LMFDB - Embedded newform 38.6.c.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,6,Mod(7,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("38.7");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	38.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:	$6.09458515289$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 386x^{6} + 3436x^{5} + 128708x^{4} + 568528x^{3} + 7340704x^{2} - 19430784x + 211527936 $ x^8 - 2x^7 + 386x^6 + 3436x^5 + 128708x^4 + 568528x^3 + 7340704x^2 - 19430784*x + 211527936
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$2.36148 + 4.09020i$ of defining polynomial
Character	$\chi$	$=$	38.11
Dual form			38.6.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 + 3.46410i) q^{2} +(-3.86148 + 6.68827i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(46.3693 - 80.3140i) q^{5} +(-15.4459 - 26.7531i) q^{6} +13.5472 q^{7} +64.0000 q^{8} +(91.6780 + 158.791i) q^{9} +O(q^{10})$	\(q+(-2.00000 + 3.46410i) q^{2} +(-3.86148 + 6.68827i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(46.3693 - 80.3140i) q^{5} +(-15.4459 - 26.7531i) q^{6} +13.5472 q^{7} +64.0000 q^{8} +(91.6780 + 158.791i) q^{9} +(185.477 + 321.256i) q^{10} +407.324 q^{11} +123.567 q^{12} +(-86.6070 - 150.008i) q^{13} +(-27.0944 + 46.9288i) q^{14} +(358.108 + 620.262i) q^{15} +(-128.000 + 221.703i) q^{16} +(822.219 - 1424.13i) q^{17} -733.424 q^{18} +(1573.31 + 27.9814i) q^{19} -1483.82 q^{20} +(-52.3121 + 90.6073i) q^{21} +(-814.647 + 1411.01i) q^{22} +(778.168 + 1347.83i) q^{23} +(-247.135 + 428.050i) q^{24} +(-2737.73 - 4741.89i) q^{25} +692.856 q^{26} -3292.73 q^{27} +(-108.377 - 187.715i) q^{28} +(-2204.59 - 3818.47i) q^{29} -2864.87 q^{30} -1489.86 q^{31} +(-512.000 - 886.810i) q^{32} +(-1572.87 + 2724.29i) q^{33} +(3288.88 + 5696.50i) q^{34} +(628.174 - 1088.03i) q^{35} +(1466.85 - 2540.66i) q^{36} +7117.66 q^{37} +(-3243.56 + 5394.16i) q^{38} +1337.72 q^{39} +(2967.64 - 5140.10i) q^{40} +(-9665.80 + 16741.7i) q^{41} +(-209.249 - 362.429i) q^{42} +(7845.40 - 13588.6i) q^{43} +(-3258.59 - 5644.04i) q^{44} +17004.2 q^{45} -6225.34 q^{46} +(6510.80 + 11277.0i) q^{47} +(-988.538 - 1712.20i) q^{48} -16623.5 q^{49} +21901.8 q^{50} +(6349.96 + 10998.5i) q^{51} +(-1385.71 + 2400.12i) q^{52} +(820.131 + 1420.51i) q^{53} +(6585.45 - 11406.3i) q^{54} +(18887.3 - 32713.8i) q^{55} +867.020 q^{56} +(-6262.46 + 10414.7i) q^{57} +17636.8 q^{58} +(-23457.7 + 40629.9i) q^{59} +(5729.73 - 9924.19i) q^{60} +(-13828.9 - 23952.4i) q^{61} +(2979.71 - 5161.01i) q^{62} +(1241.98 + 2151.17i) q^{63} +4096.00 q^{64} -16063.6 q^{65} +(-6291.48 - 10897.2i) q^{66} +(-6090.69 - 10549.4i) q^{67} -26311.0 q^{68} -12019.5 q^{69} +(2512.70 + 4352.12i) q^{70} +(-6079.27 + 10529.6i) q^{71} +(5867.39 + 10162.6i) q^{72} +(-23003.1 + 39842.6i) q^{73} +(-14235.3 + 24656.3i) q^{74} +42286.7 q^{75} +(-12198.8 - 22024.3i) q^{76} +5518.09 q^{77} +(-2675.45 + 4634.01i) q^{78} +(-22669.4 + 39264.5i) q^{79} +(11870.5 + 20560.4i) q^{80} +(-9562.96 + 16563.5i) q^{81} +(-38663.2 - 66966.6i) q^{82} +23692.9 q^{83} +1673.99 q^{84} +(-76251.5 - 132072. i) q^{85} +(31381.6 + 54354.5i) q^{86} +34052.0 q^{87} +26068.7 q^{88} +(-57570.6 - 99715.3i) q^{89} +(-34008.4 + 58904.2i) q^{90} +(-1173.28 - 2032.18i) q^{91} +(12450.7 - 21565.2i) q^{92} +(5753.04 - 9964.56i) q^{93} -52086.4 q^{94} +(75200.8 - 125062. i) q^{95} +7908.30 q^{96} +(-19513.7 + 33798.7i) q^{97} +(33246.9 - 57585.4i) q^{98} +(37342.6 + 64679.3i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9}+O(q^{10}) $ 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18} + 320 q^{19} + 1152 q^{20} - 770 q^{21} - 288 q^{22} - 204 q^{23} - 896 q^{24} - 2158 q^{25} + 5392 q^{26} + 13156 q^{27} - 608 q^{28} - 5712 q^{29} + 160 q^{30} - 2324 q^{31} - 4096 q^{32} - 15650 q^{33} + 2088 q^{34} - 4188 q^{35} + 2496 q^{36} - 25508 q^{37} - 2440 q^{38} + 44156 q^{39} - 2304 q^{40} - 3480 q^{41} - 3080 q^{42} + 4066 q^{43} - 1152 q^{44} + 51560 q^{45} + 1632 q^{46} - 45768 q^{47} - 3584 q^{48} + 1416 q^{49} + 17264 q^{50} + 1506 q^{51} - 10784 q^{52} + 45654 q^{53} - 26312 q^{54} + 36570 q^{55} + 4864 q^{56} - 66702 q^{57} + 45696 q^{58} - 84006 q^{59} - 320 q^{60} - 14012 q^{61} + 4648 q^{62} - 15128 q^{63} + 32768 q^{64} - 4020 q^{65} - 62600 q^{66} - 19046 q^{67} - 16704 q^{68} + 111592 q^{69} - 16752 q^{70} - 53274 q^{71} + 9984 q^{72} - 41084 q^{73} + 51016 q^{74} + 153216 q^{75} + 4640 q^{76} + 271524 q^{77} - 88312 q^{78} - 54170 q^{79} - 9216 q^{80} - 9528 q^{81} - 13920 q^{82} + 52392 q^{83} + 24640 q^{84} - 221850 q^{85} + 16264 q^{86} - 457120 q^{87} + 9216 q^{88} - 137862 q^{89} - 103120 q^{90} + 308516 q^{91} - 3264 q^{92} + 112746 q^{93} + 366144 q^{94} + 153078 q^{95} + 28672 q^{96} - 292388 q^{97} - 2832 q^{98} - 138328 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	−3.86148	+	6.68827i	−0.247714	+	0.429053i	−0.962891	−	0.269890i	$-0.913013\pi$
$3$	−3.86148	+	6.68827i	−0.247714	+	0.429053i	0.715177	+	0.698943i	$0.246346\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	46.3693	−	80.3140i	0.829480	−	1.43670i	−0.0689670	−	0.997619i	$-0.521970\pi$
$5$	46.3693	−	80.3140i	0.829480	−	1.43670i	0.898447	−	0.439082i	$-0.144696\pi$
$6$	−15.4459	−	26.7531i	−0.175160	−	0.303386i
$7$	13.5472			0.104497			0.0522485	−	0.998634i	$-0.483361\pi$
$7$	13.5472			0.104497			0.0522485	+	0.998634i	$0.483361\pi$
$8$	64.0000			0.353553
$9$	91.6780	+	158.791i	0.377276	+	0.653461i
$10$	185.477	+	321.256i	0.586531	+	1.01590i
$11$	407.324			1.01498			0.507490	−	0.861657i	$-0.330573\pi$
$11$	407.324			1.01498			0.507490	+	0.861657i	$0.330573\pi$
$12$	123.567			0.247714
$13$	−86.6070	−	150.008i	−0.142133	−	0.246181i	0.786167	−	0.618014i	$-0.212063\pi$
$13$	−86.6070	−	150.008i	−0.142133	−	0.246181i	−0.928300	+	0.371833i	$0.878729\pi$
$14$	−27.0944	+	46.9288i	−0.0369453	+	0.0639911i
$15$	358.108	+	620.262i	0.410947	+	0.711782i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	822.219	−	1424.13i	0.690026	−	1.19516i	−0.281803	−	0.959472i	$-0.590932\pi$
$17$	822.219	−	1424.13i	0.690026	−	1.19516i	0.971829	−	0.235687i	$-0.0757342\pi$
$18$	−733.424			−0.533548
$19$	1573.31	+	27.9814i	0.999842	+	0.0177822i
$19$	1573.31	+	27.9814i	0.999842	+	0.0177822i
$20$	−1483.82			−0.829480
$21$	−52.3121	+	90.6073i	−0.0258854	+	0.0448348i
$22$	−814.647	+	1411.01i	−0.358850	+	0.621546i
$23$	778.168	+	1347.83i	0.306728	+	0.531269i	0.977645	−	0.210264i	$-0.0674324\pi$
$23$	778.168	+	1347.83i	0.306728	+	0.531269i	−0.670916	+	0.741533i	$0.734099\pi$
$24$	−247.135	+	428.050i	−0.0875801	+	0.151693i
$25$	−2737.73	−	4741.89i	−0.876074	−	1.51740i
$26$	692.856			0.201006
$27$	−3292.73			−0.869253
$28$	−108.377	−	187.715i	−0.0261243	−	0.0452486i
$29$	−2204.59	−	3818.47i	−0.486781	−	0.843129i	0.513103	−	0.858327i	$-0.328496\pi$
$29$	−2204.59	−	3818.47i	−0.486781	−	0.843129i	−0.999885	+	0.0151973i	$0.995162\pi$
$30$	−2864.87			−0.581167
$31$	−1489.86			−0.278445			−0.139223	−	0.990261i	$-0.544460\pi$
$31$	−1489.86			−0.278445			−0.139223	+	0.990261i	$0.544460\pi$
$32$	−512.000	−	886.810i	−0.0883883	−	0.153093i
$33$	−1572.87	+	2724.29i	−0.251425	+	0.435480i
$34$	3288.88	+	5696.50i	0.487922	+	0.845106i
$35$	628.174	−	1088.03i	0.0866782	−	0.150131i
$36$	1466.85	−	2540.66i	0.188638	−	0.326730i
$37$	7117.66			0.854737			0.427369	−	0.904077i	$-0.359441\pi$
$37$	7117.66			0.854737			0.427369	+	0.904077i	$0.359441\pi$
$38$	−3243.56	+	5394.16i	−0.364387	+	0.605989i
$39$	1337.72			0.140833
$40$	2967.64	−	5140.10i	0.293265	−	0.507951i
$41$	−9665.80	+	16741.7i	−0.898004	+	1.55539i	−0.0679617	+	0.997688i	$0.521650\pi$
$41$	−9665.80	+	16741.7i	−0.898004	+	1.55539i	−0.830042	+	0.557701i	$0.811684\pi$
$42$	−209.249	−	362.429i	−0.0183037	−	0.0317030i
$43$	7845.40	−	13588.6i	0.647059	−	1.12074i	−0.336763	−	0.941590i	$-0.609332\pi$
$43$	7845.40	−	13588.6i	0.647059	−	1.12074i	0.983822	−	0.179150i	$-0.0573347\pi$
$44$	−3258.59	−	5644.04i	−0.253745	−	0.439500i
$45$	17004.2			1.25177
$46$	−6225.34			−0.433779
$47$	6510.80	+	11277.0i	0.429922	+	0.744647i	0.996866	−	0.0791097i	$-0.0252077\pi$
$47$	6510.80	+	11277.0i	0.429922	+	0.744647i	−0.566944	+	0.823756i	$0.691874\pi$
$48$	−988.538	−	1712.20i	−0.0619285	−	0.107263i
$49$	−16623.5			−0.989080
$50$	21901.8			1.23896
$51$	6349.96	+	10998.5i	0.341858	+	0.592115i
$52$	−1385.71	+	2400.12i	−0.0710664	+	0.123091i
$53$	820.131	+	1420.51i	0.0401045	+	0.0694631i	0.885381	−	0.464866i	$-0.153898\pi$
$53$	820.131	+	1420.51i	0.0401045	+	0.0694631i	−0.845276	+	0.534329i	$0.820564\pi$
$54$	6585.45	−	11406.3i	0.307327	−	0.532307i
$55$	18887.3	−	32713.8i	0.841906	−	1.45822i
$56$	867.020			0.0369453
$57$	−6262.46	+	10414.7i	−0.255304	+	0.424580i
$58$	17636.8			0.688412
$59$	−23457.7	+	40629.9i	−0.877313	+	1.51955i	−0.0230358	+	0.999735i	$0.507333\pi$
$59$	−23457.7	+	40629.9i	−0.877313	+	1.51955i	−0.854278	+	0.519817i	$0.826000\pi$
$60$	5729.73	−	9924.19i	0.205474	−	0.355891i
$61$	−13828.9	−	23952.4i	−0.475843	−	0.824184i	0.523774	−	0.851857i	$-0.324524\pi$
$61$	−13828.9	−	23952.4i	−0.475843	−	0.824184i	−0.999617	+	0.0276730i	$0.991190\pi$
$62$	2979.71	−	5161.01i	0.0984453	−	0.170512i
$63$	1241.98	+	2151.17i	0.0394242	+	0.0682847i
$64$	4096.00			0.125000
$65$	−16063.6			−0.471585
$66$	−6291.48	−	10897.2i	−0.177784	−	0.307931i
$67$	−6090.69	−	10549.4i	−0.165760	−	0.287105i	0.771165	−	0.636635i	$-0.219674\pi$
$67$	−6090.69	−	10549.4i	−0.165760	−	0.287105i	−0.936925	+	0.349531i	$0.886341\pi$
$68$	−26311.0			−0.690026
$69$	−12019.5			−0.303923
$70$	2512.70	+	4352.12i	0.0612907	+	0.106159i
$71$	−6079.27	+	10529.6i	−0.143122	+	0.247894i	−0.928671	−	0.370906i	$-0.879047\pi$
$71$	−6079.27	+	10529.6i	−0.143122	+	0.247894i	0.785549	+	0.618800i	$0.212381\pi$
$72$	5867.39	+	10162.6i	0.133387	+	0.231033i
$73$	−23003.1	+	39842.6i	−0.505219	+	0.875065i	0.494763	+	0.869028i	$0.335255\pi$
$73$	−23003.1	+	39842.6i	−0.505219	+	0.875065i	−0.999982	+	0.00603695i	$0.998078\pi$
$74$	−14235.3	+	24656.3i	−0.302195	+	0.523418i
$75$	42286.7			0.868062
$76$	−12198.8	−	22024.3i	−0.242261	−	0.437390i
$77$	5518.09			0.106062
$78$	−2675.45	+	4634.01i	−0.0497920	+	0.0862423i
$79$	−22669.4	+	39264.5i	−0.408669	+	0.707835i	−0.994741	−	0.102424i	$-0.967340\pi$
$79$	−22669.4	+	39264.5i	−0.408669	+	0.707835i	0.586072	+	0.810259i	$0.300674\pi$
$80$	11870.5	+	20560.4i	0.207370	+	0.359175i
$81$	−9562.96	+	16563.5i	−0.161950	+	0.280505i
$82$	−38663.2	−	66966.6i	−0.634985	−	1.09983i
$83$	23692.9			0.377505			0.188753	−	0.982025i	$-0.439556\pi$
$83$	23692.9			0.377505			0.188753	+	0.982025i	$0.439556\pi$
$84$	1673.99			0.0258854
$85$	−76251.5	−	132072.i	−1.14473	−	1.98272i
$86$	31381.6	+	54354.5i	0.457540	+	0.792483i
$87$	34052.0			0.482330
$88$	26068.7			0.358850
$89$	−57570.6	−	99715.3i	−0.770417	−	1.33440i	−0.937334	−	0.348431i	$-0.886715\pi$
$89$	−57570.6	−	99715.3i	−0.770417	−	1.33440i	0.166917	−	0.985971i	$-0.446619\pi$
$90$	−34008.4	+	58904.2i	−0.442568	+	0.766550i
$91$	−1173.28	−	2032.18i	−0.0148525	−	0.0257252i
$92$	12450.7	−	21565.2i	0.153364	−	0.265634i
$93$	5753.04	−	9964.56i	0.0689748	−	0.119468i
$94$	−52086.4			−0.608001
$95$	75200.8	−	125062.i	0.854896	−	1.42172i
$96$	7908.30			0.0875801
$97$	−19513.7	+	33798.7i	−0.210577	+	0.364729i	−0.951895	−	0.306424i	$-0.900867\pi$
$97$	−19513.7	+	33798.7i	−0.210577	+	0.364729i	0.741319	+	0.671153i	$0.234201\pi$
$98$	33246.9	−	57585.4i	0.349693	−	0.605686i
$99$	37342.6	+	64679.3i	0.382928	+	0.663250i
$100$	−43803.7	+	75870.2i	−0.438037	+	0.758702i
$101$	99163.8	+	171757.i	0.967274	+	1.67537i	0.703376	+	0.710818i	$0.251675\pi$
$101$	99163.8	+	171757.i	0.967274	+	1.67537i	0.263898	+	0.964551i	$0.414992\pi$
$102$	−50799.7			−0.483460
$103$	182403.			1.69410			0.847052	−	0.531511i	$-0.178375\pi$
$103$	182403.			1.69410			0.847052	+	0.531511i	$0.178375\pi$
$104$	−5542.85	−	9600.49i	−0.0502516	−	0.0870383i
$105$	4851.36	+	8402.80i	0.0429428	+	0.0743791i
$106$	−6561.04			−0.0567164
$107$	26608.0			0.224674			0.112337	−	0.993670i	$-0.464166\pi$
$107$	26608.0			0.224674			0.112337	+	0.993670i	$0.464166\pi$
$108$	26341.8	+	45625.4i	0.217313	+	0.376398i
$109$	22504.5	−	38979.0i	0.181428	−	0.314242i	−0.760939	−	0.648823i	$-0.775261\pi$
$109$	22504.5	−	38979.0i	0.181428	−	0.314242i	0.942367	+	0.334581i	$0.108595\pi$
$110$	75549.3	+	130855.i	0.595318	+	1.03112i
$111$	−27484.7	+	47604.8i	−0.211730	+	0.366728i
$112$	−1734.04	+	3003.45i	−0.0130621	+	0.0226243i
$113$	12010.0			0.0884805			0.0442403	−	0.999021i	$-0.485913\pi$
$113$	12010.0			0.0884805			0.0442403	+	0.999021i	$0.485913\pi$
$114$	−23552.7	−	42523.2i	−0.169738	−	0.306453i
$115$	144332.			1.01770
$116$	−35273.5	+	61095.5i	−0.243391	+	0.421565i
$117$	15879.9	−	27504.8i	0.107247	−	0.185757i
$118$	−93830.7	−	162519.i	−0.620354	−	1.07449i
$119$	11138.8	−	19292.9i	0.0721057	−	0.124891i
$120$	22918.9	+	39696.7i	0.145292	+	0.251653i
$121$	4861.47			0.0301859
$122$	110631.			0.672944
$123$	−74648.5	−	129295.i	−0.444896	−	0.770582i
$124$	11918.8	+	20644.0i	0.0696113	+	0.120570i
$125$	−217979.			−1.24778
$126$	−9935.83			−0.0557542
$127$	−122810.	−	212713.i	−0.675654	−	1.17027i	−0.976277	−	0.216525i	$-0.930528\pi$
$127$	−122810.	−	212713.i	−0.675654	−	1.17027i	0.300623	−	0.953743i	$-0.402805\pi$
$128$	−8192.00	+	14189.0i	−0.0441942	+	0.0765466i
$129$	60589.7	+	104944.i	0.320571	+	0.555245i
$130$	32127.3	−	55646.1i	0.166731	−	0.288786i
$131$	−142223.	+	246338.i	−0.724090	+	1.25416i	0.235257	+	0.971933i	$0.424407\pi$
$131$	−142223.	+	246338.i	−0.724090	+	1.25416i	−0.959347	+	0.282228i	$0.908927\pi$
$132$	50331.9			0.251425
$133$	21314.0	+	379.070i	0.104481	+	0.00185819i
$134$	48725.5			0.234420
$135$	−152682.	+	264452.i	−0.721028	+	1.24886i
$136$	52622.0	−	91144.0i	0.243961	−	0.422553i
$137$	−124079.	−	214911.i	−0.564802	−	0.978266i	−0.997068	−	0.0765196i	$-0.975619\pi$
$137$	−124079.	−	214911.i	−0.564802	−	0.978266i	0.432266	−	0.901746i	$-0.357714\pi$
$138$	24039.0	−	41636.8i	0.107453	−	0.186114i
$139$	−22825.8	−	39535.4i	−0.100205	−	0.173560i	0.811564	−	0.584263i	$-0.198616\pi$
$139$	−22825.8	−	39535.4i	−0.100205	−	0.173560i	−0.911769	+	0.410704i	$0.865283\pi$
$140$	−20101.6			−0.0866782
$141$	−100565.			−0.425991
$142$	−24317.1	−	42118.4i	−0.101202	−	0.175288i
$143$	−35277.1	−	61101.7i	−0.144262	−	0.249869i
$144$	−46939.1			−0.188638
$145$	−408902.			−1.61510
$146$	−92012.5	−	159370.i	−0.357244	−	0.618764i
$147$	64191.2	−	111182.i	0.245009	−	0.424368i
$148$	−56941.2	−	98625.1i	−0.213684	−	0.370112i
$149$	50801.3	−	87990.4i	0.187460	−	0.324691i	−0.756943	−	0.653481i	$-0.773308\pi$
$149$	50801.3	−	87990.4i	0.187460	−	0.324691i	0.944403	+	0.328791i	$0.106641\pi$
$150$	−84573.5	+	146486.i	−0.306906	+	0.531577i
$151$	381041.			1.35997			0.679986	−	0.733225i	$-0.261986\pi$
$151$	381041.			1.35997			0.679986	+	0.733225i	$0.261986\pi$
$152$	100692.	+	1790.81i	0.353497	+	0.00628696i
$153$	301518.			1.04132
$154$	−11036.2	+	19115.2i	−0.0374988	+	0.0649497i
$155$	−69083.6	+	119656.i	−0.230965	+	0.400043i
$156$	−10701.8	−	18536.0i	−0.0352083	−	0.0609825i
$157$	−178383.	+	308969.i	−0.577570	+	1.00038i	0.418187	+	0.908361i	$0.362666\pi$
$157$	−178383.	+	308969.i	−0.577570	+	1.00038i	−0.995757	+	0.0920203i	$0.970668\pi$
$158$	−90677.4	−	157058.i	−0.288972	−	0.500515i
$159$	−12667.7			−0.0397378
$160$	−94964.4			−0.293265
$161$	10542.0	+	18259.3i	0.0320522	+	0.0555160i
$162$	−38251.9	−	66254.2i	−0.114516	−	0.198347i
$163$	−354161.			−1.04407			−0.522037	−	0.852923i	$-0.674828\pi$
$163$	−354161.			−1.04407			−0.522037	+	0.852923i	$0.674828\pi$
$164$	309306.			0.898004
$165$	145866.	+	252647.i	0.417104	+	0.722445i
$166$	−47385.8	+	82074.6i	−0.133468	+	0.231174i
$167$	306334.	+	530586.i	0.849971	+	1.47219i	0.881233	+	0.472682i	$0.156714\pi$
$167$	306334.	+	530586.i	0.849971	+	1.47219i	−0.0312618	+	0.999511i	$0.509953\pi$
$168$	−3347.98	+	5798.87i	−0.00915186	+	0.0158515i
$169$	170645.	−	295566.i	0.459596	−	0.796044i
$170$	610012.			1.61889
$171$	139795.	+	252393.i	0.365596	+	0.660066i
$172$	−251053.			−0.647059
$173$	−79786.5	+	138194.i	−0.202682	+	0.351055i	−0.949392	−	0.314095i	$-0.898299\pi$
$173$	−79786.5	+	138194.i	−0.202682	+	0.351055i	0.746710	+	0.665150i	$0.231632\pi$
$174$	−68103.9	+	117959.i	−0.170529	+	0.295365i
$175$	−37088.5	−	64239.2i	−0.0915471	−	0.158564i
$176$	−52137.4	+	90304.6i	−0.126873	+	0.219750i
$177$	−181162.	−	313783.i	−0.434645	−	0.752828i
$178$	460565.			1.08953
$179$	−221072.			−0.515706			−0.257853	−	0.966184i	$-0.583015\pi$
$179$	−221072.			−0.515706			−0.257853	+	0.966184i	$0.583015\pi$
$180$	−136034.	−	235617.i	−0.312943	−	0.542032i
$181$	63950.3	+	110765.i	0.145093	+	0.251308i	0.929408	−	0.369055i	$-0.120319\pi$
$181$	63950.3	+	110765.i	0.145093	+	0.251308i	−0.784315	+	0.620363i	$0.786985\pi$
$182$	9386.25			0.0210046
$183$	213600.			0.471492
$184$	49802.7	+	86260.9i	0.108445	+	0.187832i
$185$	330041.	−	571648.i	0.708987	−	1.22800i
$186$	23012.2	+	39858.3i	0.0487725	+	0.0844765i
$187$	334909.	−	580080.i	0.700363	−	1.21306i
$188$	104173.	−	180433.i	0.214961	−	0.372323i
$189$	−44607.2			−0.0908344
$190$	282825.	+	510627.i	0.568373	+	1.02617i
$191$	−478653.			−0.949375			−0.474687	−	0.880154i	$-0.657439\pi$
$191$	−478653.			−0.949375			−0.474687	+	0.880154i	$0.657439\pi$
$192$	−15816.6	+	27395.2i	−0.0309642	+	0.0536316i
$193$	111799.	−	193642.i	0.216046	−	0.374203i	−0.737550	−	0.675293i	$-0.764017\pi$
$193$	111799.	−	193642.i	0.216046	−	0.374203i	0.953596	+	0.301090i	$0.0973505\pi$
$194$	−78054.8	−	135195.i	−0.148900	−	0.257903i
$195$	62029.4	−	107438.i	0.116818	−	0.202335i
$196$	132988.	+	230342.i	0.247270	+	0.428284i
$197$	343584.			0.630765			0.315383	−	0.948965i	$-0.397867\pi$
$197$	343584.			0.630765			0.315383	+	0.948965i	$0.397867\pi$
$198$	−298741.			−0.541541
$199$	−241246.	−	417850.i	−0.431844	−	0.747977i	0.565188	−	0.824962i	$-0.308804\pi$
$199$	−241246.	−	417850.i	−0.431844	−	0.747977i	−0.997032	+	0.0769857i	$0.975470\pi$
$200$	−175215.	−	303481.i	−0.309739	−	0.536483i
$201$	94076.3			0.164244
$202$	−793310.			−1.36793
$203$	−29866.0	−	51729.5i	−0.0508672	−	0.0881045i
$204$	101599.	−	175975.i	0.170929	−	0.296058i
$205$	896394.	+	1.55260e6i	1.48975	+	2.58033i
$206$	−364807.	+	631864.i	−0.598956	+	1.03742i
$207$	−142682.	+	247132.i	−0.231442	+	0.400870i
$208$	44342.8			0.0710664
$209$	640848.	+	11397.5i	1.01482	+	0.0180486i
$210$	−38810.9			−0.0607303
$211$	−414026.	+	717115.i	−0.640209	+	1.10887i	0.345177	+	0.938538i	$0.387819\pi$
$211$	−414026.	+	717115.i	−0.640209	+	1.10887i	−0.985386	+	0.170337i	$0.945514\pi$
$212$	13122.1	−	22728.1i	0.0200523	−	0.0347315i
$213$	−46949.9	−	81319.6i	−0.0709065	−	0.122814i
$214$	−53216.0	+	92172.8i	−0.0794342	+	0.137584i
$215$	−727572.	−	1.26019e6i	−1.07345	−	1.85926i
$216$	−210735.			−0.307327
$217$	−20183.4			−0.0290967
$218$	90018.1	+	155916.i	0.128289	+	0.222203i
$219$	−177652.	−	307702.i	−0.250299	−	0.433531i
$220$	−604394.			−0.841906
$221$	−284840.			−0.392301
$222$	−109939.	−	190419.i	−0.149716	−	0.259316i
$223$	377744.	−	654272.i	0.508669	−	0.881041i	−0.491280	−	0.871001i	$-0.663471\pi$
$223$	377744.	−	654272.i	0.508669	−	0.881041i	0.999950	−	0.0100395i	$-0.00319572\pi$
$224$	−6936.16	−	12013.8i	−0.00923632	−	0.0159978i
$225$	501979.	−	869454.i	0.661043	−	1.14496i
$226$	−24020.0	+	41603.9i	−0.0312826	+	0.0541830i
$227$	−1.00051e6			−1.28872			−0.644358	−	0.764724i	$-0.722875\pi$
$227$	−1.00051e6			−1.28872			−0.644358	+	0.764724i	$0.722875\pi$
$228$	194410.	+	3457.59i	0.247675	+	0.00440490i
$229$	−210261.			−0.264954			−0.132477	−	0.991186i	$-0.542293\pi$
$229$	−210261.			−0.264954			−0.132477	+	0.991186i	$0.542293\pi$
$230$	−288665.	+	499982.i	−0.359811	+	0.623211i
$231$	−21308.0	+	36906.5i	−0.0262731	+	0.0455064i
$232$	−141094.	−	244382.i	−0.172103	−	0.298091i
$233$	−202554.	+	350834.i	−0.244428	+	0.423362i	−0.961971	−	0.273152i	$-0.911934\pi$
$233$	−202554.	+	350834.i	−0.244428	+	0.423362i	0.717542	+	0.696515i	$0.245267\pi$
$234$	63519.6	+	110019.i	0.0758348	+	0.131350i
$235$	1.20761e6			1.42645
$236$	750645.			0.877313
$237$	−175074.	−	303238.i	−0.202466	−	0.350681i
$238$	44555.0	+	77171.6i	0.0509864	+	0.0883110i
$239$	−1.57147e6			−1.77956			−0.889780	−	0.456390i	$-0.849142\pi$
$239$	−1.57147e6			−1.77956			−0.889780	+	0.456390i	$0.849142\pi$
$240$	−183351.			−0.205474
$241$	477803.	+	827578.i	0.529915	+	0.917839i	0.999391	+	0.0348939i	$0.0111093\pi$
$241$	477803.	+	827578.i	0.529915	+	0.917839i	−0.469476	+	0.882945i	$0.655557\pi$
$242$	−9722.93	+	16840.6i	−0.0106723	+	0.0184850i
$243$	−473921.	−	820855.i	−0.514861	−	0.891765i
$244$	−221263.	+	383238.i	−0.237922	+	0.412092i
$245$	−770819.	+	1.33510e6i	−0.820422	+	1.42101i
$246$	597188.			0.629178
$247$	−132063.	−	238433.i	−0.137733	−	0.248670i
$248$	−95350.8			−0.0984453
$249$	−91489.6	+	158465.i	−0.0935133	+	0.161970i
$250$	435957.	−	755100.i	0.441158	−	0.764108i
$251$	714398.	+	1.23737e6i	0.715741	+	1.23970i	0.962673	+	0.270667i	$0.0872443\pi$
$251$	714398.	+	1.23737e6i	0.715741	+	1.23970i	−0.246932	+	0.969033i	$0.579422\pi$
$252$	19871.7	−	34418.7i	0.0197121	−	0.0341424i
$253$	316966.	+	549001.i	0.311323	+	0.539228i
$254$	982480.			0.955520
$255$	1.17777e6			1.13426
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−822272.	−	1.42422e6i	−0.776574	−	1.34506i	−0.933906	−	0.357519i	$-0.883623\pi$
$257$	−822272.	−	1.42422e6i	−0.776574	−	1.34506i	0.157332	−	0.987546i	$-0.449711\pi$
$258$	−484717.			−0.453356
$259$	96424.2			0.0893175
$260$	128509.	+	222584.i	0.117896	+	0.204203i
$261$	404226.	−	700139.i	0.367301	−	0.636185i
$262$	−568893.	−	985352.i	−0.512009	−	0.886826i
$263$	−446870.	+	774001.i	−0.398375	+	0.690005i	−0.993526	−	0.113609i	$-0.963759\pi$
$263$	−446870.	+	774001.i	−0.398375	+	0.690005i	0.595151	+	0.803614i	$0.297092\pi$
$264$	−100664.	+	174355.i	−0.0888921	+	0.153966i
$265$	152116.			0.133064
$266$	−43941.1	+	73075.6i	−0.0380773	+	0.0633240i
$267$	889231.			0.763372
$268$	−97451.1	+	168790.i	−0.0828800	+	0.143552i
$269$	799499.	−	1.38477e6i	0.673655	−	1.16680i	−0.303206	−	0.952925i	$-0.598057\pi$
$269$	799499.	−	1.38477e6i	0.673655	−	1.16680i	0.976860	−	0.213879i	$-0.0686098\pi$
$270$	−610726.	−	1.05781e6i	−0.509844	−	0.883076i
$271$	−753944.	+	1.30587e6i	−0.623614	+	1.08013i	0.365193	+	0.930932i	$0.381003\pi$
$271$	−753944.	+	1.30587e6i	−0.623614	+	1.08013i	−0.988807	+	0.149200i	$0.952330\pi$
$272$	210488.	+	364576.i	0.172506	+	0.298790i
$273$	18122.4			0.0147166
$274$	992630.			0.798751
$275$	−1.11514e6	−	1.93148e6i	−0.889198	−	1.54014i
$276$	96156.0	+	166547.i	0.0759808	+	0.131603i
$277$	1.68831e6			1.32207			0.661034	−	0.750356i	$-0.270118\pi$
$277$	1.68831e6			1.32207			0.661034	+	0.750356i	$0.270118\pi$
$278$	182606.			0.141711
$279$	−136587.	−	236576.i	−0.105051	−	0.181953i
$280$	40203.1	−	69633.9i	0.0306454	−	0.0530793i
$281$	680516.	+	1.17869e6i	0.514129	+	0.890498i	0.999866	+	0.0163928i	$0.00521822\pi$
$281$	680516.	+	1.17869e6i	0.514129	+	0.890498i	−0.485736	+	0.874105i	$0.661448\pi$
$282$	201130.	−	348368.i	0.150610	−	0.260865i
$283$	−880309.	+	1.52474e6i	−0.653385	+	1.13170i	0.328911	+	0.944361i	$0.393318\pi$
$283$	−880309.	+	1.52474e6i	−0.653385	+	1.13170i	−0.982296	+	0.187335i	$0.940015\pi$
$284$	194537.			0.143122
$285$	546061.	+	985886.i	0.398225	+	0.718977i
$286$	282217.			0.204017
$287$	−130944.	+	226802.i	−0.0938388	+	0.162534i
$288$	93878.3	−	162602.i	0.0666936	−	0.115517i
$289$	−642160.	−	1.11225e6i	−0.452271	−	0.783357i
$290$	817804.	−	1.41648e6i	0.571024	−	0.989043i
$291$	−150703.	−	261026.i	−0.104325	−	0.180697i
$292$	736100.			0.505219
$293$	1.57450e6			1.07145			0.535727	−	0.844391i	$-0.320038\pi$
$293$	1.57450e6			1.07145			0.535727	+	0.844391i	$0.320038\pi$
$294$	256765.	+	444729.i	0.173247	+	0.300073i
$295$	2.17543e6	+	3.76796e6i	1.45543	+	2.52087i
$296$	455530.			0.302195
$297$	−1.34121e6			−0.882275
$298$	203205.	+	351962.i	0.132554	+	0.229591i
$299$	134790.	−	233462.i	0.0871923	−	0.151022i
$300$	−338294.	−	585942.i	−0.217016	−	0.375882i
$301$	106283.	−	184088.i	0.0676158	−	0.117114i
$302$	−762083.	+	1.31997e6i	−0.480823	+	0.832809i
$303$	−1.53167e6			−0.958429
$304$	−207588.	+	345226.i	−0.128830	+	0.214249i
$305$	−2.56495e6			−1.57881
$306$	−603035.	+	1.04449e6i	−0.368162	+	0.637676i
$307$	−664137.	+	1.15032e6i	−0.402172	+	0.696582i	−0.993988	−	0.109491i	$-0.965078\pi$
$307$	−664137.	+	1.15032e6i	−0.402172	+	0.696582i	0.591816	+	0.806073i	$0.298411\pi$
$308$	−44144.7	−	76460.9i	−0.0265156	−	0.0459264i
$309$	−704346.	+	1.21996e6i	−0.419653	+	0.726860i
$310$	−276335.	−	478625.i	−0.163317	−	0.282873i
$311$	2.54829e6			1.49399			0.746995	−	0.664830i	$-0.231496\pi$
$311$	2.54829e6			1.49399			0.746995	+	0.664830i	$0.231496\pi$
$312$	85614.3			0.0497920
$313$	−1.21398e6	−	2.10268e6i	−0.700408	−	1.21314i	−0.968323	−	0.249700i	$-0.919668\pi$
$313$	−1.21398e6	−	2.10268e6i	−0.700408	−	1.21314i	0.267915	−	0.963442i	$-0.413665\pi$
$314$	−713533.	−	1.23588e6i	−0.408404	−	0.707376i
$315$	230359.			0.130806
$316$	725419.			0.408669
$317$	−1.03419e6	−	1.79128e6i	−0.578035	−	1.00119i	−0.995705	−	0.0925870i	$-0.970486\pi$
$317$	−1.03419e6	−	1.79128e6i	−0.578035	−	1.00119i	0.417670	−	0.908599i	$-0.362847\pi$
$318$	25335.3	−	43882.1i	0.0140494	−	0.0243343i
$319$	−897983.	−	1.55535e6i	−0.494073	−	0.855760i
$320$	189929.	−	328966.i	0.103685	−	0.179588i
$321$	−102746.	+	177962.i	−0.0556548	+	0.0963970i
$322$	−84335.9			−0.0453286
$323$	1.33346e6	−	2.21759e6i	0.711169	−	1.18270i
$324$	306015.			0.161950
$325$	−474213.	+	821361.i	−0.249038	+	0.431346i
$326$	708322.	−	1.22685e6i	0.369136	−	0.639362i
$327$	173801.	+	301033.i	0.0898843	+	0.155684i
$328$	−618611.	+	1.07147e6i	−0.317492	+	0.549913i
$329$	88203.0	+	152772.i	0.0449256	+	0.0778134i
$330$	−1.16693e6			−0.589874
$331$	−1.75837e6			−0.882146			−0.441073	−	0.897471i	$-0.645402\pi$
$331$	−1.75837e6			−0.882146			−0.441073	+	0.897471i	$0.645402\pi$
$332$	−189543.	−	328299.i	−0.0943763	−	0.163465i
$333$	652532.	+	1.13022e6i	0.322472	+	0.558537i
$334$	−2.45067e6			−1.20204
$335$	−1.12969e6			−0.549978
$336$	−13391.9	−	23195.5i	−0.00647134	−	0.0112087i
$337$	1.02655e6	−	1.77805e6i	0.492388	−	0.852841i	−0.507574	−	0.861608i	$-0.669457\pi$
$337$	1.02655e6	−	1.77805e6i	0.492388	−	0.852841i	0.999962	+	0.00876740i	$0.00279079\pi$
$338$	682580.	+	1.18226e6i	0.324984	+	0.562888i
$339$	−46376.4	+	80326.3i	−0.0219178	+	0.0379628i
$340$	−1.22002e6	+	2.11314e6i	−0.572363	+	0.991361i
$341$	−606853.			−0.282617
$342$	−1.15391e6	−	20522.2i	−0.533464	−	0.00948767i
$343$	−452889.			−0.207853
$344$	502106.	−	869673.i	0.228770	−	0.396241i
$345$	−557336.	+	965335.i	−0.252098	+	0.436647i
$346$	−319146.	−	552777.i	−0.143318	−	0.248233i
$347$	1.97893e6	−	3.42761e6i	0.882282	−	1.52816i	0.0334848	−	0.999439i	$-0.489339\pi$
$347$	1.97893e6	−	3.42761e6i	0.882282	−	1.52816i	0.848797	−	0.528718i	$-0.177327\pi$
$348$	−272416.	−	471838.i	−0.120582	−	0.208855i
$349$	−1.77975e6			−0.782161			−0.391081	−	0.920356i	$-0.627899\pi$
$349$	−1.77975e6			−0.782161			−0.391081	+	0.920356i	$0.627899\pi$
$350$	296708.			0.129467
$351$	285173.	+	493935.i	0.123549	+	0.213994i
$352$	−208550.	−	361219.i	−0.0897125	−	0.155387i
$353$	517037.			0.220844			0.110422	−	0.993885i	$-0.464780\pi$
$353$	517037.			0.220844			0.110422	+	0.993885i	$0.464780\pi$
$354$	1.44930e6			0.614681
$355$	563783.	+	976501.i	0.237433	+	0.411246i
$356$	−921130.	+	1.59544e6i	−0.385209	+	0.667201i
$357$	86024.1	+	148998.i	0.0357231	+	0.0618743i
$358$	442145.	−	765817.i	0.182329	−	0.315804i
$359$	1.79989e6	−	3.11751e6i	0.737073	−	1.27665i	−0.216735	−	0.976231i	$-0.569541\pi$
$359$	1.79989e6	−	3.11751e6i	0.737073	−	1.27665i	0.953808	−	0.300418i	$-0.0971261\pi$
$360$	1.08827e6			0.442568
$361$	2.47453e6	+	88047.1i	0.999368	+	0.0355588i
$362$	−511602.			−0.205192
$363$	−18772.4	+	32514.8i	−0.00747746	+	0.0129513i
$364$	−18772.5	+	32514.9i	−0.00742623	+	0.0128626i
$365$	2.13328e6	+	3.69495e6i	0.838138	+	1.45170i
$366$	−427200.	+	739933.i	−0.166697	+	0.288728i
$367$	−1.59551e6	−	2.76351e6i	−0.618352	−	1.07102i	−0.989787	−	0.142557i	$-0.954467\pi$
$367$	−1.59551e6	−	2.76351e6i	−0.618352	−	1.07102i	0.371435	−	0.928459i	$-0.378866\pi$
$368$	−398422.			−0.153364
$369$	−3.54457e6			−1.35518
$370$	1.32016e6	+	2.28659e6i	0.501330	+	0.868329i
$371$	11110.5	+	19243.9i	0.00419080	+	0.00725869i
$372$	−184097.			−0.0689748
$373$	−1.28141e6			−0.476888			−0.238444	−	0.971156i	$-0.576637\pi$
$373$	−1.28141e6			−0.476888			−0.238444	+	0.971156i	$0.576637\pi$
$374$	1.33964e6	+	2.32032e6i	0.495231	+	0.857766i
$375$	841719.	−	1.45790e6i	0.309093	−	0.535365i
$376$	416691.	+	721730.i	0.152000	+	0.263272i
$377$	−381867.	+	661412.i	−0.138375	+	0.239673i
$378$	89214.4	−	154524.i	0.0321148	−	0.0556245i
$379$	2.65807e6			0.950534			0.475267	−	0.879842i	$-0.342351\pi$
$379$	2.65807e6			0.950534			0.475267	+	0.879842i	$0.342351\pi$
$380$	−2.33451e6	−	41519.4i	−0.829349	−	0.0147500i
$381$	1.89691e6			0.669476
$382$	957307.	−	1.65810e6i	0.335655	−	0.581371i
$383$	−2.45014e6	+	4.24376e6i	−0.853480	+	1.47827i	0.0245671	+	0.999698i	$0.492179\pi$
$383$	−2.45014e6	+	4.24376e6i	−0.853480	+	1.47827i	−0.878048	+	0.478573i	$0.841154\pi$
$384$	−63266.4	−	109581.i	−0.0218950	−	0.0379233i
$385$	255870.	−	443180.i	0.0879767	−	0.152380i
$386$	447198.	+	774569.i	0.152768	+	0.264601i
$387$	2.87700e6			0.976479
$388$	624438.			0.210577
$389$	2.03475e6	+	3.52430e6i	0.681770	+	1.18086i	0.974440	+	0.224647i	$0.0721228\pi$
$389$	2.03475e6	+	3.52430e6i	0.681770	+	1.18086i	−0.292671	+	0.956213i	$0.594544\pi$
$390$	248117.	+	429752.i	0.0826030	+	0.143073i
$391$	2.55930e6			0.846601
$392$	−1.06390e6			−0.349693
$393$	−1.09838e6	−	1.90246e6i	−0.358734	−	0.621346i
$394$	−687169.	+	1.19021e6i	−0.223009	+	0.386263i
$395$	2.10233e6	+	3.64133e6i	0.677965	+	1.17427i
$396$	597482.	−	1.03487e6i	0.191464	−	0.331625i
$397$	1.84561e6	−	3.19669e6i	0.587711	−	1.01795i	−0.406820	−	0.913508i	$-0.633363\pi$
$397$	1.84561e6	−	3.19669e6i	0.587711	−	1.01795i	0.994531	−	0.104437i	$-0.0333041\pi$
$398$	1.92997e6			0.610720
$399$	−84838.7	+	141090.i	−0.0266785	+	0.0443674i
$400$	1.40172e6			0.438037
$401$	756153.	−	1.30970e6i	0.234827	−	0.406733i	−0.724395	−	0.689385i	$-0.757881\pi$
$401$	756153.	−	1.30970e6i	0.234827	−	0.406733i	0.959223	+	0.282652i	$0.0912142\pi$
$402$	−188153.	+	325890.i	−0.0580691	+	0.100579i
$403$	129032.	+	223490.i	0.0395762	+	0.0685481i
$404$	1.58662e6	−	2.74811e6i	0.483637	−	0.837684i
$405$	886856.	+	1.53608e6i	0.268668	+	0.465346i
$406$	238928.			0.0719371
$407$	2.89919e6			0.867542
$408$	406397.	+	703901.i	0.120865	+	0.209344i
$409$	−2.42366e6	−	4.19791e6i	−0.716414	−	1.24087i	−0.962412	−	0.271595i	$-0.912449\pi$
$409$	−2.42366e6	−	4.19791e6i	−0.716414	−	1.24087i	0.245997	−	0.969271i	$-0.420885\pi$
$410$	−7.17115e6			−2.10683
$411$	1.91651e6			0.559637
$412$	−1.45923e6	−	2.52746e6i	−0.423526	−	0.733568i
$413$	−317785.	+	550420.i	−0.0916767	+	0.158789i
$414$	−570727.	−	988528.i	−0.163654	−	0.283458i
$415$	1.09862e6	−	1.90287e6i	0.313133	−	0.542362i
$416$	−88685.6	+	153608.i	−0.0251258	+	0.0435191i
$417$	352565.			0.0992884
$418$	−1.32118e6	+	2.19717e6i	−0.369846	+	0.615067i
$419$	−4.81922e6			−1.34104			−0.670520	−	0.741891i	$-0.733929\pi$
$419$	−4.81922e6			−1.34104			−0.670520	+	0.741891i	$0.733929\pi$
$420$	77621.7	−	134445.i	0.0214714	−	0.0371895i
$421$	135639.	−	234934.i	0.0372976	−	0.0646013i	−0.846774	−	0.531953i	$-0.821458\pi$
$421$	135639.	−	234934.i	0.0372976	−	0.0646013i	0.884072	+	0.467351i	$0.154792\pi$
$422$	−1.65611e6	−	2.86846e6i	−0.452696	−	0.784093i
$423$	−1.19379e6	+	2.06771e6i	−0.324398	+	0.561874i
$424$	52488.4	+	90912.5i	0.0141791	+	0.0245589i
$425$	−9.00406e6			−2.41805
$426$	375599.			0.100277
$427$	−187343.	−	324488.i	−0.0497242	−	0.0861248i
$428$	−212864.	−	368691.i	−0.0561685	−	0.0972867i
$429$	544886.			0.142943
$430$	5.82058e6			1.51808
$431$	−270464.	−	468458.i	−0.0701320	−	0.121472i	0.828827	−	0.559505i	$-0.189009\pi$
$431$	−270464.	−	468458.i	−0.0701320	−	0.121472i	−0.898959	+	0.438033i	$0.855675\pi$
$432$	421469.	−	730006.i	0.108657	−	0.188199i
$433$	−1.41642e6	−	2.45330e6i	−0.363054	−	0.628828i	0.625408	−	0.780298i	$-0.284933\pi$
$433$	−1.41642e6	−	2.45330e6i	−0.363054	−	0.628828i	−0.988462	+	0.151470i	$0.951599\pi$
$434$	40366.7	−	69917.2i	0.0102872	−	0.0178180i
$435$	1.57897e6	−	2.73485e6i	0.400083	−	0.692964i
$436$	−720145.			−0.181428
$437$	1.18659e6	+	2.14233e6i	0.297233	+	0.536639i
$438$	1.42122e6			0.353977
$439$	−511961.	+	886743.i	−0.126787	+	0.219602i	−0.922430	−	0.386164i	$-0.873800\pi$
$439$	−511961.	+	886743.i	−0.126787	+	0.219602i	0.795643	+	0.605766i	$0.207133\pi$
$440$	1.20879e6	−	2.09368e6i	0.297659	−	0.515560i
$441$	−1.52401e6	−	2.63966e6i	−0.373156	−	0.646325i
$442$	569680.	−	986714.i	0.138700	−	0.240235i
$443$	1.76654e6	+	3.05973e6i	0.427674	+	0.740754i	0.996666	−	0.0815897i	$-0.0259997\pi$
$443$	1.76654e6	+	3.05973e6i	0.427674	+	0.740754i	−0.568992	+	0.822343i	$0.692666\pi$
$444$	879509.			0.211730
$445$	−1.06780e7			−2.55618
$446$	1.51098e6	+	2.61709e6i	0.359683	+	0.622990i
$447$	392336.	+	679546.i	0.0928730	+	0.160861i
$448$	55489.3			0.0130621
$449$	529252.			0.123893			0.0619465	−	0.998079i	$-0.480269\pi$
$449$	529252.			0.123893			0.0619465	+	0.998079i	$0.480269\pi$
$450$	2.00792e6	+	3.47781e6i	0.467428	+	0.809609i
$451$	−3.93711e6	+	6.81927e6i	−0.911457	+	1.57869i
$452$	−96080.2	−	166416.i	−0.0221201	−	0.0383132i
$453$	−1.47138e6	+	2.54851e6i	−0.336884	+	0.583500i
$454$	2.00102e6	−	3.46587e6i	0.455630	−	0.789174i
$455$	−217617.			−0.0492793
$456$	−400798.	+	666541.i	−0.0902637	+	0.150112i
$457$	2.85284e6			0.638979			0.319489	−	0.947590i	$-0.396489\pi$
$457$	2.85284e6			0.638979			0.319489	+	0.947590i	$0.396489\pi$
$458$	420523.	−	728367.i	0.0936754	−	0.162251i
$459$	−2.70734e6	+	4.68926e6i	−0.599807	+	1.03890i
$460$	−1.15466e6	−	1.99993e6i	−0.254425	−	0.440677i
$461$	−1.78342e6	+	3.08898e6i	−0.390843	+	0.676960i	−0.992561	−	0.121749i	$-0.961150\pi$
$461$	−1.78342e6	+	3.08898e6i	−0.390843	+	0.676960i	0.601718	+	0.798709i	$0.294483\pi$
$462$	−85231.9	−	147626.i	−0.0185779	−	0.0321779i
$463$	197336.			0.0427813			0.0213907	−	0.999771i	$-0.493191\pi$
$463$	197336.			0.0427813			0.0213907	+	0.999771i	$0.493191\pi$
$464$	1.12875e6			0.243391
$465$	−533530.	−	924100.i	−0.114426	−	0.198192i
$466$	−810217.	−	1.40334e6i	−0.172837	−	0.299362i
$467$	2.41563e6			0.512552			0.256276	−	0.966604i	$-0.417504\pi$
$467$	2.41563e6			0.512552			0.256276	+	0.966604i	$0.417504\pi$
$468$	−508157.			−0.107247
$469$	−82511.8	−	142915.i	−0.0173214	−	0.0300016i
$470$	−2.41521e6	+	4.18327e6i	−0.504325	+	0.873517i
$471$	−1.37765e6	−	2.38615e6i	−0.286144	−	0.495617i
$472$	−1.50129e6	+	2.60031e6i	−0.310177	+	0.537243i
$473$	3.19562e6	−	5.53497e6i	0.656753	−	1.13753i
$474$	1.40059e6			0.286330
$475$	−4.17462e6	−	7.53708e6i	−0.848952	−	1.53274i
$476$	−356440.			−0.0721057
$477$	−150376.	+	260459.i	−0.0302609	+	0.0524135i
$478$	3.14295e6	−	5.44375e6i	0.629169	−	1.08975i
$479$	3.37480e6	+	5.84533e6i	0.672063	+	1.16405i	0.977318	+	0.211776i	$0.0679249\pi$
$479$	3.37480e6	+	5.84533e6i	0.672063	+	1.16405i	−0.305255	+	0.952271i	$0.598742\pi$
$480$	366703.	−	635148.i	0.0726459	−	0.125826i
$481$	−616439.	−	1.06770e6i	−0.121486	−	0.210420i
$482$	−3.82242e6			−0.749412
$483$	−162830.			−0.0317591
$484$	−38891.7	−	67362.5i	−0.00754647	−	0.0130709i
$485$	1.80967e6	+	3.13445e6i	0.349338	+	0.605071i
$486$	3.79137e6			0.728123
$487$	−10531.5			−0.00201219			−0.00100610	−	0.999999i	$-0.500320\pi$
$487$	−10531.5			−0.00201219			−0.00100610	+	0.999999i	$0.500320\pi$
$488$	−885051.	−	1.53295e6i	−0.168236	−	0.291393i
$489$	1.36758e6	−	2.36872e6i	0.258632	−	0.447963i
$490$	−3.08328e6	−	5.34039e6i	−0.580126	−	1.00481i
$491$	−211476.	+	366287.i	−0.0395874	+	0.0685674i	−0.885140	−	0.465324i	$-0.845938\pi$
$491$	−211476.	+	366287.i	−0.0395874	+	0.0685674i	0.845553	+	0.533892i	$0.179271\pi$
$492$	−1.19438e6	+	2.06872e6i	−0.222448	+	0.385291i
$493$	−7.25064e6			−1.34357
$494$	1.09008e6	+	19387.1i	0.200974	+	0.00357434i
$495$	6.92621e6			1.27052
$496$	190702.	−	330305.i	0.0348057	−	0.0602852i
$497$	−82357.0	+	142647.i	−0.0149558	+	0.0259042i
$498$	−365958.	−	633859.i	−0.0661239	−	0.114530i
$499$	−1.44908e6	+	2.50988e6i	−0.260520	+	0.451233i	−0.966380	−	0.257118i	$-0.917227\pi$
$499$	−1.44908e6	+	2.50988e6i	−0.260520	+	0.451233i	0.705860	+	0.708351i	$0.250561\pi$
$500$	1.74383e6	+	3.02040e6i	0.311946	+	0.540306i
$501$	−4.73161e6			−0.842199
$502$	−5.71518e6			−1.01221
$503$	−1.62618e6	−	2.81662e6i	−0.286581	−	0.496373i	0.686410	−	0.727215i	$-0.259185\pi$
$503$	−1.62618e6	−	2.81662e6i	−0.286581	−	0.496373i	−0.972991	+	0.230841i	$0.925852\pi$
$504$	79486.7	+	137675.i	0.0139386	+	0.0241423i
$505$	1.83926e7			3.20934
$506$	−2.53573e6			−0.440277
$507$	1.31788e6	+	2.28264e6i	0.227697	+	0.394382i
$508$	−1.96496e6	+	3.40341e6i	−0.337827	+	0.585134i
$509$	4.05317e6	+	7.02030e6i	0.693427	+	1.20105i	0.970708	+	0.240262i	$0.0772333\pi$
$509$	4.05317e6	+	7.02030e6i	0.693427	+	1.20105i	−0.277281	+	0.960789i	$0.589433\pi$
$510$	−2.35555e6	+	4.07993e6i	−0.401020	+	0.694588i
$511$	−311628.	+	539755.i	−0.0527939	+	0.0914417i
$512$	262144.			0.0441942
$513$	−5.18049e6	−	92135.2i	−0.869116	−	0.0154572i
$514$	6.57817e6			1.09824
$515$	8.45792e6	−	1.46496e7i	1.40522	−	2.43392i
$516$	969435.	−	1.67911e6i	0.160286	−	0.277623i
$517$	2.65200e6	+	4.59340e6i	0.436363	+	0.755802i
$518$	−192848.	+	334023.i	−0.0315785	+	0.0546956i
$519$	−616188.	−	1.06727e6i	−0.100414	−	0.173922i
$520$	−1.02807e6			−0.166731
$521$	8.35290e6			1.34816			0.674082	−	0.738656i	$-0.264539\pi$
$521$	8.35290e6			1.34816			0.674082	+	0.738656i	$0.264539\pi$
$522$	1.61690e6	+	2.80056e6i	0.259721	+	0.449850i
$523$	377576.	+	653980.i	0.0603601	+	0.104547i	0.894626	−	0.446815i	$-0.147442\pi$
$523$	377576.	+	653980.i	0.0603601	+	0.104547i	−0.834266	+	0.551362i	$0.814108\pi$
$524$	4.55115e6			0.724090
$525$	572866.			0.0907100
$526$	−1.78748e6	−	3.09600e6i	−0.281693	−	0.487907i
$527$	−1.22499e6	+	2.12174e6i	−0.192135	+	0.332787i
$528$	−402655.	−	697419.i	−0.0628562	−	0.108870i
$529$	2.00708e6	−	3.47637e6i	0.311836	−	0.540115i
$530$	−304231.	+	526944.i	−0.0470451	+	0.0814845i
$531$	−8.60221e6			−1.32396
$532$	−165259.	−	298368.i	−0.0253155	−	0.0457059i
$533$	3.34850e6			0.510544
$534$	−1.77846e6	+	3.08039e6i	−0.269893	+	0.467468i
$535$	1.23379e6	−	2.13700e6i	0.186363	−	0.322789i
$536$	−389804.	−	675161.i	−0.0586050	−	0.101507i
$537$	853666.	−	1.47859e6i	0.127747	−	0.221265i
$538$	3.19800e6	+	5.53909e6i	0.476346	+	0.825055i
$539$	−6.77113e6			−1.00390
$540$	4.88581e6			0.721028
$541$	−660689.	−	1.14435e6i	−0.0970518	−	0.168099i	0.813411	−	0.581689i	$-0.197608\pi$
$541$	−660689.	−	1.14435e6i	−0.0970518	−	0.168099i	−0.910463	+	0.413590i	$0.864275\pi$
$542$	−3.01578e6	−	5.22348e6i	−0.440962	−	0.763769i
$543$	−987770.			−0.143766
$544$	−1.68391e6			−0.243961
$545$	−2.08704e6	−	3.61486e6i	−0.300981	−	0.521315i
$546$	−36244.8	+	62777.8i	−0.00520312	+	0.00901207i
$547$	−462911.	−	801785.i	−0.0661499	−	0.114575i	0.831054	−	0.556192i	$-0.187738\pi$
$547$	−462911.	−	801785.i	−0.0661499	−	0.114575i	−0.897203	+	0.441617i	$0.854405\pi$
$548$	−1.98526e6	+	3.43857e6i	−0.282401	+	0.489133i
$549$	2.53562e6	−	4.39181e6i	0.359048	−	0.621889i
$550$	8.92114e6			1.25752
$551$	−3.36167e6	−	6.06934e6i	−0.471711	−	0.851652i
$552$	−769248.			−0.107453
$553$	−307106.	+	531923.i	−0.0427047	+	0.0739667i
$554$	−3.37663e6	+	5.84849e6i	−0.467422	+	0.809598i
$555$	2.54889e6	+	4.41481e6i	0.351252	+	0.608386i
$556$	−365212.	+	632566.i	−0.0501024	+	0.0867799i
$557$	6.32640e6	+	1.09576e7i	0.864009	+	1.49651i	0.868028	+	0.496516i	$0.165388\pi$
$557$	6.32640e6	+	1.09576e7i	0.864009	+	1.49651i	−0.00401820	+	0.999992i	$0.501279\pi$
$558$	1.09270e6			0.148564
$559$	−2.71787e6			−0.367874
$560$	160813.	+	278536.i	0.0216696	+	0.0375328i
$561$	2.58649e6	+	4.47993e6i	0.346979	+	0.600986i
$562$	−5.44413e6			−0.727089
$563$	3.01142e6			0.400406			0.200203	−	0.979754i	$-0.435840\pi$
$563$	3.01142e6			0.400406			0.200203	+	0.979754i	$0.435840\pi$
$564$	804522.	+	1.39347e6i	0.106498	+	0.184459i
$565$	556897.	−	964573.i	0.0733928	−	0.127120i
$566$	−3.52124e6	−	6.09896e6i	−0.462013	−	0.800230i
$567$	−129551.	+	224389.i	−0.0169233	+	0.0293119i
$568$	−389073.	+	673895.i	−0.0506012	+	0.0876438i
$569$	−1.15340e7			−1.49348			−0.746742	−	0.665114i	$-0.768383\pi$
$569$	−1.15340e7			−1.49348			−0.746742	+	0.665114i	$0.768383\pi$
$570$	−4.50733e6	−	80163.0i	−0.581075	−	0.0103344i
$571$	−2.07265e6			−0.266034			−0.133017	−	0.991114i	$-0.542466\pi$
$571$	−2.07265e6			−0.266034			−0.133017	+	0.991114i	$0.542466\pi$
$572$	−564433.	+	977627.i	−0.0721311	+	0.124935i
$573$	1.84831e6	−	3.20136e6i	0.235173	−	0.407332i
$574$	−523778.	−	907210.i	−0.0663540	−	0.114929i
$575$	4.26083e6	−	7.37997e6i	0.537433	−	0.930861i
$576$	375513.	+	650408.i	0.0471595	+	0.0816826i
$577$	−1.99741e6			−0.249762			−0.124881	−	0.992172i	$-0.539855\pi$
$577$	−1.99741e6			−0.249762			−0.124881	+	0.992172i	$0.539855\pi$
$578$	5.13728e6			0.639608
$579$	863422.	+	1.49549e6i	0.107035	+	0.185390i
$580$	3.27122e6	+	5.66592e6i	0.403775	+	0.699359i
$581$	320972.			0.0394482
$582$	1.20563e6			0.147539
$583$	334058.	+	578606.i	0.0407053	+	0.0705037i
$584$	−1.47220e6	+	2.54993e6i	−0.178622	+	0.309382i
$585$	−1.47268e6	−	2.55076e6i	−0.177918	−	0.308163i
$586$	−3.14900e6	+	5.45422e6i	−0.378816	+	0.656129i
$587$	−2.96558e6	+	5.13654e6i	−0.355234	+	0.615284i	−0.987158	−	0.159747i	$-0.948932\pi$
$587$	−2.96558e6	+	5.13654e6i	−0.355234	+	0.615284i	0.631924	+	0.775030i	$0.282266\pi$
$588$	−2.05412e6			−0.245009
$589$	−2.34401e6	−	41688.3i	−0.278401	−	0.00495137i
$590$	−1.74035e7			−2.05829
$591$	−1.32674e6	+	2.29799e6i	−0.156249	+	0.270632i
$592$	−911060.	+	1.57800e6i	−0.106842	+	0.185056i
$593$	926869.	+	1.60538e6i	0.108238	+	0.187474i	0.915057	−	0.403325i	$-0.132146\pi$
$593$	926869.	+	1.60538e6i	0.108238	+	0.187474i	−0.806818	+	0.590800i	$0.798812\pi$
$594$	2.68241e6	−	4.64607e6i	0.311931	−	0.540281i
$595$	−1.03299e6	−	1.78920e6i	−0.119620	−	0.207189i
$596$	−1.62564e6			−0.187460
$597$	3.72626e6			0.427895
$598$	539158.	+	933849.i	0.0616543	+	0.106788i
$599$	−3.08767e6	−	5.34800e6i	−0.351612	−	0.609010i	0.634920	−	0.772578i	$-0.281033\pi$
$599$	−3.08767e6	−	5.34800e6i	−0.351612	−	0.609010i	−0.986532	+	0.163568i	$0.947700\pi$
$600$	2.70635e6			0.306906
$601$	1.98620e6			0.224303			0.112152	−	0.993691i	$-0.464226\pi$
$601$	1.98620e6			0.224303			0.112152	+	0.993691i	$0.464226\pi$
$602$	425133.	+	736351.i	0.0478116	+	0.0828121i
$603$	1.11677e6	−	1.93429e6i	0.125074	−	0.216635i
$604$	−3.04833e6	−	5.27986e6i	−0.339993	−	0.588885i
$605$	225423.	−	390444.i	0.0250386	−	0.0433681i
$606$	3.06335e6	−	5.30588e6i	0.338856	−	0.586916i
$607$	−9.42545e6			−1.03832			−0.519159	−	0.854678i	$-0.673755\pi$
$607$	−9.42545e6			−1.03832			−0.519159	+	0.854678i	$0.673755\pi$
$608$	−780722.	−	1.40956e6i	−0.0856520	−	0.154641i
$609$	461308.			0.0504020
$610$	5.12990e6	−	8.88525e6i	0.558193	−	0.966819i
$611$	1.12776e6	−	1.95334e6i	0.122212	−	0.211678i
$612$	−2.41214e6	−	4.17795e6i	−0.260330	−	0.450905i
$613$	2.82659e6	−	4.89581e6i	0.303817	−	0.526227i	−0.673180	−	0.739479i	$-0.735072\pi$
$613$	2.82659e6	−	4.89581e6i	0.303817	−	0.526227i	0.976997	+	0.213252i	$0.0684055\pi$
$614$	−2.65655e6	−	4.60127e6i	−0.284378	−	0.492558i
$615$	−1.38456e7			−1.47613
$616$	353158.			0.0374988
$617$	5.05780e6	+	8.76036e6i	0.534871	+	0.926423i	0.999170	+	0.0407444i	$0.0129729\pi$
$617$	5.05780e6	+	8.76036e6i	0.534871	+	0.926423i	−0.464299	+	0.885678i	$0.653694\pi$
$618$	−2.81739e6	−	4.87986e6i	−0.296739	−	0.513968i
$619$	1.82708e6			0.191659			0.0958297	−	0.995398i	$-0.469450\pi$
$619$	1.82708e6			0.191659			0.0958297	+	0.995398i	$0.469450\pi$
$620$	2.21068e6			0.230965
$621$	−2.56229e6	−	4.43802e6i	−0.266624	−	0.461807i
$622$	−5.09658e6	+	8.82753e6i	−0.528205	+	0.914878i
$623$	−779920.	−	1.35086e6i	−0.0805063	−	0.139441i
$624$	−171229.	+	296577.i	−0.0176041	+	0.0304913i
$625$	−1.55212e6	+	2.68834e6i	−0.158937	+	0.275286i
$626$	9.71185e6			0.990527
$627$	−2.55085e6	+	4.24215e6i	−0.259129	+	0.430941i
$628$	5.70826e6			0.577570
$629$	5.85227e6	−	1.01364e7i	0.589791	−	1.02155i
$630$	−460718.	+	797987.i	−0.0462470	+	0.0801022i
$631$	2.21793e6	+	3.84157e6i	0.221756	+	0.384092i	0.955341	−	0.295505i	$-0.0954879\pi$
$631$	2.21793e6	+	3.84157e6i	0.221756	+	0.384092i	−0.733585	+	0.679597i	$0.762155\pi$
$632$	−1.45084e6	+	2.51293e6i	−0.144486	+	0.250257i
$633$	−3.19751e6	−	5.53824e6i	−0.317177	−	0.549367i
$634$	8.27356e6			0.817465
$635$	−2.27785e7			−2.24177
$636$	101341.	+	175528.i	0.00993444	+	0.0172070i
$637$	1.43971e6	+	2.49365e6i	0.140581	+	0.243493i
$638$	7.18386e6			0.698725
$639$	−2.22934e6			−0.215985
$640$	759715.	+	1.31587e6i	0.0733164	+	0.126988i
$641$	−3.19408e6	+	5.53230e6i	−0.307044	+	0.531815i	−0.977714	−	0.209940i	$-0.932673\pi$
$641$	−3.19408e6	+	5.53230e6i	−0.307044	+	0.531815i	0.670671	+	0.741755i	$0.266006\pi$
$642$	−410985.	−	711846.i	−0.0393539	−	0.0681630i
$643$	829278.	−	1.43635e6i	0.0790993	−	0.137004i	−0.823762	−	0.566935i	$-0.808129\pi$
$643$	829278.	−	1.43635e6i	0.0790993	−	0.137004i	0.902862	+	0.429931i	$0.141462\pi$
$644$	168672.	−	292148.i	0.0160261	−	0.0277580i
$645$	1.12380e7			1.06363
$646$	5.01504e6	+	9.05441e6i	0.472817	+	0.853648i
$647$	8.62286e6			0.809824			0.404912	−	0.914356i	$-0.367302\pi$
$647$	8.62286e6			0.809824			0.404912	+	0.914356i	$0.367302\pi$
$648$	−612030.	+	1.06007e6i	−0.0572578	+	0.0991735i
$649$	−9.55486e6	+	1.65495e7i	−0.890456	+	1.54232i
$650$	−1.89685e6	−	3.28545e6i	−0.176096	−	0.305008i
$651$	77937.6	−	134992.i	0.00720766	−	0.0124840i
$652$	2.83329e6	+	4.90740e6i	0.261019	+	0.452097i
$653$	1.73010e7			1.58777			0.793887	−	0.608065i	$-0.208054\pi$
$653$	1.73010e7			1.58777			0.793887	+	0.608065i	$0.208054\pi$
$654$	−1.39041e6			−0.127116
$655$	1.31896e7	+	2.28451e7i	1.20124	+	2.08060i
$656$	−2.47445e6	−	4.28586e6i	−0.224501	−	0.388847i
$657$	−8.43552e6			−0.762427
$658$	−705624.			−0.0635344
$659$	1.99931e6	+	3.46291e6i	0.179336	+	0.310618i	0.941653	−	0.336585i	$-0.109272\pi$
$659$	1.99931e6	+	3.46291e6i	0.179336	+	0.310618i	−0.762318	+	0.647203i	$0.775939\pi$
$660$	2.33385e6	−	4.04235e6i	0.208552	−	0.361222i
$661$	−6.01867e6	−	1.04246e7i	−0.535793	−	0.928021i	−0.999125	−	0.0418356i	$-0.986679\pi$
$661$	−6.01867e6	−	1.04246e7i	−0.535793	−	0.928021i	0.463332	−	0.886185i	$-0.346654\pi$
$662$	3.51674e6	−	6.09118e6i	0.311886	−	0.540202i
$663$	1.09990e6	−	1.90509e6i	0.0971785	−	0.168318i
$664$	1.51635e6			0.133468
$665$	1.01876e6	−	1.69423e6i	0.0893342	−	0.148566i
$666$	−5.22026e6			−0.456044
$667$	3.43109e6	−	5.94282e6i	0.298619	−	0.517223i
$668$	4.90135e6	−	8.48938e6i	0.424986	−	0.736097i
$669$	2.91730e6	+	5.05291e6i	0.252009	+	0.436492i
$670$	2.25937e6	−	3.91335e6i	0.194447	−	0.336792i
$671$	−5.63284e6	−	9.75637e6i	−0.482971	−	0.836531i
$672$	107135.			0.00915186
$673$	5.14140e6			0.437566			0.218783	−	0.975774i	$-0.429791\pi$
$673$	5.14140e6			0.437566			0.218783	+	0.975774i	$0.429791\pi$
$674$	4.10622e6	+	7.11218e6i	0.348171	+	0.603050i
$675$	9.01460e6	+	1.56137e7i	0.761530	+	1.31901i
$676$	−5.46064e6			−0.459596
$677$	9.45731e6			0.793042			0.396521	−	0.918026i	$-0.370217\pi$
$677$	9.45731e6			0.793042			0.396521	+	0.918026i	$0.370217\pi$
$678$	−185506.	−	321305.i	−0.0154983	−	0.0268438i
$679$	−264356.	+	457877.i	−0.0220046	+	0.0381131i
$680$	−4.88010e6	−	8.45258e6i	−0.404721	−	0.700998i
$681$	3.86345e6	−	6.69169e6i	0.319233	−	0.552927i
$682$	1.21371e6	−	2.10220e6i	0.0999201	−	0.173067i
$683$	1.30968e6			0.107427			0.0537136	−	0.998556i	$-0.482894\pi$
$683$	1.30968e6			0.107427			0.0537136	+	0.998556i	$0.482894\pi$
$684$	2.37890e6	−	3.95620e6i	0.194418	−	0.323324i
$685$	−2.30138e7			−1.87397
$686$	905778.	−	1.56885e6i	0.0734871	−	0.127283i
$687$	811919.	−	1.40629e6i	0.0656328	−	0.113679i
$688$	2.00842e6	+	3.47869e6i	0.161765	+	0.280185i
$689$	142058.	−	246052.i	0.0114003	−	0.0197460i
$690$	−2.22935e6	−	3.86134e6i	−0.178260	−	0.308756i
$691$	5.70771e6			0.454744			0.227372	−	0.973808i	$-0.426987\pi$
$691$	5.70771e6			0.454744			0.227372	+	0.973808i	$0.426987\pi$
$692$	2.55317e6			0.202682
$693$	505887.	+	876222.i	0.0400148	+	0.0693077i
$694$	7.91573e6	+	1.37105e7i	0.623868	+	1.08057i
$695$	−4.23366e6			−0.332471
$696$	2.17933e6			0.170529
$697$	1.58948e7	+	2.75306e7i	1.23929	+	2.14652i
$698$	3.55951e6	−	6.16525e6i	0.276536	−	0.478974i
$699$	−1.56432e6	−	2.70948e6i	−0.121097	−	0.209745i
$700$	−593417.	+	1.02783e6i	−0.0457736	+	0.0792821i
$701$	5.28777e6	−	9.15869e6i	0.406423	−	0.703945i	−0.588063	−	0.808815i	$-0.700109\pi$
$701$	5.28777e6	−	9.15869e6i	0.406423	−	0.703945i	0.994486	+	0.104870i	$0.0334427\pi$
$702$	−2.28139e6			−0.174725
$703$	1.11983e7	+	199162.i	0.854602	+	0.0151991i
$704$	1.66840e6			0.126873
$705$	−4.66314e6	+	8.07680e6i	−0.353351	+	0.612021i
$706$	−1.03407e6	+	1.79107e6i	−0.0780800	+	0.135239i
$707$	1.34339e6	+	2.32682e6i	0.101077	+	0.175071i
$708$	−2.89860e6	+	5.02052e6i	−0.217323	+	0.376414i
$709$	−4.57650e6	−	7.92674e6i	−0.341915	−	0.592214i	0.642873	−	0.765973i	$-0.277742\pi$
$709$	−4.57650e6	−	7.92674e6i	−0.341915	−	0.592214i	−0.984788	+	0.173758i	$0.944409\pi$
$710$	−4.51027e6			−0.335781
$711$	−8.31312e6			−0.616723
$712$	−3.68452e6	−	6.38178e6i	−0.272384	−	0.471782i
$713$	−1.15936e6	−	2.00807e6i	−0.0854070	−	0.147929i
$714$	−688193.			−0.0505201
$715$	−6.54310e6			−0.478650
$716$	1.76858e6	+	3.06327e6i	0.128926	+	0.223307i
$717$	6.06821e6	−	1.05105e7i	0.440822	−	0.763525i
$718$	7.19957e6	+	1.24700e7i	0.521189	+	0.902727i
$719$	3.66367e6	−	6.34567e6i	0.264298	−	0.457778i	−0.703081	−	0.711110i	$-0.748193\pi$
$719$	3.66367e6	−	6.34567e6i	0.264298	−	0.457778i	0.967380	+	0.253331i	$0.0815263\pi$
$720$	−2.17654e6	+	3.76987e6i	−0.156471	+	0.271016i
$721$	2.47105e6			0.177029
$722$	−5.25407e6	+	8.39594e6i	−0.375105	+	0.599413i
$723$	−7.38009e6			−0.525069
$724$	1.02320e6	−	1.77224e6i	0.0725464	−	0.125654i
$725$	−1.20712e7	+	2.09079e7i	−0.852912	+	1.47729i
$726$	−75089.8	−	130059.i	−0.00528736	−	0.00915798i
$727$	−6.53539e6	+	1.13196e7i	−0.458602	+	0.794321i	−0.998887	−	0.0471604i	$-0.984983\pi$
$727$	−6.53539e6	+	1.13196e7i	−0.458602	+	0.794321i	0.540286	+	0.841482i	$0.318316\pi$
$728$	−75090.0	−	130060.i	−0.00525114	−	0.00909524i
$729$	2.67253e6			0.186254
$730$	−1.70662e7			−1.18531
$731$	−1.29013e7	−	2.23457e7i	−0.892975	−	1.54668i
$732$	−1.70880e6	−	2.95973e6i	−0.117873	−	0.204162i
$733$	−2.64582e6			−0.181886			−0.0909431	−	0.995856i	$-0.528988\pi$
$733$	−2.64582e6			−0.181886			−0.0909431	+	0.995856i	$0.528988\pi$
$734$	1.27641e7			0.874481
$735$	−5.95300e6	−	1.03109e7i	−0.406460	−	0.704009i
$736$	796844.	−	1.38017e6i	0.0542224	−	0.0939159i
$737$	−2.48088e6	−	4.29701e6i	−0.168243	−	0.291406i
$738$	7.08913e6	−	1.22787e7i	0.479129	−	0.829875i
$739$	966766.	−	1.67449e6i	0.0651194	−	0.112790i	−0.831628	−	0.555334i	$-0.812591\pi$
$739$	966766.	−	1.67449e6i	0.0651194	−	0.112790i	0.896747	+	0.442544i	$0.145924\pi$
$740$	−1.05613e7			−0.708987
$741$	2.10466e6	+	37431.4i	0.140811	+	0.00250432i
$742$	−88883.7			−0.00592669
$743$	−256361.	+	444030.i	−0.0170365	+	0.0295080i	−0.874418	−	0.485173i	$-0.838756\pi$
$743$	−256361.	+	444030.i	−0.0170365	+	0.0295080i	0.857381	+	0.514681i	$0.172090\pi$
$744$	368195.	−	637732.i	0.0243863	−	0.0422383i
$745$	−4.71124e6	−	8.16011e6i	−0.310989	−	0.538649i
$746$	2.56282e6	−	4.43894e6i	0.168605	−	0.292033i
$747$	2.17212e6	+	3.76222e6i	0.142424	+	0.246685i
$748$	−1.07171e7			−0.700363
$749$	360463.			0.0234778
$750$	3.36688e6	+	5.83160e6i	0.218562	+	0.378560i
$751$	−9.12644e6	−	1.58075e7i	−0.590475	−	1.02273i	−0.994168	−	0.107839i	$-0.965607\pi$
$751$	−9.12644e6	−	1.58075e7i	−0.590475	−	1.02273i	0.403693	−	0.914894i	$-0.367726\pi$
$752$	−3.33353e6			−0.214961
$753$	−1.10345e7			−0.709196
$754$	−1.52747e6	−	2.64565e6i	−0.0978460	−	0.169474i
$755$	1.76686e7	−	3.06030e7i	1.12807	−	1.95387i
$756$	356858.	+	618095.i	0.0227086	+	0.0393325i
$757$	−4.03976e6	+	6.99707e6i	−0.256222	+	0.443789i	−0.965227	−	0.261415i	$-0.915811\pi$
$757$	−4.03976e6	+	6.99707e6i	−0.256222	+	0.443789i	0.709005	+	0.705203i	$0.249144\pi$
$758$	−5.31613e6	+	9.20781e6i	−0.336065	+	0.582081i
$759$	−4.89583e6			−0.308476
$760$	4.81285e6	−	8.00395e6i	0.302252	−	0.502655i
$761$	−2.07126e7			−1.29650			−0.648251	−	0.761427i	$-0.724499\pi$
$761$	−2.07126e7			−1.29650			−0.648251	+	0.761427i	$0.724499\pi$
$762$	−3.79382e6	+	6.57110e6i	−0.236695	+	0.409968i
$763$	304873.	−	528056.i	0.0189587	−	0.0328374i
$764$	3.82923e6	+	6.63242e6i	0.237344	+	0.411091i
$765$	1.39812e7	−	2.42161e7i	0.863754	−	1.49607i
$766$	−9.80055e6	−	1.69751e7i	−0.603502	−	1.04530i
$767$	8.12639e6			0.498780
$768$	506131.			0.0309642
$769$	−801219.	−	1.38775e6i	−0.0488579	−	0.0846244i	0.840562	−	0.541715i	$-0.182225\pi$
$769$	−801219.	−	1.38775e6i	−0.0488579	−	0.0846244i	−0.889420	+	0.457091i	$0.848891\pi$
$770$	1.02348e6	+	1.77272e6i	0.0622089	+	0.107749i
$771$	1.27007e7			0.769472
$772$	−3.57758e6			−0.216046
$773$	−7.14089e6	−	1.23684e7i	−0.429837	−	0.744499i	0.567022	−	0.823703i	$-0.308095\pi$
$773$	−7.14089e6	−	1.23684e7i	−0.429837	−	0.744499i	−0.996858	+	0.0792040i	$0.974762\pi$
$774$	−5.75401e6	+	9.96623e6i	−0.345237	+	0.597969i
$775$	4.07882e6	+	7.06473e6i	0.243939	+	0.422514i
$776$	−1.24888e6	+	2.16312e6i	−0.0744501	+	0.128951i
$777$	−372340.	+	644912.i	−0.0221252	+	0.0383220i
$778$	−1.62780e7			−0.964168
$779$	−1.56758e7	+	2.60694e7i	−0.925520	+	1.53917i
$780$	−1.98494e6			−0.116818
$781$	−2.47623e6	+	4.28896e6i	−0.145266	+	0.251608i
$782$	−5.11860e6	+	8.86567e6i	−0.299319	+	0.518435i
$783$	7.25913e6	+	1.25732e7i	0.423136	+	0.732893i
$784$	2.12780e6	−	3.68547e6i	0.123635	−	0.214142i
$785$	1.65430e7	+	2.86534e7i	0.958166	+	1.65959i
$786$	8.78707e6			0.507327
$787$	3.41257e7			1.96401			0.982007	−	0.188847i	$-0.0604750\pi$
$787$	3.41257e7			1.96401			0.982007	+	0.188847i	$0.0604750\pi$
$788$	−2.74868e6	−	4.76085e6i	−0.157691	−	0.273129i
$789$	−3.45115e6	−	5.97757e6i	−0.197366	−	0.341848i
$790$	−1.68186e7			−0.958787
$791$	162702.			0.00924595
$792$	2.38993e6	+	4.13947e6i	0.135385	+	0.234494i
$793$	−2.39536e6	+	4.14889e6i	−0.135266	+	0.234287i
$794$	7.38244e6	+	1.27868e7i	0.415574	+	0.719796i
$795$	−587391.	+	1.01739e6i	−0.0329617	+	0.0570913i
$796$	−3.85994e6	+	6.68560e6i	−0.215922	+	0.373988i
$797$	−8.99775e6			−0.501751			−0.250875	−	0.968019i	$-0.580718\pi$
$797$	−8.99775e6			−0.501751			−0.250875	+	0.968019i	$0.580718\pi$
$798$	−319072.	−	576070.i	−0.0177371	−	0.0320234i
$799$	2.14132e7			1.18663
$800$	−2.80344e6	+	4.85569e6i	−0.154869	+	0.268242i
$801$	1.05559e7	−	1.82834e7i	0.581319	−	1.00687i
$802$	3.02461e6	+	5.23878e6i	0.166048	+	0.287604i
$803$	−9.36971e6	+	1.62288e7i	−0.512788	+	0.888174i
$804$	−752610.	−	1.30356e6i	−0.0410610	−	0.0711198i
$805$	1.95530e6			0.106347
$806$	−1.03226e6			−0.0559693
$807$	6.17449e6	+	1.06945e7i	0.333747	+	0.578067i
$808$	6.34648e6	+	1.09924e7i	0.341983	+	0.592332i
$809$	7.88214e6			0.423421			0.211711	−	0.977332i	$-0.432097\pi$
$809$	7.88214e6			0.423421			0.211711	+	0.977332i	$0.432097\pi$
$810$	−7.09485e6			−0.379954
$811$	4.74871e6	+	8.22500e6i	0.253526	+	0.439121i	0.964494	−	0.264104i	$-0.0850762\pi$
$811$	4.74871e6	+	8.22500e6i	0.253526	+	0.439121i	−0.710968	+	0.703225i	$0.751743\pi$
$812$	−477857.	+	827672.i	−0.0254336	+	0.0440523i
$813$	−5.82268e6	−	1.00852e7i	−0.308956	−	0.535127i
$814$	−5.79838e6	+	1.00431e7i	−0.306722	+	0.531259i
$815$	−1.64222e7	+	2.84441e7i	−0.866039	+	1.50002i
$816$	−3.25118e6			−0.170929
$817$	1.27235e7	−	2.11597e7i	0.666886	−	1.10906i
$818$	1.93893e7			1.01316
$819$	215128.	−	372613.i	0.0112070	−	0.0194110i
$820$	1.43423e7	−	2.48416e7i	0.744876	−	1.29016i
$821$	−1.28242e7	−	2.22122e7i	−0.664008	−	1.15010i	−0.979553	−	0.201185i	$-0.935521\pi$
$821$	−1.28242e7	−	2.22122e7i	−0.664008	−	1.15010i	0.315545	−	0.948911i	$-0.397813\pi$
$822$	−3.83302e6	+	6.63898e6i	−0.197862	+	0.342706i
$823$	−2.31688e6	−	4.01296e6i	−0.119235	−	0.206521i	0.800230	−	0.599694i	$-0.204711\pi$
$823$	−2.31688e6	−	4.01296e6i	−0.119235	−	0.206521i	−0.919465	+	0.393172i	$0.871378\pi$
$824$	1.16738e7			0.598956
$825$	1.72244e7			0.881067
$826$	−1.27114e6	−	2.20168e6i	−0.0648252	−	0.112281i
$827$	−1.17966e7	−	2.04323e7i	−0.599780	−	1.03885i	−0.992853	−	0.119342i	$-0.961921\pi$
$827$	−1.17966e7	−	2.04323e7i	−0.599780	−	1.03885i	0.393073	−	0.919507i	$-0.371412\pi$
$828$	4.56581e6			0.231442
$829$	−2.79814e7			−1.41411			−0.707054	−	0.707160i	$-0.749976\pi$
$829$	−2.79814e7			−1.41411			−0.707054	+	0.707160i	$0.749976\pi$
$830$	4.39450e6	+	7.61149e6i	0.221419	+	0.383508i
$831$	−6.51939e6	+	1.12919e7i	−0.327495	+	0.567237i
$832$	−354742.	−	614432.i	−0.0177666	−	0.0307727i
$833$	−1.36681e7	+	2.36739e7i	−0.682491	+	1.18211i
$834$	−705129.	+	1.22132e6i	−0.0351038	+	0.0608015i
$835$	5.68180e7			2.82014
$836$	−4.96885e6	−	8.97103e6i	−0.245890	−	0.443942i
$837$	4.90569e6			0.242040
$838$	9.63845e6	−	1.66943e7i	0.474130	−	0.821216i
$839$	1.78055e7	−	3.08400e7i	0.873271	−	1.51255i	0.0146769	−	0.999892i	$-0.495328\pi$
$839$	1.78055e7	−	3.08400e7i	0.873271	−	1.51255i	0.858594	−	0.512657i	$-0.171339\pi$
$840$	310487.	+	537779.i	0.0151826	+	0.0262970i
$841$	535104.	−	926828.i	0.0260885	−	0.0451865i
$842$	542557.	+	939737.i	0.0263734	+	0.0456800i
$843$	−1.05112e7			−0.509428
$844$	1.32488e7			0.640209
$845$	−1.58254e7	−	2.74104e7i	−0.762452	−	1.32061i
$846$	−4.77518e6	−	8.27085e6i	−0.229384	−	0.397305i
$847$	65859.2			0.00315434
$848$	−419907.			−0.0200523
$849$	−6.79858e6	−	1.17755e7i	−0.323705	−	0.560673i
$850$	1.80081e7	−	3.11910e7i	0.854911	−	1.48075i
$851$	5.53873e6	+	9.59336e6i	0.262172	+	0.454095i
$852$	−751199.	+	1.30111e6i	−0.0354532	+	0.0614068i
$853$	−3.82673e6	+	6.62809e6i	−0.180076	+	0.311900i	−0.941906	−	0.335876i	$-0.890968\pi$
$853$	−3.82673e6	+	6.62809e6i	−0.180076	+	0.311900i	0.761830	+	0.647776i	$0.224301\pi$
$854$	1.49874e6			0.0703206
$855$	2.67529e7	+	475801.i	1.25157	+	0.0222592i
$856$	1.70291e6			0.0794342
$857$	−1.66066e7	+	2.87634e7i	−0.772374	+	1.33779i	0.163885	+	0.986479i	$0.447597\pi$
$857$	−1.66066e7	+	2.87634e7i	−0.772374	+	1.33779i	−0.936259	+	0.351311i	$0.885736\pi$
$858$	−1.08977e6	+	1.88754e6i	−0.0505380	+	0.0875343i
$859$	−8.41483e6	−	1.45749e7i	−0.389101	−	0.673943i	0.603228	−	0.797569i	$-0.293881\pi$
$859$	−8.41483e6	−	1.45749e7i	−0.389101	−	0.673943i	−0.992329	+	0.123626i	$0.960548\pi$
$860$	−1.16412e7	+	2.01631e7i	−0.536723	+	0.929631i
$861$	−1.01128e6	−	1.75158e6i	−0.0464903	−	0.0805236i
$862$	2.16371e6			0.0991817
$863$	−3.06089e6			−0.139901			−0.0699505	−	0.997550i	$-0.522284\pi$
$863$	−3.06089e6			−0.139901			−0.0699505	+	0.997550i	$0.522284\pi$
$864$	1.68588e6	+	2.92002e6i	0.0768319	+	0.133077i
$865$	7.39930e6	+	1.28160e7i	0.336241	+	0.582386i
$866$	1.13313e7			0.513436
$867$	9.91875e6			0.448135
$868$	161467.	+	279669.i	0.00727418	+	0.0125993i
$869$	−9.23376e6	+	1.59933e7i	−0.414791	+	0.718439i
$870$	6.31587e6	+	1.09394e7i	0.282901	+	0.489999i
$871$	−1.05499e6	+	1.82730e6i	−0.0471199	+	0.0816141i
$872$	1.44029e6	−	2.49465e6i	0.0641444	−	0.111101i
$873$	−7.15591e6			−0.317782
$874$	−9.79442e6	−	174194.i	−0.433711	−	0.00771355i
$875$	−2.95300e6			−0.130390
$876$	−2.84243e6	+	4.92324e6i	−0.125150	+	0.216766i
$877$	7.48891e6	−	1.29712e7i	0.328791	−	0.569482i	−0.653481	−	0.756943i	$-0.726692\pi$
$877$	7.48891e6	−	1.29712e7i	0.328791	−	0.569482i	0.982272	+	0.187460i	$0.0600256\pi$
$878$	−2.04785e6	−	3.54697e6i	−0.0896522	−	0.155282i
$879$	−6.07989e6	+	1.05307e7i	−0.265414	+	0.459710i
$880$	4.83515e6	+	8.37473e6i	0.210477	+	0.364556i
$881$	4.06522e7			1.76459			0.882295	−	0.470697i	$-0.155997\pi$
$881$	4.06522e7			1.76459			0.882295	+	0.470697i	$0.155997\pi$
$882$	1.21921e7			0.527722
$883$	−1.16198e7	−	2.01261e7i	−0.501529	−	0.868674i	−0.999998	−	0.00176685i	$-0.999438\pi$
$883$	−1.16198e7	−	2.01261e7i	−0.501529	−	0.868674i	0.498469	−	0.866907i	$-0.333896\pi$
$884$	2.27872e6	+	3.94686e6i	0.0980754	+	0.169872i
$885$	−3.36015e7			−1.44212
$886$	−1.41323e7			−0.604823
$887$	4.16037e6	+	7.20597e6i	0.177551	+	0.307527i	0.941041	−	0.338292i	$-0.109849\pi$
$887$	4.16037e6	+	7.20597e6i	0.177551	+	0.307527i	−0.763490	+	0.645819i	$0.776516\pi$
$888$	−1.75902e6	+	3.04671e6i	−0.0748580	+	0.129658i
$889$	−1.66373e6	−	2.88167e6i	−0.0706039	−	0.122290i
$890$	2.13561e7	−	3.69898e7i	0.903747	−	1.56534i
$891$	−3.89522e6	+	6.74672e6i	−0.164376	+	0.284707i
$892$	−1.20878e7			−0.508669
$893$	9.92798e6	+	1.79245e7i	0.416613	+	0.752174i
$894$	−3.13869e6			−0.131342
$895$	−1.02510e7	+	1.77552e7i	−0.427767	+	0.740915i
$896$	−110979.	+	192221.i	−0.00461816	+	0.00799889i
$897$	1.04097e6	+	1.80302e6i	0.0431975	+	0.0748202i
$898$	−1.05850e6	+	1.83338e6i	−0.0438028	+	0.0758686i
$899$	3.28453e6	+	5.68897e6i	0.135542	+	0.234766i
$900$	−1.60633e7			−0.661043
$901$	2.69731e6			0.110693
$902$	−1.57484e7	−	2.72771e7i	−0.644497	−	1.11630i
$903$	820820.	+	1.42170e6i	0.0334987	+	0.0580215i
$904$	768641.			0.0312826
$905$	1.18613e7			0.481406
$906$	−5.88553e6	−	1.01940e7i	−0.238213	−	0.412597i
$907$	−9.07944e6	+	1.57260e7i	−0.366472	+	0.634748i	−0.989011	−	0.147840i	$-0.952768\pi$
$907$	−9.07944e6	+	1.57260e7i	−0.366472	+	0.634748i	0.622539	+	0.782589i	$0.286101\pi$
$908$	8.00408e6	+	1.38635e7i	0.322179	+	0.558030i
$909$	−1.81823e7	+	3.14926e7i	−0.729858	+	1.26415i
$910$	435234.	−	753848.i	0.0174229	−	0.0301773i
$911$	−7.89177e6			−0.315049			−0.157525	−	0.987515i	$-0.550351\pi$
$911$	−7.89177e6			−0.315049			−0.157525	+	0.987515i	$0.550351\pi$
$912$	−1.50737e6	−	2.72149e6i	−0.0600113	−	0.108348i
$913$	9.65068e6			0.383161
$914$	−5.70567e6	+	9.88251e6i	−0.225913	+	0.391293i
$915$	9.90450e6	−	1.71551e7i	0.391093	−	0.677393i
$916$	1.68209e6	+	2.91347e6i	0.0662385	+	0.114729i
$917$	−1.92673e6	+	3.33719e6i	−0.0756653	+	0.131056i
$918$	−1.08294e7	−	1.87570e7i	−0.424128	−	0.734611i
$919$	−1.79687e6			−0.0701824			−0.0350912	−	0.999384i	$-0.511172\pi$
$919$	−1.79687e6			−0.0701824			−0.0350912	+	0.999384i	$0.511172\pi$
$920$	9.23728e6			0.359811
$921$	−5.12910e6	−	8.88386e6i	−0.199247	−	0.345106i
$922$	−7.13370e6	−	1.23559e7i	−0.276368	−	0.478683i
$923$	2.10603e6			0.0813692
$924$	681855.			0.0262731
$925$	−1.94862e7	−	3.37511e7i	−0.748813	−	1.29698i
$926$	−394673.	+	683593.i	−0.0151255	+	0.0261981i
$927$	1.67224e7	+	2.89640e7i	0.639144	+	1.10703i
$928$	−2.25750e6	+	3.91011e6i	−0.0860515	+	0.149046i
$929$	−1.07464e7	+	1.86132e7i	−0.408528	+	0.707591i	−0.994725	−	0.102577i	$-0.967291\pi$
$929$	−1.07464e7	+	1.86132e7i	−0.408528	+	0.707591i	0.586197	+	0.810169i	$0.300624\pi$
$930$	4.26824e6			0.161823
$931$	−2.61539e7	−	465148.i	−0.988924	−	0.0175880i
$932$	6.48174e6			0.244428
$933$	−9.84016e6	+	1.70437e7i	−0.370082	+	0.641001i
$934$	−4.83125e6	+	8.36798e6i	−0.181214	+	0.313873i
$935$	−3.10590e7	−	5.37958e7i	−1.16187	−	2.01242i
$936$	1.01631e6	−	1.76031e6i	0.0379174	−	0.0656748i
$937$	−1.00820e7	−	1.74626e7i	−0.375145	−	0.649769i	0.615204	−	0.788368i	$-0.289074\pi$
$937$	−1.00820e7	−	1.74626e7i	−0.375145	−	0.649769i	−0.990349	+	0.138598i	$0.955740\pi$
$938$	660094.			0.0244962
$939$	1.87510e7			0.694003
$940$	−9.66085e6	−	1.67331e7i	−0.356612	−	0.617669i
$941$	1.19732e7	+	2.07382e7i	0.440794	+	0.763477i	0.997749	−	0.0670657i	$-0.0213637\pi$
$941$	1.19732e7	+	2.07382e7i	0.440794	+	0.763477i	−0.556955	+	0.830543i	$0.688030\pi$
$942$	1.10212e7			0.404669
$943$	−3.00865e7			−1.10177
$944$	−6.00516e6	−	1.04012e7i	−0.219328	−	0.379888i
$945$	−2.06841e6	+	3.58258e6i	−0.0753453	+	0.130502i
$946$	1.27825e7	+	2.21399e7i	0.464394	+	0.804354i
$947$	1.42076e7	−	2.46082e7i	0.514807	−	0.891672i	−0.485046	−	0.874489i	$-0.661197\pi$
$947$	1.42076e7	−	2.46082e7i	0.514807	−	0.891672i	0.999852	−	0.0171827i	$-0.00546970\pi$
$948$	−2.80119e6	+	4.85180e6i	−0.101233	+	0.175341i
$949$	7.96893e6			0.287233
$950$	3.44585e7	+	612845.i	1.23876	+	0.0220314i
$951$	1.59741e7			0.572749
$952$	712881.	−	1.23475e6i	0.0254932	−	0.0441555i
$953$	−1.78515e7	+	3.09197e7i	−0.636712	+	1.10282i	0.349438	+	0.936959i	$0.386372\pi$
$953$	−1.78515e7	+	3.09197e7i	−0.636712	+	1.10282i	−0.986150	+	0.165857i	$0.946961\pi$
$954$	−601503.	−	1.04183e6i	−0.0213977	−	0.0370619i
$955$	−2.21948e7	+	3.84426e7i	−0.787487	+	1.36397i
$956$	1.25718e7	+	2.17750e7i	0.444890	+	0.770572i
$957$	1.38702e7			0.489555
$958$	−2.69984e7			−0.950440
$959$	−1.68092e6	−	2.91144e6i	−0.0590201	−	0.102226i
$960$	1.46681e6	+	2.54059e6i	0.0513684	+	0.0889727i
$961$	−2.64095e7			−0.922468
$962$	4.93151e6			0.171808
$963$	2.43937e6	+	4.22511e6i	0.0847640	+	0.146816i
$964$	7.64484e6	−	1.32413e7i	0.264957	−	0.458919i
$965$	−1.03681e7	−	1.79581e7i	−0.358412	−	0.620787i
$966$	325661.	−	564061.i	0.0112285	−	0.0194484i
$967$	1.15441e7	−	1.99950e7i	0.397004	−	0.687631i	−0.596351	−	0.802724i	$-0.703383\pi$
$967$	1.15441e7	−	1.99950e7i	0.397004	−	0.687631i	0.993355	+	0.115093i	$0.0367165\pi$
$968$	311134.			0.0106723
$969$	9.68273e6	+	1.74817e7i	0.331275	+	0.598101i
$970$	−1.44774e7			−0.494039
$971$	−1.79907e6	+	3.11608e6i	−0.0612350	+	0.106062i	−0.895018	−	0.446031i	$-0.852837\pi$
$971$	−1.79907e6	+	3.11608e6i	−0.0612350	+	0.106062i	0.833783	+	0.552093i	$0.186171\pi$
$972$	−7.58273e6	+	1.31337e7i	−0.257430	+	0.445883i
$973$	−309225.	−	535593.i	−0.0104711	−	0.0181365i
$974$	21063.1	−	36482.3i	0.000711417	−	0.00123221i
$975$	−3.66233e6	−	6.34334e6i	−0.123380	−	0.213701i
$976$	7.08041e6			0.237922
$977$	−4.22278e7			−1.41535			−0.707673	−	0.706540i	$-0.750255\pi$
$977$	−4.22278e7			−1.41535			−0.707673	+	0.706540i	$0.750255\pi$
$978$	5.47033e6	+	9.47490e6i	0.182880	+	0.316758i
$979$	−2.34499e7	−	4.06164e7i	−0.781959	−	1.35439i
$980$	2.46662e7			0.820422
$981$	8.25268e6			0.273793
$982$	−845903.	−	1.46515e6i	−0.0279925	−	0.0484845i
$983$	1.53664e7	−	2.66153e7i	0.507209	−	0.878512i	−0.492756	−	0.870168i	$-0.664010\pi$
$983$	1.53664e7	−	2.66153e7i	0.507209	−	0.878512i	0.999965	−	0.00834479i	$-0.00265626\pi$
$984$	−4.77751e6	−	8.27488e6i	−0.157294	−	0.272442i
$985$	1.59318e7	−	2.75947e7i	0.523207	−	0.906222i
$986$	1.45013e7	−	2.51169e7i	0.475022	−	0.822763i
$987$	−1.36238e6			−0.0445148
$988$	−2.24732e6	+	3.73737e6i	−0.0732440	+	0.121808i
$989$	2.44202e7			0.793885
$990$	−1.38524e7	+	2.39931e7i	−0.449198	+	0.778033i
$991$	2.27497e7	−	3.94036e7i	0.735854	−	1.27454i	−0.218494	−	0.975838i	$-0.570114\pi$
$991$	2.27497e7	−	3.94036e7i	0.735854	−	1.27454i	0.954348	−	0.298698i	$-0.0965523\pi$
$992$	762806.	+	1.32122e6i	0.0246113	+	0.0426281i
$993$	6.78991e6	−	1.17605e7i	0.218520	−	0.378487i
$994$	−329428.	−	570586.i	−0.0105753	−	0.0183170i
$995$	−4.47457e7			−1.43283
$996$	2.92767e6			0.0935133
$997$	434529.	+	752626.i	0.0138446	+	0.0239796i	0.872865	−	0.487962i	$-0.162260\pi$
$997$	434529.	+	752626.i	0.0138446	+	0.0239796i	−0.859020	+	0.511942i	$0.828926\pi$
$998$	−5.79631e6	−	1.00395e7i	−0.184215	−	0.319070i
$999$	−2.34365e7			−0.742983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.6.c.b.11.2	yes	8
3.2	odd	2		342.6.g.d.163.1		8
4.3	odd	2		304.6.i.b.49.3		8
19.7	even	3	inner	38.6.c.b.7.2	✓	8
19.8	odd	6		722.6.a.g.1.2		4
19.11	even	3		722.6.a.j.1.3		4
57.26	odd	6		342.6.g.d.235.1		8
76.7	odd	6		304.6.i.b.273.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.6.c.b.7.2	✓	8	19.7	even	3	inner
38.6.c.b.11.2	yes	8	1.1	even	1	trivial
304.6.i.b.49.3		8	4.3	odd	2
304.6.i.b.273.3		8	76.7	odd	6
342.6.g.d.163.1		8	3.2	odd	2
342.6.g.d.235.1		8	57.26	odd	6
722.6.a.g.1.2		4	19.8	odd	6
722.6.a.j.1.3		4	19.11	even	3

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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	38.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-3.86148 + 6.68827i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(46.3693 - 80.3140i) q^{5} +(-15.4459 - 26.7531i) q^{6} +13.5472 q^{7} +64.0000 q^{8} +(91.6780 + 158.791i) q^{9} +O(q^{10})\)	\(q+(-2.00000 + 3.46410i) q^{2} +(-3.86148 + 6.68827i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(46.3693 - 80.3140i) q^{5} +(-15.4459 - 26.7531i) q^{6} +13.5472 q^{7} +64.0000 q^{8} +(91.6780 + 158.791i) q^{9} +(185.477 + 321.256i) q^{10} +407.324 q^{11} +123.567 q^{12} +(-86.6070 - 150.008i) q^{13} +(-27.0944 + 46.9288i) q^{14} +(358.108 + 620.262i) q^{15} +(-128.000 + 221.703i) q^{16} +(822.219 - 1424.13i) q^{17} -733.424 q^{18} +(1573.31 + 27.9814i) q^{19} -1483.82 q^{20} +(-52.3121 + 90.6073i) q^{21} +(-814.647 + 1411.01i) q^{22} +(778.168 + 1347.83i) q^{23} +(-247.135 + 428.050i) q^{24} +(-2737.73 - 4741.89i) q^{25} +692.856 q^{26} -3292.73 q^{27} +(-108.377 - 187.715i) q^{28} +(-2204.59 - 3818.47i) q^{29} -2864.87 q^{30} -1489.86 q^{31} +(-512.000 - 886.810i) q^{32} +(-1572.87 + 2724.29i) q^{33} +(3288.88 + 5696.50i) q^{34} +(628.174 - 1088.03i) q^{35} +(1466.85 - 2540.66i) q^{36} +7117.66 q^{37} +(-3243.56 + 5394.16i) q^{38} +1337.72 q^{39} +(2967.64 - 5140.10i) q^{40} +(-9665.80 + 16741.7i) q^{41} +(-209.249 - 362.429i) q^{42} +(7845.40 - 13588.6i) q^{43} +(-3258.59 - 5644.04i) q^{44} +17004.2 q^{45} -6225.34 q^{46} +(6510.80 + 11277.0i) q^{47} +(-988.538 - 1712.20i) q^{48} -16623.5 q^{49} +21901.8 q^{50} +(6349.96 + 10998.5i) q^{51} +(-1385.71 + 2400.12i) q^{52} +(820.131 + 1420.51i) q^{53} +(6585.45 - 11406.3i) q^{54} +(18887.3 - 32713.8i) q^{55} +867.020 q^{56} +(-6262.46 + 10414.7i) q^{57} +17636.8 q^{58} +(-23457.7 + 40629.9i) q^{59} +(5729.73 - 9924.19i) q^{60} +(-13828.9 - 23952.4i) q^{61} +(2979.71 - 5161.01i) q^{62} +(1241.98 + 2151.17i) q^{63} +4096.00 q^{64} -16063.6 q^{65} +(-6291.48 - 10897.2i) q^{66} +(-6090.69 - 10549.4i) q^{67} -26311.0 q^{68} -12019.5 q^{69} +(2512.70 + 4352.12i) q^{70} +(-6079.27 + 10529.6i) q^{71} +(5867.39 + 10162.6i) q^{72} +(-23003.1 + 39842.6i) q^{73} +(-14235.3 + 24656.3i) q^{74} +42286.7 q^{75} +(-12198.8 - 22024.3i) q^{76} +5518.09 q^{77} +(-2675.45 + 4634.01i) q^{78} +(-22669.4 + 39264.5i) q^{79} +(11870.5 + 20560.4i) q^{80} +(-9562.96 + 16563.5i) q^{81} +(-38663.2 - 66966.6i) q^{82} +23692.9 q^{83} +1673.99 q^{84} +(-76251.5 - 132072. i) q^{85} +(31381.6 + 54354.5i) q^{86} +34052.0 q^{87} +26068.7 q^{88} +(-57570.6 - 99715.3i) q^{89} +(-34008.4 + 58904.2i) q^{90} +(-1173.28 - 2032.18i) q^{91} +(12450.7 - 21565.2i) q^{92} +(5753.04 - 9964.56i) q^{93} -52086.4 q^{94} +(75200.8 - 125062. i) q^{95} +7908.30 q^{96} +(-19513.7 + 33798.7i) q^{97} +(33246.9 - 57585.4i) q^{98} +(37342.6 + 64679.3i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9}+O(q^{10}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9	\( 8 q - 16 q^{2} - 14 q^{3} - 64 q^{4} - 36 q^{5} - 56 q^{6} + 76 q^{7} + 512 q^{8} + 156 q^{9} - 144 q^{10} + 144 q^{11} + 448 q^{12} - 674 q^{13} - 152 q^{14} - 20 q^{15} - 1024 q^{16} + 522 q^{17} - 1248 q^{18} + 320 q^{19} + 1152 q^{20} - 770 q^{21} - 288 q^{22} - 204 q^{23} - 896 q^{24} - 2158 q^{25} + 5392 q^{26} + 13156 q^{27} - 608 q^{28} - 5712 q^{29} + 160 q^{30} - 2324 q^{31} - 4096 q^{32} - 15650 q^{33} + 2088 q^{34} - 4188 q^{35} + 2496 q^{36} - 25508 q^{37} - 2440 q^{38} + 44156 q^{39} - 2304 q^{40} - 3480 q^{41} - 3080 q^{42} + 4066 q^{43} - 1152 q^{44} + 51560 q^{45} + 1632 q^{46} - 45768 q^{47} - 3584 q^{48} + 1416 q^{49} + 17264 q^{50} + 1506 q^{51} - 10784 q^{52} + 45654 q^{53} - 26312 q^{54} + 36570 q^{55} + 4864 q^{56} - 66702 q^{57} + 45696 q^{58} - 84006 q^{59} - 320 q^{60} - 14012 q^{61} + 4648 q^{62} - 15128 q^{63} + 32768 q^{64} - 4020 q^{65} - 62600 q^{66} - 19046 q^{67} - 16704 q^{68} + 111592 q^{69} - 16752 q^{70} - 53274 q^{71} + 9984 q^{72} - 41084 q^{73} + 51016 q^{74} + 153216 q^{75} + 4640 q^{76} + 271524 q^{77} - 88312 q^{78} - 54170 q^{79} - 9216 q^{80} - 9528 q^{81} - 13920 q^{82} + 52392 q^{83} + 24640 q^{84} - 221850 q^{85} + 16264 q^{86} - 457120 q^{87} + 9216 q^{88} - 137862 q^{89} - 103120 q^{90} + 308516 q^{91} - 3264 q^{92} + 112746 q^{93} + 366144 q^{94} + 153078 q^{95} + 28672 q^{96} - 292388 q^{97} - 2832 q^{98} - 138328 q^{99}+O(q^{100}) \) 8 * q - 16 * q^2 - 14 * q^3 - 64 * q^4 - 36 * q^5 - 56 * q^6 + 76 * q^7 + 512 * q^8 + 156 * q^9 - 144 * q^10 + 144 * q^11 + 448 * q^12 - 674 * q^13 - 152 * q^14 - 20 * q^15 - 1024 * q^16 + 522 * q^17 - 1248 * q^18 + 320 * q^19 + 1152 * q^20 - 770 * q^21 - 288 * q^22 - 204 * q^23 - 896 * q^24 - 2158 * q^25 + 5392 * q^26 + 13156 * q^27 - 608 * q^28 - 5712 * q^29 + 160 * q^30 - 2324 * q^31 - 4096 * q^32 - 15650 * q^33 + 2088 * q^34 - 4188 * q^35 + 2496 * q^36 - 25508 * q^37 - 2440 * q^38 + 44156 * q^39 - 2304 * q^40 - 3480 * q^41 - 3080 * q^42 + 4066 * q^43 - 1152 * q^44 + 51560 * q^45 + 1632 * q^46 - 45768 * q^47 - 3584 * q^48 + 1416 * q^49 + 17264 * q^50 + 1506 * q^51 - 10784 * q^52 + 45654 * q^53 - 26312 * q^54 + 36570 * q^55 + 4864 * q^56 - 66702 * q^57 + 45696 * q^58 - 84006 * q^59 - 320 * q^60 - 14012 * q^61 + 4648 * q^62 - 15128 * q^63 + 32768 * q^64 - 4020 * q^65 - 62600 * q^66 - 19046 * q^67 - 16704 * q^68 + 111592 * q^69 - 16752 * q^70 - 53274 * q^71 + 9984 * q^72 - 41084 * q^73 + 51016 * q^74 + 153216 * q^75 + 4640 * q^76 + 271524 * q^77 - 88312 * q^78 - 54170 * q^79 - 9216 * q^80 - 9528 * q^81 - 13920 * q^82 + 52392 * q^83 + 24640 * q^84 - 221850 * q^85 + 16264 * q^86 - 457120 * q^87 + 9216 * q^88 - 137862 * q^89 - 103120 * q^90 + 308516 * q^91 - 3264 * q^92 + 112746 * q^93 + 366144 * q^94 + 153078 * q^95 + 28672 * q^96 - 292388 * q^97 - 2832 * q^98 - 138328 * q^99

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