LMFDB - Embedded newform 21.6.e.c.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 98x^{6} + 83x^{5} + 9122x^{4} - 91x^{3} + 28567x^{2} + 2058x + 86436 $ x^8 - x^7 + 98x^6 + 83x^5 + 9122x^4 - 91x^3 + 28567x^2 + 2058x + 86436
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			4.4
Root			$5.09061 + 8.81720i$ of defining polynomial
Character	$\chi$	$=$	21.4
Dual form			21.6.e.c.16.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.59061 + 7.95118i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(-11.0358 - 19.1146i) q^{5} -82.6311 q^{6} +(126.882 + 26.6059i) q^{7} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})$	\(q+(4.59061 + 7.95118i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(-11.0358 - 19.1146i) q^{5} -82.6311 q^{6} +(126.882 + 26.6059i) q^{7} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +(101.322 - 175.495i) q^{10} +(-208.355 + 360.881i) q^{11} +(-235.327 - 407.599i) q^{12} +797.918 q^{13} +(370.920 + 1131.00i) q^{14} +198.644 q^{15} +(-18.6623 - 32.3240i) q^{16} +(687.775 - 1191.26i) q^{17} +(371.840 - 644.045i) q^{18} +(-1156.51 - 2003.14i) q^{19} +1154.23 q^{20} +(-778.343 + 869.224i) q^{21} -3825.91 q^{22} +(477.701 + 827.402i) q^{23} +(838.497 - 1452.32i) q^{24} +(1318.92 - 2284.44i) q^{25} +(3662.93 + 6344.39i) q^{26} +729.000 q^{27} +(-4522.60 + 5050.67i) q^{28} -7035.29 q^{29} +(911.900 + 1579.46i) q^{30} +(-630.596 + 1092.22i) q^{31} +(-2809.98 + 4867.03i) q^{32} +(-1875.19 - 3247.93i) q^{33} +12629.2 q^{34} +(-891.689 - 2718.92i) q^{35} +4235.89 q^{36} +(-4888.22 - 8466.65i) q^{37} +(10618.2 - 18391.3i) q^{38} +(-3590.63 + 6219.16i) q^{39} +(2056.33 + 3561.67i) q^{40} -5400.95 q^{41} +(-10484.4 - 2198.47i) q^{42} +19686.6 q^{43} +(-10895.9 - 18872.3i) q^{44} +(-893.900 + 1548.28i) q^{45} +(-4385.88 + 7596.57i) q^{46} +(-1028.28 - 1781.04i) q^{47} +335.921 q^{48} +(15391.3 + 6751.63i) q^{49} +24218.7 q^{50} +(6189.98 + 10721.4i) q^{51} +(-20863.5 + 36136.7i) q^{52} +(-9011.37 + 15608.2i) q^{53} +(3346.56 + 5796.41i) q^{54} +9197.45 q^{55} +(-23642.3 - 4957.54i) q^{56} +20817.2 q^{57} +(-32296.3 - 55938.8i) q^{58} +(-3717.84 + 6439.49i) q^{59} +(-5194.05 + 8996.36i) q^{60} +(-1747.69 - 3027.09i) q^{61} -11579.3 q^{62} +(-3272.39 - 9978.09i) q^{63} -52792.5 q^{64} +(-8805.67 - 15251.9i) q^{65} +(17216.6 - 29820.0i) q^{66} +(-7928.21 + 13732.1i) q^{67} +(35967.2 + 62297.0i) q^{68} -8598.62 q^{69} +(17525.2 - 19571.5i) q^{70} +58133.5 q^{71} +(7546.48 + 13070.9i) q^{72} +(-19555.3 + 33870.8i) q^{73} +(44879.9 - 77734.2i) q^{74} +(11870.3 + 20560.0i) q^{75} +120960. q^{76} +(-36038.1 + 40246.0i) q^{77} -65932.8 q^{78} +(-4880.35 - 8453.01i) q^{79} +(-411.906 + 713.442i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-24793.7 - 42943.9i) q^{82} -70395.7 q^{83} +(-19014.4 - 57978.2i) q^{84} -30360.6 q^{85} +(90373.4 + 156531. i) q^{86} +(31658.8 - 54834.7i) q^{87} +(38823.3 - 67243.9i) q^{88} +(-72153.1 - 124973. i) q^{89} -16414.2 q^{90} +(101242. + 21229.3i) q^{91} -49962.7 q^{92} +(-5675.36 - 9830.01i) q^{93} +(9440.90 - 16352.1i) q^{94} +(-25526.1 + 44212.5i) q^{95} +(-25289.8 - 43803.3i) q^{96} -79328.7 q^{97} +(16971.9 + 153373. i) q^{98} +33753.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.59061	+	7.95118i	0.811514	+	1.40558i	0.911804	+	0.410625i	$0.134689\pi$
$2$	4.59061	+	7.95118i	0.811514	+	1.40558i	−0.100291	+	0.994958i	$0.531977\pi$
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$3$	−4.50000	+	7.79423i	−0.288675	+	0.500000i
$4$	−26.1475	+	45.2888i	−0.817109	+	1.41527i
$5$	−11.0358	−	19.1146i	−0.197414	−	0.341932i	0.750275	−	0.661126i	$-0.229921\pi$
$5$	−11.0358	−	19.1146i	−0.197414	−	0.341932i	−0.947689	+	0.319194i	$0.896588\pi$
$6$	−82.6311			−0.937055
$7$	126.882	+	26.6059i	0.978715	+	0.205226i
$7$	126.882	+	26.6059i	0.978715	+	0.205226i
$8$	−186.333			−1.02935
$9$	−40.5000	−	70.1481i	−0.166667	−	0.288675i
$10$	101.322	−	175.495i	0.320409	−	0.554965i
$11$	−208.355	+	360.881i	−0.519184	+	0.899254i	0.480567	+	0.876958i	$0.340431\pi$
$11$	−208.355	+	360.881i	−0.519184	+	0.899254i	−0.999751	+	0.0222959i	$0.992902\pi$
$12$	−235.327	−	407.599i	−0.471758	−	0.817109i
$13$	797.918			1.30948			0.654742	−	0.755853i	$-0.272777\pi$
$13$	797.918			1.30948			0.654742	+	0.755853i	$0.272777\pi$
$14$	370.920	+	1131.00i	0.505778	+	1.54221i
$15$	198.644			0.227955
$16$	−18.6623	−	32.3240i	−0.0182249	−	0.0315664i
$17$	687.775	−	1191.26i	0.577197	−	0.999735i	−0.418602	−	0.908170i	$-0.637480\pi$
$17$	687.775	−	1191.26i	0.577197	−	0.999735i	0.995799	−	0.0915652i	$-0.0291870\pi$
$18$	371.840	−	644.045i	0.270505	−	0.468528i
$19$	−1156.51	−	2003.14i	−0.734965	−	1.27300i	−0.954739	−	0.297446i	$-0.903865\pi$
$19$	−1156.51	−	2003.14i	−0.734965	−	1.27300i	0.219774	−	0.975551i	$-0.429468\pi$
$20$	1154.23			0.645236
$21$	−778.343	+	869.224i	−0.385144	+	0.430114i
$22$	−3825.91			−1.68530
$23$	477.701	+	827.402i	0.188294	+	0.326135i	0.944682	−	0.327989i	$-0.106371\pi$
$23$	477.701	+	827.402i	0.188294	+	0.326135i	−0.756388	+	0.654124i	$0.773038\pi$
$24$	838.497	−	1452.32i	0.297149	−	0.514676i
$25$	1318.92	−	2284.44i	0.422055	−	0.731021i
$26$	3662.93	+	6344.39i	1.06266	+	1.84059i
$27$	729.000			0.192450
$28$	−4522.60	+	5050.67i	−1.09017	+	1.21746i
$29$	−7035.29			−1.55341			−0.776707	−	0.629862i	$-0.783111\pi$
$29$	−7035.29			−1.55341			−0.776707	+	0.629862i	$0.783111\pi$
$30$	911.900	+	1579.46i	0.184988	+	0.320409i
$31$	−630.596	+	1092.22i	−0.117855	+	0.204130i	−0.918917	−	0.394450i	$-0.870935\pi$
$31$	−630.596	+	1092.22i	−0.117855	+	0.204130i	0.801063	+	0.598581i	$0.204268\pi$
$32$	−2809.98	+	4867.03i	−0.485097	+	0.840212i
$33$	−1875.19	−	3247.93i	−0.299751	−	0.519184i
$34$	12629.2			1.87361
$35$	−891.689	−	2718.92i	−0.123039	−	0.375168i
$36$	4235.89			0.544739
$37$	−4888.22	−	8466.65i	−0.587012	−	1.01673i	−0.994621	−	0.103578i	$-0.966971\pi$
$37$	−4888.22	−	8466.65i	−0.587012	−	1.01673i	0.407610	−	0.913156i	$-0.366362\pi$
$38$	10618.2	−	18391.3i	1.19287	−	2.06611i
$39$	−3590.63	+	6219.16i	−0.378015	+	0.654742i
$40$	2056.33	+	3561.67i	0.203209	+	0.351968i
$41$	−5400.95			−0.501777			−0.250888	−	0.968016i	$-0.580723\pi$
$41$	−5400.95			−0.501777			−0.250888	+	0.968016i	$0.580723\pi$
$42$	−10484.4	−	2198.47i	−0.917110	−	0.192308i
$43$	19686.6			1.62367			0.811837	−	0.583885i	$-0.198468\pi$
$43$	19686.6			1.62367			0.811837	+	0.583885i	$0.198468\pi$
$44$	−10895.9	−	18872.3i	−0.848460	−	1.46958i
$45$	−893.900	+	1548.28i	−0.0658048	+	0.113977i
$46$	−4385.88	+	7596.57i	−0.305606	+	0.529326i
$47$	−1028.28	−	1781.04i	−0.0678997	−	0.117606i	0.830077	−	0.557649i	$-0.188296\pi$
$47$	−1028.28	−	1781.04i	−0.0678997	−	0.117606i	−0.897977	+	0.440043i	$0.854963\pi$
$48$	335.921			0.0210443
$49$	15391.3	+	6751.63i	0.915765	+	0.401715i
$50$	24218.7			1.37001
$51$	6189.98	+	10721.4i	0.333245	+	0.577197i
$52$	−20863.5	+	36136.7i	−1.06999	+	1.85328i
$53$	−9011.37	+	15608.2i	−0.440658	+	0.763241i	−0.997738	−	0.0672170i	$-0.978588\pi$
$53$	−9011.37	+	15608.2i	−0.440658	+	0.763241i	0.557081	+	0.830458i	$0.311921\pi$
$54$	3346.56	+	5796.41i	0.156176	+	0.270505i
$55$	9197.45			0.409978
$56$	−23642.3	−	4957.54i	−1.00744	−	0.211250i
$57$	20817.2			0.848664
$58$	−32296.3	−	55938.8i	−1.26062	−	2.18345i
$59$	−3717.84	+	6439.49i	−0.139047	+	0.240836i	−0.927136	−	0.374725i	$-0.877737\pi$
$59$	−3717.84	+	6439.49i	−0.139047	+	0.240836i	0.788089	+	0.615561i	$0.211070\pi$
$60$	−5194.05	+	8996.36i	−0.186264	+	0.322618i
$61$	−1747.69	−	3027.09i	−0.0601368	−	0.104160i	0.834390	−	0.551175i	$-0.185820\pi$
$61$	−1747.69	−	3027.09i	−0.0601368	−	0.104160i	−0.894526	+	0.447015i	$0.852487\pi$
$62$	−11579.3			−0.382563
$63$	−3272.39	−	9978.09i	−0.103875	−	0.316735i
$64$	−52792.5			−1.61110
$65$	−8805.67	−	15251.9i	−0.258511	−	0.447754i
$66$	17216.6	−	29820.0i	0.486505	−	0.842651i
$67$	−7928.21	+	13732.1i	−0.215769	+	0.373722i	−0.953510	−	0.301361i	$-0.902559\pi$
$67$	−7928.21	+	13732.1i	−0.215769	+	0.373722i	0.737741	+	0.675083i	$0.235892\pi$
$68$	35967.2	+	62297.0i	0.943266	+	1.63378i
$69$	−8598.62			−0.217423
$70$	17525.2	−	19571.5i	0.427482	−	0.477396i
$71$	58133.5			1.36861			0.684306	−	0.729195i	$-0.260105\pi$
$71$	58133.5			1.36861			0.684306	+	0.729195i	$0.260105\pi$
$72$	7546.48	+	13070.9i	0.171559	+	0.297149i
$73$	−19555.3	+	33870.8i	−0.429495	+	0.743907i	−0.996828	−	0.0795812i	$-0.974642\pi$
$73$	−19555.3	+	33870.8i	−0.429495	+	0.743907i	0.567334	+	0.823488i	$0.307975\pi$
$74$	44879.9	−	77734.2i	0.952736	−	1.65019i
$75$	11870.3	+	20560.0i	0.243674	+	0.422055i
$76$	120960.			2.40218
$77$	−36038.1	+	40246.0i	−0.692684	+	0.773563i
$78$	−65932.8			−1.22706
$79$	−4880.35	−	8453.01i	−0.0879798	−	0.152385i	0.818677	−	0.574254i	$-0.194708\pi$
$79$	−4880.35	−	8453.01i	−0.0879798	−	0.152385i	−0.906657	+	0.421868i	$0.861374\pi$
$80$	−411.906	+	713.442i	−0.00719570	+	0.0124633i
$81$	−3280.50	+	5681.99i	−0.0555556	+	0.0962250i
$82$	−24793.7	−	42943.9i	−0.407199	−	0.705289i
$83$	−70395.7			−1.12163			−0.560816	−	0.827940i	$-0.689513\pi$
$83$	−70395.7			−1.12163			−0.560816	+	0.827940i	$0.689513\pi$
$84$	−19014.4	−	57978.2i	−0.294025	−	0.896533i
$85$	−30360.6			−0.455788
$86$	90373.4	+	156531.i	1.31763	+	2.28221i
$87$	31658.8	−	54834.7i	0.448432	−	0.776707i
$88$	38823.3	−	67243.9i	0.534424	−	0.925649i
$89$	−72153.1	−	124973.i	−0.965562	−	1.67240i	−0.708098	−	0.706115i	$-0.750446\pi$
$89$	−72153.1	−	124973.i	−0.965562	−	1.67240i	−0.257464	−	0.966288i	$-0.582887\pi$
$90$	−16414.2			−0.213606
$91$	101242.	+	21229.3i	1.28161	+	0.268740i
$92$	−49962.7			−0.615427
$93$	−5675.36	−	9830.01i	−0.0680434	−	0.117855i
$94$	9440.90	−	16352.1i	0.110203	−	0.190877i
$95$	−25526.1	+	44212.5i	−0.290185	+	0.502616i
$96$	−25289.8	−	43803.3i	−0.280071	−	0.485097i
$97$	−79328.7			−0.856053			−0.428027	−	0.903766i	$-0.640791\pi$
$97$	−79328.7			−0.856053			−0.428027	+	0.903766i	$0.640791\pi$
$98$	16971.9	+	153373.i	0.178511	+	1.61318i
$99$	33753.5			0.346123
$100$	68973.0	+	119465.i	0.689730	+	1.19465i
$101$	42416.9	−	73468.2i	0.413747	−	0.716631i	−0.581549	−	0.813512i	$-0.697553\pi$
$101$	42416.9	−	73468.2i	0.413747	−	0.716631i	0.995296	+	0.0968802i	$0.0308864\pi$
$102$	−56831.6	+	98435.2i	−0.540866	+	0.936807i
$103$	−10166.1	−	17608.3i	−0.0944197	−	0.163540i	0.814947	−	0.579536i	$-0.196766\pi$
$103$	−10166.1	−	17608.3i	−0.0944197	−	0.163540i	−0.909366	+	0.415996i	$0.863433\pi$
$104$	−148678.			−1.34792
$105$	25204.5	+	5285.11i	0.223102	+	0.0467822i
$106$	−165471.			−1.43040
$107$	−3481.09	−	6029.43i	−0.0293938	−	0.0509116i	0.850954	−	0.525240i	$-0.176024\pi$
$107$	−3481.09	−	6029.43i	−0.0293938	−	0.0509116i	−0.880348	+	0.474328i	$0.842691\pi$
$108$	−19061.5	+	33015.5i	−0.157253	+	0.272370i
$109$	−56325.7	+	97559.0i	−0.454088	+	0.786504i	−0.998635	−	0.0522262i	$-0.983368\pi$
$109$	−56325.7	+	97559.0i	−0.454088	+	0.786504i	0.544547	+	0.838730i	$0.316702\pi$
$110$	42221.9	+	73130.5i	0.332703	+	0.576258i
$111$	87988.0			0.677823
$112$	−1507.90	−	4597.87i	−0.0113587	−	0.0346347i
$113$	112005.			0.825167			0.412583	−	0.910920i	$-0.364627\pi$
$113$	112005.			0.825167			0.412583	+	0.910920i	$0.364627\pi$
$114$	95563.9	+	165522.i	0.688703	+	1.19287i
$115$	10543.6	−	18262.1i	0.0743439	−	0.128767i
$116$	183955.	−	318620.i	1.26931	−	2.19851i
$117$	−32315.7	−	55972.4i	−0.218247	−	0.378015i
$118$	−68268.7			−0.451353
$119$	118961.	−	132851.i	0.770083	−	0.860000i
$120$	−37014.0			−0.234646
$121$	−6297.91	−	10908.3i	−0.0391051	−	0.0677320i
$122$	16046.0	−	27792.4i	0.0976037	−	0.169055i
$123$	24304.3	−	42096.2i	0.144850	−	0.250888i
$124$	−32977.0	−	57117.8i	−0.192600	−	0.333593i
$125$	−127195.			−0.728108
$126$	64315.3	−	71824.9i	0.360901	−	0.403040i
$127$	82224.5			0.452368			0.226184	−	0.974085i	$-0.427375\pi$
$127$	82224.5			0.452368			0.226184	+	0.974085i	$0.427375\pi$
$128$	−152431.	−	264018.i	−0.822333	−	1.42432i
$129$	−88589.5	+	153442.i	−0.468714	+	0.811837i
$130$	80846.8	−	140031.i	0.419570	−	0.726717i
$131$	87905.9	+	152258.i	0.447548	+	0.775176i	0.998226	−	0.0595417i	$-0.0189639\pi$
$131$	87905.9	+	152258.i	0.447548	+	0.775176i	−0.550677	+	0.834718i	$0.685631\pi$
$132$	196126.			0.979718
$133$	−93445.8	−	284933.i	−0.458069	−	1.39673i
$134$	−145581.			−0.700397
$135$	−8045.10	−	13934.5i	−0.0379924	−	0.0658048i
$136$	−128155.	+	221971.i	−0.594140	+	1.02908i
$137$	−15665.2	+	27132.9i	−0.0713072	+	0.123508i	−0.899474	−	0.436973i	$-0.856050\pi$
$137$	−15665.2	+	27132.9i	−0.0713072	+	0.123508i	0.828167	+	0.560481i	$0.189384\pi$
$138$	−39472.9	−	68369.1i	−0.176442	−	0.305606i
$139$	152234.			0.668305			0.334152	−	0.942519i	$-0.391550\pi$
$139$	152234.			0.668305			0.334152	+	0.942519i	$0.391550\pi$
$140$	146452.	+	30709.4i	0.631502	+	0.132419i
$141$	18509.1			0.0784038
$142$	266868.	+	462229.i	1.11065	+	1.92370i
$143$	−166250.	+	287953.i	−0.679863	+	1.17756i
$144$	−1511.64	+	2618.24i	−0.00607495	+	0.0105221i
$145$	77640.1	+	134477.i	0.306666	+	0.531162i
$146$	−359084.			−1.39416
$147$	−121884.	+	89580.6i	−0.465216	+	0.341917i
$148$	511259.			1.91861
$149$	−181430.	−	314246.i	−0.669489	−	1.15959i	−0.978047	−	0.208384i	$-0.933180\pi$
$149$	−181430.	−	314246.i	−0.669489	−	1.15959i	0.308558	−	0.951206i	$-0.400154\pi$
$150$	−108984.	+	188766.i	−0.395489	+	0.685007i
$151$	−102563.	+	177644.i	−0.366056	+	0.634027i	−0.988945	−	0.148283i	$-0.952625\pi$
$151$	−102563.	+	177644.i	−0.366056	+	0.634027i	0.622889	+	0.782310i	$0.285959\pi$
$152$	215496.	+	373250.i	0.756538	+	1.31036i
$153$	−111420.			−0.384798
$154$	−485440.	−	101792.i	−1.64943	−	0.345868i
$155$	27836.5			0.0930648
$156$	−187772.	−	325231.i	−0.617759	−	1.06999i
$157$	38636.0	−	66919.5i	0.125096	−	0.216672i	−0.796675	−	0.604409i	$-0.793409\pi$
$157$	38636.0	−	66919.5i	0.125096	−	0.216672i	0.921770	+	0.387736i	$0.126743\pi$
$158$	44807.6	−	77609.0i	0.142794	−	0.247326i
$159$	−81102.3	−	140473.i	−0.254414	−	0.440658i
$160$	124042.			0.383060
$161$	38598.1	+	117692.i	0.117355	+	0.357836i
$162$	−60238.0			−0.180336
$163$	−92465.7	−	160155.i	−0.272591	−	0.472141i	0.696934	−	0.717136i	$-0.254547\pi$
$163$	−92465.7	−	160155.i	−0.272591	−	0.472141i	−0.969525	+	0.244994i	$0.921214\pi$
$164$	141221.	−	244602.i	0.410006	−	0.710152i
$165$	−41388.5	+	71687.0i	−0.118350	+	0.204989i
$166$	−323159.	−	559728.i	−0.910220	−	1.57655i
$167$	129262.			0.358657			0.179329	−	0.983789i	$-0.442607\pi$
$167$	129262.			0.358657			0.179329	+	0.983789i	$0.442607\pi$
$168$	145031.	−	161965.i	0.396449	−	0.442739i
$169$	265380.			0.714746
$170$	−139374.	−	241403.i	−0.369878	−	0.640648i
$171$	−93677.6	+	162254.i	−0.244988	+	0.424332i
$172$	−514754.	+	891580.i	−1.32672	+	2.29794i
$173$	253934.	+	439826.i	0.645067	+	1.11729i	0.984286	+	0.176582i	$0.0565040\pi$
$173$	253934.	+	439826.i	0.645067	+	1.11729i	−0.339219	+	0.940707i	$0.610163\pi$
$174$	581334.			1.45563
$175$	228127.	−	254764.i	0.563096	−	0.628844i
$176$	15553.5			0.0378483
$177$	−33460.6	−	57955.4i	−0.0802786	−	0.139047i
$178$	662454.	−	1.14740e6i	1.56713	−	2.71435i
$179$	66294.5	−	114825.i	0.154648	−	0.267859i	−0.778283	−	0.627914i	$-0.783909\pi$
$179$	66294.5	−	114825.i	0.154648	−	0.267859i	0.932931	+	0.360056i	$0.117242\pi$
$180$	−46746.5	−	80967.3i	−0.107539	−	0.186264i
$181$	−740060.			−1.67908			−0.839538	−	0.543301i	$-0.817174\pi$
$181$	−740060.			−1.67908			−0.839538	+	0.543301i	$0.817174\pi$
$182$	295964.	+	902446.i	0.662308	+	2.01950i
$183$	31458.5			0.0694400
$184$	−89011.3	−	154172.i	−0.193821	−	0.335708i
$185$	−107891.	+	186873.i	−0.231769	+	0.401436i
$186$	52106.8	−	90251.6i	0.110436	−	0.191281i
$187$	286603.	+	496410.i	0.599344	+	1.03809i
$188$	107548.			0.221926
$189$	92497.2	+	19395.7i	0.188354	+	0.0394958i
$190$	−468722.			−0.941957
$191$	291366.	+	504661.i	0.577904	+	1.00096i	0.995719	+	0.0924273i	$0.0294626\pi$
$191$	291366.	+	504661.i	0.577904	+	1.00096i	−0.417815	+	0.908532i	$0.637204\pi$
$192$	237566.	−	411477.i	0.465085	−	0.805550i
$193$	200452.	−	347193.i	0.387362	−	0.670931i	−0.604731	−	0.796429i	$-0.706720\pi$
$193$	200452.	−	347193.i	0.387362	−	0.670931i	0.992094	+	0.125498i	$0.0400529\pi$
$194$	−364167.	−	630756.i	−0.694699	−	1.20325i
$195$	158502.			0.298503
$196$	−708216.	+	520513.i	−1.31682	+	0.967813i
$197$	671589.			1.23293			0.616464	−	0.787383i	$-0.288564\pi$
$197$	671589.			1.23293			0.616464	+	0.787383i	$0.288564\pi$
$198$	154949.	+	268380.i	0.280884	+	0.486505i
$199$	227511.	−	394060.i	0.407258	−	0.705391i	−0.587324	−	0.809352i	$-0.699818\pi$
$199$	227511.	−	394060.i	0.407258	−	0.705391i	0.994581	+	0.103961i	$0.0331518\pi$
$200$	−245758.	+	425666.i	−0.434443	+	0.752478i
$201$	−71353.9	−	123589.i	−0.124574	−	0.215769i
$202$	778878.			1.34305
$203$	−892654.	−	187180.i	−1.52035	−	0.318801i
$204$	−647409.			−1.08919
$205$	59603.8	+	103237.i	0.0990580	+	0.171573i
$206$	93337.6	−	161665.i	0.153246	−	0.265430i
$207$	38693.8	−	67019.6i	0.0627647	−	0.108712i
$208$	−14891.0	−	25791.9i	−0.0238652	−	0.0413357i
$209$	963860.			1.52633
$210$	73681.2	+	224667.i	0.115294	+	0.351553i
$211$	−1.19545e6			−1.84852			−0.924260	−	0.381764i	$-0.875317\pi$
$211$	−1.19545e6			−1.84852			−0.924260	+	0.381764i	$0.875317\pi$
$212$	−471249.	−	816228.i	−0.720130	−	1.24730i
$213$	−261601.	+	453105.i	−0.395084	+	0.684306i
$214$	31960.7	−	55357.6i	0.0477070	−	0.0826310i
$215$	−217257.	−	376300.i	−0.320537	−	0.555186i
$216$	−135837.			−0.198099
$217$	−109071.	+	121806.i	−0.157239	+	0.175598i
$218$	−1.03428e6			−1.47400
$219$	−175998.	−	304837.i	−0.247969	−	0.429495i
$220$	−240490.	+	416541.i	−0.334997	+	0.580231i
$221$	548788.	−	950529.i	0.755830	−	1.30914i
$222$	403919.	+	699608.i	0.550062	+	0.952736i
$223$	296529.			0.399305			0.199653	−	0.979867i	$-0.436019\pi$
$223$	296529.			0.399305			0.199653	+	0.979867i	$0.436019\pi$
$224$	−486029.	+	542778.i	−0.647205	+	0.722774i
$225$	−213665.			−0.281370
$226$	514172.	+	890573.i	0.669634	+	1.15984i
$227$	−109073.	+	188920.i	−0.140492	+	0.243340i	−0.927682	−	0.373371i	$-0.878202\pi$
$227$	−109073.	+	188920.i	−0.140492	+	0.243340i	0.787190	+	0.616711i	$0.211535\pi$
$228$	−544318.	+	942787.i	−0.693451	+	1.20109i
$229$	614602.	+	1.06452e6i	0.774471	+	1.34142i	0.935091	+	0.354407i	$0.115317\pi$
$229$	614602.	+	1.06452e6i	0.774471	+	1.34142i	−0.160620	+	0.987016i	$0.551349\pi$
$230$	193607.			0.241324
$231$	−151515.	−	461996.i	−0.186821	−	0.569650i
$232$	1.31090e6			1.59901
$233$	31472.1	+	54511.3i	0.0379784	+	0.0657805i	0.884390	−	0.466749i	$-0.154575\pi$
$233$	31472.1	+	54511.3i	0.0379784	+	0.0657805i	−0.846411	+	0.532530i	$0.821242\pi$
$234$	296698.	−	513895.i	0.354221	−	0.613529i
$235$	−22695.8	+	39310.4i	−0.0268088	+	0.0464341i
$236$	−194424.	−	336753.i	−0.227233	−	0.393578i
$237$	87846.2			0.101590
$238$	1.60243e6	+	336012.i	1.83373	+	0.384514i
$239$	219330.			0.248372			0.124186	−	0.992259i	$-0.460368\pi$
$239$	219330.			0.248372			0.124186	+	0.992259i	$0.460368\pi$
$240$	−3707.15	−	6420.98i	−0.00415444	−	0.00719570i
$241$	−216932.	+	375737.i	−0.240592	+	0.416717i	−0.960883	−	0.276955i	$-0.910675\pi$
$241$	−216932.	+	375737.i	−0.240592	+	0.416717i	0.720291	+	0.693672i	$0.244008\pi$
$242$	57822.6	−	100152.i	0.0634686	−	0.109931i
$243$	−29524.5	−	51137.9i	−0.0320750	−	0.0555556i
$244$	182791.			0.196553
$245$	−40800.4	−	368707.i	−0.0434259	−	0.392433i
$246$	446286.			0.470193
$247$	−922803.	−	1.59834e6i	−0.962424	−	1.66697i
$248$	117501.	−	203517.i	0.121314	−	0.210122i
$249$	316780.	−	548680.i	0.323787	−	0.560816i
$250$	−583904.	−	1.01135e6i	−0.590870	−	1.02342i
$251$	−1.71109e6			−1.71431			−0.857155	−	0.515059i	$-0.827770\pi$
$251$	−1.71109e6			−1.71431			−0.857155	+	0.515059i	$0.827770\pi$
$252$	537460.	+	112700.i	0.533144	+	0.111795i
$253$	−398125.			−0.391037
$254$	377461.	+	653782.i	0.367103	+	0.635841i
$255$	136623.	−	236638.i	0.131575	−	0.227894i
$256$	554822.	−	960979.i	0.529119	−	0.916461i
$257$	−492029.	−	852219.i	−0.464684	−	0.804856i	0.534503	−	0.845166i	$-0.320499\pi$
$257$	−492029.	−	852219.i	−0.464684	−	0.804856i	−0.999187	+	0.0403103i	$0.987165\pi$
$258$	−1.62672e6			−1.52147
$259$	−394967.	−	1.20432e6i	−0.365857	−	1.11556i
$260$	920984.			0.844926
$261$	284929.	+	493512.i	0.258902	+	0.448432i
$262$	−807084.	+	1.39791e6i	−0.726383	+	1.25813i
$263$	−273548.	+	473799.i	−0.243862	+	0.422381i	−0.961811	−	0.273714i	$-0.911748\pi$
$263$	−273548.	+	473799.i	−0.243862	+	0.422381i	0.717949	+	0.696096i	$0.245081\pi$
$264$	349410.	+	605196.i	0.308550	+	0.534424i
$265$	397791.			0.347969
$266$	1.83658e6	−	2.05102e6i	1.59150	−	1.77732i
$267$	1.29876e6			1.11493
$268$	−414605.	−	718118.i	−0.352613	−	0.610743i
$269$	320556.	−	555219.i	0.270099	−	0.467825i	−0.698788	−	0.715329i	$-0.746277\pi$
$269$	320556.	−	555219.i	0.270099	−	0.467825i	0.968887	+	0.247504i	$0.0796102\pi$
$270$	73863.9	−	127936.i	0.0616627	−	0.106803i
$271$	274006.	+	474593.i	0.226640	+	0.392552i	0.956810	−	0.290713i	$-0.0938925\pi$
$271$	274006.	+	474593.i	0.226640	+	0.392552i	−0.730170	+	0.683265i	$0.760559\pi$
$272$	−51341.8			−0.0420774
$273$	−621054.	+	693569.i	−0.504339	+	0.563227i
$274$	−287651.			−0.231467
$275$	549607.	+	951948.i	0.438249	+	0.759069i
$276$	224832.	−	389421.i	0.177658	−	0.307713i
$277$	−837070.	+	1.44985e6i	−0.655485	+	1.13533i	0.326287	+	0.945271i	$0.394202\pi$
$277$	−837070.	+	1.44985e6i	−0.655485	+	1.13533i	−0.981772	+	0.190062i	$0.939131\pi$
$278$	698847.	+	1.21044e6i	0.542338	+	0.939358i
$279$	102157.			0.0785698
$280$	166151.	+	506623.i	0.126651	+	0.386180i
$281$	1.81078e6			1.36804			0.684021	−	0.729462i	$-0.260230\pi$
$281$	1.81078e6			1.36804			0.684021	+	0.729462i	$0.260230\pi$
$282$	84968.1	+	147169.i	0.0636258	+	0.110203i
$283$	−1.25657e6	+	2.17645e6i	−0.932657	+	1.61541i	−0.153898	+	0.988087i	$0.549183\pi$
$283$	−1.25657e6	+	2.17645e6i	−0.932657	+	1.61541i	−0.778759	+	0.627323i	$0.784151\pi$
$284$	−1.52004e6	+	2.63279e6i	−1.11830	+	1.93696i
$285$	−229735.	−	397913.i	−0.167539	−	0.290185i
$286$	−3.05276e6			−2.20687
$287$	−685285.	−	143697.i	−0.491096	−	0.102978i
$288$	455217.			0.323398
$289$	−236142.	−	409009.i	−0.166314	−	0.288064i
$290$	−712831.	+	1.23466e6i	−0.497728	+	0.862090i
$291$	356979.	−	618306.i	0.247121	−	0.428027i
$292$	−1.02265e6	−	1.77127e6i	−0.701888	−	1.21571i
$293$	107228.			0.0729691			0.0364845	−	0.999334i	$-0.488384\pi$
$293$	107228.			0.0729691			0.0364845	+	0.999334i	$0.488384\pi$
$294$	−1.27180e6	−	557894.i	−0.858122	−	0.376429i
$295$	164117.			0.109799
$296$	910836.	+	1.57761e6i	0.604242	+	1.04658i
$297$	−151891.	+	263082.i	−0.0999171	+	0.173061i
$298$	1.66575e6	−	2.88517e6i	1.08660	−	1.88205i
$299$	381166.	+	660199.i	0.246568	+	0.427068i
$300$	−1.24151e6			−0.796431
$301$	2.49788e6	+	523778.i	1.58911	+	0.333220i
$302$	−1.88330e6			−1.18824
$303$	381752.	+	661214.i	0.238877	+	0.413747i
$304$	−43166.3	+	74766.2i	−0.0267893	+	0.0464004i
$305$	−38574.4	+	66812.8i	−0.0237437	+	0.0411254i
$306$	−511485.	−	885917.i	−0.312269	−	0.540866i
$307$	1.49622e6			0.906042			0.453021	−	0.891500i	$-0.350346\pi$
$307$	1.49622e6			0.906042			0.453021	+	0.891500i	$0.350346\pi$
$308$	−880385.	−	2.68445e6i	−0.528805	−	1.61242i
$309$	182990.			0.109027
$310$	127787.	+	221333.i	0.0755234	+	0.130810i
$311$	−430601.	+	745823.i	−0.252449	+	0.437255i	−0.964200	−	0.265178i	$-0.914569\pi$
$311$	−430601.	+	745823.i	−0.252449	+	0.437255i	0.711750	+	0.702433i	$0.247903\pi$
$312$	669052.	−	1.15883e6i	0.389111	−	0.673960i
$313$	251969.	+	436422.i	0.145374	+	0.251794i	0.929512	−	0.368791i	$-0.120228\pi$
$313$	251969.	+	436422.i	0.145374	+	0.251794i	−0.784139	+	0.620586i	$0.786895\pi$
$314$	709452.			0.406068
$315$	−154613.	+	172666.i	−0.0877952	+	0.0980464i
$316$	510435.			0.287556
$317$	240004.	+	415700.i	0.134144	+	0.232344i	0.925270	−	0.379309i	$-0.123838\pi$
$317$	240004.	+	415700.i	0.134144	+	0.232344i	−0.791126	+	0.611653i	$0.790505\pi$
$318$	744619.	−	1.28972e6i	0.412921	−	0.715199i
$319$	1.46584e6	−	2.53890e6i	0.806508	−	1.39691i
$320$	582608.	+	1.00911e6i	0.318055	+	0.550887i
$321$	62659.7			0.0339411
$322$	−758604.	+	847180.i	−0.407733	+	0.455340i
$323$	−3.18168e6			−1.69688
$324$	−171554.	−	297140.i	−0.0907899	−	0.157253i
$325$	1.05239e6	−	1.82280e6i	0.552674	−	0.957259i
$326$	848948.	−	1.47042e6i	0.442423	−	0.766298i
$327$	−506931.	−	878031.i	−0.262168	−	0.454088i
$328$	1.00637e6			0.516505
$329$	−83084.8	−	253341.i	−0.0423187	−	0.129037i
$330$	−759995.			−0.384172
$331$	1.09961e6	+	1.90458e6i	0.551656	+	0.955497i	0.998155	+	0.0607125i	$0.0193373\pi$
$331$	1.09961e6	+	1.90458e6i	0.551656	+	0.955497i	−0.446499	+	0.894784i	$0.647329\pi$
$332$	1.84067e6	−	3.18813e6i	0.916496	−	1.58742i
$333$	−395946.	+	685799.i	−0.195671	+	0.338911i
$334$	593392.	+	1.02778e6i	0.291055	+	0.504122i
$335$	349977.			0.170383
$336$	42622.4	+	8937.46i	0.0205963	+	0.00431883i
$337$	−1.35725e6			−0.651008			−0.325504	−	0.945541i	$-0.605534\pi$
$337$	−1.35725e6			−0.651008			−0.325504	+	0.945541i	$0.605534\pi$
$338$	1.21826e6	+	2.11008e6i	0.580026	+	1.00463i
$339$	−504023.	+	872993.i	−0.238205	+	0.412583i
$340$	793854.	−	1.37499e6i	0.372429	−	0.645065i
$341$	−262775.	−	455140.i	−0.122377	−	0.211963i
$342$	−1.72015e6			−0.795245
$343$	1.77325e6	+	1.26616e6i	0.813830	+	0.581103i
$344$	−3.66825e6			−1.67133
$345$	94892.6	+	164359.i	0.0429225	+	0.0743439i
$346$	−2.33142e6	+	4.03814e6i	−1.04696	+	1.81339i
$347$	−1.89970e6	+	3.29038e6i	−0.846959	+	1.46698i	0.0369507	+	0.999317i	$0.488236\pi$
$347$	−1.89970e6	+	3.29038e6i	−0.846959	+	1.46698i	−0.883909	+	0.467658i	$0.845098\pi$
$348$	1.65560e6	+	2.86758e6i	0.732835	+	1.26931i
$349$	−1.31753e6			−0.579024			−0.289512	−	0.957174i	$-0.593493\pi$
$349$	−1.31753e6			−0.579024			−0.289512	+	0.957174i	$0.593493\pi$
$350$	3.07292e6	+	644358.i	1.34085	+	0.281162i
$351$	581682.			0.252010
$352$	−1.17095e6	−	2.02814e6i	−0.503710	−	0.872451i
$353$	1.71253e6	−	2.96618e6i	0.731477	−	1.26695i	−0.224775	−	0.974411i	$-0.572165\pi$
$353$	1.71253e6	−	2.96618e6i	0.731477	−	1.26695i	0.956252	−	0.292544i	$-0.0945018\pi$
$354$	307209.	−	532102.i	0.130294	−	0.225677i
$355$	−641549.	−	1.11120e6i	−0.270184	−	0.467972i
$356$	7.54649e6			3.15588
$357$	500148.	+	1.52504e6i	0.207696	+	0.633302i
$358$	1.21733e6			0.501997
$359$	−735419.	−	1.27378e6i	−0.301161	−	0.521626i	0.675238	−	0.737600i	$-0.264041\pi$
$359$	−735419.	−	1.27378e6i	−0.301161	−	0.521626i	−0.976399	+	0.215974i	$0.930707\pi$
$360$	166563.	−	288495.i	0.0677364	−	0.117323i
$361$	−1.43700e6	+	2.48895e6i	−0.580347	+	1.00519i
$362$	−3.39733e6	−	5.88435e6i	−1.36259	−	2.36008i
$363$	113362.			0.0451547
$364$	−3.60866e6	+	4.03002e6i	−1.42756	+	1.59424i
$365$	863235.			0.339154
$366$	144414.	+	250132.i	0.0563515	+	0.0976037i
$367$	2.49039e6	−	4.31349e6i	0.965168	−	1.67172i	0.256006	−	0.966675i	$-0.417593\pi$
$367$	2.49039e6	−	4.31349e6i	0.965168	−	1.67172i	0.709163	−	0.705045i	$-0.249073\pi$
$368$	17830.0	−	30882.4i	0.00686326	−	0.0118875i
$369$	218738.	+	378866.i	0.0836295	+	0.144850i
$370$	−1.98114e6			−0.752335
$371$	−1.55865e6	+	1.74064e6i	−0.587915	+	0.656561i
$372$	593586.			0.222396
$373$	−1.98024e6	−	3.42987e6i	−0.736962	−	1.27646i	−0.953857	−	0.300261i	$-0.902926\pi$
$373$	−1.98024e6	−	3.42987e6i	−0.736962	−	1.27646i	0.216895	−	0.976195i	$-0.430407\pi$
$374$	−2.63136e6	+	4.55766e6i	−0.972751	+	1.68485i
$375$	572379.	−	991389.i	0.210187	−	0.364054i
$376$	191603.	+	331866.i	0.0698927	+	0.121058i
$377$	−5.61359e6			−2.03417
$378$	270401.	+	824500.i	0.0973371	+	0.296798i
$379$	−1.75155e6			−0.626359			−0.313179	−	0.949694i	$-0.601394\pi$
$379$	−1.75155e6			−0.626359			−0.313179	+	0.949694i	$0.601394\pi$
$380$	−1.33489e6	−	2.31209e6i	−0.474226	−	0.821384i
$381$	−370010.	+	640876.i	−0.130587	+	0.226184i
$382$	−2.67510e6	+	4.63341e6i	−0.937954	+	1.62458i
$383$	−1.56917e6	−	2.71788e6i	−0.546604	−	0.946745i	−0.998504	−	0.0546771i	$-0.982587\pi$
$383$	−1.56917e6	−	2.71788e6i	−0.546604	−	0.946745i	0.451900	−	0.892068i	$-0.350746\pi$
$384$	2.74375e6			0.949549
$385$	1.16699e6	+	244706.i	0.401252	+	0.0841381i
$386$	3.68079e6			1.25740
$387$	−797306.	−	1.38097e6i	−0.270612	−	0.468714i
$388$	2.07425e6	−	3.59270e6i	0.699489	−	1.21155i
$389$	526262.	−	911512.i	0.176331	−	0.305414i	−0.764290	−	0.644872i	$-0.776911\pi$
$389$	526262.	−	911512.i	0.176331	−	0.305414i	0.940621	+	0.339459i	$0.110244\pi$
$390$	727622.	+	1.26028e6i	0.242239	+	0.419570i
$391$	1.31420e6			0.434731
$392$	−2.86789e6	−	1.25805e6i	−0.942645	−	0.413507i
$393$	−1.58231e6			−0.516784
$394$	3.08301e6	+	5.33992e6i	1.00054	+	1.73298i
$395$	−107717.	+	186571.i	−0.0347370	+	0.0601662i
$396$	−882568.	+	1.52865e6i	−0.282820	+	0.489859i
$397$	−227362.	−	393803.i	−0.0724005	−	0.125401i	0.827552	−	0.561389i	$-0.189733\pi$
$397$	−227362.	−	393803.i	−0.0724005	−	0.125401i	−0.899953	+	0.435987i	$0.856399\pi$
$398$	4.17766e6			1.32198
$399$	2.64134e6	+	553861.i	0.830600	+	0.174168i
$400$	−98456.3			−0.0307676
$401$	1.44216e6	+	2.49789e6i	0.447870	+	0.775733i	0.998247	−	0.0591831i	$-0.0188496\pi$
$401$	1.44216e6	+	2.49789e6i	0.447870	+	0.775733i	−0.550378	+	0.834916i	$0.685516\pi$
$402$	655116.	−	1.13469e6i	0.202187	−	0.350198i
$403$	−503164.	+	871505.i	−0.154329	+	0.267305i
$404$	2.21819e6	+	3.84202e6i	0.676153	+	1.17113i
$405$	144812.			0.0438699
$406$	−2.60953e6	−	7.95692e6i	−0.785683	−	2.39569i
$407$	4.07394e6			1.21907
$408$	−1.15340e6	−	1.99774e6i	−0.343027	−	0.594140i
$409$	112957.	−	195647.i	0.0333891	−	0.0578317i	−0.848848	−	0.528637i	$-0.822703\pi$
$409$	112957.	−	195647.i	0.0333891	−	0.0578317i	0.882237	+	0.470805i	$0.156037\pi$
$410$	−547236.	+	947841.i	−0.160774	+	0.278468i
$411$	−140986.	−	244196.i	−0.0411692	−	0.0713072i
$412$	1.06328e6			0.308605
$413$	−643056.	+	718141.i	−0.185513	+	0.207174i
$414$	710513.			0.203738
$415$	776873.	+	1.34558e6i	0.221426	+	0.383522i
$416$	−2.24213e6	+	3.88349e6i	−0.635226	+	1.10024i
$417$	−685053.	+	1.18655e6i	−0.192923	+	0.334152i
$418$	4.42471e6	+	7.66382e6i	1.23864	+	2.14538i
$419$	4.31027e6			1.19941			0.599707	−	0.800220i	$-0.295284\pi$
$419$	4.31027e6			1.19941			0.599707	+	0.800220i	$0.295284\pi$
$420$	−898389.	+	1.00329e6i	−0.248509	+	0.277525i
$421$	1.25088e6			0.343962			0.171981	−	0.985100i	$-0.444983\pi$
$421$	1.25088e6			0.343962			0.171981	+	0.985100i	$0.444983\pi$
$422$	−5.48784e6	−	9.50521e6i	−1.50010	−	2.59825i
$423$	−83290.9	+	144264.i	−0.0226332	+	0.0392019i
$424$	1.67911e6	−	2.90831e6i	0.453592	−	0.785644i
$425$	−1.81424e6	−	3.14236e6i	−0.487218	−	0.843887i
$426$	−4.80363e6			−1.28246
$427$	−141213.	−	430583.i	−0.0374804	−	0.114285i
$428$	364087.			0.0960719
$429$	−1.49625e6	−	2.59158e6i	−0.392519	−	0.679863i
$430$	1.99469e6	−	3.45490e6i	0.520240	−	0.901081i
$431$	2.20397e6	−	3.81738e6i	0.571494	−	0.989857i	−0.424919	−	0.905231i	$-0.639697\pi$
$431$	2.20397e6	−	3.81738e6i	0.571494	−	0.989857i	0.996413	−	0.0846252i	$-0.0269693\pi$
$432$	−13604.8	−	23564.2i	−0.00350738	−	0.00607495i
$433$	−1.60951e6			−0.412549			−0.206274	−	0.978494i	$-0.566134\pi$
$433$	−1.60951e6			−0.412549			−0.206274	+	0.978494i	$0.566134\pi$
$434$	−1.46921e6	−	308077.i	−0.374420	−	0.0785118i
$435$	−1.39752e6			−0.354108
$436$	−2.94555e6	−	5.10184e6i	−0.742079	−	1.28532i
$437$	1.10493e6	−	1.91380e6i	0.276779	−	0.479395i
$438$	1.61588e6	−	2.79878e6i	0.402460	−	0.697082i
$439$	2.21226e6	+	3.83175e6i	0.547867	+	0.948933i	0.998420	+	0.0561836i	$0.0178932\pi$
$439$	2.21226e6	+	3.83175e6i	0.547867	+	0.948933i	−0.450554	+	0.892749i	$0.648773\pi$
$440$	−1.71379e6			−0.422012
$441$	−149732.	−	1.35311e6i	−0.0366622	−	0.331311i
$442$	1.00771e7			2.45347
$443$	1.80719e6	+	3.13015e6i	0.437517	+	0.757801i	0.997497	−	0.0707044i	$-0.0225247\pi$
$443$	1.80719e6	+	3.13015e6i	0.437517	+	0.757801i	−0.559980	+	0.828506i	$0.689191\pi$
$444$	−2.30066e6	+	3.98487e6i	−0.553855	+	0.959305i
$445$	−1.59254e6	+	2.75835e6i	−0.381232	+	0.660313i
$446$	1.36125e6	+	2.35776e6i	0.324042	+	0.561257i
$447$	3.26574e6			0.773060
$448$	−6.69844e6	−	1.40459e6i	−1.57681	−	0.330640i
$449$	−467024.			−0.109326			−0.0546630	−	0.998505i	$-0.517408\pi$
$449$	−467024.			−0.109326			−0.0546630	+	0.998505i	$0.517408\pi$
$450$	−980855.	−	1.69889e6i	−0.228336	−	0.395489i
$451$	1.12531e6	−	1.94910e6i	0.260515	−	0.451225i
$452$	−2.92865e6	+	5.07257e6i	−0.674251	+	1.16784i
$453$	−923065.	−	1.59880e6i	−0.211342	−	0.366056i
$454$	−2.00285e6			−0.456046
$455$	−711495.	−	2.16947e6i	−0.161118	−	0.491276i
$456$	−3.87893e6			−0.873575
$457$	300626.	+	520699.i	0.0673342	+	0.116626i	0.897727	−	0.440552i	$-0.145217\pi$
$457$	300626.	+	520699.i	0.0673342	+	0.116626i	−0.830393	+	0.557178i	$0.811884\pi$
$458$	−5.64280e6	+	9.77362e6i	−1.25699	+	2.17717i
$459$	501388.	−	868430.i	0.111082	−	0.192399i
$460$	551379.	+	955016.i	0.121494	+	0.210434i
$461$	2.87193e6			0.629392			0.314696	−	0.949192i	$-0.398097\pi$
$461$	2.87193e6			0.629392			0.314696	+	0.949192i	$0.398097\pi$
$462$	2.97787e6	−	3.32557e6i	0.649083	−	0.724871i
$463$	−2.91502e6			−0.631959			−0.315979	−	0.948766i	$-0.602333\pi$
$463$	−2.91502e6			−0.631959			−0.315979	+	0.948766i	$0.602333\pi$
$464$	131294.	+	227409.i	0.0283107	+	0.0490357i
$465$	−125264.	+	216964.i	−0.0268655	+	0.0465324i
$466$	−288953.	+	500481.i	−0.0616399	+	0.106763i
$467$	3.59688e6	+	6.22998e6i	0.763192	+	1.32189i	0.941197	+	0.337857i	$0.109702\pi$
$467$	3.59688e6	+	6.22998e6i	0.763192	+	1.32189i	−0.178006	+	0.984029i	$0.556965\pi$
$468$	3.37989e6			0.713327
$469$	−1.37130e6	+	1.53142e6i	−0.287873	+	0.321486i
$470$	−416751.			−0.0870227
$471$	347724.	+	602275.i	0.0722241	+	0.125096i
$472$	692755.	−	1.19989e6i	0.143128	−	0.247905i
$473$	−4.10179e6	+	7.10451e6i	−0.842986	+	1.46009i
$474$	403268.	+	698481.i	0.0824419	+	0.142794i
$475$	−6.10140e6			−1.24078
$476$	2.90614e6	+	8.86133e6i	0.587893	+	1.79259i
$477$	1.45984e6			0.293772
$478$	1.00686e6	+	1.74393e6i	0.201557	+	0.349108i
$479$	1.39824e6	−	2.42183e6i	0.278448	−	0.482286i	−0.692551	−	0.721369i	$-0.743513\pi$
$479$	1.39824e6	−	2.42183e6i	0.278448	−	0.482286i	0.970999	+	0.239083i	$0.0768467\pi$
$480$	−558187.	+	966808.i	−0.110580	+	0.191530i
$481$	−3.90040e6	−	6.75569e6i	−0.768682	−	1.33140i
$482$	−3.98340e6			−0.780974
$483$	−1.09101e6	−	228774.i	−0.212795	−	0.0446209i
$484$	658698.			0.127812
$485$	875456.	+	1.51633e6i	0.168997	+	0.292712i
$486$	271071.	−	469509.i	0.0520586	−	0.0901682i
$487$	1.46624e6	−	2.53960e6i	0.280144	−	0.485224i	−0.691276	−	0.722591i	$-0.742951\pi$
$487$	1.46624e6	−	2.53960e6i	0.280144	−	0.485224i	0.971420	+	0.237367i	$0.0762843\pi$
$488$	325652.	+	564046.i	0.0619020	+	0.107217i
$489$	1.66438e6			0.314761
$490$	2.74436e6	−	2.01700e6i	0.516357	−	0.379504i
$491$	−3.06121e6			−0.573046			−0.286523	−	0.958073i	$-0.592499\pi$
$491$	−3.06121e6			−0.573046			−0.286523	+	0.958073i	$0.592499\pi$
$492$	1.27099e6	+	2.20142e6i	0.236717	+	0.410006i
$493$	−4.83870e6	+	8.38087e6i	−0.896626	+	1.55300i
$494$	8.47246e6	−	1.46747e7i	1.56204	−	2.70553i
$495$	−372497.	−	645183.i	−0.0683297	−	0.118350i
$496$	47073.4			0.00859154
$497$	7.37611e6	+	1.54669e6i	1.33948	+	0.280875i
$498$	5.81687e6			1.05103
$499$	3.27577e6	+	5.67380e6i	0.588928	+	1.02005i	0.994373	+	0.105934i	$0.0337831\pi$
$499$	3.27577e6	+	5.67380e6i	0.588928	+	1.02005i	−0.405445	+	0.914119i	$0.632884\pi$
$500$	3.32583e6	−	5.76052e6i	0.594943	−	1.03047i
$501$	−581679.	+	1.00750e6i	−0.103535	+	0.179329i
$502$	−7.85497e6	−	1.36052e7i	−1.39119	−	2.40960i
$503$	−1.58524e6			−0.279367			−0.139684	−	0.990196i	$-0.544609\pi$
$503$	−1.58524e6			−0.279367			−0.139684	+	0.990196i	$0.544609\pi$
$504$	609752.	+	1.85924e6i	0.106924	+	0.326032i
$505$	−1.87242e6			−0.326719
$506$	−1.82764e6	−	3.16556e6i	−0.317332	−	0.549635i
$507$	−1.19421e6	+	2.06843e6i	−0.206329	+	0.357373i
$508$	−2.14996e6	+	3.72385e6i	−0.369634	+	0.640225i
$509$	−3.38991e6	−	5.87149e6i	−0.579953	−	1.00451i	−0.995484	−	0.0949297i	$-0.969737\pi$
$509$	−3.38991e6	−	5.87149e6i	−0.579953	−	1.00451i	0.415530	−	0.909579i	$-0.363596\pi$
$510$	2.50873e6			0.427099
$511$	−3.38239e6	+	3.77732e6i	−0.573022	+	0.639929i
$512$	432315.			0.0728829
$513$	−843098.	−	1.46029e6i	−0.141444	−	0.244988i
$514$	4.51743e6	−	7.82441e6i	0.754195	−	1.30630i
$515$	−224383.	+	388643.i	−0.0372796	+	0.0645702i
$516$	−4.63279e6	−	8.02422e6i	−0.765981	−	1.32672i
$517$	856990.			0.141010
$518$	7.76265e6	−	8.66903e6i	1.27112	−	1.41954i
$519$	−4.57081e6			−0.744859
$520$	1.64078e6	+	2.84192e6i	0.266099	+	0.460897i
$521$	5.06918e6	−	8.78008e6i	0.818170	−	1.41711i	−0.0888599	−	0.996044i	$-0.528322\pi$
$521$	5.06918e6	−	8.78008e6i	0.818170	−	1.41711i	0.907029	−	0.421067i	$-0.138344\pi$
$522$	−2.61600e6	+	4.53105e6i	−0.420205	+	0.727817i
$523$	−49998.6	−	86600.2i	−0.00799289	−	0.0138441i	0.862001	−	0.506906i	$-0.169211\pi$
$523$	−49998.6	−	86600.2i	−0.00799289	−	0.0138441i	−0.869994	+	0.493062i	$0.835878\pi$
$524$	−9.19408e6			−1.46278
$525$	959116.	+	2.92452e6i	0.151870	+	0.463080i
$526$	−5.02301e6			−0.791589
$527$	867416.	+	1.50241e6i	0.136051	+	0.235647i
$528$	−69990.7	+	121227.i	−0.0109259	+	0.0189241i
$529$	2.76178e6	−	4.78354e6i	0.429091	−	0.743207i
$530$	1.82610e6	+	3.16291e6i	0.282381	+	0.489099i
$531$	602290.			0.0926978
$532$	1.53476e7	+	3.21824e6i	2.35105	+	0.492991i
$533$	−4.30952e6			−0.657068
$534$	5.96209e6	+	1.03266e7i	0.904785	+	1.56713i
$535$	−76833.3	+	133079.i	−0.0116055	+	0.0201014i
$536$	1.47729e6	−	2.55873e6i	0.222102	−	0.384692i
$537$	596651.	+	1.03343e6i	0.0892862	+	0.154648i
$538$	5.88620e6			0.876756
$539$	−5.64338e6	+	4.14768e6i	−0.836695	+	0.614941i
$540$	841436.			0.124176
$541$	59871.4	+	103700.i	0.00879481	+	0.0152331i	0.870389	−	0.492364i	$-0.163867\pi$
$541$	59871.4	+	103700.i	0.00879481	+	0.0152331i	−0.861595	+	0.507597i	$0.830534\pi$
$542$	−2.51571e6	+	4.35734e6i	−0.367843	+	0.637123i
$543$	3.33027e6	−	5.76820e6i	0.484708	−	0.839538i
$544$	3.86527e6	+	6.69485e6i	0.559993	+	0.969937i
$545$	2.48640e6			0.358574
$546$	−8.36571e6	−	1.75420e6i	−1.20094	−	0.251824i
$547$	236568.			0.0338056			0.0169028	−	0.999857i	$-0.494619\pi$
$547$	236568.			0.0338056			0.0169028	+	0.999857i	$0.494619\pi$
$548$	−819209.	−	1.41891e6i	−0.116531	−	0.201838i
$549$	−141563.	+	245194.i	−0.0200456	+	0.0347200i
$550$	−5.04607e6	+	8.74005e6i	−0.711290	+	1.23199i
$551$	8.13641e6	+	1.40927e7i	1.14170	+	1.97749i
$552$	1.60220e6			0.223805
$553$	−394330.	−	1.20238e6i	−0.0548336	−	0.167198i
$554$	−1.53707e7			−2.12774
$555$	−971018.	−	1.68185e6i	−0.133812	−	0.231769i
$556$	−3.98054e6	+	6.89449e6i	−0.546078	+	0.945834i
$557$	2.41833e6	−	4.18867e6i	0.330277	−	0.572056i	−0.652289	−	0.757970i	$-0.726191\pi$
$557$	2.41833e6	−	4.18867e6i	0.330277	−	0.572056i	0.982566	+	0.185914i	$0.0595247\pi$
$558$	468961.	+	812264.i	0.0637604	+	0.110436i
$559$	1.57083e7			2.12617
$560$	−71245.3	+	79564.1i	−0.00960034	+	0.0107213i
$561$	−5.15885e6			−0.692063
$562$	8.31258e6	+	1.43978e7i	1.11018	+	1.92290i
$563$	2.74147e6	−	4.74837e6i	0.364513	−	0.631355i	−0.624185	−	0.781277i	$-0.714569\pi$
$563$	2.74147e6	−	4.74837e6i	0.364513	−	0.631355i	0.988698	+	0.149922i	$0.0479021\pi$
$564$	−483966.	+	838254.i	−0.0640644	+	0.110963i
$565$	−1.23607e6	−	2.14093e6i	−0.162900	−	0.282151i
$566$	−2.30738e7			−3.02746
$567$	−567412.	+	633664.i	−0.0741209	+	0.0827754i
$568$	−1.08322e7			−1.40878
$569$	3.48830e6	+	6.04191e6i	0.451682	+	0.782336i	0.998491	−	0.0549213i	$-0.0174908\pi$
$569$	3.48830e6	+	6.04191e6i	0.451682	+	0.782336i	−0.546809	+	0.837258i	$0.684157\pi$
$570$	2.10925e6	−	3.65333e6i	0.271920	−	0.470979i
$571$	5.88573e6	−	1.01944e7i	0.755458	−	1.30849i	−0.189689	−	0.981844i	$-0.560748\pi$
$571$	5.88573e6	−	1.01944e7i	0.755458	−	1.30849i	0.945146	−	0.326647i	$-0.105919\pi$
$572$	−8.69404e6	−	1.50585e7i	−1.11104	−	1.92439i
$573$	−5.24459e6			−0.667306
$574$	−2.00332e6	−	6.10848e6i	−0.253788	−	0.773844i
$575$	2.52020e6			0.317882
$576$	2.13810e6	+	3.70329e6i	0.268517	+	0.465085i
$577$	−3.38646e6	+	5.86552e6i	−0.423454	+	0.733444i	−0.996275	−	0.0862365i	$-0.972516\pi$
$577$	−3.38646e6	+	5.86552e6i	−0.423454	+	0.733444i	0.572820	+	0.819681i	$0.305849\pi$
$578$	2.16807e6	−	3.75521e6i	0.269932	−	0.467535i
$579$	1.80407e6	+	3.12474e6i	0.223644	+	0.387362i
$580$	−8.12037e6			−1.00232
$581$	−8.93197e6	−	1.87294e6i	−1.09776	−	0.230188i
$582$	6.55501e6			0.802169
$583$	−3.75512e6	−	6.50407e6i	−0.457565	−	0.792526i
$584$	3.64380e6	−	6.31124e6i	0.442102	−	0.765743i
$585$	−713259.	+	1.23540e6i	−0.0861703	+	0.149251i
$586$	492242.	+	852588.i	0.0592154	+	0.102564i
$587$	−1.05020e7			−1.25799			−0.628996	−	0.777408i	$-0.716534\pi$
$587$	−1.05020e7			−1.25799			−0.628996	+	0.777408i	$0.716534\pi$
$588$	−870027.	−	7.86230e6i	−0.103774	−	0.937792i
$589$	2.91717e6			0.346476
$590$	753400.	+	1.30493e6i	0.0891036	+	0.154332i
$591$	−3.02215e6	+	5.23452e6i	−0.355916	+	0.616464i
$592$	−182451.	+	316014.i	−0.0213964	+	0.0370597i
$593$	3.79537e6	+	6.57378e6i	0.443218	+	0.767676i	0.997926	−	0.0643687i	$-0.0205034\pi$
$593$	3.79537e6	+	6.57378e6i	0.443218	+	0.767676i	−0.554708	+	0.832045i	$0.687170\pi$
$594$	−2.78909e6			−0.324336
$595$	−3.85223e6	−	807770.i	−0.446087	−	0.0935396i
$596$	1.89758e7			2.18818
$597$	2.04760e6	+	3.54654e6i	0.235130	+	0.407258i
$598$	−3.49957e6	+	6.06144e6i	−0.400186	+	0.693143i
$599$	6.50992e6	−	1.12755e7i	0.741325	−	1.28401i	−0.210567	−	0.977580i	$-0.567531\pi$
$599$	6.50992e6	−	1.12755e7i	0.741325	−	1.28401i	0.951892	−	0.306434i	$-0.0991358\pi$
$600$	−2.21183e6	−	3.83099e6i	−0.250826	−	0.434443i
$601$	1.41821e7			1.60160			0.800801	−	0.598931i	$-0.204408\pi$
$601$	1.41821e7			1.60160			0.800801	+	0.598931i	$0.204408\pi$
$602$	7.30214e6	+	2.22655e7i	0.821219	+	2.50404i
$603$	1.28437e6			0.143846
$604$	−5.36352e6	−	9.28988e6i	−0.598215	−	1.03614i
$605$	−139005.	+	240764.i	−0.0154398	+	0.0267426i
$606$	−3.50495e6	+	6.07075e6i	−0.387704	+	0.671523i
$607$	−6.03862e6	−	1.04592e7i	−0.665221	−	1.15220i	−0.979225	−	0.202775i	$-0.935004\pi$
$607$	−6.03862e6	−	1.04592e7i	−0.665221	−	1.15220i	0.314004	−	0.949422i	$-0.398329\pi$
$608$	1.29991e7			1.42612
$609$	5.47587e6	−	6.11524e6i	0.598287	−	0.668144i
$610$	−708320.			−0.0770735
$611$	−820485.	−	1.42112e6i	−0.0889135	−	0.154003i
$612$	2.91334e6	−	5.04606e6i	0.314422	−	0.544595i
$613$	1.36265e6	−	2.36018e6i	0.146465	−	0.253684i	−0.783454	−	0.621450i	$-0.786544\pi$
$613$	1.36265e6	−	2.36018e6i	0.146465	−	0.253684i	0.929918	+	0.367766i	$0.119877\pi$
$614$	6.86855e6	+	1.18967e7i	0.735266	+	1.27352i
$615$	−1.07287e6			−0.114382
$616$	6.71508e6	−	7.49914e6i	0.713016	−	0.796269i
$617$	8.47094e6			0.895816			0.447908	−	0.894080i	$-0.352169\pi$
$617$	8.47094e6			0.895816			0.447908	+	0.894080i	$0.352169\pi$
$618$	840038.	+	1.45499e6i	0.0884765	+	0.153246i
$619$	−8.69174e6	+	1.50545e7i	−0.911759	+	1.57921i	−0.100180	+	0.994969i	$0.531942\pi$
$619$	−8.69174e6	+	1.50545e7i	−0.911759	+	1.57921i	−0.811578	+	0.584243i	$0.801391\pi$
$620$	−727855.	+	1.26068e6i	−0.0760441	+	0.131712i
$621$	348244.	+	603176.i	0.0362372	+	0.0627647i
$622$	−7.90690e6			−0.819464
$623$	−5.82995e6	−	1.77765e7i	−0.601789	−	1.83496i
$624$	268037.			0.0275571
$625$	−2.71793e6	−	4.70759e6i	−0.278316	−	0.482058i
$626$	−2.31338e6	+	4.00689e6i	−0.235945	+	0.408669i
$627$	−4.33737e6	+	7.51255e6i	−0.440613	+	0.763165i
$628$	2.02047e6	+	3.49955e6i	0.204434	+	0.354090i
$629$	−1.34480e7			−1.35529
$630$	−2.08267e6	−	436714.i	−0.209059	−	0.0438375i
$631$	−6.45149e6			−0.645040			−0.322520	−	0.946563i	$-0.604530\pi$
$631$	−6.45149e6			−0.645040			−0.322520	+	0.946563i	$0.604530\pi$
$632$	909368.	+	1.57507e6i	0.0905622	+	0.156858i
$633$	5.37951e6	−	9.31759e6i	0.533622	−	0.924260i
$634$	−2.20353e6	+	3.81663e6i	−0.217719	+	0.377101i
$635$	−907413.	−	1.57169e6i	−0.0893040	−	0.154679i
$636$	8.48249e6			0.831535
$637$	1.22810e7	+	5.38725e6i	1.19918	+	0.526039i
$638$	2.69164e7			2.61797
$639$	−2.35440e6	−	4.07795e6i	−0.228102	−	0.395084i
$640$	−3.36439e6	+	5.82730e6i	−0.324681	+	0.562364i
$641$	−8.88581e6	+	1.53907e7i	−0.854185	+	1.47949i	0.0232142	+	0.999731i	$0.492610\pi$
$641$	−8.88581e6	+	1.53907e7i	−0.854185	+	1.47949i	−0.877399	+	0.479761i	$0.840723\pi$
$642$	287647.	+	498218.i	0.0275437	+	0.0477070i
$643$	−9.34806e6			−0.891649			−0.445825	−	0.895120i	$-0.647090\pi$
$643$	−9.34806e6			−0.891649			−0.445825	+	0.895120i	$0.647090\pi$
$644$	−6.33938e6	−	1.32930e6i	−0.602327	−	0.126302i
$645$	3.91063e6			0.370124
$646$	−1.46059e7	−	2.52981e7i	−1.37704	−	2.38510i
$647$	−2.67193e6	+	4.62792e6i	−0.250937	+	0.434635i	−0.963784	−	0.266684i	$-0.914072\pi$
$647$	−2.67193e6	+	4.62792e6i	−0.250937	+	0.434635i	0.712847	+	0.701319i	$0.247405\pi$
$648$	611265.	−	1.05874e6i	0.0571863	−	0.0990495i
$649$	−1.54926e6	−	2.68340e6i	−0.144382	−	0.250077i
$650$	1.93245e7			1.79401
$651$	−458567.	−	1.39825e6i	−0.0424083	−	0.129310i
$652$	9.67098e6			0.890946
$653$	598506.	+	1.03664e6i	0.0549270	+	0.0951363i	0.892182	−	0.451677i	$-0.149174\pi$
$653$	598506.	+	1.03664e6i	0.0549270	+	0.0951363i	−0.837255	+	0.546813i	$0.815841\pi$
$654$	4.65425e6	−	8.06140e6i	0.425506	−	0.736998i
$655$	1.94022e6	−	3.36057e6i	0.176705	−	0.306062i
$656$	100794.	+	174580.i	0.00914481	+	0.0158393i
$657$	3.16796e6			0.286330
$658$	1.63295e6	−	1.82361e6i	0.147030	−	0.164198i
$659$	−1.17541e7			−1.05433			−0.527163	−	0.849764i	$-0.676744\pi$
$659$	−1.17541e7			−1.05433			−0.527163	+	0.849764i	$0.676744\pi$
$660$	−2.16441e6	−	3.74887e6i	−0.193410	−	0.334997i
$661$	9.00573e6	−	1.55984e7i	0.801706	−	1.38860i	−0.116787	−	0.993157i	$-0.537259\pi$
$661$	9.00573e6	−	1.55984e7i	0.801706	−	1.38860i	0.918493	−	0.395438i	$-0.129407\pi$
$662$	−1.00958e7	+	1.74864e7i	−0.895353	+	1.55080i
$663$	4.93910e6	+	8.55476e6i	0.436379	+	0.755830i
$664$	1.31170e7			1.15456
$665$	−4.41512e6	+	4.93064e6i	−0.387158	+	0.432364i
$666$	−7.27054e6			−0.635157
$667$	−3.36076e6	−	5.82102e6i	−0.292498	−	0.506622i
$668$	−3.37987e6	+	5.85411e6i	−0.293062	+	0.507598i
$669$	−1.33438e6	+	2.31122e6i	−0.115270	+	0.199653i
$670$	1.60661e6	+	2.78273e6i	0.138268	+	0.239488i
$671$	1.45656e6			0.124888
$672$	−2.04341e6	−	6.23072e6i	−0.174555	−	0.532249i
$673$	1.40977e7			1.19981			0.599904	−	0.800072i	$-0.295206\pi$
$673$	1.40977e7			1.19981			0.599904	+	0.800072i	$0.295206\pi$
$674$	−6.23063e6	−	1.07918e7i	−0.528302	−	0.915046i
$675$	961494.	−	1.66536e6i	0.0812245	−	0.140685i
$676$	−6.93902e6	+	1.20187e7i	−0.584025	+	1.01156i
$677$	−3.82793e6	−	6.63018e6i	−0.320991	−	0.555973i	0.659702	−	0.751527i	$-0.270683\pi$
$677$	−3.82793e6	−	6.63018e6i	−0.320991	−	0.555973i	−0.980693	+	0.195555i	$0.937349\pi$
$678$	−9.25510e6			−0.773227
$679$	−1.00654e7	−	2.11061e6i	−0.837832	−	0.175684i
$680$	5.65718e6			0.469167
$681$	−981657.	−	1.70028e6i	−0.0811133	−	0.140492i
$682$	2.41260e6	−	4.17874e6i	0.198621	−	0.344021i
$683$	5.43378e6	−	9.41158e6i	0.445708	−	0.771988i	−0.552394	−	0.833583i	$-0.686285\pi$
$683$	5.43378e6	−	9.41158e6i	0.445708	−	0.771988i	0.998101	+	0.0615953i	$0.0196188\pi$
$684$	−4.89886e6	−	8.48508e6i	−0.400364	−	0.693451i
$685$	691510.			0.0563083
$686$	−1.92718e6	+	1.99118e7i	−0.156355	+	1.61548i
$687$	−1.10628e7			−0.894283
$688$	−367396.	−	636348.i	−0.0295912	−	0.0512535i
$689$	−7.19034e6	+	1.24540e7i	−0.577034	+	0.999452i
$690$	−871231.	+	1.50902e6i	−0.0696643	+	0.120662i
$691$	7.30588e6	+	1.26542e7i	0.582073	+	1.00818i	0.995233	+	0.0975219i	$0.0310916\pi$
$691$	7.30588e6	+	1.26542e7i	0.582073	+	1.00818i	−0.413160	+	0.910658i	$0.635575\pi$
$692$	−2.65589e7			−2.10836
$693$	4.28272e6	+	898040.i	0.338756	+	0.0710334i
$694$	−3.48832e7			−2.74927
$695$	−1.68002e6	−	2.90989e6i	−0.131933	−	0.228515i
$696$	−5.89907e6	+	1.02175e7i	−0.461594	+	0.799505i
$697$	−3.71464e6	+	6.43395e6i	−0.289624	+	0.501644i
$698$	−6.04827e6	−	1.04759e7i	−0.469886	−	0.813867i
$699$	−566498.			−0.0438536
$700$	5.57299e6	+	1.69930e7i	0.429876	+	1.31077i
$701$	1.90104e7			1.46115			0.730577	−	0.682830i	$-0.239251\pi$
$701$	1.90104e7			1.46115			0.730577	+	0.682830i	$0.239251\pi$
$702$	2.67028e6	+	4.62506e6i	0.204510	+	0.354221i
$703$	−1.13066e7	+	1.95836e7i	−0.862866	+	1.49453i
$704$	1.09996e7	−	1.90518e7i	0.836458	−	1.44879i
$705$	−204263.	−	353793.i	−0.0154780	−	0.0268088i
$706$	3.14462e7			2.37441
$707$	7.33664e6	−	8.19328e6i	0.552012	−	0.616466i
$708$	3.49964e6			0.262386
$709$	5.79644e6	+	1.00397e7i	0.433058	+	0.750078i	0.997135	−	0.0756440i	$-0.0241013\pi$
$709$	5.79644e6	+	1.00397e7i	0.433058	+	0.750078i	−0.564077	+	0.825722i	$0.690768\pi$
$710$	5.89021e6	−	1.02021e7i	0.438516	−	0.759531i
$711$	−395308.	+	684693.i	−0.0293266	+	0.0507951i
$712$	1.34445e7	+	2.32865e7i	0.993904	+	1.72149i
$713$	−1.20494e6			−0.0887653
$714$	−9.82988e6	+	1.09776e7i	−0.721610	+	0.805867i
$715$	7.33881e6			0.536859
$716$	3.46687e6	+	6.00479e6i	0.252729	+	0.437739i
$717$	−986984.	+	1.70951e6i	−0.0716989	+	0.124186i
$718$	6.75205e6	−	1.16949e7i	0.488792	−	0.846613i
$719$	5.14304e6	+	8.90800e6i	0.371020	+	0.642626i	0.989723	−	0.142999i	$-0.0456747\pi$
$719$	5.14304e6	+	8.90800e6i	0.371020	+	0.642626i	−0.618703	+	0.785625i	$0.712341\pi$
$720$	66728.8			0.00479713
$721$	−821420.	−	2.50466e6i	−0.0588474	−	0.179436i
$722$	−2.63868e7			−1.88384
$723$	−1.95239e6	−	3.38163e6i	−0.138906	−	0.240592i
$724$	1.93507e7	−	3.35164e7i	1.37199	−	2.37635i
$725$	−9.27900e6	+	1.60717e7i	−0.655626	+	1.13558i
$726$	520403.	+	901365.i	0.0366436	+	0.0634686i
$727$	1.00970e7			0.708526			0.354263	−	0.935146i	$-0.384732\pi$
$727$	1.00970e7			0.708526			0.354263	+	0.935146i	$0.384732\pi$
$728$	−1.88646e7	−	3.95571e6i	−1.31923	−	0.276628i
$729$	531441.			0.0370370
$730$	3.96278e6	+	6.86373e6i	0.275228	+	0.476709i
$731$	1.35399e7	−	2.34518e7i	0.937180	−	1.62324i
$732$	−822560.	+	1.42471e6i	−0.0567400	+	0.0982766i
$733$	−962010.	−	1.66625e6i	−0.0661332	−	0.114546i	0.831063	−	0.556178i	$-0.187733\pi$
$733$	−962010.	−	1.66625e6i	−0.0661332	−	0.114546i	−0.897196	+	0.441632i	$0.854400\pi$
$734$	4.57298e7			3.13299
$735$	3.05739e6	+	1.34117e6i	0.208753	+	0.0915728i
$736$	−5.36932e6			−0.365363
$737$	−3.30376e6	−	5.72228e6i	−0.224047	−	0.388061i
$738$	−2.00829e6	+	3.47846e6i	−0.135733	+	0.235096i
$739$	−2.10136e6	+	3.63967e6i	−0.141543	+	0.245161i	−0.928078	−	0.372386i	$-0.878540\pi$
$739$	−2.10136e6	+	3.63967e6i	−0.141543	+	0.245161i	0.786535	+	0.617546i	$0.211873\pi$
$740$	−5.64215e6	−	9.77249e6i	−0.378761	−	0.656034i
$741$	1.66104e7			1.11131
$742$	−2.09953e7	−	4.40250e6i	−1.39995	−	0.293555i
$743$	−1.99659e7			−1.32684			−0.663418	−	0.748249i	$-0.730895\pi$
$743$	−1.99659e7			−1.32684			−0.663418	+	0.748249i	$0.730895\pi$
$744$	1.05751e6	+	1.83165e6i	0.0700407	+	0.121314i
$745$	−4.00445e6	+	6.93592e6i	−0.264334	+	0.457839i
$746$	1.81810e7	−	3.14904e7i	1.19611	−	2.07172i
$747$	2.85102e6	+	4.93812e6i	0.186939	+	0.323787i
$748$	−2.99757e7			−1.95892
$749$	−281271.	−	857646.i	−0.0183198	−	0.0558603i
$750$	1.05103e7			0.682277
$751$	1.81988e6	+	3.15212e6i	0.117745	+	0.203940i	0.918874	−	0.394552i	$-0.129100\pi$
$751$	1.81988e6	+	3.15212e6i	0.117745	+	0.203940i	−0.801129	+	0.598492i	$0.795767\pi$
$752$	−38380.1	+	66476.4i	−0.00247492	+	0.00428670i
$753$	7.69992e6	−	1.33366e7i	0.494878	−	0.857155i
$754$	−2.57698e7	−	4.46346e7i	−1.65076	−	2.85919i
$755$	4.52745e6			0.289059
$756$	−3.29698e6	+	3.68194e6i	−0.209803	+	0.234300i
$757$	1.73429e7			1.09997			0.549986	−	0.835174i	$-0.314633\pi$
$757$	1.73429e7			1.09997			0.549986	+	0.835174i	$0.314633\pi$
$758$	−8.04067e6	−	1.39268e7i	−0.508299	−	0.880399i
$759$	1.79156e6	−	3.10308e6i	0.112883	−	0.195519i
$760$	4.75635e6	−	8.23824e6i	0.298703	−	0.517369i
$761$	5.17841e6	+	8.96927e6i	0.324142	+	0.561430i	0.981338	−	0.192289i	$-0.0615912\pi$
$761$	5.17841e6	+	8.96927e6i	0.324142	+	0.561430i	−0.657196	+	0.753719i	$0.728258\pi$
$762$	−6.79430e6			−0.423894
$763$	−9.74238e6	+	1.08799e7i	−0.605834	+	0.676572i
$764$	−3.04740e7			−1.88884
$765$	1.22960e6	+	2.12974e6i	0.0759647	+	0.131575i
$766$	1.44069e7	−	2.49535e7i	0.887153	−	1.53659i
$767$	−2.96653e6	+	5.13818e6i	−0.182079	+	0.315371i
$768$	4.99339e6	+	8.64881e6i	0.305487	+	0.529119i
$769$	−1.81548e7			−1.10707			−0.553534	−	0.832826i	$-0.686721\pi$
$769$	−1.81548e7			−1.10707			−0.553534	+	0.832826i	$0.686721\pi$
$770$	3.41152e6	+	1.04023e7i	0.207358	+	0.632272i
$771$	8.85652e6			0.536571
$772$	1.04826e7	+	1.81565e7i	0.633034	+	1.09645i
$773$	8.17830e6	−	1.41652e7i	0.492282	−	0.852658i	−0.507678	−	0.861547i	$-0.669496\pi$
$773$	8.17830e6	−	1.41652e7i	0.492282	−	0.852658i	0.999960	+	0.00888861i	$0.00282937\pi$
$774$	7.32025e6	−	1.26790e7i	0.439211	−	0.760736i
$775$	1.66341e6	+	2.88112e6i	0.0994823	+	0.172308i
$776$	1.47815e7			0.881181
$777$	1.11641e7	+	2.34100e6i	0.663395	+	0.139107i
$778$	9.66346e6			0.572379
$779$	6.24627e6	+	1.08189e7i	0.368788	+	0.638760i
$780$	−4.14443e6	+	7.17836e6i	−0.243909	+	0.422463i
$781$	−1.21124e7	+	2.09793e7i	−0.710562	+	1.23073i
$782$	6.03300e6	+	1.04495e7i	0.352790	+	0.611051i
$783$	−5.12873e6			−0.298955
$784$	−68996.1	−	623507.i	−0.00400898	−	0.0362286i
$785$	−1.70552e6			−0.0987829
$786$	−7.26376e6	−	1.25812e7i	−0.419378	−	0.726383i
$787$	2.22364e6	−	3.85146e6i	0.127976	−	0.221661i	−0.794916	−	0.606719i	$-0.792485\pi$
$787$	2.22364e6	−	3.85146e6i	0.127976	−	0.221661i	0.922892	+	0.385058i	$0.125819\pi$
$788$	−1.75604e7	+	3.04154e7i	−1.00744	+	1.74493i
$789$	−2.46193e6	−	4.26419e6i	−0.140794	−	0.243862i
$790$	−1.97795e6			−0.112758
$791$	1.42115e7	+	2.97999e6i	0.807603	+	0.169346i
$792$	−6.28938e6			−0.356283
$793$	−1.39452e6	−	2.41537e6i	−0.0787481	−	0.136396i
$794$	2.08746e6	−	3.61559e6i	0.117508	−	0.203530i
$795$	−1.79006e6	+	3.10047e6i	−0.100450	+	0.173984i
$796$	1.18977e7	+	2.06074e7i	0.665548	+	1.15276i
$797$	−9.15303e6			−0.510410			−0.255205	−	0.966887i	$-0.582143\pi$
$797$	−9.15303e6			−0.510410			−0.255205	+	0.966887i	$0.582143\pi$
$798$	7.72153e6	+	2.35443e7i	0.429236	+	1.30882i
$799$	−2.82891e6			−0.156766
$800$	7.41229e6	+	1.28385e7i	0.409475	+	0.709232i
$801$	−5.84440e6	+	1.01228e7i	−0.321854	+	0.557467i
$802$	−1.32408e7	+	2.29337e7i	−0.726905	+	1.25904i
$803$	−8.14889e6	−	1.41143e7i	−0.445974	−	0.772450i
$804$	7.46290e6			0.407162
$805$	1.82368e6	−	2.03662e6i	0.0991879	−	0.110769i
$806$	−9.23932e6			−0.500959
$807$	2.88500e6	+	4.99697e6i	0.155942	+	0.270099i
$808$	−7.90365e6	+	1.36895e7i	−0.425892	+	0.737666i
$809$	−1.25962e7	+	2.18172e7i	−0.676654	+	1.17200i	0.299328	+	0.954150i	$0.403237\pi$
$809$	−1.25962e7	+	2.18172e7i	−0.676654	+	1.17200i	−0.975982	+	0.217849i	$0.930096\pi$
$810$	664775.	+	1.15142e6i	0.0356010	+	0.0616627i
$811$	−8.90585e6			−0.475470			−0.237735	−	0.971330i	$-0.576405\pi$
$811$	−8.90585e6			−0.475470			−0.237735	+	0.971330i	$0.576405\pi$
$812$	3.18178e7	−	3.55329e7i	1.69348	−	1.89121i
$813$	−4.93211e6			−0.261702
$814$	1.87019e7	+	3.23926e7i	0.989291	+	1.71350i
$815$	−2.04087e6	+	3.53488e6i	−0.107627	+	0.186415i
$816$	231038.	−	400170.i	0.0121467	−	0.0210387i
$817$	−2.27678e7	−	3.94349e7i	−1.19334	−	2.06693i
$818$	2.07417e6			0.108383
$819$	−2.61110e6	−	7.96170e6i	−0.136023	−	0.414759i
$820$	−6.23396e6			−0.323765
$821$	−1.67745e7	−	2.90543e7i	−0.868543	−	1.50436i	−0.863485	−	0.504374i	$-0.831723\pi$
$821$	−1.67745e7	−	2.90543e7i	−0.868543	−	1.50436i	−0.00505812	−	0.999987i	$-0.501610\pi$
$822$	1.29443e6	−	2.24202e6i	0.0668188	−	0.115734i
$823$	7.30006e6	−	1.26441e7i	0.375688	−	0.650710i	−0.614742	−	0.788728i	$-0.710740\pi$
$823$	7.30006e6	−	1.26441e7i	0.375688	−	0.650710i	0.990430	+	0.138018i	$0.0440732\pi$
$824$	1.89428e6	+	3.28100e6i	0.0971912	+	0.168340i
$825$	−9.89293e6			−0.506046
$826$	−8.66209e6	−	1.81635e6i	−0.441746	−	0.0926294i
$827$	1.97530e7			1.00431			0.502156	−	0.864777i	$-0.332540\pi$
$827$	1.97530e7			1.00431			0.502156	+	0.864777i	$0.332540\pi$
$828$	2.02349e6	+	3.50479e6i	0.102571	+	0.177658i
$829$	2.03127e6	−	3.51827e6i	0.102655	−	0.177804i	−0.810122	−	0.586261i	$-0.800599\pi$
$829$	2.03127e6	−	3.51827e6i	0.102655	−	0.177804i	0.912778	+	0.408456i	$0.133933\pi$
$830$	−7.13264e6	+	1.23541e7i	−0.359381	+	0.622467i
$831$	−7.53363e6	−	1.30486e7i	−0.378444	−	0.655485i
$832$	−4.21241e7			−2.10971
$833$	1.86287e7	−	1.36914e7i	0.930186	−	0.683653i
$834$	−1.25793e7			−0.626239
$835$	−1.42651e6	−	2.47079e6i	−0.0708041	−	0.122636i
$836$	−2.52025e7	+	4.36520e7i	−1.24718	+	2.16017i
$837$	−459704.	+	796231.i	−0.0226811	+	0.0392849i
$838$	1.97868e7	+	3.42717e7i	0.973341	+	1.68588i
$839$	−1.60509e7			−0.787217			−0.393609	−	0.919278i	$-0.628773\pi$
$839$	−1.60509e7			−0.787217			−0.393609	+	0.919278i	$0.628773\pi$
$840$	−4.69642e6	−	984788.i	−0.229651	−	0.0481554i
$841$	2.89842e7			1.41309
$842$	5.74231e6	+	9.94597e6i	0.279130	+	0.483467i
$843$	−8.14850e6	+	1.41136e7i	−0.394920	+	0.684021i
$844$	3.12579e7	−	5.41403e7i	1.51044	−	2.61616i
$845$	−2.92868e6	−	5.07263e6i	−0.141101	−	0.244394i
$846$	−1.52943e6			−0.0734687
$847$	−508869.	−	1.55163e6i	−0.0243724	−	0.0743157i
$848$	672690.			0.0321237
$849$	−1.13092e7	−	1.95881e7i	−0.538470	−	0.932657i
$850$	1.66570e7	−	2.88508e7i	0.790768	−	1.36965i
$851$	4.67022e6	−	8.08905e6i	0.221061	−	0.382890i
$852$	−1.36804e7	−	2.36951e7i	−0.645654	−	1.11830i
$853$	−1.23887e7			−0.582979			−0.291489	−	0.956574i	$-0.594151\pi$
$853$	−1.23887e7			−0.582979			−0.291489	+	0.956574i	$0.594151\pi$
$854$	2.77539e6	−	3.09945e6i	0.130221	−	0.145425i
$855$	4.13523e6			0.193457
$856$	648642.	+	1.12348e6i	0.0302566	+	0.0524060i
$857$	−1.31760e7	+	2.28214e7i	−0.612816	+	1.06143i	0.377948	+	0.925827i	$0.376630\pi$
$857$	−1.31760e7	+	2.28214e7i	−0.612816	+	1.06143i	−0.990764	+	0.135601i	$0.956703\pi$
$858$	1.37374e7	−	2.37939e7i	0.637070	−	1.10344i
$859$	6.06245e6	+	1.05005e7i	0.280327	+	0.485541i	0.971465	−	0.237182i	$-0.0762237\pi$
$859$	6.06245e6	+	1.05005e7i	0.280327	+	0.485541i	−0.691138	+	0.722723i	$0.742890\pi$
$860$	2.27229e7			1.04765
$861$	4.20379e6	−	4.69463e6i	0.193256	−	0.215821i
$862$	4.04702e7			1.85510
$863$	−1.27976e6	−	2.21661e6i	−0.0584927	−	0.101312i	0.835296	−	0.549800i	$-0.185296\pi$
$863$	−1.27976e6	−	2.21661e6i	−0.0584927	−	0.101312i	−0.893789	+	0.448488i	$0.851963\pi$
$864$	−2.04848e6	+	3.54806e6i	−0.0933569	+	0.161699i
$865$	5.60472e6	−	9.70766e6i	0.254691	−	0.441138i
$866$	−7.38866e6	−	1.27975e7i	−0.334789	−	0.579871i
$867$	4.25055e6			0.192042
$868$	−2.66453e6	−	8.12462e6i	−0.120039	−	0.366019i
$869$	4.06737e6			0.182711
$870$	−6.41548e6	−	1.11119e7i	−0.287363	−	0.497728i
$871$	−6.32606e6	+	1.09571e7i	−0.282545	+	0.489383i
$872$	1.04953e7	−	1.81784e7i	0.467417	−	0.809590i
$873$	3.21281e6	+	5.56475e6i	0.142676	+	0.247121i
$874$	2.02893e7			0.898439
$875$	−1.61388e7	−	3.38414e6i	−0.712610	−	0.149427i
$876$	1.84076e7			0.810471
$877$	−1.32910e7	−	2.30207e7i	−0.583523	−	1.01069i	−0.995058	−	0.0992977i	$-0.968340\pi$
$877$	−1.32910e7	−	2.30207e7i	−0.583523	−	1.01069i	0.411535	−	0.911394i	$-0.364993\pi$
$878$	−2.03113e7	+	3.51801e7i	−0.889203	+	1.54014i
$879$	−482526.	+	835759.i	−0.0210644	+	0.0364845i
$880$	−171645.	−	297298.i	−0.00747179	−	0.0129415i
$881$	−8.32262e6			−0.361260			−0.180630	−	0.983551i	$-0.557814\pi$
$881$	−8.32262e6			−0.361260			−0.180630	+	0.983551i	$0.557814\pi$
$882$	1.00714e7	−	7.40214e6i	0.435933	−	0.320395i
$883$	1.81133e7			0.781798			0.390899	−	0.920434i	$-0.372164\pi$
$883$	1.81133e7			0.781798			0.390899	+	0.920434i	$0.372164\pi$
$884$	2.86989e7	+	4.97079e7i	1.23519	+	2.13941i
$885$	−738528.	+	1.27917e6i	−0.0316963	+	0.0548996i
$886$	−1.65922e7	+	2.87386e7i	−0.710102	+	1.22993i
$887$	1.02128e7	+	1.76890e7i	0.435847	+	0.754909i	0.997364	−	0.0725558i	$-0.0231156\pi$
$887$	1.02128e7	+	1.76890e7i	0.435847	+	0.754909i	−0.561517	+	0.827465i	$0.689782\pi$
$888$	−1.63950e7			−0.697718
$889$	1.04328e7	+	2.18765e6i	0.442739	+	0.0928377i
$890$	−2.92429e7			−1.23750
$891$	−1.36702e6	−	2.36774e6i	−0.0576872	−	0.0999171i
$892$	−7.75349e6	+	1.34294e7i	−0.326276	+	0.565127i
$893$	−2.37844e6	+	4.11959e6i	−0.0998078	+	0.172872i
$894$	1.49918e7	+	2.59665e7i	0.627348	+	1.08660i
$895$	−2.92645e6			−0.122119
$896$	−1.23164e7	−	3.75548e7i	−0.512522	−	1.56277i
$897$	−6.86099e6			−0.284712
$898$	−2.14393e6	−	3.71339e6i	−0.0887195	−	0.153667i
$899$	4.43642e6	−	7.68411e6i	0.183077	−	0.317099i
$900$	5.58681e6	−	9.67664e6i	0.229910	−	0.398216i
$901$	1.23956e7	+	2.14698e7i	0.508693	+	0.881082i
$902$	2.06635e7			0.845645
$903$	−1.53229e7	+	1.71120e7i	−0.625347	+	0.698364i
$904$	−2.08702e7			−0.849388
$905$	8.16715e6	+	1.41459e7i	0.331474	+	0.574130i
$906$	8.47487e6	−	1.46789e7i	0.343015	−	0.594119i
$907$	1.00599e7	−	1.74242e7i	0.406044	−	0.703290i	−0.588398	−	0.808571i	$-0.700241\pi$
$907$	1.00599e7	−	1.74242e7i	0.406044	−	0.703290i	0.994442	+	0.105282i	$0.0335745\pi$
$908$	−5.70397e6	−	9.87957e6i	−0.229595	−	0.397670i
$909$	−6.87153e6			−0.275832
$910$	1.39837e7	−	1.56164e7i	0.559781	−	0.625142i
$911$	3.17075e7			1.26580			0.632902	−	0.774232i	$-0.281863\pi$
$911$	3.17075e7			1.26580			0.632902	+	0.774232i	$0.281863\pi$
$912$	−388497.	−	672896.i	−0.0154668	−	0.0267893i
$913$	1.46673e7	−	2.54045e7i	0.582334	−	1.00863i
$914$	−2.76012e6	+	4.78066e6i	−0.109285	+	0.189288i
$915$	−347169.	−	601315.i	−0.0137085	−	0.0237437i
$916$	−6.42812e7			−2.53131
$917$	7.10277e6	+	2.16576e7i	0.278936	+	0.850525i
$918$	9.20672e6			0.360577
$919$	4.35364e6	+	7.54072e6i	0.170045	+	0.294526i	0.938435	−	0.345455i	$-0.112275\pi$
$919$	4.35364e6	+	7.54072e6i	0.170045	+	0.294526i	−0.768390	+	0.639981i	$0.778942\pi$
$920$	−1.96462e6	+	3.40283e6i	−0.0765261	+	0.132547i
$921$	−6.73297e6	+	1.16619e7i	−0.261552	+	0.453021i
$922$	1.31839e7	+	2.28352e7i	0.510760	+	0.884663i
$923$	4.63857e7			1.79217
$924$	2.48850e7	+	5.21811e6i	0.958864	+	0.201064i
$925$	−2.57887e7			−0.991005
$926$	−1.33817e7	−	2.31778e7i	−0.512843	−	0.888270i
$927$	−823457.	+	1.42627e6i	−0.0314732	+	0.0545133i
$928$	1.97690e7	−	3.42410e7i	0.753556	−	1.30520i
$929$	−1.62021e7	−	2.80629e7i	−0.615931	−	1.06682i	−0.990220	−	0.139512i	$-0.955447\pi$
$929$	−1.62021e7	−	2.80629e7i	−0.615931	−	1.06682i	0.374289	−	0.927312i	$-0.377887\pi$
$930$	−2.30016e6			−0.0872069
$931$	−4.27574e6	−	3.86392e7i	−0.161673	−	1.46101i
$932$	−3.29167e6			−0.124130
$933$	−3.87541e6	−	6.71241e6i	−0.145752	−	0.252449i
$934$	−3.30238e7	+	5.71988e7i	−1.23868	+	2.14546i
$935$	6.32578e6	−	1.09566e7i	0.236638	−	0.409869i
$936$	6.02147e6	+	1.04295e7i	0.224653	+	0.389111i
$937$	−2.19155e7			−0.815458			−0.407729	−	0.913103i	$-0.633679\pi$
$937$	−2.19155e7			−0.815458			−0.407729	+	0.913103i	$0.633679\pi$
$938$	−1.84717e7	−	3.87332e6i	−0.685488	−	0.143740i
$939$	−4.53544e6			−0.167863
$940$	−1.18688e6	−	2.05573e6i	−0.0438113	−	0.0758835i
$941$	−7.30095e6	+	1.26456e7i	−0.268785	+	0.465550i	−0.968548	−	0.248825i	$-0.919956\pi$
$941$	−7.30095e6	+	1.26456e7i	−0.268785	+	0.465550i	0.699763	+	0.714375i	$0.253289\pi$
$942$	−3.19253e6	+	5.52963e6i	−0.117222	+	0.203034i
$943$	−2.58004e6	−	4.46876e6i	−0.0944815	−	0.163647i
$944$	277533.			0.0101364
$945$	−650041.	−	1.98209e6i	−0.0236789	−	0.0722012i
$946$	−7.53189e7			−2.73638
$947$	1.04189e7	+	1.80461e7i	0.377527	+	0.653895i	0.990702	−	0.136052i	$-0.0434414\pi$
$947$	1.04189e7	+	1.80461e7i	0.377527	+	0.653895i	−0.613175	+	0.789947i	$0.710108\pi$
$948$	−2.29696e6	+	3.97845e6i	−0.0830103	+	0.143778i
$949$	−1.56035e7	+	2.70261e7i	−0.562416	+	0.974134i
$950$	−2.80092e7	−	4.85133e7i	−1.00691	−	1.74402i
$951$	−4.32008e6			−0.154896
$952$	−2.21663e7	+	2.47545e7i	−0.792687	+	0.885243i
$953$	−942012.			−0.0335988			−0.0167994	−	0.999859i	$-0.505348\pi$
$953$	−942012.			−0.0335988			−0.0167994	+	0.999859i	$0.505348\pi$
$954$	6.70157e6	+	1.16075e7i	0.238400	+	0.412921i
$955$	6.43092e6	−	1.11387e7i	0.228173	−	0.395208i
$956$	−5.73492e6	+	9.93318e6i	−0.202947	+	0.351515i
$957$	1.31925e7	+	2.28501e7i	0.465638	+	0.806508i
$958$	2.56752e7			0.903857
$959$	−2.70953e6	+	3.02589e6i	−0.0951364	+	0.106245i
$960$	−1.04869e7			−0.367258
$961$	1.35193e7	+	2.34161e7i	0.472221	+	0.817910i
$962$	3.58105e7	−	6.20256e7i	1.24759	−	2.16089i
$963$	−281969.	+	488384.i	−0.00979795	+	0.0169705i
$964$	−1.13444e7	−	1.96492e7i	−0.393179	−	0.681006i
$965$	−8.84860e6			−0.305884
$966$	−3.18940e6	−	9.72505e6i	−0.109968	−	0.335312i
$967$	−2.56570e7			−0.882346			−0.441173	−	0.897422i	$-0.645438\pi$
$967$	−2.56570e7			−0.882346			−0.441173	+	0.897422i	$0.645438\pi$
$968$	1.17351e6	+	2.03257e6i	0.0402529	+	0.0697201i
$969$	1.43176e7	−	2.47988e7i	0.489847	−	0.848439i
$970$	−8.03776e6	+	1.39218e7i	−0.274287	+	0.475079i
$971$	1.07137e7	+	1.85566e7i	0.364662	+	0.631613i	0.988722	−	0.149763i	$-0.0478511\pi$
$971$	1.07137e7	+	1.85566e7i	0.364662	+	0.631613i	−0.624060	+	0.781377i	$0.714518\pi$
$972$	3.08797e6			0.104835
$973$	1.93158e7	+	4.05032e6i	0.654080	+	0.137153i
$974$	2.69237e7			0.909364
$975$	9.47153e6	+	1.64052e7i	0.319086	+	0.552674i
$976$	−65231.8	+	112985.i	−0.00219197	+	0.00379660i
$977$	1.02420e7	−	1.77397e7i	0.343281	−	0.594580i	−0.641759	−	0.766906i	$-0.721795\pi$
$977$	1.02420e7	−	1.77397e7i	0.343281	−	0.594580i	0.985040	+	0.172326i	$0.0551283\pi$
$978$	7.64054e6	+	1.32338e7i	0.255433	+	0.442423i
$979$	6.01338e7			2.00522
$980$	1.77651e7	+	7.79296e6i	0.590885	+	0.259201i
$981$	9.12476e6			0.302726
$982$	−1.40528e7	−	2.43402e7i	−0.465035	−	0.805464i
$983$	−1.38825e7	+	2.40452e7i	−0.458230	+	0.793677i	−0.998868	−	0.0475784i	$-0.984850\pi$
$983$	−1.38825e7	+	2.40452e7i	−0.458230	+	0.793677i	0.540638	+	0.841255i	$0.318183\pi$
$984$	−4.52868e6	+	7.84391e6i	−0.149102	+	0.258253i
$985$	−7.41152e6	−	1.28371e7i	−0.243398	−	0.421578i
$986$	−8.88504e7			−2.91050
$987$	2.34848e6	+	492450.i	0.0767349	+	0.0160905i
$988$	9.65159e7			3.14562
$989$	9.40429e6	+	1.62887e7i	0.305728	+	0.529536i
$990$	3.41998e6	−	5.92357e6i	0.110901	−	0.192086i
$991$	−1.73416e7	+	3.00366e7i	−0.560926	+	0.971552i	0.436490	+	0.899709i	$0.356221\pi$
$991$	−1.73416e7	+	3.00366e7i	−0.560926	+	0.971552i	−0.997416	+	0.0718429i	$0.977112\pi$
$992$	−3.54392e6	−	6.13826e6i	−0.114342	−	0.198046i
$993$	−1.97930e7			−0.636998
$994$	2.15629e7	+	6.57490e7i	0.692214	+	2.11068i
$995$	−1.00431e7			−0.321594
$996$	1.65660e7	+	2.86932e7i	0.529139	+	0.916496i
$997$	7.42861e6	−	1.28667e7i	0.236685	−	0.409950i	−0.723076	−	0.690768i	$-0.757273\pi$
$997$	7.42861e6	−	1.28667e7i	0.236685	−	0.409950i	0.959761	+	0.280818i	$0.0906059\pi$
$998$	−3.00756e7	+	5.20925e7i	−0.955846	+	1.65557i
$999$	−3.56351e6	−	6.17219e6i	−0.112970	−	0.195671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.c.4.4	✓	8
3.2	odd	2		63.6.e.e.46.1		8
4.3	odd	2		336.6.q.j.193.3		8
7.2	even	3	inner	21.6.e.c.16.4	yes	8
7.3	odd	6		147.6.a.l.1.1		4
7.4	even	3		147.6.a.m.1.1		4
7.5	odd	6		147.6.e.o.79.4		8
7.6	odd	2		147.6.e.o.67.4		8
21.2	odd	6		63.6.e.e.37.1		8
21.11	odd	6		441.6.a.w.1.4		4
21.17	even	6		441.6.a.v.1.4		4
28.23	odd	6		336.6.q.j.289.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.4	✓	8	1.1	even	1	trivial
21.6.e.c.16.4	yes	8	7.2	even	3	inner
63.6.e.e.37.1		8	21.2	odd	6
63.6.e.e.46.1		8	3.2	odd	2
147.6.a.l.1.1		4	7.3	odd	6
147.6.a.m.1.1		4	7.4	even	3
147.6.e.o.67.4		8	7.6	odd	2
147.6.e.o.79.4		8	7.5	odd	6
336.6.q.j.193.3		8	4.3	odd	2
336.6.q.j.289.3		8	28.23	odd	6
441.6.a.v.1.4		4	21.17	even	6
441.6.a.w.1.4		4	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.59061 + 7.95118i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(-11.0358 - 19.1146i) q^{5} -82.6311 q^{6} +(126.882 + 26.6059i) q^{7} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.59061 + 7.95118i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-26.1475 + 45.2888i) q^{4} +(-11.0358 - 19.1146i) q^{5} -82.6311 q^{6} +(126.882 + 26.6059i) q^{7} -186.333 q^{8} +(-40.5000 - 70.1481i) q^{9} +(101.322 - 175.495i) q^{10} +(-208.355 + 360.881i) q^{11} +(-235.327 - 407.599i) q^{12} +797.918 q^{13} +(370.920 + 1131.00i) q^{14} +198.644 q^{15} +(-18.6623 - 32.3240i) q^{16} +(687.775 - 1191.26i) q^{17} +(371.840 - 644.045i) q^{18} +(-1156.51 - 2003.14i) q^{19} +1154.23 q^{20} +(-778.343 + 869.224i) q^{21} -3825.91 q^{22} +(477.701 + 827.402i) q^{23} +(838.497 - 1452.32i) q^{24} +(1318.92 - 2284.44i) q^{25} +(3662.93 + 6344.39i) q^{26} +729.000 q^{27} +(-4522.60 + 5050.67i) q^{28} -7035.29 q^{29} +(911.900 + 1579.46i) q^{30} +(-630.596 + 1092.22i) q^{31} +(-2809.98 + 4867.03i) q^{32} +(-1875.19 - 3247.93i) q^{33} +12629.2 q^{34} +(-891.689 - 2718.92i) q^{35} +4235.89 q^{36} +(-4888.22 - 8466.65i) q^{37} +(10618.2 - 18391.3i) q^{38} +(-3590.63 + 6219.16i) q^{39} +(2056.33 + 3561.67i) q^{40} -5400.95 q^{41} +(-10484.4 - 2198.47i) q^{42} +19686.6 q^{43} +(-10895.9 - 18872.3i) q^{44} +(-893.900 + 1548.28i) q^{45} +(-4385.88 + 7596.57i) q^{46} +(-1028.28 - 1781.04i) q^{47} +335.921 q^{48} +(15391.3 + 6751.63i) q^{49} +24218.7 q^{50} +(6189.98 + 10721.4i) q^{51} +(-20863.5 + 36136.7i) q^{52} +(-9011.37 + 15608.2i) q^{53} +(3346.56 + 5796.41i) q^{54} +9197.45 q^{55} +(-23642.3 - 4957.54i) q^{56} +20817.2 q^{57} +(-32296.3 - 55938.8i) q^{58} +(-3717.84 + 6439.49i) q^{59} +(-5194.05 + 8996.36i) q^{60} +(-1747.69 - 3027.09i) q^{61} -11579.3 q^{62} +(-3272.39 - 9978.09i) q^{63} -52792.5 q^{64} +(-8805.67 - 15251.9i) q^{65} +(17216.6 - 29820.0i) q^{66} +(-7928.21 + 13732.1i) q^{67} +(35967.2 + 62297.0i) q^{68} -8598.62 q^{69} +(17525.2 - 19571.5i) q^{70} +58133.5 q^{71} +(7546.48 + 13070.9i) q^{72} +(-19555.3 + 33870.8i) q^{73} +(44879.9 - 77734.2i) q^{74} +(11870.3 + 20560.0i) q^{75} +120960. q^{76} +(-36038.1 + 40246.0i) q^{77} -65932.8 q^{78} +(-4880.35 - 8453.01i) q^{79} +(-411.906 + 713.442i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(-24793.7 - 42943.9i) q^{82} -70395.7 q^{83} +(-19014.4 - 57978.2i) q^{84} -30360.6 q^{85} +(90373.4 + 156531. i) q^{86} +(31658.8 - 54834.7i) q^{87} +(38823.3 - 67243.9i) q^{88} +(-72153.1 - 124973. i) q^{89} -16414.2 q^{90} +(101242. + 21229.3i) q^{91} -49962.7 q^{92} +(-5675.36 - 9830.01i) q^{93} +(9440.90 - 16352.1i) q^{94} +(-25526.1 + 44212.5i) q^{95} +(-25289.8 - 43803.3i) q^{96} -79328.7 q^{97} +(16971.9 + 153373. i) q^{98} +33753.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

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