47641	−0.195337
$787$	−35.4368	−1.26319	−0.631593	−	0.775300i	$-0.717599\pi$
$787$	−35.4368	−1.26319	−0.631593	+	0.775300i	$0.717599\pi$
$788$	−24.9360	−0.888308
$789$	−9.67420	−0.344411
$790$	30.9360	1.10065
$791$	−13.8966	−0.494105
$792$	0.764867	0.0271784
$793$	7.66967	0.272358
$794$	85.6307	3.03892
$795$	−11.3340	−0.401977
$796$	−43.8843	−1.55544
$797$	15.2579	0.540463	0.270232	−	0.962795i	$-0.412900\pi$
$797$	15.2579	0.540463	0.270232	+	0.962795i	$0.412900\pi$
$798$	4.00000	0.141598
$799$	3.51745	0.124438
$800$	−7.58864	−0.268299
$801$	−0.593735	−0.0209786
$802$	1.02052	0.0360358
$803$	−34.3545	−1.21235
$804$	−48.1133	−1.69682
$805$	2.52359	0.0889449
$806$	25.7899	0.908411
$807$	3.95443	0.139202
$808$	−7.57531	−0.266498
$809$	−7.16290	−0.251834	−0.125917	−	0.992041i	$-0.540187\pi$
$809$	−7.16290	−0.251834	−0.125917	+	0.992041i	$0.540187\pi$
$810$	−19.0072	−0.667845
$811$	−50.3545	−1.76819	−0.884094	−	0.467310i	$-0.845223\pi$
$811$	−50.3545	−1.76819	−0.884094	+	0.467310i	$0.845223\pi$
$812$	4.14447	0.145442
$813$	33.6742	1.18101
$814$	−73.8720	−2.58921
$815$	−2.92162	−0.102340
$816$	11.5876	0.405647
$817$	11.9155	0.416870
$818$	22.7480	0.795367
$819$	−0.115718	−0.00404350
$820$	−8.83710	−0.308605
$821$	0.952819	0.0332536	0.0166268	−	0.999862i	$-0.494707\pi$
$821$	0.952819	0.0332536	0.0166268	+	0.999862i	$0.494707\pi$
$822$	14.6225	0.510018
$823$	−44.2290	−1.54173	−0.770863	−	0.637001i	$-0.780175\pi$
$823$	−44.2290	−1.54173	−0.770863	+	0.637001i	$0.780175\pi$
$824$	9.83483	0.342613
$825$	10.8371	0.377299
$826$	−26.7214	−0.929756
$827$	−37.8615	−1.31657	−0.658287	−	0.752767i	$-0.728719\pi$
$827$	−37.8615	−1.31657	−0.658287	+	0.752767i	$0.728719\pi$
$828$	−0.496928	−0.0172695
$829$	−56.7214	−1.97002	−0.985008	−	0.172511i	$-0.944812\pi$
$829$	−56.7214	−1.97002	−0.985008	+	0.172511i	$0.944812\pi$
$830$	−31.1194	−1.08017
$831$	43.9832	1.52576
$832$	−16.8554	−0.584354
$833$	−19.0394	−0.659677
$834$	−32.8781	−1.13848
$835$	20.9132	0.723732
$836$	17.1773	0.594088
$837$	45.6742	1.57873
$838$	75.2327	2.59887
$839$	−28.3591	−0.979064	−0.489532	−	0.871985i	$-0.662832\pi$
$839$	−28.3591	−0.979064	−0.489532	+	0.871985i	$0.662832\pi$
$840$	−2.83710	−0.0978893
$841$	−26.9877	−0.930611
$842$	−75.1071	−2.58836
$843$	11.2495	0.387454
$844$	21.0928	0.726043
$845$	−11.1256	−0.382731
$846$	−0.183417	−0.00630602
$847$	31.4863	1.08188
$848$	−13.7815	−0.473259
$849$	0.849388	0.0291509
$850$	7.07838	0.242786
$851$	12.5646	0.430710
$852$	50.1855	1.71933
$853$	−17.0061	−0.582279	−0.291140	−	0.956681i	$-0.594034\pi$
$853$	−17.0061	−0.582279	−0.291140	+	0.956681i	$0.594034\pi$
$854$	13.1096	0.448600
$855$	0.0783777	0.00268046
$856$	3.52586	0.120511
$857$	15.4101	0.526400	0.263200	−	0.964741i	$-0.415222\pi$
$857$	15.4101	0.526400	0.263200	+	0.964741i	$0.415222\pi$
$858$	32.1978	1.09921
$859$	−37.7275	−1.28725	−0.643623	−	0.765342i	$-0.722570\pi$
$859$	−37.7275	−1.28725	−0.643623	+	0.765342i	$0.722570\pi$
$860$	−32.2823	−1.10082
$861$	6.01229	0.204898
$862$	14.6225	0.498044
$863$	32.1340	1.09385	0.546927	−	0.837181i	$-0.315798\pi$
$863$	32.1340	1.09385	0.546927	+	0.837181i	$0.315798\pi$
$864$	−39.9299	−1.35844
$865$	−1.05559	−0.0358912
$866$	44.4307	1.50982
$867$	10.8722	0.369238
$868$	25.3607	0.860798
$869$	−90.3833	−3.06604
$870$	−5.26180	−0.178392
$871$	14.2245	0.481977
$872$	−19.7587	−0.669115
$873$	0.696508	0.0235732
$874$	−5.07838	−0.171779
$875$	1.07838	0.0364558
$876$	−25.0928	−0.847806
$877$	−19.8927	−0.671729	−0.335864	−	0.941910i	$-0.609028\pi$
$877$	−19.8927	−0.671729	−0.335864	+	0.941910i	$0.609028\pi$
$878$	−46.5692	−1.57163
$879$	−11.3340	−0.382287
$880$	13.1773	0.444206
$881$	24.0722	0.811014	0.405507	−	0.914092i	$-0.367095\pi$
$881$	24.0722	0.811014	0.405507	+	0.914092i	$0.367095\pi$
$882$	0.992812	0.0334297
$883$	−31.1727	−1.04905	−0.524523	−	0.851396i	$-0.675756\pi$
$883$	−31.1727	−1.04905	−0.524523	+	0.851396i	$0.675756\pi$
$884$	12.0989	0.406930
$885$	19.5174	0.656072
$886$	−46.7526	−1.57068
$887$	4.86764	0.163439	0.0817197	−	0.996655i	$-0.473959\pi$
$887$	4.86764	0.163439	0.0817197	+	0.996655i	$0.473959\pi$
$888$	−14.1256	−0.474023
$889$	−8.87814	−0.297763
$890$	16.4391	0.551039
$891$	55.5318	1.86039
$892$	33.9916	1.13812
$893$	−1.07838	−0.0360865
$894$	73.2905	2.45120
$895$	0.894960	0.0299152
$896$	−12.4436	−0.415712
$897$	−5.47641	−0.182852
$898$	−18.3812	−0.613389
$899$	12.3135	0.410679
$900$	−0.212347	−0.00707823
$901$	21.6286	0.720554
$902$	44.8781	1.49428
$903$	21.9631	0.730888
$904$	−19.8348	−0.659697
$905$	−0.837101	−0.0278262
$906$	−12.6803	−0.421276
$907$	−45.4778	−1.51007	−0.755033	−	0.655686i	$-0.772379\pi$
$907$	−45.4778	−1.51007	−0.755033	+	0.655686i	$0.772379\pi$
$908$	6.20620	0.205960
$909$	0.385746	0.0127944
$910$	3.20394	0.106209
$911$	−20.9483	−0.694048	−0.347024	−	0.937856i	$-0.612808\pi$
$911$	−20.9483	−0.694048	−0.347024	+	0.937856i	$0.612808\pi$
$912$	−3.55252	−0.117636
$913$	90.9192	3.00899
$914$	24.6537	0.815471
$915$	−9.57531	−0.316550
$916$	−16.0267	−0.529536
$917$	1.59213	0.0525767
$918$	37.2450	1.22927
$919$	−59.5174	−1.96330	−0.981650	−	0.190693i	$-0.938926\pi$
$919$	−59.5174	−1.96330	−0.981650	+	0.190693i	$0.938926\pi$
$920$	3.60197	0.118753
$921$	−24.9627	−0.822548
$922$	6.61265	0.217776
$923$	−14.8371	−0.488369
$924$	31.6619	1.04160
$925$	5.36910	0.176535
$926$	−21.6430	−0.711233
$927$	−0.500804	−0.0164486
$928$	−10.7649	−0.353374
$929$	−16.7214	−0.548611	−0.274305	−	0.961643i	$-0.588448\pi$
$929$	−16.7214	−0.548611	−0.274305	+	0.961643i	$0.588448\pi$
$930$	−32.1978	−1.05581
$931$	5.83710	0.191303
$932$	36.6225	1.19961
$933$	−33.0472	−1.08192
$934$	3.23513	0.105857
$935$	−20.6803	−0.676320
$936$	−0.165166	−0.00539862
$937$	−32.4534	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$937$	−32.4534	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$938$	24.3135	0.793864
$939$	−52.4412	−1.71135
$940$	2.92162	0.0952928
$941$	−23.6742	−0.771757	−0.385878	−	0.922550i	$-0.626102\pi$
$941$	−23.6742	−0.771757	−0.385878	+	0.922550i	$0.626102\pi$
$942$	−34.9360	−1.13828
$943$	−7.63317	−0.248570
$944$	23.7321	0.772413
$945$	5.67420	0.184582
$946$	163.942	5.33021
$947$	21.9733	0.714038	0.357019	−	0.934097i	$-0.383793\pi$
$947$	21.9733	0.714038	0.357019	+	0.934097i	$0.383793\pi$
$948$	−66.0165	−2.14412
$949$	7.41855	0.240816
$950$	−2.17009	−0.0704069
$951$	−32.0144	−1.03814
$952$	5.41402	0.175469
$953$	−53.2990	−1.72652	−0.863261	−	0.504757i	$-0.831582\pi$
$953$	−53.2990	−1.72652	−0.863261	+	0.504757i	$0.831582\pi$
$954$	−1.12783	−0.0365147
$955$	22.0410	0.713231
$956$	37.5052	1.21300
$957$	15.3730	0.496938
$958$	−22.0722	−0.713122
$959$	−4.25112	−0.137276
$960$	21.0433	0.679170
$961$	44.3484	1.43059
$962$	15.9520	0.514313
$963$	−0.179542	−0.00578565
$964$	19.6742	0.633663
$965$	12.7877	0.411649
$966$	−9.36069	−0.301175
$967$	15.8166	0.508627	0.254314	−	0.967122i	$-0.418150\pi$
$967$	15.8166	0.508627	0.254314	+	0.967122i	$0.418150\pi$
$968$	44.9409	1.44446
$969$	5.57531	0.179105
$970$	−19.2846	−0.619191
$971$	−43.1506	−1.38477	−0.692385	−	0.721529i	$-0.743440\pi$
$971$	−43.1506	−1.38477	−0.692385	+	0.721529i	$0.743440\pi$
$972$	−2.20620	−0.0707640
$973$	9.55849	0.306431
$974$	−52.6863	−1.68818
$975$	−2.34017	−0.0749455
$976$	−11.6430	−0.372684
$977$	−8.47414	−0.271112	−0.135556	−	0.990770i	$-0.543282\pi$
$977$	−8.47414	−0.271112	−0.135556	+	0.990770i	$0.543282\pi$
$978$	10.8371	0.346532
$979$	−48.0288	−1.53501
$980$	−15.8143	−0.505170
$981$	1.00614	0.0321237
$982$	41.6742	1.32988
$983$	−5.59356	−0.178407	−0.0892034	−	0.996013i	$-0.528432\pi$
$983$	−5.59356	−0.178407	−0.0892034	+	0.996013i	$0.528432\pi$
$984$	8.58145	0.273567
$985$	−9.20394	−0.293262
$986$	10.0410	0.319772
$987$	−1.98771	−0.0632696
$988$	−3.70928	−0.118008
$989$	−27.8843	−0.886669
$990$	1.07838	0.0342731
$991$	32.8950	1.04494	0.522471	−	0.852657i	$-0.325010\pi$
$991$	32.8950	1.04494	0.522471	+	0.852657i	$0.325010\pi$
$992$	−65.8720	−2.09144
$993$	4.68035	0.148526
$994$	−25.3607	−0.804392
$995$	−16.1978	−0.513505
$996$	66.4079	2.10421
$997$	23.2618	0.736708	0.368354	−	0.929686i	$-0.379921\pi$
$997$	23.2618	0.736708	0.368354	+	0.929686i	$0.379921\pi$
$998$	15.9155	0.503796
$999$	28.2511	0.893826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.2.a.a.1.3	✓	3
3.2	odd	2		855.2.a.i.1.1		3
4.3	odd	2		1520.2.a.p.1.3		3
5.2	odd	4		475.2.b.d.324.6		6
5.3	odd	4		475.2.b.d.324.1		6
5.4	even	2		475.2.a.f.1.1		3
7.6	odd	2		4655.2.a.u.1.3		3
8.3	odd	2		6080.2.a.by.1.1		3
8.5	even	2		6080.2.a.bo.1.3		3
15.14	odd	2		4275.2.a.bk.1.3		3
19.18	odd	2		1805.2.a.f.1.1		3
20.19	odd	2		7600.2.a.bx.1.1		3
95.94	odd	2		9025.2.a.bb.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.a.1.3	✓	3	1.1	even	1	trivial
475.2.a.f.1.1		3	5.4	even	2
475.2.b.d.324.1		6	5.3	odd	4
475.2.b.d.324.6		6	5.2	odd	4
855.2.a.i.1.1		3	3.2	odd	2
1520.2.a.p.1.3		3	4.3	odd	2
1805.2.a.f.1.1		3	19.18	odd	2
4275.2.a.bk.1.3		3	15.14	odd	2
4655.2.a.u.1.3		3	7.6	odd	2
6080.2.a.bo.1.3		3	8.5	even	2
6080.2.a.by.1.1		3	8.3	odd	2
7600.2.a.bx.1.1		3	20.19	odd	2
9025.2.a.bb.1.3		3	95.94	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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	95.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17009 q^{2} -1.70928 q^{3} +2.70928 q^{4} +1.00000 q^{5} -3.70928 q^{6} +1.07838 q^{7} +1.53919 q^{8} -0.0783777 q^{9} +O(q^{10})\)	\(q+2.17009 q^{2} -1.70928 q^{3} +2.70928 q^{4} +1.00000 q^{5} -3.70928 q^{6} +1.07838 q^{7} +1.53919 q^{8} -0.0783777 q^{9} +2.17009 q^{10} -6.34017 q^{11} -4.63090 q^{12} +1.36910 q^{13} +2.34017 q^{14} -1.70928 q^{15} -2.07838 q^{16} +3.26180 q^{17} -0.170086 q^{18} -1.00000 q^{19} +2.70928 q^{20} -1.84324 q^{21} -13.7587 q^{22} +2.34017 q^{23} -2.63090 q^{24} +1.00000 q^{25} +2.97107 q^{26} +5.26180 q^{27} +2.92162 q^{28} +1.41855 q^{29} -3.70928 q^{30} +8.68035 q^{31} -7.58864 q^{32} +10.8371 q^{33} +7.07838 q^{34} +1.07838 q^{35} -0.212347 q^{36} +5.36910 q^{37} -2.17009 q^{38} -2.34017 q^{39} +1.53919 q^{40} -3.26180 q^{41} -4.00000 q^{42} -11.9155 q^{43} -17.1773 q^{44} -0.0783777 q^{45} +5.07838 q^{46} +1.07838 q^{47} +3.55252 q^{48} -5.83710 q^{49} +2.17009 q^{50} -5.57531 q^{51} +3.70928 q^{52} +6.63090 q^{53} +11.4186 q^{54} -6.34017 q^{55} +1.65983 q^{56} +1.70928 q^{57} +3.07838 q^{58} -11.4186 q^{59} -4.63090 q^{60} +5.60197 q^{61} +18.8371 q^{62} -0.0845208 q^{63} -12.3112 q^{64} +1.36910 q^{65} +23.5174 q^{66} +10.3896 q^{67} +8.83710 q^{68} -4.00000 q^{69} +2.34017 q^{70} -10.8371 q^{71} -0.120638 q^{72} +5.41855 q^{73} +11.6514 q^{74} -1.70928 q^{75} -2.70928 q^{76} -6.83710 q^{77} -5.07838 q^{78} +14.2557 q^{79} -2.07838 q^{80} -8.75872 q^{81} -7.07838 q^{82} -14.3402 q^{83} -4.99386 q^{84} +3.26180 q^{85} -25.8576 q^{86} -2.42469 q^{87} -9.75872 q^{88} +7.57531 q^{89} -0.170086 q^{90} +1.47641 q^{91} +6.34017 q^{92} -14.8371 q^{93} +2.34017 q^{94} -1.00000 q^{95} +12.9711 q^{96} -8.88655 q^{97} -12.6670 q^{98} +0.496928 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 2 * q^3 + q^4 + 3 * q^5 - 4 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} + 3 q^{8} + 3 q^{9} + q^{10} - 8 q^{11} - 10 q^{12} + 8 q^{13} - 4 q^{14} + 2 q^{15} - 3 q^{16} + 2 q^{17} + 5 q^{18} - 3 q^{19} + q^{20} - 12 q^{21} - 16 q^{22} - 4 q^{23} - 4 q^{24} + 3 q^{25} - 6 q^{26} + 8 q^{27} + 12 q^{28} - 10 q^{29} - 4 q^{30} + 4 q^{31} - 3 q^{32} + 4 q^{33} + 18 q^{34} - 11 q^{36} + 20 q^{37} - q^{38} + 4 q^{39} + 3 q^{40} - 2 q^{41} - 12 q^{42} - 4 q^{43} - 12 q^{44} + 3 q^{45} + 12 q^{46} + 10 q^{48} + 11 q^{49} + q^{50} + 4 q^{51} + 4 q^{52} + 16 q^{53} + 20 q^{54} - 8 q^{55} + 16 q^{56} - 2 q^{57} + 6 q^{58} - 20 q^{59} - 10 q^{60} - 2 q^{61} + 28 q^{62} - 32 q^{63} - 11 q^{64} + 8 q^{65} + 20 q^{66} + 2 q^{67} - 2 q^{68} - 12 q^{69} - 4 q^{70} - 4 q^{71} - 13 q^{72} + 2 q^{73} - 2 q^{74} + 2 q^{75} - q^{76} + 8 q^{77} - 12 q^{78} - 3 q^{80} - q^{81} - 18 q^{82} - 32 q^{83} + 20 q^{84} + 2 q^{85} - 16 q^{86} - 28 q^{87} - 4 q^{88} + 2 q^{89} + 5 q^{90} + 20 q^{91} + 8 q^{92} - 16 q^{93} - 4 q^{94} - 3 q^{95} + 24 q^{96} + 20 q^{97} - 15 q^{98} - 16 q^{99}+O(q^{100}) \) 3 * q + q^2 + 2 * q^3 + q^4 + 3 * q^5 - 4 * q^6 + 3 * q^8 + 3 * q^9 + q^10 - 8 * q^11 - 10 * q^12 + 8 * q^13 - 4 * q^14 + 2 * q^15 - 3 * q^16 + 2 * q^17 + 5 * q^18 - 3 * q^19 + q^20 - 12 * q^21 - 16 * q^22 - 4 * q^23 - 4 * q^24 + 3 * q^25 - 6 * q^26 + 8 * q^27 + 12 * q^28 - 10 * q^29 - 4 * q^30 + 4 * q^31 - 3 * q^32 + 4 * q^33 + 18 * q^34 - 11 * q^36 + 20 * q^37 - q^38 + 4 * q^39 + 3 * q^40 - 2 * q^41 - 12 * q^42 - 4 * q^43 - 12 * q^44 + 3 * q^45 + 12 * q^46 + 10 * q^48 + 11 * q^49 + q^50 + 4 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 - 8 * q^55 + 16 * q^56 - 2 * q^57 + 6 * q^58 - 20 * q^59 - 10 * q^60 - 2 * q^61 + 28 * q^62 - 32 * q^63 - 11 * q^64 + 8 * q^65 + 20 * q^66 + 2 * q^67 - 2 * q^68 - 12 * q^69 - 4 * q^70 - 4 * q^71 - 13 * q^72 + 2 * q^73 - 2 * q^74 + 2 * q^75 - q^76 + 8 * q^77 - 12 * q^78 - 3 * q^80 - q^81 - 18 * q^82 - 32 * q^83 + 20 * q^84 + 2 * q^85 - 16 * q^86 - 28 * q^87 - 4 * q^88 + 2 * q^89 + 5 * q^90 + 20 * q^91 + 8 * q^92 - 16 * q^93 - 4 * q^94 - 3 * q^95 + 24 * q^96 + 20 * q^97 - 15 * q^98 - 16 * q^99

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