LMFDB - Embedded newform 6034.2.a.o.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.804173 q^{3} +1.00000 q^{4} -3.18296 q^{5} +0.804173 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.35331 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.804173 q^{3} +1.00000 q^{4} -3.18296 q^{5} +0.804173 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.35331 q^{9} +3.18296 q^{10} -6.09311 q^{11} -0.804173 q^{12} +4.76817 q^{13} +1.00000 q^{14} +2.55965 q^{15} +1.00000 q^{16} +4.44173 q^{17} +2.35331 q^{18} -3.99081 q^{19} -3.18296 q^{20} +0.804173 q^{21} +6.09311 q^{22} -5.05427 q^{23} +0.804173 q^{24} +5.13126 q^{25} -4.76817 q^{26} +4.30498 q^{27} -1.00000 q^{28} +1.73354 q^{29} -2.55965 q^{30} +2.54048 q^{31} -1.00000 q^{32} +4.89991 q^{33} -4.44173 q^{34} +3.18296 q^{35} -2.35331 q^{36} +0.204768 q^{37} +3.99081 q^{38} -3.83443 q^{39} +3.18296 q^{40} +10.3257 q^{41} -0.804173 q^{42} +5.54792 q^{43} -6.09311 q^{44} +7.49049 q^{45} +5.05427 q^{46} -12.0517 q^{47} -0.804173 q^{48} +1.00000 q^{49} -5.13126 q^{50} -3.57192 q^{51} +4.76817 q^{52} +0.201304 q^{53} -4.30498 q^{54} +19.3941 q^{55} +1.00000 q^{56} +3.20930 q^{57} -1.73354 q^{58} +7.13561 q^{59} +2.55965 q^{60} +7.83163 q^{61} -2.54048 q^{62} +2.35331 q^{63} +1.00000 q^{64} -15.1769 q^{65} -4.89991 q^{66} -2.92364 q^{67} +4.44173 q^{68} +4.06450 q^{69} -3.18296 q^{70} -10.4869 q^{71} +2.35331 q^{72} +14.7251 q^{73} -0.204768 q^{74} -4.12642 q^{75} -3.99081 q^{76} +6.09311 q^{77} +3.83443 q^{78} -4.06038 q^{79} -3.18296 q^{80} +3.59797 q^{81} -10.3257 q^{82} -7.35519 q^{83} +0.804173 q^{84} -14.1379 q^{85} -5.54792 q^{86} -1.39406 q^{87} +6.09311 q^{88} +1.32805 q^{89} -7.49049 q^{90} -4.76817 q^{91} -5.05427 q^{92} -2.04298 q^{93} +12.0517 q^{94} +12.7026 q^{95} +0.804173 q^{96} +9.61536 q^{97} -1.00000 q^{98} +14.3389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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
$3$	−0.804173	−0.464289	−0.232145	−	0.972681i	$-0.574574\pi$
$3$	−0.804173	−0.464289	−0.232145	+	0.972681i	$0.574574\pi$
$4$	1.00000	0.500000
$5$	−3.18296	−1.42346	−0.711732	−	0.702451i	$-0.752089\pi$
$5$	−3.18296	−1.42346	−0.711732	+	0.702451i	$0.752089\pi$
$6$	0.804173	0.328302
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.35331	−0.784435
$10$	3.18296	1.00654
$11$	−6.09311	−1.83714	−0.918570	−	0.395257i	$-0.870655\pi$
$11$	−6.09311	−1.83714	−0.918570	+	0.395257i	$0.870655\pi$
$12$	−0.804173	−0.232145
$13$	4.76817	1.32245	0.661226	−	0.750186i	$-0.270036\pi$
$13$	4.76817	1.32245	0.661226	+	0.750186i	$0.270036\pi$
$14$	1.00000	0.267261
$15$	2.55965	0.660899
$16$	1.00000	0.250000
$17$	4.44173	1.07728	0.538639	−	0.842536i	$-0.318939\pi$
$17$	4.44173	1.07728	0.538639	+	0.842536i	$0.318939\pi$
$18$	2.35331	0.554680
$19$	−3.99081	−0.915555	−0.457778	−	0.889067i	$-0.651354\pi$
$19$	−3.99081	−0.915555	−0.457778	+	0.889067i	$0.651354\pi$
$20$	−3.18296	−0.711732
$21$	0.804173	0.175485
$22$	6.09311	1.29905
$23$	−5.05427	−1.05389	−0.526944	−	0.849900i	$-0.676662\pi$
$23$	−5.05427	−1.05389	−0.526944	+	0.849900i	$0.676662\pi$
$24$	0.804173	0.164151
$25$	5.13126	1.02625
$26$	−4.76817	−0.935115
$27$	4.30498	0.828494
$28$	−1.00000	−0.188982
$29$	1.73354	0.321909	0.160955	−	0.986962i	$-0.448543\pi$
$29$	1.73354	0.321909	0.160955	+	0.986962i	$0.448543\pi$
$30$	−2.55965	−0.467327
$31$	2.54048	0.456283	0.228141	−	0.973628i	$-0.426735\pi$
$31$	2.54048	0.456283	0.228141	+	0.973628i	$0.426735\pi$
$32$	−1.00000	−0.176777
$33$	4.89991	0.852965
$34$	−4.44173	−0.761751
$35$	3.18296	0.538019
$36$	−2.35331	−0.392218
$37$	0.204768	0.0336637	0.0168318	−	0.999858i	$-0.494642\pi$
$37$	0.204768	0.0336637	0.0168318	+	0.999858i	$0.494642\pi$
$38$	3.99081	0.647395
$39$	−3.83443	−0.614001
$40$	3.18296	0.503271
$41$	10.3257	1.61261	0.806304	−	0.591501i	$-0.201464\pi$
$41$	10.3257	1.61261	0.806304	+	0.591501i	$0.201464\pi$
$42$	−0.804173	−0.124087
$43$	5.54792	0.846050	0.423025	−	0.906118i	$-0.360968\pi$
$43$	5.54792	0.846050	0.423025	+	0.906118i	$0.360968\pi$
$44$	−6.09311	−0.918570
$45$	7.49049	1.11662
$46$	5.05427	0.745211
$47$	−12.0517	−1.75793	−0.878963	−	0.476889i	$-0.841764\pi$
$47$	−12.0517	−1.75793	−0.878963	+	0.476889i	$0.841764\pi$
$48$	−0.804173	−0.116072
$49$	1.00000	0.142857
$50$	−5.13126	−0.725670
$51$	−3.57192	−0.500169
$52$	4.76817	0.661226
$53$	0.201304	0.0276512	0.0138256	−	0.999904i	$-0.495599\pi$
$53$	0.201304	0.0276512	0.0138256	+	0.999904i	$0.495599\pi$
$54$	−4.30498	−0.585834
$55$	19.3941	2.61511
$56$	1.00000	0.133631
$57$	3.20930	0.425083
$58$	−1.73354	−0.227624
$59$	7.13561	0.928977	0.464489	−	0.885579i	$-0.346238\pi$
$59$	7.13561	0.928977	0.464489	+	0.885579i	$0.346238\pi$
$60$	2.55965	0.330450
$61$	7.83163	1.00274	0.501369	−	0.865234i	$-0.332830\pi$
$61$	7.83163	1.00274	0.501369	+	0.865234i	$0.332830\pi$
$62$	−2.54048	−0.322641
$63$	2.35331	0.296489
$64$	1.00000	0.125000
$65$	−15.1769	−1.88247
$66$	−4.89991	−0.603137
$67$	−2.92364	−0.357180	−0.178590	−	0.983924i	$-0.557154\pi$
$67$	−2.92364	−0.357180	−0.178590	+	0.983924i	$0.557154\pi$
$68$	4.44173	0.538639
$69$	4.06450	0.489309
$70$	−3.18296	−0.380437
$71$	−10.4869	−1.24457	−0.622284	−	0.782791i	$-0.713795\pi$
$71$	−10.4869	−1.24457	−0.622284	+	0.782791i	$0.713795\pi$
$72$	2.35331	0.277340
$73$	14.7251	1.72344	0.861721	−	0.507382i	$-0.169387\pi$
$73$	14.7251	1.72344	0.861721	+	0.507382i	$0.169387\pi$
$74$	−0.204768	−0.0238038
$75$	−4.12642	−0.476478
$76$	−3.99081	−0.457778
$77$	6.09311	0.694374
$78$	3.83443	0.434164
$79$	−4.06038	−0.456828	−0.228414	−	0.973564i	$-0.573354\pi$
$79$	−4.06038	−0.456828	−0.228414	+	0.973564i	$0.573354\pi$
$80$	−3.18296	−0.355866
$81$	3.59797	0.399774
$82$	−10.3257	−1.14029
$83$	−7.35519	−0.807337	−0.403668	−	0.914905i	$-0.632265\pi$
$83$	−7.35519	−0.807337	−0.403668	+	0.914905i	$0.632265\pi$
$84$	0.804173	0.0877424
$85$	−14.1379	−1.53347
$86$	−5.54792	−0.598248
$87$	−1.39406	−0.149459
$88$	6.09311	0.649527
$89$	1.32805	0.140773	0.0703865	−	0.997520i	$-0.477577\pi$
$89$	1.32805	0.140773	0.0703865	+	0.997520i	$0.477577\pi$
$90$	−7.49049	−0.789567
$91$	−4.76817	−0.499840
$92$	−5.05427	−0.526944
$93$	−2.04298	−0.211847
$94$	12.0517	1.24304
$95$	12.7026	1.30326
$96$	0.804173	0.0820755
$97$	9.61536	0.976292	0.488146	−	0.872762i	$-0.337673\pi$
$97$	9.61536	0.976292	0.488146	+	0.872762i	$0.337673\pi$
$98$	−1.00000	−0.101015
$99$	14.3389	1.44112
$100$	5.13126	0.513126
$101$	13.9601	1.38909	0.694543	−	0.719451i	$-0.255607\pi$
$101$	13.9601	1.38909	0.694543	+	0.719451i	$0.255607\pi$
$102$	3.57192	0.353673
$103$	−1.03811	−0.102288	−0.0511440	−	0.998691i	$-0.516287\pi$
$103$	−1.03811	−0.102288	−0.0511440	+	0.998691i	$0.516287\pi$
$104$	−4.76817	−0.467558
$105$	−2.55965	−0.249797
$106$	−0.201304	−0.0195524
$107$	−0.470297	−0.0454653	−0.0227327	−	0.999742i	$-0.507237\pi$
$107$	−0.470297	−0.0454653	−0.0227327	+	0.999742i	$0.507237\pi$
$108$	4.30498	0.414247
$109$	−0.00539596	−0.000516840 0	−0.000258420	−	1.00000i	$-0.500082\pi$
$109$	−0.00539596	−0.000516840 0	−0.000258420		1.00000i	$0.500082\pi$
$110$	−19.3941	−1.84916
$111$	−0.164669	−0.0156297
$112$	−1.00000	−0.0944911
$113$	5.15966	0.485380	0.242690	−	0.970104i	$-0.421970\pi$
$113$	5.15966	0.485380	0.242690	+	0.970104i	$0.421970\pi$
$114$	−3.20930	−0.300579
$115$	16.0875	1.50017
$116$	1.73354	0.160955
$117$	−11.2210	−1.03738
$118$	−7.13561	−0.656886
$119$	−4.44173	−0.407173
$120$	−2.55965	−0.233663
$121$	26.1259	2.37509
$122$	−7.83163	−0.709043
$123$	−8.30367	−0.748717
$124$	2.54048	0.228141
$125$	−0.417801	−0.0373693
$126$	−2.35331	−0.209649
$127$	−0.0541359	−0.00480378	−0.00240189	−	0.999997i	$-0.500765\pi$
$127$	−0.0541359	−0.00480378	−0.00240189	+	0.999997i	$0.500765\pi$
$128$	−1.00000	−0.0883883
$129$	−4.46149	−0.392812
$130$	15.1769	1.33110
$131$	14.9028	1.30206	0.651030	−	0.759052i	$-0.274337\pi$
$131$	14.9028	1.30206	0.651030	+	0.759052i	$0.274337\pi$
$132$	4.89991	0.426482
$133$	3.99081	0.346047
$134$	2.92364	0.252564
$135$	−13.7026	−1.17933
$136$	−4.44173	−0.380876
$137$	−14.2045	−1.21357	−0.606787	−	0.794864i	$-0.707542\pi$
$137$	−14.2045	−1.21357	−0.606787	+	0.794864i	$0.707542\pi$
$138$	−4.06450	−0.345993
$139$	−9.85497	−0.835887	−0.417944	−	0.908473i	$-0.637249\pi$
$139$	−9.85497	−0.835887	−0.417944	+	0.908473i	$0.637249\pi$
$140$	3.18296	0.269010
$141$	9.69168	0.816186
$142$	10.4869	0.880043
$143$	−29.0530	−2.42953
$144$	−2.35331	−0.196109
$145$	−5.51778	−0.458227
$146$	−14.7251	−1.21866
$147$	−0.804173	−0.0663270
$148$	0.204768	0.0168318
$149$	16.9385	1.38765	0.693826	−	0.720142i	$-0.255924\pi$
$149$	16.9385	1.38765	0.693826	+	0.720142i	$0.255924\pi$
$150$	4.12642	0.336921
$151$	−9.03897	−0.735581	−0.367791	−	0.929909i	$-0.619886\pi$
$151$	−9.03897	−0.735581	−0.367791	+	0.929909i	$0.619886\pi$
$152$	3.99081	0.323698
$153$	−10.4528	−0.845056
$154$	−6.09311	−0.490997
$155$	−8.08624	−0.649503
$156$	−3.83443	−0.307000
$157$	−17.1246	−1.36670	−0.683348	−	0.730093i	$-0.739477\pi$
$157$	−17.1246	−1.36670	−0.683348	+	0.730093i	$0.739477\pi$
$158$	4.06038	0.323026
$159$	−0.161883	−0.0128382
$160$	3.18296	0.251635
$161$	5.05427	0.398332
$162$	−3.59797	−0.282683
$163$	4.48976	0.351665	0.175832	−	0.984420i	$-0.443738\pi$
$163$	4.48976	0.351665	0.175832	+	0.984420i	$0.443738\pi$
$164$	10.3257	0.806304
$165$	−15.5962	−1.21417
$166$	7.35519	0.570873
$167$	−19.9940	−1.54718	−0.773592	−	0.633684i	$-0.781542\pi$
$167$	−19.9940	−1.54718	−0.773592	+	0.633684i	$0.781542\pi$
$168$	−0.804173	−0.0620433
$169$	9.73546	0.748882
$170$	14.1379	1.08433
$171$	9.39161	0.718194
$172$	5.54792	0.423025
$173$	−19.1766	−1.45797	−0.728984	−	0.684531i	$-0.760007\pi$
$173$	−19.1766	−1.45797	−0.728984	+	0.684531i	$0.760007\pi$
$174$	1.39406	0.105684
$175$	−5.13126	−0.387887
$176$	−6.09311	−0.459285
$177$	−5.73826	−0.431314
$178$	−1.32805	−0.0995416
$179$	−8.37731	−0.626149	−0.313075	−	0.949729i	$-0.601359\pi$
$179$	−8.37731	−0.626149	−0.313075	+	0.949729i	$0.601359\pi$
$180$	7.49049	0.558308
$181$	−10.3840	−0.771838	−0.385919	−	0.922533i	$-0.626116\pi$
$181$	−10.3840	−0.771838	−0.385919	+	0.922533i	$0.626116\pi$
$182$	4.76817	0.353440
$183$	−6.29799	−0.465560
$184$	5.05427	0.372605
$185$	−0.651769	−0.0479190
$186$	2.04298	0.149799
$187$	−27.0640	−1.97911
$188$	−12.0517	−0.878963
$189$	−4.30498	−0.313141
$190$	−12.7026	−0.921545
$191$	23.2688	1.68367	0.841837	−	0.539732i	$-0.181474\pi$
$191$	23.2688	1.68367	0.841837	+	0.539732i	$0.181474\pi$
$192$	−0.804173	−0.0580362
$193$	−24.7423	−1.78099	−0.890493	−	0.454996i	$-0.849641\pi$
$193$	−24.7423	−1.78099	−0.890493	+	0.454996i	$0.849641\pi$
$194$	−9.61536	−0.690343
$195$	12.2049	0.874008
$196$	1.00000	0.0714286
$197$	13.1088	0.933965	0.466983	−	0.884267i	$-0.345341\pi$
$197$	13.1088	0.933965	0.466983	+	0.884267i	$0.345341\pi$
$198$	−14.3389	−1.01902
$199$	1.11771	0.0792323	0.0396161	−	0.999215i	$-0.487386\pi$
$199$	1.11771	0.0792323	0.0396161	+	0.999215i	$0.487386\pi$
$200$	−5.13126	−0.362835
$201$	2.35111	0.165835
$202$	−13.9601	−0.982232
$203$	−1.73354	−0.121670
$204$	−3.57192	−0.250084
$205$	−32.8664	−2.29549
$206$	1.03811	0.0723285
$207$	11.8942	0.826707
$208$	4.76817	0.330613
$209$	24.3164	1.68200
$210$	2.55965	0.176633
$211$	3.08761	0.212560	0.106280	−	0.994336i	$-0.466106\pi$
$211$	3.08761	0.212560	0.106280	+	0.994336i	$0.466106\pi$
$212$	0.201304	0.0138256
$213$	8.43329	0.577840
$214$	0.470297	0.0321488
$215$	−17.6588	−1.20432
$216$	−4.30498	−0.292917
$217$	−2.54048	−0.172459
$218$	0.00539596	0.000365461 0
$219$	−11.8415	−0.800176
$220$	19.3941	1.30755
$221$	21.1789	1.42465
$222$	0.164669	0.0110518
$223$	19.2273	1.28756	0.643778	−	0.765212i	$-0.277366\pi$
$223$	19.2273	1.28756	0.643778	+	0.765212i	$0.277366\pi$
$224$	1.00000	0.0668153
$225$	−12.0754	−0.805029
$226$	−5.15966	−0.343215
$227$	−1.23730	−0.0821224	−0.0410612	−	0.999157i	$-0.513074\pi$
$227$	−1.23730	−0.0821224	−0.0410612	+	0.999157i	$0.513074\pi$
$228$	3.20930	0.212541
$229$	15.5680	1.02876	0.514381	−	0.857562i	$-0.328022\pi$
$229$	15.5680	1.02876	0.514381	+	0.857562i	$0.328022\pi$
$230$	−16.0875	−1.06078
$231$	−4.89991	−0.322390
$232$	−1.73354	−0.113812
$233$	−5.73722	−0.375858	−0.187929	−	0.982183i	$-0.560177\pi$
$233$	−5.73722	−0.375858	−0.187929	+	0.982183i	$0.560177\pi$
$234$	11.2210	0.733538
$235$	38.3603	2.50235
$236$	7.13561	0.464489
$237$	3.26524	0.212100
$238$	4.44173	0.287915
$239$	6.97957	0.451471	0.225736	−	0.974189i	$-0.427521\pi$
$239$	6.97957	0.451471	0.225736	+	0.974189i	$0.427521\pi$
$240$	2.55965	0.165225
$241$	−27.9728	−1.80189	−0.900943	−	0.433938i	$-0.857124\pi$
$241$	−27.9728	−1.80189	−0.900943	+	0.433938i	$0.857124\pi$
$242$	−26.1259	−1.67944
$243$	−15.8083	−1.01411
$244$	7.83163	0.501369
$245$	−3.18296	−0.203352
$246$	8.30367	0.529423
$247$	−19.0289	−1.21078
$248$	−2.54048	−0.161320
$249$	5.91484	0.374838
$250$	0.417801	0.0264241
$251$	−30.6186	−1.93263	−0.966315	−	0.257361i	$-0.917147\pi$
$251$	−30.6186	−1.93263	−0.966315	+	0.257361i	$0.917147\pi$
$252$	2.35331	0.148244
$253$	30.7962	1.93614
$254$	0.0541359	0.00339679
$255$	11.3693	0.711973
$256$	1.00000	0.0625000
$257$	−17.0743	−1.06507	−0.532534	−	0.846409i	$-0.678760\pi$
$257$	−17.0743	−1.06507	−0.532534	+	0.846409i	$0.678760\pi$
$258$	4.46149	0.277760
$259$	−0.204768	−0.0127237
$260$	−15.1769	−0.941233
$261$	−4.07954	−0.252517
$262$	−14.9028	−0.920696
$263$	−13.4681	−0.830478	−0.415239	−	0.909712i	$-0.636302\pi$
$263$	−13.4681	−0.830478	−0.415239	+	0.909712i	$0.636302\pi$
$264$	−4.89991	−0.301569
$265$	−0.640744	−0.0393606
$266$	−3.99081	−0.244692
$267$	−1.06798	−0.0653594
$268$	−2.92364	−0.178590
$269$	−18.3224	−1.11714	−0.558568	−	0.829459i	$-0.688649\pi$
$269$	−18.3224	−1.11714	−0.558568	+	0.829459i	$0.688649\pi$
$270$	13.7026	0.833914
$271$	−2.57028	−0.156133	−0.0780666	−	0.996948i	$-0.524875\pi$
$271$	−2.57028	−0.156133	−0.0780666	+	0.996948i	$0.524875\pi$
$272$	4.44173	0.269320
$273$	3.83443	0.232070
$274$	14.2045	0.858127
$275$	−31.2653	−1.88537
$276$	4.06450	0.244654
$277$	27.6263	1.65991	0.829953	−	0.557834i	$-0.188367\pi$
$277$	27.6263	1.65991	0.829953	+	0.557834i	$0.188367\pi$
$278$	9.85497	0.591062
$279$	−5.97852	−0.357925
$280$	−3.18296	−0.190218
$281$	−12.9499	−0.772526	−0.386263	−	0.922389i	$-0.626234\pi$
$281$	−12.9499	−0.772526	−0.386263	+	0.922389i	$0.626234\pi$
$282$	−9.69168	−0.577131
$283$	20.8235	1.23783	0.618913	−	0.785459i	$-0.287573\pi$
$283$	20.8235	1.23783	0.618913	+	0.785459i	$0.287573\pi$
$284$	−10.4869	−0.622284
$285$	−10.2151	−0.605090
$286$	29.0530	1.71794
$287$	−10.3257	−0.609509
$288$	2.35331	0.138670
$289$	2.72900	0.160529
$290$	5.51778	0.324015
$291$	−7.73241	−0.453282
$292$	14.7251	0.861721
$293$	22.9355	1.33991	0.669953	−	0.742403i	$-0.266314\pi$
$293$	22.9355	1.33991	0.669953	+	0.742403i	$0.266314\pi$
$294$	0.804173	0.0469003
$295$	−22.7124	−1.32237
$296$	−0.204768	−0.0119019
$297$	−26.2307	−1.52206
$298$	−16.9385	−0.981219
$299$	−24.0996	−1.39372
$300$	−4.12642	−0.238239
$301$	−5.54792	−0.319777
$302$	9.03897	0.520134
$303$	−11.2264	−0.644938
$304$	−3.99081	−0.228889
$305$	−24.9278	−1.42736
$306$	10.4528	0.597545
$307$	9.76068	0.557071	0.278536	−	0.960426i	$-0.410151\pi$
$307$	9.76068	0.557071	0.278536	+	0.960426i	$0.410151\pi$
$308$	6.09311	0.347187
$309$	0.834819	0.0474912
$310$	8.08624	0.459268
$311$	9.05331	0.513366	0.256683	−	0.966496i	$-0.417370\pi$
$311$	9.05331	0.513366	0.256683	+	0.966496i	$0.417370\pi$
$312$	3.83443	0.217082
$313$	4.67746	0.264386	0.132193	−	0.991224i	$-0.457798\pi$
$313$	4.67746	0.264386	0.132193	+	0.991224i	$0.457798\pi$
$314$	17.1246	0.966400
$315$	−7.49049	−0.422041
$316$	−4.06038	−0.228414
$317$	−23.2779	−1.30741	−0.653707	−	0.756747i	$-0.726787\pi$
$317$	−23.2779	−1.30741	−0.653707	+	0.756747i	$0.726787\pi$
$318$	0.161883	0.00907796
$319$	−10.5626	−0.591393
$320$	−3.18296	−0.177933
$321$	0.378200	0.0211091
$322$	−5.05427	−0.281663
$323$	−17.7261	−0.986308
$324$	3.59797	0.199887
$325$	24.4667	1.35717
$326$	−4.48976	−0.248665
$327$	0.00433929	0.000239963 0
$328$	−10.3257	−0.570143
$329$	12.0517	0.664434
$330$	15.5962	0.858545
$331$	30.8427	1.69527	0.847635	−	0.530580i	$-0.178026\pi$
$331$	30.8427	1.69527	0.847635	+	0.530580i	$0.178026\pi$
$332$	−7.35519	−0.403668
$333$	−0.481882	−0.0264070
$334$	19.9940	1.09402
$335$	9.30585	0.508433
$336$	0.804173	0.0438712
$337$	24.1465	1.31535	0.657673	−	0.753304i	$-0.271541\pi$
$337$	24.1465	1.31535	0.657673	+	0.753304i	$0.271541\pi$
$338$	−9.73546	−0.529539
$339$	−4.14926	−0.225357
$340$	−14.1379	−0.766734
$341$	−15.4794	−0.838256
$342$	−9.39161	−0.507840
$343$	−1.00000	−0.0539949
$344$	−5.54792	−0.299124
$345$	−12.9372	−0.696514
$346$	19.1766	1.03094
$347$	35.1070	1.88464	0.942321	−	0.334711i	$-0.108639\pi$
$347$	35.1070	1.88464	0.942321	+	0.334711i	$0.108639\pi$
$348$	−1.39406	−0.0747296
$349$	−12.2106	−0.653620	−0.326810	−	0.945090i	$-0.605974\pi$
$349$	−12.2106	−0.653620	−0.326810	+	0.945090i	$0.605974\pi$
$350$	5.13126	0.274277
$351$	20.5269	1.09564
$352$	6.09311	0.324764
$353$	−0.0455102	−0.00242226	−0.00121113	−	0.999999i	$-0.500386\pi$
$353$	−0.0455102	−0.00242226	−0.00121113	+	0.999999i	$0.500386\pi$
$354$	5.73826	0.304985
$355$	33.3795	1.77160
$356$	1.32805	0.0703865
$357$	3.57192	0.189046
$358$	8.37731	0.442754
$359$	22.2284	1.17317	0.586584	−	0.809888i	$-0.300472\pi$
$359$	22.2284	1.17317	0.586584	+	0.809888i	$0.300472\pi$
$360$	−7.49049	−0.394783
$361$	−3.07341	−0.161758
$362$	10.3840	0.545772
$363$	−21.0098	−1.10273
$364$	−4.76817	−0.249920
$365$	−46.8695	−2.45326
$366$	6.29799	0.329201
$367$	2.85163	0.148854	0.0744268	−	0.997226i	$-0.476287\pi$
$367$	2.85163	0.148854	0.0744268	+	0.997226i	$0.476287\pi$
$368$	−5.05427	−0.263472
$369$	−24.2996	−1.26499
$370$	0.651769	0.0338839
$371$	−0.201304	−0.0104512
$372$	−2.04298	−0.105924
$373$	−24.5935	−1.27340	−0.636701	−	0.771111i	$-0.719701\pi$
$373$	−24.5935	−1.27340	−0.636701	+	0.771111i	$0.719701\pi$
$374$	27.0640	1.39944
$375$	0.335985	0.0173502
$376$	12.0517	0.621521
$377$	8.26580	0.425710
$378$	4.30498	0.221424
$379$	−20.1534	−1.03521	−0.517604	−	0.855620i	$-0.673176\pi$
$379$	−20.1534	−1.03521	−0.517604	+	0.855620i	$0.673176\pi$
$380$	12.7026	0.651630
$381$	0.0435346	0.00223034
$382$	−23.2688	−1.19054
$383$	14.5596	0.743959	0.371980	−	0.928241i	$-0.378679\pi$
$383$	14.5596	0.743959	0.371980	+	0.928241i	$0.378679\pi$
$384$	0.804173	0.0410378
$385$	−19.3941	−0.988417
$386$	24.7423	1.25935
$387$	−13.0560	−0.663672
$388$	9.61536	0.488146
$389$	6.84944	0.347280	0.173640	−	0.984809i	$-0.444447\pi$
$389$	6.84944	0.347280	0.173640	+	0.984809i	$0.444447\pi$
$390$	−12.2049	−0.618017
$391$	−22.4497	−1.13533
$392$	−1.00000	−0.0505076
$393$	−11.9844	−0.604533
$394$	−13.1088	−0.660413
$395$	12.9240	0.650278
$396$	14.3389	0.720559
$397$	27.6407	1.38725	0.693623	−	0.720338i	$-0.256013\pi$
$397$	27.6407	1.38725	0.693623	+	0.720338i	$0.256013\pi$
$398$	−1.11771	−0.0560257
$399$	−3.20930	−0.160666
$400$	5.13126	0.256563
$401$	−11.8982	−0.594165	−0.297083	−	0.954852i	$-0.596014\pi$
$401$	−11.8982	−0.594165	−0.297083	+	0.954852i	$0.596014\pi$
$402$	−2.35111	−0.117263
$403$	12.1134	0.603413
$404$	13.9601	0.694543
$405$	−11.4522	−0.569065
$406$	1.73354	0.0860339
$407$	−1.24767	−0.0618449
$408$	3.57192	0.176836
$409$	−17.3729	−0.859036	−0.429518	−	0.903058i	$-0.641317\pi$
$409$	−17.3729	−0.859036	−0.429518	+	0.903058i	$0.641317\pi$
$410$	32.8664	1.62316
$411$	11.4229	0.563450
$412$	−1.03811	−0.0511440
$413$	−7.13561	−0.351120
$414$	−11.8942	−0.584570
$415$	23.4113	1.14922
$416$	−4.76817	−0.233779
$417$	7.92509	0.388094
$418$	−24.3164	−1.18936
$419$	4.82282	0.235610	0.117805	−	0.993037i	$-0.462414\pi$
$419$	4.82282	0.235610	0.117805	+	0.993037i	$0.462414\pi$
$420$	−2.55965	−0.124898
$421$	−21.5220	−1.04892	−0.524460	−	0.851435i	$-0.675733\pi$
$421$	−21.5220	−1.04892	−0.524460	+	0.851435i	$0.675733\pi$
$422$	−3.08761	−0.150303
$423$	28.3614	1.37898
$424$	−0.201304	−0.00977619
$425$	22.7917	1.10556
$426$	−8.43329	−0.408594
$427$	−7.83163	−0.378999
$428$	−0.470297	−0.0227327
$429$	23.3636	1.12801
$430$	17.6588	0.851585
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	4.30498	0.207124
$433$	28.3637	1.36307	0.681537	−	0.731784i	$-0.261312\pi$
$433$	28.3637	1.36307	0.681537	+	0.731784i	$0.261312\pi$
$434$	2.54048	0.121947
$435$	4.43725	0.212750
$436$	−0.00539596	−0.000258420 0
$437$	20.1706	0.964892
$438$	11.8415	0.565810
$439$	−6.26721	−0.299118	−0.149559	−	0.988753i	$-0.547785\pi$
$439$	−6.26721	−0.299118	−0.149559	+	0.988753i	$0.547785\pi$
$440$	−19.3941	−0.924579
$441$	−2.35331	−0.112062
$442$	−21.1789	−1.00738
$443$	−2.70787	−0.128655	−0.0643274	−	0.997929i	$-0.520490\pi$
$443$	−2.70787	−0.128655	−0.0643274	+	0.997929i	$0.520490\pi$
$444$	−0.164669	−0.00781484
$445$	−4.22714	−0.200386
$446$	−19.2273	−0.910440
$447$	−13.6214	−0.644272
$448$	−1.00000	−0.0472456
$449$	9.18086	0.433272	0.216636	−	0.976252i	$-0.430492\pi$
$449$	9.18086	0.433272	0.216636	+	0.976252i	$0.430492\pi$
$450$	12.0754	0.569241
$451$	−62.9158	−2.96259
$452$	5.15966	0.242690
$453$	7.26889	0.341522
$454$	1.23730	0.0580693
$455$	15.1769	0.711505
$456$	−3.20930	−0.150289
$457$	−14.0009	−0.654935	−0.327468	−	0.944862i	$-0.606195\pi$
$457$	−14.0009	−0.654935	−0.327468	+	0.944862i	$0.606195\pi$
$458$	−15.5680	−0.727445
$459$	19.1216	0.892519
$460$	16.0875	0.750086
$461$	−33.7441	−1.57162	−0.785810	−	0.618468i	$-0.787754\pi$
$461$	−33.7441	−1.57162	−0.785810	+	0.618468i	$0.787754\pi$
$462$	4.89991	0.227964
$463$	−5.66886	−0.263454	−0.131727	−	0.991286i	$-0.542052\pi$
$463$	−5.66886	−0.263454	−0.131727	+	0.991286i	$0.542052\pi$
$464$	1.73354	0.0804774
$465$	6.50274	0.301557
$466$	5.73722	0.265772
$467$	−12.9297	−0.598315	−0.299157	−	0.954204i	$-0.596706\pi$
$467$	−12.9297	−0.598315	−0.299157	+	0.954204i	$0.596706\pi$
$468$	−11.2210	−0.518689
$469$	2.92364	0.135001
$470$	−38.3603	−1.76943
$471$	13.7712	0.634542
$472$	−7.13561	−0.328443
$473$	−33.8041	−1.55431
$474$	−3.26524	−0.149978
$475$	−20.4779	−0.939591
$476$	−4.44173	−0.203587
$477$	−0.473730	−0.0216906
$478$	−6.97957	−0.319238
$479$	−29.5967	−1.35231	−0.676155	−	0.736760i	$-0.736355\pi$
$479$	−29.5967	−1.35231	−0.676155	+	0.736760i	$0.736355\pi$
$480$	−2.55965	−0.116832
$481$	0.976369	0.0445186
$482$	27.9728	1.27413
$483$	−4.06450	−0.184941
$484$	26.1259	1.18754
$485$	−30.6054	−1.38972
$486$	15.8083	0.717081
$487$	−5.29299	−0.239848	−0.119924	−	0.992783i	$-0.538265\pi$
$487$	−5.29299	−0.239848	−0.119924	+	0.992783i	$0.538265\pi$
$488$	−7.83163	−0.354521
$489$	−3.61054	−0.163274
$490$	3.18296	0.143792
$491$	14.1525	0.638692	0.319346	−	0.947638i	$-0.396537\pi$
$491$	14.1525	0.638692	0.319346	+	0.947638i	$0.396537\pi$
$492$	−8.30367	−0.374358
$493$	7.69990	0.346786
$494$	19.0289	0.856150
$495$	−45.6404	−2.05138
$496$	2.54048	0.114071
$497$	10.4869	0.470403
$498$	−5.91484	−0.265050
$499$	−6.01714	−0.269364	−0.134682	−	0.990889i	$-0.543001\pi$
$499$	−6.01714	−0.269364	−0.134682	+	0.990889i	$0.543001\pi$
$500$	−0.417801	−0.0186847
$501$	16.0786	0.718341
$502$	30.6186	1.36658
$503$	−41.1415	−1.83441	−0.917204	−	0.398418i	$-0.869559\pi$
$503$	−41.1415	−1.83441	−0.917204	+	0.398418i	$0.869559\pi$
$504$	−2.35331	−0.104825
$505$	−44.4346	−1.97732
$506$	−30.7962	−1.36906
$507$	−7.82899	−0.347698
$508$	−0.0541359	−0.00240189
$509$	−39.4860	−1.75019	−0.875093	−	0.483954i	$-0.839200\pi$
$509$	−39.4860	−1.75019	−0.875093	+	0.483954i	$0.839200\pi$
$510$	−11.3693	−0.503441
$511$	−14.7251	−0.651400
$512$	−1.00000	−0.0441942
$513$	−17.1804	−0.758532
$514$	17.0743	0.753117
$515$	3.30426	0.145603
$516$	−4.46149	−0.196406
$517$	73.4325	3.22956
$518$	0.204768	0.00899699
$519$	15.4213	0.676919
$520$	15.1769	0.665552
$521$	−33.4855	−1.46703	−0.733513	−	0.679676i	$-0.762120\pi$
$521$	−33.4855	−1.46703	−0.733513	+	0.679676i	$0.762120\pi$
$522$	4.07954	0.178557
$523$	7.28758	0.318663	0.159332	−	0.987225i	$-0.449066\pi$
$523$	7.28758	0.318663	0.159332	+	0.987225i	$0.449066\pi$
$524$	14.9028	0.651030
$525$	4.12642	0.180092
$526$	13.4681	0.587236
$527$	11.2841	0.491544
$528$	4.89991	0.213241
$529$	2.54560	0.110678
$530$	0.640744	0.0278321
$531$	−16.7923	−0.728723
$532$	3.99081	0.173024
$533$	49.2349	2.13260
$534$	1.06798	0.0462161
$535$	1.49694	0.0647183
$536$	2.92364	0.126282
$537$	6.73680	0.290714
$538$	18.3224	0.789934
$539$	−6.09311	−0.262449
$540$	−13.7026	−0.589666
$541$	24.6817	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$541$	24.6817	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$542$	2.57028	0.110403
$543$	8.35055	0.358356
$544$	−4.44173	−0.190438
$545$	0.0171752	0.000735703 0
$546$	−3.83443	−0.164099
$547$	4.37988	0.187270	0.0936352	−	0.995607i	$-0.470151\pi$
$547$	4.37988	0.187270	0.0936352	+	0.995607i	$0.470151\pi$
$548$	−14.2045	−0.606787
$549$	−18.4302	−0.786583
$550$	31.2653	1.33316
$551$	−6.91822	−0.294726
$552$	−4.06450	−0.172997
$553$	4.06038	0.172665
$554$	−27.6263	−1.17373
$555$	0.524135	0.0222483
$556$	−9.85497	−0.417944
$557$	−8.31900	−0.352487	−0.176244	−	0.984347i	$-0.556395\pi$
$557$	−8.31900	−0.352487	−0.176244	+	0.984347i	$0.556395\pi$
$558$	5.97852	0.253091
$559$	26.4534	1.11886
$560$	3.18296	0.134505
$561$	21.7641	0.918881
$562$	12.9499	0.546258
$563$	20.5069	0.864262	0.432131	−	0.901811i	$-0.357762\pi$
$563$	20.5069	0.864262	0.432131	+	0.901811i	$0.357762\pi$
$564$	9.69168	0.408093
$565$	−16.4230	−0.690921
$566$	−20.8235	−0.875276
$567$	−3.59797	−0.151101
$568$	10.4869	0.440021
$569$	−28.6185	−1.19975	−0.599875	−	0.800094i	$-0.704783\pi$
$569$	−28.6185	−1.19975	−0.599875	+	0.800094i	$0.704783\pi$
$570$	10.2151	0.427863
$571$	−38.4416	−1.60873	−0.804366	−	0.594134i	$-0.797495\pi$
$571$	−38.4416	−1.60873	−0.804366	+	0.594134i	$0.797495\pi$
$572$	−29.0530	−1.21477
$573$	−18.7122	−0.781712
$574$	10.3257	0.430988
$575$	−25.9348	−1.08155
$576$	−2.35331	−0.0980544
$577$	1.26851	0.0528087	0.0264043	−	0.999651i	$-0.491594\pi$
$577$	1.26851	0.0528087	0.0264043	+	0.999651i	$0.491594\pi$
$578$	−2.72900	−0.113511
$579$	19.8970	0.826893
$580$	−5.51778	−0.229113
$581$	7.35519	0.305145
$582$	7.73241	0.320519
$583$	−1.22657	−0.0507992
$584$	−14.7251	−0.609329
$585$	35.7159	1.47667
$586$	−22.9355	−0.947457
$587$	−20.6050	−0.850461	−0.425230	−	0.905085i	$-0.639807\pi$
$587$	−20.6050	−0.850461	−0.425230	+	0.905085i	$0.639807\pi$
$588$	−0.804173	−0.0331635
$589$	−10.1386	−0.417752
$590$	22.7124	0.935054
$591$	−10.5418	−0.433630
$592$	0.204768	0.00841591
$593$	3.10683	0.127582	0.0637911	−	0.997963i	$-0.479681\pi$
$593$	3.10683	0.127582	0.0637911	+	0.997963i	$0.479681\pi$
$594$	26.2307	1.07626
$595$	14.1379	0.579597
$596$	16.9385	0.693826
$597$	−0.898831	−0.0367867
$598$	24.0996	0.985506
$599$	17.6229	0.720054	0.360027	−	0.932942i	$-0.382768\pi$
$599$	17.6229	0.720054	0.360027	+	0.932942i	$0.382768\pi$
$600$	4.12642	0.168460
$601$	0.531381	0.0216755	0.0108377	−	0.999941i	$-0.496550\pi$
$601$	0.531381	0.0216755	0.0108377	+	0.999941i	$0.496550\pi$
$602$	5.54792	0.226116
$603$	6.88022	0.280184
$604$	−9.03897	−0.367791
$605$	−83.1580	−3.38085
$606$	11.2264	0.456040
$607$	−14.3297	−0.581624	−0.290812	−	0.956780i	$-0.593925\pi$
$607$	−14.3297	−0.581624	−0.290812	+	0.956780i	$0.593925\pi$
$608$	3.99081	0.161849
$609$	1.39406	0.0564902
$610$	24.9278	1.00930
$611$	−57.4648	−2.32478
$612$	−10.4528	−0.422528
$613$	−28.9630	−1.16980	−0.584902	−	0.811104i	$-0.698867\pi$
$613$	−28.9630	−1.16980	−0.584902	+	0.811104i	$0.698867\pi$
$614$	−9.76068	−0.393909
$615$	26.4303	1.06577
$616$	−6.09311	−0.245498
$617$	−32.4723	−1.30729	−0.653644	−	0.756802i	$-0.726760\pi$
$617$	−32.4723	−1.30729	−0.653644	+	0.756802i	$0.726760\pi$
$618$	−0.834819	−0.0335813
$619$	26.1926	1.05277	0.526385	−	0.850246i	$-0.323547\pi$
$619$	26.1926	1.05277	0.526385	+	0.850246i	$0.323547\pi$
$620$	−8.08624	−0.324751
$621$	−21.7585	−0.873140
$622$	−9.05331	−0.363005
$623$	−1.32805	−0.0532072
$624$	−3.83443	−0.153500
$625$	−24.3265	−0.973058
$626$	−4.67746	−0.186949
$627$	−19.5546	−0.780936
$628$	−17.1246	−0.683348
$629$	0.909525	0.0362651
$630$	7.49049	0.298428
$631$	−32.8575	−1.30804	−0.654019	−	0.756478i	$-0.726918\pi$
$631$	−32.8575	−1.30804	−0.654019	+	0.756478i	$0.726918\pi$
$632$	4.06038	0.161513
$633$	−2.48298	−0.0986894
$634$	23.2779	0.924482
$635$	0.172313	0.00683801
$636$	−0.161883	−0.00641909
$637$	4.76817	0.188922
$638$	10.5626	0.418178
$639$	24.6789	0.976284
$640$	3.18296	0.125818
$641$	21.6957	0.856929	0.428464	−	0.903559i	$-0.359055\pi$
$641$	21.6957	0.856929	0.428464	+	0.903559i	$0.359055\pi$
$642$	−0.378200	−0.0149264
$643$	38.7193	1.52694	0.763470	−	0.645844i	$-0.223494\pi$
$643$	38.7193	1.52694	0.763470	+	0.645844i	$0.223494\pi$
$644$	5.05427	0.199166
$645$	14.2008	0.559154
$646$	17.7261	0.697425
$647$	34.0599	1.33903	0.669517	−	0.742797i	$-0.266501\pi$
$647$	34.0599	1.33903	0.669517	+	0.742797i	$0.266501\pi$
$648$	−3.59797	−0.141342
$649$	−43.4780	−1.70666
$650$	−24.4667	−0.959664
$651$	2.04298	0.0800707
$652$	4.48976	0.175832
$653$	33.2782	1.30227	0.651137	−	0.758960i	$-0.274292\pi$
$653$	33.2782	1.30227	0.651137	+	0.758960i	$0.274292\pi$
$654$	−0.00433929	−0.000169680 0
$655$	−47.4350	−1.85344
$656$	10.3257	0.403152
$657$	−34.6527	−1.35193
$658$	−12.0517	−0.469826
$659$	35.2695	1.37390	0.686951	−	0.726703i	$-0.258948\pi$
$659$	35.2695	1.37390	0.686951	+	0.726703i	$0.258948\pi$
$660$	−15.5962	−0.607083
$661$	−2.01218	−0.0782648	−0.0391324	−	0.999234i	$-0.512459\pi$
$661$	−2.01218	−0.0782648	−0.0391324	+	0.999234i	$0.512459\pi$
$662$	−30.8427	−1.19874
$663$	−17.0315	−0.661450
$664$	7.35519	0.285437
$665$	−12.7026	−0.492586
$666$	0.481882	0.0186725
$667$	−8.76175	−0.339256
$668$	−19.9940	−0.773592
$669$	−15.4621	−0.597798
$670$	−9.30585	−0.359516
$671$	−47.7190	−1.84217
$672$	−0.804173	−0.0310216
$673$	−0.709332	−0.0273427	−0.0136714	−	0.999907i	$-0.504352\pi$
$673$	−0.709332	−0.0273427	−0.0136714	+	0.999907i	$0.504352\pi$
$674$	−24.1465	−0.930090
$675$	22.0900	0.850244
$676$	9.73546	0.374441
$677$	20.9150	0.803828	0.401914	−	0.915677i	$-0.368345\pi$
$677$	20.9150	0.803828	0.401914	+	0.915677i	$0.368345\pi$
$678$	4.14926	0.159351
$679$	−9.61536	−0.369004
$680$	14.1379	0.542163
$681$	0.995002	0.0381286
$682$	15.4794	0.592737
$683$	8.01041	0.306510	0.153255	−	0.988187i	$-0.451024\pi$
$683$	8.01041	0.306510	0.153255	+	0.988187i	$0.451024\pi$
$684$	9.39161	0.359097
$685$	45.2125	1.72748
$686$	1.00000	0.0381802
$687$	−12.5194	−0.477643
$688$	5.54792	0.211513
$689$	0.959852	0.0365675
$690$	12.9372	0.492509
$691$	7.89275	0.300254	0.150127	−	0.988667i	$-0.452032\pi$
$691$	7.89275	0.300254	0.150127	+	0.988667i	$0.452032\pi$
$692$	−19.1766	−0.728984
$693$	−14.3389	−0.544692
$694$	−35.1070	−1.33264
$695$	31.3680	1.18986
$696$	1.39406	0.0528418
$697$	45.8641	1.73723
$698$	12.2106	0.462179
$699$	4.61372	0.174507
$700$	−5.13126	−0.193943
$701$	2.92396	0.110436	0.0552182	−	0.998474i	$-0.482415\pi$
$701$	2.92396	0.110436	0.0552182	+	0.998474i	$0.482415\pi$
$702$	−20.5269	−0.774738
$703$	−0.817191	−0.0308209
$704$	−6.09311	−0.229643
$705$	−30.8483	−1.16181
$706$	0.0455102	0.00171280
$707$	−13.9601	−0.525025
$708$	−5.73826	−0.215657
$709$	−5.98496	−0.224770	−0.112385	−	0.993665i	$-0.535849\pi$
$709$	−5.98496	−0.224770	−0.112385	+	0.993665i	$0.535849\pi$
$710$	−33.3795	−1.25271
$711$	9.55531	0.358352
$712$	−1.32805	−0.0497708
$713$	−12.8402	−0.480871
$714$	−3.57192	−0.133676
$715$	92.4746	3.45835
$716$	−8.37731	−0.313075
$717$	−5.61278	−0.209613
$718$	−22.2284	−0.829555
$719$	−0.319618	−0.0119197	−0.00595987	−	0.999982i	$-0.501897\pi$
$719$	−0.319618	−0.0119197	−0.00595987	+	0.999982i	$0.501897\pi$
$720$	7.49049	0.279154
$721$	1.03811	0.0386612
$722$	3.07341	0.114381
$723$	22.4950	0.836596
$724$	−10.3840	−0.385919
$725$	8.89523	0.330360
$726$	21.0098	0.779746
$727$	45.5712	1.69014	0.845072	−	0.534653i	$-0.179558\pi$
$727$	45.5712	1.69014	0.845072	+	0.534653i	$0.179558\pi$
$728$	4.76817	0.176720
$729$	1.91872	0.0710637
$730$	46.8695	1.73472
$731$	24.6424	0.911432
$732$	−6.29799	−0.232780
$733$	−24.5603	−0.907156	−0.453578	−	0.891217i	$-0.649853\pi$
$733$	−24.5603	−0.907156	−0.453578	+	0.891217i	$0.649853\pi$
$734$	−2.85163	−0.105255
$735$	2.55965	0.0944142
$736$	5.05427	0.186303
$737$	17.8141	0.656189
$738$	24.2996	0.894481
$739$	−19.5338	−0.718564	−0.359282	−	0.933229i	$-0.616978\pi$
$739$	−19.5338	−0.718564	−0.359282	+	0.933229i	$0.616978\pi$
$740$	−0.651769	−0.0239595
$741$	15.3025	0.562152
$742$	0.201304	0.00739010
$743$	−41.9910	−1.54050	−0.770250	−	0.637741i	$-0.779869\pi$
$743$	−41.9910	−1.54050	−0.770250	+	0.637741i	$0.779869\pi$
$744$	2.04298	0.0748993
$745$	−53.9145	−1.97527
$746$	24.5935	0.900431
$747$	17.3090	0.633304
$748$	−27.0640	−0.989556
$749$	0.470297	0.0171843
$750$	−0.335985	−0.0122684
$751$	−24.2339	−0.884307	−0.442153	−	0.896939i	$-0.645785\pi$
$751$	−24.2339	−0.884307	−0.442153	+	0.896939i	$0.645785\pi$
$752$	−12.0517	−0.439482
$753$	24.6227	0.897300
$754$	−8.26580	−0.301023
$755$	28.7707	1.04707
$756$	−4.30498	−0.156571
$757$	−41.8995	−1.52286	−0.761431	−	0.648246i	$-0.775503\pi$
$757$	−41.8995	−1.52286	−0.761431	+	0.648246i	$0.775503\pi$
$758$	20.1534	0.732003
$759$	−24.7654	−0.898929
$760$	−12.7026	−0.460772
$761$	31.2339	1.13223	0.566115	−	0.824327i	$-0.308446\pi$
$761$	31.2339	1.13223	0.566115	+	0.824327i	$0.308446\pi$
$762$	−0.0435346	−0.00157709
$763$	0.00539596	0.000195347 0
$764$	23.2688	0.841837
$765$	33.2708	1.20291
$766$	−14.5596	−0.526058
$767$	34.0238	1.22853
$768$	−0.804173	−0.0290181
$769$	−21.3615	−0.770315	−0.385158	−	0.922851i	$-0.625853\pi$
$769$	−21.3615	−0.770315	−0.385158	+	0.922851i	$0.625853\pi$
$770$	19.3941	0.698916
$771$	13.7307	0.494500
$772$	−24.7423	−0.890493
$773$	−47.4352	−1.70612	−0.853062	−	0.521810i	$-0.825257\pi$
$773$	−47.4352	−1.70612	−0.853062	+	0.521810i	$0.825257\pi$
$774$	13.0560	0.469287
$775$	13.0358	0.468261
$776$	−9.61536	−0.345171
$777$	0.164669	0.00590746
$778$	−6.84944	−0.245564
$779$	−41.2081	−1.47643
$780$	12.2049	0.437004
$781$	63.8979	2.28645
$782$	22.4497	0.802800
$783$	7.46284	0.266700
$784$	1.00000	0.0357143
$785$	54.5071	1.94544
$786$	11.9844	0.427469
$787$	−33.5143	−1.19466	−0.597329	−	0.801997i	$-0.703771\pi$
$787$	−33.5143	−1.19466	−0.597329	+	0.801997i	$0.703771\pi$
$788$	13.1088	0.466983
$789$	10.8307	0.385582
$790$	−12.9240	−0.459816
$791$	−5.15966	−0.183456
$792$	−14.3389	−0.509512
$793$	37.3426	1.32607
$794$	−27.6407	−0.980932
$795$	0.515268	0.0182747
$796$	1.11771	0.0396161
$797$	−8.84264	−0.313223	−0.156611	−	0.987660i	$-0.550057\pi$
$797$	−8.84264	−0.313223	−0.156611	+	0.987660i	$0.550057\pi$
$798$	3.20930	0.113608
$799$	−53.5306	−1.89378
$800$	−5.13126	−0.181417
$801$	−3.12531	−0.110427
$802$	11.8982	0.420138
$803$	−89.7216	−3.16621
$804$	2.35111	0.0829173
$805$	−16.0875	−0.567012
$806$	−12.1134	−0.426677
$807$	14.7344	0.518674
$808$	−13.9601	−0.491116
$809$	−7.05205	−0.247937	−0.123968	−	0.992286i	$-0.539562\pi$
$809$	−7.05205	−0.247937	−0.123968	+	0.992286i	$0.539562\pi$
$810$	11.4522	0.402390
$811$	15.1734	0.532809	0.266405	−	0.963861i	$-0.414164\pi$
$811$	15.1734	0.532809	0.266405	+	0.963861i	$0.414164\pi$
$812$	−1.73354	−0.0608352
$813$	2.06695	0.0724909
$814$	1.24767	0.0437309
$815$	−14.2907	−0.500583
$816$	−3.57192	−0.125042
$817$	−22.1407	−0.774606
$818$	17.3729	0.607430
$819$	11.2210	0.392092
$820$	−32.8664	−1.14775
$821$	16.4476	0.574024	0.287012	−	0.957927i	$-0.407338\pi$
$821$	16.4476	0.574024	0.287012	+	0.957927i	$0.407338\pi$
$822$	−11.4229	−0.398419
$823$	10.5968	0.369380	0.184690	−	0.982797i	$-0.440872\pi$
$823$	10.5968	0.369380	0.184690	+	0.982797i	$0.440872\pi$
$824$	1.03811	0.0361642
$825$	25.1427	0.875357
$826$	7.13561	0.248280
$827$	29.4273	1.02329	0.511644	−	0.859198i	$-0.329037\pi$
$827$	29.4273	1.02329	0.511644	+	0.859198i	$0.329037\pi$
$828$	11.8942	0.413353
$829$	−43.2917	−1.50358	−0.751791	−	0.659401i	$-0.770810\pi$
$829$	−43.2917	−1.50358	−0.751791	+	0.659401i	$0.770810\pi$
$830$	−23.4113	−0.812618
$831$	−22.2163	−0.770676
$832$	4.76817	0.165307
$833$	4.44173	0.153897
$834$	−7.92509	−0.274424
$835$	63.6403	2.20236
$836$	24.3164	0.841002
$837$	10.9367	0.378028
$838$	−4.82282	−0.166601
$839$	41.6506	1.43794	0.718969	−	0.695042i	$-0.244614\pi$
$839$	41.6506	1.43794	0.718969	+	0.695042i	$0.244614\pi$
$840$	2.55965	0.0883164
$841$	−25.9949	−0.896374
$842$	21.5220	0.741699
$843$	10.4139	0.358675
$844$	3.08761	0.106280
$845$	−30.9876	−1.06601
$846$	−28.3614	−0.975086
$847$	−26.1259	−0.897698
$848$	0.201304	0.00691281
$849$	−16.7457	−0.574710
$850$	−22.7917	−0.781749
$851$	−1.03495	−0.0354777
$852$	8.43329	0.288920
$853$	13.3985	0.458755	0.229378	−	0.973338i	$-0.426331\pi$
$853$	13.3985	0.458755	0.229378	+	0.973338i	$0.426331\pi$
$854$	7.83163	0.267993
$855$	−29.8931	−1.02232
$856$	0.470297	0.0160744
$857$	−5.48254	−0.187280	−0.0936400	−	0.995606i	$-0.529850\pi$
$857$	−5.48254	−0.187280	−0.0936400	+	0.995606i	$0.529850\pi$
$858$	−23.3636	−0.797620
$859$	18.1000	0.617565	0.308782	−	0.951133i	$-0.400079\pi$
$859$	18.1000	0.617565	0.308782	+	0.951133i	$0.400079\pi$
$860$	−17.6588	−0.602161
$861$	8.30367	0.282988
$862$	1.00000	0.0340601
$863$	−11.5522	−0.393241	−0.196621	−	0.980480i	$-0.562997\pi$
$863$	−11.5522	−0.393241	−0.196621	+	0.980480i	$0.562997\pi$
$864$	−4.30498	−0.146458
$865$	61.0384	2.07537
$866$	−28.3637	−0.963839
$867$	−2.19458	−0.0745320
$868$	−2.54048	−0.0862294
$869$	24.7403	0.839257
$870$	−4.43725	−0.150437
$871$	−13.9404	−0.472353
$872$	0.00539596	0.000182730 0
$873$	−22.6279	−0.765838
$874$	−20.1706	−0.682282
$875$	0.417801	0.0141243
$876$	−11.8415	−0.400088
$877$	7.03362	0.237509	0.118754	−	0.992924i	$-0.462110\pi$
$877$	7.03362	0.237509	0.118754	+	0.992924i	$0.462110\pi$
$878$	6.26721	0.211508
$879$	−18.4441	−0.622104
$880$	19.3941	0.653776
$881$	55.1864	1.85928	0.929638	−	0.368474i	$-0.120119\pi$
$881$	55.1864	1.85928	0.929638	+	0.368474i	$0.120119\pi$
$882$	2.35331	0.0792399
$883$	−18.8319	−0.633743	−0.316871	−	0.948469i	$-0.602632\pi$
$883$	−18.8319	−0.633743	−0.316871	+	0.948469i	$0.602632\pi$
$884$	21.1789	0.712325
$885$	18.2647	0.613961
$886$	2.70787	0.0909726
$887$	−13.4601	−0.451947	−0.225974	−	0.974133i	$-0.572556\pi$
$887$	−13.4601	−0.451947	−0.225974	+	0.974133i	$0.572556\pi$
$888$	0.164669	0.00552592
$889$	0.0541359	0.00181566
$890$	4.22714	0.141694
$891$	−21.9228	−0.734442
$892$	19.2273	0.643778
$893$	48.0962	1.60948
$894$	13.6214	0.455569
$895$	26.6647	0.891301
$896$	1.00000	0.0334077
$897$	19.3802	0.647088
$898$	−9.18086	−0.306369
$899$	4.40401	0.146882
$900$	−12.0754	−0.402514
$901$	0.894139	0.0297881
$902$	62.9158	2.09487
$903$	4.46149	0.148469
$904$	−5.15966	−0.171608
$905$	33.0520	1.09868
$906$	−7.26889	−0.241493
$907$	49.8700	1.65591	0.827953	−	0.560797i	$-0.189505\pi$
$907$	49.8700	1.65591	0.827953	+	0.560797i	$0.189505\pi$
$908$	−1.23730	−0.0410612
$909$	−32.8525	−1.08965
$910$	−15.1769	−0.503110
$911$	50.8953	1.68624	0.843118	−	0.537728i	$-0.180717\pi$
$911$	50.8953	1.68624	0.843118	+	0.537728i	$0.180717\pi$
$912$	3.20930	0.106271
$913$	44.8160	1.48319
$914$	14.0009	0.463109
$915$	20.0463	0.662709
$916$	15.5680	0.514381
$917$	−14.9028	−0.492133
$918$	−19.1216	−0.631106
$919$	39.0812	1.28917	0.644585	−	0.764533i	$-0.277030\pi$
$919$	39.0812	1.28917	0.644585	+	0.764533i	$0.277030\pi$
$920$	−16.0875	−0.530391
$921$	−7.84927	−0.258642
$922$	33.7441	1.11130
$923$	−50.0034	−1.64588
$924$	−4.89991	−0.161195
$925$	1.05072	0.0345474
$926$	5.66886	0.186290
$927$	2.44299	0.0802383
$928$	−1.73354	−0.0569061
$929$	4.30822	0.141348	0.0706740	−	0.997499i	$-0.477485\pi$
$929$	4.30822	0.141348	0.0706740	+	0.997499i	$0.477485\pi$
$930$	−6.50274	−0.213233
$931$	−3.99081	−0.130794
$932$	−5.73722	−0.187929
$933$	−7.28043	−0.238350
$934$	12.9297	0.423073
$935$	86.1436	2.81720
$936$	11.2210	0.366769
$937$	−56.6734	−1.85144	−0.925720	−	0.378209i	$-0.876540\pi$
$937$	−56.6734	−1.85144	−0.925720	+	0.378209i	$0.876540\pi$
$938$	−2.92364	−0.0954603
$939$	−3.76149	−0.122751
$940$	38.3603	1.25117
$941$	21.4637	0.699696	0.349848	−	0.936806i	$-0.386233\pi$
$941$	21.4637	0.699696	0.349848	+	0.936806i	$0.386233\pi$
$942$	−13.7712	−0.448689
$943$	−52.1890	−1.69951
$944$	7.13561	0.232244
$945$	13.7026	0.445746
$946$	33.8041	1.09907
$947$	55.8797	1.81585	0.907923	−	0.419137i	$-0.137667\pi$
$947$	55.8797	1.81585	0.907923	+	0.419137i	$0.137667\pi$
$948$	3.26524	0.106050
$949$	70.2118	2.27917
$950$	20.4779	0.664391
$951$	18.7194	0.607019
$952$	4.44173	0.143957
$953$	1.22936	0.0398227	0.0199114	−	0.999802i	$-0.493662\pi$
$953$	1.22936	0.0398227	0.0199114	+	0.999802i	$0.493662\pi$
$954$	0.473730	0.0153376
$955$	−74.0639	−2.39665
$956$	6.97957	0.225736
$957$	8.49417	0.274577
$958$	29.5967	0.956227
$959$	14.2045	0.458688
$960$	2.55965	0.0826124
$961$	−24.5460	−0.791806
$962$	−0.976369	−0.0314794
$963$	1.10675	0.0356646
$964$	−27.9728	−0.900943
$965$	78.7537	2.53517
$966$	4.06450	0.130773
$967$	−30.6658	−0.986145	−0.493073	−	0.869988i	$-0.664126\pi$
$967$	−30.6658	−0.986145	−0.493073	+	0.869988i	$0.664126\pi$
$968$	−26.1259	−0.839720
$969$	14.2549	0.457932
$970$	30.6054	0.982679
$971$	56.8224	1.82352	0.911759	−	0.410725i	$-0.134724\pi$
$971$	56.8224	1.82352	0.911759	+	0.410725i	$0.134724\pi$
$972$	−15.8083	−0.507053
$973$	9.85497	0.315936
$974$	5.29299	0.169598
$975$	−19.6755	−0.630120
$976$	7.83163	0.250684
$977$	−2.38637	−0.0763468	−0.0381734	−	0.999271i	$-0.512154\pi$
$977$	−2.38637	−0.0763468	−0.0381734	+	0.999271i	$0.512154\pi$
$978$	3.61054	0.115452
$979$	−8.09195	−0.258620
$980$	−3.18296	−0.101676
$981$	0.0126984	0.000405427 0
$982$	−14.1525	−0.451623
$983$	−35.8768	−1.14429	−0.572146	−	0.820152i	$-0.693889\pi$
$983$	−35.8768	−1.14429	−0.572146	+	0.820152i	$0.693889\pi$
$984$	8.30367	0.264711
$985$	−41.7249	−1.32947
$986$	−7.69990	−0.245215
$987$	−9.69168	−0.308489
$988$	−19.0289	−0.605389
$989$	−28.0407	−0.891642
$990$	45.6404	1.45055
$991$	29.3311	0.931734	0.465867	−	0.884855i	$-0.345743\pi$
$991$	29.3311	0.931734	0.465867	+	0.884855i	$0.345743\pi$
$992$	−2.54048	−0.0806602
$993$	−24.8029	−0.787096
$994$	−10.4869	−0.332625
$995$	−3.55763	−0.112784
$996$	5.91484	0.187419
$997$	−29.9973	−0.950023	−0.475011	−	0.879980i	$-0.657556\pi$
$997$	−29.9973	−0.950023	−0.475011	+	0.879980i	$0.657556\pi$
$998$	6.01714	0.190469
$999$	0.881523	0.0278901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.10	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.10	✓	25	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.804173 q^{3} +1.00000 q^{4} -3.18296 q^{5} +0.804173 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.35331 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.804173 q^{3} +1.00000 q^{4} -3.18296 q^{5} +0.804173 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.35331 q^{9} +3.18296 q^{10} -6.09311 q^{11} -0.804173 q^{12} +4.76817 q^{13} +1.00000 q^{14} +2.55965 q^{15} +1.00000 q^{16} +4.44173 q^{17} +2.35331 q^{18} -3.99081 q^{19} -3.18296 q^{20} +0.804173 q^{21} +6.09311 q^{22} -5.05427 q^{23} +0.804173 q^{24} +5.13126 q^{25} -4.76817 q^{26} +4.30498 q^{27} -1.00000 q^{28} +1.73354 q^{29} -2.55965 q^{30} +2.54048 q^{31} -1.00000 q^{32} +4.89991 q^{33} -4.44173 q^{34} +3.18296 q^{35} -2.35331 q^{36} +0.204768 q^{37} +3.99081 q^{38} -3.83443 q^{39} +3.18296 q^{40} +10.3257 q^{41} -0.804173 q^{42} +5.54792 q^{43} -6.09311 q^{44} +7.49049 q^{45} +5.05427 q^{46} -12.0517 q^{47} -0.804173 q^{48} +1.00000 q^{49} -5.13126 q^{50} -3.57192 q^{51} +4.76817 q^{52} +0.201304 q^{53} -4.30498 q^{54} +19.3941 q^{55} +1.00000 q^{56} +3.20930 q^{57} -1.73354 q^{58} +7.13561 q^{59} +2.55965 q^{60} +7.83163 q^{61} -2.54048 q^{62} +2.35331 q^{63} +1.00000 q^{64} -15.1769 q^{65} -4.89991 q^{66} -2.92364 q^{67} +4.44173 q^{68} +4.06450 q^{69} -3.18296 q^{70} -10.4869 q^{71} +2.35331 q^{72} +14.7251 q^{73} -0.204768 q^{74} -4.12642 q^{75} -3.99081 q^{76} +6.09311 q^{77} +3.83443 q^{78} -4.06038 q^{79} -3.18296 q^{80} +3.59797 q^{81} -10.3257 q^{82} -7.35519 q^{83} +0.804173 q^{84} -14.1379 q^{85} -5.54792 q^{86} -1.39406 q^{87} +6.09311 q^{88} +1.32805 q^{89} -7.49049 q^{90} -4.76817 q^{91} -5.05427 q^{92} -2.04298 q^{93} +12.0517 q^{94} +12.7026 q^{95} +0.804173 q^{96} +9.61536 q^{97} -1.00000 q^{98} +14.3389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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