LMFDB - Embedded newform 60.5.f.a.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,5,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$6.20219778503$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	60.19
Dual form			60.5.f.a.19.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988963 - 3.87582i) q^{2} -5.19615 q^{3} +(-14.0439 - 7.66608i) q^{4} +(11.6321 + 22.1290i) q^{5} +(-5.13880 + 20.1393i) q^{6} -66.7450 q^{7} +(-43.6012 + 46.8501i) q^{8} +27.0000 q^{9} +O(q^{10})$	\(q+(0.988963 - 3.87582i) q^{2} -5.19615 q^{3} +(-14.0439 - 7.66608i) q^{4} +(11.6321 + 22.1290i) q^{5} +(-5.13880 + 20.1393i) q^{6} -66.7450 q^{7} +(-43.6012 + 46.8501i) q^{8} +27.0000 q^{9} +(97.2718 - 23.1992i) q^{10} +100.606i q^{11} +(72.9743 + 39.8341i) q^{12} +184.052i q^{13} +(-66.0083 + 258.691i) q^{14} +(-60.4423 - 114.986i) q^{15} +(138.462 + 215.323i) q^{16} -312.494i q^{17} +(26.7020 - 104.647i) q^{18} -18.4151i q^{19} +(6.28246 - 399.951i) q^{20} +346.817 q^{21} +(389.931 + 99.4958i) q^{22} -983.914 q^{23} +(226.559 - 243.440i) q^{24} +(-354.387 + 514.815i) q^{25} +(713.353 + 182.021i) q^{26} -140.296 q^{27} +(937.360 + 511.672i) q^{28} -1082.68 q^{29} +(-505.439 + 120.546i) q^{30} -572.196i q^{31} +(971.488 - 323.708i) q^{32} -522.765i q^{33} +(-1211.17 - 309.045i) q^{34} +(-776.386 - 1477.00i) q^{35} +(-379.185 - 206.984i) q^{36} +776.520i q^{37} +(-71.3735 - 18.2119i) q^{38} -956.363i q^{39} +(-1543.92 - 419.886i) q^{40} +261.516 q^{41} +(342.989 - 1344.20i) q^{42} +808.608 q^{43} +(771.255 - 1412.90i) q^{44} +(314.067 + 597.484i) q^{45} +(-973.054 + 3813.47i) q^{46} +2527.71 q^{47} +(-719.472 - 1118.85i) q^{48} +2053.89 q^{49} +(1644.85 + 1882.67i) q^{50} +1623.77i q^{51} +(1410.96 - 2584.81i) q^{52} -3491.13i q^{53} +(-138.748 + 543.762i) q^{54} +(-2226.32 + 1170.26i) q^{55} +(2910.16 - 3127.01i) q^{56} +95.6877i q^{57} +(-1070.74 + 4196.29i) q^{58} +5318.33i q^{59} +(-32.6446 + 2078.20i) q^{60} -1237.57 q^{61} +(-2217.73 - 565.881i) q^{62} -1802.11 q^{63} +(-293.867 - 4085.44i) q^{64} +(-4072.90 + 2140.92i) q^{65} +(-2026.14 - 516.995i) q^{66} +6820.52 q^{67} +(-2395.60 + 4388.63i) q^{68} +5112.56 q^{69} +(-6492.40 + 1548.43i) q^{70} -268.568i q^{71} +(-1177.23 + 1264.95i) q^{72} +6217.06i q^{73} +(3009.65 + 767.950i) q^{74} +(1841.45 - 2675.06i) q^{75} +(-141.172 + 258.620i) q^{76} -6714.96i q^{77} +(-3706.69 - 945.808i) q^{78} +9284.59i q^{79} +(-3154.28 + 5568.71i) q^{80} +729.000 q^{81} +(258.630 - 1013.59i) q^{82} +46.6428 q^{83} +(-4870.66 - 2658.73i) q^{84} +(6915.18 - 3634.97i) q^{85} +(799.683 - 3134.01i) q^{86} +5625.79 q^{87} +(-4713.41 - 4386.55i) q^{88} -7769.57 q^{89} +(2626.34 - 626.378i) q^{90} -12284.6i q^{91} +(13818.0 + 7542.76i) q^{92} +2973.22i q^{93} +(2499.81 - 9796.92i) q^{94} +(407.508 - 214.207i) q^{95} +(-5048.00 + 1682.04i) q^{96} -8948.56i q^{97} +(2031.22 - 7960.50i) q^{98} +2716.37i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	$ 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) $ 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.988963	−	3.87582i	0.247241	−	0.968954i
$2$	0.988963	−	3.87582i	0.247241	−	0.968954i
$3$	−5.19615			−0.577350
$3$	−5.19615			−0.577350
$4$	−14.0439	−	7.66608i	−0.877744	−	0.479130i
$5$	11.6321	+	22.1290i	0.465285	+	0.885161i
$5$	11.6321	+	22.1290i	0.465285	+	0.885161i
$6$	−5.13880	+	20.1393i	−0.142745	+	0.559426i
$7$	−66.7450			−1.36214			−0.681071	−	0.732217i	$-0.738486\pi$
$7$	−66.7450			−1.36214			−0.681071	+	0.732217i	$0.738486\pi$
$8$	−43.6012	+	46.8501i	−0.681269	+	0.732033i
$9$	27.0000			0.333333
$10$	97.2718	−	23.1992i	0.972718	−	0.231992i
$11$			100.606i			0.831456i	0.909489	+	0.415728i	$0.136473\pi$
$11$			100.606i			0.831456i	−0.909489	+	0.415728i	$0.863527\pi$
$12$	72.9743	+	39.8341i	0.506766	+	0.276626i
$13$			184.052i			1.08907i	0.838739	+	0.544533i	$0.183293\pi$
$13$			184.052i			1.08907i	−0.838739	+	0.544533i	$0.816707\pi$
$14$	−66.0083	+	258.691i	−0.336777	+	1.31985i
$15$	−60.4423	−	114.986i	−0.268632	−	0.511048i
$16$	138.462	+	215.323i	0.540869	+	0.841107i
$17$		−	312.494i		−	1.08129i	−0.841250	−	0.540647i	$-0.818180\pi$
$17$		−	312.494i		−	1.08129i	0.841250	−	0.540647i	$-0.181820\pi$
$18$	26.7020	−	104.647i	0.0824136	−	0.322985i
$19$		−	18.4151i		−	0.0510114i	−0.999675	−	0.0255057i	$-0.991880\pi$
$19$		−	18.4151i		−	0.0510114i	0.999675	−	0.0255057i	$-0.00811959\pi$
$20$	6.28246	−	399.951i	0.0157062	−	0.999877i
$21$	346.817			0.786433
$22$	389.931	+	99.4958i	0.805643	+	0.205570i
$23$	−983.914			−1.85995			−0.929975	−	0.367623i	$-0.880172\pi$
$23$	−983.914			−1.85995			−0.929975	+	0.367623i	$0.880172\pi$
$24$	226.559	−	243.440i	0.393331	−	0.422639i
$25$	−354.387	+	514.815i	−0.567020	+	0.823704i
$26$	713.353	+	182.021i	1.05526	+	0.269262i
$27$	−140.296			−0.192450
$28$	937.360	+	511.672i	1.19561	+	0.652643i
$29$	−1082.68			−1.28738			−0.643689	−	0.765287i	$-0.722597\pi$
$29$	−1082.68			−1.28738			−0.643689	+	0.765287i	$0.722597\pi$
$30$	−505.439	+	120.546i	−0.561599	+	0.133941i
$31$		−	572.196i		−	0.595417i	−0.954657	−	0.297709i	$-0.903778\pi$
$31$		−	572.196i		−	0.595417i	0.954657	−	0.297709i	$-0.0962224\pi$
$32$	971.488	−	323.708i	0.948719	−	0.316121i
$33$		−	522.765i		−	0.480041i
$34$	−1211.17	−	309.045i	−1.04772	−	0.267340i
$35$	−776.386	−	1477.00i	−0.633784	−	1.20571i
$36$	−379.185	−	206.984i	−0.292581	−	0.159710i
$37$			776.520i			0.567217i	0.958940	+	0.283609i	$0.0915316\pi$
$37$			776.520i			0.567217i	−0.958940	+	0.283609i	$0.908468\pi$
$38$	−71.3735	−	18.2119i	−0.0494277	−	0.0126121i
$39$		−	956.363i		−	0.628773i
$40$	−1543.92	−	419.886i	−0.964951	−	0.262429i
$41$	261.516			0.155572			0.0777859	−	0.996970i	$-0.475215\pi$
$41$	261.516			0.155572			0.0777859	+	0.996970i	$0.475215\pi$
$42$	342.989	−	1344.20i	0.194438	−	0.762018i
$43$	808.608			0.437322			0.218661	−	0.975801i	$-0.429831\pi$
$43$	808.608			0.437322			0.218661	+	0.975801i	$0.429831\pi$
$44$	771.255	−	1412.90i	0.398376	−	0.729806i
$45$	314.067	+	597.484i	0.155095	+	0.295054i
$46$	−973.054	+	3813.47i	−0.459856	+	1.80221i
$47$	2527.71			1.14428			0.572138	−	0.820157i	$-0.306114\pi$
$47$	2527.71			1.14428			0.572138	+	0.820157i	$0.306114\pi$
$48$	−719.472	−	1118.85i	−0.312271	−	0.485613i
$49$	2053.89			0.855431
$50$	1644.85	+	1882.67i	0.657941	+	0.753070i
$51$			1623.77i			0.624285i
$52$	1410.96	−	2584.81i	0.521804	−	0.955921i
$53$		−	3491.13i		−	1.24284i	−0.783479	−	0.621418i	$-0.786557\pi$
$53$		−	3491.13i		−	1.24284i	0.783479	−	0.621418i	$-0.213443\pi$
$54$	−138.748	+	543.762i	−0.0475815	+	0.186475i
$55$	−2226.32	+	1170.26i	−0.735973	+	0.386864i
$56$	2910.16	−	3127.01i	0.927985	−	0.997133i
$57$			95.6877i			0.0294514i
$58$	−1070.74	+	4196.29i	−0.318292	+	1.24741i
$59$			5318.33i			1.52782i	0.645325	+	0.763909i	$0.276722\pi$
$59$			5318.33i			1.52782i	−0.645325	+	0.763909i	$0.723278\pi$
$60$	−32.6446	+	2078.20i	−0.00906795	+	0.577279i
$61$	−1237.57			−0.332592			−0.166296	−	0.986076i	$-0.553181\pi$
$61$	−1237.57			−0.332592			−0.166296	+	0.986076i	$0.553181\pi$
$62$	−2217.73	−	565.881i	−0.576932	−	0.147211i
$63$	−1802.11			−0.454047
$64$	−293.867	−	4085.44i	−0.0717448	−	0.997423i
$65$	−4072.90	+	2140.92i	−0.963999	+	0.506726i
$66$	−2026.14	−	516.995i	−0.465138	−	0.118686i
$67$	6820.52			1.51939			0.759693	−	0.650282i	$-0.225349\pi$
$67$	6820.52			1.51939			0.759693	+	0.650282i	$0.225349\pi$
$68$	−2395.60	+	4388.63i	−0.518080	+	0.949099i
$69$	5112.56			1.07384
$70$	−6492.40	+	1548.43i	−1.32498	+	0.316006i
$71$		−	268.568i		−	0.0532767i	−0.999645	−	0.0266384i	$-0.991520\pi$
$71$		−	268.568i		−	0.0532767i	0.999645	−	0.0266384i	$-0.00848026\pi$
$72$	−1177.23	+	1264.95i	−0.227090	+	0.244011i
$73$			6217.06i			1.16665i	0.812240	+	0.583324i	$0.198248\pi$
$73$			6217.06i			1.16665i	−0.812240	+	0.583324i	$0.801752\pi$
$74$	3009.65	+	767.950i	0.549607	+	0.140239i
$75$	1841.45	−	2675.06i	0.327369	−	0.475566i
$76$	−141.172	+	258.620i	−0.0244411	+	0.0447749i
$77$		−	6714.96i		−	1.13256i
$78$	−3706.69	−	945.808i	−0.609252	−	0.155458i
$79$			9284.59i			1.48768i	0.668359	+	0.743839i	$0.266997\pi$
$79$			9284.59i			1.48768i	−0.668359	+	0.743839i	$0.733003\pi$
$80$	−3154.28	+	5568.71i	−0.492857	+	0.870110i
$81$	729.000			0.111111
$82$	258.630	−	1013.59i	0.0384637	−	0.150742i
$83$	46.6428			0.00677063			0.00338531	−	0.999994i	$-0.498922\pi$
$83$	46.6428			0.00677063			0.00338531	+	0.999994i	$0.498922\pi$
$84$	−4870.66	−	2658.73i	−0.690287	−	0.376804i
$85$	6915.18	−	3634.97i	0.957119	−	0.503110i
$86$	799.683	−	3134.01i	0.108124	−	0.423745i
$87$	5625.79			0.743268
$88$	−4713.41	−	4386.55i	−0.608653	−	0.566445i
$89$	−7769.57			−0.980883			−0.490441	−	0.871474i	$-0.663164\pi$
$89$	−7769.57			−0.980883			−0.490441	+	0.871474i	$0.663164\pi$
$90$	2626.34	−	626.378i	0.324239	−	0.0773306i
$91$		−	12284.6i		−	1.48346i
$92$	13818.0	+	7542.76i	1.63256	+	0.891158i
$93$			2973.22i			0.343764i
$94$	2499.81	−	9796.92i	0.282912	−	1.10875i
$95$	407.508	−	214.207i	0.0451533	−	0.0237348i
$96$	−5048.00	+	1682.04i	−0.547743	+	0.182513i
$97$		−	8948.56i		−	0.951063i	−0.879699	−	0.475532i	$-0.842256\pi$
$97$		−	8948.56i		−	0.951063i	0.879699	−	0.475532i	$-0.157744\pi$
$98$	2031.22	−	7960.50i	0.211497	−	0.828873i
$99$			2716.37i			0.277152i
$100$	8923.60	−	4513.25i	0.892360	−	0.451325i
$101$	−11088.3			−1.08698			−0.543491	−	0.839415i	$-0.682898\pi$
$101$	−11088.3			−1.08698			−0.543491	+	0.839415i	$0.682898\pi$
$102$	6293.42	+	1605.84i	0.604904	+	0.154349i
$103$	3629.00			0.342068			0.171034	−	0.985265i	$-0.445289\pi$
$103$	3629.00			0.342068			0.171034	+	0.985265i	$0.445289\pi$
$104$	−8622.87	−	8024.90i	−0.797233	−	0.741947i
$105$	4034.22	+	7674.72i	0.365915	+	0.696120i
$106$	−13531.0	−	3452.60i	−1.20425	−	0.307280i
$107$	−1947.83			−0.170131			−0.0850656	−	0.996375i	$-0.527110\pi$
$107$	−1947.83			−0.170131			−0.0850656	+	0.996375i	$0.527110\pi$
$108$	1970.31	+	1075.52i	0.168922	+	0.0922086i
$109$	10919.0			0.919028			0.459514	−	0.888170i	$-0.348024\pi$
$109$	10919.0			0.919028			0.459514	+	0.888170i	$0.348024\pi$
$110$	2333.98	+	9786.14i	0.192891	+	0.808772i
$111$		−	4034.92i		−	0.327483i
$112$	−9241.67	−	14371.7i	−0.736740	−	1.14571i
$113$			2020.10i			0.158204i	0.996867	+	0.0791019i	$0.0252052\pi$
$113$			2020.10i			0.158204i	−0.996867	+	0.0791019i	$0.974795\pi$
$114$	370.868	+	94.6316i	0.0285371	+	0.00728159i
$115$	−11445.0	−	21773.0i	−0.865407	−	1.64636i
$116$	15205.1	+	8299.95i	1.12999	+	0.616821i
$117$			4969.41i			0.363022i
$118$	20612.9	+	5259.63i	1.48038	+	0.377739i
$119$			20857.4i			1.47288i
$120$	8022.45	+	2181.79i	0.557115	+	0.151513i
$121$	4519.39			0.308681
$122$	−1223.92	+	4796.61i	−0.0822303	+	0.322266i
$123$	−1358.88			−0.0898194
$124$	−4386.50	+	8035.86i	−0.285282	+	0.522624i
$125$	−15514.6	−	1853.86i	−0.992937	−	0.118647i
$126$	−1782.22	+	6984.66i	−0.112259	+	0.439951i
$127$	−25825.9			−1.60121			−0.800606	−	0.599192i	$-0.795489\pi$
$127$	−25825.9			−1.60121			−0.800606	+	0.599192i	$0.795489\pi$
$128$	−16125.1	−	2901.38i	−0.984195	−	0.177086i
$129$	−4201.65			−0.252488
$130$	4269.86	+	17903.1i	0.252654	+	1.05935i
$131$		−	26351.6i		−	1.53555i	−0.640718	−	0.767776i	$-0.721363\pi$
$131$		−	26351.6i		−	1.53555i	0.640718	−	0.767776i	$-0.278637\pi$
$132$	−4007.56	+	7341.66i	−0.230002	+	0.421353i
$133$			1229.12i			0.0694847i
$134$	6745.24	−	26435.1i	0.375654	−	1.47221i
$135$	−1631.94	−	3104.62i	−0.0895441	−	0.170349i
$136$	14640.4	+	13625.1i	0.791543	+	0.736652i
$137$			12791.5i			0.681523i	0.940150	+	0.340762i	$0.110685\pi$
$137$			12791.5i			0.681523i	−0.940150	+	0.340762i	$0.889315\pi$
$138$	5056.14	−	19815.4i	0.265498	−	1.04050i
$139$			6998.42i			0.362218i	0.983463	+	0.181109i	$0.0579687\pi$
$139$			6998.42i			0.362218i	−0.983463	+	0.181109i	$0.942031\pi$
$140$	−419.323	+	26694.7i	−0.0213940	+	1.36197i
$141$	−13134.3			−0.660648
$142$	−1040.92	−	265.604i	−0.0516227	−	0.0131722i
$143$	−18516.8			−0.905511
$144$	3738.49	+	5813.73i	0.180290	+	0.280369i
$145$	−12593.9	−	23958.8i	−0.598997	−	1.13954i
$146$	24096.2	+	6148.45i	1.13043	+	0.288443i
$147$	−10672.3			−0.493883
$148$	5952.87	−	10905.4i	0.271771	−	0.497871i
$149$	14522.2			0.654123			0.327062	−	0.945003i	$-0.393942\pi$
$149$	14522.2			0.654123			0.327062	+	0.945003i	$0.393942\pi$
$150$	−8546.90	−	9782.66i	−0.379862	−	0.434785i
$151$			41722.9i			1.82987i	0.403601	+	0.914935i	$0.367758\pi$
$151$			41722.9i			1.82987i	−0.403601	+	0.914935i	$0.632242\pi$
$152$	862.750	+	802.921i	0.0373420	+	0.0347525i
$153$		−	8437.33i		−	0.360431i
$154$	−26025.9	−	6640.85i	−1.09740	−	0.280015i
$155$	12662.1	−	6655.85i	0.527040	−	0.277039i
$156$	−7331.56	+	13431.1i	−0.301264	+	0.551901i
$157$			44689.9i			1.81305i	0.422150	+	0.906526i	$0.361276\pi$
$157$			44689.9i			1.81305i	−0.422150	+	0.906526i	$0.638724\pi$
$158$	35985.4	+	9182.12i	1.44149	+	0.367815i
$159$			18140.4i			0.717552i
$160$	18463.8	+	17732.7i	0.721243	+	0.692682i
$161$	65671.3			2.53352
$162$	720.954	−	2825.47i	0.0274712	−	0.107662i
$163$	12008.5			0.451976			0.225988	−	0.974130i	$-0.427439\pi$
$163$	12008.5			0.451976			0.225988	+	0.974130i	$0.427439\pi$
$164$	−3672.71	−	2004.80i	−0.136552	−	0.0745391i
$165$	11568.3	−	6080.87i	0.424914	−	0.223356i
$166$	46.1281	−	180.779i	0.00167398	−	0.00656043i
$167$	−13114.4			−0.470235			−0.235118	−	0.971967i	$-0.575548\pi$
$167$	−13114.4			−0.470235			−0.235118	+	0.971967i	$0.575548\pi$
$168$	−15121.6	+	16248.4i	−0.535773	+	0.575695i
$169$	−5314.21			−0.186065
$170$	−7249.60	−	30396.8i	−0.250851	−	1.05179i
$171$		−	497.208i		−	0.0170038i
$172$	−11356.0	−	6198.85i	−0.383856	−	0.209534i
$173$			8562.05i			0.286079i	0.989717	+	0.143039i	$0.0456876\pi$
$173$			8562.05i			0.286079i	−0.989717	+	0.143039i	$0.954312\pi$
$174$	5563.70	−	21804.5i	0.183766	−	0.720192i
$175$	23653.6	−	34361.3i	0.772362	−	1.12200i
$176$	−21662.9	+	13930.2i	−0.699343	+	0.449709i
$177$		−	27634.9i		−	0.882086i
$178$	−7683.82	+	30113.4i	−0.242514	+	0.950430i
$179$			1009.72i			0.0315134i	0.999876	+	0.0157567i	$0.00501572\pi$
$179$			1009.72i			0.0315134i	−0.999876	+	0.0157567i	$0.994984\pi$
$180$	169.627	−	10798.7i	0.00523539	−	0.333292i
$181$	−50758.3			−1.54935			−0.774676	−	0.632359i	$-0.782087\pi$
$181$	−50758.3			−1.54935			−0.774676	+	0.632359i	$0.782087\pi$
$182$	−47612.7	−	12149.0i	−1.43741	−	0.366773i
$183$	6430.62			0.192022
$184$	42899.8	−	46096.5i	1.26713	−	1.36154i
$185$	−17183.6	+	9032.58i	−0.502079	+	0.263918i
$186$	11523.6	+	2940.40i	0.333092	+	0.0849926i
$187$	31438.8			0.899048
$188$	−35498.9	−	19377.6i	−1.00438	−	0.548257i
$189$	9364.06			0.262144
$190$	−427.215	−	1791.27i	−0.0118342	−	0.0496196i
$191$		−	19016.4i		−	0.521269i	−0.965438	−	0.260634i	$-0.916068\pi$
$191$		−	19016.4i		−	0.521269i	0.965438	−	0.260634i	$-0.0839317\pi$
$192$	1526.98	+	21228.6i	0.0414219	+	0.575862i
$193$		−	24278.6i		−	0.651792i	−0.945406	−	0.325896i	$-0.894334\pi$
$193$		−	24278.6i		−	0.651792i	0.945406	−	0.325896i	$-0.105666\pi$
$194$	−34683.0	−	8849.79i	−0.921537	−	0.235142i
$195$	21163.4	−	11124.5i	0.556565	−	0.292558i
$196$	−28844.6	−	15745.3i	−0.750849	−	0.409863i
$197$		−	35233.5i		−	0.907870i	−0.891035	−	0.453935i	$-0.850020\pi$
$197$		−	35233.5i		−	0.907870i	0.891035	−	0.453935i	$-0.149980\pi$
$198$	10528.1	+	2686.39i	0.268548	+	0.0685233i
$199$			35903.8i			0.906639i	0.891348	+	0.453320i	$0.149760\pi$
$199$			35903.8i			0.906639i	−0.891348	+	0.453320i	$0.850240\pi$
$200$	−8667.42	−	39049.7i	−0.216686	−	0.976241i
$201$	−35440.5			−0.877217
$202$	−10965.9	+	42976.2i	−0.268746	+	1.05324i
$203$	72263.7			1.75359
$204$	12447.9	−	22804.0i	0.299114	−	0.547962i
$205$	3041.99	+	5787.09i	0.0723852	+	0.137706i
$206$	3588.95	−	14065.3i	0.0845732	−	0.331448i
$207$	−26565.7			−0.619983
$208$	−39630.7	+	25484.3i	−0.916021	+	0.589042i
$209$	1852.67			0.0424137
$210$	33735.5	−	8045.87i	0.764977	−	0.182446i
$211$		−	18257.1i		−	0.410077i	−0.978754	−	0.205039i	$-0.934268\pi$
$211$		−	18257.1i		−	0.410077i	0.978754	−	0.205039i	$-0.0657320\pi$
$212$	−26763.3	+	49029.1i	−0.595480	+	1.09089i
$213$			1395.52i			0.0307593i
$214$	−1926.33	+	7549.44i	−0.0420634	+	0.164849i
$215$	9405.82	+	17893.7i	0.203479	+	0.387100i
$216$	6117.08	−	6572.89i	0.131110	−	0.140880i
$217$			38191.2i			0.811043i
$218$	10798.5	−	42319.9i	0.227221	−	0.890496i
$219$		−	32304.8i		−	0.673564i
$220$	40237.5	+	632.055i	0.831354	+	0.0130590i
$221$	57515.2			1.17760
$222$	−15638.6	−	3990.39i	−0.317316	−	0.0809672i
$223$	−12650.1			−0.254380			−0.127190	−	0.991878i	$-0.540596\pi$
$223$	−12650.1			−0.254380			−0.127190	+	0.991878i	$0.540596\pi$
$224$	−64841.9	+	21605.9i	−1.29229	+	0.430602i
$225$	−9568.46	+	13900.0i	−0.189007	+	0.274568i
$226$	7829.55	+	1997.81i	0.153292	+	0.0391144i
$227$	−14722.6			−0.285716			−0.142858	−	0.989743i	$-0.545629\pi$
$227$	−14722.6			−0.285716			−0.142858	+	0.989743i	$0.545629\pi$
$228$	733.549	−	1343.83i	0.0141111	−	0.0258508i
$229$	−10205.2			−0.194603			−0.0973015	−	0.995255i	$-0.531021\pi$
$229$	−10205.2			−0.194603			−0.0973015	+	0.995255i	$0.531021\pi$
$230$	−95707.0	+	22826.0i	−1.80921	+	0.431493i
$231$			34891.9i			0.653885i
$232$	47206.4	−	50723.9i	0.877051	−	0.942403i
$233$		−	14945.0i		−	0.275286i	−0.990482	−	0.137643i	$-0.956047\pi$
$233$		−	14945.0i		−	0.275286i	0.990482	−	0.137643i	$-0.0439526\pi$
$234$	19260.5	+	4914.56i	0.351752	+	0.0897539i
$235$	29402.6	+	55935.7i	0.532414	+	1.01287i
$236$	40770.8	−	74690.1i	0.732023	−	1.34103i
$237$		−	48244.2i		−	0.858911i
$238$	80839.4	+	20627.2i	1.42715	+	0.364155i
$239$			77854.6i			1.36298i	0.731829	+	0.681488i	$0.238667\pi$
$239$			77854.6i			1.36298i	−0.731829	+	0.681488i	$0.761333\pi$
$240$	16390.1	−	28935.8i	0.284551	−	0.502358i
$241$	−13021.1			−0.224188			−0.112094	−	0.993698i	$-0.535756\pi$
$241$	−13021.1			−0.224188			−0.112094	+	0.993698i	$0.535756\pi$
$242$	4469.52	−	17516.3i	0.0763185	−	0.299097i
$243$	−3788.00			−0.0641500
$244$	17380.4	+	9487.34i	0.291930	+	0.159355i
$245$	23891.1	+	45450.6i	0.398019	+	0.757194i
$246$	−1343.88	+	5266.76i	−0.0222070	+	0.0870308i
$247$	3389.34			0.0555547
$248$	26807.4	+	24948.4i	0.435865	+	0.405639i
$249$	−242.363			−0.00390902
$250$	−22528.6	+	58298.5i	−0.360458	+	0.932776i
$251$		−	49009.3i		−	0.777914i	−0.921256	−	0.388957i	$-0.872836\pi$
$251$		−	49009.3i		−	0.777914i	0.921256	−	0.388957i	$-0.127164\pi$
$252$	25308.7	+	13815.1i	0.398537	+	0.217548i
$253$		−	98987.8i		−	1.54647i
$254$	−25540.9	+	100097.i	−0.395885	+	1.55150i
$255$	−35932.3	+	18887.8i	−0.552593	+	0.290470i
$256$	−27192.3	+	59628.4i	−0.414922	+	0.909857i
$257$			50807.7i			0.769242i	0.923075	+	0.384621i	$0.125668\pi$
$257$			50807.7i			0.769242i	−0.923075	+	0.384621i	$0.874332\pi$
$258$	−4155.28	+	16284.8i	−0.0624253	+	0.244649i
$259$		−	51828.8i		−	0.772630i
$260$	73611.8	+	1156.30i	1.08893	+	0.0171050i
$261$	−29232.5			−0.429126
$262$	−102134.	−	26060.8i	−1.48788	−	0.379651i
$263$	−45257.6			−0.654304			−0.327152	−	0.944972i	$-0.606089\pi$
$263$	−45257.6			−0.654304			−0.327152	+	0.944972i	$0.606089\pi$
$264$	24491.6	+	22793.2i	0.351406	+	0.327037i
$265$	77255.3	−	40609.2i	1.10011	−	0.578273i
$266$	4763.82	+	1215.55i	0.0673275	+	0.0171795i
$267$	40371.9			0.566313
$268$	−95786.7	−	52286.6i	−1.33363	−	0.727983i
$269$	17631.6			0.243661			0.121831	−	0.992551i	$-0.461124\pi$
$269$	17631.6			0.243661			0.121831	+	0.992551i	$0.461124\pi$
$270$	−13646.9	+	3254.75i	−0.187200	+	0.0446468i
$271$		−	21664.6i		−	0.294993i	−0.989063	−	0.147496i	$-0.952879\pi$
$271$		−	21664.6i		−	0.294993i	0.989063	−	0.147496i	$-0.0471215\pi$
$272$	67287.2	−	43268.7i	0.909483	−	0.584838i
$273$			63832.4i			0.856478i
$274$	49577.5	+	12650.3i	0.660365	+	0.168500i
$275$	−51793.6	−	35653.6i	−0.684874	−	0.471452i
$276$	−71800.4	−	39193.3i	−0.942559	−	0.514510i
$277$			104980.i			1.36819i	0.729391	+	0.684097i	$0.239804\pi$
$277$			104980.i			1.36819i	−0.729391	+	0.684097i	$0.760196\pi$
$278$	27124.6	+	6921.18i	0.350973	+	0.0895552i
$279$		−	15449.3i		−	0.198472i
$280$	103049.	+	28025.3i	1.31440	+	0.357465i
$281$	2344.68			0.0296941			0.0148470	−	0.999890i	$-0.495274\pi$
$281$	2344.68			0.0296941			0.0148470	+	0.999890i	$0.495274\pi$
$282$	−12989.4	+	50906.3i	−0.163339	+	0.640138i
$283$	−139458.			−1.74129			−0.870644	−	0.491914i	$-0.836297\pi$
$283$	−139458.			−1.74129			−0.870644	+	0.491914i	$0.836297\pi$
$284$	−2058.86	+	3771.74i	−0.0255265	+	0.0467633i
$285$	−2117.47	+	1113.05i	−0.0260692	+	0.0137033i
$286$	−18312.4	+	71767.7i	−0.223879	+	0.877398i
$287$	−17454.9			−0.211911
$288$	26230.2	−	8740.12i	0.316240	−	0.105374i
$289$	−14131.4			−0.169196
$290$	−105315.	+	25117.4i	−1.25225	+	0.298661i
$291$			46498.1i			0.549097i
$292$	47660.5	−	87311.8i	0.558976	−	1.02402i
$293$			149239.i			1.73839i	0.494471	+	0.869194i	$0.335362\pi$
$293$			149239.i			1.73839i	−0.494471	+	0.869194i	$0.664638\pi$
$294$	−10554.5	+	41364.0i	−0.122108	+	0.478550i
$295$	−117689.	+	61863.5i	−1.35236	+	0.710870i
$296$	−36380.1	−	33857.2i	−0.415222	−	0.386428i
$297$		−	14114.7i		−	0.160014i
$298$	14361.9	−	56285.3i	0.161726	−	0.633815i
$299$		−	181091.i		−	2.02561i
$300$	−46368.4	+	23451.5i	−0.515204	+	0.260573i
$301$	−53970.5			−0.595694
$302$	161710.	+	41262.4i	1.77306	+	0.452419i
$303$	57616.5			0.627569
$304$	3965.20	−	2549.80i	0.0429060	−	0.0275905i
$305$	−14395.6	−	27386.3i	−0.154750	−	0.294397i
$306$	−32701.6	−	8344.21i	−0.349241	−	0.0891133i
$307$	62472.6			0.662847			0.331423	−	0.943482i	$-0.392471\pi$
$307$	62472.6			0.662847			0.331423	+	0.943482i	$0.392471\pi$
$308$	−51477.4	+	94304.2i	−0.542644	+	0.994099i
$309$	−18856.8			−0.197493
$310$	−13274.5	−	55658.5i	−0.138132	−	0.579173i
$311$			56486.6i			0.584016i	0.956416	+	0.292008i	$0.0943235\pi$
$311$			56486.6i			0.584016i	−0.956416	+	0.292008i	$0.905677\pi$
$312$	44805.7	+	41698.6i	0.460282	+	0.428363i
$313$		−	64738.6i		−	0.660807i	−0.943840	−	0.330404i	$-0.892815\pi$
$313$		−	64738.6i		−	0.660807i	0.943840	−	0.330404i	$-0.107185\pi$
$314$	173210.	+	44196.7i	1.75676	+	0.448260i
$315$	−20962.4	−	39879.0i	−0.211261	−	0.401905i
$316$	71176.4	−	130392.i	0.712791	−	1.30580i
$317$		−	194545.i		−	1.93599i	−0.250975	−	0.967994i	$-0.580751\pi$
$317$		−	194545.i		−	1.93599i	0.250975	−	0.967994i	$-0.419249\pi$
$318$	70309.0	+	17940.2i	0.695275	+	0.177408i
$319$		−	108925.i		−	1.07040i
$320$	86988.6	−	54025.4i	0.849498	−	0.527592i
$321$	10121.2			0.0982253
$322$	64946.5	−	254530.i	0.626389	−	2.45486i
$323$	−5754.60			−0.0551582
$324$	−10238.0	−	5588.57i	−0.0975271	−	0.0532367i
$325$	−94752.8	−	65225.8i	−0.897068	−	0.617522i
$326$	11876.0	−	46542.9i	0.111747	−	0.437944i
$327$	−56736.7			−0.530601
$328$	−11402.4	+	12252.1i	−0.105986	+	0.113884i
$329$	−168712.			−1.55867
$330$	−12127.7	−	50850.3i	−0.111366	−	0.466945i
$331$		−	58276.2i		−	0.531906i	−0.963986	−	0.265953i	$-0.914313\pi$
$331$		−	58276.2i		−	0.531906i	0.963986	−	0.265953i	$-0.0856867\pi$
$332$	−655.048	−	357.568i	−0.00594288	−	0.00324401i
$333$			20966.0i			0.189072i
$334$	−12969.7	+	50829.0i	−0.116261	+	0.455637i
$335$	79337.1	+	150931.i	0.706947	+	1.34490i
$336$	48021.1	+	74677.8i	0.425357	+	0.661474i
$337$		−	5112.92i		−	0.0450204i	−0.999747	−	0.0225102i	$-0.992834\pi$
$337$		−	5112.92i		−	0.0450204i	0.999747	−	0.0225102i	$-0.00716582\pi$
$338$	−5255.56	+	20596.9i	−0.0460030	+	0.180289i
$339$		−	10496.8i		−	0.0913390i
$340$	−124982.	−	1963.23i	−1.08116	−	0.0169830i
$341$	57566.4			0.495063
$342$	−1927.09	−	491.720i	−0.0164759	−	0.00420403i
$343$	23167.9			0.196924
$344$	−35256.3	+	37883.4i	−0.297934	+	0.320134i
$345$	59470.0	+	113136.i	0.499643	+	0.950524i
$346$	33185.0	+	8467.56i	0.277197	+	0.0707304i
$347$	120635.			1.00188			0.500940	−	0.865482i	$-0.332988\pi$
$347$	120635.			1.00188			0.500940	+	0.865482i	$0.332988\pi$
$348$	−79008.1	−	43127.8i	−0.652399	−	0.356122i
$349$	142108.			1.16673			0.583363	−	0.812212i	$-0.301737\pi$
$349$	142108.			1.16673			0.583363	+	0.812212i	$0.301737\pi$
$350$	−109786.	−	125659.i	−0.896209	−	1.02579i
$351$		−	25821.8i		−	0.209591i
$352$	32567.0	+	97737.7i	0.262841	+	0.788818i
$353$			67025.6i			0.537887i	0.963156	+	0.268943i	$0.0866745\pi$
$353$			67025.6i			0.537887i	−0.963156	+	0.268943i	$0.913326\pi$
$354$	−107108.	−	27329.9i	−0.854700	−	0.218088i
$355$	5943.15	−	3124.02i	0.0471585	−	0.0247889i
$356$	109115.	+	59562.2i	0.860964	+	0.469970i
$357$		−	108378.i		−	0.850365i
$358$	3913.49	+	998.577i	0.0305350	+	0.00779140i
$359$		−	151652.i		−	1.17668i	−0.808613	−	0.588340i	$-0.799781\pi$
$359$		−	151652.i		−	1.17668i	0.808613	−	0.588340i	$-0.200219\pi$
$360$	−41685.9	−	11336.9i	−0.321650	−	0.0874763i
$361$	129982.			0.997398
$362$	−50198.1	+	196730.i	−0.383063	+	1.50125i
$363$	−23483.5			−0.178217
$364$	−94174.4	+	172523.i	−0.710772	+	1.30210i
$365$	−137578.	+	72317.6i	−1.03267	+	0.542823i
$366$	6359.65	−	24923.9i	0.0474757	−	0.186060i
$367$	137234.			1.01890			0.509448	−	0.860501i	$-0.329850\pi$
$367$	137234.			1.01890			0.509448	+	0.860501i	$0.329850\pi$
$368$	−136235.	−	211860.i	−1.00599	−	1.56442i
$369$	7060.93			0.0518572
$370$	18014.6	+	75533.5i	0.131590	+	0.551742i
$371$			233015.i			1.69292i
$372$	22792.9	−	41755.6i	0.164708	−	0.301737i
$373$			120875.i			0.868801i	0.900720	+	0.434400i	$0.143040\pi$
$373$			120875.i			0.868801i	−0.900720	+	0.434400i	$0.856960\pi$
$374$	31091.8	−	121851.i	0.222281	−	0.871136i
$375$	80616.4	+	9632.92i	0.573272	+	0.0685008i
$376$	−110211.	+	118423.i	−0.779560	+	0.837648i
$377$		−	199270.i		−	1.40204i
$378$	9260.71	−	36293.4i	0.0648128	−	0.254006i
$379$		−	58409.6i		−	0.406636i	−0.979113	−	0.203318i	$-0.934827\pi$
$379$		−	58409.6i		−	0.406636i	0.979113	−	0.203318i	$-0.0651726\pi$
$380$	−7365.13	−	115.692i	−0.0510051	−	0.000801192i
$381$	134195.			0.924460
$382$	−73704.1	−	18806.5i	−0.505085	−	0.128879i
$383$	−8096.40			−0.0551944			−0.0275972	−	0.999619i	$-0.508786\pi$
$383$	−8096.40			−0.0551944			−0.0275972	+	0.999619i	$0.508786\pi$
$384$	83788.3	+	15076.0i	0.568225	+	0.102241i
$385$	148595.	−	78109.2i	1.00250	−	0.526964i
$386$	−94099.4	−	24010.6i	−0.631557	−	0.161150i
$387$	21832.4			0.145774
$388$	−68600.3	+	125673.i	−0.455683	+	0.834790i
$389$	−27852.6			−0.184063			−0.0920316	−	0.995756i	$-0.529336\pi$
$389$	−27852.6			−0.184063			−0.0920316	+	0.995756i	$0.529336\pi$
$390$	−22186.8	−	93027.2i	−0.145870	−	0.611618i
$391$			307467.i			2.01115i
$392$	−89552.1	+	96225.0i	−0.582779	+	0.626204i
$393$			136927.i			0.886552i
$394$	−136559.	−	34844.7i	−0.879685	−	0.224463i
$395$	−205459.	+	108000.i	−1.31683	+	0.692194i
$396$	20823.9	−	38148.4i	0.132792	−	0.243269i
$397$			283517.i			1.79887i	0.437059	+	0.899433i	$0.356020\pi$
$397$			283517.i			1.79887i	−0.437059	+	0.899433i	$0.643980\pi$
$398$	139157.	+	35507.6i	0.878492	+	0.224158i
$399$		−	6386.67i		−	0.0401170i
$400$	−159921.	−	5025.35i	−0.999507	−	0.0314084i
$401$	−309097.			−1.92224			−0.961118	−	0.276139i	$-0.910945\pi$
$401$	−309097.			−1.92224			−0.961118	+	0.276139i	$0.910945\pi$
$402$	−35049.3	+	137361.i	−0.216884	+	0.849983i
$403$	105314.			0.648449
$404$	155723.	+	85003.8i	0.954092	+	0.520806i
$405$	8479.82	+	16132.1i	0.0516983	+	0.0983512i
$406$	71466.2	−	280081.i	0.433559	−	1.69915i
$407$	−78122.8			−0.471616
$408$	−76073.6	−	70798.2i	−0.456997	−	0.425306i
$409$	−130574.			−0.780565			−0.390283	−	0.920695i	$-0.627623\pi$
$409$	−130574.			−0.780565			−0.390283	+	0.920695i	$0.627623\pi$
$410$	25438.1	−	6066.96i	0.151327	−	0.0360914i
$411$		−	66466.6i		−	0.393478i
$412$	−50965.3	−	27820.2i	−0.300248	−	0.163895i
$413$		−	354972.i		−	2.08110i
$414$	−26272.5	+	102964.i	−0.153285	+	0.600735i
$415$	542.555	+	1032.16i	0.00315027	+	0.00599309i
$416$	59579.2	+	178805.i	0.344277	+	1.03322i
$417$		−	36364.9i		−	0.209127i
$418$	1832.23	−	7180.62i	0.0104864	−	0.0410969i
$419$			183987.i			1.04800i	0.851720	+	0.523998i	$0.175560\pi$
$419$			183987.i			1.04800i	−0.851720	+	0.523998i	$0.824440\pi$
$420$	2178.87	−	138710.i	0.0123518	−	0.786336i
$421$	259474.			1.46396			0.731980	−	0.681326i	$-0.238596\pi$
$421$	259474.			1.46396			0.731980	+	0.681326i	$0.238596\pi$
$422$	−70761.0	−	18055.6i	−0.397346	−	0.101388i
$423$	68248.1			0.381425
$424$	163560.	+	152217.i	0.909798	+	0.846706i
$425$	160877.	+	110744.i	0.890666	+	0.613115i
$426$	5408.78	+	1380.12i	0.0298044	+	0.00760496i
$427$	82601.8			0.453037
$428$	27355.2	+	14932.2i	0.149332	+	0.0815150i
$429$	96216.1			0.522797
$430$	78654.7	−	18759.0i	0.425391	−	0.101455i
$431$		−	63999.9i		−	0.344528i	−0.985051	−	0.172264i	$-0.944892\pi$
$431$		−	63999.9i		−	0.344528i	0.985051	−	0.172264i	$-0.0551083\pi$
$432$	−19425.7	−	30209.0i	−0.104090	−	0.161871i
$433$		−	151046.i		−	0.805628i	−0.915282	−	0.402814i	$-0.868032\pi$
$433$		−	151046.i		−	0.805628i	0.915282	−	0.402814i	$-0.131968\pi$
$434$	148022.	+	37769.7i	0.785863	+	0.200523i
$435$	65439.9	+	124493.i	0.345831	+	0.657912i
$436$	−153345.	−	83705.7i	−0.806672	−	0.440334i
$437$			18118.9i			0.0948786i
$438$	−125207.	−	31948.3i	−0.652653	−	0.166533i
$439$		−	135756.i		−	0.704418i	−0.935921	−	0.352209i	$-0.885431\pi$
$439$		−	135756.i		−	0.704418i	0.935921	−	0.352209i	$-0.114569\pi$
$440$	42243.2	−	155328.i	0.218198	−	0.802315i
$441$	55455.0			0.285144
$442$	56880.4	−	222918.i	0.291151	−	1.14104i
$443$	148460.			0.756488			0.378244	−	0.925706i	$-0.376528\pi$
$443$	148460.			0.756488			0.378244	+	0.925706i	$0.376528\pi$
$444$	−30932.0	+	56666.0i	−0.156907	+	0.287446i
$445$	−90376.6	−	171933.i	−0.456390	−	0.868239i
$446$	−12510.4	+	49029.3i	−0.0628931	+	0.246483i
$447$	−75459.5			−0.377658
$448$	19614.1	+	272683.i	0.0977267	+	1.35863i
$449$	70805.3			0.351215			0.175607	−	0.984460i	$-0.443811\pi$
$449$	70805.3			0.351215			0.175607	+	0.984460i	$0.443811\pi$
$450$	44411.0	+	50832.2i	0.219314	+	0.251023i
$451$			26310.1i			0.129351i
$452$	15486.3	−	28370.1i	0.0758002	−	0.138862i
$453$		−	216798.i		−	1.05648i
$454$	−14560.2	+	57062.3i	−0.0706406	+	0.276845i
$455$	271845.	−	142895.i	1.31310	−	0.690233i
$456$	−4482.98	−	4172.10i	−0.0215594	−	0.0200643i
$457$			356840.i			1.70860i	0.519777	+	0.854302i	$0.326015\pi$
$457$			356840.i			1.70860i	−0.519777	+	0.854302i	$0.673985\pi$
$458$	−10092.5	+	39553.4i	−0.0481138	+	0.188561i
$459$			43841.7i			0.208095i
$460$	−6181.40	+	393517.i	−0.0292127	+	1.85972i
$461$	−198521.			−0.934123			−0.467062	−	0.884225i	$-0.654687\pi$
$461$	−198521.			−0.934123			−0.467062	+	0.884225i	$0.654687\pi$
$462$	135235.	+	34506.8i	0.633584	+	0.161667i
$463$	158591.			0.739805			0.369902	−	0.929071i	$-0.379391\pi$
$463$	158591.			0.739805			0.369902	+	0.929071i	$0.379391\pi$
$464$	−149911.	−	233127.i	−0.696302	−	1.08282i
$465$	−65794.4	+	34584.8i	−0.304287	+	0.159948i
$466$	−57924.0	−	14780.0i	−0.266739	−	0.0680619i
$467$	−122147.			−0.560080			−0.280040	−	0.959988i	$-0.590348\pi$
$467$	−122147.			−0.560080			−0.280040	+	0.959988i	$0.590348\pi$
$468$	38095.9	−	69789.9i	0.173935	−	0.318640i
$469$	−455235.			−2.06962
$470$	245874.	−	58640.7i	1.11306	−	0.265463i
$471$		−	232216.i		−	1.04677i
$472$	−249164.	−	231886.i	−1.11841	−	1.04085i
$473$			81350.9i			0.363614i
$474$	−186985.	−	47711.7i	−0.832245	−	0.212358i
$475$	9480.37	+	6526.08i	0.0420183	+	0.0289245i
$476$	159894.	−	292919.i	0.705699	−	1.29281i
$477$		−	94260.5i		−	0.414279i
$478$	301750.	+	76995.3i	1.32066	+	0.336983i
$479$		−	339002.i		−	1.47751i	−0.673972	−	0.738757i	$-0.735413\pi$
$479$		−	339002.i		−	1.47751i	0.673972	−	0.738757i	$-0.264587\pi$
$480$	−95940.8	−	92141.7i	−0.416410	−	0.399920i
$481$	−142920.			−0.617737
$482$	−12877.4	+	50467.3i	−0.0554285	+	0.217228i
$483$	−341238.			−1.46273
$484$	−63469.9	−	34646.0i	−0.270943	−	0.147898i
$485$	198023.	−	104091.i	0.841844	−	0.442515i
$486$	−3746.19	+	14681.6i	−0.0158605	+	0.0621584i
$487$	−348477.			−1.46932			−0.734659	−	0.678437i	$-0.762658\pi$
$487$	−348477.			−1.46932			−0.734659	+	0.678437i	$0.762658\pi$
$488$	53959.7	−	57980.5i	0.226585	−	0.243468i
$489$	−62398.2			−0.260948
$490$	199785.	−	47648.5i	0.832093	−	0.198453i
$491$		−	150786.i		−	0.625457i	−0.949843	−	0.312728i	$-0.898757\pi$
$491$		−	150786.i		−	0.625457i	0.949843	−	0.312728i	$-0.101243\pi$
$492$	19083.9	+	10417.3i	0.0788384	+	0.0430352i
$493$			338332.i			1.39203i
$494$	3351.93	−	13136.5i	0.0137354	−	0.0538300i
$495$	−60110.6	+	31597.1i	−0.245324	+	0.128955i
$496$	123207.	−	79227.6i	0.500809	−	0.322043i
$497$			17925.6i			0.0725705i
$498$	−239.688	+	939.356i	−0.000966470	+	0.00378766i
$499$			190194.i			0.763830i	0.924198	+	0.381915i	$0.124735\pi$
$499$			190194.i			0.763830i	−0.924198	+	0.381915i	$0.875265\pi$
$500$	203674.	+	144972.i	0.814697	+	0.579887i
$501$	68144.4			0.271491
$502$	−189951.	−	48468.4i	−0.753763	−	0.192332i
$503$	−323057.			−1.27686			−0.638430	−	0.769680i	$-0.720416\pi$
$503$	−323057.			−1.27686			−0.638430	+	0.769680i	$0.720416\pi$
$504$	78574.4	−	84429.2i	0.309328	−	0.332378i
$505$	−128980.	−	245373.i	−0.505756	−	0.962154i
$506$	−383658.	−	97895.3i	−1.49846	−	0.382350i
$507$	27613.5			0.107425
$508$	362697.	+	197984.i	1.40545	+	0.767188i
$509$	293025.			1.13102			0.565508	−	0.824743i	$-0.308680\pi$
$509$	293025.			1.13102			0.565508	+	0.824743i	$0.308680\pi$
$510$	37670.0	+	157947.i	0.144829	+	0.607253i
$511$		−	414958.i		−	1.58914i
$512$	204217.	+	164363.i	0.779024	+	0.626994i
$513$			2583.57i			0.00981714i
$514$	196921.	+	50246.9i	0.745360	+	0.190188i
$515$	42213.0	+	80306.2i	0.159159	+	0.302785i
$516$	59007.5	+	32210.2i	0.221620	+	0.120974i
$517$			254303.i			0.951415i
$518$	−200879.	−	51256.8i	−0.748643	−	0.191026i
$519$		−	44489.7i		−	0.165168i
$520$	77281.0	−	284162.i	0.285802	−	1.05090i
$521$	−48739.7			−0.179559			−0.0897796	−	0.995962i	$-0.528616\pi$
$521$	−48739.7			−0.179559			−0.0897796	+	0.995962i	$0.528616\pi$
$522$	−28909.9	+	113300.i	−0.106097	+	0.415803i
$523$	−212087.			−0.775373			−0.387687	−	0.921791i	$-0.626726\pi$
$523$	−212087.			−0.775373			−0.387687	+	0.921791i	$0.626726\pi$
$524$	−202014.	+	370080.i	−0.735729	+	1.34782i
$525$	−122908.	+	178547.i	−0.445923	+	0.647788i
$526$	−44758.1	+	175410.i	−0.161771	+	0.633991i
$527$	−178808.			−0.643821
$528$	112564.	−	72383.3i	0.403766	−	0.259639i
$529$	688245.			2.45941
$530$	−80991.3	−	339588.i	−0.288328	−	1.20893i
$531$			143595.i			0.509272i
$532$	9422.49	−	17261.6i	0.0332922	−	0.0609898i
$533$			48132.6i			0.169428i
$534$	39926.3	−	156474.i	0.140016	−	0.548731i
$535$	−22657.4	−	43103.6i	−0.0791595	−	0.150594i
$536$	−297383.	+	319542.i	−1.03511	+	1.11224i
$537$		−	5246.67i		−	0.0181943i
$538$	17437.0	−	68336.7i	0.0602430	−	0.236096i
$539$			206634.i			0.711253i
$540$	−881.405	+	56111.5i	−0.00302265	+	0.192426i
$541$	−247896.			−0.846982			−0.423491	−	0.905900i	$-0.639196\pi$
$541$	−247896.			−0.846982			−0.423491	+	0.905900i	$0.639196\pi$
$542$	−83967.9	−	21425.5i	−0.285835	−	0.0729343i
$543$	263748.			0.894518
$544$	−101157.	−	303584.i	−0.341820	−	1.02584i
$545$	127011.	+	241626.i	0.427610	+	0.813488i
$546$	247403.	+	63127.9i	0.829888	+	0.211756i
$547$	−108718.			−0.363351			−0.181675	−	0.983359i	$-0.558152\pi$
$547$	−108718.			−0.363351			−0.181675	+	0.983359i	$0.558152\pi$
$548$	98060.8	−	179643.i	0.326538	−	0.598203i
$549$	−33414.5			−0.110864
$550$	−189409.	+	165482.i	−0.626144	+	0.547049i
$551$			19937.7i			0.0656709i
$552$	−222914.	+	239524.i	−0.731576	+	0.786088i
$553$		−	619700.i		−	2.02643i
$554$	406884.	+	103822.i	1.32572	+	0.338274i
$555$	89288.8	−	46934.7i	0.289875	−	0.152373i
$556$	53650.5	−	98285.1i	0.173550	−	0.317935i
$557$			200089.i			0.644931i	0.946581	+	0.322465i	$0.104512\pi$
$557$			200089.i			0.644931i	−0.946581	+	0.322465i	$0.895488\pi$
$558$	−59878.6	−	15278.8i	−0.192311	−	0.0490705i
$559$			148826.i			0.476272i
$560$	210533.	−	371683.i	0.671341	−	1.18521i
$561$	−163361.			−0.519066
$562$	2318.80	−	9087.53i	0.00734159	−	0.0287722i
$563$	−32986.7			−0.104069			−0.0520346	−	0.998645i	$-0.516571\pi$
$563$	−32986.7			−0.104069			−0.0520346	+	0.998645i	$0.516571\pi$
$564$	184457.	+	100689.i	0.579880	+	0.316536i
$565$	−44702.9	+	23498.1i	−0.140036	+	0.0736098i
$566$	−137919.	+	540513.i	−0.430517	+	1.68723i
$567$	−48657.1			−0.151349
$568$	12582.4	+	11709.9i	0.0390003	+	0.0362958i
$569$	−145202.			−0.448486			−0.224243	−	0.974533i	$-0.571991\pi$
$569$	−145202.			−0.448486			−0.224243	+	0.974533i	$0.571991\pi$
$570$	2219.88	+	9307.71i	0.00683249	+	0.0286479i
$571$			58161.6i			0.178387i	0.996014	+	0.0891937i	$0.0284290\pi$
$571$			58161.6i			0.178387i	−0.996014	+	0.0891937i	$0.971571\pi$
$572$	260048.	+	141951.i	0.794807	+	0.433857i
$573$			98812.1i			0.300955i
$574$	−17262.2	+	67651.9i	−0.0523930	+	0.205332i
$575$	348687.	−	506534.i	1.05463	−	1.53205i
$576$	−7934.40	−	110307.i	−0.0239149	−	0.332474i
$577$		−	569231.i		−	1.70977i	−0.518820	−	0.854884i	$-0.673628\pi$
$577$		−	569231.i		−	1.70977i	0.518820	−	0.854884i	$-0.326372\pi$
$578$	−13975.4	+	54770.7i	−0.0418321	+	0.163943i
$579$			126155.i			0.376312i
$580$	−6801.93	+	433020.i	−0.0202198	+	1.28722i
$581$	−3113.17			−0.00922256
$582$	180218.	+	45984.9i	0.532050	+	0.135759i
$583$	351229.			1.03336
$584$	−291270.	−	271072.i	−0.854024	−	0.794801i
$585$	−109968.	+	57804.8i	−0.321333	+	0.168909i
$586$	578422.	+	147592.i	1.68442	+	0.429801i
$587$	−278696.			−0.808826			−0.404413	−	0.914576i	$-0.632524\pi$
$587$	−278696.			−0.808826			−0.404413	+	0.914576i	$0.632524\pi$
$588$	149881.	+	81814.9i	0.433503	+	0.236634i
$589$	−10537.0			−0.0303730
$590$	123381.	+	517324.i	0.354441	+	1.48613i
$591$			183079.i			0.524159i
$592$	−167203.	+	107519.i	−0.477090	+	0.306790i
$593$			362167.i			1.02991i	0.857217	+	0.514955i	$0.172191\pi$
$593$			362167.i			1.02991i	−0.857217	+	0.514955i	$0.827809\pi$
$594$	−54705.8	−	13958.9i	−0.155046	−	0.0395619i
$595$	−461554.	+	242616.i	−1.30373	+	0.685307i
$596$	−203948.	−	111328.i	−0.574153	−	0.313410i
$597$		−	186562.i		−	0.523449i
$598$	−701877.	−	179093.i	−1.96272	−	0.500813i
$599$			688704.i			1.91946i	0.280926	+	0.959729i	$0.409359\pi$
$599$			688704.i			1.91946i	−0.280926	+	0.959729i	$0.590641\pi$
$600$	45037.2	+	202908.i	0.125103	+	0.563633i
$601$	513464.			1.42155			0.710774	−	0.703421i	$-0.248345\pi$
$601$	513464.			1.42155			0.710774	+	0.703421i	$0.248345\pi$
$602$	−53374.8	+	209180.i	−0.147280	+	0.577200i
$603$	184154.			0.506462
$604$	319851.	−	585952.i	0.876746	−	1.60616i
$605$	52570.2	+	100010.i	0.143624	+	0.273232i
$606$	56980.6	−	223311.i	0.155161	−	0.608086i
$607$	−24516.1			−0.0665387			−0.0332693	−	0.999446i	$-0.510592\pi$
$607$	−24516.1			−0.0665387			−0.0332693	+	0.999446i	$0.510592\pi$
$608$	−5961.12	−	17890.0i	−0.0161258	−	0.0483954i
$609$	−375493.			−1.01244
$610$	−120381.	+	28710.7i	−0.323518	+	0.0771586i
$611$			465230.i			1.24619i
$612$	−64681.3	+	118493.i	−0.172693	+	0.316366i
$613$			51417.8i			0.136833i	0.997657	+	0.0684167i	$0.0217947\pi$
$613$			51417.8i			0.136833i	−0.997657	+	0.0684167i	$0.978205\pi$
$614$	61783.1	−	242132.i	0.163883	−	0.642268i
$615$	−15806.6	−	30070.6i	−0.0417916	−	0.0795046i
$616$	314596.	+	292780.i	0.829072	+	0.771579i
$617$		−	2653.59i		−	0.00697048i	−0.999994	−	0.00348524i	$-0.998891\pi$
$617$		−	2653.59i		−	0.00697048i	0.999994	−	0.00348524i	$-0.00110939\pi$
$618$	−18648.7	+	73085.6i	−0.0488284	+	0.191362i
$619$			139655.i			0.364480i	0.983254	+	0.182240i	$0.0583348\pi$
$619$			139655.i			0.364480i	−0.983254	+	0.182240i	$0.941665\pi$
$620$	−228850.	−	3594.80i	−0.595344	−	0.00935172i
$621$	138039.			0.357948
$622$	218932.	+	55863.2i	0.565885	+	0.144393i
$623$	518580.			1.33610
$624$	205927.	−	132420.i	0.528865	−	0.340084i
$625$	−139444.	−	364888.i	−0.356977	−	0.934113i
$626$	−250915.	−	64024.1i	−0.640292	−	0.163379i
$627$	−9626.77			−0.0244876
$628$	342596.	−	627621.i	0.868688	−	1.59140i
$629$	242658.			0.613328
$630$	−175295.	+	41807.6i	−0.441660	+	0.105335i
$631$		−	563210.i		−	1.41453i	−0.706950	−	0.707264i	$-0.749929\pi$
$631$		−	563210.i		−	1.41453i	0.706950	−	0.707264i	$-0.250071\pi$
$632$	−434984.	−	404820.i	−1.08903	−	1.01351i
$633$			94866.4i			0.236758i
$634$	−754022.	−	192398.i	−1.87588	−	0.478655i
$635$	−300410.	−	571503.i	−0.745019	−	1.41733i
$636$	139066.	−	254763.i	0.343801	−	0.629827i
$637$			378023.i			0.931621i
$638$	−422172.	−	107723.i	−1.03717	−	0.264646i
$639$		−	7251.34i		−	0.0177589i
$640$	−123364.	−	390581.i	−0.301181	−	0.953567i
$641$	453402.			1.10349			0.551744	−	0.834014i	$-0.313963\pi$
$641$	453402.			1.10349			0.551744	+	0.834014i	$0.313963\pi$
$642$	10009.5	−	39228.0i	0.0242853	−	0.0951758i
$643$	−384017.			−0.928813			−0.464406	−	0.885622i	$-0.653732\pi$
$643$	−384017.			−0.928813			−0.464406	+	0.885622i	$0.653732\pi$
$644$	−922281.	−	503441.i	−2.22378	−	1.21388i
$645$	−48874.1	−	92978.4i	−0.117479	−	0.223492i
$646$	−5691.09	+	22303.8i	−0.0136374	+	0.0534458i
$647$	652568.			1.55890			0.779448	−	0.626467i	$-0.215500\pi$
$647$	652568.			1.55890			0.779448	+	0.626467i	$0.215500\pi$
$648$	−31785.3	+	34153.7i	−0.0756966	+	0.0813370i
$649$	−535057.			−1.27031
$650$	−346510.	+	302739.i	−0.820143	+	0.716541i
$651$		−	198447.i		−	0.468256i
$652$	−168647.	−	92058.4i	−0.396719	−	0.216555i
$653$		−	104224.i		−	0.244423i	−0.992504	−	0.122211i	$-0.961001\pi$
$653$		−	104224.i		−	0.244423i	0.992504	−	0.122211i	$-0.0389986\pi$
$654$	−56110.5	+	219901.i	−0.131186	+	0.514128i
$655$	583136.	−	306525.i	1.35921	−	0.714470i
$656$	36210.1	+	56310.5i	0.0841439	+	0.130852i
$657$			167861.i			0.388882i
$658$	−166850.	+	653895.i	−0.385366	+	1.51028i
$659$		−	5763.37i		−	0.0132711i	−0.999978	−	0.00663554i	$-0.997888\pi$
$659$		−	5763.37i		−	0.0132711i	0.999978	−	0.00663554i	$-0.00211217\pi$
$660$	−209080.	−	3284.25i	−0.479982	−	0.00753961i
$661$	−242250.			−0.554447			−0.277224	−	0.960805i	$-0.589414\pi$
$661$	−242250.			−0.554447			−0.277224	+	0.960805i	$0.589414\pi$
$662$	−225868.	−	57633.0i	−0.515393	−	0.131509i
$663$	−298858.			−0.679888
$664$	−2033.69	+	2185.22i	−0.00461262	+	0.00495632i
$665$	−27199.1	+	14297.2i	−0.0615052	+	0.0323302i
$666$	81260.6	+	20734.7i	0.183202	+	0.0467464i
$667$	1.06527e6			2.39446
$668$	184177.	+	100536.i	0.412746	+	0.225304i
$669$	65731.6			0.146866
$670$	663444.	−	158230.i	1.47793	−	0.352485i
$671$		−	124508.i		−	0.276536i
$672$	336929.	−	112267.i	0.746104	−	0.248608i
$673$		−	67857.9i		−	0.149820i	−0.997190	−	0.0749100i	$-0.976133\pi$
$673$		−	67857.9i		−	0.149820i	0.997190	−	0.0749100i	$-0.0238670\pi$
$674$	−19816.7	−	5056.49i	−0.0436227	−	0.0111309i
$675$	49719.2	−	72226.6i	0.109123	−	0.158522i
$676$	74632.3	+	40739.2i	0.163318	+	0.0891495i
$677$		−	578606.i		−	1.26243i	−0.775610	−	0.631213i	$-0.782557\pi$
$677$		−	578606.i		−	1.26243i	0.775610	−	0.631213i	$-0.217443\pi$
$678$	−40683.5	−	10380.9i	−0.0885033	−	0.0225827i
$679$			597271.i			1.29548i
$680$	−131212.	+	482466.i	−0.283763	+	1.04340i
$681$	76501.1			0.164958
$682$	56931.1	−	223117.i	0.122400	−	0.479694i
$683$	243658.			0.522324			0.261162	−	0.965295i	$-0.415894\pi$
$683$	243658.			0.522324			0.261162	+	0.965295i	$0.415894\pi$
$684$	−3811.63	+	6982.74i	−0.00814702	+	0.0149250i
$685$	−283064.	+	148792.i	−0.603258	+	0.317103i
$686$	22912.2	−	89794.4i	0.0486876	−	0.190810i
$687$	53027.6			0.112354
$688$	111962.	+	174112.i	0.236534	+	0.367834i
$689$	642550.			1.35353
$690$	497308.	−	118607.i	1.04455	−	0.249123i
$691$			427648.i			0.895634i	0.894125	+	0.447817i	$0.147798\pi$
$691$			427648.i			0.895634i	−0.894125	+	0.447817i	$0.852202\pi$
$692$	65637.4	−	120245.i	0.137069	−	0.251104i
$693$		−	181304.i		−	0.377520i
$694$	119304.	−	467561.i	0.247706	−	0.970776i
$695$	−154868.	+	81406.5i	−0.320622	+	0.168535i
$696$	−245291.	+	263569.i	−0.506365	+	0.544097i
$697$		−	81722.2i		−	0.168219i
$698$	140540.	−	550786.i	0.288462	−	1.13050i
$699$			77656.5i			0.158936i
$700$	−595605.	+	301237.i	−1.21552	+	0.614769i
$701$	−447764.			−0.911198			−0.455599	−	0.890185i	$-0.650575\pi$
$701$	−447764.			−0.911198			−0.455599	+	0.890185i	$0.650575\pi$
$702$	−100081.	−	25536.8i	−0.203084	−	0.0518194i
$703$	14299.7			0.0289345
$704$	411021.	−	29564.8i	0.829313	−	0.0596527i
$705$	−152780.	−	290650.i	−0.307390	−	0.584780i
$706$	259779.	+	66285.8i	0.521188	+	0.132988i
$707$	740088.			1.48062
$708$	−211851.	+	388101.i	−0.422634	+	0.774245i
$709$	245828.			0.489034			0.244517	−	0.969645i	$-0.421371\pi$
$709$	245828.			0.489034			0.244517	+	0.969645i	$0.421371\pi$
$710$	−6230.56	−	26124.1i	−0.0123598	−	0.0518232i
$711$			250684.i			0.495892i
$712$	338763.	−	364005.i	0.668245	−	0.718039i
$713$			562991.i			1.10745i
$714$	−420054.	−	107182.i	−0.823965	−	0.210245i
$715$	−215390.	−	409759.i	−0.421321	−	0.801523i
$716$	7740.60	−	14180.4i	0.0150990	−	0.0276607i
$717$		−	404544.i		−	0.786915i
$718$	−587775.	−	149978.i	−1.14015	−	0.290924i
$719$		−	532263.i		−	1.02960i	−0.857310	−	0.514800i	$-0.827866\pi$
$719$		−	532263.i		−	1.02960i	0.857310	−	0.514800i	$-0.172134\pi$
$720$	−85165.7	+	150355.i	−0.164286	+	0.290037i
$721$	−242217.			−0.465945
$722$	128547.	−	503786.i	0.246597	−	0.966433i
$723$	67659.5			0.129435
$724$	712845.	+	389117.i	1.35993	+	0.742341i
$725$	383690.	−	557382.i	0.729969	−	1.06042i
$726$	−23224.3	+	91017.6i	−0.0440625	+	0.172684i
$727$	−613857.			−1.16144			−0.580722	−	0.814102i	$-0.697230\pi$
$727$	−613857.			−1.16144			−0.580722	+	0.814102i	$0.697230\pi$
$728$	575533.	+	535622.i	1.08594	+	1.01064i
$729$	19683.0			0.0370370
$730$	144231.	+	604745.i	0.270653	+	1.13482i
$731$		−	252685.i		−	0.472873i
$732$	−90311.1	−	49297.7i	−0.168546	−	0.0920035i
$733$			424876.i			0.790777i	0.918514	+	0.395388i	$0.129390\pi$
$733$			424876.i			0.790777i	−0.918514	+	0.395388i	$0.870610\pi$
$734$	135719.	−	531894.i	0.251913	−	0.987263i
$735$	−124142.	−	236168.i	−0.229796	−	0.437166i
$736$	−955860.	+	318501.i	−1.76457	+	0.587970i
$737$			686186.i			1.26330i
$738$	6983.00	−	27366.9i	0.0128212	−	0.0502473i
$739$			925500.i			1.69468i	0.531051	+	0.847340i	$0.321797\pi$
$739$			925500.i			1.69468i	−0.531051	+	0.847340i	$0.678203\pi$
$740$	310570.	+	4878.46i	0.567147	+	0.00890880i
$741$	−17611.5			−0.0320745
$742$	903124.	+	230444.i	1.64036	+	0.418559i
$743$	−513412.			−0.930012			−0.465006	−	0.885308i	$-0.653948\pi$
$743$	−513412.			−0.930012			−0.465006	+	0.885308i	$0.653948\pi$
$744$	−139296.	−	129636.i	−0.251647	−	0.234196i
$745$	168924.	+	321362.i	0.304354	+	0.579004i
$746$	468491.	+	119541.i	0.841828	+	0.214803i
$747$	1259.36			0.00225688
$748$	−441524.	−	241012.i	−0.789134	−	0.430761i
$749$	130008.			0.231743
$750$	117062.	−	302928.i	0.208110	−	0.538538i
$751$		−	578721.i		−	1.02610i	−0.858359	−	0.513050i	$-0.828516\pi$
$751$		−	578721.i		−	1.02610i	0.858359	−	0.513050i	$-0.171484\pi$
$752$	349992.	+	544274.i	0.618903	+	0.962458i
$753$			254660.i			0.449129i
$754$	−772336.	−	197071.i	−1.35851	−	0.346641i
$755$	−923286.	+	485326.i	−1.61973	+	0.851411i
$756$	−131508.	−	71785.6i	−0.230096	−	0.125601i
$757$		−	351402.i		−	0.613214i	−0.951836	−	0.306607i	$-0.900806\pi$
$757$		−	351402.i		−	0.613214i	0.951836	−	0.306607i	$-0.0991937\pi$
$758$	−226385.	−	57765.0i	−0.394012	−	0.100537i
$759$			514356.i			0.892853i
$760$	−7732.25	+	28431.5i	−0.0133869	+	0.0492235i
$761$	20239.4			0.0349486			0.0174743	−	0.999847i	$-0.494437\pi$
$761$	20239.4			0.0349486			0.0174743	+	0.999847i	$0.494437\pi$
$762$	132714.	−	520117.i	0.228564	−	0.895759i
$763$	−728787.			−1.25185
$764$	−145781.	+	267065.i	−0.249755	+	0.457540i
$765$	186710.	−	98144.1i	0.319040	−	0.167703i
$766$	−8007.05	+	31380.2i	−0.0136463	+	0.0534808i
$767$	−978851.			−1.66389
$768$	141295.	−	309838.i	0.239555	−	0.525306i
$769$	−300388.			−0.507961			−0.253981	−	0.967209i	$-0.581740\pi$
$769$	−300388.			−0.507961			−0.253981	+	0.967209i	$0.581740\pi$
$770$	−155781.	−	653176.i	−0.262745	−	1.10166i
$771$		−	264004.i		−	0.444122i
$772$	−186122.	+	340966.i	−0.312293	+	0.572106i
$773$		−	362531.i		−	0.606718i	−0.952876	−	0.303359i	$-0.901892\pi$
$773$		−	362531.i		−	0.606718i	0.952876	−	0.303359i	$-0.0981081\pi$
$774$	21591.4	−	84618.4i	0.0360413	−	0.141248i
$775$	294575.	+	202779.i	0.490448	+	0.337613i
$776$	419241.	+	390168.i	0.696210	+	0.647930i
$777$			269310.i			0.446078i
$778$	−27545.2	+	107952.i	−0.0455079	+	0.178349i
$779$		−	4815.84i		−	0.00793592i
$780$	−382498.	−	6008.32i	−0.628695	−	0.00987560i
$781$	27019.6			0.0442973
$782$	1.19169e6	+	304073.i	1.94871	+	0.497239i
$783$	151896.			0.247756
$784$	284387.	+	442250.i	0.462676	+	0.719509i
$785$	−988944.	+	519839.i	−1.60484	+	0.843586i
$786$	530704.	+	135416.i	0.859028	+	0.219192i
$787$	187283.			0.302377			0.151188	−	0.988505i	$-0.451690\pi$
$787$	187283.			0.302377			0.151188	+	0.988505i	$0.451690\pi$
$788$	−270103.	+	494816.i	−0.434988	+	0.796878i
$789$	235165.			0.377763
$790$	215395.	+	903129.i	0.345129	+	1.44709i
$791$		−	134832.i		−	0.215496i
$792$	−127262.	−	118437.i	−0.202884	−	0.188815i
$793$		−	227778.i		−	0.362215i
$794$	1.09886e6	+	280388.i	1.74302	+	0.444753i
$795$	−401430.	+	211012.i	−0.635149	+	0.333866i
$796$	275242.	−	504230.i	0.434398	−	0.795797i
$797$		−	503521.i		−	0.792686i	−0.918102	−	0.396343i	$-0.870279\pi$
$797$		−	503521.i		−	0.792686i	0.918102	−	0.396343i	$-0.129721\pi$
$798$	−24753.6	−	6316.18i	−0.0388715	−	0.00991856i
$799$		−	789892.i		−	1.23730i
$800$	−177633.	+	614855.i	−0.277552	+	0.960711i
$801$	−209778.			−0.326961
$802$	−305686.	+	1.19800e6i	−0.475255	+	1.86256i
$803$	−625475.			−0.970016
$804$	497722.	+	271689.i	0.769972	+	0.420301i
$805$	763896.	+	1.45324e6i	1.17881	+	2.24257i
$806$	104152.	−	408177.i	0.160323	−	0.628317i
$807$	−91616.3			−0.140678
$808$	483463.	−	519488.i	0.740527	−	0.795707i
$809$	−552787.			−0.844620			−0.422310	−	0.906452i	$-0.638781\pi$
$809$	−552787.			−0.844620			−0.422310	+	0.906452i	$0.638781\pi$
$810$	70911.1	−	16912.2i	0.108080	−	0.0257769i
$811$			184681.i			0.280789i	0.990096	+	0.140395i	$0.0448371\pi$
$811$			184681.i			0.280789i	−0.990096	+	0.140395i	$0.955163\pi$
$812$	−1.01486e6	−	553980.i	−1.53920	−	0.840198i
$813$			112572.i			0.170314i
$814$	−77260.5	+	302789.i	−0.116603	+	0.456974i
$815$	139685.	+	265737.i	0.210297	+	0.400071i
$816$	−349635.	+	224831.i	−0.525091	+	0.337656i
$817$		−	14890.6i		−	0.0223084i
$818$	−129133.	+	506080.i	−0.192988	+	0.756332i
$819$		−	331683.i		−	0.494488i
$820$	1642.97	−	104594.i	0.00244343	−	0.155553i
$821$	−130708.			−0.193918			−0.0969588	−	0.995288i	$-0.530912\pi$
$821$	−130708.			−0.193918			−0.0969588	+	0.995288i	$0.530912\pi$
$822$	−257613.	−	65733.1i	−0.381262	−	0.0972837i
$823$	358990.			0.530008			0.265004	−	0.964247i	$-0.414627\pi$
$823$	358990.			0.530008			0.265004	+	0.964247i	$0.414627\pi$
$824$	−158229.	+	170019.i	−0.233040	+	0.250405i
$825$	269127.	+	185261.i	0.395412	+	0.272193i
$826$	−1.37581e6	−	351054.i	−2.01649	−	0.514534i
$827$	639994.			0.935761			0.467880	−	0.883792i	$-0.345018\pi$
$827$	639994.			0.935761			0.467880	+	0.883792i	$0.345018\pi$
$828$	373086.	+	203655.i	0.544187	+	0.297053i
$829$	14158.4			0.0206018			0.0103009	−	0.999947i	$-0.496721\pi$
$829$	14158.4			0.0206018			0.0103009	+	0.999947i	$0.496721\pi$
$830$	4537.03	−	1082.08i	0.00658591	−	0.00157073i
$831$		−	545493.i		−	0.789927i
$832$	751935.	−	54086.8i	1.08626	−	0.0781349i
$833$		−	641828.i		−	0.924972i
$834$	−140944.	−	35963.5i	−0.202634	−	0.0517047i
$835$	−152548.	−	290209.i	−0.218793	−	0.416234i
$836$	−26018.8	−	14202.7i	−0.0372284	−	0.0203217i
$837$			80276.9i			0.114588i
$838$	713100.	+	181956.i	1.01546	+	0.259107i
$839$			642075.i			0.912140i	0.889944	+	0.456070i	$0.150743\pi$
$839$			642075.i			0.912140i	−0.889944	+	0.456070i	$0.849257\pi$
$840$	−535458.	−	145624.i	−0.758870	−	0.206383i
$841$	464925.			0.657341
$842$	256610.	−	1.00567e6i	0.361951	−	1.41851i
$843$	−12183.3			−0.0171439
$844$	−139960.	+	256400.i	−0.196480	+	0.359943i
$845$	−61815.6	−	117598.i	−0.0865734	−	0.164698i
$846$	67494.8	−	264517.i	0.0943039	−	0.369584i
$847$	−301647.			−0.420467
$848$	751722.	−	483390.i	1.04536	−	0.672212i
$849$	724645.			1.00533
$850$	588324.	−	514006.i	0.814289	−	0.711427i
$851$		−	764029.i		−	1.05500i
$852$	10698.2	−	19598.6i	0.0147377	−	0.0269988i
$853$			67120.3i			0.0922478i	0.998936	+	0.0461239i	$0.0146869\pi$
$853$			67120.3i			0.0922478i	−0.998936	+	0.0461239i	$0.985313\pi$
$854$	81690.2	−	320150.i	0.112009	−	0.438972i
$855$	11002.7	−	5783.58i	0.0150511	−	0.00791160i
$856$	84927.9	−	91256.2i	0.115905	−	0.124542i
$857$		−	892435.i		−	1.21511i	−0.794279	−	0.607554i	$-0.792151\pi$
$857$		−	892435.i		−	1.21511i	0.794279	−	0.607554i	$-0.207849\pi$
$858$	95154.2	−	372916.i	0.129257	−	0.506566i
$859$		−	1.26346e6i		−	1.71229i	−0.516738	−	0.856143i	$-0.672854\pi$
$859$		−	1.26346e6i		−	1.71229i	0.516738	−	0.856143i	$-0.327146\pi$
$860$	5080.05	−	323403.i	0.00686864	−	0.437268i
$861$	90698.2			0.122347
$862$	−248052.	−	63293.6i	−0.333832	−	0.0851815i
$863$	405341.			0.544250			0.272125	−	0.962262i	$-0.412274\pi$
$863$	405341.			0.544250			0.272125	+	0.962262i	$0.412274\pi$
$864$	−136296.	+	45415.0i	−0.182581	+	0.0608375i
$865$	−189470.	+	99594.9i	−0.253226	+	0.133108i
$866$	−585428.	−	149379.i	−0.780617	−	0.199184i
$867$	73428.9			0.0976852
$868$	292777.	−	536353.i	0.388595	−	0.711888i
$869$	−934088.			−1.23694
$870$	547231.	−	130514.i	0.722990	−	0.172432i
$871$			1.25533e6i			1.65471i
$872$	−476081.	+	511555.i	−0.626106	+	0.672759i
$873$		−	241611.i		−	0.317021i
$874$	70225.4	+	17918.9i	0.0919330	+	0.0234579i
$875$	1.03552e6	+	123736.i	1.35252	+	0.161614i
$876$	−247651.	+	453686.i	−0.322725	+	0.591217i
$877$		−	93859.2i		−	0.122033i	−0.998137	−	0.0610166i	$-0.980566\pi$
$877$		−	93859.2i		−	0.122033i	0.998137	−	0.0610166i	$-0.0194342\pi$
$878$	−526166.	−	134258.i	−0.682549	−	0.174161i
$879$		−	775468.i		−	1.00366i
$880$	−560246.	−	317341.i	−0.723459	−	0.409789i
$881$	−462334.			−0.595668			−0.297834	−	0.954618i	$-0.596264\pi$
$881$	−462334.			−0.595668			−0.297834	+	0.954618i	$0.596264\pi$
$882$	54843.0	−	214933.i	0.0704991	−	0.276291i
$883$	111865.			0.143474			0.0717369	−	0.997424i	$-0.477146\pi$
$883$	111865.			0.143474			0.0717369	+	0.997424i	$0.477146\pi$
$884$	−807738.	−	440916.i	−1.03363	−	0.564224i
$885$	611532.	−	321452.i	0.780788	−	0.410421i
$886$	146822.	−	575404.i	0.187035	−	0.733002i
$887$	−1.34030e6			−1.70355			−0.851773	−	0.523911i	$-0.824472\pi$
$887$	−1.34030e6			−1.70355			−0.851773	+	0.523911i	$0.824472\pi$
$888$	189036.	+	175927.i	0.239728	+	0.223104i
$889$	1.72375e6			2.18108
$890$	−755760.	+	180248.i	−0.954122	+	0.227557i
$891$			73341.9i			0.0923840i
$892$	177656.	+	96976.4i	0.223280	+	0.121881i
$893$		−	46548.0i		−	0.0583711i
$894$	−74626.7	+	292467.i	−0.0933725	+	0.365933i
$895$	−22344.1	+	11745.2i	−0.0278944	+	0.0146627i
$896$	1.07627e6	+	193653.i	1.34061	+	0.241217i
$897$			940979.i			1.16949i
$898$	70023.8	−	274428.i	0.0868347	−	0.340311i
$899$			619508.i			0.766527i
$900$	240937.	−	121858.i	0.297453	−	0.150442i
$901$	−1.09096e6			−1.34387
$902$	101973.	+	26019.8i	0.125335	+	0.0319809i
$903$	280439.			0.343924
$904$	−94642.1	−	88079.0i	−0.115810	−	0.107779i
$905$	−590427.	−	1.12323e6i	−0.720890	−	1.37143i
$906$	−840271.	−	214406.i	−1.02368	−	0.261204i
$907$	957858.			1.16436			0.582179	−	0.813060i	$-0.302200\pi$
$907$	957858.			1.16436			0.582179	+	0.813060i	$0.302200\pi$
$908$	206763.	+	112865.i	0.250785	+	0.136895i
$909$	−299384.			−0.362327
$910$	−284992.	−	1.19494e6i	−0.344151	−	1.44299i
$911$			104975.i			0.126488i	0.997998	+	0.0632442i	$0.0201447\pi$
$911$			104975.i			0.126488i	−0.997998	+	0.0632442i	$0.979855\pi$
$912$	−20603.8	+	13249.1i	−0.0247718	+	0.0159294i
$913$			4692.56i			0.00562948i
$914$	1.38305e6	+	352902.i	1.65556	+	0.422437i
$915$	74801.8	+	142303.i	0.0893449	+	0.169970i
$916$	143320.	+	78233.7i	0.170812	+	0.0932401i
$917$			1.75884e6i			2.09164i
$918$	169922.	+	43357.8i	0.201635	+	0.0514496i
$919$		−	382575.i		−	0.452987i	−0.974013	−	0.226494i	$-0.927274\pi$
$919$		−	382575.i		−	0.452987i	0.974013	−	0.226494i	$-0.0727263\pi$
$920$	1.51909e6	+	413132.i	1.79476	+	0.488105i
$921$	−324617.			−0.382695
$922$	−196330.	+	769430.i	−0.230953	+	0.905123i
$923$	49430.5			0.0580219
$924$	267484.	−	490019.i	0.313296	−	0.573943i
$925$	−399764.	−	275189.i	−0.467219	−	0.321623i
$926$	156841.	−	614670.i	0.182910	−	0.716837i
$927$	97983.0			0.114023
$928$	−1.05182e6	+	350474.i	−1.22136	+	0.406967i
$929$	−1.07228e6			−1.24244			−0.621222	−	0.783635i	$-0.713363\pi$
$929$	−1.07228e6			−1.24244			−0.621222	+	0.783635i	$0.713363\pi$
$930$	68976.2	+	289210.i	0.0797505	+	0.334386i
$931$		−	37822.6i		−	0.0436367i
$932$	−114570.	+	209886.i	−0.131898	+	0.241630i
$933$		−	293513.i		−	0.337182i
$934$	−120799.	+	473420.i	−0.138475	+	0.542692i
$935$	365700.	+	695710.i	0.418314	+	0.795802i
$936$	−232817.	−	216672.i	−0.265744	−	0.247316i
$937$		−	769557.i		−	0.876520i	−0.898848	−	0.438260i	$-0.855595\pi$
$937$		−	769557.i		−	0.876520i	0.898848	−	0.438260i	$-0.144405\pi$
$938$	−450211.	+	1.76441e6i	−0.511694	+	2.00536i
$939$			336392.i			0.381517i
$940$	15880.2	−	1.01096e6i	0.0179722	−	1.14413i
$941$	1.22022e6			1.37804			0.689018	−	0.724744i	$-0.258042\pi$
$941$	1.22022e6			1.37804			0.689018	+	0.724744i	$0.258042\pi$
$942$	−900025.	−	229653.i	−1.01427	−	0.258803i
$943$	−257309.			−0.289356
$944$	−1.14516e6	+	736389.i	−1.28506	+	0.826349i
$945$	108924.	+	207217.i	0.121972	+	0.232040i
$946$	315301.	+	80453.1i	0.352325	+	0.0899002i
$947$	767240.			0.855523			0.427761	−	0.903892i	$-0.359302\pi$
$947$	767240.			0.855523			0.427761	+	0.903892i	$0.359302\pi$
$948$	−369844.	+	677536.i	−0.411530	+	0.753904i
$949$	−1.14426e6			−1.27056
$950$	34669.6	−	30290.1i	0.0384151	−	0.0335625i
$951$			1.01089e6i			1.11774i
$952$	−977171.	−	909408.i	−1.07819	−	1.00342i
$953$		−	493072.i		−	0.542905i	−0.962452	−	0.271453i	$-0.912496\pi$
$953$		−	493072.i		−	0.542905i	0.962452	−	0.271453i	$-0.0875040\pi$
$954$	−365336.	−	93220.2i	−0.401417	−	0.102427i
$955$	420814.	−	221201.i	0.461407	−	0.242538i
$956$	596839.	−	1.09338e6i	0.653043	−	1.19634i
$957$			565990.i			0.617995i
$958$	−1.31391e6	−	335261.i	−1.43164	−	0.365302i
$959$		−	853769.i		−	0.928332i
$960$	−452006.	+	280724.i	−0.490458	+	0.304605i
$961$	596113.			0.645478
$962$	−141343.	+	553933.i	−0.152730	+	0.598559i
$963$	−52591.5			−0.0567104
$964$	182867.	+	99820.7i	0.196780	+	0.107415i
$965$	537262.	−	282412.i	0.576941	−	0.303269i
$966$	−337472.	+	1.32258e6i	−0.361646	+	1.41731i
$967$	−1.20283e6			−1.28632			−0.643161	−	0.765731i	$-0.722378\pi$
$967$	−1.20283e6			−1.28632			−0.643161	+	0.765731i	$0.722378\pi$
$968$	−197051.	+	211734.i	−0.210295	+	0.225964i
$969$	29901.8			0.0318456
$970$	−207599.	−	870442.i	−0.220639	−	0.925116i
$971$		−	17749.6i		−	0.0188257i	−0.999956	−	0.00941285i	$-0.997004\pi$
$971$		−	17749.6i		−	0.0188257i	0.999956	−	0.00941285i	$-0.00299625\pi$
$972$	53198.2	+	29039.1i	0.0563073	+	0.0307362i
$973$		−	467109.i		−	0.493393i
$974$	−344631.	+	1.35063e6i	−0.363275	+	1.42370i
$975$	492350.	+	338923.i	0.517923	+	0.356527i
$976$	−171358.	−	266479.i	−0.179889	−	0.279745i
$977$			908670.i			0.951956i	0.879457	+	0.475978i	$0.157906\pi$
$977$			908670.i			0.951956i	−0.879457	+	0.475978i	$0.842094\pi$
$978$	−61709.5	+	241844.i	−0.0645170	+	0.252847i
$979$		−	781667.i		−	0.815561i
$980$	12903.5	−	821454.i	0.0134355	−	0.855325i
$981$	294812.			0.306343
$982$	−584418.	−	149122.i	−0.606039	−	0.154638i
$983$	1.17515e6			1.21615			0.608076	−	0.793879i	$-0.291942\pi$
$983$	1.17515e6			1.21615			0.608076	+	0.793879i	$0.291942\pi$
$984$	59248.7	−	63663.6i	0.0611912	−	0.0657507i
$985$	779684.	−	409841.i	0.803611	−	0.422418i
$986$	1.31131e6	+	334598.i	1.34882	+	0.344167i
$987$	876651.			0.899897
$988$	−47599.6	−	25982.9i	−0.0487628	−	0.0266179i
$989$	−795600.			−0.813396
$990$	63017.5	+	264226.i	0.0642970	+	0.269591i
$991$			1.73448e6i			1.76613i	0.469249	+	0.883066i	$0.344525\pi$
$991$			1.73448e6i			1.76613i	−0.469249	+	0.883066i	$0.655475\pi$
$992$	−185224.	−	555881.i	−0.188224	−	0.564883i
$993$			302812.i			0.307096i
$994$	69476.2	+	17727.7i	0.0703175	+	0.0179424i
$995$	−794517.	+	417638.i	−0.802522	+	0.421846i
$996$	3403.73	+	1857.98i	0.00343112	+	0.00187293i
$997$		−	563011.i		−	0.566404i	−0.959060	−	0.283202i	$-0.908603\pi$
$997$		−	563011.i		−	0.566404i	0.959060	−	0.283202i	$-0.0913967\pi$
$998$	737158.	+	188095.i	0.740116	+	0.188850i
$999$		−	108943.i		−	0.109161i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.5.f.a.19.15	yes	24
3.2	odd	2		180.5.f.i.19.10		24
4.3	odd	2	inner	60.5.f.a.19.9	✓	24
5.2	odd	4		300.5.c.e.151.22		24
5.3	odd	4		300.5.c.e.151.3		24
5.4	even	2	inner	60.5.f.a.19.10	yes	24
8.3	odd	2		960.5.j.d.319.10		24
8.5	even	2		960.5.j.d.319.15		24
12.11	even	2		180.5.f.i.19.16		24
15.14	odd	2		180.5.f.i.19.15		24
20.3	even	4		300.5.c.e.151.4		24
20.7	even	4		300.5.c.e.151.21		24
20.19	odd	2	inner	60.5.f.a.19.16	yes	24
40.19	odd	2		960.5.j.d.319.22		24
40.29	even	2		960.5.j.d.319.3		24
60.59	even	2		180.5.f.i.19.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.5.f.a.19.9	✓	24	4.3	odd	2	inner
60.5.f.a.19.10	yes	24	5.4	even	2	inner
60.5.f.a.19.15	yes	24	1.1	even	1	trivial
60.5.f.a.19.16	yes	24	20.19	odd	2	inner
180.5.f.i.19.9		24	60.59	even	2
180.5.f.i.19.10		24	3.2	odd	2
180.5.f.i.19.15		24	15.14	odd	2
180.5.f.i.19.16		24	12.11	even	2
300.5.c.e.151.3		24	5.3	odd	4
300.5.c.e.151.4		24	20.3	even	4
300.5.c.e.151.21		24	20.7	even	4
300.5.c.e.151.22		24	5.2	odd	4
960.5.j.d.319.3		24	40.29	even	2
960.5.j.d.319.10		24	8.3	odd	2
960.5.j.d.319.15		24	8.5	even	2
960.5.j.d.319.22		24	40.19	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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988963 - 3.87582i) q^{2} -5.19615 q^{3} +(-14.0439 - 7.66608i) q^{4} +(11.6321 + 22.1290i) q^{5} +(-5.13880 + 20.1393i) q^{6} -66.7450 q^{7} +(-43.6012 + 46.8501i) q^{8} +27.0000 q^{9} +O(q^{10})\)	\(q+(0.988963 - 3.87582i) q^{2} -5.19615 q^{3} +(-14.0439 - 7.66608i) q^{4} +(11.6321 + 22.1290i) q^{5} +(-5.13880 + 20.1393i) q^{6} -66.7450 q^{7} +(-43.6012 + 46.8501i) q^{8} +27.0000 q^{9} +(97.2718 - 23.1992i) q^{10} +100.606i q^{11} +(72.9743 + 39.8341i) q^{12} +184.052i q^{13} +(-66.0083 + 258.691i) q^{14} +(-60.4423 - 114.986i) q^{15} +(138.462 + 215.323i) q^{16} -312.494i q^{17} +(26.7020 - 104.647i) q^{18} -18.4151i q^{19} +(6.28246 - 399.951i) q^{20} +346.817 q^{21} +(389.931 + 99.4958i) q^{22} -983.914 q^{23} +(226.559 - 243.440i) q^{24} +(-354.387 + 514.815i) q^{25} +(713.353 + 182.021i) q^{26} -140.296 q^{27} +(937.360 + 511.672i) q^{28} -1082.68 q^{29} +(-505.439 + 120.546i) q^{30} -572.196i q^{31} +(971.488 - 323.708i) q^{32} -522.765i q^{33} +(-1211.17 - 309.045i) q^{34} +(-776.386 - 1477.00i) q^{35} +(-379.185 - 206.984i) q^{36} +776.520i q^{37} +(-71.3735 - 18.2119i) q^{38} -956.363i q^{39} +(-1543.92 - 419.886i) q^{40} +261.516 q^{41} +(342.989 - 1344.20i) q^{42} +808.608 q^{43} +(771.255 - 1412.90i) q^{44} +(314.067 + 597.484i) q^{45} +(-973.054 + 3813.47i) q^{46} +2527.71 q^{47} +(-719.472 - 1118.85i) q^{48} +2053.89 q^{49} +(1644.85 + 1882.67i) q^{50} +1623.77i q^{51} +(1410.96 - 2584.81i) q^{52} -3491.13i q^{53} +(-138.748 + 543.762i) q^{54} +(-2226.32 + 1170.26i) q^{55} +(2910.16 - 3127.01i) q^{56} +95.6877i q^{57} +(-1070.74 + 4196.29i) q^{58} +5318.33i q^{59} +(-32.6446 + 2078.20i) q^{60} -1237.57 q^{61} +(-2217.73 - 565.881i) q^{62} -1802.11 q^{63} +(-293.867 - 4085.44i) q^{64} +(-4072.90 + 2140.92i) q^{65} +(-2026.14 - 516.995i) q^{66} +6820.52 q^{67} +(-2395.60 + 4388.63i) q^{68} +5112.56 q^{69} +(-6492.40 + 1548.43i) q^{70} -268.568i q^{71} +(-1177.23 + 1264.95i) q^{72} +6217.06i q^{73} +(3009.65 + 767.950i) q^{74} +(1841.45 - 2675.06i) q^{75} +(-141.172 + 258.620i) q^{76} -6714.96i q^{77} +(-3706.69 - 945.808i) q^{78} +9284.59i q^{79} +(-3154.28 + 5568.71i) q^{80} +729.000 q^{81} +(258.630 - 1013.59i) q^{82} +46.6428 q^{83} +(-4870.66 - 2658.73i) q^{84} +(6915.18 - 3634.97i) q^{85} +(799.683 - 3134.01i) q^{86} +5625.79 q^{87} +(-4713.41 - 4386.55i) q^{88} -7769.57 q^{89} +(2626.34 - 626.378i) q^{90} -12284.6i q^{91} +(13818.0 + 7542.76i) q^{92} +2973.22i q^{93} +(2499.81 - 9796.92i) q^{94} +(407.508 - 214.207i) q^{95} +(-5048.00 + 1682.04i) q^{96} -8948.56i q^{97} +(2031.22 - 7960.50i) q^{98} +2716.37i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9}+O(q^{10}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9	\( 24 q + 14 q^{4} - 24 q^{5} - 18 q^{6} + 648 q^{9} + 274 q^{10} - 36 q^{14} + 594 q^{16} - 12 q^{20} - 594 q^{24} + 1208 q^{25} - 2868 q^{26} - 1680 q^{29} + 468 q^{30} + 3076 q^{34} + 378 q^{36} - 7222 q^{40} - 4848 q^{41} - 3828 q^{44} - 648 q^{45} - 15280 q^{46} + 5416 q^{49} + 14472 q^{50} - 486 q^{54} + 32172 q^{56} - 7506 q^{60} + 2896 q^{61} - 18298 q^{64} - 2688 q^{65} - 15588 q^{66} + 9792 q^{69} + 27608 q^{70} + 31836 q^{74} + 50136 q^{76} - 27348 q^{80} + 17496 q^{81} - 4284 q^{84} - 15680 q^{85} - 58152 q^{86} - 38544 q^{89} + 7398 q^{90} + 4808 q^{94} + 21978 q^{96}+O(q^{100}) \) 24 * q + 14 * q^4 - 24 * q^5 - 18 * q^6 + 648 * q^9 + 274 * q^10 - 36 * q^14 + 594 * q^16 - 12 * q^20 - 594 * q^24 + 1208 * q^25 - 2868 * q^26 - 1680 * q^29 + 468 * q^30 + 3076 * q^34 + 378 * q^36 - 7222 * q^40 - 4848 * q^41 - 3828 * q^44 - 648 * q^45 - 15280 * q^46 + 5416 * q^49 + 14472 * q^50 - 486 * q^54 + 32172 * q^56 - 7506 * q^60 + 2896 * q^61 - 18298 * q^64 - 2688 * q^65 - 15588 * q^66 + 9792 * q^69 + 27608 * q^70 + 31836 * q^74 + 50136 * q^76 - 27348 * q^80 + 17496 * q^81 - 4284 * q^84 - 15680 * q^85 - 58152 * q^86 - 38544 * q^89 + 7398 * q^90 + 4808 * q^94 + 21978 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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