LMFDB - Embedded newform 74.6.c.b.63.8

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			63.8
Root			$-13.4393 + 23.2776i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.6.c.b.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(12.9393 - 22.4116i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5138 - 52.8515i) q^{5} +103.515 q^{6} +(-3.03701 + 5.26025i) q^{7} -64.0000 q^{8} +(-213.352 - 369.536i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(12.9393 - 22.4116i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5138 - 52.8515i) q^{5} +103.515 q^{6} +(-3.03701 + 5.26025i) q^{7} -64.0000 q^{8} +(-213.352 - 369.536i) q^{9} +244.111 q^{10} +118.542 q^{11} +(207.029 + 358.585i) q^{12} +(-74.4626 + 128.973i) q^{13} -24.2961 q^{14} +(-789.656 - 1367.72i) q^{15} +(-128.000 - 221.703i) q^{16} +(-1142.59 - 1979.02i) q^{17} +(853.408 - 1478.15i) q^{18} +(-441.224 + 764.223i) q^{19} +(488.221 + 845.624i) q^{20} +(78.5936 + 136.128i) q^{21} +(237.084 + 410.641i) q^{22} +3994.63 q^{23} +(-828.116 + 1434.34i) q^{24} +(-299.686 - 519.071i) q^{25} -595.701 q^{26} -4754.01 q^{27} +(-48.5921 - 84.1640i) q^{28} +41.3565 q^{29} +(3158.62 - 5470.90i) q^{30} +6071.89 q^{31} +(512.000 - 886.810i) q^{32} +(1533.85 - 2656.71i) q^{33} +(4570.34 - 7916.07i) q^{34} +(185.341 + 321.021i) q^{35} +6827.26 q^{36} +(3571.31 + 7522.61i) q^{37} -3529.79 q^{38} +(1926.99 + 3337.65i) q^{39} +(-1952.88 + 3382.49i) q^{40} +(2816.75 - 4878.76i) q^{41} +(-314.375 + 544.513i) q^{42} -556.662 q^{43} +(-948.336 + 1642.57i) q^{44} -26040.7 q^{45} +(7989.25 + 13837.8i) q^{46} -17833.1 q^{47} -6624.93 q^{48} +(8385.05 + 14523.3i) q^{49} +(1198.74 - 2076.28i) q^{50} -59137.1 q^{51} +(-1191.40 - 2063.57i) q^{52} +(7402.46 + 12821.4i) q^{53} +(-9508.01 - 16468.4i) q^{54} +(3617.17 - 6265.12i) q^{55} +(194.369 - 336.656i) q^{56} +(11418.3 + 19777.0i) q^{57} +(82.7130 + 143.263i) q^{58} +(-2764.44 - 4788.15i) q^{59} +25269.0 q^{60} +(-14067.4 + 24365.5i) q^{61} +(12143.8 + 21033.6i) q^{62} +2591.81 q^{63} +4096.00 q^{64} +(4544.28 + 7870.92i) q^{65} +12270.8 q^{66} +(-13741.7 + 23801.4i) q^{67} +36562.8 q^{68} +(51687.8 - 89525.8i) q^{69} +(-741.366 + 1284.08i) q^{70} +(-19700.4 + 34122.1i) q^{71} +(13654.5 + 23650.3i) q^{72} +84029.3 q^{73} +(-18916.5 + 27416.6i) q^{74} -15510.9 q^{75} +(-7059.59 - 12227.6i) q^{76} +(-360.013 + 623.561i) q^{77} +(-7707.96 + 13350.6i) q^{78} +(30683.5 - 53145.3i) q^{79} -15623.1 q^{80} +(-9669.09 + 16747.3i) q^{81} +22534.0 q^{82} +(5187.34 + 8984.73i) q^{83} -2515.00 q^{84} -139459. q^{85} +(-1113.32 - 1928.33i) q^{86} +(535.125 - 926.864i) q^{87} -7586.68 q^{88} +(5024.13 + 8702.05i) q^{89} +(-52081.5 - 90207.7i) q^{90} +(-452.287 - 783.384i) q^{91} +(-31957.0 + 55351.2i) q^{92} +(78566.1 - 136081. i) q^{93} +(-35666.2 - 61775.7i) q^{94} +(26926.9 + 46638.7i) q^{95} +(-13249.9 - 22949.4i) q^{96} -130592. q^{97} +(-33540.2 + 58093.4i) q^{98} +(-25291.2 - 43805.6i) 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
$3$	12.9393	−	22.4116i	0.830058	−	1.43770i	−0.0679340	−	0.997690i	$-0.521641\pi$
$3$	12.9393	−	22.4116i	0.830058	−	1.43770i	0.897992	−	0.440012i	$-0.145026\pi$
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	30.5138	−	52.8515i	0.545848	−	0.945436i	−0.452705	−	0.891660i	$-0.649541\pi$
$5$	30.5138	−	52.8515i	0.545848	−	0.945436i	0.998553	−	0.0537758i	$-0.0171256\pi$
$6$	103.515			1.17388
$7$	−3.03701	+	5.26025i	−0.0234261	+	0.0405753i	−0.877501	−	0.479575i	$-0.840791\pi$
$7$	−3.03701	+	5.26025i	−0.0234261	+	0.0405753i	0.854075	+	0.520150i	$0.174124\pi$
$8$	−64.0000			−0.353553
$9$	−213.352	−	369.536i	−0.877992	−	1.52073i
$10$	244.111			0.771945
$11$	118.542			0.295386			0.147693	−	0.989033i	$-0.452815\pi$
$11$	118.542			0.295386			0.147693	+	0.989033i	$0.452815\pi$
$12$	207.029	+	358.585i	0.415029	+	0.718851i
$13$	−74.4626	+	128.973i	−0.122202	+	0.211661i	−0.920636	−	0.390422i	$-0.872329\pi$
$13$	−74.4626	+	128.973i	−0.122202	+	0.211661i	0.798433	+	0.602083i	$0.205662\pi$
$14$	−24.2961			−0.0331296
$15$	−789.656	−	1367.72i	−0.906170	−	1.56953i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	−1142.59	−	1979.02i	−0.958885	−	1.66084i	−0.725215	−	0.688522i	$-0.758260\pi$
$17$	−1142.59	−	1979.02i	−0.958885	−	1.66084i	−0.233670	−	0.972316i	$-0.575074\pi$
$18$	853.408	−	1478.15i	0.620834	−	1.07532i
$19$	−441.224	+	764.223i	−0.280398	+	0.485664i	−0.971483	−	0.237110i	$-0.923800\pi$
$19$	−441.224	+	764.223i	−0.280398	+	0.485664i	0.691085	+	0.722774i	$0.257133\pi$
$20$	488.221	+	845.624i	0.272924	+	0.472718i
$21$	78.5936	+	136.128i	0.0388901	+	0.0673596i
$22$	237.084	+	410.641i	0.104435	+	0.180886i
$23$	3994.63			1.57455			0.787275	−	0.616602i	$-0.211491\pi$
$23$	3994.63			1.57455			0.787275	+	0.616602i	$0.211491\pi$
$24$	−828.116	+	1434.34i	−0.293470	+	0.508304i
$25$	−299.686	−	519.071i	−0.0958994	−	0.166103i
$26$	−595.701			−0.172820
$27$	−4754.01			−1.25502
$28$	−48.5921	−	84.1640i	−0.0117131	−	0.0202876i
$29$	41.3565			0.00913164			0.00456582	−	0.999990i	$-0.498547\pi$
$29$	41.3565			0.00913164			0.00456582	+	0.999990i	$0.498547\pi$
$30$	3158.62	−	5470.90i	0.640759	−	1.10983i
$31$	6071.89			1.13480			0.567400	−	0.823442i	$-0.307949\pi$
$31$	6071.89			1.13480			0.567400	+	0.823442i	$0.307949\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	1533.85	−	2656.71i	0.245188	−	0.424678i
$34$	4570.34	−	7916.07i	0.678034	−	1.17439i
$35$	185.341	+	321.021i	0.0255742	+	0.0442958i
$36$	6827.26			0.877992
$37$	3571.31	+	7522.61i	0.428867	+	0.903368i
$37$	3571.31	+	7522.61i	0.428867	+	0.903368i
$38$	−3529.79			−0.396543
$39$	1926.99	+	3337.65i	0.202870	+	0.351381i
$40$	−1952.88	+	3382.49i	−0.192986	+	0.334262i
$41$	2816.75	−	4878.76i	0.261691	−	0.453262i	−0.705000	−	0.709207i	$-0.749053\pi$
$41$	2816.75	−	4878.76i	0.261691	−	0.453262i	0.966691	+	0.255945i	$0.0823865\pi$
$42$	−314.375	+	544.513i	−0.0274995	+	0.0476305i
$43$	−556.662			−0.0459114			−0.0229557	−	0.999736i	$-0.507308\pi$
$43$	−556.662			−0.0459114			−0.0229557	+	0.999736i	$0.507308\pi$
$44$	−948.336	+	1642.57i	−0.0738466	+	0.127906i
$45$	−26040.7			−1.91700
$46$	7989.25	+	13837.8i	0.556688	+	0.964211i
$47$	−17833.1			−1.17756			−0.588779	−	0.808294i	$-0.700391\pi$
$47$	−17833.1			−1.17756			−0.588779	+	0.808294i	$0.700391\pi$
$48$	−6624.93			−0.415029
$49$	8385.05	+	14523.3i	0.498902	+	0.864124i
$50$	1198.74	−	2076.28i	0.0678111	−	0.117452i
$51$	−59137.1			−3.18372
$52$	−1191.40	−	2063.57i	−0.0611012	−	0.105830i
$53$	7402.46	+	12821.4i	0.361981	+	0.626970i	0.988287	−	0.152608i	$-0.0487671\pi$
$53$	7402.46	+	12821.4i	0.361981	+	0.626970i	−0.626306	+	0.779578i	$0.715434\pi$
$54$	−9508.01	−	16468.4i	−0.443716	−	0.768539i
$55$	3617.17	−	6265.12i	0.161236	−	0.279269i
$56$	194.369	−	336.656i	0.00828239	−	0.0143455i
$57$	11418.3	+	19777.0i	0.465494	+	0.806258i
$58$	82.7130	+	143.263i	0.00322852	+	0.00559197i
$59$	−2764.44	−	4788.15i	−0.103390	−	0.179076i	0.809689	−	0.586859i	$-0.199636\pi$
$59$	−2764.44	−	4788.15i	−0.103390	−	0.179076i	−0.913079	+	0.407782i	$0.866302\pi$
$60$	25269.0			0.906170
$61$	−14067.4	+	24365.5i	−0.484050	+	0.838399i	−0.999832	−	0.0183209i	$-0.994168\pi$
$61$	−14067.4	+	24365.5i	−0.484050	+	0.838399i	0.515782	+	0.856720i	$0.327501\pi$
$62$	12143.8	+	21033.6i	0.401213	+	0.694921i
$63$	2591.81			0.0822718
$64$	4096.00			0.125000
$65$	4544.28	+	7870.92i	0.133408	+	0.231069i
$66$	12270.8			0.346748
$67$	−13741.7	+	23801.4i	−0.373986	+	0.647762i	−0.990175	−	0.139836i	$-0.955342\pi$
$67$	−13741.7	+	23801.4i	−0.373986	+	0.647762i	0.616189	+	0.787598i	$0.288676\pi$
$68$	36562.8			0.958885
$69$	51687.8	−	89525.8i	1.30697	−	2.26373i
$70$	−741.366	+	1284.08i	−0.0180837	+	0.0313219i
$71$	−19700.4	+	34122.1i	−0.463798	+	0.803322i	−0.999146	−	0.0413094i	$-0.986847\pi$
$71$	−19700.4	+	34122.1i	−0.463798	+	0.803322i	0.535348	+	0.844631i	$0.320180\pi$
$72$	13654.5	+	23650.3i	0.310417	+	0.537658i
$73$	84029.3			1.84554			0.922770	−	0.385350i	$-0.125919\pi$
$73$	84029.3			1.84554			0.922770	+	0.385350i	$0.125919\pi$
$74$	−18916.5	+	27416.6i	−0.401570	+	0.582015i
$75$	−15510.9			−0.318408
$76$	−7059.59	−	12227.6i	−0.140199	−	0.242832i
$77$	−360.013	+	623.561i	−0.00691976	+	0.0119854i
$78$	−7707.96	+	13350.6i	−0.143451	+	0.248464i
$79$	30683.5	−	53145.3i	0.553142	−	0.958070i	−0.444903	−	0.895579i	$-0.646762\pi$
$79$	30683.5	−	53145.3i	0.553142	−	0.958070i	0.998045	−	0.0624917i	$-0.0199047\pi$
$80$	−15623.1			−0.272924
$81$	−9669.09	+	16747.3i	−0.163747	+	0.283618i
$82$	22534.0			0.370087
$83$	5187.34	+	8984.73i	0.0826512	+	0.143156i	0.904388	−	0.426711i	$-0.140328\pi$
$83$	5187.34	+	8984.73i	0.0826512	+	0.143156i	−0.821737	+	0.569867i	$0.806995\pi$
$84$	−2515.00			−0.0388901
$85$	−139459.			−2.09362
$86$	−1113.32	−	1928.33i	−0.0162321	−	0.0281149i
$87$	535.125	−	926.864i	0.00757979	−	0.0131286i
$88$	−7586.68			−0.104435
$89$	5024.13	+	8702.05i	0.0672335	+	0.116452i	0.897683	−	0.440643i	$-0.145249\pi$
$89$	5024.13	+	8702.05i	0.0672335	+	0.116452i	−0.830449	+	0.557095i	$0.811916\pi$
$90$	−52081.5	−	90207.7i	−0.677761	−	1.17392i
$91$	−452.287	−	783.384i	−0.00572547	−	0.00991680i
$92$	−31957.0	+	55351.2i	−0.393638	+	0.681800i
$93$	78566.1	−	136081.i	0.941950	−	1.63151i
$94$	−35666.2	−	61775.7i	−0.416329	−	0.721104i
$95$	26926.9	+	46638.7i	0.306110	+	0.530197i
$96$	−13249.9	−	22949.4i	−0.146735	−	0.254152i
$97$	−130592.			−1.40925			−0.704626	−	0.709579i	$-0.748885\pi$
$97$	−130592.			−1.40925			−0.704626	+	0.709579i	$0.748885\pi$
$98$	−33540.2	+	58093.4i	−0.352777	+	0.611028i
$99$	−25291.2	−	43805.6i	−0.259347	−	0.449202i
$100$	9589.94			0.0958994
$101$	168353.			1.64216			0.821082	−	0.570810i	$-0.193371\pi$
$101$	168353.			1.64216			0.821082	+	0.570810i	$0.193371\pi$
$102$	−118274.	−	204857.i	−1.12562	−	1.94962i
$103$	−54508.0			−0.506253			−0.253126	−	0.967433i	$-0.581459\pi$
$103$	−54508.0			−0.506253			−0.253126	+	0.967433i	$0.581459\pi$
$104$	4765.61	−	8254.27i	0.0432051	−	0.0748334i
$105$	9592.77			0.0849123
$106$	−29609.8	+	51285.7i	−0.255959	+	0.443335i
$107$	87759.9	−	152005.i	0.741031	−	1.28350i	−0.210995	−	0.977487i	$-0.567670\pi$
$107$	87759.9	−	152005.i	0.741031	−	1.28350i	0.952026	−	0.306017i	$-0.0989964\pi$
$108$	38032.1	−	65873.4i	0.313755	−	0.543439i
$109$	90350.5	+	156492.i	0.728390	+	1.26161i	0.957563	+	0.288223i	$0.0930645\pi$
$109$	90350.5	+	156492.i	0.728390	+	1.26161i	−0.229173	+	0.973386i	$0.573602\pi$
$110$	28937.3			0.228022
$111$	214804.	+	17299.0i	1.65476	+	0.133264i
$112$	1554.95			0.0117131
$113$	85612.8	+	148286.i	0.630729	+	1.09245i	0.987403	+	0.158226i	$0.0505774\pi$
$113$	85612.8	+	148286.i	0.630729	+	1.09245i	−0.356674	+	0.934229i	$0.616089\pi$
$114$	−45673.1	+	79108.2i	−0.329154	+	0.570111i
$115$	121891.	−	211122.i	0.859465	−	1.48864i
$116$	−330.852	+	573.053i	−0.00228291	+	0.00395412i
$117$	63547.0			0.429171
$118$	11057.8	−	19152.6i	0.0731076	−	0.126626i
$119$	13880.2			0.0898520
$120$	50538.0	+	87534.4i	0.320380	+	0.554914i
$121$	−146999.			−0.912747
$122$	−112539.			−0.684550
$123$	−72893.7	−	126256.i	−0.434437	−	0.752468i
$124$	−48575.1	+	84134.6i	−0.283700	+	0.491383i
$125$	154133.			0.882309
$126$	5183.61	+	8978.28i	0.0290875	+	0.0503810i
$127$	−158488.	−	274510.i	−0.871943	−	1.51025i	−0.859984	−	0.510321i	$-0.829527\pi$
$127$	−158488.	−	274510.i	−0.871943	−	1.51025i	−0.0119587	−	0.999928i	$-0.503807\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	−7202.83	+	12475.7i	−0.0381091	+	0.0660069i
$130$	−18177.1	+	31483.7i	−0.0943336	+	0.163391i
$131$	76284.7	+	132129.i	0.388382	+	0.672698i	0.992232	−	0.124400i	$-0.0397007\pi$
$131$	76284.7	+	132129.i	0.388382	+	0.672698i	−0.603850	+	0.797098i	$0.706367\pi$
$132$	24541.6	+	42507.4i	0.122594	+	0.212339i
$133$	−2680.00	−	4641.90i	−0.0131373	−	0.0227545i
$134$	−109934.			−0.528896
$135$	−145063.	+	251256.i	−0.685049	+	1.18654i
$136$	73125.5	+	126657.i	0.339017	+	0.587195i
$137$	−394700.			−1.79666			−0.898329	−	0.439323i	$-0.855218\pi$
$137$	−394700.			−1.79666			−0.898329	+	0.439323i	$0.855218\pi$
$138$	413502.			1.84833
$139$	24536.5	+	42498.4i	0.107715	+	0.186567i	0.914844	−	0.403807i	$-0.132313\pi$
$139$	24536.5	+	42498.4i	0.107715	+	0.186567i	−0.807129	+	0.590375i	$0.798980\pi$
$140$	−5930.93			−0.0255742
$141$	−230748.	+	399668.i	−0.977441	+	1.69298i
$142$	−157603.			−0.655910
$143$	−8826.94	+	15288.7i	−0.0360969	+	0.0625217i
$144$	−54618.1	+	94601.3i	−0.219498	+	0.380182i
$145$	1261.94	−	2185.75i	0.00498449	−	0.00863338i
$146$	168059.	+	291086.i	0.652497	+	1.13016i
$147$	433988.			1.65647
$148$	−132807.	−	10695.5i	−0.498386	−	0.0401370i
$149$	−256565.			−0.946742			−0.473371	−	0.880863i	$-0.656963\pi$
$149$	−256565.			−0.946742			−0.473371	+	0.880863i	$0.656963\pi$
$150$	−31021.8	−	53731.4i	−0.112574	−	0.194984i
$151$	422.805	−	732.320i	0.00150903	−	0.00261372i	−0.865270	−	0.501306i	$-0.832853\pi$
$151$	422.805	−	732.320i	0.00150903	−	0.00261372i	0.866779	+	0.498693i	$0.166186\pi$
$152$	28238.4	−	48910.3i	0.0991358	−	0.171708i
$153$	−487546.	+	844454.i	−1.68379	+	2.91640i
$154$	−2880.10			−0.00978602
$155$	185277.	−	320908.i	0.619428	−	1.07288i
$156$	−61663.7			−0.202870
$157$	−151013.	−	261562.i	−0.488951	−	0.846889i	0.510968	−	0.859600i	$-0.329287\pi$
$157$	−151013.	−	261562.i	−0.488951	−	0.846889i	−0.999919	+	0.0127112i	$0.995954\pi$
$158$	245468.			0.782261
$159$	383131.			1.20186
$160$	−31246.1	−	54119.9i	−0.0964932	−	0.167131i
$161$	−12131.7	+	21012.7i	−0.0368857	+	0.0638878i
$162$	−77352.7			−0.231573
$163$	−111136.	−	192494.i	−0.327633	−	0.567477i	0.654409	−	0.756141i	$-0.272918\pi$
$163$	−111136.	−	192494.i	−0.327633	−	0.567477i	−0.982042	+	0.188664i	$0.939584\pi$
$164$	45068.0	+	78060.1i	0.130846	+	0.226631i
$165$	−93607.4	−	162133.i	−0.267670	−	0.463618i
$166$	−20749.3	+	35938.9i	−0.0584432	+	0.101227i
$167$	117360.	−	203273.i	0.325633	−	0.564013i	−0.656007	−	0.754755i	$-0.727756\pi$
$167$	117360.	−	203273.i	0.325633	−	0.564013i	0.981640	+	0.190742i	$0.0610892\pi$
$168$	−5029.99	−	8712.20i	−0.0137497	−	0.0238152i
$169$	174557.	+	302342.i	0.470133	+	0.814294i
$170$	−278917.	−	483099.i	−0.740207	−	1.28208i
$171$	376544.			0.984749
$172$	4453.29	−	7713.33i	0.0114778	−	0.0198802i
$173$	−241838.	−	418876.i	−0.614342	−	1.06407i	−0.990500	−	0.137515i	$-0.956088\pi$
$173$	−241838.	−	418876.i	−0.614342	−	1.06407i	0.376158	−	0.926556i	$-0.377245\pi$
$174$	4281.00			0.0107194
$175$	3640.59			0.00898622
$176$	−15173.4	−	26281.0i	−0.0369233	−	0.0639530i
$177$	−143080.			−0.343278
$178$	−20096.5	+	34808.2i	−0.0475413	+	0.0823439i
$179$	−305520.			−0.712700			−0.356350	−	0.934352i	$-0.615979\pi$
$179$	−305520.			−0.712700			−0.356350	+	0.934352i	$0.615979\pi$
$180$	208326.	−	360831.i	0.479250	−	0.830085i
$181$	−159026.	+	275441.i	−0.360804	+	0.624930i	−0.988093	−	0.153856i	$-0.950831\pi$
$181$	−159026.	+	275441.i	−0.360804	+	0.624930i	0.627290	+	0.778786i	$0.284164\pi$
$182$	1809.15	−	3133.54i	0.00404852	−	0.00701223i
$183$	364046.	+	630546.i	0.803578	+	1.39184i
$184$	−255656.			−0.556688
$185$	506555.	+	40794.9i	1.08817	+	0.0876348i
$186$	628529.			1.33212
$187$	−135444.	−	234597.i	−0.283242	−	0.490589i
$188$	142665.	−	247103.i	0.294389	−	0.509897i
$189$	14438.0	−	25007.3i	0.0294003	−	0.0509228i
$190$	−107707.	+	186555.i	−0.216452	+	0.374906i
$191$	563528.			1.11772			0.558859	−	0.829263i	$-0.311239\pi$
$191$	563528.			1.11772			0.558859	+	0.829263i	$0.311239\pi$
$192$	52999.5	−	91797.7i	0.103757	−	0.179713i
$193$	−369873.			−0.714759			−0.357380	−	0.933959i	$-0.616330\pi$
$193$	−369873.			−0.714759			−0.357380	+	0.933959i	$0.616330\pi$
$194$	−261185.	−	452386.i	−0.498246	−	0.862987i
$195$	235199.			0.442945
$196$	−268322.			−0.498902
$197$	−178654.	−	309437.i	−0.327979	−	0.568077i	0.654131	−	0.756381i	$-0.273034\pi$
$197$	−178654.	−	309437.i	−0.327979	−	0.568077i	−0.982111	+	0.188304i	$0.939701\pi$
$198$	101165.	−	175222.i	0.183386	−	0.317634i
$199$	−983461.			−1.76045			−0.880226	−	0.474554i	$-0.842609\pi$
$199$	−983461.			−1.76045			−0.880226	+	0.474554i	$0.842609\pi$
$200$	19179.9	+	33220.5i	0.0339056	+	0.0587262i
$201$	355618.	+	615948.i	0.620859	+	1.07536i
$202$	336705.	+	583191.i	0.580593	+	1.00562i
$203$	−125.600	+	217.546i	−0.000213919	+	0.000370519i
$204$	473097.	−	819428.i	0.795930	−	1.37859i
$205$	−171900.	−	297739.i	−0.285687	−	0.494824i
$206$	−109016.	−	188821.i	−0.178987	−	0.310015i
$207$	−852261.	−	1.47616e6i	−1.38244	−	2.39446i
$208$	38124.9			0.0611012
$209$	−52303.6	+	90592.5i	−0.0828258	+	0.143459i
$210$	19185.5	+	33230.3i	0.0300210	+	0.0519980i
$211$	−478733.			−0.740264			−0.370132	−	0.928979i	$-0.620688\pi$
$211$	−478733.			−0.740264			−0.370132	+	0.928979i	$0.620688\pi$
$212$	−236879.			−0.361981
$213$	509819.	+	883033.i	0.769959	+	1.33361i
$214$	702079.			1.04798
$215$	−16985.9	+	29420.4i	−0.0250606	+	0.0434063i
$216$	304256.			0.443716
$217$	−18440.4	+	31939.7i	−0.0265840	+	0.0460449i
$218$	−361402.	+	625966.i	−0.515050	+	0.892092i
$219$	1.08728e6	−	1.88323e6i	1.53191	−	2.65334i
$220$	57874.7	+	100242.i	0.0806180	+	0.139634i
$221$	340320.			0.468713
$222$	369682.	+	778700.i	0.503438	+	1.06044i
$223$	−585419.			−0.788324			−0.394162	−	0.919041i	$-0.628965\pi$
$223$	−585419.			−0.788324			−0.394162	+	0.919041i	$0.628965\pi$
$224$	3109.90	+	5386.50i	0.00414120	+	0.00717276i
$225$	−127877.	+	221490.i	−0.168398	+	0.291674i
$226$	−342451.	+	593143.i	−0.445993	+	0.772482i
$227$	−469787.	+	813695.i	−0.605113	+	1.04809i	0.386921	+	0.922113i	$0.373539\pi$
$227$	−469787.	+	813695.i	−0.605113	+	1.04809i	−0.992034	+	0.125973i	$0.959795\pi$
$228$	−365385.			−0.465494
$229$	249304.	−	431807.i	0.314153	−	0.544128i	−0.665104	−	0.746750i	$-0.731613\pi$
$229$	249304.	−	431807.i	0.314153	−	0.544128i	0.979257	+	0.202622i	$0.0649463\pi$
$230$	975130.			1.21547
$231$	9316.64	+	16136.9i	0.0114876	+	0.0198971i
$232$	−2646.82			−0.00322852
$233$	20810.0			0.0251121			0.0125560	−	0.999921i	$-0.496003\pi$
$233$	20810.0			0.0251121			0.0125560	+	0.999921i	$0.496003\pi$
$234$	127094.	+	220133.i	0.151735	+	0.262812i
$235$	−544156.	+	942506.i	−0.642767	+	1.11331i
$236$	88462.1			0.103390
$237$	−794046.	−	1.37533e6i	−0.918280	−	1.59051i
$238$	27760.4	+	48082.3i	0.0317675	+	0.0550229i
$239$	−398936.	−	690977.i	−0.451760	−	0.782472i	0.546735	−	0.837306i	$-0.315871\pi$
$239$	−398936.	−	690977.i	−0.451760	−	0.782472i	−0.998496	+	0.0548336i	$0.982537\pi$
$240$	−202152.	+	350137.i	−0.226543	+	0.392383i
$241$	−220344.	+	381647.i	−0.244376	+	0.423272i	−0.961956	−	0.273204i	$-0.911917\pi$
$241$	−220344.	+	381647.i	−0.244376	+	0.423272i	0.717580	+	0.696476i	$0.245250\pi$
$242$	−293998.	−	509219.i	−0.322705	−	0.558941i
$243$	−327389.	−	567054.i	−0.355671	−	0.616040i
$244$	−225079.	−	389848.i	−0.242025	−	0.419199i
$245$	1.02344e6			1.08930
$246$	291575.	−	505022.i	0.307194	−	0.532075i
$247$	−65709.4	−	113812.i	−0.0685307	−	0.118699i
$248$	−388601.			−0.401213
$249$	268482.			0.274421
$250$	308266.	+	533933.i	0.311944	+	0.540302i
$251$	1.69402e6			1.69720			0.848602	−	0.529032i	$-0.177445\pi$
$251$	1.69402e6			1.69720			0.848602	+	0.529032i	$0.177445\pi$
$252$	−20734.5	+	35913.1i	−0.0205680	+	0.0356248i
$253$	473531.			0.465101
$254$	633953.	−	1.09804e6i	0.616557	−	1.06791i
$255$	−1.80450e6	+	3.12549e6i	−1.73783	+	3.01000i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	977548.	+	1.69316e6i	0.923220	+	1.59906i	0.794399	+	0.607396i	$0.207786\pi$
$257$	977548.	+	1.69316e6i	0.923220	+	1.59906i	0.128821	+	0.991668i	$0.458881\pi$
$258$	−57622.6			−0.0538944
$259$	−50416.9	−	4060.27i	−0.0467011	−	0.00376102i
$260$	−145417.			−0.133408
$261$	−8823.49	−	15282.7i	−0.00801750	−	0.0138867i
$262$	−305139.	+	528516.i	−0.274628	+	0.475669i
$263$	406704.	−	704431.i	0.362567	−	0.627985i	−0.625815	−	0.779971i	$-0.715234\pi$
$263$	406704.	−	704431.i	0.362567	−	0.627985i	0.988383	+	0.151986i	$0.0485670\pi$
$264$	−98166.5	+	170029.i	−0.0866869	+	0.150146i
$265$	903509.			0.790347
$266$	10720.0	−	18567.6i	0.00928948	−	0.0160898i
$267$	260035.			0.223231
$268$	−219868.	−	380823.i	−0.186993	−	0.323881i
$269$	655943.			0.552694			0.276347	−	0.961058i	$-0.410876\pi$
$269$	655943.			0.552694			0.276347	+	0.961058i	$0.410876\pi$
$270$	−1.16050e6			−0.968806
$271$	9541.03	+	16525.6i	0.00789173	+	0.0136689i	0.869944	−	0.493150i	$-0.164155\pi$
$271$	9541.03	+	16525.6i	0.00789173	+	0.0136689i	−0.862053	+	0.506819i	$0.830821\pi$
$272$	−292502.	+	506628.i	−0.239721	+	0.415210i
$273$	−23409.2			−0.0190099
$274$	−789400.	−	1.36728e6i	−0.635215	−	1.10022i
$275$	−35525.3	−	61531.7i	−0.0283274	−	0.0490645i
$276$	827004.	+	1.43241e6i	0.653484	+	1.13187i
$277$	882204.	−	1.52802e6i	0.690827	−	1.19655i	−0.280740	−	0.959784i	$-0.590580\pi$
$277$	882204.	−	1.52802e6i	0.690827	−	1.19655i	0.971567	−	0.236764i	$-0.0760869\pi$
$278$	−98145.8	+	169994.i	−0.0761658	+	0.131923i
$279$	−1.29545e6	−	2.24378e6i	−0.996346	−	1.72572i
$280$	−11861.9	−	20545.3i	−0.00904185	−	0.0156609i
$281$	−416861.	−	722025.i	−0.314938	−	0.545489i	0.664486	−	0.747301i	$-0.268651\pi$
$281$	−416861.	−	722025.i	−0.314938	−	0.545489i	−0.979424	+	0.201811i	$0.935317\pi$
$282$	−1.84599e6			−1.38231
$283$	−323181.	+	559766.i	−0.239872	+	0.415471i	−0.960677	−	0.277667i	$-0.910439\pi$
$283$	−323181.	+	559766.i	−0.239872	+	0.415471i	0.720805	+	0.693138i	$0.243772\pi$
$284$	−315206.	−	545953.i	−0.231899	−	0.401661i
$285$	1.39366e6			1.01635
$286$	−70615.5			−0.0510488
$287$	17109.0	+	29633.7i	0.0122608	+	0.0212364i
$288$	−436945.			−0.310417
$289$	−1.90108e6	+	3.29276e6i	−1.33892	+	2.31908i
$290$	10095.6			0.00704913
$291$	−1.68978e6	+	2.92678e6i	−1.16976	+	2.02608i
$292$	−672234.	+	1.16434e6i	−0.461385	+	0.799143i
$293$	−127659.	+	221112.i	−0.0868725	+	0.150468i	−0.906188	−	0.422876i	$-0.861021\pi$
$293$	−127659.	+	221112.i	−0.0868725	+	0.150468i	0.819315	+	0.573344i	$0.194354\pi$
$294$	867975.	+	1.50338e6i	0.585651	+	1.01438i
$295$	−337415.			−0.225740
$296$	−228564.	−	481447.i	−0.151627	−	0.319389i
$297$	−563549.			−0.370715
$298$	−513130.	−	888767.i	−0.334724	−	0.579759i
$299$	−297450.	+	515199.i	−0.192414	+	0.333271i
$300$	124087.	−	214926.i	0.0796021	−	0.137875i
$301$	1690.59	−	2928.18i	0.00107553	−	0.00186287i
$302$	3382.44			0.00213409
$303$	2.17837e6	−	3.77304e6i	1.36309	−	2.36094i
$304$	225907.			0.140199
$305$	858501.	+	1.48697e6i	0.528435	+	0.915276i
$306$	−3.90037e6			−2.38123
$307$	−160838.			−0.0973963			−0.0486982	−	0.998814i	$-0.515507\pi$
$307$	−160838.			−0.0973963			−0.0486982	+	0.998814i	$0.515507\pi$
$308$	−5760.21	−	9976.97i	−0.00345988	−	0.00599269i
$309$	−705296.	+	1.22161e6i	−0.420219	+	0.727840i
$310$	1.48221e6			0.876004
$311$	1.29551e6	+	2.24389e6i	0.759520	+	1.31553i	0.943095	+	0.332522i	$0.107900\pi$
$311$	1.29551e6	+	2.24389e6i	0.759520	+	1.31553i	−0.183575	+	0.983006i	$0.558767\pi$
$312$	−123327.	−	213609.i	−0.0717254	−	0.124232i
$313$	959896.	+	1.66259e6i	0.553813	+	0.959233i	0.997995	+	0.0632959i	$0.0201612\pi$
$313$	959896.	+	1.66259e6i	0.553813	+	0.959233i	−0.444182	+	0.895937i	$0.646505\pi$
$314$	604053.	−	1.04625e6i	0.345741	−	0.598841i
$315$	79085.9	−	136981.i	0.0449079	−	0.0777828i
$316$	490936.	+	850325.i	0.276571	+	0.479035i
$317$	−112213.	−	194359.i	−0.0627184	−	0.108632i	0.832961	−	0.553331i	$-0.186644\pi$
$317$	−112213.	−	194359.i	−0.0627184	−	0.108632i	−0.895680	+	0.444700i	$0.853310\pi$
$318$	766262.	+	1.32720e6i	0.424922	+	0.735987i
$319$	4902.48			0.00269736
$320$	124985.	−	216480.i	0.0682310	−	0.118179i
$321$	−2.27111e6	−	3.93367e6i	−1.23020	−	2.13076i
$322$	−97053.7			−0.0521642
$323$	2.01655e6			1.07548
$324$	−154705.	−	267958.i	−0.0818734	−	0.141809i
$325$	89261.5			0.0468766
$326$	444546.	−	769976.i	0.231671	−	0.401267i
$327$	4.67629e6			2.41842
$328$	−180272.	+	312240.i	−0.0925218	+	0.160252i
$329$	54159.3	−	93806.6i	0.0275856	−	0.0477797i
$330$	374429.	−	648531.i	0.189271	−	0.327828i
$331$	−864532.	−	1.49741e6i	−0.433722	−	0.751228i	0.563469	−	0.826137i	$-0.309467\pi$
$331$	−864532.	−	1.49741e6i	−0.433722	−	0.751228i	−0.997190	+	0.0749094i	$0.976133\pi$
$332$	−165995.			−0.0826512
$333$	2.01794e6	−	2.92469e6i	0.997233	−	1.44534i
$334$	938879.			0.460515
$335$	838626.	+	1.45254e6i	0.408279	+	0.707159i
$336$	20120.0	−	34848.8i	0.00972253	−	0.0168399i
$337$	−193951.	+	335932.i	−0.0930286	+	0.161130i	−0.908784	−	0.417267i	$-0.862988\pi$
$337$	−193951.	+	335932.i	−0.0930286	+	0.161130i	0.815756	+	0.578397i	$0.196321\pi$
$338$	−698229.	+	1.20937e6i	−0.332434	+	0.575793i
$339$	4.43109e6			2.09417
$340$	1.11567e6	−	1.93240e6i	0.523405	−	0.906565i
$341$	719774.			0.335205
$342$	753088.	+	1.30439e6i	0.348161	+	0.603033i
$343$	−203948.			−0.0936018
$344$	35626.4			0.0162321
$345$	−3.15438e6	−	5.46355e6i	−1.42681	−	2.47131i
$346$	967353.	−	1.67551e6i	0.434405	−	0.752412i
$347$	−3.49830e6			−1.55967			−0.779835	−	0.625985i	$-0.784697\pi$
$347$	−3.49830e6			−1.55967			−0.779835	+	0.625985i	$0.784697\pi$
$348$	8562.00	+	14829.8i	0.00378989	+	0.00656429i
$349$	−2.09228e6	−	3.62393e6i	−0.919508	−	1.59263i	−0.800164	−	0.599781i	$-0.795254\pi$
$349$	−2.09228e6	−	3.62393e6i	−0.919508	−	1.59263i	−0.119344	−	0.992853i	$-0.538079\pi$
$350$	7281.18	+	12611.4i	0.00317711	+	0.00550291i
$351$	353996.	−	613139.i	0.153366	−	0.265638i
$352$	60693.5	−	105124.i	0.0261087	−	0.0452216i
$353$	1.23347e6	+	2.13643e6i	0.526856	+	0.912541i	0.999510	+	0.0312933i	$0.00996259\pi$
$353$	1.23347e6	+	2.13643e6i	0.526856	+	0.912541i	−0.472654	+	0.881248i	$0.656704\pi$
$354$	−286160.	−	495644.i	−0.121367	−	0.210214i
$355$	1.20227e6	+	2.08239e6i	0.506326	+	0.876983i
$356$	−160772.			−0.0672335
$357$	179600.	−	311076.i	0.0745823	−	0.129180i
$358$	−611040.	−	1.05835e6i	−0.251978	−	0.436438i
$359$	−3.17967e6			−1.30210			−0.651052	−	0.759033i	$-0.725672\pi$
$359$	−3.17967e6			−1.30210			−0.651052	+	0.759033i	$0.725672\pi$
$360$	1.66661e6			0.677761
$361$	848692.	+	1.46998e6i	0.342754	+	0.593667i
$362$	−1.27221e6			−0.510254
$363$	−1.90206e6	+	3.29447e6i	−0.757633	+	1.31226i
$364$	14473.2			0.00572547
$365$	2.56405e6	−	4.44107e6i	1.00738	−	1.74484i
$366$	−1.45618e6	+	2.52218e6i	−0.568216	+	0.984179i
$367$	774386.	−	1.34128e6i	0.300118	−	0.519820i	−0.676044	−	0.736861i	$-0.736307\pi$
$367$	774386.	−	1.34128e6i	0.300118	−	0.519820i	0.976162	+	0.217041i	$0.0696406\pi$
$368$	−511312.	−	885619.i	−0.196819	−	0.340900i
$369$	−2.40384e6			−0.919050
$370$	871793.	+	1.83635e6i	0.331062	+	0.697350i
$371$	−89925.3			−0.0339193
$372$	1.25706e6	+	2.17729e6i	0.470975	+	0.815753i
$373$	−2.26741e6	+	3.92727e6i	−0.843836	+	1.46157i	0.0427931	+	0.999084i	$0.486374\pi$
$373$	−2.26741e6	+	3.92727e6i	−0.843836	+	1.46157i	−0.886629	+	0.462482i	$0.846959\pi$
$374$	541778.	−	938386.i	0.200282	−	0.346899i
$375$	1.99438e6	−	3.45436e6i	0.732368	−	1.26850i
$376$	1.14132e6			0.416329
$377$	−3079.51	+	5333.87i	−0.00111591	+	0.00193281i
$378$	115504.			0.0415783
$379$	168142.	+	291230.i	0.0601282	+	0.104145i	0.894523	−	0.447023i	$-0.147516\pi$
$379$	168142.	+	291230.i	0.0601282	+	0.104145i	−0.834394	+	0.551168i	$0.814182\pi$
$380$	−861660.			−0.306110
$381$	−8.20292e6			−2.89505
$382$	1.12706e6	+	1.95212e6i	0.395173	+	0.684460i
$383$	537995.	−	931835.i	0.187405	−	0.324595i	−0.756979	−	0.653439i	$-0.773326\pi$
$383$	537995.	−	931835.i	0.187405	−	0.324595i	0.944384	+	0.328844i	$0.106659\pi$
$384$	423996.			0.146735
$385$	21970.7	+	38054.4i	0.00755427	+	0.0130844i
$386$	−739747.	−	1.28128e6i	−0.252706	−	0.437699i
$387$	118765.	+	205707.i	0.0403098	+	0.0698186i
$388$	1.04474e6	−	1.80954e6i	0.352313	−	0.610224i
$389$	−1.26179e6	+	2.18549e6i	−0.422779	+	0.732275i	−0.996210	−	0.0869791i	$-0.972279\pi$
$389$	−1.26179e6	+	2.18549e6i	−0.422779	+	0.732275i	0.573431	+	0.819254i	$0.305612\pi$
$390$	470399.	+	814755.i	0.156605	+	0.271247i
$391$	−4.56421e6	−	7.90544e6i	−1.50981	−	2.61507i
$392$	−536643.	−	929494.i	−0.176389	−	0.305514i
$393$	3.94829e6			1.28952
$394$	714615.	−	1.23775e6i	0.231916	−	0.401691i
$395$	−1.87254e6	−	3.24333e6i	−0.603863	−	1.04592i
$396$	809317.			0.259347
$397$	1.91479e6			0.609739			0.304869	−	0.952394i	$-0.401387\pi$
$397$	1.91479e6			0.609739			0.304869	+	0.952394i	$0.401387\pi$
$398$	−1.96692e6	−	3.40681e6i	−0.622414	−	1.07805i
$399$	−138710.			−0.0436189
$400$	−76719.5	+	132882.i	−0.0239749	+	0.0415257i
$401$	−3.29991e6			−1.02480			−0.512402	−	0.858746i	$-0.671244\pi$
$401$	−3.29991e6			−1.02480			−0.512402	+	0.858746i	$0.671244\pi$
$402$	−1.42247e6	+	2.46379e6i	−0.439014	+	0.760394i
$403$	−452129.	+	783110.i	−0.138675	+	0.240193i
$404$	−1.34682e6	+	2.33276e6i	−0.410541	+	0.711078i
$405$	590081.	+	1.02205e6i	0.178762	+	0.309624i
$406$	−1004.80			−0.000302527
$407$	423350.	+	891745.i	0.126681	+	0.266842i
$408$	3.78478e6			1.12562
$409$	1.80935e6	+	3.13389e6i	0.534829	+	0.926350i	0.999172	+	0.0406950i	$0.0129572\pi$
$409$	1.80935e6	+	3.13389e6i	0.534829	+	0.926350i	−0.464343	+	0.885655i	$0.653709\pi$
$410$	687599.	−	1.19096e6i	0.202011	−	0.349894i
$411$	−5.10715e6	+	8.84584e6i	−1.49133	+	2.58306i
$412$	436064.	−	755285.i	0.126563	−	0.219214i
$413$	33582.5			0.00968809
$414$	3.40905e6	−	5.90464e6i	0.977534	−	1.69314i
$415$	633142.			0.180460
$416$	76249.7	+	132068.i	0.0216025	+	0.0374167i
$417$	1.26994e6			0.357638
$418$	−418429.			−0.117133
$419$	1.27461e6	+	2.20769e6i	0.354685	+	0.614333i	0.987064	−	0.160326i	$-0.0512547\pi$
$419$	1.27461e6	+	2.20769e6i	0.354685	+	0.614333i	−0.632379	+	0.774659i	$0.717921\pi$
$420$	−76742.1	+	132921.i	−0.0212281	+	0.0367681i
$421$	2.54349e6			0.699400			0.349700	−	0.936862i	$-0.386284\pi$
$421$	2.54349e6			0.699400			0.349700	+	0.936862i	$0.386284\pi$
$422$	−957465.	−	1.65838e6i	−0.261723	−	0.453318i
$423$	3.80473e6	+	6.58998e6i	1.03389	+	1.79074i
$424$	−473757.	−	820572.i	−0.127980	−	0.221667i
$425$	−684834.	+	1.18617e6i	−0.183913	+	0.318547i
$426$	−2.03928e6	+	3.53213e6i	−0.544443	+	0.943003i
$427$	−85445.8	−	147996.i	−0.0226788	−	0.0392809i
$428$	1.40416e6	+	2.43207e6i	0.370516	+	0.641752i
$429$	228429.	+	395651.i	0.0599251	+	0.103793i
$430$	−135887.			−0.0354411
$431$	−2.93066e6	+	5.07605e6i	−0.759928	+	1.31623i	0.182959	+	0.983120i	$0.441432\pi$
$431$	−2.93066e6	+	5.07605e6i	−0.759928	+	1.31623i	−0.942887	+	0.333113i	$0.891901\pi$
$432$	608513.	+	1.05398e6i	0.156877	+	0.271720i
$433$	2.18597e6			0.560306			0.280153	−	0.959955i	$-0.409615\pi$
$433$	2.18597e6			0.560306			0.280153	+	0.959955i	$0.409615\pi$
$434$	−147523.			−0.0375955
$435$	−32657.4	−	56564.3i	−0.00827482	−	0.0143324i
$436$	−2.89122e6			−0.728390
$437$	−1.76253e6	+	3.05279e6i	−0.441501	+	0.764703i
$438$	8.69826e6			2.16644
$439$	2.90908e6	−	5.03867e6i	0.720433	−	1.24783i	−0.240393	−	0.970676i	$-0.577276\pi$
$439$	2.90908e6	−	5.03867e6i	0.720433	−	1.24783i	0.960826	−	0.277152i	$-0.0893904\pi$
$440$	−231499.	+	400967.i	−0.0570055	+	0.0987364i
$441$	3.57793e6	−	6.19717e6i	0.876064	−	1.51739i
$442$	680640.	+	1.17890e6i	0.165715	+	0.287027i
$443$	264127.			0.0639445			0.0319723	−	0.999489i	$-0.489821\pi$
$443$	264127.			0.0639445			0.0319723	+	0.999489i	$0.489821\pi$
$444$	−1.95813e6	+	2.83802e6i	−0.471395	+	0.683215i
$445$	613222.			0.146797
$446$	−1.17084e6	−	2.02795e6i	−0.278714	−	0.482748i
$447$	−3.31978e6	+	5.75002e6i	−0.785850	+	1.36113i
$448$	−12439.6	+	21546.0i	−0.00292827	+	0.00507191i
$449$	−990208.	+	1.71509e6i	−0.231799	+	0.401487i	−0.958337	−	0.285638i	$-0.907794\pi$
$449$	−990208.	+	1.71509e6i	−0.231799	+	0.401487i	0.726539	+	0.687125i	$0.241128\pi$
$450$	−1.02302e6			−0.238150
$451$	333903.	−	578337.i	0.0773000	−	0.133887i
$452$	−2.73961e6			−0.630729
$453$	−10941.6	−	18951.5i	−0.00250517	−	0.00433907i
$454$	−3.75830e6			−0.855759
$455$	−55204.0			−0.0125009
$456$	−730770.	−	1.26573e6i	−0.164577	−	0.285055i
$457$	1.19998e6	−	2.07843e6i	0.268773	−	0.465528i	−0.699772	−	0.714366i	$-0.746715\pi$
$457$	1.19998e6	−	2.07843e6i	0.268773	−	0.465528i	0.968545	+	0.248838i	$0.0800486\pi$
$458$	1.99443e6			0.444279
$459$	5.43186e6	+	9.40826e6i	1.20342	+	2.08438i
$460$	1.95026e6	+	3.37795e6i	0.429732	+	0.744318i
$461$	−7526.87	−	13036.9i	−0.00164954	−	0.00285708i	0.865199	−	0.501428i	$-0.167192\pi$
$461$	−7526.87	−	13036.9i	−0.00164954	−	0.00285708i	−0.866849	+	0.498571i	$0.833858\pi$
$462$	−37266.6	+	64547.6i	−0.00812296	+	0.0140694i
$463$	173011.	−	299665.i	0.0375079	−	0.0649655i	−0.846662	−	0.532131i	$-0.821391\pi$
$463$	173011.	−	299665.i	0.0375079	−	0.0649655i	0.884170	+	0.467165i	$0.154725\pi$
$464$	−5293.63	−	9168.84i	−0.00114146	−	0.00197706i
$465$	−4.79470e6	−	8.30467e6i	−1.02832	−	1.78111i
$466$	41620.0	+	72088.0i	0.00887846	+	0.0153779i
$467$	6.52183e6			1.38381			0.691906	−	0.721988i	$-0.256771\pi$
$467$	6.52183e6			1.38381			0.691906	+	0.721988i	$0.256771\pi$
$468$	−508376.	+	880533.i	−0.107293	+	0.185836i
$469$	−83467.6	−	144570.i	−0.0175221	−	0.0303492i
$470$	−4.35325e6			−0.909010
$471$	−7.81603e6			−1.62343
$472$	176924.	+	306442.i	0.0365538	+	0.0633130i
$473$	−65987.8			−0.0135616
$474$	3.17619e6	−	5.50131e6i	0.649322	−	1.12466i
$475$	528914.			0.107560
$476$	−111041.	+	192329.i	−0.0224630	+	0.0389070i
$477$	3.15866e6	−	5.47095e6i	0.635633	−	1.10095i
$478$	1.59574e6	−	2.76391e6i	0.319443	−	0.553291i
$479$	3.88219e6	+	6.72414e6i	0.773103	+	1.33905i	0.935854	+	0.352387i	$0.114630\pi$
$479$	3.88219e6	+	6.72414e6i	0.773103	+	1.33905i	−0.162751	+	0.986667i	$0.552037\pi$
$480$	−1.61722e6			−0.320380
$481$	−1.23614e6	−	99551.4i	−0.243616	−	0.0196194i
$482$	−1.76275e6			−0.345600
$483$	313952.	+	543781.i	0.0612345	+	0.106061i
$484$	1.17599e6	−	2.03688e6i	0.228187	−	0.395231i
$485$	−3.98487e6	+	6.90200e6i	−0.769237	+	1.33236i
$486$	1.30956e6	−	2.26822e6i	0.251497	−	0.435606i
$487$	−6.09892e6			−1.16528			−0.582641	−	0.812730i	$-0.697980\pi$
$487$	−6.09892e6			−1.16528			−0.582641	+	0.812730i	$0.697980\pi$
$488$	900315.	−	1.55939e6i	0.171137	−	0.296419i
$489$	−5.75212e6			−1.08782
$490$	2.04688e6	+	3.54530e6i	0.385125	+	0.667057i
$491$	−5.84697e6			−1.09453			−0.547265	−	0.836960i	$-0.684331\pi$
$491$	−5.84697e6			−1.09453			−0.547265	+	0.836960i	$0.684331\pi$
$492$	2.33260e6			0.434437
$493$	−47253.4	−	81845.2i	−0.00875620	−	0.0151662i
$494$	262838.	−	455248.i	0.0484585	−	0.0839326i
$495$	−3.08692e6			−0.566255
$496$	−777202.	−	1.34615e6i	−0.141850	−	0.245692i
$497$	−119661.	−	207258.i	−0.0217300	−	0.0376375i
$498$	536965.	+	930050.i	0.0970225	+	0.168048i
$499$	59400.5	−	102885.i	0.0106792	−	0.0184969i	−0.860636	−	0.509220i	$-0.829934\pi$
$499$	59400.5	−	102885.i	0.0106792	−	0.0184969i	0.871316	+	0.490723i	$0.163267\pi$
$500$	−1.23306e6	+	2.13573e6i	−0.220577	+	0.382051i
$501$	−3.03711e6	−	5.26044e6i	−0.540589	−	0.936327i
$502$	3.38804e6	+	5.86826e6i	0.600052	+	1.03932i
$503$	−2.61674e6	−	4.53232e6i	−0.461148	−	0.798731i	0.537871	−	0.843027i	$-0.319229\pi$
$503$	−2.61674e6	−	4.53232e6i	−0.461148	−	0.798731i	−0.999018	+	0.0442959i	$0.985896\pi$
$504$	−165876.			−0.0290875
$505$	5.13708e6	−	8.89769e6i	0.896371	−	1.55256i
$506$	947062.	+	1.64036e6i	0.164438	+	0.284815i
$507$	9.03460e6			1.56095
$508$	5.07163e6			0.871943
$509$	−365648.	−	633320.i	−0.0625559	−	0.108350i	0.833051	−	0.553196i	$-0.186592\pi$
$509$	−365648.	−	633320.i	−0.0625559	−	0.108350i	−0.895607	+	0.444846i	$0.853259\pi$
$510$	−1.44360e7			−2.45766
$511$	−255198.	+	442015.i	−0.0432339	+	0.0748833i
$512$	−262144.			−0.0441942
$513$	2.09758e6	−	3.63312e6i	0.351905	−	0.609518i
$514$	−3.91019e6	+	6.77265e6i	−0.652815	+	1.13071i
$515$	−1.66325e6	+	2.88083e6i	−0.276337	+	0.478629i
$516$	−115245.	−	199611.i	−0.0190545	−	0.0330034i
$517$	−2.11397e6			−0.347834
$518$	−86768.7	−	182770.i	−0.0142082	−	0.0299282i
$519$	−1.25169e7			−2.03976
$520$	−290834.	−	503739.i	−0.0471668	−	0.0816953i
$521$	5.67365e6	−	9.82705e6i	0.915732	−	1.58609i	0.109905	−	0.993942i	$-0.464945\pi$
$521$	5.67365e6	−	9.82705e6i	0.915732	−	1.58609i	0.805826	−	0.592152i	$-0.201721\pi$
$522$	35294.0	−	61130.9i	0.00566923	−	0.00981940i
$523$	5.80455e6	−	1.00538e7i	0.927928	−	1.60722i	0.141146	−	0.989989i	$-0.454921\pi$
$523$	5.80455e6	−	1.00538e7i	0.927928	−	1.60722i	0.786783	−	0.617230i	$-0.211745\pi$
$524$	−2.44111e6			−0.388382
$525$	47106.8	−	81591.3i	0.00745908	−	0.0129195i
$526$	3.25363e6			0.512748
$527$	−6.93766e6	−	1.20164e7i	−1.08814	−	1.88472i
$528$	−785332.			−0.122594
$529$	9.52070e6			1.47921
$530$	1.80702e6	+	3.12985e6i	0.279430	+	0.483987i
$531$	−1.17960e6	+	2.04312e6i	−0.181551	+	0.314455i
$532$	85760.1			0.0131373
$533$	419485.	+	726570.i	0.0639586	+	0.110780i
$534$	520071.	+	900789.i	0.0789240	+	0.136700i
$535$	−5.35578e6	−	9.27648e6i	−0.808981	−	1.40120i
$536$	879472.	−	1.52329e6i	0.132224	−	0.229019i
$537$	−3.95322e6	+	6.84718e6i	−0.591582	+	1.02465i
$538$	1.31189e6	+	2.27225e6i	0.195407	+	0.338455i
$539$	993981.	+	1.72162e6i	0.147369	+	0.255251i
$540$	−2.32101e6	−	4.02010e6i	−0.342525	−	0.593270i
$541$	1.13698e6			0.167017			0.0835083	−	0.996507i	$-0.473387\pi$
$541$	1.13698e6			0.167017			0.0835083	+	0.996507i	$0.473387\pi$
$542$	−38164.1	+	66102.2i	−0.00558029	+	0.00966535i
$543$	4.11537e6	+	7.12803e6i	0.598976	+	1.03746i
$544$	−2.34002e6			−0.339017
$545$	1.10277e7			1.59036
$546$	−46818.3	−	81091.7i	−0.00672100	−	0.0116411i
$547$	4.13492e6			0.590880			0.295440	−	0.955361i	$-0.404534\pi$
$547$	4.13492e6			0.590880			0.295440	+	0.955361i	$0.404534\pi$
$548$	3.15760e6	−	5.46912e6i	0.449165	−	0.777976i
$549$	1.20052e7			1.69997
$550$	142101.	−	246127.i	0.0200305	−	0.0346938i
$551$	−18247.5	+	31605.6i	−0.00256050	+	0.00443491i
$552$	−3.30802e6	+	5.72965e6i	−0.462083	+	0.800351i
$553$	186372.	+	322806.i	0.0259160	+	0.0448878i
$554$	7.05763e6			0.976978
$555$	7.46876e6	−	1.08248e7i	1.02924	−	1.49173i
$556$	−785167.			−0.107715
$557$	4.60018e6	+	7.96774e6i	0.628256	+	1.08817i	0.987902	+	0.155083i	$0.0495643\pi$
$557$	4.60018e6	+	7.96774e6i	0.628256	+	1.08817i	−0.359645	+	0.933089i	$0.617102\pi$
$558$	5.18180e6	−	8.97514e6i	0.704523	−	1.22027i
$559$	41450.5	−	71794.4i	0.00561048	−	0.00971764i
$560$	47447.4	−	82181.3i	0.00639355	−	0.0110740i
$561$	−7.01023e6			−0.940427
$562$	1.66744e6	−	2.88810e6i	0.222695	−	0.385719i
$563$	8.78496e6			1.16807			0.584035	−	0.811728i	$-0.301473\pi$
$563$	8.78496e6			1.16807			0.584035	+	0.811728i	$0.301473\pi$
$564$	−3.69197e6	−	6.39468e6i	−0.488720	−	0.846489i
$565$	1.04495e7			1.37713
$566$	−2.58545e6			−0.339231
$567$	−58730.2	−	101724.i	−0.00767191	−	0.0132881i
$568$	1.26083e6	−	2.18381e6i	0.163977	−	0.284017i
$569$	9.84924e6			1.27533			0.637664	−	0.770314i	$-0.279901\pi$
$569$	9.84924e6			1.27533			0.637664	+	0.770314i	$0.279901\pi$
$570$	2.78732e6	+	4.82778e6i	0.359336	+	0.622387i
$571$	4.96024e6	+	8.59140e6i	0.636668	+	1.10274i	0.986159	+	0.165801i	$0.0530210\pi$
$571$	4.96024e6	+	8.59140e6i	0.636668	+	1.10274i	−0.349491	+	0.936940i	$0.613646\pi$
$572$	−141231.	−	244619.i	−0.0180485	−	0.0312609i
$573$	7.29167e6	−	1.26295e7i	0.927771	−	1.60695i
$574$	−68436.0	+	118535.i	−0.00866972	+	0.0150164i
$575$	−1.19713e6	−	2.07349e6i	−0.150999	−	0.261537i
$576$	−873890.	−	1.51362e6i	−0.109749	−	0.190091i
$577$	1.55179e6	+	2.68778e6i	0.194041	+	0.336089i	0.946586	−	0.322452i	$-0.104507\pi$
$577$	1.55179e6	+	2.68778e6i	0.194041	+	0.336089i	−0.752545	+	0.658541i	$0.771174\pi$
$578$	−1.52086e7			−1.89352
$579$	−4.78591e6	+	8.28944e6i	−0.593291	+	1.02761i
$580$	20191.1	+	34972.0i	0.00249224	+	0.00431669i
$581$	−63015.9			−0.00774480
$582$	−1.35182e7			−1.65429
$583$	877502.	+	1.51988e6i	0.106924	+	0.185198i
$584$	−5.37788e6			−0.652497
$585$	1.93906e6	−	3.35855e6i	0.234262	−	0.405754i
$586$	−1.02127e6			−0.122856
$587$	−128330.	+	222273.i	−0.0153720	+	0.0266252i	−0.873609	−	0.486628i	$-0.838227\pi$
$587$	−128330.	+	222273.i	−0.0153720	+	0.0266252i	0.858237	+	0.513254i	$0.171560\pi$
$588$	−3.47190e6	+	6.01351e6i	−0.414118	+	0.717273i
$589$	−2.67906e6	+	4.64028e6i	−0.318196	+	0.551132i
$590$	−674829.	−	1.16884e6i	−0.0798112	−	0.138237i
$591$	−9.24663e6			−1.08897
$592$	1.21066e6	−	1.75466e6i	0.141976	−	0.205773i
$593$	−1.33953e7			−1.56429			−0.782145	−	0.623097i	$-0.785874\pi$
$593$	−1.33953e7			−1.56429			−0.782145	+	0.623097i	$0.785874\pi$
$594$	−1.12710e6	−	1.95219e6i	−0.131068	−	0.227016i
$595$	423537.	−	733588.i	0.0490455	−	0.0849493i
$596$	2.05252e6	−	3.55507e6i	0.236685	−	0.409951i
$597$	−1.27253e7	+	2.20409e7i	−1.46128	+	2.53101i
$598$	−2.37960e6			−0.272114
$599$	−5.77876e6	+	1.00091e7i	−0.658064	+	1.13980i	0.323053	+	0.946381i	$0.395291\pi$
$599$	−5.77876e6	+	1.00091e7i	−0.658064	+	1.13980i	−0.981116	+	0.193419i	$0.938042\pi$
$600$	992699.			0.112574
$601$	−6.69015e6	−	1.15877e7i	−0.755526	−	1.30861i	−0.945112	−	0.326746i	$-0.894048\pi$
$601$	−6.69015e6	−	1.15877e7i	−0.755526	−	1.30861i	0.189586	−	0.981864i	$-0.439285\pi$
$602$	13524.7			0.00152102
$603$	1.17273e7			1.31343
$604$	6764.89	+	11717.1i	0.000754515	+	0.00130686i
$605$	−4.48549e6	+	7.76910e6i	−0.498221	+	0.862944i
$606$	1.74269e7			1.92770
$607$	5.80789e6	+	1.00596e7i	0.639803	+	1.10817i	0.985476	+	0.169817i	$0.0543175\pi$
$607$	5.80789e6	+	1.00596e7i	0.639803	+	1.10817i	−0.345672	+	0.938355i	$0.612349\pi$
$608$	451814.	+	782564.i	0.0495679	+	0.0858541i
$609$	3250.36	+	5629.79i	0.000355131	+	0.000615104i
$610$	−3.43401e6	+	5.94787e6i	−0.373660	+	0.647198i
$611$	1.32790e6	−	2.29999e6i	0.143900	−	0.249243i
$612$	−7.80074e6	−	1.35113e7i	−0.841893	−	1.45820i
$613$	5.36809e6	+	9.29781e6i	0.576991	+	0.999377i	0.995822	+	0.0913131i	$0.0291064\pi$
$613$	5.36809e6	+	9.29781e6i	0.576991	+	0.999377i	−0.418832	+	0.908064i	$0.637560\pi$
$614$	−321676.	−	557159.i	−0.0344348	−	0.0596428i
$615$	−8.89706e6			−0.948547
$616$	23040.8	−	39907.9i	0.00244651	−	0.00423747i
$617$	9.17624e6	+	1.58937e7i	0.970402	+	1.68079i	0.694342	+	0.719645i	$0.255695\pi$
$617$	9.17624e6	+	1.58937e7i	0.970402	+	1.68079i	0.276060	+	0.961140i	$0.410971\pi$
$618$	−5.64237e6			−0.594279
$619$	−1.10781e7			−1.16209			−0.581043	−	0.813873i	$-0.697355\pi$
$619$	−1.10781e7			−1.16209			−0.581043	+	0.813873i	$0.697355\pi$
$620$	2.96442e6	+	5.13453e6i	0.309714	+	0.536441i
$621$	−1.89905e7			−1.97609
$622$	−5.18204e6	+	8.97555e6i	−0.537062	+	0.930219i
$623$	−61033.3			−0.00630009
$624$	493310.	−	854437.i	0.0507175	−	0.0878454i
$625$	5.63971e6	−	9.76826e6i	0.577506	−	1.00027i
$626$	−3.83958e6	+	6.65036e6i	−0.391605	+	0.678280i
$627$	1.35355e6	+	2.34441e6i	0.137500	+	0.238158i
$628$	4.83242e6			0.488951
$629$	1.08069e7	−	1.56629e7i	1.08911	−	1.57850i
$630$	632687.			0.0635094
$631$	−619591.	−	1.07316e6i	−0.0619486	−	0.107298i	0.833388	−	0.552689i	$-0.186398\pi$
$631$	−619591.	−	1.07316e6i	−0.0619486	−	0.107298i	−0.895336	+	0.445391i	$0.853065\pi$
$632$	−1.96374e6	+	3.40130e6i	−0.195565	+	0.338729i
$633$	−6.19447e6	+	1.07291e7i	−0.614462	+	1.06428i
$634$	448852.	−	777435.i	0.0443486	−	0.0768141i
$635$	−1.93443e7			−1.90379
$636$	−3.06505e6	+	5.30882e6i	−0.300465	+	0.520421i
$637$	−2.49749e6			−0.243868
$638$	9804.96	+	16982.7i	0.000953661	+	0.00165179i
$639$	1.68125e7			1.62884
$640$	999877.			0.0964932
$641$	−6.30735e6	−	1.09247e7i	−0.606320	−	1.05018i	−0.991841	−	0.127478i	$-0.959312\pi$
$641$	−6.30735e6	−	1.09247e7i	−0.606320	−	1.05018i	0.385521	−	0.922699i	$-0.374022\pi$
$642$	9.08442e6	−	1.57347e7i	0.869881	−	1.50668i
$643$	−926062.			−0.0883309			−0.0441654	−	0.999024i	$-0.514063\pi$
$643$	−926062.			−0.0883309			−0.0441654	+	0.999024i	$0.514063\pi$
$644$	−194107.	−	336204.i	−0.0184428	−	0.0319439i
$645$	439571.	+	761360.i	0.0416035	+	0.0720594i
$646$	4.03309e6	+	6.98552e6i	0.380239	+	0.658594i
$647$	4.85598e6	−	8.41081e6i	0.456054	−	0.789909i	−0.542694	−	0.839931i	$-0.682596\pi$
$647$	4.85598e6	−	8.41081e6i	0.456054	−	0.789909i	0.998748	+	0.0500215i	$0.0159290\pi$
$648$	618821.	−	1.07183e6i	0.0578932	−	0.100274i
$649$	−327702.	−	567597.i	−0.0305399	−	0.0528967i
$650$	178523.	+	309211.i	0.0165734	+	0.0287059i
$651$	477212.	+	826555.i	0.0441325	+	0.0764398i
$652$	3.55637e6			0.327633
$653$	−1.53181e6	+	2.65317e6i	−0.140579	+	0.243491i	−0.927715	−	0.373289i	$-0.878230\pi$
$653$	−1.53181e6	+	2.65317e6i	−0.140579	+	0.243491i	0.787136	+	0.616780i	$0.211563\pi$
$654$	9.35259e6	+	1.61992e7i	0.855042	+	1.48098i
$655$	9.31095e6			0.847990
$656$	−1.44218e6			−0.130846
$657$	−1.79278e7	−	3.10519e7i	−1.62037	−	2.80656i
$658$	433274.			0.0390120
$659$	2.21567e6	−	3.83766e6i	0.198743	−	0.344233i	−0.749378	−	0.662142i	$-0.769647\pi$
$659$	2.21567e6	−	3.83766e6i	0.198743	−	0.344233i	0.948121	+	0.317909i	$0.102981\pi$
$660$	2.99544e6			0.267670
$661$	336143.	−	582217.i	0.0299241	−	0.0518300i	−0.850676	−	0.525691i	$-0.823807\pi$
$661$	336143.	−	582217.i	0.0299241	−	0.0518300i	0.880600	+	0.473861i	$0.157140\pi$
$662$	3.45813e6	−	5.98966e6i	0.306688	−	0.531199i
$663$	4.40351e6	−	7.62710e6i	0.389058	−	0.673869i
$664$	−331989.	−	575023.i	−0.0292216	−	0.0506133i
$665$	−327109.			−0.0286839
$666$	1.41673e7	+	1.14095e6i	1.23766	+	0.0996736i
$667$	165204.			0.0143782
$668$	1.87776e6	+	3.25237e6i	0.162817	+	0.282007i
$669$	−7.57492e6	+	1.31201e7i	−0.654354	+	1.13337i
$670$	−3.35451e6	+	5.81017e6i	−0.288697	+	0.500037i
$671$	−1.66758e6	+	2.88833e6i	−0.142982	+	0.247651i
$672$	160960.			0.0137497
$673$	1.29194e6	−	2.23771e6i	0.109953	−	0.190444i	−0.805798	−	0.592190i	$-0.798263\pi$
$673$	1.29194e6	−	2.23771e6i	0.109953	−	0.190444i	0.915751	+	0.401747i	$0.131597\pi$
$674$	−1.55161e6			−0.131562
$675$	1.42471e6	+	2.46767e6i	0.120356	+	0.208462i
$676$	−5.58583e6			−0.470133
$677$	1.30790e7			1.09674			0.548368	−	0.836237i	$-0.315249\pi$
$677$	1.30790e7			1.09674			0.548368	+	0.836237i	$0.315249\pi$
$678$	8.86218e6	+	1.53497e7i	0.740399	+	1.28241i
$679$	396610.	−	686949.i	0.0330134	−	0.0571808i
$680$	8.92535e6			0.740207
$681$	1.21574e7	+	2.10573e7i	1.00456	+	1.73994i
$682$	1.43955e6	+	2.49337e6i	0.118513	+	0.205270i
$683$	−8.28221e6	−	1.43452e7i	−0.679351	−	1.17667i	−0.975176	−	0.221429i	$-0.928928\pi$
$683$	−8.28221e6	−	1.43452e7i	−0.679351	−	1.17667i	0.295825	−	0.955242i	$-0.404405\pi$
$684$	−3.01235e6	+	5.21755e6i	−0.246187	+	0.426409i
$685$	−1.20438e7	+	2.08605e7i	−0.980702	+	1.69863i
$686$	−407896.	−	706496.i	−0.0330932	−	0.0573191i
$687$	−6.45165e6	−	1.11746e7i	−0.521529	−	0.903315i
$688$	71252.7	+	123413.i	0.00573892	+	0.00994010i
$689$	−2.20482e6			−0.176940
$690$	1.26175e7	−	2.18542e7i	1.00891	−	1.74748i
$691$	9.55930e6	+	1.65572e7i	0.761607	+	1.31914i	0.942022	+	0.335552i	$0.108923\pi$
$691$	9.55930e6	+	1.65572e7i	0.761607	+	1.31914i	−0.180414	+	0.983591i	$0.557744\pi$
$692$	7.73883e6			0.614342
$693$	307238.			0.0243020
$694$	−6.99659e6	−	1.21185e7i	−0.551427	−	0.955099i
$695$	2.99480e6			0.235183
$696$	−34248.0	+	59319.3i	−0.00267986	+	0.00464165i
$697$	−1.28735e7			−1.00373
$698$	8.36910e6	−	1.44957e7i	0.650190	−	1.12616i
$699$	269267.	−	466385.i	0.0208445	−	0.0361037i
$700$	−29124.7	+	50445.5i	−0.00224655	+	0.00389115i
$701$	−7.02795e6	−	1.21728e7i	−0.540174	−	0.935609i	−0.998894	−	0.0470276i	$-0.985025\pi$
$701$	−7.02795e6	−	1.21728e7i	−0.540174	−	0.935609i	0.458720	−	0.888581i	$-0.348308\pi$
$702$	2.83197e6			0.216893
$703$	−7.32470e6	−	589887.i	−0.558987	−	0.0450174i
$704$	485548.			0.0369233
$705$	1.40820e7	+	2.43908e7i	1.06707	+	1.84822i
$706$	−4.93388e6	+	8.54573e6i	−0.372543	+	0.645264i
$707$	−511288.	+	885577.i	−0.0384696	+	0.0666313i
$708$	1.14464e6	−	1.98257e6i	0.0858194	−	0.148644i
$709$	−1.62189e7			−1.21173			−0.605863	−	0.795569i	$-0.707172\pi$
$709$	−1.62189e7			−1.21173			−0.605863	+	0.795569i	$0.707172\pi$
$710$	−4.80907e6	+	8.32956e6i	−0.358027	+	0.620121i
$711$	−2.61855e7			−1.94262
$712$	−321544.	−	556931.i	−0.0237706	−	0.0411720i
$713$	2.42549e7			1.78680
$714$	1.43680e6			0.105475
$715$	538687.	+	933034.i	0.0394069	+	0.0682547i
$716$	2.44416e6	−	4.23341e6i	0.178175	−	0.308608i
$717$	−2.06478e7			−1.49995
$718$	−6.35933e6	−	1.10147e7i	−0.460363	−	0.797372i
$719$	−5.73759e6	−	9.93780e6i	−0.413911	−	0.716916i	0.581402	−	0.813616i	$-0.302504\pi$
$719$	−5.73759e6	−	9.93780e6i	−0.413911	−	0.716916i	−0.995314	+	0.0967007i	$0.969171\pi$
$720$	3.33321e6	+	5.77329e6i	0.239625	+	0.415042i
$721$	165541.	−	286726.i	0.0118595	−	0.0205413i
$722$	−3.39477e6	+	5.87991e6i	−0.242363	+	0.419786i
$723$	5.70221e6	+	9.87652e6i	0.405693	+	0.702681i
$724$	−2.54441e6	−	4.40705e6i	−0.180402	−	0.312465i
$725$	−12394.0	−	21467.0i	−0.000875719	−	0.00151679i
$726$	−1.52165e7			−1.07145
$727$	7.81337e6	−	1.35332e7i	0.548280	−	0.949649i	−0.450112	−	0.892972i	$-0.648616\pi$
$727$	7.81337e6	−	1.35332e7i	0.548280	−	0.949649i	0.998393	−	0.0566772i	$-0.0180506\pi$
$728$	28946.4	+	50136.6i	0.00202426	+	0.00350612i
$729$	−2.16439e7			−1.50840
$730$	2.05124e7			1.42466
$731$	636034.	+	1.10164e6i	0.0440237	+	0.0762514i
$732$	−1.16495e7			−0.803578
$733$	1.89978e6	−	3.29052e6i	0.130600	−	0.226206i	−0.793308	−	0.608821i	$-0.791643\pi$
$733$	1.89978e6	−	3.29052e6i	0.130600	−	0.226206i	0.923908	+	0.382614i	$0.124976\pi$
$734$	6.19508e6			0.424431
$735$	1.32426e7	−	2.29369e7i	0.904181	−	1.56609i
$736$	2.04525e6	−	3.54248e6i	0.139172	−	0.241053i
$737$	−1.62897e6	+	2.82147e6i	−0.110470	+	0.191340i
$738$	−4.80768e6	−	8.32714e6i	−0.324933	−	0.562801i
$739$	−4.55610e6			−0.306890			−0.153445	−	0.988157i	$-0.549037\pi$
$739$	−4.55610e6			−0.306890			−0.153445	+	0.988157i	$0.549037\pi$
$740$	−4.61771e6	+	6.69268e6i	−0.309990	+	0.449284i
$741$	−3.40094e6			−0.227538
$742$	−179851.	−	311510.i	−0.0119923	−	0.0207713i
$743$	−317656.	+	550196.i	−0.0211098	+	0.0365633i	−0.876387	−	0.481607i	$-0.840053\pi$
$743$	−317656.	+	550196.i	−0.0211098	+	0.0365633i	0.855278	+	0.518170i	$0.173387\pi$
$744$	−5.02823e6	+	8.70915e6i	−0.333030	+	0.576824i
$745$	−7.82877e6	+	1.35598e7i	−0.516777	+	0.895084i
$746$	−1.81393e7			−1.19336
$747$	2.21346e6	−	3.83382e6i	0.145134	−	0.251380i
$748$	4.33422e6			0.283242
$749$	533055.	+	923278.i	0.0347190	+	0.0601351i
$750$	1.59550e7			1.03572
$751$	1.18598e7			0.767323			0.383662	−	0.923474i	$-0.374663\pi$
$751$	1.18598e7			0.767323			0.383662	+	0.923474i	$0.374663\pi$
$752$	2.28264e6	+	3.95364e6i	0.147195	+	0.254949i
$753$	2.19195e7	−	3.79656e7i	1.40878	−	2.44007i
$754$	−24636.1			−0.00157813
$755$	−25802.8	−	44691.8i	−0.00164740	−	0.00285338i
$756$	231007.	+	400116.i	0.0147001	+	0.0254614i
$757$	−9.35027e6	−	1.61951e7i	−0.593041	−	1.02718i	−0.993820	−	0.111002i	$-0.964594\pi$
$757$	−9.35027e6	−	1.61951e7i	−0.593041	−	1.02718i	0.400779	−	0.916175i	$-0.368739\pi$
$758$	−672568.	+	1.16492e6i	−0.0425170	+	0.0736417i
$759$	6.12717e6	−	1.06126e7i	0.386060	−	0.668676i
$760$	−1.72332e6	−	2.98488e6i	−0.108226	−	0.187453i
$761$	2.71827e6	+	4.70819e6i	0.170150	+	0.294708i	0.938472	−	0.345355i	$-0.112241\pi$
$761$	2.71827e6	+	4.70819e6i	0.170150	+	0.294708i	−0.768322	+	0.640063i	$0.778908\pi$
$762$	−1.64058e7	−	2.84158e7i	−1.02356	−	1.77285i
$763$	−1.09758e6			−0.0682535
$764$	−4.50823e6	+	7.80848e6i	−0.279430	+	0.483986i
$765$	2.97538e7	+	5.15350e7i	1.83818	+	3.18382i
$766$	4.30396e6			0.265031
$767$	823390.			0.0505379
$768$	847991.	+	1.46876e6i	0.0518786	+	0.0898564i
$769$	−2.81402e6			−0.171597			−0.0857987	−	0.996312i	$-0.527344\pi$
$769$	−2.81402e6			−0.171597			−0.0857987	+	0.996312i	$0.527344\pi$
$770$	−87882.9	+	152218.i	−0.00534168	+	0.00925206i
$771$	5.05952e7			3.06530
$772$	2.95899e6	−	5.12512e6i	0.178690	−	0.309500i
$773$	−1.69078e6	+	2.92852e6i	−0.101775	+	0.176279i	−0.912416	−	0.409264i	$-0.865785\pi$
$773$	−1.69078e6	+	2.92852e6i	−0.101775	+	0.176279i	0.810641	+	0.585543i	$0.199119\pi$
$774$	−475060.	+	822827.i	−0.0285033	+	0.0493692i
$775$	−1.81966e6	−	3.15174e6i	−0.108827	−	0.188493i
$776$	8.35792e6			0.498246
$777$	−743358.	+	1.07739e6i	−0.0441718	+	0.0640204i
$778$	−1.00943e7			−0.597900
$779$	2.48564e6	+	4.30525e6i	0.146755	+	0.254188i
$780$	−1.88160e6	+	3.25902e6i	−0.110736	+	0.191801i
$781$	−2.33532e6	+	4.04490e6i	−0.137000	+	0.237290i
$782$	1.82568e7	−	3.16217e7i	1.06760	−	1.84914i
$783$	−196609.			−0.0114604
$784$	2.14657e6	−	3.71797e6i	0.124726	−	0.216031i
$785$	−1.84319e7			−1.06757
$786$	7.89658e6	+	1.36773e7i	0.455914	+	0.789665i
$787$	−2.59745e7			−1.49490			−0.747448	−	0.664320i	$-0.768721\pi$
$787$	−2.59745e7			−1.49490			−0.747448	+	0.664320i	$0.768721\pi$
$788$	5.71692e6			0.327979
$789$	−1.05249e7	−	1.82297e7i	−0.601904	−	1.04253i
$790$	7.49016e6	−	1.29733e7i	0.426995	−	0.739578i
$791$	−1.04003e6			−0.0591022
$792$	1.61863e6	+	2.80356e6i	0.0916929	+	0.158817i
$793$	−2.09499e6	−	3.62864e6i	−0.118304	−	0.204909i
$794$	3.82957e6	+	6.63301e6i	0.215575	+	0.373387i
$795$	1.16908e7	−	2.02490e7i	0.656033	−	1.13628i
$796$	7.86769e6	−	1.36272e7i	0.440113	−	0.762298i
$797$	5.29325e6	+	9.16819e6i	0.295173	+	0.511255i	0.975025	−	0.222094i	$-0.0712893\pi$
$797$	5.29325e6	+	9.16819e6i	0.295173	+	0.511255i	−0.679852	+	0.733349i	$0.737956\pi$
$798$	−277419.	−	480504.i	−0.0154216	−	0.0267110i
$799$	2.03759e7	+	3.52920e7i	1.12914	+	1.95573i
$800$	−613756.			−0.0339056
$801$	2.14382e6	−	3.71320e6i	0.118061	−	0.204488i
$802$	−6.59982e6	−	1.14312e7i	−0.362323	−	0.627562i
$803$	9.96100e6			0.545147
$804$	−1.13798e7			−0.620859
$805$	740370.	+	1.28236e6i	0.0402679	+	0.0697461i
$806$	−3.61703e6			−0.196117
$807$	8.48745e6	−	1.47007e7i	0.458768	−	0.794610i
$808$	−1.07746e7			−0.580593
$809$	−1.27918e7	+	2.21561e7i	−0.687165	+	1.19021i	0.285586	+	0.958353i	$0.407812\pi$
$809$	−1.27918e7	+	2.21561e7i	−0.687165	+	1.19021i	−0.972751	+	0.231852i	$0.925521\pi$
$810$	−2.36033e6	+	4.08820e6i	−0.126404	+	0.218937i
$811$	257454.	−	445923.i	0.0137451	−	0.0238072i	−0.859071	−	0.511856i	$-0.828958\pi$
$811$	257454.	−	445923.i	0.0137451	−	0.0238072i	0.872816	+	0.488049i	$0.162291\pi$
$812$	−2009.60	−	3480.73i	−0.000106960	−	0.000185259i
$813$	493818.			0.0262024
$814$	−2.24240e6	+	3.25002e6i	−0.118618	+	0.171919i
$815$	−1.35648e7			−0.715350
$816$	7.56955e6	+	1.31109e7i	0.397965	+	0.689296i
$817$	245613.	−	425414.i	0.0128735	−	0.0222975i
$818$	−7.23741e6	+	1.25356e7i	−0.378181	+	0.655029i
$819$	−192993.	+	334273.i	−0.0100538	+	0.0174137i
$820$	5.50079e6			0.285687
$821$	3.28129e6	−	5.68335e6i	0.169897	−	0.294271i	−0.768486	−	0.639866i	$-0.778990\pi$
$821$	3.28129e6	−	5.68335e6i	0.169897	−	0.294271i	0.938384	+	0.345596i	$0.112323\pi$
$822$	−4.08572e7			−2.10906
$823$	−2.82561e6	−	4.89410e6i	−0.145416	−	0.251868i	0.784112	−	0.620619i	$-0.213119\pi$
$823$	−2.82561e6	−	4.89410e6i	−0.145416	−	0.251868i	−0.929528	+	0.368751i	$0.879785\pi$
$824$	3.48851e6			0.178987
$825$	−1.83869e6			−0.0940534
$826$	67165.1	+	116333.i	0.00342526	+	0.00593272i
$827$	1.40432e7	−	2.43236e7i	0.714009	−	1.23670i	−0.249332	−	0.968418i	$-0.580211\pi$
$827$	1.40432e7	−	2.43236e7i	0.714009	−	1.23670i	0.963341	−	0.268281i	$-0.0864556\pi$
$828$	2.72724e7			1.38244
$829$	8.70035e6	+	1.50694e7i	0.439694	+	0.761572i	0.997666	−	0.0682879i	$-0.0217536\pi$
$829$	8.70035e6	+	1.50694e7i	0.439694	+	0.761572i	−0.557972	+	0.829860i	$0.688420\pi$
$830$	1.26628e6	+	2.19327e6i	0.0638022	+	0.110509i
$831$	−2.28302e7	−	3.95431e7i	−1.14685	−	1.98641i
$832$	−304999.	+	528274.i	−0.0152753	+	0.0264576i
$833$	1.91613e7	−	3.31883e7i	0.956780	−	1.65719i
$834$	2.53988e6	+	4.39920e6i	0.126444	+	0.219007i
$835$	−7.16220e6	−	1.24053e7i	−0.355492	−	0.615731i
$836$	−836857.	−	1.44948e6i	−0.0414129	−	0.0717293i
$837$	−2.88658e7			−1.42420
$838$	−5.09845e6	+	8.83078e6i	−0.250800	+	0.434399i
$839$	−1.37295e7	−	2.37802e7i	−0.673365	−	1.16630i	−0.976944	−	0.213496i	$-0.931515\pi$
$839$	−1.37295e7	−	2.37802e7i	−0.673365	−	1.16630i	0.303579	−	0.952806i	$-0.401818\pi$
$840$	−613937.			−0.0300210
$841$	−2.05094e7			−0.999917
$842$	5.08699e6	+	8.81092e6i	0.247275	+	0.428293i
$843$	−2.15756e7			−1.04567
$844$	3.82986e6	−	6.63351e6i	0.185066	−	0.320544i
$845$	2.13056e7			1.02648
$846$	−1.52189e7	+	2.63599e7i	−0.731068	+	1.26625i
$847$	446437.	−	773251.i	0.0213821	−	0.0370350i
$848$	1.89503e6	−	3.28229e6i	0.0904953	−	0.156743i
$849$	8.36349e6	+	1.44860e7i	0.398216	+	0.689730i
$850$	−5.47867e6			−0.260092
$851$	1.42660e7	+	3.00500e7i	0.675273	+	1.42240i
$852$	−1.63142e7			−0.769959
$853$	9.55967e6	+	1.65578e7i	0.449853	+	0.779167i	0.998376	−	0.0569677i	$-0.0181432\pi$
$853$	9.55967e6	+	1.65578e7i	0.449853	+	0.779167i	−0.548524	+	0.836135i	$0.684810\pi$
$854$	341783.	−	591986.i	0.0160364	−	0.0277758i
$855$	1.14898e7	−	1.99009e7i	0.537523	−	0.931017i
$856$	−5.61663e6	+	9.72829e6i	−0.261994	+	0.453787i
$857$	−184022.			−0.00855888			−0.00427944	−	0.999991i	$-0.501362\pi$
$857$	−184022.			−0.00855888			−0.00427944	+	0.999991i	$0.501362\pi$
$858$	−913717.	+	1.58260e6i	−0.0423734	+	0.0733929i
$859$	−3.00417e7			−1.38913			−0.694563	−	0.719432i	$-0.744402\pi$
$859$	−3.00417e7			−1.38913			−0.694563	+	0.719432i	$0.744402\pi$
$860$	−271774.	−	470726.i	−0.0125303	−	0.0217031i
$861$	885515.			0.0407088
$862$	−2.34453e7			−1.07470
$863$	−5.30082e6	−	9.18129e6i	−0.242279	−	0.419640i	0.719084	−	0.694923i	$-0.244562\pi$
$863$	−5.30082e6	−	9.18129e6i	−0.242279	−	0.419640i	−0.961363	+	0.275283i	$0.911228\pi$
$864$	−2.43405e6	+	4.21590e6i	−0.110929	+	0.192135i
$865$	−2.95176e7			−1.34135
$866$	4.37195e6	+	7.57244e6i	0.198098	+	0.343116i
$867$	4.91973e7	+	8.52122e7i	2.22277	+	3.84994i
$868$	−295046.	−	511035.i	−0.0132920	−	0.0230224i
$869$	3.63728e6	−	6.29995e6i	0.163391	−	0.283001i
$870$	130630.	−	226257.i	0.00585118	−	0.0101345i
$871$	−2.04649e6	−	3.54463e6i	−0.0914039	−	0.158316i
$872$	−5.78243e6	−	1.00155e7i	−0.257525	−	0.446046i
$873$	2.78622e7	+	4.82587e7i	1.23731	+	2.14309i
$874$	−1.41002e7			−0.624377
$875$	−468104.	+	810779.i	−0.0206691	+	0.0358000i
$876$	1.73965e7	+	3.01316e7i	0.765953	+	1.32667i
$877$	−9.18126e6			−0.403091			−0.201546	−	0.979479i	$-0.564596\pi$
$877$	−9.18126e6			−0.403091			−0.201546	+	0.979479i	$0.564596\pi$
$878$	2.32726e7			1.01885
$879$	3.30364e6	+	5.72207e6i	0.144218	+	0.249794i
$880$	−1.85199e6			−0.0806180
$881$	−2.22609e7	+	3.85569e7i	−0.966278	+	1.67364i	−0.260138	+	0.965571i	$0.583768\pi$
$881$	−2.22609e7	+	3.85569e7i	−0.966278	+	1.67364i	−0.706140	+	0.708072i	$0.749565\pi$
$882$	2.86235e7			1.23894
$883$	1.64766e7	−	2.85383e7i	0.711158	−	1.23176i	−0.253264	−	0.967397i	$-0.581504\pi$
$883$	1.64766e7	−	2.85383e7i	0.711158	−	1.23176i	0.964423	−	0.264365i	$-0.0851625\pi$
$884$	−2.72256e6	+	4.71561e6i	−0.117178	+	0.202958i
$885$	−4.36592e6	+	7.56199e6i	−0.187377	+	0.324547i
$886$	528254.	+	914963.i	0.0226078	+	0.0391579i
$887$	−2.61285e7			−1.11508			−0.557539	−	0.830150i	$-0.688254\pi$
$887$	−2.61285e7			−1.11508			−0.557539	+	0.830150i	$0.688254\pi$
$888$	−1.37474e7	−	1.10714e6i	−0.585045	−	0.0471160i
$889$	1.92532e6			0.0817051
$890$	1.22644e6	+	2.12426e6i	0.0519006	+	0.0898945i
$891$	−1.14619e6	+	1.98526e6i	−0.0483686	+	0.0837768i
$892$	4.68335e6	−	8.11180e6i	0.197081	−	0.341354i
$893$	7.86840e6	−	1.36285e7i	0.330185	−	0.571897i
$894$	−2.65582e7			−1.11136
$895$	−9.32258e6	+	1.61472e7i	−0.389026	+	0.673813i
$896$	−99516.7			−0.00414120
$897$	7.69761e6	+	1.33327e7i	0.319429	+	0.553268i
$898$	−7.92167e6			−0.327813
$899$	251112.			0.0103626
$900$	−2.04603e6	−	3.54383e6i	−0.0841989	−	0.145837i
$901$	1.69159e7	−	2.92992e7i	0.694197	−	1.20238i
$902$	2.67123e6			0.109319
$903$	−43750.1	−	75777.4i	−0.00178550	−	0.00309257i
$904$	−5.47922e6	−	9.49029e6i	−0.222996	−	0.386241i
$905$	9.70497e6	+	1.68095e7i	0.393888	+	0.682234i
$906$	43766.5	−	75805.8i	0.00177142	−	0.00306819i
$907$	−1.69683e7	+	2.93899e7i	−0.684887	+	1.18626i	0.288585	+	0.957454i	$0.406815\pi$
$907$	−1.69683e7	+	2.93899e7i	−0.684887	+	1.18626i	−0.973472	+	0.228806i	$0.926518\pi$
$908$	−7.51659e6	−	1.30191e7i	−0.302556	−	0.524043i
$909$	−3.59184e7	−	6.22124e7i	−1.44181	−	2.49728i
$910$	−110408.	−	191232.i	−0.00441975	−	0.00765522i
$911$	−2.68448e7			−1.07168			−0.535838	−	0.844321i	$-0.680004\pi$
$911$	−2.68448e7			−1.07168			−0.535838	+	0.844321i	$0.680004\pi$
$912$	2.92308e6	−	5.06292e6i	0.116373	−	0.201565i
$913$	614917.	+	1.06507e6i	0.0244140	+	0.0422863i
$914$	9.59988e6			0.380102
$915$	4.44337e7			1.75453
$916$	3.98886e6	+	6.90891e6i	0.157076	+	0.272064i
$917$	−926709.			−0.0363932
$918$	−2.17274e7	+	3.76330e7i	−0.850946	+	1.47388i
$919$	2.29750e6			0.0897360			0.0448680	−	0.998993i	$-0.485713\pi$
$919$	2.29750e6			0.0897360			0.0448680	+	0.998993i	$0.485713\pi$
$920$	−7.80104e6	+	1.35118e7i	−0.303867	+	0.526313i
$921$	−2.08113e6	+	3.60463e6i	−0.0808446	+	0.140027i
$922$	30107.5	−	52147.7i	0.00116640	−	0.00202026i
$923$	−2.93389e6	−	5.08164e6i	−0.113355	−	0.196336i
$924$	−298133.			−0.0114876
$925$	2.83450e6	−	4.10818e6i	0.108924	−	0.157868i
$926$	1.38409e6			0.0530441
$927$	1.16294e7	+	2.01427e7i	0.444485	+	0.769871i
$928$	21174.5	−	36675.4i	0.000807131	−	0.00139799i
$929$	8.62257e6	−	1.49347e7i	0.327791	−	0.567751i	−0.654282	−	0.756251i	$-0.727029\pi$
$929$	8.62257e6	−	1.49347e7i	0.327791	−	0.567751i	0.982073	+	0.188500i	$0.0603624\pi$
$930$	1.91788e7	−	3.32187e7i	0.727134	−	1.25943i
$931$	−1.47988e7			−0.559566
$932$	−166480.	+	288352.i	−0.00627802	+	0.0108738i
$933$	6.70520e7			2.52178
$934$	1.30437e7	+	2.25923e7i	0.489251	+	0.847408i
$935$	−1.65317e7			−0.618427
$936$	−4.06701e6			−0.151735
$937$	1.39959e7	+	2.42417e7i	0.520779	+	0.902015i	0.999708	+	0.0241619i	$0.00769174\pi$
$937$	1.39959e7	+	2.42417e7i	0.520779	+	0.902015i	−0.478929	+	0.877854i	$0.658975\pi$
$938$	333870.	−	578281.i	0.0123900	−	0.0214601i
$939$	4.96816e7			1.83879
$940$	−8.70649e6	−	1.50801e7i	−0.321384	−	0.556653i
$941$	−7.83593e6	−	1.35722e7i	−0.288481	−	0.499663i	0.684967	−	0.728574i	$-0.259817\pi$
$941$	−7.83593e6	−	1.35722e7i	−0.288481	−	0.499663i	−0.973447	+	0.228911i	$0.926483\pi$
$942$	−1.56321e7	−	2.70755e7i	−0.573970	−	0.994145i
$943$	1.12519e7	−	1.94888e7i	0.412046	−	0.713684i
$944$	−707697.	+	1.22577e6i	−0.0258474	+	0.0447691i
$945$	−881114.	−	1.52613e6i	−0.0320961	−	0.0555921i
$946$	−131976.	−	228588.i	−0.00479475	−	0.00830475i
$947$	2.03249e7	+	3.52037e7i	0.736466	+	1.27560i	0.954077	+	0.299560i	$0.0968400\pi$
$947$	2.03249e7	+	3.52037e7i	0.736466	+	1.27560i	−0.217612	+	0.976035i	$0.569827\pi$
$948$	2.54095e7			0.918280
$949$	−6.25704e6	+	1.08375e7i	−0.225530	+	0.390629i
$950$	1.05783e6	+	1.83221e6i	0.0380283	+	0.0658669i
$951$	−5.80784e6			−0.208240
$952$	−888331.			−0.0317675
$953$	−776033.	−	1.34413e6i	−0.0276788	−	0.0479412i	0.851854	−	0.523779i	$-0.175478\pi$
$953$	−776033.	−	1.34413e6i	−0.0276788	−	0.0479412i	−0.879533	+	0.475838i	$0.842145\pi$
$954$	2.52693e7			0.898921
$955$	1.71954e7	−	2.97833e7i	0.610104	−	1.05673i
$956$	1.27659e7			0.451760
$957$	63434.8	−	109872.i	0.00223897	−	0.00387800i
$958$	−1.55287e7	+	2.68966e7i	−0.546667	+	0.946855i
$959$	1.19871e6	−	2.07622e6i	0.0420888	−	0.0728999i
$960$	−3.23443e6	−	5.60220e6i	−0.113271	−	0.196192i
$961$	8.23869e6			0.287773
$962$	−2.12743e6	−	4.48123e6i	−0.0741170	−	0.156120i
$963$	−7.48950e7			−2.60248
$964$	−3.52551e6	−	6.10636e6i	−0.122188	−	0.211636i
$965$	−1.12862e7	+	1.95484e7i	−0.390150	+	0.675759i
$966$	−1.25581e6	+	2.17513e6i	−0.0432993	+	0.0749966i
$967$	−9.33444e6	+	1.61677e7i	−0.321012	+	0.556010i	−0.980697	−	0.195533i	$-0.937356\pi$
$967$	−9.33444e6	+	1.61677e7i	−0.321012	+	0.556010i	0.659685	+	0.751542i	$0.270690\pi$
$968$	9.40792e6			0.322705
$969$	2.60927e7	−	4.51940e7i	0.892710	−	1.54622i
$970$	−3.18790e7			−1.08787
$971$	1.07983e7	+	1.87033e7i	0.367543	+	0.636604i	0.989181	−	0.146701i	$-0.0468656\pi$
$971$	1.07983e7	+	1.87033e7i	0.367543	+	0.636604i	−0.621637	+	0.783305i	$0.713532\pi$
$972$	1.04764e7			0.355671
$973$	−298070.			−0.0100934
$974$	−1.21978e7	−	2.11273e7i	−0.411989	−	0.713586i
$975$	1.15498e6	−	2.00049e6i	0.0389103	−	0.0673946i
$976$	7.20252e6			0.242025
$977$	−2.18161e6	−	3.77866e6i	−0.0731207	−	0.126649i	0.827147	−	0.561986i	$-0.189962\pi$
$977$	−2.18161e6	−	3.77866e6i	−0.0731207	−	0.126649i	−0.900267	+	0.435337i	$0.856629\pi$
$978$	−1.15042e7	−	1.99259e7i	−0.384601	−	0.666149i
$979$	595570.	+	1.03156e6i	0.0198599	+	0.0343983i
$980$	−8.18752e6	+	1.41812e7i	−0.272325	+	0.471680i
$981$	3.85529e7	−	6.67756e7i	1.27904	−	2.21536i
$982$	−1.16939e7	−	2.02545e7i	−0.386975	−	0.670260i
$983$	−1.47819e7	−	2.56029e7i	−0.487916	−	0.845096i	0.511987	−	0.858993i	$-0.328910\pi$
$983$	−1.47819e7	−	2.56029e7i	−0.487916	−	0.845096i	−0.999903	+	0.0138974i	$0.995576\pi$
$984$	4.66520e6	+	8.08036e6i	0.153597	+	0.266037i
$985$	−2.18056e7			−0.716107
$986$	189013.	−	327381.i	0.00619157	−	0.0107241i
$987$	−1.40157e6	−	2.42759e6i	−0.0457953	−	0.0793199i
$988$	2.10270e6			0.0685307
$989$	−2.22366e6			−0.0722898
$990$	−6.17384e6	−	1.06934e7i	−0.200201	−	0.346759i
$991$	3.19117e7			1.03220			0.516102	−	0.856527i	$-0.327383\pi$
$991$	3.19117e7			1.03220			0.516102	+	0.856527i	$0.327383\pi$
$992$	3.10881e6	−	5.38461e6i	0.100303	−	0.173730i
$993$	−4.47458e7			−1.44006
$994$	478642.	−	829033.i	0.0153654	−	0.0266137i
$995$	−3.00091e7	+	5.19774e7i	−0.960939	+	1.66440i
$996$	−2.14786e6	+	3.72020e6i	−0.0686053	+	0.118828i
$997$	1.13360e7	+	1.96345e7i	0.361178	+	0.625579i	0.988155	−	0.153459i	$-0.0490413\pi$
$997$	1.13360e7	+	1.96345e7i	0.361178	+	0.625579i	−0.626977	+	0.779038i	$0.715708\pi$
$998$	475204.			0.0151027
$999$	−1.69780e7	−	3.57626e7i	−0.538236	−	1.13374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.c.b.63.8	yes	16
37.10	even	3	inner	74.6.c.b.47.8	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.c.b.47.8	✓	16	37.10	even	3	inner
74.6.c.b.63.8	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)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(12.9393 - 22.4116i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5138 - 52.8515i) q^{5} +103.515 q^{6} +(-3.03701 + 5.26025i) q^{7} -64.0000 q^{8} +(-213.352 - 369.536i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(12.9393 - 22.4116i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(30.5138 - 52.8515i) q^{5} +103.515 q^{6} +(-3.03701 + 5.26025i) q^{7} -64.0000 q^{8} +(-213.352 - 369.536i) q^{9} +244.111 q^{10} +118.542 q^{11} +(207.029 + 358.585i) q^{12} +(-74.4626 + 128.973i) q^{13} -24.2961 q^{14} +(-789.656 - 1367.72i) q^{15} +(-128.000 - 221.703i) q^{16} +(-1142.59 - 1979.02i) q^{17} +(853.408 - 1478.15i) q^{18} +(-441.224 + 764.223i) q^{19} +(488.221 + 845.624i) q^{20} +(78.5936 + 136.128i) q^{21} +(237.084 + 410.641i) q^{22} +3994.63 q^{23} +(-828.116 + 1434.34i) q^{24} +(-299.686 - 519.071i) q^{25} -595.701 q^{26} -4754.01 q^{27} +(-48.5921 - 84.1640i) q^{28} +41.3565 q^{29} +(3158.62 - 5470.90i) q^{30} +6071.89 q^{31} +(512.000 - 886.810i) q^{32} +(1533.85 - 2656.71i) q^{33} +(4570.34 - 7916.07i) q^{34} +(185.341 + 321.021i) q^{35} +6827.26 q^{36} +(3571.31 + 7522.61i) q^{37} -3529.79 q^{38} +(1926.99 + 3337.65i) q^{39} +(-1952.88 + 3382.49i) q^{40} +(2816.75 - 4878.76i) q^{41} +(-314.375 + 544.513i) q^{42} -556.662 q^{43} +(-948.336 + 1642.57i) q^{44} -26040.7 q^{45} +(7989.25 + 13837.8i) q^{46} -17833.1 q^{47} -6624.93 q^{48} +(8385.05 + 14523.3i) q^{49} +(1198.74 - 2076.28i) q^{50} -59137.1 q^{51} +(-1191.40 - 2063.57i) q^{52} +(7402.46 + 12821.4i) q^{53} +(-9508.01 - 16468.4i) q^{54} +(3617.17 - 6265.12i) q^{55} +(194.369 - 336.656i) q^{56} +(11418.3 + 19777.0i) q^{57} +(82.7130 + 143.263i) q^{58} +(-2764.44 - 4788.15i) q^{59} +25269.0 q^{60} +(-14067.4 + 24365.5i) q^{61} +(12143.8 + 21033.6i) q^{62} +2591.81 q^{63} +4096.00 q^{64} +(4544.28 + 7870.92i) q^{65} +12270.8 q^{66} +(-13741.7 + 23801.4i) q^{67} +36562.8 q^{68} +(51687.8 - 89525.8i) q^{69} +(-741.366 + 1284.08i) q^{70} +(-19700.4 + 34122.1i) q^{71} +(13654.5 + 23650.3i) q^{72} +84029.3 q^{73} +(-18916.5 + 27416.6i) q^{74} -15510.9 q^{75} +(-7059.59 - 12227.6i) q^{76} +(-360.013 + 623.561i) q^{77} +(-7707.96 + 13350.6i) q^{78} +(30683.5 - 53145.3i) q^{79} -15623.1 q^{80} +(-9669.09 + 16747.3i) q^{81} +22534.0 q^{82} +(5187.34 + 8984.73i) q^{83} -2515.00 q^{84} -139459. q^{85} +(-1113.32 - 1928.33i) q^{86} +(535.125 - 926.864i) q^{87} -7586.68 q^{88} +(5024.13 + 8702.05i) q^{89} +(-52081.5 - 90207.7i) q^{90} +(-452.287 - 783.384i) q^{91} +(-31957.0 + 55351.2i) q^{92} +(78566.1 - 136081. i) q^{93} +(-35666.2 - 61775.7i) q^{94} +(26926.9 + 46638.7i) q^{95} +(-13249.9 - 22949.4i) q^{96} -130592. q^{97} +(-33540.2 + 58093.4i) q^{98} +(-25291.2 - 43805.6i) 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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