LMFDB - Embedded newform 80.6.q.a.29.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.15
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.03469 + 3.96501i) q^{2} +(-19.4902 + 19.4902i) q^{3} +(0.557416 - 31.9951i) q^{4} +(-49.1605 - 26.6128i) q^{5} +(1.35807 - 155.915i) q^{6} +138.003 q^{7} +(124.612 + 131.301i) q^{8} -516.733i q^{9} +O(q^{10})$	\(q+(-4.03469 + 3.96501i) q^{2} +(-19.4902 + 19.4902i) q^{3} +(0.557416 - 31.9951i) q^{4} +(-49.1605 - 26.6128i) q^{5} +(1.35807 - 155.915i) q^{6} +138.003 q^{7} +(124.612 + 131.301i) q^{8} -516.733i q^{9} +(303.867 - 87.5474i) q^{10} +(148.749 - 148.749i) q^{11} +(612.726 + 634.455i) q^{12} +(-395.811 + 395.811i) q^{13} +(-556.798 + 547.182i) q^{14} +(1476.83 - 439.458i) q^{15} +(-1023.38 - 35.6692i) q^{16} -1342.37i q^{17} +(2048.85 + 2084.86i) q^{18} +(-338.856 - 338.856i) q^{19} +(-878.884 + 1558.06i) q^{20} +(-2689.70 + 2689.70i) q^{21} +(-10.3648 + 1189.95i) q^{22} -3130.03 q^{23} +(-4987.78 - 130.361i) q^{24} +(1708.51 + 2616.60i) q^{25} +(27.5800 - 3166.37i) q^{26} +(5335.09 + 5335.09i) q^{27} +(76.9250 - 4415.42i) q^{28} +(3342.83 + 3342.83i) q^{29} +(-4216.11 + 7628.74i) q^{30} +8975.16 q^{31} +(4270.44 - 3913.79i) q^{32} +5798.30i q^{33} +(5322.50 + 5416.03i) q^{34} +(-6784.29 - 3672.65i) q^{35} +(-16532.9 - 288.035i) q^{36} +(3912.71 + 3912.71i) q^{37} +(2710.74 + 23.6114i) q^{38} -15428.8i q^{39} +(-2631.71 - 9771.08i) q^{40} +11553.2i q^{41} +(187.417 - 21516.8i) q^{42} +(9090.09 + 9090.09i) q^{43} +(-4676.34 - 4842.17i) q^{44} +(-13751.7 + 25402.8i) q^{45} +(12628.7 - 12410.6i) q^{46} -23172.4i q^{47} +(20641.0 - 19250.6i) q^{48} +2237.78 q^{49} +(-17268.2 - 3782.90i) q^{50} +(26162.9 + 26162.9i) q^{51} +(12443.4 + 12884.7i) q^{52} +(-4387.18 - 4387.18i) q^{53} +(-42679.1 - 371.748i) q^{54} +(-11271.2 + 3353.95i) q^{55} +(17196.8 + 18119.9i) q^{56} +13208.7 q^{57} +(-26741.6 - 232.927i) q^{58} +(10109.8 - 10109.8i) q^{59} +(-13237.3 - 47496.5i) q^{60} +(-7489.74 - 7489.74i) q^{61} +(-36212.0 + 35586.6i) q^{62} -71310.6i q^{63} +(-1711.69 + 32723.3i) q^{64} +(29991.9 - 8924.63i) q^{65} +(-22990.3 - 23394.3i) q^{66} +(-41365.5 + 41365.5i) q^{67} +(-42949.2 - 748.257i) q^{68} +(61004.7 - 61004.7i) q^{69} +(41934.6 - 12081.8i) q^{70} +25331.5i q^{71} +(67847.3 - 64391.1i) q^{72} +71908.6 q^{73} +(-31300.5 - 272.637i) q^{74} +(-84297.2 - 17698.8i) q^{75} +(-11030.6 + 10652.9i) q^{76} +(20527.8 - 20527.8i) q^{77} +(61175.5 + 62250.6i) q^{78} +83505.6 q^{79} +(49360.6 + 28988.5i) q^{80} -82397.6 q^{81} +(-45808.4 - 46613.4i) q^{82} +(57163.1 - 57163.1i) q^{83} +(84558.0 + 87556.5i) q^{84} +(-35724.2 + 65991.5i) q^{85} +(-72718.0 - 633.395i) q^{86} -130305. q^{87} +(38066.8 + 994.921i) q^{88} -48501.3i q^{89} +(-45238.6 - 157018. i) q^{90} +(-54623.1 + 54623.1i) q^{91} +(-1744.73 + 100146. i) q^{92} +(-174927. + 174927. i) q^{93} +(91878.6 + 93493.2i) q^{94} +(7640.41 + 25676.2i) q^{95} +(-6951.20 + 159512. i) q^{96} +85142.5i q^{97} +(-9028.73 + 8872.80i) q^{98} +(-76863.6 - 76863.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−4.03469	+	3.96501i	−0.713239	+	0.700921i
$2$	−4.03469	+	3.96501i	−0.713239	+	0.700921i
$3$	−19.4902	+	19.4902i	−1.25029	+	1.25029i	−0.294707	+	0.955588i	$0.595222\pi$
$3$	−19.4902	+	19.4902i	−1.25029	+	1.25029i	−0.955588	+	0.294707i	$0.904778\pi$
$4$	0.557416	−	31.9951i	0.0174193	−	0.999848i
$5$	−49.1605	−	26.6128i	−0.879410	−	0.476065i
$5$	−49.1605	−	26.6128i	−0.879410	−	0.476065i
$6$	1.35807	−	155.915i	0.0154008	−	1.76812i
$7$	138.003			1.06449			0.532247	−	0.846589i	$-0.321348\pi$
$7$	138.003			1.06449			0.532247	+	0.846589i	$0.321348\pi$
$8$	124.612	+	131.301i	0.688391	+	0.725340i
$9$		−	516.733i		−	2.12647i
$10$	303.867	−	87.5474i	0.960913	−	0.276849i
$11$	148.749	−	148.749i	0.370658	−	0.370658i	−0.497059	−	0.867717i	$-0.665587\pi$
$11$	148.749	−	148.749i	0.370658	−	0.370658i	0.867717	+	0.497059i	$0.165587\pi$
$12$	612.726	+	634.455i	1.22833	+	1.27188i
$13$	−395.811	+	395.811i	−0.649576	+	0.649576i	−0.952890	−	0.303315i	$-0.901907\pi$
$13$	−395.811	+	395.811i	−0.649576	+	0.649576i	0.303315	+	0.952890i	$0.401907\pi$
$14$	−556.798	+	547.182i	−0.759238	+	0.746126i
$15$	1476.83	−	439.458i	1.69474	−	0.504300i
$16$	−1023.38	−	35.6692i	−0.999393	−	0.0348332i
$17$		−	1342.37i		−	1.12655i	−0.826271	−	0.563273i	$-0.809542\pi$
$17$		−	1342.37i		−	1.12655i	0.826271	−	0.563273i	$-0.190458\pi$
$18$	2048.85	+	2084.86i	1.49049	+	1.51668i
$19$	−338.856	−	338.856i	−0.215343	−	0.215343i	0.591190	−	0.806533i	$-0.298659\pi$
$19$	−338.856	−	338.856i	−0.215343	−	0.215343i	−0.806533	+	0.591190i	$0.798659\pi$
$20$	−878.884	+	1558.06i	−0.491311	+	0.870984i
$21$	−2689.70	+	2689.70i	−1.33093	+	1.33093i
$22$	−10.3648	+	1189.95i	−0.00456567	+	0.524170i
$23$	−3130.03			−1.23375			−0.616877	−	0.787060i	$-0.711602\pi$
$23$	−3130.03			−1.23375			−0.616877	+	0.787060i	$0.711602\pi$
$24$	−4987.78	−	130.361i	−1.76758	−	0.0461977i
$25$	1708.51	+	2616.60i	0.546724	+	0.837313i
$26$	27.5800	−	3166.37i	0.00800131	−	0.918604i
$27$	5335.09	+	5335.09i	1.40842	+	1.40842i
$28$	76.9250	−	4415.42i	0.0185427	−	1.06433i
$29$	3342.83	+	3342.83i	0.738107	+	0.738107i	0.972211	−	0.234104i	$-0.0752157\pi$
$29$	3342.83	+	3342.83i	0.738107	+	0.738107i	−0.234104	+	0.972211i	$0.575216\pi$
$30$	−4216.11	+	7628.74i	−0.855282	+	1.54757i
$31$	8975.16			1.67741			0.838703	−	0.544589i	$-0.183314\pi$
$31$	8975.16			1.67741			0.838703	+	0.544589i	$0.183314\pi$
$32$	4270.44	−	3913.79i	0.737221	−	0.675651i
$33$			5798.30i			0.926863i
$34$	5322.50	+	5416.03i	0.789620	+	0.803496i
$35$	−6784.29	−	3672.65i	−0.936126	−	0.506768i
$36$	−16532.9	−	288.035i	−2.12615	−	0.0370416i
$37$	3912.71	+	3912.71i	0.469866	+	0.469866i	0.901871	−	0.432005i	$-0.142194\pi$
$37$	3912.71	+	3912.71i	0.469866	+	0.469866i	−0.432005	+	0.901871i	$0.642194\pi$
$38$	2710.74	+	23.6114i	0.304530	+	0.00265254i
$39$		−	15428.8i		−	1.62432i
$40$	−2631.71	−	9771.08i	−0.260069	−	0.965590i
$41$			11553.2i			1.07335i	0.843789	+	0.536675i	$0.180320\pi$
$41$			11553.2i			1.07335i	−0.843789	+	0.536675i	$0.819680\pi$
$42$	187.417	−	21516.8i	0.0163941	−	1.88215i
$43$	9090.09	+	9090.09i	0.749717	+	0.749717i	0.974426	−	0.224709i	$-0.0721432\pi$
$43$	9090.09	+	9090.09i	0.749717	+	0.749717i	−0.224709	+	0.974426i	$0.572143\pi$
$44$	−4676.34	−	4842.17i	−0.364145	−	0.377058i
$45$	−13751.7	+	25402.8i	−1.01234	+	1.87004i
$46$	12628.7	−	12410.6i	0.879961	−	0.864764i
$47$		−	23172.4i		−	1.53012i	−0.643959	−	0.765060i	$-0.722709\pi$
$47$		−	23172.4i		−	1.53012i	0.643959	−	0.765060i	$-0.277291\pi$
$48$	20641.0	−	19250.6i	1.29309	−	1.20598i
$49$	2237.78			0.133146
$50$	−17268.2	−	3782.90i	−0.976835	−	0.213993i
$51$	26162.9	+	26162.9i	1.40851	+	1.40851i
$52$	12443.4	+	12884.7i	0.638162	+	0.660792i
$53$	−4387.18	−	4387.18i	−0.214534	−	0.214534i	0.591657	−	0.806190i	$-0.298474\pi$
$53$	−4387.18	−	4387.18i	−0.214534	−	0.214534i	−0.806190	+	0.591657i	$0.798474\pi$
$54$	−42679.1	−	371.748i	−1.99173	−	0.0173486i
$55$	−11271.2	+	3353.95i	−0.502418	+	0.149503i
$56$	17196.8	+	18119.9i	0.732787	+	0.772120i
$57$	13208.7			0.538484
$58$	−26741.6	−	232.927i	−1.04380	−	0.00909182i
$59$	10109.8	−	10109.8i	0.378105	−	0.378105i	−0.492313	−	0.870418i	$-0.663849\pi$
$59$	10109.8	−	10109.8i	0.378105	−	0.378105i	0.870418	+	0.492313i	$0.163849\pi$
$60$	−13237.3	−	47496.5i	−0.474703	−	1.70327i
$61$	−7489.74	−	7489.74i	−0.257716	−	0.257716i	0.566408	−	0.824125i	$-0.308333\pi$
$61$	−7489.74	−	7489.74i	−0.257716	−	0.257716i	−0.824125	+	0.566408i	$0.808333\pi$
$62$	−36212.0	+	35586.6i	−1.19639	+	1.17573i
$63$		−	71310.6i		−	2.26361i
$64$	−1711.69	+	32723.3i	−0.0522366	+	0.998635i
$65$	29991.9	−	8924.63i	0.880483	−	0.262003i
$66$	−22990.3	−	23394.3i	−0.649658	−	0.661075i
$67$	−41365.5	+	41365.5i	−1.12577	+	1.12577i	−0.134916	+	0.990857i	$0.543077\pi$
$67$	−41365.5	+	41365.5i	−1.12577	+	1.12577i	−0.990857	+	0.134916i	$0.956923\pi$
$68$	−42949.2	−	748.257i	−1.12637	−	0.0196236i
$69$	61004.7	−	61004.7i	1.54255	−	1.54255i
$70$	41934.6	−	12081.8i	1.02289	−	0.294704i
$71$			25331.5i			0.596369i	0.954508	+	0.298185i	$0.0963811\pi$
$71$			25331.5i			0.596369i	−0.954508	+	0.298185i	$0.903619\pi$
$72$	67847.3	−	64391.1i	1.54242	−	1.46384i
$73$	71908.6			1.57933			0.789666	−	0.613537i	$-0.210254\pi$
$73$	71908.6			1.57933			0.789666	+	0.613537i	$0.210254\pi$
$74$	−31300.5	−	272.637i	−0.664465	−	0.00578768i
$75$	−84297.2	−	17698.8i	−1.73045	−	0.363321i
$76$	−11030.6	+	10652.9i	−0.219061	+	0.211559i
$77$	20527.8	−	20527.8i	0.394563	−	0.394563i
$78$	61175.5	+	62250.6i	1.13852	+	1.15853i
$79$	83505.6			1.50539			0.752693	−	0.658371i	$-0.228754\pi$
$79$	83505.6			1.50539			0.752693	+	0.658371i	$0.228754\pi$
$80$	49360.6	+	28988.5i	0.862294	+	0.506409i
$81$	−82397.6			−1.39541
$82$	−45808.4	−	46613.4i	−0.752334	−	0.765555i
$83$	57163.1	−	57163.1i	0.910795	−	0.910795i	−0.0855399	−	0.996335i	$-0.527262\pi$
$83$	57163.1	−	57163.1i	0.910795	−	0.910795i	0.996335	+	0.0855399i	$0.0272615\pi$
$84$	84558.0	+	87556.5i	1.30754	+	1.35391i
$85$	−35724.2	+	65991.5i	−0.536309	+	0.990696i
$86$	−72718.0	−	633.395i	−1.06022	−	0.00923482i
$87$	−130305.			−1.84570
$88$	38066.8	+	994.921i	0.524010	+	0.0136956i
$89$		−	48501.3i		−	0.649051i	−0.945877	−	0.324525i	$-0.894795\pi$
$89$		−	48501.3i		−	0.649051i	0.945877	−	0.324525i	$-0.105205\pi$
$90$	−45238.6	−	157018.i	−0.588712	−	2.04336i
$91$	−54623.1	+	54623.1i	−0.691469	+	0.691469i
$92$	−1744.73	+	100146.i	−0.0214911	+	1.23357i
$93$	−174927.	+	174927.i	−2.09725	+	2.09725i
$94$	91878.6	+	93493.2i	1.07249	+	1.09134i
$95$	7640.41	+	25676.2i	0.0868576	+	0.291892i
$96$	−6951.20	+	159512.i	−0.0769807	+	1.76651i
$97$			85142.5i			0.918791i	0.888232	+	0.459396i	$0.151934\pi$
$97$			85142.5i			0.918791i	−0.888232	+	0.459396i	$0.848066\pi$
$98$	−9028.73	+	8872.80i	−0.0949645	+	0.0933245i
$99$	−76863.6	−	76863.6i	−0.788194	−	0.788194i
$100$	84670.9	−	53205.6i	0.846709	−	0.532056i
$101$	−30049.1	+	30049.1i	−0.293108	+	0.293108i	−0.838307	−	0.545199i	$-0.816454\pi$
$101$	−30049.1	+	30049.1i	−0.293108	+	0.293108i	0.545199	+	0.838307i	$0.316454\pi$
$102$	−209296.	−	1823.03i	−1.99186	−	0.0173497i
$103$	187982.			1.74591			0.872956	−	0.487799i	$-0.162200\pi$
$103$	187982.			1.74591			0.872956	+	0.487799i	$0.162200\pi$
$104$	−101293.	−	2647.41i	−0.918325	−	0.0240015i
$105$	203807.	−	60646.4i	1.80404	−	0.536824i
$106$	35096.1	+	305.697i	0.303385	+	0.00264257i
$107$	84721.0	+	84721.0i	0.715371	+	0.715371i	0.967654	−	0.252282i	$-0.0811811\pi$
$107$	84721.0	+	84721.0i	0.715371	+	0.715371i	−0.252282	+	0.967654i	$0.581181\pi$
$108$	173671.	−	167723.i	1.43274	−	1.38367i
$109$	−27406.1	−	27406.1i	−0.220943	−	0.220943i	0.587952	−	0.808896i	$-0.299934\pi$
$109$	−27406.1	−	27406.1i	−0.220943	−	0.220943i	−0.808896	+	0.587952i	$0.799934\pi$
$110$	32177.5	−	58222.7i	0.253554	−	0.458786i
$111$	−152519.			−1.17494
$112$	−141229.	−	4922.45i	−1.06385	−	0.0370797i
$113$			41936.1i			0.308952i	0.987997	+	0.154476i	$0.0493690\pi$
$113$			41936.1i			0.308952i	−0.987997	+	0.154476i	$0.950631\pi$
$114$	−53293.0	+	52372.6i	−0.384068	+	0.377435i
$115$	153874.	+	83298.9i	1.08498	+	0.587347i
$116$	108818.	−	105091.i	0.750853	−	0.725138i
$117$	204529.	+	204529.i	1.38130	+	1.38130i
$118$	−704.448	+	80875.3i	−0.00465740	+	0.534701i
$119$		−	185250.i		−	1.19920i
$120$	241732.	+	139148.i	1.53243	+	0.882109i
$121$			116798.i			0.725225i
$122$	59915.6	+	521.883i	0.364452	+	0.00317449i
$123$	−225173.	−	225173.i	−1.34200	−	1.34200i
$124$	5002.90	−	287162.i	0.0292192	−	1.67715i
$125$	−14356.2	−	174102.i	−0.0821799	−	0.996618i
$126$	282747.	+	287716.i	1.58662	+	1.61450i
$127$		−	169532.i		−	0.932699i	−0.884601	−	0.466350i	$-0.845569\pi$
$127$		−	169532.i		−	0.932699i	0.884601	−	0.466350i	$-0.154431\pi$
$128$	−122842.	−	138815.i	−0.662707	−	0.748879i
$129$	−354335.			−1.87473
$130$	−85621.9	+	154926.i	−0.444351	+	0.804020i
$131$	−23331.2	−	23331.2i	−0.118784	−	0.118784i	0.645216	−	0.764000i	$-0.276767\pi$
$131$	−23331.2	−	23331.2i	−0.118784	−	0.118784i	−0.764000	+	0.645216i	$0.776767\pi$
$132$	185517.	+	3232.06i	0.926722	+	0.0161453i
$133$	−46763.0	−	46763.0i	−0.229231	−	0.229231i
$134$	2882.33	−	330911.i	0.0138670	−	1.59202i
$135$	−120294.	−	404258.i	−0.568080	−	1.90908i
$136$	176254.	−	167275.i	0.817129	−	0.775504i
$137$	−194267.			−0.884294			−0.442147	−	0.896943i	$-0.645783\pi$
$137$	−194267.			−0.884294			−0.442147	+	0.896943i	$0.645783\pi$
$138$	−4250.79	+	488019.i	−0.0190008	+	2.18142i
$139$	75878.8	−	75878.8i	0.333107	−	0.333107i	−0.520658	−	0.853765i	$-0.674313\pi$
$139$	75878.8	−	75878.8i	0.333107	−	0.333107i	0.853765	+	0.520658i	$0.174313\pi$
$140$	−121289.	+	215017.i	−0.522998	+	0.927156i
$141$	451633.	+	451633.i	1.91310	+	1.91310i
$142$	−100440.	−	102205.i	−0.418008	−	0.425354i
$143$			117753.i			0.481541i
$144$	−18431.5	+	528813.i	−0.0740719	+	2.12518i
$145$	−75373.1	−	253298.i	−0.297712	−	1.00049i
$146$	−290129.	+	285118.i	−1.12644	+	1.10699i
$147$	−43614.6	+	43614.6i	−0.166471	+	0.166471i
$148$	127369.	−	123007.i	0.477979	−	0.461610i
$149$	−89405.9	+	89405.9i	−0.329914	+	0.329914i	−0.852554	−	0.522640i	$-0.824947\pi$
$149$	−89405.9	+	89405.9i	−0.329914	+	0.329914i	0.522640	+	0.852554i	$0.324947\pi$
$150$	410289.	−	262830.i	1.48889	−	0.953777i
$151$		−	55419.6i		−	0.197798i	−0.995097	−	0.0988988i	$-0.968468\pi$
$151$		−	55419.6i		−	0.197798i	0.995097	−	0.0988988i	$-0.0315320\pi$
$152$	2266.46	−	86717.5i	0.00795682	−	0.304437i
$153$	−693645.			−2.39557
$154$	−1430.37	+	164216.i	−0.00486012	+	0.557975i
$155$	−441224.	−	238855.i	−1.47513	−	0.798554i
$156$	−493648.	−	8600.29i	−1.62407	−	0.0282945i
$157$	352916.	−	352916.i	1.14267	−	1.14267i	0.154713	−	0.987959i	$-0.450555\pi$
$157$	352916.	−	352916.i	1.14267	−	1.14267i	0.987959	−	0.154713i	$-0.0494453\pi$
$158$	−336919.	+	331101.i	−1.07370	+	1.05516i
$159$	171013.			0.536460
$160$	−314094.	+	78755.4i	−0.969974	+	0.243209i
$161$	−431952.			−1.31332
$162$	332449.	−	326707.i	0.995261	−	0.978073i
$163$	308778.	−	308778.i	0.910286	−	0.910286i	−0.0860087	−	0.996294i	$-0.527411\pi$
$163$	308778.	−	308778.i	0.910286	−	0.910286i	0.996294	+	0.0860087i	$0.0274113\pi$
$164$	369645.	+	6439.93i	1.07319	+	0.0186970i
$165$	154309.	−	285047.i	0.441247	−	0.815093i
$166$	−3983.11	+	457287.i	−0.0112189	+	1.28801i
$167$	437490.			1.21388			0.606942	−	0.794746i	$-0.292396\pi$
$167$	437490.			1.21388			0.606942	+	0.794746i	$0.292396\pi$
$168$	−688327.	−	17990.2i	−1.88158	−	0.0491772i
$169$			57960.0i			0.156103i
$170$	−117521.	−	407902.i	−0.311883	−	1.08251i
$171$	−175098.	+	175098.i	−0.457921	+	0.457921i
$172$	295906.	−	285772.i	0.762663	−	0.736544i
$173$	11958.9	−	11958.9i	0.0303791	−	0.0303791i	−0.691754	−	0.722133i	$-0.743162\pi$
$173$	11958.9	−	11958.9i	0.0303791	−	0.0303791i	0.722133	+	0.691754i	$0.243162\pi$
$174$	525739.	−	516659.i	1.31643	−	1.29369i
$175$	235780.	+	361098.i	0.581984	+	0.891313i
$176$	−157533.	+	146921.i	−0.383344	+	0.357522i
$177$			394083.i			0.945485i
$178$	192308.	+	195688.i	0.454933	+	0.462928i
$179$	137059.	+	137059.i	0.319723	+	0.319723i	0.848661	−	0.528938i	$-0.177410\pi$
$179$	137059.	+	137059.i	0.319723	+	0.319723i	−0.528938	+	0.848661i	$0.677410\pi$
$180$	805102.	+	454148.i	1.85212	+	1.04476i
$181$	81282.8	−	81282.8i	0.184418	−	0.184418i	−0.608860	−	0.793278i	$-0.708373\pi$
$181$	81282.8	−	81282.8i	0.184418	−	0.184418i	0.793278	+	0.608860i	$0.208373\pi$
$182$	3806.12	−	436968.i	0.00851734	−	0.977847i
$183$	291952.			0.644443
$184$	−390039.	−	410974.i	−0.849304	−	0.894891i
$185$	−88222.6	−	296479.i	−0.189518	−	0.636891i
$186$	12188.9	−	1.39937e6i	0.0258334	−	2.96585i
$187$	−199676.	−	199676.i	−0.417563	−	0.417563i
$188$	−741403.	−	12916.6i	−1.52989	−	0.0266536i
$189$	736258.	+	736258.i	1.49925	+	1.49925i
$190$	−132633.	−	73301.3i	−0.266544	−	0.147308i
$191$	260451.			0.516586			0.258293	−	0.966067i	$-0.416840\pi$
$191$	260451.			0.516586			0.258293	+	0.966067i	$0.416840\pi$
$192$	−604421.	−	671143.i	−1.18328	−	1.31390i
$193$			193276.i			0.373495i	0.982408	+	0.186747i	$0.0597946\pi$
$193$			193276.i			0.373495i	−0.982408	+	0.186747i	$0.940205\pi$
$194$	−337591.	−	343523.i	−0.644000	−	0.655318i
$195$	−410605.	+	758490.i	−0.773282	+	1.42844i
$196$	1247.37	−	71598.0i	0.00231930	−	0.133125i
$197$	426655.	+	426655.i	0.783270	+	0.783270i	0.980381	−	0.197111i	$-0.0631560\pi$
$197$	426655.	+	426655.i	0.783270	+	0.783270i	−0.197111	+	0.980381i	$0.563156\pi$
$198$	614886.	+	5355.83i	1.11463	+	0.00970877i
$199$			175233.i			0.313678i	0.987624	+	0.156839i	$0.0501303\pi$
$199$			175233.i			0.313678i	−0.987624	+	0.156839i	$0.949870\pi$
$200$	−130660.	+	550389.i	−0.230976	+	0.972959i
$201$		−	1.61244e6i		−	2.81510i
$202$	2093.81	−	240383.i	0.00361043	−	0.414501i
$203$	461320.	+	461320.i	0.785710	+	0.785710i
$204$	851671.	−	822503.i	1.43284	−	1.38376i
$205$	307463.	−	567960.i	0.510984	−	0.943915i
$206$	−758447.	+	745349.i	−1.24525	+	1.22375i
$207$			1.61739e6i			2.62354i
$208$	419183.	−	390946.i	0.671808	−	0.626555i
$209$	−100809.			−0.159637
$210$	−581836.	+	1.05279e6i	−0.910441	+	1.64737i
$211$	290980.	+	290980.i	0.449942	+	0.449942i	0.895335	−	0.445393i	$-0.146936\pi$
$211$	290980.	+	290980.i	0.449942	+	0.449942i	−0.445393	+	0.895335i	$0.646936\pi$
$212$	−142814.	+	137923.i	−0.218238	+	0.210764i
$213$	−493715.	−	493715.i	−0.745637	−	0.745637i
$214$	−677742.	−	5903.33i	−1.01165	−	0.00881176i
$215$	−204961.	−	688787.i	−0.302395	−	1.01622i
$216$	−35684.2	+	1.36532e6i	−0.0520405	+	1.99113i
$217$	1.23860e6			1.78559
$218$	219240.	+	1909.65i	0.312449	+	0.00272152i
$219$	−1.40151e6	+	1.40151e6i	−1.97463	+	1.97463i
$220$	101027.	+	362494.i	0.140729	+	0.504946i
$221$	531324.	+	531324.i	0.731777	+	0.731777i
$222$	615366.	−	604738.i	0.838013	−	0.823541i
$223$		−	278222.i		−	0.374653i	−0.982298	−	0.187326i	$-0.940018\pi$
$223$		−	278222.i		−	0.374653i	0.982298	−	0.187326i	$-0.0599822\pi$
$224$	589333.	−	540114.i	0.784767	−	0.719226i
$225$	1.35208e6	−	882845.i	1.78052	−	1.16259i
$226$	−166277.	−	169199.i	−0.216551	−	0.220357i
$227$	−416592.	+	416592.i	−0.536594	+	0.536594i	−0.922527	−	0.385933i	$-0.873880\pi$
$227$	−416592.	+	416592.i	−0.536594	+	0.536594i	0.385933	+	0.922527i	$0.373880\pi$
$228$	7362.75	−	422614.i	0.00938000	−	0.538403i
$229$	480894.	−	480894.i	0.605983	−	0.605983i	−0.335911	−	0.941894i	$-0.609044\pi$
$229$	480894.	−	480894.i	0.605983	−	0.605983i	0.941894	+	0.335911i	$0.109044\pi$
$230$	−951113.	+	274026.i	−1.18553	+	0.341564i
$231$			800181.i			0.986639i
$232$	−22358.8	+	855473.i	−0.0272727	+	1.04348i
$233$	−475884.			−0.574264			−0.287132	−	0.957891i	$-0.592702\pi$
$233$	−475884.			−0.574264			−0.287132	+	0.957891i	$0.592702\pi$
$234$	−1.63617e6	−	14251.5i	−1.95338	−	0.0170146i
$235$	−616682.	+	1.13917e6i	−0.728436	+	1.34560i
$236$	−317829.	−	329100.i	−0.371461	−	0.384634i
$237$	−1.62754e6	+	1.62754e6i	−1.88218	+	1.88218i
$238$	734519.	+	747428.i	0.840545	+	0.855316i
$239$	187684.			0.212536			0.106268	−	0.994338i	$-0.466110\pi$
$239$	187684.			0.212536			0.106268	+	0.994338i	$0.466110\pi$
$240$	−1.52704e6	+	397054.i	−1.71128	+	0.444961i
$241$	−1.52222e6			−1.68825			−0.844123	−	0.536149i	$-0.819878\pi$
$241$	−1.52222e6			−1.68825			−0.844123	+	0.536149i	$0.819878\pi$
$242$	−463106.	−	471245.i	−0.508326	−	0.517259i
$243$	309515.	−	309515.i	0.336253	−	0.336253i
$244$	−243810.	+	235460.i	−0.262167	+	0.253188i
$245$	−110010.	−	59553.6i	−0.117090	−	0.0633859i
$246$	1.80132e6	+	15690.0i	1.89781	+	0.0165305i
$247$	268246.			0.279763
$248$	1.11841e6	+	1.17844e6i	1.15471	+	1.21669i
$249$			2.22824e6i			2.27752i
$250$	748239.	+	645524.i	0.757164	+	0.653225i
$251$	1.30956e6	−	1.30956e6i	1.31202	−	1.31202i	0.392092	−	0.919926i	$-0.371752\pi$
$251$	1.30956e6	−	1.30956e6i	1.31202	−	1.31202i	0.919926	−	0.392092i	$-0.128248\pi$
$252$	−2.28159e6	−	39749.7i	−2.26327	−	0.0394305i
$253$	−465589.	+	465589.i	−0.457300	+	0.457300i
$254$	672194.	+	684007.i	0.653748	+	0.665237i
$255$	−589914.	−	1.98245e6i	−0.568117	−	1.90921i
$256$	1.04603e6	+	73006.3i	0.997573	+	0.0696242i
$257$		−	1.63033e6i		−	1.53973i	−0.638210	−	0.769863i	$-0.720325\pi$
$257$		−	1.63033e6i		−	1.53973i	0.638210	−	0.769863i	$-0.279675\pi$
$258$	1.42963e6	−	1.40494e6i	1.33713	−	1.31404i
$259$	539965.	+	539965.i	0.500169	+	0.500169i
$260$	−268827.	−	964571.i	−0.246626	−	0.884914i
$261$	1.72735e6	−	1.72735e6i	1.56956	−	1.56956i
$262$	186643.	+	1625.71i	0.167980	+	0.00146316i
$263$	229574.			0.204660			0.102330	−	0.994751i	$-0.467370\pi$
$263$	229574.			0.204660			0.102330	+	0.994751i	$0.467370\pi$
$264$	−761320.	+	722537.i	−0.672291	+	0.638044i
$265$	98920.6	+	332431.i	0.0865311	+	0.290795i
$266$	374090.	+	3258.43i	0.324170	+	0.00282361i
$267$	945299.	+	945299.i	0.811505	+	0.811505i
$268$	1.30044e6	+	1.34655e6i	1.10599	+	1.14521i
$269$	−661431.	−	661431.i	−0.557319	−	0.557319i	0.371224	−	0.928543i	$-0.378938\pi$
$269$	−661431.	−	661431.i	−0.557319	−	0.557319i	−0.928543	+	0.371224i	$0.878938\pi$
$270$	2.08823e6	+	1.15409e6i	1.74329	+	0.963451i
$271$	−100315.			−0.0829741			−0.0414871	−	0.999139i	$-0.513210\pi$
$271$	−100315.			−0.0829741			−0.0414871	+	0.999139i	$0.513210\pi$
$272$	−47881.2	+	1.37375e6i	−0.0392412	+	1.12586i
$273$		−	2.12922e6i		−	1.72908i
$274$	783805.	−	770269.i	0.630713	−	0.619821i
$275$	643358.	+	135077.i	0.513004	+	0.107709i
$276$	−1.91785e6	−	1.98586e6i	−1.51545	−	1.56919i
$277$	−1.50934e6	−	1.50934e6i	−1.18192	−	1.18192i	−0.979246	−	0.202674i	$-0.935037\pi$
$277$	−1.50934e6	−	1.50934e6i	−1.18192	−	1.18192i	−0.202674	−	0.979246i	$-0.564963\pi$
$278$	−5287.21	+	607007.i	−0.00410312	+	0.471066i
$279$		−	4.63776e6i		−	3.56696i
$280$	−363183.	−	1.34844e6i	−0.276841	−	1.02786i
$281$			258255.i			0.195111i	0.995230	+	0.0975557i	$0.0311024\pi$
$281$			258255.i			0.195111i	−0.995230	+	0.0975557i	$0.968898\pi$
$282$	−3.61293e6	−	31469.6i	−2.70543	−	0.0235651i
$283$	507241.	+	507241.i	0.376485	+	0.376485i	0.869832	−	0.493347i	$-0.164227\pi$
$283$	507241.	+	507241.i	0.376485	+	0.376485i	−0.493347	+	0.869832i	$0.664227\pi$
$284$	810486.	+	14120.2i	0.596279	+	0.0103883i
$285$	−649347.	−	351521.i	−0.473549	−	0.256354i
$286$	−466893.	−	475098.i	−0.337522	−	0.343453i
$287$			1.59437e6i			1.14257i
$288$	−2.02238e6	−	2.20668e6i	−1.43675	−	1.56768i
$289$	−382091.			−0.269106
$290$	1.30843e6	+	723122.i	0.913602	+	0.504913i
$291$	−1.65944e6	−	1.65944e6i	−1.14876	−	1.14876i
$292$	40083.0	−	2.30072e6i	0.0275108	−	1.57909i
$293$	−171442.	−	171442.i	−0.116667	−	0.116667i	0.646363	−	0.763030i	$-0.276289\pi$
$293$	−171442.	−	171442.i	−0.116667	−	0.116667i	−0.763030	+	0.646363i	$0.776289\pi$
$294$	3039.05	−	348904.i	0.00205055	−	0.235417i
$295$	−766053.	+	227953.i	−0.512512	+	0.152507i
$296$	−26170.5	+	1.00131e6i	−0.0173613	+	0.664263i
$297$	1.58718e6			1.04408
$298$	6229.78	−	715220.i	0.00406380	−	0.466551i
$299$	1.23890e6	−	1.23890e6i	0.801416	−	0.801416i
$300$	−613264.	+	2.68724e6i	−0.393409	+	1.72386i
$301$	1.25446e6	+	1.25446e6i	0.798068	+	0.798068i
$302$	219739.	+	223601.i	0.138641	+	0.141077i
$303$		−	1.17132e6i		−	0.732942i
$304$	334691.	+	358864.i	0.207711	+	0.222713i
$305$	168876.	+	567523.i	0.103949	+	0.349328i
$306$	2.79864e6	−	2.75031e6i	1.70861	−	1.67910i
$307$	−1.20853e6	+	1.20853e6i	−0.731830	+	0.731830i	−0.970982	−	0.239152i	$-0.923131\pi$
$307$	−1.20853e6	+	1.20853e6i	−0.731830	+	0.731830i	0.239152	+	0.970982i	$0.423131\pi$
$308$	−645348.	−	668233.i	−0.387630	−	0.401376i
$309$	−3.66379e6	+	3.66379e6i	−2.18290	+	2.18290i
$310$	2.72726e6	−	785752.i	1.61184	−	0.464388i
$311$			2.01801e6i			1.18310i	0.806268	+	0.591550i	$0.201484\pi$
$311$			2.01801e6i			1.18310i	−0.806268	+	0.591550i	$0.798516\pi$
$312$	2.02582e6	−	1.92262e6i	1.17819	−	1.11817i
$313$	2.49523e6			1.43962			0.719812	−	0.694169i	$-0.244228\pi$
$313$	2.49523e6			1.43962			0.719812	+	0.694169i	$0.244228\pi$
$314$	−24591.1	+	2.82322e6i	−0.0140752	+	1.61592i
$315$	−1.89778e6	+	3.50566e6i	−1.07763	+	1.99065i
$316$	46547.4	−	2.67177e6i	0.0262227	−	1.50516i
$317$	−523934.	+	523934.i	−0.292839	+	0.292839i	−0.838201	−	0.545362i	$-0.816392\pi$
$317$	−523934.	+	523934.i	−0.292839	+	0.292839i	0.545362	+	0.838201i	$0.316392\pi$
$318$	−689986.	+	678070.i	−0.382624	+	0.376016i
$319$	994488.			0.547171
$320$	955006.	−	1.56314e6i	0.521352	−	0.853341i
$321$	−3.30245e6			−1.78885
$322$	1.74279e6	−	1.71269e6i	0.936712	−	0.920535i
$323$	−454869.	+	454869.i	−0.242594	+	0.242594i
$324$	−45929.8	+	2.63632e6i	−0.0243070	+	1.39520i
$325$	−1.71193e6	−	359431.i	−0.899037	−	0.188759i
$326$	−21515.6	+	2.47013e6i	−0.0112127	+	1.28729i
$327$	1.06830e6			0.552488
$328$	−1.51694e6	+	1.43966e6i	−0.778544	+	0.738884i
$329$		−	3.19785e6i		−	1.62880i
$330$	507626.	+	1.76191e6i	0.256601	+	0.890635i
$331$	551718.	−	551718.i	0.276788	−	0.276788i	−0.555038	−	0.831825i	$-0.687296\pi$
$331$	551718.	−	551718.i	0.276788	−	0.276788i	0.831825	+	0.555038i	$0.187296\pi$
$332$	−1.79708e6	−	1.86081e6i	−0.894791	−	0.926522i
$333$	2.02183e6	−	2.02183e6i	0.999156	−	0.999156i
$334$	−1.76514e6	+	1.73465e6i	−0.865789	+	0.850837i
$335$	3.13440e6	−	932696.i	1.52596	−	0.454075i
$336$	2.84852e6	−	2.65664e6i	1.37648	−	1.28376i
$337$			1.93506e6i			0.928152i	0.885795	+	0.464076i	$0.153614\pi$
$337$			1.93506e6i			0.928152i	−0.885795	+	0.464076i	$0.846386\pi$
$338$	−229812.	−	233851.i	−0.109416	−	0.111339i
$339$	−817340.	−	817340.i	−0.386281	−	0.386281i
$340$	2.09149e6	+	1.17979e6i	0.981203	+	0.553485i
$341$	1.33505e6	−	1.33505e6i	0.621744	−	0.621744i
$342$	12200.8	−	1.40073e6i	0.00564055	−	0.647573i
$343$	−2.01059e6			−0.922761
$344$	−60799.8	+	2.32627e6i	−0.0277017	+	1.05990i
$345$	−4.62253e6	+	1.37552e6i	−2.09089	+	0.622182i
$346$	−833.290	+	95667.2i	−0.000374202	+	0.0429609i
$347$	9351.62	+	9351.62i	0.00416930	+	0.00416930i	0.709188	−	0.705019i	$-0.249062\pi$
$347$	9351.62	+	9351.62i	0.00416930	+	0.00416930i	−0.705019	+	0.709188i	$0.749062\pi$
$348$	−72633.9	+	4.16912e6i	−0.0321508	+	1.84542i
$349$	−1.06874e6	−	1.06874e6i	−0.469687	−	0.469687i	0.432126	−	0.901813i	$-0.357764\pi$
$349$	−1.06874e6	−	1.06874e6i	−0.469687	−	0.469687i	−0.901813	+	0.432126i	$0.857764\pi$
$350$	−2.38306e6	−	522051.i	−1.03983	−	0.227794i
$351$	−4.22338e6			−1.82975
$352$	53051.7	−	1.21740e6i	0.0228214	−	0.523692i
$353$			2.37666e6i			1.01515i	0.861608	+	0.507574i	$0.169458\pi$
$353$			2.37666e6i			1.01515i	−0.861608	+	0.507574i	$0.830542\pi$
$354$	−1.56254e6	−	1.59000e6i	−0.662710	−	0.674357i
$355$	674144.	−	1.24531e6i	0.283911	−	0.524453i
$356$	−1.55181e6	−	27035.4i	−0.648952	−	0.0113060i
$357$	3.61056e6	+	3.61056e6i	1.49935	+	1.49935i
$358$	−1.09643e6	−	9550.20i	−0.452139	−	0.00393826i
$359$		−	1.02902e6i		−	0.421391i	−0.977552	−	0.210696i	$-0.932427\pi$
$359$		−	1.02902e6i		−	0.421391i	0.977552	−	0.210696i	$-0.0675729\pi$
$360$	−5.04904e6	+	1.35989e6i	−2.05330	+	0.553029i
$361$		−	2.24645e6i		−	0.907255i
$362$	−5663.76	+	650238.i	−0.00227161	+	0.260796i
$363$	−2.27642e6	−	2.27642e6i	−0.906745	−	0.906745i
$364$	1.71722e6	+	1.77812e6i	0.679319	+	0.703409i
$365$	−3.53506e6	−	1.91369e6i	−1.38888	−	0.751864i
$366$	−1.17794e6	+	1.15759e6i	−0.459642	+	0.451704i
$367$		−	2.36805e6i		−	0.917754i	−0.888500	−	0.458877i	$-0.848252\pi$
$367$		−	2.36805e6i		−	0.917754i	0.888500	−	0.458877i	$-0.151748\pi$
$368$	3.20320e6	+	111646.i	1.23300	+	0.0429756i
$369$	5.96990e6			2.28245
$370$	1.53149e6	+	846398.i	0.581582	+	0.321418i
$371$	−605443.	−	605443.i	−0.228370	−	0.228370i
$372$	5.49932e6	+	5.69433e6i	2.06040	+	2.13347i
$373$	−179910.	−	179910.i	−0.0669550	−	0.0669550i	0.672836	−	0.739791i	$-0.265076\pi$
$373$	−179910.	−	179910.i	−0.0669550	−	0.0669550i	−0.739791	+	0.672836i	$0.765076\pi$
$374$	1.59735e6	+	13913.4i	0.590501	+	0.00514344i
$375$	3.67308e6	+	3.11347e6i	1.34881	+	1.14332i
$376$	3.04254e6	−	2.88755e6i	1.10986	−	1.05332i
$377$	−2.64626e6			−0.958913
$378$	−5.88984e6	−	51302.2i	−2.12019	−	0.0184674i
$379$	566555.	−	566555.i	0.202602	−	0.202602i	−0.598512	−	0.801114i	$-0.704241\pi$
$379$	566555.	−	566555.i	0.202602	−	0.202602i	0.801114	+	0.598512i	$0.204241\pi$
$380$	825774.	−	230144.i	0.293361	−	0.0817599i
$381$	3.30420e6	+	3.30420e6i	1.16615	+	1.16615i
$382$	−1.05084e6	+	1.03269e6i	−0.368449	+	0.362086i
$383$			1.80323e6i			0.628136i	0.949401	+	0.314068i	$0.101692\pi$
$383$			1.80323e6i			0.628136i	−0.949401	+	0.314068i	$0.898308\pi$
$384$	5.09973e6	+	311319.i	1.76490	+	0.107740i
$385$	−1.55546e6	+	462855.i	−0.534820	+	0.159145i
$386$	−766341.	−	779809.i	−0.261791	−	0.266391i
$387$	4.69715e6	−	4.69715e6i	1.59425	−	1.59425i
$388$	2.72415e6	+	47459.8i	0.918652	+	0.0160047i
$389$	303240.	−	303240.i	0.101604	−	0.101604i	−0.654477	−	0.756082i	$-0.727111\pi$
$389$	303240.	−	303240.i	0.101604	−	0.101604i	0.756082	+	0.654477i	$0.227111\pi$
$390$	−1.35076e6	−	4.68832e6i	−0.449692	−	1.56083i
$391$			4.20164e6i			1.38988i
$392$	278854.	+	293821.i	0.0916561	+	0.0965758i
$393$	909459.			0.297031
$394$	−3.41311e6	−	29729.2i	−1.10767	−	0.00964812i
$395$	−4.10518e6	−	2.22232e6i	−1.32385	−	0.716662i
$396$	−2.50211e6	+	2.41642e6i	−0.801804	+	0.774344i
$397$	3.07647e6	−	3.07647e6i	0.979663	−	0.979663i	−0.0201345	−	0.999797i	$-0.506409\pi$
$397$	3.07647e6	−	3.07647e6i	0.979663	−	0.979663i	0.999797	+	0.0201345i	$0.00640946\pi$
$398$	−694801.	−	707011.i	−0.219863	−	0.223727i
$399$	1.82284e6			0.573213
$400$	−1.65512e6	−	2.73872e6i	−0.517226	−	0.855849i
$401$	1.66432e6			0.516863			0.258431	−	0.966030i	$-0.416794\pi$
$401$	1.66432e6			0.516863			0.258431	+	0.966030i	$0.416794\pi$
$402$	6.39333e6	+	6.50569e6i	1.97316	+	2.00784i
$403$	−3.55247e6	+	3.55247e6i	−1.08960	+	1.08960i
$404$	944674.	+	978174.i	0.287958	+	0.298169i
$405$	4.05071e6	+	2.19283e6i	1.22714	+	0.664306i
$406$	−3.69042e6	−	32144.6i	−1.11112	−	0.00967818i
$407$	1.16403e6			0.348319
$408$	−174993.	+	6.69543e6i	−0.0520439	+	1.99126i
$409$			5.50637e6i			1.62763i	0.581121	+	0.813817i	$0.302614\pi$
$409$			5.50637e6i			1.62763i	−0.581121	+	0.813817i	$0.697386\pi$
$410$	1.01145e6	+	3.51063e6i	0.297156	+	1.03140i
$411$	3.78629e6	−	3.78629e6i	1.10563	−	1.10563i
$412$	104784.	−	6.01450e6i	0.0304125	−	1.74565i
$413$	1.39518e6	−	1.39518e6i	0.402490	−	0.402490i
$414$	−6.41295e6	−	6.52565e6i	−1.83890	−	1.87121i
$415$	−4.33144e6	+	1.28890e6i	−1.23456	+	0.367365i
$416$	−141167.	+	3.23941e6i	−0.0399944	+	0.917768i
$417$			2.95778e6i			0.832963i
$418$	406733.	−	399709.i	0.113859	−	0.111893i
$419$	795452.	+	795452.i	0.221350	+	0.221350i	0.809067	−	0.587717i	$-0.199973\pi$
$419$	795452.	+	795452.i	0.221350	+	0.221350i	−0.587717	+	0.809067i	$0.699973\pi$
$420$	−1.82679e6	−	6.55465e6i	−0.505318	−	1.81312i
$421$	1.68608e6	−	1.68608e6i	0.463630	−	0.463630i	−0.436213	−	0.899843i	$-0.643681\pi$
$421$	1.68608e6	−	1.68608e6i	0.463630	−	0.463630i	0.899843	+	0.436213i	$0.143681\pi$
$422$	−2.32775e6	−	20275.4i	−0.636291	−	0.00554228i
$423$	−1.19739e7			−3.25376
$424$	29343.9	−	1.12273e6i	0.00792691	−	0.303293i
$425$	3.51244e6	−	2.29345e6i	0.943271	−	0.615910i
$426$	3.94957e6	+	34401.9i	1.05445	+	0.00918457i
$427$	−1.03361e6	−	1.03361e6i	−0.274337	−	0.274337i
$428$	2.75789e6	−	2.66344e6i	0.727724	−	0.702802i
$429$	−2.29503e6	−	2.29503e6i	−0.602068	−	0.602068i
$430$	3.55800e6	+	1.96637e6i	0.927971	+	0.512854i
$431$	−1.77017e6			−0.459010			−0.229505	−	0.973308i	$-0.573711\pi$
$431$	−1.77017e6			−0.459010			−0.229505	+	0.973308i	$0.573711\pi$
$432$	−5.26952e6	−	5.65012e6i	−1.35851	−	1.45663i
$433$			6.20991e6i			1.59172i	0.605484	+	0.795858i	$0.292980\pi$
$433$			6.20991e6i			1.59172i	−0.605484	+	0.795858i	$0.707020\pi$
$434$	−4.99736e6	+	4.91105e6i	−1.27355	+	1.25156i
$435$	6.40584e6	+	3.46778e6i	1.62313	+	0.878674i
$436$	−892139.	+	861585.i	−0.224758	+	0.217061i
$437$	1.06063e6	+	1.06063e6i	0.265680	+	0.265680i
$438$	97656.7	−	1.12116e7i	0.0243230	−	2.79244i
$439$		−	2.59345e6i		−	0.642270i	−0.947033	−	0.321135i	$-0.895936\pi$
$439$		−	2.59345e6i		−	0.642270i	0.947033	−	0.321135i	$-0.104064\pi$
$440$	−1.84491e6	−	1.06198e6i	−0.454300	−	0.261507i
$441$		−	1.15633e6i		−	0.283130i
$442$	−4.25043e6	−	37022.5i	−1.03485	−	0.00901384i
$443$	13450.1	+	13450.1i	0.00325625	+	0.00325625i	0.708733	−	0.705477i	$-0.249267\pi$
$443$	13450.1	+	13450.1i	0.00325625	+	0.00325625i	−0.705477	+	0.708733i	$0.749267\pi$
$444$	−85016.5	+	4.87986e6i	−0.0204666	+	1.17476i
$445$	−1.29076e6	+	2.38435e6i	−0.308990	+	0.570782i
$446$	1.10315e6	+	1.12254e6i	0.262602	+	0.267217i
$447$		−	3.48507e6i		−	0.824979i
$448$	−236218.	+	4.51590e6i	−0.0556055	+	1.06304i
$449$	−3.00429e6			−0.703277			−0.351639	−	0.936136i	$-0.614375\pi$
$449$	−3.00429e6			−0.703277			−0.351639	+	0.936136i	$0.614375\pi$
$450$	−1.95475e6	+	8.92303e6i	−0.455050	+	2.07721i
$451$	1.71853e6	+	1.71853e6i	0.397846	+	0.397846i
$452$	1.34175e6	+	23375.8i	0.308905	+	0.00538172i
$453$	1.08014e6	+	1.08014e6i	0.247305	+	0.247305i
$454$	29028.0	−	3.33261e6i	0.00660963	−	0.758830i
$455$	4.13897e6	−	1.23162e6i	0.937269	−	0.278901i
$456$	1.64596e6	+	1.73431e6i	0.370688	+	0.390584i
$457$	−8.52504e6			−1.90944			−0.954720	−	0.297507i	$-0.903845\pi$
$457$	−8.52504e6			−1.90944			−0.954720	+	0.297507i	$0.903845\pi$
$458$	−33508.5	+	3.84701e6i	−0.00746435	+	0.856957i
$459$	7.16165e6	−	7.16165e6i	1.58665	−	1.58665i
$460$	2.75093e6	−	4.87678e6i	0.606157	−	1.07458i
$461$	−5.29064e6	−	5.29064e6i	−1.15946	−	1.15946i	−0.984592	−	0.174868i	$-0.944050\pi$
$461$	−5.29064e6	−	5.29064e6i	−1.15946	−	1.15946i	−0.174868	−	0.984592i	$-0.555950\pi$
$462$	−3.17272e6	−	3.22848e6i	−0.691556	−	0.703709i
$463$			5.39407e6i			1.16940i	0.811249	+	0.584701i	$0.198788\pi$
$463$			5.39407e6i			1.16940i	−0.811249	+	0.584701i	$0.801212\pi$
$464$	−3.30175e6	−	3.54022e6i	−0.711949	−	0.763370i
$465$	1.32548e7	−	3.94421e6i	2.84277	−	0.845916i
$466$	1.92005e6	−	1.88689e6i	0.409587	−	0.402514i
$467$	−2.89183e6	+	2.89183e6i	−0.613594	+	0.613594i	−0.943881	−	0.330287i	$-0.892855\pi$
$467$	−2.89183e6	+	2.89183e6i	−0.613594	+	0.613594i	0.330287	+	0.943881i	$0.392855\pi$
$468$	6.65793e6	−	6.42991e6i	1.40516	−	1.35703i
$469$	−5.70855e6	+	5.70855e6i	−1.19838	+	1.19838i
$470$	−2.02868e6	−	7.04133e6i	−0.423612	−	1.47031i
$471$			1.37568e7i			2.85735i
$472$	2.58722e6	+	67620.1i	0.534539	+	0.0139708i
$473$	2.70429e6			0.555777
$474$	113406.	−	1.30198e7i	0.0231842	−	2.66170i
$475$	307711.	−	1.46559e6i	0.0625761	−	0.298043i
$476$	−5.92711e6	−	103262.i	−1.19902	−	0.0208892i
$477$	−2.26700e6	+	2.26700e6i	−0.456200	+	0.456200i
$478$	−757247.	+	744169.i	−0.151589	+	0.148971i
$479$	28762.8			0.00572785			0.00286393	−	0.999996i	$-0.499088\pi$
$479$	28762.8			0.00572785			0.00286393	+	0.999996i	$0.499088\pi$
$480$	4.58679e6	−	7.65670e6i	0.908669	−	1.51684i
$481$	−3.09739e6			−0.610426
$482$	6.14170e6	−	6.03563e6i	1.20412	−	1.18333i
$483$	8.41882e6	−	8.41882e6i	1.64204	−	1.64204i
$484$	3.73698e6	+	65105.3i	0.725115	+	0.0126329i
$485$	2.26588e6	−	4.18565e6i	0.437404	−	0.807994i
$486$	−21566.9	+	2.47602e6i	−0.00414187	+	0.475515i
$487$	−1.00936e6			−0.192853			−0.0964263	−	0.995340i	$-0.530741\pi$
$487$	−1.00936e6			−0.192853			−0.0964263	+	0.995340i	$0.530741\pi$
$488$	50095.7	−	1.91672e6i	0.00952249	−	0.364342i
$489$			1.20363e7i			2.27625i
$490$	679988.	−	195911.i	0.127941	−	0.0368612i
$491$	3.49614e6	−	3.49614e6i	0.654462	−	0.654462i	−0.299602	−	0.954064i	$-0.596854\pi$
$491$	3.49614e6	−	3.49614e6i	0.654462	−	0.654462i	0.954064	+	0.299602i	$0.0968539\pi$
$492$	−7.32996e6	+	7.07893e6i	−1.36518	+	1.31842i
$493$	4.48731e6	−	4.48731e6i	0.831512	−	0.831512i
$494$	−1.08229e6	+	1.06360e6i	−0.199538	+	0.196092i
$495$	1.73310e6	+	5.82422e6i	0.317914	+	1.06838i
$496$	−9.18499e6	−	320137.i	−1.67639	−	0.0584295i
$497$			3.49582e6i			0.634831i
$498$	−8.83497e6	−	8.99024e6i	−1.59636	−	1.62442i
$499$	−3.24295e6	−	3.24295e6i	−0.583028	−	0.583028i	0.352706	−	0.935734i	$-0.385262\pi$
$499$	−3.24295e6	−	3.24295e6i	−0.583028	−	0.583028i	−0.935734	+	0.352706i	$0.885262\pi$
$500$	−5.57842e6	+	362283.i	−0.997898	+	0.0648071i
$501$	−8.52675e6	+	8.52675e6i	−1.51771	+	1.51771i
$502$	−91249.4	+	1.04760e7i	−0.0161611	+	1.85540i
$503$	8.33969e6			1.46970			0.734852	−	0.678227i	$-0.237252\pi$
$503$	8.33969e6			1.46970			0.734852	+	0.678227i	$0.237252\pi$
$504$	9.36312e6	−	8.88615e6i	1.64189	−	1.55825i
$505$	2.27692e6	−	677537.i	0.397300	−	0.118224i
$506$	32442.1	−	3.72457e6i	0.00563291	−	0.646696i
$507$	−1.12965e6	−	1.12965e6i	−0.195175	−	0.195175i
$508$	−5.42419e6	−	94499.7i	−0.932558	−	0.0162469i
$509$	4.29380e6	+	4.29380e6i	0.734593	+	0.734593i	0.971526	−	0.236933i	$-0.0761421\pi$
$509$	4.29380e6	+	4.29380e6i	0.734593	+	0.734593i	−0.236933	+	0.971526i	$0.576142\pi$
$510$	1.02406e7	+	5.65957e6i	1.74341	+	0.963514i
$511$	9.92358e6			1.68119
$512$	−4.50988e6	+	3.85297e6i	−0.760309	+	0.649561i
$513$		−	3.61565e6i		−	0.606587i
$514$	6.46428e6	+	6.57788e6i	1.07923	+	1.09819i
$515$	−9.24128e6	−	5.00273e6i	−1.53537	−	0.831168i
$516$	−197512.	+	1.13370e7i	−0.0326565	+	1.87445i
$517$	−3.44687e6	−	3.44687e6i	−0.567151	−	0.567151i
$518$	−4.31956e6	−	37624.6i	−0.707318	−	0.00616095i
$519$			466160.i			0.0759656i
$520$	4.90917e6	+	2.82584e6i	0.796158	+	0.458289i
$521$		−	2.16011e6i		−	0.348644i	−0.984689	−	0.174322i	$-0.944227\pi$
$521$		−	2.16011e6i		−	0.348644i	0.984689	−	0.174322i	$-0.0557734\pi$
$522$	−120361.	+	1.38183e7i	−0.0193335	+	2.21961i
$523$	−3.07264e6	−	3.07264e6i	−0.491199	−	0.491199i	0.417485	−	0.908684i	$-0.362912\pi$
$523$	−3.07264e6	−	3.07264e6i	−0.491199	−	0.491199i	−0.908684	+	0.417485i	$0.862912\pi$
$524$	−759492.	+	733481.i	−0.120836	+	0.116697i
$525$	−1.16333e7	−	2.44248e6i	−1.84206	−	0.386752i
$526$	−926259.	+	910262.i	−0.145971	+	0.143451i
$527$		−	1.20480e7i		−	1.88967i
$528$	206821.	−	5.93385e6i	0.0322856	−	0.926300i
$529$	3.36072e6			0.522148
$530$	−1.71721e6	−	949034.i	−0.265542	−	0.146755i
$531$	−5.22406e6	−	5.22406e6i	−0.804030	−	0.804030i
$532$	−1.52226e6	+	1.47012e6i	−0.233189	+	0.225203i
$533$	−4.57287e6	−	4.57287e6i	−0.697222	−	0.697222i
$534$	−7.56210e6	−	65868.1i	−1.14760	−	0.00999591i
$535$	−1.91026e6	−	6.41959e6i	−0.288542	−	0.969668i
$536$	−1.05859e7	−	276676.i	−1.59154	−	0.0415968i
$537$	−5.34259e6			−0.799495
$538$	5.29125e6	+	46088.3i	0.788138	+	0.00686491i
$539$	332868.	−	332868.i	0.0493514	−	0.0493514i
$540$	−1.30013e7	+	3.62348e6i	−1.91869	+	0.534739i
$541$	3.66127e6	+	3.66127e6i	0.537822	+	0.537822i	0.922889	−	0.385067i	$-0.125822\pi$
$541$	3.66127e6	+	3.66127e6i	0.537822	+	0.537822i	−0.385067	+	0.922889i	$0.625822\pi$
$542$	404740.	−	397750.i	0.0591804	−	0.0581583i
$543$			3.16843e6i			0.461153i
$544$	−5.25374e6	−	5.73250e6i	−0.761152	−	0.830514i
$545$	617944.	+	2.07665e6i	0.0891165	+	0.299483i
$546$	8.44239e6	+	8.59076e6i	1.21195	+	1.23325i
$547$	−4.30382e6	+	4.30382e6i	−0.615015	+	0.615015i	−0.944248	−	0.329234i	$-0.893210\pi$
$547$	−4.30382e6	+	4.30382e6i	−0.615015	+	0.615015i	0.329234	+	0.944248i	$0.393210\pi$
$548$	−108287.	+	6.21559e6i	−0.0154038	+	0.884160i
$549$	−3.87019e6	+	3.87019e6i	−0.548027	+	0.548027i
$550$	−3.13133e6	+	2.00592e6i	−0.441390	+	0.282753i
$551$		−	2.26548e6i		−	0.317893i
$552$	1.56119e7	+	408035.i	2.18076	+	0.0569966i
$553$	1.15240e7			1.60247
$554$	1.20743e7	+	105170.i	1.67142	+	0.0145586i
$555$	7.49790e6	+	4.05896e6i	1.03325	+	0.559348i
$556$	−2.38546e6	−	2.47005e6i	−0.327254	−	0.338859i
$557$	5.05402e6	−	5.05402e6i	0.690238	−	0.690238i	−0.272046	−	0.962284i	$-0.587700\pi$
$557$	5.05402e6	−	5.05402e6i	0.690238	−	0.690238i	0.962284	+	0.272046i	$0.0877003\pi$
$558$	1.83888e7	+	1.87119e7i	2.50016	+	2.54409i
$559$	−7.19592e6			−0.973995
$560$	6.81190e6	+	4.00050e6i	0.917906	+	0.539069i
$561$	7.78344e6			1.04415
$562$	−1.02398e6	−	1.04198e6i	−0.136758	−	0.139161i
$563$	1.09726e6	−	1.09726e6i	0.145895	−	0.145895i	−0.630387	−	0.776281i	$-0.717104\pi$
$563$	1.09726e6	−	1.09726e6i	0.145895	−	0.145895i	0.776281	+	0.630387i	$0.217104\pi$
$564$	1.47018e7	−	1.41983e7i	1.94614	−	1.87949i
$565$	1.11604e6	−	2.06160e6i	0.147081	−	0.271696i
$566$	−4.05777e6	−	35344.4i	−0.532410	−	0.00463745i
$567$	−1.13711e7			−1.48540
$568$	−3.32604e6	+	3.15661e6i	−0.432571	+	0.410535i
$569$			4.40927e6i			0.570934i	0.958388	+	0.285467i	$0.0921488\pi$
$569$			4.40927e6i			0.570934i	−0.958388	+	0.285467i	$0.907851\pi$
$570$	4.01370e6	−	1.15639e6i	0.517437	−	0.149079i
$571$	−5.21349e6	+	5.21349e6i	−0.669173	+	0.669173i	−0.957525	−	0.288352i	$-0.906893\pi$
$571$	−5.21349e6	+	5.21349e6i	−0.669173	+	0.669173i	0.288352	+	0.957525i	$0.406893\pi$
$572$	3.76753e6	+	65637.6i	0.481468	+	0.00838808i
$573$	−5.07623e6	+	5.07623e6i	−0.645884	+	0.645884i
$574$	−6.32169e6	−	6.43279e6i	−0.800854	−	0.814928i
$575$	−5.34769e6	−	8.19003e6i	−0.674523	−	1.03304i
$576$	1.69092e7	+	884486.i	2.12357	+	0.111080i
$577$		−	1.27570e7i		−	1.59518i	−0.603201	−	0.797590i	$-0.706108\pi$
$577$		−	1.27570e7i		−	1.59518i	0.603201	−	0.797590i	$-0.293892\pi$
$578$	1.54162e6	−	1.51500e6i	0.191937	−	0.188622i
$579$	−3.76698e6	−	3.76698e6i	−0.466979	−	0.466979i
$580$	−8.14631e6	+	2.27038e6i	−1.00552	+	0.280239i
$581$	7.88867e6	−	7.88867e6i	0.969535	−	0.969535i
$582$	1.32750e7	+	115629.i	1.62453	+	0.0141501i
$583$	−1.30518e6			−0.159037
$584$	8.96067e6	+	9.44164e6i	1.08720	+	1.14555i
$585$	−4.61165e6	−	1.54978e7i	−0.557142	−	1.87232i
$586$	1.37149e6	+	11946.0i	0.164986	+	0.00143708i
$587$	8.37792e6	+	8.37792e6i	1.00355	+	1.00355i	0.999994	+	0.00356051i	$0.00113335\pi$
$587$	8.37792e6	+	8.37792e6i	1.00355	+	1.00355i	0.00356051	+	0.999994i	$0.498867\pi$
$588$	1.37114e6	+	1.41977e6i	0.163546	+	0.169346i
$589$	−3.04129e6	−	3.04129e6i	−0.361218	−	0.361218i
$590$	2.18695e6	−	3.95713e6i	0.258648	−	0.468004i
$591$	−1.66312e7			−1.95864
$592$	−3.86462e6	−	4.14375e6i	−0.453214	−	0.485947i
$593$			7.60813e6i			0.888467i	0.895911	+	0.444234i	$0.146524\pi$
$593$			7.60813e6i			0.888467i	−0.895911	+	0.444234i	$0.853476\pi$
$594$	−6.40379e6	+	6.29319e6i	−0.744682	+	0.731821i
$595$	−4.93004e6	+	9.10701e6i	−0.570897	+	1.05459i
$596$	2.81072e6	+	2.91039e6i	0.324117	+	0.335611i
$597$	−3.41532e6	−	3.41532e6i	−0.392190	−	0.392190i
$598$	−86326.1	+	9.91082e6i	−0.00987164	+	1.13333i
$599$			256241.i			0.0291798i	0.999894	+	0.0145899i	$0.00464427\pi$
$599$			256241.i			0.0291798i	−0.999894	+	0.0145899i	$0.995356\pi$
$600$	−8.18058e6	−	1.32738e7i	−0.927697	−	1.50527i
$601$			1.07628e7i			1.21546i	0.794144	+	0.607729i	$0.207919\pi$
$601$			1.07628e7i			1.21546i	−0.794144	+	0.607729i	$0.792081\pi$
$602$	−1.00353e7	−	87410.3i	−1.12860	−	0.00983040i
$603$	2.13749e7	+	2.13749e7i	2.39393	+	2.39393i
$604$	−1.77316e6	−	30891.8i	−0.197768	−	0.00344549i
$605$	3.10833e6	−	5.74186e6i	0.345254	−	0.637771i
$606$	4.64430e6	+	4.72592e6i	0.513735	+	0.522763i
$607$			523259.i			0.0576428i	0.999585	+	0.0288214i	$0.00917540\pi$
$607$			523259.i			0.0576428i	−0.999585	+	0.0288214i	$0.990825\pi$
$608$	−2.77327e6	−	120853.i	−0.304252	−	0.0132587i
$609$	−1.79824e7			−1.96474
$610$	−2.93160e6	−	1.62018e6i	−0.318992	−	0.176295i
$611$	9.17188e6	+	9.17188e6i	0.993929	+	0.993929i
$612$	−386649.	+	2.21933e7i	−0.0417290	+	2.39520i
$613$	−4.28573e6	−	4.28573e6i	−0.460653	−	0.460653i	0.438216	−	0.898870i	$-0.355610\pi$
$613$	−4.28573e6	−	4.28573e6i	−0.460653	−	0.460653i	−0.898870	+	0.438216i	$0.855610\pi$
$614$	84209.7	−	9.66784e6i	0.00901450	−	1.03492i
$615$	5.07713e6	+	1.70621e7i	0.541291	+	1.81905i
$616$	5.25333e6	+	137302.i	0.557806	+	0.0145789i
$617$	1.66349e7			1.75917			0.879585	−	0.475741i	$-0.157820\pi$
$617$	1.66349e7			1.75917			0.879585	+	0.475741i	$0.157820\pi$
$618$	255292.	−	2.93092e7i	0.0268885	−	3.08698i
$619$	3.15889e6	−	3.15889e6i	0.331365	−	0.331365i	−0.521739	−	0.853105i	$-0.674717\pi$
$619$	3.15889e6	−	3.15889e6i	0.331365	−	0.331365i	0.853105	+	0.521739i	$0.174717\pi$
$620$	−7.88813e6	+	1.39839e7i	−0.824129	+	1.46099i
$621$	−1.66990e7	−	1.66990e7i	−1.73764	−	1.73764i
$622$	−8.00141e6	−	8.14203e6i	−0.829260	−	0.843833i
$623$		−	6.69332e6i		−	0.690910i
$624$	−550335.	+	1.57896e7i	−0.0565804	+	1.62334i
$625$	−3.92759e6	+	8.94100e6i	−0.402185	+	0.915559i
$626$	−1.00675e7	+	9.89359e6i	−1.02680	+	1.00906i
$627$	1.96479e6	−	1.96479e6i	0.199593	−	0.199593i
$628$	−1.10949e7	−	1.14883e7i	−1.12259	−	1.16240i
$629$	5.25230e6	−	5.25230e6i	0.529325	−	0.529325i
$630$	−6.24305e6	−	2.16690e7i	−0.626680	−	2.17514i
$631$		−	3.05902e6i		−	0.305850i	−0.988238	−	0.152925i	$-0.951131\pi$
$631$		−	3.05902e6i		−	0.305850i	0.988238	−	0.152925i	$-0.0488694\pi$
$632$	1.04058e7	+	1.09643e7i	1.03629	+	1.09192i
$633$	−1.13425e7			−1.12512
$634$	36507.6	−	4.19131e6i	0.00360711	−	0.414121i
$635$	−4.51172e6	+	8.33427e6i	−0.444025	+	0.820225i
$636$	95325.7	−	5.47160e6i	0.00934474	−	0.536379i
$637$	−885737.	+	885737.i	−0.0864881	+	0.0864881i
$638$	−4.01245e6	+	3.94315e6i	−0.390263	+	0.383523i
$639$	1.30896e7			1.26816
$640$	2.34471e6	+	1.00934e7i	0.226276	+	0.974063i
$641$	1.09355e7			1.05122			0.525611	−	0.850725i	$-0.323837\pi$
$641$	1.09355e7			1.05122			0.525611	+	0.850725i	$0.323837\pi$
$642$	1.33244e7	−	1.30942e7i	1.27588	−	1.25384i
$643$	18781.2	−	18781.2i	0.00179142	−	0.00179142i	−0.706211	−	0.708002i	$-0.749597\pi$
$643$	18781.2	−	18781.2i	0.00179142	−	0.00179142i	0.708002	+	0.706211i	$0.249597\pi$
$644$	−240777.	+	1.38204e7i	−0.0228771	+	1.31312i
$645$	1.74193e7	+	9.42985e6i	1.64866	+	0.892495i
$646$	31695.1	−	3.63881e6i	0.00298821	−	0.343066i
$647$	1.61622e7			1.51789			0.758943	−	0.651157i	$-0.225716\pi$
$647$	1.61622e7			1.51789			0.758943	+	0.651157i	$0.225716\pi$
$648$	−1.02677e7	−	1.08189e7i	−0.960588	−	1.01215i
$649$		−	3.00765e6i		−	0.280295i
$650$	8.33225e6	−	5.33762e6i	0.773533	−	0.495524i
$651$	−2.41405e7	+	2.41405e7i	−2.23251	+	2.23251i
$652$	−9.70729e6	−	1.00515e7i	−0.894291	−	0.926004i
$653$	−8.34030e6	+	8.34030e6i	−0.765418	+	0.765418i	−0.977296	−	0.211878i	$-0.932042\pi$
$653$	−8.34030e6	+	8.34030e6i	−0.765418	+	0.765418i	0.211878	+	0.977296i	$0.432042\pi$
$654$	−4.31025e6	+	4.23581e6i	−0.394056	+	0.387251i
$655$	526066.	+	1.76789e6i	0.0479112	+	0.161009i
$656$	412093.	−	1.18233e7i	0.0373883	−	1.07270i
$657$		−	3.71575e7i		−	3.35840i
$658$	1.26795e7	+	1.29023e7i	1.14166	+	1.16173i
$659$	−3.79829e6	−	3.79829e6i	−0.340702	−	0.340702i	0.515929	−	0.856631i	$-0.327447\pi$
$659$	−3.79829e6	−	3.79829e6i	−0.340702	−	0.340702i	−0.856631	+	0.515929i	$0.827447\pi$
$660$	−9.03411e6	−	5.09603e6i	−0.807283	−	0.455378i
$661$	−420683.	+	420683.i	−0.0374499	+	0.0374499i	−0.725584	−	0.688134i	$-0.758430\pi$
$661$	−420683.	+	420683.i	−0.0374499	+	0.0374499i	0.688134	+	0.725584i	$0.258430\pi$
$662$	−38443.5	+	4.41357e6i	−0.00340940	+	0.391422i
$663$	−2.07112e7			−1.82987
$664$	1.46288e7	+	382340.i	1.28762	+	0.0336534i
$665$	1.05440e6	+	3.54339e6i	0.0924593	+	0.310717i
$666$	−140880.	+	1.61740e7i	−0.0123073	+	1.41297i
$667$	−1.04631e7	−	1.04631e7i	−0.910642	−	0.910642i
$668$	243864.	−	1.39976e7i	0.0211450	−	1.21370i
$669$	5.42259e6	+	5.42259e6i	0.468426	+	0.468426i
$670$	−8.94818e6	+	1.61911e7i	−0.770101	+	1.39344i
$671$	−2.22819e6			−0.191049
$672$	−959285.	+	2.20131e7i	−0.0819454	+	1.88043i
$673$			5.36149e6i			0.456297i	0.973626	+	0.228148i	$0.0732672\pi$
$673$			5.36149e6i			0.456297i	−0.973626	+	0.228148i	$0.926733\pi$
$674$	−7.67252e6	−	7.80735e6i	−0.650561	−	0.661994i
$675$	−4.84473e6	+	2.30749e7i	−0.409271	+	1.94931i
$676$	1.85444e6	+	32307.9i	0.156079	+	0.00271920i
$677$	−7.96962e6	−	7.96962e6i	−0.668292	−	0.668292i	0.289029	−	0.957320i	$-0.406668\pi$
$677$	−7.96962e6	−	7.96962e6i	−0.668292	−	0.668292i	−0.957320	+	0.289029i	$0.906668\pi$
$678$	6.53848e6	+	56952.0i	0.546264	+	0.00475812i
$679$			1.17499e7i			0.978047i
$680$	−1.31164e7	+	3.53272e6i	−1.08778	+	0.292979i
$681$		−	1.62389e7i		−	1.34180i
$682$	−93025.8	+	1.06800e7i	−0.00765848	+	0.879245i
$683$	4.54873e6	+	4.54873e6i	0.373111	+	0.373111i	0.868609	−	0.495498i	$-0.165014\pi$
$683$	4.54873e6	+	4.54873e6i	0.373111	+	0.373111i	−0.495498	+	0.868609i	$0.665014\pi$
$684$	5.50468e6	+	5.69988e6i	0.449875	+	0.465828i
$685$	9.55025e6	+	5.16999e6i	0.777657	+	0.420982i
$686$	8.11212e6	−	7.97202e6i	0.658149	−	0.646782i
$687$			1.87454e7i			1.51531i
$688$	−8.97837e6	−	9.62684e6i	−0.723147	−	0.775377i
$689$	3.47299e6			0.278712
$690$	1.31965e7	−	2.38782e7i	1.05521	−	1.90932i
$691$	−6.54528e6	−	6.54528e6i	−0.521475	−	0.521475i	0.396542	−	0.918017i	$-0.370210\pi$
$691$	−6.54528e6	−	6.54528e6i	−0.521475	−	0.521475i	−0.918017	+	0.396542i	$0.870210\pi$
$692$	−375959.	−	389291.i	−0.0298453	−	0.0309036i
$693$	−1.06074e7	−	1.06074e7i	−0.839027	−	0.839027i
$694$	−74810.1	−	651.618i	−0.00589606	−	5.13564e-5i
$695$	−5.74959e6	+	1.71089e6i	−0.451518	+	0.134357i
$696$	−1.62375e7	−	1.71091e7i	−1.27056	−	1.33876i
$697$	1.55086e7			1.20918
$698$	8.54960e6	+	74469.5i	0.664213	+	0.00578549i
$699$	9.27506e6	−	9.27506e6i	0.717999	−	0.717999i
$700$	1.16848e7	−	7.34252e6i	0.901316	−	0.566370i
$701$	5.46002e6	+	5.46002e6i	0.419662	+	0.419662i	0.885087	−	0.465425i	$-0.154099\pi$
$701$	5.46002e6	+	5.46002e6i	0.419662	+	0.419662i	−0.465425	+	0.885087i	$0.654099\pi$
$702$	1.70400e7	−	1.67457e7i	1.30505	−	1.28251i
$703$		−	2.65169e6i		−	0.202365i
$704$	4.61295e6	+	5.12218e6i	0.350790	+	0.389514i
$705$	−1.01833e7	−	3.42217e7i	−0.771640	−	2.59316i
$706$	−9.42346e6	−	9.58907e6i	−0.711539	−	0.724043i
$707$	−4.14685e6	+	4.14685e6i	−0.312011	+	0.312011i
$708$	1.26087e7	+	219668.i	0.945342	+	0.0164697i
$709$	3.98168e6	−	3.98168e6i	0.297475	−	0.297475i	−0.542549	−	0.840024i	$-0.682541\pi$
$709$	3.98168e6	−	3.98168e6i	0.297475	−	0.297475i	0.840024	+	0.542549i	$0.182541\pi$
$710$	2.21771e6	+	7.69742e6i	0.165104	+	0.573059i
$711$		−	4.31501e7i		−	3.20116i
$712$	6.36826e6	−	6.04385e6i	0.470783	−	0.446801i
$713$	−2.80925e7			−2.06951
$714$	−2.88834e7	−	251583.i	−2.12033	−	0.0184687i
$715$	3.13375e6	−	5.78881e6i	0.229245	−	0.423472i
$716$	4.46161e6	−	4.30881e6i	0.325244	−	0.314105i
$717$	−3.65799e6	+	3.65799e6i	−0.265733	+	0.265733i
$718$	4.08005e6	+	4.15175e6i	0.295362	+	0.300553i
$719$	1.68325e7			1.21430			0.607150	−	0.794587i	$-0.292313\pi$
$719$	1.68325e7			1.21430			0.607150	+	0.794587i	$0.292313\pi$
$720$	1.49793e7	−	2.55062e7i	1.07686	−	1.83364i
$721$	2.59420e7			1.85851
$722$	8.90720e6	+	9.06374e6i	0.635914	+	0.647089i
$723$	2.96684e7	−	2.96684e7i	2.11080	−	2.11080i
$724$	−2.55535e6	−	2.64596e6i	−0.181177	−	0.187602i
$725$	−3.03558e6	+	1.44581e7i	−0.214485	+	1.02157i
$726$	1.82106e7	+	158620.i	1.28228	+	0.0111691i
$727$	−3.55923e6			−0.249758			−0.124879	−	0.992172i	$-0.539854\pi$
$727$	−3.55923e6			−0.249758			−0.124879	+	0.992172i	$0.539854\pi$
$728$	−1.39787e7	−	365350.i	−0.977551	−	0.0255494i
$729$		−	7.95763e6i		−	0.554581i
$730$	2.18507e7	−	6.29541e6i	1.51760	−	0.437237i
$731$	1.22022e7	−	1.22022e7i	0.844590	−	0.844590i
$732$	162739.	−	9.34106e6i	0.0112257	−	0.644345i
$733$	1.20275e7	−	1.20275e7i	0.826828	−	0.826828i	−0.160249	−	0.987077i	$-0.551230\pi$
$733$	1.20275e7	−	1.20275e7i	0.826828	−	0.826828i	0.987077	+	0.160249i	$0.0512297\pi$
$734$	9.38935e6	+	9.55435e6i	0.643273	+	0.654578i
$735$	3.30483e6	−	983409.i	0.225647	−	0.0671453i
$736$	−1.33666e7	+	1.22503e7i	−0.909549	+	0.833587i
$737$			1.23062e7i			0.834553i
$738$	−2.40867e7	+	2.36707e7i	−1.62793	+	1.59982i
$739$	−1.78493e7	−	1.78493e7i	−1.20229	−	1.20229i	−0.973468	−	0.228822i	$-0.926513\pi$
$739$	−1.78493e7	−	1.78493e7i	−1.20229	−	1.20229i	−0.228822	−	0.973468i	$-0.573487\pi$
$740$	−9.53508e6	+	2.65743e6i	−0.640096	+	0.178395i
$741$	−5.22815e6	+	5.22815e6i	−0.349786	+	0.349786i
$742$	4.84336e6	+	42187.0i	0.322951	+	0.00281300i
$743$	2.57200e7			1.70923			0.854613	−	0.519265i	$-0.173794\pi$
$743$	2.57200e7			1.70923			0.854613	+	0.519265i	$0.173794\pi$
$744$	−4.47661e7	−	1.17001e6i	−2.96495	−	0.0774924i
$745$	6.77459e6	−	2.01590e6i	0.447190	−	0.133069i
$746$	1.43922e6	+	12536.1i	0.0946850	+	0.000824734i
$747$	−2.95380e7	−	2.95380e7i	−1.93678	−	1.93678i
$748$	−6.49997e6	+	6.27736e6i	−0.424773	+	0.410226i
$749$	1.16917e7	+	1.16917e7i	0.761508	+	0.761508i
$750$	−2.71647e7	+	2.00192e6i	−1.76340	+	0.129955i
$751$	8.31331e6			0.537866			0.268933	−	0.963159i	$-0.413329\pi$
$751$	8.31331e6			0.537866			0.268933	+	0.963159i	$0.413329\pi$
$752$	−826540.	+	2.37141e7i	−0.0532990	+	1.52919i
$753$			5.10469e7i			3.28082i
$754$	1.06768e7	−	1.04924e7i	0.683934	−	0.672122i
$755$	−1.47487e6	+	2.72446e6i	−0.0941645	+	0.173945i
$756$	2.39671e7	−	2.31463e7i	1.52514	−	1.47291i
$757$	−1.15755e6	−	1.15755e6i	−0.0734176	−	0.0734176i	0.669444	−	0.742862i	$-0.266532\pi$
$757$	−1.15755e6	−	1.15755e6i	−0.0734176	−	0.0734176i	−0.742862	+	0.669444i	$0.766532\pi$
$758$	−39477.4	+	4.53227e6i	−0.00249560	+	0.286512i
$759$		−	1.81488e7i		−	1.14352i
$760$	−2.41922e6	+	4.20276e6i	−0.151929	+	0.263937i
$761$			2.25118e7i			1.40912i	0.709642	+	0.704562i	$0.248857\pi$
$761$			2.25118e7i			1.40912i	−0.709642	+	0.704562i	$0.751143\pi$
$762$	−2.64326e7	−	230236.i	−1.64912	−	0.0143643i
$763$	−3.78212e6	−	3.78212e6i	−0.235193	−	0.235193i
$764$	145180.	−	8.33316e6i	0.00899854	−	0.516507i
$765$	3.40999e7	+	1.84599e7i	2.10669	+	1.14045i
$766$	−7.14981e6	−	7.27546e6i	−0.440274	−	0.448011i
$767$			8.00314e6i			0.491216i
$768$	−2.18102e7	+	1.89644e7i	−1.33431	+	1.16021i
$769$	−4.80706e6			−0.293133			−0.146566	−	0.989201i	$-0.546822\pi$
$769$	−4.80706e6			−0.293133			−0.146566	+	0.989201i	$0.546822\pi$
$770$	4.44058e6	−	8.03490e6i	0.269906	−	0.488375i
$771$	3.17754e7	+	3.17754e7i	1.92511	+	1.92511i
$772$	6.18390e6	+	107735.i	0.373438	+	0.00650601i
$773$	−1.93687e7	−	1.93687e7i	−1.16587	−	1.16587i	−0.983167	−	0.182707i	$-0.941514\pi$
$773$	−1.93687e7	−	1.93687e7i	−1.16587	−	1.16587i	−0.182707	−	0.983167i	$-0.558486\pi$
$774$	−327296.	+	3.75758e7i	−0.0196376	+	2.25453i
$775$	1.53342e7	+	2.34844e7i	0.917079	+	1.40451i
$776$	−1.11793e7	+	1.06098e7i	−0.666436	+	0.632487i
$777$	−2.10480e7			−1.25072
$778$	−21129.7	+	2.42583e6i	−0.00125154	+	0.143685i
$779$	3.91486e6	−	3.91486e6i	0.231139	−	0.231139i
$780$	2.40391e7	+	1.35602e7i	1.41476	+	0.798047i
$781$	3.76805e6	+	3.76805e6i	0.221049	+	0.221049i
$782$	−1.66596e7	−	1.69523e7i	−0.974196	−	0.991316i
$783$			3.56686e7i			2.07913i
$784$	−2.29009e6	−	79819.8i	−0.133065	−	0.00463789i
$785$	−2.67416e7	+	7.95743e6i	−1.54886	+	0.460892i
$786$	−3.66939e6	+	3.60601e6i	−0.211854	+	0.208195i
$787$	−8.58801e6	+	8.58801e6i	−0.494260	+	0.494260i	−0.909646	−	0.415385i	$-0.863647\pi$
$787$	−8.58801e6	+	8.58801e6i	−0.494260	+	0.494260i	0.415385	+	0.909646i	$0.363647\pi$
$788$	1.38887e7	−	1.34131e7i	0.796795	−	0.769507i
$789$	−4.47443e6	+	4.47443e6i	−0.255885	+	0.255885i
$790$	2.53746e7	−	7.31070e6i	1.44655	−	0.416765i
$791$			5.78729e6i			0.328878i
$792$	514108.	−	1.96704e7i	0.0291234	−	1.11429i
$793$	5.92904e6			0.334813
$794$	−214368.	+	2.46108e7i	−0.0120672	+	1.38540i
$795$	−8.40711e6	−	4.55115e6i	−0.471769	−	0.255390i
$796$	5.60661e6	+	97677.9i	0.313630	+	0.00546404i
$797$	−1.66157e7	+	1.66157e7i	−0.926557	+	0.926557i	−0.997482	−	0.0709247i	$-0.977405\pi$
$797$	−1.66157e7	+	1.66157e7i	−0.926557	+	0.926557i	0.0709247	+	0.997482i	$0.477405\pi$
$798$	−7.35458e6	+	7.22757e6i	−0.408838	+	0.401777i
$799$	−3.11058e7			−1.72375
$800$	1.75369e7	+	4.48728e6i	0.968788	+	0.247890i
$801$	−2.50622e7			−1.38019
$802$	−6.71500e6	+	6.59904e6i	−0.368647	+	0.362280i
$803$	1.06963e7	−	1.06963e7i	0.585392	−	0.585392i
$804$	−5.15902e7	−	898800.i	−2.81467	−	0.0490369i
$805$	2.12350e7	+	1.14955e7i	1.15495	+	0.625226i
$806$	247535.	−	2.84187e7i	0.0134214	−	1.54087i
$807$	2.57828e7			1.39363
$808$	−7.68993e6	−	200985.i	−0.414376	−	0.0108302i
$809$		−	1.83317e6i		−	0.0984763i	−0.998787	−	0.0492382i	$-0.984321\pi$
$809$		−	1.83317e6i		−	0.0984763i	0.998787	−	0.0492382i	$-0.0156793\pi$
$810$	−2.50380e7	+	7.21369e6i	−1.34087	+	0.386318i
$811$	−1.84288e7	+	1.84288e7i	−0.983888	+	0.983888i	−0.999872	−	0.0159840i	$-0.994912\pi$
$811$	−1.84288e7	+	1.84288e7i	−0.983888	+	0.983888i	0.0159840	+	0.999872i	$0.494912\pi$
$812$	1.50172e7	−	1.45029e7i	0.799277	−	0.771904i
$813$	1.95516e6	−	1.95516e6i	0.103742	−	0.103742i
$814$	−4.69648e6	+	4.61538e6i	−0.248434	+	0.244144i
$815$	−2.33972e7	+	6.96224e6i	−1.23387	+	0.367159i
$816$	−2.58414e7	−	2.77078e7i	−1.35860	−	1.45672i
$817$		−	6.16046e6i		−	0.322893i
$818$	−2.18328e7	−	2.22165e7i	−1.14084	−	1.16089i
$819$	2.82255e7	+	2.82255e7i	1.47039	+	1.47039i
$820$	−1.80006e7	−	1.01539e7i	−0.934871	−	0.527349i
$821$	8.20093e6	−	8.20093e6i	0.424625	−	0.424625i	−0.462168	−	0.886792i	$-0.652928\pi$
$821$	8.20093e6	−	8.20093e6i	0.424625	−	0.424625i	0.886792	+	0.462168i	$0.152928\pi$
$822$	−263827.	+	3.02892e7i	−0.0136188	+	1.56354i
$823$	−1.12909e7			−0.581071			−0.290536	−	0.956864i	$-0.593834\pi$
$823$	−1.12909e7			−0.581071			−0.290536	+	0.956864i	$0.593834\pi$
$824$	2.34248e7	+	2.46821e7i	1.20187	+	1.26638i
$825$	−1.51718e7	+	9.90647e6i	−0.776074	+	0.506739i
$826$	−97215.7	+	1.11610e7i	−0.00495777	+	0.569185i
$827$	−4.06637e6	−	4.06637e6i	−0.206749	−	0.206749i	0.596135	−	0.802884i	$-0.296702\pi$
$827$	−4.06637e6	−	4.06637e6i	−0.206749	−	0.206749i	−0.802884	+	0.596135i	$0.796702\pi$
$828$	5.17485e7	+	901558.i	2.62314	+	0.0457002i
$829$	1.19420e7	+	1.19420e7i	0.603519	+	0.603519i	0.941245	−	0.337726i	$-0.109658\pi$
$829$	1.19420e7	+	1.19420e7i	0.603519	+	0.603519i	−0.337726	+	0.941245i	$0.609658\pi$
$830$	1.23655e7	−	2.23745e7i	0.623042	−	1.12735i
$831$	5.88346e7			2.95550
$832$	−1.22747e7	−	1.36297e7i	−0.614757	−	0.682620i
$833$		−	3.00392e6i		−	0.149995i
$834$	−1.17276e7	−	1.19337e7i	−0.583841	−	0.594102i
$835$	−2.15072e7	−	1.16429e7i	−1.06750	−	0.577888i
$836$	−56192.7	+	3.22540e6i	−0.00278076	+	0.159613i
$837$	4.78833e7	+	4.78833e7i	2.36249	+	2.36249i
$838$	−6.36337e6	−	55426.8i	−0.313024	−	0.00272653i
$839$		−	2.66734e7i		−	1.30820i	−0.756409	−	0.654099i	$-0.773048\pi$
$839$		−	2.66734e7i		−	1.30820i	0.756409	−	0.654099i	$-0.226952\pi$
$840$	3.33598e7	+	1.92028e7i	1.63127	+	0.938999i
$841$			1.83789e6i			0.0896046i
$842$	−117485.	+	1.34881e7i	−0.00571088	+	0.655647i
$843$	−5.03343e6	−	5.03343e6i	−0.243947	−	0.243947i
$844$	9.47214e6	−	9.14775e6i	0.457712	−	0.442036i
$845$	1.54248e6	−	2.84934e6i	0.0743152	−	0.137279i
$846$	4.83110e7	−	4.74767e7i	2.32071	−	2.28063i
$847$			1.61185e7i			0.771997i
$848$	4.33325e6	+	4.64623e6i	0.206930	+	0.221876i
$849$	−1.97724e7			−0.941435
$850$	−5.07804e6	+	2.31802e7i	−0.241073	+	1.10045i
$851$	−1.22469e7	−	1.22469e7i	−0.579698	−	0.579698i
$852$	−1.60717e7	+	1.55213e7i	−0.758513	+	0.732536i
$853$	2.12552e7	+	2.12552e7i	1.00022	+	1.00022i	1.00000		0.000215401i	$6.85643e-5\pi$
$853$	2.12552e7	+	2.12552e7i	1.00022	+	1.00022i	0.000215401		1.00000i	$0.499931\pi$
$854$	8.26853e6	+	72021.3i	0.387957	+	0.00337922i
$855$	1.32678e7	−	3.94805e6i	0.620700	−	0.184700i
$856$	−566663.	+	2.16812e7i	−0.0264326	+	1.01134i
$857$	−1.84381e7			−0.857557			−0.428778	−	0.903410i	$-0.641056\pi$
$857$	−1.84381e7			−0.857557			−0.428778	+	0.903410i	$0.641056\pi$
$858$	1.83595e7	+	159917.i	0.851420	+	0.00741611i
$859$	724022.	−	724022.i	0.0334787	−	0.0334787i	−0.690169	−	0.723648i	$-0.742464\pi$
$859$	724022.	−	724022.i	0.0334787	−	0.0334787i	0.723648	+	0.690169i	$0.242464\pi$
$860$	−2.21521e7	+	6.17380e6i	−1.02134	+	0.284647i
$861$	−3.10745e7	−	3.10745e7i	−1.42855	−	1.42855i
$862$	7.14209e6	−	7.01874e6i	0.327384	−	0.321730i
$863$		−	1.09525e7i		−	0.500596i	−0.968169	−	0.250298i	$-0.919471\pi$
$863$		−	1.09525e7i		−	0.500596i	0.968169	−	0.250298i	$-0.0805286\pi$
$864$	4.36636e7	+	1.90277e6i	1.98992	+	0.0867166i
$865$	−906163.	+	269645.i	−0.0411781	+	0.0122533i
$866$	−2.46223e7	−	2.50550e7i	−1.11567	−	1.13527i
$867$	7.44702e6	−	7.44702e6i	0.336461	−	0.336461i
$868$	690415.	−	3.96291e7i	0.0311036	−	1.78532i
$869$	1.24214e7	−	1.24214e7i	0.557983	−	0.557983i
$870$	−3.95953e7	+	1.14078e7i	−1.77356	+	0.510981i
$871$		−	3.27458e7i		−	1.46255i
$872$	183308.	−	7.01357e6i	0.00816375	−	0.312354i
$873$	4.39959e7			1.95378
$874$	−8.48470e6	−	73904.2i	−0.375714	−	0.00327258i
$875$	−1.98120e6	−	2.40266e7i	−0.0874800	−	1.06089i
$876$	4.40603e7	+	4.56227e7i	1.93993	+	2.00873i
$877$	2.28514e7	−	2.28514e7i	1.00326	−	1.00326i	0.00326582	−	0.999995i	$-0.498960\pi$
$877$	2.28514e7	−	2.28514e7i	1.00326	−	1.00326i	0.999995	−	0.00326582i	$-0.00103954\pi$
$878$	1.02831e7	+	1.04638e7i	0.450180	+	0.458092i
$879$	6.68287e6			0.291737
$880$	1.16544e7	−	3.03033e6i	0.507320	−	0.131912i
$881$	−1.75647e7			−0.762431			−0.381215	−	0.924486i	$-0.624494\pi$
$881$	−1.75647e7			−0.762431			−0.381215	+	0.924486i	$0.624494\pi$
$882$	4.58487e6	+	4.66544e6i	0.198452	+	0.201939i
$883$	−2.20335e7	+	2.20335e7i	−0.951005	+	0.951005i	−0.998855	−	0.0478500i	$-0.984763\pi$
$883$	−2.20335e7	+	2.20335e7i	−0.951005	+	0.951005i	0.0478500	+	0.998855i	$0.484763\pi$
$884$	1.72959e7	−	1.67036e7i	0.744413	−	0.718919i
$885$	1.04877e7	−	1.93733e7i	0.450112	−	0.831469i
$886$	−107597.	−	937.201i	−0.00460485	−	4.01096e-5i
$887$	−1.09130e7			−0.465730			−0.232865	−	0.972509i	$-0.574810\pi$
$887$	−1.09130e7			−0.465730			−0.232865	+	0.972509i	$0.574810\pi$
$888$	−1.90057e7	−	2.00258e7i	−0.808818	−	0.852232i
$889$		−	2.33958e7i		−	0.992852i
$890$	−4.24617e6	−	1.47380e7i	−0.179689	−	0.623682i
$891$	−1.22566e7	+	1.22566e7i	−0.517220	+	0.517220i
$892$	−8.90175e6	−	155085.i	−0.374596	−	0.00652618i
$893$	−7.85209e6	+	7.85209e6i	−0.329501	+	0.329501i
$894$	1.38183e7	+	1.40612e7i	0.578245	+	0.588407i
$895$	−3.09035e6	−	1.03854e7i	−0.128959	−	0.433376i
$896$	−1.69525e7	−	1.91569e7i	−0.705447	−	0.797176i
$897$			4.82927e7i			2.00401i
$898$	1.21214e7	−	1.19121e7i	0.501605	−	0.492942i
$899$	3.00025e7	+	3.00025e7i	1.23811	+	1.23811i
$900$	−2.74931e7	−	4.37522e7i	−1.13140	−	1.80050i
$901$	−5.88920e6	+	5.88920e6i	−0.241682	+	0.241682i
$902$	−1.37477e7	−	119746.i	−0.562618	−	0.00490056i
$903$	−4.88992e7			−1.99564
$904$	−5.50623e6	+	5.22574e6i	−0.224096	+	0.212680i
$905$	−6.15907e6	+	1.83274e6i	−0.249973	+	0.0743840i
$906$	−8.64077e6	−	75263.6i	−0.349729	−	0.00304624i
$907$	7.58550e6	+	7.58550e6i	0.306172	+	0.306172i	0.843423	−	0.537250i	$-0.180537\pi$
$907$	7.58550e6	+	7.58550e6i	0.306172	+	0.306172i	−0.537250	+	0.843423i	$0.680537\pi$
$908$	1.30967e7	+	1.35611e7i	0.527166	+	0.545860i
$909$	1.55273e7	+	1.55273e7i	0.623286	+	0.623286i
$910$	−1.18161e7	+	2.13803e7i	−0.473009	+	0.855874i
$911$	−2.58735e7			−1.03290			−0.516452	−	0.856316i	$-0.672747\pi$
$911$	−2.58735e7			−1.03290			−0.516452	+	0.856316i	$0.672747\pi$
$912$	−1.35175e7	−	471144.i	−0.538158	−	0.0187572i
$913$		−	1.70059e7i		−	0.675187i
$914$	3.43959e7	−	3.38019e7i	1.36189	−	1.33837i
$915$	−1.43525e7	−	7.76968e6i	−0.566730	−	0.306797i
$916$	−1.51182e7	−	1.56543e7i	−0.595336	−	0.616447i
$917$	−3.21978e6	−	3.21978e6i	−0.126445	−	0.126445i
$918$	−499022.	+	5.72910e7i	−0.0195440	+	2.24378i
$919$			8.52098e6i			0.332813i	0.986057	+	0.166407i	$0.0532164\pi$
$919$			8.52098e6i			0.332813i	−0.986057	+	0.166407i	$0.946784\pi$
$920$	8.23732e6	+	3.05838e7i	0.320861	+	1.19130i
$921$		−	4.71087e7i		−	1.83001i
$922$	4.23235e7	+	368650.i	1.63966	+	0.0142819i
$923$	−1.00265e7	−	1.00265e7i	−0.387387	−	0.387387i
$924$	2.56019e7	+	446034.i	0.986489	+	0.0171865i
$925$	−3.55309e6	+	1.69229e7i	−0.136537	+	0.650311i
$926$	−2.13875e7	−	2.17634e7i	−0.819658	−	0.834063i
$927$		−	9.71363e7i		−	3.71263i
$928$	2.73585e7	+	1.19223e6i	1.04285	+	0.0454453i
$929$	−7.46593e6			−0.283821			−0.141911	−	0.989879i	$-0.545325\pi$
$929$	−7.46593e6			−0.283821			−0.141911	+	0.989879i	$0.545325\pi$
$930$	−3.78403e7	+	6.84692e7i	−1.43465	+	2.59590i
$931$	−758283.	−	758283.i	−0.0286720	−	0.0286720i
$932$	−265266.	+	1.52260e7i	−0.0100033	+	0.574177i
$933$	−3.93313e7	−	3.93313e7i	−1.47922	−	1.47922i
$934$	201502.	−	2.31338e7i	0.00755809	−	0.867720i
$935$	4.50223e6	+	1.51301e7i	0.168422	+	0.565996i
$936$	−1.36800e6	+	5.23414e7i	−0.0510385	+	1.95279i
$937$	7.95156e6			0.295872			0.147936	−	0.988997i	$-0.452737\pi$
$937$	7.95156e6			0.295872			0.147936	+	0.988997i	$0.452737\pi$
$938$	397770.	−	4.56667e7i	0.0147613	−	1.69470i
$939$	−4.86323e7	+	4.86323e7i	−1.79995	+	1.79995i
$940$	3.61040e7	+	2.03658e7i	1.33271	+	0.751765i
$941$	6.07874e6	+	6.07874e6i	0.223789	+	0.223789i	0.810092	−	0.586303i	$-0.199417\pi$
$941$	6.07874e6	+	6.07874e6i	0.223789	+	0.223789i	−0.586303	+	0.810092i	$0.699417\pi$
$942$	−5.45457e7	−	5.55043e7i	−2.00278	−	2.03798i
$943$		−	3.61617e7i		−	1.32425i
$944$	−1.07068e7	+	9.98554e6i	−0.391046	+	0.364705i
$945$	−1.66009e7	−	5.57887e7i	−0.604717	−	2.03220i
$946$	−1.09110e7	+	1.07225e7i	−0.396402	+	0.389556i
$947$	4.08655e6	−	4.08655e6i	0.148075	−	0.148075i	−0.629183	−	0.777258i	$-0.716610\pi$
$947$	4.08655e6	−	4.08655e6i	0.148075	−	0.148075i	0.777258	+	0.629183i	$0.216610\pi$
$948$	5.11661e7	+	5.29805e7i	1.84910	+	1.91468i
$949$	−2.84622e7	+	2.84622e7i	−1.02590	+	1.02590i
$950$	4.56956e6	+	7.13328e6i	0.164273	+	0.256437i
$951$		−	2.04231e7i		−	0.732269i
$952$	2.43235e7	−	2.30844e7i	0.869828	−	0.825518i
$953$	2.76137e7			0.984901			0.492451	−	0.870340i	$-0.336101\pi$
$953$	2.76137e7			0.984901			0.492451	+	0.870340i	$0.336101\pi$
$954$	157964.	−	1.81353e7i	0.00561935	−	0.645139i
$955$	−1.28039e7	−	6.93133e6i	−0.454291	−	0.245928i
$956$	104618.	−	6.00498e6i	0.00370222	−	0.212504i
$957$	−1.93827e7	+	1.93827e7i	−0.684124	+	0.684124i
$958$	−116049.	+	114045.i	−0.00408533	+	0.00401477i
$959$	−2.68093e7			−0.941325
$960$	1.18526e7	+	4.90791e7i	0.415084	+	1.71877i
$961$	5.19244e7			1.81369
$962$	1.24970e7	−	1.22812e7i	0.435380	−	0.427861i
$963$	4.37781e7	−	4.37781e7i	1.52122	−	1.52122i
$964$	−848512.	+	4.87038e7i	−0.0294080	+	1.68799i
$965$	5.14362e6	−	9.50155e6i	0.177808	−	0.328455i
$966$	−586621.	+	6.73480e7i	−0.0202262	+	2.32211i
$967$	2.36209e6			0.0812326			0.0406163	−	0.999175i	$-0.487068\pi$
$967$	2.36209e6			0.0812326			0.0406163	+	0.999175i	$0.487068\pi$
$968$	−1.53357e7	+	1.45545e7i	−0.526035	+	0.499238i
$969$		−	1.77309e7i		−	0.606627i
$970$	7.45400e6	+	2.58720e7i	0.254367	+	0.882879i
$971$	−2.73016e7	+	2.73016e7i	−0.929265	+	0.929265i	−0.997658	−	0.0683937i	$-0.978213\pi$
$971$	−2.73016e7	+	2.73016e7i	−0.929265	+	0.929265i	0.0683937	+	0.997658i	$0.478213\pi$
$972$	−9.73044e6	−	1.00755e7i	−0.330344	−	0.342059i
$973$	1.04715e7	−	1.04715e7i	0.354590	−	0.354590i
$974$	4.07247e6	−	4.00214e6i	0.137550	−	0.135174i
$975$	4.03711e7	−	2.63604e7i	1.36006	−	0.888056i
$976$	7.39769e6	+	7.93199e6i	0.248583	+	0.266537i
$977$		−	2.52638e7i		−	0.846763i	−0.905951	−	0.423382i	$-0.860843\pi$
$977$		−	2.52638e7i		−	0.846763i	0.905951	−	0.423382i	$-0.139157\pi$
$978$	−4.77239e7	−	4.85626e7i	−1.59547	−	1.62351i
$979$	−7.21454e6	−	7.21454e6i	−0.240576	−	0.240576i
$980$	−1.96675e6	+	3.48660e6i	−0.0654159	+	0.115968i
$981$	−1.41616e7	+	1.41616e7i	−0.469830	+	0.469830i
$982$	−243610.	+	2.79680e7i	−0.00806150	+	0.925514i
$983$	−4.55499e7			−1.50350			−0.751750	−	0.659448i	$-0.770790\pi$
$983$	−4.55499e7			−1.50350			−0.751750	+	0.659448i	$0.770790\pi$
$984$	1.50609e6	−	5.76246e7i	0.0495864	−	1.89723i
$985$	−9.62009e6	−	3.23291e7i	−0.315928	−	1.06170i
$986$	−312674.	+	3.58971e7i	−0.0102423	+	1.17589i
$987$	6.23266e7	+	6.23266e7i	2.03648	+	2.03648i
$988$	149525.	−	8.58256e6i	0.00487327	−	0.279721i
$989$	−2.84522e7	−	2.84522e7i	−0.924966	−	0.924966i
$990$	−3.00856e7	−	1.66271e7i	−0.975596	−	0.539175i
$991$	5.88669e7			1.90409			0.952044	−	0.305960i	$-0.0989775\pi$
$991$	5.88669e7			1.90409			0.952044	+	0.305960i	$0.0989775\pi$
$992$	3.83279e7	−	3.51269e7i	1.23662	−	1.13334i
$993$			2.15061e7i			0.692132i
$994$	−1.38610e7	−	1.41045e7i	−0.444966	−	0.452786i
$995$	4.66345e6	−	8.61456e6i	0.149331	−	0.275851i
$996$	7.12927e7	+	1.24206e6i	2.27718	+	0.0396728i
$997$	5.66640e6	+	5.66640e6i	0.180538	+	0.180538i	0.791590	−	0.611052i	$-0.209253\pi$
$997$	5.66640e6	+	5.66640e6i	0.180538	+	0.180538i	−0.611052	+	0.791590i	$0.709253\pi$
$998$	2.59426e7	+	225968.i	0.824495	+	0.00718159i
$999$			4.17494e7i			1.32354i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.15	✓	116
5.4	even	2	inner	80.6.q.a.29.44	yes	116
16.5	even	4	inner	80.6.q.a.69.44	yes	116
80.69	even	4	inner	80.6.q.a.69.15	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.15	✓	116	1.1	even	1	trivial
80.6.q.a.29.44	yes	116	5.4	even	2	inner
80.6.q.a.69.15	yes	116	80.69	even	4	inner
80.6.q.a.69.44	yes	116	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.03469 + 3.96501i) q^{2} +(-19.4902 + 19.4902i) q^{3} +(0.557416 - 31.9951i) q^{4} +(-49.1605 - 26.6128i) q^{5} +(1.35807 - 155.915i) q^{6} +138.003 q^{7} +(124.612 + 131.301i) q^{8} -516.733i q^{9} +O(q^{10})\)	\(q+(-4.03469 + 3.96501i) q^{2} +(-19.4902 + 19.4902i) q^{3} +(0.557416 - 31.9951i) q^{4} +(-49.1605 - 26.6128i) q^{5} +(1.35807 - 155.915i) q^{6} +138.003 q^{7} +(124.612 + 131.301i) q^{8} -516.733i q^{9} +(303.867 - 87.5474i) q^{10} +(148.749 - 148.749i) q^{11} +(612.726 + 634.455i) q^{12} +(-395.811 + 395.811i) q^{13} +(-556.798 + 547.182i) q^{14} +(1476.83 - 439.458i) q^{15} +(-1023.38 - 35.6692i) q^{16} -1342.37i q^{17} +(2048.85 + 2084.86i) q^{18} +(-338.856 - 338.856i) q^{19} +(-878.884 + 1558.06i) q^{20} +(-2689.70 + 2689.70i) q^{21} +(-10.3648 + 1189.95i) q^{22} -3130.03 q^{23} +(-4987.78 - 130.361i) q^{24} +(1708.51 + 2616.60i) q^{25} +(27.5800 - 3166.37i) q^{26} +(5335.09 + 5335.09i) q^{27} +(76.9250 - 4415.42i) q^{28} +(3342.83 + 3342.83i) q^{29} +(-4216.11 + 7628.74i) q^{30} +8975.16 q^{31} +(4270.44 - 3913.79i) q^{32} +5798.30i q^{33} +(5322.50 + 5416.03i) q^{34} +(-6784.29 - 3672.65i) q^{35} +(-16532.9 - 288.035i) q^{36} +(3912.71 + 3912.71i) q^{37} +(2710.74 + 23.6114i) q^{38} -15428.8i q^{39} +(-2631.71 - 9771.08i) q^{40} +11553.2i q^{41} +(187.417 - 21516.8i) q^{42} +(9090.09 + 9090.09i) q^{43} +(-4676.34 - 4842.17i) q^{44} +(-13751.7 + 25402.8i) q^{45} +(12628.7 - 12410.6i) q^{46} -23172.4i q^{47} +(20641.0 - 19250.6i) q^{48} +2237.78 q^{49} +(-17268.2 - 3782.90i) q^{50} +(26162.9 + 26162.9i) q^{51} +(12443.4 + 12884.7i) q^{52} +(-4387.18 - 4387.18i) q^{53} +(-42679.1 - 371.748i) q^{54} +(-11271.2 + 3353.95i) q^{55} +(17196.8 + 18119.9i) q^{56} +13208.7 q^{57} +(-26741.6 - 232.927i) q^{58} +(10109.8 - 10109.8i) q^{59} +(-13237.3 - 47496.5i) q^{60} +(-7489.74 - 7489.74i) q^{61} +(-36212.0 + 35586.6i) q^{62} -71310.6i q^{63} +(-1711.69 + 32723.3i) q^{64} +(29991.9 - 8924.63i) q^{65} +(-22990.3 - 23394.3i) q^{66} +(-41365.5 + 41365.5i) q^{67} +(-42949.2 - 748.257i) q^{68} +(61004.7 - 61004.7i) q^{69} +(41934.6 - 12081.8i) q^{70} +25331.5i q^{71} +(67847.3 - 64391.1i) q^{72} +71908.6 q^{73} +(-31300.5 - 272.637i) q^{74} +(-84297.2 - 17698.8i) q^{75} +(-11030.6 + 10652.9i) q^{76} +(20527.8 - 20527.8i) q^{77} +(61175.5 + 62250.6i) q^{78} +83505.6 q^{79} +(49360.6 + 28988.5i) q^{80} -82397.6 q^{81} +(-45808.4 - 46613.4i) q^{82} +(57163.1 - 57163.1i) q^{83} +(84558.0 + 87556.5i) q^{84} +(-35724.2 + 65991.5i) q^{85} +(-72718.0 - 633.395i) q^{86} -130305. q^{87} +(38066.8 + 994.921i) q^{88} -48501.3i q^{89} +(-45238.6 - 157018. i) q^{90} +(-54623.1 + 54623.1i) q^{91} +(-1744.73 + 100146. i) q^{92} +(-174927. + 174927. i) q^{93} +(91878.6 + 93493.2i) q^{94} +(7640.41 + 25676.2i) q^{95} +(-6951.20 + 159512. i) q^{96} +85142.5i q^{97} +(-9028.73 + 8872.80i) q^{98} +(-76863.6 - 76863.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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