LMFDB - Embedded newform 230.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, 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("230.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} -2.85410 q^{11} +1.61803 q^{12} -7.09017 q^{13} -0.618034 q^{14} +1.61803 q^{15} +1.00000 q^{16} +6.09017 q^{17} -0.381966 q^{18} +1.85410 q^{19} +1.00000 q^{20} -1.00000 q^{21} -2.85410 q^{22} +1.00000 q^{23} +1.61803 q^{24} +1.00000 q^{25} -7.09017 q^{26} -5.47214 q^{27} -0.618034 q^{28} -9.23607 q^{29} +1.61803 q^{30} +9.09017 q^{31} +1.00000 q^{32} -4.61803 q^{33} +6.09017 q^{34} -0.618034 q^{35} -0.381966 q^{36} +6.47214 q^{37} +1.85410 q^{38} -11.4721 q^{39} +1.00000 q^{40} +3.32624 q^{41} -1.00000 q^{42} -2.85410 q^{44} -0.381966 q^{45} +1.00000 q^{46} -3.70820 q^{47} +1.61803 q^{48} -6.61803 q^{49} +1.00000 q^{50} +9.85410 q^{51} -7.09017 q^{52} +0.472136 q^{53} -5.47214 q^{54} -2.85410 q^{55} -0.618034 q^{56} +3.00000 q^{57} -9.23607 q^{58} +1.70820 q^{59} +1.61803 q^{60} -9.32624 q^{61} +9.09017 q^{62} +0.236068 q^{63} +1.00000 q^{64} -7.09017 q^{65} -4.61803 q^{66} +14.4721 q^{67} +6.09017 q^{68} +1.61803 q^{69} -0.618034 q^{70} -4.09017 q^{71} -0.381966 q^{72} +3.23607 q^{73} +6.47214 q^{74} +1.61803 q^{75} +1.85410 q^{76} +1.76393 q^{77} -11.4721 q^{78} +1.52786 q^{79} +1.00000 q^{80} -7.70820 q^{81} +3.32624 q^{82} -6.94427 q^{83} -1.00000 q^{84} +6.09017 q^{85} -14.9443 q^{87} -2.85410 q^{88} -10.4721 q^{89} -0.381966 q^{90} +4.38197 q^{91} +1.00000 q^{92} +14.7082 q^{93} -3.70820 q^{94} +1.85410 q^{95} +1.61803 q^{96} +12.3820 q^{97} -6.61803 q^{98} +1.09017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + q^{11} + q^{12} - 3 q^{13} + q^{14} + q^{15} + 2 q^{16} + q^{17} - 3 q^{18} - 3 q^{19} + 2 q^{20} - 2 q^{21} + q^{22} + 2 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 14 q^{29} + q^{30} + 7 q^{31} + 2 q^{32} - 7 q^{33} + q^{34} + q^{35} - 3 q^{36} + 4 q^{37} - 3 q^{38} - 14 q^{39} + 2 q^{40} - 9 q^{41} - 2 q^{42} + q^{44} - 3 q^{45} + 2 q^{46} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} + 13 q^{51} - 3 q^{52} - 8 q^{53} - 2 q^{54} + q^{55} + q^{56} + 6 q^{57} - 14 q^{58} - 10 q^{59} + q^{60} - 3 q^{61} + 7 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{65} - 7 q^{66} + 20 q^{67} + q^{68} + q^{69} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} + 4 q^{74} + q^{75} - 3 q^{76} + 8 q^{77} - 14 q^{78} + 12 q^{79} + 2 q^{80} - 2 q^{81} - 9 q^{82} + 4 q^{83} - 2 q^{84} + q^{85} - 12 q^{87} + q^{88} - 12 q^{89} - 3 q^{90} + 11 q^{91} + 2 q^{92} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} + 27 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + q^11 + q^12 - 3 * q^13 + q^14 + q^15 + 2 * q^16 + q^17 - 3 * q^18 - 3 * q^19 + 2 * q^20 - 2 * q^21 + q^22 + 2 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 14 * q^29 + q^30 + 7 * q^31 + 2 * q^32 - 7 * q^33 + q^34 + q^35 - 3 * q^36 + 4 * q^37 - 3 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^44 - 3 * q^45 + 2 * q^46 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 + 13 * q^51 - 3 * q^52 - 8 * q^53 - 2 * q^54 + q^55 + q^56 + 6 * q^57 - 14 * q^58 - 10 * q^59 + q^60 - 3 * q^61 + 7 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^65 - 7 * q^66 + 20 * q^67 + q^68 + q^69 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 + 4 * q^74 + q^75 - 3 * q^76 + 8 * q^77 - 14 * q^78 + 12 * q^79 + 2 * q^80 - 2 * q^81 - 9 * q^82 + 4 * q^83 - 2 * q^84 + q^85 - 12 * q^87 + q^88 - 12 * q^89 - 3 * q^90 + 11 * q^91 + 2 * q^92 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 + 27 * q^97 - 11 * 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
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.61803	0.660560
$7$	−0.618034	−0.233595	−0.116797	−	0.993156i	$-0.537263\pi$
$7$	−0.618034	−0.233595	−0.116797	+	0.993156i	$0.537263\pi$
$8$	1.00000	0.353553
$9$	−0.381966	−0.127322
$10$	1.00000	0.316228
$11$	−2.85410	−0.860544	−0.430272	−	0.902699i	$-0.641582\pi$
$11$	−2.85410	−0.860544	−0.430272	+	0.902699i	$0.641582\pi$
$12$	1.61803	0.467086
$13$	−7.09017	−1.96646	−0.983230	−	0.182372i	$-0.941623\pi$
$13$	−7.09017	−1.96646	−0.983230	+	0.182372i	$0.941623\pi$
$14$	−0.618034	−0.165177
$15$	1.61803	0.417775
$16$	1.00000	0.250000
$17$	6.09017	1.47708	0.738542	−	0.674208i	$-0.235515\pi$
$17$	6.09017	1.47708	0.738542	+	0.674208i	$0.235515\pi$
$18$	−0.381966	−0.0900303
$19$	1.85410	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$19$	1.85410	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$20$	1.00000	0.223607
$21$	−1.00000	−0.218218
$22$	−2.85410	−0.608497
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.61803	0.330280
$25$	1.00000	0.200000
$26$	−7.09017	−1.39050
$27$	−5.47214	−1.05311
$28$	−0.618034	−0.116797
$29$	−9.23607	−1.71509	−0.857547	−	0.514405i	$-0.828013\pi$
$29$	−9.23607	−1.71509	−0.857547	+	0.514405i	$0.828013\pi$
$30$	1.61803	0.295411
$31$	9.09017	1.63264	0.816321	−	0.577598i	$-0.196010\pi$
$31$	9.09017	1.63264	0.816321	+	0.577598i	$0.196010\pi$
$32$	1.00000	0.176777
$33$	−4.61803	−0.803897
$34$	6.09017	1.04446
$35$	−0.618034	−0.104467
$36$	−0.381966	−0.0636610
$37$	6.47214	1.06401	0.532006	−	0.846740i	$-0.321438\pi$
$37$	6.47214	1.06401	0.532006	+	0.846740i	$0.321438\pi$
$38$	1.85410	0.300775
$39$	−11.4721	−1.83701
$40$	1.00000	0.158114
$41$	3.32624	0.519471	0.259736	−	0.965680i	$-0.416365\pi$
$41$	3.32624	0.519471	0.259736	+	0.965680i	$0.416365\pi$
$42$	−1.00000	−0.154303
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	−2.85410	−0.430272
$45$	−0.381966	−0.0569401
$46$	1.00000	0.147442
$47$	−3.70820	−0.540897	−0.270449	−	0.962734i	$-0.587172\pi$
$47$	−3.70820	−0.540897	−0.270449	+	0.962734i	$0.587172\pi$
$48$	1.61803	0.233543
$49$	−6.61803	−0.945433
$50$	1.00000	0.141421
$51$	9.85410	1.37985
$52$	−7.09017	−0.983230
$53$	0.472136	0.0648529	0.0324264	−	0.999474i	$-0.489677\pi$
$53$	0.472136	0.0648529	0.0324264	+	0.999474i	$0.489677\pi$
$54$	−5.47214	−0.744663
$55$	−2.85410	−0.384847
$56$	−0.618034	−0.0825883
$57$	3.00000	0.397360
$58$	−9.23607	−1.21276
$59$	1.70820	0.222389	0.111195	−	0.993799i	$-0.464532\pi$
$59$	1.70820	0.222389	0.111195	+	0.993799i	$0.464532\pi$
$60$	1.61803	0.208887
$61$	−9.32624	−1.19410	−0.597051	−	0.802203i	$-0.703661\pi$
$61$	−9.32624	−1.19410	−0.597051	+	0.802203i	$0.703661\pi$
$62$	9.09017	1.15445
$63$	0.236068	0.0297418
$64$	1.00000	0.125000
$65$	−7.09017	−0.879427
$66$	−4.61803	−0.568441
$67$	14.4721	1.76805	0.884026	−	0.467437i	$-0.154823\pi$
$67$	14.4721	1.76805	0.884026	+	0.467437i	$0.154823\pi$
$68$	6.09017	0.738542
$69$	1.61803	0.194788
$70$	−0.618034	−0.0738692
$71$	−4.09017	−0.485414	−0.242707	−	0.970100i	$-0.578035\pi$
$71$	−4.09017	−0.485414	−0.242707	+	0.970100i	$0.578035\pi$
$72$	−0.381966	−0.0450151
$73$	3.23607	0.378753	0.189377	−	0.981905i	$-0.439353\pi$
$73$	3.23607	0.378753	0.189377	+	0.981905i	$0.439353\pi$
$74$	6.47214	0.752371
$75$	1.61803	0.186834
$76$	1.85410	0.212680
$77$	1.76393	0.201019
$78$	−11.4721	−1.29896
$79$	1.52786	0.171898	0.0859491	−	0.996300i	$-0.472608\pi$
$79$	1.52786	0.171898	0.0859491	+	0.996300i	$0.472608\pi$
$80$	1.00000	0.111803
$81$	−7.70820	−0.856467
$82$	3.32624	0.367322
$83$	−6.94427	−0.762233	−0.381116	−	0.924527i	$-0.624460\pi$
$83$	−6.94427	−0.762233	−0.381116	+	0.924527i	$0.624460\pi$
$84$	−1.00000	−0.109109
$85$	6.09017	0.660572
$86$	0	0
$87$	−14.9443	−1.60219
$88$	−2.85410	−0.304248
$89$	−10.4721	−1.11004	−0.555022	−	0.831836i	$-0.687290\pi$
$89$	−10.4721	−1.11004	−0.555022	+	0.831836i	$0.687290\pi$
$90$	−0.381966	−0.0402628
$91$	4.38197	0.459355
$92$	1.00000	0.104257
$93$	14.7082	1.52517
$94$	−3.70820	−0.382472
$95$	1.85410	0.190227
$96$	1.61803	0.165140
$97$	12.3820	1.25720	0.628599	−	0.777730i	$-0.283629\pi$
$97$	12.3820	1.25720	0.628599	+	0.777730i	$0.283629\pi$
$98$	−6.61803	−0.668522
$99$	1.09017	0.109566
$100$	1.00000	0.100000
$101$	−0.291796	−0.0290348	−0.0145174	−	0.999895i	$-0.504621\pi$
$101$	−0.291796	−0.0290348	−0.0145174	+	0.999895i	$0.504621\pi$
$102$	9.85410	0.975701
$103$	16.5623	1.63193	0.815966	−	0.578100i	$-0.196205\pi$
$103$	16.5623	1.63193	0.815966	+	0.578100i	$0.196205\pi$
$104$	−7.09017	−0.695248
$105$	−1.00000	−0.0975900
$106$	0.472136	0.0458579
$107$	18.1803	1.75756	0.878780	−	0.477227i	$-0.158358\pi$
$107$	18.1803	1.75756	0.878780	+	0.477227i	$0.158358\pi$
$108$	−5.47214	−0.526557
$109$	−11.5623	−1.10747	−0.553734	−	0.832694i	$-0.686798\pi$
$109$	−11.5623	−1.10747	−0.553734	+	0.832694i	$0.686798\pi$
$110$	−2.85410	−0.272128
$111$	10.4721	0.993971
$112$	−0.618034	−0.0583987
$113$	1.05573	0.0993145	0.0496573	−	0.998766i	$-0.484187\pi$
$113$	1.05573	0.0993145	0.0496573	+	0.998766i	$0.484187\pi$
$114$	3.00000	0.280976
$115$	1.00000	0.0932505
$116$	−9.23607	−0.857547
$117$	2.70820	0.250374
$118$	1.70820	0.157253
$119$	−3.76393	−0.345039
$120$	1.61803	0.147706
$121$	−2.85410	−0.259464
$122$	−9.32624	−0.844358
$123$	5.38197	0.485276
$124$	9.09017	0.816321
$125$	1.00000	0.0894427
$126$	0.236068	0.0210306
$127$	16.1803	1.43577	0.717886	−	0.696160i	$-0.245110\pi$
$127$	16.1803	1.43577	0.717886	+	0.696160i	$0.245110\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−7.09017	−0.621849
$131$	2.94427	0.257242	0.128621	−	0.991694i	$-0.458945\pi$
$131$	2.94427	0.257242	0.128621	+	0.991694i	$0.458945\pi$
$132$	−4.61803	−0.401948
$133$	−1.14590	−0.0993620
$134$	14.4721	1.25020
$135$	−5.47214	−0.470966
$136$	6.09017	0.522228
$137$	−10.3262	−0.882230	−0.441115	−	0.897451i	$-0.645417\pi$
$137$	−10.3262	−0.882230	−0.441115	+	0.897451i	$0.645417\pi$
$138$	1.61803	0.137736
$139$	12.7639	1.08262	0.541311	−	0.840822i	$-0.317928\pi$
$139$	12.7639	1.08262	0.541311	+	0.840822i	$0.317928\pi$
$140$	−0.618034	−0.0522334
$141$	−6.00000	−0.505291
$142$	−4.09017	−0.343239
$143$	20.2361	1.69223
$144$	−0.381966	−0.0318305
$145$	−9.23607	−0.767014
$146$	3.23607	0.267819
$147$	−10.7082	−0.883198
$148$	6.47214	0.532006
$149$	−7.85410	−0.643433	−0.321717	−	0.946836i	$-0.604260\pi$
$149$	−7.85410	−0.643433	−0.321717	+	0.946836i	$0.604260\pi$
$150$	1.61803	0.132112
$151$	−2.56231	−0.208517	−0.104259	−	0.994550i	$-0.533247\pi$
$151$	−2.56231	−0.208517	−0.104259	+	0.994550i	$0.533247\pi$
$152$	1.85410	0.150388
$153$	−2.32624	−0.188065
$154$	1.76393	0.142142
$155$	9.09017	0.730140
$156$	−11.4721	−0.918506
$157$	−3.70820	−0.295947	−0.147973	−	0.988991i	$-0.547275\pi$
$157$	−3.70820	−0.295947	−0.147973	+	0.988991i	$0.547275\pi$
$158$	1.52786	0.121550
$159$	0.763932	0.0605838
$160$	1.00000	0.0790569
$161$	−0.618034	−0.0487079
$162$	−7.70820	−0.605614
$163$	1.38197	0.108244	0.0541220	−	0.998534i	$-0.482764\pi$
$163$	1.38197	0.108244	0.0541220	+	0.998534i	$0.482764\pi$
$164$	3.32624	0.259736
$165$	−4.61803	−0.359513
$166$	−6.94427	−0.538980
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	−1.00000	−0.0771517
$169$	37.2705	2.86696
$170$	6.09017	0.467095
$171$	−0.708204	−0.0541577
$172$	0	0
$173$	−1.43769	−0.109306	−0.0546529	−	0.998505i	$-0.517405\pi$
$173$	−1.43769	−0.109306	−0.0546529	+	0.998505i	$0.517405\pi$
$174$	−14.9443	−1.13292
$175$	−0.618034	−0.0467190
$176$	−2.85410	−0.215136
$177$	2.76393	0.207750
$178$	−10.4721	−0.784920
$179$	2.18034	0.162966	0.0814831	−	0.996675i	$-0.474034\pi$
$179$	2.18034	0.162966	0.0814831	+	0.996675i	$0.474034\pi$
$180$	−0.381966	−0.0284701
$181$	−12.1459	−0.902797	−0.451399	−	0.892322i	$-0.649075\pi$
$181$	−12.1459	−0.902797	−0.451399	+	0.892322i	$0.649075\pi$
$182$	4.38197	0.324813
$183$	−15.0902	−1.11550
$184$	1.00000	0.0737210
$185$	6.47214	0.475841
$186$	14.7082	1.07846
$187$	−17.3820	−1.27110
$188$	−3.70820	−0.270449
$189$	3.38197	0.246002
$190$	1.85410	0.134511
$191$	−13.7082	−0.991891	−0.495945	−	0.868354i	$-0.665178\pi$
$191$	−13.7082	−0.991891	−0.495945	+	0.868354i	$0.665178\pi$
$192$	1.61803	0.116772
$193$	0.763932	0.0549890	0.0274945	−	0.999622i	$-0.491247\pi$
$193$	0.763932	0.0549890	0.0274945	+	0.999622i	$0.491247\pi$
$194$	12.3820	0.888973
$195$	−11.4721	−0.821537
$196$	−6.61803	−0.472717
$197$	−22.5623	−1.60750	−0.803749	−	0.594969i	$-0.797164\pi$
$197$	−22.5623	−1.60750	−0.803749	+	0.594969i	$0.797164\pi$
$198$	1.09017	0.0774750
$199$	2.00000	0.141776	0.0708881	−	0.997484i	$-0.477417\pi$
$199$	2.00000	0.141776	0.0708881	+	0.997484i	$0.477417\pi$
$200$	1.00000	0.0707107
$201$	23.4164	1.65167
$202$	−0.291796	−0.0205307
$203$	5.70820	0.400637
$204$	9.85410	0.689925
$205$	3.32624	0.232315
$206$	16.5623	1.15395
$207$	−0.381966	−0.0265485
$208$	−7.09017	−0.491615
$209$	−5.29180	−0.366041
$210$	−1.00000	−0.0690066
$211$	14.0000	0.963800	0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000	0.963800	0.481900	+	0.876226i	$0.339947\pi$
$212$	0.472136	0.0324264
$213$	−6.61803	−0.453460
$214$	18.1803	1.24278
$215$	0	0
$216$	−5.47214	−0.372332
$217$	−5.61803	−0.381377
$218$	−11.5623	−0.783098
$219$	5.23607	0.353821
$220$	−2.85410	−0.192424
$221$	−43.1803	−2.90462
$222$	10.4721	0.702844
$223$	−20.9443	−1.40253	−0.701266	−	0.712900i	$-0.747382\pi$
$223$	−20.9443	−1.40253	−0.701266	+	0.712900i	$0.747382\pi$
$224$	−0.618034	−0.0412941
$225$	−0.381966	−0.0254644
$226$	1.05573	0.0702260
$227$	−18.7639	−1.24541	−0.622703	−	0.782458i	$-0.713965\pi$
$227$	−18.7639	−1.24541	−0.622703	+	0.782458i	$0.713965\pi$
$228$	3.00000	0.198680
$229$	10.0000	0.660819	0.330409	−	0.943838i	$-0.392813\pi$
$229$	10.0000	0.660819	0.330409	+	0.943838i	$0.392813\pi$
$230$	1.00000	0.0659380
$231$	2.85410	0.187786
$232$	−9.23607	−0.606378
$233$	6.29180	0.412189	0.206095	−	0.978532i	$-0.433925\pi$
$233$	6.29180	0.412189	0.206095	+	0.978532i	$0.433925\pi$
$234$	2.70820	0.177041
$235$	−3.70820	−0.241897
$236$	1.70820	0.111195
$237$	2.47214	0.160582
$238$	−3.76393	−0.243979
$239$	−20.3607	−1.31702	−0.658511	−	0.752571i	$-0.728814\pi$
$239$	−20.3607	−1.31702	−0.658511	+	0.752571i	$0.728814\pi$
$240$	1.61803	0.104444
$241$	0	0		−	1.00000i	$-0.5\pi$
$241$	0	0			1.00000i	$0.5\pi$
$242$	−2.85410	−0.183469
$243$	3.94427	0.253025
$244$	−9.32624	−0.597051
$245$	−6.61803	−0.422811
$246$	5.38197	0.343142
$247$	−13.1459	−0.836453
$248$	9.09017	0.577226
$249$	−11.2361	−0.712057
$250$	1.00000	0.0632456
$251$	6.14590	0.387926	0.193963	−	0.981009i	$-0.437866\pi$
$251$	6.14590	0.387926	0.193963	+	0.981009i	$0.437866\pi$
$252$	0.236068	0.0148709
$253$	−2.85410	−0.179436
$254$	16.1803	1.01524
$255$	9.85410	0.617088
$256$	1.00000	0.0625000
$257$	−7.81966	−0.487777	−0.243888	−	0.969803i	$-0.578423\pi$
$257$	−7.81966	−0.487777	−0.243888	+	0.969803i	$0.578423\pi$
$258$	0	0
$259$	−4.00000	−0.248548
$260$	−7.09017	−0.439714
$261$	3.52786	0.218369
$262$	2.94427	0.181898
$263$	20.7426	1.27905	0.639523	−	0.768772i	$-0.279132\pi$
$263$	20.7426	1.27905	0.639523	+	0.768772i	$0.279132\pi$
$264$	−4.61803	−0.284220
$265$	0.472136	0.0290031
$266$	−1.14590	−0.0702595
$267$	−16.9443	−1.03697
$268$	14.4721	0.884026
$269$	−14.1803	−0.864591	−0.432295	−	0.901732i	$-0.642296\pi$
$269$	−14.1803	−0.864591	−0.432295	+	0.901732i	$0.642296\pi$
$270$	−5.47214	−0.333024
$271$	−30.3262	−1.84219	−0.921094	−	0.389341i	$-0.872703\pi$
$271$	−30.3262	−1.84219	−0.921094	+	0.389341i	$0.872703\pi$
$272$	6.09017	0.369271
$273$	7.09017	0.429117
$274$	−10.3262	−0.623831
$275$	−2.85410	−0.172109
$276$	1.61803	0.0973942
$277$	29.4164	1.76746	0.883730	−	0.467996i	$-0.155024\pi$
$277$	29.4164	1.76746	0.883730	+	0.467996i	$0.155024\pi$
$278$	12.7639	0.765530
$279$	−3.47214	−0.207871
$280$	−0.618034	−0.0369346
$281$	22.7639	1.35798	0.678991	−	0.734146i	$-0.262417\pi$
$281$	22.7639	1.35798	0.678991	+	0.734146i	$0.262417\pi$
$282$	−6.00000	−0.357295
$283$	−26.9443	−1.60167	−0.800835	−	0.598885i	$-0.795611\pi$
$283$	−26.9443	−1.60167	−0.800835	+	0.598885i	$0.795611\pi$
$284$	−4.09017	−0.242707
$285$	3.00000	0.177705
$286$	20.2361	1.19658
$287$	−2.05573	−0.121346
$288$	−0.381966	−0.0225076
$289$	20.0902	1.18177
$290$	−9.23607	−0.542361
$291$	20.0344	1.17444
$292$	3.23607	0.189377
$293$	−19.8885	−1.16190	−0.580951	−	0.813939i	$-0.697319\pi$
$293$	−19.8885	−1.16190	−0.580951	+	0.813939i	$0.697319\pi$
$294$	−10.7082	−0.624515
$295$	1.70820	0.0994555
$296$	6.47214	0.376185
$297$	15.6180	0.906250
$298$	−7.85410	−0.454976
$299$	−7.09017	−0.410035
$300$	1.61803	0.0934172
$301$	0	0
$302$	−2.56231	−0.147444
$303$	−0.472136	−0.0271235
$304$	1.85410	0.106340
$305$	−9.32624	−0.534019
$306$	−2.32624	−0.132982
$307$	−28.4508	−1.62378	−0.811888	−	0.583813i	$-0.801560\pi$
$307$	−28.4508	−1.62378	−0.811888	+	0.583813i	$0.801560\pi$
$308$	1.76393	0.100509
$309$	26.7984	1.52451
$310$	9.09017	0.516287
$311$	4.00000	0.226819	0.113410	−	0.993548i	$-0.463823\pi$
$311$	4.00000	0.226819	0.113410	+	0.993548i	$0.463823\pi$
$312$	−11.4721	−0.649482
$313$	12.7984	0.723407	0.361703	−	0.932293i	$-0.382195\pi$
$313$	12.7984	0.723407	0.361703	+	0.932293i	$0.382195\pi$
$314$	−3.70820	−0.209266
$315$	0.236068	0.0133009
$316$	1.52786	0.0859491
$317$	−11.0902	−0.622886	−0.311443	−	0.950265i	$-0.600812\pi$
$317$	−11.0902	−0.622886	−0.311443	+	0.950265i	$0.600812\pi$
$318$	0.763932	0.0428392
$319$	26.3607	1.47591
$320$	1.00000	0.0559017
$321$	29.4164	1.64186
$322$	−0.618034	−0.0344417
$323$	11.2918	0.628292
$324$	−7.70820	−0.428234
$325$	−7.09017	−0.393292
$326$	1.38197	0.0765400
$327$	−18.7082	−1.03457
$328$	3.32624	0.183661
$329$	2.29180	0.126351
$330$	−4.61803	−0.254214
$331$	19.2361	1.05731	0.528655	−	0.848837i	$-0.322697\pi$
$331$	19.2361	1.05731	0.528655	+	0.848837i	$0.322697\pi$
$332$	−6.94427	−0.381116
$333$	−2.47214	−0.135472
$334$	−8.00000	−0.437741
$335$	14.4721	0.790697
$336$	−1.00000	−0.0545545
$337$	13.6738	0.744857	0.372429	−	0.928061i	$-0.378525\pi$
$337$	13.6738	0.744857	0.372429	+	0.928061i	$0.378525\pi$
$338$	37.2705	2.02725
$339$	1.70820	0.0927769
$340$	6.09017	0.330286
$341$	−25.9443	−1.40496
$342$	−0.708204	−0.0382953
$343$	8.41641	0.454443
$344$	0	0
$345$	1.61803	0.0871120
$346$	−1.43769	−0.0772909
$347$	−6.38197	−0.342602	−0.171301	−	0.985219i	$-0.554797\pi$
$347$	−6.38197	−0.342602	−0.171301	+	0.985219i	$0.554797\pi$
$348$	−14.9443	−0.801097
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−0.618034	−0.0330353
$351$	38.7984	2.07090
$352$	−2.85410	−0.152124
$353$	24.0000	1.27739	0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000	1.27739	0.638696	+	0.769460i	$0.279474\pi$
$354$	2.76393	0.146901
$355$	−4.09017	−0.217084
$356$	−10.4721	−0.555022
$357$	−6.09017	−0.322326
$358$	2.18034	0.115235
$359$	26.3607	1.39126	0.695632	−	0.718399i	$-0.255125\pi$
$359$	26.3607	1.39126	0.695632	+	0.718399i	$0.255125\pi$
$360$	−0.381966	−0.0201314
$361$	−15.5623	−0.819069
$362$	−12.1459	−0.638374
$363$	−4.61803	−0.242384
$364$	4.38197	0.229677
$365$	3.23607	0.169384
$366$	−15.0902	−0.788776
$367$	6.47214	0.337843	0.168921	−	0.985630i	$-0.445972\pi$
$367$	6.47214	0.337843	0.168921	+	0.985630i	$0.445972\pi$
$368$	1.00000	0.0521286
$369$	−1.27051	−0.0661401
$370$	6.47214	0.336470
$371$	−0.291796	−0.0151493
$372$	14.7082	0.762585
$373$	20.1803	1.04490	0.522449	−	0.852670i	$-0.325018\pi$
$373$	20.1803	1.04490	0.522449	+	0.852670i	$0.325018\pi$
$374$	−17.3820	−0.898800
$375$	1.61803	0.0835549
$376$	−3.70820	−0.191236
$377$	65.4853	3.37266
$378$	3.38197	0.173950
$379$	−22.4508	−1.15322	−0.576611	−	0.817019i	$-0.695625\pi$
$379$	−22.4508	−1.15322	−0.576611	+	0.817019i	$0.695625\pi$
$380$	1.85410	0.0951134
$381$	26.1803	1.34126
$382$	−13.7082	−0.701373
$383$	−17.8885	−0.914062	−0.457031	−	0.889451i	$-0.651087\pi$
$383$	−17.8885	−0.914062	−0.457031	+	0.889451i	$0.651087\pi$
$384$	1.61803	0.0825700
$385$	1.76393	0.0898983
$386$	0.763932	0.0388831
$387$	0	0
$388$	12.3820	0.628599
$389$	21.3262	1.08128	0.540642	−	0.841253i	$-0.318182\pi$
$389$	21.3262	1.08128	0.540642	+	0.841253i	$0.318182\pi$
$390$	−11.4721	−0.580914
$391$	6.09017	0.307993
$392$	−6.61803	−0.334261
$393$	4.76393	0.240309
$394$	−22.5623	−1.13667
$395$	1.52786	0.0768752
$396$	1.09017	0.0547831
$397$	7.32624	0.367693	0.183847	−	0.982955i	$-0.441145\pi$
$397$	7.32624	0.367693	0.183847	+	0.982955i	$0.441145\pi$
$398$	2.00000	0.100251
$399$	−1.85410	−0.0928212
$400$	1.00000	0.0500000
$401$	−1.70820	−0.0853036	−0.0426518	−	0.999090i	$-0.513581\pi$
$401$	−1.70820	−0.0853036	−0.0426518	+	0.999090i	$0.513581\pi$
$402$	23.4164	1.16790
$403$	−64.4508	−3.21053
$404$	−0.291796	−0.0145174
$405$	−7.70820	−0.383024
$406$	5.70820	0.283293
$407$	−18.4721	−0.915630
$408$	9.85410	0.487851
$409$	−30.2148	−1.49402	−0.747012	−	0.664810i	$-0.768512\pi$
$409$	−30.2148	−1.49402	−0.747012	+	0.664810i	$0.768512\pi$
$410$	3.32624	0.164271
$411$	−16.7082	−0.824155
$412$	16.5623	0.815966
$413$	−1.05573	−0.0519490
$414$	−0.381966	−0.0187726
$415$	−6.94427	−0.340881
$416$	−7.09017	−0.347624
$417$	20.6525	1.01136
$418$	−5.29180	−0.258830
$419$	14.4721	0.707010	0.353505	−	0.935433i	$-0.384990\pi$
$419$	14.4721	0.707010	0.353505	+	0.935433i	$0.384990\pi$
$420$	−1.00000	−0.0487950
$421$	13.7426	0.669776	0.334888	−	0.942258i	$-0.391302\pi$
$421$	13.7426	0.669776	0.334888	+	0.942258i	$0.391302\pi$
$422$	14.0000	0.681509
$423$	1.41641	0.0688681
$424$	0.472136	0.0229289
$425$	6.09017	0.295417
$426$	−6.61803	−0.320645
$427$	5.76393	0.278936
$428$	18.1803	0.878780
$429$	32.7426	1.58083
$430$	0	0
$431$	3.34752	0.161245	0.0806223	−	0.996745i	$-0.474309\pi$
$431$	3.34752	0.161245	0.0806223	+	0.996745i	$0.474309\pi$
$432$	−5.47214	−0.263278
$433$	8.50658	0.408800	0.204400	−	0.978887i	$-0.434476\pi$
$433$	8.50658	0.408800	0.204400	+	0.978887i	$0.434476\pi$
$434$	−5.61803	−0.269674
$435$	−14.9443	−0.716523
$436$	−11.5623	−0.553734
$437$	1.85410	0.0886937
$438$	5.23607	0.250189
$439$	−13.3820	−0.638686	−0.319343	−	0.947639i	$-0.603462\pi$
$439$	−13.3820	−0.638686	−0.319343	+	0.947639i	$0.603462\pi$
$440$	−2.85410	−0.136064
$441$	2.52786	0.120374
$442$	−43.1803	−2.05388
$443$	25.0902	1.19207	0.596035	−	0.802958i	$-0.296742\pi$
$443$	25.0902	1.19207	0.596035	+	0.802958i	$0.296742\pi$
$444$	10.4721	0.496986
$445$	−10.4721	−0.496427
$446$	−20.9443	−0.991740
$447$	−12.7082	−0.601077
$448$	−0.618034	−0.0291994
$449$	−1.56231	−0.0737298	−0.0368649	−	0.999320i	$-0.511737\pi$
$449$	−1.56231	−0.0737298	−0.0368649	+	0.999320i	$0.511737\pi$
$450$	−0.381966	−0.0180061
$451$	−9.49342	−0.447028
$452$	1.05573	0.0496573
$453$	−4.14590	−0.194791
$454$	−18.7639	−0.880635
$455$	4.38197	0.205430
$456$	3.00000	0.140488
$457$	−37.7771	−1.76714	−0.883569	−	0.468301i	$-0.844866\pi$
$457$	−37.7771	−1.76714	−0.883569	+	0.468301i	$0.844866\pi$
$458$	10.0000	0.467269
$459$	−33.3262	−1.55554
$460$	1.00000	0.0466252
$461$	−39.2361	−1.82741	−0.913703	−	0.406383i	$-0.866790\pi$
$461$	−39.2361	−1.82741	−0.913703	+	0.406383i	$0.866790\pi$
$462$	2.85410	0.132785
$463$	2.00000	0.0929479	0.0464739	−	0.998920i	$-0.485202\pi$
$463$	2.00000	0.0929479	0.0464739	+	0.998920i	$0.485202\pi$
$464$	−9.23607	−0.428774
$465$	14.7082	0.682077
$466$	6.29180	0.291462
$467$	−17.1246	−0.792433	−0.396216	−	0.918157i	$-0.629677\pi$
$467$	−17.1246	−0.792433	−0.396216	+	0.918157i	$0.629677\pi$
$468$	2.70820	0.125187
$469$	−8.94427	−0.413008
$470$	−3.70820	−0.171047
$471$	−6.00000	−0.276465
$472$	1.70820	0.0786265
$473$	0	0
$474$	2.47214	0.113549
$475$	1.85410	0.0850720
$476$	−3.76393	−0.172520
$477$	−0.180340	−0.00825720
$478$	−20.3607	−0.931276
$479$	−31.8885	−1.45702	−0.728512	−	0.685033i	$-0.759788\pi$
$479$	−31.8885	−1.45702	−0.728512	+	0.685033i	$0.759788\pi$
$480$	1.61803	0.0738528
$481$	−45.8885	−2.09234
$482$	0	0
$483$	−1.00000	−0.0455016
$484$	−2.85410	−0.129732
$485$	12.3820	0.562236
$486$	3.94427	0.178916
$487$	−19.8197	−0.898115	−0.449057	−	0.893503i	$-0.648240\pi$
$487$	−19.8197	−0.898115	−0.449057	+	0.893503i	$0.648240\pi$
$488$	−9.32624	−0.422179
$489$	2.23607	0.101118
$490$	−6.61803	−0.298972
$491$	6.18034	0.278915	0.139457	−	0.990228i	$-0.455464\pi$
$491$	6.18034	0.278915	0.139457	+	0.990228i	$0.455464\pi$
$492$	5.38197	0.242638
$493$	−56.2492	−2.53334
$494$	−13.1459	−0.591462
$495$	1.09017	0.0489995
$496$	9.09017	0.408161
$497$	2.52786	0.113390
$498$	−11.2361	−0.503500
$499$	12.3607	0.553340	0.276670	−	0.960965i	$-0.410769\pi$
$499$	12.3607	0.553340	0.276670	+	0.960965i	$0.410769\pi$
$500$	1.00000	0.0447214
$501$	−12.9443	−0.578307
$502$	6.14590	0.274305
$503$	36.3262	1.61971	0.809853	−	0.586632i	$-0.199547\pi$
$503$	36.3262	1.61971	0.809853	+	0.586632i	$0.199547\pi$
$504$	0.236068	0.0105153
$505$	−0.291796	−0.0129848
$506$	−2.85410	−0.126880
$507$	60.3050	2.67824
$508$	16.1803	0.717886
$509$	36.6525	1.62459	0.812296	−	0.583245i	$-0.198217\pi$
$509$	36.6525	1.62459	0.812296	+	0.583245i	$0.198217\pi$
$510$	9.85410	0.436347
$511$	−2.00000	−0.0884748
$512$	1.00000	0.0441942
$513$	−10.1459	−0.447952
$514$	−7.81966	−0.344910
$515$	16.5623	0.729822
$516$	0	0
$517$	10.5836	0.465466
$518$	−4.00000	−0.175750
$519$	−2.32624	−0.102111
$520$	−7.09017	−0.310925
$521$	−15.5279	−0.680288	−0.340144	−	0.940373i	$-0.610476\pi$
$521$	−15.5279	−0.680288	−0.340144	+	0.940373i	$0.610476\pi$
$522$	3.52786	0.154410
$523$	−26.0000	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$524$	2.94427	0.128621
$525$	−1.00000	−0.0436436
$526$	20.7426	0.904422
$527$	55.3607	2.41155
$528$	−4.61803	−0.200974
$529$	1.00000	0.0434783
$530$	0.472136	0.0205083
$531$	−0.652476	−0.0283150
$532$	−1.14590	−0.0496810
$533$	−23.5836	−1.02152
$534$	−16.9443	−0.733250
$535$	18.1803	0.786005
$536$	14.4721	0.625101
$537$	3.52786	0.152239
$538$	−14.1803	−0.611358
$539$	18.8885	0.813587
$540$	−5.47214	−0.235483
$541$	22.8328	0.981659	0.490830	−	0.871256i	$-0.336694\pi$
$541$	22.8328	0.981659	0.490830	+	0.871256i	$0.336694\pi$
$542$	−30.3262	−1.30262
$543$	−19.6525	−0.843368
$544$	6.09017	0.261114
$545$	−11.5623	−0.495275
$546$	7.09017	0.303431
$547$	27.9230	1.19390	0.596950	−	0.802278i	$-0.296379\pi$
$547$	27.9230	1.19390	0.596950	+	0.802278i	$0.296379\pi$
$548$	−10.3262	−0.441115
$549$	3.56231	0.152036
$550$	−2.85410	−0.121699
$551$	−17.1246	−0.729533
$552$	1.61803	0.0688681
$553$	−0.944272	−0.0401545
$554$	29.4164	1.24978
$555$	10.4721	0.444517
$556$	12.7639	0.541311
$557$	−22.8328	−0.967457	−0.483729	−	0.875218i	$-0.660718\pi$
$557$	−22.8328	−0.967457	−0.483729	+	0.875218i	$0.660718\pi$
$558$	−3.47214	−0.146987
$559$	0	0
$560$	−0.618034	−0.0261167
$561$	−28.1246	−1.18742
$562$	22.7639	0.960239
$563$	−13.8885	−0.585332	−0.292666	−	0.956215i	$-0.594542\pi$
$563$	−13.8885	−0.585332	−0.292666	+	0.956215i	$0.594542\pi$
$564$	−6.00000	−0.252646
$565$	1.05573	0.0444148
$566$	−26.9443	−1.13255
$567$	4.76393	0.200066
$568$	−4.09017	−0.171620
$569$	−2.00000	−0.0838444	−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000	−0.0838444	−0.0419222	+	0.999121i	$0.513348\pi$
$570$	3.00000	0.125656
$571$	15.9787	0.668688	0.334344	−	0.942451i	$-0.391485\pi$
$571$	15.9787	0.668688	0.334344	+	0.942451i	$0.391485\pi$
$572$	20.2361	0.846113
$573$	−22.1803	−0.926597
$574$	−2.05573	−0.0858044
$575$	1.00000	0.0417029
$576$	−0.381966	−0.0159153
$577$	−3.52786	−0.146867	−0.0734335	−	0.997300i	$-0.523396\pi$
$577$	−3.52786	−0.146867	−0.0734335	+	0.997300i	$0.523396\pi$
$578$	20.0902	0.835641
$579$	1.23607	0.0513692
$580$	−9.23607	−0.383507
$581$	4.29180	0.178054
$582$	20.0344	0.830454
$583$	−1.34752	−0.0558087
$584$	3.23607	0.133909
$585$	2.70820	0.111970
$586$	−19.8885	−0.821588
$587$	13.6180	0.562076	0.281038	−	0.959697i	$-0.409321\pi$
$587$	13.6180	0.562076	0.281038	+	0.959697i	$0.409321\pi$
$588$	−10.7082	−0.441599
$589$	16.8541	0.694461
$590$	1.70820	0.0703256
$591$	−36.5066	−1.50168
$592$	6.47214	0.266003
$593$	39.2361	1.61123	0.805616	−	0.592438i	$-0.201834\pi$
$593$	39.2361	1.61123	0.805616	+	0.592438i	$0.201834\pi$
$594$	15.6180	0.640816
$595$	−3.76393	−0.154306
$596$	−7.85410	−0.321717
$597$	3.23607	0.132443
$598$	−7.09017	−0.289939
$599$	−18.3820	−0.751067	−0.375533	−	0.926809i	$-0.622540\pi$
$599$	−18.3820	−0.751067	−0.375533	+	0.926809i	$0.622540\pi$
$600$	1.61803	0.0660560
$601$	−33.2705	−1.35713	−0.678566	−	0.734539i	$-0.737398\pi$
$601$	−33.2705	−1.35713	−0.678566	+	0.734539i	$0.737398\pi$
$602$	0	0
$603$	−5.52786	−0.225112
$604$	−2.56231	−0.104259
$605$	−2.85410	−0.116036
$606$	−0.472136	−0.0191792
$607$	26.4721	1.07447	0.537235	−	0.843432i	$-0.319469\pi$
$607$	26.4721	1.07447	0.537235	+	0.843432i	$0.319469\pi$
$608$	1.85410	0.0751938
$609$	9.23607	0.374264
$610$	−9.32624	−0.377608
$611$	26.2918	1.06365
$612$	−2.32624	−0.0940326
$613$	19.3050	0.779720	0.389860	−	0.920874i	$-0.372523\pi$
$613$	19.3050	0.779720	0.389860	+	0.920874i	$0.372523\pi$
$614$	−28.4508	−1.14818
$615$	5.38197	0.217022
$616$	1.76393	0.0710708
$617$	34.0902	1.37242	0.686209	−	0.727404i	$-0.259273\pi$
$617$	34.0902	1.37242	0.686209	+	0.727404i	$0.259273\pi$
$618$	26.7984	1.07799
$619$	−2.79837	−0.112476	−0.0562381	−	0.998417i	$-0.517911\pi$
$619$	−2.79837	−0.112476	−0.0562381	+	0.998417i	$0.517911\pi$
$620$	9.09017	0.365070
$621$	−5.47214	−0.219589
$622$	4.00000	0.160385
$623$	6.47214	0.259301
$624$	−11.4721	−0.459253
$625$	1.00000	0.0400000
$626$	12.7984	0.511526
$627$	−8.56231	−0.341946
$628$	−3.70820	−0.147973
$629$	39.4164	1.57164
$630$	0.236068	0.00940517
$631$	42.0689	1.67474	0.837368	−	0.546640i	$-0.184093\pi$
$631$	42.0689	1.67474	0.837368	+	0.546640i	$0.184093\pi$
$632$	1.52786	0.0607752
$633$	22.6525	0.900355
$634$	−11.0902	−0.440447
$635$	16.1803	0.642097
$636$	0.763932	0.0302919
$637$	46.9230	1.85916
$638$	26.3607	1.04363
$639$	1.56231	0.0618039
$640$	1.00000	0.0395285
$641$	0.360680	0.0142460	0.00712300	−	0.999975i	$-0.497733\pi$
$641$	0.360680	0.0142460	0.00712300	+	0.999975i	$0.497733\pi$
$642$	29.4164	1.16097
$643$	−8.29180	−0.326997	−0.163498	−	0.986544i	$-0.552278\pi$
$643$	−8.29180	−0.326997	−0.163498	+	0.986544i	$0.552278\pi$
$644$	−0.618034	−0.0243540
$645$	0	0
$646$	11.2918	0.444270
$647$	−36.2492	−1.42510	−0.712552	−	0.701619i	$-0.752461\pi$
$647$	−36.2492	−1.42510	−0.712552	+	0.701619i	$0.752461\pi$
$648$	−7.70820	−0.302807
$649$	−4.87539	−0.191376
$650$	−7.09017	−0.278099
$651$	−9.09017	−0.356272
$652$	1.38197	0.0541220
$653$	−8.03444	−0.314412	−0.157206	−	0.987566i	$-0.550249\pi$
$653$	−8.03444	−0.314412	−0.157206	+	0.987566i	$0.550249\pi$
$654$	−18.7082	−0.731549
$655$	2.94427	0.115042
$656$	3.32624	0.129868
$657$	−1.23607	−0.0482236
$658$	2.29180	0.0893435
$659$	−46.2492	−1.80161	−0.900807	−	0.434220i	$-0.857024\pi$
$659$	−46.2492	−1.80161	−0.900807	+	0.434220i	$0.857024\pi$
$660$	−4.61803	−0.179757
$661$	18.6738	0.726325	0.363163	−	0.931726i	$-0.381697\pi$
$661$	18.6738	0.726325	0.363163	+	0.931726i	$0.381697\pi$
$662$	19.2361	0.747631
$663$	−69.8673	−2.71342
$664$	−6.94427	−0.269490
$665$	−1.14590	−0.0444360
$666$	−2.47214	−0.0957933
$667$	−9.23607	−0.357622
$668$	−8.00000	−0.309529
$669$	−33.8885	−1.31021
$670$	14.4721	0.559107
$671$	26.6180	1.02758
$672$	−1.00000	−0.0385758
$673$	−10.9443	−0.421871	−0.210935	−	0.977500i	$-0.567651\pi$
$673$	−10.9443	−0.421871	−0.210935	+	0.977500i	$0.567651\pi$
$674$	13.6738	0.526694
$675$	−5.47214	−0.210623
$676$	37.2705	1.43348
$677$	−50.9443	−1.95795	−0.978974	−	0.203986i	$-0.934610\pi$
$677$	−50.9443	−1.95795	−0.978974	+	0.203986i	$0.934610\pi$
$678$	1.70820	0.0656032
$679$	−7.65248	−0.293675
$680$	6.09017	0.233547
$681$	−30.3607	−1.16342
$682$	−25.9443	−0.993458
$683$	−31.5623	−1.20770	−0.603849	−	0.797099i	$-0.706367\pi$
$683$	−31.5623	−1.20770	−0.603849	+	0.797099i	$0.706367\pi$
$684$	−0.708204	−0.0270789
$685$	−10.3262	−0.394545
$686$	8.41641	0.321340
$687$	16.1803	0.617318
$688$	0	0
$689$	−3.34752	−0.127531
$690$	1.61803	0.0615975
$691$	−29.2361	−1.11219	−0.556096	−	0.831118i	$-0.687701\pi$
$691$	−29.2361	−1.11219	−0.556096	+	0.831118i	$0.687701\pi$
$692$	−1.43769	−0.0546529
$693$	−0.673762	−0.0255941
$694$	−6.38197	−0.242256
$695$	12.7639	0.484164
$696$	−14.9443	−0.566461
$697$	20.2574	0.767302
$698$	−2.00000	−0.0757011
$699$	10.1803	0.385056
$700$	−0.618034	−0.0233595
$701$	43.3394	1.63691	0.818453	−	0.574573i	$-0.194832\pi$
$701$	43.3394	1.63691	0.818453	+	0.574573i	$0.194832\pi$
$702$	38.7984	1.46435
$703$	12.0000	0.452589
$704$	−2.85410	−0.107568
$705$	−6.00000	−0.225973
$706$	24.0000	0.903252
$707$	0.180340	0.00678238
$708$	2.76393	0.103875
$709$	−26.0902	−0.979837	−0.489918	−	0.871768i	$-0.662973\pi$
$709$	−26.0902	−0.979837	−0.489918	+	0.871768i	$0.662973\pi$
$710$	−4.09017	−0.153501
$711$	−0.583592	−0.0218864
$712$	−10.4721	−0.392460
$713$	9.09017	0.340430
$714$	−6.09017	−0.227919
$715$	20.2361	0.756786
$716$	2.18034	0.0814831
$717$	−32.9443	−1.23033
$718$	26.3607	0.983772
$719$	35.2705	1.31537	0.657684	−	0.753294i	$-0.271536\pi$
$719$	35.2705	1.31537	0.657684	+	0.753294i	$0.271536\pi$
$720$	−0.381966	−0.0142350
$721$	−10.2361	−0.381211
$722$	−15.5623	−0.579169
$723$	0	0
$724$	−12.1459	−0.451399
$725$	−9.23607	−0.343019
$726$	−4.61803	−0.171391
$727$	28.2016	1.04594	0.522970	−	0.852351i	$-0.324824\pi$
$727$	28.2016	1.04594	0.522970	+	0.852351i	$0.324824\pi$
$728$	4.38197	0.162406
$729$	29.5066	1.09284
$730$	3.23607	0.119772
$731$	0	0
$732$	−15.0902	−0.557749
$733$	−29.4164	−1.08652	−0.543260	−	0.839565i	$-0.682810\pi$
$733$	−29.4164	−1.08652	−0.543260	+	0.839565i	$0.682810\pi$
$734$	6.47214	0.238891
$735$	−10.7082	−0.394978
$736$	1.00000	0.0368605
$737$	−41.3050	−1.52149
$738$	−1.27051	−0.0467681
$739$	−13.8885	−0.510898	−0.255449	−	0.966822i	$-0.582223\pi$
$739$	−13.8885	−0.510898	−0.255449	+	0.966822i	$0.582223\pi$
$740$	6.47214	0.237920
$741$	−21.2705	−0.781392
$742$	−0.291796	−0.0107122
$743$	33.6312	1.23381	0.616904	−	0.787038i	$-0.288387\pi$
$743$	33.6312	1.23381	0.616904	+	0.787038i	$0.288387\pi$
$744$	14.7082	0.539229
$745$	−7.85410	−0.287752
$746$	20.1803	0.738855
$747$	2.65248	0.0970490
$748$	−17.3820	−0.635548
$749$	−11.2361	−0.410557
$750$	1.61803	0.0590822
$751$	−47.0132	−1.71553	−0.857767	−	0.514038i	$-0.828149\pi$
$751$	−47.0132	−1.71553	−0.857767	+	0.514038i	$0.828149\pi$
$752$	−3.70820	−0.135224
$753$	9.94427	0.362389
$754$	65.4853	2.38483
$755$	−2.56231	−0.0932519
$756$	3.38197	0.123001
$757$	−17.8885	−0.650170	−0.325085	−	0.945685i	$-0.605393\pi$
$757$	−17.8885	−0.650170	−0.325085	+	0.945685i	$0.605393\pi$
$758$	−22.4508	−0.815452
$759$	−4.61803	−0.167624
$760$	1.85410	0.0672553
$761$	46.8673	1.69894	0.849468	−	0.527640i	$-0.176923\pi$
$761$	46.8673	1.69894	0.849468	+	0.527640i	$0.176923\pi$
$762$	26.1803	0.948414
$763$	7.14590	0.258699
$764$	−13.7082	−0.495945
$765$	−2.32624	−0.0841053
$766$	−17.8885	−0.646339
$767$	−12.1115	−0.437319
$768$	1.61803	0.0583858
$769$	−6.58359	−0.237410	−0.118705	−	0.992930i	$-0.537874\pi$
$769$	−6.58359	−0.237410	−0.118705	+	0.992930i	$0.537874\pi$
$770$	1.76393	0.0635677
$771$	−12.6525	−0.455668
$772$	0.763932	0.0274945
$773$	28.9443	1.04105	0.520527	−	0.853845i	$-0.325736\pi$
$773$	28.9443	1.04105	0.520527	+	0.853845i	$0.325736\pi$
$774$	0	0
$775$	9.09017	0.326529
$776$	12.3820	0.444487
$777$	−6.47214	−0.232187
$778$	21.3262	0.764583
$779$	6.16718	0.220962
$780$	−11.4721	−0.410768
$781$	11.6738	0.417720
$782$	6.09017	0.217784
$783$	50.5410	1.80619
$784$	−6.61803	−0.236358
$785$	−3.70820	−0.132351
$786$	4.76393	0.169924
$787$	−2.87539	−0.102497	−0.0512483	−	0.998686i	$-0.516320\pi$
$787$	−2.87539	−0.102497	−0.0512483	+	0.998686i	$0.516320\pi$
$788$	−22.5623	−0.803749
$789$	33.5623	1.19485
$790$	1.52786	0.0543590
$791$	−0.652476	−0.0231994
$792$	1.09017	0.0387375
$793$	66.1246	2.34815
$794$	7.32624	0.259998
$795$	0.763932	0.0270939
$796$	2.00000	0.0708881
$797$	13.7082	0.485569	0.242785	−	0.970080i	$-0.421939\pi$
$797$	13.7082	0.485569	0.242785	+	0.970080i	$0.421939\pi$
$798$	−1.85410	−0.0656345
$799$	−22.5836	−0.798950
$800$	1.00000	0.0353553
$801$	4.00000	0.141333
$802$	−1.70820	−0.0603188
$803$	−9.23607	−0.325934
$804$	23.4164	0.825833
$805$	−0.618034	−0.0217828
$806$	−64.4508	−2.27018
$807$	−22.9443	−0.807677
$808$	−0.291796	−0.0102653
$809$	−46.7426	−1.64338	−0.821692	−	0.569932i	$-0.806970\pi$
$809$	−46.7426	−1.64338	−0.821692	+	0.569932i	$0.806970\pi$
$810$	−7.70820	−0.270839
$811$	21.8197	0.766192	0.383096	−	0.923709i	$-0.374858\pi$
$811$	21.8197	0.766192	0.383096	+	0.923709i	$0.374858\pi$
$812$	5.70820	0.200319
$813$	−49.0689	−1.72092
$814$	−18.4721	−0.647448
$815$	1.38197	0.0484082
$816$	9.85410	0.344963
$817$	0	0
$818$	−30.2148	−1.05644
$819$	−1.67376	−0.0584860
$820$	3.32624	0.116157
$821$	−33.0557	−1.15365	−0.576826	−	0.816867i	$-0.695709\pi$
$821$	−33.0557	−1.15365	−0.576826	+	0.816867i	$0.695709\pi$
$822$	−16.7082	−0.582766
$823$	25.4164	0.885960	0.442980	−	0.896531i	$-0.353921\pi$
$823$	25.4164	0.885960	0.442980	+	0.896531i	$0.353921\pi$
$824$	16.5623	0.576975
$825$	−4.61803	−0.160779
$826$	−1.05573	−0.0367335
$827$	21.7082	0.754868	0.377434	−	0.926036i	$-0.376806\pi$
$827$	21.7082	0.754868	0.377434	+	0.926036i	$0.376806\pi$
$828$	−0.381966	−0.0132742
$829$	18.9443	0.657962	0.328981	−	0.944337i	$-0.393295\pi$
$829$	18.9443	0.657962	0.328981	+	0.944337i	$0.393295\pi$
$830$	−6.94427	−0.241039
$831$	47.5967	1.65111
$832$	−7.09017	−0.245807
$833$	−40.3050	−1.39648
$834$	20.6525	0.715137
$835$	−8.00000	−0.276851
$836$	−5.29180	−0.183021
$837$	−49.7426	−1.71936
$838$	14.4721	0.499932
$839$	33.0132	1.13974	0.569870	−	0.821735i	$-0.306993\pi$
$839$	33.0132	1.13974	0.569870	+	0.821735i	$0.306993\pi$
$840$	−1.00000	−0.0345033
$841$	56.3050	1.94155
$842$	13.7426	0.473603
$843$	36.8328	1.26859
$844$	14.0000	0.481900
$845$	37.2705	1.28214
$846$	1.41641	0.0486971
$847$	1.76393	0.0606094
$848$	0.472136	0.0162132
$849$	−43.5967	−1.49624
$850$	6.09017	0.208891
$851$	6.47214	0.221862
$852$	−6.61803	−0.226730
$853$	−10.7984	−0.369729	−0.184865	−	0.982764i	$-0.559185\pi$
$853$	−10.7984	−0.369729	−0.184865	+	0.982764i	$0.559185\pi$
$854$	5.76393	0.197238
$855$	−0.708204	−0.0242201
$856$	18.1803	0.621391
$857$	−6.58359	−0.224891	−0.112446	−	0.993658i	$-0.535868\pi$
$857$	−6.58359	−0.224891	−0.112446	+	0.993658i	$0.535868\pi$
$858$	32.7426	1.11782
$859$	−24.0689	−0.821220	−0.410610	−	0.911811i	$-0.634684\pi$
$859$	−24.0689	−0.821220	−0.410610	+	0.911811i	$0.634684\pi$
$860$	0	0
$861$	−3.32624	−0.113358
$862$	3.34752	0.114017
$863$	32.7639	1.11530	0.557649	−	0.830077i	$-0.311704\pi$
$863$	32.7639	1.11530	0.557649	+	0.830077i	$0.311704\pi$
$864$	−5.47214	−0.186166
$865$	−1.43769	−0.0488831
$866$	8.50658	0.289065
$867$	32.5066	1.10398
$868$	−5.61803	−0.190688
$869$	−4.36068	−0.147926
$870$	−14.9443	−0.506658
$871$	−102.610	−3.47680
$872$	−11.5623	−0.391549
$873$	−4.72949	−0.160069
$874$	1.85410	0.0627159
$875$	−0.618034	−0.0208934
$876$	5.23607	0.176910
$877$	18.7426	0.632894	0.316447	−	0.948610i	$-0.397510\pi$
$877$	18.7426	0.632894	0.316447	+	0.948610i	$0.397510\pi$
$878$	−13.3820	−0.451619
$879$	−32.1803	−1.08542
$880$	−2.85410	−0.0962118
$881$	8.58359	0.289189	0.144594	−	0.989491i	$-0.453812\pi$
$881$	8.58359	0.289189	0.144594	+	0.989491i	$0.453812\pi$
$882$	2.52786	0.0851176
$883$	15.5623	0.523713	0.261857	−	0.965107i	$-0.415665\pi$
$883$	15.5623	0.523713	0.261857	+	0.965107i	$0.415665\pi$
$884$	−43.1803	−1.45231
$885$	2.76393	0.0929086
$886$	25.0902	0.842921
$887$	−5.16718	−0.173497	−0.0867485	−	0.996230i	$-0.527648\pi$
$887$	−5.16718	−0.173497	−0.0867485	+	0.996230i	$0.527648\pi$
$888$	10.4721	0.351422
$889$	−10.0000	−0.335389
$890$	−10.4721	−0.351027
$891$	22.0000	0.737028
$892$	−20.9443	−0.701266
$893$	−6.87539	−0.230076
$894$	−12.7082	−0.425026
$895$	2.18034	0.0728807
$896$	−0.618034	−0.0206471
$897$	−11.4721	−0.383043
$898$	−1.56231	−0.0521348
$899$	−83.9574	−2.80014
$900$	−0.381966	−0.0127322
$901$	2.87539	0.0957931
$902$	−9.49342	−0.316096
$903$	0	0
$904$	1.05573	0.0351130
$905$	−12.1459	−0.403743
$906$	−4.14590	−0.137738
$907$	7.12461	0.236569	0.118284	−	0.992980i	$-0.462261\pi$
$907$	7.12461	0.236569	0.118284	+	0.992980i	$0.462261\pi$
$908$	−18.7639	−0.622703
$909$	0.111456	0.00369677
$910$	4.38197	0.145261
$911$	36.0689	1.19502	0.597508	−	0.801863i	$-0.296158\pi$
$911$	36.0689	1.19502	0.597508	+	0.801863i	$0.296158\pi$
$912$	3.00000	0.0993399
$913$	19.8197	0.655935
$914$	−37.7771	−1.24955
$915$	−15.0902	−0.498866
$916$	10.0000	0.330409
$917$	−1.81966	−0.0600905
$918$	−33.3262	−1.09993
$919$	40.0000	1.31948	0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000	1.31948	0.659739	+	0.751495i	$0.270667\pi$
$920$	1.00000	0.0329690
$921$	−46.0344	−1.51689
$922$	−39.2361	−1.29217
$923$	29.0000	0.954547
$924$	2.85410	0.0938931
$925$	6.47214	0.212803
$926$	2.00000	0.0657241
$927$	−6.32624	−0.207781
$928$	−9.23607	−0.303189
$929$	−3.52786	−0.115745	−0.0578727	−	0.998324i	$-0.518432\pi$
$929$	−3.52786	−0.115745	−0.0578727	+	0.998324i	$0.518432\pi$
$930$	14.7082	0.482301
$931$	−12.2705	−0.402150
$932$	6.29180	0.206095
$933$	6.47214	0.211888
$934$	−17.1246	−0.560334
$935$	−17.3820	−0.568451
$936$	2.70820	0.0885204
$937$	−36.7984	−1.20215	−0.601075	−	0.799192i	$-0.705261\pi$
$937$	−36.7984	−1.20215	−0.601075	+	0.799192i	$0.705261\pi$
$938$	−8.94427	−0.292041
$939$	20.7082	0.675787
$940$	−3.70820	−0.120948
$941$	−22.4934	−0.733265	−0.366632	−	0.930366i	$-0.619489\pi$
$941$	−22.4934	−0.733265	−0.366632	+	0.930366i	$0.619489\pi$
$942$	−6.00000	−0.195491
$943$	3.32624	0.108317
$944$	1.70820	0.0555973
$945$	3.38197	0.110015
$946$	0	0
$947$	−54.6869	−1.77709	−0.888543	−	0.458793i	$-0.848282\pi$
$947$	−54.6869	−1.77709	−0.888543	+	0.458793i	$0.848282\pi$
$948$	2.47214	0.0802912
$949$	−22.9443	−0.744803
$950$	1.85410	0.0601550
$951$	−17.9443	−0.581883
$952$	−3.76393	−0.121990
$953$	3.79837	0.123041	0.0615207	−	0.998106i	$-0.480405\pi$
$953$	3.79837	0.123041	0.0615207	+	0.998106i	$0.480405\pi$
$954$	−0.180340	−0.00583872
$955$	−13.7082	−0.443587
$956$	−20.3607	−0.658511
$957$	42.6525	1.37876
$958$	−31.8885	−1.03027
$959$	6.38197	0.206084
$960$	1.61803	0.0522218
$961$	51.6312	1.66552
$962$	−45.8885	−1.47951
$963$	−6.94427	−0.223776
$964$	0	0
$965$	0.763932	0.0245918
$966$	−1.00000	−0.0321745
$967$	−16.5410	−0.531923	−0.265962	−	0.963984i	$-0.585689\pi$
$967$	−16.5410	−0.531923	−0.265962	+	0.963984i	$0.585689\pi$
$968$	−2.85410	−0.0917343
$969$	18.2705	0.586933
$970$	12.3820	0.397561
$971$	34.2705	1.09979	0.549896	−	0.835233i	$-0.314667\pi$
$971$	34.2705	1.09979	0.549896	+	0.835233i	$0.314667\pi$
$972$	3.94427	0.126513
$973$	−7.88854	−0.252895
$974$	−19.8197	−0.635063
$975$	−11.4721	−0.367402
$976$	−9.32624	−0.298526
$977$	−23.5623	−0.753825	−0.376912	−	0.926249i	$-0.623014\pi$
$977$	−23.5623	−0.753825	−0.376912	+	0.926249i	$0.623014\pi$
$978$	2.23607	0.0715016
$979$	29.8885	0.955242
$980$	−6.61803	−0.211405
$981$	4.41641	0.141005
$982$	6.18034	0.197223
$983$	−14.2705	−0.455159	−0.227579	−	0.973760i	$-0.573081\pi$
$983$	−14.2705	−0.455159	−0.227579	+	0.973760i	$0.573081\pi$
$984$	5.38197	0.171571
$985$	−22.5623	−0.718895
$986$	−56.2492	−1.79134
$987$	3.70820	0.118033
$988$	−13.1459	−0.418227
$989$	0	0
$990$	1.09017	0.0346479
$991$	27.5066	0.873775	0.436888	−	0.899516i	$-0.356081\pi$
$991$	27.5066	0.873775	0.436888	+	0.899516i	$0.356081\pi$
$992$	9.09017	0.288613
$993$	31.1246	0.987710
$994$	2.52786	0.0801790
$995$	2.00000	0.0634043
$996$	−11.2361	−0.356028
$997$	57.1935	1.81134	0.905668	−	0.423987i	$-0.139370\pi$
$997$	57.1935	1.81134	0.905668	+	0.423987i	$0.139370\pi$
$998$	12.3607	0.391270
$999$	−35.4164	−1.12053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.a.c.1.2	✓	2
3.2	odd	2		2070.2.a.u.1.1		2
4.3	odd	2		1840.2.a.l.1.1		2
5.2	odd	4		1150.2.b.i.599.3		4
5.3	odd	4		1150.2.b.i.599.2		4
5.4	even	2		1150.2.a.j.1.1		2
8.3	odd	2		7360.2.a.bn.1.2		2
8.5	even	2		7360.2.a.bh.1.1		2
20.19	odd	2		9200.2.a.bu.1.2		2
23.22	odd	2		5290.2.a.o.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.c.1.2	✓	2	1.1	even	1	trivial
1150.2.a.j.1.1		2	5.4	even	2
1150.2.b.i.599.2		4	5.3	odd	4
1150.2.b.i.599.3		4	5.2	odd	4
1840.2.a.l.1.1		2	4.3	odd	2
2070.2.a.u.1.1		2	3.2	odd	2
5290.2.a.o.1.2		2	23.22	odd	2
7360.2.a.bh.1.1		2	8.5	even	2
7360.2.a.bn.1.2		2	8.3	odd	2
9200.2.a.bu.1.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -0.618034 q^{7} +1.00000 q^{8} -0.381966 q^{9} +1.00000 q^{10} -2.85410 q^{11} +1.61803 q^{12} -7.09017 q^{13} -0.618034 q^{14} +1.61803 q^{15} +1.00000 q^{16} +6.09017 q^{17} -0.381966 q^{18} +1.85410 q^{19} +1.00000 q^{20} -1.00000 q^{21} -2.85410 q^{22} +1.00000 q^{23} +1.61803 q^{24} +1.00000 q^{25} -7.09017 q^{26} -5.47214 q^{27} -0.618034 q^{28} -9.23607 q^{29} +1.61803 q^{30} +9.09017 q^{31} +1.00000 q^{32} -4.61803 q^{33} +6.09017 q^{34} -0.618034 q^{35} -0.381966 q^{36} +6.47214 q^{37} +1.85410 q^{38} -11.4721 q^{39} +1.00000 q^{40} +3.32624 q^{41} -1.00000 q^{42} -2.85410 q^{44} -0.381966 q^{45} +1.00000 q^{46} -3.70820 q^{47} +1.61803 q^{48} -6.61803 q^{49} +1.00000 q^{50} +9.85410 q^{51} -7.09017 q^{52} +0.472136 q^{53} -5.47214 q^{54} -2.85410 q^{55} -0.618034 q^{56} +3.00000 q^{57} -9.23607 q^{58} +1.70820 q^{59} +1.61803 q^{60} -9.32624 q^{61} +9.09017 q^{62} +0.236068 q^{63} +1.00000 q^{64} -7.09017 q^{65} -4.61803 q^{66} +14.4721 q^{67} +6.09017 q^{68} +1.61803 q^{69} -0.618034 q^{70} -4.09017 q^{71} -0.381966 q^{72} +3.23607 q^{73} +6.47214 q^{74} +1.61803 q^{75} +1.85410 q^{76} +1.76393 q^{77} -11.4721 q^{78} +1.52786 q^{79} +1.00000 q^{80} -7.70820 q^{81} +3.32624 q^{82} -6.94427 q^{83} -1.00000 q^{84} +6.09017 q^{85} -14.9443 q^{87} -2.85410 q^{88} -10.4721 q^{89} -0.381966 q^{90} +4.38197 q^{91} +1.00000 q^{92} +14.7082 q^{93} -3.70820 q^{94} +1.85410 q^{95} +1.61803 q^{96} +12.3820 q^{97} -6.61803 q^{98} +1.09017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + 2 q^{5} + q^{6} + q^{7} + 2 q^{8} - 3 q^{9} + 2 q^{10} + q^{11} + q^{12} - 3 q^{13} + q^{14} + q^{15} + 2 q^{16} + q^{17} - 3 q^{18} - 3 q^{19} + 2 q^{20} - 2 q^{21} + q^{22} + 2 q^{23} + q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} + q^{28} - 14 q^{29} + q^{30} + 7 q^{31} + 2 q^{32} - 7 q^{33} + q^{34} + q^{35} - 3 q^{36} + 4 q^{37} - 3 q^{38} - 14 q^{39} + 2 q^{40} - 9 q^{41} - 2 q^{42} + q^{44} - 3 q^{45} + 2 q^{46} + 6 q^{47} + q^{48} - 11 q^{49} + 2 q^{50} + 13 q^{51} - 3 q^{52} - 8 q^{53} - 2 q^{54} + q^{55} + q^{56} + 6 q^{57} - 14 q^{58} - 10 q^{59} + q^{60} - 3 q^{61} + 7 q^{62} - 4 q^{63} + 2 q^{64} - 3 q^{65} - 7 q^{66} + 20 q^{67} + q^{68} + q^{69} + q^{70} + 3 q^{71} - 3 q^{72} + 2 q^{73} + 4 q^{74} + q^{75} - 3 q^{76} + 8 q^{77} - 14 q^{78} + 12 q^{79} + 2 q^{80} - 2 q^{81} - 9 q^{82} + 4 q^{83} - 2 q^{84} + q^{85} - 12 q^{87} + q^{88} - 12 q^{89} - 3 q^{90} + 11 q^{91} + 2 q^{92} + 16 q^{93} + 6 q^{94} - 3 q^{95} + q^{96} + 27 q^{97} - 11 q^{98} - 9 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + 2 * q^5 + q^6 + q^7 + 2 * q^8 - 3 * q^9 + 2 * q^10 + q^11 + q^12 - 3 * q^13 + q^14 + q^15 + 2 * q^16 + q^17 - 3 * q^18 - 3 * q^19 + 2 * q^20 - 2 * q^21 + q^22 + 2 * q^23 + q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 + q^28 - 14 * q^29 + q^30 + 7 * q^31 + 2 * q^32 - 7 * q^33 + q^34 + q^35 - 3 * q^36 + 4 * q^37 - 3 * q^38 - 14 * q^39 + 2 * q^40 - 9 * q^41 - 2 * q^42 + q^44 - 3 * q^45 + 2 * q^46 + 6 * q^47 + q^48 - 11 * q^49 + 2 * q^50 + 13 * q^51 - 3 * q^52 - 8 * q^53 - 2 * q^54 + q^55 + q^56 + 6 * q^57 - 14 * q^58 - 10 * q^59 + q^60 - 3 * q^61 + 7 * q^62 - 4 * q^63 + 2 * q^64 - 3 * q^65 - 7 * q^66 + 20 * q^67 + q^68 + q^69 + q^70 + 3 * q^71 - 3 * q^72 + 2 * q^73 + 4 * q^74 + q^75 - 3 * q^76 + 8 * q^77 - 14 * q^78 + 12 * q^79 + 2 * q^80 - 2 * q^81 - 9 * q^82 + 4 * q^83 - 2 * q^84 + q^85 - 12 * q^87 + q^88 - 12 * q^89 - 3 * q^90 + 11 * q^91 + 2 * q^92 + 16 * q^93 + 6 * q^94 - 3 * q^95 + q^96 + 27 * q^97 - 11 * q^98 - 9 * q^99

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