LMFDB - Embedded newform 140.6.g.a.111.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,6,Mod(111,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("140.111");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	140.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$22.4537347738$
Analytic rank:	$0$
Dimension:	$80$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			111.19
Character	$\chi$	$=$	140.111
Dual form			140.6.g.a.111.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.03990 + 3.95970i) q^{2} -8.42590 q^{3} +(0.641579 - 31.9936i) q^{4} +25.0000i q^{5} +(34.0398 - 33.3640i) q^{6} +(-129.634 + 1.38412i) q^{7} +(124.093 + 131.791i) q^{8} -172.004 q^{9} +O(q^{10})$	\(q+(-4.03990 + 3.95970i) q^{2} -8.42590 q^{3} +(0.641579 - 31.9936i) q^{4} +25.0000i q^{5} +(34.0398 - 33.3640i) q^{6} +(-129.634 + 1.38412i) q^{7} +(124.093 + 131.791i) q^{8} -172.004 q^{9} +(-98.9925 - 100.997i) q^{10} +236.451i q^{11} +(-5.40588 + 269.575i) q^{12} -80.3721i q^{13} +(518.229 - 518.905i) q^{14} -210.648i q^{15} +(-1023.18 - 41.0528i) q^{16} +665.963i q^{17} +(694.880 - 681.085i) q^{18} -2744.67 q^{19} +(799.839 + 16.0395i) q^{20} +(1092.29 - 11.6624i) q^{21} +(-936.274 - 955.238i) q^{22} -4368.68i q^{23} +(-1045.60 - 1110.46i) q^{24} -625.000 q^{25} +(318.249 + 324.695i) q^{26} +3496.78 q^{27} +(-38.8878 + 4148.36i) q^{28} +2918.69 q^{29} +(834.101 + 850.995i) q^{30} +1442.43 q^{31} +(4296.09 - 3885.62i) q^{32} -1992.31i q^{33} +(-2637.01 - 2690.42i) q^{34} +(-34.6029 - 3240.86i) q^{35} +(-110.354 + 5503.03i) q^{36} +11063.9 q^{37} +(11088.2 - 10868.1i) q^{38} +677.207i q^{39} +(-3294.78 + 3102.32i) q^{40} +11678.7i q^{41} +(-4366.55 + 4372.24i) q^{42} +9167.01i q^{43} +(7564.91 + 151.702i) q^{44} -4300.10i q^{45} +(17298.7 + 17649.0i) q^{46} -2648.21 q^{47} +(8621.19 + 345.907i) q^{48} +(16803.2 - 358.858i) q^{49} +(2524.94 - 2474.81i) q^{50} -5611.34i q^{51} +(-2571.39 - 51.5650i) q^{52} +38013.8 q^{53} +(-14126.7 + 13846.2i) q^{54} -5911.27 q^{55} +(-16269.1 - 16912.9i) q^{56} +23126.3 q^{57} +(-11791.2 + 11557.1i) q^{58} -17964.2 q^{59} +(-6739.37 - 135.147i) q^{60} +577.717i q^{61} +(-5827.27 + 5711.58i) q^{62} +(22297.7 - 238.074i) q^{63} +(-1969.87 + 32708.7i) q^{64} +2009.30 q^{65} +(7888.95 + 8048.74i) q^{66} -37763.1i q^{67} +(21306.5 + 427.268i) q^{68} +36810.1i q^{69} +(12972.6 + 12955.7i) q^{70} -62852.9i q^{71} +(-21344.5 - 22668.6i) q^{72} -64985.9i q^{73} +(-44696.9 + 43809.6i) q^{74} +5266.19 q^{75} +(-1760.92 + 87811.7i) q^{76} +(-327.276 - 30652.2i) q^{77} +(-2681.54 - 2735.85i) q^{78} -14789.0i q^{79} +(1026.32 - 25579.4i) q^{80} +12333.4 q^{81} +(-46244.1 - 47180.7i) q^{82} +69004.9 q^{83} +(327.665 - 34953.6i) q^{84} -16649.1 q^{85} +(-36298.6 - 37033.8i) q^{86} -24592.6 q^{87} +(-31162.2 + 29341.9i) q^{88} -101082. i q^{89} +(17027.1 + 17372.0i) q^{90} +(111.244 + 10419.0i) q^{91} +(-139770. - 2802.85i) q^{92} -12153.8 q^{93} +(10698.5 - 10486.1i) q^{94} -68616.7i q^{95} +(-36198.4 + 32739.9i) q^{96} +66005.1i q^{97} +(-66462.1 + 67985.2i) q^{98} -40670.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{2} - 22 q^{4} - 178 q^{8} + 6480 q^{9}+O(q^{10}) $ 80 * q + 2 * q^2 - 22 * q^4 - 178 * q^8 + 6480 * q^9	$ 80 q + 2 q^{2} - 22 q^{4} - 178 q^{8} + 6480 q^{9} + 390 q^{14} + 2850 q^{16} + 8830 q^{18} + 3428 q^{21} + 1248 q^{22} - 50000 q^{25} + 9382 q^{28} - 16104 q^{29} - 19298 q^{32} - 56470 q^{36} + 16992 q^{37} - 17116 q^{42} - 44404 q^{44} - 51340 q^{46} + 37516 q^{49} - 1250 q^{50} - 14432 q^{53} - 494 q^{56} + 77328 q^{57} + 107480 q^{58} - 7700 q^{60} - 98494 q^{64} - 42200 q^{65} + 36400 q^{70} - 210642 q^{72} - 229924 q^{74} - 39912 q^{77} + 122676 q^{78} + 300680 q^{81} + 256808 q^{84} + 82348 q^{86} + 98692 q^{88} - 607884 q^{92} + 667696 q^{93} - 397470 q^{98}+O(q^{100}) $ 80 * q + 2 * q^2 - 22 * q^4 - 178 * q^8 + 6480 * q^9 + 390 * q^14 + 2850 * q^16 + 8830 * q^18 + 3428 * q^21 + 1248 * q^22 - 50000 * q^25 + 9382 * q^28 - 16104 * q^29 - 19298 * q^32 - 56470 * q^36 + 16992 * q^37 - 17116 * q^42 - 44404 * q^44 - 51340 * q^46 + 37516 * q^49 - 1250 * q^50 - 14432 * q^53 - 494 * q^56 + 77328 * q^57 + 107480 * q^58 - 7700 * q^60 - 98494 * q^64 - 42200 * q^65 + 36400 * q^70 - 210642 * q^72 - 229924 * q^74 - 39912 * q^77 + 122676 * q^78 + 300680 * q^81 + 256808 * q^84 + 82348 * q^86 + 98692 * q^88 - 607884 * q^92 + 667696 * q^93 - 397470 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−4.03990	+	3.95970i	−0.714160	+	0.699982i
$2$	−4.03990	+	3.95970i	−0.714160	+	0.699982i
$3$	−8.42590			−0.540522			−0.270261	−	0.962787i	$-0.587110\pi$
$3$	−8.42590			−0.540522			−0.270261	+	0.962787i	$0.587110\pi$
$4$	0.641579	−	31.9936i	0.0200493	−	0.999799i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	34.0398	−	33.3640i	0.386019	−	0.378356i
$7$	−129.634	+	1.38412i	−0.999943	+	0.0106765i
$7$	−129.634	+	1.38412i	−0.999943	+	0.0106765i
$8$	124.093	+	131.791i	0.685523	+	0.728051i
$9$	−172.004			−0.707836
$10$	−98.9925	−	100.997i	−0.313042	−	0.319382i
$11$			236.451i			0.589195i	0.955621	+	0.294598i	$0.0951856\pi$
$11$			236.451i			0.589195i	−0.955621	+	0.294598i	$0.904814\pi$
$12$	−5.40588	+	269.575i	−0.0108371	+	0.540413i
$13$		−	80.3721i		−	0.131901i	−0.997823	−	0.0659503i	$-0.978992\pi$
$13$		−	80.3721i		−	0.131901i	0.997823	−	0.0659503i	$-0.0210079\pi$
$14$	518.229	−	518.905i	0.706646	−	0.707567i
$15$		−	210.648i		−	0.241729i
$16$	−1023.18	−	41.0528i	−0.999196	−	0.0400906i
$17$			665.963i			0.558892i	0.960161	+	0.279446i	$0.0901508\pi$
$17$			665.963i			0.558892i	−0.960161	+	0.279446i	$0.909849\pi$
$18$	694.880	−	681.085i	0.505508	−	0.495473i
$19$	−2744.67			−1.74424			−0.872119	−	0.489294i	$-0.837255\pi$
$19$	−2744.67			−1.74424			−0.872119	+	0.489294i	$0.837255\pi$
$20$	799.839	+	16.0395i	0.447124	+	0.00896633i
$21$	1092.29	−	11.6624i	0.540491	−	0.00577087i
$22$	−936.274	−	955.238i	−0.412426	−	0.420780i
$23$		−	4368.68i		−	1.72199i	−0.508612	−	0.860996i	$-0.669841\pi$
$23$		−	4368.68i		−	1.72199i	0.508612	−	0.860996i	$-0.330159\pi$
$24$	−1045.60	−	1110.46i	−0.370540	−	0.393527i
$25$	−625.000			−0.200000
$26$	318.249	+	324.695i	0.0923281	+	0.0941981i
$27$	3496.78			0.923123
$28$	−38.8878	+	4148.36i	−0.00937386	+	0.999956i
$29$	2918.69			0.644456			0.322228	−	0.946662i	$-0.395568\pi$
$29$	2918.69			0.644456			0.322228	+	0.946662i	$0.395568\pi$
$30$	834.101	+	850.995i	0.169206	+	0.172633i
$31$	1442.43			0.269582			0.134791	−	0.990874i	$-0.456964\pi$
$31$	1442.43			0.269582			0.134791	+	0.990874i	$0.456964\pi$
$32$	4296.09	−	3885.62i	0.741649	−	0.670789i
$33$		−	1992.31i		−	0.318473i
$34$	−2637.01	−	2690.42i	−0.391214	−	0.399138i
$35$	−34.6029	−	3240.86i	−0.00477466	−	0.447188i
$36$	−110.354	+	5503.03i	−0.0141916	+	0.707694i
$37$	11063.9			1.32862			0.664312	−	0.747455i	$-0.268724\pi$
$37$	11063.9			1.32862			0.664312	+	0.747455i	$0.268724\pi$
$38$	11088.2	−	10868.1i	1.24567	−	1.22094i
$39$			677.207i			0.0712952i
$40$	−3294.78	+	3102.32i	−0.325594	+	0.306575i
$41$			11678.7i			1.08501i	0.840052	+	0.542506i	$0.182524\pi$
$41$			11678.7i			1.08501i	−0.840052	+	0.542506i	$0.817476\pi$
$42$	−4366.55	+	4372.24i	−0.381958	+	0.382456i
$43$			9167.01i			0.756060i	0.925793	+	0.378030i	$0.123398\pi$
$43$			9167.01i			0.756060i	−0.925793	+	0.378030i	$0.876602\pi$
$44$	7564.91	+	151.702i	0.589077	+	0.0118130i
$45$		−	4300.10i		−	0.316554i
$46$	17298.7	+	17649.0i	1.20536	+	1.22978i
$47$	−2648.21			−0.174867			−0.0874334	−	0.996170i	$-0.527866\pi$
$47$	−2648.21			−0.174867			−0.0874334	+	0.996170i	$0.527866\pi$
$48$	8621.19	+	345.907i	0.540087	+	0.0216698i
$49$	16803.2	−	358.858i	0.999772	−	0.0213517i
$50$	2524.94	−	2474.81i	0.142832	−	0.139996i
$51$		−	5611.34i		−	0.302093i
$52$	−2571.39	−	51.5650i	−0.131874	−	0.00264452i
$53$	38013.8			1.85888			0.929440	−	0.368974i	$-0.120291\pi$
$53$	38013.8			1.85888			0.929440	+	0.368974i	$0.120291\pi$
$54$	−14126.7	+	13846.2i	−0.659258	+	0.646170i
$55$	−5911.27			−0.263496
$56$	−16269.1	−	16912.9i	−0.693257	−	0.720690i
$57$	23126.3			0.942799
$58$	−11791.2	+	11557.1i	−0.460245	+	0.451108i
$59$	−17964.2			−0.671857			−0.335929	−	0.941887i	$-0.609050\pi$
$59$	−17964.2			−0.671857			−0.335929	+	0.941887i	$0.609050\pi$
$60$	−6739.37	−	135.147i	−0.241680	−	0.00484650i
$61$			577.717i			0.0198788i	0.999951	+	0.00993941i	$0.00316386\pi$
$61$			577.717i			0.0198788i	−0.999951	+	0.00993941i	$0.996836\pi$
$62$	−5827.27	+	5711.58i	−0.192524	+	0.188702i
$63$	22297.7	−	238.074i	0.707796	−	0.00755719i
$64$	−1969.87	+	32708.7i	−0.0601158	+	0.998191i
$65$	2009.30			0.0589877
$66$	7888.95	+	8048.74i	0.222925	+	0.227441i
$67$		−	37763.1i		−	1.02773i	−0.857870	−	0.513867i	$-0.828212\pi$
$67$		−	37763.1i		−	1.02773i	0.857870	−	0.513867i	$-0.171788\pi$
$68$	21306.5	+	427.268i	0.558779	+	0.0112054i
$69$			36810.1i			0.930774i
$70$	12972.6	+	12955.7i	0.316434	+	0.316022i
$71$		−	62852.9i		−	1.47972i	−0.672761	−	0.739860i	$-0.734892\pi$
$71$		−	62852.9i		−	1.47972i	0.672761	−	0.739860i	$-0.265108\pi$
$72$	−21344.5	−	22668.6i	−0.485238	−	0.515341i
$73$		−	64985.9i		−	1.42729i	−0.700508	−	0.713644i	$-0.747043\pi$
$73$		−	64985.9i		−	1.42729i	0.700508	−	0.713644i	$-0.252957\pi$
$74$	−44696.9	+	43809.6i	−0.948851	+	0.930014i
$75$	5266.19			0.108104
$76$	−1760.92	+	87811.7i	−0.0349708	+	1.74389i
$77$	−327.276	−	30652.2i	−0.00629052	−	0.589161i
$78$	−2681.54	−	2735.85i	−0.0499054	−	0.0509162i
$79$		−	14789.0i		−	0.266606i	−0.991075	−	0.133303i	$-0.957442\pi$
$79$		−	14789.0i		−	0.266606i	0.991075	−	0.133303i	$-0.0425584\pi$
$80$	1026.32	−	25579.4i	0.0179291	−	0.446854i
$81$	12333.4			0.208868
$82$	−46244.1	−	47180.7i	−0.759489	−	0.774872i
$83$	69004.9			1.09947			0.549737	−	0.835338i	$-0.314728\pi$
$83$	69004.9			1.09947			0.549737	+	0.835338i	$0.314728\pi$
$84$	327.665	−	34953.6i	0.00506678	−	0.540498i
$85$	−16649.1			−0.249944
$86$	−36298.6	−	37033.8i	−0.529229	−	0.539948i
$87$	−24592.6			−0.348342
$88$	−31162.2	+	29341.9i	−0.428964	+	0.403907i
$89$		−	101082.i		−	1.35269i	−0.736584	−	0.676346i	$-0.763563\pi$
$89$		−	101082.i		−	1.35269i	0.736584	−	0.676346i	$-0.236437\pi$
$90$	17027.1	+	17372.0i	0.221582	+	0.226070i
$91$	111.244	+	10419.0i	0.00140823	+	0.131893i
$92$	−139770.	−	2802.85i	−1.72165	−	0.0345248i
$93$	−12153.8			−0.145715
$94$	10698.5	−	10486.1i	0.124883	−	0.122404i
$95$		−	68616.7i		−	0.780047i
$96$	−36198.4	+	32739.9i	−0.400877	+	0.362576i
$97$			66005.1i			0.712276i	0.934433	+	0.356138i	$0.115907\pi$
$97$			66005.1i			0.712276i	−0.934433	+	0.356138i	$0.884093\pi$
$98$	−66462.1	+	67985.2i	−0.699051	+	0.715071i
$99$		−	40670.5i		−	0.417054i
$100$	−400.987	+	19996.0i	−0.00400987	+	0.199960i
$101$			184851.i			1.80310i	0.432679	+	0.901548i	$0.357568\pi$
$101$			184851.i			1.80310i	−0.432679	+	0.901548i	$0.642432\pi$
$102$	22219.2	+	22669.2i	0.211460	+	0.215743i
$103$	−37459.2			−0.347909			−0.173954	−	0.984754i	$-0.555655\pi$
$103$	−37459.2			−0.347909			−0.173954	+	0.984754i	$0.555655\pi$
$104$	10592.3	−	9973.61i	0.0960303	−	0.0904209i
$105$	291.561	+	27307.2i	0.00258081	+	0.241715i
$106$	−153572.	+	150523.i	−1.32754	+	1.30118i
$107$		−	273.739i		−	0.00231141i	−0.999999	−	0.00115571i	$-0.999632\pi$
$107$		−	273.739i		−	0.00231141i	0.999999	−	0.00115571i	$-0.000367872\pi$
$108$	2243.46	−	111875.i	0.0185080	−	0.922937i
$109$	−65384.8			−0.527121			−0.263560	−	0.964643i	$-0.584897\pi$
$109$	−65384.8			−0.527121			−0.263560	+	0.964643i	$0.584897\pi$
$110$	23880.9	−	23406.8i	0.188178	−	0.184443i
$111$	−93223.0			−0.718151
$112$	132696.	+	3905.66i	0.999567	+	0.0294204i
$113$	−107336.			−0.790768			−0.395384	−	0.918516i	$-0.629388\pi$
$113$	−107336.			−0.790768			−0.395384	+	0.918516i	$0.629388\pi$
$114$	−93428.0	+	91573.2i	−0.673309	+	0.659943i
$115$	109217.			0.770098
$116$	1872.57	−	93379.3i	0.0129209	−	0.644326i
$117$			13824.3i			0.0933640i
$118$	72573.4	−	71132.7i	0.479814	−	0.470288i
$119$	−921.771	−	86331.7i	−0.00596699	−	0.558860i
$120$	27761.5	−	26139.9i	0.175991	−	0.165711i
$121$	105142.			0.652849
$122$	−2287.58	−	2333.92i	−0.0139148	−	0.0141967i
$123$		−	98403.5i		−	0.586473i
$124$	925.431	−	46148.4i	0.00540493	−	0.269527i
$125$		−	15625.0i		−	0.0894427i
$126$	−89137.6	+	89253.8i	−0.500190	+	0.500842i
$127$		−	51341.9i		−	0.282464i	−0.989977	−	0.141232i	$-0.954894\pi$
$127$		−	51341.9i		−	0.282464i	0.989977	−	0.141232i	$-0.0451063\pi$
$128$	−121559.	−	139940.i	−0.655784	−	0.754948i
$129$		−	77240.3i		−	0.408667i
$130$	−8117.38	+	7956.23i	−0.0421267	+	0.0412904i
$131$	−278204.			−1.41640			−0.708198	−	0.706014i	$-0.750492\pi$
$131$	−278204.			−1.41640			−0.708198	+	0.706014i	$0.750492\pi$
$132$	−63741.2	−	1278.22i	−0.318409	−	0.00638517i
$133$	355803.	−	3798.94i	1.74414	−	0.0186223i
$134$	149531.	+	152559.i	0.719396	+	0.733967i
$135$			87419.6i			0.412833i
$136$	−87768.1	+	82641.3i	−0.406902	+	0.383133i
$137$	−77617.2			−0.353310			−0.176655	−	0.984273i	$-0.556528\pi$
$137$	−77617.2			−0.353310			−0.176655	+	0.984273i	$0.556528\pi$
$138$	−145757.	−	148709.i	−0.651526	−	0.664722i
$139$	227957.			1.00073			0.500365	−	0.865815i	$-0.333199\pi$
$139$	227957.			1.00073			0.500365	+	0.865815i	$0.333199\pi$
$140$	−103709.	−	972.196i	−0.447194	−	0.00419212i
$141$	22313.5			0.0945193
$142$	248879.	+	253919.i	1.03578	+	1.05676i
$143$	19004.0			0.0777152
$144$	175991.	+	7061.25i	0.707267	+	0.0283776i
$145$			72967.3i			0.288209i
$146$	257324.	+	262536.i	0.999077	+	1.01931i
$147$	−141582.	+	3023.71i	−0.540399	+	0.0115411i
$148$	7098.34	−	353972.i	0.0266380	−	1.32836i
$149$	−253431.			−0.935178			−0.467589	−	0.883946i	$-0.654877\pi$
$149$	−253431.			−0.935178			−0.467589	+	0.883946i	$0.654877\pi$
$150$	−21274.9	+	20852.5i	−0.0772038	+	0.0756712i
$151$			409163.i			1.46034i	0.683265	+	0.730171i	$0.260559\pi$
$151$			409163.i			1.46034i	−0.683265	+	0.730171i	$0.739441\pi$
$152$	−340594.	−	361723.i	−1.19572	−	1.26989i
$153$		−	114548.i		−	0.395604i
$154$	122695.	+	122536.i	0.416895	+	0.416352i
$155$			36060.7i			0.120561i
$156$	21666.3	+	434.482i	0.0712808	+	0.00142942i
$157$		−	483404.i		−	1.56517i	−0.622545	−	0.782584i	$-0.713901\pi$
$157$		−	483404.i		−	1.56517i	0.622545	−	0.782584i	$-0.286099\pi$
$158$	58559.9	+	59746.0i	0.186620	+	0.190400i
$159$	−320300.			−1.00477
$160$	97140.6	+	107402.i	0.299986	+	0.331675i
$161$	6046.77	+	566332.i	0.0183848	+	1.72189i
$162$	−49825.9	+	48836.7i	−0.149165	+	0.146204i
$163$			390106.i			1.15004i	0.818139	+	0.575021i	$0.195006\pi$
$163$			390106.i			1.15004i	−0.818139	+	0.575021i	$0.804994\pi$
$164$	373643.	+	7492.80i	1.08479	+	0.0217538i
$165$	49807.8			0.142425
$166$	−278773.	+	273239.i	−0.785200	+	0.769612i
$167$	457751.			1.27010			0.635050	−	0.772471i	$-0.280980\pi$
$167$	457751.			1.27010			0.635050	+	0.772471i	$0.280980\pi$
$168$	137082.	+	142507.i	0.374721	+	0.389549i
$169$	364833.			0.982602
$170$	67260.6	−	65925.3i	0.178500	−	0.174956i
$171$	472094.			1.23463
$172$	293285.	+	5881.36i	0.755908	+	0.0151585i
$173$		−	414399.i		−	1.05270i	−0.850269	−	0.526349i	$-0.823561\pi$
$173$		−	414399.i		−	1.05270i	0.850269	−	0.526349i	$-0.176439\pi$
$174$	99351.7	−	97379.3i	0.248772	−	0.243834i
$175$	81021.5	−	865.073i	0.199989	−	0.00213529i
$176$	9706.96	−	241931.i	0.0236212	−	0.588721i
$177$	151364.			0.363154
$178$	400254.	+	408361.i	0.946860	+	0.966038i
$179$		−	499741.i		−	1.16577i	−0.812555	−	0.582885i	$-0.801924\pi$
$179$		−	499741.i		−	1.16577i	0.812555	−	0.582885i	$-0.198076\pi$
$180$	−137576.	−	2758.85i	−0.316490	−	0.00634669i
$181$			1253.13i			0.00284315i	0.999999	+	0.00142157i	$0.000452501\pi$
$181$			1253.13i			0.00284315i	−0.999999	+	0.00142157i	$0.999547\pi$
$182$	−41705.5	−	41651.2i	−0.0933285	−	0.0932070i
$183$		−	4867.79i		−	0.0107449i
$184$	575754.	−	542123.i	1.25370	−	1.18047i
$185$			276597.i			0.594179i
$186$	49100.0	−	48125.2i	0.104064	−	0.101998i
$187$	−157467.			−0.329296
$188$	−1699.03	+	84725.6i	−0.00350596	+	0.174832i
$189$	−453304.	+	4839.96i	−0.923070	+	0.00985569i
$190$	271701.	+	277205.i	0.546019	+	0.557078i
$191$			22393.6i			0.0444160i	0.999753	+	0.0222080i	$0.00706961\pi$
$191$			22393.6i			0.0444160i	−0.999753	+	0.0222080i	$0.992930\pi$
$192$	16598.0	−	275601.i	0.0324939	−	0.539544i
$193$	−153182.			−0.296015			−0.148008	−	0.988986i	$-0.547286\pi$
$193$	−153182.			−0.296015			−0.148008	+	0.988986i	$0.547286\pi$
$194$	−261360.	−	266654.i	−0.498581	−	0.508679i
$195$	−16930.2			−0.0318842
$196$	−700.609	−	537824.i	−0.00130267	−	0.999999i
$197$	−162307.			−0.297969			−0.148984	−	0.988840i	$-0.547600\pi$
$197$	−162307.			−0.297969			−0.148984	+	0.988840i	$0.547600\pi$
$198$	161043.	+	164305.i	0.291930	+	0.297843i
$199$	−359843.			−0.644139			−0.322070	−	0.946716i	$-0.604379\pi$
$199$	−359843.			−0.644139			−0.322070	+	0.946716i	$0.604379\pi$
$200$	−77558.1	−	82369.5i	−0.137105	−	0.145610i
$201$			318188.i			0.555513i
$202$	−731955.	−	746780.i	−1.26214	−	1.28770i
$203$	−378363.	+	4039.81i	−0.644419	+	0.00688051i
$204$	−179527.	−	3600.11i	−0.302033	−	0.00605677i
$205$	−291967.			−0.485232
$206$	151331.	−	148327.i	0.248463	−	0.243530i
$207$			751432.i			1.21889i
$208$	−3299.50	+	82234.8i	−0.00528797	+	0.131795i
$209$		−	648979.i		−	1.02770i
$210$	−109306.	−	109164.i	−0.171039	−	0.170817i
$211$		−	358445.i		−	0.554264i	−0.960832	−	0.277132i	$-0.910616\pi$
$211$		−	358445.i		−	0.554264i	0.960832	−	0.277132i	$-0.0893839\pi$
$212$	24388.8	−	1.21620e6i	0.0372693	−	1.85851i
$213$			529593.i			0.799821i
$214$	1083.92	+	1105.88i	0.00161795	+	0.00165072i
$215$	−229175.			−0.338120
$216$	433926.	+	460846.i	0.632822	+	0.672080i
$217$	−186988.	+	1996.49i	−0.269566	+	0.00287818i
$218$	264148.	−	258904.i	0.376449	−	0.368975i
$219$			547565.i			0.771481i
$220$	−3792.54	+	189123.i	−0.00528292	+	0.263443i
$221$	53524.8			0.0737182
$222$	376612.	−	369135.i	0.512875	−	0.502693i
$223$	308644.			0.415619			0.207810	−	0.978169i	$-0.433367\pi$
$223$	308644.			0.415619			0.207810	+	0.978169i	$0.433367\pi$
$224$	−551543.	+	509657.i	−0.734445	+	0.678668i
$225$	107503.			0.141567
$226$	433626.	−	425018.i	0.564735	−	0.553524i
$227$	1.26833e6			1.63368			0.816842	−	0.576861i	$-0.195723\pi$
$227$	1.26833e6			1.63368			0.816842	+	0.576861i	$0.195723\pi$
$228$	14837.3	−	739893.i	0.0189025	−	0.942609i
$229$		−	1.09699e6i		−	1.38233i	−0.722696	−	0.691166i	$-0.757097\pi$
$229$		−	1.09699e6i		−	1.38233i	0.722696	−	0.691166i	$-0.242903\pi$
$230$	−441226.	+	432467.i	−0.549973	+	0.539055i
$231$	2757.59	+	258272.i	0.00340017	+	0.318455i
$232$	362189.	+	384658.i	0.441789	+	0.469197i
$233$	−1.16203e6			−1.40226			−0.701130	−	0.713033i	$-0.747321\pi$
$233$	−1.16203e6			−1.40226			−0.701130	+	0.713033i	$0.747321\pi$
$234$	−54740.2	−	55848.9i	−0.0653532	−	0.0666768i
$235$		−	66205.2i		−	0.0782028i
$236$	−11525.4	+	574738.i	−0.0134703	+	0.671722i
$237$			124611.i			0.144107i
$238$	345571.	+	345122.i	0.395453	+	0.394939i
$239$			730266.i			0.826964i	0.910512	+	0.413482i	$0.135688\pi$
$239$			730266.i			0.826964i	−0.910512	+	0.413482i	$0.864312\pi$
$240$	−8647.67	+	215530.i	−0.00969105	+	0.241534i
$241$			812841.i			0.901495i	0.892652	+	0.450747i	$0.148842\pi$
$241$			812841.i			0.901495i	−0.892652	+	0.450747i	$0.851158\pi$
$242$	−424763.	+	416331.i	−0.466239	+	0.456983i
$243$	−953639.			−1.03602
$244$	18483.2	+	370.651i	0.0198748	+	0.000398557i
$245$	8971.46	+	420079.i	0.00954878	+	0.447112i
$246$	389648.	+	397540.i	0.410520	+	0.418835i
$247$			220595.i			0.230066i
$248$	178995.	+	190100.i	0.184804	+	0.196269i
$249$	−581428.			−0.594289
$250$	61870.3	+	63123.4i	0.0626083	+	0.0638764i
$251$	559979.			0.561031			0.280516	−	0.959849i	$-0.409495\pi$
$251$	559979.			0.561031			0.280516	+	0.959849i	$0.409495\pi$
$252$	6688.87	−	713534.i	0.00663516	−	0.707805i
$253$	1.03298e6			1.01459
$254$	203299.	+	207416.i	0.197720	+	0.201724i
$255$	140283.			0.135100
$256$	1.04521e6	+	84008.5i	0.996785	+	0.0801167i
$257$		−	493425.i		−	0.466003i	−0.972476	−	0.233001i	$-0.925145\pi$
$257$		−	493425.i		−	0.466003i	0.972476	−	0.233001i	$-0.0748547\pi$
$258$	305848.	+	312043.i	0.286060	+	0.291854i
$259$	−1.43426e6	+	15313.7i	−1.32855	+	0.0141850i
$260$	1289.12	−	64284.7i	0.00118266	−	0.0589759i
$261$	−502027.			−0.456169
$262$	1.12392e6	−	1.10160e6i	1.01153	−	0.991452i
$263$			1.18983e6i			1.06071i	0.847777	+	0.530353i	$0.177941\pi$
$263$			1.18983e6i			1.06071i	−0.847777	+	0.530353i	$0.822059\pi$
$264$	262569.	−	247232.i	0.231864	−	0.218321i
$265$			950344.i			0.831316i
$266$	−1.42237e6	+	1.42422e6i	−1.23256	+	1.23417i
$267$			851707.i			0.731159i
$268$	−1.20818e6	−	24228.0i	−1.02753	−	0.0206054i
$269$		−	555697.i		−	0.468228i	−0.972209	−	0.234114i	$-0.924781\pi$
$269$		−	555697.i		−	0.468228i	0.972209	−	0.234114i	$-0.0752189\pi$
$270$	−346155.	−	353166.i	−0.288976	−	0.294829i
$271$	9517.38			0.00787216			0.00393608	−	0.999992i	$-0.498747\pi$
$271$	9517.38			0.00787216			0.00393608	+	0.999992i	$0.498747\pi$
$272$	27339.6	−	681398.i	0.0224063	−	0.558442i
$273$	−937.334	−	87789.4i	−0.000761181	−	0.0712911i
$274$	313566.	−	307341.i	0.252320	−	0.247311i
$275$		−	147782.i		−	0.117839i
$276$	1.17769e6	+	23616.6i	0.930587	+	0.0186614i
$277$	−496319.			−0.388652			−0.194326	−	0.980937i	$-0.562252\pi$
$277$	−496319.			−0.388652			−0.194326	+	0.980937i	$0.562252\pi$
$278$	−920925.	+	902642.i	−0.714681	+	0.700493i
$279$	−248104.			−0.190820
$280$	422823.	−	406728.i	0.322302	−	0.310034i
$281$	−2.06154e6			−1.55749			−0.778746	−	0.627339i	$-0.784144\pi$
$281$	−2.06154e6			−1.55749			−0.778746	+	0.627339i	$0.784144\pi$
$282$	−90144.4	+	88354.9i	−0.0675019	+	0.0661619i
$283$	−289035.			−0.214528			−0.107264	−	0.994231i	$-0.534209\pi$
$283$	−289035.			−0.214528			−0.107264	+	0.994231i	$0.534209\pi$
$284$	−2.01089e6	−	40325.1i	−1.47942	−	0.0296674i
$285$			578158.i			0.421633i
$286$	−76774.4	+	75250.3i	−0.0555011	+	0.0543993i
$287$	−16164.7	−	1.51396e6i	−0.0115841	−	1.08495i
$288$	−738945.	+	668343.i	−0.524966	+	0.474808i
$289$	976350.			0.687640
$290$	−288928.	−	294780.i	−0.201741	−	0.205828i
$291$		−	556153.i		−	0.385001i
$292$	−2.07913e6	−	41693.6i	−1.42700	−	0.0286162i
$293$		−	1.44909e6i		−	0.986109i	−0.869998	−	0.493054i	$-0.835880\pi$
$293$		−	1.44909e6i		−	0.986109i	0.869998	−	0.493054i	$-0.164120\pi$
$294$	560004.	−	572837.i	0.377853	−	0.386512i
$295$		−	449104.i		−	0.300464i
$296$	1.37295e6	+	1.45812e6i	0.910803	+	0.967306i
$297$			826818.i			0.543899i
$298$	1.02384e6	−	1.00351e6i	0.667867	−	0.654608i
$299$	−351120.			−0.227132
$300$	3378.67	−	168484.i	0.00216742	−	0.108083i
$301$	−12688.2	−	1.18836e6i	−0.00807206	−	0.756017i
$302$	−1.62016e6	−	1.65298e6i	−1.02221	−	1.04292i
$303$		−	1.55754e6i		−	0.974613i
$304$	2.80828e6	+	112676.i	1.74284	+	0.0699276i
$305$	−14442.9			−0.00889008
$306$	453577.	+	462764.i	0.276916	+	0.282524i
$307$	1.40327e6			0.849758			0.424879	−	0.905250i	$-0.360317\pi$
$307$	1.40327e6			0.849758			0.424879	+	0.905250i	$0.360317\pi$
$308$	−980882.	−	9195.06i	−0.589169	−	0.00552303i
$309$	315628.			0.188052
$310$	−142790.	−	145682.i	−0.0843902	−	0.0860995i
$311$	106742.			0.0625800			0.0312900	−	0.999510i	$-0.490038\pi$
$311$	106742.			0.0625800			0.0312900	+	0.999510i	$0.490038\pi$
$312$	−89250.0	+	84036.7i	−0.0519065	+	0.0488745i
$313$			2.53013e6i			1.45976i	0.683574	+	0.729881i	$0.260425\pi$
$313$			2.53013e6i			1.45976i	−0.683574	+	0.729881i	$0.739575\pi$
$314$	1.91413e6	+	1.95290e6i	1.09559	+	1.11778i
$315$	5951.85	+	557442.i	0.00337968	+	0.316536i
$316$	−473152.	−	9488.29i	−0.266553	−	0.00534528i
$317$	467480.			0.261285			0.130643	−	0.991430i	$-0.458296\pi$
$317$	467480.			0.261285			0.130643	+	0.991430i	$0.458296\pi$
$318$	1.29398e6	−	1.26829e6i	0.717563	−	0.703318i
$319$			690127.i			0.379710i
$320$	−817718.	−	49246.8i	−0.446405	−	0.0268846i
$321$			2306.50i			0.00124937i
$322$	−2.26693e6	−	2.26398e6i	−1.21842	−	1.21684i
$323$		−	1.82785e6i		−	0.974840i
$324$	7912.87	−	394591.i	0.00418766	−	0.208826i
$325$			50232.5i			0.0263801i
$326$	−1.54470e6	−	1.57599e6i	−0.805009	−	0.821314i
$327$	550926.			0.284920
$328$	−1.53915e6	+	1.44924e6i	−0.789943	+	0.743801i
$329$	343299.	−	3665.43i	0.174857	−	0.00186696i
$330$	−201218.	+	197224.i	−0.101715	+	0.0996953i
$331$		−	304294.i		−	0.152659i	−0.997083	−	0.0763297i	$-0.975680\pi$
$331$		−	304294.i		−	0.152659i	0.997083	−	0.0763297i	$-0.0243201\pi$
$332$	44272.1	−	2.20771e6i	0.0220437	−	1.09925i
$333$	−1.90303e6			−0.940449
$334$	−1.84927e6	+	1.81255e6i	−0.907055	+	0.889047i
$335$	944078.			0.459617
$336$	−1.11808e6	−	32908.7i	−0.540288	−	0.0159024i
$337$	1.74463e6			0.836814			0.418407	−	0.908260i	$-0.362589\pi$
$337$	1.74463e6			0.836814			0.418407	+	0.908260i	$0.362589\pi$
$338$	−1.47389e6	+	1.44463e6i	−0.701735	+	0.687804i
$339$	904402.			0.427427
$340$	−10681.7	+	532663.i	−0.00501121	+	0.249894i
$341$			341063.i			0.158836i
$342$	−1.90721e6	+	1.86935e6i	−0.881727	+	0.864223i
$343$	−2.17777e6	+	69778.0i	−0.999487	+	0.0320245i
$344$	−1.20813e6	+	1.13756e6i	−0.550450	+	0.518297i
$345$	−920253.			−0.416255
$346$	1.64090e6	+	1.67413e6i	0.736870	+	0.751795i
$347$		−	3.22517e6i		−	1.43790i	−0.695062	−	0.718950i	$-0.744623\pi$
$347$		−	3.22517e6i		−	1.43790i	0.695062	−	0.718950i	$-0.255377\pi$
$348$	−15778.1	+	786805.i	−0.00698403	+	0.348272i
$349$		−	2.79466e6i		−	1.22819i	−0.789233	−	0.614094i	$-0.789522\pi$
$349$		−	2.79466e6i		−	1.22819i	0.789233	−	0.614094i	$-0.210478\pi$
$350$	−323893.	+	324316.i	−0.141329	+	0.141513i
$351$		−	281044.i		−	0.121760i
$352$	918759.	+	1.01581e6i	0.395225	+	0.436976i
$353$		−	1.62909e6i		−	0.695839i	−0.937524	−	0.347919i	$-0.886888\pi$
$353$		−	1.62909e6i		−	0.695839i	0.937524	−	0.347919i	$-0.113112\pi$
$354$	−611497.	+	599357.i	−0.259350	+	0.254201i
$355$	1.57132e6			0.661751
$356$	−3.23397e6	−	64852.0i	−1.35242	−	0.0271206i
$357$	7766.75	+	727423.i	0.00322529	+	0.302076i
$358$	1.97882e6	+	2.01890e6i	0.816018	+	0.832546i
$359$			365607.i			0.149719i	0.997194	+	0.0748597i	$0.0238509\pi$
$359$			365607.i			0.149719i	−0.997194	+	0.0748597i	$0.976149\pi$
$360$	566716.	−	533613.i	0.230467	−	0.217005i
$361$	5.05710e6			2.04237
$362$	−4962.01	−	5062.51i	−0.00199015	−	0.00203046i
$363$	−885916.			−0.352879
$364$	333412.	+	3125.50i	0.131895	+	0.00123642i
$365$	1.62465e6			0.638303
$366$	19275.0	+	19665.4i	0.00752126	+	0.00767360i
$367$	4.25423e6			1.64875			0.824376	−	0.566042i	$-0.191526\pi$
$367$	4.25423e6			1.64875			0.824376	+	0.566042i	$0.191526\pi$
$368$	−179347.	+	4.46994e6i	−0.0690357	+	1.72061i
$369$		−	2.00878e6i		−	0.768010i
$370$	−1.09524e6	−	1.11742e6i	−0.415915	−	0.424339i
$371$	−4.92789e6	+	52615.5i	−1.85877	+	0.0198463i
$372$	−7797.60	+	388842.i	−0.00292148	+	0.145685i
$373$	686057.			0.255322			0.127661	−	0.991818i	$-0.459253\pi$
$373$	686057.			0.255322			0.127661	+	0.991818i	$0.459253\pi$
$374$	636153.	−	623524.i	0.235170	−	0.230502i
$375$			131655.i			0.0483458i
$376$	−328624.	−	349011.i	−0.119875	−	0.127312i
$377$		−	234581.i		−	0.0850041i
$378$	1.81214e6	−	1.81450e6i	0.652321	−	0.653171i
$379$		−	2.72936e6i		−	0.976029i	−0.872835	−	0.488015i	$-0.837721\pi$
$379$		−	2.72936e6i		−	0.976029i	0.872835	−	0.488015i	$-0.162279\pi$
$380$	−2.19529e6	−	44023.0i	−0.779890	−	0.0156394i
$381$			432602.i			0.152678i
$382$	−88671.7	−	90467.7i	−0.0310904	−	0.0317201i
$383$	146103.			0.0508934			0.0254467	−	0.999676i	$-0.491899\pi$
$383$	146103.			0.0508934			0.0254467	+	0.999676i	$0.491899\pi$
$384$	1.02424e6	+	1.17912e6i	0.354466	+	0.408066i
$385$	766304.	−	8181.89i	0.263481	−	0.00281321i
$386$	618839.	−	606554.i	0.211402	−	0.207205i
$387$		−	1.57676e6i		−	0.535167i
$388$	2.11174e6	+	42347.5i	0.712133	+	0.0142807i
$389$	5.23192e6			1.75302			0.876510	−	0.481384i	$-0.159866\pi$
$389$	5.23192e6			1.75302			0.876510	+	0.481384i	$0.159866\pi$
$390$	68396.2	−	67038.4i	0.0227704	−	0.0223184i
$391$	2.90938e6			0.962407
$392$	2.13245e6	+	2.16998e6i	0.700912	+	0.713248i
$393$	2.34412e6			0.765593
$394$	655703.	−	642686.i	0.212798	−	0.208573i
$395$	369724.			0.119230
$396$	−1.30120e6	−	26093.3i	−0.416970	−	0.00836164i
$397$			4.87575e6i			1.55262i	0.630352	+	0.776309i	$0.282911\pi$
$397$			4.87575e6i			1.55262i	−0.630352	+	0.776309i	$0.717089\pi$
$398$	1.45373e6	−	1.42487e6i	0.460019	−	0.450886i
$399$	−2.99797e6	+	32009.5i	−0.942745	+	0.0100658i
$400$	639485.	+	25658.0i	0.199839	+	0.00801812i
$401$	4.31488e6			1.34001			0.670005	−	0.742356i	$-0.266292\pi$
$401$	4.31488e6			1.34001			0.670005	+	0.742356i	$0.266292\pi$
$402$	−1.25993e6	−	1.28545e6i	−0.388849	−	0.396725i
$403$		−	115931.i		−	0.0355580i
$404$	5.91405e6	+	118597.i	1.80273	+	0.0361509i
$405$			308336.i			0.0934086i
$406$	1.51255e6	−	1.51452e6i	0.455402	−	0.455996i
$407$			2.61606e6i			0.782819i
$408$	739525.	−	696328.i	0.219939	−	0.207092i
$409$		−	157683.i		−	0.0466097i	−0.999728	−	0.0233049i	$-0.992581\pi$
$409$		−	157683.i		−	0.0466097i	0.999728	−	0.0233049i	$-0.00741884\pi$
$410$	1.17952e6	−	1.15610e6i	0.346533	−	0.339654i
$411$	653995.			0.190972
$412$	−24033.0	+	1.19845e6i	−0.00697534	+	0.347839i
$413$	2.32877e6	−	24864.5i	0.671819	−	0.00717307i
$414$	−2.97544e6	−	3.03571e6i	−0.853200	−	0.870481i
$415$			1.72512e6i			0.491699i
$416$	−312295.	−	345285.i	−0.0884774	−	0.0978239i
$417$	−1.92075e6			−0.540916
$418$	2.56976e6	+	2.62181e6i	0.719369	+	0.733940i
$419$	−545905.			−0.151909			−0.0759543	−	0.997111i	$-0.524200\pi$
$419$	−545905.			−0.151909			−0.0759543	+	0.997111i	$0.524200\pi$
$420$	873841.	+	8191.63i	0.241718	+	0.00226593i
$421$	−1.98944e6			−0.547047			−0.273524	−	0.961865i	$-0.588189\pi$
$421$	−1.98944e6			−0.547047			−0.273524	+	0.961865i	$0.588189\pi$
$422$	1.41933e6	+	1.44808e6i	0.387975	+	0.395833i
$423$	455503.			0.123777
$424$	4.71724e6	+	5.00988e6i	1.27431	+	1.35336i
$425$		−	416227.i		−	0.111778i
$426$	−2.09703e6	−	2.13950e6i	−0.559861	−	0.571200i
$427$	−799.628	−	74892.0i	−0.000212236	−	0.0198777i
$428$	−8757.88	−	175.625i	−0.00231095	−	4.63422e-5i
$429$	−160126.			−0.0420068
$430$	925845.	−	907465.i	0.241472	−	0.236678i
$431$		−	3.13853e6i		−	0.813828i	−0.913466	−	0.406914i	$-0.866605\pi$
$431$		−	3.13853e6i		−	0.813828i	0.913466	−	0.406914i	$-0.133395\pi$
$432$	−3.57783e6	−	143553.i	−0.922381	−	0.0370086i
$433$		−	7.69064e6i		−	1.97125i	−0.168935	−	0.985627i	$-0.554033\pi$
$433$		−	7.69064e6i		−	1.97125i	0.168935	−	0.985627i	$-0.445967\pi$
$434$	747509.	−	748483.i	0.190499	−	0.190747i
$435$		−	614815.i		−	0.155783i
$436$	−41949.5	+	2.09189e6i	−0.0105684	+	0.527015i
$437$			1.19906e7i			3.00356i
$438$	−2.16819e6	−	2.21211e6i	−0.540023	−	0.550961i
$439$	−6.14820e6			−1.52260			−0.761302	−	0.648397i	$-0.775440\pi$
$439$	−6.14820e6			−1.52260			−0.761302	+	0.648397i	$0.775440\pi$
$440$	−733547.	−	779054.i	−0.180633	−	0.191838i
$441$	−2.89021e6	+	61725.1i	−0.707675	+	0.0151135i
$442$	−216235.	+	211942.i	−0.0526466	+	0.0516014i
$443$		−	2.35177e6i		−	0.569358i	−0.958623	−	0.284679i	$-0.908113\pi$
$443$		−	2.35177e6i		−	0.569358i	0.958623	−	0.284679i	$-0.0918870\pi$
$444$	−59809.9	+	2.98254e6i	−0.0143984	+	0.718007i
$445$	2.52705e6			0.604942
$446$	−1.24689e6	+	1.22214e6i	−0.296819	+	0.290926i
$447$	2.13539e6			0.505484
$448$	210091.	−	4.24290e6i	0.0494552	−	0.998776i
$449$	−3.08364e6			−0.721851			−0.360925	−	0.932595i	$-0.617539\pi$
$449$	−3.08364e6			−0.721851			−0.360925	+	0.932595i	$0.617539\pi$
$450$	−434300.	+	425678.i	−0.101102	+	0.0990946i
$451$	−2.76144e6			−0.639283
$452$	−68864.4	+	3.43406e6i	−0.0158544	+	0.790609i
$453$		−	3.44757e6i		−	0.789346i
$454$	−5.12393e6	+	5.02221e6i	−1.16671	+	1.14355i
$455$	−260475.	+	2781.11i	−0.0589844	+	0.000629781i
$456$	2.86981e6	+	3.04784e6i	0.646311	+	0.686406i
$457$	4.84495e6			1.08517			0.542587	−	0.840000i	$-0.317445\pi$
$457$	4.84495e6			1.08517			0.542587	+	0.840000i	$0.317445\pi$
$458$	4.34374e6	+	4.43172e6i	0.967609	+	0.987207i
$459$			2.32873e6i			0.515926i
$460$	70071.3	−	3.49424e6i	0.0154399	−	0.769943i
$461$		−	4.68302e6i		−	1.02630i	−0.858299	−	0.513149i	$-0.828479\pi$
$461$		−	4.68302e6i		−	1.02630i	0.858299	−	0.513149i	$-0.171521\pi$
$462$	−1.03382e6	−	1.03247e6i	−0.225341	−	0.225048i
$463$			4.89526e6i			1.06126i	0.847603	+	0.530631i	$0.178045\pi$
$463$			4.89526e6i			1.06126i	−0.847603	+	0.530631i	$0.821955\pi$
$464$	−2.98634e6	−	119820.i	−0.643938	−	0.0258366i
$465$		−	303844.i		−	0.0651656i
$466$	4.69450e6	−	4.60130e6i	1.00144	−	0.981558i
$467$	5.65385e6			1.19964			0.599822	−	0.800133i	$-0.295238\pi$
$467$	5.65385e6			1.19964			0.599822	+	0.800133i	$0.295238\pi$
$468$	442290.	+	8869.39i	0.0933452	+	0.00187189i
$469$	52268.6	+	4.89540e6i	0.0109726	+	1.02768i
$470$	262153.	+	267462.i	0.0547406	+	0.0558493i
$471$			4.07312e6i			0.846008i
$472$	−2.22923e6	−	2.36752e6i	−0.460574	−	0.489146i
$473$	−2.16755e6			−0.445467
$474$	−493420.	−	503414.i	−0.100872	−	0.102915i
$475$	1.71542e6			0.348848
$476$	−2.76265e6	−	25897.8i	−0.558867	−	0.00523897i
$477$	−6.53853e6			−1.31578
$478$	−2.89163e6	−	2.95020e6i	−0.578860	−	0.590585i
$479$	−4.86995e6			−0.969807			−0.484904	−	0.874568i	$-0.661145\pi$
$479$	−4.86995e6			−0.969807			−0.484904	+	0.874568i	$0.661145\pi$
$480$	−818497.	−	904961.i	−0.162149	−	0.179278i
$481$		−	889225.i		−	0.175246i
$482$	−3.21861e6	−	3.28380e6i	−0.631030	−	0.643812i
$483$	−50949.5	−	4.77186e6i	−0.00993738	−	0.930721i
$484$	67456.9	−	3.36387e6i	0.0130892	−	0.652718i
$485$	−1.65013e6			−0.318539
$486$	3.85261e6	−	3.77612e6i	0.739885	−	0.725196i
$487$			4.81362e6i			0.919708i	0.887995	+	0.459854i	$0.152098\pi$
$487$			4.81362e6i			0.919708i	−0.887995	+	0.459854i	$0.847902\pi$
$488$	−76138.0	+	71690.6i	−0.0144728	+	0.0136274i
$489$		−	3.28699e6i		−	0.621623i
$490$	−1.69963e6	−	1.66155e6i	−0.319790	−	0.312625i
$491$		−	3.22794e6i		−	0.604257i	−0.953267	−	0.302128i	$-0.902303\pi$
$491$		−	3.22794e6i		−	0.604257i	0.953267	−	0.302128i	$-0.0976971\pi$
$492$	−3.14828e6	−	63133.6i	−0.586355	−	0.0117584i
$493$			1.94374e6i			0.360181i
$494$	−873488.	−	891180.i	−0.161042	−	0.164304i
$495$	1.01676e6			0.186512
$496$	−1.47586e6	−	59215.7i	−0.269365	−	0.0108077i
$497$	86995.8	+	8.14790e6i	0.0157982	+	1.47964i
$498$	2.34891e6	−	2.30228e6i	0.424418	−	0.415992i
$499$		−	7.64814e6i		−	1.37501i	−0.726182	−	0.687503i	$-0.758707\pi$
$499$		−	7.64814e6i		−	1.37501i	0.726182	−	0.687503i	$-0.241293\pi$
$500$	−499899.	−	10024.7i	−0.0894247	−	0.00179327i
$501$	−3.85696e6			−0.686517
$502$	−2.26226e6	+	2.21735e6i	−0.400666	+	0.392712i
$503$	6.54114e6			1.15275			0.576373	−	0.817187i	$-0.304467\pi$
$503$	6.54114e6			1.15275			0.576373	+	0.817187i	$0.304467\pi$
$504$	2.79836e6	+	2.90909e6i	0.490712	+	0.510131i
$505$	−4.62128e6			−0.806369
$506$	−4.17313e6	+	4.09028e6i	−0.724579	+	0.710194i
$507$	−3.07405e6			−0.531118
$508$	−1.64261e6	−	32939.9i	−0.282407	−	0.00566321i
$509$		−	6.67039e6i		−	1.14119i	−0.821232	−	0.570594i	$-0.806713\pi$
$509$		−	6.67039e6i		−	1.14119i	0.821232	−	0.570594i	$-0.193287\pi$
$510$	−566731.	+	555480.i	−0.0964832	+	0.0945678i
$511$	89948.1	+	8.42441e6i	0.0152384	+	1.42721i
$512$	−4.55517e6	+	3.79931e6i	−0.767945	+	0.640516i
$513$	−9.59751e6			−1.61015
$514$	1.95382e6	+	1.99339e6i	0.326194	+	0.332801i
$515$		−	936480.i		−	0.155590i
$516$	−2.47119e6	−	49555.7i	−0.408585	−	0.00819350i
$517$		−	626171.i		−	0.103031i
$518$	5.73362e6	−	5.74109e6i	0.938868	−	0.940091i
$519$			3.49169e6i			0.569006i
$520$	249340.	+	264808.i	0.0404375	+	0.0429461i
$521$		−	4.27421e6i		−	0.689861i	−0.938628	−	0.344931i	$-0.887902\pi$
$521$		−	4.27421e6i		−	0.689861i	0.938628	−	0.344931i	$-0.112098\pi$
$522$	2.02814e6	−	1.98788e6i	0.325778	−	0.319310i
$523$	2.81053e6			0.449297			0.224649	−	0.974440i	$-0.427877\pi$
$523$	2.81053e6			0.449297			0.224649	+	0.974440i	$0.427877\pi$
$524$	−178490.	+	8.90073e6i	−0.0283978	+	1.41611i
$525$	−682679.	+	7289.02i	−0.108098	+	0.00115417i
$526$	−4.71136e6	−	4.80679e6i	−0.742476	−	0.757514i
$527$			960604.i			0.150667i
$528$	−81789.9	+	2.03849e6i	−0.0127678	+	0.318217i
$529$	−1.26491e7			−1.96525
$530$	−3.76308e6	−	3.83930e6i	−0.581907	−	0.593693i
$531$	3.08991e6			0.475565
$532$	106734.	−	1.13859e7i	0.0163503	−	1.74416i
$533$	938640.			0.143114
$534$	−3.37250e6	−	3.44081e6i	−0.511799	−	0.522165i
$535$	6843.47			0.00103369
$536$	4.97685e6	−	4.68614e6i	0.748243	−	0.704536i
$537$			4.21077e6i			0.630124i
$538$	2.20039e6	+	2.24496e6i	0.327751	+	0.334390i
$539$	84852.4	+	3.97312e6i	0.0125803	+	0.589061i
$540$	2.79687e6	+	56086.6i	0.412750	+	0.00827703i
$541$	−4.28781e6			−0.629857			−0.314929	−	0.949115i	$-0.601981\pi$
$541$	−4.28781e6			−0.629857			−0.314929	+	0.949115i	$0.601981\pi$
$542$	−38449.3	+	37685.9i	−0.00562199	+	0.00551038i
$543$		−	10558.7i		−	0.00153678i
$544$	2.58768e6	+	2.86104e6i	0.374898	+	0.414501i
$545$		−	1.63462e6i		−	0.235736i
$546$	351406.	+	350949.i	0.0504461	+	0.0503804i
$547$			3.00247e6i			0.429052i	0.976718	+	0.214526i	$0.0688206\pi$
$547$			3.00247e6i			0.429052i	−0.976718	+	0.214526i	$0.931179\pi$
$548$	−49797.5	+	2.48325e6i	−0.00708364	+	0.353239i
$549$		−	99369.7i		−	0.0140709i
$550$	585171.	+	597023.i	0.0824852	+	0.0841559i
$551$	−8.01084e6			−1.12408
$552$	−4.85125e6	+	4.56787e6i	−0.677651	+	0.638067i
$553$	20469.7	+	1.91716e6i	0.00284641	+	0.266591i
$554$	2.00508e6	−	1.96527e6i	0.277560	−	0.272050i
$555$		−	2.33058e6i		−	0.321167i
$556$	146253.	−	7.29317e6i	0.0200639	−	1.00053i
$557$	−4.24976e6			−0.580398			−0.290199	−	0.956966i	$-0.593722\pi$
$557$	−4.24976e6			−0.580398			−0.290199	+	0.956966i	$0.593722\pi$
$558$	1.00231e6	−	982416.i	0.136276	−	0.133570i
$559$	736771.			0.0997248
$560$	−97641.4	+	3.31739e6i	−0.0131572	+	0.447020i
$561$	1.32681e6			0.177992
$562$	8.32841e6	−	8.16307e6i	1.11230	−	1.09022i
$563$	−1.00722e7			−1.33923			−0.669614	−	0.742709i	$-0.733540\pi$
$563$	−1.00722e7			−1.33923			−0.669614	+	0.742709i	$0.733540\pi$
$564$	14315.9	−	713890.i	0.00189505	−	0.0945003i
$565$		−	2.68340e6i		−	0.353642i
$566$	1.16767e6	−	1.14449e6i	0.153207	−	0.150166i
$567$	−1.59884e6	+	17070.9i	−0.208856	+	0.00222997i
$568$	8.28347e6	−	7.79960e6i	1.07731	−	1.01438i
$569$	5.99679e6			0.776494			0.388247	−	0.921555i	$-0.373081\pi$
$569$	5.99679e6			0.776494			0.388247	+	0.921555i	$0.373081\pi$
$570$	−2.28933e6	−	2.33570e6i	−0.295135	−	0.301113i
$571$		−	5.52939e6i		−	0.709720i	−0.934919	−	0.354860i	$-0.884529\pi$
$571$		−	5.52939e6i		−	0.709720i	0.934919	−	0.354860i	$-0.115471\pi$
$572$	12192.6	−	608007.i	0.00155814	−	0.0776996i
$573$		−	188686.i		−	0.0240078i
$574$	6.06013e6	+	6.05224e6i	0.767719	+	0.766719i
$575$			2.73043e6i			0.344398i
$576$	338826.	−	5.62604e6i	0.0425521	−	0.706556i
$577$			6.41190e6i			0.801765i	0.916129	+	0.400883i	$0.131296\pi$
$577$			6.41190e6i			0.801765i	−0.916129	+	0.400883i	$0.868704\pi$
$578$	−3.94436e6	+	3.86605e6i	−0.491085	+	0.481336i
$579$	1.29070e6			0.160003
$580$	2.33448e6	+	46814.2i	0.288151	+	0.00577841i
$581$	−8.94541e6	+	95510.8i	−1.09941	+	0.0117385i
$582$	2.20220e6	+	2.24680e6i	0.269494	+	0.274952i
$583$			8.98839e6i			1.09524i
$584$	8.56457e6	−	8.06429e6i	1.03914	−	0.978440i
$585$	−345608.			−0.0417536
$586$	5.73794e6	+	5.85416e6i	0.690259	+	0.704240i
$587$	1.59665e7			1.91256			0.956281	−	0.292451i	$-0.0944708\pi$
$587$	1.59665e7			1.91256			0.956281	+	0.292451i	$0.0944708\pi$
$588$	5903.27	+	4.53165e6i	0.000704124	+	0.540521i
$589$	−3.95899e6			−0.470214
$590$	1.77832e6	+	1.81434e6i	0.210319	+	0.214579i
$591$	1.36758e6			0.161059
$592$	−1.13203e7	−	454202.i	−1.32756	−	0.0532654i
$593$			1.35247e6i			0.157940i	0.996877	+	0.0789700i	$0.0251631\pi$
$593$			1.35247e6i			0.157940i	−0.996877	+	0.0789700i	$0.974837\pi$
$594$	−3.27395e6	−	3.34026e6i	−0.380720	−	0.388431i
$595$	2.15829e6	−	23044.3i	0.249930	−	0.00266852i
$596$	−162596.	+	8.10817e6i	−0.0187497	+	0.934990i
$597$	3.03200e6			0.348171
$598$	1.41849e6	−	1.39033e6i	0.162208	−	0.158988i
$599$			3.78831e6i			0.431399i	0.976460	+	0.215699i	$0.0692031\pi$
$599$			3.78831e6i			0.431399i	−0.976460	+	0.215699i	$0.930797\pi$
$600$	653497.	+	694038.i	0.0741081	+	0.0787055i
$601$		−	1.61531e7i		−	1.82419i	−0.409977	−	0.912096i	$-0.634463\pi$
$601$		−	1.61531e7i		−	1.82419i	0.409977	−	0.912096i	$-0.365537\pi$
$602$	4.75681e6	+	4.75061e6i	0.534964	+	0.534267i
$603$			6.49541e6i			0.727467i
$604$	1.30906e7	+	262510.i	1.46005	+	0.0292789i
$605$			2.62855e6i			0.291963i
$606$	6.16738e6	+	6.29230e6i	0.682212	+	0.696030i
$607$	7.29279e6			0.803382			0.401691	−	0.915775i	$-0.368423\pi$
$607$	7.29279e6			0.803382			0.401691	+	0.915775i	$0.368423\pi$
$608$	−1.17913e7	+	1.06647e7i	−1.29361	+	1.17001i
$609$	3.18805e6	−	34039.1i	0.348323	−	0.00371907i
$610$	58348.0	−	57189.6i	0.00634894	−	0.00622290i
$611$			212842.i			0.0230650i
$612$	−3.66481e6	−	73491.8i	−0.395524	−	0.00793159i
$613$	9.20964e6			0.989901			0.494950	−	0.868921i	$-0.335186\pi$
$613$	9.20964e6			0.989901			0.494950	+	0.868921i	$0.335186\pi$
$614$	−5.66907e6	+	5.55653e6i	−0.606863	+	0.594816i
$615$	2.46009e6			0.262279
$616$	3.99907e6	−	3.84685e6i	0.424627	−	0.408464i
$617$	6.34735e6			0.671242			0.335621	−	0.941997i	$-0.391054\pi$
$617$	6.34735e6			0.671242			0.335621	+	0.941997i	$0.391054\pi$
$618$	−1.27510e6	+	1.24979e6i	−0.134300	+	0.131633i
$619$	−1.18848e7			−1.24670			−0.623352	−	0.781941i	$-0.714230\pi$
$619$	−1.18848e7			−1.24670			−0.623352	+	0.781941i	$0.714230\pi$
$620$	1.15371e6	+	23135.8i	0.120536	+	0.00241716i
$621$		−	1.52763e7i		−	1.58961i
$622$	−431228.	+	422668.i	−0.0446922	+	0.0438049i
$623$	139909.	+	1.31037e7i	0.0144420	+	1.35261i
$624$	27801.2	−	692903.i	0.00285827	−	0.0712378i
$625$	390625.			0.0400000
$626$	−1.00186e7	−	1.02215e7i	−1.02181	−	1.04250i
$627$			5.46823e6i			0.555493i
$628$	−1.54658e7	−	310142.i	−1.56485	−	0.0313806i
$629$			7.36812e6i			0.742558i
$630$	−2.23135e6	−	2.22844e6i	−0.223983	−	0.223692i
$631$			490544.i			0.0490461i	0.999699	+	0.0245231i	$0.00780672\pi$
$631$			490544.i			0.0490461i	−0.999699	+	0.0245231i	$0.992193\pi$
$632$	1.94906e6	−	1.83521e6i	0.194103	−	0.182765i
$633$			3.02022e6i			0.299592i
$634$	−1.88857e6	+	1.85108e6i	−0.186600	+	0.182895i
$635$	1.28355e6			0.126322
$636$	−205498.	+	1.02476e7i	−0.0201449	+	1.00456i
$637$	−28842.2	−	1.35051e6i	−0.00281631	−	0.131871i
$638$	−2.73269e6	−	2.78804e6i	−0.265790	−	0.271174i
$639$			1.08110e7i			1.04740i
$640$	3.49850e6	−	3.03897e6i	0.337623	−	0.293276i
$641$	1.31818e7			1.26715			0.633576	−	0.773680i	$-0.281586\pi$
$641$	1.31818e7			1.26715			0.633576	+	0.773680i	$0.281586\pi$
$642$	−9133.03	−	9318.02i	−0.000874536	−	0.000892249i
$643$	−6.05188e6			−0.577248			−0.288624	−	0.957442i	$-0.593198\pi$
$643$	−6.05188e6			−0.577248			−0.288624	+	0.957442i	$0.593198\pi$
$644$	1.81229e7	+	169889.i	1.72192	+	0.0161417i
$645$	1.93101e6			0.182762
$646$	7.23772e6	+	7.38432e6i	0.682371	+	0.696192i
$647$	−1.09720e7			−1.03044			−0.515222	−	0.857057i	$-0.672291\pi$
$647$	−1.09720e7			−1.03044			−0.515222	+	0.857057i	$0.672291\pi$
$648$	1.53049e6	+	1.62544e6i	0.143184	+	0.152066i
$649$		−	4.24764e6i		−	0.395855i
$650$	−198906.	−	202934.i	−0.0184656	−	0.0188396i
$651$	1.57555e6	−	16822.2i	0.145706	−	0.00155572i
$652$	1.24809e7	+	250284.i	1.14981	+	0.0230576i
$653$	1.22336e7			1.12272			0.561360	−	0.827572i	$-0.310278\pi$
$653$	1.22336e7			1.12272			0.561360	+	0.827572i	$0.310278\pi$
$654$	−2.22568e6	+	2.18150e6i	−0.203479	+	0.199439i
$655$		−	6.95509e6i		−	0.633432i
$656$	479443.	−	1.19494e7i	0.0434988	−	1.08414i
$657$			1.11778e7i			1.01029i
$658$	−1.37238e6	+	1.37417e6i	−0.123569	+	0.123730i
$659$		−	1.63789e7i		−	1.46916i	−0.678520	−	0.734582i	$-0.737378\pi$
$659$		−	1.63789e7i		−	1.46916i	0.678520	−	0.734582i	$-0.262622\pi$
$660$	31955.6	−	1.59353e6i	0.00285553	−	0.142397i
$661$			1.71239e7i			1.52440i	0.647342	+	0.762199i	$0.275880\pi$
$661$			1.71239e7i			1.52440i	−0.647342	+	0.762199i	$0.724120\pi$
$662$	1.20491e6	+	1.22932e6i	0.106859	+	0.109023i
$663$	−450995.			−0.0398463
$664$	8.56302e6	+	9.09424e6i	0.753714	+	0.800472i
$665$	94973.5	+	8.89509e6i	0.00832815	+	0.780003i
$666$	7.68805e6	−	7.53543e6i	0.671631	−	0.658297i
$667$		−	1.27508e7i		−	1.10975i
$668$	293683.	−	1.46451e7i	0.0254646	−	1.26984i
$669$	−2.60060e6			−0.224651
$670$	−3.81398e6	+	3.73826e6i	−0.328240	+	0.321724i
$671$	−136602.			−0.0117125
$672$	4.64725e6	−	4.29432e6i	0.396983	−	0.366835i
$673$	−4.71142e6			−0.400972			−0.200486	−	0.979697i	$-0.564252\pi$
$673$	−4.71142e6			−0.400972			−0.200486	+	0.979697i	$0.564252\pi$
$674$	−7.04814e6	+	6.90822e6i	−0.597619	+	0.585755i
$675$	−2.18549e6			−0.184625
$676$	234069.	−	1.16723e7i	0.0197005	−	0.982405i
$677$		−	4.12694e6i		−	0.346064i	−0.984916	−	0.173032i	$-0.944644\pi$
$677$		−	4.12694e6i		−	0.346064i	0.984916	−	0.173032i	$-0.0553565\pi$
$678$	−3.65369e6	+	3.58116e6i	−0.305252	+	0.299192i
$679$	−91358.8	−	8.55654e6i	−0.00760459	−	0.712235i
$680$	−2.06603e6	−	2.19420e6i	−0.171342	−	0.181972i
$681$	−1.06868e7			−0.883042
$682$	−1.35051e6	−	1.37786e6i	−0.111182	−	0.113434i
$683$		−	1.15537e7i		−	0.947694i	−0.880607	−	0.473847i	$-0.842865\pi$
$683$		−	1.15537e7i		−	0.947694i	0.880607	−	0.473847i	$-0.157135\pi$
$684$	302886.	−	1.51040e7i	0.0247536	−	1.23439i
$685$		−	1.94043e6i		−	0.158005i
$686$	8.52168e6	−	8.90522e6i	0.691377	−	0.722494i
$687$			9.24310e6i			0.747181i
$688$	376331.	−	9.37947e6i	0.0303109	−	0.755453i
$689$		−	3.05525e6i		−	0.245187i
$690$	3.71773e6	−	3.64392e6i	0.297273	−	0.291371i
$691$	1.08673e7			0.865819			0.432910	−	0.901437i	$-0.357487\pi$
$691$	1.08673e7			0.865819			0.432910	+	0.901437i	$0.357487\pi$
$692$	−1.32581e7	−	265870.i	−1.05249	−	0.0211059i
$693$	56292.8	+	5.27230e6i	0.00445266	+	0.417030i
$694$	1.27707e7	+	1.30293e7i	1.00650	+	1.02689i
$695$			5.69893e6i			0.447540i
$696$	−3.05177e6	−	3.24109e6i	−0.238797	−	0.253611i
$697$	−7.77757e6			−0.606404
$698$	1.10660e7	+	1.12901e7i	0.859710	+	0.877123i
$699$	9.79118e6			0.757953
$700$	24304.9	−	2.59272e6i	0.00187477	−	0.199991i
$701$	2.41919e7			1.85941			0.929705	−	0.368305i	$-0.120062\pi$
$701$	2.41919e7			1.85941			0.929705	+	0.368305i	$0.120062\pi$
$702$	1.11285e6	+	1.13539e6i	0.0852302	+	0.0869565i
$703$	−3.03666e7			−2.31744
$704$	−7.73401e6	−	465778.i	−0.588129	−	0.0354199i
$705$			557838.i			0.0422703i
$706$	6.45071e6	+	6.58137e6i	0.487075	+	0.496940i
$707$	−255856.	−	2.39631e7i	−0.0192507	−	1.80299i
$708$	97112.1	−	4.84269e6i	0.00728099	−	0.363081i
$709$	−681159.			−0.0508901			−0.0254450	−	0.999676i	$-0.508100\pi$
$709$	−681159.			−0.0508901			−0.0254450	+	0.999676i	$0.508100\pi$
$710$	−6.34799e6	+	6.22196e6i	−0.472596	+	0.463214i
$711$			2.54377e6i			0.188714i
$712$	1.33217e7	−	1.25436e7i	0.984828	−	0.927302i
$713$		−	6.30151e6i		−	0.464217i
$714$	−2.91175e6	−	2.90796e6i	−0.213751	−	0.213473i
$715$			475101.i			0.0347553i
$716$	−1.59885e7	−	320623.i	−1.16553	−	0.0233729i
$717$		−	6.15315e6i		−	0.446992i
$718$	−1.44769e6	−	1.47702e6i	−0.104801	−	0.106924i
$719$	2.03593e7			1.46872			0.734361	−	0.678759i	$-0.237482\pi$
$719$	2.03593e7			1.46872			0.734361	+	0.678759i	$0.237482\pi$
$720$	−176531.	+	4.39977e6i	−0.0126908	+	0.316299i
$721$	4.85600e6	−	51847.9i	0.347889	−	0.00371444i
$722$	−2.04302e7	+	2.00246e7i	−1.45858	+	1.42962i
$723$		−	6.84892e6i		−	0.487278i
$724$	40092.1	+	803.981i	0.00284257	+	5.70032e-5i
$725$	−1.82418e6			−0.128891
$726$	3.57901e6	−	3.50796e6i	0.252012	−	0.247009i
$727$	1.54952e7			1.08733			0.543663	−	0.839303i	$-0.317037\pi$
$727$	1.54952e7			1.08733			0.543663	+	0.839303i	$0.317037\pi$
$728$	−1.35933e6	+	1.30758e6i	−0.0950595	+	0.0914410i
$729$	5.03824e6			0.351124
$730$	−6.56341e6	+	6.43311e6i	−0.455851	+	0.446801i
$731$	−6.10489e6			−0.422556
$732$	−155738.	−	3123.07i	−0.0107428	−	0.000215429i
$733$			2.05377e7i			1.41186i	0.708283	+	0.705929i	$0.249470\pi$
$733$			2.05377e7i			1.41186i	−0.708283	+	0.705929i	$0.750530\pi$
$734$	−1.71866e7	+	1.68455e7i	−1.17747	+	1.15410i
$735$	−75592.7	−	3.53955e6i	−0.00516133	−	0.241674i
$736$	−1.69751e7	−	1.87682e7i	−1.15509	−	1.27711i
$737$	8.92912e6			0.605536
$738$	7.95417e6	+	8.11528e6i	0.537594	+	0.548482i
$739$			1.97507e7i			1.33037i	0.746679	+	0.665185i	$0.231647\pi$
$739$			1.97507e7i			1.33037i	−0.746679	+	0.665185i	$0.768353\pi$
$740$	8.84931e6	+	177458.i	0.594060	+	0.0119129i
$741$		−	1.85871e6i		−	0.124356i
$742$	1.96999e7	−	1.97255e7i	1.31357	−	1.31528i
$743$		−	2.87632e7i		−	1.91146i	−0.294250	−	0.955729i	$-0.595070\pi$
$743$		−	2.87632e7i		−	1.91146i	0.294250	−	0.955729i	$-0.404930\pi$
$744$	−1.50820e6	−	1.60176e6i	−0.0998908	−	0.106088i
$745$		−	6.33578e6i		−	0.418224i
$746$	−2.77160e6	+	2.71658e6i	−0.182341	+	0.178721i
$747$	−1.18691e7			−0.778247
$748$	−101028.	+	5.03795e6i	−0.00660217	+	0.329230i
$749$	378.887	+	35486.0i	2.46777e−5	+	0.00231128i
$750$	−521313.	−	531872.i	−0.0338412	−	0.0345266i
$751$			1.07977e7i			0.698604i	0.937010	+	0.349302i	$0.113581\pi$
$751$			1.07977e7i			0.698604i	−0.937010	+	0.349302i	$0.886419\pi$
$752$	2.70958e6	+	108716.i	0.174726	+	0.00701051i
$753$	−4.71833e6			−0.303250
$754$	928871.	+	947685.i	0.0595014	+	0.0607065i
$755$	−1.02291e7			−0.653084
$756$	−135982.	+	1.45059e7i	−0.00865323	+	0.923082i
$757$	−1.04322e7			−0.661659			−0.330830	−	0.943691i	$-0.607329\pi$
$757$	−1.04322e7			−0.661659			−0.330830	+	0.943691i	$0.607329\pi$
$758$	1.08074e7	+	1.10263e7i	0.683203	+	0.697041i
$759$	−8.70378e6			−0.548408
$760$	9.04308e6	−	8.51485e6i	0.567914	−	0.534740i
$761$		−	672525.i		−	0.0420965i	−0.999778	−	0.0210483i	$-0.993300\pi$
$761$		−	672525.i		−	0.0420965i	0.999778	−	0.0210483i	$-0.00670037\pi$
$762$	−1.71297e6	−	1.74767e6i	−0.106872	−	0.109036i
$763$	8.47612e6	−	90500.2i	0.527091	−	0.00562779i
$764$	716450.	+	14367.2i	0.0444071	+	0.000890511i
$765$	2.86371e6			0.176919
$766$	−590241.	+	578523.i	−0.0363460	+	0.0356245i
$767$			1.44382e6i			0.0886184i
$768$	−8.80680e6	−	707847.i	−0.538784	−	0.0433049i
$769$		−	2.22607e6i		−	0.135745i	−0.997694	−	0.0678725i	$-0.978379\pi$
$769$		−	2.22607e6i		−	0.135745i	0.997694	−	0.0678725i	$-0.0216211\pi$
$770$	−3.06339e6	+	3.06739e6i	−0.186198	+	0.186441i
$771$			4.15755e6i			0.251885i
$772$	−98278.2	+	4.90083e6i	−0.00593491	+	0.295956i
$773$		−	1.53133e7i		−	0.921768i	−0.887460	−	0.460884i	$-0.847532\pi$
$773$		−	1.53133e7i		−	0.921768i	0.887460	−	0.460884i	$-0.152468\pi$
$774$	6.24351e6	+	6.36997e6i	0.374607	+	0.382195i
$775$	−901518.			−0.0539163
$776$	−8.69890e6	+	8.19077e6i	−0.518573	+	0.488282i
$777$	1.20849e7	−	129032.i	0.718110	−	0.00766732i
$778$	−2.11364e7	+	2.07168e7i	−1.25194	+	1.22708i
$779$		−	3.20541e7i		−	1.89252i
$780$	−10862.0	+	541657.i	−0.000639256	+	0.0318778i
$781$	1.48616e7			0.871844
$782$	−1.17536e7	+	1.15203e7i	−0.687313	+	0.673668i
$783$	1.02060e7			0.594912
$784$	−1.72073e7	−	322641.i	−0.999824	−	0.0187469i
$785$	1.20851e7			0.699965
$786$	−9.47000e6	+	9.28200e6i	−0.546756	+	0.535902i
$787$	−1.06160e7			−0.610974			−0.305487	−	0.952196i	$-0.598819\pi$
$787$	−1.06160e7			−0.610974			−0.305487	+	0.952196i	$0.598819\pi$
$788$	−104133.	+	5.19277e6i	−0.00597408	+	0.297909i
$789$		−	1.00254e7i		−	0.573335i
$790$	−1.49365e6	+	1.46400e6i	−0.0851493	+	0.0834589i
$791$	1.39144e7	−	148566.i	0.790723	−	0.00844261i
$792$	5.36002e6	−	5.04693e6i	0.303636	−	0.285900i
$793$	46432.3			0.00262203
$794$	−1.93065e7	−	1.96975e7i	−1.08681	−	1.10882i
$795$		−	8.00751e6i		−	0.449345i
$796$	−230867.	+	1.15126e7i	−0.0129146	+	0.644010i
$797$		−	2.51922e7i		−	1.40482i	−0.711774	−	0.702408i	$-0.752108\pi$
$797$		−	2.51922e7i		−	1.40482i	0.711774	−	0.702408i	$-0.247892\pi$
$798$	1.19847e7	−	1.20004e7i	0.666225	−	0.667094i
$799$		−	1.76361e6i		−	0.0977316i
$800$	−2.68506e6	+	2.42851e6i	−0.148330	+	0.134158i
$801$			1.73865e7i			0.957484i
$802$	−1.74317e7	+	1.70856e7i	−0.956982	+	0.937984i
$803$	1.53660e7			0.840952
$804$	1.01800e7	+	204143.i	0.555401	+	0.0111377i
$805$	−1.41583e7	+	151169.i	−0.770054	+	0.00822193i
$806$	459052.	+	468350.i	0.0248899	+	0.0253941i
$807$			4.68225e6i			0.253088i
$808$	−2.43618e7	+	2.29387e7i	−1.31275	+	1.23606i
$809$	6.35279e6			0.341266			0.170633	−	0.985335i	$-0.445419\pi$
$809$	6.35279e6			0.341266			0.170633	+	0.985335i	$0.445419\pi$
$810$	−1.22092e6	−	1.24565e6i	−0.0653844	−	0.0667087i
$811$	7.44624e6			0.397544			0.198772	−	0.980046i	$-0.436305\pi$
$811$	7.44624e6			0.397544			0.198772	+	0.980046i	$0.436305\pi$
$812$	−113502.	+	1.21078e7i	−0.00604104	+	0.644427i
$813$	−80192.5			−0.00425508
$814$	−1.03588e7	−	1.05686e7i	−0.547960	−	0.559058i
$815$	−9.75265e6			−0.514314
$816$	−230361.	+	5.74139e6i	−0.0121111	+	0.301850i
$817$		−	2.51604e7i		−	1.31875i
$818$	624377.	+	637023.i	0.0326260	+	0.0332868i
$819$	−19134.5	−	1.79211e6i	−0.000996798	−	0.0933587i
$820$	−187320.	+	9.34107e6i	−0.00972858	+	0.485134i
$821$	−1.95801e7			−1.01381			−0.506906	−	0.862002i	$-0.669211\pi$
$821$	−1.95801e7			−1.01381			−0.506906	+	0.862002i	$0.669211\pi$
$822$	−2.64207e6	+	2.58962e6i	−0.136385	+	0.133677i
$823$			3.32948e7i			1.71347i	0.515758	+	0.856734i	$0.327510\pi$
$823$			3.32948e7i			1.71347i	−0.515758	+	0.856734i	$0.672490\pi$
$824$	−4.64843e6	−	4.93680e6i	−0.238500	−	0.253295i
$825$			1.24519e6i			0.0636946i
$826$	−9.30956e6	+	9.32169e6i	−0.474765	+	0.475384i
$827$			2.34392e6i			0.119173i	0.998223	+	0.0595866i	$0.0189782\pi$
$827$			2.34392e6i			0.119173i	−0.998223	+	0.0595866i	$0.981022\pi$
$828$	2.40410e7	+	482103.i	1.21864	+	0.0244379i
$829$			2.09019e7i			1.05633i	0.849142	+	0.528165i	$0.177120\pi$
$829$			2.09019e7i			1.05633i	−0.849142	+	0.528165i	$0.822880\pi$
$830$	−6.83096e6	−	6.96932e6i	−0.344181	−	0.351152i
$831$	4.18193e6			0.210075
$832$	2.62887e6	+	158323.i	0.131662	+	0.00792930i
$833$	238986.	+	1.11903e7i	0.0119333	+	0.558764i
$834$	7.75962e6	−	7.60557e6i	0.386301	−	0.378632i
$835$			1.14438e7i			0.568006i
$836$	−2.07632e7	−	416371.i	−1.02749	−	0.0206046i
$837$	5.04386e6			0.248857
$838$	2.20540e6	−	2.16162e6i	0.108487	−	0.106333i
$839$	516190.			0.0253165			0.0126583	−	0.999920i	$-0.495971\pi$
$839$	516190.			0.0253165			0.0126583	+	0.999920i	$0.495971\pi$
$840$	−3.56267e6	+	3.42705e6i	−0.174212	+	0.167580i
$841$	−1.19924e7			−0.584677
$842$	8.03713e6	−	7.87757e6i	0.390679	−	0.382924i
$843$	1.73703e7			0.841858
$844$	−1.14679e7	−	229971.i	−0.554152	−	0.0111126i
$845$			9.12083e6i			0.439433i
$846$	−1.84018e6	+	1.80365e6i	−0.0883966	+	0.0866417i
$847$	−1.36300e7	+	145529.i	−0.652812	+	0.00697013i
$848$	−3.88948e7	−	1.56057e6i	−1.85739	−	0.0745236i
$849$	2.43538e6			0.115957
$850$	1.64813e6	+	1.68151e6i	0.0782429	+	0.0798276i
$851$		−	4.83345e7i		−	2.28788i
$852$	1.69436e7	+	339775.i	0.799660	+	0.0160359i
$853$		−	1.01498e7i		−	0.477625i	−0.971066	−	0.238812i	$-0.923242\pi$
$853$		−	1.01498e7i		−	0.477625i	0.971066	−	0.238812i	$-0.0767581\pi$
$854$	299780.	+	299390.i	0.0140656	+	0.0140473i
$855$			1.18024e7i			0.552145i
$856$	36076.4	−	33969.1i	0.00168282	−	0.00158453i
$857$		−	6.65406e6i		−	0.309481i	−0.987955	−	0.154741i	$-0.950546\pi$
$857$		−	6.65406e6i		−	0.309481i	0.987955	−	0.154741i	$-0.0494542\pi$
$858$	646894.	−	634051.i	0.0299996	−	0.0294040i
$859$	−1.63484e7			−0.755947			−0.377974	−	0.925816i	$-0.623379\pi$
$859$	−1.63484e7			−0.755947			−0.377974	+	0.925816i	$0.623379\pi$
$860$	−147034.	+	7.33213e6i	−0.00677909	+	0.338053i
$861$	136202.	+	1.27565e7i	0.00626146	+	0.586439i
$862$	1.24276e7	+	1.26793e7i	0.569665	+	0.581203i
$863$		−	1.62408e7i		−	0.742302i	−0.928572	−	0.371151i	$-0.878963\pi$
$863$		−	1.62408e7i		−	0.742302i	0.928572	−	0.371151i	$-0.121037\pi$
$864$	1.50225e7	−	1.35872e7i	0.684633	−	0.619220i
$865$	1.03600e7			0.470781
$866$	3.04526e7	+	3.10694e7i	1.37984	+	1.40779i
$867$	−8.22663e6			−0.371684
$868$	−56092.9	+	5.98371e6i	−0.00252702	+	0.269570i
$869$	3.49687e6			0.157083
$870$	2.43448e6	+	2.48379e6i	0.109046	+	0.111254i
$871$	−3.03510e6			−0.135559
$872$	−8.11379e6	−	8.61714e6i	−0.361354	−	0.383771i
$873$		−	1.13532e7i		−	0.504175i
$874$	−4.74791e7	−	4.84408e7i	−2.10244	−	2.14503i
$875$	21626.8	+	2.02554e6i	0.000954933	+	0.0894376i
$876$	1.75185e7	+	351306.i	0.771326	+	0.0154677i
$877$	−3.46859e7			−1.52284			−0.761420	−	0.648259i	$-0.775498\pi$
$877$	−3.46859e7			−1.52284			−0.761420	+	0.648259i	$0.775498\pi$
$878$	2.48381e7	−	2.43450e7i	1.08738	−	1.06580i
$879$			1.22099e7i			0.533014i
$880$	6.04827e6	+	242674.i	0.263284	+	0.0105637i
$881$			1.81027e7i			0.785786i	0.919584	+	0.392893i	$0.128526\pi$
$881$			1.81027e7i			0.785786i	−0.919584	+	0.392893i	$0.871474\pi$
$882$	1.14318e7	−	1.16937e7i	0.494814	−	0.506153i
$883$		−	1.35643e7i		−	0.585459i	−0.956195	−	0.292730i	$-0.905436\pi$
$883$		−	1.35643e7i		−	0.585459i	0.956195	−	0.292730i	$-0.0945636\pi$
$884$	34340.4	−	1.71245e6i	0.00147800	−	0.0737033i
$885$			3.78411e6i			0.162407i
$886$	9.31230e6	+	9.50091e6i	0.398541	+	0.406613i
$887$	−4.99812e6			−0.213303			−0.106652	−	0.994296i	$-0.534013\pi$
$887$	−4.99812e6			−0.213303			−0.106652	+	0.994296i	$0.534013\pi$
$888$	−1.15683e7	−	1.22860e7i	−0.492309	−	0.522850i
$889$	71063.2	+	6.65568e6i	0.00301572	+	0.282448i
$890$	−1.02090e7	+	1.00064e7i	−0.432026	+	0.423449i
$891$			2.91625e6i			0.123064i
$892$	198019.	−	9.87462e6i	0.00833288	−	0.415536i
$893$	7.26845e6			0.305009
$894$	−8.62675e6	+	8.45549e6i	−0.360997	+	0.353830i
$895$	1.24935e7			0.521348
$896$	1.59519e7	+	1.79728e7i	0.663807	+	0.747904i
$897$	2.95850e6			0.122770
$898$	1.24576e7	−	1.22103e7i	0.515517	−	0.505283i
$899$	4.21000e6			0.173733
$900$	68971.4	−	3.43939e6i	0.00283833	−	0.141539i
$901$			2.53158e7i			1.03891i
$902$	1.11559e7	−	1.09344e7i	0.456551	−	0.447487i
$903$	106910.	+	1.00130e7i	0.00436312	+	0.408644i
$904$	−1.33196e7	−	1.41459e7i	−0.542090	−	0.575719i
$905$	−31328.2			−0.00127149
$906$	1.36513e7	+	1.39278e7i	0.552529	+	0.563720i
$907$		−	1.73172e7i		−	0.698971i	−0.936942	−	0.349486i	$-0.886356\pi$
$907$		−	1.73172e7i		−	0.698971i	0.936942	−	0.349486i	$-0.113644\pi$
$908$	813734.	−	4.05784e7i	0.0327543	−	1.63336i
$909$		−	3.17952e7i		−	1.27630i
$910$	1.04128e6	−	1.04264e6i	0.0416835	−	0.0417378i
$911$		−	1.11339e6i		−	0.0444480i	−0.999753	−	0.0222240i	$-0.992925\pi$
$911$		−	1.11339e6i		−	0.0444480i	0.999753	−	0.0222240i	$-0.00707470\pi$
$912$	−2.36623e7	−	949399.i	−0.942041	−	0.0377974i
$913$			1.63163e7i			0.647804i
$914$	−1.95731e7	+	1.91845e7i	−0.774987	+	0.759602i
$915$	121695.			0.00480528
$916$	−3.50965e7	−	703803.i	−1.38206	−	0.0277149i
$917$	3.60648e7	−	385067.i	1.41632	−	0.0151221i
$918$	−9.22106e6	−	9.40783e6i	−0.361139	−	0.368454i
$919$			3.31076e7i			1.29312i	0.762863	+	0.646560i	$0.223793\pi$
$919$			3.31076e7i			1.29312i	−0.762863	+	0.646560i	$0.776207\pi$
$920$	1.35531e7	+	1.43939e7i	0.527920	+	0.560670i
$921$	−1.18238e7			−0.459313
$922$	1.85434e7	+	1.89189e7i	0.718391	+	0.732942i
$923$	−5.05162e6			−0.195176
$924$	8.26482e6	+	77476.7i	0.318459	+	0.00298532i
$925$	−6.91491e6			−0.265725
$926$	−1.93837e7	−	1.97763e7i	−0.742865	−	0.757912i
$927$	6.44314e6			0.246263
$928$	1.25390e7	−	1.13409e7i	0.477960	−	0.432294i
$929$			3.47703e7i			1.32181i	0.750469	+	0.660906i	$0.229828\pi$
$929$			3.47703e7i			1.32181i	−0.750469	+	0.660906i	$0.770172\pi$
$930$	1.20313e6	+	1.22750e6i	0.0456148	+	0.0465387i
$931$	−4.61191e7	+	984947.i	−1.74384	+	0.0372425i
$932$	−745536.	+	3.71776e7i	−0.0281144	+	1.40198i
$933$	−899401.			−0.0338259
$934$	−2.28410e7	+	2.23876e7i	−0.856738	+	0.839730i
$935$		−	3.93669e6i		−	0.147266i
$936$	−1.82193e6	+	1.71550e6i	−0.0679737	+	0.0640032i
$937$		−	5.10591e7i		−	1.89987i	−0.312444	−	0.949936i	$-0.601148\pi$
$937$		−	5.10591e7i		−	1.89987i	0.312444	−	0.949936i	$-0.398852\pi$
$938$	−1.95955e7	−	1.95700e7i	−0.727191	−	0.726244i
$939$		−	2.13186e7i		−	0.789034i
$940$	−2.11814e6	−	42475.8i	−0.0781871	−	0.00156791i
$941$			1.31510e7i			0.484155i	0.970257	+	0.242077i	$0.0778288\pi$
$941$			1.31510e7i			0.484155i	−0.970257	+	0.242077i	$0.922171\pi$
$942$	−1.61283e7	−	1.64550e7i	−0.592191	−	0.604185i
$943$	5.10205e7			1.86838
$944$	1.83805e7	+	737479.i	0.671317	+	0.0269352i
$945$	−120999.	−	1.13326e7i	−0.00440760	−	0.412810i
$946$	8.75667e6	−	8.58283e6i	0.318135	−	0.311819i
$947$			1.30211e7i			0.471817i	0.971775	+	0.235908i	$0.0758065\pi$
$947$			1.30211e7i			0.471817i	−0.971775	+	0.235908i	$0.924193\pi$
$948$	3.98673e6	+	79947.4i	0.144078	+	0.00288924i
$949$	−5.22305e6			−0.188260
$950$	−6.93011e6	+	6.79254e6i	−0.249133	+	0.244187i
$951$	−3.93894e6			−0.141230
$952$	1.12634e7	−	1.08346e7i	0.402788	−	0.387456i
$953$	−1.24183e7			−0.442926			−0.221463	−	0.975169i	$-0.571083\pi$
$953$	−1.24183e7			−0.442926			−0.221463	+	0.975169i	$0.571083\pi$
$954$	2.64150e7	−	2.58906e7i	0.939679	−	0.921024i
$955$	−559839.			−0.0198634
$956$	2.33638e7	+	468523.i	0.826798	+	0.0165801i
$957$		−	5.81494e6i		−	0.205242i
$958$	1.96741e7	−	1.92835e7i	0.692598	−	0.678848i
$959$	1.00619e7	−	107431.i	0.353290	−	0.00377211i
$960$	6.89002e6	+	414949.i	0.241292	+	0.0145317i
$961$	−2.65486e7			−0.927326
$962$	3.52106e6	+	3.59238e6i	0.122669	+	0.125154i
$963$			47084.2i			0.00163610i
$964$	2.60057e7	+	521502.i	0.901314	+	0.0180744i
$965$		−	3.82955e6i		−	0.132382i
$966$	1.91009e7	+	1.90761e7i	0.658585	+	0.657728i
$967$			4.12687e7i			1.41924i	0.704587	+	0.709618i	$0.251132\pi$
$967$			4.12687e7i			1.41924i	−0.704587	+	0.709618i	$0.748868\pi$
$968$	1.30474e7	+	1.38568e7i	0.447543	+	0.475307i
$969$			1.54013e7i			0.526923i
$970$	6.66635e6	−	6.53401e6i	0.227488	−	0.222972i
$971$	1.00474e7			0.341985			0.170992	−	0.985272i	$-0.445303\pi$
$971$	1.00474e7			0.341985			0.170992	+	0.985272i	$0.445303\pi$
$972$	−611834.	+	3.05103e7i	−0.0207715	+	1.03581i
$973$	−2.95511e7	+	315520.i	−1.00067	+	0.0106843i
$974$	−1.90605e7	−	1.94466e7i	−0.643779	−	0.656818i
$975$		−	423255.i		−	0.0142590i
$976$	23716.9	−	591106.i	0.000796954	−	0.0198628i
$977$	−1.45648e7			−0.488167			−0.244084	−	0.969754i	$-0.578487\pi$
$977$	−1.45648e7			−0.488167			−0.244084	+	0.969754i	$0.578487\pi$
$978$	1.30155e7	+	1.32791e7i	0.435125	+	0.443938i
$979$	2.39009e7			0.796999
$980$	1.34456e7	−	17515.2i	0.447213	−	0.000582573i
$981$	1.12465e7			0.373115
$982$	1.27817e7	+	1.30405e7i	0.422969	+	0.431536i
$983$	−3.58933e7			−1.18476			−0.592378	−	0.805660i	$-0.701811\pi$
$983$	−3.58933e7			−1.18476			−0.592378	+	0.805660i	$0.701811\pi$
$984$	1.29687e7	−	1.22112e7i	0.426982	−	0.402041i
$985$		−	4.05767e6i		−	0.133256i
$986$	−7.69662e6	−	7.85251e6i	−0.252120	−	0.257227i
$987$	−2.89260e6	+	30884.5i	−0.0945139	+	0.00100913i
$988$	7.05761e6	+	141529.i	0.230020	+	0.00461267i
$989$	4.00478e7			1.30193
$990$	−4.10762e6	+	4.02608e6i	−0.133199	+	0.130555i
$991$			9.80319e6i			0.317090i	0.987352	+	0.158545i	$0.0506804\pi$
$991$			9.80319e6i			0.317090i	−0.987352	+	0.158545i	$0.949320\pi$
$992$	6.19680e6	−	5.60473e6i	0.199935	−	0.180832i
$993$			2.56395e6i			0.0825157i
$994$	−3.26147e7	−	3.25722e7i	−1.04700	−	1.04564i
$995$		−	8.99606e6i		−	0.288068i
$996$	−373032.	+	1.86020e7i	−0.0119151	+	0.594170i
$997$		−	2.57309e7i		−	0.819816i	−0.912127	−	0.409908i	$-0.865561\pi$
$997$		−	2.57309e7i		−	0.819816i	0.912127	−	0.409908i	$-0.134439\pi$
$998$	3.02843e7	+	3.08977e7i	0.962480	+	0.981974i
$999$	3.86879e7			1.22648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.6.g.a.111.19	yes	80
4.3	odd	2	inner	140.6.g.a.111.18	yes	80
7.6	odd	2	inner	140.6.g.a.111.20	yes	80
28.27	even	2	inner	140.6.g.a.111.17	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.6.g.a.111.17	✓	80	28.27	even	2	inner
140.6.g.a.111.18	yes	80	4.3	odd	2	inner
140.6.g.a.111.19	yes	80	1.1	even	1	trivial
140.6.g.a.111.20	yes	80	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	140.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.03990 + 3.95970i) q^{2} -8.42590 q^{3} +(0.641579 - 31.9936i) q^{4} +25.0000i q^{5} +(34.0398 - 33.3640i) q^{6} +(-129.634 + 1.38412i) q^{7} +(124.093 + 131.791i) q^{8} -172.004 q^{9} +O(q^{10})\)	\(q+(-4.03990 + 3.95970i) q^{2} -8.42590 q^{3} +(0.641579 - 31.9936i) q^{4} +25.0000i q^{5} +(34.0398 - 33.3640i) q^{6} +(-129.634 + 1.38412i) q^{7} +(124.093 + 131.791i) q^{8} -172.004 q^{9} +(-98.9925 - 100.997i) q^{10} +236.451i q^{11} +(-5.40588 + 269.575i) q^{12} -80.3721i q^{13} +(518.229 - 518.905i) q^{14} -210.648i q^{15} +(-1023.18 - 41.0528i) q^{16} +665.963i q^{17} +(694.880 - 681.085i) q^{18} -2744.67 q^{19} +(799.839 + 16.0395i) q^{20} +(1092.29 - 11.6624i) q^{21} +(-936.274 - 955.238i) q^{22} -4368.68i q^{23} +(-1045.60 - 1110.46i) q^{24} -625.000 q^{25} +(318.249 + 324.695i) q^{26} +3496.78 q^{27} +(-38.8878 + 4148.36i) q^{28} +2918.69 q^{29} +(834.101 + 850.995i) q^{30} +1442.43 q^{31} +(4296.09 - 3885.62i) q^{32} -1992.31i q^{33} +(-2637.01 - 2690.42i) q^{34} +(-34.6029 - 3240.86i) q^{35} +(-110.354 + 5503.03i) q^{36} +11063.9 q^{37} +(11088.2 - 10868.1i) q^{38} +677.207i q^{39} +(-3294.78 + 3102.32i) q^{40} +11678.7i q^{41} +(-4366.55 + 4372.24i) q^{42} +9167.01i q^{43} +(7564.91 + 151.702i) q^{44} -4300.10i q^{45} +(17298.7 + 17649.0i) q^{46} -2648.21 q^{47} +(8621.19 + 345.907i) q^{48} +(16803.2 - 358.858i) q^{49} +(2524.94 - 2474.81i) q^{50} -5611.34i q^{51} +(-2571.39 - 51.5650i) q^{52} +38013.8 q^{53} +(-14126.7 + 13846.2i) q^{54} -5911.27 q^{55} +(-16269.1 - 16912.9i) q^{56} +23126.3 q^{57} +(-11791.2 + 11557.1i) q^{58} -17964.2 q^{59} +(-6739.37 - 135.147i) q^{60} +577.717i q^{61} +(-5827.27 + 5711.58i) q^{62} +(22297.7 - 238.074i) q^{63} +(-1969.87 + 32708.7i) q^{64} +2009.30 q^{65} +(7888.95 + 8048.74i) q^{66} -37763.1i q^{67} +(21306.5 + 427.268i) q^{68} +36810.1i q^{69} +(12972.6 + 12955.7i) q^{70} -62852.9i q^{71} +(-21344.5 - 22668.6i) q^{72} -64985.9i q^{73} +(-44696.9 + 43809.6i) q^{74} +5266.19 q^{75} +(-1760.92 + 87811.7i) q^{76} +(-327.276 - 30652.2i) q^{77} +(-2681.54 - 2735.85i) q^{78} -14789.0i q^{79} +(1026.32 - 25579.4i) q^{80} +12333.4 q^{81} +(-46244.1 - 47180.7i) q^{82} +69004.9 q^{83} +(327.665 - 34953.6i) q^{84} -16649.1 q^{85} +(-36298.6 - 37033.8i) q^{86} -24592.6 q^{87} +(-31162.2 + 29341.9i) q^{88} -101082. i q^{89} +(17027.1 + 17372.0i) q^{90} +(111.244 + 10419.0i) q^{91} +(-139770. - 2802.85i) q^{92} -12153.8 q^{93} +(10698.5 - 10486.1i) q^{94} -68616.7i q^{95} +(-36198.4 + 32739.9i) q^{96} +66005.1i q^{97} +(-66462.1 + 67985.2i) q^{98} -40670.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{2} - 22 q^{4} - 178 q^{8} + 6480 q^{9}+O(q^{10}) \) 80 * q + 2 * q^2 - 22 * q^4 - 178 * q^8 + 6480 * q^9	\( 80 q + 2 q^{2} - 22 q^{4} - 178 q^{8} + 6480 q^{9} + 390 q^{14} + 2850 q^{16} + 8830 q^{18} + 3428 q^{21} + 1248 q^{22} - 50000 q^{25} + 9382 q^{28} - 16104 q^{29} - 19298 q^{32} - 56470 q^{36} + 16992 q^{37} - 17116 q^{42} - 44404 q^{44} - 51340 q^{46} + 37516 q^{49} - 1250 q^{50} - 14432 q^{53} - 494 q^{56} + 77328 q^{57} + 107480 q^{58} - 7700 q^{60} - 98494 q^{64} - 42200 q^{65} + 36400 q^{70} - 210642 q^{72} - 229924 q^{74} - 39912 q^{77} + 122676 q^{78} + 300680 q^{81} + 256808 q^{84} + 82348 q^{86} + 98692 q^{88} - 607884 q^{92} + 667696 q^{93} - 397470 q^{98}+O(q^{100}) \) 80 * q + 2 * q^2 - 22 * q^4 - 178 * q^8 + 6480 * q^9 + 390 * q^14 + 2850 * q^16 + 8830 * q^18 + 3428 * q^21 + 1248 * q^22 - 50000 * q^25 + 9382 * q^28 - 16104 * q^29 - 19298 * q^32 - 56470 * q^36 + 16992 * q^37 - 17116 * q^42 - 44404 * q^44 - 51340 * q^46 + 37516 * q^49 - 1250 * q^50 - 14432 * q^53 - 494 * q^56 + 77328 * q^57 + 107480 * q^58 - 7700 * q^60 - 98494 * q^64 - 42200 * q^65 + 36400 * q^70 - 210642 * q^72 - 229924 * q^74 - 39912 * q^77 + 122676 * q^78 + 300680 * q^81 + 256808 * q^84 + 82348 * q^86 + 98692 * q^88 - 607884 * q^92 + 667696 * q^93 - 397470 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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