LMFDB - Embedded newform 8034.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.72329.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 2x + 15 $ x^4 - x^3 - 9x^2 + 2x + 15
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.46917$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.31071 q^{5} +1.00000 q^{6} +3.84154 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.31071 q^{5} +1.00000 q^{6} +3.84154 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.31071 q^{10} +5.49163 q^{11} +1.00000 q^{12} +1.00000 q^{13} +3.84154 q^{14} -3.31071 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +0.938340 q^{19} -3.31071 q^{20} +3.84154 q^{21} +5.49163 q^{22} +3.93834 q^{23} +1.00000 q^{24} +5.96080 q^{25} +1.00000 q^{26} +1.00000 q^{27} +3.84154 q^{28} +2.02246 q^{29} -3.31071 q^{30} -0.938340 q^{31} +1.00000 q^{32} +5.49163 q^{33} +2.00000 q^{34} -12.7182 q^{35} +1.00000 q^{36} -7.49163 q^{37} +0.938340 q^{38} +1.00000 q^{39} -3.31071 q^{40} +11.6214 q^{41} +3.84154 q^{42} +2.50837 q^{43} +5.49163 q^{44} -3.31071 q^{45} +3.93834 q^{46} -5.51408 q^{47} +1.00000 q^{48} +7.75742 q^{49} +5.96080 q^{50} +2.00000 q^{51} +1.00000 q^{52} -9.60467 q^{53} +1.00000 q^{54} -18.1812 q^{55} +3.84154 q^{56} +0.938340 q^{57} +2.02246 q^{58} +4.34991 q^{59} -3.31071 q^{60} -1.44671 q^{61} -0.938340 q^{62} +3.84154 q^{63} +1.00000 q^{64} -3.31071 q^{65} +5.49163 q^{66} -4.24905 q^{67} +2.00000 q^{68} +3.93834 q^{69} -12.7182 q^{70} -9.79180 q^{71} +1.00000 q^{72} +2.33938 q^{73} -7.49163 q^{74} +5.96080 q^{75} +0.938340 q^{76} +21.0963 q^{77} +1.00000 q^{78} -15.5598 q^{79} -3.31071 q^{80} +1.00000 q^{81} +11.6214 q^{82} -0.689291 q^{83} +3.84154 q^{84} -6.62142 q^{85} +2.50837 q^{86} +2.02246 q^{87} +5.49163 q^{88} -2.36183 q^{89} -3.31071 q^{90} +3.84154 q^{91} +3.93834 q^{92} -0.938340 q^{93} -5.51408 q^{94} -3.10657 q^{95} +1.00000 q^{96} -19.1644 q^{97} +7.75742 q^{98} +5.49163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 9 q^{11} + 4 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} + 2 q^{20} + 5 q^{21} + 9 q^{22} + 6 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 5 q^{28} + 2 q^{30} + 6 q^{31} + 4 q^{32} + 9 q^{33} + 8 q^{34} - 21 q^{35} + 4 q^{36} - 17 q^{37} - 6 q^{38} + 4 q^{39} + 2 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 9 q^{44} + 2 q^{45} + 6 q^{46} - q^{47} + 4 q^{48} + 19 q^{49} + 6 q^{50} + 8 q^{51} + 4 q^{52} + 18 q^{53} + 4 q^{54} - 2 q^{55} + 5 q^{56} - 6 q^{57} + 20 q^{59} + 2 q^{60} - 9 q^{61} + 6 q^{62} + 5 q^{63} + 4 q^{64} + 2 q^{65} + 9 q^{66} + 8 q^{67} + 8 q^{68} + 6 q^{69} - 21 q^{70} - 21 q^{71} + 4 q^{72} + 22 q^{73} - 17 q^{74} + 6 q^{75} - 6 q^{76} + 15 q^{77} + 4 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 16 q^{82} - 18 q^{83} + 5 q^{84} + 4 q^{85} + 23 q^{86} + 9 q^{88} - 14 q^{89} + 2 q^{90} + 5 q^{91} + 6 q^{92} + 6 q^{93} - q^{94} - 6 q^{95} + 4 q^{96} + 20 q^{97} + 19 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 9 * q^11 + 4 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 + 2 * q^20 + 5 * q^21 + 9 * q^22 + 6 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 5 * q^28 + 2 * q^30 + 6 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 - 21 * q^35 + 4 * q^36 - 17 * q^37 - 6 * q^38 + 4 * q^39 + 2 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 9 * q^44 + 2 * q^45 + 6 * q^46 - q^47 + 4 * q^48 + 19 * q^49 + 6 * q^50 + 8 * q^51 + 4 * q^52 + 18 * q^53 + 4 * q^54 - 2 * q^55 + 5 * q^56 - 6 * q^57 + 20 * q^59 + 2 * q^60 - 9 * q^61 + 6 * q^62 + 5 * q^63 + 4 * q^64 + 2 * q^65 + 9 * q^66 + 8 * q^67 + 8 * q^68 + 6 * q^69 - 21 * q^70 - 21 * q^71 + 4 * q^72 + 22 * q^73 - 17 * q^74 + 6 * q^75 - 6 * q^76 + 15 * q^77 + 4 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 16 * q^82 - 18 * q^83 + 5 * q^84 + 4 * q^85 + 23 * q^86 + 9 * q^88 - 14 * q^89 + 2 * q^90 + 5 * q^91 + 6 * q^92 + 6 * q^93 - q^94 - 6 * q^95 + 4 * q^96 + 20 * q^97 + 19 * q^98 + 9 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−3.31071	−1.48059	−0.740297	−	0.672280i	$-0.765315\pi$
$5$	−3.31071	−1.48059	−0.740297	+	0.672280i	$0.765315\pi$
$6$	1.00000	0.408248
$7$	3.84154	1.45197	0.725983	−	0.687713i	$-0.241385\pi$
$7$	3.84154	1.45197	0.725983	+	0.687713i	$0.241385\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.31071	−1.04694
$11$	5.49163	1.65579	0.827894	−	0.560885i	$-0.189539\pi$
$11$	5.49163	1.65579	0.827894	+	0.560885i	$0.189539\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.84154	1.02669
$15$	−3.31071	−0.854821
$16$	1.00000	0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	1.00000	0.235702
$19$	0.938340	0.215270	0.107635	−	0.994190i	$-0.465672\pi$
$19$	0.938340	0.215270	0.107635	+	0.994190i	$0.465672\pi$
$20$	−3.31071	−0.740297
$21$	3.84154	0.838293
$22$	5.49163	1.17082
$23$	3.93834	0.821201	0.410600	−	0.911815i	$-0.365319\pi$
$23$	3.93834	0.821201	0.410600	+	0.911815i	$0.365319\pi$
$24$	1.00000	0.204124
$25$	5.96080	1.19216
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	3.84154	0.725983
$29$	2.02246	0.375561	0.187780	−	0.982211i	$-0.439871\pi$
$29$	2.02246	0.375561	0.187780	+	0.982211i	$0.439871\pi$
$30$	−3.31071	−0.604450
$31$	−0.938340	−0.168531	−0.0842654	−	0.996443i	$-0.526854\pi$
$31$	−0.938340	−0.168531	−0.0842654	+	0.996443i	$0.526854\pi$
$32$	1.00000	0.176777
$33$	5.49163	0.955969
$34$	2.00000	0.342997
$35$	−12.7182	−2.14977
$36$	1.00000	0.166667
$37$	−7.49163	−1.23162	−0.615808	−	0.787896i	$-0.711170\pi$
$37$	−7.49163	−1.23162	−0.615808	+	0.787896i	$0.711170\pi$
$38$	0.938340	0.152219
$39$	1.00000	0.160128
$40$	−3.31071	−0.523469
$41$	11.6214	1.81496	0.907480	−	0.420095i	$-0.138003\pi$
$41$	11.6214	1.81496	0.907480	+	0.420095i	$0.138003\pi$
$42$	3.84154	0.592762
$43$	2.50837	0.382523	0.191262	−	0.981539i	$-0.438742\pi$
$43$	2.50837	0.382523	0.191262	+	0.981539i	$0.438742\pi$
$44$	5.49163	0.827894
$45$	−3.31071	−0.493531
$46$	3.93834	0.580677
$47$	−5.51408	−0.804312	−0.402156	−	0.915571i	$-0.631739\pi$
$47$	−5.51408	−0.804312	−0.402156	+	0.915571i	$0.631739\pi$
$48$	1.00000	0.144338
$49$	7.75742	1.10820
$50$	5.96080	0.842984
$51$	2.00000	0.280056
$52$	1.00000	0.138675
$53$	−9.60467	−1.31930	−0.659651	−	0.751572i	$-0.729296\pi$
$53$	−9.60467	−1.31930	−0.659651	+	0.751572i	$0.729296\pi$
$54$	1.00000	0.136083
$55$	−18.1812	−2.45155
$56$	3.84154	0.513347
$57$	0.938340	0.124286
$58$	2.02246	0.265561
$59$	4.34991	0.566310	0.283155	−	0.959074i	$-0.408619\pi$
$59$	4.34991	0.566310	0.283155	+	0.959074i	$0.408619\pi$
$60$	−3.31071	−0.427411
$61$	−1.44671	−0.185233	−0.0926164	−	0.995702i	$-0.529523\pi$
$61$	−1.44671	−0.185233	−0.0926164	+	0.995702i	$0.529523\pi$
$62$	−0.938340	−0.119169
$63$	3.84154	0.483988
$64$	1.00000	0.125000
$65$	−3.31071	−0.410643
$66$	5.49163	0.675972
$67$	−4.24905	−0.519104	−0.259552	−	0.965729i	$-0.583575\pi$
$67$	−4.24905	−0.519104	−0.259552	+	0.965729i	$0.583575\pi$
$68$	2.00000	0.242536
$69$	3.93834	0.474120
$70$	−12.7182	−1.52012
$71$	−9.79180	−1.16207	−0.581036	−	0.813878i	$-0.697353\pi$
$71$	−9.79180	−1.16207	−0.581036	+	0.813878i	$0.697353\pi$
$72$	1.00000	0.117851
$73$	2.33938	0.273803	0.136902	−	0.990585i	$-0.456286\pi$
$73$	2.33938	0.273803	0.136902	+	0.990585i	$0.456286\pi$
$74$	−7.49163	−0.870884
$75$	5.96080	0.688293
$76$	0.938340	0.107635
$77$	21.0963	2.40415
$78$	1.00000	0.113228
$79$	−15.5598	−1.75061	−0.875305	−	0.483572i	$-0.839339\pi$
$79$	−15.5598	−1.75061	−0.875305	+	0.483572i	$0.839339\pi$
$80$	−3.31071	−0.370149
$81$	1.00000	0.111111
$82$	11.6214	1.28337
$83$	−0.689291	−0.0756595	−0.0378297	−	0.999284i	$-0.512044\pi$
$83$	−0.689291	−0.0756595	−0.0378297	+	0.999284i	$0.512044\pi$
$84$	3.84154	0.419146
$85$	−6.62142	−0.718194
$86$	2.50837	0.270485
$87$	2.02246	0.216830
$88$	5.49163	0.585409
$89$	−2.36183	−0.250354	−0.125177	−	0.992134i	$-0.539950\pi$
$89$	−2.36183	−0.250354	−0.125177	+	0.992134i	$0.539950\pi$
$90$	−3.31071	−0.348979
$91$	3.84154	0.402703
$92$	3.93834	0.410600
$93$	−0.938340	−0.0973013
$94$	−5.51408	−0.568734
$95$	−3.10657	−0.318728
$96$	1.00000	0.102062
$97$	−19.1644	−1.94585	−0.972927	−	0.231115i	$-0.925763\pi$
$97$	−19.1644	−1.94585	−0.972927	+	0.231115i	$0.925763\pi$
$98$	7.75742	0.783618
$99$	5.49163	0.551929
$100$	5.96080	0.596080
$101$	7.08488	0.704972	0.352486	−	0.935817i	$-0.385336\pi$
$101$	7.08488	0.704972	0.352486	+	0.935817i	$0.385336\pi$
$102$	2.00000	0.198030
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−12.7182	−1.24117
$106$	−9.60467	−0.932888
$107$	16.9833	1.64183	0.820916	−	0.571048i	$-0.193463\pi$
$107$	16.9833	1.64183	0.820916	+	0.571048i	$0.193463\pi$
$108$	1.00000	0.0962250
$109$	19.6279	1.88001	0.940006	−	0.341159i	$-0.110820\pi$
$109$	19.6279	1.88001	0.940006	+	0.341159i	$0.110820\pi$
$110$	−18.1812	−1.73351
$111$	−7.49163	−0.711074
$112$	3.84154	0.362991
$113$	−4.16900	−0.392186	−0.196093	−	0.980585i	$-0.562825\pi$
$113$	−4.16900	−0.392186	−0.196093	+	0.980585i	$0.562825\pi$
$114$	0.938340	0.0878836
$115$	−13.0387	−1.21587
$116$	2.02246	0.187780
$117$	1.00000	0.0924500
$118$	4.34991	0.400442
$119$	7.68308	0.704307
$120$	−3.31071	−0.302225
$121$	19.1580	1.74163
$122$	−1.44671	−0.130979
$123$	11.6214	1.04787
$124$	−0.938340	−0.0842654
$125$	−3.18092	−0.284510
$126$	3.84154	0.342232
$127$	1.23851	0.109900	0.0549502	−	0.998489i	$-0.482500\pi$
$127$	1.23851	0.109900	0.0549502	+	0.998489i	$0.482500\pi$
$128$	1.00000	0.0883883
$129$	2.50837	0.220850
$130$	−3.31071	−0.290368
$131$	−3.30017	−0.288338	−0.144169	−	0.989553i	$-0.546051\pi$
$131$	−3.30017	−0.288338	−0.144169	+	0.989553i	$0.546051\pi$
$132$	5.49163	0.477985
$133$	3.60467	0.312565
$134$	−4.24905	−0.367062
$135$	−3.31071	−0.284940
$136$	2.00000	0.171499
$137$	3.71822	0.317669	0.158834	−	0.987305i	$-0.449226\pi$
$137$	3.71822	0.317669	0.158834	+	0.987305i	$0.449226\pi$
$138$	3.93834	0.335254
$139$	18.9897	1.61069	0.805344	−	0.592808i	$-0.201981\pi$
$139$	18.9897	1.61069	0.805344	+	0.592808i	$0.201981\pi$
$140$	−12.7182	−1.07489
$141$	−5.51408	−0.464369
$142$	−9.79180	−0.821710
$143$	5.49163	0.459233
$144$	1.00000	0.0833333
$145$	−6.69576	−0.556053
$146$	2.33938	0.193608
$147$	7.75742	0.639822
$148$	−7.49163	−0.615808
$149$	−5.12979	−0.420249	−0.210124	−	0.977675i	$-0.567387\pi$
$149$	−5.12979	−0.420249	−0.210124	+	0.977675i	$0.567387\pi$
$150$	5.96080	0.486697
$151$	14.1363	1.15039	0.575196	−	0.818015i	$-0.304926\pi$
$151$	14.1363	1.15039	0.575196	+	0.818015i	$0.304926\pi$
$152$	0.938340	0.0761094
$153$	2.00000	0.161690
$154$	21.0963	1.69999
$155$	3.10657	0.249526
$156$	1.00000	0.0800641
$157$	−10.2820	−0.820596	−0.410298	−	0.911951i	$-0.634575\pi$
$157$	−10.2820	−0.820596	−0.410298	+	0.911951i	$0.634575\pi$
$158$	−15.5598	−1.23787
$159$	−9.60467	−0.761700
$160$	−3.31071	−0.261735
$161$	15.1293	1.19235
$162$	1.00000	0.0785674
$163$	−17.1298	−1.34171	−0.670854	−	0.741589i	$-0.734072\pi$
$163$	−17.1298	−1.34171	−0.670854	+	0.741589i	$0.734072\pi$
$164$	11.6214	0.907480
$165$	−18.1812	−1.41540
$166$	−0.689291	−0.0534993
$167$	−19.1979	−1.48558	−0.742790	−	0.669524i	$-0.766498\pi$
$167$	−19.1979	−1.48558	−0.742790	+	0.669524i	$0.766498\pi$
$168$	3.84154	0.296381
$169$	1.00000	0.0769231
$170$	−6.62142	−0.507840
$171$	0.938340	0.0717567
$172$	2.50837	0.191262
$173$	−8.55329	−0.650294	−0.325147	−	0.945663i	$-0.605414\pi$
$173$	−8.55329	−0.650294	−0.325147	+	0.945663i	$0.605414\pi$
$174$	2.02246	0.153322
$175$	22.8986	1.73097
$176$	5.49163	0.413947
$177$	4.34991	0.326959
$178$	−2.36183	−0.177027
$179$	18.0346	1.34797	0.673986	−	0.738744i	$-0.264581\pi$
$179$	18.0346	1.34797	0.673986	+	0.738744i	$0.264581\pi$
$180$	−3.31071	−0.246766
$181$	−15.2428	−1.13299	−0.566496	−	0.824065i	$-0.691701\pi$
$181$	−15.2428	−1.13299	−0.566496	+	0.824065i	$0.691701\pi$
$182$	3.84154	0.284754
$183$	−1.44671	−0.106944
$184$	3.93834	0.290338
$185$	24.8026	1.82352
$186$	−0.938340	−0.0688024
$187$	10.9833	0.803175
$188$	−5.51408	−0.402156
$189$	3.84154	0.279431
$190$	−3.10657	−0.225374
$191$	12.0449	0.871539	0.435770	−	0.900058i	$-0.356476\pi$
$191$	12.0449	0.871539	0.435770	+	0.900058i	$0.356476\pi$
$192$	1.00000	0.0721688
$193$	20.0801	1.44539	0.722697	−	0.691165i	$-0.242902\pi$
$193$	20.0801	1.44539	0.722697	+	0.691165i	$0.242902\pi$
$194$	−19.1644	−1.37593
$195$	−3.31071	−0.237085
$196$	7.75742	0.554102
$197$	16.6439	1.18583	0.592913	−	0.805266i	$-0.297978\pi$
$197$	16.6439	1.18583	0.592913	+	0.805266i	$0.297978\pi$
$198$	5.49163	0.390273
$199$	4.77988	0.338837	0.169418	−	0.985544i	$-0.445811\pi$
$199$	4.77988	0.338837	0.169418	+	0.985544i	$0.445811\pi$
$200$	5.96080	0.421492
$201$	−4.24905	−0.299705
$202$	7.08488	0.498490
$203$	7.76934	0.545301
$204$	2.00000	0.140028
$205$	−38.4751	−2.68722
$206$	−1.00000	−0.0696733
$207$	3.93834	0.273734
$208$	1.00000	0.0693375
$209$	5.15301	0.356441
$210$	−12.7182	−0.877641
$211$	14.6446	1.00818	0.504089	−	0.863652i	$-0.331828\pi$
$211$	14.6446	1.00818	0.504089	+	0.863652i	$0.331828\pi$
$212$	−9.60467	−0.659651
$213$	−9.79180	−0.670923
$214$	16.9833	1.16095
$215$	−8.30450	−0.566362
$216$	1.00000	0.0680414
$217$	−3.60467	−0.244701
$218$	19.6279	1.32937
$219$	2.33938	0.158080
$220$	−18.1812	−1.22577
$221$	2.00000	0.134535
$222$	−7.49163	−0.502805
$223$	18.8802	1.26431	0.632157	−	0.774840i	$-0.282170\pi$
$223$	18.8802	1.26431	0.632157	+	0.774840i	$0.282170\pi$
$224$	3.84154	0.256674
$225$	5.96080	0.397386
$226$	−4.16900	−0.277318
$227$	6.57651	0.436498	0.218249	−	0.975893i	$-0.429965\pi$
$227$	6.57651	0.436498	0.218249	+	0.975893i	$0.429965\pi$
$228$	0.938340	0.0621431
$229$	−19.6896	−1.30112	−0.650561	−	0.759454i	$-0.725466\pi$
$229$	−19.6896	−1.30112	−0.650561	+	0.759454i	$0.725466\pi$
$230$	−13.0387	−0.859746
$231$	21.0963	1.38803
$232$	2.02246	0.132781
$233$	−23.8026	−1.55936	−0.779680	−	0.626178i	$-0.784618\pi$
$233$	−23.8026	−1.55936	−0.779680	+	0.626178i	$0.784618\pi$
$234$	1.00000	0.0653720
$235$	18.2555	1.19086
$236$	4.34991	0.283155
$237$	−15.5598	−1.01071
$238$	7.68308	0.498020
$239$	28.9962	1.87561	0.937804	−	0.347165i	$-0.112856\pi$
$239$	28.9962	1.87561	0.937804	+	0.347165i	$0.112856\pi$
$240$	−3.31071	−0.213705
$241$	−11.4278	−0.736130	−0.368065	−	0.929800i	$-0.619980\pi$
$241$	−11.4278	−0.736130	−0.368065	+	0.929800i	$0.619980\pi$
$242$	19.1580	1.23152
$243$	1.00000	0.0641500
$244$	−1.44671	−0.0926164
$245$	−25.6826	−1.64080
$246$	11.6214	0.740955
$247$	0.938340	0.0597052
$248$	−0.938340	−0.0595847
$249$	−0.689291	−0.0436820
$250$	−3.18092	−0.201179
$251$	−4.92780	−0.311040	−0.155520	−	0.987833i	$-0.549705\pi$
$251$	−4.92780	−0.311040	−0.155520	+	0.987833i	$0.549705\pi$
$252$	3.84154	0.241994
$253$	21.6279	1.35973
$254$	1.23851	0.0777113
$255$	−6.62142	−0.414649
$256$	1.00000	0.0625000
$257$	17.1649	1.07072	0.535360	−	0.844624i	$-0.320176\pi$
$257$	17.1649	1.07072	0.535360	+	0.844624i	$0.320176\pi$
$258$	2.50837	0.156165
$259$	−28.7794	−1.78826
$260$	−3.31071	−0.205321
$261$	2.02246	0.125187
$262$	−3.30017	−0.203885
$263$	−31.3327	−1.93205	−0.966027	−	0.258440i	$-0.916792\pi$
$263$	−31.3327	−1.93205	−0.966027	+	0.258440i	$0.916792\pi$
$264$	5.49163	0.337986
$265$	31.7983	1.95335
$266$	3.60467	0.221017
$267$	−2.36183	−0.144542
$268$	−4.24905	−0.259552
$269$	9.96562	0.607615	0.303807	−	0.952733i	$-0.401742\pi$
$269$	9.96562	0.607615	0.303807	+	0.952733i	$0.401742\pi$
$270$	−3.31071	−0.201483
$271$	−11.6382	−0.706968	−0.353484	−	0.935441i	$-0.615003\pi$
$271$	−11.6382	−0.706968	−0.353484	+	0.935441i	$0.615003\pi$
$272$	2.00000	0.121268
$273$	3.84154	0.232501
$274$	3.71822	0.224626
$275$	32.7345	1.97396
$276$	3.93834	0.237060
$277$	−2.27151	−0.136482	−0.0682408	−	0.997669i	$-0.521739\pi$
$277$	−2.27151	−0.136482	−0.0682408	+	0.997669i	$0.521739\pi$
$278$	18.9897	1.13893
$279$	−0.938340	−0.0561770
$280$	−12.7182	−0.760059
$281$	−0.486683	−0.0290331	−0.0145165	−	0.999895i	$-0.504621\pi$
$281$	−0.486683	−0.0290331	−0.0145165	+	0.999895i	$0.504621\pi$
$282$	−5.51408	−0.328359
$283$	−21.8410	−1.29831	−0.649157	−	0.760654i	$-0.724878\pi$
$283$	−21.8410	−1.29831	−0.649157	+	0.760654i	$0.724878\pi$
$284$	−9.79180	−0.581036
$285$	−3.10657	−0.184017
$286$	5.49163	0.324727
$287$	44.6441	2.63526
$288$	1.00000	0.0589256
$289$	−13.0000	−0.764706
$290$	−6.69576	−0.393189
$291$	−19.1644	−1.12344
$292$	2.33938	0.136902
$293$	−0.470555	−0.0274901	−0.0137451	−	0.999906i	$-0.504375\pi$
$293$	−0.470555	−0.0274901	−0.0137451	+	0.999906i	$0.504375\pi$
$294$	7.75742	0.452422
$295$	−14.4013	−0.838476
$296$	−7.49163	−0.435442
$297$	5.49163	0.318656
$298$	−5.12979	−0.297161
$299$	3.93834	0.227760
$300$	5.96080	0.344147
$301$	9.63602	0.555411
$302$	14.1363	0.813451
$303$	7.08488	0.407016
$304$	0.938340	0.0538175
$305$	4.78965	0.274255
$306$	2.00000	0.114332
$307$	3.66848	0.209371	0.104686	−	0.994505i	$-0.466616\pi$
$307$	3.66848	0.209371	0.104686	+	0.994505i	$0.466616\pi$
$308$	21.0963	1.20207
$309$	−1.00000	−0.0568880
$310$	3.10657	0.176441
$311$	21.1517	1.19941	0.599703	−	0.800223i	$-0.295286\pi$
$311$	21.1517	1.19941	0.599703	+	0.800223i	$0.295286\pi$
$312$	1.00000	0.0566139
$313$	3.14171	0.177580	0.0887901	−	0.996050i	$-0.471700\pi$
$313$	3.14171	0.177580	0.0887901	+	0.996050i	$0.471700\pi$
$314$	−10.2820	−0.580249
$315$	−12.7182	−0.716590
$316$	−15.5598	−0.875305
$317$	11.2877	0.633983	0.316992	−	0.948428i	$-0.397327\pi$
$317$	11.2877	0.633983	0.316992	+	0.948428i	$0.397327\pi$
$318$	−9.60467	−0.538603
$319$	11.1066	0.621849
$320$	−3.31071	−0.185074
$321$	16.9833	0.947913
$322$	15.1293	0.843122
$323$	1.87668	0.104421
$324$	1.00000	0.0555556
$325$	5.96080	0.330645
$326$	−17.1298	−0.948731
$327$	19.6279	1.08542
$328$	11.6214	0.641685
$329$	−21.1826	−1.16783
$330$	−18.1812	−1.00084
$331$	1.45890	0.0801881	0.0400941	−	0.999196i	$-0.487234\pi$
$331$	1.45890	0.0801881	0.0400941	+	0.999196i	$0.487234\pi$
$332$	−0.689291	−0.0378297
$333$	−7.49163	−0.410539
$334$	−19.1979	−1.05046
$335$	14.0674	0.768582
$336$	3.84154	0.209573
$337$	−20.8767	−1.13723	−0.568613	−	0.822605i	$-0.692520\pi$
$337$	−20.8767	−1.13723	−0.568613	+	0.822605i	$0.692520\pi$
$338$	1.00000	0.0543928
$339$	−4.16900	−0.226429
$340$	−6.62142	−0.359097
$341$	−5.15301	−0.279051
$342$	0.938340	0.0507396
$343$	2.90967	0.157108
$344$	2.50837	0.135242
$345$	−13.0387	−0.701980
$346$	−8.55329	−0.459827
$347$	5.73827	0.308046	0.154023	−	0.988067i	$-0.450777\pi$
$347$	5.73827	0.308046	0.154023	+	0.988067i	$0.450777\pi$
$348$	2.02246	0.108415
$349$	−28.2022	−1.50963	−0.754816	−	0.655937i	$-0.772274\pi$
$349$	−28.2022	−1.50963	−0.754816	+	0.655937i	$0.772274\pi$
$350$	22.8986	1.22398
$351$	1.00000	0.0533761
$352$	5.49163	0.292705
$353$	−13.3212	−0.709018	−0.354509	−	0.935053i	$-0.615352\pi$
$353$	−13.3212	−0.709018	−0.354509	+	0.935053i	$0.615352\pi$
$354$	4.34991	0.231195
$355$	32.4178	1.72056
$356$	−2.36183	−0.125177
$357$	7.68308	0.406632
$358$	18.0346	0.953160
$359$	0.868058	0.0458143	0.0229072	−	0.999738i	$-0.492708\pi$
$359$	0.868058	0.0458143	0.0229072	+	0.999738i	$0.492708\pi$
$360$	−3.31071	−0.174490
$361$	−18.1195	−0.953659
$362$	−15.2428	−0.801146
$363$	19.1580	1.00553
$364$	3.84154	0.201351
$365$	−7.74500	−0.405392
$366$	−1.44671	−0.0756210
$367$	−27.9345	−1.45817	−0.729086	−	0.684423i	$-0.760054\pi$
$367$	−27.9345	−1.45817	−0.729086	+	0.684423i	$0.760054\pi$
$368$	3.93834	0.205300
$369$	11.6214	0.604987
$370$	24.8026	1.28943
$371$	−36.8967	−1.91558
$372$	−0.938340	−0.0486507
$373$	−22.7583	−1.17838	−0.589190	−	0.807994i	$-0.700553\pi$
$373$	−22.7583	−1.17838	−0.589190	+	0.807994i	$0.700553\pi$
$374$	10.9833	0.567930
$375$	−3.18092	−0.164262
$376$	−5.51408	−0.284367
$377$	2.02246	0.104162
$378$	3.84154	0.197587
$379$	0.735587	0.0377846	0.0188923	−	0.999822i	$-0.493986\pi$
$379$	0.735587	0.0377846	0.0188923	+	0.999822i	$0.493986\pi$
$380$	−3.10657	−0.159364
$381$	1.23851	0.0634510
$382$	12.0449	0.616271
$383$	−24.8167	−1.26807	−0.634036	−	0.773303i	$-0.718603\pi$
$383$	−24.8167	−1.26807	−0.634036	+	0.773303i	$0.718603\pi$
$384$	1.00000	0.0510310
$385$	−69.8437	−3.55956
$386$	20.0801	1.02205
$387$	2.50837	0.127508
$388$	−19.1644	−0.972927
$389$	−4.85778	−0.246299	−0.123150	−	0.992388i	$-0.539300\pi$
$389$	−4.85778	−0.246299	−0.123150	+	0.992388i	$0.539300\pi$
$390$	−3.31071	−0.167644
$391$	7.87668	0.398341
$392$	7.75742	0.391809
$393$	−3.30017	−0.166472
$394$	16.6439	0.838506
$395$	51.5138	2.59194
$396$	5.49163	0.275965
$397$	16.6663	0.836459	0.418230	−	0.908341i	$-0.362651\pi$
$397$	16.6663	0.836459	0.418230	+	0.908341i	$0.362651\pi$
$398$	4.77988	0.239594
$399$	3.60467	0.180459
$400$	5.96080	0.298040
$401$	−1.52462	−0.0761358	−0.0380679	−	0.999275i	$-0.512120\pi$
$401$	−1.52462	−0.0761358	−0.0380679	+	0.999275i	$0.512120\pi$
$402$	−4.24905	−0.211923
$403$	−0.938340	−0.0467421
$404$	7.08488	0.352486
$405$	−3.31071	−0.164510
$406$	7.76934	0.385586
$407$	−41.1412	−2.03929
$408$	2.00000	0.0990148
$409$	−17.4814	−0.864397	−0.432199	−	0.901778i	$-0.642262\pi$
$409$	−17.4814	−0.864397	−0.432199	+	0.901778i	$0.642262\pi$
$410$	−38.4751	−1.90015
$411$	3.71822	0.183406
$412$	−1.00000	−0.0492665
$413$	16.7104	0.822263
$414$	3.93834	0.193559
$415$	2.28204	0.112021
$416$	1.00000	0.0490290
$417$	18.9897	0.929931
$418$	5.15301	0.252042
$419$	21.8200	1.06597	0.532987	−	0.846123i	$-0.321069\pi$
$419$	21.8200	1.06597	0.532987	+	0.846123i	$0.321069\pi$
$420$	−12.7182	−0.620586
$421$	−4.33938	−0.211488	−0.105744	−	0.994393i	$-0.533722\pi$
$421$	−4.33938	−0.211488	−0.105744	+	0.994393i	$0.533722\pi$
$422$	14.6446	0.712890
$423$	−5.51408	−0.268104
$424$	−9.60467	−0.466444
$425$	11.9216	0.578282
$426$	−9.79180	−0.474414
$427$	−5.55761	−0.268952
$428$	16.9833	0.820916
$429$	5.49163	0.265138
$430$	−8.30450	−0.400478
$431$	8.16823	0.393450	0.196725	−	0.980459i	$-0.436969\pi$
$431$	8.16823	0.393450	0.196725	+	0.980459i	$0.436969\pi$
$432$	1.00000	0.0481125
$433$	13.0731	0.628252	0.314126	−	0.949381i	$-0.398289\pi$
$433$	13.0731	0.628252	0.314126	+	0.949381i	$0.398289\pi$
$434$	−3.60467	−0.173030
$435$	−6.69576	−0.321037
$436$	19.6279	0.940006
$437$	3.69550	0.176780
$438$	2.33938	0.111780
$439$	−4.23687	−0.202215	−0.101107	−	0.994876i	$-0.532239\pi$
$439$	−4.23687	−0.202215	−0.101107	+	0.994876i	$0.532239\pi$
$440$	−18.1812	−0.866754
$441$	7.75742	0.369401
$442$	2.00000	0.0951303
$443$	8.15872	0.387633	0.193816	−	0.981038i	$-0.437913\pi$
$443$	8.15872	0.387633	0.193816	+	0.981038i	$0.437913\pi$
$444$	−7.49163	−0.355537
$445$	7.81934	0.370672
$446$	18.8802	0.894005
$447$	−5.12979	−0.242631
$448$	3.84154	0.181496
$449$	9.11952	0.430377	0.215188	−	0.976573i	$-0.430963\pi$
$449$	9.11952	0.430377	0.215188	+	0.976573i	$0.430963\pi$
$450$	5.96080	0.280995
$451$	63.8205	3.00519
$452$	−4.16900	−0.196093
$453$	14.1363	0.664180
$454$	6.57651	0.308651
$455$	−12.7182	−0.596239
$456$	0.938340	0.0439418
$457$	8.74550	0.409097	0.204549	−	0.978856i	$-0.434427\pi$
$457$	8.74550	0.409097	0.204549	+	0.978856i	$0.434427\pi$
$458$	−19.6896	−0.920032
$459$	2.00000	0.0933520
$460$	−13.0387	−0.607933
$461$	27.8859	1.29878	0.649389	−	0.760456i	$-0.275025\pi$
$461$	27.8859	1.29878	0.649389	+	0.760456i	$0.275025\pi$
$462$	21.0963	0.981489
$463$	−2.60035	−0.120848	−0.0604242	−	0.998173i	$-0.519245\pi$
$463$	−2.60035	−0.120848	−0.0604242	+	0.998173i	$0.519245\pi$
$464$	2.02246	0.0938902
$465$	3.10657	0.144064
$466$	−23.8026	−1.10263
$467$	0.519790	0.0240530	0.0120265	−	0.999928i	$-0.496172\pi$
$467$	0.519790	0.0240530	0.0120265	+	0.999928i	$0.496172\pi$
$468$	1.00000	0.0462250
$469$	−16.3229	−0.753721
$470$	18.2555	0.842064
$471$	−10.2820	−0.473771
$472$	4.34991	0.200221
$473$	13.7751	0.633378
$474$	−15.5598	−0.714683
$475$	5.59325	0.256636
$476$	7.68308	0.352153
$477$	−9.60467	−0.439768
$478$	28.9962	1.32626
$479$	25.9892	1.18748	0.593739	−	0.804658i	$-0.297651\pi$
$479$	25.9892	1.18748	0.593739	+	0.804658i	$0.297651\pi$
$480$	−3.31071	−0.151113
$481$	−7.49163	−0.341589
$482$	−11.4278	−0.520523
$483$	15.1293	0.688406
$484$	19.1580	0.870816
$485$	63.4479	2.88102
$486$	1.00000	0.0453609
$487$	−7.15301	−0.324134	−0.162067	−	0.986780i	$-0.551816\pi$
$487$	−7.15301	−0.324134	−0.162067	+	0.986780i	$0.551816\pi$
$488$	−1.44671	−0.0654897
$489$	−17.1298	−0.774636
$490$	−25.6826	−1.16022
$491$	35.0157	1.58024	0.790119	−	0.612953i	$-0.210019\pi$
$491$	35.0157	1.58024	0.790119	+	0.612953i	$0.210019\pi$
$492$	11.6214	0.523934
$493$	4.04491	0.182174
$494$	0.938340	0.0422179
$495$	−18.1812	−0.817183
$496$	−0.938340	−0.0421327
$497$	−37.6156	−1.68729
$498$	−0.689291	−0.0308879
$499$	17.2813	0.773616	0.386808	−	0.922160i	$-0.373578\pi$
$499$	17.2813	0.773616	0.386808	+	0.922160i	$0.373578\pi$
$500$	−3.18092	−0.142255
$501$	−19.1979	−0.857700
$502$	−4.92780	−0.219939
$503$	43.1858	1.92556	0.962779	−	0.270290i	$-0.0871196\pi$
$503$	43.1858	1.92556	0.962779	+	0.270290i	$0.0871196\pi$
$504$	3.84154	0.171116
$505$	−23.4560	−1.04378
$506$	21.6279	0.961477
$507$	1.00000	0.0444116
$508$	1.23851	0.0549502
$509$	1.73014	0.0766871	0.0383436	−	0.999265i	$-0.487792\pi$
$509$	1.73014	0.0766871	0.0383436	+	0.999265i	$0.487792\pi$
$510$	−6.62142	−0.293201
$511$	8.98681	0.397553
$512$	1.00000	0.0441942
$513$	0.938340	0.0414287
$514$	17.1649	0.757113
$515$	3.31071	0.145887
$516$	2.50837	0.110425
$517$	−30.2813	−1.33177
$518$	−28.7794	−1.26449
$519$	−8.55329	−0.375448
$520$	−3.31071	−0.145184
$521$	17.7870	0.779261	0.389631	−	0.920971i	$-0.372603\pi$
$521$	17.7870	0.779261	0.389631	+	0.920971i	$0.372603\pi$
$522$	2.02246	0.0885205
$523$	−14.8824	−0.650761	−0.325381	−	0.945583i	$-0.605492\pi$
$523$	−14.8824	−0.650761	−0.325381	+	0.945583i	$0.605492\pi$
$524$	−3.30017	−0.144169
$525$	22.8986	0.999378
$526$	−31.3327	−1.36617
$527$	−1.87668	−0.0817495
$528$	5.49163	0.238992
$529$	−7.48948	−0.325629
$530$	31.7983	1.38123
$531$	4.34991	0.188770
$532$	3.60467	0.156282
$533$	11.6214	0.503380
$534$	−2.36183	−0.102207
$535$	−56.2266	−2.43089
$536$	−4.24905	−0.183531
$537$	18.0346	0.778252
$538$	9.96562	0.429649
$539$	42.6009	1.83495
$540$	−3.31071	−0.142470
$541$	23.8872	1.02699	0.513496	−	0.858092i	$-0.328350\pi$
$541$	23.8872	1.02699	0.513496	+	0.858092i	$0.328350\pi$
$542$	−11.6382	−0.499902
$543$	−15.2428	−0.654133
$544$	2.00000	0.0857493
$545$	−64.9822	−2.78353
$546$	3.84154	0.164403
$547$	30.0235	1.28371	0.641856	−	0.766825i	$-0.278165\pi$
$547$	30.0235	1.28371	0.641856	+	0.766825i	$0.278165\pi$
$548$	3.71822	0.158834
$549$	−1.44671	−0.0617443
$550$	32.7345	1.39580
$551$	1.89775	0.0808469
$552$	3.93834	0.167627
$553$	−59.7734	−2.54182
$554$	−2.27151	−0.0965070
$555$	24.8026	1.05281
$556$	18.9897	0.805344
$557$	15.9665	0.676522	0.338261	−	0.941052i	$-0.390161\pi$
$557$	15.9665	0.676522	0.338261	+	0.941052i	$0.390161\pi$
$558$	−0.938340	−0.0397231
$559$	2.50837	0.106093
$560$	−12.7182	−0.537443
$561$	10.9833	0.463713
$562$	−0.486683	−0.0205295
$563$	20.3838	0.859074	0.429537	−	0.903049i	$-0.358677\pi$
$563$	20.3838	0.859074	0.429537	+	0.903049i	$0.358677\pi$
$564$	−5.51408	−0.232185
$565$	13.8023	0.580669
$566$	−21.8410	−0.918047
$567$	3.84154	0.161329
$568$	−9.79180	−0.410855
$569$	2.14604	0.0899665	0.0449833	−	0.998988i	$-0.485677\pi$
$569$	2.14604	0.0899665	0.0449833	+	0.998988i	$0.485677\pi$
$570$	−3.10657	−0.130120
$571$	27.1306	1.13538	0.567689	−	0.823243i	$-0.307838\pi$
$571$	27.1306	1.13538	0.567689	+	0.823243i	$0.307838\pi$
$572$	5.49163	0.229616
$573$	12.0449	0.503183
$574$	44.6441	1.86341
$575$	23.4756	0.979002
$576$	1.00000	0.0416667
$577$	−29.4476	−1.22592	−0.612960	−	0.790114i	$-0.710021\pi$
$577$	−29.4476	−1.22592	−0.612960	+	0.790114i	$0.710021\pi$
$578$	−13.0000	−0.540729
$579$	20.0801	0.834499
$580$	−6.69576	−0.278026
$581$	−2.64794	−0.109855
$582$	−19.1644	−0.794391
$583$	−52.7453	−2.18449
$584$	2.33938	0.0968041
$585$	−3.31071	−0.136881
$586$	−0.470555	−0.0194384
$587$	27.4140	1.13150	0.565748	−	0.824578i	$-0.308587\pi$
$587$	27.4140	1.13150	0.565748	+	0.824578i	$0.308587\pi$
$588$	7.75742	0.319911
$589$	−0.880482	−0.0362796
$590$	−14.4013	−0.592892
$591$	16.6439	0.684638
$592$	−7.49163	−0.307904
$593$	1.77443	0.0728672	0.0364336	−	0.999336i	$-0.488400\pi$
$593$	1.77443	0.0728672	0.0364336	+	0.999336i	$0.488400\pi$
$594$	5.49163	0.225324
$595$	−25.4364	−1.04279
$596$	−5.12979	−0.210124
$597$	4.77988	0.195627
$598$	3.93834	0.161051
$599$	36.0693	1.47375	0.736875	−	0.676029i	$-0.236300\pi$
$599$	36.0693	1.47375	0.736875	+	0.676029i	$0.236300\pi$
$600$	5.96080	0.243348
$601$	7.15301	0.291778	0.145889	−	0.989301i	$-0.453396\pi$
$601$	7.15301	0.291778	0.145889	+	0.989301i	$0.453396\pi$
$602$	9.63602	0.392735
$603$	−4.24905	−0.173035
$604$	14.1363	0.575196
$605$	−63.4264	−2.57865
$606$	7.08488	0.287804
$607$	−28.8150	−1.16957	−0.584783	−	0.811190i	$-0.698820\pi$
$607$	−28.8150	−1.16957	−0.584783	+	0.811190i	$0.698820\pi$
$608$	0.938340	0.0380547
$609$	7.76934	0.314830
$610$	4.78965	0.193927
$611$	−5.51408	−0.223076
$612$	2.00000	0.0808452
$613$	−23.5327	−0.950478	−0.475239	−	0.879857i	$-0.657638\pi$
$613$	−23.5327	−0.950478	−0.475239	+	0.879857i	$0.657638\pi$
$614$	3.66848	0.148048
$615$	−38.4751	−1.55147
$616$	21.0963	0.849994
$617$	−17.9427	−0.722344	−0.361172	−	0.932499i	$-0.617623\pi$
$617$	−17.9427	−0.722344	−0.361172	+	0.932499i	$0.617623\pi$
$618$	−1.00000	−0.0402259
$619$	4.11090	0.165231	0.0826154	−	0.996582i	$-0.473673\pi$
$619$	4.11090	0.165231	0.0826154	+	0.996582i	$0.473673\pi$
$620$	3.10657	0.124763
$621$	3.93834	0.158040
$622$	21.1517	0.848108
$623$	−9.07308	−0.363505
$624$	1.00000	0.0400320
$625$	−19.2729	−0.770916
$626$	3.14171	0.125568
$627$	5.15301	0.205792
$628$	−10.2820	−0.410298
$629$	−14.9833	−0.597421
$630$	−12.7182	−0.506706
$631$	0.915119	0.0364303	0.0182152	−	0.999834i	$-0.494202\pi$
$631$	0.915119	0.0364303	0.0182152	+	0.999834i	$0.494202\pi$
$632$	−15.5598	−0.618934
$633$	14.6446	0.582072
$634$	11.2877	0.448294
$635$	−4.10036	−0.162718
$636$	−9.60467	−0.380850
$637$	7.75742	0.307360
$638$	11.1066	0.439713
$639$	−9.79180	−0.387358
$640$	−3.31071	−0.130867
$641$	−12.6679	−0.500350	−0.250175	−	0.968201i	$-0.580488\pi$
$641$	−12.6679	−0.500350	−0.250175	+	0.968201i	$0.580488\pi$
$642$	16.9833	0.670275
$643$	−24.1130	−0.950926	−0.475463	−	0.879736i	$-0.657719\pi$
$643$	−24.1130	−0.950926	−0.475463	+	0.879736i	$0.657719\pi$
$644$	15.1293	0.596177
$645$	−8.30450	−0.326989
$646$	1.87668	0.0738370
$647$	−23.8783	−0.938754	−0.469377	−	0.882998i	$-0.655521\pi$
$647$	−23.8783	−0.938754	−0.469377	+	0.882998i	$0.655521\pi$
$648$	1.00000	0.0392837
$649$	23.8881	0.937690
$650$	5.96080	0.233802
$651$	−3.60467	−0.141278
$652$	−17.1298	−0.670854
$653$	−25.1747	−0.985162	−0.492581	−	0.870267i	$-0.663947\pi$
$653$	−25.1747	−0.985162	−0.492581	+	0.870267i	$0.663947\pi$
$654$	19.6279	0.767511
$655$	10.9259	0.426911
$656$	11.6214	0.453740
$657$	2.33938	0.0912678
$658$	−21.1826	−0.825782
$659$	−27.9541	−1.08894	−0.544468	−	0.838782i	$-0.683268\pi$
$659$	−27.9541	−1.08894	−0.544468	+	0.838782i	$0.683268\pi$
$660$	−18.1812	−0.707701
$661$	−16.6793	−0.648749	−0.324374	−	0.945929i	$-0.605154\pi$
$661$	−16.6793	−0.648749	−0.324374	+	0.945929i	$0.605154\pi$
$662$	1.45890	0.0567016
$663$	2.00000	0.0776736
$664$	−0.689291	−0.0267497
$665$	−11.9340	−0.462781
$666$	−7.49163	−0.290295
$667$	7.96512	0.308411
$668$	−19.1979	−0.742790
$669$	18.8802	0.729952
$670$	14.0674	0.543470
$671$	−7.94481	−0.306706
$672$	3.84154	0.148191
$673$	24.9835	0.963044	0.481522	−	0.876434i	$-0.340084\pi$
$673$	24.9835	0.963044	0.481522	+	0.876434i	$0.340084\pi$
$674$	−20.8767	−0.804140
$675$	5.96080	0.229431
$676$	1.00000	0.0384615
$677$	5.84369	0.224591	0.112296	−	0.993675i	$-0.464180\pi$
$677$	5.84369	0.224591	0.112296	+	0.993675i	$0.464180\pi$
$678$	−4.16900	−0.160109
$679$	−73.6209	−2.82531
$680$	−6.62142	−0.253920
$681$	6.57651	0.252012
$682$	−5.15301	−0.197319
$683$	−23.7084	−0.907179	−0.453589	−	0.891211i	$-0.649857\pi$
$683$	−23.7084	−0.907179	−0.453589	+	0.891211i	$0.649857\pi$
$684$	0.938340	0.0358783
$685$	−12.3099	−0.470339
$686$	2.90967	0.111092
$687$	−19.6896	−0.751203
$688$	2.50837	0.0956309
$689$	−9.60467	−0.365909
$690$	−13.0387	−0.496375
$691$	−30.2366	−1.15026	−0.575128	−	0.818064i	$-0.695048\pi$
$691$	−30.2366	−1.15026	−0.575128	+	0.818064i	$0.695048\pi$
$692$	−8.55329	−0.325147
$693$	21.0963	0.801382
$694$	5.73827	0.217822
$695$	−62.8695	−2.38477
$696$	2.02246	0.0766610
$697$	23.2428	0.880385
$698$	−28.2022	−1.06747
$699$	−23.8026	−0.900297
$700$	22.8986	0.865487
$701$	−14.4637	−0.546287	−0.273144	−	0.961973i	$-0.588063\pi$
$701$	−14.4637	−0.546287	−0.273144	+	0.961973i	$0.588063\pi$
$702$	1.00000	0.0377426
$703$	−7.02969	−0.265130
$704$	5.49163	0.206973
$705$	18.2555	0.687543
$706$	−13.3212	−0.501352
$707$	27.2168	1.02359
$708$	4.34991	0.163480
$709$	0.159226	0.00597985	0.00298992	−	0.999996i	$-0.499048\pi$
$709$	0.159226	0.00597985	0.00298992	+	0.999996i	$0.499048\pi$
$710$	32.4178	1.21662
$711$	−15.5598	−0.583537
$712$	−2.36183	−0.0885135
$713$	−3.69550	−0.138398
$714$	7.68308	0.287532
$715$	−18.1812	−0.679937
$716$	18.0346	0.673986
$717$	28.9962	1.08288
$718$	0.868058	0.0323956
$719$	−23.3776	−0.871836	−0.435918	−	0.899986i	$-0.643576\pi$
$719$	−23.3776	−0.871836	−0.435918	+	0.899986i	$0.643576\pi$
$720$	−3.31071	−0.123383
$721$	−3.84154	−0.143066
$722$	−18.1195	−0.674339
$723$	−11.4278	−0.425005
$724$	−15.2428	−0.566496
$725$	12.0554	0.447728
$726$	19.1580	0.711018
$727$	17.8313	0.661325	0.330662	−	0.943749i	$-0.392728\pi$
$727$	17.8313	0.661325	0.330662	+	0.943749i	$0.392728\pi$
$728$	3.84154	0.142377
$729$	1.00000	0.0370370
$730$	−7.74500	−0.286655
$731$	5.01675	0.185551
$732$	−1.44671	−0.0534721
$733$	−21.7063	−0.801740	−0.400870	−	0.916135i	$-0.631292\pi$
$733$	−21.7063	−0.801740	−0.400870	+	0.916135i	$0.631292\pi$
$734$	−27.9345	−1.03108
$735$	−25.6826	−0.947316
$736$	3.93834	0.145169
$737$	−23.3342	−0.859526
$738$	11.6214	0.427790
$739$	−16.2617	−0.598198	−0.299099	−	0.954222i	$-0.596686\pi$
$739$	−16.2617	−0.598198	−0.299099	+	0.954222i	$0.596686\pi$
$740$	24.8026	0.911762
$741$	0.938340	0.0344708
$742$	−36.8967	−1.35452
$743$	2.65871	0.0975386	0.0487693	−	0.998810i	$-0.484470\pi$
$743$	2.65871	0.0975386	0.0487693	+	0.998810i	$0.484470\pi$
$744$	−0.938340	−0.0344012
$745$	16.9833	0.622218
$746$	−22.7583	−0.833241
$747$	−0.689291	−0.0252198
$748$	10.9833	0.401587
$749$	65.2418	2.38388
$750$	−3.18092	−0.116151
$751$	36.2499	1.32278	0.661389	−	0.750043i	$-0.269967\pi$
$751$	36.2499	1.32278	0.661389	+	0.750043i	$0.269967\pi$
$752$	−5.51408	−0.201078
$753$	−4.92780	−0.179579
$754$	2.02246	0.0736535
$755$	−46.8011	−1.70327
$756$	3.84154	0.139715
$757$	20.3965	0.741322	0.370661	−	0.928768i	$-0.379131\pi$
$757$	20.3965	0.741322	0.370661	+	0.928768i	$0.379131\pi$
$758$	0.735587	0.0267177
$759$	21.6279	0.785043
$760$	−3.10657	−0.112687
$761$	−19.5473	−0.708590	−0.354295	−	0.935134i	$-0.615279\pi$
$761$	−19.5473	−0.708590	−0.354295	+	0.935134i	$0.615279\pi$
$762$	1.23851	0.0448666
$763$	75.4013	2.72971
$764$	12.0449	0.435770
$765$	−6.62142	−0.239398
$766$	−24.8167	−0.896663
$767$	4.34991	0.157066
$768$	1.00000	0.0360844
$769$	−50.4056	−1.81767	−0.908837	−	0.417152i	$-0.863028\pi$
$769$	−50.4056	−1.81767	−0.908837	+	0.417152i	$0.863028\pi$
$770$	−69.8437	−2.51699
$771$	17.1649	0.618180
$772$	20.0801	0.722697
$773$	13.6614	0.491366	0.245683	−	0.969350i	$-0.420988\pi$
$773$	13.6614	0.491366	0.245683	+	0.969350i	$0.420988\pi$
$774$	2.50837	0.0901616
$775$	−5.59325	−0.200916
$776$	−19.1644	−0.687963
$777$	−28.7794	−1.03245
$778$	−4.85778	−0.174160
$779$	10.9048	0.390707
$780$	−3.31071	−0.118542
$781$	−53.7729	−1.92415
$782$	7.87668	0.281670
$783$	2.02246	0.0722767
$784$	7.75742	0.277051
$785$	34.0408	1.21497
$786$	−3.30017	−0.117713
$787$	−38.7583	−1.38158	−0.690792	−	0.723053i	$-0.742738\pi$
$787$	−38.7583	−1.38158	−0.690792	+	0.723053i	$0.742738\pi$
$788$	16.6439	0.592913
$789$	−31.3327	−1.11547
$790$	51.5138	1.83278
$791$	−16.0154	−0.569441
$792$	5.49163	0.195136
$793$	−1.44671	−0.0513743
$794$	16.6663	0.591466
$795$	31.7983	1.12777
$796$	4.77988	0.169418
$797$	−48.1328	−1.70495	−0.852476	−	0.522766i	$-0.824900\pi$
$797$	−48.1328	−1.70495	−0.852476	+	0.522766i	$0.824900\pi$
$798$	3.60467	0.127604
$799$	−11.0282	−0.390148
$800$	5.96080	0.210746
$801$	−2.36183	−0.0834513
$802$	−1.52462	−0.0538361
$803$	12.8470	0.453360
$804$	−4.24905	−0.149852
$805$	−50.0887	−1.76539
$806$	−0.938340	−0.0330516
$807$	9.96562	0.350807
$808$	7.08488	0.249245
$809$	−33.8667	−1.19069	−0.595344	−	0.803471i	$-0.702984\pi$
$809$	−33.8667	−1.19069	−0.595344	+	0.803471i	$0.702984\pi$
$810$	−3.31071	−0.116326
$811$	0.767698	0.0269575	0.0134788	−	0.999909i	$-0.495709\pi$
$811$	0.767698	0.0269575	0.0134788	+	0.999909i	$0.495709\pi$
$812$	7.76934	0.272651
$813$	−11.6382	−0.408168
$814$	−41.1412	−1.44200
$815$	56.7118	1.98653
$816$	2.00000	0.0700140
$817$	2.35371	0.0823458
$818$	−17.4814	−0.611221
$819$	3.84154	0.134234
$820$	−38.4751	−1.34361
$821$	−44.1374	−1.54041	−0.770203	−	0.637799i	$-0.779845\pi$
$821$	−44.1374	−1.54041	−0.770203	+	0.637799i	$0.779845\pi$
$822$	3.71822	0.129688
$823$	10.2469	0.357184	0.178592	−	0.983923i	$-0.442846\pi$
$823$	10.2469	0.357184	0.178592	+	0.983923i	$0.442846\pi$
$824$	−1.00000	−0.0348367
$825$	32.7345	1.13967
$826$	16.7104	0.581428
$827$	−13.1633	−0.457732	−0.228866	−	0.973458i	$-0.573502\pi$
$827$	−13.1633	−0.457732	−0.228866	+	0.973458i	$0.573502\pi$
$828$	3.93834	0.136867
$829$	5.88722	0.204471	0.102236	−	0.994760i	$-0.467400\pi$
$829$	5.88722	0.204471	0.102236	+	0.994760i	$0.467400\pi$
$830$	2.28204	0.0792108
$831$	−2.27151	−0.0787977
$832$	1.00000	0.0346688
$833$	15.5148	0.537558
$834$	18.9897	0.657560
$835$	63.5588	2.19954
$836$	5.15301	0.178221
$837$	−0.938340	−0.0324338
$838$	21.8200	0.753758
$839$	−55.5712	−1.91853	−0.959265	−	0.282508i	$-0.908834\pi$
$839$	−55.5712	−1.91853	−0.959265	+	0.282508i	$0.908834\pi$
$840$	−12.7182	−0.438820
$841$	−24.9097	−0.858954
$842$	−4.33938	−0.149545
$843$	−0.486683	−0.0167623
$844$	14.6446	0.504089
$845$	−3.31071	−0.113892
$846$	−5.51408	−0.189578
$847$	73.5960	2.52879
$848$	−9.60467	−0.329826
$849$	−21.8410	−0.749582
$850$	11.9216	0.408907
$851$	−29.5046	−1.01140
$852$	−9.79180	−0.335462
$853$	24.2701	0.830993	0.415497	−	0.909595i	$-0.363608\pi$
$853$	24.2701	0.830993	0.415497	+	0.909595i	$0.363608\pi$
$854$	−5.55761	−0.190177
$855$	−3.10657	−0.106243
$856$	16.9833	0.580476
$857$	−29.3776	−1.00352	−0.501759	−	0.865007i	$-0.667314\pi$
$857$	−29.3776	−1.00352	−0.501759	+	0.865007i	$0.667314\pi$
$858$	5.49163	0.187481
$859$	30.2828	1.03324	0.516618	−	0.856216i	$-0.327191\pi$
$859$	30.2828	1.03324	0.516618	+	0.856216i	$0.327191\pi$
$860$	−8.30450	−0.283181
$861$	44.6441	1.52147
$862$	8.16823	0.278211
$863$	−38.8611	−1.32285	−0.661423	−	0.750013i	$-0.730047\pi$
$863$	−38.8611	−1.32285	−0.661423	+	0.750013i	$0.730047\pi$
$864$	1.00000	0.0340207
$865$	28.3174	0.962822
$866$	13.0731	0.444241
$867$	−13.0000	−0.441503
$868$	−3.60467	−0.122350
$869$	−85.4484	−2.89864
$870$	−6.69576	−0.227008
$871$	−4.24905	−0.143974
$872$	19.6279	0.664684
$873$	−19.1644	−0.648618
$874$	3.69550	0.125002
$875$	−12.2196	−0.413098
$876$	2.33938	0.0790402
$877$	−19.6165	−0.662401	−0.331201	−	0.943560i	$-0.607454\pi$
$877$	−19.6165	−0.662401	−0.331201	+	0.943560i	$0.607454\pi$
$878$	−4.23687	−0.142987
$879$	−0.470555	−0.0158714
$880$	−18.1812	−0.612887
$881$	−15.6111	−0.525953	−0.262976	−	0.964802i	$-0.584704\pi$
$881$	−15.6111	−0.525953	−0.262976	+	0.964802i	$0.584704\pi$
$882$	7.75742	0.261206
$883$	37.8583	1.27403	0.637017	−	0.770850i	$-0.280168\pi$
$883$	37.8583	1.27403	0.637017	+	0.770850i	$0.280168\pi$
$884$	2.00000	0.0672673
$885$	−14.4013	−0.484094
$886$	8.15872	0.274098
$887$	−19.1160	−0.641852	−0.320926	−	0.947104i	$-0.603994\pi$
$887$	−19.1160	−0.641852	−0.320926	+	0.947104i	$0.603994\pi$
$888$	−7.49163	−0.251403
$889$	4.75780	0.159571
$890$	7.81934	0.262105
$891$	5.49163	0.183976
$892$	18.8802	0.632157
$893$	−5.17408	−0.173144
$894$	−5.12979	−0.171566
$895$	−59.7074	−1.99580
$896$	3.84154	0.128337
$897$	3.93834	0.131497
$898$	9.11952	0.304322
$899$	−1.89775	−0.0632936
$900$	5.96080	0.198693
$901$	−19.2093	−0.639956
$902$	63.8205	2.12499
$903$	9.63602	0.320667
$904$	−4.16900	−0.138659
$905$	50.4646	1.67750
$906$	14.1363	0.469646
$907$	33.4800	1.11168	0.555842	−	0.831288i	$-0.312396\pi$
$907$	33.4800	1.11168	0.555842	+	0.831288i	$0.312396\pi$
$908$	6.57651	0.218249
$909$	7.08488	0.234991
$910$	−12.7182	−0.421605
$911$	54.6247	1.80980	0.904899	−	0.425627i	$-0.139946\pi$
$911$	54.6247	1.80980	0.904899	+	0.425627i	$0.139946\pi$
$912$	0.938340	0.0310715
$913$	−3.78533	−0.125276
$914$	8.74550	0.289276
$915$	4.78965	0.158341
$916$	−19.6896	−0.650561
$917$	−12.6777	−0.418656
$918$	2.00000	0.0660098
$919$	−15.3578	−0.506606	−0.253303	−	0.967387i	$-0.581517\pi$
$919$	−15.3578	−0.506606	−0.253303	+	0.967387i	$0.581517\pi$
$920$	−13.0387	−0.429873
$921$	3.66848	0.120881
$922$	27.8859	0.918375
$923$	−9.79180	−0.322301
$924$	21.0963	0.694017
$925$	−44.6561	−1.46828
$926$	−2.60035	−0.0854527
$927$	−1.00000	−0.0328443
$928$	2.02246	0.0663904
$929$	−0.822381	−0.0269814	−0.0134907	−	0.999909i	$-0.504294\pi$
$929$	−0.822381	−0.0269814	−0.0134907	+	0.999909i	$0.504294\pi$
$930$	3.10657	0.101868
$931$	7.27910	0.238563
$932$	−23.8026	−0.779680
$933$	21.1517	0.692477
$934$	0.519790	0.0170080
$935$	−36.3624	−1.18918
$936$	1.00000	0.0326860
$937$	−32.4661	−1.06062	−0.530311	−	0.847803i	$-0.677925\pi$
$937$	−32.4661	−1.06062	−0.530311	+	0.847803i	$0.677925\pi$
$938$	−16.3229	−0.532961
$939$	3.14171	0.102526
$940$	18.2555	0.595429
$941$	59.3667	1.93530	0.967649	−	0.252299i	$-0.0811868\pi$
$941$	59.3667	1.93530	0.967649	+	0.252299i	$0.0811868\pi$
$942$	−10.2820	−0.335007
$943$	45.7691	1.49045
$944$	4.34991	0.141578
$945$	−12.7182	−0.413724
$946$	13.7751	0.447866
$947$	−58.5203	−1.90165	−0.950827	−	0.309722i	$-0.899764\pi$
$947$	−58.5203	−1.90165	−0.950827	+	0.309722i	$0.899764\pi$
$948$	−15.5598	−0.505357
$949$	2.33938	0.0759394
$950$	5.59325	0.181469
$951$	11.2877	0.366030
$952$	7.68308	0.249010
$953$	35.0411	1.13509	0.567546	−	0.823341i	$-0.307893\pi$
$953$	35.0411	1.13509	0.567546	+	0.823341i	$0.307893\pi$
$954$	−9.60467	−0.310963
$955$	−39.8772	−1.29040
$956$	28.9962	0.937804
$957$	11.1066	0.359024
$958$	25.9892	0.839674
$959$	14.2837	0.461244
$960$	−3.31071	−0.106853
$961$	−30.1195	−0.971597
$962$	−7.49163	−0.241540
$963$	16.9833	0.547278
$964$	−11.4278	−0.368065
$965$	−66.4792	−2.14004
$966$	15.1293	0.486777
$967$	37.4354	1.20384	0.601921	−	0.798556i	$-0.294402\pi$
$967$	37.4354	1.20384	0.601921	+	0.798556i	$0.294402\pi$
$968$	19.1580	0.615760
$969$	1.87668	0.0602877
$970$	63.4479	2.03719
$971$	−6.55493	−0.210358	−0.105179	−	0.994453i	$-0.533542\pi$
$971$	−6.55493	−0.210358	−0.105179	+	0.994453i	$0.533542\pi$
$972$	1.00000	0.0320750
$973$	72.9498	2.33866
$974$	−7.15301	−0.229197
$975$	5.96080	0.190898
$976$	−1.44671	−0.0463082
$977$	56.7409	1.81530	0.907652	−	0.419724i	$-0.137873\pi$
$977$	56.7409	1.81530	0.907652	+	0.419724i	$0.137873\pi$
$978$	−17.1298	−0.547750
$979$	−12.9703	−0.414533
$980$	−25.6826	−0.820400
$981$	19.6279	0.626670
$982$	35.0157	1.11740
$983$	−35.7280	−1.13955	−0.569773	−	0.821802i	$-0.692969\pi$
$983$	−35.7280	−1.13955	−0.569773	+	0.821802i	$0.692969\pi$
$984$	11.6214	0.370477
$985$	−55.1030	−1.75573
$986$	4.04491	0.128816
$987$	−21.1826	−0.674248
$988$	0.938340	0.0298526
$989$	9.87883	0.314129
$990$	−18.1812	−0.577836
$991$	19.2413	0.611220	0.305610	−	0.952157i	$-0.401140\pi$
$991$	19.2413	0.611220	0.305610	+	0.952157i	$0.401140\pi$
$992$	−0.938340	−0.0297923
$993$	1.45890	0.0462966
$994$	−37.6156	−1.19309
$995$	−15.8248	−0.501680
$996$	−0.689291	−0.0218410
$997$	−26.5903	−0.842124	−0.421062	−	0.907032i	$-0.638343\pi$
$997$	−26.5903	−0.842124	−0.421062	+	0.907032i	$0.638343\pi$
$998$	17.2813	0.547029
$999$	−7.49163	−0.237025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.n.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.n.1.1	✓	4	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.31071 q^{5} +1.00000 q^{6} +3.84154 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.31071 q^{5} +1.00000 q^{6} +3.84154 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.31071 q^{10} +5.49163 q^{11} +1.00000 q^{12} +1.00000 q^{13} +3.84154 q^{14} -3.31071 q^{15} +1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +0.938340 q^{19} -3.31071 q^{20} +3.84154 q^{21} +5.49163 q^{22} +3.93834 q^{23} +1.00000 q^{24} +5.96080 q^{25} +1.00000 q^{26} +1.00000 q^{27} +3.84154 q^{28} +2.02246 q^{29} -3.31071 q^{30} -0.938340 q^{31} +1.00000 q^{32} +5.49163 q^{33} +2.00000 q^{34} -12.7182 q^{35} +1.00000 q^{36} -7.49163 q^{37} +0.938340 q^{38} +1.00000 q^{39} -3.31071 q^{40} +11.6214 q^{41} +3.84154 q^{42} +2.50837 q^{43} +5.49163 q^{44} -3.31071 q^{45} +3.93834 q^{46} -5.51408 q^{47} +1.00000 q^{48} +7.75742 q^{49} +5.96080 q^{50} +2.00000 q^{51} +1.00000 q^{52} -9.60467 q^{53} +1.00000 q^{54} -18.1812 q^{55} +3.84154 q^{56} +0.938340 q^{57} +2.02246 q^{58} +4.34991 q^{59} -3.31071 q^{60} -1.44671 q^{61} -0.938340 q^{62} +3.84154 q^{63} +1.00000 q^{64} -3.31071 q^{65} +5.49163 q^{66} -4.24905 q^{67} +2.00000 q^{68} +3.93834 q^{69} -12.7182 q^{70} -9.79180 q^{71} +1.00000 q^{72} +2.33938 q^{73} -7.49163 q^{74} +5.96080 q^{75} +0.938340 q^{76} +21.0963 q^{77} +1.00000 q^{78} -15.5598 q^{79} -3.31071 q^{80} +1.00000 q^{81} +11.6214 q^{82} -0.689291 q^{83} +3.84154 q^{84} -6.62142 q^{85} +2.50837 q^{86} +2.02246 q^{87} +5.49163 q^{88} -2.36183 q^{89} -3.31071 q^{90} +3.84154 q^{91} +3.93834 q^{92} -0.938340 q^{93} -5.51408 q^{94} -3.10657 q^{95} +1.00000 q^{96} -19.1644 q^{97} +7.75742 q^{98} +5.49163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 5 q^{7} + 4 q^{8} + 4 q^{9} + 2 q^{10} + 9 q^{11} + 4 q^{12} + 4 q^{13} + 5 q^{14} + 2 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} + 2 q^{20} + 5 q^{21} + 9 q^{22} + 6 q^{23} + 4 q^{24} + 6 q^{25} + 4 q^{26} + 4 q^{27} + 5 q^{28} + 2 q^{30} + 6 q^{31} + 4 q^{32} + 9 q^{33} + 8 q^{34} - 21 q^{35} + 4 q^{36} - 17 q^{37} - 6 q^{38} + 4 q^{39} + 2 q^{40} + 16 q^{41} + 5 q^{42} + 23 q^{43} + 9 q^{44} + 2 q^{45} + 6 q^{46} - q^{47} + 4 q^{48} + 19 q^{49} + 6 q^{50} + 8 q^{51} + 4 q^{52} + 18 q^{53} + 4 q^{54} - 2 q^{55} + 5 q^{56} - 6 q^{57} + 20 q^{59} + 2 q^{60} - 9 q^{61} + 6 q^{62} + 5 q^{63} + 4 q^{64} + 2 q^{65} + 9 q^{66} + 8 q^{67} + 8 q^{68} + 6 q^{69} - 21 q^{70} - 21 q^{71} + 4 q^{72} + 22 q^{73} - 17 q^{74} + 6 q^{75} - 6 q^{76} + 15 q^{77} + 4 q^{78} - 22 q^{79} + 2 q^{80} + 4 q^{81} + 16 q^{82} - 18 q^{83} + 5 q^{84} + 4 q^{85} + 23 q^{86} + 9 q^{88} - 14 q^{89} + 2 q^{90} + 5 q^{91} + 6 q^{92} + 6 q^{93} - q^{94} - 6 q^{95} + 4 q^{96} + 20 q^{97} + 19 q^{98} + 9 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 5 * q^7 + 4 * q^8 + 4 * q^9 + 2 * q^10 + 9 * q^11 + 4 * q^12 + 4 * q^13 + 5 * q^14 + 2 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 6 * q^19 + 2 * q^20 + 5 * q^21 + 9 * q^22 + 6 * q^23 + 4 * q^24 + 6 * q^25 + 4 * q^26 + 4 * q^27 + 5 * q^28 + 2 * q^30 + 6 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 - 21 * q^35 + 4 * q^36 - 17 * q^37 - 6 * q^38 + 4 * q^39 + 2 * q^40 + 16 * q^41 + 5 * q^42 + 23 * q^43 + 9 * q^44 + 2 * q^45 + 6 * q^46 - q^47 + 4 * q^48 + 19 * q^49 + 6 * q^50 + 8 * q^51 + 4 * q^52 + 18 * q^53 + 4 * q^54 - 2 * q^55 + 5 * q^56 - 6 * q^57 + 20 * q^59 + 2 * q^60 - 9 * q^61 + 6 * q^62 + 5 * q^63 + 4 * q^64 + 2 * q^65 + 9 * q^66 + 8 * q^67 + 8 * q^68 + 6 * q^69 - 21 * q^70 - 21 * q^71 + 4 * q^72 + 22 * q^73 - 17 * q^74 + 6 * q^75 - 6 * q^76 + 15 * q^77 + 4 * q^78 - 22 * q^79 + 2 * q^80 + 4 * q^81 + 16 * q^82 - 18 * q^83 + 5 * q^84 + 4 * q^85 + 23 * q^86 + 9 * q^88 - 14 * q^89 + 2 * q^90 + 5 * q^91 + 6 * q^92 + 6 * q^93 - q^94 - 6 * q^95 + 4 * q^96 + 20 * q^97 + 19 * q^98 + 9 * q^99

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