LMFDB - Embedded newform 230.4.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,4,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, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
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:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.318165.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 45x + 60 $ x^3 - x^2 - 45*x + 60
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			$6.50182$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} -6.50182 q^{3} +4.00000 q^{4} +5.00000 q^{5} +13.0036 q^{6} +2.73001 q^{7} -8.00000 q^{8} +15.2736 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -6.50182 q^{3} +4.00000 q^{4} +5.00000 q^{5} +13.0036 q^{6} +2.73001 q^{7} -8.00000 q^{8} +15.2736 q^{9} -10.0000 q^{10} -58.0600 q^{11} -26.0073 q^{12} +60.8209 q^{13} -5.46001 q^{14} -32.5091 q^{15} +16.0000 q^{16} -25.5200 q^{17} -30.5473 q^{18} -135.292 q^{19} +20.0000 q^{20} -17.7500 q^{21} +116.120 q^{22} +23.0000 q^{23} +52.0145 q^{24} +25.0000 q^{25} -121.642 q^{26} +76.2427 q^{27} +10.9200 q^{28} +76.0691 q^{29} +65.0182 q^{30} +146.654 q^{31} -32.0000 q^{32} +377.495 q^{33} +51.0400 q^{34} +13.6500 q^{35} +61.0945 q^{36} +411.565 q^{37} +270.584 q^{38} -395.446 q^{39} -40.0000 q^{40} +279.340 q^{41} +35.5000 q^{42} +444.971 q^{43} -232.240 q^{44} +76.3681 q^{45} -46.0000 q^{46} +60.4237 q^{47} -104.029 q^{48} -335.547 q^{49} -50.0000 q^{50} +165.926 q^{51} +243.284 q^{52} -417.414 q^{53} -152.485 q^{54} -290.300 q^{55} -21.8401 q^{56} +879.643 q^{57} -152.138 q^{58} +474.367 q^{59} -130.036 q^{60} +430.793 q^{61} -293.307 q^{62} +41.6971 q^{63} +64.0000 q^{64} +304.104 q^{65} -754.991 q^{66} +444.731 q^{67} -102.080 q^{68} -149.542 q^{69} -27.3001 q^{70} -425.418 q^{71} -122.189 q^{72} -835.514 q^{73} -823.131 q^{74} -162.545 q^{75} -541.167 q^{76} -158.504 q^{77} +790.893 q^{78} -169.644 q^{79} +80.0000 q^{80} -908.104 q^{81} -558.680 q^{82} +623.154 q^{83} -71.0000 q^{84} -127.600 q^{85} -889.942 q^{86} -494.587 q^{87} +464.480 q^{88} +1674.53 q^{89} -152.736 q^{90} +166.041 q^{91} +92.0000 q^{92} -953.515 q^{93} -120.847 q^{94} -676.459 q^{95} +208.058 q^{96} +1010.47 q^{97} +671.094 q^{98} -886.787 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} - q^{3} + 12 q^{4} + 15 q^{5} + 2 q^{6} + 7 q^{7} - 24 q^{8} + 10 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 - q^3 + 12 * q^4 + 15 * q^5 + 2 * q^6 + 7 * q^7 - 24 * q^8 + 10 * q^9	\( 3 q - 6 q^{2} - q^{3} + 12 q^{4} + 15 q^{5} + 2 q^{6} + 7 q^{7} - 24 q^{8} + 10 q^{9} - 30 q^{10} + 27 q^{11} - 4 q^{12} + 75 q^{13} - 14 q^{14} - 5 q^{15} + 48 q^{16} + 127 q^{17} - 20 q^{18} - 185 q^{19} + 60 q^{20} - 258 q^{21} - 54 q^{22} + 69 q^{23} + 8 q^{24} + 75 q^{25} - 150 q^{26} + 98 q^{27} + 28 q^{28} + 344 q^{29} + 10 q^{30} + 397 q^{31} - 96 q^{32} + 477 q^{33} - 254 q^{34} + 35 q^{35} + 40 q^{36} + 978 q^{37} + 370 q^{38} + 198 q^{39} - 120 q^{40} - 575 q^{41} + 516 q^{42} + 812 q^{43} + 108 q^{44} + 50 q^{45} - 138 q^{46} - 270 q^{47} - 16 q^{48} + 878 q^{49} - 150 q^{50} + 955 q^{51} + 300 q^{52} + 510 q^{53} - 196 q^{54} + 135 q^{55} - 56 q^{56} + 894 q^{57} - 688 q^{58} + 142 q^{59} - 20 q^{60} - 49 q^{61} - 794 q^{62} - 1356 q^{63} + 192 q^{64} + 375 q^{65} - 954 q^{66} + 1616 q^{67} + 508 q^{68} - 23 q^{69} - 70 q^{70} - 471 q^{71} - 80 q^{72} - 780 q^{73} - 1956 q^{74} - 25 q^{75} - 740 q^{76} + 1032 q^{77} - 396 q^{78} - 860 q^{79} + 240 q^{80} - 1193 q^{81} + 1150 q^{82} - 288 q^{83} - 1032 q^{84} + 635 q^{85} - 1624 q^{86} + 1452 q^{87} - 216 q^{88} - 90 q^{89} - 100 q^{90} - 3963 q^{91} + 276 q^{92} - 1592 q^{93} + 540 q^{94} - 925 q^{95} + 32 q^{96} + 1321 q^{97} - 1756 q^{98} - 1851 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - q^3 + 12 * q^4 + 15 * q^5 + 2 * q^6 + 7 * q^7 - 24 * q^8 + 10 * q^9 - 30 * q^10 + 27 * q^11 - 4 * q^12 + 75 * q^13 - 14 * q^14 - 5 * q^15 + 48 * q^16 + 127 * q^17 - 20 * q^18 - 185 * q^19 + 60 * q^20 - 258 * q^21 - 54 * q^22 + 69 * q^23 + 8 * q^24 + 75 * q^25 - 150 * q^26 + 98 * q^27 + 28 * q^28 + 344 * q^29 + 10 * q^30 + 397 * q^31 - 96 * q^32 + 477 * q^33 - 254 * q^34 + 35 * q^35 + 40 * q^36 + 978 * q^37 + 370 * q^38 + 198 * q^39 - 120 * q^40 - 575 * q^41 + 516 * q^42 + 812 * q^43 + 108 * q^44 + 50 * q^45 - 138 * q^46 - 270 * q^47 - 16 * q^48 + 878 * q^49 - 150 * q^50 + 955 * q^51 + 300 * q^52 + 510 * q^53 - 196 * q^54 + 135 * q^55 - 56 * q^56 + 894 * q^57 - 688 * q^58 + 142 * q^59 - 20 * q^60 - 49 * q^61 - 794 * q^62 - 1356 * q^63 + 192 * q^64 + 375 * q^65 - 954 * q^66 + 1616 * q^67 + 508 * q^68 - 23 * q^69 - 70 * q^70 - 471 * q^71 - 80 * q^72 - 780 * q^73 - 1956 * q^74 - 25 * q^75 - 740 * q^76 + 1032 * q^77 - 396 * q^78 - 860 * q^79 + 240 * q^80 - 1193 * q^81 + 1150 * q^82 - 288 * q^83 - 1032 * q^84 + 635 * q^85 - 1624 * q^86 + 1452 * q^87 - 216 * q^88 - 90 * q^89 - 100 * q^90 - 3963 * q^91 + 276 * q^92 - 1592 * q^93 + 540 * q^94 - 925 * q^95 + 32 * q^96 + 1321 * q^97 - 1756 * q^98 - 1851 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−6.50182	−1.25128	−0.625638	−	0.780114i	$-0.715161\pi$
$3$	−6.50182	−1.25128	−0.625638	+	0.780114i	$0.715161\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	13.0036	0.884785
$7$	2.73001	0.147406	0.0737032	−	0.997280i	$-0.476518\pi$
$7$	2.73001	0.147406	0.0737032	+	0.997280i	$0.476518\pi$
$8$	−8.00000	−0.353553
$9$	15.2736	0.565690
$10$	−10.0000	−0.316228
$11$	−58.0600	−1.59143	−0.795716	−	0.605671i	$-0.792905\pi$
$11$	−58.0600	−1.59143	−0.795716	+	0.605671i	$0.792905\pi$
$12$	−26.0073	−0.625638
$13$	60.8209	1.29759	0.648795	−	0.760963i	$-0.275273\pi$
$13$	60.8209	1.29759	0.648795	+	0.760963i	$0.275273\pi$
$14$	−5.46001	−0.104232
$15$	−32.5091	−0.559587
$16$	16.0000	0.250000
$17$	−25.5200	−0.364089	−0.182044	−	0.983290i	$-0.558271\pi$
$17$	−25.5200	−0.364089	−0.182044	+	0.983290i	$0.558271\pi$
$18$	−30.5473	−0.400003
$19$	−135.292	−1.63358	−0.816791	−	0.576933i	$-0.804249\pi$
$19$	−135.292	−1.63358	−0.816791	+	0.576933i	$0.804249\pi$
$20$	20.0000	0.223607
$21$	−17.7500	−0.184446
$22$	116.120	1.12531
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	52.0145	0.442393
$25$	25.0000	0.200000
$26$	−121.642	−0.917535
$27$	76.2427	0.543441
$28$	10.9200	0.0737032
$29$	76.0691	0.487092	0.243546	−	0.969889i	$-0.421689\pi$
$29$	76.0691	0.487092	0.243546	+	0.969889i	$0.421689\pi$
$30$	65.0182	0.395688
$31$	146.654	0.849670	0.424835	−	0.905271i	$-0.360332\pi$
$31$	146.654	0.849670	0.424835	+	0.905271i	$0.360332\pi$
$32$	−32.0000	−0.176777
$33$	377.495	1.99132
$34$	51.0400	0.257450
$35$	13.6500	0.0659222
$36$	61.0945	0.282845
$37$	411.565	1.82867	0.914337	−	0.404954i	$-0.132712\pi$
$37$	411.565	1.82867	0.914337	+	0.404954i	$0.132712\pi$
$38$	270.584	1.15512
$39$	−395.446	−1.62364
$40$	−40.0000	−0.158114
$41$	279.340	1.06404	0.532019	−	0.846732i	$-0.321433\pi$
$41$	279.340	1.06404	0.532019	+	0.846732i	$0.321433\pi$
$42$	35.5000	0.130423
$43$	444.971	1.57808	0.789040	−	0.614342i	$-0.210578\pi$
$43$	444.971	1.57808	0.789040	+	0.614342i	$0.210578\pi$
$44$	−232.240	−0.795716
$45$	76.3681	0.252984
$46$	−46.0000	−0.147442
$47$	60.4237	0.187525	0.0937627	−	0.995595i	$-0.470110\pi$
$47$	60.4237	0.187525	0.0937627	+	0.995595i	$0.470110\pi$
$48$	−104.029	−0.312819
$49$	−335.547	−0.978271
$50$	−50.0000	−0.141421
$51$	165.926	0.455575
$52$	243.284	0.648795
$53$	−417.414	−1.08182	−0.540908	−	0.841082i	$-0.681919\pi$
$53$	−417.414	−1.08182	−0.540908	+	0.841082i	$0.681919\pi$
$54$	−152.485	−0.384271
$55$	−290.300	−0.711710
$56$	−21.8401	−0.0521161
$57$	879.643	2.04406
$58$	−152.138	−0.344426
$59$	474.367	1.04673	0.523367	−	0.852107i	$-0.324676\pi$
$59$	474.367	1.04673	0.523367	+	0.852107i	$0.324676\pi$
$60$	−130.036	−0.279794
$61$	430.793	0.904219	0.452109	−	0.891963i	$-0.350672\pi$
$61$	430.793	0.904219	0.452109	+	0.891963i	$0.350672\pi$
$62$	−293.307	−0.600808
$63$	41.6971	0.0833864
$64$	64.0000	0.125000
$65$	304.104	0.580300
$66$	−754.991	−1.40807
$67$	444.731	0.810933	0.405467	−	0.914110i	$-0.367109\pi$
$67$	444.731	0.810933	0.405467	+	0.914110i	$0.367109\pi$
$68$	−102.080	−0.182044
$69$	−149.542	−0.260909
$70$	−27.3001	−0.0466140
$71$	−425.418	−0.711096	−0.355548	−	0.934658i	$-0.615706\pi$
$71$	−425.418	−0.711096	−0.355548	+	0.934658i	$0.615706\pi$
$72$	−122.189	−0.200002
$73$	−835.514	−1.33958	−0.669791	−	0.742549i	$-0.733616\pi$
$73$	−835.514	−1.33958	−0.669791	+	0.742549i	$0.733616\pi$
$74$	−823.131	−1.29307
$75$	−162.545	−0.250255
$76$	−541.167	−0.816791
$77$	−158.504	−0.234587
$78$	790.893	1.14809
$79$	−169.644	−0.241600	−0.120800	−	0.992677i	$-0.538546\pi$
$79$	−169.644	−0.241600	−0.120800	+	0.992677i	$0.538546\pi$
$80$	80.0000	0.111803
$81$	−908.104	−1.24568
$82$	−558.680	−0.752388
$83$	623.154	0.824097	0.412049	−	0.911162i	$-0.364813\pi$
$83$	623.154	0.824097	0.412049	+	0.911162i	$0.364813\pi$
$84$	−71.0000	−0.0922231
$85$	−127.600	−0.162825
$86$	−889.942	−1.11587
$87$	−494.587	−0.609486
$88$	464.480	0.562656
$89$	1674.53	1.99437	0.997187	−	0.0749529i	$-0.0238807\pi$
$89$	1674.53	1.99437	0.997187	+	0.0749529i	$0.0238807\pi$
$90$	−152.736	−0.178887
$91$	166.041	0.191273
$92$	92.0000	0.104257
$93$	−953.515	−1.06317
$94$	−120.847	−0.132601
$95$	−676.459	−0.730560
$96$	208.058	0.221196
$97$	1010.47	1.05771	0.528855	−	0.848712i	$-0.322621\pi$
$97$	1010.47	1.05771	0.528855	+	0.848712i	$0.322621\pi$
$98$	671.094	0.691742
$99$	−886.787	−0.900257
$100$	100.000	0.100000
$101$	793.592	0.781836	0.390918	−	0.920426i	$-0.372158\pi$
$101$	793.592	0.781836	0.390918	+	0.920426i	$0.372158\pi$
$102$	−331.853	−0.322140
$103$	−675.460	−0.646165	−0.323083	−	0.946371i	$-0.604719\pi$
$103$	−675.460	−0.646165	−0.323083	+	0.946371i	$0.604719\pi$
$104$	−486.567	−0.458768
$105$	−88.7500	−0.0824868
$106$	834.829	0.764960
$107$	−779.649	−0.704407	−0.352203	−	0.935924i	$-0.614567\pi$
$107$	−779.649	−0.704407	−0.352203	+	0.935924i	$0.614567\pi$
$108$	304.971	0.271721
$109$	985.830	0.866288	0.433144	−	0.901325i	$-0.357404\pi$
$109$	985.830	0.866288	0.433144	+	0.901325i	$0.357404\pi$
$110$	580.600	0.503255
$111$	−2675.92	−2.28817
$112$	43.6801	0.0368516
$113$	213.916	0.178084	0.0890422	−	0.996028i	$-0.471619\pi$
$113$	213.916	0.178084	0.0890422	+	0.996028i	$0.471619\pi$
$114$	−1759.29	−1.44537
$115$	115.000	0.0932505
$116$	304.276	0.243546
$117$	928.956	0.734034
$118$	−948.734	−0.740153
$119$	−69.6697	−0.0536690
$120$	260.073	0.197844
$121$	2039.96	1.53265
$122$	−861.585	−0.639379
$123$	−1816.22	−1.33140
$124$	586.615	0.424835
$125$	125.000	0.0894427
$126$	−83.3942	−0.0589631
$127$	1990.90	1.39105	0.695527	−	0.718500i	$-0.255171\pi$
$127$	1990.90	1.39105	0.695527	+	0.718500i	$0.255171\pi$
$128$	−128.000	−0.0883883
$129$	−2893.12	−1.97461
$130$	−608.209	−0.410334
$131$	−1128.87	−0.752897	−0.376449	−	0.926437i	$-0.622855\pi$
$131$	−1128.87	−0.752897	−0.376449	+	0.926437i	$0.622855\pi$
$132$	1509.98	0.995659
$133$	−369.347	−0.240801
$134$	−889.462	−0.573417
$135$	381.214	0.243034
$136$	204.160	0.128725
$137$	651.068	0.406018	0.203009	−	0.979177i	$-0.434928\pi$
$137$	651.068	0.406018	0.203009	+	0.979177i	$0.434928\pi$
$138$	299.084	0.184490
$139$	227.553	0.138855	0.0694273	−	0.997587i	$-0.477883\pi$
$139$	227.553	0.138855	0.0694273	+	0.997587i	$0.477883\pi$
$140$	54.6001	0.0329611
$141$	−392.864	−0.234646
$142$	850.836	0.502821
$143$	−3531.26	−2.06503
$144$	244.378	0.141422
$145$	380.345	0.217834
$146$	1671.03	0.947228
$147$	2181.67	1.22409
$148$	1646.26	0.914337
$149$	−3190.52	−1.75421	−0.877107	−	0.480295i	$-0.840530\pi$
$149$	−3190.52	−1.75421	−0.877107	+	0.480295i	$0.840530\pi$
$150$	325.091	0.176957
$151$	−954.094	−0.514193	−0.257096	−	0.966386i	$-0.582766\pi$
$151$	−954.094	−0.514193	−0.257096	+	0.966386i	$0.582766\pi$
$152$	1082.33	0.577559
$153$	−389.783	−0.205961
$154$	317.008	0.165878
$155$	733.268	0.379984
$156$	−1581.79	−0.811822
$157$	2828.19	1.43767	0.718834	−	0.695181i	$-0.244676\pi$
$157$	2828.19	1.43767	0.718834	+	0.695181i	$0.244676\pi$
$158$	339.288	0.170837
$159$	2713.95	1.35365
$160$	−160.000	−0.0790569
$161$	62.7901	0.0307364
$162$	1816.21	0.880832
$163$	457.019	0.219610	0.109805	−	0.993953i	$-0.464977\pi$
$163$	457.019	0.219610	0.109805	+	0.993953i	$0.464977\pi$
$164$	1117.36	0.532019
$165$	1887.48	0.890545
$166$	−1246.31	−0.582725
$167$	−1914.18	−0.886969	−0.443484	−	0.896282i	$-0.646258\pi$
$167$	−1914.18	−0.886969	−0.443484	+	0.896282i	$0.646258\pi$
$168$	142.000	0.0652115
$169$	1502.18	0.683741
$170$	255.200	0.115135
$171$	−2066.40	−0.924101
$172$	1779.88	0.789040
$173$	−3334.32	−1.46534	−0.732670	−	0.680584i	$-0.761726\pi$
$173$	−3334.32	−1.46534	−0.732670	+	0.680584i	$0.761726\pi$
$174$	989.174	0.430972
$175$	68.2502	0.0294813
$176$	−928.960	−0.397858
$177$	−3084.25	−1.30975
$178$	−3349.05	−1.41024
$179$	−4516.88	−1.88607	−0.943037	−	0.332688i	$-0.892044\pi$
$179$	−4516.88	−1.88607	−0.943037	+	0.332688i	$0.892044\pi$
$180$	305.473	0.126492
$181$	4463.52	1.83299	0.916494	−	0.400048i	$-0.131007\pi$
$181$	4463.52	1.83299	0.916494	+	0.400048i	$0.131007\pi$
$182$	−332.083	−0.135251
$183$	−2800.93	−1.13143
$184$	−184.000	−0.0737210
$185$	2057.83	0.817808
$186$	1907.03	0.751776
$187$	1481.69	0.579422
$188$	241.695	0.0937627
$189$	208.143	0.0801068
$190$	1352.92	0.516584
$191$	1766.54	0.669227	0.334614	−	0.942355i	$-0.391394\pi$
$191$	1766.54	0.669227	0.334614	+	0.942355i	$0.391394\pi$
$192$	−416.116	−0.156409
$193$	598.155	0.223089	0.111544	−	0.993759i	$-0.464420\pi$
$193$	598.155	0.223089	0.111544	+	0.993759i	$0.464420\pi$
$194$	−2020.94	−0.747914
$195$	−1977.23	−0.726115
$196$	−1342.19	−0.489136
$197$	2354.76	0.851623	0.425812	−	0.904812i	$-0.359989\pi$
$197$	2354.76	0.851623	0.425812	+	0.904812i	$0.359989\pi$
$198$	1773.57	0.636577
$199$	2728.83	0.972070	0.486035	−	0.873939i	$-0.338443\pi$
$199$	2728.83	0.972070	0.486035	+	0.873939i	$0.338443\pi$
$200$	−200.000	−0.0707107
$201$	−2891.56	−1.01470
$202$	−1587.18	−0.552841
$203$	207.669	0.0718005
$204$	663.705	0.227788
$205$	1396.70	0.475852
$206$	1350.92	0.456908
$207$	351.293	0.117955
$208$	973.134	0.324398
$209$	7855.04	2.59973
$210$	177.500	0.0583270
$211$	3649.23	1.19063	0.595315	−	0.803492i	$-0.297027\pi$
$211$	3649.23	1.19063	0.595315	+	0.803492i	$0.297027\pi$
$212$	−1669.66	−0.540908
$213$	2765.99	0.889777
$214$	1559.30	0.498091
$215$	2224.85	0.705739
$216$	−609.942	−0.192136
$217$	400.365	0.125247
$218$	−1971.66	−0.612558
$219$	5432.36	1.67619
$220$	−1161.20	−0.355855
$221$	−1552.15	−0.472438
$222$	5351.85	1.61798
$223$	−825.309	−0.247833	−0.123916	−	0.992293i	$-0.539545\pi$
$223$	−825.309	−0.247833	−0.123916	+	0.992293i	$0.539545\pi$
$224$	−87.3602	−0.0260580
$225$	381.841	0.113138
$226$	−427.832	−0.125925
$227$	6047.64	1.76826	0.884132	−	0.467238i	$-0.154751\pi$
$227$	6047.64	1.76826	0.884132	+	0.467238i	$0.154751\pi$
$228$	3518.57	1.02203
$229$	−4557.36	−1.31510	−0.657551	−	0.753410i	$-0.728408\pi$
$229$	−4557.36	−1.31510	−0.657551	+	0.753410i	$0.728408\pi$
$230$	−230.000	−0.0659380
$231$	1030.56	0.293533
$232$	−608.553	−0.172213
$233$	−4755.29	−1.33704	−0.668518	−	0.743696i	$-0.733071\pi$
$233$	−4755.29	−1.33704	−0.668518	+	0.743696i	$0.733071\pi$
$234$	−1857.91	−0.519040
$235$	302.118	0.0838639
$236$	1897.47	0.523367
$237$	1102.99	0.302308
$238$	139.339	0.0379497
$239$	−4935.94	−1.33590	−0.667948	−	0.744208i	$-0.732827\pi$
$239$	−4935.94	−1.33590	−0.667948	+	0.744208i	$0.732827\pi$
$240$	−520.145	−0.139897
$241$	−2511.38	−0.671253	−0.335626	−	0.941995i	$-0.608948\pi$
$241$	−2511.38	−0.671253	−0.335626	+	0.941995i	$0.608948\pi$
$242$	−4079.92	−1.08375
$243$	3845.77	1.01525
$244$	1723.17	0.452109
$245$	−1677.74	−0.437496
$246$	3632.43	0.941445
$247$	−8228.57	−2.11972
$248$	−1173.23	−0.300404
$249$	−4051.64	−1.03117
$250$	−250.000	−0.0632456
$251$	−5.50802	−0.00138511	−0.000692556	−	1.00000i	$-0.500220\pi$
$251$	−5.50802	−0.00138511	−0.000692556		1.00000i	$0.500220\pi$
$252$	166.788	0.0416932
$253$	−1335.38	−0.331836
$254$	−3981.80	−0.983624
$255$	829.632	0.203739
$256$	256.000	0.0625000
$257$	1516.34	0.368041	0.184021	−	0.982922i	$-0.441089\pi$
$257$	1516.34	0.368041	0.184021	+	0.982922i	$0.441089\pi$
$258$	5786.24	1.39626
$259$	1123.58	0.269558
$260$	1216.42	0.290150
$261$	1161.85	0.275543
$262$	2257.73	0.532379
$263$	1712.56	0.401524	0.200762	−	0.979640i	$-0.435658\pi$
$263$	1712.56	0.401524	0.200762	+	0.979640i	$0.435658\pi$
$264$	−3019.96	−0.704037
$265$	−2087.07	−0.483803
$266$	738.695	0.170272
$267$	−10887.5	−2.49551
$268$	1778.92	0.405467
$269$	−4081.95	−0.925208	−0.462604	−	0.886565i	$-0.653085\pi$
$269$	−4081.95	−0.925208	−0.462604	+	0.886565i	$0.653085\pi$
$270$	−762.427	−0.171851
$271$	−1313.70	−0.294471	−0.147235	−	0.989101i	$-0.547037\pi$
$271$	−1313.70	−0.294471	−0.147235	+	0.989101i	$0.547037\pi$
$272$	−408.320	−0.0910222
$273$	−1079.57	−0.239336
$274$	−1302.14	−0.287098
$275$	−1451.50	−0.318286
$276$	−598.167	−0.130454
$277$	2787.83	0.604709	0.302355	−	0.953196i	$-0.402227\pi$
$277$	2787.83	0.604709	0.302355	+	0.953196i	$0.402227\pi$
$278$	−455.106	−0.0981850
$279$	2239.93	0.480650
$280$	−109.200	−0.0233070
$281$	−2017.23	−0.428249	−0.214124	−	0.976806i	$-0.568690\pi$
$281$	−2017.23	−0.428249	−0.214124	+	0.976806i	$0.568690\pi$
$282$	785.727	0.165920
$283$	−325.902	−0.0684554	−0.0342277	−	0.999414i	$-0.510897\pi$
$283$	−325.902	−0.0684554	−0.0342277	+	0.999414i	$0.510897\pi$
$284$	−1701.67	−0.355548
$285$	4398.21	0.914132
$286$	7062.52	1.46019
$287$	762.600	0.156846
$288$	−488.756	−0.100001
$289$	−4261.73	−0.867439
$290$	−760.691	−0.154032
$291$	−6569.91	−1.32349
$292$	−3342.06	−0.669791
$293$	2696.09	0.537568	0.268784	−	0.963200i	$-0.413378\pi$
$293$	2696.09	0.537568	0.268784	+	0.963200i	$0.413378\pi$
$294$	−4363.33	−0.865560
$295$	2371.84	0.468114
$296$	−3292.52	−0.646534
$297$	−4426.65	−0.864850
$298$	6381.05	1.24042
$299$	1398.88	0.270566
$300$	−650.182	−0.125128
$301$	1214.77	0.232619
$302$	1908.19	0.363589
$303$	−5159.79	−0.978292
$304$	−2164.67	−0.408396
$305$	2153.96	0.404379
$306$	779.566	0.145637
$307$	−2411.07	−0.448232	−0.224116	−	0.974562i	$-0.571949\pi$
$307$	−2411.07	−0.448232	−0.224116	+	0.974562i	$0.571949\pi$
$308$	−634.016	−0.117294
$309$	4391.72	0.808531
$310$	−1466.54	−0.268689
$311$	−7951.50	−1.44980	−0.724901	−	0.688853i	$-0.758114\pi$
$311$	−7951.50	−1.44980	−0.724901	+	0.688853i	$0.758114\pi$
$312$	3163.57	0.574045
$313$	−989.412	−0.178674	−0.0893368	−	0.996001i	$-0.528475\pi$
$313$	−989.412	−0.178674	−0.0893368	+	0.996001i	$0.528475\pi$
$314$	−5656.38	−1.01659
$315$	208.486	0.0372915
$316$	−678.575	−0.120800
$317$	−2862.59	−0.507189	−0.253594	−	0.967311i	$-0.581613\pi$
$317$	−2862.59	−0.507189	−0.253594	+	0.967311i	$0.581613\pi$
$318$	−5427.90	−0.957175
$319$	−4416.57	−0.775174
$320$	320.000	0.0559017
$321$	5069.14	0.881407
$322$	−125.580	−0.0217339
$323$	3452.65	0.594769
$324$	−3632.42	−0.622842
$325$	1520.52	0.259518
$326$	−914.038	−0.155288
$327$	−6409.69	−1.08396
$328$	−2234.72	−0.376194
$329$	164.957	0.0276425
$330$	−3774.95	−0.629710
$331$	6982.52	1.15950	0.579749	−	0.814795i	$-0.303151\pi$
$331$	6982.52	1.15950	0.579749	+	0.814795i	$0.303151\pi$
$332$	2492.62	0.412049
$333$	6286.10	1.03446
$334$	3828.36	0.627182
$335$	2223.66	0.362660
$336$	−284.000	−0.0461115
$337$	5037.32	0.814244	0.407122	−	0.913374i	$-0.366532\pi$
$337$	5037.32	0.814244	0.407122	+	0.913374i	$0.366532\pi$
$338$	−3004.36	−0.483478
$339$	−1390.84	−0.222833
$340$	−510.400	−0.0814127
$341$	−8514.71	−1.35219
$342$	4132.79	0.653438
$343$	−1852.44	−0.291610
$344$	−3559.77	−0.557935
$345$	−747.709	−0.116682
$346$	6668.64	1.03615
$347$	9612.35	1.48708	0.743542	−	0.668690i	$-0.233145\pi$
$347$	9612.35	1.48708	0.743542	+	0.668690i	$0.233145\pi$
$348$	−1978.35	−0.304743
$349$	−841.492	−0.129066	−0.0645330	−	0.997916i	$-0.520556\pi$
$349$	−841.492	−0.129066	−0.0645330	+	0.997916i	$0.520556\pi$
$350$	−136.500	−0.0208464
$351$	4637.15	0.705165
$352$	1857.92	0.281328
$353$	−3687.33	−0.555968	−0.277984	−	0.960586i	$-0.589666\pi$
$353$	−3687.33	−0.555968	−0.277984	+	0.960586i	$0.589666\pi$
$354$	6168.50	0.926135
$355$	−2127.09	−0.318012
$356$	6698.10	0.997187
$357$	452.980	0.0671547
$358$	9033.75	1.33366
$359$	3947.28	0.580305	0.290153	−	0.956980i	$-0.406294\pi$
$359$	3947.28	0.580305	0.290153	+	0.956980i	$0.406294\pi$
$360$	−610.945	−0.0894434
$361$	11444.9	1.66859
$362$	−8927.04	−1.29612
$363$	−13263.5	−1.91777
$364$	664.166	0.0956366
$365$	−4177.57	−0.599080
$366$	5601.87	0.800039
$367$	−7067.93	−1.00529	−0.502647	−	0.864492i	$-0.667640\pi$
$367$	−7067.93	−1.00529	−0.502647	+	0.864492i	$0.667640\pi$
$368$	368.000	0.0521286
$369$	4266.53	0.601916
$370$	−4115.65	−0.578278
$371$	−1139.54	−0.159467
$372$	−3814.06	−0.531586
$373$	3798.67	0.527313	0.263657	−	0.964617i	$-0.415071\pi$
$373$	3798.67	0.527313	0.263657	+	0.964617i	$0.415071\pi$
$374$	−2963.38	−0.409713
$375$	−812.727	−0.111917
$376$	−483.389	−0.0663003
$377$	4626.59	0.632046
$378$	−416.286	−0.0566441
$379$	−5405.21	−0.732577	−0.366289	−	0.930501i	$-0.619372\pi$
$379$	−5405.21	−0.732577	−0.366289	+	0.930501i	$0.619372\pi$
$380$	−2705.84	−0.365280
$381$	−12944.5	−1.74059
$382$	−3533.08	−0.473215
$383$	8357.40	1.11500	0.557498	−	0.830178i	$-0.311761\pi$
$383$	8357.40	1.11500	0.557498	+	0.830178i	$0.311761\pi$
$384$	832.233	0.110598
$385$	−792.521	−0.104911
$386$	−1196.31	−0.157748
$387$	6796.32	0.892704
$388$	4041.89	0.528855
$389$	8070.10	1.05185	0.525926	−	0.850530i	$-0.323719\pi$
$389$	8070.10	1.05185	0.525926	+	0.850530i	$0.323719\pi$
$390$	3954.46	0.513441
$391$	−586.960	−0.0759177
$392$	2684.38	0.345871
$393$	7339.69	0.942082
$394$	−4709.52	−0.602189
$395$	−848.219	−0.108047
$396$	−3547.15	−0.450128
$397$	7274.45	0.919633	0.459816	−	0.888014i	$-0.347915\pi$
$397$	7274.45	0.919633	0.459816	+	0.888014i	$0.347915\pi$
$398$	−5457.67	−0.687357
$399$	2401.43	0.301308
$400$	400.000	0.0500000
$401$	13501.5	1.68138	0.840692	−	0.541514i	$-0.182149\pi$
$401$	13501.5	1.68138	0.840692	+	0.541514i	$0.182149\pi$
$402$	5783.12	0.717502
$403$	8919.61	1.10252
$404$	3174.37	0.390918
$405$	−4540.52	−0.557087
$406$	−415.338	−0.0507707
$407$	−23895.5	−2.91021
$408$	−1327.41	−0.161070
$409$	−3887.99	−0.470046	−0.235023	−	0.971990i	$-0.575517\pi$
$409$	−3887.99	−0.470046	−0.235023	+	0.971990i	$0.575517\pi$
$410$	−2793.40	−0.336478
$411$	−4233.13	−0.508041
$412$	−2701.84	−0.323083
$413$	1295.03	0.154295
$414$	−702.587	−0.0834064
$415$	3115.77	0.368547
$416$	−1946.27	−0.229384
$417$	−1479.51	−0.173745
$418$	−15710.1	−1.83829
$419$	4416.78	0.514973	0.257486	−	0.966282i	$-0.417106\pi$
$419$	4416.78	0.514973	0.257486	+	0.966282i	$0.417106\pi$
$420$	−355.000	−0.0412434
$421$	−14065.5	−1.62829	−0.814145	−	0.580661i	$-0.802794\pi$
$421$	−14065.5	−1.62829	−0.814145	+	0.580661i	$0.802794\pi$
$422$	−7298.45	−0.841903
$423$	922.888	0.106081
$424$	3339.32	0.382480
$425$	−638.000	−0.0728177
$426$	−5531.98	−0.629168
$427$	1176.07	0.133288
$428$	−3118.60	−0.352203
$429$	22959.6	2.58392
$430$	−4449.71	−0.499033
$431$	12344.3	1.37959	0.689794	−	0.724006i	$-0.257701\pi$
$431$	12344.3	1.37959	0.689794	+	0.724006i	$0.257701\pi$
$432$	1219.88	0.135860
$433$	5439.20	0.603675	0.301837	−	0.953359i	$-0.402400\pi$
$433$	5439.20	0.603675	0.301837	+	0.953359i	$0.402400\pi$
$434$	−800.731	−0.0885629
$435$	−2472.94	−0.272571
$436$	3943.32	0.433144
$437$	−3111.71	−0.340626
$438$	−10864.7	−1.18524
$439$	1216.82	0.132290	0.0661452	−	0.997810i	$-0.478930\pi$
$439$	1216.82	0.132290	0.0661452	+	0.997810i	$0.478930\pi$
$440$	2322.40	0.251627
$441$	−5125.02	−0.553398
$442$	3104.30	0.334064
$443$	14338.4	1.53779	0.768893	−	0.639378i	$-0.220808\pi$
$443$	14338.4	1.53779	0.768893	+	0.639378i	$0.220808\pi$
$444$	−10703.7	−1.14409
$445$	8372.63	0.891911
$446$	1650.62	0.175244
$447$	20744.2	2.19500
$448$	174.720	0.0184258
$449$	−3502.78	−0.368166	−0.184083	−	0.982911i	$-0.558932\pi$
$449$	−3502.78	−0.368166	−0.184083	+	0.982911i	$0.558932\pi$
$450$	−763.681	−0.0800006
$451$	−16218.5	−1.69334
$452$	855.664	0.0890422
$453$	6203.35	0.643397
$454$	−12095.3	−1.25035
$455$	830.207	0.0855400
$456$	−7037.14	−0.722685
$457$	−4207.17	−0.430641	−0.215321	−	0.976543i	$-0.569080\pi$
$457$	−4207.17	−0.430641	−0.215321	+	0.976543i	$0.569080\pi$
$458$	9114.71	0.929918
$459$	−1945.71	−0.197861
$460$	460.000	0.0466252
$461$	−468.801	−0.0473628	−0.0236814	−	0.999720i	$-0.507539\pi$
$461$	−468.801	−0.0473628	−0.0236814	+	0.999720i	$0.507539\pi$
$462$	−2061.13	−0.207559
$463$	−3612.40	−0.362598	−0.181299	−	0.983428i	$-0.558030\pi$
$463$	−3612.40	−0.362598	−0.181299	+	0.983428i	$0.558030\pi$
$464$	1217.11	0.121773
$465$	−4767.58	−0.475465
$466$	9510.58	0.945427
$467$	4794.07	0.475038	0.237519	−	0.971383i	$-0.423666\pi$
$467$	4794.07	0.475038	0.237519	+	0.971383i	$0.423666\pi$
$468$	3715.82	0.367017
$469$	1214.12	0.119537
$470$	−604.237	−0.0593008
$471$	−18388.4	−1.79892
$472$	−3794.94	−0.370077
$473$	−25835.0	−2.51141
$474$	−2205.99	−0.213764
$475$	−3382.30	−0.326717
$476$	−278.679	−0.0268345
$477$	−6375.43	−0.611973
$478$	9871.87	0.944621
$479$	1544.58	0.147335	0.0736677	−	0.997283i	$-0.476530\pi$
$479$	1544.58	0.147335	0.0736677	+	0.997283i	$0.476530\pi$
$480$	1040.29	0.0989220
$481$	25031.8	2.37287
$482$	5022.75	0.474647
$483$	−408.250	−0.0384597
$484$	8159.84	0.766326
$485$	5052.36	0.473023
$486$	−7691.55	−0.717892
$487$	−14437.6	−1.34339	−0.671695	−	0.740828i	$-0.734433\pi$
$487$	−14437.6	−1.34339	−0.671695	+	0.740828i	$0.734433\pi$
$488$	−3446.34	−0.319690
$489$	−2971.46	−0.274793
$490$	3355.47	0.309357
$491$	17252.2	1.58570	0.792851	−	0.609416i	$-0.208596\pi$
$491$	17252.2	1.58570	0.792851	+	0.609416i	$0.208596\pi$
$492$	−7264.87	−0.665702
$493$	−1941.28	−0.177345
$494$	16457.1	1.49887
$495$	−4433.93	−0.402607
$496$	2346.46	0.212418
$497$	−1161.39	−0.104820
$498$	8103.27	0.729149
$499$	20118.4	1.80486	0.902430	−	0.430836i	$-0.141781\pi$
$499$	20118.4	1.80486	0.902430	+	0.430836i	$0.141781\pi$
$500$	500.000	0.0447214
$501$	12445.7	1.10984
$502$	11.0160	0.000979422 0
$503$	−1537.38	−0.136279	−0.0681397	−	0.997676i	$-0.521706\pi$
$503$	−1537.38	−0.136279	−0.0681397	+	0.997676i	$0.521706\pi$
$504$	−333.577	−0.0294815
$505$	3967.96	0.349648
$506$	2670.76	0.234644
$507$	−9766.90	−0.855549
$508$	7963.60	0.695527
$509$	7757.27	0.675511	0.337755	−	0.941234i	$-0.390332\pi$
$509$	7757.27	0.675511	0.337755	+	0.941234i	$0.390332\pi$
$510$	−1659.26	−0.144066
$511$	−2280.96	−0.197463
$512$	−512.000	−0.0441942
$513$	−10315.0	−0.887756
$514$	−3032.68	−0.260245
$515$	−3377.30	−0.288974
$516$	−11572.5	−0.987306
$517$	−3508.20	−0.298434
$518$	−2247.15	−0.190607
$519$	21679.2	1.83354
$520$	−2432.84	−0.205167
$521$	−19463.5	−1.63668	−0.818342	−	0.574732i	$-0.805106\pi$
$521$	−19463.5	−1.63668	−0.818342	+	0.574732i	$0.805106\pi$
$522$	−2323.70	−0.194838
$523$	8640.74	0.722435	0.361217	−	0.932482i	$-0.382361\pi$
$523$	8640.74	0.722435	0.361217	+	0.932482i	$0.382361\pi$
$524$	−4515.47	−0.376449
$525$	−443.750	−0.0368892
$526$	−3425.11	−0.283920
$527$	−3742.60	−0.309355
$528$	6039.93	0.497830
$529$	529.000	0.0434783
$530$	4174.14	0.342100
$531$	7245.31	0.592127
$532$	−1477.39	−0.120400
$533$	16989.7	1.38069
$534$	21774.9	1.76459
$535$	−3898.25	−0.315020
$536$	−3557.85	−0.286708
$537$	29367.9	2.36000
$538$	8163.91	0.654221
$539$	19481.9	1.55685
$540$	1524.85	0.121517
$541$	−3428.37	−0.272453	−0.136226	−	0.990678i	$-0.543497\pi$
$541$	−3428.37	−0.272453	−0.136226	+	0.990678i	$0.543497\pi$
$542$	2627.40	0.208222
$543$	−29021.0	−2.29357
$544$	816.640	0.0643624
$545$	4929.15	0.387416
$546$	2159.14	0.169236
$547$	6246.03	0.488228	0.244114	−	0.969746i	$-0.421503\pi$
$547$	6246.03	0.488228	0.244114	+	0.969746i	$0.421503\pi$
$548$	2604.27	0.203009
$549$	6579.77	0.511507
$550$	2903.00	0.225062
$551$	−10291.5	−0.795705
$552$	1196.33	0.0922452
$553$	−463.129	−0.0356134
$554$	−5575.66	−0.427594
$555$	−13379.6	−1.02330
$556$	910.211	0.0694273
$557$	19065.0	1.45028	0.725142	−	0.688599i	$-0.241774\pi$
$557$	19065.0	1.45028	0.725142	+	0.688599i	$0.241774\pi$
$558$	−4479.87	−0.339871
$559$	27063.5	2.04770
$560$	218.401	0.0164805
$561$	−9633.68	−0.725016
$562$	4034.46	0.302817
$563$	−14965.2	−1.12027	−0.560133	−	0.828403i	$-0.689250\pi$
$563$	−14965.2	−1.12027	−0.560133	+	0.828403i	$0.689250\pi$
$564$	−1571.45	−0.117323
$565$	1069.58	0.0796417
$566$	651.805	0.0484053
$567$	−2479.13	−0.183622
$568$	3403.35	0.251411
$569$	12421.6	0.915185	0.457593	−	0.889162i	$-0.348712\pi$
$569$	12421.6	0.915185	0.457593	+	0.889162i	$0.348712\pi$
$570$	−8796.43	−0.646389
$571$	4517.92	0.331120	0.165560	−	0.986200i	$-0.447057\pi$
$571$	4517.92	0.331120	0.165560	+	0.986200i	$0.447057\pi$
$572$	−14125.0	−1.03251
$573$	−11485.7	−0.837388
$574$	−1525.20	−0.110907
$575$	575.000	0.0417029
$576$	977.512	0.0707112
$577$	−18827.0	−1.35837	−0.679184	−	0.733968i	$-0.737666\pi$
$577$	−18827.0	−1.35837	−0.679184	+	0.733968i	$0.737666\pi$
$578$	8523.46	0.613372
$579$	−3889.10	−0.279146
$580$	1521.38	0.108917
$581$	1701.22	0.121477
$582$	13139.8	0.935847
$583$	24235.1	1.72164
$584$	6684.11	0.473614
$585$	4644.78	0.328270
$586$	−5392.19	−0.380118
$587$	−11036.1	−0.775993	−0.387996	−	0.921661i	$-0.626833\pi$
$587$	−11036.1	−0.775993	−0.387996	+	0.921661i	$0.626833\pi$
$588$	8726.66	0.612043
$589$	−19841.0	−1.38801
$590$	−4743.67	−0.331007
$591$	−15310.2	−1.06562
$592$	6585.05	0.457169
$593$	−5459.17	−0.378046	−0.189023	−	0.981973i	$-0.560532\pi$
$593$	−5459.17	−0.378046	−0.189023	+	0.981973i	$0.560532\pi$
$594$	8853.30	0.611541
$595$	−348.349	−0.0240015
$596$	−12762.1	−0.877107
$597$	−17742.4	−1.21633
$598$	−2797.76	−0.191319
$599$	4065.23	0.277297	0.138648	−	0.990342i	$-0.455724\pi$
$599$	4065.23	0.277297	0.138648	+	0.990342i	$0.455724\pi$
$600$	1300.36	0.0884785
$601$	13664.7	0.927443	0.463722	−	0.885981i	$-0.346514\pi$
$601$	13664.7	0.927443	0.463722	+	0.885981i	$0.346514\pi$
$602$	−2429.55	−0.164487
$603$	6792.66	0.458737
$604$	−3816.38	−0.257096
$605$	10199.8	0.685423
$606$	10319.6	0.691757
$607$	−22214.5	−1.48543	−0.742716	−	0.669606i	$-0.766463\pi$
$607$	−22214.5	−1.48543	−0.742716	+	0.669606i	$0.766463\pi$
$608$	4329.34	0.288779
$609$	−1350.23	−0.0898422
$610$	−4307.93	−0.285939
$611$	3675.02	0.243331
$612$	−1559.13	−0.102981
$613$	18941.2	1.24800	0.624002	−	0.781423i	$-0.285506\pi$
$613$	18941.2	1.24800	0.624002	+	0.781423i	$0.285506\pi$
$614$	4822.15	0.316948
$615$	−9081.08	−0.595422
$616$	1268.03	0.0829391
$617$	13188.8	0.860550	0.430275	−	0.902698i	$-0.358417\pi$
$617$	13188.8	0.860550	0.430275	+	0.902698i	$0.358417\pi$
$618$	−8783.43	−0.571718
$619$	15094.4	0.980124	0.490062	−	0.871688i	$-0.336974\pi$
$619$	15094.4	0.980124	0.490062	+	0.871688i	$0.336974\pi$
$620$	2933.07	0.189992
$621$	1753.58	0.113315
$622$	15903.0	1.02516
$623$	4571.46	0.293984
$624$	−6327.14	−0.405911
$625$	625.000	0.0400000
$626$	1978.82	0.126341
$627$	−51072.0	−3.25298
$628$	11312.8	0.718834
$629$	−10503.1	−0.665799
$630$	−416.971	−0.0263691
$631$	−9183.83	−0.579401	−0.289701	−	0.957117i	$-0.593556\pi$
$631$	−9183.83	−0.579401	−0.289701	+	0.957117i	$0.593556\pi$
$632$	1357.15	0.0854186
$633$	−23726.6	−1.48981
$634$	5725.17	0.358637
$635$	9954.51	0.622098
$636$	10855.8	0.676825
$637$	−20408.3	−1.26940
$638$	8833.14	0.548130
$639$	−6497.68	−0.402260
$640$	−640.000	−0.0395285
$641$	5367.34	0.330729	0.165364	−	0.986233i	$-0.447120\pi$
$641$	5367.34	0.330729	0.165364	+	0.986233i	$0.447120\pi$
$642$	−10138.3	−0.623249
$643$	−27594.2	−1.69240	−0.846198	−	0.532868i	$-0.821114\pi$
$643$	−27594.2	−1.69240	−0.846198	+	0.532868i	$0.821114\pi$
$644$	251.161	0.0153682
$645$	−14465.6	−0.883073
$646$	−6905.29	−0.420565
$647$	−4129.95	−0.250951	−0.125475	−	0.992097i	$-0.540046\pi$
$647$	−4129.95	−0.250951	−0.125475	+	0.992097i	$0.540046\pi$
$648$	7264.83	0.440416
$649$	−27541.7	−1.66581
$650$	−3041.04	−0.183507
$651$	−2603.10	−0.156718
$652$	1828.08	0.109805
$653$	17419.5	1.04391	0.521957	−	0.852972i	$-0.325202\pi$
$653$	17419.5	1.04391	0.521957	+	0.852972i	$0.325202\pi$
$654$	12819.4	0.766479
$655$	−5644.33	−0.336706
$656$	4469.44	0.266009
$657$	−12761.3	−0.757788
$658$	−329.914	−0.0195462
$659$	577.196	0.0341189	0.0170594	−	0.999854i	$-0.494570\pi$
$659$	577.196	0.0341189	0.0170594	+	0.999854i	$0.494570\pi$
$660$	7549.91	0.445272
$661$	−3858.11	−0.227024	−0.113512	−	0.993537i	$-0.536210\pi$
$661$	−3858.11	−0.227024	−0.113512	+	0.993537i	$0.536210\pi$
$662$	−13965.0	−0.819889
$663$	10091.8	0.591150
$664$	−4985.23	−0.291362
$665$	−1846.74	−0.107689
$666$	−12572.2	−0.731475
$667$	1749.59	0.101566
$668$	−7656.72	−0.443484
$669$	5366.01	0.310107
$670$	−4447.31	−0.256440
$671$	−25011.8	−1.43900
$672$	568.000	0.0326058
$673$	−28439.6	−1.62892	−0.814461	−	0.580218i	$-0.802967\pi$
$673$	−28439.6	−1.62892	−0.814461	+	0.580218i	$0.802967\pi$
$674$	−10074.6	−0.575758
$675$	1906.07	0.108688
$676$	6008.72	0.341871
$677$	−13186.6	−0.748601	−0.374300	−	0.927308i	$-0.622117\pi$
$677$	−13186.6	−0.748601	−0.374300	+	0.927308i	$0.622117\pi$
$678$	2781.69	0.157566
$679$	2758.60	0.155913
$680$	1020.80	0.0575675
$681$	−39320.6	−2.21258
$682$	17029.4	0.956144
$683$	3508.39	0.196552	0.0982758	−	0.995159i	$-0.468667\pi$
$683$	3508.39	0.196552	0.0982758	+	0.995159i	$0.468667\pi$
$684$	−8265.59	−0.462051
$685$	3255.34	0.181577
$686$	3704.88	0.206199
$687$	29631.1	1.64556
$688$	7119.53	0.394520
$689$	−25387.5	−1.40375
$690$	1495.42	0.0825067
$691$	22652.9	1.24712	0.623558	−	0.781777i	$-0.285687\pi$
$691$	22652.9	1.24712	0.623558	+	0.781777i	$0.285687\pi$
$692$	−13337.3	−0.732670
$693$	−2420.93	−0.132704
$694$	−19224.7	−1.05153
$695$	1137.76	0.0620976
$696$	3956.70	0.215486
$697$	−7128.75	−0.387404
$698$	1682.98	0.0912635
$699$	30918.0	1.67300
$700$	273.001	0.0147406
$701$	15393.8	0.829412	0.414706	−	0.909956i	$-0.363885\pi$
$701$	15393.8	0.829412	0.414706	+	0.909956i	$0.363885\pi$
$702$	−9274.30	−0.498627
$703$	−55681.4	−2.98729
$704$	−3715.84	−0.198929
$705$	−1964.32	−0.104937
$706$	7374.66	0.393129
$707$	2166.51	0.115248
$708$	−12337.0	−0.654877
$709$	−33826.6	−1.79180	−0.895898	−	0.444260i	$-0.853467\pi$
$709$	−33826.6	−1.79180	−0.895898	+	0.444260i	$0.853467\pi$
$710$	4254.18	0.224868
$711$	−2591.08	−0.136671
$712$	−13396.2	−0.705118
$713$	3373.03	0.177168
$714$	−905.960	−0.0474856
$715$	−17656.3	−0.923508
$716$	−18067.5	−0.943037
$717$	32092.6	1.67157
$718$	−7894.57	−0.410338
$719$	−20975.5	−1.08798	−0.543988	−	0.839093i	$-0.683086\pi$
$719$	−20975.5	−1.08798	−0.543988	+	0.839093i	$0.683086\pi$
$720$	1221.89	0.0632461
$721$	−1844.01	−0.0952490
$722$	−22889.7	−1.17987
$723$	16328.5	0.839922
$724$	17854.1	0.916494
$725$	1901.73	0.0974184
$726$	26526.9	1.35607
$727$	24780.4	1.26417	0.632086	−	0.774898i	$-0.282199\pi$
$727$	24780.4	1.26417	0.632086	+	0.774898i	$0.282199\pi$
$728$	−1328.33	−0.0676253
$729$	−485.707	−0.0246765
$730$	8355.14	0.423613
$731$	−11355.7	−0.574561
$732$	−11203.7	−0.565713
$733$	−16951.6	−0.854189	−0.427094	−	0.904207i	$-0.640463\pi$
$733$	−16951.6	−0.854189	−0.427094	+	0.904207i	$0.640463\pi$
$734$	14135.9	0.710850
$735$	10908.3	0.547428
$736$	−736.000	−0.0368605
$737$	−25821.1	−1.29054
$738$	−8533.07	−0.425619
$739$	−9849.67	−0.490292	−0.245146	−	0.969486i	$-0.578836\pi$
$739$	−9849.67	−0.490292	−0.245146	+	0.969486i	$0.578836\pi$
$740$	8231.31	0.408904
$741$	53500.6	2.65236
$742$	2279.09	0.112760
$743$	37095.1	1.83161	0.915805	−	0.401623i	$-0.131554\pi$
$743$	37095.1	1.83161	0.915805	+	0.401623i	$0.131554\pi$
$744$	7628.12	0.375888
$745$	−15952.6	−0.784508
$746$	−7597.35	−0.372867
$747$	9517.83	0.466184
$748$	5926.76	0.289711
$749$	−2128.45	−0.103834
$750$	1625.45	0.0791376
$751$	10943.1	0.531718	0.265859	−	0.964012i	$-0.414344\pi$
$751$	10943.1	0.531718	0.265859	+	0.964012i	$0.414344\pi$
$752$	966.778	0.0468814
$753$	35.8121	0.00173316
$754$	−9253.18	−0.446924
$755$	−4770.47	−0.229954
$756$	832.573	0.0400534
$757$	36604.3	1.75747	0.878737	−	0.477307i	$-0.158387\pi$
$757$	36604.3	1.75747	0.878737	+	0.477307i	$0.158387\pi$
$758$	10810.4	0.518010
$759$	8682.39	0.415219
$760$	5411.67	0.258292
$761$	12046.3	0.573823	0.286912	−	0.957957i	$-0.407371\pi$
$761$	12046.3	0.573823	0.286912	+	0.957957i	$0.407371\pi$
$762$	25889.0	1.23078
$763$	2691.32	0.127696
$764$	7066.16	0.334614
$765$	−1948.91	−0.0921087
$766$	−16714.8	−0.788421
$767$	28851.4	1.35823
$768$	−1664.47	−0.0782047
$769$	−27690.3	−1.29849	−0.649243	−	0.760581i	$-0.724914\pi$
$769$	−27690.3	−1.29849	−0.649243	+	0.760581i	$0.724914\pi$
$770$	1585.04	0.0741830
$771$	−9858.96	−0.460521
$772$	2392.62	0.111544
$773$	−26922.2	−1.25268	−0.626341	−	0.779550i	$-0.715448\pi$
$773$	−26922.2	−1.25268	−0.626341	+	0.779550i	$0.715448\pi$
$774$	−13592.6	−0.631237
$775$	3666.34	0.169934
$776$	−8083.78	−0.373957
$777$	−7305.29	−0.337292
$778$	−16140.2	−0.743772
$779$	−37792.4	−1.73819
$780$	−7908.93	−0.363058
$781$	24699.8	1.13166
$782$	1173.92	0.0536819
$783$	5799.71	0.264706
$784$	−5368.75	−0.244568
$785$	14140.9	0.642945
$786$	−14679.4	−0.666152
$787$	36138.1	1.63683	0.818414	−	0.574629i	$-0.194853\pi$
$787$	36138.1	1.63683	0.818414	+	0.574629i	$0.194853\pi$
$788$	9419.05	0.425812
$789$	−11134.7	−0.502417
$790$	1696.44	0.0764007
$791$	583.992	0.0262508
$792$	7094.29	0.318289
$793$	26201.2	1.17331
$794$	−14548.9	−0.650279
$795$	13569.8	0.605371
$796$	10915.3	0.486035
$797$	12371.9	0.549855	0.274928	−	0.961465i	$-0.411346\pi$
$797$	12371.9	0.549855	0.274928	+	0.961465i	$0.411346\pi$
$798$	−4802.86	−0.213057
$799$	−1542.01	−0.0682759
$800$	−800.000	−0.0353553
$801$	25576.1	1.12820
$802$	−27003.1	−1.18892
$803$	48509.9	2.13185
$804$	−11566.2	−0.507350
$805$	313.951	0.0137457
$806$	−17839.2	−0.779602
$807$	26540.1	1.15769
$808$	−6348.74	−0.276421
$809$	−21068.0	−0.915588	−0.457794	−	0.889058i	$-0.651360\pi$
$809$	−21068.0	−0.915588	−0.457794	+	0.889058i	$0.651360\pi$
$810$	9081.04	0.393920
$811$	−12595.5	−0.545360	−0.272680	−	0.962105i	$-0.587910\pi$
$811$	−12595.5	−0.545360	−0.272680	+	0.962105i	$0.587910\pi$
$812$	830.676	0.0359003
$813$	8541.43	0.368464
$814$	47791.0	2.05783
$815$	2285.10	0.0982128
$816$	2654.82	0.113894
$817$	−60200.9	−2.57792
$818$	7775.98	0.332373
$819$	2536.05	0.108201
$820$	5586.80	0.237926
$821$	33947.7	1.44310	0.721549	−	0.692363i	$-0.243430\pi$
$821$	33947.7	1.44310	0.721549	+	0.692363i	$0.243430\pi$
$822$	8466.26	0.359239
$823$	13026.1	0.551715	0.275857	−	0.961199i	$-0.411038\pi$
$823$	13026.1	0.551715	0.275857	+	0.961199i	$0.411038\pi$
$824$	5403.68	0.228454
$825$	9437.38	0.398264
$826$	−2590.05	−0.109103
$827$	6209.08	0.261077	0.130539	−	0.991443i	$-0.458329\pi$
$827$	6209.08	0.261077	0.130539	+	0.991443i	$0.458329\pi$
$828$	1405.17	0.0589773
$829$	7291.20	0.305469	0.152735	−	0.988267i	$-0.451192\pi$
$829$	7291.20	0.305469	0.152735	+	0.988267i	$0.451192\pi$
$830$	−6231.54	−0.260602
$831$	−18126.0	−0.756658
$832$	3892.54	0.162199
$833$	8563.16	0.356177
$834$	2959.01	0.122856
$835$	−9570.91	−0.396664
$836$	31420.2	1.29987
$837$	11181.3	0.461746
$838$	−8833.55	−0.364141
$839$	764.741	0.0314682	0.0157341	−	0.999876i	$-0.494991\pi$
$839$	764.741	0.0314682	0.0157341	+	0.999876i	$0.494991\pi$
$840$	710.000	0.0291635
$841$	−18602.5	−0.762741
$842$	28131.0	1.15138
$843$	13115.7	0.535857
$844$	14596.9	0.595315
$845$	7510.90	0.305778
$846$	−1845.78	−0.0750108
$847$	5569.11	0.225923
$848$	−6678.63	−0.270454
$849$	2118.96	0.0856566
$850$	1276.00	0.0514899
$851$	9466.00	0.381305
$852$	11064.0	0.444889
$853$	−2306.94	−0.0926003	−0.0463002	−	0.998928i	$-0.514743\pi$
$853$	−2306.94	−0.0926003	−0.0463002	+	0.998928i	$0.514743\pi$
$854$	−2352.13	−0.0942486
$855$	−10332.0	−0.413271
$856$	6237.19	0.249045
$857$	−34838.6	−1.38864	−0.694320	−	0.719666i	$-0.744295\pi$
$857$	−34838.6	−1.38864	−0.694320	+	0.719666i	$0.744295\pi$
$858$	−45919.2	−1.82710
$859$	−38882.0	−1.54440	−0.772199	−	0.635380i	$-0.780843\pi$
$859$	−38882.0	−1.54440	−0.772199	+	0.635380i	$0.780843\pi$
$860$	8899.42	0.352869
$861$	−4958.28	−0.196258
$862$	−24688.5	−0.975516
$863$	19124.0	0.754334	0.377167	−	0.926145i	$-0.376898\pi$
$863$	19124.0	0.754334	0.377167	+	0.926145i	$0.376898\pi$
$864$	−2439.77	−0.0960678
$865$	−16671.6	−0.655320
$866$	−10878.4	−0.426862
$867$	27709.0	1.08541
$868$	1601.46	0.0626235
$869$	9849.51	0.384490
$870$	4945.87	0.192737
$871$	27048.9	1.05226
$872$	−7886.64	−0.306279
$873$	15433.6	0.598336
$874$	6223.42	0.240859
$875$	341.251	0.0131844
$876$	21729.4	0.838093
$877$	−38827.9	−1.49501	−0.747505	−	0.664256i	$-0.768749\pi$
$877$	−38827.9	−1.49501	−0.747505	+	0.664256i	$0.768749\pi$
$878$	−2433.63	−0.0935434
$879$	−17529.5	−0.672646
$880$	−4644.80	−0.177927
$881$	30392.1	1.16224	0.581121	−	0.813817i	$-0.302614\pi$
$881$	30392.1	1.16224	0.581121	+	0.813817i	$0.302614\pi$
$882$	10250.0	0.391312
$883$	2520.10	0.0960453	0.0480226	−	0.998846i	$-0.484708\pi$
$883$	2520.10	0.0960453	0.0480226	+	0.998846i	$0.484708\pi$
$884$	−6208.59	−0.236219
$885$	−15421.2	−0.585739
$886$	−28676.8	−1.08738
$887$	16141.7	0.611032	0.305516	−	0.952187i	$-0.401171\pi$
$887$	16141.7	0.611032	0.305516	+	0.952187i	$0.401171\pi$
$888$	21407.4	0.808992
$889$	5435.17	0.205050
$890$	−16745.3	−0.630676
$891$	52724.5	1.98242
$892$	−3301.23	−0.123916
$893$	−8174.82	−0.306338
$894$	−41488.4	−1.55210
$895$	−22584.4	−0.843478
$896$	−349.441	−0.0130290
$897$	−9095.26	−0.338553
$898$	7005.57	0.260333
$899$	11155.8	0.413868
$900$	1527.36	0.0565690
$901$	10652.4	0.393877
$902$	32436.9	1.19737
$903$	−7898.24	−0.291071
$904$	−1711.33	−0.0629623
$905$	22317.6	0.819737
$906$	−12406.7	−0.454950
$907$	54155.5	1.98258	0.991292	−	0.131684i	$-0.0420384\pi$
$907$	54155.5	1.98258	0.991292	+	0.131684i	$0.0420384\pi$
$908$	24190.5	0.884132
$909$	12121.0	0.442277
$910$	−1660.41	−0.0604859
$911$	−20067.1	−0.729805	−0.364903	−	0.931046i	$-0.618898\pi$
$911$	−20067.1	−0.729805	−0.364903	+	0.931046i	$0.618898\pi$
$912$	14074.3	0.511015
$913$	−36180.3	−1.31149
$914$	8414.34	0.304509
$915$	−14004.7	−0.505989
$916$	−18229.4	−0.657551
$917$	−3081.81	−0.110982
$918$	3891.43	0.139909
$919$	34816.2	1.24971	0.624854	−	0.780742i	$-0.285159\pi$
$919$	34816.2	1.24971	0.624854	+	0.780742i	$0.285159\pi$
$920$	−920.000	−0.0329690
$921$	15676.4	0.560862
$922$	937.602	0.0334906
$923$	−25874.3	−0.922712
$924$	4122.26	0.146767
$925$	10289.1	0.365735
$926$	7224.81	0.256395
$927$	−10316.7	−0.365529
$928$	−2434.21	−0.0861065
$929$	10936.8	0.386250	0.193125	−	0.981174i	$-0.438138\pi$
$929$	10936.8	0.386250	0.193125	+	0.981174i	$0.438138\pi$
$930$	9535.15	0.336204
$931$	45396.8	1.59809
$932$	−19021.2	−0.668518
$933$	51699.2	1.81410
$934$	−9588.13	−0.335903
$935$	7408.45	0.259125
$936$	−7431.64	−0.259520
$937$	−41240.6	−1.43786	−0.718928	−	0.695085i	$-0.755367\pi$
$937$	−41240.6	−1.43786	−0.718928	+	0.695085i	$0.755367\pi$
$938$	−2428.24	−0.0845253
$939$	6432.97	0.223570
$940$	1208.47	0.0419320
$941$	−39978.4	−1.38497	−0.692486	−	0.721431i	$-0.743485\pi$
$941$	−39978.4	−1.38497	−0.692486	+	0.721431i	$0.743485\pi$
$942$	36776.7	1.27203
$943$	6424.82	0.221867
$944$	7589.87	0.261684
$945$	1040.72	0.0358249
$946$	51670.0	1.77583
$947$	−23729.0	−0.814242	−0.407121	−	0.913374i	$-0.633467\pi$
$947$	−23729.0	−0.814242	−0.407121	+	0.913374i	$0.633467\pi$
$948$	4411.97	0.151154
$949$	−50816.7	−1.73823
$950$	6764.59	0.231023
$951$	18612.0	0.634633
$952$	557.358	0.0189749
$953$	−1214.35	−0.0412767	−0.0206383	−	0.999787i	$-0.506570\pi$
$953$	−1214.35	−0.0412767	−0.0206383	+	0.999787i	$0.506570\pi$
$954$	12750.9	0.432730
$955$	8832.70	0.299288
$956$	−19743.7	−0.667948
$957$	28715.7	0.969956
$958$	−3089.16	−0.104182
$959$	1777.42	0.0598498
$960$	−2080.58	−0.0699484
$961$	−8283.70	−0.278061
$962$	−50063.5	−1.67787
$963$	−11908.1	−0.398476
$964$	−10045.5	−0.335626
$965$	2990.78	0.0997684
$966$	816.500	0.0271951
$967$	42431.8	1.41108	0.705540	−	0.708670i	$-0.250704\pi$
$967$	42431.8	1.41108	0.705540	+	0.708670i	$0.250704\pi$
$968$	−16319.7	−0.541875
$969$	−22448.5	−0.744220
$970$	−10104.7	−0.334477
$971$	−3273.42	−0.108187	−0.0540933	−	0.998536i	$-0.517227\pi$
$971$	−3273.42	−0.108187	−0.0540933	+	0.998536i	$0.517227\pi$
$972$	15383.1	0.507627
$973$	621.221	0.0204681
$974$	28875.2	0.949920
$975$	−9886.16	−0.324729
$976$	6892.68	0.226055
$977$	−32057.9	−1.04977	−0.524884	−	0.851174i	$-0.675891\pi$
$977$	−32057.9	−1.04977	−0.524884	+	0.851174i	$0.675891\pi$
$978$	5942.91	0.194308
$979$	−97222.9	−3.17391
$980$	−6710.94	−0.218748
$981$	15057.2	0.490050
$982$	−34504.3	−1.12126
$983$	21721.1	0.704777	0.352388	−	0.935854i	$-0.385370\pi$
$983$	21721.1	0.704777	0.352388	+	0.935854i	$0.385370\pi$
$984$	14529.7	0.470723
$985$	11773.8	0.380858
$986$	3882.56	0.125402
$987$	−1072.52	−0.0345883
$988$	−32914.3	−1.05986
$989$	10234.3	0.329052
$990$	8867.87	0.284686
$991$	5969.62	0.191353	0.0956767	−	0.995412i	$-0.469499\pi$
$991$	5969.62	0.191353	0.0956767	+	0.995412i	$0.469499\pi$
$992$	−4692.92	−0.150202
$993$	−45399.0	−1.45085
$994$	2322.79	0.0741191
$995$	13644.2	0.434723
$996$	−16206.5	−0.515586
$997$	35140.4	1.11626	0.558128	−	0.829755i	$-0.311520\pi$
$997$	35140.4	1.11626	0.558128	+	0.829755i	$0.311520\pi$
$998$	−40236.9	−1.27623
$999$	31378.9	0.993777

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.g.1.1	✓	3
3.2	odd	2		2070.4.a.ba.1.2		3
4.3	odd	2		1840.4.a.j.1.3		3
5.2	odd	4		1150.4.b.l.599.3		6
5.3	odd	4		1150.4.b.l.599.4		6
5.4	even	2		1150.4.a.m.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.g.1.1	✓	3	1.1	even	1	trivial
1150.4.a.m.1.3		3	5.4	even	2
1150.4.b.l.599.3		6	5.2	odd	4
1150.4.b.l.599.4		6	5.3	odd	4
1840.4.a.j.1.3		3	4.3	odd	2
2070.4.a.ba.1.2		3	3.2	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -6.50182 q^{3} +4.00000 q^{4} +5.00000 q^{5} +13.0036 q^{6} +2.73001 q^{7} -8.00000 q^{8} +15.2736 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -6.50182 q^{3} +4.00000 q^{4} +5.00000 q^{5} +13.0036 q^{6} +2.73001 q^{7} -8.00000 q^{8} +15.2736 q^{9} -10.0000 q^{10} -58.0600 q^{11} -26.0073 q^{12} +60.8209 q^{13} -5.46001 q^{14} -32.5091 q^{15} +16.0000 q^{16} -25.5200 q^{17} -30.5473 q^{18} -135.292 q^{19} +20.0000 q^{20} -17.7500 q^{21} +116.120 q^{22} +23.0000 q^{23} +52.0145 q^{24} +25.0000 q^{25} -121.642 q^{26} +76.2427 q^{27} +10.9200 q^{28} +76.0691 q^{29} +65.0182 q^{30} +146.654 q^{31} -32.0000 q^{32} +377.495 q^{33} +51.0400 q^{34} +13.6500 q^{35} +61.0945 q^{36} +411.565 q^{37} +270.584 q^{38} -395.446 q^{39} -40.0000 q^{40} +279.340 q^{41} +35.5000 q^{42} +444.971 q^{43} -232.240 q^{44} +76.3681 q^{45} -46.0000 q^{46} +60.4237 q^{47} -104.029 q^{48} -335.547 q^{49} -50.0000 q^{50} +165.926 q^{51} +243.284 q^{52} -417.414 q^{53} -152.485 q^{54} -290.300 q^{55} -21.8401 q^{56} +879.643 q^{57} -152.138 q^{58} +474.367 q^{59} -130.036 q^{60} +430.793 q^{61} -293.307 q^{62} +41.6971 q^{63} +64.0000 q^{64} +304.104 q^{65} -754.991 q^{66} +444.731 q^{67} -102.080 q^{68} -149.542 q^{69} -27.3001 q^{70} -425.418 q^{71} -122.189 q^{72} -835.514 q^{73} -823.131 q^{74} -162.545 q^{75} -541.167 q^{76} -158.504 q^{77} +790.893 q^{78} -169.644 q^{79} +80.0000 q^{80} -908.104 q^{81} -558.680 q^{82} +623.154 q^{83} -71.0000 q^{84} -127.600 q^{85} -889.942 q^{86} -494.587 q^{87} +464.480 q^{88} +1674.53 q^{89} -152.736 q^{90} +166.041 q^{91} +92.0000 q^{92} -953.515 q^{93} -120.847 q^{94} -676.459 q^{95} +208.058 q^{96} +1010.47 q^{97} +671.094 q^{98} -886.787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - q^{3} + 12 q^{4} + 15 q^{5} + 2 q^{6} + 7 q^{7} - 24 q^{8} + 10 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 - q^3 + 12 * q^4 + 15 * q^5 + 2 * q^6 + 7 * q^7 - 24 * q^8 + 10 * q^9	\( 3 q - 6 q^{2} - q^{3} + 12 q^{4} + 15 q^{5} + 2 q^{6} + 7 q^{7} - 24 q^{8} + 10 q^{9} - 30 q^{10} + 27 q^{11} - 4 q^{12} + 75 q^{13} - 14 q^{14} - 5 q^{15} + 48 q^{16} + 127 q^{17} - 20 q^{18} - 185 q^{19} + 60 q^{20} - 258 q^{21} - 54 q^{22} + 69 q^{23} + 8 q^{24} + 75 q^{25} - 150 q^{26} + 98 q^{27} + 28 q^{28} + 344 q^{29} + 10 q^{30} + 397 q^{31} - 96 q^{32} + 477 q^{33} - 254 q^{34} + 35 q^{35} + 40 q^{36} + 978 q^{37} + 370 q^{38} + 198 q^{39} - 120 q^{40} - 575 q^{41} + 516 q^{42} + 812 q^{43} + 108 q^{44} + 50 q^{45} - 138 q^{46} - 270 q^{47} - 16 q^{48} + 878 q^{49} - 150 q^{50} + 955 q^{51} + 300 q^{52} + 510 q^{53} - 196 q^{54} + 135 q^{55} - 56 q^{56} + 894 q^{57} - 688 q^{58} + 142 q^{59} - 20 q^{60} - 49 q^{61} - 794 q^{62} - 1356 q^{63} + 192 q^{64} + 375 q^{65} - 954 q^{66} + 1616 q^{67} + 508 q^{68} - 23 q^{69} - 70 q^{70} - 471 q^{71} - 80 q^{72} - 780 q^{73} - 1956 q^{74} - 25 q^{75} - 740 q^{76} + 1032 q^{77} - 396 q^{78} - 860 q^{79} + 240 q^{80} - 1193 q^{81} + 1150 q^{82} - 288 q^{83} - 1032 q^{84} + 635 q^{85} - 1624 q^{86} + 1452 q^{87} - 216 q^{88} - 90 q^{89} - 100 q^{90} - 3963 q^{91} + 276 q^{92} - 1592 q^{93} + 540 q^{94} - 925 q^{95} + 32 q^{96} + 1321 q^{97} - 1756 q^{98} - 1851 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 - q^3 + 12 * q^4 + 15 * q^5 + 2 * q^6 + 7 * q^7 - 24 * q^8 + 10 * q^9 - 30 * q^10 + 27 * q^11 - 4 * q^12 + 75 * q^13 - 14 * q^14 - 5 * q^15 + 48 * q^16 + 127 * q^17 - 20 * q^18 - 185 * q^19 + 60 * q^20 - 258 * q^21 - 54 * q^22 + 69 * q^23 + 8 * q^24 + 75 * q^25 - 150 * q^26 + 98 * q^27 + 28 * q^28 + 344 * q^29 + 10 * q^30 + 397 * q^31 - 96 * q^32 + 477 * q^33 - 254 * q^34 + 35 * q^35 + 40 * q^36 + 978 * q^37 + 370 * q^38 + 198 * q^39 - 120 * q^40 - 575 * q^41 + 516 * q^42 + 812 * q^43 + 108 * q^44 + 50 * q^45 - 138 * q^46 - 270 * q^47 - 16 * q^48 + 878 * q^49 - 150 * q^50 + 955 * q^51 + 300 * q^52 + 510 * q^53 - 196 * q^54 + 135 * q^55 - 56 * q^56 + 894 * q^57 - 688 * q^58 + 142 * q^59 - 20 * q^60 - 49 * q^61 - 794 * q^62 - 1356 * q^63 + 192 * q^64 + 375 * q^65 - 954 * q^66 + 1616 * q^67 + 508 * q^68 - 23 * q^69 - 70 * q^70 - 471 * q^71 - 80 * q^72 - 780 * q^73 - 1956 * q^74 - 25 * q^75 - 740 * q^76 + 1032 * q^77 - 396 * q^78 - 860 * q^79 + 240 * q^80 - 1193 * q^81 + 1150 * q^82 - 288 * q^83 - 1032 * q^84 + 635 * q^85 - 1624 * q^86 + 1452 * q^87 - 216 * q^88 - 90 * q^89 - 100 * q^90 - 3963 * q^91 + 276 * q^92 - 1592 * q^93 + 540 * q^94 - 925 * q^95 + 32 * q^96 + 1321 * q^97 - 1756 * q^98 - 1851 * q^99

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