LMFDB - Embedded newform 21.6.e.b.16.1

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-83})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 20x^{2} - 21x + 441 $ x^4 - x^3 - 20x^2 - 21x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.1
Root			$4.19493 - 1.84460i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.6.e.b.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.19493 + 5.53379i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-4.41520 - 7.64735i) q^{4} +(-19.3645 + 33.5404i) q^{5} -57.5088 q^{6} +(-87.5000 - 95.6596i) q^{7} -148.051 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(-3.19493 + 5.53379i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-4.41520 - 7.64735i) q^{4} +(-19.3645 + 33.5404i) q^{5} -57.5088 q^{6} +(-87.5000 - 95.6596i) q^{7} -148.051 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-123.737 - 214.318i) q^{10} +(288.195 + 499.168i) q^{11} +(39.7368 - 68.8262i) q^{12} +391.491 q^{13} +(808.916 - 178.580i) q^{14} -348.562 q^{15} +(614.298 - 1064.00i) q^{16} +(664.850 + 1151.55i) q^{17} +(-258.790 - 448.237i) q^{18} +(-471.237 + 816.206i) q^{19} +341.993 q^{20} +(351.842 - 1112.46i) q^{21} -3683.05 q^{22} +(816.040 - 1413.42i) q^{23} +(-666.228 - 1153.94i) q^{24} +(812.530 + 1407.34i) q^{25} +(-1250.79 + 2166.43i) q^{26} -729.000 q^{27} +(-345.212 + 1091.50i) q^{28} -1463.54 q^{29} +(1113.63 - 1928.87i) q^{30} +(1956.21 + 3388.25i) q^{31} +(1556.47 + 2695.89i) q^{32} +(-2593.75 + 4492.51i) q^{33} -8496.61 q^{34} +(4902.85 - 1082.38i) q^{35} +715.262 q^{36} +(8150.17 - 14116.5i) q^{37} +(-3011.14 - 5215.45i) q^{38} +(1761.71 + 3051.37i) q^{39} +(2866.93 - 4965.67i) q^{40} -13103.8 q^{41} +(5032.02 + 5501.27i) q^{42} +14733.5 q^{43} +(2544.88 - 4407.86i) q^{44} +(-1568.53 - 2716.77i) q^{45} +(5214.38 + 9031.58i) q^{46} +(3407.26 - 5901.55i) q^{47} +11057.4 q^{48} +(-1494.50 + 16740.4i) q^{49} -10383.9 q^{50} +(-5983.65 + 10364.0i) q^{51} +(-1728.51 - 2993.87i) q^{52} +(1005.67 + 1741.87i) q^{53} +(2329.11 - 4034.13i) q^{54} -22323.0 q^{55} +(12954.4 + 14162.5i) q^{56} -8482.26 q^{57} +(4675.93 - 8098.94i) q^{58} +(-25726.6 - 44559.7i) q^{59} +(1538.97 + 2665.57i) q^{60} +(-20548.9 + 35591.8i) q^{61} -24999.8 q^{62} +(10254.1 - 2263.74i) q^{63} +19423.8 q^{64} +(-7581.04 + 13130.8i) q^{65} +(-16573.7 - 28706.6i) q^{66} +(-25289.1 - 43802.0i) q^{67} +(5870.89 - 10168.7i) q^{68} +14688.7 q^{69} +(-9674.63 + 30589.5i) q^{70} +39970.6 q^{71} +(5996.05 - 10385.5i) q^{72} +(27843.3 + 48226.0i) q^{73} +(52078.5 + 90202.6i) q^{74} +(-7312.77 + 12666.1i) q^{75} +8322.42 q^{76} +(22533.2 - 71245.8i) q^{77} -22514.2 q^{78} +(31575.7 - 54690.7i) q^{79} +(23791.2 + 41207.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(41865.9 - 72513.8i) q^{82} +45572.4 q^{83} +(-10060.8 + 2221.08i) q^{84} -51498.1 q^{85} +(-47072.5 + 81532.0i) q^{86} +(-6585.95 - 11407.2i) q^{87} +(-42667.5 - 73902.2i) q^{88} +(-7843.34 + 13585.1i) q^{89} +20045.4 q^{90} +(-34255.5 - 37449.9i) q^{91} -14411.9 q^{92} +(-17605.9 + 30494.3i) q^{93} +(21771.9 + 37710.1i) q^{94} +(-18250.6 - 31610.9i) q^{95} +(-14008.3 + 24263.0i) q^{96} +3128.49 q^{97} +(-87863.1 - 61754.8i) q^{98} -46687.6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 18 q^{3} - 65 q^{4} + 33 q^{5} + 54 q^{6} - 350 q^{7} - 750 q^{8} - 162 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 18 * q^3 - 65 * q^4 + 33 * q^5 + 54 * q^6 - 350 * q^7 - 750 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} + 18 q^{3} - 65 q^{4} + 33 q^{5} + 54 q^{6} - 350 q^{7} - 750 q^{8} - 162 q^{9} - 921 q^{10} + 1137 q^{11} + 585 q^{12} + 1850 q^{13} + 2352 q^{14} + 594 q^{15} + 895 q^{16} + 324 q^{17} + 243 q^{18} - 2311 q^{19} - 7374 q^{20} - 1575 q^{21} + 3162 q^{22} - 1596 q^{23} - 3375 q^{24} - 395 q^{25} + 2508 q^{26} - 2916 q^{27} + 13531 q^{28} - 4434 q^{29} + 8289 q^{30} - 4294 q^{31} - 1017 q^{32} - 10233 q^{33} - 35880 q^{34} + 15414 q^{35} + 10530 q^{36} + 19109 q^{37} + 6828 q^{38} + 8325 q^{39} - 10545 q^{40} - 25716 q^{41} - 4725 q^{42} - 5542 q^{43} + 36579 q^{44} + 2673 q^{45} + 40740 q^{46} + 23160 q^{47} + 16110 q^{48} - 5978 q^{49} - 58704 q^{50} - 2916 q^{51} - 33424 q^{52} + 31653 q^{53} - 2187 q^{54} + 35778 q^{55} + 65625 q^{56} - 41598 q^{57} + 2277 q^{58} - 41097 q^{59} - 33183 q^{60} - 42052 q^{61} - 204114 q^{62} + 14175 q^{63} - 60062 q^{64} + 23106 q^{65} + 14229 q^{66} - 30763 q^{67} - 44748 q^{68} - 28728 q^{69} + 151179 q^{70} + 204192 q^{71} + 30375 q^{72} + 28577 q^{73} + 77784 q^{74} + 3555 q^{75} + 170384 q^{76} - 96873 q^{77} + 45144 q^{78} + 18464 q^{79} + 71511 q^{80} - 13122 q^{81} + 86040 q^{82} + 122358 q^{83} + 19404 q^{84} - 247272 q^{85} - 258510 q^{86} - 19953 q^{87} - 212565 q^{88} - 29322 q^{89} + 149202 q^{90} - 161875 q^{91} + 333816 q^{92} + 38646 q^{93} - 109938 q^{94} + 61662 q^{95} + 9153 q^{96} - 19582 q^{97} - 462021 q^{98} - 184194 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 18 * q^3 - 65 * q^4 + 33 * q^5 + 54 * q^6 - 350 * q^7 - 750 * q^8 - 162 * q^9 - 921 * q^10 + 1137 * q^11 + 585 * q^12 + 1850 * q^13 + 2352 * q^14 + 594 * q^15 + 895 * q^16 + 324 * q^17 + 243 * q^18 - 2311 * q^19 - 7374 * q^20 - 1575 * q^21 + 3162 * q^22 - 1596 * q^23 - 3375 * q^24 - 395 * q^25 + 2508 * q^26 - 2916 * q^27 + 13531 * q^28 - 4434 * q^29 + 8289 * q^30 - 4294 * q^31 - 1017 * q^32 - 10233 * q^33 - 35880 * q^34 + 15414 * q^35 + 10530 * q^36 + 19109 * q^37 + 6828 * q^38 + 8325 * q^39 - 10545 * q^40 - 25716 * q^41 - 4725 * q^42 - 5542 * q^43 + 36579 * q^44 + 2673 * q^45 + 40740 * q^46 + 23160 * q^47 + 16110 * q^48 - 5978 * q^49 - 58704 * q^50 - 2916 * q^51 - 33424 * q^52 + 31653 * q^53 - 2187 * q^54 + 35778 * q^55 + 65625 * q^56 - 41598 * q^57 + 2277 * q^58 - 41097 * q^59 - 33183 * q^60 - 42052 * q^61 - 204114 * q^62 + 14175 * q^63 - 60062 * q^64 + 23106 * q^65 + 14229 * q^66 - 30763 * q^67 - 44748 * q^68 - 28728 * q^69 + 151179 * q^70 + 204192 * q^71 + 30375 * q^72 + 28577 * q^73 + 77784 * q^74 + 3555 * q^75 + 170384 * q^76 - 96873 * q^77 + 45144 * q^78 + 18464 * q^79 + 71511 * q^80 - 13122 * q^81 + 86040 * q^82 + 122358 * q^83 + 19404 * q^84 - 247272 * q^85 - 258510 * q^86 - 19953 * q^87 - 212565 * q^88 - 29322 * q^89 + 149202 * q^90 - 161875 * q^91 + 333816 * q^92 + 38646 * q^93 - 109938 * q^94 + 61662 * q^95 + 9153 * q^96 - 19582 * q^97 - 462021 * q^98 - 184194 * 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 $

$2$	−3.19493	+	5.53379i	−0.564790	+	0.978245i	0.432279	+	0.901740i	$0.357709\pi$
$2$	−3.19493	+	5.53379i	−0.564790	+	0.978245i	−0.997069	+	0.0765049i	$0.975624\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−4.41520	−	7.64735i	−0.137975	−	0.238980i
$5$	−19.3645	+	33.5404i	−0.346403	+	0.599988i	−0.985608	−	0.169049i	$-0.945930\pi$
$5$	−19.3645	+	33.5404i	−0.346403	+	0.599988i	0.639204	+	0.769037i	$0.279264\pi$
$6$	−57.5088			−0.652163
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$7$	−87.5000	−	95.6596i	−0.674937	−	0.737876i
$8$	−148.051			−0.817872
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−123.737	−	214.318i	−0.391290	−	0.677734i
$11$	288.195	+	499.168i	0.718133	+	1.24384i	0.961739	+	0.273968i	$0.0883362\pi$
$11$	288.195	+	499.168i	0.718133	+	1.24384i	−0.243606	+	0.969874i	$0.578330\pi$
$12$	39.7368	−	68.8262i	0.0796599	−	0.137975i
$13$	391.491			0.642486			0.321243	−	0.946997i	$-0.395899\pi$
$13$	391.491			0.642486			0.321243	+	0.946997i	$0.395899\pi$
$14$	808.916	−	178.580i	1.10302	−	0.243508i
$15$	−348.562			−0.399992
$16$	614.298	−	1064.00i	0.599901	−	1.03906i
$17$	664.850	+	1151.55i	0.557958	+	0.966412i	0.997667	+	0.0682711i	$0.0217483\pi$
$17$	664.850	+	1151.55i	0.557958	+	0.966412i	−0.439709	+	0.898140i	$0.644918\pi$
$18$	−258.790	−	448.237i	−0.188263	−	0.326082i
$19$	−471.237	+	816.206i	−0.299471	+	0.518699i	−0.976015	−	0.217703i	$-0.930144\pi$
$19$	−471.237	+	816.206i	−0.299471	+	0.518699i	0.676544	+	0.736402i	$0.263477\pi$
$20$	341.993			0.191180
$21$	351.842	−	1112.46i	0.174100	−	0.550475i
$22$	−3683.05			−1.62238
$23$	816.040	−	1413.42i	0.321656	−	0.557124i	−0.659174	−	0.751991i	$-0.729094\pi$
$23$	816.040	−	1413.42i	0.321656	−	0.557124i	0.980830	+	0.194866i	$0.0624272\pi$
$24$	−666.228	−	1153.94i	−0.236099	−	0.408936i
$25$	812.530	+	1407.34i	0.260009	+	0.450350i
$26$	−1250.79	+	2166.43i	−0.362869	+	0.628508i
$27$	−729.000			−0.192450
$28$	−345.212	+	1091.50i	−0.0832130	+	0.263105i
$29$	−1463.54			−0.323155			−0.161577	−	0.986860i	$-0.551658\pi$
$29$	−1463.54			−0.323155			−0.161577	+	0.986860i	$0.551658\pi$
$30$	1113.63	−	1928.87i	0.225911	−	0.391290i
$31$	1956.21	+	3388.25i	0.365604	+	0.633245i	0.988873	−	0.148763i	$-0.0475291\pi$
$31$	1956.21	+	3388.25i	0.365604	+	0.633245i	−0.623269	+	0.782008i	$0.714196\pi$
$32$	1556.47	+	2695.89i	0.268700	+	0.465401i
$33$	−2593.75	+	4492.51i	−0.414614	+	0.718133i
$34$	−8496.61			−1.26052
$35$	4902.85	−	1082.38i	0.676517	−	0.149351i
$36$	715.262			0.0919833
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.311691	−	0.950184i	$-0.399105\pi$
$37$	8150.17	−	14116.5i	0.978729	−	1.69521i	0.667038	−	0.745024i	$-0.267562\pi$
$38$	−3011.14	−	5215.45i	−0.338277	−	0.585912i
$39$	1761.71	+	3051.37i	0.185470	+	0.321243i
$40$	2866.93	−	4965.67i	0.283314	−	0.490714i
$41$	−13103.8			−1.21741			−0.608707	−	0.793395i	$-0.708312\pi$
$41$	−13103.8			−1.21741			−0.608707	+	0.793395i	$0.708312\pi$
$42$	5032.02	+	5501.27i	0.440169	+	0.481215i
$43$	14733.5			1.21516			0.607582	−	0.794257i	$-0.292140\pi$
$43$	14733.5			1.21516			0.607582	+	0.794257i	$0.292140\pi$
$44$	2544.88	−	4407.86i	0.198169	−	0.343238i
$45$	−1568.53	−	2716.77i	−0.115468	−	0.199996i
$46$	5214.38	+	9031.58i	0.363336	+	0.629316i
$47$	3407.26	−	5901.55i	0.224989	−	0.389692i	−0.731327	−	0.682027i	$-0.761099\pi$
$47$	3407.26	−	5901.55i	0.224989	−	0.389692i	0.956316	+	0.292335i	$0.0944322\pi$
$48$	11057.4			0.692706
$49$	−1494.50	+	16740.4i	−0.0889213	+	0.996039i
$50$	−10383.9			−0.587403
$51$	−5983.65	+	10364.0i	−0.322137	+	0.557958i
$52$	−1728.51	−	2993.87i	−0.0886470	−	0.153541i
$53$	1005.67	+	1741.87i	0.0491775	+	0.0851779i	0.889566	−	0.456806i	$-0.151007\pi$
$53$	1005.67	+	1741.87i	0.0491775	+	0.0851779i	−0.840389	+	0.541984i	$0.817673\pi$
$54$	2329.11	−	4034.13i	0.108694	−	0.188263i
$55$	−22323.0			−0.995054
$56$	12954.4	+	14162.5i	0.552012	+	0.603488i
$57$	−8482.26			−0.345800
$58$	4675.93	−	8098.94i	0.182515	−	0.316125i
$59$	−25726.6	−	44559.7i	−0.962170	−	1.66653i	−0.717035	−	0.697037i	$-0.754501\pi$
$59$	−25726.6	−	44559.7i	−0.962170	−	1.66653i	−0.245135	−	0.969489i	$-0.578832\pi$
$60$	1538.97	+	2665.57i	0.0551889	+	0.0955900i
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	0.258865	+	0.965913i	$0.416651\pi$
$61$	−20548.9	+	35591.8i	−0.707073	+	1.22469i	−0.965938	+	0.258773i	$0.916682\pi$
$62$	−24999.8			−0.825958
$63$	10254.1	−	2263.74i	0.325496	−	0.0718581i
$64$	19423.8			0.592766
$65$	−7581.04	+	13130.8i	−0.222559	+	0.385484i
$66$	−16573.7	−	28706.6i	−0.468340	−	0.811188i
$67$	−25289.1	−	43802.0i	−0.688250	−	1.19208i	−0.972404	−	0.233305i	$-0.925046\pi$
$67$	−25289.1	−	43802.0i	−0.688250	−	1.19208i	0.284153	−	0.958779i	$-0.408288\pi$
$68$	5870.89	−	10168.7i	0.153968	−	0.266681i
$69$	14688.7			0.371416
$70$	−9674.63	+	30589.5i	−0.235988	+	0.746151i
$71$	39970.6			0.941012			0.470506	−	0.882397i	$-0.344071\pi$
$71$	39970.6			0.941012			0.470506	+	0.882397i	$0.344071\pi$
$72$	5996.05	−	10385.5i	0.136312	−	0.236099i
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	0.990984	+	0.133983i	$0.0427767\pi$
$73$	27843.3	+	48226.0i	0.611524	+	1.05919i	−0.379459	+	0.925208i	$0.623890\pi$
$74$	52078.5	+	90202.6i	1.10555	+	1.91487i
$75$	−7312.77	+	12666.1i	−0.150117	+	0.260009i
$76$	8322.42			0.165278
$77$	22533.2	−	71245.8i	0.433107	−	1.36941i
$78$	−22514.2			−0.419006
$79$	31575.7	−	54690.7i	0.569226	−	0.985929i	−0.427416	−	0.904055i	$-0.640576\pi$
$79$	31575.7	−	54690.7i	0.569226	−	0.985929i	0.996643	−	0.0818739i	$-0.0260905\pi$
$80$	23791.2	+	41207.6i	0.415615	+	0.719867i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	41865.9	−	72513.8i	0.687583	−	1.19093i
$83$	45572.4			0.726116			0.363058	−	0.931766i	$-0.381733\pi$
$83$	45572.4			0.726116			0.363058	+	0.931766i	$0.381733\pi$
$84$	−10060.8	+	2221.08i	−0.155574	+	0.0343453i
$85$	−51498.1			−0.773114
$86$	−47072.5	+	81532.0i	−0.686312	+	1.18873i
$87$	−6585.95	−	11407.2i	−0.0932868	−	0.161577i
$88$	−42667.5	−	73902.2i	−0.587341	−	1.01730i
$89$	−7843.34	+	13585.1i	−0.104961	+	0.181797i	−0.913722	−	0.406340i	$-0.866805\pi$
$89$	−7843.34	+	13585.1i	−0.104961	+	0.181797i	0.808762	+	0.588137i	$0.200138\pi$
$90$	20045.4			0.260860
$91$	−34255.5	−	37449.9i	−0.433637	−	0.474075i
$92$	−14411.9			−0.177522
$93$	−17605.9	+	30494.3i	−0.211082	+	0.365604i
$94$	21771.9	+	37710.1i	0.254143	+	0.440188i
$95$	−18250.6	−	31610.9i	−0.207476	−	0.359358i
$96$	−14008.3	+	24263.0i	−0.155134	+	0.268700i
$97$	3128.49			0.0337603			0.0168801	−	0.999858i	$-0.494627\pi$
$97$	3128.49			0.0337603			0.0168801	+	0.999858i	$0.494627\pi$
$98$	−87863.1	−	61754.8i	−0.924148	−	0.649539i
$99$	−46687.6			−0.478755
$100$	7174.96	−	12427.4i	0.0717496	−	0.124274i
$101$	84505.5	+	146368.i	0.824292	+	1.42772i	0.902459	+	0.430776i	$0.141760\pi$
$101$	84505.5	+	146368.i	0.824292	+	1.42772i	−0.0781663	+	0.996940i	$0.524907\pi$
$102$	−38234.7	−	66224.5i	−0.363880	−	0.630258i
$103$	−56410.1	+	97705.1i	−0.523918	+	0.907453i	0.475694	+	0.879611i	$0.342197\pi$
$103$	−56410.1	+	97705.1i	−0.523918	+	0.907453i	−0.999612	+	0.0278422i	$0.991136\pi$
$104$	−57960.5			−0.525471
$105$	30499.1	+	33343.2i	0.269969	+	0.295144i
$106$	−12852.2			−0.111100
$107$	11154.7	−	19320.6i	0.0941890	−	0.163140i	−0.815081	−	0.579347i	$-0.803308\pi$
$107$	11154.7	−	19320.6i	0.0941890	−	0.163140i	0.909270	+	0.416207i	$0.136641\pi$
$108$	3218.68	+	5574.92i	0.0265533	+	0.0459917i
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	0.984032	−	0.177993i	$-0.0569604\pi$
$109$	41909.8	+	72589.8i	0.337869	+	0.585207i	−0.646162	+	0.763200i	$0.723627\pi$
$110$	71320.6	−	123531.i	0.561996	−	0.973406i
$111$	146703.			1.13014
$112$	−155532.	+	34336.1i	−1.17159	+	0.258646i
$113$	−40928.4			−0.301529			−0.150764	−	0.988570i	$-0.548174\pi$
$113$	−40928.4			−0.301529			−0.150764	+	0.988570i	$0.548174\pi$
$114$	27100.3	−	46939.0i	0.195304	−	0.338277i
$115$	31604.4	+	54740.5i	0.222845	+	0.385980i
$116$	6461.84	+	11192.2i	0.0445873	+	0.0772275i
$117$	−15855.4	+	27462.3i	−0.107081	+	0.185470i
$118$	328779.			2.17369
$119$	51982.8	−	164360.i	0.336505	−	1.06397i
$120$	51604.8			0.327142
$121$	−85587.1	+	148241.i	−0.531429	+	0.920462i
$122$	−131305.	−	227427.i	−0.798695	−	1.38338i
$123$	−58967.2	−	102134.i	−0.351437	−	0.608707i
$124$	17274.1	−	29919.6i	0.100888	−	0.174744i
$125$	−183965.			−1.05308
$126$	−20234.0	+	63976.4i	−0.113542	+	0.358999i
$127$	83270.1			0.458120			0.229060	−	0.973412i	$-0.426435\pi$
$127$	83270.1			0.458120			0.229060	+	0.973412i	$0.426435\pi$
$128$	−111865.	+	193756.i	−0.603488	+	1.04527i
$129$	66300.7	+	114836.i	0.350788	+	0.607582i
$130$	−48441.9	−	83903.8i	−0.251398	−	0.435435i
$131$	83437.4	−	144518.i	0.424798	−	0.735772i	−0.571603	−	0.820530i	$-0.693678\pi$
$131$	83437.4	−	144518.i	0.424798	−	0.735772i	0.996402	+	0.0847580i	$0.0270117\pi$
$132$	45807.8			0.228825
$133$	119311.	−	26339.7i	0.584860	−	0.129117i
$134$	323188.			1.55487
$135$	14116.7	−	24450.9i	0.0666653	−	0.115468i
$136$	−98431.5	−	170488.i	−0.456338	−	0.790401i
$137$	−19111.9	−	33102.9i	−0.0869969	−	0.150683i	0.819244	−	0.573446i	$-0.194394\pi$
$137$	−19111.9	−	33102.9i	−0.0869969	−	0.150683i	−0.906240	+	0.422763i	$0.861060\pi$
$138$	−46929.5	+	81284.2i	−0.209772	+	0.363336i
$139$	106263.			0.466492			0.233246	−	0.972418i	$-0.425065\pi$
$139$	106263.			0.466492			0.233246	+	0.972418i	$0.425065\pi$
$140$	−29924.4	−	32714.9i	−0.129034	−	0.141067i
$141$	61330.7			0.259795
$142$	−127703.	+	221189.i	−0.531474	+	0.920540i
$143$	112826.	+	195420.i	0.461390	+	0.799151i
$144$	49758.2	+	86183.7i	0.199967	+	0.346353i
$145$	28340.8	−	49087.8i	0.111942	−	0.193889i
$146$	−355830.			−1.38153
$147$	−137204.	+	63683.4i	−0.523689	+	0.243071i
$148$	−143938.			−0.540160
$149$	−96277.8	+	166758.i	−0.355271	+	0.615348i	−0.987164	−	0.159708i	$-0.948945\pi$
$149$	−96277.8	+	166758.i	−0.355271	+	0.615348i	0.631893	+	0.775056i	$0.282278\pi$
$150$	−46727.6	−	80934.6i	−0.169569	−	0.293701i
$151$	−70849.3	−	122715.i	−0.252868	−	0.437980i	0.711447	−	0.702740i	$-0.248040\pi$
$151$	−70849.3	−	122715.i	−0.252868	−	0.437980i	−0.964314	+	0.264761i	$0.914707\pi$
$152$	69766.9	−	120840.i	0.244929	−	0.424230i
$153$	−107706.			−0.371972
$154$	322267.	+	352319.i	1.09500	+	1.19711i
$155$	−151524.			−0.506586
$156$	15556.6	−	26944.8i	0.0511804	−	0.0886470i
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.805536	−	0.592546i	$-0.798123\pi$
$157$	−282885.	−	489972.i	−0.915928	−	1.58643i	−0.110392	−	0.993888i	$-0.535211\pi$
$158$	201764.	+	349466.i	0.642986	+	1.11368i
$159$	−9051.04	+	15676.9i	−0.0283926	+	0.0491775i
$160$	−120562.			−0.372314
$161$	−206611.	+	45612.4i	−0.628186	+	0.138682i
$162$	41923.9			0.125509
$163$	215101.	−	372565.i	0.634121	−	1.09833i	−0.352579	−	0.935782i	$-0.614695\pi$
$163$	215101.	−	372565.i	0.634121	−	1.09833i	0.986701	−	0.162549i	$-0.0519714\pi$
$164$	57856.0	+	100210.i	0.167973	+	0.290937i
$165$	−100454.	−	173991.i	−0.287247	−	0.497527i
$166$	−145601.	+	252188.i	−0.410103	+	0.710319i
$167$	−240265.			−0.666653			−0.333327	−	0.942811i	$-0.608171\pi$
$167$	−240265.			−0.666653			−0.333327	+	0.942811i	$0.608171\pi$
$168$	−52090.5	+	164701.i	−0.142392	+	0.450218i
$169$	−218028.			−0.587212
$170$	164533.	−	284979.i	0.436647	−	0.756295i
$171$	−38170.2	−	66112.7i	−0.0998238	−	0.172900i
$172$	−65051.3	−	112672.i	−0.167662	−	0.290399i
$173$	89650.1	−	155279.i	0.227738	−	0.394454i	−0.729399	−	0.684088i	$-0.760200\pi$
$173$	89650.1	−	155279.i	0.227738	−	0.394454i	0.957137	+	0.289634i	$0.0935337\pi$
$174$	84166.7			0.210750
$175$	63529.4	−	200869.i	0.156812	−	0.495812i
$176$	708151.			1.72323
$177$	231539.	−	401037.i	0.555509	−	0.962170i
$178$	−50117.9	−	86806.8i	−0.118561	−	0.205354i
$179$	287780.	+	498449.i	0.671317	+	1.16275i	0.977531	+	0.210792i	$0.0676043\pi$
$179$	287780.	+	498449.i	0.671317	+	1.16275i	−0.306214	+	0.951963i	$0.599062\pi$
$180$	−13850.7	+	23990.2i	−0.0318633	+	0.0551889i
$181$	581006.			1.31821			0.659105	−	0.752051i	$-0.270935\pi$
$181$	581006.			1.31821			0.659105	+	0.752051i	$0.270935\pi$
$182$	316684.	−	69912.7i	0.708675	−	0.156451i
$183$	−369880.			−0.816458
$184$	−120815.	+	209258.i	−0.263073	+	0.455657i
$185$	315648.	+	546719.i	0.678070	+	1.17445i
$186$	−112499.	−	194854.i	−0.238433	−	0.412979i
$187$	−383213.	+	663744.i	−0.801376	+	1.38802i
$188$	−60174.9			−0.124171
$189$	63787.5	+	69735.8i	0.129892	+	0.142004i
$190$	233237.			0.468721
$191$	330280.	−	572062.i	0.655087	−	1.13464i	−0.326785	−	0.945099i	$-0.605965\pi$
$191$	330280.	−	572062.i	0.655087	−	1.13464i	0.981872	−	0.189545i	$-0.0607013\pi$
$192$	87407.0	+	151393.i	0.171117	+	0.296383i
$193$	278655.	+	482645.i	0.538485	+	0.932684i	0.998986	+	0.0450243i	$0.0143365\pi$
$193$	278655.	+	482645.i	0.538485	+	0.932684i	−0.460501	+	0.887659i	$0.652330\pi$
$194$	−9995.33	+	17312.4i	−0.0190675	+	0.0330258i
$195$	−136459.			−0.256989
$196$	134618.	−	62483.3i	0.250302	−	0.116178i
$197$	−761400.			−1.39781			−0.698904	−	0.715216i	$-0.746328\pi$
$197$	−761400.			−1.39781			−0.698904	+	0.715216i	$0.746328\pi$
$198$	149164.	−	258359.i	0.270396	−	0.468340i
$199$	67929.9	+	117658.i	0.121598	+	0.210615i	0.920398	−	0.390982i	$-0.127865\pi$
$199$	67929.9	+	117658.i	0.121598	+	0.210615i	−0.798800	+	0.601597i	$0.794531\pi$
$200$	−120296.	−	208358.i	−0.212655	−	0.368328i
$201$	227602.	−	394218.i	0.397361	−	0.688250i
$202$	−1.07996e6			−1.86221
$203$	128060.	+	140002.i	0.218109	+	0.238448i
$204$	105676.			0.177787
$205$	253750.	−	439507.i	0.421716	−	0.730434i
$206$	−360453.	−	624323.i	−0.591807	−	1.02504i
$207$	66099.2	+	114487.i	0.107219	+	0.185708i
$208$	240492.	−	416545.i	0.385428	−	0.667581i
$209$	−543232.			−0.860240
$210$	−281957.	+	62246.3i	−0.441199	+	0.0974014i
$211$	−991157.			−1.53263			−0.766313	−	0.642467i	$-0.777911\pi$
$211$	−991157.			−1.53263			−0.766313	+	0.642467i	$0.777911\pi$
$212$	8880.48	−	15381.4i	0.0135705	−	0.0235048i
$213$	179868.	+	311540.i	0.271647	+	0.470506i
$214$	71277.3	+	123456.i	0.106394	+	0.184280i
$215$	−285307.	+	494167.i	−0.420937	+	0.729084i
$216$	107929.			0.157400
$217$	152951.	−	483602.i	0.220496	−	0.697170i
$218$	−535596.			−0.763301
$219$	−250590.	+	434034.i	−0.353064	+	0.611524i
$220$	98560.7	+	170712.i	0.137293	+	0.237798i
$221$	260283.	+	450823.i	0.358480	+	0.620906i
$222$	−468706.	+	811823.i	−0.638291	+	1.10555i
$223$	543344.			0.731666			0.365833	−	0.930681i	$-0.380784\pi$
$223$	543344.			0.731666			0.365833	+	0.930681i	$0.380784\pi$
$224$	121696.	−	384782.i	0.162053	−	0.512383i
$225$	−131630.			−0.173340
$226$	130764.	−	226489.i	0.170300	−	0.294969i
$227$	−8.16704	−	14.1457i	−1.05196e−5	−	1.82205e-5i	0.866020	−	0.500009i	$-0.166670\pi$
$227$	−8.16704	−	14.1457i	−1.05196e−5	−	1.82205e-5i	−0.866031	+	0.499991i	$0.833337\pi$
$228$	37450.9	+	64866.8i	0.0477117	+	0.0826391i
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	−0.840619	−	0.541627i	$-0.817808\pi$
$229$	38689.5	−	67012.2i	0.0487534	−	0.0844433i	0.889372	+	0.457184i	$0.151142\pi$
$230$	−403896.			−0.503443
$231$	656705.	−	144978.i	0.809731	−	0.178760i
$232$	216679.			0.264299
$233$	51828.6	−	89769.9i	0.0625432	−	0.108328i	−0.833058	−	0.553185i	$-0.813412\pi$
$233$	51828.6	−	89769.9i	0.0625432	−	0.108328i	0.895602	+	0.444857i	$0.146746\pi$
$234$	−101314.	−	175481.i	−0.120956	−	0.209503i
$235$	131960.	+	228561.i	0.155874	+	0.269981i
$236$	−227176.	+	393480.i	−0.265511	+	0.459878i
$237$	568362.			0.657286
$238$	743453.	+	812782.i	0.850768	+	0.930104i
$239$	689109.			0.780356			0.390178	−	0.920739i	$-0.372413\pi$
$239$	689109.			0.780356			0.390178	+	0.920739i	$0.372413\pi$
$240$	−214121.	+	370868.i	−0.239956	+	0.415615i
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	0.798458	−	0.602050i	$-0.205649\pi$
$241$	−110148.	−	190782.i	−0.122161	−	0.211590i	−0.920620	+	0.390460i	$0.872316\pi$
$242$	−546890.	−	947242.i	−0.600291	−	1.03973i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	362910.			0.390234
$245$	−532539.	−	374297.i	−0.566809	−	0.398383i
$246$	753585.			0.793953
$247$	−184485.	+	319537.i	−0.192406	+	0.333257i
$248$	−289618.	−	501633.i	−0.299017	−	0.517913i
$249$	205076.	+	355201.i	0.209612	+	0.363058i
$250$	587757.	−	1.01803e6i	0.594768	−	1.03017i
$251$	1.43641e6			1.43912			0.719558	−	0.694433i	$-0.244345\pi$
$251$	1.43641e6			1.43912			0.719558	+	0.694433i	$0.244345\pi$
$252$	−62585.5	−	68421.7i	−0.0620829	−	0.0678723i
$253$	940714.			0.923966
$254$	−266042.	+	460799.i	−0.258742	+	0.448154i
$255$	−231741.	−	401388.i	−0.223179	−	0.386557i
$256$	−404021.	−	699785.i	−0.385305	−	0.667367i
$257$	454598.	−	787388.i	0.429334	−	0.743628i	−0.567480	−	0.823387i	$-0.692082\pi$
$257$	454598.	−	787388.i	0.429334	−	0.743628i	0.996814	+	0.0797589i	$0.0254151\pi$
$258$	−847306.			−0.792485
$259$	−2.06352e6	+	455553.i	−1.91143	+	0.421977i
$260$	133887.			0.122830
$261$	59273.5	−	102665.i	0.0538592	−	0.0932868i
$262$	533154.	+	923450.i	0.479843	+	0.831113i
$263$	−374528.	−	648702.i	−0.333884	−	0.578304i	0.649386	−	0.760459i	$-0.275026\pi$
$263$	−374528.	−	648702.i	−0.333884	−	0.578304i	−0.983270	+	0.182155i	$0.941693\pi$
$264$	384007.	−	665120.i	0.339101	−	0.587341i
$265$	−77897.4			−0.0681410
$266$	−235433.	+	744396.i	−0.204015	+	0.645060i
$267$	−141180.			−0.121198
$268$	−223313.	+	386789.i	−0.189923	+	0.328956i
$269$	−334972.	−	580189.i	−0.282246	−	0.488865i	0.689691	−	0.724104i	$-0.257746\pi$
$269$	−334972.	−	580189.i	−0.282246	−	0.488865i	−0.971938	+	0.235238i	$0.924413\pi$
$270$	90204.1	+	156238.i	0.0753038	+	0.130430i
$271$	−270330.	+	468225.i	−0.223599	+	0.387285i	−0.955898	−	0.293698i	$-0.905114\pi$
$271$	−270330.	+	468225.i	−0.223599	+	0.387285i	0.732299	+	0.680983i	$0.238447\pi$
$272$	1.63367e6			1.33888
$273$	137743.	−	435519.i	0.111857	−	0.353672i
$274$	244246.			0.196540
$275$	−468334.	+	811178.i	−0.373443	+	0.646821i
$276$	−64853.6	−	112330.i	−0.0512462	−	0.0887610i
$277$	200955.	+	348064.i	0.157362	+	0.272558i	0.933916	−	0.357491i	$-0.116368\pi$
$277$	200955.	+	348064.i	0.157362	+	0.272558i	−0.776555	+	0.630050i	$0.783035\pi$
$278$	−339502.	+	588035.i	−0.263470	+	0.456343i
$279$	−316906.			−0.243736
$280$	−725871.	+	160247.i	−0.553304	+	0.122150i
$281$	−429139.			−0.324214			−0.162107	−	0.986773i	$-0.551829\pi$
$281$	−429139.			−0.324214			−0.162107	+	0.986773i	$0.551829\pi$
$282$	−195947.	+	339391.i	−0.146729	+	0.254143i
$283$	170463.	+	295251.i	0.126522	+	0.219142i	0.922327	−	0.386411i	$-0.126285\pi$
$283$	170463.	+	295251.i	0.126522	+	0.219142i	−0.795805	+	0.605553i	$0.792952\pi$
$284$	−176478.	−	305669.i	−0.129836	−	0.224883i
$285$	164255.	−	284498.i	0.119786	−	0.207476i
$286$	−1.44188e6			−1.04235
$287$	1.14658e6	+	1.25351e6i	0.821678	+	0.898301i
$288$	−252149.			−0.179133
$289$	−174123.	+	301590.i	−0.122634	+	0.212409i
$290$	181094.	+	313664.i	0.126447	+	0.219013i
$291$	14078.2	+	24384.2i	0.00974575	+	0.0168801i
$292$	245868.	−	425855.i	0.168750	−	0.292284i
$293$	−388847.			−0.264612			−0.132306	−	0.991209i	$-0.542238\pi$
$293$	−388847.			−0.264612			−0.132306	+	0.991209i	$0.542238\pi$
$294$	85946.9	−	962722.i	0.0579912	−	0.649580i
$295$	1.99273e6			1.33319
$296$	−1.20664e6	+	2.08996e6i	−0.800475	+	1.38646i
$297$	−210094.	−	363894.i	−0.138205	−	0.239378i
$298$	−615202.	−	1.06556e6i	−0.401307	−	0.695085i
$299$	319472.	−	553342.i	0.206659	−	0.357945i
$300$	129149.			0.0828493
$301$	−1.28918e6	−	1.40940e6i	−0.820158	−	0.896640i
$302$	905435.			0.571268
$303$	−760549.	+	1.31731e6i	−0.475905	+	0.824292i
$304$	578960.	+	1.00279e6i	0.359306	+	0.622336i
$305$	−795840.	−	1.37844e6i	−0.489865	−	0.848471i
$306$	344113.	−	596021.i	0.210086	−	0.363880i
$307$	−2.35747e6			−1.42758			−0.713789	−	0.700361i	$-0.753022\pi$
$307$	−2.35747e6			−1.42758			−0.713789	+	0.700361i	$0.753022\pi$
$308$	−644330.	+	142246.i	−0.387018	+	0.0854402i
$309$	−1.01538e6			−0.604969
$310$	484110.	−	838503.i	0.286114	−	0.495565i
$311$	718314.	+	1.24416e6i	0.421127	+	0.729414i	0.996050	−	0.0887939i	$-0.0283013\pi$
$311$	718314.	+	1.24416e6i	0.421127	+	0.729414i	−0.574923	+	0.818208i	$0.694968\pi$
$312$	−260822.	−	451758.i	−0.151691	−	0.262736i
$313$	411400.	−	712566.i	0.237358	−	0.411116i	−0.722598	−	0.691269i	$-0.757052\pi$
$313$	411400.	−	712566.i	0.237358	−	0.411116i	0.959955	+	0.280153i	$0.0903853\pi$
$314$	3.61520e6			2.06923
$315$	−122639.	+	387762.i	−0.0696388	+	0.220186i
$316$	−557652.			−0.314156
$317$	883467.	−	1.53021e6i	0.493790	−	0.855269i	−0.506184	−	0.862425i	$-0.668944\pi$
$317$	883467.	−	1.53021e6i	0.493790	−	0.855269i	0.999974	+	0.00715584i	$0.00227779\pi$
$318$	−57835.0	−	100173.i	−0.0320718	−	0.0555499i
$319$	−421786.	−	730555.i	−0.232068	−	0.401954i
$320$	−376132.	+	651480.i	−0.205336	+	0.355653i
$321$	200785.			0.108760
$322$	407698.	−	1.28907e6i	0.219129	−	0.692845i
$323$	−1.25321e6			−0.668370
$324$	−28968.1	+	50174.3i	−0.0153306	+	0.0265533i
$325$	318098.	+	550962.i	0.167052	+	0.289343i
$326$	1.37446e6	+	2.38064e6i	0.716291	+	1.24065i
$327$	−377188.	+	653309.i	−0.195069	+	0.337869i
$328$	1.94003e6			0.995689
$329$	−862675.	+	190448.i	−0.439397	+	0.0970036i
$330$	1.28377e6			0.648937
$331$	1526.14	−	2643.35i	0.000765638	−	0.00132612i	−0.865642	−	0.500663i	$-0.833090\pi$
$331$	1526.14	−	2643.35i	0.000765638	−	0.00132612i	0.866408	+	0.499337i	$0.166423\pi$
$332$	−201211.	−	348508.i	−0.100186	−	0.173527i
$333$	660164.	+	1.14344e6i	0.326243	+	0.565069i
$334$	767632.	−	1.32958e6i	0.376519	−	0.652150i
$335$	1.95885e6			0.953649
$336$	−967520.	−	1.05774e6i	−0.467532	−	0.511131i
$337$	2.02939e6			0.973398			0.486699	−	0.873570i	$-0.338201\pi$
$337$	2.02939e6			0.973398			0.486699	+	0.873570i	$0.338201\pi$
$338$	696584.	−	1.20652e6i	0.331651	−	0.574437i
$339$	−184178.	−	319006.i	−0.0870439	−	0.150764i
$340$	227374.	+	393824.i	0.106670	+	0.184759i
$341$	−1.12754e6	+	1.95295e6i	−0.525104	+	0.909507i
$342$	487805.			0.225518
$343$	1.73215e6	−	1.32182e6i	0.794969	−	0.606650i
$344$	−2.18130e6			−0.993848
$345$	−284440.	+	492665.i	−0.128660	+	0.222845i
$346$	572852.	+	992209.i	0.257248	+	0.445567i
$347$	−1.89109e6	−	3.27547e6i	−0.843119	−	1.46033i	−0.887245	−	0.461299i	$-0.847383\pi$
$347$	−1.89109e6	−	3.27547e6i	−0.843119	−	1.46033i	0.0441252	−	0.999026i	$-0.485950\pi$
$348$	−58156.6	+	100730.i	−0.0257425	+	0.0445873i
$349$	291147.			0.127953			0.0639763	−	0.997951i	$-0.479622\pi$
$349$	291147.			0.127953			0.0639763	+	0.997951i	$0.479622\pi$
$350$	908592.	+	993320.i	0.396460	+	0.433430i
$351$	−285397.			−0.123646
$352$	−897136.	+	1.55389e6i	−0.385924	+	0.668440i
$353$	−192538.	−	333486.i	−0.0822394	−	0.142443i	0.821972	−	0.569528i	$-0.192874\pi$
$353$	−192538.	−	333486.i	−0.0822394	−	0.142443i	−0.904212	+	0.427085i	$0.859541\pi$
$354$	1.47950e6	+	2.56257e6i	0.627491	+	1.08685i
$355$	−774013.	+	1.34063e6i	−0.325970	+	0.564596i
$356$	138520.			0.0579277
$357$	1.51498e6	−	334456.i	0.629126	−	0.138889i
$358$	−3.67775e6			−1.51661
$359$	1.61507e6	−	2.79738e6i	0.661385	−	1.14555i	−0.318866	−	0.947800i	$-0.603302\pi$
$359$	1.61507e6	−	2.79738e6i	0.661385	−	1.14555i	0.980252	−	0.197753i	$-0.0633645\pi$
$360$	232222.	+	402219.i	0.0944379	+	0.163571i
$361$	793921.	+	1.37511e6i	0.320634	+	0.555354i
$362$	−1.85628e6	+	3.21517e6i	−0.744511	+	1.28953i
$363$	−1.54057e6			−0.613641
$364$	−135148.	+	427312.i	−0.0534632	+	0.169041i
$365$	−2.15669e6			−0.847336
$366$	1.18174e6	−	2.04684e6i	0.461127	−	0.798695i
$367$	239779.	+	415310.i	0.0929280	+	0.160956i	0.908742	−	0.417358i	$-0.137044\pi$
$367$	239779.	+	415310.i	0.0929280	+	0.160956i	−0.815814	+	0.578314i	$0.803711\pi$
$368$	−1.00258e6	−	1.73653e6i	−0.385923	−	0.668439i
$369$	530705.	−	919208.i	0.202902	−	0.351437i
$370$	−4.03390e6			−1.53187
$371$	78630.6	−	248616.i	0.0296590	−	0.0937766i
$372$	310934.			0.116496
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	−0.935724	−	0.352734i	$-0.885252\pi$
$373$	−436333.	+	755751.i	−0.162385	+	0.281259i	0.773339	+	0.633993i	$0.218585\pi$
$374$	−2.44868e6	−	4.24124e6i	−0.905217	−	1.56788i
$375$	−827844.	−	1.43387e6i	−0.303998	−	0.526540i
$376$	−504447.	+	873728.i	−0.184012	+	0.318718i
$377$	−572965.			−0.207622
$378$	−589700.	+	130185.i	−0.212276	+	0.0468632i
$379$	−2.43493e6			−0.870742			−0.435371	−	0.900251i	$-0.643383\pi$
$379$	−2.43493e6			−0.870742			−0.435371	+	0.900251i	$0.643383\pi$
$380$	−161160.	+	279137.i	−0.0572529	+	0.0991650i
$381$	374715.	+	649026.i	0.132248	+	0.229060i
$382$	2.11044e6	+	3.65540e6i	0.739973	+	1.28167i
$383$	1.80584e6	−	3.12781e6i	0.629047	−	1.08954i	−0.358696	−	0.933454i	$-0.616778\pi$
$383$	1.80584e6	−	3.12781e6i	0.629047	−	1.08954i	0.987743	−	0.156087i	$-0.0498882\pi$
$384$	−2.01357e6			−0.696848
$385$	1.95327e6	+	2.13541e6i	0.671598	+	0.734226i
$386$	−3.56114e6			−1.21652
$387$	−596707.	+	1.03353e6i	−0.202527	+	0.350788i
$388$	−13812.9	−	23924.7i	−0.00465807	−	0.00806802i
$389$	87616.2	+	151756.i	0.0293569	+	0.0508477i	0.880331	−	0.474361i	$-0.157321\pi$
$389$	87616.2	+	151756.i	0.0293569	+	0.0508477i	−0.850974	+	0.525208i	$0.823987\pi$
$390$	435977.	−	755134.i	0.145145	−	0.251398i
$391$	2.17018e6			0.717882
$392$	221262.	−	2.47843e6i	0.0727262	−	0.814632i
$393$	1.50187e6			0.490515
$394$	2.43262e6	−	4.21343e6i	0.789467	−	1.36740i
$395$	1.22290e6	+	2.11812e6i	0.394364	+	0.683058i
$396$	206135.	+	357036.i	0.0660562	+	0.114413i
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	−0.976170	−	0.217007i	$-0.930371\pi$
$397$	−942577.	+	1.63259e6i	−0.300152	+	0.519878i	0.676019	+	0.736885i	$0.263704\pi$
$398$	−868126.			−0.274710
$399$	742198.	+	811409.i	0.233393	+	0.255157i
$400$	1.99654e6			0.623920
$401$	−669915.	+	1.16033e6i	−0.208046	+	0.360346i	−0.951099	−	0.308887i	$-0.900044\pi$
$401$	−669915.	+	1.16033e6i	−0.208046	+	0.360346i	0.743053	+	0.669232i	$0.233377\pi$
$402$	1.45435e6	+	2.51900e6i	0.448851	+	0.777433i
$403$	765839.	+	1.32647e6i	0.234895	+	0.406851i
$404$	746217.	−	1.29249e6i	0.227463	−	0.393978i
$405$	254101.			0.0769785
$406$	−1.18388e6	+	261360.i	−0.356446	+	0.0786909i
$407$	9.39535e6			2.81143
$408$	885884.	−	1.53440e6i	0.263467	−	0.456338i
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.685043	−	0.728503i	$-0.740217\pi$
$409$	−3.29314e6	−	5.70388e6i	−0.973423	−	1.68602i	−0.288381	−	0.957516i	$-0.593117\pi$
$410$	1.62143e6	+	2.80839e6i	0.476362	+	0.825084i
$411$	172008.	−	297926.i	0.0502277	−	0.0869969i
$412$	996247.			0.289150
$413$	−2.01149e6	+	6.35996e6i	−0.580286	+	1.83476i
$414$	−844730.			−0.242224
$415$	−882487.	+	1.52851e6i	−0.251529	+	0.435661i
$416$	609346.	+	1.05542e6i	0.172636	+	0.299014i
$417$	478182.	+	828236.i	0.134665	+	0.233246i
$418$	1.73559e6	−	3.00613e6i	0.485855	−	0.841525i
$419$	−6.96869e6			−1.93917			−0.969585	−	0.244754i	$-0.921293\pi$
$419$	−6.96869e6			−1.93917			−0.969585	+	0.244754i	$0.921293\pi$
$420$	120328.	−	380455.i	0.0332845	−	0.105240i
$421$	3.84041e6			1.05602			0.528010	−	0.849238i	$-0.322938\pi$
$421$	3.84041e6			1.05602			0.528010	+	0.849238i	$0.322938\pi$
$422$	3.16668e6	−	5.48485e6i	0.865612	−	1.49928i
$423$	275988.	+	478025.i	0.0749962	+	0.129897i
$424$	−148890.	−	257886.i	−0.0402209	−	0.0696647i
$425$	−1.08042e6	+	1.87134e6i	−0.290149	+	0.502552i
$426$	−2.29866e6			−0.613693
$427$	5.20272e6	−	1.14858e6i	1.38090	−	0.304854i
$428$	−197002.			−0.0519829
$429$	−1.01543e6	+	1.75878e6i	−0.266384	+	0.461390i
$430$	−1.82308e6	−	3.15766e6i	−0.475481	−	0.823558i
$431$	−1.51818e6	−	2.62957e6i	−0.393668	−	0.681854i	0.599262	−	0.800553i	$-0.295461\pi$
$431$	−1.51818e6	−	2.62957e6i	−0.393668	−	0.681854i	−0.992930	+	0.118699i	$0.962128\pi$
$432$	−447824.	+	775653.i	−0.115451	+	0.199967i
$433$	−941529.			−0.241332			−0.120666	−	0.992693i	$-0.538503\pi$
$433$	−941529.			−0.241332			−0.120666	+	0.992693i	$0.538503\pi$
$434$	2.18749e6	+	2.39147e6i	0.557469	+	0.609454i
$435$	510135.			0.129259
$436$	370080.	−	640997.i	0.0932351	−	0.161488i
$437$	769096.	+	1.33211e6i	0.192653	+	0.333686i
$438$	−1.60124e6	−	2.77342e6i	−0.398814	−	0.690765i
$439$	−670546.	+	1.16142e6i	−0.166061	+	0.287626i	−0.937031	−	0.349245i	$-0.886438\pi$
$439$	−670546.	+	1.16142e6i	−0.166061	+	0.287626i	0.770971	+	0.636871i	$0.219771\pi$
$440$	3.30494e6			0.813827
$441$	−1.11378e6	−	782823.i	−0.272711	−	0.191676i
$442$	−3.32635e6			−0.809864
$443$	386171.	−	668867.i	0.0934910	−	0.161931i	−0.815487	−	0.578776i	$-0.803531\pi$
$443$	386171.	−	668867.i	0.0934910	−	0.161931i	0.908978	+	0.416844i	$0.136864\pi$
$444$	−647723.	−	1.12189e6i	−0.155931	−	0.270080i
$445$	−303765.	−	526137.i	−0.0727174	−	0.125950i
$446$	−1.73595e6	+	3.00675e6i	−0.413238	+	0.715748i
$447$	−1.73300e6			−0.410232
$448$	−1.69958e6	−	1.85807e6i	−0.400080	−	0.437388i
$449$	2.25684e6			0.528304			0.264152	−	0.964481i	$-0.414908\pi$
$449$	2.25684e6			0.528304			0.264152	+	0.964481i	$0.414908\pi$
$450$	420548.	−	728411.i	0.0979005	−	0.169569i
$451$	−3.77646e6	−	6.54101e6i	−0.874265	−	1.51427i
$452$	180707.	+	312994.i	0.0416034	+	0.0720593i
$453$	637644.	−	1.10443e6i	0.145993	−	0.252868i
$454$	104.373			2.37655e−5
$455$	1.91942e6	−	423742.i	0.434653	−	0.0959561i
$456$	1.25580e6			0.282820
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	−0.999733	−	0.0231196i	$-0.992640\pi$
$457$	−2.14235e6	+	3.71066e6i	−0.479844	+	0.831114i	0.519889	+	0.854234i	$0.325973\pi$
$458$	247221.	+	428199.i	0.0550708	+	0.0953854i
$459$	−484676.	−	839483.i	−0.107379	−	0.185986i
$460$	279080.	−	483381.i	0.0614942	−	0.106511i
$461$	−3.10462e6			−0.680387			−0.340193	−	0.940355i	$-0.610493\pi$
$461$	−3.10462e6			−0.680387			−0.340193	+	0.940355i	$0.610493\pi$
$462$	−1.29585e6	+	4.09726e6i	−0.282456	+	0.893077i
$463$	−3.53386e6			−0.766121			−0.383060	−	0.923723i	$-0.625130\pi$
$463$	−3.53386e6			−0.766121			−0.383060	+	0.923723i	$0.625130\pi$
$464$	−899053.	+	1.55721e6i	−0.193861	+	0.335777i
$465$	−681859.	−	1.18102e6i	−0.146239	−	0.253293i
$466$	331178.	+	573617.i	0.0706475	+	0.122365i
$467$	−1.36230e6	+	2.35957e6i	−0.289054	+	0.500657i	−0.973584	−	0.228328i	$-0.926674\pi$
$467$	−1.36230e6	+	2.35957e6i	−0.289054	+	0.500657i	0.684530	+	0.728985i	$0.260007\pi$
$468$	280019.			0.0590980
$469$	−1.97728e6	+	6.25182e6i	−0.415085	+	1.31242i
$470$	−1.68641e6			−0.352143
$471$	2.54597e6	−	4.40975e6i	0.528812	−	0.915928i
$472$	3.80883e6	+	6.59709e6i	0.786932	+	1.36301i
$473$	4.24612e6	+	7.35449e6i	0.872649	+	1.51147i
$474$	−1.81588e6	+	3.14520e6i	−0.371228	+	0.642986i
$475$	−1.53158e6			−0.311461
$476$	−1.48643e6	+	328153.i	−0.300697	+	0.0663833i
$477$	−162919.			−0.0327850
$478$	−2.20166e6	+	3.81338e6i	−0.440737	+	0.763379i
$479$	−489342.	−	847566.i	−0.0974482	−	0.168785i	0.813180	−	0.582013i	$-0.197735\pi$
$479$	−489342.	−	847566.i	−0.0974482	−	0.168785i	−0.910628	+	0.413228i	$0.864401\pi$
$480$	−542527.	−	939685.i	−0.107478	−	0.186157i
$481$	3.19072e6	−	5.52649e6i	0.628819	−	1.08915i
$482$	1.40766e6			0.275982
$483$	−1.28526e6	−	1.40512e6i	−0.250682	−	0.274059i
$484$	1.51154e6			0.293296
$485$	−60581.8	+	104931.i	−0.0116947	+	0.0202558i
$486$	188658.	+	326765.i	0.0362313	+	0.0627544i
$487$	−1.96372e6	−	3.40126e6i	−0.375195	−	0.649857i	0.615161	−	0.788401i	$-0.289091\pi$
$487$	−1.96372e6	−	3.40126e6i	−0.375195	−	0.649857i	−0.990356	+	0.138544i	$0.955758\pi$
$488$	3.04228e6	−	5.26938e6i	0.578295	−	1.00164i
$489$	3.87181e6			0.732220
$490$	3.77271e6	−	1.75111e6i	0.709844	−	0.329475i
$491$	2.63241e6			0.492777			0.246388	−	0.969171i	$-0.420756\pi$
$491$	2.63241e6			0.492777			0.246388	+	0.969171i	$0.420756\pi$
$492$	−520704.	+	901886.i	−0.0969791	+	0.167973i
$493$	−973037.	−	1.68535e6i	−0.180307	−	0.312301i
$494$	−1.17883e6	−	2.04180e6i	−0.217338	−	0.376440i
$495$	904083.	−	1.56592e6i	0.165842	−	0.287247i
$496$	4.80678e6			0.877305
$497$	−3.49743e6	−	3.82357e6i	−0.635123	−	0.694350i
$498$	−2.62081e6			−0.473546
$499$	−1.06272e6	+	1.84069e6i	−0.191059	+	0.330924i	−0.945601	−	0.325327i	$-0.894526\pi$
$499$	−1.06272e6	+	1.84069e6i	−0.191059	+	0.330924i	0.754542	+	0.656251i	$0.227859\pi$
$500$	812244.	+	1.40685e6i	0.145299	+	0.251665i
$501$	−1.08119e6	−	1.87268e6i	−0.192446	−	0.333327i
$502$	−4.58925e6	+	7.94881e6i	−0.812798	+	1.40781i
$503$	2.60929e6			0.459835			0.229917	−	0.973210i	$-0.426154\pi$
$503$	2.60929e6			0.459835			0.229917	+	0.973210i	$0.426154\pi$
$504$	−1.51812e6	+	335149.i	−0.266214	+	0.0587707i
$505$	−6.54564e6			−1.14215
$506$	−3.00552e6	+	5.20571e6i	−0.521847	+	0.903865i
$507$	−981124.	−	1.69936e6i	−0.169513	−	0.293606i
$508$	−367654.	−	636795.i	−0.0632092	−	0.109481i
$509$	5.00911e6	−	8.67603e6i	0.856970	−	1.48432i	−0.0178348	−	0.999841i	$-0.505677\pi$
$509$	5.00911e6	−	8.67603e6i	0.856970	−	1.48432i	0.874805	−	0.484475i	$-0.160989\pi$
$510$	2.96159e6			0.504196
$511$	2.17699e6	−	6.88326e6i	0.368811	−	1.16612i
$512$	−1.99607e6			−0.336512
$513$	343532.	−	595014.i	0.0576333	−	0.0998238i
$514$	2.90482e6	+	5.03130e6i	0.484967	+	0.839987i
$515$	−2.18471e6	−	3.78403e6i	−0.362974	−	0.628689i
$516$	585462.	−	1.01405e6i	0.0967998	−	0.167662i
$517$	3.92782e6			0.646287
$518$	4.07187e6	−	1.28745e7i	0.666760	−	2.10818i
$519$	1.61370e6			0.262969
$520$	1.12238e6	−	1.94402e6i	0.182025	−	0.315277i
$521$	2.08970e6	+	3.61947e6i	0.337280	+	0.584186i	0.983920	−	0.178609i	$-0.0571598\pi$
$521$	2.08970e6	+	3.61947e6i	0.337280	+	0.584186i	−0.646640	+	0.762795i	$0.723826\pi$
$522$	378750.	+	656014.i	0.0608382	+	0.105375i
$523$	−1.80263e6	+	3.12224e6i	−0.288172	+	0.499128i	−0.973373	−	0.229225i	$-0.926381\pi$
$523$	−1.80263e6	+	3.12224e6i	−0.288172	+	0.499128i	0.685202	+	0.728353i	$0.259714\pi$
$524$	−1.47357e6			−0.234446
$525$	1.85150e6	−	408746.i	0.293174	−	0.0647225i
$526$	4.78637e6			0.754297
$527$	−2.60117e6	+	4.50536e6i	−0.407983	+	0.706648i
$528$	3.18668e6	+	5.51949e6i	0.497455	+	0.861617i
$529$	1.88633e6	+	3.26722e6i	0.293075	+	0.507621i
$530$	248877.	−	431068.i	0.0384853	−	0.0666586i
$531$	4.16770e6			0.641446
$532$	−728212.	−	796119.i	−0.111552	−	0.121955i
$533$	−5.13003e6			−0.782172
$534$	451061.	−	781261.i	0.0684514	−	0.118561i
$535$	432013.	+	748268.i	0.0652547	+	0.113025i
$536$	3.74407e6	+	6.48492e6i	0.562901	+	0.974972i
$537$	−2.59002e6	+	4.48604e6i	−0.387585	+	0.671317i
$538$	4.28086e6			0.637640
$539$	−8.78699e6	+	4.07850e6i	−1.30277	+	0.604684i
$540$	−249313.			−0.0367926
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	−0.509193	−	0.860653i	$-0.670056\pi$
$541$	3.34083e6	−	5.78648e6i	0.490751	−	0.850005i	0.999943	+	0.0106475i	$0.00338926\pi$
$542$	−1.72737e6	−	2.99189e6i	−0.252573	−	0.437470i
$543$	2.61453e6	+	4.52850e6i	0.380534	+	0.659105i
$544$	−2.06964e6	+	3.58473e6i	−0.299846	+	0.519349i
$545$	−3.24625e6			−0.468156
$546$	1.96999e6	+	2.15370e6i	0.282802	+	0.309174i
$547$	8.69076e6			1.24191			0.620954	−	0.783847i	$-0.286745\pi$
$547$	8.69076e6			1.24191			0.620954	+	0.783847i	$0.286745\pi$
$548$	−168766.	+	292312.i	−0.0240068	+	0.0415810i
$549$	−1.66446e6	−	2.88293e6i	−0.235691	−	0.408229i
$550$	−2.99259e6	−	5.18332e6i	−0.421833	−	0.730636i
$551$	689676.	−	1.19455e6i	0.0967756	−	0.167620i
$552$	−2.17467e6			−0.303771
$553$	−7.99456e6	+	1.76492e6i	−1.11168	+	0.245421i
$554$	−2.56815e6			−0.355505
$555$	−2.84084e6	+	4.92047e6i	−0.391484	+	0.678070i
$556$	−469171.	−	812628.i	−0.0643642	−	0.111482i
$557$	−3.12371e6	−	5.41042e6i	−0.426612	−	0.738913i	0.569958	−	0.821674i	$-0.306960\pi$
$557$	−3.12371e6	−	5.41042e6i	−0.426612	−	0.738913i	−0.996569	+	0.0827611i	$0.973626\pi$
$558$	1.01249e6	−	1.75369e6i	0.137660	−	0.238433i
$559$	5.76803e6			0.780725
$560$	1.86017e6	−	5.88152e6i	0.250658	−	0.792537i
$561$	−6.89783e6			−0.925349
$562$	1.37107e6	−	2.37476e6i	0.183113	−	0.317161i
$563$	5.95223e6	+	1.03096e7i	0.791423	+	1.37078i	0.925086	+	0.379758i	$0.123993\pi$
$563$	5.95223e6	+	1.03096e7i	0.791423	+	1.37078i	−0.133663	+	0.991027i	$0.542674\pi$
$564$	−270787.	−	469017.i	−0.0358451	−	0.0620856i
$565$	792560.	−	1.37275e6i	0.104451	−	0.180914i
$566$	−2.17848e6			−0.285833
$567$	−256493.	+	810986.i	−0.0335057	+	0.105939i
$568$	−5.91768e6			−0.769627
$569$	−10707.2	+	18545.4i	−0.00138642	+	0.00240135i	−0.866718	−	0.498799i	$-0.833775\pi$
$569$	−10707.2	+	18545.4i	−0.00138642	+	0.00240135i	0.865331	+	0.501200i	$0.167108\pi$
$570$	1.04957e6	+	1.81791e6i	0.135308	+	0.234360i
$571$	−3.55823e6	−	6.16304e6i	−0.456714	−	0.791051i	0.542071	−	0.840333i	$-0.317640\pi$
$571$	−3.55823e6	−	6.16304e6i	−0.456714	−	0.791051i	−0.998785	+	0.0492811i	$0.984307\pi$
$572$	996297.	−	1.72564e6i	0.127321	−	0.220526i
$573$	5.94504e6			0.756429
$574$	−1.05999e7	+	2.34009e6i	−1.34283	+	0.296451i
$575$	2.65223e6			0.334534
$576$	−786663.	+	1.36254e6i	−0.0987944	+	0.171117i
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	0.978793	+	0.204854i	$0.0656719\pi$
$577$	5.33259e6	+	9.23632e6i	0.666805	+	1.15494i	−0.311988	+	0.950086i	$0.600995\pi$
$578$	−1.11262e6	−	1.92712e6i	−0.138525	−	0.239932i
$579$	−2.50790e6	+	4.34380e6i	−0.310895	+	0.538485i
$580$	−500522.			−0.0617808
$581$	−3.98758e6	−	4.35943e6i	−0.490083	−	0.535784i
$582$	−179916.			−0.0220172
$583$	−579659.	+	1.00400e6i	−0.0706319	+	0.122338i
$584$	−4.12222e6	−	7.13990e6i	−0.500149	−	0.866283i
$585$	−614065.	−	1.06359e6i	−0.0741864	−	0.128495i
$586$	1.24234e6	−	2.15180e6i	0.149450	−	0.258856i
$587$	−1.30101e7			−1.55843			−0.779213	−	0.626759i	$-0.784381\pi$
$587$	−1.30101e7			−1.55843			−0.779213	+	0.626759i	$0.784381\pi$
$588$	1.09279e6	+	768071.i	0.130345	+	0.0916132i
$589$	−3.68735e6			−0.437952
$590$	−6.36664e6	+	1.10273e7i	−0.752975	+	1.30419i
$591$	−3.42630e6	−	5.93453e6i	−0.403512	−	0.698904i
$592$	−1.00133e7	−	1.73435e7i	−1.17428	−	2.03391i
$593$	−2.13043e6	+	3.69002e6i	−0.248789	+	0.430915i	−0.963190	−	0.268821i	$-0.913366\pi$
$593$	−2.13043e6	+	3.69002e6i	−0.248789	+	0.430915i	0.714401	+	0.699736i	$0.246699\pi$
$594$	2.68495e6			0.312226
$595$	4.50608e6	+	4.92628e6i	0.521803	+	0.570462i
$596$	1.70034e6			0.196074
$597$	−611369.	+	1.05892e6i	−0.0702049	+	0.121598i
$598$	2.04139e6	+	3.53578e6i	0.233438	+	0.404327i
$599$	6.89790e6	+	1.19475e7i	0.785507	+	1.36054i	0.928696	+	0.370842i	$0.120931\pi$
$599$	6.89790e6	+	1.19475e7i	0.785507	+	1.36054i	−0.143189	+	0.989695i	$0.545736\pi$
$600$	1.08266e6	−	1.87522e6i	0.122776	−	0.212655i
$601$	4.99695e6			0.564311			0.282155	−	0.959369i	$-0.408951\pi$
$601$	4.99695e6			0.564311			0.282155	+	0.959369i	$0.408951\pi$
$602$	1.19182e7	−	2.63111e6i	1.34035	−	0.295902i
$603$	4.09683e6			0.458833
$604$	−625628.	+	1.08362e6i	−0.0697788	+	0.120860i
$605$	−3.31471e6	−	5.74125e6i	−0.368177	−	0.637702i
$606$	−4.85981e6	−	8.41743e6i	−0.537573	−	0.931104i
$607$	1.52473e6	−	2.64091e6i	0.167966	−	0.290926i	−0.769739	−	0.638359i	$-0.779613\pi$
$607$	1.52473e6	−	2.64091e6i	0.167966	−	0.290926i	0.937705	+	0.347434i	$0.112947\pi$
$608$	−2.93387e6			−0.321871
$609$	−514937.	+	1.62814e6i	−0.0562614	+	0.177889i
$610$	1.01706e7			1.10668
$611$	1.33391e6	−	2.31040e6i	0.144552	−	0.250372i
$612$	475542.	+	823663.i	0.0513228	+	0.0888937i
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	0.990793	−	0.135388i	$-0.0432282\pi$
$613$	3.51813e6	+	6.09357e6i	0.378147	+	0.654969i	−0.612646	+	0.790357i	$0.709895\pi$
$614$	7.53195e6	−	1.30457e7i	0.806281	−	1.39652i
$615$	4.56749e6			0.486956
$616$	−3.33605e6	+	1.05480e7i	−0.354226	+	1.12000i
$617$	1.00066e7			1.05822			0.529108	−	0.848554i	$-0.322527\pi$
$617$	1.00066e7			1.05822			0.529108	+	0.848554i	$0.322527\pi$
$618$	3.24408e6	−	5.61890e6i	0.341680	−	0.591807i
$619$	3.27533e6	+	5.67304e6i	0.343581	+	0.595099i	0.985095	−	0.172012i	$-0.0550268\pi$
$619$	3.27533e6	+	5.67304e6i	0.343581	+	0.595099i	−0.641514	+	0.767111i	$0.721693\pi$
$620$	669010.	+	1.15876e6i	0.0698962	+	0.121064i
$621$	−594893.	+	1.03038e6i	−0.0619027	+	0.107219i
$622$	−9.17986e6			−0.951393
$623$	1.98583e6	−	438403.i	0.204985	−	0.0452536i
$624$	4.32886e6			0.445054
$625$	1.02325e6	−	1.77232e6i	0.104781	−	0.181485i
$626$	2.62879e6	+	4.55320e6i	0.268114	+	0.464388i
$627$	−2.44455e6	−	4.23408e6i	−0.248330	−	0.430120i
$628$	−2.49799e6	+	4.32665e6i	−0.252750	+	0.437777i
$629$	2.16746e7			2.18436
$630$	−1.75397e6	−	1.91753e6i	−0.176064	−	0.192482i
$631$	2.22672e6			0.222635			0.111317	−	0.993785i	$-0.464493\pi$
$631$	2.22672e6			0.222635			0.111317	+	0.993785i	$0.464493\pi$
$632$	−4.67480e6	+	8.09699e6i	−0.465554	+	0.806364i
$633$	−4.46021e6	−	7.72531e6i	−0.442431	−	0.766313i
$634$	5.64524e6	+	9.77784e6i	0.557775	+	0.966095i
$635$	−1.61249e6	+	2.79291e6i	−0.158694	+	0.274867i
$636$	159849.			0.0156699
$637$	−585084.	+	6.55373e6i	−0.0571307	+	0.639941i
$638$	5.39031e6			0.524279
$639$	−1.61881e6	+	2.80386e6i	−0.156835	+	0.271647i
$640$	−4.33242e6	−	7.50397e6i	−0.418101	−	0.724171i
$641$	7.96698e6	+	1.37992e7i	0.765859	+	1.32651i	0.939791	+	0.341749i	$0.111019\pi$
$641$	7.96698e6	+	1.37992e7i	0.765859	+	1.32651i	−0.173932	+	0.984758i	$0.555647\pi$
$642$	−641496.	+	1.11110e6i	−0.0614266	+	0.106394i
$643$	−1.49933e7			−1.43011			−0.715056	−	0.699067i	$-0.753599\pi$
$643$	−1.49933e7			−1.43011			−0.715056	+	0.699067i	$0.753599\pi$
$644$	1.26104e6	+	1.37864e6i	0.119816	+	0.130989i
$645$	−5.13553e6			−0.486056
$646$	4.00391e6	−	6.93498e6i	0.377488	−	0.653829i
$647$	−6.49027e6	−	1.12415e7i	−0.609540	−	1.05575i	−0.991316	−	0.131500i	$-0.958021\pi$
$647$	−6.49027e6	−	1.12415e7i	−0.609540	−	1.05575i	0.381776	−	0.924255i	$-0.375313\pi$
$648$	485680.	+	841223.i	0.0454373	+	0.0786998i
$649$	1.48285e7	−	2.56838e7i	1.38193	−	2.39357i
$650$	−4.06521e6			−0.377398
$651$	4.45758e6	−	984079.i	0.412237	−	0.0910075i
$652$	−3.79885e6			−0.349972
$653$	8.27460e6	−	1.43320e7i	0.759389	−	1.31530i	−0.183774	−	0.982969i	$-0.558831\pi$
$653$	8.27460e6	−	1.43320e7i	0.759389	−	1.31530i	0.943163	−	0.332332i	$-0.107835\pi$
$654$	−2.41018e6	−	4.17455e6i	−0.220346	−	0.381650i
$655$	3.23145e6	+	5.59704e6i	0.294303	+	0.509748i
$656$	−8.04966e6	+	1.39424e7i	−0.730328	+	1.26497i
$657$	−4.51062e6			−0.407683
$658$	1.70229e6	−	5.38233e6i	0.153274	−	0.484625i
$659$	5.86879e6			0.526423			0.263212	−	0.964738i	$-0.415218\pi$
$659$	5.86879e6			0.526423			0.263212	+	0.964738i	$0.415218\pi$
$660$	−887046.	+	1.53641e6i	−0.0792659	+	0.137293i
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	0.657389	−	0.753551i	$-0.271661\pi$
$661$	−3.63843e6	−	6.30195e6i	−0.323900	−	0.561011i	−0.981289	+	0.192540i	$0.938327\pi$
$662$	9751.81	+	16890.6i	0.000864849	+	0.00149796i
$663$	−2.34255e6	+	4.05741e6i	−0.206969	+	0.358480i
$664$	−6.74702e6			−0.593870
$665$	−1.42696e6	+	4.51179e6i	−0.125129	+	0.395635i
$666$	−8.43672e6			−0.737035
$667$	−1.19431e6	+	2.06861e6i	−0.103945	+	0.180038i
$668$	1.06082e6	+	1.83739e6i	0.0919815	+	0.159317i
$669$	2.44505e6	+	4.23495e6i	0.211214	+	0.365833i
$670$	−6.25838e6	+	1.08398e7i	−0.538611	+	0.932902i
$671$	−2.36884e7			−2.03109
$672$	3.54671e6	−	782991.i	0.302972	−	0.0668857i
$673$	−1.82417e7			−1.55248			−0.776241	−	0.630437i	$-0.782876\pi$
$673$	−1.82417e7			−1.55248			−0.776241	+	0.630437i	$0.782876\pi$
$674$	−6.48376e6	+	1.12302e7i	−0.549765	+	0.952222i
$675$	−592334.	−	1.02595e6i	−0.0500388	−	0.0866698i
$676$	962636.	+	1.66733e6i	0.0810205	+	0.140332i
$677$	3.88203e6	−	6.72387e6i	0.325527	−	0.563829i	−0.656092	−	0.754681i	$-0.727792\pi$
$677$	3.88203e6	−	6.72387e6i	0.325527	−	0.563829i	0.981619	+	0.190852i	$0.0611250\pi$
$678$	2.35374e6			0.196646
$679$	−273743.	−	299270.i	−0.0227860	−	0.0249109i
$680$	7.62432e6			0.632308
$681$	73.5034	−	127.312i	6.07351e−6	−	1.05196e-5i
$682$	−7.20482e6	−	1.24791e7i	−0.593147	−	1.02736i
$683$	−4.28162e6	−	7.41598e6i	−0.351201	−	0.608299i	0.635259	−	0.772299i	$-0.280893\pi$
$683$	−4.28162e6	−	7.41598e6i	−0.351201	−	0.608299i	−0.986460	+	0.164001i	$0.947560\pi$
$684$	−337058.	+	583801.i	−0.0275464	+	0.0477117i
$685$	1.48038e6			0.120544
$686$	1.78059e6	+	1.38085e7i	0.144462	+	1.12030i
$687$	696411.			0.0562955
$688$	9.05076e6	−	1.56764e7i	0.728978	−	1.26263i
$689$	393712.	+	681928.i	0.0315959	+	0.0547256i
$690$	−1.81753e6	−	3.14806e6i	−0.145332	−	0.251722i
$691$	−8.22547e6	+	1.42469e7i	−0.655338	+	1.13508i	0.326471	+	0.945207i	$0.394140\pi$
$691$	−8.22547e6	+	1.42469e7i	−0.655338	+	1.13508i	−0.981809	+	0.189872i	$0.939193\pi$
$692$	−1.58329e6			−0.125689
$693$	4.08516e6	+	4.46611e6i	0.323129	+	0.353262i
$694$	2.41677e7			1.90474
$695$	−2.05773e6	+	3.56409e6i	−0.161594	+	0.279890i
$696$	975054.	+	1.68884e6i	0.0762967	+	0.132150i
$697$	−8.71208e6	−	1.50898e7i	−0.679266	−	1.17652i
$698$	−930197.	+	1.61115e6i	−0.0722664	+	0.125169i
$699$	932916.			0.0722187
$700$	−1.81661e6	+	401044.i	−0.140125	+	0.0309347i
$701$	−1.66928e7			−1.28302			−0.641512	−	0.767113i	$-0.721693\pi$
$701$	−1.66928e7			−1.28302			−0.641512	+	0.767113i	$0.721693\pi$
$702$	911825.	−	1.57933e6i	0.0698343	−	0.120956i
$703$	7.68132e6	+	1.33044e7i	0.586202	+	1.01533i
$704$	5.59783e6	+	9.69573e6i	0.425685	+	0.737308i
$705$	−1.18764e6	+	2.05705e6i	−0.0899937	+	0.155874i
$706$	2.46059e6			0.185792
$707$	6.60725e6	−	2.08909e7i	0.497132	−	1.57184i
$708$	−4.08916e6			−0.306585
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	−0.951669	−	0.307126i	$-0.900633\pi$
$709$	−2.80890e6	+	4.86515e6i	−0.209855	+	0.363480i	0.741813	+	0.670606i	$0.233966\pi$
$710$	−4.94584e6	−	8.56644e6i	−0.368209	−	0.637756i
$711$	2.55763e6	+	4.42994e6i	0.189742	+	0.328643i
$712$	1.16121e6	−	2.01128e6i	0.0858443	−	0.148687i
$713$	6.38537e6			0.470395
$714$	−2.98947e6	+	9.45216e6i	−0.219456	+	0.693882i
$715$	−8.73927e6			−0.639308
$716$	2.54121e6	−	4.40150e6i	0.185250	−	0.320862i
$717$	3.10099e6	+	5.37107e6i	0.225269	+	0.390178i
$718$	1.03201e7	+	1.78749e7i	0.747087	+	1.29399i
$719$	−5.18592e6	+	8.98227e6i	−0.374113	+	0.647983i	−0.990194	−	0.139700i	$-0.955386\pi$
$719$	−5.18592e6	+	8.98227e6i	−0.374113	+	0.647983i	0.616081	+	0.787683i	$0.288720\pi$
$720$	−3.85418e6			−0.277077
$721$	1.42823e7	−	3.15303e6i	1.02320	−	0.225887i
$722$	−1.01461e7			−0.724363
$723$	991332.	−	1.71704e6i	0.0705299	−	0.122161i
$724$	−2.56526e6	−	4.44316e6i	−0.181880	−	0.315025i
$725$	−1.18917e6	−	2.05971e6i	−0.0840233	−	0.145533i
$726$	4.92201e6	−	8.52518e6i	0.346578	−	0.600291i
$727$	1.15369e7			0.809565			0.404783	−	0.914413i	$-0.367347\pi$
$727$	1.15369e7			0.809565			0.404783	+	0.914413i	$0.367347\pi$
$728$	5.07155e6	+	5.54448e6i	0.354660	+	0.387733i
$729$	531441.			0.0370370
$730$	6.89049e6	−	1.19347e7i	0.478567	−	0.828902i
$731$	9.79557e6	+	1.69664e7i	0.678010	+	1.17435i
$732$	1.63310e6	+	2.82860e6i	0.112651	+	0.195117i
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	0.486109	+	0.873898i	$0.338416\pi$
$733$	−7.47349e6	+	1.29445e7i	−0.513764	+	0.889865i	−0.999873	+	0.0159667i	$0.994917\pi$
$734$	−3.06432e6			−0.209939
$735$	520925.	−	5.83507e6i	0.0355678	−	0.398408i
$736$	5.08058e6			0.345715
$737$	1.45764e7	−	2.52470e7i	0.988510	−	1.71215i
$738$	3.39113e6	+	5.87362e6i	0.229194	+	0.396976i
$739$	−4.50682e6	−	7.80604e6i	−0.303570	−	0.525799i	0.673372	−	0.739304i	$-0.264845\pi$
$739$	−4.50682e6	−	7.80604e6i	−0.303570	−	0.525799i	−0.976942	+	0.213505i	$0.931512\pi$
$740$	2.78730e6	−	4.82775e6i	0.187113	−	0.324090i
$741$	−3.32073e6			−0.222171
$742$	1.12457e6	+	1.22944e6i	0.0749853	+	0.0819779i
$743$	−2.10239e7			−1.39714			−0.698571	−	0.715541i	$-0.746180\pi$
$743$	−2.10239e7			−1.39714			−0.698571	+	0.715541i	$0.746180\pi$
$744$	2.60656e6	−	4.51470e6i	0.172638	−	0.299017i
$745$	−3.72875e6	−	6.45838e6i	−0.246134	−	0.426317i
$746$	−2.78811e6	−	4.82915e6i	−0.183427	−	0.317705i
$747$	−1.84568e6	+	3.19681e6i	−0.121019	+	0.209612i
$748$	6.76785e6			0.442279
$749$	−2.82424e6	+	623493.i	−0.183949	+	0.0406094i
$750$	1.05796e7			0.686779
$751$	−2.02110e6	+	3.50064e6i	−0.130764	+	0.226489i	−0.923971	−	0.382462i	$-0.875076\pi$
$751$	−2.02110e6	+	3.50064e6i	−0.130764	+	0.226489i	0.793207	+	0.608952i	$0.208410\pi$
$752$	−4.18615e6	−	7.25062e6i	−0.269942	−	0.467553i
$753$	6.46387e6	+	1.11957e7i	0.415437	+	0.719558i
$754$	1.83058e6	−	3.17066e6i	0.117263	−	0.203106i
$755$	5.48786e6			0.350377
$756$	251660.	−	795703.i	0.0160143	−	0.0506345i
$757$	−1.82059e7			−1.15471			−0.577353	−	0.816495i	$-0.695914\pi$
$757$	−1.82059e7			−1.15471			−0.577353	+	0.816495i	$0.695914\pi$
$758$	7.77945e6	−	1.34744e7i	0.491786	−	0.851798i
$759$	4.23321e6	+	7.33214e6i	0.266726	+	0.461983i
$760$	2.70201e6	+	4.68001e6i	0.169689	+	0.293909i
$761$	9.45999e6	−	1.63852e7i	0.592146	−	1.02563i	−0.401797	−	0.915729i	$-0.631614\pi$
$761$	9.45999e6	−	1.63852e7i	0.592146	−	1.02563i	0.993943	−	0.109898i	$-0.0350526\pi$
$762$	−4.78876e6			−0.298769
$763$	3.27681e6	−	1.03607e7i	0.203770	−	0.644283i
$764$	−5.83301e6			−0.361542
$765$	2.08567e6	−	3.61249e6i	0.128852	−	0.223179i
$766$	1.15391e7	+	1.99863e7i	0.710559	+	1.23072i
$767$	−1.00717e7	−	1.74447e7i	−0.618180	−	1.07072i
$768$	3.63619e6	−	6.29807e6i	0.222456	−	0.385305i
$769$	−1.12831e7			−0.688037			−0.344019	−	0.938963i	$-0.611788\pi$
$769$	−1.12831e7			−0.688037			−0.344019	+	0.938963i	$0.611788\pi$
$770$	−1.80575e7	+	3.98646e6i	−1.09756	+	0.242304i
$771$	8.18277e6			0.495752
$772$	2.46064e6	−	4.26195e6i	0.148595	−	0.257374i
$773$	1.84282e6	+	3.19186e6i	0.110926	+	0.192130i	0.916144	−	0.400849i	$-0.131285\pi$
$773$	1.84282e6	+	3.19186e6i	0.110926	+	0.192130i	−0.805218	+	0.592979i	$0.797952\pi$
$774$	−3.81288e6	−	6.60410e6i	−0.228771	−	0.396242i
$775$	−3.17896e6	+	5.50611e6i	−0.190121	+	0.329299i
$776$	−463176.			−0.0276116
$777$	−1.28365e7	−	1.40335e7i	−0.762772	−	0.833902i
$778$	−1.11971e6			−0.0663219
$779$	6.17501e6	−	1.06954e7i	0.364581	−	0.631472i
$780$	602493.	+	1.04355e6i	0.0354581	+	0.0614152i
$781$	1.15193e7	+	1.99521e7i	0.675771	+	1.17047i
$782$	−6.93357e6	+	1.20093e7i	−0.405452	+	0.702264i
$783$	1.06692e6			0.0621912
$784$	1.68937e7	+	1.18738e7i	0.981599	+	0.689919i
$785$	2.19118e7			1.26912
$786$	−4.79839e6	+	8.31105e6i	−0.277038	+	0.479843i
$787$	7.03741e6	+	1.21891e7i	0.405019	+	0.701514i	0.994324	−	0.106397i	$-0.0339314\pi$
$787$	7.03741e6	+	1.21891e7i	0.405019	+	0.701514i	−0.589304	+	0.807911i	$0.700598\pi$
$788$	3.36173e6	+	5.82269e6i	0.192862	+	0.334048i
$789$	3.37076e6	−	5.83832e6i	0.192768	−	0.333884i
$790$	−1.56283e7			−0.890930
$791$	3.58124e6	+	3.91519e6i	0.203513	+	0.222491i
$792$	6.91213e6			0.391560
$793$	−8.04472e6	+	1.39339e7i	−0.454284	+	0.786844i
$794$	−6.02294e6	−	1.04320e7i	−0.339045	−	0.587243i
$795$	−350538.	−	607150.i	−0.0196706	−	0.0340705i
$796$	599848.	−	1.03897e6i	0.0335551	−	0.0581191i
$797$	−1.75191e7			−0.976937			−0.488469	−	0.872582i	$-0.662444\pi$
$797$	−1.75191e7			−0.976937			−0.488469	+	0.872582i	$0.662444\pi$
$798$	−6.86144e6	+	1.51477e6i	−0.381424	+	0.0842051i
$799$	9.06127e6			0.502137
$800$	−2.52936e6	+	4.38099e6i	−0.139729	+	0.242018i
$801$	−635311.	−	1.10039e6i	−0.0349869	−	0.0605990i
$802$	−4.28067e6	−	7.41433e6i	−0.235004	−	0.407039i
$803$	−1.60486e7	+	2.77970e7i	−0.878311	+	1.52128i
$804$	−4.01963e6			−0.219304
$805$	2.47106e6	−	7.81306e6i	0.134398	−	0.424944i
$806$	−9.78721e6			−0.530666
$807$	3.01475e6	−	5.22170e6i	0.162955	−	0.282246i
$808$	−1.25111e7	−	2.16698e7i	−0.674166	−	1.16769i
$809$	−407261.	−	705396.i	−0.0218777	−	0.0378932i	0.854879	−	0.518827i	$-0.173631\pi$
$809$	−407261.	−	705396.i	−0.0218777	−	0.0378932i	−0.876757	+	0.480934i	$0.840298\pi$
$810$	−811837.	+	1.40614e6i	−0.0434767	+	0.0753038i
$811$	1.26533e7			0.675540			0.337770	−	0.941229i	$-0.390327\pi$
$811$	1.26533e7			0.675540			0.337770	+	0.941229i	$0.390327\pi$
$812$	505233.	−	1.59746e6i	0.0268907	−	0.0850235i
$813$	−4.86593e6			−0.258190
$814$	−3.00175e7	+	5.19919e7i	−1.58787	+	2.75026i
$815$	8.33064e6	+	1.44291e7i	0.439324	+	0.760931i
$816$	7.35150e6	+	1.27332e7i	0.386501	+	0.669439i
$817$	−6.94297e6	+	1.20256e7i	−0.363907	+	0.630305i
$818$	4.20854e7			2.19912
$819$	4.01438e6	−	886236.i	0.209126	−	0.0461678i
$820$	−4.48142e6			−0.232745
$821$	−2.13697e6	+	3.70133e6i	−0.110647	+	0.191646i	−0.916031	−	0.401107i	$-0.868626\pi$
$821$	−2.13697e6	+	3.70133e6i	−0.110647	+	0.191646i	0.805384	+	0.592753i	$0.201959\pi$
$822$	1.09911e6	+	1.90371e6i	0.0567361	+	0.0982699i
$823$	−8.52317e6	−	1.47626e7i	−0.438633	−	0.759735i	0.558951	−	0.829201i	$-0.311204\pi$
$823$	−8.52317e6	−	1.47626e7i	−0.438633	−	0.759735i	−0.997584	+	0.0694656i	$0.977871\pi$
$824$	8.35155e6	−	1.44653e7i	0.428498	−	0.742180i
$825$	−8.43001e6			−0.431214
$826$	−2.87681e7	−	3.14508e7i	−1.46711	−	1.60392i
$827$	2.60828e6			0.132614			0.0663071	−	0.997799i	$-0.478878\pi$
$827$	2.60828e6			0.132614			0.0663071	+	0.997799i	$0.478878\pi$
$828$	583682.	−	1.01097e6i	0.0295870	−	0.0512462i
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	−0.998880	−	0.0473066i	$-0.984936\pi$
$829$	−1.06932e7	−	1.85212e7i	−0.540409	−	0.936016i	0.458471	−	0.888709i	$-0.348397\pi$
$830$	−5.63898e6	−	9.76700e6i	−0.284122	−	0.492114i
$831$	−1.80859e6	+	3.13257e6i	−0.0908528	+	0.157362i
$832$	7.60423e6			0.380844
$833$	−2.02711e7	+	9.40887e6i	−1.01220	+	0.469813i
$834$	−6.11104e6			−0.304229
$835$	4.65263e6	−	8.05859e6i	0.230931	−	0.399984i
$836$	2.39848e6	+	4.15429e6i	0.118692	+	0.205580i
$837$	−1.42608e6	−	2.47004e6i	−0.0703605	−	0.121868i
$838$	2.22645e7	−	3.85632e7i	1.09522	−	1.89698i
$839$	771393.			0.0378330			0.0189165	−	0.999821i	$-0.493978\pi$
$839$	771393.			0.0378330			0.0189165	+	0.999821i	$0.493978\pi$
$840$	−4.51542e6	−	4.93649e6i	−0.220800	−	0.241390i
$841$	−1.83692e7			−0.895571
$842$	−1.22699e7	+	2.12520e7i	−0.596430	+	1.03305i
$843$	−1.93112e6	−	3.34480e6i	−0.0935925	−	0.162107i
$844$	4.37616e6	+	7.57973e6i	0.211464	+	0.366267i
$845$	4.22200e6	−	7.31272e6i	0.203412	−	0.352320i
$846$	−3.52705e6			−0.169428
$847$	2.16696e7	−	4.78388e6i	1.03787	−	0.229125i
$848$	2.47113e6			0.118006
$849$	−1.53417e6	+	2.65726e6i	−0.0730474	+	0.126522i
$850$	−6.90375e6	−	1.19576e7i	−0.327746	−	0.567673i
$851$	−1.33017e7	−	2.30393e7i	−0.629628	−	1.09055i
$852$	1.58830e6	−	2.75102e6i	0.0749609	−	0.129836i
$853$	2.94032e7			1.38364			0.691818	−	0.722072i	$-0.256810\pi$
$853$	2.94032e7			1.38364			0.691818	+	0.722072i	$0.256810\pi$
$854$	−1.02664e7	+	3.24604e7i	−0.481694	+	1.52303i
$855$	2.95659e6			0.138317
$856$	−1.65147e6	+	2.86042e6i	−0.0770345	+	0.133428i
$857$	1.32505e7	+	2.29505e7i	0.616283	+	1.06743i	0.990158	+	0.139954i	$0.0446955\pi$
$857$	1.32505e7	+	2.29505e7i	0.616283	+	1.06743i	−0.373875	+	0.927479i	$0.621971\pi$
$858$	−6.48848e6	−	1.12384e7i	−0.300902	−	0.521177i
$859$	1.83759e7	−	3.18281e7i	0.849702	−	1.47173i	−0.0317727	−	0.999495i	$-0.510115\pi$
$859$	1.83759e7	−	3.18281e7i	0.849702	−	1.47173i	0.881475	−	0.472232i	$-0.156551\pi$
$860$	5.03876e6			0.232315
$861$	−4.61048e6	+	1.45775e7i	−0.211952	+	0.670156i
$862$	1.94020e7			0.889360
$863$	−5.90946e6	+	1.02355e7i	−0.270098	+	0.467823i	−0.968887	−	0.247505i	$-0.920389\pi$
$863$	−5.90946e6	+	1.02355e7i	−0.270098	+	0.467823i	0.698789	+	0.715328i	$0.253723\pi$
$864$	−1.13467e6	−	1.96531e6i	−0.0517113	−	0.0895665i
$865$	3.47207e6	+	6.01379e6i	0.157778	+	0.273280i
$866$	3.00812e6	−	5.21022e6i	0.136302	−	0.236081i
$867$	−3.13421e6			−0.141606
$868$	−4.37358e6	+	965534.i	−0.197033	+	0.0434979i
$869$	3.63998e7			1.63512
$870$	−1.62985e6	+	2.82298e6i	−0.0730044	+	0.126447i
$871$	−9.90046e6	−	1.71481e7i	−0.442191	−	0.765897i
$872$	−6.20477e6	−	1.07470e7i	−0.276334	−	0.478625i
$873$	−126704.	+	219458.i	−0.00562671	+	0.00974575i
$874$	−9.82884e6			−0.435235
$875$	1.60970e7	+	1.75980e7i	0.710762	+	0.777042i
$876$	4.42562e6			0.194856
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	−0.939881	−	0.341503i	$-0.889064\pi$
$877$	−3.96754e6	+	6.87199e6i	−0.174190	+	0.301706i	0.765691	+	0.643209i	$0.222397\pi$
$878$	−4.28470e6	−	7.42131e6i	−0.187579	−	0.324896i
$879$	−1.74981e6	−	3.03077e6i	−0.0763870	−	0.132306i
$880$	−1.37130e7	+	2.37516e7i	−0.596934	+	1.03392i
$881$	4.20152e7			1.82375			0.911877	−	0.410464i	$-0.134633\pi$
$881$	4.20152e7			1.82375			0.911877	+	0.410464i	$0.134633\pi$
$882$	7.89043e6	−	3.66236e6i	0.341530	−	0.158522i
$883$	2.12461e7			0.917016			0.458508	−	0.888690i	$-0.348384\pi$
$883$	2.12461e7			0.917016			0.458508	+	0.888690i	$0.348384\pi$
$884$	2.29840e6	−	3.98095e6i	0.0989226	−	0.171339i
$885$	8.96729e6	+	1.55318e7i	0.384860	+	0.666597i
$886$	2.46758e6	+	4.27397e6i	0.105606	+	0.182914i
$887$	−9.42452e6	+	1.63238e7i	−0.402208	+	0.696644i	−0.993992	−	0.109452i	$-0.965090\pi$
$887$	−9.42452e6	+	1.63238e7i	−0.402208	+	0.696644i	0.591784	+	0.806096i	$0.298424\pi$
$888$	−2.17195e7			−0.924309
$889$	−7.28613e6	−	7.96558e6i	−0.309202	−	0.338036i
$890$	3.88204e6			0.164280
$891$	1.89085e6	−	3.27504e6i	0.0797925	−	0.138205i
$892$	−2.39897e6	−	4.15514e6i	−0.100952	−	0.174853i
$893$	3.21125e6	+	5.56205e6i	0.134755	+	0.233403i
$894$	5.53682e6	−	9.59005e6i	0.231695	−	0.401307i
$895$	−2.22909e7			−0.930186
$896$	2.83227e7	−	6.25267e6i	1.17860	−	0.260193i
$897$	5.75050e6			0.238630
$898$	−7.21044e6	+	1.24889e7i	−0.298381	+	0.516811i
$899$	−2.86300e6	−	4.95886e6i	−0.118147	−	0.204636i
$900$	581172.	+	1.00662e6i	0.0239165	+	0.0414247i
$901$	−1.33724e6	+	2.31617e6i	−0.0548780	+	0.0950514i
$902$	4.82621e7			1.97510
$903$	5.18387e6	−	1.63905e7i	0.211561	−	0.668917i
$904$	6.05948e6			0.246612
$905$	−1.12509e7	+	1.94872e7i	−0.456632	+	0.790910i
$906$	4.07446e6	+	7.05717e6i	0.164911	+	0.285634i
$907$	3.09723e6	+	5.36456e6i	0.125013	+	0.216529i	0.921738	−	0.387813i	$-0.126769\pi$
$907$	3.09723e6	+	5.36456e6i	0.125013	+	0.216529i	−0.796725	+	0.604342i	$0.793436\pi$
$908$	−72.1183	+	124.912i	−2.90289e−6	+	5.02795e-6i
$909$	−1.36899e7			−0.549528
$910$	−3.78753e6	+	1.19755e7i	−0.151619	+	0.479392i
$911$	−2.50171e7			−0.998712			−0.499356	−	0.866397i	$-0.666430\pi$
$911$	−2.50171e7			−0.998712			−0.499356	+	0.866397i	$0.666430\pi$
$912$	−5.21064e6	+	9.02509e6i	−0.207445	+	0.359306i
$913$	1.31337e7	+	2.27483e7i	0.521448	+	0.903174i
$914$	−1.36893e7	−	2.37106e7i	−0.542022	−	0.938810i
$915$	7.16256e6	−	1.24059e7i	0.282824	−	0.489865i
$916$	−683288.			−0.0269070
$917$	−2.11253e7	+	4.66373e6i	−0.829620	+	0.183151i
$918$	6.19403e6			0.242586
$919$	−7.74961e6	+	1.34227e7i	−0.302685	+	0.524266i	−0.976743	−	0.214412i	$-0.931216\pi$
$919$	−7.74961e6	+	1.34227e7i	−0.302685	+	0.524266i	0.674058	+	0.738678i	$0.264550\pi$
$920$	−4.67906e6	−	8.10437e6i	−0.182259	−	0.315682i
$921$	−1.06086e7	−	1.83746e7i	−0.412106	−	0.713789i
$922$	9.91905e6	−	1.71803e7i	0.384276	−	0.665585i
$923$	1.56481e7			0.604587
$924$	−4.00818e6	−	4.38195e6i	−0.154443	−	0.168845i
$925$	2.64890e7			1.01791
$926$	1.12905e7	−	1.95556e7i	0.432697	−	0.749453i
$927$	−4.56921e6	−	7.91411e6i	−0.174639	−	0.302484i
$928$	−2.27797e6	−	3.94556e6i	−0.0868316	−	0.150397i
$929$	−1.87643e7	+	3.25007e7i	−0.713333	+	1.23553i	0.250266	+	0.968177i	$0.419482\pi$
$929$	−1.87643e7	+	3.25007e7i	−0.713333	+	1.23553i	−0.963599	+	0.267352i	$0.913852\pi$
$930$	8.71398e6			0.330377
$931$	−1.29594e7	−	9.10852e6i	−0.490015	−	0.344408i
$932$	−915335.			−0.0345176
$933$	−6.46483e6	+	1.11974e7i	−0.243138	+	0.421127i
$934$	−8.70489e6	−	1.50773e7i	−0.326510	−	0.565532i
$935$	−1.48415e7	−	2.57062e7i	−0.555198	−	0.961632i
$936$	2.34740e6	−	4.06582e6i	0.0875786	−	0.151691i
$937$	−1.08298e7			−0.402969			−0.201485	−	0.979492i	$-0.564577\pi$
$937$	−1.08298e7			−0.402969			−0.201485	+	0.979492i	$0.564577\pi$
$938$	−2.82789e7	−	3.09160e7i	−1.04944	−	1.14730i
$939$	7.40520e6			0.274077
$940$	1.16526e6	−	2.01829e6i	0.0430133	−	0.0745013i
$941$	−1.62295e7	−	2.81104e7i	−0.597492	−	1.03489i	−0.993190	−	0.116505i	$-0.962831\pi$
$941$	−1.62295e7	−	2.81104e7i	−0.597492	−	1.03489i	0.395699	−	0.918380i	$-0.370503\pi$
$942$	1.62684e7	+	2.81777e7i	0.597335	+	1.03461i
$943$	−1.06932e7	+	1.85212e7i	−0.391589	+	0.678251i
$944$	−6.32151e7			−2.30883
$945$	−3.57418e6	+	789054.i	−0.130196	+	0.0287427i
$946$	−5.42643e7			−1.97145
$947$	−3.76939e6	+	6.52877e6i	−0.136583	+	0.236568i	−0.926201	−	0.377030i	$-0.876945\pi$
$947$	−3.76939e6	+	6.52877e6i	−0.136583	+	0.236568i	0.789618	+	0.613598i	$0.210279\pi$
$948$	−2.50943e6	−	4.34646e6i	−0.0906890	−	0.157078i
$949$	1.09004e7	+	1.88801e7i	0.392896	+	0.680516i
$950$	4.89328e6	−	8.47541e6i	0.175910	−	0.304686i
$951$	1.59024e7			0.570180
$952$	−7.69608e6	+	2.43336e7i	−0.275218	+	0.870191i
$953$	−3.01356e7			−1.07485			−0.537424	−	0.843312i	$-0.680602\pi$
$953$	−3.01356e7			−1.07485			−0.537424	+	0.843312i	$0.680602\pi$
$954$	520515.	−	901558.i	0.0185166	−	0.0320718i
$955$	1.27914e7	+	2.21554e7i	0.453848	+	0.786089i
$956$	−3.04255e6	−	5.26986e6i	−0.107670	−	0.186489i
$957$	3.79607e6	−	6.57499e6i	0.133985	−	0.232068i
$958$	6.25366e6			0.220151
$959$	−1.49431e6	+	4.72474e6i	−0.0524680	+	0.165894i
$960$	−6.77038e6			−0.237102
$961$	6.66107e6	−	1.15373e7i	0.232667	−	0.402992i
$962$	2.03883e7	+	3.53135e7i	0.710301	+	1.23028i
$963$	903534.	+	1.56497e6i	0.0313963	+	0.0543800i
$964$	−972650.	+	1.68468e6i	−0.0337104	+	0.0583882i
$965$	−2.15841e7			−0.746132
$966$	1.18819e7	−	2.62312e6i	0.409680	−	0.0904430i
$967$	2.88021e6			0.0990509			0.0495255	−	0.998773i	$-0.484229\pi$
$967$	2.88021e6			0.0990509			0.0495255	+	0.998773i	$0.484229\pi$
$968$	1.26712e7	−	2.19472e7i	0.434641	−	0.752820i
$969$	−5.63943e6	−	9.76779e6i	−0.192942	−	0.334185i
$970$	−387110.	−	670494.i	−0.0132101	−	0.0228805i
$971$	1.37245e7	−	2.37715e7i	0.467142	−	0.809113i	−0.532154	−	0.846648i	$-0.678617\pi$
$971$	1.37245e7	−	2.37715e7i	0.467142	−	0.809113i	0.999295	+	0.0375347i	$0.0119505\pi$
$972$	−521426.			−0.0177022
$973$	−9.29799e6	−	1.01650e7i	−0.314852	−	0.344213i
$974$	2.50958e7			0.847626
$975$	−2.86288e6	+	4.95866e6i	−0.0964478	+	0.167052i
$976$	2.52463e7	+	4.37279e7i	0.848347	+	1.46938i
$977$	2.94262e7	+	5.09676e7i	0.986274	+	1.70828i	0.636133	+	0.771579i	$0.280533\pi$
$977$	2.94262e7	+	5.09676e7i	0.986274	+	1.70828i	0.350141	+	0.936697i	$0.386134\pi$
$978$	−1.23702e7	+	2.14258e7i	−0.413551	+	0.716291i
$979$	−9.04164e6			−0.301502
$980$	−511109.	+	5.72511e6i	−0.0170000	+	0.190423i
$981$	−6.78938e6			−0.225246
$982$	−8.41039e6	+	1.45672e7i	−0.278315	+	0.482056i
$983$	−9.30384e6	−	1.61147e7i	−0.307099	−	0.531911i	0.670627	−	0.741794i	$-0.266025\pi$
$983$	−9.30384e6	−	1.61147e7i	−0.307099	−	0.531911i	−0.977726	+	0.209883i	$0.932692\pi$
$984$	8.73014e6	+	1.51210e7i	0.287431	+	0.497845i
$985$	1.47442e7	−	2.55376e7i	0.484205	−	0.838668i
$986$	1.24352e7			0.407342
$987$	−5.36643e6	−	5.86687e6i	−0.175345	−	0.191696i
$988$	3.25815e6			0.106189
$989$	1.20231e7	−	2.08246e7i	0.390865	−	0.676997i
$990$	5.77697e6	+	1.00060e7i	0.187332	+	0.324469i
$991$	−1.23577e7	−	2.14041e7i	−0.399718	−	0.692331i	0.593973	−	0.804485i	$-0.297558\pi$
$991$	−1.23577e7	−	2.14041e7i	−0.399718	−	0.692331i	−0.993691	+	0.112154i	$0.964225\pi$
$992$	−6.08958e6	+	1.05475e7i	−0.196475	+	0.340305i
$993$	27470.5			0.000884083
$994$	3.23329e7	−	7.13797e6i	1.03796	−	0.229144i
$995$	−5.26172e6			−0.168488
$996$	1.81090e6	−	3.13657e6i	0.0578424	−	0.100186i
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	0.972871	−	0.231347i	$-0.0743131\pi$
$997$	8.97906e6	+	1.55522e7i	0.286084	+	0.495511i	−0.686788	+	0.726858i	$0.740980\pi$
$998$	−6.79064e6	−	1.17617e7i	−0.215816	−	0.373805i
$999$	−5.94147e6	+	1.02909e7i	−0.188356	+	0.326243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.b.16.1	yes	4
3.2	odd	2		63.6.e.c.37.2		4
4.3	odd	2		336.6.q.e.289.1		4
7.2	even	3		147.6.a.i.1.2		2
7.3	odd	6		147.6.e.l.67.1		4
7.4	even	3	inner	21.6.e.b.4.1	✓	4
7.5	odd	6		147.6.a.k.1.2		2
7.6	odd	2		147.6.e.l.79.1		4
21.2	odd	6		441.6.a.t.1.1		2
21.5	even	6		441.6.a.s.1.1		2
21.11	odd	6		63.6.e.c.46.2		4
28.11	odd	6		336.6.q.e.193.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.1	✓	4	7.4	even	3	inner
21.6.e.b.16.1	yes	4	1.1	even	1	trivial
63.6.e.c.37.2		4	3.2	odd	2
63.6.e.c.46.2		4	21.11	odd	6
147.6.a.i.1.2		2	7.2	even	3
147.6.a.k.1.2		2	7.5	odd	6
147.6.e.l.67.1		4	7.3	odd	6
147.6.e.l.79.1		4	7.6	odd	2
336.6.q.e.193.1		4	28.11	odd	6
336.6.q.e.289.1		4	4.3	odd	2
441.6.a.s.1.1		2	21.5	even	6
441.6.a.t.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-3.19493 + 5.53379i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-4.41520 - 7.64735i) q^{4} +(-19.3645 + 33.5404i) q^{5} -57.5088 q^{6} +(-87.5000 - 95.6596i) q^{7} -148.051 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(-3.19493 + 5.53379i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-4.41520 - 7.64735i) q^{4} +(-19.3645 + 33.5404i) q^{5} -57.5088 q^{6} +(-87.5000 - 95.6596i) q^{7} -148.051 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-123.737 - 214.318i) q^{10} +(288.195 + 499.168i) q^{11} +(39.7368 - 68.8262i) q^{12} +391.491 q^{13} +(808.916 - 178.580i) q^{14} -348.562 q^{15} +(614.298 - 1064.00i) q^{16} +(664.850 + 1151.55i) q^{17} +(-258.790 - 448.237i) q^{18} +(-471.237 + 816.206i) q^{19} +341.993 q^{20} +(351.842 - 1112.46i) q^{21} -3683.05 q^{22} +(816.040 - 1413.42i) q^{23} +(-666.228 - 1153.94i) q^{24} +(812.530 + 1407.34i) q^{25} +(-1250.79 + 2166.43i) q^{26} -729.000 q^{27} +(-345.212 + 1091.50i) q^{28} -1463.54 q^{29} +(1113.63 - 1928.87i) q^{30} +(1956.21 + 3388.25i) q^{31} +(1556.47 + 2695.89i) q^{32} +(-2593.75 + 4492.51i) q^{33} -8496.61 q^{34} +(4902.85 - 1082.38i) q^{35} +715.262 q^{36} +(8150.17 - 14116.5i) q^{37} +(-3011.14 - 5215.45i) q^{38} +(1761.71 + 3051.37i) q^{39} +(2866.93 - 4965.67i) q^{40} -13103.8 q^{41} +(5032.02 + 5501.27i) q^{42} +14733.5 q^{43} +(2544.88 - 4407.86i) q^{44} +(-1568.53 - 2716.77i) q^{45} +(5214.38 + 9031.58i) q^{46} +(3407.26 - 5901.55i) q^{47} +11057.4 q^{48} +(-1494.50 + 16740.4i) q^{49} -10383.9 q^{50} +(-5983.65 + 10364.0i) q^{51} +(-1728.51 - 2993.87i) q^{52} +(1005.67 + 1741.87i) q^{53} +(2329.11 - 4034.13i) q^{54} -22323.0 q^{55} +(12954.4 + 14162.5i) q^{56} -8482.26 q^{57} +(4675.93 - 8098.94i) q^{58} +(-25726.6 - 44559.7i) q^{59} +(1538.97 + 2665.57i) q^{60} +(-20548.9 + 35591.8i) q^{61} -24999.8 q^{62} +(10254.1 - 2263.74i) q^{63} +19423.8 q^{64} +(-7581.04 + 13130.8i) q^{65} +(-16573.7 - 28706.6i) q^{66} +(-25289.1 - 43802.0i) q^{67} +(5870.89 - 10168.7i) q^{68} +14688.7 q^{69} +(-9674.63 + 30589.5i) q^{70} +39970.6 q^{71} +(5996.05 - 10385.5i) q^{72} +(27843.3 + 48226.0i) q^{73} +(52078.5 + 90202.6i) q^{74} +(-7312.77 + 12666.1i) q^{75} +8322.42 q^{76} +(22533.2 - 71245.8i) q^{77} -22514.2 q^{78} +(31575.7 - 54690.7i) q^{79} +(23791.2 + 41207.6i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(41865.9 - 72513.8i) q^{82} +45572.4 q^{83} +(-10060.8 + 2221.08i) q^{84} -51498.1 q^{85} +(-47072.5 + 81532.0i) q^{86} +(-6585.95 - 11407.2i) q^{87} +(-42667.5 - 73902.2i) q^{88} +(-7843.34 + 13585.1i) q^{89} +20045.4 q^{90} +(-34255.5 - 37449.9i) q^{91} -14411.9 q^{92} +(-17605.9 + 30494.3i) q^{93} +(21771.9 + 37710.1i) q^{94} +(-18250.6 - 31610.9i) q^{95} +(-14008.3 + 24263.0i) q^{96} +3128.49 q^{97} +(-87863.1 - 61754.8i) q^{98} -46687.6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 18 q^{3} - 65 q^{4} + 33 q^{5} + 54 q^{6} - 350 q^{7} - 750 q^{8} - 162 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 18 * q^3 - 65 * q^4 + 33 * q^5 + 54 * q^6 - 350 * q^7 - 750 * q^8 - 162 * q^9	\( 4 q + 3 q^{2} + 18 q^{3} - 65 q^{4} + 33 q^{5} + 54 q^{6} - 350 q^{7} - 750 q^{8} - 162 q^{9} - 921 q^{10} + 1137 q^{11} + 585 q^{12} + 1850 q^{13} + 2352 q^{14} + 594 q^{15} + 895 q^{16} + 324 q^{17} + 243 q^{18} - 2311 q^{19} - 7374 q^{20} - 1575 q^{21} + 3162 q^{22} - 1596 q^{23} - 3375 q^{24} - 395 q^{25} + 2508 q^{26} - 2916 q^{27} + 13531 q^{28} - 4434 q^{29} + 8289 q^{30} - 4294 q^{31} - 1017 q^{32} - 10233 q^{33} - 35880 q^{34} + 15414 q^{35} + 10530 q^{36} + 19109 q^{37} + 6828 q^{38} + 8325 q^{39} - 10545 q^{40} - 25716 q^{41} - 4725 q^{42} - 5542 q^{43} + 36579 q^{44} + 2673 q^{45} + 40740 q^{46} + 23160 q^{47} + 16110 q^{48} - 5978 q^{49} - 58704 q^{50} - 2916 q^{51} - 33424 q^{52} + 31653 q^{53} - 2187 q^{54} + 35778 q^{55} + 65625 q^{56} - 41598 q^{57} + 2277 q^{58} - 41097 q^{59} - 33183 q^{60} - 42052 q^{61} - 204114 q^{62} + 14175 q^{63} - 60062 q^{64} + 23106 q^{65} + 14229 q^{66} - 30763 q^{67} - 44748 q^{68} - 28728 q^{69} + 151179 q^{70} + 204192 q^{71} + 30375 q^{72} + 28577 q^{73} + 77784 q^{74} + 3555 q^{75} + 170384 q^{76} - 96873 q^{77} + 45144 q^{78} + 18464 q^{79} + 71511 q^{80} - 13122 q^{81} + 86040 q^{82} + 122358 q^{83} + 19404 q^{84} - 247272 q^{85} - 258510 q^{86} - 19953 q^{87} - 212565 q^{88} - 29322 q^{89} + 149202 q^{90} - 161875 q^{91} + 333816 q^{92} + 38646 q^{93} - 109938 q^{94} + 61662 q^{95} + 9153 q^{96} - 19582 q^{97} - 462021 q^{98} - 184194 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 18 * q^3 - 65 * q^4 + 33 * q^5 + 54 * q^6 - 350 * q^7 - 750 * q^8 - 162 * q^9 - 921 * q^10 + 1137 * q^11 + 585 * q^12 + 1850 * q^13 + 2352 * q^14 + 594 * q^15 + 895 * q^16 + 324 * q^17 + 243 * q^18 - 2311 * q^19 - 7374 * q^20 - 1575 * q^21 + 3162 * q^22 - 1596 * q^23 - 3375 * q^24 - 395 * q^25 + 2508 * q^26 - 2916 * q^27 + 13531 * q^28 - 4434 * q^29 + 8289 * q^30 - 4294 * q^31 - 1017 * q^32 - 10233 * q^33 - 35880 * q^34 + 15414 * q^35 + 10530 * q^36 + 19109 * q^37 + 6828 * q^38 + 8325 * q^39 - 10545 * q^40 - 25716 * q^41 - 4725 * q^42 - 5542 * q^43 + 36579 * q^44 + 2673 * q^45 + 40740 * q^46 + 23160 * q^47 + 16110 * q^48 - 5978 * q^49 - 58704 * q^50 - 2916 * q^51 - 33424 * q^52 + 31653 * q^53 - 2187 * q^54 + 35778 * q^55 + 65625 * q^56 - 41598 * q^57 + 2277 * q^58 - 41097 * q^59 - 33183 * q^60 - 42052 * q^61 - 204114 * q^62 + 14175 * q^63 - 60062 * q^64 + 23106 * q^65 + 14229 * q^66 - 30763 * q^67 - 44748 * q^68 - 28728 * q^69 + 151179 * q^70 + 204192 * q^71 + 30375 * q^72 + 28577 * q^73 + 77784 * q^74 + 3555 * q^75 + 170384 * q^76 - 96873 * q^77 + 45144 * q^78 + 18464 * q^79 + 71511 * q^80 - 13122 * q^81 + 86040 * q^82 + 122358 * q^83 + 19404 * q^84 - 247272 * q^85 - 258510 * q^86 - 19953 * q^87 - 212565 * q^88 - 29322 * q^89 + 149202 * q^90 - 161875 * q^91 + 333816 * q^92 + 38646 * q^93 - 109938 * q^94 + 61662 * q^95 + 9153 * q^96 - 19582 * q^97 - 462021 * q^98 - 184194 * q^99

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