LMFDB - Embedded newform 5.7.c.a.2.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,7,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$1.15027041810$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{201})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 101x^{2} + 2500 $ x^4 + 101*x^2 + 2500
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.2
Root			$7.58872i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.7.c.a.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.58872 + 4.58872i) q^{2} +(0.411277 - 0.411277i) q^{3} -21.8872i q^{4} +(-123.831 - 17.0564i) q^{5} +3.77447 q^{6} +(215.476 + 215.476i) q^{7} +(394.113 - 394.113i) q^{8} +728.662i q^{9} +O(q^{10})$	\(q+(4.58872 + 4.58872i) q^{2} +(0.411277 - 0.411277i) q^{3} -21.8872i q^{4} +(-123.831 - 17.0564i) q^{5} +3.77447 q^{6} +(215.476 + 215.476i) q^{7} +(394.113 - 394.113i) q^{8} +728.662i q^{9} +(-489.959 - 646.493i) q^{10} -1326.31 q^{11} +(-9.00171 - 9.00171i) q^{12} +(1439.89 - 1439.89i) q^{13} +1977.52i q^{14} +(-57.9436 + 43.9138i) q^{15} +2216.17 q^{16} +(1349.15 + 1349.15i) q^{17} +(-3343.63 + 3343.63i) q^{18} -9191.14i q^{19} +(-373.317 + 2710.31i) q^{20} +177.240 q^{21} +(-6086.06 - 6086.06i) q^{22} +(-7491.20 + 7491.20i) q^{23} -324.179i q^{24} +(15043.2 + 4224.21i) q^{25} +13214.5 q^{26} +(599.502 + 599.502i) q^{27} +(4716.17 - 4716.17i) q^{28} +5438.74i q^{29} +(-467.396 - 64.3788i) q^{30} -32749.1 q^{31} +(-15053.8 - 15053.8i) q^{32} +(-545.480 + 545.480i) q^{33} +12381.7i q^{34} +(-23007.3 - 30357.8i) q^{35} +15948.4 q^{36} +(56535.1 + 56535.1i) q^{37} +(42175.6 - 42175.6i) q^{38} -1184.39i q^{39} +(-55525.5 + 42081.2i) q^{40} +17758.7 q^{41} +(813.307 + 813.307i) q^{42} +(-6394.08 + 6394.08i) q^{43} +29029.2i q^{44} +(12428.3 - 90230.8i) q^{45} -68750.1 q^{46} +(-35299.9 - 35299.9i) q^{47} +(911.457 - 911.457i) q^{48} -24789.2i q^{49} +(49645.2 + 88412.6i) q^{50} +1109.75 q^{51} +(-31515.2 - 31515.2i) q^{52} +(-60400.3 + 60400.3i) q^{53} +5501.90i q^{54} +(164238. + 22622.0i) q^{55} +169844. q^{56} +(-3780.10 - 3780.10i) q^{57} +(-24956.9 + 24956.9i) q^{58} -46091.2i q^{59} +(961.152 + 1268.23i) q^{60} -75611.9 q^{61} +(-150277. - 150277. i) q^{62} +(-157009. + 157009. i) q^{63} -279990. i q^{64} +(-202862. + 153743. i) q^{65} -5006.11 q^{66} +(154883. + 154883. i) q^{67} +(29529.1 - 29529.1i) q^{68} +6161.91i q^{69} +(33729.3 - 244878. i) q^{70} +184000. q^{71} +(287175. + 287175. i) q^{72} +(301029. - 301029. i) q^{73} +518848. i q^{74} +(7924.22 - 4449.58i) q^{75} -201169. q^{76} +(-285788. - 285788. i) q^{77} +(5434.82 - 5434.82i) q^{78} +178743. i q^{79} +(-274430. - 37799.8i) q^{80} -530701. q^{81} +(81489.6 + 81489.6i) q^{82} +(565063. - 565063. i) q^{83} -3879.30i q^{84} +(-144055. - 190078. i) q^{85} -58681.4 q^{86} +(2236.83 + 2236.83i) q^{87} +(-522715. + 522715. i) q^{88} +249057. i q^{89} +(471074. - 357014. i) q^{90} +620523. q^{91} +(163962. + 163962. i) q^{92} +(-13468.9 + 13468.9i) q^{93} -323963. i q^{94} +(-156768. + 1.13815e6i) q^{95} -12382.6 q^{96} +(30626.2 + 30626.2i) q^{97} +(113751. - 113751. i) q^{98} -966430. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8}+O(q^{10}) $ 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} - 4370 q^{10} - 1052 q^{11} + 3480 q^{12} + 1960 q^{13} - 90 q^{15} - 776 q^{16} - 3280 q^{17} - 870 q^{18} + 20340 q^{20} + 3828 q^{21} - 27520 q^{22} - 39010 q^{23} + 30400 q^{25} + 44068 q^{26} + 31320 q^{27} - 4840 q^{28} - 50640 q^{30} - 33172 q^{31} - 48760 q^{32} + 22260 q^{33} - 24970 q^{35} - 40836 q^{36} + 146860 q^{37} + 218040 q^{38} - 110100 q^{40} - 213932 q^{41} - 31680 q^{42} - 72050 q^{43} + 78210 q^{45} + 323288 q^{46} + 830 q^{47} - 74160 q^{48} - 203350 q^{50} - 172212 q^{51} - 173300 q^{52} - 29620 q^{53} + 470660 q^{55} + 467280 q^{56} + 195840 q^{57} - 554640 q^{58} + 620280 q^{60} - 111052 q^{61} - 610520 q^{62} - 350130 q^{63} - 406540 q^{65} - 457824 q^{66} - 146930 q^{67} + 775780 q^{68} - 133320 q^{70} + 1310188 q^{71} + 899460 q^{72} + 553540 q^{73} - 435450 q^{75} - 2073840 q^{76} - 476300 q^{77} + 268200 q^{78} - 1011520 q^{80} - 624816 q^{81} + 2554880 q^{82} + 536870 q^{83} - 1344920 q^{85} + 1019128 q^{86} - 763440 q^{87} - 187680 q^{88} + 947310 q^{90} + 1131548 q^{91} - 2552680 q^{92} + 444660 q^{93} + 912600 q^{95} - 568992 q^{96} - 59420 q^{97} - 1892810 q^{98}+O(q^{100}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8 - 4370 * q^10 - 1052 * q^11 + 3480 * q^12 + 1960 * q^13 - 90 * q^15 - 776 * q^16 - 3280 * q^17 - 870 * q^18 + 20340 * q^20 + 3828 * q^21 - 27520 * q^22 - 39010 * q^23 + 30400 * q^25 + 44068 * q^26 + 31320 * q^27 - 4840 * q^28 - 50640 * q^30 - 33172 * q^31 - 48760 * q^32 + 22260 * q^33 - 24970 * q^35 - 40836 * q^36 + 146860 * q^37 + 218040 * q^38 - 110100 * q^40 - 213932 * q^41 - 31680 * q^42 - 72050 * q^43 + 78210 * q^45 + 323288 * q^46 + 830 * q^47 - 74160 * q^48 - 203350 * q^50 - 172212 * q^51 - 173300 * q^52 - 29620 * q^53 + 470660 * q^55 + 467280 * q^56 + 195840 * q^57 - 554640 * q^58 + 620280 * q^60 - 111052 * q^61 - 610520 * q^62 - 350130 * q^63 - 406540 * q^65 - 457824 * q^66 - 146930 * q^67 + 775780 * q^68 - 133320 * q^70 + 1310188 * q^71 + 899460 * q^72 + 553540 * q^73 - 435450 * q^75 - 2073840 * q^76 - 476300 * q^77 + 268200 * q^78 - 1011520 * q^80 - 624816 * q^81 + 2554880 * q^82 + 536870 * q^83 - 1344920 * q^85 + 1019128 * q^86 - 763440 * q^87 - 187680 * q^88 + 947310 * q^90 + 1131548 * q^91 - 2552680 * q^92 + 444660 * q^93 + 912600 * q^95 - 568992 * q^96 - 59420 * q^97 - 1892810 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	4.58872	+	4.58872i	0.573590	+	0.573590i	0.933130	−	0.359539i	$-0.117066\pi$
$2$	4.58872	+	4.58872i	0.573590	+	0.573590i	−0.359539	+	0.933130i	$0.617066\pi$
$3$	0.411277	−	0.411277i	0.0152325	−	0.0152325i	−0.699450	−	0.714682i	$-0.746571\pi$
$3$	0.411277	−	0.411277i	0.0152325	−	0.0152325i	0.714682	+	0.699450i	$0.246571\pi$
$4$		−	21.8872i		−	0.341988i
$5$	−123.831	−	17.0564i	−0.990647	−	0.136451i
$5$	−123.831	−	17.0564i	−0.990647	−	0.136451i
$6$	3.77447			0.0174744
$7$	215.476	+	215.476i	0.628210	+	0.628210i	0.947617	−	0.319408i	$-0.103484\pi$
$7$	215.476	+	215.476i	0.628210	+	0.628210i	−0.319408	+	0.947617i	$0.603484\pi$
$8$	394.113	−	394.113i	0.769751	−	0.769751i
$9$			728.662i			0.999536i
$10$	−489.959	−	646.493i	−0.489959	−	0.646493i
$11$	−1326.31			−0.996475			−0.498238	−	0.867041i	$-0.666019\pi$
$11$	−1326.31			−0.996475			−0.498238	+	0.867041i	$0.666019\pi$
$12$	−9.00171	−	9.00171i	−0.00520932	−	0.00520932i
$13$	1439.89	−	1439.89i	0.655389	−	0.655389i	−0.298897	−	0.954285i	$-0.596619\pi$
$13$	1439.89	−	1439.89i	0.655389	−	0.655389i	0.954285	+	0.298897i	$0.0966186\pi$
$14$			1977.52i			0.720670i
$15$	−57.9436	+	43.9138i	−0.0171685	+	0.0130115i
$16$	2216.17			0.541056
$17$	1349.15	+	1349.15i	0.274608	+	0.274608i	0.830952	−	0.556344i	$-0.187796\pi$
$17$	1349.15	+	1349.15i	0.274608	+	0.274608i	−0.556344	+	0.830952i	$0.687796\pi$
$18$	−3343.63	+	3343.63i	−0.573324	+	0.573324i
$19$		−	9191.14i		−	1.34001i	−0.742356	−	0.670006i	$-0.766291\pi$
$19$		−	9191.14i		−	1.34001i	0.742356	−	0.670006i	$-0.233709\pi$
$20$	−373.317	+	2710.31i	−0.0466646	+	0.338789i
$21$	177.240			0.0191384
$22$	−6086.06	−	6086.06i	−0.571569	−	0.571569i
$23$	−7491.20	+	7491.20i	−0.615698	+	0.615698i	−0.944425	−	0.328727i	$-0.893380\pi$
$23$	−7491.20	+	7491.20i	−0.615698	+	0.615698i	0.328727	+	0.944425i	$0.393380\pi$
$24$		−	324.179i		−	0.0234504i
$25$	15043.2	+	4224.21i	0.962762	+	0.270350i
$26$	13214.5			0.751849
$27$	599.502	+	599.502i	0.0304579	+	0.0304579i
$28$	4716.17	−	4716.17i	0.214840	−	0.214840i
$29$			5438.74i			0.223000i	0.993764	+	0.111500i	$0.0355655\pi$
$29$			5438.74i			0.223000i	−0.993764	+	0.111500i	$0.964435\pi$
$30$	−467.396	−	64.3788i	−0.0173110	−	0.00238440i
$31$	−32749.1			−1.09929			−0.549647	−	0.835397i	$-0.685238\pi$
$31$	−32749.1			−1.09929			−0.549647	+	0.835397i	$0.685238\pi$
$32$	−15053.8	−	15053.8i	−0.459407	−	0.459407i
$33$	−545.480	+	545.480i	−0.0151788	+	0.0151788i
$34$			12381.7i			0.315025i
$35$	−23007.3	−	30357.8i	−0.536614	−	0.708054i
$36$	15948.4			0.341829
$37$	56535.1	+	56535.1i	1.11612	+	1.11612i	0.992305	+	0.123820i	$0.0395146\pi$
$37$	56535.1	+	56535.1i	1.11612	+	1.11612i	0.123820	+	0.992305i	$0.460485\pi$
$38$	42175.6	−	42175.6i	0.768618	−	0.768618i
$39$		−	1184.39i		−	0.0199664i
$40$	−55525.5	+	42081.2i	−0.867585	+	0.657518i
$41$	17758.7			0.257667			0.128834	−	0.991666i	$-0.458877\pi$
$41$	17758.7			0.257667			0.128834	+	0.991666i	$0.458877\pi$
$42$	813.307	+	813.307i	0.0109776	+	0.0109776i
$43$	−6394.08	+	6394.08i	−0.0804216	+	0.0804216i	−0.746173	−	0.665752i	$-0.768111\pi$
$43$	−6394.08	+	6394.08i	−0.0804216	+	0.0804216i	0.665752	+	0.746173i	$0.268111\pi$
$44$			29029.2i			0.340783i
$45$	12428.3	−	90230.8i	0.136388	−	0.990187i
$46$	−68750.1			−0.706317
$47$	−35299.9	−	35299.9i	−0.340001	−	0.340001i	0.516367	−	0.856368i	$-0.327284\pi$
$47$	−35299.9	−	35299.9i	−0.340001	−	0.340001i	−0.856368	+	0.516367i	$0.827284\pi$
$48$	911.457	−	911.457i	0.00824162	−	0.00824162i
$49$		−	24789.2i		−	0.210705i
$50$	49645.2	+	88412.6i	0.397161	+	0.707301i
$51$	1109.75			0.00836592
$52$	−31515.2	−	31515.2i	−0.224135	−	0.224135i
$53$	−60400.3	+	60400.3i	−0.405706	+	0.405706i	−0.880238	−	0.474532i	$-0.842617\pi$
$53$	−60400.3	+	60400.3i	−0.405706	+	0.405706i	0.474532	+	0.880238i	$0.342617\pi$
$54$			5501.90i			0.0349407i
$55$	164238.	+	22622.0i	0.987155	+	0.135970i
$56$	169844.			0.967131
$57$	−3780.10	−	3780.10i	−0.0204117	−	0.0204117i
$58$	−24956.9	+	24956.9i	−0.127911	+	0.127911i
$59$		−	46091.2i		−	0.224420i	−0.993685	−	0.112210i	$-0.964207\pi$
$59$		−	46091.2i		−	0.224420i	0.993685	−	0.112210i	$-0.0357930\pi$
$60$	961.152	+	1268.23i	0.00444978	+	0.00587141i
$61$	−75611.9			−0.333120			−0.166560	−	0.986031i	$-0.553266\pi$
$61$	−75611.9			−0.333120			−0.166560	+	0.986031i	$0.553266\pi$
$62$	−150277.	−	150277.i	−0.630545	−	0.630545i
$63$	−157009.	+	157009.i	−0.627918	+	0.627918i
$64$		−	279990.i		−	1.06808i
$65$	−202862.	+	153743.i	−0.738687	+	0.559830i
$66$	−5006.11			−0.0174128
$67$	154883.	+	154883.i	0.514966	+	0.514966i	0.916044	−	0.401078i	$-0.131364\pi$
$67$	154883.	+	154883.i	0.514966	+	0.514966i	−0.401078	+	0.916044i	$0.631364\pi$
$68$	29529.1	−	29529.1i	0.0939127	−	0.0939127i
$69$			6161.91i			0.0187572i
$70$	33729.3	−	244878.i	0.0983362	−	0.713930i
$71$	184000.			0.514095			0.257048	−	0.966399i	$-0.417250\pi$
$71$	184000.			0.514095			0.257048	+	0.966399i	$0.417250\pi$
$72$	287175.	+	287175.i	0.769394	+	0.769394i
$73$	301029.	−	301029.i	0.773819	−	0.773819i	−0.204953	−	0.978772i	$-0.565704\pi$
$73$	301029.	−	301029.i	0.773819	−	0.773819i	0.978772	+	0.204953i	$0.0657042\pi$
$74$			518848.i			1.28040i
$75$	7924.22	−	4449.58i	0.0187833	−	0.0105472i
$76$	−201169.			−0.458268
$77$	−285788.	−	285788.i	−0.625995	−	0.625995i
$78$	5434.82	−	5434.82i	0.0114525	−	0.0114525i
$79$			178743.i			0.362532i	0.983434	+	0.181266i	$0.0580195\pi$
$79$			178743.i			0.362532i	−0.983434	+	0.181266i	$0.941980\pi$
$80$	−274430.	−	37799.8i	−0.535996	−	0.0738277i
$81$	−530701.			−0.998608
$82$	81489.6	+	81489.6i	0.147795	+	0.147795i
$83$	565063.	−	565063.i	0.988240	−	0.988240i	−0.0116912	−	0.999932i	$-0.503722\pi$
$83$	565063.	−	565063.i	0.988240	−	0.988240i	0.999932	+	0.0116912i	$0.00372152\pi$
$84$		−	3879.30i		−	0.00654509i
$85$	−144055.	−	190078.i	−0.234569	−	0.309510i
$86$	−58681.4			−0.0922582
$87$	2236.83	+	2236.83i	0.00339684	+	0.00339684i
$88$	−522715.	+	522715.i	−0.767038	+	0.767038i
$89$			249057.i			0.353289i	0.984275	+	0.176644i	$0.0565242\pi$
$89$			249057.i			0.353289i	−0.984275	+	0.176644i	$0.943476\pi$
$90$	471074.	−	357014.i	0.646193	−	0.489731i
$91$	620523.			0.823443
$92$	163962.	+	163962.i	0.210561	+	0.210561i
$93$	−13468.9	+	13468.9i	−0.0167450	+	0.0167450i
$94$		−	323963.i		−	0.390043i
$95$	−156768.	+	1.13815e6i	−0.182846	+	1.32748i
$96$	−12382.6			−0.0139958
$97$	30626.2	+	30626.2i	0.0335567	+	0.0335567i	0.723686	−	0.690129i	$-0.242446\pi$
$97$	30626.2	+	30626.2i	0.0335567	+	0.0335567i	−0.690129	+	0.723686i	$0.742446\pi$
$98$	113751.	−	113751.i	0.120858	−	0.120858i
$99$		−	966430.i		−	0.996013i
$100$	92456.3	−	329253.i	0.0924563	−	0.329253i
$101$	797915.			0.774448			0.387224	−	0.921986i	$-0.373434\pi$
$101$	797915.			0.774448			0.387224	+	0.921986i	$0.373434\pi$
$102$	5092.32	+	5092.32i	0.00479861	+	0.00479861i
$103$	−1.44814e6	+	1.44814e6i	−1.32526	+	1.32526i	−0.415798	+	0.909457i	$0.636498\pi$
$103$	−1.44814e6	+	1.44814e6i	−1.32526	+	1.32526i	−0.909457	+	0.415798i	$0.863502\pi$
$104$		−	1.13496e6i		−	1.00897i
$105$	−21947.8	−	3023.08i	−0.0189594	−	0.00261145i
$106$	−554321.			−0.465418
$107$	−1.50954e6	−	1.50954e6i	−1.23224	−	1.23224i	−0.963102	−	0.269136i	$-0.913262\pi$
$107$	−1.50954e6	−	1.50954e6i	−1.23224	−	1.23224i	−0.269136	−	0.963102i	$-0.586738\pi$
$108$	13121.4	−	13121.4i	0.0104162	−	0.0104162i
$109$			1.32041e6i			1.01960i	0.860294	+	0.509798i	$0.170280\pi$
$109$			1.32041e6i			1.01960i	−0.860294	+	0.509798i	$0.829720\pi$
$110$	649836.	+	857449.i	0.488232	+	0.644214i
$111$	46503.1			0.0340027
$112$	477530.	+	477530.i	0.339897	+	0.339897i
$113$	783429.	−	783429.i	0.542955	−	0.542955i	−0.381439	−	0.924394i	$-0.624571\pi$
$113$	783429.	−	783429.i	0.542955	−	0.542955i	0.924394	+	0.381439i	$0.124571\pi$
$114$		−	34691.7i		−	0.0234159i
$115$	1.05541e6	−	799869.i	0.693952	−	0.525927i
$116$	119039.			0.0762632
$117$	1.04919e6	+	1.04919e6i	0.655085	+	0.655085i
$118$	211500.	−	211500.i	0.128725	−	0.128725i
$119$			581419.i			0.345023i
$120$	−5529.32	+	40143.3i	−0.00319984	+	0.0232311i
$121$	−12466.7			−0.00703714
$122$	−346962.	−	346962.i	−0.191074	−	0.191074i
$123$	7303.72	−	7303.72i	0.00392490	−	0.00392490i
$124$			716787.i			0.375946i
$125$	−1.79076e6	−	779670.i	−0.916868	−	0.399191i
$126$	−1.44094e6			−0.720336
$127$	−456295.	−	456295.i	−0.222759	−	0.222759i	0.586901	−	0.809659i	$-0.300348\pi$
$127$	−456295.	−	456295.i	−0.222759	−	0.222759i	−0.809659	+	0.586901i	$0.800348\pi$
$128$	321353.	−	321353.i	0.153233	−	0.153233i
$129$			5259.47i			0.00245004i
$130$	−1.63636e6	−	225392.i	−0.744817	−	0.102591i
$131$	−580402.			−0.258176			−0.129088	−	0.991633i	$-0.541205\pi$
$131$	−580402.			−0.258176			−0.129088	+	0.991633i	$0.541205\pi$
$132$	11939.0	+	11939.0i	0.00519096	+	0.00519096i
$133$	1.98047e6	−	1.98047e6i	0.841809	−	0.841809i
$134$			1.42143e6i			0.590759i
$135$	−64011.5	−	84462.2i	−0.0260170	−	0.0343290i
$136$	1.06343e6			0.422760
$137$	2.50818e6	+	2.50818e6i	0.975431	+	0.975431i	0.999705	−	0.0242745i	$-0.00772756\pi$
$137$	2.50818e6	+	2.50818e6i	0.975431	+	0.975431i	−0.0242745	+	0.999705i	$0.507728\pi$
$138$	−28275.3	+	28275.3i	−0.0107589	+	0.0107589i
$139$		−	3.08650e6i		−	1.14927i	−0.818409	−	0.574636i	$-0.805144\pi$
$139$		−	3.08650e6i		−	1.14927i	0.818409	−	0.574636i	$-0.194856\pi$
$140$	−664449.	+	503567.i	−0.242146	+	0.183516i
$141$	−29036.1			−0.0103581
$142$	844327.	+	844327.i	0.294880	+	0.294880i
$143$	−1.90974e6	+	1.90974e6i	−0.653079	+	0.653079i
$144$			1.61484e6i			0.540805i
$145$	92765.2	−	673484.i	0.0304286	−	0.220914i
$146$	2.76267e6			0.887710
$147$	−10195.2	−	10195.2i	−0.00320956	−	0.00320956i
$148$	1.23740e6	−	1.23740e6i	0.381701	−	0.381701i
$149$			1.18378e6i			0.357860i	0.983862	+	0.178930i	$0.0572635\pi$
$149$			1.18378e6i			0.357860i	−0.983862	+	0.178930i	$0.942736\pi$
$150$	56779.9	+	15944.2i	0.0168237	+	0.00472420i
$151$	−3.01484e6			−0.875656			−0.437828	−	0.899059i	$-0.644252\pi$
$151$	−3.01484e6			−0.875656			−0.437828	+	0.899059i	$0.644252\pi$
$152$	−3.62235e6	−	3.62235e6i	−1.03148	−	1.03148i
$153$	−983073.	+	983073.i	−0.274481	+	0.274481i
$154$		−	2.62280e6i		−	0.718130i
$155$	4.05535e6	+	558581.i	1.08901	+	0.150000i
$156$	−25922.9			−0.00682826
$157$	−965155.	−	965155.i	−0.249401	−	0.249401i	0.571324	−	0.820725i	$-0.306430\pi$
$157$	−965155.	−	965155.i	−0.249401	−	0.249401i	−0.820725	+	0.571324i	$0.806430\pi$
$158$	−820200.	+	820200.i	−0.207945	+	0.207945i
$159$			49682.5i			0.0123598i
$160$	1.60737e6	+	2.12089e6i	0.392423	+	0.517797i
$161$	−3.22835e6			−0.773575
$162$	−2.43524e6	−	2.43524e6i	−0.572792	−	0.572792i
$163$	−2.59213e6	+	2.59213e6i	−0.598542	+	0.598542i	−0.939924	−	0.341383i	$-0.889105\pi$
$163$	−2.59213e6	+	2.59213e6i	−0.598542	+	0.598542i	0.341383	+	0.939924i	$0.389105\pi$
$164$		−	388688.i		−	0.0881190i
$165$	76851.1	−	58243.3i	0.0171080	−	0.0129656i
$166$	5.18584e6			1.13369
$167$	2.49297e6	+	2.49297e6i	0.535263	+	0.535263i	0.922134	−	0.386871i	$-0.126444\pi$
$167$	2.49297e6	+	2.49297e6i	0.535263	+	0.535263i	−0.386871	+	0.922134i	$0.626444\pi$
$168$	69852.7	−	69852.7i	0.0147318	−	0.0147318i
$169$			680249.i			0.140931i
$170$	211188.	−	1.53324e6i	0.0429855	−	0.312079i
$171$	6.69724e6			1.33939
$172$	139949.	+	139949.i	0.0275032	+	0.0275032i
$173$	1.00408e6	−	1.00408e6i	0.193923	−	0.193923i	−0.603466	−	0.797389i	$-0.706214\pi$
$173$	1.00408e6	−	1.00408e6i	0.193923	−	0.193923i	0.797389	+	0.603466i	$0.206214\pi$
$174$			20528.4i			0.00389678i
$175$	2.33122e6	+	4.15166e6i	0.434980	+	0.774653i
$176$	−2.93932e6			−0.539149
$177$	−18956.2	−	18956.2i	−0.00341847	−	0.00341847i
$178$	−1.14286e6	+	1.14286e6i	−0.202643	+	0.202643i
$179$		−	8.39831e6i		−	1.46431i	−0.681139	−	0.732154i	$-0.738515\pi$
$179$		−	8.39831e6i		−	1.46431i	0.681139	−	0.732154i	$-0.261485\pi$
$180$	−1.97490e6	−	272022.i	−0.338632	−	0.0466430i
$181$	−8.17816e6			−1.37918			−0.689588	−	0.724202i	$-0.742208\pi$
$181$	−8.17816e6			−1.37918			−0.689588	+	0.724202i	$0.742208\pi$
$182$	2.84741e6	+	2.84741e6i	0.472319	+	0.472319i
$183$	−31097.4	+	31097.4i	−0.00507424	+	0.00507424i
$184$			5.90475e6i			0.947869i
$185$	−6.03650e6	−	7.96507e6i	−0.953389	−	1.25798i
$186$	−123610.			−0.0192095
$187$	−1.78939e6	−	1.78939e6i	−0.273640	−	0.273640i
$188$	−772618.	+	772618.i	−0.116276	+	0.116276i
$189$			258357.i			0.0382679i
$190$	−5.94201e6	+	4.50328e6i	−0.866308	+	0.656550i
$191$	6.45566e6			0.926489			0.463245	−	0.886230i	$-0.346685\pi$
$191$	6.45566e6			0.926489			0.463245	+	0.886230i	$0.346685\pi$
$192$	−115154.	−	115154.i	−0.0162695	−	0.0162695i
$193$	6.32306e6	−	6.32306e6i	0.879539	−	0.879539i	−0.113948	−	0.993487i	$-0.536350\pi$
$193$	6.32306e6	−	6.32306e6i	0.879539	−	0.879539i	0.993487	+	0.113948i	$0.0363497\pi$
$194$			281071.i			0.0384955i
$195$	−20201.3	+	146663.i	−0.00272443	+	0.0197796i
$196$	−542568.			−0.0720586
$197$	4.61427e6	+	4.61427e6i	0.603538	+	0.603538i	0.941250	−	0.337712i	$-0.109653\pi$
$197$	4.61427e6	+	4.61427e6i	0.603538	+	0.603538i	−0.337712	+	0.941250i	$0.609653\pi$
$198$	4.43468e6	−	4.43468e6i	0.571303	−	0.571303i
$199$			9.33452e6i			1.18449i	0.805756	+	0.592247i	$0.201759\pi$
$199$			9.33452e6i			1.18449i	−0.805756	+	0.592247i	$0.798241\pi$
$200$	7.59352e6	−	4.26389e6i	0.949190	−	0.532986i
$201$	127399.			0.0156884
$202$	3.66141e6	+	3.66141e6i	0.444216	+	0.444216i
$203$	−1.17192e6	+	1.17192e6i	−0.140091	+	0.140091i
$204$		−	24289.3i		−	0.00286104i
$205$	−2.19907e6	−	302899.i	−0.255257	−	0.0351589i
$206$	−1.32902e7			−1.52031
$207$	−5.45855e6	−	5.45855e6i	−0.615412	−	0.615412i
$208$	3.19103e6	−	3.19103e6i	0.354602	−	0.354602i
$209$			1.21903e7i			1.33529i
$210$	−86840.5	−	114585.i	−0.00937701	−	0.0123728i
$211$	2.21170e6			0.235439			0.117720	−	0.993047i	$-0.462442\pi$
$211$	2.21170e6			0.235439			0.117720	+	0.993047i	$0.462442\pi$
$212$	1.32200e6	+	1.32200e6i	0.138747	+	0.138747i
$213$	75675.0	−	75675.0i	0.00783094	−	0.00783094i
$214$		−	1.38538e7i		−	1.41360i
$215$	900845.	−	682725.i	0.0906430	−	0.0686958i
$216$	472543.			0.0468900
$217$	−7.05664e6	−	7.05664e6i	−0.690588	−	0.690588i
$218$	−6.05898e6	+	6.05898e6i	−0.584831	+	0.584831i
$219$		−	247612.i		−	0.0235743i
$220$	495134.	−	3.59471e6i	0.0465001	−	0.337595i
$221$	3.88525e6			0.359950
$222$	213390.	+	213390.i	0.0195036	+	0.0195036i
$223$	−5.52712e6	+	5.52712e6i	−0.498407	+	0.498407i	−0.910942	−	0.412535i	$-0.864644\pi$
$223$	−5.52712e6	+	5.52712e6i	−0.498407	+	0.498407i	0.412535	+	0.910942i	$0.364644\pi$
$224$		−	6.48748e6i		−	0.577208i
$225$	−3.07802e6	+	1.09614e7i	−0.270224	+	0.962315i
$226$	7.18988e6			0.622868
$227$	2.23679e6	+	2.23679e6i	0.191227	+	0.191227i	0.796226	−	0.604999i	$-0.206827\pi$
$227$	2.23679e6	+	2.23679e6i	0.191227	+	0.191227i	−0.604999	+	0.796226i	$0.706827\pi$
$228$	−82736.0	+	82736.0i	−0.00698055	+	0.00698055i
$229$		−	8.27450e6i		−	0.689025i	−0.938782	−	0.344513i	$-0.888044\pi$
$229$		−	8.27450e6i		−	0.689025i	0.938782	−	0.344513i	$-0.111956\pi$
$230$	8.51338e6	+	1.17263e6i	0.699711	+	0.0963777i
$231$	−235075.			−0.0190709
$232$	2.14348e6	+	2.14348e6i	0.171654	+	0.171654i
$233$	−2.68203e6	+	2.68203e6i	−0.212029	+	0.212029i	−0.805129	−	0.593100i	$-0.797904\pi$
$233$	−2.68203e6	+	2.68203e6i	−0.212029	+	0.212029i	0.593100	+	0.805129i	$0.297904\pi$
$234$			9.62890e6i			0.751500i
$235$	3.76913e6	+	4.97331e6i	0.290427	+	0.383214i
$236$	−1.00881e6			−0.0767490
$237$	73512.6	+	73512.6i	0.00552226	+	0.00552226i
$238$	−2.66797e6	+	2.66797e6i	−0.197902	+	0.197902i
$239$		−	1.80178e7i		−	1.31980i	−0.751352	−	0.659902i	$-0.770598\pi$
$239$		−	1.80178e7i		−	1.31980i	0.751352	−	0.659902i	$-0.229402\pi$
$240$	−128413.	+	97320.3i	−0.00928911	+	0.00703996i
$241$	2.39062e7			1.70789			0.853945	−	0.520363i	$-0.174203\pi$
$241$	2.39062e7			1.70789			0.853945	+	0.520363i	$0.174203\pi$
$242$	−57206.3	−	57206.3i	−0.00403644	−	0.00403644i
$243$	−655302.	+	655302.i	−0.0456691	+	0.0456691i
$244$			1.65494e6i			0.113923i
$245$	−422814.	+	3.06967e6i	−0.0287509	+	0.208734i
$246$	67029.5			0.00450258
$247$	−1.32342e7	−	1.32342e7i	−0.878229	−	0.878229i
$248$	−1.29068e7	+	1.29068e7i	−0.846184	+	0.846184i
$249$		−	464794.i		−	0.0301067i
$250$	−4.63960e6	−	1.17950e7i	−0.296935	−	0.754879i
$251$	−2.61747e7			−1.65524			−0.827620	−	0.561289i	$-0.810306\pi$
$251$	−2.61747e7			−1.65524			−0.827620	+	0.561289i	$0.810306\pi$
$252$	3.43649e6	+	3.43649e6i	0.214741	+	0.214741i
$253$	9.93564e6	−	9.93564e6i	0.613528	−	0.613528i
$254$		−	4.18762e6i		−	0.255544i
$255$	−137421.	−	18928.3i	−0.00828767	−	0.00114154i
$256$	−1.49702e7			−0.892293
$257$	6.82647e6	+	6.82647e6i	0.402158	+	0.402158i	0.878993	−	0.476835i	$-0.158216\pi$
$257$	6.82647e6	+	6.82647e6i	0.402158	+	0.402158i	−0.476835	+	0.878993i	$0.658216\pi$
$258$	−24134.3	+	24134.3i	−0.00140532	+	0.00140532i
$259$			2.43639e7i			1.40232i
$260$	3.36502e6	+	4.44009e6i	0.191455	+	0.252622i
$261$	−3.96300e6			−0.222896
$262$	−2.66331e6	−	2.66331e6i	−0.148087	−	0.148087i
$263$	2.01956e7	−	2.01956e7i	1.11017	−	1.11017i	0.117045	−	0.993127i	$-0.462658\pi$
$263$	2.01956e7	−	2.01956e7i	1.11017	−	1.11017i	0.993127	−	0.117045i	$-0.0373423\pi$
$264$			429961.i			0.0233678i
$265$	8.50963e6	−	6.44921e6i	0.457270	−	0.346552i
$266$	1.81757e7			0.965707
$267$	102432.	+	102432.i	0.00538146	+	0.00538146i
$268$	3.38996e6	−	3.38996e6i	0.176112	−	0.176112i
$269$			1.52094e7i			0.781368i	0.920525	+	0.390684i	$0.127762\pi$
$269$			1.52094e7i			0.781368i	−0.920525	+	0.390684i	$0.872238\pi$
$270$	93842.5	−	681305.i	0.00476769	−	0.0346139i
$271$	1.17759e7			0.591677			0.295838	−	0.955238i	$-0.404401\pi$
$271$	1.17759e7			0.591677			0.295838	+	0.955238i	$0.404401\pi$
$272$	2.98994e6	+	2.98994e6i	0.148578	+	0.148578i
$273$	255207.	−	255207.i	0.0125431	−	0.0125431i
$274$			2.30187e7i			1.11900i
$275$	−1.99519e7	−	5.60261e6i	−0.959369	−	0.269397i
$276$	134867.			0.00641474
$277$	1.37835e7	+	1.37835e7i	0.648515	+	0.648515i	0.952634	−	0.304119i	$-0.0983621\pi$
$277$	1.37835e7	+	1.37835e7i	0.648515	+	0.648515i	−0.304119	+	0.952634i	$0.598362\pi$
$278$	1.41631e7	−	1.41631e7i	0.659211	−	0.659211i
$279$		−	2.38630e7i		−	1.09878i
$280$	−2.10319e7	−	2.89692e6i	−0.958085	−	0.131966i
$281$	−2.56366e7			−1.15543			−0.577713	−	0.816240i	$-0.696055\pi$
$281$	−2.56366e7			−1.15543			−0.577713	+	0.816240i	$0.696055\pi$
$282$	−133238.	−	133238.i	−0.00594131	−	0.00594131i
$283$	−1.99807e7	+	1.99807e7i	−0.881559	+	0.881559i	−0.993693	−	0.112134i	$-0.964231\pi$
$283$	−1.99807e7	+	1.99807e7i	−0.881559	+	0.881559i	0.112134	+	0.993693i	$0.464231\pi$
$284$		−	4.02726e6i		−	0.175814i
$285$	403618.	+	532568.i	0.0174356	+	0.0230060i
$286$	−1.75265e7			−0.749199
$287$	3.82657e6	+	3.82657e6i	0.161869	+	0.161869i
$288$	1.09692e7	−	1.09692e7i	0.459194	−	0.459194i
$289$		−	2.04972e7i		−	0.849181i
$290$	3.51611e6	−	2.66476e6i	0.144168	−	0.109261i
$291$	25191.7			0.00102230
$292$	−6.58869e6	−	6.58869e6i	−0.264637	−	0.264637i
$293$	−5.27401e6	+	5.27401e6i	−0.209671	+	0.209671i	−0.804128	−	0.594457i	$-0.797367\pi$
$293$	−5.27401e6	+	5.27401e6i	−0.209671	+	0.209671i	0.594457	+	0.804128i	$0.297367\pi$
$294$		−	93566.1i		−	0.00368194i
$295$	−786149.	+	5.70751e6i	−0.0306224	+	0.222321i
$296$	4.45624e7			1.71828
$297$	−795125.	−	795125.i	−0.0303505	−	0.0303505i
$298$	−5.43205e6	+	5.43205e6i	−0.205265	+	0.205265i
$299$			2.15730e7i			0.807043i
$300$	−97389.0	−	173439.i	−0.00360700	−	0.00642368i
$301$	−2.75554e6			−0.101043
$302$	−1.38343e7	−	1.38343e7i	−0.502268	−	0.502268i
$303$	328164.	−	328164.i	0.0117968	−	0.0117968i
$304$		−	2.03691e7i		−	0.725022i
$305$	9.36308e6	+	1.28967e6i	0.330004	+	0.0454546i
$306$	−9.02210e6			−0.314879
$307$	3.02867e7	+	3.02867e7i	1.04674	+	1.04674i	0.998853	+	0.0478836i	$0.0152477\pi$
$307$	3.02867e7	+	3.02867e7i	1.04674	+	1.04674i	0.0478836	+	0.998853i	$0.484752\pi$
$308$	−6.25510e6	+	6.25510e6i	−0.214083	+	0.214083i
$309$			1.19117e6i			0.0403738i
$310$	1.60457e7	+	2.11720e7i	0.538609	+	0.710686i
$311$	1.87774e7			0.624244			0.312122	−	0.950042i	$-0.398960\pi$
$311$	1.87774e7			0.624244			0.312122	+	0.950042i	$0.398960\pi$
$312$	−466781.	−	466781.i	−0.0153691	−	0.0153691i
$313$	−2.13347e7	+	2.13347e7i	−0.695750	+	0.695750i	−0.963491	−	0.267741i	$-0.913723\pi$
$313$	−2.13347e7	+	2.13347e7i	−0.695750	+	0.695750i	0.267741	+	0.963491i	$0.413723\pi$
$314$		−	8.85766e6i		−	0.286108i
$315$	2.21206e7	−	1.67646e7i	0.707725	−	0.536365i
$316$	3.91218e6			0.123982
$317$	−4.19358e7	−	4.19358e7i	−1.31646	−	1.31646i	−0.916558	−	0.399901i	$-0.869045\pi$
$317$	−4.19358e7	−	4.19358e7i	−1.31646	−	1.31646i	−0.399901	−	0.916558i	$-0.630955\pi$
$318$	−227979.	+	227979.i	−0.00708947	+	0.00708947i
$319$		−	7.21345e6i		−	0.222214i
$320$	−4.77562e6	+	3.46715e7i	−0.145741	+	1.05809i
$321$	−1.24168e6			−0.0375400
$322$	−1.48140e7	−	1.48140e7i	−0.443715	−	0.443715i
$323$	1.24002e7	−	1.24002e7i	0.367978	−	0.367978i
$324$			1.16156e7i			0.341512i
$325$	2.77429e7	−	1.55781e7i	0.808168	−	0.453799i
$326$	−2.37892e7			−0.686636
$327$	543053.	+	543053.i	0.0155310	+	0.0155310i
$328$	6.99892e6	−	6.99892e6i	0.198340	−	0.198340i
$329$		−	1.52126e7i		−	0.427184i
$330$	619911.	+	85386.1i	0.0172499	+	0.00237599i
$331$	−2.36910e7			−0.653279			−0.326640	−	0.945149i	$-0.605916\pi$
$331$	−2.36910e7			−0.653279			−0.326640	+	0.945149i	$0.605916\pi$
$332$	−1.23677e7	−	1.23677e7i	−0.337966	−	0.337966i
$333$	−4.11949e7	+	4.11949e7i	−1.11561	+	1.11561i
$334$			2.28791e7i			0.614044i
$335$	−1.65375e7	−	2.18210e7i	−0.439882	−	0.580417i
$336$	392794.			0.0103549
$337$	−4.12007e6	−	4.12007e6i	−0.107650	−	0.107650i	0.651230	−	0.758880i	$-0.274253\pi$
$337$	−4.12007e6	−	4.12007e6i	−0.107650	−	0.107650i	−0.758880	+	0.651230i	$0.774253\pi$
$338$	−3.12147e6	+	3.12147e6i	−0.0808369	+	0.0808369i
$339$		−	644412.i		−	0.0165411i
$340$	−4.16028e6	+	3.15296e6i	−0.105849	+	0.0802198i
$341$	4.34354e7			1.09542
$342$	3.07318e7	+	3.07318e7i	0.768262	+	0.768262i
$343$	3.06920e7	−	3.06920e7i	0.760577	−	0.760577i
$344$			5.03998e6i			0.123809i
$345$	105100.	−	763034.i	0.00255944	−	0.0185818i
$346$	9.21487e6			0.222465
$347$	3.58847e7	+	3.58847e7i	0.858857	+	0.858857i	0.991203	−	0.132347i	$-0.0422513\pi$
$347$	3.58847e7	+	3.58847e7i	0.858857	+	0.858857i	−0.132347	+	0.991203i	$0.542251\pi$
$348$	48957.9	−	48957.9i	0.00116168	−	0.00116168i
$349$		−	5.38706e7i		−	1.26729i	−0.773624	−	0.633645i	$-0.781558\pi$
$349$		−	5.38706e7i		−	1.26729i	0.773624	−	0.633645i	$-0.218442\pi$
$350$	−8.35346e6	+	2.97481e7i	−0.194833	+	0.693834i
$351$	1.72643e6			0.0399235
$352$	1.99660e7	+	1.99660e7i	0.457788	+	0.457788i
$353$	9.94346e6	−	9.94346e6i	0.226055	−	0.226055i	−0.584988	−	0.811042i	$-0.698901\pi$
$353$	9.94346e6	−	9.94346e6i	0.226055	−	0.226055i	0.811042	+	0.584988i	$0.198901\pi$
$354$		−	173970.i		−	0.00392161i
$355$	−2.27849e7	−	3.13838e6i	−0.509287	−	0.0701488i
$356$	5.45118e6			0.120820
$357$	239124.	+	239124.i	0.00525555	+	0.00525555i
$358$	3.85375e7	−	3.85375e7i	0.839913	−	0.839913i
$359$			8.32978e7i			1.80032i	0.435556	+	0.900162i	$0.356552\pi$
$359$			8.32978e7i			1.80032i	−0.435556	+	0.900162i	$0.643448\pi$
$360$	−3.06629e7	−	4.04593e7i	−0.657213	−	0.867183i
$361$	−3.74313e7			−0.795633
$362$	−3.75273e7	−	3.75273e7i	−0.791082	−	0.791082i
$363$	−5127.27	+	5127.27i	−0.000107193	+	0.000107193i
$364$		−	1.35815e7i		−	0.281608i
$365$	−4.24111e7	+	3.21422e7i	−0.872170	+	0.660993i
$366$	−285395.			−0.00582107
$367$	6.36276e6	+	6.36276e6i	0.128720	+	0.128720i	0.768532	−	0.639811i	$-0.220988\pi$
$367$	6.36276e6	+	6.36276e6i	0.128720	+	0.128720i	−0.639811	+	0.768532i	$0.720988\pi$
$368$	−1.66017e7	+	1.66017e7i	−0.333127	+	0.333127i
$369$			1.29401e7i			0.257547i
$370$	8.84966e6	−	6.42493e7i	0.174712	−	1.26842i
$371$	−2.60296e7			−0.509737
$372$	294798.	+	294798.i	0.00572658	+	0.00572658i
$373$	−4.79779e6	+	4.79779e6i	−0.0924517	+	0.0924517i	−0.751820	−	0.659368i	$-0.770824\pi$
$373$	−4.79779e6	+	4.79779e6i	−0.0924517	+	0.0924517i	0.659368	+	0.751820i	$0.270824\pi$
$374$		−	1.64220e7i		−	0.313915i
$375$	−1.05716e6	+	415837.i	−0.0200468	+	0.00788550i
$376$	−2.78243e7			−0.523432
$377$	7.83118e6	+	7.83118e6i	0.146152	+	0.146152i
$378$	−1.18553e6	+	1.18553e6i	−0.0219501	+	0.0219501i
$379$			1.31093e6i			0.0240803i	0.999928	+	0.0120401i	$0.00383259\pi$
$379$			1.31093e6i			0.0240803i	−0.999928	+	0.0120401i	$0.996167\pi$
$380$	2.49109e7	+	3.43121e6i	0.453982	+	0.0625312i
$381$	−375327.			−0.00678632
$382$	2.96232e7	+	2.96232e7i	0.531425	+	0.531425i
$383$	5.50901e7	−	5.50901e7i	0.980566	−	0.980566i	−0.0192483	−	0.999815i	$-0.506127\pi$
$383$	5.50901e7	−	5.50901e7i	0.980566	−	0.980566i	0.999815	+	0.0192483i	$0.00612731\pi$
$384$		−	264330.i		−	0.00466823i
$385$	3.05148e7	+	4.02638e7i	0.534723	+	0.705558i
$386$	5.80295e7			1.00899
$387$	−4.65912e6	−	4.65912e6i	−0.0803843	−	0.0803843i
$388$	670324.	−	670324.i	0.0114760	−	0.0114760i
$389$			3.10657e7i			0.527755i	0.964556	+	0.263877i	$0.0850014\pi$
$389$			3.10657e7i			0.527755i	−0.964556	+	0.263877i	$0.914999\pi$
$390$	−765696.	+	580300.i	−0.0129081	+	0.00978269i
$391$	−2.02135e7			−0.338151
$392$	−9.76975e6	−	9.76975e6i	−0.162190	−	0.162190i
$393$	−238706.	+	238706.i	−0.00393265	+	0.00393265i
$394$			4.23472e7i			0.692367i
$395$	3.04870e6	−	2.21338e7i	0.0494679	−	0.359141i
$396$	−2.11525e7			−0.340624
$397$	−2.74272e7	−	2.74272e7i	−0.438339	−	0.438339i	0.453114	−	0.891453i	$-0.350313\pi$
$397$	−2.74272e7	−	2.74272e7i	−0.438339	−	0.438339i	−0.891453	+	0.453114i	$0.850313\pi$
$398$	−4.28335e7	+	4.28335e7i	−0.679414	+	0.679414i
$399$		−	1.62904e6i		−	0.0256456i
$400$	3.33381e7	+	9.36156e6i	0.520908	+	0.146274i
$401$	5.39359e7			0.836459			0.418230	−	0.908341i	$-0.362651\pi$
$401$	5.39359e7			0.836459			0.418230	+	0.908341i	$0.362651\pi$
$402$	584600.	+	584600.i	0.00899872	+	0.00899872i
$403$	−4.71551e7	+	4.71551e7i	−0.720465	+	0.720465i
$404$		−	1.74642e7i		−	0.264852i
$405$	6.57172e7	+	9.05184e6i	0.989268	+	0.136261i
$406$	−1.07552e7			−0.160709
$407$	−7.49829e7	−	7.49829e7i	−1.11219	−	1.11219i
$408$	437365.	−	437365.i	0.00643968	−	0.00643968i
$409$		−	8.00992e7i		−	1.17073i	−0.810769	−	0.585367i	$-0.800951\pi$
$409$		−	8.00992e7i		−	1.17073i	0.810769	−	0.585367i	$-0.199049\pi$
$410$	−8.70101e6	−	1.14808e7i	−0.126246	−	0.166580i
$411$	2.06311e6			0.0297164
$412$	3.16958e7	+	3.16958e7i	0.453221	+	0.453221i
$413$	9.93154e6	−	9.93154e6i	0.140983	−	0.140983i
$414$		−	5.00955e7i		−	0.705989i
$415$	−7.96102e7	+	6.03343e7i	−1.11384	+	0.844151i
$416$	−4.33517e7			−0.602180
$417$	−1.26941e6	−	1.26941e6i	−0.0175062	−	0.0175062i
$418$	−5.59379e7	+	5.59379e7i	−0.765909	+	0.765909i
$419$		−	7.63894e7i		−	1.03846i	−0.854634	−	0.519231i	$-0.826218\pi$
$419$		−	7.63894e7i		−	1.03846i	0.854634	−	0.519231i	$-0.173782\pi$
$420$	−66166.9	+	480377.i	−0.000893085	+	0.00648388i
$421$	8.62618e7			1.15604			0.578019	−	0.816023i	$-0.303826\pi$
$421$	8.62618e7			1.15604			0.578019	+	0.816023i	$0.303826\pi$
$422$	1.01489e7	+	1.01489e7i	0.135046	+	0.135046i
$423$	2.57217e7	−	2.57217e7i	0.339843	−	0.339843i
$424$			4.76091e7i			0.624586i
$425$	1.45964e7	+	2.59946e7i	0.190142	+	0.338622i
$426$	694504.			0.00898350
$427$	−1.62925e7	−	1.62925e7i	−0.209269	−	0.209269i
$428$	−3.30398e7	+	3.30398e7i	−0.421411	+	0.421411i
$429$			1.57086e6i			0.0198960i
$430$	7.26656e6	+	1.00089e6i	0.0913952	+	0.0125887i
$431$	1.52887e7			0.190959			0.0954795	−	0.995431i	$-0.469562\pi$
$431$	1.52887e7			0.190959			0.0954795	+	0.995431i	$0.469562\pi$
$432$	1.32860e6	+	1.32860e6i	0.0164794	+	0.0164794i
$433$	−3.40552e7	+	3.40552e7i	−0.419489	+	0.419489i	−0.885028	−	0.465539i	$-0.845861\pi$
$433$	−3.40552e7	+	3.40552e7i	−0.419489	+	0.419489i	0.465539	+	0.885028i	$0.345861\pi$
$434$		−	6.47620e7i		−	0.792229i
$435$	−238836.	−	315140.i	−0.00290156	−	0.00382857i
$436$	2.89001e7			0.348690
$437$	6.88527e7	+	6.88527e7i	0.825043	+	0.825043i
$438$	1.13622e6	−	1.13622e6i	0.0135220	−	0.0135220i
$439$			7.90801e7i			0.934703i	0.884072	+	0.467351i	$0.154792\pi$
$439$			7.90801e7i			0.934703i	−0.884072	+	0.467351i	$0.845208\pi$
$440$	7.36439e7	−	5.58126e7i	0.864527	−	0.655201i
$441$	1.80630e7			0.210607
$442$	1.78283e7	+	1.78283e7i	0.206464	+	0.206464i
$443$	5.21596e7	−	5.21596e7i	0.599961	−	0.599961i	−0.340341	−	0.940302i	$-0.610542\pi$
$443$	5.21596e7	−	5.21596e7i	0.599961	−	0.599961i	0.940302	+	0.340341i	$0.110542\pi$
$444$		−	1.01782e6i		−	0.0116285i
$445$	4.24802e6	−	3.08410e7i	0.0482066	−	0.349984i
$446$	−5.07249e7			−0.571763
$447$	486862.	+	486862.i	0.00545108	+	0.00545108i
$448$	6.03312e7	−	6.03312e7i	0.670978	−	0.670978i
$449$			7.16826e7i			0.791908i	0.918270	+	0.395954i	$0.129586\pi$
$449$			7.16826e7i			0.791908i	−0.918270	+	0.395954i	$0.870414\pi$
$450$	−6.44229e7	+	3.61745e7i	−0.706973	+	0.396977i
$451$	−2.35535e7			−0.256759
$452$	−1.71471e7	−	1.71471e7i	−0.185684	−	0.185684i
$453$	−1.23993e6	+	1.23993e6i	−0.0133384	+	0.0133384i
$454$			2.05281e7i			0.219372i
$455$	−7.68399e7	−	1.05839e7i	−0.815741	−	0.112360i
$456$	−2.97957e6			−0.0314239
$457$	−9.43530e7	−	9.43530e7i	−0.988570	−	0.988570i	0.0113658	−	0.999935i	$-0.496382\pi$
$457$	−9.43530e7	−	9.43530e7i	−0.988570	−	0.988570i	−0.999935	+	0.0113658i	$0.996382\pi$
$458$	3.79694e7	−	3.79694e7i	0.395218	−	0.395218i
$459$			1.61764e6i			0.0167279i
$460$	−1.75069e7	−	2.31001e7i	−0.179861	−	0.237323i
$461$	−1.52870e8			−1.56034			−0.780168	−	0.625570i	$-0.784867\pi$
$461$	−1.52870e8			−1.56034			−0.780168	+	0.625570i	$0.784867\pi$
$462$	−1.07870e6	−	1.07870e6i	−0.0109389	−	0.0109389i
$463$	−8.33930e6	+	8.33930e6i	−0.0840207	+	0.0840207i	−0.747868	−	0.663847i	$-0.768922\pi$
$463$	−8.33930e6	+	8.33930e6i	−0.0840207	+	0.0840207i	0.663847	+	0.747868i	$0.268922\pi$
$464$			1.20532e7i			0.120655i
$465$	1.89760e6	−	1.43814e6i	0.0188732	−	0.0143035i
$466$	−2.46142e7			−0.243236
$467$	9.10189e7	+	9.10189e7i	0.893678	+	0.893678i	0.994867	−	0.101189i	$-0.0322647\pi$
$467$	9.10189e7	+	9.10189e7i	0.893678	+	0.893678i	−0.101189	+	0.994867i	$0.532265\pi$
$468$	2.29639e7	−	2.29639e7i	0.224031	−	0.224031i
$469$			6.67470e7i			0.647014i
$470$	−5.52564e6	+	4.01166e7i	−0.0532217	+	0.386394i
$471$	−793891.			−0.00759798
$472$	−1.81651e7	−	1.81651e7i	−0.172748	−	0.172748i
$473$	8.48053e6	−	8.48053e6i	0.0801382	−	0.0801382i
$474$			674658.i			0.00633503i
$475$	3.88254e7	−	1.38264e8i	0.362272	−	1.29011i
$476$	1.27256e7			0.117994
$477$	−4.40114e7	−	4.40114e7i	−0.405518	−	0.405518i
$478$	8.26789e7	−	8.26789e7i	0.757027	−	0.757027i
$479$			1.10830e8i			1.00845i	0.863574	+	0.504223i	$0.168221\pi$
$479$			1.10830e8i			1.00845i	−0.863574	+	0.504223i	$0.831779\pi$
$480$	1.53335e6	+	211202.i	0.0138649	+	0.00190974i
$481$	1.62808e8			1.46299
$482$	1.09699e8	+	1.09699e8i	0.979630	+	0.979630i
$483$	−1.32774e6	+	1.32774e6i	−0.0117835	+	0.0117835i
$484$			272862.i			0.00240662i
$485$	−3.27010e6	−	4.31485e6i	−0.0286639	−	0.0378216i
$486$	−6.01400e6			−0.0523907
$487$	4.44091e7	+	4.44091e7i	0.384490	+	0.384490i	0.872717	−	0.488227i	$-0.162356\pi$
$487$	4.44091e7	+	4.44091e7i	0.384490	+	0.384490i	−0.488227	+	0.872717i	$0.662356\pi$
$488$	−2.97996e7	+	2.97996e7i	−0.256420	+	0.256420i
$489$			2.13217e6i			0.0182345i
$490$	−1.60260e7	+	1.21457e7i	−0.136219	+	0.103237i
$491$	−4.56855e7			−0.385953			−0.192976	−	0.981203i	$-0.561814\pi$
$491$	−4.56855e7			−0.385953			−0.192976	+	0.981203i	$0.561814\pi$
$492$	−159858.	−	159858.i	−0.00134227	−	0.00134227i
$493$	−7.33767e6	+	7.33767e6i	−0.0612375	+	0.0612375i
$494$		−	1.21456e8i		−	1.00749i
$495$	−1.64838e7	+	1.19674e8i	−0.135907	+	0.986697i
$496$	−7.25774e7			−0.594780
$497$	3.96477e7	+	3.96477e7i	0.322960	+	0.322960i
$498$	2.13281e6	−	2.13281e6i	0.0172689	−	0.0172689i
$499$		−	1.98876e8i		−	1.60059i	−0.599604	−	0.800297i	$-0.704675\pi$
$499$		−	1.98876e8i		−	1.60059i	0.599604	−	0.800297i	$-0.295325\pi$
$500$	−1.70648e7	+	3.91947e7i	−0.136519	+	0.313558i
$501$	2.05060e6			0.0163068
$502$	−1.20109e8	−	1.20109e8i	−0.949430	−	0.949430i
$503$	−1.40471e8	+	1.40471e8i	−1.10378	+	1.10378i	−0.109831	+	0.993950i	$0.535031\pi$
$503$	−1.40471e8	+	1.40471e8i	−1.10378	+	1.10378i	−0.993950	+	0.109831i	$0.964969\pi$
$504$			1.23759e8i			0.966682i
$505$	−9.88065e7	−	1.36095e7i	−0.767205	−	0.105674i
$506$	9.11838e7			0.703827
$507$	279770.	+	279770.i	0.00214673	+	0.00214673i
$508$	−9.98703e6	+	9.98703e6i	−0.0761807	+	0.0761807i
$509$		−	2.05461e8i		−	1.55803i	−0.627005	−	0.779015i	$-0.715719\pi$
$509$		−	2.05461e8i		−	1.55803i	0.627005	−	0.779015i	$-0.284281\pi$
$510$	−543730.	−	717443.i	−0.00409895	−	0.00540850i
$511$	1.29729e8			0.972241
$512$	−8.92607e7	−	8.92607e7i	−0.665044	−	0.665044i
$513$	5.51011e6	−	5.51011e6i	0.0408139	−	0.0408139i
$514$			6.26496e7i			0.461348i
$515$	2.04025e8	−	1.54625e8i	1.49369	−	1.13203i
$516$	115115.			0.000837884
$517$	4.68186e7	+	4.68186e7i	0.338802	+	0.338802i
$518$	−1.11799e8	+	1.11799e8i	−0.804358	+	0.804358i
$519$		−	825908.i		−	0.00590785i
$520$	−1.93583e7	+	1.40543e8i	−0.137675	+	0.999536i
$521$	−2.38512e8			−1.68654			−0.843271	−	0.537488i	$-0.819373\pi$
$521$	−2.38512e8			−1.68654			−0.843271	+	0.537488i	$0.819373\pi$
$522$	−1.81851e7	−	1.81851e7i	−0.127851	−	0.127851i
$523$	5.77184e7	−	5.77184e7i	0.403468	−	0.403468i	−0.475985	−	0.879453i	$-0.657908\pi$
$523$	5.77184e7	−	5.77184e7i	0.403468	−	0.403468i	0.879453	+	0.475985i	$0.157908\pi$
$524$			1.27034e7i			0.0882930i
$525$	2.66626e6	+	748701.i	0.0184257	+	0.00517405i
$526$	1.85344e8			1.27357
$527$	−4.41834e7	−	4.41834e7i	−0.301875	−	0.301875i
$528$	−1.20887e6	+	1.20887e6i	−0.00821257	+	0.00821257i
$529$			3.57998e7i			0.241832i
$530$	6.86420e7	+	9.45470e6i	0.461065	+	0.0635068i
$531$	3.35849e7			0.224316
$532$	−4.33470e7	−	4.33470e7i	−0.287889	−	0.287889i
$533$	2.55705e7	−	2.55705e7i	0.168872	−	0.168872i
$534$			940060.i			0.00617350i
$535$	1.61181e8	+	2.12676e8i	1.05257	+	1.38885i
$536$	1.22083e8			0.792792
$537$	−3.45403e6	−	3.45403e6i	−0.0223050	−	0.0223050i
$538$	−6.97918e7	+	6.97918e7i	−0.448185	+	0.448185i
$539$			3.28782e7i			0.209962i
$540$	−1.84864e6	+	1.40104e6i	−0.0117401	+	0.00889749i
$541$	−1.95129e8			−1.23234			−0.616169	−	0.787614i	$-0.711316\pi$
$541$	−1.95129e8			−1.23234			−0.616169	+	0.787614i	$0.711316\pi$
$542$	5.40361e7	+	5.40361e7i	0.339380	+	0.339380i
$543$	−3.36348e6	+	3.36348e6i	−0.0210083	+	0.0210083i
$544$		−	4.06198e7i		−	0.252314i
$545$	2.25214e7	−	1.63507e8i	0.139125	−	1.01006i
$546$	2.34214e6			0.0143892
$547$	3.48848e7	+	3.48848e7i	0.213145	+	0.213145i	0.805602	−	0.592457i	$-0.201842\pi$
$547$	3.48848e7	+	3.48848e7i	0.213145	+	0.213145i	−0.592457	+	0.805602i	$0.701842\pi$
$548$	5.48971e7	−	5.48971e7i	0.333586	−	0.333586i
$549$		−	5.50955e7i		−	0.332965i
$550$	−6.58448e7	−	1.17262e8i	−0.395761	−	0.704808i
$551$	4.99883e7			0.298822
$552$	2.42849e6	+	2.42849e6i	0.0144384	+	0.0144384i
$553$	−3.85147e7	+	3.85147e7i	−0.227746	+	0.227746i
$554$			1.26497e8i			0.743964i
$555$	−5.75852e6	−	793175.i	−0.0336846	−	0.00463970i
$556$	−6.75551e7			−0.393037
$557$	2.29154e7	+	2.29154e7i	0.132606	+	0.132606i	0.770294	−	0.637689i	$-0.220109\pi$
$557$	2.29154e7	+	2.29154e7i	0.132606	+	0.132606i	−0.637689	+	0.770294i	$0.720109\pi$
$558$	1.09501e8	−	1.09501e8i	0.630252	−	0.630252i
$559$			1.84135e7i			0.105415i
$560$	−5.09881e7	−	6.72779e7i	−0.290338	−	0.383097i
$561$	−1.47187e6			−0.00833643
$562$	−1.17639e8	−	1.17639e8i	−0.662741	−	0.662741i
$563$	−7.98554e7	+	7.98554e7i	−0.447486	+	0.447486i	−0.894518	−	0.447032i	$-0.852481\pi$
$563$	−7.98554e7	+	7.98554e7i	−0.447486	+	0.447486i	0.447032	+	0.894518i	$0.352481\pi$
$564$			635519.i			0.00354235i
$565$	−1.10375e8	+	8.36502e7i	−0.611964	+	0.463790i
$566$	−1.83372e8			−1.01131
$567$	−1.14353e8	−	1.14353e8i	−0.627335	−	0.627335i
$568$	7.25169e7	−	7.25169e7i	0.395726	−	0.395726i
$569$			6.42351e7i			0.348687i	0.984685	+	0.174343i	$0.0557803\pi$
$569$			6.42351e7i			0.348687i	−0.984685	+	0.174343i	$0.944220\pi$
$570$	−591715.	+	4.29590e6i	−0.00319512	+	0.0231969i
$571$	−1.63954e8			−0.880672			−0.440336	−	0.897833i	$-0.645141\pi$
$571$	−1.63954e8			−0.880672			−0.440336	+	0.897833i	$0.645141\pi$
$572$	4.17989e7	+	4.17989e7i	0.223345	+	0.223345i
$573$	2.65506e6	−	2.65506e6i	0.0141127	−	0.0141127i
$574$			3.51181e7i			0.185693i
$575$	−1.44336e8	+	8.10469e7i	−0.759224	+	0.426317i
$576$	2.04018e8			1.06758
$577$	2.43201e8	+	2.43201e8i	1.26601	+	1.26601i	0.948130	+	0.317884i	$0.102972\pi$
$577$	2.43201e8	+	2.43201e8i	1.26601	+	1.26601i	0.317884	+	0.948130i	$0.397028\pi$
$578$	9.40558e7	−	9.40558e7i	0.487082	−	0.487082i
$579$		−	5.20105e6i		−	0.0267951i
$580$	−1.47407e7	−	2.03037e6i	−0.0755499	−	0.0104062i
$581$	2.43515e8			1.24164
$582$	115598.	+	115598.i	0.000586382	+	0.000586382i
$583$	8.01094e7	−	8.01094e7i	0.404276	−	0.404276i
$584$		−	2.37278e8i		−	1.19130i
$585$	−1.12027e8	−	1.47818e8i	−0.559570	−	0.738344i
$586$	−4.84019e7			−0.240530
$587$	1.89685e8	+	1.89685e8i	0.937819	+	0.937819i	0.998177	−	0.0603574i	$-0.0192240\pi$
$587$	1.89685e8	+	1.89685e8i	0.937819	+	0.937819i	−0.0603574	+	0.998177i	$0.519224\pi$
$588$	−223145.	+	223145.i	−0.00109763	+	0.00109763i
$589$			3.01002e8i			1.47307i
$590$	−2.97976e7	+	2.25828e7i	−0.145086	+	0.109957i
$591$	3.79548e6			0.0183867
$592$	1.25291e8	+	1.25291e8i	0.603886	+	0.603886i
$593$	1.53385e8	−	1.53385e8i	0.735561	−	0.735561i	−0.236155	−	0.971715i	$-0.575887\pi$
$593$	1.53385e8	−	1.53385e8i	0.735561	−	0.735561i	0.971715	+	0.236155i	$0.0758873\pi$
$594$		−	7.29721e6i		−	0.0348175i
$595$	9.91690e6	−	7.19975e7i	0.0470787	−	0.341796i
$596$	2.59097e7			0.122384
$597$	3.83907e6	+	3.83907e6i	0.0180428	+	0.0180428i
$598$	−9.89925e7	+	9.89925e7i	−0.462912	+	0.462912i
$599$		−	1.58011e8i		−	0.735201i	−0.929984	−	0.367601i	$-0.880179\pi$
$599$		−	1.58011e8i		−	0.735201i	0.929984	−	0.367601i	$-0.119821\pi$
$600$	1.36940e6	−	4.87667e6i	0.00633981	−	0.0225772i
$601$	−6.50644e7			−0.299723			−0.149861	−	0.988707i	$-0.547883\pi$
$601$	−6.50644e7			−0.299723			−0.149861	+	0.988707i	$0.547883\pi$
$602$	−1.26444e7	−	1.26444e7i	−0.0579575	−	0.0579575i
$603$	−1.12857e8	+	1.12857e8i	−0.514727	+	0.514727i
$604$			6.59865e7i			0.299464i
$605$	1.54376e6	+	212637.i	0.00697132	+	0.000960225i
$606$	3.01171e6			0.0135330
$607$	−2.99149e8	−	2.99149e8i	−1.33759	−	1.33759i	−0.898393	−	0.439192i	$-0.855265\pi$
$607$	−2.99149e8	−	2.99149e8i	−1.33759	−	1.33759i	−0.439192	−	0.898393i	$-0.644735\pi$
$608$	−1.38362e8	+	1.38362e8i	−0.615611	+	0.615611i
$609$			963965.i			0.00426785i
$610$	3.70467e7	+	4.88825e7i	0.163215	+	0.215360i
$611$	−1.01656e8			−0.445666
$612$	2.15168e7	+	2.15168e7i	0.0938691	+	0.0938691i
$613$	1.98366e8	−	1.98366e8i	0.861164	−	0.861164i	−0.130310	−	0.991473i	$-0.541597\pi$
$613$	1.98366e8	−	1.98366e8i	0.861164	−	0.861164i	0.991473	+	0.130310i	$0.0415971\pi$
$614$			2.77955e8i			1.20080i
$615$	−1.02900e6	+	779851.i	−0.00442375	+	0.00335264i
$616$	−2.25265e8			−0.963722
$617$	−2.29329e8	−	2.29329e8i	−0.976347	−	0.976347i	0.0233799	−	0.999727i	$-0.492557\pi$
$617$	−2.29329e8	−	2.29329e8i	−0.976347	−	0.976347i	−0.999727	+	0.0233799i	$0.992557\pi$
$618$	−5.46597e6	+	5.46597e6i	−0.0231580	+	0.0231580i
$619$		−	2.71801e8i		−	1.14598i	−0.819561	−	0.572992i	$-0.805783\pi$
$619$		−	2.71801e8i		−	1.14598i	0.819561	−	0.572992i	$-0.194217\pi$
$620$	1.22258e7	−	8.87604e7i	0.0512982	−	0.372429i
$621$	−8.98198e6			−0.0375057
$622$	8.61643e7	+	8.61643e7i	0.358060	+	0.358060i
$623$	−5.36659e7	+	5.36659e7i	−0.221939	+	0.221939i
$624$		−	2.62479e6i		−	0.0108029i
$625$	2.08453e8	+	1.27091e8i	0.853822	+	0.520565i
$626$	−1.95798e8			−0.798151
$627$	5.01358e6	+	5.01358e6i	0.0203397	+	0.0203397i
$628$	−2.11246e7	+	2.11246e7i	−0.0852922	+	0.0852922i
$629$			1.52549e8i			0.612994i
$630$	1.78433e8	+	2.45773e7i	0.713598	+	0.0982906i
$631$	4.20768e8			1.67477			0.837384	−	0.546615i	$-0.184084\pi$
$631$	4.20768e8			1.67477			0.837384	+	0.546615i	$0.184084\pi$
$632$	7.04447e7	+	7.04447e7i	0.279060	+	0.279060i
$633$	909620.	−	909620.i	0.00358632	−	0.00358632i
$634$		−	3.84864e8i		−	1.51022i
$635$	4.87206e7	+	6.42861e7i	0.190279	+	0.251071i
$636$	1.08741e6			0.00422691
$637$	−3.56937e7	−	3.56937e7i	−0.138094	−	0.138094i
$638$	3.31005e7	−	3.31005e7i	0.127460	−	0.127460i
$639$			1.34074e8i			0.513857i
$640$	−4.52745e7	+	3.43123e7i	−0.172709	+	0.130891i
$641$	2.64309e8			1.00355			0.501773	−	0.864999i	$-0.332681\pi$
$641$	2.64309e8			1.00355			0.501773	+	0.864999i	$0.332681\pi$
$642$	−5.69773e6	−	5.69773e6i	−0.0215326	−	0.0215326i
$643$	−2.46084e8	+	2.46084e8i	−0.925659	+	0.925659i	−0.997422	−	0.0717631i	$-0.977137\pi$
$643$	−2.46084e8	+	2.46084e8i	−0.925659	+	0.925659i	0.0717631	+	0.997422i	$0.477137\pi$
$644$			7.06596e7i			0.264553i
$645$	89707.6	−	651285.i	0.000334310	−	0.00242712i
$646$	1.13802e8			0.422138
$647$	−2.80240e8	−	2.80240e8i	−1.03471	−	1.03471i	−0.999376	−	0.0353306i	$-0.988752\pi$
$647$	−2.80240e8	−	2.80240e8i	−1.03471	−	1.03471i	−0.0353306	−	0.999376i	$-0.511248\pi$
$648$	−2.09156e8	+	2.09156e8i	−0.768680	+	0.768680i
$649$			6.11311e7i			0.223629i
$650$	1.98788e8	+	5.58209e7i	0.723852	+	0.203262i
$651$	−5.80446e6			−0.0210387
$652$	5.67346e7	+	5.67346e7i	0.204694	+	0.204694i
$653$	6.29176e7	−	6.29176e7i	0.225961	−	0.225961i	−0.585042	−	0.811003i	$-0.698922\pi$
$653$	6.29176e7	−	6.29176e7i	0.225961	−	0.225961i	0.811003	+	0.585042i	$0.198922\pi$
$654$			4.98384e6i			0.0178168i
$655$	7.18717e7	+	9.89956e6i	0.255761	+	0.0352283i
$656$	3.93562e7			0.139412
$657$	2.19348e8	+	2.19348e8i	0.773460	+	0.773460i
$658$	6.98063e7	−	6.98063e7i	0.245029	−	0.245029i
$659$		−	1.20587e8i		−	0.421351i	−0.977556	−	0.210676i	$-0.932434\pi$
$659$		−	1.20587e8i		−	0.421351i	0.977556	−	0.210676i	$-0.0675664\pi$
$660$	−1.27478e6	−	1.68206e6i	−0.00443410	−	0.00585072i
$661$	−7.06531e7			−0.244640			−0.122320	−	0.992491i	$-0.539033\pi$
$661$	−7.06531e7			−0.244640			−0.122320	+	0.992491i	$0.539033\pi$
$662$	−1.08711e8	−	1.08711e8i	−0.374715	−	0.374715i
$663$	1.59791e6	−	1.59791e6i	0.00548293	−	0.00548293i
$664$		−	4.45397e8i		−	1.52140i
$665$	−2.79023e8	+	2.11464e8i	−0.948801	+	0.719070i
$666$	−3.78064e8			−1.27980
$667$	−4.07427e7	−	4.07427e7i	−0.137300	−	0.137300i
$668$	5.45642e7	−	5.45642e7i	0.183054	−	0.183054i
$669$			4.54635e6i			0.0151839i
$670$	2.42444e7	−	1.76017e8i	0.0806097	−	0.585234i
$671$	1.00285e8			0.331946
$672$	−2.66815e6	−	2.66815e6i	−0.00879230	−	0.00879230i
$673$	−3.05643e7	+	3.05643e7i	−0.100270	+	0.100270i	−0.755462	−	0.655192i	$-0.772588\pi$
$673$	−3.05643e7	+	3.05643e7i	−0.100270	+	0.100270i	0.655192	+	0.755462i	$0.272588\pi$
$674$		−	3.78117e7i		−	0.123494i
$675$	6.48598e6	+	1.15508e7i	0.0210894	+	0.0375579i
$676$	1.48888e7			0.0481968
$677$	3.25627e7	+	3.25627e7i	0.104943	+	0.104943i	0.757629	−	0.652686i	$-0.226358\pi$
$677$	3.25627e7	+	3.25627e7i	0.104943	+	0.104943i	−0.652686	+	0.757629i	$0.726358\pi$
$678$	2.95703e6	−	2.95703e6i	0.00948782	−	0.00948782i
$679$			1.31984e7i			0.0421612i
$680$	−1.31686e8	−	1.81383e7i	−0.418806	−	0.0576860i
$681$	1.83988e6			0.00582571
$682$	1.99313e8	+	1.99313e8i	0.628323	+	0.628323i
$683$	−3.30544e8	+	3.30544e8i	−1.03745	+	1.03745i	−0.0381800	+	0.999271i	$0.512156\pi$
$683$	−3.30544e8	+	3.30544e8i	−1.03745	+	1.03745i	−0.999271	+	0.0381800i	$0.987844\pi$
$684$		−	1.46584e8i		−	0.458056i
$685$	−2.67809e8	−	3.53370e8i	−0.833209	−	1.09941i
$686$	2.81674e8			0.872519
$687$	−3.40311e6	−	3.40311e6i	−0.0104956	−	0.0104956i
$688$	−1.41703e7	+	1.41703e7i	−0.0435126	+	0.0435126i
$689$			1.73939e8i			0.531790i
$690$	3.98363e6	−	3.01908e6i	0.0121264	−	0.00919025i
$691$	−1.82764e8			−0.553931			−0.276965	−	0.960880i	$-0.589329\pi$
$691$	−1.82764e8			−0.553931			−0.276965	+	0.960880i	$0.589329\pi$
$692$	−2.19765e7	−	2.19765e7i	−0.0663193	−	0.0663193i
$693$	2.08242e8	−	2.08242e8i	0.625705	−	0.625705i
$694$			3.29330e8i			0.985264i
$695$	−5.26446e7	+	3.82205e8i	−0.156819	+	1.13852i
$696$	1.76312e6			0.00522944
$697$	2.39591e7	+	2.39591e7i	0.0707574	+	0.0707574i
$698$	2.47197e8	−	2.47197e8i	0.726905	−	0.726905i
$699$			2.20611e6i			0.00645945i
$700$	9.08683e7	−	5.10240e7i	0.264922	−	0.148758i
$701$	9.24516e7			0.268386			0.134193	−	0.990955i	$-0.457156\pi$
$701$	9.24516e7			0.268386			0.134193	+	0.990955i	$0.457156\pi$
$702$	7.92212e6	+	7.92212e6i	0.0228997	+	0.0228997i
$703$	5.19622e8	−	5.19622e8i	1.49562	−	1.49562i
$704$			3.71354e8i			1.06431i
$705$	3.59556e6	+	495250.i	0.0102612	+	0.00141337i
$706$	9.12556e7			0.259326
$707$	1.71931e8	+	1.71931e8i	0.486516	+	0.486516i
$708$	−414899.	+	414899.i	−0.00116908	+	0.00116908i
$709$			3.04366e8i			0.853999i	0.904252	+	0.427000i	$0.140429\pi$
$709$			3.04366e8i			0.853999i	−0.904252	+	0.427000i	$0.859571\pi$
$710$	−9.01525e7	−	1.18955e8i	−0.251885	−	0.332359i
$711$	−1.30243e8			−0.362364
$712$	9.81567e7	+	9.81567e7i	0.271944	+	0.271944i
$713$	2.45330e8	−	2.45330e8i	0.676834	−	0.676834i
$714$			2.19455e6i			0.00602907i
$715$	2.69058e8	−	2.03911e8i	0.736083	−	0.557857i
$716$	−1.83816e8			−0.500776
$717$	−7.41032e6	−	7.41032e6i	−0.0201039	−	0.0201039i
$718$	−3.82231e8	+	3.82231e8i	−1.03265	+	1.03265i
$719$		−	7.55310e7i		−	0.203207i	−0.994825	−	0.101604i	$-0.967603\pi$
$719$		−	7.55310e7i		−	0.203207i	0.994825	−	0.101604i	$-0.0323973\pi$
$720$	2.75432e7	−	1.99966e8i	0.0737934	−	0.535747i
$721$	−6.24080e8			−1.66508
$722$	−1.71762e8	−	1.71762e8i	−0.456368	−	0.456368i
$723$	9.83207e6	−	9.83207e6i	0.0260154	−	0.0260154i
$724$			1.78997e8i			0.471662i
$725$	−2.29744e7	+	8.18158e7i	−0.0602879	+	0.214696i
$726$	−47055.2			−0.000122970
$727$	−7.46010e7	−	7.46010e7i	−0.194152	−	0.194152i	0.603336	−	0.797487i	$-0.293838\pi$
$727$	−7.46010e7	−	7.46010e7i	−0.194152	−	0.194152i	−0.797487	+	0.603336i	$0.793838\pi$
$728$	2.44556e8	−	2.44556e8i	0.633847	−	0.633847i
$729$		−	3.86342e8i		−	0.997217i
$730$	−3.42104e8	−	4.71212e7i	−0.879407	−	0.121129i
$731$	−1.72531e7			−0.0441689
$732$	680636.	+	680636.i	0.00173533	+	0.00173533i
$733$	−4.35999e8	+	4.35999e8i	−1.10707	+	1.10707i	−0.113531	+	0.993534i	$0.536216\pi$
$733$	−4.35999e8	+	4.35999e8i	−1.10707	+	1.10707i	−0.993534	+	0.113531i	$0.963784\pi$
$734$			5.83939e7i			0.147666i
$735$	1.08859e6	+	1.43638e6i	0.00274159	+	0.00361748i
$736$	2.25543e8			0.565712
$737$	−2.05422e8	−	2.05422e8i	−0.513151	−	0.513151i
$738$	−5.93784e7	+	5.93784e7i	−0.147727	+	0.147727i
$739$			3.93731e8i			0.975587i	0.872959	+	0.487794i	$0.162198\pi$
$739$			3.93731e8i			0.975587i	−0.872959	+	0.487794i	$0.837802\pi$
$740$	−1.74333e8	+	1.32122e8i	−0.430215	+	0.326048i
$741$	−1.08859e7			−0.0267552
$742$	−1.19443e8	−	1.19443e8i	−0.292380	−	0.292380i
$743$	3.05130e8	−	3.05130e8i	0.743906	−	0.743906i	−0.229421	−	0.973327i	$-0.573683\pi$
$743$	3.05130e8	−	3.05130e8i	0.743906	−	0.743906i	0.973327	+	0.229421i	$0.0736834\pi$
$744$			1.06166e7i			0.0257789i
$745$	2.01910e7	−	1.46589e8i	0.0488303	−	0.354513i
$746$	−4.40315e7			−0.106059
$747$	4.11740e8	+	4.11740e8i	0.987782	+	0.987782i
$748$	−3.91648e7	+	3.91648e7i	−0.0935816	+	0.0935816i
$749$		−	6.50541e8i		−	1.54821i
$750$	−6.75916e6	−	2.94284e6i	−0.0160217	−	0.00697562i
$751$	3.96683e8			0.936534			0.468267	−	0.883587i	$-0.344879\pi$
$751$	3.96683e8			0.936534			0.468267	+	0.883587i	$0.344879\pi$
$752$	−7.82305e7	−	7.82305e7i	−0.183960	−	0.183960i
$753$	−1.07651e7	+	1.07651e7i	−0.0252134	+	0.0252134i
$754$			7.18703e7i			0.167662i
$755$	3.73330e8	+	5.14223e7i	0.867466	+	0.119484i
$756$	5.65471e6			0.0130871
$757$	1.91605e8	+	1.91605e8i	0.441691	+	0.441691i	0.892580	−	0.450889i	$-0.148893\pi$
$757$	1.91605e8	+	1.91605e8i	0.441691	+	0.441691i	−0.450889	+	0.892580i	$0.648893\pi$
$758$	−6.01549e6	+	6.01549e6i	−0.0138122	+	0.0138122i
$759$		−	8.17259e6i		−	0.0186911i
$760$	3.86774e8	+	5.10343e8i	0.881083	+	1.16257i
$761$	5.82598e7			0.132195			0.0660975	−	0.997813i	$-0.478945\pi$
$761$	5.82598e7			0.132195			0.0660975	+	0.997813i	$0.478945\pi$
$762$	−1.72227e6	−	1.72227e6i	−0.00389257	−	0.00389257i
$763$	−2.84516e8	+	2.84516e8i	−0.640521	+	0.640521i
$764$		−	1.41296e8i		−	0.316848i
$765$	1.38503e8	−	1.04967e8i	0.309367	−	0.234460i
$766$	5.05586e8			1.12489
$767$	−6.63662e7	−	6.63662e7i	−0.147082	−	0.147082i
$768$	−6.15689e6	+	6.15689e6i	−0.0135918	+	0.0135918i
$769$		−	3.41834e8i		−	0.751687i	−0.926683	−	0.375843i	$-0.877353\pi$
$769$		−	3.41834e8i		−	0.751687i	0.926683	−	0.375843i	$-0.122647\pi$
$770$	−4.47355e7	+	3.24784e8i	−0.0979896	+	0.711413i
$771$	5.61513e6			0.0122517
$772$	−1.38394e8	−	1.38394e8i	−0.300792	−	0.300792i
$773$	−3.94613e8	+	3.94613e8i	−0.854344	+	0.854344i	−0.990665	−	0.136321i	$-0.956472\pi$
$773$	−3.94613e8	+	3.94613e8i	−0.854344	+	0.854344i	0.136321	+	0.990665i	$0.456472\pi$
$774$		−	4.27589e7i		−	0.0922153i
$775$	−4.92650e8	−	1.38339e8i	−1.05836	−	0.297194i
$776$	2.41404e7			0.0516606
$777$	1.00203e7	+	1.00203e7i	0.0213608	+	0.0213608i
$778$	−1.42552e8	+	1.42552e8i	−0.302715	+	0.302715i
$779$		−	1.63223e8i		−	0.345277i
$780$	3.21006e6	+	442151.i	0.00676439	+	0.000931723i
$781$	−2.44041e8			−0.512283
$782$	−9.27541e7	−	9.27541e7i	−0.193960	−	0.193960i
$783$	−3.26054e6	+	3.26054e6i	−0.00679210	+	0.00679210i
$784$		−	5.49370e7i		−	0.114003i
$785$	1.03054e8	+	1.35978e8i	0.213037	+	0.281099i
$786$	−2.19071e6			−0.00451146
$787$	−1.24249e7	−	1.24249e7i	−0.0254899	−	0.0254899i	0.694247	−	0.719737i	$-0.255738\pi$
$787$	−1.24249e7	−	1.24249e7i	−0.0254899	−	0.0254899i	−0.719737	+	0.694247i	$0.755738\pi$
$788$	1.00994e8	−	1.00994e8i	0.206403	−	0.206403i
$789$		−	1.66120e7i		−	0.0338213i
$790$	1.15556e8	−	8.75764e7i	0.234374	−	0.177626i
$791$	3.37620e8			0.682180
$792$	−3.80882e8	−	3.80882e8i	−0.766682	−	0.766682i
$793$	−1.08873e8	+	1.08873e8i	−0.218323	+	0.218323i
$794$		−	2.51712e8i		−	0.502854i
$795$	847403.	−	6.15222e6i	0.00168651	−	0.0122442i
$796$	2.04307e8			0.405083
$797$	−2.16052e8	−	2.16052e8i	−0.426760	−	0.426760i	0.460763	−	0.887523i	$-0.347576\pi$
$797$	−2.16052e8	−	2.16052e8i	−0.426760	−	0.426760i	−0.887523	+	0.460763i	$0.847576\pi$
$798$	7.47522e6	−	7.47522e6i	0.0147101	−	0.0147101i
$799$		−	9.52497e7i		−	0.186734i
$800$	−1.62867e8	−	2.90048e8i	−0.318099	−	0.566500i
$801$	−1.81479e8			−0.353125
$802$	2.47497e8	+	2.47497e8i	0.479785	+	0.479785i
$803$	−3.99257e8	+	3.99257e8i	−0.771091	+	0.771091i
$804$		−	2.78842e6i		−	0.00536525i
$805$	3.99769e8	+	5.50639e7i	0.766340	+	0.105555i
$806$	−4.32763e8			−0.826504
$807$	6.25528e6	+	6.25528e6i	0.0119022	+	0.0119022i
$808$	3.14468e8	−	3.14468e8i	0.596133	−	0.596133i
$809$			7.65363e8i			1.44551i	0.691102	+	0.722757i	$0.257125\pi$
$809$			7.65363e8i			1.44551i	−0.691102	+	0.722757i	$0.742875\pi$
$810$	2.60022e8	+	3.43094e8i	0.489277	+	0.645593i
$811$	−7.53196e8			−1.41203			−0.706017	−	0.708195i	$-0.749510\pi$
$811$	−7.53196e8			−1.41203			−0.706017	+	0.708195i	$0.749510\pi$
$812$	2.56500e7	+	2.56500e7i	0.0479093	+	0.0479093i
$813$	4.84313e6	−	4.84313e6i	0.00901269	−	0.00901269i
$814$		−	6.88152e8i		−	1.27588i
$815$	3.65199e8	−	2.76774e8i	0.674615	−	0.511272i
$816$	2.45938e6			0.00452643
$817$	5.87689e7	+	5.87689e7i	0.107766	+	0.107766i
$818$	3.67553e8	−	3.67553e8i	0.671521	−	0.671521i
$819$			4.52151e8i			0.823061i
$820$	−6.62961e6	+	4.81316e7i	−0.0120239	+	0.0872949i
$821$	3.57195e8			0.645469			0.322734	−	0.946490i	$-0.395398\pi$
$821$	3.57195e8			0.645469			0.322734	+	0.946490i	$0.395398\pi$
$822$	9.46704e6	+	9.46704e6i	0.0170451	+	0.0170451i
$823$	3.47845e8	−	3.47845e8i	0.624002	−	0.624002i	−0.322550	−	0.946552i	$-0.604540\pi$
$823$	3.47845e8	−	3.47845e8i	0.624002	−	0.624002i	0.946552	+	0.322550i	$0.104540\pi$
$824$			1.14146e9i			2.04023i
$825$	−1.05100e7	+	5.90151e6i	−0.0187171	+	0.0105100i
$826$	9.11462e7			0.161733
$827$	4.91730e8	+	4.91730e8i	0.869380	+	0.869380i	0.992404	−	0.123023i	$-0.0392590\pi$
$827$	4.91730e8	+	4.91730e8i	0.869380	+	0.869380i	−0.123023	+	0.992404i	$0.539259\pi$
$828$	−1.19473e8	+	1.19473e8i	−0.210464	+	0.210464i
$829$			8.41407e7i			0.147687i	0.997270	+	0.0738435i	$0.0235265\pi$
$829$			8.41407e7i			0.147687i	−0.997270	+	0.0738435i	$0.976473\pi$
$830$	−6.42166e8	−	8.84516e7i	−1.12309	−	0.154693i
$831$	1.13377e7			0.0197570
$832$	−4.03155e8	−	4.03155e8i	−0.700007	−	0.700007i
$833$	3.34444e7	−	3.34444e7i	0.0578613	−	0.0578613i
$834$		−	1.16499e7i		−	0.0200828i
$835$	−2.66185e8	−	3.51228e8i	−0.457220	−	0.603294i
$836$	2.66812e8			0.456653
$837$	−1.96332e7	−	1.96332e7i	−0.0334822	−	0.0334822i
$838$	3.50530e8	−	3.50530e8i	0.595652	−	0.595652i
$839$		−	1.92325e8i		−	0.325650i	−0.986655	−	0.162825i	$-0.947939\pi$
$839$		−	1.92325e8i		−	0.325650i	0.986655	−	0.162825i	$-0.0520605\pi$
$840$	−9.84136e6	+	7.45849e6i	−0.0166042	+	0.0125838i
$841$	5.65243e8			0.950271
$842$	3.95831e8	+	3.95831e8i	0.663092	+	0.663092i
$843$	−1.05438e7	+	1.05438e7i	−0.0176000	+	0.0176000i
$844$		−	4.84080e7i		−	0.0805174i
$845$	1.16026e7	−	8.42358e7i	0.0192302	−	0.139613i
$846$	2.36060e8			0.389862
$847$	−2.68628e6	−	2.68628e6i	−0.00442080	−	0.00442080i
$848$	−1.33857e8	+	1.33857e8i	−0.219510	+	0.219510i
$849$			1.64352e7i			0.0268566i
$850$	−5.23031e7	+	1.86261e8i	−0.0851669	+	0.303294i
$851$	−8.47031e8			−1.37439
$852$	−1.65632e6	−	1.65632e6i	−0.00267809	−	0.00267809i
$853$	4.32334e8	−	4.32334e8i	0.696582	−	0.696582i	−0.267090	−	0.963672i	$-0.586062\pi$
$853$	4.32334e8	−	4.32334e8i	0.696582	−	0.696582i	0.963672	+	0.267090i	$0.0860620\pi$
$854$		−	1.49524e8i		−	0.240070i
$855$	−8.29324e8	−	1.14231e8i	−1.32686	−	0.182761i
$856$	−1.18986e9			−1.89703
$857$	−1.34271e8	−	1.34271e8i	−0.213323	−	0.213323i	0.592354	−	0.805678i	$-0.298199\pi$
$857$	−1.34271e8	−	1.34271e8i	−0.213323	−	0.213323i	−0.805678	+	0.592354i	$0.798199\pi$
$858$	−7.20824e6	+	7.20824e6i	−0.0114122	+	0.0114122i
$859$		−	2.62687e8i		−	0.414438i	−0.978295	−	0.207219i	$-0.933559\pi$
$859$		−	2.62687e8i		−	0.414438i	0.978295	−	0.207219i	$-0.0664413\pi$
$860$	−1.49430e7	−	1.97170e7i	−0.0234931	−	0.0309988i
$861$	3.14755e6			0.00493133
$862$	7.01558e7	+	7.01558e7i	0.109532	+	0.109532i
$863$	−1.09116e8	+	1.09116e8i	−0.169769	+	0.169769i	−0.786878	−	0.617109i	$-0.788304\pi$
$863$	−1.09116e8	+	1.09116e8i	−0.169769	+	0.169769i	0.617109	+	0.786878i	$0.288304\pi$
$864$		−	1.80496e7i		−	0.0279851i
$865$	−1.41462e8	+	1.07210e8i	−0.218570	+	0.165648i
$866$	−3.12540e8			−0.481230
$867$	−8.43000e6	−	8.43000e6i	−0.0129351	−	0.0129351i
$868$	−1.54450e8	+	1.54450e8i	−0.236173	+	0.236173i
$869$		−	2.37068e8i		−	0.361254i
$870$	350140.	−	2.54204e6i	0.000531720	−	0.00386034i
$871$	4.46028e8			0.675006
$872$	5.20389e8	+	5.20389e8i	0.784836	+	0.784836i
$873$	−2.23162e7	+	2.23162e7i	−0.0335411	+	0.0335411i
$874$			6.31892e8i			0.946473i
$875$	−2.17865e8	−	5.53865e8i	−0.325210	−	0.826761i
$876$	−5.41954e6			−0.00806214
$877$	3.07353e7	+	3.07353e7i	0.0455658	+	0.0455658i	0.729523	−	0.683957i	$-0.239742\pi$
$877$	3.07353e7	+	3.07353e7i	0.0455658	+	0.0455658i	−0.683957	+	0.729523i	$0.739742\pi$
$878$	−3.62877e8	+	3.62877e8i	−0.536137	+	0.536137i
$879$			4.33815e6i			0.00638760i
$880$	3.63978e8	+	5.01342e7i	0.534106	+	0.0735675i
$881$	6.97712e8			1.02035			0.510174	−	0.860071i	$-0.329581\pi$
$881$	6.97712e8			1.02035			0.510174	+	0.860071i	$0.329581\pi$
$882$	8.28859e7	+	8.28859e7i	0.120802	+	0.120802i
$883$	7.66490e8	−	7.66490e8i	1.11333	−	1.11333i	0.120635	−	0.992697i	$-0.461507\pi$
$883$	7.66490e8	−	7.66490e8i	1.11333	−	1.11333i	0.992697	−	0.120635i	$-0.0384930\pi$
$884$		−	8.50374e7i		−	0.123099i
$885$	2.02404e6	+	2.67069e6i	0.00292004	+	0.00385295i
$886$	4.78692e8			0.688264
$887$	−1.80718e8	−	1.80718e8i	−0.258959	−	0.258959i	0.565672	−	0.824631i	$-0.308617\pi$
$887$	−1.80718e8	−	1.80718e8i	−0.258959	−	0.258959i	−0.824631	+	0.565672i	$0.808617\pi$
$888$	1.83275e7	−	1.83275e7i	0.0261736	−	0.0261736i
$889$		−	1.96641e8i		−	0.279878i
$890$	1.61014e8	−	1.22028e8i	0.228398	−	0.173097i
$891$	7.03874e8			0.995088
$892$	1.20973e8	+	1.20973e8i	0.170449	+	0.170449i
$893$	−3.24447e8	+	3.24447e8i	−0.455605	+	0.455605i
$894$			4.46815e6i			0.00625338i
$895$	−1.43245e8	+	1.03997e9i	−0.199806	+	1.45061i
$896$	1.38488e8			0.192525
$897$	8.87246e6	+	8.87246e6i	0.0122933	+	0.0122933i
$898$	−3.28932e8	+	3.28932e8i	−0.454231	+	0.454231i
$899$		−	1.78114e8i		−	0.245142i
$900$	2.39914e8	+	6.73694e7i	0.329100	+	0.0924134i
$901$	−1.62978e8			−0.222820
$902$	−1.08080e8	−	1.08080e8i	−0.147274	−	0.147274i
$903$	−1.13329e6	+	1.13329e6i	−0.00153914	+	0.00153914i
$904$		−	6.17519e8i		−	0.835882i
$905$	1.01271e9	+	1.39490e8i	1.36628	+	0.188190i
$906$	−1.13794e7			−0.0153016
$907$	−2.51326e8	−	2.51326e8i	−0.336834	−	0.336834i	0.518341	−	0.855174i	$-0.326550\pi$
$907$	−2.51326e8	−	2.51326e8i	−0.336834	−	0.336834i	−0.855174	+	0.518341i	$0.826550\pi$
$908$	4.89572e7	−	4.89572e7i	0.0653972	−	0.0653972i
$909$			5.81410e8i			0.774089i
$910$	−3.04030e8	−	4.01163e8i	−0.403453	−	0.532350i
$911$	−1.32793e9			−1.75639			−0.878193	−	0.478306i	$-0.841251\pi$
$911$	−1.32793e9			−1.75639			−0.878193	+	0.478306i	$0.841251\pi$
$912$	−8.37733e6	−	8.37733e6i	−0.0110439	−	0.0110439i
$913$	−7.49448e8	+	7.49448e8i	−0.984757	+	0.984757i
$914$		−	8.65920e8i		−	1.13407i
$915$	4.38123e6	−	3.32041e6i	0.00571916	−	0.00433439i
$916$	−1.81106e8			−0.235638
$917$	−1.25063e8	−	1.25063e8i	−0.162188	−	0.162188i
$918$	−7.42288e6	+	7.42288e6i	−0.00959499	+	0.00959499i
$919$			1.31280e9i			1.69143i	0.533638	+	0.845713i	$0.320825\pi$
$919$			1.31280e9i			1.69143i	−0.533638	+	0.845713i	$0.679175\pi$
$920$	1.00714e8	−	7.31191e8i	0.129338	−	0.939003i
$921$	2.49125e7			0.0318888
$922$	−7.01476e8	−	7.01476e8i	−0.894994	−	0.894994i
$923$	2.64940e8	−	2.64940e8i	0.336932	−	0.336932i
$924$			5.14515e6i			0.00652202i
$925$	6.11650e8	+	1.08928e9i	0.772819	+	1.37631i
$926$	−7.65334e7			−0.0963870
$927$	−1.05521e9	−	1.05521e9i	−1.32464	−	1.32464i
$928$	8.18740e7	−	8.18740e7i	0.102448	−	0.102448i
$929$		−	1.28584e9i		−	1.60377i	−0.597481	−	0.801883i	$-0.703832\pi$
$929$		−	1.28584e9i		−	1.60377i	0.597481	−	0.801883i	$-0.296168\pi$
$930$	1.53068e7	+	2.10835e6i	0.0190298	+	0.00262116i
$931$	−2.27841e8			−0.282347
$932$	5.87022e7	+	5.87022e7i	0.0725114	+	0.0725114i
$933$	7.72270e6	−	7.72270e6i	0.00950877	−	0.00950877i
$934$			8.35322e8i			1.02521i
$935$	1.91061e8	+	2.52102e8i	0.233742	+	0.308419i
$936$	8.27000e8			1.00850
$937$	1.61452e8	+	1.61452e8i	0.196256	+	0.196256i	0.798393	−	0.602137i	$-0.205684\pi$
$937$	1.61452e8	+	1.61452e8i	0.196256	+	0.196256i	−0.602137	+	0.798393i	$0.705684\pi$
$938$	−3.06284e8	+	3.06284e8i	−0.371121	+	0.371121i
$939$			1.75489e7i			0.0211960i
$940$	1.08852e8	−	8.24958e7i	0.131055	−	0.0993227i
$941$	7.40996e8			0.889297			0.444649	−	0.895705i	$-0.353329\pi$
$941$	7.40996e8			0.889297			0.444649	+	0.895705i	$0.353329\pi$
$942$	−3.64295e6	−	3.64295e6i	−0.00435813	−	0.00435813i
$943$	−1.33034e8	+	1.33034e8i	−0.158645	+	0.158645i
$944$		−	1.02146e8i		−	0.121424i
$945$	4.40663e6	−	3.19925e7i	0.00522169	−	0.0379099i
$946$	7.78296e7			0.0919330
$947$	4.84666e8	+	4.84666e8i	0.570680	+	0.570680i	0.932318	−	0.361639i	$-0.117783\pi$
$947$	4.84666e8	+	4.84666e8i	0.570680	+	0.570680i	−0.361639	+	0.932318i	$0.617783\pi$
$948$	1.60899e6	−	1.60899e6i	0.00188855	−	0.00188855i
$949$		−	8.66896e8i		−	1.01430i
$950$	8.12613e8	−	4.56296e8i	0.947792	−	0.532201i
$951$	−3.44944e7			−0.0401058
$952$	2.29144e8	+	2.29144e8i	0.265582	+	0.265582i
$953$	−6.04027e8	+	6.04027e8i	−0.697876	+	0.697876i	−0.963952	−	0.266076i	$-0.914273\pi$
$953$	−6.04027e8	+	6.04027e8i	−0.697876	+	0.697876i	0.266076	+	0.963952i	$0.414273\pi$
$954$		−	4.03912e8i		−	0.465202i
$955$	−7.99410e8	−	1.10110e8i	−0.917824	−	0.126420i
$956$	−3.94361e8			−0.451357
$957$	−2.96672e6	−	2.96672e6i	−0.00338486	−	0.00338486i
$958$	−5.08570e8	+	5.08570e8i	−0.578435	+	0.578435i
$959$			1.08090e9i			1.22555i
$960$	1.22955e7	+	1.62237e7i	0.0138973	+	0.0183373i
$961$	1.85000e8			0.208449
$962$	7.47083e8	+	7.47083e8i	0.839158	+	0.839158i
$963$	1.09995e9	−	1.09995e9i	1.23167	−	1.23167i
$964$		−	5.23241e8i		−	0.584078i
$965$	−8.90838e8	+	6.75141e8i	−0.991327	+	0.751298i
$966$	−1.21853e7			−0.0135178
$967$	9.16779e8	+	9.16779e8i	1.01388	+	1.01388i	0.999902	+	0.0139747i	$0.00444843\pi$
$967$	9.16779e8	+	9.16779e8i	1.01388	+	1.01388i	0.0139747	+	0.999902i	$0.495552\pi$
$968$	−4.91329e6	+	4.91329e6i	−0.00541685	+	0.00541685i
$969$		−	1.01998e7i		−	0.0112104i
$970$	4.79405e6	−	3.48052e7i	0.00525276	−	0.0381355i
$971$	4.28954e8			0.468547			0.234273	−	0.972171i	$-0.424729\pi$
$971$	4.28954e8			0.468547			0.234273	+	0.972171i	$0.424729\pi$
$972$	1.43427e7	+	1.43427e7i	0.0156183	+	0.0156183i
$973$	6.65068e8	−	6.65068e8i	0.721983	−	0.721983i
$974$			4.07562e8i			0.441080i
$975$	5.00309e6	−	1.78169e7i	0.00539790	−	0.0192229i
$976$	−1.67568e8			−0.180237
$977$	−9.78728e8	−	9.78728e8i	−1.04949	−	1.04949i	−0.998710	−	0.0507801i	$-0.983829\pi$
$977$	−9.78728e8	−	9.78728e8i	−1.04949	−	1.04949i	−0.0507801	−	0.998710i	$-0.516171\pi$
$978$	−9.78393e6	+	9.78393e6i	−0.0104592	+	0.0104592i
$979$		−	3.30327e8i		−	0.352043i
$980$	6.71866e7	+	9.25424e6i	0.0713846	+	0.00983247i
$981$	−9.62130e8			−1.01912
$982$	−2.09638e8	−	2.09638e8i	−0.221379	−	0.221379i
$983$	1.22302e6	−	1.22302e6i	0.00128758	−	0.00128758i	−0.706463	−	0.707750i	$-0.749710\pi$
$983$	1.22302e6	−	1.22302e6i	0.00128758	−	0.00128758i	0.707750	+	0.706463i	$0.249710\pi$
$984$		−	5.75698e6i		−	0.00604240i
$985$	−4.92687e8	−	6.50092e8i	−0.515540	−	0.680246i
$986$	−6.73411e7			−0.0702505
$987$	−6.25657e6	−	6.25657e6i	−0.00650706	−	0.00650706i
$988$	−2.89661e8	+	2.89661e8i	−0.300344	+	0.300344i
$989$		−	9.57987e7i		−	0.0990309i
$990$	−6.24790e8	+	4.73511e8i	−0.643915	+	0.488005i
$991$	1.28005e9			1.31524			0.657620	−	0.753349i	$-0.271563\pi$
$991$	1.28005e9			1.31524			0.657620	+	0.753349i	$0.271563\pi$
$992$	4.93000e8	+	4.93000e8i	0.505024	+	0.505024i
$993$	−9.74354e6	+	9.74354e6i	−0.00995105	+	0.00995105i
$994$			3.63864e8i			0.370493i
$995$	1.59213e8	−	1.15590e9i	0.161625	−	1.17342i
$996$	−1.01731e7			−0.0102961
$997$	−6.11907e8	−	6.11907e8i	−0.617447	−	0.617447i	0.327429	−	0.944876i	$-0.393818\pi$
$997$	−6.11907e8	−	6.11907e8i	−0.617447	−	0.617447i	−0.944876	+	0.327429i	$0.893818\pi$
$998$	9.12587e8	−	9.12587e8i	0.918085	−	0.918085i
$999$			6.77858e7i			0.0679896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.7.c.a.2.2	✓	4
3.2	odd	2		45.7.g.a.37.1		4
4.3	odd	2		80.7.p.b.17.2		4
5.2	odd	4		25.7.c.c.18.1		4
5.3	odd	4	inner	5.7.c.a.3.2	yes	4
5.4	even	2		25.7.c.c.7.1		4
15.2	even	4		225.7.g.c.118.2		4
15.8	even	4		45.7.g.a.28.1		4
15.14	odd	2		225.7.g.c.82.2		4
20.3	even	4		80.7.p.b.33.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.7.c.a.2.2	✓	4	1.1	even	1	trivial
5.7.c.a.3.2	yes	4	5.3	odd	4	inner
25.7.c.c.7.1		4	5.4	even	2
25.7.c.c.18.1		4	5.2	odd	4
45.7.g.a.28.1		4	15.8	even	4
45.7.g.a.37.1		4	3.2	odd	2
80.7.p.b.17.2		4	4.3	odd	2
80.7.p.b.33.2		4	20.3	even	4
225.7.g.c.82.2		4	15.14	odd	2
225.7.g.c.118.2		4	15.2	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.58872 + 4.58872i) q^{2} +(0.411277 - 0.411277i) q^{3} -21.8872i q^{4} +(-123.831 - 17.0564i) q^{5} +3.77447 q^{6} +(215.476 + 215.476i) q^{7} +(394.113 - 394.113i) q^{8} +728.662i q^{9} +O(q^{10})\)	\(q+(4.58872 + 4.58872i) q^{2} +(0.411277 - 0.411277i) q^{3} -21.8872i q^{4} +(-123.831 - 17.0564i) q^{5} +3.77447 q^{6} +(215.476 + 215.476i) q^{7} +(394.113 - 394.113i) q^{8} +728.662i q^{9} +(-489.959 - 646.493i) q^{10} -1326.31 q^{11} +(-9.00171 - 9.00171i) q^{12} +(1439.89 - 1439.89i) q^{13} +1977.52i q^{14} +(-57.9436 + 43.9138i) q^{15} +2216.17 q^{16} +(1349.15 + 1349.15i) q^{17} +(-3343.63 + 3343.63i) q^{18} -9191.14i q^{19} +(-373.317 + 2710.31i) q^{20} +177.240 q^{21} +(-6086.06 - 6086.06i) q^{22} +(-7491.20 + 7491.20i) q^{23} -324.179i q^{24} +(15043.2 + 4224.21i) q^{25} +13214.5 q^{26} +(599.502 + 599.502i) q^{27} +(4716.17 - 4716.17i) q^{28} +5438.74i q^{29} +(-467.396 - 64.3788i) q^{30} -32749.1 q^{31} +(-15053.8 - 15053.8i) q^{32} +(-545.480 + 545.480i) q^{33} +12381.7i q^{34} +(-23007.3 - 30357.8i) q^{35} +15948.4 q^{36} +(56535.1 + 56535.1i) q^{37} +(42175.6 - 42175.6i) q^{38} -1184.39i q^{39} +(-55525.5 + 42081.2i) q^{40} +17758.7 q^{41} +(813.307 + 813.307i) q^{42} +(-6394.08 + 6394.08i) q^{43} +29029.2i q^{44} +(12428.3 - 90230.8i) q^{45} -68750.1 q^{46} +(-35299.9 - 35299.9i) q^{47} +(911.457 - 911.457i) q^{48} -24789.2i q^{49} +(49645.2 + 88412.6i) q^{50} +1109.75 q^{51} +(-31515.2 - 31515.2i) q^{52} +(-60400.3 + 60400.3i) q^{53} +5501.90i q^{54} +(164238. + 22622.0i) q^{55} +169844. q^{56} +(-3780.10 - 3780.10i) q^{57} +(-24956.9 + 24956.9i) q^{58} -46091.2i q^{59} +(961.152 + 1268.23i) q^{60} -75611.9 q^{61} +(-150277. - 150277. i) q^{62} +(-157009. + 157009. i) q^{63} -279990. i q^{64} +(-202862. + 153743. i) q^{65} -5006.11 q^{66} +(154883. + 154883. i) q^{67} +(29529.1 - 29529.1i) q^{68} +6161.91i q^{69} +(33729.3 - 244878. i) q^{70} +184000. q^{71} +(287175. + 287175. i) q^{72} +(301029. - 301029. i) q^{73} +518848. i q^{74} +(7924.22 - 4449.58i) q^{75} -201169. q^{76} +(-285788. - 285788. i) q^{77} +(5434.82 - 5434.82i) q^{78} +178743. i q^{79} +(-274430. - 37799.8i) q^{80} -530701. q^{81} +(81489.6 + 81489.6i) q^{82} +(565063. - 565063. i) q^{83} -3879.30i q^{84} +(-144055. - 190078. i) q^{85} -58681.4 q^{86} +(2236.83 + 2236.83i) q^{87} +(-522715. + 522715. i) q^{88} +249057. i q^{89} +(471074. - 357014. i) q^{90} +620523. q^{91} +(163962. + 163962. i) q^{92} +(-13468.9 + 13468.9i) q^{93} -323963. i q^{94} +(-156768. + 1.13815e6i) q^{95} -12382.6 q^{96} +(30626.2 + 30626.2i) q^{97} +(113751. - 113751. i) q^{98} -966430. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8}+O(q^{10}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8	\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} - 4370 q^{10} - 1052 q^{11} + 3480 q^{12} + 1960 q^{13} - 90 q^{15} - 776 q^{16} - 3280 q^{17} - 870 q^{18} + 20340 q^{20} + 3828 q^{21} - 27520 q^{22} - 39010 q^{23} + 30400 q^{25} + 44068 q^{26} + 31320 q^{27} - 4840 q^{28} - 50640 q^{30} - 33172 q^{31} - 48760 q^{32} + 22260 q^{33} - 24970 q^{35} - 40836 q^{36} + 146860 q^{37} + 218040 q^{38} - 110100 q^{40} - 213932 q^{41} - 31680 q^{42} - 72050 q^{43} + 78210 q^{45} + 323288 q^{46} + 830 q^{47} - 74160 q^{48} - 203350 q^{50} - 172212 q^{51} - 173300 q^{52} - 29620 q^{53} + 470660 q^{55} + 467280 q^{56} + 195840 q^{57} - 554640 q^{58} + 620280 q^{60} - 111052 q^{61} - 610520 q^{62} - 350130 q^{63} - 406540 q^{65} - 457824 q^{66} - 146930 q^{67} + 775780 q^{68} - 133320 q^{70} + 1310188 q^{71} + 899460 q^{72} + 553540 q^{73} - 435450 q^{75} - 2073840 q^{76} - 476300 q^{77} + 268200 q^{78} - 1011520 q^{80} - 624816 q^{81} + 2554880 q^{82} + 536870 q^{83} - 1344920 q^{85} + 1019128 q^{86} - 763440 q^{87} - 187680 q^{88} + 947310 q^{90} + 1131548 q^{91} - 2552680 q^{92} + 444660 q^{93} + 912600 q^{95} - 568992 q^{96} - 59420 q^{97} - 1892810 q^{98}+O(q^{100}) \) 4 * q - 10 * q^2 + 30 * q^3 - 70 * q^5 - 552 * q^6 + 550 * q^7 + 1860 * q^8 - 4370 * q^10 - 1052 * q^11 + 3480 * q^12 + 1960 * q^13 - 90 * q^15 - 776 * q^16 - 3280 * q^17 - 870 * q^18 + 20340 * q^20 + 3828 * q^21 - 27520 * q^22 - 39010 * q^23 + 30400 * q^25 + 44068 * q^26 + 31320 * q^27 - 4840 * q^28 - 50640 * q^30 - 33172 * q^31 - 48760 * q^32 + 22260 * q^33 - 24970 * q^35 - 40836 * q^36 + 146860 * q^37 + 218040 * q^38 - 110100 * q^40 - 213932 * q^41 - 31680 * q^42 - 72050 * q^43 + 78210 * q^45 + 323288 * q^46 + 830 * q^47 - 74160 * q^48 - 203350 * q^50 - 172212 * q^51 - 173300 * q^52 - 29620 * q^53 + 470660 * q^55 + 467280 * q^56 + 195840 * q^57 - 554640 * q^58 + 620280 * q^60 - 111052 * q^61 - 610520 * q^62 - 350130 * q^63 - 406540 * q^65 - 457824 * q^66 - 146930 * q^67 + 775780 * q^68 - 133320 * q^70 + 1310188 * q^71 + 899460 * q^72 + 553540 * q^73 - 435450 * q^75 - 2073840 * q^76 - 476300 * q^77 + 268200 * q^78 - 1011520 * q^80 - 624816 * q^81 + 2554880 * q^82 + 536870 * q^83 - 1344920 * q^85 + 1019128 * q^86 - 763440 * q^87 - 187680 * q^88 + 947310 * q^90 + 1131548 * q^91 - 2552680 * q^92 + 444660 * q^93 + 912600 * q^95 - 568992 * q^96 - 59420 * q^97 - 1892810 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more