LMFDB - Embedded newform 6023.2.a.a.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.01585 q^{2} +1.02156 q^{3} +2.06364 q^{4} +0.907276 q^{5} -2.05931 q^{6} +1.44669 q^{7} -0.128285 q^{8} -1.95642 q^{9} +O(q^{10})$	\(q-2.01585 q^{2} +1.02156 q^{3} +2.06364 q^{4} +0.907276 q^{5} -2.05931 q^{6} +1.44669 q^{7} -0.128285 q^{8} -1.95642 q^{9} -1.82893 q^{10} +1.64263 q^{11} +2.10813 q^{12} +3.28313 q^{13} -2.91630 q^{14} +0.926835 q^{15} -3.86867 q^{16} -5.85334 q^{17} +3.94384 q^{18} +1.00000 q^{19} +1.87229 q^{20} +1.47787 q^{21} -3.31128 q^{22} -2.18399 q^{23} -0.131051 q^{24} -4.17685 q^{25} -6.61828 q^{26} -5.06327 q^{27} +2.98544 q^{28} +1.38582 q^{29} -1.86836 q^{30} +8.80877 q^{31} +8.05522 q^{32} +1.67804 q^{33} +11.7994 q^{34} +1.31254 q^{35} -4.03734 q^{36} -7.98191 q^{37} -2.01585 q^{38} +3.35391 q^{39} -0.116390 q^{40} -0.480022 q^{41} -2.97917 q^{42} -1.11356 q^{43} +3.38979 q^{44} -1.77501 q^{45} +4.40258 q^{46} +0.283513 q^{47} -3.95208 q^{48} -4.90710 q^{49} +8.41989 q^{50} -5.97953 q^{51} +6.77518 q^{52} +0.685261 q^{53} +10.2068 q^{54} +1.49031 q^{55} -0.185588 q^{56} +1.02156 q^{57} -2.79360 q^{58} +11.0139 q^{59} +1.91265 q^{60} -10.2931 q^{61} -17.7571 q^{62} -2.83032 q^{63} -8.50075 q^{64} +2.97870 q^{65} -3.38267 q^{66} -10.1028 q^{67} -12.0792 q^{68} -2.23107 q^{69} -2.64588 q^{70} -2.43086 q^{71} +0.250979 q^{72} -9.19020 q^{73} +16.0903 q^{74} -4.26690 q^{75} +2.06364 q^{76} +2.37636 q^{77} -6.76096 q^{78} -4.06342 q^{79} -3.50995 q^{80} +0.696820 q^{81} +0.967651 q^{82} -16.0101 q^{83} +3.04980 q^{84} -5.31059 q^{85} +2.24477 q^{86} +1.41570 q^{87} -0.210724 q^{88} +0.906021 q^{89} +3.57815 q^{90} +4.74965 q^{91} -4.50696 q^{92} +8.99868 q^{93} -0.571518 q^{94} +0.907276 q^{95} +8.22889 q^{96} +5.47112 q^{97} +9.89196 q^{98} -3.21366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) $ 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * 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 $

$2$	−2.01585	−1.42542	−0.712709	−	0.701459i	$-0.752532\pi$
$2$	−2.01585	−1.42542	−0.712709	+	0.701459i	$0.752532\pi$
$3$	1.02156	0.589797	0.294899	−	0.955529i	$-0.404714\pi$
$3$	1.02156	0.589797	0.294899	+	0.955529i	$0.404714\pi$
$4$	2.06364	1.03182
$5$	0.907276	0.405746	0.202873	−	0.979205i	$-0.434972\pi$
$5$	0.907276	0.405746	0.202873	+	0.979205i	$0.434972\pi$
$6$	−2.05931	−0.840708
$7$	1.44669	0.546796	0.273398	−	0.961901i	$-0.411852\pi$
$7$	1.44669	0.546796	0.273398	+	0.961901i	$0.411852\pi$
$8$	−0.128285	−0.0453556
$9$	−1.95642	−0.652139
$10$	−1.82893	−0.578358
$11$	1.64263	0.495270	0.247635	−	0.968853i	$-0.420347\pi$
$11$	1.64263	0.495270	0.247635	+	0.968853i	$0.420347\pi$
$12$	2.10813	0.608564
$13$	3.28313	0.910575	0.455288	−	0.890344i	$-0.349536\pi$
$13$	3.28313	0.910575	0.455288	+	0.890344i	$0.349536\pi$
$14$	−2.91630	−0.779413
$15$	0.926835	0.239308
$16$	−3.86867	−0.967168
$17$	−5.85334	−1.41964	−0.709821	−	0.704382i	$-0.751224\pi$
$17$	−5.85334	−1.41964	−0.709821	+	0.704382i	$0.751224\pi$
$18$	3.94384	0.929571
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.87229	0.418656
$21$	1.47787	0.322499
$22$	−3.31128	−0.705968
$23$	−2.18399	−0.455393	−0.227696	−	0.973732i	$-0.573119\pi$
$23$	−2.18399	−0.455393	−0.227696	+	0.973732i	$0.573119\pi$
$24$	−0.131051	−0.0267506
$25$	−4.17685	−0.835370
$26$	−6.61828	−1.29795
$27$	−5.06327	−0.974427
$28$	2.98544	0.564194
$29$	1.38582	0.257340	0.128670	−	0.991687i	$-0.458929\pi$
$29$	1.38582	0.257340	0.128670	+	0.991687i	$0.458929\pi$
$30$	−1.86836	−0.341114
$31$	8.80877	1.58210	0.791051	−	0.611751i	$-0.209534\pi$
$31$	8.80877	1.58210	0.791051	+	0.611751i	$0.209534\pi$
$32$	8.05522	1.42398
$33$	1.67804	0.292109
$34$	11.7994	2.02359
$35$	1.31254	0.221860
$36$	−4.03734	−0.672890
$37$	−7.98191	−1.31222	−0.656109	−	0.754667i	$-0.727799\pi$
$37$	−7.98191	−1.31222	−0.656109	+	0.754667i	$0.727799\pi$
$38$	−2.01585	−0.327014
$39$	3.35391	0.537055
$40$	−0.116390	−0.0184029
$41$	−0.480022	−0.0749669	−0.0374834	−	0.999297i	$-0.511934\pi$
$41$	−0.480022	−0.0749669	−0.0374834	+	0.999297i	$0.511934\pi$
$42$	−2.97917	−0.459696
$43$	−1.11356	−0.169817	−0.0849084	−	0.996389i	$-0.527060\pi$
$43$	−1.11356	−0.169817	−0.0849084	+	0.996389i	$0.527060\pi$
$44$	3.38979	0.511029
$45$	−1.77501	−0.264603
$46$	4.40258	0.649125
$47$	0.283513	0.0413546	0.0206773	−	0.999786i	$-0.493418\pi$
$47$	0.283513	0.0413546	0.0206773	+	0.999786i	$0.493418\pi$
$48$	−3.95208	−0.570433
$49$	−4.90710	−0.701014
$50$	8.41989	1.19075
$51$	−5.97953	−0.837301
$52$	6.77518	0.939549
$53$	0.685261	0.0941279	0.0470639	−	0.998892i	$-0.485014\pi$
$53$	0.685261	0.0941279	0.0470639	+	0.998892i	$0.485014\pi$
$54$	10.2068	1.38897
$55$	1.49031	0.200954
$56$	−0.185588	−0.0248003
$57$	1.02156	0.135309
$58$	−2.79360	−0.366818
$59$	11.0139	1.43388	0.716942	−	0.697133i	$-0.245541\pi$
$59$	11.0139	1.43388	0.716942	+	0.697133i	$0.245541\pi$
$60$	1.91265	0.246922
$61$	−10.2931	−1.31790	−0.658948	−	0.752189i	$-0.728998\pi$
$61$	−10.2931	−1.31790	−0.658948	+	0.752189i	$0.728998\pi$
$62$	−17.7571	−2.25516
$63$	−2.83032	−0.356587
$64$	−8.50075	−1.06259
$65$	2.97870	0.369462
$66$	−3.38267	−0.416378
$67$	−10.1028	−1.23425	−0.617126	−	0.786864i	$-0.711703\pi$
$67$	−10.1028	−1.23425	−0.617126	+	0.786864i	$0.711703\pi$
$68$	−12.0792	−1.46481
$69$	−2.23107	−0.268589
$70$	−2.64588	−0.316244
$71$	−2.43086	−0.288490	−0.144245	−	0.989542i	$-0.546075\pi$
$71$	−2.43086	−0.288490	−0.144245	+	0.989542i	$0.546075\pi$
$72$	0.250979	0.0295782
$73$	−9.19020	−1.07563	−0.537815	−	0.843063i	$-0.680750\pi$
$73$	−9.19020	−1.07563	−0.537815	+	0.843063i	$0.680750\pi$
$74$	16.0903	1.87046
$75$	−4.26690	−0.492699
$76$	2.06364	0.236716
$77$	2.37636	0.270812
$78$	−6.76096	−0.765528
$79$	−4.06342	−0.457170	−0.228585	−	0.973524i	$-0.573410\pi$
$79$	−4.06342	−0.457170	−0.228585	+	0.973524i	$0.573410\pi$
$80$	−3.50995	−0.392425
$81$	0.696820	0.0774245
$82$	0.967651	0.106859
$83$	−16.0101	−1.75734	−0.878668	−	0.477434i	$-0.841567\pi$
$83$	−16.0101	−1.75734	−0.878668	+	0.477434i	$0.841567\pi$
$84$	3.04980	0.332760
$85$	−5.31059	−0.576014
$86$	2.24477	0.242060
$87$	1.41570	0.151779
$88$	−0.210724	−0.0224633
$89$	0.906021	0.0960381	0.0480190	−	0.998846i	$-0.484709\pi$
$89$	0.906021	0.0960381	0.0480190	+	0.998846i	$0.484709\pi$
$90$	3.57815	0.377170
$91$	4.74965	0.497899
$92$	−4.50696	−0.469883
$93$	8.99868	0.933119
$94$	−0.571518	−0.0589476
$95$	0.907276	0.0930845
$96$	8.22889	0.839857
$97$	5.47112	0.555508	0.277754	−	0.960652i	$-0.410410\pi$
$97$	5.47112	0.555508	0.277754	+	0.960652i	$0.410410\pi$
$98$	9.89196	0.999239
$99$	−3.21366	−0.322985
$100$	−8.61951	−0.861951
$101$	9.88023	0.983120	0.491560	−	0.870844i	$-0.336427\pi$
$101$	9.88023	0.983120	0.491560	+	0.870844i	$0.336427\pi$
$102$	12.0538	1.19351
$103$	−16.9633	−1.67144	−0.835722	−	0.549152i	$-0.814951\pi$
$103$	−16.9633	−1.67144	−0.835722	+	0.549152i	$0.814951\pi$
$104$	−0.421176	−0.0412997
$105$	1.34084	0.130853
$106$	−1.38138	−0.134172
$107$	−3.47482	−0.335924	−0.167962	−	0.985793i	$-0.553719\pi$
$107$	−3.47482	−0.335924	−0.167962	+	0.985793i	$0.553719\pi$
$108$	−10.4488	−1.00543
$109$	16.2966	1.56093	0.780466	−	0.625199i	$-0.214982\pi$
$109$	16.2966	1.56093	0.780466	+	0.625199i	$0.214982\pi$
$110$	−3.00424	−0.286443
$111$	−8.15399	−0.773942
$112$	−5.59675	−0.528844
$113$	0.278153	0.0261665	0.0130832	−	0.999914i	$-0.495835\pi$
$113$	0.278153	0.0261665	0.0130832	+	0.999914i	$0.495835\pi$
$114$	−2.05931	−0.192872
$115$	−1.98148	−0.184774
$116$	2.85983	0.265529
$117$	−6.42316	−0.593822
$118$	−22.2023	−2.04389
$119$	−8.46794	−0.776255
$120$	−0.118899	−0.0108540
$121$	−8.30178	−0.754707
$122$	20.7493	1.87855
$123$	−0.490371	−0.0442153
$124$	18.1781	1.63244
$125$	−8.32593	−0.744694
$126$	5.70549	0.508286
$127$	1.59467	0.141504	0.0707522	−	0.997494i	$-0.477460\pi$
$127$	1.59467	0.141504	0.0707522	+	0.997494i	$0.477460\pi$
$128$	1.02576	0.0906653
$129$	−1.13757	−0.100157
$130$	−6.00460	−0.526638
$131$	−10.0059	−0.874217	−0.437108	−	0.899409i	$-0.643997\pi$
$131$	−10.0059	−0.874217	−0.437108	+	0.899409i	$0.643997\pi$
$132$	3.46287	0.301404
$133$	1.44669	0.125444
$134$	20.3657	1.75933
$135$	−4.59378	−0.395370
$136$	0.750896	0.0643888
$137$	15.3464	1.31114	0.655568	−	0.755136i	$-0.272429\pi$
$137$	15.3464	1.31114	0.655568	+	0.755136i	$0.272429\pi$
$138$	4.49750	0.382852
$139$	2.34310	0.198739	0.0993697	−	0.995051i	$-0.468317\pi$
$139$	2.34310	0.198739	0.0993697	+	0.995051i	$0.468317\pi$
$140$	2.70861	0.228920
$141$	0.289625	0.0243908
$142$	4.90024	0.411219
$143$	5.39295	0.450981
$144$	7.56874	0.630728
$145$	1.25732	0.104415
$146$	18.5260	1.53322
$147$	−5.01289	−0.413456
$148$	−16.4718	−1.35397
$149$	5.14134	0.421195	0.210597	−	0.977573i	$-0.432459\pi$
$149$	5.14134	0.421195	0.210597	+	0.977573i	$0.432459\pi$
$150$	8.60142	0.702303
$151$	−23.8848	−1.94372	−0.971859	−	0.235562i	$-0.924307\pi$
$151$	−23.8848	−1.94372	−0.971859	+	0.235562i	$0.924307\pi$
$152$	−0.128285	−0.0104053
$153$	11.4516	0.925804
$154$	−4.79038	−0.386020
$155$	7.99198	0.641931
$156$	6.92125	0.554143
$157$	18.8329	1.50303	0.751514	−	0.659717i	$-0.229324\pi$
$157$	18.8329	1.50303	0.751514	+	0.659717i	$0.229324\pi$
$158$	8.19123	0.651659
$159$	0.700035	0.0555164
$160$	7.30831	0.577772
$161$	−3.15954	−0.249007
$162$	−1.40468	−0.110362
$163$	−18.9087	−1.48105	−0.740523	−	0.672031i	$-0.765422\pi$
$163$	−18.9087	−1.48105	−0.740523	+	0.672031i	$0.765422\pi$
$164$	−0.990592	−0.0773522
$165$	1.52244	0.118522
$166$	32.2739	2.50494
$167$	−8.98057	−0.694937	−0.347469	−	0.937692i	$-0.612959\pi$
$167$	−8.98057	−0.694937	−0.347469	+	0.937692i	$0.612959\pi$
$168$	−0.189589	−0.0146271
$169$	−2.22109	−0.170853
$170$	10.7053	0.821062
$171$	−1.95642	−0.149611
$172$	−2.29799	−0.175220
$173$	7.73983	0.588448	0.294224	−	0.955736i	$-0.404939\pi$
$173$	7.73983	0.588448	0.294224	+	0.955736i	$0.404939\pi$
$174$	−2.85383	−0.216348
$175$	−6.04259	−0.456777
$176$	−6.35478	−0.479010
$177$	11.2513	0.845701
$178$	−1.82640	−0.136895
$179$	4.06539	0.303861	0.151931	−	0.988391i	$-0.451451\pi$
$179$	4.06539	0.303861	0.151931	+	0.988391i	$0.451451\pi$
$180$	−3.66298	−0.273022
$181$	−8.54765	−0.635342	−0.317671	−	0.948201i	$-0.602901\pi$
$181$	−8.54765	−0.635342	−0.317671	+	0.948201i	$0.602901\pi$
$182$	−9.57457	−0.709714
$183$	−10.5150	−0.777292
$184$	0.280173	0.0206546
$185$	−7.24179	−0.532427
$186$	−18.1400	−1.33009
$187$	−9.61484	−0.703107
$188$	0.585068	0.0426705
$189$	−7.32496	−0.532813
$190$	−1.82893	−0.132684
$191$	−18.2218	−1.31848	−0.659241	−	0.751932i	$-0.729122\pi$
$191$	−18.2218	−1.31848	−0.659241	+	0.751932i	$0.729122\pi$
$192$	−8.68402	−0.626715
$193$	12.4382	0.895324	0.447662	−	0.894203i	$-0.352257\pi$
$193$	12.4382	0.895324	0.447662	+	0.894203i	$0.352257\pi$
$194$	−11.0289	−0.791832
$195$	3.04292	0.217908
$196$	−10.1265	−0.723320
$197$	−13.7993	−0.983162	−0.491581	−	0.870832i	$-0.663581\pi$
$197$	−13.7993	−0.983162	−0.491581	+	0.870832i	$0.663581\pi$
$198$	6.47825	0.460389
$199$	−12.2065	−0.865296	−0.432648	−	0.901563i	$-0.642421\pi$
$199$	−12.2065	−0.865296	−0.432648	+	0.901563i	$0.642421\pi$
$200$	0.535828	0.0378887
$201$	−10.3206	−0.727959
$202$	−19.9170	−1.40136
$203$	2.00485	0.140713
$204$	−12.3396	−0.863944
$205$	−0.435512	−0.0304175
$206$	34.1954	2.38251
$207$	4.27279	0.296979
$208$	−12.7013	−0.880679
$209$	1.64263	0.113623
$210$	−2.70293	−0.186520
$211$	23.0898	1.58957	0.794784	−	0.606893i	$-0.207584\pi$
$211$	23.0898	1.58957	0.794784	+	0.606893i	$0.207584\pi$
$212$	1.41413	0.0971229
$213$	−2.48327	−0.170151
$214$	7.00471	0.478832
$215$	−1.01031	−0.0689024
$216$	0.649542	0.0441958
$217$	12.7435	0.865086
$218$	−32.8515	−2.22498
$219$	−9.38833	−0.634404
$220$	3.07547	0.207348
$221$	−19.2172	−1.29269
$222$	16.4372	1.10319
$223$	10.7784	0.721773	0.360887	−	0.932610i	$-0.382474\pi$
$223$	10.7784	0.721773	0.360887	+	0.932610i	$0.382474\pi$
$224$	11.6534	0.778624
$225$	8.17166	0.544778
$226$	−0.560714	−0.0372982
$227$	−12.1183	−0.804321	−0.402160	−	0.915569i	$-0.631741\pi$
$227$	−12.1183	−0.804321	−0.402160	+	0.915569i	$0.631741\pi$
$228$	2.10813	0.139614
$229$	−0.552548	−0.0365134	−0.0182567	−	0.999833i	$-0.505812\pi$
$229$	−0.552548	−0.0365134	−0.0182567	+	0.999833i	$0.505812\pi$
$230$	3.99436	0.263380
$231$	2.42759	0.159724
$232$	−0.177780	−0.0116718
$233$	−7.02335	−0.460115	−0.230057	−	0.973177i	$-0.573891\pi$
$233$	−7.02335	−0.460115	−0.230057	+	0.973177i	$0.573891\pi$
$234$	12.9481	0.846445
$235$	0.257224	0.0167795
$236$	22.7287	1.47951
$237$	−4.15102	−0.269638
$238$	17.0701	1.10649
$239$	25.4005	1.64302	0.821509	−	0.570195i	$-0.193132\pi$
$239$	25.4005	1.64302	0.821509	+	0.570195i	$0.193132\pi$
$240$	−3.58562	−0.231451
$241$	0.790547	0.0509236	0.0254618	−	0.999676i	$-0.491894\pi$
$241$	0.790547	0.0509236	0.0254618	+	0.999676i	$0.491894\pi$
$242$	16.7351	1.07577
$243$	15.9017	1.02009
$244$	−21.2412	−1.35983
$245$	−4.45209	−0.284434
$246$	0.988513	0.0630253
$247$	3.28313	0.208900
$248$	−1.13003	−0.0717572
$249$	−16.3552	−1.03647
$250$	16.7838	1.06150
$251$	1.03776	0.0655028	0.0327514	−	0.999464i	$-0.489573\pi$
$251$	1.03776	0.0655028	0.0327514	+	0.999464i	$0.489573\pi$
$252$	−5.84076	−0.367933
$253$	−3.58747	−0.225542
$254$	−3.21462	−0.201703
$255$	−5.42508	−0.339732
$256$	14.9337	0.933358
$257$	16.6016	1.03558	0.517788	−	0.855509i	$-0.326755\pi$
$257$	16.6016	1.03558	0.517788	+	0.855509i	$0.326755\pi$
$258$	2.29317	0.142766
$259$	−11.5473	−0.717515
$260$	6.14696	0.381218
$261$	−2.71124	−0.167822
$262$	20.1703	1.24613
$263$	−28.1721	−1.73716	−0.868582	−	0.495545i	$-0.834968\pi$
$263$	−28.1721	−1.73716	−0.868582	+	0.495545i	$0.834968\pi$
$264$	−0.215267	−0.0132488
$265$	0.621721	0.0381920
$266$	−2.91630	−0.178810
$267$	0.925554	0.0566430
$268$	−20.8485	−1.27352
$269$	6.42353	0.391650	0.195825	−	0.980639i	$-0.437262\pi$
$269$	6.42353	0.391650	0.195825	+	0.980639i	$0.437262\pi$
$270$	9.26036	0.563568
$271$	−15.7820	−0.958686	−0.479343	−	0.877628i	$-0.659125\pi$
$271$	−15.7820	−0.958686	−0.479343	+	0.877628i	$0.659125\pi$
$272$	22.6446	1.37303
$273$	4.85205	0.293659
$274$	−30.9361	−1.86892
$275$	−6.86100	−0.413734
$276$	−4.60412	−0.277136
$277$	6.96639	0.418570	0.209285	−	0.977855i	$-0.432886\pi$
$277$	6.96639	0.418570	0.209285	+	0.977855i	$0.432886\pi$
$278$	−4.72334	−0.283287
$279$	−17.2336	−1.03175
$280$	−0.168380	−0.0100626
$281$	1.97196	0.117637	0.0588186	−	0.998269i	$-0.481267\pi$
$281$	1.97196	0.117637	0.0588186	+	0.998269i	$0.481267\pi$
$282$	−0.583840	−0.0347671
$283$	10.3965	0.618008	0.309004	−	0.951061i	$-0.400004\pi$
$283$	10.3965	0.618008	0.309004	+	0.951061i	$0.400004\pi$
$284$	−5.01641	−0.297669
$285$	0.926835	0.0549010
$286$	−10.8714	−0.642836
$287$	−0.694441	−0.0409916
$288$	−15.7594	−0.928630
$289$	17.2615	1.01538
$290$	−2.53457	−0.148835
$291$	5.58907	0.327637
$292$	−18.9652	−1.10986
$293$	−8.00136	−0.467444	−0.233722	−	0.972303i	$-0.575091\pi$
$293$	−8.00136	−0.467444	−0.233722	+	0.972303i	$0.575091\pi$
$294$	10.1052	0.589349
$295$	9.99262	0.581793
$296$	1.02396	0.0595164
$297$	−8.31706	−0.482605
$298$	−10.3641	−0.600379
$299$	−7.17030	−0.414669
$300$	−8.80534	−0.508376
$301$	−1.61098	−0.0928551
$302$	48.1481	2.77061
$303$	10.0932	0.579841
$304$	−3.86867	−0.221884
$305$	−9.33867	−0.534731
$306$	−23.0846	−1.31966
$307$	9.18143	0.524012	0.262006	−	0.965066i	$-0.415616\pi$
$307$	9.18143	0.524012	0.262006	+	0.965066i	$0.415616\pi$
$308$	4.90395	0.279429
$309$	−17.3290	−0.985814
$310$	−16.1106	−0.915021
$311$	16.7973	0.952486	0.476243	−	0.879314i	$-0.341998\pi$
$311$	16.7973	0.952486	0.476243	+	0.879314i	$0.341998\pi$
$312$	−0.430256	−0.0243585
$313$	31.3593	1.77253	0.886267	−	0.463174i	$-0.153289\pi$
$313$	31.3593	1.77253	0.886267	+	0.463174i	$0.153289\pi$
$314$	−37.9642	−2.14244
$315$	−2.56788	−0.144684
$316$	−8.38543	−0.471717
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	−1.41116	−0.0791341
$319$	2.27638	0.127453
$320$	−7.71252	−0.431143
$321$	−3.54974	−0.198127
$322$	6.36915	0.354939
$323$	−5.85334	−0.325688
$324$	1.43798	0.0798880
$325$	−13.7131	−0.760667
$326$	38.1171	2.11111
$327$	16.6479	0.920633
$328$	0.0615797	0.00340017
$329$	0.410154	0.0226125
$330$	−3.06901	−0.168944
$331$	−20.9197	−1.14985	−0.574926	−	0.818205i	$-0.694969\pi$
$331$	−20.9197	−1.14985	−0.574926	+	0.818205i	$0.694969\pi$
$332$	−33.0390	−1.81325
$333$	15.6159	0.855748
$334$	18.1035	0.990577
$335$	−9.16601	−0.500793
$336$	−5.71742	−0.311911
$337$	8.89829	0.484721	0.242360	−	0.970186i	$-0.422078\pi$
$337$	8.89829	0.484721	0.242360	+	0.970186i	$0.422078\pi$
$338$	4.47738	0.243537
$339$	0.284150	0.0154329
$340$	−10.9591	−0.594343
$341$	14.4695	0.783568
$342$	3.94384	0.213258
$343$	−17.2258	−0.930108
$344$	0.142853	0.00770214
$345$	−2.02420	−0.108979
$346$	−15.6023	−0.838785
$347$	23.8188	1.27866	0.639330	−	0.768933i	$-0.279212\pi$
$347$	23.8188	1.27866	0.639330	+	0.768933i	$0.279212\pi$
$348$	2.92149	0.156608
$349$	−32.1769	−1.72239	−0.861195	−	0.508275i	$-0.830283\pi$
$349$	−32.1769	−1.72239	−0.861195	+	0.508275i	$0.830283\pi$
$350$	12.1809	0.651098
$351$	−16.6234	−0.887289
$352$	13.2317	0.705253
$353$	−18.2097	−0.969205	−0.484602	−	0.874735i	$-0.661036\pi$
$353$	−18.2097	−0.969205	−0.484602	+	0.874735i	$0.661036\pi$
$354$	−22.6809	−1.20548
$355$	−2.20546	−0.117054
$356$	1.86970	0.0990939
$357$	−8.65050	−0.457833
$358$	−8.19520	−0.433130
$359$	−3.93521	−0.207692	−0.103846	−	0.994593i	$-0.533115\pi$
$359$	−3.93521	−0.207692	−0.103846	+	0.994593i	$0.533115\pi$
$360$	0.227707	0.0120012
$361$	1.00000	0.0526316
$362$	17.2308	0.905628
$363$	−8.48076	−0.445124
$364$	9.80156	0.513741
$365$	−8.33804	−0.436433
$366$	21.1966	1.10797
$367$	6.09527	0.318171	0.159085	−	0.987265i	$-0.449146\pi$
$367$	6.09527	0.318171	0.159085	+	0.987265i	$0.449146\pi$
$368$	8.44913	0.440441
$369$	0.939124	0.0488888
$370$	14.5983	0.758931
$371$	0.991358	0.0514687
$372$	18.5700	0.962810
$373$	−31.2583	−1.61849	−0.809247	−	0.587469i	$-0.800124\pi$
$373$	−31.2583	−1.61849	−0.809247	+	0.587469i	$0.800124\pi$
$374$	19.3820	1.00222
$375$	−8.50543	−0.439219
$376$	−0.0363705	−0.00187566
$377$	4.54982	0.234328
$378$	14.7660	0.759481
$379$	−13.6436	−0.700826	−0.350413	−	0.936595i	$-0.613959\pi$
$379$	−13.6436	−0.700826	−0.350413	+	0.936595i	$0.613959\pi$
$380$	1.87229	0.0960464
$381$	1.62905	0.0834589
$382$	36.7323	1.87939
$383$	25.1627	1.28575	0.642876	−	0.765970i	$-0.277741\pi$
$383$	25.1627	1.28575	0.642876	+	0.765970i	$0.277741\pi$
$384$	1.04788	0.0534742
$385$	2.15602	0.109881
$386$	−25.0736	−1.27621
$387$	2.17859	0.110744
$388$	11.2904	0.573184
$389$	−19.8649	−1.00719	−0.503595	−	0.863940i	$-0.667990\pi$
$389$	−19.8649	−1.00719	−0.503595	+	0.863940i	$0.667990\pi$
$390$	−6.13405	−0.310610
$391$	12.7836	0.646495
$392$	0.629508	0.0317949
$393$	−10.2216	−0.515611
$394$	27.8174	1.40142
$395$	−3.68664	−0.185495
$396$	−6.63183	−0.333262
$397$	9.76992	0.490338	0.245169	−	0.969480i	$-0.421156\pi$
$397$	9.76992	0.490338	0.245169	+	0.969480i	$0.421156\pi$
$398$	24.6064	1.23341
$399$	1.47787	0.0739863
$400$	16.1589	0.807944
$401$	8.89121	0.444006	0.222003	−	0.975046i	$-0.428741\pi$
$401$	8.89121	0.444006	0.222003	+	0.975046i	$0.428741\pi$
$402$	20.8047	1.03765
$403$	28.9203	1.44062
$404$	20.3892	1.01440
$405$	0.632208	0.0314147
$406$	−4.04146	−0.200574
$407$	−13.1113	−0.649902
$408$	0.767084	0.0379763
$409$	−21.9352	−1.08463	−0.542313	−	0.840177i	$-0.682451\pi$
$409$	−21.9352	−1.08463	−0.542313	+	0.840177i	$0.682451\pi$
$410$	0.877926	0.0433577
$411$	15.6773	0.773304
$412$	−35.0061	−1.72463
$413$	15.9336	0.784042
$414$	−8.61329	−0.423320
$415$	−14.5256	−0.713032
$416$	26.4463	1.29664
$417$	2.39362	0.117216
$418$	−3.31128	−0.161960
$419$	35.5812	1.73826	0.869128	−	0.494587i	$-0.164681\pi$
$419$	35.5812	1.73826	0.869128	+	0.494587i	$0.164681\pi$
$420$	2.76701	0.135016
$421$	−3.95694	−0.192850	−0.0964248	−	0.995340i	$-0.530741\pi$
$421$	−3.95694	−0.192850	−0.0964248	+	0.995340i	$0.530741\pi$
$422$	−46.5455	−2.26580
$423$	−0.554669	−0.0269689
$424$	−0.0879088	−0.00426923
$425$	24.4485	1.18593
$426$	5.00588	0.242536
$427$	−14.8909	−0.720620
$428$	−7.17078	−0.346613
$429$	5.50921	0.265987
$430$	2.03663	0.0982148
$431$	16.2847	0.784407	0.392204	−	0.919878i	$-0.371713\pi$
$431$	16.2847	0.784407	0.392204	+	0.919878i	$0.371713\pi$
$432$	19.5881	0.942435
$433$	−22.5977	−1.08598	−0.542988	−	0.839740i	$-0.682707\pi$
$433$	−22.5977	−1.08598	−0.542988	+	0.839740i	$0.682707\pi$
$434$	−25.6890	−1.23311
$435$	1.28443	0.0615836
$436$	33.6303	1.61060
$437$	−2.18399	−0.104474
$438$	18.9254	0.904292
$439$	−2.12983	−0.101651	−0.0508257	−	0.998708i	$-0.516185\pi$
$439$	−2.12983	−0.101651	−0.0508257	+	0.998708i	$0.516185\pi$
$440$	−0.191185	−0.00911439
$441$	9.60034	0.457159
$442$	38.7390	1.84263
$443$	−20.2422	−0.961737	−0.480868	−	0.876793i	$-0.659678\pi$
$443$	−20.2422	−0.961737	−0.480868	+	0.876793i	$0.659678\pi$
$444$	−16.8269	−0.798568
$445$	0.822011	0.0389671
$446$	−21.7276	−1.02883
$447$	5.25218	0.248420
$448$	−12.2979	−0.581022
$449$	3.55632	0.167833	0.0839166	−	0.996473i	$-0.473257\pi$
$449$	3.55632	0.167833	0.0839166	+	0.996473i	$0.473257\pi$
$450$	−16.4728	−0.776536
$451$	−0.788497	−0.0371289
$452$	0.574008	0.0269991
$453$	−24.3997	−1.14640
$454$	24.4287	1.14649
$455$	4.30924	0.202020
$456$	−0.131051	−0.00613702
$457$	−3.64586	−0.170546	−0.0852730	−	0.996358i	$-0.527176\pi$
$457$	−3.64586	−0.170546	−0.0852730	+	0.996358i	$0.527176\pi$
$458$	1.11385	0.0520469
$459$	29.6370	1.38334
$460$	−4.08905	−0.190653
$461$	14.2964	0.665848	0.332924	−	0.942954i	$-0.391965\pi$
$461$	14.2964	0.665848	0.332924	+	0.942954i	$0.391965\pi$
$462$	−4.89366	−0.227674
$463$	−12.0142	−0.558348	−0.279174	−	0.960241i	$-0.590061\pi$
$463$	−12.0142	−0.558348	−0.279174	+	0.960241i	$0.590061\pi$
$464$	−5.36129	−0.248891
$465$	8.16428	0.378609
$466$	14.1580	0.655857
$467$	32.0862	1.48477	0.742385	−	0.669973i	$-0.233695\pi$
$467$	32.0862	1.48477	0.742385	+	0.669973i	$0.233695\pi$
$468$	−13.2551	−0.612716
$469$	−14.6156	−0.674884
$470$	−0.518525	−0.0239178
$471$	19.2389	0.886482
$472$	−1.41292	−0.0650347
$473$	−1.82917	−0.0841052
$474$	8.36783	0.384347
$475$	−4.17685	−0.191647
$476$	−17.4748	−0.800954
$477$	−1.34066	−0.0613845
$478$	−51.2034	−2.34199
$479$	11.8572	0.541772	0.270886	−	0.962611i	$-0.412683\pi$
$479$	11.8572	0.541772	0.270886	+	0.962611i	$0.412683\pi$
$480$	7.46587	0.340769
$481$	−26.2056	−1.19487
$482$	−1.59362	−0.0725875
$483$	−3.22766	−0.146864
$484$	−17.1319	−0.778722
$485$	4.96381	0.225395
$486$	−32.0553	−1.45406
$487$	8.35561	0.378629	0.189315	−	0.981917i	$-0.439373\pi$
$487$	8.35561	0.378629	0.189315	+	0.981917i	$0.439373\pi$
$488$	1.32045	0.0597740
$489$	−19.3164	−0.873517
$490$	8.97474	0.405437
$491$	11.1921	0.505091	0.252546	−	0.967585i	$-0.418732\pi$
$491$	11.1921	0.505091	0.252546	+	0.967585i	$0.418732\pi$
$492$	−1.01195	−0.0456221
$493$	−8.11167	−0.365331
$494$	−6.61828	−0.297770
$495$	−2.91568	−0.131050
$496$	−34.0782	−1.53016
$497$	−3.51669	−0.157745
$498$	32.9697	1.47741
$499$	39.4693	1.76689	0.883444	−	0.468537i	$-0.155219\pi$
$499$	39.4693	1.76689	0.883444	+	0.468537i	$0.155219\pi$
$500$	−17.1817	−0.768390
$501$	−9.17418	−0.409872
$502$	−2.09197	−0.0933690
$503$	−5.07367	−0.226224	−0.113112	−	0.993582i	$-0.536082\pi$
$503$	−5.07367	−0.226224	−0.113112	+	0.993582i	$0.536082\pi$
$504$	0.363088	0.0161732
$505$	8.96409	0.398897
$506$	7.23179	0.321492
$507$	−2.26897	−0.100769
$508$	3.29083	0.146007
$509$	−37.1936	−1.64858	−0.824288	−	0.566171i	$-0.808424\pi$
$509$	−37.1936	−1.64858	−0.824288	+	0.566171i	$0.808424\pi$
$510$	10.9361	0.484260
$511$	−13.2953	−0.588151
$512$	−32.1556	−1.42109
$513$	−5.06327	−0.223549
$514$	−33.4662	−1.47613
$515$	−15.3904	−0.678182
$516$	−2.34753	−0.103344
$517$	0.465705	0.0204817
$518$	23.2776	1.02276
$519$	7.90669	0.347065
$520$	−0.382123	−0.0167572
$521$	8.50815	0.372749	0.186374	−	0.982479i	$-0.440326\pi$
$521$	8.50815	0.372749	0.186374	+	0.982479i	$0.440326\pi$
$522$	5.46545	0.239216
$523$	−17.4855	−0.764587	−0.382294	−	0.924041i	$-0.624866\pi$
$523$	−17.4855	−0.764587	−0.382294	+	0.924041i	$0.624866\pi$
$524$	−20.6485	−0.902034
$525$	−6.17286	−0.269406
$526$	56.7906	2.47619
$527$	−51.5607	−2.24602
$528$	−6.49178	−0.282519
$529$	−18.2302	−0.792617
$530$	−1.25329	−0.0544396
$531$	−21.5477	−0.935092
$532$	2.98544	0.129435
$533$	−1.57597	−0.0682630
$534$	−1.86578	−0.0807400
$535$	−3.15262	−0.136300
$536$	1.29604	0.0559803
$537$	4.15303	0.179217
$538$	−12.9489	−0.558265
$539$	−8.06053	−0.347192
$540$	−9.47991	−0.407950
$541$	11.7088	0.503399	0.251700	−	0.967805i	$-0.419010\pi$
$541$	11.7088	0.503399	0.251700	+	0.967805i	$0.419010\pi$
$542$	31.8140	1.36653
$543$	−8.73193	−0.374723
$544$	−47.1499	−2.02154
$545$	14.7855	0.633342
$546$	−9.78099	−0.418588
$547$	0.208133	0.00889914	0.00444957	−	0.999990i	$-0.498584\pi$
$547$	0.208133	0.00889914	0.00444957	+	0.999990i	$0.498584\pi$
$548$	31.6695	1.35285
$549$	20.1376	0.859451
$550$	13.8307	0.589744
$551$	1.38582	0.0590379
$552$	0.286213	0.0121820
$553$	−5.87849	−0.249979
$554$	−14.0432	−0.596637
$555$	−7.39791	−0.314024
$556$	4.83532	0.205063
$557$	13.3686	0.566448	0.283224	−	0.959054i	$-0.408596\pi$
$557$	13.3686	0.566448	0.283224	+	0.959054i	$0.408596\pi$
$558$	34.7403	1.47068
$559$	−3.65597	−0.154631
$560$	−5.07780	−0.214576
$561$	−9.82213	−0.414690
$562$	−3.97517	−0.167682
$563$	−43.9386	−1.85179	−0.925895	−	0.377781i	$-0.876687\pi$
$563$	−43.9386	−1.85179	−0.925895	+	0.377781i	$0.876687\pi$
$564$	0.597681	0.0251669
$565$	0.252362	0.0106169
$566$	−20.9578	−0.880921
$567$	1.00808	0.0423354
$568$	0.311843	0.0130846
$569$	−10.5988	−0.444324	−0.222162	−	0.975010i	$-0.571311\pi$
$569$	−10.5988	−0.444324	−0.222162	+	0.975010i	$0.571311\pi$
$570$	−1.86836	−0.0782569
$571$	−2.00232	−0.0837946	−0.0418973	−	0.999122i	$-0.513340\pi$
$571$	−2.00232	−0.0837946	−0.0418973	+	0.999122i	$0.513340\pi$
$572$	11.1291	0.465331
$573$	−18.6146	−0.777637
$574$	1.39989	0.0584302
$575$	9.12219	0.380421
$576$	16.6310	0.692959
$577$	−12.0860	−0.503148	−0.251574	−	0.967838i	$-0.580948\pi$
$577$	−12.0860	−0.503148	−0.251574	+	0.967838i	$0.580948\pi$
$578$	−34.7966	−1.44735
$579$	12.7064	0.528060
$580$	2.59465	0.107737
$581$	−23.1616	−0.960903
$582$	−11.2667	−0.467020
$583$	1.12563	0.0466187
$584$	1.17897	0.0487859
$585$	−5.82758	−0.240941
$586$	16.1295	0.666304
$587$	−4.47541	−0.184720	−0.0923600	−	0.995726i	$-0.529441\pi$
$587$	−4.47541	−0.184720	−0.0923600	+	0.995726i	$0.529441\pi$
$588$	−10.3448	−0.426612
$589$	8.80877	0.362959
$590$	−20.1436	−0.829299
$591$	−14.0968	−0.579866
$592$	30.8794	1.26913
$593$	−29.5242	−1.21241	−0.606207	−	0.795307i	$-0.707310\pi$
$593$	−29.5242	−1.21241	−0.606207	+	0.795307i	$0.707310\pi$
$594$	16.7659	0.687914
$595$	−7.68275	−0.314962
$596$	10.6099	0.434597
$597$	−12.4697	−0.510349
$598$	14.4542	0.591077
$599$	−32.3835	−1.32316	−0.661578	−	0.749876i	$-0.730113\pi$
$599$	−32.3835	−1.32316	−0.661578	+	0.749876i	$0.730113\pi$
$600$	0.547380	0.0223467
$601$	−17.5211	−0.714700	−0.357350	−	0.933971i	$-0.616320\pi$
$601$	−17.5211	−0.714700	−0.357350	+	0.933971i	$0.616320\pi$
$602$	3.24748	0.132357
$603$	19.7653	0.804904
$604$	−49.2896	−2.00557
$605$	−7.53200	−0.306219
$606$	−20.3464	−0.826517
$607$	−28.1372	−1.14205	−0.571027	−	0.820931i	$-0.693455\pi$
$607$	−28.1372	−1.14205	−0.571027	+	0.820931i	$0.693455\pi$
$608$	8.05522	0.326682
$609$	2.04807	0.0829919
$610$	18.8253	0.762216
$611$	0.930808	0.0376565
$612$	23.6319	0.955263
$613$	−44.6499	−1.80339	−0.901696	−	0.432371i	$-0.857677\pi$
$613$	−44.6499	−1.80339	−0.901696	+	0.432371i	$0.857677\pi$
$614$	−18.5084	−0.746937
$615$	−0.444902	−0.0179402
$616$	−0.304852	−0.0122828
$617$	9.37645	0.377482	0.188741	−	0.982027i	$-0.439559\pi$
$617$	9.37645	0.377482	0.188741	+	0.982027i	$0.439559\pi$
$618$	34.9327	1.40520
$619$	−7.40946	−0.297811	−0.148906	−	0.988851i	$-0.547575\pi$
$619$	−7.40946	−0.297811	−0.148906	+	0.988851i	$0.547575\pi$
$620$	16.4926	0.662357
$621$	11.0581	0.443747
$622$	−33.8607	−1.35769
$623$	1.31073	0.0525132
$624$	−12.9752	−0.519422
$625$	13.3303	0.533214
$626$	−63.2156	−2.52660
$627$	1.67804	0.0670144
$628$	38.8643	1.55085
$629$	46.7208	1.86288
$630$	5.17645	0.206235
$631$	−30.7215	−1.22300	−0.611502	−	0.791243i	$-0.709435\pi$
$631$	−30.7215	−1.22300	−0.611502	+	0.791243i	$0.709435\pi$
$632$	0.521276	0.0207353
$633$	23.5876	0.937523
$634$	−2.01585	−0.0800595
$635$	1.44681	0.0574148
$636$	1.44462	0.0572828
$637$	−16.1106	−0.638326
$638$	−4.58884	−0.181674
$639$	4.75577	0.188135
$640$	0.930648	0.0367871
$641$	−35.3752	−1.39724	−0.698618	−	0.715495i	$-0.746201\pi$
$641$	−35.3752	−1.39724	−0.698618	+	0.715495i	$0.746201\pi$
$642$	7.15572	0.282414
$643$	−33.5251	−1.32210	−0.661050	−	0.750342i	$-0.729889\pi$
$643$	−33.5251	−1.32210	−0.661050	+	0.750342i	$0.729889\pi$
$644$	−6.52015	−0.256930
$645$	−1.03209	−0.0406385
$646$	11.7994	0.464242
$647$	−21.7425	−0.854788	−0.427394	−	0.904066i	$-0.640568\pi$
$647$	−21.7425	−0.854788	−0.427394	+	0.904066i	$0.640568\pi$
$648$	−0.0893916	−0.00351163
$649$	18.0917	0.710160
$650$	27.6436	1.08427
$651$	13.0183	0.510226
$652$	−39.0208	−1.52817
$653$	−10.3339	−0.404396	−0.202198	−	0.979345i	$-0.564809\pi$
$653$	−10.3339	−0.404396	−0.202198	+	0.979345i	$0.564809\pi$
$654$	−33.5597	−1.31229
$655$	−9.07808	−0.354710
$656$	1.85705	0.0725056
$657$	17.9799	0.701461
$658$	−0.826807	−0.0322323
$659$	41.6400	1.62206	0.811032	−	0.585001i	$-0.198906\pi$
$659$	41.6400	1.62206	0.811032	+	0.585001i	$0.198906\pi$
$660$	3.14177	0.122293
$661$	−15.7206	−0.611462	−0.305731	−	0.952118i	$-0.598901\pi$
$661$	−15.7206	−0.611462	−0.305731	+	0.952118i	$0.598901\pi$
$662$	42.1710	1.63902
$663$	−19.6315	−0.762426
$664$	2.05386	0.0797050
$665$	1.31254	0.0508982
$666$	−31.4793	−1.21980
$667$	−3.02661	−0.117191
$668$	−18.5326	−0.717050
$669$	11.0107	0.425700
$670$	18.4773	0.713839
$671$	−16.9077	−0.652715
$672$	11.9046	0.459230
$673$	32.2527	1.24325	0.621625	−	0.783315i	$-0.286473\pi$
$673$	32.2527	1.24325	0.621625	+	0.783315i	$0.286473\pi$
$674$	−17.9376	−0.690930
$675$	21.1485	0.814008
$676$	−4.58353	−0.176289
$677$	−6.63477	−0.254995	−0.127497	−	0.991839i	$-0.540694\pi$
$677$	−6.63477	−0.254995	−0.127497	+	0.991839i	$0.540694\pi$
$678$	−0.572803	−0.0219984
$679$	7.91499	0.303750
$680$	0.681269	0.0261255
$681$	−12.3796	−0.474386
$682$	−29.1683	−1.11691
$683$	38.3194	1.46625	0.733125	−	0.680094i	$-0.238061\pi$
$683$	38.3194	1.46625	0.733125	+	0.680094i	$0.238061\pi$
$684$	−4.03734	−0.154371
$685$	13.9235	0.531988
$686$	34.7246	1.32579
$687$	−0.564461	−0.0215355
$688$	4.30801	0.164241
$689$	2.24980	0.0857105
$690$	4.08047	0.155341
$691$	−9.22391	−0.350894	−0.175447	−	0.984489i	$-0.556137\pi$
$691$	−9.22391	−0.350894	−0.175447	+	0.984489i	$0.556137\pi$
$692$	15.9722	0.607172
$693$	−4.64916	−0.176607
$694$	−48.0150	−1.82263
$695$	2.12584	0.0806377
$696$	−0.181613	−0.00688402
$697$	2.80973	0.106426
$698$	64.8637	2.45513
$699$	−7.17477	−0.271375
$700$	−12.4697	−0.471311
$701$	7.50979	0.283641	0.141820	−	0.989892i	$-0.454704\pi$
$701$	7.50979	0.283641	0.141820	+	0.989892i	$0.454704\pi$
$702$	33.5101	1.26476
$703$	−7.98191	−0.301043
$704$	−13.9635	−0.526271
$705$	0.262770	0.00989648
$706$	36.7080	1.38152
$707$	14.2936	0.537566
$708$	23.2187	0.872611
$709$	21.6586	0.813405	0.406702	−	0.913561i	$-0.366679\pi$
$709$	21.6586	0.813405	0.406702	+	0.913561i	$0.366679\pi$
$710$	4.44587	0.166850
$711$	7.94975	0.298139
$712$	−0.116229	−0.00435587
$713$	−19.2382	−0.720477
$714$	17.4381	0.652604
$715$	4.89289	0.182984
$716$	8.38949	0.313530
$717$	25.9481	0.969048
$718$	7.93277	0.296049
$719$	27.7237	1.03392	0.516959	−	0.856010i	$-0.327064\pi$
$719$	27.7237	1.03392	0.516959	+	0.856010i	$0.327064\pi$
$720$	6.86693	0.255915
$721$	−24.5406	−0.913939
$722$	−2.01585	−0.0750220
$723$	0.807590	0.0300346
$724$	−17.6393	−0.655558
$725$	−5.78836	−0.214974
$726$	17.0959	0.634489
$727$	−22.5171	−0.835111	−0.417556	−	0.908651i	$-0.637113\pi$
$727$	−22.5171	−0.835111	−0.417556	+	0.908651i	$0.637113\pi$
$728$	−0.609309	−0.0225825
$729$	14.1540	0.524223
$730$	16.8082	0.622100
$731$	6.51806	0.241079
$732$	−21.6992	−0.802024
$733$	34.0977	1.25943	0.629713	−	0.776828i	$-0.283172\pi$
$733$	34.0977	1.25943	0.629713	+	0.776828i	$0.283172\pi$
$734$	−12.2871	−0.453526
$735$	−4.54807	−0.167758
$736$	−17.5925	−0.648468
$737$	−16.5951	−0.611288
$738$	−1.89313	−0.0696870
$739$	−48.8266	−1.79612	−0.898058	−	0.439878i	$-0.855022\pi$
$739$	−48.8266	−1.79612	−0.898058	+	0.439878i	$0.855022\pi$
$740$	−14.9444	−0.549368
$741$	3.35391	0.123209
$742$	−1.99843	−0.0733645
$743$	0.383233	0.0140594	0.00702972	−	0.999975i	$-0.497762\pi$
$743$	0.383233	0.0140594	0.00702972	+	0.999975i	$0.497762\pi$
$744$	−1.15440	−0.0423222
$745$	4.66461	0.170898
$746$	63.0119	2.30703
$747$	31.3224	1.14603
$748$	−19.8416	−0.725479
$749$	−5.02698	−0.183682
$750$	17.1456	0.626070
$751$	4.71448	0.172034	0.0860168	−	0.996294i	$-0.472586\pi$
$751$	4.71448	0.172034	0.0860168	+	0.996294i	$0.472586\pi$
$752$	−1.09682	−0.0399968
$753$	1.06013	0.0386334
$754$	−9.17174	−0.334015
$755$	−21.6701	−0.788656
$756$	−15.1161	−0.549766
$757$	−7.99903	−0.290730	−0.145365	−	0.989378i	$-0.546436\pi$
$757$	−7.99903	−0.290730	−0.145365	+	0.989378i	$0.546436\pi$
$758$	27.5035	0.998971
$759$	−3.66481	−0.133024
$760$	−0.116390	−0.00422191
$761$	45.7471	1.65833	0.829165	−	0.559004i	$-0.188817\pi$
$761$	45.7471	1.65833	0.829165	+	0.559004i	$0.188817\pi$
$762$	−3.28392	−0.118964
$763$	23.5761	0.853511
$764$	−37.6032	−1.36043
$765$	10.3897	0.375641
$766$	−50.7241	−1.83274
$767$	36.1599	1.30566
$768$	15.2557	0.550492
$769$	−11.0515	−0.398527	−0.199263	−	0.979946i	$-0.563855\pi$
$769$	−11.0515	−0.398527	−0.199263	+	0.979946i	$0.563855\pi$
$770$	−4.34620	−0.156626
$771$	16.9595	0.610780
$772$	25.6680	0.923813
$773$	−1.05859	−0.0380748	−0.0190374	−	0.999819i	$-0.506060\pi$
$773$	−1.05859	−0.0380748	−0.0190374	+	0.999819i	$0.506060\pi$
$774$	−4.39171	−0.157857
$775$	−36.7929	−1.32164
$776$	−0.701863	−0.0251954
$777$	−11.7963	−0.423188
$778$	40.0446	1.43567
$779$	−0.480022	−0.0171986
$780$	6.27948	0.224841
$781$	−3.99299	−0.142880
$782$	−25.7698	−0.921526
$783$	−7.01678	−0.250759
$784$	18.9840	0.677999
$785$	17.0866	0.609847
$786$	20.6052	0.734961
$787$	−26.0461	−0.928445	−0.464222	−	0.885719i	$-0.653666\pi$
$787$	−26.0461	−0.928445	−0.464222	+	0.885719i	$0.653666\pi$
$788$	−28.4768	−1.01445
$789$	−28.7794	−1.02458
$790$	7.43170	0.264408
$791$	0.402400	0.0143077
$792$	0.412265	0.0146492
$793$	−33.7935	−1.20004
$794$	−19.6947	−0.698938
$795$	0.635124	0.0225255
$796$	−25.1898	−0.892829
$797$	−18.8295	−0.666976	−0.333488	−	0.942754i	$-0.608226\pi$
$797$	−18.8295	−0.666976	−0.333488	+	0.942754i	$0.608226\pi$
$798$	−2.97917	−0.105461
$799$	−1.65950	−0.0587087
$800$	−33.6455	−1.18955
$801$	−1.77256	−0.0626302
$802$	−17.9233	−0.632894
$803$	−15.0960	−0.532728
$804$	−21.2980	−0.751122
$805$	−2.86658	−0.101034
$806$	−58.2989	−2.05349
$807$	6.56202	0.230994
$808$	−1.26749	−0.0445900
$809$	−1.02320	−0.0359739	−0.0179869	−	0.999838i	$-0.505726\pi$
$809$	−1.02320	−0.0359739	−0.0179869	+	0.999838i	$0.505726\pi$
$810$	−1.27443	−0.0447791
$811$	−38.0714	−1.33687	−0.668434	−	0.743771i	$-0.733035\pi$
$811$	−38.0714	−1.33687	−0.668434	+	0.743771i	$0.733035\pi$
$812$	4.13728	0.145190
$813$	−16.1222	−0.565431
$814$	26.4303	0.926383
$815$	−17.1554	−0.600928
$816$	23.1328	0.809811
$817$	−1.11356	−0.0389586
$818$	44.2180	1.54605
$819$	−9.29230	−0.324699
$820$	−0.898740	−0.0313854
$821$	−43.2256	−1.50858	−0.754292	−	0.656539i	$-0.772020\pi$
$821$	−43.2256	−1.50858	−0.754292	+	0.656539i	$0.772020\pi$
$822$	−31.6030	−1.10228
$823$	−23.4786	−0.818412	−0.409206	−	0.912442i	$-0.634194\pi$
$823$	−23.4786	−0.818412	−0.409206	+	0.912442i	$0.634194\pi$
$824$	2.17614	0.0758094
$825$	−7.00892	−0.244019
$826$	−32.1197	−1.11759
$827$	−37.6806	−1.31028	−0.655142	−	0.755506i	$-0.727391\pi$
$827$	−37.6806	−1.31028	−0.655142	+	0.755506i	$0.727391\pi$
$828$	8.81749	0.306429
$829$	28.1512	0.977732	0.488866	−	0.872359i	$-0.337411\pi$
$829$	28.1512	0.977732	0.488866	+	0.872359i	$0.337411\pi$
$830$	29.2813	1.01637
$831$	7.11658	0.246871
$832$	−27.9090	−0.967571
$833$	28.7229	0.995190
$834$	−4.82517	−0.167082
$835$	−8.14785	−0.281968
$836$	3.38979	0.117238
$837$	−44.6012	−1.54164
$838$	−71.7263	−2.47774
$839$	15.4016	0.531722	0.265861	−	0.964011i	$-0.414344\pi$
$839$	15.4016	0.531722	0.265861	+	0.964011i	$0.414344\pi$
$840$	−0.172010	−0.00593490
$841$	−27.0795	−0.933776
$842$	7.97659	0.274891
$843$	2.01447	0.0693821
$844$	47.6490	1.64015
$845$	−2.01514	−0.0693229
$846$	1.11813	0.0384420
$847$	−12.0101	−0.412671
$848$	−2.65105	−0.0910375
$849$	10.6206	0.364500
$850$	−49.2845	−1.69044
$851$	17.4324	0.597574
$852$	−5.12456	−0.175565
$853$	−20.9338	−0.716761	−0.358380	−	0.933576i	$-0.616671\pi$
$853$	−20.9338	−0.716761	−0.358380	+	0.933576i	$0.616671\pi$
$854$	30.0177	1.02719
$855$	−1.77501	−0.0607040
$856$	0.445768	0.0152360
$857$	−12.9525	−0.442448	−0.221224	−	0.975223i	$-0.571005\pi$
$857$	−12.9525	−0.442448	−0.221224	+	0.975223i	$0.571005\pi$
$858$	−11.1057	−0.379143
$859$	−3.38497	−0.115494	−0.0577468	−	0.998331i	$-0.518392\pi$
$859$	−3.38497	−0.115494	−0.0577468	+	0.998331i	$0.518392\pi$
$860$	−2.08491	−0.0710949
$861$	−0.709413	−0.0241767
$862$	−32.8275	−1.11811
$863$	49.7042	1.69195	0.845976	−	0.533221i	$-0.179019\pi$
$863$	49.7042	1.69195	0.845976	+	0.533221i	$0.179019\pi$
$864$	−40.7858	−1.38756
$865$	7.02216	0.238761
$866$	45.5535	1.54797
$867$	17.6337	0.598871
$868$	26.2980	0.892613
$869$	−6.67468	−0.226423
$870$	−2.58921	−0.0877824
$871$	−33.1687	−1.12388
$872$	−2.09061	−0.0707970
$873$	−10.7038	−0.362269
$874$	4.40258	0.148920
$875$	−12.0450	−0.407196
$876$	−19.3741	−0.654591
$877$	17.6056	0.594498	0.297249	−	0.954800i	$-0.403931\pi$
$877$	17.6056	0.594498	0.297249	+	0.954800i	$0.403931\pi$
$878$	4.29342	0.144896
$879$	−8.17386	−0.275697
$880$	−5.76554	−0.194356
$881$	−33.5907	−1.13170	−0.565850	−	0.824508i	$-0.691452\pi$
$881$	−33.5907	−1.13170	−0.565850	+	0.824508i	$0.691452\pi$
$882$	−19.3528	−0.651643
$883$	−16.5266	−0.556164	−0.278082	−	0.960557i	$-0.589699\pi$
$883$	−16.5266	−0.556164	−0.278082	+	0.960557i	$0.589699\pi$
$884$	−39.6574	−1.33382
$885$	10.2081	0.343140
$886$	40.8052	1.37088
$887$	−17.0667	−0.573045	−0.286523	−	0.958074i	$-0.592499\pi$
$887$	−17.0667	−0.573045	−0.286523	+	0.958074i	$0.592499\pi$
$888$	1.04603	0.0351026
$889$	2.30699	0.0773740
$890$	−1.65705	−0.0555444
$891$	1.14461	0.0383460
$892$	22.2427	0.744740
$893$	0.283513	0.00948739
$894$	−10.5876	−0.354102
$895$	3.68843	0.123290
$896$	1.48395	0.0495754
$897$	−7.32489	−0.244571
$898$	−7.16900	−0.239233
$899$	12.2074	0.407138
$900$	16.8634	0.562112
$901$	−4.01106	−0.133628
$902$	1.58949	0.0529242
$903$	−1.64571	−0.0547657
$904$	−0.0356829	−0.00118680
$905$	−7.75507	−0.257787
$906$	49.1861	1.63410
$907$	−24.6163	−0.817371	−0.408685	−	0.912675i	$-0.634013\pi$
$907$	−24.6163	−0.817371	−0.408685	+	0.912675i	$0.634013\pi$
$908$	−25.0078	−0.829914
$909$	−19.3299	−0.641131
$910$	−8.68677	−0.287964
$911$	53.7873	1.78205	0.891027	−	0.453950i	$-0.149986\pi$
$911$	53.7873	1.78205	0.891027	+	0.453950i	$0.149986\pi$
$912$	−3.95208	−0.130866
$913$	−26.2986	−0.870356
$914$	7.34949	0.243099
$915$	−9.54001	−0.315383
$916$	−1.14026	−0.0376752
$917$	−14.4753	−0.478018
$918$	−59.7437	−1.97184
$919$	28.0054	0.923813	0.461906	−	0.886929i	$-0.347166\pi$
$919$	28.0054	0.923813	0.461906	+	0.886929i	$0.347166\pi$
$920$	0.254194	0.00838053
$921$	9.37938	0.309061
$922$	−28.8193	−0.949113
$923$	−7.98081	−0.262692
$924$	5.00968	0.164806
$925$	33.3392	1.09619
$926$	24.2188	0.795880
$927$	33.1873	1.09001
$928$	11.1631	0.366446
$929$	25.2287	0.827727	0.413863	−	0.910339i	$-0.364179\pi$
$929$	25.2287	0.827727	0.413863	+	0.910339i	$0.364179\pi$
$930$	−16.4579	−0.539677
$931$	−4.90710	−0.160824
$932$	−14.4937	−0.474755
$933$	17.1594	0.561774
$934$	−64.6808	−2.11642
$935$	−8.72331	−0.285283
$936$	0.823996	0.0269332
$937$	−16.8775	−0.551365	−0.275683	−	0.961249i	$-0.588904\pi$
$937$	−16.8775	−0.551365	−0.275683	+	0.961249i	$0.588904\pi$
$938$	29.4627	0.961992
$939$	32.0354	1.04544
$940$	0.530818	0.0173134
$941$	−38.6482	−1.25990	−0.629948	−	0.776637i	$-0.716924\pi$
$941$	−38.6482	−1.25990	−0.629948	+	0.776637i	$0.716924\pi$
$942$	−38.7827	−1.26361
$943$	1.04836	0.0341394
$944$	−42.6091	−1.38681
$945$	−6.64576	−0.216187
$946$	3.68732	0.119885
$947$	−43.3651	−1.40918	−0.704588	−	0.709616i	$-0.748868\pi$
$947$	−43.3651	−1.40918	−0.704588	+	0.709616i	$0.748868\pi$
$948$	−8.56621	−0.278218
$949$	−30.1726	−0.979443
$950$	8.41989	0.273177
$951$	1.02156	0.0331263
$952$	1.08631	0.0352075
$953$	33.7587	1.09355	0.546776	−	0.837279i	$-0.315855\pi$
$953$	33.7587	1.09355	0.546776	+	0.837279i	$0.315855\pi$
$954$	2.70256	0.0874986
$955$	−16.5322	−0.534969
$956$	52.4173	1.69530
$957$	2.32546	0.0751714
$958$	−23.9024	−0.772251
$959$	22.2015	0.716923
$960$	−7.87880	−0.254287
$961$	46.5944	1.50304
$962$	52.8265	1.70319
$963$	6.79820	0.219069
$964$	1.63140	0.0525440
$965$	11.2849	0.363274
$966$	6.50647	0.209342
$967$	39.2895	1.26347	0.631733	−	0.775186i	$-0.282344\pi$
$967$	39.2895	1.26347	0.631733	+	0.775186i	$0.282344\pi$
$968$	1.06499	0.0342302
$969$	−5.97953	−0.192090
$970$	−10.0063	−0.321283
$971$	−4.55264	−0.146101	−0.0730506	−	0.997328i	$-0.523273\pi$
$971$	−4.55264	−0.146101	−0.0730506	+	0.997328i	$0.523273\pi$
$972$	32.8153	1.05255
$973$	3.38973	0.108670
$974$	−16.8436	−0.539705
$975$	−14.0088	−0.448640
$976$	39.8206	1.27463
$977$	36.8781	1.17984	0.589918	−	0.807463i	$-0.299160\pi$
$977$	36.8781	1.17984	0.589918	+	0.807463i	$0.299160\pi$
$978$	38.9388	1.24513
$979$	1.48825	0.0475648
$980$	−9.18751	−0.293484
$981$	−31.8830	−1.01794
$982$	−22.5615	−0.719967
$983$	−12.8946	−0.411274	−0.205637	−	0.978628i	$-0.565927\pi$
$983$	−12.8946	−0.411274	−0.205637	+	0.978628i	$0.565927\pi$
$984$	0.0629073	0.00200541
$985$	−12.5198	−0.398914
$986$	16.3519	0.520750
$987$	0.418996	0.0133368
$988$	6.77518	0.215547
$989$	2.43201	0.0773333
$990$	5.87756	0.186801
$991$	−23.2665	−0.739084	−0.369542	−	0.929214i	$-0.620485\pi$
$991$	−23.2665	−0.739084	−0.369542	+	0.929214i	$0.620485\pi$
$992$	70.9566	2.25287
$993$	−21.3707	−0.678180
$994$	7.08910	0.224853
$995$	−11.0747	−0.351090
$996$	−33.7513	−1.06945
$997$	−4.65339	−0.147374	−0.0736871	−	0.997281i	$-0.523477\pi$
$997$	−4.65339	−0.147374	−0.0736871	+	0.997281i	$0.523477\pi$
$998$	−79.5640	−2.51856
$999$	40.4146	1.27866

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.a.1.18	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.a.1.18	✓	98	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.01585 q^{2} +1.02156 q^{3} +2.06364 q^{4} +0.907276 q^{5} -2.05931 q^{6} +1.44669 q^{7} -0.128285 q^{8} -1.95642 q^{9} +O(q^{10})\)	\(q-2.01585 q^{2} +1.02156 q^{3} +2.06364 q^{4} +0.907276 q^{5} -2.05931 q^{6} +1.44669 q^{7} -0.128285 q^{8} -1.95642 q^{9} -1.82893 q^{10} +1.64263 q^{11} +2.10813 q^{12} +3.28313 q^{13} -2.91630 q^{14} +0.926835 q^{15} -3.86867 q^{16} -5.85334 q^{17} +3.94384 q^{18} +1.00000 q^{19} +1.87229 q^{20} +1.47787 q^{21} -3.31128 q^{22} -2.18399 q^{23} -0.131051 q^{24} -4.17685 q^{25} -6.61828 q^{26} -5.06327 q^{27} +2.98544 q^{28} +1.38582 q^{29} -1.86836 q^{30} +8.80877 q^{31} +8.05522 q^{32} +1.67804 q^{33} +11.7994 q^{34} +1.31254 q^{35} -4.03734 q^{36} -7.98191 q^{37} -2.01585 q^{38} +3.35391 q^{39} -0.116390 q^{40} -0.480022 q^{41} -2.97917 q^{42} -1.11356 q^{43} +3.38979 q^{44} -1.77501 q^{45} +4.40258 q^{46} +0.283513 q^{47} -3.95208 q^{48} -4.90710 q^{49} +8.41989 q^{50} -5.97953 q^{51} +6.77518 q^{52} +0.685261 q^{53} +10.2068 q^{54} +1.49031 q^{55} -0.185588 q^{56} +1.02156 q^{57} -2.79360 q^{58} +11.0139 q^{59} +1.91265 q^{60} -10.2931 q^{61} -17.7571 q^{62} -2.83032 q^{63} -8.50075 q^{64} +2.97870 q^{65} -3.38267 q^{66} -10.1028 q^{67} -12.0792 q^{68} -2.23107 q^{69} -2.64588 q^{70} -2.43086 q^{71} +0.250979 q^{72} -9.19020 q^{73} +16.0903 q^{74} -4.26690 q^{75} +2.06364 q^{76} +2.37636 q^{77} -6.76096 q^{78} -4.06342 q^{79} -3.50995 q^{80} +0.696820 q^{81} +0.967651 q^{82} -16.0101 q^{83} +3.04980 q^{84} -5.31059 q^{85} +2.24477 q^{86} +1.41570 q^{87} -0.210724 q^{88} +0.906021 q^{89} +3.57815 q^{90} +4.74965 q^{91} -4.50696 q^{92} +8.99868 q^{93} -0.571518 q^{94} +0.907276 q^{95} +8.22889 q^{96} +5.47112 q^{97} +9.89196 q^{98} -3.21366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9	\( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 98 * q - 8 * q^2 - 25 * q^3 + 82 * q^4 - 10 * q^5 - 4 * q^6 - 18 * q^7 - 18 * q^8 + 61 * q^9 - 24 * q^10 - 12 * q^11 - 51 * q^12 - 58 * q^13 - 15 * q^14 - 18 * q^15 + 58 * q^16 - 25 * q^17 - 40 * q^18 + 98 * q^19 - 12 * q^20 - 24 * q^21 - 59 * q^22 - 38 * q^23 - 9 * q^24 - 12 * q^25 - 3 * q^26 - 85 * q^27 - 33 * q^28 - 24 * q^29 - 22 * q^30 - 56 * q^31 - 29 * q^32 - 51 * q^33 - 38 * q^34 - 10 * q^35 + 50 * q^36 - 124 * q^37 - 8 * q^38 - 4 * q^39 - 80 * q^40 - 28 * q^41 - 37 * q^42 - 63 * q^43 - 7 * q^44 - 32 * q^45 - 47 * q^46 - 10 * q^47 - 88 * q^48 + 6 * q^49 - 17 * q^50 - 22 * q^51 - 119 * q^52 - 65 * q^53 + 24 * q^54 - 30 * q^55 - 39 * q^56 - 25 * q^57 - 91 * q^58 - 26 * q^59 - 60 * q^60 - 60 * q^61 + 6 * q^62 - 26 * q^63 + 50 * q^64 - 40 * q^65 + 57 * q^66 - 108 * q^67 - 41 * q^68 - 15 * q^69 - 36 * q^70 - 19 * q^71 - 47 * q^72 - 136 * q^73 + 22 * q^74 - 48 * q^75 + 82 * q^76 - 35 * q^77 - 56 * q^78 - 98 * q^79 - 42 * q^80 + 6 * q^81 - 37 * q^82 - 31 * q^83 - 24 * q^84 - 71 * q^85 - 24 * q^86 + 7 * q^87 - 166 * q^88 - 38 * q^89 + 26 * q^90 - 100 * q^91 - 59 * q^92 - 21 * q^93 - 48 * q^94 - 10 * q^95 - 16 * q^96 - 190 * q^97 - 80 * q^98 - 17 * q^99

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