LMFDB - Embedded newform 63.8.f.b.22.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,8,Mod(22,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("63.22");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$N$	$=$	$63 = 3^{2} \cdot 7$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	63.f (of order $3$ , degree $2$ , 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:	$19.6802566055$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.13
Character	$\chi$	$=$	63.22
Dual form			63.8.f.b.43.13

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.20811 + 7.28866i) q^{2} +(33.7867 + 32.3336i) q^{3} +(28.5836 - 49.5082i) q^{4} +(126.650 - 219.365i) q^{5} +(-93.4907 + 382.323i) q^{6} +(-171.500 - 297.047i) q^{7} +1558.41 q^{8} +(96.0764 + 2184.89i) q^{9} +2131.84 q^{10} +(-1527.37 - 2645.48i) q^{11} +(2566.52 - 748.507i) q^{12} +(7499.07 - 12988.8i) q^{13} +(1443.38 - 2500.01i) q^{14} +(11372.0 - 3316.54i) q^{15} +(2899.26 + 5021.67i) q^{16} +1553.31 q^{17} +(-15520.6 + 9894.53i) q^{18} +12984.0 q^{19} +(-7240.24 - 12540.5i) q^{20} +(3810.18 - 15581.4i) q^{21} +(12854.7 - 22265.0i) q^{22} +(-12578.1 + 21785.9i) q^{23} +(52653.4 + 50389.0i) q^{24} +(6981.84 + 12092.9i) q^{25} +126228. q^{26} +(-67399.2 + 76926.6i) q^{27} -19608.3 q^{28} +(57844.9 + 100190. i) q^{29} +(72027.6 + 68930.0i) q^{30} +(-47101.5 + 81582.2i) q^{31} +(75337.3 - 130488. i) q^{32} +(33933.2 - 138767. i) q^{33} +(6536.51 + 11321.6i) q^{34} -86882.2 q^{35} +(110916. + 57695.4i) q^{36} -92758.4 q^{37} +(54638.1 + 94635.9i) q^{38} +(673342. - 196375. i) q^{39} +(197373. - 341860. i) q^{40} +(-158340. + 274252. i) q^{41} +(129601. - 37797.3i) q^{42} +(-64347.6 - 111453. i) q^{43} -174631. q^{44} +(491456. + 255641. i) q^{45} -211720. q^{46} +(449906. + 779260. i) q^{47} +(-64412.2 + 263409. i) q^{48} +(-58824.5 + 101887. i) q^{49} +(-58760.8 + 101777. i) q^{50} +(52481.2 + 50224.1i) q^{51} +(-428700. - 742531. i) q^{52} +96320.1 q^{53} +(-844316. - 167535. i) q^{54} -773768. q^{55} +(-267267. - 462920. i) q^{56} +(438685. + 419819. i) q^{57} +(-486836. + 843224. i) q^{58} +(498012. - 862582. i) q^{59} +(160855. - 657804. i) q^{60} +(-1.17512e6 - 2.03536e6i) q^{61} -792834. q^{62} +(632537. - 403248. i) q^{63} +2.01032e6 q^{64} +(-1.89952e6 - 3.29007e6i) q^{65} +(1.15422e6 - 336621. i) q^{66} +(-2.30243e6 + 3.98793e6i) q^{67} +(44399.2 - 76901.6i) q^{68} +(-1.12939e6 + 329377. i) q^{69} +(-365610. - 633255. i) q^{70} +1.27305e6 q^{71} +(149726. + 3.40495e6i) q^{72} -2.67508e6 q^{73} +(-390338. - 676085. i) q^{74} +(-155114. + 634327. i) q^{75} +(371129. - 642814. i) q^{76} +(-523888. + 907400. i) q^{77} +(4.26481e6 + 4.08140e6i) q^{78} +(-2.57679e6 - 4.46312e6i) q^{79} +1.46877e6 q^{80} +(-4.76451e6 + 419832. i) q^{81} -2.66525e6 q^{82} +(-4.09232e6 - 7.08810e6i) q^{83} +(-662500. - 634008. i) q^{84} +(196727. - 340742. i) q^{85} +(541564. - 938016. i) q^{86} +(-1.28513e6 + 5.25543e6i) q^{87} +(-2.38027e6 - 4.12274e6i) q^{88} +7.41641e6 q^{89} +(204819. + 4.65783e6i) q^{90} -5.14436e6 q^{91} +(719053. + 1.24544e6i) q^{92} +(-4.22925e6 + 1.23343e6i) q^{93} +(-3.78651e6 + 6.55843e6i) q^{94} +(1.64443e6 - 2.84823e6i) q^{95} +(6.76454e6 - 1.97283e6i) q^{96} +(3.74232e6 + 6.48189e6i) q^{97} -990160. q^{98} +(5.63334e6 - 3.59130e6i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$42 q + 24 q^{2} - 108 q^{3} - 1344 q^{4} + 429 q^{5} - 414 q^{6} - 7203 q^{7} - 11814 q^{8} - 4590 q^{9} + 12306 q^{11} + 24264 q^{12} + 6177 q^{13} + 8232 q^{14} - 3789 q^{15} - 86016 q^{16} - 96324 q^{17}+ \cdots + 47404458 q^{99}+O(q^{100})$ 42 * q + 24 * q^2 - 108 * q^3 - 1344 * q^4 + 429 * q^5 - 414 * q^6 - 7203 * q^7 - 11814 * q^8 - 4590 * q^9 + 12306 * q^11 + 24264 * q^12 + 6177 * q^13 + 8232 * q^14 - 3789 * q^15 - 86016 * q^16 - 96324 * q^17 - 54261 * q^18 - 2094 * q^19 + 87162 * q^20 + 18522 * q^21 - 20340 * q^22 + 88872 * q^23 - 126036 * q^24 - 284160 * q^25 - 91698 * q^26 + 43281 * q^27 + 921984 * q^28 + 314811 * q^29 + 425484 * q^30 + 99327 * q^31 + 598995 * q^32 - 158922 * q^33 - 154962 * q^34 - 294294 * q^35 - 218214 * q^36 - 151782 * q^37 + 1943481 * q^38 + 81846 * q^39 - 493605 * q^40 + 1523556 * q^41 + 373527 * q^42 - 360321 * q^43 - 7126080 * q^44 + 2263473 * q^45 + 2949156 * q^46 + 1437693 * q^47 + 2807595 * q^48 - 2470629 * q^49 + 3263631 * q^50 - 4812579 * q^51 + 459525 * q^52 - 10590036 * q^53 + 4286250 * q^54 - 473580 * q^55 + 2026101 * q^56 + 3095001 * q^57 + 1294767 * q^58 + 3175149 * q^59 - 3823848 * q^60 - 1085874 * q^61 - 19233024 * q^62 + 1370628 * q^63 - 6306654 * q^64 + 10809597 * q^65 - 3038166 * q^66 - 3324480 * q^67 + 6041055 * q^68 - 7681131 * q^69 - 25439166 * q^71 + 21174903 * q^72 + 4361610 * q^73 + 17948712 * q^74 - 4822317 * q^75 + 7715820 * q^76 + 4220958 * q^77 - 12430908 * q^78 + 3451017 * q^79 - 9652098 * q^80 + 24846102 * q^81 + 13987116 * q^82 + 1496952 * q^83 - 11273724 * q^84 + 961623 * q^85 - 1371957 * q^86 - 34244685 * q^87 + 7278228 * q^88 + 10267044 * q^89 + 61654149 * q^90 - 4237422 * q^91 + 7124595 * q^92 - 33666435 * q^93 - 16935300 * q^94 + 10747956 * q^95 - 38960325 * q^96 - 1435137 * q^97 - 5647152 * q^98 + 47404458 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$ .

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	4.20811	+	7.28866i	0.371948	+	0.644233i	0.989865	−	0.142010i	$-0.0453566\pi$
$2$	4.20811	+	7.28866i	0.371948	+	0.644233i	−0.617917	+	0.786243i	$0.712023\pi$
$3$	33.7867	+	32.3336i	0.722472	+	0.691401i
$3$	33.7867	+	32.3336i	0.722472	+	0.691401i
$4$	28.5836	−	49.5082i	0.223309	−	0.386783i
$5$	126.650	−	219.365i	0.453118	−	0.784824i	−0.545460	−	0.838137i	$-0.683645\pi$
$5$	126.650	−	219.365i	0.453118	−	0.784824i	0.998578	+	0.0533132i	$0.0169782\pi$
$6$	−93.4907	+	382.323i	−0.176701	+	0.722605i
$7$	−171.500	−	297.047i	−0.188982	−	0.327327i
$7$	−171.500	−	297.047i	−0.188982	−	0.327327i
$8$	1558.41			1.07613
$9$	96.0764	+	2184.89i	0.0439307	+	0.999035i
$10$	2131.84			0.674146
$11$	−1527.37	−	2645.48i	−0.345995	−	0.599281i	0.639539	−	0.768759i	$-0.279125\pi$
$11$	−1527.37	−	2645.48i	−0.345995	−	0.599281i	−0.985534	+	0.169478i	$0.945792\pi$
$12$	2566.52	−	748.507i	0.428756	−	0.125044i
$13$	7499.07	−	12988.8i	0.946685	−	1.63971i	0.194344	−	0.980933i	$-0.437742\pi$
$13$	7499.07	−	12988.8i	0.946685	−	1.63971i	0.752341	−	0.658774i	$-0.228925\pi$
$14$	1443.38	−	2500.01i	0.140583	−	0.243497i
$15$	11372.0	−	3316.54i	0.869993	−	0.253727i
$16$	2899.26	+	5021.67i	0.176957	+	0.306498i
$17$	1553.31			0.0766809			0.0383404	−	0.999265i	$-0.487793\pi$
$17$	1553.31			0.0766809			0.0383404	+	0.999265i	$0.487793\pi$
$18$	−15520.6	+	9894.53i	−0.627271	+	0.399891i
$19$	12984.0			0.434281			0.217140	−	0.976140i	$-0.430327\pi$
$19$	12984.0			0.434281			0.217140	+	0.976140i	$0.430327\pi$
$20$	−7240.24	−	12540.5i	−0.202371	−	0.350517i
$21$	3810.18	−	15581.4i	0.0897796	−	0.367147i
$22$	12854.7	−	22265.0i	0.257384	−	0.445803i
$23$	−12578.1	+	21785.9i	−0.215559	+	0.373360i	−0.953445	−	0.301566i	$-0.902491\pi$
$23$	−12578.1	+	21785.9i	−0.215559	+	0.373360i	0.737886	+	0.674925i	$0.235824\pi$
$24$	52653.4	+	50389.0i	0.777476	+	0.744040i
$25$	6981.84	+	12092.9i	0.0893676	+	0.154789i
$26$	126228.			1.40847
$27$	−67399.2	+	76926.6i	−0.658994	+	0.752148i
$28$	−19608.3			−0.168806
$29$	57844.9	+	100190.i	0.440425	+	0.762839i	0.997721	−	0.0674753i	$-0.0214944\pi$
$29$	57844.9	+	100190.i	0.440425	+	0.762839i	−0.557296	+	0.830314i	$0.688161\pi$
$30$	72027.6	+	68930.0i	0.487051	+	0.466105i
$31$	−47101.5	+	81582.2i	−0.283968	+	0.491846i	−0.972358	−	0.233494i	$-0.924984\pi$
$31$	−47101.5	+	81582.2i	−0.283968	+	0.491846i	0.688391	+	0.725340i	$0.258317\pi$
$32$	75337.3	−	130488.i	0.406429	−	0.703957i
$33$	33933.2	−	138767.i	0.164372	−	0.672185i
$34$	6536.51	+	11321.6i	0.0285213	+	0.0494004i
$35$	−86882.2			−0.342525
$36$	110916.	+	57695.4i	0.396220	+	0.206102i
$37$	−92758.4			−0.301056			−0.150528	−	0.988606i	$-0.548097\pi$
$37$	−92758.4			−0.301056			−0.150528	+	0.988606i	$0.548097\pi$
$38$	54638.1	+	94635.9i	0.161530	+	0.279778i
$39$	673342.	−	196375.i	1.81765	−	0.530103i
$40$	197373.	−	341860.i	0.487616	−	0.844576i
$41$	−158340.	+	274252.i	−0.358795	+	0.621451i	−0.987760	−	0.155983i	$-0.950146\pi$
$41$	−158340.	+	274252.i	−0.358795	+	0.621451i	0.628965	+	0.777434i	$0.283479\pi$
$42$	129601.	−	37797.3i	0.269921	−	0.0787206i
$43$	−64347.6	−	111453.i	−0.123422	−	0.213773i	0.797693	−	0.603064i	$-0.206054\pi$
$43$	−64347.6	−	111453.i	−0.123422	−	0.213773i	−0.921115	+	0.389290i	$0.872720\pi$
$44$	−174631.			−0.309055
$45$	491456.	+	255641.i	0.803972	+	0.418203i
$46$	−211720.			−0.320708
$47$	449906.	+	779260.i	0.632091	+	1.09481i	0.987124	+	0.159959i	$0.0511363\pi$
$47$	449906.	+	779260.i	0.632091	+	1.09481i	−0.355033	+	0.934854i	$0.615530\pi$
$48$	−64412.2	+	263409.i	−0.0840667	+	0.343784i
$49$	−58824.5	+	101887.i	−0.0714286	+	0.123718i
$50$	−58760.8	+	101777.i	−0.0664802	+	0.115147i
$51$	52481.2	+	50224.1i	0.0553998	+	0.0530172i
$52$	−428700.	−	742531.i	−0.422807	−	0.732323i
$53$	96320.1			0.0888692			0.0444346	−	0.999012i	$-0.485851\pi$
$53$	96320.1			0.0888692			0.0444346	+	0.999012i	$0.485851\pi$
$54$	−844316.	−	167535.i	−0.729670	−	0.144786i
$55$	−773768.			−0.627107
$56$	−267267.	−	462920.i	−0.203370	−	0.352248i
$57$	438685.	+	419819.i	0.313755	+	0.300262i
$58$	−486836.	+	843224.i	−0.327631	+	0.567473i
$59$	498012.	−	862582.i	0.315688	−	0.546787i	−0.663896	−	0.747825i	$-0.731098\pi$
$59$	498012.	−	862582.i	0.315688	−	0.546787i	0.979583	+	0.201038i	$0.0644315\pi$
$60$	160855.	−	657804.i	0.0961402	−	0.393158i
$61$	−1.17512e6	−	2.03536e6i	−0.662868	−	1.14812i	−0.979859	−	0.199693i	$-0.936006\pi$
$61$	−1.17512e6	−	2.03536e6i	−0.662868	−	1.14812i	0.316990	−	0.948429i	$-0.397328\pi$
$62$	−792834.			−0.422485
$63$	632537.	−	403248.i	0.318709	−	0.203179i
$64$	2.01032e6			0.958596
$65$	−1.89952e6	−	3.29007e6i	−0.857921	−	1.48596i
$66$	1.15422e6	−	336621.i	0.494181	−	0.144124i
$67$	−2.30243e6	+	3.98793e6i	−0.935244	+	1.61989i	−0.161046	+	0.986947i	$0.551487\pi$
$67$	−2.30243e6	+	3.98793e6i	−0.935244	+	1.61989i	−0.774198	+	0.632944i	$0.781846\pi$
$68$	44399.2	−	76901.6i	0.0171235	−	0.0296589i
$69$	−1.12939e6	+	329377.i	−0.413877	+	0.120704i
$70$	−365610.	−	633255.i	−0.127402	−	0.220666i
$71$	1.27305e6			0.422125			0.211063	−	0.977473i	$-0.432308\pi$
$71$	1.27305e6			0.422125			0.211063	+	0.977473i	$0.432308\pi$
$72$	149726.	+	3.40495e6i	0.0472753	+	1.07510i
$73$	−2.67508e6			−0.804834			−0.402417	−	0.915457i	$-0.631830\pi$
$73$	−2.67508e6			−0.804834			−0.402417	+	0.915457i	$0.631830\pi$
$74$	−390338.	−	676085.i	−0.111977	−	0.193950i
$75$	−155114.	+	634327.i	−0.0424558	+	0.173620i
$76$	371129.	−	642814.i	0.0969788	−	0.167972i
$77$	−523888.	+	907400.i	−0.130774	+	0.226507i
$78$	4.26481e6	+	4.08140e6i	1.01758	+	0.973818i
$79$	−2.57679e6	−	4.46312e6i	−0.588008	−	1.01846i	−0.994493	−	0.104803i	$-0.966579\pi$
$79$	−2.57679e6	−	4.46312e6i	−0.588008	−	1.01846i	0.406485	−	0.913658i	$-0.366754\pi$
$80$	1.46877e6			0.320729
$81$	−4.76451e6	+	419832.i	−0.996140	+	0.0877765i
$82$	−2.66525e6			−0.533813
$83$	−4.09232e6	−	7.08810e6i	−0.785590	−	1.36068i	−0.928646	−	0.370967i	$-0.879026\pi$
$83$	−4.09232e6	−	7.08810e6i	−0.785590	−	1.36068i	0.143056	−	0.989715i	$-0.454307\pi$
$84$	−662500.	−	634008.i	−0.121957	−	0.116712i
$85$	196727.	−	340742.i	0.0347455	−	0.0601810i
$86$	541564.	−	938016.i	0.0918132	−	0.159025i
$87$	−1.28513e6	+	5.25543e6i	−0.209232	+	0.855640i
$88$	−2.38027e6	−	4.12274e6i	−0.372337	−	0.644907i
$89$	7.41641e6			1.11514			0.557569	−	0.830131i	$-0.311734\pi$
$89$	7.41641e6			1.11514			0.557569	+	0.830131i	$0.311734\pi$
$90$	204819.	+	4.65783e6i	0.0296157	+	0.673495i
$91$	−5.14436e6			−0.715627
$92$	719053.	+	1.24544e6i	0.0962728	+	0.166749i
$93$	−4.22925e6	+	1.23343e6i	−0.545221	+	0.159010i
$94$	−3.78651e6	+	6.55843e6i	−0.470210	+	0.814427i
$95$	1.64443e6	−	2.84823e6i	0.196780	−	0.340834i
$96$	6.76454e6	−	1.97283e6i	0.780350	−	0.227583i
$97$	3.74232e6	+	6.48189e6i	0.416332	+	0.721109i	0.995567	−	0.0940518i	$-0.0299819\pi$
$97$	3.74232e6	+	6.48189e6i	0.416332	+	0.721109i	−0.579235	+	0.815161i	$0.696649\pi$
$98$	−990160.			−0.106271
$99$	5.63334e6	−	3.59130e6i	0.583503	−	0.371988i
$100$	798264.			0.0798264
$101$	5.72998e6	+	9.92462e6i	0.553386	+	0.958493i	0.998027	+	0.0627843i	$0.0199980\pi$
$101$	5.72998e6	+	9.92462e6i	0.553386	+	0.958493i	−0.444641	+	0.895709i	$0.646669\pi$
$102$	−145220.	+	593866.i	−0.0135496	+	0.0554100i
$103$	−7.60747e6	+	1.31765e7i	−0.685978	+	1.18815i	0.287151	+	0.957885i	$0.407292\pi$
$103$	−7.60747e6	+	1.31765e7i	−0.685978	+	1.18815i	−0.973128	+	0.230263i	$0.926041\pi$
$104$	1.16866e7	−	2.02418e7i	1.01876	−	1.76454i
$105$	−2.93546e6	−	2.80921e6i	−0.247465	−	0.236822i
$106$	405326.	+	702045.i	0.0330547	+	0.0572525i
$107$	3.45989e6			0.273035			0.136518	−	0.990638i	$-0.456409\pi$
$107$	3.45989e6			0.273035			0.136518	+	0.990638i	$0.456409\pi$
$108$	1.88199e6	+	5.53565e6i	0.143758	+	0.422849i
$109$	−2.85960e6			−0.211501			−0.105750	−	0.994393i	$-0.533724\pi$
$109$	−2.85960e6			−0.211501			−0.105750	+	0.994393i	$0.533724\pi$
$110$	−3.25610e6	−	5.63974e6i	−0.233251	−	0.404003i
$111$	−3.13400e6	−	2.99921e6i	−0.217504	−	0.208150i
$112$	994446.	−	1.72243e6i	0.0668834	−	0.115845i
$113$	1.04941e7	−	1.81764e7i	0.684182	−	1.18504i	−0.289511	−	0.957175i	$-0.593493\pi$
$113$	1.04941e7	−	1.81764e7i	0.684182	−	1.18504i	0.973693	−	0.227864i	$-0.0731740\pi$
$114$	−1.21388e6	+	4.96408e6i	−0.0767378	+	0.313813i
$115$	3.18604e6	+	5.51838e6i	0.195348	+	0.338352i
$116$	6.61366e6			0.393404
$117$	2.90995e7	+	1.51367e7i	1.67971	+	0.873738i
$118$	8.38276e6			0.469678
$119$	−266393.	−	461406.i	−0.0144913	−	0.0250997i
$120$	1.77221e7	−	5.16853e6i	0.936229	−	0.273044i
$121$	5.07787e6	−	8.79512e6i	0.260575	−	0.451329i
$122$	9.89006e6	−	1.71301e7i	0.493105	−	0.854083i
$123$	−1.42173e7	+	4.14638e6i	−0.688891	+	0.200910i
$124$	2.69266e6	+	4.66382e6i	0.126825	+	0.219668i
$125$	2.33261e7			1.06821
$126$	5.60092e6	+	2.91344e6i	0.249438	+	0.129750i
$127$	−1.50219e7			−0.650746			−0.325373	−	0.945586i	$-0.605490\pi$
$127$	−1.50219e7			−0.650746			−0.325373	+	0.945586i	$0.605490\pi$
$128$	−1.18351e6	−	2.04991e6i	−0.0498814	−	0.0863971i
$129$	1.42960e6	−	5.84623e6i	0.0586340	−	0.239779i
$130$	1.59868e7	−	2.76899e7i	0.638204	−	1.10540i
$131$	−2.46158e6	+	4.26357e6i	−0.0956673	+	0.165701i	−0.909887	−	0.414856i	$-0.863832\pi$
$131$	−2.46158e6	+	4.26357e6i	−0.0956673	+	0.165701i	0.814220	+	0.580557i	$0.197165\pi$
$132$	−5.90019e6	−	5.64644e6i	−0.223284	−	0.213681i
$133$	−2.22675e6	−	3.85685e6i	−0.0820713	−	0.142152i
$134$	−3.87556e7			−1.39145
$135$	8.33886e6	+	2.45278e7i	0.291701	+	0.858007i
$136$	2.42069e6			0.0825189
$137$	−2.82785e6	−	4.89798e6i	−0.0939580	−	0.162740i	0.815215	−	0.579158i	$-0.196619\pi$
$137$	−2.82785e6	−	4.89798e6i	−0.0939580	−	0.162740i	−0.909173	+	0.416418i	$0.863285\pi$
$138$	−7.15331e6	−	6.84567e6i	−0.231702	−	0.221737i
$139$	−2.73217e7	+	4.73227e7i	−0.862892	+	1.49457i	0.00623223	+	0.999981i	$0.498016\pi$
$139$	−2.73217e7	+	4.73227e7i	−0.862892	+	1.49457i	−0.869125	+	0.494593i	$0.835317\pi$
$140$	−2.48340e6	+	4.30138e6i	−0.0764890	+	0.132483i
$141$	−9.99547e6	+	4.08757e7i	−0.300287	+	1.22800i
$142$	5.35714e6	+	9.27884e6i	0.157009	+	0.271947i
$143$	−4.58154e7			−1.31019
$144$	−1.06932e7	+	6.81702e6i	−0.298428	+	0.190251i
$145$	2.93043e7			0.798259
$146$	−1.12570e7	−	1.94977e7i	−0.299356	−	0.518500i
$147$	−5.28186e6	+	1.54041e6i	−0.137144	+	0.0399969i
$148$	−2.65137e6	+	4.59230e6i	−0.0672286	+	0.116443i
$149$	−3.14454e7	+	5.44651e7i	−0.778764	+	1.34886i	0.153891	+	0.988088i	$0.450819\pi$
$149$	−3.14454e7	+	5.44651e7i	−0.778764	+	1.34886i	−0.932655	+	0.360770i	$0.882514\pi$
$150$	−5.27613e6	+	1.53874e6i	−0.127643	+	0.0372261i
$151$	−1.13249e7	−	1.96153e7i	−0.267679	−	0.463634i	0.700583	−	0.713571i	$-0.252923\pi$
$151$	−1.13249e7	−	1.96153e7i	−0.267679	−	0.463634i	−0.968262	+	0.249937i	$0.919590\pi$
$152$	2.02344e7			0.467344
$153$	149236.	+	3.39381e6i	0.00336864	+	0.0766069i
$154$	−8.81832e6			−0.194564
$155$	1.19308e7	+	2.06648e7i	0.257342	+	0.445729i
$156$	9.52435e6	−	3.89491e7i	0.200863	−	0.821412i
$157$	−2.43724e7	+	4.22143e7i	−0.502632	+	0.870584i	0.497363	+	0.867542i	$0.334302\pi$
$157$	−2.43724e7	+	4.22143e7i	−0.502632	+	0.870584i	−0.999995	+	0.00304172i	$0.999032\pi$
$158$	2.16868e7	−	3.75626e7i	0.437417	−	0.757629i
$159$	3.25433e6	+	3.11438e6i	0.0642055	+	0.0614442i
$160$	−1.90830e7	−	3.30527e7i	−0.368321	−	0.637951i
$161$	8.62856e6			0.162948
$162$	−2.31096e7	−	3.29602e7i	−0.427061	−	0.609098i
$163$	−8.69334e7			−1.57228			−0.786140	−	0.618048i	$-0.787924\pi$
$163$	−8.69334e7			−1.57228			−0.786140	+	0.618048i	$0.787924\pi$
$164$	9.05183e6	+	1.56782e7i	0.160244	+	0.277552i
$165$	−2.61430e7	−	2.50187e7i	−0.453067	−	0.433582i
$166$	3.44419e7	−	5.96550e7i	0.584397	−	1.01221i
$167$	−5.16217e6	+	8.94115e6i	−0.0857679	+	0.148554i	−0.905718	−	0.423880i	$-0.860668\pi$
$167$	−5.16217e6	+	8.94115e6i	−0.0857679	+	0.148554i	0.819950	+	0.572435i	$0.194001\pi$
$168$	5.93781e6	−	2.42822e7i	0.0966149	−	0.395099i
$169$	−8.10978e7	−	1.40466e8i	−1.29243	−	2.23855i
$170$	3.31140e6			0.0516941
$171$	1.24745e6	+	2.83686e7i	0.0190782	+	0.433861i
$172$	−7.35714e6			−0.110245
$173$	5.52079e7	+	9.56229e7i	0.810662	+	1.40411i	0.912401	+	0.409297i	$0.134226\pi$
$173$	5.52079e7	+	9.56229e7i	0.810662	+	1.40411i	−0.101739	+	0.994811i	$0.532441\pi$
$174$	−4.37130e7	+	1.27486e7i	−0.629055	+	0.183459i
$175$	2.39477e6	−	4.14787e6i	0.0337778	−	0.0585048i
$176$	8.85649e6	−	1.53399e7i	0.122452	−	0.212094i
$177$	4.47165e7	−	1.30412e7i	0.606124	−	0.176772i
$178$	3.12091e7	+	5.40557e7i	0.414774	+	0.718409i
$179$	−1.11941e8			−1.45883			−0.729416	−	0.684071i	$-0.760208\pi$
$179$	−1.11941e8			−1.45883			−0.729416	+	0.684071i	$0.760208\pi$
$180$	2.67039e7	−	1.70240e7i	0.341288	−	0.217574i
$181$	1.18847e8			1.48975			0.744873	−	0.667207i	$-0.232510\pi$
$181$	1.18847e8			1.48975			0.744873	+	0.667207i	$0.232510\pi$
$182$	−2.16481e7	−	3.74955e7i	−0.266176	−	0.461030i
$183$	2.61073e7	−	1.06764e8i	0.314908	−	1.28779i
$184$	−1.96018e7	+	3.39513e7i	−0.231971	+	0.401785i
$185$	−1.17479e7	+	2.03479e7i	−0.136414	+	0.236276i
$186$	−2.67872e7	−	2.56352e7i	−0.305233	−	0.292106i
$187$	−2.37248e6	−	4.10926e6i	−0.0265312	−	0.0459534i
$188$	5.14397e7			0.564607
$189$	3.44098e7	+	6.82781e6i	0.370736	+	0.0735639i
$190$	2.76797e7			0.292769
$191$	8.51763e7	+	1.47530e8i	0.884509	+	1.53201i	0.846276	+	0.532745i	$0.178839\pi$
$191$	8.51763e7	+	1.47530e8i	0.884509	+	1.53201i	0.0382327	+	0.999269i	$0.487827\pi$
$192$	6.79221e7	+	6.50010e7i	0.692559	+	0.662774i
$193$	1.09229e7	−	1.89191e7i	0.109368	−	0.189430i	−0.806147	−	0.591716i	$-0.798451\pi$
$193$	1.09229e7	−	1.89191e7i	0.109368	−	0.189430i	0.915514	+	0.402286i	$0.131784\pi$
$194$	−3.14962e7	+	5.45531e7i	−0.309708	+	0.536430i
$195$	4.22012e7	−	1.72579e8i	0.407572	−	1.66673i
$196$	3.36283e6	+	5.82459e6i	0.0319013	+	0.0552547i
$197$	−1.78421e8			−1.66270			−0.831349	−	0.555751i	$-0.812431\pi$
$197$	−1.78421e8			−1.66270			−0.831349	+	0.555751i	$0.812431\pi$
$198$	4.98815e7	+	2.59469e7i	0.456680	+	0.237551i
$199$	1.79189e8			1.61186			0.805928	−	0.592013i	$-0.201667\pi$
$199$	1.79189e8			1.61186			0.805928	+	0.592013i	$0.201667\pi$
$200$	1.08806e7	+	1.88457e7i	0.0961715	+	0.166574i
$201$	−2.06736e8	+	6.02929e7i	−1.79568	+	0.523697i
$202$	−4.82248e7	+	8.35278e7i	−0.411662	+	0.713020i
$203$	1.98408e7	−	3.43653e7i	0.166465	−	0.288326i
$204$	3.98661e6	−	1.16266e6i	0.0328774	−	0.00958845i
$205$	4.01076e7	+	6.94684e7i	0.325153	+	0.563182i
$206$	−1.28052e8			−1.02059
$207$	−4.88082e7	−	2.53886e7i	−0.382469	−	0.198949i
$208$	8.69670e7			0.670090
$209$	−1.98313e7	−	3.43489e7i	−0.150259	−	0.260256i
$210$	8.12268e6	−	3.32171e7i	0.0605246	−	0.247511i
$211$	1.12919e8	−	1.95581e8i	0.827518	−	1.43330i	−0.0724625	−	0.997371i	$-0.523086\pi$
$211$	1.12919e8	−	1.95581e8i	0.827518	−	1.43330i	0.899980	−	0.435931i	$-0.143581\pi$
$212$	2.75317e6	−	4.76864e6i	0.0198453	−	0.0343731i
$213$	4.30121e7	+	4.11623e7i	0.304974	+	0.291858i
$214$	1.45596e7	+	2.52179e7i	0.101555	+	0.175898i
$215$	−3.25986e7			−0.223699
$216$	−1.05036e8	+	1.19883e8i	−0.709166	+	0.809412i
$217$	3.23116e7			0.214659
$218$	−1.20335e7	−	2.08427e7i	−0.0786674	−	0.136256i
$219$	−9.03819e7	−	8.64948e7i	−0.581470	−	0.556462i
$220$	−2.21171e7	+	3.83079e7i	−0.140039	+	0.242554i
$221$	1.16484e7	−	2.01756e7i	0.0725927	−	0.125734i
$222$	8.67205e6	−	3.54637e7i	0.0531969	−	0.217545i
$223$	−6.48503e7	−	1.12324e8i	−0.391602	−	0.678275i	0.601059	−	0.799205i	$-0.294746\pi$
$223$	−6.48503e7	−	1.12324e8i	−0.391602	−	0.678275i	−0.992661	+	0.120930i	$0.961412\pi$
$224$	−5.16814e7			−0.307232
$225$	−2.57509e7	+	1.64164e7i	−0.150714	+	0.0960813i
$226$	1.76642e8			1.01792
$227$	1.52000e8	+	2.63271e8i	0.862487	+	1.49387i	0.869521	+	0.493896i	$0.164428\pi$
$227$	1.52000e8	+	2.63271e8i	0.862487	+	1.49387i	−0.00703360	+	0.999975i	$0.502239\pi$
$228$	3.33237e7	−	9.71860e6i	0.186201	−	0.0543040i
$229$	−1.25641e8	+	2.17617e8i	−0.691364	+	1.19748i	0.280027	+	0.959992i	$0.409657\pi$
$229$	−1.25641e8	+	2.17617e8i	−0.691364	+	1.19748i	−0.971391	+	0.237486i	$0.923677\pi$
$230$	−2.68144e7	+	4.64439e7i	−0.145318	+	0.251699i
$231$	−4.70399e7	+	1.37188e7i	−0.251087	+	0.0732277i
$232$	9.01460e7	+	1.56137e8i	0.473957	+	0.820917i
$233$	3.26554e8			1.69126			0.845628	−	0.533773i	$-0.179226\pi$
$233$	3.26554e8			1.69126			0.845628	+	0.533773i	$0.179226\pi$
$234$	1.21275e7	+	2.75794e8i	0.0618751	+	1.40711i
$235$	2.27923e8			1.14565
$236$	−2.84699e7	−	4.93114e7i	−0.140992	−	0.244205i
$237$	5.72479e7	−	2.34111e8i	0.279345	−	1.14236i
$238$	2.24202e6	−	3.88330e6i	0.0107800	−	0.0186716i
$239$	3.57106e7	−	6.18525e7i	0.169201	−	0.293065i	−0.768938	−	0.639323i	$-0.779214\pi$
$239$	3.57106e7	−	6.18525e7i	0.169201	−	0.293065i	0.938139	+	0.346258i	$0.112548\pi$
$240$	4.96248e7	+	4.74906e7i	0.231718	+	0.221753i
$241$	9.58242e7	+	1.65972e8i	0.440977	+	0.763794i	0.997762	−	0.0668621i	$-0.0212988\pi$
$241$	9.58242e7	+	1.65972e8i	0.440977	+	0.763794i	−0.556785	+	0.830656i	$0.687965\pi$
$242$	8.54730e7			0.387681
$243$	−1.74551e8	−	1.39869e8i	−0.780372	−	0.625316i
$244$	−1.34356e8			−0.592098
$245$	1.49003e7	+	2.58081e7i	0.0647312	+	0.112118i
$246$	−9.00497e7	−	8.61770e7i	−0.385664	−	0.369078i
$247$	9.73678e7	−	1.68646e8i	0.411127	−	0.712093i
$248$	−7.34034e7	+	1.27138e8i	−0.305587	+	0.529292i
$249$	9.09181e7	−	3.71803e8i	0.373209	−	1.52621i
$250$	9.81590e7	+	1.70016e8i	0.397320	+	0.688178i
$251$	−1.40499e8			−0.560810			−0.280405	−	0.959882i	$-0.590469\pi$
$251$	−1.40499e8			−0.560810			−0.280405	+	0.959882i	$0.590469\pi$
$252$	−1.88390e6	−	4.28420e7i	−0.00741575	−	0.168643i
$253$	7.68455e7			0.298330
$254$	−6.32138e7	−	1.09490e8i	−0.242044	−	0.419232i
$255$	1.76642e7	−	5.15162e6i	0.0667118	−	0.0194560i
$256$	1.38621e8	−	2.40099e8i	0.516405	−	0.894439i
$257$	1.47789e8	−	2.55977e8i	0.543094	−	0.940667i	−0.455630	−	0.890169i	$-0.650586\pi$
$257$	1.47789e8	−	2.55977e8i	0.543094	−	0.940667i	0.998724	−	0.0504973i	$-0.0160806\pi$
$258$	4.86271e7	−	1.41817e7i	0.176283	−	0.0514115i
$259$	1.59081e7	+	2.75536e7i	0.0568942	+	0.0985437i
$260$	−2.17180e8			−0.766327
$261$	−2.13347e8	+	1.36011e8i	−0.742754	+	0.473512i
$262$	−4.14343e7			−0.142333
$263$	1.23899e8	+	2.14600e8i	0.419976	+	0.727420i	0.995937	−	0.0900578i	$-0.0287052\pi$
$263$	1.23899e8	+	2.14600e8i	0.419976	+	0.727420i	−0.575961	+	0.817477i	$0.695372\pi$
$264$	5.28819e7	−	2.16256e8i	0.176886	−	0.723361i
$265$	1.21990e7	−	2.11293e7i	0.0402683	−	0.0697467i
$266$	1.87409e7	−	3.24601e7i	0.0610525	−	0.105746i
$267$	2.50576e8	+	2.39799e8i	0.805656	+	0.771007i
$268$	1.31623e8	+	2.27979e8i	0.417697	+	0.723473i
$269$	2.29446e8			0.718700			0.359350	−	0.933203i	$-0.382998\pi$
$269$	2.29446e8			0.718700			0.359350	+	0.933203i	$0.382998\pi$
$270$	−1.43684e8	+	1.63995e8i	−0.444258	+	0.507057i
$271$	−5.67244e8			−1.73132			−0.865660	−	0.500632i	$-0.833101\pi$
$271$	−5.67244e8			−1.73132			−0.865660	+	0.500632i	$0.833101\pi$
$272$	4.50345e6	+	7.80021e6i	0.0135692	+	0.0235026i
$273$	−1.73811e8	−	1.66336e8i	−0.517020	−	0.494785i
$274$	2.37998e7	−	4.12225e7i	0.0698950	−	0.121062i
$275$	2.13277e7	−	3.69407e7i	0.0618415	−	0.107113i
$276$	−1.59750e7	+	6.53287e7i	−0.0457362	+	0.187035i
$277$	−9.66172e7	−	1.67346e8i	−0.273134	−	0.473081i	0.696529	−	0.717529i	$-0.254727\pi$
$277$	−9.66172e7	−	1.67346e8i	−0.273134	−	0.473081i	−0.969663	+	0.244447i	$0.921393\pi$
$278$	−4.59892e8			−1.28380
$279$	−1.82773e8	−	9.50734e7i	−0.503846	−	0.262086i
$280$	−1.35398e8			−0.368603
$281$	−2.06009e8	−	3.56818e8i	−0.553877	−	0.959343i	−0.997990	−	0.0633725i	$-0.979814\pi$
$281$	−2.06009e8	−	3.56818e8i	−0.553877	−	0.959343i	0.444113	−	0.895971i	$-0.353519\pi$
$282$	−3.39991e8	+	9.91559e7i	−0.902809	+	0.263297i
$283$	6.95228e7	−	1.20417e8i	0.182337	−	0.315817i	−0.760339	−	0.649526i	$-0.774967\pi$
$283$	6.95228e7	−	1.20417e8i	0.182337	−	0.315817i	0.942676	+	0.333710i	$0.108301\pi$
$284$	3.63883e7	−	6.30264e7i	0.0942645	−	0.163271i
$285$	1.47653e8	−	4.30620e7i	0.377821	−	0.110189i
$286$	−1.92796e8	−	3.33933e8i	−0.487324	−	0.844070i
$287$	1.08621e8			0.271224
$288$	2.92340e8	+	1.52067e8i	0.721132	+	0.375112i
$289$	−4.07926e8			−0.994120
$290$	1.23316e8	+	2.13589e8i	0.296911	+	0.514265i
$291$	−8.31424e7	+	3.40004e8i	−0.197787	+	0.808833i
$292$	−7.64632e7	+	1.32438e8i	−0.179727	+	0.311296i
$293$	2.83738e8	−	4.91449e8i	0.658994	−	1.14141i	−0.321882	−	0.946780i	$-0.604316\pi$
$293$	2.83738e8	−	4.91449e8i	0.658994	−	1.14141i	0.980876	−	0.194632i	$-0.0623512\pi$
$294$	−3.34542e7	−	3.20155e7i	−0.0767777	−	0.0734757i
$295$	−1.26147e8	−	2.18493e8i	−0.286088	−	0.495519i
$296$	−1.44555e8			−0.323977
$297$	3.06451e8	+	6.08081e7i	0.678757	+	0.134683i
$298$	−5.29304e8			−1.15864
$299$	1.88648e8	+	3.26747e8i	0.408134	+	0.706908i
$300$	2.69707e7	+	2.58108e7i	0.0576723	+	0.0551920i
$301$	−2.20712e7	+	3.82285e7i	−0.0466492	+	0.0807987i
$302$	9.53128e7	−	1.65087e8i	0.199125	−	0.344895i
$303$	−1.27302e8	+	5.20591e8i	−0.262897	+	1.07510i
$304$	3.76440e7	+	6.52012e7i	0.0768489	+	0.133106i
$305$	−5.95317e8			−1.20143
$306$	−2.41083e7	+	1.53693e7i	−0.0480997	+	0.0306640i
$307$	2.06412e7			0.0407147			0.0203574	−	0.999793i	$-0.493520\pi$
$307$	2.06412e7			0.0407147			0.0203574	+	0.999793i	$0.493520\pi$
$308$	2.99492e7	+	5.18735e7i	0.0584060	+	0.101162i
$309$	−6.83076e8	+	1.99214e8i	−1.31709	+	0.384118i
$310$	−1.00413e8	+	1.73920e8i	−0.191436	+	0.331576i
$311$	−2.07734e8	+	3.59805e8i	−0.391603	+	0.678276i	−0.992661	−	0.120929i	$-0.961413\pi$
$311$	−2.07734e8	+	3.59805e8i	−0.391603	+	0.678276i	0.601058	+	0.799205i	$0.294746\pi$
$312$	1.04934e9	−	3.06033e8i	1.95603	−	0.570462i
$313$	1.87486e8	+	3.24735e8i	0.345591	+	0.598581i	0.985461	−	0.169902i	$-0.0543451\pi$
$313$	1.87486e8	+	3.24735e8i	0.345591	+	0.598581i	−0.639870	+	0.768483i	$0.721012\pi$
$314$	−4.10248e8			−0.747812
$315$	−8.34732e6	−	1.89828e8i	−0.0150474	−	0.342195i
$316$	−2.94615e8			−0.525231
$317$	2.35619e8	+	4.08104e8i	0.415435	+	0.719554i	0.995474	−	0.0950344i	$-0.0302961\pi$
$317$	2.35619e8	+	4.08104e8i	0.415435	+	0.719554i	−0.580039	+	0.814589i	$0.696963\pi$
$318$	−9.00504e6	+	3.68254e7i	−0.0157033	+	0.0642174i
$319$	1.76701e8	−	3.06055e8i	0.304770	−	0.527877i
$320$	2.54608e8	−	4.40994e8i	0.434358	−	0.752329i
$321$	1.16898e8	+	1.11871e8i	0.197260	+	0.188777i
$322$	3.63100e7	+	6.28907e7i	0.0606080	+	0.104976i
$323$	2.01682e7			0.0333010
$324$	−1.15402e8	+	2.47883e8i	−0.188497	+	0.404891i
$325$	2.09429e8			0.338412
$326$	−3.65825e8	−	6.33628e8i	−0.584807	−	1.01291i
$327$	−9.66163e7	−	9.24611e7i	−0.152803	−	0.146232i
$328$	−2.46758e8	+	4.27397e8i	−0.386112	+	0.668765i
$329$	1.54318e8	−	2.67286e8i	0.238908	−	0.413801i
$330$	7.23401e7	−	2.95829e8i	0.110810	−	0.453151i
$331$	3.00093e8	+	5.19776e8i	0.454839	+	0.787803i	0.998679	−	0.0513853i	$-0.0163636\pi$
$331$	3.00093e8	+	5.19776e8i	0.454839	+	0.787803i	−0.543840	+	0.839189i	$0.683030\pi$
$332$	−4.67892e8			−0.701718
$333$	−8.91189e6	−	2.02667e8i	−0.0132256	−	0.300765i
$334$	−8.68920e7			−0.127605
$335$	5.83208e8	+	1.01015e9i	0.847553	+	1.46800i
$336$	8.92914e7	−	2.60412e7i	0.128417	−	0.0374518i
$337$	5.62143e8	−	9.73661e8i	0.800097	−	1.38581i	−0.119455	−	0.992840i	$-0.538115\pi$
$337$	5.62143e8	−	9.73661e8i	0.800097	−	1.38581i	0.919552	−	0.392969i	$-0.128552\pi$
$338$	6.82538e8	−	1.18219e9i	0.961431	−	1.66525i
$339$	9.42269e8	−	2.74806e8i	1.31364	−	0.383113i
$340$	−1.12463e7	−	1.94792e7i	−0.0155180	−	0.0268779i
$341$	2.87766e8			0.393005
$342$	−2.01520e8	+	1.28470e8i	−0.272412	+	0.173665i
$343$	4.03536e7			0.0539949
$344$	−1.00280e8	−	1.73690e8i	−0.132819	−	0.230049i
$345$	−7.07835e7	+	2.89464e8i	−0.0928037	+	0.379513i
$346$	−4.64642e8	+	8.04784e8i	−0.603048	+	1.04451i
$347$	1.38822e6	−	2.40447e6i	0.00178363	−	0.00308934i	−0.865132	−	0.501544i	$-0.832766\pi$
$347$	1.38822e6	−	2.40447e6i	0.00178363	−	0.00308934i	0.866916	+	0.498455i	$0.166099\pi$
$348$	2.23453e8	+	2.13843e8i	0.284223	+	0.272000i
$349$	−4.69978e8	−	8.14025e8i	−0.591818	−	1.02506i	−0.993988	−	0.109494i	$-0.965077\pi$
$349$	−4.69978e8	−	8.14025e8i	−0.591818	−	1.02506i	0.402170	−	0.915565i	$-0.368256\pi$
$350$	4.03099e7			0.0502543
$351$	4.93750e8	+	1.45231e9i	0.609442	+	1.79261i
$352$	−4.60272e8			−0.562490
$353$	−2.92980e8	−	5.07456e8i	−0.354508	−	0.614026i	0.632526	−	0.774539i	$-0.282018\pi$
$353$	−2.92980e8	−	5.07456e8i	−0.354508	−	0.614026i	−0.987034	+	0.160514i	$0.948685\pi$
$354$	2.83226e8	+	2.71045e8i	0.339329	+	0.324736i
$355$	1.61232e8	−	2.79263e8i	0.191273	−	0.331294i
$356$	2.11988e8	−	3.67173e8i	0.249021	−	0.431316i
$357$	5.91839e6	−	2.42028e7i	0.00688438	−	0.0281531i
$358$	−4.71062e8	−	8.15903e8i	−0.542610	−	0.939827i
$359$	−2.26089e7			−0.0257898			−0.0128949	−	0.999917i	$-0.504105\pi$
$359$	−2.26089e7			−0.0257898			−0.0128949	+	0.999917i	$0.504105\pi$
$360$	7.65889e8	+	3.98394e8i	0.865182	+	0.450042i
$361$	−7.25288e8			−0.811400
$362$	5.00120e8	+	8.66233e8i	0.554108	+	0.959743i
$363$	4.55942e8	−	1.32972e8i	0.500307	−	0.145911i
$364$	−1.47044e8	+	2.54688e8i	−0.159806	+	0.276792i
$365$	−3.38800e8	+	5.86818e8i	−0.364685	+	0.631653i
$366$	8.88029e8	−	2.58987e8i	0.946768	−	0.276118i
$367$	−4.24466e8	−	7.35196e8i	−0.448241	−	0.776376i	0.550031	−	0.835144i	$-0.314616\pi$
$367$	−4.24466e8	−	7.35196e8i	−0.448241	−	0.776376i	−0.998272	+	0.0587687i	$0.981283\pi$
$368$	−1.45868e8			−0.152579
$369$	−6.14424e8	−	3.19605e8i	−0.636613	−	0.331148i
$370$	−1.97746e8			−0.202956
$371$	−1.65189e7	−	2.86116e7i	−0.0167947	−	0.0290893i
$372$	−5.98222e7	+	2.44638e8i	−0.0602507	+	0.246391i
$373$	1.76373e8	−	3.05487e8i	0.175975	−	0.304798i	−0.764523	−	0.644596i	$-0.777026\pi$
$373$	1.76373e8	−	3.05487e8i	0.175975	−	0.304798i	0.940498	+	0.339799i	$0.110359\pi$
$374$	1.99673e7	−	3.45844e7i	0.0197365	−	0.0341846i
$375$	7.88112e8	+	7.54218e8i	0.771754	+	0.738563i
$376$	7.01138e8	+	1.21441e9i	0.680214	+	1.17817i
$377$	1.73513e9			1.66778
$378$	9.50345e7	+	2.79533e8i	0.0905024	+	0.266203i
$379$	7.71353e8			0.727806			0.363903	−	0.931437i	$-0.381444\pi$
$379$	7.71353e8			0.727806			0.363903	+	0.931437i	$0.381444\pi$
$380$	−9.40072e7	−	1.62825e8i	−0.0878858	−	0.152223i
$381$	−5.07539e8	−	4.85712e8i	−0.470146	−	0.449926i
$382$	−7.16863e8	+	1.24164e9i	−0.657983	+	1.13966i
$383$	3.28658e8	−	5.69253e8i	0.298916	−	0.517737i	−0.676972	−	0.736008i	$-0.736708\pi$
$383$	3.28658e8	−	5.69253e8i	0.298916	−	0.517737i	0.975888	+	0.218271i	$0.0700417\pi$
$384$	2.62939e7	−	1.07527e8i	0.0236971	−	0.0969075i
$385$	1.32701e8	+	2.29845e8i	0.118512	+	0.205269i
$386$	1.83860e8			0.162716
$387$	2.37331e8	−	1.51300e8i	0.208145	−	0.132694i
$388$	4.27876e8			0.371883
$389$	−2.64685e8	−	4.58448e8i	−0.227985	−	0.394881i	0.729226	−	0.684273i	$-0.239880\pi$
$389$	−2.64685e8	−	4.58448e8i	−0.227985	−	0.394881i	−0.957211	+	0.289392i	$0.906547\pi$
$390$	1.43546e9	−	4.18640e8i	1.22536	−	0.357367i
$391$	−1.95377e7	+	3.38402e7i	−0.0165293	+	0.0286296i
$392$	−9.16726e7	+	1.58782e8i	−0.0768667	+	0.133137i
$393$	−2.21025e8	+	6.44603e7i	−0.183682	+	0.0535696i
$394$	−7.50814e8	−	1.30045e9i	−0.618437	−	1.07116i
$395$	−1.30540e9			−1.06575
$396$	−1.67779e7	−	3.81549e8i	−0.0135770	−	0.308757i
$397$	−1.40516e8			−0.112709			−0.0563544	−	0.998411i	$-0.517948\pi$
$397$	−1.40516e8			−0.112709			−0.0563544	+	0.998411i	$0.517948\pi$
$398$	7.54049e8	+	1.30605e9i	0.599527	+	1.03841i
$399$	4.94713e7	−	2.02309e8i	0.0389895	−	0.159445i
$400$	−4.04844e7	+	7.01210e7i	−0.0316284	+	0.0547820i
$401$	3.81769e8	−	6.61244e8i	0.295662	−	0.512102i	−0.679477	−	0.733697i	$-0.737793\pi$
$401$	3.81769e8	−	6.61244e8i	0.295662	−	0.512102i	0.975139	+	0.221595i	$0.0711264\pi$
$402$	−1.30942e9	−	1.25311e9i	−1.00528	−	0.962049i
$403$	7.06435e8	+	1.22358e9i	0.537656	+	0.931247i
$404$	6.55134e8			0.494305
$405$	−5.11330e8	+	1.09834e9i	−0.382480	+	0.821568i
$406$	3.33969e8			0.247665
$407$	1.41676e8	+	2.45391e8i	0.104164	+	0.180417i
$408$	8.17871e7	+	7.82697e7i	0.0596176	+	0.0570536i
$409$	5.86311e8	−	1.01552e9i	0.423737	−	0.733934i	−0.572564	−	0.819860i	$-0.694051\pi$
$409$	5.86311e8	−	1.01552e9i	0.423737	−	0.733934i	0.996302	+	0.0859255i	$0.0273847\pi$
$410$	−3.37554e8	+	5.84661e8i	−0.241880	+	0.418949i
$411$	6.28257e7	−	2.56921e8i	0.0446366	−	0.182538i
$412$	4.34898e8	+	7.53265e8i	0.306370	+	0.530649i
$413$	−3.41636e8			−0.238638
$414$	−2.03413e7	−	4.62584e8i	−0.0140889	−	0.320398i
$415$	−2.07317e9			−1.42386
$416$	−1.12992e9	−	1.95708e9i	−0.769522	−	1.33285i
$417$	−2.45322e9	+	7.15464e8i	−1.65676	+	0.483183i
$418$	1.66905e8	−	2.89088e8i	0.111777	−	0.193604i
$419$	7.73439e8	−	1.33964e9i	0.513662	−	0.889688i	−0.486213	−	0.873840i	$-0.661622\pi$
$419$	7.73439e8	−	1.33964e9i	0.513662	−	0.889688i	0.999874	−	0.0158477i	$-0.00504469\pi$
$420$	−2.22985e8	+	6.50319e7i	−0.146860	+	0.0428306i
$421$	−2.42362e8	−	4.19783e8i	−0.158299	−	0.274181i	0.775957	−	0.630786i	$-0.217268\pi$
$421$	−2.42362e8	−	4.19783e8i	−0.158299	−	0.274181i	−0.934255	+	0.356605i	$0.883934\pi$
$422$	1.90070e9			1.23117
$423$	−1.65937e9	+	1.05786e9i	−1.06599	+	0.679576i
$424$	1.50106e8			0.0956352
$425$	1.08450e7	+	1.87840e7i	0.00685279	+	0.0118694i
$426$	−1.19018e8	+	4.86717e8i	−0.0745900	+	0.305030i
$427$	−4.03066e8	+	6.98130e8i	−0.250541	+	0.433949i
$428$	9.88959e7	−	1.71293e8i	0.0609712	−	0.105605i
$429$	−1.54795e9	−	1.48138e9i	−0.946578	−	0.905869i
$430$	−1.37179e8	−	2.37600e8i	−0.0832045	−	0.144114i
$431$	−6.42962e8			−0.386825			−0.193413	−	0.981117i	$-0.561956\pi$
$431$	−6.42962e8			−0.386825			−0.193413	+	0.981117i	$0.561956\pi$
$432$	−5.81707e8	−	1.15426e8i	−0.347146	−	0.0688829i
$433$	1.44149e9			0.853306			0.426653	−	0.904415i	$-0.359692\pi$
$433$	1.44149e9			0.853306			0.426653	+	0.904415i	$0.359692\pi$
$434$	1.35971e8	+	2.35509e8i	0.0798421	+	0.138291i
$435$	9.90095e8	+	9.47514e8i	0.576719	+	0.551917i
$436$	−8.17376e7	+	1.41574e8i	−0.0472301	+	0.0818050i
$437$	−1.63314e8	+	2.82867e8i	−0.0936132	+	0.162143i
$438$	2.50095e8	−	1.02274e9i	0.142215	−	0.581577i
$439$	1.25401e9	+	2.17201e9i	0.707417	+	1.22528i	0.965812	+	0.259243i	$0.0834730\pi$
$439$	1.25401e9	+	2.17201e9i	0.707417	+	1.22528i	−0.258395	+	0.966039i	$0.583194\pi$
$440$	−1.20585e9			−0.674851
$441$	−2.28263e8	−	1.18736e8i	−0.126736	−	0.0659246i
$442$	1.96071e8			0.108003
$443$	1.27744e9	+	2.21260e9i	0.698118	+	1.20918i	0.969118	+	0.246596i	$0.0793122\pi$
$443$	1.27744e9	+	2.21260e9i	0.698118	+	1.20918i	−0.271001	+	0.962579i	$0.587355\pi$
$444$	−2.38066e8	+	6.94303e7i	−0.129080	+	0.0376451i
$445$	9.39291e8	−	1.62690e9i	0.505290	−	0.875187i
$446$	5.45795e8	−	9.45345e8i	0.291311	−	0.504566i
$447$	−2.82349e9	+	8.23449e8i	−1.49524	+	0.436074i
$448$	−3.44770e8	−	5.97160e8i	−0.181158	−	0.313774i
$449$	−2.89111e9			−1.50731			−0.753656	−	0.657269i	$-0.771711\pi$
$449$	−2.89111e9			−1.50731			−0.753656	+	0.657269i	$0.771711\pi$
$450$	−2.28016e8	−	1.18607e8i	−0.117956	−	0.0613575i
$451$	9.67373e8			0.496565
$452$	−5.99919e8	−	1.03909e9i	−0.305568	−	0.529260i
$453$	2.51602e8	−	1.02891e9i	0.127166	−	0.520036i
$454$	−1.27926e9	+	2.21575e9i	−0.641601	+	1.11129i
$455$	−6.51536e8	+	1.12849e9i	−0.324264	+	0.561641i
$456$	6.83651e8	+	6.54249e8i	0.337643	+	0.323122i
$457$	−1.53956e9	−	2.66660e9i	−0.754554	−	1.30693i	−0.945596	−	0.325343i	$-0.894520\pi$
$457$	−1.53956e9	−	2.66660e9i	−0.754554	−	1.30693i	0.191042	−	0.981582i	$-0.438813\pi$
$458$	−2.11484e9			−1.02861
$459$	−1.04692e8	+	1.19491e8i	−0.0505323	+	0.0576754i
$460$	3.64273e8			0.174492
$461$	−6.93800e8	−	1.20170e9i	−0.329823	−	0.571270i	0.652653	−	0.757657i	$-0.273656\pi$
$461$	−6.93800e8	−	1.20170e9i	−0.329823	−	0.571270i	−0.982477	+	0.186386i	$0.940322\pi$
$462$	−2.97941e8	−	2.85128e8i	−0.140567	−	0.134522i
$463$	−2.76077e8	+	4.78179e8i	−0.129270	+	0.223902i	−0.923394	−	0.383854i	$-0.874597\pi$
$463$	−2.76077e8	+	4.78179e8i	−0.129270	+	0.223902i	0.794124	+	0.607756i	$0.207930\pi$
$464$	−3.35415e8	+	5.80956e8i	−0.155872	+	0.269979i
$465$	−2.65065e8	+	1.08396e9i	−0.122255	+	0.499953i
$466$	1.37418e9	+	2.38014e9i	0.629059	+	1.08956i
$467$	−3.83312e9			−1.74158			−0.870790	−	0.491654i	$-0.836392\pi$
$467$	−3.83312e9			−1.74158			−0.870790	+	0.491654i	$0.836392\pi$
$468$	1.58116e9	−	1.00800e9i	0.713042	−	0.454570i
$469$	1.57947e9			0.706978
$470$	9.59127e8	+	1.66126e9i	0.426121	+	0.738064i
$471$	−2.18840e9	+	6.38231e8i	−0.965060	+	0.281452i
$472$	7.76106e8	−	1.34426e9i	0.339722	−	0.588416i
$473$	−1.96565e8	+	3.40461e8i	−0.0854068	+	0.147929i
$474$	1.94726e9	−	5.67904e8i	0.839846	−	0.244935i
$475$	9.06521e7	+	1.57014e8i	0.0388106	+	0.0672219i
$476$	−3.04578e7			−0.0129442
$477$	9.25408e6	+	2.10449e8i	0.00390408	+	0.0887834i
$478$	6.01096e8			0.251737
$479$	2.47923e8	+	4.29416e8i	0.103073	+	0.178527i	0.912949	−	0.408074i	$-0.133799\pi$
$479$	2.47923e8	+	4.29416e8i	0.103073	+	0.178527i	−0.809877	+	0.586600i	$0.800466\pi$
$480$	4.23963e8	−	1.73376e9i	0.174978	−	0.715559i
$481$	−6.95602e8	+	1.20482e9i	−0.285005	+	0.493644i
$482$	−8.06478e8	+	1.39686e9i	−0.328041	+	0.568184i
$483$	2.91530e8	+	2.78992e8i	0.117725	+	0.112662i
$484$	−2.90287e8	−	5.02792e8i	−0.116378	−	0.201572i
$485$	1.89587e9			0.754591
$486$	2.84926e8	−	1.86083e9i	0.112591	−	0.735326i
$487$	2.75096e9			1.07928			0.539639	−	0.841896i	$-0.318561\pi$
$487$	2.75096e9			1.07928			0.539639	+	0.841896i	$0.318561\pi$
$488$	−1.83131e9	−	3.17193e9i	−0.713335	−	1.23553i
$489$	−2.93719e9	−	2.81087e9i	−1.13593	−	1.08708i
$490$	−1.25404e8	+	2.17207e8i	−0.0481533	+	0.0834039i
$491$	−1.18853e9	+	2.05859e9i	−0.453132	+	0.784848i	−0.998579	−	0.0532975i	$-0.983027\pi$
$491$	−1.18853e9	+	2.05859e9i	−0.453132	+	0.784848i	0.545446	+	0.838146i	$0.316360\pi$
$492$	−2.01103e8	+	8.22393e8i	−0.0761272	+	0.311316i
$493$	8.98511e7	+	1.55627e8i	0.0337722	+	0.0584952i
$494$	1.63894e9			0.611672
$495$	−7.43408e7	−	1.69060e9i	−0.0275492	−	0.626501i
$496$	−5.46238e8			−0.201000
$497$	−2.18328e8	−	3.78155e8i	−0.0797742	−	0.138173i
$498$	3.09254e9	−	9.01915e8i	1.12205	−	0.327237i
$499$	9.08113e8	−	1.57290e9i	0.327181	−	0.566694i	−0.654770	−	0.755828i	$-0.727235\pi$
$499$	9.08113e8	−	1.57290e9i	0.327181	−	0.566694i	0.981951	+	0.189134i	$0.0605680\pi$
$500$	6.66745e8	−	1.15484e9i	0.238542	−	0.413166i
$501$	−4.63512e8	+	1.35180e8i	−0.164676	+	0.0480264i
$502$	−5.91236e8	−	1.02405e9i	−0.208592	−	0.361292i
$503$	5.32699e9			1.86635			0.933177	−	0.359418i	$-0.117025\pi$
$503$	5.32699e9			1.86635			0.933177	+	0.359418i	$0.117025\pi$
$504$	9.85751e8	−	6.28424e8i	0.342973	−	0.218648i
$505$	2.90282e9			1.00300
$506$	3.23375e8	+	5.60101e8i	0.110963	+	0.192194i
$507$	1.80173e9	−	7.36805e9i	0.613992	−	2.51087i
$508$	−4.29379e8	+	7.43707e8i	−0.145318	+	0.251697i
$509$	−2.27282e9	+	3.93663e9i	−0.763927	+	1.32316i	0.176885	+	0.984232i	$0.443398\pi$
$509$	−2.27282e9	+	3.93663e9i	−0.763927	+	1.32316i	−0.940812	+	0.338929i	$0.889935\pi$
$510$	1.11881e8	+	1.07070e8i	0.0373475	+	0.0357413i
$511$	4.58776e8	+	7.94623e8i	0.152099	+	0.263444i
$512$	2.03036e9			0.668540
$513$	−8.75110e8	+	9.98814e8i	−0.286188	+	0.326643i
$514$	2.48764e9			0.808011
$515$	1.92698e9	+	3.33763e9i	0.621658	+	1.07674i
$516$	−2.48573e8	−	2.37883e8i	−0.0796490	−	0.0762235i
$517$	1.37435e9	−	2.38044e9i	0.437400	−	0.757600i
$518$	−1.33886e8	+	2.31897e8i	−0.0423234	+	0.0733063i
$519$	−1.22654e9	+	5.01585e9i	−0.385120	+	1.57492i
$520$	−2.96023e9	−	5.12727e9i	−0.923238	−	1.59909i
$521$	2.61558e9			0.810283			0.405141	−	0.914254i	$-0.367222\pi$
$521$	2.61558e9			0.810283			0.405141	+	0.914254i	$0.367222\pi$
$522$	−1.88912e9	−	9.82668e8i	−0.581318	−	0.302385i
$523$	−4.89917e8			−0.149750			−0.0748750	−	0.997193i	$-0.523856\pi$
$523$	−4.89917e8			−0.149750			−0.0748750	+	0.997193i	$0.523856\pi$
$524$	1.40721e8	+	2.43736e8i	0.0427268	+	0.0740050i
$525$	2.15027e8	−	6.27110e7i	0.0648538	−	0.0189141i
$526$	−1.04277e9	+	1.80612e9i	−0.312419	+	0.541125i
$527$	−7.31633e7	+	1.26722e8i	−0.0217749	+	0.0377152i
$528$	7.95225e8	−	2.31921e8i	0.235110	−	0.0685681i
$529$	1.38600e9	+	2.40062e9i	0.407068	+	0.705063i
$530$	2.05339e8			0.0599108
$531$	1.93249e9	+	1.00523e9i	0.560128	+	0.291362i
$532$	−2.54594e8			−0.0733091
$533$	2.37480e9	+	4.11328e9i	0.679332	+	1.17664i
$534$	−6.93366e8	+	2.83546e9i	−0.197046	+	0.805805i
$535$	4.38196e8	−	7.58978e8i	0.123717	−	0.214284i
$536$	−3.58813e9	+	6.21482e9i	−1.00645	+	1.74322i
$537$	−3.78212e9	−	3.61947e9i	−1.05396	−	1.00864i
$538$	9.65535e8	+	1.67236e9i	0.267319	+	0.463010i
$539$	3.59387e8			0.0988557
$540$	1.45268e9	+	2.88251e8i	0.397002	+	0.0787757i
$541$	−1.06891e9			−0.290237			−0.145118	−	0.989414i	$-0.546356\pi$
$541$	−1.06891e9			−0.290237			−0.145118	+	0.989414i	$0.546356\pi$
$542$	−2.38703e9	−	4.13445e9i	−0.643962	−	1.11537i
$543$	4.01543e9	+	3.84274e9i	1.07630	+	1.03001i
$544$	1.17022e8	−	2.02688e8i	0.0311654	−	0.0539800i
$545$	−3.62169e8	+	6.27296e8i	−0.0958350	+	0.165991i
$546$	4.80950e8	−	1.96681e9i	0.126452	−	0.517116i
$547$	3.38531e8	+	5.86353e8i	0.0884389	+	0.153181i	0.906851	−	0.421450i	$-0.138479\pi$
$547$	3.38531e8	+	5.86353e8i	0.0884389	+	0.153181i	−0.818413	+	0.574631i	$0.805146\pi$
$548$	−3.23320e8			−0.0839268
$549$	4.33414e9	−	2.76305e9i	1.11789	−	0.712666i
$550$	3.58998e8			0.0920073
$551$	7.51057e8	+	1.30087e9i	0.191268	+	0.331286i
$552$	−1.76005e9	+	5.13304e8i	−0.445387	+	0.129894i
$553$	−8.83837e8	+	1.53085e9i	−0.222246	+	0.384942i
$554$	8.13152e8	−	1.40842e9i	0.203183	−	0.351923i
$555$	−1.05484e9	+	3.07637e8i	−0.261917	+	0.0763860i
$556$	1.56191e9	+	2.70530e9i	0.385384	+	0.667504i
$557$	−1.29962e9			−0.318658			−0.159329	−	0.987226i	$-0.550933\pi$
$557$	−1.29962e9			−0.318658			−0.159329	+	0.987226i	$0.550933\pi$
$558$	−7.61726e7	−	1.73225e9i	−0.0185600	−	0.422077i
$559$	−1.93019e9			−0.467367
$560$	−2.51894e8	−	4.36293e8i	−0.0606122	−	0.104983i
$561$	5.27089e7	−	2.15549e8i	0.0126042	−	0.0515437i
$562$	1.73382e9	−	3.00306e9i	0.412027	−	0.713652i
$563$	−1.68060e9	+	2.91088e9i	−0.396902	+	0.687455i	−0.993342	−	0.115203i	$-0.963248\pi$
$563$	−1.68060e9	+	2.91088e9i	−0.396902	+	0.687455i	0.596440	+	0.802658i	$0.296582\pi$
$564$	1.73798e9	+	1.66323e9i	0.407912	+	0.390369i
$565$	−2.65817e9	−	4.60409e9i	−0.620031	−	1.07393i
$566$	1.17024e9			0.271279
$567$	9.41823e8	+	1.34328e9i	0.216984	+	0.309475i
$568$	1.98393e9			0.454263
$569$	−1.73372e9	−	3.00290e9i	−0.394536	−	0.683356i	0.598506	−	0.801118i	$-0.295761\pi$
$569$	−1.73372e9	−	3.00290e9i	−0.394536	−	0.683356i	−0.993042	+	0.117762i	$0.962428\pi$
$570$	9.35206e8	+	8.94986e8i	0.211517	+	0.202420i
$571$	7.09815e8	−	1.22944e9i	0.159558	−	0.276363i	−0.775151	−	0.631776i	$-0.782326\pi$
$571$	7.09815e8	−	1.22944e9i	0.159558	−	0.276363i	0.934709	+	0.355413i	$0.115660\pi$
$572$	−1.30957e9	+	2.26824e9i	−0.292578	+	0.506760i
$573$	−1.89234e9	+	7.73859e9i	−0.420203	+	1.71839i
$574$	4.57090e8	+	7.91702e8i	0.100881	+	0.174731i
$575$	−3.51273e8			−0.0770561
$576$	1.93144e8	+	4.39233e9i	0.0421118	+	0.957671i
$577$	−5.21400e9			−1.12994			−0.564970	−	0.825111i	$-0.691112\pi$
$577$	−5.21400e9			−1.12994			−0.564970	+	0.825111i	$0.691112\pi$
$578$	−1.71660e9	−	2.97324e9i	−0.369761	−	0.640445i
$579$	9.80770e8	−	2.86034e8i	0.209987	−	0.0612411i
$580$	8.37622e8	−	1.45080e9i	0.178259	−	0.308753i
$581$	−1.40366e9	+	2.43122e9i	−0.296925	+	0.514289i
$582$	−2.82805e9	+	8.24779e8i	−0.594643	+	0.173423i
$583$	−1.47116e8	−	2.54813e8i	−0.0307483	−	0.0532576i
$584$	−4.16886e9			−0.866109
$585$	7.00593e9	−	4.46634e9i	1.44684	−	0.922372i
$586$	4.77601e9			0.980447
$587$	−2.03273e9	−	3.52080e9i	−0.414808	−	0.718469i	0.580600	−	0.814189i	$-0.302818\pi$
$587$	−2.03273e9	−	3.52080e9i	−0.414808	−	0.718469i	−0.995408	+	0.0957200i	$0.969485\pi$
$588$	−7.47113e7	+	3.05526e8i	−0.0151553	+	0.0619765i
$589$	−6.11565e8	+	1.05926e9i	−0.123322	+	0.213599i
$590$	1.06168e9	−	1.83888e9i	0.212820	−	0.368614i
$591$	−6.02823e9	−	5.76898e9i	−1.20125	−	1.14959i
$592$	−2.68931e8	−	4.65802e8i	−0.0532739	−	0.0922731i
$593$	−3.12593e9			−0.615586			−0.307793	−	0.951453i	$-0.599590\pi$
$593$	−3.12593e9			−0.615586			−0.307793	+	0.951453i	$0.599590\pi$
$594$	8.46372e8	+	2.48951e9i	0.165695	+	0.487373i
$595$	−1.34955e8			−0.0262651
$596$	1.79765e9	+	3.11361e9i	0.347810	+	0.602425i
$597$	6.05421e9	+	5.79384e9i	1.16452	+	1.11444i
$598$	−1.58770e9	+	2.74998e9i	−0.303609	+	0.525866i
$599$	3.03460e9	−	5.25608e9i	0.576909	−	0.999235i	−0.418923	−	0.908022i	$-0.637592\pi$
$599$	3.03460e9	−	5.25608e9i	0.576909	−	0.999235i	0.995831	−	0.0912134i	$-0.0290745\pi$
$600$	−2.41731e8	+	9.88541e8i	−0.0456881	+	0.186838i
$601$	−2.03521e9	−	3.52509e9i	−0.382428	−	0.662384i	0.608981	−	0.793185i	$-0.291579\pi$
$601$	−2.03521e9	−	3.52509e9i	−0.382428	−	0.662384i	−0.991409	+	0.130800i	$0.958245\pi$
$602$	−3.71513e8			−0.0694043
$603$	−8.93439e9	−	4.64741e9i	−1.65941	−	0.863178i
$604$	−1.29482e9			−0.239101
$605$	−1.28623e9	−	2.22781e9i	−0.236143	−	0.409011i
$606$	−4.33011e9	+	1.26284e9i	−0.790396	+	0.230513i
$607$	6.30211e8	−	1.09156e9i	0.114373	−	0.198101i	−0.803156	−	0.595769i	$-0.796847\pi$
$607$	6.30211e8	−	1.09156e9i	0.114373	−	0.198101i	0.917529	+	0.397669i	$0.130181\pi$
$608$	9.78179e8	−	1.69425e9i	0.176504	−	0.305715i
$609$	1.78151e9	−	5.19563e8i	0.319615	−	0.0932133i
$610$	−2.50516e9	−	4.33906e9i	−0.446870	−	0.774001i
$611$	1.34955e10			2.39356
$612$	1.72287e8	+	8.96188e7i	0.0303825	+	0.0158041i
$613$	1.09591e9			0.192160			0.0960801	−	0.995374i	$-0.469369\pi$
$613$	1.09591e9			0.192160			0.0960801	+	0.995374i	$0.469369\pi$
$614$	8.68606e7	+	1.50447e8i	0.0151438	+	0.0262298i
$615$	−8.91062e8	+	3.64393e9i	−0.154470	+	0.631694i
$616$	−8.16431e8	+	1.41410e9i	−0.140730	+	0.243752i
$617$	4.14948e9	−	7.18711e9i	0.711206	−	1.23185i	−0.253199	−	0.967414i	$-0.581483\pi$
$617$	4.14948e9	−	7.18711e9i	0.711206	−	1.23185i	0.964405	−	0.264431i	$-0.0851841\pi$
$618$	−4.32646e9	−	4.14040e9i	−0.737349	−	0.705638i
$619$	4.13379e9	+	7.15993e9i	0.700537	+	1.21336i	0.968278	+	0.249874i	$0.0803893\pi$
$619$	4.13379e9	+	7.15993e9i	0.700537	+	1.21336i	−0.267742	+	0.963491i	$0.586277\pi$
$620$	1.36411e9			0.229867
$621$	−8.28160e8	−	2.43594e9i	−0.138769	−	0.408174i
$622$	−3.49667e9			−0.582624
$623$	−1.27191e9	−	2.20302e9i	−0.210741	−	0.365015i
$624$	2.93832e9	+	2.81196e9i	0.484121	+	0.463300i
$625$	2.40881e9	−	4.17218e9i	0.394659	−	0.683570i
$626$	−1.57792e9	+	2.73304e9i	−0.257084	+	0.445283i
$627$	4.40589e8	−	1.80175e9i	0.0713834	−	0.291917i
$628$	1.39330e9	+	2.41327e9i	0.224485	+	0.388819i
$629$	−1.44083e8			−0.0230852
$630$	1.34847e9	−	8.59658e8i	0.214856	−	0.136973i
$631$	−7.52813e9			−1.19285			−0.596423	−	0.802670i	$-0.703412\pi$
$631$	−7.52813e9			−1.19285			−0.596423	+	0.802670i	$0.703412\pi$
$632$	−4.01568e9	−	6.95537e9i	−0.632776	−	1.09600i
$633$	1.01390e10	−	2.95696e9i	1.58884	−	0.463374i
$634$	−1.98302e9	+	3.43470e9i	−0.309040	+	0.535274i
$635$	−1.90253e9	+	3.29528e9i	−0.294865	+	0.510721i
$636$	2.47208e8	−	7.20962e7i	0.0381032	−	0.0111125i
$637$	8.82258e8	+	1.52812e9i	0.135241	+	0.234244i
$638$	2.97431e9			0.453434
$639$	1.22310e8	+	2.78147e9i	0.0185442	+	0.421718i
$640$	−5.99570e8			−0.0904087
$641$	1.66944e9	+	2.89156e9i	0.250362	+	0.433639i	0.963625	−	0.267257i	$-0.0861171\pi$
$641$	1.66944e9	+	2.89156e9i	0.250362	+	0.433639i	−0.713264	+	0.700896i	$0.752784\pi$
$642$	−3.23467e8	+	1.32279e9i	−0.0482456	+	0.197297i
$643$	−1.10901e8	+	1.92085e8i	−0.0164511	+	0.0284942i	−0.874134	−	0.485685i	$-0.838570\pi$
$643$	−1.10901e8	+	1.92085e8i	−0.0164511	+	0.0284942i	0.857683	+	0.514179i	$0.171903\pi$
$644$	2.46635e8	−	4.27185e8i	0.0363877	−	0.0630253i
$645$	−1.10140e9	−	1.05403e9i	−0.161616	−	0.154666i
$646$	8.48699e7	+	1.46999e8i	0.0123863	+	0.0214536i
$647$	−5.23430e9			−0.759789			−0.379895	−	0.925030i	$-0.624040\pi$
$647$	−5.23430e9			−0.759789			−0.379895	+	0.925030i	$0.624040\pi$
$648$	−7.42505e9	+	6.54270e8i	−1.07198	+	0.0944593i
$649$	−3.04259e9			−0.436906
$650$	8.81302e8	+	1.52646e9i	0.125872	+	0.218016i
$651$	1.09170e9	+	1.04475e9i	0.155085	+	0.148416i
$652$	−2.48487e9	+	4.30392e9i	−0.351105	+	0.608131i
$653$	4.89700e9	−	8.48186e9i	0.688231	−	1.19205i	−0.284179	−	0.958771i	$-0.591721\pi$
$653$	4.89700e9	−	8.48186e9i	0.688231	−	1.19205i	0.972410	−	0.233280i	$-0.0749457\pi$
$654$	2.67346e8	−	1.09329e9i	0.0373725	−	0.152832i
$655$	6.23519e8	+	1.07997e9i	0.0866972	+	0.150164i
$656$	−1.83627e9			−0.253965
$657$	−2.57012e8	−	5.84474e9i	−0.0353569	−	0.804057i
$658$	2.59755e9			0.355445
$659$	−6.21730e9	−	1.07687e10i	−0.846258	−	1.46576i	−0.884524	−	0.466495i	$-0.845517\pi$
$659$	−6.21730e9	−	1.07687e10i	−0.846258	−	1.46576i	0.0382657	−	0.999268i	$-0.487817\pi$
$660$	−1.98589e9	+	5.79171e8i	−0.268876	+	0.0784157i
$661$	−4.61781e9	+	7.99829e9i	−0.621915	+	1.07719i	0.367214	+	0.930137i	$0.380312\pi$
$661$	−4.61781e9	+	7.99829e9i	−0.621915	+	1.07719i	−0.989129	+	0.147052i	$0.953022\pi$
$662$	−2.52565e9	+	4.37455e9i	−0.338353	+	0.586044i
$663$	1.04591e9	−	3.05032e8i	0.139379	−	0.0406488i
$664$	−6.37750e9	−	1.10462e10i	−0.845400	−	1.46428i
$665$	−1.12808e9			−0.148752
$666$	1.43967e9	−	9.17800e8i	0.188844	−	0.120389i
$667$	−2.91031e9			−0.379751
$668$	2.95107e8	+	5.11140e8i	0.0383055	+	0.0663471i
$669$	1.44077e9	−	5.89190e9i	0.186038	−	0.760789i
$670$	−4.90841e9	+	8.50161e9i	−0.630491	+	1.09204i
$671$	−3.58968e9	+	6.21751e9i	−0.458698	+	0.794488i
$672$	−1.74614e9	−	1.67105e9i	−0.221966	−	0.212420i
$673$	−2.40213e9	−	4.16061e9i	−0.303769	−	0.526143i	0.673217	−	0.739445i	$-0.264912\pi$
$673$	−2.40213e9	−	4.16061e9i	−0.303769	−	0.526143i	−0.976986	+	0.213301i	$0.931578\pi$
$674$	9.46225e9			1.19038
$675$	−1.40084e9	−	2.77963e8i	−0.175317	−	0.0347876i
$676$	−9.27226e9			−1.15444
$677$	−5.29933e9	−	9.17871e9i	−0.656388	−	1.13690i	−0.981544	−	0.191237i	$-0.938750\pi$
$677$	−5.29933e9	−	9.17871e9i	−0.656388	−	1.13690i	0.325156	−	0.945660i	$-0.394583\pi$
$678$	5.96814e9	+	5.71147e9i	0.735419	+	0.703791i
$679$	1.28362e9	−	2.22329e9i	0.157359	−	0.272554i
$680$	3.06582e8	−	5.31015e8i	0.0373908	−	0.0647628i
$681$	−3.37695e9	+	1.38098e10i	−0.409741	+	1.67560i
$682$	1.21095e9	+	2.09743e9i	0.146178	+	0.253187i
$683$	1.19057e9			0.142982			0.0714910	−	0.997441i	$-0.477224\pi$
$683$	1.19057e9			0.142982			0.0714910	+	0.997441i	$0.477224\pi$
$684$	1.44013e9	+	7.49116e8i	0.172070	+	0.0895061i
$685$	−1.43259e9			−0.170296
$686$	1.69813e8	+	2.94124e8i	0.0200833	+	0.0347853i
$687$	−1.12813e10	+	3.29011e9i	−1.32743	+	0.387134i
$688$	3.73121e8	−	6.46264e8i	0.0436808	−	0.0756573i
$689$	7.22311e8	−	1.25108e9i	0.0841312	−	0.145719i
$690$	−2.40767e9	+	7.02178e8i	−0.279013	+	0.0813721i
$691$	6.27618e9	+	1.08707e10i	0.723640	+	1.25338i	0.959531	+	0.281601i	$0.0908656\pi$
$691$	6.27618e9	+	1.08707e10i	0.723640	+	1.25338i	−0.235892	+	0.971779i	$0.575801\pi$
$692$	6.31216e9			0.724113
$693$	−2.03290e9	−	1.05746e9i	−0.232033	−	0.120697i
$694$	2.33671e7			0.00265367
$695$	6.92062e9	+	1.19869e10i	0.781985	+	1.35444i
$696$	−2.00275e9	+	8.19011e9i	−0.225162	+	0.920783i
$697$	−2.45951e8	+	4.25999e8i	−0.0275127	+	0.0476534i
$698$	3.95544e9	−	6.85102e9i	0.440251	−	0.762537i
$699$	1.10332e10	+	1.05587e10i	1.22188	+	1.16933i
$700$	−1.36902e8	−	2.37122e8i	−0.0150858	−	0.0261293i
$701$	1.15800e10			1.26969			0.634844	−	0.772641i	$-0.281065\pi$
$701$	1.15800e10			1.26969			0.634844	+	0.772641i	$0.281065\pi$
$702$	−8.50765e9	+	9.71027e9i	−0.928175	+	1.05938i
$703$	−1.20437e9			−0.130743
$704$	−3.07051e9	−	5.31827e9i	−0.331670	−	0.574469i
$705$	7.70076e9	+	7.36958e9i	0.827698	+	0.792101i
$706$	2.46578e9	−	4.27086e9i	0.263717	−	0.456771i
$707$	1.96538e9	−	3.40414e9i	0.209160	−	0.362276i
$708$	6.32510e8	−	2.58660e9i	0.0669809	−	0.273913i
$709$	−7.66189e9	−	1.32708e10i	−0.807372	−	1.39841i	−0.914678	−	0.404184i	$-0.867556\pi$
$709$	−7.66189e9	−	1.32708e10i	−0.807372	−	1.39841i	0.107305	−	0.994226i	$-0.465778\pi$
$710$	2.71394e9			0.284574
$711$	9.50386e9	−	6.05879e9i	0.991645	−	0.632182i
$712$	1.15578e10			1.20004
$713$	−1.18489e9	−	2.05229e9i	−0.122424	−	0.212044i
$714$	2.01311e8	−	5.87109e7i	0.0206978	−	0.00603636i
$715$	−5.80254e9	+	1.00503e10i	−0.593673	+	1.02827i
$716$	−3.19968e9	+	5.54202e9i	−0.325770	+	0.564251i
$717$	3.20646e9	−	9.35138e8i	0.324869	−	0.0947456i
$718$	−9.51408e7	−	1.64789e8i	−0.00959249	−	0.0166147i
$719$	−9.87877e9			−0.991178			−0.495589	−	0.868557i	$-0.665048\pi$
$719$	−9.87877e9			−0.991178			−0.495589	+	0.868557i	$0.665048\pi$
$720$	1.41114e8	+	3.20910e9i	0.0140899	+	0.320420i
$721$	5.21873e9			0.518551
$722$	−3.05209e9	−	5.28638e9i	−0.301799	−	0.522731i
$723$	−2.12891e9	+	8.70600e9i	−0.209494	+	0.856711i
$724$	3.39706e9	−	5.88388e9i	0.332674	−	0.576208i
$725$	−8.07728e8	+	1.39903e9i	−0.0787195	+	0.136346i
$726$	2.88785e9	+	2.76365e9i	0.280089	+	0.268043i
$727$	−1.29191e9	−	2.23766e9i	−0.124699	−	0.215985i	0.796916	−	0.604090i	$-0.206463\pi$
$727$	−1.29191e9	−	2.23766e9i	−0.124699	−	0.215985i	−0.921615	+	0.388105i	$0.873130\pi$
$728$	−8.01702e9			−0.770110
$729$	−1.37504e9	−	1.03696e10i	−0.131453	−	0.991322i
$730$	−5.70283e9			−0.542575
$731$	−9.99518e7	−	1.73122e8i	−0.00946411	−	0.0163923i
$732$	−4.53945e9	−	4.34422e9i	−0.427774	−	0.409377i
$733$	3.10258e9	−	5.37382e9i	0.290977	−	0.503987i	−0.683064	−	0.730358i	$-0.739353\pi$
$733$	3.10258e9	−	5.37382e9i	0.290977	−	0.503987i	0.974041	+	0.226372i	$0.0726864\pi$
$734$	3.57240e9	−	6.18757e9i	0.333445	−	0.577543i
$735$	−3.31037e8	+	1.35375e9i	−0.0307518	+	0.125757i
$736$	1.89520e9	+	3.28258e9i	0.175219	+	0.303489i
$737$	1.40667e10			1.29436
$738$	−2.56067e8	−	5.82326e9i	−0.0234507	−	0.533297i
$739$	7.58363e9			0.691229			0.345614	−	0.938377i	$-0.387671\pi$
$739$	7.58363e9			0.691229			0.345614	+	0.938377i	$0.387671\pi$
$740$	6.71593e8	+	1.16323e9i	0.0609250	+	0.105525i
$741$	8.74267e9	−	2.54973e9i	0.789369	−	0.230214i
$742$	1.39027e8	−	2.40801e8i	0.0124935	−	0.0216394i
$743$	6.01484e9	−	1.04180e10i	0.537976	−	0.931802i	−0.461037	−	0.887381i	$-0.652522\pi$
$743$	6.01484e9	−	1.04180e10i	0.537976	−	0.931802i	0.999013	−	0.0444211i	$-0.0141443\pi$
$744$	−6.59090e9	+	1.92218e9i	−0.586731	+	0.171116i
$745$	7.96515e9	+	1.37961e10i	0.705744	+	1.22238i
$746$	2.96879e9			0.261814
$747$	1.50935e10	−	9.62225e9i	1.32486	−	0.844607i
$748$	−2.71256e8			−0.0236986
$749$	−5.93370e8	−	1.02775e9i	−0.0515988	−	0.0893717i
$750$	−2.18078e9	+	8.91812e9i	−0.188754	+	0.771896i
$751$	4.12475e9	−	7.14428e9i	0.355351	−	0.615486i	−0.631827	−	0.775110i	$-0.717695\pi$
$751$	4.12475e9	−	7.14428e9i	0.355351	−	0.615486i	0.987178	+	0.159623i	$0.0510279\pi$
$752$	−2.60879e9	+	4.51856e9i	−0.223706	+	0.387469i
$753$	−4.74700e9	−	4.54285e9i	−0.405169	−	0.387744i
$754$	7.30163e9	+	1.26468e10i	0.620326	+	1.07444i
$755$	−5.73720e9			−0.485161
$756$	1.32159e9	−	1.50840e9i	0.111242	−	0.126967i
$757$	−4.68482e9			−0.392516			−0.196258	−	0.980552i	$-0.562879\pi$
$757$	−4.68482e9			−0.392516			−0.196258	+	0.980552i	$0.562879\pi$
$758$	3.24594e9	+	5.62213e9i	0.270706	+	0.468877i
$759$	2.59635e9	+	2.48469e9i	0.215535	+	0.206265i
$760$	2.56269e9	−	4.43871e9i	0.211762	−	0.366783i
$761$	2.79317e9	−	4.83791e9i	0.229747	−	0.397934i	−0.727986	−	0.685592i	$-0.759543\pi$
$761$	2.79317e9	−	4.83791e9i	0.229747	−	0.397934i	0.957733	+	0.287658i	$0.0928767\pi$
$762$	1.40441e9	−	5.74322e9i	0.114988	−	0.470233i
$763$	4.90421e8	+	8.49435e8i	0.0399699	+	0.0692299i
$764$	9.73857e9			0.790076
$765$	7.63384e8	+	3.97090e8i	0.0616493	+	0.0320682i
$766$	5.53212e9			0.444725
$767$	−7.46925e9	−	1.29371e10i	−0.597714	−	1.03527i
$768$	1.24468e10	−	3.63002e9i	0.991504	−	0.289165i
$769$	2.71041e9	−	4.69458e9i	0.214928	−	0.372267i	−0.738322	−	0.674448i	$-0.764382\pi$
$769$	2.71041e9	−	4.69458e9i	0.214928	−	0.372267i	0.953250	+	0.302182i	$0.0977149\pi$
$770$	−1.11684e9	+	1.93443e9i	−0.0881606	+	0.152699i
$771$	1.32700e10	−	3.87008e9i	1.04275	−	0.304109i
$772$	−6.24432e8	−	1.08155e9i	−0.0488455	−	0.0846030i
$773$	5.75445e9			0.448100			0.224050	−	0.974578i	$-0.428072\pi$
$773$	5.75445e9			0.448100			0.224050	+	0.974578i	$0.428072\pi$
$774$	2.10149e9	+	1.09314e9i	0.162905	+	0.0847385i
$775$	−1.31542e9			−0.101510
$776$	5.83207e9	+	1.01014e10i	0.448029	+	0.776010i
$777$	−3.53426e8	+	1.44531e9i	−0.0270287	+	0.110532i
$778$	2.22765e9	−	3.85840e9i	0.169597	−	0.293751i
$779$	−2.05588e9	+	3.56089e9i	−0.155818	+	0.269884i
$780$	−7.33780e9	−	7.02222e9i	−0.553649	−	0.529839i
$781$	−1.94442e9	−	3.36783e9i	−0.146053	−	0.252972i
$782$	−3.28867e8			−0.0245921
$783$	−1.16060e10	−	2.30294e9i	−0.864005	−	0.171442i
$784$	−6.82190e8			−0.0505591
$785$	6.17356e9	+	1.06929e10i	0.455503	+	0.788955i
$786$	−1.39993e9	−	1.33972e9i	−0.102832	−	0.0984092i
$787$	4.06402e9	−	7.03909e9i	0.297197	−	0.514760i	−0.678297	−	0.734788i	$-0.737282\pi$
$787$	4.06402e9	−	7.03909e9i	0.297197	−	0.514760i	0.975494	+	0.220028i	$0.0706149\pi$
$788$	−5.09990e9	+	8.83328e9i	−0.371296	+	0.643103i
$789$	−2.75265e9	+	1.12567e10i	−0.199518	+	0.815912i
$790$	−5.49329e9	−	9.51465e9i	−0.396403	−	0.686591i
$791$	−7.19897e9			−0.517193
$792$	8.77904e9	−	5.59671e9i	0.627927	−	0.400309i
$793$	−3.52492e10			−2.51011
$794$	−5.91306e8	−	1.02417e9i	−0.0419218	−	0.0726107i
$795$	1.09535e9	−	3.19450e8i	0.0773156	−	0.0225485i
$796$	5.12187e9	−	8.87134e9i	0.359942	−	0.623438i
$797$	−3.45299e9	+	5.98075e9i	−0.241597	+	0.418458i	−0.961169	−	0.275959i	$-0.911004\pi$
$797$	−3.45299e9	+	5.98075e9i	−0.241597	+	0.418458i	0.719572	+	0.694417i	$0.244338\pi$
$798$	1.68274e9	−	4.90759e8i	0.117222	−	0.0341868i
$799$	6.98844e8	+	1.21043e9i	0.0484693	+	0.0839512i
$800$	2.10397e9			0.145287
$801$	7.12542e8	+	1.62040e10i	0.0489888	+	1.11406i
$802$	6.42611e9			0.439884
$803$	4.08583e9	+	7.07687e9i	0.278468	+	0.482321i
$804$	−2.92425e9	+	1.19585e10i	−0.198435	+	0.811485i
$805$	1.09281e9	−	1.89280e9i	0.0738345	−	0.127885i
$806$	−5.94551e9	+	1.02979e10i	−0.399960	+	0.692751i
$807$	7.75222e9	+	7.41882e9i	0.519240	+	0.496910i
$808$	8.92965e9	+	1.54666e10i	0.595518	+	1.03147i
$809$	−2.05077e10			−1.36175			−0.680873	−	0.732401i	$-0.738400\pi$
$809$	−2.05077e10			−1.36175			−0.680873	+	0.732401i	$0.738400\pi$
$810$	−1.01572e10	+	8.95014e8i	−0.671544	+	0.0591742i
$811$	−7.66838e9			−0.504813			−0.252407	−	0.967621i	$-0.581222\pi$
$811$	−7.66838e9			−0.504813			−0.252407	+	0.967621i	$0.581222\pi$
$812$	−1.13424e9	−	1.96457e9i	−0.0743464	−	0.128772i
$813$	−1.91653e10	−	1.83410e10i	−1.25083	−	1.19704i
$814$	−1.19238e9	+	2.06526e9i	−0.0774871	+	0.134212i
$815$	−1.10101e10	+	1.90701e10i	−0.712429	+	1.23396i
$816$	−1.00052e8	+	4.09156e8i	−0.00644631	+	0.0263617i
$817$	−8.35488e8	−	1.44711e9i	−0.0535998	−	0.0928376i
$818$	9.86905e9			0.630433
$819$	−4.94252e8	−	1.12399e10i	−0.0314380	−	0.714936i
$820$	4.58567e9			0.290439
$821$	5.27527e9	+	9.13704e9i	0.332693	+	0.576241i	0.983039	−	0.183397i	$-0.0587094\pi$
$821$	5.27527e9	+	9.13704e9i	0.332693	+	0.576241i	−0.650346	+	0.759638i	$0.725376\pi$
$822$	2.13699e9	−	6.23236e8i	0.134199	−	0.0391382i
$823$	−1.13792e10	+	1.97094e10i	−0.711564	+	1.23247i	0.252705	+	0.967543i	$0.418680\pi$
$823$	−1.13792e10	+	1.97094e10i	−0.711564	+	1.23247i	−0.964270	+	0.264922i	$0.914654\pi$
$824$	−1.18555e10	+	2.05344e10i	−0.738204	+	1.27861i
$825$	1.91502e9	−	5.58500e8i	0.118736	−	0.0346286i
$826$	−1.43764e9	−	2.49007e9i	−0.0887608	−	0.153738i
$827$	1.39780e10			0.859362			0.429681	−	0.902981i	$-0.358626\pi$
$827$	1.39780e10			0.859362			0.429681	+	0.902981i	$0.358626\pi$
$828$	−2.65206e9	+	1.69071e9i	−0.162359	+	0.103505i
$829$	−1.59098e10			−0.969896			−0.484948	−	0.874543i	$-0.661161\pi$
$829$	−1.59098e10			−0.969896			−0.484948	+	0.874543i	$0.661161\pi$
$830$	−8.72415e9	−	1.51107e10i	−0.529602	−	0.917298i
$831$	2.14652e9	−	8.77804e9i	0.129757	−	0.530633i
$832$	1.50755e10	−	2.61116e10i	0.907489	−	1.57182i
$833$	−9.13727e7	+	1.58262e8i	−0.00547721	+	0.00948680i
$834$	−1.55382e10	−	1.48700e10i	−0.927513	−	0.887623i
$835$	1.30758e9	+	2.26480e9i	0.0777260	+	0.134625i
$836$	−2.26740e9			−0.134217
$837$	−3.10123e9	−	9.12193e9i	−0.182808	−	0.537710i
$838$	1.30189e10			0.764222
$839$	−9.20824e9	−	1.59491e10i	−0.538282	−	0.932331i	−0.998997	−	0.0447830i	$-0.985740\pi$
$839$	−9.20824e9	−	1.59491e10i	−0.538282	−	0.932331i	0.460715	−	0.887548i	$-0.347593\pi$
$840$	−4.57464e9	−	4.37790e9i	−0.266305	−	0.254852i
$841$	1.93287e9	−	3.34783e9i	0.112051	−	0.194079i
$842$	2.03977e9	−	3.53299e9i	0.117758	−	0.203962i
$843$	4.57685e9	−	1.87167e10i	0.263130	−	1.07605i
$844$	−6.45524e9	−	1.11808e10i	−0.369585	−	0.640139i
$845$	−4.10843e10			−2.34249
$846$	−1.46932e10	−	7.64300e9i	−0.834298	−	0.433978i
$847$	−3.48342e9			−0.196976
$848$	2.79257e8	+	4.83687e8i	0.0157260	+	0.0272383i
$849$	6.24246e9	−	1.82056e9i	0.350089	−	0.102101i
$850$	−9.12737e7	+	1.58091e8i	−0.00509776	+	0.00882958i
$851$	1.16672e9	−	2.02082e9i	0.0648954	−	0.112402i
$852$	3.26731e9	−	9.52887e8i	0.180989	−	0.0527841i
$853$	−6.57611e9	−	1.13902e10i	−0.362783	−	0.628359i	0.625634	−	0.780116i	$-0.284840\pi$
$853$	−6.57611e9	−	1.13902e10i	−0.362783	−	0.628359i	−0.988418	+	0.151757i	$0.951507\pi$
$854$	−6.78458e9			−0.372752
$855$	6.38106e9	+	3.31924e9i	0.349149	+	0.181617i
$856$	5.39191e9			0.293822
$857$	8.93113e9	+	1.54692e10i	0.484700	+	0.839526i	0.999846	−	0.0175773i	$-0.00559530\pi$
$857$	8.93113e9	+	1.54692e10i	0.484700	+	0.839526i	−0.515145	+	0.857103i	$0.672262\pi$
$858$	4.28332e9	−	1.75163e10i	0.231513	−	0.946753i
$859$	−8.15278e8	+	1.41210e9i	−0.0438864	+	0.0760134i	−0.887134	−	0.461512i	$-0.847307\pi$
$859$	−8.15278e8	+	1.41210e9i	−0.0438864	+	0.0760134i	0.843248	+	0.537525i	$0.180641\pi$
$860$	−9.31785e8	+	1.61390e9i	−0.0499541	+	0.0865230i
$861$	3.66994e9	+	3.51211e9i	0.195951	+	0.187524i
$862$	−2.70566e9	−	4.68634e9i	−0.143879	−	0.249206i
$863$	−1.95334e10			−1.03452			−0.517262	−	0.855827i	$-0.673049\pi$
$863$	−1.95334e10			−1.03452			−0.517262	+	0.855827i	$0.673049\pi$
$864$	4.96032e9	+	1.45902e10i	0.261645	+	0.769598i
$865$	2.79684e10			1.46930
$866$	6.06597e9	+	1.05066e10i	0.317386	+	0.549728i
$867$	−1.37825e10	−	1.31897e10i	−0.718224	−	0.687335i
$868$	9.23582e8	−	1.59969e9i	0.0479354	−	0.0830265i
$869$	−7.87141e9	+	1.36337e10i	−0.406896	+	0.704764i
$870$	−2.73968e9	+	1.12037e10i	−0.141053	+	0.576826i
$871$	3.45322e10	+	5.98115e10i	1.77076	+	3.06705i
$872$	−4.45642e9			−0.227603
$873$	−1.38027e10	+	8.79932e9i	−0.702123	+	0.447609i
$874$	−2.74897e9			−0.139277
$875$	−4.00043e9	−	6.92895e9i	−0.201873	−	0.349655i
$876$	−6.86564e9	+	2.00231e9i	−0.345078	+	0.100639i
$877$	1.09949e10	−	1.90437e10i	0.550417	−	0.953351i	−0.447827	−	0.894120i	$-0.647802\pi$
$877$	1.09949e10	−	1.90437e10i	0.550417	−	0.953351i	0.998244	−	0.0592307i	$-0.0188648\pi$
$878$	−1.05540e10	+	1.82801e10i	−0.526245	+	0.911483i
$879$	2.54769e10	−	7.43015e9i	1.26528	−	0.369009i
$880$	−2.24336e9	−	3.88561e9i	−0.110971	−	0.192207i
$881$	7.05184e9			0.347446			0.173723	−	0.984795i	$-0.444420\pi$
$881$	7.05184e9			0.347446			0.173723	+	0.984795i	$0.444420\pi$
$882$	−9.51310e7	−	2.16339e9i	−0.00466855	−	0.106168i
$883$	−1.86573e9			−0.0911981			−0.0455990	−	0.998960i	$-0.514520\pi$
$883$	−1.86573e9			−0.0911981			−0.0455990	+	0.998960i	$0.514520\pi$
$884$	−6.65905e8	−	1.15338e9i	−0.0324212	−	0.0561552i
$885$	2.80258e9	−	1.14609e10i	0.135911	−	0.555799i
$886$	−1.07513e10	+	1.86217e10i	−0.519327	+	0.899501i
$887$	−1.41621e9	+	2.45295e9i	−0.0681389	+	0.118020i	−0.898082	−	0.439828i	$-0.855039\pi$
$887$	−1.41621e9	+	2.45295e9i	−0.0681389	+	0.118020i	0.829943	+	0.557848i	$0.188373\pi$
$888$	−4.88405e9	−	4.67400e9i	−0.234064	−	0.223998i
$889$	2.57625e9	+	4.46220e9i	0.122979	+	0.213007i
$890$	1.58106e10			0.751766
$891$	8.38782e9	+	1.19632e10i	0.397262	+	0.566598i
$892$	−7.41462e9			−0.349794
$893$	5.84157e9	+	1.01179e10i	0.274505	+	0.475456i
$894$	−1.78834e10	−	1.71143e10i	−0.837084	−	0.801083i
$895$	−1.41774e10	+	2.45560e10i	−0.661023	+	1.14493i
$896$	−4.05945e8	+	7.03118e8i	−0.0188534	+	0.0326550i
$897$	−4.19115e9	+	1.71394e10i	−0.193892	+	0.792905i
$898$	−1.21661e10	−	2.10724e10i	−0.560642	−	0.971060i
$899$	−1.08983e10			−0.500266
$900$	7.66943e7	+	1.74412e9i	0.00350683	+	0.0797494i
$901$	1.49615e8			0.00681457
$902$	4.07082e9	+	7.05086e9i	0.184696	+	0.319904i
$903$	−1.98178e9	+	5.77971e8i	−0.0895670	+	0.0261215i
$904$	1.63541e10	−	2.83262e10i	0.736272	−	1.27526i
$905$	1.50520e10	−	2.60708e10i	0.675031	−	1.16919i
$906$	8.55814e9	−	2.49592e9i	0.382323	−	0.111502i
$907$	−8.33012e9	−	1.44282e10i	−0.370703	−	0.642076i	0.618971	−	0.785414i	$-0.287550\pi$
$907$	−8.33012e9	−	1.44282e10i	−0.370703	−	0.642076i	−0.989674	+	0.143338i	$0.954216\pi$
$908$	1.73788e10			0.770405
$909$	−2.11337e10	+	1.34729e10i	−0.933257	+	0.594959i
$910$	−1.09669e10			−0.482437
$911$	1.13582e9	+	1.96729e9i	0.0497730	+	0.0862094i	0.889839	−	0.456276i	$-0.150817\pi$
$911$	1.13582e9	+	1.96729e9i	0.0497730	+	0.0862094i	−0.840065	+	0.542485i	$0.817484\pi$
$912$	−8.36328e8	+	3.42010e9i	−0.0365085	+	0.149299i
$913$	−1.25010e10	+	2.16523e10i	−0.543620	+	0.941578i
$914$	1.29573e10	−	2.24427e10i	0.561310	−	0.972217i
$915$	−2.01138e10	−	1.92487e10i	−0.868000	−	0.830670i
$916$	7.18254e9	+	1.24405e10i	0.308776	+	0.534816i
$917$	1.68864e9			0.0723177
$918$	−1.31148e9	−	2.60233e8i	−0.0559518	−	0.0111023i
$919$	3.54341e10			1.50597			0.752987	−	0.658035i	$-0.228612\pi$
$919$	3.54341e10			1.50597			0.752987	+	0.658035i	$0.228612\pi$
$920$	4.96515e9	+	8.59989e9i	0.210220	+	0.364112i
$921$	6.97398e8	+	6.67405e8i	0.0294152	+	0.0281502i
$922$	5.83918e9	−	1.01138e10i	0.245354	−	0.424966i
$923$	9.54669e9	−	1.65354e10i	0.399620	−	0.692162i
$924$	−6.65374e8	+	2.72100e9i	−0.0277469	+	0.113469i
$925$	−6.47625e8	−	1.12172e9i	−0.0269046	−	0.0466002i
$926$	−4.64705e9			−0.192326
$927$	−2.95201e10	−	1.53555e10i	−1.21714	−	0.633119i
$928$	1.74315e10			0.716007
$929$	−5.44456e9	−	9.43026e9i	−0.222796	−	0.385895i	0.732860	−	0.680380i	$-0.238185\pi$
$929$	−5.44456e9	−	9.43026e9i	−0.222796	−	0.385895i	−0.955656	+	0.294485i	$0.904852\pi$
$930$	−9.01607e9	+	2.62947e9i	−0.367559	+	0.107196i
$931$	−7.63776e8	+	1.32290e9i	−0.0310200	+	0.0537283i
$932$	9.33408e9	−	1.61671e10i	0.377673	−	0.654149i
$933$	−1.86524e10	+	5.43984e9i	−0.751882	+	0.219281i
$934$	−1.61302e10	−	2.79383e10i	−0.647778	−	1.12198i
$935$	−1.20190e9			−0.0480871
$936$	4.53489e10	+	2.35892e10i	1.80760	+	0.940259i
$937$	4.39030e10			1.74343			0.871716	−	0.490011i	$-0.163007\pi$
$937$	4.39030e10			1.74343			0.871716	+	0.490011i	$0.163007\pi$
$938$	6.64658e9	+	1.15122e10i	0.262959	+	0.455459i
$939$	−4.16533e9	+	1.70338e10i	−0.164180	+	0.671400i
$940$	6.51486e9	−	1.12841e10i	0.255834	−	0.443117i
$941$	1.84978e10	−	3.20391e10i	0.723697	−	1.25348i	−0.235811	−	0.971799i	$-0.575775\pi$
$941$	1.84978e10	−	3.20391e10i	0.723697	−	1.25348i	0.959508	−	0.281681i	$-0.0908919\pi$
$942$	−1.38609e10	−	1.32648e10i	−0.540273	−	0.517038i
$943$	−3.98322e9	−	6.89914e9i	−0.154683	−	0.267919i
$944$	5.77547e9			0.223452
$945$	5.85579e9	−	6.68355e9i	0.225722	−	0.257630i
$946$	−3.30867e9			−0.127068
$947$	1.34497e10	+	2.32956e10i	0.514623	+	0.891353i	0.999856	+	0.0169683i	$0.00540145\pi$
$947$	1.34497e10	+	2.32956e10i	0.514623	+	0.891353i	−0.485233	+	0.874385i	$0.661265\pi$
$948$	−9.95405e9	−	9.52596e9i	−0.379464	−	0.363145i
$949$	−2.00606e10	+	3.47459e10i	−0.761924	+	1.31969i
$950$	−7.62949e8	+	1.32147e9i	−0.0288711	+	0.0500062i
$951$	−5.23470e9	+	2.14069e10i	−0.197360	+	0.807089i
$952$	−4.15149e8	−	7.19059e8i	−0.0155946	−	0.0270107i
$953$	−2.90847e10			−1.08853			−0.544263	−	0.838914i	$-0.683191\pi$
$953$	−2.90847e10			−1.08853			−0.544263	+	0.838914i	$0.683191\pi$
$954$	−1.49495e9	+	9.53042e8i	−0.0557451	+	0.0355380i
$955$	4.31505e10			1.60315
$956$	−2.04147e9	−	3.53593e9i	−0.0755685	−	0.130888i
$957$	1.58660e10	−	4.62720e9i	0.585162	−	0.170658i
$958$	−2.08658e9	+	3.61406e9i	−0.0766753	+	0.132805i
$959$	−9.69952e8	+	1.68001e9i	−0.0355128	+	0.0615100i
$960$	2.28613e10	−	6.66732e9i	0.833972	−	0.243222i
$961$	9.31921e9	+	1.61413e10i	0.338725	+	0.586689i
$962$	−1.17087e10			−0.424029
$963$	3.32413e8	+	7.55946e9i	0.0119946	+	0.272771i
$964$	1.09560e10			0.393897
$965$	−2.76679e9	−	4.79221e9i	−0.0991128	−	0.171668i
$966$	−8.06690e8	+	3.29890e9i	−0.0287930	+	0.117747i
$967$	−3.15245e9	+	5.46019e9i	−0.112113	+	0.194185i	−0.916622	−	0.399755i	$-0.869095\pi$
$967$	−3.15245e9	+	5.46019e9i	−0.112113	+	0.194185i	0.804509	+	0.593940i	$0.202428\pi$
$968$	7.91339e9	−	1.37064e10i	0.280414	−	0.485690i
$969$	6.81415e8	+	6.52109e8i	0.0240590	+	0.0230243i
$970$	7.97802e9	+	1.38183e10i	0.280669	+	0.486133i
$971$	−2.28311e10			−0.800312			−0.400156	−	0.916447i	$-0.631044\pi$
$971$	−2.28311e10			−0.800312			−0.400156	+	0.916447i	$0.631044\pi$
$972$	−1.19140e10	+	4.64378e9i	−0.416126	+	0.162196i
$973$	1.87427e10			0.652285
$974$	1.15764e10	+	2.00509e10i	0.401436	+	0.695307i
$975$	7.07592e9	+	6.77160e9i	0.244493	+	0.233978i
$976$	6.81395e9	−	1.18021e10i	0.234598	−	0.406336i
$977$	−1.17492e10	+	2.03501e10i	−0.403066	+	0.698130i	−0.994094	−	0.108521i	$-0.965389\pi$
$977$	−1.17492e10	+	2.03501e10i	−0.403066	+	0.698130i	0.591029	+	0.806651i	$0.298722\pi$
$978$	8.12747e9	−	3.32366e10i	0.277824	−	1.13614i
$979$	−1.13276e10	−	1.96200e10i	−0.385832	−	0.668281i
$980$	1.70361e9			0.0578203
$981$	−2.74740e8	−	6.24791e9i	−0.00929138	−	0.211297i
$982$	−2.00059e10			−0.674167
$983$	−6.59837e9	−	1.14287e10i	−0.221564	−	0.383760i	0.733719	−	0.679453i	$-0.237783\pi$
$983$	−6.59837e9	−	1.14287e10i	−0.221564	−	0.383760i	−0.955283	+	0.295693i	$0.904450\pi$
$984$	−2.21564e10	+	6.46175e9i	−0.741339	+	0.216206i
$985$	−2.25970e10	+	3.91392e10i	−0.753399	+	1.30492i
$986$	−7.56207e8	+	1.30979e9i	−0.0251230	+	0.0435143i
$987$	1.38562e10	−	4.04106e9i	0.458706	−	0.133778i
$988$	−5.56624e9	−	9.64101e9i	−0.183617	−	0.318034i
$989$	3.23748e9			0.106419
$990$	1.20094e10	−	7.65607e9i	0.393366	−	0.250774i
$991$	2.06952e10			0.675480			0.337740	−	0.941239i	$-0.390337\pi$
$991$	2.06952e10			0.675480			0.337740	+	0.941239i	$0.390337\pi$
$992$	7.09700e9	+	1.22924e10i	0.230826	+	0.399802i
$993$	−6.66709e9	+	2.72646e10i	−0.216080	+	0.883641i
$994$	1.83750e9	−	3.18264e9i	0.0593437	−	0.102786i
$995$	2.26944e10	−	3.93079e10i	0.730362	−	1.26502i
$996$	−1.58085e10	−	1.51286e10i	−0.506971	−	0.485168i
$997$	−3.41729e9	−	5.91891e9i	−0.109206	−	0.189151i	0.806243	−	0.591585i	$-0.201498\pi$
$997$	−3.41729e9	−	5.91891e9i	−0.109206	−	0.189151i	−0.915449	+	0.402434i	$0.868164\pi$
$998$	1.52858e10			0.486778
$999$	6.25184e9	−	7.13559e9i	0.198394	−	0.226439i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.8.f.b.22.13	✓	42
3.2	odd	2		189.8.f.a.64.9		42
9.2	odd	6		189.8.f.a.127.9		42
9.4	even	3		567.8.a.f.1.9		21
9.5	odd	6		567.8.a.i.1.13		21
9.7	even	3	inner	63.8.f.b.43.13	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.8.f.b.22.13	✓	42	1.1	even	1	trivial
63.8.f.b.43.13	yes	42	9.7	even	3	inner
189.8.f.a.64.9		42	3.2	odd	2
189.8.f.a.127.9		42	9.2	odd	6
567.8.a.f.1.9		21	9.4	even	3
567.8.a.i.1.13		21	9.5	odd	6

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	63.8.f.b.22.13

Level	$63$
Weight	$8$
Character	63.22
Analytic conductor	$19.680$
Analytic rank	$0$
Dimension	$42$
Inner twists	$2$