LMFDB - Embedded newform 74.6.c.b.63.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.c (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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
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} + 1317 x^{14} - 2712 x^{13} + 1206654 x^{12} - 2683704 x^{11} + 572597881 x^{10} + \cdots + 683643854869056 $ x^16 + 1317x^14 - 2712x^13 + 1206654x^12 - 2683704x^11 + 572597881x^10 - 1472178324x^9 + 197936317446x^8 - 538366712748x^7 + 33466187997381x^6 - 131063526625884x^5 + 4041550479749833x^4 - 11057529820868736x^3 + 29709621477714456x^2 - 4628457422701056x + 683643854869056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.1
Root			$11.6855 - 20.2399i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.6.c.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(-12.1855 + 21.1059i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-5.21821 + 9.03821i) q^{5} -97.4840 q^{6} +(-70.8626 + 122.738i) q^{7} -64.0000 q^{8} +(-175.473 - 303.928i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(-12.1855 + 21.1059i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-5.21821 + 9.03821i) q^{5} -97.4840 q^{6} +(-70.8626 + 122.738i) q^{7} -64.0000 q^{8} +(-175.473 - 303.928i) q^{9} -41.7457 q^{10} +313.369 q^{11} +(-194.968 - 337.695i) q^{12} +(-152.674 + 264.440i) q^{13} -566.901 q^{14} +(-127.173 - 220.270i) q^{15} +(-128.000 - 221.703i) q^{16} +(26.6401 + 46.1420i) q^{17} +(701.892 - 1215.71i) q^{18} +(1487.28 - 2576.04i) q^{19} +(-83.4914 - 144.611i) q^{20} +(-1726.99 - 2991.24i) q^{21} +(626.737 + 1085.54i) q^{22} -253.103 q^{23} +(779.872 - 1350.78i) q^{24} +(1508.04 + 2612.00i) q^{25} -1221.39 q^{26} +2630.76 q^{27} +(-1133.80 - 1963.80i) q^{28} -7631.98 q^{29} +(508.692 - 881.081i) q^{30} -145.337 q^{31} +(512.000 - 886.810i) q^{32} +(-3818.56 + 6613.93i) q^{33} +(-106.560 + 184.568i) q^{34} +(-739.552 - 1280.94i) q^{35} +5615.14 q^{36} +(-1778.48 + 8135.17i) q^{37} +11898.2 q^{38} +(-3720.83 - 6444.66i) q^{39} +(333.966 - 578.445i) q^{40} +(-1873.82 + 3245.55i) q^{41} +(6907.97 - 11965.0i) q^{42} -5795.78 q^{43} +(-2506.95 + 4342.16i) q^{44} +3662.62 q^{45} +(-506.206 - 876.775i) q^{46} -10570.8 q^{47} +6238.98 q^{48} +(-1639.52 - 2839.73i) q^{49} +(-6032.16 + 10448.0i) q^{50} -1298.49 q^{51} +(-2442.79 - 4231.03i) q^{52} +(-5143.83 - 8909.37i) q^{53} +(5261.52 + 9113.22i) q^{54} +(-1635.22 + 2832.29i) q^{55} +(4535.21 - 7855.21i) q^{56} +(36246.4 + 62780.6i) q^{57} +(-15264.0 - 26437.9i) q^{58} +(12117.5 + 20988.1i) q^{59} +4069.54 q^{60} +(-15836.3 + 27429.3i) q^{61} +(-290.674 - 503.462i) q^{62} +49737.9 q^{63} +4096.00 q^{64} +(-1593.37 - 2759.80i) q^{65} -30548.4 q^{66} +(-8626.30 + 14941.2i) q^{67} -852.484 q^{68} +(3084.19 - 5341.97i) q^{69} +(2958.21 - 5123.77i) q^{70} +(14262.2 - 24702.9i) q^{71} +(11230.3 + 19451.4i) q^{72} -23858.5 q^{73} +(-31738.0 + 10109.5i) q^{74} -73504.9 q^{75} +(23796.4 + 41216.6i) q^{76} +(-22206.1 + 38462.1i) q^{77} +(14883.3 - 25778.7i) q^{78} +(37862.4 - 65579.6i) q^{79} +2671.72 q^{80} +(10582.8 - 18330.0i) q^{81} -14990.5 q^{82} +(52802.5 + 91456.6i) q^{83} +55263.8 q^{84} -556.055 q^{85} +(-11591.6 - 20077.2i) q^{86} +(92999.5 - 161080. i) q^{87} -20055.6 q^{88} +(-48874.3 - 84652.8i) q^{89} +(7325.25 + 12687.7i) q^{90} +(-21637.8 - 37477.8i) q^{91} +(2024.82 - 3507.10i) q^{92} +(1771.00 - 3067.47i) q^{93} +(-21141.7 - 36618.4i) q^{94} +(15521.8 + 26884.6i) q^{95} +(12478.0 + 21612.5i) q^{96} -63377.1 q^{97} +(6558.08 - 11358.9i) q^{98} +(-54987.8 - 95241.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9}+O(q^{10}) $ 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9} + 560 q^{10} - 240 q^{11} - 128 q^{12} + 1614 q^{13} - 256 q^{14} + 728 q^{15} - 2048 q^{16} + 216 q^{17} + 2792 q^{18} - 950 q^{19} + 1120 q^{20} + 1718 q^{21} - 480 q^{22} + 1716 q^{23} + 512 q^{24} - 11760 q^{25} + 12912 q^{26} - 92 q^{27} - 512 q^{28} + 1112 q^{29} - 2912 q^{30} - 16816 q^{31} + 8192 q^{32} + 4744 q^{33} - 864 q^{34} - 5004 q^{35} + 22336 q^{36} + 3556 q^{37} - 7600 q^{38} + 17710 q^{39} - 4480 q^{40} - 8080 q^{41} - 6872 q^{42} - 19012 q^{43} + 1920 q^{44} - 58672 q^{45} + 3432 q^{46} + 29392 q^{47} + 4096 q^{48} + 474 q^{49} + 47040 q^{50} - 17856 q^{51} + 25824 q^{52} - 29250 q^{53} - 184 q^{54} + 15772 q^{55} + 2048 q^{56} + 16182 q^{57} + 2224 q^{58} + 61478 q^{59} - 23296 q^{60} - 132002 q^{61} - 33632 q^{62} - 103324 q^{63} + 65536 q^{64} - 37426 q^{65} + 37952 q^{66} - 45658 q^{67} - 6912 q^{68} - 23816 q^{69} + 20016 q^{70} + 13236 q^{71} + 44672 q^{72} + 270632 q^{73} - 81304 q^{74} + 419904 q^{75} - 15200 q^{76} - 184084 q^{77} - 70840 q^{78} + 123974 q^{79} - 35840 q^{80} + 96448 q^{81} - 64640 q^{82} - 16936 q^{83} - 54976 q^{84} - 251316 q^{85} - 38024 q^{86} + 168290 q^{87} + 15360 q^{88} + 52892 q^{89} - 117344 q^{90} - 432546 q^{91} - 13728 q^{92} + 220328 q^{93} + 58784 q^{94} + 47026 q^{95} + 8192 q^{96} - 546140 q^{97} - 1896 q^{98} - 9800 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9 + 560 * q^10 - 240 * q^11 - 128 * q^12 + 1614 * q^13 - 256 * q^14 + 728 * q^15 - 2048 * q^16 + 216 * q^17 + 2792 * q^18 - 950 * q^19 + 1120 * q^20 + 1718 * q^21 - 480 * q^22 + 1716 * q^23 + 512 * q^24 - 11760 * q^25 + 12912 * q^26 - 92 * q^27 - 512 * q^28 + 1112 * q^29 - 2912 * q^30 - 16816 * q^31 + 8192 * q^32 + 4744 * q^33 - 864 * q^34 - 5004 * q^35 + 22336 * q^36 + 3556 * q^37 - 7600 * q^38 + 17710 * q^39 - 4480 * q^40 - 8080 * q^41 - 6872 * q^42 - 19012 * q^43 + 1920 * q^44 - 58672 * q^45 + 3432 * q^46 + 29392 * q^47 + 4096 * q^48 + 474 * q^49 + 47040 * q^50 - 17856 * q^51 + 25824 * q^52 - 29250 * q^53 - 184 * q^54 + 15772 * q^55 + 2048 * q^56 + 16182 * q^57 + 2224 * q^58 + 61478 * q^59 - 23296 * q^60 - 132002 * q^61 - 33632 * q^62 - 103324 * q^63 + 65536 * q^64 - 37426 * q^65 + 37952 * q^66 - 45658 * q^67 - 6912 * q^68 - 23816 * q^69 + 20016 * q^70 + 13236 * q^71 + 44672 * q^72 + 270632 * q^73 - 81304 * q^74 + 419904 * q^75 - 15200 * q^76 - 184084 * q^77 - 70840 * q^78 + 123974 * q^79 - 35840 * q^80 + 96448 * q^81 - 64640 * q^82 - 16936 * q^83 - 54976 * q^84 - 251316 * q^85 - 38024 * q^86 + 168290 * q^87 + 15360 * q^88 + 52892 * q^89 - 117344 * q^90 - 432546 * q^91 - 13728 * q^92 + 220328 * q^93 + 58784 * q^94 + 47026 * q^95 + 8192 * q^96 - 546140 * q^97 - 1896 * q^98 - 9800 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	−12.1855	+	21.1059i	−0.781701	+	1.35395i	0.149250	+	0.988800i	$0.452314\pi$
$3$	−12.1855	+	21.1059i	−0.781701	+	1.35395i	−0.930950	+	0.365146i	$0.881019\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	−5.21821	+	9.03821i	−0.0933462	+	0.161680i	−0.908917	−	0.416977i	$-0.863090\pi$
$5$	−5.21821	+	9.03821i	−0.0933462	+	0.161680i	0.815571	+	0.578657i	$0.196423\pi$
$6$	−97.4840			−1.10549
$7$	−70.8626	+	122.738i	−0.546603	+	0.946744i	0.451901	+	0.892068i	$0.350746\pi$
$7$	−70.8626	+	122.738i	−0.546603	+	0.946744i	−0.998504	+	0.0546762i	$0.982587\pi$
$8$	−64.0000			−0.353553
$9$	−175.473	−	303.928i	−0.722112	−	1.25073i
$10$	−41.7457			−0.132011
$11$	313.369			0.780861			0.390431	−	0.920632i	$-0.372326\pi$
$11$	313.369			0.780861			0.390431	+	0.920632i	$0.372326\pi$
$12$	−194.968	−	337.695i	−0.390850	−	0.676973i
$13$	−152.674	+	264.440i	−0.250558	+	0.433979i	−0.963679	−	0.267062i	$-0.913947\pi$
$13$	−152.674	+	264.440i	−0.250558	+	0.433979i	0.713122	+	0.701040i	$0.247281\pi$
$14$	−566.901			−0.773013
$15$	−127.173	−	220.270i	−0.145938	−	0.252771i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	26.6401	+	46.1420i	0.0223570	+	0.0387235i	0.876987	−	0.480513i	$-0.159550\pi$
$17$	26.6401	+	46.1420i	0.0223570	+	0.0387235i	−0.854630	+	0.519237i	$0.826216\pi$
$18$	701.892	−	1215.71i	0.510610	−	0.884402i
$19$	1487.28	−	2576.04i	0.945164	−	1.63707i	0.189743	−	0.981834i	$-0.439235\pi$
$19$	1487.28	−	2576.04i	0.945164	−	1.63707i	0.755422	−	0.655239i	$-0.227432\pi$
$20$	−83.4914	−	144.611i	−0.0466731	−	0.0808402i
$21$	−1726.99	−	2991.24i	−0.854560	−	1.48014i
$22$	626.737	+	1085.54i	0.276076	+	0.478178i
$23$	−253.103			−0.0997649			−0.0498824	−	0.998755i	$-0.515885\pi$
$23$	−253.103			−0.0997649			−0.0498824	+	0.998755i	$0.515885\pi$
$24$	779.872	−	1350.78i	0.276373	−	0.478692i
$25$	1508.04	+	2612.00i	0.482573	+	0.835841i
$26$	−1221.39			−0.354342
$27$	2630.76			0.694499
$28$	−1133.80	−	1963.80i	−0.273302	−	0.473372i
$29$	−7631.98			−1.68516			−0.842582	−	0.538569i	$-0.818965\pi$
$29$	−7631.98			−1.68516			−0.842582	+	0.538569i	$0.818965\pi$
$30$	508.692	−	881.081i	0.103193	−	0.178736i
$31$	−145.337			−0.0271626			−0.0135813	−	0.999908i	$-0.504323\pi$
$31$	−145.337			−0.0271626			−0.0135813	+	0.999908i	$0.504323\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−3818.56	+	6613.93i	−0.610400	+	1.05724i
$34$	−106.560	+	184.568i	−0.0158088	+	0.0273816i
$35$	−739.552	−	1280.94i	−0.102047	−	0.176750i
$36$	5615.14			0.722112
$37$	−1778.48	+	8135.17i	−0.213572	+	0.976927i
$37$	−1778.48	+	8135.17i	−0.213572	+	0.976927i
$38$	11898.2			1.33666
$39$	−3720.83	−	6444.66i	−0.391722	−	0.678483i
$40$	333.966	−	578.445i	0.0330029	−	0.0571626i
$41$	−1873.82	+	3245.55i	−0.174088	+	0.301528i	−0.939845	−	0.341601i	$-0.889031\pi$
$41$	−1873.82	+	3245.55i	−0.174088	+	0.301528i	0.765758	+	0.643129i	$0.222364\pi$
$42$	6907.97	−	11965.0i	0.604265	−	1.04662i
$43$	−5795.78			−0.478014			−0.239007	−	0.971018i	$-0.576822\pi$
$43$	−5795.78			−0.478014			−0.239007	+	0.971018i	$0.576822\pi$
$44$	−2506.95	+	4342.16i	−0.195215	+	0.338123i
$45$	3662.62			0.269625
$46$	−506.206	−	876.775i	−0.0352722	−	0.0610933i
$47$	−10570.8			−0.698015			−0.349007	−	0.937120i	$-0.613481\pi$
$47$	−10570.8			−0.698015			−0.349007	+	0.937120i	$0.613481\pi$
$48$	6238.98			0.390850
$49$	−1639.52	−	2839.73i	−0.0975498	−	0.168961i
$50$	−6032.16	+	10448.0i	−0.341231	+	0.591029i
$51$	−1298.49			−0.0699060
$52$	−2442.79	−	4231.03i	−0.125279	−	0.216989i
$53$	−5143.83	−	8909.37i	−0.251534	−	0.435670i	0.712414	−	0.701759i	$-0.247602\pi$
$53$	−5143.83	−	8909.37i	−0.251534	−	0.435670i	−0.963948	+	0.266089i	$0.914268\pi$
$54$	5261.52	+	9113.22i	0.245543	+	0.425292i
$55$	−1635.22	+	2832.29i	−0.0728904	+	0.126250i
$56$	4535.21	−	7855.21i	0.193253	−	0.334725i
$57$	36246.4	+	62780.6i	1.47767	+	2.55940i
$58$	−15264.0	−	26437.9i	−0.595795	−	1.03195i
$59$	12117.5	+	20988.1i	0.453193	+	0.784953i	0.998582	−	0.0532300i	$-0.0169516\pi$
$59$	12117.5	+	20988.1i	0.453193	+	0.784953i	−0.545390	+	0.838183i	$0.683618\pi$
$60$	4069.54			0.145938
$61$	−15836.3	+	27429.3i	−0.544916	+	0.943822i	0.453697	+	0.891156i	$0.350105\pi$
$61$	−15836.3	+	27429.3i	−0.544916	+	0.943822i	−0.998612	+	0.0526653i	$0.983228\pi$
$62$	−290.674	−	503.462i	−0.00960344	−	0.0166336i
$63$	49737.9			1.57883
$64$	4096.00			0.125000
$65$	−1593.37	−	2759.80i	−0.0467772	−	0.0810205i
$66$	−30548.4			−0.863235
$67$	−8626.30	+	14941.2i	−0.234767	+	0.406629i	−0.959205	−	0.282711i	$-0.908766\pi$
$67$	−8626.30	+	14941.2i	−0.234767	+	0.406629i	0.724438	+	0.689340i	$0.242100\pi$
$68$	−852.484			−0.0223570
$69$	3084.19	−	5341.97i	0.0779863	−	0.135076i
$70$	2958.21	−	5123.77i	0.0721579	−	0.124981i
$71$	14262.2	−	24702.9i	0.335769	−	0.581569i	−0.647863	−	0.761757i	$-0.724337\pi$
$71$	14262.2	−	24702.9i	0.335769	−	0.581569i	0.983632	+	0.180188i	$0.0576705\pi$
$72$	11230.3	+	19451.4i	0.255305	+	0.442201i
$73$	−23858.5			−0.524006			−0.262003	−	0.965067i	$-0.584383\pi$
$73$	−23858.5			−0.524006			−0.262003	+	0.965067i	$0.584383\pi$
$74$	−31738.0	+	10109.5i	−0.673753	+	0.214610i
$75$	−73504.9			−1.50891
$76$	23796.4	+	41216.6i	0.472582	+	0.818536i
$77$	−22206.1	+	38462.1i	−0.426821	+	0.739276i
$78$	14883.3	−	25778.7i	0.276989	−	0.479760i
$79$	37862.4	−	65579.6i	0.682559	−	1.18223i	−0.291638	−	0.956529i	$-0.594200\pi$
$79$	37862.4	−	65579.6i	0.682559	−	1.18223i	0.974197	−	0.225698i	$-0.0724663\pi$
$80$	2671.72			0.0466731
$81$	10582.8	−	18330.0i	0.179221	−	0.310420i
$82$	−14990.5			−0.246197
$83$	52802.5	+	91456.6i	0.841316	+	1.45720i	0.888782	+	0.458329i	$0.151552\pi$
$83$	52802.5	+	91456.6i	0.841316	+	1.45720i	−0.0474664	+	0.998873i	$0.515115\pi$
$84$	55263.8			0.854560
$85$	−556.055			−0.00834777
$86$	−11591.6	−	20077.2i	−0.169004	−	0.292723i
$87$	92999.5	−	161080.i	1.31729	−	2.28162i
$88$	−20055.6			−0.276076
$89$	−48874.3	−	84652.8i	−0.654042	−	1.13283i	−0.982133	−	0.188188i	$-0.939739\pi$
$89$	−48874.3	−	84652.8i	−0.654042	−	1.13283i	0.328091	−	0.944646i	$-0.393595\pi$
$90$	7325.25	+	12687.7i	0.0953270	+	0.165111i
$91$	−21637.8	−	37477.8i	−0.273911	−	0.474428i
$92$	2024.82	−	3507.10i	0.0249412	−	0.0431995i
$93$	1771.00	−	3067.47i	0.0212330	−	0.0367767i
$94$	−21141.7	−	36618.4i	−0.246785	−	0.427445i
$95$	15521.8	+	26884.6i	0.176455	+	0.305629i
$96$	12478.0	+	21612.5i	0.138186	+	0.239346i
$97$	−63377.1			−0.683916			−0.341958	−	0.939715i	$-0.611090\pi$
$97$	−63377.1			−0.683916			−0.341958	+	0.939715i	$0.611090\pi$
$98$	6558.08	−	11358.9i	0.0689781	−	0.119474i
$99$	−54987.8	−	95241.6i	−0.563869	−	0.976650i
$100$	−48257.3			−0.482573
$101$	−24980.0			−0.243663			−0.121831	−	0.992551i	$-0.538877\pi$
$101$	−24980.0			−0.243663			−0.121831	+	0.992551i	$0.538877\pi$
$102$	−2596.99	−	4498.11i	−0.0247155	−	0.0428085i
$103$	−153068.			−1.42165			−0.710825	−	0.703369i	$-0.751678\pi$
$103$	−153068.			−1.42165			−0.710825	+	0.703369i	$0.751678\pi$
$104$	9771.16	−	16924.1i	0.0885855	−	0.153435i
$105$	36047.3			0.319080
$106$	20575.3	−	35637.5i	0.177861	−	0.308065i
$107$	78361.3	−	135726.i	0.661671	−	1.14605i	−0.318506	−	0.947921i	$-0.603181\pi$
$107$	78361.3	−	135726.i	0.661671	−	1.14605i	0.980176	−	0.198127i	$-0.0634857\pi$
$108$	−21046.1	+	36452.9i	−0.173625	+	0.300727i
$109$	−18963.4	−	32845.6i	−0.152880	−	0.264796i	0.779405	−	0.626520i	$-0.215521\pi$
$109$	−18963.4	−	32845.6i	−0.152880	−	0.264796i	−0.932285	+	0.361724i	$0.882188\pi$
$110$	−13081.8			−0.103083
$111$	−150028.	−	136668.i	−1.15576	−	1.05283i
$112$	36281.7			0.273302
$113$	123733.	+	214312.i	0.911569	+	1.57888i	0.811848	+	0.583869i	$0.198462\pi$
$113$	123733.	+	214312.i	0.911569	+	1.57888i	0.0997212	+	0.995015i	$0.468205\pi$
$114$	−144986.	+	251122.i	−1.04487	+	1.80977i
$115$	1320.75	−	2287.60i	0.00931267	−	0.0161300i
$116$	61055.8	−	105752.i	0.421291	−	0.729697i
$117$	107161.			0.723722
$118$	−48470.0	+	83952.5i	−0.320456	+	0.555045i
$119$	−7551.15			−0.0488817
$120$	8139.08	+	14097.3i	0.0515967	+	0.0893681i
$121$	−62851.1			−0.390256
$122$	−126690.			−0.770627
$123$	−45666.8	−	79097.3i	−0.272169	−	0.471410i
$124$	1162.70	−	2013.85i	0.00679066	−	0.0117618i
$125$	−64090.9			−0.366878
$126$	99475.9	+	172297.i	0.558202	+	0.966834i
$127$	83255.5	+	144203.i	0.458040	+	0.793349i	0.998857	−	0.0477911i	$-0.0152182\pi$
$127$	83255.5	+	144203.i	0.458040	+	0.793349i	−0.540817	+	0.841140i	$0.681885\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	70624.5	−	122325.i	0.373664	−	0.647205i
$130$	6373.49	−	11039.2i	0.0330765	−	0.0572901i
$131$	24323.9	+	42130.1i	0.123838	+	0.214494i	0.921278	−	0.388904i	$-0.127146\pi$
$131$	24323.9	+	42130.1i	0.123838	+	0.214494i	−0.797440	+	0.603398i	$0.793813\pi$
$132$	−61096.9	−	105823.i	−0.305200	−	0.528622i
$133$	210784.	+	365089.i	1.03326	+	1.78966i
$134$	−69010.4			−0.332011
$135$	−13727.9	+	23777.3i	−0.0648288	+	0.112287i
$136$	−1704.97	−	2953.09i	−0.00790440	−	0.0136908i
$137$	260791.			1.18711			0.593555	−	0.804793i	$-0.297724\pi$
$137$	260791.			1.18711			0.593555	+	0.804793i	$0.297724\pi$
$138$	24673.5			0.110289
$139$	85624.0	+	148305.i	0.375888	+	0.651057i	0.990460	−	0.137804i	$-0.0440044\pi$
$139$	85624.0	+	148305.i	0.375888	+	0.651057i	−0.614572	+	0.788861i	$0.710671\pi$
$140$	23665.7			0.102047
$141$	128811.	−	223107.i	0.545639	−	0.945074i
$142$	114098.			0.474849
$143$	−47843.3	+	82867.1i	−0.195651	+	0.338877i
$144$	−44921.1	+	77805.7i	−0.180528	+	0.312683i
$145$	39825.3	−	68979.4i	0.157304	−	0.272458i
$146$	−47717.1	−	82648.4i	−0.185264	−	0.320887i
$147$	79913.5			0.305019
$148$	−98496.4	−	89724.7i	−0.369629	−	0.336711i
$149$	418712.			1.54508			0.772538	−	0.634968i	$-0.218987\pi$
$149$	418712.			1.54508			0.772538	+	0.634968i	$0.218987\pi$
$150$	−147010.	−	254629.i	−0.533480	−	0.924015i
$151$	−136113.	+	235754.i	−0.485799	+	0.841428i	−0.999867	−	0.0163213i	$-0.994805\pi$
$151$	−136113.	+	235754.i	−0.485799	+	0.841428i	0.514068	+	0.857749i	$0.328138\pi$
$152$	−95185.6	+	164866.i	−0.334166	+	0.578793i
$153$	9349.25	−	16193.4i	0.0322885	−	0.0559254i
$154$	−177649.			−0.603616
$155$	758.399	−	1313.59i	0.00253553	−	0.00439166i
$156$	119066.			0.391722
$157$	−79189.6	−	137160.i	−0.256400	−	0.444099i	0.708875	−	0.705335i	$-0.249203\pi$
$157$	−79189.6	−	137160.i	−0.256400	−	0.444099i	−0.965275	+	0.261236i	$0.915870\pi$
$158$	302899.			0.965284
$159$	250721.			0.786497
$160$	5343.45	+	9255.12i	0.0165014	+	0.0285813i
$161$	17935.5	−	31065.3i	0.0545318	−	0.0944518i
$162$	84662.7			0.253457
$163$	−43102.6	−	74655.8i	−0.127067	−	0.220087i	0.795472	−	0.605991i	$-0.207223\pi$
$163$	−43102.6	−	74655.8i	−0.127067	−	0.220087i	−0.922539	+	0.385903i	$0.873890\pi$
$164$	−29981.1	−	51928.8i	−0.0870438	−	0.150764i
$165$	−39852.1	−	69025.8i	−0.113957	−	0.197379i
$166$	−211210.	+	365826.i	−0.594900	+	1.03040i
$167$	−147018.	+	254643.i	−0.407925	+	0.706547i	−0.994657	−	0.103234i	$-0.967081\pi$
$167$	−147018.	+	254643.i	−0.407925	+	0.706547i	0.586732	+	0.809781i	$0.300414\pi$
$168$	110528.	+	191439.i	0.302133	+	0.523309i
$169$	139028.	+	240803.i	0.374442	+	0.648552i
$170$	−1112.11	−	1926.23i	−0.00295138	−	0.00511194i
$171$	−1.04391e6			−2.73006
$172$	46366.3	−	80308.7i	0.119504	−	0.206986i
$173$	206656.	+	357938.i	0.524967	+	0.909269i	0.999577	+	0.0290733i	$0.00925562\pi$
$173$	206656.	+	357938.i	0.524967	+	0.909269i	−0.474610	+	0.880196i	$0.657411\pi$
$174$	743996.			1.86293
$175$	−427455.			−1.05510
$176$	−40111.2	−	69474.6i	−0.0976077	−	0.169061i
$177$	−590631.			−1.41704
$178$	195497.	−	338611.i	0.462477	−	0.801034i
$179$	279929.			0.653002			0.326501	−	0.945197i	$-0.394130\pi$
$179$	279929.			0.653002			0.326501	+	0.945197i	$0.394130\pi$
$180$	−29301.0	+	50750.8i	−0.0674064	+	0.116751i
$181$	−246077.	+	426218.i	−0.558309	+	0.967020i	0.439328	+	0.898327i	$0.355216\pi$
$181$	−246077.	+	426218.i	−0.558309	+	0.967020i	−0.997638	+	0.0686937i	$0.978117\pi$
$182$	86551.2	−	149911.i	0.193684	−	0.335471i
$183$	−385947.	−	668479.i	−0.851922	−	1.47557i
$184$	16198.6			0.0352722
$185$	−64246.8	−	58525.3i	−0.138014	−	0.125723i
$186$	14168.0			0.0300281
$187$	8348.18	+	14459.5i	0.0174577	+	0.0302377i
$188$	84566.7	−	146474.i	0.174504	−	0.302249i
$189$	−186422.	+	322893.i	−0.379615	+	0.657513i
$190$	−62087.3	+	107538.i	−0.124773	+	0.216112i
$191$	−604329.			−1.19864			−0.599322	−	0.800508i	$-0.704563\pi$
$191$	−604329.			−1.19864			−0.599322	+	0.800508i	$0.704563\pi$
$192$	−49911.8	+	86449.8i	−0.0977126	+	0.169243i
$193$	−877076.			−1.69490			−0.847449	−	0.530876i	$-0.821863\pi$
$193$	−877076.			−1.69490			−0.847449	+	0.530876i	$0.821863\pi$
$194$	−126754.	−	219545.i	−0.241801	−	0.418812i
$195$	77664.3			0.146263
$196$	52464.6			0.0975498
$197$	243587.	+	421904.i	0.447186	+	0.774548i	0.998202	−	0.0599463i	$-0.0190930\pi$
$197$	243587.	+	421904.i	0.447186	+	0.774548i	−0.551016	+	0.834495i	$0.685760\pi$
$198$	219951.	−	380966.i	0.398716	−	0.690596i
$199$	644418.			1.15355			0.576773	−	0.816904i	$-0.304312\pi$
$199$	644418.			1.15355			0.576773	+	0.816904i	$0.304312\pi$
$200$	−96514.6	−	167168.i	−0.170615	−	0.295514i
$201$	−210232.	−	364132.i	−0.367036	−	0.635724i
$202$	−49960.0	−	86533.2i	−0.0861477	−	0.149212i
$203$	540822.	−	936731.i	0.921115	−	1.59542i
$204$	10387.9	−	17992.5i	0.0174765	−	0.0302702i
$205$	−19556.0	−	33871.9i	−0.0325008	−	0.0562931i
$206$	−306137.	−	530245.i	−0.502629	−	0.870579i
$207$	44412.8	+	76925.2i	0.0720414	+	0.124779i
$208$	78169.3			0.125279
$209$	466065.	−	807249.i	0.738042	−	1.27833i
$210$	72094.5	+	124871.i	0.112812	+	0.195396i
$211$	293124.			0.453258			0.226629	−	0.973981i	$-0.427229\pi$
$211$	293124.			0.453258			0.226629	+	0.973981i	$0.427229\pi$
$212$	164603.			0.251534
$213$	347584.	+	602034.i	0.524942	+	0.909226i
$214$	626890.			0.935744
$215$	30243.6	−	52383.5i	0.0446208	−	0.0772855i
$216$	−168369.			−0.245543
$217$	10299.0	−	17838.3i	0.0148472	−	0.0257161i
$218$	75853.7	−	131382.i	0.108102	−	0.187239i
$219$	290728.	−	503556.i	0.409616	−	0.709476i
$220$	−26163.6	−	45316.7i	−0.0364452	−	0.0631250i
$221$	−16269.0			−0.0224069
$222$	173373.	−	793049.i	0.236102	−	1.07998i
$223$	20324.3			0.0273687			0.0136844	−	0.999906i	$-0.495644\pi$
$223$	20324.3			0.0273687			0.0136844	+	0.999906i	$0.495644\pi$
$224$	72563.3	+	125683.i	0.0966267	+	0.167362i
$225$	529241.	−	916673.i	0.696943	−	1.20714i
$226$	−494932.	+	857248.i	−0.644577	+	1.11644i
$227$	153588.	−	266022.i	0.197830	−	0.342652i	−0.749994	−	0.661444i	$-0.769944\pi$
$227$	153588.	−	266022.i	0.197830	−	0.342652i	0.947825	+	0.318792i	$0.103277\pi$
$228$	−1.15988e6			−1.47767
$229$	−463853.	+	803417.i	−0.584509	+	1.01240i	0.410427	+	0.911893i	$0.365380\pi$
$229$	−463853.	+	803417.i	−0.584509	+	1.01240i	−0.994936	+	0.100506i	$0.967954\pi$
$230$	10566.0			0.0131701
$231$	−541186.	−	937361.i	−0.667293	−	1.15578i
$232$	488446.			0.595795
$233$	1.58148e6			1.90842			0.954208	−	0.299145i	$-0.0967016\pi$
$233$	1.58148e6			1.90842			0.954208	+	0.299145i	$0.0967016\pi$
$234$	214322.	+	371216.i	0.255874	+	0.443188i
$235$	55160.8	−	95541.4i	0.0651570	−	0.112855i
$236$	−387760.			−0.453193
$237$	922744.	+	1.59824e6i	1.06711	+	1.84829i
$238$	−15102.3	−	26158.0i	−0.0172823	−	0.0299338i
$239$	−637437.	−	1.10407e6i	−0.721842	−	1.25027i	−0.960261	−	0.279105i	$-0.909962\pi$
$239$	−637437.	−	1.10407e6i	−0.721842	−	1.25027i	0.238418	−	0.971163i	$-0.423371\pi$
$240$	−32556.3	+	56389.2i	−0.0364844	+	0.0631928i
$241$	−808871.	+	1.40101e6i	−0.897092	+	1.55381i	−0.0658973	+	0.997826i	$0.520991\pi$
$241$	−808871.	+	1.40101e6i	−0.897092	+	1.55381i	−0.831194	+	0.555982i	$0.812342\pi$
$242$	−125702.	−	217723.i	−0.137976	−	0.238982i
$243$	577552.	+	1.00035e6i	0.627444	+	1.08677i
$244$	−253381.	−	438869.i	−0.272458	−	0.471911i
$245$	34221.4			0.0364236
$246$	182667.	−	316389.i	0.192452	−	0.333337i
$247$	454137.	+	786589.i	0.473636	+	0.820362i
$248$	9301.56			0.00960344
$249$	−2.57370e6			−2.63063
$250$	−128182.	−	222017.i	−0.129711	−	0.224666i
$251$	−1.59727e6			−1.60027			−0.800135	−	0.599820i	$-0.795239\pi$
$251$	−1.59727e6			−1.60027			−0.800135	+	0.599820i	$0.795239\pi$
$252$	−397903.	+	689189.i	−0.394708	+	0.683655i
$253$	−79314.6			−0.0779025
$254$	−333022.	+	576811.i	−0.323883	+	0.560983i
$255$	6775.81	−	11736.1i	0.00652546	−	0.0113024i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−256647.	−	444525.i	−0.242383	−	0.419821i	0.719009	−	0.695001i	$-0.244596\pi$
$257$	−256647.	−	444525.i	−0.242383	−	0.419821i	−0.961393	+	0.275180i	$0.911263\pi$
$258$	564996.			0.528441
$259$	−872464.	−	794766.i	−0.808161	−	0.736190i
$260$	50988.0			0.0467772
$261$	1.33921e6	+	2.31957e6i	1.21688	+	2.10769i
$262$	−97295.4	+	168521.i	−0.0875667	+	0.151670i
$263$	671711.	−	1.16344e6i	0.598816	−	1.03718i	−0.394180	−	0.919033i	$-0.628971\pi$
$263$	671711.	−	1.16344e6i	0.598816	−	1.03718i	0.992996	−	0.118147i	$-0.0376953\pi$
$264$	244388.	−	423292.i	0.215809	−	0.373792i
$265$	107366.			0.0939190
$266$	−843138.	+	1.46036e6i	−0.730625	+	1.26548i
$267$	2.38223e6			2.04506
$268$	−138021.	−	239059.i	−0.117384	−	0.203315i
$269$	−208919.			−0.176034			−0.0880171	−	0.996119i	$-0.528053\pi$
$269$	−208919.			−0.176034			−0.0880171	+	0.996119i	$0.528053\pi$
$270$	−109823.			−0.0916818
$271$	252095.	+	436641.i	0.208516	+	0.361161i	0.951247	−	0.308429i	$-0.0998032\pi$
$271$	252095.	+	436641.i	0.208516	+	0.361161i	−0.742731	+	0.669590i	$0.766470\pi$
$272$	6819.87	−	11812.4i	0.00558925	−	0.00968087i
$273$	1.05467e6			0.856466
$274$	521582.	+	903407.i	0.419707	+	0.726954i
$275$	472573.	+	818520.i	0.376823	+	0.652676i
$276$	49347.0	+	85471.5i	0.0389931	+	0.0675381i
$277$	−1.27340e6	+	2.20559e6i	−0.997158	+	1.72713i	−0.433333	+	0.901234i	$0.642663\pi$
$277$	−1.27340e6	+	2.20559e6i	−0.997158	+	1.72713i	−0.563825	+	0.825894i	$0.690671\pi$
$278$	−342496.	+	593220.i	−0.265793	+	0.460367i
$279$	25502.7	+	44172.0i	0.0196144	+	0.0339732i
$280$	47331.3	+	81980.3i	0.0360789	+	0.0624905i
$281$	−1.30116e6	−	2.25368e6i	−0.983029	−	1.70266i	−0.650386	−	0.759604i	$-0.725393\pi$
$281$	−1.30116e6	−	2.25368e6i	−0.983029	−	1.70266i	−0.332644	−	0.943053i	$-0.607941\pi$
$282$	1.03049e6			0.771649
$283$	344594.	−	596855.i	0.255766	−	0.442999i	−0.709338	−	0.704869i	$-0.751006\pi$
$283$	344594.	−	596855.i	0.255766	−	0.442999i	0.965103	+	0.261870i	$0.0843392\pi$
$284$	228195.	+	395246.i	0.167885	+	0.290785i
$285$	−756565.			−0.551740
$286$	−382747.			−0.276692
$287$	−265567.	−	459976.i	−0.190314	−	0.329633i
$288$	−359369.			−0.255305
$289$	708509.	−	1.22717e6i	0.499000	−	0.864294i
$290$	318602.			0.222461
$291$	772282.	−	1.33763e6i	0.534618	−	0.925985i
$292$	190868.	−	330594.i	0.131002	−	0.226901i
$293$	−764722.	+	1.32454e6i	−0.520396	+	0.901353i	0.479322	+	0.877639i	$0.340882\pi$
$293$	−764722.	+	1.32454e6i	−0.520396	+	0.901353i	−0.999719	+	0.0237141i	$0.992451\pi$
$294$	159827.	+	276828.i	0.107840	+	0.186785i
$295$	−252927.			−0.169215
$296$	113823.	−	520651.i	0.0755092	−	0.345396i
$297$	824397.			0.542307
$298$	837425.	+	1.45046e6i	0.546267	+	0.946163i
$299$	38642.3	−	66930.5i	0.0249969	−	0.0432958i
$300$	588040.	−	1.01851e6i	0.377228	−	0.653377i
$301$	410704.	−	711361.i	0.261284	−	0.452557i
$302$	−1.08890e6			−0.687023
$303$	304394.	−	527226.i	0.190471	−	0.329906i
$304$	−761485.			−0.472582
$305$	−165274.	−	286264.i	−0.101732	−	0.176204i
$306$	74794.0			0.0456629
$307$	772743.			0.467939			0.233970	−	0.972244i	$-0.424828\pi$
$307$	772743.			0.467939			0.233970	+	0.972244i	$0.424828\pi$
$308$	−355298.	−	615394.i	−0.213411	−	0.369638i
$309$	1.86522e6	−	3.23065e6i	1.11130	−	1.92484i
$310$	6067.19			0.00358578
$311$	1.18116e6	+	2.04582e6i	0.692479	+	1.19941i	0.971023	+	0.238986i	$0.0768150\pi$
$311$	1.18116e6	+	2.04582e6i	0.692479	+	1.19941i	−0.278544	+	0.960424i	$0.589852\pi$
$312$	238133.	+	412458.i	0.138495	+	0.239880i
$313$	−1.56724e6	−	2.71454e6i	−0.904223	−	1.56616i	−0.821957	−	0.569550i	$-0.807118\pi$
$313$	−1.56724e6	−	2.71454e6i	−0.904223	−	1.56616i	−0.0822662	−	0.996610i	$-0.526216\pi$
$314$	316758.	−	548641.i	0.181302	−	0.314025i
$315$	−259543.	+	449542.i	−0.147378	+	0.255266i
$316$	605798.	+	1.04927e6i	0.341279	+	0.591113i
$317$	375172.	+	649817.i	0.209692	+	0.363198i	0.951618	−	0.307285i	$-0.0994204\pi$
$317$	375172.	+	649817.i	0.209692	+	0.363198i	−0.741925	+	0.670483i	$0.766087\pi$
$318$	501441.	+	868522.i	0.278069	+	0.481629i
$319$	−2.39162e6			−1.31588
$320$	−21373.8	+	37020.5i	−0.0116683	+	0.0202100i
$321$	1.90974e6	+	3.30777e6i	1.03446	+	1.79173i
$322$	143484.			0.0771196
$323$	158485.			0.0845242
$324$	169325.	+	293280.i	0.0896106	+	0.155210i
$325$	−920956.			−0.483649
$326$	172410.	−	298623.i	0.0898502	−	0.155625i
$327$	924316.			0.478025
$328$	119924.	−	207715.i	0.0615492	−	0.106606i
$329$	749077.	−	1.29744e6i	0.381537	−	0.660841i
$330$	159408.	−	276103.i	0.0805797	−	0.139568i
$331$	1.15362e6	+	1.99814e6i	0.578754	+	1.00243i	0.995623	+	0.0934650i	$0.0297943\pi$
$331$	1.15362e6	+	1.99814e6i	0.578754	+	1.00243i	−0.416868	+	0.908967i	$0.636872\pi$
$332$	−1.68968e6			−0.841316
$333$	2.78458e6	−	886973.i	1.37610	−	0.438329i
$334$	−1.17615e6			−0.576893
$335$	−90027.8	−	155933.i	−0.0438293	−	0.0759146i
$336$	−442110.	+	765758.i	−0.213640	+	0.370035i
$337$	−1.38712e6	+	2.40257e6i	−0.665335	+	1.15239i	0.313859	+	0.949469i	$0.398378\pi$
$337$	−1.38712e6	+	2.40257e6i	−0.665335	+	1.15239i	−0.979194	+	0.202925i	$0.934955\pi$
$338$	−556110.	+	963211.i	−0.264770	+	0.458596i
$339$	−6.03100e6			−2.85030
$340$	4448.44	−	7704.93i	0.00208694	−	0.00361469i
$341$	−45544.0			−0.0212102
$342$	−2.08781e6	−	3.61620e6i	−0.965221	−	1.67181i
$343$	−1.91725e6			−0.879922
$344$	370930.			0.169004
$345$	32187.9	+	55751.1i	0.0145594	+	0.0252177i
$346$	−826622.	+	1.43175e6i	−0.371208	+	0.642950i
$347$	−452905.			−0.201922			−0.100961	−	0.994890i	$-0.532192\pi$
$347$	−452905.			−0.201922			−0.100961	+	0.994890i	$0.532192\pi$
$348$	1.48799e6	+	2.57728e6i	0.658647	+	1.14081i
$349$	−1.59989e6	−	2.77109e6i	−0.703116	−	1.21783i	−0.967367	−	0.253379i	$-0.918458\pi$
$349$	−1.59989e6	−	2.77109e6i	−0.703116	−	1.21783i	0.264251	−	0.964454i	$-0.414875\pi$
$350$	−854910.	−	1.48075e6i	−0.373035	−	0.646116i
$351$	−401649.	+	695677.i	−0.174012	+	0.301398i
$352$	160445.	−	277898.i	0.0690190	−	0.119544i
$353$	771213.	+	1.33578e6i	0.329411	+	0.570556i	0.982395	−	0.186815i	$-0.0598166\pi$
$353$	771213.	+	1.33578e6i	0.329411	+	0.570556i	−0.652984	+	0.757371i	$0.726483\pi$
$354$	−1.18126e6	−	2.04601e6i	−0.501001	−	0.867759i
$355$	148846.	+	257810.i	0.0626855	+	0.108575i
$356$	1.56398e6			0.654042
$357$	92014.6	−	159374.i	0.0382108	−	0.0661831i
$358$	559857.	+	969701.i	0.230871	+	0.399881i
$359$	4.40899e6			1.80552			0.902761	−	0.430143i	$-0.141537\pi$
$359$	4.40899e6			1.80552			0.902761	+	0.430143i	$0.141537\pi$
$360$	−234408.			−0.0953270
$361$	−3.18593e6	−	5.51818e6i	−1.28667	−	2.22858i
$362$	−1.96862e6			−0.789569
$363$	765872.	−	1.32653e6i	0.305063	−	0.528385i
$364$	692410.			0.273911
$365$	124499.	−	215638.i	0.0489140	−	0.0847216i
$366$	1.54379e6	−	2.67392e6i	0.602400	−	1.04339i
$367$	−6885.82	+	11926.6i	−0.00266864	+	0.00462222i	−0.867357	−	0.497687i	$-0.834183\pi$
$367$	−6885.82	+	11926.6i	−0.00266864	+	0.00462222i	0.864688	+	0.502309i	$0.167516\pi$
$368$	32397.2	+	56113.6i	0.0124706	+	0.0215997i
$369$	1.31522e6			0.502843
$370$	74243.9	−	339608.i	0.0281940	−	0.128966i
$371$	1.45802e6			0.549957
$372$	28336.1	+	49079.5i	0.0106165	+	0.0183884i
$373$	2.01195e6	−	3.48480e6i	0.748765	−	1.29690i	−0.199650	−	0.979867i	$-0.563981\pi$
$373$	2.01195e6	−	3.48480e6i	0.748765	−	1.29690i	0.948415	−	0.317032i	$-0.102686\pi$
$374$	−33392.7	+	57837.9i	−0.0123445	+	0.0213813i
$375$	780980.	−	1.35270e6i	0.286789	−	0.496732i
$376$	676533.			0.246785
$377$	1.16521e6	−	2.01820e6i	0.422231	−	0.731325i
$378$	−1.49138e6			−0.536857
$379$	1.39585e6	+	2.41769e6i	0.499162	+	0.864573i	1.00000		0.000967822i	$-0.000308067\pi$
$379$	1.39585e6	+	2.41769e6i	0.499162	+	0.864573i	−0.500838	+	0.865541i	$0.666975\pi$
$380$	−496699.			−0.176455
$381$	−4.05804e6			−1.43220
$382$	−1.20866e6	−	2.09346e6i	−0.423784	−	0.734016i
$383$	454686.	−	787540.i	0.158385	−	0.274331i	−0.775901	−	0.630854i	$-0.782705\pi$
$383$	454686.	−	787540.i	0.158385	−	0.274331i	0.934287	+	0.356523i	$0.116038\pi$
$384$	−399295.			−0.138186
$385$	−231752.	−	401407.i	−0.0796843	−	0.138017i
$386$	−1.75415e6	−	3.03828e6i	−0.599237	−	1.03791i
$387$	1.01700e6	+	1.76150e6i	0.345180	+	0.597869i
$388$	507017.	−	878179.i	0.170979	−	0.296145i
$389$	−956062.	+	1.65595e6i	−0.320341	+	0.554847i	−0.980558	−	0.196228i	$-0.937131\pi$
$389$	−956062.	+	1.65595e6i	−0.320341	+	0.554847i	0.660218	+	0.751074i	$0.270464\pi$
$390$	155329.	+	269037.i	0.0517118	+	0.0895675i
$391$	−6742.70	−	11678.7i	−0.00223045	−	0.00386325i
$392$	104929.	+	181743.i	0.0344891	+	0.0597368i
$393$	−1.18559e6			−0.387217
$394$	−974347.	+	1.68762e6i	−0.316208	+	0.547688i
$395$	395148.	+	684416.i	0.127429	+	0.220713i
$396$	1.75961e6			0.563869
$397$	2.56909e6			0.818093			0.409047	−	0.912513i	$-0.365861\pi$
$397$	2.56909e6			0.818093			0.409047	+	0.912513i	$0.365861\pi$
$398$	1.28884e6	+	2.23233e6i	0.407840	+	0.706400i
$399$	−1.02741e7			−3.23080
$400$	386058.	−	668673.i	0.120643	−	0.208960i
$401$	2.23253e6			0.693325			0.346662	−	0.937990i	$-0.387315\pi$
$401$	2.23253e6			0.693325			0.346662	+	0.937990i	$0.387315\pi$
$402$	840927.	−	1.45653e6i	0.259533	−	0.449525i
$403$	22189.2	−	38432.9i	0.00680580	−	0.0117880i
$404$	199840.	−	346133.i	0.0609157	−	0.105509i
$405$	110447.	+	191300.i	0.0334592	+	0.0579531i
$406$	4.32657e6			1.30265
$407$	−557320.	+	2.54931e6i	−0.166770	+	0.762845i
$408$	83103.6			0.0247155
$409$	2.53769e6	+	4.39540e6i	0.750118	+	1.29924i	0.947765	+	0.318970i	$0.103337\pi$
$409$	2.53769e6	+	4.39540e6i	0.750118	+	1.29924i	−0.197647	+	0.980273i	$0.563330\pi$
$410$	78223.8	−	135488.i	0.0229815	−	0.0398052i
$411$	−3.17787e6	+	5.50423e6i	−0.927965	+	1.60728i
$412$	1.22455e6	−	2.12098e6i	0.355412	−	0.615592i
$413$	−3.43471e6			−0.990866
$414$	−177651.	+	307701.i	−0.0509410	+	0.0882323i
$415$	−1.10214e6			−0.314135
$416$	156339.	+	270786.i	0.0442927	+	0.0767173i
$417$	−4.17349e6			−1.17533
$418$	3.72852e6			1.04375
$419$	2.84297e6	+	4.92417e6i	0.791110	+	1.37024i	0.925280	+	0.379285i	$0.123830\pi$
$419$	2.84297e6	+	4.92417e6i	0.791110	+	1.37024i	−0.134170	+	0.990958i	$0.542837\pi$
$420$	−288378.	+	499486.i	−0.0797699	+	0.138166i
$421$	4.33398e6			1.19174			0.595870	−	0.803081i	$-0.296808\pi$
$421$	4.33398e6			1.19174			0.595870	+	0.803081i	$0.296808\pi$
$422$	586248.	+	1.01541e6i	0.160251	+	0.277563i
$423$	1.85490e6	+	3.21278e6i	0.504045	+	0.873031i
$424$	329205.	+	570200.i	0.0889307	+	0.154033i
$425$	−80348.8	+	139168.i	−0.0215778	+	0.0373738i
$426$	−1.39034e6	+	2.40814e6i	−0.371190	+	0.642920i
$427$	−2.24440e6	−	3.88742e6i	−0.595705	−	1.03179i
$428$	1.25378e6	+	2.17161e6i	0.330835	+	0.573024i
$429$	−1.16599e6	−	2.01956e6i	−0.305881	−	0.529801i
$430$	241949.			0.0631034
$431$	−1.87205e6	+	3.24249e6i	−0.485428	+	0.840786i	−0.999860	−	0.0167451i	$-0.994670\pi$
$431$	−1.87205e6	+	3.24249e6i	−0.485428	+	0.840786i	0.514432	+	0.857531i	$0.328003\pi$
$432$	−336737.	−	583246.i	−0.0868124	−	0.150363i
$433$	9946.56			0.00254949			0.00127474	−	0.999999i	$-0.499594\pi$
$433$	9946.56			0.00254949			0.00127474	+	0.999999i	$0.499594\pi$
$434$	82391.6			0.0209971
$435$	970582.	+	1.68110e6i	0.245929	+	0.425961i
$436$	606830.			0.152880
$437$	−376434.	+	652003.i	−0.0942942	+	0.163322i
$438$	2.32583e6			0.579285
$439$	2.90816e6	−	5.03709e6i	0.720208	−	1.24744i	−0.240709	−	0.970597i	$-0.577380\pi$
$439$	2.90816e6	−	5.03709e6i	0.720208	−	1.24744i	0.960916	−	0.276839i	$-0.0892868\pi$
$440$	104654.	−	181267.i	0.0257707	−	0.0446361i
$441$	−575383.	+	996593.i	−0.140884	+	0.244018i
$442$	−32538.1	−	56357.6i	−0.00792203	−	0.0137214i
$443$	3.23419e6			0.782990			0.391495	−	0.920180i	$-0.371958\pi$
$443$	3.23419e6			0.782990			0.391495	+	0.920180i	$0.371958\pi$
$444$	3.09395e6	−	985515.i	0.744828	−	0.237250i
$445$	1.02015e6			0.244209
$446$	40648.7	+	70405.6i	0.00967630	+	0.0167598i
$447$	−5.10222e6	+	8.83731e6i	−1.20779	+	2.09195i
$448$	−290253.	+	502733.i	−0.0683254	+	0.118343i
$449$	−142385.	+	246618.i	−0.0333310	+	0.0577310i	−0.882210	−	0.470857i	$-0.843945\pi$
$449$	−142385.	+	246618.i	−0.0333310	+	0.0577310i	0.848879	+	0.528588i	$0.177278\pi$
$450$	4.23393e6			0.985626
$451$	−587196.	+	1.01705e6i	−0.135938	+	0.235452i
$452$	−3.95946e6			−0.911569
$453$	−3.31721e6	−	5.74557e6i	−0.759498	−	1.31549i
$454$	1.22870e6			0.279774
$455$	451642.			0.102274
$456$	−2.31977e6	−	4.01796e6i	−0.522436	−	0.904885i
$457$	840377.	−	1.45558e6i	0.188228	−	0.326020i	−0.756432	−	0.654073i	$-0.773059\pi$
$457$	840377.	−	1.45558e6i	0.188228	−	0.326020i	0.944659	+	0.328053i	$0.106392\pi$
$458$	−3.71082e6			−0.826621
$459$	70083.7	+	121389.i	0.0155269	+	0.0268934i
$460$	21131.9	+	36601.6i	0.00465634	+	0.00806501i
$461$	2.71715e6	+	4.70624e6i	0.595472	+	1.03139i	0.993480	+	0.114006i	$0.0363682\pi$
$461$	2.71715e6	+	4.70624e6i	0.595472	+	1.03139i	−0.398008	+	0.917382i	$0.630298\pi$
$462$	2.16474e6	−	3.74944e6i	0.471847	−	0.817263i
$463$	−572453.	+	991518.i	−0.124105	+	0.214955i	−0.921383	−	0.388657i	$-0.872939\pi$
$463$	−572453.	+	991518.i	−0.124105	+	0.214955i	0.797278	+	0.603612i	$0.206272\pi$
$464$	976893.	+	1.69203e6i	0.210645	+	0.364849i
$465$	18482.9	+	32013.4i	0.00396405	+	0.00686593i
$466$	3.16295e6	+	5.47839e6i	0.674727	+	1.16866i
$467$	−251214.			−0.0533030			−0.0266515	−	0.999645i	$-0.508484\pi$
$467$	−251214.			−0.0533030			−0.0266515	+	0.999645i	$0.508484\pi$
$468$	−857288.	+	1.48487e6i	−0.180931	+	0.313381i
$469$	−1.22256e6	−	2.11754e6i	−0.256649	−	0.444529i
$470$	441287.			0.0921459
$471$	3.85986e6			0.801713
$472$	−775520.	−	1.34324e6i	−0.160228	−	0.277523i
$473$	−1.81622e6			−0.373263
$474$	−3.69098e6	+	6.39296e6i	−0.754563	+	1.30694i
$475$	8.97149e6			1.82444
$476$	60409.2	−	104632.i	0.0122204	−	0.0211664i
$477$	−1.80521e6	+	3.12671e6i	−0.363271	+	0.629204i
$478$	2.54975e6	−	4.41629e6i	0.510420	−	0.884073i
$479$	−1.08979e6	−	1.88757e6i	−0.217021	−	0.375892i	0.736875	−	0.676030i	$-0.236301\pi$
$479$	−1.08979e6	−	1.88757e6i	−0.217021	−	0.375892i	−0.953896	+	0.300137i	$0.902968\pi$
$480$	−260450.			−0.0515967
$481$	−1.87973e6	−	1.71233e6i	−0.370453	−	0.337462i
$482$	−6.47097e6			−1.26868
$483$	437107.	+	757092.i	0.0852551	+	0.147666i
$484$	502809.	−	870890.i	0.0975639	−	0.168986i
$485$	330715.	−	572815.i	0.0638410	−	0.110576i
$486$	−2.31021e6	+	4.00140e6i	−0.443670	+	0.768459i
$487$	4.66383e6			0.891087			0.445543	−	0.895260i	$-0.353011\pi$
$487$	4.66383e6			0.891087			0.445543	+	0.895260i	$0.353011\pi$
$488$	1.01352e6	−	1.75547e6i	0.192657	−	0.333691i
$489$	2.10091e6			0.397315
$490$	68442.9	+	118547.i	0.0128777	+	0.0223048i
$491$	1.03992e7			1.94669			0.973345	−	0.229344i	$-0.0736581\pi$
$491$	1.03992e7			1.94669			0.973345	+	0.229344i	$0.0736581\pi$
$492$	1.46134e6			0.272169
$493$	−203317.	−	352155.i	−0.0376752	−	0.0652554i
$494$	−1.81655e6	+	3.14636e6i	−0.334911	+	0.580084i
$495$	1.14775e6			0.210540
$496$	18603.1	+	32221.6i	0.00339533	+	0.00588088i
$497$	2.02131e6	+	3.50102e6i	0.367065	+	0.635775i
$498$	−5.14740e6	−	8.91556e6i	−0.930068	−	1.61092i
$499$	−577116.	+	999594.i	−0.103756	+	0.179710i	−0.913229	−	0.407446i	$-0.866419\pi$
$499$	−577116.	+	999594.i	−0.103756	+	0.179710i	0.809473	+	0.587156i	$0.199753\pi$
$500$	512727.	−	888070.i	0.0917194	−	0.158863i
$501$	−3.58299e6	−	6.20591e6i	−0.637750	−	1.10462i
$502$	−3.19454e6	−	5.53310e6i	−0.565781	−	0.979962i
$503$	−1.49966e6	−	2.59750e6i	−0.264286	−	0.457757i	0.703090	−	0.711101i	$-0.251803\pi$
$503$	−1.49966e6	−	2.59750e6i	−0.264286	−	0.457757i	−0.967376	+	0.253344i	$0.918470\pi$
$504$	−3.18323e6			−0.558202
$505$	130351.	−	225774.i	0.0227450	−	0.0393955i
$506$	−158629.	−	274754.i	−0.0275427	−	0.0477054i
$507$	−6.77649e6			−1.17081
$508$	−2.66418e6			−0.458040
$509$	−3.27643e6	−	5.67494e6i	−0.560539	−	0.970882i	−0.997449	−	0.0713772i	$-0.977261\pi$
$509$	−3.27643e6	−	5.67494e6i	−0.560539	−	0.970882i	0.436910	−	0.899505i	$-0.356073\pi$
$510$	54206.5			0.00922839
$511$	1.69068e6	−	2.92834e6i	0.286424	−	0.496100i
$512$	−262144.			−0.0441942
$513$	3.91266e6	−	6.77693e6i	0.656416	−	1.13695i
$514$	1.02659e6	−	1.77810e6i	0.171391	−	0.296858i
$515$	798743.	−	1.38346e6i	0.132706	−	0.229853i
$516$	1.12999e6	+	1.95720e6i	0.186832	+	0.323603i
$517$	−3.31257e6			−0.545053
$518$	1.00822e6	−	4.61183e6i	0.165094	−	0.755178i
$519$	−1.00728e7			−1.64147
$520$	101976.	+	176627.i	0.0165382	+	0.0286451i
$521$	−2.51401e6	+	4.35440e6i	−0.405764	+	0.702803i	−0.994410	−	0.105588i	$-0.966328\pi$
$521$	−2.51401e6	+	4.35440e6i	−0.405764	+	0.702803i	0.588646	+	0.808391i	$0.299661\pi$
$522$	−5.35683e6	+	9.27830e6i	−0.860461	+	1.49036i
$523$	3.37373e6	−	5.84348e6i	0.539333	−	0.934151i	−0.459608	−	0.888122i	$-0.652010\pi$
$523$	3.37373e6	−	5.84348e6i	0.539333	−	0.934151i	0.998940	−	0.0460292i	$-0.0146567\pi$
$524$	−778363.			−0.123838
$525$	5.20875e6	−	9.02182e6i	0.824775	−	1.42855i
$526$	5.37369e6			0.846854
$527$	−3871.79	−	6706.14i	−0.000607275	−	0.00105183i
$528$	1.95510e6			0.305200
$529$	−6.37228e6			−0.990047
$530$	214733.	+	371928.i	0.0332054	+	0.0575134i
$531$	4.25259e6	−	7.36570e6i	0.654511	−	1.13365i
$532$	−6.74510e6			−1.03326
$533$	−572168.	−	991023.i	−0.0872379	−	0.151101i
$534$	4.76446e6	+	8.25229e6i	0.723038	+	1.25234i
$535$	817811.	+	1.41649e6i	0.123529	+	0.213958i
$536$	552084.	−	956237.i	0.0830028	−	0.143765i
$537$	−3.41107e6	+	5.90815e6i	−0.510452	+	0.884129i
$538$	−417838.	−	723716.i	−0.0622375	−	0.107798i
$539$	−513774.	−	889883.i	−0.0761729	−	0.131935i
$540$	−219646.	−	380438.i	−0.0324144	−	0.0561434i
$541$	−4.34424e6			−0.638147			−0.319074	−	0.947730i	$-0.603372\pi$
$541$	−4.34424e6			−0.638147			−0.319074	+	0.947730i	$0.603372\pi$
$542$	−1.00838e6	+	1.74656e6i	−0.147443	+	0.255379i
$543$	−5.99715e6	−	1.03874e7i	−0.872862	−	1.51184i
$544$	54559.0			0.00790440
$545$	395821.			0.0570831
$546$	2.10934e6	+	3.65349e6i	0.302806	+	0.524476i
$547$	2.45331e6			0.350578			0.175289	−	0.984517i	$-0.443914\pi$
$547$	2.45331e6			0.350578			0.175289	+	0.984517i	$0.443914\pi$
$548$	−2.08633e6	+	3.61363e6i	−0.296778	+	0.514034i
$549$	1.11154e7			1.57396
$550$	−1.89029e6	+	3.27408e6i	−0.266454	+	0.461511i
$551$	−1.13508e7	+	1.96602e7i	−1.59276	+	2.75873i
$552$	−197388.	+	341886.i	−0.0275723	+	0.0477566i
$553$	5.36605e6	+	9.29428e6i	0.746178	+	1.29242i
$554$	−1.01872e7			−1.41019
$555$	2.01811e6	−	642828.i	0.278107	−	0.0885855i
$556$	−2.73997e6			−0.375888
$557$	−2.40514e6	−	4.16583e6i	−0.328476	−	0.568936i	0.653734	−	0.756724i	$-0.273202\pi$
$557$	−2.40514e6	−	4.16583e6i	−0.328476	−	0.568936i	−0.982210	+	0.187788i	$0.939868\pi$
$558$	−102011.	+	176688.i	−0.0138695	+	0.0240227i
$559$	884867.	−	1.53263e6i	0.119770	−	0.207448i
$560$	−189325.	+	327921.i	−0.0255117	+	0.0441875i
$561$	−406907.			−0.0545869
$562$	5.20466e6	−	9.01473e6i	0.695107	−	1.20396i
$563$	3.20684e6			0.426389			0.213194	−	0.977010i	$-0.431613\pi$
$563$	3.20684e6			0.426389			0.213194	+	0.977010i	$0.431613\pi$
$564$	2.06098e6	+	3.56971e6i	0.272819	+	0.472537i
$565$	−2.58266e6			−0.340366
$566$	2.75675e6			0.361707
$567$	1.49985e6	+	2.59782e6i	0.195926	+	0.339353i
$568$	−912781.	+	1.58098e6i	−0.118712	+	0.205616i
$569$	1.07760e7			1.39533			0.697665	−	0.716425i	$-0.254223\pi$
$569$	1.07760e7			1.39533			0.697665	+	0.716425i	$0.254223\pi$
$570$	−1.51313e6	−	2.62082e6i	−0.195070	−	0.337870i
$571$	5.19317e6	+	8.99484e6i	0.666565	+	1.15452i	0.978858	+	0.204539i	$0.0655694\pi$
$571$	5.19317e6	+	8.99484e6i	0.666565	+	1.15452i	−0.312293	+	0.949986i	$0.601097\pi$
$572$	−765494.	−	1.32587e6i	−0.0978254	−	0.169438i
$573$	7.36405e6	−	1.27549e7i	0.936980	−	1.62290i
$574$	1.06227e6	−	1.83990e6i	0.134572	−	0.233086i
$575$	−381690.	−	661106.i	−0.0481438	−	0.0833876i
$576$	−718738.	−	1.24489e6i	−0.0902640	−	0.156342i
$577$	−2.34599e6	−	4.06337e6i	−0.293350	−	0.508098i	0.681250	−	0.732051i	$-0.261437\pi$
$577$	−2.34599e6	−	4.06337e6i	−0.293350	−	0.508098i	−0.974600	+	0.223954i	$0.928104\pi$
$578$	5.66807e6			0.705693
$579$	1.06876e7	−	1.85115e7i	1.32490	−	2.29480i
$580$	637204.	+	1.10367e6i	0.0786518	+	0.136229i
$581$	−1.49669e7			−1.83946
$582$	6.17826e6			0.756064
$583$	−1.61191e6	−	2.79192e6i	−0.196413	−	0.340198i
$584$	1.52695e6			0.185264
$585$	−559188.	+	968543.i	−0.0675567	+	0.117012i
$586$	−6.11777e6			−0.735952
$587$	468714.	−	811836.i	0.0561452	−	0.0972464i	−0.836587	−	0.547834i	$-0.815452\pi$
$587$	468714.	−	811836.i	0.0561452	−	0.0972464i	0.892732	+	0.450588i	$0.148786\pi$
$588$	−639308.	+	1.10731e6i	−0.0762547	+	0.132077i
$589$	−216156.	+	374393.i	−0.0256731	+	0.0444672i
$590$	−505853.	−	876163.i	−0.0598266	−	0.103623i
$591$	−1.18729e7			−1.39826
$592$	2.03123e6	−	647008.i	0.238207	−	0.0758762i
$593$	1.12391e6			0.131248			0.0656241	−	0.997844i	$-0.479096\pi$
$593$	1.12391e6			0.131248			0.0656241	+	0.997844i	$0.479096\pi$
$594$	1.64879e6	+	2.85580e6i	0.191735	+	0.332094i
$595$	39403.5	−	68248.9i	0.00456292	−	0.00790320i
$596$	−3.34970e6	+	5.80185e6i	−0.386269	+	0.669038i
$597$	−7.85256e6	+	1.36010e7i	−0.901728	+	1.56184i
$598$	309139.			0.0353509
$599$	5.51411e6	−	9.55072e6i	0.627926	−	1.08760i	−0.360042	−	0.932936i	$-0.617237\pi$
$599$	5.51411e6	−	9.55072e6i	0.627926	−	1.08760i	0.987967	−	0.154663i	$-0.0494292\pi$
$600$	4.70432e6			0.533480
$601$	−169654.	−	293849.i	−0.0191592	−	0.0331848i	0.856287	−	0.516501i	$-0.172766\pi$
$601$	−169654.	−	293849.i	−0.0191592	−	0.0331848i	−0.875446	+	0.483316i	$0.839432\pi$
$602$	3.28563e6			0.369511
$603$	6.05474e6			0.678113
$604$	−2.17780e6	−	3.77207e6i	−0.242899	−	0.420714i
$605$	327970.	−	568061.i	0.0364289	−	0.0630967i
$606$	2.43515e6			0.269367
$607$	−7.67869e6	−	1.32999e7i	−0.845893	−	1.46513i	−0.884844	−	0.465888i	$-0.845735\pi$
$607$	−7.67869e6	−	1.32999e7i	−0.845893	−	1.46513i	0.0389508	−	0.999241i	$-0.487598\pi$
$608$	−1.52297e6	−	2.63786e6i	−0.167083	−	0.289396i
$609$	1.31804e7	+	2.28291e7i	1.44007	+	2.49428i
$610$	661097.	−	1.14505e6i	0.0719351	−	0.124595i
$611$	1.61389e6	−	2.79535e6i	0.174893	−	0.302923i
$612$	149588.	+	259094.i	0.0161443	+	0.0279627i
$613$	−3.88773e6	−	6.73374e6i	−0.417873	−	0.723778i	0.577852	−	0.816141i	$-0.303891\pi$
$613$	−3.88773e6	−	6.73374e6i	−0.417873	−	0.723778i	−0.995725	+	0.0923639i	$0.970558\pi$
$614$	1.54549e6	+	2.67686e6i	0.165441	+	0.286553i
$615$	953197.			0.101624
$616$	1.42119e6	−	2.46158e6i	0.150904	−	0.261373i
$617$	−360495.	−	624396.i	−0.0381230	−	0.0660309i	0.846334	−	0.532652i	$-0.178805\pi$
$617$	−360495.	−	624396.i	−0.0381230	−	0.0660309i	−0.884457	+	0.466621i	$0.845471\pi$
$618$	1.49217e7			1.57162
$619$	−1.57048e6			−0.164743			−0.0823713	−	0.996602i	$-0.526249\pi$
$619$	−1.57048e6			−0.164743			−0.0823713	+	0.996602i	$0.526249\pi$
$620$	12134.4	+	21017.4i	0.00126776	+	0.00219583i
$621$	−665853.			−0.0692866
$622$	−4.72463e6	+	8.18330e6i	−0.489657	+	0.848111i
$623$	1.38534e7			1.43000
$624$	−952532.	+	1.64983e6i	−0.0979305	+	0.169621i
$625$	−4.37819e6	+	7.58324e6i	−0.448326	+	0.776524i
$626$	6.26897e6	−	1.08582e7i	0.639382	−	1.10744i
$627$	1.13585e7	+	1.96735e7i	1.15386	+	1.99854i
$628$	2.53407e6			0.256400
$629$	−422752.	+	134659.i	−0.0426049	+	0.0135709i
$630$	−2.07634e6			−0.208424
$631$	58512.0	+	101346.i	0.00585021	+	0.0101329i	0.868936	−	0.494925i	$-0.164804\pi$
$631$	58512.0	+	101346.i	0.00585021	+	0.0101329i	−0.863085	+	0.505058i	$0.831471\pi$
$632$	−2.42319e6	+	4.19709e6i	−0.241321	+	0.417980i
$633$	−3.57187e6	+	6.18666e6i	−0.354312	+	0.613687i
$634$	−1.50069e6	+	2.59927e6i	−0.148275	+	0.256820i
$635$	−1.73778e6			−0.171025
$636$	−2.00577e6	+	3.47409e6i	−0.196624	+	0.340563i
$637$	1.00125e6			0.0977674
$638$	−4.78324e6	−	8.28482e6i	−0.465233	−	0.805808i
$639$	−1.00105e7			−0.969851
$640$	−170990.			−0.0165014
$641$	−5.96503e6	−	1.03317e7i	−0.573413	−	0.993180i	−0.996212	−	0.0869568i	$-0.972286\pi$
$641$	−5.96503e6	−	1.03317e7i	−0.573413	−	0.993180i	0.422799	−	0.906223i	$-0.361048\pi$
$642$	−7.63897e6	+	1.32311e7i	−0.731472	+	1.26695i
$643$	−7.16644e6			−0.683559			−0.341780	−	0.939780i	$-0.611030\pi$
$643$	−7.16644e6			−0.683559			−0.341780	+	0.939780i	$0.611030\pi$
$644$	286969.	+	497044.i	0.0272659	+	0.0472259i
$645$	737067.	+	1.27664e6i	0.0697602	+	0.120828i
$646$	316970.	+	549007.i	0.0298838	+	0.0517603i
$647$	707262.	−	1.22501e6i	0.0664231	−	0.115048i	−0.830901	−	0.556420i	$-0.812175\pi$
$647$	707262.	−	1.22501e6i	0.0664231	−	0.115048i	0.897324	+	0.441372i	$0.145508\pi$
$648$	−677301.	+	1.17312e6i	−0.0633643	+	0.109750i
$649$	3.79724e6	+	6.57702e6i	0.353881	+	0.612939i
$650$	−1.84191e6	−	3.19029e6i	−0.170996	−	0.296174i
$651$	250996.	+	434738.i	0.0232121	+	0.0402045i
$652$	1.37928e6			0.127067
$653$	−1.69416e6	+	2.93436e6i	−0.155479	+	0.269297i	−0.933233	−	0.359271i	$-0.883025\pi$
$653$	−1.69416e6	+	2.93436e6i	−0.155479	+	0.269297i	0.777755	+	0.628568i	$0.216359\pi$
$654$	1.84863e6	+	3.20192e6i	0.169008	+	0.292730i
$655$	−507708.			−0.0462392
$656$	959395.			0.0870438
$657$	4.18653e6	+	7.25129e6i	0.378391	+	0.655393i
$658$	5.99261e6			0.539575
$659$	−4.11547e6	+	7.12820e6i	−0.369152	+	0.639391i	−0.989433	−	0.144989i	$-0.953685\pi$
$659$	−4.11547e6	+	7.12820e6i	−0.369152	+	0.639391i	0.620281	+	0.784380i	$0.287019\pi$
$660$	1.27527e6			0.113957
$661$	−7.35564e6	+	1.27403e7i	−0.654812	+	1.13417i	0.327128	+	0.944980i	$0.393919\pi$
$661$	−7.35564e6	+	1.27403e7i	−0.654812	+	1.13417i	−0.981941	+	0.189188i	$0.939414\pi$
$662$	−4.61450e6	+	7.99254e6i	−0.409241	+	0.708826i
$663$	198247.	−	343373.i	0.0175155	−	0.0303377i
$664$	−3.37936e6	−	5.85322e6i	−0.297450	−	0.515199i
$665$	−4.39967e6			−0.385803
$666$	8.64173e6	+	7.87214e6i	0.754945	+	0.687713i
$667$	1.93168e6			0.168120
$668$	−2.35229e6	−	4.07429e6i	−0.203963	−	0.353273i
$669$	−247662.	+	428964.i	−0.0213941	+	0.0370557i
$670$	360111.	−	623731.i	0.0309920	−	0.0536797i
$671$	−4.96260e6	+	8.59548e6i	−0.425503	+	0.736994i
$672$	−3.53688e6			−0.302133
$673$	5.45173e6	−	9.44267e6i	0.463977	−	0.803632i	−0.535178	−	0.844739i	$-0.679755\pi$
$673$	5.45173e6	−	9.44267e6i	0.463977	−	0.803632i	0.999155	+	0.0411079i	$0.0130887\pi$
$674$	−1.10970e7			−0.940926
$675$	3.96729e6	+	6.87155e6i	0.335146	+	0.580491i
$676$	−4.44888e6			−0.374442
$677$	−502631.			−0.0421480			−0.0210740	−	0.999778i	$-0.506709\pi$
$677$	−502631.			−0.0421480			−0.0210740	+	0.999778i	$0.506709\pi$
$678$	−1.20620e7	−	2.08920e7i	−1.00773	−	1.74544i
$679$	4.49107e6	−	7.77876e6i	0.373831	−	0.647494i
$680$	35587.5			0.00295138
$681$	3.74310e6	+	6.48323e6i	0.309288	+	0.535703i
$682$	−91088.1	−	157769.i	−0.00749895	−	0.0129886i
$683$	3.16916e6	+	5.48915e6i	0.259952	+	0.450250i	0.966229	−	0.257686i	$-0.0829600\pi$
$683$	3.16916e6	+	5.48915e6i	0.259952	+	0.450250i	−0.706277	+	0.707936i	$0.749627\pi$
$684$	8.35126e6	−	1.44648e7i	0.682514	−	1.18215i
$685$	−1.36086e6	+	2.35708e6i	−0.110812	+	0.191933i
$686$	−3.83451e6	−	6.64156e6i	−0.311099	−	0.538840i
$687$	−1.13046e7	−	1.95801e7i	−0.913823	−	1.58279i
$688$	741860.	+	1.28494e6i	0.0597518	+	0.103493i
$689$	3.14132e6			0.252095
$690$	−128752.	+	223004.i	−0.0102951	+	0.0178316i
$691$	3.30848e6	+	5.73045e6i	0.263592	+	0.456556i	0.967194	−	0.254039i	$-0.0817593\pi$
$691$	3.30848e6	+	5.73045e6i	0.263592	+	0.456556i	−0.703601	+	0.710595i	$0.748426\pi$
$692$	−6.61298e6			−0.524967
$693$	1.55863e7			1.23285
$694$	−905809.	−	1.56891e6i	−0.0713901	−	0.123651i
$695$	−1.78722e6			−0.140351
$696$	−5.95197e6	+	1.03091e7i	−0.465733	+	0.806674i
$697$	−199675.			−0.0155683
$698$	6.39957e6	−	1.10844e7i	0.497178	−	0.861138i
$699$	−1.92711e7	+	3.33785e7i	−1.49181	+	2.58389i
$700$	3.41964e6	−	5.92299e6i	0.263776	−	0.456873i
$701$	−4.40499e6	−	7.62967e6i	−0.338571	−	0.586423i	0.645593	−	0.763682i	$-0.276610\pi$
$701$	−4.40499e6	−	7.62967e6i	−0.338571	−	0.586423i	−0.984164	+	0.177259i	$0.943277\pi$
$702$	−3.21319e6			−0.246090
$703$	1.83114e7	+	1.66807e7i	1.39744	+	1.27299i
$704$	1.28356e6			0.0976077
$705$	1.34433e6	+	2.32844e6i	0.101867	+	0.176438i
$706$	−3.08485e6	+	5.34312e6i	−0.232929	+	0.403444i
$707$	1.77015e6	−	3.06599e6i	0.133187	−	0.230686i
$708$	4.72505e6	−	8.18403e6i	0.354261	−	0.613598i
$709$	2.04697e7			1.52931			0.764655	−	0.644440i	$-0.222910\pi$
$709$	2.04697e7			1.52931			0.764655	+	0.644440i	$0.222910\pi$
$710$	−595386.	+	1.03124e6i	−0.0443254	+	0.0767738i
$711$	−2.65753e7			−1.97153
$712$	3.12795e6	+	5.41778e6i	0.231239	+	0.400517i
$713$	36785.2			0.00270988
$714$	736117.			0.0540383
$715$	−499313.	−	864836.i	−0.0365265	−	0.0632658i
$716$	−2.23943e6	+	3.87880e6i	−0.163251	+	0.282758i
$717$	3.10700e7			2.25706
$718$	8.81797e6	+	1.52732e7i	0.638348	+	1.10565i
$719$	6.05245e6	+	1.04831e7i	0.436625	+	0.756257i	0.997427	−	0.0716933i	$-0.0228403\pi$
$719$	6.05245e6	+	1.04831e7i	0.436625	+	0.756257i	−0.560802	+	0.827950i	$0.689507\pi$
$720$	−468816.	−	812013.i	−0.0337032	−	0.0583756i
$721$	1.08468e7	−	1.87873e7i	0.777078	−	1.34594i
$722$	1.27437e7	−	2.20727e7i	0.909814	−	1.57584i
$723$	−1.97130e7	−	3.41439e7i	−1.40251	−	2.42923i
$724$	−3.93724e6	−	6.81949e6i	−0.279155	−	0.483510i
$725$	−1.15093e7	−	1.99347e7i	−0.813214	−	1.40853i
$726$	6.12698e6			0.431424
$727$	−2.94702e6	+	5.10439e6i	−0.206798	+	0.358185i	−0.950704	−	0.310099i	$-0.899638\pi$
$727$	−2.94702e6	+	5.10439e6i	−0.206798	+	0.358185i	0.743906	+	0.668284i	$0.232971\pi$
$728$	1.38482e6	+	2.39858e6i	0.0968422	+	0.167736i
$729$	−2.30078e7			−1.60345
$730$	995991.			0.0691749
$731$	−154400.	−	267429.i	−0.0106870	−	0.0185104i
$732$	1.23503e7			0.851922
$733$	−9.51520e6	+	1.64808e7i	−0.654121	+	1.13297i	0.327992	+	0.944680i	$0.393628\pi$
$733$	−9.51520e6	+	1.64808e7i	−0.654121	+	1.13297i	−0.982113	+	0.188291i	$0.939705\pi$
$734$	−55086.5			−0.00377403
$735$	−417005.	+	722275.i	−0.0284724	+	0.0493156i
$736$	−129589.	+	224454.i	−0.00881805	+	0.0152733i
$737$	−2.70321e6	+	4.68210e6i	−0.183321	+	0.317521i
$738$	2.63044e6	+	4.55605e6i	0.177782	+	0.307927i
$739$	−2.68947e6			−0.181158			−0.0905788	−	0.995889i	$-0.528872\pi$
$739$	−2.68947e6			−0.181158			−0.0905788	+	0.995889i	$0.528872\pi$
$740$	1.32493e6	−	422028.i	0.0889430	−	0.0283310i
$741$	−2.21356e7			−1.48097
$742$	2.91604e6	+	5.05073e6i	0.194439	+	0.336779i
$743$	1.05857e7	−	1.83349e7i	0.703472	−	1.21845i	−0.263768	−	0.964586i	$-0.584965\pi$
$743$	1.05857e7	−	1.83349e7i	0.703472	−	1.21845i	0.967240	−	0.253863i	$-0.0817013\pi$
$744$	−113344.	+	196318.i	−0.00750701	+	0.0130025i
$745$	−2.18493e6	+	3.78441e6i	−0.144227	+	0.249809i
$746$	1.60956e7			1.05891
$747$	1.85308e7	−	3.20963e7i	1.21505	−	2.10453i
$748$	−267142.			−0.0174577
$749$	1.11058e7	+	1.92358e7i	0.723343	+	1.25287i
$750$	6.24784e6			0.405580
$751$	−2.24260e7			−1.45095			−0.725474	−	0.688249i	$-0.758379\pi$
$751$	−2.24260e7			−1.45095			−0.725474	+	0.688249i	$0.758379\pi$
$752$	1.35307e6	+	2.34358e6i	0.0872518	+	0.151125i
$753$	1.94635e7	−	3.37118e7i	1.25093	−	2.16668i
$754$	9.32165e6			0.597124
$755$	−1.42053e6	−	2.46043e6i	−0.0906949	−	0.157088i
$756$	−2.98276e6	−	5.16629e6i	−0.189808	−	0.328757i
$757$	−4.45601e6	−	7.71804e6i	−0.282623	−	0.489517i	0.689407	−	0.724374i	$-0.257871\pi$
$757$	−4.45601e6	−	7.71804e6i	−0.282623	−	0.489517i	−0.972030	+	0.234857i	$0.924538\pi$
$758$	−5.58341e6	+	9.67074e6i	−0.352961	+	0.611346i
$759$	966488.	−	1.67401e6i	0.0608965	−	0.105476i
$760$	−993397.	−	1.72061e6i	−0.0623863	−	0.108056i
$761$	−251456.	−	435534.i	−0.0157398	−	0.0272622i	0.858048	−	0.513569i	$-0.171677\pi$
$761$	−251456.	−	435534.i	−0.0157398	−	0.0272622i	−0.873788	+	0.486307i	$0.838344\pi$
$762$	−8.11609e6	−	1.40575e7i	−0.506360	−	0.877041i
$763$	5.37519e6			0.334259
$764$	4.83463e6	−	8.37383e6i	0.299661	−	0.519028i
$765$	97572.7	+	169001.i	0.00602802	+	0.0104408i
$766$	3.63749e6			0.223991
$767$	−7.40012e6			−0.454203
$768$	−798589.	−	1.38320e6i	−0.0488563	−	0.0846216i
$769$	−2.56101e7			−1.56169			−0.780847	−	0.624722i	$-0.785212\pi$
$769$	−2.56101e7			−1.56169			−0.780847	+	0.624722i	$0.785212\pi$
$770$	927010.	−	1.60563e6i	0.0563453	−	0.0975929i
$771$	1.25095e7			0.757885
$772$	7.01661e6	−	1.21531e7i	0.423725	−	0.733913i
$773$	4.64981e6	−	8.05371e6i	0.279890	−	0.484783i	−0.691467	−	0.722408i	$-0.743035\pi$
$773$	4.64981e6	−	8.05371e6i	0.279890	−	0.484783i	0.971357	+	0.237625i	$0.0763688\pi$
$774$	−4.06802e6	+	7.04601e6i	−0.244079	+	0.422757i
$775$	−219174.	−	379621.i	−0.0131080	−	0.0227036i
$776$	4.05613e6			0.241801
$777$	2.74057e7	−	8.72952e6i	1.62850	−	0.518726i
$778$	−7.64850e6			−0.453030
$779$	5.57376e6	+	9.65404e6i	0.329083	+	0.569988i
$780$	−621314.	+	1.07615e6i	−0.0365658	+	0.0633338i
$781$	4.46933e6	−	7.74110e6i	0.262189	−	0.454125i
$782$	26970.8	−	46714.8i	0.00157716	−	0.00273173i
$783$	−2.00779e7			−1.17034
$784$	−419717.	+	726971.i	−0.0243874	+	0.0422403i
$785$	1.65291e6			0.0957360
$786$	−2.37119e6	−	4.10702e6i	−0.136902	−	0.237121i
$787$	−2.48572e7			−1.43059			−0.715295	−	0.698823i	$-0.753707\pi$
$787$	−2.48572e7			−1.43059			−0.715295	+	0.698823i	$0.753707\pi$
$788$	−7.79477e6			−0.447186
$789$	1.63703e7	+	2.83542e7i	0.936190	+	1.62153i
$790$	−1.58059e6	+	2.73766e6i	−0.0901056	+	0.156067i
$791$	−3.50722e7			−1.99307
$792$	3.51922e6	+	6.09546e6i	0.199358	+	0.345298i
$793$	−4.83559e6	−	8.37549e6i	−0.273066	−	0.472963i
$794$	5.13818e6	+	8.89958e6i	0.289240	+	0.500978i
$795$	−1.30831e6	+	2.26606e6i	−0.0734165	+	0.127161i
$796$	−5.15534e6	+	8.92932e6i	−0.288386	+	0.499500i
$797$	4.98612e6	+	8.63622e6i	0.278046	+	0.481591i	0.970899	−	0.239489i	$-0.0769797\pi$
$797$	4.98612e6	+	8.63622e6i	0.278046	+	0.481591i	−0.692853	+	0.721079i	$0.743646\pi$
$798$	−2.05481e7	−	3.55904e7i	−1.14226	−	1.97845i
$799$	−281608.	−	487760.i	−0.0156055	−	0.0270296i
$800$	3.08847e6			0.170615
$801$	−1.71523e7	+	2.97086e7i	−0.944582	+	1.63606i
$802$	4.46506e6	+	7.73371e6i	0.245127	+	0.424573i
$803$	−7.47652e6			−0.409176
$804$	6.72742e6			0.367036
$805$	187183.	+	324210.i	0.0101807	+	0.0176334i
$806$	177514.			0.00962486
$807$	2.54578e6	−	4.40942e6i	0.137606	−	0.238341i
$808$	1.59872e6			0.0861477
$809$	2.60329e6	−	4.50902e6i	0.139846	−	0.242221i	−0.787592	−	0.616197i	$-0.788673\pi$
$809$	2.60329e6	−	4.50902e6i	0.139846	−	0.242221i	0.927438	+	0.373976i	$0.122006\pi$
$810$	−441788.	+	765199.i	−0.0236593	+	0.0409790i
$811$	−6.82868e6	+	1.18276e7i	−0.364573	+	0.631460i	−0.988708	−	0.149858i	$-0.952118\pi$
$811$	−6.82868e6	+	1.18276e7i	−0.364573	+	0.631460i	0.624134	+	0.781317i	$0.285452\pi$
$812$	8.65315e6	+	1.49877e7i	0.460558	+	0.797709i
$813$	−1.22876e7			−0.651990
$814$	−9.94570e6	+	3.16800e6i	−0.526107	+	0.167581i
$815$	899673.			0.0474450
$816$	166207.	+	287879.i	0.00873825	+	0.0151351i
$817$	−8.61992e6	+	1.49301e7i	−0.451802	+	0.782544i
$818$	−1.01507e7	+	1.75816e7i	−0.530414	+	0.918704i
$819$	−7.59371e6	+	1.31527e7i	−0.395589	+	0.685180i
$820$	625790.			0.0325008
$821$	1.13000e7	−	1.95721e7i	0.585086	−	1.01340i	−0.409779	−	0.912185i	$-0.634394\pi$
$821$	1.13000e7	−	1.95721e7i	0.585086	−	1.01340i	0.994865	−	0.101213i	$-0.0322725\pi$
$822$	−2.54230e7			−1.31234
$823$	1.35800e7	+	2.35213e7i	0.698876	+	1.21049i	0.968856	+	0.247623i	$0.0796495\pi$
$823$	1.35800e7	+	2.35213e7i	0.698876	+	1.21049i	−0.269980	+	0.962866i	$0.587017\pi$
$824$	9.79638e6			0.502629
$825$	−2.30341e7			−1.17825
$826$	−6.86942e6	−	1.18982e7i	−0.350324	−	0.606779i
$827$	3.80727e6	−	6.59439e6i	0.193575	−	0.335283i	−0.752857	−	0.658184i	$-0.771325\pi$
$827$	3.80727e6	−	6.59439e6i	0.193575	−	0.335283i	0.946433	+	0.322901i	$0.104658\pi$
$828$	−1.42121e6			−0.0720414
$829$	8.19852e6	+	1.42002e7i	0.414333	+	0.717645i	0.995358	−	0.0962403i	$-0.0306817\pi$
$829$	8.19852e6	+	1.42002e7i	0.414333	+	0.717645i	−0.581026	+	0.813885i	$0.697348\pi$
$830$	−2.20428e6	−	3.81792e6i	−0.111063	−	0.192367i
$831$	−3.10339e7	−	5.37524e7i	−1.55896	−	2.70019i
$832$	−625354.	+	1.08314e6i	−0.0313197	+	0.0542473i
$833$	87354.0	−	151302.i	0.00436185	−	0.00755494i
$834$	−8.34697e6	−	1.44574e7i	−0.415541	−	0.719738i
$835$	−1.53435e6	−	2.65756e6i	−0.0761565	−	0.131907i
$836$	7.45705e6	+	1.29160e7i	0.369021	+	0.639163i
$837$	−382347.			−0.0188644
$838$	−1.13719e7	+	1.96967e7i	−0.559400	+	0.968908i
$839$	−854674.	−	1.48034e6i	−0.0419175	−	0.0726033i	0.844305	−	0.535862i	$-0.180013\pi$
$839$	−854674.	−	1.48034e6i	−0.0419175	−	0.0726033i	−0.886223	+	0.463259i	$0.846680\pi$
$840$	−2.30703e6			−0.112812
$841$	3.77359e7			1.83978
$842$	8.66795e6	+	1.50133e7i	0.421343	+	0.729788i
$843$	6.34214e7			3.07374
$844$	−2.34499e6	+	4.06165e6i	−0.113315	+	0.196267i
$845$	−2.90190e6			−0.139811
$846$	−7.41959e6	+	1.28511e7i	−0.356413	+	0.617326i
$847$	4.45379e6	−	7.71419e6i	0.213315	−	0.369472i
$848$	−1.31682e6	+	2.28080e6i	−0.0628835	+	0.108917i
$849$	8.39811e6	+	1.45460e7i	0.399864	+	0.692585i
$850$	−642790.			−0.0305156
$851$	450139.	−	2.05904e6i	0.0213070	−	0.0974631i
$852$	−1.11227e7			−0.524942
$853$	1.13752e7	+	1.97024e7i	0.535286	+	0.927143i	0.999149	+	0.0412360i	$0.0131296\pi$
$853$	1.13752e7	+	1.97024e7i	0.535286	+	0.927143i	−0.463863	+	0.885907i	$0.653537\pi$
$854$	8.97761e6	−	1.55497e7i	0.421227	−	0.729587i
$855$	5.44733e6	−	9.43505e6i	0.254840	−	0.441397i
$856$	−5.01512e6	+	8.68644e6i	−0.233936	+	0.405189i
$857$	1.40521e7			0.653568			0.326784	−	0.945099i	$-0.394035\pi$
$857$	1.40521e7			0.653568			0.326784	+	0.945099i	$0.394035\pi$
$858$	4.66396e6	−	8.07822e6i	0.216290	−	0.374626i
$859$	2.12827e7			0.984110			0.492055	−	0.870564i	$-0.336246\pi$
$859$	2.12827e7			0.984110			0.492055	+	0.870564i	$0.336246\pi$
$860$	483898.	+	838135.i	0.0223104	+	0.0386428i
$861$	1.29443e7			0.595073
$862$	−1.49764e7			−0.686499
$863$	−5.69803e6	−	9.86928e6i	−0.260434	−	0.451085i	0.705923	−	0.708288i	$-0.250532\pi$
$863$	−5.69803e6	−	9.86928e6i	−0.260434	−	0.451085i	−0.966357	+	0.257203i	$0.917199\pi$
$864$	1.34695e6	−	2.33298e6i	0.0613856	−	0.106323i
$865$	−4.31349e6			−0.196015
$866$	19893.1	+	34455.9i	0.000901380	+	0.00156124i
$867$	1.72671e7	+	2.99075e7i	0.780138	+	1.35124i
$868$	164783.	+	285413.i	0.00742359	+	0.0128580i
$869$	1.18649e7	−	2.05506e7i	0.532984	−	0.923155i
$870$	−3.88233e6	+	6.72439e6i	−0.173898	+	0.301200i
$871$	−2.63403e6	−	4.56227e6i	−0.117646	−	0.203768i
$872$	1.21366e6	+	2.10212e6i	0.0540512	+	0.0936195i
$873$	1.11210e7	+	1.92621e7i	0.493864	+	0.855398i
$874$	−3.01147e6			−0.133352
$875$	4.54165e6	−	7.86637e6i	0.200537	−	0.347339i
$876$	4.65165e6	+	8.05690e6i	0.204808	+	0.354738i
$877$	−2.57592e7			−1.13093			−0.565463	−	0.824774i	$-0.691302\pi$
$877$	−2.57592e7			−1.13093			−0.565463	+	0.824774i	$0.691302\pi$
$878$	2.32653e7			1.01853
$879$	−1.86370e7	−	3.22803e7i	−0.813588	−	1.40918i
$880$	837235.			0.0364452
$881$	2.47132e6	−	4.28045e6i	0.107273	−	0.185802i	−0.807392	−	0.590016i	$-0.799122\pi$
$881$	2.47132e6	−	4.28045e6i	0.107273	−	0.185802i	0.914664	+	0.404214i	$0.132455\pi$
$882$	−4.60307e6			−0.199240
$883$	1.29460e7	−	2.24232e7i	0.558772	−	0.967822i	−0.438827	−	0.898572i	$-0.644606\pi$
$883$	1.29460e7	−	2.24232e7i	0.558772	−	0.967822i	0.997599	−	0.0692505i	$-0.0220608\pi$
$884$	130152.	−	225431.i	0.00560172	−	0.00970247i
$885$	3.08204e6	−	5.33825e6i	0.132276	−	0.229108i
$886$	6.46838e6	+	1.12036e7i	0.276829	+	0.479482i
$887$	3.58333e7			1.52925			0.764624	−	0.644476i	$-0.222924\pi$
$887$	3.58333e7			1.52925			0.764624	+	0.644476i	$0.222924\pi$
$888$	9.60182e6	+	8.74673e6i	0.408622	+	0.372231i
$889$	−2.35988e7			−1.00147
$890$	2.04029e6	+	3.53389e6i	0.0863410	+	0.149547i
$891$	3.31633e6	−	5.74405e6i	0.139947	−	0.242395i
$892$	−162595.	+	281622.i	−0.00684218	+	0.0118510i
$893$	−1.57217e7	+	2.72308e7i	−0.659739	+	1.14270i
$894$	−4.08178e7			−1.70807
$895$	−1.46073e6	+	2.53005e6i	−0.0609553	+	0.105578i
$896$	−2.32203e6			−0.0966267
$897$	941753.	+	1.63116e6i	0.0390801	+	0.0676887i
$898$	−1.13908e6			−0.0471372
$899$	1.10921e6			0.0457735
$900$	8.46786e6	+	1.46668e7i	0.348472	+	0.603570i
$901$	274064.	−	474694.i	0.0112471	−	0.0194806i
$902$	−4.69757e6			−0.192246
$903$	1.00093e7	+	1.73366e7i	0.408492	+	0.707529i
$904$	−7.91892e6	−	1.37160e7i	−0.322288	−	0.558220i
$905$	−2.56817e6	−	4.44819e6i	−0.104232	−	0.180535i
$906$	1.32688e7	−	2.29823e7i	0.537046	−	0.930192i
$907$	2.01609e7	−	3.49198e7i	0.813753	−	1.40946i	−0.0964677	−	0.995336i	$-0.530754\pi$
$907$	2.01609e7	−	3.49198e7i	0.813753	−	1.40946i	0.910220	−	0.414125i	$-0.135912\pi$
$908$	2.45741e6	+	4.25636e6i	0.0989151	+	0.171326i
$909$	4.38332e6	+	7.59213e6i	0.175952	+	0.304757i
$910$	903285.	+	1.56454e6i	0.0361594	+	0.0626299i
$911$	−1.95768e7			−0.781530			−0.390765	−	0.920490i	$-0.627790\pi$
$911$	−1.95768e7			−0.781530			−0.390765	+	0.920490i	$0.627790\pi$
$912$	9.27908e6	−	1.60718e7i	0.369418	−	0.639850i
$913$	1.65466e7	+	2.86596e7i	0.656951	+	1.13787i
$914$	6.72302e6			0.266194
$915$	8.05581e6			0.318095
$916$	−7.42164e6	−	1.28547e7i	−0.292255	−	0.506200i
$917$	−6.89461e6			−0.270761
$918$	−280335.	+	485554.i	−0.0109792	+	0.0190165i
$919$	2.79433e7			1.09141			0.545707	−	0.837976i	$-0.316261\pi$
$919$	2.79433e7			1.09141			0.545707	+	0.837976i	$0.316261\pi$
$920$	−84527.7	+	146406.i	−0.00329253	+	0.00570282i
$921$	−9.41627e6	+	1.63095e7i	−0.365788	+	0.633564i
$922$	−1.08686e7	+	1.88250e7i	−0.421062	+	0.729301i
$923$	4.35495e6	+	7.54299e6i	0.168259	+	0.291433i
$924$	1.73179e7			0.667293
$925$	−2.39311e7	+	7.62277e6i	−0.919620	+	0.292926i
$926$	−4.57963e6			−0.175510
$927$	2.68594e7	+	4.65218e7i	1.02659	+	1.77811i
$928$	−3.90757e6	+	6.76811e6i	−0.148949	+	0.257987i
$929$	8.07066e6	−	1.39788e7i	0.306810	−	0.531411i	−0.670852	−	0.741591i	$-0.734072\pi$
$929$	8.07066e6	−	1.39788e7i	0.306810	−	0.531411i	0.977663	+	0.210180i	$0.0674049\pi$
$930$	−73931.8	+	128054.i	−0.00280300	+	0.00485495i
$931$	−9.75367e6			−0.368802
$932$	−1.26518e7	+	2.19136e7i	−0.477104	+	0.826368i
$933$	−5.75720e7			−2.16525
$934$	−502428.	−	870231.i	−0.0188455	−	0.0326413i
$935$	−174250.			−0.00651845
$936$	−6.85830e6			−0.255874
$937$	1.03492e7	+	1.79253e7i	0.385085	+	0.666986i	0.991781	−	0.127947i	$-0.0408389\pi$
$937$	1.03492e7	+	1.79253e7i	0.385085	+	0.666986i	−0.606696	+	0.794934i	$0.707506\pi$
$938$	4.89026e6	−	8.47018e6i	0.181478	−	0.314330i
$939$	7.63906e7			2.82733
$940$	882573.	+	1.52866e6i	0.0325785	+	0.0564276i
$941$	1.91555e7	+	3.31784e7i	0.705213	+	1.22146i	0.966615	+	0.256235i	$0.0824820\pi$
$941$	1.91555e7	+	3.31784e7i	0.705213	+	1.22146i	−0.261401	+	0.965230i	$0.584185\pi$
$942$	7.71972e6	+	1.33709e7i	0.283449	+	0.490947i
$943$	474269.	−	821458.i	0.0173678	−	0.0300820i
$944$	3.10208e6	−	5.37296e6i	0.113298	−	0.196238i
$945$	−1.94558e6	−	3.36985e6i	−0.0708713	−	0.122753i
$946$	−3.63243e6	−	6.29156e6i	−0.131968	−	0.228576i
$947$	−7.41626e6	−	1.28453e7i	−0.268726	−	0.465448i	0.699807	−	0.714332i	$-0.253269\pi$
$947$	−7.41626e6	−	1.28453e7i	−0.268726	−	0.465448i	−0.968533	+	0.248885i	$0.919936\pi$
$948$	−2.95278e7			−1.06711
$949$	3.64259e6	−	6.30914e6i	0.131294	−	0.227408i
$950$	1.79430e7	+	3.10781e7i	0.645038	+	1.11724i
$951$	−1.82867e7			−0.655666
$952$	483274.			0.0172823
$953$	−1.07743e7	−	1.86617e7i	−0.384290	−	0.665609i	0.607381	−	0.794411i	$-0.292220\pi$
$953$	−1.07743e7	−	1.86617e7i	−0.384290	−	0.665609i	−0.991670	+	0.128802i	$0.958887\pi$
$954$	−1.44417e7			−0.513743
$955$	3.15352e6	−	5.46205e6i	0.111889	−	0.193797i
$956$	2.03980e7			0.721842
$957$	2.91431e7	−	5.04774e7i	1.02862	−	1.78163i
$958$	4.35915e6	−	7.55026e6i	0.153457	−	0.265796i
$959$	−1.84803e7	+	3.20089e7i	−0.648878	+	1.12389i
$960$	−520901.	−	902227.i	−0.0182422	−	0.0315964i
$961$	−2.86080e7			−0.999262
$962$	2.17223e6	−	9.93625e6i	0.0756776	−	0.346166i
$963$	−5.50012e7			−1.91120
$964$	−1.29419e7	−	2.24161e7i	−0.448546	−	0.776904i
$965$	4.57677e6	−	7.92719e6i	0.158212	−	0.274032i
$966$	−1.74843e6	+	3.02837e6i	−0.0602844	+	0.104416i
$967$	−3.90060e6	+	6.75603e6i	−0.134142	+	0.232341i	−0.925269	−	0.379311i	$-0.876161\pi$
$967$	−3.90060e6	+	6.75603e6i	−0.134142	+	0.232341i	0.791127	+	0.611651i	$0.209495\pi$
$968$	4.02247e6			0.137976
$969$	−1.93122e6	+	3.34497e6i	−0.0660726	+	0.114441i
$970$	2.64572e6			0.0902848
$971$	−1.55926e7	−	2.70073e7i	−0.530728	−	0.919247i	−0.999357	−	0.0358524i	$-0.988585\pi$
$971$	−1.55926e7	−	2.70073e7i	−0.530728	−	0.919247i	0.468629	−	0.883395i	$-0.344748\pi$
$972$	−1.84817e7			−0.627444
$973$	−2.42702e7			−0.821846
$974$	9.32765e6	+	1.61560e7i	0.315047	+	0.545677i
$975$	1.12223e7	−	1.94376e7i	0.378069	−	0.654835i
$976$	8.10819e6			0.272458
$977$	2.93149e6	+	5.07749e6i	0.0982543	+	0.170181i	0.910962	−	0.412490i	$-0.135341\pi$
$977$	2.93149e6	+	5.07749e6i	0.0982543	+	0.170181i	−0.812708	+	0.582671i	$0.802007\pi$
$978$	4.20181e6	+	7.27775e6i	0.140472	+	0.243304i
$979$	−1.53157e7	−	2.65275e7i	−0.510716	−	0.884586i
$980$	−273771.	+	474186.i	−0.00910590	+	0.0157719i
$981$	−6.65514e6	+	1.15270e7i	−0.220793	+	0.382424i
$982$	2.07984e7	+	3.60239e7i	0.688259	+	1.19210i
$983$	−1.52960e7	−	2.64934e7i	−0.504886	−	0.874489i	−0.999984	−	0.00565134i	$-0.998201\pi$
$983$	−1.52960e7	−	2.64934e7i	−0.504886	−	0.874489i	0.495098	−	0.868837i	$-0.335132\pi$
$984$	2.92268e6	+	5.06223e6i	0.0962262	+	0.166669i
$985$	−5.08435e6			−0.166972
$986$	813267.	−	1.40862e6i	0.0266404	−	0.0461425i
$987$	1.82558e7	+	3.16199e7i	0.596495	+	1.03316i
$988$	−1.45324e7			−0.473636
$989$	1.46693e6			0.0476890
$990$	2.29550e6	+	3.97593e6i	0.0744372	+	0.128929i
$991$	−5.68084e7			−1.83751			−0.918753	−	0.394834i	$-0.870802\pi$
$991$	−5.68084e7			−1.83751			−0.918753	+	0.394834i	$0.870802\pi$
$992$	−74412.5	+	128886.i	−0.00240086	+	0.00415841i
$993$	−5.62300e7			−1.80965
$994$	−8.08526e6	+	1.40041e7i	−0.259554	+	0.449561i
$995$	−3.36271e6	+	5.82438e6i	−0.107679	+	0.186506i
$996$	2.05896e7	−	3.56622e7i	0.657657	−	1.13910i
$997$	−9.27045e6	−	1.60569e7i	−0.295368	−	0.511592i	0.679703	−	0.733488i	$-0.262109\pi$
$997$	−9.27045e6	−	1.60569e7i	−0.295368	−	0.511592i	−0.975070	+	0.221896i	$0.928775\pi$
$998$	−4.61693e6			−0.146733
$999$	−4.67875e6	+	2.14017e7i	−0.148326	+	0.678475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.c.b.63.1	yes	16
37.10	even	3	inner	74.6.c.b.47.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.c.b.47.1	✓	16	37.10	even	3	inner
74.6.c.b.63.1	yes	16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(-12.1855 + 21.1059i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-5.21821 + 9.03821i) q^{5} -97.4840 q^{6} +(-70.8626 + 122.738i) q^{7} -64.0000 q^{8} +(-175.473 - 303.928i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(-12.1855 + 21.1059i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-5.21821 + 9.03821i) q^{5} -97.4840 q^{6} +(-70.8626 + 122.738i) q^{7} -64.0000 q^{8} +(-175.473 - 303.928i) q^{9} -41.7457 q^{10} +313.369 q^{11} +(-194.968 - 337.695i) q^{12} +(-152.674 + 264.440i) q^{13} -566.901 q^{14} +(-127.173 - 220.270i) q^{15} +(-128.000 - 221.703i) q^{16} +(26.6401 + 46.1420i) q^{17} +(701.892 - 1215.71i) q^{18} +(1487.28 - 2576.04i) q^{19} +(-83.4914 - 144.611i) q^{20} +(-1726.99 - 2991.24i) q^{21} +(626.737 + 1085.54i) q^{22} -253.103 q^{23} +(779.872 - 1350.78i) q^{24} +(1508.04 + 2612.00i) q^{25} -1221.39 q^{26} +2630.76 q^{27} +(-1133.80 - 1963.80i) q^{28} -7631.98 q^{29} +(508.692 - 881.081i) q^{30} -145.337 q^{31} +(512.000 - 886.810i) q^{32} +(-3818.56 + 6613.93i) q^{33} +(-106.560 + 184.568i) q^{34} +(-739.552 - 1280.94i) q^{35} +5615.14 q^{36} +(-1778.48 + 8135.17i) q^{37} +11898.2 q^{38} +(-3720.83 - 6444.66i) q^{39} +(333.966 - 578.445i) q^{40} +(-1873.82 + 3245.55i) q^{41} +(6907.97 - 11965.0i) q^{42} -5795.78 q^{43} +(-2506.95 + 4342.16i) q^{44} +3662.62 q^{45} +(-506.206 - 876.775i) q^{46} -10570.8 q^{47} +6238.98 q^{48} +(-1639.52 - 2839.73i) q^{49} +(-6032.16 + 10448.0i) q^{50} -1298.49 q^{51} +(-2442.79 - 4231.03i) q^{52} +(-5143.83 - 8909.37i) q^{53} +(5261.52 + 9113.22i) q^{54} +(-1635.22 + 2832.29i) q^{55} +(4535.21 - 7855.21i) q^{56} +(36246.4 + 62780.6i) q^{57} +(-15264.0 - 26437.9i) q^{58} +(12117.5 + 20988.1i) q^{59} +4069.54 q^{60} +(-15836.3 + 27429.3i) q^{61} +(-290.674 - 503.462i) q^{62} +49737.9 q^{63} +4096.00 q^{64} +(-1593.37 - 2759.80i) q^{65} -30548.4 q^{66} +(-8626.30 + 14941.2i) q^{67} -852.484 q^{68} +(3084.19 - 5341.97i) q^{69} +(2958.21 - 5123.77i) q^{70} +(14262.2 - 24702.9i) q^{71} +(11230.3 + 19451.4i) q^{72} -23858.5 q^{73} +(-31738.0 + 10109.5i) q^{74} -73504.9 q^{75} +(23796.4 + 41216.6i) q^{76} +(-22206.1 + 38462.1i) q^{77} +(14883.3 - 25778.7i) q^{78} +(37862.4 - 65579.6i) q^{79} +2671.72 q^{80} +(10582.8 - 18330.0i) q^{81} -14990.5 q^{82} +(52802.5 + 91456.6i) q^{83} +55263.8 q^{84} -556.055 q^{85} +(-11591.6 - 20077.2i) q^{86} +(92999.5 - 161080. i) q^{87} -20055.6 q^{88} +(-48874.3 - 84652.8i) q^{89} +(7325.25 + 12687.7i) q^{90} +(-21637.8 - 37477.8i) q^{91} +(2024.82 - 3507.10i) q^{92} +(1771.00 - 3067.47i) q^{93} +(-21141.7 - 36618.4i) q^{94} +(15521.8 + 26884.6i) q^{95} +(12478.0 + 21612.5i) q^{96} -63377.1 q^{97} +(6558.08 - 11358.9i) q^{98} +(-54987.8 - 95241.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9}+O(q^{10}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9} + 560 q^{10} - 240 q^{11} - 128 q^{12} + 1614 q^{13} - 256 q^{14} + 728 q^{15} - 2048 q^{16} + 216 q^{17} + 2792 q^{18} - 950 q^{19} + 1120 q^{20} + 1718 q^{21} - 480 q^{22} + 1716 q^{23} + 512 q^{24} - 11760 q^{25} + 12912 q^{26} - 92 q^{27} - 512 q^{28} + 1112 q^{29} - 2912 q^{30} - 16816 q^{31} + 8192 q^{32} + 4744 q^{33} - 864 q^{34} - 5004 q^{35} + 22336 q^{36} + 3556 q^{37} - 7600 q^{38} + 17710 q^{39} - 4480 q^{40} - 8080 q^{41} - 6872 q^{42} - 19012 q^{43} + 1920 q^{44} - 58672 q^{45} + 3432 q^{46} + 29392 q^{47} + 4096 q^{48} + 474 q^{49} + 47040 q^{50} - 17856 q^{51} + 25824 q^{52} - 29250 q^{53} - 184 q^{54} + 15772 q^{55} + 2048 q^{56} + 16182 q^{57} + 2224 q^{58} + 61478 q^{59} - 23296 q^{60} - 132002 q^{61} - 33632 q^{62} - 103324 q^{63} + 65536 q^{64} - 37426 q^{65} + 37952 q^{66} - 45658 q^{67} - 6912 q^{68} - 23816 q^{69} + 20016 q^{70} + 13236 q^{71} + 44672 q^{72} + 270632 q^{73} - 81304 q^{74} + 419904 q^{75} - 15200 q^{76} - 184084 q^{77} - 70840 q^{78} + 123974 q^{79} - 35840 q^{80} + 96448 q^{81} - 64640 q^{82} - 16936 q^{83} - 54976 q^{84} - 251316 q^{85} - 38024 q^{86} + 168290 q^{87} + 15360 q^{88} + 52892 q^{89} - 117344 q^{90} - 432546 q^{91} - 13728 q^{92} + 220328 q^{93} + 58784 q^{94} + 47026 q^{95} + 8192 q^{96} - 546140 q^{97} - 1896 q^{98} - 9800 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9 + 560 * q^10 - 240 * q^11 - 128 * q^12 + 1614 * q^13 - 256 * q^14 + 728 * q^15 - 2048 * q^16 + 216 * q^17 + 2792 * q^18 - 950 * q^19 + 1120 * q^20 + 1718 * q^21 - 480 * q^22 + 1716 * q^23 + 512 * q^24 - 11760 * q^25 + 12912 * q^26 - 92 * q^27 - 512 * q^28 + 1112 * q^29 - 2912 * q^30 - 16816 * q^31 + 8192 * q^32 + 4744 * q^33 - 864 * q^34 - 5004 * q^35 + 22336 * q^36 + 3556 * q^37 - 7600 * q^38 + 17710 * q^39 - 4480 * q^40 - 8080 * q^41 - 6872 * q^42 - 19012 * q^43 + 1920 * q^44 - 58672 * q^45 + 3432 * q^46 + 29392 * q^47 + 4096 * q^48 + 474 * q^49 + 47040 * q^50 - 17856 * q^51 + 25824 * q^52 - 29250 * q^53 - 184 * q^54 + 15772 * q^55 + 2048 * q^56 + 16182 * q^57 + 2224 * q^58 + 61478 * q^59 - 23296 * q^60 - 132002 * q^61 - 33632 * q^62 - 103324 * q^63 + 65536 * q^64 - 37426 * q^65 + 37952 * q^66 - 45658 * q^67 - 6912 * q^68 - 23816 * q^69 + 20016 * q^70 + 13236 * q^71 + 44672 * q^72 + 270632 * q^73 - 81304 * q^74 + 419904 * q^75 - 15200 * q^76 - 184084 * q^77 - 70840 * q^78 + 123974 * q^79 - 35840 * q^80 + 96448 * q^81 - 64640 * q^82 - 16936 * q^83 - 54976 * q^84 - 251316 * q^85 - 38024 * q^86 + 168290 * q^87 + 15360 * q^88 + 52892 * q^89 - 117344 * q^90 - 432546 * q^91 - 13728 * q^92 + 220328 * q^93 + 58784 * q^94 + 47026 * q^95 + 8192 * q^96 - 546140 * q^97 - 1896 * q^98 - 9800 * q^99

Introduction

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