LMFDB - Embedded newform 24.6.f.b.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [24,6,Mod(11,24)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(24, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("24.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	24.f (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:	$3.84921167551$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 26 x^{14} + 904 x^{12} - 55232 x^{10} + 1401856 x^{8} - 56557568 x^{6} + 947912704 x^{4} + \cdots + 1099511627776 $ x^16 - 26x^14 + 904x^12 - 55232x^10 + 1401856x^8 - 56557568x^6 + 947912704x^4 - 27917287424*x^2 + 1099511627776
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.8
Root			$-2.35284 + 5.14433i$ of defining polynomial
Character	$\chi$	$=$	24.11
Dual form			24.6.f.b.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.35284 + 5.14433i) q^{2} +(8.05622 - 13.3453i) q^{3} +(-20.9283 - 24.2076i) q^{4} -95.9504 q^{5} +(49.6977 + 72.8433i) q^{6} -122.802i q^{7} +(173.773 - 50.7054i) q^{8} +(-113.195 - 215.026i) q^{9} +O(q^{10})$	\(q+(-2.35284 + 5.14433i) q^{2} +(8.05622 - 13.3453i) q^{3} +(-20.9283 - 24.2076i) q^{4} -95.9504 q^{5} +(49.6977 + 72.8433i) q^{6} -122.802i q^{7} +(173.773 - 50.7054i) q^{8} +(-113.195 - 215.026i) q^{9} +(225.756 - 493.600i) q^{10} +77.6307i q^{11} +(-491.661 + 84.2728i) q^{12} +267.974i q^{13} +(631.734 + 288.934i) q^{14} +(-772.997 + 1280.49i) q^{15} +(-148.014 + 1013.25i) q^{16} -958.891i q^{17} +(1372.49 - 76.3900i) q^{18} -1992.07 q^{19} +(2008.08 + 2322.73i) q^{20} +(-1638.83 - 989.320i) q^{21} +(-399.358 - 182.653i) q^{22} +2142.09 q^{23} +(723.272 - 2727.54i) q^{24} +6081.47 q^{25} +(-1378.55 - 630.500i) q^{26} +(-3781.50 - 221.674i) q^{27} +(-2972.74 + 2570.03i) q^{28} +1413.81 q^{29} +(-4768.51 - 6989.34i) q^{30} -535.205i q^{31} +(-4864.22 - 3145.44i) q^{32} +(1036.01 + 625.410i) q^{33} +(4932.85 + 2256.12i) q^{34} +11782.9i q^{35} +(-2836.28 + 7240.28i) q^{36} -15204.5i q^{37} +(4687.03 - 10247.9i) q^{38} +(3576.19 + 2158.85i) q^{39} +(-16673.6 + 4865.20i) q^{40} -7477.78i q^{41} +(8945.29 - 6102.97i) q^{42} +8815.59 q^{43} +(1879.25 - 1624.68i) q^{44} +(10861.1 + 20631.8i) q^{45} +(-5040.01 + 11019.6i) q^{46} +4179.37 q^{47} +(12329.6 + 10138.2i) q^{48} +1726.68 q^{49} +(-14308.7 + 31285.1i) q^{50} +(-12796.7 - 7725.03i) q^{51} +(6487.00 - 5608.23i) q^{52} -23903.6 q^{53} +(10037.6 - 18931.7i) q^{54} -7448.70i q^{55} +(-6226.72 - 21339.6i) q^{56} +(-16048.6 + 26584.8i) q^{57} +(-3326.47 + 7273.11i) q^{58} -18735.4i q^{59} +(47175.0 - 8086.00i) q^{60} +12429.5i q^{61} +(2753.27 + 1259.25i) q^{62} +(-26405.6 + 13900.5i) q^{63} +(27625.9 - 17622.4i) q^{64} -25712.2i q^{65} +(-5654.88 + 3858.07i) q^{66} +13418.7 q^{67} +(-23212.4 + 20067.9i) q^{68} +(17257.2 - 28586.9i) q^{69} +(-60615.1 - 27723.3i) q^{70} -34353.4 q^{71} +(-30573.1 - 31626.0i) q^{72} -29787.6 q^{73} +(78216.8 + 35773.7i) q^{74} +(48993.7 - 81159.1i) q^{75} +(41690.6 + 48223.3i) q^{76} +9533.21 q^{77} +(-19520.1 + 13317.7i) q^{78} -42918.9i q^{79} +(14202.0 - 97221.3i) q^{80} +(-33422.9 + 48679.5i) q^{81} +(38468.2 + 17594.0i) q^{82} +98756.8i q^{83} +(10348.9 + 60376.9i) q^{84} +92005.9i q^{85} +(-20741.7 + 45350.3i) q^{86} +(11390.0 - 18867.7i) q^{87} +(3936.30 + 13490.1i) q^{88} +3595.76i q^{89} +(-131691. + 7329.65i) q^{90} +32907.7 q^{91} +(-44830.3 - 51854.9i) q^{92} +(-7142.48 - 4311.73i) q^{93} +(-9833.38 + 21500.0i) q^{94} +191140. q^{95} +(-81164.1 + 39574.1i) q^{96} -49022.1 q^{97} +(-4062.60 + 8882.60i) q^{98} +(16692.6 - 8787.39i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 52 q^{4} + 264 q^{6} + 480 q^{9}+O(q^{10}) $ 16 * q + 52 * q^4 + 264 * q^6 + 480 * q^9	$ 16 q + 52 q^{4} + 264 q^{6} + 480 q^{9} + 168 q^{10} - 156 q^{12} - 2264 q^{16} + 24 q^{18} - 8128 q^{19} + 7808 q^{22} - 7992 q^{24} + 12496 q^{25} - 5184 q^{27} - 6864 q^{28} + 6672 q^{30} + 23472 q^{33} + 26480 q^{34} - 8196 q^{36} + 5856 q^{40} - 16728 q^{42} - 45760 q^{43} - 25056 q^{46} - 26184 q^{48} - 33392 q^{49} + 36480 q^{51} - 54240 q^{52} + 14616 q^{54} - 10128 q^{57} + 58056 q^{58} + 105456 q^{60} + 225520 q^{64} - 149496 q^{66} + 183296 q^{67} - 199248 q^{70} - 172848 q^{72} - 153376 q^{73} + 50880 q^{75} + 4856 q^{76} + 251664 q^{78} - 148464 q^{81} + 111872 q^{82} + 317856 q^{84} + 151088 q^{88} - 468792 q^{90} - 32832 q^{91} - 523200 q^{94} - 392496 q^{96} + 178496 q^{97} - 91968 q^{99}+O(q^{100}) $ 16 * q + 52 * q^4 + 264 * q^6 + 480 * q^9 + 168 * q^10 - 156 * q^12 - 2264 * q^16 + 24 * q^18 - 8128 * q^19 + 7808 * q^22 - 7992 * q^24 + 12496 * q^25 - 5184 * q^27 - 6864 * q^28 + 6672 * q^30 + 23472 * q^33 + 26480 * q^34 - 8196 * q^36 + 5856 * q^40 - 16728 * q^42 - 45760 * q^43 - 25056 * q^46 - 26184 * q^48 - 33392 * q^49 + 36480 * q^51 - 54240 * q^52 + 14616 * q^54 - 10128 * q^57 + 58056 * q^58 + 105456 * q^60 + 225520 * q^64 - 149496 * q^66 + 183296 * q^67 - 199248 * q^70 - 172848 * q^72 - 153376 * q^73 + 50880 * q^75 + 4856 * q^76 + 251664 * q^78 - 148464 * q^81 + 111872 * q^82 + 317856 * q^84 + 151088 * q^88 - 468792 * q^90 - 32832 * q^91 - 523200 * q^94 - 392496 * q^96 + 178496 * q^97 - 91968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−2.35284	+	5.14433i	−0.415927	+	0.909398i
$2$	−2.35284	+	5.14433i	−0.415927	+	0.909398i
$3$	8.05622	−	13.3453i	0.516807	−	0.856102i
$3$	8.05622	−	13.3453i	0.516807	−	0.856102i
$4$	−20.9283	−	24.2076i	−0.654009	−	0.756487i
$5$	−95.9504			−1.71641			−0.858206	−	0.513305i	$-0.828421\pi$
$5$	−95.9504			−1.71641			−0.858206	+	0.513305i	$0.828421\pi$
$6$	49.6977	+	72.8433i	0.563583	+	0.826059i
$7$		−	122.802i		−	0.947240i	−0.880729	−	0.473620i	$-0.842947\pi$
$7$		−	122.802i		−	0.947240i	0.880729	−	0.473620i	$-0.157053\pi$
$8$	173.773	−	50.7054i	0.959968	−	0.280110i
$9$	−113.195	−	215.026i	−0.465822	−	0.884879i
$10$	225.756	−	493.600i	0.713903	−	1.56090i
$11$			77.6307i			0.193443i	0.995312	+	0.0967213i	$0.0308355\pi$
$11$			77.6307i			0.193443i	−0.995312	+	0.0967213i	$0.969164\pi$
$12$	−491.661	+	84.2728i	−0.985626	+	0.168941i
$13$			267.974i			0.439778i	0.975525	+	0.219889i	$0.0705696\pi$
$13$			267.974i			0.439778i	−0.975525	+	0.219889i	$0.929430\pi$
$14$	631.734	+	288.934i	0.861418	+	0.393983i
$15$	−772.997	+	1280.49i	−0.887053	+	1.46942i
$16$	−148.014	+	1013.25i	−0.144545	+	0.989498i
$17$		−	958.891i		−	0.804724i	−0.915481	−	0.402362i	$-0.868189\pi$
$17$		−	958.891i		−	0.804724i	0.915481	−	0.402362i	$-0.131811\pi$
$18$	1372.49	−	76.3900i	0.998455	−	0.0555719i
$19$	−1992.07			−1.26596			−0.632982	−	0.774167i	$-0.718169\pi$
$19$	−1992.07			−1.26596			−0.632982	+	0.774167i	$0.718169\pi$
$20$	2008.08	+	2322.73i	1.12255	+	1.29844i
$21$	−1638.83	−	989.320i	−0.810935	−	0.489540i
$22$	−399.358	−	182.653i	−0.175916	−	0.0804581i
$23$	2142.09			0.844343			0.422171	−	0.906516i	$-0.361268\pi$
$23$	2142.09			0.844343			0.422171	+	0.906516i	$0.361268\pi$
$24$	723.272	−	2727.54i	0.256315	−	0.966593i
$25$	6081.47			1.94607
$26$	−1378.55	−	630.500i	−0.399933	−	0.182916i
$27$	−3781.50	−	221.674i	−0.998286	−	0.0585203i
$28$	−2972.74	+	2570.03i	−0.716575	+	0.619503i
$29$	1413.81			0.312174			0.156087	−	0.987743i	$-0.450112\pi$
$29$	1413.81			0.312174			0.156087	+	0.987743i	$0.450112\pi$
$30$	−4768.51	−	6989.34i	−0.967341	−	1.41786i
$31$		−	535.205i		−	0.100027i	−0.998749	−	0.0500134i	$-0.984074\pi$
$31$		−	535.205i		−	0.100027i	0.998749	−	0.0500134i	$-0.0159264\pi$
$32$	−4864.22	−	3145.44i	−0.839727	−	0.543009i
$33$	1036.01	+	625.410i	0.165607	+	0.0999724i
$34$	4932.85	+	2256.12i	0.731814	+	0.334707i
$35$			11782.9i			1.62585i
$36$	−2836.28	+	7240.28i	−0.364748	+	0.931106i
$37$		−	15204.5i		−	1.82586i	−0.408120	−	0.912928i	$-0.633815\pi$
$37$		−	15204.5i		−	1.82586i	0.408120	−	0.912928i	$-0.366185\pi$
$38$	4687.03	−	10247.9i	0.526549	−	1.15126i
$39$	3576.19	+	2158.85i	0.376495	+	0.227280i
$40$	−16673.6	+	4865.20i	−1.64770	+	0.480785i
$41$		−	7477.78i		−	0.694725i	−0.937731	−	0.347363i	$-0.887077\pi$
$41$		−	7477.78i		−	0.694725i	0.937731	−	0.347363i	$-0.112923\pi$
$42$	8945.29	−	6102.97i	0.782477	−	0.533849i
$43$	8815.59			0.727076			0.363538	−	0.931579i	$-0.381569\pi$
$43$	8815.59			0.727076			0.363538	+	0.931579i	$0.381569\pi$
$44$	1879.25	−	1624.68i	0.146337	−	0.126513i
$45$	10861.1	+	20631.8i	0.799542	+	1.51882i
$46$	−5040.01	+	11019.6i	−0.351185	+	0.767843i
$47$	4179.37			0.275972			0.137986	−	0.990434i	$-0.455937\pi$
$47$	4179.37			0.275972			0.137986	+	0.990434i	$0.455937\pi$
$48$	12329.6	+	10138.2i	0.772410	+	0.635125i
$49$	1726.68			0.102736
$50$	−14308.7	+	31285.1i	−0.809424	+	1.76975i
$51$	−12796.7	−	7725.03i	−0.688926	−	0.415887i
$52$	6487.00	−	5608.23i	0.332687	−	0.287619i
$53$	−23903.6			−1.16889			−0.584444	−	0.811434i	$-0.698687\pi$
$53$	−23903.6			−1.16889			−0.584444	+	0.811434i	$0.698687\pi$
$54$	10037.6	−	18931.7i	0.468433	−	0.883499i
$55$		−	7448.70i		−	0.332027i
$56$	−6226.72	−	21339.6i	−0.265332	−	0.909320i
$57$	−16048.6	+	26584.8i	−0.654258	+	1.08379i
$58$	−3326.47	+	7273.11i	−0.129842	+	0.283890i
$59$		−	18735.4i		−	0.700701i	−0.936619	−	0.350351i	$-0.886062\pi$
$59$		−	18735.4i		−	0.700701i	0.936619	−	0.350351i	$-0.113938\pi$
$60$	47175.0	−	8086.00i	1.69174	−	0.289972i
$61$			12429.5i			0.427691i	0.976867	+	0.213846i	$0.0685990\pi$
$61$			12429.5i			0.427691i	−0.976867	+	0.213846i	$0.931401\pi$
$62$	2753.27	+	1259.25i	0.0909641	+	0.0416039i
$63$	−26405.6	+	13900.5i	−0.838193	+	0.441245i
$64$	27625.9	−	17622.4i	0.843076	−	0.537794i
$65$		−	25712.2i		−	0.754841i
$66$	−5654.88	+	3858.07i	−0.159795	+	0.109021i
$67$	13418.7			0.365195			0.182597	−	0.983188i	$-0.441550\pi$
$67$	13418.7			0.365195			0.182597	+	0.983188i	$0.441550\pi$
$68$	−23212.4	+	20067.9i	−0.608763	+	0.526296i
$69$	17257.2	−	28586.9i	0.436362	−	0.722844i
$70$	−60615.1	−	27723.3i	−1.47855	−	0.676238i
$71$	−34353.4			−0.808768			−0.404384	−	0.914589i	$-0.632514\pi$
$71$	−34353.4			−0.808768			−0.404384	+	0.914589i	$0.632514\pi$
$72$	−30573.1	−	31626.0i	−0.695037	−	0.718974i
$73$	−29787.6			−0.654226			−0.327113	−	0.944985i	$-0.606076\pi$
$73$	−29787.6			−0.654226			−0.327113	+	0.944985i	$0.606076\pi$
$74$	78216.8	+	35773.7i	1.66043	+	0.759424i
$75$	48993.7	−	81159.1i	1.00574	−	1.66604i
$76$	41690.6	+	48223.3i	0.827951	+	0.957685i
$77$	9533.21			0.183237
$78$	−19520.1	+	13317.7i	−0.363283	+	0.247852i
$79$		−	42918.9i		−	0.773715i	−0.922139	−	0.386858i	$-0.873560\pi$
$79$		−	42918.9i		−	0.773715i	0.922139	−	0.386858i	$-0.126440\pi$
$80$	14202.0	−	97221.3i	0.248099	−	1.69839i
$81$	−33422.9	+	48679.5i	−0.566020	+	0.824391i
$82$	38468.2	+	17594.0i	0.631782	+	0.288955i
$83$			98756.8i			1.57352i	0.617260	+	0.786759i	$0.288243\pi$
$83$			98756.8i			1.57352i	−0.617260	+	0.786759i	$0.711757\pi$
$84$	10348.9	+	60376.9i	0.160027	+	0.933625i
$85$			92005.9i			1.38124i
$86$	−20741.7	+	45350.3i	−0.302411	+	0.661202i
$87$	11390.0	−	18867.7i	0.161333	−	0.267252i
$88$	3936.30	+	13490.1i	0.0541853	+	0.185699i
$89$			3595.76i			0.0481189i	0.999711	+	0.0240595i	$0.00765910\pi$
$89$			3595.76i			0.0481189i	−0.999711	+	0.0240595i	$0.992341\pi$
$90$	−131691.	+	7329.65i	−1.71376	+	0.0953843i
$91$	32907.7			0.416576
$92$	−44830.3	−	51854.9i	−0.552208	−	0.638734i
$93$	−7142.48	−	4311.73i	−0.0856331	−	0.0516945i
$94$	−9833.38	+	21500.0i	−0.114785	+	0.250969i
$95$	191140.			2.17291
$96$	−81164.1	+	39574.1i	−0.898847	+	0.438262i
$97$	−49022.1			−0.529009			−0.264504	−	0.964385i	$-0.585208\pi$
$97$	−49022.1			−0.529009			−0.264504	+	0.964385i	$0.585208\pi$
$98$	−4062.60	+	8882.60i	−0.0427306	+	0.0934275i
$99$	16692.6	−	8787.39i	0.171173	−	0.0901097i
$100$	−127275.	−	147218.i	−1.27275	−	1.47218i
$101$	54961.1			0.536107			0.268054	−	0.963404i	$-0.413620\pi$
$101$	54961.1			0.536107			0.268054	+	0.963404i	$0.413620\pi$
$102$	69848.7	−	47654.7i	0.664749	−	0.453529i
$103$			87301.5i			0.810828i	0.914133	+	0.405414i	$0.132873\pi$
$103$			87301.5i			0.810828i	−0.914133	+	0.405414i	$0.867127\pi$
$104$	13587.7	+	46566.5i	0.123186	+	0.422173i
$105$	157246.	+	94925.6i	1.39190	+	0.840253i
$106$	56241.3	−	122968.i	0.486172	−	1.06298i
$107$			67209.0i			0.567503i	0.958898	+	0.283751i	$0.0915790\pi$
$107$			67209.0i			0.567503i	−0.958898	+	0.283751i	$0.908421\pi$
$108$	73774.1	+	96180.3i	0.608618	+	0.793463i
$109$		−	213990.i		−	1.72515i	−0.505927	−	0.862576i	$-0.668850\pi$
$109$		−	213990.i		−	1.72515i	0.505927	−	0.862576i	$-0.331150\pi$
$110$	38318.6	+	17525.6i	0.301945	+	0.138099i
$111$	−202908.	−	122490.i	−1.56312	−	0.943615i
$112$	124429.	+	18176.5i	0.937293	+	0.136919i
$113$		−	201896.i		−	1.48741i	−0.668507	−	0.743706i	$-0.733066\pi$
$113$		−	201896.i		−	1.48741i	0.668507	−	0.743706i	$-0.266934\pi$
$114$	−99001.4	−	145109.i	−0.713476	−	1.04576i
$115$	−205535.			−1.44924
$116$	−29588.6	−	34224.9i	−0.204164	−	0.236155i
$117$	57621.2	−	30333.2i	0.389150	−	0.204858i
$118$	96381.1	+	44081.4i	0.637216	+	0.291441i
$119$	−117754.			−0.762267
$120$	−69398.2	+	261709.i	−0.439942	+	1.65907i
$121$	155024.			0.962580
$122$	−63941.6	−	29244.7i	−0.388941	−	0.177889i
$123$	−99793.3	−	60242.6i	−0.594756	−	0.359039i
$124$	−12956.0	+	11200.9i	−0.0756689	+	0.0654184i
$125$	−283674.			−1.62385
$126$	−9380.84	−	168545.i	−0.0526399	−	0.945777i
$127$			308686.i			1.69827i	0.528172	+	0.849137i	$0.322878\pi$
$127$			308686.i			1.69827i	−0.528172	+	0.849137i	$0.677122\pi$
$128$	25656.2	+	183580.i	0.138410	+	0.990375i
$129$	71020.3	−	117647.i	0.375758	−	0.622452i
$130$	132272.	+	60496.7i	0.686451	+	0.313959i
$131$			45723.8i			0.232790i	0.993203	+	0.116395i	$0.0371338\pi$
$131$			45723.8i			0.232790i	−0.993203	+	0.116395i	$0.962866\pi$
$132$	−6542.16	−	38168.0i	−0.0326803	−	0.190662i
$133$			244630.i			1.19917i
$134$	−31572.1	+	69030.4i	−0.151894	+	0.332107i
$135$	362837.	+	21269.7i	1.71347	+	0.100445i
$136$	−48620.9	−	166629.i	−0.225411	−	0.772509i
$137$			15965.7i			0.0726753i	0.999340	+	0.0363376i	$0.0115692\pi$
$137$			15965.7i			0.0726753i	−0.999340	+	0.0363376i	$0.988431\pi$
$138$	106457.	+	156037.i	0.475857	+	0.697477i
$139$	−167306.			−0.734470			−0.367235	−	0.930128i	$-0.619696\pi$
$139$	−167306.			−0.734470			−0.367235	+	0.930128i	$0.619696\pi$
$140$	285235.	−	246596.i	1.22994	−	1.06332i
$141$	33669.9	−	55774.9i	0.142624	−	0.236261i
$142$	80828.1	−	176725.i	0.336389	−	0.735492i
$143$	−20803.0			−0.0850718
$144$	234628.	−	82867.2i	0.942918	−	0.333025i
$145$	−135656.			−0.535818
$146$	70085.4	−	153237.i	0.272111	−	0.594952i
$147$	13910.5	−	23043.0i	0.0530944	−	0.0879522i
$148$	−368063.	+	318203.i	−1.38124	+	1.19413i
$149$	−38149.9			−0.140776			−0.0703878	−	0.997520i	$-0.522424\pi$
$149$	−38149.9			−0.140776			−0.0703878	+	0.997520i	$0.522424\pi$
$150$	302235.	+	442994.i	1.09677	+	1.60757i
$151$		−	306895.i		−	1.09534i	−0.836695	−	0.547669i	$-0.815515\pi$
$151$		−	306895.i		−	1.09534i	0.836695	−	0.547669i	$-0.184485\pi$
$152$	−346168.	+	101009.i	−1.21528	+	0.354609i
$153$	−206186.	+	108541.i	−0.712083	+	0.374858i
$154$	−22430.1	+	49042.0i	−0.0762131	+	0.166635i
$155$			51353.1i			0.171687i
$156$	−22582.9	−	131752.i	−0.0742964	−	0.433457i
$157$			80487.9i			0.260604i	0.991474	+	0.130302i	$0.0415947\pi$
$157$			80487.9i			0.260604i	−0.991474	+	0.130302i	$0.958405\pi$
$158$	220789.	+	100981.i	0.703615	+	0.321809i
$159$	−192572.	+	319000.i	−0.604089	+	1.00069i
$160$	466724.	+	301806.i	1.44132	+	0.932027i
$161$		−	263053.i		−	0.799796i
$162$	−171785.	−	286474.i	−0.514276	−	0.857625i
$163$	480855.			1.41757			0.708786	−	0.705424i	$-0.249243\pi$
$163$	480855.			1.41757			0.708786	+	0.705424i	$0.249243\pi$
$164$	−181019.	+	156497.i	−0.525551	+	0.454356i
$165$	−99405.2	−	60008.3i	−0.284249	−	0.171594i
$166$	−508038.	−	232359.i	−1.43095	−	0.654469i
$167$	−257793.			−0.715288			−0.357644	−	0.933858i	$-0.616420\pi$
$167$	−257793.			−0.715288			−0.357644	+	0.933858i	$0.616420\pi$
$168$	−334948.	−	88819.2i	−0.915596	−	0.242792i
$169$	299483.			0.806595
$170$	−473309.	−	216475.i	−1.25609	−	0.574495i
$171$	225492.	+	428346.i	0.589713	+	1.12022i
$172$	−184495.	−	213404.i	−0.475514	−	0.550024i
$173$	623593.			1.58411			0.792056	−	0.610449i	$-0.209011\pi$
$173$	623593.			1.58411			0.792056	+	0.610449i	$0.209011\pi$
$174$	70263.1	+	102987.i	0.175936	+	0.257874i
$175$		−	746817.i		−	1.84340i
$176$	−78659.0	−	11490.5i	−0.191411	−	0.0279612i
$177$	−250030.	−	150937.i	−0.599872	−	0.362127i
$178$	−18497.8	−	8460.25i	−0.0437592	−	0.0200140i
$179$		−	596594.i		−	1.39170i	−0.718186	−	0.695851i	$-0.755027\pi$
$179$		−	596594.i		−	1.39170i	0.718186	−	0.695851i	$-0.244973\pi$
$180$	272142.	−	694708.i	0.626058	−	1.59816i
$181$		−	686635.i		−	1.55786i	−0.627108	−	0.778932i	$-0.715762\pi$
$181$		−	686635.i		−	1.55786i	0.627108	−	0.778932i	$-0.284238\pi$
$182$	−77426.6	+	169288.i	−0.173265	+	0.378833i
$183$	165876.	+	100135.i	0.366147	+	0.221034i
$184$	372237.	−	108616.i	0.810542	−	0.236509i
$185$			1.45887e6i			3.13392i
$186$	38986.1	−	26598.5i	0.0826280	−	0.0563734i
$187$	74439.4			0.155668
$188$	−87466.9	−	101172.i	−0.180488	−	0.208770i
$189$	−27222.1	+	464376.i	−0.0554328	+	0.945617i
$190$	−449722.	+	983288.i	−0.903775	+	1.97604i
$191$	672971.			1.33479			0.667395	−	0.744704i	$-0.267409\pi$
$191$	672971.			1.33479			0.667395	+	0.744704i	$0.267409\pi$
$192$	−12616.2	−	510647.i	−0.0246988	−	0.999695i
$193$	−351825.			−0.679881			−0.339941	−	0.940447i	$-0.610407\pi$
$193$	−351825.			−0.679881			−0.339941	+	0.940447i	$0.610407\pi$
$194$	115341.	−	252186.i	0.220029	−	0.481079i
$195$	−343137.	−	207143.i	−0.646221	−	0.390107i
$196$	−36136.4	−	41798.7i	−0.0671900	−	0.0777181i
$197$	−35429.7			−0.0650432			−0.0325216	−	0.999471i	$-0.510354\pi$
$197$	−35429.7			−0.0650432			−0.0325216	+	0.999471i	$0.510354\pi$
$198$	5930.21	+	106548.i	0.0107500	+	0.193144i
$199$			423770.i			0.758574i	0.925279	+	0.379287i	$0.123831\pi$
$199$			423770.i			0.758574i	−0.925279	+	0.379287i	$0.876169\pi$
$200$	1.05679e6	−	308363.i	1.86817	−	0.545114i
$201$	108104.	−	179077.i	0.188735	−	0.312644i
$202$	−129315.	+	282738.i	−0.222982	+	0.487535i
$203$		−	173619.i		−	0.295703i
$204$	80808.4	+	471449.i	0.135951	+	0.793157i
$205$			717496.i			1.19243i
$206$	−449108.	−	205407.i	−0.737365	−	0.337246i
$207$	−242474.	−	460605.i	−0.393313	−	0.747141i
$208$	−271523.	−	39664.0i	−0.435160	−	0.0635679i
$209$		−	154646.i		−	0.244891i
$210$	−858304.	+	585583.i	−1.34305	+	0.916305i
$211$	848868.			1.31260			0.656302	−	0.754498i	$-0.272120\pi$
$211$	848868.			1.31260			0.656302	+	0.754498i	$0.272120\pi$
$212$	500260.	+	578647.i	0.764463	+	0.884248i
$213$	−276759.	+	458457.i	−0.417977	+	0.692388i
$214$	−345745.	−	158132.i	−0.516086	−	0.236040i
$215$	−845859.			−1.24796
$216$	−668362.	+	153222.i	−0.974715	+	0.223453i
$217$	−65724.3			−0.0947494
$218$	1.10084e6	+	503485.i	1.56885	+	0.717538i
$219$	−239975.	+	397524.i	−0.338108	+	0.560084i
$220$	−180315.	+	155888.i	−0.251174	+	0.217149i
$221$	256958.			0.353900
$222$	1.10754e6	−	755627.i	1.50827	−	1.02902i
$223$			660509.i			0.889440i	0.895670	+	0.444720i	$0.146697\pi$
$223$			660509.i			0.889440i	−0.895670	+	0.444720i	$0.853303\pi$
$224$	−386266.	+	597336.i	−0.514360	+	0.795423i
$225$	−688390.	−	1.30767e6i	−0.906522	−	1.72204i
$226$	1.03862e6	+	475029.i	1.35265	+	0.618655i
$227$		−	691910.i		−	0.891221i	−0.895227	−	0.445610i	$-0.852987\pi$
$227$		−	691910.i		−	0.891221i	0.895227	−	0.445610i	$-0.147013\pi$
$228$	979423.	−	167877.i	1.24777	−	0.213873i
$229$		−	782249.i		−	0.985727i	−0.870107	−	0.492863i	$-0.835950\pi$
$229$		−	782249.i		−	0.985727i	0.870107	−	0.492863i	$-0.164050\pi$
$230$	483590.	−	1.05734e6i	0.602779	−	1.31794i
$231$	76801.6	−	127224.i	0.0946979	−	0.156869i
$232$	245682.	−	71687.8i	0.299677	−	0.0874430i
$233$			109785.i			0.132481i	0.997804	+	0.0662404i	$0.0211004\pi$
$233$			109785.i			0.132481i	−0.997804	+	0.0662404i	$0.978900\pi$
$234$	20470.5	+	367792.i	0.0244393	+	0.439099i
$235$	−401012.			−0.473682
$236$	−453539.	+	392100.i	−0.530072	+	0.458265i
$237$	−572767.	−	345764.i	−0.662379	−	0.399861i
$238$	277056.	−	605764.i	0.317048	−	0.693204i
$239$	−762355.			−0.863302			−0.431651	−	0.902041i	$-0.642069\pi$
$239$	−762355.			−0.863302			−0.431651	+	0.902041i	$0.642069\pi$
$240$	−1.18303e6	−	972767.i	−1.32577	−	1.09014i
$241$	−735138.			−0.815317			−0.407658	−	0.913134i	$-0.633655\pi$
$241$	−735138.			−0.815317			−0.407658	+	0.913134i	$0.633655\pi$
$242$	−364748.	+	797497.i	−0.400363	+	0.875368i
$243$	380380.	+	838212.i	0.413240	+	0.910622i
$244$	300889.	−	260129.i	0.323543	−	0.279714i
$245$	−165675.			−0.176337
$246$	544706.	−	371628.i	0.573884	−	0.391536i
$247$		−	533823.i		−	0.556743i
$248$	−27137.8	−	93004.1i	−0.0280185	−	0.0960225i
$249$	1.31794e6	+	795606.i	1.34709	+	0.813205i
$250$	667441.	−	1.45932e6i	0.675403	−	1.47672i
$251$			48664.3i			0.0487558i	0.999703	+	0.0243779i	$0.00776049\pi$
$251$			48664.3i			0.0487558i	−0.999703	+	0.0243779i	$0.992240\pi$
$252$	889121.	+	348301.i	0.881982	+	0.345504i
$253$			166292.i			0.163332i
$254$	−1.58798e6	−	726290.i	−1.54441	−	0.706359i
$255$	1.22785e6	+	741220.i	1.18248	+	0.713833i
$256$	−1.00476e6	−	299950.i	−0.958213	−	0.286055i
$257$		−	1.12964e6i		−	1.06686i	−0.845845	−	0.533428i	$-0.820903\pi$
$257$		−	1.12964e6i		−	1.06686i	0.845845	−	0.533428i	$-0.179097\pi$
$258$	438114.	+	642156.i	0.409768	+	0.600608i
$259$	−1.86714e6			−1.72953
$260$	−622430.	+	538112.i	−0.571027	+	0.493672i
$261$	−160036.	−	304005.i	−0.145417	−	0.276236i
$262$	−235218.	−	107581.i	−0.211698	−	0.0968236i
$263$	1.09552e6			0.976629			0.488315	−	0.872668i	$-0.337612\pi$
$263$	1.09552e6			0.976629			0.488315	+	0.872668i	$0.337612\pi$
$264$	211741.	+	56148.2i	0.186980	+	0.0495822i
$265$	2.29355e6			2.00629
$266$	−1.25846e6	−	575576.i	−1.09052	−	0.498768i
$267$	47986.5	+	28968.2i	0.0411947	+	0.0248682i
$268$	−280831.	−	324835.i	−0.238840	−	0.276265i
$269$	−725401.			−0.611220			−0.305610	−	0.952157i	$-0.598860\pi$
$269$	−725401.			−0.611220			−0.305610	+	0.952157i	$0.598860\pi$
$270$	−963115.	+	1.81651e6i	−0.804024	+	1.51645i
$271$		−	229201.i		−	0.189580i	−0.995497	−	0.0947901i	$-0.969782\pi$
$271$		−	229201.i		−	0.189580i	0.995497	−	0.0947901i	$-0.0302180\pi$
$272$	971592.	+	141930.i	0.796273	+	0.116319i
$273$	265112.	−	439163.i	0.215289	−	0.356631i
$274$	−82132.9	−	37564.8i	−0.0660907	−	0.0302276i
$275$			472109.i			0.376453i
$276$	−1.05318e6	+	180520.i	−0.832206	+	0.142644i
$277$			1.38041e6i			1.08096i	0.841357	+	0.540479i	$0.181757\pi$
$277$			1.38041e6i			1.08096i	−0.841357	+	0.540479i	$0.818243\pi$
$278$	393644.	−	860677.i	0.305486	−	0.667926i
$279$	−115083.	+	60582.4i	−0.0885115	+	0.0465946i
$280$	597456.	+	2.04755e6i	0.455419	+	1.56077i
$281$			1.92505e6i			1.45437i	0.686440	+	0.727186i	$0.259172\pi$
$281$			1.92505e6i			1.45437i	−0.686440	+	0.727186i	$0.740828\pi$
$282$	207705.	+	304439.i	0.155533	+	0.227970i
$283$	−1.09550e6			−0.813105			−0.406553	−	0.913627i	$-0.633269\pi$
$283$	−1.09550e6			−0.813105			−0.406553	+	0.913627i	$0.633269\pi$
$284$	718958.	+	831613.i	0.528941	+	0.611823i
$285$	1.53987e6	−	2.55082e6i	1.12298	−	1.86024i
$286$	48946.1	−	107017.i	0.0353837	−	0.0773641i
$287$	−918286.			−0.658072
$288$	−125747.	+	1.40198e6i	−0.0893336	+	0.996002i
$289$	500386.			0.352420
$290$	319176.	−	697857.i	0.222862	−	0.487272i
$291$	−394933.	+	654215.i	−0.273395	+	0.452885i
$292$	623402.	+	721085.i	0.427870	+	0.494914i
$293$	1.20976e6			0.823244			0.411622	−	0.911355i	$-0.364962\pi$
$293$	1.20976e6			0.823244			0.411622	+	0.911355i	$0.364962\pi$
$294$	85811.9	+	125777.i	0.0579001	+	0.0848657i
$295$			1.79767e6i			1.20269i
$296$	−770948.	−	2.64212e6i	−0.511441	−	1.75276i
$297$	17208.8	−	293561.i	0.0113203	−	0.193111i
$298$	89760.6	−	196256.i	0.0585524	−	0.128021i
$299$			574025.i			0.371324i
$300$	−2.99002e6	+	512502.i	−1.91810	+	0.328770i
$301$		−	1.08257e6i		−	0.688716i
$302$	1.57877e6	+	722076.i	0.996097	+	0.455581i
$303$	442778.	−	733472.i	0.277064	−	0.458962i
$304$	294855.	−	2.01846e6i	0.182989	−	1.25267i
$305$		−	1.19262e6i		−	0.734094i
$306$	−73249.6	−	1.31607e6i	−0.0447200	−	0.803480i
$307$	960442.			0.581601			0.290801	−	0.956784i	$-0.406078\pi$
$307$	960442.			0.581601			0.290801	+	0.956784i	$0.406078\pi$
$308$	−199514.	−	230776.i	−0.119838	−	0.138616i
$309$	1.16507e6	+	703320.i	0.694152	+	0.419041i
$310$	−264178.	−	120826.i	−0.156132	−	0.0714094i
$311$	2.06246e6			1.20916			0.604581	−	0.796543i	$-0.293340\pi$
$311$	2.06246e6			1.20916			0.604581	+	0.796543i	$0.293340\pi$
$312$	730910.	+	193818.i	0.425087	+	0.112722i
$313$	−2.37601e6			−1.37084			−0.685422	−	0.728146i	$-0.740382\pi$
$313$	−2.37601e6			−1.37084			−0.685422	+	0.728146i	$0.740382\pi$
$314$	−414056.	−	189375.i	−0.236993	−	0.108392i
$315$	2.53362e6	−	1.33376e6i	1.43868	−	0.757359i
$316$	−1.03896e6	+	898219.i	−0.585306	+	0.506017i
$317$	−1.65110e6			−0.922835			−0.461418	−	0.887183i	$-0.652659\pi$
$317$	−1.65110e6			−0.922835			−0.461418	+	0.887183i	$0.652659\pi$
$318$	−1.18795e6	−	1.74121e6i	−0.658765	−	0.965570i
$319$			109755.i			0.0603876i
$320$	−2.65072e6	+	1.69088e6i	−1.44707	+	0.923076i
$321$	896925.	+	541450.i	0.485840	+	0.293289i
$322$	1.35323e6	+	618923.i	0.727332	+	0.332657i
$323$			1.91018e6i			1.01875i
$324$	1.87790e6	−	209689.i	0.993824	−	0.110972i
$325$			1.62967e6i			0.855840i
$326$	−1.13138e6	+	2.47368e6i	−0.589607	+	1.28914i
$327$	−2.85576e6	−	1.72395e6i	−1.47691	−	0.891570i
$328$	−379164.	−	1.29943e6i	−0.194600	−	0.666914i
$329$		−	513234.i		−	0.261412i
$330$	542587.	−	370183.i	0.274274	−	0.187125i
$331$	974506.			0.488894			0.244447	−	0.969663i	$-0.421394\pi$
$331$	974506.			0.488894			0.244447	+	0.969663i	$0.421394\pi$
$332$	2.39066e6	−	2.06681e6i	1.19035	−	1.02909i
$333$	−3.26935e6	+	1.72106e6i	−1.61566	+	0.850524i
$334$	606547.	−	1.32617e6i	0.297508	−	0.650481i
$335$	−1.28753e6			−0.626825
$336$	1.24499e6	−	1.51411e6i	0.601616	−	0.731658i
$337$	−2.71091e6			−1.30029			−0.650145	−	0.759810i	$-0.725292\pi$
$337$	−2.71091e6			−1.30029			−0.650145	+	0.759810i	$0.725292\pi$
$338$	−704636.	+	1.54064e6i	−0.335485	+	0.733516i
$339$	−2.69436e6	−	1.62652e6i	−1.27338	−	0.768704i
$340$	2.22724e6	−	1.92553e6i	1.04489	−	0.903341i
$341$	41548.4			0.0193494
$342$	−2.73410e6	+	152174.i	−1.26401	+	0.0703520i
$343$		−	2.27597e6i		−	1.04456i
$344$	1.53191e6	−	446998.i	0.697970	−	0.203662i
$345$	−1.65583e6	+	2.74292e6i	−0.748977	+	1.24070i
$346$	−1.46721e6	+	3.20797e6i	−0.658875	+	1.44059i
$347$		−	4.10907e6i		−	1.83198i	−0.401204	−	0.915989i	$-0.631408\pi$
$347$		−	4.10907e6i		−	1.83198i	0.401204	−	0.915989i	$-0.368592\pi$
$348$	−695115.	+	119146.i	−0.307686	+	0.0527388i
$349$		−	705038.i		−	0.309848i	−0.987926	−	0.154924i	$-0.950487\pi$
$349$		−	705038.i		−	0.309848i	0.987926	−	0.154924i	$-0.0495133\pi$
$350$	3.84187e6	+	1.75714e6i	1.67638	+	0.766719i
$351$	59402.9	−	1.01334e6i	0.0257359	−	0.439025i
$352$	244183.	−	377613.i	0.105041	−	0.162439i
$353$		−	2.46743e6i		−	1.05392i	−0.849889	−	0.526961i	$-0.823331\pi$
$353$		−	2.46743e6i		−	1.05392i	0.849889	−	0.526961i	$-0.176669\pi$
$354$	1.36475e6	−	931106.i	0.578821	−	0.394904i
$355$	3.29622e6			1.38818
$356$	87044.7	−	75253.1i	0.0364013	−	0.0314702i
$357$	−948649.	+	1.57146e6i	−0.393945	+	0.652578i
$358$	3.06908e6	+	1.40369e6i	1.26561	+	0.578847i
$359$	1.64484e6			0.673579			0.336790	−	0.941580i	$-0.390659\pi$
$359$	1.64484e6			0.673579			0.336790	+	0.941580i	$0.390659\pi$
$360$	2.93350e6	+	3.03453e6i	1.19297	+	1.23405i
$361$	1.49225e6			0.602663
$362$	3.53228e6	+	1.61554e6i	1.41672	+	0.647959i
$363$	1.24891e6	−	2.06885e6i	0.497468	−	0.824067i
$364$	−688701.	−	796616.i	−0.272444	−	0.315134i
$365$	2.85813e6			1.12292
$366$	−905408.	+	617719.i	−0.353298	+	0.241040i
$367$			3.16599e6i			1.22700i	0.789695	+	0.613499i	$0.210239\pi$
$367$			3.16599e6i			1.22700i	−0.789695	+	0.613499i	$0.789761\pi$
$368$	−317061.	+	2.17047e6i	−0.122046	+	0.835476i
$369$	−1.60791e6	+	846445.i	−0.614747	+	0.323618i
$370$	−7.50493e6	−	3.43250e6i	−2.84998	−	1.30348i
$371$			2.93540e6i			1.10722i
$372$	45103.2	+	263139.i	0.0168986	+	0.0985890i
$373$		−	2.30383e6i		−	0.857390i	−0.903449	−	0.428695i	$-0.858973\pi$
$373$		−	2.30383e6i		−	0.857390i	0.903449	−	0.428695i	$-0.141027\pi$
$374$	−175144.	+	382941.i	−0.0647465	+	0.141564i
$375$	−2.28534e6	+	3.78572e6i	−0.839215	+	1.39018i
$376$	726260.	−	211916.i	0.264925	−	0.0773027i
$377$			378864.i			0.137287i
$378$	−2.32485e6	−	1.23264e6i	−0.836886	−	0.443719i
$379$	−1.58202e6			−0.565737			−0.282869	−	0.959159i	$-0.591286\pi$
$379$	−1.58202e6			−0.565737			−0.282869	+	0.959159i	$0.591286\pi$
$380$	−4.00023e6	−	4.62704e6i	−1.42111	−	1.64378i
$381$	4.11951e6	+	2.48684e6i	1.45390	+	0.877680i
$382$	−1.58339e6	+	3.46199e6i	−0.555176	+	1.21386i
$383$	−2.32359e6			−0.809398			−0.404699	−	0.914450i	$-0.632624\pi$
$383$	−2.32359e6			−0.809398			−0.404699	+	0.914450i	$0.632624\pi$
$384$	2.65662e6	+	1.13657e6i	0.919393	+	0.393340i
$385$	−914715.			−0.314510
$386$	827788.	−	1.80990e6i	0.282781	−	0.618283i
$387$	−997877.	−	1.89558e6i	−0.338688	−	0.643374i
$388$	1.02595e6	+	1.18671e6i	0.345976	+	0.400188i
$389$	−2.17293e6			−0.728066			−0.364033	−	0.931386i	$-0.618600\pi$
$389$	−2.17293e6			−0.728066			−0.364033	+	0.931386i	$0.618600\pi$
$390$	1.87296e6	−	1.27784e6i	0.623543	−	0.425416i
$391$		−	2.05403e6i		−	0.679463i
$392$	300049.	−	87551.8i	0.0986229	−	0.0287773i
$393$	610198.	+	368361.i	0.199292	+	0.120307i
$394$	83360.4	−	182262.i	0.0270532	−	0.0591501i
$395$			4.11809e6i			1.32801i
$396$	−562069.	−	220182.i	−0.180116	−	0.0705577i
$397$			1.40092e6i			0.446105i	0.974806	+	0.223052i	$0.0716021\pi$
$397$			1.40092e6i			0.446105i	−0.974806	+	0.223052i	$0.928398\pi$
$398$	−2.18001e6	−	997064.i	−0.689845	−	0.315512i
$399$	3.26467e6	+	1.97080e6i	1.02661	+	0.619740i
$400$	−900145.	+	6.16203e6i	−0.281295	+	1.92563i
$401$			3.52043e6i			1.09329i	0.837365	+	0.546644i	$0.184095\pi$
$401$			3.52043e6i			1.09329i	−0.837365	+	0.546644i	$0.815905\pi$
$402$	666880.	+	977464.i	0.205818	+	0.301672i
$403$	143421.			0.0439896
$404$	−1.15024e6	−	1.33047e6i	−0.350619	−	0.405558i
$405$	3.20694e6	−	4.67081e6i	0.971524	−	1.41500i
$406$	893152.	+	408497.i	0.268912	+	0.122991i
$407$	1.18033e6			0.353198
$408$	−2.61542e6	−	693539.i	−0.777841	−	0.206263i
$409$	3.40295e6			1.00588			0.502941	−	0.864321i	$-0.332251\pi$
$409$	3.40295e6			1.00588			0.502941	+	0.864321i	$0.332251\pi$
$410$	−3.69104e6	−	1.68815e6i	−1.08440	−	0.495966i
$411$	213067.	+	128623.i	0.0622175	+	0.0375591i
$412$	2.11336e6	−	1.82707e6i	0.613381	−	0.530289i
$413$	−2.30074e6			−0.663733
$414$	2.94000e6	−	163634.i	0.843038	−	0.0469217i
$415$		−	9.47575e6i		−	2.70081i
$416$	842896.	−	1.30348e6i	0.238803	−	0.369294i
$417$	−1.34785e6	+	2.23275e6i	−0.379579	+	0.628781i
$418$	795550.	+	363858.i	0.222703	+	0.101857i
$419$		−	1.25923e6i		−	0.350404i	−0.984532	−	0.175202i	$-0.943942\pi$
$419$		−	1.25923e6i		−	0.350404i	0.984532	−	0.175202i	$-0.0560579\pi$
$420$	−992977.	−	5.79318e6i	−0.274673	−	1.60249i
$421$		−	384209.i		−	0.105648i	−0.998604	−	0.0528242i	$-0.983178\pi$
$421$		−	384209.i		−	0.105648i	0.998604	−	0.0528242i	$-0.0168223\pi$
$422$	−1.99725e6	+	4.36686e6i	−0.545948	+	1.19368i
$423$	−473082.	−	898670.i	−0.128554	−	0.244202i
$424$	−4.15379e6	+	1.21204e6i	−1.12209	+	0.327417i
$425$		−	5.83147e6i		−	1.56605i
$426$	−1.70729e6	−	2.50241e6i	−0.455808	−	0.668090i
$427$	1.52637e6			0.405126
$428$	1.62697e6	−	1.40657e6i	0.429308	−	0.371152i
$429$	−167594.	+	277622.i	−0.0439657	+	0.0728302i
$430$	1.99017e6	−	4.35138e6i	0.519062	−	1.13489i
$431$	6.02229e6			1.56160			0.780798	−	0.624784i	$-0.214813\pi$
$431$	6.02229e6			1.56160			0.780798	+	0.624784i	$0.214813\pi$
$432$	784328.	−	3.79878e6i	0.202203	−	0.979344i
$433$	6.39865e6			1.64009			0.820047	−	0.572296i	$-0.193947\pi$
$433$	6.39865e6			1.64009			0.820047	+	0.572296i	$0.193947\pi$
$434$	154639.	−	338107.i	0.0394089	−	0.0861649i
$435$	−1.09287e6	+	1.81037e6i	−0.276915	+	0.458715i
$436$	−5.18018e6	+	4.47844e6i	−1.30506	+	1.12826i
$437$	−4.26721e6			−1.06891
$438$	−1.48037e6	−	2.16982e6i	−0.368711	−	0.540429i
$439$			4.17217e6i			1.03324i	0.856215	+	0.516620i	$0.172810\pi$
$439$			4.17217e6i			1.03324i	−0.856215	+	0.516620i	$0.827190\pi$
$440$	−377689.	−	1.29438e6i	−0.0930042	−	0.318735i
$441$	−195451.	−	371280.i	−0.0478565	−	0.0909085i
$442$	−604580.	+	1.32187e6i	−0.147197	+	0.321836i
$443$			2.23399e6i			0.540843i	0.962742	+	0.270421i	$0.0871630\pi$
$443$			2.23399e6i			0.540843i	−0.962742	+	0.270421i	$0.912837\pi$
$444$	1.28132e6	+	7.47543e6i	0.308461	+	1.79961i
$445$		−	345015.i		−	0.0825919i
$446$	−3.39788e6	−	1.55407e6i	−0.808855	−	0.369943i
$447$	−307344.	+	509122.i	−0.0727538	+	0.120518i
$448$	−2.16407e6	−	3.39252e6i	−0.509420	−	0.798596i
$449$		−	4.06503e6i		−	0.951585i	−0.879557	−	0.475793i	$-0.842161\pi$
$449$		−	4.06503e6i		−	0.951585i	0.879557	−	0.475793i	$-0.157839\pi$
$450$	8.34677e6	−	464563.i	1.94306	−	0.108147i
$451$	580506.			0.134389
$452$	−4.88741e6	+	4.22533e6i	−1.12521	+	0.972780i
$453$	−4.09561e6	−	2.47242e6i	−0.937721	−	0.566078i
$454$	3.55942e6	+	1.62796e6i	0.810474	+	0.370683i
$455$	−3.15751e6			−0.715016
$456$	−1.44081e6	+	5.43347e6i	−0.324485	+	1.22367i
$457$	−5.17400e6			−1.15887			−0.579437	−	0.815017i	$-0.696728\pi$
$457$	−5.17400e6			−1.15887			−0.579437	+	0.815017i	$0.696728\pi$
$458$	4.02415e6	+	1.84051e6i	0.896418	+	0.409991i
$459$	−212562.	+	3.62605e6i	−0.0470926	+	0.803345i
$460$	4.30149e6	+	4.97550e6i	0.947816	+	1.09633i
$461$	3.92825e6			0.860887			0.430444	−	0.902617i	$-0.358357\pi$
$461$	3.92825e6			0.860887			0.430444	+	0.902617i	$0.358357\pi$
$462$	473778.	+	694430.i	0.103269	+	0.151364i
$463$			6.38891e6i			1.38508i	0.721381	+	0.692539i	$0.243508\pi$
$463$			6.38891e6i			1.38508i	−0.721381	+	0.692539i	$0.756492\pi$
$464$	−209264.	+	1.43254e6i	−0.0451232	+	0.308895i
$465$	685324.	+	413712.i	0.146982	+	0.0887291i
$466$	−564770.	−	258306.i	−0.120478	−	0.0551024i
$467$		−	216481.i		−	0.0459334i	−0.999736	−	0.0229667i	$-0.992689\pi$
$467$		−	216481.i		−	0.0459334i	0.999736	−	0.0229667i	$-0.00731117\pi$
$468$	−1.94021e6	−	760048.i	−0.409480	−	0.160408i
$469$		−	1.64785e6i		−	0.345927i
$470$	943517.	−	2.06294e6i	0.197018	−	0.430766i
$471$	1.07414e6	+	648428.i	0.223104	+	0.134682i
$472$	−949986.	−	3.25570e6i	−0.196274	−	0.672651i
$473$			684360.i			0.140648i
$474$	3.12635e6	−	2.13297e6i	0.639135	−	0.436053i
$475$	−1.21147e7			−2.46365
$476$	2.46438e6	+	2.85053e6i	0.498529	+	0.576645i
$477$	2.70575e6	+	5.13987e6i	0.544493	+	1.03432i
$478$	1.79370e6	−	3.92181e6i	0.359071	−	0.785085i
$479$	−5.62295e6			−1.11976			−0.559880	−	0.828573i	$-0.689153\pi$
$479$	−5.62295e6			−1.11976			−0.559880	+	0.828573i	$0.689153\pi$
$480$	7.78773e6	−	3.79715e6i	1.54279	−	0.752238i
$481$	4.07440e6			0.802972
$482$	1.72966e6	−	3.78179e6i	0.339113	−	0.741447i
$483$	−3.51053e6	−	2.11921e6i	−0.684707	−	0.413340i
$484$	−3.24440e6	−	3.75277e6i	−0.629536	−	0.728179i
$485$	4.70369e6			0.907997
$486$	−5.20701e6	−	15377.3i	−0.999996	−	0.00295317i
$487$			3.08869e6i			0.590135i	0.955476	+	0.295068i	$0.0953422\pi$
$487$			3.08869e6i			0.590135i	−0.955476	+	0.295068i	$0.904658\pi$
$488$	630244.	+	2.15991e6i	0.119801	+	0.410570i
$489$	3.87387e6	−	6.41716e6i	0.732611	−	1.21359i
$490$	389808.	−	852288.i	0.0733432	−	0.160360i
$491$			1.22473e6i			0.229265i	0.993408	+	0.114633i	$0.0365691\pi$
$491$			1.22473e6i			0.229265i	−0.993408	+	0.114633i	$0.963431\pi$
$492$	630173.	+	3.67653e6i	0.117367	+	0.684739i
$493$		−	1.35569e6i		−	0.251213i
$494$	2.74616e6	+	1.25600e6i	0.506301	+	0.231565i
$495$	−1.60166e6	+	843153.i	−0.293804	+	0.154665i
$496$	542295.	+	79218.1i	0.0989763	+	0.0144584i
$497$			4.21867e6i			0.766098i
$498$	−7.19377e6	+	4.90799e6i	−1.29982	+	0.886809i
$499$	4.64777e6			0.835590			0.417795	−	0.908541i	$-0.362803\pi$
$499$	4.64777e6			0.835590			0.417795	+	0.908541i	$0.362803\pi$
$500$	5.93682e6	+	6.86707e6i	1.06201	+	1.22842i
$501$	−2.07684e6	+	3.44033e6i	−0.369665	+	0.612359i
$502$	−250345.	−	114499.i	−0.0443384	−	0.0202789i
$503$	2.58619e6			0.455764			0.227882	−	0.973689i	$-0.426820\pi$
$503$	2.58619e6			0.455764			0.227882	+	0.973689i	$0.426820\pi$
$504$	−3.88373e6	+	3.75444e6i	−0.681041	+	0.658368i
$505$	−5.27353e6			−0.920181
$506$	−855463.	−	391259.i	−0.148534	−	0.0679342i
$507$	2.41270e6	−	3.99670e6i	0.416854	−	0.690528i
$508$	7.47255e6	−	6.46027e6i	1.28472	−	1.11069i
$509$	−7.59068e6			−1.29863			−0.649316	−	0.760519i	$-0.724945\pi$
$509$	−7.59068e6			−1.29863			−0.649316	+	0.760519i	$0.724945\pi$
$510$	−6.70201e6	+	4.57248e6i	−1.14098	+	0.778442i
$511$			3.65797e6i			0.619709i
$512$	3.90708e6	−	4.46308e6i	0.658685	−	0.752419i
$513$	7.53303e6	+	441592.i	1.26379	+	0.0740845i
$514$	5.81123e6	+	2.65786e6i	0.970197	+	0.443735i
$515$		−	8.37661e6i		−	1.39172i
$516$	−4.33428e6	+	742914.i	−0.716626	+	0.122833i
$517$			324447.i			0.0533848i
$518$	4.39308e6	−	9.60517e6i	0.719357	−	1.57283i
$519$	5.02380e6	−	8.32204e6i	0.818679	−	1.35616i
$520$	−1.30375e6	−	4.46807e6i	−0.211439	−	0.724623i
$521$		−	2.45550e6i		−	0.396319i	−0.980170	−	0.198160i	$-0.936504\pi$
$521$		−	2.45550e6i		−	0.396319i	0.980170	−	0.198160i	$-0.0634964\pi$
$522$	1.94044e6	−	108001.i	0.311691	−	0.0173481i
$523$	−3.50564e6			−0.560419			−0.280209	−	0.959939i	$-0.590404\pi$
$523$	−3.50564e6			−0.560419			−0.280209	+	0.959939i	$0.590404\pi$
$524$	1.10686e6	−	956920.i	0.176102	−	0.152246i
$525$	−9.96650e6	−	6.01652e6i	−1.57814	−	0.952680i
$526$	−2.57758e6	+	5.63570e6i	−0.406207	+	0.888144i
$527$	−513203.			−0.0804939
$528$	−787038.	+	957160.i	−0.122860	+	0.149417i
$529$	−1.84778e6			−0.287085
$530$	−5.39637e6	+	1.17988e7i	−0.834472	+	1.82452i
$531$	−4.02859e6	+	2.12075e6i	−0.620036	+	0.326402i
$532$	5.92191e6	−	5.11969e6i	0.907158	−	0.784269i
$533$	2.00385e6			0.305525
$534$	−261927.	+	178701.i	−0.0397491	+	0.0271190i
$535$		−	6.44873e6i		−	0.974068i
$536$	2.33181e6	−	680402.i	0.350575	−	0.102295i
$537$	−7.96173e6	−	4.80629e6i	−1.19144	−	0.719241i
$538$	1.70675e6	−	3.73171e6i	0.254223	−	0.555842i
$539$			134043.i			0.0198734i
$540$	−7.07866e6	−	9.22854e6i	−1.04464	−	1.36191i
$541$		−	1.46207e6i		−	0.214770i	−0.994218	−	0.107385i	$-0.965752\pi$
$541$		−	1.46207e6i		−	0.214770i	0.994218	−	0.107385i	$-0.0342477\pi$
$542$	1.17908e6	+	539273.i	0.172404	+	0.0788516i
$543$	−9.16336e6	−	5.53168e6i	−1.33369	−	0.805115i
$544$	−3.01614e6	+	4.66425e6i	−0.436972	+	0.675748i
$545$			2.05324e7i			2.96107i
$546$	1.63544e6	+	2.39710e6i	0.234775	+	0.344116i
$547$	1.11773e7			1.59724			0.798620	−	0.601836i	$-0.205564\pi$
$547$	1.11773e7			1.59724			0.798620	+	0.601836i	$0.205564\pi$
$548$	386491.	−	334135.i	0.0549779	−	0.0475303i
$549$	2.67267e6	−	1.40696e6i	0.378455	−	0.199228i
$550$	−2.42869e6	−	1.11080e6i	−0.342345	−	0.156577i
$551$	−2.81641e6			−0.395200
$552$	1.54932e6	−	5.84266e6i	0.216418	−	0.816136i
$553$	−5.27053e6			−0.732894
$554$	−7.10129e6	−	3.24789e6i	−0.983022	−	0.449600i
$555$	1.94691e7	+	1.17530e7i	2.68296	+	1.61963i
$556$	3.50142e6	+	4.05007e6i	0.480350	+	0.555617i
$557$	1.22276e7			1.66994			0.834972	−	0.550293i	$-0.185484\pi$
$557$	1.22276e7			1.66994			0.834972	+	0.550293i	$0.185484\pi$
$558$	−40884.3	−	734565.i	−0.00555867	−	0.0998722i
$559$			2.36235e6i			0.319752i
$560$	−1.19390e7	−	1.74404e6i	−1.60878	−	0.235010i
$561$	599700.	−	993417.i	0.0804502	−	0.133268i
$562$	−9.90308e6	−	4.52933e6i	−1.32260	−	0.604913i
$563$		−	9.14920e6i		−	1.21650i	−0.793746	−	0.608250i	$-0.791872\pi$
$563$		−	9.14920e6i		−	1.21650i	0.793746	−	0.608250i	$-0.208128\pi$
$564$	−2.05483e6	+	352207.i	−0.272006	+	0.0466230i
$565$			1.93720e7i			2.55301i
$566$	2.57754e6	−	5.63562e6i	0.338193	−	0.739436i
$567$	5.97794e6	+	4.10440e6i	0.780897	+	0.536157i
$568$	−5.96969e6	+	1.74190e6i	−0.776391	+	0.226544i
$569$		−	7.58186e6i		−	0.981737i	−0.871234	−	0.490868i	$-0.836680\pi$
$569$		−	7.58186e6i		−	0.981737i	0.871234	−	0.490868i	$-0.163320\pi$
$570$	9.49922e6	+	1.39233e7i	1.22462	+	1.79496i
$571$	−3.53008e6			−0.453101			−0.226550	−	0.973999i	$-0.572745\pi$
$571$	−3.53008e6			−0.453101			−0.226550	+	0.973999i	$0.572745\pi$
$572$	435371.	+	503590.i	0.0556377	+	0.0643557i
$573$	5.42160e6	−	8.98101e6i	0.689829	−	1.14272i
$574$	2.16058e6	−	4.72397e6i	0.273710	−	0.598449i
$575$	1.30271e7			1.64315
$576$	−6.91638e6	−	3.94551e6i	−0.868605	−	0.495504i
$577$	−6.44129e6			−0.805440			−0.402720	−	0.915323i	$-0.631935\pi$
$577$	−6.44129e6			−0.805440			−0.402720	+	0.915323i	$0.631935\pi$
$578$	−1.17733e6	+	2.57415e6i	−0.146581	+	0.320490i
$579$	−2.83438e6	+	4.69521e6i	−0.351367	+	0.582048i
$580$	2.83904e6	+	3.28389e6i	0.350430	+	0.405340i
$581$	1.21275e7			1.49050
$582$	−2.43629e6	−	3.57093e6i	−0.298140	−	0.436992i
$583$		−	1.85565e6i		−	0.226113i
$584$	−5.17627e6	+	1.51039e6i	−0.628036	+	0.183255i
$585$	−5.52877e6	+	2.91048e6i	−0.667943	+	0.351621i
$586$	−2.84636e6	+	6.22338e6i	−0.342410	+	0.748656i
$587$			2.76141e6i			0.330778i	0.986228	+	0.165389i	$0.0528879\pi$
$587$			2.76141e6i			0.330778i	−0.986228	+	0.165389i	$0.947112\pi$
$588$	−848939.	+	145512.i	−0.101259	+	0.0173562i
$589$			1.06617e6i			0.126630i
$590$	−9.24780e6	−	4.22963e6i	−1.09373	−	0.500233i
$591$	−285429.	+	472820.i	−0.0336147	+	0.0556836i
$592$	1.54059e7	+	2.25048e6i	1.80668	+	0.263919i
$593$			5.54593e6i			0.647646i	0.946118	+	0.323823i	$0.104968\pi$
$593$			5.54593e6i			0.647646i	−0.946118	+	0.323823i	$0.895032\pi$
$594$	1.46968e6	+	779230.i	0.170906	+	0.0906148i
$595$	1.12985e7			1.30836
$596$	798411.	+	923516.i	0.0920685	+	0.106495i
$597$	5.65535e6	+	3.41399e6i	0.649417	+	0.392036i
$598$	−2.95297e6	−	1.35059e6i	−0.337681	−	0.154444i
$599$	−1.53803e7			−1.75145			−0.875726	−	0.482808i	$-0.839617\pi$
$599$	−1.53803e7			−1.75145			−0.875726	+	0.482808i	$0.839617\pi$
$600$	4.39856e6	−	1.65875e7i	0.498807	−	1.88106i
$601$	2.11507e6			0.238857			0.119428	−	0.992843i	$-0.461894\pi$
$601$	2.11507e6			0.238857			0.119428	+	0.992843i	$0.461894\pi$
$602$	5.56910e6	+	2.54712e6i	0.626317	+	0.286456i
$603$	−1.51893e6	−	2.88537e6i	−0.170116	−	0.323153i
$604$	−7.42920e6	+	6.42279e6i	−0.828609	+	0.716360i
$605$	−1.48747e7			−1.65218
$606$	2.73144e6	+	4.00354e6i	0.302141	+	0.442856i
$607$		−	1.33213e7i		−	1.46749i	−0.679423	−	0.733747i	$-0.737770\pi$
$607$		−	1.33213e7i		−	1.46749i	0.679423	−	0.733747i	$-0.262230\pi$
$608$	9.68988e6	+	6.26595e6i	1.06306	+	0.687429i
$609$	−2.31700e6	−	1.39871e6i	−0.253152	−	0.152821i
$610$	6.13522e6	+	2.80604e6i	0.667584	+	0.305330i
$611$			1.11996e6i			0.121367i
$612$	6.94264e6	+	2.71968e6i	0.749283	+	0.293521i
$613$		−	7.09506e6i		−	0.762614i	−0.924448	−	0.381307i	$-0.875474\pi$
$613$		−	7.09506e6i		−	0.762614i	0.924448	−	0.381307i	$-0.124526\pi$
$614$	−2.25977e6	+	4.94083e6i	−0.241904	+	0.528907i
$615$	9.57520e6	+	5.78030e6i	1.02085	+	0.616258i
$616$	1.65661e6	−	483385.i	0.175901	−	0.0513265i
$617$			8.98551e6i			0.950232i	0.879923	+	0.475116i	$0.157594\pi$
$617$			8.98551e6i			0.950232i	−0.879923	+	0.475116i	$0.842406\pi$
$618$	−6.35933e6	+	4.33869e6i	−0.669792	+	0.456969i
$619$	−9.40970e6			−0.987073			−0.493536	−	0.869725i	$-0.664296\pi$
$619$	−9.40970e6			−0.987073			−0.493536	+	0.869725i	$0.664296\pi$
$620$	1.24314e6	−	1.07473e6i	0.129879	−	0.112285i
$621$	−8.10033e6	−	474847.i	−0.842896	−	0.0494112i
$622$	−4.85264e6	+	1.06100e7i	−0.502924	+	1.09961i
$623$	441566.			0.0455802
$624$	−2.71678e6	+	3.30402e6i	−0.279314	+	0.339689i
$625$	8.21407e6			0.841121
$626$	5.59038e6	−	1.22230e7i	0.570172	−	1.24664i
$627$	−2.06380e6	−	1.24586e6i	−0.209652	−	0.126561i
$628$	1.94842e6	−	1.68447e6i	0.197144	−	0.170437i
$629$	−1.45794e7			−1.46931
$630$	900095.	+	1.61719e7i	0.0903518	+	1.62334i
$631$			7.51210e6i			0.751083i	0.926806	+	0.375542i	$0.122543\pi$
$631$			7.51210e6i			0.751083i	−0.926806	+	0.375542i	$0.877457\pi$
$632$	−2.17622e6	−	7.45814e6i	−0.216726	−	0.742742i
$633$	6.83866e6	−	1.13284e7i	0.678363	−	1.12372i
$634$	3.88477e6	−	8.49378e6i	0.383832	−	0.839224i
$635$		−	2.96186e7i		−	2.91494i
$636$	1.17524e7	−	2.01442e6i	1.15209	−	0.197473i
$637$			462704.i			0.0451809i
$638$	−564617.	−	258236.i	−0.0549164	−	0.0251169i
$639$	3.88862e6	+	7.38686e6i	0.376742	+	0.715662i
$640$	−2.46172e6	−	1.76145e7i	−0.237568	−	1.69989i
$641$			3.47610e6i			0.334154i	0.985944	+	0.167077i	$0.0534329\pi$
$641$			3.47610e6i			0.334154i	−0.985944	+	0.167077i	$0.946567\pi$
$642$	−4.89572e6	+	3.34013e6i	−0.468791	+	0.319835i
$643$	−1.00185e7			−0.955600			−0.477800	−	0.878469i	$-0.658566\pi$
$643$	−1.00185e7			−0.955600			−0.477800	+	0.878469i	$0.658566\pi$
$644$	−6.36788e6	+	5.50525e6i	−0.605035	+	0.523073i
$645$	−6.81442e6	+	1.12882e7i	−0.644955	+	1.06838i
$646$	−9.82660e6	−	4.49435e6i	−0.926450	−	0.423726i
$647$	−1.82105e7			−1.71026			−0.855128	−	0.518417i	$-0.826522\pi$
$647$	−1.82105e7			−1.71026			−0.855128	+	0.518417i	$0.826522\pi$
$648$	−3.33968e6	+	1.01539e7i	−0.312441	+	0.949937i
$649$	1.45444e6			0.135545
$650$	−8.38358e6	−	3.83436e6i	−0.778299	−	0.355967i
$651$	−529489.	+	877111.i	−0.0489671	+	0.0811151i
$652$	−1.00635e7	−	1.16403e7i	−0.927104	−	1.07237i
$653$	1.43747e7			1.31921			0.659607	−	0.751611i	$-0.270723\pi$
$653$	1.43747e7			1.31921			0.659607	+	0.751611i	$0.270723\pi$
$654$	1.55877e7	−	1.06348e7i	1.42508	−	0.972267i
$655$		−	4.38721e6i		−	0.399563i
$656$	7.57683e6	+	1.10682e6i	0.687429	+	0.100419i
$657$	3.37179e6	+	6.40509e6i	0.304753	+	0.578911i
$658$	2.64025e6	+	1.20756e6i	0.237728	+	0.108729i
$659$			2.04263e7i			1.83222i	0.400932	+	0.916108i	$0.368687\pi$
$659$			2.04263e7i			1.83222i	−0.400932	+	0.916108i	$0.631313\pi$
$660$	627722.	+	3.66223e6i	0.0560929	+	0.327255i
$661$		−	2.00837e7i		−	1.78789i	−0.448177	−	0.893945i	$-0.647927\pi$
$661$		−	2.00837e7i		−	1.78789i	0.448177	−	0.893945i	$-0.352073\pi$
$662$	−2.29286e6	+	5.01318e6i	−0.203344	+	0.444599i
$663$	2.07011e6	−	3.42918e6i	0.182898	−	0.302975i
$664$	5.00750e6	+	1.71612e7i	0.440759	+	1.51053i
$665$		−	2.34724e7i		−	2.05827i
$666$	−1.16147e6	−	2.08680e7i	−0.101466	−	1.82304i
$667$	3.02851e6			0.263581
$668$	5.39517e6	+	6.24056e6i	0.467804	+	0.541106i
$669$	8.81470e6	+	5.32121e6i	0.761452	+	0.459669i
$670$	3.02936e6	−	6.62349e6i	0.260714	−	0.570033i
$671$	−964914.			−0.0827337
$672$	4.85978e6	+	9.96711e6i	0.415139	+	0.851425i
$673$	1.08749e7			0.925526			0.462763	−	0.886482i	$-0.346858\pi$
$673$	1.08749e7			0.925526			0.462763	+	0.886482i	$0.346858\pi$
$674$	6.37834e6	−	1.39458e7i	0.540826	−	1.18248i
$675$	−2.29971e7	−	1.34811e6i	−1.94274	−	0.113885i
$676$	−6.26767e6	−	7.24976e6i	−0.527520	−	0.610179i
$677$	−2.04934e6			−0.171847			−0.0859236	−	0.996302i	$-0.527384\pi$
$677$	−2.04934e6			−0.171847			−0.0859236	+	0.996302i	$0.527384\pi$
$678$	1.47067e7	−	1.00338e7i	1.22869	−	0.838280i
$679$			6.02001e6i			0.501098i
$680$	4.66519e6	+	1.59881e7i	0.386899	+	1.32594i
$681$	−9.23376e6	−	5.57418e6i	−0.762976	−	0.460589i
$682$	−97756.7	+	213739.i	−0.00804796	+	0.0175963i
$683$			2.00660e7i			1.64592i	0.568096	+	0.822962i	$0.307680\pi$
$683$			2.00660e7i			1.64592i	−0.568096	+	0.822962i	$0.692320\pi$
$684$	5.65007e6	−	1.44232e7i	0.461757	−	1.17875i
$685$		−	1.53192e6i		−	0.124741i
$686$	1.17084e7	+	5.35500e6i	0.949917	+	0.434459i
$687$	−1.04394e7	−	6.30197e6i	−0.843883	−	0.509430i
$688$	−1.30483e6	+	8.93236e6i	−0.105095	+	0.719441i
$689$		−	6.40552e6i		−	0.514051i
$690$	−1.02146e7	−	1.49718e7i	−0.816768	−	1.19716i
$691$	8.87967e6			0.707459			0.353730	−	0.935348i	$-0.384913\pi$
$691$	8.87967e6			0.707459			0.353730	+	0.935348i	$0.384913\pi$
$692$	−1.30507e7	−	1.50957e7i	−1.03602	−	1.19836i
$693$	−1.07911e6	−	2.04988e6i	−0.0853556	−	0.162142i
$694$	2.11384e7	+	9.66799e6i	1.66600	+	0.761970i
$695$	1.60531e7			1.26065
$696$	1.02257e6	−	3.85623e6i	0.0800147	−	0.301745i
$697$	−7.17037e6			−0.559062
$698$	3.62695e6	+	1.65884e6i	0.281775	+	0.128874i
$699$	1.46511e6	+	884451.i	0.113417	+	0.0684669i
$700$	−1.80786e7	+	1.56296e7i	−1.39451	+	1.20560i
$701$	−1.13692e7			−0.873845			−0.436922	−	0.899499i	$-0.643932\pi$
$701$	−1.13692e7			−0.873845			−0.436922	+	0.899499i	$0.643932\pi$
$702$	5.07321e6	+	2.68982e6i	0.388544	+	0.206007i
$703$			3.02884e7i			2.31147i
$704$	1.36804e6	+	2.14462e6i	0.104032	+	0.163087i
$705$	−3.23064e6	+	5.35162e6i	−0.244802	+	0.405521i
$706$	1.26933e7	+	5.80548e6i	0.958434	+	0.438355i
$707$		−	6.74933e6i		−	0.507822i
$708$	1.57888e6	+	9.21146e6i	0.118377	+	0.690630i
$709$		−	1.02551e7i		−	0.766170i	−0.923713	−	0.383085i	$-0.874862\pi$
$709$		−	1.02551e7i		−	0.766170i	0.923713	−	0.383085i	$-0.125138\pi$
$710$	−7.75549e6	+	1.69569e7i	−0.577382	+	1.26241i
$711$	−9.22867e6	+	4.85819e6i	−0.684644	+	0.360413i
$712$	182324.	+	624845.i	0.0134786	+	0.0461926i
$713$		−	1.14646e6i		−	0.0844569i
$714$	−5.85209e6	−	8.57756e6i	−0.429601	−	0.629678i
$715$	1.99606e6			0.146018
$716$	−1.44421e7	+	1.24857e7i	−1.05280	+	0.910186i
$717$	−6.14170e6	+	1.01739e7i	−0.446160	+	0.739074i
$718$	−3.87006e6	+	8.46162e6i	−0.280160	+	0.612552i
$719$	1.56434e7			1.12852			0.564260	−	0.825597i	$-0.309161\pi$
$719$	1.56434e7			1.12852			0.564260	+	0.825597i	$0.309161\pi$
$720$	−2.25127e7	+	7.95114e6i	−1.61844	+	0.571608i
$721$	1.07208e7			0.768049
$722$	−3.51104e6	+	7.67665e6i	−0.250664	+	0.548061i
$723$	−5.92244e6	+	9.81065e6i	−0.421361	+	0.697995i
$724$	−1.66218e7	+	1.43701e7i	−1.17850	+	1.01886i
$725$	8.59805e6			0.607512
$726$	7.70436e6	+	1.12925e7i	0.542494	+	0.795148i
$727$		−	2.23879e7i		−	1.57100i	−0.618860	−	0.785501i	$-0.712405\pi$
$727$		−	2.23879e7i		−	1.57100i	0.618860	−	0.785501i	$-0.287595\pi$
$728$	5.71846e6	−	1.66860e6i	0.399899	−	0.116687i
$729$	1.42506e7	+	1.67653e6i	0.993151	+	0.116840i
$730$	−6.72472e6	+	1.47032e7i	−0.467054	+	1.02118i
$731$		−	8.45318e6i		−	0.585096i
$732$	−1.04747e6	−	6.11111e6i	−0.0722544	−	0.421544i
$733$			2.09009e7i			1.43683i	0.695617	+	0.718413i	$0.255131\pi$
$733$			2.09009e7i			1.43683i	−0.695617	+	0.718413i	$0.744869\pi$
$734$	−1.62869e7	−	7.44907e6i	−1.11583	−	0.510342i
$735$	−1.33472e6	+	2.21099e6i	−0.0911319	+	0.150962i
$736$	−1.04196e7	−	6.73783e6i	−0.709018	−	0.458485i
$737$			1.04171e6i			0.0706442i
$738$	−571228.	−	1.02632e7i	−0.0386072	−	0.693652i
$739$	467556.			0.0314936			0.0157468	−	0.999876i	$-0.494987\pi$
$739$	467556.			0.0314936			0.0157468	+	0.999876i	$0.494987\pi$
$740$	3.53158e7	−	3.05317e7i	2.37077	−	2.04961i
$741$	−7.12403e6	−	4.30060e6i	−0.476629	−	0.287729i
$742$	−1.51007e7	−	6.90654e6i	−1.00690	−	0.460522i
$743$	2.41151e7			1.60257			0.801287	−	0.598281i	$-0.204149\pi$
$743$	2.41151e7			1.60257			0.801287	+	0.598281i	$0.204149\pi$
$744$	−1.45980e6	−	387099.i	−0.0966852	−	0.0256383i
$745$	3.66049e6			0.241629
$746$	1.18517e7	+	5.42055e6i	0.779709	+	0.356612i
$747$	2.12352e7	−	1.11787e7i	1.39237	−	0.732979i
$748$	−1.55789e6	−	1.80200e6i	−0.101808	−	0.117761i
$749$	8.25339e6			0.537561
$750$	−1.40980e7	−	2.06638e7i	−0.915173	−	1.34139i
$751$		−	1.99272e7i		−	1.28928i	−0.764486	−	0.644640i	$-0.777007\pi$
$751$		−	1.99272e7i		−	1.28928i	0.764486	−	0.644640i	$-0.222993\pi$
$752$	−618606.	+	4.23473e6i	−0.0398905	+	0.273074i
$753$	649440.	+	392050.i	0.0417399	+	0.0251973i
$754$	−1.94900e6	−	891407.i	−0.124849	−	0.0571015i
$755$			2.94467e7i			1.88005i
$756$	1.18111e7	−	9.05961e6i	0.751601	−	0.576508i
$757$		−	1.51893e7i		−	0.963382i	−0.876341	−	0.481691i	$-0.840023\pi$
$757$		−	1.51893e7i		−	0.963382i	0.876341	−	0.481691i	$-0.159977\pi$
$758$	3.72225e6	−	8.13845e6i	0.235306	−	0.514480i
$759$	2.21922e6	+	1.33969e6i	0.139829	+	0.0844110i
$760$	3.32149e7	−	9.69183e6i	2.08593	−	0.608656i
$761$			9.79195e6i			0.612926i	0.951883	+	0.306463i	$0.0991455\pi$
$761$			9.79195e6i			0.612926i	−0.951883	+	0.306463i	$0.900854\pi$
$762$	−2.24857e7	+	1.53410e7i	−1.40288	+	0.957119i
$763$	−2.62784e7			−1.63413
$764$	−1.40841e7	−	1.62910e7i	−0.872965	−	1.00975i
$765$	1.97836e7	−	1.04146e7i	1.22223	−	0.643410i
$766$	5.46703e6	−	1.19533e7i	0.336651	−	0.736065i
$767$	5.02060e6			0.308153
$768$	−1.20975e7	+	1.09924e7i	−0.740103	+	0.672494i
$769$	7.53372e6			0.459403			0.229701	−	0.973261i	$-0.426225\pi$
$769$	7.53372e6			0.459403			0.229701	+	0.973261i	$0.426225\pi$
$770$	2.15218e6	−	4.70559e6i	0.130813	−	0.286014i
$771$	−1.50754e7	−	9.10060e6i	−0.913338	−	0.551359i
$772$	7.36309e6	+	8.51683e6i	0.444648	+	0.514321i
$773$	−1.42355e7			−0.856889			−0.428444	−	0.903568i	$-0.640938\pi$
$773$	−1.42355e7			−0.856889			−0.428444	+	0.903568i	$0.640938\pi$
$774$	1.20993e7	−	673422.i	0.725953	−	0.0404050i
$775$		−	3.25484e6i		−	0.194659i
$776$	−8.51871e6	+	2.48569e6i	−0.507831	+	0.148181i
$777$	−1.50421e7	+	2.49175e7i	−0.893830	+	1.48065i
$778$	5.11255e6	−	1.11782e7i	0.302823	−	0.662102i
$779$			1.48963e7i			0.879497i
$780$	2.16684e6	+	1.26417e7i	0.127523	+	0.743991i
$781$		−	2.66688e6i		−	0.156450i
$782$	1.05666e7	+	4.83281e6i	0.617902	+	0.282607i
$783$	−5.34633e6	−	313406.i	−0.311639	−	0.0182685i
$784$	−255573.	+	1.74955e6i	−0.0148499	+	0.101657i
$785$		−	7.72284e6i		−	0.447304i
$786$	−3.33067e6	+	2.27237e6i	−0.192298	+	0.131196i
$787$	2.16332e7			1.24504			0.622522	−	0.782602i	$-0.286108\pi$
$787$	2.16332e7			1.24504			0.622522	+	0.782602i	$0.286108\pi$
$788$	741482.	+	857667.i	0.0425388	+	0.0492043i
$789$	8.82572e6	−	1.46200e7i	0.504728	−	0.836094i
$790$	−2.11848e7	−	9.68920e6i	−1.20769	−	0.552358i
$791$	−2.47932e7			−1.40894
$792$	2.45515e6	−	2.37341e6i	0.139080	−	0.134450i
$793$	−3.33079e6			−0.188089
$794$	−7.20679e6	−	3.29614e6i	−0.405687	−	0.185547i
$795$	1.84774e7	−	3.06082e7i	1.03687	−	1.71759i
$796$	1.02585e7	−	8.86878e6i	0.573851	−	0.496114i
$797$	1.53108e7			0.853794			0.426897	−	0.904300i	$-0.359607\pi$
$797$	1.53108e7			0.853794			0.426897	+	0.904300i	$0.359607\pi$
$798$	−1.78197e7	+	1.21576e7i	−0.990587	+	0.675833i
$799$		−	4.00755e6i		−	0.222082i
$800$	−2.95816e7	−	1.91289e7i	−1.63417	−	1.05673i
$801$	773180.	−	407021.i	0.0425794	−	0.0224148i
$802$	−1.81102e7	−	8.28300e6i	−0.994233	−	0.454728i
$803$		−	2.31243e6i		−	0.126555i
$804$	−6.59746e6	+	1.13083e6i	−0.359945	+	0.0616962i
$805$			2.52401e7i			1.37278i
$806$	−337447.	+	737805.i	−0.0182965	+	0.0400040i
$807$	−5.84399e6	+	9.68071e6i	−0.315883	+	0.523267i
$808$	9.55073e6	−	2.78682e6i	0.514646	−	0.150169i
$809$		−	9.98433e6i		−	0.536349i	−0.963370	−	0.268175i	$-0.913580\pi$
$809$		−	9.98433e6i		−	0.536349i	0.963370	−	0.268175i	$-0.0864204\pi$
$810$	1.64828e7	+	2.74873e7i	0.882710	+	1.47204i
$811$	−1.93260e6			−0.103178			−0.0515892	−	0.998668i	$-0.516429\pi$
$811$	−1.93260e6			−0.103178			−0.0515892	+	0.998668i	$0.516429\pi$
$812$	−4.20289e6	+	3.63354e6i	−0.223696	+	0.193393i
$813$	−3.05876e6	−	1.84649e6i	−0.162300	−	0.0979763i
$814$	−2.77714e6	+	6.07203e6i	−0.146905	+	0.321198i
$815$	−4.61382e7			−2.43314
$816$	9.72146e6	−	1.18228e7i	0.511100	−	0.621576i
$817$	−1.75613e7			−0.920452
$818$	−8.00660e6	+	1.75059e7i	−0.418374	+	0.914747i
$819$	−3.72498e6	−	7.07599e6i	−0.194050	−	0.368619i
$820$	1.73688e7	−	1.50159e7i	0.902061	−	0.779863i
$821$	−5.93570e6			−0.307336			−0.153668	−	0.988123i	$-0.549109\pi$
$821$	−5.93570e6			−0.307336			−0.153668	+	0.988123i	$0.549109\pi$
$822$	−1.16299e6	+	793459.i	−0.0600341	+	0.0409586i
$823$			2.50579e7i			1.28957i	0.764363	+	0.644786i	$0.223054\pi$
$823$			2.50579e7i			1.28957i	−0.764363	+	0.644786i	$0.776946\pi$
$824$	4.42666e6	+	1.51706e7i	0.227121	+	0.778369i
$825$	6.30044e6	+	3.80341e6i	0.322282	+	0.194553i
$826$	5.41329e6	−	1.18358e7i	0.276065	−	0.603597i
$827$		−	1.56538e7i		−	0.795895i	−0.917408	−	0.397947i	$-0.869723\pi$
$827$		−	1.56538e7i		−	0.795895i	0.917408	−	0.397947i	$-0.130277\pi$
$828$	−6.07557e6	+	1.55094e7i	−0.307972	+	0.786173i
$829$			3.02149e6i			0.152698i	0.997081	+	0.0763492i	$0.0243264\pi$
$829$			3.02149e6i			0.152698i	−0.997081	+	0.0763492i	$0.975674\pi$
$830$	4.87464e7	+	2.22949e7i	2.45611	+	1.12334i
$831$	1.84220e7	+	1.11209e7i	0.925411	+	0.558647i
$832$	4.72235e6	+	7.40302e6i	0.236510	+	0.370767i
$833$		−	1.65569e6i		−	0.0826738i
$834$	−8.31472e6	−	1.21871e7i	−0.413935	−	0.606716i
$835$	2.47354e7			1.22773
$836$	−3.74361e6	+	3.23648e6i	−0.185257	+	0.160161i
$837$	−118641.	+	2.02388e6i	−0.00585359	+	0.0998553i
$838$	6.47789e6	+	2.96277e6i	0.318657	+	0.145743i
$839$	3.35142e7			1.64371			0.821853	−	0.569700i	$-0.192941\pi$
$839$	3.35142e7			1.64371			0.821853	+	0.569700i	$0.192941\pi$
$840$	3.21384e7	+	8.52224e6i	1.57154	+	0.416731i
$841$	−1.85123e7			−0.902548
$842$	1.97650e6	+	903983.i	0.0960764	+	0.0439420i
$843$	2.56904e7	+	1.55086e7i	1.24509	+	0.751629i
$844$	−1.77653e7	−	2.05490e7i	−0.858455	−	0.992968i
$845$	−2.87355e7			−1.38445
$846$	5.73614e6	−	319262.i	0.275546	−	0.0153363i
$847$		−	1.90373e7i		−	0.911795i
$848$	3.53807e6	−	2.42202e7i	0.168957	−	1.15661i
$849$	−8.82560e6	+	1.46198e7i	−0.420218	+	0.696101i
$850$	2.99990e7	+	1.37205e7i	1.42416	+	0.651363i
$851$		−	3.25694e7i		−	1.54165i
$852$	1.68902e7	−	2.89506e6i	0.797143	−	0.136634i
$853$			2.84777e7i			1.34009i	0.742322	+	0.670043i	$0.233724\pi$
$853$			2.84777e7i			1.34009i	−0.742322	+	0.670043i	$0.766276\pi$
$854$	−3.59131e6	+	7.85216e6i	−0.168503	+	0.368421i
$855$	−2.16360e7	−	4.11000e7i	−1.01219	−	1.92277i
$856$	3.40786e6	+	1.16791e7i	0.158963	+	0.544784i
$857$		−	1.17081e7i		−	0.544547i	−0.962220	−	0.272274i	$-0.912224\pi$
$857$		−	1.17081e7i		−	0.544547i	0.962220	−	0.272274i	$-0.0877756\pi$
$858$	−1.03386e6	−	1.51536e6i	−0.0479451	−	0.0702744i
$859$	−3.97251e7			−1.83689			−0.918444	−	0.395552i	$-0.870553\pi$
$859$	−3.97251e7			−1.83689			−0.918444	+	0.395552i	$0.870553\pi$
$860$	1.77024e7	+	2.04762e7i	0.816178	+	0.944068i
$861$	−7.39791e6	+	1.22548e7i	−0.340096	+	0.563377i
$862$	−1.41695e7	+	3.09807e7i	−0.649510	+	1.42011i
$863$	6.93805e6			0.317111			0.158555	−	0.987350i	$-0.449316\pi$
$863$	6.93805e6			0.317111			0.158555	+	0.987350i	$0.449316\pi$
$864$	1.76968e7	+	1.29728e7i	0.806511	+	0.591219i
$865$	−5.98339e7			−2.71899
$866$	−1.50550e7	+	3.29168e7i	−0.682160	+	1.49150i
$867$	4.03122e6	−	6.67780e6i	0.182133	−	0.301707i
$868$	1.37550e6	+	1.59103e6i	0.0619669	+	0.0716767i
$869$	3.33183e6			0.149669
$870$	−6.74177e6	−	9.88159e6i	−0.301978	−	0.442618i
$871$			3.59587e6i			0.160605i
$872$	−1.08504e7	−	3.71856e7i	−0.483233	−	1.65609i
$873$	5.54904e6	+	1.05410e7i	0.246424	+	0.468108i
$874$	1.00401e7	−	2.19519e7i	0.444588	−	0.972062i
$875$			3.48358e7i			1.53817i
$876$	1.46454e7	−	2.51028e6i	0.644822	−	0.110525i
$877$			3.98910e6i			0.175136i	0.996159	+	0.0875681i	$0.0279095\pi$
$877$			3.98910e6i			0.175136i	−0.996159	+	0.0875681i	$0.972090\pi$
$878$	−2.14630e7	−	9.81646e6i	−0.939626	−	0.429753i
$879$	9.74605e6	−	1.61446e7i	0.425458	−	0.704781i
$880$	7.54736e6	+	1.10251e6i	0.328540	+	0.0479930i
$881$		−	4.52952e7i		−	1.96613i	−0.183257	−	0.983065i	$-0.558664\pi$
$881$		−	4.52952e7i		−	1.96613i	0.183257	−	0.983065i	$-0.441336\pi$
$882$	2.36985e6	−	131901.i	0.102577	−	0.00570921i
$883$	3.36305e6			0.145155			0.0725774	−	0.997363i	$-0.476878\pi$
$883$	3.36305e6			0.145155			0.0725774	+	0.997363i	$0.476878\pi$
$884$	−5.37768e6	−	6.22032e6i	−0.231454	−	0.267721i
$885$	2.39904e7	+	1.44824e7i	1.02963	+	0.621560i
$886$	−1.14924e7	−	5.25621e6i	−0.491841	−	0.224951i
$887$	1.26548e7			0.540066			0.270033	−	0.962851i	$-0.412965\pi$
$887$	1.26548e7			0.540066			0.270033	+	0.962851i	$0.412965\pi$
$888$	−4.14708e7	−	1.09970e7i	−1.76486	−	0.467994i
$889$	3.79073e7			1.60867
$890$	1.77487e6	+	811764.i	0.0751089	+	0.0343522i
$891$	−3.77902e6	−	2.59465e6i	−0.159472	−	0.109492i
$892$	1.59893e7	−	1.38233e7i	0.672850	−	0.581702i
$893$	−8.32560e6			−0.349371
$894$	−1.89596e6	−	2.77896e6i	−0.0793388	−	0.116289i
$895$			5.72434e7i			2.38874i
$896$	2.25439e7	−	3.15063e6i	0.938123	−	0.131107i
$897$	7.66054e6	+	4.62447e6i	0.317891	+	0.191903i
$898$	2.09118e7	+	9.56437e6i	0.865370	+	0.395790i
$899$		−	756679.i		−	0.0312257i
$900$	−1.72487e7	+	4.40316e7i	−0.709825	+	1.81200i
$901$			2.29209e7i			0.940632i
$902$	−1.36584e6	+	2.98631e6i	−0.0558962	+	0.122213i
$903$	−1.44472e7	−	8.72143e6i	−0.589611	−	0.355933i
$904$	−1.02372e7	−	3.50840e7i	−0.416639	−	1.42787i
$905$			6.58829e7i			2.67394i
$906$	2.23553e7	−	1.52520e7i	0.904814	−	0.617314i
$907$	4.82723e7			1.94841			0.974204	−	0.225671i	$-0.0724574\pi$
$907$	4.82723e7			1.94841			0.974204	+	0.225671i	$0.0724574\pi$
$908$	−1.67495e7	+	1.44805e7i	−0.674197	+	0.582866i
$909$	−6.22130e6	−	1.18180e7i	−0.249730	−	0.474390i
$910$	7.42911e6	−	1.62433e7i	0.297395	−	0.650234i
$911$	−2.04653e7			−0.817001			−0.408501	−	0.912758i	$-0.633948\pi$
$911$	−2.04653e7			−0.817001			−0.408501	+	0.912758i	$0.633948\pi$
$912$	−2.45616e7	−	2.01961e7i	−0.977842	−	0.804045i
$913$	−7.66656e6			−0.304385
$914$	1.21736e7	−	2.66168e7i	0.482008	−	1.05388i
$915$	−1.59159e7	−	9.60800e6i	−0.628460	−	0.379385i
$916$	−1.89364e7	+	1.63711e7i	−0.745689	+	0.644674i
$917$	5.61497e6			0.220508
$918$	−1.81535e7	−	9.62500e6i	−0.710973	−	0.376959i
$919$		−	2.51001e6i		−	0.0980364i	−0.998798	−	0.0490182i	$-0.984391\pi$
$919$		−	2.51001e6i		−	0.0980364i	0.998798	−	0.0490182i	$-0.0156092\pi$
$920$	−3.57163e7	+	1.04217e7i	−1.39122	+	0.405947i
$921$	7.73753e6	−	1.28174e7i	0.300575	−	0.497910i
$922$	−9.24254e6	+	2.02082e7i	−0.358067	+	0.782889i
$923$		−	9.20581e6i		−	0.355679i
$924$	−4.68710e6	+	803390.i	−0.180603	+	0.0309561i
$925$		−	9.24655e7i		−	3.55325i
$926$	−3.28667e7	−	1.50321e7i	−1.25959	−	0.576092i
$927$	1.87721e7	−	9.88207e6i	0.717485	−	0.377701i
$928$	−6.87708e6	−	4.44706e6i	−0.262141	−	0.169513i
$929$		−	1.41318e7i		−	0.537228i	−0.963248	−	0.268614i	$-0.913434\pi$
$929$		−	1.41318e7i		−	0.537228i	0.963248	−	0.268614i	$-0.0865656\pi$
$930$	−3.74073e6	+	2.55213e6i	−0.141824	+	0.0967600i
$931$	−3.43967e6			−0.130059
$932$	2.65763e6	−	2.29761e6i	0.100220	−	0.0866436i
$933$	1.66156e7	−	2.75242e7i	0.624904	−	1.03517i
$934$	1.11365e6	+	509346.i	0.0417717	+	0.0191050i
$935$	−7.14249e6			−0.267190
$936$	8.47493e6	−	8.19279e6i	0.316189	−	0.305662i
$937$	3.22481e7			1.19993			0.599964	−	0.800027i	$-0.295182\pi$
$937$	3.22481e7			1.19993			0.599964	+	0.800027i	$0.295182\pi$
$938$	8.47707e6	+	3.87712e6i	0.314585	+	0.143881i
$939$	−1.91417e7	+	3.17086e7i	−0.708461	+	1.17358i
$940$	8.39248e6	+	9.70752e6i	0.309792	+	0.358335i
$941$	−7.20257e6			−0.265163			−0.132582	−	0.991172i	$-0.542327\pi$
$941$	−7.20257e6			−0.265163			−0.132582	+	0.991172i	$0.542327\pi$
$942$	−5.86300e6	+	4.00006e6i	−0.215275	+	0.146872i
$943$		−	1.60181e7i		−	0.586586i
$944$	1.89836e7	+	2.77311e6i	0.693343	+	0.101283i
$945$	2.61197e6	−	4.45570e7i	0.0951454	−	1.62307i
$946$	−3.52058e6	−	1.61019e6i	−0.127905	−	0.0584992i
$947$			2.54136e7i			0.920855i	0.887697	+	0.460427i	$0.152304\pi$
$947$			2.54136e7i			0.920855i	−0.887697	+	0.460427i	$0.847696\pi$
$948$	3.61690e6	+	2.11015e7i	0.130712	+	0.762594i
$949$		−	7.98228e6i		−	0.287714i
$950$	2.85040e7	−	6.23222e7i	1.02470	−	2.24044i
$951$	−1.33016e7	+	2.20344e7i	−0.476927	+	0.790041i
$952$	−2.04624e7	+	5.97074e6i	−0.731752	+	0.213519i
$953$			582665.i			0.0207820i	0.999946	+	0.0103910i	$0.00330761\pi$
$953$			582665.i			0.0207820i	−0.999946	+	0.0103910i	$0.996692\pi$
$954$	−3.28074e7	+	1.82599e6i	−1.16708	+	0.0649573i
$955$	−6.45718e7			−2.29105
$956$	1.59548e7	+	1.84548e7i	0.564607	+	0.653077i
$957$	1.46472e6	+	884211.i	0.0516980	+	0.0312087i
$958$	1.32299e7	−	2.89263e7i	0.465739	−	1.01831i
$959$	1.96062e6			0.0688410
$960$	1.21053e6	+	4.89967e7i	0.0423934	+	1.71589i
$961$	2.83427e7			0.989995
$962$	−9.58640e6	+	2.09600e7i	−0.333978	+	0.730221i
$963$	1.44516e7	−	7.60770e6i	0.502171	−	0.264355i
$964$	1.53852e7	+	1.77959e7i	0.533224	+	0.616777i
$965$	3.37577e7			1.16696
$966$	1.91617e7	−	1.30731e7i	0.660679	−	0.450751i
$967$		−	1.08963e7i		−	0.374727i	−0.982291	−	0.187363i	$-0.940006\pi$
$967$		−	1.08963e7i		−	0.374727i	0.982291	−	0.187363i	$-0.0599942\pi$
$968$	2.69390e7	−	7.86057e6i	0.924046	−	0.269629i
$969$	2.54919e7	+	1.53888e7i	0.872155	+	0.526497i
$970$	−1.10670e7	+	2.41973e7i	−0.377661	+	0.825730i
$971$			3.13080e7i			1.06563i	0.846231	+	0.532816i	$0.178866\pi$
$971$			3.13080e7i			1.06563i	−0.846231	+	0.532816i	$0.821134\pi$
$972$	1.23304e7	−	2.67504e7i	0.418611	−	0.908166i
$973$			2.05455e7i			0.695720i
$974$	−1.58892e7	−	7.26719e6i	−0.536668	−	0.245453i
$975$	2.17485e7	+	1.31290e7i	0.732686	+	0.442304i
$976$	−1.25942e7	−	1.83975e6i	−0.423200	−	0.0618208i
$977$			3.13362e7i			1.05029i	0.851012	+	0.525146i	$0.175989\pi$
$977$			3.13362e7i			1.05029i	−0.851012	+	0.525146i	$0.824011\pi$
$978$	2.38974e7	+	3.50270e7i	0.798920	+	1.17100i
$979$	−279142.			−0.00930824
$980$	3.46730e6	+	4.01060e6i	0.115326	+	0.133396i
$981$	−4.60133e7	+	2.42225e7i	−1.52655	+	0.803613i
$982$	−6.30044e6	−	2.88161e6i	−0.208493	−	0.0953577i
$983$	3.59771e7			1.18752			0.593762	−	0.804641i	$-0.297642\pi$
$983$	3.59771e7			1.18752			0.593762	+	0.804641i	$0.297642\pi$
$984$	−2.03960e7	−	5.40847e6i	−0.671517	−	0.178068i
$985$	3.39949e6			0.111641
$986$	6.97411e6	+	3.18972e6i	0.228453	+	0.104487i
$987$	−6.84927e6	−	4.13473e6i	−0.223796	−	0.135100i
$988$	−1.29226e7	+	1.11720e7i	−0.421169	+	0.364115i
$989$	1.88838e7			0.613902
$990$	−569006.	−	1.02233e7i	−0.0184514	−	0.331514i
$991$		−	4.45701e7i		−	1.44165i	−0.693118	−	0.720824i	$-0.743764\pi$
$991$		−	4.45701e7i		−	1.44165i	0.693118	−	0.720824i	$-0.256236\pi$
$992$	−1.68346e6	+	2.60336e6i	−0.0543154	+	0.0839952i
$993$	7.85084e6	−	1.30051e7i	0.252664	−	0.418543i
$994$	−2.17022e7	−	9.92585e6i	−0.696688	−	0.318641i
$995$		−	4.06609e7i		−	1.30203i
$996$	−8.32251e6	−	4.85548e7i	−0.265831	−	1.55090i
$997$		−	1.25671e7i		−	0.400404i	−0.979755	−	0.200202i	$-0.935840\pi$
$997$		−	1.25671e7i		−	0.400404i	0.979755	−	0.200202i	$-0.0641598\pi$
$998$	−1.09355e7	+	2.39097e7i	−0.347545	+	0.759884i
$999$	−3.37044e6	+	5.74957e7i	−0.106850	+	1.82273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	24.6.f.b.11.8	yes	16
3.2	odd	2	inner	24.6.f.b.11.9	yes	16
4.3	odd	2		96.6.f.b.47.7		16
8.3	odd	2	inner	24.6.f.b.11.10	yes	16
8.5	even	2		96.6.f.b.47.8		16
12.11	even	2		96.6.f.b.47.6		16
24.5	odd	2		96.6.f.b.47.5		16
24.11	even	2	inner	24.6.f.b.11.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.6.f.b.11.7	✓	16	24.11	even	2	inner
24.6.f.b.11.8	yes	16	1.1	even	1	trivial
24.6.f.b.11.9	yes	16	3.2	odd	2	inner
24.6.f.b.11.10	yes	16	8.3	odd	2	inner
96.6.f.b.47.5		16	24.5	odd	2
96.6.f.b.47.6		16	12.11	even	2
96.6.f.b.47.7		16	4.3	odd	2
96.6.f.b.47.8		16	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	24.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.35284 + 5.14433i) q^{2} +(8.05622 - 13.3453i) q^{3} +(-20.9283 - 24.2076i) q^{4} -95.9504 q^{5} +(49.6977 + 72.8433i) q^{6} -122.802i q^{7} +(173.773 - 50.7054i) q^{8} +(-113.195 - 215.026i) q^{9} +O(q^{10})\)	\(q+(-2.35284 + 5.14433i) q^{2} +(8.05622 - 13.3453i) q^{3} +(-20.9283 - 24.2076i) q^{4} -95.9504 q^{5} +(49.6977 + 72.8433i) q^{6} -122.802i q^{7} +(173.773 - 50.7054i) q^{8} +(-113.195 - 215.026i) q^{9} +(225.756 - 493.600i) q^{10} +77.6307i q^{11} +(-491.661 + 84.2728i) q^{12} +267.974i q^{13} +(631.734 + 288.934i) q^{14} +(-772.997 + 1280.49i) q^{15} +(-148.014 + 1013.25i) q^{16} -958.891i q^{17} +(1372.49 - 76.3900i) q^{18} -1992.07 q^{19} +(2008.08 + 2322.73i) q^{20} +(-1638.83 - 989.320i) q^{21} +(-399.358 - 182.653i) q^{22} +2142.09 q^{23} +(723.272 - 2727.54i) q^{24} +6081.47 q^{25} +(-1378.55 - 630.500i) q^{26} +(-3781.50 - 221.674i) q^{27} +(-2972.74 + 2570.03i) q^{28} +1413.81 q^{29} +(-4768.51 - 6989.34i) q^{30} -535.205i q^{31} +(-4864.22 - 3145.44i) q^{32} +(1036.01 + 625.410i) q^{33} +(4932.85 + 2256.12i) q^{34} +11782.9i q^{35} +(-2836.28 + 7240.28i) q^{36} -15204.5i q^{37} +(4687.03 - 10247.9i) q^{38} +(3576.19 + 2158.85i) q^{39} +(-16673.6 + 4865.20i) q^{40} -7477.78i q^{41} +(8945.29 - 6102.97i) q^{42} +8815.59 q^{43} +(1879.25 - 1624.68i) q^{44} +(10861.1 + 20631.8i) q^{45} +(-5040.01 + 11019.6i) q^{46} +4179.37 q^{47} +(12329.6 + 10138.2i) q^{48} +1726.68 q^{49} +(-14308.7 + 31285.1i) q^{50} +(-12796.7 - 7725.03i) q^{51} +(6487.00 - 5608.23i) q^{52} -23903.6 q^{53} +(10037.6 - 18931.7i) q^{54} -7448.70i q^{55} +(-6226.72 - 21339.6i) q^{56} +(-16048.6 + 26584.8i) q^{57} +(-3326.47 + 7273.11i) q^{58} -18735.4i q^{59} +(47175.0 - 8086.00i) q^{60} +12429.5i q^{61} +(2753.27 + 1259.25i) q^{62} +(-26405.6 + 13900.5i) q^{63} +(27625.9 - 17622.4i) q^{64} -25712.2i q^{65} +(-5654.88 + 3858.07i) q^{66} +13418.7 q^{67} +(-23212.4 + 20067.9i) q^{68} +(17257.2 - 28586.9i) q^{69} +(-60615.1 - 27723.3i) q^{70} -34353.4 q^{71} +(-30573.1 - 31626.0i) q^{72} -29787.6 q^{73} +(78216.8 + 35773.7i) q^{74} +(48993.7 - 81159.1i) q^{75} +(41690.6 + 48223.3i) q^{76} +9533.21 q^{77} +(-19520.1 + 13317.7i) q^{78} -42918.9i q^{79} +(14202.0 - 97221.3i) q^{80} +(-33422.9 + 48679.5i) q^{81} +(38468.2 + 17594.0i) q^{82} +98756.8i q^{83} +(10348.9 + 60376.9i) q^{84} +92005.9i q^{85} +(-20741.7 + 45350.3i) q^{86} +(11390.0 - 18867.7i) q^{87} +(3936.30 + 13490.1i) q^{88} +3595.76i q^{89} +(-131691. + 7329.65i) q^{90} +32907.7 q^{91} +(-44830.3 - 51854.9i) q^{92} +(-7142.48 - 4311.73i) q^{93} +(-9833.38 + 21500.0i) q^{94} +191140. q^{95} +(-81164.1 + 39574.1i) q^{96} -49022.1 q^{97} +(-4062.60 + 8882.60i) q^{98} +(16692.6 - 8787.39i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 52 q^{4} + 264 q^{6} + 480 q^{9}+O(q^{10}) \) 16 * q + 52 * q^4 + 264 * q^6 + 480 * q^9	\( 16 q + 52 q^{4} + 264 q^{6} + 480 q^{9} + 168 q^{10} - 156 q^{12} - 2264 q^{16} + 24 q^{18} - 8128 q^{19} + 7808 q^{22} - 7992 q^{24} + 12496 q^{25} - 5184 q^{27} - 6864 q^{28} + 6672 q^{30} + 23472 q^{33} + 26480 q^{34} - 8196 q^{36} + 5856 q^{40} - 16728 q^{42} - 45760 q^{43} - 25056 q^{46} - 26184 q^{48} - 33392 q^{49} + 36480 q^{51} - 54240 q^{52} + 14616 q^{54} - 10128 q^{57} + 58056 q^{58} + 105456 q^{60} + 225520 q^{64} - 149496 q^{66} + 183296 q^{67} - 199248 q^{70} - 172848 q^{72} - 153376 q^{73} + 50880 q^{75} + 4856 q^{76} + 251664 q^{78} - 148464 q^{81} + 111872 q^{82} + 317856 q^{84} + 151088 q^{88} - 468792 q^{90} - 32832 q^{91} - 523200 q^{94} - 392496 q^{96} + 178496 q^{97} - 91968 q^{99}+O(q^{100}) \) 16 * q + 52 * q^4 + 264 * q^6 + 480 * q^9 + 168 * q^10 - 156 * q^12 - 2264 * q^16 + 24 * q^18 - 8128 * q^19 + 7808 * q^22 - 7992 * q^24 + 12496 * q^25 - 5184 * q^27 - 6864 * q^28 + 6672 * q^30 + 23472 * q^33 + 26480 * q^34 - 8196 * q^36 + 5856 * q^40 - 16728 * q^42 - 45760 * q^43 - 25056 * q^46 - 26184 * q^48 - 33392 * q^49 + 36480 * q^51 - 54240 * q^52 + 14616 * q^54 - 10128 * q^57 + 58056 * q^58 + 105456 * q^60 + 225520 * q^64 - 149496 * q^66 + 183296 * q^67 - 199248 * q^70 - 172848 * q^72 - 153376 * q^73 + 50880 * q^75 + 4856 * q^76 + 251664 * q^78 - 148464 * q^81 + 111872 * q^82 + 317856 * q^84 + 151088 * q^88 - 468792 * q^90 - 32832 * q^91 - 523200 * q^94 - 392496 * q^96 + 178496 * q^97 - 91968 * q^99

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