LMFDB - Embedded newform 82.6.c.a.73.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,6,Mod(9,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.9"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	82.c (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.1514732247$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 3744 x^{13} + 591440 x^{12} + 1165004 x^{11} + 3495880 x^{10} + \cdots + 22\!\cdots\!00 $ x^16 - 2x^15 + 2x^14 + 3744x^13 + 591440x^12 + 1165004x^11 + 3495880x^10 + 907468956x^9 + 96107185444x^8 + 493242636448x^7 + 829878020288x^6 - 41617693936080x^5 + 1256161442994900x^4 + 450348141276000x^3 + 347688450000000x^2 - 12637466505000000*x + 229667622932250000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			73.8
Root			$-15.3135 - 15.3135i$ of defining polynomial
Character	$\chi$	$=$	82.73
Dual form			82.6.c.a.9.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.00000i q^{2} +(15.3135 - 15.3135i) q^{3} -16.0000 q^{4} +59.4099i q^{5} +(61.2538 + 61.2538i) q^{6} +(-111.655 + 111.655i) q^{7} -64.0000i q^{8} -226.004i q^{9} -237.640 q^{10} +(13.6671 - 13.6671i) q^{11} +(-245.015 + 245.015i) q^{12} +(-546.015 + 546.015i) q^{13} +(-446.620 - 446.620i) q^{14} +(909.771 + 909.771i) q^{15} +256.000 q^{16} +(475.377 + 475.377i) q^{17} +904.014 q^{18} +(1573.62 + 1573.62i) q^{19} -950.559i q^{20} +3419.65i q^{21} +(54.6684 + 54.6684i) q^{22} -2910.69 q^{23} +(-980.061 - 980.061i) q^{24} -404.541 q^{25} +(-2184.06 - 2184.06i) q^{26} +(260.273 + 260.273i) q^{27} +(1786.48 - 1786.48i) q^{28} +(101.789 - 101.789i) q^{29} +(-3639.09 + 3639.09i) q^{30} -5765.43 q^{31} +1024.00i q^{32} -418.581i q^{33} +(-1901.51 + 1901.51i) q^{34} +(-6633.42 - 6633.42i) q^{35} +3616.06i q^{36} +5267.63 q^{37} +(-6294.50 + 6294.50i) q^{38} +16722.8i q^{39} +3802.24 q^{40} +(-8663.74 - 6387.16i) q^{41} -13678.6 q^{42} -7337.12i q^{43} +(-218.674 + 218.674i) q^{44} +13426.9 q^{45} -11642.8i q^{46} +(20040.8 + 20040.8i) q^{47} +(3920.24 - 3920.24i) q^{48} -8126.70i q^{49} -1618.17i q^{50} +14559.3 q^{51} +(8736.25 - 8736.25i) q^{52} +(16131.4 - 16131.4i) q^{53} +(-1041.09 + 1041.09i) q^{54} +(811.961 + 811.961i) q^{55} +(7145.92 + 7145.92i) q^{56} +48195.2 q^{57} +(407.156 + 407.156i) q^{58} -648.258 q^{59} +(-14556.3 - 14556.3i) q^{60} -43907.4i q^{61} -23061.7i q^{62} +(25234.4 + 25234.4i) q^{63} -4096.00 q^{64} +(-32438.7 - 32438.7i) q^{65} +1674.32 q^{66} +(25258.3 + 25258.3i) q^{67} +(-7606.03 - 7606.03i) q^{68} +(-44572.7 + 44572.7i) q^{69} +(26533.7 - 26533.7i) q^{70} +(-36466.2 + 36466.2i) q^{71} -14464.2 q^{72} -38756.3i q^{73} +21070.5i q^{74} +(-6194.93 + 6194.93i) q^{75} +(-25178.0 - 25178.0i) q^{76} +3052.00i q^{77} -66891.0 q^{78} +(-13182.3 + 13182.3i) q^{79} +15208.9i q^{80} +62890.2 q^{81} +(25548.6 - 34655.0i) q^{82} -12127.7 q^{83} -54714.4i q^{84} +(-28242.1 + 28242.1i) q^{85} +29348.5 q^{86} -3117.48i q^{87} +(-874.694 - 874.694i) q^{88} +(74101.6 - 74101.6i) q^{89} +53707.4i q^{90} -121931. i q^{91} +46571.0 q^{92} +(-88288.7 + 88288.7i) q^{93} +(-80163.2 + 80163.2i) q^{94} +(-93488.9 + 93488.9i) q^{95} +(15681.0 + 15681.0i) q^{96} +(25241.5 + 25241.5i) q^{97} +32506.8 q^{98} +(-3088.81 - 3088.81i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{3} - 256 q^{4} - 8 q^{6} - 100 q^{7} - 160 q^{10} - 418 q^{11} + 32 q^{12} - 194 q^{13} - 400 q^{14} + 1576 q^{15} + 4096 q^{16} + 2508 q^{17} + 3888 q^{18} + 1458 q^{19} - 1672 q^{22} + 11312 q^{23}+ \cdots + 266182 q^{99}+O(q^{100}) $ 16 * q - 2 * q^3 - 256 * q^4 - 8 * q^6 - 100 * q^7 - 160 * q^10 - 418 * q^11 + 32 * q^12 - 194 * q^13 - 400 * q^14 + 1576 * q^15 + 4096 * q^16 + 2508 * q^17 + 3888 * q^18 + 1458 * q^19 - 1672 * q^22 + 11312 * q^23 + 128 * q^24 - 1408 * q^25 - 776 * q^26 + 10264 * q^27 + 1600 * q^28 + 6942 * q^29 - 6304 * q^30 - 2064 * q^31 - 10032 * q^34 - 896 * q^35 - 42716 * q^37 - 5832 * q^38 + 2560 * q^40 + 24566 * q^41 + 12000 * q^42 + 6688 * q^44 + 33760 * q^45 - 8740 * q^47 - 512 * q^48 - 45076 * q^51 + 3104 * q^52 + 16066 * q^53 - 41056 * q^54 + 31288 * q^55 + 6400 * q^56 - 12948 * q^57 + 27768 * q^58 - 35932 * q^59 - 25216 * q^60 + 61456 * q^63 - 65536 * q^64 - 3908 * q^65 + 46384 * q^66 - 6270 * q^67 - 40128 * q^68 - 98616 * q^69 + 3584 * q^70 - 130568 * q^71 - 62208 * q^72 - 139070 * q^75 - 23328 * q^76 - 51648 * q^78 - 18212 * q^79 + 202436 * q^81 + 59784 * q^82 - 245784 * q^83 - 153632 * q^85 + 218336 * q^86 + 26752 * q^88 + 301716 * q^89 - 180992 * q^92 + 44488 * q^93 + 34960 * q^94 - 54892 * q^95 - 2048 * q^96 + 224176 * q^97 + 302336 * q^98 + 266182 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			4.00000i			0.707107i
$2$			4.00000i			0.707107i
$3$	15.3135	−	15.3135i	0.982358	−	0.982358i	−0.0174887	−	0.999847i	$-0.505567\pi$
$3$	15.3135	−	15.3135i	0.982358	−	0.982358i	0.999847	+	0.0174887i	$0.00556710\pi$
$4$	−16.0000			−0.500000
$5$			59.4099i			1.06276i	0.847134	+	0.531379i	$0.178326\pi$
$5$			59.4099i			1.06276i	−0.847134	+	0.531379i	$0.821674\pi$
$6$	61.2538	+	61.2538i	0.694632	+	0.694632i
$7$	−111.655	+	111.655i	−0.861258	+	0.861258i	−0.991484	−	0.130226i	$-0.958430\pi$
$7$	−111.655	+	111.655i	−0.861258	+	0.861258i	0.130226	+	0.991484i	$0.458430\pi$
$8$		−	64.0000i		−	0.353553i
$9$		−	226.004i		−	0.930056i
$10$	−237.640			−0.751483
$11$	13.6671	−	13.6671i	0.0340561	−	0.0340561i	−0.689874	−	0.723930i	$-0.742334\pi$
$11$	13.6671	−	13.6671i	0.0340561	−	0.0340561i	0.723930	+	0.689874i	$0.242334\pi$
$12$	−245.015	+	245.015i	−0.491179	+	0.491179i
$13$	−546.015	+	546.015i	−0.896079	+	0.896079i	−0.995087	−	0.0990074i	$-0.968433\pi$
$13$	−546.015	+	546.015i	−0.896079	+	0.896079i	0.0990074	+	0.995087i	$0.468433\pi$
$14$	−446.620	−	446.620i	−0.609001	−	0.609001i
$15$	909.771	+	909.771i	1.04401	+	1.04401i
$16$	256.000			0.250000
$17$	475.377	+	475.377i	0.398948	+	0.398948i	0.877862	−	0.478914i	$-0.158969\pi$
$17$	475.377	+	475.377i	0.398948	+	0.398948i	−0.478914	+	0.877862i	$0.658969\pi$
$18$	904.014			0.657649
$19$	1573.62	+	1573.62i	1.00004	+	1.00004i	1.00000		3.89536e-5i	$1.23993e-5\pi$
$19$	1573.62	+	1573.62i	1.00004	+	1.00004i	3.89536e−5		1.00000i	$0.499988\pi$
$20$		−	950.559i		−	0.531379i
$21$			3419.65i			1.69213i
$22$	54.6684	+	54.6684i	0.0240813	+	0.0240813i
$23$	−2910.69			−1.14730			−0.573649	−	0.819101i	$-0.694473\pi$
$23$	−2910.69			−1.14730			−0.573649	+	0.819101i	$0.694473\pi$
$24$	−980.061	−	980.061i	−0.347316	−	0.347316i
$25$	−404.541			−0.129453
$26$	−2184.06	−	2184.06i	−0.633624	−	0.633624i
$27$	260.273	+	260.273i	0.0687101	+	0.0687101i
$28$	1786.48	−	1786.48i	0.430629	−	0.430629i
$29$	101.789	−	101.789i	0.0224753	−	0.0224753i	−0.695780	−	0.718255i	$-0.744941\pi$
$29$	101.789	−	101.789i	0.0224753	−	0.0224753i	0.718255	+	0.695780i	$0.244941\pi$
$30$	−3639.09	+	3639.09i	−0.738226	+	0.738226i
$31$	−5765.43			−1.07753			−0.538763	−	0.842457i	$-0.681108\pi$
$31$	−5765.43			−1.07753			−0.538763	+	0.842457i	$0.681108\pi$
$32$			1024.00i			0.176777i
$33$		−	418.581i		−	0.0669105i
$34$	−1901.51	+	1901.51i	−0.282099	+	0.282099i
$35$	−6633.42	−	6633.42i	−0.915308	−	0.915308i
$36$			3616.06i			0.465028i
$37$	5267.63			0.632573			0.316287	−	0.948664i	$-0.397564\pi$
$37$	5267.63			0.632573			0.316287	+	0.948664i	$0.397564\pi$
$38$	−6294.50	+	6294.50i	−0.707134	+	0.707134i
$39$			16722.8i			1.76054i
$40$	3802.24			0.375741
$41$	−8663.74	−	6387.16i	−0.804907	−	0.593401i
$41$	−8663.74	−	6387.16i	−0.804907	−	0.593401i
$42$	−13678.6			−1.19652
$43$		−	7337.12i		−	0.605138i	−0.953127	−	0.302569i	$-0.902156\pi$
$43$		−	7337.12i		−	0.605138i	0.953127	−	0.302569i	$-0.0978443\pi$
$44$	−218.674	+	218.674i	−0.0170280	+	0.0170280i
$45$	13426.9			0.988424
$46$		−	11642.8i		−	0.811262i
$47$	20040.8	+	20040.8i	1.32334	+	1.32334i	0.911058	+	0.412279i	$0.135267\pi$
$47$	20040.8	+	20040.8i	1.32334	+	1.32334i	0.412279	+	0.911058i	$0.364733\pi$
$48$	3920.24	−	3920.24i	0.245590	−	0.245590i
$49$		−	8126.70i		−	0.483531i
$50$		−	1618.17i		−	0.0915373i
$51$	14559.3			0.783819
$52$	8736.25	−	8736.25i	0.448040	−	0.448040i
$53$	16131.4	−	16131.4i	0.788829	−	0.788829i	−0.192473	−	0.981302i	$-0.561651\pi$
$53$	16131.4	−	16131.4i	0.788829	−	0.788829i	0.981302	+	0.192473i	$0.0616508\pi$
$54$	−1041.09	+	1041.09i	−0.0485854	+	0.0485854i
$55$	811.961	+	811.961i	0.0361933	+	0.0361933i
$56$	7145.92	+	7145.92i	0.304501	+	0.304501i
$57$	48195.2			1.96479
$58$	407.156	+	407.156i	0.0158924	+	0.0158924i
$59$	−648.258			−0.0242448			−0.0121224	−	0.999927i	$-0.503859\pi$
$59$	−648.258			−0.0242448			−0.0121224	+	0.999927i	$0.503859\pi$
$60$	−14556.3	−	14556.3i	−0.522004	−	0.522004i
$61$		−	43907.4i		−	1.51082i	−0.655251	−	0.755411i	$-0.727437\pi$
$61$		−	43907.4i		−	1.51082i	0.655251	−	0.755411i	$-0.272563\pi$
$62$		−	23061.7i		−	0.761926i
$63$	25234.4	+	25234.4i	0.801018	+	0.801018i
$64$	−4096.00			−0.125000
$65$	−32438.7	−	32438.7i	−0.952315	−	0.952315i
$66$	1674.32			0.0473129
$67$	25258.3	+	25258.3i	0.687413	+	0.687413i	0.961659	−	0.274247i	$-0.0884285\pi$
$67$	25258.3	+	25258.3i	0.687413	+	0.687413i	−0.274247	+	0.961659i	$0.588429\pi$
$68$	−7606.03	−	7606.03i	−0.199474	−	0.199474i
$69$	−44572.7	+	44572.7i	−1.12706	+	1.12706i
$70$	26533.7	−	26533.7i	0.647221	−	0.647221i
$71$	−36466.2	+	36466.2i	−0.858509	+	0.858509i	−0.991162	−	0.132654i	$-0.957650\pi$
$71$	−36466.2	+	36466.2i	−0.858509	+	0.858509i	0.132654	+	0.991162i	$0.457650\pi$
$72$	−14464.2			−0.328824
$73$		−	38756.3i		−	0.851208i	−0.904910	−	0.425604i	$-0.860062\pi$
$73$		−	38756.3i		−	0.851208i	0.904910	−	0.425604i	$-0.139938\pi$
$74$			21070.5i			0.447297i
$75$	−6194.93	+	6194.93i	−0.127169	+	0.127169i
$76$	−25178.0	−	25178.0i	−0.500019	−	0.500019i
$77$			3052.00i			0.0586621i
$78$	−66891.0			−1.24489
$79$	−13182.3	+	13182.3i	−0.237641	+	0.237641i	−0.815873	−	0.578231i	$-0.803743\pi$
$79$	−13182.3	+	13182.3i	−0.237641	+	0.237641i	0.578231	+	0.815873i	$0.303743\pi$
$80$			15208.9i			0.265689i
$81$	62890.2			1.06505
$82$	25548.6	−	34655.0i	0.419598	−	0.569155i
$83$	−12127.7			−0.193234			−0.0966169	−	0.995322i	$-0.530802\pi$
$83$	−12127.7			−0.193234			−0.0966169	+	0.995322i	$0.530802\pi$
$84$		−	54714.4i		−	0.846064i
$85$	−28242.1	+	28242.1i	−0.423984	+	0.423984i
$86$	29348.5			0.427897
$87$		−	3117.48i		−	0.0441576i
$88$	−874.694	−	874.694i	−0.0120406	−	0.0120406i
$89$	74101.6	−	74101.6i	0.991636	−	0.991636i	−0.00832915	−	0.999965i	$-0.502651\pi$
$89$	74101.6	−	74101.6i	0.991636	−	0.991636i	0.999965	+	0.00832915i	$0.00265128\pi$
$90$			53707.4i			0.698921i
$91$		−	121931.i		−	1.54351i
$92$	46571.0			0.573649
$93$	−88288.7	+	88288.7i	−1.05852	+	1.05852i
$94$	−80163.2	+	80163.2i	−0.935740	+	0.935740i
$95$	−93488.9	+	93488.9i	−1.06280	+	1.06280i
$96$	15681.0	+	15681.0i	0.173658	+	0.173658i
$97$	25241.5	+	25241.5i	0.272387	+	0.272387i	0.830060	−	0.557674i	$-0.188306\pi$
$97$	25241.5	+	25241.5i	0.272387	+	0.272387i	−0.557674	+	0.830060i	$0.688306\pi$
$98$	32506.8			0.341908
$99$	−3088.81	−	3088.81i	−0.0316741	−	0.0316741i
$100$	6472.66			0.0647266
$101$	−17219.3	−	17219.3i	−0.167962	−	0.167962i	0.618121	−	0.786083i	$-0.287894\pi$
$101$	−17219.3	−	17219.3i	−0.167962	−	0.167962i	−0.786083	+	0.618121i	$0.787894\pi$
$102$			58237.3i			0.554244i
$103$		−	120103.i		−	1.11548i	−0.830017	−	0.557738i	$-0.811669\pi$
$103$		−	120103.i		−	1.11548i	0.830017	−	0.557738i	$-0.188331\pi$
$104$	34945.0	+	34945.0i	0.316812	+	0.316812i
$105$	−203161.			−1.79832
$106$	64525.7	+	64525.7i	0.557786	+	0.557786i
$107$	140265.			1.18438			0.592188	−	0.805800i	$-0.298264\pi$
$107$	140265.			1.18438			0.592188	+	0.805800i	$0.298264\pi$
$108$	−4164.37	−	4164.37i	−0.0343550	−	0.0343550i
$109$	126743.	+	126743.i	1.02178	+	1.02178i	0.999758	+	0.0220210i	$0.00701005\pi$
$109$	126743.	+	126743.i	1.02178	+	1.02178i	0.0220210	+	0.999758i	$0.492990\pi$
$110$	−3247.85	+	3247.85i	−0.0255926	+	0.0255926i
$111$	80665.6	−	80665.6i	0.621414	−	0.621414i
$112$	−28583.7	+	28583.7i	−0.215315	+	0.215315i
$113$	−41402.3			−0.305020			−0.152510	−	0.988302i	$-0.548736\pi$
$113$	−41402.3			−0.305020			−0.152510	+	0.988302i	$0.548736\pi$
$114$			192781.i			1.38932i
$115$		−	172924.i		−	1.21930i
$116$	−1628.62	+	1628.62i	−0.0112376	+	0.0112376i
$117$	123401.	+	123401.i	0.833404	+	0.833404i
$118$		−	2593.03i		−	0.0171436i
$119$	−106156.			−0.687194
$120$	58225.4	−	58225.4i	0.369113	−	0.369113i
$121$			160677.i			0.997680i
$122$	175630.			1.06831
$123$	−230481.	+	34862.4i	−1.37364	+	0.207775i
$124$	92247.0			0.538763
$125$			161622.i			0.925180i
$126$	−100938.	+	100938.i	−0.566405	+	0.566405i
$127$	−213488.			−1.17453			−0.587265	−	0.809395i	$-0.699795\pi$
$127$	−213488.			−1.17453			−0.587265	+	0.809395i	$0.699795\pi$
$128$		−	16384.0i		−	0.0883883i
$129$	−112357.	−	112357.i	−0.594462	−	0.594462i
$130$	129755.	−	129755.i	0.673388	−	0.673388i
$131$		−	21770.3i		−	0.110837i	−0.998463	−	0.0554186i	$-0.982351\pi$
$131$		−	21770.3i		−	0.110837i	0.998463	−	0.0554186i	$-0.0176493\pi$
$132$			6697.29i			0.0334553i
$133$	−351406.			−1.72258
$134$	−101033.	+	101033.i	−0.486074	+	0.486074i
$135$	−15462.8	+	15462.8i	−0.0730221	+	0.0730221i
$136$	30424.1	−	30424.1i	0.141049	−	0.141049i
$137$	−110327.	−	110327.i	−0.502206	−	0.502206i	0.409917	−	0.912123i	$-0.365558\pi$
$137$	−110327.	−	110327.i	−0.502206	−	0.502206i	−0.912123	+	0.409917i	$0.865558\pi$
$138$	−178291.	−	178291.i	−0.796950	−	0.796950i
$139$	−161854.			−0.710537			−0.355268	−	0.934764i	$-0.615611\pi$
$139$	−161854.			−0.710537			−0.355268	+	0.934764i	$0.615611\pi$
$140$	106135.	+	106135.i	0.457654	+	0.457654i
$141$	613788.			2.59998
$142$	−145865.	−	145865.i	−0.607057	−	0.607057i
$143$			14924.9i			0.0610339i
$144$		−	57856.9i		−	0.232514i
$145$	6047.27	+	6047.27i	0.0238858	+	0.0238858i
$146$	155025.			0.601895
$147$	−124448.	−	124448.i	−0.475001	−	0.475001i
$148$	−84282.1			−0.316287
$149$	245659.	+	245659.i	0.906498	+	0.906498i	0.995988	−	0.0894901i	$-0.0285237\pi$
$149$	245659.	+	245659.i	0.906498	+	0.906498i	−0.0894901	+	0.995988i	$0.528524\pi$
$150$	−24779.7	−	24779.7i	−0.0899224	−	0.0899224i
$151$	−194244.	+	194244.i	−0.693275	+	0.693275i	−0.962951	−	0.269676i	$-0.913083\pi$
$151$	−194244.	+	194244.i	−0.693275	+	0.693275i	0.269676	+	0.962951i	$0.413083\pi$
$152$	100712.	−	100712.i	0.353567	−	0.353567i
$153$	107437.	−	107437.i	0.371044	−	0.371044i
$154$	−12208.0			−0.0414804
$155$		−	342524.i		−	1.14515i
$156$		−	267564.i		−	0.880271i
$157$	330693.	−	330693.i	1.07072	−	1.07072i	0.0734192	−	0.997301i	$-0.476609\pi$
$157$	330693.	−	330693.i	1.07072	−	1.07072i	0.997301	−	0.0734192i	$-0.0233911\pi$
$158$	−52729.0	−	52729.0i	−0.168038	−	0.168038i
$159$		−	494056.i		−	1.54983i
$160$	−60835.8			−0.187871
$161$	324993.	−	324993.i	0.988120	−	0.988120i
$162$			251561.i			0.753105i
$163$	407181.			1.20038			0.600190	−	0.799858i	$-0.295092\pi$
$163$	407181.			1.20038			0.600190	+	0.799858i	$0.295092\pi$
$164$	138620.	+	102195.i	0.402454	+	0.296700i
$165$	24867.9			0.0711097
$166$		−	48510.8i		−	0.136637i
$167$	−338103.	+	338103.i	−0.938119	+	0.938119i	−0.998194	−	0.0600747i	$-0.980866\pi$
$167$	−338103.	+	338103.i	−0.938119	+	0.938119i	0.0600747	+	0.998194i	$0.480866\pi$
$168$	218858.			0.598258
$169$		−	224972.i		−	0.605916i
$170$	−112968.	−	112968.i	−0.299802	−	0.299802i
$171$	355645.	−	355645.i	0.930092	−	0.930092i
$172$			117394.i			0.302569i
$173$			715111.i			1.81660i	0.418323	+	0.908298i	$0.362618\pi$
$173$			715111.i			1.81660i	−0.418323	+	0.908298i	$0.637382\pi$
$174$	12469.9			0.0312241
$175$	45169.1	−	45169.1i	0.111493	−	0.111493i
$176$	3498.78	−	3498.78i	0.00851402	−	0.00851402i
$177$	−9927.07	+	9927.07i	−0.0238170	+	0.0238170i
$178$	296406.	+	296406.i	0.701193	+	0.701193i
$179$	251891.	+	251891.i	0.587597	+	0.587597i	0.936980	−	0.349383i	$-0.113609\pi$
$179$	251891.	+	251891.i	0.587597	+	0.587597i	−0.349383	+	0.936980i	$0.613609\pi$
$180$	−214830.			−0.494212
$181$	97009.1	+	97009.1i	0.220098	+	0.220098i	0.808540	−	0.588442i	$-0.200258\pi$
$181$	97009.1	+	97009.1i	0.220098	+	0.220098i	−0.588442	+	0.808540i	$0.700258\pi$
$182$	487723.			1.09143
$183$	−672374.	−	672374.i	−1.48417	−	1.48417i
$184$			186284.i			0.405631i
$185$			312950.i			0.672272i
$186$	−353155.	−	353155.i	−0.748484	−	0.748484i
$187$	12994.0			0.0271732
$188$	−320653.	−	320653.i	−0.661668	−	0.661668i
$189$	−58121.7			−0.118354
$190$	−373956.	−	373956.i	−0.751512	−	0.751512i
$191$	459503.	+	459503.i	0.911392	+	0.911392i	0.996382	−	0.0849898i	$-0.0270858\pi$
$191$	459503.	+	459503.i	0.911392	+	0.911392i	−0.0849898	+	0.996382i	$0.527086\pi$
$192$	−62723.9	+	62723.9i	−0.122795	+	0.122795i
$193$	−187128.	+	187128.i	−0.361614	+	0.361614i	−0.864407	−	0.502793i	$-0.832306\pi$
$193$	−187128.	+	187128.i	−0.361614	+	0.361614i	0.502793	+	0.864407i	$0.332306\pi$
$194$	−100966.	+	100966.i	−0.192607	+	0.192607i
$195$	−993498.			−1.87103
$196$			130027.i			0.241765i
$197$			849072.i			1.55876i	0.626552	+	0.779379i	$0.284465\pi$
$197$			849072.i			1.55876i	−0.626552	+	0.779379i	$0.715535\pi$
$198$	12355.3	−	12355.3i	0.0223969	−	0.0223969i
$199$	−385129.	−	385129.i	−0.689403	−	0.689403i	0.272697	−	0.962100i	$-0.412084\pi$
$199$	−385129.	−	385129.i	−0.689403	−	0.689403i	−0.962100	+	0.272697i	$0.912084\pi$
$200$			25890.6i			0.0457686i
$201$	773584.			1.35057
$202$	68877.1	−	68877.1i	0.118767	−	0.118767i
$203$			22730.5i			0.0387141i
$204$	−232949.			−0.391909
$205$	379461.	−	514712.i	0.630641	−	0.855421i
$206$	480411.			0.788761
$207$			657826.i			1.06705i
$208$	−139780.	+	139780.i	−0.224020	+	0.224020i
$209$	43013.7			0.0681148
$210$		−	812645.i		−	1.27161i
$211$	−524629.	−	524629.i	−0.811235	−	0.811235i	0.173584	−	0.984819i	$-0.444465\pi$
$211$	−524629.	−	524629.i	−0.811235	−	0.811235i	−0.984819	+	0.173584i	$0.944465\pi$
$212$	−258103.	+	258103.i	−0.394415	+	0.394415i
$213$			1.11685e6i			1.68673i
$214$			561059.i			0.837480i
$215$	435898.			0.643115
$216$	16657.5	−	16657.5i	0.0242927	−	0.0242927i
$217$	643740.	−	643740.i	0.928028	−	0.928028i
$218$	−506971.	+	506971.i	−0.722506	+	0.722506i
$219$	−593493.	−	593493.i	−0.836191	−	0.836191i
$220$	−12991.4	−	12991.4i	−0.0180967	−	0.0180967i
$221$	−519126.			−0.714977
$222$	322662.	+	322662.i	0.439406	+	0.439406i
$223$	1.35749e6			1.82799			0.913995	−	0.405725i	$-0.132981\pi$
$223$	1.35749e6			1.82799			0.913995	+	0.405725i	$0.132981\pi$
$224$	−114335.	−	114335.i	−0.152250	−	0.152250i
$225$			91427.8i			0.120399i
$226$		−	165609.i		−	0.215682i
$227$	534475.	+	534475.i	0.688435	+	0.688435i	0.961886	−	0.273451i	$-0.0881652\pi$
$227$	534475.	+	534475.i	0.688435	+	0.688435i	−0.273451	+	0.961886i	$0.588165\pi$
$228$	−771124.			−0.982397
$229$	−365126.	−	365126.i	−0.460103	−	0.460103i	0.438586	−	0.898689i	$-0.355479\pi$
$229$	−365126.	−	365126.i	−0.460103	−	0.460103i	−0.898689	+	0.438586i	$0.855479\pi$
$230$	691696.			0.862175
$231$	46736.7	+	46736.7i	0.0576272	+	0.0576272i
$232$	−6514.49	−	6514.49i	−0.00794622	−	0.00794622i
$233$	−433959.	+	433959.i	−0.523672	+	0.523672i	−0.918678	−	0.395006i	$-0.870742\pi$
$233$	−433959.	+	433959.i	−0.523672	+	0.523672i	0.395006	+	0.918678i	$0.370742\pi$
$234$	−493606.	+	493606.i	−0.589306	+	0.589306i
$235$	−1.19062e6	+	1.19062e6i	−1.40639	+	1.40639i
$236$	10372.1			0.0121224
$237$			403732.i			0.466898i
$238$		−	424626.i		−	0.485919i
$239$	874959.	−	874959.i	0.990816	−	0.990816i	−0.00914189	−	0.999958i	$-0.502910\pi$
$239$	874959.	−	874959.i	0.990816	−	0.990816i	0.999958	+	0.00914189i	$0.00290999\pi$
$240$	232901.	+	232901.i	0.261002	+	0.261002i
$241$			822355.i			0.912046i	0.889968	+	0.456023i	$0.150726\pi$
$241$			822355.i			0.912046i	−0.889968	+	0.456023i	$0.849274\pi$
$242$	−642710.			−0.705467
$243$	899820.	−	899820.i	0.977553	−	0.977553i
$244$			702519.i			0.755411i
$245$	482807.			0.513876
$246$	−139449.	−	921925.i	−0.146919	−	0.971310i
$247$	−1.71845e6			−1.79223
$248$			368988.i			0.380963i
$249$	−185717.	+	185717.i	−0.189825	+	0.189825i
$250$	−646489.			−0.654201
$251$			1.28351e6i			1.28592i	0.765900	+	0.642960i	$0.222294\pi$
$251$			1.28351e6i			1.28592i	−0.765900	+	0.642960i	$0.777706\pi$
$252$	−403751.	−	403751.i	−0.400509	−	0.400509i
$253$	−39780.7	+	39780.7i	−0.0390725	+	0.0390725i
$254$		−	853951.i		−	0.830518i
$255$			864969.i			0.833009i
$256$	65536.0			0.0625000
$257$	913980.	−	913980.i	0.863185	−	0.863185i	−0.128522	−	0.991707i	$-0.541023\pi$
$257$	913980.	−	913980.i	0.863185	−	0.863185i	0.991707	+	0.128522i	$0.0410233\pi$
$258$	449426.	−	449426.i	0.420348	−	0.420348i
$259$	−588157.	+	588157.i	−0.544809	+	0.544809i
$260$	519020.	+	519020.i	0.476157	+	0.476157i
$261$	−23004.7	−	23004.7i	−0.0209033	−	0.0209033i
$262$	87081.1			0.0783737
$263$	−263775.	−	263775.i	−0.235150	−	0.235150i	0.579688	−	0.814838i	$-0.303174\pi$
$263$	−263775.	−	263775.i	−0.235150	−	0.235150i	−0.814838	+	0.579688i	$0.803174\pi$
$264$	−26789.2			−0.0236564
$265$	958367.	+	958367.i	0.838334	+	0.838334i
$266$		−	1.40562e6i		−	1.21805i
$267$		−	2.26950e6i		−	1.94828i
$268$	−404133.	−	404133.i	−0.343706	−	0.343706i
$269$	−103774.			−0.0874393			−0.0437197	−	0.999044i	$-0.513921\pi$
$269$	−103774.			−0.0874393			−0.0437197	+	0.999044i	$0.513921\pi$
$270$	−61851.3	−	61851.3i	−0.0516344	−	0.0516344i
$271$	−749984.			−0.620338			−0.310169	−	0.950681i	$-0.600386\pi$
$271$	−749984.			−0.620338			−0.310169	+	0.950681i	$0.600386\pi$
$272$	121697.	+	121697.i	0.0997369	+	0.0997369i
$273$	−1.86718e6	−	1.86718e6i	−1.51628	−	1.51628i
$274$	441310.	−	441310.i	0.355114	−	0.355114i
$275$	−5528.91	+	5528.91i	−0.00440867	+	0.00440867i
$276$	713163.	−	713163.i	0.563529	−	0.563529i
$277$	504092.			0.394740			0.197370	−	0.980329i	$-0.436760\pi$
$277$	504092.			0.394740			0.197370	+	0.980329i	$0.436760\pi$
$278$		−	647416.i		−	0.502426i
$279$			1.30301e6i			1.00216i
$280$	−424539.	+	424539.i	−0.323610	+	0.323610i
$281$	559472.	+	559472.i	0.422681	+	0.422681i	0.886126	−	0.463445i	$-0.153387\pi$
$281$	559472.	+	559472.i	0.422681	+	0.422681i	−0.463445	+	0.886126i	$0.653387\pi$
$282$			2.45515e6i			1.83846i
$283$	−1.74111e6			−1.29229			−0.646147	−	0.763213i	$-0.723621\pi$
$283$	−1.74111e6			−1.29229			−0.646147	+	0.763213i	$0.723621\pi$
$284$	583459.	−	583459.i	0.429254	−	0.429254i
$285$			2.86328e6i			2.08810i
$286$	−59699.5			−0.0431575
$287$	1.68051e6	−	254192.i	1.20430	−	0.182162i
$288$	231428.			0.164412
$289$		−	967890.i		−	0.681682i
$290$	−24189.1	+	24189.1i	−0.0168898	+	0.0168898i
$291$	773069.			0.535163
$292$			620102.i			0.425604i
$293$	−686907.	−	686907.i	−0.467443	−	0.467443i	0.433642	−	0.901085i	$-0.357228\pi$
$293$	−686907.	−	686907.i	−0.467443	−	0.467443i	−0.901085	+	0.433642i	$0.857228\pi$
$294$	497792.	−	497792.i	0.335876	−	0.335876i
$295$		−	38513.0i		−	0.0257663i
$296$		−	337128.i		−	0.223648i
$297$	7114.36			0.00467999
$298$	−982635.	+	982635.i	−0.640991	+	0.640991i
$299$	1.58928e6	−	1.58928e6i	1.02807	−	1.02807i
$300$	99118.8	−	99118.8i	0.0635847	−	0.0635847i
$301$	819226.	+	819226.i	0.521180	+	0.521180i
$302$	−776977.	−	776977.i	−0.490220	−	0.490220i
$303$	−527373.			−0.329998
$304$	402848.	+	402848.i	0.250010	+	0.250010i
$305$	2.60854e6			1.60564
$306$	429748.	+	429748.i	0.262367	+	0.262367i
$307$		−	842820.i		−	0.510374i	−0.966892	−	0.255187i	$-0.917863\pi$
$307$		−	842820.i		−	0.510374i	0.966892	−	0.255187i	$-0.0821371\pi$
$308$		−	48832.0i		−	0.0293311i
$309$	−1.83919e6	−	1.83919e6i	−1.09580	−	1.09580i
$310$	1.37010e6			0.809742
$311$	−1.51582e6	−	1.51582e6i	−0.888682	−	0.888682i	0.105714	−	0.994397i	$-0.466287\pi$
$311$	−1.51582e6	−	1.51582e6i	−0.888682	−	0.888682i	−0.994397	+	0.105714i	$0.966287\pi$
$312$	1.07026e6			0.622446
$313$	−498526.	−	498526.i	−0.287625	−	0.287625i	0.548515	−	0.836140i	$-0.315193\pi$
$313$	−498526.	−	498526.i	−0.287625	−	0.287625i	−0.836140	+	0.548515i	$0.815193\pi$
$314$	1.32277e6	+	1.32277e6i	0.757114	+	0.757114i
$315$	−1.49918e6	+	1.49918e6i	−0.851288	+	0.851288i
$316$	210916.	−	210916.i	0.118821	−	0.118821i
$317$	2.04918e6	−	2.04918e6i	1.14533	−	1.14533i	0.157875	−	0.987459i	$-0.449536\pi$
$317$	2.04918e6	−	2.04918e6i	1.14533	−	1.14533i	0.987459	−	0.157875i	$-0.0504643\pi$
$318$	1.97622e6			1.09589
$319$		−	2782.32i		−	0.00153084i
$320$		−	243343.i		−	0.132845i
$321$	2.14794e6	−	2.14794e6i	1.16348	−	1.16348i
$322$	1.29997e6	+	1.29997e6i	0.698706	+	0.698706i
$323$			1.49613e6i			0.797926i
$324$	−1.00624e6			−0.532526
$325$	220886.	−	220886.i	0.116000	−	0.116000i
$326$			1.62872e6i			0.848797i
$327$	3.88174e6			2.00751
$328$	−408778.	+	554479.i	−0.209799	+	0.284578i
$329$	−4.47531e6			−2.27947
$330$			99471.5i			0.0502821i
$331$	2.06208e6	−	2.06208e6i	1.03451	−	1.03451i	0.0351270	−	0.999383i	$-0.488816\pi$
$331$	2.06208e6	−	2.06208e6i	1.03451	−	1.03451i	0.999383	−	0.0351270i	$-0.0111836\pi$
$332$	194043.			0.0966169
$333$		−	1.19050e6i		−	0.588329i
$334$	−1.35241e6	−	1.35241e6i	−0.663350	−	0.663350i
$335$	−1.50060e6	+	1.50060e6i	−0.730553	+	0.730553i
$336$			875430.i			0.423032i
$337$		−	2.45553e6i		−	1.17780i	−0.808207	−	0.588898i	$-0.799562\pi$
$337$		−	2.45553e6i		−	1.17780i	0.808207	−	0.588898i	$-0.200438\pi$
$338$	899890.			0.428448
$339$	−634012.	+	634012.i	−0.299639	+	0.299639i
$340$	451874.	−	451874.i	0.211992	−	0.211992i
$341$	−78796.7	+	78796.7i	−0.0366963	+	0.0366963i
$342$	1.42258e6	+	1.42258e6i	0.657675	+	0.657675i
$343$	−969199.	−	969199.i	−0.444813	−	0.444813i
$344$	−469576.			−0.213949
$345$	−2.64806e6	−	2.64806e6i	−1.19779	−	1.19779i
$346$	−2.86045e6			−1.28453
$347$	−477195.	−	477195.i	−0.212752	−	0.212752i	0.592684	−	0.805435i	$-0.298068\pi$
$347$	−477195.	−	477195.i	−0.212752	−	0.212752i	−0.805435	+	0.592684i	$0.798068\pi$
$348$			49879.7i			0.0220788i
$349$		−	1.70664e6i		−	0.750027i	−0.927019	−	0.375014i	$-0.877638\pi$
$349$		−	1.70664e6i		−	0.750027i	0.927019	−	0.375014i	$-0.122362\pi$
$350$	180676.	+	180676.i	0.0788372	+	0.0788372i
$351$	−284227.			−0.123139
$352$	13995.1	+	13995.1i	0.00602032	+	0.00602032i
$353$	−2.87493e6			−1.22798			−0.613988	−	0.789315i	$-0.710436\pi$
$353$	−2.87493e6			−1.22798			−0.613988	+	0.789315i	$0.710436\pi$
$354$	−39708.3	−	39708.3i	−0.0168412	−	0.0168412i
$355$	−2.16645e6	−	2.16645e6i	−0.912386	−	0.912386i
$356$	−1.18563e6	+	1.18563e6i	−0.495818	+	0.495818i
$357$	−1.62562e6	+	1.62562e6i	−0.675070	+	0.675070i
$358$	−1.00756e6	+	1.00756e6i	−0.415494	+	0.415494i
$359$	2.06012e6			0.843639			0.421820	−	0.906680i	$-0.361392\pi$
$359$	2.06012e6			0.843639			0.421820	+	0.906680i	$0.361392\pi$
$360$		−	859319.i		−	0.349461i
$361$			2.47648e6i			1.00016i
$362$	−388036.	+	388036.i	−0.155633	+	0.155633i
$363$	2.46053e6	+	2.46053e6i	0.980080	+	0.980080i
$364$			1.95089e6i			0.771756i
$365$	2.30251e6			0.904628
$366$	2.68950e6	−	2.68950e6i	1.04947	−	1.04947i
$367$			2.70793e6i			1.04948i	0.851264	+	0.524738i	$0.175837\pi$
$367$			2.70793e6i			1.04948i	−0.851264	+	0.524738i	$0.824163\pi$
$368$	−745136.			−0.286825
$369$	−1.44352e6	+	1.95804e6i	−0.551896	+	0.748609i
$370$	−1.25180e6			−0.475368
$371$			3.60231e6i			1.35877i
$372$	1.41262e6	−	1.41262e6i	0.529258	−	0.529258i
$373$	3.18603e6			1.18571			0.592855	−	0.805309i	$-0.298001\pi$
$373$	3.18603e6			1.18571			0.592855	+	0.805309i	$0.298001\pi$
$374$			51976.2i			0.0192143i
$375$	2.47500e6	+	2.47500e6i	0.908858	+	0.908858i
$376$	1.28261e6	−	1.28261e6i	0.467870	−	0.467870i
$377$			111157.i			0.0402793i
$378$		−	232487.i		−	0.0836891i
$379$	−4.57739e6			−1.63689			−0.818446	−	0.574584i	$-0.805164\pi$
$379$	−4.57739e6			−1.63689			−0.818446	+	0.574584i	$0.805164\pi$
$380$	1.49582e6	−	1.49582e6i	0.531399	−	0.531399i
$381$	−3.26924e6	+	3.26924e6i	−1.15381	+	1.15381i
$382$	−1.83801e6	+	1.83801e6i	−0.644451	+	0.644451i
$383$	−1.55220e6	−	1.55220e6i	−0.540693	−	0.540693i	0.383039	−	0.923732i	$-0.374877\pi$
$383$	−1.55220e6	−	1.55220e6i	−0.540693	−	0.540693i	−0.923732	+	0.383039i	$0.874877\pi$
$384$	−250896.	−	250896.i	−0.0868290	−	0.0868290i
$385$	−181319.			−0.0623436
$386$	−748512.	−	748512.i	−0.255700	−	0.255700i
$387$	−1.65822e6			−0.562812
$388$	−403864.	−	403864.i	−0.136193	−	0.136193i
$389$			3.74318e6i			1.25420i	0.778939	+	0.627100i	$0.215758\pi$
$389$			3.74318e6i			1.25420i	−0.778939	+	0.627100i	$0.784242\pi$
$390$		−	3.97399e6i		−	1.32302i
$391$	−1.38367e6	−	1.38367e6i	−0.457712	−	0.457712i
$392$	−520109.			−0.170954
$393$	−333378.	−	333378.i	−0.108882	−	0.108882i
$394$	−3.39629e6			−1.10221
$395$	−783157.	−	783157.i	−0.252555	−	0.252555i
$396$	49421.0	+	49421.0i	0.0158370	+	0.0158370i
$397$	1.36197e6	−	1.36197e6i	0.433703	−	0.433703i	−0.456183	−	0.889886i	$-0.650784\pi$
$397$	1.36197e6	−	1.36197e6i	0.433703	−	0.433703i	0.889886	+	0.456183i	$0.150784\pi$
$398$	1.54052e6	−	1.54052e6i	0.487482	−	0.487482i
$399$	−5.38124e6	+	5.38124e6i	−1.69219	+	1.69219i
$400$	−103563.			−0.0323633
$401$		−	1.40614e6i		−	0.436683i	−0.975872	−	0.218342i	$-0.929935\pi$
$401$		−	1.40614e6i		−	0.436683i	0.975872	−	0.218342i	$-0.0700647\pi$
$402$			3.09434e6i			0.954998i
$403$	3.14802e6	−	3.14802e6i	0.965549	−	0.965549i
$404$	275508.	+	275508.i	0.0839811	+	0.0839811i
$405$			3.73631e6i			1.13189i
$406$	−90922.0			−0.0273750
$407$	71993.2	−	71993.2i	0.0215430	−	0.0215430i
$408$		−	931797.i		−	0.277122i
$409$	4.25862e6			1.25881			0.629406	−	0.777077i	$-0.283298\pi$
$409$	4.25862e6			1.25881			0.629406	+	0.777077i	$0.283298\pi$
$410$	2.05885e6	+	1.51784e6i	0.604874	+	0.445930i
$411$	−3.37899e6			−0.986693
$412$			1.92165e6i			0.557738i
$413$	72381.3	−	72381.3i	0.0208810	−	0.0208810i
$414$	−2.63131e6			−0.754519
$415$		−	720506.i		−	0.205361i
$416$	−559120.	−	559120.i	−0.158406	−	0.158406i
$417$	−2.47854e6	+	2.47854e6i	−0.698002	+	0.698002i
$418$			172055.i			0.0481644i
$419$			5.77168e6i			1.60608i	0.595925	+	0.803040i	$0.296786\pi$
$419$			5.77168e6i			1.60608i	−0.595925	+	0.803040i	$0.703214\pi$
$420$	3.25058e6			0.899161
$421$	3.32384e6	−	3.32384e6i	0.913977	−	0.913977i	−0.0826052	−	0.996582i	$-0.526324\pi$
$421$	3.32384e6	−	3.32384e6i	0.913977	−	0.913977i	0.996582	+	0.0826052i	$0.0263241\pi$
$422$	2.09852e6	−	2.09852e6i	0.573630	−	0.573630i
$423$	4.52929e6	−	4.52929e6i	1.23078	−	1.23078i
$424$	−1.03241e6	−	1.03241e6i	−0.278893	−	0.278893i
$425$	−192310.	−	192310.i	−0.0516451	−	0.0516451i
$426$	−4.46739e6			−1.19270
$427$	4.90249e6	+	4.90249e6i	1.30121	+	1.30121i
$428$	−2.24424e6			−0.592188
$429$	228552.	+	228552.i	0.0599571	+	0.0599571i
$430$			1.74359e6i			0.454751i
$431$			1.94687e6i			0.504829i	0.967619	+	0.252415i	$0.0812247\pi$
$431$			1.94687e6i			0.504829i	−0.967619	+	0.252415i	$0.918775\pi$
$432$	66630.0	+	66630.0i	0.0171775	+	0.0171775i
$433$	6.11452e6			1.56727			0.783633	−	0.621224i	$-0.213364\pi$
$433$	6.11452e6			1.56727			0.783633	+	0.621224i	$0.213364\pi$
$434$	2.57496e6	+	2.57496e6i	0.656215	+	0.656215i
$435$	185209.			0.0469288
$436$	−2.02788e6	−	2.02788e6i	−0.510889	−	0.510889i
$437$	−4.58033e6	−	4.58033e6i	−1.14734	−	1.14734i
$438$	2.37397e6	−	2.37397e6i	0.591277	−	0.591277i
$439$	5.12339e6	−	5.12339e6i	1.26881	−	1.26881i	0.322104	−	0.946704i	$-0.395610\pi$
$439$	5.12339e6	−	5.12339e6i	1.26881	−	1.26881i	0.946704	−	0.322104i	$-0.104390\pi$
$440$	51965.5	−	51965.5i	0.0127963	−	0.0127963i
$441$	−1.83666e6			−0.449711
$442$		−	2.07650e6i		−	0.505565i
$443$		−	5.66966e6i		−	1.37261i	−0.727313	−	0.686306i	$-0.759231\pi$
$443$		−	5.66966e6i		−	1.37261i	0.727313	−	0.686306i	$-0.240769\pi$
$444$	−1.29065e6	+	1.29065e6i	−0.310707	+	0.310707i
$445$	4.40237e6	+	4.40237e6i	1.05387	+	1.05387i
$446$			5.42995e6i			1.29258i
$447$	7.52377e6			1.78101
$448$	457339.	−	457339.i	0.107657	−	0.107657i
$449$			6.32951e6i			1.48168i	0.671681	+	0.740840i	$0.265572\pi$
$449$			6.32951e6i			1.48168i	−0.671681	+	0.740840i	$0.734428\pi$
$450$	−365711.			−0.0851348
$451$	−205702.	+	31114.3i	−0.0476209	+	0.00720308i
$452$	662437.			0.152510
$453$			5.94910e6i			1.36209i
$454$	−2.13790e6	+	2.13790e6i	−0.486797	+	0.486797i
$455$	7.24390e6			1.64038
$456$		−	3.08449e6i		−	0.694659i
$457$	631271.	+	631271.i	0.141392	+	0.141392i	0.774260	−	0.632868i	$-0.218122\pi$
$457$	631271.	+	631271.i	0.141392	+	0.141392i	−0.632868	+	0.774260i	$0.718122\pi$
$458$	1.46051e6	−	1.46051e6i	0.325342	−	0.325342i
$459$			247456.i			0.0548234i
$460$			2.76678e6i			0.609650i
$461$	−3.69120e6			−0.808938			−0.404469	−	0.914552i	$-0.632544\pi$
$461$	−3.69120e6			−0.808938			−0.404469	+	0.914552i	$0.632544\pi$
$462$	−186947.	+	186947.i	−0.0407486	+	0.0407486i
$463$	5.56214e6	−	5.56214e6i	1.20584	−	1.20584i	0.233477	−	0.972362i	$-0.424990\pi$
$463$	5.56214e6	−	5.56214e6i	1.20584	−	1.20584i	0.972362	−	0.233477i	$-0.0750103\pi$
$464$	26058.0	−	26058.0i	0.00561882	−	0.00561882i
$465$	−5.24523e6	−	5.24523e6i	−1.12495	−	1.12495i
$466$	−1.73584e6	−	1.73584e6i	−0.370292	−	0.370292i
$467$	−2.56874e6			−0.545040			−0.272520	−	0.962150i	$-0.587857\pi$
$467$	−2.56874e6			−0.545040			−0.272520	+	0.962150i	$0.587857\pi$
$468$	−1.97442e6	−	1.97442e6i	−0.416702	−	0.416702i
$469$	−5.64044e6			−1.18408
$470$	−4.76249e6	−	4.76249e6i	−0.994465	−	0.994465i
$471$		−	1.01281e7i		−	2.10366i
$472$			41488.5i			0.00857182i
$473$	−100277.	−	100277.i	−0.0206086	−	0.0206086i
$474$	−1.61493e6			−0.330147
$475$	−636596.	−	636596.i	−0.129458	−	0.129458i
$476$	1.69850e6			0.343597
$477$	−3.64576e6	−	3.64576e6i	−0.733655	−	0.733655i
$478$	3.49984e6	+	3.49984e6i	0.700613	+	0.700613i
$479$	−6.16864e6	+	6.16864e6i	−1.22843	+	1.22843i	−0.263874	+	0.964557i	$0.585000\pi$
$479$	−6.16864e6	+	6.16864e6i	−1.22843	+	1.22843i	−0.964557	+	0.263874i	$0.915000\pi$
$480$	−931606.	+	931606.i	−0.184556	+	0.184556i
$481$	−2.87621e6	+	2.87621e6i	−0.566836	+	0.566836i
$482$	−3.28942e6			−0.644914
$483$		−	9.95354e6i		−	1.94138i
$484$		−	2.57084e6i		−	0.498840i
$485$	−1.49960e6	+	1.49960e6i	−0.289481	+	0.289481i
$486$	3.59928e6	+	3.59928e6i	0.691234	+	0.691234i
$487$		−	3.72545e6i		−	0.711798i	−0.934524	−	0.355899i	$-0.884175\pi$
$487$		−	3.72545e6i		−	0.711798i	0.934524	−	0.355899i	$-0.115825\pi$
$488$	−2.81007e6			−0.534156
$489$	6.23535e6	−	6.23535e6i	1.17920	−	1.17920i
$490$			1.93123e6i			0.363365i
$491$	−1.12891e6			−0.211327			−0.105663	−	0.994402i	$-0.533697\pi$
$491$	−1.12891e6			−0.211327			−0.105663	+	0.994402i	$0.533697\pi$
$492$	3.68770e6	−	557798.i	0.686820	−	0.103888i
$493$	96776.2			0.0179329
$494$		−	6.87378e6i		−	1.26730i
$495$	183506.	−	183506.i	0.0336618	−	0.0336618i
$496$	−1.47595e6			−0.269382
$497$		−	8.14327e6i		−	1.47879i
$498$	−742867.	−	742867.i	−0.134226	−	0.134226i
$499$	−6.36082e6	+	6.36082e6i	−1.14357	+	1.14357i	−0.155775	+	0.987793i	$0.549787\pi$
$499$	−6.36082e6	+	6.36082e6i	−1.14357	+	1.14357i	−0.987793	+	0.155775i	$0.950213\pi$
$500$		−	2.58596e6i		−	0.462590i
$501$			1.03551e7i			1.84314i
$502$	−5.13402e6			−0.909282
$503$	−3.31860e6	+	3.31860e6i	−0.584836	+	0.584836i	−0.936228	−	0.351392i	$-0.885708\pi$
$503$	−3.31860e6	+	3.31860e6i	−0.584836	+	0.584836i	0.351392	+	0.936228i	$0.385708\pi$
$504$	1.61500e6	−	1.61500e6i	0.283203	−	0.283203i
$505$	1.02300e6	−	1.02300e6i	0.178503	−	0.178503i
$506$	−159123.	−	159123.i	−0.0276284	−	0.0276284i
$507$	−3.44511e6	−	3.44511e6i	−0.595227	−	0.595227i
$508$	3.41581e6			0.587265
$509$	−6.16715e6	−	6.16715e6i	−1.05509	−	1.05509i	−0.998391	−	0.0566993i	$-0.981942\pi$
$509$	−6.16715e6	−	6.16715e6i	−1.05509	−	1.05509i	−0.0566993	−	0.998391i	$-0.518058\pi$
$510$	−3.45987e6			−0.589027
$511$	4.32734e6	+	4.32734e6i	0.733110	+	0.733110i
$512$			262144.i			0.0441942i
$513$			819145.i			0.137425i
$514$	3.65592e6	+	3.65592e6i	0.610364	+	0.610364i
$515$	7.13530e6			1.18548
$516$	1.79771e6	+	1.79771e6i	0.297231	+	0.297231i
$517$	547799.			0.0901353
$518$	−2.35263e6	−	2.35263e6i	−0.385238	−	0.385238i
$519$	1.09508e7	+	1.09508e7i	1.78455	+	1.78455i
$520$	−2.07608e6	+	2.07608e6i	−0.336694	+	0.336694i
$521$	1.00156e6	−	1.00156e6i	0.161652	−	0.161652i	−0.621646	−	0.783298i	$-0.713536\pi$
$521$	1.00156e6	−	1.00156e6i	0.161652	−	0.161652i	0.783298	+	0.621646i	$0.213536\pi$
$522$	92018.6	−	92018.6i	0.0147809	−	0.0147809i
$523$	6.93475e6			1.10860			0.554302	−	0.832315i	$-0.312985\pi$
$523$	6.93475e6			1.10860			0.554302	+	0.832315i	$0.312985\pi$
$524$			348324.i			0.0554186i
$525$		−	1.38339e6i		−	0.219051i
$526$	1.05510e6	−	1.05510e6i	0.166276	−	0.166276i
$527$	−2.74075e6	−	2.74075e6i	−0.429876	−	0.429876i
$528$		−	107157.i		−	0.0167276i
$529$	2.03577e6			0.316293
$530$	−3.83347e6	+	3.83347e6i	−0.592792	+	0.592792i
$531$			146509.i			0.0225490i
$532$	5.62250e6			0.861292
$533$	8.21802e6	−	1.24305e6i	1.25299	−	0.189527i
$534$	9.07801e6			1.37764
$535$			8.33312e6i			1.25870i
$536$	1.61653e6	−	1.61653e6i	0.243037	−	0.243037i
$537$	7.71463e6			1.15446
$538$		−	415095.i		−	0.0618289i
$539$	−111068.	−	111068.i	−0.0164672	−	0.0164672i
$540$	247405.	−	247405.i	0.0365111	−	0.0365111i
$541$		−	6.77764e6i		−	0.995602i	−0.867291	−	0.497801i	$-0.834141\pi$
$541$		−	6.77764e6i		−	0.995602i	0.867291	−	0.497801i	$-0.165859\pi$
$542$		−	2.99993e6i		−	0.438645i
$543$	2.97109e6			0.432430
$544$	−486786.	+	486786.i	−0.0705246	+	0.0705246i
$545$	−7.52978e6	+	7.52978e6i	−1.08590	+	1.08590i
$546$	7.46872e6	−	7.46872e6i	1.07217	−	1.07217i
$547$	−2.94320e6	−	2.94320e6i	−0.420583	−	0.420583i	0.464822	−	0.885404i	$-0.346118\pi$
$547$	−2.94320e6	−	2.94320e6i	−0.420583	−	0.420583i	−0.885404	+	0.464822i	$0.846118\pi$
$548$	1.76524e6	+	1.76524e6i	0.251103	+	0.251103i
$549$	−9.92324e6			−1.40515
$550$	−22115.6	−	22115.6i	−0.00311740	−	0.00311740i
$551$	320355.			0.0449523
$552$	2.85265e6	+	2.85265e6i	0.398475	+	0.398475i
$553$		−	2.94373e6i		−	0.409341i
$554$			2.01637e6i			0.279123i
$555$	4.79234e6	+	4.79234e6i	0.660412	+	0.660412i
$556$	2.58967e6			0.355268
$557$	−3.96331e6	−	3.96331e6i	−0.541277	−	0.541277i	0.382626	−	0.923903i	$-0.375020\pi$
$557$	−3.96331e6	−	3.96331e6i	−0.541277	−	0.541277i	−0.923903	+	0.382626i	$0.875020\pi$
$558$	−5.21204e6			−0.708634
$559$	4.00618e6	+	4.00618e6i	0.542252	+	0.542252i
$560$	−1.69816e6	−	1.69816e6i	−0.228827	−	0.228827i
$561$	198984.	−	198984.i	0.0266938	−	0.0266938i
$562$	−2.23789e6	+	2.23789e6i	−0.298881	+	0.298881i
$563$	4.95154e6	−	4.95154e6i	0.658368	−	0.658368i	−0.296626	−	0.954994i	$-0.595861\pi$
$563$	4.95154e6	−	4.95154e6i	0.658368	−	0.658368i	0.954994	+	0.296626i	$0.0958613\pi$
$564$	−9.82060e6			−1.29999
$565$		−	2.45971e6i		−	0.324162i
$566$		−	6.96446e6i		−	0.913790i
$567$	−7.02201e6	+	7.02201e6i	−0.917284	+	0.917284i
$568$	2.33384e6	+	2.33384e6i	0.303529	+	0.303529i
$569$		−	6.00322e6i		−	0.777326i	−0.921380	−	0.388663i	$-0.872937\pi$
$569$		−	6.00322e6i		−	0.777326i	0.921380	−	0.388663i	$-0.127063\pi$
$570$	−1.14531e7			−1.47651
$571$	−8.37236e6	+	8.37236e6i	−1.07463	+	1.07463i	−0.0776459	+	0.996981i	$0.524740\pi$
$571$	−8.37236e6	+	8.37236e6i	−1.07463	+	1.07463i	−0.996981	+	0.0776459i	$0.975260\pi$
$572$		−	238798.i		−	0.0305169i
$573$	1.40732e7			1.79063
$574$	1.01677e6	+	6.72204e6i	0.128808	+	0.851571i
$575$	1.17749e6			0.148521
$576$			925711.i			0.116257i
$577$	−3.02191e6	+	3.02191e6i	−0.377870	+	0.377870i	−0.870333	−	0.492463i	$-0.836097\pi$
$577$	−3.02191e6	+	3.02191e6i	−0.377870	+	0.377870i	0.492463	+	0.870333i	$0.336097\pi$
$578$	3.87156e6			0.482022
$579$			5.73116e6i			0.710470i
$580$	−96756.4	−	96756.4i	−0.0119429	−	0.0119429i
$581$	1.35412e6	−	1.35412e6i	0.166424	−	0.166424i
$582$			3.09228e6i			0.378417i
$583$		−	440939.i		−	0.0537288i
$584$	−2.48041e6			−0.300947
$585$	−7.33127e6	+	7.33127e6i	−0.885706	+	0.885706i
$586$	2.74763e6	−	2.74763e6i	0.330532	−	0.330532i
$587$	−6.80234e6	+	6.80234e6i	−0.814823	+	0.814823i	−0.985353	−	0.170530i	$-0.945452\pi$
$587$	−6.80234e6	+	6.80234e6i	−0.814823	+	0.814823i	0.170530	+	0.985353i	$0.445452\pi$
$588$	1.99117e6	+	1.99117e6i	0.237500	+	0.237500i
$589$	−9.07262e6	−	9.07262e6i	−1.07757	−	1.07757i
$590$	154052.			0.0182195
$591$	1.30022e7	+	1.30022e7i	1.53126	+	1.53126i
$592$	1.34851e6			0.158143
$593$	3.59558e6	+	3.59558e6i	0.419887	+	0.419887i	0.885165	−	0.465278i	$-0.154045\pi$
$593$	3.59558e6	+	3.59558e6i	0.419887	+	0.419887i	−0.465278	+	0.885165i	$0.654045\pi$
$594$			28457.5i			0.00330925i
$595$		−	6.30675e6i		−	0.730320i
$596$	−3.93054e6	−	3.93054e6i	−0.453249	−	0.453249i
$597$	−1.17953e7			−1.35448
$598$	6.35712e6	+	6.35712e6i	0.726955	+	0.726955i
$599$	−1.13490e7			−1.29239			−0.646193	−	0.763174i	$-0.723640\pi$
$599$	−1.13490e7			−1.29239			−0.646193	+	0.763174i	$0.723640\pi$
$600$	396475.	+	396475.i	0.0449612	+	0.0449612i
$601$	−8.14940e6	−	8.14940e6i	−0.920321	−	0.920321i	0.0767306	−	0.997052i	$-0.475552\pi$
$601$	−8.14940e6	−	8.14940e6i	−0.920321	−	0.920321i	−0.997052	+	0.0767306i	$0.975552\pi$
$602$	−3.27691e6	+	3.27691e6i	−0.368530	+	0.368530i
$603$	5.70847e6	−	5.70847e6i	0.639332	−	0.639332i
$604$	3.10791e6	−	3.10791e6i	0.346638	−	0.346638i
$605$	−9.54584e6			−1.06029
$606$		−	2.10949e6i		−	0.233344i
$607$			1.34408e7i			1.48066i	0.672246	+	0.740328i	$0.265330\pi$
$607$			1.34408e7i			1.48066i	−0.672246	+	0.740328i	$0.734670\pi$
$608$	−1.61139e6	+	1.61139e6i	−0.176784	+	0.176784i
$609$	348082.	+	348082.i	0.0380311	+	0.0380311i
$610$			1.04341e7i			1.13536i
$611$	−2.18852e7			−2.37163
$612$	−1.71899e6	+	1.71899e6i	−0.185522	+	0.185522i
$613$		−	6.95779e6i		−	0.747860i	−0.927457	−	0.373930i	$-0.878010\pi$
$613$		−	6.95779e6i		−	0.747860i	0.927457	−	0.373930i	$-0.121990\pi$
$614$	3.37128e6			0.360889
$615$	−2.07117e6	−	1.36929e7i	−0.220815	−	1.45985i
$616$	195328.			0.0207402
$617$			5.68522e6i			0.601222i	0.953747	+	0.300611i	$0.0971905\pi$
$617$			5.68522e6i			0.601222i	−0.953747	+	0.300611i	$0.902809\pi$
$618$	7.35676e6	−	7.35676e6i	0.774846	−	0.774846i
$619$	2.05947e6			0.216037			0.108019	−	0.994149i	$-0.465549\pi$
$619$	2.05947e6			0.216037			0.108019	+	0.994149i	$0.465549\pi$
$620$			5.48039e6i			0.572574i
$621$	−757575.	−	757575.i	−0.0788309	−	0.0788309i
$622$	6.06328e6	−	6.06328e6i	0.628393	−	0.628393i
$623$			1.65476e7i			1.70811i
$624$			4.28103e6i			0.440136i
$625$	−1.08662e7			−1.11270
$626$	1.99410e6	−	1.99410e6i	0.203382	−	0.203382i
$627$	658689.	−	658689.i	0.0669131	−	0.0669131i
$628$	−5.29109e6	+	5.29109e6i	−0.535360	+	0.535360i
$629$	2.50411e6	+	2.50411e6i	0.252364	+	0.252364i
$630$	−5.99671e6	−	5.99671e6i	−0.601952	−	0.601952i
$631$	4.16311e6			0.416240			0.208120	−	0.978103i	$-0.433265\pi$
$631$	4.16311e6			0.416240			0.208120	+	0.978103i	$0.433265\pi$
$632$	843665.	+	843665.i	0.0840189	+	0.0840189i
$633$	−1.60678e7			−1.59385
$634$	8.19672e6	+	8.19672e6i	0.809873	+	0.809873i
$635$		−	1.26833e7i		−	1.24824i
$636$			7.90489e6i			0.774913i
$637$	4.43730e6	+	4.43730e6i	0.433282	+	0.433282i
$638$	11129.3			0.00108247
$639$	8.24149e6	+	8.24149e6i	0.798461	+	0.798461i
$640$	973373.			0.0939354
$641$	7.14026e6	+	7.14026e6i	0.686387	+	0.686387i	0.961431	−	0.275045i	$-0.0886927\pi$
$641$	7.14026e6	+	7.14026e6i	0.686387	+	0.686387i	−0.275045	+	0.961431i	$0.588693\pi$
$642$	8.59175e6	+	8.59175e6i	0.822705	+	0.822705i
$643$	1.05059e6	−	1.05059e6i	0.100209	−	0.100209i	−0.655225	−	0.755434i	$-0.727426\pi$
$643$	1.05059e6	−	1.05059e6i	0.100209	−	0.100209i	0.755434	+	0.655225i	$0.227426\pi$
$644$	−5.19989e6	+	5.19989e6i	−0.494060	+	0.494060i
$645$	6.67510e6	−	6.67510e6i	0.631769	−	0.631769i
$646$	−5.98452e6			−0.564219
$647$		−	8.60269e6i		−	0.807930i	−0.914774	−	0.403965i	$-0.867632\pi$
$647$		−	8.60269e6i		−	0.807930i	0.914774	−	0.403965i	$-0.132368\pi$
$648$		−	4.02498e6i		−	0.376553i
$649$	−8859.80	+	8859.80i	−0.000825681	+	0.000825681i
$650$	883543.	+	883543.i	0.0820247	+	0.0820247i
$651$		−	1.97158e7i		−	1.82331i
$652$	−6.51490e6			−0.600190
$653$	1.39043e7	−	1.39043e7i	1.27605	−	1.27605i	0.333184	−	0.942862i	$-0.391877\pi$
$653$	1.39043e7	−	1.39043e7i	1.27605	−	1.27605i	0.942862	−	0.333184i	$-0.108123\pi$
$654$			1.55269e7i			1.41952i
$655$	1.29337e6			0.117793
$656$	−2.21792e6	−	1.63511e6i	−0.201227	−	0.148350i
$657$	−8.75907e6			−0.791671
$658$		−	1.79013e7i		−	1.61183i
$659$	−6.35836e6	+	6.35836e6i	−0.570337	+	0.570337i	−0.932223	−	0.361885i	$-0.882133\pi$
$659$	−6.35836e6	+	6.35836e6i	−0.570337	+	0.570337i	0.361885	+	0.932223i	$0.382133\pi$
$660$	−397886.			−0.0355548
$661$		−	1.18946e7i		−	1.05888i	−0.848349	−	0.529438i	$-0.822403\pi$
$661$		−	1.18946e7i		−	1.05888i	0.848349	−	0.529438i	$-0.177597\pi$
$662$	8.24830e6	+	8.24830e6i	0.731509	+	0.731509i
$663$	−7.94961e6	+	7.94961e6i	−0.702364	+	0.702364i
$664$			776172.i			0.0683184i
$665$		−	2.08770e7i		−	1.83069i
$666$	4.76201e6			0.416011
$667$	−296276.	+	296276.i	−0.0257859	+	0.0257859i
$668$	5.40965e6	−	5.40965e6i	0.469060	−	0.469060i
$669$	2.07878e7	−	2.07878e7i	1.79574	−	1.79574i
$670$	−6.00238e6	−	6.00238e6i	−0.516579	−	0.516579i
$671$	−600087.	−	600087.i	−0.0514527	−	0.0514527i
$672$	−3.50172e6			−0.299129
$673$	3.18643e6	+	3.18643e6i	0.271185	+	0.271185i	0.829577	−	0.558392i	$-0.188581\pi$
$673$	3.18643e6	+	3.18643e6i	0.271185	+	0.271185i	−0.558392	+	0.829577i	$0.688581\pi$
$674$	9.82212e6			0.832828
$675$	−105291.	−	105291.i	−0.00889474	−	0.00889474i
$676$			3.59956e6i			0.302958i
$677$			7.44105e6i			0.623968i	0.950087	+	0.311984i	$0.100994\pi$
$677$			7.44105e6i			0.623968i	−0.950087	+	0.311984i	$0.899006\pi$
$678$	−2.53605e6	−	2.53605e6i	−0.211877	−	0.211877i
$679$	−5.63669e6			−0.469191
$680$	1.80750e6	+	1.80750e6i	0.149901	+	0.149901i
$681$	1.63693e7			1.35258
$682$	−315187.	−	315187.i	−0.0259482	−	0.0259482i
$683$	−6.42073e6	−	6.42073e6i	−0.526663	−	0.526663i	0.392913	−	0.919576i	$-0.371467\pi$
$683$	−6.42073e6	−	6.42073e6i	−0.526663	−	0.526663i	−0.919576	+	0.392913i	$0.871467\pi$
$684$	−5.69031e6	+	5.69031e6i	−0.465046	+	0.465046i
$685$	6.55455e6	−	6.55455e6i	0.533724	−	0.533724i
$686$	3.87680e6	−	3.87680e6i	0.314530	−	0.314530i
$687$	−1.11827e7			−0.903971
$688$		−	1.87830e6i		−	0.151285i
$689$			1.76160e7i			1.41371i
$690$	1.05922e7	−	1.05922e7i	0.846965	−	0.846965i
$691$	−7.89473e6	−	7.89473e6i	−0.628988	−	0.628988i	0.318826	−	0.947813i	$-0.396712\pi$
$691$	−7.89473e6	−	7.89473e6i	−0.628988	−	0.628988i	−0.947813	+	0.318826i	$0.896712\pi$
$692$		−	1.14418e7i		−	0.908298i
$693$	689763.			0.0545591
$694$	1.90878e6	−	1.90878e6i	0.150438	−	0.150438i
$695$		−	9.61574e6i		−	0.755128i
$696$	−199519.			−0.0156121
$697$	−1.08224e6	−	7.15485e6i	−0.0843801	−	0.557852i
$698$	6.82654e6			0.530350
$699$			1.32908e7i			1.02887i
$700$	−722705.	+	722705.i	−0.0557463	+	0.0557463i
$701$	2.74383e6			0.210893			0.105446	−	0.994425i	$-0.466373\pi$
$701$	2.74383e6			0.210893			0.105446	+	0.994425i	$0.466373\pi$
$702$		−	1.13691e6i		−	0.0870727i
$703$	8.28927e6	+	8.28927e6i	0.632598	+	0.632598i
$704$	−55980.4	+	55980.4i	−0.00425701	+	0.00425701i
$705$			3.64651e7i			2.76315i
$706$		−	1.14997e7i		−	0.868310i
$707$	3.84524e6			0.289317
$708$	158833.	−	158833.i	0.0119085	−	0.0119085i
$709$	−4.13423e6	+	4.13423e6i	−0.308872	+	0.308872i	−0.844472	−	0.535600i	$-0.820086\pi$
$709$	−4.13423e6	+	4.13423e6i	−0.308872	+	0.308872i	0.535600	+	0.844472i	$0.320086\pi$
$710$	8.66582e6	−	8.66582e6i	0.645155	−	0.645155i
$711$	2.97924e6	+	2.97924e6i	0.221020	+	0.221020i
$712$	−4.74250e6	−	4.74250e6i	−0.350596	−	0.350596i
$713$	1.67814e7			1.23624
$714$	−6.50249e6	−	6.50249e6i	−0.477347	−	0.477347i
$715$	−886687.			−0.0648642
$716$	−4.03025e6	−	4.03025e6i	−0.293799	−	0.293799i
$717$		−	2.67973e7i		−	1.94667i
$718$			8.24049e6i			0.596543i
$719$	6.43374e6	+	6.43374e6i	0.464131	+	0.464131i	0.900007	−	0.435875i	$-0.143561\pi$
$719$	6.43374e6	+	6.43374e6i	0.464131	+	0.464131i	−0.435875	+	0.900007i	$0.643561\pi$
$720$	3.43728e6			0.247106
$721$	1.34101e7	+	1.34101e7i	0.960713	+	0.960713i
$722$	−9.90594e6			−0.707217
$723$	1.25931e7	+	1.25931e7i	0.895956	+	0.895956i
$724$	−1.55215e6	−	1.55215e6i	−0.110049	−	0.110049i
$725$	−41177.8	+	41177.8i	−0.00290950	+	0.00290950i
$726$	−9.84210e6	+	9.84210e6i	−0.693021	+	0.693021i
$727$	1.42958e7	−	1.42958e7i	1.00317	−	1.00317i	0.00317284	−	0.999995i	$-0.498990\pi$
$727$	1.42958e7	−	1.42958e7i	1.00317	−	1.00317i	0.999995	−	0.00317284i	$-0.00100995\pi$
$728$	−7.80357e6			−0.545714
$729$		−	1.22764e7i		−	0.855562i
$730$			9.21005e6i			0.639668i
$731$	3.48790e6	−	3.48790e6i	0.241418	−	0.241418i
$732$	1.07580e7	+	1.07580e7i	0.742084	+	0.742084i
$733$		−	2.84845e6i		−	0.195816i	−0.995195	−	0.0979081i	$-0.968785\pi$
$733$		−	2.84845e6i		−	0.195816i	0.995195	−	0.0979081i	$-0.0312151\pi$
$734$	−1.08317e7			−0.742092
$735$	7.39344e6	−	7.39344e6i	0.504810	−	0.504810i
$736$		−	2.98055e6i		−	0.202816i
$737$	690416.			0.0468211
$738$	−7.83215e6	−	5.77408e6i	−0.529346	−	0.390249i
$739$	7.85361e6			0.529003			0.264502	−	0.964385i	$-0.414793\pi$
$739$	7.85361e6			0.529003			0.264502	+	0.964385i	$0.414793\pi$
$740$		−	5.00719e6i		−	0.336136i
$741$	−2.63153e7	+	2.63153e7i	−1.76061	+	1.76061i
$742$	−1.44092e7			−0.960796
$743$		−	1.13682e7i		−	0.755477i	−0.925912	−	0.377738i	$-0.876702\pi$
$743$		−	1.13682e7i		−	0.755477i	0.925912	−	0.377738i	$-0.123298\pi$
$744$	5.65048e6	+	5.65048e6i	0.374242	+	0.374242i
$745$	−1.45946e7	+	1.45946e7i	−0.963387	+	0.963387i
$746$			1.27441e7i			0.838424i
$747$			2.74090e6i			0.179718i
$748$	−207905.			−0.0135866
$749$	−1.56613e7	+	1.56613e7i	−1.02005	+	1.02005i
$750$	−9.89998e6	+	9.89998e6i	−0.642660	+	0.642660i
$751$	1.82965e7	−	1.82965e7i	1.18377	−	1.18377i	0.205010	−	0.978760i	$-0.434277\pi$
$751$	1.82965e7	−	1.82965e7i	1.18377	−	1.18377i	0.978760	−	0.205010i	$-0.0657227\pi$
$752$	5.13044e6	+	5.13044e6i	0.330834	+	0.330834i
$753$	1.96549e7	+	1.96549e7i	1.26323	+	1.26323i
$754$	−444626.			−0.0284818
$755$	−1.15400e7	−	1.15400e7i	−0.736784	−	0.736784i
$756$	929947.			0.0591771
$757$	5.67397e6	+	5.67397e6i	0.359871	+	0.359871i	0.863765	−	0.503894i	$-0.168100\pi$
$757$	5.67397e6	+	5.67397e6i	0.359871	+	0.359871i	−0.503894	+	0.863765i	$0.668100\pi$
$758$		−	1.83096e7i		−	1.15746i
$759$			1.21836e6i			0.0767663i
$760$	5.98329e6	+	5.98329e6i	0.375756	+	0.375756i
$761$	1.82708e6			0.114366			0.0571829	−	0.998364i	$-0.481788\pi$
$761$	1.82708e6			0.114366			0.0571829	+	0.998364i	$0.481788\pi$
$762$	−1.30769e7	−	1.30769e7i	−0.815866	−	0.815866i
$763$	−2.83029e7			−1.76003
$764$	−7.35205e6	−	7.35205e6i	−0.455696	−	0.455696i
$765$	6.38282e6	+	6.38282e6i	0.394329	+	0.394329i
$766$	6.20880e6	−	6.20880e6i	0.382328	−	0.382328i
$767$	353959.	−	353959.i	0.0217252	−	0.0217252i
$768$	1.00358e6	−	1.00358e6i	0.0613974	−	0.0613974i
$769$	−5.37745e6			−0.327914			−0.163957	−	0.986467i	$-0.552426\pi$
$769$	−5.37745e6			−0.327914			−0.163957	+	0.986467i	$0.552426\pi$
$770$		−	725277.i		−	0.0440836i
$771$		−	2.79924e7i		−	1.69591i
$772$	2.99405e6	−	2.99405e6i	0.180807	−	0.180807i
$773$	−1.97010e7	−	1.97010e7i	−1.18588	−	1.18588i	−0.978197	−	0.207681i	$-0.933408\pi$
$773$	−1.97010e7	−	1.97010e7i	−1.18588	−	1.18588i	−0.207681	−	0.978197i	$-0.566592\pi$
$774$		−	6.63286e6i		−	0.397968i
$775$	2.33236e6			0.139489
$776$	1.61546e6	−	1.61546e6i	0.0963033	−	0.0963033i
$777$			1.80134e7i			1.07040i
$778$	−1.49727e7			−0.886853
$779$	−3.58249e6	−	2.36845e7i	−0.211515	−	1.39836i
$780$	1.58960e7			0.935515
$781$			996774.i			0.0584749i
$782$	5.53470e6	−	5.53470e6i	0.323651	−	0.323651i
$783$	52985.9			0.00308856
$784$		−	2.08044e6i		−	0.120883i
$785$	1.96465e7	+	1.96465e7i	1.13792	+	1.13792i
$786$	1.33351e6	−	1.33351e6i	0.0769911	−	0.0769911i
$787$		−	1.47773e7i		−	0.850470i	−0.905083	−	0.425235i	$-0.860191\pi$
$787$		−	1.47773e7i		−	0.850470i	0.905083	−	0.425235i	$-0.139809\pi$
$788$		−	1.35852e7i		−	0.779379i
$789$	−8.07861e6			−0.462003
$790$	3.13263e6	−	3.13263e6i	0.178583	−	0.178583i
$791$	4.62278e6	−	4.62278e6i	0.262701	−	0.262701i
$792$	−197684.	+	197684.i	−0.0111985	+	0.0111985i
$793$	2.39741e7	+	2.39741e7i	1.35382	+	1.35382i
$794$	5.44789e6	+	5.44789e6i	0.306674	+	0.306674i
$795$	2.93518e7			1.64709
$796$	6.16206e6	+	6.16206e6i	0.344702	+	0.344702i
$797$	−1.56507e7			−0.872744			−0.436372	−	0.899766i	$-0.643737\pi$
$797$	−1.56507e7			−0.872744			−0.436372	+	0.899766i	$0.643737\pi$
$798$	−2.15250e7	−	2.15250e7i	−1.19656	−	1.19656i
$799$			1.90539e7i			1.05588i
$800$		−	414250.i		−	0.0228843i
$801$	−1.67472e7	−	1.67472e7i	−0.922277	−	0.922277i
$802$	5.62455e6			0.308782
$803$	−529687.	−	529687.i	−0.0289888	−	0.0289888i
$804$	−1.23773e7			−0.675285
$805$	1.93078e7	+	1.93078e7i	1.05013	+	1.05013i
$806$	1.25921e7	+	1.25921e7i	0.682746	+	0.682746i
$807$	−1.58913e6	+	1.58913e6i	−0.0858968	+	0.0858968i
$808$	−1.10203e6	+	1.10203e6i	−0.0593836	+	0.0593836i
$809$	5.67170e6	−	5.67170e6i	0.304679	−	0.304679i	−0.538162	−	0.842841i	$-0.680881\pi$
$809$	5.67170e6	−	5.67170e6i	0.304679	−	0.304679i	0.842841	+	0.538162i	$0.180881\pi$
$810$	−1.49452e7			−0.800368
$811$			1.36785e7i			0.730272i	0.930954	+	0.365136i	$0.118978\pi$
$811$			1.36785e7i			0.730272i	−0.930954	+	0.365136i	$0.881022\pi$
$812$		−	363688.i		−	0.0193570i
$813$	−1.14848e7	+	1.14848e7i	−0.609394	+	0.609394i
$814$	287973.	+	287973.i	0.0152332	+	0.0152332i
$815$			2.41906e7i			1.27571i
$816$	3.72719e6			0.195955
$817$	1.15459e7	−	1.15459e7i	0.605162	−	0.605162i
$818$			1.70345e7i			0.890114i
$819$	−2.75568e7			−1.43555
$820$	−6.07137e6	+	8.23540e6i	−0.315320	+	0.427711i
$821$	2.48377e7			1.28604			0.643019	−	0.765850i	$-0.277681\pi$
$821$	2.48377e7			1.28604			0.643019	+	0.765850i	$0.277681\pi$
$822$		−	1.35160e7i		−	0.697698i
$823$	−1.90881e7	+	1.90881e7i	−0.982341	+	0.982341i	−0.999847	−	0.0175057i	$-0.994427\pi$
$823$	−1.90881e7	+	1.90881e7i	−0.982341	+	0.982341i	0.0175057	+	0.999847i	$0.494427\pi$
$824$	−7.68658e6			−0.394380
$825$			169333.i			0.00866179i
$826$	289525.	+	289525.i	0.0147651	+	0.0147651i
$827$	−1.15768e7	+	1.15768e7i	−0.588608	+	0.588608i	−0.937254	−	0.348647i	$-0.886641\pi$
$827$	−1.15768e7	+	1.15768e7i	−0.588608	+	0.588608i	0.348647	+	0.937254i	$0.386641\pi$
$828$		−	1.05252e7i		−	0.533526i
$829$			1.37041e7i			0.692569i	0.938130	+	0.346284i	$0.112557\pi$
$829$			1.37041e7i			0.692569i	−0.938130	+	0.346284i	$0.887443\pi$
$830$	2.88202e6			0.145212
$831$	7.71940e6	−	7.71940e6i	0.387776	−	0.387776i
$832$	2.23648e6	−	2.23648e6i	0.112010	−	0.112010i
$833$	3.86325e6	−	3.86325e6i	0.192903	−	0.192903i
$834$	−9.91418e6	−	9.91418e6i	−0.493562	−	0.493562i
$835$	−2.00867e7	−	2.00867e7i	−0.996993	−	0.996993i
$836$	−688220.			−0.0340574
$837$	−1.50059e6	−	1.50059e6i	−0.0740369	−	0.0740369i
$838$	−2.30867e7			−1.13567
$839$	−8.17870e6	−	8.17870e6i	−0.401125	−	0.401125i	0.477505	−	0.878629i	$-0.341541\pi$
$839$	−8.17870e6	−	8.17870e6i	−0.401125	−	0.401125i	−0.878629	+	0.477505i	$0.841541\pi$
$840$			1.30023e7i			0.635803i
$841$			2.04904e7i			0.998990i
$842$	1.32954e7	+	1.32954e7i	0.646279	+	0.646279i
$843$	1.71349e7			0.830448
$844$	8.39407e6	+	8.39407e6i	0.405617	+	0.405617i
$845$	1.33656e7			0.643942
$846$	1.81172e7	+	1.81172e7i	0.870291	+	0.870291i
$847$	−1.79404e7	−	1.79404e7i	−0.859260	−	0.859260i
$848$	4.12964e6	−	4.12964e6i	0.197207	−	0.197207i
$849$	−2.66625e7	+	2.66625e7i	−1.26950	+	1.26950i
$850$	769239.	−	769239.i	0.0365186	−	0.0365186i
$851$	−1.53324e7			−0.725750
$852$		−	1.78695e7i		−	0.843363i
$853$		−	2.39894e7i		−	1.12888i	−0.825476	−	0.564438i	$-0.809093\pi$
$853$		−	2.39894e7i		−	1.12888i	0.825476	−	0.564438i	$-0.190907\pi$
$854$	−1.96099e7	+	1.96099e7i	−0.920093	+	0.920093i
$855$	2.11288e7	+	2.11288e7i	0.988462	+	0.988462i
$856$		−	8.97695e6i		−	0.418740i
$857$	4.05571e7			1.88632			0.943160	−	0.332340i	$-0.107838\pi$
$857$	4.05571e7			1.88632			0.943160	+	0.332340i	$0.107838\pi$
$858$	−914206.	+	914206.i	−0.0423961	+	0.0423961i
$859$			1.88386e7i			0.871095i	0.900166	+	0.435548i	$0.143445\pi$
$859$			1.88386e7i			0.871095i	−0.900166	+	0.435548i	$0.856555\pi$
$860$	−6.97437e6			−0.321557
$861$	2.18418e7	−	2.96270e7i	1.00411	−	1.36201i
$862$	−7.78749e6			−0.356968
$863$			7.59157e6i			0.346980i	0.984836	+	0.173490i	$0.0555045\pi$
$863$			7.59157e6i			0.346980i	−0.984836	+	0.173490i	$0.944496\pi$
$864$	−266520.	+	266520.i	−0.0121463	+	0.0121463i
$865$	−4.24847e7			−1.93060
$866$			2.44581e7i			1.10822i
$867$	−1.48217e7	−	1.48217e7i	−0.669656	−	0.669656i
$868$	−1.02998e7	+	1.02998e7i	−0.464014	+	0.464014i
$869$			360326.i			0.0161863i
$870$			740837.i			0.0331837i
$871$	−2.75829e7			−1.23195
$872$	8.11153e6	−	8.11153e6i	0.361253	−	0.361253i
$873$	5.70467e6	−	5.70467e6i	0.253335	−	0.253335i
$874$	1.83213e7	−	1.83213e7i	0.811294	−	0.811294i
$875$	−1.80459e7	−	1.80459e7i	−0.796819	−	0.796819i
$876$	9.49589e6	+	9.49589e6i	0.418096	+	0.418096i
$877$	1.08046e7			0.474360			0.237180	−	0.971466i	$-0.423777\pi$
$877$	1.08046e7			0.474360			0.237180	+	0.971466i	$0.423777\pi$
$878$	2.04936e7	+	2.04936e7i	0.897183	+	0.897183i
$879$	−2.10378e7			−0.918394
$880$	207862.	+	207862.i	0.00904833	+	0.00904833i
$881$		−	1.53139e7i		−	0.664731i	−0.943151	−	0.332365i	$-0.892153\pi$
$881$		−	1.53139e7i		−	0.664731i	0.943151	−	0.332365i	$-0.107847\pi$
$882$		−	7.34666e6i		−	0.317994i
$883$	−2.63579e7	−	2.63579e7i	−1.13765	−	1.13765i	−0.988870	−	0.148779i	$-0.952466\pi$
$883$	−2.63579e7	−	2.63579e7i	−1.13765	−	1.13765i	−0.148779	−	0.988870i	$-0.547534\pi$
$884$	8.30602e6			0.357489
$885$	−589767.	−	589767.i	−0.0253117	−	0.0253117i
$886$	2.26787e7			0.970583
$887$	2.03362e7	+	2.03362e7i	0.867881	+	0.867881i	0.992238	−	0.124356i	$-0.0396866\pi$
$887$	2.03362e7	+	2.03362e7i	0.867881	+	0.867881i	−0.124356	+	0.992238i	$0.539687\pi$
$888$	−5.16260e6	−	5.16260e6i	−0.219703	−	0.219703i
$889$	2.38370e7	−	2.38370e7i	1.01157	−	1.01157i
$890$	−1.76095e7	+	1.76095e7i	−0.745198	+	0.745198i
$891$	859527.	−	859527.i	0.0362715	−	0.0362715i
$892$	−2.17198e7			−0.913995
$893$			6.30734e7i			2.64678i
$894$			3.00951e7i			1.25937i
$895$	−1.49648e7	+	1.49648e7i	−0.624473	+	0.624473i
$896$	1.82936e6	+	1.82936e6i	0.0761252	+	0.0761252i
$897$		−	4.86748e7i		−	2.01987i
$898$	−2.53181e7			−1.04771
$899$	−586857.	+	586857.i	−0.0242177	+	0.0242177i
$900$		−	1.46285e6i		−	0.0601994i
$901$	1.53370e7			0.629403
$902$	−124457.	−	822808.i	−0.00509335	−	0.0336730i
$903$	2.50904e7			1.02397
$904$			2.64975e6i			0.107841i
$905$	−5.76331e6	+	5.76331e6i	−0.233911	+	0.233911i
$906$	−2.37964e7			−0.963143
$907$			4.25606e7i			1.71787i	0.512087	+	0.858934i	$0.328873\pi$
$907$			4.25606e7i			1.71787i	−0.512087	+	0.858934i	$0.671127\pi$
$908$	−8.55160e6	−	8.55160e6i	−0.344217	−	0.344217i
$909$	−3.89162e6	+	3.89162e6i	−0.156214	+	0.156214i
$910$			2.89756e7i			1.15992i
$911$			8.36014e6i			0.333747i	0.985978	+	0.166874i	$0.0533672\pi$
$911$			8.36014e6i			0.333747i	−0.985978	+	0.166874i	$0.946633\pi$
$912$	1.23380e7			0.491198
$913$	−165750.	+	165750.i	−0.00658078	+	0.00658078i
$914$	−2.52509e6	+	2.52509e6i	−0.0999794	+	0.0999794i
$915$	3.99457e7	−	3.99457e7i	1.57731	−	1.57731i
$916$	5.84202e6	+	5.84202e6i	0.230051	+	0.230051i
$917$	2.43076e6	+	2.43076e6i	0.0954594	+	0.0954594i
$918$	−989824.			−0.0387660
$919$	−9.36273e6	−	9.36273e6i	−0.365690	−	0.365690i	0.500212	−	0.865903i	$-0.333255\pi$
$919$	−9.36273e6	−	9.36273e6i	−0.365690	−	0.365690i	−0.865903	+	0.500212i	$0.833255\pi$
$920$	−1.10671e7			−0.431087
$921$	−1.29065e7	−	1.29065e7i	−0.501371	−	0.501371i
$922$		−	1.47648e7i		−	0.572006i
$923$		−	3.98222e7i		−	1.53858i
$924$	−747787.	−	747787.i	−0.0288136	−	0.0288136i
$925$	−2.13097e6			−0.0818887
$926$	2.22486e7	+	2.22486e7i	0.852657	+	0.852657i
$927$	−2.71437e7			−1.03746
$928$	104232.	+	104232.i	0.00397311	+	0.00397311i
$929$	2.66622e7	+	2.66622e7i	1.01358	+	1.01358i	0.999907	+	0.0136686i	$0.00435099\pi$
$929$	2.66622e7	+	2.66622e7i	1.01358	+	1.01358i	0.0136686	+	0.999907i	$0.495649\pi$
$930$	2.09809e7	−	2.09809e7i	0.795457	−	0.795457i
$931$	1.27884e7	−	1.27884e7i	0.483550	−	0.483550i
$932$	6.94335e6	−	6.94335e6i	0.261836	−	0.261836i
$933$	−4.64249e7			−1.74601
$934$		−	1.02750e7i		−	0.385402i
$935$			771975.i			0.0288785i
$936$	7.89769e6	−	7.89769e6i	0.294653	−	0.294653i
$937$	−2.79936e6	−	2.79936e6i	−0.104162	−	0.104162i	0.653105	−	0.757267i	$-0.273466\pi$
$937$	−2.79936e6	−	2.79936e6i	−0.104162	−	0.104162i	−0.757267	+	0.653105i	$0.773466\pi$
$938$		−	2.25618e7i		−	0.837270i
$939$	−1.52683e7			−0.565102
$940$	1.90500e7	−	1.90500e7i	0.703193	−	0.703193i
$941$			1.72126e7i			0.633683i	0.948478	+	0.316842i	$0.102622\pi$
$941$			1.72126e7i			0.633683i	−0.948478	+	0.316842i	$0.897378\pi$
$942$	4.05124e7			1.48751
$943$	2.52175e7	+	1.85910e7i	0.923469	+	0.680807i
$944$	−165954.			−0.00606119
$945$		−	3.45301e6i		−	0.125782i
$946$	401108.	−	401108.i	0.0145725	−	0.0145725i
$947$	1.30939e7			0.474455			0.237228	−	0.971454i	$-0.423761\pi$
$947$	1.30939e7			0.474455			0.237228	+	0.971454i	$0.423761\pi$
$948$		−	6.45971e6i		−	0.233449i
$949$	2.11616e7	+	2.11616e7i	0.762750	+	0.762750i
$950$	2.54638e6	−	2.54638e6i	0.0915408	−	0.0915408i
$951$		−	6.27601e7i		−	2.25026i
$952$			6.79402e6i			0.242960i
$953$	−5.34224e6			−0.190542			−0.0952712	−	0.995451i	$-0.530372\pi$
$953$	−5.34224e6			−0.190542			−0.0952712	+	0.995451i	$0.530372\pi$
$954$	1.45830e7	−	1.45830e7i	0.518773	−	0.518773i
$955$	−2.72991e7	+	2.72991e7i	−0.968589	+	0.968589i
$956$	−1.39994e7	+	1.39994e7i	−0.495408	+	0.495408i
$957$	−42606.9	−	42606.9i	−0.00150383	−	0.00150383i
$958$	−2.46746e7	−	2.46746e7i	−0.868632	−	0.868632i
$959$	2.46372e7			0.865059
$960$	−3.72642e6	−	3.72642e6i	−0.130501	−	0.130501i
$961$	4.61108e6			0.161063
$962$	−1.15048e7	−	1.15048e7i	−0.400813	−	0.400813i
$963$		−	3.17004e7i		−	1.10154i
$964$		−	1.31577e7i		−	0.456023i
$965$	−1.11173e7	−	1.11173e7i	−0.384308	−	0.384308i
$966$	3.98141e7			1.37276
$967$	1.29058e7	+	1.29058e7i	0.443831	+	0.443831i	0.893297	−	0.449466i	$-0.148386\pi$
$967$	1.29058e7	+	1.29058e7i	0.443831	+	0.443831i	−0.449466	+	0.893297i	$0.648386\pi$
$968$	1.02834e7			0.352733
$969$	2.29109e7	+	2.29109e7i	0.783850	+	0.783850i
$970$	−5.99839e6	−	5.99839e6i	−0.204694	−	0.204694i
$971$	1.18191e6	−	1.18191e6i	0.0402286	−	0.0402286i	−0.686706	−	0.726935i	$-0.740944\pi$
$971$	1.18191e6	−	1.18191e6i	0.0402286	−	0.0402286i	0.726935	+	0.686706i	$0.240944\pi$
$972$	−1.43971e7	+	1.43971e7i	−0.488776	+	0.488776i
$973$	1.80718e7	−	1.80718e7i	0.611956	−	0.611956i
$974$	1.49018e7			0.503317
$975$		−	6.76505e6i		−	0.227908i
$976$		−	1.12403e7i		−	0.377706i
$977$	−9.07592e6	+	9.07592e6i	−0.304196	+	0.304196i	−0.842653	−	0.538457i	$-0.819008\pi$
$977$	−9.07592e6	+	9.07592e6i	−0.304196	+	0.304196i	0.538457	+	0.842653i	$0.319008\pi$
$978$	2.49414e7	+	2.49414e7i	0.833823	+	0.833823i
$979$		−	2.02551e6i		−	0.0675425i
$980$	−7.72491e6			−0.256938
$981$	2.86443e7	−	2.86443e7i	0.950311	−	0.950311i
$982$		−	4.51563e6i		−	0.149431i
$983$	1.38808e7			0.458175			0.229088	−	0.973406i	$-0.426426\pi$
$983$	1.38808e7			0.458175			0.229088	+	0.973406i	$0.426426\pi$
$984$	2.23119e6	+	1.47508e7i	0.0734597	+	0.485655i
$985$	−5.04433e7			−1.65658
$986$			387105.i			0.0126805i
$987$	−6.85325e7	+	6.85325e7i	−2.23926	+	2.23926i
$988$	2.74951e7			0.896114
$989$			2.13561e7i			0.694274i
$990$	734025.	+	734025.i	0.0238025	+	0.0238025i
$991$	−2.70792e6	+	2.70792e6i	−0.0875894	+	0.0875894i	−0.749544	−	0.661955i	$-0.769727\pi$
$991$	−2.70792e6	+	2.70792e6i	−0.0875894	+	0.0875894i	0.661955	+	0.749544i	$0.269727\pi$
$992$		−	5.90380e6i		−	0.190482i
$993$		−	6.31550e7i		−	2.03252i
$994$	3.25731e7			1.04567
$995$	2.28805e7	−	2.28805e7i	0.732669	−	0.732669i
$996$	2.97147e6	−	2.97147e6i	0.0949124	−	0.0949124i
$997$	3.77834e7	−	3.77834e7i	1.20383	−	1.20383i	0.230832	−	0.972994i	$-0.425855\pi$
$997$	3.77834e7	−	3.77834e7i	1.20383	−	1.20383i	0.972994	−	0.230832i	$-0.0741447\pi$
$998$	−2.54433e7	−	2.54433e7i	−0.808624	−	0.808624i
$999$	1.37102e6	+	1.37102e6i	0.0434642	+	0.0434642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.c.a.73.8	yes	16
41.9	even	4	inner	82.6.c.a.9.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.c.a.9.8	✓	16	41.9	even	4	inner
82.6.c.a.73.8	yes	16	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	82.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+4.00000i q^{2} +(15.3135 - 15.3135i) q^{3} -16.0000 q^{4} +59.4099i q^{5} +(61.2538 + 61.2538i) q^{6} +(-111.655 + 111.655i) q^{7} -64.0000i q^{8} -226.004i q^{9} -237.640 q^{10} +(13.6671 - 13.6671i) q^{11} +(-245.015 + 245.015i) q^{12} +(-546.015 + 546.015i) q^{13} +(-446.620 - 446.620i) q^{14} +(909.771 + 909.771i) q^{15} +256.000 q^{16} +(475.377 + 475.377i) q^{17} +904.014 q^{18} +(1573.62 + 1573.62i) q^{19} -950.559i q^{20} +3419.65i q^{21} +(54.6684 + 54.6684i) q^{22} -2910.69 q^{23} +(-980.061 - 980.061i) q^{24} -404.541 q^{25} +(-2184.06 - 2184.06i) q^{26} +(260.273 + 260.273i) q^{27} +(1786.48 - 1786.48i) q^{28} +(101.789 - 101.789i) q^{29} +(-3639.09 + 3639.09i) q^{30} -5765.43 q^{31} +1024.00i q^{32} -418.581i q^{33} +(-1901.51 + 1901.51i) q^{34} +(-6633.42 - 6633.42i) q^{35} +3616.06i q^{36} +5267.63 q^{37} +(-6294.50 + 6294.50i) q^{38} +16722.8i q^{39} +3802.24 q^{40} +(-8663.74 - 6387.16i) q^{41} -13678.6 q^{42} -7337.12i q^{43} +(-218.674 + 218.674i) q^{44} +13426.9 q^{45} -11642.8i q^{46} +(20040.8 + 20040.8i) q^{47} +(3920.24 - 3920.24i) q^{48} -8126.70i q^{49} -1618.17i q^{50} +14559.3 q^{51} +(8736.25 - 8736.25i) q^{52} +(16131.4 - 16131.4i) q^{53} +(-1041.09 + 1041.09i) q^{54} +(811.961 + 811.961i) q^{55} +(7145.92 + 7145.92i) q^{56} +48195.2 q^{57} +(407.156 + 407.156i) q^{58} -648.258 q^{59} +(-14556.3 - 14556.3i) q^{60} -43907.4i q^{61} -23061.7i q^{62} +(25234.4 + 25234.4i) q^{63} -4096.00 q^{64} +(-32438.7 - 32438.7i) q^{65} +1674.32 q^{66} +(25258.3 + 25258.3i) q^{67} +(-7606.03 - 7606.03i) q^{68} +(-44572.7 + 44572.7i) q^{69} +(26533.7 - 26533.7i) q^{70} +(-36466.2 + 36466.2i) q^{71} -14464.2 q^{72} -38756.3i q^{73} +21070.5i q^{74} +(-6194.93 + 6194.93i) q^{75} +(-25178.0 - 25178.0i) q^{76} +3052.00i q^{77} -66891.0 q^{78} +(-13182.3 + 13182.3i) q^{79} +15208.9i q^{80} +62890.2 q^{81} +(25548.6 - 34655.0i) q^{82} -12127.7 q^{83} -54714.4i q^{84} +(-28242.1 + 28242.1i) q^{85} +29348.5 q^{86} -3117.48i q^{87} +(-874.694 - 874.694i) q^{88} +(74101.6 - 74101.6i) q^{89} +53707.4i q^{90} -121931. i q^{91} +46571.0 q^{92} +(-88288.7 + 88288.7i) q^{93} +(-80163.2 + 80163.2i) q^{94} +(-93488.9 + 93488.9i) q^{95} +(15681.0 + 15681.0i) q^{96} +(25241.5 + 25241.5i) q^{97} +32506.8 q^{98} +(-3088.81 - 3088.81i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{3} - 256 q^{4} - 8 q^{6} - 100 q^{7} - 160 q^{10} - 418 q^{11} + 32 q^{12} - 194 q^{13} - 400 q^{14} + 1576 q^{15} + 4096 q^{16} + 2508 q^{17} + 3888 q^{18} + 1458 q^{19} - 1672 q^{22} + 11312 q^{23}+ \cdots + 266182 q^{99}+O(q^{100}) \) 16 * q - 2 * q^3 - 256 * q^4 - 8 * q^6 - 100 * q^7 - 160 * q^10 - 418 * q^11 + 32 * q^12 - 194 * q^13 - 400 * q^14 + 1576 * q^15 + 4096 * q^16 + 2508 * q^17 + 3888 * q^18 + 1458 * q^19 - 1672 * q^22 + 11312 * q^23 + 128 * q^24 - 1408 * q^25 - 776 * q^26 + 10264 * q^27 + 1600 * q^28 + 6942 * q^29 - 6304 * q^30 - 2064 * q^31 - 10032 * q^34 - 896 * q^35 - 42716 * q^37 - 5832 * q^38 + 2560 * q^40 + 24566 * q^41 + 12000 * q^42 + 6688 * q^44 + 33760 * q^45 - 8740 * q^47 - 512 * q^48 - 45076 * q^51 + 3104 * q^52 + 16066 * q^53 - 41056 * q^54 + 31288 * q^55 + 6400 * q^56 - 12948 * q^57 + 27768 * q^58 - 35932 * q^59 - 25216 * q^60 + 61456 * q^63 - 65536 * q^64 - 3908 * q^65 + 46384 * q^66 - 6270 * q^67 - 40128 * q^68 - 98616 * q^69 + 3584 * q^70 - 130568 * q^71 - 62208 * q^72 - 139070 * q^75 - 23328 * q^76 - 51648 * q^78 - 18212 * q^79 + 202436 * q^81 + 59784 * q^82 - 245784 * q^83 - 153632 * q^85 + 218336 * q^86 + 26752 * q^88 + 301716 * q^89 - 180992 * q^92 + 44488 * q^93 + 34960 * q^94 - 54892 * q^95 - 2048 * q^96 + 224176 * q^97 + 302336 * q^98 + 266182 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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