LMFDB - Embedded newform 80.6.l.a.61.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (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:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.15
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.38570 + 5.12917i) q^{2} +(2.82595 + 2.82595i) q^{3} +(-20.6168 - 24.4734i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-21.2367 + 7.75292i) q^{6} +197.416i q^{7} +(174.714 - 47.3612i) q^{8} -227.028i q^{9} +O(q^{10})$	\(q+(-2.38570 + 5.12917i) q^{2} +(2.82595 + 2.82595i) q^{3} +(-20.6168 - 24.4734i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-21.2367 + 7.75292i) q^{6} +197.416i q^{7} +(174.714 - 47.3612i) q^{8} -227.028i q^{9} +(48.4982 + 132.846i) q^{10} +(-541.655 + 541.655i) q^{11} +(10.8984 - 127.423i) q^{12} +(-657.010 - 657.010i) q^{13} +(-1012.58 - 470.975i) q^{14} +99.9125 q^{15} +(-173.892 + 1009.13i) q^{16} +152.646 q^{17} +(1164.47 + 541.621i) q^{18} +(-428.008 - 428.008i) q^{19} +(-797.090 - 68.1744i) q^{20} +(-557.887 + 557.887i) q^{21} +(-1486.01 - 4070.47i) q^{22} -2103.77i q^{23} +(627.574 + 359.893i) q^{24} -625.000i q^{25} +(4937.35 - 1802.49i) q^{26} +(1328.28 - 1328.28i) q^{27} +(4831.42 - 4070.09i) q^{28} +(-1313.03 - 1313.03i) q^{29} +(-238.362 + 512.469i) q^{30} -8014.55 q^{31} +(-4761.13 - 3299.40i) q^{32} -3061.38 q^{33} +(-364.167 + 782.947i) q^{34} +(3489.85 + 3489.85i) q^{35} +(-5556.14 + 4680.60i) q^{36} +(-4174.18 + 4174.18i) q^{37} +(3216.43 - 1174.23i) q^{38} -3713.36i q^{39} +(2251.30 - 3925.77i) q^{40} -6836.92i q^{41} +(-1530.55 - 4192.45i) q^{42} +(367.257 - 367.257i) q^{43} +(24423.3 + 2088.91i) q^{44} +(-4013.33 - 4013.33i) q^{45} +(10790.6 + 5018.97i) q^{46} -6123.69 q^{47} +(-3343.16 + 2360.34i) q^{48} -22165.9 q^{49} +(3205.73 + 1491.06i) q^{50} +(431.370 + 431.370i) q^{51} +(-2533.78 + 29624.7i) q^{52} +(-8837.44 + 8837.44i) q^{53} +(3644.09 + 9981.84i) q^{54} +19150.4i q^{55} +(9349.83 + 34491.2i) q^{56} -2419.06i q^{57} +(9867.26 - 3602.26i) q^{58} +(-23628.5 + 23628.5i) q^{59} +(-2059.88 - 2445.20i) q^{60} +(34685.8 + 34685.8i) q^{61} +(19120.3 - 41108.0i) q^{62} +44818.9 q^{63} +(28281.8 - 16549.3i) q^{64} -23228.8 q^{65} +(7303.55 - 15702.4i) q^{66} +(-12889.4 - 12889.4i) q^{67} +(-3147.07 - 3735.76i) q^{68} +(5945.16 - 5945.16i) q^{69} +(-26225.8 + 9574.29i) q^{70} +56725.7i q^{71} +(-10752.3 - 39664.9i) q^{72} +41485.9i q^{73} +(-11451.7 - 31368.5i) q^{74} +(1766.22 - 1766.22i) q^{75} +(-1650.63 + 19299.0i) q^{76} +(-106931. - 106931. i) q^{77} +(19046.5 + 8858.97i) q^{78} +106416. q^{79} +(14765.0 + 20913.0i) q^{80} -47660.5 q^{81} +(35067.7 + 16310.9i) q^{82} +(-49167.0 - 49167.0i) q^{83} +(25155.3 + 2151.51i) q^{84} +(2698.42 - 2698.42i) q^{85} +(1007.56 + 2759.89i) q^{86} -7421.13i q^{87} +(-68981.2 + 120288. i) q^{88} -62632.3i q^{89} +(30159.6 - 11010.4i) q^{90} +(129704. - 129704. i) q^{91} +(-51486.4 + 43373.1i) q^{92} +(-22648.8 - 22648.8i) q^{93} +(14609.3 - 31409.4i) q^{94} -15132.4 q^{95} +(-4130.80 - 22778.7i) q^{96} +27802.9 q^{97} +(52881.3 - 113693. i) q^{98} +(122971. + 122971. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * 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 $

$2$	−2.38570	+	5.12917i	−0.421737	+	0.906718i
$2$	−2.38570	+	5.12917i	−0.421737	+	0.906718i
$3$	2.82595	+	2.82595i	0.181285	+	0.181285i	0.791916	−	0.610631i	$-0.209084\pi$
$3$	2.82595	+	2.82595i	0.181285	+	0.181285i	−0.610631	+	0.791916i	$0.709084\pi$
$4$	−20.6168	−	24.4734i	−0.644276	−	0.764793i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$5$	17.6777	−	17.6777i	0.316228	−	0.316228i
$6$	−21.2367	+	7.75292i	−0.240829	+	0.0879199i
$7$			197.416i			1.52278i	0.648296	+	0.761389i	$0.275482\pi$
$7$			197.416i			1.52278i	−0.648296	+	0.761389i	$0.724518\pi$
$8$	174.714	−	47.3612i	0.965167	−	0.261636i
$9$		−	227.028i		−	0.934272i
$10$	48.4982	+	132.846i	0.153365	+	0.420094i
$11$	−541.655	+	541.655i	−1.34971	+	1.34971i	−0.463739	+	0.885972i	$0.653493\pi$
$11$	−541.655	+	541.655i	−1.34971	+	1.34971i	−0.885972	+	0.463739i	$0.846507\pi$
$12$	10.8984	−	127.423i	0.0218478	−	0.255443i
$13$	−657.010	−	657.010i	−1.07824	−	1.07824i	−0.996668	−	0.0815680i	$-0.974007\pi$
$13$	−657.010	−	657.010i	−1.07824	−	1.07824i	−0.0815680	−	0.996668i	$-0.525993\pi$
$14$	−1012.58	−	470.975i	−1.38073	−	0.642211i
$15$	99.9125			0.114655
$16$	−173.892	+	1009.13i	−0.169816	+	0.985476i
$17$	152.646			0.128104			0.0640520	−	0.997947i	$-0.479598\pi$
$17$	152.646			0.128104			0.0640520	+	0.997947i	$0.479598\pi$
$18$	1164.47	+	541.621i	0.847121	+	0.394017i
$19$	−428.008	−	428.008i	−0.272000	−	0.272000i	0.557905	−	0.829905i	$-0.311605\pi$
$19$	−428.008	−	428.008i	−0.272000	−	0.272000i	−0.829905	+	0.557905i	$0.811605\pi$
$20$	−797.090	−	68.1744i	−0.445587	−	0.0381107i
$21$	−557.887	+	557.887i	−0.276057	+	0.276057i
$22$	−1486.01	−	4070.47i	−0.654585	−	1.79303i
$23$		−	2103.77i		−	0.829237i	−0.909995	−	0.414619i	$-0.863915\pi$
$23$		−	2103.77i		−	0.829237i	0.909995	−	0.414619i	$-0.136085\pi$
$24$	627.574	+	359.893i	0.222401	+	0.127540i
$25$		−	625.000i		−	0.200000i
$26$	4937.35	−	1802.49i	1.43239	−	0.522925i
$27$	1328.28	−	1328.28i	0.350654	−	0.350654i
$28$	4831.42	−	4070.09i	1.16461	−	0.981089i
$29$	−1313.03	−	1313.03i	−0.289921	−	0.289921i	0.547128	−	0.837049i	$-0.315721\pi$
$29$	−1313.03	−	1313.03i	−0.289921	−	0.289921i	−0.837049	+	0.547128i	$0.815721\pi$
$30$	−238.362	+	512.469i	−0.0483541	+	0.103960i
$31$	−8014.55			−1.49787			−0.748937	−	0.662642i	$-0.769435\pi$
$31$	−8014.55			−1.49787			−0.748937	+	0.662642i	$0.769435\pi$
$32$	−4761.13	−	3299.40i	−0.821931	−	0.569587i
$33$	−3061.38			−0.489365
$34$	−364.167	+	782.947i	−0.0540261	+	0.116154i
$35$	3489.85	+	3489.85i	0.481544	+	0.481544i
$36$	−5556.14	+	4680.60i	−0.714524	+	0.601929i
$37$	−4174.18	+	4174.18i	−0.501265	+	0.501265i	−0.911831	−	0.410566i	$-0.865331\pi$
$37$	−4174.18	+	4174.18i	−0.501265	+	0.501265i	0.410566	+	0.911831i	$0.365331\pi$
$38$	3216.43	−	1174.23i	0.361339	−	0.131915i
$39$		−	3713.36i		−	0.390936i
$40$	2251.30	−	3925.77i	0.222476	−	0.387949i
$41$		−	6836.92i		−	0.635186i	−0.948227	−	0.317593i	$-0.897126\pi$
$41$		−	6836.92i		−	0.635186i	0.948227	−	0.317593i	$-0.102874\pi$
$42$	−1530.55	−	4192.45i	−0.133882	−	0.366729i
$43$	367.257	−	367.257i	0.0302900	−	0.0302900i	−0.691800	−	0.722090i	$-0.743182\pi$
$43$	367.257	−	367.257i	0.0302900	−	0.0302900i	0.722090	+	0.691800i	$0.243182\pi$
$44$	24423.3	+	2088.91i	1.90184	+	0.162662i
$45$	−4013.33	−	4013.33i	−0.295443	−	0.295443i
$46$	10790.6	+	5018.97i	0.751885	+	0.349720i
$47$	−6123.69			−0.404360			−0.202180	−	0.979348i	$-0.564803\pi$
$47$	−6123.69			−0.404360			−0.202180	+	0.979348i	$0.564803\pi$
$48$	−3343.16	+	2360.34i	−0.209437	+	0.147867i
$49$	−22165.9			−1.31885
$50$	3205.73	+	1491.06i	0.181344	+	0.0843473i
$51$	431.370	+	431.370i	0.0232233	+	0.0232233i
$52$	−2533.78	+	29624.7i	−0.129945	+	1.51931i
$53$	−8837.44	+	8837.44i	−0.432152	+	0.432152i	−0.889360	−	0.457208i	$-0.848850\pi$
$53$	−8837.44	+	8837.44i	−0.432152	+	0.432152i	0.457208	+	0.889360i	$0.348850\pi$
$54$	3644.09	+	9981.84i	0.170061	+	0.465829i
$55$			19150.4i			0.853632i
$56$	9349.83	+	34491.2i	0.398413	+	1.46973i
$57$		−	2419.06i		−	0.0986189i
$58$	9867.26	−	3602.26i	0.385147	−	0.140606i
$59$	−23628.5	+	23628.5i	−0.883704	+	0.883704i	−0.993909	−	0.110205i	$-0.964849\pi$
$59$	−23628.5	+	23628.5i	−0.883704	+	0.883704i	0.110205	+	0.993909i	$0.464849\pi$
$60$	−2059.88	−	2445.20i	−0.0738693	−	0.0876871i
$61$	34685.8	+	34685.8i	1.19351	+	1.19351i	0.976074	+	0.217437i	$0.0697698\pi$
$61$	34685.8	+	34685.8i	1.19351	+	1.19351i	0.217437	+	0.976074i	$0.430230\pi$
$62$	19120.3	−	41108.0i	0.631708	−	1.35815i
$63$	44818.9			1.42269
$64$	28281.8	−	16549.3i	0.863093	−	0.505045i
$65$	−23228.8			−0.681936
$66$	7303.55	−	15702.4i	0.206383	−	0.443716i
$67$	−12889.4	−	12889.4i	−0.350790	−	0.350790i	0.509613	−	0.860403i	$-0.329788\pi$
$67$	−12889.4	−	12889.4i	−0.350790	−	0.350790i	−0.860403	+	0.509613i	$0.829788\pi$
$68$	−3147.07	−	3735.76i	−0.0825343	−	0.0979730i
$69$	5945.16	−	5945.16i	0.150328	−	0.150328i
$70$	−26225.8	+	9574.29i	−0.639710	+	0.233540i
$71$			56725.7i			1.33547i	0.744399	+	0.667735i	$0.232736\pi$
$71$			56725.7i			1.33547i	−0.744399	+	0.667735i	$0.767264\pi$
$72$	−10752.3	−	39664.9i	−0.244439	−	0.901728i
$73$			41485.9i			0.911158i	0.890195	+	0.455579i	$0.150568\pi$
$73$			41485.9i			0.911158i	−0.890195	+	0.455579i	$0.849432\pi$
$74$	−11451.7	−	31368.5i	−0.243104	−	0.665907i
$75$	1766.22	−	1766.22i	0.0362570	−	0.0362570i
$76$	−1650.63	+	19299.0i	−0.0327804	+	0.383266i
$77$	−106931.	−	106931.i	−2.05531	−	2.05531i
$78$	19046.5	+	8858.97i	0.354469	+	0.164872i
$79$	106416.			1.91839			0.959196	−	0.282743i	$-0.0912444\pi$
$79$	106416.			1.91839			0.959196	+	0.282743i	$0.0912444\pi$
$80$	14765.0	+	20913.0i	0.257934	+	0.365335i
$81$	−47660.5			−0.807135
$82$	35067.7	+	16310.9i	0.575934	+	0.267881i
$83$	−49167.0	−	49167.0i	−0.783390	−	0.783390i	0.197011	−	0.980401i	$-0.436876\pi$
$83$	−49167.0	−	49167.0i	−0.783390	−	0.783390i	−0.980401	+	0.197011i	$0.936876\pi$
$84$	25155.3	+	2151.51i	0.388983	+	0.0332694i
$85$	2698.42	−	2698.42i	0.0405100	−	0.0405100i
$86$	1007.56	+	2759.89i	0.0146901	+	0.0402389i
$87$		−	7421.13i		−	0.105117i
$88$	−68981.2	+	120288.i	−0.949563	+	1.65583i
$89$		−	62632.3i		−	0.838154i	−0.907951	−	0.419077i	$-0.862354\pi$
$89$		−	62632.3i		−	0.838154i	0.907951	−	0.419077i	$-0.137646\pi$
$90$	30159.6	−	11010.4i	0.392482	−	0.143284i
$91$	129704.	−	129704.i	1.64191	−	1.64191i
$92$	−51486.4	+	43373.1i	−0.634195	+	0.534258i
$93$	−22648.8	−	22648.8i	−0.271542	−	0.271542i
$94$	14609.3	−	31409.4i	0.170533	−	0.366641i
$95$	−15132.4			−0.172028
$96$	−4130.80	−	22778.7i	−0.0457463	−	0.252261i
$97$	27802.9			0.300027			0.150014	−	0.988684i	$-0.452068\pi$
$97$	27802.9			0.300027			0.150014	+	0.988684i	$0.452068\pi$
$98$	52881.3	−	113693.i	0.556207	−	1.19583i
$99$	122971.	+	122971.i	1.26100	+	1.26100i
$100$	−15295.9	+	12885.5i	−0.152959	+	0.128855i
$101$	−86867.1	+	86867.1i	−0.847328	+	0.847328i	−0.989799	−	0.142471i	$-0.954495\pi$
$101$	−86867.1	+	86867.1i	−0.847328	+	0.847328i	0.142471	+	0.989799i	$0.454495\pi$
$102$	−3241.69	+	1183.45i	−0.0308511	+	0.0112629i
$103$			37838.9i			0.351436i	0.984441	+	0.175718i	$0.0562246\pi$
$103$			37838.9i			0.351436i	−0.984441	+	0.175718i	$0.943775\pi$
$104$	−145906.	−	83672.0i	−1.32278	−	0.758572i
$105$			19724.3i			0.174594i
$106$	−24245.2	−	66412.2i	−0.209586	−	0.574095i
$107$	1871.29	−	1871.29i	0.0158009	−	0.0158009i	−0.699162	−	0.714963i	$-0.746443\pi$
$107$	1871.29	−	1871.29i	0.0158009	−	0.0158009i	0.714963	+	0.699162i	$0.246443\pi$
$108$	−59892.3	−	5122.54i	−0.494096	−	0.0422596i
$109$	39905.8	+	39905.8i	0.321714	+	0.321714i	0.849424	−	0.527710i	$-0.176949\pi$
$109$	39905.8	+	39905.8i	0.321714	+	0.321714i	−0.527710	+	0.849424i	$0.676949\pi$
$110$	−98225.6	−	45687.1i	−0.774004	−	0.360008i
$111$	−23592.1			−0.181743
$112$	−199217.	−	34328.9i	−1.50066	−	0.258592i
$113$	179127.			1.31967			0.659834	−	0.751412i	$-0.270627\pi$
$113$	179127.			1.31967			0.659834	+	0.751412i	$0.270627\pi$
$114$	12407.8	+	5771.17i	0.0894196	+	0.0415912i
$115$	−37189.8	−	37189.8i	−0.262228	−	0.262228i
$116$	−5063.74	+	59204.8i	−0.0349403	+	0.408519i
$117$	−149160.	+	149160.i	−1.00736	+	1.00736i
$118$	−64824.2	−	177565.i	−0.428580	−	1.17396i
$119$			30134.7i			0.195074i
$120$	17456.1	−	4731.97i	0.110661	−	0.0299978i
$121$		−	425729.i		−	2.64344i
$122$	−260659.	+	95159.4i	−1.58553	+	0.578831i
$123$	19320.8	−	19320.8i	0.115150	−	0.115150i
$124$	165235.	+	196143.i	0.965044	+	1.14556i
$125$	−11048.5	−	11048.5i	−0.0632456	−	0.0632456i
$126$	−106924.	+	229884.i	−0.599999	+	1.28998i
$127$	54658.8			0.300712			0.150356	−	0.988632i	$-0.451958\pi$
$127$	54658.8			0.300712			0.150356	+	0.988632i	$0.451958\pi$
$128$	17412.2	+	184544.i	0.0939351	+	0.995578i
$129$	2075.70			0.0109822
$130$	55417.1	−	119145.i	0.287598	−	0.618324i
$131$	75263.3	+	75263.3i	0.383182	+	0.383182i	0.872247	−	0.489065i	$-0.162662\pi$
$131$	75263.3	+	75263.3i	0.383182	+	0.383182i	−0.489065	+	0.872247i	$0.662662\pi$
$132$	63116.0	+	74922.3i	0.315286	+	0.374263i
$133$	84495.5	−	84495.5i	0.414195	−	0.414195i
$134$	96862.6	−	35361.8i	0.466009	−	0.170127i
$135$		−	46961.7i		−	0.221773i
$136$	26669.3	−	7229.48i	0.123642	−	0.0335166i
$137$		−	82268.7i		−	0.374484i	−0.982314	−	0.187242i	$-0.940045\pi$
$137$		−	82268.7i		−	0.374484i	0.982314	−	0.187242i	$-0.0599549\pi$
$138$	16310.4	+	44677.1i	0.0729065	+	0.199704i
$139$	−30619.7	+	30619.7i	−0.134420	+	0.134420i	−0.771115	−	0.636696i	$-0.780301\pi$
$139$	−30619.7	+	30619.7i	−0.134420	+	0.134420i	0.636696	+	0.771115i	$0.280301\pi$
$140$	13458.7	−	157358.i	0.0580340	−	0.678529i
$141$	−17305.2	−	17305.2i	−0.0733044	−	0.0733044i
$142$	−290956.	−	135331.i	−1.21089	−	0.563217i
$143$	711745.			2.91061
$144$	229100.	+	39478.3i	0.920702	+	0.158654i
$145$	−46422.6			−0.183362
$146$	−212788.	−	98973.1i	−0.826163	−	0.384269i
$147$	−62639.8	−	62639.8i	−0.239088	−	0.239088i
$148$	188215.	+	16097.8i	0.706316	+	0.0604107i
$149$	−209646.	+	209646.i	−0.773607	+	0.773607i	−0.978735	−	0.205128i	$-0.934239\pi$
$149$	−209646.	+	209646.i	−0.773607	+	0.773607i	0.205128	+	0.978735i	$0.434239\pi$
$150$	4845.57	+	13272.9i	0.0175840	+	0.0481658i
$151$			202737.i			0.723586i	0.932258	+	0.361793i	$0.117835\pi$
$151$			202737.i			0.723586i	−0.932258	+	0.361793i	$0.882165\pi$
$152$	−95050.0	−	54508.0i	−0.333690	−	0.191360i
$153$		−	34654.9i		−	0.119684i
$154$	803574.	−	293362.i	2.73039	−	0.996787i
$155$	−141679.	+	141679.i	−0.473669	+	0.473669i
$156$	−90878.4	+	76557.8i	−0.298985	+	0.251871i
$157$	343510.	+	343510.i	1.11222	+	1.11222i	0.992850	+	0.119369i	$0.0380872\pi$
$157$	343510.	+	343510.i	1.11222	+	1.11222i	0.119369	+	0.992850i	$0.461913\pi$
$158$	−253876.	+	545824.i	−0.809056	+	1.73944i
$159$	−49948.4			−0.156685
$160$	−142491.	+	25840.1i	−0.440037	+	0.0797984i
$161$	415317.			1.26274
$162$	113704.	−	244459.i	0.340398	−	0.731844i
$163$	−163012.	−	163012.i	−0.480564	−	0.480564i	0.424748	−	0.905312i	$-0.360363\pi$
$163$	−163012.	−	163012.i	−0.480564	−	0.480564i	−0.905312	+	0.424748i	$0.860363\pi$
$164$	−167322.	+	140956.i	−0.485785	+	0.409235i
$165$	−54118.1	+	54118.1i	−0.154751	+	0.154751i
$166$	369484.	−	134888.i	1.04070	−	0.379930i
$167$		−	12174.1i		−	0.0337790i	−0.999857	−	0.0168895i	$-0.994624\pi$
$167$		−	12174.1i		−	0.0337790i	0.999857	−	0.0168895i	$-0.00537634\pi$
$168$	−71048.4	+	123893.i	−0.194214	+	0.338667i
$169$			492032.i			1.32518i
$170$	7403.04	+	20278.3i	0.0196466	+	0.0538157i
$171$	−97169.9	+	97169.9i	−0.254121	+	0.254121i
$172$	−16559.7	−	1416.34i	−0.0426807	−	0.00365044i
$173$	−536526.	−	536526.i	−1.36294	−	1.36294i	−0.870152	−	0.492783i	$-0.835980\pi$
$173$	−536526.	−	536526.i	−1.36294	−	1.36294i	−0.492783	−	0.870152i	$-0.664020\pi$
$174$	38064.2	+	17704.6i	0.0953112	+	0.0443316i
$175$	123385.			0.304555
$176$	−452409.	−	640788.i	−1.10090	−	1.55931i
$177$	−133546.			−0.320404
$178$	321252.	+	149422.i	0.759969	+	0.353480i
$179$	−496149.	−	496149.i	−1.15739	−	1.15739i	−0.985035	−	0.172356i	$-0.944862\pi$
$179$	−496149.	−	496149.i	−1.15739	−	1.15739i	−0.172356	−	0.985035i	$-0.555138\pi$
$180$	−15477.5	+	180962.i	−0.0356057	+	0.416299i
$181$	189857.	−	189857.i	0.430754	−	0.430754i	−0.458131	−	0.888885i	$-0.651481\pi$
$181$	189857.	−	189857.i	0.430754	−	0.430754i	0.888885	+	0.458131i	$0.151481\pi$
$182$	355839.	+	974710.i	0.796298	+	2.18121i
$183$			196041.i			0.432731i
$184$	−99637.1	−	367558.i	−0.216958	−	0.800352i
$185$			147580.i			0.317028i
$186$	170203.	−	62136.2i	0.360731	−	0.131693i
$187$	−82681.3	+	82681.3i	−0.172903	+	0.172903i
$188$	126251.	+	149867.i	0.260520	+	0.309252i
$189$	262223.	+	262223.i	0.533968	+	0.533968i
$190$	36101.4	−	77616.6i	0.0725504	−	0.155981i
$191$	−216777.			−0.429962			−0.214981	−	0.976618i	$-0.568969\pi$
$191$	−216777.			−0.429962			−0.214981	+	0.976618i	$0.568969\pi$
$192$	126691.	+	33155.6i	0.248023	+	0.0649089i
$193$	−129059.			−0.249399			−0.124700	−	0.992195i	$-0.539797\pi$
$193$	−129059.			−0.249399			−0.124700	+	0.992195i	$0.539797\pi$
$194$	−66329.4	+	142606.i	−0.126532	+	0.272040i
$195$	−65643.6	−	65643.6i	−0.123625	−	0.123625i
$196$	456991.	+	542475.i	0.849704	+	1.00865i
$197$	−384351.	+	384351.i	−0.705607	+	0.705607i	−0.965608	−	0.260001i	$-0.916277\pi$
$197$	−384351.	+	384351.i	−0.705607	+	0.705607i	0.260001	+	0.965608i	$0.416277\pi$
$198$	−924110.	+	337367.i	−1.67518	+	0.611560i
$199$			754358.i			1.35035i	0.737660	+	0.675173i	$0.235931\pi$
$199$			754358.i			1.35035i	−0.737660	+	0.675173i	$0.764069\pi$
$200$	−29600.7	−	109196.i	−0.0523272	−	0.193033i
$201$		−	72849.9i		−	0.127186i
$202$	−238317.	−	652795.i	−0.410939	−	1.12564i
$203$	259213.	−	259213.i	0.441485	−	0.441485i
$204$	1663.59	−	19450.6i	0.00279879	−	0.0327233i
$205$	−120861.	−	120861.i	−0.200863	−	0.200863i
$206$	−194082.	−	90272.4i	−0.318653	−	0.148213i
$207$	−477615.			−0.774733
$208$	777255.	−	548758.i	1.24568	−	0.879473i
$209$	463665.			0.734242
$210$	−101169.	−	47056.3i	−0.158307	−	0.0736325i
$211$	−508214.	−	508214.i	−0.785851	−	0.785851i	0.194960	−	0.980811i	$-0.437542\pi$
$211$	−508214.	−	508214.i	−0.785851	−	0.785851i	−0.980811	+	0.194960i	$0.937542\pi$
$212$	398482.	+	34081.8i	0.608932	+	0.0520815i
$213$	−160304.	+	160304.i	−0.242101	+	0.242101i
$214$	5133.84	+	14062.5i	0.00766316	+	0.0209908i
$215$		−	12984.5i		−	0.0191571i
$216$	169160.	−	294977.i	0.246696	−	0.430184i
$217$		−	1.58220e6i		−	2.28093i
$218$	−299887.	+	109480.i	−0.427383	+	0.156025i
$219$	−117237.	+	117237.i	−0.165179	+	0.165179i
$220$	468674.	−	394820.i	0.652852	−	0.549975i
$221$	−100290.	−	100290.i	−0.138126	−	0.138126i
$222$	56283.7	−	121008.i	0.0766479	−	0.164790i
$223$	162588.			0.218940			0.109470	−	0.993990i	$-0.465085\pi$
$223$	162588.			0.218940			0.109470	+	0.993990i	$0.465085\pi$
$224$	651353.	−	939922.i	0.867354	−	1.25162i
$225$	−141892.			−0.186854
$226$	−427343.	+	918773.i	−0.556552	+	1.19657i
$227$	−517939.	−	517939.i	−0.667135	−	0.667135i	0.289917	−	0.957052i	$-0.406372\pi$
$227$	−517939.	−	517939.i	−0.667135	−	0.667135i	−0.957052	+	0.289917i	$0.906372\pi$
$228$	−59202.6	+	49873.4i	−0.0754230	+	0.0635378i
$229$	−814473.	+	814473.i	−1.02633	+	1.02633i	−0.0266888	+	0.999644i	$0.508496\pi$
$229$	−814473.	+	814473.i	−1.02633	+	1.02633i	−0.999644	+	0.0266888i	$0.991504\pi$
$230$	279477.	−	102029.i	0.348358	−	0.127176i
$231$		−	604364.i		−	0.745193i
$232$	−291591.	−	167218.i	−0.355676	−	0.203968i
$233$		−	453287.i		−	0.546995i	−0.961873	−	0.273498i	$-0.911819\pi$
$233$		−	453287.i		−	0.546995i	0.961873	−	0.273498i	$-0.0881805\pi$
$234$	−409215.	−	1.12092e6i	−0.488554	−	1.33824i
$235$	−108252.	+	108252.i	−0.127870	+	0.127870i
$236$	1.06542e6	+	91124.1i	1.24520	+	0.106501i
$237$	300725.	+	300725.i	0.347776	+	0.347776i
$238$	−154566.	−	71892.3i	−0.176877	−	0.0822697i
$239$	−1.02509e6			−1.16083			−0.580413	−	0.814322i	$-0.697109\pi$
$239$	−1.02509e6			−1.16083			−0.580413	+	0.814322i	$0.697109\pi$
$240$	−17374.0	+	100824.i	−0.0194702	+	0.112989i
$241$	1.33741e6			1.48328			0.741638	−	0.670800i	$-0.234049\pi$
$241$	1.33741e6			1.48328			0.741638	+	0.670800i	$0.234049\pi$
$242$	2.18364e6	+	1.01566e6i	2.39685	+	1.11484i
$243$	−457458.	−	457458.i	−0.496976	−	0.496976i
$244$	133767.	−	1.56399e6i	0.143838	−	1.68174i
$245$	−391842.	+	391842.i	−0.417057	+	0.417057i
$246$	53006.1	+	145193.i	0.0558454	+	0.152971i
$247$			562412.i			0.586559i
$248$	−1.40025e6	+	379579.i	−1.44570	+	0.391897i
$249$		−	277887.i		−	0.284034i
$250$	83028.4	−	30311.4i	0.0840189	−	0.0306729i
$251$	−949915.	+	949915.i	−0.951701	+	0.951701i	−0.998886	−	0.0471855i	$-0.984975\pi$
$251$	−949915.	+	949915.i	−0.951701	+	0.951701i	0.0471855	+	0.998886i	$0.484975\pi$
$252$	−924023.	−	1.09687e6i	−0.916604	−	1.08806i
$253$	1.13952e6	+	1.13952e6i	1.11923	+	1.11923i
$254$	−130400.	+	280355.i	−0.126821	+	0.272661i
$255$	15251.2			0.0146877
$256$	−988099.	−	350958.i	−0.942325	−	0.334699i
$257$	1.04686e6			0.988681			0.494341	−	0.869268i	$-0.335410\pi$
$257$	1.04686e6			0.988681			0.494341	+	0.869268i	$0.335410\pi$
$258$	−4952.01	+	10646.6i	−0.00463161	+	0.00995779i
$259$	−824048.	−	824048.i	−0.763314	−	0.763314i
$260$	478905.	+	568487.i	0.439355	+	0.521540i
$261$	−298095.	+	298095.i	−0.270865	+	0.270865i
$262$	−565594.	+	206483.i	−0.509040	+	0.185836i
$263$		−	1.88612e6i		−	1.68144i	−0.541472	−	0.840719i	$-0.682133\pi$
$263$		−	1.88612e6i		−	1.68144i	0.541472	−	0.840719i	$-0.317867\pi$
$264$	−534866.	+	144991.i	−0.472318	+	0.128035i
$265$			312451.i			0.273317i
$266$	231811.	+	634973.i	0.200877	+	0.550239i
$267$	176996.	−	176996.i	0.151945	−	0.151945i
$268$	−49708.5	+	581188.i	−0.0422760	+	0.494287i
$269$	−225955.	−	225955.i	−0.190388	−	0.190388i	0.605476	−	0.795864i	$-0.292983\pi$
$269$	−225955.	−	225955.i	−0.190388	−	0.190388i	−0.795864	+	0.605476i	$0.792983\pi$
$270$	240875.	+	112037.i	0.201086	+	0.0935299i
$271$	751159.			0.621310			0.310655	−	0.950523i	$-0.399452\pi$
$271$	751159.			0.621310			0.310655	+	0.950523i	$0.399452\pi$
$272$	−26543.8	+	154039.i	−0.0217541	+	0.126243i
$273$	733075.			0.595308
$274$	421971.	+	196269.i	0.339552	+	0.157934i
$275$	338534.	+	338534.i	0.269942	+	0.269942i
$276$	−268068.	−	22927.7i	−0.211823	−	0.0181170i
$277$	991598.	−	991598.i	0.776491	−	0.776491i	−0.202742	−	0.979232i	$-0.564985\pi$
$277$	991598.	−	991598.i	0.776491	−	0.776491i	0.979232	+	0.202742i	$0.0649852\pi$
$278$	−84004.1	−	230103.i	−0.0651911	−	0.178571i
$279$			1.81953e6i			1.39942i
$280$	775008.	+	444441.i	0.590760	+	0.338781i
$281$			1.15437e6i			0.872126i	0.899916	+	0.436063i	$0.143627\pi$
$281$			1.15437e6i			0.872126i	−0.899916	+	0.436063i	$0.856373\pi$
$282$	130047.	−	47476.4i	0.0973816	−	0.0355513i
$283$	1.22003e6	−	1.22003e6i	0.905530	−	0.905530i	−0.0903777	−	0.995908i	$-0.528807\pi$
$283$	1.22003e6	−	1.22003e6i	0.905530	−	0.905530i	0.995908	+	0.0903777i	$0.0288074\pi$
$284$	1.38827e6	−	1.16950e6i	1.02136	−	0.860411i
$285$	−42763.4	−	42763.4i	−0.0311860	−	0.0311860i
$286$	−1.69801e6	+	3.65066e6i	−1.22751	+	2.63911i
$287$	1.34971e6			0.967246
$288$	−749056.	+	1.08091e6i	−0.532149	+	0.767907i
$289$	−1.39656e6			−0.983589
$290$	110751.	−	238110.i	0.0773306	−	0.166258i
$291$	78569.6	+	78569.6i	0.0543904	+	0.0543904i
$292$	1.01530e6	−	855308.i	0.696847	−	0.587037i
$293$	203103.	−	203103.i	0.138213	−	0.138213i	−0.634615	−	0.772828i	$-0.718841\pi$
$293$	203103.	−	203103.i	0.138213	−	0.138213i	0.772828	+	0.634615i	$0.218841\pi$
$294$	470731.	−	171851.i	0.317617	−	0.115953i
$295$			835395.i			0.558903i
$296$	−531593.	+	926981.i	−0.352655	+	0.614953i
$297$			1.43893e6i			0.946564i
$298$	−575157.	−	1.57546e6i	−0.375185	−	1.02770i
$299$	−1.38220e6	+	1.38220e6i	−0.894114	+	0.894114i
$300$	−79639.3	−	6811.48i	−0.0510886	−	0.00436957i
$301$	72502.2	+	72502.2i	0.0461249	+	0.0461249i
$302$	−1.03987e6	−	483670.i	−0.656089	−	0.305163i
$303$	−490965.			−0.307216
$304$	506342.	−	357488.i	0.314239	−	0.221859i
$305$	1.22633e6			0.754843
$306$	177751.	+	82676.2i	0.108520	+	0.0504751i
$307$	559308.	+	559308.i	0.338692	+	0.338692i	0.855875	−	0.517183i	$-0.173019\pi$
$307$	559308.	+	559308.i	0.338692	+	0.338692i	−0.517183	+	0.855875i	$0.673019\pi$
$308$	−412383.	+	4.82154e6i	−0.247699	+	2.89607i
$309$	−106931.	+	106931.i	−0.0637100	+	0.0637100i
$310$	−388691.	−	1.06470e6i	−0.229721	−	0.629248i
$311$			1.23935e6i			0.726598i	0.931673	+	0.363299i	$0.118350\pi$
$311$			1.23935e6i			0.726598i	−0.931673	+	0.363299i	$0.881650\pi$
$312$	−175869.	−	648775.i	−0.102283	−	0.377318i
$313$		−	859630.i		−	0.495965i	−0.968765	−	0.247982i	$-0.920233\pi$
$313$		−	859630.i		−	0.495965i	0.968765	−	0.247982i	$-0.0797675\pi$
$314$	−2.58144e6	+	942410.i	−1.47753	+	0.539406i
$315$	792293.	−	792293.i	0.449893	−	0.449893i
$316$	−2.19395e6	−	2.60435e6i	−1.23597	−	1.46717i
$317$	227313.	+	227313.i	0.127051	+	0.127051i	0.767773	−	0.640722i	$-0.221365\pi$
$317$	227313.	+	227313.i	0.127051	+	0.127051i	−0.640722	+	0.767773i	$0.721365\pi$
$318$	119162.	−	256194.i	0.0660800	−	0.142069i
$319$	1.42242e6			0.782619
$320$	207404.	−	792510.i	0.113225	−	0.432643i
$321$	10576.4			0.00572894
$322$	−990824.	+	2.13023e6i	−0.532545	+	1.14495i
$323$	−65333.7	−	65333.7i	−0.0348442	−	0.0348442i
$324$	982609.	+	1.16641e6i	0.520018	+	0.617291i
$325$	−410631.	+	410631.i	−0.215647	+	0.215647i
$326$	1.22502e6	−	447219.i	0.638407	−	0.233065i
$327$			225544.i			0.116644i
$328$	−323804.	−	1.19450e6i	−0.166187	−	0.613060i
$329$		−	1.20891e6i		−	0.615750i
$330$	−148471.	−	406691.i	−0.0750512	−	0.205579i
$331$	781848.	−	781848.i	0.392240	−	0.392240i	−0.483245	−	0.875485i	$-0.660542\pi$
$331$	781848.	−	781848.i	0.392240	−	0.392240i	0.875485	+	0.483245i	$0.160542\pi$
$332$	−189614.	+	2.21695e6i	−0.0944114	+	1.10385i
$333$	947656.	+	947656.i	0.468317	+	0.468317i
$334$	62443.2	+	29043.8i	0.0306280	+	0.0142458i
$335$	−455711.			−0.221859
$336$	−465967.	−	659991.i	−0.225168	−	0.318926i
$337$	3.22360e6			1.54620			0.773102	−	0.634282i	$-0.218704\pi$
$337$	3.22360e6			1.54620			0.773102	+	0.634282i	$0.218704\pi$
$338$	−2.52372e6	−	1.17384e6i	−1.20157	−	0.558879i
$339$	506204.	+	506204.i	0.239236	+	0.239236i
$340$	−121672.	−	10406.5i	−0.0570814	−	0.00488213i
$341$	4.34112e6	−	4.34112e6i	2.02170	−	2.02170i
$342$	−266583.	−	730220.i	−0.123244	−	0.337589i
$343$		−	1.05793e6i		−	0.485537i
$344$	46771.1	−	81558.6i	0.0213099	−	0.0371598i
$345$		−	210193.i		−	0.0950760i
$346$	4.03192e6	−	1.47194e6i	1.81060	−	0.660999i
$347$	336317.	−	336317.i	0.149942	−	0.149942i	−0.628150	−	0.778092i	$-0.716188\pi$
$347$	336317.	−	336317.i	0.149942	−	0.149942i	0.778092	+	0.628150i	$0.216188\pi$
$348$	−181620.	+	153000.i	−0.0803925	+	0.0677242i
$349$	−1.30701e6	−	1.30701e6i	−0.574400	−	0.574400i	0.358955	−	0.933355i	$-0.383133\pi$
$349$	−1.30701e6	−	1.30701e6i	−0.574400	−	0.574400i	−0.933355	+	0.358955i	$0.883133\pi$
$350$	−294359.	+	632862.i	−0.128442	+	0.276146i
$351$	−1.74538e6			−0.756176
$352$	4.36603e6	−	791756.i	1.87815	−	0.340592i
$353$	−4.18476e6			−1.78745			−0.893725	−	0.448615i	$-0.851917\pi$
$353$	−4.18476e6			−1.78745			−0.893725	+	0.448615i	$0.851917\pi$
$354$	318602.	−	684982.i	0.135126	−	0.290517i
$355$	1.00278e6	+	1.00278e6i	0.422313	+	0.422313i
$356$	−1.53282e6	+	1.29128e6i	−0.641014	+	0.540003i
$357$	−85159.1	+	85159.1i	−0.0353639	+	0.0353639i
$358$	3.72850e6	−	1.36117e6i	1.53754	−	0.561313i
$359$		−	1.30242e6i		−	0.533354i	−0.963786	−	0.266677i	$-0.914074\pi$
$359$		−	1.30242e6i		−	0.533354i	0.963786	−	0.266677i	$-0.0859257\pi$
$360$	−891259.	−	511108.i	−0.362450	−	0.207853i
$361$		−	2.10972e6i		−	0.852032i
$362$	520866.	+	1.42675e6i	0.208908	+	0.572237i
$363$	1.20309e6	−	1.20309e6i	0.479216	−	0.479216i
$364$	−5.84838e6	−	500207.i	−2.31357	−	0.197878i
$365$	733374.	+	733374.i	0.288133	+	0.288133i
$366$	−1.00553e6	−	467695.i	−0.392366	−	0.182499i
$367$	442787.			0.171605			0.0858025	−	0.996312i	$-0.472655\pi$
$367$	442787.			0.171605			0.0858025	+	0.996312i	$0.472655\pi$
$368$	2.12297e6	+	365828.i	0.817193	+	0.140818i
$369$	−1.55217e6			−0.593436
$370$	−756961.	−	352081.i	−0.287455	−	0.133702i
$371$	−1.74465e6	−	1.74465e6i	−0.658071	−	0.658071i
$372$	−87345.5	+	1.02124e6i	−0.0327253	+	0.382621i
$373$	−3.38472e6	+	3.38472e6i	−1.25965	+	1.25965i	−0.308392	+	0.951259i	$0.599791\pi$
$373$	−3.38472e6	+	3.38472e6i	−1.25965	+	1.25965i	−0.951259	+	0.308392i	$0.900209\pi$
$374$	−226834.	−	621340.i	−0.0838549	−	0.229694i
$375$		−	62445.3i		−	0.0229309i
$376$	−1.06989e6	+	290025.i	−0.390275	+	0.105795i
$377$			1.72535e6i			0.625207i
$378$	−1.97057e6	+	719400.i	−0.709353	+	0.258965i
$379$	−1.74454e6	+	1.74454e6i	−0.623852	+	0.623852i	−0.946514	−	0.322662i	$-0.895422\pi$
$379$	−1.74454e6	+	1.74454e6i	−0.623852	+	0.623852i	0.322662	+	0.946514i	$0.395422\pi$
$380$	311982.	+	370340.i	0.110833	+	0.131566i
$381$	154463.	+	154463.i	0.0545146	+	0.0545146i
$382$	517166.	−	1.11189e6i	0.181331	−	0.389855i
$383$	3.91329e6			1.36315			0.681577	−	0.731746i	$-0.261294\pi$
$383$	3.91329e6			1.36315			0.681577	+	0.731746i	$0.261294\pi$
$384$	−472307.	+	570719.i	−0.163454	+	0.197512i
$385$	−3.78058e6			−1.29989
$386$	307896.	−	661966.i	0.105181	−	0.226135i
$387$	−83377.6	−	83377.6i	−0.0282991	−	0.0282991i
$388$	−573207.	−	680430.i	−0.193300	−	0.229458i
$389$	521316.	−	521316.i	0.174674	−	0.174674i	−0.614356	−	0.789029i	$-0.710584\pi$
$389$	521316.	−	521316.i	0.174674	−	0.174674i	0.789029	+	0.614356i	$0.210584\pi$
$390$	493303.	−	180091.i	0.164230	−	0.0599558i
$391$		−	321132.i		−	0.106229i
$392$	−3.87269e6	+	1.04980e6i	−1.27291	+	0.345059i
$393$			425381.i			0.138930i
$394$	−1.05446e6	−	2.88835e6i	−0.342206	−	0.937367i
$395$	1.88118e6	−	1.88118e6i	0.606649	−	0.606649i
$396$	474240.	−	5.54478e6i	0.151971	−	1.77683i
$397$	−2.14350e6	−	2.14350e6i	−0.682569	−	0.682569i	0.278009	−	0.960578i	$-0.410325\pi$
$397$	−2.14350e6	−	2.14350e6i	−0.682569	−	0.682569i	−0.960578	+	0.278009i	$0.910325\pi$
$398$	−3.86923e6	−	1.79967e6i	−1.22438	−	0.569490i
$399$	477561.			0.150175
$400$	630704.	+	108682.i	0.197095	+	0.0339632i
$401$	−2.38412e6			−0.740403			−0.370201	−	0.928952i	$-0.620711\pi$
$401$	−2.38412e6			−0.740403			−0.370201	+	0.928952i	$0.620711\pi$
$402$	373660.	+	173798.i	0.115322	+	0.0536390i
$403$	5.26564e6	+	5.26564e6i	1.61506	+	1.61506i
$404$	3.91685e6	+	335005.i	1.19394	+	0.102117i
$405$	−842527.	+	842527.i	−0.255238	+	0.255238i
$406$	711142.	+	1.94795e6i	0.214112	+	0.586493i
$407$		−	4.52193e6i		−	1.35312i
$408$	95796.4	+	54936.1i	0.0284904	+	0.0163383i
$409$			4.74247e6i			1.40183i	0.713244	+	0.700916i	$0.247225\pi$
$409$			4.74247e6i			1.40183i	−0.713244	+	0.700916i	$0.752775\pi$
$410$	908254.	−	331578.i	0.266838	−	0.0974150i
$411$	232488.	−	232488.i	0.0678883	−	0.0678883i
$412$	926046.	−	780119.i	0.268775	−	0.226422i
$413$	−4.66464e6	−	4.66464e6i	−1.34568	−	1.34568i
$414$	1.13945e6	−	2.44977e6i	0.326733	−	0.702465i
$415$	−1.73831e6			−0.495459
$416$	960376.	+	5.29585e6i	0.272087	+	1.50038i
$417$	−173059.			−0.0487366
$418$	−1.10617e6	+	2.37822e6i	−0.309657	+	0.665750i
$419$	1.30162e6	+	1.30162e6i	0.362199	+	0.362199i	0.864622	−	0.502423i	$-0.167558\pi$
$419$	1.30162e6	+	1.30162e6i	0.362199	+	0.362199i	−0.502423	+	0.864622i	$0.667558\pi$
$420$	482720.	−	406653.i	0.133528	−	0.112486i
$421$	945631.	−	945631.i	0.260026	−	0.260026i	−0.565039	−	0.825064i	$-0.691139\pi$
$421$	945631.	−	945631.i	0.260026	−	0.260026i	0.825064	+	0.565039i	$0.191139\pi$
$422$	3.81916e6	−	1.39427e6i	1.04397	−	0.381123i
$423$			1.39025e6i			0.377782i
$424$	−1.12547e6	+	1.96257e6i	−0.304032	+	0.530165i
$425$		−	95403.6i		−	0.0256208i
$426$	−439790.	−	1.20467e6i	−0.117414	−	0.321620i
$427$	−6.84751e6	+	6.84751e6i	−1.81745	+	1.81745i
$428$	−84377.0	−	7216.69i	−0.0222646	−	0.00190427i
$429$	2.01136e6	+	2.01136e6i	0.527650	+	0.527650i
$430$	66599.7	+	30977.1i	0.0173701	+	0.00807923i
$431$	−5.90106e6			−1.53016			−0.765080	−	0.643935i	$-0.777301\pi$
$431$	−5.90106e6			−1.53016			−0.765080	+	0.643935i	$0.777301\pi$
$432$	1.10942e6	+	1.57138e6i	0.286015	+	0.405108i
$433$	−3.70654e6			−0.950055			−0.475027	−	0.879971i	$-0.657562\pi$
$433$	−3.70654e6			−0.950055			−0.475027	+	0.879971i	$0.657562\pi$
$434$	8.11537e6	+	3.77465e6i	2.06816	+	0.961951i
$435$	−131188.	−	131188.i	−0.0332408	−	0.0332408i
$436$	153898.	−	1.79936e6i	0.0387719	−	0.453317i
$437$	−900432.	+	900432.i	−0.225552	+	0.225552i
$438$	−321637.	−	881023.i	−0.0801089	−	0.219433i
$439$		−	2.43564e6i		−	0.603186i	−0.953437	−	0.301593i	$-0.902482\pi$
$439$		−	2.43564e6i		−	0.603186i	0.953437	−	0.301593i	$-0.0975184\pi$
$440$	906984.	+	3.34584e6i	0.223341	+	0.823897i
$441$			5.03228e6i			1.23216i
$442$	753666.	−	275142.i	0.183494	−	0.0669887i
$443$	4.75839e6	−	4.75839e6i	1.15200	−	1.15200i	0.165843	−	0.986152i	$-0.446966\pi$
$443$	4.75839e6	−	4.75839e6i	1.15200	−	1.15200i	0.986152	−	0.165843i	$-0.0530345\pi$
$444$	486394.	+	577378.i	0.117093	+	0.138996i
$445$	−1.10719e6	−	1.10719e6i	−0.265047	−	0.265047i
$446$	−387886.	+	833941.i	−0.0923352	+	0.198517i
$447$	−1.18490e6			−0.280487
$448$	3.26709e6	+	5.58328e6i	0.769070	+	1.31430i
$449$	1.20625e6			0.282372			0.141186	−	0.989983i	$-0.454908\pi$
$449$	1.20625e6			0.282372			0.141186	+	0.989983i	$0.454908\pi$
$450$	338513.	−	727791.i	0.0788033	−	0.169424i
$451$	3.70325e6	+	3.70325e6i	0.857317	+	0.857317i
$452$	−3.69303e6	−	4.38384e6i	−0.850231	−	1.00927i
$453$	−572925.	+	572925.i	−0.131175	+	0.131175i
$454$	3.89225e6	−	1.42095e6i	0.886259	−	0.323548i
$455$		−	4.58573e6i		−	1.03844i
$456$	−114570.	−	422644.i	−0.0258022	−	0.0951837i
$457$		−	8.30542e6i		−	1.86025i	−0.367245	−	0.930124i	$-0.619699\pi$
$457$		−	8.30542e6i		−	1.86025i	0.367245	−	0.930124i	$-0.380301\pi$
$458$	−2.23448e6	−	6.12067e6i	−0.497752	−	1.36344i
$459$	202756.	−	202756.i	0.0449202	−	0.0449202i
$460$	−143423.	+	1.67689e6i	−0.0316028	+	0.369497i
$461$	−3.51089e6	−	3.51089e6i	−0.769422	−	0.769422i	0.208583	−	0.978005i	$-0.433115\pi$
$461$	−3.51089e6	−	3.51089e6i	−0.769422	−	0.769422i	−0.978005	+	0.208583i	$0.933115\pi$
$462$	3.09989e6	+	1.44183e6i	0.675680	+	0.314275i
$463$	558945.			0.121176			0.0605880	−	0.998163i	$-0.480702\pi$
$463$	558945.			0.121176			0.0605880	+	0.998163i	$0.480702\pi$
$464$	1.55334e6	−	1.09669e6i	0.334944	−	0.236477i
$465$	−800754.			−0.171738
$466$	2.32499e6	+	1.08141e6i	0.495970	+	0.230688i
$467$	2.74891e6	+	2.74891e6i	0.583268	+	0.583268i	0.935800	−	0.352532i	$-0.114679\pi$
$467$	2.74891e6	+	2.74891e6i	0.583268	+	0.583268i	−0.352532	+	0.935800i	$0.614679\pi$
$468$	6.72564e6	+	575239.i	1.41945	+	0.121404i
$469$	2.54458e6	−	2.54458e6i	0.534175	−	0.534175i
$470$	−296987.	−	813504.i	−0.0620145	−	0.169869i
$471$			1.94149e6i			0.403257i
$472$	−3.00916e6	+	5.24731e6i	−0.621713	+	1.08413i
$473$			397853.i			0.0817654i
$474$	−2.25991e6	+	825031.i	−0.462004	+	0.168665i
$475$	−267505.	+	267505.i	−0.0543999	+	0.0543999i
$476$	737496.	−	621281.i	0.149191	−	0.125681i
$477$	2.00634e6	+	2.00634e6i	0.403747	+	0.403747i
$478$	2.44556e6	−	5.25786e6i	0.489563	−	1.05254i
$479$	−1.32442e6			−0.263746			−0.131873	−	0.991267i	$-0.542099\pi$
$479$	−1.32442e6			−0.263746			−0.131873	+	0.991267i	$0.542099\pi$
$480$	−475697.	−	329651.i	−0.0942383	−	0.0653058i
$481$	5.48496e6			1.08096
$482$	−3.19066e6	+	6.85981e6i	−0.625552	+	1.34491i
$483$	1.17367e6	+	1.17367e6i	0.228916	+	0.228916i
$484$	−1.04190e7	+	8.77718e6i	−2.02168	+	1.70311i
$485$	491490.	−	491490.i	0.0948769	−	0.0948769i
$486$	3.43774e6	−	1.25502e6i	0.660210	−	0.241024i
$487$			8.10722e6i			1.54899i	0.632578	+	0.774496i	$0.281997\pi$
$487$			8.10722e6i			1.54899i	−0.632578	+	0.774496i	$0.718003\pi$
$488$	7.70284e6	+	4.41732e6i	1.46420	+	0.839672i
$489$		−	921329.i		−	0.174238i
$490$	−1.07501e6	−	2.94464e6i	−0.202265	−	0.554041i
$491$	−406525.	+	406525.i	−0.0760998	+	0.0760998i	−0.744132	−	0.668032i	$-0.767137\pi$
$491$	−406525.	+	406525.i	−0.0760998	+	0.0760998i	0.668032	+	0.744132i	$0.267137\pi$
$492$	−871179.	−	74511.2i	−0.162254	−	0.0138774i
$493$	−200429.	−	200429.i	−0.0371400	−	0.0371400i
$494$	−2.88471e6	−	1.34175e6i	−0.531844	−	0.247374i
$495$	4.34767e6			0.797524
$496$	1.39366e6	−	8.08770e6i	0.254363	−	1.47612i
$497$	−1.11985e7			−2.03362
$498$	1.42533e6	+	662956.i	0.257539	+	0.119787i
$499$	193908.	+	193908.i	0.0348614	+	0.0348614i	0.724323	−	0.689461i	$-0.242153\pi$
$499$	193908.	+	193908.i	0.0348614	+	0.0348614i	−0.689461	+	0.724323i	$0.742153\pi$
$500$	−42609.0	+	498181.i	−0.00762213	+	0.0891174i
$501$	34403.5	−	34403.5i	0.00612362	−	0.00612362i
$502$	−2.60606e6	−	7.13849e6i	−0.461557	−	1.26429i
$503$			1.67379e6i			0.294973i	0.989064	+	0.147486i	$0.0471183\pi$
$503$			1.67379e6i			0.294973i	−0.989064	+	0.147486i	$0.952882\pi$
$504$	7.83047e6	−	2.12267e6i	1.37313	−	0.372226i
$505$			3.07121e6i			0.535897i
$506$	−8.56333e6	+	3.12623e6i	−1.48685	+	0.542806i
$507$	−1.39046e6	+	1.39046e6i	−0.240236	+	0.240236i
$508$	−1.12689e6	−	1.33769e6i	−0.193742	−	0.229982i
$509$	1.50765e6	+	1.50765e6i	0.257932	+	0.257932i	0.824213	−	0.566280i	$-0.191618\pi$
$509$	1.50765e6	+	1.50765e6i	0.257932	+	0.257932i	−0.566280	+	0.824213i	$0.691618\pi$
$510$	−36384.9	+	78226.2i	−0.00619435	+	0.0133176i
$511$	−8.18996e6			−1.38749
$512$	4.15743e6	−	4.23085e6i	0.700891	−	0.713268i
$513$	−1.13703e6			−0.190756
$514$	−2.49750e6	+	5.36953e6i	−0.416963	+	0.896455i
$515$	668904.	+	668904.i	0.111134	+	0.111134i
$516$	−42794.4	−	50799.4i	−0.00707559	−	0.00839913i
$517$	3.31692e6	−	3.31692e6i	0.545769	−	0.545769i
$518$	6.19262e6	−	2.26075e6i	1.01403	−	0.370193i
$519$		−	3.03239e6i		−	0.494159i
$520$	−4.05840e6	+	1.10014e6i	−0.658182	+	0.178419i
$521$			2.57563e6i			0.415708i	0.978160	+	0.207854i	$0.0666479\pi$
$521$			2.57563e6i			0.415708i	−0.978160	+	0.207854i	$0.933352\pi$
$522$	−817814.	−	2.24014e6i	−0.131365	−	0.359832i
$523$	−2.13633e6	+	2.13633e6i	−0.341518	+	0.341518i	−0.856938	−	0.515420i	$-0.827636\pi$
$523$	−2.13633e6	+	2.13633e6i	−0.341518	+	0.341518i	0.515420	+	0.856938i	$0.327636\pi$
$524$	290255.	−	3.39364e6i	0.0461797	−	0.539930i
$525$	348679.	+	348679.i	0.0552113	+	0.0552113i
$526$	9.67426e6	+	4.49973e6i	1.52459	+	0.709124i
$527$	−1.22339e6			−0.191883
$528$	532349.	−	3.08932e6i	0.0831020	−	0.482257i
$529$	2.01049e6			0.312365
$530$	−1.60261e6	−	745414.i	−0.247821	−	0.115268i
$531$	5.36434e6	+	5.36434e6i	0.825619	+	0.825619i
$532$	−3.80992e6	−	325859.i	−0.583629	−	0.0499173i
$533$	−4.49192e6	+	4.49192e6i	−0.684880	+	0.684880i
$534$	485583.	+	1.33010e6i	0.0736904	+	0.201852i
$535$		−	66160.2i		−	0.00999338i
$536$	−2.86242e6	−	1.64150e6i	−0.430350	−	0.246792i
$537$		−	2.80419e6i		−	0.419635i
$538$	1.69802e6	−	619900.i	0.252922	−	0.0923349i
$539$	1.20063e7	−	1.20063e7i	1.78007	−	1.78007i
$540$	−1.14931e6	+	968202.i	−0.169611	+	0.142883i
$541$	1.65184e6	+	1.65184e6i	0.242647	+	0.242647i	0.817944	−	0.575297i	$-0.195114\pi$
$541$	1.65184e6	+	1.65184e6i	0.242647	+	0.242647i	−0.575297	+	0.817944i	$0.695114\pi$
$542$	−1.79204e6	+	3.85282e6i	−0.262029	+	0.563353i
$543$	1.07305e6			0.156178
$544$	−726767.	−	503639.i	−0.105293	−	0.0729663i
$545$	1.41088e6			0.203470
$546$	−1.74890e6	+	3.76007e6i	−0.251063	+	0.539777i
$547$	−6.74481e6	−	6.74481e6i	−0.963833	−	0.963833i	0.0355356	−	0.999368i	$-0.488686\pi$
$547$	−6.74481e6	−	6.74481e6i	−0.963833	−	0.963833i	−0.999368	+	0.0355356i	$0.988686\pi$
$548$	−2.01339e6	+	1.69612e6i	−0.286403	+	0.241271i
$549$	7.87464e6	−	7.87464e6i	1.11506	−	1.11506i
$550$	−2.54404e6	+	928758.i	−0.358606	+	0.130917i
$551$			1.12398e6i			0.157717i
$552$	757132.	−	1.32027e6i	0.105761	−	0.184423i
$553$			2.10081e7i			2.92128i
$554$	2.72042e6	+	7.45174e6i	0.376584	+	1.03153i
$555$	−417053.	+	417053.i	−0.0574723	+	0.0574723i
$556$	1.38065e6	+	118086.i	0.189407	+	0.0161998i
$557$	3.42824e6	+	3.42824e6i	0.468202	+	0.468202i	0.901332	−	0.433130i	$-0.142591\pi$
$557$	3.42824e6	+	3.42824e6i	0.468202	+	0.468202i	−0.433130	+	0.901332i	$0.642591\pi$
$558$	−9.33267e6	−	4.34085e6i	−1.26888	−	0.590187i
$559$	−482583.			−0.0653194
$560$	−4.12856e6	+	2.91484e6i	−0.556324	+	0.392776i
$561$	−467307.			−0.0626895
$562$	−5.92096e6	−	2.75398e6i	−0.790772	−	0.367807i
$563$	−9.10019e6	−	9.10019e6i	−1.20998	−	1.20998i	−0.971031	−	0.238952i	$-0.923196\pi$
$563$	−9.10019e6	−	9.10019e6i	−1.20998	−	1.20998i	−0.238952	−	0.971031i	$-0.576804\pi$
$564$	−66738.2	+	780297.i	−0.00883439	+	0.103291i
$565$	3.16654e6	−	3.16654e6i	0.417316	−	0.417316i
$566$	3.34710e6	+	9.16834e6i	0.439165	+	1.20296i
$567$		−	9.40893e6i		−	1.22909i
$568$	2.68660e6	+	9.91076e6i	0.349407	+	1.28895i
$569$		−	5.49614e6i		−	0.711668i	−0.934549	−	0.355834i	$-0.884197\pi$
$569$		−	5.49614e6i		−	0.711668i	0.934549	−	0.355834i	$-0.115803\pi$
$570$	321362.	−	117320.i	0.0414292	−	0.0151247i
$571$	−6.26904e6	+	6.26904e6i	−0.804657	+	0.804657i	−0.983820	−	0.179162i	$-0.942661\pi$
$571$	−6.26904e6	+	6.26904e6i	−0.804657	+	0.804657i	0.179162	+	0.983820i	$0.442661\pi$
$572$	−1.46739e7	−	1.74188e7i	−1.87524	−	2.22602i
$573$	−612602.	−	612602.i	−0.0779457	−	0.0779457i
$574$	−3.22002e6	+	6.92292e6i	−0.407923	+	0.877020i
$575$	−1.31486e6			−0.165847
$576$	−3.75715e6	−	6.42077e6i	−0.471849	−	0.806363i
$577$	2.00756e6			0.251031			0.125516	−	0.992092i	$-0.459941\pi$
$577$	2.00756e6			0.251031			0.125516	+	0.992092i	$0.459941\pi$
$578$	3.33177e6	−	7.16318e6i	0.414816	−	0.891839i
$579$	−364714.	−	364714.i	−0.0452123	−	0.0452123i
$580$	957088.	+	1.13612e6i	0.118136	+	0.140234i
$581$	9.70632e6	−	9.70632e6i	1.19293	−	1.19293i
$582$	−590441.	+	215553.i	−0.0722552	+	0.0263783i
$583$		−	9.57368e6i		−	1.16656i
$584$	1.96482e6	+	7.24816e6i	0.238392	+	0.879419i
$585$			5.27359e6i			0.637114i
$586$	557208.	+	1.52630e6i	0.0670306	+	0.183609i
$587$	5.11196e6	−	5.11196e6i	0.612339	−	0.612339i	−0.331216	−	0.943555i	$-0.607459\pi$
$587$	5.11196e6	−	5.11196e6i	0.612339	−	0.612339i	0.943555	+	0.331216i	$0.107459\pi$
$588$	−241572.	+	2.82444e6i	−0.0288140	+	0.336891i
$589$	3.43030e6	+	3.43030e6i	0.407421	+	0.407421i
$590$	−4.28488e6	−	1.99300e6i	−0.506768	−	0.235710i
$591$	−2.17232e6			−0.255832
$592$	−3.48642e6	−	4.93814e6i	−0.408861	−	0.579107i
$593$	−5.60846e6			−0.654948			−0.327474	−	0.944860i	$-0.606197\pi$
$593$	−5.60846e6			−0.654948			−0.327474	+	0.944860i	$0.606197\pi$
$594$	−7.38055e6	−	3.43287e6i	−0.858267	−	0.399201i
$595$	532710.	+	532710.i	0.0616877	+	0.0616877i
$596$	9.45298e6	+	808505.i	1.09007	+	0.0932325i
$597$	−2.13178e6	+	2.13178e6i	−0.244797	+	0.244797i
$598$	−3.79202e6	−	1.03871e7i	−0.433629	−	1.18779i
$599$		−	3.57303e6i		−	0.406883i	−0.979087	−	0.203441i	$-0.934787\pi$
$599$		−	3.57303e6i		−	0.406883i	0.979087	−	0.203441i	$-0.0652126\pi$
$600$	224933.	−	392233.i	0.0255079	−	0.0444802i
$601$			7.00344e6i			0.790907i	0.918486	+	0.395453i	$0.129413\pi$
$601$			7.00344e6i			0.790907i	−0.918486	+	0.395453i	$0.870587\pi$
$602$	−544845.	+	198908.i	−0.0612748	+	0.0223697i
$603$	−2.92626e6	+	2.92626e6i	−0.327733	+	0.327733i
$604$	4.96166e6	−	4.17979e6i	0.553394	−	0.466190i
$605$	−7.52589e6	−	7.52589e6i	−0.835929	−	0.835929i
$606$	1.17130e6	−	2.51824e6i	0.129564	−	0.278558i
$607$	−7.15190e6			−0.787861			−0.393930	−	0.919140i	$-0.628885\pi$
$607$	−7.15190e6			−0.787861			−0.393930	+	0.919140i	$0.628885\pi$
$608$	625635.	+	3.44998e6i	0.0686376	+	0.378492i
$609$	1.46505e6			0.160069
$610$	−2.92565e6	+	6.29004e6i	−0.318345	+	0.684430i
$611$	4.02332e6	+	4.02332e6i	0.435995	+	0.435995i
$612$	−848121.	+	714474.i	−0.0915333	+	0.0771095i
$613$	1.00171e7	−	1.00171e7i	1.07669	−	1.07669i	0.0798818	−	0.996804i	$-0.474546\pi$
$613$	1.00171e7	−	1.00171e7i	1.07669	−	1.07669i	0.996804	−	0.0798818i	$-0.0254543\pi$
$614$	−4.20313e6	+	1.53444e6i	−0.449937	+	0.164259i
$615$		−	683094.i		−	0.0728270i
$616$	−2.37467e7	−	1.36180e7i	−2.52146	−	1.44597i
$617$		−	6.37727e6i		−	0.674407i	−0.941432	−	0.337203i	$-0.890519\pi$
$617$		−	6.37727e6i		−	0.674407i	0.941432	−	0.337203i	$-0.109481\pi$
$618$	−293362.	−	803573.i	−0.0308982	−	0.0846359i
$619$	−1.04107e7	+	1.04107e7i	−1.09208	+	1.09208i	−0.0967688	+	0.995307i	$0.530851\pi$
$619$	−1.04107e7	+	1.04107e7i	−1.09208	+	1.09208i	−0.995307	+	0.0967688i	$0.969149\pi$
$620$	6.38832e6	+	546388.i	0.667432	+	0.0570849i
$621$	−2.79439e6	−	2.79439e6i	−0.290776	−	0.290776i
$622$	−6.35686e6	−	2.95673e6i	−0.658819	−	0.306433i
$623$	1.23646e7			1.27632
$624$	3.74725e6	+	645722.i	0.385258	+	0.0663872i
$625$	−390625.			−0.0400000
$626$	4.40919e6	+	2.05082e6i	0.449700	+	0.209166i
$627$	1.31030e6	+	1.31030e6i	0.133107	+	0.133107i
$628$	1.32476e6	−	1.54889e7i	0.134041	−	1.56719i
$629$	−637171.	+	637171.i	−0.0642140	+	0.0642140i
$630$	2.17363e6	+	5.95398e6i	0.218190	+	0.597663i
$631$			7.50163e6i			0.750036i	0.927018	+	0.375018i	$0.122363\pi$
$631$			7.50163e6i			0.750036i	−0.927018	+	0.375018i	$0.877637\pi$
$632$	1.85923e7	−	5.03996e6i	1.85157	−	0.501920i
$633$		−	2.87238e6i		−	0.284926i
$634$	−1.70823e6	+	623628.i	−0.168781	+	0.0616172i
$635$	966241.	−	966241.i	0.0950935	−	0.0950935i
$636$	1.02978e6	+	1.22240e6i	0.100949	+	0.119832i
$637$	1.45632e7	+	1.45632e7i	1.42203	+	1.42203i
$638$	−3.39347e6	+	7.29583e6i	−0.330059	+	0.709615i
$639$	1.28783e7			1.24769
$640$	3.57012e6	+	2.95450e6i	0.344534	+	0.285125i
$641$	1.89084e7			1.81765			0.908825	−	0.417177i	$-0.136980\pi$
$641$	1.89084e7			1.81765			0.908825	+	0.417177i	$0.136980\pi$
$642$	−25232.1	+	54248.1i	−0.00241610	+	0.00519453i
$643$	5.88611e6	+	5.88611e6i	0.561437	+	0.561437i	0.929716	−	0.368278i	$-0.120053\pi$
$643$	5.88611e6	+	5.88611e6i	0.561437	+	0.561437i	−0.368278	+	0.929716i	$0.620053\pi$
$644$	−8.56253e6	−	1.01642e7i	−0.813556	−	0.965737i
$645$	36693.6	−	36693.6i	0.00347289	−	0.00347289i
$646$	490974.	−	179241.i	0.0462890	−	0.0168988i
$647$			1.84161e6i			0.172956i	0.996254	+	0.0864782i	$0.0275613\pi$
$647$			1.84161e6i			0.172956i	−0.996254	+	0.0864782i	$0.972439\pi$
$648$	−8.32695e6	+	2.25726e6i	−0.779020	+	0.211175i
$649$		−	2.55970e7i		−	2.38549i
$650$	−1.12656e6	−	3.08584e6i	−0.104585	−	0.286478i
$651$	4.47122e6	−	4.47122e6i	0.413498	−	0.413498i
$652$	−628661.	+	7.35025e6i	−0.0579158	+	0.677147i
$653$	7.63776e6	+	7.63776e6i	0.700944	+	0.700944i	0.964613	−	0.263670i	$-0.0849328\pi$
$653$	7.63776e6	+	7.63776e6i	0.700944	+	0.700944i	−0.263670	+	0.964613i	$0.584933\pi$
$654$	−1.15685e6	−	538081.i	−0.105763	−	0.0491930i
$655$	2.66096e6			0.242345
$656$	6.89932e6	+	1.18888e6i	0.625960	+	0.107865i
$657$	9.41846e6			0.851269
$658$	6.20071e6	+	2.88410e6i	0.558312	+	0.259684i
$659$	4.80399e6	+	4.80399e6i	0.430912	+	0.430912i	0.888939	−	0.458027i	$-0.151444\pi$
$659$	4.80399e6	+	4.80399e6i	0.430912	+	0.430912i	−0.458027	+	0.888939i	$0.651444\pi$
$660$	2.44020e6	+	208708.i	0.218054	+	0.0186500i
$661$	2.67220e6	−	2.67220e6i	0.237884	−	0.237884i	−0.578089	−	0.815974i	$-0.696201\pi$
$661$	2.67220e6	−	2.67220e6i	0.237884	−	0.237884i	0.815974	+	0.578089i	$0.196201\pi$
$662$	2.14498e6	+	5.87549e6i	0.190229	+	0.521074i
$663$		−	566829.i		−	0.0500804i
$664$	−1.09188e7	−	6.26154e6i	−0.961065	−	0.551139i
$665$		−	2.98737e6i		−	0.261960i
$666$	−7.12152e6	+	2.59987e6i	−0.622138	+	0.227125i
$667$	−2.76232e6	+	2.76232e6i	−0.240413	+	0.240413i
$668$	−297942.	+	250992.i	−0.0258339	+	0.0217630i
$669$	459465.	+	459465.i	0.0396906	+	0.0396906i
$670$	1.08719e6	−	2.33742e6i	0.0935661	−	0.201164i
$671$	−3.75754e7			−3.22179
$672$	4.49687e6	−	815484.i	0.384138	−	0.0696614i
$673$	−7.91971e6			−0.674019			−0.337009	−	0.941501i	$-0.609415\pi$
$673$	−7.91971e6			−0.674019			−0.337009	+	0.941501i	$0.609415\pi$
$674$	−7.69056e6	+	1.65344e7i	−0.652091	+	1.40197i
$675$	−830173.	−	830173.i	−0.0701309	−	0.0701309i
$676$	1.20417e7	−	1.01441e7i	1.01349	−	0.853785i
$677$	−8.95269e6	+	8.95269e6i	−0.750727	+	0.750727i	−0.974615	−	0.223888i	$-0.928125\pi$
$677$	−8.95269e6	+	8.95269e6i	−0.750727	+	0.750727i	0.223888	+	0.974615i	$0.428125\pi$
$678$	−3.80406e6	+	1.38876e6i	−0.317814	+	0.116025i
$679$			5.48872e6i			0.456874i
$680$	343651.	−	599252.i	0.0285000	−	0.0496978i
$681$		−	2.92734e6i		−	0.241883i
$682$	1.19097e7	+	3.26230e7i	0.980485	+	2.68573i
$683$	−843476.	+	843476.i	−0.0691865	+	0.0691865i	−0.740853	−	0.671667i	$-0.765579\pi$
$683$	−843476.	+	843476.i	−0.0691865	+	0.0691865i	0.671667	+	0.740853i	$0.265579\pi$
$684$	4.38141e6	+	374738.i	0.358075	+	0.0306258i
$685$	−1.45432e6	−	1.45432e6i	−0.118422	−	0.118422i
$686$	5.42632e6	+	2.52391e6i	0.440246	+	0.204769i
$687$	−4.60333e6			−0.372117
$688$	306746.	+	434472.i	0.0247063	+	0.0349937i
$689$	1.16126e7			0.931924
$690$	1.07812e6	+	501458.i	0.0862071	+	0.0400970i
$691$	−5.68228e6	−	5.68228e6i	−0.452717	−	0.452717i	0.443538	−	0.896256i	$-0.353723\pi$
$691$	−5.68228e6	−	5.68228e6i	−0.452717	−	0.452717i	−0.896256	+	0.443538i	$0.853723\pi$
$692$	−2.06913e6	+	2.41921e7i	−0.164256	+	1.92047i
$693$	−2.42763e7	+	2.42763e7i	−1.92022	+	1.92022i
$694$	922675.	+	2.52738e6i	0.0727193	+	0.199192i
$695$			1.08257e6i			0.0850146i
$696$	−351473.	−	1.29657e6i	−0.0275023	−	0.101455i
$697$		−	1.04363e6i		−	0.0813698i
$698$	9.82199e6	−	3.58573e6i	0.763064	−	0.278573i
$699$	1.28097e6	−	1.28097e6i	0.0991620	−	0.0991620i
$700$	−2.54380e6	−	3.01964e6i	−0.196218	−	0.232922i
$701$	1.14378e7	+	1.14378e7i	0.879118	+	0.879118i	0.993443	−	0.114325i	$-0.0364705\pi$
$701$	1.14378e7	+	1.14378e7i	0.879118	+	0.879118i	−0.114325	+	0.993443i	$0.536471\pi$
$702$	4.16397e6	−	8.95237e6i	0.318907	−	0.685639i
$703$	3.57317e6			0.272688
$704$	−6.35498e6	+	2.42830e7i	−0.483262	+	1.84659i
$705$	−611833.			−0.0463618
$706$	9.98360e6	−	2.14644e7i	0.753833	−	1.62071i
$707$	−1.71489e7	−	1.71489e7i	−1.29029	−	1.29029i
$708$	2.75330e6	+	3.26833e6i	0.206429	+	0.245043i
$709$	−1.13313e7	+	1.13313e7i	−0.846576	+	0.846576i	−0.989704	−	0.143128i	$-0.954284\pi$
$709$	−1.13313e7	+	1.13313e7i	−0.846576	+	0.846576i	0.143128	+	0.989704i	$0.454284\pi$
$710$	−7.53575e6	+	2.75109e6i	−0.561023	+	0.204814i
$711$		−	2.41593e7i		−	1.79230i
$712$	−2.96634e6	−	1.09427e7i	−0.219291	−	0.808958i
$713$			1.68608e7i			1.24209i
$714$	−233632.	−	639960.i	−0.0171509	−	0.0469794i
$715$	1.25820e7	−	1.25820e7i	0.920417	−	0.920417i
$716$	−1.91341e6	+	2.23715e7i	−0.139485	+	1.63084i
$717$	−2.89685e6	−	2.89685e6i	−0.210440	−	0.210440i
$718$	6.68035e6	+	3.10719e6i	0.483602	+	0.224935i
$719$	3.31295e6			0.238997			0.119499	−	0.992834i	$-0.461871\pi$
$719$	3.31295e6			0.238997			0.119499	+	0.992834i	$0.461871\pi$
$720$	4.74784e6	−	3.35207e6i	0.341322	−	0.240981i
$721$	−7.46999e6			−0.535158
$722$	1.08211e7	+	5.03316e6i	0.772553	+	0.359333i
$723$	3.77946e6	+	3.77946e6i	0.268896	+	0.268896i
$724$	−8.56068e6	−	732187.i	−0.606962	−	0.0519130i
$725$	−820644.	+	820644.i	−0.0579842	+	0.0579842i
$726$	3.30064e6	+	9.04106e6i	0.232411	+	0.636617i
$727$			1.99116e7i			1.39723i	0.715496	+	0.698617i	$0.246201\pi$
$727$			1.99116e7i			1.39723i	−0.715496	+	0.698617i	$0.753799\pi$
$728$	1.65182e7	−	2.88040e7i	1.15514	−	2.01430i
$729$			8.99599e6i			0.626946i
$730$	−5.51122e6	+	2.01199e6i	−0.382772	+	0.139739i
$731$	56060.2	−	56060.2i	0.00388026	−	0.00388026i
$732$	4.79778e6	−	4.04174e6i	0.330950	−	0.278799i
$733$	−7.01608e6	−	7.01608e6i	−0.482319	−	0.482319i	0.423553	−	0.905872i	$-0.360783\pi$
$733$	−7.01608e6	−	7.01608e6i	−0.482319	−	0.482319i	−0.905872	+	0.423553i	$0.860783\pi$
$734$	−1.05636e6	+	2.27113e6i	−0.0723721	+	0.155597i
$735$	−2.21465e6			−0.151212
$736$	−6.94118e6	+	1.00163e7i	−0.472323	+	0.681576i
$737$	1.39633e7			0.946930
$738$	3.70302e6	−	7.96136e6i	0.250274	−	0.538079i
$739$	−1.40622e7	−	1.40622e7i	−0.947199	−	0.947199i	0.0514751	−	0.998674i	$-0.483608\pi$
$739$	−1.40622e7	−	1.40622e7i	−0.947199	−	0.947199i	−0.998674	+	0.0514751i	$0.983608\pi$
$740$	3.61177e6	−	3.04263e6i	0.242460	−	0.204253i
$741$	−1.58935e6	+	1.58935e6i	−0.106334	+	0.106334i
$742$	1.31108e7	−	4.78639e6i	0.874218	−	0.319152i
$743$			6.27904e6i			0.417274i	0.977993	+	0.208637i	$0.0669027\pi$
$743$			6.27904e6i			0.417274i	−0.977993	+	0.208637i	$0.933097\pi$
$744$	−5.02972e6	−	2.88438e6i	−0.333128	−	0.191038i
$745$			7.41210e6i			0.489272i
$746$	−9.28587e6	−	2.54357e7i	−0.610908	−	1.67339i
$747$	−1.11623e7	+	1.11623e7i	−0.731899	+	0.731899i
$748$	3.72812e6	+	318863.i	0.243633	+	0.0208377i
$749$	369422.	+	369422.i	0.0240613	+	0.0240613i
$750$	320293.	+	148976.i	0.0207919	+	0.00967082i
$751$	−6.01668e6			−0.389275			−0.194638	−	0.980875i	$-0.562353\pi$
$751$	−6.01668e6			−0.389275			−0.194638	+	0.980875i	$0.562353\pi$
$752$	1.06486e6	−	6.17958e6i	0.0686668	−	0.398487i
$753$	−5.36883e6			−0.345058
$754$	−8.84962e6	−	4.11617e6i	−0.566886	−	0.263673i
$755$	3.58392e6	+	3.58392e6i	0.228818	+	0.228818i
$756$	1.01127e6	−	1.18237e7i	0.0643520	−	0.752398i
$757$	3.36457e6	−	3.36457e6i	0.213398	−	0.213398i	−0.592311	−	0.805709i	$-0.701784\pi$
$757$	3.36457e6	−	3.36457e6i	0.213398	−	0.213398i	0.805709	+	0.592311i	$0.201784\pi$
$758$	−4.78608e6	−	1.31100e7i	−0.302557	−	0.828760i
$759$			6.44045e6i			0.405799i
$760$	−2.64384e6	+	716687.i	−0.166035	+	0.0450086i
$761$			1.95367e7i			1.22290i	0.791284	+	0.611448i	$0.209413\pi$
$761$			1.95367e7i			1.22290i	−0.791284	+	0.611448i	$0.790587\pi$
$762$	−1.16077e6	+	423765.i	−0.0724202	+	0.0264386i
$763$	−7.87803e6	+	7.87803e6i	−0.489899	+	0.489899i
$764$	4.46926e6	+	5.30527e6i	0.277014	+	0.328832i
$765$	−612617.	−	612617.i	−0.0378474	−	0.0378474i
$766$	−9.33595e6	+	2.00719e7i	−0.574892	+	1.23600i
$767$	3.10484e7			1.90568
$768$	−1.80053e6	−	3.78411e6i	−0.110153	−	0.231505i
$769$	−2.30217e6			−0.140386			−0.0701928	−	0.997533i	$-0.522361\pi$
$769$	−2.30217e6			−0.140386			−0.0701928	+	0.997533i	$0.522361\pi$
$770$	9.01935e6	−	1.93913e7i	0.548212	−	1.17864i
$771$	2.95838e6	+	2.95838e6i	0.179233	+	0.179233i
$772$	2.66079e6	+	3.15851e6i	0.160682	+	0.190739i
$773$	3.83662e6	−	3.83662e6i	0.230941	−	0.230941i	−0.582145	−	0.813085i	$-0.697786\pi$
$773$	3.83662e6	−	3.83662e6i	0.230941	−	0.230941i	0.813085	+	0.582145i	$0.197786\pi$
$774$	626572.	−	228744.i	0.0375940	−	0.0137245i
$775$			5.00910e6i			0.299575i
$776$	4.85755e6	−	1.31678e6i	0.289576	−	0.0784978i
$777$		−	4.65744e6i		−	0.276755i
$778$	1.43022e6	+	3.91763e6i	0.0847135	+	0.232046i
$779$	−2.92626e6	+	2.92626e6i	−0.172770	+	0.172770i
$780$	−253156.	+	2.95988e6i	−0.0148988	+	0.174196i
$781$	−3.07257e7	−	3.07257e7i	−1.80250	−	1.80250i
$782$	1.64714e6	+	766125.i	0.0963194	+	0.0448005i
$783$	−3.48814e6			−0.203324
$784$	3.85447e6	−	2.23682e7i	0.223962	−	1.29969i
$785$	1.21449e7			0.703429
$786$	−2.18185e6	−	1.01483e6i	−0.125971	−	0.0585920i
$787$	1.11181e6	+	1.11181e6i	0.0639874	+	0.0639874i	0.738376	−	0.674389i	$-0.235593\pi$
$787$	1.11181e6	+	1.11181e6i	0.0639874	+	0.0639874i	−0.674389	+	0.738376i	$0.735593\pi$
$788$	1.73305e7	+	1.48226e6i	0.994249	+	0.0850373i
$789$	5.33010e6	−	5.33010e6i	0.304819	−	0.304819i
$790$	5.16096e6	+	1.41368e7i	0.294213	+	0.805905i
$791$			3.53624e7i			2.00956i
$792$	2.73087e7	+	1.56607e7i	1.54699	+	0.887150i
$793$		−	4.55778e7i		−	2.57377i
$794$	1.61081e7	−	5.88062e6i	0.906763	−	0.331034i
$795$	−882971.	+	882971.i	−0.0495483	+	0.0495483i
$796$	1.84617e7	−	1.55525e7i	1.03273	−	0.869995i
$797$	−8.17500e6	−	8.17500e6i	−0.455871	−	0.455871i	0.441426	−	0.897297i	$-0.354473\pi$
$797$	−8.17500e6	−	8.17500e6i	−0.455871	−	0.455871i	−0.897297	+	0.441426i	$0.854473\pi$
$798$	−1.13932e6	+	2.44949e6i	−0.0633341	+	0.136166i
$799$	−934755.			−0.0518001
$800$	−2.06212e6	+	2.97571e6i	−0.113917	+	0.164386i
$801$	−1.42193e7			−0.783063
$802$	5.68781e6	−	1.22286e7i	0.312255	−	0.671337i
$803$	−2.24710e7	−	2.24710e7i	−1.22980	−	1.22980i
$804$	−1.78288e6	+	1.50194e6i	−0.0972709	+	0.0819429i
$805$	7.34184e6	−	7.34184e6i	0.399315	−	0.399315i
$806$	−3.95707e7	+	1.44461e7i	−2.14554	+	0.783275i
$807$		−	1.27707e6i		−	0.0690291i
$808$	−1.10628e7	+	1.92910e7i	−0.596121	+	1.03950i
$809$		−	1.30916e7i		−	0.703266i	−0.936138	−	0.351633i	$-0.885626\pi$
$809$		−	1.30916e7i		−	0.703266i	0.936138	−	0.351633i	$-0.114374\pi$
$810$	−2.31145e6	−	6.33148e6i	−0.123786	−	0.339073i
$811$	1.54235e7	−	1.54235e7i	0.823438	−	0.823438i	−0.163162	−	0.986599i	$-0.552169\pi$
$811$	1.54235e7	−	1.54235e7i	0.823438	−	0.823438i	0.986599	+	0.163162i	$0.0521692\pi$
$812$	−1.16880e7	−	999661.i	−0.622083	−	0.0532063i
$813$	2.12274e6	+	2.12274e6i	0.112634	+	0.112634i
$814$	2.31938e7	+	1.07880e7i	1.22690	+	0.570662i
$815$	−5.76335e6			−0.303935
$816$	−510319.	+	360295.i	−0.0268297	+	0.0189423i
$817$	−314378.			−0.0164777
$818$	−2.43249e7	−	1.13141e7i	−1.27107	−	0.591204i
$819$	−2.94464e7	−	2.94464e7i	−1.53399	−	1.53399i
$820$	−466103.	+	5.44964e6i	−0.0242073	+	0.283030i
$821$	1.29282e7	−	1.29282e7i	0.669393	−	0.669393i	−0.288182	−	0.957576i	$-0.593051\pi$
$821$	1.29282e7	−	1.29282e7i	0.669393	−	0.669393i	0.957576	+	0.288182i	$0.0930509\pi$
$822$	637823.	+	1.74712e6i	0.0329246	+	0.0901866i
$823$			2.14212e6i			0.110241i	0.998480	+	0.0551207i	$0.0175544\pi$
$823$			2.14212e6i			0.110241i	−0.998480	+	0.0551207i	$0.982446\pi$
$824$	1.79210e6	+	6.61098e6i	0.0919482	+	0.339194i
$825$			1.91336e6i			0.0978729i
$826$	3.50542e7	−	1.27973e7i	1.78768	−	0.652632i
$827$	−1.68100e7	+	1.68100e7i	−0.854681	+	0.854681i	−0.990705	−	0.136024i	$-0.956567\pi$
$827$	−1.68100e7	+	1.68100e7i	−0.854681	+	0.854681i	0.136024	+	0.990705i	$0.456567\pi$
$828$	9.84691e6	+	1.16888e7i	0.499142	+	0.592510i
$829$	−1.41517e7	−	1.41517e7i	−0.715192	−	0.715192i	0.252424	−	0.967617i	$-0.418772\pi$
$829$	−1.41517e7	−	1.41517e7i	−0.715192	−	0.715192i	−0.967617	+	0.252424i	$0.918772\pi$
$830$	4.14710e6	−	8.91612e6i	0.208953	−	0.449242i
$831$	5.60442e6			0.281532
$832$	−2.94545e7	−	7.70840e6i	−1.47518	−	0.386061i
$833$	−3.38353e6			−0.168950
$834$	412868.	−	887652.i	0.0205540	−	0.0441904i
$835$	−215210.	−	215210.i	−0.0106818	−	0.0106818i
$836$	−9.55932e6	−	1.13475e7i	−0.473055	−	0.561543i
$837$	−1.06455e7	+	1.06455e7i	−0.525236	+	0.525236i
$838$	−9.78148e6	+	3.57094e6i	−0.481166	+	0.175660i
$839$		−	2.57808e7i		−	1.26442i	−0.774797	−	0.632210i	$-0.782148\pi$
$839$		−	2.57808e7i		−	1.26442i	0.774797	−	0.632210i	$-0.217852\pi$
$840$	934165.	+	3.44611e6i	0.0456799	+	0.168512i
$841$		−	1.70630e7i		−	0.831891i
$842$	2.59431e6	+	7.10630e6i	0.126108	+	0.345433i
$843$	−3.26219e6	+	3.26219e6i	−0.158103	+	0.158103i
$844$	−1.95994e6	+	2.29155e7i	−0.0947080	+	1.10732i
$845$	8.69798e6	+	8.69798e6i	0.419060	+	0.419060i
$846$	−7.13082e6	−	3.31672e6i	−0.342542	−	0.159325i
$847$	8.40454e7			4.02537
$848$	−7.38134e6	−	1.04549e7i	−0.352489	−	0.499262i
$849$	6.89547e6			0.328318
$850$	489342.	+	227605.i	0.0232308	+	0.0108052i
$851$	8.78152e6	+	8.78152e6i	0.415667	+	0.415667i
$852$	7.22815e6	+	618218.i	0.341136	+	0.0291771i
$853$	−1.33299e7	+	1.33299e7i	−0.627270	+	0.627270i	−0.947380	−	0.320110i	$-0.896280\pi$
$853$	−1.33299e7	+	1.33299e7i	−0.627270	+	0.627270i	0.320110	+	0.947380i	$0.396280\pi$
$854$	−1.87859e7	−	5.14582e7i	−0.881431	−	2.41440i
$855$			3.43547e6i			0.160721i
$856$	238314.	−	415567.i	0.0111164	−	0.0193846i
$857$		−	1.84183e6i		−	0.0856637i	−0.999082	−	0.0428318i	$-0.986362\pi$
$857$		−	1.84183e6i		−	0.0856637i	0.999082	−	0.0428318i	$-0.0136380\pi$
$858$	−1.51151e7	+	5.51810e6i	−0.700960	+	0.255901i
$859$	−1.06784e7	+	1.06784e7i	−0.493768	+	0.493768i	−0.909491	−	0.415723i	$-0.863529\pi$
$859$	−1.06784e7	+	1.06784e7i	−0.493768	+	0.493768i	0.415723	+	0.909491i	$0.363529\pi$
$860$	−317774.	+	267699.i	−0.0146512	+	0.0123424i
$861$	3.81423e6	+	3.81423e6i	0.175347	+	0.175347i
$862$	1.40782e7	−	3.02676e7i	0.645325	−	1.38742i
$863$	−1.02613e7			−0.469004			−0.234502	−	0.972116i	$-0.575346\pi$
$863$	−1.02613e7			−0.469004			−0.234502	+	0.972116i	$0.575346\pi$
$864$	−1.07066e7	+	1.94159e6i	−0.487942	+	0.0884857i
$865$	−1.89690e7			−0.861996
$866$	8.84270e6	−	1.90115e7i	0.400673	−	0.861432i
$867$	−3.94660e6	−	3.94660e6i	−0.178310	−	0.178310i
$868$	−3.87217e7	+	3.26199e7i	−1.74444	+	1.46955i
$869$	−5.76405e7	+	5.76405e7i	−2.58927	+	2.58927i
$870$	985863.	−	359911.i	0.0441589	−	0.0161212i
$871$			1.69370e7i			0.756469i
$872$	8.86208e6	+	5.08211e6i	0.394680	+	0.226336i
$873$		−	6.31203e6i		−	0.280307i
$874$	−2.47031e6	−	6.76663e6i	−0.109389	−	0.299636i
$875$	2.18115e6	−	2.18115e6i	0.0963089	−	0.0963089i
$876$	5.28625e6	+	452129.i	0.232749	+	0.0199068i
$877$	1.60206e7	+	1.60206e7i	0.703364	+	0.703364i	0.965131	−	0.261767i	$-0.0843053\pi$
$877$	1.60206e7	+	1.60206e7i	0.703364	+	0.703364i	−0.261767	+	0.965131i	$0.584305\pi$
$878$	1.24928e7	+	5.81071e6i	0.546920	+	0.254386i
$879$	1.14792e6			0.0501118
$880$	−1.93252e7	−	3.33009e6i	−0.841234	−	0.144960i
$881$	−1.47936e7			−0.642146			−0.321073	−	0.947054i	$-0.604043\pi$
$881$	−1.47936e7			−0.642146			−0.321073	+	0.947054i	$0.604043\pi$
$882$	−2.58114e7	−	1.20055e7i	−1.11723	−	0.519649i
$883$	2.96145e7	+	2.96145e7i	1.27821	+	1.27821i	0.941667	+	0.336546i	$0.109259\pi$
$883$	2.96145e7	+	2.96145e7i	1.27821	+	1.27821i	0.336546	+	0.941667i	$0.390741\pi$
$884$	−386771.	+	4.52209e6i	−0.0166465	+	0.194629i
$885$	−2.36079e6	+	2.36079e6i	−0.101321	+	0.101321i
$886$	1.30545e7	+	3.57587e7i	0.558697	+	1.53037i
$887$		−	2.34254e7i		−	0.999720i	−0.866106	−	0.499860i	$-0.833385\pi$
$887$		−	2.34254e7i		−	0.999720i	0.866106	−	0.499860i	$-0.166615\pi$
$888$	−4.12186e6	+	1.11735e6i	−0.175413	+	0.0475506i
$889$			1.07905e7i			0.457918i
$890$	8.32043e6	−	3.03755e6i	0.352104	−	0.128543i
$891$	2.58155e7	−	2.58155e7i	1.08940	−	1.08940i
$892$	−3.35205e6	−	3.97907e6i	−0.141058	−	0.167444i
$893$	2.62099e6	+	2.62099e6i	0.109986	+	0.109986i
$894$	2.82682e6	−	6.07755e6i	0.118292	−	0.254323i
$895$	−1.75415e7			−0.731998
$896$	−3.64319e7	+	3.43743e6i	−1.51604	+	0.143042i
$897$	−7.81206e6			−0.324179
$898$	−2.87776e6	+	6.18707e6i	−0.119087	+	0.256032i
$899$	1.05234e7	+	1.05234e7i	0.434265	+	0.434265i
$900$	2.92537e6	+	3.47259e6i	0.120386	+	0.142905i
$901$	−1.34900e6	+	1.34900e6i	−0.0553604	+	0.0553604i
$902$	−2.78294e7	+	1.01598e7i	−1.13891	+	0.415783i
$903$			409776.i			0.0167235i
$904$	3.12959e7	−	8.48366e6i	1.27370	−	0.345272i
$905$		−	6.71245e6i		−	0.272433i
$906$	−1.57180e6	−	4.30546e6i	−0.0636176	−	0.174261i
$907$	−4.48366e6	+	4.48366e6i	−0.180973	+	0.180973i	−0.791780	−	0.610806i	$-0.790845\pi$
$907$	−4.48366e6	+	4.48366e6i	−0.180973	+	0.180973i	0.610806	+	0.791780i	$0.290845\pi$
$908$	−1.99745e6	+	2.33540e7i	−0.0804008	+	0.940040i
$909$	1.97213e7	+	1.97213e7i	0.791635	+	0.791635i
$910$	2.35210e7	+	1.09402e7i	0.941570	+	0.437947i
$911$	2.32020e7			0.926251			0.463126	−	0.886293i	$-0.346728\pi$
$911$	2.32020e7			0.926251			0.463126	+	0.886293i	$0.346728\pi$
$912$	2.44114e6	+	420655.i	0.0971865	+	0.0167471i
$913$	5.32630e7			2.11470
$914$	4.25999e7	+	1.98143e7i	1.68672	+	0.784535i
$915$	3.46554e6	+	3.46554e6i	0.136842	+	0.136842i
$916$	3.67248e7	+	3.14104e6i	1.44617	+	0.123690i
$917$	−1.48581e7	+	1.48581e7i	−0.583500	+	0.583500i
$918$	556255.	+	1.52369e6i	0.0217855	+	0.0596745i
$919$			1.53427e7i			0.599258i	0.954056	+	0.299629i	$0.0968629\pi$
$919$			1.53427e7i			0.599258i	−0.954056	+	0.299629i	$0.903137\pi$
$920$	−8.25892e6	−	4.73622e6i	−0.321702	−	0.184485i
$921$			3.16116e6i			0.122800i
$922$	2.63839e7	−	9.63201e6i	1.02214	−	0.373155i
$923$	3.72694e7	−	3.72694e7i	1.43995	−	1.43995i
$924$	−1.47908e7	+	1.24601e7i	−0.569918	+	0.480110i
$925$	2.60886e6	+	2.60886e6i	0.100253	+	0.100253i
$926$	−1.33348e6	+	2.86692e6i	−0.0511043	+	0.109872i
$927$	8.59049e6			0.328336
$928$	1.91930e6	+	1.05837e7i	0.0731600	+	0.403430i
$929$	−2.42104e7			−0.920369			−0.460184	−	0.887823i	$-0.652217\pi$
$929$	−2.42104e7			−0.920369			−0.460184	+	0.887823i	$0.652217\pi$
$930$	1.91036e6	−	4.10721e6i	0.0724283	−	0.155718i
$931$	9.48720e6	+	9.48720e6i	0.358727	+	0.358727i
$932$	−1.10935e7	+	9.34534e6i	−0.418338	+	0.352416i
$933$	−3.50235e6	+	3.50235e6i	−0.131721	+	0.131721i
$934$	−2.06577e7	+	7.54155e6i	−0.774845	+	0.282874i
$935$			2.92322e6i			0.109354i
$936$	−1.89959e7	+	3.31246e7i	−0.708712	+	1.23584i
$937$		−	4.92615e7i		−	1.83298i	−0.400054	−	0.916492i	$-0.631009\pi$
$937$		−	4.92615e7i		−	1.83298i	0.400054	−	0.916492i	$-0.368991\pi$
$938$	6.98097e6	+	1.91222e7i	0.259065	+	0.709627i
$939$	2.42927e6	−	2.42927e6i	0.0899109	−	0.0899109i
$940$	4.88113e6	+	417479.i	0.180177	+	0.0154104i
$941$	−2.82940e7	−	2.82940e7i	−1.04165	−	1.04165i	−0.999094	−	0.0425521i	$-0.986451\pi$
$941$	−2.82940e7	−	2.82940e7i	−1.04165	−	1.04165i	−0.0425521	−	0.999094i	$-0.513549\pi$
$942$	−9.95822e6	−	4.63181e6i	−0.365641	−	0.170068i
$943$	−1.43833e7			−0.526720
$944$	−1.97354e7	−	2.79530e7i	−0.720802	−	1.02094i
$945$	9.27097e6			0.337711
$946$	−2.04066e6	−	949159.i	−0.0741382	−	0.0344835i
$947$	8.26404e6	+	8.26404e6i	0.299445	+	0.299445i	0.840797	−	0.541351i	$-0.182087\pi$
$947$	8.26404e6	+	8.26404e6i	0.299445	+	0.299445i	−0.541351	+	0.840797i	$0.682087\pi$
$948$	1.15976e6	−	1.35598e7i	0.0419127	−	0.490040i
$949$	2.72567e7	−	2.72567e7i	0.982443	−	0.982443i
$950$	−733893.	−	2.01027e6i	−0.0263830	−	0.0722678i
$951$			1.28475e6i			0.0460647i
$952$	1.42721e6	+	5.26494e6i	0.0510383	+	0.188279i
$953$		−	3.54568e7i		−	1.26464i	−0.774707	−	0.632321i	$-0.782103\pi$
$953$		−	3.54568e7i		−	1.26464i	0.774707	−	0.632321i	$-0.217897\pi$
$954$	−1.50774e7	+	5.50435e6i	−0.536360	+	0.195810i
$955$	−3.83212e6	+	3.83212e6i	−0.135966	+	0.135966i
$956$	2.11341e7	+	2.50874e7i	0.747892	+	0.887791i
$957$	4.01969e6	+	4.01969e6i	0.141877	+	0.141877i
$958$	3.15967e6	−	6.79317e6i	0.111231	−	0.239144i
$959$	1.62411e7			0.570256
$960$	2.82571e6	−	1.65348e6i	0.0989577	−	0.0579057i
$961$	3.56039e7			1.24362
$962$	−1.30855e7	+	2.81333e7i	−0.455882	+	0.980129i
$963$	−424836.	−	424836.i	−0.0147623	−	0.0147623i
$964$	−2.75732e7	−	3.27309e7i	−0.955640	−	1.13440i
$965$	−2.28146e6	+	2.28146e6i	−0.0788669	+	0.0788669i
$966$	−8.81996e6	+	3.21992e6i	−0.304105	+	0.111020i
$967$			8.52361e6i			0.293128i	0.989201	+	0.146564i	$0.0468214\pi$
$967$			8.52361e6i			0.293128i	−0.989201	+	0.146564i	$0.953179\pi$
$968$	−2.01630e7	−	7.43807e7i	−0.691619	−	2.55136i
$969$		−	369260.i		−	0.0126335i
$970$	1.34839e6	+	3.69349e6i	0.0460135	+	0.126040i
$971$	−2.55609e6	+	2.55609e6i	−0.0870019	+	0.0870019i	−0.749268	−	0.662266i	$-0.769595\pi$
$971$	−2.55609e6	+	2.55609e6i	−0.0870019	+	0.0870019i	0.662266	+	0.749268i	$0.269595\pi$
$972$	−1.76420e6	+	2.06269e7i	−0.0598938	+	0.700273i
$973$	−6.04480e6	−	6.04480e6i	−0.204691	−	0.204691i
$974$	−4.15833e7	−	1.93414e7i	−1.40450	−	0.653267i
$975$	−2.32085e6			−0.0781872
$976$	−4.10339e7	+	2.89708e7i	−1.37885	+	0.973499i
$977$	−1.27814e7			−0.428392			−0.214196	−	0.976791i	$-0.568713\pi$
$977$	−1.27814e7			−0.428392			−0.214196	+	0.976791i	$0.568713\pi$
$978$	4.72566e6	+	2.19802e6i	0.157985	+	0.0734825i
$979$	3.39251e7	+	3.39251e7i	1.13127	+	1.13127i
$980$	1.76682e7	+	1.51115e6i	0.587662	+	0.0502623i
$981$	9.05974e6	−	9.05974e6i	0.300568	−	0.300568i
$982$	−1.11529e6	−	3.05499e6i	−0.0369070	−	0.101095i
$983$			3.00862e7i			0.993079i	0.868014	+	0.496539i	$0.165396\pi$
$983$			3.00862e7i			0.993079i	−0.868014	+	0.496539i	$0.834604\pi$
$984$	2.46056e6	−	4.29067e6i	0.0810113	−	0.141266i
$985$			1.35889e7i			0.446265i
$986$	1.50620e6	−	549870.i	0.0493389	−	0.0180122i
$987$	3.41633e6	−	3.41633e6i	0.111626	−	0.111626i
$988$	1.37641e7	−	1.15952e7i	0.448596	−	0.377906i
$989$	−772624.	−	772624.i	−0.0251176	−	0.0251176i
$990$	−1.03723e7	+	2.23000e7i	−0.336345	+	0.723130i
$991$	−8.58399e6			−0.277655			−0.138827	−	0.990317i	$-0.544333\pi$
$991$	−8.58399e6			−0.277655			−0.138827	+	0.990317i	$0.544333\pi$
$992$	3.81584e7	+	2.64432e7i	1.23115	+	0.853169i
$993$	4.41893e6			0.142215
$994$	2.67164e7	−	5.74392e7i	0.857653	−	1.84392i
$995$	1.33353e7	+	1.33353e7i	0.427017	+	0.427017i
$996$	−6.80083e6	+	5.72915e6i	−0.217227	+	0.182996i
$997$	−3.57413e6	+	3.57413e6i	−0.113876	+	0.113876i	−0.761749	−	0.647873i	$-0.775659\pi$
$997$	−3.57413e6	+	3.57413e6i	−0.113876	+	0.113876i	0.647873	+	0.761749i	$0.275659\pi$
$998$	−1.45720e6	+	531982.i	−0.0463119	+	0.0169072i
$999$			1.10889e7i			0.351541i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.15	yes	80
4.3	odd	2		320.6.l.a.81.19		80
16.5	even	4	inner	80.6.l.a.21.15	✓	80
16.11	odd	4		320.6.l.a.241.19		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.15	✓	80	16.5	even	4	inner
80.6.l.a.61.15	yes	80	1.1	even	1	trivial
320.6.l.a.81.19		80	4.3	odd	2
320.6.l.a.241.19		80	16.11	odd	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.38570 + 5.12917i) q^{2} +(2.82595 + 2.82595i) q^{3} +(-20.6168 - 24.4734i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-21.2367 + 7.75292i) q^{6} +197.416i q^{7} +(174.714 - 47.3612i) q^{8} -227.028i q^{9} +O(q^{10})\)	\(q+(-2.38570 + 5.12917i) q^{2} +(2.82595 + 2.82595i) q^{3} +(-20.6168 - 24.4734i) q^{4} +(17.6777 - 17.6777i) q^{5} +(-21.2367 + 7.75292i) q^{6} +197.416i q^{7} +(174.714 - 47.3612i) q^{8} -227.028i q^{9} +(48.4982 + 132.846i) q^{10} +(-541.655 + 541.655i) q^{11} +(10.8984 - 127.423i) q^{12} +(-657.010 - 657.010i) q^{13} +(-1012.58 - 470.975i) q^{14} +99.9125 q^{15} +(-173.892 + 1009.13i) q^{16} +152.646 q^{17} +(1164.47 + 541.621i) q^{18} +(-428.008 - 428.008i) q^{19} +(-797.090 - 68.1744i) q^{20} +(-557.887 + 557.887i) q^{21} +(-1486.01 - 4070.47i) q^{22} -2103.77i q^{23} +(627.574 + 359.893i) q^{24} -625.000i q^{25} +(4937.35 - 1802.49i) q^{26} +(1328.28 - 1328.28i) q^{27} +(4831.42 - 4070.09i) q^{28} +(-1313.03 - 1313.03i) q^{29} +(-238.362 + 512.469i) q^{30} -8014.55 q^{31} +(-4761.13 - 3299.40i) q^{32} -3061.38 q^{33} +(-364.167 + 782.947i) q^{34} +(3489.85 + 3489.85i) q^{35} +(-5556.14 + 4680.60i) q^{36} +(-4174.18 + 4174.18i) q^{37} +(3216.43 - 1174.23i) q^{38} -3713.36i q^{39} +(2251.30 - 3925.77i) q^{40} -6836.92i q^{41} +(-1530.55 - 4192.45i) q^{42} +(367.257 - 367.257i) q^{43} +(24423.3 + 2088.91i) q^{44} +(-4013.33 - 4013.33i) q^{45} +(10790.6 + 5018.97i) q^{46} -6123.69 q^{47} +(-3343.16 + 2360.34i) q^{48} -22165.9 q^{49} +(3205.73 + 1491.06i) q^{50} +(431.370 + 431.370i) q^{51} +(-2533.78 + 29624.7i) q^{52} +(-8837.44 + 8837.44i) q^{53} +(3644.09 + 9981.84i) q^{54} +19150.4i q^{55} +(9349.83 + 34491.2i) q^{56} -2419.06i q^{57} +(9867.26 - 3602.26i) q^{58} +(-23628.5 + 23628.5i) q^{59} +(-2059.88 - 2445.20i) q^{60} +(34685.8 + 34685.8i) q^{61} +(19120.3 - 41108.0i) q^{62} +44818.9 q^{63} +(28281.8 - 16549.3i) q^{64} -23228.8 q^{65} +(7303.55 - 15702.4i) q^{66} +(-12889.4 - 12889.4i) q^{67} +(-3147.07 - 3735.76i) q^{68} +(5945.16 - 5945.16i) q^{69} +(-26225.8 + 9574.29i) q^{70} +56725.7i q^{71} +(-10752.3 - 39664.9i) q^{72} +41485.9i q^{73} +(-11451.7 - 31368.5i) q^{74} +(1766.22 - 1766.22i) q^{75} +(-1650.63 + 19299.0i) q^{76} +(-106931. - 106931. i) q^{77} +(19046.5 + 8858.97i) q^{78} +106416. q^{79} +(14765.0 + 20913.0i) q^{80} -47660.5 q^{81} +(35067.7 + 16310.9i) q^{82} +(-49167.0 - 49167.0i) q^{83} +(25155.3 + 2151.51i) q^{84} +(2698.42 - 2698.42i) q^{85} +(1007.56 + 2759.89i) q^{86} -7421.13i q^{87} +(-68981.2 + 120288. i) q^{88} -62632.3i q^{89} +(30159.6 - 11010.4i) q^{90} +(129704. - 129704. i) q^{91} +(-51486.4 + 43373.1i) q^{92} +(-22648.8 - 22648.8i) q^{93} +(14609.3 - 31409.4i) q^{94} -15132.4 q^{95} +(-4130.80 - 22778.7i) q^{96} +27802.9 q^{97} +(52881.3 - 113693. i) q^{98} +(122971. + 122971. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Introduction

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