LMFDB - Embedded newform 21.6.e.c.16.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("21.4");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			16.2
Root			$-0.874091 + 1.51397i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.6.e.c.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37409 + 2.37999i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(12.2237 + 21.1722i) q^{4} +(-29.1836 + 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 + 127.857i) q^{7} -155.128 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-1.37409 + 2.37999i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(12.2237 + 21.1722i) q^{4} +(-29.1836 + 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 + 127.857i) q^{7} -155.128 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-80.2019 - 138.914i) q^{10} +(-8.71205 - 15.0897i) q^{11} +(110.014 - 190.549i) q^{12} +889.933 q^{13} +(-274.844 - 226.706i) q^{14} +525.305 q^{15} +(-178.000 + 308.305i) q^{16} +(-513.318 - 889.092i) q^{17} +(-111.301 - 192.780i) q^{18} +(869.702 - 1506.37i) q^{19} -1426.93 q^{20} +(1093.01 - 408.276i) q^{21} +47.8846 q^{22} +(-1968.11 + 3408.87i) q^{23} +(698.076 + 1209.10i) q^{24} +(-140.869 - 243.993i) q^{25} +(-1222.85 + 2118.04i) q^{26} +729.000 q^{27} +(-2969.05 + 1109.04i) q^{28} +5633.53 q^{29} +(-721.817 + 1250.22i) q^{30} +(1548.27 + 2681.68i) q^{31} +(-2971.22 - 5146.31i) q^{32} +(-78.4084 + 135.807i) q^{33} +2821.38 q^{34} +(-5837.27 - 4814.91i) q^{35} -1980.25 q^{36} +(-2513.43 + 4353.39i) q^{37} +(2390.10 + 4139.77i) q^{38} +(-4004.70 - 6936.34i) q^{39} +(4527.20 - 7841.34i) q^{40} +18367.0 q^{41} +(-530.205 + 3162.37i) q^{42} -1630.91 q^{43} +(212.988 - 368.906i) q^{44} +(-2363.87 - 4094.35i) q^{45} +(-5408.72 - 9368.19i) q^{46} +(4802.62 - 8318.38i) q^{47} +3204.00 q^{48} +(-15887.9 - 5481.65i) q^{49} +774.269 q^{50} +(-4619.86 + 8001.83i) q^{51} +(10878.3 + 18841.8i) q^{52} +(11628.3 + 20140.7i) q^{53} +(-1001.71 + 1735.02i) q^{54} +1017.00 q^{55} +(3325.41 - 19834.2i) q^{56} -15654.6 q^{57} +(-7740.98 + 13407.8i) q^{58} +(1801.62 + 3120.50i) q^{59} +(6421.20 + 11121.8i) q^{60} +(-11438.3 + 19811.7i) q^{61} -8509.83 q^{62} +(-8100.75 - 6681.95i) q^{63} +4938.92 q^{64} +(-25971.5 + 44983.9i) q^{65} +(-215.481 - 373.223i) q^{66} +(-23506.4 - 40714.2i) q^{67} +(12549.3 - 21736.1i) q^{68} +35426.0 q^{69} +(19480.4 - 7276.56i) q^{70} -1599.63 q^{71} +(6282.68 - 10881.9i) q^{72} +(-2965.67 - 5136.70i) q^{73} +(-6907.36 - 11963.9i) q^{74} +(-1267.82 + 2195.93i) q^{75} +42524.1 q^{76} +(2116.09 - 790.427i) q^{77} +22011.3 q^{78} +(44234.4 - 76616.3i) q^{79} +(-10389.4 - 17994.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-25237.9 + 43713.3i) q^{82} -95823.9 q^{83} +(22004.8 + 18150.8i) q^{84} +59921.9 q^{85} +(2241.02 - 3881.56i) q^{86} +(-25350.9 - 43909.0i) q^{87} +(1351.48 + 2340.84i) q^{88} +(23253.9 - 40277.0i) q^{89} +12992.7 q^{90} +(-19077.1 + 113784. i) q^{91} -96230.8 q^{92} +(13934.4 - 24135.1i) q^{93} +(13198.5 + 22860.4i) q^{94} +(50762.1 + 87922.5i) q^{95} +(-26741.0 + 46316.8i) q^{96} -75981.8 q^{97} +(34877.8 - 30281.0i) q^{98} +1411.35 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9}+O(q^{10}) $ 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9	\( 8 q - 3 q^{2} - 36 q^{3} - 69 q^{4} + 54 q^{6} + 258 q^{7} + 246 q^{8} - 324 q^{9} - 283 q^{10} - 402 q^{11} - 621 q^{12} + 924 q^{13} + 1926 q^{14} - 3273 q^{16} - 276 q^{17} - 243 q^{18} - 510 q^{19} + 9438 q^{20} - 3564 q^{21} + 2750 q^{22} - 6900 q^{23} - 1107 q^{24} - 2814 q^{25} + 15138 q^{26} + 5832 q^{27} - 26221 q^{28} + 1080 q^{29} - 2547 q^{30} + 6410 q^{31} - 15519 q^{32} - 3618 q^{33} + 42288 q^{34} - 33108 q^{35} + 11178 q^{36} - 15250 q^{37} + 41250 q^{38} - 4158 q^{39} + 8547 q^{40} + 8616 q^{41} - 16281 q^{42} + 58396 q^{43} - 70743 q^{44} - 61800 q^{46} + 15060 q^{47} + 58914 q^{48} - 64252 q^{49} - 14604 q^{50} - 2484 q^{51} + 47476 q^{52} - 13692 q^{53} - 2187 q^{54} + 146248 q^{55} - 15921 q^{56} + 9180 q^{57} - 52309 q^{58} - 34830 q^{59} - 42471 q^{60} + 5364 q^{61} + 32058 q^{62} + 11178 q^{63} - 146974 q^{64} - 66864 q^{65} - 12375 q^{66} + 5994 q^{67} + 58272 q^{68} + 124200 q^{69} - 4307 q^{70} + 178536 q^{71} - 9963 q^{72} - 59638 q^{73} + 185442 q^{74} - 25326 q^{75} + 42616 q^{76} - 75660 q^{77} - 272484 q^{78} + 44062 q^{79} + 33381 q^{80} - 26244 q^{81} - 57596 q^{82} - 416892 q^{83} + 63036 q^{84} + 72648 q^{85} + 136968 q^{86} - 4860 q^{87} - 87597 q^{88} + 77520 q^{89} + 45846 q^{90} + 104722 q^{91} + 316512 q^{92} + 57690 q^{93} + 73722 q^{94} + 221376 q^{95} - 139671 q^{96} - 377260 q^{97} + 382479 q^{98} + 65124 q^{99}+O(q^{100}) \) 8 * q - 3 * q^2 - 36 * q^3 - 69 * q^4 + 54 * q^6 + 258 * q^7 + 246 * q^8 - 324 * q^9 - 283 * q^10 - 402 * q^11 - 621 * q^12 + 924 * q^13 + 1926 * q^14 - 3273 * q^16 - 276 * q^17 - 243 * q^18 - 510 * q^19 + 9438 * q^20 - 3564 * q^21 + 2750 * q^22 - 6900 * q^23 - 1107 * q^24 - 2814 * q^25 + 15138 * q^26 + 5832 * q^27 - 26221 * q^28 + 1080 * q^29 - 2547 * q^30 + 6410 * q^31 - 15519 * q^32 - 3618 * q^33 + 42288 * q^34 - 33108 * q^35 + 11178 * q^36 - 15250 * q^37 + 41250 * q^38 - 4158 * q^39 + 8547 * q^40 + 8616 * q^41 - 16281 * q^42 + 58396 * q^43 - 70743 * q^44 - 61800 * q^46 + 15060 * q^47 + 58914 * q^48 - 64252 * q^49 - 14604 * q^50 - 2484 * q^51 + 47476 * q^52 - 13692 * q^53 - 2187 * q^54 + 146248 * q^55 - 15921 * q^56 + 9180 * q^57 - 52309 * q^58 - 34830 * q^59 - 42471 * q^60 + 5364 * q^61 + 32058 * q^62 + 11178 * q^63 - 146974 * q^64 - 66864 * q^65 - 12375 * q^66 + 5994 * q^67 + 58272 * q^68 + 124200 * q^69 - 4307 * q^70 + 178536 * q^71 - 9963 * q^72 - 59638 * q^73 + 185442 * q^74 - 25326 * q^75 + 42616 * q^76 - 75660 * q^77 - 272484 * q^78 + 44062 * q^79 + 33381 * q^80 - 26244 * q^81 - 57596 * q^82 - 416892 * q^83 + 63036 * q^84 + 72648 * q^85 + 136968 * q^86 - 4860 * q^87 - 87597 * q^88 + 77520 * q^89 + 45846 * q^90 + 104722 * q^91 + 316512 * q^92 + 57690 * q^93 + 73722 * q^94 + 221376 * q^95 - 139671 * q^96 - 377260 * q^97 + 382479 * q^98 + 65124 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.37409	+	2.37999i	−0.242907	+	0.420728i	−0.961541	−	0.274661i	$-0.911434\pi$
$2$	−1.37409	+	2.37999i	−0.242907	+	0.420728i	0.718634	+	0.695389i	$0.244768\pi$
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$3$	−4.50000	−	7.79423i	−0.288675	−	0.500000i
$4$	12.2237	+	21.1722i	0.381992	+	0.661630i
$5$	−29.1836	+	50.5475i	−0.522053	+	0.904222i	0.477618	+	0.878568i	$0.341500\pi$
$5$	−29.1836	+	50.5475i	−0.522053	+	0.904222i	−0.999671	+	0.0256544i	$0.991833\pi$
$6$	24.7336			0.280485
$7$	−21.4366	+	127.857i	−0.165352	+	0.986235i
$7$	−21.4366	+	127.857i	−0.165352	+	0.986235i
$8$	−155.128			−0.856969
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−80.2019	−	138.914i	−0.253621	−	0.439284i
$11$	−8.71205	−	15.0897i	−0.0217089	−	0.0376010i	0.854967	−	0.518683i	$-0.173577\pi$
$11$	−8.71205	−	15.0897i	−0.0217089	−	0.0376010i	−0.876676	+	0.481082i	$0.840244\pi$
$12$	110.014	−	190.549i	0.220543	−	0.381992i
$13$	889.933			1.46049			0.730246	−	0.683185i	$-0.239406\pi$
$13$	889.933			1.46049			0.730246	+	0.683185i	$0.239406\pi$
$14$	−274.844	−	226.706i	−0.374771	−	0.309132i
$15$	525.305			0.602815
$16$	−178.000	+	308.305i	−0.173828	+	0.301079i
$17$	−513.318	−	889.092i	−0.430788	−	0.746147i	0.566153	−	0.824300i	$-0.308431\pi$
$17$	−513.318	−	889.092i	−0.430788	−	0.746147i	−0.996941	+	0.0781529i	$0.975098\pi$
$18$	−111.301	−	192.780i	−0.0809691	−	0.140243i
$19$	869.702	−	1506.37i	0.552696	−	0.957297i	−0.445383	−	0.895340i	$-0.646932\pi$
$19$	869.702	−	1506.37i	0.552696	−	0.957297i	0.998079	−	0.0619572i	$-0.0197342\pi$
$20$	−1426.93			−0.797680
$21$	1093.01	−	408.276i	0.540850	−	0.202025i
$22$	47.8846			0.0210930
$23$	−1968.11	+	3408.87i	−0.775764	+	1.34366i	0.158599	+	0.987343i	$0.449302\pi$
$23$	−1968.11	+	3408.87i	−0.775764	+	1.34366i	−0.934364	+	0.356320i	$0.884031\pi$
$24$	698.076	+	1209.10i	0.247386	+	0.428485i
$25$	−140.869	−	243.993i	−0.0450782	−	0.0780777i
$26$	−1222.85	+	2118.04i	−0.354764	+	0.614469i
$27$	729.000			0.192450
$28$	−2969.05	+	1109.04i	−0.715686	+	0.267332i
$29$	5633.53			1.24390			0.621950	−	0.783057i	$-0.286341\pi$
$29$	5633.53			1.24390			0.621950	+	0.783057i	$0.286341\pi$
$30$	−721.817	+	1250.22i	−0.146428	+	0.253621i
$31$	1548.27	+	2681.68i	0.289362	+	0.501190i	0.973658	−	0.228015i	$-0.0732236\pi$
$31$	1548.27	+	2681.68i	0.289362	+	0.501190i	−0.684296	+	0.729205i	$0.739890\pi$
$32$	−2971.22	−	5146.31i	−0.512933	−	0.888426i
$33$	−78.4084	+	135.807i	−0.0125337	+	0.0217089i
$34$	2821.38			0.418566
$35$	−5837.27	−	4814.91i	−0.805452	−	0.664382i
$36$	−1980.25			−0.254661
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	−0.976551	−	0.215288i	$-0.930931\pi$
$37$	−2513.43	+	4353.39i	−0.301830	+	0.522785i	0.674720	+	0.738073i	$0.264264\pi$
$38$	2390.10	+	4139.77i	0.268508	+	0.465069i
$39$	−4004.70	−	6936.34i	−0.421608	−	0.730246i
$40$	4527.20	−	7841.34i	0.447383	−	0.774890i
$41$	18367.0			1.70639			0.853195	−	0.521592i	$-0.174662\pi$
$41$	18367.0			1.70639			0.853195	+	0.521592i	$0.174662\pi$
$42$	−530.205	+	3162.37i	−0.0463789	+	0.276624i
$43$	−1630.91			−0.134511			−0.0672557	−	0.997736i	$-0.521424\pi$
$43$	−1630.91			−0.134511			−0.0672557	+	0.997736i	$0.521424\pi$
$44$	212.988	−	368.906i	0.0165853	−	0.0287266i
$45$	−2363.87	−	4094.35i	−0.174018	−	0.301407i
$46$	−5408.72	−	9368.19i	−0.376878	−	0.652771i
$47$	4802.62	−	8318.38i	0.317127	−	0.549280i	−0.662760	−	0.748832i	$-0.730615\pi$
$47$	4802.62	−	8318.38i	0.317127	−	0.549280i	0.979887	+	0.199551i	$0.0639485\pi$
$48$	3204.00			0.200720
$49$	−15887.9	−	5481.65i	−0.945317	−	0.326153i
$50$	774.269			0.0437992
$51$	−4619.86	+	8001.83i	−0.248716	+	0.430788i
$52$	10878.3	+	18841.8i	0.557896	+	0.966305i
$53$	11628.3	+	20140.7i	0.568624	+	0.984886i	0.996702	+	0.0811440i	$0.0258574\pi$
$53$	11628.3	+	20140.7i	0.568624	+	0.984886i	−0.428078	+	0.903742i	$0.640809\pi$
$54$	−1001.71	+	1735.02i	−0.0467475	+	0.0809691i
$55$	1017.00			0.0453328
$56$	3325.41	−	19834.2i	0.141702	−	0.845172i
$57$	−15654.6			−0.638198
$58$	−7740.98	+	13407.8i	−0.302152	+	0.523343i
$59$	1801.62	+	3120.50i	0.0673803	+	0.116706i	0.897747	−	0.440511i	$-0.145203\pi$
$59$	1801.62	+	3120.50i	0.0673803	+	0.116706i	−0.830367	+	0.557217i	$0.811869\pi$
$60$	6421.20	+	11121.8i	0.230270	+	0.398840i
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	−0.992919	−	0.118791i	$-0.962098\pi$
$61$	−11438.3	+	19811.7i	−0.393584	+	0.681707i	0.599336	+	0.800498i	$0.295431\pi$
$62$	−8509.83			−0.281152
$63$	−8100.75	−	6681.95i	−0.257143	−	0.212106i
$64$	4938.92			0.150724
$65$	−25971.5	+	44983.9i	−0.762454	+	1.32061i
$66$	−215.481	−	373.223i	−0.00608903	−	0.0105465i
$67$	−23506.4	−	40714.2i	−0.639733	−	1.10805i	−0.985491	−	0.169726i	$-0.945712\pi$
$67$	−23506.4	−	40714.2i	−0.639733	−	1.10805i	0.345758	−	0.938324i	$-0.387622\pi$
$68$	12549.3	−	21736.1i	0.329116	−	0.570045i
$69$	35426.0			0.895776
$70$	19480.4	−	7276.56i	0.475174	−	0.177493i
$71$	−1599.63			−0.0376595			−0.0188298	−	0.999823i	$-0.505994\pi$
$71$	−1599.63			−0.0376595			−0.0188298	+	0.999823i	$0.505994\pi$
$72$	6282.68	−	10881.9i	0.142828	−	0.247386i
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	0.831619	−	0.555347i	$-0.187415\pi$
$73$	−2965.67	−	5136.70i	−0.0651353	−	0.112818i	−0.896754	+	0.442529i	$0.854081\pi$
$74$	−6907.36	−	11963.9i	−0.146633	−	0.253976i
$75$	−1267.82	+	2195.93i	−0.0260259	+	0.0450782i
$76$	42524.1			0.844502
$77$	2116.09	−	790.427i	0.0406730	−	0.0151927i
$78$	22011.3			0.409646
$79$	44234.4	−	76616.3i	0.797431	−	1.38119i	−0.123854	−	0.992300i	$-0.539525\pi$
$79$	44234.4	−	76616.3i	0.797431	−	1.38119i	0.921284	−	0.388890i	$-0.127141\pi$
$80$	−10389.4	−	17994.9i	−0.181495	−	0.314359i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	−25237.9	+	43713.3i	−0.414495	+	0.717926i
$83$	−95823.9			−1.52679			−0.763394	−	0.645933i	$-0.776469\pi$
$83$	−95823.9			−1.52679			−0.763394	+	0.645933i	$0.776469\pi$
$84$	22004.8	+	18150.8i	0.340267	+	0.280671i
$85$	59921.9			0.899577
$86$	2241.02	−	3881.56i	0.0326738	−	0.0565927i
$87$	−25350.9	−	43909.0i	−0.359083	−	0.621950i
$88$	1351.48	+	2340.84i	0.0186039	+	0.0322229i
$89$	23253.9	−	40277.0i	0.311187	−	0.538992i	−0.667433	−	0.744670i	$-0.732607\pi$
$89$	23253.9	−	40277.0i	0.311187	−	0.538992i	0.978620	+	0.205679i	$0.0659401\pi$
$90$	12992.7			0.169081
$91$	−19077.1	+	113784.i	−0.241496	+	1.44039i
$92$	−96230.8			−1.18534
$93$	13934.4	−	24135.1i	0.167063	−	0.289362i
$94$	13198.5	+	22860.4i	0.154065	+	0.266848i
$95$	50762.1	+	87922.5i	0.577073	+	0.999519i
$96$	−26741.0	+	46316.8i	−0.296142	+	0.512933i
$97$	−75981.8			−0.819937			−0.409968	−	0.912100i	$-0.634460\pi$
$97$	−75981.8			−0.819937			−0.409968	+	0.912100i	$0.634460\pi$
$98$	34877.8	−	30281.0i	0.366846	−	0.318496i
$99$	1411.35			0.0144726
$100$	3443.90	−	5965.01i	0.0344390	−	0.0596501i
$101$	23078.7	+	39973.5i	0.225117	+	0.389914i	0.956355	−	0.292209i	$-0.0943903\pi$
$101$	23078.7	+	39973.5i	0.225117	+	0.389914i	−0.731238	+	0.682123i	$0.761057\pi$
$102$	−12696.2	−	21990.5i	−0.120830	−	0.209283i
$103$	40986.8	−	70991.2i	0.380672	−	0.659343i	−0.610487	−	0.792027i	$-0.709026\pi$
$103$	40986.8	−	70991.2i	0.380672	−	0.659343i	0.991158	+	0.132683i	$0.0423594\pi$
$104$	−138054.			−1.25160
$105$	−11260.8	+	67164.1i	−0.0996769	+	0.594517i
$106$	−63913.2			−0.552491
$107$	1426.84	−	2471.35i	0.0120480	−	0.0208677i	−0.859939	−	0.510398i	$-0.829498\pi$
$107$	1426.84	−	2471.35i	0.0120480	−	0.0208677i	0.871987	+	0.489530i	$0.162832\pi$
$108$	8911.11	+	15434.5i	0.0735144	+	0.127331i
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	0.977832	+	0.209391i	$0.0671483\pi$
$109$	83139.2	+	144001.i	0.670254	+	1.16091i	−0.307578	+	0.951523i	$0.599518\pi$
$110$	−1397.45	+	2420.45i	−0.0110117	+	0.0190728i
$111$	45241.7			0.348523
$112$	−35603.3	−	29367.6i	−0.268192	−	0.221220i
$113$	260304.			1.91772			0.958858	−	0.283886i	$-0.0916237\pi$
$113$	260304.			1.91772			0.958858	+	0.283886i	$0.0916237\pi$
$114$	21510.9	−	37257.9i	0.155023	−	0.268508i
$115$	−114873.	−	198966.i	−0.809980	−	1.40293i
$116$	68862.8	+	119274.i	0.475160	+	0.823001i
$117$	−36042.3	+	62427.1i	−0.243415	+	0.421608i
$118$	−9902.35			−0.0654687
$119$	124681.	−	46572.3i	0.807108	−	0.301481i
$120$	−81489.6			−0.516593
$121$	80373.7	−	139211.i	0.499057	−	0.864393i
$122$	−31434.5	−	54446.2i	−0.191209	−	0.331183i
$123$	−82651.5	−	143157.i	−0.492592	−	0.853195i
$124$	−37851.2	+	65560.3i	−0.221068	+	0.382901i
$125$	−165953.			−0.949973
$126$	27034.2	−	10098.1i	0.151700	−	0.0566651i
$127$	−233743.			−1.28596			−0.642982	−	0.765882i	$-0.722303\pi$
$127$	−233743.			−1.28596			−0.642982	+	0.765882i	$0.722303\pi$
$128$	88292.6	−	152927.i	0.476321	−	0.825012i
$129$	7339.10	+	12711.7i	0.0388301	+	0.0672557i
$130$	−71374.4	−	123624.i	−0.370411	−	0.641571i
$131$	78644.9	−	136217.i	0.400398	−	0.693510i	−0.593376	−	0.804926i	$-0.702205\pi$
$131$	78644.9	−	136217.i	0.400398	−	0.693510i	0.993774	+	0.111415i	$0.0355384\pi$
$132$	−3833.78			−0.0191510
$133$	173957.	+	143489.i	0.852730	+	0.703379i
$134$	129200.			0.621583
$135$	−21274.9	+	36849.2i	−0.100469	+	0.174018i
$136$	79629.9	+	137923.i	0.369172	+	0.639425i
$137$	85773.8	+	148564.i	0.390439	+	0.676260i	0.992507	−	0.122185i	$-0.0389900\pi$
$137$	85773.8	+	148564.i	0.390439	+	0.676260i	−0.602069	+	0.798444i	$0.705657\pi$
$138$	−48678.5	+	84313.7i	−0.217590	+	0.376878i
$139$	210625.			0.924642			0.462321	−	0.886713i	$-0.347017\pi$
$139$	210625.			0.924642			0.462321	+	0.886713i	$0.347017\pi$
$140$	30588.6	−	182444.i	0.131898	−	0.786700i
$141$	−86447.1			−0.366187
$142$	2198.04	−	3807.12i	0.00914777	−	0.0158444i
$143$	−7753.14	−	13428.8i	−0.0317057	−	0.0549159i
$144$	−14418.0	−	24972.7i	−0.0579427	−	0.100360i
$145$	−164407.	+	284761.i	−0.649381	+	1.12476i
$146$	16300.4			0.0632873
$147$	28770.6	+	148502.i	0.109813	+	0.566811i
$148$	−122894.			−0.461187
$149$	−119706.	+	207338.i	−0.441725	+	0.765090i	−0.997818	−	0.0660304i	$-0.978967\pi$
$149$	−119706.	+	207338.i	−0.441725	+	0.765090i	0.556093	+	0.831120i	$0.312300\pi$
$150$	−3484.21	−	6034.83i	−0.0126438	−	0.0218996i
$151$	−108520.	−	187962.i	−0.387317	−	0.670852i	0.604771	−	0.796400i	$-0.293265\pi$
$151$	−108520.	−	187962.i	−0.387317	−	0.670852i	−0.992088	+	0.125547i	$0.959931\pi$
$152$	−134915.	+	233680.i	−0.473643	+	0.820374i
$153$	83157.5			0.287192
$154$	−1026.48	+	6122.39i	−0.00348778	+	0.0208027i
$155$	−180736.			−0.604249
$156$	97904.9	−	169576.i	0.322102	−	0.557896i
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	0.698711	−	0.715404i	$-0.253757\pi$
$157$	−83452.2	−	144543.i	−0.270202	−	0.468004i	−0.968913	+	0.247400i	$0.920424\pi$
$158$	121564.	+	210556.i	0.387403	+	0.671002i
$159$	104654.	−	181267.i	0.328295	−	0.568624i
$160$	346844.			1.07111
$161$	−393659.	−	324712.i	−1.19689	−	0.987264i
$162$	18030.8			0.0539794
$163$	−253086.	+	438358.i	−0.746104	+	1.29229i	0.203574	+	0.979060i	$0.434744\pi$
$163$	−253086.	+	438358.i	−0.746104	+	1.29229i	−0.949677	+	0.313230i	$0.898589\pi$
$164$	224514.	+	388869.i	0.651828	+	1.12900i
$165$	−4576.49	−	7926.71i	−0.0130865	−	0.0226664i
$166$	131671.	−	228061.i	0.370868	−	0.642362i
$167$	−565560.			−1.56923			−0.784616	−	0.619982i	$-0.787140\pi$
$167$	−565560.			−1.56923			−0.784616	+	0.619982i	$0.787140\pi$
$168$	−169557.	+	63335.0i	−0.463492	+	0.173129i
$169$	420688.			1.13304
$170$	−82338.1	+	142614.i	−0.218514	+	0.378477i
$171$	70445.8	+	122016.i	0.184232	+	0.319099i
$172$	−19935.9	−	34529.9i	−0.0513823	−	0.0889968i
$173$	329718.	−	571088.i	0.837581	−	1.45073i	−0.0543304	−	0.998523i	$-0.517302\pi$
$173$	329718.	−	571088.i	0.837581	−	1.45073i	0.891911	−	0.452210i	$-0.149364\pi$
$174$	139338.			0.348895
$175$	34216.0	−	12780.8i	0.0844567	−	0.0315473i
$176$	6202.98			0.0150945
$177$	16214.6	−	28084.5i	0.0389020	−	0.0673803i
$178$	63906.0	+	110688.i	0.151179	+	0.261850i
$179$	−82645.0	−	143145.i	−0.192790	−	0.333922i	0.753384	−	0.657581i	$-0.228420\pi$
$179$	−82645.0	−	143145.i	−0.192790	−	0.333922i	−0.946174	+	0.323659i	$0.895087\pi$
$180$	57790.8	−	100097.i	0.132947	−	0.230270i
$181$	148492.			0.336904			0.168452	−	0.985710i	$-0.446123\pi$
$181$	148492.			0.336904			0.168452	+	0.985710i	$0.446123\pi$
$182$	−244593.	−	201754.i	−0.547350	−	0.451484i
$183$	205889.			0.454471
$184$	305309.	−	528811.i	0.664806	−	1.15148i
$185$	−146702.	−	254095.i	−0.315142	−	0.545843i
$186$	38294.2	+	66327.6i	0.0811617	+	0.140576i
$187$	−8944.10	+	15491.6i	−0.0187039	+	0.0323961i
$188$	234824.			0.484560
$189$	−15627.3	+	93207.9i	−0.0318221	+	0.189801i
$190$	−279007.			−0.560701
$191$	−192955.	+	334208.i	−0.382713	+	0.662879i	−0.991449	−	0.130494i	$-0.958344\pi$
$191$	−192955.	+	334208.i	−0.382713	+	0.662879i	0.608736	+	0.793373i	$0.291677\pi$
$192$	−22225.1	−	38495.1i	−0.0435102	−	0.0753619i
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	0.520193	−	0.854049i	$-0.325860\pi$
$193$	−248148.	−	429805.i	−0.479531	−	0.830573i	−0.999724	+	0.0234760i	$0.992527\pi$
$194$	104406.	−	180836.i	0.199169	−	0.344970i
$195$	467487.			0.880406
$196$	−78152.0	−	403388.i	−0.145312	−	0.750038i
$197$	441439.			0.810411			0.405206	−	0.914226i	$-0.367200\pi$
$197$	441439.			0.810411			0.405206	+	0.914226i	$0.367200\pi$
$198$	−1939.33	+	3359.01i	−0.00351551	+	0.00608903i
$199$	37919.4	+	65678.3i	0.0678779	+	0.117568i	0.897967	−	0.440063i	$-0.145044\pi$
$199$	37919.4	+	65678.3i	0.0678779	+	0.117568i	−0.830089	+	0.557631i	$0.811710\pi$
$200$	21852.8	+	37850.1i	0.0386306	+	0.0669102i
$201$	−211557.	+	366428.i	−0.369350	+	0.639733i
$202$	−126849.			−0.218730
$203$	−120764.	+	720287.i	−0.205682	+	1.22678i
$204$	−225888.			−0.380030
$205$	−536016.	+	928406.i	−0.890826	+	1.54296i
$206$	112639.	+	195097.i	0.184936	+	0.320318i
$207$	−159417.	−	276118.i	−0.258588	−	0.447888i
$208$	−158408.	+	274371.i	−0.253875	+	0.439724i
$209$	−30307.5			−0.0479938
$210$	−144377.	−	119090.i	−0.225917	−	0.186349i
$211$	778704.			1.20411			0.602055	−	0.798454i	$-0.294349\pi$
$211$	778704.			1.20411			0.602055	+	0.798454i	$0.294349\pi$
$212$	−284282.	+	492391.i	−0.434420	+	0.752437i
$213$	7198.35	+	12467.9i	0.0108714	+	0.0188298i
$214$	3921.21	+	6791.73i	0.00585309	+	0.0101379i
$215$	47595.9	−	82438.6i	0.0702221	−	0.121628i
$216$	−113088.			−0.164924
$217$	−376061.	+	140471.i	−0.542137	+	0.202506i
$218$	−456963.			−0.651238
$219$	−26691.1	+	46230.3i	−0.0376059	+	0.0651353i
$220$	12431.5	+	21532.0i	0.0173168	+	0.0299936i
$221$	−456818.	−	791233.i	−0.629163	−	1.08974i
$222$	−62166.3	+	107675.i	−0.0846588	+	0.146633i
$223$	738085.			0.993903			0.496951	−	0.867778i	$-0.334453\pi$
$223$	738085.			0.993903			0.496951	+	0.867778i	$0.334453\pi$
$224$	721686.	−	269573.i	0.961011	−	0.358969i
$225$	22820.8			0.0300521
$226$	−357681.	+	619522.i	−0.465827	+	0.806836i
$227$	272058.	+	471218.i	0.350426	+	0.606956i	0.986324	−	0.164817i	$-0.0527035\pi$
$227$	272058.	+	471218.i	0.350426	+	0.606956i	−0.635898	+	0.771773i	$0.719370\pi$
$228$	−191358.	−	331442.i	−0.243787	−	0.422251i
$229$	116781.	−	202271.i	0.147158	−	0.254885i	−0.783018	−	0.621999i	$-0.786321\pi$
$229$	116781.	−	202271.i	0.147158	−	0.254885i	0.930176	+	0.367114i	$0.119654\pi$
$230$	631385.			0.787000
$231$	−15683.2	−	12936.3i	−0.0193376	−	0.0159508i
$232$	−873917.			−1.06598
$233$	309050.	−	535290.i	0.372940	−	0.645951i	−0.617077	−	0.786903i	$-0.711683\pi$
$233$	309050.	−	535290.i	0.372940	−	0.645951i	0.990016	+	0.140952i	$0.0450164\pi$
$234$	−99050.8	−	171561.i	−0.118255	−	0.204823i
$235$	280316.	+	485521.i	0.331114	+	0.573506i
$236$	−44045.1	+	76288.3i	−0.0514775	+	0.0891617i
$237$	−796220.			−0.920794
$238$	−60480.8	+	360734.i	−0.0692110	+	0.412805i
$239$	937500.			1.06164			0.530819	−	0.847485i	$-0.321884\pi$
$239$	937500.			1.06164			0.530819	+	0.847485i	$0.321884\pi$
$240$	−93504.4	+	161954.i	−0.104786	+	0.181495i
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	−0.999809	−	0.0195613i	$-0.993773\pi$
$241$	−466018.	−	807167.i	−0.516845	−	0.895202i	0.482964	−	0.875640i	$-0.339560\pi$
$242$	220882.	+	382578.i	0.242449	+	0.419935i
$243$	−29524.5	+	51137.9i	−0.0320750	+	0.0555556i
$244$	−559276.			−0.601383
$245$	740752.	−	643122.i	0.788420	−	0.684508i
$246$	454282.			0.478617
$247$	773976.	−	1.34057e6i	0.807208	−	1.39812i
$248$	−240179.	−	416003.i	−0.247974	−	0.429504i
$249$	431208.	+	746874.i	0.440746	+	0.763394i
$250$	228035.	−	394968.i	0.230755	−	0.399680i
$251$	214975.			0.215379			0.107690	−	0.994185i	$-0.465655\pi$
$251$	214975.			0.215379			0.107690	+	0.994185i	$0.465655\pi$
$252$	42449.7	−	253189.i	0.0421089	−	0.251156i
$253$	68585.1			0.0673641
$254$	321184.	−	556306.i	0.312370	−	0.541040i
$255$	−269649.	−	467045.i	−0.259685	−	0.449788i
$256$	321667.	+	557143.i	0.306765	+	0.531333i
$257$	−39593.5	+	68578.0i	−0.0373931	+	0.0647667i	−0.884116	−	0.467267i	$-0.845239\pi$
$257$	−39593.5	+	68578.0i	−0.0373931	+	0.0647667i	0.846723	+	0.532034i	$0.178572\pi$
$258$	−40338.4			−0.0377285
$259$	−502733.	−	414682.i	−0.465680	−	0.384119i
$260$	−1.26988e6			−1.16501
$261$	−228158.	+	395181.i	−0.207317	+	0.359083i
$262$	216130.	+	374349.i	0.194519	+	0.336917i
$263$	216414.	+	374840.i	0.192928	+	0.334162i	0.946219	−	0.323526i	$-0.104868\pi$
$263$	216414.	+	374840.i	0.192928	+	0.334162i	−0.753291	+	0.657687i	$0.771535\pi$
$264$	12163.3	−	21067.5i	0.0107410	−	0.0186039i
$265$	−1.35742e6			−1.18741
$266$	−580535.	+	216849.i	−0.503065	+	0.187911i
$267$	−418571.			−0.359328
$268$	574672.	−	995361.i	0.488746	−	0.846533i
$269$	2345.93	+	4063.27i	0.00197667	+	0.00342369i	0.867012	−	0.498287i	$-0.166037\pi$
$269$	2345.93	+	4063.27i	0.00197667	+	0.00342369i	−0.865035	+	0.501711i	$0.832704\pi$
$270$	−58467.2	−	101268.i	−0.0488093	−	0.0845403i
$271$	−52632.1	+	91161.5i	−0.0435339	+	0.0754029i	−0.886971	−	0.461825i	$-0.847195\pi$
$271$	−52632.1	+	91161.5i	−0.0435339	+	0.0754029i	0.843437	+	0.537227i	$0.180528\pi$
$272$	365482.			0.299533
$273$	972709.	−	363338.i	0.789907	−	0.295056i
$274$	−471444.			−0.379362
$275$	−2454.52	+	4251.35i	−0.00195720	+	0.00338997i
$276$	433038.	+	750045.i	0.342179	+	0.592672i
$277$	381558.	+	660879.i	0.298787	+	0.517514i	0.975859	−	0.218403i	$-0.0700847\pi$
$277$	381558.	+	660879.i	0.298787	+	0.517514i	−0.677072	+	0.735917i	$0.736751\pi$
$278$	−289418.	+	501287.i	−0.224602	+	0.389023i
$279$	−250819.			−0.192908
$280$	905524.	+	746927.i	0.690248	+	0.569355i
$281$	−729540.			−0.551167			−0.275584	−	0.961277i	$-0.588871\pi$
$281$	−729540.			−0.551167			−0.275584	+	0.961277i	$0.588871\pi$
$282$	118786.	−	205744.i	0.0889494	−	0.154065i
$283$	595214.	+	1.03094e6i	0.441781	+	0.765188i	0.997822	−	0.0659675i	$-0.0210134\pi$
$283$	595214.	+	1.03094e6i	0.441781	+	0.765188i	−0.556040	+	0.831155i	$0.687680\pi$
$284$	−19553.5	−	33867.7i	−0.0143856	−	0.0249167i
$285$	456859.	−	791303.i	0.333173	−	0.577073i
$286$	42614.1			0.0308062
$287$	−393726.	+	2.34835e6i	−0.282156	+	1.68290i
$288$	481338.			0.341955
$289$	182938.	−	316859.i	0.128843	−	0.223162i
$290$	−451820.	−	782575.i	−0.315479	−	0.546425i
$291$	341918.	+	592220.i	0.236695	+	0.409968i
$292$	72503.3	−	125579.i	0.0497623	−	0.0861909i
$293$	−1.02503e6			−0.697537			−0.348769	−	0.937209i	$-0.613400\pi$
$293$	−1.02503e6			−0.697537			−0.348769	+	0.937209i	$0.613400\pi$
$294$	−392967.	−	135581.i	−0.265147	−	0.0914809i
$295$	−210311.			−0.140704
$296$	389903.	−	675332.i	0.258659	−	0.448011i
$297$	−6351.08	−	11000.4i	−0.00417789	−	0.00723631i
$298$	−328975.	−	569801.i	−0.214596	−	0.371692i
$299$	−1.75149e6	+	3.03366e6i	−1.13300	+	1.96241i
$300$	−61990.2			−0.0397667
$301$	34961.2	−	208524.i	0.0222418	−	0.132660i
$302$	596464.			0.376328
$303$	207708.	−	359762.i	0.129971	−	0.225117i
$304$	309614.	+	536267.i	0.192148	+	0.332811i
$305$	−667623.	−	1.15636e6i	−0.410943	−	0.711774i
$306$	−114266.	+	197914.i	−0.0697611	+	0.120830i
$307$	−709845.			−0.429850			−0.214925	−	0.976631i	$-0.568951\pi$
$307$	−709845.			−0.429850			−0.214925	+	0.976631i	$0.568951\pi$
$308$	42601.5	+	35140.1i	0.0255887	+	0.0211070i
$309$	−737762.			−0.439562
$310$	248348.	−	430151.i	0.146776	−	0.254224i
$311$	−783816.	−	1.35761e6i	−0.459529	−	0.795928i	0.539407	−	0.842045i	$-0.318648\pi$
$311$	−783816.	−	1.35761e6i	−0.459529	−	0.795928i	−0.998936	+	0.0461175i	$0.985315\pi$
$312$	621241.	+	1.07602e6i	0.361305	+	0.625798i
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	−0.914792	−	0.403924i	$-0.867646\pi$
$313$	−186476.	+	322986.i	−0.107588	+	0.186347i	0.807205	+	0.590271i	$0.200979\pi$
$314$	458684.			0.262536
$315$	574166.	−	214470.i	0.326033	−	0.121784i
$316$	2.16284e6			1.21845
$317$	1.51408e6	−	2.62246e6i	0.846253	−	1.46575i	−0.0382747	−	0.999267i	$-0.512186\pi$
$317$	1.51408e6	−	2.62246e6i	0.846253	−	1.46575i	0.884528	−	0.466487i	$-0.154480\pi$
$318$	287609.	+	498154.i	0.159491	+	0.276246i
$319$	−49079.6	−	85008.3i	−0.0270037	−	0.0467719i
$320$	−144136.	+	249650.i	−0.0786858	+	0.136288i
$321$	−25683.1			−0.0139118
$322$	1.31373e6	−	490723.i	0.706103	−	0.263752i
$323$	−1.78573e6			−0.952380
$324$	80200.0	−	138911.i	0.0424436	−	0.0735144i
$325$	−125364.	−	217137.i	−0.0658363	−	0.114032i
$326$	−695526.	−	1.20469e6i	−0.362468	−	0.627813i
$327$	748253.	−	1.29601e6i	0.386971	−	0.670254i
$328$	−2.84923e6			−1.46232
$329$	960613.	+	792367.i	0.489281	+	0.403586i
$330$	25154.0			0.0127152
$331$	−533448.	+	923959.i	−0.267622	+	0.463535i	−0.968247	−	0.249995i	$-0.919571\pi$
$331$	−533448.	+	923959.i	−0.267622	+	0.463535i	0.700625	+	0.713529i	$0.252905\pi$
$332$	−1.17133e6	−	2.02880e6i	−0.583221	−	1.01017i
$333$	−203588.	−	352624.i	−0.100610	−	0.174262i
$334$	777130.	−	1.34603e6i	0.381178	−	0.660219i
$335$	2.74401e6			1.33590
$336$	−68682.9	+	409655.i	−0.0331895	+	0.197957i
$337$	1.55734e6			0.746981			0.373490	−	0.927634i	$-0.378161\pi$
$337$	1.55734e6			0.746981			0.373490	+	0.927634i	$0.378161\pi$
$338$	−578064.	+	1.00124e6i	−0.275222	+	0.476699i
$339$	−1.17137e6	−	2.02887e6i	−0.553597	−	0.958858i
$340$	732470.	+	1.26868e6i	0.343631	+	0.595187i
$341$	26977.1	−	46725.8i	0.0125635	−	0.0217606i
$342$	−387196.			−0.179005
$343$	1.04145e6	−	1.91388e6i	0.477973	−	0.878374i
$344$	253000.			0.115272
$345$	−1.03386e6	+	1.79070e6i	−0.467642	+	0.809980i
$346$	906124.	+	1.56945e6i	0.406909	+	0.704787i
$347$	1.11748e6	+	1.93553e6i	0.498214	+	0.862932i	0.999998	−	0.00206105i	$-0.000656052\pi$
$347$	1.11748e6	+	1.93553e6i	0.498214	+	0.862932i	−0.501784	+	0.864993i	$0.667323\pi$
$348$	619765.	−	1.07347e6i	0.274334	−	0.475160i
$349$	−1.72982e6			−0.760218			−0.380109	−	0.924942i	$-0.624114\pi$
$349$	−1.72982e6			−0.760218			−0.380109	+	0.924942i	$0.624114\pi$
$350$	−16597.7	+	98995.8i	−0.00724231	+	0.0431963i
$351$	648761.			0.281072
$352$	−51770.9	+	89669.8i	−0.0222705	+	0.0385736i
$353$	1.18287e6	+	2.04879e6i	0.505242	+	0.875105i	0.999982	+	0.00606386i	$0.00193020\pi$
$353$	1.18287e6	+	2.04879e6i	0.505242	+	0.875105i	−0.494739	+	0.869041i	$0.664736\pi$
$354$	44560.6	+	77181.2i	0.0188992	+	0.0327343i
$355$	46683.1	−	80857.6i	0.0196603	−	0.0340526i
$356$	1.13700e6			0.475484
$357$	−924058.	−	762214.i	−0.383733	−	0.316524i
$358$	454247.			0.187320
$359$	−25514.3	+	44192.1i	−0.0104484	+	0.0180971i	−0.871202	−	0.490924i	$-0.836659\pi$
$359$	−25514.3	+	44192.1i	−0.0104484	+	0.0180971i	0.860754	+	0.509021i	$0.169993\pi$
$360$	366703.	+	635148.i	0.149128	+	0.258297i
$361$	−274712.	−	475815.i	−0.110945	−	0.192163i
$362$	−204041.	+	353410.i	−0.0818364	+	0.141745i
$363$	−1.44673e6			−0.576262
$364$	−2.64226e6	+	986968.i	−1.04525	+	0.390436i
$365$	346197.			0.136016
$366$	−282911.	+	490016.i	−0.110394	+	0.191209i
$367$	−1.88411e6	−	3.26338e6i	−0.730200	−	1.26474i	−0.956797	−	0.290755i	$-0.906093\pi$
$367$	−1.88411e6	−	3.26338e6i	−0.730200	−	1.26474i	0.226597	−	0.973989i	$-0.427240\pi$
$368$	−700648.	−	1.21356e6i	−0.269699	−	0.467133i
$369$	−743863.	+	1.28841e6i	−0.284398	+	0.492592i
$370$	806328.			0.306201
$371$	−2.82441e6	+	1.05501e6i	−1.06535	+	0.397943i
$372$	681322.			0.255267
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	0.00727258	+	0.999974i	$0.497685\pi$
$373$	−2.31720e6	+	4.01351e6i	−0.862366	+	1.49366i	−0.869639	+	0.493689i	$0.835648\pi$
$374$	−24580.0	−	42573.8i	−0.00908663	−	0.0157385i
$375$	746790.	+	1.29348e6i	0.274234	+	0.474986i
$376$	−745020.	+	1.29041e6i	−0.271768	+	0.470716i
$377$	5.01346e6			1.81670
$378$	−200361.	−	165269.i	−0.0721247	−	0.0594924i
$379$	−4.17169e6			−1.49181			−0.745905	−	0.666052i	$-0.767983\pi$
$379$	−4.17169e6			−1.49181			−0.745905	+	0.666052i	$0.767983\pi$
$380$	−1.24101e6	+	2.14949e6i	−0.440875	+	0.763617i
$381$	1.05184e6	+	1.82184e6i	0.371226	+	0.642982i
$382$	−530276.	−	918465.i	−0.185928	−	0.322036i
$383$	2.08586e6	−	3.61281e6i	0.726588	−	1.25849i	−0.231730	−	0.972780i	$-0.574438\pi$
$383$	2.08586e6	−	3.61281e6i	0.726588	−	1.25849i	0.958317	−	0.285706i	$-0.0922282\pi$
$384$	−1.58927e6			−0.550008
$385$	−21800.9	+	130030.i	−0.00749590	+	0.0447088i
$386$	1.36391e6			0.465927
$387$	66051.9	−	114405.i	0.0224186	−	0.0388301i
$388$	−928783.	−	1.60870e6i	−0.313209	−	0.542495i
$389$	−1.37697e6	−	2.38498e6i	−0.461371	−	0.799119i	0.537658	−	0.843163i	$-0.319309\pi$
$389$	−1.37697e6	−	2.38498e6i	−0.461371	−	0.799119i	−0.999030	+	0.0440442i	$0.985976\pi$
$390$	−642369.	+	1.11262e6i	−0.213857	+	0.370411i
$391$	4.04106e6			1.33676
$392$	2.46466e6	+	850357.i	0.810108	+	0.279503i
$393$	−1.41561e6			−0.462340
$394$	−606578.	+	1.05062e6i	−0.196855	+	0.340962i
$395$	2.58184e6	+	4.47189e6i	0.832602	+	1.44211i
$396$	17252.0	+	29881.4i	0.00552843	+	0.00957552i
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	−0.590956	−	0.806704i	$-0.701249\pi$
$397$	1.26602e6	−	2.19281e6i	0.403148	−	0.698274i	0.994104	+	0.108430i	$0.0345825\pi$
$398$	−208419.			−0.0659522
$399$	335582.	−	2.00156e6i	0.105528	−	0.629413i
$400$	100299.			0.0313434
$401$	1.07873e6	−	1.86842e6i	0.335007	−	0.580249i	−0.648479	−	0.761232i	$-0.724595\pi$
$401$	1.07873e6	−	1.86842e6i	0.335007	−	0.580249i	0.983486	+	0.180983i	$0.0579280\pi$
$402$	−581398.	−	1.00701e6i	−0.179436	−	0.310791i
$403$	1.37785e6	+	2.38651e6i	0.422611	+	0.731983i
$404$	−564217.	+	977252.i	−0.171986	+	0.297888i
$405$	382948.			0.116012
$406$	−1.54834e6	−	1.27716e6i	−0.466177	−	0.384529i
$407$	87588.5			0.0262096
$408$	716669.	−	1.24131e6i	0.213142	−	0.369172i
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	0.985506	+	0.169640i	$0.0542604\pi$
$409$	2.16402e6	+	3.74819e6i	0.639665	+	1.10793i	−0.345841	+	0.938293i	$0.612406\pi$
$410$	−1.47307e6	−	2.55143e6i	−0.432776	−	0.749590i
$411$	771964.	−	1.33708e6i	0.225420	−	0.390439i
$412$	2.00405e6			0.581655
$413$	−437599.	+	163457.i	−0.126241	+	0.0471552i
$414$	876213.			0.251252
$415$	2.79649e6	−	4.84366e6i	0.797064	−	1.38056i
$416$	−2.64419e6	−	4.57987e6i	−0.749134	−	1.29754i
$417$	−947814.	−	1.64166e6i	−0.266921	−	0.462321i
$418$	41645.3	−	72131.8i	0.0116580	−	0.0201923i
$419$	−1.51129e6			−0.420544			−0.210272	−	0.977643i	$-0.567435\pi$
$419$	−1.51129e6			−0.420544			−0.210272	+	0.977643i	$0.567435\pi$
$420$	−1.55966e6	+	582583.i	−0.431426	+	0.161152i
$421$	1.11586e6			0.306835			0.153418	−	0.988161i	$-0.450972\pi$
$421$	1.11586e6			0.306835			0.153418	+	0.988161i	$0.450972\pi$
$422$	−1.07001e6	+	1.85331e6i	−0.292487	+	0.506603i
$423$	389012.	+	673788.i	0.105709	+	0.183093i
$424$	−1.80387e6	−	3.12439e6i	−0.487293	−	0.844016i
$425$	−144621.	+	250492.i	−0.0388383	+	0.0672699i
$426$	−39564.8			−0.0105629
$427$	−2.28787e6	−	1.88717e6i	−0.607243	−	0.500888i
$428$	69765.2			0.0184090
$429$	−69778.3	+	120860.i	−0.0183053	+	0.0317057i
$430$	130802.	+	226556.i	0.0341149	+	0.0590887i
$431$	−3.10672e6	−	5.38100e6i	−0.805581	−	1.39531i	−0.915898	−	0.401411i	$-0.868520\pi$
$431$	−3.10672e6	−	5.38100e6i	−0.805581	−	1.39531i	0.110317	−	0.993896i	$-0.464813\pi$
$432$	−129762.	+	224754.i	−0.0334533	+	0.0579427i
$433$	3.24118e6			0.830775			0.415388	−	0.909644i	$-0.363646\pi$
$433$	3.24118e6			0.830775			0.415388	+	0.909644i	$0.363646\pi$
$434$	182422.	−	1.08804e6i	0.0464892	−	0.277282i
$435$	2.95932e6			0.749841
$436$	−2.03255e6	+	3.52047e6i	−0.512064	+	0.886920i
$437$	3.42334e6	+	5.92939e6i	0.857524	+	1.48527i
$438$	−73351.9	−	127049.i	−0.0182695	−	0.0316437i
$439$	−1.15248e6	+	1.99616e6i	−0.285413	+	0.494349i	−0.972709	−	0.232028i	$-0.925464\pi$
$439$	−1.15248e6	+	1.99616e6i	−0.285413	+	0.494349i	0.687297	+	0.726377i	$0.258797\pi$
$440$	−157765.			−0.0388488
$441$	1.02799e6	−	892502.i	0.251705	−	0.218531i
$442$	2.51084e6			0.611313
$443$	−766328.	+	1.32732e6i	−0.185526	+	0.321341i	−0.943754	−	0.330649i	$-0.892732\pi$
$443$	−766328.	+	1.32732e6i	−0.185526	+	0.321341i	0.758228	+	0.651990i	$0.226066\pi$
$444$	553024.	+	957865.i	0.133133	+	0.230593i
$445$	1.35727e6	+	2.35086e6i	0.324912	+	0.562764i
$446$	−1.01420e6	+	1.75664e6i	−0.241426	+	0.418162i
$447$	2.15472e6			0.510060
$448$	−105874.	+	631476.i	−0.0249226	+	0.148649i
$449$	−3.55718e6			−0.832702			−0.416351	−	0.909204i	$-0.636691\pi$
$449$	−3.55718e6			−0.832702			−0.416351	+	0.909204i	$0.636691\pi$
$450$	−31357.9	+	54313.4i	−0.00729987	+	0.0126438i
$451$	−160014.	−	277153.i	−0.0370439	−	0.0641620i
$452$	3.18189e6	+	5.51119e6i	0.732553	+	1.26882i
$453$	−976678.	+	1.69166e6i	−0.223617	+	0.387317i
$454$	−1.49533e6			−0.340484
$455$	−5.19478e6	−	4.28494e6i	−1.17636	−	0.970324i
$456$	2.42847e6			0.546916
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	−0.971898	−	0.235403i	$-0.924359\pi$
$457$	−1.25941e6	+	2.18137e6i	−0.282083	+	0.488583i	0.689814	+	0.723986i	$0.257692\pi$
$458$	320936.	+	555877.i	0.0714915	+	0.123827i
$459$	−374209.	−	648148.i	−0.0829053	−	0.143596i
$460$	2.80836e6	−	4.86423e6i	0.618812	−	1.07181i
$461$	−6.63271e6			−1.45358			−0.726789	−	0.686861i	$-0.758988\pi$
$461$	−6.63271e6			−1.45358			−0.726789	+	0.686861i	$0.758988\pi$
$462$	52338.5	−	19550.1i	0.0114082	−	0.00426132i
$463$	−4.40432e6			−0.954830			−0.477415	−	0.878678i	$-0.658426\pi$
$463$	−4.40432e6			−0.954830			−0.477415	+	0.878678i	$0.658426\pi$
$464$	−1.00277e6	+	1.73685e6i	−0.216225	+	0.374512i
$465$	813313.	+	1.40870e6i	0.174432	+	0.302124i
$466$	849325.	+	1.47107e6i	0.181180	+	0.313812i
$467$	−122922.	+	212908.i	−0.0260819	+	0.0451751i	−0.878772	−	0.477242i	$-0.841636\pi$
$467$	−122922.	+	212908.i	−0.0260819	+	0.0451751i	0.852690	+	0.522417i	$0.174970\pi$
$468$	−1.76229e6			−0.371931
$469$	5.70951e6	−	2.13269e6i	1.19858	−	0.447708i
$470$	−1.54072e6			−0.321720
$471$	−751070.	+	1.30089e6i	−0.156001	+	0.270202i
$472$	−279482.	−	484076.i	−0.0577428	−	0.100014i
$473$	14208.6	+	24610.0i	0.00292010	+	0.00505776i
$474$	1.09408e6	−	1.89500e6i	0.223667	−	0.387403i
$475$	−490057.			−0.0996581
$476$	2.51010e6	+	2.07047e6i	0.507778	+	0.418843i
$477$	−1.88378e6			−0.379083
$478$	−1.28821e6	+	2.23125e6i	−0.257880	+	0.446661i
$479$	20175.6	+	34945.1i	0.00401779	+	0.00695901i	0.868027	−	0.496516i	$-0.165388\pi$
$479$	20175.6	+	34945.1i	0.00401779	+	0.00695901i	−0.864010	+	0.503475i	$0.832054\pi$
$480$	−1.56080e6	−	2.70339e6i	−0.309203	−	0.535556i
$481$	−2.23678e6	+	3.87422e6i	−0.440820	+	0.763523i
$482$	2.56140e6			0.502181
$483$	−759412.	+	4.52947e6i	−0.148119	+	0.883445i
$484$	3.92987e6			0.762544
$485$	2.21743e6	−	3.84069e6i	0.428050	−	0.741405i
$486$	−81138.7	−	140536.i	−0.0155825	−	0.0269897i
$487$	1.65484e6	+	2.86627e6i	0.316180	+	0.547639i	0.979688	−	0.200530i	$-0.0642664\pi$
$487$	1.65484e6	+	2.86627e6i	0.316180	+	0.547639i	−0.663508	+	0.748169i	$0.730933\pi$
$488$	1.77440e6	−	3.07335e6i	0.337289	−	0.584202i
$489$	4.55555e6			0.861526
$490$	512768.	+	2.64669e6i	0.0964785	+	0.497982i
$491$	−1.97959e6			−0.370570			−0.185285	−	0.982685i	$-0.559321\pi$
$491$	−1.97959e6			−0.370570			−0.185285	+	0.982685i	$0.559321\pi$
$492$	2.02062e6	−	3.49982e6i	0.376333	−	0.651828i
$493$	−2.89179e6	−	5.00872e6i	−0.535857	−	0.928132i
$494$	2.12703e6	+	3.68412e6i	0.392153	+	0.679229i
$495$	−41188.4	+	71340.4i	−0.00755547	+	0.0130865i
$496$	−1.10237e6			−0.201197
$497$	34290.7	−	204525.i	0.00622709	−	0.0371411i
$498$	−2.37007e6			−0.428241
$499$	1.58498e6	−	2.74526e6i	0.284952	−	0.493551i	−0.687646	−	0.726046i	$-0.741356\pi$
$499$	1.58498e6	−	2.74526e6i	0.284952	−	0.493551i	0.972597	+	0.232495i	$0.0746891\pi$
$500$	−2.02857e6	−	3.51359e6i	−0.362882	−	0.628530i
$501$	2.54502e6	+	4.40810e6i	0.452998	+	0.784616i
$502$	−295396.	+	511640.i	−0.0523172	+	0.0906161i
$503$	−4.01273e6			−0.707164			−0.353582	−	0.935403i	$-0.615037\pi$
$503$	−4.01273e6			−0.707164			−0.353582	+	0.935403i	$0.615037\pi$
$504$	1.25665e6	+	1.03656e6i	0.220363	+	0.181768i
$505$	−2.69408e6			−0.470092
$506$	−94242.1	+	163232.i	−0.0163632	+	0.0283419i
$507$	−1.89310e6	−	3.27894e6i	−0.327079	−	0.566518i
$508$	−2.85721e6	−	4.94884e6i	−0.491228	−	0.850832i
$509$	−2.05629e6	+	3.56159e6i	−0.351795	+	0.609326i	−0.986564	−	0.163375i	$-0.947762\pi$
$509$	−2.05629e6	+	3.56159e6i	−0.351795	+	0.609326i	0.634769	+	0.772702i	$0.281095\pi$
$510$	1.48209e6			0.252318
$511$	720338.	−	269070.i	0.122035	−	0.0455840i
$512$	3.88273e6			0.654580
$513$	634012.	−	1.09814e6i	0.106366	−	0.184232i
$514$	−108810.	−	188465.i	−0.0181661	−	0.0314646i
$515$	2.39229e6	+	4.14356e6i	0.397462	+	0.688424i
$516$	−179423.	+	310769.i	−0.0296656	+	0.0513823i
$517$	−167363.			−0.0275380
$518$	1.67774e6	−	626691.i	0.274727	−	0.102619i
$519$	−5.93492e6			−0.967155
$520$	4.02890e6	−	6.97827e6i	0.653399	−	1.13172i
$521$	−4.27758e6	−	7.40898e6i	−0.690404	−	1.19582i	−0.971705	−	0.236196i	$-0.924099\pi$
$521$	−4.27758e6	−	7.40898e6i	−0.690404	−	1.19582i	0.281301	−	0.959620i	$-0.409234\pi$
$522$	−627019.	−	1.08603e6i	−0.100717	−	0.174448i
$523$	896820.	−	1.55334e6i	0.143368	−	0.248320i	−0.785395	−	0.618995i	$-0.787540\pi$
$523$	896820.	−	1.55334e6i	0.143368	−	0.248320i	0.928763	+	0.370675i	$0.120874\pi$
$524$	3.84534e6			0.611796
$525$	−253588.	−	209174.i	−0.0401542	−	0.0331214i
$526$	−1.18949e6			−0.187455
$527$	1.58950e6	−	2.75310e6i	0.249307	−	0.431813i
$528$	−27913.4	−	48347.5i	−0.00435741	−	0.00754725i
$529$	−4.52875e6	−	7.84402e6i	−0.703621	−	1.21871i
$530$	1.86522e6	−	3.23065e6i	0.288430	−	0.499575i
$531$	−291862.			−0.0449202
$532$	−911571.	+	5.43701e6i	−0.139640	+	0.832877i
$533$	1.63454e7			2.49217
$534$	575154.	−	996196.i	0.0872833	−	0.151179i
$535$	83280.6	+	144246.i	0.0125794	+	0.0217881i
$536$	3.64650e6	+	6.31592e6i	0.548231	+	0.949565i
$537$	−743805.	+	1.28831e6i	−0.111307	+	0.192790i
$538$	−12894.1			−0.00192059
$539$	55700.1	+	287501.i	0.00825818	+	0.0426253i
$540$	−1.04023e6			−0.153514
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	−0.852596	−	0.522571i	$-0.824973\pi$
$541$	178780.	−	309657.i	0.0262619	−	0.0454870i	0.878858	+	0.477084i	$0.158306\pi$
$542$	−144643.	−	250528.i	−0.0211494	−	0.0366318i
$543$	−668213.	−	1.15738e6i	−0.0972558	−	0.168452i
$544$	−3.05036e6	+	5.28338e6i	−0.441931	+	0.765447i
$545$	−9.70522e6			−1.39963
$546$	−471847.	+	2.81430e6i	−0.0677360	+	0.404007i
$547$	−3.79404e6			−0.542167			−0.271084	−	0.962556i	$-0.587382\pi$
$547$	−3.79404e6			−0.542167			−0.271084	+	0.962556i	$0.587382\pi$
$548$	−2.09695e6	+	3.63203e6i	−0.298289	+	0.516652i
$549$	−926502.	−	1.60475e6i	−0.131195	−	0.227236i
$550$	−6745.47	−	11683.5i	−0.000950835	−	0.00164689i
$551$	4.89949e6	−	8.48616e6i	0.687498	−	1.19078i
$552$	−5.49556e6			−0.767652
$553$	8.84771e6	+	7.29809e6i	1.23032	+	1.01484i
$554$	−2.09718e6			−0.290310
$555$	−1.32032e6	+	2.28686e6i	−0.181948	+	0.315142i
$556$	2.57463e6	+	4.45939e6i	0.353206	+	0.611771i
$557$	2.44799e6	+	4.24005e6i	0.334328	+	0.579072i	0.983355	−	0.181692i	$-0.0581575\pi$
$557$	2.44799e6	+	4.24005e6i	0.334328	+	0.579072i	−0.649028	+	0.760765i	$0.724824\pi$
$558$	344648.	−	596948.i	0.0468587	−	0.0811617i
$559$	−1.45140e6			−0.196453
$560$	2.52350e6	−	942607.i	0.340042	−	0.127017i
$561$	160994.			0.0215974
$562$	1.00245e6	−	1.73630e6i	0.133882	−	0.231891i
$563$	2.16583e6	+	3.75133e6i	0.287974	+	0.498786i	0.973326	−	0.229426i	$-0.0736849\pi$
$563$	2.16583e6	+	3.75133e6i	0.287974	+	0.498786i	−0.685352	+	0.728212i	$0.740352\pi$
$564$	−1.05671e6	−	1.83027e6i	−0.139880	−	0.242280i
$565$	−7.59661e6	+	1.31577e7i	−1.00115	+	1.73404i
$566$	−3.27151e6			−0.429248
$567$	796807.	−	297633.i	0.104087	−	0.0388798i
$568$	248148.			0.0322730
$569$	1.09848e6	−	1.90262e6i	0.142236	−	0.246361i	−0.786102	−	0.618097i	$-0.787904\pi$
$569$	1.09848e6	−	1.90262e6i	0.142236	−	0.246361i	0.928338	+	0.371736i	$0.121237\pi$
$570$	1.25553e6	+	2.17464e6i	0.161860	+	0.280350i
$571$	3.73846e6	+	6.47520e6i	0.479846	+	0.831118i	0.999733	−	0.0231172i	$-0.00735908\pi$
$571$	3.73846e6	+	6.47520e6i	0.479846	+	0.831118i	−0.519886	+	0.854235i	$0.674026\pi$
$572$	189545.	−	328301.i	0.0242227	−	0.0419549i
$573$	3.47320e6			0.441919
$574$	−5.04805e6	−	4.16391e6i	−0.639505	−	0.527500i
$575$	1.10899e6			0.139880
$576$	−200026.	+	346456.i	−0.0251206	+	0.0435102i
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	0.905569	−	0.424198i	$-0.139444\pi$
$577$	683110.	+	1.18318e6i	0.0854183	+	0.147949i	−0.820151	+	0.572147i	$0.806111\pi$
$578$	502748.	+	870785.i	0.0625937	+	0.108415i
$579$	−2.23333e6	+	3.86824e6i	−0.276858	+	0.479531i
$580$	−8.03867e6			−0.992234
$581$	2.05414e6	−	1.22518e7i	0.252458	−	1.50577i
$582$	−1.87931e6			−0.229980
$583$	202612.	−	350934.i	0.0246884	−	0.0427616i
$584$	460059.	+	796845.i	0.0558189	+	0.0966812i
$585$	−2.10369e6	−	3.64370e6i	−0.254151	−	0.440203i
$586$	1.40848e6	−	2.43956e6i	0.169437	−	0.293473i
$587$	−9.27217e6			−1.11067			−0.555336	−	0.831626i	$-0.687410\pi$
$587$	−9.27217e6			−1.11067			−0.555336	+	0.831626i	$0.687410\pi$
$588$	−2.79242e6	+	2.42438e6i	−0.333071	+	0.289173i
$589$	5.38612e6			0.639717
$590$	288987.	−	500540.i	0.0341781	−	0.0591982i
$591$	−1.98648e6	−	3.44068e6i	−0.233946	−	0.405206i
$592$	−894782.	−	1.54981e6i	−0.104933	−	0.181750i
$593$	−4.60523e6	+	7.97649e6i	−0.537792	+	0.931483i	0.461231	+	0.887280i	$0.347408\pi$
$593$	−4.60523e6	+	7.97649e6i	−0.537792	+	0.931483i	−0.999023	+	0.0442028i	$0.985925\pi$
$594$	34907.9			0.00405936
$595$	−1.28452e6	+	7.66145e6i	−0.148747	+	0.887194i
$596$	−5.85305e6			−0.674942
$597$	341275.	−	591105.i	0.0391894	−	0.0678779i
$598$	−4.81340e6	−	8.33706e6i	−0.550426	−	0.953367i
$599$	6.84581e6	+	1.18573e7i	0.779575	+	1.35026i	0.932187	+	0.361977i	$0.117898\pi$
$599$	6.84581e6	+	1.18573e7i	0.779575	+	1.35026i	−0.152612	+	0.988286i	$0.548769\pi$
$600$	196675.	−	340651.i	0.0223034	−	0.0386306i
$601$	1.61113e6			0.181946			0.0909732	−	0.995853i	$-0.471002\pi$
$601$	1.61113e6			0.181946			0.0909732	+	0.995853i	$0.471002\pi$
$602$	448246.	+	369738.i	0.0504110	+	0.0415818i
$603$	3.80803e6			0.426489
$604$	2.65304e6	−	4.59519e6i	0.295904	−	0.512521i
$605$	4.69119e6	+	8.12539e6i	0.521069	+	0.902517i
$606$	570820.	+	988690.i	0.0631419	+	0.109365i
$607$	7.03281e6	−	1.21812e7i	0.774742	−	1.34189i	−0.160198	−	0.987085i	$-0.551213\pi$
$607$	7.03281e6	−	1.21812e7i	0.774742	−	1.34189i	0.934940	−	0.354807i	$-0.115453\pi$
$608$	−1.03363e7			−1.13398
$609$	6.15752e6	−	2.30003e6i	0.672764	−	0.251299i
$610$	3.66950e6			0.399284
$611$	4.27401e6	−	7.40280e6i	0.463161	−	0.802219i
$612$	1.01650e6	+	1.76062e6i	0.109705	+	0.190015i
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	−0.956572	−	0.291497i	$-0.905847\pi$
$613$	−6.79842e6	−	1.17752e7i	−0.730729	−	1.26566i	0.225842	−	0.974164i	$-0.427487\pi$
$614$	975391.	−	1.68943e6i	0.104414	−	0.180850i
$615$	9.64828e6			1.02864
$616$	−328264.	+	122617.i	−0.0348555	+	0.0130197i
$617$	−5.74287e6			−0.607318			−0.303659	−	0.952781i	$-0.598208\pi$
$617$	−5.74287e6			−0.607318			−0.303659	+	0.952781i	$0.598208\pi$
$618$	1.01375e6	−	1.75587e6i	0.106773	−	0.184936i
$619$	3.01299e6	+	5.21865e6i	0.316061	+	0.547434i	0.979662	−	0.200653i	$-0.0643063\pi$
$619$	3.01299e6	+	5.21865e6i	0.316061	+	0.547434i	−0.663602	+	0.748086i	$0.730973\pi$
$620$	−2.20927e6	−	3.82657e6i	−0.230818	−	0.399789i
$621$	−1.43475e6	+	2.48506e6i	−0.149296	+	0.258588i
$622$	4.30814e6			0.446492
$623$	4.65122e6	+	3.83658e6i	0.480117	+	0.396027i
$624$	2.85135e6			0.293149
$625$	5.28334e6	−	9.15101e6i	0.541014	−	0.937064i
$626$	−512470.	−	887625.i	−0.0522676	−	0.0905302i
$627$	136384.	+	236224.i	0.0138546	+	0.0239969i
$628$	2.04020e6	−	3.53373e6i	0.206430	−	0.357547i
$629$	5.16075e6			0.520099
$630$	−278519.	+	1.66121e6i	−0.0279579	+	0.166753i
$631$	−6.90670e6			−0.690554			−0.345277	−	0.938501i	$-0.612215\pi$
$631$	−6.90670e6			−0.690554			−0.345277	+	0.938501i	$0.612215\pi$
$632$	−6.86200e6	+	1.18853e7i	−0.683373	+	1.18364i
$633$	−3.50417e6	−	6.06940e6i	−0.347597	−	0.602055i
$634$	4.16096e6	+	7.20700e6i	0.411122	+	0.712084i
$635$	6.82146e6	−	1.18151e7i	0.671341	−	1.16280i
$636$	5.11708e6			0.501625
$637$	−1.41392e7	−	4.87830e6i	−1.38063	−	0.476343i
$638$	269759.			0.0262376
$639$	64785.2	−	112211.i	0.00627659	−	0.0108714i
$640$	5.15340e6	+	8.92595e6i	0.497329	+	0.861400i
$641$	−8.24828e6	−	1.42864e7i	−0.792900	−	1.37334i	−0.924164	−	0.381995i	$-0.875237\pi$
$641$	−8.24828e6	−	1.42864e7i	−0.792900	−	1.37334i	0.131265	−	0.991347i	$-0.458096\pi$
$642$	35290.9	−	61125.6i	0.00337928	−	0.00585309i
$643$	1.70171e7			1.62315			0.811576	−	0.584247i	$-0.198610\pi$
$643$	1.70171e7			1.62315			0.811576	+	0.584247i	$0.198610\pi$
$644$	2.06286e6	−	1.23038e7i	0.195999	−	1.16903i
$645$	−856727.			−0.0810855
$646$	2.45376e6	−	4.25003e6i	0.231340	−	0.400692i
$647$	−1.74287e6	−	3.01873e6i	−0.163683	−	0.283507i	0.772504	−	0.635010i	$-0.219004\pi$
$647$	−1.74287e6	−	3.01873e6i	−0.163683	−	0.283507i	−0.936187	+	0.351503i	$0.885671\pi$
$648$	508897.	+	881436.i	0.0476094	+	0.0824619i
$649$	31391.6	−	54371.8i	0.00292551	−	0.00506713i
$650$	689047.			0.0639684
$651$	2.78714e6	+	2.29899e6i	0.257754	+	0.212610i
$652$	−1.23746e7			−1.14002
$653$	−7.72245e6	+	1.33757e7i	−0.708716	+	1.22753i	0.256618	+	0.966513i	$0.417392\pi$
$653$	−7.72245e6	+	1.33757e7i	−0.708716	+	1.22753i	−0.965334	+	0.261019i	$0.915941\pi$
$654$	2.05633e6	+	3.56168e6i	0.187996	+	0.325619i
$655$	4.59029e6	+	7.95061e6i	0.418058	+	0.724098i
$656$	−3.26933e6	+	5.66264e6i	−0.296619	+	0.513759i
$657$	480439.			0.0434235
$658$	−3.20580e6	+	1.19747e6i	−0.288650	+	0.107820i
$659$	−3.11193e6			−0.279136			−0.139568	−	0.990212i	$-0.544571\pi$
$659$	−3.11193e6			−0.279136			−0.139568	+	0.990212i	$0.544571\pi$
$660$	111884.	−	193788.i	0.00999785	−	0.0173168i
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	0.624823	−	0.780766i	$-0.285171\pi$
$661$	−4.08610e6	−	7.07733e6i	−0.363752	−	0.630037i	−0.988575	+	0.150729i	$0.951838\pi$
$662$	−1.46601e6	−	2.53921e6i	−0.130015	−	0.225192i
$663$	−4.11137e6	+	7.12110e6i	−0.363247	+	0.629163i
$664$	1.48650e7			1.30841
$665$	−1.23297e7	+	4.60554e6i	−1.08118	+	0.403856i
$666$	1.11899e6			0.0977556
$667$	−1.10874e7	+	1.92039e7i	−0.964973	+	1.67138i
$668$	−6.91326e6	−	1.19741e7i	−0.599434	−	1.03825i
$669$	−3.32138e6	−	5.75280e6i	−0.286915	−	0.496951i
$670$	−3.77051e6	+	6.53072e6i	−0.324499	+	0.562049i
$671$	398604.			0.0341771
$672$	−5.34870e6	−	4.41191e6i	−0.456904	−	0.376880i
$673$	1.60182e7			1.36325			0.681627	−	0.731700i	$-0.261273\pi$
$673$	1.60182e7			1.36325			0.681627	+	0.731700i	$0.261273\pi$
$674$	−2.13993e6	+	3.70647e6i	−0.181447	+	0.314276i
$675$	−102694.	−	177871.i	−0.00867530	−	0.0150261i
$676$	5.14239e6	+	8.90687e6i	0.432811	+	0.749650i
$677$	−512185.	+	887131.i	−0.0429492	+	0.0743902i	−0.886701	−	0.462344i	$-0.847009\pi$
$677$	−512185.	+	887131.i	−0.0429492	+	0.0743902i	0.843752	+	0.536734i	$0.180342\pi$
$678$	6.43826e6			0.537891
$679$	1.62879e6	−	9.71483e6i	0.135579	−	0.808650i
$680$	−9.29556e6			−0.770910
$681$	2.44852e6	−	4.24096e6i	0.202319	−	0.350426i
$682$	74138.1	+	128411.i	0.00610352	+	0.0105716i
$683$	2.69688e6	+	4.67114e6i	0.221213	+	0.383152i	0.955177	−	0.296037i	$-0.0956651\pi$
$683$	2.69688e6	+	4.67114e6i	0.221213	+	0.383152i	−0.733964	+	0.679189i	$0.762332\pi$
$684$	−1.72222e6	+	2.98298e6i	−0.140750	+	0.243787i
$685$	−1.00128e7			−0.815319
$686$	3.12398e6	+	5.10850e6i	0.253453	+	0.414460i
$687$	−2.10206e6			−0.169924
$688$	290302.	−	502819.i	0.0233819	−	0.0404986i
$689$	1.03484e7	+	1.79239e7i	0.830470	+	1.43842i
$690$	−2.84123e6	−	4.92116e6i	−0.227187	−	0.393500i
$691$	452826.	−	784318.i	0.0360775	−	0.0624881i	−0.847423	−	0.530919i	$-0.821847\pi$
$691$	452826.	−	784318.i	0.0360775	−	0.0624881i	0.883500	+	0.468430i	$0.155180\pi$
$692$	1.61215e7			1.27980
$693$	−30254.6	+	180452.i	−0.00239308	+	0.0142734i
$694$	−6.14207e6			−0.484079
$695$	−6.14682e6	+	1.06466e7i	−0.482712	+	0.836082i
$696$	3.93263e6	+	6.81151e6i	0.307723	+	0.532992i
$697$	−9.42810e6	−	1.63300e7i	−0.735093	−	1.27322i
$698$	2.37693e6	−	4.11697e6i	0.184662	−	0.319845i
$699$	−5.56290e6			−0.430634
$700$	688845.	+	568197.i	0.0531344	+	0.0438282i
$701$	1.12573e7			0.865246			0.432623	−	0.901575i	$-0.357588\pi$
$701$	1.12573e7			0.865246			0.432623	+	0.901575i	$0.357588\pi$
$702$	−891457.	+	1.54405e6i	−0.0682743	+	0.118255i
$703$	4.37187e6	+	7.57230e6i	0.333640	+	0.577882i
$704$	−43028.1	−	74526.9i	−0.00327205	−	0.00566736i
$705$	2.52284e6	−	4.36969e6i	0.191169	−	0.331114i
$706$	−6.50147e6			−0.490908
$707$	−5.60563e6	+	2.09388e6i	−0.421770	+	0.157545i
$708$	792812.			0.0594411
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	−0.935831	−	0.352448i	$-0.885349\pi$
$709$	−2.17755e6	+	3.77162e6i	−0.162687	+	0.281781i	0.773145	+	0.634230i	$0.218683\pi$
$710$	128294.	+	222211.i	0.00955123	+	0.0165432i
$711$	3.58299e6	+	6.20592e6i	0.265810	+	0.460397i
$712$	−3.60733e6	+	6.24809e6i	−0.266678	+	0.461899i
$713$	−1.21886e7			−0.897907
$714$	3.08381e6	−	1.15190e6i	0.226382	−	0.0845609i
$715$	905060.			0.0662082
$716$	2.02046e6	−	3.49955e6i	0.147288	−	0.255111i
$717$	−4.21875e6	−	7.30709e6i	−0.306469	−	0.530819i
$718$	−70118.0	−	121448.i	−0.00507597	−	0.00879183i
$719$	7.07221e6	−	1.22494e7i	0.510191	−	0.883676i	−0.489739	−	0.871869i	$-0.662908\pi$
$719$	7.07221e6	−	1.22494e7i	0.510191	−	0.883676i	0.999930	−	0.0118076i	$-0.00375858\pi$
$720$	1.68308e6			0.120997
$721$	8.19812e6	+	6.76227e6i	0.587322	+	0.484456i
$722$	1.50992e6			0.107798
$723$	−4.19416e6	+	7.26450e6i	−0.298401	+	0.516845i
$724$	1.81513e6	+	3.14389e6i	0.128695	+	0.222906i
$725$	−793591.	−	1.37454e6i	−0.0560727	−	0.0971208i
$726$	1.98793e6	−	3.44320e6i	0.139978	−	0.242449i
$727$	−6.26406e6			−0.439561			−0.219781	−	0.975549i	$-0.570534\pi$
$727$	−6.26406e6			−0.439561			−0.219781	+	0.975549i	$0.570534\pi$
$728$	2.95940e6	−	1.76511e7i	0.206954	−	1.23437i
$729$	531441.			0.0370370
$730$	−475705.	+	823946.i	−0.0330393	+	0.0572258i
$731$	837176.	+	1.45003e6i	0.0579460	+	0.100365i
$732$	2.51674e6	+	4.35912e6i	0.173604	+	0.300692i
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	−0.266025	−	0.963966i	$-0.585710\pi$
$733$	1.02089e7	−	1.76823e7i	0.701806	−	1.21556i	0.967832	−	0.251598i	$-0.0809562\pi$
$734$	1.03558e7			0.709484
$735$	−8.34602e6	−	2.87954e6i	−0.569851	−	0.196610i
$736$	2.33908e7			1.59166
$737$	−409577.	+	709409.i	−0.0277758	+	0.0481092i
$738$	−2.04427e6	−	3.54078e6i	−0.138165	−	0.239309i
$739$	−7.42256e6	−	1.28563e7i	−0.499969	−	0.865971i	0.500031	−	0.866007i	$-0.333322\pi$
$739$	−7.42256e6	−	1.28563e7i	−0.499969	−	0.865971i	−1.00000		3.61537e-5i	$0.999988\pi$
$740$	3.58650e6	−	6.21200e6i	0.240764	−	0.417015i
$741$	−1.39316e7			−0.932083
$742$	1.37008e6	−	8.17176e6i	0.0913558	−	0.544886i
$743$	2.36601e7			1.57234			0.786168	−	0.618013i	$-0.212062\pi$
$743$	2.36601e7			1.57234			0.786168	+	0.618013i	$0.212062\pi$
$744$	−2.16161e6	+	3.74403e6i	−0.143168	+	0.247974i
$745$	−6.98694e6	−	1.21017e7i	−0.461207	−	0.798834i
$746$	−6.36809e6	−	1.10299e7i	−0.418950	−	0.725643i
$747$	3.88087e6	−	6.72186e6i	0.254465	−	0.440746i
$748$	−437322.			−0.0285790
$749$	285394.	+	235409.i	0.0185883	+	0.0153327i
$750$	−4.10463e6			−0.266453
$751$	−1.03287e7	+	1.78898e7i	−0.668258	+	1.15746i	0.310133	+	0.950693i	$0.399627\pi$
$751$	−1.03287e7	+	1.78898e7i	−0.668258	+	1.15746i	−0.978391	+	0.206764i	$0.933707\pi$
$752$	1.70973e6	+	2.96134e6i	0.110251	+	0.190961i
$753$	−967389.	−	1.67557e6i	−0.0621747	−	0.107690i
$754$	−6.88895e6	+	1.19320e7i	−0.441291	+	0.764338i
$755$	1.26680e7			0.808799
$756$	−2.16444e6	+	808487.i	−0.137734	+	0.0514480i
$757$	−1.26697e7			−0.803573			−0.401787	−	0.915733i	$-0.631611\pi$
$757$	−1.26697e7			−0.803573			−0.401787	+	0.915733i	$0.631611\pi$
$758$	5.73228e6	−	9.92860e6i	0.362372	−	0.627646i
$759$	−308633.	−	534568.i	−0.0194463	−	0.0336820i
$760$	−7.87462e6	−	1.36392e7i	−0.494534	−	0.856557i
$761$	−8.13761e6	+	1.40948e7i	−0.509372	+	0.882259i	0.490569	+	0.871402i	$0.336789\pi$
$761$	−8.13761e6	+	1.40948e7i	−0.509372	+	0.882259i	−0.999941	+	0.0108563i	$0.996544\pi$
$762$	−5.78130e6			−0.360694
$763$	−2.01938e7	+	7.54305e6i	−1.25576	+	0.469068i
$764$	−9.43455e6			−0.584774
$765$	−2.42684e6	+	4.20341e6i	−0.149929	+	0.259685i
$766$	5.73232e6	+	9.92867e6i	0.352987	+	0.611391i
$767$	1.60332e6	+	2.77703e6i	0.0984084	+	0.170448i
$768$	2.89500e6	−	5.01429e6i	0.177111	−	0.306765i
$769$	1.60471e7			0.978547			0.489273	−	0.872130i	$-0.337262\pi$
$769$	1.60471e7			0.978547			0.489273	+	0.872130i	$0.337262\pi$
$770$	−279515.	−	230560.i	−0.0169894	−	0.0140138i
$771$	712683.			0.0431778
$772$	6.06659e6	−	1.05076e7i	0.366355	−	0.634545i
$773$	−1.07839e6	−	1.86782e6i	−0.0649121	−	0.112431i	0.831743	−	0.555161i	$-0.187343\pi$
$773$	−1.07839e6	−	1.86782e6i	−0.0649121	−	0.112431i	−0.896655	+	0.442730i	$0.854010\pi$
$774$	181523.	+	314406.i	0.0108913	+	0.0188642i
$775$	436206.	−	755531.i	0.0260878	−	0.0451854i
$776$	1.17869e7			0.702661
$777$	−969828.	+	5.78448e6i	−0.0576292	+	0.343726i
$778$	7.56833e6			0.448282
$779$	1.59738e7	−	2.76674e7i	0.943115	−	1.63352i
$780$	5.71444e6	+	9.89770e6i	0.336308	+	0.582503i
$781$	13936.1	+	24138.0i	0.000817548	+	0.00141603i
$782$	−5.55279e6	+	9.61771e6i	−0.324709	+	0.562412i
$783$	4.10684e6			0.239389
$784$	4.51808e6	−	3.92260e6i	0.262521	−	0.227921i
$785$	9.74175e6			0.564239
$786$	1.94517e6	−	3.36914e6i	0.112306	−	0.194519i
$787$	−7.00503e6	−	1.21331e7i	−0.403156	−	0.698286i	0.590949	−	0.806709i	$-0.298753\pi$
$787$	−7.00503e6	−	1.21331e7i	−0.403156	−	0.698286i	−0.994105	+	0.108423i	$0.965420\pi$
$788$	5.39604e6	+	9.34622e6i	0.309571	+	0.536192i
$789$	1.94773e6	−	3.37356e6i	0.111387	−	0.192928i
$790$	−1.41908e7			−0.808980
$791$	−5.58002e6	+	3.32817e7i	−0.317099	+	1.89132i
$792$	−218940.			−0.0124026
$793$	−1.01793e7	+	1.76311e7i	−0.574825	+	0.995627i
$794$	3.47926e6	+	6.02625e6i	0.195855	+	0.339231i
$795$	6.10839e6	+	1.05800e7i	0.342775	+	0.593703i
$796$	−927034.	+	1.60567e6i	−0.0518577	+	0.0898202i
$797$	4.73289e6			0.263925			0.131963	−	0.991255i	$-0.457872\pi$
$797$	4.73289e6			0.263925			0.131963	+	0.991255i	$0.457872\pi$
$798$	4.30258e6	+	3.54900e6i	0.239178	+	0.197287i
$799$	−9.86107e6			−0.546459
$800$	−837108.	+	1.44991e6i	−0.0462441	+	0.0800972i
$801$	1.88357e6	+	3.26244e6i	0.103729	+	0.179664i
$802$	2.96456e6	+	5.13477e6i	0.162751	+	0.281893i
$803$	−51674.2	+	89502.3i	−0.00282804	+	0.00489830i
$804$	−1.03441e7			−0.564355
$805$	2.79018e7	−	1.04222e7i	1.51755	−	0.566853i
$806$	−7.57318e6			−0.410621
$807$	21113.4	−	36569.4i	0.00114123	−	0.00197667i
$808$	−3.58015e6	−	6.20101e6i	−0.192918	−	0.334144i
$809$	−4.05446e6	−	7.02253e6i	−0.217802	−	0.377244i	0.736334	−	0.676618i	$-0.236555\pi$
$809$	−4.05446e6	−	7.02253e6i	−0.217802	−	0.377244i	−0.954136	+	0.299375i	$0.903222\pi$
$810$	−526205.	+	911414.i	−0.0281801	+	0.0488093i
$811$	−9.13444e6			−0.487674			−0.243837	−	0.969816i	$-0.578406\pi$
$811$	−9.13444e6			−0.487674			−0.243837	+	0.969816i	$0.578406\pi$
$812$	−1.67262e7	+	6.24778e6i	−0.890241	+	0.332534i
$813$	947378.			0.0502686
$814$	−120355.	+	208460.i	−0.00636651	+	0.0110271i
$815$	−1.47719e7	−	2.55858e7i	−0.779011	−	1.34929i
$816$	−1.64467e6	−	2.84865e6i	−0.0864676	−	0.149766i
$817$	−1.41841e6	+	2.45675e6i	−0.0743439	+	0.128767i
$818$	−1.18942e7			−0.621517
$819$	−7.20913e6	−	5.94649e6i	−0.375555	−	0.309778i
$820$	−2.62085e7			−1.36115
$821$	−850776.	+	1.47359e6i	−0.0440511	+	0.0762988i	−0.887210	−	0.461365i	$-0.847360\pi$
$821$	−850776.	+	1.47359e6i	−0.0440511	+	0.0762988i	0.843159	+	0.537664i	$0.180693\pi$
$822$	2.12150e6	+	3.67454e6i	0.109512	+	0.189681i
$823$	1.24604e7	+	2.15820e7i	0.641256	+	1.11069i	0.985153	+	0.171680i	$0.0549196\pi$
$823$	1.24604e7	+	2.15820e7i	0.641256	+	1.11069i	−0.343897	+	0.939007i	$0.611747\pi$
$824$	−6.35820e6	+	1.10127e7i	−0.326224	+	0.565037i
$825$	44181.4			0.00225998
$826$	212273.	−	1.26609e6i	0.0108254	−	0.0645674i
$827$	−1.91232e7			−0.972292			−0.486146	−	0.873878i	$-0.661598\pi$
$827$	−1.91232e7			−0.972292			−0.486146	+	0.873878i	$0.661598\pi$
$828$	3.89735e6	−	6.75040e6i	0.197557	−	0.342179i
$829$	1.10134e7	+	1.90757e7i	0.556588	+	0.964038i	0.997778	+	0.0666248i	$0.0212231\pi$
$829$	1.10134e7	+	1.90757e7i	0.556588	+	0.964038i	−0.441190	+	0.897414i	$0.645444\pi$
$830$	7.68527e6	+	1.33113e7i	0.387225	+	0.670694i
$831$	3.43403e6	−	5.94791e6i	0.172505	−	0.298787i
$832$	4.39531e6			0.220131
$833$	3.28187e6	+	1.69397e7i	0.163874	+	0.845849i
$834$	5.20953e6			0.259348
$835$	1.65051e7	−	2.85877e7i	0.819222	−	1.41893i
$836$	−370472.	−	641676.i	−0.0183332	−	0.0317541i
$837$	1.12869e6	+	1.95494e6i	0.0556877	+	0.0964540i
$838$	2.07664e6	−	3.59685e6i	0.102153	−	0.176935i
$839$	4.28039e6			0.209932			0.104966	−	0.994476i	$-0.466527\pi$
$839$	4.28039e6			0.209932			0.104966	+	0.994476i	$0.466527\pi$
$840$	1.74686e6	−	1.04190e7i	0.0854200	−	0.509482i
$841$	1.12255e7			0.547286
$842$	−1.53330e6	+	2.65575e6i	−0.0745325	+	0.129094i
$843$	3.28293e6	+	5.68620e6i	0.159108	+	0.275584i
$844$	9.51869e6	+	1.64869e7i	0.459961	+	0.796676i
$845$	−1.22772e7	+	2.12648e7i	−0.591504	+	1.02452i
$846$	−2.13815e6			−0.102710
$847$	1.60762e7	+	1.32606e7i	0.769974	+	0.635117i
$848$	−8.27933e6			−0.395372
$849$	5.35693e6	−	9.27848e6i	0.255063	−	0.441781i
$850$	−397446.	−	688396.i	−0.0188682	−	0.0326807i
$851$	−9.89342e6	−	1.71359e7i	−0.468298	−	0.811116i
$852$	−175982.	+	304809.i	−0.00830555	+	0.0143856i
$853$	−1.72415e7			−0.811341			−0.405670	−	0.914019i	$-0.632962\pi$
$853$	−1.72415e7			−0.811341			−0.405670	+	0.914019i	$0.632962\pi$
$854$	7.63519e6	−	2.85199e6i	0.358241	−	0.133815i
$855$	−8.22346e6			−0.384715
$856$	−221342.	+	383376.i	−0.0103248	+	0.0178830i
$857$	−1.04170e7	−	1.80427e7i	−0.484495	−	0.839171i	0.515346	−	0.856982i	$-0.327663\pi$
$857$	−1.04170e7	−	1.80427e7i	−0.484495	−	0.839171i	−0.999841	+	0.0178115i	$0.994330\pi$
$858$	−191763.	−	332144.i	−0.00889298	−	0.0154031i
$859$	7.91782e6	−	1.37141e7i	0.366119	−	0.634137i	−0.622836	−	0.782353i	$-0.714020\pi$
$859$	7.91782e6	−	1.37141e7i	0.366119	−	0.634137i	0.988955	+	0.148215i	$0.0473529\pi$
$860$	2.32720e6			0.107297
$861$	2.00754e7	−	7.49880e6i	0.922902	−	0.344734i
$862$	1.70757e7			0.782726
$863$	7.96408e6	−	1.37942e7i	0.364006	−	0.630477i	−0.624610	−	0.780937i	$-0.714742\pi$
$863$	7.96408e6	−	1.37942e7i	0.364006	−	0.630477i	0.988616	+	0.150460i	$0.0480754\pi$
$864$	−2.16602e6	−	3.75166e6i	−0.0987140	−	0.170978i
$865$	1.92447e7	+	3.33328e7i	0.874523	+	1.51472i
$866$	−4.45368e6	+	7.71400e6i	−0.201801	+	0.349530i
$867$	−3.29289e6			−0.148775
$868$	−7.57095e6	−	6.24494e6i	−0.341076	−	0.281338i
$869$	−1.54149e6			−0.0692455
$870$	−4.06638e6	+	7.04317e6i	−0.182142	+	0.315479i
$871$	−2.09191e7	−	3.62330e7i	−0.934325	−	1.61830i
$872$	−1.28972e7	−	2.23386e7i	−0.574387	−	0.994868i
$873$	3.07726e6	−	5.32998e6i	0.136656	−	0.236695i
$874$	−1.88159e7			−0.833195
$875$	3.55747e6	−	2.12183e7i	0.157080	−	0.936896i
$876$	−1.30506e6			−0.0574606
$877$	−2.60367e6	+	4.50969e6i	−0.114311	+	0.197992i	−0.917504	−	0.397727i	$-0.869799\pi$
$877$	−2.60367e6	+	4.50969e6i	−0.114311	+	0.197992i	0.803193	+	0.595718i	$0.203133\pi$
$878$	−3.16723e6	−	5.48581e6i	−0.138658	−	0.240162i
$879$	4.61263e6	+	7.98931e6i	0.201362	+	0.348769i
$880$	−181026.	+	313546.i	−0.00788013	+	0.0136488i
$881$	−932829.			−0.0404913			−0.0202457	−	0.999795i	$-0.506445\pi$
$881$	−932829.			−0.0404913			−0.0202457	+	0.999795i	$0.506445\pi$
$882$	711600.	+	3.67299e6i	0.0308010	+	0.158982i
$883$	1.33789e7			0.577457			0.288728	−	0.957411i	$-0.406768\pi$
$883$	1.33789e7			0.577457			0.288728	+	0.957411i	$0.406768\pi$
$884$	1.11681e7	−	1.93437e7i	0.480670	−	0.832546i
$885$	946401.	+	1.63921e6i	0.0406178	+	0.0703522i
$886$	−2.10601e6	−	3.64771e6i	−0.0901313	−	0.156112i
$887$	3.48450e6	−	6.03533e6i	0.148707	−	0.257568i	−0.782043	−	0.623225i	$-0.785822\pi$
$887$	3.48450e6	−	6.03533e6i	0.148707	−	0.257568i	0.930750	+	0.365657i	$0.119156\pi$
$888$	−7.01826e6			−0.298674
$889$	5.01064e6	−	2.98857e7i	0.212637	−	1.26826i
$890$	−7.46004e6			−0.315694
$891$	−57159.8	+	99003.6i	−0.00241210	+	0.00417789i
$892$	9.02216e6	+	1.56268e7i	0.379663	+	0.657596i
$893$	−8.35369e6	−	1.44690e7i	−0.350550	−	0.607170i
$894$	−2.96077e6	+	5.12821e6i	−0.123897	+	0.214596i
$895$	9.64753e6			0.402586
$896$	1.76602e7	+	1.45671e7i	0.734894	+	0.606182i
$897$	3.15268e7			1.30827
$898$	4.88788e6	−	8.46606e6i	0.202269	−	0.350341i
$899$	8.72220e6	+	1.51073e7i	0.359937	+	0.623429i
$900$	278956.	+	483166.i	0.0114797	+	0.0198834i
$901$	1.19380e7	−	2.06772e7i	0.489913	−	0.848554i
$902$	879496.			0.0359929
$903$	−1.78261e6	+	665862.i	−0.0727506	+	0.0271747i
$904$	−4.03804e7			−1.64342
$905$	−4.33353e6	+	7.50590e6i	−0.175882	+	0.304636i
$906$	−2.68409e6	−	4.64898e6i	−0.108637	−	0.188164i
$907$	1.88282e7	+	3.26113e7i	0.759959	+	1.31629i	0.942871	+	0.333158i	$0.108114\pi$
$907$	1.88282e7	+	3.26113e7i	0.759959	+	1.31629i	−0.182913	+	0.983129i	$0.558553\pi$
$908$	−6.65113e6	+	1.15201e7i	−0.267720	+	0.463705i
$909$	−3.73875e6			−0.150078
$910$	1.73362e7	−	6.47565e6i	0.693987	−	0.259227i
$911$	−3.09942e7			−1.23733			−0.618663	−	0.785657i	$-0.712325\pi$
$911$	−3.09942e7			−1.23733			−0.618663	+	0.785657i	$0.712325\pi$
$912$	2.78653e6	−	4.82640e6i	0.110937	−	0.192148i
$913$	834823.	+	1.44596e6i	0.0331450	+	0.0574087i
$914$	−3.46110e6	−	5.99479e6i	−0.137040	−	0.237361i
$915$	−6.00860e6	+	1.04072e7i	−0.237258	+	0.410943i
$916$	5.71002e6			0.224853
$917$	1.57304e7	+	1.29753e7i	0.617757	+	0.509560i
$918$	2.05679e6			0.0805531
$919$	−358007.	+	620086.i	−0.0139831	+	0.0242194i	−0.872932	−	0.487841i	$-0.837784\pi$
$919$	−358007.	+	620086.i	−0.0139831	+	0.0242194i	0.858949	+	0.512061i	$0.171118\pi$
$920$	1.78201e7	+	3.08652e7i	0.694128	+	1.20226i
$921$	3.19430e6	+	5.53269e6i	0.124087	+	0.214925i
$922$	9.11394e6	−	1.57858e7i	0.353085	−	0.611561i
$923$	−1.42357e6			−0.0550014
$924$	82183.2	−	490177.i	0.00316667	−	0.0188874i
$925$	1.41626e6			0.0544238
$926$	6.05193e6	−	1.04823e7i	0.231935	−	0.401723i
$927$	3.31993e6	+	5.75029e6i	0.126891	+	0.219781i
$928$	−1.67385e7	−	2.89919e7i	−0.638037	−	1.10511i
$929$	−2.08815e7	+	3.61678e7i	−0.793820	+	1.37494i	0.129766	+	0.991545i	$0.458577\pi$
$929$	−2.08815e7	+	3.61678e7i	−0.793820	+	1.37494i	−0.923586	+	0.383392i	$0.874756\pi$
$930$	−4.47026e6			−0.169483
$931$	−2.20751e7	+	1.91657e7i	−0.834698	+	0.724686i
$932$	1.51110e7			0.569840
$933$	−7.05434e6	+	1.22185e7i	−0.265309	+	0.459529i
$934$	−337813.	−	585109.i	−0.0126709	−	0.0219467i
$935$	−522043.	−	904204.i	−0.0195289	−	0.0338250i
$936$	5.59117e6	−	9.68419e6i	0.208599	−	0.361305i
$937$	−2.17917e7			−0.810854			−0.405427	−	0.914127i	$-0.632877\pi$
$937$	−2.17917e7			−0.810854			−0.405427	+	0.914127i	$0.632877\pi$
$938$	−2.76960e6	+	1.65191e7i	−0.102780	+	0.613027i
$939$	3.35657e6			0.124232
$940$	−6.85302e6	+	1.18698e7i	−0.252966	+	0.438150i
$941$	1.07609e6	+	1.86385e6i	0.0396164	+	0.0686177i	0.885154	−	0.465299i	$-0.154053\pi$
$941$	1.07609e6	+	1.86385e6i	0.0396164	+	0.0686177i	−0.845537	+	0.533916i	$0.820720\pi$
$942$	−2.06408e6	−	3.57508e6i	−0.0757876	−	0.131268i
$943$	−3.61483e7	+	6.26106e7i	−1.32376	+	2.29281i
$944$	−1.28275e6			−0.0468504
$945$	−4.25537e6	−	3.51007e6i	−0.155009	−	0.127860i
$946$	−78095.5			−0.00283725
$947$	1.32125e7	−	2.28847e7i	0.478750	−	0.829220i	−0.520953	−	0.853585i	$-0.674423\pi$
$947$	1.32125e7	−	2.28847e7i	0.478750	−	0.829220i	0.999703	+	0.0243656i	$0.00775658\pi$
$948$	−9.73279e6	−	1.68577e7i	−0.351736	−	0.609224i
$949$	−2.63925e6	−	4.57132e6i	−0.0951295	−	0.164769i
$950$	673383.	−	1.16633e6i	0.0242077	−	0.0419289i
$951$	−2.72534e7			−0.977169
$952$	−1.93415e7	+	7.22466e6i	−0.691667	+	0.258360i
$953$	9.07051e6			0.323519			0.161759	−	0.986830i	$-0.448283\pi$
$953$	9.07051e6			0.323519			0.161759	+	0.986830i	$0.448283\pi$
$954$	2.58848e6	−	4.48338e6i	0.0920819	−	0.159491i
$955$	−1.12623e7	−	1.95068e7i	−0.399593	−	0.692115i
$956$	1.14598e7	+	1.98489e7i	0.405538	+	0.702412i
$957$	−441716.	+	765075.i	−0.0155906	+	0.0270037i
$958$	−110892.			−0.00390380
$959$	−2.08337e7	+	7.78208e6i	−0.731511	+	0.273243i
$960$	2.59444e6			0.0908585
$961$	9.52032e6	−	1.64897e7i	0.332539	−	0.575975i
$962$	−6.14709e6	−	1.06471e7i	−0.214157	−	0.370930i
$963$	115574.	+	200180.i	0.00401600	+	0.00695592i
$964$	1.13930e7	−	1.97332e7i	0.394861	−	0.683920i
$965$	2.89674e7			1.00136
$966$	−9.73661e6	−	8.03130e6i	−0.335711	−	0.276913i
$967$	1.80108e7			0.619395			0.309698	−	0.950835i	$-0.399772\pi$
$967$	1.80108e7			0.619395			0.309698	+	0.950835i	$0.399772\pi$
$968$	−1.24682e7	+	2.15956e7i	−0.427677	+	0.740758i
$969$	8.03580e6	+	1.39184e7i	0.274928	+	0.476190i
$970$	6.09389e6	+	1.05549e7i	0.207953	+	0.360185i
$971$	2.33815e7	−	4.04980e7i	0.795838	−	1.37843i	−0.126467	−	0.991971i	$-0.540364\pi$
$971$	2.33815e7	−	4.04980e7i	0.795838	−	1.37843i	0.922305	−	0.386462i	$-0.126303\pi$
$972$	−1.44360e6			−0.0490096
$973$	−4.51509e6	+	2.69300e7i	−0.152892	+	0.911914i
$974$	−9.09561e6			−0.307209
$975$	−1.12828e6	+	1.95424e6i	−0.0380106	+	0.0658363i
$976$	−4.07204e6	−	7.05298e6i	−0.136832	−	0.237000i
$977$	−2.16217e6	−	3.74498e6i	−0.0724690	−	0.125520i	0.827514	−	0.561445i	$-0.189755\pi$
$977$	−2.16217e6	−	3.74498e6i	−0.0724690	−	0.125520i	−0.899983	+	0.435925i	$0.856421\pi$
$978$	−6.25974e6	+	1.08422e7i	−0.209271	+	0.362468i
$979$	−810357.			−0.0270221
$980$	2.26710e7	+	7.82195e6i	0.754061	+	0.260165i
$981$	−1.34685e7			−0.446836
$982$	2.72013e6	−	4.71140e6i	0.0900142	−	0.155909i
$983$	−1.04367e7	−	1.80768e7i	−0.344491	−	0.596676i	0.640770	−	0.767733i	$-0.278615\pi$
$983$	−1.04367e7	−	1.80768e7i	−0.344491	−	0.596676i	−0.985261	+	0.171057i	$0.945282\pi$
$984$	1.28216e7	+	2.22076e7i	0.422136	+	0.731162i
$985$	−1.28828e7	+	2.23137e7i	−0.423077	+	0.732792i
$986$	1.58943e7			0.520655
$987$	1.85313e6	−	1.10529e7i	0.0605499	−	0.361146i
$988$	3.78436e7			1.23339
$989$	3.20981e6	−	5.55956e6i	0.104349	−	0.180738i
$990$	−113193.	−	196056.i	−0.00367056	−	0.00635759i
$991$	−2.06104e7	−	3.56983e7i	−0.666658	−	1.15469i	−0.978833	−	0.204661i	$-0.934391\pi$
$991$	−2.06104e7	−	3.56983e7i	−0.666658	−	1.15469i	0.312175	−	0.950025i	$-0.398942\pi$
$992$	9.20049e6	−	1.59357e7i	0.296846	−	0.514153i
$993$	9.60206e6			0.309023
$994$	439649.	+	362647.i	0.0141137	+	0.0116418i
$995$	−4.42650e6			−0.141743
$996$	−1.05420e7	+	1.82592e7i	−0.336723	+	0.583221i
$997$	2.67307e7	+	4.62990e7i	0.851674	+	1.47514i	0.879697	+	0.475535i	$0.157745\pi$
$997$	2.67307e7	+	4.62990e7i	0.851674	+	1.47514i	−0.0280235	+	0.999607i	$0.508921\pi$
$998$	4.35580e6	+	7.54447e6i	0.138434	+	0.239774i
$999$	−1.83229e6	+	3.17362e6i	−0.0580872	+	0.100610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.c.16.2	yes	8
3.2	odd	2		63.6.e.e.37.3		8
4.3	odd	2		336.6.q.j.289.1		8
7.2	even	3		147.6.a.m.1.3		4
7.3	odd	6		147.6.e.o.67.2		8
7.4	even	3	inner	21.6.e.c.4.2	✓	8
7.5	odd	6		147.6.a.l.1.3		4
7.6	odd	2		147.6.e.o.79.2		8
21.2	odd	6		441.6.a.w.1.2		4
21.5	even	6		441.6.a.v.1.2		4
21.11	odd	6		63.6.e.e.46.3		8
28.11	odd	6		336.6.q.j.193.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.c.4.2	✓	8	7.4	even	3	inner
21.6.e.c.16.2	yes	8	1.1	even	1	trivial
63.6.e.e.37.3		8	3.2	odd	2
63.6.e.e.46.3		8	21.11	odd	6
147.6.a.l.1.3		4	7.5	odd	6
147.6.a.m.1.3		4	7.2	even	3
147.6.e.o.67.2		8	7.3	odd	6
147.6.e.o.79.2		8	7.6	odd	2
336.6.q.j.193.1		8	28.11	odd	6
336.6.q.j.289.1		8	4.3	odd	2
441.6.a.v.1.2		4	21.5	even	6
441.6.a.w.1.2		4	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.37409 + 2.37999i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(12.2237 + 21.1722i) q^{4} +(-29.1836 + 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 + 127.857i) q^{7} -155.128 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-1.37409 + 2.37999i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(12.2237 + 21.1722i) q^{4} +(-29.1836 + 50.5475i) q^{5} +24.7336 q^{6} +(-21.4366 + 127.857i) q^{7} -155.128 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-80.2019 - 138.914i) q^{10} +(-8.71205 - 15.0897i) q^{11} +(110.014 - 190.549i) q^{12} +889.933 q^{13} +(-274.844 - 226.706i) q^{14} +525.305 q^{15} +(-178.000 + 308.305i) q^{16} +(-513.318 - 889.092i) q^{17} +(-111.301 - 192.780i) q^{18} +(869.702 - 1506.37i) q^{19} -1426.93 q^{20} +(1093.01 - 408.276i) q^{21} +47.8846 q^{22} +(-1968.11 + 3408.87i) q^{23} +(698.076 + 1209.10i) q^{24} +(-140.869 - 243.993i) q^{25} +(-1222.85 + 2118.04i) q^{26} +729.000 q^{27} +(-2969.05 + 1109.04i) q^{28} +5633.53 q^{29} +(-721.817 + 1250.22i) q^{30} +(1548.27 + 2681.68i) q^{31} +(-2971.22 - 5146.31i) q^{32} +(-78.4084 + 135.807i) q^{33} +2821.38 q^{34} +(-5837.27 - 4814.91i) q^{35} -1980.25 q^{36} +(-2513.43 + 4353.39i) q^{37} +(2390.10 + 4139.77i) q^{38} +(-4004.70 - 6936.34i) q^{39} +(4527.20 - 7841.34i) q^{40} +18367.0 q^{41} +(-530.205 + 3162.37i) q^{42} -1630.91 q^{43} +(212.988 - 368.906i) q^{44} +(-2363.87 - 4094.35i) q^{45} +(-5408.72 - 9368.19i) q^{46} +(4802.62 - 8318.38i) q^{47} +3204.00 q^{48} +(-15887.9 - 5481.65i) q^{49} +774.269 q^{50} +(-4619.86 + 8001.83i) q^{51} +(10878.3 + 18841.8i) q^{52} +(11628.3 + 20140.7i) q^{53} +(-1001.71 + 1735.02i) q^{54} +1017.00 q^{55} +(3325.41 - 19834.2i) q^{56} -15654.6 q^{57} +(-7740.98 + 13407.8i) q^{58} +(1801.62 + 3120.50i) q^{59} +(6421.20 + 11121.8i) q^{60} +(-11438.3 + 19811.7i) q^{61} -8509.83 q^{62} +(-8100.75 - 6681.95i) q^{63} +4938.92 q^{64} +(-25971.5 + 44983.9i) q^{65} +(-215.481 - 373.223i) q^{66} +(-23506.4 - 40714.2i) q^{67} +(12549.3 - 21736.1i) q^{68} +35426.0 q^{69} +(19480.4 - 7276.56i) q^{70} -1599.63 q^{71} +(6282.68 - 10881.9i) q^{72} +(-2965.67 - 5136.70i) q^{73} +(-6907.36 - 11963.9i) q^{74} +(-1267.82 + 2195.93i) q^{75} +42524.1 q^{76} +(2116.09 - 790.427i) q^{77} +22011.3 q^{78} +(44234.4 - 76616.3i) q^{79} +(-10389.4 - 17994.9i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-25237.9 + 43713.3i) q^{82} -95823.9 q^{83} +(22004.8 + 18150.8i) q^{84} +59921.9 q^{85} +(2241.02 - 3881.56i) q^{86} +(-25350.9 - 43909.0i) q^{87} +(1351.48 + 2340.84i) q^{88} +(23253.9 - 40277.0i) q^{89} +12992.7 q^{90} +(-19077.1 + 113784. i) q^{91} -96230.8 q^{92} +(13934.4 - 24135.1i) q^{93} +(13198.5 + 22860.4i) q^{94} +(50762.1 + 87922.5i) q^{95} +(-26741.0 + 46316.8i) q^{96} -75981.8 q^{97} +(34877.8 - 30281.0i) q^{98} +1411.35 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more