LMFDB - Embedded newform 8018.2.a.f.1.29

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:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.29
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.92980 q^{3} +1.00000 q^{4} -0.949986 q^{5} -1.92980 q^{6} -5.12113 q^{7} -1.00000 q^{8} +0.724133 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.92980 q^{3} +1.00000 q^{4} -0.949986 q^{5} -1.92980 q^{6} -5.12113 q^{7} -1.00000 q^{8} +0.724133 q^{9} +0.949986 q^{10} +5.68753 q^{11} +1.92980 q^{12} +1.19251 q^{13} +5.12113 q^{14} -1.83329 q^{15} +1.00000 q^{16} +1.38339 q^{17} -0.724133 q^{18} -1.00000 q^{19} -0.949986 q^{20} -9.88277 q^{21} -5.68753 q^{22} -0.766006 q^{23} -1.92980 q^{24} -4.09753 q^{25} -1.19251 q^{26} -4.39197 q^{27} -5.12113 q^{28} +1.61710 q^{29} +1.83329 q^{30} -1.26936 q^{31} -1.00000 q^{32} +10.9758 q^{33} -1.38339 q^{34} +4.86501 q^{35} +0.724133 q^{36} +4.06278 q^{37} +1.00000 q^{38} +2.30130 q^{39} +0.949986 q^{40} -2.57235 q^{41} +9.88277 q^{42} +11.8290 q^{43} +5.68753 q^{44} -0.687917 q^{45} +0.766006 q^{46} -8.05851 q^{47} +1.92980 q^{48} +19.2260 q^{49} +4.09753 q^{50} +2.66966 q^{51} +1.19251 q^{52} -3.78994 q^{53} +4.39197 q^{54} -5.40308 q^{55} +5.12113 q^{56} -1.92980 q^{57} -1.61710 q^{58} +3.49062 q^{59} -1.83329 q^{60} -6.12383 q^{61} +1.26936 q^{62} -3.70838 q^{63} +1.00000 q^{64} -1.13286 q^{65} -10.9758 q^{66} +9.03635 q^{67} +1.38339 q^{68} -1.47824 q^{69} -4.86501 q^{70} -1.73461 q^{71} -0.724133 q^{72} -12.9260 q^{73} -4.06278 q^{74} -7.90741 q^{75} -1.00000 q^{76} -29.1266 q^{77} -2.30130 q^{78} +4.84810 q^{79} -0.949986 q^{80} -10.6480 q^{81} +2.57235 q^{82} -0.862341 q^{83} -9.88277 q^{84} -1.31420 q^{85} -11.8290 q^{86} +3.12069 q^{87} -5.68753 q^{88} +4.83486 q^{89} +0.687917 q^{90} -6.10698 q^{91} -0.766006 q^{92} -2.44962 q^{93} +8.05851 q^{94} +0.949986 q^{95} -1.92980 q^{96} -1.09528 q^{97} -19.2260 q^{98} +4.11853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	1.92980	1.11417	0.557086	−	0.830455i	$-0.311920\pi$
$3$	1.92980	1.11417	0.557086	+	0.830455i	$0.311920\pi$
$4$	1.00000	0.500000
$5$	−0.949986	−0.424847	−0.212423	−	0.977178i	$-0.568136\pi$
$5$	−0.949986	−0.424847	−0.212423	+	0.977178i	$0.568136\pi$
$6$	−1.92980	−0.787838
$7$	−5.12113	−1.93561	−0.967803	−	0.251708i	$-0.919008\pi$
$7$	−5.12113	−1.93561	−0.967803	+	0.251708i	$0.919008\pi$
$8$	−1.00000	−0.353553
$9$	0.724133	0.241378
$10$	0.949986	0.300412
$11$	5.68753	1.71486	0.857428	−	0.514604i	$-0.172061\pi$
$11$	5.68753	1.71486	0.857428	+	0.514604i	$0.172061\pi$
$12$	1.92980	0.557086
$13$	1.19251	0.330742	0.165371	−	0.986231i	$-0.447118\pi$
$13$	1.19251	0.330742	0.165371	+	0.986231i	$0.447118\pi$
$14$	5.12113	1.36868
$15$	−1.83329	−0.473352
$16$	1.00000	0.250000
$17$	1.38339	0.335521	0.167760	−	0.985828i	$-0.446347\pi$
$17$	1.38339	0.335521	0.167760	+	0.985828i	$0.446347\pi$
$18$	−0.724133	−0.170680
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.949986	−0.212423
$21$	−9.88277	−2.15660
$22$	−5.68753	−1.21259
$23$	−0.766006	−0.159723	−0.0798616	−	0.996806i	$-0.525448\pi$
$23$	−0.766006	−0.159723	−0.0798616	+	0.996806i	$0.525448\pi$
$24$	−1.92980	−0.393919
$25$	−4.09753	−0.819505
$26$	−1.19251	−0.233870
$27$	−4.39197	−0.845235
$28$	−5.12113	−0.967803
$29$	1.61710	0.300288	0.150144	−	0.988664i	$-0.452026\pi$
$29$	1.61710	0.300288	0.150144	+	0.988664i	$0.452026\pi$
$30$	1.83329	0.334711
$31$	−1.26936	−0.227984	−0.113992	−	0.993482i	$-0.536364\pi$
$31$	−1.26936	−0.227984	−0.113992	+	0.993482i	$0.536364\pi$
$32$	−1.00000	−0.176777
$33$	10.9758	1.91064
$34$	−1.38339	−0.237249
$35$	4.86501	0.822336
$36$	0.724133	0.120689
$37$	4.06278	0.667917	0.333958	−	0.942588i	$-0.391615\pi$
$37$	4.06278	0.667917	0.333958	+	0.942588i	$0.391615\pi$
$38$	1.00000	0.162221
$39$	2.30130	0.368503
$40$	0.949986	0.150206
$41$	−2.57235	−0.401733	−0.200866	−	0.979619i	$-0.564376\pi$
$41$	−2.57235	−0.401733	−0.200866	+	0.979619i	$0.564376\pi$
$42$	9.88277	1.52494
$43$	11.8290	1.80391	0.901956	−	0.431828i	$-0.142131\pi$
$43$	11.8290	1.80391	0.901956	+	0.431828i	$0.142131\pi$
$44$	5.68753	0.857428
$45$	−0.687917	−0.102549
$46$	0.766006	0.112941
$47$	−8.05851	−1.17545	−0.587727	−	0.809059i	$-0.699977\pi$
$47$	−8.05851	−1.17545	−0.587727	+	0.809059i	$0.699977\pi$
$48$	1.92980	0.278543
$49$	19.2260	2.74657
$50$	4.09753	0.579478
$51$	2.66966	0.373827
$52$	1.19251	0.165371
$53$	−3.78994	−0.520588	−0.260294	−	0.965529i	$-0.583820\pi$
$53$	−3.78994	−0.520588	−0.260294	+	0.965529i	$0.583820\pi$
$54$	4.39197	0.597672
$55$	−5.40308	−0.728551
$56$	5.12113	0.684340
$57$	−1.92980	−0.255608
$58$	−1.61710	−0.212336
$59$	3.49062	0.454440	0.227220	−	0.973843i	$-0.427036\pi$
$59$	3.49062	0.454440	0.227220	+	0.973843i	$0.427036\pi$
$60$	−1.83329	−0.236676
$61$	−6.12383	−0.784076	−0.392038	−	0.919949i	$-0.628230\pi$
$61$	−6.12383	−0.784076	−0.392038	+	0.919949i	$0.628230\pi$
$62$	1.26936	0.161209
$63$	−3.70838	−0.467212
$64$	1.00000	0.125000
$65$	−1.13286	−0.140515
$66$	−10.9758	−1.35103
$67$	9.03635	1.10397	0.551983	−	0.833855i	$-0.313871\pi$
$67$	9.03635	1.10397	0.551983	+	0.833855i	$0.313871\pi$
$68$	1.38339	0.167760
$69$	−1.47824	−0.177959
$70$	−4.86501	−0.581480
$71$	−1.73461	−0.205861	−0.102930	−	0.994689i	$-0.532822\pi$
$71$	−1.73461	−0.205861	−0.102930	+	0.994689i	$0.532822\pi$
$72$	−0.724133	−0.0853399
$73$	−12.9260	−1.51287	−0.756436	−	0.654068i	$-0.773061\pi$
$73$	−12.9260	−1.51287	−0.756436	+	0.654068i	$0.773061\pi$
$74$	−4.06278	−0.472288
$75$	−7.90741	−0.913069
$76$	−1.00000	−0.114708
$77$	−29.1266	−3.31929
$78$	−2.30130	−0.260571
$79$	4.84810	0.545453	0.272727	−	0.962092i	$-0.412075\pi$
$79$	4.84810	0.545453	0.272727	+	0.962092i	$0.412075\pi$
$80$	−0.949986	−0.106212
$81$	−10.6480	−1.18311
$82$	2.57235	0.284068
$83$	−0.862341	−0.0946542	−0.0473271	−	0.998879i	$-0.515070\pi$
$83$	−0.862341	−0.0946542	−0.0473271	+	0.998879i	$0.515070\pi$
$84$	−9.88277	−1.07830
$85$	−1.31420	−0.142545
$86$	−11.8290	−1.27556
$87$	3.12069	0.334573
$88$	−5.68753	−0.606293
$89$	4.83486	0.512494	0.256247	−	0.966611i	$-0.417514\pi$
$89$	4.83486	0.512494	0.256247	+	0.966611i	$0.417514\pi$
$90$	0.687917	0.0725128
$91$	−6.10698	−0.640186
$92$	−0.766006	−0.0798616
$93$	−2.44962	−0.254014
$94$	8.05851	0.831171
$95$	0.949986	0.0974666
$96$	−1.92980	−0.196960
$97$	−1.09528	−0.111209	−0.0556044	−	0.998453i	$-0.517709\pi$
$97$	−1.09528	−0.111209	−0.0556044	+	0.998453i	$0.517709\pi$
$98$	−19.2260	−1.94212
$99$	4.11853	0.413928
$100$	−4.09753	−0.409753
$101$	6.53440	0.650197	0.325098	−	0.945680i	$-0.394603\pi$
$101$	6.53440	0.650197	0.325098	+	0.945680i	$0.394603\pi$
$102$	−2.66966	−0.264336
$103$	−13.8795	−1.36759	−0.683793	−	0.729676i	$-0.739671\pi$
$103$	−13.8795	−1.36759	−0.683793	+	0.729676i	$0.739671\pi$
$104$	−1.19251	−0.116935
$105$	9.38850	0.916223
$106$	3.78994	0.368112
$107$	−17.2579	−1.66838	−0.834192	−	0.551474i	$-0.814066\pi$
$107$	−17.2579	−1.66838	−0.834192	+	0.551474i	$0.814066\pi$
$108$	−4.39197	−0.422618
$109$	−0.289833	−0.0277610	−0.0138805	−	0.999904i	$-0.504418\pi$
$109$	−0.289833	−0.0277610	−0.0138805	+	0.999904i	$0.504418\pi$
$110$	5.40308	0.515163
$111$	7.84036	0.744174
$112$	−5.12113	−0.483902
$113$	−8.98798	−0.845518	−0.422759	−	0.906242i	$-0.638938\pi$
$113$	−8.98798	−0.845518	−0.422759	+	0.906242i	$0.638938\pi$
$114$	1.92980	0.180742
$115$	0.727695	0.0678579
$116$	1.61710	0.150144
$117$	0.863533	0.0798337
$118$	−3.49062	−0.321338
$119$	−7.08451	−0.649436
$120$	1.83329	0.167355
$121$	21.3480	1.94073
$122$	6.12383	0.554425
$123$	−4.96412	−0.447599
$124$	−1.26936	−0.113992
$125$	8.64253	0.773011
$126$	3.70838	0.330369
$127$	1.41891	0.125908	0.0629538	−	0.998016i	$-0.479948\pi$
$127$	1.41891	0.125908	0.0629538	+	0.998016i	$0.479948\pi$
$128$	−1.00000	−0.0883883
$129$	22.8277	2.00987
$130$	1.13286	0.0993588
$131$	−8.51530	−0.743985	−0.371993	−	0.928236i	$-0.621325\pi$
$131$	−8.51530	−0.743985	−0.371993	+	0.928236i	$0.621325\pi$
$132$	10.9758	0.955322
$133$	5.12113	0.444059
$134$	−9.03635	−0.780622
$135$	4.17231	0.359096
$136$	−1.38339	−0.118624
$137$	−0.154510	−0.0132007	−0.00660035	−	0.999978i	$-0.502101\pi$
$137$	−0.154510	−0.0132007	−0.00660035	+	0.999978i	$0.502101\pi$
$138$	1.47824	0.125836
$139$	0.244437	0.0207329	0.0103664	−	0.999946i	$-0.496700\pi$
$139$	0.244437	0.0207329	0.0103664	+	0.999946i	$0.496700\pi$
$140$	4.86501	0.411168
$141$	−15.5513	−1.30966
$142$	1.73461	0.145565
$143$	6.78242	0.567174
$144$	0.724133	0.0603444
$145$	−1.53623	−0.127577
$146$	12.9260	1.06976
$147$	37.1024	3.06015
$148$	4.06278	0.333958
$149$	13.8687	1.13617	0.568085	−	0.822970i	$-0.307685\pi$
$149$	13.8687	1.13617	0.568085	+	0.822970i	$0.307685\pi$
$150$	7.90741	0.645637
$151$	−13.8568	−1.12765	−0.563827	−	0.825893i	$-0.690671\pi$
$151$	−13.8568	−1.12765	−0.563827	+	0.825893i	$0.690671\pi$
$152$	1.00000	0.0811107
$153$	1.00176	0.0809872
$154$	29.1266	2.34709
$155$	1.20588	0.0968584
$156$	2.30130	0.184251
$157$	−2.98622	−0.238326	−0.119163	−	0.992875i	$-0.538021\pi$
$157$	−2.98622	−0.238326	−0.119163	+	0.992875i	$0.538021\pi$
$158$	−4.84810	−0.385694
$159$	−7.31383	−0.580025
$160$	0.949986	0.0751030
$161$	3.92282	0.309161
$162$	10.6480	0.836588
$163$	5.48205	0.429388	0.214694	−	0.976681i	$-0.431125\pi$
$163$	5.48205	0.429388	0.214694	+	0.976681i	$0.431125\pi$
$164$	−2.57235	−0.200866
$165$	−10.4269	−0.811731
$166$	0.862341	0.0669306
$167$	1.39723	0.108121	0.0540603	−	0.998538i	$-0.482784\pi$
$167$	1.39723	0.108121	0.0540603	+	0.998538i	$0.482784\pi$
$168$	9.88277	0.762472
$169$	−11.5779	−0.890610
$170$	1.31420	0.100794
$171$	−0.724133	−0.0553758
$172$	11.8290	0.901956
$173$	−20.1474	−1.53178	−0.765890	−	0.642972i	$-0.777701\pi$
$173$	−20.1474	−1.53178	−0.765890	+	0.642972i	$0.777701\pi$
$174$	−3.12069	−0.236579
$175$	20.9840	1.58624
$176$	5.68753	0.428714
$177$	6.73620	0.506324
$178$	−4.83486	−0.362388
$179$	20.9209	1.56370	0.781852	−	0.623464i	$-0.214275\pi$
$179$	20.9209	1.56370	0.781852	+	0.623464i	$0.214275\pi$
$180$	−0.687917	−0.0512743
$181$	−9.35437	−0.695305	−0.347652	−	0.937624i	$-0.613021\pi$
$181$	−9.35437	−0.695305	−0.347652	+	0.937624i	$0.613021\pi$
$182$	6.10698	0.452680
$183$	−11.8178	−0.873594
$184$	0.766006	0.0564707
$185$	−3.85959	−0.283762
$186$	2.44962	0.179615
$187$	7.86806	0.575369
$188$	−8.05851	−0.587727
$189$	22.4919	1.63604
$190$	−0.949986	−0.0689193
$191$	−22.7670	−1.64736	−0.823682	−	0.567052i	$-0.808084\pi$
$191$	−22.7670	−1.64736	−0.823682	+	0.567052i	$0.808084\pi$
$192$	1.92980	0.139271
$193$	−9.54829	−0.687301	−0.343650	−	0.939098i	$-0.611664\pi$
$193$	−9.54829	−0.687301	−0.343650	+	0.939098i	$0.611664\pi$
$194$	1.09528	0.0786365
$195$	−2.18620	−0.156557
$196$	19.2260	1.37329
$197$	−0.138228	−0.00984835	−0.00492418	−	0.999988i	$-0.501567\pi$
$197$	−0.138228	−0.00984835	−0.00492418	+	0.999988i	$0.501567\pi$
$198$	−4.11853	−0.292691
$199$	−3.25501	−0.230741	−0.115371	−	0.993323i	$-0.536806\pi$
$199$	−3.25501	−0.230741	−0.115371	+	0.993323i	$0.536806\pi$
$200$	4.09753	0.289739
$201$	17.4384	1.23001
$202$	−6.53440	−0.459759
$203$	−8.28140	−0.581240
$204$	2.66966	0.186914
$205$	2.44369	0.170675
$206$	13.8795	0.967030
$207$	−0.554690	−0.0385536
$208$	1.19251	0.0826854
$209$	−5.68753	−0.393415
$210$	−9.38850	−0.647868
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.78994	−0.260294
$213$	−3.34746	−0.229364
$214$	17.2579	1.17973
$215$	−11.2374	−0.766386
$216$	4.39197	0.298836
$217$	6.50058	0.441288
$218$	0.289833	0.0196300
$219$	−24.9446	−1.68560
$220$	−5.40308	−0.364276
$221$	1.64970	0.110971
$222$	−7.84036	−0.526210
$223$	0.580405	0.0388668	0.0194334	−	0.999811i	$-0.493814\pi$
$223$	0.580405	0.0388668	0.0194334	+	0.999811i	$0.493814\pi$
$224$	5.12113	0.342170
$225$	−2.96715	−0.197810
$226$	8.98798	0.597872
$227$	−8.27867	−0.549475	−0.274737	−	0.961519i	$-0.588591\pi$
$227$	−8.27867	−0.549475	−0.274737	+	0.961519i	$0.588591\pi$
$228$	−1.92980	−0.127804
$229$	−8.81746	−0.582674	−0.291337	−	0.956620i	$-0.594100\pi$
$229$	−8.81746	−0.582674	−0.291337	+	0.956620i	$0.594100\pi$
$230$	−0.727695	−0.0479828
$231$	−56.2086	−3.69825
$232$	−1.61710	−0.106168
$233$	−6.24109	−0.408868	−0.204434	−	0.978880i	$-0.565535\pi$
$233$	−6.24109	−0.408868	−0.204434	+	0.978880i	$0.565535\pi$
$234$	−0.863533	−0.0564509
$235$	7.65547	0.499388
$236$	3.49062	0.227220
$237$	9.35586	0.607729
$238$	7.08451	0.459220
$239$	−16.4430	−1.06361	−0.531805	−	0.846867i	$-0.678486\pi$
$239$	−16.4430	−1.06361	−0.531805	+	0.846867i	$0.678486\pi$
$240$	−1.83329	−0.118338
$241$	3.12390	0.201228	0.100614	−	0.994926i	$-0.467919\pi$
$241$	3.12390	0.201228	0.100614	+	0.994926i	$0.467919\pi$
$242$	−21.3480	−1.37230
$243$	−7.37267	−0.472957
$244$	−6.12383	−0.392038
$245$	−18.2644	−1.16687
$246$	4.96412	0.316501
$247$	−1.19251	−0.0758773
$248$	1.26936	0.0806046
$249$	−1.66415	−0.105461
$250$	−8.64253	−0.546601
$251$	15.6621	0.988583	0.494292	−	0.869296i	$-0.335427\pi$
$251$	15.6621	0.988583	0.494292	+	0.869296i	$0.335427\pi$
$252$	−3.70838	−0.233606
$253$	−4.35668	−0.273902
$254$	−1.41891	−0.0890301
$255$	−2.53614	−0.158819
$256$	1.00000	0.0625000
$257$	−11.0823	−0.691296	−0.345648	−	0.938364i	$-0.612341\pi$
$257$	−11.0823	−0.691296	−0.345648	+	0.938364i	$0.612341\pi$
$258$	−22.8277	−1.42119
$259$	−20.8060	−1.29282
$260$	−1.13286	−0.0702573
$261$	1.17100	0.0724829
$262$	8.51530	0.526077
$263$	−21.4484	−1.32256	−0.661282	−	0.750138i	$-0.729987\pi$
$263$	−21.4484	−1.32256	−0.661282	+	0.750138i	$0.729987\pi$
$264$	−10.9758	−0.675514
$265$	3.60039	0.221170
$266$	−5.12113	−0.313997
$267$	9.33032	0.571006
$268$	9.03635	0.551983
$269$	−7.01921	−0.427969	−0.213984	−	0.976837i	$-0.568644\pi$
$269$	−7.01921	−0.427969	−0.213984	+	0.976837i	$0.568644\pi$
$270$	−4.17231	−0.253919
$271$	18.4171	1.11876	0.559380	−	0.828911i	$-0.311039\pi$
$271$	18.4171	1.11876	0.559380	+	0.828911i	$0.311039\pi$
$272$	1.38339	0.0838801
$273$	−11.7853	−0.713277
$274$	0.154510	0.00933430
$275$	−23.3048	−1.40533
$276$	−1.47824	−0.0889795
$277$	−2.57767	−0.154877	−0.0774387	−	0.996997i	$-0.524674\pi$
$277$	−2.57767	−0.154877	−0.0774387	+	0.996997i	$0.524674\pi$
$278$	−0.244437	−0.0146604
$279$	−0.919188	−0.0550303
$280$	−4.86501	−0.290740
$281$	−13.7142	−0.818120	−0.409060	−	0.912508i	$-0.634143\pi$
$281$	−13.7142	−0.818120	−0.409060	+	0.912508i	$0.634143\pi$
$282$	15.5513	0.926067
$283$	−6.74555	−0.400981	−0.200491	−	0.979696i	$-0.564254\pi$
$283$	−6.74555	−0.400981	−0.200491	+	0.979696i	$0.564254\pi$
$284$	−1.73461	−0.102930
$285$	1.83329	0.108594
$286$	−6.78242	−0.401053
$287$	13.1733	0.777597
$288$	−0.724133	−0.0426699
$289$	−15.0862	−0.887426
$290$	1.53623	0.0902103
$291$	−2.11367	−0.123906
$292$	−12.9260	−0.756436
$293$	−3.47945	−0.203272	−0.101636	−	0.994822i	$-0.532408\pi$
$293$	−3.47945	−0.203272	−0.101636	+	0.994822i	$0.532408\pi$
$294$	−37.1024	−2.16385
$295$	−3.31604	−0.193067
$296$	−4.06278	−0.236144
$297$	−24.9795	−1.44946
$298$	−13.8687	−0.803393
$299$	−0.913466	−0.0528271
$300$	−7.90741	−0.456535
$301$	−60.5781	−3.49166
$302$	13.8568	0.797371
$303$	12.6101	0.724431
$304$	−1.00000	−0.0573539
$305$	5.81755	0.333112
$306$	−1.00176	−0.0572666
$307$	24.1915	1.38068	0.690342	−	0.723483i	$-0.257460\pi$
$307$	24.1915	1.38068	0.690342	+	0.723483i	$0.257460\pi$
$308$	−29.1266	−1.65964
$309$	−26.7847	−1.52373
$310$	−1.20588	−0.0684893
$311$	−23.9501	−1.35809	−0.679044	−	0.734098i	$-0.737605\pi$
$311$	−23.9501	−1.35809	−0.679044	+	0.734098i	$0.737605\pi$
$312$	−2.30130	−0.130285
$313$	8.61435	0.486912	0.243456	−	0.969912i	$-0.421719\pi$
$313$	8.61435	0.486912	0.243456	+	0.969912i	$0.421719\pi$
$314$	2.98622	0.168522
$315$	3.52291	0.198494
$316$	4.84810	0.272727
$317$	1.70835	0.0959504	0.0479752	−	0.998849i	$-0.484723\pi$
$317$	1.70835	0.0959504	0.0479752	+	0.998849i	$0.484723\pi$
$318$	7.31383	0.410139
$319$	9.19733	0.514951
$320$	−0.949986	−0.0531059
$321$	−33.3043	−1.85887
$322$	−3.92282	−0.218610
$323$	−1.38339	−0.0769737
$324$	−10.6480	−0.591557
$325$	−4.88632	−0.271045
$326$	−5.48205	−0.303623
$327$	−0.559320	−0.0309305
$328$	2.57235	0.142034
$329$	41.2687	2.27522
$330$	10.4269	0.573980
$331$	−7.13434	−0.392139	−0.196069	−	0.980590i	$-0.562818\pi$
$331$	−7.13434	−0.392139	−0.196069	+	0.980590i	$0.562818\pi$
$332$	−0.862341	−0.0473271
$333$	2.94199	0.161220
$334$	−1.39723	−0.0764528
$335$	−8.58441	−0.469016
$336$	−9.88277	−0.539149
$337$	20.5702	1.12053	0.560266	−	0.828313i	$-0.310699\pi$
$337$	20.5702	1.12053	0.560266	+	0.828313i	$0.310699\pi$
$338$	11.5779	0.629756
$339$	−17.3450	−0.942052
$340$	−1.31420	−0.0712724
$341$	−7.21955	−0.390960
$342$	0.724133	0.0391566
$343$	−62.6110	−3.38068
$344$	−11.8290	−0.637779
$345$	1.40431	0.0756053
$346$	20.1474	1.08313
$347$	−12.7865	−0.686415	−0.343208	−	0.939260i	$-0.611513\pi$
$347$	−12.7865	−0.686415	−0.343208	+	0.939260i	$0.611513\pi$
$348$	3.12069	0.167286
$349$	37.0602	1.98379	0.991895	−	0.127063i	$-0.0405550\pi$
$349$	37.0602	1.98379	0.991895	+	0.127063i	$0.0405550\pi$
$350$	−20.9840	−1.12164
$351$	−5.23745	−0.279555
$352$	−5.68753	−0.303147
$353$	11.2263	0.597516	0.298758	−	0.954329i	$-0.403428\pi$
$353$	11.2263	0.597516	0.298758	+	0.954329i	$0.403428\pi$
$354$	−6.73620	−0.358025
$355$	1.64786	0.0874593
$356$	4.83486	0.256247
$357$	−13.6717	−0.723583
$358$	−20.9209	−1.10571
$359$	−0.395404	−0.0208686	−0.0104343	−	0.999946i	$-0.503321\pi$
$359$	−0.395404	−0.0208686	−0.0104343	+	0.999946i	$0.503321\pi$
$360$	0.687917	0.0362564
$361$	1.00000	0.0526316
$362$	9.35437	0.491655
$363$	41.1975	2.16231
$364$	−6.10698	−0.320093
$365$	12.2795	0.642739
$366$	11.8178	0.617725
$367$	−9.21862	−0.481208	−0.240604	−	0.970623i	$-0.577346\pi$
$367$	−9.21862	−0.481208	−0.240604	+	0.970623i	$0.577346\pi$
$368$	−0.766006	−0.0399308
$369$	−1.86272	−0.0969694
$370$	3.85959	0.200650
$371$	19.4088	1.00765
$372$	−2.44962	−0.127007
$373$	−30.5660	−1.58265	−0.791324	−	0.611397i	$-0.790608\pi$
$373$	−30.5660	−1.58265	−0.791324	+	0.611397i	$0.790608\pi$
$374$	−7.86806	−0.406848
$375$	16.6784	0.861267
$376$	8.05851	0.415586
$377$	1.92840	0.0993179
$378$	−22.4919	−1.15686
$379$	−20.8883	−1.07296	−0.536479	−	0.843914i	$-0.680246\pi$
$379$	−20.8883	−1.07296	−0.536479	+	0.843914i	$0.680246\pi$
$380$	0.949986	0.0487333
$381$	2.73821	0.140283
$382$	22.7670	1.16486
$383$	−30.4293	−1.55487	−0.777433	−	0.628965i	$-0.783479\pi$
$383$	−30.4293	−1.55487	−0.777433	+	0.628965i	$0.783479\pi$
$384$	−1.92980	−0.0984798
$385$	27.6699	1.41019
$386$	9.54829	0.485995
$387$	8.56580	0.435424
$388$	−1.09528	−0.0556044
$389$	−17.7475	−0.899832	−0.449916	−	0.893071i	$-0.648546\pi$
$389$	−17.7475	−0.899832	−0.449916	+	0.893071i	$0.648546\pi$
$390$	2.18620	0.110703
$391$	−1.05968	−0.0535904
$392$	−19.2260	−0.971060
$393$	−16.4328	−0.828927
$394$	0.138228	0.00696384
$395$	−4.60563	−0.231734
$396$	4.11853	0.206964
$397$	−9.89965	−0.496849	−0.248425	−	0.968651i	$-0.579913\pi$
$397$	−9.89965	−0.496849	−0.248425	+	0.968651i	$0.579913\pi$
$398$	3.25501	0.163159
$399$	9.88277	0.494757
$400$	−4.09753	−0.204876
$401$	−27.8478	−1.39065	−0.695327	−	0.718693i	$-0.744741\pi$
$401$	−27.8478	−1.39065	−0.695327	+	0.718693i	$0.744741\pi$
$402$	−17.4384	−0.869746
$403$	−1.51372	−0.0754039
$404$	6.53440	0.325098
$405$	10.1155	0.502642
$406$	8.28140	0.410999
$407$	23.1072	1.14538
$408$	−2.66966	−0.132168
$409$	−3.79119	−0.187462	−0.0937312	−	0.995598i	$-0.529879\pi$
$409$	−3.79119	−0.187462	−0.0937312	+	0.995598i	$0.529879\pi$
$410$	−2.44369	−0.120685
$411$	−0.298174	−0.0147078
$412$	−13.8795	−0.683793
$413$	−17.8759	−0.879617
$414$	0.554690	0.0272615
$415$	0.819212	0.0402135
$416$	−1.19251	−0.0584674
$417$	0.471715	0.0231000
$418$	5.68753	0.278186
$419$	−32.6477	−1.59494	−0.797472	−	0.603355i	$-0.793830\pi$
$419$	−32.6477	−1.59494	−0.797472	+	0.603355i	$0.793830\pi$
$420$	9.38850	0.458112
$421$	−7.75759	−0.378082	−0.189041	−	0.981969i	$-0.560538\pi$
$421$	−7.75759	−0.378082	−0.189041	+	0.981969i	$0.560538\pi$
$422$	1.00000	0.0486792
$423$	−5.83543	−0.283728
$424$	3.78994	0.184056
$425$	−5.66846	−0.274961
$426$	3.34746	0.162185
$427$	31.3609	1.51766
$428$	−17.2579	−0.834192
$429$	13.0887	0.631929
$430$	11.2374	0.541917
$431$	−15.1975	−0.732036	−0.366018	−	0.930608i	$-0.619279\pi$
$431$	−15.1975	−0.732036	−0.366018	+	0.930608i	$0.619279\pi$
$432$	−4.39197	−0.211309
$433$	−1.18951	−0.0571641	−0.0285820	−	0.999591i	$-0.509099\pi$
$433$	−1.18951	−0.0571641	−0.0285820	+	0.999591i	$0.509099\pi$
$434$	−6.50058	−0.312038
$435$	−2.96461	−0.142142
$436$	−0.289833	−0.0138805
$437$	0.766006	0.0366430
$438$	24.9446	1.19190
$439$	3.20207	0.152827	0.0764133	−	0.997076i	$-0.475653\pi$
$439$	3.20207	0.152827	0.0764133	+	0.997076i	$0.475653\pi$
$440$	5.40308	0.257582
$441$	13.9222	0.662961
$442$	−1.64970	−0.0784681
$443$	16.4498	0.781554	0.390777	−	0.920485i	$-0.372206\pi$
$443$	16.4498	0.781554	0.390777	+	0.920485i	$0.372206\pi$
$444$	7.84036	0.372087
$445$	−4.59305	−0.217732
$446$	−0.580405	−0.0274830
$447$	26.7639	1.26589
$448$	−5.12113	−0.241951
$449$	16.5768	0.782306	0.391153	−	0.920326i	$-0.372076\pi$
$449$	16.5768	0.782306	0.391153	+	0.920326i	$0.372076\pi$
$450$	2.96715	0.139873
$451$	−14.6303	−0.688914
$452$	−8.98798	−0.422759
$453$	−26.7409	−1.25640
$454$	8.27867	0.388537
$455$	5.80155	0.271981
$456$	1.92980	0.0903712
$457$	−18.0168	−0.842791	−0.421395	−	0.906877i	$-0.638460\pi$
$457$	−18.0168	−0.842791	−0.421395	+	0.906877i	$0.638460\pi$
$458$	8.81746	0.412013
$459$	−6.07579	−0.283594
$460$	0.727695	0.0339290
$461$	20.4524	0.952563	0.476282	−	0.879293i	$-0.341984\pi$
$461$	20.4524	0.952563	0.476282	+	0.879293i	$0.341984\pi$
$462$	56.2086	2.61506
$463$	22.9144	1.06492	0.532461	−	0.846454i	$-0.321267\pi$
$463$	22.9144	1.06492	0.532461	+	0.846454i	$0.321267\pi$
$464$	1.61710	0.0750721
$465$	2.32710	0.107917
$466$	6.24109	0.289113
$467$	11.2564	0.520883	0.260442	−	0.965490i	$-0.416132\pi$
$467$	11.2564	0.520883	0.260442	+	0.965490i	$0.416132\pi$
$468$	0.863533	0.0399168
$469$	−46.2763	−2.13684
$470$	−7.65547	−0.353121
$471$	−5.76281	−0.265536
$472$	−3.49062	−0.160669
$473$	67.2781	3.09345
$474$	−9.35586	−0.429729
$475$	4.09753	0.188007
$476$	−7.08451	−0.324718
$477$	−2.74442	−0.125658
$478$	16.4430	0.752086
$479$	12.3932	0.566258	0.283129	−	0.959082i	$-0.408628\pi$
$479$	12.3932	0.566258	0.283129	+	0.959082i	$0.408628\pi$
$480$	1.83329	0.0836776
$481$	4.84489	0.220908
$482$	−3.12390	−0.142290
$483$	7.57026	0.344459
$484$	21.3480	0.970365
$485$	1.04050	0.0472467
$486$	7.37267	0.334431
$487$	−17.4243	−0.789568	−0.394784	−	0.918774i	$-0.629181\pi$
$487$	−17.4243	−0.789568	−0.394784	+	0.918774i	$0.629181\pi$
$488$	6.12383	0.277213
$489$	10.5793	0.478411
$490$	18.2644	0.825103
$491$	25.4495	1.14852	0.574261	−	0.818672i	$-0.305290\pi$
$491$	25.4495	1.14852	0.574261	+	0.818672i	$0.305290\pi$
$492$	−4.96412	−0.223800
$493$	2.23708	0.100753
$494$	1.19251	0.0536534
$495$	−3.91255	−0.175856
$496$	−1.26936	−0.0569961
$497$	8.88318	0.398465
$498$	1.66415	0.0745722
$499$	−39.6165	−1.77348	−0.886738	−	0.462272i	$-0.847034\pi$
$499$	−39.6165	−1.77348	−0.886738	+	0.462272i	$0.847034\pi$
$500$	8.64253	0.386506
$501$	2.69637	0.120465
$502$	−15.6621	−0.699034
$503$	19.2517	0.858391	0.429195	−	0.903212i	$-0.358797\pi$
$503$	19.2517	0.858391	0.429195	+	0.903212i	$0.358797\pi$
$504$	3.70838	0.165184
$505$	−6.20759	−0.276234
$506$	4.35668	0.193678
$507$	−22.3431	−0.992292
$508$	1.41891	0.0629538
$509$	37.4460	1.65976	0.829882	−	0.557939i	$-0.188408\pi$
$509$	37.4460	1.65976	0.829882	+	0.557939i	$0.188408\pi$
$510$	2.53614	0.112302
$511$	66.1956	2.92832
$512$	−1.00000	−0.0441942
$513$	4.39197	0.193910
$514$	11.0823	0.488820
$515$	13.1853	0.581015
$516$	22.8277	1.00493
$517$	−45.8330	−2.01573
$518$	20.8060	0.914165
$519$	−38.8805	−1.70666
$520$	1.13286	0.0496794
$521$	10.4028	0.455754	0.227877	−	0.973690i	$-0.426822\pi$
$521$	10.4028	0.455754	0.227877	+	0.973690i	$0.426822\pi$
$522$	−1.17100	−0.0512532
$523$	−21.5066	−0.940418	−0.470209	−	0.882555i	$-0.655822\pi$
$523$	−21.5066	−0.940418	−0.470209	+	0.882555i	$0.655822\pi$
$524$	−8.51530	−0.371993
$525$	40.4949	1.76734
$526$	21.4484	0.935193
$527$	−1.75602	−0.0764934
$528$	10.9758	0.477661
$529$	−22.4132	−0.974488
$530$	−3.60039	−0.156391
$531$	2.52767	0.109692
$532$	5.12113	0.222029
$533$	−3.06754	−0.132870
$534$	−9.33032	−0.403763
$535$	16.3948	0.708808
$536$	−9.03635	−0.390311
$537$	40.3733	1.74223
$538$	7.01921	0.302620
$539$	109.349	4.70997
$540$	4.17231	0.179548
$541$	−30.3732	−1.30585	−0.652923	−	0.757425i	$-0.726457\pi$
$541$	−30.3732	−1.30585	−0.652923	+	0.757425i	$0.726457\pi$
$542$	−18.4171	−0.791083
$543$	−18.0521	−0.774688
$544$	−1.38339	−0.0593122
$545$	0.275337	0.0117942
$546$	11.7853	0.504363
$547$	2.57884	0.110263	0.0551316	−	0.998479i	$-0.482442\pi$
$547$	2.57884	0.110263	0.0551316	+	0.998479i	$0.482442\pi$
$548$	−0.154510	−0.00660035
$549$	−4.43446	−0.189258
$550$	23.3048	0.993721
$551$	−1.61710	−0.0688909
$552$	1.47824	0.0629180
$553$	−24.8277	−1.05578
$554$	2.57767	0.109515
$555$	−7.44823	−0.316160
$556$	0.244437	0.0103664
$557$	−18.7602	−0.794896	−0.397448	−	0.917625i	$-0.630104\pi$
$557$	−18.7602	−0.794896	−0.397448	+	0.917625i	$0.630104\pi$
$558$	0.919188	0.0389123
$559$	14.1062	0.596629
$560$	4.86501	0.205584
$561$	15.1838	0.641060
$562$	13.7142	0.578498
$563$	−16.7373	−0.705393	−0.352696	−	0.935738i	$-0.614735\pi$
$563$	−16.7373	−0.705393	−0.352696	+	0.935738i	$0.614735\pi$
$564$	−15.5513	−0.654829
$565$	8.53846	0.359216
$566$	6.74555	0.283536
$567$	54.5300	2.29004
$568$	1.73461	0.0727827
$569$	8.79572	0.368736	0.184368	−	0.982857i	$-0.440976\pi$
$569$	8.79572	0.368736	0.184368	+	0.982857i	$0.440976\pi$
$570$	−1.83329	−0.0767879
$571$	−23.5769	−0.986661	−0.493330	−	0.869842i	$-0.664221\pi$
$571$	−23.5769	−0.986661	−0.493330	+	0.869842i	$0.664221\pi$
$572$	6.78242	0.283587
$573$	−43.9358	−1.83545
$574$	−13.1733	−0.549844
$575$	3.13873	0.130894
$576$	0.724133	0.0301722
$577$	20.3266	0.846206	0.423103	−	0.906081i	$-0.360941\pi$
$577$	20.3266	0.846206	0.423103	+	0.906081i	$0.360941\pi$
$578$	15.0862	0.627505
$579$	−18.4263	−0.765771
$580$	−1.53623	−0.0637883
$581$	4.41616	0.183213
$582$	2.11367	0.0876145
$583$	−21.5554	−0.892734
$584$	12.9260	0.534881
$585$	−0.820345	−0.0339171
$586$	3.47945	0.143735
$587$	−6.36433	−0.262684	−0.131342	−	0.991337i	$-0.541929\pi$
$587$	−6.36433	−0.262684	−0.131342	+	0.991337i	$0.541929\pi$
$588$	37.1024	1.53008
$589$	1.26936	0.0523032
$590$	3.31604	0.136519
$591$	−0.266753	−0.0109728
$592$	4.06278	0.166979
$593$	40.1432	1.64848	0.824242	−	0.566237i	$-0.191601\pi$
$593$	40.1432	1.64848	0.824242	+	0.566237i	$0.191601\pi$
$594$	24.9795	1.02492
$595$	6.73019	0.275911
$596$	13.8687	0.568085
$597$	−6.28152	−0.257086
$598$	0.913466	0.0373544
$599$	25.9052	1.05846	0.529229	−	0.848479i	$-0.322481\pi$
$599$	25.9052	1.05846	0.529229	+	0.848479i	$0.322481\pi$
$600$	7.90741	0.322819
$601$	2.87979	0.117469	0.0587346	−	0.998274i	$-0.481293\pi$
$601$	2.87979	0.117469	0.0587346	+	0.998274i	$0.481293\pi$
$602$	60.5781	2.46898
$603$	6.54352	0.266473
$604$	−13.8568	−0.563827
$605$	−20.2803	−0.824513
$606$	−12.6101	−0.512250
$607$	18.7117	0.759484	0.379742	−	0.925093i	$-0.376013\pi$
$607$	18.7117	0.759484	0.379742	+	0.925093i	$0.376013\pi$
$608$	1.00000	0.0405554
$609$	−15.9815	−0.647601
$610$	−5.81755	−0.235546
$611$	−9.60982	−0.388772
$612$	1.00176	0.0404936
$613$	−14.6821	−0.593006	−0.296503	−	0.955032i	$-0.595820\pi$
$613$	−14.6821	−0.593006	−0.296503	+	0.955032i	$0.595820\pi$
$614$	−24.1915	−0.976291
$615$	4.71584	0.190161
$616$	29.1266	1.17354
$617$	−40.8310	−1.64380	−0.821898	−	0.569635i	$-0.807085\pi$
$617$	−40.8310	−1.64380	−0.821898	+	0.569635i	$0.807085\pi$
$618$	26.7847	1.07744
$619$	16.5684	0.665938	0.332969	−	0.942938i	$-0.391949\pi$
$619$	16.5684	0.665938	0.332969	+	0.942938i	$0.391949\pi$
$620$	1.20588	0.0484292
$621$	3.36427	0.135004
$622$	23.9501	0.960313
$623$	−24.7600	−0.991987
$624$	2.30130	0.0921257
$625$	12.2773	0.491094
$626$	−8.61435	−0.344299
$627$	−10.9758	−0.438332
$628$	−2.98622	−0.119163
$629$	5.62039	0.224100
$630$	−3.52291	−0.140356
$631$	−37.7068	−1.50109	−0.750543	−	0.660822i	$-0.770208\pi$
$631$	−37.7068	−1.50109	−0.750543	+	0.660822i	$0.770208\pi$
$632$	−4.84810	−0.192847
$633$	−1.92980	−0.0767027
$634$	−1.70835	−0.0678472
$635$	−1.34794	−0.0534914
$636$	−7.31383	−0.290012
$637$	22.9271	0.908406
$638$	−9.19733	−0.364126
$639$	−1.25609	−0.0496902
$640$	0.949986	0.0375515
$641$	29.4367	1.16268	0.581339	−	0.813661i	$-0.302529\pi$
$641$	29.4367	1.16268	0.581339	+	0.813661i	$0.302529\pi$
$642$	33.3043	1.31442
$643$	40.8561	1.61121	0.805603	−	0.592456i	$-0.201841\pi$
$643$	40.8561	1.61121	0.805603	+	0.592456i	$0.201841\pi$
$644$	3.92282	0.154581
$645$	−21.6860	−0.853886
$646$	1.38339	0.0544286
$647$	2.16460	0.0850994	0.0425497	−	0.999094i	$-0.486452\pi$
$647$	2.16460	0.0850994	0.0425497	+	0.999094i	$0.486452\pi$
$648$	10.6480	0.418294
$649$	19.8530	0.779299
$650$	4.88632	0.191657
$651$	12.5448	0.491670
$652$	5.48205	0.214694
$653$	−44.7455	−1.75103	−0.875514	−	0.483194i	$-0.839477\pi$
$653$	−44.7455	−1.75103	−0.875514	+	0.483194i	$0.839477\pi$
$654$	0.559320	0.0218712
$655$	8.08942	0.316080
$656$	−2.57235	−0.100433
$657$	−9.36013	−0.365173
$658$	−41.2687	−1.60882
$659$	21.0904	0.821566	0.410783	−	0.911733i	$-0.365255\pi$
$659$	21.0904	0.821566	0.410783	+	0.911733i	$0.365255\pi$
$660$	−10.4269	−0.405865
$661$	−1.50992	−0.0587290	−0.0293645	−	0.999569i	$-0.509348\pi$
$661$	−1.50992	−0.0587290	−0.0293645	+	0.999569i	$0.509348\pi$
$662$	7.13434	0.277284
$663$	3.18359	0.123640
$664$	0.862341	0.0334653
$665$	−4.86501	−0.188657
$666$	−2.94199	−0.114000
$667$	−1.23871	−0.0479630
$668$	1.39723	0.0540603
$669$	1.12007	0.0433043
$670$	8.58441	0.331645
$671$	−34.8295	−1.34458
$672$	9.88277	0.381236
$673$	−39.1941	−1.51082	−0.755410	−	0.655252i	$-0.772562\pi$
$673$	−39.1941	−1.51082	−0.755410	+	0.655252i	$0.772562\pi$
$674$	−20.5702	−0.792336
$675$	17.9962	0.692675
$676$	−11.5779	−0.445305
$677$	24.6916	0.948975	0.474488	−	0.880262i	$-0.342633\pi$
$677$	24.6916	0.948975	0.474488	+	0.880262i	$0.342633\pi$
$678$	17.3450	0.666132
$679$	5.60907	0.215256
$680$	1.31420	0.0503972
$681$	−15.9762	−0.612209
$682$	7.21955	0.276451
$683$	−26.1170	−0.999338	−0.499669	−	0.866216i	$-0.666545\pi$
$683$	−26.1170	−0.999338	−0.499669	+	0.866216i	$0.666545\pi$
$684$	−0.724133	−0.0276879
$685$	0.146783	0.00560827
$686$	62.6110	2.39050
$687$	−17.0159	−0.649199
$688$	11.8290	0.450978
$689$	−4.51953	−0.172180
$690$	−1.40431	−0.0534610
$691$	9.61146	0.365637	0.182819	−	0.983147i	$-0.441478\pi$
$691$	9.61146	0.365637	0.182819	+	0.983147i	$0.441478\pi$
$692$	−20.1474	−0.765890
$693$	−21.0915	−0.801202
$694$	12.7865	0.485369
$695$	−0.232212	−0.00880830
$696$	−3.12069	−0.118289
$697$	−3.55855	−0.134790
$698$	−37.0602	−1.40275
$699$	−12.0441	−0.455549
$700$	20.9840	0.793120
$701$	14.8159	0.559589	0.279794	−	0.960060i	$-0.409734\pi$
$701$	14.8159	0.559589	0.279794	+	0.960060i	$0.409734\pi$
$702$	5.23745	0.197675
$703$	−4.06278	−0.153231
$704$	5.68753	0.214357
$705$	14.7735	0.556404
$706$	−11.2263	−0.422508
$707$	−33.4635	−1.25853
$708$	6.73620	0.253162
$709$	−21.5840	−0.810603	−0.405302	−	0.914183i	$-0.632834\pi$
$709$	−21.5840	−0.810603	−0.405302	+	0.914183i	$0.632834\pi$
$710$	−1.64786	−0.0618430
$711$	3.51067	0.131660
$712$	−4.83486	−0.181194
$713$	0.972339	0.0364144
$714$	13.6717	0.511650
$715$	−6.44321	−0.240962
$716$	20.9209	0.781852
$717$	−31.7317	−1.18504
$718$	0.395404	0.0147563
$719$	−46.3014	−1.72675	−0.863375	−	0.504563i	$-0.831654\pi$
$719$	−46.3014	−1.72675	−0.863375	+	0.504563i	$0.831654\pi$
$720$	−0.687917	−0.0256371
$721$	71.0787	2.64711
$722$	−1.00000	−0.0372161
$723$	6.02851	0.224203
$724$	−9.35437	−0.347652
$725$	−6.62612	−0.246088
$726$	−41.1975	−1.52898
$727$	−11.1820	−0.414717	−0.207358	−	0.978265i	$-0.566487\pi$
$727$	−11.1820	−0.414717	−0.207358	+	0.978265i	$0.566487\pi$
$728$	6.10698	0.226340
$729$	17.7163	0.656159
$730$	−12.2795	−0.454485
$731$	16.3641	0.605250
$732$	−11.8178	−0.436797
$733$	19.1742	0.708217	0.354109	−	0.935204i	$-0.384784\pi$
$733$	19.1742	0.708217	0.354109	+	0.935204i	$0.384784\pi$
$734$	9.21862	0.340266
$735$	−35.2467	−1.30010
$736$	0.766006	0.0282353
$737$	51.3945	1.89314
$738$	1.86272	0.0685677
$739$	−14.8202	−0.545171	−0.272586	−	0.962132i	$-0.587879\pi$
$739$	−14.8202	−0.545171	−0.272586	+	0.962132i	$0.587879\pi$
$740$	−3.85959	−0.141881
$741$	−2.30130	−0.0845404
$742$	−19.4088	−0.712519
$743$	11.1501	0.409057	0.204529	−	0.978861i	$-0.434434\pi$
$743$	11.1501	0.409057	0.204529	+	0.978861i	$0.434434\pi$
$744$	2.44962	0.0898074
$745$	−13.1751	−0.482698
$746$	30.5660	1.11910
$747$	−0.624449	−0.0228474
$748$	7.86806	0.287685
$749$	88.3800	3.22933
$750$	−16.6784	−0.609008
$751$	−13.8536	−0.505525	−0.252763	−	0.967528i	$-0.581339\pi$
$751$	−13.8536	−0.505525	−0.252763	+	0.967528i	$0.581339\pi$
$752$	−8.05851	−0.293863
$753$	30.2247	1.10145
$754$	−1.92840	−0.0702284
$755$	13.1638	0.479080
$756$	22.4919	0.818021
$757$	−16.1070	−0.585418	−0.292709	−	0.956202i	$-0.594557\pi$
$757$	−16.1070	−0.585418	−0.292709	+	0.956202i	$0.594557\pi$
$758$	20.8883	0.758696
$759$	−8.40753	−0.305174
$760$	−0.949986	−0.0344596
$761$	11.4498	0.415054	0.207527	−	0.978229i	$-0.433459\pi$
$761$	11.4498	0.415054	0.207527	+	0.978229i	$0.433459\pi$
$762$	−2.73821	−0.0991948
$763$	1.48427	0.0537343
$764$	−22.7670	−0.823682
$765$	−0.951655	−0.0344071
$766$	30.4293	1.09946
$767$	4.16259	0.150302
$768$	1.92980	0.0696357
$769$	−6.85961	−0.247364	−0.123682	−	0.992322i	$-0.539470\pi$
$769$	−6.85961	−0.247364	−0.123682	+	0.992322i	$0.539470\pi$
$770$	−27.6699	−0.997154
$771$	−21.3867	−0.770222
$772$	−9.54829	−0.343650
$773$	1.68065	0.0604488	0.0302244	−	0.999543i	$-0.490378\pi$
$773$	1.68065	0.0604488	0.0302244	+	0.999543i	$0.490378\pi$
$774$	−8.56580	−0.307891
$775$	5.20125	0.186834
$776$	1.09528	0.0393183
$777$	−40.1515	−1.44043
$778$	17.7475	0.636277
$779$	2.57235	0.0921639
$780$	−2.18620	−0.0782786
$781$	−9.86567	−0.353021
$782$	1.05968	0.0378942
$783$	−7.10227	−0.253814
$784$	19.2260	0.686643
$785$	2.83687	0.101252
$786$	16.4328	0.586140
$787$	−39.7721	−1.41772	−0.708862	−	0.705347i	$-0.750791\pi$
$787$	−39.7721	−1.41772	−0.708862	+	0.705347i	$0.750791\pi$
$788$	−0.138228	−0.00492418
$789$	−41.3911	−1.47356
$790$	4.60563	0.163861
$791$	46.0287	1.63659
$792$	−4.11853	−0.146346
$793$	−7.30270	−0.259326
$794$	9.89965	0.351325
$795$	6.94804	0.246422
$796$	−3.25501	−0.115371
$797$	23.0749	0.817354	0.408677	−	0.912679i	$-0.365990\pi$
$797$	23.0749	0.817354	0.408677	+	0.912679i	$0.365990\pi$
$798$	−9.88277	−0.349846
$799$	−11.1480	−0.394389
$800$	4.09753	0.144869
$801$	3.50108	0.123705
$802$	27.8478	0.983342
$803$	−73.5169	−2.59436
$804$	17.4384	0.615003
$805$	−3.72662	−0.131346
$806$	1.51372	0.0533186
$807$	−13.5457	−0.476831
$808$	−6.53440	−0.229879
$809$	15.9183	0.559657	0.279828	−	0.960050i	$-0.409722\pi$
$809$	15.9183	0.559657	0.279828	+	0.960050i	$0.409722\pi$
$810$	−10.1155	−0.355422
$811$	1.35628	0.0476253	0.0238127	−	0.999716i	$-0.492419\pi$
$811$	1.35628	0.0476253	0.0238127	+	0.999716i	$0.492419\pi$
$812$	−8.28140	−0.290620
$813$	35.5414	1.24649
$814$	−23.1072	−0.809907
$815$	−5.20788	−0.182424
$816$	2.66966	0.0934569
$817$	−11.8290	−0.413846
$818$	3.79119	0.132556
$819$	−4.42227	−0.154527
$820$	2.44369	0.0853375
$821$	−40.6616	−1.41910	−0.709550	−	0.704655i	$-0.751102\pi$
$821$	−40.6616	−1.41910	−0.709550	+	0.704655i	$0.751102\pi$
$822$	0.298174	0.0104000
$823$	−56.1155	−1.95606	−0.978031	−	0.208457i	$-0.933156\pi$
$823$	−56.1155	−1.95606	−0.978031	+	0.208457i	$0.933156\pi$
$824$	13.8795	0.483515
$825$	−44.9737	−1.56578
$826$	17.8759	0.621983
$827$	28.4662	0.989866	0.494933	−	0.868931i	$-0.335193\pi$
$827$	28.4662	0.989866	0.494933	+	0.868931i	$0.335193\pi$
$828$	−0.554690	−0.0192768
$829$	10.3172	0.358332	0.179166	−	0.983819i	$-0.442660\pi$
$829$	10.3172	0.358332	0.179166	+	0.983819i	$0.442660\pi$
$830$	−0.819212	−0.0284353
$831$	−4.97440	−0.172560
$832$	1.19251	0.0413427
$833$	26.5970	0.921531
$834$	−0.471715	−0.0163342
$835$	−1.32734	−0.0459347
$836$	−5.68753	−0.196707
$837$	5.57501	0.192700
$838$	32.6477	1.12780
$839$	23.5321	0.812420	0.406210	−	0.913780i	$-0.366850\pi$
$839$	23.5321	0.812420	0.406210	+	0.913780i	$0.366850\pi$
$840$	−9.38850	−0.323934
$841$	−26.3850	−0.909827
$842$	7.75759	0.267344
$843$	−26.4657	−0.911526
$844$	−1.00000	−0.0344214
$845$	10.9989	0.378373
$846$	5.83543	0.200626
$847$	−109.326	−3.75649
$848$	−3.78994	−0.130147
$849$	−13.0176	−0.446762
$850$	5.66846	0.194427
$851$	−3.11211	−0.106682
$852$	−3.34746	−0.114682
$853$	44.1548	1.51183	0.755915	−	0.654670i	$-0.227192\pi$
$853$	44.1548	1.51183	0.755915	+	0.654670i	$0.227192\pi$
$854$	−31.3609	−1.07315
$855$	0.687917	0.0235263
$856$	17.2579	0.589863
$857$	28.7334	0.981515	0.490758	−	0.871296i	$-0.336720\pi$
$857$	28.7334	0.981515	0.490758	+	0.871296i	$0.336720\pi$
$858$	−13.0887	−0.446842
$859$	−21.7971	−0.743706	−0.371853	−	0.928292i	$-0.621277\pi$
$859$	−21.7971	−0.743706	−0.371853	+	0.928292i	$0.621277\pi$
$860$	−11.2374	−0.383193
$861$	25.4219	0.866376
$862$	15.1975	0.517627
$863$	34.8859	1.18753	0.593766	−	0.804638i	$-0.297641\pi$
$863$	34.8859	1.18753	0.593766	+	0.804638i	$0.297641\pi$
$864$	4.39197	0.149418
$865$	19.1398	0.650772
$866$	1.18951	0.0404211
$867$	−29.1134	−0.988745
$868$	6.50058	0.220644
$869$	27.5737	0.935374
$870$	2.96461	0.100510
$871$	10.7759	0.365127
$872$	0.289833	0.00981499
$873$	−0.793128	−0.0268433
$874$	−0.766006	−0.0259105
$875$	−44.2595	−1.49625
$876$	−24.9446	−0.842799
$877$	−13.9021	−0.469440	−0.234720	−	0.972063i	$-0.575417\pi$
$877$	−13.9021	−0.469440	−0.234720	+	0.972063i	$0.575417\pi$
$878$	−3.20207	−0.108065
$879$	−6.71465	−0.226480
$880$	−5.40308	−0.182138
$881$	39.6836	1.33697	0.668487	−	0.743724i	$-0.266942\pi$
$881$	39.6836	1.33697	0.668487	+	0.743724i	$0.266942\pi$
$882$	−13.9222	−0.468784
$883$	28.7650	0.968019	0.484010	−	0.875063i	$-0.339180\pi$
$883$	28.7650	0.968019	0.484010	+	0.875063i	$0.339180\pi$
$884$	1.64970	0.0554853
$885$	−6.39930	−0.215110
$886$	−16.4498	−0.552642
$887$	24.8181	0.833310	0.416655	−	0.909065i	$-0.363202\pi$
$887$	24.8181	0.833310	0.416655	+	0.909065i	$0.363202\pi$
$888$	−7.84036	−0.263105
$889$	−7.26641	−0.243707
$890$	4.59305	0.153959
$891$	−60.5610	−2.02887
$892$	0.580405	0.0194334
$893$	8.05851	0.269668
$894$	−26.7639	−0.895118
$895$	−19.8746	−0.664335
$896$	5.12113	0.171085
$897$	−1.76281	−0.0588585
$898$	−16.5768	−0.553174
$899$	−2.05269	−0.0684611
$900$	−2.96715	−0.0989051
$901$	−5.24295	−0.174668
$902$	14.6303	0.487136
$903$	−116.904	−3.89031
$904$	8.98798	0.298936
$905$	8.88652	0.295398
$906$	26.7409	0.888408
$907$	−34.3176	−1.13950	−0.569749	−	0.821819i	$-0.692959\pi$
$907$	−34.3176	−1.13950	−0.569749	+	0.821819i	$0.692959\pi$
$908$	−8.27867	−0.274737
$909$	4.73177	0.156943
$910$	−5.80155	−0.192320
$911$	12.5604	0.416146	0.208073	−	0.978113i	$-0.433281\pi$
$911$	12.5604	0.416146	0.208073	+	0.978113i	$0.433281\pi$
$912$	−1.92980	−0.0639021
$913$	−4.90459	−0.162318
$914$	18.0168	0.595943
$915$	11.2267	0.371144
$916$	−8.81746	−0.291337
$917$	43.6080	1.44006
$918$	6.07579	0.200531
$919$	−15.5466	−0.512834	−0.256417	−	0.966566i	$-0.582542\pi$
$919$	−15.5466	−0.512834	−0.256417	+	0.966566i	$0.582542\pi$
$920$	−0.727695	−0.0239914
$921$	46.6849	1.53832
$922$	−20.4524	−0.673564
$923$	−2.06854	−0.0680867
$924$	−56.2086	−1.84913
$925$	−16.6473	−0.547361
$926$	−22.9144	−0.753014
$927$	−10.0506	−0.330105
$928$	−1.61710	−0.0530840
$929$	48.6157	1.59503	0.797515	−	0.603299i	$-0.206147\pi$
$929$	48.6157	1.59503	0.797515	+	0.603299i	$0.206147\pi$
$930$	−2.32710	−0.0763088
$931$	−19.2260	−0.630107
$932$	−6.24109	−0.204434
$933$	−46.2190	−1.51314
$934$	−11.2564	−0.368320
$935$	−7.47455	−0.244444
$936$	−0.863533	−0.0282255
$937$	−16.0716	−0.525036	−0.262518	−	0.964927i	$-0.584553\pi$
$937$	−16.0716	−0.525036	−0.262518	+	0.964927i	$0.584553\pi$
$938$	46.2763	1.51098
$939$	16.6240	0.542503
$940$	7.65547	0.249694
$941$	6.68619	0.217963	0.108982	−	0.994044i	$-0.465241\pi$
$941$	6.68619	0.217963	0.108982	+	0.994044i	$0.465241\pi$
$942$	5.76281	0.187763
$943$	1.97043	0.0641661
$944$	3.49062	0.113610
$945$	−21.3670	−0.695068
$946$	−67.2781	−2.18740
$947$	−45.0059	−1.46250	−0.731248	−	0.682112i	$-0.761062\pi$
$947$	−45.0059	−1.46250	−0.731248	+	0.682112i	$0.761062\pi$
$948$	9.35586	0.303864
$949$	−15.4143	−0.500370
$950$	−4.09753	−0.132941
$951$	3.29677	0.106905
$952$	7.08451	0.229610
$953$	38.2738	1.23981	0.619906	−	0.784676i	$-0.287171\pi$
$953$	38.2738	1.23981	0.619906	+	0.784676i	$0.287171\pi$
$954$	2.74442	0.0888539
$955$	21.6284	0.699877
$956$	−16.4430	−0.531805
$957$	17.7490	0.573744
$958$	−12.3932	−0.400405
$959$	0.791267	0.0255513
$960$	−1.83329	−0.0591690
$961$	−29.3887	−0.948023
$962$	−4.84489	−0.156205
$963$	−12.4970	−0.402711
$964$	3.12390	0.100614
$965$	9.07074	0.291998
$966$	−7.57026	−0.243569
$967$	−5.74055	−0.184604	−0.0923019	−	0.995731i	$-0.529422\pi$
$967$	−5.74055	−0.184604	−0.0923019	+	0.995731i	$0.529422\pi$
$968$	−21.3480	−0.686152
$969$	−2.66966	−0.0857619
$970$	−1.04050	−0.0334085
$971$	−53.4240	−1.71446	−0.857229	−	0.514935i	$-0.827816\pi$
$971$	−53.4240	−1.71446	−0.857229	+	0.514935i	$0.827816\pi$
$972$	−7.37267	−0.236479
$973$	−1.25179	−0.0401307
$974$	17.4243	0.558309
$975$	−9.42964	−0.301990
$976$	−6.12383	−0.196019
$977$	−7.19858	−0.230303	−0.115151	−	0.993348i	$-0.536735\pi$
$977$	−7.19858	−0.230303	−0.115151	+	0.993348i	$0.536735\pi$
$978$	−10.5793	−0.338288
$979$	27.4984	0.878854
$980$	−18.2644	−0.583436
$981$	−0.209878	−0.00670088
$982$	−25.4495	−0.812127
$983$	17.8868	0.570502	0.285251	−	0.958453i	$-0.407923\pi$
$983$	17.8868	0.570502	0.285251	+	0.958453i	$0.407923\pi$
$984$	4.96412	0.158250
$985$	0.131315	0.00418404
$986$	−2.23708	−0.0712431
$987$	79.6404	2.53498
$988$	−1.19251	−0.0379387
$989$	−9.06111	−0.288127
$990$	3.91255	0.124349
$991$	0.427357	0.0135755	0.00678773	−	0.999977i	$-0.497839\pi$
$991$	0.427357	0.0135755	0.00678773	+	0.999977i	$0.497839\pi$
$992$	1.26936	0.0403023
$993$	−13.7679	−0.436910
$994$	−8.88318	−0.281757
$995$	3.09221	0.0980298
$996$	−1.66415	−0.0527305
$997$	23.9308	0.757897	0.378948	−	0.925418i	$-0.376286\pi$
$997$	23.9308	0.757897	0.378948	+	0.925418i	$0.376286\pi$
$998$	39.6165	1.25404
$999$	−17.8436	−0.564547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.29	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.29	✓	34	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.92980 q^{3} +1.00000 q^{4} -0.949986 q^{5} -1.92980 q^{6} -5.12113 q^{7} -1.00000 q^{8} +0.724133 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.92980 q^{3} +1.00000 q^{4} -0.949986 q^{5} -1.92980 q^{6} -5.12113 q^{7} -1.00000 q^{8} +0.724133 q^{9} +0.949986 q^{10} +5.68753 q^{11} +1.92980 q^{12} +1.19251 q^{13} +5.12113 q^{14} -1.83329 q^{15} +1.00000 q^{16} +1.38339 q^{17} -0.724133 q^{18} -1.00000 q^{19} -0.949986 q^{20} -9.88277 q^{21} -5.68753 q^{22} -0.766006 q^{23} -1.92980 q^{24} -4.09753 q^{25} -1.19251 q^{26} -4.39197 q^{27} -5.12113 q^{28} +1.61710 q^{29} +1.83329 q^{30} -1.26936 q^{31} -1.00000 q^{32} +10.9758 q^{33} -1.38339 q^{34} +4.86501 q^{35} +0.724133 q^{36} +4.06278 q^{37} +1.00000 q^{38} +2.30130 q^{39} +0.949986 q^{40} -2.57235 q^{41} +9.88277 q^{42} +11.8290 q^{43} +5.68753 q^{44} -0.687917 q^{45} +0.766006 q^{46} -8.05851 q^{47} +1.92980 q^{48} +19.2260 q^{49} +4.09753 q^{50} +2.66966 q^{51} +1.19251 q^{52} -3.78994 q^{53} +4.39197 q^{54} -5.40308 q^{55} +5.12113 q^{56} -1.92980 q^{57} -1.61710 q^{58} +3.49062 q^{59} -1.83329 q^{60} -6.12383 q^{61} +1.26936 q^{62} -3.70838 q^{63} +1.00000 q^{64} -1.13286 q^{65} -10.9758 q^{66} +9.03635 q^{67} +1.38339 q^{68} -1.47824 q^{69} -4.86501 q^{70} -1.73461 q^{71} -0.724133 q^{72} -12.9260 q^{73} -4.06278 q^{74} -7.90741 q^{75} -1.00000 q^{76} -29.1266 q^{77} -2.30130 q^{78} +4.84810 q^{79} -0.949986 q^{80} -10.6480 q^{81} +2.57235 q^{82} -0.862341 q^{83} -9.88277 q^{84} -1.31420 q^{85} -11.8290 q^{86} +3.12069 q^{87} -5.68753 q^{88} +4.83486 q^{89} +0.687917 q^{90} -6.10698 q^{91} -0.766006 q^{92} -2.44962 q^{93} +8.05851 q^{94} +0.949986 q^{95} -1.92980 q^{96} -1.09528 q^{97} -19.2260 q^{98} +4.11853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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