LMFDB - Embedded newform 8018.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} -0.567392 q^{10} +1.83375 q^{11} -2.47683 q^{12} -5.69770 q^{13} -4.82108 q^{14} +1.40533 q^{15} +1.00000 q^{16} +4.15123 q^{17} +3.13468 q^{18} +1.00000 q^{19} -0.567392 q^{20} +11.9410 q^{21} +1.83375 q^{22} +3.32654 q^{23} -2.47683 q^{24} -4.67807 q^{25} -5.69770 q^{26} -0.333577 q^{27} -4.82108 q^{28} +0.666868 q^{29} +1.40533 q^{30} +1.19796 q^{31} +1.00000 q^{32} -4.54189 q^{33} +4.15123 q^{34} +2.73544 q^{35} +3.13468 q^{36} -1.66156 q^{37} +1.00000 q^{38} +14.1122 q^{39} -0.567392 q^{40} +12.1142 q^{41} +11.9410 q^{42} -0.920599 q^{43} +1.83375 q^{44} -1.77859 q^{45} +3.32654 q^{46} +5.33894 q^{47} -2.47683 q^{48} +16.2428 q^{49} -4.67807 q^{50} -10.2819 q^{51} -5.69770 q^{52} -6.95873 q^{53} -0.333577 q^{54} -1.04046 q^{55} -4.82108 q^{56} -2.47683 q^{57} +0.666868 q^{58} -9.75807 q^{59} +1.40533 q^{60} +3.51810 q^{61} +1.19796 q^{62} -15.1125 q^{63} +1.00000 q^{64} +3.23283 q^{65} -4.54189 q^{66} -10.6946 q^{67} +4.15123 q^{68} -8.23928 q^{69} +2.73544 q^{70} +13.2989 q^{71} +3.13468 q^{72} -0.562291 q^{73} -1.66156 q^{74} +11.5868 q^{75} +1.00000 q^{76} -8.84067 q^{77} +14.1122 q^{78} +7.21166 q^{79} -0.567392 q^{80} -8.57782 q^{81} +12.1142 q^{82} +13.7036 q^{83} +11.9410 q^{84} -2.35538 q^{85} -0.920599 q^{86} -1.65172 q^{87} +1.83375 q^{88} -8.31843 q^{89} -1.77859 q^{90} +27.4691 q^{91} +3.32654 q^{92} -2.96713 q^{93} +5.33894 q^{94} -0.567392 q^{95} -2.47683 q^{96} +6.85317 q^{97} +16.2428 q^{98} +5.74823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.47683	−1.43000	−0.714999	−	0.699126i	$-0.753573\pi$
$3$	−2.47683	−1.43000	−0.714999	+	0.699126i	$0.753573\pi$
$4$	1.00000	0.500000
$5$	−0.567392	−0.253746	−0.126873	−	0.991919i	$-0.540494\pi$
$5$	−0.567392	−0.253746	−0.126873	+	0.991919i	$0.540494\pi$
$6$	−2.47683	−1.01116
$7$	−4.82108	−1.82220	−0.911099	−	0.412188i	$-0.864765\pi$
$7$	−4.82108	−1.82220	−0.911099	+	0.412188i	$0.864765\pi$
$8$	1.00000	0.353553
$9$	3.13468	1.04489
$10$	−0.567392	−0.179425
$11$	1.83375	0.552897	0.276449	−	0.961029i	$-0.410842\pi$
$11$	1.83375	0.552897	0.276449	+	0.961029i	$0.410842\pi$
$12$	−2.47683	−0.714999
$13$	−5.69770	−1.58026	−0.790128	−	0.612942i	$-0.789986\pi$
$13$	−5.69770	−1.58026	−0.790128	+	0.612942i	$0.789986\pi$
$14$	−4.82108	−1.28849
$15$	1.40533	0.362856
$16$	1.00000	0.250000
$17$	4.15123	1.00682	0.503410	−	0.864047i	$-0.332078\pi$
$17$	4.15123	1.00682	0.503410	+	0.864047i	$0.332078\pi$
$18$	3.13468	0.738851
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.567392	−0.126873
$21$	11.9410	2.60574
$22$	1.83375	0.390958
$23$	3.32654	0.693632	0.346816	−	0.937933i	$-0.387263\pi$
$23$	3.32654	0.693632	0.346816	+	0.937933i	$0.387263\pi$
$24$	−2.47683	−0.505580
$25$	−4.67807	−0.935613
$26$	−5.69770	−1.11741
$27$	−0.333577	−0.0641969
$28$	−4.82108	−0.911099
$29$	0.666868	0.123834	0.0619171	−	0.998081i	$-0.480279\pi$
$29$	0.666868	0.123834	0.0619171	+	0.998081i	$0.480279\pi$
$30$	1.40533	0.256578
$31$	1.19796	0.215159	0.107580	−	0.994196i	$-0.465690\pi$
$31$	1.19796	0.215159	0.107580	+	0.994196i	$0.465690\pi$
$32$	1.00000	0.176777
$33$	−4.54189	−0.790642
$34$	4.15123	0.711930
$35$	2.73544	0.462375
$36$	3.13468	0.522447
$37$	−1.66156	−0.273159	−0.136579	−	0.990629i	$-0.543611\pi$
$37$	−1.66156	−0.273159	−0.136579	+	0.990629i	$0.543611\pi$
$38$	1.00000	0.162221
$39$	14.1122	2.25976
$40$	−0.567392	−0.0897126
$41$	12.1142	1.89193	0.945963	−	0.324274i	$-0.105120\pi$
$41$	12.1142	1.89193	0.945963	+	0.324274i	$0.105120\pi$
$42$	11.9410	1.84254
$43$	−0.920599	−0.140390	−0.0701950	−	0.997533i	$-0.522362\pi$
$43$	−0.920599	−0.140390	−0.0701950	+	0.997533i	$0.522362\pi$
$44$	1.83375	0.276449
$45$	−1.77859	−0.265137
$46$	3.32654	0.490472
$47$	5.33894	0.778764	0.389382	−	0.921076i	$-0.372689\pi$
$47$	5.33894	0.778764	0.389382	+	0.921076i	$0.372689\pi$
$48$	−2.47683	−0.357499
$49$	16.2428	2.32040
$50$	−4.67807	−0.661578
$51$	−10.2819	−1.43975
$52$	−5.69770	−0.790128
$53$	−6.95873	−0.955856	−0.477928	−	0.878399i	$-0.658612\pi$
$53$	−6.95873	−0.955856	−0.477928	+	0.878399i	$0.658612\pi$
$54$	−0.333577	−0.0453941
$55$	−1.04046	−0.140295
$56$	−4.82108	−0.644244
$57$	−2.47683	−0.328064
$58$	0.666868	0.0875640
$59$	−9.75807	−1.27039	−0.635196	−	0.772351i	$-0.719081\pi$
$59$	−9.75807	−1.27039	−0.635196	+	0.772351i	$0.719081\pi$
$60$	1.40533	0.181428
$61$	3.51810	0.450447	0.225223	−	0.974307i	$-0.427689\pi$
$61$	3.51810	0.450447	0.225223	+	0.974307i	$0.427689\pi$
$62$	1.19796	0.152141
$63$	−15.1125	−1.90400
$64$	1.00000	0.125000
$65$	3.23283	0.400983
$66$	−4.54189	−0.559068
$67$	−10.6946	−1.30655	−0.653274	−	0.757122i	$-0.726605\pi$
$67$	−10.6946	−1.30655	−0.653274	+	0.757122i	$0.726605\pi$
$68$	4.15123	0.503410
$69$	−8.23928	−0.991892
$70$	2.73544	0.326948
$71$	13.2989	1.57828	0.789142	−	0.614211i	$-0.210525\pi$
$71$	13.2989	1.57828	0.789142	+	0.614211i	$0.210525\pi$
$72$	3.13468	0.369425
$73$	−0.562291	−0.0658111	−0.0329056	−	0.999458i	$-0.510476\pi$
$73$	−0.562291	−0.0658111	−0.0329056	+	0.999458i	$0.510476\pi$
$74$	−1.66156	−0.193152
$75$	11.5868	1.33792
$76$	1.00000	0.114708
$77$	−8.84067	−1.00749
$78$	14.1122	1.59789
$79$	7.21166	0.811375	0.405688	−	0.914012i	$-0.367032\pi$
$79$	7.21166	0.811375	0.405688	+	0.914012i	$0.367032\pi$
$80$	−0.567392	−0.0634364
$81$	−8.57782	−0.953092
$82$	12.1142	1.33779
$83$	13.7036	1.50416	0.752081	−	0.659071i	$-0.229050\pi$
$83$	13.7036	1.50416	0.752081	+	0.659071i	$0.229050\pi$
$84$	11.9410	1.30287
$85$	−2.35538	−0.255476
$86$	−0.920599	−0.0992707
$87$	−1.65172	−0.177083
$88$	1.83375	0.195479
$89$	−8.31843	−0.881752	−0.440876	−	0.897568i	$-0.645332\pi$
$89$	−8.31843	−0.881752	−0.440876	+	0.897568i	$0.645332\pi$
$90$	−1.77859	−0.187480
$91$	27.4691	2.87954
$92$	3.32654	0.346816
$93$	−2.96713	−0.307677
$94$	5.33894	0.550669
$95$	−0.567392	−0.0582132
$96$	−2.47683	−0.252790
$97$	6.85317	0.695834	0.347917	−	0.937525i	$-0.386889\pi$
$97$	6.85317	0.695834	0.347917	+	0.937525i	$0.386889\pi$
$98$	16.2428	1.64077
$99$	5.74823	0.577719
$100$	−4.67807	−0.467807
$101$	−6.59279	−0.656007	−0.328004	−	0.944676i	$-0.606376\pi$
$101$	−6.59279	−0.656007	−0.328004	+	0.944676i	$0.606376\pi$
$102$	−10.2819	−1.01806
$103$	12.3679	1.21864	0.609321	−	0.792924i	$-0.291442\pi$
$103$	12.3679	1.21864	0.609321	+	0.792924i	$0.291442\pi$
$104$	−5.69770	−0.558705
$105$	−6.77523	−0.661194
$106$	−6.95873	−0.675892
$107$	−5.73409	−0.554335	−0.277168	−	0.960822i	$-0.589396\pi$
$107$	−5.73409	−0.554335	−0.277168	+	0.960822i	$0.589396\pi$
$108$	−0.333577	−0.0320985
$109$	7.07403	0.677569	0.338785	−	0.940864i	$-0.389984\pi$
$109$	7.07403	0.677569	0.338785	+	0.940864i	$0.389984\pi$
$110$	−1.04046	−0.0992037
$111$	4.11540	0.390616
$112$	−4.82108	−0.455549
$113$	2.29029	0.215452	0.107726	−	0.994181i	$-0.465643\pi$
$113$	2.29029	0.215452	0.107726	+	0.994181i	$0.465643\pi$
$114$	−2.47683	−0.231976
$115$	−1.88746	−0.176006
$116$	0.666868	0.0619171
$117$	−17.8604	−1.65120
$118$	−9.75807	−0.898303
$119$	−20.0134	−1.83463
$120$	1.40533	0.128289
$121$	−7.63735	−0.694304
$122$	3.51810	0.318514
$123$	−30.0049	−2.70545
$124$	1.19796	0.107580
$125$	5.49126	0.491153
$126$	−15.1125	−1.34633
$127$	4.06565	0.360768	0.180384	−	0.983596i	$-0.442266\pi$
$127$	4.06565	0.360768	0.180384	+	0.983596i	$0.442266\pi$
$128$	1.00000	0.0883883
$129$	2.28017	0.200757
$130$	3.23283	0.283538
$131$	−22.0302	−1.92479	−0.962395	−	0.271655i	$-0.912429\pi$
$131$	−22.0302	−1.92479	−0.962395	+	0.271655i	$0.912429\pi$
$132$	−4.54189	−0.395321
$133$	−4.82108	−0.418041
$134$	−10.6946	−0.923868
$135$	0.189269	0.0162897
$136$	4.15123	0.355965
$137$	−21.1806	−1.80958	−0.904791	−	0.425857i	$-0.859973\pi$
$137$	−21.1806	−1.80958	−0.904791	+	0.425857i	$0.859973\pi$
$138$	−8.23928	−0.701374
$139$	9.81593	0.832576	0.416288	−	0.909233i	$-0.363331\pi$
$139$	9.81593	0.832576	0.416288	+	0.909233i	$0.363331\pi$
$140$	2.73544	0.231187
$141$	−13.2236	−1.11363
$142$	13.2989	1.11602
$143$	−10.4482	−0.873720
$144$	3.13468	0.261223
$145$	−0.378376	−0.0314224
$146$	−0.562291	−0.0465355
$147$	−40.2307	−3.31817
$148$	−1.66156	−0.136579
$149$	−9.83654	−0.805840	−0.402920	−	0.915235i	$-0.632005\pi$
$149$	−9.83654	−0.805840	−0.402920	+	0.915235i	$0.632005\pi$
$150$	11.5868	0.946056
$151$	0.426888	0.0347397	0.0173698	−	0.999849i	$-0.494471\pi$
$151$	0.426888	0.0347397	0.0173698	+	0.999849i	$0.494471\pi$
$152$	1.00000	0.0811107
$153$	13.0128	1.05202
$154$	−8.84067	−0.712402
$155$	−0.679711	−0.0545957
$156$	14.1122	1.12988
$157$	−8.18977	−0.653614	−0.326807	−	0.945091i	$-0.605973\pi$
$157$	−8.18977	−0.653614	−0.326807	+	0.945091i	$0.605973\pi$
$158$	7.21166	0.573729
$159$	17.2356	1.36687
$160$	−0.567392	−0.0448563
$161$	−16.0375	−1.26393
$162$	−8.57782	−0.673938
$163$	−20.4062	−1.59833	−0.799167	−	0.601109i	$-0.794726\pi$
$163$	−20.4062	−1.59833	−0.799167	+	0.601109i	$0.794726\pi$
$164$	12.1142	0.945963
$165$	2.57703	0.200622
$166$	13.7036	1.06360
$167$	−2.47910	−0.191839	−0.0959194	−	0.995389i	$-0.530579\pi$
$167$	−2.47910	−0.191839	−0.0959194	+	0.995389i	$0.530579\pi$
$168$	11.9410	0.921268
$169$	19.4637	1.49721
$170$	−2.35538	−0.180649
$171$	3.13468	0.239715
$172$	−0.920599	−0.0701950
$173$	−9.31587	−0.708273	−0.354136	−	0.935194i	$-0.615225\pi$
$173$	−9.31587	−0.708273	−0.354136	+	0.935194i	$0.615225\pi$
$174$	−1.65172	−0.125216
$175$	22.5533	1.70487
$176$	1.83375	0.138224
$177$	24.1691	1.81666
$178$	−8.31843	−0.623493
$179$	9.64188	0.720668	0.360334	−	0.932823i	$-0.382663\pi$
$179$	9.64188	0.720668	0.360334	+	0.932823i	$0.382663\pi$
$180$	−1.77859	−0.132568
$181$	−9.03298	−0.671416	−0.335708	−	0.941966i	$-0.608976\pi$
$181$	−9.03298	−0.671416	−0.335708	+	0.941966i	$0.608976\pi$
$182$	27.4691	2.03614
$183$	−8.71373	−0.644138
$184$	3.32654	0.245236
$185$	0.942755	0.0693128
$186$	−2.96713	−0.217561
$187$	7.61233	0.556669
$188$	5.33894	0.389382
$189$	1.60820	0.116979
$190$	−0.567392	−0.0411630
$191$	20.8399	1.50792	0.753962	−	0.656918i	$-0.228140\pi$
$191$	20.8399	1.50792	0.753962	+	0.656918i	$0.228140\pi$
$192$	−2.47683	−0.178750
$193$	1.05471	0.0759197	0.0379599	−	0.999279i	$-0.487914\pi$
$193$	1.05471	0.0759197	0.0379599	+	0.999279i	$0.487914\pi$
$194$	6.85317	0.492029
$195$	−8.00716	−0.573405
$196$	16.2428	1.16020
$197$	−13.1104	−0.934074	−0.467037	−	0.884238i	$-0.654679\pi$
$197$	−13.1104	−0.934074	−0.467037	+	0.884238i	$0.654679\pi$
$198$	5.74823	0.408509
$199$	2.27122	0.161002	0.0805012	−	0.996755i	$-0.474348\pi$
$199$	2.27122	0.161002	0.0805012	+	0.996755i	$0.474348\pi$
$200$	−4.67807	−0.330789
$201$	26.4886	1.86836
$202$	−6.59279	−0.463867
$203$	−3.21502	−0.225650
$204$	−10.2819	−0.719876
$205$	−6.87353	−0.480068
$206$	12.3679	0.861710
$207$	10.4276	0.724771
$208$	−5.69770	−0.395064
$209$	1.83375	0.126843
$210$	−6.77523	−0.467535
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−6.95873	−0.477928
$213$	−32.9390	−2.25694
$214$	−5.73409	−0.391974
$215$	0.522341	0.0356233
$216$	−0.333577	−0.0226970
$217$	−5.77544	−0.392063
$218$	7.07403	0.479114
$219$	1.39270	0.0941098
$220$	−1.04046	−0.0701476
$221$	−23.6524	−1.59103
$222$	4.11540	0.276207
$223$	17.4547	1.16885	0.584426	−	0.811447i	$-0.301320\pi$
$223$	17.4547	1.16885	0.584426	+	0.811447i	$0.301320\pi$
$224$	−4.82108	−0.322122
$225$	−14.6642	−0.977616
$226$	2.29029	0.152348
$227$	−18.6335	−1.23675	−0.618374	−	0.785884i	$-0.712208\pi$
$227$	−18.6335	−1.23675	−0.618374	+	0.785884i	$0.712208\pi$
$228$	−2.47683	−0.164032
$229$	9.79335	0.647162	0.323581	−	0.946200i	$-0.395113\pi$
$229$	9.79335	0.647162	0.323581	+	0.946200i	$0.395113\pi$
$230$	−1.88746	−0.124455
$231$	21.8968	1.44071
$232$	0.666868	0.0437820
$233$	−17.5426	−1.14926	−0.574628	−	0.818415i	$-0.694853\pi$
$233$	−17.5426	−1.14926	−0.574628	+	0.818415i	$0.694853\pi$
$234$	−17.8604	−1.16757
$235$	−3.02927	−0.197608
$236$	−9.75807	−0.635196
$237$	−17.8620	−1.16026
$238$	−20.0134	−1.29728
$239$	4.72853	0.305863	0.152932	−	0.988237i	$-0.451129\pi$
$239$	4.72853	0.305863	0.152932	+	0.988237i	$0.451129\pi$
$240$	1.40533	0.0907139
$241$	−3.70715	−0.238799	−0.119399	−	0.992846i	$-0.538097\pi$
$241$	−3.70715	−0.238799	−0.119399	+	0.992846i	$0.538097\pi$
$242$	−7.63735	−0.490947
$243$	22.2465	1.42712
$244$	3.51810	0.225223
$245$	−9.21605	−0.588792
$246$	−30.0049	−1.91304
$247$	−5.69770	−0.362536
$248$	1.19796	0.0760703
$249$	−33.9414	−2.15095
$250$	5.49126	0.347298
$251$	−16.9366	−1.06903	−0.534515	−	0.845159i	$-0.679506\pi$
$251$	−16.9366	−1.06903	−0.534515	+	0.845159i	$0.679506\pi$
$252$	−15.1125	−0.952001
$253$	6.10006	0.383507
$254$	4.06565	0.255102
$255$	5.83386	0.365330
$256$	1.00000	0.0625000
$257$	−6.96918	−0.434726	−0.217363	−	0.976091i	$-0.569745\pi$
$257$	−6.96918	−0.434726	−0.217363	+	0.976091i	$0.569745\pi$
$258$	2.28017	0.141957
$259$	8.01051	0.497749
$260$	3.23283	0.200492
$261$	2.09042	0.129393
$262$	−22.0302	−1.36103
$263$	6.22817	0.384045	0.192023	−	0.981391i	$-0.438495\pi$
$263$	6.22817	0.384045	0.192023	+	0.981391i	$0.438495\pi$
$264$	−4.54189	−0.279534
$265$	3.94833	0.242544
$266$	−4.82108	−0.295599
$267$	20.6033	1.26090
$268$	−10.6946	−0.653274
$269$	20.3744	1.24225	0.621124	−	0.783712i	$-0.286676\pi$
$269$	20.3744	1.24225	0.621124	+	0.783712i	$0.286676\pi$
$270$	0.189269	0.0115185
$271$	−16.5363	−1.00451	−0.502254	−	0.864720i	$-0.667496\pi$
$271$	−16.5363	−1.00451	−0.502254	+	0.864720i	$0.667496\pi$
$272$	4.15123	0.251705
$273$	−68.0361	−4.11773
$274$	−21.1806	−1.27957
$275$	−8.57842	−0.517298
$276$	−8.23928	−0.495946
$277$	17.2738	1.03788	0.518940	−	0.854810i	$-0.326327\pi$
$277$	17.2738	1.03788	0.518940	+	0.854810i	$0.326327\pi$
$278$	9.81593	0.588720
$279$	3.75521	0.224818
$280$	2.73544	0.163474
$281$	−2.67698	−0.159695	−0.0798476	−	0.996807i	$-0.525443\pi$
$281$	−2.67698	−0.159695	−0.0798476	+	0.996807i	$0.525443\pi$
$282$	−13.2236	−0.787456
$283$	11.6554	0.692840	0.346420	−	0.938079i	$-0.387397\pi$
$283$	11.6554	0.692840	0.346420	+	0.938079i	$0.387397\pi$
$284$	13.2989	0.789142
$285$	1.40533	0.0832448
$286$	−10.4482	−0.617813
$287$	−58.4037	−3.44746
$288$	3.13468	0.184713
$289$	0.232697	0.0136881
$290$	−0.378376	−0.0222190
$291$	−16.9741	−0.995041
$292$	−0.562291	−0.0329056
$293$	20.0736	1.17271	0.586357	−	0.810053i	$-0.300562\pi$
$293$	20.0736	1.17271	0.586357	+	0.810053i	$0.300562\pi$
$294$	−40.2307	−2.34630
$295$	5.53665	0.322356
$296$	−1.66156	−0.0965761
$297$	−0.611698	−0.0354943
$298$	−9.83654	−0.569815
$299$	−18.9536	−1.09612
$300$	11.5868	0.668962
$301$	4.43828	0.255818
$302$	0.426888	0.0245647
$303$	16.3292	0.938089
$304$	1.00000	0.0573539
$305$	−1.99614	−0.114299
$306$	13.0128	0.743890
$307$	−4.90950	−0.280200	−0.140100	−	0.990137i	$-0.544742\pi$
$307$	−4.90950	−0.280200	−0.140100	+	0.990137i	$0.544742\pi$
$308$	−8.84067	−0.503744
$309$	−30.6331	−1.74266
$310$	−0.679711	−0.0386050
$311$	−27.4826	−1.55840	−0.779199	−	0.626777i	$-0.784374\pi$
$311$	−27.4826	−1.55840	−0.779199	+	0.626777i	$0.784374\pi$
$312$	14.1122	0.798947
$313$	−13.3112	−0.752395	−0.376197	−	0.926540i	$-0.622769\pi$
$313$	−13.3112	−0.752395	−0.376197	+	0.926540i	$0.622769\pi$
$314$	−8.18977	−0.462175
$315$	8.57474	0.483132
$316$	7.21166	0.405688
$317$	−13.3881	−0.751952	−0.375976	−	0.926629i	$-0.622693\pi$
$317$	−13.3881	−0.751952	−0.375976	+	0.926629i	$0.622693\pi$
$318$	17.2356	0.966524
$319$	1.22287	0.0684676
$320$	−0.567392	−0.0317182
$321$	14.2024	0.792698
$322$	−16.0375	−0.893737
$323$	4.15123	0.230981
$324$	−8.57782	−0.476546
$325$	26.6542	1.47851
$326$	−20.4062	−1.13019
$327$	−17.5212	−0.968923
$328$	12.1142	0.668897
$329$	−25.7395	−1.41906
$330$	2.57703	0.141861
$331$	18.7133	1.02858	0.514288	−	0.857618i	$-0.328056\pi$
$331$	18.7133	1.02858	0.514288	+	0.857618i	$0.328056\pi$
$332$	13.7036	0.752081
$333$	−5.20845	−0.285421
$334$	−2.47910	−0.135650
$335$	6.06801	0.331531
$336$	11.9410	0.651434
$337$	−26.5988	−1.44893	−0.724464	−	0.689312i	$-0.757913\pi$
$337$	−26.5988	−1.44893	−0.724464	+	0.689312i	$0.757913\pi$
$338$	19.4637	1.05869
$339$	−5.67264	−0.308096
$340$	−2.35538	−0.127738
$341$	2.19676	0.118961
$342$	3.13468	0.169504
$343$	−44.5604	−2.40604
$344$	−0.920599	−0.0496354
$345$	4.67490	0.251688
$346$	−9.31587	−0.500824
$347$	11.5652	0.620851	0.310425	−	0.950598i	$-0.399529\pi$
$347$	11.5652	0.620851	0.310425	+	0.950598i	$0.399529\pi$
$348$	−1.65172	−0.0885413
$349$	−14.2528	−0.762934	−0.381467	−	0.924382i	$-0.624581\pi$
$349$	−14.2528	−0.762934	−0.381467	+	0.924382i	$0.624581\pi$
$350$	22.5533	1.20553
$351$	1.90062	0.101448
$352$	1.83375	0.0977394
$353$	9.49285	0.505253	0.252627	−	0.967564i	$-0.418706\pi$
$353$	9.49285	0.505253	0.252627	+	0.967564i	$0.418706\pi$
$354$	24.1691	1.28457
$355$	−7.54567	−0.400483
$356$	−8.31843	−0.440876
$357$	49.5698	2.62351
$358$	9.64188	0.509589
$359$	−19.1533	−1.01087	−0.505436	−	0.862864i	$-0.668668\pi$
$359$	−19.1533	−1.01087	−0.505436	+	0.862864i	$0.668668\pi$
$360$	−1.77859	−0.0937401
$361$	1.00000	0.0526316
$362$	−9.03298	−0.474763
$363$	18.9164	0.992854
$364$	27.4691	1.43977
$365$	0.319039	0.0166993
$366$	−8.71373	−0.455474
$367$	−9.02112	−0.470899	−0.235449	−	0.971887i	$-0.575656\pi$
$367$	−9.02112	−0.470899	−0.235449	+	0.971887i	$0.575656\pi$
$368$	3.32654	0.173408
$369$	37.9742	1.97686
$370$	0.942755	0.0490115
$371$	33.5486	1.74176
$372$	−2.96713	−0.153839
$373$	−15.6364	−0.809621	−0.404811	−	0.914401i	$-0.632663\pi$
$373$	−15.6364	−0.809621	−0.404811	+	0.914401i	$0.632663\pi$
$374$	7.61233	0.393624
$375$	−13.6009	−0.702348
$376$	5.33894	0.275335
$377$	−3.79961	−0.195690
$378$	1.60820	0.0827170
$379$	−15.7259	−0.807786	−0.403893	−	0.914806i	$-0.632343\pi$
$379$	−15.7259	−0.807786	−0.403893	+	0.914806i	$0.632343\pi$
$380$	−0.567392	−0.0291066
$381$	−10.0699	−0.515898
$382$	20.8399	1.06626
$383$	−1.06145	−0.0542376	−0.0271188	−	0.999632i	$-0.508633\pi$
$383$	−1.06145	−0.0542376	−0.0271188	+	0.999632i	$0.508633\pi$
$384$	−2.47683	−0.126395
$385$	5.01613	0.255646
$386$	1.05471	0.0536834
$387$	−2.88578	−0.146693
$388$	6.85317	0.347917
$389$	17.3400	0.879172	0.439586	−	0.898200i	$-0.355125\pi$
$389$	17.3400	0.879172	0.439586	+	0.898200i	$0.355125\pi$
$390$	−8.00716	−0.405458
$391$	13.8092	0.698363
$392$	16.2428	0.820387
$393$	54.5651	2.75244
$394$	−13.1104	−0.660490
$395$	−4.09184	−0.205883
$396$	5.74823	0.288859
$397$	−20.1357	−1.01058	−0.505291	−	0.862949i	$-0.668615\pi$
$397$	−20.1357	−1.01058	−0.505291	+	0.862949i	$0.668615\pi$
$398$	2.27122	0.113846
$399$	11.9410	0.597797
$400$	−4.67807	−0.233903
$401$	−26.6269	−1.32969	−0.664843	−	0.746983i	$-0.731502\pi$
$401$	−26.6269	−1.32969	−0.664843	+	0.746983i	$0.731502\pi$
$402$	26.4886	1.32113
$403$	−6.82559	−0.340007
$404$	−6.59279	−0.328004
$405$	4.86699	0.241843
$406$	−3.21502	−0.159559
$407$	−3.04689	−0.151029
$408$	−10.2819	−0.509029
$409$	−4.92119	−0.243337	−0.121669	−	0.992571i	$-0.538825\pi$
$409$	−4.92119	−0.243337	−0.121669	+	0.992571i	$0.538825\pi$
$410$	−6.87353	−0.339459
$411$	52.4607	2.58770
$412$	12.3679	0.609321
$413$	47.0445	2.31491
$414$	10.4276	0.512491
$415$	−7.77530	−0.381674
$416$	−5.69770	−0.279353
$417$	−24.3124	−1.19058
$418$	1.83375	0.0896918
$419$	25.3212	1.23702	0.618511	−	0.785776i	$-0.287736\pi$
$419$	25.3212	1.23702	0.618511	+	0.785776i	$0.287736\pi$
$420$	−6.77523	−0.330597
$421$	10.0646	0.490521	0.245260	−	0.969457i	$-0.421127\pi$
$421$	10.0646	0.490521	0.245260	+	0.969457i	$0.421127\pi$
$422$	−1.00000	−0.0486792
$423$	16.7359	0.813725
$424$	−6.95873	−0.337946
$425$	−19.4197	−0.941995
$426$	−32.9390	−1.59590
$427$	−16.9611	−0.820803
$428$	−5.73409	−0.277168
$429$	25.8783	1.24942
$430$	0.522341	0.0251895
$431$	6.56730	0.316336	0.158168	−	0.987412i	$-0.449441\pi$
$431$	6.56730	0.316336	0.158168	+	0.987412i	$0.449441\pi$
$432$	−0.333577	−0.0160492
$433$	−34.5132	−1.65860	−0.829299	−	0.558805i	$-0.811260\pi$
$433$	−34.5132	−1.65860	−0.829299	+	0.558805i	$0.811260\pi$
$434$	−5.77544	−0.277230
$435$	0.937171	0.0449339
$436$	7.07403	0.338785
$437$	3.32654	0.159130
$438$	1.39270	0.0665456
$439$	8.56863	0.408958	0.204479	−	0.978871i	$-0.434450\pi$
$439$	8.56863	0.408958	0.204479	+	0.978871i	$0.434450\pi$
$440$	−1.04046	−0.0496019
$441$	50.9160	2.42457
$442$	−23.6524	−1.12503
$443$	−16.3904	−0.778732	−0.389366	−	0.921083i	$-0.627306\pi$
$443$	−16.3904	−0.778732	−0.389366	+	0.921083i	$0.627306\pi$
$444$	4.11540	0.195308
$445$	4.71981	0.223741
$446$	17.4547	0.826503
$447$	24.3634	1.15235
$448$	−4.82108	−0.227775
$449$	−0.0363439	−0.00171518	−0.000857588	−	1.00000i	$-0.500273\pi$
$449$	−0.0363439	−0.00171518	−0.000857588		1.00000i	$0.500273\pi$
$450$	−14.6642	−0.691279
$451$	22.2145	1.04604
$452$	2.29029	0.107726
$453$	−1.05733	−0.0496777
$454$	−18.6335	−0.874513
$455$	−15.5857	−0.730670
$456$	−2.47683	−0.115988
$457$	−2.88094	−0.134765	−0.0673823	−	0.997727i	$-0.521465\pi$
$457$	−2.88094	−0.134765	−0.0673823	+	0.997727i	$0.521465\pi$
$458$	9.79335	0.457613
$459$	−1.38475	−0.0646348
$460$	−1.88746	−0.0880030
$461$	−20.5742	−0.958238	−0.479119	−	0.877750i	$-0.659044\pi$
$461$	−20.5742	−0.958238	−0.479119	+	0.877750i	$0.659044\pi$
$462$	21.8968	1.01873
$463$	5.76886	0.268102	0.134051	−	0.990974i	$-0.457201\pi$
$463$	5.76886	0.268102	0.134051	+	0.990974i	$0.457201\pi$
$464$	0.666868	0.0309585
$465$	1.68353	0.0780717
$466$	−17.5426	−0.812646
$467$	−0.843417	−0.0390287	−0.0195143	−	0.999810i	$-0.506212\pi$
$467$	−0.843417	−0.0390287	−0.0195143	+	0.999810i	$0.506212\pi$
$468$	−17.8604	−0.825599
$469$	51.5593	2.38079
$470$	−3.02927	−0.139730
$471$	20.2846	0.934667
$472$	−9.75807	−0.449152
$473$	−1.68815	−0.0776213
$474$	−17.8620	−0.820431
$475$	−4.67807	−0.214644
$476$	−20.0134	−0.917313
$477$	−21.8134	−0.998767
$478$	4.72853	0.216278
$479$	−18.0326	−0.823931	−0.411965	−	0.911199i	$-0.635158\pi$
$479$	−18.0326	−0.823931	−0.411965	+	0.911199i	$0.635158\pi$
$480$	1.40533	0.0641444
$481$	9.46705	0.431660
$482$	−3.70715	−0.168856
$483$	39.7222	1.80742
$484$	−7.63735	−0.347152
$485$	−3.88844	−0.176565
$486$	22.2465	1.00912
$487$	−42.0650	−1.90615	−0.953073	−	0.302742i	$-0.902098\pi$
$487$	−42.0650	−1.90615	−0.953073	+	0.302742i	$0.902098\pi$
$488$	3.51810	0.159257
$489$	50.5426	2.28561
$490$	−9.21605	−0.416339
$491$	−14.2502	−0.643101	−0.321551	−	0.946892i	$-0.604204\pi$
$491$	−14.2502	−0.643101	−0.321551	+	0.946892i	$0.604204\pi$
$492$	−30.0049	−1.35272
$493$	2.76832	0.124679
$494$	−5.69770	−0.256351
$495$	−3.26150	−0.146594
$496$	1.19796	0.0537898
$497$	−64.1149	−2.87595
$498$	−33.9414	−1.52095
$499$	9.56768	0.428308	0.214154	−	0.976800i	$-0.431301\pi$
$499$	9.56768	0.428308	0.214154	+	0.976800i	$0.431301\pi$
$500$	5.49126	0.245577
$501$	6.14031	0.274329
$502$	−16.9366	−0.755919
$503$	13.1297	0.585423	0.292711	−	0.956201i	$-0.405442\pi$
$503$	13.1297	0.585423	0.292711	+	0.956201i	$0.405442\pi$
$504$	−15.1125	−0.673166
$505$	3.74070	0.166459
$506$	6.10006	0.271181
$507$	−48.2083	−2.14101
$508$	4.06565	0.180384
$509$	42.3360	1.87651	0.938256	−	0.345942i	$-0.112441\pi$
$509$	42.3360	1.87651	0.938256	+	0.345942i	$0.112441\pi$
$510$	5.83386	0.258328
$511$	2.71085	0.119921
$512$	1.00000	0.0441942
$513$	−0.333577	−0.0147278
$514$	−6.96918	−0.307398
$515$	−7.01743	−0.309225
$516$	2.28017	0.100379
$517$	9.79029	0.430577
$518$	8.01051	0.351962
$519$	23.0738	1.01283
$520$	3.23283	0.141769
$521$	−6.93772	−0.303947	−0.151974	−	0.988385i	$-0.548563\pi$
$521$	−6.93772	−0.303947	−0.151974	+	0.988385i	$0.548563\pi$
$522$	2.09042	0.0914950
$523$	28.9900	1.26765	0.633823	−	0.773478i	$-0.281485\pi$
$523$	28.9900	1.26765	0.633823	+	0.773478i	$0.281485\pi$
$524$	−22.0302	−0.962395
$525$	−55.8607	−2.43796
$526$	6.22817	0.271561
$527$	4.97299	0.216627
$528$	−4.54189	−0.197660
$529$	−11.9341	−0.518874
$530$	3.94833	0.171505
$531$	−30.5884	−1.32742
$532$	−4.82108	−0.209020
$533$	−69.0232	−2.98973
$534$	20.6033	0.891593
$535$	3.25348	0.140660
$536$	−10.6946	−0.461934
$537$	−23.8813	−1.03055
$538$	20.3744	0.878402
$539$	29.7853	1.28295
$540$	0.189269	0.00814484
$541$	25.5107	1.09679	0.548395	−	0.836220i	$-0.315239\pi$
$541$	25.5107	1.09679	0.548395	+	0.836220i	$0.315239\pi$
$542$	−16.5363	−0.710295
$543$	22.3731	0.960124
$544$	4.15123	0.177982
$545$	−4.01375	−0.171930
$546$	−68.0361	−2.91168
$547$	−3.26142	−0.139448	−0.0697242	−	0.997566i	$-0.522212\pi$
$547$	−3.26142	−0.139448	−0.0697242	+	0.997566i	$0.522212\pi$
$548$	−21.1806	−0.904791
$549$	11.0281	0.470669
$550$	−8.57842	−0.365785
$551$	0.666868	0.0284095
$552$	−8.23928	−0.350687
$553$	−34.7680	−1.47849
$554$	17.2738	0.733893
$555$	−2.33504	−0.0991171
$556$	9.81593	0.416288
$557$	−11.3735	−0.481912	−0.240956	−	0.970536i	$-0.577461\pi$
$557$	−11.3735	−0.481912	−0.240956	+	0.970536i	$0.577461\pi$
$558$	3.75521	0.158971
$559$	5.24529	0.221852
$560$	2.73544	0.115594
$561$	−18.8544	−0.796035
$562$	−2.67698	−0.112922
$563$	15.4769	0.652275	0.326137	−	0.945322i	$-0.394253\pi$
$563$	15.4769	0.652275	0.326137	+	0.945322i	$0.394253\pi$
$564$	−13.2236	−0.556815
$565$	−1.29949	−0.0546700
$566$	11.6554	0.489912
$567$	41.3544	1.73672
$568$	13.2989	0.558008
$569$	−12.4033	−0.519975	−0.259987	−	0.965612i	$-0.583718\pi$
$569$	−12.4033	−0.519975	−0.259987	+	0.965612i	$0.583718\pi$
$570$	1.40533	0.0588629
$571$	−17.6149	−0.737162	−0.368581	−	0.929596i	$-0.620156\pi$
$571$	−17.6149	−0.737162	−0.368581	+	0.929596i	$0.620156\pi$
$572$	−10.4482	−0.436860
$573$	−51.6169	−2.15633
$574$	−58.4037	−2.43772
$575$	−15.5618	−0.648971
$576$	3.13468	0.130612
$577$	24.7686	1.03113	0.515565	−	0.856850i	$-0.327582\pi$
$577$	24.7686	1.03113	0.515565	+	0.856850i	$0.327582\pi$
$578$	0.232697	0.00967894
$579$	−2.61234	−0.108565
$580$	−0.378376	−0.0157112
$581$	−66.0660	−2.74088
$582$	−16.9741	−0.703600
$583$	−12.7606	−0.528490
$584$	−0.562291	−0.0232677
$585$	10.1339	0.418984
$586$	20.0736	0.829234
$587$	3.74142	0.154425	0.0772124	−	0.997015i	$-0.475398\pi$
$587$	3.74142	0.154425	0.0772124	+	0.997015i	$0.475398\pi$
$588$	−40.2307	−1.65909
$589$	1.19796	0.0493609
$590$	5.53665	0.227940
$591$	32.4721	1.33572
$592$	−1.66156	−0.0682896
$593$	−39.8877	−1.63799	−0.818996	−	0.573799i	$-0.805469\pi$
$593$	−39.8877	−1.63799	−0.818996	+	0.573799i	$0.805469\pi$
$594$	−0.611698	−0.0250983
$595$	11.3555	0.465528
$596$	−9.83654	−0.402920
$597$	−5.62541	−0.230233
$598$	−18.9536	−0.775072
$599$	6.36217	0.259951	0.129976	−	0.991517i	$-0.458510\pi$
$599$	6.36217	0.259951	0.129976	+	0.991517i	$0.458510\pi$
$600$	11.5868	0.473028
$601$	−28.0361	−1.14362	−0.571809	−	0.820387i	$-0.693758\pi$
$601$	−28.0361	−1.14362	−0.571809	+	0.820387i	$0.693758\pi$
$602$	4.43828	0.180891
$603$	−33.5240	−1.36520
$604$	0.426888	0.0173698
$605$	4.33337	0.176177
$606$	16.3292	0.663329
$607$	18.3805	0.746042	0.373021	−	0.927823i	$-0.378322\pi$
$607$	18.3805	0.746042	0.373021	+	0.927823i	$0.378322\pi$
$608$	1.00000	0.0405554
$609$	7.96306	0.322679
$610$	−1.99614	−0.0808215
$611$	−30.4196	−1.23065
$612$	13.0128	0.526010
$613$	−16.5269	−0.667515	−0.333757	−	0.942659i	$-0.608317\pi$
$613$	−16.5269	−0.667515	−0.333757	+	0.942659i	$0.608317\pi$
$614$	−4.90950	−0.198131
$615$	17.0245	0.686496
$616$	−8.84067	−0.356201
$617$	0.181132	0.00729209	0.00364605	−	0.999993i	$-0.498839\pi$
$617$	0.181132	0.00729209	0.00364605	+	0.999993i	$0.498839\pi$
$618$	−30.6331	−1.23224
$619$	25.3398	1.01849	0.509246	−	0.860621i	$-0.329924\pi$
$619$	25.3398	1.01849	0.509246	+	0.860621i	$0.329924\pi$
$620$	−0.679711	−0.0272978
$621$	−1.10966	−0.0445291
$622$	−27.4826	−1.10195
$623$	40.1038	1.60673
$624$	14.1122	0.564941
$625$	20.2746	0.810985
$626$	−13.3112	−0.532023
$627$	−4.54189	−0.181386
$628$	−8.18977	−0.326807
$629$	−6.89751	−0.275022
$630$	8.57474	0.341626
$631$	18.5985	0.740395	0.370197	−	0.928953i	$-0.379290\pi$
$631$	18.5985	0.740395	0.370197	+	0.928953i	$0.379290\pi$
$632$	7.21166	0.286864
$633$	2.47683	0.0984451
$634$	−13.3881	−0.531711
$635$	−2.30682	−0.0915434
$636$	17.2356	0.683436
$637$	−92.5467	−3.66683
$638$	1.22287	0.0484139
$639$	41.6877	1.64914
$640$	−0.567392	−0.0224282
$641$	27.8553	1.10022	0.550109	−	0.835093i	$-0.314586\pi$
$641$	27.8553	1.10022	0.550109	+	0.835093i	$0.314586\pi$
$642$	14.2024	0.560522
$643$	−15.2251	−0.600420	−0.300210	−	0.953873i	$-0.597057\pi$
$643$	−15.2251	−0.600420	−0.300210	+	0.953873i	$0.597057\pi$
$644$	−16.0375	−0.631967
$645$	−1.29375	−0.0509413
$646$	4.15123	0.163328
$647$	26.8519	1.05566	0.527828	−	0.849351i	$-0.323006\pi$
$647$	26.8519	1.05566	0.527828	+	0.849351i	$0.323006\pi$
$648$	−8.57782	−0.336969
$649$	−17.8939	−0.702397
$650$	26.6542	1.04546
$651$	14.3048	0.560648
$652$	−20.4062	−0.799167
$653$	−40.0131	−1.56583	−0.782917	−	0.622126i	$-0.786269\pi$
$653$	−40.0131	−1.56583	−0.782917	+	0.622126i	$0.786269\pi$
$654$	−17.5212	−0.685132
$655$	12.4998	0.488407
$656$	12.1142	0.472982
$657$	−1.76260	−0.0687656
$658$	−25.7395	−1.00343
$659$	−37.3563	−1.45519	−0.727597	−	0.686004i	$-0.759363\pi$
$659$	−37.3563	−1.45519	−0.727597	+	0.686004i	$0.759363\pi$
$660$	2.57703	0.100311
$661$	6.81868	0.265216	0.132608	−	0.991169i	$-0.457665\pi$
$661$	6.81868	0.265216	0.132608	+	0.991169i	$0.457665\pi$
$662$	18.7133	0.727312
$663$	58.5830	2.27518
$664$	13.7036	0.531801
$665$	2.73544	0.106076
$666$	−5.20845	−0.201823
$667$	2.21836	0.0858954
$668$	−2.47910	−0.0959194
$669$	−43.2322	−1.67145
$670$	6.06801	0.234428
$671$	6.45133	0.249051
$672$	11.9410	0.460634
$673$	2.68173	0.103373	0.0516866	−	0.998663i	$-0.483540\pi$
$673$	2.68173	0.103373	0.0516866	+	0.998663i	$0.483540\pi$
$674$	−26.5988	−1.02455
$675$	1.56050	0.0600635
$676$	19.4637	0.748605
$677$	−40.2480	−1.54686	−0.773429	−	0.633883i	$-0.781460\pi$
$677$	−40.2480	−1.54686	−0.773429	+	0.633883i	$0.781460\pi$
$678$	−5.67264	−0.217857
$679$	−33.0397	−1.26795
$680$	−2.35538	−0.0903245
$681$	46.1519	1.76855
$682$	2.19676	0.0841181
$683$	18.9980	0.726938	0.363469	−	0.931606i	$-0.381592\pi$
$683$	18.9980	0.726938	0.363469	+	0.931606i	$0.381592\pi$
$684$	3.13468	0.119857
$685$	12.0177	0.459173
$686$	−44.5604	−1.70132
$687$	−24.2564	−0.925441
$688$	−0.920599	−0.0350975
$689$	39.6487	1.51050
$690$	4.67490	0.177970
$691$	3.89630	0.148222	0.0741111	−	0.997250i	$-0.476388\pi$
$691$	3.89630	0.148222	0.0741111	+	0.997250i	$0.476388\pi$
$692$	−9.31587	−0.354136
$693$	−27.7127	−1.05272
$694$	11.5652	0.439008
$695$	−5.56948	−0.211263
$696$	−1.65172	−0.0626082
$697$	50.2890	1.90483
$698$	−14.2528	−0.539476
$699$	43.4501	1.64343
$700$	22.5533	0.852436
$701$	6.16398	0.232810	0.116405	−	0.993202i	$-0.462863\pi$
$701$	6.16398	0.232810	0.116405	+	0.993202i	$0.462863\pi$
$702$	1.90062	0.0717343
$703$	−1.66156	−0.0626669
$704$	1.83375	0.0691122
$705$	7.50299	0.282579
$706$	9.49285	0.357268
$707$	31.7844	1.19538
$708$	24.1691	0.908329
$709$	−47.7828	−1.79452	−0.897261	−	0.441500i	$-0.854446\pi$
$709$	−47.7828	−1.79452	−0.897261	+	0.441500i	$0.854446\pi$
$710$	−7.54567	−0.283184
$711$	22.6062	0.847800
$712$	−8.31843	−0.311746
$713$	3.98505	0.149241
$714$	49.5698	1.85510
$715$	5.92821	0.221702
$716$	9.64188	0.360334
$717$	−11.7118	−0.437384
$718$	−19.1533	−0.714794
$719$	50.2312	1.87331	0.936653	−	0.350257i	$-0.113906\pi$
$719$	50.2312	1.87331	0.936653	+	0.350257i	$0.113906\pi$
$720$	−1.77859	−0.0662842
$721$	−59.6265	−2.22061
$722$	1.00000	0.0372161
$723$	9.18198	0.341481
$724$	−9.03298	−0.335708
$725$	−3.11965	−0.115861
$726$	18.9164	0.702054
$727$	−11.2442	−0.417024	−0.208512	−	0.978020i	$-0.566862\pi$
$727$	−11.2442	−0.417024	−0.208512	+	0.978020i	$0.566862\pi$
$728$	27.4691	1.01807
$729$	−29.3674	−1.08768
$730$	0.319039	0.0118082
$731$	−3.82162	−0.141348
$732$	−8.71373	−0.322069
$733$	34.3250	1.26782	0.633911	−	0.773406i	$-0.281449\pi$
$733$	34.3250	1.26782	0.633911	+	0.773406i	$0.281449\pi$
$734$	−9.02112	−0.332976
$735$	22.8266	0.841971
$736$	3.32654	0.122618
$737$	−19.6112	−0.722387
$738$	37.9742	1.39785
$739$	−41.8021	−1.53771	−0.768857	−	0.639421i	$-0.779174\pi$
$739$	−41.8021	−1.53771	−0.768857	+	0.639421i	$0.779174\pi$
$740$	0.942755	0.0346564
$741$	14.1122	0.518425
$742$	33.5486	1.23161
$743$	−14.4206	−0.529042	−0.264521	−	0.964380i	$-0.585214\pi$
$743$	−14.4206	−0.529042	−0.264521	+	0.964380i	$0.585214\pi$
$744$	−2.96713	−0.108780
$745$	5.58118	0.204478
$746$	−15.6364	−0.572489
$747$	42.9563	1.57169
$748$	7.61233	0.278334
$749$	27.6445	1.01011
$750$	−13.6009	−0.496635
$751$	9.10593	0.332280	0.166140	−	0.986102i	$-0.446870\pi$
$751$	9.10593	0.332280	0.166140	+	0.986102i	$0.446870\pi$
$752$	5.33894	0.194691
$753$	41.9491	1.52871
$754$	−3.79961	−0.138374
$755$	−0.242213	−0.00881504
$756$	1.60820	0.0584897
$757$	−3.27757	−0.119125	−0.0595626	−	0.998225i	$-0.518971\pi$
$757$	−3.27757	−0.119125	−0.0595626	+	0.998225i	$0.518971\pi$
$758$	−15.7259	−0.571191
$759$	−15.1088	−0.548415
$760$	−0.567392	−0.0205815
$761$	4.59832	0.166689	0.0833445	−	0.996521i	$-0.473440\pi$
$761$	4.59832	0.166689	0.0833445	+	0.996521i	$0.473440\pi$
$762$	−10.0699	−0.364795
$763$	−34.1045	−1.23467
$764$	20.8399	0.753962
$765$	−7.38335	−0.266945
$766$	−1.06145	−0.0383518
$767$	55.5985	2.00755
$768$	−2.47683	−0.0893748
$769$	28.7812	1.03787	0.518937	−	0.854812i	$-0.326328\pi$
$769$	28.7812	1.03787	0.518937	+	0.854812i	$0.326328\pi$
$770$	5.01613	0.180769
$771$	17.2615	0.621657
$772$	1.05471	0.0379599
$773$	22.2648	0.800809	0.400405	−	0.916338i	$-0.368870\pi$
$773$	22.2648	0.800809	0.400405	+	0.916338i	$0.368870\pi$
$774$	−2.88578	−0.103727
$775$	−5.60412	−0.201306
$776$	6.85317	0.246014
$777$	−19.8407	−0.711780
$778$	17.3400	0.621669
$779$	12.1142	0.434038
$780$	−8.00716	−0.286702
$781$	24.3868	0.872629
$782$	13.8092	0.493817
$783$	−0.222452	−0.00794978
$784$	16.2428	0.580101
$785$	4.64681	0.165852
$786$	54.5651	1.94627
$787$	11.8770	0.423368	0.211684	−	0.977338i	$-0.432105\pi$
$787$	11.8770	0.423368	0.211684	+	0.977338i	$0.432105\pi$
$788$	−13.1104	−0.467037
$789$	−15.4261	−0.549184
$790$	−4.09184	−0.145581
$791$	−11.0417	−0.392596
$792$	5.74823	0.204254
$793$	−20.0451	−0.711821
$794$	−20.1357	−0.714589
$795$	−9.77934	−0.346837
$796$	2.27122	0.0805012
$797$	−7.58194	−0.268566	−0.134283	−	0.990943i	$-0.542873\pi$
$797$	−7.58194	−0.268566	−0.134283	+	0.990943i	$0.542873\pi$
$798$	11.9410	0.422707
$799$	22.1631	0.784076
$800$	−4.67807	−0.165395
$801$	−26.0756	−0.921336
$802$	−26.6269	−0.940230
$803$	−1.03110	−0.0363868
$804$	26.4886	0.934180
$805$	9.09957	0.320718
$806$	−6.82559	−0.240421
$807$	−50.4639	−1.77641
$808$	−6.59279	−0.231934
$809$	17.3062	0.608454	0.304227	−	0.952600i	$-0.401602\pi$
$809$	17.3062	0.608454	0.304227	+	0.952600i	$0.401602\pi$
$810$	4.86699	0.171009
$811$	31.7744	1.11575	0.557874	−	0.829925i	$-0.311617\pi$
$811$	31.7744	1.11575	0.557874	+	0.829925i	$0.311617\pi$
$812$	−3.21502	−0.112825
$813$	40.9576	1.43644
$814$	−3.04689	−0.106793
$815$	11.5783	0.405570
$816$	−10.2819	−0.359938
$817$	−0.920599	−0.0322077
$818$	−4.92119	−0.172065
$819$	86.1067	3.00881
$820$	−6.87353	−0.240034
$821$	−36.7926	−1.28407	−0.642035	−	0.766675i	$-0.721910\pi$
$821$	−36.7926	−1.28407	−0.642035	+	0.766675i	$0.721910\pi$
$822$	52.4607	1.82978
$823$	−47.3954	−1.65210	−0.826050	−	0.563597i	$-0.809417\pi$
$823$	−47.3954	−1.65210	−0.826050	+	0.563597i	$0.809417\pi$
$824$	12.3679	0.430855
$825$	21.2473	0.739735
$826$	47.0445	1.63689
$827$	23.0157	0.800334	0.400167	−	0.916442i	$-0.368952\pi$
$827$	23.0157	0.800334	0.400167	+	0.916442i	$0.368952\pi$
$828$	10.4276	0.362386
$829$	−43.1140	−1.49741	−0.748705	−	0.662903i	$-0.769324\pi$
$829$	−43.1140	−1.49741	−0.748705	+	0.662903i	$0.769324\pi$
$830$	−7.77530	−0.269884
$831$	−42.7842	−1.48417
$832$	−5.69770	−0.197532
$833$	67.4277	2.33623
$834$	−24.3124	−0.841869
$835$	1.40662	0.0486782
$836$	1.83375	0.0634217
$837$	−0.399610	−0.0138126
$838$	25.3212	0.874707
$839$	20.4668	0.706594	0.353297	−	0.935511i	$-0.385061\pi$
$839$	20.4668	0.706594	0.353297	+	0.935511i	$0.385061\pi$
$840$	−6.77523	−0.233768
$841$	−28.5553	−0.984665
$842$	10.0646	0.346850
$843$	6.63042	0.228364
$844$	−1.00000	−0.0344214
$845$	−11.0436	−0.379910
$846$	16.7359	0.575391
$847$	36.8203	1.26516
$848$	−6.95873	−0.238964
$849$	−28.8684	−0.990760
$850$	−19.4197	−0.666091
$851$	−5.52725	−0.189472
$852$	−32.9390	−1.12847
$853$	11.2293	0.384483	0.192242	−	0.981348i	$-0.438424\pi$
$853$	11.2293	0.384483	0.192242	+	0.981348i	$0.438424\pi$
$854$	−16.9611	−0.580395
$855$	−1.77859	−0.0608266
$856$	−5.73409	−0.195987
$857$	27.9813	0.955822	0.477911	−	0.878408i	$-0.341394\pi$
$857$	27.9813	0.955822	0.477911	+	0.878408i	$0.341394\pi$
$858$	25.8783	0.883471
$859$	−0.633749	−0.0216232	−0.0108116	−	0.999942i	$-0.503442\pi$
$859$	−0.633749	−0.0216232	−0.0108116	+	0.999942i	$0.503442\pi$
$860$	0.522341	0.0178117
$861$	144.656	4.92986
$862$	6.56730	0.223683
$863$	−29.6830	−1.01042	−0.505211	−	0.862996i	$-0.668585\pi$
$863$	−29.6830	−1.01042	−0.505211	+	0.862996i	$0.668585\pi$
$864$	−0.333577	−0.0113485
$865$	5.28575	0.179721
$866$	−34.5132	−1.17281
$867$	−0.576352	−0.0195739
$868$	−5.77544	−0.196031
$869$	13.2244	0.448607
$870$	0.937171	0.0317731
$871$	60.9343	2.06468
$872$	7.07403	0.239557
$873$	21.4825	0.727072
$874$	3.32654	0.112522
$875$	−26.4738	−0.894978
$876$	1.39270	0.0470549
$877$	−21.4846	−0.725482	−0.362741	−	0.931890i	$-0.618159\pi$
$877$	−21.4846	−0.725482	−0.362741	+	0.931890i	$0.618159\pi$
$878$	8.56863	0.289177
$879$	−49.7189	−1.67698
$880$	−1.04046	−0.0350738
$881$	−8.74990	−0.294792	−0.147396	−	0.989078i	$-0.547089\pi$
$881$	−8.74990	−0.294792	−0.147396	+	0.989078i	$0.547089\pi$
$882$	50.9160	1.71443
$883$	17.2547	0.580666	0.290333	−	0.956926i	$-0.406234\pi$
$883$	17.2547	0.580666	0.290333	+	0.956926i	$0.406234\pi$
$884$	−23.6524	−0.795517
$885$	−13.7133	−0.460969
$886$	−16.3904	−0.550647
$887$	30.3658	1.01958	0.509792	−	0.860298i	$-0.329722\pi$
$887$	30.3658	1.01958	0.509792	+	0.860298i	$0.329722\pi$
$888$	4.11540	0.138104
$889$	−19.6008	−0.657391
$890$	4.71981	0.158208
$891$	−15.7296	−0.526962
$892$	17.4547	0.584426
$893$	5.33894	0.178661
$894$	24.3634	0.814834
$895$	−5.47073	−0.182866
$896$	−4.82108	−0.161061
$897$	46.9449	1.56744
$898$	−0.0363439	−0.00121281
$899$	0.798878	0.0266441
$900$	−14.6642	−0.488808
$901$	−28.8873	−0.962375
$902$	22.2145	0.739663
$903$	−10.9929	−0.365820
$904$	2.29029	0.0761738
$905$	5.12524	0.170369
$906$	−1.05733	−0.0351274
$907$	−12.2095	−0.405410	−0.202705	−	0.979240i	$-0.564973\pi$
$907$	−12.2095	−0.405410	−0.202705	+	0.979240i	$0.564973\pi$
$908$	−18.6335	−0.618374
$909$	−20.6663	−0.685458
$910$	−15.5857	−0.516662
$911$	−33.1195	−1.09730	−0.548649	−	0.836053i	$-0.684858\pi$
$911$	−33.1195	−1.09730	−0.548649	+	0.836053i	$0.684858\pi$
$912$	−2.47683	−0.0820160
$913$	25.1290	0.831647
$914$	−2.88094	−0.0952930
$915$	4.94411	0.163447
$916$	9.79335	0.323581
$917$	106.209	3.50735
$918$	−1.38475	−0.0457037
$919$	30.2242	0.997004	0.498502	−	0.866888i	$-0.333884\pi$
$919$	30.2242	0.997004	0.498502	+	0.866888i	$0.333884\pi$
$920$	−1.88746	−0.0622276
$921$	12.1600	0.400685
$922$	−20.5742	−0.677576
$923$	−75.7729	−2.49409
$924$	21.8968	0.720353
$925$	7.77288	0.255571
$926$	5.76886	0.189576
$927$	38.7693	1.27335
$928$	0.666868	0.0218910
$929$	−24.7144	−0.810854	−0.405427	−	0.914127i	$-0.632877\pi$
$929$	−24.7144	−0.810854	−0.405427	+	0.914127i	$0.632877\pi$
$930$	1.68353	0.0552050
$931$	16.2428	0.532337
$932$	−17.5426	−0.574628
$933$	68.0698	2.22850
$934$	−0.843417	−0.0275974
$935$	−4.31918	−0.141252
$936$	−17.8604	−0.583787
$937$	−0.140002	−0.00457366	−0.00228683	−	0.999997i	$-0.500728\pi$
$937$	−0.140002	−0.00457366	−0.00228683	+	0.999997i	$0.500728\pi$
$938$	51.5593	1.68347
$939$	32.9696	1.07592
$940$	−3.02927	−0.0988040
$941$	10.5083	0.342560	0.171280	−	0.985222i	$-0.445210\pi$
$941$	10.5083	0.342560	0.171280	+	0.985222i	$0.445210\pi$
$942$	20.2846	0.660909
$943$	40.2985	1.31230
$944$	−9.75807	−0.317598
$945$	−0.912482	−0.0296830
$946$	−1.68815	−0.0548865
$947$	−9.12492	−0.296520	−0.148260	−	0.988948i	$-0.547367\pi$
$947$	−9.12492	−0.296520	−0.148260	+	0.988948i	$0.547367\pi$
$948$	−17.8620	−0.580132
$949$	3.20376	0.103998
$950$	−4.67807	−0.151777
$951$	33.1601	1.07529
$952$	−20.0134	−0.648638
$953$	7.07306	0.229119	0.114559	−	0.993416i	$-0.463454\pi$
$953$	7.07306	0.229119	0.114559	+	0.993416i	$0.463454\pi$
$954$	−21.8134	−0.706235
$955$	−11.8244	−0.382629
$956$	4.72853	0.152932
$957$	−3.02884	−0.0979085
$958$	−18.0326	−0.582607
$959$	102.113	3.29741
$960$	1.40533	0.0453569
$961$	−29.5649	−0.953707
$962$	9.46705	0.305230
$963$	−17.9745	−0.579221
$964$	−3.70715	−0.119399
$965$	−0.598435	−0.0192643
$966$	39.7222	1.27804
$967$	20.3506	0.654430	0.327215	−	0.944950i	$-0.393890\pi$
$967$	20.3506	0.654430	0.327215	+	0.944950i	$0.393890\pi$
$968$	−7.63735	−0.245474
$969$	−10.2819	−0.330302
$970$	−3.88844	−0.124850
$971$	−12.1285	−0.389222	−0.194611	−	0.980880i	$-0.562344\pi$
$971$	−12.1285	−0.389222	−0.194611	+	0.980880i	$0.562344\pi$
$972$	22.2465	0.713558
$973$	−47.3234	−1.51712
$974$	−42.0650	−1.34785
$975$	−66.0179	−2.11426
$976$	3.51810	0.112612
$977$	−57.9253	−1.85319	−0.926597	−	0.376057i	$-0.877280\pi$
$977$	−57.9253	−1.85319	−0.926597	+	0.376057i	$0.877280\pi$
$978$	50.5426	1.61617
$979$	−15.2539	−0.487518
$980$	−9.21605	−0.294396
$981$	22.1748	0.707988
$982$	−14.2502	−0.454741
$983$	17.9013	0.570962	0.285481	−	0.958384i	$-0.407847\pi$
$983$	17.9013	0.570962	0.285481	+	0.958384i	$0.407847\pi$
$984$	−30.0049	−0.956521
$985$	7.43872	0.237017
$986$	2.76832	0.0881613
$987$	63.7522	2.02926
$988$	−5.69770	−0.181268
$989$	−3.06241	−0.0973790
$990$	−3.26150	−0.103657
$991$	5.21954	0.165804	0.0829021	−	0.996558i	$-0.473581\pi$
$991$	5.21954	0.165804	0.0829021	+	0.996558i	$0.473581\pi$
$992$	1.19796	0.0380351
$993$	−46.3496	−1.47086
$994$	−64.1149	−2.03360
$995$	−1.28867	−0.0408536
$996$	−33.9414	−1.07547
$997$	−13.1277	−0.415758	−0.207879	−	0.978155i	$-0.566656\pi$
$997$	−13.1277	−0.415758	−0.207879	+	0.978155i	$0.566656\pi$
$998$	9.56768	0.302860
$999$	0.554258	0.0175359

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.5	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.5	✓	30	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} -0.567392 q^{10} +1.83375 q^{11} -2.47683 q^{12} -5.69770 q^{13} -4.82108 q^{14} +1.40533 q^{15} +1.00000 q^{16} +4.15123 q^{17} +3.13468 q^{18} +1.00000 q^{19} -0.567392 q^{20} +11.9410 q^{21} +1.83375 q^{22} +3.32654 q^{23} -2.47683 q^{24} -4.67807 q^{25} -5.69770 q^{26} -0.333577 q^{27} -4.82108 q^{28} +0.666868 q^{29} +1.40533 q^{30} +1.19796 q^{31} +1.00000 q^{32} -4.54189 q^{33} +4.15123 q^{34} +2.73544 q^{35} +3.13468 q^{36} -1.66156 q^{37} +1.00000 q^{38} +14.1122 q^{39} -0.567392 q^{40} +12.1142 q^{41} +11.9410 q^{42} -0.920599 q^{43} +1.83375 q^{44} -1.77859 q^{45} +3.32654 q^{46} +5.33894 q^{47} -2.47683 q^{48} +16.2428 q^{49} -4.67807 q^{50} -10.2819 q^{51} -5.69770 q^{52} -6.95873 q^{53} -0.333577 q^{54} -1.04046 q^{55} -4.82108 q^{56} -2.47683 q^{57} +0.666868 q^{58} -9.75807 q^{59} +1.40533 q^{60} +3.51810 q^{61} +1.19796 q^{62} -15.1125 q^{63} +1.00000 q^{64} +3.23283 q^{65} -4.54189 q^{66} -10.6946 q^{67} +4.15123 q^{68} -8.23928 q^{69} +2.73544 q^{70} +13.2989 q^{71} +3.13468 q^{72} -0.562291 q^{73} -1.66156 q^{74} +11.5868 q^{75} +1.00000 q^{76} -8.84067 q^{77} +14.1122 q^{78} +7.21166 q^{79} -0.567392 q^{80} -8.57782 q^{81} +12.1142 q^{82} +13.7036 q^{83} +11.9410 q^{84} -2.35538 q^{85} -0.920599 q^{86} -1.65172 q^{87} +1.83375 q^{88} -8.31843 q^{89} -1.77859 q^{90} +27.4691 q^{91} +3.32654 q^{92} -2.96713 q^{93} +5.33894 q^{94} -0.567392 q^{95} -2.47683 q^{96} +6.85317 q^{97} +16.2428 q^{98} +5.74823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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