LMFDB - Embedded newform 230.2.a.d.1.1

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:	$3$
Coefficient field:	3.3.1101.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 9x + 12 $ x^3 - x^2 - 9*x + 12
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			1.1
Root			$-3.11903$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} -1.00000 q^{10} +4.33763 q^{11} -3.11903 q^{12} -3.72833 q^{13} +4.50973 q^{14} +3.11903 q^{15} +1.00000 q^{16} +1.11903 q^{17} +6.72833 q^{18} +4.50973 q^{19} -1.00000 q^{20} -14.0660 q^{21} +4.33763 q^{22} -1.00000 q^{23} -3.11903 q^{24} +1.00000 q^{25} -3.72833 q^{26} -11.6288 q^{27} +4.50973 q^{28} -8.23805 q^{29} +3.11903 q^{30} +1.72833 q^{31} +1.00000 q^{32} -13.5292 q^{33} +1.11903 q^{34} -4.50973 q^{35} +6.72833 q^{36} -0.781399 q^{37} +4.50973 q^{38} +11.6288 q^{39} -1.00000 q^{40} +3.90043 q^{41} -14.0660 q^{42} +8.00000 q^{43} +4.33763 q^{44} -6.72833 q^{45} -1.00000 q^{46} -11.4567 q^{47} -3.11903 q^{48} +13.3376 q^{49} +1.00000 q^{50} -3.49027 q^{51} -3.72833 q^{52} -6.00000 q^{53} -11.6288 q^{54} -4.33763 q^{55} +4.50973 q^{56} -14.0660 q^{57} -8.23805 q^{58} -2.23805 q^{59} +3.11903 q^{60} +3.55623 q^{61} +1.72833 q^{62} +30.3429 q^{63} +1.00000 q^{64} +3.72833 q^{65} -13.5292 q^{66} +2.43720 q^{67} +1.11903 q^{68} +3.11903 q^{69} -4.50973 q^{70} +7.11903 q^{71} +6.72833 q^{72} -9.45665 q^{73} -0.781399 q^{74} -3.11903 q^{75} +4.50973 q^{76} +19.5615 q^{77} +11.6288 q^{78} -14.9133 q^{79} -1.00000 q^{80} +16.0854 q^{81} +3.90043 q^{82} +2.78140 q^{83} -14.0660 q^{84} -1.11903 q^{85} +8.00000 q^{86} +25.6947 q^{87} +4.33763 q^{88} -7.69471 q^{89} -6.72833 q^{90} -16.8137 q^{91} -1.00000 q^{92} -5.39070 q^{93} -11.4567 q^{94} -4.50973 q^{95} -3.11903 q^{96} -0.642920 q^{97} +13.3376 q^{98} +29.1850 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 10 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - q^{13} + 3 q^{14} - q^{15} + 3 q^{16} - 7 q^{17} + 10 q^{18} + 3 q^{19} - 3 q^{20} - 22 q^{21} + 3 q^{22} - 3 q^{23} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} + 3 q^{28} - 4 q^{29} - q^{30} - 5 q^{31} + 3 q^{32} - 9 q^{33} - 7 q^{34} - 3 q^{35} + 10 q^{36} - 2 q^{37} + 3 q^{38} + 14 q^{39} - 3 q^{40} + q^{41} - 22 q^{42} + 24 q^{43} + 3 q^{44} - 10 q^{45} - 3 q^{46} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} - 21 q^{51} - q^{52} - 18 q^{53} - 14 q^{54} - 3 q^{55} + 3 q^{56} - 22 q^{57} - 4 q^{58} + 14 q^{59} - q^{60} + q^{61} - 5 q^{62} + 8 q^{63} + 3 q^{64} + q^{65} - 9 q^{66} + 8 q^{67} - 7 q^{68} - q^{69} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} - 2 q^{74} + q^{75} + 3 q^{76} - 24 q^{77} + 14 q^{78} - 4 q^{79} - 3 q^{80} + 7 q^{81} + q^{82} + 8 q^{83} - 22 q^{84} + 7 q^{85} + 24 q^{86} + 36 q^{87} + 3 q^{88} + 18 q^{89} - 10 q^{90} + q^{91} - 3 q^{92} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} - 33 q^{97} + 30 q^{98} + 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 10 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - q^13 + 3 * q^14 - q^15 + 3 * q^16 - 7 * q^17 + 10 * q^18 + 3 * q^19 - 3 * q^20 - 22 * q^21 + 3 * q^22 - 3 * q^23 + q^24 + 3 * q^25 - q^26 - 14 * q^27 + 3 * q^28 - 4 * q^29 - q^30 - 5 * q^31 + 3 * q^32 - 9 * q^33 - 7 * q^34 - 3 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 + 14 * q^39 - 3 * q^40 + q^41 - 22 * q^42 + 24 * q^43 + 3 * q^44 - 10 * q^45 - 3 * q^46 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 - 21 * q^51 - q^52 - 18 * q^53 - 14 * q^54 - 3 * q^55 + 3 * q^56 - 22 * q^57 - 4 * q^58 + 14 * q^59 - q^60 + q^61 - 5 * q^62 + 8 * q^63 + 3 * q^64 + q^65 - 9 * q^66 + 8 * q^67 - 7 * q^68 - q^69 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 - 2 * q^74 + q^75 + 3 * q^76 - 24 * q^77 + 14 * q^78 - 4 * q^79 - 3 * q^80 + 7 * q^81 + q^82 + 8 * q^83 - 22 * q^84 + 7 * q^85 + 24 * q^86 + 36 * q^87 + 3 * q^88 + 18 * q^89 - 10 * q^90 + q^91 - 3 * q^92 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 - 33 * q^97 + 30 * q^98 + 57 * 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
$3$	−3.11903	−1.80077	−0.900385	−	0.435093i	$-0.856715\pi$
$3$	−3.11903	−1.80077	−0.900385	+	0.435093i	$0.856715\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.11903	−1.27334
$7$	4.50973	1.70452	0.852258	−	0.523122i	$-0.175233\pi$
$7$	4.50973	1.70452	0.852258	+	0.523122i	$0.175233\pi$
$8$	1.00000	0.353553
$9$	6.72833	2.24278
$10$	−1.00000	−0.316228
$11$	4.33763	1.30784	0.653922	−	0.756562i	$-0.273122\pi$
$11$	4.33763	1.30784	0.653922	+	0.756562i	$0.273122\pi$
$12$	−3.11903	−0.900385
$13$	−3.72833	−1.03405	−0.517026	−	0.855970i	$-0.672961\pi$
$13$	−3.72833	−1.03405	−0.517026	+	0.855970i	$0.672961\pi$
$14$	4.50973	1.20527
$15$	3.11903	0.805329
$16$	1.00000	0.250000
$17$	1.11903	0.271404	0.135702	−	0.990750i	$-0.456671\pi$
$17$	1.11903	0.271404	0.135702	+	0.990750i	$0.456671\pi$
$18$	6.72833	1.58588
$19$	4.50973	1.03460	0.517301	−	0.855803i	$-0.326937\pi$
$19$	4.50973	1.03460	0.517301	+	0.855803i	$0.326937\pi$
$20$	−1.00000	−0.223607
$21$	−14.0660	−3.06944
$22$	4.33763	0.924785
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.11903	−0.636669
$25$	1.00000	0.200000
$26$	−3.72833	−0.731185
$27$	−11.6288	−2.23795
$28$	4.50973	0.852258
$29$	−8.23805	−1.52977	−0.764884	−	0.644168i	$-0.777204\pi$
$29$	−8.23805	−1.52977	−0.764884	+	0.644168i	$0.777204\pi$
$30$	3.11903	0.569454
$31$	1.72833	0.310417	0.155208	−	0.987882i	$-0.450395\pi$
$31$	1.72833	0.310417	0.155208	+	0.987882i	$0.450395\pi$
$32$	1.00000	0.176777
$33$	−13.5292	−2.35513
$34$	1.11903	0.191911
$35$	−4.50973	−0.762283
$36$	6.72833	1.12139
$37$	−0.781399	−0.128461	−0.0642306	−	0.997935i	$-0.520459\pi$
$37$	−0.781399	−0.128461	−0.0642306	+	0.997935i	$0.520459\pi$
$38$	4.50973	0.731574
$39$	11.6288	1.86209
$40$	−1.00000	−0.158114
$41$	3.90043	0.609144	0.304572	−	0.952489i	$-0.401487\pi$
$41$	3.90043	0.609144	0.304572	+	0.952489i	$0.401487\pi$
$42$	−14.0660	−2.17042
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	4.33763	0.653922
$45$	−6.72833	−1.00300
$46$	−1.00000	−0.147442
$47$	−11.4567	−1.67112	−0.835562	−	0.549396i	$-0.814858\pi$
$47$	−11.4567	−1.67112	−0.835562	+	0.549396i	$0.814858\pi$
$48$	−3.11903	−0.450193
$49$	13.3376	1.90538
$50$	1.00000	0.141421
$51$	−3.49027	−0.488736
$52$	−3.72833	−0.517026
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	−11.6288	−1.58247
$55$	−4.33763	−0.584886
$56$	4.50973	0.602637
$57$	−14.0660	−1.86308
$58$	−8.23805	−1.08171
$59$	−2.23805	−0.291370	−0.145685	−	0.989331i	$-0.546539\pi$
$59$	−2.23805	−0.291370	−0.145685	+	0.989331i	$0.546539\pi$
$60$	3.11903	0.402665
$61$	3.55623	0.455329	0.227664	−	0.973740i	$-0.426891\pi$
$61$	3.55623	0.455329	0.227664	+	0.973740i	$0.426891\pi$
$62$	1.72833	0.219498
$63$	30.3429	3.82285
$64$	1.00000	0.125000
$65$	3.72833	0.462442
$66$	−13.5292	−1.66533
$67$	2.43720	0.297752	0.148876	−	0.988856i	$-0.452435\pi$
$67$	2.43720	0.297752	0.148876	+	0.988856i	$0.452435\pi$
$68$	1.11903	0.135702
$69$	3.11903	0.375487
$70$	−4.50973	−0.539015
$71$	7.11903	0.844873	0.422437	−	0.906393i	$-0.361175\pi$
$71$	7.11903	0.844873	0.422437	+	0.906393i	$0.361175\pi$
$72$	6.72833	0.792941
$73$	−9.45665	−1.10682	−0.553409	−	0.832910i	$-0.686673\pi$
$73$	−9.45665	−1.10682	−0.553409	+	0.832910i	$0.686673\pi$
$74$	−0.781399	−0.0908357
$75$	−3.11903	−0.360154
$76$	4.50973	0.517301
$77$	19.5615	2.22924
$78$	11.6288	1.31670
$79$	−14.9133	−1.67788	−0.838939	−	0.544225i	$-0.816824\pi$
$79$	−14.9133	−1.67788	−0.838939	+	0.544225i	$0.816824\pi$
$80$	−1.00000	−0.111803
$81$	16.0854	1.78727
$82$	3.90043	0.430730
$83$	2.78140	0.305298	0.152649	−	0.988280i	$-0.451220\pi$
$83$	2.78140	0.305298	0.152649	+	0.988280i	$0.451220\pi$
$84$	−14.0660	−1.53472
$85$	−1.11903	−0.121375
$86$	8.00000	0.862662
$87$	25.6947	2.75476
$88$	4.33763	0.462393
$89$	−7.69471	−0.815637	−0.407819	−	0.913063i	$-0.633710\pi$
$89$	−7.69471	−0.815637	−0.407819	+	0.913063i	$0.633710\pi$
$90$	−6.72833	−0.709228
$91$	−16.8137	−1.76256
$92$	−1.00000	−0.104257
$93$	−5.39070	−0.558989
$94$	−11.4567	−1.18166
$95$	−4.50973	−0.462688
$96$	−3.11903	−0.318334
$97$	−0.642920	−0.0652786	−0.0326393	−	0.999467i	$-0.510391\pi$
$97$	−0.642920	−0.0652786	−0.0326393	+	0.999467i	$0.510391\pi$
$98$	13.3376	1.34730
$99$	29.1850	2.93320
$100$	1.00000	0.100000
$101$	−8.23805	−0.819717	−0.409858	−	0.912149i	$-0.634422\pi$
$101$	−8.23805	−0.819717	−0.409858	+	0.912149i	$0.634422\pi$
$102$	−3.49027	−0.345589
$103$	12.3376	1.21566	0.607831	−	0.794066i	$-0.292040\pi$
$103$	12.3376	1.21566	0.607831	+	0.794066i	$0.292040\pi$
$104$	−3.72833	−0.365593
$105$	14.0660	1.37270
$106$	−6.00000	−0.582772
$107$	−15.9328	−1.54028	−0.770139	−	0.637876i	$-0.779813\pi$
$107$	−15.9328	−1.54028	−0.770139	+	0.637876i	$0.779813\pi$
$108$	−11.6288	−1.11898
$109$	−1.49027	−0.142742	−0.0713712	−	0.997450i	$-0.522737\pi$
$109$	−1.49027	−0.142742	−0.0713712	+	0.997450i	$0.522737\pi$
$110$	−4.33763	−0.413577
$111$	2.43720	0.231329
$112$	4.50973	0.426129
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−14.0660	−1.31740
$115$	1.00000	0.0932505
$116$	−8.23805	−0.764884
$117$	−25.0854	−2.31915
$118$	−2.23805	−0.206030
$119$	5.04650	0.462612
$120$	3.11903	0.284727
$121$	7.81502	0.710456
$122$	3.55623	0.321966
$123$	−12.1655	−1.09693
$124$	1.72833	0.155208
$125$	−1.00000	−0.0894427
$126$	30.3429	2.70316
$127$	−0.675256	−0.0599193	−0.0299597	−	0.999551i	$-0.509538\pi$
$127$	−0.675256	−0.0599193	−0.0299597	+	0.999551i	$0.509538\pi$
$128$	1.00000	0.0883883
$129$	−24.9522	−2.19692
$130$	3.72833	0.326996
$131$	−13.6947	−1.19651	−0.598256	−	0.801305i	$-0.704139\pi$
$131$	−13.6947	−1.19651	−0.598256	+	0.801305i	$0.704139\pi$
$132$	−13.5292	−1.17756
$133$	20.3376	1.76350
$134$	2.43720	0.210542
$135$	11.6288	1.00084
$136$	1.11903	0.0959557
$137$	7.52918	0.643261	0.321631	−	0.946865i	$-0.395769\pi$
$137$	7.52918	0.643261	0.321631	+	0.946865i	$0.395769\pi$
$138$	3.11903	0.265509
$139$	4.67526	0.396550	0.198275	−	0.980146i	$-0.436466\pi$
$139$	4.67526	0.396550	0.198275	+	0.980146i	$0.436466\pi$
$140$	−4.50973	−0.381141
$141$	35.7336	3.00931
$142$	7.11903	0.597415
$143$	−16.1721	−1.35238
$144$	6.72833	0.560694
$145$	8.23805	0.684133
$146$	−9.45665	−0.782638
$147$	−41.6004	−3.43114
$148$	−0.781399	−0.0642306
$149$	7.52918	0.616814	0.308407	−	0.951254i	$-0.400204\pi$
$149$	7.52918	0.616814	0.308407	+	0.951254i	$0.400204\pi$
$150$	−3.11903	−0.254667
$151$	−13.3571	−1.08698	−0.543492	−	0.839414i	$-0.682898\pi$
$151$	−13.3571	−1.08698	−0.543492	+	0.839414i	$0.682898\pi$
$152$	4.50973	0.365787
$153$	7.52918	0.608698
$154$	19.5615	1.57631
$155$	−1.72833	−0.138823
$156$	11.6288	0.931045
$157$	16.2381	1.29594	0.647969	−	0.761667i	$-0.275619\pi$
$157$	16.2381	1.29594	0.647969	+	0.761667i	$0.275619\pi$
$158$	−14.9133	−1.18644
$159$	18.7142	1.48413
$160$	−1.00000	−0.0790569
$161$	−4.50973	−0.355416
$162$	16.0854	1.26379
$163$	−3.29112	−0.257781	−0.128890	−	0.991659i	$-0.541142\pi$
$163$	−3.29112	−0.257781	−0.128890	+	0.991659i	$0.541142\pi$
$164$	3.90043	0.304572
$165$	13.5292	1.05325
$166$	2.78140	0.215878
$167$	22.9133	1.77309	0.886543	−	0.462647i	$-0.153100\pi$
$167$	22.9133	1.77309	0.886543	+	0.462647i	$0.153100\pi$
$168$	−14.0660	−1.08521
$169$	0.900425	0.0692635
$170$	−1.11903	−0.0858254
$171$	30.3429	2.32038
$172$	8.00000	0.609994
$173$	0.575681	0.0437683	0.0218841	−	0.999761i	$-0.493034\pi$
$173$	0.575681	0.0437683	0.0218841	+	0.999761i	$0.493034\pi$
$174$	25.6947	1.94791
$175$	4.50973	0.340903
$176$	4.33763	0.326961
$177$	6.98055	0.524690
$178$	−7.69471	−0.576743
$179$	5.01945	0.375171	0.187586	−	0.982248i	$-0.439934\pi$
$179$	5.01945	0.375171	0.187586	+	0.982248i	$0.439934\pi$
$180$	−6.72833	−0.501500
$181$	−11.5292	−0.856957	−0.428479	−	0.903552i	$-0.640950\pi$
$181$	−11.5292	−0.856957	−0.428479	+	0.903552i	$0.640950\pi$
$182$	−16.8137	−1.24632
$183$	−11.0920	−0.819942
$184$	−1.00000	−0.0737210
$185$	0.781399	0.0574496
$186$	−5.39070	−0.395265
$187$	4.85392	0.354954
$188$	−11.4567	−0.835562
$189$	−52.4425	−3.81463
$190$	−4.50973	−0.327170
$191$	−18.7142	−1.35411	−0.677055	−	0.735933i	$-0.736744\pi$
$191$	−18.7142	−1.35411	−0.677055	+	0.735933i	$0.736744\pi$
$192$	−3.11903	−0.225096
$193$	23.4956	1.69125	0.845624	−	0.533780i	$-0.179229\pi$
$193$	23.4956	1.69125	0.845624	+	0.533780i	$0.179229\pi$
$194$	−0.642920	−0.0461590
$195$	−11.6288	−0.832752
$196$	13.3376	0.952688
$197$	−18.1385	−1.29231	−0.646157	−	0.763205i	$-0.723625\pi$
$197$	−18.1385	−1.29231	−0.646157	+	0.763205i	$0.723625\pi$
$198$	29.1850	2.07409
$199$	−23.2575	−1.64868	−0.824340	−	0.566094i	$-0.808454\pi$
$199$	−23.2575	−1.64868	−0.824340	+	0.566094i	$0.808454\pi$
$200$	1.00000	0.0707107
$201$	−7.60170	−0.536183
$202$	−8.23805	−0.579627
$203$	−37.1514	−2.60751
$204$	−3.49027	−0.244368
$205$	−3.90043	−0.272418
$206$	12.3376	0.859603
$207$	−6.72833	−0.467651
$208$	−3.72833	−0.258513
$209$	19.5615	1.35310
$210$	14.0660	0.970643
$211$	4.34420	0.299067	0.149533	−	0.988757i	$-0.452223\pi$
$211$	4.34420	0.299067	0.149533	+	0.988757i	$0.452223\pi$
$212$	−6.00000	−0.412082
$213$	−22.2044	−1.52142
$214$	−15.9328	−1.08914
$215$	−8.00000	−0.545595
$216$	−11.6288	−0.791236
$217$	7.79428	0.529110
$218$	−1.49027	−0.100934
$219$	29.4956	1.99313
$220$	−4.33763	−0.292443
$221$	−4.17210	−0.280646
$222$	2.43720	0.163574
$223$	12.4761	0.835462	0.417731	−	0.908571i	$-0.362825\pi$
$223$	12.4761	0.835462	0.417731	+	0.908571i	$0.362825\pi$
$224$	4.50973	0.301319
$225$	6.72833	0.448555
$226$	−6.00000	−0.399114
$227$	15.9328	1.05749	0.528747	−	0.848779i	$-0.322662\pi$
$227$	15.9328	1.05749	0.528747	+	0.848779i	$0.322662\pi$
$228$	−14.0660	−0.931541
$229$	−3.56280	−0.235436	−0.117718	−	0.993047i	$-0.537558\pi$
$229$	−3.56280	−0.235436	−0.117718	+	0.993047i	$0.537558\pi$
$230$	1.00000	0.0659380
$231$	−61.0129	−4.01435
$232$	−8.23805	−0.540855
$233$	−27.4956	−1.80129	−0.900647	−	0.434552i	$-0.856907\pi$
$233$	−27.4956	−1.80129	−0.900647	+	0.434552i	$0.856907\pi$
$234$	−25.0854	−1.63988
$235$	11.4567	0.747350
$236$	−2.23805	−0.145685
$237$	46.5150	3.02147
$238$	5.04650	0.327116
$239$	10.0389	0.649363	0.324681	−	0.945823i	$-0.394743\pi$
$239$	10.0389	0.649363	0.324681	+	0.945823i	$0.394743\pi$
$240$	3.11903	0.201332
$241$	−23.6947	−1.52631	−0.763155	−	0.646215i	$-0.776351\pi$
$241$	−23.6947	−1.52631	−0.763155	+	0.646215i	$0.776351\pi$
$242$	7.81502	0.502368
$243$	−15.2846	−0.980505
$244$	3.55623	0.227664
$245$	−13.3376	−0.852110
$246$	−12.1655	−0.775646
$247$	−16.8137	−1.06983
$248$	1.72833	0.109749
$249$	−8.67526	−0.549772
$250$	−1.00000	−0.0632456
$251$	12.4425	0.785363	0.392681	−	0.919675i	$-0.371548\pi$
$251$	12.4425	0.785363	0.392681	+	0.919675i	$0.371548\pi$
$252$	30.3429	1.91142
$253$	−4.33763	−0.272704
$254$	−0.675256	−0.0423693
$255$	3.49027	0.218569
$256$	1.00000	0.0625000
$257$	5.45665	0.340377	0.170188	−	0.985412i	$-0.445562\pi$
$257$	5.45665	0.340377	0.170188	+	0.985412i	$0.445562\pi$
$258$	−24.9522	−1.55346
$259$	−3.52389	−0.218964
$260$	3.72833	0.231221
$261$	−55.4283	−3.43093
$262$	−13.6947	−0.846062
$263$	0.138479	0.00853895	0.00426948	−	0.999991i	$-0.498641\pi$
$263$	0.138479	0.00853895	0.00426948	+	0.999991i	$0.498641\pi$
$264$	−13.5292	−0.832663
$265$	6.00000	0.368577
$266$	20.3376	1.24698
$267$	24.0000	1.46878
$268$	2.43720	0.148876
$269$	14.6753	0.894766	0.447383	−	0.894342i	$-0.352356\pi$
$269$	14.6753	0.894766	0.447383	+	0.894342i	$0.352356\pi$
$270$	11.6288	0.707703
$271$	−8.31058	−0.504832	−0.252416	−	0.967619i	$-0.581225\pi$
$271$	−8.31058	−0.504832	−0.252416	+	0.967619i	$0.581225\pi$
$272$	1.11903	0.0678510
$273$	52.4425	3.17396
$274$	7.52918	0.454854
$275$	4.33763	0.261569
$276$	3.11903	0.187743
$277$	12.9133	0.775886	0.387943	−	0.921683i	$-0.373186\pi$
$277$	12.9133	0.775886	0.387943	+	0.921683i	$0.373186\pi$
$278$	4.67526	0.280403
$279$	11.6288	0.696195
$280$	−4.50973	−0.269508
$281$	2.67526	0.159592	0.0797962	−	0.996811i	$-0.474573\pi$
$281$	2.67526	0.159592	0.0797962	+	0.996811i	$0.474573\pi$
$282$	35.7336	2.12791
$283$	0.742495	0.0441367	0.0220684	−	0.999756i	$-0.492975\pi$
$283$	0.742495	0.0441367	0.0220684	+	0.999756i	$0.492975\pi$
$284$	7.11903	0.422437
$285$	14.0660	0.833195
$286$	−16.1721	−0.956276
$287$	17.5898	1.03830
$288$	6.72833	0.396470
$289$	−15.7478	−0.926340
$290$	8.23805	0.483755
$291$	2.00528	0.117552
$292$	−9.45665	−0.553409
$293$	−6.00000	−0.350524	−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000	−0.350524	−0.175262	+	0.984522i	$0.556077\pi$
$294$	−41.6004	−2.42619
$295$	2.23805	0.130305
$296$	−0.781399	−0.0454179
$297$	−50.4412	−2.92690
$298$	7.52918	0.436154
$299$	3.72833	0.215615
$300$	−3.11903	−0.180077
$301$	36.0778	2.07949
$302$	−13.3571	−0.768614
$303$	25.6947	1.47612
$304$	4.50973	0.258651
$305$	−3.55623	−0.203629
$306$	7.52918	0.430414
$307$	30.5084	1.74121	0.870604	−	0.491984i	$-0.163728\pi$
$307$	30.5084	1.74121	0.870604	+	0.491984i	$0.163728\pi$
$308$	19.5615	1.11462
$309$	−38.4814	−2.18913
$310$	−1.72833	−0.0981624
$311$	5.56280	0.315437	0.157719	−	0.987484i	$-0.449586\pi$
$311$	5.56280	0.315437	0.157719	+	0.987484i	$0.449586\pi$
$312$	11.6288	0.658348
$313$	4.07252	0.230193	0.115096	−	0.993354i	$-0.463282\pi$
$313$	4.07252	0.230193	0.115096	+	0.993354i	$0.463282\pi$
$314$	16.2381	0.916366
$315$	−30.3429	−1.70963
$316$	−14.9133	−0.838939
$317$	−6.16553	−0.346291	−0.173145	−	0.984896i	$-0.555393\pi$
$317$	−6.16553	−0.346291	−0.173145	+	0.984896i	$0.555393\pi$
$318$	18.7142	1.04944
$319$	−35.7336	−2.00070
$320$	−1.00000	−0.0559017
$321$	49.6947	2.77369
$322$	−4.50973	−0.251317
$323$	5.04650	0.280795
$324$	16.0854	0.893634
$325$	−3.72833	−0.206810
$326$	−3.29112	−0.182279
$327$	4.64820	0.257046
$328$	3.90043	0.215365
$329$	−51.6664	−2.84846
$330$	13.5292	0.744757
$331$	27.5886	1.51640	0.758202	−	0.652019i	$-0.226078\pi$
$331$	27.5886	1.51640	0.758202	+	0.652019i	$0.226078\pi$
$332$	2.78140	0.152649
$333$	−5.25751	−0.288110
$334$	22.9133	1.25376
$335$	−2.43720	−0.133159
$336$	−14.0660	−0.767361
$337$	−17.4230	−0.949093	−0.474547	−	0.880230i	$-0.657388\pi$
$337$	−17.4230	−0.949093	−0.474547	+	0.880230i	$0.657388\pi$
$338$	0.900425	0.0489767
$339$	18.7142	1.01641
$340$	−1.11903	−0.0606877
$341$	7.49684	0.405977
$342$	30.3429	1.64076
$343$	28.5810	1.54323
$344$	8.00000	0.431331
$345$	−3.11903	−0.167923
$346$	0.575681	0.0309488
$347$	4.88097	0.262024	0.131012	−	0.991381i	$-0.458177\pi$
$347$	4.88097	0.262024	0.131012	+	0.991381i	$0.458177\pi$
$348$	25.6947	1.37738
$349$	24.0389	1.28677	0.643387	−	0.765542i	$-0.277529\pi$
$349$	24.0389	1.28677	0.643387	+	0.765542i	$0.277529\pi$
$350$	4.50973	0.241055
$351$	43.3558	2.31416
$352$	4.33763	0.231196
$353$	−14.3442	−0.763464	−0.381732	−	0.924273i	$-0.624672\pi$
$353$	−14.3442	−0.763464	−0.381732	+	0.924273i	$0.624672\pi$
$354$	6.98055	0.371012
$355$	−7.11903	−0.377839
$356$	−7.69471	−0.407819
$357$	−15.7402	−0.833059
$358$	5.01945	0.265286
$359$	26.7814	1.41347	0.706734	−	0.707479i	$-0.250168\pi$
$359$	26.7814	1.41347	0.706734	+	0.707479i	$0.250168\pi$
$360$	−6.72833	−0.354614
$361$	1.33763	0.0704015
$362$	−11.5292	−0.605960
$363$	−24.3752	−1.27937
$364$	−16.8137	−0.881279
$365$	9.45665	0.494984
$366$	−11.0920	−0.579787
$367$	−20.4761	−1.06884	−0.534422	−	0.845218i	$-0.679471\pi$
$367$	−20.4761	−1.06884	−0.534422	+	0.845218i	$0.679471\pi$
$368$	−1.00000	−0.0521286
$369$	26.2433	1.36617
$370$	0.781399	0.0406230
$371$	−27.0584	−1.40480
$372$	−5.39070	−0.279495
$373$	−3.89386	−0.201616	−0.100808	−	0.994906i	$-0.532143\pi$
$373$	−3.89386	−0.201616	−0.100808	+	0.994906i	$0.532143\pi$
$374$	4.85392	0.250990
$375$	3.11903	0.161066
$376$	−11.4567	−0.590832
$377$	30.7142	1.58186
$378$	−52.4425	−2.69735
$379$	−30.3765	−1.56034	−0.780169	−	0.625569i	$-0.784867\pi$
$379$	−30.3765	−1.56034	−0.780169	+	0.625569i	$0.784867\pi$
$380$	−4.50973	−0.231344
$381$	2.10614	0.107901
$382$	−18.7142	−0.957500
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	−3.11903	−0.159167
$385$	−19.5615	−0.996947
$386$	23.4956	1.19589
$387$	53.8266	2.73616
$388$	−0.642920	−0.0326393
$389$	−18.6818	−0.947206	−0.473603	−	0.880738i	$-0.657047\pi$
$389$	−18.6818	−0.947206	−0.473603	+	0.880738i	$0.657047\pi$
$390$	−11.6288	−0.588845
$391$	−1.11903	−0.0565916
$392$	13.3376	0.673652
$393$	42.7142	2.15464
$394$	−18.1385	−0.913803
$395$	14.9133	0.750370
$396$	29.1850	1.46660
$397$	−28.5757	−1.43417	−0.717086	−	0.696985i	$-0.754525\pi$
$397$	−28.5757	−1.43417	−0.717086	+	0.696985i	$0.754525\pi$
$398$	−23.2575	−1.16579
$399$	−63.4336	−3.17565
$400$	1.00000	0.0500000
$401$	12.1061	0.604552	0.302276	−	0.953220i	$-0.402254\pi$
$401$	12.1061	0.604552	0.302276	+	0.953220i	$0.402254\pi$
$402$	−7.60170	−0.379138
$403$	−6.44377	−0.320987
$404$	−8.23805	−0.409858
$405$	−16.0854	−0.799290
$406$	−37.1514	−1.84379
$407$	−3.38942	−0.168007
$408$	−3.49027	−0.172794
$409$	25.2911	1.25057	0.625283	−	0.780398i	$-0.284984\pi$
$409$	25.2911	1.25057	0.625283	+	0.780398i	$0.284984\pi$
$410$	−3.90043	−0.192628
$411$	−23.4837	−1.15837
$412$	12.3376	0.607831
$413$	−10.0930	−0.496644
$414$	−6.72833	−0.330679
$415$	−2.78140	−0.136533
$416$	−3.72833	−0.182796
$417$	−14.5822	−0.714096
$418$	19.5615	0.956785
$419$	−17.3505	−0.847628	−0.423814	−	0.905749i	$-0.639309\pi$
$419$	−17.3505	−0.847628	−0.423814	+	0.905749i	$0.639309\pi$
$420$	14.0660	0.686348
$421$	21.4230	1.04409	0.522047	−	0.852916i	$-0.325168\pi$
$421$	21.4230	1.04409	0.522047	+	0.852916i	$0.325168\pi$
$422$	4.34420	0.211472
$423$	−77.0841	−3.74796
$424$	−6.00000	−0.291386
$425$	1.11903	0.0542808
$426$	−22.2044	−1.07581
$427$	16.0376	0.776115
$428$	−15.9328	−0.770139
$429$	50.4412	2.43532
$430$	−8.00000	−0.385794
$431$	22.5822	1.08775	0.543874	−	0.839167i	$-0.316957\pi$
$431$	22.5822	1.08775	0.543874	+	0.839167i	$0.316957\pi$
$432$	−11.6288	−0.559489
$433$	1.01417	0.0487378	0.0243689	−	0.999703i	$-0.492242\pi$
$433$	1.01417	0.0487378	0.0243689	+	0.999703i	$0.492242\pi$
$434$	7.79428	0.374138
$435$	−25.6947	−1.23197
$436$	−1.49027	−0.0713712
$437$	−4.50973	−0.215729
$438$	29.4956	1.40935
$439$	−26.7478	−1.27660	−0.638301	−	0.769787i	$-0.720362\pi$
$439$	−26.7478	−1.27660	−0.638301	+	0.769787i	$0.720362\pi$
$440$	−4.33763	−0.206788
$441$	89.7399	4.27333
$442$	−4.17210	−0.198446
$443$	10.2044	0.484827	0.242414	−	0.970173i	$-0.422061\pi$
$443$	10.2044	0.484827	0.242414	+	0.970173i	$0.422061\pi$
$444$	2.43720	0.115665
$445$	7.69471	0.364764
$446$	12.4761	0.590761
$447$	−23.4837	−1.11074
$448$	4.50973	0.213065
$449$	38.7867	1.83046	0.915228	−	0.402936i	$-0.132010\pi$
$449$	38.7867	1.83046	0.915228	+	0.402936i	$0.132010\pi$
$450$	6.72833	0.317176
$451$	16.9186	0.796665
$452$	−6.00000	−0.282216
$453$	41.6611	1.95741
$454$	15.9328	0.747762
$455$	16.8137	0.788240
$456$	−14.0660	−0.658699
$457$	34.9522	1.63500	0.817498	−	0.575932i	$-0.195361\pi$
$457$	34.9522	1.63500	0.817498	+	0.575932i	$0.195361\pi$
$458$	−3.56280	−0.166479
$459$	−13.0129	−0.607389
$460$	1.00000	0.0466252
$461$	16.3700	0.762425	0.381213	−	0.924487i	$-0.375507\pi$
$461$	16.3700	0.762425	0.381213	+	0.924487i	$0.375507\pi$
$462$	−61.0129	−2.83858
$463$	29.2186	1.35790	0.678952	−	0.734183i	$-0.262435\pi$
$463$	29.2186	1.35790	0.678952	+	0.734183i	$0.262435\pi$
$464$	−8.23805	−0.382442
$465$	5.39070	0.249988
$466$	−27.4956	−1.27371
$467$	24.2770	1.12340	0.561702	−	0.827340i	$-0.310147\pi$
$467$	24.2770	1.12340	0.561702	+	0.827340i	$0.310147\pi$
$468$	−25.0854	−1.15957
$469$	10.9911	0.507523
$470$	11.4567	0.528456
$471$	−50.6469	−2.33369
$472$	−2.23805	−0.103015
$473$	34.7010	1.59555
$474$	46.5150	2.13651
$475$	4.50973	0.206920
$476$	5.04650	0.231306
$477$	−40.3700	−1.84841
$478$	10.0389	0.459169
$479$	24.6080	1.12437	0.562185	−	0.827012i	$-0.309961\pi$
$479$	24.6080	1.12437	0.562185	+	0.827012i	$0.309961\pi$
$480$	3.11903	0.142363
$481$	2.91331	0.132835
$482$	−23.6947	−1.07926
$483$	14.0660	0.640023
$484$	7.81502	0.355228
$485$	0.642920	0.0291935
$486$	−15.2846	−0.693322
$487$	−30.2381	−1.37022	−0.685108	−	0.728441i	$-0.740245\pi$
$487$	−30.2381	−1.37022	−0.685108	+	0.728441i	$0.740245\pi$
$488$	3.55623	0.160983
$489$	10.2651	0.464204
$490$	−13.3376	−0.602533
$491$	12.3311	0.556493	0.278246	−	0.960510i	$-0.410247\pi$
$491$	12.3311	0.556493	0.278246	+	0.960510i	$0.410247\pi$
$492$	−12.1655	−0.548464
$493$	−9.21860	−0.415185
$494$	−16.8137	−0.756486
$495$	−29.1850	−1.31177
$496$	1.72833	0.0776042
$497$	32.1049	1.44010
$498$	−8.67526	−0.388748
$499$	−26.9133	−1.20481	−0.602403	−	0.798192i	$-0.705790\pi$
$499$	−26.9133	−1.20481	−0.602403	+	0.798192i	$0.705790\pi$
$500$	−1.00000	−0.0447214
$501$	−71.4672	−3.19292
$502$	12.4425	0.555335
$503$	20.5097	0.914483	0.457242	−	0.889342i	$-0.348837\pi$
$503$	20.5097	0.914483	0.457242	+	0.889342i	$0.348837\pi$
$504$	30.3429	1.35158
$505$	8.23805	0.366589
$506$	−4.33763	−0.192831
$507$	−2.80845	−0.124728
$508$	−0.675256	−0.0299597
$509$	−36.7142	−1.62733	−0.813663	−	0.581336i	$-0.802530\pi$
$509$	−36.7142	−1.62733	−0.813663	+	0.581336i	$0.802530\pi$
$510$	3.49027	0.154552
$511$	−42.6469	−1.88659
$512$	1.00000	0.0441942
$513$	−52.4425	−2.31539
$514$	5.45665	0.240683
$515$	−12.3376	−0.543661
$516$	−24.9522	−1.09846
$517$	−49.6947	−2.18557
$518$	−3.52389	−0.154831
$519$	−1.79557	−0.0788166
$520$	3.72833	0.163498
$521$	−4.91331	−0.215256	−0.107628	−	0.994191i	$-0.534326\pi$
$521$	−4.91331	−0.215256	−0.107628	+	0.994191i	$0.534326\pi$
$522$	−55.4283	−2.42603
$523$	−0.344196	−0.0150506	−0.00752531	−	0.999972i	$-0.502395\pi$
$523$	−0.344196	−0.0150506	−0.00752531	+	0.999972i	$0.502395\pi$
$524$	−13.6947	−0.598256
$525$	−14.0660	−0.613889
$526$	0.138479	0.00603795
$527$	1.93404	0.0842483
$528$	−13.5292	−0.588782
$529$	1.00000	0.0434783
$530$	6.00000	0.260623
$531$	−15.0584	−0.653477
$532$	20.3376	0.881748
$533$	−14.5421	−0.629887
$534$	24.0000	1.03858
$535$	15.9328	0.688833
$536$	2.43720	0.105271
$537$	−15.6558	−0.675598
$538$	14.6753	0.632695
$539$	57.8537	2.49193
$540$	11.6288	0.500422
$541$	−6.13191	−0.263631	−0.131816	−	0.991274i	$-0.542081\pi$
$541$	−6.13191	−0.263631	−0.131816	+	0.991274i	$0.542081\pi$
$542$	−8.31058	−0.356970
$543$	35.9598	1.54318
$544$	1.11903	0.0479779
$545$	1.49027	0.0638363
$546$	52.4425	2.24433
$547$	−9.18498	−0.392721	−0.196361	−	0.980532i	$-0.562912\pi$
$547$	−9.18498	−0.392721	−0.196361	+	0.980532i	$0.562912\pi$
$548$	7.52918	0.321631
$549$	23.9275	1.02120
$550$	4.33763	0.184957
$551$	−37.1514	−1.58270
$552$	3.11903	0.132755
$553$	−67.2549	−2.85997
$554$	12.9133	0.548634
$555$	−2.43720	−0.103454
$556$	4.67526	0.198275
$557$	−4.30529	−0.182421	−0.0912105	−	0.995832i	$-0.529074\pi$
$557$	−4.30529	−0.182421	−0.0912105	+	0.995832i	$0.529074\pi$
$558$	11.6288	0.492284
$559$	−29.8266	−1.26153
$560$	−4.50973	−0.190571
$561$	−15.1395	−0.639191
$562$	2.67526	0.112849
$563$	11.1256	0.468888	0.234444	−	0.972130i	$-0.424673\pi$
$563$	11.1256	0.468888	0.234444	+	0.972130i	$0.424673\pi$
$564$	35.7336	1.50466
$565$	6.00000	0.252422
$566$	0.742495	0.0312094
$567$	72.5408	3.04643
$568$	7.11903	0.298708
$569$	−16.0389	−0.672386	−0.336193	−	0.941793i	$-0.609139\pi$
$569$	−16.0389	−0.672386	−0.336193	+	0.941793i	$0.609139\pi$
$570$	14.0660	0.589158
$571$	17.9004	0.749109	0.374555	−	0.927205i	$-0.377796\pi$
$571$	17.9004	0.749109	0.374555	+	0.927205i	$0.377796\pi$
$572$	−16.1721	−0.676189
$573$	58.3700	2.43844
$574$	17.5898	0.734186
$575$	−1.00000	−0.0417029
$576$	6.72833	0.280347
$577$	−9.12559	−0.379903	−0.189952	−	0.981793i	$-0.560833\pi$
$577$	−9.12559	−0.379903	−0.189952	+	0.981793i	$0.560833\pi$
$578$	−15.7478	−0.655021
$579$	−73.2833	−3.04555
$580$	8.23805	0.342067
$581$	12.5433	0.520386
$582$	2.00528	0.0831217
$583$	−26.0258	−1.07788
$584$	−9.45665	−0.391319
$585$	25.0854	1.03715
$586$	−6.00000	−0.247858
$587$	−33.6340	−1.38823	−0.694113	−	0.719866i	$-0.744203\pi$
$587$	−33.6340	−1.38823	−0.694113	+	0.719866i	$0.744203\pi$
$588$	−41.6004	−1.71557
$589$	7.79428	0.321158
$590$	2.23805	0.0921392
$591$	56.5744	2.32716
$592$	−0.781399	−0.0321153
$593$	−17.4567	−0.716859	−0.358429	−	0.933557i	$-0.616688\pi$
$593$	−17.4567	−0.716859	−0.358429	+	0.933557i	$0.616688\pi$
$594$	−50.4412	−2.06963
$595$	−5.04650	−0.206886
$596$	7.52918	0.308407
$597$	72.5408	2.96890
$598$	3.72833	0.152463
$599$	−11.5951	−0.473764	−0.236882	−	0.971538i	$-0.576126\pi$
$599$	−11.5951	−0.473764	−0.236882	+	0.971538i	$0.576126\pi$
$600$	−3.11903	−0.127334
$601$	−31.6611	−1.29148	−0.645741	−	0.763556i	$-0.723452\pi$
$601$	−31.6611	−1.29148	−0.645741	+	0.763556i	$0.723452\pi$
$602$	36.0778	1.47042
$603$	16.3983	0.667790
$604$	−13.3571	−0.543492
$605$	−7.81502	−0.317726
$606$	25.6947	1.04378
$607$	−36.0778	−1.46435	−0.732177	−	0.681115i	$-0.761495\pi$
$607$	−36.0778	−1.46435	−0.732177	+	0.681115i	$0.761495\pi$
$608$	4.50973	0.182894
$609$	115.876	4.69554
$610$	−3.55623	−0.143988
$611$	42.7142	1.72803
$612$	7.52918	0.304349
$613$	−32.0389	−1.29404	−0.647020	−	0.762473i	$-0.723985\pi$
$613$	−32.0389	−1.29404	−0.647020	+	0.762473i	$0.723985\pi$
$614$	30.5084	1.23122
$615$	12.1655	0.490562
$616$	19.5615	0.788156
$617$	−13.3960	−0.539302	−0.269651	−	0.962958i	$-0.586908\pi$
$617$	−13.3960	−0.539302	−0.269651	+	0.962958i	$0.586908\pi$
$618$	−38.4814	−1.54795
$619$	37.1309	1.49242	0.746208	−	0.665713i	$-0.231872\pi$
$619$	37.1309	1.49242	0.746208	+	0.665713i	$0.231872\pi$
$620$	−1.72833	−0.0694113
$621$	11.6288	0.466646
$622$	5.56280	0.223048
$623$	−34.7010	−1.39027
$624$	11.6288	0.465523
$625$	1.00000	0.0400000
$626$	4.07252	0.162771
$627$	−61.0129	−2.43662
$628$	16.2381	0.647969
$629$	−0.874406	−0.0348648
$630$	−30.3429	−1.20889
$631$	11.1125	0.442380	0.221190	−	0.975231i	$-0.429006\pi$
$631$	11.1125	0.442380	0.221190	+	0.975231i	$0.429006\pi$
$632$	−14.9133	−0.593220
$633$	−13.5497	−0.538551
$634$	−6.16553	−0.244864
$635$	0.675256	0.0267967
$636$	18.7142	0.742065
$637$	−49.7270	−1.97026
$638$	−35.7336	−1.41471
$639$	47.8991	1.89486
$640$	−1.00000	−0.0395285
$641$	12.3831	0.489103	0.244552	−	0.969636i	$-0.421359\pi$
$641$	12.3831	0.489103	0.244552	+	0.969636i	$0.421359\pi$
$642$	49.6947	1.96129
$643$	−37.4956	−1.47868	−0.739340	−	0.673332i	$-0.764862\pi$
$643$	−37.4956	−1.47868	−0.739340	+	0.673332i	$0.764862\pi$
$644$	−4.50973	−0.177708
$645$	24.9522	0.982492
$646$	5.04650	0.198552
$647$	14.5691	0.572771	0.286385	−	0.958114i	$-0.407546\pi$
$647$	14.5691	0.572771	0.286385	+	0.958114i	$0.407546\pi$
$648$	16.0854	0.631894
$649$	−9.70784	−0.381066
$650$	−3.72833	−0.146237
$651$	−24.3106	−0.952807
$652$	−3.29112	−0.128890
$653$	−4.41672	−0.172840	−0.0864198	−	0.996259i	$-0.527543\pi$
$653$	−4.41672	−0.172840	−0.0864198	+	0.996259i	$0.527543\pi$
$654$	4.64820	0.181759
$655$	13.6947	0.535097
$656$	3.90043	0.152286
$657$	−63.6275	−2.48234
$658$	−51.6664	−2.01416
$659$	−31.8655	−1.24130	−0.620652	−	0.784086i	$-0.713132\pi$
$659$	−31.8655	−1.24130	−0.620652	+	0.784086i	$0.713132\pi$
$660$	13.5292	0.526623
$661$	33.1190	1.28818	0.644090	−	0.764949i	$-0.277236\pi$
$661$	33.1190	1.28818	0.644090	+	0.764949i	$0.277236\pi$
$662$	27.5886	1.07226
$663$	13.0129	0.505379
$664$	2.78140	0.107939
$665$	−20.3376	−0.788659
$666$	−5.25751	−0.203724
$667$	8.23805	0.318979
$668$	22.9133	0.886543
$669$	−38.9133	−1.50448
$670$	−2.43720	−0.0941574
$671$	15.4256	0.595499
$672$	−14.0660	−0.542606
$673$	19.3505	0.745907	0.372954	−	0.927850i	$-0.378345\pi$
$673$	19.3505	0.745907	0.372954	+	0.927850i	$0.378345\pi$
$674$	−17.4230	−0.671110
$675$	−11.6288	−0.447591
$676$	0.900425	0.0346317
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	18.7142	0.718713
$679$	−2.89939	−0.111268
$680$	−1.11903	−0.0429127
$681$	−49.6947	−1.90431
$682$	7.49684	0.287069
$683$	38.3495	1.46740	0.733701	−	0.679472i	$-0.237791\pi$
$683$	38.3495	1.46740	0.733701	+	0.679472i	$0.237791\pi$
$684$	30.3429	1.16019
$685$	−7.52918	−0.287675
$686$	28.5810	1.09123
$687$	11.1125	0.423967
$688$	8.00000	0.304997
$689$	22.3700	0.852228
$690$	−3.11903	−0.118739
$691$	−21.0195	−0.799618	−0.399809	−	0.916599i	$-0.630923\pi$
$691$	−21.0195	−0.799618	−0.399809	+	0.916599i	$0.630923\pi$
$692$	0.575681	0.0218841
$693$	131.616	4.99969
$694$	4.88097	0.185279
$695$	−4.67526	−0.177343
$696$	25.6947	0.973955
$697$	4.36468	0.165324
$698$	24.0389	0.909886
$699$	85.7594	3.24372
$700$	4.50973	0.170452
$701$	19.3169	0.729589	0.364794	−	0.931088i	$-0.381139\pi$
$701$	19.3169	0.729589	0.364794	+	0.931088i	$0.381139\pi$
$702$	43.3558	1.63636
$703$	−3.52389	−0.132906
$704$	4.33763	0.163481
$705$	−35.7336	−1.34581
$706$	−14.3442	−0.539851
$707$	−37.1514	−1.39722
$708$	6.98055	0.262345
$709$	12.2315	0.459363	0.229682	−	0.973266i	$-0.426232\pi$
$709$	12.2315	0.459363	0.229682	+	0.973266i	$0.426232\pi$
$710$	−7.11903	−0.267172
$711$	−100.342	−3.76311
$712$	−7.69471	−0.288371
$713$	−1.72833	−0.0647264
$714$	−15.7402	−0.589061
$715$	16.1721	0.604802
$716$	5.01945	0.187586
$717$	−31.3116	−1.16935
$718$	26.7814	0.999473
$719$	−40.6416	−1.51568	−0.757839	−	0.652442i	$-0.773745\pi$
$719$	−40.6416	−1.51568	−0.757839	+	0.652442i	$0.773745\pi$
$720$	−6.72833	−0.250750
$721$	55.6393	2.07212
$722$	1.33763	0.0497814
$723$	73.9044	2.74854
$724$	−11.5292	−0.428479
$725$	−8.23805	−0.305954
$726$	−24.3752	−0.904650
$727$	−23.4501	−0.869716	−0.434858	−	0.900499i	$-0.643201\pi$
$727$	−23.4501	−0.869716	−0.434858	+	0.900499i	$0.643201\pi$
$728$	−16.8137	−0.623158
$729$	−0.583281	−0.0216030
$730$	9.45665	0.350006
$731$	8.95221	0.331110
$732$	−11.0920	−0.409971
$733$	−12.5150	−0.462252	−0.231126	−	0.972924i	$-0.574241\pi$
$733$	−12.5150	−0.462252	−0.231126	+	0.972924i	$0.574241\pi$
$734$	−20.4761	−0.755787
$735$	41.6004	1.53445
$736$	−1.00000	−0.0368605
$737$	10.5717	0.389413
$738$	26.2433	0.966031
$739$	−21.3505	−0.785391	−0.392696	−	0.919668i	$-0.628457\pi$
$739$	−21.3505	−0.785391	−0.392696	+	0.919668i	$0.628457\pi$
$740$	0.781399	0.0287248
$741$	52.4425	1.92652
$742$	−27.0584	−0.993343
$743$	24.9858	0.916641	0.458321	−	0.888787i	$-0.348451\pi$
$743$	24.9858	0.916641	0.458321	+	0.888787i	$0.348451\pi$
$744$	−5.39070	−0.197633
$745$	−7.52918	−0.275848
$746$	−3.89386	−0.142564
$747$	18.7142	0.684715
$748$	4.85392	0.177477
$749$	−71.8524	−2.62543
$750$	3.11903	0.113891
$751$	−33.6275	−1.22708	−0.613542	−	0.789662i	$-0.710256\pi$
$751$	−33.6275	−1.22708	−0.613542	+	0.789662i	$0.710256\pi$
$752$	−11.4567	−0.417781
$753$	−38.8085	−1.41426
$754$	30.7142	1.11854
$755$	13.3571	0.486114
$756$	−52.4425	−1.90731
$757$	−37.1230	−1.34926	−0.674630	−	0.738156i	$-0.735697\pi$
$757$	−37.1230	−1.34926	−0.674630	+	0.738156i	$0.735697\pi$
$758$	−30.3765	−1.10333
$759$	13.5292	0.491078
$760$	−4.50973	−0.163585
$761$	−3.87337	−0.140410	−0.0702048	−	0.997533i	$-0.522365\pi$
$761$	−3.87337	−0.140410	−0.0702048	+	0.997533i	$0.522365\pi$
$762$	2.10614	0.0762975
$763$	−6.72073	−0.243307
$764$	−18.7142	−0.677055
$765$	−7.52918	−0.272218
$766$	0	0
$767$	8.34420	0.301291
$768$	−3.11903	−0.112548
$769$	23.1645	0.835333	0.417667	−	0.908600i	$-0.362848\pi$
$769$	23.1645	0.835333	0.417667	+	0.908600i	$0.362848\pi$
$770$	−19.5615	−0.704948
$771$	−17.0195	−0.612941
$772$	23.4956	0.845624
$773$	−8.78140	−0.315845	−0.157922	−	0.987452i	$-0.550480\pi$
$773$	−8.78140	−0.315845	−0.157922	+	0.987452i	$0.550480\pi$
$774$	53.8266	1.93476
$775$	1.72833	0.0620834
$776$	−0.642920	−0.0230795
$777$	10.9911	0.394304
$778$	−18.6818	−0.669776
$779$	17.5898	0.630222
$780$	−11.6288	−0.416376
$781$	30.8797	1.10496
$782$	−1.11903	−0.0400163
$783$	95.7983	3.42355
$784$	13.3376	0.476344
$785$	−16.2381	−0.579561
$786$	42.7142	1.52356
$787$	49.6275	1.76903	0.884514	−	0.466513i	$-0.154490\pi$
$787$	49.6275	1.76903	0.884514	+	0.466513i	$0.154490\pi$
$788$	−18.1385	−0.646157
$789$	−0.431918	−0.0153767
$790$	14.9133	0.530592
$791$	−27.0584	−0.962084
$792$	29.1850	1.03704
$793$	−13.2588	−0.470833
$794$	−28.5757	−1.01411
$795$	−18.7142	−0.663723
$796$	−23.2575	−0.824340
$797$	18.3311	0.649319	0.324660	−	0.945831i	$-0.394750\pi$
$797$	18.3311	0.649319	0.324660	+	0.945831i	$0.394750\pi$
$798$	−63.4336	−2.24553
$799$	−12.8203	−0.453550
$800$	1.00000	0.0353553
$801$	−51.7725	−1.82929
$802$	12.1061	0.427483
$803$	−41.0195	−1.44755
$804$	−7.60170	−0.268091
$805$	4.50973	0.158947
$806$	−6.44377	−0.226972
$807$	−45.7725	−1.61127
$808$	−8.23805	−0.289814
$809$	−1.93933	−0.0681832	−0.0340916	−	0.999419i	$-0.510854\pi$
$809$	−1.93933	−0.0681832	−0.0340916	+	0.999419i	$0.510854\pi$
$810$	−16.0854	−0.565184
$811$	−5.41775	−0.190243	−0.0951215	−	0.995466i	$-0.530324\pi$
$811$	−5.41775	−0.190243	−0.0951215	+	0.995466i	$0.530324\pi$
$812$	−37.1514	−1.30376
$813$	25.9209	0.909086
$814$	−3.38942	−0.118799
$815$	3.29112	0.115283
$816$	−3.49027	−0.122184
$817$	36.0778	1.26220
$818$	25.2911	0.884283
$819$	−113.128	−3.95302
$820$	−3.90043	−0.136209
$821$	37.8655	1.32152	0.660758	−	0.750599i	$-0.270235\pi$
$821$	37.8655	1.32152	0.660758	+	0.750599i	$0.270235\pi$
$822$	−23.4837	−0.819088
$823$	43.7336	1.52446	0.762229	−	0.647308i	$-0.224105\pi$
$823$	43.7336	1.52446	0.762229	+	0.647308i	$0.224105\pi$
$824$	12.3376	0.429802
$825$	−13.5292	−0.471026
$826$	−10.0930	−0.351181
$827$	28.1991	0.980581	0.490290	−	0.871559i	$-0.336891\pi$
$827$	28.1991	0.980581	0.490290	+	0.871559i	$0.336891\pi$
$828$	−6.72833	−0.233826
$829$	1.12559	0.0390935	0.0195468	−	0.999809i	$-0.493778\pi$
$829$	1.12559	0.0390935	0.0195468	+	0.999809i	$0.493778\pi$
$830$	−2.78140	−0.0965438
$831$	−40.2770	−1.39719
$832$	−3.72833	−0.129256
$833$	14.9252	0.517126
$834$	−14.5822	−0.504942
$835$	−22.9133	−0.792948
$836$	19.5615	0.676549
$837$	−20.0983	−0.694699
$838$	−17.3505	−0.599364
$839$	39.9328	1.37863	0.689316	−	0.724461i	$-0.257911\pi$
$839$	39.9328	1.37863	0.689316	+	0.724461i	$0.257911\pi$
$840$	14.0660	0.485322
$841$	38.8655	1.34019
$842$	21.4230	0.738287
$843$	−8.34420	−0.287389
$844$	4.34420	0.149533
$845$	−0.900425	−0.0309756
$846$	−77.0841	−2.65021
$847$	35.2436	1.21098
$848$	−6.00000	−0.206041
$849$	−2.31586	−0.0794801
$850$	1.11903	0.0383823
$851$	0.781399	0.0267860
$852$	−22.2044	−0.760711
$853$	47.9921	1.64322	0.821610	−	0.570050i	$-0.193076\pi$
$853$	47.9921	1.64322	0.821610	+	0.570050i	$0.193076\pi$
$854$	16.0376	0.548796
$855$	−30.3429	−1.03771
$856$	−15.9328	−0.544571
$857$	−43.4283	−1.48348	−0.741742	−	0.670686i	$-0.766000\pi$
$857$	−43.4283	−1.48348	−0.741742	+	0.670686i	$0.766000\pi$
$858$	50.4412	1.72203
$859$	32.5433	1.11036	0.555182	−	0.831729i	$-0.312648\pi$
$859$	32.5433	1.11036	0.555182	+	0.831729i	$0.312648\pi$
$860$	−8.00000	−0.272798
$861$	−54.8632	−1.86973
$862$	22.5822	0.769154
$863$	46.1036	1.56938	0.784692	−	0.619886i	$-0.212821\pi$
$863$	46.1036	1.56938	0.784692	+	0.619886i	$0.212821\pi$
$864$	−11.6288	−0.395618
$865$	−0.575681	−0.0195738
$866$	1.01417	0.0344628
$867$	49.1177	1.66813
$868$	7.79428	0.264555
$869$	−64.6884	−2.19440
$870$	−25.6947	−0.871132
$871$	−9.08669	−0.307891
$872$	−1.49027	−0.0504670
$873$	−4.32578	−0.146405
$874$	−4.50973	−0.152544
$875$	−4.50973	−0.152457
$876$	29.4956	0.996563
$877$	−24.0996	−0.813785	−0.406892	−	0.913476i	$-0.633388\pi$
$877$	−24.0996	−0.813785	−0.406892	+	0.913476i	$0.633388\pi$
$878$	−26.7478	−0.902694
$879$	18.7142	0.631213
$880$	−4.33763	−0.146221
$881$	2.34420	0.0789780	0.0394890	−	0.999220i	$-0.487427\pi$
$881$	2.34420	0.0789780	0.0394890	+	0.999220i	$0.487427\pi$
$882$	89.7399	3.02170
$883$	−41.0505	−1.38146	−0.690730	−	0.723113i	$-0.742711\pi$
$883$	−41.0505	−1.38146	−0.690730	+	0.723113i	$0.742711\pi$
$884$	−4.17210	−0.140323
$885$	−6.98055	−0.234649
$886$	10.2044	0.342825
$887$	54.7788	1.83929	0.919647	−	0.392747i	$-0.128475\pi$
$887$	54.7788	1.83929	0.919647	+	0.392747i	$0.128475\pi$
$888$	2.43720	0.0817872
$889$	−3.04522	−0.102133
$890$	7.69471	0.257927
$891$	69.7725	2.33747
$892$	12.4761	0.417731
$893$	−51.6664	−1.72895
$894$	−23.4837	−0.785413
$895$	−5.01945	−0.167782
$896$	4.50973	0.150659
$897$	−11.6288	−0.388273
$898$	38.7867	1.29433
$899$	−14.2381	−0.474866
$900$	6.72833	0.224278
$901$	−6.71416	−0.223681
$902$	16.9186	0.563328
$903$	−112.528	−3.74469
$904$	−6.00000	−0.199557
$905$	11.5292	0.383243
$906$	41.6611	1.38410
$907$	−10.1061	−0.335569	−0.167784	−	0.985824i	$-0.553661\pi$
$907$	−10.1061	−0.335569	−0.167784	+	0.985824i	$0.553661\pi$
$908$	15.9328	0.528747
$909$	−55.4283	−1.83844
$910$	16.8137	0.557370
$911$	−25.4178	−0.842128	−0.421064	−	0.907031i	$-0.638343\pi$
$911$	−25.4178	−0.842128	−0.421064	+	0.907031i	$0.638343\pi$
$912$	−14.0660	−0.465770
$913$	12.0647	0.399282
$914$	34.9522	1.15612
$915$	11.0920	0.366689
$916$	−3.56280	−0.117718
$917$	−61.7594	−2.03947
$918$	−13.0129	−0.429489
$919$	23.6017	0.778548	0.389274	−	0.921122i	$-0.372726\pi$
$919$	23.6017	0.778548	0.389274	+	0.921122i	$0.372726\pi$
$920$	1.00000	0.0329690
$921$	−95.1566	−3.13552
$922$	16.3700	0.539116
$923$	−26.5421	−0.873643
$924$	−61.0129	−2.00718
$925$	−0.781399	−0.0256922
$926$	29.2186	0.960183
$927$	83.0116	2.72646
$928$	−8.23805	−0.270427
$929$	−7.08669	−0.232507	−0.116253	−	0.993220i	$-0.537088\pi$
$929$	−7.08669	−0.232507	−0.116253	+	0.993220i	$0.537088\pi$
$930$	5.39070	0.176768
$931$	60.1490	1.97131
$932$	−27.4956	−0.900647
$933$	−17.3505	−0.568030
$934$	24.2770	0.794366
$935$	−4.85392	−0.158740
$936$	−25.0854	−0.819942
$937$	27.3169	0.892404	0.446202	−	0.894932i	$-0.352776\pi$
$937$	27.3169	0.892404	0.446202	+	0.894932i	$0.352776\pi$
$938$	10.9911	0.358873
$939$	−12.7023	−0.414524
$940$	11.4567	0.373675
$941$	55.8979	1.82222	0.911109	−	0.412165i	$-0.135227\pi$
$941$	55.8979	1.82222	0.911109	+	0.412165i	$0.135227\pi$
$942$	−50.6469	−1.65017
$943$	−3.90043	−0.127015
$944$	−2.23805	−0.0728424
$945$	52.4425	1.70595
$946$	34.7010	1.12823
$947$	37.5939	1.22164	0.610818	−	0.791771i	$-0.290841\pi$
$947$	37.5939	1.22164	0.610818	+	0.791771i	$0.290841\pi$
$948$	46.5150	1.51074
$949$	35.2575	1.14451
$950$	4.50973	0.146315
$951$	19.2305	0.623590
$952$	5.04650	0.163558
$953$	−29.3828	−0.951804	−0.475902	−	0.879498i	$-0.657878\pi$
$953$	−29.3828	−0.951804	−0.475902	+	0.879498i	$0.657878\pi$
$954$	−40.3700	−1.30703
$955$	18.7142	0.605576
$956$	10.0389	0.324681
$957$	111.454	3.60280
$958$	24.6080	0.795049
$959$	33.9545	1.09645
$960$	3.11903	0.100666
$961$	−28.0129	−0.903641
$962$	2.91331	0.0939289
$963$	−107.201	−3.45450
$964$	−23.6947	−0.763155
$965$	−23.4956	−0.756349
$966$	14.0660	0.452565
$967$	−49.2292	−1.58310	−0.791552	−	0.611102i	$-0.790726\pi$
$967$	−49.2292	−1.58310	−0.791552	+	0.611102i	$0.790726\pi$
$968$	7.81502	0.251184
$969$	−15.7402	−0.505647
$970$	0.642920	0.0206429
$971$	9.62347	0.308832	0.154416	−	0.988006i	$-0.450650\pi$
$971$	9.62347	0.308832	0.154416	+	0.988006i	$0.450650\pi$
$972$	−15.2846	−0.490252
$973$	21.0841	0.675926
$974$	−30.2381	−0.968890
$975$	11.6288	0.372418
$976$	3.55623	0.113832
$977$	18.9858	0.607411	0.303705	−	0.952766i	$-0.401776\pi$
$977$	18.9858	0.607411	0.303705	+	0.952766i	$0.401776\pi$
$978$	10.2651	0.328242
$979$	−33.3768	−1.06673
$980$	−13.3376	−0.426055
$981$	−10.0271	−0.320139
$982$	12.3311	0.393500
$983$	4.33763	0.138349	0.0691744	−	0.997605i	$-0.477963\pi$
$983$	4.33763	0.138349	0.0691744	+	0.997605i	$0.477963\pi$
$984$	−12.1655	−0.387823
$985$	18.1385	0.577940
$986$	−9.21860	−0.293580
$987$	161.149	5.12942
$988$	−16.8137	−0.534916
$989$	−8.00000	−0.254385
$990$	−29.1850	−0.927560
$991$	1.96766	0.0625049	0.0312524	−	0.999512i	$-0.490050\pi$
$991$	1.96766	0.0625049	0.0312524	+	0.999512i	$0.490050\pi$
$992$	1.72833	0.0548744
$993$	−86.0495	−2.73070
$994$	32.1049	1.01830
$995$	23.2575	0.737312
$996$	−8.67526	−0.274886
$997$	3.96110	0.125449	0.0627246	−	0.998031i	$-0.480021\pi$
$997$	3.96110	0.125449	0.0627246	+	0.998031i	$0.480021\pi$
$998$	−26.9133	−0.851926
$999$	9.08669	0.287490

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.a.d.1.1	✓	3
3.2	odd	2		2070.2.a.z.1.3		3
4.3	odd	2		1840.2.a.r.1.3		3
5.2	odd	4		1150.2.b.j.599.6		6
5.3	odd	4		1150.2.b.j.599.1		6
5.4	even	2		1150.2.a.q.1.3		3
8.3	odd	2		7360.2.a.ce.1.1		3
8.5	even	2		7360.2.a.bz.1.3		3
20.19	odd	2		9200.2.a.cf.1.1		3
23.22	odd	2		5290.2.a.r.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.a.d.1.1	✓	3	1.1	even	1	trivial
1150.2.a.q.1.3		3	5.4	even	2
1150.2.b.j.599.1		6	5.3	odd	4
1150.2.b.j.599.6		6	5.2	odd	4
1840.2.a.r.1.3		3	4.3	odd	2
2070.2.a.z.1.3		3	3.2	odd	2
5290.2.a.r.1.1		3	23.22	odd	2
7360.2.a.bz.1.3		3	8.5	even	2
7360.2.a.ce.1.1		3	8.3	odd	2
9200.2.a.cf.1.1		3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.11903 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.11903 q^{6} +4.50973 q^{7} +1.00000 q^{8} +6.72833 q^{9} -1.00000 q^{10} +4.33763 q^{11} -3.11903 q^{12} -3.72833 q^{13} +4.50973 q^{14} +3.11903 q^{15} +1.00000 q^{16} +1.11903 q^{17} +6.72833 q^{18} +4.50973 q^{19} -1.00000 q^{20} -14.0660 q^{21} +4.33763 q^{22} -1.00000 q^{23} -3.11903 q^{24} +1.00000 q^{25} -3.72833 q^{26} -11.6288 q^{27} +4.50973 q^{28} -8.23805 q^{29} +3.11903 q^{30} +1.72833 q^{31} +1.00000 q^{32} -13.5292 q^{33} +1.11903 q^{34} -4.50973 q^{35} +6.72833 q^{36} -0.781399 q^{37} +4.50973 q^{38} +11.6288 q^{39} -1.00000 q^{40} +3.90043 q^{41} -14.0660 q^{42} +8.00000 q^{43} +4.33763 q^{44} -6.72833 q^{45} -1.00000 q^{46} -11.4567 q^{47} -3.11903 q^{48} +13.3376 q^{49} +1.00000 q^{50} -3.49027 q^{51} -3.72833 q^{52} -6.00000 q^{53} -11.6288 q^{54} -4.33763 q^{55} +4.50973 q^{56} -14.0660 q^{57} -8.23805 q^{58} -2.23805 q^{59} +3.11903 q^{60} +3.55623 q^{61} +1.72833 q^{62} +30.3429 q^{63} +1.00000 q^{64} +3.72833 q^{65} -13.5292 q^{66} +2.43720 q^{67} +1.11903 q^{68} +3.11903 q^{69} -4.50973 q^{70} +7.11903 q^{71} +6.72833 q^{72} -9.45665 q^{73} -0.781399 q^{74} -3.11903 q^{75} +4.50973 q^{76} +19.5615 q^{77} +11.6288 q^{78} -14.9133 q^{79} -1.00000 q^{80} +16.0854 q^{81} +3.90043 q^{82} +2.78140 q^{83} -14.0660 q^{84} -1.11903 q^{85} +8.00000 q^{86} +25.6947 q^{87} +4.33763 q^{88} -7.69471 q^{89} -6.72833 q^{90} -16.8137 q^{91} -1.00000 q^{92} -5.39070 q^{93} -11.4567 q^{94} -4.50973 q^{95} -3.11903 q^{96} -0.642920 q^{97} +13.3376 q^{98} +29.1850 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 10 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 10 * q^9	\( 3 q + 3 q^{2} + q^{3} + 3 q^{4} - 3 q^{5} + q^{6} + 3 q^{7} + 3 q^{8} + 10 q^{9} - 3 q^{10} + 3 q^{11} + q^{12} - q^{13} + 3 q^{14} - q^{15} + 3 q^{16} - 7 q^{17} + 10 q^{18} + 3 q^{19} - 3 q^{20} - 22 q^{21} + 3 q^{22} - 3 q^{23} + q^{24} + 3 q^{25} - q^{26} - 14 q^{27} + 3 q^{28} - 4 q^{29} - q^{30} - 5 q^{31} + 3 q^{32} - 9 q^{33} - 7 q^{34} - 3 q^{35} + 10 q^{36} - 2 q^{37} + 3 q^{38} + 14 q^{39} - 3 q^{40} + q^{41} - 22 q^{42} + 24 q^{43} + 3 q^{44} - 10 q^{45} - 3 q^{46} - 14 q^{47} + q^{48} + 30 q^{49} + 3 q^{50} - 21 q^{51} - q^{52} - 18 q^{53} - 14 q^{54} - 3 q^{55} + 3 q^{56} - 22 q^{57} - 4 q^{58} + 14 q^{59} - q^{60} + q^{61} - 5 q^{62} + 8 q^{63} + 3 q^{64} + q^{65} - 9 q^{66} + 8 q^{67} - 7 q^{68} - q^{69} - 3 q^{70} + 11 q^{71} + 10 q^{72} - 8 q^{73} - 2 q^{74} + q^{75} + 3 q^{76} - 24 q^{77} + 14 q^{78} - 4 q^{79} - 3 q^{80} + 7 q^{81} + q^{82} + 8 q^{83} - 22 q^{84} + 7 q^{85} + 24 q^{86} + 36 q^{87} + 3 q^{88} + 18 q^{89} - 10 q^{90} + q^{91} - 3 q^{92} - 16 q^{93} - 14 q^{94} - 3 q^{95} + q^{96} - 33 q^{97} + 30 q^{98} + 57 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + q^3 + 3 * q^4 - 3 * q^5 + q^6 + 3 * q^7 + 3 * q^8 + 10 * q^9 - 3 * q^10 + 3 * q^11 + q^12 - q^13 + 3 * q^14 - q^15 + 3 * q^16 - 7 * q^17 + 10 * q^18 + 3 * q^19 - 3 * q^20 - 22 * q^21 + 3 * q^22 - 3 * q^23 + q^24 + 3 * q^25 - q^26 - 14 * q^27 + 3 * q^28 - 4 * q^29 - q^30 - 5 * q^31 + 3 * q^32 - 9 * q^33 - 7 * q^34 - 3 * q^35 + 10 * q^36 - 2 * q^37 + 3 * q^38 + 14 * q^39 - 3 * q^40 + q^41 - 22 * q^42 + 24 * q^43 + 3 * q^44 - 10 * q^45 - 3 * q^46 - 14 * q^47 + q^48 + 30 * q^49 + 3 * q^50 - 21 * q^51 - q^52 - 18 * q^53 - 14 * q^54 - 3 * q^55 + 3 * q^56 - 22 * q^57 - 4 * q^58 + 14 * q^59 - q^60 + q^61 - 5 * q^62 + 8 * q^63 + 3 * q^64 + q^65 - 9 * q^66 + 8 * q^67 - 7 * q^68 - q^69 - 3 * q^70 + 11 * q^71 + 10 * q^72 - 8 * q^73 - 2 * q^74 + q^75 + 3 * q^76 - 24 * q^77 + 14 * q^78 - 4 * q^79 - 3 * q^80 + 7 * q^81 + q^82 + 8 * q^83 - 22 * q^84 + 7 * q^85 + 24 * q^86 + 36 * q^87 + 3 * q^88 + 18 * q^89 - 10 * q^90 + q^91 - 3 * q^92 - 16 * q^93 - 14 * q^94 - 3 * q^95 + q^96 - 33 * q^97 + 30 * q^98 + 57 * q^99

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