LMFDB - Embedded newform 76.8.d.a.75.13

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			75.13
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.59747 - 5.99070i) q^{2} -1.36022 q^{3} +(56.2230 + 114.991i) q^{4} +59.9018 q^{5} +(13.0547 + 8.14867i) q^{6} -254.899i q^{7} +(149.279 - 1440.44i) q^{8} -2185.15 q^{9} +O(q^{10})$	\(q+(-9.59747 - 5.99070i) q^{2} -1.36022 q^{3} +(56.2230 + 114.991i) q^{4} +59.9018 q^{5} +(13.0547 + 8.14867i) q^{6} -254.899i q^{7} +(149.279 - 1440.44i) q^{8} -2185.15 q^{9} +(-574.906 - 358.854i) q^{10} +5031.67i q^{11} +(-76.4756 - 156.413i) q^{12} -5860.07i q^{13} +(-1527.02 + 2446.39i) q^{14} -81.4796 q^{15} +(-10061.9 + 12930.3i) q^{16} +23510.7 q^{17} +(20971.9 + 13090.6i) q^{18} +(26650.7 + 13550.3i) q^{19} +(3367.86 + 6888.18i) q^{20} +346.719i q^{21} +(30143.2 - 48291.3i) q^{22} -18898.7i q^{23} +(-203.052 + 1959.31i) q^{24} -74536.8 q^{25} +(-35105.9 + 56241.8i) q^{26} +5947.08 q^{27} +(29311.1 - 14331.2i) q^{28} -116601. i q^{29} +(781.998 + 488.120i) q^{30} +28852.9 q^{31} +(174031. - 63820.1i) q^{32} -6844.17i q^{33} +(-225643. - 140845. i) q^{34} -15268.9i q^{35} +(-122856. - 251273. i) q^{36} -412015. i q^{37} +(-174603. - 289705. i) q^{38} +7970.98i q^{39} +(8942.09 - 86284.9i) q^{40} -42123.5i q^{41} +(2077.09 - 3327.62i) q^{42} -377606. i q^{43} +(-578597. + 282895. i) q^{44} -130894. q^{45} +(-113217. + 181380. i) q^{46} -1.20215e6i q^{47} +(13686.5 - 17588.0i) q^{48} +758570. q^{49} +(715365. + 446528. i) q^{50} -31979.7 q^{51} +(673856. - 329471. i) q^{52} -1.22067e6i q^{53} +(-57077.0 - 35627.2i) q^{54} +301406. i q^{55} +(-367167. - 38051.1i) q^{56} +(-36250.8 - 18431.4i) q^{57} +(-698522. + 1.11907e6i) q^{58} -618478. q^{59} +(-4581.03 - 9369.43i) q^{60} +1.20389e6 q^{61} +(-276914. - 172849. i) q^{62} +556992. i q^{63} +(-2.05258e6 - 430055. i) q^{64} -351029. i q^{65} +(-41001.4 + 65686.7i) q^{66} +3.49955e6 q^{67} +(1.32184e6 + 2.70352e6i) q^{68} +25706.4i q^{69} +(-91471.5 + 146543. i) q^{70} -5.00869e6 q^{71} +(-326197. + 3.14758e6i) q^{72} +4.87137e6 q^{73} +(-2.46826e6 + 3.95430e6i) q^{74} +101386. q^{75} +(-59785.9 + 3.82644e6i) q^{76} +1.28257e6 q^{77} +(47751.7 - 76501.3i) q^{78} -2.80653e6 q^{79} +(-602729. + 774548. i) q^{80} +4.77083e6 q^{81} +(-252349. + 404279. i) q^{82} -5.18427e6i q^{83} +(-39869.6 + 19493.6i) q^{84} +1.40833e6 q^{85} +(-2.26212e6 + 3.62406e6i) q^{86} +158603. i q^{87} +(7.24781e6 + 751123. i) q^{88} +2.38832e6i q^{89} +(1.25626e6 + 784149. i) q^{90} -1.49373e6 q^{91} +(2.17318e6 - 1.06254e6i) q^{92} -39246.2 q^{93} +(-7.20173e6 + 1.15376e7i) q^{94} +(1.59643e6 + 811689. i) q^{95} +(-236720. + 86809.3i) q^{96} +7.55047e6i q^{97} +(-7.28035e6 - 4.54436e6i) q^{98} -1.09949e7i 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 $

$2$	−9.59747	−	5.99070i	−0.848305	−	0.529508i
$2$	−9.59747	−	5.99070i	−0.848305	−	0.529508i
$3$	−1.36022			−0.0290860			−0.0145430	−	0.999894i	$-0.504629\pi$
$3$	−1.36022			−0.0290860			−0.0145430	+	0.999894i	$0.504629\pi$
$4$	56.2230	+	114.991i	0.439242	+	0.898369i
$5$	59.9018			0.214311			0.107156	−	0.994242i	$-0.465826\pi$
$5$	59.9018			0.214311			0.107156	+	0.994242i	$0.465826\pi$
$6$	13.0547	+	8.14867i	0.0246738	+	0.0154013i
$7$		−	254.899i		−	0.280883i	−0.990089	−	0.140441i	$-0.955148\pi$
$7$		−	254.899i		−	0.280883i	0.990089	−	0.140441i	$-0.0448521\pi$
$8$	149.279	−	1440.44i	0.103082	−	0.994673i
$9$	−2185.15			−0.999154
$10$	−574.906	−	358.854i	−0.181801	−	0.113480i
$11$			5031.67i			1.13982i	0.821706	+	0.569912i	$0.193023\pi$
$11$			5031.67i			1.13982i	−0.821706	+	0.569912i	$0.806977\pi$
$12$	−76.4756	−	156.413i	−0.0127758	−	0.0261300i
$13$		−	5860.07i		−	0.739777i	−0.929076	−	0.369889i	$-0.879396\pi$
$13$		−	5860.07i		−	0.739777i	0.929076	−	0.369889i	$-0.120604\pi$
$14$	−1527.02	+	2446.39i	−0.148730	+	0.238274i
$15$	−81.4796			−0.00623346
$16$	−10061.9	+	12930.3i	−0.614133	+	0.789203i
$17$	23510.7			1.16063			0.580315	−	0.814392i	$-0.302929\pi$
$17$	23510.7			1.16063			0.580315	+	0.814392i	$0.302929\pi$
$18$	20971.9	+	13090.6i	0.847587	+	0.529060i
$19$	26650.7	+	13550.3i	0.891397	+	0.453223i
$19$	26650.7	+	13550.3i	0.891397	+	0.453223i
$20$	3367.86	+	6888.18i	0.0941345	+	0.192530i
$21$			346.719i			0.00816976i
$22$	30143.2	−	48291.3i	0.603546	−	0.966917i
$23$		−	18898.7i		−	0.323880i	−0.986801	−	0.161940i	$-0.948225\pi$
$23$		−	18898.7i		−	0.323880i	0.986801	−	0.161940i	$-0.0517752\pi$
$24$	−203.052	+	1959.31i	−0.00299826	+	0.0289311i
$25$	−74536.8			−0.954071
$26$	−35105.9	+	56241.8i	−0.391718	+	0.627557i
$27$	5947.08			0.0581475
$28$	29311.1	−	14331.2i	0.252336	−	0.123376i
$29$		−	116601.i		−	0.887788i	−0.896079	−	0.443894i	$-0.853597\pi$
$29$		−	116601.i		−	0.887788i	0.896079	−	0.443894i	$-0.146403\pi$
$30$	781.998	+	488.120i	0.00528788	+	0.00330067i
$31$	28852.9			0.173949			0.0869747	−	0.996211i	$-0.472280\pi$
$31$	28852.9			0.173949			0.0869747	+	0.996211i	$0.472280\pi$
$32$	174031.	−	63820.1i	0.938861	−	0.344296i
$33$		−	6844.17i		−	0.0331529i
$34$	−225643.	−	140845.i	−0.984568	−	0.614563i
$35$		−	15268.9i		−	0.0601963i
$36$	−122856.	−	251273.i	−0.438871	−	0.897609i
$37$		−	412015.i		−	1.33723i	−0.743608	−	0.668616i	$-0.766887\pi$
$37$		−	412015.i		−	1.33723i	0.743608	−	0.668616i	$-0.233113\pi$
$38$	−174603.	−	289705.i	−0.516191	−	0.856474i
$39$			7970.98i			0.0215172i
$40$	8942.09	−	86284.9i	0.0220917	−	0.213170i
$41$		−	42123.5i		−	0.0954511i	−0.998860	−	0.0477255i	$-0.984803\pi$
$41$		−	42123.5i		−	0.0954511i	0.998860	−	0.0477255i	$-0.0151973\pi$
$42$	2077.09	−	3327.62i	0.00432596	−	0.00693045i
$43$		−	377606.i		−	0.724267i	−0.932126	−	0.362134i	$-0.882048\pi$
$43$		−	377606.i		−	0.724267i	0.932126	−	0.362134i	$-0.117952\pi$
$44$	−578597.	+	282895.i	−1.02398	+	0.500658i
$45$	−130894.			−0.214130
$46$	−113217.	+	181380.i	−0.171497	+	0.274749i
$47$		−	1.20215e6i		−	1.68895i	−0.535595	−	0.844475i	$-0.679913\pi$
$47$		−	1.20215e6i		−	1.68895i	0.535595	−	0.844475i	$-0.320087\pi$
$48$	13686.5	−	17588.0i	0.0178627	−	0.0229548i
$49$	758570.			0.921105
$50$	715365.	+	446528.i	0.809343	+	0.505188i
$51$	−31979.7			−0.0337581
$52$	673856.	−	329471.i	0.664593	−	0.324941i
$53$		−	1.22067e6i		−	1.12624i	−0.826375	−	0.563120i	$-0.809601\pi$
$53$		−	1.22067e6i		−	1.12624i	0.826375	−	0.563120i	$-0.190399\pi$
$54$	−57077.0	−	35627.2i	−0.0493268	−	0.0307896i
$55$			301406.i			0.244277i
$56$	−367167.	−	38051.1i	−0.279386	−	0.0289540i
$57$	−36250.8	−	18431.4i	−0.0259272	−	0.0131825i
$58$	−698522.	+	1.11907e6i	−0.470091	+	0.753115i
$59$	−618478.			−0.392051			−0.196025	−	0.980599i	$-0.562803\pi$
$59$	−618478.			−0.392051			−0.196025	+	0.980599i	$0.562803\pi$
$60$	−4581.03	−	9369.43i	−0.00273800	−	0.00559995i
$61$	1.20389e6			0.679098			0.339549	−	0.940588i	$-0.389726\pi$
$61$	1.20389e6			0.679098			0.339549	+	0.940588i	$0.389726\pi$
$62$	−276914.	−	172849.i	−0.147562	−	0.0921076i
$63$			556992.i			0.280645i
$64$	−2.05258e6	−	430055.i	−0.978748	−	0.205066i
$65$		−	351029.i		−	0.158543i
$66$	−41001.4	+	65686.7i	−0.0175548	+	0.0281238i
$67$	3.49955e6			1.42151			0.710756	−	0.703438i	$-0.248353\pi$
$67$	3.49955e6			1.42151			0.710756	+	0.703438i	$0.248353\pi$
$68$	1.32184e6	+	2.70352e6i	0.509798	+	1.04267i
$69$			25706.4i			0.00942040i
$70$	−91471.5	+	146543.i	−0.0318744	+	0.0510648i
$71$	−5.00869e6			−1.66081			−0.830405	−	0.557161i	$-0.811891\pi$
$71$	−5.00869e6			−1.66081			−0.830405	+	0.557161i	$0.811891\pi$
$72$	−326197.	+	3.14758e6i	−0.102995	+	0.993831i
$73$	4.87137e6			1.46562			0.732809	−	0.680434i	$-0.238209\pi$
$73$	4.87137e6			1.46562			0.732809	+	0.680434i	$0.238209\pi$
$74$	−2.46826e6	+	3.95430e6i	−0.708075	+	1.13438i
$75$	101386.			0.0277501
$76$	−59785.9	+	3.82644e6i	−0.0156225	+	0.999878i
$77$	1.28257e6			0.320157
$78$	47751.7	−	76501.3i	0.0113935	−	0.0182531i
$79$	−2.80653e6			−0.640435			−0.320218	−	0.947344i	$-0.603756\pi$
$79$	−2.80653e6			−0.640435			−0.320218	+	0.947344i	$0.603756\pi$
$80$	−602729.	+	774548.i	−0.131615	+	0.169135i
$81$	4.77083e6			0.997463
$82$	−252349.	+	404279.i	−0.0505421	+	0.0809716i
$83$		−	5.18427e6i		−	0.995209i	−0.867404	−	0.497604i	$-0.834213\pi$
$83$		−	5.18427e6i		−	0.995209i	0.867404	−	0.497604i	$-0.165787\pi$
$84$	−39869.6	+	19493.6i	−0.00733946	+	0.00358851i
$85$	1.40833e6			0.248736
$86$	−2.26212e6	+	3.62406e6i	−0.383506	+	0.614400i
$87$			158603.i			0.0258222i
$88$	7.24781e6	+	751123.i	1.13375	+	0.117496i
$89$			2.38832e6i			0.359109i	0.983748	+	0.179555i	$0.0574657\pi$
$89$			2.38832e6i			0.359109i	−0.983748	+	0.179555i	$0.942534\pi$
$90$	1.25626e6	+	784149.i	0.181647	+	0.113384i
$91$	−1.49373e6			−0.207791
$92$	2.17318e6	−	1.06254e6i	0.290964	−	0.142262i
$93$	−39246.2			−0.00505950
$94$	−7.20173e6	+	1.15376e7i	−0.894313	+	1.43274i
$95$	1.59643e6	+	811689.i	0.191036	+	0.0971308i
$96$	−236720.	+	86809.3i	−0.0273077	+	0.0100142i
$97$			7.55047e6i			0.839987i	0.907527	+	0.419994i	$0.137968\pi$
$97$			7.55047e6i			0.839987i	−0.907527	+	0.419994i	$0.862032\pi$
$98$	−7.28035e6	−	4.54436e6i	−0.781378	−	0.487733i
$99$		−	1.09949e7i		−	1.13886i
$100$	−4.19068e6	−	8.57107e6i	−0.419068	−	0.857107i
$101$	1.19892e7			1.15789			0.578943	−	0.815368i	$-0.303465\pi$
$101$	1.19892e7			1.15789			0.578943	+	0.815368i	$0.303465\pi$
$102$	306924.	+	191581.i	0.0286372	+	0.0178752i
$103$	−9.61064e6			−0.866607			−0.433303	−	0.901248i	$-0.642652\pi$
$103$	−9.61064e6			−0.866607			−0.433303	+	0.901248i	$0.642652\pi$
$104$	−8.44108e6	−	874786.i	−0.735836	−	0.0762579i
$105$			20769.1i			0.00175087i
$106$	−7.31264e6	+	1.17153e7i	−0.596354	+	0.955395i
$107$	−6.47522e6			−0.510989			−0.255494	−	0.966811i	$-0.582238\pi$
$107$	−6.47522e6			−0.510989			−0.255494	+	0.966811i	$0.582238\pi$
$108$	334363.	+	683862.i	0.0255408	+	0.0522379i
$109$		−	1.06715e7i		−	0.789280i	−0.918836	−	0.394640i	$-0.870869\pi$
$109$		−	1.06715e7i		−	0.789280i	0.918836	−	0.394640i	$-0.129131\pi$
$110$	1.80563e6	−	2.89273e6i	0.129347	−	0.207221i
$111$			560431.i			0.0388948i
$112$	3.29592e6	+	2.56478e6i	0.221673	+	0.172499i
$113$		−	2.42665e7i		−	1.58210i	−0.611753	−	0.791049i	$-0.709535\pi$
$113$		−	2.42665e7i		−	1.58210i	0.611753	−	0.791049i	$-0.290465\pi$
$114$	237499.	+	394063.i	0.0150139	+	0.0249114i
$115$		−	1.13207e6i		−	0.0694112i
$116$	1.34081e7	−	6.55566e6i	0.797561	−	0.389954i
$117$			1.28051e7i			0.739151i
$118$	5.93583e6	+	3.70512e6i	0.332578	+	0.207594i
$119$		−	5.99285e6i		−	0.326001i
$120$	−12163.2	+	117366.i	−0.000642560	+	0.00620026i
$121$	−5.83050e6			−0.299197
$122$	−1.15543e7	−	7.21214e6i	−0.576082	−	0.359588i
$123$			57297.2i			0.00277629i
$124$	1.62219e6	+	3.31782e6i	0.0764059	+	0.156271i
$125$	−9.14471e6			−0.418779
$126$	3.33678e6	−	5.34572e6i	0.148604	−	0.238073i
$127$	3.61018e7			1.56392			0.781962	−	0.623327i	$-0.214219\pi$
$127$	3.61018e7			1.56392			0.781962	+	0.623327i	$0.214219\pi$
$128$	1.71233e7	+	1.64239e7i	0.721692	+	0.692214i
$129$			513627.i			0.0210661i
$130$	−2.10291e6	+	3.36899e6i	−0.0839496	+	0.134492i
$131$			8.16284e6i			0.317243i	0.987339	+	0.158621i	$0.0507049\pi$
$131$			8.16284e6i			0.317243i	−0.987339	+	0.158621i	$0.949295\pi$
$132$	787019.	−	384800.i	0.0297836	−	0.0145622i
$133$	3.45397e6	−	6.79324e6i	0.127303	−	0.250378i
$134$	−3.35869e7	−	2.09648e7i	−1.20588	−	0.752702i
$135$	356241.			0.0124617
$136$	3.50965e6	−	3.38657e7i	0.119640	−	1.15445i
$137$	−1.46485e7			−0.486710			−0.243355	−	0.969937i	$-0.578248\pi$
$137$	−1.46485e7			−0.486710			−0.243355	+	0.969937i	$0.578248\pi$
$138$	153999.	−	246716.i	0.00498818	−	0.00799137i
$139$			4.99434e7i			1.57734i	0.614815	+	0.788671i	$0.289231\pi$
$139$			4.99434e7i			1.57734i	−0.614815	+	0.788671i	$0.710769\pi$
$140$	1.75579e6	−	858464.i	0.0540785	−	0.0264408i
$141$			1.63519e6i			0.0491249i
$142$	4.80708e7	+	3.00056e7i	1.40887	+	0.879412i
$143$	2.94859e7			0.843215
$144$	2.19869e7	−	2.82546e7i	0.613613	−	0.788535i
$145$		−	6.98461e6i		−	0.190263i
$146$	−4.67528e7	−	2.91829e7i	−1.24329	−	0.776057i
$147$	−1.03182e6			−0.0267913
$148$	4.73781e7	−	2.31647e7i	1.20133	−	0.587369i
$149$	−1.04112e7			−0.257839			−0.128919	−	0.991655i	$-0.541151\pi$
$149$	−1.04112e7			−0.257839			−0.128919	+	0.991655i	$0.541151\pi$
$150$	−973053.	−	607375.i	−0.0235406	−	0.0146939i
$151$	1.45002e7			0.342732			0.171366	−	0.985207i	$-0.445182\pi$
$151$	1.45002e7			0.342732			0.171366	+	0.985207i	$0.445182\pi$
$152$	2.34968e7	−	3.63660e7i	0.542696	−	0.839929i
$153$	−5.13743e7			−1.15965
$154$	−1.23094e7	−	7.68347e6i	−0.271590	−	0.169526i
$155$	1.72834e6			0.0372793
$156$	−916592.	+	448152.i	−0.0193304	+	0.00945126i
$157$	−6.31804e7			−1.30297			−0.651483	−	0.758663i	$-0.725853\pi$
$157$	−6.31804e7			−1.30297			−0.651483	+	0.758663i	$0.725853\pi$
$158$	2.69356e7	+	1.68131e7i	0.543284	+	0.339116i
$159$			1.66037e6i			0.0327579i
$160$	1.04248e7	−	3.82294e6i	0.201208	−	0.0737866i
$161$	−4.81726e6			−0.0909724
$162$	−4.57879e7	−	2.85806e7i	−0.846152	−	0.528165i
$163$		−	2.10168e7i		−	0.380110i	−0.981773	−	0.190055i	$-0.939133\pi$
$163$		−	2.10168e7i		−	0.380110i	0.981773	−	0.190055i	$-0.0608667\pi$
$164$	4.84383e6	−	2.36831e6i	0.0857503	−	0.0419261i
$165$		−	409978.i		−	0.00710505i
$166$	−3.10574e7	+	4.97559e7i	−0.526971	+	0.844240i
$167$	−7.39391e7			−1.22848			−0.614238	−	0.789121i	$-0.710536\pi$
$167$	−7.39391e7			−1.22848			−0.614238	+	0.789121i	$0.710536\pi$
$168$	499427.	+	51757.8i	0.00812624	+	0.000842158i
$169$	2.84081e7			0.452730
$170$	−1.35164e7	−	8.43689e6i	−0.211004	−	0.131708i
$171$	−5.82358e7	−	2.96095e7i	−0.890643	−	0.452840i
$172$	4.34213e7	−	2.12301e7i	0.650659	−	0.318129i
$173$			5.29824e7i			0.777983i	0.921241	+	0.388992i	$0.127176\pi$
$173$			5.29824e7i			0.777983i	−0.921241	+	0.388992i	$0.872824\pi$
$174$	950143.	−	1.52219e6i	0.0136731	−	0.0219051i
$175$			1.89993e7i			0.267982i
$176$	−6.50610e7	−	5.06284e7i	−0.899552	−	0.700003i
$177$	841266.			0.0114032
$178$	1.43077e7	−	2.29218e7i	0.190151	−	0.304634i
$179$	1.29684e8			1.69005			0.845027	−	0.534724i	$-0.179584\pi$
$179$	1.29684e8			1.69005			0.845027	+	0.534724i	$0.179584\pi$
$180$	−7.35928e6	−	1.50517e7i	−0.0940549	−	0.192368i
$181$			4.90787e7i			0.615202i	0.951515	+	0.307601i	$0.0995262\pi$
$181$			4.90787e7i			0.615202i	−0.951515	+	0.307601i	$0.900474\pi$
$182$	1.43360e7	+	8.94846e6i	0.176270	+	0.110027i
$183$	−1.63755e6			−0.0197523
$184$	−2.72225e7	−	2.82118e6i	−0.322155	−	0.0333863i
$185$		−	2.46804e7i		−	0.286584i
$186$	376664.	+	235112.i	0.00429200	+	0.00267905i
$187$			1.18298e8i			1.32291i
$188$	1.38237e8	−	6.75886e7i	1.51730	−	0.741858i
$189$		−	1.51591e6i		−	0.0163326i
$190$	−1.04591e7	−	1.73539e7i	−0.110625	−	0.183552i
$191$		−	8.28854e7i		−	0.860718i	−0.902658	−	0.430359i	$-0.858387\pi$
$191$		−	8.28854e7i		−	0.860718i	0.902658	−	0.430359i	$-0.141613\pi$
$192$	2.79196e6	+	584969.i	0.0284679	+	0.00596457i
$193$			1.64768e8i			1.64977i	0.565302	+	0.824884i	$0.308760\pi$
$193$			1.64768e8i			1.64977i	−0.565302	+	0.824884i	$0.691240\pi$
$194$	4.52326e7	−	7.24654e7i	0.444780	−	0.712565i
$195$			477476.i			0.00461137i
$196$	4.26491e7	+	8.72288e7i	0.404588	+	0.827492i
$197$	−4.79190e7			−0.446556			−0.223278	−	0.974755i	$-0.571676\pi$
$197$	−4.79190e7			−0.446556			−0.223278	+	0.974755i	$0.571676\pi$
$198$	−6.58674e7	+	1.05524e8i	−0.603035	+	0.966099i
$199$			1.30874e8i			1.17725i	0.808407	+	0.588624i	$0.200330\pi$
$199$			1.30874e8i			1.17725i	−0.808407	+	0.588624i	$0.799670\pi$
$200$	−1.11268e7	+	1.07366e8i	−0.0983478	+	0.948988i
$201$	−4.76016e6			−0.0413462
$202$	−1.15066e8	−	7.18238e7i	−0.982241	−	0.613111i
$203$	−2.97215e7			−0.249364
$204$	−1.79799e6	−	3.67738e6i	−0.0148280	−	0.0303273i
$205$		−	2.52327e6i		−	0.0204562i
$206$	9.22379e7	+	5.75745e7i	0.735147	+	0.458875i
$207$			4.12965e7i			0.323606i
$208$	7.57724e7	+	5.89637e7i	0.583834	+	0.454321i
$209$	−6.81807e7	+	1.34097e8i	−0.516594	+	1.01603i
$210$	124421.	−	199331.i	0.000927101	−	0.00148527i
$211$	−8.86686e7			−0.649802			−0.324901	−	0.945748i	$-0.605331\pi$
$211$	−8.86686e7			−0.649802			−0.324901	+	0.945748i	$0.605331\pi$
$212$	1.40366e8	−	6.86295e7i	1.01178	−	0.494692i
$213$	6.81292e6			0.0483064
$214$	6.21458e7	+	3.87911e7i	0.433474	+	0.270573i
$215$		−	2.26193e7i		−	0.155219i
$216$	887775.	−	8.56642e6i	0.00599397	−	0.0578377i
$217$		−	7.35456e6i		−	0.0488594i
$218$	−6.39295e7	+	1.02419e8i	−0.417930	+	0.669550i
$219$	−6.62613e6			−0.0426291
$220$	−3.46590e7	+	1.69459e7i	−0.219451	+	0.107297i
$221$		−	1.37774e8i		−	0.858608i
$222$	3.35737e6	−	5.37872e6i	0.0205951	−	0.0329946i
$223$	6.78902e7			0.409959			0.204979	−	0.978766i	$-0.434287\pi$
$223$	6.78902e7			0.409959			0.204979	+	0.978766i	$0.434287\pi$
$224$	−1.62677e7	−	4.43603e7i	−0.0967069	−	0.263710i
$225$	1.62874e8			0.953264
$226$	−1.45374e8	+	2.32897e8i	−0.837734	+	1.34210i
$227$	1.99723e7			0.113328			0.0566641	−	0.998393i	$-0.481954\pi$
$227$	1.99723e7			0.113328			0.0566641	+	0.998393i	$0.481954\pi$
$228$	81322.0	−	5.20479e6i	0.000454398	−	0.0290825i
$229$	8.04097e7			0.442470			0.221235	−	0.975220i	$-0.428991\pi$
$229$	8.04097e7			0.442470			0.221235	+	0.975220i	$0.428991\pi$
$230$	−6.78187e6	+	1.08650e7i	−0.0367538	+	0.0588819i
$231$	−1.74457e6			−0.00931209
$232$	−1.67957e8	−	1.74061e7i	−0.883059	−	0.0915152i
$233$	−9.38810e6			−0.0486219			−0.0243110	−	0.999704i	$-0.507739\pi$
$233$	−9.38810e6			−0.0486219			−0.0243110	+	0.999704i	$0.507739\pi$
$234$	7.67117e7	−	1.22897e8i	0.391387	−	0.627026i
$235$		−	7.20110e7i		−	0.361961i
$236$	−3.47727e7	−	7.11195e7i	−0.172205	−	0.352206i
$237$	3.81750e6			0.0186277
$238$	−3.59014e7	+	5.75162e7i	−0.172620	+	0.276548i
$239$			1.71095e8i			0.810672i	0.914168	+	0.405336i	$0.132845\pi$
$239$			1.71095e8i			0.810672i	−0.914168	+	0.405336i	$0.867155\pi$
$240$	819843.	−	1.05356e6i	0.00382817	−	0.00491947i
$241$		−	3.36062e8i		−	1.54654i	−0.634080	−	0.773268i	$-0.718621\pi$
$241$		−	3.36062e8i		−	1.54654i	0.634080	−	0.773268i	$-0.281379\pi$
$242$	5.59580e7	+	3.49288e7i	0.253810	+	0.158427i
$243$	−1.94957e7			−0.0871597
$244$	6.76863e7	+	1.38437e8i	0.298288	+	0.610080i
$245$	4.54397e7			0.197403
$246$	343250.	−	549908.i	0.00147007	−	0.00235514i
$247$	7.94059e7	−	1.56175e8i	0.335284	−	0.659435i
$248$	4.30713e6	−	4.15608e7i	0.0179311	−	0.173023i
$249$			7.05174e6i			0.0289467i
$250$	8.77662e7	+	5.47832e7i	0.355252	+	0.221747i
$251$		−	1.13733e8i		−	0.453972i	−0.973898	−	0.226986i	$-0.927113\pi$
$251$		−	1.13733e8i		−	0.453972i	0.973898	−	0.226986i	$-0.0728871\pi$
$252$	−6.40492e7	+	3.13158e7i	−0.252123	+	0.123271i
$253$	9.50920e7			0.369166
$254$	−3.46486e8	−	2.16275e8i	−1.32668	−	0.828110i
$255$	−1.91564e6			−0.00723475
$256$	−6.59498e7	−	2.60208e8i	−0.245682	−	0.969350i
$257$			3.84283e7i			0.141217i	0.997504	+	0.0706083i	$0.0224940\pi$
$257$			3.84283e7i			0.141217i	−0.997504	+	0.0706083i	$0.977506\pi$
$258$	3.07698e6	−	4.92952e6i	0.0111547	−	0.0178704i
$259$	−1.05022e8			−0.375605
$260$	4.03652e7	−	1.97359e7i	0.142430	−	0.0696386i
$261$			2.54791e8i			0.887037i
$262$	4.89011e7	−	7.83426e7i	0.167983	−	0.269118i
$263$		−	2.54125e8i		−	0.861396i	−0.902496	−	0.430698i	$-0.858267\pi$
$263$		−	2.54125e8i		−	0.861396i	0.902496	−	0.430698i	$-0.141733\pi$
$264$	−9.85862e6	−	1.02169e6i	−0.0329763	−	0.00341748i
$265$		−	7.31201e7i		−	0.241366i
$266$	−7.38456e7	+	4.45063e7i	−0.240569	+	0.144989i
$267$		−	3.24863e6i		−	0.0104451i
$268$	1.96755e8	+	4.02418e8i	0.624388	+	1.27704i
$269$		−	5.05355e8i		−	1.58294i	−0.611209	−	0.791469i	$-0.709317\pi$
$269$		−	5.05355e8i		−	1.58294i	0.611209	−	0.791469i	$-0.290683\pi$
$270$	−3.41901e6	−	2.13413e6i	−0.0105713	−	0.00659855i
$271$		−	3.71301e8i		−	1.13327i	−0.823969	−	0.566635i	$-0.808245\pi$
$271$		−	3.71301e8i		−	1.13327i	0.823969	−	0.566635i	$-0.191755\pi$
$272$	−2.36563e8	+	3.04000e8i	−0.712781	+	0.915973i
$273$	2.03179e6			0.00604381
$274$	1.40588e8	+	8.77546e7i	0.412878	+	0.257717i
$275$		−	3.75044e8i		−	1.08747i
$276$	−2.95601e6	+	1.44529e6i	−0.00846299	+	0.00413784i
$277$	2.33010e8			0.658711			0.329356	−	0.944206i	$-0.393169\pi$
$277$	2.33010e8			0.658711			0.329356	+	0.944206i	$0.393169\pi$
$278$	2.99196e8	−	4.79330e8i	0.835216	−	1.33807i
$279$	−6.30478e7			−0.173802
$280$	−2.19939e7	−	2.27933e6i	−0.0598756	−	0.00620517i
$281$		−	5.89101e8i		−	1.58386i	−0.610609	−	0.791932i	$-0.709075\pi$
$281$		−	5.89101e8i		−	1.58386i	0.610609	−	0.791932i	$-0.290925\pi$
$282$	9.79593e6	−	1.56937e7i	0.0260120	−	0.0416729i
$283$			1.56644e8i			0.410828i	0.978675	+	0.205414i	$0.0658541\pi$
$283$			1.56644e8i			0.410828i	−0.978675	+	0.205414i	$0.934146\pi$
$284$	−2.81603e8	−	5.75955e8i	−0.729498	−	1.49202i
$285$	−2.17149e6	−	1.10408e6i	−0.00555649	−	0.00282515i
$286$	−2.82990e8	−	1.76641e8i	−0.715303	−	0.446489i
$287$	−1.07372e7			−0.0268106
$288$	−3.80283e8	+	1.39456e8i	−0.938067	+	0.344005i
$289$	1.42413e8			0.347063
$290$	−4.18427e7	+	6.70346e7i	−0.100746	+	0.161401i
$291$		−	1.02703e7i		−	0.0244319i
$292$	2.73883e8	+	5.60165e8i	0.643762	+	1.31667i
$293$			1.29551e8i			0.300888i	0.988619	+	0.150444i	$0.0480704\pi$
$293$			1.29551e8i			0.300888i	−0.988619	+	0.150444i	$0.951930\pi$
$294$	9.90287e6	+	6.18133e6i	0.0227272	+	0.0141862i
$295$	−3.70479e7			−0.0840208
$296$	−5.93483e8	−	6.15052e7i	−1.33011	−	0.137845i
$297$			2.99237e7i			0.0662778i
$298$	9.99210e7	+	6.23703e7i	0.218726	+	0.136528i
$299$	−1.10748e8			−0.239599
$300$	5.70025e6	+	1.16585e7i	0.0121890	+	0.0249299i
$301$	−9.62513e7			−0.203434
$302$	−1.39165e8	−	8.68664e7i	−0.290741	−	0.181480i
$303$	−1.63080e7			−0.0336783
$304$	−4.43368e8	+	2.08259e8i	−0.905121	+	0.425154i
$305$	7.21152e7			0.145538
$306$	4.93064e8	+	3.07768e8i	0.983735	+	0.614043i
$307$	−3.37575e8			−0.665864			−0.332932	−	0.942951i	$-0.608038\pi$
$307$	−3.37575e8			−0.665864			−0.332932	+	0.942951i	$0.608038\pi$
$308$	7.21097e7	+	1.47484e8i	0.140626	+	0.287619i
$309$	1.30726e7			0.0252062
$310$	−1.65877e7	−	1.03540e7i	−0.0316242	−	0.0197397i
$311$			3.39278e8i			0.639580i	0.947488	+	0.319790i	$0.103612\pi$
$311$			3.39278e8i			0.639580i	−0.947488	+	0.319790i	$0.896388\pi$
$312$	1.14817e7	+	1.18990e6i	0.0214026	+	0.00221804i
$313$	6.02290e8			1.11020			0.555099	−	0.831784i	$-0.312680\pi$
$313$	6.02290e8			1.11020			0.555099	+	0.831784i	$0.312680\pi$
$314$	6.06372e8	+	3.78495e8i	1.10531	+	0.689931i
$315$			3.33648e7i			0.0601454i
$316$	−1.57792e8	−	3.22727e8i	−0.281306	−	0.575347i
$317$		−	6.39970e8i		−	1.12837i	−0.825648	−	0.564186i	$-0.809190\pi$
$317$		−	6.39970e8i		−	1.12837i	0.825648	−	0.564186i	$-0.190810\pi$
$318$	9.94680e6	−	1.59354e7i	0.0173456	−	0.0277887i
$319$	5.86697e8			1.01192
$320$	−1.22953e8	−	2.57611e7i	−0.209757	−	0.0439480i
$321$	8.80772e6			0.0148626
$322$	4.62335e7	+	2.88588e7i	0.0771723	+	0.0481706i
$323$	6.26576e8	+	3.18577e8i	1.03458	+	0.526025i
$324$	2.68231e8	+	5.48604e8i	0.438128	+	0.896089i
$325$			4.36791e8i			0.705800i
$326$	−1.25905e8	+	2.01708e8i	−0.201271	+	0.322449i
$327$			1.45155e7i			0.0229570i
$328$	−6.06764e7	−	6.28816e6i	−0.0949426	−	0.00983931i
$329$	−3.06427e8			−0.474397
$330$	−2.45606e6	+	3.93475e6i	−0.00376218	+	0.00602724i
$331$	−8.36585e8			−1.26798			−0.633989	−	0.773342i	$-0.718584\pi$
$331$	−8.36585e8			−1.26798			−0.633989	+	0.773342i	$0.718584\pi$
$332$	5.96145e8	−	2.91475e8i	0.894064	−	0.437138i
$333$			9.00314e8i			1.33610i
$334$	7.09628e8	+	4.42947e8i	1.04212	+	0.650488i
$335$	2.09629e8			0.304646
$336$	−4.48317e6	−	3.48866e6i	−0.00644760	−	0.00501732i
$337$			7.49773e8i			1.06715i	0.845753	+	0.533574i	$0.179152\pi$
$337$			7.49773e8i			1.06715i	−0.845753	+	0.533574i	$0.820848\pi$
$338$	−2.72646e8	−	1.70185e8i	−0.384053	−	0.239724i
$339$			3.30078e7i			0.0460170i
$340$	7.91806e7	+	1.61946e8i	0.109255	+	0.223457i
$341$			1.45178e8i			0.198271i
$342$	3.81535e8	+	6.33050e8i	0.515754	+	0.855749i
$343$		−	4.03279e8i		−	0.539605i
$344$	−5.43918e8	−	5.63686e7i	−0.720409	−	0.0746591i
$345$			1.53986e6i			0.00201890i
$346$	3.17402e8	−	5.08497e8i	0.411948	−	0.659967i
$347$			1.13846e9i			1.46273i	0.681987	+	0.731364i	$0.261116\pi$
$347$			1.13846e9i			1.46273i	−0.681987	+	0.731364i	$0.738884\pi$
$348$	−1.82379e7	+	8.91713e6i	−0.0231979	+	0.0113422i
$349$	3.28510e8			0.413675			0.206838	−	0.978375i	$-0.433683\pi$
$349$	3.28510e8			0.413675			0.206838	+	0.978375i	$0.433683\pi$
$350$	1.13819e8	−	1.82346e8i	0.141899	−	0.227330i
$351$		−	3.48503e7i		−	0.0430162i
$352$	3.21121e8	+	8.75665e8i	0.392437	+	1.07014i
$353$	−8.16440e8			−0.987900			−0.493950	−	0.869490i	$-0.664447\pi$
$353$	−8.16440e8			−0.987900			−0.493950	+	0.869490i	$0.664447\pi$
$354$	−8.07403e6	−	5.03977e6i	−0.00967339	−	0.00603809i
$355$	−3.00029e8			−0.355930
$356$	−2.74635e8	+	1.34278e8i	−0.322613	+	0.157736i
$357$			8.15159e6i			0.00948208i
$358$	−1.24464e9	−	7.76897e8i	−1.43368	−	0.894897i
$359$		−	2.50076e8i		−	0.285260i	−0.989776	−	0.142630i	$-0.954444\pi$
$359$		−	2.50076e8i		−	0.285260i	0.989776	−	0.142630i	$-0.0455560\pi$
$360$	−1.95398e7	+	1.88546e8i	−0.0220730	+	0.212989i
$361$	5.26649e8	+	7.22252e8i	0.589177	+	0.808004i
$362$	2.94016e8	−	4.71031e8i	0.325754	−	0.521879i
$363$	7.93075e6			0.00870245
$364$	−8.39817e7	−	1.71765e8i	−0.0912704	−	0.186673i
$365$	2.91804e8			0.314099
$366$	1.57164e7	+	9.81010e6i	0.0167559	+	0.0104590i
$367$		−	2.85531e8i		−	0.301524i	−0.988570	−	0.150762i	$-0.951827\pi$
$367$		−	2.85531e8i		−	0.301524i	0.988570	−	0.150762i	$-0.0481727\pi$
$368$	2.44366e8	+	1.90158e8i	0.255607	+	0.198906i
$369$			9.20461e7i			0.0953703i
$370$	−1.47853e8	+	2.36870e8i	−0.151748	+	0.243110i
$371$	−3.11146e8			−0.316341
$372$	−2.20654e6	−	4.51297e6i	−0.00222234	−	0.00454529i
$373$		−	9.83051e8i		−	0.980833i	−0.871488	−	0.490416i	$-0.836845\pi$
$373$		−	9.83051e8i		−	0.980833i	0.871488	−	0.490416i	$-0.163155\pi$
$374$	7.08687e8	−	1.13536e9i	0.700493	−	1.12223i
$375$	1.24388e7			0.0121806
$376$	−1.73163e9	−	1.79456e8i	−1.67995	−	0.174101i
$377$	−6.83290e8			−0.656765
$378$	−9.08134e6	+	1.45489e7i	−0.00864825	+	0.0138550i
$379$	−1.01345e9			−0.956237			−0.478118	−	0.878295i	$-0.658681\pi$
$379$	−1.01345e9			−0.956237			−0.478118	+	0.878295i	$0.658681\pi$
$380$	−3.58128e6	+	2.29210e8i	−0.00334808	+	0.214285i
$381$	−4.91063e7			−0.0454883
$382$	−4.96541e8	+	7.95490e8i	−0.455757	+	0.730151i
$383$	7.20156e8			0.654985			0.327492	−	0.944854i	$-0.393796\pi$
$383$	7.20156e8			0.654985			0.327492	+	0.944854i	$0.393796\pi$
$384$	−2.32914e7	−	2.23401e7i	−0.0209912	−	0.0201338i
$385$	7.68280e7			0.0686131
$386$	9.87077e8	−	1.58136e9i	0.873566	−	1.39951i
$387$			8.25125e8i			0.723655i
$388$	−8.68237e8	+	4.24510e8i	−0.754618	+	0.368958i
$389$	−1.55137e9			−1.33627			−0.668133	−	0.744042i	$-0.732906\pi$
$389$	−1.55137e9			−1.33627			−0.668133	+	0.744042i	$0.732906\pi$
$390$	2.86042e6	−	4.58256e6i	0.00244176	−	0.00391185i
$391$		−	4.44321e8i		−	0.375905i
$392$	1.13239e8	−	1.09267e9i	0.0949496	−	0.916198i
$393$		−	1.11032e7i		−	0.00922733i
$394$	4.59901e8	+	2.87068e8i	0.378816	+	0.236455i
$395$	−1.68116e8			−0.137252
$396$	1.26432e9	−	6.18169e8i	1.02312	−	0.500235i
$397$	−1.62177e9			−1.30083			−0.650416	−	0.759578i	$-0.725405\pi$
$397$	−1.62177e9			−1.30083			−0.650416	+	0.759578i	$0.725405\pi$
$398$	7.84028e8	−	1.25606e9i	0.623363	−	0.998665i
$399$	−4.69815e6	+	9.24030e6i	−0.00370273	+	0.00728250i
$400$	7.49985e8	−	9.63783e8i	0.585926	−	0.752955i
$401$			6.46218e8i			0.500465i	0.968186	+	0.250233i	$0.0805071\pi$
$401$			6.46218e8i			0.500465i	−0.968186	+	0.250233i	$0.919493\pi$
$402$	4.56855e7	+	2.85167e7i	0.0350742	+	0.0218931i
$403$		−	1.69080e8i		−	0.128684i
$404$	6.74070e8	+	1.37865e9i	0.508593	+	1.04021i
$405$	2.85781e8			0.213767
$406$	2.85251e8	+	1.78052e8i	0.211537	+	0.132040i
$407$	2.07312e9			1.52421
$408$	−4.77390e6	+	4.60648e7i	−0.00347987	+	0.0335783i
$409$			1.95371e9i			1.41198i	0.708223	+	0.705989i	$0.249497\pi$
$409$			1.95371e9i			1.41198i	−0.708223	+	0.705989i	$0.750503\pi$
$410$	−1.51162e7	+	2.42170e7i	−0.0108317	+	0.0173531i
$411$	1.99251e7			0.0141565
$412$	−5.40339e8	−	1.10514e9i	−0.380650	−	0.778532i
$413$			1.57649e8i			0.110120i
$414$	2.47395e8	−	3.96342e8i	0.171352	−	0.274517i
$415$		−	3.10547e8i		−	0.213284i
$416$	−3.73990e8	−	1.01983e9i	−0.254703	−	0.694548i
$417$		−	6.79339e7i		−	0.0458786i
$418$	1.45770e9	−	8.78547e8i	0.976228	−	0.588366i
$419$			1.86031e8i			0.123548i	0.998090	+	0.0617742i	$0.0196759\pi$
$419$			1.86031e8i			0.123548i	−0.998090	+	0.0617742i	$0.980324\pi$
$420$	−2.38826e6	+	1.16770e6i	−0.00157293	+	0.000769057i
$421$			2.21882e8i			0.144922i	0.997371	+	0.0724609i	$0.0230853\pi$
$421$			2.21882e8i			0.144922i	−0.997371	+	0.0724609i	$0.976915\pi$
$422$	8.50994e8	+	5.31187e8i	0.551230	+	0.344076i
$423$			2.62688e9i			1.68752i
$424$	−1.75830e9	−	1.82220e8i	−1.12024	−	0.116095i
$425$	−1.75241e9			−1.10732
$426$	−6.53868e7	−	4.08141e7i	−0.0409785	−	0.0255786i
$427$		−	3.06870e8i		−	0.190747i
$428$	−3.64056e8	−	7.44593e8i	−0.224448	−	0.459056i
$429$	−4.01073e7			−0.0245258
$430$	−1.35505e8	+	2.17088e8i	−0.0821895	+	0.131673i
$431$	2.25776e8			0.135833			0.0679167	−	0.997691i	$-0.478365\pi$
$431$	2.25776e8			0.135833			0.0679167	+	0.997691i	$0.478365\pi$
$432$	−5.98392e7	+	7.68976e7i	−0.0357103	+	0.0458902i
$433$		−	2.32222e9i		−	1.37466i	−0.726344	−	0.687331i	$-0.758782\pi$
$433$		−	2.32222e9i		−	1.37466i	0.726344	−	0.687331i	$-0.241218\pi$
$434$	−4.40590e7	+	7.05852e7i	−0.0258714	+	0.0414476i
$435$			9.50060e6i			0.00553399i
$436$	1.22712e9	−	5.99981e8i	0.709064	−	0.346685i
$437$	2.56084e8	−	5.03664e8i	0.146790	−	0.288706i
$438$	6.35941e7	+	3.96952e7i	0.0361624	+	0.0225724i
$439$	1.95077e9			1.10047			0.550237	−	0.835008i	$-0.314537\pi$
$439$	1.95077e9			1.10047			0.550237	+	0.835008i	$0.314537\pi$
$440$	4.34157e8	+	4.49936e7i	0.242976	+	0.0251806i
$441$	−1.65759e9			−0.920326
$442$	−8.25364e8	+	1.32228e9i	−0.454640	+	0.728361i
$443$		−	1.02331e6i		−	0.000559236i	−1.00000		0.000279618i	$-0.999911\pi$
$443$		−	1.02331e6i		−	0.000559236i	1.00000		0.000279618i	$-8.90051e-5\pi$
$444$	−6.44446e7	+	3.15091e7i	−0.0349419	+	0.0170842i
$445$			1.43064e8i			0.0769611i
$446$	−6.51574e8	−	4.06710e8i	−0.347770	−	0.217076i
$447$	1.41615e7			0.00749950
$448$	−1.09621e8	+	5.23201e8i	−0.0575996	+	0.274913i
$449$		−	3.36338e9i		−	1.75353i	−0.480918	−	0.876765i	$-0.659697\pi$
$449$		−	3.36338e9i		−	1.75353i	0.480918	−	0.876765i	$-0.340303\pi$
$450$	−1.56318e9	−	9.75730e8i	−0.808658	−	0.504761i
$451$	2.11951e8			0.108797
$452$	2.79044e9	−	1.36434e9i	1.42131	−	0.694924i
$453$	−1.97235e7			−0.00996872
$454$	−1.91684e8	−	1.19648e8i	−0.0961368	−	0.0600082i
$455$	−8.94768e7			−0.0445318
$456$	−3.19609e7	+	4.94657e7i	−0.0157849	+	0.0244302i
$457$	2.71435e9			1.33033			0.665164	−	0.746697i	$-0.268362\pi$
$457$	2.71435e9			1.33033			0.665164	+	0.746697i	$0.268362\pi$
$458$	−7.71730e8	−	4.81710e8i	−0.375350	−	0.234292i
$459$	1.39820e8			0.0674877
$460$	1.30178e8	−	6.36482e7i	0.0623568	−	0.0304883i
$461$	−3.25986e8			−0.154969			−0.0774847	−	0.996994i	$-0.524689\pi$
$461$	−3.25986e8			−0.154969			−0.0774847	+	0.996994i	$0.524689\pi$
$462$	1.67435e7	+	1.04512e7i	0.00789949	+	0.00493083i
$463$			6.99885e8i			0.327713i	0.986484	+	0.163856i	$0.0523934\pi$
$463$			6.99885e8i			0.327713i	−0.986484	+	0.163856i	$0.947607\pi$
$464$	1.50769e9	+	1.17323e9i	0.700645	+	0.545220i
$465$	−2.35092e6			−0.00108431
$466$	9.01021e7	+	5.62413e7i	0.0412462	+	0.0257457i
$467$			2.25108e9i			1.02278i	0.859349	+	0.511390i	$0.170869\pi$
$467$			2.25108e9i			1.02278i	−0.859349	+	0.511390i	$0.829131\pi$
$468$	−1.47248e9	+	7.19943e8i	−0.664030	+	0.324666i
$469$		−	8.92032e8i		−	0.399278i
$470$	−4.31397e8	+	6.91124e8i	−0.191661	+	0.307053i
$471$	8.59391e7			0.0378981
$472$	−9.23258e7	+	8.90880e8i	−0.0404135	+	0.389962i
$473$	1.89999e9			0.825537
$474$	−3.66384e7	−	2.28695e7i	−0.0158020	−	0.00986353i
$475$	−1.98646e9	−	1.01000e9i	−0.850456	−	0.432407i
$476$	6.89125e8	−	3.36936e8i	0.292869	−	0.143193i
$477$			2.66734e9i			1.12529i
$478$	1.02498e9	−	1.64208e9i	0.429257	−	0.687697i
$479$		−	2.78889e9i		−	1.15947i	−0.814807	−	0.579733i	$-0.803157\pi$
$479$		−	2.78889e9i		−	1.15947i	0.814807	−	0.579733i	$-0.196843\pi$
$480$	−1.41800e7	+	5.20003e6i	−0.00585236	+	0.00214616i
$481$	−2.41443e9			−0.989254
$482$	−2.01325e9	+	3.22535e9i	−0.818903	+	1.31193i
$483$	6.55253e6			0.00264603
$484$	−3.27808e8	−	6.70456e8i	−0.131420	−	0.268789i
$485$			4.52286e8i			0.180019i
$486$	1.87109e8	+	1.16793e8i	0.0739380	+	0.0461518i
$487$	−1.24636e9			−0.488983			−0.244491	−	0.969651i	$-0.578621\pi$
$487$	−1.24636e9			−0.488983			−0.244491	+	0.969651i	$0.578621\pi$
$488$	1.79716e8	−	1.73413e9i	0.0700030	−	0.675480i
$489$			2.85874e7i			0.0110559i
$490$	−4.36106e8	−	2.72216e8i	−0.167458	−	0.104527i
$491$		−	1.35954e9i		−	0.518331i	−0.965833	−	0.259165i	$-0.916553\pi$
$491$		−	1.35954e9i		−	0.518331i	0.965833	−	0.259165i	$-0.0834474\pi$
$492$	−6.58867e6	+	3.22142e6i	−0.00249414	+	0.00121947i
$493$		−	2.74137e9i		−	1.03039i
$494$	−1.69769e9	+	1.02319e9i	−0.633600	+	0.381866i
$495$		−	6.58617e8i		−	0.244070i
$496$	−2.90316e8	+	3.73076e8i	−0.106828	+	0.137281i
$497$			1.27671e9i			0.466493i
$498$	4.22449e7	−	6.76789e7i	0.0153275	−	0.0245556i
$499$		−	6.40004e7i		−	0.0230585i	−0.999934	−	0.0115292i	$-0.996330\pi$
$499$		−	6.40004e7i		−	0.0230585i	0.999934	−	0.0115292i	$-0.00366995\pi$
$500$	−5.14143e8	−	1.05156e9i	−0.183945	−	0.376218i
$501$	1.00573e8			0.0357315
$502$	−6.81341e8	+	1.09155e9i	−0.240382	+	0.385106i
$503$		−	2.53991e9i		−	0.889878i	−0.895561	−	0.444939i	$-0.853225\pi$
$503$		−	2.53991e9i		−	0.889878i	0.895561	−	0.444939i	$-0.146775\pi$
$504$	8.02314e8	+	8.31473e7i	0.279150	+	0.0289295i
$505$	7.18176e8			0.248148
$506$	−9.12643e8	−	5.69668e8i	−0.313166	−	0.195477i
$507$	−3.86413e7			−0.0131681
$508$	2.02975e9	+	4.15139e9i	0.686941	+	1.40498i
$509$			2.89291e9i			0.972351i	0.873861	+	0.486176i	$0.161608\pi$
$509$			2.89291e9i			0.972351i	−0.873861	+	0.486176i	$0.838392\pi$
$510$	1.83853e7	+	1.14760e7i	0.00613727	+	0.00383086i
$511$		−	1.24171e9i		−	0.411667i
$512$	−9.25877e8	+	2.89243e9i	−0.304865	+	0.952395i
$513$	1.58494e8	+	8.05849e7i	0.0518325	+	0.0263538i
$514$	2.30213e8	−	3.68815e8i	0.0747753	−	0.119795i
$515$	−5.75695e8			−0.185723
$516$	−5.90625e7	+	2.88776e7i	−0.0189251	+	0.00925311i
$517$	6.04883e9			1.92510
$518$	1.00795e9	+	6.29156e8i	0.318628	+	0.198886i
$519$		−	7.20677e7i		−	0.0226284i
$520$	−5.05636e8	−	5.24012e7i	−0.157698	−	0.0163429i
$521$		−	1.31837e8i		−	0.0408419i	−0.999791	−	0.0204209i	$-0.993499\pi$
$521$		−	1.31837e8i		−	0.0408419i	0.999791	−	0.0204209i	$-0.00650064\pi$
$522$	1.52637e9	−	2.44535e9i	0.469693	−	0.752478i
$523$	−2.71287e9			−0.829226			−0.414613	−	0.909998i	$-0.636083\pi$
$523$	−2.71287e9			−0.829226			−0.414613	+	0.909998i	$0.636083\pi$
$524$	−9.38654e8	+	4.58939e8i	−0.285001	+	0.139346i
$525$		−	2.58433e7i		−	0.00779453i
$526$	−1.52239e9	+	2.43896e9i	−0.456116	+	0.730726i
$527$	6.78350e8			0.201891
$528$	8.84972e7	+	6.88657e7i	0.0261644	+	0.0203603i
$529$	3.04766e9			0.895101
$530$	−4.38040e8	+	7.01768e8i	−0.127805	+	0.204752i
$531$	1.35147e9			0.391719
$532$	9.75355e8	+	1.52394e7i	0.280848	+	0.00438810i
$533$	−2.46846e8			−0.0706125
$534$	−1.94616e7	+	3.11787e7i	−0.00553075	+	0.00886060i
$535$	−3.87877e8			−0.109511
$536$	5.22410e8	−	5.04090e9i	0.146533	−	1.41394i
$537$	−1.76399e8			−0.0491570
$538$	−3.02743e9	+	4.85014e9i	−0.838179	+	1.34281i
$539$			3.81687e9i			1.04990i
$540$	2.00289e7	+	4.09646e7i	0.00547368	+	0.0111952i
$541$	4.95285e9			1.34482			0.672411	−	0.740178i	$-0.265259\pi$
$541$	4.95285e9			1.34482			0.672411	+	0.740178i	$0.265259\pi$
$542$	−2.22435e9	+	3.56355e9i	−0.600076	+	0.961358i
$543$		−	6.67578e7i		−	0.0178938i
$544$	4.09158e9	−	1.50045e9i	1.08967	−	0.399601i
$545$		−	6.39239e8i		−	0.169151i
$546$	−1.95001e7	−	1.21719e7i	−0.00512699	−	0.00320024i
$547$	−4.01383e9			−1.04859			−0.524293	−	0.851538i	$-0.675670\pi$
$547$	−4.01383e9			−1.04859			−0.524293	+	0.851538i	$0.675670\pi$
$548$	−8.23581e8	−	1.68444e9i	−0.213784	−	0.437245i
$549$	−2.63068e9			−0.678523
$550$	−2.24678e9	+	3.59948e9i	−0.575825	+	0.922508i
$551$	1.57998e9	−	3.10750e9i	0.402366	−	0.791372i
$552$	3.70285e7	+	3.83743e6i	0.00937021	+	0.000971076i
$553$			7.15382e8i			0.179887i
$554$	−2.23631e9	−	1.39589e9i	−0.558788	−	0.348793i
$555$			3.35708e7i			0.00833559i
$556$	−5.74305e9	+	2.80797e9i	−1.41704	+	0.692835i
$557$	2.94615e9			0.722373			0.361187	−	0.932494i	$-0.382372\pi$
$557$	2.94615e9			0.722373			0.361187	+	0.932494i	$0.382372\pi$
$558$	6.05100e8	+	3.77701e8i	0.147437	+	0.0920297i
$559$	−2.21279e9			−0.535796
$560$	1.97432e8	+	1.53635e8i	0.0475071	+	0.0369685i
$561$		−	1.60911e8i		−	0.0384783i
$562$	−3.52913e9	+	5.65388e9i	−0.838669	+	1.34360i
$563$	−4.53737e9			−1.07158			−0.535790	−	0.844351i	$-0.679986\pi$
$563$	−4.53737e9			−1.07158			−0.535790	+	0.844351i	$0.679986\pi$
$564$	−1.88032e8	+	9.19353e7i	−0.0441322	+	0.0215777i
$565$		−	1.45361e9i		−	0.339061i
$566$	9.38405e8	−	1.50338e9i	0.217537	−	0.348507i
$567$		−	1.21608e9i		−	0.280170i
$568$	−7.47692e8	+	7.21472e9i	−0.171200	+	1.65196i
$569$		−	1.56073e9i		−	0.355170i	−0.984106	−	0.177585i	$-0.943172\pi$
$569$		−	1.56073e9i		−	0.355170i	0.984106	−	0.177585i	$-0.0568284\pi$
$570$	1.42266e7	+	2.36051e7i	0.00321766	+	0.00533880i
$571$		−	6.88077e9i		−	1.54672i	−0.633970	−	0.773358i	$-0.718576\pi$
$571$		−	6.88077e9i		−	1.54672i	0.633970	−	0.773358i	$-0.281424\pi$
$572$	1.65779e9	+	3.39062e9i	0.370376	+	0.757518i
$573$			1.12742e8i			0.0250349i
$574$	1.03050e8	+	6.43236e7i	0.0227435	+	0.0141964i
$575$			1.40865e9i			0.309005i
$576$	4.48520e9	+	9.39735e8i	0.977920	+	0.204893i
$577$	2.69810e9			0.584713			0.292357	−	0.956309i	$-0.405561\pi$
$577$	2.69810e9			0.584713			0.292357	+	0.956309i	$0.405561\pi$
$578$	−1.36681e9	−	8.53155e8i	−0.294415	−	0.183772i
$579$		−	2.24121e8i		−	0.0479852i
$580$	8.03168e8	−	3.92696e8i	0.170926	−	0.0835715i
$581$	−1.32146e9			−0.279537
$582$	−6.15262e7	+	9.85688e7i	−0.0129369	+	0.0207257i
$583$	6.14198e9			1.28372
$584$	7.27194e8	−	7.01692e9i	0.151079	−	1.45781i
$585$			7.67050e8i			0.158408i
$586$	7.76104e8	−	1.24337e9i	0.159323	−	0.255245i
$587$			9.46703e9i			1.93188i	0.258762	+	0.965941i	$0.416685\pi$
$587$			9.46703e9i			1.93188i	−0.258762	+	0.965941i	$0.583315\pi$
$588$	−5.80121e7	−	1.18650e8i	−0.0117679	−	0.0240685i
$589$	7.68949e8	+	3.90966e8i	0.155058	+	0.0788379i
$590$	3.55567e8	+	2.21943e8i	0.0712753	+	0.0444897i
$591$	6.51803e7			0.0129885
$592$	5.32747e9	+	4.14567e9i	1.05535	+	0.821238i
$593$	−1.17249e9			−0.230896			−0.115448	−	0.993314i	$-0.536830\pi$
$593$	−1.17249e9			−0.230896			−0.115448	+	0.993314i	$0.536830\pi$
$594$	1.79264e8	−	2.87192e8i	0.0350947	−	0.0562238i
$595$		−	3.58982e8i		−	0.0698656i
$596$	−5.85348e8	−	1.19719e9i	−0.113254	−	0.231634i
$597$		−	1.78018e8i		−	0.0342415i
$598$	1.06290e9	+	6.63456e8i	0.203253	+	0.126870i
$599$	7.02381e9			1.33530			0.667650	−	0.744475i	$-0.267300\pi$
$599$	7.02381e9			1.33530			0.667650	+	0.744475i	$0.267300\pi$
$600$	1.51349e7	−	1.46041e8i	0.00286055	−	0.0276023i
$601$			1.58778e9i			0.298353i	0.988811	+	0.149176i	$0.0476622\pi$
$601$			1.58778e9i			0.298353i	−0.988811	+	0.149176i	$0.952338\pi$
$602$	9.23769e8	+	5.76613e8i	0.172574	+	0.107720i
$603$	−7.64705e9			−1.42031
$604$	8.15245e8	+	1.66740e9i	0.150542	+	0.307900i
$605$	−3.49257e8			−0.0641212
$606$	1.56515e8	+	9.76962e7i	0.0285695	+	0.0178330i
$607$	8.31064e9			1.50825			0.754126	−	0.656730i	$-0.228061\pi$
$607$	8.31064e9			1.50825			0.754126	+	0.656730i	$0.228061\pi$
$608$	5.50283e9	+	6.57325e8i	0.992941	+	0.118609i
$609$	4.04277e7			0.00725302
$610$	−6.92123e8	−	4.32020e8i	−0.123461	−	0.0770637i
$611$	−7.04469e9			−1.24945
$612$	−2.88842e9	−	5.90760e9i	−0.509366	−	1.04179i
$613$	−6.80459e9			−1.19314			−0.596569	−	0.802562i	$-0.703470\pi$
$613$	−6.80459e9			−1.19314			−0.596569	+	0.802562i	$0.703470\pi$
$614$	3.23986e9	+	2.02231e9i	0.564855	+	0.352580i
$615$			3.43220e6i			0.000594991i
$616$	1.91460e8	−	1.84746e9i	0.0330025	−	0.318451i
$617$	7.23729e8			0.124045			0.0620223	−	0.998075i	$-0.480245\pi$
$617$	7.23729e8			0.124045			0.0620223	+	0.998075i	$0.480245\pi$
$618$	−1.25464e8	−	7.83139e7i	−0.0213825	−	0.0133469i
$619$			9.10263e9i			1.54259i	0.636480	+	0.771293i	$0.280390\pi$
$619$			9.10263e9i			1.54259i	−0.636480	+	0.771293i	$0.719610\pi$
$620$	9.71723e7	+	1.98744e8i	0.0163746	+	0.0334905i
$621$		−	1.12392e8i		−	0.0188328i
$622$	2.03252e9	−	3.25622e9i	0.338663	−	0.542559i
$623$	6.08779e8			0.100868
$624$	−1.03067e8	−	8.02036e7i	−0.0169814	−	0.0132144i
$625$	5.27540e9			0.864322
$626$	−5.78047e9	−	3.60814e9i	−0.941787	−	0.587859i
$627$	9.27408e7	−	1.82402e8i	0.0150257	−	0.0295524i
$628$	−3.55219e9	−	7.26518e9i	−0.572318	−	1.17054i
$629$		−	9.68675e9i		−	1.55203i
$630$	1.99879e8	−	3.20218e8i	0.0318475	−	0.0510216i
$631$		−	8.64278e9i		−	1.36946i	−0.728795	−	0.684732i	$-0.759919\pi$
$631$		−	8.64278e9i		−	1.36946i	0.728795	−	0.684732i	$-0.240081\pi$
$632$	−4.18957e8	+	4.04264e9i	−0.0660175	+	0.637024i
$633$	1.20609e8			0.0189002
$634$	−3.83387e9	+	6.14209e9i	−0.597482	+	0.957203i
$635$	2.16256e9			0.335166
$636$	−1.90928e8	+	9.33512e7i	−0.0294287	+	0.0143886i
$637$		−	4.44527e9i		−	0.681412i
$638$	−5.63081e9	−	3.51473e9i	−0.858418	−	0.535821i
$639$	1.09447e10			1.65940
$640$	1.02572e9	+	9.83819e8i	0.154667	+	0.148349i
$641$			7.51851e9i			1.12753i	0.825935	+	0.563766i	$0.190648\pi$
$641$			7.51851e9i			1.12753i	−0.825935	+	0.563766i	$0.809352\pi$
$642$	−8.45319e7	−	5.27644e7i	−0.0126080	−	0.00786989i
$643$		−	1.48432e9i		−	0.220185i	−0.993921	−	0.110093i	$-0.964885\pi$
$643$		−	1.48432e9i		−	0.220185i	0.993921	−	0.110093i	$-0.0351148\pi$
$644$	−2.70841e8	−	5.53943e8i	−0.0399589	−	0.0817268i
$645$			3.07672e7i			0.00451469i
$646$	−4.10505e9	−	6.81117e9i	−0.599107	−	0.994049i
$647$		−	9.12649e9i		−	1.32476i	−0.749166	−	0.662382i	$-0.769545\pi$
$647$		−	9.12649e9i		−	1.32476i	0.749166	−	0.662382i	$-0.230455\pi$
$648$	7.12186e8	−	6.87210e9i	0.102821	−	0.992149i
$649$		−	3.11197e9i		−	0.446868i
$650$	2.61668e9	−	4.19209e9i	0.373727	−	0.598733i
$651$			1.00038e7i			0.00142113i
$652$	2.41674e9	−	1.18163e9i	0.341479	−	0.166960i
$653$	−1.01661e10			−1.42876			−0.714381	−	0.699757i	$-0.753292\pi$
$653$	−1.01661e10			−1.42876			−0.714381	+	0.699757i	$0.753292\pi$
$654$	8.69582e7	−	1.39312e8i	0.0121559	−	0.0194746i
$655$			4.88968e8i			0.0679886i
$656$	5.44669e8	+	4.23844e8i	0.0753303	+	0.0586196i
$657$	−1.06447e10			−1.46438
$658$	2.94093e9	+	1.83571e9i	0.402433	+	0.251197i
$659$	−8.99411e9			−1.22422			−0.612109	−	0.790773i	$-0.709679\pi$
$659$	−8.99411e9			−1.22422			−0.612109	+	0.790773i	$0.709679\pi$
$660$	4.71439e7	−	2.30502e7i	0.00638295	−	0.00312084i
$661$		−	2.45281e9i		−	0.330339i	−0.986265	−	0.165169i	$-0.947183\pi$
$661$		−	2.45281e9i		−	0.330339i	0.986265	−	0.165169i	$-0.0528171\pi$
$662$	8.02910e9	+	5.01173e9i	1.07563	+	0.671405i
$663$			1.87403e8i			0.0249735i
$664$	−7.46763e9	−	7.73903e8i	−0.989907	−	0.102588i
$665$	2.06899e8	−	4.06927e8i	0.0272824	−	0.0536588i
$666$	5.39351e9	−	8.64074e9i	0.707476	−	1.13342i
$667$	−2.20361e9			−0.287537
$668$	−4.15708e9	−	8.50234e9i	−0.539598	−	1.10362i
$669$	−9.23456e7			−0.0119241
$670$	−2.01191e9	−	1.25583e9i	−0.258433	−	0.161313i
$671$			6.05757e9i			0.774051i
$672$	2.21276e7	+	6.03397e7i	0.00281282	+	0.00767027i
$673$		−	5.45607e9i		−	0.689965i	−0.938609	−	0.344982i	$-0.887885\pi$
$673$		−	5.45607e9i		−	0.689965i	0.938609	−	0.344982i	$-0.112115\pi$
$674$	4.49166e9	−	7.19592e9i	0.565064	−	0.905267i
$675$	−4.43276e8			−0.0554768
$676$	1.59719e9	+	3.26668e9i	0.198858	+	0.406718i
$677$			1.39469e10i			1.72750i	0.503924	+	0.863748i	$0.331889\pi$
$677$			1.39469e10i			1.72750i	−0.503924	+	0.863748i	$0.668111\pi$
$678$	1.97740e8	−	3.16792e8i	0.0243664	−	0.0390364i
$679$	1.92461e9			0.235938
$680$	2.10234e8	−	2.02862e9i	0.0256403	−	0.247411i
$681$	−2.71667e7			−0.00329627
$682$	8.69718e8	−	1.39334e9i	0.104986	−	0.168195i
$683$	−1.66071e9			−0.199445			−0.0997223	−	0.995015i	$-0.531795\pi$
$683$	−1.66071e9			−0.199445			−0.0997223	+	0.995015i	$0.531795\pi$
$684$	1.30641e8	−	8.36134e9i	0.0156093	−	0.999032i
$685$	−8.77470e8			−0.104307
$686$	−2.41592e9	+	3.87046e9i	−0.285725	+	0.457750i
$687$	−1.09375e8			−0.0128697
$688$	4.88255e9	+	3.79945e9i	0.571594	+	0.444796i
$689$	−7.15318e9			−0.833167
$690$	9.22483e6	−	1.47788e7i	0.00106902	−	0.00171264i
$691$			1.21758e10i			1.40387i	0.712243	+	0.701933i	$0.247679\pi$
$691$			1.21758e10i			1.40387i	−0.712243	+	0.701933i	$0.752321\pi$
$692$	−6.09251e9	+	2.97883e9i	−0.698916	+	0.341723i
$693$	−2.80260e9			−0.319886
$694$	6.82016e9	−	1.09263e10i	0.774527	−	1.24084i
$695$			2.99170e9i			0.338042i
$696$	2.28458e8	+	2.36761e7i	0.0256847	+	0.00266182i
$697$		−	9.90352e8i		−	0.110783i
$698$	−3.15286e9	−	1.96800e9i	−0.350923	−	0.219044i
$699$	1.27699e7			0.00141422
$700$	−2.18476e9	+	1.06820e9i	−0.240747	+	0.117709i
$701$	−9.34466e9			−1.02459			−0.512295	−	0.858809i	$-0.671205\pi$
$701$	−9.34466e9			−1.02459			−0.512295	+	0.858809i	$0.671205\pi$
$702$	−2.08778e8	+	3.34475e8i	−0.0227774	+	0.0364908i
$703$	5.58294e9	−	1.09805e10i	0.606065	−	1.19200i
$704$	2.16389e9	−	1.03279e10i	0.233739	−	1.11560i
$705$			9.79508e7i			0.0105280i
$706$	7.83577e9	+	4.89105e9i	0.838040	+	0.523101i
$707$		−	3.05604e9i		−	0.325230i
$708$	4.72985e7	+	9.67381e7i	0.00500877	+	0.0102443i
$709$	2.60492e9			0.274494			0.137247	−	0.990537i	$-0.456175\pi$
$709$	2.60492e9			0.274494			0.137247	+	0.990537i	$0.456175\pi$
$710$	2.87952e9	+	1.79739e9i	0.301937	+	0.188468i
$711$	6.13269e9			0.639894
$712$	3.44023e9	+	3.56526e8i	0.357196	+	0.0370178i
$713$		−	5.45282e8i		−	0.0563388i
$714$	4.88337e7	−	7.82346e7i	0.00502084	−	0.00804369i
$715$	1.76626e9			0.180710
$716$	7.29122e9	+	1.49125e10i	0.742343	+	1.51829i
$717$		−	2.32727e8i		−	0.0235792i
$718$	−1.49813e9	+	2.40010e9i	−0.151048	+	0.241988i
$719$			9.98115e9i			1.00145i	0.865606	+	0.500725i	$0.166933\pi$
$719$			9.98115e9i			1.00145i	−0.865606	+	0.500725i	$0.833067\pi$
$720$	1.31705e9	−	1.69250e9i	0.131504	−	0.168992i
$721$			2.44974e9i			0.243415i
$722$	−7.27703e8	−	1.00868e10i	−0.0719571	−	0.997408i
$723$			4.57118e8i			0.0449826i
$724$	−5.64361e9	+	2.75935e9i	−0.552678	+	0.270223i
$725$			8.69106e9i			0.847013i
$726$	−7.61152e7	−	4.75108e7i	−0.00738233	−	0.00460802i
$727$			1.61060e10i			1.55459i	0.629135	+	0.777296i	$0.283409\pi$
$727$			1.61060e10i			1.55459i	−0.629135	+	0.777296i	$0.716591\pi$
$728$	−2.22982e8	+	2.15162e9i	−0.0214195	+	0.206684i
$729$	−1.04073e10			−0.994928
$730$	−2.80058e9	−	1.74811e9i	−0.266451	−	0.166318i
$731$		−	8.87777e9i		−	0.840607i
$732$	−9.20682e7	−	1.88304e8i	−0.00867603	−	0.0177448i
$733$	1.68574e10			1.58098			0.790489	−	0.612476i	$-0.209826\pi$
$733$	1.68574e10			1.58098			0.790489	+	0.612476i	$0.209826\pi$
$734$	−1.71053e9	+	2.74037e9i	−0.159659	+	0.255784i
$735$	−6.18079e7			−0.00574167
$736$	−1.20612e9	−	3.28896e9i	−0.111511	−	0.304079i
$737$			1.76086e10i			1.62027i
$738$	5.51421e8	−	8.83410e8i	0.0504994	−	0.0809031i
$739$			1.22933e9i			0.112051i	0.998429	+	0.0560253i	$0.0178427\pi$
$739$			1.22933e9i			0.112051i	−0.998429	+	0.0560253i	$0.982157\pi$
$740$	2.83803e9	−	1.38761e9i	0.257458	−	0.125880i
$741$	−1.08009e8	+	2.12432e8i	−0.00975209	+	0.0191804i
$742$	2.98622e9	+	1.86399e9i	0.268354	+	0.167505i
$743$	1.49196e10			1.33443			0.667216	−	0.744864i	$-0.267486\pi$
$743$	1.49196e10			1.33443			0.667216	+	0.744864i	$0.267486\pi$
$744$	−5.85864e6	+	5.65318e7i	−0.000521545	+	0.00503254i
$745$	−6.23648e8			−0.0552577
$746$	−5.88916e9	+	9.43480e9i	−0.519359	+	0.832045i
$747$			1.13284e10i			0.994367i
$748$	−1.36032e10	+	6.65106e9i	−1.18846	+	0.581079i
$749$			1.65053e9i			0.143528i
$750$	−1.19381e8	−	7.45172e7i	−0.0103329	−	0.00644974i
$751$	−1.93559e10			−1.66753			−0.833766	−	0.552118i	$-0.813820\pi$
$751$	−1.93559e10			−1.66753			−0.833766	+	0.552118i	$0.813820\pi$
$752$	1.55442e10	+	1.20960e10i	1.33292	+	1.03724i
$753$			1.54702e8i			0.0132042i
$754$	6.55786e9	+	4.09338e9i	0.557137	+	0.347763i
$755$	8.68589e8			0.0734514
$756$	1.74316e8	−	8.52288e7i	0.0146727	−	0.00717397i
$757$	7.36792e8			0.0617318			0.0308659	−	0.999524i	$-0.490174\pi$
$757$	7.36792e8			0.0617318			0.0308659	+	0.999524i	$0.490174\pi$
$758$	9.72657e9	+	6.07128e9i	0.811180	+	0.506335i
$759$	−1.29346e8			−0.0107376
$760$	1.40750e9	−	2.17839e9i	0.116306	−	0.180006i
$761$	1.27424e10			1.04811			0.524055	−	0.851685i	$-0.324419\pi$
$761$	1.27424e10			1.04811			0.524055	+	0.851685i	$0.324419\pi$
$762$	4.71297e8	+	2.94181e8i	0.0385880	+	0.0240864i
$763$	−2.72014e9			−0.221695
$764$	9.53109e9	−	4.66006e9i	0.773242	−	0.378064i
$765$	−3.07742e9			−0.248526
$766$	−6.91168e9	−	4.31424e9i	−0.555627	−	0.346820i
$767$			3.62432e9i			0.290030i
$768$	8.97063e7	+	3.53940e8i	0.00714593	+	0.0281946i
$769$	5.13236e9			0.406981			0.203491	−	0.979077i	$-0.434771\pi$
$769$	5.13236e9			0.406981			0.203491	+	0.979077i	$0.434771\pi$
$770$	−7.37355e8	−	4.60254e8i	−0.0582048	−	0.0363312i
$771$		−	5.22709e7i		−	0.00410743i
$772$	−1.89469e10	+	9.26376e9i	−1.48210	+	0.724648i
$773$			1.44754e10i			1.12721i	0.826045	+	0.563604i	$0.190585\pi$
$773$			1.44754e10i			1.12721i	−0.826045	+	0.563604i	$0.809415\pi$
$774$	4.94308e9	−	7.91912e9i	0.383181	−	0.613880i
$775$	−2.15060e9			−0.165960
$776$	1.08760e10	+	1.12713e9i	0.835512	+	0.0865878i
$777$	1.42853e8			0.0109249
$778$	1.48893e10	+	9.29382e9i	1.13356	+	0.707564i
$779$	5.70787e8	−	1.12262e9i	0.0432607	−	0.0850848i
$780$	−5.49055e7	+	2.68451e7i	−0.00414271	+	0.00202551i
$781$		−	2.52020e10i		−	1.89303i
$782$	−2.66180e9	+	4.26436e9i	−0.199045	+	0.318882i
$783$		−	6.93436e8i		−	0.0516226i
$784$	−7.63269e9	+	9.80853e9i	−0.565681	+	0.726939i
$785$	−3.78462e9			−0.279240
$786$	−6.65162e7	+	1.06563e8i	−0.00488595	+	0.00782759i
$787$	−5.75058e9			−0.420533			−0.210267	−	0.977644i	$-0.567433\pi$
$787$	−5.75058e9			−0.420533			−0.210267	+	0.977644i	$0.567433\pi$
$788$	−2.69415e9	−	5.51026e9i	−0.196146	−	0.401172i
$789$			3.45666e8i			0.0250546i
$790$	1.61349e9	+	1.00713e9i	0.116432	+	0.0726763i
$791$	−6.18552e9			−0.444384
$792$	−1.58376e10	−	1.64132e9i	−1.13279	−	0.117396i
$793$		−	7.05488e9i		−	0.502381i
$794$	1.55649e10	+	9.71551e9i	1.10350	+	0.688801i
$795$			9.94593e7i			0.00702038i
$796$	−1.50494e10	+	7.35814e9i	−1.05760	+	0.517097i
$797$			2.32146e10i			1.62427i	0.583471	+	0.812134i	$0.301694\pi$
$797$			2.32146e10i			1.62427i	−0.583471	+	0.812134i	$0.698306\pi$
$798$	1.00446e8	−	6.05383e7i	0.00699719	−	0.00421716i
$799$		−	2.82634e10i		−	1.96025i
$800$	−1.29717e10	+	4.75694e9i	−0.895740	+	0.328483i
$801$		−	5.21883e9i		−	0.358806i
$802$	3.87130e9	−	6.20206e9i	0.265000	−	0.424547i
$803$			2.45111e10i			1.67055i
$804$	−2.67630e8	−	5.47376e8i	−0.0181610	−	0.0371441i
$805$	−2.88563e8			−0.0194964
$806$	−1.01291e9	+	1.62274e9i	−0.0681391	+	0.109163i
$807$			6.87394e8i			0.0460414i
$808$	1.78974e9	−	1.72698e10i	0.119358	−	1.15172i
$809$	−1.95032e10			−1.29505			−0.647523	−	0.762046i	$-0.724195\pi$
$809$	−1.95032e10			−1.29505			−0.647523	+	0.762046i	$0.724195\pi$
$810$	−2.74278e9	−	1.71203e9i	−0.181340	−	0.113192i
$811$	9.57085e9			0.630054			0.315027	−	0.949083i	$-0.397986\pi$
$811$	9.57085e9			0.630054			0.315027	+	0.949083i	$0.397986\pi$
$812$	−1.67103e9	−	3.41771e9i	−0.109531	−	0.224021i
$813$			5.05051e8i			0.0329623i
$814$	−1.98967e10	−	1.24194e10i	−1.29299	−	0.807081i
$815$		−	1.25894e9i		−	0.0814619i
$816$	3.21778e8	−	4.13507e8i	0.0207320	−	0.0266420i
$817$	5.11668e9	−	1.00635e10i	0.328255	−	0.645610i
$818$	1.17041e10	−	1.87506e10i	0.747654	−	1.19779i
$819$	3.26401e9			0.207615
$820$	2.90154e8	−	1.41866e8i	0.0183772	−	0.00898524i
$821$	1.53216e10			0.966283			0.483142	−	0.875542i	$-0.339496\pi$
$821$	1.53216e10			0.966283			0.483142	+	0.875542i	$0.339496\pi$
$822$	−1.91231e8	−	1.19366e8i	−0.0120090	−	0.00749596i
$823$		−	1.91024e10i		−	1.19450i	−0.802054	−	0.597252i	$-0.796259\pi$
$823$		−	1.91024e10i		−	1.19450i	0.802054	−	0.597252i	$-0.203741\pi$
$824$	−1.43467e9	+	1.38436e10i	−0.0893318	+	0.861990i
$825$			5.10142e8i			0.0316302i
$826$	9.44430e8	−	1.51304e9i	0.0583096	−	0.0934155i
$827$	−2.43449e10			−1.49671			−0.748356	−	0.663297i	$-0.769157\pi$
$827$	−2.43449e10			−1.49671			−0.748356	+	0.663297i	$0.769157\pi$
$828$	−4.74873e9	+	2.32181e9i	−0.290718	+	0.142142i
$829$			3.82880e9i			0.233411i	0.993167	+	0.116706i	$0.0372334\pi$
$829$			3.82880e9i			0.233411i	−0.993167	+	0.116706i	$0.962767\pi$
$830$	−1.86039e9	+	2.98047e9i	−0.112936	+	0.180930i
$831$	−3.16944e8			−0.0191593
$832$	−2.52015e9	+	1.20283e10i	−0.151703	+	0.724055i
$833$	1.78345e10			1.06906
$834$	−4.06972e8	+	6.51994e8i	−0.0242931	+	0.0389191i
$835$	−4.42908e9			−0.263276
$836$	−1.92534e10	−	3.00823e8i	−1.13968	−	0.0178069i
$837$	1.71590e8			0.0101147
$838$	1.11446e9	−	1.78543e9i	0.0654198	−	0.104807i
$839$	1.19767e10			0.700118			0.350059	−	0.936728i	$-0.386162\pi$
$839$	1.19767e10			0.700118			0.350059	+	0.936728i	$0.386162\pi$
$840$	2.99166e7	+	3.10039e6i	0.00174154	+	0.000180484i
$841$	3.65408e9			0.211833
$842$	1.32923e9	−	2.12950e9i	0.0767373	−	0.122938i
$843$			8.01307e8i			0.0460683i
$844$	−4.98521e9	−	1.01961e10i	−0.285421	−	0.583762i
$845$	1.70170e9			0.0970250
$846$	1.57369e10	−	2.52114e10i	0.893556	−	1.43153i
$847$			1.48619e9i			0.0840392i
$848$	1.57836e10	+	1.22823e10i	0.888832	+	0.691661i
$849$		−	2.13070e8i		−	0.0119494i
$850$	1.68187e10	+	1.04982e10i	0.939348	+	0.586337i
$851$	−7.78655e9			−0.433103
$852$	3.83043e8	+	7.83425e8i	0.0212182	+	0.0433969i
$853$	2.40197e9			0.132509			0.0662546	−	0.997803i	$-0.478895\pi$
$853$	2.40197e9			0.132509			0.0662546	+	0.997803i	$0.478895\pi$
$854$	−1.83837e9	+	2.94518e9i	−0.101002	+	0.161811i
$855$	−3.48843e9	−	1.77366e9i	−0.190875	−	0.0970487i
$856$	−9.66615e8	+	9.32717e9i	−0.0526739	+	0.508267i
$857$		−	1.19967e10i		−	0.651073i	−0.945530	−	0.325536i	$-0.894455\pi$
$857$		−	1.19967e10i		−	0.651073i	0.945530	−	0.325536i	$-0.105545\pi$
$858$	3.84929e8	+	2.40271e8i	0.0208053	+	0.0129866i
$859$		−	3.45337e10i		−	1.85895i	−0.368888	−	0.929474i	$-0.620262\pi$
$859$		−	3.45337e10i		−	1.85895i	0.368888	−	0.929474i	$-0.379738\pi$
$860$	2.60102e9	−	1.27172e9i	0.139444	−	0.0681786i
$861$	1.46050e7			0.000779813
$862$	−2.16688e9	−	1.35255e9i	−0.115228	−	0.0719249i
$863$	2.77540e10			1.46990			0.734951	−	0.678120i	$-0.237205\pi$
$863$	2.77540e10			1.46990			0.734951	+	0.678120i	$0.237205\pi$
$864$	1.03498e9	−	3.79543e8i	0.0545924	−	0.0200200i
$865$			3.17374e9i			0.166730i
$866$	−1.39117e10	+	2.22875e10i	−0.727895	+	1.16613i
$867$	−1.93713e8			−0.0100947
$868$	8.45710e8	−	4.13496e8i	0.0438937	−	0.0214611i
$869$		−	1.41215e10i		−	0.729983i
$870$	5.69153e7	−	9.11818e7i	0.00293029	−	0.00469451i
$871$		−	2.05076e10i		−	1.05160i
$872$	−1.53716e10	−	1.59303e9i	−0.785075	−	0.0813608i
$873$		−	1.64989e10i		−	0.839277i
$874$	−5.47506e9	+	3.29978e9i	−0.277395	+	0.167184i
$875$			2.33098e9i			0.117628i
$876$	−3.72541e8	−	7.61947e8i	−0.0187245	−	0.0382966i
$877$			5.71928e9i			0.286314i	0.989700	+	0.143157i	$0.0457254\pi$
$877$			5.71928e9i			0.286314i	−0.989700	+	0.143157i	$0.954275\pi$
$878$	−1.87224e10	−	1.16865e10i	−0.933538	−	0.582710i
$879$		−	1.76218e8i		−	0.00875165i
$880$	−3.89727e9	−	3.03273e9i	−0.192784	−	0.150018i
$881$	1.01339e10			0.499300			0.249650	−	0.968336i	$-0.419684\pi$
$881$	1.01339e10			0.499300			0.249650	+	0.968336i	$0.419684\pi$
$882$	1.59087e10	+	9.93011e9i	0.780717	+	0.487320i
$883$		−	3.62081e10i		−	1.76988i	−0.465705	−	0.884940i	$-0.654199\pi$
$883$		−	3.62081e10i		−	1.76988i	0.465705	−	0.884940i	$-0.345801\pi$
$884$	1.58428e10	−	7.74608e9i	0.771346	−	0.377137i
$885$	5.03933e7			0.00244383
$886$	−6.13035e6	+	9.82120e6i	−0.000296120	+	0.000474402i
$887$	−1.39192e10			−0.669704			−0.334852	−	0.942271i	$-0.608686\pi$
$887$	−1.39192e10			−0.669704			−0.334852	+	0.942271i	$0.608686\pi$
$888$	8.07267e8	+	8.36606e7i	0.0386876	+	0.00400936i
$889$		−	9.20230e9i		−	0.439279i
$890$	8.57056e8	−	1.37306e9i	0.0407516	−	0.0652865i
$891$			2.40052e10i			1.13693i
$892$	3.81699e9	+	7.80678e9i	0.180071	+	0.368294i
$893$	1.62896e10	−	3.20382e10i	0.765472	−	1.50552i
$894$	−1.35915e8	−	8.48372e7i	−0.00636187	−	0.00397105i
$895$	7.76830e9			0.362197
$896$	4.18642e9	−	4.36471e9i	0.194431	−	0.202711i
$897$	1.50641e8			0.00696900
$898$	−2.01490e10	+	3.22799e10i	−0.928509	+	1.48753i
$899$		−	3.36427e9i		−	0.154430i
$900$	9.15727e9	+	1.87291e10i	0.418714	+	0.856382i
$901$		−	2.86987e10i		−	1.30715i
$902$	−2.03420e9	−	1.26974e9i	−0.0922933	−	0.0576091i
$903$	1.30923e8			0.00591709
$904$	−3.49545e10	−	3.62249e9i	−1.57367	−	0.163086i
$905$			2.93990e9i			0.131845i
$906$	1.89295e8	+	1.18157e8i	0.00845652	+	0.00527852i
$907$	−3.42557e10			−1.52443			−0.762214	−	0.647325i	$-0.775888\pi$
$907$	−3.42557e10			−1.52443			−0.762214	+	0.647325i	$0.775888\pi$
$908$	1.12290e9	+	2.29664e9i	0.0497785	+	0.101810i
$909$	−2.61982e10			−1.15691
$910$	8.58751e8	+	5.36029e8i	0.0377766	+	0.0235800i
$911$	9.48213e9			0.415520			0.207760	−	0.978180i	$-0.433383\pi$
$911$	9.48213e9			0.415520			0.207760	+	0.978180i	$0.433383\pi$
$912$	6.03078e8	−	2.83278e8i	0.0263264	−	0.0123660i
$913$	2.60855e10			1.13436
$914$	−2.60509e10	−	1.62608e10i	−1.12852	−	0.704419i
$915$	−9.80924e7			−0.00423313
$916$	4.52087e9	+	9.24641e9i	0.194352	+	0.397502i
$917$	2.08070e9			0.0891080
$918$	−1.34192e9	−	8.37620e8i	−0.0572502	−	0.0357353i
$919$			3.80658e10i			1.61782i	0.587932	+	0.808910i	$0.299942\pi$
$919$			3.80658e10i			1.61782i	−0.587932	+	0.808910i	$0.700058\pi$
$920$	−1.63067e9	−	1.68994e8i	−0.0690414	−	0.00715506i
$921$	4.59175e8			0.0193673
$922$	3.12864e9	+	1.95288e9i	0.131461	+	0.0820575i
$923$			2.93513e10i			1.22863i
$924$	−9.80851e7	−	2.00610e8i	−0.00409026	−	0.00836569i
$925$			3.07103e10i			1.27581i
$926$	4.19280e9	−	6.71713e9i	0.173527	−	0.278000i
$927$	2.10007e10			0.865873
$928$	−7.44149e9	−	2.02922e10i	−0.305662	−	0.833510i
$929$	−1.04108e10			−0.426019			−0.213010	−	0.977050i	$-0.568327\pi$
$929$	−1.04108e10			−0.426019			−0.213010	+	0.977050i	$0.568327\pi$
$930$	2.25629e7	+	1.40836e7i	0.000919823	+	0.000574149i
$931$	2.02164e10	+	1.02789e10i	0.821070	+	0.417466i
$932$	−5.27827e8	−	1.07955e9i	−0.0213568	−	0.0436804i
$933$		−	4.61493e8i		−	0.0186028i
$934$	1.34856e10	−	2.16047e10i	0.541570	−	0.867629i
$935$			7.08626e9i			0.283515i
$936$	1.84450e10	+	1.91154e9i	0.735214	+	0.0761934i
$937$	1.58124e10			0.627926			0.313963	−	0.949435i	$-0.398343\pi$
$937$	1.58124e10			0.627926			0.313963	+	0.949435i	$0.398343\pi$
$938$	−5.34390e9	+	8.56126e9i	−0.211421	+	0.338710i
$939$	−8.19247e8			−0.0322913
$940$	8.28064e9	−	4.04868e9i	0.325174	−	0.158988i
$941$		−	2.44262e10i		−	0.955635i	−0.878459	−	0.477817i	$-0.841428\pi$
$941$		−	2.44262e10i		−	0.955635i	0.878459	−	0.477817i	$-0.158572\pi$
$942$	−8.24799e8	−	5.14836e8i	−0.0321492	−	0.0200674i
$943$	−7.96079e8			−0.0309147
$944$	6.22309e9	−	7.99710e9i	0.240771	−	0.309407i
$945$		−	9.08055e7i		−	0.00350026i
$946$	−1.82351e10	−	1.13822e10i	−0.700307	−	0.437128i
$947$		−	3.06234e10i		−	1.17173i	−0.810407	−	0.585867i	$-0.800754\pi$
$947$		−	3.06234e10i		−	1.17173i	0.810407	−	0.585867i	$-0.199246\pi$
$948$	2.14631e8	+	4.38979e8i	0.00818208	+	0.0167346i
$949$		−	2.85466e10i		−	1.08423i
$950$	1.30144e10	+	2.15937e10i	0.492483	+	0.817136i
$951$			8.70500e8i			0.0328199i
$952$	−8.63234e9	−	8.94607e8i	−0.324264	−	0.0336049i
$953$			3.29377e10i			1.23273i	0.787461	+	0.616364i	$0.211395\pi$
$953$			3.29377e10i			1.23273i	−0.787461	+	0.616364i	$0.788605\pi$
$954$	1.59792e10	−	2.55997e10i	0.595849	−	0.954587i
$955$		−	4.96498e9i		−	0.184462i
$956$	−1.96744e10	+	9.61948e9i	−0.728282	+	0.356081i
$957$	−7.98037e8			−0.0294328
$958$	−1.67074e10	+	2.67663e10i	−0.613946	+	0.983580i
$959$			3.73388e9i			0.136708i
$960$	1.67244e8	+	3.50407e7i	0.00610099	+	0.00127827i
$961$	−2.66801e10			−0.969742
$962$	2.31725e10	+	1.44642e10i	0.839189	+	0.523818i
$963$	1.41493e10			0.510556
$964$	3.86442e10	−	1.88944e10i	1.38936	−	0.679303i
$965$			9.86991e9i			0.353564i
$966$	−6.28878e7	−	3.92543e7i	−0.00224464	−	0.00140109i
$967$		−	2.21774e10i		−	0.788712i	−0.918958	−	0.394356i	$-0.870968\pi$
$967$		−	2.21774e10i		−	0.788712i	0.918958	−	0.394356i	$-0.129032\pi$
$968$	−8.70371e8	+	8.39848e9i	−0.0308419	+	0.297603i
$969$	−8.52281e8	−	4.33335e8i	−0.0300919	−	0.0153000i
$970$	2.70951e9	−	4.34081e9i	0.0953213	−	0.152711i
$971$	3.11054e10			1.09036			0.545178	−	0.838320i	$-0.316462\pi$
$971$	3.11054e10			1.09036			0.545178	+	0.838320i	$0.316462\pi$
$972$	−1.09610e9	−	2.24183e9i	−0.0382842	−	0.0783016i
$973$	1.27305e10			0.443048
$974$	1.19619e10	+	7.46660e9i	0.414806	+	0.258920i
$975$		−	5.94131e8i		−	0.0205289i
$976$	−1.21135e10	+	1.55667e10i	−0.417056	+	0.535946i
$977$			1.32690e10i			0.455206i	0.973754	+	0.227603i	$0.0730888\pi$
$977$			1.32690e10i			0.455206i	−0.973754	+	0.227603i	$0.926911\pi$
$978$	1.71259e8	−	2.74367e8i	0.00585419	−	0.00937878i
$979$	−1.20172e10			−0.409321
$980$	2.55475e9	+	5.22516e9i	0.0867078	+	0.177341i
$981$			2.33187e10i			0.788612i
$982$	−8.14460e9	+	1.30482e10i	−0.274460	+	0.439702i
$983$	−4.58040e10			−1.53803			−0.769017	−	0.639228i	$-0.779254\pi$
$983$	−4.58040e10			−1.53803			−0.769017	+	0.639228i	$0.779254\pi$
$984$	8.25332e7	+	8.55327e6i	0.00276150	+	0.000286187i
$985$	−2.87043e9			−0.0957019
$986$	−1.64227e10	+	2.63102e10i	−0.545602	+	0.874088i
$987$	4.16808e8			0.0137983
$988$	2.24232e10	+	3.50350e8i	0.739687	+	0.0115572i
$989$	−7.13626e9			−0.234576
$990$	−3.94558e9	+	6.32106e9i	−0.129237	+	0.207046i
$991$	−3.09073e10			−1.00880			−0.504399	−	0.863471i	$-0.668286\pi$
$991$	−3.09073e10			−1.00880			−0.504399	+	0.863471i	$0.668286\pi$
$992$	5.02129e9	−	1.84139e9i	0.163314	−	0.0598901i
$993$	1.13794e9			0.0368805
$994$	7.64839e9	−	1.22532e10i	0.247012	−	0.395728i
$995$			7.83960e9i			0.252297i
$996$	−8.10888e8	+	3.96470e8i	−0.0260048	+	0.0127146i
$997$	3.82590e10			1.22265			0.611323	−	0.791381i	$-0.290638\pi$
$997$	3.82590e10			1.22265			0.611323	+	0.791381i	$0.290638\pi$
$998$	−3.83407e8	+	6.14242e8i	−0.0122097	+	0.0195606i
$999$		−	2.45029e9i		−	0.0777567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.13	✓	68
4.3	odd	2	inner	76.8.d.a.75.55	yes	68
19.18	odd	2	inner	76.8.d.a.75.56	yes	68
76.75	even	2	inner	76.8.d.a.75.14	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.13	✓	68	1.1	even	1	trivial
76.8.d.a.75.14	yes	68	76.75	even	2	inner
76.8.d.a.75.55	yes	68	4.3	odd	2	inner
76.8.d.a.75.56	yes	68	19.18	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)

\(f(q)\)	\(=\)	\(q+(-9.59747 - 5.99070i) q^{2} -1.36022 q^{3} +(56.2230 + 114.991i) q^{4} +59.9018 q^{5} +(13.0547 + 8.14867i) q^{6} -254.899i q^{7} +(149.279 - 1440.44i) q^{8} -2185.15 q^{9} +O(q^{10})\)	\(q+(-9.59747 - 5.99070i) q^{2} -1.36022 q^{3} +(56.2230 + 114.991i) q^{4} +59.9018 q^{5} +(13.0547 + 8.14867i) q^{6} -254.899i q^{7} +(149.279 - 1440.44i) q^{8} -2185.15 q^{9} +(-574.906 - 358.854i) q^{10} +5031.67i q^{11} +(-76.4756 - 156.413i) q^{12} -5860.07i q^{13} +(-1527.02 + 2446.39i) q^{14} -81.4796 q^{15} +(-10061.9 + 12930.3i) q^{16} +23510.7 q^{17} +(20971.9 + 13090.6i) q^{18} +(26650.7 + 13550.3i) q^{19} +(3367.86 + 6888.18i) q^{20} +346.719i q^{21} +(30143.2 - 48291.3i) q^{22} -18898.7i q^{23} +(-203.052 + 1959.31i) q^{24} -74536.8 q^{25} +(-35105.9 + 56241.8i) q^{26} +5947.08 q^{27} +(29311.1 - 14331.2i) q^{28} -116601. i q^{29} +(781.998 + 488.120i) q^{30} +28852.9 q^{31} +(174031. - 63820.1i) q^{32} -6844.17i q^{33} +(-225643. - 140845. i) q^{34} -15268.9i q^{35} +(-122856. - 251273. i) q^{36} -412015. i q^{37} +(-174603. - 289705. i) q^{38} +7970.98i q^{39} +(8942.09 - 86284.9i) q^{40} -42123.5i q^{41} +(2077.09 - 3327.62i) q^{42} -377606. i q^{43} +(-578597. + 282895. i) q^{44} -130894. q^{45} +(-113217. + 181380. i) q^{46} -1.20215e6i q^{47} +(13686.5 - 17588.0i) q^{48} +758570. q^{49} +(715365. + 446528. i) q^{50} -31979.7 q^{51} +(673856. - 329471. i) q^{52} -1.22067e6i q^{53} +(-57077.0 - 35627.2i) q^{54} +301406. i q^{55} +(-367167. - 38051.1i) q^{56} +(-36250.8 - 18431.4i) q^{57} +(-698522. + 1.11907e6i) q^{58} -618478. q^{59} +(-4581.03 - 9369.43i) q^{60} +1.20389e6 q^{61} +(-276914. - 172849. i) q^{62} +556992. i q^{63} +(-2.05258e6 - 430055. i) q^{64} -351029. i q^{65} +(-41001.4 + 65686.7i) q^{66} +3.49955e6 q^{67} +(1.32184e6 + 2.70352e6i) q^{68} +25706.4i q^{69} +(-91471.5 + 146543. i) q^{70} -5.00869e6 q^{71} +(-326197. + 3.14758e6i) q^{72} +4.87137e6 q^{73} +(-2.46826e6 + 3.95430e6i) q^{74} +101386. q^{75} +(-59785.9 + 3.82644e6i) q^{76} +1.28257e6 q^{77} +(47751.7 - 76501.3i) q^{78} -2.80653e6 q^{79} +(-602729. + 774548. i) q^{80} +4.77083e6 q^{81} +(-252349. + 404279. i) q^{82} -5.18427e6i q^{83} +(-39869.6 + 19493.6i) q^{84} +1.40833e6 q^{85} +(-2.26212e6 + 3.62406e6i) q^{86} +158603. i q^{87} +(7.24781e6 + 751123. i) q^{88} +2.38832e6i q^{89} +(1.25626e6 + 784149. i) q^{90} -1.49373e6 q^{91} +(2.17318e6 - 1.06254e6i) q^{92} -39246.2 q^{93} +(-7.20173e6 + 1.15376e7i) q^{94} +(1.59643e6 + 811689. i) q^{95} +(-236720. + 86809.3i) q^{96} +7.55047e6i q^{97} +(-7.28035e6 - 4.54436e6i) q^{98} -1.09949e7i 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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