LMFDB - Embedded newform 76.8.d.a.75.15

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			75.15
Character	$\chi$	$=$	76.75
Dual form			76.8.d.a.75.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-8.06300 - 7.93650i) q^{2} +49.8474 q^{3} +(2.02391 + 127.984i) q^{4} +33.4044 q^{5} +(-401.919 - 395.614i) q^{6} +865.446i q^{7} +(999.426 - 1048.00i) q^{8} +297.759 q^{9} +O(q^{10})$	\(q+(-8.06300 - 7.93650i) q^{2} +49.8474 q^{3} +(2.02391 + 127.984i) q^{4} +33.4044 q^{5} +(-401.919 - 395.614i) q^{6} +865.446i q^{7} +(999.426 - 1048.00i) q^{8} +297.759 q^{9} +(-269.340 - 265.114i) q^{10} +2130.37i q^{11} +(100.887 + 6379.66i) q^{12} +4558.41i q^{13} +(6868.61 - 6978.09i) q^{14} +1665.12 q^{15} +(-16375.8 + 518.056i) q^{16} -19626.8 q^{17} +(-2400.83 - 2363.16i) q^{18} +(-29487.3 + 4936.67i) q^{19} +(67.6075 + 4275.23i) q^{20} +43140.2i q^{21} +(16907.7 - 17177.1i) q^{22} -96048.6i q^{23} +(49818.8 - 52239.9i) q^{24} -77009.1 q^{25} +(36177.9 - 36754.5i) q^{26} -94173.7 q^{27} +(-110763. + 1751.58i) q^{28} +155472. i q^{29} +(-13425.9 - 13215.2i) q^{30} +63620.4 q^{31} +(136150. + 125790. i) q^{32} +106193. i q^{33} +(158251. + 155768. i) q^{34} +28909.7i q^{35} +(602.637 + 38108.4i) q^{36} +247273. i q^{37} +(276936. + 194222. i) q^{38} +227225. i q^{39} +(33385.2 - 35007.7i) q^{40} +200821. i q^{41} +(342382. - 347839. i) q^{42} +691830. i q^{43} +(-272653. + 4311.67i) q^{44} +9946.45 q^{45} +(-762290. + 774440. i) q^{46} +425638. i q^{47} +(-816291. + 25823.7i) q^{48} +74546.7 q^{49} +(620925. + 611183. i) q^{50} -978344. q^{51} +(-583404. + 9225.82i) q^{52} -556470. i q^{53} +(759322. + 747409. i) q^{54} +71163.6i q^{55} +(906985. + 864949. i) q^{56} +(-1.46986e6 + 246080. i) q^{57} +(1.23390e6 - 1.25357e6i) q^{58} +2.70200e6 q^{59} +(3370.05 + 213109. i) q^{60} -2.75987e6 q^{61} +(-512971. - 504923. i) q^{62} +257694. i q^{63} +(-99446.0 - 2.09479e6i) q^{64} +152271. i q^{65} +(842802. - 856235. i) q^{66} +1.44778e6 q^{67} +(-39722.9 - 2.51192e6i) q^{68} -4.78777e6i q^{69} +(229442. - 233099. i) q^{70} +571173. q^{71} +(297588. - 312050. i) q^{72} +1.63064e6 q^{73} +(1.96248e6 - 1.99376e6i) q^{74} -3.83870e6 q^{75} +(-691494. - 3.76391e6i) q^{76} -1.84372e6 q^{77} +(1.80337e6 - 1.83211e6i) q^{78} -3.39532e6 q^{79} +(-547024. + 17305.3i) q^{80} -5.34551e6 q^{81} +(1.59382e6 - 1.61922e6i) q^{82} +7.19377e6i q^{83} +(-5.52125e6 + 87311.8i) q^{84} -655622. q^{85} +(5.49071e6 - 5.57823e6i) q^{86} +7.74985e6i q^{87} +(2.23262e6 + 2.12915e6i) q^{88} -3.56648e6i q^{89} +(-80198.2 - 78940.0i) q^{90} -3.94506e6 q^{91} +(1.22927e7 - 194394. i) q^{92} +3.17131e6 q^{93} +(3.37808e6 - 3.43192e6i) q^{94} +(-985006. + 164906. i) q^{95} +(6.78670e6 + 6.27028e6i) q^{96} +2.27472e6i q^{97} +(-601070. - 591640. i) q^{98} +634335. i 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 $

$2$	−8.06300	−	7.93650i	−0.712675	−	0.701494i
$2$	−8.06300	−	7.93650i	−0.712675	−	0.701494i
$3$	49.8474			1.06590			0.532952	−	0.846146i	$-0.321083\pi$
$3$	49.8474			1.06590			0.532952	+	0.846146i	$0.321083\pi$
$4$	2.02391	+	127.984i	0.0158118	+	0.999875i
$5$	33.4044			0.119511			0.0597556	−	0.998213i	$-0.480968\pi$
$5$	33.4044			0.119511			0.0597556	+	0.998213i	$0.480968\pi$
$6$	−401.919	−	395.614i	−0.759643	−	0.747725i
$7$			865.446i			0.953667i	0.878994	+	0.476833i	$0.158216\pi$
$7$			865.446i			0.953667i	−0.878994	+	0.476833i	$0.841784\pi$
$8$	999.426	−	1048.00i	0.690138	−	0.723678i
$9$	297.759			0.136149
$10$	−269.340	−	265.114i	−0.0851727	−	0.0838364i
$11$			2130.37i			0.482592i	0.970452	+	0.241296i	$0.0775725\pi$
$11$			2130.37i			0.482592i	−0.970452	+	0.241296i	$0.922428\pi$
$12$	100.887	+	6379.66i	0.0168538	+	1.06577i
$13$			4558.41i			0.575456i	0.957712	+	0.287728i	$0.0928999\pi$
$13$			4558.41i			0.575456i	−0.957712	+	0.287728i	$0.907100\pi$
$14$	6868.61	−	6978.09i	0.668992	−	0.679655i
$15$	1665.12			0.127387
$16$	−16375.8	+	518.056i	−0.999500	+	0.0316196i
$17$	−19626.8			−0.968899			−0.484449	−	0.874819i	$-0.660980\pi$
$17$	−19626.8			−0.968899			−0.484449	+	0.874819i	$0.660980\pi$
$18$	−2400.83	−	2363.16i	−0.0970303	−	0.0955080i
$19$	−29487.3	+	4936.67i	−0.986274	+	0.165119i
$19$	−29487.3	+	4936.67i	−0.986274	+	0.165119i
$20$	67.6075	+	4275.23i	0.00188969	+	0.119496i
$21$			43140.2i			1.01652i
$22$	16907.7	−	17177.1i	0.338535	−	0.343931i
$23$		−	96048.6i		−	1.64605i	−0.568003	−	0.823026i	$-0.692284\pi$
$23$		−	96048.6i		−	1.64605i	0.568003	−	0.823026i	$-0.307716\pi$
$24$	49818.8	−	52239.9i	0.735620	−	0.771371i
$25$	−77009.1			−0.985717
$26$	36177.9	−	36754.5i	0.403679	−	0.410113i
$27$	−94173.7			−0.920781
$28$	−110763.	+	1751.58i	−0.953548	+	0.0150792i
$29$			155472.i			1.18374i	0.806032	+	0.591872i	$0.201611\pi$
$29$			155472.i			1.18374i	−0.806032	+	0.591872i	$0.798389\pi$
$30$	−13425.9	−	13215.2i	−0.0907858	−	0.0893615i
$31$	63620.4			0.383557			0.191779	−	0.981438i	$-0.438574\pi$
$31$	63620.4			0.383557			0.191779	+	0.981438i	$0.438574\pi$
$32$	136150.	+	125790.i	0.734500	+	0.678609i
$33$			106193.i			0.514396i
$34$	158251.	+	155768.i	0.690510	+	0.679677i
$35$			28909.7i			0.113974i
$36$	602.637	+	38108.4i	0.00215277	+	0.136132i
$37$			247273.i			0.802548i	0.915958	+	0.401274i	$0.131433\pi$
$37$			247273.i			0.802548i	−0.915958	+	0.401274i	$0.868567\pi$
$38$	276936.	+	194222.i	0.818723	+	0.574189i
$39$			227225.i			0.613380i
$40$	33385.2	−	35007.7i	0.0824792	−	0.0864876i
$41$			200821.i			0.455057i	0.973771	+	0.227528i	$0.0730645\pi$
$41$			200821.i			0.455057i	−0.973771	+	0.227528i	$0.926936\pi$
$42$	342382.	−	347839.i	0.713080	−	0.724446i
$43$			691830.i			1.32697i	0.748191	+	0.663483i	$0.230923\pi$
$43$			691830.i			1.32697i	−0.748191	+	0.663483i	$0.769077\pi$
$44$	−272653.	+	4311.67i	−0.482532	+	0.00763064i
$45$	9946.45			0.0162714
$46$	−762290.	+	774440.i	−1.15470	+	1.17310i
$47$			425638.i			0.597995i	0.954254	+	0.298998i	$0.0966523\pi$
$47$			425638.i			0.597995i	−0.954254	+	0.298998i	$0.903348\pi$
$48$	−816291.	+	25823.7i	−1.06537	+	0.0337035i
$49$	74546.7			0.0905195
$50$	620925.	+	611183.i	0.702496	+	0.691475i
$51$	−978344.			−1.03275
$52$	−583404.	+	9225.82i	−0.575384	+	0.00909899i
$53$		−	556470.i		−	0.513424i	−0.966488	−	0.256712i	$-0.917361\pi$
$53$		−	556470.i		−	0.513424i	0.966488	−	0.256712i	$-0.0826392\pi$
$54$	759322.	+	747409.i	0.656218	+	0.645923i
$55$			71163.6i			0.0576751i
$56$	906985.	+	864949.i	0.690148	+	0.658162i
$57$	−1.46986e6	+	246080.i	−1.05127	+	0.176001i
$58$	1.23390e6	−	1.25357e6i	0.830390	−	0.843625i
$59$	2.70200e6			1.71279			0.856395	−	0.516322i	$-0.172699\pi$
$59$	2.70200e6			1.71279			0.856395	+	0.516322i	$0.172699\pi$
$60$	3370.05	+	213109.i	0.00201422	+	0.127371i
$61$	−2.75987e6			−1.55681			−0.778403	−	0.627765i	$-0.783970\pi$
$61$	−2.75987e6			−1.55681			−0.778403	+	0.627765i	$0.783970\pi$
$62$	−512971.	−	504923.i	−0.273352	−	0.269063i
$63$			257694.i			0.129841i
$64$	−99446.0	−	2.09479e6i	−0.0474196	−	0.998875i
$65$			152271.i			0.0687734i
$66$	842802.	−	856235.i	0.360846	−	0.366597i
$67$	1.44778e6			0.588084			0.294042	−	0.955792i	$-0.404999\pi$
$67$	1.44778e6			0.588084			0.294042	+	0.955792i	$0.404999\pi$
$68$	−39722.9	−	2.51192e6i	−0.0153200	−	0.968778i
$69$		−	4.78777e6i		−	1.75453i
$70$	229442.	−	233099.i	0.0799520	−	0.0812263i
$71$	571173.			0.189393			0.0946963	−	0.995506i	$-0.469812\pi$
$71$	571173.			0.189393			0.0946963	+	0.995506i	$0.469812\pi$
$72$	297588.	−	312050.i	0.0939618	−	0.0985283i
$73$	1.63064e6			0.490601			0.245300	−	0.969447i	$-0.421113\pi$
$73$	1.63064e6			0.490601			0.245300	+	0.969447i	$0.421113\pi$
$74$	1.96248e6	−	1.99376e6i	0.562983	−	0.571956i
$75$	−3.83870e6			−1.05068
$76$	−691494.	−	3.76391e6i	−0.180693	−	0.983540i
$77$	−1.84372e6			−0.460232
$78$	1.80337e6	−	1.83211e6i	0.430283	−	0.437141i
$79$	−3.39532e6			−0.774794			−0.387397	−	0.921913i	$-0.626626\pi$
$79$	−3.39532e6			−0.774794			−0.387397	+	0.921913i	$0.626626\pi$
$80$	−547024.	+	17305.3i	−0.119451	+	0.00377890i
$81$	−5.34551e6			−1.11761
$82$	1.59382e6	−	1.61922e6i	0.319220	−	0.324308i
$83$			7.19377e6i			1.38097i	0.723348	+	0.690483i	$0.242602\pi$
$83$			7.19377e6i			1.38097i	−0.723348	+	0.690483i	$0.757398\pi$
$84$	−5.52125e6	+	87311.8i	−1.01639	+	0.0160729i
$85$	−655622.			−0.115794
$86$	5.49071e6	−	5.57823e6i	0.930860	−	0.945696i
$87$			7.74985e6i			1.26176i
$88$	2.23262e6	+	2.12915e6i	0.349241	+	0.333055i
$89$		−	3.56648e6i		−	0.536259i	−0.963383	−	0.268129i	$-0.913595\pi$
$89$		−	3.56648e6i		−	0.536259i	0.963383	−	0.268129i	$-0.0864054\pi$
$90$	−80198.2	−	78940.0i	−0.0115962	−	0.0114143i
$91$	−3.94506e6			−0.548793
$92$	1.22927e7	−	194394.i	1.64585	−	0.0260270i
$93$	3.17131e6			0.408835
$94$	3.37808e6	−	3.43192e6i	0.419490	−	0.426176i
$95$	−985006.	+	164906.i	−0.117871	+	0.0197335i
$96$	6.78670e6	+	6.27028e6i	0.782906	+	0.723331i
$97$			2.27472e6i			0.253062i	0.991963	+	0.126531i	$0.0403843\pi$
$97$			2.27472e6i			0.253062i	−0.991963	+	0.126531i	$0.959616\pi$
$98$	−601070.	−	591640.i	−0.0645110	−	0.0634989i
$99$			634335.i			0.0657046i
$100$	−155860.	−	9.85594e6i	−0.0155860	−	0.985594i
$101$	−1.16227e7			−1.12249			−0.561247	−	0.827648i	$-0.689678\pi$
$101$	−1.16227e7			−1.12249			−0.561247	+	0.827648i	$0.689678\pi$
$102$	7.88839e6	+	7.76463e6i	0.736017	+	0.724470i
$103$	−2.78297e6			−0.250945			−0.125472	−	0.992097i	$-0.540045\pi$
$103$	−2.78297e6			−0.250945			−0.125472	+	0.992097i	$0.540045\pi$
$104$	4.77721e6	+	4.55580e6i	0.416445	+	0.397144i
$105$			1.44107e6i			0.121485i
$106$	−4.41643e6	+	4.48682e6i	−0.360164	+	0.365905i
$107$	3.40505e6			0.268708			0.134354	−	0.990933i	$-0.457104\pi$
$107$	3.40505e6			0.268708			0.134354	+	0.990933i	$0.457104\pi$
$108$	−190599.	−	1.20527e7i	−0.0145592	−	0.920666i
$109$		−	8.92703e6i		−	0.660259i	−0.943936	−	0.330130i	$-0.892908\pi$
$109$		−	8.92703e6i		−	0.660259i	0.943936	−	0.330130i	$-0.107092\pi$
$110$	564790.	−	573792.i	0.0404588	−	0.0411036i
$111$			1.23259e7i			0.855439i
$112$	−448349.	−	1.41724e7i	−0.0301546	−	0.953190i
$113$			3.21226e6i			0.209428i	0.994502	+	0.104714i	$0.0333928\pi$
$113$			3.21226e6i			0.209428i	−0.994502	+	0.104714i	$0.966607\pi$
$114$	1.38045e7	+	9.68144e6i	0.872679	+	0.612030i
$115$		−	3.20845e6i		−	0.196722i
$116$	−1.98979e7	+	314660.i	−1.18360	+	0.0187171i
$117$			1.35731e6i			0.0783480i
$118$	−2.17863e7	−	2.14445e7i	−1.22066	−	1.20151i
$119$		−	1.69859e7i		−	0.924007i
$120$	1.66417e6	−	1.74504e6i	0.0879148	−	0.0921874i
$121$	1.49487e7			0.767105
$122$	2.22528e7	+	2.19037e7i	1.10950	+	1.09209i
$123$			1.00104e7i			0.485047i
$124$	128762.	+	8.14239e6i	0.00606473	+	0.383509i
$125$	−5.18216e6			−0.237315
$126$	2.04519e6	−	2.07779e6i	0.0910828	−	0.0925346i
$127$	3.02184e7			1.30906			0.654528	−	0.756038i	$-0.272867\pi$
$127$	3.02184e7			1.30906			0.654528	+	0.756038i	$0.272867\pi$
$128$	−1.58235e7	+	1.76796e7i	−0.666910	+	0.745138i
$129$			3.44859e7i			1.41442i
$130$	1.20850e6	−	1.22776e6i	0.0482442	−	0.0490131i
$131$		−	1.57796e7i		−	0.613262i	−0.951828	−	0.306631i	$-0.900798\pi$
$131$		−	1.57796e7i		−	0.613262i	0.951828	−	0.306631i	$-0.0992018\pi$
$132$	−1.35910e7	+	214925.i	−0.514332	+	0.00813353i
$133$	−4.27242e6	−	2.55197e7i	−0.157468	−	0.940577i
$134$	−1.16734e7	−	1.14903e7i	−0.419113	−	0.412538i
$135$	−3.14581e6			−0.110044
$136$	−1.96155e7	+	2.05688e7i	−0.668674	+	0.701171i
$137$	−1.38168e7			−0.459077			−0.229538	−	0.973300i	$-0.573722\pi$
$137$	−1.38168e7			−0.459077			−0.229538	+	0.973300i	$0.573722\pi$
$138$	−3.79981e7	+	3.86038e7i	−1.23079	+	1.25041i
$139$		−	1.89128e7i		−	0.597317i	−0.954360	−	0.298658i	$-0.903461\pi$
$139$		−	1.89128e7i		−	0.597317i	0.954360	−	0.298658i	$-0.0965391\pi$
$140$	−3.69998e6	+	58510.6i	−0.113960	+	0.00180213i
$141$			2.12169e7i			0.637405i
$142$	−4.60536e6	−	4.53311e6i	−0.134975	−	0.132858i
$143$	−9.71110e6			−0.277710
$144$	−4.87604e6	+	154256.i	−0.136081	+	0.00430499i
$145$			5.19343e6i			0.141471i
$146$	−1.31479e7	−	1.29416e7i	−0.349639	−	0.344154i
$147$	3.71596e6			0.0964850
$148$	−3.16470e7	+	500459.i	−0.802448	+	0.0126897i
$149$	5.51963e7			1.36697			0.683484	−	0.729965i	$-0.260464\pi$
$149$	5.51963e7			1.36697			0.683484	+	0.729965i	$0.260464\pi$
$150$	3.09515e7	+	3.04659e7i	0.748793	+	0.737045i
$151$	−1.20703e7			−0.285298			−0.142649	−	0.989773i	$-0.545562\pi$
$151$	−1.20703e7			−0.285298			−0.142649	+	0.989773i	$0.545562\pi$
$152$	−2.42968e7	+	3.58365e7i	−0.561172	+	0.827699i
$153$	−5.84405e6			−0.131915
$154$	1.48659e7	+	1.46327e7i	0.327996	+	0.322850i
$155$	2.12520e6			0.0458394
$156$	−2.90811e7	+	459883.i	−0.613304	+	0.00969864i
$157$	−7.55831e7			−1.55875			−0.779374	−	0.626558i	$-0.784463\pi$
$157$	−7.55831e7			−1.55875			−0.779374	+	0.626558i	$0.784463\pi$
$158$	2.73765e7	+	2.69470e7i	0.552176	+	0.543513i
$159$		−	2.77386e7i		−	0.547260i
$160$	4.54800e6	+	4.20192e6i	0.0877809	+	0.0811014i
$161$	8.31249e7			1.56979
$162$	4.31008e7	+	4.24246e7i	0.796495	+	0.783999i
$163$		−	1.07412e7i		−	0.194266i	−0.995271	−	0.0971331i	$-0.969033\pi$
$163$		−	1.07412e7i		−	0.194266i	0.995271	−	0.0971331i	$-0.0309672\pi$
$164$	−2.57019e7	+	406444.i	−0.455000	+	0.00719526i
$165$			3.54732e6i			0.0614761i
$166$	5.70934e7	−	5.80034e7i	0.968740	−	0.984181i
$167$	7.31317e7			1.21506			0.607531	−	0.794296i	$-0.292160\pi$
$167$	7.31317e7			1.21506			0.607531	+	0.794296i	$0.292160\pi$
$168$	4.52108e7	+	4.31154e7i	0.735631	+	0.701536i
$169$	4.19694e7			0.668850
$170$	5.28628e6	+	5.20334e6i	0.0825237	+	0.0812290i
$171$	−8.78010e6	+	1.46994e6i	−0.134281	+	0.0224808i
$172$	−8.85432e7	+	1.40020e6i	−1.32680	+	0.0209817i
$173$			6.61723e7i			0.971662i	0.874053	+	0.485831i	$0.161483\pi$
$173$			6.61723e7i			0.971662i	−0.874053	+	0.485831i	$0.838517\pi$
$174$	6.15067e7	−	6.24870e7i	0.885115	−	0.899223i
$175$		−	6.66472e7i		−	0.940046i
$176$	−1.10365e6	−	3.48865e7i	−0.0152594	−	0.482351i
$177$	1.34688e8			1.82567
$178$	−2.83053e7	+	2.87565e7i	−0.376182	+	0.382178i
$179$	−1.11482e7			−0.145285			−0.0726423	−	0.997358i	$-0.523143\pi$
$179$	−1.11482e7			−0.145285			−0.0726423	+	0.997358i	$0.523143\pi$
$180$	20130.7	+	1.27299e6i	0.000257280	+	0.0162693i
$181$			8.12822e7i			1.01887i	0.860508	+	0.509437i	$0.170146\pi$
$181$			8.12822e7i			1.01887i	−0.860508	+	0.509437i	$0.829854\pi$
$182$	3.18090e7	+	3.13100e7i	0.391111	+	0.384975i
$183$	−1.37572e8			−1.65940
$184$	−1.00659e8	−	9.59935e7i	−1.19121	−	1.13600i
$185$			8.26002e6i			0.0959135i
$186$	−2.55702e7	−	2.51691e7i	−0.291366	−	0.286795i
$187$		−	4.18123e7i		−	0.467583i
$188$	−5.44748e7	+	861453.i	−0.597921	+	0.00945538i
$189$		−	8.15022e7i		−	0.878118i
$190$	9.25088e6	+	6.48786e6i	0.0978465	+	0.0686220i
$191$			3.87269e7i			0.402158i	0.979575	+	0.201079i	$0.0644447\pi$
$191$			3.87269e7i			0.402158i	−0.979575	+	0.201079i	$0.935555\pi$
$192$	−4.95712e6	−	1.04420e8i	−0.0505447	−	1.06470i
$193$		−	1.83291e8i		−	1.83523i	−0.397469	−	0.917615i	$-0.630111\pi$
$193$		−	1.83291e8i		−	1.83523i	0.397469	−	0.917615i	$-0.369889\pi$
$194$	1.80533e7	−	1.83411e7i	0.177522	−	0.180351i
$195$			7.59031e6i			0.0733058i
$196$	150876.	+	9.54078e6i	0.00143128	+	0.0905082i
$197$	−6.19596e7			−0.577400			−0.288700	−	0.957420i	$-0.593223\pi$
$197$	−6.19596e7			−0.577400			−0.288700	+	0.957420i	$0.593223\pi$
$198$	5.03440e6	−	5.11465e6i	0.0460914	−	0.0468260i
$199$		−	6.52384e7i		−	0.586837i	−0.955984	−	0.293419i	$-0.905207\pi$
$199$		−	6.52384e7i		−	0.586837i	0.955984	−	0.293419i	$-0.0947929\pi$
$200$	−7.69650e7	+	8.07054e7i	−0.680281	+	0.713342i
$201$	7.21678e7			0.626841
$202$	9.37142e7	+	9.22439e7i	0.799973	+	0.787423i
$203$	−1.34552e8			−1.12890
$204$	−1.98008e6	−	1.25212e8i	−0.0163297	−	1.03262i
$205$			6.70831e6i			0.0543844i
$206$	2.24391e7	+	2.20871e7i	0.178842	+	0.176036i
$207$		−	2.85993e7i		−	0.224109i
$208$	−2.36151e6	−	7.46477e7i	−0.0181957	−	0.575168i
$209$	−1.05169e7	−	6.28188e7i	−0.0796850	−	0.475968i
$210$	1.14371e7	−	1.16194e7i	0.0852211	−	0.0865794i
$211$	2.40250e8			1.76066			0.880329	−	0.474364i	$-0.157322\pi$
$211$	2.40250e8			1.76066			0.880329	+	0.474364i	$0.157322\pi$
$212$	7.12193e7	−	1.12625e6i	0.513360	−	0.00811816i
$213$	2.84714e7			0.201874
$214$	−2.74549e7	−	2.70242e7i	−0.191501	−	0.188497i
$215$			2.31102e7i			0.158587i
$216$	−9.41197e7	+	9.86938e7i	−0.635466	+	0.666349i
$217$			5.50600e7i			0.365786i
$218$	−7.08494e7	+	7.19787e7i	−0.463168	+	0.470550i
$219$	8.12831e7			0.522933
$220$	−9.10781e6	+	144029.i	−0.0576679	+	0.000911947i
$221$		−	8.94671e7i		−	0.557559i
$222$	9.78247e7	−	9.93839e7i	0.600085	−	0.609650i
$223$	1.16839e8			0.705538			0.352769	−	0.935710i	$-0.385240\pi$
$223$	1.16839e8			0.705538			0.352769	+	0.935710i	$0.385240\pi$
$224$	−1.08864e8	+	1.17830e8i	−0.647167	+	0.700468i
$225$	−2.29301e7			−0.134205
$226$	2.54941e7	−	2.59004e7i	0.146913	−	0.149254i
$227$	9.63420e7			0.546670			0.273335	−	0.961919i	$-0.411873\pi$
$227$	9.63420e7			0.546670			0.273335	+	0.961919i	$0.411873\pi$
$228$	−3.44692e7	−	1.87621e8i	−0.192601	−	1.04836i
$229$	−2.75840e8			−1.51787			−0.758934	−	0.651168i	$-0.774279\pi$
$229$	−2.75840e8			−1.51787			−0.758934	+	0.651168i	$0.774279\pi$
$230$	−2.54638e7	+	2.58697e7i	−0.137999	+	0.140199i
$231$	−9.19044e7			−0.490563
$232$	1.62934e8	+	1.55382e8i	0.856650	+	0.816947i
$233$	7.17196e7			0.371443			0.185722	−	0.982602i	$-0.440538\pi$
$233$	7.17196e7			0.371443			0.185722	+	0.982602i	$0.440538\pi$
$234$	1.07723e7	−	1.09440e7i	0.0549606	−	0.0558367i
$235$			1.42182e7i			0.0714671i
$236$	5.46861e6	+	3.45813e8i	0.0270823	+	1.71258i
$237$	−1.69248e8			−0.825855
$238$	−1.34809e8	+	1.36958e8i	−0.648185	+	0.658517i
$239$			1.36330e8i			0.645950i	0.946408	+	0.322975i	$0.104683\pi$
$239$			1.36330e8i			0.645950i	−0.946408	+	0.322975i	$0.895317\pi$
$240$	−2.72677e7	+	862626.i	−0.127324	+	0.00402794i
$241$		−	4.19425e8i		−	1.93016i	−0.261947	−	0.965082i	$-0.584365\pi$
$241$		−	4.19425e8i		−	1.93016i	0.261947	−	0.965082i	$-0.415635\pi$
$242$	−1.20531e8	−	1.18640e8i	−0.546697	−	0.538120i
$243$	−6.05015e7			−0.270486
$244$	−5.58573e6	−	3.53219e8i	−0.0246159	−	1.55661i
$245$	2.49019e6			0.0108181
$246$	7.94475e7	−	8.07138e7i	0.340257	−	0.345681i
$247$	−2.25034e7	−	1.34415e8i	−0.0950186	−	0.567557i
$248$	6.35839e7	−	6.66740e7i	0.264707	−	0.277572i
$249$			3.58590e8i			1.47198i
$250$	4.17838e7	+	4.11282e7i	0.169129	+	0.166475i
$251$			2.23233e8i			0.891048i	0.895270	+	0.445524i	$0.146983\pi$
$251$			2.23233e8i			0.891048i	−0.895270	+	0.445524i	$0.853017\pi$
$252$	−3.29807e7	+	521549.i	−0.129825	+	0.00205302i
$253$	2.04619e8			0.794372
$254$	−2.43651e8	−	2.39828e8i	−0.932932	−	0.918295i
$255$	−3.26810e7			−0.123425
$256$	2.67899e8	−	1.69672e7i	0.998000	−	0.0632076i
$257$			3.75518e8i			1.37995i	0.723831	+	0.689977i	$0.242380\pi$
$257$			3.75518e8i			1.37995i	−0.723831	+	0.689977i	$0.757620\pi$
$258$	2.73698e8	−	2.78060e8i	0.992206	−	1.00802i
$259$	−2.14002e8			−0.765364
$260$	−1.94883e7	+	308183.i	−0.0687648	+	0.00108743i
$261$			4.62930e7i			0.161166i
$262$	−1.25235e8	+	1.27231e8i	−0.430200	+	0.437057i
$263$			2.30830e8i			0.782432i	0.920299	+	0.391216i	$0.127945\pi$
$263$			2.30830e8i			0.782432i	−0.920299	+	0.391216i	$0.872055\pi$
$264$	1.11290e8	+	1.06132e8i	0.372257	+	0.355004i
$265$		−	1.85885e7i		−	0.0613599i
$266$	−1.68088e8	+	2.39673e8i	−0.547585	+	0.780789i
$267$		−	1.77779e8i		−	0.571600i
$268$	2.93017e6	+	1.85292e8i	0.00929867	+	0.588011i
$269$		−	1.70225e8i		−	0.533202i	−0.963807	−	0.266601i	$-0.914099\pi$
$269$		−	1.70225e8i		−	0.533202i	0.963807	−	0.266601i	$-0.0859005\pi$
$270$	2.53647e7	+	2.49668e7i	0.0784254	+	0.0771950i
$271$			5.08371e8i			1.55163i	0.630959	+	0.775816i	$0.282661\pi$
$271$			5.08371e8i			1.55163i	−0.630959	+	0.775816i	$0.717339\pi$
$272$	3.21405e8	−	1.01678e7i	0.968414	−	0.0306362i
$273$	−1.96651e8			−0.584960
$274$	1.11405e8	+	1.09657e8i	0.327173	+	0.322040i
$275$		−	1.64058e8i		−	0.475699i
$276$	6.12758e8	−	9.69001e6i	1.75431	−	0.0277423i
$277$	−4.20602e8			−1.18903			−0.594514	−	0.804086i	$-0.702655\pi$
$277$	−4.20602e8			−1.18903			−0.594514	+	0.804086i	$0.702655\pi$
$278$	−1.50102e8	+	1.52494e8i	−0.419014	+	0.425693i
$279$	1.89435e7			0.0522211
$280$	3.02973e7	+	2.88931e7i	0.0824804	+	0.0786577i
$281$			6.57138e8i			1.76679i	0.468630	+	0.883394i	$0.344748\pi$
$281$			6.57138e8i			1.76679i	−0.468630	+	0.883394i	$0.655252\pi$
$282$	1.68388e8	−	1.71072e8i	0.447136	−	0.454263i
$283$			5.25734e8i			1.37884i	0.724362	+	0.689420i	$0.242134\pi$
$283$			5.25734e8i			1.37884i	−0.724362	+	0.689420i	$0.757866\pi$
$284$	1.15600e6	+	7.31010e7i	0.00299464	+	0.189369i
$285$	−4.90999e7	+	8.22015e6i	−0.125639	+	0.0210340i
$286$	7.83006e7	+	7.70721e7i	0.197917	+	0.194812i
$287$	−1.73800e8			−0.433973
$288$	4.05398e7	+	3.74549e7i	0.100002	+	0.0923922i
$289$	−2.51271e7			−0.0612350
$290$	4.12177e7	−	4.18746e7i	0.0992409	−	0.100823i
$291$			1.13389e8i			0.269740i
$292$	3.30027e6	+	2.08696e8i	0.00775728	+	0.490540i
$293$			4.35073e8i			1.01047i	0.862981	+	0.505237i	$0.168595\pi$
$293$			4.35073e8i			1.01047i	−0.862981	+	0.505237i	$0.831405\pi$
$294$	−2.99617e7	−	2.94917e7i	−0.0687625	−	0.0676837i
$295$	9.02588e7			0.204698
$296$	2.59142e8	+	2.47131e8i	0.580787	+	0.553869i
$297$		−	2.00625e8i		−	0.444362i
$298$	−4.45048e8	−	4.38066e8i	−0.974204	−	0.958920i
$299$	4.37829e8			0.947231
$300$	−7.76918e6	−	4.91292e8i	−0.0166131	−	1.05055i
$301$	−5.98742e8			−1.26548
$302$	9.73229e7	+	9.57961e7i	0.203325	+	0.200135i
$303$	−5.79363e8			−1.19647
$304$	4.80321e8	−	9.61180e7i	0.980560	−	0.196222i
$305$	−9.21918e7			−0.186056
$306$	4.71206e7	+	4.63813e7i	0.0940125	+	0.0925376i
$307$	−4.73992e8			−0.934947			−0.467474	−	0.884007i	$-0.654836\pi$
$307$	−4.73992e8			−0.934947			−0.467474	+	0.884007i	$0.654836\pi$
$308$	−3.73152e6	−	2.35966e8i	−0.00727709	−	0.460174i
$309$	−1.38724e8			−0.267483
$310$	−1.71355e7	−	1.68666e7i	−0.0326686	−	0.0321561i
$311$		−	3.91767e8i		−	0.738527i	−0.929325	−	0.369264i	$-0.879610\pi$
$311$		−	3.91767e8i		−	0.738527i	0.929325	−	0.369264i	$-0.120390\pi$
$312$	2.38131e8	+	2.27095e8i	0.443890	+	0.423317i
$313$	3.76376e8			0.693772			0.346886	−	0.937907i	$-0.387239\pi$
$313$	3.76376e8			0.693772			0.346886	+	0.937907i	$0.387239\pi$
$314$	6.09427e8	+	5.99866e8i	1.11088	+	1.09345i
$315$			8.60811e6i			0.0155175i
$316$	−6.87182e6	−	4.34547e8i	−0.0122509	−	0.774697i
$317$		−	6.70685e8i		−	1.18253i	−0.806479	−	0.591263i	$-0.798629\pi$
$317$		−	6.70685e8i		−	1.18253i	0.806479	−	0.591263i	$-0.201371\pi$
$318$	−2.20147e8	+	2.23656e8i	−0.383900	+	0.390019i
$319$	−3.31212e8			−0.571266
$320$	−3.32193e6	−	6.99753e7i	−0.00566717	−	0.119377i
$321$	1.69733e8			0.286416
$322$	−6.70236e8	−	6.59721e8i	−1.11875	−	1.10120i
$323$	5.78742e8	−	9.68910e7i	0.955599	−	0.159983i
$324$	−1.08188e7	−	6.84139e8i	−0.0176715	−	1.11747i
$325$		−	3.51040e8i		−	0.567237i
$326$	−8.52477e7	+	8.66065e7i	−0.136277	+	0.138449i
$327$		−	4.44989e8i		−	0.703772i
$328$	2.10460e8	+	2.00706e8i	0.329315	+	0.314052i
$329$	−3.68367e8			−0.570288
$330$	2.81533e7	−	2.86020e7i	0.0431251	−	0.0438125i
$331$	4.00714e8			0.607346			0.303673	−	0.952776i	$-0.401787\pi$
$331$	4.00714e8			0.607346			0.303673	+	0.952776i	$0.401787\pi$
$332$	−9.20687e8	+	1.45595e7i	−1.38079	+	0.0218356i
$333$			7.36278e7i			0.109266i
$334$	−5.89661e8	−	5.80410e8i	−0.865944	−	0.852358i
$335$	4.83621e7			0.0702827
$336$	−2.23490e7	−	7.06455e8i	−0.0321419	−	1.01601i
$337$		−	5.52271e8i		−	0.786046i	−0.919529	−	0.393023i	$-0.871429\pi$
$337$		−	5.52271e8i		−	0.786046i	0.919529	−	0.393023i	$-0.128571\pi$
$338$	−3.38399e8	−	3.33090e8i	−0.476673	−	0.469195i
$339$			1.60122e8i			0.223230i
$340$	−1.32692e6	−	8.39091e7i	−0.00183091	−	0.115780i
$341$			1.35535e8i			0.185102i
$342$	8.24601e7	+	5.78312e7i	0.111469	+	0.0781755i
$343$			7.77248e8i			1.03999i
$344$	7.25037e8	+	6.91434e8i	0.960297	+	0.915790i
$345$		−	1.59933e8i		−	0.209686i
$346$	5.25177e8	−	5.33547e8i	0.681615	−	0.692479i
$347$			476096.i			0.000611704i	1.00000		0.000305852i	$9.73558e-5\pi$
$347$			476096.i			0.000611704i	−1.00000		0.000305852i	$0.999903\pi$
$348$	−9.91856e8	+	1.56850e7i	−1.26160	+	0.0199506i
$349$	1.48215e9			1.86639			0.933197	−	0.359366i	$-0.117007\pi$
$349$	1.48215e9			1.86639			0.933197	+	0.359366i	$0.117007\pi$
$350$	−5.28946e8	+	5.37377e8i	−0.659437	+	0.669947i
$351$		−	4.29283e8i		−	0.529869i
$352$	−2.67978e8	+	2.90049e8i	−0.327491	+	0.354464i
$353$	−5.39147e8			−0.652372			−0.326186	−	0.945306i	$-0.605764\pi$
$353$	−5.39147e8			−0.652372			−0.326186	+	0.945306i	$0.605764\pi$
$354$	−1.08599e9	−	1.06895e9i	−1.30111	−	1.28070i
$355$	1.90797e7			0.0226345
$356$	4.56452e8	−	7.21822e6i	0.536192	−	0.00847921i
$357$		−	8.46704e8i		−	0.984902i
$358$	8.98880e7	+	8.84777e7i	0.103541	+	0.101916i
$359$		−	1.11733e9i		−	1.27454i	−0.770642	−	0.637268i	$-0.780064\pi$
$359$		−	1.11733e9i		−	1.27454i	0.770642	−	0.637268i	$-0.219936\pi$
$360$	9.94074e6	−	1.04239e7i	0.0112295	−	0.0117752i
$361$	8.45130e8	−	2.91138e8i	0.945472	−	0.325705i
$362$	6.45096e8	−	6.55378e8i	0.714734	−	0.726126i
$363$	7.45153e8			0.817660
$364$	−7.98444e6	−	5.04905e8i	−0.00867740	−	0.548725i
$365$	5.44706e7			0.0586323
$366$	1.10924e9	+	1.09184e9i	1.18262	+	1.16406i
$367$		−	6.95436e8i		−	0.734388i	−0.930144	−	0.367194i	$-0.880318\pi$
$367$		−	6.95436e8i		−	0.734388i	0.930144	−	0.367194i	$-0.119682\pi$
$368$	4.97586e7	+	1.57287e9i	0.0520476	+	1.64523i
$369$			5.97962e7i			0.0619557i
$370$	6.55556e7	−	6.66005e7i	0.0672828	−	0.0683552i
$371$	4.81595e8			0.489636
$372$	6.41844e6	+	4.05876e8i	0.00646441	+	0.408784i
$373$		−	6.81765e8i		−	0.680227i	−0.940384	−	0.340113i	$-0.889535\pi$
$373$		−	6.81765e8i		−	0.680227i	0.940384	−	0.340113i	$-0.110465\pi$
$374$	−3.31843e8	+	3.37133e8i	−0.328007	+	0.333235i
$375$	−2.58317e8			−0.252955
$376$	4.46068e8	+	4.25394e8i	0.432756	+	0.412699i
$377$	−7.08704e8			−0.681193
$378$	−6.46842e8	+	6.57152e8i	−0.615995	+	0.625813i
$379$	2.82913e8			0.266941			0.133471	−	0.991053i	$-0.457388\pi$
$379$	2.82913e8			0.266941			0.133471	+	0.991053i	$0.457388\pi$
$380$	−2.30989e7	−	1.25731e8i	−0.0215948	−	0.117544i
$381$	1.50631e9			1.39533
$382$	3.07356e8	−	3.12255e8i	0.282111	−	0.286608i
$383$	3.76658e8			0.342572			0.171286	−	0.985221i	$-0.445208\pi$
$383$	3.76658e8			0.342572			0.171286	+	0.985221i	$0.445208\pi$
$384$	−7.88759e8	+	8.81280e8i	−0.710862	+	0.794245i
$385$	−6.15883e7			−0.0550029
$386$	−1.45469e9	+	1.47788e9i	−1.28740	+	1.30792i
$387$			2.05999e8i			0.180666i
$388$	−2.91128e8	+	4.60383e6i	−0.253030	+	0.00400136i
$389$	1.16854e9			1.00651			0.503256	−	0.864138i	$-0.332135\pi$
$389$	1.16854e9			1.00651			0.503256	+	0.864138i	$0.332135\pi$
$390$	6.02405e7	−	6.12007e7i	0.0514236	−	0.0522432i
$391$			1.88513e9i			1.59486i
$392$	7.45039e7	−	7.81248e7i	0.0624709	−	0.0655070i
$393$		−	7.86571e8i		−	0.653678i
$394$	4.99580e8	+	4.91742e8i	0.411499	+	0.405043i
$395$	−1.13419e8			−0.0925965
$396$	−8.11848e7	+	1.28384e6i	−0.0656964	+	0.00103891i
$397$	1.57017e8			0.125945			0.0629723	−	0.998015i	$-0.479942\pi$
$397$	1.57017e8			0.125945			0.0629723	+	0.998015i	$0.479942\pi$
$398$	−5.17765e8	+	5.26017e8i	−0.411663	+	0.418224i
$399$	−2.12969e8	−	1.27209e9i	−0.167846	−	1.00256i
$400$	1.26109e9	−	3.98950e7i	0.985224	−	0.0311680i
$401$			1.32751e9i			1.02809i	0.857763	+	0.514045i	$0.171854\pi$
$401$			1.32751e9i			1.02809i	−0.857763	+	0.514045i	$0.828146\pi$
$402$	−5.81889e8	−	5.72760e8i	−0.446734	−	0.439725i
$403$			2.90008e8i			0.220720i
$404$	−2.35234e7	−	1.48753e9i	−0.0177486	−	1.12235i
$405$	−1.78563e8			−0.133567
$406$	1.08489e9	+	1.06787e9i	0.804537	+	0.791915i
$407$	−5.26783e8			−0.387303
$408$	−9.77783e8	+	1.02530e9i	−0.712741	+	0.747380i
$409$			1.81517e9i			1.31186i	0.754823	+	0.655928i	$0.227723\pi$
$409$			1.81517e9i			1.31186i	−0.754823	+	0.655928i	$0.772277\pi$
$410$	5.32405e7	−	5.40891e7i	0.0381503	−	0.0387584i
$411$	−6.88731e8			−0.489332
$412$	−5.63248e6	−	3.56176e8i	−0.00396789	−	0.250914i
$413$			2.33844e9i			1.63343i
$414$	−2.26978e8	+	2.30596e8i	−0.157211	+	0.159717i
$415$			2.40304e8i			0.165041i
$416$	−5.73401e8	+	6.20627e8i	−0.390510	+	0.422672i
$417$		−	9.42755e8i		−	0.636682i
$418$	−4.13763e8	+	5.89975e8i	−0.277099	+	0.395109i
$419$		−	1.74758e9i		−	1.16061i	−0.814398	−	0.580307i	$-0.802933\pi$
$419$		−	1.74758e9i		−	1.16061i	0.814398	−	0.580307i	$-0.197067\pi$
$420$	−1.84434e8	+	2.91660e6i	−0.121470	+	0.00192090i
$421$			1.82622e9i			1.19279i	0.802690	+	0.596396i	$0.203401\pi$
$421$			1.82622e9i			1.19279i	−0.802690	+	0.596396i	$0.796599\pi$
$422$	−1.93714e9	−	1.90674e9i	−1.25478	−	1.23509i
$423$			1.26737e8i			0.0814167i
$424$	−5.83179e8	−	5.56151e8i	−0.371554	−	0.354333i
$425$	1.51144e9			0.955060
$426$	−2.29565e8	−	2.25964e8i	−0.143871	−	0.141614i
$427$		−	2.38852e9i		−	1.48467i
$428$	6.89151e6	+	4.35792e8i	0.00424875	+	0.268674i
$429$	−4.84072e8			−0.296012
$430$	1.83414e8	−	1.86337e8i	0.111248	−	0.113021i
$431$	−3.23382e9			−1.94556			−0.972781	−	0.231725i	$-0.925563\pi$
$431$	−3.23382e9			−1.94556			−0.972781	+	0.231725i	$0.925563\pi$
$432$	1.54217e9	−	4.87872e7i	0.920321	−	0.0291148i
$433$		−	2.38163e9i		−	1.40983i	−0.709291	−	0.704916i	$-0.750985\pi$
$433$		−	2.38163e9i		−	1.40983i	0.709291	−	0.704916i	$-0.249015\pi$
$434$	4.36983e8	−	4.43948e8i	0.256597	−	0.260686i
$435$			2.58879e8i			0.150794i
$436$	1.14252e9	−	1.80675e7i	0.660177	−	0.0104399i
$437$	4.74160e8	+	2.83221e9i	0.271794	+	1.62346i
$438$	−6.55386e8	−	6.45104e8i	−0.372681	−	0.366835i
$439$	4.86985e8			0.274720			0.137360	−	0.990521i	$-0.456138\pi$
$439$	4.86985e8			0.274720			0.137360	+	0.990521i	$0.456138\pi$
$440$	7.45793e7	+	7.11228e7i	0.0417382	+	0.0398038i
$441$	2.21969e7			0.0123242
$442$	−7.10056e8	+	7.21373e8i	−0.391124	+	0.397358i
$443$		−	2.45223e9i		−	1.34014i	−0.742300	−	0.670068i	$-0.766265\pi$
$443$		−	2.45223e9i		−	1.34014i	0.742300	−	0.670068i	$-0.233735\pi$
$444$	−1.57752e9	+	2.49465e7i	−0.855332	+	0.0135260i
$445$		−	1.19136e8i		−	0.0640889i
$446$	−9.42072e8	−	9.27293e8i	−0.502820	−	0.494931i
$447$	2.75139e9			1.45706
$448$	1.81293e9	−	8.60651e7i	0.952594	−	0.0452225i
$449$			6.39281e8i			0.333296i	0.986016	+	0.166648i	$0.0532943\pi$
$449$			6.39281e8i			0.333296i	−0.986016	+	0.166648i	$0.946706\pi$
$450$	1.84886e8	+	1.81985e8i	0.0956444	+	0.0941439i
$451$	−4.27823e8			−0.219607
$452$	−4.11117e8	+	6.50131e6i	−0.209402	+	0.00331144i
$453$	−6.01673e8			−0.304100
$454$	−7.76805e8	−	7.64618e8i	−0.389598	−	0.383486i
$455$	−1.31782e8			−0.0655869
$456$	−1.21113e9	+	1.78635e9i	−0.598155	+	0.882247i
$457$	−3.05168e9			−1.49566			−0.747828	−	0.663892i	$-0.768903\pi$
$457$	−3.05168e9			−1.49566			−0.747828	+	0.663892i	$0.768903\pi$
$458$	2.22410e9	+	2.18921e9i	1.08175	+	1.06478i
$459$	1.84833e9			0.892144
$460$	4.10630e8	−	6.49360e6i	0.196697	−	0.00311052i
$461$	2.83876e8			0.134951			0.0674754	−	0.997721i	$-0.478506\pi$
$461$	2.83876e8			0.134951			0.0674754	+	0.997721i	$0.478506\pi$
$462$	7.41025e8	+	7.29400e8i	0.349612	+	0.344127i
$463$			5.58634e8i			0.261574i	0.991411	+	0.130787i	$0.0417503\pi$
$463$			5.58634e8i			0.261574i	−0.991411	+	0.130787i	$0.958250\pi$
$464$	−8.05430e7	−	2.54597e9i	−0.0374296	−	1.18315i
$465$	1.05936e8			0.0488603
$466$	−5.78275e8	−	5.69203e8i	−0.264718	−	0.260565i
$467$			2.72047e9i			1.23605i	0.786159	+	0.618024i	$0.212067\pi$
$467$			2.72047e9i			1.23605i	−0.786159	+	0.618024i	$0.787933\pi$
$468$	−1.73714e8	+	2.74707e6i	−0.0783382	+	0.00123882i
$469$			1.25297e9i			0.560837i
$470$	1.12843e8	−	1.14641e8i	0.0501338	−	0.0509329i
$471$	−3.76762e9			−1.66148
$472$	2.70045e9	−	2.83169e9i	1.18206	−	1.23951i
$473$	−1.47385e9			−0.640384
$474$	1.36464e9	+	1.34324e9i	0.588566	+	0.579332i
$475$	2.27079e9	−	3.80169e8i	0.972187	−	0.162760i
$476$	2.17393e9	−	3.43780e7i	0.923891	−	0.0146102i
$477$		−	1.65694e8i		−	0.0699024i
$478$	1.08198e9	−	1.09923e9i	0.453130	−	0.460352i
$479$		−	4.55132e9i		−	1.89218i	−0.323898	−	0.946092i	$-0.604993\pi$
$479$		−	4.55132e9i		−	1.89218i	0.323898	−	0.946092i	$-0.395007\pi$
$480$	2.26706e8	+	2.09455e8i	0.0935660	+	0.0864462i
$481$	−1.12717e9			−0.461831
$482$	−3.32876e9	+	3.38182e9i	−1.35400	+	1.37558i
$483$	4.14355e9			1.67324
$484$	3.02548e7	+	1.91320e9i	0.0121293	+	0.767009i
$485$			7.59857e7i			0.0302437i
$486$	4.87824e8	+	4.80171e8i	0.192769	+	0.189744i
$487$	−3.79091e9			−1.48728			−0.743638	−	0.668582i	$-0.766902\pi$
$487$	−3.79091e9			−1.48728			−0.743638	+	0.668582i	$0.766902\pi$
$488$	−2.75829e9	+	2.89234e9i	−1.07441	+	1.12663i
$489$		−	5.35422e8i		−	0.207069i
$490$	−2.00784e7	−	1.97634e7i	−0.00770979	−	0.00758883i
$491$			5.11597e9i			1.95049i	0.221135	+	0.975243i	$0.429024\pi$
$491$			5.11597e9i			1.95049i	−0.221135	+	0.975243i	$0.570976\pi$
$492$	−1.28117e9	+	2.02601e7i	−0.484986	+	0.00766945i
$493$		−	3.05141e9i		−	1.14693i
$494$	−8.85343e8	+	1.26239e9i	−0.330421	+	0.471139i
$495$			2.11896e7i			0.00785244i
$496$	−1.04183e9	+	3.29589e7i	−0.383365	+	0.0121279i
$497$			4.94319e8i			0.180618i
$498$	2.84595e9	−	2.89131e9i	1.03258	−	1.04904i
$499$			5.16718e9i			1.86167i	0.365443	+	0.930834i	$0.380917\pi$
$499$			5.16718e9i			1.86167i	−0.365443	+	0.930834i	$0.619083\pi$
$500$	−1.04882e7	−	6.63234e8i	−0.00375238	−	0.237286i
$501$	3.64542e9			1.29514
$502$	1.77169e9	−	1.79993e9i	0.625065	−	0.635028i
$503$			3.16079e8i			0.110741i	0.998466	+	0.0553705i	$0.0176340\pi$
$503$			3.16079e8i			0.110741i	−0.998466	+	0.0553705i	$0.982366\pi$
$504$	2.70063e8	+	2.57546e8i	0.0939632	+	0.0896083i
$505$	−3.88251e8			−0.134151
$506$	−1.64984e9	−	1.62396e9i	−0.566129	−	0.557247i
$507$	2.09206e9			0.712930
$508$	6.11593e7	+	3.86747e9i	0.0206985	+	1.30889i
$509$		−	3.26123e9i		−	1.09615i	−0.836430	−	0.548074i	$-0.815361\pi$
$509$		−	3.26123e9i		−	1.09615i	0.836430	−	0.548074i	$-0.184639\pi$
$510$	2.63507e8	+	2.59373e8i	0.0879623	+	0.0865822i
$511$			1.41123e9i			0.467870i
$512$	−2.29473e9	−	1.98937e9i	−0.755590	−	0.655045i
$513$	2.77693e9	−	4.64904e8i	0.908142	−	0.152038i
$514$	2.98030e9	−	3.02780e9i	0.968030	−	0.983460i
$515$	−9.29635e7			−0.0299907
$516$	−4.41365e9	+	6.97964e7i	−1.41424	+	0.0223645i
$517$	−9.06765e8			−0.288588
$518$	1.72549e9	+	1.69842e9i	0.545456	+	0.536898i
$519$			3.29852e9i			1.03570i
$520$	1.59580e8	+	1.52184e8i	0.0497698	+	0.0474631i
$521$		−	2.57123e9i		−	0.796542i	−0.917268	−	0.398271i	$-0.869610\pi$
$521$		−	2.57123e9i		−	0.796542i	0.917268	−	0.398271i	$-0.130390\pi$
$522$	3.67405e8	−	3.73261e8i	0.113057	−	0.114859i
$523$	−2.34473e9			−0.716699			−0.358349	−	0.933588i	$-0.616660\pi$
$523$	−2.34473e9			−0.716699			−0.358349	+	0.933588i	$0.616660\pi$
$524$	2.01954e9	−	3.19365e7i	0.613186	−	0.00969678i
$525$		−	3.32219e9i		−	1.00200i
$526$	1.83198e9	−	1.86118e9i	0.548872	−	0.557620i
$527$	−1.24866e9			−0.371628
$528$	−5.50140e7	−	1.73900e9i	−0.0162650	−	0.514139i
$529$	−5.82051e9			−1.70949
$530$	−1.47528e8	+	1.49879e8i	−0.0430436	+	0.0437297i
$531$	8.04545e8			0.233195
$532$	3.25746e9	−	5.98451e8i	0.937969	−	0.172321i
$533$	−9.15425e8			−0.261865
$534$	−1.41095e9	+	1.43344e9i	−0.400974	+	0.407365i
$535$	1.13744e8			0.0321136
$536$	1.44695e9	−	1.51727e9i	0.405859	−	0.425584i
$537$	−5.55709e8			−0.154859
$538$	−1.35099e9	+	1.37253e9i	−0.374038	+	0.380000i
$539$			1.58812e8i			0.0436840i
$540$	−6.36684e6	−	4.02614e8i	−0.00173999	−	0.110030i
$541$	−5.85988e8			−0.159110			−0.0795552	−	0.996830i	$-0.525350\pi$
$541$	−5.85988e8			−0.159110			−0.0795552	+	0.996830i	$0.525350\pi$
$542$	4.03469e9	−	4.09900e9i	1.08846	−	1.10581i
$543$			4.05170e9i			1.08602i
$544$	−2.67218e9	−	2.46885e9i	−0.711656	−	0.657503i
$545$		−	2.98202e8i		−	0.0789084i
$546$	1.58560e9	+	1.56072e9i	0.416887	+	0.410346i
$547$	8.10458e8			0.211726			0.105863	−	0.994381i	$-0.466239\pi$
$547$	8.10458e8			0.211726			0.105863	+	0.994381i	$0.466239\pi$
$548$	−2.79639e7	−	1.76833e9i	−0.00725883	−	0.459020i
$549$	−8.21776e8			−0.211958
$550$	−1.30204e9	+	1.32280e9i	−0.333700	+	0.339019i
$551$	−7.67512e8	−	4.58444e9i	−0.195458	−	1.16750i
$552$	−5.01757e9	−	4.78502e9i	−1.26972	−	1.21087i
$553$		−	2.93847e9i		−	0.738895i
$554$	3.39131e9	+	3.33811e9i	0.847390	+	0.834096i
$555$			4.11740e8i			0.102235i
$556$	2.42054e9	−	3.82779e7i	0.597242	−	0.00944465i
$557$	5.87524e9			1.44056			0.720282	−	0.693682i	$-0.244013\pi$
$557$	5.87524e9			1.44056			0.720282	+	0.693682i	$0.244013\pi$
$558$	−1.52742e8	−	1.50345e8i	−0.0372167	−	0.0366328i
$559$	−3.15365e9			−0.763611
$560$	−1.49768e7	−	4.73420e8i	−0.00360381	−	0.113917i
$561$		−	2.08423e9i		−	0.498398i
$562$	5.21538e9	−	5.29850e9i	1.23939	−	1.25915i
$563$	7.24225e9			1.71039			0.855193	−	0.518309i	$-0.173438\pi$
$563$	7.24225e9			1.71039			0.855193	+	0.518309i	$0.173438\pi$
$564$	−2.71543e9	+	4.29411e7i	−0.637325	+	0.0100785i
$565$			1.07303e8i			0.0250290i
$566$	4.17249e9	−	4.23899e9i	0.967248	−	0.982665i
$567$		−	4.62625e9i		−	1.06583i
$568$	5.70845e8	−	5.98588e8i	0.130707	−	0.137059i
$569$			5.91875e9i			1.34690i	0.739231	+	0.673452i	$0.235189\pi$
$569$			5.91875e9i			1.34690i	−0.739231	+	0.673452i	$0.764811\pi$
$570$	4.61132e8	+	3.23402e8i	0.104295	+	0.0731444i
$571$			3.51334e8i			0.0789758i	0.999220	+	0.0394879i	$0.0125727\pi$
$571$			3.51334e8i			0.0789758i	−0.999220	+	0.0394879i	$0.987427\pi$
$572$	−1.96544e7	−	1.24286e9i	−0.00439110	−	0.277676i
$573$			1.93044e9i			0.428661i
$574$	1.40135e9	+	1.37936e9i	0.309282	+	0.304429i
$575$			7.39662e9i			1.62254i
$576$	−2.96109e7	−	6.23743e8i	−0.00645614	−	0.135996i
$577$	−6.32470e9			−1.37064			−0.685321	−	0.728241i	$-0.740338\pi$
$577$	−6.32470e9			−1.37064			−0.685321	+	0.728241i	$0.740338\pi$
$578$	2.02600e8	+	1.99421e8i	0.0436407	+	0.0429560i
$579$		−	9.13658e9i		−	1.95618i
$580$	−6.64676e8	+	1.05110e7i	−0.141453	+	0.00223691i
$581$	−6.22582e9			−1.31698
$582$	8.99910e8	−	9.14254e8i	0.189221	−	0.192237i
$583$	1.18549e9			0.247774
$584$	1.62971e9	−	1.70891e9i	0.338582	−	0.355037i
$585$			4.53400e7i			0.00936346i
$586$	3.45295e9	−	3.50799e9i	0.708842	−	0.720140i
$587$			2.78723e9i			0.568773i	0.958710	+	0.284387i	$0.0917899\pi$
$587$			2.78723e9i			0.568773i	−0.958710	+	0.284387i	$0.908210\pi$
$588$	7.52076e6	+	4.75583e8i	0.00152560	+	0.0964729i
$589$	−1.87599e9	+	3.14073e8i	−0.378292	+	0.0633325i
$590$	−7.27757e8	−	7.16339e8i	−0.145883	−	0.143594i
$591$	−3.08852e9			−0.615452
$592$	−1.28101e8	−	4.04930e9i	−0.0253763	−	0.802147i
$593$	−1.20596e9			−0.237487			−0.118744	−	0.992925i	$-0.537887\pi$
$593$	−1.20596e9			−0.237487			−0.118744	+	0.992925i	$0.537887\pi$
$594$	−1.59226e9	+	1.61764e9i	−0.311717	+	0.316685i
$595$		−	5.67405e8i		−	0.110429i
$596$	1.11712e8	+	7.06425e9i	0.0216142	+	1.36680i
$597$		−	3.25196e9i		−	0.625511i
$598$	−3.53022e9	−	3.47483e9i	−0.675068	−	0.664477i
$599$	−6.49770e9			−1.23528			−0.617641	−	0.786460i	$-0.711911\pi$
$599$	−6.49770e9			−1.23528			−0.617641	+	0.786460i	$0.711911\pi$
$600$	−3.83650e9	+	4.02295e9i	−0.725113	+	0.760353i
$601$			3.81691e9i			0.717218i	0.933488	+	0.358609i	$0.116749\pi$
$601$			3.81691e9i			0.717218i	−0.933488	+	0.358609i	$0.883251\pi$
$602$	4.82765e9	+	4.75191e9i	0.901879	+	0.887730i
$603$	4.31088e8			0.0800673
$604$	−2.44292e7	−	1.54481e9i	−0.00451108	−	0.285263i
$605$	4.99352e8			0.0916776
$606$	4.67140e9	+	4.59812e9i	0.852694	+	0.839317i
$607$	−5.96819e9			−1.08313			−0.541567	−	0.840657i	$-0.682169\pi$
$607$	−5.96819e9			−1.08313			−0.541567	+	0.840657i	$0.682169\pi$
$608$	−4.63567e9	−	3.03707e9i	−0.836469	−	0.548014i
$609$	−6.70707e9			−1.20330
$610$	7.43342e8	+	7.31680e8i	0.132597	+	0.130517i
$611$	−1.94023e9			−0.344120
$612$	−1.18278e7	−	7.47945e8i	−0.00208581	−	0.131899i
$613$	−7.52207e9			−1.31894			−0.659471	−	0.751730i	$-0.729220\pi$
$613$	−7.52207e9			−1.31894			−0.659471	+	0.751730i	$0.729220\pi$
$614$	3.82180e9	+	3.76184e9i	0.666314	+	0.655860i
$615$			3.34391e8i			0.0579685i
$616$	−1.84266e9	+	1.93221e9i	−0.317623	+	0.333060i
$617$	9.54841e9			1.63656			0.818282	−	0.574817i	$-0.194927\pi$
$617$	9.54841e9			1.63656			0.818282	+	0.574817i	$0.194927\pi$
$618$	1.11853e9	+	1.10098e9i	0.190628	+	0.187638i
$619$			5.15322e9i			0.873296i	0.899632	+	0.436648i	$0.143834\pi$
$619$			5.15322e9i			0.873296i	−0.899632	+	0.436648i	$0.856166\pi$
$620$	4.30121e6	+	2.71992e8i	0.000724803	+	0.0458337i
$621$			9.04525e9i			1.51565i
$622$	−3.10926e9	+	3.15882e9i	−0.518073	+	0.526330i
$623$	3.08659e9			0.511412
$624$	−1.17715e8	−	3.72099e9i	−0.0193949	−	0.613074i
$625$	5.84323e9			0.957355
$626$	−3.03472e9	−	2.98711e9i	−0.494434	−	0.486677i
$627$	−5.24241e8	−	3.13135e9i	−0.0849365	−	0.507336i
$628$	−1.52973e8	−	9.67343e9i	−0.0246466	−	1.55855i
$629$		−	4.85319e9i		−	0.777588i
$630$	6.83183e7	−	6.94072e7i	0.0108854	−	0.0110589i
$631$		−	9.95626e8i		−	0.157759i	−0.996884	−	0.0788794i	$-0.974866\pi$
$631$		−	9.95626e8i		−	0.157759i	0.996884	−	0.0788794i	$-0.0251342\pi$
$632$	−3.39337e9	+	3.55829e9i	−0.534714	+	0.560701i
$633$	1.19758e10			1.87669
$634$	−5.32289e9	+	5.40773e9i	−0.829536	+	0.842757i
$635$	1.00943e9			0.156447
$636$	3.55009e9	−	5.61403e7i	0.547192	−	0.00865317i
$637$			3.39815e8i			0.0520900i
$638$	2.67056e9	+	2.62866e9i	0.407127	+	0.400739i
$639$	1.70072e8			0.0257857
$640$	−5.28574e8	+	5.90575e8i	−0.0797033	+	0.0890523i
$641$			7.73979e9i			1.16072i	0.814361	+	0.580358i	$0.197087\pi$
$641$			7.73979e9i			1.16072i	−0.814361	+	0.580358i	$0.802913\pi$
$642$	−1.36855e9	−	1.34708e9i	−0.204122	−	0.200919i
$643$			4.69901e9i			0.697056i	0.937298	+	0.348528i	$0.113318\pi$
$643$			4.69901e9i			0.697056i	−0.937298	+	0.348528i	$0.886682\pi$
$644$	1.68237e8	+	1.06387e10i	0.0248211	+	1.56959i
$645$			1.15198e9i			0.169039i
$646$	−5.43537e9	−	3.81195e9i	−0.793259	−	0.556331i
$647$		−	3.25346e9i		−	0.472259i	−0.971722	−	0.236130i	$-0.924121\pi$
$647$		−	3.25346e9i		−	0.472259i	0.971722	−	0.236130i	$-0.0758790\pi$
$648$	−5.34244e9	+	5.60208e9i	−0.771307	+	0.808792i
$649$			5.75626e9i			0.826578i
$650$	−2.78603e9	+	2.83043e9i	−0.397913	+	0.404256i
$651$			2.74459e9i			0.389892i
$652$	1.37470e9	−	2.17393e7i	0.194242	−	0.00307170i
$653$	2.04890e9			0.287955			0.143978	−	0.989581i	$-0.454011\pi$
$653$	2.04890e9			0.287955			0.143978	+	0.989581i	$0.454011\pi$
$654$	−3.53166e9	+	3.58795e9i	−0.493692	+	0.501561i
$655$		−	5.27108e8i		−	0.0732917i
$656$	−1.04037e8	−	3.28861e9i	−0.0143887	−	0.454829i
$657$	4.85538e8			0.0667950
$658$	2.97014e9	+	2.92354e9i	0.406430	+	0.400054i
$659$	−1.98469e8			−0.0270143			−0.0135072	−	0.999909i	$-0.504300\pi$
$659$	−1.98469e8			−0.0270143			−0.0135072	+	0.999909i	$0.504300\pi$
$660$	−4.54000e8	+	7.17945e6i	−0.0614684	+	0.000972047i
$661$			7.74590e9i			1.04320i	0.853191	+	0.521599i	$0.174664\pi$
$661$			7.74590e9i			1.04320i	−0.853191	+	0.521599i	$0.825336\pi$
$662$	−3.23095e9	−	3.18026e9i	−0.432840	−	0.426050i
$663$		−	4.45970e9i		−	0.594303i
$664$	7.53905e9	+	7.18964e9i	0.999375	+	0.953057i
$665$	−1.42718e8	−	8.52469e8i	−0.0188192	−	0.112409i
$666$	5.84347e8	−	5.93661e8i	0.0766498	−	0.0778715i
$667$	1.49328e10			1.94851
$668$	1.48012e8	+	9.35969e9i	0.0192123	+	1.21491i
$669$	5.82411e9			0.752036
$670$	−3.89944e8	−	3.83826e8i	−0.0500887	−	0.0493029i
$671$		−	5.87954e9i		−	0.751302i
$672$	−5.42658e9	+	5.87352e9i	−0.689817	+	0.746631i
$673$		−	3.60932e9i		−	0.456428i	−0.973611	−	0.228214i	$-0.926711\pi$
$673$		−	3.60932e9i		−	0.456428i	0.973611	−	0.228214i	$-0.0732886\pi$
$674$	−4.38310e9	+	4.45296e9i	−0.551407	+	0.560195i
$675$	7.25223e9			0.907630
$676$	8.49422e7	+	5.37141e9i	0.0105757	+	0.668767i
$677$		−	9.54799e9i		−	1.18264i	−0.806438	−	0.591319i	$-0.798608\pi$
$677$		−	9.54799e9i		−	1.18264i	0.806438	−	0.591319i	$-0.201392\pi$
$678$	1.27081e9	−	1.29107e9i	0.156595	−	0.159091i
$679$	−1.96865e9			−0.241337
$680$	−6.55246e8	+	6.87090e8i	−0.0799140	+	0.0837978i
$681$	4.80239e9			0.582697
$682$	1.07567e9	−	1.09282e9i	0.129848	−	0.131917i
$683$	1.17627e10			1.41266			0.706328	−	0.707885i	$-0.250350\pi$
$683$	1.17627e10			1.41266			0.706328	+	0.707885i	$0.250350\pi$
$684$	−2.05898e8	−	1.12074e9i	−0.0246012	−	0.133908i
$685$	−4.61542e8			−0.0548648
$686$	6.16863e9	−	6.26695e9i	0.729549	−	0.741177i
$687$	−1.37499e10			−1.61790
$688$	−3.58407e8	−	1.13293e10i	−0.0419582	−	1.32630i
$689$	2.53662e9			0.295453
$690$	−1.26930e9	+	1.28954e9i	−0.147094	+	0.149438i
$691$			2.53148e9i			0.291878i	0.989294	+	0.145939i	$0.0466203\pi$
$691$			2.53148e9i			0.291878i	−0.989294	+	0.145939i	$0.953380\pi$
$692$	−8.46900e9	+	1.33927e8i	−0.971540	+	0.0153637i
$693$	−5.48983e8			−0.0626603
$694$	3.77854e6	−	3.83876e6i	0.000429107	−	0.000435947i
$695$		−	6.31772e8i		−	0.0713861i
$696$	8.12182e9	+	7.74540e9i	0.913106	+	0.870786i
$697$		−	3.94148e9i		−	0.440904i
$698$	−1.19506e10	−	1.17631e10i	−1.33013	−	1.30926i
$699$	3.57503e9			0.395922
$700$	8.52978e9	−	1.34888e8i	0.939928	−	0.0148638i
$701$	1.43587e10			1.57436			0.787179	−	0.616725i	$-0.211541\pi$
$701$	1.43587e10			1.57436			0.787179	+	0.616725i	$0.211541\pi$
$702$	−3.40700e9	+	3.46131e9i	−0.371700	+	0.377624i
$703$	−1.22071e9	−	7.29142e9i	−0.132516	−	0.791532i
$704$	4.46268e9	−	2.11857e8i	0.482049	−	0.0228843i
$705$			7.08739e8i			0.0761771i
$706$	4.34714e9	+	4.27894e9i	0.464929	+	0.457635i
$707$		−	1.00589e10i		−	1.07049i
$708$	2.72596e8	+	1.72379e10i	0.0288671	+	1.82544i
$709$	−1.13789e10			−1.19905			−0.599524	−	0.800357i	$-0.704643\pi$
$709$	−1.13789e10			−1.19905			−0.599524	+	0.800357i	$0.704643\pi$
$710$	−1.53839e8	−	1.51426e8i	−0.0161311	−	0.0158780i
$711$	−1.01099e9			−0.105488
$712$	−3.73766e9	−	3.56443e9i	−0.388079	−	0.370092i
$713$		−	6.11065e9i		−	0.631355i
$714$	−6.71987e9	+	6.82697e9i	−0.690903	+	0.701915i
$715$	−3.24393e8			−0.0331895
$716$	−2.25630e7	−	1.42679e9i	−0.00229721	−	0.145266i
$717$			6.79569e9i			0.688520i
$718$	−8.86772e9	+	9.00906e9i	−0.894080	+	0.908331i
$719$		−	7.18692e9i		−	0.721093i	−0.932741	−	0.360547i	$-0.882590\pi$
$719$		−	7.18692e9i		−	0.721093i	0.932741	−	0.360547i	$-0.117410\pi$
$720$	−1.62881e8	+	5.15282e6i	−0.0162632	+	0.000514495i
$721$		−	2.40851e9i		−	0.239318i
$722$	−9.12490e9	−	4.35993e9i	−0.902294	−	0.431121i
$723$		−	2.09072e10i		−	2.05737i
$724$	−1.04028e10	+	1.64508e8i	−1.01875	+	0.0161102i
$725$		−	1.19727e10i		−	1.16684i
$726$	−6.00817e9	−	5.91391e9i	−0.582726	−	0.573583i
$727$			1.31873e10i			1.27287i	0.771330	+	0.636436i	$0.219592\pi$
$727$			1.31873e10i			1.27287i	−0.771330	+	0.636436i	$0.780408\pi$
$728$	−3.94280e9	+	4.13441e9i	−0.378743	+	0.397150i
$729$	8.67478e9			0.829301
$730$	−4.39196e8	−	4.32306e8i	−0.0417858	−	0.0411302i
$731$		−	1.35784e10i		−	1.28570i
$732$	−2.78434e8	−	1.76070e10i	−0.0262381	−	1.65920i
$733$	−1.02131e10			−0.957844			−0.478922	−	0.877858i	$-0.658972\pi$
$733$	−1.02131e10			−0.957844			−0.478922	+	0.877858i	$0.658972\pi$
$734$	−5.51933e9	+	5.60730e9i	−0.515169	+	0.523380i
$735$	1.24129e8			0.0115310
$736$	1.20819e10	−	1.30770e10i	1.11703	−	1.20903i
$737$			3.08430e9i			0.283805i
$738$	4.74573e8	−	4.82137e8i	0.0434616	−	0.0441543i
$739$			1.76440e10i			1.60820i	0.594491	+	0.804102i	$0.297354\pi$
$739$			1.76440e10i			1.60820i	−0.594491	+	0.804102i	$0.702646\pi$
$740$	−1.05715e9	+	1.67175e7i	−0.0959015	+	0.00151656i
$741$	−1.12173e9	−	6.70025e9i	−0.101281	−	0.604961i
$742$	−3.88310e9	−	3.82218e9i	−0.348951	−	0.343477i
$743$	−6.62893e9			−0.592902			−0.296451	−	0.955048i	$-0.595803\pi$
$743$	−6.62893e9			−0.592902			−0.296451	+	0.955048i	$0.595803\pi$
$744$	3.16949e9	−	3.32352e9i	0.282152	−	0.295865i
$745$	1.84380e9			0.163368
$746$	−5.41083e9	+	5.49707e9i	−0.477175	+	0.484781i
$747$			2.14201e9i			0.188018i
$748$	5.35131e9	−	8.46243e7i	0.467524	−	0.00739332i
$749$			2.94688e9i			0.256258i
$750$	2.08281e9	+	2.05013e9i	0.180275	+	0.177447i
$751$	−1.46244e10			−1.25991			−0.629954	−	0.776632i	$-0.716926\pi$
$751$	−1.46244e10			−1.25991			−0.629954	+	0.776632i	$0.716926\pi$
$752$	−2.20504e8	−	6.97017e9i	−0.0189084	−	0.597696i
$753$			1.11276e10i			0.949771i
$754$	5.71428e9	+	5.62463e9i	0.485469	+	0.477853i
$755$	−4.03202e8			−0.0340964
$756$	1.04310e10	−	1.64953e8i	0.878009	−	0.0138846i
$757$	1.95864e9			0.164104			0.0820521	−	0.996628i	$-0.473853\pi$
$757$	1.95864e9			0.164104			0.0820521	+	0.996628i	$0.473853\pi$
$758$	−2.28113e9	−	2.24534e9i	−0.190242	−	0.187258i
$759$	1.01997e10			0.846723
$760$	−8.11619e8	+	1.19710e9i	−0.0670663	+	0.0989193i
$761$	1.25846e10			1.03512			0.517562	−	0.855646i	$-0.326840\pi$
$761$	1.25846e10			1.03512			0.517562	+	0.855646i	$0.326840\pi$
$762$	−1.21453e10	−	1.19548e10i	−0.994415	−	0.978814i
$763$	7.72586e9			0.629667
$764$	−4.95643e9	+	7.83798e7i	−0.402107	+	0.00635883i
$765$	−1.95217e8			−0.0157653
$766$	−3.03700e9	−	2.98935e9i	−0.244143	−	0.240312i
$767$			1.23169e10i			0.985635i
$768$	1.33540e10	−	8.45768e8i	1.06377	−	0.0673732i
$769$	−2.39727e9			−0.190097			−0.0950484	−	0.995473i	$-0.530301\pi$
$769$	−2.39727e9			−0.190097			−0.0950484	+	0.995473i	$0.530301\pi$
$770$	4.96586e8	+	4.88795e8i	0.0391992	+	0.0385842i
$771$			1.87186e10i			1.47090i
$772$	2.34583e10	−	3.70964e8i	1.83500	−	0.0290183i
$773$		−	1.25629e10i		−	0.978274i	−0.872207	−	0.489137i	$-0.837312\pi$
$773$		−	1.25629e10i		−	0.978274i	0.872207	−	0.489137i	$-0.162688\pi$
$774$	1.63491e9	−	1.66097e9i	0.126736	−	0.128756i
$775$	−4.89935e9			−0.378079
$776$	2.38390e9	+	2.27342e9i	0.183135	+	0.174648i
$777$	−1.06674e10			−0.815804
$778$	−9.42191e9	−	9.27409e9i	−0.717316	−	0.706062i
$779$	−9.91387e8	−	5.92167e9i	−0.0751384	−	0.448811i
$780$	−9.71438e8	+	1.53621e7i	−0.0732966	+	0.00115910i
$781$			1.21681e9i			0.0913994i
$782$	1.49613e10	−	1.51998e10i	1.11878	−	1.13662i
$783$		−	1.46413e10i		−	1.08997i
$784$	−1.22076e9	+	3.86194e7i	−0.0904742	+	0.00286219i
$785$	−2.52481e9			−0.186288
$786$	−6.24262e9	+	6.34212e9i	−0.458552	+	0.465860i
$787$	−4.82261e9			−0.352672			−0.176336	−	0.984330i	$-0.556424\pi$
$787$	−4.82261e9			−0.352672			−0.176336	+	0.984330i	$0.556424\pi$
$788$	−1.25401e8	−	7.92984e9i	−0.00912973	−	0.577328i
$789$			1.15063e10i			0.833997i
$790$	9.14494e8	+	9.00147e8i	0.0659912	+	0.0649559i
$791$	−2.78003e9			−0.199725
$792$	6.64782e8	+	6.33972e8i	0.0475490	+	0.0453452i
$793$		−	1.25806e10i		−	0.895873i
$794$	−1.26603e9	−	1.24616e9i	−0.0897575	−	0.0883493i
$795$		−	9.26590e8i		−	0.0654038i
$796$	8.34947e9	−	1.32037e8i	0.586764	−	0.00927894i
$797$		−	1.44734e10i		−	1.01266i	−0.862339	−	0.506332i	$-0.831001\pi$
$797$		−	1.44734e10i		−	1.01266i	0.862339	−	0.506332i	$-0.168999\pi$
$798$	−8.37876e9	+	1.19471e10i	−0.583673	+	0.832245i
$799$		−	8.35391e9i		−	0.579397i
$800$	−1.04848e10	−	9.68694e9i	−0.724009	−	0.668916i
$801$		−	1.06195e9i		−	0.0730113i
$802$	1.05358e10	−	1.07037e10i	0.721199	−	0.732694i
$803$			3.47386e9i			0.236760i
$804$	1.46061e8	+	9.23633e9i	0.00991148	+	0.626763i
$805$	2.77674e9			0.187607
$806$	2.30165e9	−	2.33833e9i	0.154834	−	0.157302i
$807$		−	8.48529e9i		−	0.568341i
$808$	−1.16161e10	+	1.21806e10i	−0.774675	+	0.812324i
$809$	2.45503e10			1.63018			0.815092	−	0.579331i	$-0.196686\pi$
$809$	2.45503e10			1.63018			0.815092	+	0.579331i	$0.196686\pi$
$810$	1.43976e9	+	1.41717e9i	0.0951901	+	0.0936966i
$811$	1.80710e10			1.18962			0.594812	−	0.803865i	$-0.297227\pi$
$811$	1.80710e10			1.18962			0.594812	+	0.803865i	$0.297227\pi$
$812$	−2.72321e8	−	1.72205e10i	−0.0178499	−	1.12876i
$813$			2.53410e10i			1.65389i
$814$	4.24745e9	+	4.18081e9i	0.276022	+	0.271691i
$815$		−	3.58804e8i		−	0.0232170i
$816$	1.60212e10	−	5.06837e8i	1.03224	−	0.0326552i
$817$	−3.41534e9	−	2.04002e10i	−0.219107	−	1.30875i
$818$	1.44061e10	−	1.46357e10i	0.920260	−	0.934928i
$819$	−1.17468e9			−0.0747179
$820$	−8.58556e8	+	1.35770e7i	−0.0543776	+	0.000859915i
$821$	−2.78652e10			−1.75736			−0.878681	−	0.477409i	$-0.841576\pi$
$821$	−2.78652e10			−1.75736			−0.878681	+	0.477409i	$0.841576\pi$
$822$	5.55324e9	+	5.46611e9i	0.348734	+	0.343263i
$823$			3.88911e9i			0.243193i	0.992580	+	0.121596i	$0.0388014\pi$
$823$			3.88911e9i			0.243193i	−0.992580	+	0.121596i	$0.961199\pi$
$824$	−2.78137e9	+	2.91655e9i	−0.173187	+	0.181603i
$825$		−	8.17785e9i		−	0.507049i
$826$	1.85590e10	−	1.88548e10i	1.14584	−	1.16411i
$827$	−2.11541e10			−1.30054			−0.650272	−	0.759701i	$-0.725345\pi$
$827$	−2.11541e10			−1.30054			−0.650272	+	0.759701i	$0.725345\pi$
$828$	3.66025e9	−	5.78824e7i	0.224081	−	0.00354357i
$829$			2.72672e10i			1.66226i	0.556076	+	0.831132i	$0.312306\pi$
$829$			2.72672e10i			1.66226i	−0.556076	+	0.831132i	$0.687694\pi$
$830$	1.90717e9	−	1.93757e9i	0.115775	−	0.117621i
$831$	−2.09659e10			−1.26739
$832$	9.54893e9	−	4.53316e8i	0.574809	−	0.0272879i
$833$	−1.46311e9			−0.0877042
$834$	−7.48217e9	+	7.60143e9i	−0.446629	+	0.453747i
$835$	2.44292e9			0.145213
$836$	8.01851e9	−	1.47314e9i	0.474648	−	0.0872009i
$837$	−5.99136e9			−0.353172
$838$	−1.38697e10	+	1.40907e10i	−0.814164	+	0.827141i
$839$	−6.09974e9			−0.356570			−0.178285	−	0.983979i	$-0.557055\pi$
$839$	−6.09974e9			−0.356570			−0.178285	+	0.983979i	$0.557055\pi$
$840$	1.51024e9	+	1.44024e9i	0.0879161	+	0.0838415i
$841$	−6.92153e9			−0.401251
$842$	1.44938e10	−	1.47248e10i	0.836737	−	0.850073i
$843$			3.27566e10i			1.88323i
$844$	4.86244e8	+	3.07482e10i	0.0278391	+	1.76044i
$845$	1.40196e9			0.0799351
$846$	1.00585e9	−	1.02188e9i	0.0571134	−	0.0580237i
$847$			1.29373e10i			0.731563i
$848$	2.88283e8	+	9.11265e9i	0.0162343	+	0.513167i
$849$			2.62065e10i			1.46971i
$850$	−1.21868e10	−	1.19956e10i	−0.680648	−	0.669969i
$851$	2.37503e10			1.32104
$852$	5.76236e7	+	3.64389e9i	0.00319199	+	0.201849i
$853$	−9.88474e9			−0.545310			−0.272655	−	0.962112i	$-0.587902\pi$
$853$	−9.88474e9			−0.545310			−0.272655	+	0.962112i	$0.587902\pi$
$854$	−1.89565e10	+	1.92586e10i	−1.04149	+	1.05809i
$855$	−2.93294e8	+	4.91023e7i	−0.0160480	+	0.00268671i
$856$	3.40310e9	−	3.56848e9i	0.185445	−	0.194458i
$857$		−	2.12913e10i		−	1.15550i	−0.816215	−	0.577749i	$-0.803931\pi$
$857$		−	2.12913e10i		−	1.15550i	0.816215	−	0.577749i	$-0.196069\pi$
$858$	3.90308e9	+	3.84184e9i	0.210961	+	0.207651i
$859$		−	1.10128e10i		−	0.592818i	−0.955061	−	0.296409i	$-0.904211\pi$
$859$		−	1.10128e10i		−	0.592818i	0.955061	−	0.296409i	$-0.0957892\pi$
$860$	−2.95773e9	+	4.67729e7i	−0.158568	+	0.00250755i
$861$	−8.66346e9			−0.462573
$862$	2.60743e10	+	2.56652e10i	1.38655	+	1.36480i
$863$	1.66519e10			0.881911			0.440955	−	0.897529i	$-0.354640\pi$
$863$	1.66519e10			0.881911			0.440955	+	0.897529i	$0.354640\pi$
$864$	−1.28217e10	−	1.18461e10i	−0.676313	−	0.624850i
$865$			2.21045e9i			0.116124i
$866$	−1.89018e10	+	1.92031e10i	−0.988989	+	1.00475i
$867$	−1.25252e9			−0.0652706
$868$	−7.04679e9	+	1.11436e8i	−0.365740	+	0.00578373i
$869$		−	7.23328e9i		−	0.373909i
$870$	2.05459e9	−	2.08734e9i	0.105781	−	0.107467i
$871$			6.59956e9i			0.338417i
$872$	−9.35551e9	−	8.92191e9i	−0.477815	−	0.455670i
$873$			6.77318e8i			0.0344542i
$874$	1.86547e10	−	2.65993e10i	0.945146	−	1.34766i
$875$		−	4.48488e9i		−	0.226320i
$876$	1.64510e8	+	1.04029e10i	0.00826851	+	0.522868i
$877$		−	1.22205e10i		−	0.611772i	−0.952068	−	0.305886i	$-0.901047\pi$
$877$		−	1.22205e10i		−	0.611772i	0.952068	−	0.305886i	$-0.0989527\pi$
$878$	−3.92656e9	−	3.86496e9i	−0.195786	−	0.192714i
$879$			2.16872e10i			1.07707i
$880$	−3.68667e7	−	1.16536e9i	−0.00182367	−	0.0576463i
$881$	−1.24907e10			−0.615417			−0.307708	−	0.951481i	$-0.599562\pi$
$881$	−1.24907e10			−0.615417			−0.307708	+	0.951481i	$0.599562\pi$
$882$	−1.78974e8	−	1.76166e8i	−0.00878313	−	0.00864534i
$883$			2.85138e10i			1.39377i	0.717181	+	0.696887i	$0.245432\pi$
$883$			2.85138e10i			1.39377i	−0.717181	+	0.696887i	$0.754568\pi$
$884$	1.14504e10	−	1.81073e8i	0.557489	−	0.00881600i
$885$	4.49916e9			0.218188
$886$	−1.94621e10	+	1.97724e10i	−0.940097	+	0.955081i
$887$	1.89303e10			0.910806			0.455403	−	0.890286i	$-0.349495\pi$
$887$	1.89303e10			0.910806			0.455403	+	0.890286i	$0.349495\pi$
$888$	1.29175e10	+	1.23188e10i	0.619062	+	0.590371i
$889$			2.61524e10i			1.24840i
$890$	−9.45523e8	+	9.60593e8i	−0.0449580	+	0.0456746i
$891$		−	1.13879e10i		−	0.539351i
$892$	2.36471e8	+	1.49535e10i	0.0111558	+	0.705450i
$893$	−2.10123e9	−	1.25509e10i	−0.0987402	−	0.589787i
$894$	−2.21845e10	−	2.18364e10i	−1.03841	−	1.02212i
$895$	−3.72399e8			−0.0173631
$896$	−1.53007e10	−	1.36944e10i	−0.710613	−	0.636010i
$897$	2.18246e10			1.00966
$898$	5.07366e9	−	5.15452e9i	0.233805	−	0.237532i
$899$			9.89116e9i			0.454034i
$900$	−4.64085e7	−	2.93469e9i	−0.00212202	−	0.134188i
$901$			1.09217e10i			0.497456i
$902$	3.44953e9	+	3.39541e9i	0.156508	+	0.154053i
$903$	−2.98457e10			−1.34888
$904$	3.36644e9	+	3.21041e9i	0.151559	+	0.144534i
$905$			2.71518e9i			0.121767i
$906$	4.85129e9	+	4.77518e9i	0.216725	+	0.213325i
$907$	1.37469e9			0.0611759			0.0305880	−	0.999532i	$-0.490262\pi$
$907$	1.37469e9			0.0611759			0.0305880	+	0.999532i	$0.490262\pi$
$908$	1.94987e8	+	1.23302e10i	0.00864383	+	0.546601i
$909$	−3.46077e9			−0.152827
$910$	1.06256e9	+	1.04589e9i	0.0467422	+	0.0460089i
$911$	5.55774e9			0.243548			0.121774	−	0.992558i	$-0.461142\pi$
$911$	5.55774e9			0.243548			0.121774	+	0.992558i	$0.461142\pi$
$912$	2.39427e10	−	4.79123e9i	1.04518	−	0.209153i
$913$	−1.53254e10			−0.666443
$914$	2.46057e10	+	2.42196e10i	1.06592	+	1.04919i
$915$	−4.59552e9			−0.198317
$916$	−5.58276e8	−	3.53032e10i	−0.0240002	−	1.51768i
$917$	1.36564e10			0.584848
$918$	−1.49031e10	−	1.46693e10i	−0.635809	−	0.625834i
$919$			3.03476e10i			1.28979i	0.764269	+	0.644897i	$0.223100\pi$
$919$			3.03476e10i			1.28979i	−0.764269	+	0.644897i	$0.776900\pi$
$920$	−3.36244e9	−	3.20661e9i	−0.142363	−	0.135765i
$921$	−2.36273e10			−0.996563
$922$	−2.28889e9	−	2.25298e9i	−0.0961760	−	0.0946671i
$923$			2.60364e9i			0.108987i
$924$	−1.86006e8	−	1.17623e10i	−0.00775667	−	0.490501i
$925$		−	1.90423e10i		−	0.791086i
$926$	4.43360e9	−	4.50426e9i	0.183492	−	0.186417i
$927$	−8.28654e8			−0.0341660
$928$	−1.95567e10	+	2.11674e10i	−0.803300	+	0.869460i
$929$	−3.98580e10			−1.63102			−0.815511	−	0.578741i	$-0.803544\pi$
$929$	−3.98580e10			−1.63102			−0.815511	+	0.578741i	$0.803544\pi$
$930$	−8.54158e8	−	8.40758e8i	−0.0348216	−	0.0342752i
$931$	−2.19818e9	+	3.68012e8i	−0.0892770	+	0.0149465i
$932$	1.45154e8	+	9.17896e9i	0.00587318	+	0.371397i
$933$		−	1.95286e10i		−	0.787199i
$934$	2.15910e10	−	2.19352e10i	0.867080	−	0.880901i
$935$		−	1.39671e9i		−	0.0558814i
$936$	1.42246e9	+	1.35653e9i	0.0566987	+	0.0540709i
$937$	−1.10136e10			−0.437362			−0.218681	−	0.975796i	$-0.570175\pi$
$937$	−1.10136e10			−0.437362			−0.218681	+	0.975796i	$0.570175\pi$
$938$	9.94421e9	−	1.01027e10i	0.393424	−	0.399694i
$939$	1.87613e10			0.739493
$940$	−1.81970e9	+	2.87763e7i	−0.0714582	+	0.00113002i
$941$			2.61000e10i			1.02112i	0.859842	+	0.510560i	$0.170562\pi$
$941$			2.61000e10i			1.02112i	−0.859842	+	0.510560i	$0.829438\pi$
$942$	3.03783e10	+	2.99017e10i	1.18409	+	1.16552i
$943$	1.92886e10			0.749048
$944$	−4.42475e10	+	1.39979e9i	−1.71193	+	0.0541578i
$945$		−	2.72253e9i		−	0.104945i
$946$	1.18837e10	+	1.16972e10i	0.456385	+	0.449225i
$947$		−	3.75116e10i		−	1.43529i	−0.696407	−	0.717647i	$-0.745219\pi$
$947$		−	3.75116e10i		−	1.43529i	0.696407	−	0.717647i	$-0.254781\pi$
$948$	−3.42542e8	−	2.16610e10i	−0.0130582	−	0.825752i
$949$			7.43314e9i			0.282319i
$950$	−2.13266e10	−	1.49568e10i	−0.807029	−	0.565988i
$951$		−	3.34319e10i		−	1.26046i
$952$	−1.78012e10	−	1.69762e10i	−0.668683	−	0.637692i
$953$			3.97340e10i			1.48709i	0.668686	+	0.743545i	$0.266857\pi$
$953$			3.97340e10i			1.48709i	−0.668686	+	0.743545i	$0.733143\pi$
$954$	−1.31503e9	+	1.33599e9i	−0.0490361	+	0.0498177i
$955$			1.29365e9i			0.0480623i
$956$	−1.74481e10	+	2.75919e8i	−0.645869	+	0.0102136i
$957$	−1.65100e10			−0.608914
$958$	−3.61216e10	+	3.66973e10i	−1.32736	+	1.34851i
$959$		−	1.19577e10i		−	0.437806i
$960$	−1.65590e8	−	3.48808e9i	−0.00604065	−	0.127244i
$961$	−2.34651e10			−0.852884
$962$	9.08840e9	+	8.94582e9i	0.329136	+	0.323972i
$963$	1.01388e9			0.0365844
$964$	5.36796e10	−	8.48877e8i	1.92992	−	0.0305194i
$965$		−	6.12273e9i		−	0.219331i
$966$	−3.34095e10	−	3.28853e10i	−1.19248	−	1.17377i
$967$			1.52114e10i			0.540973i	0.962724	+	0.270487i	$0.0871846\pi$
$967$			1.52114e10i			0.540973i	−0.962724	+	0.270487i	$0.912815\pi$
$968$	1.49401e10	−	1.56662e10i	0.529408	−	0.555137i
$969$	2.88487e10	−	4.82976e9i	1.01858	−	0.170527i
$970$	6.03060e8	−	6.12672e8i	0.0212158	−	0.0215540i
$971$	7.26245e9			0.254575			0.127288	−	0.991866i	$-0.459373\pi$
$971$	7.26245e9			0.254575			0.127288	+	0.991866i	$0.459373\pi$
$972$	−1.22450e8	−	7.74323e9i	−0.00427687	−	0.270452i
$973$	1.63680e10			0.569641
$974$	3.05661e10	+	3.00865e10i	1.05995	+	1.04332i
$975$		−	1.74984e10i		−	0.604619i
$976$	4.51951e10	−	1.42977e9i	1.55603	−	0.0492256i
$977$		−	1.44675e10i		−	0.496322i	−0.968719	−	0.248161i	$-0.920174\pi$
$977$		−	1.44675e10i		−	0.496322i	0.968719	−	0.248161i	$-0.0798262\pi$
$978$	−4.24937e9	+	4.31710e9i	−0.145258	+	0.147573i
$979$	7.59790e9			0.258794
$980$	5.03991e6	+	3.18704e8i	0.000171053	+	0.0108167i
$981$		−	2.65810e9i		−	0.0898939i
$982$	4.06029e10	−	4.12501e10i	1.36825	−	1.39006i
$983$	−3.57450e10			−1.20027			−0.600133	−	0.799900i	$-0.704886\pi$
$983$	−3.57450e10			−1.20027			−0.600133	+	0.799900i	$0.704886\pi$
$984$	1.04909e10	+	1.00047e10i	0.351017	+	0.334749i
$985$	−2.06972e9			−0.0690058
$986$	−2.42175e10	+	2.46035e10i	−0.804564	+	0.817388i
$987$	−1.83621e10			−0.607872
$988$	1.71575e10	−	3.15212e9i	0.565984	−	0.103981i
$989$	6.64494e10			2.18426
$990$	1.68171e8	−	1.70852e8i	0.00550844	−	0.00559624i
$991$	−1.78857e10			−0.583777			−0.291889	−	0.956452i	$-0.594284\pi$
$991$	−1.78857e10			−0.583777			−0.291889	+	0.956452i	$0.594284\pi$
$992$	8.66189e9	+	8.00277e9i	0.281723	+	0.260285i
$993$	1.99745e10			0.647372
$994$	3.92316e9	−	3.98569e9i	0.126702	−	0.128722i
$995$		−	2.17925e9i		−	0.0701336i
$996$	−4.58938e10	+	7.25754e8i	−1.47179	+	0.0232746i
$997$	−7.96864e9			−0.254654			−0.127327	−	0.991861i	$-0.540640\pi$
$997$	−7.96864e9			−0.254654			−0.127327	+	0.991861i	$0.540640\pi$
$998$	4.10094e10	−	4.16630e10i	1.30595	−	1.32676i
$999$		−	2.32866e10i		−	0.738971i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.d.a.75.15	✓	68
4.3	odd	2	inner	76.8.d.a.75.53	yes	68
19.18	odd	2	inner	76.8.d.a.75.54	yes	68
76.75	even	2	inner	76.8.d.a.75.16	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.d.a.75.15	✓	68	1.1	even	1	trivial
76.8.d.a.75.16	yes	68	76.75	even	2	inner
76.8.d.a.75.53	yes	68	4.3	odd	2	inner
76.8.d.a.75.54	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)

\(f(q)\)	\(=\)	\(q+(-8.06300 - 7.93650i) q^{2} +49.8474 q^{3} +(2.02391 + 127.984i) q^{4} +33.4044 q^{5} +(-401.919 - 395.614i) q^{6} +865.446i q^{7} +(999.426 - 1048.00i) q^{8} +297.759 q^{9} +O(q^{10})\)	\(q+(-8.06300 - 7.93650i) q^{2} +49.8474 q^{3} +(2.02391 + 127.984i) q^{4} +33.4044 q^{5} +(-401.919 - 395.614i) q^{6} +865.446i q^{7} +(999.426 - 1048.00i) q^{8} +297.759 q^{9} +(-269.340 - 265.114i) q^{10} +2130.37i q^{11} +(100.887 + 6379.66i) q^{12} +4558.41i q^{13} +(6868.61 - 6978.09i) q^{14} +1665.12 q^{15} +(-16375.8 + 518.056i) q^{16} -19626.8 q^{17} +(-2400.83 - 2363.16i) q^{18} +(-29487.3 + 4936.67i) q^{19} +(67.6075 + 4275.23i) q^{20} +43140.2i q^{21} +(16907.7 - 17177.1i) q^{22} -96048.6i q^{23} +(49818.8 - 52239.9i) q^{24} -77009.1 q^{25} +(36177.9 - 36754.5i) q^{26} -94173.7 q^{27} +(-110763. + 1751.58i) q^{28} +155472. i q^{29} +(-13425.9 - 13215.2i) q^{30} +63620.4 q^{31} +(136150. + 125790. i) q^{32} +106193. i q^{33} +(158251. + 155768. i) q^{34} +28909.7i q^{35} +(602.637 + 38108.4i) q^{36} +247273. i q^{37} +(276936. + 194222. i) q^{38} +227225. i q^{39} +(33385.2 - 35007.7i) q^{40} +200821. i q^{41} +(342382. - 347839. i) q^{42} +691830. i q^{43} +(-272653. + 4311.67i) q^{44} +9946.45 q^{45} +(-762290. + 774440. i) q^{46} +425638. i q^{47} +(-816291. + 25823.7i) q^{48} +74546.7 q^{49} +(620925. + 611183. i) q^{50} -978344. q^{51} +(-583404. + 9225.82i) q^{52} -556470. i q^{53} +(759322. + 747409. i) q^{54} +71163.6i q^{55} +(906985. + 864949. i) q^{56} +(-1.46986e6 + 246080. i) q^{57} +(1.23390e6 - 1.25357e6i) q^{58} +2.70200e6 q^{59} +(3370.05 + 213109. i) q^{60} -2.75987e6 q^{61} +(-512971. - 504923. i) q^{62} +257694. i q^{63} +(-99446.0 - 2.09479e6i) q^{64} +152271. i q^{65} +(842802. - 856235. i) q^{66} +1.44778e6 q^{67} +(-39722.9 - 2.51192e6i) q^{68} -4.78777e6i q^{69} +(229442. - 233099. i) q^{70} +571173. q^{71} +(297588. - 312050. i) q^{72} +1.63064e6 q^{73} +(1.96248e6 - 1.99376e6i) q^{74} -3.83870e6 q^{75} +(-691494. - 3.76391e6i) q^{76} -1.84372e6 q^{77} +(1.80337e6 - 1.83211e6i) q^{78} -3.39532e6 q^{79} +(-547024. + 17305.3i) q^{80} -5.34551e6 q^{81} +(1.59382e6 - 1.61922e6i) q^{82} +7.19377e6i q^{83} +(-5.52125e6 + 87311.8i) q^{84} -655622. q^{85} +(5.49071e6 - 5.57823e6i) q^{86} +7.74985e6i q^{87} +(2.23262e6 + 2.12915e6i) q^{88} -3.56648e6i q^{89} +(-80198.2 - 78940.0i) q^{90} -3.94506e6 q^{91} +(1.22927e7 - 194394. i) q^{92} +3.17131e6 q^{93} +(3.37808e6 - 3.43192e6i) q^{94} +(-985006. + 164906. i) q^{95} +(6.78670e6 + 6.27028e6i) q^{96} +2.27472e6i q^{97} +(-601070. - 591640. i) q^{98} +634335. i 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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