LMFDB - Embedded newform 31.7.h.a.3.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,7,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13167659222$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$15$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	31.3
Dual form			31.7.h.a.21.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-10.5954 + 7.69802i) q^{2} +(-9.40640 - 0.988652i) q^{3} +(33.2262 - 102.260i) q^{4} +(3.18721 - 5.52041i) q^{5} +(107.275 - 61.9354i) q^{6} +(559.643 - 118.956i) q^{7} +(176.139 + 542.099i) q^{8} +(-625.567 - 132.968i) q^{9} +(8.72642 + 83.0263i) q^{10} +(-555.336 + 500.027i) q^{11} +(-413.638 + 929.047i) q^{12} +(1220.19 + 2740.60i) q^{13} +(-5013.92 + 5568.52i) q^{14} +(-35.4380 + 48.7762i) q^{15} +(-472.158 - 343.043i) q^{16} +(-999.257 - 899.735i) q^{17} +(7651.73 - 3406.77i) q^{18} +(4266.78 + 1899.69i) q^{19} +(-458.617 - 509.346i) q^{20} +(-5381.83 + 565.653i) q^{21} +(2034.80 - 9572.98i) q^{22} +(5249.87 - 1705.79i) q^{23} +(-1120.88 - 5273.34i) q^{24} +(7792.18 + 13496.5i) q^{25} +(-34025.6 - 19644.7i) q^{26} +(12310.4 + 3999.90i) q^{27} +(6430.42 - 61181.4i) q^{28} +(14796.9 + 20366.3i) q^{29} -789.606i q^{30} +(29507.3 - 4101.57i) q^{31} -28836.3 q^{32} +(5718.07 - 4154.42i) q^{33} +(17513.7 + 1840.77i) q^{34} +(1127.02 - 3468.60i) q^{35} +(-34382.5 + 59552.3i) q^{36} +(-41277.6 + 23831.6i) q^{37} +(-59832.1 + 12717.7i) q^{38} +(-8768.12 - 26985.5i) q^{39} +(3554.00 + 755.426i) q^{40} +(4606.66 + 43829.4i) q^{41} +(52668.3 - 47422.7i) q^{42} +(-3430.25 + 7704.46i) q^{43} +(32680.9 + 73402.6i) q^{44} +(-2727.85 + 3029.59i) q^{45} +(-42493.3 + 58487.1i) q^{46} +(47102.9 + 34222.2i) q^{47} +(4102.15 + 3693.59i) q^{48} +(191572. - 85293.2i) q^{49} +(-186457. - 83016.2i) q^{50} +(8509.88 + 9451.18i) q^{51} +(320795. - 33716.9i) q^{52} +(32831.4 - 154460. i) q^{53} +(-161226. + 52385.3i) q^{54} +(990.382 + 4659.38i) q^{55} +(163060. + 282429. i) q^{56} +(-38256.9 - 22087.6i) q^{57} +(-313560. - 101882. i) q^{58} +(-28486.2 + 271028. i) q^{59} +(3810.37 + 5244.53i) q^{60} -270534. i q^{61} +(-281068. + 270606. i) q^{62} -365911. q^{63} +(335751. - 243937. i) q^{64} +(19018.2 + 1998.90i) q^{65} +(-28604.5 + 88035.6i) q^{66} +(-92993.5 + 161070. i) q^{67} +(-125208. + 72289.0i) q^{68} +(-51068.8 + 10855.0i) q^{69} +(14760.1 + 45427.0i) q^{70} +(437139. + 92916.7i) q^{71} +(-38104.5 - 362540. i) q^{72} +(411513. - 370528. i) q^{73} +(253897. - 570262. i) q^{74} +(-59953.1 - 134657. i) q^{75} +(336031. - 373200. i) q^{76} +(-251309. + 345897. i) q^{77} +(300637. + 218425. i) q^{78} +(-624756. - 562532. i) q^{79} +(-3398.60 + 1513.16i) q^{80} +(314077. + 139836. i) q^{81} +(-386209. - 428929. i) q^{82} +(-11857.0 + 1246.22i) q^{83} +(-120974. + 569139. i) q^{84} +(-8151.75 + 2648.67i) q^{85} +(-22964.2 - 108038. i) q^{86} +(-119051. - 206202. i) q^{87} +(-368880. - 212973. i) q^{88} +(703557. + 228600. i) q^{89} +(5580.91 - 53098.8i) q^{90} +(1.00888e6 + 1.38861e6i) q^{91} -593527. i q^{92} +(-281612. + 9408.56i) q^{93} -762518. q^{94} +(24086.2 - 17499.7i) q^{95} +(271246. + 28509.1i) q^{96} +(-441321. + 1.35824e6i) q^{97} +(-1.37319e6 + 2.37844e6i) q^{98} +(413888. - 238958. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) $ 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{30}\right)$

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 $

$2$	−10.5954	+	7.69802i	−1.32443	+	0.962252i	−0.324561	+	0.945865i	$0.605217\pi$
$2$	−10.5954	+	7.69802i	−1.32443	+	0.962252i	−0.999866	+	0.0163877i	$0.994783\pi$
$3$	−9.40640	−	0.988652i	−0.348385	−	0.0366167i	−0.0712799	−	0.997456i	$-0.522708\pi$
$3$	−9.40640	−	0.988652i	−0.348385	−	0.0366167i	−0.277105	+	0.960840i	$0.589375\pi$
$4$	33.2262	−	102.260i	0.519160	−	1.59781i
$5$	3.18721	−	5.52041i	0.0254977	−	0.0441633i	−0.852995	−	0.521919i	$-0.825216\pi$
$5$	3.18721	−	5.52041i	0.0254977	−	0.0441633i	0.878493	+	0.477756i	$0.158550\pi$
$6$	107.275	−	61.9354i	0.496645	−	0.286738i
$7$	559.643	−	118.956i	1.63161	−	0.346810i	0.701097	−	0.713066i	$-0.252694\pi$
$7$	559.643	−	118.956i	1.63161	−	0.346810i	0.930514	+	0.366256i	$0.119361\pi$
$8$	176.139	+	542.099i	0.344021	+	1.05879i
$9$	−625.567	−	132.968i	−0.858116	−	0.182398i
$10$	8.72642	+	83.0263i	0.00872642	+	0.0830263i
$11$	−555.336	+	500.027i	−0.417232	+	0.375678i	−0.850841	−	0.525424i	$-0.823907\pi$
$11$	−555.336	+	500.027i	−0.417232	+	0.375678i	0.433608	+	0.901101i	$0.357240\pi$
$12$	−413.638	+	929.047i	−0.239374	+	0.537643i
$13$	1220.19	+	2740.60i	0.555390	+	1.24743i	0.945188	+	0.326527i	$0.105878\pi$
$13$	1220.19	+	2740.60i	0.555390	+	1.24743i	−0.389798	+	0.920901i	$0.627455\pi$
$14$	−5013.92	+	5568.52i	−1.82723	+	2.02935i
$15$	−35.4380	+	48.7762i	−0.0105001	+	0.0144522i
$16$	−472.158	−	343.043i	−0.115273	−	0.0837506i
$17$	−999.257	−	899.735i	−0.203390	−	0.183133i	0.561141	−	0.827720i	$-0.310363\pi$
$17$	−999.257	−	899.735i	−0.203390	−	0.183133i	−0.764531	+	0.644587i	$0.777029\pi$
$18$	7651.73	−	3406.77i	1.31203	−	0.584151i
$19$	4266.78	+	1899.69i	0.622070	+	0.276963i	0.693471	−	0.720484i	$-0.256080\pi$
$19$	4266.78	+	1899.69i	0.622070	+	0.276963i	−0.0714015	+	0.997448i	$0.522747\pi$
$20$	−458.617	−	509.346i	−0.0573272	−	0.0636683i
$21$	−5381.83	+	565.653i	−0.581128	+	0.0610790i
$22$	2034.80	−	9572.98i	0.191097	−	0.899040i
$23$	5249.87	−	1705.79i	0.431484	−	0.140198i	−0.0852192	−	0.996362i	$-0.527159\pi$
$23$	5249.87	−	1705.79i	0.431484	−	0.140198i	0.516703	+	0.856165i	$0.327159\pi$
$24$	−1120.88	−	5273.34i	−0.0810824	−	0.381462i
$25$	7792.18	+	13496.5i	0.498700	+	0.863773i
$26$	−34025.6	−	19644.7i	−1.93591	−	1.11770i
$27$	12310.4	+	3999.90i	0.625435	+	0.203216i
$28$	6430.42	−	61181.4i	0.292931	−	2.78705i
$29$	14796.9	+	20366.3i	0.606706	+	0.835059i	0.996301	−	0.0859271i	$-0.0273852\pi$
$29$	14796.9	+	20366.3i	0.606706	+	0.835059i	−0.389596	+	0.920986i	$0.627385\pi$
$30$		−	789.606i		−	0.0292447i
$31$	29507.3	−	4101.57i	0.990477	−	0.137678i
$31$	29507.3	−	4101.57i	0.990477	−	0.137678i
$32$	−28836.3			−0.880015
$33$	5718.07	−	4154.42i	0.159114	−	0.115603i
$34$	17513.7	+	1840.77i	0.445596	+	0.0468341i
$35$	1127.02	−	3468.60i	0.0262861	−	0.0809002i
$36$	−34382.5	+	59552.3i	−0.736937	+	1.27641i
$37$	−41277.6	+	23831.6i	−0.814909	+	0.470488i	−0.848658	−	0.528942i	$-0.822589\pi$
$37$	−41277.6	+	23831.6i	−0.814909	+	0.470488i	0.0337485	+	0.999430i	$0.489255\pi$
$38$	−59832.1	+	12717.7i	−1.09039	+	0.231770i
$39$	−8768.12	−	26985.5i	−0.147813	−	0.454922i
$40$	3554.00	+	755.426i	0.0555313	+	0.0118035i
$41$	4606.66	+	43829.4i	0.0668397	+	0.635937i	0.975741	+	0.218926i	$0.0702555\pi$
$41$	4606.66	+	43829.4i	0.0668397	+	0.635937i	−0.908902	+	0.417010i	$0.863078\pi$
$42$	52668.3	−	47422.7i	0.710888	−	0.640086i
$43$	−3430.25	+	7704.46i	−0.0431440	+	0.0969029i	−0.933832	−	0.357713i	$-0.883557\pi$
$43$	−3430.25	+	7704.46i	−0.0431440	+	0.0969029i	0.890688	+	0.454616i	$0.150223\pi$
$44$	32680.9	+	73402.6i	0.383651	+	0.861694i
$45$	−2727.85	+	3029.59i	−0.0299353	+	0.0332465i
$46$	−42493.3	+	58487.1i	−0.436564	+	0.600878i
$47$	47102.9	+	34222.2i	0.453684	+	0.329621i	0.791049	−	0.611753i	$-0.209535\pi$
$47$	47102.9	+	34222.2i	0.453684	+	0.329621i	−0.337364	+	0.941374i	$0.609535\pi$
$48$	4102.15	+	3693.59i	0.0370927	+	0.0333984i
$49$	191572.	−	85293.2i	1.62833	−	0.724980i
$50$	−186457.	−	83016.2i	−1.49166	−	0.664129i
$51$	8509.88	+	9451.18i	0.0641524	+	0.0712485i
$52$	320795.	−	33716.9i	2.28149	−	0.239794i
$53$	32831.4	−	154460.i	0.220527	−	1.03750i	−0.718996	−	0.695014i	$-0.755398\pi$
$53$	32831.4	−	154460.i	0.220527	−	1.03750i	0.939523	−	0.342485i	$-0.111269\pi$
$54$	−161226.	+	52385.3i	−1.02389	+	0.332681i
$55$	990.382	+	4659.38i	0.00595271	+	0.0280053i
$56$	163060.	+	282429.i	0.928506	+	1.60822i
$57$	−38256.9	−	22087.6i	−0.206578	−	0.119268i
$58$	−313560.	−	101882.i	−1.60707	−	0.522170i
$59$	−28486.2	+	271028.i	−0.138700	+	1.31965i	0.674765	+	0.738033i	$0.264245\pi$
$59$	−28486.2	+	271028.i	−0.138700	+	1.31965i	−0.813465	+	0.581613i	$0.802422\pi$
$60$	3810.37	+	5244.53i	0.0176406	+	0.0242802i
$61$		−	270534.i		−	1.19188i	−0.803029	−	0.595940i	$-0.796780\pi$
$61$		−	270534.i		−	1.19188i	0.803029	−	0.595940i	$-0.203220\pi$
$62$	−281068.	+	270606.i	−1.17933	+	1.13543i
$63$	−365911.			−1.46337
$64$	335751.	−	243937.i	1.28079	−	0.930547i
$65$	19018.2	+	1998.90i	0.0692517	+	0.00727865i
$66$	−28604.5	+	88035.6i	−0.0994953	+	0.306215i
$67$	−92993.5	+	161070.i	−0.309192	+	0.535536i	−0.978186	−	0.207732i	$-0.933392\pi$
$67$	−92993.5	+	161070.i	−0.309192	+	0.535536i	0.668994	+	0.743268i	$0.266725\pi$
$68$	−125208.	+	72289.0i	−0.398204	+	0.229903i
$69$	−51068.8	+	10855.0i	−0.155456	+	0.0330432i
$70$	14760.1	+	45427.0i	0.0430324	+	0.132440i
$71$	437139.	+	92916.7i	1.22136	+	0.259608i	0.773094	−	0.634291i	$-0.218708\pi$
$71$	437139.	+	92916.7i	1.22136	+	0.259608i	0.448267	+	0.893900i	$0.352041\pi$
$72$	−38104.5	−	362540.i	−0.102089	−	0.971311i
$73$	411513.	−	370528.i	1.05783	−	0.952472i	0.0588765	−	0.998265i	$-0.481248\pi$
$73$	411513.	−	370528.i	1.05783	−	0.952472i	0.998951	+	0.0457931i	$0.0145815\pi$
$74$	253897.	−	570262.i	0.626559	−	1.40728i
$75$	−59953.1	−	134657.i	−0.142111	−	0.319186i
$76$	336031.	−	373200.i	0.765488	−	0.850161i
$77$	−251309.	+	345897.i	−0.550472	+	0.757660i
$78$	300637.	+	218425.i	0.633517	+	0.460277i
$79$	−624756.	−	562532.i	−1.26715	−	1.14095i	−0.983283	−	0.182086i	$-0.941715\pi$
$79$	−624756.	−	562532.i	−1.26715	−	1.14095i	−0.283870	−	0.958863i	$-0.591618\pi$
$80$	−3398.60	+	1513.16i	−0.00663790	+	0.00295538i
$81$	314077.	+	139836.i	0.590990	+	0.263126i
$82$	−386209.	−	428929.i	−0.700456	−	0.777935i
$83$	−11857.0	+	1246.22i	−0.0207368	+	0.00217953i	−0.114891	−	0.993378i	$-0.536652\pi$
$83$	−11857.0	+	1246.22i	−0.0207368	+	0.00217953i	0.0941544	+	0.995558i	$0.469985\pi$
$84$	−120974.	+	569139.i	−0.204106	+	0.960241i
$85$	−8151.75	+	2648.67i	−0.0132738	+	0.00431291i
$86$	−22964.2	−	108038.i	−0.0361041	−	0.169856i
$87$	−119051.	−	206202.i	−0.180790	−	0.313138i
$88$	−368880.	−	212973.i	−0.541299	−	0.312519i
$89$	703557.	+	228600.i	0.997997	+	0.324269i	0.762065	−	0.647501i	$-0.224186\pi$
$89$	703557.	+	228600.i	0.997997	+	0.324269i	0.235932	+	0.971770i	$0.424186\pi$
$90$	5580.91	−	53098.8i	0.00765557	−	0.0728379i
$91$	1.00888e6	+	1.38861e6i	1.33880	+	1.84270i
$92$		−	593527.i		−	0.762214i
$93$	−281612.	+	9408.56i	−0.350109	+	0.0116970i
$94$	−762518.			−0.918050
$95$	24086.2	−	17499.7i	0.0280930	−	0.0204107i
$96$	271246.	+	28509.1i	0.306584	+	0.0322233i
$97$	−441321.	+	1.35824e6i	−0.483547	+	1.48821i	0.350527	+	0.936553i	$0.386003\pi$
$97$	−441321.	+	1.35824e6i	−0.483547	+	1.48821i	−0.834074	+	0.551653i	$0.813997\pi$
$98$	−1.37319e6	+	2.37844e6i	−1.45899	+	2.52705i
$99$	413888.	−	238958.i	0.426557	−	0.246273i
$100$	1.63905e6	−	348391.i	1.63905	−	0.348391i
$101$	−155830.	−	479594.i	−0.151247	−	0.465489i	0.846515	−	0.532365i	$-0.178697\pi$
$101$	−155830.	−	479594.i	−0.151247	−	0.465489i	−0.997761	+	0.0668762i	$0.978697\pi$
$102$	−162921.	−	34629.9i	−0.153524	−	0.0326326i
$103$	−80427.3	−	765215.i	−0.0736024	−	0.700280i	−0.967648	−	0.252304i	$-0.918812\pi$
$103$	−80427.3	−	765215.i	−0.0736024	−	0.700280i	0.894046	−	0.447976i	$-0.147855\pi$
$104$	−1.27075e6	+	1.14419e6i	−1.12969	+	1.01718i
$105$	−14030.4	+	31512.8i	−0.0121200	+	0.0272219i
$106$	841171.	+	1.88930e6i	0.706264	+	1.58629i
$107$	−1.40404e6	+	1.55935e6i	−1.14612	+	1.27289i	−0.189390	+	0.981902i	$0.560651\pi$
$107$	−1.40404e6	+	1.55935e6i	−1.14612	+	1.27289i	−0.956726	+	0.290990i	$0.906016\pi$
$108$	818059.	−	1.12596e6i	0.649401	−	0.893824i
$109$	−165495.	−	120239.i	−0.127792	−	0.0928465i	0.522053	−	0.852913i	$-0.325166\pi$
$109$	−165495.	−	120239.i	−0.127792	−	0.0928465i	−0.649845	+	0.760067i	$0.725166\pi$
$110$	−46361.5	−	41744.1i	−0.0348321	−	0.0313629i
$111$	411835.	−	183361.i	0.301130	−	0.134072i
$112$	−305046.	−	135815.i	−0.217126	−	0.0966707i
$113$	−1.48668e6	−	1.65112e6i	−1.03034	−	1.14431i	−0.989410	−	0.145151i	$-0.953633\pi$
$113$	−1.48668e6	−	1.65112e6i	−1.03034	−	1.14431i	−0.0409339	−	0.999162i	$-0.513033\pi$
$114$	575378.	−	60474.7i	0.388364	−	0.0408187i
$115$	7315.80	−	34418.1i	0.00481026	−	0.0226305i
$116$	2.57430e6	−	836439.i	1.64924	−	0.535871i
$117$	−398899.	−	1.87667e6i	−0.249061	−	1.17174i
$118$	−1.78455e6	−	3.09094e6i	−1.08613	−	1.88124i
$119$	−666255.	−	384663.i	−0.395366	−	0.228265i
$120$	−32683.5	−	10619.5i	−0.0189141	−	0.00614555i
$121$	−126807.	+	1.20649e6i	−0.0715794	+	0.681032i
$122$	2.08258e6	+	2.86642e6i	1.14689	+	1.57856i
$123$		−	416831.i		−	0.223998i
$124$	560990.	−	3.15369e6i	0.294232	−	1.65407i
$125$	198942.			0.101858
$126$	3.87698e6	−	2.81679e6i	1.93813	−	1.40813i
$127$	−1.72577e6	−	181386.i	−0.842504	−	0.0885507i	−0.326563	−	0.945175i	$-0.605891\pi$
$127$	−1.72577e6	−	181386.i	−0.842504	−	0.0885507i	−0.515940	+	0.856625i	$0.672557\pi$
$128$	−1.10929e6	+	3.41404e6i	−0.528949	+	1.62794i
$129$	39883.3	−	69079.9i	0.0185790	−	0.0321797i
$130$	−216894.	+	125224.i	−0.0987227	+	0.0569976i
$131$	3.04440e6	−	647107.i	1.35421	−	0.287847i	0.527063	−	0.849826i	$-0.323293\pi$
$131$	3.04440e6	−	647107.i	1.35421	−	0.287847i	0.827152	+	0.561979i	$0.189960\pi$
$132$	−234840.	−	722764.i	−0.102106	−	0.314250i
$133$	2.61385e6	+	555591.i	1.11103	+	0.236157i
$134$	−254611.	−	2.42246e6i	−0.105819	−	1.00680i
$135$	61317.1	−	55210.2i	0.0249219	−	0.0224397i
$136$	311738.	−	700174.i	0.123929	−	0.278349i
$137$	−1.97522e6	−	4.43643e6i	−0.768165	−	1.72533i	−0.684710	−	0.728816i	$-0.740071\pi$
$137$	−1.97522e6	−	4.43643e6i	−0.768165	−	1.72533i	−0.0834558	−	0.996511i	$-0.526596\pi$
$138$	457533.	−	508141.i	0.174094	−	0.193351i
$139$	−2.88220e6	+	3.96700e6i	−1.07320	+	1.47713i	−0.206398	+	0.978468i	$0.566174\pi$
$139$	−2.88220e6	+	3.96700e6i	−1.07320	+	1.47713i	−0.866798	+	0.498659i	$0.833826\pi$
$140$	−317251.	−	230497.i	−0.115616	−	0.0840003i
$141$	−409234.	−	368476.i	−0.145987	−	0.131447i
$142$	−5.34694e6	+	2.38061e6i	−1.86741	+	0.831426i
$143$	−2.04799e6	−	911824.i	−0.700357	−	0.311819i
$144$	249752.	+	277378.i	0.0836416	+	0.0928934i
$145$	159591.	−	16773.7i	0.0523486	−	0.00550206i
$146$	−1.50782e6	+	7.09373e6i	−0.484496	+	2.27938i
$147$	−1.88632e6	+	612904.i	−0.593833	+	0.192948i
$148$	1.06552e6	+	5.01287e6i	0.328682	+	1.54633i
$149$	624324.	+	1.08136e6i	0.188735	+	0.326898i	0.944829	−	0.327565i	$-0.106228\pi$
$149$	624324.	+	1.08136e6i	0.188735	+	0.326898i	−0.756094	+	0.654463i	$0.772895\pi$
$150$	1.67182e6	+	965225.i	0.495354	+	0.285993i
$151$	−3.40059e6	−	1.10492e6i	−0.987698	−	0.320922i	−0.229758	−	0.973248i	$-0.573794\pi$
$151$	−3.40059e6	−	1.10492e6i	−0.987698	−	0.320922i	−0.757939	+	0.652325i	$0.773794\pi$
$152$	−278276.	+	2.64762e6i	−0.0792402	+	0.753920i
$153$	505466.	+	695714.i	0.141129	+	0.194248i
$154$		−	5.59950e6i		−	1.53316i
$155$	71403.7	−	175965.i	0.0191746	−	0.0472532i
$156$	−3.05086e6			−0.803616
$157$	4.06156e6	−	2.95089e6i	1.04953	−	0.762526i	0.0774042	−	0.997000i	$-0.475337\pi$
$157$	4.06156e6	−	2.95089e6i	1.04953	−	0.762526i	0.972122	+	0.234474i	$0.0753368\pi$
$158$	1.09499e7	+	1.15088e6i	2.77613	+	0.291783i
$159$	−461532.	+	1.42045e6i	−0.114818	+	0.353374i
$160$	−91907.5	+	159188.i	−0.0224384	+	0.0388644i
$161$	2.73514e6	−	1.57913e6i	0.655392	−	0.378391i
$162$	−4.40423e6	+	936148.i	−1.03592	+	0.220191i
$163$	−428788.	−	1.31967e6i	−0.0990101	−	0.304722i	0.889268	−	0.457387i	$-0.151214\pi$
$163$	−428788.	−	1.31967e6i	−0.0990101	−	0.304722i	−0.988278	+	0.152665i	$0.951214\pi$
$164$	4.63505e6	+	985210.i	1.05081	+	0.223356i
$165$	−4709.42	−	44807.1i	−0.00104837	−	0.00997459i
$166$	116037.	−	104480.i	0.0253671	−	0.0228407i
$167$	810399.	−	1.82019e6i	0.174000	−	0.390811i	−0.805402	−	0.592728i	$-0.798051\pi$
$167$	810399.	−	1.82019e6i	0.174000	−	0.390811i	0.979402	+	0.201918i	$0.0647174\pi$
$168$	−1.25459e6	−	2.81785e6i	−0.264590	−	0.594278i
$169$	−2.79224e6	+	3.10109e6i	−0.578485	+	0.642473i
$170$	65981.7	−	90816.1i	0.0134300	−	0.0184848i
$171$	−2.41655e6	−	1.75573e6i	−0.483290	−	0.351131i
$172$	673882.	+	606767.i	0.132434	+	0.119244i
$173$	5.19259e6	−	2.31189e6i	1.00287	−	0.446508i	0.161448	−	0.986881i	$-0.448384\pi$
$173$	5.19259e6	−	2.31189e6i	1.00287	−	0.446508i	0.841425	+	0.540373i	$0.181717\pi$
$174$	2.84874e6	+	1.26834e6i	0.540761	+	0.240762i
$175$	5.96632e6	+	6.62627e6i	1.11325	+	1.23639i
$176$	433737.	−	45587.6i	0.0795588	−	0.00836197i
$177$	535904.	−	2.52123e6i	0.0966423	−	0.454666i
$178$	−9.21424e6	+	2.99389e6i	−1.63380	+	0.530855i
$179$	1.18634e6	+	5.58130e6i	0.206848	+	0.973142i	0.951965	+	0.306208i	$0.0990604\pi$
$179$	1.18634e6	+	5.58130e6i	0.206848	+	0.973142i	−0.745117	+	0.666934i	$0.767606\pi$
$180$	219169.	+	379612.i	0.0375804	+	0.0650912i
$181$	−517017.	−	298500.i	−0.0871905	−	0.0503394i	0.455771	−	0.890097i	$-0.349364\pi$
$181$	−517017.	−	298500.i	−0.0871905	−	0.0503394i	−0.542961	+	0.839758i	$0.682697\pi$
$182$	−2.13790e7	−	6.94647e6i	−3.54629	−	1.15226i
$183$	−267464.	+	2.54475e6i	−0.0436428	+	0.415233i
$184$	1.84941e6	+	2.54549e6i	0.296879	+	0.408619i
$185$			303826.i			0.0479855i
$186$	2.91137e6	−	2.26755e6i	0.452438	−	0.352385i
$187$	1.00482e6			0.153660
$188$	5.06461e6	−	3.67965e6i	0.762206	−	0.553775i
$189$	7.36526e6	+	774120.i	1.09094	+	0.114663i
$190$	−120491.	+	370832.i	−0.0175668	+	0.0540650i
$191$	−703004.	+	1.21764e6i	−0.100892	+	0.174751i	−0.912053	−	0.410073i	$-0.865503\pi$
$191$	−703004.	+	1.21764e6i	−0.100892	+	0.174751i	0.811160	+	0.584824i	$0.198836\pi$
$192$	−3.39938e6	+	1.96263e6i	−0.480281	+	0.277290i
$193$	1.02094e7	−	2.17007e6i	1.42013	−	0.301858i	0.567069	−	0.823671i	$-0.308077\pi$
$193$	1.02094e7	−	2.17007e6i	1.42013	−	0.301858i	0.853060	+	0.521813i	$0.174744\pi$
$194$	−5.77982e6	−	1.77885e7i	−0.791606	−	2.43631i
$195$	−176917.	−	37604.9i	−0.0238597	−	0.00507154i
$196$	−2.35686e6	−	2.24240e7i	−0.313016	−	2.97814i
$197$	−1.08932e7	+	9.80824e6i	−1.42480	+	1.28290i	−0.521934	+	0.852986i	$0.674789\pi$
$197$	−1.08932e7	+	9.80824e6i	−1.42480	+	1.28290i	−0.902870	+	0.429914i	$0.858544\pi$
$198$	−2.54581e6	+	5.71798e6i	−0.327967	+	0.736625i
$199$	982806.	+	2.20742e6i	0.124712	+	0.280108i	0.965102	−	0.261874i	$-0.0843406\pi$
$199$	982806.	+	2.20742e6i	0.124712	+	0.280108i	−0.840390	+	0.541982i	$0.817674\pi$
$200$	−5.94391e6	+	6.60138e6i	−0.742989	+	0.825173i
$201$	1.03398e6	−	1.42315e6i	0.127328	−	0.175251i
$202$	5.34300e6	+	3.88192e6i	0.648233	+	0.470969i
$203$	1.07037e7	+	9.63764e6i	1.27951	+	1.15208i
$204$	1.24923e6	−	556192.i	0.147147	−	0.0655140i
$205$	256639.	+	114263.i	0.0297893	+	0.0132631i
$206$	6.74280e6	+	7.48864e6i	0.771327	+	0.856646i
$207$	−3.51096e6	+	369016.i	−0.395835	+	0.0416040i
$208$	364018.	−	1.71257e6i	0.0404514	−	0.190309i
$209$	−3.31939e6	+	1.07854e6i	−0.363597	+	0.118140i
$210$	−93928.1	−	441897.i	−0.0101423	−	0.0477159i
$211$	1.76428e6	+	3.05582e6i	0.187810	+	0.325297i	0.944520	−	0.328454i	$-0.106528\pi$
$211$	1.76428e6	+	3.05582e6i	0.187810	+	0.325297i	−0.756710	+	0.653751i	$0.773194\pi$
$212$	−1.47042e7	−	8.48945e6i	−1.54324	−	0.890988i
$213$	−4.02004e6	−	1.30619e6i	−0.415998	−	0.135166i
$214$	2.87253e6	−	2.73303e7i	0.293105	−	2.78870i
$215$	31598.9	+	43492.1i	0.00317948	+	0.00437618i
$216$			7.37801e6i			0.732113i
$217$	1.60256e7	−	5.80548e6i	1.56833	−	0.568144i
$218$	2.67909e6			0.258593
$219$	−4.23718e6	+	3.07849e6i	−0.403408	+	0.293093i
$220$	509374.	+	53537.3i	0.0478375	+	0.00502792i
$221$	1.24653e6	−	3.83641e6i	0.115485	−	0.355425i
$222$	−2.95205e6	+	5.11309e6i	−0.269814	+	0.467331i
$223$	−9.83546e6	+	5.67851e6i	−0.886911	+	0.512058i	−0.872931	−	0.487844i	$-0.837784\pi$
$223$	−9.83546e6	+	5.67851e6i	−0.886911	+	0.512058i	−0.0139803	+	0.999902i	$0.504450\pi$
$224$	−1.61380e7	+	3.43025e6i	−1.43584	+	0.305198i
$225$	−3.07993e6	−	9.47905e6i	−0.270392	−	0.832180i
$226$	2.84624e7	+	6.04987e6i	2.46573	+	0.524108i
$227$	−1.75969e6	−	1.67424e7i	−0.150439	−	1.43133i	−0.765798	−	0.643082i	$-0.777656\pi$
$227$	−1.75969e6	−	1.67424e7i	−0.150439	−	1.43133i	0.615359	−	0.788247i	$-0.289011\pi$
$228$	−3.52980e6	+	3.17825e6i	−0.297815	+	0.268154i
$229$	5.18365e6	−	1.16427e7i	0.431647	−	0.969495i	−0.558505	−	0.829501i	$-0.688625\pi$
$229$	5.18365e6	−	1.16427e7i	0.431647	−	0.969495i	0.990152	−	0.139994i	$-0.0447084\pi$
$230$	187438.	+	420992.i	0.0154054	+	0.0346011i
$231$	2.70588e6	−	3.00519e6i	0.219519	−	0.243801i
$232$	−8.43421e6	+	1.16087e7i	−0.675430	+	0.929650i
$233$	−1.11313e7	−	8.08735e6i	−0.879989	−	0.639350i	0.0532594	−	0.998581i	$-0.483039\pi$
$233$	−1.11313e7	−	8.08735e6i	−0.879989	−	0.639350i	−0.933249	+	0.359231i	$0.883039\pi$
$234$	1.86732e7	+	1.68134e7i	1.45737	+	1.31222i
$235$	339048.	−	150954.i	0.0261251	−	0.0116316i
$236$	2.67687e7	+	1.19182e7i	2.03654	+	0.906724i
$237$	5.32055e6	+	5.90907e6i	0.399679	+	0.443889i
$238$	1.00204e7	−	1.05319e6i	0.743282	−	0.0781221i
$239$	−1.47267e6	+	6.92838e6i	−0.107873	+	0.507502i	0.890724	+	0.454545i	$0.150198\pi$
$239$	−1.47267e6	+	6.92838e6i	−0.107873	+	0.507502i	−0.998597	+	0.0529574i	$0.983135\pi$
$240$	33464.6	−	10873.3i	0.00242076	−	0.000786553i
$241$	2.77658e6	+	1.30628e7i	0.198362	+	0.933221i	0.958860	+	0.283880i	$0.0916218\pi$
$241$	2.77658e6	+	1.30628e7i	0.198362	+	0.933221i	−0.760497	+	0.649341i	$0.775045\pi$
$242$	−7.94401e6	−	1.37594e7i	−0.560523	−	0.970855i
$243$	−1.09880e7	−	6.34394e6i	−0.765774	−	0.442120i
$244$	−2.76648e7	−	8.98883e6i	−1.90440	−	0.618776i
$245$	139726.	−	1.32940e6i	0.00950120	−	0.0903979i
$246$	3.20877e6	+	4.41650e6i	0.215543	+	0.296669i
$247$			1.40115e7i			0.929809i
$248$	7.42083e6	+	1.52734e7i	0.486517	+	1.00134i
$249$	112764.			0.00730420
$250$	−2.10787e6	+	1.53146e6i	−0.134904	+	0.0980133i
$251$	−747239.	−	78537.9i	−0.0472540	−	0.00496659i	0.0808720	−	0.996724i	$-0.474230\pi$
$251$	−747239.	−	78537.9i	−0.0472540	−	0.00496659i	−0.128126	+	0.991758i	$0.540896\pi$
$252$	−1.21578e7	+	3.74180e7i	−0.759722	+	2.33819i
$253$	−2.06250e6	+	3.57236e6i	−0.127360	+	0.220594i
$254$	1.96816e7	−	1.13632e7i	1.20104	−	0.693422i
$255$	79297.2	−	16855.1i	0.00478231	−	0.00101651i
$256$	−6.32024e6	−	1.94517e7i	−0.376716	−	1.15941i
$257$	−1.22208e6	−	259761.i	−0.0719947	−	0.0153029i	0.171774	−	0.985136i	$-0.445050\pi$
$257$	−1.22208e6	−	259761.i	−0.0719947	−	0.0153029i	−0.243768	+	0.969834i	$0.578384\pi$
$258$	109198.	+	1.03895e6i	0.00635853	+	0.0604974i
$259$	−2.02658e7	+	1.82474e7i	−1.16645	+	1.05027i
$260$	836311.	−	1.87839e6i	0.0475826	−	0.106872i
$261$	−6.54841e6	−	1.47080e7i	−0.368311	−	0.827240i
$262$	−2.72752e7	+	3.02922e7i	−1.51658	+	1.68433i
$263$	1.58178e7	−	2.17713e7i	0.869518	−	1.19679i	−0.109697	−	0.993965i	$-0.534988\pi$
$263$	1.58178e7	−	2.17713e7i	0.869518	−	1.19679i	0.979215	−	0.202824i	$-0.0650120\pi$
$264$	3.25928e6	+	2.36800e6i	0.177137	+	0.128698i
$265$	−748041.	−	673539.i	−0.0401965	−	0.0361931i
$266$	−3.19718e7	+	1.42347e7i	−1.69872	+	0.756319i
$267$	−6.39193e6	−	2.84587e6i	−0.335814	−	0.149514i
$268$	1.33811e7	+	1.48612e7i	0.695165	+	0.772059i
$269$	1.58278e7	−	1.66357e6i	0.813136	−	0.0854640i	0.311173	−	0.950353i	$-0.399278\pi$
$269$	1.58278e7	−	1.66357e6i	0.813136	−	0.0854640i	0.501963	+	0.864889i	$0.332611\pi$
$270$	−224671.	+	1.05699e6i	−0.0114145	+	0.0537009i
$271$	−1.66687e7	+	5.41598e6i	−0.837515	+	0.272125i	−0.696208	−	0.717840i	$-0.745131\pi$
$271$	−1.66687e7	+	5.41598e6i	−0.837515	+	0.272125i	−0.141308	+	0.989966i	$0.545131\pi$
$272$	163159.	+	767604.i	0.00810784	+	0.0381444i
$273$	−8.11709e6	−	1.40592e7i	−0.398944	−	0.690992i
$274$	5.50800e7	+	3.18005e7i	2.67758	+	1.54590i
$275$	−1.10759e7	−	3.59877e6i	−0.532574	−	0.173044i
$276$	−586792.	+	5.58295e6i	−0.0279098	+	0.265544i
$277$	−2.01549e6	−	2.77408e6i	−0.0948290	−	0.130521i	0.758966	−	0.651130i	$-0.225705\pi$
$277$	−2.01549e6	−	2.77408e6i	−0.0948290	−	0.130521i	−0.853795	+	0.520609i	$0.825705\pi$
$278$		−	6.42192e7i		−	2.98903i
$279$	−1.90042e7	−	1.35773e6i	−0.875057	−	0.0625173i
$280$	2.07883e6			0.0946990
$281$	1.33697e7	−	9.71365e6i	0.602563	−	0.437788i	−0.244225	−	0.969719i	$-0.578533\pi$
$281$	1.33697e7	−	9.71365e6i	0.602563	−	0.437788i	0.846788	+	0.531931i	$0.178533\pi$
$282$	7.17254e6	+	753865.i	0.319835	+	0.0336160i
$283$	4.46440e6	−	1.37400e7i	0.196972	−	0.606217i	−0.802976	−	0.596011i	$-0.796751\pi$
$283$	4.46440e6	−	1.37400e7i	0.196972	−	0.606217i	0.999948	−	0.0102058i	$-0.00324867\pi$
$284$	2.40261e7	−	4.16144e7i	1.04889	−	1.81672i
$285$	−243865.	+	140796.i	−0.0105345	+	0.00608212i
$286$	2.87185e7	−	6.10431e6i	1.22762	−	0.260939i
$287$	7.79184e6	+	2.39808e7i	0.329605	+	1.01442i
$288$	1.80390e7	+	3.83432e6i	0.755155	+	0.160513i
$289$	−2.33407e6	−	2.22072e7i	−0.0966987	−	0.920027i
$290$	−1.56181e6	+	1.40626e6i	−0.0640375	+	0.0576596i
$291$	5.49407e6	−	1.23399e7i	0.222954	−	0.500763i
$292$	−2.42171e7	−	5.43925e7i	−0.972687	−	2.18469i
$293$	5.11463e6	−	5.68037e6i	0.203335	−	0.225826i	−0.632850	−	0.774275i	$-0.718115\pi$
$293$	5.11463e6	−	5.68037e6i	0.203335	−	0.225826i	0.836184	+	0.548449i	$0.184781\pi$
$294$	1.52682e7	−	2.10149e7i	0.600824	−	0.826963i
$295$	1.40539e6	+	1.02108e6i	0.0547434	+	0.0397734i
$296$	−2.01897e7	−	1.81789e7i	−0.778492	−	0.700958i
$297$	−8.83649e6	+	3.93426e6i	−0.337295	+	0.150174i
$298$	−1.49393e7	−	6.65141e6i	−0.564523	−	0.251342i
$299$	1.10807e7	+	1.23064e7i	0.414528	+	0.460380i
$300$	−1.57620e7	+	1.65665e6i	−0.583777	+	0.0613575i
$301$	−1.00322e6	+	4.71979e6i	−0.0367873	+	0.173071i
$302$	4.45364e7	−	1.44708e7i	1.61694	−	0.525376i
$303$	991643.	+	4.66531e6i	0.0356474	+	0.167708i
$304$	−1.36292e6	−	2.36064e6i	−0.0485119	−	0.0840251i
$305$	−1.49346e6	−	862250.i	−0.0526374	−	0.0303902i
$306$	−1.07112e7	−	3.48029e6i	−0.373831	−	0.121465i
$307$	−3.26229e6	+	3.10387e7i	−0.112748	+	1.07272i	0.781116	+	0.624386i	$0.214651\pi$
$307$	−3.26229e6	+	3.10387e7i	−0.112748	+	1.07272i	−0.893864	+	0.448338i	$0.852016\pi$
$308$	2.70213e7	+	3.71916e7i	0.924813	+	1.27290i
$309$			7.27743e6i			0.246662i
$310$	598031.	+	2.41409e6i	0.0200742	+	0.0810342i
$311$	−1.40836e7			−0.468200			−0.234100	−	0.972213i	$-0.575214\pi$
$311$	−1.40836e7			−0.468200			−0.234100	+	0.972213i	$0.575214\pi$
$312$	1.30844e7	−	9.50637e6i	0.430814	−	0.313005i
$313$	−4.73190e7	−	4.97343e6i	−1.54313	−	0.162190i	−0.705612	−	0.708599i	$-0.749328\pi$
$313$	−4.73190e7	−	4.97343e6i	−1.54313	−	0.162190i	−0.837518	+	0.546409i	$0.815994\pi$
$314$	−2.03178e7	+	6.25319e7i	−0.656279	+	2.01982i
$315$	−1.16624e6	+	2.01998e6i	−0.0373126	+	0.0646272i
$316$	−7.82827e7	+	4.51965e7i	−2.48087	+	1.43233i
$317$	1.01211e7	−	2.15131e6i	0.317724	−	0.0675344i	−0.0462891	−	0.998928i	$-0.514740\pi$
$317$	1.01211e7	−	2.15131e6i	0.317724	−	0.0675344i	0.364013	+	0.931394i	$0.381406\pi$
$318$	−6.04453e6	−	1.86031e7i	−0.187967	−	0.578502i
$319$	−1.84010e7	−	3.91124e6i	−0.566850	−	0.120488i
$320$	−276525.	−	2.63096e6i	−0.00843889	−	0.0802907i
$321$	1.47486e7	−	1.32797e7i	0.445899	−	0.401489i
$322$	−1.68237e7	+	3.77867e7i	−0.503912	+	1.13180i
$323$	−2.55439e6	−	5.73725e6i	−0.0758017	−	0.170253i
$324$	2.47352e7	−	2.74712e7i	0.727243	−	0.807686i
$325$	−2.74804e7	+	3.78235e7i	−0.800521	+	1.10182i
$326$	1.47021e7	+	1.06817e7i	0.424351	+	0.308309i
$327$	1.43783e6	+	1.29463e6i	0.0411212	+	0.0370257i
$328$	−2.29485e7	+	1.02173e7i	−0.650327	+	0.289544i
$329$	3.04317e7	+	1.35491e7i	0.854552	+	0.380471i
$330$	394824.	+	438497.i	0.0109866	+	0.0122018i
$331$	1.11677e7	−	1.17378e6i	0.307951	−	0.0323669i	0.0507073	−	0.998714i	$-0.483852\pi$
$331$	1.11677e7	−	1.17378e6i	0.307951	−	0.0323669i	0.257243	+	0.966347i	$0.417186\pi$
$332$	−266526.	+	1.25391e6i	−0.00728325	+	0.0342650i
$333$	2.89907e7	−	9.41967e6i	0.785103	−	0.255095i
$334$	5.42531e6	+	2.55241e7i	0.145608	+	0.685032i
$335$	592780.	+	1.02673e6i	0.0157674	+	0.0273099i
$336$	2.73511e6	+	1.57912e6i	0.0721037	+	0.0416291i
$337$	6.01262e7	+	1.95362e7i	1.57099	+	0.510446i	0.959716	−	0.280972i	$-0.0906569\pi$
$337$	6.01262e7	+	1.95362e7i	1.57099	+	0.510446i	0.611275	+	0.791418i	$0.290657\pi$
$338$	5.71263e6	−	5.43521e7i	0.147940	−	1.40756i
$339$	1.23519e7	+	1.70009e7i	0.317055	+	0.436389i
$340$			921602.i			0.0234480i
$341$	−1.43356e7	+	1.70322e7i	−0.361536	+	0.429544i
$342$	3.91200e7			0.977960
$343$	4.26087e7	−	3.09571e7i	1.05588	−	0.767145i
$344$	−4.78078e6	−	502480.i	−0.117442	−	0.0123436i
$345$	−102843.	+	316518.i	−0.00250448	+	0.00770799i
$346$	−3.72207e7	+	6.44681e7i	−0.898579	+	1.55638i
$347$	−1.16201e7	+	6.70889e6i	−0.278114	+	0.160569i	−0.632569	−	0.774504i	$-0.718000\pi$
$347$	−1.16201e7	+	6.70889e6i	−0.278114	+	0.160569i	0.354455	+	0.935073i	$0.384666\pi$
$348$	−2.50418e7	+	5.32280e6i	−0.594193	+	0.126300i
$349$	−4.73901e6	−	1.45852e7i	−0.111484	−	0.343111i	0.879714	−	0.475504i	$-0.157734\pi$
$349$	−4.73901e6	−	1.45852e7i	−0.111484	−	0.343111i	−0.991197	+	0.132392i	$0.957734\pi$
$350$	−1.14225e8	−	2.42792e7i	−2.66413	−	0.566279i
$351$	4.05898e6	+	3.86186e7i	0.0938632	+	0.893049i
$352$	1.60139e7	−	1.44189e7i	0.367171	−	0.330602i
$353$	−3.38402e7	+	7.60062e7i	−0.769322	+	1.72793i	−0.0877884	+	0.996139i	$0.527980\pi$
$353$	−3.38402e7	+	7.60062e7i	−0.769322	+	1.72793i	−0.681534	+	0.731787i	$0.738687\pi$
$354$	1.37304e7	+	3.08389e7i	0.309508	+	0.695167i
$355$	1.90619e6	−	2.11704e6i	0.0426071	−	0.0473199i
$356$	4.67531e7	−	6.43501e7i	1.03624	−	1.42626i
$357$	5.88676e6	+	4.27698e6i	0.129381	+	0.0940011i
$358$	−5.55347e7	−	5.00037e7i	−1.21036	−	1.08982i
$359$	2.44552e7	−	1.08882e7i	0.528552	−	0.235327i	−0.125070	−	0.992148i	$-0.539915\pi$
$359$	2.44552e7	−	1.08882e7i	0.528552	−	0.235327i	0.653622	+	0.756821i	$0.273249\pi$
$360$	−2.12282e6	−	945139.i	−0.0454993	−	0.0202576i
$361$	−1.68833e7	−	1.87508e7i	−0.358869	−	0.398564i
$362$	7.77586e6	−	817276.i	0.163917	−	0.0172283i
$363$	2.38560e6	−	1.12234e7i	0.0498744	−	0.234640i
$364$	1.75520e8	−	5.70299e7i	3.63934	−	1.18249i
$365$	−733888.	−	3.45267e6i	−0.0150922	−	0.0710030i
$366$	−1.67557e7	−	2.90216e7i	−0.341758	−	0.591942i
$367$	−2.78277e7	−	1.60663e7i	−0.562961	−	0.325026i	0.191372	−	0.981518i	$-0.438706\pi$
$367$	−2.78277e7	−	1.60663e7i	−0.562961	−	0.325026i	−0.754333	+	0.656492i	$0.772040\pi$
$368$	−3.06392e6	−	995528.i	−0.0614800	−	0.0199761i
$369$	2.94615e6	−	2.80308e7i	0.0586376	−	0.557899i
$370$	−2.33886e6	−	3.21916e6i	−0.0461741	−	0.0635532i
$371$		−	9.03477e7i		−	1.76928i
$372$	−8.39480e6	+	2.91102e7i	−0.163073	+	0.565480i
$373$	1.45065e7			0.279534			0.139767	−	0.990184i	$-0.455365\pi$
$373$	1.45065e7			0.279534			0.139767	+	0.990184i	$0.455365\pi$
$374$	−1.06464e7	+	7.73509e6i	−0.203512	+	0.147860i
$375$	−1.87133e6	−	196684.i	−0.0354859	−	0.00372972i
$376$	−1.02552e7	+	3.15623e7i	−0.192922	+	0.593751i
$377$	−3.77606e7	+	6.54032e7i	−0.704717	+	1.22060i
$378$	−8.39971e7	+	4.84958e7i	−1.55521	+	0.897901i
$379$	3.68223e7	−	7.82682e6i	0.676384	−	0.143770i	0.143103	−	0.989708i	$-0.454292\pi$
$379$	3.68223e7	−	7.82682e6i	0.676384	−	0.143770i	0.533281	+	0.845938i	$0.320959\pi$
$380$	−989217.	−	3.04450e6i	−0.0180277	−	0.0554836i
$381$	1.60540e7	+	3.41237e6i	0.290273	+	0.0616995i
$382$	−1.92479e6	−	1.83131e7i	−0.0345297	−	0.328528i
$383$	7.28336e7	−	6.55797e7i	1.29639	−	1.16728i	0.320929	−	0.947103i	$-0.396005\pi$
$383$	7.28336e7	−	6.55797e7i	1.29639	−	1.16728i	0.975461	−	0.220172i	$-0.0706618\pi$
$384$	1.38097e7	−	3.10171e7i	0.243888	−	0.547781i
$385$	1.10852e6	+	2.48978e6i	0.0194250	+	0.0436293i
$386$	−9.14674e7	+	1.01585e8i	−1.59039	+	1.76631i
$387$	3.17030e6	−	4.36354e6i	0.0546975	−	0.0752846i
$388$	1.24230e8	+	9.02587e7i	2.12683	+	1.54523i
$389$	−5.42186e7	−	4.88187e7i	−0.921085	−	0.829349i	0.0646058	−	0.997911i	$-0.479421\pi$
$389$	−5.42186e7	−	4.88187e7i	−0.921085	−	0.829349i	−0.985691	+	0.168562i	$0.946088\pi$
$390$	2.16399e6	−	963471.i	0.0364806	−	0.0162422i
$391$	−6.78072e6	−	3.01897e6i	−0.113435	−	0.0505043i
$392$	7.99805e7	+	8.88274e7i	1.32778	+	1.47465i
$393$	−2.92766e7	+	3.07709e6i	−0.482328	+	0.0506947i
$394$	3.99135e7	−	1.87778e8i	0.652576	−	3.07013i
$395$	−5.09664e6	+	1.65600e6i	−0.0826976	+	0.0268701i
$396$	−1.06839e7	−	5.02637e7i	−0.172046	−	0.809411i
$397$	1.84316e6	+	3.19244e6i	0.0294571	+	0.0510213i	0.880378	−	0.474272i	$-0.157289\pi$
$397$	1.84316e6	+	3.19244e6i	0.0294571	+	0.0510213i	−0.850921	+	0.525294i	$0.823955\pi$
$398$	−2.74060e7	−	1.58229e7i	−0.434707	−	0.250978i
$399$	−2.40376e7	−	7.81029e6i	−0.378419	−	0.122956i
$400$	950721.	−	9.04551e6i	0.0148550	−	0.141336i
$401$	−1.82479e7	−	2.51161e7i	−0.282996	−	0.389510i	0.643728	−	0.765255i	$-0.277387\pi$
$401$	−1.82479e7	−	2.51161e7i	−0.282996	−	0.389510i	−0.926723	+	0.375745i	$0.877387\pi$
$402$			2.30384e7i			0.354629i
$403$	4.72453e7	+	7.58629e7i	0.721845	+	1.15908i
$404$	−5.42208e7			−0.822284
$405$	1.77298e6	−	1.28815e6i	0.0266894	−	0.0193910i
$406$	−1.87601e8	−	1.97176e7i	−2.80321	−	0.294630i
$407$	1.10065e7	−	3.38745e7i	0.163255	−	0.502446i
$408$	−3.62456e6	+	6.27792e6i	−0.0533672	+	0.0924347i
$409$	−2.15624e7	+	1.24491e7i	−0.315158	+	0.181956i	−0.649232	−	0.760590i	$-0.724910\pi$
$409$	−2.15624e7	+	1.24491e7i	−0.315158	+	0.181956i	0.334074	+	0.942547i	$0.391576\pi$
$410$	−3.59879e6	+	764947.i	−0.0522162	+	0.0110989i
$411$	1.41937e7	+	4.36836e7i	0.204441	+	0.629206i
$412$	−8.09230e7	−	1.72007e7i	−1.15713	−	0.245955i
$413$	1.62982e7	+	1.55067e8i	0.231361	+	2.20125i
$414$	3.43594e7	−	3.09373e7i	0.484221	−	0.435995i
$415$	−30911.2	+	69427.8i	−0.000432486	+	0.000971379i
$416$	−3.51859e7	−	7.90288e7i	−0.488752	−	1.09775i
$417$	3.10331e7	−	3.44657e7i	0.427973	−	0.475312i
$418$	2.68677e7	−	3.69803e7i	0.367877	−	0.506339i
$419$	6.27919e7	+	4.56210e7i	0.853614	+	0.620187i	0.926140	−	0.377180i	$-0.123106\pi$
$419$	6.27919e7	+	4.56210e7i	0.853614	+	0.620187i	−0.0725260	+	0.997367i	$0.523106\pi$
$420$	2.75631e6	+	2.48179e6i	0.0372032	+	0.0334979i
$421$	−3.11455e7	+	1.38669e7i	−0.417396	+	0.185837i	−0.604679	−	0.796469i	$-0.706699\pi$
$421$	−3.11455e7	+	1.38669e7i	−0.417396	+	0.185837i	0.187283	+	0.982306i	$0.440032\pi$
$422$	−4.22170e7	−	1.87962e7i	−0.561759	−	0.250111i
$423$	−2.49155e7	−	2.76715e7i	−0.329192	−	0.365604i
$424$	8.95153e7	−	9.40844e6i	1.17436	−	0.123430i
$425$	4.35684e6	−	2.04973e7i	0.0567551	−	0.267012i
$426$	5.26490e7	−	1.71067e7i	0.681023	−	0.221278i
$427$	−3.21816e7	−	1.51402e8i	−0.413356	−	1.94469i
$428$	1.12807e8	+	1.95388e8i	1.43882	+	2.49211i
$429$	1.83627e7	+	1.06017e7i	0.232576	+	0.134278i
$430$	−669607.	−	217568.i	−0.00842198	−	0.00273647i
$431$	−478204.	+	4.54981e6i	−0.00597285	+	0.0568279i	−0.997102	−	0.0760719i	$-0.975762\pi$
$431$	−478204.	+	4.54981e6i	−0.00597285	+	0.0568279i	0.991129	+	0.132900i	$0.0424288\pi$
$432$	−4.44033e6	−	6.11159e6i	−0.0550762	−	0.0758059i
$433$		−	4.08938e7i		−	0.503726i	−0.967763	−	0.251863i	$-0.918957\pi$
$433$		−	4.08938e7i		−	0.503726i	0.967763	−	0.251863i	$-0.0810432\pi$
$434$	−1.25108e8	+	1.84877e8i	−1.53043	+	2.26159i
$435$	−1.51776e6			−0.0184389
$436$	−1.77944e7	+	1.29284e7i	−0.214696	+	0.155986i
$437$	2.56405e7	+	2.69492e6i	0.307243	+	0.0322925i
$438$	2.11964e7	−	6.52357e7i	0.252255	−	0.776360i
$439$	3.65716e7	−	6.33438e7i	0.432265	−	0.748705i	−0.564803	−	0.825226i	$-0.691048\pi$
$439$	3.65716e7	−	6.33438e7i	0.432265	−	0.748705i	0.997068	+	0.0765207i	$0.0243811\pi$
$440$	−2.35140e6	+	1.35758e6i	−0.0276038	+	0.0159370i
$441$	−1.31182e8	+	2.78836e7i	−1.52953	+	0.325112i
$442$	1.63253e7	+	5.02441e7i	0.189058	+	0.581860i
$443$	1.27044e8	+	2.70040e7i	1.46131	+	0.310612i	0.868886	−	0.495013i	$-0.164837\pi$
$443$	1.27044e8	+	2.70040e7i	1.46131	+	0.310612i	0.592427	+	0.805624i	$0.298170\pi$
$444$	−5.06671e6	−	4.82065e7i	−0.0578865	−	0.550753i
$445$	3.50435e6	−	3.15533e6i	0.0397674	−	0.0358068i
$446$	6.04975e7	−	1.35880e8i	0.681920	−	1.53162i
$447$	−4.80355e6	−	1.07890e7i	−0.0537824	−	0.120797i
$448$	1.58883e8	−	1.76457e8i	1.76703	−	1.96248i
$449$	3.12246e7	−	4.29770e7i	0.344951	−	0.474785i	−0.600928	−	0.799303i	$-0.705202\pi$
$449$	3.12246e7	−	4.29770e7i	0.344951	−	0.474785i	0.945879	+	0.324518i	$0.105202\pi$
$450$	1.05603e8	+	7.67251e7i	1.15888	+	0.841976i
$451$	−2.44741e7	−	2.20366e7i	−0.266795	−	0.240223i
$452$	−2.18240e8	+	9.71669e7i	−2.36331	+	1.05221i
$453$	3.08950e7	+	1.37553e7i	0.332348	+	0.147971i
$454$	1.47528e8	+	1.63846e8i	1.57654	+	1.75093i
$455$	1.08812e7	−	1.14366e6i	0.115516	−	0.0121412i
$456$	5.23516e6	−	2.46295e7i	0.0552122	−	0.259753i
$457$	−2.07346e7	+	6.73708e6i	−0.217244	+	0.0705867i	−0.415617	−	0.909540i	$-0.636434\pi$
$457$	−2.07346e7	+	6.73708e6i	−0.217244	+	0.0705867i	0.198373	+	0.980127i	$0.436434\pi$
$458$	3.47025e7	+	1.63263e8i	0.361214	+	1.69938i
$459$	−8.70244e6	−	1.50731e7i	−0.0899918	−	0.155870i
$460$	−3.27652e6	−	1.89170e6i	−0.0336619	−	0.0194347i
$461$	5.97588e7	+	1.94168e7i	0.609957	+	0.198187i	0.597676	−	0.801738i	$-0.296091\pi$
$461$	5.97588e7	+	1.94168e7i	0.609957	+	0.198187i	0.0122808	+	0.999925i	$0.496091\pi$
$462$	−5.53596e6	+	5.26711e7i	−0.0561393	+	0.534130i
$463$	−5.01699e7	−	6.90529e7i	−0.505475	−	0.695727i	0.477673	−	0.878538i	$-0.341480\pi$
$463$	−5.01699e7	−	6.90529e7i	−0.505475	−	0.695727i	−0.983148	+	0.182811i	$0.941480\pi$
$464$		−	1.46921e7i		−	0.147072i
$465$	−845620.	+	1.58460e6i	−0.00841039	+	0.0157602i
$466$	1.80197e8			1.78070
$467$	−9.77385e7	+	7.10112e7i	−0.959655	+	0.697230i	−0.953070	−	0.302748i	$-0.902096\pi$
$467$	−9.77385e7	+	7.10112e7i	−0.959655	+	0.697230i	−0.00658407	+	0.999978i	$0.502096\pi$
$468$	−2.05162e8	−	2.15634e7i	−2.00152	−	0.210368i
$469$	−3.28830e7	+	1.01203e8i	−0.318752	+	0.981018i
$470$	−2.43031e6	+	4.20941e6i	−0.0234082	+	0.0405441i
$471$	−4.11220e7	+	2.37418e7i	−0.393561	+	0.227222i
$472$	−1.51941e8	+	3.22961e7i	−1.44494	+	0.307132i
$473$	−1.94750e6	−	5.99378e6i	−0.0184032	−	0.0566393i
$474$	−1.01862e8	−	2.16513e7i	−0.956479	−	0.203306i
$475$	7.60840e6	+	7.23891e7i	0.0709925	+	0.675449i
$476$	−6.14727e7	+	5.53502e7i	−0.569982	+	0.513214i
$477$	−4.10765e7	+	9.22593e7i	−0.378476	+	0.850071i
$478$	−3.77312e7	−	8.47457e7i	−0.345476	−	0.775951i
$479$	−1.20985e8	+	1.34368e8i	−1.10084	+	1.22261i	−0.127845	+	0.991794i	$0.540806\pi$
$479$	−1.20985e8	+	1.34368e8i	−1.10084	+	1.22261i	−0.972998	+	0.230815i	$0.925861\pi$
$480$	1.02190e6	−	1.40653e6i	0.00924027	−	0.0127181i
$481$	−1.15680e8	−	8.40461e7i	−1.03949	−	0.755235i
$482$	−1.29977e8	−	1.17031e8i	−1.16071	−	1.04511i
$483$	−2.72890e7	+	1.21498e7i	−0.242184	+	0.107827i
$484$	1.19162e8	+	5.30544e7i	1.05100	+	0.467935i
$485$	6.09149e6	+	6.76529e6i	0.0533947	+	0.0593009i
$486$	1.65258e8	−	1.73694e7i	1.43964	−	0.151313i
$487$	1.46847e7	−	6.90860e7i	0.127139	−	0.598140i	−0.867736	−	0.497025i	$-0.834426\pi$
$487$	1.46847e7	−	6.90860e7i	0.127139	−	0.598140i	0.994875	−	0.101115i	$-0.0322410\pi$
$488$	1.46656e8	−	4.76515e7i	1.26195	−	0.410032i
$489$	2.72865e6	+	1.28373e7i	0.0233357	+	0.109786i
$490$	8.75331e6	+	1.51612e7i	0.0744019	+	0.128868i
$491$	1.46431e8	+	8.45420e7i	1.23705	+	0.714213i	0.968491	−	0.249049i	$-0.0801180\pi$
$491$	1.46431e8	+	8.45420e7i	1.23705	+	0.714213i	0.268563	+	0.963262i	$0.413451\pi$
$492$	−4.26251e7	−	1.38497e7i	−0.357907	−	0.116291i
$493$	3.53828e6	−	3.36644e7i	0.0295291	−	0.280951i
$494$	−1.07861e8	−	1.48458e8i	−0.894711	−	1.23146i
$495$		−	3.04644e6i		−	0.0251175i
$496$	−1.53391e7	−	8.18567e6i	−0.125706	−	0.0670825i
$497$	2.55694e8			2.08282
$498$	−1.19478e6	+	868060.i	−0.00967388	+	0.00702849i
$499$	−9.66239e7	−	1.01556e7i	−0.777648	−	0.0817341i	−0.292615	−	0.956230i	$-0.594526\pi$
$499$	−9.66239e7	−	1.01556e7i	−0.777648	−	0.0817341i	−0.485032	+	0.874496i	$0.661192\pi$
$500$	6.61008e6	−	2.03437e7i	0.0528807	−	0.162750i
$501$	−9.42246e6	+	1.63202e7i	−0.0749292	+	0.129781i
$502$	8.52189e6	−	4.92012e6i	0.0673635	−	0.0388923i
$503$	1.09120e7	−	2.31942e6i	0.0857434	−	0.0182253i	−0.164840	−	0.986320i	$-0.552711\pi$
$503$	1.09120e7	−	2.31942e6i	0.0857434	−	0.0182253i	0.250584	+	0.968095i	$0.419378\pi$
$504$	−6.44511e7	−	1.98360e8i	−0.503429	−	1.54940i
$505$	−3.14422e6	−	668324.i	−0.0244140	−	0.00518935i
$506$	−5.64702e6	−	5.37278e7i	−0.0435881	−	0.414713i
$507$	2.93308e7	−	2.64096e7i	0.225061	−	0.202646i
$508$	−7.58893e7	+	1.70450e8i	−0.578881	+	1.30019i
$509$	6.01018e7	+	1.34991e8i	0.455758	+	1.02365i	0.984583	+	0.174918i	$0.0559660\pi$
$509$	6.01018e7	+	1.34991e8i	0.455758	+	1.02365i	−0.528825	+	0.848731i	$0.677367\pi$
$510$	−710436.	+	789019.i	−0.00535568	+	0.00594808i
$511$	1.86224e8	−	2.56315e8i	1.39564	−	1.92093i
$512$	3.08395e7	+	2.24062e7i	0.229772	+	0.166939i
$513$	4.49273e7	+	4.04527e7i	0.332781	+	0.299637i
$514$	1.49481e7	−	6.65532e6i	0.110077	−	0.0490094i
$515$	−4.48064e6	−	1.99491e6i	−0.0328034	−	0.0146050i
$516$	−5.73893e6	−	6.37372e6i	−0.0417716	−	0.0463921i
$517$	−4.32700e7	+	4.54786e6i	−0.313123	+	0.0329105i
$518$	7.42556e7	−	3.49345e8i	0.534245	−	2.51342i
$519$	−5.11292e7	+	1.66129e7i	−0.365736	+	0.118835i
$520$	2.26625e6	+	1.06619e7i	0.0161175	+	0.0758268i
$521$	−4.96466e7	−	8.59904e7i	−0.351056	−	0.608047i	0.635379	−	0.772201i	$-0.280844\pi$
$521$	−4.96466e7	−	8.59904e7i	−0.351056	−	0.608047i	−0.986435	+	0.164154i	$0.947511\pi$
$522$	1.82605e8	+	1.05427e8i	1.28381	+	0.741210i
$523$	−1.67501e7	−	5.44245e6i	−0.117088	−	0.0380443i	0.249887	−	0.968275i	$-0.419607\pi$
$523$	−1.67501e7	−	5.44245e6i	−0.117088	−	0.0380443i	−0.366975	+	0.930231i	$0.619607\pi$
$524$	3.49808e7	−	3.32820e8i	0.243129	−	2.31322i
$525$	−4.95705e7	−	6.82279e7i	−0.342567	−	0.471503i
$526$			3.52442e8i			2.42176i
$527$	−3.31757e7	−	2.24502e7i	−0.226667	−	0.153387i
$528$	−4.12497e6			−0.0280233
$529$	−9.51122e7	+	6.91030e7i	−0.642494	+	0.466799i
$530$	1.31107e7	+	1.37799e6i	0.0880641	+	0.00925591i
$531$	5.38581e7	−	1.65758e8i	0.359722	−	1.10711i
$532$	1.43663e8	−	2.48831e8i	0.954135	−	1.65261i
$533$	−1.14498e8	+	6.61053e7i	−0.756163	+	0.436571i
$534$	8.96327e7	−	1.90520e7i	0.588631	−	0.125117i
$535$	4.13326e6	+	1.27209e7i	0.0269918	+	0.0830721i
$536$	−1.03695e8	−	2.20411e7i	−0.673387	−	0.143133i
$537$	−5.64124e6	−	5.36728e7i	−0.0364294	−	0.346602i
$538$	−1.54896e8	+	1.39469e8i	−0.994701	+	0.895633i
$539$	−6.37378e7	+	1.43157e8i	−0.407034	+	0.914213i
$540$	−3.60845e6	−	8.10470e6i	−0.0229160	−	0.0514702i
$541$	7.37929e7	−	8.19553e7i	0.466040	−	0.517589i	−0.463607	−	0.886041i	$-0.653445\pi$
$541$	7.37929e7	−	8.19553e7i	0.466040	−	0.517589i	0.929647	+	0.368451i	$0.120112\pi$
$542$	1.34919e8	−	1.85700e8i	0.847375	−	1.16631i
$543$	4.56815e6	+	3.31896e6i	0.0285326	+	0.0207301i
$544$	2.88149e7	+	2.59450e7i	0.178987	+	0.161160i
$545$	−1.19124e6	+	530372.i	−0.00735882	+	0.00327636i
$546$	1.94232e8	+	8.64777e7i	1.19328	+	0.531283i
$547$	−4.92366e6	−	5.46828e6i	−0.0300833	−	0.0334109i	0.727915	−	0.685667i	$-0.240489\pi$
$547$	−4.92366e6	−	5.46828e6i	−0.0300833	−	0.0334109i	−0.757999	+	0.652256i	$0.773823\pi$
$548$	−5.19297e8	+	5.45803e7i	−3.15554	+	0.331661i
$549$	−3.59725e7	+	1.69237e8i	−0.217397	+	1.02277i
$550$	1.45057e8	−	4.71318e7i	0.871867	−	0.283287i
$551$	2.44457e7	+	1.15008e8i	0.146133	+	0.687500i
$552$	−1.48797e7	−	2.57723e7i	−0.0884659	−	0.153227i
$553$	−4.16556e8	−	2.40499e8i	−2.46319	−	1.42212i
$554$	4.27099e7	+	1.38773e7i	0.251188	+	0.0816159i
$555$	300378.	−	2.85791e6i	0.00175707	−	0.0167174i
$556$	3.09900e8	+	4.26541e8i	1.80301	+	2.48163i
$557$		−	3.61877e7i		−	0.209409i	−0.994503	−	0.104705i	$-0.966610\pi$
$557$		−	3.61877e7i		−	0.209409i	0.994503	−	0.104705i	$-0.0333897\pi$
$558$	2.11809e8	−	1.31909e8i	1.21911	−	0.759226i
$559$	−2.53004e7			−0.144841
$560$	−1.72201e6	+	1.25111e6i	−0.00980551	+	0.00712412i
$561$	−9.45169e6	−	993413.i	−0.0535329	−	0.00562654i
$562$	−6.68816e7	+	2.05840e8i	−0.376788	+	1.15964i
$563$	6.97404e7	−	1.20794e8i	0.390804	−	0.676892i	−0.601752	−	0.798683i	$-0.705530\pi$
$563$	6.97404e7	−	1.20794e8i	0.390804	−	0.676892i	0.992556	+	0.121791i	$0.0388637\pi$
$564$	−5.12776e7	+	2.96051e7i	−0.285819	+	0.165017i
$565$	−1.38533e7	+	2.94460e6i	−0.0768080	+	0.0163260i
$566$	5.84688e7	+	1.79948e8i	0.322459	+	0.992427i
$567$	1.92405e8	+	4.08969e7i	1.05552	+	0.224358i
$568$	2.66270e7	+	2.53339e8i	0.145304	+	1.38247i
$569$	−1.26250e8	+	1.13676e8i	−0.685323	+	0.617068i	−0.936415	−	0.350896i	$-0.885877\pi$
$569$	−1.26250e8	+	1.13676e8i	−0.685323	+	0.617068i	0.251091	+	0.967963i	$0.419211\pi$
$570$	1.50001e6	−	3.36907e6i	0.00809970	−	0.0181922i
$571$	−8.50935e7	−	1.91123e8i	−0.457075	−	1.02661i	−0.984239	−	0.176844i	$-0.943411\pi$
$571$	−8.50935e7	−	1.91123e8i	−0.457075	−	1.02661i	0.527163	−	0.849764i	$-0.323256\pi$
$572$	−1.61290e8	+	1.79131e8i	−0.861825	+	0.957153i
$573$	7.81656e6	−	1.07586e7i	0.0415482	−	0.0571861i
$574$	−2.67163e8	−	1.94105e8i	−1.41267	−	1.02636i
$575$	6.39300e7	+	5.75628e7i	0.336280	+	0.302788i
$576$	−2.42471e8	+	1.07955e8i	−1.26880	+	0.564904i
$577$	1.88315e7	+	8.38432e6i	0.0980296	+	0.0436456i	0.455166	−	0.890407i	$-0.349580\pi$
$577$	1.88315e7	+	8.38432e6i	0.0980296	+	0.0436456i	−0.357136	+	0.934052i	$0.616247\pi$
$578$	1.95682e8	+	2.17327e8i	1.01337	+	1.12546i
$579$	−9.81790e7	+	1.03190e7i	−0.505805	+	0.0531622i
$580$	3.58734e6	−	1.68771e7i	0.0183860	−	0.0864995i
$581$	−6.48746e6	+	2.10790e6i	−0.0330785	+	0.0107479i
$582$	3.67807e7	+	1.73040e8i	0.186574	+	0.877761i
$583$	5.90016e7	+	1.02194e8i	0.297754	+	0.515725i
$584$	2.73346e8	+	1.57816e8i	1.37238	+	0.792344i
$585$	−1.16314e7	−	3.77927e6i	−0.0580984	−	0.0188773i
$586$	−1.04640e7	+	9.95584e7i	−0.0520002	+	0.494749i
$587$	−2.07650e8	−	2.85805e8i	−1.02664	−	1.41305i	−0.907443	−	0.420175i	$-0.861969\pi$
$587$	−2.07650e8	−	2.85805e8i	−1.02664	−	1.41305i	−0.119195	−	0.992871i	$-0.538031\pi$
$588$			2.13260e8i			1.04900i
$589$	1.33693e8	+	3.85543e7i	0.654278	+	0.188680i
$590$	−2.27510e7			−0.110776
$591$	1.12162e8	−	8.14907e7i	0.543356	−	0.394771i
$592$	2.76648e7	+	2.90769e6i	0.133341	+	0.0140147i
$593$	7.75323e7	−	2.38620e8i	0.371808	−	1.14431i	−0.573799	−	0.818996i	$-0.694531\pi$
$593$	7.75323e7	−	2.38620e8i	0.371808	−	1.14431i	0.945607	−	0.325311i	$-0.105469\pi$
$594$	6.33403e7	−	1.09709e8i	0.302218	−	0.523457i
$595$	−4.24699e6	+	2.45200e6i	−0.0201619	+	0.0116405i
$596$	1.31324e8	−	2.79137e7i	0.620304	−	0.131850i
$597$	−7.06230e6	−	2.17355e7i	−0.0331912	−	0.102152i
$598$	−2.12140e8	−	4.50917e7i	−0.992015	−	0.210859i
$599$	1.93816e7	+	1.84404e8i	0.0901798	+	0.858003i	0.942325	+	0.334698i	$0.108634\pi$
$599$	1.93816e7	+	1.84404e8i	0.0901798	+	0.858003i	−0.852146	+	0.523305i	$0.824699\pi$
$600$	6.24373e7	−	5.62188e7i	0.289061	−	0.260272i
$601$	−4.57947e7	+	1.02857e8i	−0.210956	+	0.473815i	−0.987771	−	0.155914i	$-0.950168\pi$
$601$	−4.57947e7	+	1.02857e8i	−0.210956	+	0.473815i	0.776815	+	0.629729i	$0.216834\pi$
$602$	−2.57035e7	−	5.77310e7i	−0.117816	−	0.264618i
$603$	7.95908e7	−	8.83945e7i	0.363004	−	0.403156i
$604$	−2.25978e8	+	3.11032e8i	−1.02555	+	1.41154i
$605$	6.25616e6	+	4.54537e6i	0.0282515	+	0.0205259i
$606$	−4.64205e7	−	4.17972e7i	−0.208589	−	0.187815i
$607$	−1.62622e8	+	7.24038e7i	−0.727130	+	0.323739i	−0.736704	−	0.676215i	$-0.763619\pi$
$607$	−1.62622e8	+	7.24038e7i	−0.727130	+	0.323739i	0.00957425	+	0.999954i	$0.496952\pi$
$608$	−1.23038e8	−	5.47801e7i	−0.547431	−	0.243732i
$609$	−9.11548e7	−	1.01238e8i	−0.403578	−	0.448219i
$610$	2.24615e7	−	2.36079e6i	0.0989574	−	0.0104008i
$611$	−3.63148e7	+	1.70848e8i	−0.159206	+	0.749006i
$612$	8.79382e7	−	2.85729e7i	0.383640	−	0.124652i
$613$	7.46912e7	+	3.51395e8i	0.324256	+	1.52551i	0.774485	+	0.632592i	$0.218009\pi$
$613$	7.46912e7	+	3.51395e8i	0.324256	+	1.52551i	−0.450229	+	0.892913i	$0.648658\pi$
$614$	−2.04371e8	−	3.53981e8i	−0.882905	−	1.52924i
$615$	−2.30108e6	−	1.32853e6i	−0.00989251	−	0.00571144i
$616$	−2.31775e8	−	7.53084e7i	−0.991574	−	0.322182i
$617$	1.96647e7	−	1.87097e8i	0.0837204	−	0.796546i	−0.869431	−	0.494054i	$-0.835515\pi$
$617$	1.96647e7	−	1.87097e8i	0.0837204	−	0.796546i	0.953152	−	0.302492i	$-0.0978187\pi$
$618$	−5.60218e7	−	7.71074e7i	−0.237351	−	0.326686i
$619$		−	3.30365e8i		−	1.39290i	−0.717603	−	0.696452i	$-0.754761\pi$
$619$		−	3.30365e8i		−	1.39290i	0.717603	−	0.696452i	$-0.245239\pi$
$620$	−1.56217e7	−	1.31484e7i	−0.0655470	−	0.0551693i
$621$	7.14511e7			0.298356
$622$	1.49221e8	−	1.08415e8i	0.620096	−	0.450526i
$623$	4.20934e8	+	4.42419e7i	1.74080	+	0.182966i
$624$	−5.11724e6	+	1.57492e7i	−0.0210611	+	0.0648195i
$625$	−1.21119e8	+	2.09784e8i	−0.496103	+	0.859275i
$626$	5.39650e8	−	3.11567e8i	2.19983	−	1.27007i
$627$	3.22898e7	−	6.86341e6i	0.130997	−	0.0278444i
$628$	−1.66808e8	−	5.13381e8i	−0.673499	−	2.07282i
$629$	6.26891e7	+	1.33250e7i	0.251907	+	0.0535445i
$630$	−3.19309e6	−	3.03802e7i	−0.0127700	−	0.121498i
$631$	4.75553e7	−	4.28189e7i	0.189283	−	0.170431i	−0.569041	−	0.822309i	$-0.692685\pi$
$631$	4.75553e7	−	4.28189e7i	0.189283	−	0.170431i	0.758323	+	0.651878i	$0.226019\pi$
$632$	1.94905e8	−	4.37763e8i	0.772095	−	1.73415i
$633$	−1.35743e7	−	3.04885e7i	−0.0535190	−	0.120206i
$634$	−9.06766e7	+	1.00707e8i	−0.355818	+	0.395175i
$635$	−6.50172e6	+	8.94885e6i	−0.0253926	+	0.0349499i
$636$	1.29920e8	+	9.43924e7i	0.505015	+	0.366915i
$637$	4.67509e8	+	4.20947e8i	1.80872	+	1.62858i
$638$	2.25075e8	−	1.00210e8i	0.866691	−	0.385876i
$639$	−2.61104e8	−	1.16251e8i	−1.00072	−	0.445548i
$640$	1.53114e7	+	1.70050e7i	0.0584082	+	0.0648689i
$641$	4.18422e8	−	4.39780e7i	1.58870	−	0.166979i	0.731453	−	0.681891i	$-0.238842\pi$
$641$	4.18422e8	−	4.39780e7i	1.58870	−	0.166979i	0.857243	+	0.514913i	$0.172176\pi$
$642$	−5.40403e7	+	2.54239e8i	−0.204227	+	0.960811i
$643$	2.54689e7	−	8.27535e6i	0.0958026	−	0.0311282i	−0.260723	−	0.965414i	$-0.583961\pi$
$643$	2.54689e7	−	8.27535e6i	0.0958026	−	0.0311282i	0.356526	+	0.934285i	$0.383961\pi$
$644$	−7.06034e7	−	3.32163e8i	−0.264343	−	1.24364i
$645$	−254233.	−	440345.i	−0.000947443	−	0.00164102i
$646$	7.12302e7	+	4.11248e7i	0.264221	+	0.152548i
$647$	−3.50774e8	−	1.13973e8i	−1.29513	−	0.420814i	−0.421247	−	0.906946i	$-0.638408\pi$
$647$	−3.50774e8	−	1.13973e8i	−1.29513	−	0.420814i	−0.873886	+	0.486131i	$0.838408\pi$
$648$	−2.04839e7	+	1.94891e8i	−0.0752813	+	0.716254i
$649$	−1.19702e8	−	1.64755e8i	−0.437891	−	0.602706i
$650$		−	6.12300e8i		−	2.22959i
$651$	−1.56483e8	+	3.87648e7i	−0.567185	+	0.140506i
$652$	−1.49197e8			−0.538289
$653$	3.15831e8	−	2.29465e8i	1.13427	−	0.824093i	0.147957	−	0.988994i	$-0.452730\pi$
$653$	3.15831e8	−	2.29465e8i	1.13427	−	0.824093i	0.986310	+	0.164901i	$0.0527303\pi$
$654$	−2.52006e7	−	2.64869e6i	−0.0900901	−	0.00946885i
$655$	6.13085e6	−	1.88688e7i	0.0218171	−	0.0671461i
$656$	1.28603e7	−	2.22747e7i	0.0455553	−	0.0789041i
$657$	−3.06697e8	+	1.77072e8i	−1.08147	+	0.624386i
$658$	−4.26737e8	+	9.07058e7i	−1.49790	+	0.318389i
$659$	1.29476e8	+	3.98486e8i	0.452410	+	1.39238i	0.874149	+	0.485659i	$0.161420\pi$
$659$	1.29476e8	+	3.98486e8i	0.452410	+	1.39238i	−0.421738	+	0.906718i	$0.638580\pi$
$660$	−4.73844e6	−	1.00719e6i	−0.0164818	−	0.00350331i
$661$	−4.34000e7	−	4.12924e8i	−0.150275	−	1.42977i	−0.766524	−	0.642216i	$-0.778015\pi$
$661$	−4.34000e7	−	4.12924e8i	−0.150275	−	1.42977i	0.616249	−	0.787551i	$-0.288651\pi$
$662$	−1.09291e8	+	9.84061e7i	−0.376713	+	0.339194i
$663$	−1.55182e7	+	3.48544e7i	−0.0532476	+	0.119596i
$664$	−2.76406e6	−	6.20818e6i	−0.00944155	−	0.0212061i
$665$	1.13980e7	−	1.26587e7i	0.0387582	−	0.0430453i
$666$	−2.34656e8	+	3.22977e8i	−0.794345	+	1.09332i
$667$	1.12422e8	+	8.16797e7i	0.378857	+	0.275256i
$668$	−1.59205e8	−	1.43349e8i	−0.534107	−	0.480912i
$669$	9.81303e7	−	4.36904e7i	0.327737	−	0.145918i
$670$	−1.41845e7	−	6.31535e6i	−0.0471617	−	0.0209978i
$671$	1.35274e8	+	1.50237e8i	0.447763	+	0.497291i
$672$	1.55192e8	−	1.63113e7i	0.511401	−	0.0537504i
$673$	4.11694e6	−	1.93687e7i	0.0135061	−	0.0635412i	−0.970878	−	0.239573i	$-0.922993\pi$
$673$	4.11694e6	−	1.93687e7i	0.0135061	−	0.0635412i	0.984385	+	0.176031i	$0.0563260\pi$
$674$	−7.87451e8	+	2.55858e8i	−2.57184	+	0.835642i
$675$	4.19407e7	+	1.97315e8i	0.136372	+	0.641578i
$676$	2.24342e8	+	3.88571e8i	0.726223	+	1.25786i
$677$	−8.25225e7	−	4.76444e7i	−0.265954	−	0.153549i	0.361094	−	0.932530i	$-0.382404\pi$
$677$	−8.25225e7	−	4.76444e7i	−0.265954	−	0.153549i	−0.627048	+	0.778981i	$0.715737\pi$
$678$	−2.61747e8	−	8.50468e7i	−0.839833	−	0.272878i
$679$	−8.54108e7	+	8.12629e8i	−0.272837	+	2.59587i
$680$	−2.87168e6	−	3.95252e6i	−0.00913290	−	0.0125704i
$681$			1.59225e8i			0.504162i
$682$	2.07772e7	−	2.90819e8i	0.0654988	−	0.916789i
$683$	−4.13710e8			−1.29848			−0.649238	−	0.760585i	$-0.724912\pi$
$683$	−4.13710e8			−1.29848			−0.649238	+	0.760585i	$0.724912\pi$
$684$	−2.59834e8	+	1.88780e8i	−0.811945	+	0.589913i
$685$	−3.07864e7	−	3.23578e6i	−0.0957826	−	0.0100672i
$686$	−2.13149e8	+	6.56006e8i	−0.660254	+	2.03205i
$687$	−6.02700e7	+	1.04391e8i	−0.185879	+	0.321952i
$688$	4.26258e6	−	2.46100e6i	0.0130890	−	0.00755694i
$689$	4.63373e8	−	9.84929e7i	1.41668	−	0.301125i
$690$	−1.34690e6	−	4.14532e6i	−0.00410003	−	0.0126186i
$691$	4.73157e8	+	1.00573e8i	1.43407	+	0.304822i	0.858451	−	0.512895i	$-0.171427\pi$
$691$	4.73157e8	+	1.00573e8i	1.43407	+	0.304822i	0.575621	+	0.817716i	$0.304760\pi$
$692$	−6.38833e7	−	6.07809e8i	−0.192783	−	1.83421i
$693$	2.03204e8	−	1.82965e8i	0.610565	−	0.549755i
$694$	7.14751e7	−	1.60536e8i	0.213834	−	0.480278i
$695$	1.27133e7	+	2.85546e7i	0.0378708	+	0.0850593i
$696$	9.08125e7	−	1.00857e8i	0.269351	−	0.299144i
$697$	3.48316e7	−	4.79416e7i	0.102867	−	0.141584i
$698$	1.62489e8	+	1.18055e8i	0.477811	+	0.347150i
$699$	9.67097e7	+	8.70778e7i	0.283164	+	0.254962i
$700$	8.75839e8	−	3.89949e8i	2.55347	−	1.13688i
$701$	−3.74319e7	−	1.66657e7i	−0.108664	−	0.0483805i	0.351684	−	0.936119i	$-0.385609\pi$
$701$	−3.74319e7	−	1.66657e7i	−0.108664	−	0.0483805i	−0.460349	+	0.887738i	$0.652276\pi$
$702$	−3.40293e8	−	3.77934e8i	−0.983653	−	1.09246i
$703$	−2.21395e8	+	2.32696e7i	−0.637238	+	0.0669764i
$704$	−6.44794e7	+	3.03352e8i	−0.184800	+	0.869418i
$705$	−3.33846e6	+	1.08473e6i	−0.00952749	+	0.00309567i
$706$	−2.26547e8	−	1.06582e9i	−0.643790	−	3.02879i
$707$	−1.44259e8	−	2.49864e8i	−0.408212	−	0.707043i
$708$	−2.40014e8	−	1.38572e8i	−0.676297	−	0.390460i
$709$	6.14312e8	+	1.99602e8i	1.72366	+	0.560050i	0.992509	−	0.122170i	$-0.0389854\pi$
$709$	6.14312e8	+	1.99602e8i	1.72366	+	0.560050i	0.731147	+	0.682220i	$0.238985\pi$
$710$	−3.89988e6	+	3.71048e7i	−0.0108962	+	0.103671i
$711$	3.16027e8	+	4.34974e8i	0.879257	+	1.21019i
$712$			4.21663e8i			1.16822i
$713$	1.47913e8	−	7.18658e7i	0.408073	−	0.198269i
$714$	−9.52970e7			−0.261809
$715$	−1.15610e7	+	8.39958e6i	−0.0316285	+	0.0229794i
$716$	6.10160e8	+	6.41304e7i	1.66228	+	0.174713i
$717$	2.07023e7	−	6.37151e7i	0.0561644	−	0.172856i
$718$	−1.75296e8	+	3.03621e8i	−0.473585	+	0.820273i
$719$	1.24060e8	−	7.16258e7i	0.333767	−	0.192701i	−0.323745	−	0.946144i	$-0.604942\pi$
$719$	1.24060e8	−	7.16258e7i	0.333767	−	0.192701i	0.657512	+	0.753444i	$0.271609\pi$
$720$	2.32726e6	−	494673.i	0.00623515	−	0.00132532i
$721$	−1.36037e8	−	4.18680e8i	−0.362954	−	1.11706i
$722$	3.23229e8	+	6.87045e7i	0.858814	+	0.182547i
$723$	−1.32031e7	−	1.25619e8i	−0.0349349	−	0.332384i
$724$	−4.77030e7	+	4.29520e7i	−0.125699	+	0.113180i
$725$	−1.59572e8	+	3.58404e8i	−0.418738	+	0.940500i
$726$	6.11212e7	+	1.37280e8i	0.159728	+	0.358756i
$727$	4.06093e7	−	4.51011e7i	0.105687	−	0.117377i	−0.687980	−	0.725729i	$-0.741502\pi$
$727$	4.06093e7	−	4.51011e7i	0.105687	−	0.117377i	0.793667	+	0.608352i	$0.208169\pi$
$728$	−5.75059e8	+	7.91501e8i	−1.49045	+	2.05143i
$729$	−1.05678e8	−	7.67796e7i	−0.272774	−	0.198182i
$730$	3.43546e7	+	3.09330e7i	0.0883113	+	0.0795158i
$731$	1.03597e7	−	4.61242e6i	0.0265212	−	0.0118080i
$732$	2.51339e8	+	1.11903e8i	0.640806	+	0.285305i
$733$	−3.14499e8	−	3.49287e8i	−0.798560	−	0.886891i	0.197059	−	0.980392i	$-0.436861\pi$
$733$	−3.14499e8	−	3.49287e8i	−0.798560	−	0.886891i	−0.995619	+	0.0935010i	$0.970194\pi$
$734$	4.18524e8	−	4.39887e7i	1.05836	−	0.111238i
$735$	−2.62863e6	+	1.23667e7i	−0.00662015	+	0.0311454i
$736$	−1.51387e8	+	4.91886e7i	−0.379712	+	0.123376i
$737$	−2.88964e7	−	1.35947e8i	−0.0721841	−	0.339600i
$738$	1.84566e8	+	3.19677e8i	0.459179	+	0.795321i
$739$	−5.77628e8	−	3.33493e8i	−1.43125	−	0.826331i	−0.434031	−	0.900898i	$-0.642909\pi$
$739$	−5.77628e8	−	3.33493e8i	−1.43125	−	0.826331i	−0.997216	+	0.0745668i	$0.976243\pi$
$740$	3.10692e7	+	1.00950e7i	0.0766716	+	0.0249121i
$741$	1.38525e7	−	1.31798e8i	0.0340466	−	0.323932i
$742$	6.95499e8	+	9.57272e8i	1.70249	+	2.34328i
$743$		−	5.64461e8i		−	1.37616i	−0.725637	−	0.688078i	$-0.758455\pi$
$743$		−	5.64461e8i		−	1.37616i	0.725637	−	0.688078i	$-0.241545\pi$
$744$	−5.47032e7	−	1.51005e8i	−0.132829	−	0.366667i
$745$	7.95942e6			0.0192492
$746$	−1.53702e8	+	1.11671e8i	−0.370223	+	0.268983i
$747$	7.58308e6	+	797014.i	0.0181921	+	0.00191207i
$748$	3.33862e7	−	1.02752e8i	0.0797742	−	0.245520i
$749$	−6.00269e8	+	1.03970e9i	−1.42857	+	2.47435i
$750$	2.13415e7	−	1.23215e7i	0.0505874	−	0.0292066i
$751$	4.98980e8	−	1.06062e8i	1.17805	−	0.250402i	0.423037	−	0.906112i	$-0.360964\pi$
$751$	4.98980e8	−	1.06062e8i	1.17805	−	0.250402i	0.755013	+	0.655710i	$0.227631\pi$
$752$	−1.05003e7	−	3.23166e7i	−0.0246915	−	0.0759927i
$753$	6.95118e6	+	1.47752e6i	0.0162807	+	0.00346057i
$754$	−1.03386e8	−	9.83656e8i	−0.241184	−	2.29472i
$755$	−1.69380e7	+	1.52511e7i	−0.0393570	+	0.0354372i
$756$	3.23881e8	−	7.27449e8i	0.749584	−	1.68359i
$757$	6.59959e7	+	1.48229e8i	0.152135	+	0.341701i	0.973495	−	0.228710i	$-0.0734507\pi$
$757$	6.59959e7	+	1.48229e8i	0.152135	+	0.341701i	−0.821360	+	0.570411i	$0.806784\pi$
$758$	−3.29897e8	+	3.66387e8i	−0.757478	+	0.841265i
$759$	2.29325e7	−	3.15639e7i	0.0524477	−	0.0721881i
$760$	1.37291e7	+	9.97474e6i	0.0312752	+	0.0227227i
$761$	−4.67017e8	−	4.20504e8i	−1.05969	−	0.954149i	−0.0606584	−	0.998159i	$-0.519320\pi$
$761$	−4.67017e8	−	4.20504e8i	−1.05969	−	0.954149i	−0.999031	+	0.0440098i	$0.985987\pi$
$762$	−1.96367e8	+	8.74281e7i	−0.443816	+	0.197600i
$763$	−1.06921e8	−	4.76043e7i	−0.240707	−	0.107170i
$764$	1.01157e8	+	1.12347e8i	0.226839	+	0.251930i
$765$	5.45165e6	−	572992.i	0.0121771	−	0.00127987i
$766$	−2.66869e8	+	1.25552e9i	−0.593761	+	2.79342i
$767$	−7.77536e8	+	2.52637e8i	−1.72320	+	0.559900i
$768$	4.02197e7	+	1.89219e8i	0.0887883	+	0.417716i
$769$	−2.91405e8	−	5.04728e8i	−0.640793	−	1.10989i	−0.985256	−	0.171086i	$-0.945272\pi$
$769$	−2.91405e8	−	5.04728e8i	−0.640793	−	1.10989i	0.344463	−	0.938800i	$-0.388061\pi$
$770$	−3.09116e7	−	1.78468e7i	−0.0677094	−	0.0390920i
$771$	1.12386e7	+	3.65163e6i	0.0245215	+	0.00796753i
$772$	1.17308e8	−	1.11611e9i	0.254963	−	2.42581i
$773$	1.28691e8	+	1.77128e8i	0.278618	+	0.383485i	0.925276	−	0.379295i	$-0.123834\pi$
$773$	1.28691e8	+	1.77128e8i	0.278618	+	0.383485i	−0.646657	+	0.762781i	$0.723834\pi$
$774$			7.06385e7i			0.152342i
$775$	2.85283e8	+	3.66284e8i	0.612873	+	0.786887i
$776$	−8.14037e8			−1.74204
$777$	2.08668e8	−	1.51607e8i	0.444830	−	0.323188i
$778$	9.50276e8	+	9.98780e7i	2.01795	+	0.212095i
$779$	−6.36068e7	+	1.95761e8i	−0.134552	+	0.414109i
$780$	−9.72375e6	+	1.68420e7i	−0.0204904	+	0.0354904i
$781$	−2.89220e8	+	1.66981e8i	−0.607121	+	0.350521i
$782$	9.50846e7	−	2.02109e7i	0.198834	−	0.0422634i
$783$	1.00694e8	+	3.09904e8i	0.209758	+	0.645567i
$784$	−1.19711e8	−	2.54454e7i	−0.248420	−	0.0528033i
$785$	−3.34511e6	−	3.18266e7i	−0.00691515	−	0.0657932i
$786$	2.86510e8	−	2.57975e8i	0.590027	−	0.531263i
$787$	1.14199e8	−	2.56495e8i	0.234281	−	0.526205i	−0.757698	−	0.652606i	$-0.773676\pi$
$787$	1.14199e8	−	2.56495e8i	0.234281	−	0.526205i	0.991979	+	0.126401i	$0.0403425\pi$
$788$	6.41051e8	+	1.43982e9i	1.31013	+	2.94259i
$789$	−1.70313e8	+	1.89151e8i	−0.346750	+	0.385105i
$790$	4.12531e7	−	5.67800e7i	0.0836711	−	0.115163i
$791$	−1.02842e9	−	7.47191e8i	−2.07798	−	1.50974i
$792$	2.02441e8	+	1.82278e8i	0.407495	+	0.366910i
$793$	7.41425e8	−	3.30104e8i	1.48678	−	0.661959i
$794$	−4.41045e7	−	1.96366e7i	−0.0881092	−	0.0392287i
$795$	6.37047e6	+	7.07513e6i	0.0126786	+	0.0140810i
$796$	2.58385e8	−	2.71574e7i	0.512305	−	0.0538454i
$797$	1.29351e8	−	6.08549e8i	0.255502	−	1.20204i	−0.643964	−	0.765056i	$-0.722711\pi$
$797$	1.29351e8	−	6.08549e8i	0.255502	−	1.20204i	0.899467	−	0.436989i	$-0.143955\pi$
$798$	3.14812e8	−	1.02289e8i	0.619502	−	0.201289i
$799$	−1.62769e7	−	7.65769e7i	−0.0319104	−	0.150126i
$800$	−2.24698e8	−	3.89188e8i	−0.438863	−	0.760133i
$801$	−4.09725e8	−	2.36555e8i	−0.797252	−	0.460293i
$802$	3.86688e8	+	1.25643e8i	0.749614	+	0.243564i
$803$	−4.32541e7	+	4.11535e8i	−0.0835373	+	0.794804i
$804$	−1.11175e8	−	1.53020e8i	−0.213915	−	0.294428i
$805$		−	2.01321e7i		−	0.0385924i
$806$	−1.08458e9	−	4.40104e8i	−2.07136	−	0.840523i
$807$	−1.50527e8			−0.286414
$808$	2.32540e8	−	1.68950e8i	0.440822	−	0.320276i
$809$	−2.29828e7	−	2.41559e6i	−0.0434067	−	0.00456223i	0.0828002	−	0.996566i	$-0.473614\pi$
$809$	−2.29828e7	−	2.41559e6i	−0.0434067	−	0.00456223i	−0.126207	+	0.992004i	$0.540280\pi$
$810$	−8.86930e6	+	2.72969e7i	−0.0166891	+	0.0513639i
$811$	−9.01335e7	+	1.56116e8i	−0.168975	+	0.292674i	−0.938060	−	0.346473i	$-0.887379\pi$
$811$	−9.01335e7	+	1.56116e8i	−0.168975	+	0.292674i	0.769084	+	0.639147i	$0.220713\pi$
$812$	1.34119e9	−	7.74334e8i	2.50508	−	1.44631i
$813$	1.62147e8	−	3.44653e7i	0.301742	−	0.0641373i
$814$	1.44148e8	+	4.43642e8i	0.267261	+	0.822545i
$815$	−8.65178e6	−	1.83899e6i	−0.0159821	−	0.00339709i
$816$	−775848.	−	7.38170e6i	−0.00142793	−	0.0135858i
$817$	−2.92722e7	+	2.63568e7i	−0.0536771	+	0.0483311i
$818$	1.32630e8	−	2.97891e8i	0.242315	−	0.544249i
$819$	−4.46482e8	−	1.00282e9i	−0.812741	−	1.82545i
$820$	2.02117e7	−	2.24473e7i	0.0366573	−	0.0407120i
$821$	8.27965e7	−	1.13960e8i	0.149618	−	0.205931i	−0.727629	−	0.685971i	$-0.759378\pi$
$821$	8.27965e7	−	1.13960e8i	0.149618	−	0.205931i	0.877247	+	0.480040i	$0.159378\pi$
$822$	−4.86665e8	−	3.53583e8i	−0.876223	−	0.636613i
$823$	−1.85935e8	−	1.67417e8i	−0.333551	−	0.300331i	0.485288	−	0.874355i	$-0.338715\pi$
$823$	−1.85935e8	−	1.67417e8i	−0.333551	−	0.300331i	−0.818838	+	0.574024i	$0.805382\pi$
$824$	4.00656e8	−	1.78383e8i	0.716127	−	0.318840i
$825$	1.00626e8	+	4.48016e7i	0.179205	+	0.0797870i
$826$	−1.36640e9	−	1.51754e9i	−2.42458	−	2.69277i
$827$	4.89076e8	−	5.14040e7i	0.864689	−	0.0908825i	0.338210	−	0.941071i	$-0.390179\pi$
$827$	4.89076e8	−	5.14040e7i	0.864689	−	0.0908825i	0.526479	+	0.850188i	$0.323512\pi$
$828$	−7.89203e7	+	3.71291e8i	−0.139027	+	0.654068i
$829$	−4.08612e8	+	1.32766e8i	−0.717212	+	0.233036i	−0.644814	−	0.764340i	$-0.723065\pi$
$829$	−4.08612e8	+	1.32766e8i	−0.717212	+	0.233036i	−0.0723980	+	0.997376i	$0.523065\pi$
$830$	−206939.	−	973571.i	−0.000361916	−	0.00170268i
$831$	1.62159e7	+	2.80867e7i	0.0282577	+	0.0489438i
$832$	1.07821e9	+	6.22508e8i	1.87213	+	1.08087i
$833$	−2.68171e8	−	8.71339e7i	−0.463955	−	0.150748i
$834$	−6.34905e7	+	6.04072e8i	−0.109449	+	1.04133i
$835$	−7.46527e6	−	1.02751e7i	−0.0128229	−	0.0176492i
$836$			3.75276e8i			0.642291i
$837$	3.79654e8	+	6.75342e7i	0.647457	+	0.115172i
$838$	−1.01650e9			−1.72733
$839$	5.76051e8	−	4.18526e8i	0.975383	−	0.708657i	0.0187107	−	0.999825i	$-0.494044\pi$
$839$	5.76051e8	−	4.18526e8i	0.975383	−	0.708657i	0.956672	+	0.291168i	$0.0940439\pi$
$840$	−1.95543e7	−	2.05524e6i	−0.0329917	−	0.00346757i
$841$	−1.20240e7	+	3.70061e7i	−0.0202144	+	0.0622136i
$842$	2.23252e8	−	3.86684e8i	0.373989	−	0.647768i
$843$	−1.35364e8	+	7.81525e7i	−0.225954	+	0.130455i
$844$	3.71107e8	−	7.88813e7i	0.617266	−	0.131204i
$845$	8.21987e6	+	2.52982e7i	0.0136237	+	0.0419294i
$846$	4.77006e8	+	1.01391e8i	0.787794	+	0.167451i
$847$	7.25522e7	+	6.90288e8i	0.119399	+	1.13600i
$848$	−6.84879e7	+	6.16668e7i	−0.112312	+	0.101126i
$849$	−5.55781e7	+	1.24830e8i	−0.0908198	+	0.203985i
$850$	1.11626e8	+	2.50717e8i	0.181765	+	0.408250i
$851$	−1.76050e8	+	1.95524e8i	−0.285659	+	0.317257i
$852$	−2.67141e8	+	3.67688e8i	−0.431939	+	0.594513i
$853$	4.26067e8	+	3.09556e8i	0.686485	+	0.498760i	0.875503	−	0.483213i	$-0.160530\pi$
$853$	4.26067e8	+	3.09556e8i	0.686485	+	0.498760i	−0.189018	+	0.981974i	$0.560530\pi$
$854$	1.50648e9	+	1.35644e9i	2.41874	+	2.17784i
$855$	−1.73944e7	+	7.74450e6i	−0.0278299	+	0.0123907i
$856$	−1.09263e9	−	4.86469e8i	−1.74201	−	0.775592i
$857$	−1.74440e8	−	1.93735e8i	−0.277142	−	0.307797i	0.588464	−	0.808524i	$-0.299733\pi$
$857$	−1.74440e8	−	1.93735e8i	−0.277142	−	0.307797i	−0.865606	+	0.500726i	$0.833066\pi$
$858$	−2.76173e8	+	2.90270e7i	−0.437239	+	0.0459557i
$859$	−2.12752e8	+	1.00092e9i	−0.335655	+	1.57913i	0.409543	+	0.912291i	$0.365688\pi$
$859$	−2.12752e8	+	1.00092e9i	−0.335655	+	1.57913i	−0.745198	+	0.666843i	$0.767645\pi$
$860$	5.49741e6	−	1.78622e6i	0.00864296	−	0.00280827i
$861$	−4.95844e7	−	2.33276e8i	−0.0776848	−	0.365478i
$862$	−2.99577e7	−	5.18883e7i	−0.0467721	−	0.0810117i
$863$	3.26658e8	+	1.88596e8i	0.508230	+	0.293427i	0.732106	−	0.681191i	$-0.238538\pi$
$863$	3.26658e8	+	1.88596e8i	0.508230	+	0.293427i	−0.223876	+	0.974618i	$0.571871\pi$
$864$	−3.54988e8	−	1.15343e8i	−0.550392	−	0.178833i
$865$	3.78730e6	−	3.60338e7i	0.00585169	−	0.0556751i
$866$	3.14801e8	+	4.33287e8i	0.484711	+	0.667148i
$867$			2.11197e8i			0.324064i
$868$	−6.11954e7	−	1.83167e9i	−0.0935750	−	2.80084i
$869$	6.28231e8			0.957326
$870$	1.60813e7	−	1.16838e7i	0.0244210	−	0.0177429i
$871$	−5.54897e8	−	5.83220e7i	−0.839765	−	0.0882628i
$872$	3.60314e7	−	1.10893e8i	0.0543415	−	0.167246i
$873$	4.56679e8	−	7.90991e8i	0.686386	−	1.18886i
$874$	−2.92417e8	+	1.68827e8i	−0.437994	+	0.252876i
$875$	1.11336e8	−	2.36653e7i	0.166193	−	0.0353254i
$876$	1.74020e8	+	5.35579e8i	0.258873	+	0.796731i
$877$	1.06537e9	+	2.26452e8i	1.57944	+	0.335720i	0.912399	−	0.409301i	$-0.134228\pi$
$877$	1.06537e9	+	2.26452e8i	1.57944	+	0.335720i	0.667040	+	0.745022i	$0.267561\pi$
$878$	1.00131e8	+	9.52683e8i	0.147940	+	1.40755i
$879$	−5.37261e7	+	4.83752e7i	−0.0791077	+	0.0712289i
$880$	1.13075e6	−	2.53970e6i	0.00165927	−	0.00372679i
$881$	−1.01427e8	−	2.27810e8i	−0.148330	−	0.333154i	0.824065	−	0.566495i	$-0.191701\pi$
$881$	−1.01427e8	−	2.27810e8i	−0.148330	−	0.333154i	−0.972395	+	0.233341i	$0.925034\pi$
$882$	1.17528e9	−	1.30528e9i	1.71292	−	1.90238i
$883$	−6.00155e8	+	8.26043e8i	−0.871729	+	1.19983i	0.106914	+	0.994268i	$0.465903\pi$
$883$	−6.00155e8	+	8.26043e8i	−0.871729	+	1.19983i	−0.978644	+	0.205564i	$0.934097\pi$
$884$	−3.50893e8	−	2.54939e8i	−0.507947	−	0.369045i
$885$	−1.22102e7	−	1.09941e7i	−0.0176154	−	0.0158610i
$886$	−1.55396e9	+	6.91869e8i	−2.23429	+	0.994769i
$887$	−7.67244e8	−	3.41599e8i	−1.09942	−	0.489492i	−0.224849	−	0.974394i	$-0.572189\pi$
$887$	−7.67244e8	−	3.41599e8i	−1.09942	−	0.489492i	−0.874569	+	0.484901i	$0.838856\pi$
$888$	1.71940e8	+	1.90958e8i	0.245548	+	0.272709i
$889$	−9.87391e8	+	1.03779e8i	−1.40535	+	0.147708i
$890$	−1.28402e7	+	6.04086e7i	−0.0182139	+	0.0856897i
$891$	−2.44340e8	+	7.93908e7i	−0.345431	+	0.112237i
$892$	2.53888e8	+	1.19445e9i	0.357723	+	1.68296i
$893$	1.35966e8	+	2.35499e8i	0.190930	+	0.330701i
$894$	1.33949e8	+	7.73356e7i	0.187468	+	0.108235i
$895$	3.45922e7	+	1.12397e7i	0.0482513	+	0.0156778i
$896$	−2.14685e8	+	2.04260e9i	−0.298455	+	2.83961i
$897$	−9.20629e7	−	1.26714e8i	−0.127558	−	0.175568i
$898$			6.95726e8i			0.960748i
$899$	5.20152e8	+	5.40262e8i	0.715898	+	0.743576i
$900$	−1.07166e9			−1.47004
$901$	−1.71780e8	+	1.24805e8i	−0.234854	+	0.170631i
$902$	4.28952e8	+	4.50846e7i	0.584506	+	0.0614340i
$903$	1.41029e7	−	4.34044e7i	0.0191534	−	0.0589482i
$904$	6.33211e8	−	1.09675e9i	0.857124	−	1.48458i
$905$	−3.29569e6	+	1.90276e6i	−0.00444631	+	0.00256708i
$906$	−4.33234e8	+	9.20867e7i	−0.582556	+	0.123826i
$907$	1.28100e8	+	3.94251e8i	0.171683	+	0.528386i	0.999466	−	0.0326620i	$-0.0103985\pi$
$907$	1.28100e8	+	3.94251e8i	0.171683	+	0.528386i	−0.827784	+	0.561048i	$0.810398\pi$
$908$	−1.77054e9	−	3.76340e8i	−2.36509	−	0.502716i
$909$	3.37110e7	+	3.20738e8i	0.0448828	+	0.427031i
$910$	−1.06487e8	+	9.58813e7i	−0.141310	+	0.127236i
$911$	1.29757e7	−	2.91439e7i	0.0171623	−	0.0385472i	−0.904761	−	0.425920i	$-0.859951\pi$
$911$	1.29757e7	−	2.91439e7i	0.0171623	−	0.0385472i	0.921923	+	0.387373i	$0.126617\pi$
$912$	1.04863e7	+	2.35526e7i	0.0138241	+	0.0310494i
$913$	5.96150e6	−	6.62091e6i	0.00783327	−	0.00869973i
$914$	1.67829e8	−	2.30997e8i	0.219801	−	0.302530i
$915$	1.31956e7	+	9.58718e6i	0.0172253	+	0.0125149i
$916$	−1.01834e9	−	9.16920e8i	−1.32497	−	1.19301i
$917$	1.62680e9	−	7.24297e8i	2.10972	−	0.939309i
$918$	2.08239e8	+	9.27138e7i	0.269174	+	0.119844i
$919$	1.65738e8	+	1.84071e8i	0.213539	+	0.237159i	0.840393	−	0.541978i	$-0.182324\pi$
$919$	1.65738e8	+	1.84071e8i	0.213539	+	0.237159i	−0.626854	+	0.779137i	$0.715658\pi$
$920$	1.99466e7	−	2.09648e6i	0.0256157	−	0.00269232i
$921$	6.13729e7	−	2.88737e8i	0.0785593	−	0.369592i
$922$	−7.82641e8	+	2.54295e8i	−0.998549	+	0.324448i
$923$	2.78746e8	+	1.31140e9i	0.354490	+	1.66774i
$924$	−2.17403e8	−	3.76554e8i	−0.275582	−	0.477322i
$925$	−6.43285e8	−	3.71401e8i	−0.812790	−	0.469265i
$926$	1.06314e9	+	3.45436e8i	1.33893	+	0.435045i
$927$	−5.14367e7	+	4.89387e8i	−0.0645704	+	0.614347i
$928$	−4.26690e8	−	5.87288e8i	−0.533910	−	0.734864i
$929$		−	6.95083e8i		−	0.866941i	−0.901168	−	0.433471i	$-0.857289\pi$
$929$		−	6.95083e8i		−	0.866941i	0.901168	−	0.433471i	$-0.142711\pi$
$930$	−3.23863e6	−	2.32991e7i	−0.00402635	−	0.0289662i
$931$	9.79424e8			1.21373
$932$	−1.19686e9	+	8.69570e8i	−1.47841	+	1.07413i
$933$	1.32476e8	+	1.39237e7i	0.163114	+	0.0171439i
$934$	4.88934e8	−	1.50479e9i	0.600081	−	1.84686i
$935$	3.20256e6	−	5.54700e6i	0.00391798	−	0.00678614i
$936$	9.47081e8	−	5.46798e8i	1.15494	−	0.666805i
$937$	−4.81297e7	+	1.02303e7i	−0.0585051	+	0.0124357i	−0.237071	−	0.971492i	$-0.576187\pi$
$937$	−4.81297e7	+	1.02303e7i	−0.0585051	+	0.0124357i	0.178566	+	0.983928i	$0.442854\pi$
$938$	−4.30657e8	−	1.32543e9i	−0.521823	−	1.60601i
$939$	4.40184e8	+	9.35641e7i	0.531665	+	0.113009i
$940$	−4.17123e6	−	3.96866e7i	−0.00502204	−	0.0477815i
$941$	−3.12555e8	+	2.81426e8i	−0.375109	+	0.337749i	−0.835024	−	0.550213i	$-0.814546\pi$
$941$	−3.12555e8	+	2.81426e8i	−0.375109	+	0.337749i	0.459915	+	0.887963i	$0.347880\pi$
$942$	2.52940e8	−	5.68112e8i	0.302597	−	0.679644i
$943$	9.89479e7	+	2.22241e8i	0.117997	+	0.265026i
$944$	1.06424e8	−	1.18196e8i	0.126510	−	0.140503i
$945$	2.77481e7	−	3.81920e7i	0.0328805	−	0.0452561i
$946$	6.67748e7	+	4.85147e7i	0.0788750	+	0.0573060i
$947$	1.93107e8	+	1.73874e8i	0.227378	+	0.204732i	0.774943	−	0.632031i	$-0.217778\pi$
$947$	1.93107e8	+	1.73874e8i	0.227378	+	0.204732i	−0.547565	+	0.836763i	$0.684445\pi$
$948$	7.81042e8	−	3.47742e8i	0.916747	−	0.408162i
$949$	1.51759e9	+	6.75676e8i	1.77565	+	0.790569i
$950$	−6.37867e8	−	7.08423e8i	−0.743977	−	0.826270i
$951$	−9.73301e7	+	1.02298e7i	−0.113163	+	0.0118939i
$952$	9.11719e7	−	4.28930e8i	0.105670	−	0.497137i
$953$	−3.64652e8	+	1.18483e8i	−0.421308	+	0.136891i	−0.511996	−	0.858988i	$-0.671094\pi$
$953$	−3.64652e8	+	1.18483e8i	−0.421308	+	0.136891i	0.0906874	+	0.995879i	$0.471094\pi$
$954$	−2.74992e8	−	1.29373e9i	−0.316719	−	1.49005i
$955$	4.48125e6	+	7.76175e6i	0.00514504	+	0.00891147i
$956$	6.59563e8	+	3.80799e8i	0.754889	+	0.435835i
$957$	1.69220e8	+	5.49829e7i	0.193070	+	0.0627323i
$958$	2.47523e8	−	2.35502e9i	0.281526	−	2.67854i
$959$	−1.63316e9	−	2.24785e9i	−1.85171	−	2.54866i
$960$			2.50213e7i			0.0282811i
$961$	8.53858e8	−	2.42053e8i	0.962089	−	0.272734i
$962$	1.87266e9			2.10346
$963$	1.08567e9	−	7.88782e8i	1.21567	−	0.883239i
$964$	1.42805e9	+	1.50094e8i	1.59409	+	0.167546i
$965$	2.05598e7	−	6.32765e7i	0.0228790	−	0.0704143i
$966$	1.95608e8	−	3.38804e8i	0.216998	−	0.375852i
$967$	7.66104e8	−	4.42310e8i	0.847243	−	0.489156i	−0.0124765	−	0.999922i	$-0.503972\pi$
$967$	7.66104e8	−	4.42310e8i	0.847243	−	0.489156i	0.859720	+	0.510766i	$0.170638\pi$
$968$	−6.76373e8	+	1.43767e8i	−0.745693	+	0.158502i
$969$	1.83554e7	+	5.64922e7i	0.0201741	+	0.0620894i
$970$	−1.16621e8	−	2.47886e7i	−0.127780	−	0.0271604i
$971$	1.29681e8	+	1.23384e9i	0.141651	+	1.34772i	0.802253	+	0.596984i	$0.203634\pi$
$971$	1.29681e8	+	1.23384e9i	0.141651	+	1.34772i	−0.660602	+	0.750736i	$0.729699\pi$
$972$	−1.01382e9	+	9.12848e8i	−1.10398	+	0.994030i
$973$	−1.14110e9	+	2.56296e9i	−1.23876	+	2.78229i
$974$	3.76235e8	+	8.45038e8i	0.407176	+	0.914533i
$975$	2.95886e8	−	3.28614e8i	0.319235	−	0.354546i
$976$	−9.28048e7	+	1.27735e8i	−0.0998207	+	0.137391i
$977$	−1.12262e9	−	8.15631e8i	−1.20379	−	0.874602i	−0.209134	−	0.977887i	$-0.567064\pi$
$977$	−1.12262e9	−	8.15631e8i	−1.20379	−	0.874602i	−0.994652	+	0.103285i	$0.967064\pi$
$978$	−1.27733e8	−	1.15011e8i	−0.136548	−	0.122949i
$979$	−5.05017e8	+	2.24848e8i	−0.538217	+	0.239630i
$980$	−1.31302e8	−	5.84594e7i	−0.139506	−	0.0621120i
$981$	8.75400e7	+	9.72230e7i	0.0927256	+	0.102982i
$982$	−2.20230e9	+	2.31471e8i	−2.32564	+	0.244435i
$983$	2.06019e8	−	9.69241e8i	0.216893	−	1.02040i	−0.726100	−	0.687589i	$-0.758669\pi$
$983$	2.06019e8	−	9.69241e8i	0.216893	−	1.02040i	0.942993	−	0.332813i	$-0.107998\pi$
$984$	2.25964e8	−	7.34201e7i	0.237167	−	0.0770601i
$985$	1.94268e7	+	9.13957e7i	0.0203279	+	0.0956351i
$986$	2.21660e8	+	3.83926e8i	0.231237	+	0.400514i
$987$	−2.72857e8	−	1.57534e8i	−0.283782	−	0.163841i
$988$	1.43281e9	+	4.65549e8i	1.48566	+	0.482720i
$989$	−4.86619e6	+	4.62987e7i	−0.00503037	+	0.0478608i
$990$	2.34516e7	+	3.22783e7i	0.0241694	+	0.0332664i
$991$		−	1.37193e9i		−	1.40965i	−0.709380	−	0.704827i	$-0.751025\pi$
$991$		−	1.37193e9i		−	1.40965i	0.709380	−	0.704827i	$-0.248975\pi$
$992$	−8.50882e8	+	1.18274e8i	−0.871634	+	0.121159i
$993$	−1.06209e8			−0.108471
$994$	−2.70919e9	+	1.96834e9i	−2.75854	+	2.00420i
$995$	1.53183e7	+	1.61002e6i	0.0155504	+	0.00163441i
$996$	3.74672e6	−	1.15312e7i	0.00379205	−	0.0116707i
$997$	−8.67652e7	+	1.50282e8i	−0.0875508	+	0.151642i	−0.906475	−	0.422259i	$-0.861237\pi$
$997$	−8.67652e7	+	1.50282e8i	−0.0875508	+	0.151642i	0.818924	+	0.573901i	$0.194571\pi$
$998$	1.10195e9	−	6.36210e8i	1.10859	−	0.640043i
$999$	−6.03470e8	+	1.28271e8i	−0.605284	+	0.128657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.7.h.a.3.2	✓	120
31.21	odd	30	inner	31.7.h.a.21.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.7.h.a.3.2	✓	120	1.1	even	1	trivial
31.7.h.a.21.2	yes	120	31.21	odd	30	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.5954 + 7.69802i) q^{2} +(-9.40640 - 0.988652i) q^{3} +(33.2262 - 102.260i) q^{4} +(3.18721 - 5.52041i) q^{5} +(107.275 - 61.9354i) q^{6} +(559.643 - 118.956i) q^{7} +(176.139 + 542.099i) q^{8} +(-625.567 - 132.968i) q^{9} +(8.72642 + 83.0263i) q^{10} +(-555.336 + 500.027i) q^{11} +(-413.638 + 929.047i) q^{12} +(1220.19 + 2740.60i) q^{13} +(-5013.92 + 5568.52i) q^{14} +(-35.4380 + 48.7762i) q^{15} +(-472.158 - 343.043i) q^{16} +(-999.257 - 899.735i) q^{17} +(7651.73 - 3406.77i) q^{18} +(4266.78 + 1899.69i) q^{19} +(-458.617 - 509.346i) q^{20} +(-5381.83 + 565.653i) q^{21} +(2034.80 - 9572.98i) q^{22} +(5249.87 - 1705.79i) q^{23} +(-1120.88 - 5273.34i) q^{24} +(7792.18 + 13496.5i) q^{25} +(-34025.6 - 19644.7i) q^{26} +(12310.4 + 3999.90i) q^{27} +(6430.42 - 61181.4i) q^{28} +(14796.9 + 20366.3i) q^{29} -789.606i q^{30} +(29507.3 - 4101.57i) q^{31} -28836.3 q^{32} +(5718.07 - 4154.42i) q^{33} +(17513.7 + 1840.77i) q^{34} +(1127.02 - 3468.60i) q^{35} +(-34382.5 + 59552.3i) q^{36} +(-41277.6 + 23831.6i) q^{37} +(-59832.1 + 12717.7i) q^{38} +(-8768.12 - 26985.5i) q^{39} +(3554.00 + 755.426i) q^{40} +(4606.66 + 43829.4i) q^{41} +(52668.3 - 47422.7i) q^{42} +(-3430.25 + 7704.46i) q^{43} +(32680.9 + 73402.6i) q^{44} +(-2727.85 + 3029.59i) q^{45} +(-42493.3 + 58487.1i) q^{46} +(47102.9 + 34222.2i) q^{47} +(4102.15 + 3693.59i) q^{48} +(191572. - 85293.2i) q^{49} +(-186457. - 83016.2i) q^{50} +(8509.88 + 9451.18i) q^{51} +(320795. - 33716.9i) q^{52} +(32831.4 - 154460. i) q^{53} +(-161226. + 52385.3i) q^{54} +(990.382 + 4659.38i) q^{55} +(163060. + 282429. i) q^{56} +(-38256.9 - 22087.6i) q^{57} +(-313560. - 101882. i) q^{58} +(-28486.2 + 271028. i) q^{59} +(3810.37 + 5244.53i) q^{60} -270534. i q^{61} +(-281068. + 270606. i) q^{62} -365911. q^{63} +(335751. - 243937. i) q^{64} +(19018.2 + 1998.90i) q^{65} +(-28604.5 + 88035.6i) q^{66} +(-92993.5 + 161070. i) q^{67} +(-125208. + 72289.0i) q^{68} +(-51068.8 + 10855.0i) q^{69} +(14760.1 + 45427.0i) q^{70} +(437139. + 92916.7i) q^{71} +(-38104.5 - 362540. i) q^{72} +(411513. - 370528. i) q^{73} +(253897. - 570262. i) q^{74} +(-59953.1 - 134657. i) q^{75} +(336031. - 373200. i) q^{76} +(-251309. + 345897. i) q^{77} +(300637. + 218425. i) q^{78} +(-624756. - 562532. i) q^{79} +(-3398.60 + 1513.16i) q^{80} +(314077. + 139836. i) q^{81} +(-386209. - 428929. i) q^{82} +(-11857.0 + 1246.22i) q^{83} +(-120974. + 569139. i) q^{84} +(-8151.75 + 2648.67i) q^{85} +(-22964.2 - 108038. i) q^{86} +(-119051. - 206202. i) q^{87} +(-368880. - 212973. i) q^{88} +(703557. + 228600. i) q^{89} +(5580.91 - 53098.8i) q^{90} +(1.00888e6 + 1.38861e6i) q^{91} -593527. i q^{92} +(-281612. + 9408.56i) q^{93} -762518. q^{94} +(24086.2 - 17499.7i) q^{95} +(271246. + 28509.1i) q^{96} +(-441321. + 1.35824e6i) q^{97} +(-1.37319e6 + 2.37844e6i) q^{98} +(413888. - 238958. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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