LMFDB - Embedded newform 76.8.d.a.75.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,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, 8, names="a")

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

chi := DirichletCharacter("76.75");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			75.20
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.35548 + 8.59633i) q^{2} -83.0232 q^{3} +(-19.7938 - 126.460i) q^{4} -447.252 q^{5} +(610.676 - 713.695i) q^{6} -106.200i q^{7} +(1232.69 + 760.022i) q^{8} +4705.86 q^{9} +O(q^{10})$	\(q+(-7.35548 + 8.59633i) q^{2} -83.0232 q^{3} +(-19.7938 - 126.460i) q^{4} -447.252 q^{5} +(610.676 - 713.695i) q^{6} -106.200i q^{7} +(1232.69 + 760.022i) q^{8} +4705.86 q^{9} +(3289.75 - 3844.72i) q^{10} -7457.91i q^{11} +(1643.35 + 10499.1i) q^{12} -996.063i q^{13} +(912.932 + 781.153i) q^{14} +37132.3 q^{15} +(-15600.4 + 5006.27i) q^{16} -14144.3 q^{17} +(-34613.8 + 40453.1i) q^{18} +(10708.7 - 27914.1i) q^{19} +(8852.83 + 56559.6i) q^{20} +8817.08i q^{21} +(64110.7 + 54856.5i) q^{22} -49089.2i q^{23} +(-102342. - 63099.5i) q^{24} +121909. q^{25} +(8562.49 + 7326.52i) q^{26} -209124. q^{27} +(-13430.1 + 2102.11i) q^{28} -195745. i q^{29} +(-273126. + 319201. i) q^{30} -243107. q^{31} +(71712.9 - 170930. i) q^{32} +619180. i q^{33} +(104038. - 121589. i) q^{34} +47498.2i q^{35} +(-93147.0 - 595104. i) q^{36} +152241. i q^{37} +(161191. + 297377. i) q^{38} +82696.4i q^{39} +(-551322. - 339921. i) q^{40} -581032. i q^{41} +(-75794.6 - 64853.9i) q^{42} -675783. i q^{43} +(-943130. + 147621. i) q^{44} -2.10470e6 q^{45} +(421987. + 361075. i) q^{46} +165475. i q^{47} +(1.29520e6 - 415637. i) q^{48} +812265. q^{49} +(-896699. + 1.04797e6i) q^{50} +1.17431e6 q^{51} +(-125962. + 19715.9i) q^{52} +38212.1i q^{53} +(1.53820e6 - 1.79770e6i) q^{54} +3.33556e6i q^{55} +(80714.4 - 130912. i) q^{56} +(-889070. + 2.31752e6i) q^{57} +(1.68269e6 + 1.43980e6i) q^{58} -2.24545e6 q^{59} +(-734990. - 4.69576e6i) q^{60} +368923. q^{61} +(1.78817e6 - 2.08983e6i) q^{62} -499763. i q^{63} +(941886. + 1.87374e6i) q^{64} +445491. i q^{65} +(-5.32268e6 - 4.55437e6i) q^{66} -762681. q^{67} +(279970. + 1.78869e6i) q^{68} +4.07555e6i q^{69} +(-408310. - 349372. i) q^{70} +336990. q^{71} +(5.80085e6 + 3.57655e6i) q^{72} +2.02383e6 q^{73} +(-1.30872e6 - 1.11981e6i) q^{74} -1.01213e7 q^{75} +(-3.74199e6 - 801697. i) q^{76} -792032. q^{77} +(-710885. - 608271. i) q^{78} +3.58420e6 q^{79} +(6.97731e6 - 2.23906e6i) q^{80} +7.07041e6 q^{81} +(4.99474e6 + 4.27377e6i) q^{82} -8.23737e6i q^{83} +(1.11501e6 - 174524. i) q^{84} +6.32606e6 q^{85} +(5.80926e6 + 4.97071e6i) q^{86} +1.62514e7i q^{87} +(5.66818e6 - 9.19328e6i) q^{88} -4.68170e6i q^{89} +(1.54811e7 - 1.80927e7i) q^{90} -105782. q^{91} +(-6.20784e6 + 971664. i) q^{92} +2.01835e7 q^{93} +(-1.42247e6 - 1.21714e6i) q^{94} +(-4.78948e6 + 1.24846e7i) q^{95} +(-5.95384e6 + 1.41911e7i) q^{96} +1.14401e7i q^{97} +(-5.97460e6 + 6.98250e6i) q^{98} -3.50959e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	$ 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) $ 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * 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 $

$2$	−7.35548	+	8.59633i	−0.650139	+	0.759816i
$2$	−7.35548	+	8.59633i	−0.650139	+	0.759816i
$3$	−83.0232			−1.77531			−0.887657	−	0.460505i	$-0.847668\pi$
$3$	−83.0232			−1.77531			−0.887657	+	0.460505i	$0.847668\pi$
$4$	−19.7938	−	126.460i	−0.154639	−	0.987971i
$5$	−447.252			−1.60014			−0.800068	−	0.599909i	$-0.795203\pi$
$5$	−447.252			−1.60014			−0.800068	+	0.599909i	$0.795203\pi$
$6$	610.676	−	713.695i	1.15420	−	1.34891i
$7$		−	106.200i		−	0.117026i	−0.998287	−	0.0585130i	$-0.981364\pi$
$7$		−	106.200i		−	0.117026i	0.998287	−	0.0585130i	$-0.0186359\pi$
$8$	1232.69	+	760.022i	0.851213	+	0.524821i
$9$	4705.86			2.15174
$10$	3289.75	−	3844.72i	1.04031	−	1.21581i
$11$		−	7457.91i		−	1.68944i	−0.535208	−	0.844720i	$-0.679767\pi$
$11$		−	7457.91i		−	1.68944i	0.535208	−	0.844720i	$-0.320233\pi$
$12$	1643.35	+	10499.1i	0.274533	+	1.75396i
$13$		−	996.063i		−	0.125743i	−0.998022	−	0.0628717i	$-0.979974\pi$
$13$		−	996.063i		−	0.125743i	0.998022	−	0.0628717i	$-0.0200259\pi$
$14$	912.932	+	781.153i	0.0889181	+	0.0760831i
$15$	37132.3			2.84074
$16$	−15600.4	+	5006.27i	−0.952173	+	0.305558i
$17$	−14144.3			−0.698249			−0.349124	−	0.937076i	$-0.613521\pi$
$17$	−14144.3			−0.698249			−0.349124	+	0.937076i	$0.613521\pi$
$18$	−34613.8	+	40453.1i	−1.39893	+	1.63493i
$19$	10708.7	−	27914.1i	0.358178	−	0.933653i
$19$	10708.7	−	27914.1i	0.358178	−	0.933653i
$20$	8852.83	+	56559.6i	0.247444	+	1.58089i
$21$			8817.08i			0.207758i
$22$	64110.7	+	54856.5i	1.28366	+	1.09837i
$23$		−	49089.2i		−	0.841276i	−0.907228	−	0.420638i	$-0.861806\pi$
$23$		−	49089.2i		−	0.841276i	0.907228	−	0.420638i	$-0.138194\pi$
$24$	−102342.	−	63099.5i	−1.51117	−	0.931722i
$25$	121909.			1.56044
$26$	8562.49	+	7326.52i	0.0955418	+	0.0817506i
$27$	−209124.			−2.04470
$28$	−13430.1	+	2102.11i	−0.115618	+	0.0180968i
$29$		−	195745.i		−	1.49038i	−0.666849	−	0.745192i	$-0.732358\pi$
$29$		−	195745.i		−	1.49038i	0.666849	−	0.745192i	$-0.267642\pi$
$30$	−273126.	+	319201.i	−1.84688	+	2.15844i
$31$	−243107.			−1.46566			−0.732828	−	0.680414i	$-0.761800\pi$
$31$	−243107.			−1.46566			−0.732828	+	0.680414i	$0.761800\pi$
$32$	71712.9	−	170930.i	0.386877	−	0.922131i
$33$			619180.i			2.99929i
$34$	104038.	−	121589.i	0.453958	−	0.530540i
$35$			47498.2i			0.187257i
$36$	−93147.0	−	595104.i	−0.332744	−	2.12586i
$37$			152241.i			0.494113i	0.969001	+	0.247057i	$0.0794634\pi$
$37$			152241.i			0.494113i	−0.969001	+	0.247057i	$0.920537\pi$
$38$	161191.	+	297377.i	0.476539	+	0.879153i
$39$			82696.4i			0.223234i
$40$	−551322.	−	339921.i	−1.36206	−	0.839785i
$41$		−	581032.i		−	1.31661i	−0.752752	−	0.658304i	$-0.771274\pi$
$41$		−	581032.i		−	1.31661i	0.752752	−	0.658304i	$-0.228726\pi$
$42$	−75794.6	−	64853.9i	−0.157858	−	0.135071i
$43$		−	675783.i		−	1.29619i	−0.761561	−	0.648094i	$-0.775567\pi$
$43$		−	675783.i		−	1.29619i	0.761561	−	0.648094i	$-0.224433\pi$
$44$	−943130.	+	147621.i	−1.66912	+	0.261254i
$45$	−2.10470e6			−3.44308
$46$	421987.	+	361075.i	0.639215	+	0.546946i
$47$			165475.i			0.232482i	0.993221	+	0.116241i	$0.0370844\pi$
$47$			165475.i			0.232482i	−0.993221	+	0.116241i	$0.962916\pi$
$48$	1.29520e6	−	415637.i	1.69041	−	0.542462i
$49$	812265.			0.986305
$50$	−896699.	+	1.04797e6i	−1.01450	+	1.18564i
$51$	1.17431e6			1.23961
$52$	−125962.	+	19715.9i	−0.124231	+	0.0194449i
$53$			38212.1i			0.0352562i	0.999845	+	0.0176281i	$0.00561148\pi$
$53$			38212.1i			0.0352562i	−0.999845	+	0.0176281i	$0.994389\pi$
$54$	1.53820e6	−	1.79770e6i	1.32934	−	1.55360i
$55$			3.33556e6i			2.70333i
$56$	80714.4	−	130912.i	0.0614176	−	0.0996140i
$57$	−889070.	+	2.31752e6i	−0.635878	+	1.65753i
$58$	1.68269e6	+	1.43980e6i	1.13242	+	0.968957i
$59$	−2.24545e6			−1.42338			−0.711692	−	0.702492i	$-0.752071\pi$
$59$	−2.24545e6			−1.42338			−0.711692	+	0.702492i	$0.752071\pi$
$60$	−734990.	−	4.69576e6i	−0.439291	−	2.80657i
$61$	368923.			0.208105			0.104052	−	0.994572i	$-0.466819\pi$
$61$	368923.			0.208105			0.104052	+	0.994572i	$0.466819\pi$
$62$	1.78817e6	−	2.08983e6i	0.952879	−	1.11363i
$63$		−	499763.i		−	0.251810i
$64$	941886.	+	1.87374e6i	0.449126	+	0.893468i
$65$			445491.i			0.201206i
$66$	−5.32268e6	−	4.55437e6i	−2.27891	−	1.94995i
$67$	−762681.			−0.309800			−0.154900	−	0.987930i	$-0.549505\pi$
$67$	−762681.			−0.309800			−0.154900	+	0.987930i	$0.549505\pi$
$68$	279970.	+	1.78869e6i	0.107977	+	0.689849i
$69$			4.07555e6i			1.49353i
$70$	−408310.	−	349372.i	−0.142281	−	0.121743i
$71$	336990.			0.111741			0.0558705	−	0.998438i	$-0.482207\pi$
$71$	336990.			0.111741			0.0558705	+	0.998438i	$0.482207\pi$
$72$	5.80085e6	+	3.57655e6i	1.83159	+	1.12928i
$73$	2.02383e6			0.608898			0.304449	−	0.952529i	$-0.401528\pi$
$73$	2.02383e6			0.608898			0.304449	+	0.952529i	$0.401528\pi$
$74$	−1.30872e6	−	1.11981e6i	−0.375435	−	0.321242i
$75$	−1.01213e7			−2.77026
$76$	−3.74199e6	−	801697.i	−0.977811	−	0.209490i
$77$	−792032.			−0.197708
$78$	−710885.	−	608271.i	−0.169617	−	0.145133i
$79$	3.58420e6			0.817894			0.408947	−	0.912558i	$-0.365896\pi$
$79$	3.58420e6			0.817894			0.408947	+	0.912558i	$0.365896\pi$
$80$	6.97731e6	−	2.23906e6i	1.52361	−	0.488935i
$81$	7.07041e6			1.47825
$82$	4.99474e6	+	4.27377e6i	1.00038	+	0.855978i
$83$		−	8.23737e6i		−	1.58130i	−0.612266	−	0.790652i	$-0.709742\pi$
$83$		−	8.23737e6i		−	1.58130i	0.612266	−	0.790652i	$-0.290258\pi$
$84$	1.11501e6	−	174524.i	0.205259	−	0.0321275i
$85$	6.32606e6			1.11729
$86$	5.80926e6	+	4.97071e6i	0.984863	+	0.842701i
$87$			1.62514e7i			2.64590i
$88$	5.66818e6	−	9.19328e6i	0.886654	−	1.43807i
$89$		−	4.68170e6i		−	0.703945i	−0.936010	−	0.351973i	$-0.885511\pi$
$89$		−	4.68170e6i		−	0.703945i	0.936010	−	0.351973i	$-0.114489\pi$
$90$	1.54811e7	−	1.80927e7i	2.23848	−	2.61610i
$91$	−105782.			−0.0147152
$92$	−6.20784e6	+	971664.i	−0.831157	+	0.130094i
$93$	2.01835e7			2.60200
$94$	−1.42247e6	−	1.21714e6i	−0.176643	−	0.151145i
$95$	−4.78948e6	+	1.24846e7i	−0.573133	+	1.49397i
$96$	−5.95384e6	+	1.41911e7i	−0.686828	+	1.63707i
$97$			1.14401e7i			1.27271i	0.771397	+	0.636354i	$0.219558\pi$
$97$			1.14401e7i			1.27271i	−0.771397	+	0.636354i	$0.780442\pi$
$98$	−5.97460e6	+	6.98250e6i	−0.641235	+	0.749410i
$99$		−	3.50959e7i		−	3.63524i
$100$	−2.41305e6	−	1.54166e7i	−0.241305	−	1.54166i
$101$	−1.21597e7			−1.17435			−0.587176	−	0.809459i	$-0.699761\pi$
$101$	−1.21597e7			−1.17435			−0.587176	+	0.809459i	$0.699761\pi$
$102$	−8.63758e6	+	1.00947e7i	−0.805919	+	0.941875i
$103$	−1.22848e7			−1.10774			−0.553869	−	0.832604i	$-0.686849\pi$
$103$	−1.22848e7			−1.10774			−0.553869	+	0.832604i	$0.686849\pi$
$104$	757029.	−	1.22783e6i	0.0659927	−	0.107034i
$105$		−	3.94345e6i		−	0.332441i
$106$	−328484.	−	281068.i	−0.0267882	−	0.0229214i
$107$	1.66914e6			0.131719			0.0658596	−	0.997829i	$-0.479021\pi$
$107$	1.66914e6			0.131719			0.0658596	+	0.997829i	$0.479021\pi$
$108$	4.13936e6	+	2.64458e7i	0.316191	+	2.02011i
$109$		−	5.54615e6i		−	0.410203i	−0.978741	−	0.205101i	$-0.934248\pi$
$109$		−	5.54615e6i		−	0.410203i	0.978741	−	0.205101i	$-0.0657524\pi$
$110$	−2.86736e7	−	2.45347e7i	−2.05404	−	1.75754i
$111$		−	1.26396e7i		−	0.877207i
$112$	531667.	+	1.65677e6i	0.0357583	+	0.111429i
$113$		−	1.55694e7i		−	1.01507i	−0.861630	−	0.507536i	$-0.830556\pi$
$113$		−	1.55694e7i		−	1.01507i	0.861630	−	0.507536i	$-0.169444\pi$
$114$	−1.33826e7	−	2.46892e7i	−0.846007	−	1.56077i
$115$			2.19552e7i			1.34616i
$116$	−2.47540e7	+	3.87455e6i	−1.47246	+	0.230472i
$117$		−	4.68733e6i		−	0.270567i
$118$	1.65164e7	−	1.93027e7i	0.925397	−	1.08151i
$119$			1.50213e6i			0.0817132i
$120$	4.57725e7	+	2.82213e7i	2.41808	+	1.49088i
$121$	−3.61333e7			−1.85421
$122$	−2.71361e6	+	3.17139e6i	−0.135297	+	0.158121i
$123$			4.82391e7i			2.33739i
$124$	4.81202e6	+	3.07434e7i	0.226648	+	1.44802i
$125$	−1.95825e7			−0.896772
$126$	4.29613e6	+	3.67600e6i	0.191329	+	0.163711i
$127$	−1.65404e7			−0.716526			−0.358263	−	0.933621i	$-0.616631\pi$
$127$	−1.65404e7			−0.716526			−0.358263	+	0.933621i	$0.616631\pi$
$128$	−2.30353e7	−	5.68548e6i	−0.970865	−	0.239625i
$129$			5.61057e7i			2.30114i
$130$	−3.82959e6	−	3.27680e6i	−0.152880	−	0.130812i
$131$		−	2.32760e7i		−	0.904604i	−0.891865	−	0.452302i	$-0.850603\pi$
$131$		−	2.32760e7i		−	0.904604i	0.891865	−	0.452302i	$-0.149397\pi$
$132$	7.83017e7	−	1.22560e7i	2.96321	−	0.463808i
$133$	−2.96448e6	−	1.13726e6i	−0.109262	−	0.0419161i
$134$	5.60988e6	−	6.55626e6i	0.201413	−	0.235391i
$135$	9.35309e7			3.27180
$136$	−1.74355e7	−	1.07500e7i	−0.594358	−	0.366455i
$137$	2.59781e7			0.863148			0.431574	−	0.902077i	$-0.357958\pi$
$137$	2.59781e7			0.863148			0.431574	+	0.902077i	$0.357958\pi$
$138$	−3.50347e7	−	2.99776e7i	−1.13481	−	0.971002i
$139$		−	5.33514e6i		−	0.168498i	−0.996445	−	0.0842488i	$-0.973151\pi$
$139$		−	5.33514e6i		−	0.168498i	0.996445	−	0.0842488i	$-0.0268491\pi$
$140$	6.00664e6	−	940172.i	0.185005	−	0.0289574i
$141$		−	1.37382e7i		−	0.412728i
$142$	−2.47872e6	+	2.89688e6i	−0.0726472	+	0.0849026i
$143$	−7.42855e6			−0.212436
$144$	−7.34133e7	+	2.35588e7i	−2.04883	+	0.657483i
$145$			8.75474e7i			2.38482i
$146$	−1.48863e7	+	1.73975e7i	−0.395868	+	0.462650i
$147$	−6.74368e7			−1.75100
$148$	1.92525e7	−	3.01344e6i	0.488170	−	0.0764094i
$149$	−4.81028e7			−1.19129			−0.595646	−	0.803247i	$-0.703104\pi$
$149$	−4.81028e7			−1.19129			−0.595646	+	0.803247i	$0.703104\pi$
$150$	7.44469e7	−	8.70059e7i	1.80105	−	2.10489i
$151$	−2.65180e7			−0.626788			−0.313394	−	0.949623i	$-0.601466\pi$
$151$	−2.65180e7			−0.626788			−0.313394	+	0.949623i	$0.601466\pi$
$152$	3.44158e7	−	2.62705e7i	0.794886	−	0.606759i
$153$	−6.65610e7			−1.50245
$154$	5.82577e6	−	6.80857e6i	0.128538	−	0.150222i
$155$	1.08730e8			2.34525
$156$	1.04578e7	−	1.63688e6i	0.220549	−	0.0345208i
$157$	−2.00364e7			−0.413211			−0.206606	−	0.978424i	$-0.566242\pi$
$157$	−2.00364e7			−0.413211			−0.206606	+	0.978424i	$0.566242\pi$
$158$	−2.63635e7	+	3.08109e7i	−0.531745	+	0.621449i
$159$		−	3.17249e6i		−	0.0625908i
$160$	−3.20737e7	+	7.64486e7i	−0.619055	+	1.47554i
$161$	−5.21329e6			−0.0984512
$162$	−5.20063e7	+	6.07796e7i	−0.961066	+	1.12320i
$163$		−	2.69656e7i		−	0.487701i	−0.969813	−	0.243851i	$-0.921589\pi$
$163$		−	2.69656e7i		−	0.487701i	0.969813	−	0.243851i	$-0.0784107\pi$
$164$	−7.34775e7	+	1.15009e7i	−1.30077	+	0.203599i
$165$		−	2.76929e8i		−	4.79927i
$166$	7.08112e7	+	6.05898e7i	1.20150	+	1.02807i
$167$	3.10719e7			0.516250			0.258125	−	0.966112i	$-0.416895\pi$
$167$	3.10719e7			0.516250			0.258125	+	0.966112i	$0.416895\pi$
$168$	−6.70117e6	+	1.08687e7i	−0.109036	+	0.176846i
$169$	6.17564e7			0.984189
$170$	−4.65312e7	+	5.43809e7i	−0.726395	+	0.848936i
$171$	5.03935e7	−	1.31360e8i	0.770706	−	2.00898i
$172$	−8.54597e7	+	1.33763e7i	−1.28060	+	0.200442i
$173$		−	2.64643e7i		−	0.388597i	−0.980942	−	0.194298i	$-0.937757\pi$
$173$		−	2.64643e7i		−	0.388597i	0.980942	−	0.194298i	$-0.0622430\pi$
$174$	−1.39703e8	−	1.19537e8i	−2.01040	−	1.72020i
$175$		−	1.29468e7i		−	0.182611i
$176$	3.73363e7	+	1.16346e8i	0.516223	+	1.60864i
$177$	1.86425e8			2.52695
$178$	4.02455e7	+	3.44362e7i	0.534869	+	0.457662i
$179$	−3.02694e7			−0.394474			−0.197237	−	0.980356i	$-0.563197\pi$
$179$	−3.02694e7			−0.394474			−0.197237	+	0.980356i	$0.563197\pi$
$180$	4.16601e7	+	2.66161e8i	0.532435	+	3.40166i
$181$		−	9.65258e7i		−	1.20995i	−0.796244	−	0.604976i	$-0.793183\pi$
$181$		−	9.65258e7i		−	1.20995i	0.796244	−	0.604976i	$-0.206817\pi$
$182$	778078.	−	909338.i	0.00956694	−	0.0111809i
$183$	−3.06292e7			−0.369451
$184$	3.73089e7	−	6.05117e7i	0.441519	−	0.716105i
$185$		−	6.80902e7i		−	0.790649i
$186$	−1.48460e8	+	1.73504e8i	−1.69166	+	1.97704i
$187$			1.05487e8i			1.17965i
$188$	2.09260e7	−	3.27538e6i	0.229685	−	0.0359508i
$189$			2.22090e7i			0.239283i
$190$	−7.20930e7	−	1.33002e8i	−0.762528	−	1.40676i
$191$			1.94105e7i			0.201567i	0.994908	+	0.100784i	$0.0321350\pi$
$191$			1.94105e7i			0.201567i	−0.994908	+	0.100784i	$0.967865\pi$
$192$	−7.81984e7	−	1.55564e8i	−0.797340	−	1.58619i
$193$			5.06797e7i			0.507439i	0.967278	+	0.253719i	$0.0816540\pi$
$193$			5.06797e7i			0.507439i	−0.967278	+	0.253719i	$0.918346\pi$
$194$	−9.83428e7	−	8.41474e7i	−0.967023	−	0.827436i
$195$		−	3.69861e7i		−	0.357205i
$196$	−1.60778e7	−	1.02719e8i	−0.152522	−	0.974441i
$197$	1.51253e7			0.140953			0.0704763	−	0.997513i	$-0.477548\pi$
$197$	1.51253e7			0.140953			0.0704763	+	0.997513i	$0.477548\pi$
$198$	3.01696e8	+	2.58147e8i	2.76211	+	2.36341i
$199$			1.28443e7i			0.115538i	0.998330	+	0.0577690i	$0.0183987\pi$
$199$			1.28443e7i			0.115538i	−0.998330	+	0.0577690i	$0.981601\pi$
$200$	1.50276e8	+	9.26535e7i	1.32826	+	0.818949i
$201$	6.33202e7			0.549992
$202$	8.94405e7	−	1.04529e8i	0.763492	−	0.892292i
$203$	−2.07882e7			−0.174414
$204$	−2.32440e7	−	1.48503e8i	−0.191693	−	1.22470i
$205$			2.59867e8i			2.10675i
$206$	9.03604e7	−	1.05604e8i	0.720183	−	0.841677i
$207$		−	2.31007e8i		−	1.81021i
$208$	4.98656e6	+	1.55390e7i	0.0384219	+	0.119729i
$209$	−2.08181e8	−	7.98645e7i	−1.57735	−	0.605120i
$210$	3.38992e7	+	2.90060e7i	0.252594	+	0.216133i
$211$	1.51484e8			1.11014			0.555069	−	0.831804i	$-0.312692\pi$
$211$	1.51484e8			1.11014			0.555069	+	0.831804i	$0.312692\pi$
$212$	4.83231e6	−	756363.i	0.0348321	−	0.00545199i
$213$	−2.79780e7			−0.198375
$214$	−1.22773e7	+	1.43485e7i	−0.0856358	+	0.100082i
$215$			3.02245e8i			2.07408i
$216$	−2.57784e8	−	1.58939e8i	−1.74048	−	1.07310i
$217$			2.58180e7i			0.171520i
$218$	4.76765e7	+	4.07946e7i	0.311679	+	0.266689i
$219$	−1.68025e8			−1.08099
$220$	4.21816e8	−	6.60236e7i	2.67082	−	0.418042i
$221$			1.40886e7i			0.0878001i
$222$	1.08654e8	+	9.29701e7i	0.666515	+	0.570306i
$223$	2.80414e8			1.69329			0.846646	−	0.532156i	$-0.178618\pi$
$223$	2.80414e8			1.69329			0.846646	+	0.532156i	$0.178618\pi$
$224$	−1.81528e7	−	7.61593e6i	−0.107913	−	0.0452746i
$225$	5.73686e8			3.35765
$226$	1.33840e8	+	1.14520e8i	0.771268	+	0.659938i
$227$	−1.54180e7			−0.0874858			−0.0437429	−	0.999043i	$-0.513928\pi$
$227$	−1.54180e7			−0.0874858			−0.0437429	+	0.999043i	$0.513928\pi$
$228$	3.10672e8	+	6.65594e7i	1.73592	+	0.371910i
$229$	2.05480e8			1.13070			0.565349	−	0.824852i	$-0.308742\pi$
$229$	2.05480e8			1.13070			0.565349	+	0.824852i	$0.308742\pi$
$230$	−1.88734e8	−	1.61491e8i	−1.02283	−	0.875189i
$231$	6.57570e7			0.350995
$232$	1.48771e8	−	2.41293e8i	0.782185	−	1.26863i
$233$	−3.43211e8			−1.77752			−0.888762	−	0.458369i	$-0.848434\pi$
$233$	−3.43211e8			−1.77752			−0.888762	+	0.458369i	$0.848434\pi$
$234$	4.02938e7	+	3.44776e7i	0.205581	+	0.175906i
$235$		−	7.40087e7i		−	0.372002i
$236$	4.44461e7	+	2.83961e8i	0.220111	+	1.40626i
$237$	−2.97572e8			−1.45202
$238$	−1.29128e7	−	1.10489e7i	−0.0620870	−	0.0531249i
$239$			1.41496e8i			0.670426i	0.942142	+	0.335213i	$0.108808\pi$
$239$			1.41496e8i			0.670426i	−0.942142	+	0.335213i	$0.891192\pi$
$240$	−5.79279e8	+	1.85894e8i	−2.70488	+	0.868013i
$241$		−	7.11607e7i		−	0.327477i	−0.986504	−	0.163738i	$-0.947645\pi$
$241$		−	7.11607e7i		−	0.327477i	0.986504	−	0.163738i	$-0.0523553\pi$
$242$	2.65778e8	−	3.10614e8i	1.20549	−	1.40886i
$243$	−1.29655e8			−0.579653
$244$	−7.30241e6	−	4.66542e7i	−0.0321812	−	0.205601i
$245$	−3.63287e8			−1.57822
$246$	−4.14680e8	−	3.54822e8i	−1.77599	−	1.51963i
$247$	−2.78042e7	−	1.06665e7i	−0.117401	−	0.0450385i
$248$	−2.99675e8	−	1.84767e8i	−1.24758	−	0.769206i
$249$			6.83893e8i			2.80731i
$250$	1.44038e8	−	1.68337e8i	0.583026	−	0.681381i
$251$			3.40204e8i			1.35794i	0.734164	+	0.678972i	$0.237574\pi$
$251$			3.40204e8i			1.35794i	−0.734164	+	0.678972i	$0.762426\pi$
$252$	−6.32002e7	+	9.89223e6i	−0.248780	+	0.0389397i
$253$	−3.66103e8			−1.42129
$254$	1.21662e8	−	1.42186e8i	0.465841	−	0.544428i
$255$	−5.25210e8			−1.98355
$256$	2.18310e8	−	1.56200e8i	0.813268	−	0.581889i
$257$			4.39945e8i			1.61671i	0.588695	+	0.808355i	$0.299642\pi$
$257$			4.39945e8i			1.61671i	−0.588695	+	0.808355i	$0.700358\pi$
$258$	−4.82303e8	−	4.12684e8i	−1.74844	−	1.49606i
$259$	1.61681e7			0.0578241
$260$	5.63369e7	−	8.81797e6i	0.198786	−	0.0311144i
$261$		−	9.21150e8i		−	3.20692i
$262$	2.00088e8	+	1.71206e8i	0.687332	+	0.588118i
$263$		−	6.92242e7i		−	0.234646i	−0.993094	−	0.117323i	$-0.962569\pi$
$263$		−	6.92242e7i		−	0.234646i	0.993094	−	0.117323i	$-0.0374313\pi$
$264$	−4.70590e8	+	7.63256e8i	−1.57409	+	2.55303i
$265$		−	1.70904e7i		−	0.0564146i
$266$	3.15815e7	−	1.71185e7i	0.102884	−	0.0557675i
$267$			3.88690e8i			1.24972i
$268$	1.50964e7	+	9.64488e7i	0.0479072	+	0.306073i
$269$			2.17640e8i			0.681720i	0.940114	+	0.340860i	$0.110718\pi$
$269$			2.17640e8i			0.681720i	−0.940114	+	0.340860i	$0.889282\pi$
$270$	−6.87965e8	+	8.04023e8i	−2.12712	+	2.48597i
$271$		−	684637.i		−	0.00208962i	−0.999999	−	0.00104481i	$-0.999667\pi$
$271$		−	684637.i		−	0.00208962i	0.999999	−	0.00104481i	$-0.000332574\pi$
$272$	2.20657e8	−	7.08101e7i	0.664854	−	0.213356i
$273$	8.78237e6			0.0261242
$274$	−1.91081e8	+	2.23316e8i	−0.561166	+	0.655834i
$275$		−	9.09187e8i		−	2.63626i
$276$	5.15395e8	−	8.06707e7i	1.47556	−	0.230959i
$277$	4.58005e8			1.29476			0.647382	−	0.762166i	$-0.275864\pi$
$277$	4.58005e8			1.29476			0.647382	+	0.762166i	$0.275864\pi$
$278$	4.58626e7	+	3.92425e7i	0.128027	+	0.109547i
$279$	−1.14403e9			−3.15371
$280$	−3.60997e7	+	5.85505e7i	−0.0982766	+	0.159396i
$281$		−	1.01473e8i		−	0.272822i	−0.990652	−	0.136411i	$-0.956443\pi$
$281$		−	1.01473e8i		−	0.272822i	0.990652	−	0.136411i	$-0.0435568\pi$
$282$	1.18098e8	+	1.01051e8i	0.313597	+	0.268330i
$283$			7.49619e8i			1.96602i	0.183548	+	0.983011i	$0.441242\pi$
$283$			7.49619e8i			1.96602i	−0.183548	+	0.983011i	$0.558758\pi$
$284$	−6.67032e6	−	4.26158e7i	−0.0172796	−	0.110397i
$285$	3.97638e8	−	1.03651e9i	1.01749	−	2.65227i
$286$	5.46406e7	−	6.38583e7i	0.138113	−	0.161412i
$287$	−6.17057e7			−0.154077
$288$	3.37471e8	−	8.04371e8i	0.832458	−	1.98419i
$289$	−2.10278e8			−0.512449
$290$	−7.52587e8	−	6.43953e8i	−1.81202	−	1.55046i
$291$		−	9.49794e8i		−	2.25946i
$292$	−4.00594e7	−	2.55935e8i	−0.0941597	−	0.601574i
$293$			7.91184e8i			1.83756i	0.394772	+	0.918779i	$0.370823\pi$
$293$			7.91184e8i			1.83756i	−0.394772	+	0.918779i	$0.629177\pi$
$294$	4.96030e8	−	5.79709e8i	1.13839	−	1.33044i
$295$	1.00428e9			2.27761
$296$	−1.15707e8	+	1.87666e8i	−0.259321	+	0.420596i
$297$			1.55963e9i			3.45440i
$298$	3.53819e8	−	4.13507e8i	0.774505	−	0.905162i
$299$	−4.88960e7			−0.105785
$300$	2.00339e8	+	1.27994e9i	0.428392	+	2.73694i
$301$	−7.17683e7			−0.151688
$302$	1.95052e8	−	2.27957e8i	0.407499	−	0.476244i
$303$	1.00954e9			2.08485
$304$	−2.73145e7	+	4.89082e8i	−0.0557616	+	0.998444i
$305$	−1.65002e8			−0.332996
$306$	4.89588e8	−	5.72181e8i	0.976801	−	1.14158i
$307$	−5.63617e8			−1.11173			−0.555865	−	0.831272i	$-0.687613\pi$
$307$	−5.63617e8			−1.11173			−0.555865	+	0.831272i	$0.687613\pi$
$308$	1.56774e7	+	1.00161e8i	0.0305735	+	0.195330i
$309$	1.01992e9			1.96658
$310$	−7.99762e8	+	9.34680e8i	−1.52474	+	1.78196i
$311$		−	7.72031e8i		−	1.45537i	−0.685912	−	0.727685i	$-0.740596\pi$
$311$		−	7.72031e8i		−	1.45537i	0.685912	−	0.727685i	$-0.259404\pi$
$312$	−6.28510e7	+	1.01939e8i	−0.117158	+	0.190020i
$313$	4.52014e8			0.833195			0.416597	−	0.909091i	$-0.363223\pi$
$313$	4.52014e8			0.833195			0.416597	+	0.909091i	$0.363223\pi$
$314$	1.47378e8	−	1.72240e8i	0.268644	−	0.313964i
$315$			2.23520e8i			0.402929i
$316$	−7.09450e7	−	4.53259e8i	−0.126479	−	0.808056i
$317$		−	7.32387e8i		−	1.29132i	−0.763626	−	0.645659i	$-0.776583\pi$
$317$		−	7.32387e8i		−	1.29132i	0.763626	−	0.645659i	$-0.223417\pi$
$318$	2.72718e7	+	2.33352e7i	0.0475574	+	0.0406927i
$319$	−1.45985e9			−2.51792
$320$	−4.21260e8	−	8.38033e8i	−0.718663	−	1.42967i
$321$	−1.38577e8			−0.233843
$322$	3.83462e7	−	4.48151e7i	0.0640069	−	0.0748047i
$323$	−1.51467e8	+	3.94825e8i	−0.250097	+	0.651922i
$324$	−1.39951e8	−	8.94127e8i	−0.228595	−	1.46047i
$325$		−	1.21429e8i		−	0.196214i
$326$	2.31805e8	+	1.98345e8i	0.370563	+	0.317073i
$327$			4.60459e8i			0.728239i
$328$	4.41597e8	−	7.16231e8i	0.690983	−	1.12071i
$329$	1.75734e7			0.0272064
$330$	2.38058e9	+	2.03695e9i	3.64656	+	3.12019i
$331$	−5.46189e7			−0.0827838			−0.0413919	−	0.999143i	$-0.513179\pi$
$331$	−5.46189e7			−0.0827838			−0.0413919	+	0.999143i	$0.513179\pi$
$332$	−1.04170e9	+	1.63049e8i	−1.56228	+	0.244532i
$333$			7.16426e8i			1.06320i
$334$	−2.28549e8	+	2.67104e8i	−0.335634	+	0.392255i
$335$	3.41110e8			0.495722
$336$	−4.41407e7	−	1.37550e8i	−0.0634822	−	0.197821i
$337$		−	3.48422e8i		−	0.495908i	−0.968772	−	0.247954i	$-0.920242\pi$
$337$		−	3.48422e8i		−	0.495908i	0.968772	−	0.247954i	$-0.0797581\pi$
$338$	−4.54248e8	+	5.30878e8i	−0.639859	+	0.747802i
$339$			1.29262e9i			1.80207i
$340$	−1.25217e8	−	7.99995e8i	−0.172777	−	1.10385i
$341$			1.81307e9i			2.47614i
$342$	7.58543e8	+	1.39941e9i	1.02539	+	1.89171i
$343$		−	1.73723e8i		−	0.232449i
$344$	5.13610e8	−	8.33029e8i	0.680266	−	1.10333i
$345$		−	1.82279e9i		−	2.38985i
$346$	2.27496e8	+	1.94658e8i	0.295262	+	0.252642i
$347$			2.50612e8i			0.321994i	0.986955	+	0.160997i	$0.0514710\pi$
$347$			2.50612e8i			0.321994i	−0.986955	+	0.160997i	$0.948529\pi$
$348$	2.05516e9	−	3.21678e8i	2.61407	−	0.409161i
$349$	−1.13646e9			−1.43108			−0.715542	−	0.698569i	$-0.753820\pi$
$349$	−1.13646e9			−1.43108			−0.715542	+	0.698569i	$0.753820\pi$
$350$	1.11295e8	+	9.52296e7i	0.138751	+	0.118723i
$351$			2.08300e8i			0.257108i
$352$	−1.27478e9	−	5.34829e8i	−1.55789	−	0.653605i
$353$	4.89645e8			0.592475			0.296237	−	0.955114i	$-0.404268\pi$
$353$	4.89645e8			0.592475			0.296237	+	0.955114i	$0.404268\pi$
$354$	−1.37124e9	+	1.60257e9i	−1.64287	+	1.92002i
$355$	−1.50719e8			−0.178801
$356$	−5.92050e8	+	9.26689e7i	−0.695477	+	0.108858i
$357$		−	1.24711e8i		−	0.145067i
$358$	2.22646e8	−	2.60206e8i	0.256463	−	0.299727i
$359$			7.62380e8i			0.869643i	0.900517	+	0.434822i	$0.143189\pi$
$359$			7.62380e8i			0.869643i	−0.900517	+	0.434822i	$0.856811\pi$
$360$	−2.59444e9	−	1.59962e9i	−2.93079	−	1.80700i
$361$	−6.64520e8	−	5.97846e8i	−0.743417	−	0.668828i
$362$	8.29767e8	+	7.09993e8i	0.919340	+	0.786637i
$363$	2.99990e9			3.29181
$364$	2.09383e6	+	1.33772e7i	0.00227555	+	0.0145382i
$365$	−9.05163e8			−0.974320
$366$	2.25293e8	−	2.63299e8i	0.240195	−	0.280715i
$367$		−	1.43283e9i		−	1.51309i	−0.653941	−	0.756545i	$-0.726886\pi$
$367$		−	1.43283e9i		−	1.51309i	0.653941	−	0.756545i	$-0.273114\pi$
$368$	2.45754e8	+	7.65812e8i	0.257059	+	0.801041i
$369$		−	2.73425e9i		−	2.83300i
$370$	5.85326e8	+	5.00836e8i	0.600747	+	0.514031i
$371$	4.05813e6			0.00412588
$372$	−3.99510e8	−	2.55242e9i	−0.402371	−	2.57070i
$373$		−	3.69312e8i		−	0.368479i	−0.982881	−	0.184239i	$-0.941018\pi$
$373$		−	3.69312e8i		−	0.368479i	0.982881	−	0.184239i	$-0.0589822\pi$
$374$	−9.06801e8	−	7.75907e8i	−0.896316	−	0.766936i
$375$	1.62580e9			1.59205
$376$	−1.25764e8	+	2.03978e8i	−0.122011	+	0.197891i
$377$	−1.94975e8			−0.187406
$378$	−1.90916e8	−	1.63358e8i	−0.181811	−	0.155567i
$379$	7.66263e8			0.723004			0.361502	−	0.932371i	$-0.382264\pi$
$379$	7.66263e8			0.723004			0.361502	+	0.932371i	$0.382264\pi$
$380$	1.67361e9	+	3.58560e8i	1.56463	+	0.335212i
$381$	1.37323e9			1.27206
$382$	−1.66859e8	−	1.42774e8i	−0.153154	−	0.131047i
$383$	−6.19328e8			−0.563281			−0.281640	−	0.959520i	$-0.590878\pi$
$383$	−6.19328e8			−0.563281			−0.281640	+	0.959520i	$0.590878\pi$
$384$	1.91247e9	+	4.72027e8i	1.72359	+	0.425410i
$385$	3.54238e8			0.316360
$386$	−4.35660e8	−	3.72774e8i	−0.385560	−	0.329906i
$387$		−	3.18014e9i		−	2.78906i
$388$	1.44672e9	−	2.26443e8i	1.25740	−	0.196811i
$389$	−3.09742e8			−0.266794			−0.133397	−	0.991063i	$-0.542589\pi$
$389$	−3.09742e8			−0.266794			−0.133397	+	0.991063i	$0.542589\pi$
$390$	3.17945e8	+	2.72050e8i	0.271410	+	0.232233i
$391$			6.94332e8i			0.587420i
$392$	1.00127e9	+	6.17339e8i	0.839555	+	0.517633i
$393$			1.93245e9i			1.60596i
$394$	−1.11254e8	+	1.30022e8i	−0.0916387	+	0.107098i
$395$	−1.60304e9			−1.30874
$396$	−4.43823e9	+	6.94682e8i	−3.59151	+	0.562151i
$397$	1.74154e9			1.39690			0.698452	−	0.715657i	$-0.253873\pi$
$397$	1.74154e9			1.39690			0.698452	+	0.715657i	$0.253873\pi$
$398$	−1.10414e8	−	9.44760e7i	−0.0877875	−	0.0751157i
$399$	2.46121e8	+	9.44194e7i	0.193974	+	0.0744142i
$400$	−1.90183e9	+	6.10309e8i	−1.48580	+	0.476804i
$401$		−	1.11977e9i		−	0.867212i	−0.901103	−	0.433606i	$-0.857241\pi$
$401$		−	1.11977e9i		−	0.867212i	0.901103	−	0.433606i	$-0.142759\pi$
$402$	−4.65751e8	+	5.44322e8i	−0.357571	+	0.417892i
$403$			2.42150e8i			0.184296i
$404$	2.40687e8	+	1.53772e9i	0.181601	+	1.16023i
$405$	−3.16225e9			−2.36540
$406$	1.52907e8	−	1.78702e8i	0.113393	−	0.132522i
$407$	1.13540e9			0.834775
$408$	1.44755e9	+	8.92497e8i	1.05517	+	0.650573i
$409$		−	6.06144e8i		−	0.438071i	−0.975717	−	0.219035i	$-0.929709\pi$
$409$		−	6.06144e8i		−	0.438071i	0.975717	−	0.219035i	$-0.0702910\pi$
$410$	−2.23391e9	−	1.91145e9i	−1.60074	−	1.36968i
$411$	−2.15679e9			−1.53236
$412$	2.43163e8	+	1.55354e9i	0.171300	+	1.09441i
$413$			2.38468e8i			0.166573i
$414$	1.98581e9	+	1.69917e9i	1.37542	+	1.17689i
$415$			3.68418e9i			2.53030i
$416$	−1.70257e8	−	7.14306e7i	−0.115952	−	0.0486472i
$417$			4.42940e8i			0.299136i
$418$	2.21781e9	−	1.20215e9i	1.48528	−	0.805085i
$419$			6.76363e7i			0.0449191i	0.999748	+	0.0224595i	$0.00714969\pi$
$419$			6.76363e7i			0.0449191i	−0.999748	+	0.0224595i	$0.992850\pi$
$420$	−4.98690e8	+	7.80561e7i	−0.328442	+	0.0514084i
$421$			2.41699e9i			1.57866i	0.613971	+	0.789329i	$0.289571\pi$
$421$			2.41699e9i			1.57866i	−0.613971	+	0.789329i	$0.710429\pi$
$422$	−1.11424e9	+	1.30220e9i	−0.721744	+	0.843501i
$423$			7.78699e8i			0.500240i
$424$	−2.90420e7	+	4.71035e7i	−0.0185032	+	0.0300105i
$425$	−1.72432e9			−1.08957
$426$	2.05792e8	−	2.40508e8i	0.128972	−	0.150729i
$427$		−	3.91797e7i		−	0.0243537i
$428$	−3.30387e7	−	2.11080e8i	−0.0203690	−	0.130135i
$429$	6.16742e8			0.377141
$430$	−2.59820e9	−	2.22316e9i	−1.57591	−	1.34844i
$431$	1.87453e9			1.12778			0.563888	−	0.825851i	$-0.309305\pi$
$431$	1.87453e9			1.12778			0.563888	+	0.825851i	$0.309305\pi$
$432$	3.26241e9	−	1.04693e9i	1.94691	−	0.624776i
$433$		−	3.14975e9i		−	1.86453i	−0.361780	−	0.932263i	$-0.617831\pi$
$433$		−	3.14975e9i		−	1.86453i	0.361780	−	0.932263i	$-0.382169\pi$
$434$	−2.21940e8	−	1.89904e8i	−0.130323	−	0.111512i
$435$		−	7.26847e9i		−	4.23380i
$436$	−7.01367e8	+	1.09780e8i	−0.405269	+	0.0634335i
$437$	−1.37028e9	−	5.25681e8i	−0.785461	−	0.301326i
$438$	1.23591e9	−	1.44440e9i	0.702791	−	0.821350i
$439$	−3.03555e9			−1.71243			−0.856213	−	0.516623i	$-0.827189\pi$
$439$	−3.03555e9			−1.71243			−0.856213	+	0.516623i	$0.827189\pi$
$440$	−2.53510e9	+	4.11171e9i	−1.41877	+	2.30111i
$441$	3.82240e9			2.12227
$442$	−1.21110e8	−	1.03628e8i	−0.0667119	−	0.0570823i
$443$		−	1.15236e9i		−	0.629758i	−0.949132	−	0.314879i	$-0.898036\pi$
$443$		−	1.15236e9i		−	0.629758i	0.949132	−	0.314879i	$-0.101964\pi$
$444$	−1.59840e9	+	2.50186e8i	−0.866655	+	0.135651i
$445$			2.09390e9i			1.12641i
$446$	−2.06258e9	+	2.41053e9i	−1.10088	+	1.28659i
$447$	3.99365e9			2.11492
$448$	1.98991e8	−	1.00028e8i	0.104559	−	0.0525594i
$449$		−	8.59070e8i		−	0.447885i	−0.974602	−	0.223942i	$-0.928107\pi$
$449$		−	8.59070e8i		−	0.447885i	0.974602	−	0.223942i	$-0.0718928\pi$
$450$	−4.21974e9	+	4.93160e9i	−2.18294	+	2.55120i
$451$	−4.33329e9			−2.22433
$452$	−1.96891e9	+	3.08178e8i	−1.00286	+	0.156970i
$453$	2.20161e9			1.11275
$454$	1.13407e8	−	1.32538e8i	0.0568779	−	0.0664731i
$455$	4.73112e7			0.0235464
$456$	−2.85731e9	+	2.18106e9i	−1.41117	+	1.07719i
$457$	3.34517e9			1.63950			0.819749	−	0.572723i	$-0.194113\pi$
$457$	3.34517e9			1.63950			0.819749	+	0.572723i	$0.194113\pi$
$458$	−1.51141e9	+	1.76638e9i	−0.735110	+	0.859121i
$459$	2.95791e9			1.42771
$460$	2.77647e9	−	4.34578e8i	1.32996	−	0.208169i
$461$	3.27440e9			1.55661			0.778303	−	0.627889i	$-0.216081\pi$
$461$	3.27440e9			1.55661			0.778303	+	0.627889i	$0.216081\pi$
$462$	−4.83675e8	+	5.65269e8i	−0.228195	+	0.266691i
$463$			7.33860e8i			0.343621i	0.985130	+	0.171811i	$0.0549617\pi$
$463$			7.33860e8i			0.343621i	−0.985130	+	0.171811i	$0.945038\pi$
$464$	9.79954e8	+	3.05371e9i	0.455400	+	1.41910i
$465$	−9.02712e9			−4.16355
$466$	2.52448e9	−	2.95035e9i	1.15564	−	1.35059i
$467$			5.17347e8i			0.235057i	0.993070	+	0.117528i	$0.0374971\pi$
$467$			5.17347e8i			0.235057i	−0.993070	+	0.117528i	$0.962503\pi$
$468$	−5.92761e8	+	9.27803e7i	−0.267312	+	0.0418403i
$469$			8.09968e7i			0.0362546i
$470$	6.36204e8	+	5.44370e8i	0.282653	+	0.241853i
$471$	1.66349e9			0.733579
$472$	−2.76794e9	−	1.70659e9i	−1.21160	−	0.747021i
$473$	−5.03993e9			−2.18983
$474$	2.18878e9	−	2.55802e9i	0.944014	−	1.10327i
$475$	1.30548e9	−	3.40298e9i	0.558913	−	1.45691i
$476$	1.89959e8	−	2.97329e7i	0.0807303	−	0.0126361i
$477$			1.79821e8i			0.0758621i
$478$	−1.21634e9	−	1.04077e9i	−0.509400	−	0.435870i
$479$		−	3.33597e8i		−	0.138691i	−0.997593	−	0.0693454i	$-0.977909\pi$
$479$		−	3.33597e8i		−	0.138691i	0.997593	−	0.0693454i	$-0.0220911\pi$
$480$	2.66286e9	−	6.34701e9i	1.09902	−	2.61954i
$481$	1.51642e8			0.0621315
$482$	6.11721e8	+	5.23421e8i	0.248822	+	0.212905i
$483$	4.32824e8			0.174782
$484$	7.15217e8	+	4.56943e9i	0.286734	+	1.83191i
$485$		−	5.11660e9i		−	2.03650i
$486$	9.53676e8	−	1.11456e9i	0.376855	−	0.440429i
$487$	−1.85149e9			−0.726390			−0.363195	−	0.931713i	$-0.618314\pi$
$487$	−1.85149e9			−0.726390			−0.363195	+	0.931713i	$0.618314\pi$
$488$	4.54767e8	+	2.80390e8i	0.177141	+	0.109218i
$489$			2.23877e9i			0.865823i
$490$	2.67215e9	−	3.12293e9i	1.02606	−	1.19916i
$491$			1.07948e9i			0.411557i	0.978599	+	0.205778i	$0.0659726\pi$
$491$			1.07948e9i			0.411557i	−0.978599	+	0.205778i	$0.934027\pi$
$492$	6.10034e9	−	9.54838e8i	2.30928	−	0.361453i
$493$			2.76868e9i			1.04066i
$494$	2.96206e8	−	1.60557e8i	0.110548	−	0.0599216i
$495$			1.56967e10i			5.81688i
$496$	3.79257e9	−	1.21706e9i	1.39556	−	0.447843i
$497$		−	3.57884e7i		−	0.0130766i
$498$	−5.87897e9	−	5.03036e9i	−2.13304	−	1.82514i
$499$		−	2.14498e9i		−	0.772808i	−0.922330	−	0.386404i	$-0.873717\pi$
$499$		−	2.14498e9i		−	0.772808i	0.922330	−	0.386404i	$-0.126283\pi$
$500$	3.87612e8	+	2.47640e9i	0.138676	+	0.885985i
$501$	−2.57969e9			−0.916506
$502$	−2.92451e9	−	2.50237e9i	−1.03179	−	0.882852i
$503$		−	3.18072e9i		−	1.11439i	−0.830381	−	0.557196i	$-0.811877\pi$
$503$		−	3.18072e9i		−	1.11439i	0.830381	−	0.557196i	$-0.188123\pi$
$504$	3.79831e8	−	6.16052e8i	0.132155	−	0.214343i
$505$	5.43845e9			1.87912
$506$	2.69286e9	−	3.14714e9i	0.924033	−	1.07992i
$507$	−5.12721e9			−1.74724
$508$	3.27397e8	+	2.09170e9i	0.110803	+	0.707907i
$509$			3.97902e9i			1.33741i	0.743529	+	0.668704i	$0.233150\pi$
$509$			3.97902e9i			1.33741i	−0.743529	+	0.668704i	$0.766850\pi$
$510$	3.86317e9	−	4.51488e9i	1.28958	−	1.50713i
$511$		−	2.14932e8i		−	0.0712569i
$512$	−2.63030e8	+	3.02559e9i	−0.0866086	+	0.996242i
$513$	−2.23944e9	+	5.83749e9i	−0.732367	+	1.90904i
$514$	−3.78191e9	−	3.23600e9i	−1.22840	−	1.05109i
$515$	5.49439e9			1.77253
$516$	7.09514e9	−	1.11055e9i	2.27346	−	0.355847i
$517$	1.23409e9			0.392764
$518$	−1.18924e8	+	1.38986e8i	−0.0375937	+	0.0439357i
$519$			2.19715e9i			0.689881i
$520$	−3.38583e8	+	5.49151e8i	−0.105597	+	0.171270i
$521$		−	4.72489e9i		−	1.46372i	−0.681453	−	0.731862i	$-0.738651\pi$
$521$		−	4.72489e9i		−	1.46372i	0.681453	−	0.731862i	$-0.261349\pi$
$522$	7.91851e9	+	6.77550e9i	2.43667	+	2.08494i
$523$	−4.12799e9			−1.26178			−0.630888	−	0.775874i	$-0.717309\pi$
$523$	−4.12799e9			−1.26178			−0.630888	+	0.775874i	$0.717309\pi$
$524$	−2.94349e9	+	4.60721e8i	−0.893722	+	0.139887i
$525$			1.07488e9i			0.324193i
$526$	5.95074e8	+	5.09177e8i	0.178288	+	0.152552i
$527$	3.43858e9			1.02339
$528$	−3.09978e9	−	9.65946e9i	−0.916458	−	2.85584i
$529$	9.95074e8			0.292254
$530$	1.46915e8	+	1.25708e8i	0.0428647	+	0.0366773i
$531$	−1.05668e10			−3.06275
$532$	−8.51403e7	+	3.97400e8i	−0.0245157	+	0.114429i
$533$	−5.78744e8			−0.165555
$534$	−3.34131e9	−	2.85900e9i	−0.949560	−	0.812494i
$535$	−7.46525e8			−0.210769
$536$	−9.40147e8	−	5.79654e8i	−0.263705	−	0.162589i
$537$	2.51306e9			0.700315
$538$	−1.87091e9	−	1.60085e9i	−0.517981	−	0.443212i
$539$		−	6.05780e9i		−	1.66630i
$540$	−1.85134e9	−	1.18279e10i	−0.505949	−	3.23244i
$541$	1.99704e9			0.542247			0.271124	−	0.962545i	$-0.412605\pi$
$541$	1.99704e9			0.542247			0.271124	+	0.962545i	$0.412605\pi$
$542$	5.88537e6	+	5.03584e6i	0.00158773	+	0.00135854i
$543$			8.01388e9i			2.14805i
$544$	−1.01433e9	+	2.41768e9i	−0.270136	+	0.643877i
$545$			2.48052e9i			0.656380i
$546$	−6.45985e7	+	7.54962e7i	−0.0169843	+	0.0198496i
$547$	1.88840e9			0.493331			0.246666	−	0.969101i	$-0.420665\pi$
$547$	1.88840e9			0.493331			0.246666	+	0.969101i	$0.420665\pi$
$548$	−5.14206e8	−	3.28520e9i	−0.133477	−	0.852766i
$549$	1.73610e9			0.447787
$550$	7.81567e9	+	6.68750e9i	2.00307	+	1.71394i
$551$	−5.46405e9	−	2.09618e9i	−1.39150	−	0.533823i
$552$	−3.09750e9	+	5.02388e9i	−0.783836	+	1.27131i
$553$		−	3.80642e8i		−	0.0957148i
$554$	−3.36884e9	+	3.93716e9i	−0.841776	+	0.983782i
$555$			5.65307e9i			1.40365i
$556$	−6.74683e8	+	1.05603e8i	−0.166471	+	0.0260564i
$557$	5.09331e9			1.24884			0.624421	−	0.781088i	$-0.285335\pi$
$557$	5.09331e9			1.24884			0.624421	+	0.781088i	$0.285335\pi$
$558$	8.41487e9	−	9.83444e9i	2.05035	−	2.39624i
$559$	−6.73122e8			−0.162987
$560$	−2.37789e8	−	7.40991e8i	−0.0572181	−	0.178302i
$561$		−	8.75787e9i		−	2.09425i
$562$	8.72298e8	+	7.46385e8i	0.207294	+	0.177372i
$563$	8.42481e8			0.198967			0.0994834	−	0.995039i	$-0.468281\pi$
$563$	8.42481e8			0.198967			0.0994834	+	0.995039i	$0.468281\pi$
$564$	−1.73734e9	+	2.71932e8i	−0.407763	+	0.0638240i
$565$			6.96343e9i			1.62425i
$566$	−6.44398e9	−	5.51381e9i	−1.49381	−	1.27819i
$567$		−	7.50879e8i		−	0.172993i
$568$	4.15403e8	+	2.56120e8i	0.0951154	+	0.0586440i
$569$		−	2.30834e9i		−	0.525300i	−0.964891	−	0.262650i	$-0.915403\pi$
$569$		−	2.30834e9i		−	0.525300i	0.964891	−	0.262650i	$-0.0845965\pi$
$570$	5.98539e9	+	1.10423e10i	1.35373	+	2.49745i
$571$			3.46898e8i			0.0779785i	0.999240	+	0.0389893i	$0.0124138\pi$
$571$			3.46898e8i			0.0779785i	−0.999240	+	0.0389893i	$0.987586\pi$
$572$	1.47040e8	+	9.39417e8i	0.0328510	+	0.209881i
$573$		−	1.61152e9i		−	0.357845i
$574$	4.53875e8	−	5.30443e8i	0.100172	−	0.117070i
$575$		−	5.98442e9i		−	1.31276i
$576$	4.43238e9	+	8.81755e9i	0.966403	+	1.92251i
$577$	4.03219e9			0.873827			0.436914	−	0.899504i	$-0.356072\pi$
$577$	4.03219e9			0.873827			0.436914	+	0.899504i	$0.356072\pi$
$578$	1.54669e9	−	1.80762e9i	0.333163	−	0.389367i
$579$		−	4.20760e9i		−	0.900864i
$580$	1.10713e10	−	1.73290e9i	2.35613	−	0.368787i
$581$	−8.74810e8			−0.185054
$582$	8.16474e9	+	6.98619e9i	1.71677	+	1.46896i
$583$	2.84982e8			0.0595632
$584$	2.49475e9	+	1.53816e9i	0.518302	+	0.319562i
$585$			2.09642e9i			0.432944i
$586$	−6.80128e9	−	5.81954e9i	−1.39621	−	1.19467i
$587$			3.71265e9i			0.757618i	0.925475	+	0.378809i	$0.123666\pi$
$587$			3.71265e9i			0.757618i	−0.925475	+	0.378809i	$0.876334\pi$
$588$	1.33483e9	+	8.52808e9i	0.270774	+	1.72994i
$589$	−2.60336e9	+	6.78611e9i	−0.524965	+	1.36841i
$590$	−7.38698e9	+	8.63315e9i	−1.48076	+	1.73056i
$591$	−1.25575e9			−0.250235
$592$	−7.62161e8	−	2.37503e9i	−0.150981	−	0.470482i
$593$	−3.54071e9			−0.697266			−0.348633	−	0.937259i	$-0.613354\pi$
$593$	−3.54071e9			−0.697266			−0.348633	+	0.937259i	$0.613354\pi$
$594$	−1.34071e10	−	1.14718e10i	−2.62471	−	2.24584i
$595$		−	6.71829e8i		−	0.130752i
$596$	9.52138e8	+	6.08309e9i	0.184221	+	1.17696i
$597$		−	1.06638e9i		−	0.205116i
$598$	3.59653e8	−	4.20326e8i	0.0687749	−	0.0803770i
$599$	8.48019e8			0.161217			0.0806087	−	0.996746i	$-0.474314\pi$
$599$	8.48019e8			0.161217			0.0806087	+	0.996746i	$0.474314\pi$
$600$	−1.24764e10	−	7.69239e9i	−2.35808	−	1.45389i
$601$		−	3.01276e9i		−	0.566114i	−0.959103	−	0.283057i	$-0.908652\pi$
$601$		−	3.01276e9i		−	0.566114i	0.959103	−	0.283057i	$-0.0913485\pi$
$602$	5.27890e8	−	6.16944e8i	0.0986179	−	0.115255i
$603$	−3.58907e9			−0.666609
$604$	5.24892e8	+	3.35347e9i	0.0969262	+	0.619249i
$605$	1.61607e10			2.96699
$606$	−7.42564e9	+	8.67833e9i	−1.35544	+	1.58410i
$607$	2.39524e9			0.434700			0.217350	−	0.976094i	$-0.430259\pi$
$607$	2.39524e9			0.434700			0.217350	+	0.976094i	$0.430259\pi$
$608$	−4.00340e9	−	3.83223e9i	−0.722381	−	0.691496i
$609$	1.72590e9			0.309639
$610$	1.21367e9	−	1.41841e9i	0.216493	−	0.253015i
$611$	1.64823e8			0.0292330
$612$	1.31750e9	+	8.41733e9i	0.232338	+	1.48438i
$613$	−1.02628e10			−1.79951			−0.899755	−	0.436395i	$-0.856255\pi$
$613$	−1.02628e10			−1.79951			−0.899755	+	0.436395i	$0.856255\pi$
$614$	4.14567e9	−	4.84503e9i	0.722779	−	0.844710i
$615$		−	2.15750e10i		−	3.74015i
$616$	−9.76328e8	−	6.01961e8i	−0.168292	−	0.103761i
$617$	3.36122e9			0.576101			0.288051	−	0.957615i	$-0.406993\pi$
$617$	3.36122e9			0.576101			0.288051	+	0.957615i	$0.406993\pi$
$618$	−7.50202e9	+	8.76759e9i	−1.27855	+	1.49424i
$619$		−	6.15064e9i		−	1.04232i	−0.853457	−	0.521162i	$-0.825499\pi$
$619$		−	6.15064e9i		−	1.04232i	0.853457	−	0.521162i	$-0.174501\pi$
$620$	−2.15219e9	−	1.37500e10i	−0.362668	−	2.31704i
$621$			1.02657e10i			1.72016i
$622$	6.63663e9	+	5.67866e9i	1.10581	+	0.946192i
$623$	−4.97198e8			−0.0823799
$624$	−4.14000e8	−	1.29010e9i	−0.0682110	−	0.212557i
$625$	−7.65854e8			−0.125478
$626$	−3.32478e9	+	3.88566e9i	−0.541692	+	0.633074i
$627$	1.72838e10	+	6.63061e9i	2.80030	+	1.07428i
$628$	3.96598e8	+	2.53381e9i	0.0638987	+	0.408240i
$629$		−	2.15335e9i		−	0.345014i
$630$	−1.92145e9	−	1.64410e9i	−0.306152	−	0.261960i
$631$			2.57771e9i			0.408444i	0.978925	+	0.204222i	$0.0654664\pi$
$631$			2.57771e9i			0.408444i	−0.978925	+	0.204222i	$0.934534\pi$
$632$	4.41820e9	+	2.72407e9i	0.696202	+	0.429248i
$633$	−1.25767e10			−1.97085
$634$	6.29584e9	+	5.38706e9i	0.981163	+	0.839536i
$635$	7.39770e9			1.14654
$636$	−4.01194e8	+	6.27957e7i	−0.0618378	+	0.00967899i
$637$		−	8.09067e8i		−	0.124021i
$638$	1.07379e10	−	1.25494e10i	1.63700	−	1.91315i
$639$	1.58583e9			0.240438
$640$	1.03026e10	+	2.54284e9i	1.55352	+	0.383433i
$641$		−	4.66718e9i		−	0.699924i	−0.936764	−	0.349962i	$-0.886194\pi$
$641$		−	4.66718e9i		−	0.699924i	0.936764	−	0.349962i	$-0.113806\pi$
$642$	1.01930e9	−	1.19126e9i	0.152030	−	0.177678i
$643$			1.11696e10i			1.65691i	0.560058	+	0.828453i	$0.310779\pi$
$643$			1.11696e10i			1.65691i	−0.560058	+	0.828453i	$0.689221\pi$
$644$	1.03191e8	+	6.59274e8i	0.0152244	+	0.0972669i
$645$		−	2.50934e10i		−	3.68214i
$646$	−2.27994e9	−	4.20619e9i	−0.332743	−	0.613867i
$647$			4.43545e9i			0.643832i	0.946768	+	0.321916i	$0.104327\pi$
$647$			4.43545e9i			0.643832i	−0.946768	+	0.321916i	$0.895673\pi$
$648$	8.71561e9	+	5.37367e9i	1.25830	+	0.775815i
$649$			1.67464e10i			2.40472i
$650$	1.04384e9	+	8.93169e8i	0.149087	+	0.127567i
$651$		−	2.14350e9i		−	0.304501i
$652$	−3.41008e9	+	5.33753e8i	−0.481835	+	0.0754178i
$653$	−1.23995e10			−1.74264			−0.871320	−	0.490716i	$-0.836735\pi$
$653$	−1.23995e10			−1.74264			−0.871320	+	0.490716i	$0.836735\pi$
$654$	−3.95826e9	−	3.38690e9i	−0.553327	−	0.473456i
$655$			1.04102e10i			1.44749i
$656$	2.90880e9	+	9.06433e9i	0.402301	+	1.25364i
$657$	9.52387e9			1.31019
$658$	−1.29261e8	+	1.51067e8i	−0.0176879	+	0.0206718i
$659$	3.16574e9			0.430900			0.215450	−	0.976515i	$-0.430878\pi$
$659$	3.16574e9			0.430900			0.215450	+	0.976515i	$0.430878\pi$
$660$	−3.50206e10	+	5.48149e9i	−4.74154	+	0.742156i
$661$		−	9.70152e9i		−	1.30658i	−0.757110	−	0.653288i	$-0.773389\pi$
$661$		−	9.70152e9i		−	1.30658i	0.757110	−	0.653288i	$-0.226611\pi$
$662$	4.01748e8	−	4.69523e8i	0.0538209	−	0.0629004i
$663$		−	1.16968e9i		−	0.155873i
$664$	6.26058e9	−	1.01541e10i	0.829901	−	1.34603i
$665$	1.32587e9	+	5.08643e8i	0.174834	+	0.0670714i
$666$	−6.15864e9	−	5.26966e9i	−0.807839	−	0.691230i
$667$	−9.60899e9			−1.25383
$668$	−6.15032e8	−	3.92936e9i	−0.0798326	−	0.510040i
$669$	−2.32808e10			−3.00613
$670$	−2.50903e9	+	2.93230e9i	−0.322288	+	0.376657i
$671$		−	2.75140e9i		−	0.351581i
$672$	1.50710e9	+	6.32299e8i	0.191580	+	0.0803767i
$673$			9.49005e9i			1.20010i	0.799964	+	0.600048i	$0.204852\pi$
$673$			9.49005e9i			1.20010i	−0.799964	+	0.600048i	$0.795148\pi$
$674$	2.99515e9	+	2.56281e9i	0.376798	+	0.322409i
$675$	−2.54941e10			−3.19062
$676$	−1.22240e9	−	7.80973e9i	−0.152194	−	0.972350i
$677$		−	6.38172e9i		−	0.790455i	−0.918583	−	0.395228i	$-0.870666\pi$
$677$		−	6.38172e9i		−	0.790455i	0.918583	−	0.395228i	$-0.129334\pi$
$678$	−1.11118e10	−	9.50785e9i	−1.36924	−	1.17160i
$679$	1.21494e9			0.148940
$680$	7.79805e9	+	4.80794e9i	0.951054	+	0.586378i
$681$	1.28005e9			0.155315
$682$	−1.55858e10	−	1.33360e10i	−1.88141	−	1.60983i
$683$	−4.32806e9			−0.519782			−0.259891	−	0.965638i	$-0.583687\pi$
$683$	−4.32806e9			−0.519782			−0.259891	+	0.965638i	$0.583687\pi$
$684$	−1.76093e10	−	3.77267e9i	−2.10400	−	0.450767i
$685$	−1.16187e10			−1.38115
$686$	1.49338e9	+	1.27782e9i	0.176619	+	0.151124i
$687$	−1.70597e10			−2.00734
$688$	3.38315e9	+	1.05425e10i	0.396061	+	1.23419i
$689$	3.80616e7			0.00443323
$690$	1.56693e10	+	1.34075e10i	1.81585	+	1.55373i
$691$		−	1.20117e10i		−	1.38495i	−0.721444	−	0.692473i	$-0.756521\pi$
$691$		−	1.20117e10i		−	1.38495i	0.721444	−	0.692473i	$-0.243479\pi$
$692$	−3.34668e9	+	5.23830e8i	−0.383922	+	0.0600923i
$693$	−3.72719e9			−0.425417
$694$	−2.15434e9	−	1.84337e9i	−0.244656	−	0.209341i
$695$			2.38615e9i			0.269619i
$696$	−1.23514e10	+	2.00329e10i	−1.38862	+	2.25223i
$697$			8.21829e9i			0.919320i
$698$	8.35921e9	−	9.76939e9i	0.930403	−	1.08736i
$699$	2.84945e10			3.15566
$700$	−1.63725e9	+	2.56266e8i	−0.180415	+	0.0282389i
$701$	6.81686e9			0.747432			0.373716	−	0.927543i	$-0.378084\pi$
$701$	6.81686e9			0.747432			0.373716	+	0.927543i	$0.378084\pi$
$702$	−1.79062e9	−	1.53215e9i	−0.195354	−	0.167156i
$703$	4.24968e9	+	1.63031e9i	0.461331	+	0.176980i
$704$	1.39742e10	−	7.02451e9i	1.50946	−	0.758772i
$705$			6.14445e9i			0.660421i
$706$	−3.60157e9	+	4.20915e9i	−0.385191	+	0.450171i
$707$			1.29136e9i			0.137430i
$708$	−3.69006e9	−	2.35753e10i	−0.390766	−	2.49656i
$709$	3.98257e8			0.0419663			0.0209832	−	0.999780i	$-0.493320\pi$
$709$	3.98257e8			0.0419663			0.0209832	+	0.999780i	$0.493320\pi$
$710$	1.10861e9	−	1.29563e9i	0.116245	−	0.135856i
$711$	1.68667e10			1.75990
$712$	3.55820e9	−	5.77108e9i	0.369445	−	0.599207i
$713$			1.19339e10i			1.23302i
$714$	1.07206e9	+	9.17312e8i	0.110224	+	0.0943134i
$715$	3.32243e9			0.339926
$716$	5.99148e8	+	3.82788e9i	0.0610012	+	0.389729i
$717$		−	1.17474e10i		−	1.19022i
$718$	−6.55367e9	−	5.60767e9i	−0.660768	−	0.565389i
$719$			1.37676e10i			1.38136i	0.723162	+	0.690678i	$0.242688\pi$
$719$			1.37676e10i			1.38136i	−0.723162	+	0.690678i	$0.757312\pi$
$720$	3.28342e10	−	1.05367e10i	3.27841	−	1.05206i
$721$			1.30465e9i			0.129634i
$722$	1.00271e10	−	1.31499e9i	0.991510	−	0.130029i
$723$			5.90799e9i			0.581374i
$724$	−1.22067e10	+	1.91062e9i	−1.19540	+	0.187106i
$725$		−	2.38631e10i		−	2.32565i
$726$	−2.20657e10	+	2.57882e10i	−2.14013	+	2.50116i
$727$			5.42026e9i			0.523178i	0.965179	+	0.261589i	$0.0842465\pi$
$727$			5.42026e9i			0.523178i	−0.965179	+	0.261589i	$0.915753\pi$
$728$	−1.30396e8	−	8.03967e7i	−0.0125258	−	0.00772286i
$729$	−4.69861e9			−0.449182
$730$	6.65791e9	−	7.78108e9i	0.633443	−	0.740304i
$731$			9.55847e9i			0.905061i
$732$	6.06270e8	+	3.87338e9i	0.0571317	+	0.365007i
$733$	6.95448e9			0.652230			0.326115	−	0.945330i	$-0.394260\pi$
$733$	6.95448e9			0.652230			0.326115	+	0.945330i	$0.394260\pi$
$734$	1.23171e10	+	1.05392e10i	1.14967	+	0.983719i
$735$	3.01612e10			2.80184
$736$	−8.39081e9	−	3.52033e9i	−0.775767	−	0.325470i
$737$			5.68801e9i			0.523388i
$738$	2.35045e10	+	2.01117e10i	2.15256	+	1.84184i
$739$		−	1.03818e10i		−	0.946271i	−0.880990	−	0.473136i	$-0.843122\pi$
$739$		−	1.03818e10i		−	0.946271i	0.880990	−	0.473136i	$-0.156878\pi$
$740$	−8.61071e9	+	1.34777e9i	−0.781138	+	0.122265i
$741$	2.30839e9	+	8.85569e8i	0.208423	+	0.0799574i
$742$	−2.98495e7	+	3.48850e7i	−0.00268240	+	0.00313491i
$743$	−1.29366e10			−1.15707			−0.578536	−	0.815657i	$-0.696376\pi$
$743$	−1.29366e10			−1.15707			−0.578536	+	0.815657i	$0.696376\pi$
$744$	2.48800e10	+	1.53399e10i	2.21485	+	1.36558i
$745$	2.15140e10			1.90623
$746$	3.17473e9	+	2.71647e9i	0.279976	+	0.239562i
$747$		−	3.87639e10i		−	3.40255i
$748$	1.33399e10	−	2.08799e9i	1.16546	−	0.182420i
$749$		−	1.77263e8i		−	0.0154146i
$750$	−1.19585e10	+	1.39759e10i	−1.03505	+	1.20967i
$751$	1.47832e10			1.27358			0.636792	−	0.771036i	$-0.280261\pi$
$751$	1.47832e10			1.27358			0.636792	+	0.771036i	$0.280261\pi$
$752$	−8.28410e8	−	2.58147e9i	−0.0710367	−	0.221363i
$753$		−	2.82449e10i		−	2.41078i
$754$	1.43413e9	−	1.67607e9i	0.121840	−	0.142394i
$755$	1.18602e10			1.00295
$756$	2.80855e9	−	4.39601e8i	0.236405	−	0.0370026i
$757$	−3.97261e9			−0.332844			−0.166422	−	0.986055i	$-0.553221\pi$
$757$	−3.97261e9			−0.332844			−0.166422	+	0.986055i	$0.553221\pi$
$758$	−5.63623e9	+	6.58705e9i	−0.470053	+	0.549349i
$759$	3.03951e10			2.52323
$760$	−1.53925e10	+	1.17495e10i	−1.27193	+	0.970896i
$761$	−2.76070e9			−0.227077			−0.113539	−	0.993534i	$-0.536219\pi$
$761$	−2.76070e9			−0.227077			−0.113539	+	0.993534i	$0.536219\pi$
$762$	−1.01008e10	+	1.18048e10i	−0.827015	+	0.966530i
$763$	−5.89002e8			−0.0480044
$764$	2.45466e9	−	3.84209e8i	0.199143	−	0.0311702i
$765$	2.97695e10			2.40412
$766$	4.55545e9	−	5.32395e9i	0.366211	−	0.427989i
$767$			2.23661e9i			0.178981i
$768$	−1.81248e10	+	1.29682e10i	−1.44381	+	1.03304i
$769$	3.09668e9			0.245558			0.122779	−	0.992434i	$-0.460819\pi$
$769$	3.09668e9			0.245558			0.122779	+	0.992434i	$0.460819\pi$
$770$	−2.60559e9	+	3.04514e9i	−0.205678	+	0.240375i
$771$		−	3.65256e10i		−	2.87017i
$772$	6.40897e9	−	1.00315e9i	0.501335	−	0.0784700i
$773$		−	4.92236e9i		−	0.383306i	−0.981463	−	0.191653i	$-0.938615\pi$
$773$		−	4.92236e9i		−	0.383306i	0.981463	−	0.191653i	$-0.0613848\pi$
$774$	2.73375e10	+	2.33914e10i	2.11917	+	1.81328i
$775$	−2.96369e10			−2.28706
$776$	−8.69472e9	+	1.41021e10i	−0.667943	+	1.08334i
$777$	−1.34233e9			−0.102656
$778$	2.27830e9	−	2.66264e9i	0.173453	−	0.202714i
$779$	−1.62190e10	−	6.22209e9i	−1.22926	−	0.471580i
$780$	−4.67727e9	+	7.32097e8i	−0.352908	+	0.0552379i
$781$		−	2.51324e9i		−	0.188780i
$782$	−5.96871e9	−	5.10715e9i	−0.446331	−	0.381905i
$783$			4.09350e10i			3.04739i
$784$	−1.26717e10	+	4.06641e9i	−0.939133	+	0.301374i
$785$	8.96133e9			0.661194
$786$	−1.66120e10	−	1.42141e10i	−1.22023	−	1.04409i
$787$	−2.34994e10			−1.71848			−0.859241	−	0.511571i	$-0.829064\pi$
$787$	−2.34994e10			−1.71848			−0.859241	+	0.511571i	$0.829064\pi$
$788$	−2.99388e8	−	1.91275e9i	−0.0217968	−	0.139257i
$789$			5.74722e9i			0.416570i
$790$	1.17911e10	−	1.37802e10i	0.850864	−	0.994402i
$791$	−1.65347e9			−0.118790
$792$	2.66736e10	−	4.32623e10i	1.90785	−	3.09436i
$793$		−	3.67471e8i		−	0.0261678i
$794$	−1.28099e10	+	1.49709e10i	−0.908181	+	1.06139i
$795$			1.41890e9i			0.100154i
$796$	1.62429e9	−	2.54238e8i	0.114148	−	0.0178667i
$797$			1.98702e10i			1.39026i	0.718882	+	0.695132i	$0.244654\pi$
$797$			1.98702e10i			1.39026i	−0.718882	+	0.695132i	$0.755346\pi$
$798$	−2.62200e9	+	1.42124e9i	−0.182651	+	0.0990048i
$799$		−	2.34052e9i		−	0.162330i
$800$	8.74245e9	−	2.08379e10i	0.603696	−	1.43893i
$801$		−	2.20314e10i		−	1.51471i
$802$	9.62595e9	+	8.23647e9i	0.658921	+	0.563808i
$803$		−	1.50936e10i		−	1.02870i
$804$	−1.25335e9	−	8.00749e9i	−0.0850504	−	0.543376i
$805$	2.33165e9			0.157535
$806$	−2.08160e9	−	1.78113e9i	−0.140031	−	0.119818i
$807$		−	1.80692e10i		−	1.21027i
$808$	−1.49891e10	−	9.24165e9i	−0.999624	−	0.616325i
$809$	1.11935e10			0.743270			0.371635	−	0.928379i	$-0.378797\pi$
$809$	1.11935e10			0.743270			0.371635	+	0.928379i	$0.378797\pi$
$810$	2.32599e10	−	2.71838e10i	1.53784	−	1.79727i
$811$	−1.84475e10			−1.21441			−0.607203	−	0.794547i	$-0.707709\pi$
$811$	−1.84475e10			−1.21441			−0.607203	+	0.794547i	$0.707709\pi$
$812$	4.11478e8	+	2.62888e9i	0.0269712	+	0.172316i
$813$			5.68408e7i			0.00370974i
$814$	−8.35143e9	+	9.76030e9i	−0.542720	+	0.634275i
$815$			1.20604e10i			0.780388i
$816$	−1.83196e10	+	5.87889e9i	−1.18032	+	0.378773i
$817$	−1.88639e10	−	7.23675e9i	−1.21019	−	0.464265i
$818$	5.21062e9	+	4.45848e9i	0.332853	+	0.284807i
$819$	−4.97795e8			−0.0316634
$820$	3.28629e10	−	5.14377e9i	2.08141	−	0.325787i
$821$	8.29733e9			0.523284			0.261642	−	0.965165i	$-0.415736\pi$
$821$	8.29733e9			0.523284			0.261642	+	0.965165i	$0.415736\pi$
$822$	1.58642e10	−	1.85404e10i	0.996246	−	1.16431i
$823$			2.57639e10i			1.61106i	0.592552	+	0.805532i	$0.298120\pi$
$823$			2.57639e10i			1.61106i	−0.592552	+	0.805532i	$0.701880\pi$
$824$	−1.51433e10	−	9.33670e9i	−0.942921	−	0.581364i
$825$			7.54836e10i			4.68019i
$826$	−2.04995e9	−	1.75404e9i	−0.126565	−	0.108295i
$827$	−1.38746e10			−0.853007			−0.426504	−	0.904486i	$-0.640255\pi$
$827$	−1.38746e10			−0.853007			−0.426504	+	0.904486i	$0.640255\pi$
$828$	−2.92132e10	+	4.57251e9i	−1.78843	+	0.279930i
$829$			1.91143e10i			1.16525i	0.812742	+	0.582624i	$0.197974\pi$
$829$			1.91143e10i			1.16525i	−0.812742	+	0.582624i	$0.802026\pi$
$830$	−3.16704e10	−	2.70989e10i	−1.92256	−	1.64505i
$831$	−3.80250e10			−2.29861
$832$	1.86636e9	−	9.38178e8i	0.112348	−	0.0564747i
$833$	−1.14889e10			−0.688686
$834$	−3.80766e9	−	3.25804e9i	−0.227288	−	0.194480i
$835$	−1.38970e10			−0.826070
$836$	−5.97898e9	+	2.79074e10i	−0.353920	+	1.65195i
$837$	5.08395e10			2.99683
$838$	−5.81424e8	−	4.97497e8i	−0.0341302	−	0.0292036i
$839$	5.76495e8			0.0336999			0.0168500	−	0.999858i	$-0.494636\pi$
$839$	5.76495e8			0.0336999			0.0168500	+	0.999858i	$0.494636\pi$
$840$	2.99711e9	−	4.86105e9i	0.174472	−	0.282978i
$841$	−2.10664e10			−1.22125
$842$	−2.07773e10	−	1.77781e10i	−1.19949	−	1.02635i
$843$			8.42464e9i			0.484345i
$844$	−2.99844e9	−	1.91567e10i	−0.171671	−	1.09679i
$845$	−2.76206e10			−1.57484
$846$	−6.69396e9	−	5.72771e9i	−0.380090	−	0.325226i
$847$			3.83736e9i			0.216991i
$848$	−1.91300e8	−	5.96124e8i	−0.0107728	−	0.0335700i
$849$		−	6.22358e10i		−	3.49031i
$850$	1.26832e10	−	1.48228e10i	0.708373	−	0.827873i
$851$	7.47341e9			0.415686
$852$	5.53792e8	+	3.53811e9i	0.0306767	+	0.195989i
$853$	−2.05019e9			−0.113102			−0.0565512	−	0.998400i	$-0.518010\pi$
$853$	−2.05019e9			−0.113102			−0.0565512	+	0.998400i	$0.518010\pi$
$854$	3.36802e8	+	2.88186e8i	0.0185043	+	0.0158333i
$855$	−2.25386e10	+	5.87508e10i	−1.23323	+	3.21464i
$856$	2.05753e9	+	1.26858e9i	0.112121	+	0.0691290i
$857$		−	5.83437e9i		−	0.316637i	−0.987388	−	0.158318i	$-0.949393\pi$
$857$		−	5.83437e9i		−	0.316637i	0.987388	−	0.158318i	$-0.0506072\pi$
$858$	−4.53644e9	+	5.30172e9i	−0.245194	+	0.286557i
$859$			8.97485e9i			0.483116i	0.970386	+	0.241558i	$0.0776583\pi$
$859$			8.97485e9i			0.483116i	−0.970386	+	0.241558i	$0.922342\pi$
$860$	3.82220e10	−	5.98259e9i	2.04913	−	0.320734i
$861$	5.12301e9			0.273536
$862$	−1.37881e10	+	1.61141e10i	−0.733211	+	0.856902i
$863$	2.74440e10			1.45348			0.726742	−	0.686911i	$-0.241034\pi$
$863$	2.74440e10			1.45348			0.726742	+	0.686911i	$0.241034\pi$
$864$	−1.49969e10	+	3.57455e10i	−0.791048	+	1.88548i
$865$			1.18362e10i			0.621807i
$866$	2.70763e10	+	2.31679e10i	1.41670	+	1.21220i
$867$	1.74579e10			0.909758
$868$	3.26496e9	−	5.11038e8i	0.169456	−	0.0265237i
$869$		−	2.67306e10i		−	1.38178i
$870$	6.24822e10	+	5.34631e10i	3.21691	+	2.75256i
$871$			7.59678e8i			0.0389552i
$872$	4.21519e9	−	6.83667e9i	0.215283	−	0.349170i
$873$			5.38354e10i			2.73854i
$874$	1.45980e10	−	7.91275e9i	0.739611	−	0.400901i
$875$			2.07966e9i			0.104946i
$876$	3.32586e9	+	2.12485e10i	0.167163	+	1.06798i
$877$		−	1.47541e10i		−	0.738610i	−0.929308	−	0.369305i	$-0.879596\pi$
$877$		−	1.47541e10i		−	0.738610i	0.929308	−	0.369305i	$-0.120404\pi$
$878$	2.23279e10	−	2.60946e10i	1.11331	−	1.30113i
$879$		−	6.56867e10i		−	3.26224i
$880$	−1.66987e10	−	5.20362e10i	−0.826027	−	2.57404i
$881$	6.76561e9			0.333343			0.166672	−	0.986012i	$-0.446698\pi$
$881$	6.76561e9			0.333343			0.166672	+	0.986012i	$0.446698\pi$
$882$	−2.81156e10	+	3.28586e10i	−1.37977	+	1.61254i
$883$			2.06807e10i			1.01089i	0.862860	+	0.505443i	$0.168671\pi$
$883$			2.06807e10i			1.01089i	−0.862860	+	0.505443i	$0.831329\pi$
$884$	1.78165e9	−	2.78868e8i	0.0867440	−	0.0135774i
$885$	−8.33788e10			−4.04347
$886$	9.90604e9	+	8.47614e9i	0.478500	+	0.409430i
$887$	3.04308e10			1.46414			0.732068	−	0.681232i	$-0.238555\pi$
$887$	3.04308e10			1.46414			0.732068	+	0.681232i	$0.238555\pi$
$888$	9.60635e9	−	1.55806e10i	0.460376	−	0.746690i
$889$			1.75659e9i			0.0838521i
$890$	−1.79999e10	−	1.54016e10i	−0.855862	−	0.732321i
$891$		−	5.27305e10i		−	2.49741i
$892$	−5.55046e9	−	3.54612e10i	−0.261850	−	1.67292i
$893$	4.61907e9	+	1.77201e9i	0.217057	+	0.0832697i
$894$	−2.93752e10	+	3.43307e10i	−1.37499	+	1.60695i
$895$	1.35380e10			0.631212
$896$	−6.03799e8	+	2.44635e9i	−0.0280424	+	0.113616i
$897$	4.05950e9			0.187801
$898$	7.38485e9	+	6.31887e9i	0.340310	+	0.291187i
$899$			4.75871e10i			2.18439i
$900$	−1.13555e10	−	7.25485e10i	−0.519225	−	3.31726i
$901$		−	5.40483e8i		−	0.0246176i
$902$	3.18734e10	−	3.72504e10i	1.44612	−	1.69008i
$903$	5.95844e9			0.269293
$904$	1.18331e10	−	1.91922e10i	0.532731	−	0.864042i
$905$			4.31713e10i			1.93609i
$906$	−1.61939e10	+	1.89257e10i	−0.723440	+	0.845482i
$907$	−1.08794e10			−0.484149			−0.242074	−	0.970258i	$-0.577828\pi$
$907$	−1.08794e10			−0.484149			−0.242074	+	0.970258i	$0.577828\pi$
$908$	3.05181e8	+	1.94976e9i	0.0135287	+	0.0864334i
$909$	−5.72219e10			−2.52690
$910$	−3.47997e8	+	4.06703e8i	−0.0153084	+	0.0178909i
$911$	4.07735e10			1.78675			0.893374	−	0.449313i	$-0.148331\pi$
$911$	4.07735e10			1.78675			0.893374	+	0.449313i	$0.148331\pi$
$912$	2.26774e9	−	4.06051e10i	0.0989944	−	1.77255i
$913$	−6.14336e10			−2.67152
$914$	−2.46053e10	+	2.87562e10i	−1.06590	+	1.24572i
$915$	1.36990e10			0.591172
$916$	−4.06725e9	−	2.59851e10i	−0.174850	−	1.11710i
$917$	−2.47191e9			−0.105862
$918$	−2.17568e10	+	2.54271e10i	−0.928210	+	1.08480i
$919$			2.57661e10i			1.09508i	0.836781	+	0.547538i	$0.184435\pi$
$919$			2.57661e10i			1.09508i	−0.836781	+	0.547538i	$0.815565\pi$
$920$	−1.66865e10	+	2.70639e10i	−0.706491	+	1.14587i
$921$	4.67933e10			1.97367
$922$	−2.40848e10	+	2.81478e10i	−1.01201	+	1.18273i
$923$		−	3.35663e8i		−	0.0140507i
$924$	−1.30158e9	−	8.31566e9i	−0.0542776	−	0.346772i
$925$			1.85596e10i			0.771032i
$926$	−6.30851e9	−	5.39790e9i	−0.261089	−	0.223401i
$927$	−5.78104e10			−2.38357
$928$	−3.34587e10	−	1.40375e10i	−1.37433	−	0.576595i
$929$	1.46881e10			0.601050			0.300525	−	0.953774i	$-0.402838\pi$
$929$	1.46881e10			0.601050			0.300525	+	0.953774i	$0.402838\pi$
$930$	6.63988e10	−	7.76001e10i	2.70689	−	3.16353i
$931$	8.69829e9	−	2.26736e10i	0.353272	−	0.920867i
$932$	6.79346e9	+	4.34025e10i	0.274875	+	1.75614i
$933$			6.40965e10i			2.58374i
$934$	−4.44729e9	−	3.80534e9i	−0.178600	−	0.152820i
$935$		−	4.71792e10i		−	1.88760i
$936$	3.56247e9	−	5.77801e9i	0.141999	−	0.230310i
$937$	2.17946e10			0.865487			0.432744	−	0.901517i	$-0.357546\pi$
$937$	2.17946e10			0.865487			0.432744	+	0.901517i	$0.357546\pi$
$938$	−6.96276e8	−	5.95771e8i	−0.0275468	−	0.0235705i
$939$	−3.75276e10			−1.47918
$940$	−9.35917e9	+	1.46492e9i	−0.367527	+	0.0575262i
$941$			2.95166e10i			1.15479i	0.816466	+	0.577394i	$0.195930\pi$
$941$			2.95166e10i			1.15479i	−0.816466	+	0.577394i	$0.804070\pi$
$942$	−1.22358e10	+	1.42999e10i	−0.476928	+	0.557385i
$943$	−2.85224e10			−1.10763
$944$	3.50300e10	−	1.12413e10i	1.35531	−	0.434927i
$945$		−	9.93300e9i		−	0.382886i
$946$	3.70711e10	−	4.33249e10i	1.42369	−	1.66387i
$947$		−	1.05941e10i		−	0.405358i	−0.979245	−	0.202679i	$-0.935035\pi$
$947$		−	1.05941e10i		−	0.405358i	0.979245	−	0.202679i	$-0.0649648\pi$
$948$	5.89009e9	+	3.76310e10i	0.224539	+	1.43455i
$949$		−	2.01587e9i		−	0.0765649i
$950$	1.96507e10	+	3.62529e10i	0.743608	+	1.37186i
$951$			6.08051e10i			2.29249i
$952$	−1.14165e9	+	1.85165e9i	−0.0428848	+	0.0695553i
$953$		−	2.76760e10i		−	1.03581i	−0.855439	−	0.517903i	$-0.826713\pi$
$953$		−	2.76760e10i		−	1.03581i	0.855439	−	0.517903i	$-0.173287\pi$
$954$	−1.54580e9	−	1.32267e9i	−0.0576412	−	0.0493209i
$955$		−	8.68138e9i		−	0.322535i
$956$	1.78936e10	−	2.80074e9i	0.662361	−	0.103674i
$957$	1.21202e11			4.47009
$958$	2.86771e9	+	2.45376e9i	0.105379	+	0.0901682i
$959$		−	2.75888e9i		−	0.101011i
$960$	3.49744e10	+	6.95762e10i	1.27585	+	2.53811i
$961$	3.15885e10			1.14815
$962$	−1.11540e9	+	1.30357e9i	−0.0403941	+	0.0472085i
$963$	7.85473e9			0.283426
$964$	−8.99901e9	+	1.40854e9i	−0.323538	+	0.0506408i
$965$		−	2.26666e10i		−	0.811971i
$966$	−3.18363e9	+	3.72070e9i	−0.113632	+	0.132802i
$967$			3.10111e10i			1.10287i	0.834217	+	0.551436i	$0.185920\pi$
$967$			3.10111e10i			1.10287i	−0.834217	+	0.551436i	$0.814080\pi$
$968$	−4.45411e10	−	2.74621e10i	−1.57833	−	0.973128i
$969$	1.25753e10	−	3.27796e10i	0.444001	−	1.15737i
$970$	4.39840e10	+	3.76350e10i	1.54737	+	1.32401i
$971$	2.13027e10			0.746736			0.373368	−	0.927683i	$-0.378203\pi$
$971$	2.13027e10			0.746736			0.373368	+	0.927683i	$0.378203\pi$
$972$	2.56637e9	+	1.63962e10i	0.0896371	+	0.572680i
$973$	−5.66593e8			−0.0197186
$974$	1.36186e10	−	1.59160e10i	0.472254	−	0.551922i
$975$			1.00814e10i			0.348342i
$976$	−5.75536e9	+	1.84693e9i	−0.198152	+	0.0635881i
$977$		−	2.76538e10i		−	0.948688i	−0.880340	−	0.474344i	$-0.842685\pi$
$977$		−	2.76538e10i		−	0.948688i	0.880340	−	0.474344i	$-0.157315\pi$
$978$	−1.92452e10	−	1.64673e10i	−0.657866	−	0.562905i
$979$	−3.49157e10			−1.18927
$980$	7.19084e9	+	4.59413e10i	0.244055	+	1.55924i
$981$		−	2.60994e10i		−	0.882650i
$982$	−9.27957e9	−	7.94010e9i	−0.312707	−	0.267569i
$983$	−1.68773e10			−0.566715			−0.283357	−	0.959014i	$-0.591448\pi$
$983$	−1.68773e10			−0.566715			−0.283357	+	0.959014i	$0.591448\pi$
$984$	−3.66628e10	+	5.94638e10i	−1.22671	+	1.98962i
$985$	−6.76483e9			−0.225543
$986$	−2.38005e10	−	2.03650e10i	−0.790709	−	0.676573i
$987$	−1.45900e9			−0.0482999
$988$	−7.98540e8	+	3.72726e9i	−0.0263419	+	0.122953i
$989$	−3.31737e10			−1.09045
$990$	−1.34934e11	−	1.15457e11i	−4.41975	−	3.78178i
$991$	−4.78133e10			−1.56060			−0.780299	−	0.625407i	$-0.784933\pi$
$991$	−4.78133e10			−1.56060			−0.780299	+	0.625407i	$0.784933\pi$
$992$	−1.74339e10	+	4.15543e10i	−0.567028	+	1.35153i
$993$	4.53464e9			0.146967
$994$	3.07649e8	+	2.63241e8i	0.00993581	+	0.00850160i
$995$		−	5.74463e9i		−	0.184876i
$996$	8.64853e10	−	1.35369e10i	2.77354	−	0.434121i
$997$	−1.83879e10			−0.587623			−0.293812	−	0.955863i	$-0.594924\pi$
$997$	−1.83879e10			−0.587623			−0.293812	+	0.955863i	$0.594924\pi$
$998$	1.84390e10	+	1.57774e10i	0.587191	+	0.502432i
$999$		−	3.18373e10i		−	1.01031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.20	yes	68
4.3	odd	2	inner	76.8.d.a.75.50	yes	68
19.18	odd	2	inner	76.8.d.a.75.49	yes	68
76.75	even	2	inner	76.8.d.a.75.19	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.19	✓	68	76.75	even	2	inner
76.8.d.a.75.20	yes	68	1.1	even	1	trivial
76.8.d.a.75.49	yes	68	19.18	odd	2	inner
76.8.d.a.75.50	yes	68	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.35548 + 8.59633i) q^{2} -83.0232 q^{3} +(-19.7938 - 126.460i) q^{4} -447.252 q^{5} +(610.676 - 713.695i) q^{6} -106.200i q^{7} +(1232.69 + 760.022i) q^{8} +4705.86 q^{9} +O(q^{10})\)	\(q+(-7.35548 + 8.59633i) q^{2} -83.0232 q^{3} +(-19.7938 - 126.460i) q^{4} -447.252 q^{5} +(610.676 - 713.695i) q^{6} -106.200i q^{7} +(1232.69 + 760.022i) q^{8} +4705.86 q^{9} +(3289.75 - 3844.72i) q^{10} -7457.91i q^{11} +(1643.35 + 10499.1i) q^{12} -996.063i q^{13} +(912.932 + 781.153i) q^{14} +37132.3 q^{15} +(-15600.4 + 5006.27i) q^{16} -14144.3 q^{17} +(-34613.8 + 40453.1i) q^{18} +(10708.7 - 27914.1i) q^{19} +(8852.83 + 56559.6i) q^{20} +8817.08i q^{21} +(64110.7 + 54856.5i) q^{22} -49089.2i q^{23} +(-102342. - 63099.5i) q^{24} +121909. q^{25} +(8562.49 + 7326.52i) q^{26} -209124. q^{27} +(-13430.1 + 2102.11i) q^{28} -195745. i q^{29} +(-273126. + 319201. i) q^{30} -243107. q^{31} +(71712.9 - 170930. i) q^{32} +619180. i q^{33} +(104038. - 121589. i) q^{34} +47498.2i q^{35} +(-93147.0 - 595104. i) q^{36} +152241. i q^{37} +(161191. + 297377. i) q^{38} +82696.4i q^{39} +(-551322. - 339921. i) q^{40} -581032. i q^{41} +(-75794.6 - 64853.9i) q^{42} -675783. i q^{43} +(-943130. + 147621. i) q^{44} -2.10470e6 q^{45} +(421987. + 361075. i) q^{46} +165475. i q^{47} +(1.29520e6 - 415637. i) q^{48} +812265. q^{49} +(-896699. + 1.04797e6i) q^{50} +1.17431e6 q^{51} +(-125962. + 19715.9i) q^{52} +38212.1i q^{53} +(1.53820e6 - 1.79770e6i) q^{54} +3.33556e6i q^{55} +(80714.4 - 130912. i) q^{56} +(-889070. + 2.31752e6i) q^{57} +(1.68269e6 + 1.43980e6i) q^{58} -2.24545e6 q^{59} +(-734990. - 4.69576e6i) q^{60} +368923. q^{61} +(1.78817e6 - 2.08983e6i) q^{62} -499763. i q^{63} +(941886. + 1.87374e6i) q^{64} +445491. i q^{65} +(-5.32268e6 - 4.55437e6i) q^{66} -762681. q^{67} +(279970. + 1.78869e6i) q^{68} +4.07555e6i q^{69} +(-408310. - 349372. i) q^{70} +336990. q^{71} +(5.80085e6 + 3.57655e6i) q^{72} +2.02383e6 q^{73} +(-1.30872e6 - 1.11981e6i) q^{74} -1.01213e7 q^{75} +(-3.74199e6 - 801697. i) q^{76} -792032. q^{77} +(-710885. - 608271. i) q^{78} +3.58420e6 q^{79} +(6.97731e6 - 2.23906e6i) q^{80} +7.07041e6 q^{81} +(4.99474e6 + 4.27377e6i) q^{82} -8.23737e6i q^{83} +(1.11501e6 - 174524. i) q^{84} +6.32606e6 q^{85} +(5.80926e6 + 4.97071e6i) q^{86} +1.62514e7i q^{87} +(5.66818e6 - 9.19328e6i) q^{88} -4.68170e6i q^{89} +(1.54811e7 - 1.80927e7i) q^{90} -105782. q^{91} +(-6.20784e6 + 971664. i) q^{92} +2.01835e7 q^{93} +(-1.42247e6 - 1.21714e6i) q^{94} +(-4.78948e6 + 1.24846e7i) q^{95} +(-5.95384e6 + 1.41911e7i) q^{96} +1.14401e7i q^{97} +(-5.97460e6 + 6.98250e6i) q^{98} -3.50959e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9	\( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) 68 * q - 54 * q^4 - 4 * q^5 - 150 * q^6 + 48888 * q^9 + 13050 * q^16 + 23968 * q^17 - 79660 * q^20 - 232154 * q^24 + 937496 * q^25 - 391242 * q^26 - 37666 * q^28 - 468496 * q^30 - 1128652 * q^36 - 530466 * q^38 + 651806 * q^42 + 1433776 * q^44 - 321252 * q^45 - 4014380 * q^49 + 1697586 * q^54 + 137420 * q^57 + 2227894 * q^58 - 3042164 * q^61 + 2261524 * q^62 + 9825150 * q^64 - 749476 * q^66 - 11176962 * q^68 + 598424 * q^73 - 6195964 * q^74 - 1714536 * q^76 - 2556764 * q^77 + 16623216 * q^80 + 43726748 * q^81 - 20460388 * q^82 + 27222844 * q^85 - 61733582 * q^92 + 17778200 * q^93 - 36370886 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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