LMFDB - Embedded newform 82.6.c.a.73.7

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			73.7
Root			$-15.0753 - 15.0753i$ of defining polynomial
Character	$\chi$	$=$	82.73
Dual form			82.6.c.a.9.7

$q$-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} +(15.0753 - 15.0753i) q^{3} -16.0000 q^{4} -29.0716i q^{5} +(60.3011 + 60.3011i) q^{6} +(1.29408 - 1.29408i) q^{7} -64.0000i q^{8} -211.528i q^{9} +116.286 q^{10} +(90.7123 - 90.7123i) q^{11} +(-241.205 + 241.205i) q^{12} +(438.083 - 438.083i) q^{13} +(5.17633 + 5.17633i) q^{14} +(-438.262 - 438.262i) q^{15} +256.000 q^{16} +(-1538.58 - 1538.58i) q^{17} +846.114 q^{18} +(-1320.70 - 1320.70i) q^{19} +465.145i q^{20} -39.0173i q^{21} +(362.849 + 362.849i) q^{22} +796.221 q^{23} +(-964.818 - 964.818i) q^{24} +2279.84 q^{25} +(1752.33 + 1752.33i) q^{26} +(474.443 + 474.443i) q^{27} +(-20.7053 + 20.7053i) q^{28} +(2187.02 - 2187.02i) q^{29} +(1753.05 - 1753.05i) q^{30} +174.422 q^{31} +1024.00i q^{32} -2735.03i q^{33} +(6154.33 - 6154.33i) q^{34} +(-37.6210 - 37.6210i) q^{35} +3384.45i q^{36} -1072.33 q^{37} +(5282.80 - 5282.80i) q^{38} -13208.4i q^{39} -1860.58 q^{40} +(7458.36 + 7760.74i) q^{41} +156.069 q^{42} -4353.29i q^{43} +(-1451.40 + 1451.40i) q^{44} -6149.46 q^{45} +3184.88i q^{46} +(9984.85 + 9984.85i) q^{47} +(3859.27 - 3859.27i) q^{48} +16803.7i q^{49} +9119.38i q^{50} -46389.2 q^{51} +(-7009.33 + 7009.33i) q^{52} +(-7743.18 + 7743.18i) q^{53} +(-1897.77 + 1897.77i) q^{54} +(-2637.15 - 2637.15i) q^{55} +(-82.8212 - 82.8212i) q^{56} -39819.9 q^{57} +(8748.08 + 8748.08i) q^{58} -18613.4 q^{59} +(7012.19 + 7012.19i) q^{60} +12279.5i q^{61} +697.690i q^{62} +(-273.735 - 273.735i) q^{63} -4096.00 q^{64} +(-12735.8 - 12735.8i) q^{65} +10940.1 q^{66} +(-1586.86 - 1586.86i) q^{67} +(24617.3 + 24617.3i) q^{68} +(12003.3 - 12003.3i) q^{69} +(150.484 - 150.484i) q^{70} +(-3331.87 + 3331.87i) q^{71} -13537.8 q^{72} +53891.1i q^{73} -4289.33i q^{74} +(34369.3 - 34369.3i) q^{75} +(21131.2 + 21131.2i) q^{76} -234.778i q^{77} +52833.8 q^{78} +(25621.2 - 25621.2i) q^{79} -7442.32i q^{80} +65706.1 q^{81} +(-31043.0 + 29833.4i) q^{82} +39021.7 q^{83} +624.277i q^{84} +(-44729.0 + 44729.0i) q^{85} +17413.2 q^{86} -65939.9i q^{87} +(-5805.59 - 5805.59i) q^{88} +(26981.0 - 26981.0i) q^{89} -24597.8i q^{90} -1133.83i q^{91} -12739.5 q^{92} +(2629.47 - 2629.47i) q^{93} +(-39939.4 + 39939.4i) q^{94} +(-38394.8 + 38394.8i) q^{95} +(15437.1 + 15437.1i) q^{96} +(19676.4 + 19676.4i) q^{97} -67214.6 q^{98} +(-19188.2 - 19188.2i) 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
$3$	15.0753	−	15.0753i	0.967080	−	0.967080i	−0.0323952	−	0.999475i	$-0.510314\pi$
$3$	15.0753	−	15.0753i	0.967080	−	0.967080i	0.999475	+	0.0323952i	$0.0103135\pi$
$4$	−16.0000			−0.500000
$5$		−	29.0716i		−	0.520048i	−0.965602	−	0.260024i	$-0.916270\pi$
$5$		−	29.0716i		−	0.520048i	0.965602	−	0.260024i	$-0.0837305\pi$
$6$	60.3011	+	60.3011i	0.683829	+	0.683829i
$7$	1.29408	−	1.29408i	0.00998198	−	0.00998198i	−0.702098	−	0.712080i	$-0.747753\pi$
$7$	1.29408	−	1.29408i	0.00998198	−	0.00998198i	0.712080	+	0.702098i	$0.247753\pi$
$8$		−	64.0000i		−	0.353553i
$9$		−	211.528i		−	0.870487i
$10$	116.286			0.367729
$11$	90.7123	−	90.7123i	0.226040	−	0.226040i	−0.584996	−	0.811036i	$-0.698904\pi$
$11$	90.7123	−	90.7123i	0.226040	−	0.226040i	0.811036	+	0.584996i	$0.198904\pi$
$12$	−241.205	+	241.205i	−0.483540	+	0.483540i
$13$	438.083	−	438.083i	0.718949	−	0.718949i	−0.249441	−	0.968390i	$-0.580247\pi$
$13$	438.083	−	438.083i	0.718949	−	0.718949i	0.968390	+	0.249441i	$0.0802470\pi$
$14$	5.17633	+	5.17633i	0.00705832	+	0.00705832i
$15$	−438.262	−	438.262i	−0.502928	−	0.502928i
$16$	256.000			0.250000
$17$	−1538.58	−	1538.58i	−1.29122	−	1.29122i	−0.934036	−	0.357180i	$-0.883738\pi$
$17$	−1538.58	−	1538.58i	−1.29122	−	1.29122i	−0.357180	−	0.934036i	$-0.616262\pi$
$18$	846.114			0.615527
$19$	−1320.70	−	1320.70i	−0.839306	−	0.839306i	0.149461	−	0.988768i	$-0.452246\pi$
$19$	−1320.70	−	1320.70i	−0.839306	−	0.839306i	−0.988768	+	0.149461i	$0.952246\pi$
$20$			465.145i			0.260024i
$21$		−	39.0173i		−	0.0193067i
$22$	362.849	+	362.849i	0.159834	+	0.159834i
$23$	796.221			0.313844			0.156922	−	0.987611i	$-0.449843\pi$
$23$	796.221			0.313844			0.156922	+	0.987611i	$0.449843\pi$
$24$	−964.818	−	964.818i	−0.341914	−	0.341914i
$25$	2279.84			0.729550
$26$	1752.33	+	1752.33i	0.508373	+	0.508373i
$27$	474.443	+	474.443i	0.125249	+	0.125249i
$28$	−20.7053	+	20.7053i	−0.00499099	+	0.00499099i
$29$	2187.02	−	2187.02i	0.482900	−	0.482900i	−0.423156	−	0.906057i	$-0.639078\pi$
$29$	2187.02	−	2187.02i	0.482900	−	0.482900i	0.906057	+	0.423156i	$0.139078\pi$
$30$	1753.05	−	1753.05i	0.355624	−	0.355624i
$31$	174.422			0.0325985			0.0162993	−	0.999867i	$-0.494812\pi$
$31$	174.422			0.0325985			0.0162993	+	0.999867i	$0.494812\pi$
$32$			1024.00i			0.176777i
$33$		−	2735.03i		−	0.437197i
$34$	6154.33	−	6154.33i	0.913027	−	0.913027i
$35$	−37.6210	−	37.6210i	−0.00519111	−	0.00519111i
$36$			3384.45i			0.435244i
$37$	−1072.33			−0.128773			−0.0643865	−	0.997925i	$-0.520509\pi$
$37$	−1072.33			−0.128773			−0.0643865	+	0.997925i	$0.520509\pi$
$38$	5282.80	−	5282.80i	0.593479	−	0.593479i
$39$		−	13208.4i		−	1.39056i
$40$	−1860.58			−0.183865
$41$	7458.36	+	7760.74i	0.692921	+	0.721014i
$41$	7458.36	+	7760.74i	0.692921	+	0.721014i
$42$	156.069			0.0136519
$43$		−	4353.29i		−	0.359043i	−0.983754	−	0.179522i	$-0.942545\pi$
$43$		−	4353.29i		−	0.359043i	0.983754	−	0.179522i	$-0.0574550\pi$
$44$	−1451.40	+	1451.40i	−0.113020	+	0.113020i
$45$	−6149.46			−0.452695
$46$			3184.88i			0.221921i
$47$	9984.85	+	9984.85i	0.659321	+	0.659321i	0.955219	−	0.295898i	$-0.0956189\pi$
$47$	9984.85	+	9984.85i	0.659321	+	0.659321i	−0.295898	+	0.955219i	$0.595619\pi$
$48$	3859.27	−	3859.27i	0.241770	−	0.241770i
$49$			16803.7i			0.999801i
$50$			9119.38i			0.515870i
$51$	−46389.2			−2.49742
$52$	−7009.33	+	7009.33i	−0.359474	+	0.359474i
$53$	−7743.18	+	7743.18i	−0.378643	+	0.378643i	−0.870612	−	0.491970i	$-0.836277\pi$
$53$	−7743.18	+	7743.18i	−0.378643	+	0.378643i	0.491970	+	0.870612i	$0.336277\pi$
$54$	−1897.77	+	1897.77i	−0.0885646	+	0.0885646i
$55$	−2637.15	−	2637.15i	−0.117551	−	0.117551i
$56$	−82.8212	−	82.8212i	−0.00352916	−	0.00352916i
$57$	−39819.9			−1.62335
$58$	8748.08	+	8748.08i	0.341462	+	0.341462i
$59$	−18613.4			−0.696139			−0.348070	−	0.937469i	$-0.613163\pi$
$59$	−18613.4			−0.696139			−0.348070	+	0.937469i	$0.613163\pi$
$60$	7012.19	+	7012.19i	0.251464	+	0.251464i
$61$			12279.5i			0.422528i	0.977429	+	0.211264i	$0.0677580\pi$
$61$			12279.5i			0.422528i	−0.977429	+	0.211264i	$0.932242\pi$
$62$			697.690i			0.0230506i
$63$	−273.735	−	273.735i	−0.00868918	−	0.00868918i
$64$	−4096.00			−0.125000
$65$	−12735.8	−	12735.8i	−0.373888	−	0.373888i
$66$	10940.1			0.309145
$67$	−1586.86	−	1586.86i	−0.0431870	−	0.0431870i	0.685184	−	0.728370i	$-0.259722\pi$
$67$	−1586.86	−	1586.86i	−0.0431870	−	0.0431870i	−0.728370	+	0.685184i	$0.759722\pi$
$68$	24617.3	+	24617.3i	0.645608	+	0.645608i
$69$	12003.3	−	12003.3i	0.303512	−	0.303512i
$70$	150.484	−	150.484i	0.00367067	−	0.00367067i
$71$	−3331.87	+	3331.87i	−0.0784408	+	0.0784408i	−0.745239	−	0.666798i	$-0.767664\pi$
$71$	−3331.87	+	3331.87i	−0.0784408	+	0.0784408i	0.666798	+	0.745239i	$0.267664\pi$
$72$	−13537.8			−0.307764
$73$			53891.1i			1.18361i	0.806080	+	0.591807i	$0.201585\pi$
$73$			53891.1i			1.18361i	−0.806080	+	0.591807i	$0.798415\pi$
$74$		−	4289.33i		−	0.0910563i
$75$	34369.3	−	34369.3i	0.705533	−	0.705533i
$76$	21131.2	+	21131.2i	0.419653	+	0.419653i
$77$		−	234.778i		−	0.00451264i
$78$	52833.8			0.983276
$79$	25621.2	−	25621.2i	0.461883	−	0.461883i	−0.437389	−	0.899272i	$-0.644097\pi$
$79$	25621.2	−	25621.2i	0.461883	−	0.461883i	0.899272	+	0.437389i	$0.144097\pi$
$80$		−	7442.32i		−	0.130012i
$81$	65706.1			1.11274
$82$	−31043.0	+	29833.4i	−0.509834	+	0.489969i
$83$	39021.7			0.621743			0.310872	−	0.950452i	$-0.399379\pi$
$83$	39021.7			0.621743			0.310872	+	0.950452i	$0.399379\pi$
$84$			624.277i			0.00965337i
$85$	−44729.0	+	44729.0i	−0.671494	+	0.671494i
$86$	17413.2			0.253882
$87$		−	65939.9i		−	0.934007i
$88$	−5805.59	−	5805.59i	−0.0799170	−	0.0799170i
$89$	26981.0	−	26981.0i	0.361064	−	0.361064i	−0.503141	−	0.864204i	$-0.667822\pi$
$89$	26981.0	−	26981.0i	0.361064	−	0.361064i	0.864204	+	0.503141i	$0.167822\pi$
$90$		−	24597.8i		−	0.320104i
$91$		−	1133.83i		−	0.0143531i
$92$	−12739.5			−0.156922
$93$	2629.47	−	2629.47i	0.0315254	−	0.0315254i
$94$	−39939.4	+	39939.4i	−0.466211	+	0.466211i
$95$	−38394.8	+	38394.8i	−0.436479	+	0.436479i
$96$	15437.1	+	15437.1i	0.170957	+	0.170957i
$97$	19676.4	+	19676.4i	0.212333	+	0.212333i	0.805258	−	0.592925i	$-0.202027\pi$
$97$	19676.4	+	19676.4i	0.212333	+	0.212333i	−0.592925	+	0.805258i	$0.702027\pi$
$98$	−67214.6			−0.706966
$99$	−19188.2	−	19188.2i	−0.196765	−	0.196765i
$100$	−36477.5			−0.364775
$101$	−94917.4	−	94917.4i	−0.925854	−	0.925854i	0.0715807	−	0.997435i	$-0.477196\pi$
$101$	−94917.4	−	94917.4i	−0.925854	−	0.925854i	−0.997435	+	0.0715807i	$0.977196\pi$
$102$		−	185557.i		−	1.76594i
$103$			39232.3i			0.364377i	0.983264	+	0.182188i	$0.0583181\pi$
$103$			39232.3i			0.364377i	−0.983264	+	0.182188i	$0.941682\pi$
$104$	−28037.3	−	28037.3i	−0.254187	−	0.254187i
$105$	−1134.29			−0.0100404
$106$	−30972.7	−	30972.7i	−0.267741	−	0.267741i
$107$	56249.6			0.474964			0.237482	−	0.971392i	$-0.423678\pi$
$107$	56249.6			0.474964			0.237482	+	0.971392i	$0.423678\pi$
$108$	−7591.09	−	7591.09i	−0.0626246	−	0.0626246i
$109$	74716.8	+	74716.8i	0.602354	+	0.602354i	0.940937	−	0.338582i	$-0.109947\pi$
$109$	74716.8	+	74716.8i	0.602354	+	0.602354i	−0.338582	+	0.940937i	$0.609947\pi$
$110$	10548.6	−	10548.6i	0.0831214	−	0.0831214i
$111$	−16165.7	+	16165.7i	−0.124534	+	0.124534i
$112$	331.285	−	331.285i	0.00249549	−	0.00249549i
$113$	101323.			0.746468			0.373234	−	0.927737i	$-0.378249\pi$
$113$	101323.			0.746468			0.373234	+	0.927737i	$0.378249\pi$
$114$		−	159280.i		−	1.14788i
$115$		−	23147.4i		−	0.163214i
$116$	−34992.3	+	34992.3i	−0.241450	+	0.241450i
$117$	−92667.0	−	92667.0i	−0.625836	−	0.625836i
$118$		−	74453.7i		−	0.492245i
$119$	−3982.10			−0.0257778
$120$	−28048.8	+	28048.8i	−0.177812	+	0.177812i
$121$			144594.i			0.897812i
$122$	−49118.0			−0.298773
$123$	229432.	+	4558.53i	1.36739	+	0.0271683i
$124$	−2790.76			−0.0162993
$125$		−	157127.i		−	0.899449i
$126$	1094.94	−	1094.94i	0.00614418	−	0.00614418i
$127$	350446.			1.92802			0.964011	−	0.265864i	$-0.0856572\pi$
$127$	350446.			1.92802			0.964011	+	0.265864i	$0.0856572\pi$
$128$		−	16384.0i		−	0.0883883i
$129$	−65627.1	−	65627.1i	−0.347223	−	0.347223i
$130$	50943.0	−	50943.0i	0.264379	−	0.264379i
$131$			132949.i			0.676872i	0.940989	+	0.338436i	$0.109898\pi$
$131$			132949.i			0.676872i	−0.940989	+	0.338436i	$0.890102\pi$
$132$			43760.4i			0.218598i
$133$	−3418.19			−0.0167559
$134$	6347.46	−	6347.46i	0.0305378	−	0.0305378i
$135$	13792.8	−	13792.8i	0.0651356	−	0.0651356i
$136$	−98469.3	+	98469.3i	−0.456514	+	0.456514i
$137$	−209109.	−	209109.i	−0.951855	−	0.951855i	0.0470384	−	0.998893i	$-0.485022\pi$
$137$	−209109.	−	209109.i	−0.951855	−	0.951855i	−0.998893	+	0.0470384i	$0.985022\pi$
$138$	48013.0	+	48013.0i	0.214616	+	0.214616i
$139$	53031.6			0.232808			0.116404	−	0.993202i	$-0.462863\pi$
$139$	53031.6			0.232808			0.116404	+	0.993202i	$0.462863\pi$
$140$	601.936	+	601.936i	0.00259555	+	0.00259555i
$141$	301049.			1.27523
$142$	−13327.5	−	13327.5i	−0.0554660	−	0.0554660i
$143$		−	79479.0i		−	0.325022i
$144$		−	54151.3i		−	0.217622i
$145$	−63580.1	−	63580.1i	−0.251131	−	0.251131i
$146$	−215564.			−0.836941
$147$	253320.	+	253320.i	0.966887	+	0.966887i
$148$	17157.3			0.0643865
$149$	−194432.	−	194432.i	−0.717468	−	0.717468i	0.250618	−	0.968086i	$-0.419366\pi$
$149$	−194432.	−	194432.i	−0.717468	−	0.717468i	−0.968086	+	0.250618i	$0.919366\pi$
$150$	137477.	+	137477.i	0.498887	+	0.498887i
$151$	−355880.	+	355880.i	−1.27017	+	1.27017i	−0.324167	+	0.946000i	$0.605084\pi$
$151$	−355880.	+	355880.i	−1.27017	+	1.27017i	−0.946000	+	0.324167i	$0.894916\pi$
$152$	−84524.8	+	84524.8i	−0.296740	+	0.296740i
$153$	−325454.	+	325454.i	−1.12399	+	1.12399i
$154$	939.113			0.00319092
$155$		−	5070.73i		−	0.0169528i
$156$			211335.i			0.695281i
$157$	−169591.	+	169591.i	−0.549102	+	0.549102i	−0.926181	−	0.377079i	$-0.876928\pi$
$157$	−169591.	+	169591.i	−0.549102	+	0.549102i	0.377079	+	0.926181i	$0.376928\pi$
$158$	102485.	+	102485.i	0.326601	+	0.326601i
$159$			233461.i			0.732355i
$160$	29769.3			0.0919324
$161$	1030.38	−	1030.38i	0.00313279	−	0.00313279i
$162$			262825.i			0.786825i
$163$	640203.			1.88733			0.943667	−	0.330897i	$-0.107351\pi$
$163$	640203.			1.88733			0.943667	+	0.330897i	$0.107351\pi$
$164$	−119334.	−	124172.i	−0.346460	−	0.360507i
$165$	−79511.5			−0.227363
$166$			156087.i			0.439639i
$167$	−70046.6	+	70046.6i	−0.194355	+	0.194355i	−0.797575	−	0.603220i	$-0.793884\pi$
$167$	−70046.6	+	70046.6i	−0.194355	+	0.194355i	0.603220	+	0.797575i	$0.293884\pi$
$168$	−2497.11			−0.00682596
$169$		−	12540.1i		−	0.0337742i
$170$	−178916.	−	178916.i	−0.474818	−	0.474818i
$171$	−279366.	+	279366.i	−0.730605	+	0.730605i
$172$			69652.7i			0.179522i
$173$		−	526318.i		−	1.33700i	−0.743710	−	0.668502i	$-0.766936\pi$
$173$		−	526318.i		−	1.33700i	0.743710	−	0.668502i	$-0.233064\pi$
$174$	263759.			0.660442
$175$	2950.30	−	2950.30i	0.00728235	−	0.00728235i
$176$	23222.3	−	23222.3i	0.0565099	−	0.0565099i
$177$	−280603.	+	280603.i	−0.673222	+	0.673222i
$178$	107924.	+	107924.i	0.255310	+	0.255310i
$179$	73671.0	+	73671.0i	0.171856	+	0.171856i	0.787794	−	0.615938i	$-0.211223\pi$
$179$	73671.0	+	73671.0i	0.171856	+	0.171856i	−0.615938	+	0.787794i	$0.711223\pi$
$180$	98391.4			0.226348
$181$	−545651.	−	545651.i	−1.23799	−	1.23799i	−0.960819	−	0.277176i	$-0.910602\pi$
$181$	−545651.	−	545651.i	−1.23799	−	1.23799i	−0.277176	−	0.960819i	$-0.589398\pi$
$182$	4535.32			0.0101491
$183$	185117.	+	185117.i	0.408619	+	0.408619i
$184$		−	50958.2i		−	0.110961i
$185$			31174.4i			0.0669682i
$186$	10517.9	+	10517.9i	0.0222918	+	0.0222918i
$187$	−279137.			−0.583731
$188$	−159758.	−	159758.i	−0.329661	−	0.329661i
$189$	1227.94			0.00250047
$190$	−153579.	−	153579.i	−0.308638	−	0.308638i
$191$	−48418.4	−	48418.4i	−0.0960345	−	0.0960345i	0.657457	−	0.753492i	$-0.271632\pi$
$191$	−48418.4	−	48418.4i	−0.0960345	−	0.0960345i	−0.753492	+	0.657457i	$0.771632\pi$
$192$	−61748.4	+	61748.4i	−0.120885	+	0.120885i
$193$	527106.	−	527106.i	1.01860	−	1.01860i	0.0187796	−	0.999824i	$-0.494022\pi$
$193$	527106.	−	527106.i	1.01860	−	1.01860i	0.999824	−	0.0187796i	$-0.00597809\pi$
$194$	−78705.7	+	78705.7i	−0.150142	+	0.150142i
$195$	−383990.			−0.723159
$196$		−	268858.i		−	0.499900i
$197$		−	30753.1i		−	0.0564576i	−0.999601	−	0.0282288i	$-0.991013\pi$
$197$		−	30753.1i		−	0.0564576i	0.999601	−	0.0282288i	$-0.00898671\pi$
$198$	76752.9	−	76752.9i	0.139134	−	0.139134i
$199$	475668.	+	475668.i	0.851475	+	0.851475i	0.990315	−	0.138840i	$-0.0443375\pi$
$199$	475668.	+	475668.i	0.851475	+	0.851475i	−0.138840	+	0.990315i	$0.544337\pi$
$200$		−	145910.i		−	0.257935i
$201$	−47844.9			−0.0835305
$202$	379670.	−	379670.i	0.654678	−	0.654678i
$203$		−	5660.36i		−	0.00964060i
$204$	742227.			1.24871
$205$	225617.	−	216826.i	0.374962	−	0.360352i
$206$	−156929.			−0.257653
$207$		−	168423.i		−	0.273197i
$208$	112149.	−	112149.i	0.179737	−	0.179737i
$209$	−239608.			−0.379433
$210$		−	4537.18i		−	0.00709966i
$211$	−106423.	−	106423.i	−0.164561	−	0.164561i	0.620023	−	0.784584i	$-0.287123\pi$
$211$	−106423.	−	106423.i	−0.164561	−	0.164561i	−0.784584	+	0.620023i	$0.787123\pi$
$212$	123891.	−	123891.i	0.189321	−	0.189321i
$213$			100458.i			0.151717i
$214$			224999.i			0.335850i
$215$	−126557.			−0.186720
$216$	30364.4	−	30364.4i	0.0442823	−	0.0442823i
$217$	225.717	−	225.717i	0.000325398	−	0.000325398i
$218$	−298867.	+	298867.i	−0.425929	+	0.425929i
$219$	812423.	+	812423.i	1.14465	+	1.14465i
$220$	42194.4	+	42194.4i	0.0587757	+	0.0587757i
$221$	−1.34805e6			−1.85663
$222$	−64662.9	−	64662.9i	−0.0880587	−	0.0880587i
$223$	1.22912e6			1.65513			0.827564	−	0.561372i	$-0.189726\pi$
$223$	1.22912e6			1.65513			0.827564	+	0.561372i	$0.189726\pi$
$224$	1325.14	+	1325.14i	0.00176458	+	0.00176458i
$225$		−	482252.i		−	0.635064i
$226$			405291.i			0.527832i
$227$	−701903.	−	701903.i	−0.904091	−	0.904091i	0.0916960	−	0.995787i	$-0.470771\pi$
$227$	−701903.	−	701903.i	−0.904091	−	0.904091i	−0.995787	+	0.0916960i	$0.970771\pi$
$228$	637118.			0.811676
$229$	−816924.	−	816924.i	−1.02942	−	1.02942i	−0.999554	−	0.0298673i	$-0.990492\pi$
$229$	−816924.	−	816924.i	−1.02942	−	1.02942i	−0.0298673	−	0.999554i	$-0.509508\pi$
$230$	92589.6			0.115410
$231$	−3539.35	−	3539.35i	−0.00436409	−	0.00436409i
$232$	−139969.	−	139969.i	−0.170731	−	0.170731i
$233$	−584569.	+	584569.i	−0.705418	+	0.705418i	−0.965568	−	0.260151i	$-0.916228\pi$
$233$	−584569.	+	584569.i	−0.705418	+	0.705418i	0.260151	+	0.965568i	$0.416228\pi$
$234$	370668.	−	370668.i	0.442533	−	0.442533i
$235$	290275.	−	290275.i	0.342879	−	0.342879i
$236$	297815.			0.348070
$237$		−	772494.i		−	0.893356i
$238$		−	15928.4i		−	0.0182276i
$239$	718011.	−	718011.i	0.813085	−	0.813085i	−0.172010	−	0.985095i	$-0.555026\pi$
$239$	718011.	−	718011.i	0.813085	−	0.813085i	0.985095	+	0.172010i	$0.0550261\pi$
$240$	−112195.	−	112195.i	−0.125732	−	0.125732i
$241$			879782.i			0.975737i	0.872917	+	0.487868i	$0.162225\pi$
$241$			879782.i			0.975737i	−0.872917	+	0.487868i	$0.837775\pi$
$242$	−578374.			−0.634849
$243$	875249.	−	875249.i	0.950859	−	0.950859i
$244$		−	196472.i		−	0.211264i
$245$	488508.			0.519944
$246$	−18234.1	+	917729.i	−0.0192109	+	0.966889i
$247$	−1.15715e6			−1.20684
$248$		−	11163.0i		−	0.0115253i
$249$	588263.	−	588263.i	0.601275	−	0.601275i
$250$	628509.			0.636007
$251$		−	881026.i		−	0.882682i	−0.897339	−	0.441341i	$-0.854503\pi$
$251$		−	881026.i		−	0.882682i	0.897339	−	0.441341i	$-0.145497\pi$
$252$	4379.76	+	4379.76i	0.00434459	+	0.00434459i
$253$	72227.1	−	72227.1i	0.0709412	−	0.0709412i
$254$			1.40178e6i			1.36332i
$255$			1.34861e6i			1.29878i
$256$	65536.0			0.0625000
$257$	−476350.	+	476350.i	−0.449876	+	0.449876i	−0.895313	−	0.445437i	$-0.853048\pi$
$257$	−476350.	+	476350.i	−0.449876	+	0.449876i	0.445437	+	0.895313i	$0.353048\pi$
$258$	262508.	−	262508.i	0.245524	−	0.245524i
$259$	−1387.69	+	1387.69i	−0.00128541	+	0.00128541i
$260$	203772.	+	203772.i	0.186944	+	0.186944i
$261$	−462617.	−	462617.i	−0.420359	−	0.420359i
$262$	−531796.			−0.478621
$263$	−387994.	−	387994.i	−0.345888	−	0.345888i	0.512687	−	0.858575i	$-0.328650\pi$
$263$	−387994.	−	387994.i	−0.345888	−	0.345888i	−0.858575	+	0.512687i	$0.828650\pi$
$264$	−175042.			−0.154572
$265$	225106.	+	225106.i	0.196912	+	0.196912i
$266$		−	13672.8i		−	0.0118482i
$267$		−	813494.i		−	0.698355i
$268$	25389.8	+	25389.8i	0.0215935	+	0.0215935i
$269$	264165.			0.222584			0.111292	−	0.993788i	$-0.464501\pi$
$269$	264165.			0.222584			0.111292	+	0.993788i	$0.464501\pi$
$270$	55171.2	+	55171.2i	0.0460578	+	0.0460578i
$271$	−190896.			−0.157897			−0.0789486	−	0.996879i	$-0.525156\pi$
$271$	−190896.			−0.157897			−0.0789486	+	0.996879i	$0.525156\pi$
$272$	−393877.	−	393877.i	−0.322804	−	0.322804i
$273$	−17092.8	−	17092.8i	−0.0138806	−	0.0138806i
$274$	836435.	−	836435.i	0.673063	−	0.673063i
$275$	206810.	−	206810.i	0.164907	−	0.164907i
$276$	−192052.	+	192052.i	−0.151756	+	0.151756i
$277$	−348476.			−0.272881			−0.136441	−	0.990648i	$-0.543566\pi$
$277$	−348476.			−0.272881			−0.136441	+	0.990648i	$0.543566\pi$
$278$			212126.i			0.164620i
$279$		−	36895.3i		−	0.0283766i
$280$	−2407.74	+	2407.74i	−0.00183533	+	0.00183533i
$281$	1.23000e6	+	1.23000e6i	0.929265	+	0.929265i	0.997658	−	0.0683938i	$-0.0217874\pi$
$281$	1.23000e6	+	1.23000e6i	0.929265	+	0.929265i	−0.0683938	+	0.997658i	$0.521787\pi$
$282$			1.20420e6i			0.901726i
$283$	990383.			0.735084			0.367542	−	0.930007i	$-0.380199\pi$
$283$	990383.			0.735084			0.367542	+	0.930007i	$0.380199\pi$
$284$	53309.9	−	53309.9i	0.0392204	−	0.0392204i
$285$			1.15763e6i			0.844221i
$286$	317916.			0.229825
$287$	19694.8	+	391.310i	0.0141139	+	0.000280425i
$288$	216605.			0.153882
$289$			3.31462e6i			2.33447i
$290$	254320.	−	254320.i	0.177577	−	0.177577i
$291$	593256.			0.410686
$292$		−	862257.i		−	0.591807i
$293$	−1.09966e6	−	1.09966e6i	−0.748324	−	0.748324i	0.225841	−	0.974164i	$-0.427487\pi$
$293$	−1.09966e6	−	1.09966e6i	−0.748324	−	0.748324i	−0.974164	+	0.225841i	$0.927487\pi$
$294$	−1.01328e6	+	1.01328e6i	−0.683693	+	0.683693i
$295$			541121.i			0.362026i
$296$			68629.3i			0.0455282i
$297$	86075.7			0.0566225
$298$	777729.	−	777729.i	0.507327	−	0.507327i
$299$	348811.	−	348811.i	0.225638	−	0.225638i
$300$	−549909.	+	549909.i	−0.352767	+	0.352767i
$301$	−5633.51	−	5633.51i	−0.00358396	−	0.00358396i
$302$	−1.42352e6	−	1.42352e6i	−0.898144	−	0.898144i
$303$	−2.86181e6			−1.79075
$304$	−338099.	−	338099.i	−0.209827	−	0.209827i
$305$	356984.			0.219735
$306$	−1.30182e6	−	1.30182e6i	−0.794778	−	0.794778i
$307$			236383.i			0.143143i	0.997435	+	0.0715716i	$0.0228014\pi$
$307$			236383.i			0.143143i	−0.997435	+	0.0715716i	$0.977199\pi$
$308$			3756.45i			0.00225632i
$309$	591438.	+	591438.i	0.352381	+	0.352381i
$310$	20282.9			0.0119874
$311$	−1.42271e6	−	1.42271e6i	−0.834096	−	0.834096i	0.153978	−	0.988074i	$-0.450792\pi$
$311$	−1.42271e6	−	1.42271e6i	−0.834096	−	0.834096i	−0.988074	+	0.153978i	$0.950792\pi$
$312$	−845341.			−0.491638
$313$	755614.	+	755614.i	0.435953	+	0.435953i	0.890647	−	0.454695i	$-0.150252\pi$
$313$	755614.	+	755614.i	0.435953	+	0.435953i	−0.454695	+	0.890647i	$0.650252\pi$
$314$	−678363.	−	678363.i	−0.388274	−	0.388274i
$315$	−7957.91	+	7957.91i	−0.00451879	+	0.00451879i
$316$	−409939.	+	409939.i	−0.230942	+	0.230942i
$317$	−2.16182e6	+	2.16182e6i	−1.20829	+	1.20829i	−0.236710	+	0.971580i	$0.576069\pi$
$317$	−2.16182e6	+	2.16182e6i	−1.20829	+	1.20829i	−0.971580	+	0.236710i	$0.923931\pi$
$318$	−933845.			−0.517854
$319$		−	396779.i		−	0.218309i
$320$			119077.i			0.0650060i
$321$	847979.	−	847979.i	0.459328	−	0.459328i
$322$	4121.50	+	4121.50i	0.00221521	+	0.00221521i
$323$			4.06402e6i			2.16745i
$324$	−1.05130e6			−0.556370
$325$	998760.	−	998760.i	0.524509	−	0.524509i
$326$			2.56081e6i			1.33455i
$327$	2.25275e6			1.16505
$328$	496687.	−	477335.i	0.254917	−	0.244984i
$329$	25842.4			0.0131627
$330$		−	318046.i		−	0.160770i
$331$	−1.08830e6	+	1.08830e6i	−0.545984	+	0.545984i	−0.925277	−	0.379293i	$-0.876167\pi$
$331$	−1.08830e6	+	1.08830e6i	−0.545984	+	0.545984i	0.379293	+	0.925277i	$0.376167\pi$
$332$	−624347.			−0.310872
$333$			226829.i			0.112095i
$334$	−280186.	−	280186.i	−0.137430	−	0.137430i
$335$	−46132.6	+	46132.6i	−0.0224593	+	0.0224593i
$336$		−	9988.43i		−	0.00482668i
$337$			2.29343e6i			1.10005i	0.835150	+	0.550023i	$0.185381\pi$
$337$			2.29343e6i			1.10005i	−0.835150	+	0.550023i	$0.814619\pi$
$338$	50160.5			0.0238820
$339$	1.52747e6	−	1.52747e6i	0.721894	−	0.721894i
$340$	715664.	−	715664.i	0.335747	−	0.335747i
$341$	15822.3	−	15822.3i	0.00736856	−	0.00736856i
$342$	−1.11746e6	−	1.11746e6i	−0.516616	−	0.516616i
$343$	43494.9	+	43494.9i	0.0199620	+	0.0199620i
$344$	−278611.			−0.126941
$345$	−348954.	−	348954.i	−0.157841	−	0.157841i
$346$	2.10527e6			0.945404
$347$	1.24204e6	+	1.24204e6i	0.553747	+	0.553747i	0.927520	−	0.373773i	$-0.121936\pi$
$347$	1.24204e6	+	1.24204e6i	0.553747	+	0.553747i	−0.373773	+	0.927520i	$0.621936\pi$
$348$			1.05504e6i			0.467003i
$349$		−	2.67812e6i		−	1.17697i	−0.808506	−	0.588487i	$-0.799724\pi$
$349$		−	2.67812e6i		−	1.17697i	0.808506	−	0.588487i	$-0.200276\pi$
$350$	11801.2	+	11801.2i	0.00514940	+	0.00514940i
$351$	415691.			0.180095
$352$	92889.4	+	92889.4i	0.0399585	+	0.0399585i
$353$	−2.71246e6			−1.15858			−0.579290	−	0.815122i	$-0.696670\pi$
$353$	−2.71246e6			−1.15858			−0.579290	+	0.815122i	$0.696670\pi$
$354$	−1.12241e6	−	1.12241e6i	−0.476040	−	0.476040i
$355$	96862.6	+	96862.6i	0.0407930	+	0.0407930i
$356$	−431697.	+	431697.i	−0.180532	+	0.180532i
$357$	−60031.4	+	60031.4i	−0.0249292	+	0.0249292i
$358$	−294684.	+	294684.i	−0.121520	+	0.121520i
$359$	3.99187e6			1.63471			0.817354	−	0.576136i	$-0.195440\pi$
$359$	3.99187e6			1.63471			0.817354	+	0.576136i	$0.195440\pi$
$360$			393566.i			0.160052i
$361$			1.01240e6i			0.408870i
$362$	2.18261e6	−	2.18261e6i	0.875395	−	0.875395i
$363$	2.17979e6	+	2.17979e6i	0.868256	+	0.868256i
$364$			18141.3i			0.00717653i
$365$	1.56670e6			0.615536
$366$	−740467.	+	740467.i	−0.288937	+	0.288937i
$367$			1.50364e6i			0.582746i	0.956610	+	0.291373i	$0.0941120\pi$
$367$			1.50364e6i			0.582746i	−0.956610	+	0.291373i	$0.905888\pi$
$368$	203833.			0.0784611
$369$	1.64162e6	−	1.57765e6i	0.627633	−	0.603179i
$370$	−124698.			−0.0473537
$371$			20040.6i			0.00755920i
$372$	−42071.5	+	42071.5i	−0.0157627	+	0.0157627i
$373$	3.96397e6			1.47523			0.737613	−	0.675224i	$-0.235953\pi$
$373$	3.96397e6			1.47523			0.737613	+	0.675224i	$0.235953\pi$
$374$		−	1.11655e6i		−	0.412760i
$375$	−2.36874e6	−	2.36874e6i	−0.869839	−	0.869839i
$376$	639031.	−	639031.i	0.233105	−	0.233105i
$377$		−	1.91619e6i		−	0.694361i
$378$			4911.75i			0.00176810i
$379$	−1.56055e6			−0.558059			−0.279029	−	0.960283i	$-0.590013\pi$
$379$	−1.56055e6			−0.558059			−0.279029	+	0.960283i	$0.590013\pi$
$380$	614317.	−	614317.i	0.218240	−	0.218240i
$381$	5.28307e6	−	5.28307e6i	1.86455	−	1.86455i
$382$	193674.	−	193674.i	0.0679067	−	0.0679067i
$383$	−2.61684e6	−	2.61684e6i	−0.911549	−	0.911549i	0.0848454	−	0.996394i	$-0.472960\pi$
$383$	−2.61684e6	−	2.61684e6i	−0.911549	−	0.911549i	−0.996394	+	0.0848454i	$0.972960\pi$
$384$	−246993.	−	246993.i	−0.0854786	−	0.0854786i
$385$	−6825.37			−0.00234679
$386$	2.10843e6	+	2.10843e6i	0.720261	+	0.720261i
$387$	−920845.			−0.312542
$388$	−314823.	−	314823.i	−0.106166	−	0.106166i
$389$		−	5.53656e6i		−	1.85510i	−0.373704	−	0.927548i	$-0.621913\pi$
$389$		−	5.53656e6i		−	1.85510i	0.373704	−	0.927548i	$-0.378087\pi$
$390$		−	1.53596e6i		−	0.511350i
$391$	−1.22505e6	−	1.22505e6i	−0.405240	−	0.405240i
$392$	1.07543e6			0.353483
$393$	2.00424e6	+	2.00424e6i	0.654589	+	0.654589i
$394$	123012.			0.0399216
$395$	−744849.	−	744849.i	−0.240201	−	0.240201i
$396$	307012.	+	307012.i	0.0983823	+	0.0983823i
$397$	−3.57890e6	+	3.57890e6i	−1.13965	+	1.13965i	−0.151141	+	0.988512i	$0.548295\pi$
$397$	−3.57890e6	+	3.57890e6i	−1.13965	+	1.13965i	−0.988512	+	0.151141i	$0.951705\pi$
$398$	−1.90267e6	+	1.90267e6i	−0.602083	+	0.602083i
$399$	−51530.2	+	51530.2i	−0.0162043	+	0.0162043i
$400$	583640.			0.182388
$401$		−	1.27802e6i		−	0.396895i	−0.980112	−	0.198447i	$-0.936410\pi$
$401$		−	1.27802e6i		−	0.396895i	0.980112	−	0.198447i	$-0.0635899\pi$
$402$		−	191380.i		−	0.0590650i
$403$	76411.5	−	76411.5i	0.0234367	−	0.0234367i
$404$	1.51868e6	+	1.51868e6i	0.462927	+	0.462927i
$405$		−	1.91018e6i		−	0.578678i
$406$	22641.4			0.00681693
$407$	−97273.7	+	97273.7i	−0.0291078	+	0.0291078i
$408$			2.96891e6i			0.882970i
$409$	−321785.			−0.0951169			−0.0475584	−	0.998868i	$-0.515144\pi$
$409$	−321785.			−0.0951169			−0.0475584	+	0.998868i	$0.515144\pi$
$410$	867305.	+	902468.i	0.254807	+	0.265138i
$411$	−6.30475e6			−1.84104
$412$		−	627717.i		−	0.182188i
$413$	−24087.3	+	24087.3i	−0.00694885	+	0.00694885i
$414$	673694.			0.193180
$415$		−	1.13442e6i		−	0.323336i
$416$	448597.	+	448597.i	0.127093	+	0.127093i
$417$	799466.	−	799466.i	0.225144	−	0.225144i
$418$		−	958430.i		−	0.268299i
$419$			5.24453e6i			1.45939i	0.683773	+	0.729695i	$0.260338\pi$
$419$			5.24453e6i			1.45939i	−0.683773	+	0.729695i	$0.739662\pi$
$420$	18148.7			0.00502022
$421$	−1.23496e6	+	1.23496e6i	−0.339585	+	0.339585i	−0.856211	−	0.516626i	$-0.827188\pi$
$421$	−1.23496e6	+	1.23496e6i	−0.339585	+	0.339585i	0.516626	+	0.856211i	$0.327188\pi$
$422$	425691.	−	425691.i	0.116362	−	0.116362i
$423$	2.11208e6	−	2.11208e6i	0.573931	−	0.573931i
$424$	495563.	+	495563.i	0.133870	+	0.133870i
$425$	−3.50773e6	−	3.50773e6i	−0.942006	−	0.942006i
$426$	−401831.			−0.107280
$427$	15890.7	+	15890.7i	0.00421767	+	0.00421767i
$428$	−899994.			−0.237482
$429$	−1.19817e6	−	1.19817e6i	−0.314322	−	0.314322i
$430$		−	506228.i		−	0.132031i
$431$		−	7.04222e6i		−	1.82606i	−0.407887	−	0.913032i	$-0.633734\pi$
$431$		−	7.04222e6i		−	1.82606i	0.407887	−	0.913032i	$-0.366266\pi$
$432$	121458.	+	121458.i	0.0313123	+	0.0313123i
$433$	−4.02436e6			−1.03152			−0.515759	−	0.856734i	$-0.672490\pi$
$433$	−4.02436e6			−1.03152			−0.515759	+	0.856734i	$0.672490\pi$
$434$	902.867	+	902.867i	0.000230091	+	0.000230091i
$435$	−1.91698e6			−0.485728
$436$	−1.19547e6	−	1.19547e6i	−0.301177	−	0.301177i
$437$	−1.05157e6	−	1.05157e6i	−0.263411	−	0.263411i
$438$	−3.24969e6	+	3.24969e6i	−0.809389	+	0.809389i
$439$	1.69237e6	−	1.69237e6i	0.419117	−	0.419117i	−0.465783	−	0.884899i	$-0.654227\pi$
$439$	1.69237e6	−	1.69237e6i	0.419117	−	0.419117i	0.884899	+	0.465783i	$0.154227\pi$
$440$	−168778.	+	168778.i	−0.0415607	+	0.0415607i
$441$	3.55445e6			0.870314
$442$		−	5.39222e6i		−	1.31284i
$443$			3.70906e6i			0.897954i	0.893543	+	0.448977i	$0.148212\pi$
$443$			3.70906e6i			0.897954i	−0.893543	+	0.448977i	$0.851788\pi$
$444$	258651.	−	258651.i	0.0622669	−	0.0622669i
$445$	−784381.	−	784381.i	−0.187770	−	0.187770i
$446$			4.91647e6i			1.17035i
$447$	−5.86224e6			−1.38770
$448$	−5300.56	+	5300.56i	−0.00124775	+	0.00124775i
$449$			7.31892e6i			1.71329i	0.515905	+	0.856646i	$0.327456\pi$
$449$			7.31892e6i			1.71329i	−0.515905	+	0.856646i	$0.672544\pi$
$450$	1.92901e6			0.449058
$451$	1.38056e6	+	27430.0i	0.319605	+	0.00635015i
$452$	−1.62116e6			−0.373234
$453$			1.07300e7i			2.45671i
$454$	2.80761e6	−	2.80761e6i	0.639289	−	0.639289i
$455$	−32962.2			−0.00746428
$456$			2.54847e6i			0.573942i
$457$	2.27205e6	+	2.27205e6i	0.508895	+	0.508895i	0.914187	−	0.405292i	$-0.132830\pi$
$457$	2.27205e6	+	2.27205e6i	0.508895	+	0.508895i	−0.405292	+	0.914187i	$0.632830\pi$
$458$	3.26770e6	−	3.26770e6i	0.727911	−	0.727911i
$459$		−	1.45994e6i		−	0.323447i
$460$			370358.i			0.0816070i
$461$	−3.99752e6			−0.876070			−0.438035	−	0.898958i	$-0.644325\pi$
$461$	−3.99752e6			−0.876070			−0.438035	+	0.898958i	$0.644325\pi$
$462$	14157.4	−	14157.4i	0.00308588	−	0.00308588i
$463$	−3.10875e6	+	3.10875e6i	−0.673959	+	0.673959i	−0.958626	−	0.284667i	$-0.908117\pi$
$463$	−3.10875e6	+	3.10875e6i	−0.673959	+	0.673959i	0.284667	+	0.958626i	$0.408117\pi$
$464$	559877.	−	559877.i	0.120725	−	0.120725i
$465$	−76442.7	−	76442.7i	−0.0163947	−	0.0163947i
$466$	−2.33828e6	−	2.33828e6i	−0.498806	−	0.498806i
$467$	6.59950e6			1.40029			0.700147	−	0.713999i	$-0.253118\pi$
$467$	6.59950e6			1.40029			0.700147	+	0.713999i	$0.253118\pi$
$468$	1.48267e6	+	1.48267e6i	0.312918	+	0.312918i
$469$	−4107.07			−0.000862183
$470$	1.16110e6	+	1.16110e6i	0.242452	+	0.242452i
$471$			5.11326e6i			1.06205i
$472$			1.19126e6i			0.246122i
$473$	−394897.	−	394897.i	−0.0811579	−	0.0811579i
$474$	3.08998e6			0.631698
$475$	−3.01099e6	−	3.01099e6i	−0.612316	−	0.612316i
$476$	63713.7			0.0128889
$477$	1.63790e6	+	1.63790e6i	0.329604	+	0.329604i
$478$	2.87204e6	+	2.87204e6i	0.574938	+	0.574938i
$479$	3.46258e6	−	3.46258e6i	0.689542	−	0.689542i	−0.272589	−	0.962131i	$-0.587880\pi$
$479$	3.46258e6	−	3.46258e6i	0.689542	−	0.689542i	0.962131	+	0.272589i	$0.0878798\pi$
$480$	448780.	−	448780.i	0.0889059	−	0.0889059i
$481$	−469770.	+	469770.i	−0.0925812	+	0.0925812i
$482$	−3.51913e6			−0.689950
$483$		−	31066.4i		−	0.00605931i
$484$		−	2.31350e6i		−	0.448906i
$485$	572025.	−	572025.i	0.110423	−	0.110423i
$486$	3.50100e6	+	3.50100e6i	0.672359	+	0.672359i
$487$			4.97835e6i			0.951181i	0.879667	+	0.475590i	$0.157765\pi$
$487$			4.97835e6i			0.951181i	−0.879667	+	0.475590i	$0.842235\pi$
$488$	785887.			0.149386
$489$	9.65124e6	−	9.65124e6i	1.82520	−	1.82520i
$490$			1.95403e6i			0.367656i
$491$	9.12861e6			1.70884			0.854419	−	0.519585i	$-0.173913\pi$
$491$	9.12861e6			1.70884			0.854419	+	0.519585i	$0.173913\pi$
$492$	−3.67092e6	−	72936.5i	−0.683694	−	0.0135841i
$493$	−6.72982e6			−1.24706
$494$		−	4.62861e6i		−	0.853362i
$495$	−557832.	+	557832.i	−0.102327	+	0.102327i
$496$	44652.1			0.00814963
$497$			8623.42i			0.00156599i
$498$	2.35305e6	+	2.35305e6i	0.425166	+	0.425166i
$499$	−3.64397e6	+	3.64397e6i	−0.655124	+	0.655124i	−0.954222	−	0.299099i	$-0.903314\pi$
$499$	−3.64397e6	+	3.64397e6i	−0.655124	+	0.655124i	0.299099	+	0.954222i	$0.403314\pi$
$500$			2.51404e6i			0.449725i
$501$			2.11194e6i			0.375914i
$502$	3.52410e6			0.624151
$503$	−6.15017e6	+	6.15017e6i	−1.08384	+	1.08384i	−0.0876973	+	0.996147i	$0.527951\pi$
$503$	−6.15017e6	+	6.15017e6i	−1.08384	+	1.08384i	−0.996147	+	0.0876973i	$0.972049\pi$
$504$	−17519.0	+	17519.0i	−0.00307209	+	0.00307209i
$505$	−2.75940e6	+	2.75940e6i	−0.481489	+	0.481489i
$506$	288908.	+	288908.i	0.0501630	+	0.0501630i
$507$	−189046.	−	189046.i	−0.0326624	−	0.0326624i
$508$	−5.60714e6			−0.964011
$509$	6.38525e6	+	6.38525e6i	1.09240	+	1.09240i	0.995271	+	0.0971326i	$0.0309671\pi$
$509$	6.38525e6	+	6.38525e6i	1.09240	+	1.09240i	0.0971326	+	0.995271i	$0.469033\pi$
$510$	−5.39442e6			−0.918374
$511$	69739.5	+	69739.5i	0.0118148	+	0.0118148i
$512$			262144.i			0.0441942i
$513$		−	1.25320e6i		−	0.210245i
$514$	−1.90540e6	−	1.90540e6i	−0.318111	−	0.318111i
$515$	1.14054e6			0.189493
$516$	1.05003e6	+	1.05003e6i	0.173612	+	0.173612i
$517$	1.81150e6			0.298065
$518$	−5550.74	−	5550.74i	−0.000908922	−	0.000908922i
$519$	−7.93439e6	−	7.93439e6i	−1.29299	−	1.29299i
$520$	−815088.	+	815088.i	−0.132189	+	0.132189i
$521$	6.28797e6	−	6.28797e6i	1.01488	−	1.01488i	0.0149953	−	0.999888i	$-0.495227\pi$
$521$	6.28797e6	−	6.28797e6i	1.01488	−	1.01488i	0.999888	−	0.0149953i	$-0.00477334\pi$
$522$	1.85047e6	−	1.85047e6i	0.297238	−	0.297238i
$523$	−1.12668e7			−1.80113			−0.900567	−	0.434718i	$-0.856848\pi$
$523$	−1.12668e7			−1.80113			−0.900567	+	0.434718i	$0.856848\pi$
$524$		−	2.12718e6i		−	0.338436i
$525$		−	88953.3i		−	0.0140852i
$526$	1.55198e6	−	1.55198e6i	0.244580	−	0.244580i
$527$	−268363.	−	268363.i	−0.0420917	−	0.0420917i
$528$		−	700167.i		−	0.109299i
$529$	−5.80237e6			−0.901502
$530$	−900425.	+	900425.i	−0.139238	+	0.139238i
$531$			3.93727e6i			0.605980i
$532$	54691.0			0.00837793
$533$	6.66723e6	+	132469.i	1.01655	+	0.0201975i
$534$	3.25397e6			0.493811
$535$		−	1.63527e6i		−	0.247004i
$536$	−101559.	+	101559.i	−0.0152689	+	0.0152689i
$537$	2.22122e6			0.332397
$538$			1.05666e6i			0.157391i
$539$	1.52430e6	+	1.52430e6i	0.225994	+	0.225994i
$540$	−220685.	+	220685.i	−0.0325678	+	0.0325678i
$541$			6.26323e6i			0.920037i	0.887909	+	0.460019i	$0.152157\pi$
$541$			6.26323e6i			0.920037i	−0.887909	+	0.460019i	$0.847843\pi$
$542$		−	763585.i		−	0.111650i
$543$	−1.64517e7			−2.39448
$544$	1.57551e6	−	1.57551e6i	0.228257	−	0.228257i
$545$	2.17213e6	−	2.17213e6i	0.313253	−	0.313253i
$546$	68371.2	−	68371.2i	0.00981503	−	0.00981503i
$547$	716056.	+	716056.i	0.102324	+	0.102324i	0.756416	−	0.654091i	$-0.226949\pi$
$547$	716056.	+	716056.i	0.102324	+	0.102324i	−0.654091	+	0.756416i	$0.726949\pi$
$548$	3.34574e6	+	3.34574e6i	0.475927	+	0.475927i
$549$	2.59746e6			0.367805
$550$	827239.	+	827239.i	0.116607	+	0.116607i
$551$	−5.77679e6			−0.810603
$552$	−768209.	−	768209.i	−0.107308	−	0.107308i
$553$		−	66311.9i		−	0.00922101i
$554$		−	1.39391e6i		−	0.192956i
$555$	469963.	+	469963.i	0.0647636	+	0.0647636i
$556$	−848505.			−0.116404
$557$	1.17587e6	+	1.17587e6i	0.160592	+	0.160592i	0.782829	−	0.622237i	$-0.213776\pi$
$557$	1.17587e6	+	1.17587e6i	0.160592	+	0.160592i	−0.622237	+	0.782829i	$0.713776\pi$
$558$	147581.			0.0200653
$559$	−1.90710e6	−	1.90710e6i	−0.258134	−	0.258134i
$560$	−9630.97	−	9630.97i	−0.00129778	−	0.00129778i
$561$	−4.20807e6	+	4.20807e6i	−0.564515	+	0.564515i
$562$	−4.92000e6	+	4.92000e6i	−0.657089	+	0.657089i
$563$	3.17808e6	−	3.17808e6i	0.422565	−	0.422565i	−0.463521	−	0.886086i	$-0.653414\pi$
$563$	3.17808e6	−	3.17808e6i	0.422565	−	0.422565i	0.886086	+	0.463521i	$0.153414\pi$
$564$	−4.81678e6			−0.637616
$565$		−	2.94561e6i		−	0.388199i
$566$			3.96153e6i			0.519783i
$567$	85029.1	−	85029.1i	0.0111073	−	0.0111073i
$568$	213240.	+	213240.i	0.0277330	+	0.0277330i
$569$		−	1.10902e7i		−	1.43601i	−0.696036	−	0.718006i	$-0.745055\pi$
$569$		−	1.10902e7i		−	1.43601i	0.696036	−	0.718006i	$-0.254945\pi$
$570$	−4.63050e6			−0.596954
$571$	9.40293e6	−	9.40293e6i	1.20690	−	1.20690i	0.234880	−	0.972024i	$-0.424530\pi$
$571$	9.40293e6	−	9.40293e6i	1.20690	−	1.20690i	0.972024	−	0.234880i	$-0.0754697\pi$
$572$			1.27166e6i			0.162511i
$573$	−1.45984e6			−0.185746
$574$	−1565.24	+	78779.0i	−0.000198290	+	0.00998001i
$575$	1.81526e6			0.228965
$576$			866420.i			0.108811i
$577$	−1.42013e6	+	1.42013e6i	−0.177578	+	0.177578i	−0.790299	−	0.612721i	$-0.790075\pi$
$577$	−1.42013e6	+	1.42013e6i	−0.177578	+	0.177578i	0.612721	+	0.790299i	$0.290075\pi$
$578$	−1.32585e7			−1.65072
$579$		−	1.58926e7i		−	1.97014i
$580$	1.01728e6	+	1.01728e6i	0.125566	+	0.125566i
$581$	50497.3	−	50497.3i	0.00620623	−	0.00620623i
$582$			2.37302e6i			0.290399i
$583$			1.40480e6i			0.171176i
$584$	3.44903e6			0.418470
$585$	−2.69397e6	+	2.69397e6i	−0.325465	+	0.325465i
$586$	4.39864e6	−	4.39864e6i	0.529145	−	0.529145i
$587$	1.03846e7	−	1.03846e7i	1.24393	−	1.24393i	0.285573	−	0.958357i	$-0.407816\pi$
$587$	1.03846e7	−	1.03846e7i	1.24393	−	1.24393i	0.958357	−	0.285573i	$-0.0921838\pi$
$588$	−4.05312e6	−	4.05312e6i	−0.483444	−	0.483444i
$589$	−230360.	−	230360.i	−0.0273602	−	0.0273602i
$590$	−2.16448e6			−0.255991
$591$	−463611.	−	463611.i	−0.0545991	−	0.0545991i
$592$	−274517.			−0.0321933
$593$	4.75316e6	+	4.75316e6i	0.555067	+	0.555067i	0.927899	−	0.372832i	$-0.121613\pi$
$593$	4.75316e6	+	4.75316e6i	0.555067	+	0.555067i	−0.372832	+	0.927899i	$0.621613\pi$
$594$			344303.i			0.0400382i
$595$			115766.i			0.0134057i
$596$	3.11092e6	+	3.11092e6i	0.358734	+	0.358734i
$597$	1.43417e7			1.64689
$598$	1.39524e6	+	1.39524e6i	0.159550	+	0.159550i
$599$	1.64547e6			0.187380			0.0936899	−	0.995601i	$-0.470134\pi$
$599$	1.64547e6			0.187380			0.0936899	+	0.995601i	$0.470134\pi$
$600$	−2.19963e6	−	2.19963e6i	−0.249444	−	0.249444i
$601$	1.34324e6	+	1.34324e6i	0.151694	+	0.151694i	0.778874	−	0.627180i	$-0.215791\pi$
$601$	1.34324e6	+	1.34324e6i	0.151694	+	0.151694i	−0.627180	+	0.778874i	$0.715791\pi$
$602$	22534.1	−	22534.1i	0.00253424	−	0.00253424i
$603$	−335667.	+	335667.i	−0.0375937	+	0.0375937i
$604$	5.69407e6	−	5.69407e6i	0.635083	−	0.635083i
$605$	4.20356e6			0.466905
$606$		−	1.14473e7i		−	1.26625i
$607$		−	8.35307e6i		−	0.920184i	−0.887871	−	0.460092i	$-0.847817\pi$
$607$		−	8.35307e6i		−	0.920184i	0.887871	−	0.460092i	$-0.152183\pi$
$608$	1.35240e6	−	1.35240e6i	0.148370	−	0.148370i
$609$	−85331.6	−	85331.6i	−0.00932323	−	0.00932323i
$610$			1.42794e6i			0.155376i
$611$	8.74839e6			0.948036
$612$	5.20726e6	−	5.20726e6i	0.561993	−	0.561993i
$613$			4.17508e6i			0.448759i	0.974502	+	0.224380i	$0.0720355\pi$
$613$			4.17508e6i			0.448759i	−0.974502	+	0.224380i	$0.927964\pi$
$614$	−945533.			−0.101218
$615$	132524.	−	6.66995e6i	0.0141288	−	0.711107i
$616$	−15025.8			−0.00159546
$617$			3.79973e6i			0.401828i	0.979609	+	0.200914i	$0.0643912\pi$
$617$			3.79973e6i			0.401828i	−0.979609	+	0.200914i	$0.935609\pi$
$618$	−2.36575e6	+	2.36575e6i	−0.249171	+	0.249171i
$619$	1.32599e7			1.39096			0.695478	−	0.718548i	$-0.255193\pi$
$619$	1.32599e7			1.39096			0.695478	+	0.718548i	$0.255193\pi$
$620$			81131.7i			0.00847640i
$621$	377762.	+	377762.i	0.0393087	+	0.0393087i
$622$	5.69085e6	−	5.69085e6i	0.589795	−	0.589795i
$623$		−	69831.3i		−	0.00720826i
$624$		−	3.38136e6i		−	0.347640i
$625$	2.55658e6			0.261793
$626$	−3.02246e6	+	3.02246e6i	−0.308265	+	0.308265i
$627$	−3.61215e6	+	3.61215e6i	−0.366942	+	0.366942i
$628$	2.71345e6	−	2.71345e6i	0.274551	−	0.274551i
$629$	1.64987e6	+	1.64987e6i	0.166274	+	0.166274i
$630$	−31831.6	−	31831.6i	−0.00319527	−	0.00319527i
$631$	5.03250e6			0.503165			0.251582	−	0.967836i	$-0.419049\pi$
$631$	5.03250e6			0.503165			0.251582	+	0.967836i	$0.419049\pi$
$632$	−1.63976e6	−	1.63976e6i	−0.163300	−	0.163300i
$633$	−3.20870e6			−0.318288
$634$	−8.64728e6	−	8.64728e6i	−0.854390	−	0.854390i
$635$		−	1.01880e7i		−	1.00266i
$636$		−	3.73538e6i		−	0.366178i
$637$	7.36139e6	+	7.36139e6i	0.718805	+	0.718805i
$638$	1.58712e6			0.154368
$639$	704785.	+	704785.i	0.0682817	+	0.0682817i
$640$	−476309.			−0.0459662
$641$	7.91859e6	+	7.91859e6i	0.761207	+	0.761207i	0.976541	−	0.215334i	$-0.0690839\pi$
$641$	7.91859e6	+	7.91859e6i	0.761207	+	0.761207i	−0.215334	+	0.976541i	$0.569084\pi$
$642$	3.39192e6	+	3.39192e6i	0.324794	+	0.324794i
$643$	−6.02274e6	+	6.02274e6i	−0.574469	+	0.574469i	−0.933374	−	0.358905i	$-0.883150\pi$
$643$	−6.02274e6	+	6.02274e6i	−0.574469	+	0.574469i	0.358905	+	0.933374i	$0.383150\pi$
$644$	−16486.0	+	16486.0i	−0.00156639	+	0.00156639i
$645$	−1.90788e6	+	1.90788e6i	−0.180573	+	0.180573i
$646$	−1.62561e7			−1.53262
$647$			7.18492e6i			0.674778i	0.941365	+	0.337389i	$0.109544\pi$
$647$			7.18492e6i			0.674778i	−0.941365	+	0.337389i	$0.890456\pi$
$648$		−	4.20519e6i		−	0.393413i
$649$	−1.68847e6	+	1.68847e6i	−0.157355	+	0.157355i
$650$	3.99504e6	+	3.99504e6i	0.370884	+	0.370884i
$651$		−	6805.49i		−	0.000629371i
$652$	−1.02432e7			−0.943667
$653$	−6.82064e6	+	6.82064e6i	−0.625954	+	0.625954i	−0.947047	−	0.321094i	$-0.895950\pi$
$653$	−6.82064e6	+	6.82064e6i	−0.625954	+	0.625954i	0.321094	+	0.947047i	$0.395950\pi$
$654$			9.01102e6i			0.823814i
$655$	3.86503e6			0.352006
$656$	1.90934e6	+	1.98675e6i	0.173230	+	0.180253i
$657$	1.13995e7			1.03032
$658$			103370.i			0.00930741i
$659$	−7.20001e6	+	7.20001e6i	−0.645832	+	0.645832i	−0.951983	−	0.306151i	$-0.900959\pi$
$659$	−7.20001e6	+	7.20001e6i	−0.645832	+	0.645832i	0.306151	+	0.951983i	$0.400959\pi$
$660$	1.27218e6			0.113682
$661$			1.03342e7i			0.919969i	0.887927	+	0.459984i	$0.152145\pi$
$661$			1.03342e7i			0.919969i	−0.887927	+	0.459984i	$0.847855\pi$
$662$	−4.35321e6	−	4.35321e6i	−0.386069	−	0.386069i
$663$	−2.03223e7	+	2.03223e7i	−1.79551	+	1.79551i
$664$		−	2.49739e6i		−	0.219819i
$665$			99372.1i			0.00871386i
$666$	−907315.			−0.0792634
$667$	1.74135e6	−	1.74135e6i	0.151556	−	0.151556i
$668$	1.12074e6	−	1.12074e6i	0.0971775	−	0.0971775i
$669$	1.85293e7	−	1.85293e7i	1.60064	−	1.60064i
$670$	−184531.	−	184531.i	−0.0158811	−	0.0158811i
$671$	1.11390e6	+	1.11390e6i	0.0955081	+	0.0955081i
$672$	39953.7			0.00341298
$673$	−1.08728e7	−	1.08728e7i	−0.925345	−	0.925345i	0.0720560	−	0.997401i	$-0.477044\pi$
$673$	−1.08728e7	−	1.08728e7i	−0.925345	−	0.925345i	−0.997401	+	0.0720560i	$0.977044\pi$
$674$	−9.17372e6			−0.777850
$675$	1.08166e6	+	1.08166e6i	0.0913756	+	0.0913756i
$676$			200642.i			0.0168871i
$677$			2.16243e7i			1.81331i	0.421876	+	0.906653i	$0.361372\pi$
$677$			2.16243e7i			1.81331i	−0.421876	+	0.906653i	$0.638628\pi$
$678$	6.10988e6	+	6.10988e6i	0.510456	+	0.510456i
$679$	50925.8			0.00423900
$680$	2.86266e6	+	2.86266e6i	0.237409	+	0.237409i
$681$	−2.11628e7			−1.74866
$682$	63289.0	+	63289.0i	0.00521036	+	0.00521036i
$683$	−463407.	−	463407.i	−0.0380112	−	0.0380112i	0.687846	−	0.725857i	$-0.258557\pi$
$683$	−463407.	−	463407.i	−0.0380112	−	0.0380112i	−0.725857	+	0.687846i	$0.758557\pi$
$684$	4.46985e6	−	4.46985e6i	0.365303	−	0.365303i
$685$	−6.07912e6	+	6.07912e6i	−0.495010	+	0.495010i
$686$	−173980.	+	173980.i	−0.0141152	+	0.0141152i
$687$	−2.46307e7			−1.99107
$688$		−	1.11444e6i		−	0.0897608i
$689$			6.78431e6i			0.544449i
$690$	1.39581e6	−	1.39581e6i	0.111610	−	0.111610i
$691$	8.30925e6	+	8.30925e6i	0.662013	+	0.662013i	0.955854	−	0.293841i	$-0.0949337\pi$
$691$	8.30925e6	+	8.30925e6i	0.662013	+	0.662013i	−0.293841	+	0.955854i	$0.594934\pi$
$692$			8.42108e6i			0.668502i
$693$	−49662.3			−0.00392820
$694$	−4.96815e6	+	4.96815e6i	−0.391558	+	0.391558i
$695$		−	1.54171e6i		−	0.121071i
$696$	−4.22015e6			−0.330221
$697$	465243.	−	2.34158e7i	0.0362742	−	1.82569i
$698$	1.07125e7			0.832247
$699$			1.76251e7i			1.36439i
$700$	−47204.9	+	47204.9i	−0.00364118	+	0.00364118i
$701$	5.56323e6			0.427595			0.213797	−	0.976878i	$-0.431417\pi$
$701$	5.56323e6			0.427595			0.213797	+	0.976878i	$0.431417\pi$
$702$			1.66276e6i			0.127347i
$703$	1.41623e6	+	1.41623e6i	0.108080	+	0.108080i
$704$	−371558.	+	371558.i	−0.0282549	+	0.0282549i
$705$		−	8.75197e6i		−	0.663182i
$706$		−	1.08498e7i		−	0.819240i
$707$	−245662.			−0.0184837
$708$	4.48964e6	−	4.48964e6i	0.336611	−	0.336611i
$709$	−1.65007e7	+	1.65007e7i	−1.23278	+	1.23278i	−0.269890	+	0.962891i	$0.586987\pi$
$709$	−1.65007e7	+	1.65007e7i	−1.23278	+	1.23278i	−0.962891	+	0.269890i	$0.913013\pi$
$710$	−387451.	+	387451.i	−0.0288450	+	0.0288450i
$711$	−5.41961e6	−	5.41961e6i	−0.402063	−	0.402063i
$712$	−1.72679e6	−	1.72679e6i	−0.127655	−	0.127655i
$713$	138879.			0.0102309
$714$	−240125.	−	240125.i	−0.0176276	−	0.0176276i
$715$	−2.31058e6			−0.169027
$716$	−1.17874e6	−	1.17874e6i	−0.0859279	−	0.0859279i
$717$		−	2.16484e7i		−	1.57264i
$718$			1.59675e7i			1.15591i
$719$	−1.05670e7	−	1.05670e7i	−0.762303	−	0.762303i	0.214435	−	0.976738i	$-0.431209\pi$
$719$	−1.05670e7	−	1.05670e7i	−0.762303	−	0.762303i	−0.976738	+	0.214435i	$0.931209\pi$
$720$	−1.57426e6			−0.113174
$721$	50769.8	+	50769.8i	0.00363720	+	0.00363720i
$722$	−4.04961e6			−0.289114
$723$	1.32630e7	+	1.32630e7i	0.943615	+	0.943615i
$724$	8.73042e6	+	8.73042e6i	0.618997	+	0.618997i
$725$	4.98606e6	−	4.98606e6i	0.352300	−	0.352300i
$726$	−8.71916e6	+	8.71916e6i	−0.613950	+	0.613950i
$727$	1.10210e7	−	1.10210e7i	0.773364	−	0.773364i	−0.205329	−	0.978693i	$-0.565827\pi$
$727$	1.10210e7	−	1.10210e7i	0.773364	−	0.773364i	0.978693	+	0.205329i	$0.0658265\pi$
$728$	−72565.1			−0.00507457
$729$		−	1.04227e7i		−	0.726373i
$730$			6.26679e6i			0.435249i
$731$	−6.69790e6	+	6.69790e6i	−0.463602	+	0.463602i
$732$	−2.96187e6	−	2.96187e6i	−0.204309	−	0.204309i
$733$		−	2.27369e7i		−	1.56304i	−0.623879	−	0.781521i	$-0.714444\pi$
$733$		−	2.27369e7i		−	1.56304i	0.623879	−	0.781521i	$-0.285556\pi$
$734$	−6.01457e6			−0.412063
$735$	7.36440e6	−	7.36440e6i	0.502828	−	0.502828i
$736$			815331.i			0.0554803i
$737$	−287896.			−0.0195239
$738$	6.31062e6	+	6.56647e6i	0.426512	+	0.443804i
$739$	1.62481e7			1.09444			0.547220	−	0.836989i	$-0.315686\pi$
$739$	1.62481e7			1.09444			0.547220	+	0.836989i	$0.315686\pi$
$740$		−	498790.i		−	0.0334841i
$741$	−1.74444e7	+	1.74444e7i	−1.16711	+	1.16711i
$742$	−80162.4			−0.00534516
$743$			8.39787e6i			0.558081i	0.960279	+	0.279040i	$0.0900163\pi$
$743$			8.39787e6i			0.558081i	−0.960279	+	0.279040i	$0.909984\pi$
$744$	−168286.	−	168286.i	−0.0111459	−	0.0111459i
$745$	−5.65245e6	+	5.65245e6i	−0.373118	+	0.373118i
$746$			1.58559e7i			1.04314i
$747$		−	8.25420e6i		−	0.541220i
$748$	4.46619e6			0.291866
$749$	72791.6	−	72791.6i	0.00474108	−	0.00474108i
$750$	9.47495e6	−	9.47495e6i	0.615069	−	0.615069i
$751$	1.19566e7	−	1.19566e7i	0.773583	−	0.773583i	−0.205148	−	0.978731i	$-0.565768\pi$
$751$	1.19566e7	−	1.19566e7i	0.773583	−	0.773583i	0.978731	+	0.205148i	$0.0657676\pi$
$752$	2.55612e6	+	2.55612e6i	0.164830	+	0.164830i
$753$	−1.32817e7	−	1.32817e7i	−0.853624	−	0.853624i
$754$	7.66476e6			0.490987
$755$	1.03460e7	+	1.03460e7i	0.660548	+	0.660548i
$756$	−19647.0			−0.00125023
$757$	424720.	+	424720.i	0.0269378	+	0.0269378i	0.720447	−	0.693510i	$-0.243936\pi$
$757$	424720.	+	424720.i	0.0269378	+	0.0269378i	−0.693510	+	0.720447i	$0.743936\pi$
$758$		−	6.24220e6i		−	0.394607i
$759$		−	2.17769e6i		−	0.137212i
$760$	2.45727e6	+	2.45727e6i	0.154319	+	0.154319i
$761$	−2.76470e7			−1.73056			−0.865280	−	0.501289i	$-0.832859\pi$
$761$	−2.76470e7			−1.73056			−0.865280	+	0.501289i	$0.832859\pi$
$762$	2.11323e7	+	2.11323e7i	1.31844	+	1.31844i
$763$	193379.			0.0120254
$764$	774695.	+	774695.i	0.0480173	+	0.0480173i
$765$	9.46146e6	+	9.46146e6i	0.584527	+	0.584527i
$766$	1.04674e7	−	1.04674e7i	0.644562	−	0.644562i
$767$	−8.15422e6	+	8.15422e6i	−0.500488	+	0.500488i
$768$	987974.	−	987974.i	0.0604425	−	0.0604425i
$769$	−2.55706e6			−0.155928			−0.0779641	−	0.996956i	$-0.524842\pi$
$769$	−2.55706e6			−0.155928			−0.0779641	+	0.996956i	$0.524842\pi$
$770$		−	27301.5i		−	0.00165943i
$771$			1.43622e7i			0.870133i
$772$	−8.43370e6	+	8.43370e6i	−0.509302	+	0.509302i
$773$	−1.13148e7	−	1.13148e7i	−0.681082	−	0.681082i	0.279162	−	0.960244i	$-0.409943\pi$
$773$	−1.13148e7	−	1.13148e7i	−0.681082	−	0.681082i	−0.960244	+	0.279162i	$0.909943\pi$
$774$		−	3.68338e6i		−	0.221001i
$775$	397656.			0.0237823
$776$	1.25929e6	−	1.25929e6i	0.0750710	−	0.0750710i
$777$			41839.5i			0.00248619i
$778$	2.21463e7			1.31175
$779$	399359.	−	2.00999e7i	0.0235787	−	1.18672i
$780$	6.14384e6			0.361579
$781$			604483.i			0.0354614i
$782$	4.90021e6	−	4.90021e6i	0.286548	−	0.286548i
$783$	2.07523e6			0.120966
$784$			4.30173e6i			0.249950i
$785$	4.93027e6	+	4.93027e6i	0.285559	+	0.285559i
$786$	−8.01697e6	+	8.01697e6i	−0.462865	+	0.462865i
$787$			2.07217e7i			1.19258i	0.802769	+	0.596290i	$0.203359\pi$
$787$			2.07217e7i			1.19258i	−0.802769	+	0.596290i	$0.796641\pi$
$788$			492049.i			0.0282288i
$789$	−1.16982e7			−0.669003
$790$	2.97940e6	−	2.97940e6i	0.169848	−	0.169848i
$791$	131120.	−	131120.i	0.00745123	−	0.00745123i
$792$	−1.22805e6	+	1.22805e6i	−0.0695668	+	0.0695668i
$793$	5.37943e6	+	5.37943e6i	0.303776	+	0.303776i
$794$	−1.43156e7	−	1.43156e7i	−0.805857	−	0.805857i
$795$	6.78708e6			0.380860
$796$	−7.61070e6	−	7.61070e6i	−0.425737	−	0.425737i
$797$	−1.63440e7			−0.911408			−0.455704	−	0.890131i	$-0.650613\pi$
$797$	−1.63440e7			−0.911408			−0.455704	+	0.890131i	$0.650613\pi$
$798$	−206121.	−	206121.i	−0.0114581	−	0.0114581i
$799$		−	3.07251e7i		−	1.70265i
$800$			2.33456e6i			0.128967i
$801$	−5.70726e6	−	5.70726e6i	−0.314301	−	0.314301i
$802$	5.11206e6			0.280647
$803$	4.88858e6	+	4.88858e6i	0.267543	+	0.267543i
$804$	765518.			0.0417653
$805$	−29954.6	−	29954.6i	−0.00162920	−	0.00162920i
$806$	305646.	+	305646.i	0.0165722	+	0.0165722i
$807$	3.98236e6	−	3.98236e6i	0.215257	−	0.215257i
$808$	−6.07472e6	+	6.07472e6i	−0.327339	+	0.327339i
$809$	1.11480e7	−	1.11480e7i	0.598860	−	0.598860i	−0.341149	−	0.940009i	$-0.610816\pi$
$809$	1.11480e7	−	1.11480e7i	0.598860	−	0.598860i	0.940009	+	0.341149i	$0.110816\pi$
$810$	7.64072e6			0.409187
$811$			9.51335e6i			0.507904i	0.967217	+	0.253952i	$0.0817305\pi$
$811$			9.51335e6i			0.507904i	−0.967217	+	0.253952i	$0.918270\pi$
$812$			90565.8i			0.00482030i
$813$	−2.87782e6	+	2.87782e6i	−0.152699	+	0.152699i
$814$	−389095.	−	389095.i	−0.0205823	−	0.0205823i
$815$		−	1.86117e7i		−	0.981504i
$816$	−1.18756e7			−0.624354
$817$	−5.74939e6	+	5.74939e6i	−0.301347	+	0.301347i
$818$		−	1.28714e6i		−	0.0672578i
$819$	−239837.			−0.0124942
$820$	−3.60987e6	+	3.46922e6i	−0.187481	+	0.180176i
$821$	−1.67324e7			−0.866364			−0.433182	−	0.901307i	$-0.642609\pi$
$821$	−1.67324e7			−0.866364			−0.433182	+	0.901307i	$0.642609\pi$
$822$		−	2.52190e7i		−	1.30181i
$823$	−1.53825e7	+	1.53825e7i	−0.791641	+	0.791641i	−0.981761	−	0.190120i	$-0.939112\pi$
$823$	−1.53825e7	+	1.53825e7i	−0.791641	+	0.791641i	0.190120	+	0.981761i	$0.439112\pi$
$824$	2.51087e6			0.128827
$825$		−	6.23544e6i		−	0.318957i
$826$	−96349.1	−	96349.1i	−0.00491358	−	0.00491358i
$827$	−1.05375e7	+	1.05375e7i	−0.535764	+	0.535764i	−0.922282	−	0.386518i	$-0.873678\pi$
$827$	−1.05375e7	+	1.05375e7i	−0.535764	+	0.535764i	0.386518	+	0.922282i	$0.373678\pi$
$828$			2.69477e6i			0.136599i
$829$		−	2.09961e7i		−	1.06109i	−0.847656	−	0.530546i	$-0.821987\pi$
$829$		−	2.09961e7i		−	1.06109i	0.847656	−	0.530546i	$-0.178013\pi$
$830$	4.53769e6			0.228633
$831$	−5.25338e6	+	5.25338e6i	−0.263898	+	0.263898i
$832$	−1.79439e6	+	1.79439e6i	−0.0898686	+	0.0898686i
$833$	2.58538e7	−	2.58538e7i	1.29096	−	1.29096i
$834$	3.19786e6	+	3.19786e6i	0.159201	+	0.159201i
$835$	2.03636e6	+	2.03636e6i	0.101074	+	0.101074i
$836$	3.83372e6			0.189716
$837$	82753.6	+	82753.6i	0.00408294	+	0.00408294i
$838$	−2.09781e7			−1.03194
$839$	8.92837e6	+	8.92837e6i	0.437892	+	0.437892i	0.891302	−	0.453410i	$-0.149793\pi$
$839$	8.92837e6	+	8.92837e6i	0.437892	+	0.437892i	−0.453410	+	0.891302i	$0.649793\pi$
$840$			72594.8i			0.00354983i
$841$			1.09450e7i			0.533614i
$842$	−4.93985e6	−	4.93985e6i	−0.240123	−	0.240123i
$843$	3.70852e7			1.79735
$844$	1.70276e6	+	1.70276e6i	0.0822807	+	0.0822807i
$845$	−364561.			−0.0175642
$846$	8.44832e6	+	8.44832e6i	0.405830	+	0.405830i
$847$	187116.	+	187116.i	0.00896194	+	0.00896194i
$848$	−1.98225e6	+	1.98225e6i	−0.0946607	+	0.0946607i
$849$	1.49303e7	−	1.49303e7i	0.710885	−	0.710885i
$850$	1.40309e7	−	1.40309e7i	0.666099	−	0.666099i
$851$	−853814.			−0.0404147
$852$		−	1.60732e6i		−	0.0758585i
$853$		−	1.54675e6i		−	0.0727860i	−0.999338	−	0.0363930i	$-0.988413\pi$
$853$		−	1.54675e6i		−	0.0727860i	0.999338	−	0.0363930i	$-0.0115868\pi$
$854$	−63562.6	+	63562.6i	−0.00298234	+	0.00298234i
$855$	8.12160e6	+	8.12160e6i	0.379950	+	0.379950i
$856$		−	3.59998e6i		−	0.167925i
$857$	−1.11246e7			−0.517408			−0.258704	−	0.965957i	$-0.583295\pi$
$857$	−1.11246e7			−0.517408			−0.258704	+	0.965957i	$0.583295\pi$
$858$	4.79267e6	−	4.79267e6i	0.222259	−	0.222259i
$859$		−	2.95227e7i		−	1.36513i	−0.730825	−	0.682565i	$-0.760865\pi$
$859$		−	2.95227e7i		−	1.36513i	0.730825	−	0.682565i	$-0.239135\pi$
$860$	2.02491e6			0.0933598
$861$	302803.	−	291005.i	0.0139204	−	0.0133780i
$862$	2.81689e7			1.29122
$863$		−	3.76504e6i		−	0.172085i	−0.996291	−	0.0860424i	$-0.972578\pi$
$863$		−	3.76504e6i		−	0.172085i	0.996291	−	0.0860424i	$-0.0274220\pi$
$864$	−485830.	+	485830.i	−0.0221411	+	0.0221411i
$865$	−1.53009e7			−0.695306
$866$		−	1.60974e7i		−	0.729393i
$867$	4.99688e7	+	4.99688e7i	2.25762	+	2.25762i
$868$	−3611.47	+	3611.47i	−0.000162699	+	0.000162699i
$869$		−	4.64832e6i		−	0.208808i
$870$		−	7.66790e6i		−	0.343462i
$871$	−1.39036e6			−0.0620985
$872$	4.78188e6	−	4.78188e6i	0.212964	−	0.212964i
$873$	4.16213e6	−	4.16213e6i	0.184833	−	0.184833i
$874$	4.20628e6	−	4.20628e6i	0.186260	−	0.186260i
$875$	−203336.	−	203336.i	−0.00897828	−	0.00897828i
$876$	−1.29988e7	−	1.29988e7i	−0.572324	−	0.572324i
$877$	2.18337e6			0.0958581			0.0479290	−	0.998851i	$-0.484738\pi$
$877$	2.18337e6			0.0958581			0.0479290	+	0.998851i	$0.484738\pi$
$878$	6.76949e6	+	6.76949e6i	0.296360	+	0.296360i
$879$	−3.31554e7			−1.44738
$880$	−675110.	−	675110.i	−0.0293879	−	0.0293879i
$881$		−	1.69081e7i		−	0.733933i	−0.930234	−	0.366966i	$-0.880396\pi$
$881$		−	1.69081e7i		−	0.733933i	0.930234	−	0.366966i	$-0.119604\pi$
$882$			1.42178e7i			0.615405i
$883$	4.91158e6	+	4.91158e6i	0.211992	+	0.211992i	0.805113	−	0.593121i	$-0.202104\pi$
$883$	4.91158e6	+	4.91158e6i	0.211992	+	0.211992i	−0.593121	+	0.805113i	$0.702104\pi$
$884$	2.15689e7			0.928317
$885$	8.15756e6	+	8.15756e6i	0.350108	+	0.350108i
$886$	−1.48362e7			−0.634949
$887$	1.24711e7	+	1.24711e7i	0.532225	+	0.532225i	0.921234	−	0.389009i	$-0.127183\pi$
$887$	1.24711e7	+	1.24711e7i	0.532225	+	0.532225i	−0.389009	+	0.921234i	$0.627183\pi$
$888$	1.03461e6	+	1.03461e6i	0.0440294	+	0.0440294i
$889$	453506.	−	453506.i	0.0192455	−	0.0192455i
$890$	3.13752e6	−	3.13752e6i	0.132774	−	0.132774i
$891$	5.96035e6	−	5.96035e6i	0.251523	−	0.251523i
$892$	−1.96659e7			−0.827564
$893$		−	2.63740e7i		−	1.10674i
$894$		−	2.34490e7i		−	0.981251i
$895$	2.14173e6	−	2.14173e6i	0.0893733	−	0.0893733i
$896$	−21202.2	−	21202.2i	−0.000882290	−	0.000882290i
$897$		−	1.05168e7i		−	0.436420i
$898$	−2.92757e7			−1.21148
$899$	381465.	−	381465.i	0.0157418	−	0.0157418i
$900$			7.71603e6i			0.317532i
$901$	2.38270e7			0.977818
$902$	−109720.	+	5.52224e6i	−0.00449023	+	0.225995i
$903$	−169854.			−0.00693195
$904$		−	6.48466e6i		−	0.263916i
$905$	−1.58629e7	+	1.58629e7i	−0.643817	+	0.643817i
$906$	−4.29199e7			−1.73715
$907$			6.54693e6i			0.264253i	0.991233	+	0.132126i	$0.0421805\pi$
$907$			6.54693e6i			0.264253i	−0.991233	+	0.132126i	$0.957820\pi$
$908$	1.12304e7	+	1.12304e7i	0.452046	+	0.452046i
$909$	−2.00777e7	+	2.00777e7i	−0.805944	+	0.805944i
$910$		−	131849.i		−	0.00527804i
$911$		−	1.02691e6i		−	0.0409956i	−0.999790	−	0.0204978i	$-0.993475\pi$
$911$		−	1.02691e6i		−	0.0409956i	0.999790	−	0.0204978i	$-0.00652510\pi$
$912$	−1.01939e7			−0.405838
$913$	3.53975e6	−	3.53975e6i	0.140539	−	0.140539i
$914$	−9.08821e6	+	9.08821e6i	−0.359843	+	0.359843i
$915$	5.38164e6	−	5.38164e6i	0.212501	−	0.212501i
$916$	1.30708e7	+	1.30708e7i	0.514711	+	0.514711i
$917$	172047.	+	172047.i	0.00675652	+	0.00675652i
$918$	5.83976e6			0.228712
$919$	−2.52302e7	−	2.52302e7i	−0.985444	−	0.985444i	0.0144520	−	0.999896i	$-0.495400\pi$
$919$	−2.52302e7	−	2.52302e7i	−0.985444	−	0.985444i	−0.999896	+	0.0144520i	$0.995400\pi$
$920$	−1.48143e6			−0.0577049
$921$	3.56354e6	+	3.56354e6i	0.138431	+	0.138431i
$922$		−	1.59901e7i		−	0.619475i
$923$			2.91927e6i			0.112790i
$924$	56629.6	+	56629.6i	0.00218204	+	0.00218204i
$925$	−2.44475e6			−0.0939464
$926$	−1.24350e7	−	1.24350e7i	−0.476561	−	0.476561i
$927$	8.29874e6			0.317185
$928$	2.23951e6	+	2.23951e6i	0.0853655	+	0.0853655i
$929$	−3.50138e7	−	3.50138e7i	−1.33107	−	1.33107i	−0.904415	−	0.426653i	$-0.859692\pi$
$929$	−3.50138e7	−	3.50138e7i	−1.33107	−	1.33107i	−0.426653	−	0.904415i	$-0.640308\pi$
$930$	305771.	−	305771.i	0.0115928	−	0.0115928i
$931$	2.21926e7	−	2.21926e7i	0.839139	−	0.839139i
$932$	9.35311e6	−	9.35311e6i	0.352709	−	0.352709i
$933$	−4.28956e7			−1.61328
$934$			2.63980e7i			0.990157i
$935$			8.11494e6i			0.303568i
$936$	−5.93069e6	+	5.93069e6i	−0.221266	+	0.221266i
$937$	1.24419e7	+	1.24419e7i	0.462955	+	0.462955i	0.899623	−	0.436668i	$-0.143841\pi$
$937$	1.24419e7	+	1.24419e7i	0.462955	+	0.462955i	−0.436668	+	0.899623i	$0.643841\pi$
$938$		−	16428.3i		−	0.000609656i
$939$	2.27822e7			0.843202
$940$	−4.64441e6	+	4.64441e6i	−0.171439	+	0.171439i
$941$			9.95768e6i			0.366593i	0.983058	+	0.183296i	$0.0586768\pi$
$941$			9.95768e6i			0.366593i	−0.983058	+	0.183296i	$0.941323\pi$
$942$	−2.04530e7			−0.750983
$943$	5.93850e6	+	6.17927e6i	0.217469	+	0.226286i
$944$	−4.76503e6			−0.174035
$945$		−	35698.0i		−	0.00130036i
$946$	1.57959e6	−	1.57959e6i	0.0573873	−	0.0573873i
$947$	−1.33532e7			−0.483851			−0.241926	−	0.970295i	$-0.577779\pi$
$947$	−1.33532e7			−0.483851			−0.241926	+	0.970295i	$0.577779\pi$
$948$			1.23599e7i			0.446678i
$949$	2.36088e7	+	2.36088e7i	0.850957	+	0.850957i
$950$	1.20440e7	−	1.20440e7i	0.432973	−	0.432973i
$951$			6.51801e7i			2.33703i
$952$			254855.i			0.00911382i
$953$	−1.74086e7			−0.620914			−0.310457	−	0.950587i	$-0.600482\pi$
$953$	−1.74086e7			−0.620914			−0.310457	+	0.950587i	$0.600482\pi$
$954$	−6.55161e6	+	6.55161e6i	−0.233065	+	0.233065i
$955$	−1.40760e6	+	1.40760e6i	−0.0499426	+	0.0499426i
$956$	−1.14882e7	+	1.14882e7i	−0.406543	+	0.406543i
$957$	−5.98156e6	−	5.98156e6i	−0.211122	−	0.211122i
$958$	1.38503e7	+	1.38503e7i	0.487580	+	0.487580i
$959$	−541207.			−0.0190028
$960$	1.79512e6	+	1.79512e6i	0.0628660	+	0.0628660i
$961$	−2.85987e7			−0.998937
$962$	−1.87908e6	−	1.87908e6i	−0.0654648	−	0.0654648i
$963$		−	1.18984e7i		−	0.413450i
$964$		−	1.40765e7i		−	0.487868i
$965$	−1.53238e7	−	1.53238e7i	−0.529723	−	0.529723i
$966$	124266.			0.00428458
$967$	1.57761e7	+	1.57761e7i	0.542543	+	0.542543i	0.924274	−	0.381730i	$-0.124672\pi$
$967$	1.57761e7	+	1.57761e7i	0.542543	+	0.542543i	−0.381730	+	0.924274i	$0.624672\pi$
$968$	9.25399e6			0.317425
$969$	6.12662e7	+	6.12662e7i	2.09610	+	2.09610i
$970$	2.28810e6	+	2.28810e6i	0.0780810	+	0.0780810i
$971$	−1.64926e7	+	1.64926e7i	−0.561359	+	0.561359i	−0.929693	−	0.368334i	$-0.879928\pi$
$971$	−1.64926e7	+	1.64926e7i	−0.561359	+	0.561359i	0.368334	+	0.929693i	$0.379928\pi$
$972$	−1.40040e7	+	1.40040e7i	−0.475429	+	0.475429i
$973$	68627.2	−	68627.2i	0.00232388	−	0.00232388i
$974$	−1.99134e7			−0.672586
$975$		−	3.01132e7i		−	1.01448i
$976$			3.14355e6i			0.105632i
$977$	−3.47968e7	+	3.47968e7i	−1.16628	+	1.16628i	−0.183206	+	0.983075i	$0.558648\pi$
$977$	−3.47968e7	+	3.47968e7i	−1.16628	+	1.16628i	−0.983075	+	0.183206i	$0.941352\pi$
$978$	3.86050e7	+	3.86050e7i	1.29061	+	1.29061i
$979$		−	4.89502e6i		−	0.163229i
$980$	−7.81614e6			−0.259972
$981$	1.58047e7	−	1.58047e7i	0.524342	−	0.524342i
$982$			3.65144e7i			1.20833i
$983$	−4.75192e7			−1.56850			−0.784251	−	0.620444i	$-0.786952\pi$
$983$	−4.75192e7			−1.56850			−0.784251	+	0.620444i	$0.786952\pi$
$984$	291746.	−	1.46837e7i	0.00960543	−	0.483445i
$985$	−894040.			−0.0293607
$986$		−	2.69193e7i		−	0.881802i
$987$	389582.	−	389582.i	0.0127293	−	0.0127293i
$988$	1.85144e7			0.603418
$989$		−	3.46618e6i		−	0.112684i
$990$	−2.23133e6	−	2.23133e6i	−0.0723561	−	0.0723561i
$991$	−5.58171e6	+	5.58171e6i	−0.180544	+	0.180544i	−0.791593	−	0.611049i	$-0.790748\pi$
$991$	−5.58171e6	+	5.58171e6i	−0.180544	+	0.180544i	0.611049	+	0.791593i	$0.290748\pi$
$992$			178609.i			0.00576266i
$993$			3.28130e7i			1.05602i
$994$	−34493.7			−0.00110732
$995$	1.38284e7	−	1.38284e7i	0.442808	−	0.442808i
$996$	−9.41221e6	+	9.41221e6i	−0.300638	+	0.300638i
$997$	6.13168e6	−	6.13168e6i	0.195363	−	0.195363i	−0.602646	−	0.798009i	$-0.705887\pi$
$997$	6.13168e6	−	6.13168e6i	0.195363	−	0.195363i	0.798009	+	0.602646i	$0.205887\pi$
$998$	−1.45759e7	−	1.45759e7i	−0.463242	−	0.463242i
$999$	−508761.	−	508761.i	−0.0161287	−	0.0161287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.6.c.a.73.7	yes	16
41.9	even	4	inner	82.6.c.a.9.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.6.c.a.9.7	✓	16	41.9	even	4	inner
82.6.c.a.73.7	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} +(15.0753 - 15.0753i) q^{3} -16.0000 q^{4} -29.0716i q^{5} +(60.3011 + 60.3011i) q^{6} +(1.29408 - 1.29408i) q^{7} -64.0000i q^{8} -211.528i q^{9} +116.286 q^{10} +(90.7123 - 90.7123i) q^{11} +(-241.205 + 241.205i) q^{12} +(438.083 - 438.083i) q^{13} +(5.17633 + 5.17633i) q^{14} +(-438.262 - 438.262i) q^{15} +256.000 q^{16} +(-1538.58 - 1538.58i) q^{17} +846.114 q^{18} +(-1320.70 - 1320.70i) q^{19} +465.145i q^{20} -39.0173i q^{21} +(362.849 + 362.849i) q^{22} +796.221 q^{23} +(-964.818 - 964.818i) q^{24} +2279.84 q^{25} +(1752.33 + 1752.33i) q^{26} +(474.443 + 474.443i) q^{27} +(-20.7053 + 20.7053i) q^{28} +(2187.02 - 2187.02i) q^{29} +(1753.05 - 1753.05i) q^{30} +174.422 q^{31} +1024.00i q^{32} -2735.03i q^{33} +(6154.33 - 6154.33i) q^{34} +(-37.6210 - 37.6210i) q^{35} +3384.45i q^{36} -1072.33 q^{37} +(5282.80 - 5282.80i) q^{38} -13208.4i q^{39} -1860.58 q^{40} +(7458.36 + 7760.74i) q^{41} +156.069 q^{42} -4353.29i q^{43} +(-1451.40 + 1451.40i) q^{44} -6149.46 q^{45} +3184.88i q^{46} +(9984.85 + 9984.85i) q^{47} +(3859.27 - 3859.27i) q^{48} +16803.7i q^{49} +9119.38i q^{50} -46389.2 q^{51} +(-7009.33 + 7009.33i) q^{52} +(-7743.18 + 7743.18i) q^{53} +(-1897.77 + 1897.77i) q^{54} +(-2637.15 - 2637.15i) q^{55} +(-82.8212 - 82.8212i) q^{56} -39819.9 q^{57} +(8748.08 + 8748.08i) q^{58} -18613.4 q^{59} +(7012.19 + 7012.19i) q^{60} +12279.5i q^{61} +697.690i q^{62} +(-273.735 - 273.735i) q^{63} -4096.00 q^{64} +(-12735.8 - 12735.8i) q^{65} +10940.1 q^{66} +(-1586.86 - 1586.86i) q^{67} +(24617.3 + 24617.3i) q^{68} +(12003.3 - 12003.3i) q^{69} +(150.484 - 150.484i) q^{70} +(-3331.87 + 3331.87i) q^{71} -13537.8 q^{72} +53891.1i q^{73} -4289.33i q^{74} +(34369.3 - 34369.3i) q^{75} +(21131.2 + 21131.2i) q^{76} -234.778i q^{77} +52833.8 q^{78} +(25621.2 - 25621.2i) q^{79} -7442.32i q^{80} +65706.1 q^{81} +(-31043.0 + 29833.4i) q^{82} +39021.7 q^{83} +624.277i q^{84} +(-44729.0 + 44729.0i) q^{85} +17413.2 q^{86} -65939.9i q^{87} +(-5805.59 - 5805.59i) q^{88} +(26981.0 - 26981.0i) q^{89} -24597.8i q^{90} -1133.83i q^{91} -12739.5 q^{92} +(2629.47 - 2629.47i) q^{93} +(-39939.4 + 39939.4i) q^{94} +(-38394.8 + 38394.8i) q^{95} +(15437.1 + 15437.1i) q^{96} +(19676.4 + 19676.4i) q^{97} -67214.6 q^{98} +(-19188.2 - 19188.2i) 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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