LMFDB - Embedded newform 80.6.l.a.21.3

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			21.3
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.62667 + 0.583586i) q^{2} +(-13.2011 + 13.2011i) q^{3} +(31.3189 - 6.56730i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(66.5744 - 81.9824i) q^{6} +190.109i q^{7} +(-172.388 + 55.2293i) q^{8} -105.540i q^{9} +O(q^{10})$	\(q+(-5.62667 + 0.583586i) q^{2} +(-13.2011 + 13.2011i) q^{3} +(31.3189 - 6.56730i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(66.5744 - 81.9824i) q^{6} +190.109i q^{7} +(-172.388 + 55.2293i) q^{8} -105.540i q^{9} +(109.783 + 89.1500i) q^{10} +(436.822 + 436.822i) q^{11} +(-326.748 + 500.140i) q^{12} +(-460.621 + 460.621i) q^{13} +(-110.945 - 1069.68i) q^{14} +466.730 q^{15} +(937.741 - 411.360i) q^{16} -541.113 q^{17} +(61.5914 + 593.836i) q^{18} +(317.998 - 317.998i) q^{19} +(-669.739 - 437.550i) q^{20} +(-2509.65 - 2509.65i) q^{21} +(-2712.78 - 2202.93i) q^{22} -2557.06i q^{23} +(1546.63 - 3004.81i) q^{24} +625.000i q^{25} +(2322.95 - 2860.58i) q^{26} +(-1814.63 - 1814.63i) q^{27} +(1248.50 + 5954.00i) q^{28} +(-690.500 + 690.500i) q^{29} +(-2626.14 + 272.377i) q^{30} -6618.22 q^{31} +(-5036.30 + 2861.84i) q^{32} -11533.1 q^{33} +(3044.66 - 315.786i) q^{34} +(3360.69 - 3360.69i) q^{35} +(-693.109 - 3305.38i) q^{36} +(2981.43 + 2981.43i) q^{37} +(-1603.69 + 1974.85i) q^{38} -12161.4i q^{39} +(4023.75 + 2071.10i) q^{40} -14704.0i q^{41} +(15585.6 + 12656.4i) q^{42} +(783.164 + 783.164i) q^{43} +(16549.5 + 10812.0i) q^{44} +(-1865.69 + 1865.69i) q^{45} +(1492.26 + 14387.7i) q^{46} +17953.6 q^{47} +(-6948.82 + 17809.7i) q^{48} -19334.5 q^{49} +(-364.741 - 3516.67i) q^{50} +(7143.30 - 7143.30i) q^{51} +(-11401.1 + 17451.2i) q^{52} +(5900.43 + 5900.43i) q^{53} +(11269.3 + 9151.35i) q^{54} -15444.0i q^{55} +(-10499.6 - 32772.6i) q^{56} +8395.88i q^{57} +(3482.25 - 4288.18i) q^{58} +(-14624.8 - 14624.8i) q^{59} +(14617.5 - 3065.16i) q^{60} +(-34636.5 + 34636.5i) q^{61} +(37238.5 - 3862.30i) q^{62} +20064.0 q^{63} +(26667.5 - 19041.8i) q^{64} +16285.4 q^{65} +(64892.8 - 6730.55i) q^{66} +(-48789.6 + 48789.6i) q^{67} +(-16947.0 + 3553.65i) q^{68} +(33756.1 + 33756.1i) q^{69} +(-16948.2 + 20870.7i) q^{70} +18965.7i q^{71} +(5828.87 + 18193.8i) q^{72} -81785.7i q^{73} +(-18515.4 - 15035.6i) q^{74} +(-8250.70 - 8250.70i) q^{75} +(7870.96 - 12047.7i) q^{76} +(-83043.8 + 83043.8i) q^{77} +(7097.25 + 68428.5i) q^{78} +27688.8 q^{79} +(-23849.0 - 9305.19i) q^{80} +73556.5 q^{81} +(8581.03 + 82734.3i) q^{82} +(40272.0 - 40272.0i) q^{83} +(-95081.1 - 62117.9i) q^{84} +(9565.61 + 9565.61i) q^{85} +(-4863.65 - 3949.56i) q^{86} -18230.7i q^{87} +(-99428.3 - 51177.6i) q^{88} +20256.6i q^{89} +(9408.85 - 11586.4i) q^{90} +(-87568.3 - 87568.3i) q^{91} +(-16793.0 - 80084.2i) q^{92} +(87368.0 - 87368.0i) q^{93} +(-101019. + 10477.5i) q^{94} -11242.9 q^{95} +(28705.2 - 104264. i) q^{96} -76865.8 q^{97} +(108789. - 11283.3i) q^{98} +(46101.9 - 46101.9i) 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 $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

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

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 $

$2$	−5.62667	+	0.583586i	−0.994664	+	0.103164i
$2$	−5.62667	+	0.583586i	−0.994664	+	0.103164i
$3$	−13.2011	+	13.2011i	−0.846853	+	0.846853i	−0.989739	−	0.142886i	$-0.954362\pi$
$3$	−13.2011	+	13.2011i	−0.846853	+	0.846853i	0.142886	+	0.989739i	$0.454362\pi$
$4$	31.3189	−	6.56730i	0.978714	−	0.205228i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$5$	−17.6777	−	17.6777i	−0.316228	−	0.316228i
$6$	66.5744	−	81.9824i	0.754969	−	0.929699i
$7$			190.109i			1.46642i	0.680003	+	0.733209i	$0.261978\pi$
$7$			190.109i			1.46642i	−0.680003	+	0.733209i	$0.738022\pi$
$8$	−172.388	+	55.2293i	−0.952320	+	0.305102i
$9$		−	105.540i		−	0.434319i
$10$	109.783	+	89.1500i	0.347164	+	0.281917i
$11$	436.822	+	436.822i	1.08849	+	1.08849i	0.995685	+	0.0928004i	$0.0295818\pi$
$11$	436.822	+	436.822i	1.08849	+	1.08849i	0.0928004	+	0.995685i	$0.470418\pi$
$12$	−326.748	+	500.140i	−0.655029	+	1.00262i
$13$	−460.621	+	460.621i	−0.755937	+	0.755937i	−0.975580	−	0.219643i	$-0.929511\pi$
$13$	−460.621	+	460.621i	−0.755937	+	0.755937i	0.219643	+	0.975580i	$0.429511\pi$
$14$	−110.945	−	1069.68i	−0.151282	−	1.45859i
$15$	466.730			0.535597
$16$	937.741	−	411.360i	0.915763	−	0.401719i
$17$	−541.113			−0.454115			−0.227057	−	0.973881i	$-0.572910\pi$
$17$	−541.113			−0.454115			−0.227057	+	0.973881i	$0.572910\pi$
$18$	61.5914	+	593.836i	0.0448063	+	0.432002i
$19$	317.998	−	317.998i	0.202088	−	0.202088i	−0.598806	−	0.800894i	$-0.704358\pi$
$19$	317.998	−	317.998i	0.202088	−	0.202088i	0.800894	+	0.598806i	$0.204358\pi$
$20$	−669.739	−	437.550i	−0.374395	−	0.244598i
$21$	−2509.65	−	2509.65i	−1.24184	−	1.24184i
$22$	−2712.78	−	2202.93i	−1.19497	−	0.970384i
$23$		−	2557.06i		−	1.00791i	−0.863730	−	0.503954i	$-0.831878\pi$
$23$		−	2557.06i		−	1.00791i	0.863730	−	0.503954i	$-0.168122\pi$
$24$	1546.63	−	3004.81i	0.548099	−	1.06485i
$25$			625.000i			0.200000i
$26$	2322.95	−	2860.58i	0.673918	−	0.829890i
$27$	−1814.63	−	1814.63i	−0.479049	−	0.479049i
$28$	1248.50	+	5954.00i	0.300950	+	1.43520i
$29$	−690.500	+	690.500i	−0.152464	+	0.152464i	−0.779218	−	0.626753i	$-0.784383\pi$
$29$	−690.500	+	690.500i	−0.152464	+	0.152464i	0.626753	+	0.779218i	$0.284383\pi$
$30$	−2626.14	+	272.377i	−0.532739	+	0.0552545i
$31$	−6618.22			−1.23691			−0.618453	−	0.785821i	$-0.712240\pi$
$31$	−6618.22			−1.23691			−0.618453	+	0.785821i	$0.712240\pi$
$32$	−5036.30	+	2861.84i	−0.869434	+	0.494050i
$33$	−11533.1			−1.84357
$34$	3044.66	−	315.786i	0.451692	−	0.0468485i
$35$	3360.69	−	3360.69i	0.463722	−	0.463722i
$36$	−693.109	−	3305.38i	−0.0891344	−	0.425074i
$37$	2981.43	+	2981.43i	0.358031	+	0.358031i	0.863087	−	0.505056i	$-0.168528\pi$
$37$	2981.43	+	2981.43i	0.358031	+	0.358031i	−0.505056	+	0.863087i	$0.668528\pi$
$38$	−1603.69	+	1974.85i	−0.180162	+	0.221858i
$39$		−	12161.4i		−	1.28034i
$40$	4023.75	+	2071.10i	0.397632	+	0.204668i
$41$		−	14704.0i		−	1.36608i	−0.730383	−	0.683038i	$-0.760658\pi$
$41$		−	14704.0i		−	1.36608i	0.730383	−	0.683038i	$-0.239342\pi$
$42$	15585.6	+	12656.4i	1.36333	+	1.10710i
$43$	783.164	+	783.164i	0.0645924	+	0.0645924i	0.738665	−	0.674073i	$-0.235457\pi$
$43$	783.164	+	783.164i	0.0645924	+	0.0645924i	−0.674073	+	0.738665i	$0.735457\pi$
$44$	16549.5	+	10812.0i	1.28870	+	0.841928i
$45$	−1865.69	+	1865.69i	−0.137344	+	0.137344i
$46$	1492.26	+	14387.7i	0.103980	+	1.00253i
$47$	17953.6			1.18551			0.592757	−	0.805381i	$-0.298039\pi$
$47$	17953.6			1.18551			0.592757	+	0.805381i	$0.298039\pi$
$48$	−6948.82	+	17809.7i	−0.435319	+	1.11571i
$49$	−19334.5			−1.15038
$50$	−364.741	−	3516.67i	−0.0206329	−	0.198933i
$51$	7143.30	−	7143.30i	0.384568	−	0.384568i
$52$	−11401.1	+	17451.2i	−0.584707	+	0.894986i
$53$	5900.43	+	5900.43i	0.288532	+	0.288532i	0.836500	−	0.547967i	$-0.184598\pi$
$53$	5900.43	+	5900.43i	0.288532	+	0.288532i	−0.547967	+	0.836500i	$0.684598\pi$
$54$	11269.3	+	9151.35i	0.525913	+	0.427072i
$55$		−	15444.0i		−	0.688418i
$56$	−10499.6	−	32772.6i	−0.447406	−	1.39650i
$57$			8395.88i			0.342278i
$58$	3482.25	−	4288.18i	0.135922	−	0.167380i
$59$	−14624.8	−	14624.8i	−0.546966	−	0.546966i	0.378596	−	0.925562i	$-0.376407\pi$
$59$	−14624.8	−	14624.8i	−0.546966	−	0.546966i	−0.925562	+	0.378596i	$0.876407\pi$
$60$	14617.5	−	3065.16i	0.524196	−	0.109919i
$61$	−34636.5	+	34636.5i	−1.19182	+	1.19182i	−0.215262	+	0.976556i	$0.569060\pi$
$61$	−34636.5	+	34636.5i	−1.19182	+	1.19182i	−0.976556	+	0.215262i	$0.930940\pi$
$62$	37238.5	−	3862.30i	1.23031	−	0.127605i
$63$	20064.0			0.636893
$64$	26667.5	−	19041.8i	0.813826	−	0.581108i
$65$	16285.4			0.478097
$66$	64892.8	−	6730.55i	1.83374	−	0.190191i
$67$	−48789.6	+	48789.6i	−1.32782	+	1.32782i	−0.420559	+	0.907265i	$0.638166\pi$
$67$	−48789.6	+	48789.6i	−1.32782	+	1.32782i	−0.907265	+	0.420559i	$0.861834\pi$
$68$	−16947.0	+	3553.65i	−0.444448	+	0.0931970i
$69$	33756.1	+	33756.1i	0.853550	+	0.853550i
$70$	−16948.2	+	20870.7i	−0.413408	+	0.509088i
$71$			18965.7i			0.446502i	0.974761	+	0.223251i	$0.0716669\pi$
$71$			18965.7i			0.446502i	−0.974761	+	0.223251i	$0.928333\pi$
$72$	5828.87	+	18193.8i	0.132511	+	0.413611i
$73$		−	81785.7i		−	1.79626i	−0.439726	−	0.898132i	$-0.644924\pi$
$73$		−	81785.7i		−	1.79626i	0.439726	−	0.898132i	$-0.355076\pi$
$74$	−18515.4	−	15035.6i	−0.393056	−	0.319184i
$75$	−8250.70	−	8250.70i	−0.169371	−	0.169371i
$76$	7870.96	−	12047.7i	0.156312	−	0.239261i
$77$	−83043.8	+	83043.8i	−1.59617	+	1.59617i
$78$	7097.25	+	68428.5i	0.132085	+	1.27350i
$79$	27688.8			0.499156			0.249578	−	0.968355i	$-0.419708\pi$
$79$	27688.8			0.499156			0.249578	+	0.968355i	$0.419708\pi$
$80$	−23849.0	−	9305.19i	−0.416624	−	0.162555i
$81$	73556.5			1.24569
$82$	8581.03	+	82734.3i	0.140930	+	1.35879i
$83$	40272.0	−	40272.0i	0.641665	−	0.641665i	−0.309300	−	0.950965i	$-0.600095\pi$
$83$	40272.0	−	40272.0i	0.641665	−	0.641665i	0.950965	+	0.309300i	$0.100095\pi$
$84$	−95081.1	−	62117.9i	−1.47027	−	0.960546i
$85$	9565.61	+	9565.61i	0.143604	+	0.143604i
$86$	−4863.65	−	3949.56i	−0.0709114	−	0.0575841i
$87$		−	18230.7i		−	0.258230i
$88$	−99428.3	−	51177.6i	−1.36868	−	0.704487i
$89$			20256.6i			0.271076i	0.990772	+	0.135538i	$0.0432764\pi$
$89$			20256.6i			0.271076i	−0.990772	+	0.135538i	$0.956724\pi$
$90$	9408.85	−	11586.4i	0.122442	−	0.150780i
$91$	−87568.3	−	87568.3i	−1.10852	−	1.10852i
$92$	−16793.0	−	80084.2i	−0.206851	−	0.986454i
$93$	87368.0	−	87368.0i	1.04748	−	1.04748i
$94$	−101019.	+	10477.5i	−1.17919	+	0.122303i
$95$	−11242.9			−0.127812
$96$	28705.2	−	104264.i	0.317895	−	1.15467i
$97$	−76865.8			−0.829476			−0.414738	−	0.909941i	$-0.636127\pi$
$97$	−76865.8			−0.829476			−0.414738	+	0.909941i	$0.636127\pi$
$98$	108789.	−	11283.3i	1.14424	−	0.118679i
$99$	46101.9	−	46101.9i	0.472750	−	0.472750i
$100$	4104.56	+	19574.3i	0.0410456	+	0.195743i
$101$	−11615.5	−	11615.5i	−0.113301	−	0.113301i	0.648183	−	0.761484i	$-0.275529\pi$
$101$	−11615.5	−	11615.5i	−0.113301	−	0.113301i	−0.761484	+	0.648183i	$0.775529\pi$
$102$	−36024.3	+	44361.7i	−0.342842	+	0.422190i
$103$		−	210790.i		−	1.95775i	−0.204454	−	0.978876i	$-0.565542\pi$
$103$		−	210790.i		−	1.95775i	0.204454	−	0.978876i	$-0.434458\pi$
$104$	53966.0	−	104846.i	0.489257	−	0.950532i
$105$			88729.7i			0.785409i
$106$	−36643.2	−	29756.4i	−0.316759	−	0.257226i
$107$	138862.	+	138862.i	1.17253	+	1.17253i	0.981605	+	0.190922i	$0.0611478\pi$
$107$	138862.	+	138862.i	1.17253	+	1.17253i	0.190922	+	0.981605i	$0.438852\pi$
$108$	−68749.5	−	44915.0i	−0.567166	−	0.370537i
$109$	−98758.1	+	98758.1i	−0.796171	+	0.796171i	−0.982489	−	0.186318i	$-0.940344\pi$
$109$	−98758.1	+	98758.1i	−0.796171	+	0.796171i	0.186318	+	0.982489i	$0.440344\pi$
$110$	9012.90	+	86898.2i	0.0710203	+	0.684745i
$111$	−78716.4			−0.606398
$112$	78203.4	+	178273.i	0.589088	+	1.34289i
$113$	−68434.7			−0.504174			−0.252087	−	0.967705i	$-0.581117\pi$
$113$	−68434.7			−0.504174			−0.252087	+	0.967705i	$0.581117\pi$
$114$	−4899.72	−	47240.8i	−0.0353109	−	0.340452i
$115$	−45202.8	+	45202.8i	−0.318729	+	0.318729i
$116$	−17090.9	+	26160.4i	−0.117929	+	0.180509i
$117$	48613.8	+	48613.8i	0.328318	+	0.328318i
$118$	90823.8	+	73754.1i	0.600475	+	0.487620i
$119$		−	102870.i		−	0.665922i
$120$	−80458.8	+	25777.2i	−0.510059	+	0.163411i
$121$			220575.i			1.36960i
$122$	174675.	−	215102.i	1.06251	−	1.30841i
$123$	194109.	+	194109.i	1.15686	+	1.15686i
$124$	−207275.	+	43463.8i	−1.21058	+	0.253848i
$125$	11048.5	−	11048.5i	0.0632456	−	0.0632456i
$126$	−112894.	+	11709.1i	−0.633495	+	0.0657047i
$127$	186051.			1.02358			0.511791	−	0.859110i	$-0.328982\pi$
$127$	186051.			1.02358			0.511791	+	0.859110i	$0.328982\pi$
$128$	−138936.	+	122704.i	−0.749534	+	0.661966i
$129$	−20677.3			−0.109401
$130$	−91632.8	+	9503.95i	−0.475546	+	0.0493226i
$131$	264913.	−	264913.i	1.34873	−	1.34873i	0.461685	−	0.887044i	$-0.347245\pi$
$131$	264913.	−	264913.i	1.34873	−	1.34873i	0.887044	−	0.461685i	$-0.152755\pi$
$132$	−361203.	+	75741.1i	−1.80433	+	0.378353i
$133$	60454.4	+	60454.4i	0.296346	+	0.296346i
$134$	246050.	−	302996.i	1.18375	−	1.45772i
$135$			64157.0i			0.302977i
$136$	93281.5	−	29885.3i	0.432462	−	0.138551i
$137$		−	188083.i		−	0.856148i	−0.903744	−	0.428074i	$-0.859192\pi$
$137$		−	188083.i		−	0.856148i	0.903744	−	0.428074i	$-0.140808\pi$
$138$	−209634.	−	170235.i	−0.937052	−	0.760940i
$139$	261616.	+	261616.i	1.14849	+	1.14849i	0.986850	+	0.161638i	$0.0516778\pi$
$139$	261616.	+	261616.i	1.14849	+	1.14849i	0.161638	+	0.986850i	$0.448322\pi$
$140$	83182.2	−	127323.i	0.358683	−	0.549020i
$141$	−237008.	+	237008.i	−1.00396	+	1.00396i
$142$	−11068.1	−	106714.i	−0.0460631	−	0.444119i
$143$	−402419.			−1.64565
$144$	−43414.8	−	98968.7i	−0.174474	−	0.397733i
$145$	24412.8			0.0964270
$146$	47729.0	+	460181.i	0.185311	+	1.78668i
$147$	255237.	−	255237.i	0.974204	−	0.974204i
$148$	112955.	+	73795.0i	0.423887	+	0.276932i
$149$	−224725.	−	224725.i	−0.829251	−	0.829251i	0.158162	−	0.987413i	$-0.449443\pi$
$149$	−224725.	−	224725.i	−0.829251	−	0.829251i	−0.987413	+	0.158162i	$0.949443\pi$
$150$	51239.0	+	41609.0i	0.185940	+	0.150994i
$151$			2888.53i			0.0103094i	0.999987	+	0.00515471i	$0.00164080\pi$
$151$			2888.53i			0.0103094i	−0.999987	+	0.00515471i	$0.998359\pi$
$152$	−37256.4	+	72382.0i	−0.130795	+	0.254110i
$153$			57108.8i			0.197231i
$154$	418797.	−	515723.i	1.42299	−	1.75233i
$155$	116995.	+	116995.i	0.391144	+	0.391144i
$156$	−79867.8	−	380883.i	−0.262761	−	1.25308i
$157$	−307992.	+	307992.i	−0.997217	+	0.997217i	−0.999996	−	0.00277909i	$-0.999115\pi$
$157$	−307992.	+	307992.i	−0.997217	+	0.997217i	0.00277909	+	0.999996i	$0.499115\pi$
$158$	−155796.	+	16158.8i	−0.496493	+	0.0514952i
$159$	−155785.			−0.488689
$160$	139621.	+	38439.3i	0.431171	+	0.118707i
$161$	486120.			1.47802
$162$	−413878.	+	42926.6i	−1.23904	+	0.128511i
$163$	59729.4	−	59729.4i	0.176084	−	0.176084i	−0.613563	−	0.789646i	$-0.710264\pi$
$163$	59729.4	−	59729.4i	0.176084	−	0.176084i	0.789646	+	0.613563i	$0.210264\pi$
$164$	−96565.3	−	460511.i	−0.280357	−	1.33700i
$165$	203878.	+	203878.i	0.582989	+	0.582989i
$166$	−203095.	+	250100.i	−0.572044	+	0.704438i
$167$			630406.i			1.74916i	0.484883	+	0.874579i	$0.338862\pi$
$167$			630406.i			1.74916i	−0.484883	+	0.874579i	$0.661138\pi$
$168$	571241.	+	294029.i	1.56152	+	0.803742i
$169$		−	53051.3i		−	0.142883i
$170$	−59404.9	−	48240.2i	−0.157652	−	0.128023i
$171$	−33561.4	−	33561.4i	−0.0877707	−	0.0877707i
$172$	29671.1	+	19384.5i	0.0764737	+	0.0499614i
$173$	−56816.7	+	56816.7i	−0.144331	+	0.144331i	−0.775580	−	0.631249i	$-0.782543\pi$
$173$	−56816.7	+	56816.7i	−0.144331	+	0.144331i	0.631249	+	0.775580i	$0.282543\pi$
$174$	10639.2	+	102578.i	0.0266401	+	0.256852i
$175$	−118818.			−0.293284
$176$	589317.	+	229935.i	1.43406	+	0.559529i
$177$	386128.			0.926399
$178$	−11821.5	−	113977.i	−0.0279655	−	0.269630i
$179$	−4976.81	+	4976.81i	−0.0116096	+	0.0116096i	−0.712888	−	0.701278i	$-0.752613\pi$
$179$	−4976.81	+	4976.81i	−0.0116096	+	0.0116096i	0.701278	+	0.712888i	$0.252613\pi$
$180$	−46178.8	+	70683.9i	−0.106233	+	0.162607i
$181$	197629.	+	197629.i	0.448388	+	0.448388i	0.894818	−	0.446430i	$-0.147305\pi$
$181$	197629.	+	197629.i	0.448388	+	0.448388i	−0.446430	+	0.894818i	$0.647305\pi$
$182$	543822.	+	441615.i	1.21697	+	0.988246i
$183$		−	914483.i		−	2.01859i
$184$	141225.	+	440807.i	0.307514	+	0.959851i
$185$		−	105409.i		−	0.226438i
$186$	−440604.	+	542578.i	−0.933826	+	1.14995i
$187$	−236370.	−	236370.i	−0.494297	−	0.494297i
$188$	562286.	−	117907.i	1.16028	−	0.243301i
$189$	344978.	−	344978.i	0.702485	−	0.702485i
$190$	63260.3	−	6561.23i	0.127130	−	0.0131856i
$191$	−669691.			−1.32828			−0.664142	−	0.747606i	$-0.731203\pi$
$191$	−669691.			−1.32828			−0.664142	+	0.747606i	$0.731203\pi$
$192$	−100668.	+	603413.i	−0.197078	+	1.18130i
$193$	−293474.			−0.567122			−0.283561	−	0.958954i	$-0.591516\pi$
$193$	−293474.			−0.567122			−0.283561	+	0.958954i	$0.591516\pi$
$194$	432499.	−	44857.8i	0.825050	−	0.0855725i
$195$	−214986.	+	214986.i	−0.404878	+	0.404878i
$196$	−605534.	+	126975.i	−1.12590	+	0.236091i
$197$	−483401.	−	483401.i	−0.887445	−	0.887445i	0.106832	−	0.994277i	$-0.465929\pi$
$197$	−483401.	−	483401.i	−0.887445	−	0.887445i	−0.994277	+	0.106832i	$0.965929\pi$
$198$	−232496.	+	286305.i	−0.421456	+	0.518998i
$199$			617351.i			1.10509i	0.833482	+	0.552547i	$0.186344\pi$
$199$			617351.i			1.10509i	−0.833482	+	0.552547i	$0.813656\pi$
$200$	−34518.3	−	107743.i	−0.0610203	−	0.190464i
$201$		−	1.28816e6i		−	2.24894i
$202$	72135.3	+	58578.0i	0.124385	+	0.101008i
$203$	−131270.	−	131270.i	−0.223577	−	0.223577i
$204$	176808.	−	270632.i	0.297458	−	0.455306i
$205$	−259932.	+	259932.i	−0.431991	+	0.431991i
$206$	123014.	+	1.18605e6i	0.201970	+	1.94731i
$207$	−269871.			−0.437754
$208$	−242462.	+	621425.i	−0.388585	+	0.995934i
$209$	277817.			0.439940
$210$	−51781.4	−	499253.i	−0.0810263	−	0.781218i
$211$	−460653.	+	460653.i	−0.712308	+	0.712308i	−0.967018	−	0.254710i	$-0.918020\pi$
$211$	−460653.	+	460653.i	−0.712308	+	0.712308i	0.254710	+	0.967018i	$0.418020\pi$
$212$	223545.	+	146045.i	0.341606	+	0.223176i
$213$	−250369.	−	250369.i	−0.378121	−	0.378121i
$214$	−862367.	−	700291.i	−1.28723	−	1.04531i
$215$		−	27689.0i		−	0.0408518i
$216$	413042.	+	212601.i	0.602366	+	0.310049i
$217$		−	1.25818e6i		−	1.81382i
$218$	498045.	−	613313.i	0.709787	−	0.874060i
$219$	1.07966e6	+	1.07966e6i	1.52117	+	1.52117i
$220$	−101425.	−	483688.i	−0.141283	−	0.673765i
$221$	249248.	−	249248.i	0.343282	−	0.343282i
$222$	442911.	−	45937.8i	0.603163	−	0.0625587i
$223$	−1.15488e6			−1.55516			−0.777579	−	0.628786i	$-0.783552\pi$
$223$	−1.15488e6			−1.55516			−0.777579	+	0.628786i	$0.783552\pi$
$224$	−544062.	−	957446.i	−0.724484	−	1.27495i
$225$	65962.2			0.0868638
$226$	385060.	−	39937.6i	0.501484	−	0.0520128i
$227$	148238.	−	148238.i	0.190939	−	0.190939i	−0.605163	−	0.796102i	$-0.706892\pi$
$227$	148238.	−	148238.i	0.190939	−	0.190939i	0.796102	+	0.605163i	$0.206892\pi$
$228$	55138.2	+	262949.i	0.0702450	+	0.334992i
$229$	58454.7	+	58454.7i	0.0736599	+	0.0736599i	0.742977	−	0.669317i	$-0.233413\pi$
$229$	58454.7	+	58454.7i	0.0736599	+	0.0736599i	−0.669317	+	0.742977i	$0.733413\pi$
$230$	227962.	−	280721.i	0.284147	−	0.349910i
$231$		−	2.19254e6i		−	2.70345i
$232$	80898.3	−	157170.i	0.0986778	−	0.191712i
$233$		−	546820.i		−	0.659864i	−0.944005	−	0.329932i	$-0.892974\pi$
$233$		−	546820.i		−	0.659864i	0.944005	−	0.329932i	$-0.107026\pi$
$234$	−301904.	−	245163.i	−0.360437	−	0.292695i
$235$	−317378.	−	317378.i	−0.374892	−	0.374892i
$236$	−554078.	−	361987.i	−0.647576	−	0.423070i
$237$	−365523.	+	365523.i	−0.422712	+	0.422712i
$238$	60033.8	+	578818.i	0.0686995	+	0.662369i
$239$	−1.20909e6			−1.36919			−0.684594	−	0.728925i	$-0.740020\pi$
$239$	−1.20909e6			−1.36919			−0.684594	+	0.728925i	$0.740020\pi$
$240$	437672.	−	191994.i	0.490480	−	0.215159i
$241$	10734.0			0.0119047			0.00595236	−	0.999982i	$-0.498105\pi$
$241$	10734.0			0.0119047			0.00595236	+	0.999982i	$0.498105\pi$
$242$	−128725.	−	1.24111e6i	−0.141294	−	1.36229i
$243$	−530073.	+	530073.i	−0.575864	+	0.575864i
$244$	−857308.	+	1.31225e6i	−0.921855	+	1.41104i
$245$	341788.	+	341788.i	0.363783	+	0.363783i
$246$	−1.20547e6	−	978907.i	−1.27004	−	1.03134i
$247$			292954.i			0.305532i
$248$	1.14090e6	−	365519.i	1.17793	−	0.377382i
$249$			1.06327e6i			1.08679i
$250$	−55718.7	+	68614.3i	−0.0563834	+	0.0694328i
$251$	290458.	+	290458.i	0.291004	+	0.291004i	0.837477	−	0.546473i	$-0.184030\pi$
$251$	290458.	+	290458.i	0.291004	+	0.291004i	−0.546473	+	0.837477i	$0.684030\pi$
$252$	628382.	−	131766.i	0.623336	−	0.130708i
$253$	1.11698e6	−	1.11698e6i	1.09709	−	1.09709i
$254$	−1.04685e6	+	108577.i	−1.01812	+	0.105597i
$255$	−252554.			−0.243222
$256$	710141.	−	771499.i	0.677243	−	0.735759i
$257$	−355570.			−0.335809			−0.167904	−	0.985803i	$-0.553700\pi$
$257$	−355570.			−0.335809			−0.167904	+	0.985803i	$0.553700\pi$
$258$	116344.	−	12067.0i	0.108817	−	0.0112862i
$259$	−566797.	+	566797.i	−0.525022	+	0.525022i
$260$	510041.	−	106951.i	0.467920	−	0.0981189i
$261$	72875.0	+	72875.0i	0.0662182	+	0.0662182i
$262$	−1.33598e6	+	1.64518e6i	−1.20239	+	1.48067i
$263$			1.59192e6i			1.41916i	0.704623	+	0.709582i	$0.251116\pi$
$263$			1.59192e6i			1.41916i	−0.704623	+	0.709582i	$0.748884\pi$
$264$	1.98817e6	−	636964.i	1.75567	−	0.562477i
$265$		−	208612.i		−	0.182484i
$266$	−375437.	−	304877.i	−0.325337	−	0.264192i
$267$	−267410.	−	267410.i	−0.229562	−	0.229562i
$268$	−1.20762e6	+	1.84845e6i	−1.02705	+	1.57207i
$269$	−1.42217e6	+	1.42217e6i	−1.19831	+	1.19831i	−0.223642	+	0.974671i	$0.571795\pi$
$269$	−1.42217e6	+	1.42217e6i	−1.19831	+	1.19831i	−0.974671	+	0.223642i	$0.928205\pi$
$270$	−37441.1	−	360990.i	−0.0312564	−	0.301360i
$271$	1.19243e6			0.986300			0.493150	−	0.869944i	$-0.335845\pi$
$271$	1.19243e6			0.986300			0.493150	+	0.869944i	$0.335845\pi$
$272$	−507424.	+	222592.i	−0.415861	+	0.182427i
$273$	2.31200e6			1.87751
$274$	109763.	+	1.05828e6i	0.0883241	+	0.851580i
$275$	−273014.	+	273014.i	−0.217697	+	0.217697i
$276$	1.27889e6	+	835515.i	1.01055	+	0.660209i
$277$	532826.	+	532826.i	0.417240	+	0.417240i	0.884251	−	0.467011i	$-0.154669\pi$
$277$	532826.	+	532826.i	0.417240	+	0.417240i	−0.467011	+	0.884251i	$0.654669\pi$
$278$	−1.62470e6	−	1.31935e6i	−1.26084	−	1.02388i
$279$			698484.i			0.537212i
$280$	−393735.	+	764951.i	−0.300129	+	0.583094i
$281$			115327.i			0.0871296i	0.999051	+	0.0435648i	$0.0138715\pi$
$281$			115327.i			0.0871296i	−0.999051	+	0.0435648i	$0.986129\pi$
$282$	1.19525e6	−	1.47188e6i	0.895026	−	1.10217i
$283$	169009.	+	169009.i	0.125442	+	0.125442i	0.767041	−	0.641598i	$-0.221728\pi$
$283$	169009.	+	169009.i	0.125442	+	0.125442i	−0.641598	+	0.767041i	$0.721728\pi$
$284$	124553.	+	593984.i	0.0916347	+	0.436998i
$285$	148420.	−	148420.i	0.108238	−	0.108238i
$286$	2.26428e6	−	234846.i	1.63687	−	0.169773i
$287$	2.79536e6			2.00324
$288$	302037.	+	531528.i	0.214575	+	0.377611i
$289$	−1.12705e6			−0.793780
$290$	−137363.	+	14247.0i	−0.0959124	+	0.00994784i
$291$	1.01472e6	−	1.01472e6i	0.702444	−	0.702444i
$292$	−537111.	−	2.56143e6i	−0.368644	−	1.75803i
$293$	−170154.	−	170154.i	−0.115791	−	0.115791i	0.646837	−	0.762628i	$-0.276091\pi$
$293$	−170154.	−	170154.i	−0.115791	−	0.115791i	−0.762628	+	0.646837i	$0.776091\pi$
$294$	−1.28718e6	+	1.58509e6i	−0.868503	+	1.06951i
$295$			517065.i			0.345932i
$296$	−678625.	−	349301.i	−0.450195	−	0.231724i
$297$		−	1.58534e6i		−	1.04287i
$298$	1.39560e6	+	1.13331e6i	0.910375	+	0.739277i
$299$	1.17784e6	+	1.17784e6i	0.761916	+	0.761916i
$300$	−312587.	−	204218.i	−0.200525	−	0.131006i
$301$	−148887.	+	148887.i	−0.0947195	+	0.0947195i
$302$	−1685.71	−	16252.8i	−0.00106357	−	0.0102544i
$303$	306675.			0.191899
$304$	167388.	−	429012.i	0.103882	−	0.266248i
$305$	1.22459e6			0.753772
$306$	−33327.9	−	321332.i	−0.0203472	−	0.196178i
$307$	−778959.	+	778959.i	−0.471703	+	0.471703i	−0.902465	−	0.430762i	$-0.858245\pi$
$307$	−778959.	+	778959.i	−0.471703	+	0.471703i	0.430762	+	0.902465i	$0.358245\pi$
$308$	−2.05546e6	+	3.14621e6i	−1.23462	+	1.88978i
$309$	2.78267e6	+	2.78267e6i	1.65793	+	1.65793i
$310$	−726567.	−	590014.i	−0.429409	−	0.348705i
$311$			1.12014e6i			0.656705i	0.944555	+	0.328352i	$0.106493\pi$
$311$			1.12014e6i			0.656705i	−0.944555	+	0.328352i	$0.893507\pi$
$312$	671668.	+	2.09649e6i	0.390632	+	1.21929i
$313$		−	3.38921e6i		−	1.95541i	−0.209980	−	0.977706i	$-0.567340\pi$
$313$		−	3.38921e6i		−	1.95541i	0.209980	−	0.977706i	$-0.432660\pi$
$314$	1.55323e6	−	1.91271e6i	0.889019	−	1.09477i
$315$	−354685.	−	354685.i	−0.201403	−	0.201403i
$316$	867182.	−	181841.i	0.488531	−	0.102441i
$317$	−1.30797e6	+	1.30797e6i	−0.731054	+	0.731054i	−0.970829	−	0.239774i	$-0.922927\pi$
$317$	−1.30797e6	+	1.30797e6i	−0.731054	+	0.731054i	0.239774	+	0.970829i	$0.422927\pi$
$318$	876550.	−	90913.9i	0.486081	−	0.0504153i
$319$	−603250.			−0.331910
$320$	−808032.	−	134804.i	−0.441117	−	0.0735918i
$321$	−3.66626e6			−1.98592
$322$	−2.73524e6	+	283693.i	−1.47013	+	0.152479i
$323$	−172073.	+	172073.i	−0.0917712	+	0.0917712i
$324$	2.30371e6	−	483067.i	1.21917	−	0.255650i
$325$	−287888.	−	287888.i	−0.151187	−	0.151187i
$326$	−301220.	+	370935.i	−0.156978	+	0.193310i
$327$		−	2.60744e6i		−	1.34848i
$328$	812089.	+	2.53479e6i	0.416792	+	1.30094i
$329$			3.41314e6i			1.73846i
$330$	−1.26613e6	−	1.02817e6i	−0.640022	−	0.519735i
$331$	2.48446e6	+	2.48446e6i	1.24641	+	1.24641i	0.957293	+	0.289121i	$0.0933630\pi$
$331$	2.48446e6	+	2.48446e6i	1.24641	+	1.24641i	0.289121	+	0.957293i	$0.406637\pi$
$332$	996796.	−	1.52575e6i	0.496319	−	0.759694i
$333$	314658.	−	314658.i	0.155499	−	0.155499i
$334$	−367896.	−	3.54709e6i	−0.180451	−	1.73983i
$335$	1.72497e6			0.839790
$336$	−3.38578e6	−	1.32103e6i	−1.63610	−	0.638360i
$337$	2.04358e6			0.980206			0.490103	−	0.871665i	$-0.336959\pi$
$337$	2.04358e6			0.980206			0.490103	+	0.871665i	$0.336959\pi$
$338$	30960.0	+	298502.i	0.0147404	+	0.142120i
$339$	903415.	−	903415.i	0.426961	−	0.426961i
$340$	362404.	+	236764.i	0.170018	+	0.111075i
$341$	−2.89098e6	−	2.89098e6i	−1.34635	−	1.34635i
$342$	208425.	+	169253.i	0.0963572	+	0.0782476i
$343$		−	480496.i		−	0.220523i
$344$	−178262.	−	91754.7i	−0.0812199	−	0.0418054i
$345$		−	1.19346e6i		−	0.539833i
$346$	286531.	−	352846.i	0.128671	−	0.158451i
$347$	−1.42726e6	−	1.42726e6i	−0.636325	−	0.636325i	0.313322	−	0.949647i	$-0.398558\pi$
$347$	−1.42726e6	−	1.42726e6i	−0.636325	−	0.636325i	−0.949647	+	0.313322i	$0.898558\pi$
$348$	−119727.	−	570966.i	−0.0529960	−	0.252733i
$349$	1.77197e6	−	1.77197e6i	0.778739	−	0.778739i	−0.200877	−	0.979616i	$-0.564379\pi$
$349$	1.77197e6	−	1.77197e6i	0.778739	−	0.778739i	0.979616	+	0.200877i	$0.0643792\pi$
$350$	668551.	−	69340.7i	0.291719	−	0.0302564i
$351$	1.67172e6			0.724261
$352$	−3.45008e6	−	949849.i	−1.48413	−	0.408599i
$353$	836162.			0.357153			0.178576	−	0.983926i	$-0.442851\pi$
$353$	836162.			0.357153			0.178576	+	0.983926i	$0.442851\pi$
$354$	−2.17261e6	+	225339.i	−0.921456	+	0.0955714i
$355$	335270.	−	335270.i	0.141196	−	0.141196i
$356$	133031.	+	634414.i	0.0556325	+	0.265306i
$357$	1.35801e6	+	1.35801e6i	0.563938	+	0.563938i
$358$	25098.5	−	30907.3i	0.0103500	−	0.0127454i
$359$		−	802370.i		−	0.328578i	−0.986412	−	0.164289i	$-0.947467\pi$
$359$		−	802370.i		−	0.328578i	0.986412	−	0.164289i	$-0.0525330\pi$
$360$	218583.	−	424664.i	0.0888914	−	0.172699i
$361$			2.27385e6i			0.918321i
$362$	−1.22733e6	−	996659.i	−0.492253	−	0.399738i
$363$	−2.91184e6	−	2.91184e6i	−1.15985	−	1.15985i
$364$	−3.31763e6	−	2.16745e6i	−1.31242	−	0.857425i
$365$	−1.44578e6	+	1.44578e6i	−0.568029	+	0.568029i
$366$	533680.	+	5.14549e6i	0.208247	+	2.00782i
$367$	−158829.			−0.0615550			−0.0307775	−	0.999526i	$-0.509798\pi$
$367$	−158829.			−0.0615550			−0.0307775	+	0.999526i	$0.509798\pi$
$368$	−1.05187e6	−	2.39786e6i	−0.404896	−	0.923005i
$369$	−1.55185e6			−0.593312
$370$	61515.5	+	593104.i	0.0233604	+	0.225230i
$371$	−1.12173e6	+	1.12173e6i	−0.423109	+	0.423109i
$372$	2.16249e6	−	3.31004e6i	0.810210	−	1.24015i
$373$	719302.	+	719302.i	0.267694	+	0.267694i	0.828171	−	0.560476i	$-0.189382\pi$
$373$	719302.	+	719302.i	0.267694	+	0.267694i	−0.560476	+	0.828171i	$0.689382\pi$
$374$	1.46792e6	+	1.19203e6i	0.542653	+	0.440666i
$375$			291706.i			0.107119i
$376$	−3.09499e6	+	991564.i	−1.12899	+	0.361702i
$377$		−	636118.i		−	0.230507i
$378$	−1.73976e6	+	2.14240e6i	−0.626266	+	0.771209i
$379$	−733349.	−	733349.i	−0.262248	−	0.262248i	0.563719	−	0.825967i	$-0.309370\pi$
$379$	−733349.	−	733349.i	−0.262248	−	0.262248i	−0.825967	+	0.563719i	$0.809370\pi$
$380$	−352116.	+	73835.7i	−0.125091	+	0.0262306i
$381$	−2.45608e6	+	2.45608e6i	−0.866824	+	0.866824i
$382$	3.76813e6	−	390823.i	1.32120	−	0.137032i
$383$	−3.53928e6			−1.23287			−0.616435	−	0.787406i	$-0.711424\pi$
$383$	−3.53928e6			−1.23287			−0.616435	+	0.787406i	$0.711424\pi$
$384$	214280.	−	3.45396e6i	0.0741574	−	1.19533i
$385$	2.93604e6			1.00951
$386$	1.65128e6	−	171268.i	0.564096	−	0.0585069i
$387$	82654.7	−	82654.7i	0.0280537	−	0.0280537i
$388$	−2.40735e6	+	504801.i	−0.811820	+	0.170232i
$389$	−467653.	−	467653.i	−0.156693	−	0.156693i	0.624407	−	0.781100i	$-0.285341\pi$
$389$	−467653.	−	467653.i	−0.156693	−	0.156693i	−0.781100	+	0.624407i	$0.785341\pi$
$390$	1.08419e6	−	1.33512e6i	0.360948	−	0.444486i
$391$			1.38366e6i			0.457706i
$392$	3.33304e6	−	1.06783e6i	1.09553	−	0.350983i
$393$			6.99430e6i			2.28435i
$394$	3.00204e6	+	2.43783e6i	0.974263	+	0.791157i
$395$	−489474.	−	489474.i	−0.157847	−	0.157847i
$396$	1.14109e6	−	1.74663e6i	0.365665	−	0.559708i
$397$	1.28300e6	−	1.28300e6i	0.408555	−	0.408555i	−0.472680	−	0.881234i	$-0.656713\pi$
$397$	1.28300e6	−	1.28300e6i	0.408555	−	0.408555i	0.881234	+	0.472680i	$0.156713\pi$
$398$	−360277.	−	3.47363e6i	−0.114006	−	1.09920i
$399$	−1.59613e6			−0.501923
$400$	257100.	+	586088.i	0.0803438	+	0.183153i
$401$	−1.16341e6			−0.361304			−0.180652	−	0.983547i	$-0.557821\pi$
$401$	−1.16341e6			−0.361304			−0.180652	+	0.983547i	$0.557821\pi$
$402$	751750.	+	7.24803e6i	0.232011	+	2.23694i
$403$	3.04849e6	−	3.04849e6i	0.935024	−	0.935024i
$404$	−440067.	−	287502.i	−0.134142	−	0.0876369i
$405$	−1.30031e6	−	1.30031e6i	−0.393921	−	0.393921i
$406$	815222.	+	662007.i	0.245449	+	0.199318i
$407$			2.60470e6i			0.779422i
$408$	−836902.	+	1.62594e6i	−0.248900	+	0.483564i
$409$			2.33520e6i			0.690266i	0.938554	+	0.345133i	$0.112166\pi$
$409$			2.33520e6i			0.690266i	−0.938554	+	0.345133i	$0.887834\pi$
$410$	1.31086e6	−	1.61424e6i	0.385120	−	0.474252i
$411$	2.48291e6	+	2.48291e6i	0.725032	+	0.725032i
$412$	−1.38432e6	−	6.60171e6i	−0.401786	−	1.91608i
$413$	2.78031e6	−	2.78031e6i	0.802081	−	0.802081i
$414$	1.51847e6	−	157493.i	0.435418	−	0.0451606i
$415$	−1.42383e6			−0.405825
$416$	1.00160e6	−	3.63805e6i	0.283767	−	1.03071i
$417$	−6.90724e6			−1.94520
$418$	−1.56319e6	+	162130.i	−0.437593	+	0.0453862i
$419$	591682.	−	591682.i	0.164647	−	0.164647i	−0.619975	−	0.784622i	$-0.712857\pi$
$419$	591682.	−	591682.i	0.164647	−	0.164647i	0.784622	+	0.619975i	$0.212857\pi$
$420$	582714.	+	2.77891e6i	0.161188	+	0.768691i
$421$	−463532.	−	463532.i	−0.127460	−	0.127460i	0.640499	−	0.767959i	$-0.278728\pi$
$421$	−463532.	−	463532.i	−0.127460	−	0.127460i	−0.767959	+	0.640499i	$0.778728\pi$
$422$	2.32311e6	−	2.86077e6i	0.635022	−	0.781992i
$423$		−	1.89481e6i		−	0.514891i
$424$	−1.34304e6	−	691289.i	−0.362807	−	0.186743i
$425$		−	338195.i		−	0.0908229i
$426$	1.55485e6	+	1.26263e6i	0.415112	+	0.337095i
$427$	−6.58472e6	−	6.58472e6i	−1.74770	−	1.74770i
$428$	5.26093e6	+	3.43704e6i	1.38820	+	0.906934i
$429$	5.31238e6	−	5.31238e6i	1.39363	−	1.39363i
$430$	16158.9	+	155797.i	0.00421446	+	0.0406339i
$431$	−2.47706e6			−0.642309			−0.321154	−	0.947027i	$-0.604071\pi$
$431$	−2.47706e6			−0.642309			−0.321154	+	0.947027i	$0.604071\pi$
$432$	−2.44812e6	−	955188.i	−0.631138	−	0.246252i
$433$	3.94915e6			1.01224			0.506120	−	0.862463i	$-0.331079\pi$
$433$	3.94915e6			1.01224			0.506120	+	0.862463i	$0.331079\pi$
$434$	734259.	+	7.07939e6i	0.187122	+	1.80414i
$435$	−322277.	+	322277.i	−0.0816594	+	0.0816594i
$436$	−2.44442e6	+	3.74156e6i	−0.615827	+	0.942621i
$437$	−813141.	−	813141.i	−0.203686	−	0.203686i
$438$	−6.70499e6	−	5.44483e6i	−1.66999	−	1.35612i
$439$		−	2.57617e6i		−	0.637990i	−0.947756	−	0.318995i	$-0.896655\pi$
$439$		−	2.57617e6i		−	0.637990i	0.947756	−	0.318995i	$-0.103345\pi$
$440$	852960.	+	2.66236e6i	0.210038	+	0.655595i
$441$			2.04055e6i			0.499633i
$442$	−1.25698e6	+	1.54790e6i	−0.306036	+	0.376865i
$443$	−1.36521e6	−	1.36521e6i	−0.330514	−	0.330514i	0.522268	−	0.852782i	$-0.325086\pi$
$443$	−1.36521e6	−	1.36521e6i	−0.330514	−	0.330514i	−0.852782	+	0.522268i	$0.825086\pi$
$444$	−2.46531e6	+	516954.i	−0.593491	+	0.124450i
$445$	358090.	−	358090.i	0.0857219	−	0.0857219i
$446$	6.49813e6	−	673972.i	1.54686	−	0.160437i
$447$	5.93325e6			1.40451
$448$	3.62001e6	+	5.06973e6i	0.852148	+	1.19341i
$449$	−3.34712e6			−0.783531			−0.391765	−	0.920065i	$-0.628136\pi$
$449$	−3.34712e6			−0.783531			−0.391765	+	0.920065i	$0.628136\pi$
$450$	−371148.	+	38494.6i	−0.0864003	+	0.00896126i
$451$	6.42301e6	−	6.42301e6i	1.48695	−	1.48695i
$452$	−2.14330e6	+	449431.i	−0.493442	+	0.103471i
$453$	−38131.8	−	38131.8i	−0.00873056	−	0.00873056i
$454$	−747575.	+	920593.i	−0.170222	+	0.209618i
$455$			3.09601e6i			0.701090i
$456$	−463698.	−	1.44735e6i	−0.104430	−	0.325958i
$457$			7.96562e6i			1.78414i	0.451898	+	0.892070i	$0.350747\pi$
$457$			7.96562e6i			1.78414i	−0.451898	+	0.892070i	$0.649253\pi$
$458$	−363019.	−	294792.i	−0.0808659	−	0.0656678i
$459$	981921.	+	981921.i	0.217543	+	0.217543i
$460$	−1.11884e6	+	1.71256e6i	−0.246532	+	0.377356i
$461$	−2.11325e6	+	2.11325e6i	−0.463126	+	0.463126i	−0.899679	−	0.436553i	$-0.856199\pi$
$461$	−2.11325e6	+	2.11325e6i	−0.463126	+	0.463126i	0.436553	+	0.899679i	$0.356199\pi$
$462$	1.27954e6	+	1.23367e7i	0.278900	+	2.68902i
$463$	−1.33400e6			−0.289204			−0.144602	−	0.989490i	$-0.546190\pi$
$463$	−1.33400e6			−0.289204			−0.144602	+	0.989490i	$0.546190\pi$
$464$	−363466.	+	931554.i	−0.0783734	+	0.200869i
$465$	−3.08892e6			−0.662483
$466$	319117.	+	3.07678e6i	0.0680745	+	0.656343i
$467$	1.89907e6	−	1.89907e6i	0.402948	−	0.402948i	−0.476323	−	0.879270i	$-0.658031\pi$
$467$	1.89907e6	−	1.89907e6i	0.402948	−	0.402948i	0.879270	+	0.476323i	$0.158031\pi$
$468$	1.84179e6	+	1.20327e6i	0.388709	+	0.253949i
$469$	−9.27535e6	−	9.27535e6i	−1.94715	−	1.94715i
$470$	1.97100e6	+	1.60056e6i	0.411568	+	0.334217i
$471$		−	8.13167e6i		−	1.68899i
$472$	3.32886e6	+	1.71343e6i	0.687766	+	0.354006i
$473$			684206.i			0.140616i
$474$	1.84337e6	−	2.26999e6i	0.376848	−	0.464065i
$475$	198749.	+	198749.i	0.0404176	+	0.0404176i
$476$	−675581.	−	3.22178e6i	−0.136666	−	0.651747i
$477$	622729.	−	622729.i	0.125315	−	0.125315i
$478$	6.80314e6	−	705607.i	1.36188	−	0.141251i
$479$	6.56083e6			1.30653			0.653266	−	0.757129i	$-0.273399\pi$
$479$	6.56083e6			1.30653			0.653266	+	0.757129i	$0.273399\pi$
$480$	−2.35059e6	+	1.33571e6i	−0.465666	+	0.264611i
$481$	−2.74662e6			−0.541297
$482$	−60396.7	+	6264.22i	−0.0118412	+	0.00122814i
$483$	−6.41733e6	+	6.41733e6i	−1.25166	+	1.25166i
$484$	1.44858e6	+	6.90817e6i	0.281080	+	1.34045i
$485$	1.35881e6	+	1.35881e6i	0.262303	+	0.262303i
$486$	2.67320e6	−	3.29189e6i	0.513383	−	0.632200i
$487$			3.54526e6i			0.677369i	0.940900	+	0.338685i	$0.109982\pi$
$487$			3.54526e6i			0.677369i	−0.940900	+	0.338685i	$0.890018\pi$
$488$	4.05798e6	−	7.88389e6i	0.771367	−	1.49862i
$489$			1.57699e6i			0.298234i
$490$	−2.12259e6	−	1.72367e6i	−0.399371	−	0.324312i
$491$	3.02097e6	+	3.02097e6i	0.565514	+	0.565514i	0.930868	−	0.365355i	$-0.119052\pi$
$491$	3.02097e6	+	3.02097e6i	0.565514	+	0.565514i	−0.365355	+	0.930868i	$0.619052\pi$
$492$	7.35404e6	+	4.80450e6i	1.36966	+	0.894819i
$493$	373638.	−	373638.i	0.0692363	−	0.0692363i
$494$	−170964.	−	1.64835e6i	−0.0315201	−	0.303902i
$495$	−1.62995e6			−0.298993
$496$	−6.20618e6	+	2.72247e6i	−1.13271	+	0.496889i
$497$	−3.60555e6			−0.654758
$498$	−620511.	−	5.98268e6i	−0.112118	−	1.08099i
$499$	−714396.	+	714396.i	−0.128436	+	0.128436i	−0.768403	−	0.639966i	$-0.778948\pi$
$499$	−714396.	+	714396.i	−0.128436	+	0.128436i	0.639966	+	0.768403i	$0.278948\pi$
$500$	273469.	−	418587.i	0.0489196	−	0.0748791i
$501$	−8.32207e6	−	8.32207e6i	−1.48128	−	1.48128i
$502$	−1.80382e6	−	1.46480e6i	−0.319473	−	0.259430i
$503$			5.36521e6i			0.945511i	0.881194	+	0.472756i	$0.156741\pi$
$503$			5.36521e6i			0.945511i	−0.881194	+	0.472756i	$0.843259\pi$
$504$	−3.45880e6	+	1.10812e6i	−0.606526	+	0.194317i
$505$			410670.i			0.0716580i
$506$	−5.63302e6	+	6.93673e6i	−0.978059	+	1.20442i
$507$	700337.	+	700337.i	0.121001	+	0.121001i
$508$	5.82691e6	−	1.22185e6i	1.00180	−	0.210068i
$509$	660473.	−	660473.i	0.112995	−	0.112995i	−0.648348	−	0.761344i	$-0.724540\pi$
$509$	660473.	−	660473.i	0.112995	−	0.112995i	0.761344	+	0.648348i	$0.224540\pi$
$510$	1.42104e6	−	147387.i	0.241924	−	0.0250919i
$511$	1.55482e7			2.63407
$512$	−3.54549e6	+	4.75540e6i	−0.597726	+	0.801701i
$513$	−1.15410e6			−0.193620
$514$	2.00067e6	−	207506.i	0.334017	−	0.0346435i
$515$	−3.72628e6	+	3.72628e6i	−0.619096	+	0.619096i
$516$	−647589.	+	135794.i	−0.107072	+	0.0224521i
$517$	7.84252e6	+	7.84252e6i	1.29041	+	1.29041i
$518$	2.85840e6	−	3.51995e6i	0.468057	−	0.576385i
$519$		−	1.50009e6i		−	0.244455i
$520$	−2.80742e6	+	899432.i	−0.455301	+	0.145868i
$521$		−	971519.i		−	0.156804i	−0.996922	−	0.0784020i	$-0.975018\pi$
$521$		−	971519.i		−	0.156804i	0.996922	−	0.0784020i	$-0.0249818\pi$
$522$	−452572.	−	367515.i	−0.0726962	−	0.0590335i
$523$	−2.56867e6	−	2.56867e6i	−0.410632	−	0.410632i	0.471326	−	0.881959i	$-0.343775\pi$
$523$	−2.56867e6	−	2.56867e6i	−0.410632	−	0.410632i	−0.881959	+	0.471326i	$0.843775\pi$
$524$	6.55700e6	−	1.00365e7i	1.04322	−	1.59682i
$525$	1.56853e6	−	1.56853e6i	0.248368	−	0.248368i
$526$	−929024.	−	8.95722e6i	−0.146407	−	1.41159i
$527$	3.58120e6			0.561697
$528$	−1.08150e7	+	4.74425e6i	−1.68828	+	0.740599i
$529$	−102208.			−0.0158798
$530$	121743.	+	1.17379e6i	0.0188258	+	0.181510i
$531$	−1.54349e6	+	1.54349e6i	−0.237558	+	0.237558i
$532$	2.29038e6	+	1.49634e6i	0.350856	+	0.229219i
$533$	6.77296e6	+	6.77296e6i	1.03267	+	1.03267i
$534$	1.66069e6	+	1.34857e6i	0.252020	+	0.204654i
$535$		−	4.90950e6i		−	0.741571i
$536$	5.71615e6	−	1.11054e7i	0.859392	−	1.66963i
$537$		−	131399.i		−	0.0196633i
$538$	7.17212e6	−	8.83203e6i	1.06830	−	1.31554i
$539$	−8.44572e6	−	8.44572e6i	−1.25217	−	1.25217i
$540$	421338.	+	2.00932e6i	0.0621793	+	0.296528i
$541$	−2.32096e6	+	2.32096e6i	−0.340937	+	0.340937i	−0.856719	−	0.515783i	$-0.827501\pi$
$541$	−2.32096e6	+	2.32096e6i	−0.340937	+	0.340937i	0.515783	+	0.856719i	$0.327501\pi$
$542$	−6.70940e6	+	695885.i	−0.981038	+	0.101751i
$543$	−5.21785e6			−0.759437
$544$	2.72520e6	−	1.54858e6i	0.394822	−	0.224355i
$545$	3.49163e6			0.503543
$546$	−1.30089e7	+	1.34925e6i	−1.86749	+	0.193692i
$547$	4.92582e6	−	4.92582e6i	0.703898	−	0.703898i	−0.261347	−	0.965245i	$-0.584167\pi$
$547$	4.92582e6	−	4.92582e6i	0.703898	−	0.703898i	0.965245	+	0.261347i	$0.0841666\pi$
$548$	−1.23520e6	−	5.89056e6i	−0.175706	−	0.837925i
$549$	3.65552e6	+	3.65552e6i	0.517629	+	0.517629i
$550$	1.37683e6	−	1.69548e6i	0.194077	−	0.238994i
$551$			439156.i			0.0616225i
$552$	−7.68347e6	−	3.95483e6i	−1.07327	−	0.552433i
$553$			5.26389e6i			0.731972i
$554$	−3.30899e6	−	2.68709e6i	−0.458059	−	0.371970i
$555$	1.39152e6	+	1.39152e6i	0.191760	+	0.191760i
$556$	9.91161e6	+	6.47539e6i	1.35974	+	0.888340i
$557$	−5.57524e6	+	5.57524e6i	−0.761422	+	0.761422i	−0.976579	−	0.215157i	$-0.930974\pi$
$557$	−5.57524e6	+	5.57524e6i	−0.761422	+	0.761422i	0.215157	+	0.976579i	$0.430974\pi$
$558$	−407626.	−	3.93014e6i	−0.0554212	−	0.534346i
$559$	−721484.			−0.0976557
$560$	1.76900e6	−	4.53391e6i	0.238373	−	0.610946i
$561$	6.24069e6			0.837193
$562$	−67303.3	−	648908.i	−0.00898868	−	0.0866647i
$563$	−8.90526e6	+	8.90526e6i	−1.18406	+	1.18406i	−0.205383	+	0.978682i	$0.565844\pi$
$563$	−8.90526e6	+	8.90526e6i	−1.18406	+	1.18406i	−0.978682	+	0.205383i	$0.934156\pi$
$564$	−5.86631e6	+	8.97931e6i	−0.776546	+	1.18863i
$565$	1.20977e6	+	1.20977e6i	0.159434	+	0.159434i
$566$	−1.04959e6	−	852327.i	−0.137714	−	0.111832i
$567$			1.39838e7i			1.82670i
$568$	−1.04746e6	−	3.26947e6i	−0.136228	−	0.425213i
$569$		−	9.17182e6i		−	1.18761i	−0.804608	−	0.593806i	$-0.797625\pi$
$569$		−	9.17182e6i		−	1.18761i	0.804608	−	0.593806i	$-0.202375\pi$
$570$	−748492.	+	921723.i	−0.0964940	+	0.118827i
$571$	−8.05400e6	−	8.05400e6i	−1.03376	−	1.03376i	−0.999410	−	0.0343541i	$-0.989063\pi$
$571$	−8.05400e6	−	8.05400e6i	−1.03376	−	1.03376i	−0.0343541	−	0.999410i	$-0.510937\pi$
$572$	−1.26033e7	+	2.64280e6i	−1.61062	+	0.337734i
$573$	8.84068e6	−	8.84068e6i	1.12486	−	1.12486i
$574$	−1.57286e7	+	1.63133e6i	−1.99255	+	0.206663i
$575$	1.59816e6			0.201582
$576$	−2.00966e6	−	2.81447e6i	−0.252386	−	0.353460i
$577$	6.38833e6			0.798818			0.399409	−	0.916773i	$-0.369215\pi$
$577$	6.38833e6			0.798818			0.399409	+	0.916773i	$0.369215\pi$
$578$	6.34156e6	−	657733.i	0.789545	−	0.0818899i
$579$	3.87419e6	−	3.87419e6i	0.480269	−	0.480269i
$580$	764582.	−	160326.i	0.0943744	−	0.0197895i
$581$	7.65608e6	+	7.65608e6i	0.940949	+	0.940949i
$582$	−5.11730e6	+	6.30164e6i	−0.626229	+	0.771163i
$583$			5.15488e6i			0.628126i
$584$	4.51697e6	+	1.40989e7i	0.548043	+	1.71062i
$585$		−	1.71876e6i		−	0.207646i
$586$	1.05670e6	+	858101.i	0.127118	+	0.103227i
$587$	3.14367e6	+	3.14367e6i	0.376566	+	0.376566i	0.869862	−	0.493296i	$-0.164208\pi$
$587$	3.14367e6	+	3.14367e6i	0.376566	+	0.376566i	−0.493296	+	0.869862i	$0.664208\pi$
$588$	6.31751e6	−	9.66994e6i	0.753533	−	1.15340i
$589$	−2.10458e6	+	2.10458e6i	−0.249964	+	0.249964i
$590$	−301752.	−	2.90935e6i	−0.0356878	−	0.344086i
$591$	1.27629e7			1.50307
$592$	4.02225e6	+	1.56937e6i	0.471699	+	0.184043i
$593$	−7.90117e6			−0.922688			−0.461344	−	0.887221i	$-0.652633\pi$
$593$	−7.90117e6			−0.922688			−0.461344	+	0.887221i	$0.652633\pi$
$594$	925184.	+	8.92020e6i	0.107588	+	1.03731i
$595$	−1.81851e6	+	1.81851e6i	−0.210583	+	0.210583i
$596$	−8.51397e6	−	5.56230e6i	−0.981785	−	0.641414i
$597$	−8.14972e6	−	8.14972e6i	−0.935852	−	0.935852i
$598$	−7.31467e6	−	5.93993e6i	−0.836453	−	0.679248i
$599$			7.49192e6i			0.853152i	0.904452	+	0.426576i	$0.140280\pi$
$599$			7.49192e6i			0.853152i	−0.904452	+	0.426576i	$0.859720\pi$
$600$	1.87801e6	+	966644.i	0.212970	+	0.109620i
$601$		−	8.77293e6i		−	0.990737i	−0.868683	−	0.495369i	$-0.835033\pi$
$601$		−	8.77293e6i		−	0.990737i	0.868683	−	0.495369i	$-0.164967\pi$
$602$	750848.	−	924624.i	0.0844424	−	0.103986i
$603$	5.14923e6	+	5.14923e6i	0.576699	+	0.576699i
$604$	18969.8	+	90465.4i	0.00211578	+	0.0100900i
$605$	3.89926e6	−	3.89926e6i	0.433105	−	0.433105i
$606$	−1.72556e6	+	178972.i	−0.190875	+	0.0197971i
$607$	−752225.			−0.0828660			−0.0414330	−	0.999141i	$-0.513192\pi$
$607$	−752225.			−0.0828660			−0.0414330	+	0.999141i	$0.513192\pi$
$608$	−691473.	+	2.51160e6i	−0.0758606	+	0.275544i
$609$	3.46583e6			0.378673
$610$	−6.89035e6	+	714652.i	−0.749750	+	0.0777625i
$611$	−8.26981e6	+	8.26981e6i	−0.896174	+	0.896174i
$612$	375050.	+	1.78858e6i	0.0404772	+	0.193032i
$613$	3.13608e6	+	3.13608e6i	0.337082	+	0.337082i	0.855268	−	0.518186i	$-0.173392\pi$
$613$	3.13608e6	+	3.13608e6i	0.337082	+	0.337082i	−0.518186	+	0.855268i	$0.673392\pi$
$614$	3.92836e6	−	4.83754e6i	0.420523	−	0.517849i
$615$		−	6.86278e6i		−	0.731665i
$616$	9.72933e6	−	1.89022e7i	1.03307	−	2.00706i
$617$			2.22134e6i			0.234911i	0.993078	+	0.117455i	$0.0374737\pi$
$617$			2.22134e6i			0.234911i	−0.993078	+	0.117455i	$0.962526\pi$
$618$	−1.72811e7	−	1.40332e7i	−1.82012	−	1.47804i
$619$	−1.03308e7	−	1.03308e7i	−1.08370	−	1.08370i	−0.996162	−	0.0875338i	$-0.972101\pi$
$619$	−1.03308e7	−	1.03308e7i	−1.08370	−	1.08370i	−0.0875338	−	0.996162i	$-0.527899\pi$
$620$	4.43248e6	+	2.89580e6i	0.463092	+	0.302545i
$621$	−4.64012e6	+	4.64012e6i	−0.482837	+	0.482837i
$622$	−653697.	−	6.30264e6i	−0.0677486	−	0.653201i
$623$	−3.85097e6			−0.397511
$624$	−5.00274e6	−	1.14043e7i	−0.514335	−	1.17248i
$625$	−390625.			−0.0400000
$626$	1.97790e6	+	1.90700e7i	0.201729	+	1.94498i
$627$	−3.66750e6	+	3.66750e6i	−0.372564	+	0.372564i
$628$	−7.62327e6	+	1.16686e7i	−0.771334	+	1.18065i
$629$	−1.61329e6	−	1.61329e6i	−0.162587	−	0.162587i
$630$	2.20269e6	+	1.78871e6i	0.221106	+	0.179551i
$631$		−	2.50673e6i		−	0.250631i	−0.992117	−	0.125315i	$-0.960006\pi$
$631$		−	2.50673e6i		−	0.250631i	0.992117	−	0.125315i	$-0.0399942\pi$
$632$	−4.77323e6	+	1.52923e6i	−0.475356	+	0.152293i
$633$		−	1.21623e7i		−	1.20644i
$634$	6.59620e6	−	8.12283e6i	0.651735	−	0.802572i
$635$	−3.28895e6	−	3.28895e6i	−0.323685	−	0.323685i
$636$	−4.87900e6	+	1.02308e6i	−0.478286	+	0.100293i
$637$	8.90587e6	−	8.90587e6i	0.869617	−	0.869617i
$638$	3.39429e6	−	352049.i	0.330139	−	0.0342414i
$639$	2.00163e6			0.193924
$640$	4.62520e6	+	286944.i	0.446355	+	0.0276915i
$641$	−473959.			−0.0455612			−0.0227806	−	0.999740i	$-0.507252\pi$
$641$	−473959.			−0.0455612			−0.0227806	+	0.999740i	$0.507252\pi$
$642$	2.06288e7	−	2.13958e6i	1.97532	−	0.204876i
$643$	−9.27956e6	+	9.27956e6i	−0.885115	+	0.885115i	−0.994049	−	0.108934i	$-0.965256\pi$
$643$	−9.27956e6	+	9.27956e6i	−0.885115	+	0.885115i	0.108934	+	0.994049i	$0.465256\pi$
$644$	1.52247e7	−	3.19250e6i	1.44655	−	0.303330i
$645$	365526.	+	365526.i	0.0345955	+	0.0345955i
$646$	867779.	−	1.06862e6i	0.0818140	−	0.100749i
$647$			1.14608e7i			1.07635i	0.842834	+	0.538174i	$0.180886\pi$
$647$			1.14608e7i			1.07635i	−0.842834	+	0.538174i	$0.819114\pi$
$648$	−1.26803e7	+	4.06247e6i	−1.18629	+	0.380061i
$649$		−	1.27769e7i		−	1.19073i
$650$	1.78786e6	+	1.45185e6i	0.165978	+	0.134784i
$651$	1.66094e7	+	1.66094e7i	1.53604	+	1.53604i
$652$	1.47839e6	−	2.26292e6i	0.136198	−	0.208473i
$653$	7.79263e6	−	7.79263e6i	0.715157	−	0.715157i	−0.252453	−	0.967609i	$-0.581237\pi$
$653$	7.79263e6	−	7.79263e6i	0.715157	−	0.715157i	0.967609	+	0.252453i	$0.0812372\pi$
$654$	1.52166e6	+	1.46712e7i	0.139115	+	1.34128i
$655$	−9.36608e6			−0.853011
$656$	−6.04863e6	−	1.37885e7i	−0.548779	−	1.25100i
$657$	−8.63162e6			−0.780152
$658$	−1.99186e6	−	1.92046e7i	−0.179347	−	1.72918i
$659$	1.08176e7	−	1.08176e7i	0.970327	−	0.970327i	−0.0292456	−	0.999572i	$-0.509310\pi$
$659$	1.08176e7	−	1.08176e7i	0.970327	−	0.970327i	0.999572	+	0.0292456i	$0.00931048\pi$
$660$	7.72415e6	+	5.04630e6i	0.690225	+	0.450934i
$661$	−772828.	−	772828.i	−0.0687985	−	0.0687985i	0.671870	−	0.740669i	$-0.265491\pi$
$661$	−772828.	−	772828.i	−0.0687985	−	0.0687985i	−0.740669	+	0.671870i	$0.765491\pi$
$662$	−1.54291e7	−	1.25293e7i	−1.36835	−	1.11118i
$663$			6.58071e6i			0.581419i
$664$	−4.71823e6	+	9.16662e6i	−0.415297	+	0.806843i
$665$		−	2.13739e6i		−	0.187426i
$666$	−1.58685e6	+	1.95411e6i	−0.138628	+	0.170712i
$667$	1.76565e6	+	1.76565e6i	0.153670	+	0.153670i
$668$	4.14006e6	+	1.97436e7i	0.358976	+	1.71193i
$669$	1.52457e7	−	1.52457e7i	1.31699	−	1.31699i
$670$	−9.70586e6	+	1.00667e6i	−0.835309	+	0.0866364i
$671$	−3.02600e7			−2.59455
$672$	1.98216e7	+	5.45713e6i	1.69323	+	0.466166i
$673$	2.02477e7			1.72321			0.861603	−	0.507583i	$-0.169461\pi$
$673$	2.02477e7			1.72321			0.861603	+	0.507583i	$0.169461\pi$
$674$	−1.14986e7	+	1.19261e6i	−0.974976	+	0.101122i
$675$	1.13415e6	−	1.13415e6i	0.0958097	−	0.0958097i
$676$	−348404.	−	1.66151e6i	−0.0293235	−	0.139841i
$677$	−6.86021e6	−	6.86021e6i	−0.575262	−	0.575262i	0.358332	−	0.933594i	$-0.383346\pi$
$677$	−6.86021e6	−	6.86021e6i	−0.575262	−	0.575262i	−0.933594	+	0.358332i	$0.883346\pi$
$678$	−4.55600e6	+	5.61044e6i	−0.380636	+	0.468730i
$679$		−	1.46129e7i		−	1.21636i
$680$	−2.17730e6	−	1.12070e6i	−0.180570	−	0.0929429i
$681$			3.91381e6i			0.323394i
$682$	1.79537e7	+	1.45795e7i	1.47807	+	1.20027i
$683$	9.81746e6	+	9.81746e6i	0.805281	+	0.805281i	0.983915	−	0.178635i	$-0.0571681\pi$
$683$	9.81746e6	+	9.81746e6i	0.805281	+	0.805281i	−0.178635	+	0.983915i	$0.557168\pi$
$684$	−1.27151e6	−	830697.i	−0.103915	−	0.0678895i
$685$	−3.32488e6	+	3.32488e6i	−0.270738	+	0.270738i
$686$	280411.	+	2.70359e6i	0.0227501	+	0.219346i
$687$	−1.54334e6			−0.124758
$688$	1.05657e6	+	412243.i	0.0850994	+	0.0332033i
$689$	−5.43573e6			−0.436225
$690$	696485.	+	6.71519e6i	0.0556915	+	0.536952i
$691$	−6.64037e6	+	6.64037e6i	−0.529051	+	0.529051i	−0.920289	−	0.391238i	$-0.872047\pi$
$691$	−6.64037e6	+	6.64037e6i	−0.529051	+	0.529051i	0.391238	+	0.920289i	$0.372047\pi$
$692$	−1.40630e6	+	2.15256e6i	−0.111638	+	0.170880i
$693$	8.76440e6	+	8.76440e6i	0.693249	+	0.693249i
$694$	8.86364e6	+	7.19778e6i	0.698575	+	0.567283i
$695$		−	9.24951e6i		−	0.726368i
$696$	1.00687e6	+	3.14277e6i	0.0787863	+	0.245917i
$697$			7.95650e6i			0.620355i
$698$	−8.93618e6	+	1.10044e7i	−0.694246	+	0.854922i
$699$	7.21864e6	+	7.21864e6i	0.558808	+	0.558808i
$700$	−3.72125e6	+	780314.i	−0.287041	+	0.0601900i
$701$	−1.66016e7	+	1.66016e7i	−1.27601	+	1.27601i	−0.333134	+	0.942879i	$0.608106\pi$
$701$	−1.66016e7	+	1.66016e7i	−1.27601	+	1.27601i	−0.942879	+	0.333134i	$0.891894\pi$
$702$	−9.40621e6	+	975592.i	−0.720397	+	0.0747180i
$703$	1.89618e6			0.144707
$704$	1.99668e7	+	3.33107e6i	1.51837	+	0.253310i
$705$	8.37949e6			0.634957
$706$	−4.70481e6	+	487973.i	−0.355247	+	0.0368454i
$707$	2.20821e6	−	2.20821e6i	0.166147	−	0.166147i
$708$	1.20931e7	−	2.53582e6i	0.906680	−	0.190123i
$709$	1.53831e7	+	1.53831e7i	1.14929	+	1.14929i	0.986693	+	0.162597i	$0.0519869\pi$
$709$	1.53831e7	+	1.53831e7i	1.14929	+	1.14929i	0.162597	+	0.986693i	$0.448013\pi$
$710$	−1.69079e6	+	2.08211e6i	−0.125876	+	0.155009i
$711$		−	2.92226e6i		−	0.216793i
$712$	−1.11876e6	−	3.49200e6i	−0.0827058	−	0.258151i
$713$			1.69232e7i			1.24669i
$714$	−8.43357e6	−	6.84854e6i	−0.619107	−	0.502750i
$715$	7.11383e6	+	7.11383e6i	0.520401	+	0.520401i
$716$	−123184.	+	188552.i	−0.00897989	+	0.0137451i
$717$	1.59613e7	−	1.59613e7i	1.15950	−	1.15950i
$718$	468252.	+	4.51467e6i	0.0338976	+	0.326825i
$719$	1.07413e7			0.774879			0.387439	−	0.921895i	$-0.373360\pi$
$719$	1.07413e7			0.774879			0.387439	+	0.921895i	$0.373360\pi$
$720$	−982065.	+	2.51701e6i	−0.0706007	+	0.180948i
$721$	4.00732e7			2.87088
$722$	−1.32699e6	−	1.27942e7i	−0.0947381	−	0.913421i
$723$	−141701.	+	141701.i	−0.0100815	+	0.0100815i
$724$	7.48740e6	+	4.89162e6i	0.530865	+	0.346822i
$725$	−431562.	−	431562.i	−0.0304929	−	0.0304929i
$726$	1.80833e7	+	1.46847e7i	1.27332	+	1.03401i
$727$			222223.i			0.0155939i	0.999970	+	0.00779693i	$0.00248187\pi$
$727$			222223.i			0.0155939i	−0.999970	+	0.00779693i	$0.997518\pi$
$728$	1.99321e7	+	1.02594e7i	1.39388	+	0.717455i
$729$			3.87911e6i			0.270342i
$730$	7.29119e6	−	8.97867e6i	0.506397	−	0.623598i
$731$	−423780.	−	423780.i	−0.0293324	−	0.0293324i
$732$	−6.00568e6	−	2.86406e7i	−0.414271	−	1.97562i
$733$	−1.11978e7	+	1.11978e7i	−0.769791	+	0.769791i	−0.978070	−	0.208279i	$-0.933214\pi$
$733$	−1.11978e7	+	1.11978e7i	−0.769791	+	0.769791i	0.208279	+	0.978070i	$0.433214\pi$
$734$	893676.	−	92690.2i	0.0612266	−	0.00635029i
$735$	−9.02398e6			−0.616141
$736$	7.31790e6	+	1.28781e7i	0.497957	+	0.876310i
$737$	−4.26247e7			−2.89063
$738$	8.73174e6	−	905638.i	0.590147	−	0.0612088i
$739$	−5.74562e6	+	5.74562e6i	−0.387013	+	0.387013i	−0.873621	−	0.486607i	$-0.838234\pi$
$739$	−5.74562e6	+	5.74562e6i	−0.387013	+	0.387013i	0.486607	+	0.873621i	$0.338234\pi$
$740$	−692255.	−	3.30130e6i	−0.0464715	−	0.221618i
$741$	−3.86732e6	−	3.86732e6i	−0.258741	−	0.258741i
$742$	5.65696e6	−	6.96621e6i	0.377202	−	0.464501i
$743$		−	1.03255e7i		−	0.686179i	−0.939303	−	0.343090i	$-0.888527\pi$
$743$		−	1.03255e7i		−	0.686179i	0.939303	−	0.343090i	$-0.111473\pi$
$744$	−1.02359e7	+	1.98865e7i	−0.677947	+	1.31712i
$745$			7.94523e6i			0.524464i
$746$	−4.46705e6	−	3.62750e6i	−0.293883	−	0.238649i
$747$	−4.25029e6	−	4.25029e6i	−0.278687	−	0.278687i
$748$	−8.95514e6	−	5.85052e6i	−0.585219	−	0.382332i
$749$	−2.63989e7	+	2.63989e7i	−1.71942	+	1.71942i
$750$	−170236.	−	1.64134e6i	−0.0110509	−	0.106548i
$751$	−1.14757e7			−0.742468			−0.371234	−	0.928539i	$-0.621065\pi$
$751$	−1.14757e7			−0.742468			−0.371234	+	0.928539i	$0.621065\pi$
$752$	1.68358e7	−	7.38540e6i	1.08565	−	0.476244i
$753$	−7.66875e6			−0.492875
$754$	371230.	+	3.57923e6i	0.0237801	+	0.229277i
$755$	51062.5	−	51062.5i	0.00326013	−	0.00326013i
$756$	8.53875e6	−	1.30699e7i	0.543363	−	0.831702i
$757$	−9.78035e6	−	9.78035e6i	−0.620318	−	0.620318i	0.325294	−	0.945613i	$-0.394537\pi$
$757$	−9.78035e6	−	9.78035e6i	−0.620318	−	0.620318i	−0.945613	+	0.325294i	$0.894537\pi$
$758$	4.55429e6	+	3.69834e6i	0.287904	+	0.233794i
$759$			2.94908e7i			1.85815i
$760$	1.93815e6	−	620940.i	0.121718	−	0.0389956i
$761$			2.22081e6i			0.139011i	0.997582	+	0.0695054i	$0.0221421\pi$
$761$			2.22081e6i			0.139011i	−0.997582	+	0.0695054i	$0.977858\pi$
$762$	1.23862e7	−	1.52529e7i	0.772773	−	0.951624i
$763$	−1.87748e7	−	1.87748e7i	−1.16752	−	1.16752i
$764$	−2.09740e7	+	4.39806e6i	−1.30001	+	0.272601i
$765$	1.00955e6	−	1.00955e6i	0.0623698	−	0.0623698i
$766$	1.99143e7	−	2.06547e6i	1.22629	−	0.127188i
$767$	1.34730e7			0.826944
$768$	809996.	+	1.95593e7i	0.0495541	+	1.19660i
$769$	−1.41145e7			−0.860697			−0.430349	−	0.902663i	$-0.641609\pi$
$769$	−1.41145e7			−0.860697			−0.430349	+	0.902663i	$0.641609\pi$
$770$	−1.65201e7	+	1.71343e6i	−1.00412	+	0.104145i
$771$	4.69392e6	−	4.69392e6i	0.284380	−	0.284380i
$772$	−9.19128e6	+	1.92733e6i	−0.555051	+	0.116389i
$773$	−1.95334e7	−	1.95334e7i	−1.17579	−	1.17579i	−0.980806	−	0.194985i	$-0.937534\pi$
$773$	−1.95334e7	−	1.95334e7i	−1.17579	−	1.17579i	−0.194985	−	0.980806i	$-0.562466\pi$
$774$	−416835.	+	513307.i	−0.0250099	+	0.0307982i
$775$		−	4.13639e6i		−	0.247381i
$776$	1.32508e7	−	4.24524e6i	0.789927	−	0.253074i
$777$		−	1.49647e7i		−	0.889233i
$778$	2.90425e6	+	2.35841e6i	0.172022	+	0.139692i
$779$	−4.67584e6	−	4.67584e6i	−0.276068	−	0.276068i
$780$	−5.32124e6	+	8.14499e6i	−0.313167	+	0.479352i
$781$	−8.28463e6	+	8.28463e6i	−0.486011	+	0.486011i
$782$	−807483.	−	7.78538e6i	−0.0472190	−	0.455264i
$783$	2.50601e6			0.146076
$784$	−1.81307e7	+	7.95344e6i	−1.05348	+	0.462131i
$785$	1.08891e7			0.630695
$786$	−4.08178e6	−	3.93546e7i	−0.235664	−	2.27216i
$787$	1.56745e7	−	1.56745e7i	0.902105	−	0.902105i	−0.0935131	−	0.995618i	$-0.529810\pi$
$787$	1.56745e7	−	1.56745e7i	0.902105	−	0.902105i	0.995618	+	0.0935131i	$0.0298097\pi$
$788$	−1.83142e7	−	1.19649e7i	−1.05068	−	0.686427i
$789$	−2.10152e7	−	2.10152e7i	−1.20182	−	1.20182i
$790$	3.03976e6	+	2.46846e6i	0.173289	+	0.140721i
$791$		−	1.30101e7i		−	0.739330i
$792$	−5.40126e6	+	1.04936e7i	−0.305972	+	0.594446i
$793$		−	3.19087e7i		−	1.80188i
$794$	−6.47028e6	+	7.96776e6i	−0.364226	+	0.448523i
$795$	2.75391e6	+	2.75391e6i	0.154537	+	0.154537i
$796$	4.05433e6	+	1.93347e7i	0.226796	+	1.08157i
$797$	9.69347e6	−	9.69347e6i	0.540547	−	0.540547i	−0.383142	−	0.923689i	$-0.625158\pi$
$797$	9.69347e6	−	9.69347e6i	0.540547	−	0.540547i	0.923689	+	0.383142i	$0.125158\pi$
$798$	8.98091e6	−	931481.i	0.499244	−	0.0517806i
$799$	−9.71492e6			−0.538359
$800$	−1.78865e6	−	3.14769e6i	−0.0988100	−	0.173887i
$801$	2.13787e6			0.117734
$802$	6.54613e6	−	678951.i	0.359376	−	0.0372737i
$803$	3.57258e7	−	3.57258e7i	1.95521	−	1.95521i
$804$	−8.45970e6	−	4.03436e7i	−0.461546	−	2.20107i
$805$	−8.59347e6	−	8.59347e6i	−0.467390	−	0.467390i
$806$	−1.53738e7	+	1.89319e7i	−0.833574	+	1.02650i
$807$		−	3.75485e7i		−	2.02959i
$808$	2.64389e6	+	1.36086e6i	0.142467	+	0.0733306i
$809$		−	3.45363e7i		−	1.85526i	−0.373502	−	0.927629i	$-0.621843\pi$
$809$		−	3.45363e7i		−	1.85526i	0.373502	−	0.927629i	$-0.378157\pi$
$810$	8.07525e6	+	6.55756e6i	0.432457	+	0.351180i
$811$	5.52703e6	+	5.52703e6i	0.295080	+	0.295080i	0.839083	−	0.544003i	$-0.183092\pi$
$811$	5.52703e6	+	5.52703e6i	0.295080	+	0.295080i	−0.544003	+	0.839083i	$0.683092\pi$
$812$	−4.97333e6	−	3.24914e6i	−0.264702	−	0.172933i
$813$	−1.57414e7	+	1.57414e7i	−0.835251	+	0.835251i
$814$	−1.52007e6	−	1.46558e7i	−0.0804086	−	0.775263i
$815$	−2.11175e6			−0.111365
$816$	3.76009e6	−	9.63703e6i	0.197685	−	0.506662i
$817$	498090.			0.0261067
$818$	−1.36279e6	−	1.31394e7i	−0.0712109	−	0.686583i
$819$	−9.24192e6	+	9.24192e6i	−0.481451	+	0.481451i
$820$	−6.43372e6	+	9.84781e6i	−0.334139	+	0.511452i
$821$	−1.00138e7	−	1.00138e7i	−0.518493	−	0.518493i	0.398622	−	0.917115i	$-0.369488\pi$
$821$	−1.00138e7	−	1.00138e7i	−0.518493	−	0.518493i	−0.917115	+	0.398622i	$0.869488\pi$
$822$	−1.54195e7	−	1.25215e7i	−0.795961	−	0.646366i
$823$			8.91190e6i			0.458639i	0.973351	+	0.229319i	$0.0736500\pi$
$823$			8.91190e6i			0.458639i	−0.973351	+	0.229319i	$0.926350\pi$
$824$	1.16418e7	+	3.63378e7i	0.597313	+	1.86441i
$825$		−	7.20817e6i		−	0.368715i
$826$	−1.40213e7	+	1.72664e7i	−0.715055	+	0.880547i
$827$	1.71368e7	+	1.71368e7i	0.871296	+	0.871296i	0.992614	−	0.121317i	$-0.0387119\pi$
$827$	1.71368e7	+	1.71368e7i	0.871296	+	0.871296i	−0.121317	+	0.992614i	$0.538712\pi$
$828$	−8.45204e6	+	1.77232e6i	−0.428436	+	0.0898394i
$829$	−7.26943e6	+	7.26943e6i	−0.367379	+	0.367379i	−0.866520	−	0.499142i	$-0.833649\pi$
$829$	−7.26943e6	+	7.26943e6i	−0.367379	+	0.367379i	0.499142	+	0.866520i	$0.333649\pi$
$830$	8.01143e6	−	830929.i	0.403659	−	0.0418667i
$831$	−1.40678e7			−0.706682
$832$	−3.51256e6	+	2.10546e7i	−0.175920	+	1.05448i
$833$	1.04621e7			0.522405
$834$	3.88648e7	−	4.03097e6i	1.93482	−	0.200676i
$835$	1.11441e7	−	1.11441e7i	0.553132	−	0.553132i
$836$	8.70092e6	−	1.82451e6i	0.430576	−	0.0902880i
$837$	1.20096e7	+	1.20096e7i	0.592538	+	0.592538i
$838$	−2.98390e6	+	3.67450e6i	−0.146783	+	0.180754i
$839$			2.46342e7i			1.20819i	0.796914	+	0.604093i	$0.206464\pi$
$839$			2.46342e7i			1.20819i	−0.796914	+	0.604093i	$0.793536\pi$
$840$	−4.90048e6	−	1.52960e7i	−0.239629	−	0.747960i
$841$			1.95576e7i			0.953509i
$842$	2.87865e6	+	2.33763e6i	0.139929	+	0.113631i
$843$	−1.52245e6	−	1.52245e6i	−0.0737859	−	0.0737859i
$844$	−1.14019e7	+	1.74524e7i	−0.550960	+	0.843331i
$845$	−937824.	+	937824.i	−0.0451835	+	0.0451835i
$846$	1.10579e6	+	1.06615e7i	0.0531185	+	0.512144i
$847$	−4.19334e7			−2.00841
$848$	7.96029e6	+	3.10588e6i	0.380136	+	0.148318i
$849$	−4.46222e6			−0.212462
$850$	197366.	+	1.90291e6i	0.00936970	+	0.0903383i
$851$	7.62369e6	−	7.62369e6i	0.360862	−	0.360862i
$852$	−9.48551e6	−	6.19702e6i	−0.447674	−	0.292472i
$853$	2.29987e7	+	2.29987e7i	1.08226	+	1.08226i	0.996299	+	0.0859603i	$0.0273958\pi$
$853$	2.29987e7	+	2.29987e7i	1.08226	+	1.08226i	0.0859603	+	0.996299i	$0.472604\pi$
$854$	4.08928e7	+	3.32073e7i	1.91868	+	1.55808i
$855$			1.18657e6i			0.0555111i
$856$	−3.16074e7	−	1.62689e7i	−1.47436	−	0.758881i
$857$			1.70677e7i			0.793823i	0.917857	+	0.396912i	$0.129918\pi$
$857$			1.70677e7i			0.793823i	−0.917857	+	0.396912i	$0.870082\pi$
$858$	−2.67908e7	+	3.29913e7i	−1.24242	+	1.52996i
$859$	−1.32645e7	−	1.32645e7i	−0.613351	−	0.613351i	0.330467	−	0.943818i	$-0.392794\pi$
$859$	−1.32645e7	−	1.32645e7i	−0.613351	−	0.613351i	−0.943818	+	0.330467i	$0.892794\pi$
$860$	−181842.	−	867189.i	−0.00838394	−	0.0399823i
$861$	−3.69019e7	+	3.69019e7i	−1.69645	+	1.69645i
$862$	1.39376e7	−	1.44558e6i	0.638881	−	0.0662634i
$863$	1.61706e7			0.739094			0.369547	−	0.929212i	$-0.379513\pi$
$863$	1.61706e7			0.739094			0.369547	+	0.929212i	$0.379513\pi$
$864$	1.43322e7	+	3.94584e6i	0.653175	+	0.179827i
$865$	2.00877e6			0.0912831
$866$	−2.22206e7	+	2.30467e6i	−1.00684	+	0.104427i
$867$	1.48784e7	−	1.48784e7i	0.672215	−	0.672215i
$868$	−8.26287e6	−	3.94049e7i	−0.372247	−	1.77521i
$869$	1.20951e7	+	1.20951e7i	0.543324	+	0.543324i
$870$	1.62527e6	−	2.00142e6i	0.0727994	−	0.0896481i
$871$		−	4.49471e7i		−	2.00750i
$872$	1.15704e7	−	2.24791e7i	0.515297	−	1.00112i
$873$			8.11238e6i			0.360257i
$874$	5.04981e6	+	4.10074e6i	0.223613	+	0.181586i
$875$	2.10043e6	+	2.10043e6i	0.0927444	+	0.0927444i
$876$	4.09043e7	+	2.67234e7i	1.80098	+	1.17660i
$877$	1.26350e7	−	1.26350e7i	0.554722	−	0.554722i	−0.373078	−	0.927800i	$-0.621698\pi$
$877$	1.26350e7	−	1.26350e7i	0.554722	−	0.554722i	0.927800	+	0.373078i	$0.121698\pi$
$878$	1.50342e6	+	1.44953e7i	0.0658179	+	0.634586i
$879$	4.49245e6			0.196115
$880$	−6.35304e6	−	1.44825e7i	−0.276551	−	0.630428i
$881$	7.72392e6			0.335273			0.167636	−	0.985849i	$-0.446387\pi$
$881$	7.72392e6			0.335273			0.167636	+	0.985849i	$0.446387\pi$
$882$	−1.19084e6	−	1.14815e7i	−0.0515443	−	0.496967i
$883$	−2.43397e7	+	2.43397e7i	−1.05054	+	1.05054i	−0.0518872	+	0.998653i	$0.516524\pi$
$883$	−2.43397e7	+	2.43397e7i	−1.05054	+	1.05054i	−0.998653	+	0.0518872i	$0.983476\pi$
$884$	6.16928e6	−	9.44305e6i	0.265524	−	0.406426i
$885$	−6.82584e6	−	6.82584e6i	−0.292953	−	0.292953i
$886$	8.47830e6	+	6.88487e6i	0.362848	+	0.294653i
$887$		−	8.25403e6i		−	0.352255i	−0.984367	−	0.176128i	$-0.943643\pi$
$887$		−	8.25403e6i		−	0.352255i	0.984367	−	0.176128i	$-0.0563571\pi$
$888$	1.35698e7	−	4.34745e6i	0.577485	−	0.185013i
$889$			3.53700e7i			1.50100i
$890$	−1.80588e6	+	2.22383e6i	−0.0764211	+	0.0941080i
$891$	3.21311e7	+	3.21311e7i	1.35591	+	1.35591i
$892$	−3.61695e7	+	7.58443e6i	−1.52205	+	0.319162i
$893$	5.70921e6	−	5.70921e6i	0.239578	−	0.239578i
$894$	−3.33844e7	+	3.46256e6i	−1.39701	+	0.144895i
$895$	175957.			0.00734258
$896$	−2.33272e7	−	2.64131e7i	−0.970719	−	1.09913i
$897$	−3.10975e7			−1.29046
$898$	1.88332e7	−	1.95334e6i	0.779350	−	0.0808325i
$899$	4.56988e6	−	4.56988e6i	0.188584	−	0.188584i
$900$	2.06586e6	−	433193.i	0.0850148	−	0.0178269i
$901$	−3.19280e6	−	3.19280e6i	−0.131027	−	0.131027i
$902$	−3.23918e7	+	3.98885e7i	−1.32562	+	1.63242i
$903$		−	3.93094e6i		−	0.160427i
$904$	1.17973e7	−	3.77960e6i	0.480135	−	0.153824i
$905$		−	6.98724e6i		−	0.283585i
$906$	236809.	+	192302.i	0.00958466	+	0.00778330i
$907$	1.41287e7	+	1.41287e7i	0.570275	+	0.570275i	0.932205	−	0.361930i	$-0.117882\pi$
$907$	1.41287e7	+	1.41287e7i	0.570275	+	0.570275i	−0.361930	+	0.932205i	$0.617882\pi$
$908$	3.66911e6	−	5.61615e6i	0.147688	−	0.226060i
$909$	−1.22589e6	+	1.22589e6i	−0.0492089	+	0.0492089i
$910$	−1.80679e6	−	1.74202e7i	−0.0723276	−	0.697349i
$911$	2.75193e6			0.109861			0.0549303	−	0.998490i	$-0.482506\pi$
$911$	2.75193e6			0.109861			0.0549303	+	0.998490i	$0.482506\pi$
$912$	3.45373e6	+	7.87316e6i	0.137500	+	0.313445i
$913$	3.51834e7			1.39689
$914$	−4.64862e6	−	4.48199e7i	−0.184060	−	1.77462i
$915$	−1.61659e7	+	1.61659e7i	−0.638334	+	0.638334i
$916$	2.21463e6	+	1.44685e6i	0.0872090	+	0.0569749i
$917$	5.03623e7	+	5.03623e7i	1.97780	+	1.97780i
$918$	−6.09798e6	−	4.95191e6i	−0.238825	−	0.193939i
$919$		−	1.39375e7i		−	0.544373i	−0.962244	−	0.272187i	$-0.912253\pi$
$919$		−	1.39375e7i		−	0.544373i	0.962244	−	0.272187i	$-0.0877468\pi$
$920$	5.29592e6	−	1.02890e7i	0.206287	−	0.400776i
$921$		−	2.05663e7i		−	0.798926i
$922$	1.06573e7	−	1.31238e7i	0.412877	−	0.508433i
$923$	−8.73601e6	−	8.73601e6i	−0.337527	−	0.337527i
$924$	−1.43991e7	−	6.86679e7i	−0.554824	−	2.64590i
$925$	−1.86339e6	+	1.86339e6i	−0.0716061	+	0.0716061i
$926$	7.50600e6	−	778506.i	0.287661	−	0.0298356i
$927$	−2.22467e7			−0.850289
$928$	1.50146e6	−	5.45366e6i	0.0572326	−	0.207883i
$929$	3.63709e7			1.38266			0.691330	−	0.722539i	$-0.257025\pi$
$929$	3.63709e7			1.38266			0.691330	+	0.722539i	$0.257025\pi$
$930$	1.73804e7	−	1.80265e6i	0.658948	−	0.0683447i
$931$	−6.14833e6	+	6.14833e6i	−0.232479	+	0.232479i
$932$	−3.59113e6	−	1.71258e7i	−0.135423	−	0.645818i
$933$	−1.47871e7	−	1.47871e7i	−0.556132	−	0.556132i
$934$	−9.57717e6	+	1.17937e7i	−0.359228	+	0.442368i
$935$			8.35693e6i			0.312621i
$936$	−1.10653e7	−	5.69554e6i	−0.412834	−	0.212493i
$937$			3.20456e7i			1.19239i	0.802839	+	0.596197i	$0.203322\pi$
$937$			3.20456e7i			1.19239i	−0.802839	+	0.596197i	$0.796678\pi$
$938$	5.76023e7	+	4.67764e7i	2.13763	+	1.73588i
$939$	4.47414e7	+	4.47414e7i	1.65595	+	1.65595i
$940$	−1.20242e7	−	7.85559e6i	−0.443851	−	0.289974i
$941$	3.10580e7	−	3.10580e7i	1.14340	−	1.14340i	0.155578	−	0.987824i	$-0.450276\pi$
$941$	3.10580e7	−	3.10580e7i	1.14340	−	1.14340i	0.987824	−	0.155578i	$-0.0497242\pi$
$942$	4.74553e6	+	4.57542e7i	0.174244	+	1.67998i
$943$	−3.75989e7			−1.37688
$944$	−1.97304e7	−	7.69822e6i	−0.720618	−	0.281164i
$945$	−1.21968e7			−0.444291
$946$	−399293.	−	3.84980e6i	−0.0145066	−	0.139866i
$947$	1.18742e7	−	1.18742e7i	0.430257	−	0.430257i	−0.458459	−	0.888716i	$-0.651598\pi$
$947$	1.18742e7	−	1.18742e7i	0.430257	−	0.430257i	0.888716	+	0.458459i	$0.151598\pi$
$948$	−9.04728e6	+	1.38483e7i	−0.326962	+	0.500466i
$949$	3.76723e7	+	3.76723e7i	1.35786	+	1.35786i
$950$	−1.23428e6	−	1.00231e6i	−0.0443717	−	0.0360323i
$951$		−	3.45334e7i		−	1.23819i
$952$	5.68146e6	+	1.77337e7i	0.203174	+	0.634171i
$953$		−	6.35853e6i		−	0.226790i	−0.993550	−	0.113395i	$-0.963827\pi$
$953$		−	6.35853e6i		−	0.226790i	0.993550	−	0.113395i	$-0.0361726\pi$
$954$	−3.14047e6	+	3.86731e6i	−0.111718	+	0.137574i
$955$	1.18386e7	+	1.18386e7i	0.420040	+	0.420040i
$956$	−3.78672e7	+	7.94043e6i	−1.34004	+	0.280996i
$957$	7.96359e6	−	7.96359e6i	0.281079	−	0.281079i
$958$	−3.69156e7	+	3.82881e6i	−1.29956	+	0.134788i
$959$	3.57564e7			1.25547
$960$	1.24465e7	−	8.88737e6i	0.435883	−	0.311240i
$961$	1.51717e7			0.529938
$962$	1.54543e7	−	1.60289e6i	0.538409	−	0.0558426i
$963$	1.46554e7	−	1.46554e7i	0.509251	−	0.509251i
$964$	336177.	−	70493.4i	0.0116513	−	0.00244318i
$965$	5.18794e6	+	5.18794e6i	0.179340	+	0.179340i
$966$	3.23632e7	−	3.98533e7i	1.11586	−	1.37411i
$967$			4.24344e7i			1.45933i	0.683807	+	0.729663i	$0.260323\pi$
$967$			4.24344e7i			1.45933i	−0.683807	+	0.729663i	$0.739677\pi$
$968$	−1.21822e7	−	3.80246e7i	−0.417867	−	1.30430i
$969$		−	4.54311e6i		−	0.155433i
$970$	−8.43855e6	−	6.85259e6i	−0.287964	−	0.233843i
$971$	8.42543e6	+	8.42543e6i	0.286777	+	0.286777i	0.835804	−	0.549027i	$-0.185002\pi$
$971$	8.42543e6	+	8.42543e6i	0.286777	+	0.286777i	−0.549027	+	0.835804i	$0.685002\pi$
$972$	−1.31201e7	+	2.00824e7i	−0.445423	+	0.681790i
$973$	−4.97355e7	+	4.97355e7i	−1.68416	+	1.68416i
$974$	−2.06896e6	−	1.99480e7i	−0.0698805	−	0.673755i
$975$	7.60090e6			0.256067
$976$	−1.82320e7	+	4.67282e7i	−0.612647	+	1.57020i
$977$	112748.			0.00377897			0.00188949	−	0.999998i	$-0.499399\pi$
$977$	112748.			0.00377897			0.00188949	+	0.999998i	$0.499399\pi$
$978$	−920310.	−	8.87320e6i	−0.0307671	−	0.296642i
$979$	−8.84853e6	+	8.84853e6i	−0.295063	+	0.295063i
$980$	1.29490e7	+	8.45980e6i	0.430698	+	0.281381i
$981$	1.04229e7	+	1.04229e7i	0.345792	+	0.345792i
$982$	−1.87610e7	−	1.52350e7i	−0.620837	−	0.504155i
$983$			3.41003e7i			1.12557i	0.826602	+	0.562787i	$0.190271\pi$
$983$			3.41003e7i			1.12557i	−0.826602	+	0.562787i	$0.809729\pi$
$984$	−4.41826e7	−	2.27416e7i	−1.45467	−	0.748744i
$985$			1.70908e7i			0.561270i
$986$	−1.88429e6	+	2.32039e6i	−0.0617241	+	0.0760096i
$987$	−4.50573e7	−	4.50573e7i	−1.47222	−	1.47222i
$988$	1.92391e6	+	9.17498e6i	0.0627037	+	0.299029i
$989$	2.00260e6	−	2.00260e6i	0.0651033	−	0.0651033i
$990$	9.17119e6	−	951217.i	0.297398	−	0.0308455i
$991$	1.36375e7			0.441113			0.220556	−	0.975374i	$-0.429213\pi$
$991$	1.36375e7			0.441113			0.220556	+	0.975374i	$0.429213\pi$
$992$	3.33313e7	−	1.89403e7i	1.07541	−	0.611094i
$993$	−6.55954e7			−2.11106
$994$	2.02873e7	−	2.10415e6i	0.651265	−	0.0675478i
$995$	1.09133e7	−	1.09133e7i	0.349461	−	0.349461i
$996$	6.98283e6	+	3.33005e7i	0.223040	+	1.06366i
$997$	−1.24966e7	−	1.24966e7i	−0.398158	−	0.398158i	0.479425	−	0.877583i	$-0.340845\pi$
$997$	−1.24966e7	−	1.24966e7i	−0.398158	−	0.398158i	−0.877583	+	0.479425i	$0.840845\pi$
$998$	3.60276e6	−	4.43659e6i	0.114501	−	0.141001i
$999$		−	1.08204e7i		−	0.343028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.3	✓	80
4.3	odd	2		320.6.l.a.241.32		80
16.3	odd	4		320.6.l.a.81.32		80
16.13	even	4	inner	80.6.l.a.61.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.3	✓	80	1.1	even	1	trivial
80.6.l.a.61.3	yes	80	16.13	even	4	inner
320.6.l.a.81.32		80	16.3	odd	4
320.6.l.a.241.32		80	4.3	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-5.62667 + 0.583586i) q^{2} +(-13.2011 + 13.2011i) q^{3} +(31.3189 - 6.56730i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(66.5744 - 81.9824i) q^{6} +190.109i q^{7} +(-172.388 + 55.2293i) q^{8} -105.540i q^{9} +O(q^{10})\)	\(q+(-5.62667 + 0.583586i) q^{2} +(-13.2011 + 13.2011i) q^{3} +(31.3189 - 6.56730i) q^{4} +(-17.6777 - 17.6777i) q^{5} +(66.5744 - 81.9824i) q^{6} +190.109i q^{7} +(-172.388 + 55.2293i) q^{8} -105.540i q^{9} +(109.783 + 89.1500i) q^{10} +(436.822 + 436.822i) q^{11} +(-326.748 + 500.140i) q^{12} +(-460.621 + 460.621i) q^{13} +(-110.945 - 1069.68i) q^{14} +466.730 q^{15} +(937.741 - 411.360i) q^{16} -541.113 q^{17} +(61.5914 + 593.836i) q^{18} +(317.998 - 317.998i) q^{19} +(-669.739 - 437.550i) q^{20} +(-2509.65 - 2509.65i) q^{21} +(-2712.78 - 2202.93i) q^{22} -2557.06i q^{23} +(1546.63 - 3004.81i) q^{24} +625.000i q^{25} +(2322.95 - 2860.58i) q^{26} +(-1814.63 - 1814.63i) q^{27} +(1248.50 + 5954.00i) q^{28} +(-690.500 + 690.500i) q^{29} +(-2626.14 + 272.377i) q^{30} -6618.22 q^{31} +(-5036.30 + 2861.84i) q^{32} -11533.1 q^{33} +(3044.66 - 315.786i) q^{34} +(3360.69 - 3360.69i) q^{35} +(-693.109 - 3305.38i) q^{36} +(2981.43 + 2981.43i) q^{37} +(-1603.69 + 1974.85i) q^{38} -12161.4i q^{39} +(4023.75 + 2071.10i) q^{40} -14704.0i q^{41} +(15585.6 + 12656.4i) q^{42} +(783.164 + 783.164i) q^{43} +(16549.5 + 10812.0i) q^{44} +(-1865.69 + 1865.69i) q^{45} +(1492.26 + 14387.7i) q^{46} +17953.6 q^{47} +(-6948.82 + 17809.7i) q^{48} -19334.5 q^{49} +(-364.741 - 3516.67i) q^{50} +(7143.30 - 7143.30i) q^{51} +(-11401.1 + 17451.2i) q^{52} +(5900.43 + 5900.43i) q^{53} +(11269.3 + 9151.35i) q^{54} -15444.0i q^{55} +(-10499.6 - 32772.6i) q^{56} +8395.88i q^{57} +(3482.25 - 4288.18i) q^{58} +(-14624.8 - 14624.8i) q^{59} +(14617.5 - 3065.16i) q^{60} +(-34636.5 + 34636.5i) q^{61} +(37238.5 - 3862.30i) q^{62} +20064.0 q^{63} +(26667.5 - 19041.8i) q^{64} +16285.4 q^{65} +(64892.8 - 6730.55i) q^{66} +(-48789.6 + 48789.6i) q^{67} +(-16947.0 + 3553.65i) q^{68} +(33756.1 + 33756.1i) q^{69} +(-16948.2 + 20870.7i) q^{70} +18965.7i q^{71} +(5828.87 + 18193.8i) q^{72} -81785.7i q^{73} +(-18515.4 - 15035.6i) q^{74} +(-8250.70 - 8250.70i) q^{75} +(7870.96 - 12047.7i) q^{76} +(-83043.8 + 83043.8i) q^{77} +(7097.25 + 68428.5i) q^{78} +27688.8 q^{79} +(-23849.0 - 9305.19i) q^{80} +73556.5 q^{81} +(8581.03 + 82734.3i) q^{82} +(40272.0 - 40272.0i) q^{83} +(-95081.1 - 62117.9i) q^{84} +(9565.61 + 9565.61i) q^{85} +(-4863.65 - 3949.56i) q^{86} -18230.7i q^{87} +(-99428.3 - 51177.6i) q^{88} +20256.6i q^{89} +(9408.85 - 11586.4i) q^{90} +(-87568.3 - 87568.3i) q^{91} +(-16793.0 - 80084.2i) q^{92} +(87368.0 - 87368.0i) q^{93} +(-101019. + 10477.5i) q^{94} -11242.9 q^{95} +(28705.2 - 104264. i) q^{96} -76865.8 q^{97} +(108789. - 11283.3i) q^{98} +(46101.9 - 46101.9i) 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

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