LMFDB - Embedded newform 76.6.d.a.75.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,6,Mod(75,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	76.d (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:	$12.1891703058$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.16
Character	$\chi$	$=$	76.75
Dual form			76.6.d.a.75.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.09334 + 4.73617i) q^{2} -0.774530 q^{3} +(-12.8625 - 29.3011i) q^{4} -32.1016 q^{5} +(2.39588 - 3.66830i) q^{6} +237.436i q^{7} +(178.563 + 29.7192i) q^{8} -242.400 q^{9} +O(q^{10})$	\(q+(-3.09334 + 4.73617i) q^{2} -0.774530 q^{3} +(-12.8625 - 29.3011i) q^{4} -32.1016 q^{5} +(2.39588 - 3.66830i) q^{6} +237.436i q^{7} +(178.563 + 29.7192i) q^{8} -242.400 q^{9} +(99.3011 - 152.038i) q^{10} -381.850i q^{11} +(9.96241 + 22.6946i) q^{12} -905.883i q^{13} +(-1124.54 - 734.470i) q^{14} +24.8637 q^{15} +(-693.111 + 753.773i) q^{16} +1015.54 q^{17} +(749.825 - 1148.05i) q^{18} +(1472.29 - 555.405i) q^{19} +(412.908 + 940.613i) q^{20} -183.901i q^{21} +(1808.50 + 1181.19i) q^{22} -724.790i q^{23} +(-138.302 - 23.0184i) q^{24} -2094.49 q^{25} +(4290.41 + 2802.20i) q^{26} +375.957 q^{27} +(6957.14 - 3054.03i) q^{28} -6046.58i q^{29} +(-76.9117 + 117.758i) q^{30} +3451.89 q^{31} +(-1425.97 - 5614.36i) q^{32} +295.754i q^{33} +(-3141.40 + 4809.76i) q^{34} -7622.08i q^{35} +(3117.88 + 7102.59i) q^{36} -8561.79i q^{37} +(-1923.79 + 8691.04i) q^{38} +701.633i q^{39} +(-5732.16 - 954.034i) q^{40} +17371.3i q^{41} +(870.987 + 568.869i) q^{42} -11284.8i q^{43} +(-11188.6 + 4911.55i) q^{44} +7781.43 q^{45} +(3432.72 + 2242.02i) q^{46} -10866.4i q^{47} +(536.835 - 583.820i) q^{48} -39568.9 q^{49} +(6478.96 - 9919.84i) q^{50} -786.565 q^{51} +(-26543.4 + 11651.9i) q^{52} -7043.34i q^{53} +(-1162.96 + 1780.59i) q^{54} +12258.0i q^{55} +(-7056.41 + 42397.3i) q^{56} +(-1140.33 + 430.178i) q^{57} +(28637.6 + 18704.1i) q^{58} +16203.7 q^{59} +(-319.809 - 728.533i) q^{60} -45493.7 q^{61} +(-10677.9 + 16348.7i) q^{62} -57554.5i q^{63} +(31001.5 + 10613.5i) q^{64} +29080.3i q^{65} +(-1400.74 - 914.868i) q^{66} -43584.7 q^{67} +(-13062.4 - 29756.4i) q^{68} +561.371i q^{69} +(36099.4 + 23577.7i) q^{70} +56141.9 q^{71} +(-43283.7 - 7203.94i) q^{72} +11323.6 q^{73} +(40550.1 + 26484.5i) q^{74} +1622.24 q^{75} +(-35211.3 - 35995.7i) q^{76} +90664.9 q^{77} +(-3323.05 - 2170.39i) q^{78} -90764.9 q^{79} +(22250.0 - 24197.3i) q^{80} +58612.0 q^{81} +(-82273.3 - 53735.3i) q^{82} +63238.3i q^{83} +(-5388.51 + 2365.44i) q^{84} -32600.4 q^{85} +(53446.5 + 34907.6i) q^{86} +4683.26i q^{87} +(11348.3 - 68184.3i) q^{88} -23387.3i q^{89} +(-24070.6 + 36854.1i) q^{90} +215089. q^{91} +(-21237.2 + 9322.63i) q^{92} -2673.59 q^{93} +(51464.9 + 33613.3i) q^{94} +(-47262.7 + 17829.4i) q^{95} +(1104.45 + 4348.49i) q^{96} -40004.3i q^{97} +(122400. - 187405. i) q^{98} +92560.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	$ 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) $ 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.09334	+	4.73617i	−0.546830	+	0.837244i
$2$	−3.09334	+	4.73617i	−0.546830	+	0.837244i
$3$	−0.774530			−0.0496861			−0.0248431	−	0.999691i	$-0.507909\pi$
$3$	−0.774530			−0.0496861			−0.0248431	+	0.999691i	$0.507909\pi$
$4$	−12.8625	−	29.3011i	−0.401954	−	0.915660i
$5$	−32.1016			−0.574251			−0.287125	−	0.957893i	$-0.592700\pi$
$5$	−32.1016			−0.574251			−0.287125	+	0.957893i	$0.592700\pi$
$6$	2.39588	−	3.66830i	0.0271699	−	0.0415994i
$7$			237.436i			1.83148i	0.401774	+	0.915739i	$0.368394\pi$
$7$			237.436i			1.83148i	−0.401774	+	0.915739i	$0.631606\pi$
$8$	178.563	+	29.7192i	0.986431	+	0.164177i
$9$	−242.400			−0.997531
$10$	99.3011	−	152.038i	0.314018	−	0.480788i
$11$		−	381.850i		−	0.951505i	−0.879579	−	0.475752i	$-0.842176\pi$
$11$		−	381.850i		−	0.951505i	0.879579	−	0.475752i	$-0.157824\pi$
$12$	9.96241	+	22.6946i	0.0199715	+	0.0454956i
$13$		−	905.883i		−	1.48667i	−0.668921	−	0.743334i	$-0.733244\pi$
$13$		−	905.883i		−	1.48667i	0.668921	−	0.743334i	$-0.266756\pi$
$14$	−1124.54	−	734.470i	−1.53339	−	1.00151i
$15$	24.8637			0.0285323
$16$	−693.111	+	753.773i	−0.676866	+	0.736106i
$17$	1015.54			0.852264			0.426132	−	0.904661i	$-0.359876\pi$
$17$	1015.54			0.852264			0.426132	+	0.904661i	$0.359876\pi$
$18$	749.825	−	1148.05i	0.545480	−	0.835177i
$19$	1472.29	−	555.405i	0.935638	−	0.352960i
$19$	1472.29	−	555.405i	0.935638	−	0.352960i
$20$	412.908	+	940.613i	0.230822	+	0.525819i
$21$		−	183.901i		−	0.0909990i
$22$	1808.50	+	1181.19i	0.796641	+	0.520311i
$23$		−	724.790i		−	0.285688i	−0.989745	−	0.142844i	$-0.954375\pi$
$23$		−	724.790i		−	0.285688i	0.989745	−	0.142844i	$-0.0456248\pi$
$24$	−138.302	−	23.0184i	−0.0490119	−	0.00815732i
$25$	−2094.49			−0.670236
$26$	4290.41	+	2802.20i	1.24470	+	0.812954i
$27$	375.957			0.0992496
$28$	6957.14	−	3054.03i	1.67701	−	0.736169i
$29$		−	6046.58i		−	1.33510i	−0.744564	−	0.667551i	$-0.767342\pi$
$29$		−	6046.58i		−	1.33510i	0.744564	−	0.667551i	$-0.232658\pi$
$30$	−76.9117	+	117.758i	−0.0156023	+	0.0238885i
$31$	3451.89			0.645138			0.322569	−	0.946546i	$-0.395454\pi$
$31$	3451.89			0.645138			0.322569	+	0.946546i	$0.395454\pi$
$32$	−1425.97	−	5614.36i	−0.246170	−	0.969227i
$33$			295.754i			0.0472766i
$34$	−3141.40	+	4809.76i	−0.466043	+	0.713553i
$35$		−	7622.08i		−	1.05173i
$36$	3117.88	+	7102.59i	0.400962	+	0.913399i
$37$		−	8561.79i		−	1.02816i	−0.857743	−	0.514080i	$-0.828134\pi$
$37$		−	8561.79i		−	1.02816i	0.857743	−	0.514080i	$-0.171866\pi$
$38$	−1923.79	+	8691.04i	−0.216122	+	0.976366i
$39$			701.633i			0.0738667i
$40$	−5732.16	−	954.034i	−0.566459	−	0.0942788i
$41$			17371.3i			1.61389i	0.590630	+	0.806943i	$0.298879\pi$
$41$			17371.3i			1.61389i	−0.590630	+	0.806943i	$0.701121\pi$
$42$	870.987	+	568.869i	0.0761883	+	0.0497610i
$43$		−	11284.8i		−	0.930725i	−0.885120	−	0.465363i	$-0.845924\pi$
$43$		−	11284.8i		−	0.930725i	0.885120	−	0.465363i	$-0.154076\pi$
$44$	−11188.6	+	4911.55i	−0.871255	+	0.382461i
$45$	7781.43			0.572833
$46$	3432.72	+	2242.02i	0.239191	+	0.156223i
$47$		−	10866.4i		−	0.717530i	−0.933428	−	0.358765i	$-0.883198\pi$
$47$		−	10866.4i		−	0.717530i	0.933428	−	0.358765i	$-0.116802\pi$
$48$	536.835	−	583.820i	0.0336308	−	0.0365743i
$49$	−39568.9			−2.35431
$50$	6478.96	−	9919.84i	0.366505	−	0.561151i
$51$	−786.565			−0.0423457
$52$	−26543.4	+	11651.9i	−1.36128	+	0.597572i
$53$		−	7043.34i		−	0.344421i	−0.985060	−	0.172210i	$-0.944909\pi$
$53$		−	7043.34i		−	0.344421i	0.985060	−	0.172210i	$-0.0550909\pi$
$54$	−1162.96	+	1780.59i	−0.0542726	+	0.0830961i
$55$			12258.0i			0.546402i
$56$	−7056.41	+	42397.3i	−0.300686	+	1.80663i
$57$	−1140.33	+	430.178i	−0.0464882	+	0.0175372i
$58$	28637.6	+	18704.1i	1.11781	+	0.730074i
$59$	16203.7			0.606015			0.303007	−	0.952988i	$-0.402009\pi$
$59$	16203.7			0.606015			0.303007	+	0.952988i	$0.402009\pi$
$60$	−319.809	−	728.533i	−0.0114687	−	0.0261259i
$61$	−45493.7			−1.56540			−0.782702	−	0.622396i	$-0.786159\pi$
$61$	−45493.7			−1.56540			−0.782702	+	0.622396i	$0.786159\pi$
$62$	−10677.9	+	16348.7i	−0.352781	+	0.540138i
$63$		−	57554.5i		−	1.82696i
$64$	31001.5	+	10613.5i	0.946092	+	0.323898i
$65$			29080.3i			0.853720i
$66$	−1400.74	−	914.868i	−0.0395820	−	0.0258523i
$67$	−43584.7			−1.18617			−0.593086	−	0.805139i	$-0.702090\pi$
$67$	−43584.7			−1.18617			−0.593086	+	0.805139i	$0.702090\pi$
$68$	−13062.4	−	29756.4i	−0.342571	−	0.780384i
$69$			561.371i			0.0141947i
$70$	36099.4	+	23577.7i	0.880552	+	0.575116i
$71$	56141.9			1.32173			0.660863	−	0.750507i	$-0.270190\pi$
$71$	56141.9			1.32173			0.660863	+	0.750507i	$0.270190\pi$
$72$	−43283.7	−	7203.94i	−0.983996	−	0.163772i
$73$	11323.6			0.248701			0.124351	−	0.992238i	$-0.460315\pi$
$73$	11323.6			0.248701			0.124351	+	0.992238i	$0.460315\pi$
$74$	40550.1	+	26484.5i	0.860820	+	0.562228i
$75$	1622.24			0.0333014
$76$	−35211.3	−	35995.7i	−0.699275	−	0.714853i
$77$	90664.9			1.74266
$78$	−3323.05	−	2170.39i	−0.0618444	−	0.0403925i
$79$	−90764.9			−1.63625			−0.818126	−	0.575039i	$-0.804987\pi$
$79$	−90764.9			−1.63625			−0.818126	+	0.575039i	$0.804987\pi$
$80$	22250.0	−	24197.3i	0.388691	−	0.422710i
$81$	58612.0			0.992600
$82$	−82273.3	−	53735.3i	−1.35122	−	0.882521i
$83$			63238.3i			1.00759i	0.863822	+	0.503796i	$0.168064\pi$
$83$			63238.3i			1.00759i	−0.863822	+	0.503796i	$0.831936\pi$
$84$	−5388.51	+	2365.44i	−0.0833241	+	0.0365774i
$85$	−32600.4			−0.489413
$86$	53446.5	+	34907.6i	0.779244	+	0.508949i
$87$			4683.26i			0.0663361i
$88$	11348.3	−	68184.3i	0.156215	−	0.938594i
$89$		−	23387.3i		−	0.312971i	−0.987680	−	0.156486i	$-0.949984\pi$
$89$		−	23387.3i		−	0.312971i	0.987680	−	0.156486i	$-0.0500165\pi$
$90$	−24070.6	+	36854.1i	−0.313242	+	0.479601i
$91$	215089.			2.72280
$92$	−21237.2	+	9322.63i	−0.261593	+	0.114834i
$93$	−2673.59			−0.0320544
$94$	51464.9	+	33613.3i	0.600747	+	0.392367i
$95$	−47262.7	+	17829.4i	−0.537291	+	0.202688i
$96$	1104.45	+	4348.49i	0.0122312	+	0.0481571i
$97$		−	40004.3i		−	0.431695i	−0.976427	−	0.215848i	$-0.930749\pi$
$97$		−	40004.3i		−	0.431695i	0.976427	−	0.215848i	$-0.0692514\pi$
$98$	122400.	−	187405.i	1.28741	−	1.97113i
$99$			92560.5i			0.949156i
$100$	26940.4	+	61370.8i	0.269404	+	0.613708i
$101$	−37740.6			−0.368134			−0.184067	−	0.982914i	$-0.558926\pi$
$101$	−37740.6			−0.368134			−0.184067	+	0.982914i	$0.558926\pi$
$102$	2433.11	−	3725.30i	0.0231559	−	0.0354537i
$103$	−139414.			−1.29483			−0.647416	−	0.762137i	$-0.724150\pi$
$103$	−139414.			−1.29483			−0.647416	+	0.762137i	$0.724150\pi$
$104$	26922.1	−	161757.i	0.244076	−	1.46649i
$105$			5903.53i			0.0522563i
$106$	33358.4	+	21787.4i	0.288364	+	0.188340i
$107$	−71792.1			−0.606202			−0.303101	−	0.952959i	$-0.598022\pi$
$107$	−71792.1			−0.606202			−0.303101	+	0.952959i	$0.598022\pi$
$108$	−4835.76	−	11016.0i	−0.0398938	−	0.0908789i
$109$		−	129011.i		−	1.04007i	−0.854146	−	0.520034i	$-0.825919\pi$
$109$		−	129011.i		−	1.04007i	0.854146	−	0.520034i	$-0.174081\pi$
$110$	−58055.9	−	37918.1i	−0.457472	−	0.298789i
$111$			6631.36i			0.0510852i
$112$	−178973.	−	164570.i	−1.34816	−	1.23966i
$113$		−	189572.i		−	1.39662i	−0.715797	−	0.698309i	$-0.753936\pi$
$113$		−	189572.i		−	1.39662i	0.715797	−	0.698309i	$-0.246064\pi$
$114$	1490.03	−	6731.47i	0.0107382	−	0.0485119i
$115$			23266.9i			0.164057i
$116$	−177172.	+	77774.3i	−1.22250	+	0.536650i
$117$			219586.i			1.48300i
$118$	−50123.4	+	76743.2i	−0.331387	+	0.507382i
$119$			241125.i			1.56090i
$120$	4439.73	+	738.928i	0.0281451	+	0.00468435i
$121$	15241.6			0.0946386
$122$	140727.	−	215466.i	0.856010	−	1.31063i
$123$		−	13454.6i		−	0.0801877i
$124$	−44400.0	−	101144.i	−0.259316	−	0.590727i
$125$	167554.			0.959134
$126$	272588.	+	178036.i	1.52961	+	0.999034i
$127$	160180.			0.881252			0.440626	−	0.897691i	$-0.354756\pi$
$127$	160180.			0.881252			0.440626	+	0.897691i	$0.354756\pi$
$128$	−146166.	+	113997.i	−0.788533	+	0.614992i
$129$			8740.39i			0.0462441i
$130$	−137729.	−	89955.2i	−0.714772	−	0.466840i
$131$		−	120575.i		−	0.613875i	−0.951730	−	0.306938i	$-0.900696\pi$
$131$		−	120575.i		−	0.613875i	0.951730	−	0.306938i	$-0.0993043\pi$
$132$	8665.93	−	3804.15i	0.0432893	−	0.0190030i
$133$	131873.	+	349574.i	0.646438	+	1.71360i
$134$	134822.	−	206424.i	0.648634	−	0.993114i
$135$	−12068.8			−0.0569942
$136$	181338.	+	30181.0i	0.840699	+	0.139922i
$137$	292572.			1.33178			0.665888	−	0.746052i	$-0.268053\pi$
$137$	292572.			1.33178			0.665888	+	0.746052i	$0.268053\pi$
$138$	−2658.75	−	1736.51i	−0.0118845	−	0.00776211i
$139$			54376.8i			0.238713i	0.992851	+	0.119357i	$0.0380832\pi$
$139$			54376.8i			0.238713i	−0.992851	+	0.119357i	$0.961917\pi$
$140$	−223335.	+	98039.2i	−0.963025	+	0.422746i
$141$			8416.33i			0.0356513i
$142$	−173666.	+	265897.i	−0.722759	+	1.10661i
$143$	−345911.			−1.41457
$144$	168010.	−	182715.i	0.675195	−	0.734289i
$145$			194105.i			0.766684i
$146$	−35027.7	+	53630.5i	−0.135997	+	0.208223i
$147$	30647.3			0.116976
$148$	−250870.	+	110126.i	−0.941444	+	0.413273i
$149$	−320932.			−1.18426			−0.592131	−	0.805842i	$-0.701713\pi$
$149$	−320932.			−1.18426			−0.592131	+	0.805842i	$0.701713\pi$
$150$	−5018.15	+	7683.21i	−0.0182102	+	0.0278814i
$151$	−10731.1			−0.0383001			−0.0191500	−	0.999817i	$-0.506096\pi$
$151$	−10731.1			−0.0383001			−0.0191500	+	0.999817i	$0.506096\pi$
$152$	279402.	−	55419.6i	0.980891	−	0.194560i
$153$	−246167.			−0.850160
$154$	−280457.	+	429404.i	−0.952938	+	1.45903i
$155$	−110811.			−0.370471
$156$	20558.6	−	9024.78i	0.0676368	−	0.0296910i
$157$	−107463.			−0.347944			−0.173972	−	0.984751i	$-0.555660\pi$
$157$	−107463.			−0.347944			−0.173972	+	0.984751i	$0.555660\pi$
$158$	280767.	−	429878.i	0.894752	−	1.36994i
$159$			5455.28i			0.0171129i
$160$	45775.8	+	180230.i	0.141363	+	0.556579i
$161$	172091.			0.523232
$162$	−181307.	+	277596.i	−0.542783	+	0.831048i
$163$			31482.1i			0.0928100i	0.998923	+	0.0464050i	$0.0147765\pi$
$163$			31482.1i			0.0928100i	−0.998923	+	0.0464050i	$0.985224\pi$
$164$	508998.	−	223439.i	1.47777	−	0.648707i
$165$		−	9494.18i		−	0.0271486i
$166$	−299507.	−	195617.i	−0.843600	−	0.550982i
$167$	508504.			1.41092			0.705461	−	0.708749i	$-0.250740\pi$
$167$	508504.			1.41092			0.705461	+	0.708749i	$0.250740\pi$
$168$	5465.40	−	32838.0i	0.0149399	−	0.0897642i
$169$	−449331.			−1.21018
$170$	100844.	−	154401.i	0.267626	−	0.409758i
$171$	−356882.	+	134630.i	−0.933329	+	0.352089i
$172$	−330656.	+	145151.i	−0.852228	+	0.374109i
$173$		−	540648.i		−	1.37341i	−0.726938	−	0.686704i	$-0.759057\pi$
$173$		−	540648.i		−	1.37341i	0.726938	−	0.686704i	$-0.240943\pi$
$174$	−22180.7	−	14486.9i	−0.0555395	−	0.0362746i
$175$		−	497307.i		−	1.22752i
$176$	287828.	+	264664.i	0.700409	+	0.644041i
$177$	−12550.2			−0.0301105
$178$	110766.	+	72344.7i	0.262033	+	0.171142i
$179$	85581.9			0.199641			0.0998204	−	0.995005i	$-0.468173\pi$
$179$	85581.9			0.199641			0.0998204	+	0.995005i	$0.468173\pi$
$180$	−100089.	−	228005.i	−0.230253	−	0.524520i
$181$			240662.i			0.546024i	0.962011	+	0.273012i	$0.0880198\pi$
$181$			240662.i			0.546024i	−0.962011	+	0.273012i	$0.911980\pi$
$182$	−665344.	+	1.01870e6i	−1.48891	+	2.27964i
$183$	35236.2			0.0777789
$184$	21540.2	−	129421.i	0.0469034	−	0.281812i
$185$			274847.i			0.590421i
$186$	8270.32	−	12662.6i	0.0175283	−	0.0268374i
$187$		−	387783.i		−	0.810933i
$188$	−318397.	+	139769.i	−0.657013	+	0.288414i
$189$			89265.7i			0.181773i
$190$	61756.6	−	278996.i	0.124108	−	0.560679i
$191$		−	455834.i		−	0.904114i	−0.891989	−	0.452057i	$-0.850690\pi$
$191$		−	455834.i		−	0.904114i	0.891989	−	0.452057i	$-0.149310\pi$
$192$	−24011.6	−	8220.48i	−0.0470076	−	0.0160933i
$193$		−	513774.i		−	0.992839i	−0.868083	−	0.496419i	$-0.834648\pi$
$193$		−	513774.i		−	0.992839i	0.868083	−	0.496419i	$-0.165352\pi$
$194$	189467.	+	123747.i	0.361434	+	0.236064i
$195$		−	22523.6i		−	0.0424180i
$196$	508956.	+	1.15941e6i	0.946324	+	2.15575i
$197$	−231380.			−0.424775			−0.212388	−	0.977185i	$-0.568124\pi$
$197$	−231380.			−0.424775			−0.212388	+	0.977185i	$0.568124\pi$
$198$	−438382.	−	286321.i	−0.794675	−	0.519027i
$199$		−	462260.i		−	0.827472i	−0.910397	−	0.413736i	$-0.864224\pi$
$199$		−	462260.i		−	0.827472i	0.910397	−	0.413736i	$-0.135776\pi$
$200$	−373998.	−	62246.5i	−0.661141	−	0.110037i
$201$	33757.7			0.0589362
$202$	116744.	−	178746.i	0.201306	−	0.308218i
$203$	1.43568e6			2.44521
$204$	10117.2	+	23047.2i	0.0170210	+	0.0387742i
$205$		−	557646.i		−	0.926775i
$206$	431255.	−	660288.i	0.708053	−	1.08409i
$207$			175689.i			0.284983i
$208$	682830.	+	627877.i	1.09434	+	1.00627i
$209$	−212081.	−	562192.i	−0.335843	−	0.890264i
$210$	−27960.1	−	18261.6i	−0.0437512	−	0.0285753i
$211$	−279463.			−0.432134			−0.216067	−	0.976379i	$-0.569323\pi$
$211$	−279463.			−0.432134			−0.216067	+	0.976379i	$0.569323\pi$
$212$	−206378.	+	90595.2i	−0.315372	+	0.138441i
$213$	−43483.6			−0.0656714
$214$	222077.	−	340019.i	0.331489	−	0.507538i
$215$			362259.i			0.534470i
$216$	67132.0	+	11173.1i	0.0979028	+	0.0162945i
$217$			819603.i			1.18156i
$218$	611019.	+	399076.i	0.870790	+	0.568740i
$219$	−8770.47			−0.0123570
$220$	359173.	−	157669.i	0.500319	−	0.219629i
$221$		−	919959.i		−	1.26703i
$222$	−31407.2	−	20513.0i	−0.0427708	−	0.0279349i
$223$	−677627.			−0.912491			−0.456246	−	0.889854i	$-0.650806\pi$
$223$	−677627.			−0.912491			−0.456246	+	0.889854i	$0.650806\pi$
$224$	1.33305e6	−	338576.i	1.77512	−	0.450854i
$225$	507704.			0.668581
$226$	897843.	+	586409.i	1.16931	+	0.763712i
$227$	170148.			0.219160			0.109580	−	0.993978i	$-0.465049\pi$
$227$	170148.			0.219160			0.109580	+	0.993978i	$0.465049\pi$
$228$	27272.2	+	27879.7i	0.0347443	+	0.0355183i
$229$	293285.			0.369573			0.184787	−	0.982779i	$-0.440841\pi$
$229$	293285.			0.369573			0.184787	+	0.982779i	$0.440841\pi$
$230$	−110196.	−	71972.4i	−0.137356	−	0.0897112i
$231$	−70222.7			−0.0865860
$232$	179699.	−	1.07970e6i	0.219193	−	1.31699i
$233$	−676065.			−0.815828			−0.407914	−	0.913020i	$-0.633744\pi$
$233$	−676065.			−0.815828			−0.407914	+	0.913020i	$0.633744\pi$
$234$	−1.04000e6	−	679254.i	−1.24163	−	0.810947i
$235$			348828.i			0.412042i
$236$	−208420.	−	474786.i	−0.243590	−	0.554903i
$237$	70300.1			0.0812990
$238$	−1.14201e6	−	745882.i	−1.30686	−	0.853548i
$239$			493874.i			0.559269i	0.960106	+	0.279635i	$0.0902134\pi$
$239$			493874.i			0.559269i	−0.960106	+	0.279635i	$0.909787\pi$
$240$	−17233.3	+	18741.5i	−0.0193125	+	0.0210028i
$241$			135537.i			0.150319i	0.997172	+	0.0751597i	$0.0239467\pi$
$241$			135537.i			0.150319i	−0.997172	+	0.0751597i	$0.976053\pi$
$242$	−47147.6	+	72187.0i	−0.0517513	+	0.0792356i
$243$	−136754.			−0.148568
$244$	585164.	+	1.33302e6i	0.629220	+	1.43338i
$245$	1.27022e6			1.35196
$246$	63723.2	+	41619.6i	0.0671366	+	0.0438490i
$247$	−503132.	−	1.33372e6i	−0.524734	−	1.39098i
$248$	616380.	+	102587.i	0.636384	+	0.105917i
$249$		−	48980.0i		−	0.0500634i
$250$	−518301.	+	793563.i	−0.524484	+	0.803029i
$251$		−	779268.i		−	0.780733i	−0.920660	−	0.390366i	$-0.872348\pi$
$251$		−	779268.i		−	0.780733i	0.920660	−	0.390366i	$-0.127652\pi$
$252$	−1.68641e6	+	740296.i	−1.67287	+	0.734352i
$253$	−276761.			−0.271834
$254$	−495492.	+	758641.i	−0.481895	+	0.737823i
$255$	25250.0			0.0243170
$256$	−87770.5	−	1.04490e6i	−0.0837045	−	0.996491i
$257$			59084.3i			0.0558007i	0.999611	+	0.0279003i	$0.00888211\pi$
$257$			59084.3i			0.0558007i	−0.999611	+	0.0279003i	$0.991118\pi$
$258$	−41395.9	−	27037.0i	−0.0387176	−	0.0252877i
$259$	2.03288e6			1.88305
$260$	852085.	−	374046.i	0.781717	−	0.343156i
$261$			1.46569e6i			1.33181i
$262$	571065.	+	372980.i	0.513963	+	0.335685i
$263$			517119.i			0.461000i	0.973072	+	0.230500i	$0.0740363\pi$
$263$			517119.i			0.461000i	−0.973072	+	0.230500i	$0.925964\pi$
$264$	−8789.58	+	52810.8i	−0.00776172	+	0.0466351i
$265$			226103.i			0.197784i
$266$	−2.06357e6	−	456776.i	−1.78819	−	0.395822i
$267$			18114.1i			0.0155503i
$268$	560610.	+	1.27708e6i	0.476786	+	1.08613i
$269$		−	100570.i		−	0.0847401i	−0.999102	−	0.0423701i	$-0.986509\pi$
$269$		−	100570.i		−	0.0847401i	0.999102	−	0.0423701i	$-0.0134908\pi$
$270$	37332.9	−	57159.9i	0.0311661	−	0.0477180i
$271$			247273.i			0.204528i	0.994757	+	0.102264i	$0.0326087\pi$
$271$			247273.i			0.204528i	−0.994757	+	0.102264i	$0.967391\pi$
$272$	−703881.	+	765485.i	−0.576869	+	0.627357i
$273$	−166593.			−0.135285
$274$	−905024.	+	1.38567e6i	−0.728255	+	1.11502i
$275$			799780.i			0.637733i
$276$	16448.8	−	7220.65i	0.0129976	−	0.00570563i
$277$	−2.37345e6			−1.85858			−0.929291	−	0.369349i	$-0.879581\pi$
$277$	−2.37345e6			−1.85858			−0.929291	+	0.369349i	$0.879581\pi$
$278$	−257537.	−	168206.i	−0.199861	−	0.130535i
$279$	−836739.			−0.643546
$280$	226522.	−	1.36102e6i	0.172669	−	1.03746i
$281$			1.76900e6i			1.33648i	0.743947	+	0.668238i	$0.232951\pi$
$281$			1.76900e6i			1.33648i	−0.743947	+	0.668238i	$0.767049\pi$
$282$	−39861.1	−	26034.5i	−0.0298488	−	0.0194952i
$283$			1.73146e6i			1.28513i	0.766233	+	0.642563i	$0.222129\pi$
$283$			1.73146e6i			1.28513i	−0.766233	+	0.642563i	$0.777871\pi$
$284$	−722127.	−	1.64502e6i	−0.531273	−	1.21025i
$285$	36606.4	−	13809.4i	0.0266959	−	0.0100708i
$286$	1.07002e6	−	1.63829e6i	0.773530	−	1.18434i
$287$	−4.12457e6			−2.95579
$288$	345654.	+	1.36092e6i	0.245562	+	0.966834i
$289$	−388538.			−0.273646
$290$	−919313.	−	600432.i	−0.641901	−	0.419246i
$291$			30984.5i			0.0214493i
$292$	−145650.	−	331794.i	−0.0999664	−	0.227726i
$293$		−	1.37111e6i		−	0.933049i	−0.884508	−	0.466525i	$-0.845506\pi$
$293$		−	1.37111e6i		−	0.933049i	0.884508	−	0.466525i	$-0.154494\pi$
$294$	−94802.4	+	145151.i	−0.0639663	+	0.0979378i
$295$	−520164.			−0.348005
$296$	254450.	−	1.52882e6i	0.168800	−	1.01421i
$297$		−	143559.i		−	0.0944364i
$298$	992752.	−	1.51999e6i	0.647590	−	0.991516i
$299$	−656575.			−0.424723
$300$	−20866.1	−	47533.5i	−0.0133856	−	0.0304928i
$301$	2.67941e6			1.70460
$302$	33194.8	−	50824.0i	0.0209436	−	0.0320665i
$303$	29231.2			0.0182911
$304$	−601808.	+	1.49473e6i	−0.373486	+	0.927636i
$305$	1.46042e6			0.898935
$306$	761477.	−	1.16589e6i	0.464893	−	0.711791i
$307$	3.02174e6			1.82983			0.914915	−	0.403647i	$-0.132258\pi$
$307$	3.02174e6			1.82983			0.914915	+	0.403647i	$0.132258\pi$
$308$	−1.16618e6	−	2.65658e6i	−0.700469	−	1.59568i
$309$	107980.			0.0643352
$310$	342777.	−	524820.i	0.202585	−	0.310175i
$311$			2.14138e6i			1.25543i	0.778442	+	0.627717i	$0.216010\pi$
$311$			2.14138e6i			1.25543i	−0.778442	+	0.627717i	$0.783990\pi$
$312$	−20852.0	+	125286.i	−0.0121272	+	0.0728644i
$313$	−275944.			−0.159206			−0.0796031	−	0.996827i	$-0.525365\pi$
$313$	−275944.			−0.159206			−0.0796031	+	0.996827i	$0.525365\pi$
$314$	332419.	−	508962.i	0.190266	−	0.291314i
$315$			1.84759e6i			1.04913i
$316$	1.16747e6	+	2.65951e6i	0.657698	+	1.49825i
$317$			637741.i			0.356448i	0.983990	+	0.178224i	$0.0570352\pi$
$317$			637741.i			0.356448i	−0.983990	+	0.178224i	$0.942965\pi$
$318$	−25837.1	−	16875.0i	−0.0143277	−	0.00935786i
$319$	−2.30889e6			−1.27036
$320$	−995199.	−	340710.i	−0.543294	−	0.185999i
$321$	55605.1			0.0301198
$322$	−532336.	+	815053.i	−0.286119	+	0.438072i
$323$	1.49516e6	−	564035.i	0.797411	−	0.300815i
$324$	−753899.	−	1.71740e6i	−0.398979	−	0.908884i
$325$			1.89736e6i			0.996418i
$326$	−149104.	−	97384.8i	−0.0777046	−	0.0507513i
$327$			99923.2i			0.0516769i
$328$	−516261.	+	3.10187e6i	−0.264963	+	1.59199i
$329$	2.58007e6			1.31414
$330$	44966.0	+	29368.7i	0.0227300	+	0.0148457i
$331$	598597.			0.300306			0.150153	−	0.988663i	$-0.452023\pi$
$331$	598597.			0.300306			0.150153	+	0.988663i	$0.452023\pi$
$332$	1.85295e6	−	813404.i	0.922612	−	0.405006i
$333$			2.07538e6i			1.02562i
$334$	−1.57297e6	+	2.40836e6i	−0.771534	+	1.18129i
$335$	1.39914e6			0.681160
$336$	138620.	+	127464.i	0.0669849	+	0.0615941i
$337$		−	1.56836e6i		−	0.752264i	−0.926566	−	0.376132i	$-0.877254\pi$
$337$		−	1.56836e6i		−	0.752264i	0.926566	−	0.376132i	$-0.122746\pi$
$338$	1.38993e6	−	2.12811e6i	0.661762	−	1.01321i
$339$			146829.i			0.0693925i
$340$	419324.	+	955229.i	0.196722	+	0.448136i
$341$		−	1.31810e6i		−	0.613852i
$342$	466326.	−	2.10671e6i	0.215588	−	0.973956i
$343$		−	5.40449e6i		−	2.48039i
$344$	335374.	−	2.01504e6i	0.152804	−	0.918096i
$345$		−	18020.9i		−	0.00815135i
$346$	2.56060e6	+	1.67241e6i	1.14988	+	0.751020i
$347$			3.10156e6i			1.38279i	0.722477	+	0.691395i	$0.243004\pi$
$347$			3.10156e6i			1.38279i	−0.722477	+	0.691395i	$0.756996\pi$
$348$	137225.	−	60238.5i	0.0607413	−	0.0266640i
$349$	−1.23157e6			−0.541245			−0.270622	−	0.962686i	$-0.587230\pi$
$349$	−1.23157e6			−0.541245			−0.270622	+	0.962686i	$0.587230\pi$
$350$	2.35533e6	+	1.53834e6i	1.02773	+	0.671246i
$351$		−	340573.i		−	0.147551i
$352$	−2.14384e6	+	544505.i	−0.922224	+	0.234231i
$353$	1.85138e6			0.790787			0.395393	−	0.918512i	$-0.370608\pi$
$353$	1.85138e6			0.790787			0.395393	+	0.918512i	$0.370608\pi$
$354$	38822.1	−	59439.9i	0.0164653	−	0.0252098i
$355$	−1.80225e6			−0.759002
$356$	−685273.	+	300819.i	−0.286575	+	0.125800i
$357$		−	186759.i		−	0.0775552i
$358$	−264734.	+	405330.i	−0.109170	+	0.167148i
$359$		−	207159.i		−	0.0848336i	−0.999100	−	0.0424168i	$-0.986494\pi$
$359$		−	207159.i		−	0.0848336i	0.999100	−	0.0424168i	$-0.0135057\pi$
$360$	1.38948e6	+	231258.i	0.565060	+	0.0940460i
$361$	1.85915e6	−	1.63543e6i	0.750838	−	0.660486i
$362$	−1.13982e6	−	744449.i	−0.457155	−	0.298582i
$363$	−11805.1			−0.00470223
$364$	−2.76659e6	−	6.30236e6i	−1.09444	−	2.49316i
$365$	−363506.			−0.142817
$366$	−108998.	+	166885.i	−0.0425318	+	0.0651199i
$367$		−	69761.1i		−	0.0270364i	−0.999909	−	0.0135182i	$-0.995697\pi$
$367$		−	69761.1i		−	0.0270364i	0.999909	−	0.0135182i	$-0.00430310\pi$
$368$	546327.	+	502360.i	0.210297	+	0.193373i
$369$		−	4.21080e6i		−	1.60990i
$370$	−1.30172e6	−	850195.i	−0.494326	−	0.322860i
$371$	1.67234e6			0.630799
$372$	34389.2	+	78339.3i	0.0128844	+	0.0293509i
$373$		−	1.27347e6i		−	0.473934i	−0.971518	−	0.236967i	$-0.923847\pi$
$373$		−	1.27347e6i		−	0.473934i	0.971518	−	0.236967i	$-0.0761534\pi$
$374$	1.83661e6	+	1.19954e6i	0.678949	+	0.443443i
$375$	−129776.			−0.0476557
$376$	322940.	−	1.94033e6i	0.117802	−	0.707793i
$377$	−5.47749e6			−1.98485
$378$	−422777.	−	276129.i	−0.152189	−	0.0993991i
$379$	2.08350e6			0.745067			0.372534	−	0.928019i	$-0.378489\pi$
$379$	2.08350e6			0.745067			0.372534	+	0.928019i	$0.378489\pi$
$380$	1.13034e6	+	1.15552e6i	0.401559	+	0.410505i
$381$	−124065.			−0.0437860
$382$	2.15890e6	+	1.41005e6i	0.756964	+	0.494397i
$383$	−596834.			−0.207901			−0.103950	−	0.994582i	$-0.533148\pi$
$383$	−596834.			−0.207901			−0.103950	+	0.994582i	$0.533148\pi$
$384$	113210.	−	88294.3i	0.0391792	−	0.0305566i
$385$	−2.91049e6			−1.00072
$386$	2.43332e6	+	1.58928e6i	0.831248	+	0.542914i
$387$			2.73543e6i			0.928428i
$388$	−1.17217e6	+	514556.i	−0.395286	+	0.173522i
$389$	3.18330e6			1.06660			0.533302	−	0.845925i	$-0.320951\pi$
$389$	3.18330e6			1.06660			0.533302	+	0.845925i	$0.320951\pi$
$390$	106675.	+	69673.0i	0.0355142	+	0.0231954i
$391$		−	736052.i		−	0.243482i
$392$	−7.06554e6	−	1.17596e6i	−2.32236	−	0.386523i
$393$			93389.2i			0.0305011i
$394$	715735.	−	1.09585e6i	0.232280	−	0.355641i
$395$	2.91370e6			0.939619
$396$	2.71212e6	−	1.19056e6i	0.869104	−	0.381517i
$397$	−4.17270e6			−1.32874			−0.664371	−	0.747403i	$-0.731301\pi$
$397$	−4.17270e6			−1.32874			−0.664371	+	0.747403i	$0.731301\pi$
$398$	2.18934e6	+	1.42993e6i	0.692796	+	0.452486i
$399$	−102140.	−	270755.i	−0.0321190	−	0.0851422i
$400$	1.45171e6	−	1.57877e6i	0.453660	−	0.493365i
$401$		−	2.29436e6i		−	0.712526i	−0.934386	−	0.356263i	$-0.884051\pi$
$401$		−	2.29436e6i		−	0.712526i	0.934386	−	0.356263i	$-0.115949\pi$
$402$	−104424.	+	159882.i	−0.0322281	+	0.0493440i
$403$		−	3.12701e6i		−	0.959106i
$404$	485440.	+	1.10584e6i	0.147973	+	0.337085i
$405$	−1.88154e6			−0.570001
$406$	−4.44103e6	+	6.79960e6i	−1.33711	+	2.04724i
$407$	−3.26932e6			−0.978298
$408$	−140451.	−	23376.1i	−0.0417711	−	0.00695219i
$409$		−	173040.i		−	0.0511491i	−0.999673	−	0.0255745i	$-0.991858\pi$
$409$		−	173040.i		−	0.0511491i	0.999673	−	0.0255745i	$-0.00814151\pi$
$410$	2.64111e6	+	1.72499e6i	0.775936	+	0.506788i
$411$	−226606.			−0.0661708
$412$	1.79322e6	+	4.08499e6i	0.520463	+	1.18563i
$413$			3.84733e6i			1.10990i
$414$	−832093.	−	543466.i	−0.238600	−	0.155837i
$415$		−	2.03005e6i		−	0.578611i
$416$	−5.08595e6	+	1.29176e6i	−1.44092	+	0.365972i
$417$		−	42116.4i		−	0.0118607i
$418$	3.31867e6	+	734598.i	0.929017	+	0.205641i
$419$		−	705404.i		−	0.196292i	−0.995172	−	0.0981461i	$-0.968709\pi$
$419$		−	705404.i		−	0.196292i	0.995172	−	0.0981461i	$-0.0312912\pi$
$420$	172980.	−	75934.3i	0.0478490	−	0.0210046i
$421$			1.30729e6i			0.359473i	0.983715	+	0.179736i	$0.0575245\pi$
$421$			1.30729e6i			0.359473i	−0.983715	+	0.179736i	$0.942476\pi$
$422$	864474.	−	1.32358e6i	0.236304	−	0.361802i
$423$			2.63401e6i			0.715758i
$424$	209323.	−	1.25768e6i	0.0565459	−	0.339747i
$425$	−2.12703e6			−0.571218
$426$	134509.	−	205946.i	0.0359111	−	0.0549830i
$427$		−	1.08018e7i		−	2.86700i
$428$	923427.	+	2.10359e6i	0.243665	+	0.555074i
$429$	267919.			0.0702845
$430$	−1.71572e6	−	1.12059e6i	−0.447481	−	0.292264i
$431$	−2.48235e6			−0.643680			−0.321840	−	0.946794i	$-0.604301\pi$
$431$	−2.48235e6			−0.643680			−0.321840	+	0.946794i	$0.604301\pi$
$432$	−260580.	+	283386.i	−0.0671787	+	0.0730582i
$433$			3.54652e6i			0.909040i	0.890737	+	0.454520i	$0.150189\pi$
$433$			3.54652e6i			0.909040i	−0.890737	+	0.454520i	$0.849811\pi$
$434$	−3.88178e6	−	2.53531e6i	−0.989250	−	0.646110i
$435$		−	150340.i		−	0.0380936i
$436$	−3.78018e6	+	1.65941e6i	−0.952349	+	0.418059i
$437$	−402552.	−	1.06710e6i	−0.100837	−	0.267301i
$438$	27130.0	−	41538.4i	0.00675717	−	0.0103458i
$439$	5.78237e6			1.43201			0.716003	−	0.698097i	$-0.245970\pi$
$439$	5.78237e6			1.43201			0.716003	+	0.698097i	$0.245970\pi$
$440$	−364298.	+	2.18882e6i	−0.0897067	+	0.538988i
$441$	9.59150e6			2.34850
$442$	4.35708e6	+	2.84574e6i	1.06082	+	0.692851i
$443$			224353.i			0.0543154i	0.999631	+	0.0271577i	$0.00864563\pi$
$443$			224353.i			0.0543154i	−0.999631	+	0.0271577i	$0.991354\pi$
$444$	194306.	−	85296.1i	0.0467767	−	0.0205339i
$445$			750768.i			0.179724i
$446$	2.09613e6	−	3.20935e6i	0.498978	−	0.763977i
$447$	248572.			0.0588414
$448$	−2.52003e6	+	7.36088e6i	−0.593213	+	1.73275i
$449$			6.93083e6i			1.62244i	0.584739	+	0.811221i	$0.301197\pi$
$449$			6.93083e6i			1.62244i	−0.584739	+	0.811221i	$0.698803\pi$
$450$	−1.57050e6	+	2.40457e6i	−0.365600	+	0.559765i
$451$	6.63323e6			1.53562
$452$	−5.55466e6	+	2.43837e6i	−1.27883	+	0.561376i
$453$	8311.52			0.00190298
$454$	−526324.	+	805847.i	−0.119843	+	0.183490i
$455$	−6.90471e6			−1.56357
$456$	−216405.	+	42924.2i	−0.0487366	+	0.00966696i
$457$	−2.78552e6			−0.623901			−0.311950	−	0.950098i	$-0.600982\pi$
$457$	−2.78552e6			−0.623901			−0.311950	+	0.950098i	$0.600982\pi$
$458$	−907229.	+	1.38904e6i	−0.202094	+	0.309423i
$459$	381799.			0.0845868
$460$	681747.	−	299271.i	0.150220	−	0.0659433i
$461$	648749.			0.142175			0.0710877	−	0.997470i	$-0.477353\pi$
$461$	648749.			0.142175			0.0710877	+	0.997470i	$0.477353\pi$
$462$	217223.	−	332586.i	0.0473478	−	0.0724936i
$463$		−	1.37048e6i		−	0.297112i	−0.988904	−	0.148556i	$-0.952537\pi$
$463$		−	1.37048e6i		−	0.297112i	0.988904	−	0.148556i	$-0.0474625\pi$
$464$	4.55775e6	+	4.19095e6i	0.982777	+	0.903686i
$465$	85826.6			0.0184073
$466$	2.09130e6	−	3.20195e6i	0.446119	−	0.683047i
$467$			6.02083e6i			1.27751i	0.769410	+	0.638755i	$0.220550\pi$
$467$			6.02083e6i			1.27751i	−0.769410	+	0.638755i	$0.779450\pi$
$468$	6.43412e6	−	2.82443e6i	1.35792	−	0.596096i
$469$		−	1.03486e7i		−	2.17245i
$470$	−1.65211e6	−	1.07904e6i	−0.344980	−	0.225317i
$471$	83233.3			0.0172880
$472$	2.89338e6	+	481560.i	0.597792	+	0.0994937i
$473$	−4.30909e6			−0.885590
$474$	−217462.	+	332953.i	−0.0444567	+	0.0680671i
$475$	−3.08368e6	+	1.16329e6i	−0.627098	+	0.236567i
$476$	7.06525e6	−	3.10148e6i	1.42926	−	0.627411i
$477$			1.70731e6i			0.343570i
$478$	−2.33907e6	−	1.52772e6i	−0.468245	−	0.305825i
$479$		−	6.45472e6i		−	1.28540i	−0.766118	−	0.642700i	$-0.777814\pi$
$479$		−	6.45472e6i		−	1.28540i	0.766118	−	0.642700i	$-0.222186\pi$
$480$	−35454.7	−	139594.i	−0.00702378	−	0.0276543i
$481$	−7.75598e6			−1.52853
$482$	−641925.	−	419261.i	−0.125854	−	0.0821991i
$483$	−133290.			−0.0259974
$484$	−196046.	−	446597.i	−0.0380404	−	0.0866568i
$485$			1.28420e6i			0.247901i
$486$	423027.	−	647691.i	0.0812414	−	0.124388i
$487$	−7.28417e6			−1.39174			−0.695869	−	0.718169i	$-0.744981\pi$
$487$	−7.28417e6			−1.39174			−0.695869	+	0.718169i	$0.744981\pi$
$488$	−8.12349e6	−	1.35204e6i	−1.54416	−	0.257003i
$489$		−	24383.8i		−	0.00461137i
$490$	−3.92923e6	+	6.01599e6i	−0.739295	+	1.13192i
$491$		−	7.96494e6i		−	1.49100i	−0.666503	−	0.745502i	$-0.732210\pi$
$491$		−	7.96494e6i		−	1.49100i	0.666503	−	0.745502i	$-0.267790\pi$
$492$	−394234.	+	173060.i	−0.0734246	+	0.0322318i
$493$		−	6.14053e6i		−	1.13786i
$494$	7.87307e6	+	1.74273e6i	1.45153	+	0.321301i
$495$		−	2.97134e6i		−	0.545054i
$496$	−2.39254e6	+	2.60194e6i	−0.436672	+	0.474890i
$497$			1.33301e7i			2.42071i
$498$	231977.	+	151512.i	0.0419152	+	0.0273761i
$499$			9.89073e6i			1.77819i	0.457727	+	0.889093i	$0.348664\pi$
$499$			9.89073e6i			1.77819i	−0.457727	+	0.889093i	$0.651336\pi$
$500$	−2.15517e6	−	4.90952e6i	−0.385528	−	0.878241i
$501$	−393851.			−0.0701032
$502$	3.69074e6	+	2.41054e6i	0.653664	+	0.426928i
$503$			5.50623e6i			0.970364i	0.874413	+	0.485182i	$0.161247\pi$
$503$			5.50623e6i			0.970364i	−0.874413	+	0.485182i	$0.838753\pi$
$504$	1.71047e6	−	1.02771e7i	0.299944	−	1.80217i
$505$	1.21153e6			0.211401
$506$	856115.	−	1.31079e6i	0.148647	−	0.227591i
$507$	348020.			0.0601291
$508$	−2.06032e6	−	4.69347e6i	−0.354223	−	0.806927i
$509$		−	3.47957e6i		−	0.595294i	−0.954676	−	0.297647i	$-0.903798\pi$
$509$		−	3.47957e6i		−	0.595294i	0.954676	−	0.297647i	$-0.0962019\pi$
$510$	−78106.8	+	119588.i	−0.0132973	+	0.0203593i
$511$			2.68863e6i			0.455490i
$512$	5.22030e6	+	2.81652e6i	0.880078	+	0.474830i
$513$	553516.	−	208808.i	0.0928617	−	0.0350311i
$514$	−279833.	−	182768.i	−0.0467188	−	0.0305135i
$515$	4.47541e6			0.743558
$516$	256103.	−	112423.i	0.0423439	−	0.0185880i
$517$	−4.14932e6			−0.682733
$518$	−6.28838e6	+	9.62805e6i	−1.02971	+	1.57657i
$519$			418748.i			0.0682393i
$520$	−864243.	+	5.19267e6i	−0.140161	+	0.842136i
$521$		−	4.41260e6i		−	0.712197i	−0.934448	−	0.356098i	$-0.884107\pi$
$521$		−	4.41260e6i		−	0.712197i	0.934448	−	0.356098i	$-0.115893\pi$
$522$	−6.94176e6	−	4.53388e6i	−1.11505	−	0.728272i
$523$	1.04037e7			1.66316			0.831580	−	0.555404i	$-0.187437\pi$
$523$	1.04037e7			1.66316			0.831580	+	0.555404i	$0.187437\pi$
$524$	−3.53299e6	+	1.55090e6i	−0.562101	+	0.246750i
$525$			385179.i			0.0609908i
$526$	−2.44916e6	−	1.59962e6i	−0.385970	−	0.252089i
$527$	3.50553e6			0.549828
$528$	−222931.	−	204990.i	−0.0348006	−	0.0319999i
$529$	5.91102e6			0.918382
$530$	−1.07086e6	−	699412.i	−0.165593	−	0.108154i
$531$	−3.92777e6			−0.604519
$532$	8.54668e6	−	8.36043e6i	1.30924	−	1.28071i
$533$	1.57364e7			2.39931
$534$	−85791.5	−	56033.1i	−0.0130194	−	0.00850338i
$535$	2.30464e6			0.348112
$536$	−7.78262e6	−	1.29530e6i	−1.17008	−	0.194742i
$537$	−66285.7			−0.00991937
$538$	476318.	+	311098.i	0.0709481	+	0.0463384i
$539$			1.51094e7i			2.24014i
$540$	155235.	+	353630.i	0.0229090	+	0.0521873i
$541$	−6.49157e6			−0.953579			−0.476789	−	0.879018i	$-0.658200\pi$
$541$	−6.49157e6			−0.953579			−0.476789	+	0.879018i	$0.658200\pi$
$542$	−1.17112e6	−	764898.i	−0.171240	−	0.111842i
$543$		−	186400.i		−	0.0271298i
$544$	−1.44812e6	−	5.70160e6i	−0.209801	−	0.826037i
$545$			4.14147e6i			0.597260i
$546$	515329.	−	789012.i	0.0739780	−	0.113267i
$547$	−486584.			−0.0695328			−0.0347664	−	0.999395i	$-0.511069\pi$
$547$	−486584.			−0.0695328			−0.0347664	+	0.999395i	$0.511069\pi$
$548$	−3.76321e6	−	8.57268e6i	−0.535313	−	1.21945i
$549$	1.10277e7			1.56154
$550$	−3.78789e6	−	2.47399e6i	−0.533938	−	0.348731i
$551$	−3.35830e6	−	8.90229e6i	−0.471238	−	1.24917i
$552$	−16683.5	+	100240.i	−0.00233045	+	0.0140021i
$553$		−	2.15509e7i		−	2.99676i
$554$	7.34190e6	−	1.12411e7i	1.01633	−	1.55609i
$555$		−	212877.i		−	0.0293357i
$556$	1.59330e6	−	699422.i	0.218580	−	0.0959517i
$557$	6.72820e6			0.918885			0.459442	−	0.888208i	$-0.348049\pi$
$557$	6.72820e6			0.918885			0.459442	+	0.888208i	$0.348049\pi$
$558$	2.58832e6	−	3.96293e6i	0.351910	−	0.538804i
$559$	−1.02227e7			−1.38368
$560$	5.74531e6	+	5.28294e6i	0.774183	+	0.711879i
$561$			300350.i			0.0402921i
$562$	−8.37826e6	−	5.47211e6i	−1.11896	−	0.730826i
$563$	−8.16421e6			−1.08553			−0.542767	−	0.839883i	$-0.682623\pi$
$563$	−8.16421e6			−1.08553			−0.542767	+	0.839883i	$0.682623\pi$
$564$	246608.	−	108255.i	0.0326444	−	0.0143302i
$565$			6.08555e6i			0.802009i
$566$	−8.20047e6	−	5.35598e6i	−1.07596	−	0.702745i
$567$			1.39166e7i			1.81792i
$568$	1.00249e7	+	1.66849e6i	1.30379	+	0.216997i
$569$			9.14370e6i			1.18397i	0.805948	+	0.591986i	$0.201656\pi$
$569$			9.14370e6i			1.18397i	−0.805948	+	0.591986i	$0.798344\pi$
$570$	−47832.4	+	216091.i	−0.00616644	+	0.0278580i
$571$			4.36724e6i			0.560553i	0.959919	+	0.280277i	$0.0904262\pi$
$571$			4.36724e6i			0.560553i	−0.959919	+	0.280277i	$0.909574\pi$
$572$	4.44929e6	+	1.01356e7i	0.568592	+	1.29527i
$573$			353057.i			0.0449219i
$574$	1.27587e7	−	1.95347e7i	1.61632	−	2.47472i
$575$			1.51806e6i			0.191479i
$576$	−7.51478e6	−	2.57271e6i	−0.943756	−	0.323099i
$577$	5.32768e6			0.666191			0.333095	−	0.942893i	$-0.391907\pi$
$577$	5.32768e6			0.666191			0.333095	+	0.942893i	$0.391907\pi$
$578$	1.20188e6	−	1.84018e6i	0.149638	−	0.229109i
$579$			397933.i			0.0493303i
$580$	5.68749e6	−	2.49668e6i	0.702022	−	0.308172i
$581$	−1.50151e7			−1.84538
$582$	−146748.	−	95845.5i	−0.0179583	−	0.0117291i
$583$	−2.68950e6			−0.327718
$584$	2.02198e6	+	336529.i	0.245326	+	0.0408310i
$585$		−	7.04907e6i		−	0.851612i
$586$	6.49382e6	+	4.24132e6i	0.781190	+	0.510219i
$587$			1.91830e6i			0.229784i	0.993378	+	0.114892i	$0.0366523\pi$
$587$			1.91830e6i			0.229784i	−0.993378	+	0.114892i	$0.963348\pi$
$588$	−394201.	−	897999.i	−0.0470192	−	0.107111i
$589$	5.08217e6	−	1.91720e6i	0.603616	−	0.227708i
$590$	1.60904e6	−	2.46358e6i	0.190299	−	0.291365i
$591$	179210.			0.0211054
$592$	6.45364e6	+	5.93427e6i	0.756834	+	0.695926i
$593$	−5.31161e6			−0.620283			−0.310141	−	0.950690i	$-0.600376\pi$
$593$	−5.31161e6			−0.620283			−0.310141	+	0.950690i	$0.600376\pi$
$594$	679920.	+	444077.i	0.0790663	+	0.0516407i
$595$		−	7.74051e6i		−	0.896349i
$596$	4.12800e6	+	9.40368e6i	0.476019	+	1.08438i
$597$			358034.i			0.0411139i
$598$	2.03101e6	−	3.10965e6i	0.232252	−	0.355597i
$599$	1.32311e7			1.50671			0.753355	−	0.657614i	$-0.228434\pi$
$599$	1.32311e7			1.50671			0.753355	+	0.657614i	$0.228434\pi$
$600$	289673.	+	48211.8i	0.0328495	+	0.00546733i
$601$			5.22472e6i			0.590033i	0.955492	+	0.295017i	$0.0953252\pi$
$601$			5.22472e6i			0.590033i	−0.955492	+	0.295017i	$0.904675\pi$
$602$	−8.28832e6	+	1.26901e7i	−0.932128	+	1.42717i
$603$	1.05649e7			1.18324
$604$	138028.	+	314432.i	0.0153949	+	0.0350699i
$605$	−489281.			−0.0543463
$606$	−90422.1	+	138444.i	−0.0100021	+	0.0153141i
$607$	2.50008e6			0.275411			0.137706	−	0.990473i	$-0.456027\pi$
$607$	2.50008e6			0.275411			0.137706	+	0.990473i	$0.456027\pi$
$608$	−5.21767e6	−	7.47395e6i	−0.572424	−	0.819958i
$609$	−1.11197e6			−0.121493
$610$	−4.51757e6	+	6.91679e6i	−0.491565	+	0.752628i
$611$	−9.84366e6			−1.06673
$612$	3.16632e6	+	7.21296e6i	0.341725	+	0.778457i
$613$	−2.83556e6			−0.304781			−0.152391	−	0.988320i	$-0.548697\pi$
$613$	−2.83556e6			−0.304781			−0.152391	+	0.988320i	$0.548697\pi$
$614$	−9.34725e6	+	1.43114e7i	−1.00061	+	1.53201i
$615$			431914.i			0.0460478i
$616$	1.61894e7	+	2.69449e6i	1.71901	+	0.286105i
$617$	1.63806e7			1.73227			0.866135	−	0.499810i	$-0.166597\pi$
$617$	1.63806e7			1.73227			0.866135	+	0.499810i	$0.166597\pi$
$618$	−334020.	+	511413.i	−0.0351804	+	0.0538642i
$619$			6.70763e6i			0.703627i	0.936070	+	0.351814i	$0.114435\pi$
$619$			6.70763e6i			0.703627i	−0.936070	+	0.351814i	$0.885565\pi$
$620$	1.42531e6	+	3.24689e6i	0.148912	+	0.339226i
$621$		−	272490.i		−	0.0283544i
$622$	−1.01419e7	−	6.62402e6i	−1.05110	−	0.686509i
$623$	5.55298e6			0.573200
$624$	−528872.	−	486310.i	−0.0543737	−	0.0499979i
$625$	1.16652e6			0.119452
$626$	853587.	−	1.30692e6i	0.0870587	−	0.133294i
$627$	164263.	+	435435.i	0.0166867	+	0.0442338i
$628$	1.38225e6	+	3.14879e6i	0.139858	+	0.318599i
$629$		−	8.69483e6i		−	0.876263i
$630$	−8.75050e6	−	5.71523e6i	−0.878378	−	0.573696i
$631$			1.60409e6i			0.160382i	0.996780	+	0.0801910i	$0.0255530\pi$
$631$			1.60409e6i			0.160382i	−0.996780	+	0.0801910i	$0.974447\pi$
$632$	−1.62073e7	−	2.69746e6i	−1.61405	−	0.268635i
$633$	216453.			0.0214711
$634$	−3.02045e6	−	1.97275e6i	−0.298434	−	0.194916i
$635$	−5.14205e6			−0.506060
$636$	159846.	−	70168.7i	0.0156696	−	0.00687861i
$637$			3.58448e7i			3.50007i
$638$	7.14216e6	−	1.09353e7i	0.694669	−	1.06360i
$639$	−1.36088e7			−1.31846
$640$	4.69215e6	−	3.65949e6i	0.452816	−	0.353160i
$641$			5.45759e6i			0.524633i	0.964982	+	0.262317i	$0.0844865\pi$
$641$			5.45759e6i			0.524633i	−0.964982	+	0.262317i	$0.915514\pi$
$642$	−172005.	+	263355.i	−0.0164704	+	0.0252176i
$643$		−	1.66551e7i		−	1.58862i	−0.607515	−	0.794308i	$-0.707833\pi$
$643$		−	1.66551e7i		−	1.58862i	0.607515	−	0.794308i	$-0.292167\pi$
$644$	−2.21353e6	−	5.04247e6i	−0.210315	−	0.479102i
$645$		−	280581.i		−	0.0265557i
$646$	−1.95368e6	+	8.82609e6i	−0.184193	+	0.832122i
$647$		−	1.47424e7i		−	1.38454i	−0.721638	−	0.692271i	$-0.756610\pi$
$647$		−	1.47424e7i		−	1.38454i	0.721638	−	0.692271i	$-0.243390\pi$
$648$	1.04659e7	+	1.74190e6i	0.979131	+	0.162962i
$649$		−	6.18737e6i		−	0.576626i
$650$	−8.98621e6	−	5.86918e6i	−0.834244	−	0.544871i
$651$		−	634807.i		−	0.0587069i
$652$	922461.	−	404939.i	0.0849824	−	0.0373053i
$653$	−6.05940e6			−0.556092			−0.278046	−	0.960568i	$-0.589687\pi$
$653$	−6.05940e6			−0.556092			−0.278046	+	0.960568i	$0.589687\pi$
$654$	−473253.	−	309096.i	−0.0432662	−	0.0282585i
$655$			3.87066e6i			0.352518i
$656$	−1.30940e7	−	1.20402e7i	−1.18799	−	1.09238i
$657$	−2.74484e6			−0.248087
$658$	−7.98102e6	+	1.22196e7i	−0.718611	+	1.10025i
$659$	−3.47415e6			−0.311627			−0.155813	−	0.987786i	$-0.549800\pi$
$659$	−3.47415e6			−0.311627			−0.155813	+	0.987786i	$0.549800\pi$
$660$	−278190.	+	122119.i	−0.0248589	+	0.0109125i
$661$			1.17342e7i			1.04460i	0.852761	+	0.522301i	$0.174926\pi$
$661$			1.17342e7i			1.04460i	−0.852761	+	0.522301i	$0.825074\pi$
$662$	−1.85166e6	+	2.83505e6i	−0.164216	+	0.251430i
$663$			712536.i			0.0629539i
$664$	−1.87939e6	+	1.12920e7i	−0.165423	+	0.993920i
$665$	−4.23334e6	−	1.12219e7i	−0.371218	−	0.984037i
$666$	−9.82934e6	−	6.41985e6i	−0.858695	−	0.560840i
$667$	−4.38250e6			−0.381423
$668$	−6.54064e6	−	1.48997e7i	−0.567126	−	1.29192i
$669$	524843.			0.0453381
$670$	−4.32801e6	+	6.62656e6i	−0.372479	+	0.570297i
$671$			1.73718e7i			1.48949i
$672$	−1.03249e6	+	262237.i	−0.0881987	+	0.0224012i
$673$		−	1.12124e7i		−	0.954249i	−0.878836	−	0.477124i	$-0.841679\pi$
$673$		−	1.12124e7i		−	0.954249i	0.878836	−	0.477124i	$-0.158321\pi$
$674$	7.42800e6	+	4.85146e6i	0.629829	+	0.411361i
$675$	−787437.			−0.0665206
$676$	5.77953e6	+	1.31659e7i	0.486436	+	1.10811i
$677$		−	9.01849e6i		−	0.756244i	−0.925756	−	0.378122i	$-0.876570\pi$
$677$		−	9.01849e6i		−	0.756244i	0.925756	−	0.378122i	$-0.123430\pi$
$678$	−695406.	−	454191.i	−0.0580984	−	0.0379459i
$679$	9.49846e6			0.790640
$680$	−5.82123e6	−	968858.i	−0.482772	−	0.0803504i
$681$	−131784.			−0.0108892
$682$	6.24276e6	+	4.07734e6i	0.513944	+	0.335673i
$683$	−3.90833e6			−0.320582			−0.160291	−	0.987070i	$-0.551243\pi$
$683$	−3.90833e6			−0.320582			−0.160291	+	0.987070i	$0.551243\pi$
$684$	8.53522e6	+	8.72536e6i	0.697549	+	0.713088i
$685$	−9.39203e6			−0.764774
$686$	2.55966e7	+	1.67179e7i	2.07669	+	1.35635i
$687$	−227158.			−0.0183627
$688$	8.50615e6	+	7.82160e6i	0.685113	+	0.629976i
$689$	−6.38044e6			−0.512039
$690$	85350.1	+	55744.8i	0.00682466	+	0.00445740i
$691$		−	7.96569e6i		−	0.634641i	−0.948318	−	0.317321i	$-0.897217\pi$
$691$		−	7.96569e6i		−	0.634641i	0.948318	−	0.317321i	$-0.102783\pi$
$692$	−1.58416e7	+	6.95410e6i	−1.25757	+	0.552046i
$693$	−2.19772e7			−1.73836
$694$	−1.46895e7	−	9.59417e6i	−1.15773	−	0.756151i
$695$		−	1.74558e6i		−	0.137081i
$696$	−139183.	+	836257.i	−0.0108909	+	0.0654360i
$697$			1.76412e7i			1.37546i
$698$	3.80965e6	−	5.83290e6i	0.295969	−	0.453154i
$699$	523632.			0.0405353
$700$	−1.45716e7	+	6.39662e6i	−1.12399	+	0.493407i
$701$	−1.00182e7			−0.770005			−0.385002	−	0.922916i	$-0.625799\pi$
$701$	−1.00182e7			−0.770005			−0.385002	+	0.922916i	$0.625799\pi$
$702$	1.61301e6	+	1.05351e6i	0.123536	+	0.0806854i
$703$	−4.75526e6	−	1.26054e7i	−0.362899	−	0.961985i
$704$	4.05277e6	−	1.18379e7i	0.308191	−	0.900211i
$705$		−	270178.i		−	0.0204728i
$706$	−5.72695e6	+	8.76845e6i	−0.432426	+	0.662081i
$707$		−	8.96098e6i		−	0.674228i
$708$	161428.	+	367736.i	0.0121030	+	0.0275710i
$709$	6.51189e6			0.486509			0.243255	−	0.969962i	$-0.421785\pi$
$709$	6.51189e6			0.486509			0.243255	+	0.969962i	$0.421785\pi$
$710$	5.57495e6	−	8.53573e6i	0.415045	−	0.635470i
$711$	2.20014e7			1.63221
$712$	695051.	−	4.17610e6i	0.0513826	−	0.308724i
$713$		−	2.50190e6i		−	0.184309i
$714$	884521.	+	577708.i	0.0649326	+	0.0424095i
$715$	1.11043e7			0.812319
$716$	−1.10080e6	−	2.50764e6i	−0.0802464	−	0.182803i
$717$		−	382520.i		−	0.0277879i
$718$	981140.	+	640813.i	0.0710264	+	0.0463896i
$719$			1.08477e7i			0.782555i	0.920273	+	0.391278i	$0.127967\pi$
$719$			1.08477e7i			0.782555i	−0.920273	+	0.391278i	$0.872033\pi$
$720$	−5.39340e6	+	5.86543e6i	−0.387731	+	0.421666i
$721$		−	3.31019e7i		−	2.37146i
$722$	1.99468e6	+	1.38642e7i	0.142407	+	0.989808i
$723$		−	104977.i		−	0.00746879i
$724$	7.05167e6	−	3.09552e6i	0.499972	−	0.219476i
$725$			1.26645e7i			0.894834i
$726$	36517.2	−	55911.0i	0.00257132	−	0.00393691i
$727$		−	1.30113e7i		−	0.913030i	−0.889716	−	0.456515i	$-0.849097\pi$
$727$		−	1.30113e7i		−	0.913030i	0.889716	−	0.456515i	$-0.150903\pi$
$728$	3.84070e7	+	6.39228e6i	2.68585	+	0.447020i
$729$	−1.41368e7			−0.985218
$730$	1.12445e6	−	1.72162e6i	0.0780965	−	0.119572i
$731$		−	1.14601e7i		−	0.793224i
$732$	−453227.	−	1.03246e6i	−0.0312635	−	0.0712190i
$733$	1.50098e7			1.03185			0.515923	−	0.856635i	$-0.327449\pi$
$733$	1.50098e7			1.03185			0.515923	+	0.856635i	$0.327449\pi$
$734$	330400.	+	215795.i	0.0226360	+	0.0147843i
$735$	−983827.			−0.0671739
$736$	−4.06923e6	+	1.03353e6i	−0.276897	+	0.0703278i
$737$			1.66428e7i			1.12865i
$738$	1.99431e7	+	1.30254e7i	1.34788	+	0.880342i
$739$			3.91183e6i			0.263493i	0.991283	+	0.131746i	$0.0420585\pi$
$739$			3.91183e6i			0.263493i	−0.991283	+	0.131746i	$0.957942\pi$
$740$	8.05333e6	−	3.53523e6i	0.540625	−	0.237322i
$741$	389691.	+	1.03300e6i	0.0260720	+	0.0691125i
$742$	−5.17312e6	+	7.92050e6i	−0.344940	+	0.528132i
$743$	−2.77591e7			−1.84473			−0.922366	−	0.386317i	$-0.873747\pi$
$743$	−2.77591e7			−1.84473			−0.922366	+	0.386317i	$0.873747\pi$
$744$	−477405.	−	79457.0i	−0.0316195	−	0.00526260i
$745$	1.03024e7			0.680064
$746$	6.03139e6	+	3.93929e6i	0.396799	+	0.259162i
$747$		−	1.53290e7i		−	1.00511i
$748$	−1.13625e7	+	4.98787e6i	−0.742539	+	0.325958i
$749$		−	1.70460e7i		−	1.11024i
$750$	401439.	−	614638.i	0.0260595	−	0.0398994i
$751$	9.97896e6			0.645633			0.322816	−	0.946462i	$-0.395370\pi$
$751$	9.97896e6			0.645633			0.322816	+	0.946462i	$0.395370\pi$
$752$	8.19077e6	+	7.53160e6i	0.528178	+	0.485671i
$753$			603566.i			0.0387916i
$754$	1.69437e7	−	2.59423e7i	1.08538	−	1.66181i
$755$	344484.			0.0219939
$756$	2.61559e6	−	1.14818e6i	0.166443	−	0.0730645i
$757$	1.93580e7			1.22778			0.613891	−	0.789391i	$-0.289603\pi$
$757$	1.93580e7			1.22778			0.613891	+	0.789391i	$0.289603\pi$
$758$	−6.44497e6	+	9.86780e6i	−0.407425	+	0.623803i
$759$	214360.			0.0135064
$760$	−8.96925e6	+	1.77906e6i	−0.563277	+	0.111727i
$761$	−1.68679e7			−1.05584			−0.527922	−	0.849293i	$-0.677029\pi$
$761$	−1.68679e7			−1.05584			−0.527922	+	0.849293i	$0.677029\pi$
$762$	383773.	−	587590.i	0.0239435	−	0.0366595i
$763$	3.06319e7			1.90486
$764$	−1.33564e7	+	5.86317e6i	−0.827861	+	0.363412i
$765$	7.90234e6			0.488205
$766$	1.84621e6	−	2.82670e6i	0.113686	−	0.174064i
$767$		−	1.46786e7i		−	0.900942i
$768$	67980.9	+	809303.i	0.00415895	+	0.0495118i
$769$	1.25533e7			0.765492			0.382746	−	0.923854i	$-0.374978\pi$
$769$	1.25533e7			0.765492			0.382746	+	0.923854i	$0.374978\pi$
$770$	9.00313e6	−	1.37846e7i	0.547226	−	0.837850i
$771$		−	45762.6i		−	0.00277252i
$772$	−1.50541e7	+	6.60843e6i	−0.909103	+	0.399075i
$773$		−	1.97501e7i		−	1.18883i	−0.804158	−	0.594416i	$-0.797383\pi$
$773$		−	1.97501e7i		−	1.18883i	0.804158	−	0.594416i	$-0.202617\pi$
$774$	−1.29554e7	−	8.46161e6i	−0.777320	−	0.507692i
$775$	−7.22994e6			−0.432395
$776$	1.18890e6	−	7.14329e6i	0.0708744	−	0.425837i
$777$	−1.57452e6			−0.0935614
$778$	−9.84701e6	+	1.50766e7i	−0.583251	+	0.893007i
$779$	9.64810e6	+	2.55755e7i	0.569637	+	1.51001i
$780$	−659965.	+	289710.i	−0.0388405	+	0.0170501i
$781$		−	2.14378e7i		−	1.25763i
$782$	3.48606e6	+	2.27686e6i	0.203854	+	0.133143i
$783$		−	2.27325e6i		−	0.132508i
$784$	2.74256e7	−	2.98259e7i	1.59355	−	1.73302i
$785$	3.44973e6			0.199807
$786$	−442307.	−	288884.i	−0.0255368	−	0.0166789i
$787$	−1.93097e7			−1.11132			−0.555658	−	0.831411i	$-0.687534\pi$
$787$	−1.93097e7			−1.11132			−0.555658	+	0.831411i	$0.687534\pi$
$788$	2.97613e6	+	6.77968e6i	0.170740	+	0.388950i
$789$		−	400524.i		−	0.0229053i
$790$	−9.01305e6	+	1.37998e7i	−0.513812	+	0.786690i
$791$	4.50111e7			2.55787
$792$	−2.75082e6	+	1.65279e7i	−0.155830	+	0.936277i
$793$			4.12120e7i			2.32724i
$794$	1.29076e7	−	1.97626e7i	0.726596	−	1.11248i
$795$		−	175123.i		−	0.00982711i
$796$	−1.35447e7	+	5.94583e6i	−0.757683	+	0.332606i
$797$		−	1.68577e7i		−	0.940051i	−0.882653	−	0.470026i	$-0.844245\pi$
$797$		−	1.68577e7i		−	0.940051i	0.882653	−	0.470026i	$-0.155755\pi$
$798$	1.59829e6	+	353787.i	0.0888484	+	0.0196668i
$799$		−	1.10352e7i		−	0.611525i
$800$	2.98667e6	+	1.17592e7i	0.164992	+	0.649611i
$801$			5.66907e6i			0.312198i
$802$	1.08665e7	+	7.09723e6i	0.596558	+	0.389631i
$803$		−	4.32392e6i		−	0.236640i
$804$	−434209.	−	989138.i	−0.0236897	−	0.0539656i
$805$	−5.52440e6			−0.300466
$806$	1.48100e7	+	9.67289e6i	0.803005	+	0.524468i
$807$			77894.7i			0.00421041i
$808$	−6.73908e6	−	1.12162e6i	−0.363138	−	0.0604391i
$809$	2.40583e7			1.29239			0.646196	−	0.763171i	$-0.276359\pi$
$809$	2.40583e7			1.29239			0.646196	+	0.763171i	$0.276359\pi$
$810$	5.82024e6	−	8.91129e6i	0.311694	−	0.477230i
$811$	−1.62329e7			−0.866652			−0.433326	−	0.901237i	$-0.642660\pi$
$811$	−1.62329e7			−0.866652			−0.433326	+	0.901237i	$0.642660\pi$
$812$	−1.84664e7	−	4.20669e7i	−0.982862	−	2.23898i
$813$		−	191520.i		−	0.0101622i
$814$	1.01131e7	−	1.54840e7i	0.534963	−	0.819074i
$815$		−	1.01063e6i		−	0.0532962i
$816$	545177.	−	592891.i	0.0286624	−	0.0311709i
$817$	−6.26761e6	−	1.66144e7i	−0.328509	−	0.870822i
$818$	819545.	+	535270.i	0.0428242	+	0.0279698i
$819$	−5.21377e7			−2.71608
$820$	−1.63397e7	+	7.17274e6i	−0.848611	+	0.372521i
$821$	−3.01371e6			−0.156043			−0.0780213	−	0.996952i	$-0.524860\pi$
$821$	−3.01371e6			−0.156043			−0.0780213	+	0.996952i	$0.524860\pi$
$822$	700968.	−	1.07324e6i	0.0361842	−	0.0554011i
$823$			2.74365e7i			1.41198i	0.708220	+	0.705991i	$0.249498\pi$
$823$			2.74365e7i			1.41198i	−0.708220	+	0.705991i	$0.750502\pi$
$824$	−2.48942e7	−	4.14327e6i	−1.27726	−	0.212582i
$825$		−	619453.i		−	0.0316865i
$826$	−1.82216e7	−	1.19011e7i	−0.929259	−	0.606928i
$827$	5.43017e6			0.276089			0.138045	−	0.990426i	$-0.455918\pi$
$827$	5.43017e6			0.276089			0.138045	+	0.990426i	$0.455918\pi$
$828$	5.14789e6	−	2.25981e6i	0.260948	−	0.114550i
$829$		−	1.95253e7i		−	0.986757i	−0.869815	−	0.493379i	$-0.835762\pi$
$829$		−	1.95253e7i		−	0.986757i	0.869815	−	0.493379i	$-0.164238\pi$
$830$	9.61466e6	+	6.27963e6i	0.484438	+	0.316402i
$831$	1.83831e6			0.0923457
$832$	9.61459e6	−	2.80838e7i	0.481529	−	1.40652i
$833$	−4.01837e7			−2.00649
$834$	199470.	+	130280.i	0.00993032	+	0.00648580i
$835$	−1.63238e7			−0.810223
$836$	−1.37450e7	+	1.34454e7i	−0.680186	+	0.665363i
$837$	1.29776e6			0.0640297
$838$	3.34091e6	+	2.18205e6i	0.164344	+	0.107338i
$839$	2.75028e7			1.34888			0.674438	−	0.738332i	$-0.264386\pi$
$839$	2.75028e7			1.34888			0.674438	+	0.738332i	$0.264386\pi$
$840$	−175448.	+	1.05415e6i	−0.00857927	+	0.0515472i
$841$	−1.60500e7			−0.782500
$842$	−6.19153e6	−	4.04388e6i	−0.300966	−	0.196570i
$843$		−	1.37014e6i		−	0.0664043i
$844$	3.59460e6	+	8.18859e6i	0.173698	+	0.395688i
$845$	1.44242e7			0.694946
$846$	−1.24751e7	−	8.14788e6i	−0.599264	−	0.391398i
$847$			3.61892e6i			0.173329i
$848$	5.30908e6	+	4.88182e6i	0.253530	+	0.233127i
$849$		−	1.34107e6i		−	0.0638529i
$850$	6.57963e6	−	1.00740e7i	0.312359	−	0.478249i
$851$	−6.20550e6			−0.293733
$852$	559309.	+	1.27412e6i	0.0263969	+	0.0601327i
$853$	−1.64869e7			−0.775831			−0.387916	−	0.921695i	$-0.626805\pi$
$853$	−1.64869e7			−0.775831			−0.387916	+	0.921695i	$0.626805\pi$
$854$	5.11593e7	+	3.34137e7i	2.40038	+	1.56776i
$855$	1.14565e7	−	4.32184e6i	0.535965	−	0.202187i
$856$	−1.28194e7	−	2.13360e6i	−0.597976	−	0.0995243i
$857$		−	1.99905e6i		−	0.0929760i	−0.998919	−	0.0464880i	$-0.985197\pi$
$857$		−	1.99905e6i		−	0.0929760i	0.998919	−	0.0464880i	$-0.0148029\pi$
$858$	−828763.	+	1.26891e6i	−0.0384337	+	0.0588453i
$859$			3.17728e7i			1.46917i	0.678516	+	0.734586i	$0.262623\pi$
$859$			3.17728e7i			1.46917i	−0.678516	+	0.734586i	$0.737377\pi$
$860$	1.06146e7	−	4.65957e6i	0.489393	−	0.214832i
$861$	3.19460e6			0.146862
$862$	7.67875e6	−	1.17568e7i	0.351984	−	0.538917i
$863$	−1.35141e7			−0.617677			−0.308838	−	0.951115i	$-0.599940\pi$
$863$	−1.35141e7			−0.617677			−0.308838	+	0.951115i	$0.599940\pi$
$864$	−536102.	−	2.11076e6i	−0.0244322	−	0.0961953i
$865$			1.73557e7i			0.788680i
$866$	−1.67969e7	−	1.09706e7i	−0.761088	−	0.497090i
$867$	300935.			0.0135964
$868$	2.40153e7	−	1.05422e7i	1.08190	−	0.474931i
$869$			3.46586e7i			1.55690i
$870$	712035.	+	465052.i	0.0318936	+	0.0208307i
$871$			3.94827e7i			1.76344i
$872$	3.83411e6	−	2.30367e7i	0.170755	−	1.02596i
$873$			9.69704e6i			0.430629i
$874$	6.29918e6	+	1.39434e6i	0.278937	+	0.0617434i
$875$			3.97833e7i			1.75663i
$876$	112810.	+	256985.i	0.00496694	+	0.0113148i
$877$			1.53055e7i			0.671969i	0.941868	+	0.335984i	$0.109069\pi$
$877$			1.53055e7i			0.671969i	−0.941868	+	0.335984i	$0.890931\pi$
$878$	−1.78868e7	+	2.73863e7i	−0.783064	+	1.19894i
$879$			1.06197e6i			0.0463596i
$880$	−9.23974e6	−	8.49615e6i	−0.402210	−	0.369841i
$881$	3.74126e7			1.62397			0.811986	−	0.583677i	$-0.198386\pi$
$881$	3.74126e7			1.62397			0.811986	+	0.583677i	$0.198386\pi$
$882$	−2.96697e7	+	4.54269e7i	−1.28423	+	1.96626i
$883$		−	1.53378e7i		−	0.662004i	−0.943630	−	0.331002i	$-0.892613\pi$
$883$		−	1.53378e7i		−	0.662004i	0.943630	−	0.331002i	$-0.107387\pi$
$884$	−2.69558e7	+	1.18330e7i	−1.16017	+	0.509289i
$885$	402882.			0.0172910
$886$	−1.06257e6	−	694000.i	−0.0454752	−	0.0297013i
$887$	2.25923e7			0.964166			0.482083	−	0.876126i	$-0.339880\pi$
$887$	2.25923e7			0.964166			0.482083	+	0.876126i	$0.339880\pi$
$888$	−197079.	+	1.18412e6i	−0.00838702	+	0.0503921i
$889$			3.80326e7i			1.61399i
$890$	−3.55576e6	−	2.32238e6i	−0.150473	−	0.0982784i
$891$		−	2.23810e7i		−	0.944464i
$892$	8.71600e6	+	1.98552e7i	0.366779	+	0.835532i
$893$	−6.03523e6	−	1.59984e7i	−0.253259	−	0.671348i
$894$	−768916.	+	1.17728e6i	−0.0321762	+	0.0492646i
$895$	−2.74732e6			−0.114644
$896$	−2.70671e7	−	3.47050e7i	−1.12634	−	1.44418i
$897$	508537.			0.0211029
$898$	−3.28256e7	−	2.14394e7i	−1.35838	−	0.887200i
$899$		−	2.08721e7i		−	0.861326i
$900$	−6.53035e6	−	1.48763e7i	−0.268739	−	0.612193i
$901$		−	7.15279e6i		−	0.293537i
$902$	−2.05188e7	+	3.14161e7i	−0.839723	+	1.28569i
$903$	−2.07528e6			−0.0846951
$904$	5.63392e6	−	3.38505e7i	0.229292	−	1.37767i
$905$		−	7.72564e6i		−	0.313555i
$906$	−25710.3	+	39364.7i	−0.00104061	+	0.00159326i
$907$	−2.96009e7			−1.19478			−0.597388	−	0.801952i	$-0.703795\pi$
$907$	−2.96009e7			−1.19478			−0.597388	+	0.801952i	$0.703795\pi$
$908$	−2.18853e6	−	4.98551e6i	−0.0880922	−	0.200676i
$909$	9.14833e6			0.367225
$910$	2.13586e7	−	3.27018e7i	0.855006	−	1.30909i
$911$	−2.81268e7			−1.12286			−0.561428	−	0.827526i	$-0.689748\pi$
$911$	−2.81268e7			−1.12286			−0.561428	+	0.827526i	$0.689748\pi$
$912$	466118.	−	1.15771e6i	0.0185571	−	0.0460906i
$913$	2.41475e7			0.958729
$914$	8.61655e6	−	1.31927e7i	0.341168	−	0.522357i
$915$	−1.13114e6			−0.0446646
$916$	−3.77238e6	−	8.59357e6i	−0.148551	−	0.338404i
$917$	2.86289e7			1.12430
$918$	−1.18103e6	+	1.80826e6i	−0.0462546	+	0.0708198i
$919$		−	3.30668e6i		−	0.129153i	−0.997913	−	0.0645763i	$-0.979430\pi$
$919$		−	3.30668e6i		−	0.129153i	0.997913	−	0.0645763i	$-0.0205696\pi$
$920$	−691474.	+	4.15461e6i	−0.0269343	+	0.161831i
$921$	−2.34043e6			−0.0909171
$922$	−2.00680e6	+	3.07258e6i	−0.0777458	+	0.119036i
$923$		−	5.08580e7i		−	1.96497i
$924$	903241.	+	2.05760e6i	0.0348036	+	0.0792833i
$925$			1.79326e7i			0.689109i
$926$	6.49082e6	+	4.23936e6i	0.248755	+	0.162470i
$927$	3.37940e7			1.29164
$928$	−3.39477e7	+	8.62222e6i	−1.29402	+	0.328662i
$929$	5.08478e7			1.93301			0.966503	−	0.256654i	$-0.0826202\pi$
$929$	5.08478e7			1.93301			0.966503	+	0.256654i	$0.0826202\pi$
$930$	−265491.	+	406489.i	−0.0100657	+	0.0154114i
$931$	−5.82567e7	+	2.19767e7i	−2.20278	+	0.830977i
$932$	8.69590e6	+	1.98094e7i	0.327925	+	0.747021i
$933$		−	1.65857e6i		−	0.0623776i
$934$	−2.85156e7	−	1.86245e7i	−1.06959	−	0.698580i
$935$			1.24485e7i			0.465679i
$936$	−6.52592e6	+	3.92100e7i	−0.243474	+	1.46287i
$937$	−3.98334e7			−1.48217			−0.741085	−	0.671411i	$-0.765689\pi$
$937$	−3.98334e7			−1.48217			−0.741085	+	0.671411i	$0.765689\pi$
$938$	4.90126e7	+	3.20117e7i	1.81887	+	1.18796i
$939$	213727.			0.00791034
$940$	1.02210e7	−	4.48681e6i	0.377290	−	0.165622i
$941$			2.15479e7i			0.793289i	0.917972	+	0.396645i	$0.129825\pi$
$941$			2.15479e7i			0.793289i	−0.917972	+	0.396645i	$0.870175\pi$
$942$	−257469.	+	394207.i	−0.00945360	+	0.0144743i
$943$	1.25905e7			0.461068
$944$	−1.12309e7	+	1.22139e7i	−0.410191	+	0.446091i
$945$		−	2.86557e6i		−	0.104384i
$946$	1.33295e7	−	2.04086e7i	0.484267	−	0.741454i
$947$		−	3.96621e7i		−	1.43715i	−0.695451	−	0.718573i	$-0.744795\pi$
$947$		−	3.96621e7i		−	1.43715i	0.695451	−	0.718573i	$-0.255205\pi$
$948$	−904237.	−	2.05987e6i	−0.0326785	−	0.0744423i
$949$		−	1.02579e7i		−	0.369736i
$950$	4.02935e6	−	1.82033e7i	0.144852	−	0.654396i
$951$		−	493949.i		−	0.0177105i
$952$	−7.16606e6	+	4.30561e7i	−0.256264	+	1.53972i
$953$			1.60078e7i			0.570951i	0.958386	+	0.285475i	$0.0921515\pi$
$953$			1.60078e7i			0.570951i	−0.958386	+	0.285475i	$0.907848\pi$
$954$	−8.08609e6	−	5.28128e6i	−0.287652	−	0.187875i
$955$			1.46330e7i			0.519188i
$956$	1.44710e7	−	6.35246e6i	0.512101	−	0.224801i
$957$	1.78830e6			0.0631191
$958$	3.05706e7	+	1.99666e7i	1.07619	+	0.702896i
$959$			6.94671e7i			2.43912i
$960$	770811.	+	263890.i	0.0269942	+	0.00924157i
$961$	−1.67136e7			−0.583797
$962$	2.39919e7	−	3.67336e7i	0.835846	−	1.27975i
$963$	1.74024e7			0.604705
$964$	3.97138e6	−	1.74335e6i	0.137641	−	0.0604215i
$965$			1.64930e7i			0.570139i
$966$	412310.	−	631283.i	0.0142161	−	0.0217661i
$967$			3.51967e7i			1.21042i	0.796066	+	0.605209i	$0.206911\pi$
$967$			3.51967e7i			1.21042i	−0.796066	+	0.605209i	$0.793089\pi$
$968$	2.72160e6	+	452970.i	0.0933545	+	0.0155375i
$969$	−1.15805e6	+	436862.i	−0.0396202	+	0.0149463i
$970$	−6.08219e6	−	3.97247e6i	−0.207554	−	0.135560i
$971$	−1.45207e7			−0.494240			−0.247120	−	0.968985i	$-0.579484\pi$
$971$	−1.45207e7			−0.494240			−0.247120	+	0.968985i	$0.579484\pi$
$972$	1.75901e6	+	4.00705e6i	0.0597175	+	0.136038i
$973$	−1.29110e7			−0.437198
$974$	2.25324e7	−	3.44990e7i	0.761044	−	1.16522i
$975$		−	1.46956e6i		−	0.0495081i
$976$	3.15322e7	−	3.42919e7i	1.05957	−	1.15230i
$977$		−	4.28474e7i		−	1.43611i	−0.695986	−	0.718056i	$-0.745032\pi$
$977$		−	4.28474e7i		−	1.43611i	0.695986	−	0.718056i	$-0.254968\pi$
$978$	115486.	+	75427.4i	0.00386084	+	0.00252163i
$979$	−8.93042e6			−0.297794
$980$	−1.63383e7	−	3.72190e7i	−0.543427	−	1.23794i
$981$			3.12724e7i			1.03750i
$982$	3.77233e7	+	2.46383e7i	1.24833	+	0.815326i
$983$	3.45114e7			1.13914			0.569572	−	0.821942i	$-0.307109\pi$
$983$	3.45114e7			1.13914			0.569572	+	0.821942i	$0.307109\pi$
$984$	399860.	−	2.40249e6i	0.0131650	−	0.0790996i
$985$	7.42765e6			0.243928
$986$	2.90826e7	+	1.89947e7i	0.952666	+	0.622216i
$987$	−1.99834e6			−0.0652945
$988$	−3.26079e7	+	3.18973e7i	−1.06275	+	1.03959i
$989$	−8.17909e6			−0.265897
$990$	1.40728e7	+	9.19135e6i	0.456343	+	0.298052i
$991$	3.57784e7			1.15728			0.578638	−	0.815585i	$-0.303585\pi$
$991$	3.57784e7			1.15728			0.578638	+	0.815585i	$0.303585\pi$
$992$	−4.92228e6	−	1.93802e7i	−0.158813	−	0.625285i
$993$	−463631.			−0.0149211
$994$	−6.31336e7	−	4.12346e7i	−2.02673	−	1.32372i
$995$			1.48393e7i			0.475177i
$996$	−1.43517e6	+	630006.i	−0.0458410	+	0.0201232i
$997$	−2.84787e7			−0.907365			−0.453682	−	0.891163i	$-0.649890\pi$
$997$	−2.84787e7			−0.907365			−0.453682	+	0.891163i	$0.649890\pi$
$998$	−4.68441e7	−	3.05954e7i	−1.48877	−	0.972365i
$999$		−	3.21886e6i		−	0.102044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.6.d.a.75.16	yes	48
4.3	odd	2	inner	76.6.d.a.75.34	yes	48
19.18	odd	2	inner	76.6.d.a.75.33	yes	48
76.75	even	2	inner	76.6.d.a.75.15	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.6.d.a.75.15	✓	48	76.75	even	2	inner
76.6.d.a.75.16	yes	48	1.1	even	1	trivial
76.6.d.a.75.33	yes	48	19.18	odd	2	inner
76.6.d.a.75.34	yes	48	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.09334 + 4.73617i) q^{2} -0.774530 q^{3} +(-12.8625 - 29.3011i) q^{4} -32.1016 q^{5} +(2.39588 - 3.66830i) q^{6} +237.436i q^{7} +(178.563 + 29.7192i) q^{8} -242.400 q^{9} +O(q^{10})\)	\(q+(-3.09334 + 4.73617i) q^{2} -0.774530 q^{3} +(-12.8625 - 29.3011i) q^{4} -32.1016 q^{5} +(2.39588 - 3.66830i) q^{6} +237.436i q^{7} +(178.563 + 29.7192i) q^{8} -242.400 q^{9} +(99.3011 - 152.038i) q^{10} -381.850i q^{11} +(9.96241 + 22.6946i) q^{12} -905.883i q^{13} +(-1124.54 - 734.470i) q^{14} +24.8637 q^{15} +(-693.111 + 753.773i) q^{16} +1015.54 q^{17} +(749.825 - 1148.05i) q^{18} +(1472.29 - 555.405i) q^{19} +(412.908 + 940.613i) q^{20} -183.901i q^{21} +(1808.50 + 1181.19i) q^{22} -724.790i q^{23} +(-138.302 - 23.0184i) q^{24} -2094.49 q^{25} +(4290.41 + 2802.20i) q^{26} +375.957 q^{27} +(6957.14 - 3054.03i) q^{28} -6046.58i q^{29} +(-76.9117 + 117.758i) q^{30} +3451.89 q^{31} +(-1425.97 - 5614.36i) q^{32} +295.754i q^{33} +(-3141.40 + 4809.76i) q^{34} -7622.08i q^{35} +(3117.88 + 7102.59i) q^{36} -8561.79i q^{37} +(-1923.79 + 8691.04i) q^{38} +701.633i q^{39} +(-5732.16 - 954.034i) q^{40} +17371.3i q^{41} +(870.987 + 568.869i) q^{42} -11284.8i q^{43} +(-11188.6 + 4911.55i) q^{44} +7781.43 q^{45} +(3432.72 + 2242.02i) q^{46} -10866.4i q^{47} +(536.835 - 583.820i) q^{48} -39568.9 q^{49} +(6478.96 - 9919.84i) q^{50} -786.565 q^{51} +(-26543.4 + 11651.9i) q^{52} -7043.34i q^{53} +(-1162.96 + 1780.59i) q^{54} +12258.0i q^{55} +(-7056.41 + 42397.3i) q^{56} +(-1140.33 + 430.178i) q^{57} +(28637.6 + 18704.1i) q^{58} +16203.7 q^{59} +(-319.809 - 728.533i) q^{60} -45493.7 q^{61} +(-10677.9 + 16348.7i) q^{62} -57554.5i q^{63} +(31001.5 + 10613.5i) q^{64} +29080.3i q^{65} +(-1400.74 - 914.868i) q^{66} -43584.7 q^{67} +(-13062.4 - 29756.4i) q^{68} +561.371i q^{69} +(36099.4 + 23577.7i) q^{70} +56141.9 q^{71} +(-43283.7 - 7203.94i) q^{72} +11323.6 q^{73} +(40550.1 + 26484.5i) q^{74} +1622.24 q^{75} +(-35211.3 - 35995.7i) q^{76} +90664.9 q^{77} +(-3323.05 - 2170.39i) q^{78} -90764.9 q^{79} +(22250.0 - 24197.3i) q^{80} +58612.0 q^{81} +(-82273.3 - 53735.3i) q^{82} +63238.3i q^{83} +(-5388.51 + 2365.44i) q^{84} -32600.4 q^{85} +(53446.5 + 34907.6i) q^{86} +4683.26i q^{87} +(11348.3 - 68184.3i) q^{88} -23387.3i q^{89} +(-24070.6 + 36854.1i) q^{90} +215089. q^{91} +(-21237.2 + 9322.63i) q^{92} -2673.59 q^{93} +(51464.9 + 33613.3i) q^{94} +(-47262.7 + 17829.4i) q^{95} +(1104.45 + 4348.49i) q^{96} -40004.3i q^{97} +(122400. - 187405. i) q^{98} +92560.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9}+O(q^{10}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9	\( 48 q - 22 q^{4} - 4 q^{5} - 246 q^{6} + 3516 q^{9} - 1222 q^{16} + 1000 q^{17} - 300 q^{20} + 17158 q^{24} + 24996 q^{25} + 12102 q^{26} + 6382 q^{28} - 16528 q^{30} + 27524 q^{36} + 3598 q^{38} + 35966 q^{42} - 65408 q^{44} - 13476 q^{45} - 143096 q^{49} - 148446 q^{54} - 53980 q^{57} - 117018 q^{58} + 133740 q^{61} + 28068 q^{62} - 78130 q^{64} + 128204 q^{66} - 48338 q^{68} - 104080 q^{73} + 48932 q^{74} - 251688 q^{76} + 184844 q^{77} + 80080 q^{80} + 375128 q^{81} + 175628 q^{82} - 384748 q^{85} + 139810 q^{92} + 183272 q^{93} + 601258 q^{96}+O(q^{100}) \) 48 * q - 22 * q^4 - 4 * q^5 - 246 * q^6 + 3516 * q^9 - 1222 * q^16 + 1000 * q^17 - 300 * q^20 + 17158 * q^24 + 24996 * q^25 + 12102 * q^26 + 6382 * q^28 - 16528 * q^30 + 27524 * q^36 + 3598 * q^38 + 35966 * q^42 - 65408 * q^44 - 13476 * q^45 - 143096 * q^49 - 148446 * q^54 - 53980 * q^57 - 117018 * q^58 + 133740 * q^61 + 28068 * q^62 - 78130 * q^64 + 128204 * q^66 - 48338 * q^68 - 104080 * q^73 + 48932 * q^74 - 251688 * q^76 + 184844 * q^77 + 80080 * q^80 + 375128 * q^81 + 175628 * q^82 - 384748 * q^85 + 139810 * q^92 + 183272 * q^93 + 601258 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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