LMFDB - Embedded newform 21.6.e.c.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(4,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.e (of order $3$, degree $2$, 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:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$-4.61193 + 7.98809i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.6.e.c.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.11193 + 8.85412i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(-11.8764 + 20.5705i) q^{5} +92.0147 q^{6} +(30.6840 - 125.958i) q^{7} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-5.11193 + 8.85412i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(-11.8764 + 20.5705i) q^{5} +92.0147 q^{6} +(30.6840 - 125.958i) q^{7} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-121.423 - 210.310i) q^{10} +(-232.763 - 403.157i) q^{11} +(-326.372 + 565.293i) q^{12} -1019.30 q^{13} +(958.395 + 915.570i) q^{14} +213.775 q^{15} +(-957.660 + 1658.72i) q^{16} +(-280.878 - 486.496i) q^{17} +(-414.066 - 717.183i) q^{18} +(693.789 - 1201.68i) q^{19} +1722.72 q^{20} +(-1119.83 + 327.654i) q^{21} +4759.47 q^{22} +(-2056.81 + 3562.50i) q^{23} +(-1864.55 - 3229.49i) q^{24} +(1280.40 + 2217.72i) q^{25} +(5210.59 - 9025.00i) q^{26} +729.000 q^{27} +(-9024.20 + 2640.42i) q^{28} -2381.37 q^{29} +(-1092.80 + 1892.79i) q^{30} +(-1475.33 - 2555.34i) q^{31} +(-3161.47 - 5475.84i) q^{32} +(-2094.87 + 3628.42i) q^{33} +5743.32 q^{34} +(2226.61 + 2127.12i) q^{35} +5874.70 q^{36} +(4954.48 - 8581.40i) q^{37} +(7093.20 + 12285.8i) q^{38} +(4586.85 + 7944.66i) q^{39} +(-4920.92 + 8523.28i) q^{40} -4477.13 q^{41} +(2823.38 - 11590.0i) q^{42} +5181.48 q^{43} +(-16881.6 + 29239.9i) q^{44} +(-961.989 - 1666.21i) q^{45} +(-21028.5 - 36422.5i) q^{46} +(1560.80 - 2703.38i) q^{47} +17237.9 q^{48} +(-14924.0 - 7729.82i) q^{49} -26181.3 q^{50} +(-2527.91 + 4378.46i) q^{51} +(36963.5 + 64022.6i) q^{52} +(-570.499 - 988.133i) q^{53} +(-3726.59 + 6454.65i) q^{54} +11057.6 q^{55} +(12713.7 - 52190.0i) q^{56} -12488.2 q^{57} +(12173.4 - 21085.0i) q^{58} +(-13748.5 - 23813.2i) q^{59} +(-7752.26 - 13427.3i) q^{60} +(10551.8 - 18276.2i) q^{61} +30167.1 q^{62} +(7593.03 + 7253.74i) q^{63} +3354.67 q^{64} +(12105.6 - 20967.6i) q^{65} +(-21417.6 - 37096.4i) q^{66} +(27794.2 + 48141.0i) q^{67} +(-20371.3 + 35284.2i) q^{68} +37022.6 q^{69} +(-30216.0 + 8841.02i) q^{70} -6076.90 q^{71} +(-16780.9 + 29065.4i) q^{72} +(8389.82 + 14531.6i) q^{73} +(50653.8 + 87735.0i) q^{74} +(11523.6 - 19959.5i) q^{75} -100637. q^{76} +(-57923.1 + 16947.9i) q^{77} -93790.5 q^{78} +(2422.63 - 4196.12i) q^{79} +(-22747.1 - 39399.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(22886.7 - 39641.0i) q^{82} +60145.4 q^{83} +(61189.0 + 58454.8i) q^{84} +13343.3 q^{85} +(-26487.4 + 45877.5i) q^{86} +(10716.2 + 18561.0i) q^{87} +(-96443.9 - 167046. i) q^{88} +(31248.7 - 54124.4i) q^{89} +19670.5 q^{90} +(-31276.2 + 128389. i) q^{91} +298349. q^{92} +(-13277.9 + 22998.1i) q^{93} +(15957.4 + 27639.0i) q^{94} +(16479.4 + 28543.2i) q^{95} +(-28453.3 + 49282.5i) q^{96} -63653.8 q^{97} +(144731. - 92624.4i) q^{98} +37707.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−5.11193	+	8.85412i	−0.903669	+	1.56520i	−0.0809760	+	0.996716i	$0.525804\pi$
$2$	−5.11193	+	8.85412i	−0.903669	+	1.56520i	−0.822693	+	0.568485i	$0.807530\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	−36.2636	−	62.8104i	−1.13324	−	1.96282i
$5$	−11.8764	+	20.5705i	−0.212452	+	0.367977i	−0.952481	−	0.304597i	$-0.901478\pi$
$5$	−11.8764	+	20.5705i	−0.212452	+	0.367977i	0.740030	+	0.672574i	$0.234811\pi$
$6$	92.0147			1.04347
$7$	30.6840	−	125.958i	0.236683	−	0.971587i
$7$	30.6840	−	125.958i	0.236683	−	0.971587i
$8$	414.344			2.28895
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−121.423	−	210.310i	−0.383972	−	0.665059i
$11$	−232.763	−	403.157i	−0.580006	−	1.00460i	−0.995478	−	0.0949934i	$-0.969717\pi$
$11$	−232.763	−	403.157i	−0.580006	−	1.00460i	0.415472	−	0.909606i	$-0.363616\pi$
$12$	−326.372	+	565.293i	−0.654275	+	1.13324i
$13$	−1019.30			−1.67280			−0.836399	−	0.548121i	$-0.815343\pi$
$13$	−1019.30			−1.67280			−0.836399	+	0.548121i	$0.815343\pi$
$14$	958.395	+	915.570i	1.30685	+	1.24845i
$15$	213.775			0.245318
$16$	−957.660	+	1658.72i	−0.935215	+	1.61984i
$17$	−280.878	−	486.496i	−0.235720	−	0.408279i	0.723762	−	0.690050i	$-0.242411\pi$
$17$	−280.878	−	486.496i	−0.235720	−	0.408279i	−0.959482	+	0.281771i	$0.909078\pi$
$18$	−414.066	−	717.183i	−0.301223	−	0.521734i
$19$	693.789	−	1201.68i	0.440903	−	0.763667i	−0.556853	−	0.830611i	$-0.687991\pi$
$19$	693.789	−	1201.68i	0.440903	−	0.763667i	0.997757	+	0.0669438i	$0.0213248\pi$
$20$	1722.72			0.963032
$21$	−1119.83	+	327.654i	−0.554118	+	0.162131i
$22$	4759.47			2.09653
$23$	−2056.81	+	3562.50i	−0.810727	+	1.40422i	0.101630	+	0.994822i	$0.467594\pi$
$23$	−2056.81	+	3562.50i	−0.810727	+	1.40422i	−0.912356	+	0.409397i	$0.865739\pi$
$24$	−1864.55	−	3229.49i	−0.660762	−	1.14447i
$25$	1280.40	+	2217.72i	0.409729	+	0.709671i
$26$	5210.59	−	9025.00i	1.51166	−	2.61827i
$27$	729.000			0.192450
$28$	−9024.20	+	2640.42i	−2.17527	+	0.636471i
$29$	−2381.37			−0.525814			−0.262907	−	0.964821i	$-0.584681\pi$
$29$	−2381.37			−0.525814			−0.262907	+	0.964821i	$0.584681\pi$
$30$	−1092.80	+	1892.79i	−0.221686	+	0.383972i
$31$	−1475.33	−	2555.34i	−0.275730	−	0.477579i	0.694589	−	0.719407i	$-0.255586\pi$
$31$	−1475.33	−	2555.34i	−0.275730	−	0.477579i	−0.970319	+	0.241828i	$0.922253\pi$
$32$	−3161.47	−	5475.84i	−0.545776	−	0.945313i
$33$	−2094.87	+	3628.42i	−0.334866	+	0.580006i
$34$	5743.32			0.852051
$35$	2226.61	+	2127.12i	0.307238	+	0.293509i
$36$	5874.70			0.755491
$37$	4954.48	−	8581.40i	0.594968	−	1.03051i	−0.398584	−	0.917132i	$-0.630498\pi$
$37$	4954.48	−	8581.40i	0.594968	−	1.03051i	0.993551	−	0.113382i	$-0.0361685\pi$
$38$	7093.20	+	12285.8i	0.796862	+	1.38021i
$39$	4586.85	+	7944.66i	0.482895	+	0.836399i
$40$	−4920.92	+	8523.28i	−0.486291	+	0.842280i
$41$	−4477.13			−0.415949			−0.207974	−	0.978134i	$-0.566687\pi$
$41$	−4477.13			−0.415949			−0.207974	+	0.978134i	$0.566687\pi$
$42$	2823.38	−	11590.0i	0.246971	−	1.01382i
$43$	5181.48			0.427349			0.213675	−	0.976905i	$-0.431457\pi$
$43$	5181.48			0.427349			0.213675	+	0.976905i	$0.431457\pi$
$44$	−16881.6	+	29239.9i	−1.31457	+	2.27690i
$45$	−961.989	−	1666.21i	−0.0708172	−	0.122659i
$46$	−21028.5	−	36422.5i	−1.46526	−	2.53790i
$47$	1560.80	−	2703.38i	0.103063	−	0.178510i	−0.809882	−	0.586592i	$-0.800469\pi$
$47$	1560.80	−	2703.38i	0.103063	−	0.178510i	0.912945	+	0.408082i	$0.133802\pi$
$48$	17237.9			1.07989
$49$	−14924.0	−	7729.82i	−0.887962	−	0.459917i
$50$	−26181.3			−1.48104
$51$	−2527.91	+	4378.46i	−0.136093	+	0.235720i
$52$	36963.5	+	64022.6i	1.89568	+	3.28341i
$53$	−570.499	−	988.133i	−0.0278975	−	0.0483198i	0.851740	−	0.523965i	$-0.175548\pi$
$53$	−570.499	−	988.133i	−0.0278975	−	0.0483198i	−0.879637	+	0.475645i	$0.842215\pi$
$54$	−3726.59	+	6454.65i	−0.173911	+	0.301223i
$55$	11057.6			0.492893
$56$	12713.7	−	52190.0i	0.541755	−	2.22391i
$57$	−12488.2			−0.509111
$58$	12173.4	−	21085.0i	0.475162	−	0.823005i
$59$	−13748.5	−	23813.2i	−0.514194	−	0.890610i	−0.999864	−	0.0164678i	$-0.994758\pi$
$59$	−13748.5	−	23813.2i	−0.514194	−	0.890610i	0.485671	−	0.874142i	$-0.338575\pi$
$60$	−7752.26	−	13427.3i	−0.278003	−	0.481516i
$61$	10551.8	−	18276.2i	0.363078	−	0.628870i	−0.625387	−	0.780314i	$-0.715059\pi$
$61$	10551.8	−	18276.2i	0.363078	−	0.628870i	0.988466	+	0.151444i	$0.0483924\pi$
$62$	30167.1			0.996676
$63$	7593.03	+	7253.74i	0.241026	+	0.230256i
$64$	3354.67			0.102376
$65$	12105.6	−	20967.6i	0.355389	−	0.615551i
$66$	−21417.6	−	37096.4i	−0.605217	−	1.04827i
$67$	27794.2	+	48141.0i	0.756428	+	1.31017i	0.944661	+	0.328047i	$0.106390\pi$
$67$	27794.2	+	48141.0i	0.756428	+	1.31017i	−0.188234	+	0.982124i	$0.560276\pi$
$68$	−20371.3	+	35284.2i	−0.534253	+	0.925353i
$69$	37022.6			0.936146
$70$	−30216.0	+	8841.02i	−0.737043	+	0.215654i
$71$	−6076.90			−0.143066			−0.0715330	−	0.997438i	$-0.522789\pi$
$71$	−6076.90			−0.143066			−0.0715330	+	0.997438i	$0.522789\pi$
$72$	−16780.9	+	29065.4i	−0.381491	+	0.660762i
$73$	8389.82	+	14531.6i	0.184266	+	0.319158i	0.943329	−	0.331859i	$-0.107676\pi$
$73$	8389.82	+	14531.6i	0.184266	+	0.319158i	−0.759063	+	0.651017i	$0.774343\pi$
$74$	50653.8	+	87735.0i	1.07531	+	1.86249i
$75$	11523.6	−	19959.5i	0.236557	−	0.409729i
$76$	−100637.			−1.99859
$77$	−57923.1	+	16947.9i	−1.11333	+	0.325754i
$78$	−93790.5			−1.74551
$79$	2422.63	−	4196.12i	0.0436737	−	0.0756450i	−0.843362	−	0.537345i	$-0.819427\pi$
$79$	2422.63	−	4196.12i	0.0436737	−	0.0756450i	0.887036	+	0.461700i	$0.152760\pi$
$80$	−22747.1	−	39399.2i	−0.397376	−	0.688275i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	22886.7	−	39641.0i	0.375880	−	0.651043i
$83$	60145.4			0.958313			0.479156	−	0.877730i	$-0.340943\pi$
$83$	60145.4			0.958313			0.479156	+	0.877730i	$0.340943\pi$
$84$	61189.0	+	58454.8i	0.946182	+	0.903903i
$85$	13343.3			0.200316
$86$	−26487.4	+	45877.5i	−0.386183	+	0.668888i
$87$	10716.2	+	18561.0i	0.151790	+	0.262907i
$88$	−96443.9	−	167046.i	−1.32760	−	2.29947i
$89$	31248.7	−	54124.4i	0.418174	−	0.724299i	−0.577582	−	0.816333i	$-0.696004\pi$
$89$	31248.7	−	54124.4i	0.418174	−	0.724299i	0.995756	+	0.0920340i	$0.0293368\pi$
$90$	19670.5			0.255981
$91$	−31276.2	+	128389.i	−0.395923	+	1.62527i
$92$	298349.			3.67498
$93$	−13277.9	+	22998.1i	−0.159193	+	0.275730i
$94$	15957.4	+	27639.0i	0.186269	+	0.322628i
$95$	16479.4	+	28543.2i	0.187341	+	0.324485i
$96$	−28453.3	+	49282.5i	−0.315104	+	0.545776i
$97$	−63653.8			−0.686903			−0.343451	−	0.939170i	$-0.611596\pi$
$97$	−63653.8			−0.686903			−0.343451	+	0.939170i	$0.611596\pi$
$98$	144731.	−	92624.4i	1.52229	−	0.974227i
$99$	37707.6			0.386670
$100$	92863.9	−	160845.i	0.928639	−	1.60845i
$101$	−92311.4	−	159888.i	−0.900434	−	1.55960i	−0.826932	−	0.562302i	$-0.809916\pi$
$101$	−92311.4	−	159888.i	−0.900434	−	1.55960i	−0.0735022	−	0.997295i	$-0.523418\pi$
$102$	−25844.9	−	44764.7i	−0.245966	−	0.426026i
$103$	−26021.9	+	45071.2i	−0.241683	+	0.418607i	−0.961194	−	0.275874i	$-0.911033\pi$
$103$	−26021.9	+	45071.2i	−0.241683	+	0.418607i	0.719511	+	0.694481i	$0.244366\pi$
$104$	−422341.			−3.82895
$105$	6559.49	−	26926.8i	0.0580627	−	0.238348i
$106$	11665.4			0.100840
$107$	−24088.9	+	41723.2i	−0.203403	+	0.352304i	−0.949623	−	0.313395i	$-0.898534\pi$
$107$	−24088.9	+	41723.2i	−0.203403	+	0.352304i	0.746220	+	0.665700i	$0.231867\pi$
$108$	−26436.2	−	45788.8i	−0.218092	−	0.377746i
$109$	18217.8	+	31554.1i	0.146869	+	0.254384i	0.930069	−	0.367386i	$-0.119747\pi$
$109$	18217.8	+	31554.1i	0.146869	+	0.254384i	−0.783200	+	0.621770i	$0.786414\pi$
$110$	−56525.4	+	97904.9i	−0.445412	+	0.771476i
$111$	−89180.6			−0.687010
$112$	179544.	+	171521.i	1.35247	+	1.29203i
$113$	−96711.1			−0.712492			−0.356246	−	0.934392i	$-0.615944\pi$
$113$	−96711.1			−0.712492			−0.356246	+	0.934392i	$0.615944\pi$
$114$	63838.8	−	110572.i	0.460068	−	0.796862i
$115$	−48855.0	−	84619.4i	−0.344480	−	0.596658i
$116$	86357.1	+	149575.i	0.595872	+	1.03208i
$117$	41281.6	−	71501.9i	0.278800	−	0.482895i
$118$	281126.			1.85864
$119$	−69896.6	+	20451.3i	−0.452469	+	0.132390i
$120$	88576.5			0.561520
$121$	−27831.7	+	48206.0i	−0.172813	+	0.299321i
$122$	107880.	+	186853.i	0.656206	+	1.13658i
$123$	20147.1	+	34895.7i	0.120074	+	0.207974i
$124$	−107001.	+	185332.i	−0.624935	+	1.08242i
$125$	−135054.			−0.773093
$126$	−103040.	+	30149.0i	−0.578204	+	0.169179i
$127$	23322.9			0.128314			0.0641568	−	0.997940i	$-0.479564\pi$
$127$	23322.9			0.128314			0.0641568	+	0.997940i	$0.479564\pi$
$128$	84018.4	−	145524.i	0.453262	−	0.785073i
$129$	−23316.7	−	40385.7i	−0.123365	−	0.213675i
$130$	123766.	+	214369.i	0.642308	+	1.11251i
$131$	169379.	−	293373.i	0.862345	−	1.49363i	−0.00731374	−	0.999973i	$-0.502328\pi$
$131$	169379.	−	293373.i	0.862345	−	1.49363i	0.869659	−	0.493653i	$-0.164339\pi$
$132$	303870.			1.51793
$133$	−130073.	−	124261.i	−0.637614	−	0.609123i
$134$	−568328.			−2.73424
$135$	−8657.90	+	14995.9i	−0.0408863	+	0.0708172i
$136$	−116380.	−	201576.i	−0.539550	−	0.934528i
$137$	31438.4	+	54452.9i	0.143106	+	0.247867i	0.928665	−	0.370920i	$-0.120958\pi$
$137$	31438.4	+	54452.9i	0.143106	+	0.247867i	−0.785559	+	0.618787i	$0.787624\pi$
$138$	−189257.	+	327802.i	−0.845967	+	1.46526i
$139$	211927.			0.930356			0.465178	−	0.885217i	$-0.345990\pi$
$139$	211927.			0.930356			0.465178	+	0.885217i	$0.345990\pi$
$140$	52860.2	−	216991.i	0.227934	−	0.935669i
$141$	−28094.3			−0.119007
$142$	31064.7	−	53805.6i	0.129284	−	0.223927i
$143$	237255.	+	410938.i	0.970233	+	1.68049i
$144$	−77570.5	−	134356.i	−0.311738	−	0.539947i
$145$	28282.2	−	48986.1i	0.111710	−	0.193488i
$146$	−171553.			−0.666062
$147$	6909.92	+	151105.i	0.0263742	+	0.576748i
$148$	−718668.			−2.69696
$149$	−70136.4	+	121480.i	−0.258808	+	0.448269i	−0.965923	−	0.258830i	$-0.916663\pi$
$149$	−70136.4	+	121480.i	−0.258808	+	0.448269i	0.707115	+	0.707099i	$0.249996\pi$
$150$	117816.	+	204063.i	0.427538	+	0.740518i
$151$	81995.7	+	142021.i	0.292650	+	0.506885i	0.974436	−	0.224667i	$-0.0721296\pi$
$151$	81995.7	+	142021.i	0.292650	+	0.506885i	−0.681785	+	0.731552i	$0.738796\pi$
$152$	287467.	−	497908.i	1.00920	−	1.74799i
$153$	45502.3			0.157147
$154$	146040.	−	599495.i	0.496214	−	2.03696i
$155$	70086.4			0.234317
$156$	332671.	−	576203.i	1.09447	−	1.89568i
$157$	−278272.	−	481981.i	−0.900990	−	1.56056i	−0.826212	−	0.563360i	$-0.809508\pi$
$157$	−278272.	−	481981.i	−0.900990	−	1.56056i	−0.0747781	−	0.997200i	$-0.523825\pi$
$158$	24768.6	+	42900.5i	0.0789331	+	0.136716i
$159$	−5134.49	+	8893.19i	−0.0161066	+	0.0278975i
$160$	150188.			0.463804
$161$	385615.	+	368384.i	1.17244	+	1.12005i
$162$	67078.7			0.200815
$163$	9863.32	−	17083.8i	0.0290773	−	0.0503634i	−0.851121	−	0.524970i	$-0.824076\pi$
$163$	9863.32	−	17083.8i	0.0290773	−	0.0503634i	0.880198	+	0.474607i	$0.157410\pi$
$164$	162357.	+	281210.i	0.471368	+	0.816434i
$165$	−49759.0	−	86185.1i	−0.142286	−	0.246446i
$166$	−307459.	+	532534.i	−0.865998	+	1.49995i
$167$	94776.2			0.262971			0.131486	−	0.991318i	$-0.458025\pi$
$167$	94776.2			0.262971			0.131486	+	0.991318i	$0.458025\pi$
$168$	−463993.	+	135761.i	−1.26835	+	0.371110i
$169$	667679.			1.79825
$170$	−68210.0	+	118143.i	−0.181020	+	0.313535i
$171$	56196.9	+	97335.9i	0.146968	+	0.254556i
$172$	−187899.	−	325451.i	−0.484288	−	0.838812i
$173$	−169420.	+	293445.i	−0.430379	+	0.745437i	−0.996906	−	0.0786055i	$-0.974953\pi$
$173$	−169420.	+	293445.i	−0.430379	+	0.745437i	0.566527	+	0.824043i	$0.308287\pi$
$174$	−219121.			−0.548670
$175$	318628.	−	93228.6i	0.786483	−	0.230120i
$176$	891631.			2.16972
$177$	−123737.	+	214319.i	−0.296870	+	0.514194i
$178$	319482.	+	553360.i	0.755782	+	1.30905i
$179$	−388096.	−	672203.i	−0.905330	−	1.56808i	−0.820473	−	0.571685i	$-0.806290\pi$
$179$	−388096.	−	672203.i	−0.905330	−	1.56808i	−0.0848573	−	0.996393i	$-0.527043\pi$
$180$	−69770.3	+	120846.i	−0.160505	+	0.278003i
$181$	−132697.			−0.301067			−0.150534	−	0.988605i	$-0.548099\pi$
$181$	−132697.			−0.301067			−0.150534	+	0.988605i	$0.548099\pi$
$182$	−976892.	−	933240.i	−2.18609	−	2.08841i
$183$	−189932.			−0.419247
$184$	−852226.	+	1.47610e6i	−1.85571	+	3.21418i
$185$	117683.	+	203833.i	0.252804	+	0.437869i
$186$	−135752.	−	235129.i	−0.287715	−	0.498338i
$187$	−130756.	+	226476.i	−0.273438	+	0.473608i
$188$	−226400.			−0.467178
$189$	22368.7	−	91823.6i	0.0455497	−	0.186982i
$190$	−336967.			−0.677178
$191$	−3318.71	+	5748.17i	−0.00658242	+	0.0114011i	−0.869298	−	0.494289i	$-0.835429\pi$
$191$	−3318.71	+	5748.17i	−0.00658242	+	0.0114011i	0.862715	+	0.505690i	$0.168762\pi$
$192$	−15096.0	−	26147.0i	−0.0295535	−	0.0511882i
$193$	−226295.	−	391954.i	−0.437302	−	0.757430i	0.560178	−	0.828372i	$-0.310733\pi$
$193$	−226295.	−	391954.i	−0.437302	−	0.757430i	−0.997480	+	0.0709425i	$0.977399\pi$
$194$	325394.	−	563598.i	0.620733	−	1.07514i
$195$	−217901.			−0.410368
$196$	55684.1	+	1.21769e6i	0.103536	+	2.26411i
$197$	816952.			1.49979			0.749896	−	0.661556i	$-0.230104\pi$
$197$	816952.			1.49979			0.749896	+	0.661556i	$0.230104\pi$
$198$	−192759.	+	333868.i	−0.349422	+	0.605217i
$199$	−403208.	−	698378.i	−0.721767	−	1.25014i	−0.960291	−	0.279000i	$-0.909997\pi$
$199$	−403208.	−	698378.i	−0.721767	−	1.25014i	0.238524	−	0.971137i	$-0.423336\pi$
$200$	530526.	+	918899.i	0.937847	+	1.62440i
$201$	250148.	−	433269.i	0.436724	−	0.756428i
$202$	1.88756e6			3.25478
$203$	−73070.2	+	299954.i	−0.124451	+	0.510874i
$204$	366684.			0.616902
$205$	53172.2	−	92096.9i	0.0883690	−	0.153060i
$206$	−266044.	−	460801.i	−0.436802	−	0.756564i
$207$	−166602.	−	288562.i	−0.270242	−	0.468073i
$208$	976143.	−	1.69073e6i	1.56443	−	2.70966i
$209$	−645954.			−1.02291
$210$	204881.	+	195726.i	0.320593	+	0.306267i
$211$	68773.9			0.106345			0.0531726	−	0.998585i	$-0.483067\pi$
$211$	68773.9			0.106345			0.0531726	+	0.998585i	$0.483067\pi$
$212$	−41376.6	+	71666.5i	−0.0632289	+	0.109516i
$213$	27346.1	+	47364.8i	0.0412996	+	0.0715330i
$214$	−246281.	−	426572.i	−0.367618	−	0.636734i
$215$	−61537.4	+	106586.i	−0.0907911	+	0.157255i
$216$	302057.			0.440508
$217$	−367136.	+	107421.i	−0.529270	+	0.154861i
$218$	−372512.			−0.530883
$219$	75508.4	−	130784.i	0.106386	−	0.184266i
$220$	−400987.	−	694529.i	−0.558564	−	0.967461i
$221$	286299.	+	495885.i	0.394312	+	0.682968i
$222$	455884.	−	789615.i	0.620829	−	1.07531i
$223$	−620227.			−0.835196			−0.417598	−	0.908632i	$-0.637128\pi$
$223$	−620227.			−0.835196			−0.417598	+	0.908632i	$0.637128\pi$
$224$	−786734.	+	230193.i	−1.04763	+	0.306530i
$225$	−207425.			−0.273152
$226$	494380.	−	856291.i	0.643857	−	1.11519i
$227$	−501116.	−	867959.i	−0.645467	−	1.11798i	−0.984193	−	0.177096i	$-0.943330\pi$
$227$	−501116.	−	867959.i	−0.645467	−	1.11798i	0.338727	−	0.940885i	$-0.390004\pi$
$228$	452867.	+	784388.i	0.576944	+	0.999296i
$229$	−442931.	+	767178.i	−0.558145	+	0.966735i	0.439506	+	0.898239i	$0.355153\pi$
$229$	−442931.	+	767178.i	−0.558145	+	0.966735i	−0.997651	+	0.0684960i	$0.978180\pi$
$230$	998973.			1.24519
$231$	392750.	+	375200.i	0.484269	+	0.462629i
$232$	−986707.			−1.20356
$233$	−298082.	+	516293.i	−0.359704	+	0.623026i	−0.987911	−	0.155020i	$-0.950456\pi$
$233$	−298082.	+	516293.i	−0.359704	+	0.623026i	0.628207	+	0.778046i	$0.283789\pi$
$234$	422057.	+	731025.i	0.503886	+	0.872755i
$235$	37073.3	+	64212.9i	0.0437917	+	0.0758495i
$236$	−997143.	+	1.72710e6i	−1.16541	+	2.01854i
$237$	−43607.4			−0.0504300
$238$	176228.	−	723419.i	0.201666	−	0.827842i
$239$	743111.			0.841509			0.420754	−	0.907175i	$-0.361765\pi$
$239$	743111.			0.841509			0.420754	+	0.907175i	$0.361765\pi$
$240$	−204724.	+	354593.i	−0.229425	+	0.397376i
$241$	587419.	+	1.01744e6i	0.651487	+	1.12841i	0.982762	+	0.184874i	$0.0591877\pi$
$241$	587419.	+	1.01744e6i	0.651487	+	1.12841i	−0.331276	+	0.943534i	$0.607479\pi$
$242$	−284548.	−	492851.i	−0.312332	−	0.540975i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−1.53058e6			−1.64582
$245$	336250.	−	215192.i	0.357888	−	0.229040i
$246$	−411961.			−0.434029
$247$	−707179.	+	1.22487e6i	−0.737542	+	1.27746i
$248$	−611293.	−	1.05879e6i	−0.631132	−	1.09315i
$249$	−270654.	−	468787.i	−0.276641	−	0.479156i
$250$	690385.	−	1.19578e6i	0.698621	−	1.21005i
$251$	352992.			0.353655			0.176828	−	0.984242i	$-0.443416\pi$
$251$	352992.			0.353655			0.176828	+	0.984242i	$0.443416\pi$
$252$	180260.	−	739967.i	0.178812	−	0.734025i
$253$	1.91500e6			1.88090
$254$	−119225.	+	206504.i	−0.115953	+	0.200837i
$255$	−60044.9	−	104001.i	−0.0578263	−	0.100158i
$256$	912666.	+	1.58078e6i	0.870386	+	1.50755i
$257$	−5006.34	+	8671.23i	−0.00472811	+	0.00818932i	−0.868380	−	0.495900i	$-0.834838\pi$
$257$	−5006.34	+	8671.23i	−0.00472811	+	0.00818932i	0.863652	+	0.504089i	$0.168172\pi$
$258$	476773.			0.445925
$259$	−928875.	−	887369.i	−0.860415	−	0.821968i
$260$	−1.75597e6			−1.61096
$261$	96445.6	−	167049.i	0.0876357	−	0.151790i
$262$	1.73171e6	+	2.99940e6i	1.55855	+	2.69949i
$263$	−840900.	−	1.45648e6i	−0.749644	−	1.29842i	−0.947993	−	0.318290i	$-0.896891\pi$
$263$	−840900.	−	1.45648e6i	−0.749644	−	1.29842i	0.198349	−	0.980131i	$-0.436442\pi$
$264$	−867995.	+	1.50341e6i	−0.766492	+	1.32760i
$265$	27101.9			0.0237075
$266$	1.76514e6	−	516469.i	1.52959	−	0.447549i
$267$	−562477.			−0.482866
$268$	2.01584e6	−	3.49153e6i	1.71442	−	2.96947i
$269$	958587.	+	1.66032e6i	0.807702	+	1.39898i	0.914452	+	0.404694i	$0.132622\pi$
$269$	958587.	+	1.66032e6i	0.807702	+	1.39898i	−0.106750	+	0.994286i	$0.534045\pi$
$270$	−88517.1	−	153316.i	−0.0738955	−	0.127991i
$271$	−1.14500e6	+	1.98320e6i	−0.947069	+	1.64037i	−0.195515	+	0.980701i	$0.562638\pi$
$271$	−1.14500e6	+	1.98320e6i	−0.947069	+	1.64037i	−0.751554	+	0.659672i	$0.770695\pi$
$272$	1.07594e6			0.881795
$273$	1.14144e6	−	333977.i	0.926928	−	0.271213i
$274$	−642843.			−0.517283
$275$	596060.	−	1.03241e6i	0.475290	−	0.823226i
$276$	−1.34257e6	−	2.32540e6i	−1.06088	−	1.83749i
$277$	197401.	+	341908.i	0.154579	+	0.267738i	0.932906	−	0.360121i	$-0.117265\pi$
$277$	197401.	+	341908.i	0.154579	+	0.267738i	−0.778327	+	0.627859i	$0.783931\pi$
$278$	−1.08335e6	+	1.87642e6i	−0.840734	+	1.45619i
$279$	239003.			0.183820
$280$	922584.	+	881359.i	0.703251	+	0.671827i
$281$	−1.77699e6			−1.34252			−0.671259	−	0.741223i	$-0.734246\pi$
$281$	−1.77699e6			−1.34252			−0.671259	+	0.741223i	$0.734246\pi$
$282$	143616.	−	248751.i	0.107543	−	0.186269i
$283$	−607622.	−	1.05243e6i	−0.450991	−	0.781139i	0.547457	−	0.836834i	$-0.315596\pi$
$283$	−607622.	−	1.05243e6i	−0.450991	−	0.781139i	−0.998448	+	0.0556949i	$0.982263\pi$
$284$	220370.	+	381693.i	0.162128	+	0.280813i
$285$	148315.	−	256889.i	0.108162	−	0.187341i
$286$	−4.85133e6			−3.50708
$287$	−137376.	+	563931.i	−0.0984481	+	0.404130i
$288$	512159.			0.363851
$289$	552143.	−	956340.i	0.388872	−	0.673547i
$290$	289153.	+	500827.i	0.201898	+	0.349698i
$291$	286442.	+	496132.i	0.198292	+	0.343451i
$292$	608490.	−	1.05393e6i	0.417634	−	0.723364i
$293$	−1.48897e6			−1.01325			−0.506627	−	0.862165i	$-0.669108\pi$
$293$	−1.48897e6			−1.01325			−0.506627	+	0.862165i	$0.669108\pi$
$294$	−1.37323e6	−	711257.i	−0.926560	−	0.479908i
$295$	653133.			0.436965
$296$	2.05286e6	−	3.55565e6i	1.36185	−	2.35879i
$297$	−169684.	−	293902.i	−0.111622	−	0.193335i
$298$	−717065.	−	1.24199e6i	−0.467754	−	0.810174i
$299$	2.09651e6	−	3.63125e6i	1.35618	−	2.34898i
$300$	−1.67155e6			−1.07230
$301$	158989.	−	652651.i	0.101146	−	0.415207i
$302$	−1.67662e6			−1.05784
$303$	−830803.	+	1.43899e6i	−0.519866	+	0.900434i
$304$	1.32883e6	+	2.30160e6i	0.824679	+	1.42839i
$305$	250634.	+	434111.i	0.154273	+	0.267209i
$306$	−232604.	+	402883.i	−0.142009	+	0.245966i
$307$	2.03109e6			1.22994			0.614968	−	0.788552i	$-0.289169\pi$
$307$	2.03109e6			1.22994			0.614968	+	0.788552i	$0.289169\pi$
$308$	3.16501e6	+	3.02358e6i	1.90107	+	1.81612i
$309$	468394.			0.279071
$310$	−358276.	+	620553.i	−0.211745	+	0.366754i
$311$	−144892.	−	250961.i	−0.0849463	−	0.147131i	0.820422	−	0.571758i	$-0.193739\pi$
$311$	−144892.	−	250961.i	−0.0849463	−	0.147131i	−0.905368	+	0.424627i	$0.860405\pi$
$312$	1.90053e6	+	3.29182e6i	1.10532	+	1.91447i
$313$	−109105.	+	188976.i	−0.0629484	+	0.109030i	−0.895782	−	0.444493i	$-0.853384\pi$
$313$	−109105.	+	188976.i	−0.0629484	+	0.109030i	0.832834	+	0.553523i	$0.186717\pi$
$314$	5.69002e6			3.25679
$315$	−239391.	+	70044.3i	−0.135935	+	0.0397737i
$316$	−351413.			−0.197970
$317$	−645315.	+	1.11772e6i	−0.360681	+	0.624718i	−0.988073	−	0.153985i	$-0.950789\pi$
$317$	−645315.	+	1.11772e6i	−0.360681	+	0.624718i	0.627392	+	0.778704i	$0.284122\pi$
$318$	−52494.2	−	90922.7i	−0.0291101	−	0.0504202i
$319$	554296.	+	960068.i	0.304975	+	0.528233i
$320$	−39841.4	+	69007.3i	−0.0217500	+	0.0376721i
$321$	433600.			0.234870
$322$	−5.23295e6	+	1.53113e6i	−2.81259	+	0.822947i
$323$	−779481.			−0.415719
$324$	−237925.	+	412099.i	−0.125915	+	0.218092i
$325$	−1.30511e6	−	2.26052e6i	−0.685393	−	1.18714i
$326$	100841.	+	174662.i	0.0525526	+	0.0910237i
$327$	163960.	−	283987.i	0.0847947	−	0.146869i
$328$	−1.85507e6			−0.952084
$329$	−292621.	−	279546.i	−0.149045	−	0.142385i
$330$	1.01746e6			0.514318
$331$	1.74280e6	−	3.01862e6i	0.874336	−	1.51439i	0.0168673	−	0.999858i	$-0.494631\pi$
$331$	1.74280e6	−	3.01862e6i	0.874336	−	1.51439i	0.857469	−	0.514536i	$-0.172036\pi$
$332$	−2.18109e6	−	3.77776e6i	−1.08600	−	1.88100i
$333$	401313.	+	695094.i	0.198323	+	0.343505i
$334$	−484489.	+	839160.i	−0.237639	+	0.411603i
$335$	−1.32038e6			−0.642817
$336$	528928.	−	2.17125e6i	0.255593	−	1.04921i
$337$	249198.			0.119528			0.0597641	−	0.998213i	$-0.480965\pi$
$337$	249198.			0.119528			0.0597641	+	0.998213i	$0.480965\pi$
$338$	−3.41313e6	+	5.91171e6i	−1.62503	+	2.81463i
$339$	435200.	+	753788.i	0.205679	+	0.356246i
$340$	−483876.	−	838098.i	−0.227006	−	0.393186i
$341$	−686803.	+	1.18958e6i	−0.319850	+	0.553997i
$342$	−1.14910e6			−0.531241
$343$	−1.43156e6	+	1.64262e6i	−0.657015	+	0.753878i
$344$	2.14692e6			0.978180
$345$	−439695.	+	761574.i	−0.198886	+	0.344480i
$346$	−1.73213e6	−	3.00014e6i	−0.777840	−	1.34726i
$347$	753007.	+	1.30425e6i	0.335719	+	0.581482i	0.983623	−	0.180240i	$-0.0576875\pi$
$347$	753007.	+	1.30425e6i	0.335719	+	0.581482i	−0.647904	+	0.761722i	$0.724354\pi$
$348$	777214.	−	1.34617e6i	0.344027	−	0.595872i
$349$	1.54370e6			0.678423			0.339212	−	0.940710i	$-0.389840\pi$
$349$	1.54370e6			0.678423			0.339212	+	0.940710i	$0.389840\pi$
$350$	−803348.	+	3.29775e6i	−0.350537	+	1.43896i
$351$	−743070.			−0.321930
$352$	−1.47175e6	+	2.54914e6i	−0.633107	+	1.09657i
$353$	838978.	+	1.45315e6i	0.358355	+	0.620689i	0.987686	−	0.156448i	$-0.0500043\pi$
$353$	838978.	+	1.45315e6i	0.358355	+	0.620689i	−0.629331	+	0.777137i	$0.716671\pi$
$354$	−1.26507e6	−	2.19116e6i	−0.536544	−	0.929322i
$355$	72171.8	−	125005.i	0.0303946	−	0.0526450i
$356$	−4.53276e6			−1.89556
$357$	473937.	+	452760.i	0.196811	+	0.188017i
$358$	7.93568e6			3.27248
$359$	1.24987e6	−	2.16483e6i	0.511832	−	0.886519i	−0.488074	−	0.872802i	$-0.662300\pi$
$359$	1.24987e6	−	2.16483e6i	0.511832	−	0.886519i	0.999906	−	0.0137165i	$-0.00436623\pi$
$360$	−398594.	−	690385.i	−0.162097	−	0.280760i
$361$	275363.	+	476943.i	0.111208	+	0.192619i
$362$	678335.	−	1.17491e6i	0.272065	−	0.471231i
$363$	500971.			0.199547
$364$	9.19836e6	−	2.69138e6i	3.63879	−	1.06469i
$365$	−398564.			−0.156591
$366$	970917.	−	1.68168e6i	0.378861	−	0.656206i
$367$	1.05371e6	+	1.82507e6i	0.408370	+	0.707318i	0.994707	−	0.102749i	$-0.0327639\pi$
$367$	1.05371e6	+	1.82507e6i	0.408370	+	0.707318i	−0.586337	+	0.810067i	$0.699431\pi$
$368$	−3.93945e6	−	6.82332e6i	−1.51641	−	2.62649i
$369$	181324.	−	314062.i	0.0693248	−	0.120074i
$370$	−2.40634e6			−0.913804
$371$	−141969.	+	41539.1i	−0.0535498	+	0.0156683i
$372$	1.92602e6			0.721613
$373$	−1.36612e6	+	2.36619e6i	−0.508414	+	0.880599i	0.491538	+	0.870856i	$0.336435\pi$
$373$	−1.36612e6	+	2.36619e6i	−0.508414	+	0.880599i	−0.999953	+	0.00974333i	$0.996899\pi$
$374$	−1.33683e6	−	2.31546e6i	−0.494194	−	0.855970i
$375$	607742.	+	1.05264e6i	0.223173	+	0.386547i
$376$	646706.	−	1.12013e6i	0.235905	−	0.408600i
$377$	2.42733e6			0.879581
$378$	698670.	+	667450.i	0.251503	+	0.240264i
$379$	−2.04295e6			−0.730567			−0.365283	−	0.930896i	$-0.619028\pi$
$379$	−2.04295e6			−0.730567			−0.365283	+	0.930896i	$0.619028\pi$
$380$	1.19521e6	−	2.07016e6i	0.424604	−	0.735436i
$381$	−104953.	−	181784.i	−0.0370410	−	0.0641568i
$382$	−33930.0	−	58768.4i	−0.0118967	−	0.0206056i
$383$	−754497.	+	1.30683e6i	−0.262821	+	0.455220i	−0.966991	−	0.254812i	$-0.917986\pi$
$383$	−754497.	+	1.30683e6i	−0.262821	+	0.455220i	0.704169	+	0.710032i	$0.251320\pi$
$384$	−1.51233e6			−0.523382
$385$	339290.	−	1.39279e6i	0.116659	−	0.478888i
$386$	4.62721e6			1.58071
$387$	−209850.	+	363471.i	−0.0712249	+	0.123365i
$388$	2.30832e6	+	3.99812e6i	0.778423	+	1.34827i
$389$	−2.25033e6	−	3.89768e6i	−0.754000	−	1.30597i	−0.945870	−	0.324546i	$-0.894788\pi$
$389$	−2.25033e6	−	3.89768e6i	−0.754000	−	1.30597i	0.191870	−	0.981420i	$-0.438545\pi$
$390$	1.11389e6	−	1.92932e6i	0.370837	−	0.642308i
$391$	2.31085e6			0.764417
$392$	−6.18366e6	−	3.20280e6i	−2.03250	−	1.05273i
$393$	−3.04882e6			−0.995751
$394$	−4.17620e6	+	7.23339e6i	−1.35532	+	2.34748i
$395$	57544.3	+	99669.7i	0.0185571	+	0.0321418i
$396$	−1.36741e6	−	2.36843e6i	−0.438189	−	0.758966i
$397$	1.76068e6	−	3.04958e6i	0.560665	−	0.971101i	−0.436773	−	0.899572i	$-0.643879\pi$
$397$	1.76068e6	−	3.04958e6i	0.560665	−	0.971101i	0.997439	−	0.0715292i	$-0.0227879\pi$
$398$	8.24469e6			2.60895
$399$	−383189.	+	1.57299e6i	−0.120498	+	0.494646i
$400$	−4.90476e6			−1.53274
$401$	453554.	−	785578.i	0.140853	−	0.243965i	−0.786965	−	0.616998i	$-0.788349\pi$
$401$	453554.	−	785578.i	0.140853	−	0.243965i	0.927818	+	0.373033i	$0.121682\pi$
$402$	2.55748e6	+	4.42968e6i	0.789308	+	1.36712i
$403$	1.50380e6	+	2.60466e6i	0.461241	+	0.798893i
$404$	−6.69508e6	+	1.15962e7i	−2.04081	+	3.53479i
$405$	155842.			0.0472115
$406$	−2.28230e6	−	2.18031e6i	−0.687158	−	0.656453i
$407$	−4.61287e6			−1.38034
$408$	−1.04742e6	+	1.81419e6i	−0.311509	+	0.539550i
$409$	−2.15927e6	−	3.73996e6i	−0.638260	−	1.10550i	−0.985814	−	0.167839i	$-0.946321\pi$
$409$	−2.15927e6	−	3.73996e6i	−0.638260	−	1.10550i	0.347554	−	0.937660i	$-0.387012\pi$
$410$	543624.	+	941585.i	0.159713	+	0.276630i
$411$	282945.	−	490076.i	0.0826224	−	0.143106i
$412$	3.77458e6			1.09553
$413$	−3.42133e6	+	1.00106e6i	−0.987006	+	0.288791i
$414$	3.40662e6			0.976838
$415$	−714311.	+	1.23722e6i	−0.203595	+	0.352637i
$416$	3.22249e6	+	5.58152e6i	0.912974	+	1.58132i
$417$	−953671.	−	1.65181e6i	−0.268571	−	0.465178i
$418$	3.30207e6	−	5.71935e6i	0.924369	−	1.60105i
$419$	−1.52041e6			−0.423083			−0.211541	−	0.977369i	$-0.567848\pi$
$419$	−1.52041e6			−0.423083			−0.211541	+	0.977369i	$0.567848\pi$
$420$	−1.92915e6	+	564457.i	−0.533633	+	0.156138i
$421$	−4.42050e6			−1.21553			−0.607766	−	0.794116i	$-0.707934\pi$
$421$	−4.42050e6			−1.21553			−0.607766	+	0.794116i	$0.707934\pi$
$422$	−351567.	+	608932.i	−0.0961008	+	0.166452i
$423$	126425.	+	218974.i	0.0343542	+	0.0595033i
$424$	−236383.	−	409427.i	−0.0638559	−	0.110602i
$425$	719274.	−	1.24582e6i	0.193162	−	0.334567i
$426$	−559164.			−0.149285
$427$	−1.97827e6	−	1.88987e6i	−0.525068	−	0.501605i
$428$	3.49420e6			0.922016
$429$	2.13530e6	−	3.69844e6i	0.560164	−	0.970233i
$430$	−629150.	−	1.08972e6i	−0.164090	−	0.284213i
$431$	3.42393e6	+	5.93041e6i	0.887833	+	1.53777i	0.842432	+	0.538803i	$0.181123\pi$
$431$	3.42393e6	+	5.93041e6i	0.887833	+	1.53777i	0.0454009	+	0.998969i	$0.485543\pi$
$432$	−698134.	+	1.20920e6i	−0.179982	+	0.311738i
$433$	−3.99328e6			−1.02355			−0.511777	−	0.859119i	$-0.671012\pi$
$433$	−3.99328e6			−1.02355			−0.511777	+	0.859119i	$0.671012\pi$
$434$	925648.	−	3.79979e6i	0.235896	−	0.968357i
$435$	−509079.			−0.128992
$436$	1.32128e6	−	2.28853e6i	0.332874	−	0.576555i
$437$	2.85398e6	+	4.94324e6i	0.714904	+	1.23825i
$438$	771986.	+	1.33712e6i	0.192276	+	0.333031i
$439$	−742783.	+	1.28654e6i	−0.183950	+	0.318611i	−0.943222	−	0.332162i	$-0.892222\pi$
$439$	−742783.	+	1.28654e6i	−0.183950	+	0.318611i	0.759272	+	0.650773i	$0.225555\pi$
$440$	4.58163e6			1.12821
$441$	1.14665e6	−	733830.i	0.280760	−	0.179680i
$442$	−5.85416e6			−1.42531
$443$	2.81097e6	−	4.86874e6i	0.680528	−	1.17871i	−0.294291	−	0.955716i	$-0.595084\pi$
$443$	2.81097e6	−	4.86874e6i	0.680528	−	1.17871i	0.974820	−	0.222994i	$-0.0715831\pi$
$444$	3.23401e6	+	5.60146e6i	0.778545	+	1.34848i
$445$	742245.	+	1.28561e6i	0.177684	+	0.307757i
$446$	3.17055e6	−	5.49156e6i	0.754741	−	1.30725i
$447$	1.26246e6			0.298846
$448$	102935.	−	422548.i	0.0242308	−	0.0994675i
$449$	1.94883e6			0.456202			0.228101	−	0.973637i	$-0.426748\pi$
$449$	1.94883e6			0.456202			0.228101	+	0.973637i	$0.426748\pi$
$450$	1.06034e6	−	1.83657e6i	0.246839	−	0.427538i
$451$	1.04211e6	+	1.80499e6i	0.241253	+	0.417862i
$452$	3.50709e6	+	6.07446e6i	0.807422	+	1.39850i
$453$	737961.	−	1.27819e6i	0.168962	−	0.292650i
$454$	1.02467e7			2.33315
$455$	−2.26959e6	−	2.16817e6i	−0.513947	−	0.490982i
$456$	−5.17441e6			−1.16533
$457$	1.33656e6	−	2.31499e6i	0.299363	−	0.518511i	−0.676628	−	0.736325i	$-0.736559\pi$
$457$	1.33656e6	−	2.31499e6i	0.299363	−	0.518511i	0.975990	+	0.217814i	$0.0698926\pi$
$458$	−4.52846e6	−	7.84352e6i	−1.00876	−	1.74722i
$459$	−204760.	−	354655.i	−0.0453643	−	0.0785733i
$460$	−3.54332e6	+	6.13720e6i	−0.780756	+	1.35231i
$461$	−4.65262e6			−1.01964			−0.509819	−	0.860282i	$-0.670287\pi$
$461$	−4.65262e6			−1.01964			−0.509819	+	0.860282i	$0.670287\pi$
$462$	−5.32978e6	+	1.55946e6i	−1.16173	+	0.339914i
$463$	−5.18586e6			−1.12426			−0.562132	−	0.827047i	$-0.690019\pi$
$463$	−5.18586e6			−1.12426			−0.562132	+	0.827047i	$0.690019\pi$
$464$	2.28055e6	−	3.95002e6i	0.491749	−	0.851735i
$465$	−315389.	−	546269.i	−0.0676416	−	0.117159i
$466$	−3.04754e6	−	5.27850e6i	−0.650107	−	1.12602i
$467$	2.52990e6	−	4.38192e6i	0.536799	−	0.929763i	−0.462275	−	0.886737i	$-0.652967\pi$
$467$	2.52990e6	−	4.38192e6i	0.536799	−	0.929763i	0.999074	−	0.0430263i	$-0.0136999\pi$
$468$	−5.98808e6			−1.26378
$469$	6.91660e6	−	2.02375e6i	1.45198	−	0.424840i
$470$	−758064.			−0.158293
$471$	−2.50444e6	+	4.33783e6i	−0.520187	+	0.900990i
$472$	−5.69662e6	−	9.86684e6i	−1.17696	−	2.03856i
$473$	−1.20606e6	−	2.08895e6i	−0.247865	−	0.429315i
$474$	222918.	−	386105.i	0.0455720	−	0.0789331i
$475$	3.55331e6			0.722603
$476$	3.81926e6	+	3.64860e6i	0.772612	+	0.738088i
$477$	92420.8			0.0185983
$478$	−3.79873e6	+	6.57959e6i	−0.760446	+	1.31713i
$479$	2.77543e6	+	4.80718e6i	0.552702	+	0.957308i	0.998078	+	0.0619642i	$0.0197365\pi$
$479$	2.77543e6	+	4.80718e6i	0.552702	+	0.957308i	−0.445377	+	0.895343i	$0.646930\pi$
$480$	−675845.	−	1.17060e6i	−0.133889	−	0.231902i
$481$	−5.05010e6	+	8.74702e6i	−0.995261	+	1.72384i
$482$	−1.20114e7			−2.35491
$483$	1.13600e6	−	4.66330e6i	0.221570	−	0.909548i
$484$	4.03711e6			0.783353
$485$	755979.	−	1.30939e6i	0.145934	−	0.252764i
$486$	−301854.	−	522827.i	−0.0579704	−	0.100408i
$487$	3.43905e6	+	5.95661e6i	0.657077	+	1.13809i	0.981369	+	0.192133i	$0.0615405\pi$
$487$	3.43905e6	+	5.95661e6i	0.657077	+	1.13809i	−0.324292	+	0.945957i	$0.605126\pi$
$488$	4.37206e6	−	7.57262e6i	0.831067	−	1.43945i
$489$	−177540.			−0.0335756
$490$	186449.	+	4.07724e6i	0.0350809	+	0.767143i
$491$	7.44459e6			1.39360			0.696798	−	0.717267i	$-0.254607\pi$
$491$	7.44459e6			1.39360			0.696798	+	0.717267i	$0.254607\pi$
$492$	1.46121e6	−	2.53089e6i	0.272145	−	0.471368i
$493$	668876.	+	1.15853e6i	0.123945	+	0.214679i
$494$	−7.23009e6	−	1.25229e7i	−1.33299	−	2.30880i
$495$	−447831.	+	775666.i	−0.0821488	+	0.142286i
$496$	5.65145e6			1.03147
$497$	−186464.	+	765436.i	−0.0338613	+	0.139001i
$498$	5.53426e6			0.999968
$499$	−1.07665e6	+	1.86481e6i	−0.193563	+	0.335261i	−0.946428	−	0.322914i	$-0.895338\pi$
$499$	−1.07665e6	+	1.86481e6i	−0.193563	+	0.335261i	0.752866	+	0.658174i	$0.228671\pi$
$500$	4.89754e6	+	8.48278e6i	0.876098	+	1.51745i
$501$	−426493.	−	738707.i	−0.0759132	−	0.131486i
$502$	−1.80447e6	+	3.12543e6i	−0.319588	+	0.553542i
$503$	8.61012e6			1.51736			0.758681	−	0.651463i	$-0.225844\pi$
$503$	8.61012e6			1.51736			0.758681	+	0.651463i	$0.225844\pi$
$504$	3.14612e6	+	3.00554e6i	0.551695	+	0.527043i
$505$	4.38531e6			0.765195
$506$	−9.78932e6	+	1.69556e7i	−1.69972	+	2.94399i
$507$	−3.00456e6	−	5.20404e6i	−0.519111	−	0.899127i
$508$	−845771.	−	1.46492e6i	−0.145410	−	0.251857i
$509$	−1.67100e6	+	2.89426e6i	−0.285879	+	0.495157i	−0.972822	−	0.231554i	$-0.925619\pi$
$509$	−1.67100e6	+	2.89426e6i	−0.285879	+	0.495157i	0.686943	+	0.726712i	$0.258952\pi$
$510$	1.22778e6			0.209024
$511$	2.08781e6	−	610879.i	0.353703	−	0.103491i
$512$	−1.32848e7			−2.23964
$513$	505772.	−	876023.i	0.0848519	−	0.146968i
$514$	−51184.1	−	88653.4i	−0.00854529	−	0.0148009i
$515$	−618093.	−	1.07057e6i	−0.102692	−	0.177867i
$516$	−1.69109e6	+	2.92906e6i	−0.279604	+	0.484288i
$517$	−1.45318e6			−0.239108
$518$	1.26052e7	−	3.68820e6i	2.06408	−	0.603936i
$519$	3.04957e6			0.496958
$520$	5.01589e6	−	8.68777e6i	0.813466	−	1.40896i
$521$	1.34152e6	+	2.32359e6i	0.216523	+	0.375029i	0.953743	−	0.300624i	$-0.0971950\pi$
$521$	1.34152e6	+	2.32359e6i	0.216523	+	0.375029i	−0.737220	+	0.675653i	$0.763862\pi$
$522$	986046.	+	1.70788e6i	0.158387	+	0.274335i
$523$	2.71178e6	−	4.69694e6i	0.433511	−	0.750863i	−0.563662	−	0.826005i	$-0.690608\pi$
$523$	2.71178e6	−	4.69694e6i	0.433511	−	0.750863i	0.997173	+	0.0751429i	$0.0239413\pi$
$524$	−2.45692e7			−3.90897
$525$	−2.16047e6	−	2.06393e6i	−0.342098	−	0.326811i
$526$	1.71945e7			2.70972
$527$	−828775.	+	1.43548e6i	−0.129990	+	0.225149i
$528$	−4.01234e6	−	6.94958e6i	−0.626344	−	1.08486i
$529$	−5.24276e6	−	9.08072e6i	−0.814555	−	1.41085i
$530$	−138543.	+	239963.i	−0.0214237	+	0.0371070i
$531$	2.22726e6			0.342796
$532$	−3.08795e6	+	1.26761e7i	−0.473033	+	1.94181i
$533$	4.56353e6			0.695798
$534$	2.87534e6	−	4.98024e6i	0.436351	−	0.755782i
$535$	−572179.	−	991044.i	−0.0864266	−	0.149695i
$536$	1.15164e7	+	1.99469e7i	1.73142	+	2.99891i
$537$	−3.49287e6	+	6.04983e6i	−0.522693	+	0.905330i
$538$	−1.96009e7			−2.91958
$539$	357417.	+	7.81593e6i	0.0529911	+	1.15880i
$540$	1.25587e6			0.185336
$541$	−1.09228e6	+	1.89188e6i	−0.160450	+	0.277908i	−0.935030	−	0.354568i	$-0.884628\pi$
$541$	−1.09228e6	+	1.89188e6i	−0.160450	+	0.277908i	0.774580	+	0.632476i	$0.217961\pi$
$542$	−1.17063e7	−	2.02759e7i	−1.71168	−	2.96471i
$543$	597135.	+	1.03427e6i	0.0869106	+	0.150534i
$544$	−1.77598e6	+	3.07609e6i	−0.257301	+	0.445658i
$545$	−865447.			−0.124810
$546$	−2.87787e6	+	1.18137e7i	−0.413133	+	1.69592i
$547$	−691437.			−0.0988062			−0.0494031	−	0.998779i	$-0.515732\pi$
$547$	−691437.			−0.0988062			−0.0494031	+	0.998779i	$0.515732\pi$
$548$	2.28014e6	−	3.94931e6i	0.324347	−	0.561785i
$549$	854693.	+	1.48037e6i	0.121026	+	0.209623i
$550$	6.09403e6	+	1.05552e7i	0.859010	+	1.48785i
$551$	−1.65217e6	+	2.86164e6i	−0.231833	+	0.401547i
$552$	1.53401e7			2.14279
$553$	−454200.	−	433904.i	−0.0631589	−	0.0603367i
$554$	−4.03639e6			−0.558752
$555$	1.05914e6	−	1.83449e6i	0.145956	−	0.252804i
$556$	−7.68523e6	−	1.33112e7i	−1.05431	−	1.82612i
$557$	−2.73828e6	−	4.74284e6i	−0.373973	−	0.647740i	0.616200	−	0.787590i	$-0.288671\pi$
$557$	−2.73828e6	−	4.74284e6i	−0.373973	−	0.647740i	−0.990173	+	0.139850i	$0.955338\pi$
$558$	−1.22177e6	+	2.11616e6i	−0.166113	+	0.287715i
$559$	−5.28149e6			−0.714869
$560$	−5.66063e6	+	1.65626e6i	−0.762771	+	0.223182i
$561$	2.35361e6			0.315739
$562$	9.08386e6	−	1.57337e7i	1.21319	−	2.10131i
$563$	−199488.	−	345523.i	−0.0265244	−	0.0459416i	0.852459	−	0.522795i	$-0.175111\pi$
$563$	−199488.	−	345523.i	−0.0265244	−	0.0459416i	−0.878983	+	0.476853i	$0.841777\pi$
$564$	1.01880e6	+	1.76462e6i	0.134863	+	0.233589i
$565$	1.14858e6	−	1.98940e6i	0.151370	−	0.262181i
$566$	1.24245e7			1.63019
$567$	−816353.	+	238860.i	−0.106640	+	0.0312022i
$568$	−2.51793e6			−0.327471
$569$	2.11556e6	−	3.66426e6i	0.273934	−	0.474467i	−0.695932	−	0.718108i	$-0.745008\pi$
$569$	2.11556e6	−	3.66426e6i	0.273934	−	0.474467i	0.969866	+	0.243641i	$0.0783418\pi$
$570$	1.51635e6	+	2.62640e6i	0.195485	+	0.338589i
$571$	−4.37551e6	−	7.57861e6i	−0.561615	−	0.972746i	−0.997356	−	0.0726734i	$-0.976847\pi$
$571$	−4.37551e6	−	7.57861e6i	−0.561615	−	0.972746i	0.435741	−	0.900072i	$-0.356486\pi$
$572$	1.72075e7	−	2.98042e7i	2.19901	−	3.80879i
$573$	59736.7			0.00760072
$574$	−4.29085e6	−	4.09912e6i	−0.543581	−	0.519291i
$575$	−1.05342e7			−1.32871
$576$	−135864.	+	235323.i	−0.0170627	+	0.0295535i
$577$	883558.	+	1.53037e6i	0.110483	+	0.191362i	0.915965	−	0.401258i	$-0.131427\pi$
$577$	883558.	+	1.53037e6i	0.110483	+	0.191362i	−0.805482	+	0.592620i	$0.798094\pi$
$578$	5.64503e6	+	9.77748e6i	0.702824	+	1.21733i
$579$	−2.03665e6	+	3.52759e6i	−0.252477	+	0.437302i
$580$	−4.10245e6			−0.506376
$581$	1.84550e6	−	7.57581e6i	0.226817	−	0.931084i
$582$	−5.85709e6			−0.716761
$583$	−265582.	+	460001.i	−0.0323614	+	0.0560516i
$584$	3.47627e6	+	6.02107e6i	0.421775	+	0.730536i
$585$	980555.	+	1.69837e6i	0.118463	+	0.205184i
$586$	7.61153e6	−	1.31835e7i	0.915646	−	1.58595i
$587$	−8.65009e6			−1.03616			−0.518078	−	0.855333i	$-0.673352\pi$
$587$	−8.65009e6			−1.03616			−0.518078	+	0.855333i	$0.673352\pi$
$588$	9.24039e6	−	5.91363e6i	1.10217	−	0.705360i
$589$	−4.09426e6			−0.486281
$590$	−3.33877e6	+	5.78292e6i	−0.394872	+	0.683939i
$591$	−3.67628e6	−	6.36751e6i	−0.432953	−	0.749896i
$592$	9.48941e6	+	1.64361e7i	1.11285	+	1.92750i
$593$	−7.72568e6	+	1.33813e7i	−0.902194	+	1.56265i	−0.0775549	+	0.996988i	$0.524711\pi$
$593$	−7.72568e6	+	1.33813e7i	−0.902194	+	1.56265i	−0.824640	+	0.565659i	$0.808622\pi$
$594$	3.46965e6			0.403478
$595$	409427.	−	1.68070e6i	0.0474115	−	0.194625i
$596$	1.01736e7			1.17316
$597$	−3.62888e6	+	6.28540e6i	−0.416712	+	0.721767i
$598$	2.14344e7	+	3.71254e7i	2.45108	+	4.24540i
$599$	1.92400e6	+	3.33247e6i	0.219098	+	0.379489i	0.954533	−	0.298107i	$-0.0963552\pi$
$599$	1.92400e6	+	3.33247e6i	0.219098	+	0.379489i	−0.735434	+	0.677596i	$0.763022\pi$
$600$	4.77474e6	−	8.27009e6i	0.541466	−	0.937847i
$601$	1.27578e7			1.44075			0.720376	−	0.693583i	$-0.243969\pi$
$601$	1.27578e7			1.44075			0.720376	+	0.693583i	$0.243969\pi$
$602$	4.96591e6	+	4.74401e6i	0.558480	+	0.533524i
$603$	−4.50266e6			−0.504285
$604$	5.94691e6	−	1.03004e7i	0.663284	−	1.14884i
$605$	−661082.	−	1.14503e6i	−0.0734289	−	0.127183i
$606$	−8.49400e6	−	1.47120e7i	−0.939574	−	1.62739i
$607$	6.81033e6	−	1.17958e7i	0.750233	−	1.29944i	−0.197476	−	0.980308i	$-0.563274\pi$
$607$	6.81033e6	−	1.17958e7i	0.750233	−	1.29944i	0.947709	−	0.319135i	$-0.103392\pi$
$608$	−8.77359e6			−0.962539
$609$	2.66672e6	−	780266.i	0.291363	−	0.0852510i
$610$	−5.12489e6			−0.557648
$611$	−1.59092e6	+	2.75555e6i	−0.172403	+	0.298611i
$612$	−1.65008e6	−	2.85802e6i	−0.178084	−	0.308451i
$613$	−7.67372e6	−	1.32913e7i	−0.824812	−	1.42862i	−0.902063	−	0.431605i	$-0.857948\pi$
$613$	−7.67372e6	−	1.32913e7i	−0.824812	−	1.42862i	0.0772508	−	0.997012i	$-0.475386\pi$
$614$	−1.03828e7	+	1.79835e7i	−1.11145	+	1.92510i
$615$	−957099.			−0.102040
$616$	−2.40001e7	+	7.02227e6i	−2.54836	+	0.745634i
$617$	1.18485e7			1.25300			0.626500	−	0.779421i	$-0.284487\pi$
$617$	1.18485e7			1.25300			0.626500	+	0.779421i	$0.284487\pi$
$618$	−2.39439e6	+	4.14721e6i	−0.252188	+	0.436802i
$619$	437230.	+	757304.i	0.0458652	+	0.0794408i	0.888047	−	0.459753i	$-0.152062\pi$
$619$	437230.	+	757304.i	0.0458652	+	0.0794408i	−0.842181	+	0.539194i	$0.818729\pi$
$620$	−2.54158e6	−	4.40215e6i	−0.265537	−	0.459924i
$621$	−1.49941e6	+	2.59706e6i	−0.156024	+	0.270242i
$622$	2.96272e6			0.307054
$623$	−5.85858e6	−	5.59679e6i	−0.604744	−	0.577722i
$624$	−1.75706e7			−1.80644
$625$	−2.39730e6	+	4.15225e6i	−0.245484	+	0.425190i
$626$	−1.11548e6	−	1.93206e6i	−0.113769	−	0.197054i
$627$	2.90679e6	+	5.03471e6i	0.295287	+	0.511453i
$628$	−2.01823e7	+	3.49567e7i	−2.04207	+	3.53697i
$629$	−5.56642e6			−0.560983
$630$	603570.	−	2.47766e6i	0.0605865	−	0.248708i
$631$	−4.43859e6			−0.443784			−0.221892	−	0.975071i	$-0.571223\pi$
$631$	−4.43859e6			−0.443784			−0.221892	+	0.975071i	$0.571223\pi$
$632$	1.00380e6	−	1.73864e6i	0.0999667	−	0.173147i
$633$	−309483.	−	536040.i	−0.0306992	−	0.0531726i
$634$	−6.59761e6	−	1.14274e7i	−0.651873	−	1.12908i
$635$	−276992.	+	479764.i	−0.0272605	+	0.0472165i
$636$	744780.			0.0730104
$637$	1.52120e7	+	7.87900e6i	1.48538	+	0.769348i
$638$	−1.13341e7			−1.10239
$639$	246115.	−	426283.i	0.0238443	−	0.0412996i
$640$	1.99567e6	+	3.45661e6i	0.192593	+	0.333580i
$641$	−406276.	−	703690.i	−0.0390549	−	0.0676451i	0.845837	−	0.533441i	$-0.179101\pi$
$641$	−406276.	−	703690.i	−0.0390549	−	0.0676451i	−0.884892	+	0.465796i	$0.845768\pi$
$642$	−2.21653e6	+	3.83915e6i	−0.212245	+	0.367618i
$643$	−1.17941e7			−1.12496			−0.562481	−	0.826810i	$-0.690153\pi$
$643$	−1.17941e7			−1.12496			−0.562481	+	0.826810i	$0.690153\pi$
$644$	9.15456e6	−	3.75795e7i	0.869806	−	3.57056i
$645$	1.10767e6			0.104837
$646$	3.98465e6	−	6.90162e6i	0.375672	−	0.650683i
$647$	1.21690e6	+	2.10773e6i	0.114286	+	0.197950i	0.917494	−	0.397749i	$-0.130209\pi$
$647$	1.21690e6	+	2.10773e6i	0.114286	+	0.197950i	−0.803208	+	0.595699i	$0.796875\pi$
$648$	−1.35925e6	−	2.35430e6i	−0.127164	−	0.220254i
$649$	−6.40031e6	+	1.10857e7i	−0.596471	+	1.03312i
$650$	2.66866e7			2.47748
$651$	2.48938e6	+	2.37814e6i	0.230217	+	0.219930i
$652$	−1.43072e6			−0.131806
$653$	4.73332e6	−	8.19835e6i	0.434393	−	0.752391i	−0.562853	−	0.826557i	$-0.690296\pi$
$653$	4.73332e6	−	8.19835e6i	0.434393	−	0.752391i	0.997246	+	0.0741664i	$0.0236296\pi$
$654$	1.67630e6	+	2.90344e6i	0.153253	+	0.265442i
$655$	4.02323e6	+	6.96843e6i	0.366413	+	0.634647i
$656$	4.28756e6	−	7.42628e6i	0.389001	−	0.673770i
$657$	−1.35915e6			−0.122844
$658$	3.97099e6	−	1.16189e6i	0.357548	−	0.104616i
$659$	1.40662e7			1.26172			0.630860	−	0.775896i	$-0.282702\pi$
$659$	1.40662e7			1.26172			0.630860	+	0.775896i	$0.282702\pi$
$660$	−3.60888e6	+	6.25076e6i	−0.322487	+	0.558564i
$661$	8.58029e6	+	1.48615e7i	0.763832	+	1.32300i	0.940862	+	0.338791i	$0.110018\pi$
$661$	8.58029e6	+	1.48615e7i	0.763832	+	1.32300i	−0.177029	+	0.984206i	$0.556649\pi$
$662$	1.78182e7	+	3.08620e7i	1.58022	+	2.73702i
$663$	2.57669e6	−	4.46296e6i	0.227656	−	0.394312i
$664$	2.49209e7			2.19353
$665$	4.10091e6	−	1.19990e6i	0.359606	−	0.105218i
$666$	−8.20592e6			−0.716872
$667$	4.89803e6	−	8.48364e6i	0.426292	−	0.738359i
$668$	−3.43692e6	−	5.95293e6i	−0.298009	−	0.516166i
$669$	2.79102e6	+	4.83419e6i	0.241100	+	0.417598i
$670$	6.74969e6	−	1.16908e7i	0.580894	−	1.00614i
$671$	−9.82424e6			−0.842350
$672$	5.33448e6	+	5.09611e6i	0.455689	+	0.435327i
$673$	5.87113e6			0.499671			0.249836	−	0.968288i	$-0.419623\pi$
$673$	5.87113e6			0.499671			0.249836	+	0.968288i	$0.419623\pi$
$674$	−1.27388e6	+	2.20643e6i	−0.108014	+	0.187086i
$675$	933413.	+	1.61672e6i	0.0788523	+	0.136576i
$676$	−2.42124e7	−	4.19372e7i	−2.03785	−	3.52966i
$677$	−6.96368e6	+	1.20614e7i	−0.583938	+	1.01141i	0.411069	+	0.911604i	$0.365156\pi$
$677$	−6.96368e6	+	1.20614e7i	−0.583938	+	1.01141i	−0.995007	+	0.0998062i	$0.968178\pi$
$678$	−8.89884e6			−0.743462
$679$	−1.95316e6	+	8.01773e6i	−0.162578	+	0.667386i
$680$	5.52872e6			0.458513
$681$	−4.51005e6	+	7.81163e6i	−0.372660	+	0.645467i
$682$	−7.02178e6	−	1.21621e7i	−0.578077	−	1.00126i
$683$	−9.15503e6	−	1.58570e7i	−0.750945	−	1.30067i	−0.947365	−	0.320155i	$-0.896265\pi$
$683$	−9.15503e6	−	1.58570e7i	−0.750945	−	1.30067i	0.196421	−	0.980520i	$-0.437068\pi$
$684$	4.07580e6	−	7.05950e6i	0.333099	−	0.576944i
$685$	−1.49350e6			−0.121613
$686$	−7.22587e6	−	2.10722e7i	−0.586246	−	1.70962i
$687$	7.97275e6			0.644490
$688$	−4.96210e6	+	8.59461e6i	−0.399663	+	0.692237i
$689$	581509.	+	1.00720e6i	0.0466669	+	0.0808294i
$690$	−4.49538e6	−	7.78622e6i	−0.359454	−	0.622593i
$691$	8.83583e6	−	1.53041e7i	0.703967	−	1.21931i	−0.263096	−	0.964770i	$-0.584744\pi$
$691$	8.83583e6	−	1.53041e7i	0.703967	−	1.21931i	0.967063	−	0.254537i	$-0.0819230\pi$
$692$	2.45752e7			1.95088
$693$	1.15702e6	−	4.74959e6i	0.0915184	−	0.375684i
$694$	−1.53973e7			−1.21351
$695$	−2.51693e6	+	4.35945e6i	−0.197656	+	0.342350i
$696$	4.44018e6	+	7.69062e6i	0.347438	+	0.601781i
$697$	1.25753e6	+	2.17810e6i	0.0980473	+	0.169823i
$698$	−7.89131e6	+	1.36681e7i	−0.613070	+	1.06187i
$699$	5.36547e6			0.415351
$700$	−1.74103e7	−	1.66324e7i	−1.34296	−	1.28295i
$701$	8.22993e6			0.632559			0.316279	−	0.948666i	$-0.397566\pi$
$701$	8.22993e6			0.632559			0.316279	+	0.948666i	$0.397566\pi$
$702$	3.79852e6	−	6.57922e6i	0.290918	−	0.503886i
$703$	−6.87472e6	−	1.19074e7i	−0.524646	−	0.908714i
$704$	−780843.	−	1.35246e6i	−0.0593789	−	0.102847i
$705$	333660.	−	577916.i	0.0252832	−	0.0437917i
$706$	−1.71552e7			−1.29534
$707$	−2.29717e7	+	6.72137e6i	−1.72840	+	0.505719i
$708$	1.79486e7			1.34570
$709$	−1.23183e7	+	2.13360e7i	−0.920314	+	1.59403i	−0.121386	+	0.992605i	$0.538734\pi$
$709$	−1.23183e7	+	2.13360e7i	−0.920314	+	1.59403i	−0.798929	+	0.601426i	$0.794600\pi$
$710$	737874.	+	1.27803e6i	0.0549334	+	0.0951474i
$711$	196233.	+	339886.i	0.0145579	+	0.0252150i
$712$	1.29477e7	−	2.24261e7i	0.957179	−	1.65788i
$713$	1.21379e7			0.894167
$714$	−6.43152e6	+	1.88182e6i	−0.472137	+	0.138144i
$715$	−1.12710e7			−0.824510
$716$	−2.81475e7	+	4.87530e7i	−2.05191	+	3.55401i
$717$	−3.34400e6	−	5.79197e6i	−0.242923	−	0.420754i
$718$	1.27784e7	+	2.21329e7i	0.925053	+	1.60224i
$719$	9.41269e6	−	1.63033e7i	0.679034	−	1.17612i	−0.296238	−	0.955114i	$-0.595732\pi$
$719$	9.41269e6	−	1.63033e7i	0.679034	−	1.17612i	0.975272	−	0.221007i	$-0.0709345\pi$
$720$	3.68503e6			0.264917
$721$	4.87863e6	+	4.66064e6i	0.349510	+	0.333893i
$722$	−5.63055e6			−0.401983
$723$	5.28677e6	−	9.15696e6i	0.376136	−	0.651487i
$724$	4.81205e6	+	8.33472e6i	0.341180	+	0.590942i
$725$	−3.04911e6	−	5.28122e6i	−0.215441	−	0.373155i
$726$	−2.56093e6	+	4.43566e6i	−0.180325	+	0.312332i
$727$	6.77607e6			0.475491			0.237745	−	0.971328i	$-0.423592\pi$
$727$	6.77607e6			0.475491			0.237745	+	0.971328i	$0.423592\pi$
$728$	−1.29591e7	+	5.31973e7i	−0.906248	+	3.72015i
$729$	531441.			0.0370370
$730$	2.03743e6	−	3.52893e6i	0.141506	−	0.245096i
$731$	−1.45537e6	−	2.52077e6i	−0.100735	−	0.174478i
$732$	6.88760e6	+	1.19297e7i	0.475106	+	0.822908i
$733$	8.61136e6	−	1.49153e7i	0.591986	−	1.02535i	−0.401978	−	0.915649i	$-0.631677\pi$
$733$	8.61136e6	−	1.49153e7i	0.591986	−	1.02535i	0.993965	−	0.109701i	$-0.0349894\pi$
$734$	−2.15459e7			−1.47613
$735$	−3.19038e6	−	1.65244e6i	−0.217833	−	0.112826i
$736$	2.60102e7			1.76990
$737$	1.29389e7	−	2.24109e7i	0.877465	−	1.51981i
$738$	1.85383e6	+	3.21092e6i	0.125293	+	0.217014i
$739$	8.82669e6	+	1.52883e7i	0.594548	+	1.02979i	0.993610	+	0.112864i	$0.0360023\pi$
$739$	8.82669e6	+	1.52883e7i	0.594548	+	1.02979i	−0.399062	+	0.916924i	$0.630664\pi$
$740$	8.53520e6	−	1.47834e7i	0.572973	−	0.992418i
$741$	1.27292e7			0.851641
$742$	357941.	−	1.46935e6i	0.0238672	−	0.0979752i
$743$	−1.36977e7			−0.910281			−0.455141	−	0.890420i	$-0.650411\pi$
$743$	−1.36977e7			−0.910281			−0.455141	+	0.890420i	$0.650411\pi$
$744$	−5.50163e6	+	9.52911e6i	−0.364384	+	0.631132i
$745$	−1.66594e6	−	2.88549e6i	−0.109968	−	0.190471i
$746$	−1.39670e7	−	2.41916e7i	−0.918877	−	1.59154i
$747$	−2.43589e6	+	4.21908e6i	−0.159719	+	0.276641i
$748$	1.89668e7			1.23948
$749$	4.51624e6	+	4.31443e6i	0.294152	+	0.281008i
$750$	−1.24269e7			−0.806698
$751$	−5.80446e6	+	1.00536e7i	−0.375545	+	0.650463i	−0.990408	−	0.138171i	$-0.955878\pi$
$751$	−5.80446e6	+	1.00536e7i	−0.375545	+	0.650463i	0.614864	+	0.788633i	$0.289211\pi$
$752$	2.98943e6	+	5.17784e6i	0.192772	+	0.333890i
$753$	−1.58846e6	−	2.75130e6i	−0.102092	−	0.176828i
$754$	−1.24083e7	+	2.14919e7i	−0.794851	+	1.37672i
$755$	−3.89526e6			−0.248696
$756$	−6.57864e6	+	1.92487e6i	−0.418631	+	0.122489i
$757$	6.25226e6			0.396550			0.198275	−	0.980146i	$-0.436466\pi$
$757$	6.25226e6			0.396550			0.198275	+	0.980146i	$0.436466\pi$
$758$	1.04434e7	−	1.80885e7i	0.660191	−	1.14348i
$759$	−8.61748e6	−	1.49259e7i	−0.542970	−	0.940452i
$760$	6.82815e6	+	1.18267e7i	0.428814	+	0.742728i
$761$	1.51063e7	−	2.61648e7i	0.945574	−	1.63778i	0.190977	−	0.981595i	$-0.438834\pi$
$761$	1.51063e7	−	2.61648e7i	0.945574	−	1.63778i	0.754597	−	0.656188i	$-0.227832\pi$
$762$	2.14605e6			0.133891
$763$	4.53350e6	−	1.32647e6i	0.281918	−	0.0824873i
$764$	481393.			0.0298378
$765$	−540404.	+	936007.i	−0.0333860	+	0.0578263i
$766$	−7.71386e6	−	1.33608e7i	−0.475007	−	0.822736i
$767$	1.40139e7	+	2.42728e7i	0.860142	+	1.48981i
$768$	8.21400e6	−	1.42271e7i	0.502518	−	0.870386i
$769$	−2.58756e7			−1.57788			−0.788940	−	0.614470i	$-0.789370\pi$
$769$	−2.58756e7			−1.57788			−0.788940	+	0.614470i	$0.789370\pi$
$770$	1.05975e7	+	1.01240e7i	0.644135	+	0.615352i
$771$	90114.1			0.00545955
$772$	−1.64125e7	+	2.84273e7i	−0.991134	+	1.71669i
$773$	−1.27705e7	−	2.21191e7i	−0.768701	−	1.33143i	−0.938267	−	0.345911i	$-0.887570\pi$
$773$	−1.27705e7	−	2.21191e7i	−0.768701	−	1.33143i	0.169566	−	0.985519i	$-0.445763\pi$
$774$	−2.14548e6	−	3.71607e6i	−0.128728	−	0.222963i
$775$	3.77802e6	−	6.54373e6i	0.225949	−	0.391355i
$776$	−2.63746e7			−1.57228
$777$	−2.73642e6	+	1.12330e7i	−0.162604	+	0.667489i
$778$	4.60140e7			2.72547
$779$	−3.10618e6	+	5.38006e6i	−0.183393	+	0.317646i
$780$	7.90188e6	+	1.36865e7i	0.465044	+	0.805479i
$781$	1.41448e6	+	2.44995e6i	0.0829791	+	0.143724i
$782$	−1.18129e7	+	2.04606e7i	−0.690780	+	1.19647i
$783$	−1.73602e6			−0.101193
$784$	2.71137e7	−	1.73521e7i	1.57543	−	1.00824i
$785$	1.32195e7			0.765667
$786$	1.55854e7	−	2.69946e7i	0.899829	−	1.55855i
$787$	4.40589e6	+	7.63123e6i	0.253570	+	0.439195i	0.964506	−	0.264061i	$-0.0850620\pi$
$787$	4.40589e6	+	7.63123e6i	0.253570	+	0.439195i	−0.710936	+	0.703256i	$0.751729\pi$
$788$	−2.96256e7	−	5.13130e7i	−1.69962	−	2.94383i
$789$	−7.56810e6	+	1.31083e7i	−0.432807	+	0.749644i
$790$	−1.17665e6			−0.0670779
$791$	−2.96749e6	+	1.21816e7i	−0.168635	+	0.692248i
$792$	1.56239e7			0.885068
$793$	−1.07554e7	+	1.86289e7i	−0.607357	+	1.05197i
$794$	1.80009e7	+	3.11785e7i	1.01331	+	1.75511i
$795$	−121959.	−	211238.i	−0.00684375	−	0.0118537i
$796$	−2.92436e7	+	5.06513e7i	−1.63587	+	2.83340i
$797$	−2.07624e7			−1.15780			−0.578899	−	0.815399i	$-0.696517\pi$
$797$	−2.07624e7			−1.15780			−0.578899	+	0.815399i	$0.696517\pi$
$798$	−1.19686e7	−	1.14338e7i	−0.665330	−	0.635600i
$799$	−1.75358e6			−0.0971757
$800$	8.09592e6	−	1.40225e7i	0.447240	−	0.774643i
$801$	2.53115e6	+	4.38407e6i	0.139391	+	0.241433i
$802$	4.63706e6	+	8.03163e6i	0.254570	+	0.440928i
$803$	3.90568e6	−	6.76483e6i	0.213751	−	0.370227i
$804$	−3.62850e7			−1.97965
$805$	−1.21576e7	+	3.55723e6i	−0.661237	+	0.193474i
$806$	−3.07493e7			−1.66724
$807$	8.62729e6	−	1.49429e7i	0.466327	−	0.807702i
$808$	−3.82486e7	−	6.62486e7i	−2.06105	−	3.56984i
$809$	−6.85107e6	−	1.18664e7i	−0.368034	−	0.637453i	0.621224	−	0.783633i	$-0.286636\pi$
$809$	−6.85107e6	−	1.18664e7i	−0.368034	−	0.637453i	−0.989258	+	0.146180i	$0.953302\pi$
$810$	−796654.	+	1.37985e6i	−0.0426636	+	0.0738955i
$811$	3.30799e7			1.76609			0.883043	−	0.469292i	$-0.155491\pi$
$811$	3.30799e7			1.76609			0.883043	+	0.469292i	$0.155491\pi$
$812$	2.14900e7	−	6.28783e6i	1.14379	−	0.334665i
$813$	2.06100e7			1.09358
$814$	2.35807e7	−	4.08429e7i	1.24737	−	2.16051i
$815$	234282.	+	405788.i	0.0123550	+	0.0213996i
$816$	−4.84175e6	−	8.38615e6i	−0.254552	−	0.440897i
$817$	3.59486e6	−	6.22647e6i	0.188420	−	0.326353i
$818$	4.41520e7			2.30711
$819$	−7.73957e6	−	7.39373e6i	−0.403187	−	0.385171i
$820$	−7.71285e6			−0.400572
$821$	−7.41616e6	+	1.28452e7i	−0.383991	+	0.665092i	−0.991629	−	0.129122i	$-0.958784\pi$
$821$	−7.41616e6	+	1.28452e7i	−0.383991	+	0.665092i	0.607638	+	0.794214i	$0.292117\pi$
$822$	2.89279e6	+	5.01046e6i	0.149327	+	0.258641i
$823$	−5.43612e6	−	9.41563e6i	−0.279762	−	0.484563i	0.691563	−	0.722316i	$-0.256922\pi$
$823$	−5.43612e6	−	9.41563e6i	−0.279762	−	0.484563i	−0.971326	+	0.237753i	$0.923589\pi$
$824$	−1.07820e7	+	1.86750e7i	−0.553199	+	0.958168i
$825$	−1.07291e7			−0.548817
$826$	8.62609e6	−	3.54102e7i	0.439910	−	1.80583i
$827$	−1.34267e7			−0.682662			−0.341331	−	0.939943i	$-0.610878\pi$
$827$	−1.34267e7			−0.682662			−0.341331	+	0.939943i	$0.610878\pi$
$828$	−1.20831e7	+	2.09286e7i	−0.612497	+	1.06088i
$829$	7.33770e6	+	1.27093e7i	0.370829	+	0.642295i	0.989693	−	0.143203i	$-0.0457402\pi$
$829$	7.33770e6	+	1.27093e7i	0.370829	+	0.642295i	−0.618864	+	0.785498i	$0.712407\pi$
$830$	−7.30302e6	−	1.26492e7i	−0.367965	−	0.637335i
$831$	1.77661e6	−	3.07718e6i	0.0892461	−	0.154579i
$832$	−3.41941e6			−0.171255
$833$	431300.	+	9.43159e6i	0.0215361	+	0.470947i
$834$	1.95004e7			0.970796
$835$	−1.12560e6	+	1.94960e6i	−0.0558687	+	0.0967674i
$836$	2.34246e7	+	4.05726e7i	1.15919	+	2.00778i
$837$	−1.07551e6	−	1.86284e6i	−0.0530643	−	0.0919100i
$838$	7.77222e6	−	1.34619e7i	0.382327	−	0.662210i
$839$	2.76635e7			1.35676			0.678379	−	0.734712i	$-0.262683\pi$
$839$	2.76635e7			1.35676			0.678379	+	0.734712i	$0.262683\pi$
$840$	2.71788e6	−	1.11569e7i	0.132902	−	0.545566i
$841$	−1.48402e7			−0.723519
$842$	2.25973e7	−	3.91396e7i	1.09844	−	1.90255i
$843$	7.99647e6	+	1.38503e7i	0.387552	+	0.671259i
$844$	−2.49399e6	−	4.31971e6i	−0.120514	−	0.208737i
$845$	−7.92963e6	+	1.37345e7i	−0.382042	+	0.661716i
$846$	−2.58509e6			−0.124180
$847$	5.21795e6	+	4.98479e6i	0.249915	+	0.238747i
$848$	2.18537e6			0.104361
$849$	−5.46860e6	+	9.47189e6i	−0.260380	+	0.450991i
$850$	7.35376e6	+	1.27371e7i	0.349110	+	0.604676i
$851$	2.03808e7	+	3.53006e7i	0.964712	+	1.67093i
$852$	1.98333e6	−	3.43523e6i	0.0936045	−	0.162128i
$853$	3.43515e6			0.161649			0.0808244	−	0.996728i	$-0.474245\pi$
$853$	3.43515e6			0.161649			0.0808244	+	0.996728i	$0.474245\pi$
$854$	2.68459e7	−	7.85493e6i	1.25960	−	0.368551i
$855$	−2.66967e6			−0.124894
$856$	−9.98108e6	+	1.72877e7i	−0.465579	+	0.806406i
$857$	3.20313e6	+	5.54799e6i	0.148978	+	0.258038i	0.930850	−	0.365401i	$-0.119068\pi$
$857$	3.20313e6	+	5.54799e6i	0.148978	+	0.258038i	−0.781872	+	0.623439i	$0.785735\pi$
$858$	2.18310e7	+	3.78123e7i	1.01241	+	1.75354i
$859$	−9.08695e6	+	1.57391e7i	−0.420180	+	0.727773i	−0.995957	−	0.0898340i	$-0.971366\pi$
$859$	−9.08695e6	+	1.57391e7i	−0.420180	+	0.727773i	0.575777	+	0.817607i	$0.304700\pi$
$860$	8.92627e6			0.411551
$861$	5.01360e6	−	1.46695e6i	0.230485	−	0.0674383i
$862$	−7.00114e7			−3.20923
$863$	−409387.	+	709079.i	−0.0187114	+	0.0324091i	−0.875230	−	0.483708i	$-0.839290\pi$
$863$	−409387.	+	709079.i	−0.0187114	+	0.0324091i	0.856518	+	0.516117i	$0.172623\pi$
$864$	−2.30472e6	−	3.99188e6i	−0.105035	−	0.181925i
$865$	−4.02421e6	−	6.97014e6i	−0.182869	−	0.316739i
$866$	2.04134e7	−	3.53570e7i	0.924954	−	1.60207i
$867$	−9.93858e6			−0.449031
$868$	2.00608e7	+	1.91644e7i	0.903753	+	0.863369i
$869$	−2.25560e6			−0.101324
$870$	2.60237e6	−	4.50744e6i	0.116566	−	0.201898i
$871$	−2.83306e7	−	4.90701e7i	−1.26535	−	2.19165i
$872$	7.54842e6	+	1.30743e7i	0.336175	+	0.582272i
$873$	2.57798e6	−	4.46519e6i	0.114484	−	0.198292i
$874$	−5.83574e7			−2.58415
$875$	−4.14400e6	+	1.70112e7i	−0.182978	+	0.751127i
$876$	−1.09528e7			−0.482242
$877$	1.66981e7	−	2.89219e7i	0.733108	−	1.26978i	−0.222441	−	0.974946i	$-0.571402\pi$
$877$	1.66981e7	−	2.89219e7i	0.733108	−	1.26978i	0.955549	−	0.294834i	$-0.0952642\pi$
$878$	−7.59411e6	−	1.31534e7i	−0.332461	−	0.575839i
$879$	6.70038e6	+	1.16054e7i	0.292501	+	0.506627i
$880$	−1.05894e7	+	1.83413e7i	−0.460961	+	0.798407i
$881$	−1.24325e7			−0.539658			−0.269829	−	0.962908i	$-0.586967\pi$
$881$	−1.24325e7			−0.539658			−0.269829	+	0.962908i	$0.586967\pi$
$882$	635814.	+	1.39039e7i	0.0275207	+	0.601817i
$883$	−2.33298e7			−1.00695			−0.503476	−	0.864009i	$-0.667946\pi$
$883$	−2.33298e7			−1.00695			−0.503476	+	0.864009i	$0.667946\pi$
$884$	2.07645e7	−	3.59651e7i	0.893697	−	1.54793i
$885$	−2.93910e6	−	5.09067e6i	−0.126141	−	0.218483i
$886$	2.87389e7	+	4.97772e7i	1.22995	+	2.13033i
$887$	2.37764e6	−	4.11819e6i	0.101470	−	0.175751i	−0.810821	−	0.585295i	$-0.800979\pi$
$887$	2.37764e6	−	4.11819e6i	0.101470	−	0.175751i	0.912290	+	0.409544i	$0.134312\pi$
$888$	−3.69514e7			−1.57253
$889$	715640.	−	2.93771e6i	0.0303697	−	0.124668i
$890$	−1.51772e7			−0.642269
$891$	−1.52716e6	+	2.64512e6i	−0.0644451	+	0.111622i
$892$	2.24916e7	+	3.89567e7i	0.946475	+	1.63934i
$893$	−2.16573e6	−	3.75115e6i	−0.0908814	−	0.157411i
$894$	−6.45358e6	+	1.11779e7i	−0.270058	+	0.467754i
$895$	1.84368e7			0.769356
$896$	−1.57519e7	−	1.50481e7i	−0.655487	−	0.626197i
$897$	−3.77371e7			−1.56598
$898$	−9.96226e6	+	1.72551e7i	−0.412256	+	0.714048i
$899$	3.51331e6	+	6.08522e6i	0.144983	+	0.251118i
$900$	7.52198e6	+	1.30284e7i	0.309546	+	0.536150i
$901$	−320482.	+	555090.i	−0.0131520	+	0.0227799i
$902$	−2.13087e7			−0.872050
$903$	−5.80236e6	+	1.69773e6i	−0.236802	+	0.0692867i
$904$	−4.00716e7			−1.63086
$905$	1.57596e6	−	2.72964e6i	0.0639622	−	0.110786i
$906$	7.54481e6	+	1.30680e7i	0.305371	+	0.528918i
$907$	9.54512e6	+	1.65326e7i	0.385268	+	0.667304i	0.991806	−	0.127750i	$-0.0407755\pi$
$907$	9.54512e6	+	1.65326e7i	0.385268	+	0.667304i	−0.606538	+	0.795054i	$0.707442\pi$
$908$	−3.63445e7	+	6.29506e7i	−1.46293	+	2.53388i
$909$	1.49544e7			0.600289
$910$	3.07992e7	−	9.01165e6i	1.23292	−	0.360745i
$911$	−1.22591e6			−0.0489399			−0.0244700	−	0.999701i	$-0.507790\pi$
$911$	−1.22591e6			−0.0489399			−0.0244700	+	0.999701i	$0.507790\pi$
$912$	1.19595e7	−	2.07144e7i	0.476128	−	0.824679i
$913$	−1.39996e7	−	2.42481e7i	−0.555827	−	0.962720i
$914$	1.36648e7	+	2.36681e7i	0.541050	+	0.937126i
$915$	2.25571e6	−	3.90700e6i	0.0890697	−	0.154273i
$916$	6.42490e7			2.53004
$917$	−3.17555e7	−	3.03366e7i	−1.24708	−	1.19136i
$918$	4.18688e6			0.163977
$919$	8.46136e6	−	1.46555e7i	0.330485	−	0.572417i	−0.652122	−	0.758114i	$-0.726121\pi$
$919$	8.46136e6	−	1.46555e7i	0.330485	−	0.572417i	0.982607	+	0.185697i	$0.0594544\pi$
$920$	−2.02428e7	−	3.50615e7i	−0.788497	−	1.36572i
$921$	−9.13988e6	−	1.58307e7i	−0.355052	−	0.614968i
$922$	2.37839e7	−	4.11949e7i	0.921415	−	1.59594i
$923$	6.19419e6			0.239321
$924$	9.32395e6	−	3.82749e7i	0.359269	−	1.47480i
$925$	2.53749e7			0.975101
$926$	2.65098e7	−	4.59162e7i	1.01596	−	1.75970i
$927$	−2.10777e6	−	3.65077e6i	−0.0805609	−	0.139536i
$928$	7.52865e6	+	1.30400e7i	0.286977	+	0.497059i
$929$	−3.38620e6	+	5.86507e6i	−0.128728	+	0.222964i	−0.923184	−	0.384358i	$-0.874423\pi$
$929$	−3.38620e6	+	5.86507e6i	−0.128728	+	0.222964i	0.794456	+	0.607322i	$0.207756\pi$
$930$	6.44897e6			0.244502
$931$	−1.96428e7	+	1.25709e7i	−0.742729	+	0.475329i
$932$	4.32380e7			1.63052
$933$	−1.30403e6	+	2.25865e6i	−0.0490438	+	0.0849463i
$934$	2.58653e7	+	4.48001e7i	0.970177	+	1.68040i
$935$	−3.10583e6	−	5.37945e6i	−0.116185	−	0.201238i
$936$	1.71048e7	−	2.96264e7i	0.638158	−	1.10532i
$937$	−1.41035e7			−0.524779			−0.262389	−	0.964962i	$-0.584511\pi$
$937$	−1.41035e7			−0.524779			−0.262389	+	0.964962i	$0.584511\pi$
$938$	−1.74386e7	+	7.15856e7i	−0.647149	+	2.65655i
$939$	1.96389e6			0.0726866
$940$	2.68882e6	−	4.65718e6i	0.0992527	−	0.171911i
$941$	2.81262e6	+	4.87160e6i	0.103547	+	0.179349i	0.913144	−	0.407638i	$-0.133647\pi$
$941$	2.81262e6	+	4.87160e6i	0.103547	+	0.179349i	−0.809597	+	0.586987i	$0.800314\pi$
$942$	−2.56051e7	−	4.43493e7i	−0.940154	−	1.62839i
$943$	9.20859e6	−	1.59498e7i	0.337221	−	0.584083i
$944$	5.26657e7			1.92353
$945$	1.62320e6	+	1.55067e6i	0.0591280	+	0.0564859i
$946$	2.46611e7			0.895952
$947$	−1.32063e7	+	2.28739e7i	−0.478526	+	0.828831i	−0.999697	−	0.0246212i	$-0.992162\pi$
$947$	−1.32063e7	+	2.28739e7i	−0.478526	+	0.828831i	0.521171	+	0.853452i	$0.325495\pi$
$948$	1.58136e6	+	2.73899e6i	0.0571491	+	0.0989852i
$949$	−8.55174e6	−	1.48120e7i	−0.308240	−	0.533887i
$950$	−1.81643e7	+	3.14615e7i	−0.652994	+	1.13102i
$951$	1.16157e7			0.416479
$952$	−2.89612e7	+	8.47387e6i	−1.03568	+	0.303033i
$953$	4.21824e7			1.50452			0.752262	−	0.658864i	$-0.228963\pi$
$953$	4.21824e7			1.50452			0.752262	+	0.658864i	$0.228963\pi$
$954$	−472448.	+	818304.i	−0.0168067	+	0.0291101i
$955$	−78828.6	−	136535.i	−0.00279689	−	0.00484436i
$956$	−2.69479e7	−	4.66751e7i	−0.953629	−	1.65173i
$957$	4.98866e6	−	8.64061e6i	0.176078	−	0.304975i
$958$	−5.67511e7			−1.99784
$959$	7.82344e6	−	2.28909e6i	0.274695	−	0.0803741i
$960$	717145.			0.0251148
$961$	9.96139e6	−	1.72536e7i	0.347946	−	0.602660i
$962$	−5.16314e7	−	8.94283e7i	−1.79877	−	3.11557i
$963$	−1.95120e6	−	3.37958e6i	−0.0678010	−	0.117435i
$964$	4.26038e7	−	7.37920e7i	1.47658	−	2.55751i
$965$	1.07503e7			0.371622
$966$	3.54822e7	+	3.38967e7i	1.22340	+	1.16873i
$967$	4.01501e7			1.38077			0.690384	−	0.723443i	$-0.257441\pi$
$967$	4.01501e7			1.38077			0.690384	+	0.723443i	$0.257441\pi$
$968$	−1.15319e7	+	1.99738e7i	−0.395560	+	0.685130i
$969$	3.50767e6	+	6.07546e6i	0.120008	+	0.207859i
$970$	7.72902e6	+	1.33870e7i	0.263751	+	0.456831i
$971$	−8.22756e6	+	1.42506e7i	−0.280042	+	0.485047i	−0.971395	−	0.237471i	$-0.923682\pi$
$971$	−8.22756e6	+	1.42506e7i	−0.280042	+	0.485047i	0.691353	+	0.722517i	$0.257015\pi$
$972$	4.28266e6			0.145394
$973$	6.50277e6	−	2.66939e7i	0.220200	−	0.903921i
$974$	−7.03207e7			−2.37512
$975$	−1.17460e7	+	2.03447e7i	−0.395712	+	0.685393i
$976$	2.02100e7	+	3.50048e7i	0.679113	+	1.17626i
$977$	−8.55881e6	−	1.48243e7i	−0.286865	−	0.496864i	0.686195	−	0.727418i	$-0.259280\pi$
$977$	−8.55881e6	−	1.48243e7i	−0.286865	−	0.496864i	−0.973060	+	0.230554i	$0.925946\pi$
$978$	907571.	−	1.57196e6i	0.0303412	−	0.0525526i
$979$	−2.90942e7			−0.970174
$980$	−2.57099e7	−	1.33163e7i	−0.855136	−	0.442915i
$981$	−2.95128e6			−0.0979125
$982$	−3.80562e7	+	6.59153e7i	−1.25935	+	2.18126i
$983$	1.16901e7	+	2.02479e7i	0.385865	+	0.668338i	0.991889	−	0.127108i	$-0.0405696\pi$
$983$	1.16901e7	+	2.02479e7i	0.385865	+	0.668338i	−0.606024	+	0.795447i	$0.707236\pi$
$984$	8.34781e6	+	1.44588e7i	0.274843	+	0.476042i
$985$	−9.70245e6	+	1.68051e7i	−0.318633	+	0.551889i
$986$	−1.36770e7			−0.448021
$987$	−862048.	+	3.53871e6i	−0.0281669	+	0.115625i
$988$	1.02579e8			3.34324
$989$	−1.06573e7	+	1.84590e7i	−0.346463	+	0.600092i
$990$	−4.57856e6	−	7.93029e6i	−0.148471	−	0.257159i
$991$	2.35478e6	+	4.07859e6i	0.0761667	+	0.131925i	0.901593	−	0.432585i	$-0.142399\pi$
$991$	2.35478e6	+	4.07859e6i	0.0761667	+	0.131925i	−0.825426	+	0.564510i	$0.809065\pi$
$992$	−9.32842e6	+	1.61573e7i	−0.300974	+	0.521302i
$993$	−3.13705e7			−1.00960
$994$	−5.82407e6	−	5.56383e6i	−0.186965	−	0.178611i
$995$	1.91547e7			0.613362
$996$	−1.96298e7	+	3.39998e7i	−0.627000	+	1.08600i
$997$	2.27714e7	+	3.94412e7i	0.725524	+	1.25665i	0.958758	+	0.284224i	$0.0917360\pi$
$997$	2.27714e7	+	3.94412e7i	0.725524	+	1.25665i	−0.233233	+	0.972421i	$0.574931\pi$
$998$	−1.10075e7	−	1.90655e7i	−0.349834	−	0.605930i
$999$	3.61181e6	−	6.25584e6i	0.114502	−	0.198323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.c.16.1	yes	8
3.2	odd	2		63.6.e.e.37.4		8
4.3	odd	2		336.6.q.j.289.2		8
7.2	even	3		147.6.a.m.1.4		4
7.3	odd	6		147.6.e.o.67.1		8
7.4	even	3	inner	21.6.e.c.4.1	✓	8
7.5	odd	6		147.6.a.l.1.4		4
7.6	odd	2		147.6.e.o.79.1		8
21.2	odd	6		441.6.a.w.1.1		4
21.5	even	6		441.6.a.v.1.1		4
21.11	odd	6		63.6.e.e.46.4		8
28.11	odd	6		336.6.q.j.193.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.1	✓	8	7.4	even	3	inner
21.6.e.c.16.1	yes	8	1.1	even	1	trivial
63.6.e.e.37.4		8	3.2	odd	2
63.6.e.e.46.4		8	21.11	odd	6
147.6.a.l.1.4		4	7.5	odd	6
147.6.a.m.1.4		4	7.2	even	3
147.6.e.o.67.1		8	7.3	odd	6
147.6.e.o.79.1		8	7.6	odd	2
336.6.q.j.193.2		8	28.11	odd	6
336.6.q.j.289.2		8	4.3	odd	2
441.6.a.v.1.1		4	21.5	even	6
441.6.a.w.1.1		4	21.2	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.11193 + 8.85412i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(-11.8764 + 20.5705i) q^{5} +92.0147 q^{6} +(30.6840 - 125.958i) q^{7} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-5.11193 + 8.85412i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-36.2636 - 62.8104i) q^{4} +(-11.8764 + 20.5705i) q^{5} +92.0147 q^{6} +(30.6840 - 125.958i) q^{7} +414.344 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-121.423 - 210.310i) q^{10} +(-232.763 - 403.157i) q^{11} +(-326.372 + 565.293i) q^{12} -1019.30 q^{13} +(958.395 + 915.570i) q^{14} +213.775 q^{15} +(-957.660 + 1658.72i) q^{16} +(-280.878 - 486.496i) q^{17} +(-414.066 - 717.183i) q^{18} +(693.789 - 1201.68i) q^{19} +1722.72 q^{20} +(-1119.83 + 327.654i) q^{21} +4759.47 q^{22} +(-2056.81 + 3562.50i) q^{23} +(-1864.55 - 3229.49i) q^{24} +(1280.40 + 2217.72i) q^{25} +(5210.59 - 9025.00i) q^{26} +729.000 q^{27} +(-9024.20 + 2640.42i) q^{28} -2381.37 q^{29} +(-1092.80 + 1892.79i) q^{30} +(-1475.33 - 2555.34i) q^{31} +(-3161.47 - 5475.84i) q^{32} +(-2094.87 + 3628.42i) q^{33} +5743.32 q^{34} +(2226.61 + 2127.12i) q^{35} +5874.70 q^{36} +(4954.48 - 8581.40i) q^{37} +(7093.20 + 12285.8i) q^{38} +(4586.85 + 7944.66i) q^{39} +(-4920.92 + 8523.28i) q^{40} -4477.13 q^{41} +(2823.38 - 11590.0i) q^{42} +5181.48 q^{43} +(-16881.6 + 29239.9i) q^{44} +(-961.989 - 1666.21i) q^{45} +(-21028.5 - 36422.5i) q^{46} +(1560.80 - 2703.38i) q^{47} +17237.9 q^{48} +(-14924.0 - 7729.82i) q^{49} -26181.3 q^{50} +(-2527.91 + 4378.46i) q^{51} +(36963.5 + 64022.6i) q^{52} +(-570.499 - 988.133i) q^{53} +(-3726.59 + 6454.65i) q^{54} +11057.6 q^{55} +(12713.7 - 52190.0i) q^{56} -12488.2 q^{57} +(12173.4 - 21085.0i) q^{58} +(-13748.5 - 23813.2i) q^{59} +(-7752.26 - 13427.3i) q^{60} +(10551.8 - 18276.2i) q^{61} +30167.1 q^{62} +(7593.03 + 7253.74i) q^{63} +3354.67 q^{64} +(12105.6 - 20967.6i) q^{65} +(-21417.6 - 37096.4i) q^{66} +(27794.2 + 48141.0i) q^{67} +(-20371.3 + 35284.2i) q^{68} +37022.6 q^{69} +(-30216.0 + 8841.02i) q^{70} -6076.90 q^{71} +(-16780.9 + 29065.4i) q^{72} +(8389.82 + 14531.6i) q^{73} +(50653.8 + 87735.0i) q^{74} +(11523.6 - 19959.5i) q^{75} -100637. q^{76} +(-57923.1 + 16947.9i) q^{77} -93790.5 q^{78} +(2422.63 - 4196.12i) q^{79} +(-22747.1 - 39399.2i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(22886.7 - 39641.0i) q^{82} +60145.4 q^{83} +(61189.0 + 58454.8i) q^{84} +13343.3 q^{85} +(-26487.4 + 45877.5i) q^{86} +(10716.2 + 18561.0i) q^{87} +(-96443.9 - 167046. i) q^{88} +(31248.7 - 54124.4i) q^{89} +19670.5 q^{90} +(-31276.2 + 128389. i) q^{91} +298349. q^{92} +(-13277.9 + 22998.1i) q^{93} +(15957.4 + 27639.0i) q^{94} +(16479.4 + 28543.2i) q^{95} +(-28453.3 + 49282.5i) q^{96} -63653.8 q^{97} +(144731. - 92624.4i) q^{98} +37707.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

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