LMFDB - Embedded newform 21.6.e.b.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:	$4$
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			16.2
Root			$-3.69493 + 2.71062i$ of defining polynomial
Character	$\chi$	$=$	21.16
Dual form			21.6.e.b.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.69493 - 8.13186i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(35.8645 - 62.1192i) q^{5} +84.5088 q^{6} +(-87.5000 + 95.6596i) q^{7} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})$	\(q+(4.69493 - 8.13186i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(35.8645 - 62.1192i) q^{5} +84.5088 q^{6} +(-87.5000 + 95.6596i) q^{7} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-336.763 - 583.291i) q^{10} +(280.305 + 485.503i) q^{11} +(252.763 - 437.799i) q^{12} +533.509 q^{13} +(367.084 + 1160.65i) q^{14} +645.562 q^{15} +(-166.798 + 288.903i) q^{16} +(-502.850 - 870.962i) q^{17} +(380.290 + 658.681i) q^{18} +(-684.263 + 1185.18i) q^{19} -4028.99 q^{20} +(-1139.34 - 251.527i) q^{21} +5264.05 q^{22} +(-1614.04 + 2795.60i) q^{23} +(-1021.27 - 1768.90i) q^{24} +(-1010.03 - 1749.42i) q^{25} +(2504.79 - 4338.42i) q^{26} -729.000 q^{27} +(7110.71 + 1569.80i) q^{28} -753.456 q^{29} +(3030.87 - 5249.62i) q^{30} +(-4103.21 - 7106.97i) q^{31} +(-2064.97 - 3576.64i) q^{32} +(-2522.75 + 4369.52i) q^{33} -9443.39 q^{34} +(2804.15 + 8866.21i) q^{35} +4549.74 q^{36} +(1404.33 - 2432.37i) q^{37} +(6425.14 + 11128.7i) q^{38} +(2400.79 + 4158.29i) q^{39} +(-8139.43 + 14097.9i) q^{40} +245.827 q^{41} +(-7394.52 + 8084.07i) q^{42} -17504.5 q^{43} +(15744.6 - 27270.5i) q^{44} +(2905.03 + 5031.65i) q^{45} +(15155.6 + 26250.3i) q^{46} +(8172.74 - 14155.6i) q^{47} -3002.37 q^{48} +(-1494.50 - 16740.4i) q^{49} -18968.1 q^{50} +(4525.65 - 7838.66i) q^{51} +(-14983.5 - 25952.2i) q^{52} +(14820.8 + 25670.4i) q^{53} +(-3422.61 + 5928.13i) q^{54} +40212.0 q^{55} +(19858.1 - 21709.9i) q^{56} -12316.7 q^{57} +(-3537.43 + 6127.00i) q^{58} +(5178.05 + 8968.65i) q^{59} +(-18130.5 - 31402.9i) q^{60} +(-477.089 + 826.343i) q^{61} -77057.2 q^{62} +(-3166.58 - 10012.2i) q^{63} -49454.8 q^{64} +(19134.0 - 33141.1i) q^{65} +(23688.2 + 41029.2i) q^{66} +(9907.60 + 17160.5i) q^{67} +(-28244.9 + 48921.6i) q^{68} -29052.7 q^{69} +(85264.1 + 18823.3i) q^{70} +62125.4 q^{71} +(9191.45 - 15920.1i) q^{72} +(-13554.8 - 23477.6i) q^{73} +(-13186.5 - 22839.7i) q^{74} +(9090.27 - 15744.8i) q^{75} +76869.6 q^{76} +(-70969.7 - 15667.6i) q^{77} +45086.2 q^{78} +(-22343.7 + 38700.4i) q^{79} +(11964.3 + 20722.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(1154.14 - 1999.03i) q^{82} +15606.6 q^{83} +(19762.8 + 62486.6i) q^{84} -72137.9 q^{85} +(-82182.5 + 142344. i) q^{86} +(-3390.55 - 5872.61i) q^{87} +(-63615.0 - 110184. i) q^{88} +(-6817.66 + 11808.5i) q^{89} +54555.6 q^{90} +(-46682.0 + 51035.2i) q^{91} +181320. q^{92} +(36928.9 - 63962.7i) q^{93} +(-76740.9 - 132919. i) q^{94} +(49081.6 + 85011.8i) q^{95} +(18584.8 - 32189.8i) q^{96} -12919.5 q^{97} +(-143147. - 66442.1i) q^{98} -45409.4 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 $

$2$	4.69493	−	8.13186i	0.829955	−	1.43752i	−0.0681181	−	0.997677i	$-0.521699\pi$
$2$	4.69493	−	8.13186i	0.829955	−	1.43752i	0.898073	−	0.439847i	$-0.144967\pi$
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$3$	4.50000	+	7.79423i	0.288675	+	0.500000i
$4$	−28.0848	−	48.6443i	−0.877650	−	1.52013i
$5$	35.8645	−	62.1192i	0.641564	−	1.11122i	−0.343519	−	0.939146i	$-0.611619\pi$
$5$	35.8645	−	62.1192i	0.641564	−	1.11122i	0.985084	−	0.172076i	$-0.0550476\pi$
$6$	84.5088			0.958349
$7$	−87.5000	+	95.6596i	−0.674937	+	0.737876i
$7$	−87.5000	+	95.6596i	−0.674937	+	0.737876i
$8$	−226.949			−1.25373
$9$	−40.5000	+	70.1481i	−0.166667	+	0.288675i
$10$	−336.763	−	583.291i	−1.06494	−	1.84453i
$11$	280.305	+	485.503i	0.698472	+	1.20979i	0.968996	+	0.247076i	$0.0794698\pi$
$11$	280.305	+	485.503i	0.698472	+	1.20979i	−0.270524	+	0.962713i	$0.587197\pi$
$12$	252.763	−	437.799i	0.506711	−	0.877650i
$13$	533.509			0.875555			0.437777	−	0.899083i	$-0.355766\pi$
$13$	533.509			0.875555			0.437777	+	0.899083i	$0.355766\pi$
$14$	367.084	+	1160.65i	0.500547	+	1.58264i
$15$	645.562			0.740815
$16$	−166.798	+	288.903i	−0.162889	+	0.282132i
$17$	−502.850	−	870.962i	−0.422004	−	0.730932i	0.574132	−	0.818763i	$-0.305340\pi$
$17$	−502.850	−	870.962i	−0.422004	−	0.730932i	−0.996135	+	0.0878311i	$0.972006\pi$
$18$	380.290	+	658.681i	0.276652	+	0.479175i
$19$	−684.263	+	1185.18i	−0.434850	+	0.753182i	−0.997283	−	0.0736606i	$-0.976532\pi$
$19$	−684.263	+	1185.18i	−0.434850	+	0.753182i	0.562434	+	0.826842i	$0.309865\pi$
$20$	−4028.99			−2.25228
$21$	−1139.34	−	251.527i	−0.563775	−	0.124462i
$22$	5264.05			2.31880
$23$	−1614.04	+	2795.60i	−0.636201	+	1.10193i	0.350058	+	0.936728i	$0.386162\pi$
$23$	−1614.04	+	2795.60i	−0.636201	+	1.10193i	−0.986259	+	0.165205i	$0.947171\pi$
$24$	−1021.27	−	1768.90i	−0.361921	−	0.626865i
$25$	−1010.03	−	1749.42i	−0.323209	−	0.559815i
$26$	2504.79	−	4338.42i	0.726671	−	1.25863i
$27$	−729.000			−0.192450
$28$	7110.71	+	1569.80i	1.71403	+	0.378398i
$29$	−753.456			−0.166365			−0.0831827	−	0.996534i	$-0.526508\pi$
$29$	−753.456			−0.166365			−0.0831827	+	0.996534i	$0.526508\pi$
$30$	3030.87	−	5249.62i	0.614843	−	1.06494i
$31$	−4103.21	−	7106.97i	−0.766866	−	1.32825i	−0.939254	−	0.343222i	$-0.888482\pi$
$31$	−4103.21	−	7106.97i	−0.766866	−	1.32825i	0.172389	−	0.985029i	$-0.444852\pi$
$32$	−2064.97	−	3576.64i	−0.356484	−	0.617448i
$33$	−2522.75	+	4369.52i	−0.403263	+	0.698472i
$34$	−9443.39			−1.40098
$35$	2804.15	+	8866.21i	0.386929	+	1.22340i
$36$	4549.74			0.585100
$37$	1404.33	−	2432.37i	0.168642	−	0.292096i	−0.769301	−	0.638887i	$-0.779395\pi$
$37$	1404.33	−	2432.37i	0.168642	−	0.292096i	0.937943	+	0.346791i	$0.112729\pi$
$38$	6425.14	+	11128.7i	0.721811	+	1.25021i
$39$	2400.79	+	4158.29i	0.252751	+	0.437777i
$40$	−8139.43	+	14097.9i	−0.804348	+	1.39317i
$41$	245.827			0.0228387			0.0114193	−	0.999935i	$-0.496365\pi$
$41$	245.827			0.0228387			0.0114193	+	0.999935i	$0.496365\pi$
$42$	−7394.52	+	8084.07i	−0.646825	+	0.707143i
$43$	−17504.5			−1.44371			−0.721853	−	0.692047i	$-0.756709\pi$
$43$	−17504.5			−1.44371			−0.721853	+	0.692047i	$0.756709\pi$
$44$	15744.6	−	27270.5i	1.22603	−	2.12354i
$45$	2905.03	+	5031.65i	0.213855	+	0.370407i
$46$	15155.6	+	26250.3i	1.05604	+	1.82911i
$47$	8172.74	−	14155.6i	0.539663	−	0.934725i	−0.459258	−	0.888303i	$-0.651885\pi$
$47$	8172.74	−	14155.6i	0.539663	−	0.934725i	0.998922	−	0.0464219i	$-0.0147819\pi$
$48$	−3002.37			−0.188088
$49$	−1494.50	−	16740.4i	−0.0889213	−	0.996039i
$50$	−18968.1			−1.07300
$51$	4525.65	−	7838.66i	0.243644	−	0.422004i
$52$	−14983.5	−	25952.2i	−0.768430	−	1.33096i
$53$	14820.8	+	25670.4i	0.724741	+	1.25529i	0.959081	+	0.283133i	$0.0913739\pi$
$53$	14820.8	+	25670.4i	0.724741	+	1.25529i	−0.234340	+	0.972155i	$0.575293\pi$
$54$	−3422.61	+	5928.13i	−0.159725	+	0.276652i
$55$	40212.0			1.79246
$56$	19858.1	−	21709.9i	0.846188	−	0.925097i
$57$	−12316.7			−0.502121
$58$	−3537.43	+	6127.00i	−0.138076	+	0.239154i
$59$	5178.05	+	8968.65i	0.193659	+	0.335426i	0.946460	−	0.322821i	$-0.104631\pi$
$59$	5178.05	+	8968.65i	0.193659	+	0.335426i	−0.752801	+	0.658248i	$0.771298\pi$
$60$	−18130.5	−	31402.9i	−0.650176	−	1.12614i
$61$	−477.089	+	826.343i	−0.0164163	+	0.0284339i	−0.874117	−	0.485716i	$-0.838559\pi$
$61$	−477.089	+	826.343i	−0.0164163	+	0.0284339i	0.857701	+	0.514150i	$0.171892\pi$
$62$	−77057.2			−2.54586
$63$	−3166.58	−	10012.2i	−0.100517	−	0.317817i
$64$	−49454.8			−1.50924
$65$	19134.0	−	33141.1i	0.561725	−	0.972935i
$66$	23688.2	+	41029.2i	0.669380	+	1.15940i
$67$	9907.60	+	17160.5i	0.269638	+	0.467027i	0.968768	−	0.247967i	$-0.0797626\pi$
$67$	9907.60	+	17160.5i	0.269638	+	0.467027i	−0.699130	+	0.714994i	$0.746429\pi$
$68$	−28244.9	+	48921.6i	−0.740743	+	1.28300i
$69$	−29052.7			−0.734622
$70$	85264.1	+	18823.3i	2.07980	+	0.459147i
$71$	62125.4			1.46259			0.731296	−	0.682060i	$-0.238916\pi$
$71$	62125.4			1.46259			0.731296	+	0.682060i	$0.238916\pi$
$72$	9191.45	−	15920.1i	0.208955	−	0.361921i
$73$	−13554.8	−	23477.6i	−0.297705	−	0.515641i	0.677905	−	0.735149i	$-0.262888\pi$
$73$	−13554.8	−	23477.6i	−0.297705	−	0.515641i	−0.975611	+	0.219509i	$0.929555\pi$
$74$	−13186.5	−	22839.7i	−0.279930	−	0.484853i
$75$	9090.27	−	15744.8i	0.186605	−	0.323209i
$76$	76869.6			1.52658
$77$	−70969.7	−	15667.6i	−1.36410	−	0.301145i
$78$	45086.2			0.839087
$79$	−22343.7	+	38700.4i	−0.402798	+	0.697666i	−0.994062	−	0.108812i	$-0.965295\pi$
$79$	−22343.7	+	38700.4i	−0.402798	+	0.697666i	0.591265	+	0.806477i	$0.298629\pi$
$80$	11964.3	+	20722.8i	0.209008	+	0.362012i
$81$	−3280.50	−	5681.99i	−0.0555556	−	0.0962250i
$82$	1154.14	−	1999.03i	0.0189551	−	0.0328311i
$83$	15606.6			0.248665			0.124332	−	0.992241i	$-0.460321\pi$
$83$	15606.6			0.248665			0.124332	+	0.992241i	$0.460321\pi$
$84$	19762.8	+	62486.6i	0.305599	+	0.966248i
$85$	−72137.9			−1.08297
$86$	−82182.5	+	142344.i	−1.19821	+	2.07536i
$87$	−3390.55	−	5872.61i	−0.0480255	−	0.0831827i
$88$	−63615.0	−	110184.i	−0.875696	−	1.51675i
$89$	−6817.66	+	11808.5i	−0.0912347	+	0.158023i	−0.908031	−	0.418903i	$-0.862415\pi$
$89$	−6817.66	+	11808.5i	−0.0912347	+	0.158023i	0.816796	+	0.576926i	$0.195748\pi$
$90$	54555.6			0.709959
$91$	−46682.0	+	51035.2i	−0.590944	+	0.646050i
$92$	181320.			2.23345
$93$	36928.9	−	63962.7i	0.442750	−	0.766866i
$94$	−76740.9	−	132919.i	−0.895793	−	1.55156i
$95$	49081.6	+	85011.8i	0.557968	+	0.966429i
$96$	18584.8	−	32189.8i	0.205816	−	0.356484i
$97$	−12919.5			−0.139417			−0.0697086	−	0.997567i	$-0.522207\pi$
$97$	−12919.5			−0.139417			−0.0697086	+	0.997567i	$0.522207\pi$
$98$	−143147.	−	66442.1i	−1.50563	−	0.698841i
$99$	−45409.4			−0.465648
$100$	−56733.0	+	98264.4i	−0.567330	+	0.982644i
$101$	−12571.5	−	21774.4i	−0.122626	−	0.212394i	0.798177	−	0.602424i	$-0.205798\pi$
$101$	−12571.5	−	21774.4i	−0.122626	−	0.212394i	−0.920802	+	0.390029i	$0.872465\pi$
$102$	−42495.3	−	73604.0i	−0.404427	−	0.700488i
$103$	80376.6	−	139216.i	0.746511	−	1.29300i	−0.202974	−	0.979184i	$-0.565061\pi$
$103$	80376.6	−	139216.i	0.746511	−	1.29300i	0.949485	−	0.313811i	$-0.101606\pi$
$104$	−121079.			−1.09771
$105$	−56486.6	+	61754.1i	−0.500003	+	0.546629i
$106$	278331.			2.40601
$107$	47187.8	−	81731.6i	0.398446	−	0.690129i	−0.595088	−	0.803661i	$-0.702883\pi$
$107$	47187.8	−	81731.6i	0.398446	−	0.690129i	0.993534	+	0.113531i	$0.0362162\pi$
$108$	20473.8	+	35461.7i	0.168904	+	0.292550i
$109$	41696.7	+	72220.9i	0.336152	+	0.582233i	0.983705	−	0.179788i	$-0.0575410\pi$
$109$	41696.7	+	72220.9i	0.336152	+	0.582233i	−0.647553	+	0.762020i	$0.724208\pi$
$110$	188793.	−	326999.i	1.48766	−	2.57670i
$111$	25278.0			0.194731
$112$	−13041.5	−	41234.9i	−0.0982387	−	0.310613i
$113$	−179254.			−1.32060			−0.660301	−	0.751001i	$-0.729571\pi$
$113$	−179254.			−1.32060			−0.660301	+	0.751001i	$0.729571\pi$
$114$	−57826.3	+	100158.i	−0.416738	+	0.721811i
$115$	115774.	+	200526.i	0.816328	+	1.41392i
$116$	21160.7	+	36651.3i	0.146011	+	0.252898i
$117$	−21607.1	+	37424.6i	−0.145926	+	0.252751i
$118$	97242.5			0.642911
$119$	127315.	+	28106.8i	0.824163	+	0.181946i
$120$	−146510.			−0.928781
$121$	−76616.4	+	132703.i	−0.475727	+	0.823984i
$122$	4479.80	+	7759.25i	0.0272496	+	0.0471976i
$123$	1106.22	+	1916.04i	0.00659295	+	0.0114193i
$124$	−230476.	+	399195.i	−1.34608	+	2.33148i
$125$	79256.4			0.453690
$126$	−96284.5	−	21256.2i	−0.540294	−	0.119278i
$127$	−143674.			−0.790440			−0.395220	−	0.918586i	$-0.629332\pi$
$127$	−143674.			−0.790440			−0.395220	+	0.918586i	$0.629332\pi$
$128$	−166108.	+	287707.i	−0.896117	+	1.55212i
$129$	−78770.2	−	136434.i	−0.416762	−	0.721853i
$130$	−179666.	−	311191.i	−0.932412	−	1.61498i
$131$	−26144.9	+	45284.3i	−0.133110	+	0.230553i	−0.924874	−	0.380274i	$-0.875830\pi$
$131$	−26144.9	+	45284.3i	−0.133110	+	0.230553i	0.791764	+	0.610827i	$0.209163\pi$
$132$	283403.			1.41570
$133$	−53500.6	−	169159.i	−0.262259	−	0.829215i
$134$	186062.			0.895150
$135$	−26145.2	+	45284.9i	−0.123469	+	0.213855i
$136$	114122.	+	197664.i	0.529079	+	0.916391i
$137$	−4705.05	−	8149.39i	−0.0214172	−	0.0370957i	0.855118	−	0.518433i	$-0.173484\pi$
$137$	−4705.05	−	8149.39i	−0.0214172	−	0.0370957i	−0.876535	+	0.481337i	$0.840151\pi$
$138$	−136401.	+	236253.i	−0.609703	+	1.05604i
$139$	183094.			0.803781			0.401890	−	0.915688i	$-0.368353\pi$
$139$	183094.			0.803781			0.401890	+	0.915688i	$0.368353\pi$
$140$	352537.	−	385412.i	1.52014	−	1.66190i
$141$	147109.			0.623150
$142$	291674.	−	505195.i	1.21389	−	2.10251i
$143$	149545.	+	259020.i	0.611551	+	1.05924i
$144$	−13510.7	−	23401.2i	−0.0542964	−	0.0940441i
$145$	−27022.3	+	46804.1i	−0.106734	+	0.184869i
$146$	−254556.			−0.988328
$147$	123753.	−	86980.4i	0.472350	−	0.331992i
$148$	−157762.			−0.592034
$149$	83500.8	−	144628.i	0.308123	−	0.533685i	−0.669828	−	0.742516i	$-0.733632\pi$
$149$	83500.8	−	144628.i	0.308123	−	0.533685i	0.977952	+	0.208830i	$0.0669657\pi$
$150$	−85356.4	−	147842.i	−0.309748	−	0.536499i
$151$	−188132.	−	325855.i	−0.671461	−	1.16300i	−0.977490	−	0.210982i	$-0.932334\pi$
$151$	−188132.	−	325855.i	−0.671461	−	1.16300i	0.306029	−	0.952022i	$-0.401000\pi$
$152$	155293.	−	268976.i	0.545184	−	0.944286i
$153$	81461.7			0.281336
$154$	−460605.	+	503557.i	−1.56504	+	1.71099i
$155$	−588639.			−1.96797
$156$	134851.	−	233569.i	0.443654	−	0.768430i
$157$	−19537.5	−	33840.0i	−0.0632587	−	0.109567i	0.832662	−	0.553782i	$-0.186816\pi$
$157$	−19537.5	−	33840.0i	−0.0632587	−	0.109567i	−0.895920	+	0.444215i	$0.853483\pi$
$158$	209804.	+	363391.i	0.668608	+	1.15806i
$159$	−133387.	+	231034.i	−0.418429	+	0.724741i
$160$	−296237.			−0.914829
$161$	−126197.	−	399013.i	−0.383694	−	1.21317i
$162$	−61606.9			−0.184434
$163$	238959.	−	413890.i	0.704458	−	1.22016i	−0.262428	−	0.964951i	$-0.584523\pi$
$163$	238959.	−	413890.i	0.704458	−	1.22016i	0.966887	−	0.255206i	$-0.0821433\pi$
$164$	−6904.01	−	11958.1i	−0.0200444	−	0.0347178i
$165$	180954.	+	313422.i	0.517439	+	0.896230i
$166$	73272.1	−	126911.i	0.206381	−	0.357462i
$167$	39793.4			0.110413			0.0552064	−	0.998475i	$-0.482418\pi$
$167$	39793.4			0.110413			0.0552064	+	0.998475i	$0.482418\pi$
$168$	258573.	+	57083.9i	0.706822	+	0.156042i
$169$	−86661.4			−0.233404
$170$	−338683.	+	586616.i	−0.898816	+	1.55680i
$171$	−55425.3	−	95999.5i	−0.144950	−	0.251061i
$172$	491610.	+	851494.i	1.26707	+	2.19463i
$173$	−24169.1	+	41862.1i	−0.0613968	+	0.106342i	−0.895090	−	0.445886i	$-0.852889\pi$
$173$	−24169.1	+	41862.1i	−0.0613968	+	0.106342i	0.833693	+	0.552228i	$0.186222\pi$
$174$	−63673.7			−0.159436
$175$	255727.	+	56455.5i	0.631220	+	0.139351i
$176$	−187018.			−0.455094
$177$	−46602.5	+	80717.9i	−0.111809	+	0.193659i
$178$	64016.9	+	110881.i	0.151441	+	0.262304i
$179$	71455.3	+	123764.i	0.166687	+	0.288711i	0.937253	−	0.348650i	$-0.113360\pi$
$179$	71455.3	+	123764.i	0.166687	+	0.288711i	−0.770566	+	0.637360i	$0.780026\pi$
$180$	163174.	−	282626.i	0.375379	−	0.650176i
$181$	−77245.3			−0.175257			−0.0876285	−	0.996153i	$-0.527929\pi$
$181$	−77245.3			−0.175257			−0.0876285	+	0.996153i	$0.527929\pi$
$182$	195842.	+	619219.i	0.438256	+	1.38569i
$183$	−8587.61			−0.0189559
$184$	366305.	−	634459.i	0.797625	−	1.38153i
$185$	−100731.	−	174472.i	−0.216389	−	0.374797i
$186$	−346757.	−	600601.i	−0.734925	−	1.27293i
$187$	281903.	−	488270.i	0.589516	−	1.02107i
$188$	−918119.			−1.89454
$189$	63787.5	−	69735.8i	0.129892	−	0.142004i
$190$	921739.			1.85235
$191$	−136027.	+	235606.i	−0.269800	+	0.467307i	−0.968810	−	0.247805i	$-0.920291\pi$
$191$	−136027.	+	235606.i	−0.269800	+	0.467307i	0.699010	+	0.715112i	$0.253624\pi$
$192$	−222546.	−	385462.i	−0.435680	−	0.754620i
$193$	8016.89	+	13885.7i	0.0154922	+	0.0268333i	0.873668	−	0.486523i	$-0.161735\pi$
$193$	8016.89	+	13885.7i	0.0154922	+	0.0268333i	−0.858175	+	0.513357i	$0.828402\pi$
$194$	−60656.2	+	105060.i	−0.115710	+	0.200415i
$195$	344413.			0.648624
$196$	−772353.	+	542850.i	−1.43607	+	1.00935i
$197$	1.03228e6			1.89510			0.947552	−	0.319603i	$-0.103549\pi$
$197$	1.03228e6			1.89510			0.947552	+	0.319603i	$0.103549\pi$
$198$	−213194.	+	369263.i	−0.386467	+	0.669380i
$199$	440868.	+	763606.i	0.789180	+	1.36690i	0.926470	+	0.376369i	$0.122827\pi$
$199$	440868.	+	763606.i	0.789180	+	1.36690i	−0.137290	+	0.990531i	$0.543839\pi$
$200$	229226.	+	397030.i	0.405217	+	0.701857i
$201$	−89168.4	+	154444.i	−0.155676	+	0.269638i
$202$	−236089.			−0.407096
$203$	65927.4	−	72075.3i	0.112286	−	0.122757i
$204$	−508408.			−0.855337
$205$	8816.49	−	15270.6i	0.0146525	−	0.0253788i
$206$	−754725.	−	1.30722e6i	−1.23914	−	2.14626i
$207$	−130737.	−	226443.i	−0.212067	−	0.367311i
$208$	−88988.4	+	154132.i	−0.142618	+	0.247022i
$209$	−767210.			−1.21492
$210$	236975.	+	749273.i	0.370813	+	1.17244i
$211$	−372813.			−0.576480			−0.288240	−	0.957558i	$-0.593070\pi$
$211$	−372813.			−0.576480			−0.288240	+	0.957558i	$0.593070\pi$
$212$	832480.	−	1.44190e6i	1.27214	−	2.20341i
$213$	279564.	+	484219.i	0.422214	+	0.731296i
$214$	−443087.	−	767449.i	−0.661385	−	1.14555i
$215$	−627791.	+	1.08737e6i	−0.926230	+	1.60428i
$216$	165446.			0.241280
$217$	1.03888e6	+	229348.i	1.49767	+	0.330633i
$218$	783054.			1.11596
$219$	121993.	−	211299.i	0.171880	−	0.297705i
$220$	−1.12935e6	−	1.95609e6i	−1.57315	−	2.72478i
$221$	−268275.	−	464666.i	−0.369487	−	0.639971i
$222$	118678.	−	205557.i	0.161618	−	0.279930i
$223$	−1.08205e6			−1.45708			−0.728541	−	0.685002i	$-0.759801\pi$
$223$	−1.08205e6			−1.45708			−0.728541	+	0.685002i	$0.759801\pi$
$224$	522825.	+	115422.i	0.696204	+	0.153697i
$225$	163625.			0.215473
$226$	−841584.	+	1.45767e6i	−1.09604	+	1.89840i
$227$	−276524.	−	478954.i	−0.356179	−	0.616921i	0.631140	−	0.775669i	$-0.282587\pi$
$227$	−276524.	−	478954.i	−0.356179	−	0.616921i	−0.987319	+	0.158748i	$0.949254\pi$
$228$	345913.	+	599139.i	0.440687	+	0.763292i
$229$	−261512.	+	452952.i	−0.329536	+	0.570773i	−0.982420	−	0.186685i	$-0.940226\pi$
$229$	−261512.	+	452952.i	−0.329536	+	0.570773i	0.652884	+	0.757458i	$0.273559\pi$
$230$	2.17420e6			2.71006
$231$	−197246.	−	623658.i	−0.243209	−	0.768983i
$232$	170996.			0.208577
$233$	182090.	−	315390.i	0.219734	−	0.380590i	−0.734993	−	0.678075i	$-0.762814\pi$
$233$	182090.	−	315390.i	0.219734	−	0.380590i	0.954727	+	0.297485i	$0.0961477\pi$
$234$	202888.	+	351412.i	0.242224	+	0.419544i
$235$	−586223.	−	1.01537e6i	−0.692458	−	1.19937i
$236$	290849.	−	503766.i	0.339929	−	0.588774i
$237$	−402186.			−0.465111
$238$	826297.	−	903351.i	0.945570	−	1.03375i
$239$	371841.			0.421078			0.210539	−	0.977585i	$-0.432478\pi$
$239$	371841.			0.421078			0.210539	+	0.977585i	$0.432478\pi$
$240$	−107679.	+	186505.i	−0.120671	+	0.209008i
$241$	855737.	+	1.48218e6i	0.949069	+	1.64384i	0.747391	+	0.664384i	$0.231306\pi$
$241$	855737.	+	1.48218e6i	0.949069	+	1.64384i	0.201678	+	0.979452i	$0.435360\pi$
$242$	719417.	+	1.24607e6i	0.789664	+	1.36774i
$243$	29524.5	−	51137.9i	0.0320750	−	0.0555556i
$244$	53595.8			0.0576310
$245$	−1.09350e6	−	507550.i	−1.16387	−	0.540212i
$246$	20774.6			0.0218874
$247$	−365060.	+	632303.i	−0.380735	+	0.659452i
$248$	931221.	+	1.61292e6i	0.961443	+	1.66527i
$249$	70229.9	+	121642.i	0.0717833	+	0.124332i
$250$	372103.	−	644502.i	0.376542	−	0.652190i
$251$	58134.1			0.0582434			0.0291217	−	0.999576i	$-0.490729\pi$
$251$	58134.1			0.0582434			0.0291217	+	0.999576i	$0.490729\pi$
$252$	−398102.	+	435226.i	−0.394905	+	0.431731i
$253$	−1.80969e6			−1.77748
$254$	−674540.	+	1.16834e6i	−0.656030	+	1.13628i
$255$	−324621.	−	562260.i	−0.312627	−	0.541485i
$256$	768453.	+	1.33100e6i	0.732853	+	1.26934i
$257$	155920.	−	270061.i	0.147254	−	0.255052i	−0.782957	−	0.622075i	$-0.786290\pi$
$257$	155920.	−	270061.i	0.147254	−	0.255052i	0.930212	+	0.367023i	$0.119623\pi$
$258$	−1.47928e6			−1.38357
$259$	109801.	+	347171.i	0.101708	+	0.321583i
$260$	−2.14950e6			−1.97199
$261$	30515.0	−	52853.5i	0.0277276	−	0.0480255i
$262$	245497.	+	425214.i	0.220950	+	0.382696i
$263$	−431983.	−	748216.i	−0.385103	−	0.667018i	0.606681	−	0.794946i	$-0.292501\pi$
$263$	−431983.	−	748216.i	−0.385103	−	0.667018i	−0.991783	+	0.127928i	$0.959167\pi$
$264$	572535.	−	991660.i	0.505583	−	0.875696i
$265$	2.12617e6			1.85987
$266$	−1.62676e6	−	359133.i	−1.40968	−	0.311208i
$267$	−122718.			−0.105349
$268$	556506.	−	963896.i	0.473296	−	0.819773i
$269$	560346.	+	970548.i	0.472145	+	0.817779i	0.999492	−	0.0318707i	$-0.0101465\pi$
$269$	560346.	+	970548.i	0.472145	+	0.817779i	−0.527347	+	0.849650i	$0.676813\pi$
$270$	245500.	+	425219.i	0.204948	+	0.354980i
$271$	−570058.	+	987369.i	−0.471515	+	0.816688i	−0.999469	−	0.0325848i	$-0.989626\pi$
$271$	−570058.	+	987369.i	−0.471515	+	0.816688i	0.527954	+	0.849273i	$0.322959\pi$
$272$	335498.			0.274959
$273$	−607849.	−	134192.i	−0.493616	−	0.108973i
$274$	−88359.6			−0.0711013
$275$	566233.	−	980744.i	0.451506	−	0.782031i
$276$	815940.	+	1.41325e6i	0.644741	+	1.11672i
$277$	994005.	+	1.72167e6i	0.778375	+	1.34819i	0.932878	+	0.360193i	$0.117289\pi$
$277$	994005.	+	1.72167e6i	0.778375	+	1.34819i	−0.154502	+	0.987992i	$0.549377\pi$
$278$	859615.	−	1.48890e6i	0.667102	−	1.15545i
$279$	664720.			0.511244
$280$	−636399.	−	2.01218e6i	−0.485104	−	1.53381i
$281$	532321.			0.402168			0.201084	−	0.979574i	$-0.435554\pi$
$281$	532321.			0.402168			0.201084	+	0.979574i	$0.435554\pi$
$282$	690668.	−	1.19627e6i	0.517186	−	0.895793i
$283$	−1.31237e6	−	2.27308e6i	−0.974067	−	1.68713i	−0.682980	−	0.730437i	$-0.739316\pi$
$283$	−1.31237e6	−	2.27308e6i	−0.974067	−	1.68713i	−0.291087	−	0.956697i	$-0.594017\pi$
$284$	−1.74478e6	−	3.02205e6i	−1.28364	−	2.22334i
$285$	−441734.	+	765106.i	−0.322143	+	0.557968i
$286$	2.80842e6			2.03024
$287$	−21509.9	+	23515.7i	−0.0154146	+	0.0168521i
$288$	334526.			0.237656
$289$	204212.	−	353705.i	0.143826	−	0.249113i
$290$	253736.	+	439484.i	0.177169	+	0.306866i
$291$	−58137.7	−	100697.i	−0.0402463	−	0.0697086i
$292$	−761369.	+	1.31873e6i	−0.522562	+	0.905104i
$293$	609962.			0.415082			0.207541	−	0.978226i	$-0.433454\pi$
$293$	609962.			0.415082			0.207541	+	0.978226i	$0.433454\pi$
$294$	−126298.	−	1.41471e6i	−0.0852176	−	0.954553i
$295$	742834.			0.496978
$296$	−318712.	+	552026.i	−0.211431	+	0.366210i
$297$	−204342.	−	353931.i	−0.134421	−	0.232824i
$298$	−784061.	−	1.35803e6i	−0.511457	−	0.885870i
$299$	−861104.	+	1.49148e6i	−0.557029	+	0.964802i
$300$	−1.02119e6			−0.655096
$301$	1.53164e6	−	1.67447e6i	0.974409	−	1.06528i
$302$	−3.53307e6			−2.22913
$303$	113143.	−	195970.i	0.0707981	−	0.122626i
$304$	−228268.	−	395372.i	−0.141665	−	0.245370i
$305$	34221.2	+	59272.8i	0.0210642	+	0.0364843i
$306$	382457.	−	662436.i	0.233496	−	0.404427i
$307$	−1.34843e6			−0.816551			−0.408275	−	0.912859i	$-0.633870\pi$
$307$	−1.34843e6			−0.816551			−0.408275	+	0.912859i	$0.633870\pi$
$308$	1.23103e6	+	3.89229e6i	0.739420	+	2.33791i
$309$	1.44678e6			0.861997
$310$	−2.76362e6	+	4.78673e6i	−1.63333	+	2.82901i
$311$	1.66530e6	+	2.88439e6i	0.976320	+	1.69104i	0.675507	+	0.737353i	$0.263925\pi$
$311$	1.66530e6	+	2.88439e6i	0.976320	+	1.69104i	0.300813	+	0.953683i	$0.402742\pi$
$312$	−544858.	−	943721.i	−0.316881	−	0.548854i
$313$	1.41835e6	−	2.45666e6i	0.818320	−	1.41737i	−0.0885991	−	0.996067i	$-0.528239\pi$
$313$	1.41835e6	−	2.45666e6i	0.818320	−	1.41737i	0.906919	−	0.421305i	$-0.138428\pi$
$314$	−366909.			−0.210007
$315$	−735516.	−	162376.i	−0.417653	−	0.0922032i
$316$	2.51007e6			1.41406
$317$	544195.	−	942574.i	0.304163	−	0.526826i	−0.672912	−	0.739723i	$-0.734957\pi$
$317$	544195.	−	942574.i	0.304163	−	0.526826i	0.977075	+	0.212897i	$0.0682899\pi$
$318$	1.25249e6	+	2.16938e6i	0.694555	+	1.20300i
$319$	−211198.	−	365805.i	−0.116202	−	0.201267i
$320$	−1.77367e6	+	3.07209e6i	−0.968274	+	1.67710i
$321$	849380.			0.460086
$322$	−3.83721e6	−	847122.i	−2.06241	−	0.455309i
$323$	1.37633e6			0.734033
$324$	−184264.	+	319155.i	−0.0975167	+	0.168904i
$325$	−538860.	−	933332.i	−0.282988	−	0.490149i
$326$	−2.24380e6	−	3.88637e6i	−1.16934	−	2.02535i
$327$	−375271.	+	649988.i	−0.194078	+	0.336152i
$328$	−55790.4			−0.0286335
$329$	639004.	+	2.02042e6i	0.325472	+	1.02908i
$330$	3.39827e6			1.71780
$331$	−652773.	+	1.13064e6i	−0.327485	+	0.567221i	−0.982012	−	0.188817i	$-0.939535\pi$
$331$	−652773.	+	1.13064e6i	−0.327485	+	0.567221i	0.654527	+	0.756039i	$0.272868\pi$
$332$	−438309.	−	759174.i	−0.218241	−	0.378004i
$333$	113751.	+	197022.i	0.0562140	+	0.0973654i
$334$	186827.	−	323594.i	0.0916376	−	0.158721i
$335$	1.42133e6			0.691961
$336$	262707.	−	287206.i	0.126948	−	0.138786i
$337$	−3.17016e6			−1.52057			−0.760285	−	0.649590i	$-0.774941\pi$
$337$	−3.17016e6			−1.52057			−0.760285	+	0.649590i	$0.774941\pi$
$338$	−406869.	+	704718.i	−0.193715	+	0.335524i
$339$	−806641.	−	1.39714e6i	−0.381225	−	0.660301i
$340$	2.02598e6	+	3.50910e6i	0.950469	+	1.64626i
$341$	2.30030e6	−	3.98424e6i	1.07127	−	1.85549i
$342$	−1.04087e6			−0.481207
$343$	1.73215e6	+	1.32182e6i	0.794969	+	0.606650i
$344$	3.97263e6			1.81002
$345$	−1.04196e6	+	1.80473e6i	−0.471307	+	0.816328i
$346$	226945.	+	393080.i	0.101913	+	0.176519i
$347$	857958.	+	1.48603e6i	0.382510	+	0.662526i	0.991420	−	0.130713i	$-0.0417265\pi$
$347$	857958.	+	1.48603e6i	0.382510	+	0.662526i	−0.608911	+	0.793239i	$0.708393\pi$
$348$	−190446.	+	329862.i	−0.0842992	+	0.146011i
$349$	−2.95822e6			−1.30007			−0.650034	−	0.759905i	$-0.725245\pi$
$349$	−2.95822e6			−1.30007			−0.650034	+	0.759905i	$0.725245\pi$
$350$	1.65971e6	−	1.81448e6i	0.724205	−	0.791739i
$351$	−388928.			−0.168501
$352$	1.15765e6	−	2.00510e6i	0.497988	−	0.862541i
$353$	−1.88490e6	−	3.26474e6i	−0.805103	−	1.39448i	−0.916222	−	0.400672i	$-0.868777\pi$
$353$	−1.88490e6	−	3.26474e6i	−0.805103	−	1.39448i	0.111119	−	0.993807i	$-0.464557\pi$
$354$	437591.	+	757930.i	0.185592	+	0.321456i
$355$	2.22810e6	−	3.85918e6i	0.938347	−	1.62526i
$356$	765890.			0.320289
$357$	353848.	+	1.11880e6i	0.146942	+	0.464605i
$358$	1.34191e6			0.553371
$359$	−964935.	+	1.67132e6i	−0.395150	+	0.684420i	−0.993120	−	0.117099i	$-0.962641\pi$
$359$	−964935.	+	1.67132e6i	−0.395150	+	0.684420i	0.597970	+	0.801518i	$0.295974\pi$
$360$	−659294.	−	1.14193e6i	−0.268116	−	0.464391i
$361$	301617.	+	522416.i	0.121811	+	0.210984i
$362$	−362662.	+	628148.i	−0.145455	+	0.251936i
$363$	−1.37909e6			−0.549323
$364$	3.79363e6	+	837500.i	1.50073	+	0.331308i
$365$	−1.94455e6			−0.763988
$366$	−40318.2	+	69833.2i	−0.0157325	+	0.0272496i
$367$	−1.18371e6	−	2.05025e6i	−0.458754	−	0.794586i	0.540141	−	0.841575i	$-0.318371\pi$
$367$	−1.18371e6	−	2.05025e6i	−0.458754	−	0.794586i	−0.998895	+	0.0469885i	$0.985038\pi$
$368$	−538438.	−	932603.i	−0.207260	−	0.358986i
$369$	−9956.01	+	17244.3i	−0.00380644	+	0.00659295i
$370$	−1.89171e6			−0.718373
$371$	−3.75244e6	−	828409.i	−1.41540	−	0.312471i
$372$	−4.14856e6			−1.55432
$373$	−1.76914e6	+	3.06425e6i	−0.658402	+	1.14039i	0.322627	+	0.946526i	$0.395434\pi$
$373$	−1.76914e6	+	3.06425e6i	−0.658402	+	1.14039i	−0.981029	+	0.193860i	$0.937899\pi$
$374$	−2.64703e6	−	4.58479e6i	−0.978543	−	1.69489i
$375$	356654.	+	617742.i	0.130969	+	0.226845i
$376$	−1.85480e6	+	3.21260e6i	−0.676592	+	1.17189i
$377$	−401975.			−0.145662
$378$	−267604.	−	846116.i	−0.0963304	−	0.304579i
$379$	1.79847e6			0.643139			0.321569	−	0.946886i	$-0.395790\pi$
$379$	1.79847e6			0.643139			0.321569	+	0.946886i	$0.395790\pi$
$380$	2.75689e6	−	4.77508e6i	0.979401	−	1.69637i
$381$	−646533.	−	1.11983e6i	−0.228180	−	0.395220i
$382$	1.27728e6	+	2.21231e6i	0.447843	+	0.775687i
$383$	−1.30407e6	+	2.25872e6i	−0.454261	+	0.786802i	−0.998645	−	0.0520333i	$-0.983430\pi$
$383$	−1.30407e6	+	2.25872e6i	−0.454261	+	0.786802i	0.544385	+	0.838836i	$0.316763\pi$
$384$	−2.98994e6			−1.03475
$385$	−3.51855e6	+	3.84667e6i	−1.20980	+	1.32261i
$386$	150555.			0.0514313
$387$	708932.	−	1.22791e6i	0.240618	−	0.416762i
$388$	362841.	+	628460.i	0.122359	+	0.211933i
$389$	1.41498e6	+	2.45081e6i	0.474106	+	0.821175i	0.999560	−	0.0296466i	$-0.00943818\pi$
$389$	1.41498e6	+	2.45081e6i	0.474106	+	0.821175i	−0.525455	+	0.850821i	$0.676105\pi$
$390$	1.61700e6	−	2.80072e6i	0.538328	−	0.932412i
$391$	3.24648e6			1.07392
$392$	339176.	+	3.79923e6i	0.111483	+	1.24876i
$393$	−470609.			−0.153702
$394$	4.84650e6	−	8.39438e6i	1.57285	−	2.72426i
$395$	1.60269e6	+	2.77594e6i	0.516841	+	0.895195i
$396$	1.27531e6	+	2.20891e6i	0.408676	+	0.707848i
$397$	1.21531e6	−	2.10498e6i	0.387000	−	0.670303i	−0.605045	−	0.796191i	$-0.706845\pi$
$397$	1.21531e6	−	2.10498e6i	0.387000	−	0.670303i	0.992044	+	0.125888i	$0.0401781\pi$
$398$	8.27939e6			2.61993
$399$	1.07771e6	−	1.17821e6i	0.338900	−	0.370503i
$400$	673885.			0.210589
$401$	1.21592e6	−	2.10604e6i	0.377611	−	0.654041i	−0.613103	−	0.790003i	$-0.710079\pi$
$401$	1.21592e6	−	2.10604e6i	0.377611	−	0.654041i	0.990714	+	0.135962i	$0.0434124\pi$
$402$	837279.	+	1.45021e6i	0.258408	+	0.447575i
$403$	−2.18910e6	−	3.79163e6i	−0.671433	−	1.16296i
$404$	−706134.	+	1.22306e6i	−0.215245	+	0.372816i
$405$	−470614.			−0.142570
$406$	−276581.	−	874501.i	−0.0832737	−	0.263297i
$407$	1.57457e6			0.471167
$408$	−1.02709e6	+	1.77898e6i	−0.305464	+	0.529079i
$409$	2.38733e6	+	4.13497e6i	0.705674	+	1.22226i	0.966448	+	0.256863i	$0.0826889\pi$
$409$	2.38733e6	+	4.13497e6i	0.705674	+	1.22226i	−0.260774	+	0.965400i	$0.583978\pi$
$410$	−82785.6	−	143389.i	−0.0243218	−	0.0421266i
$411$	42345.5	−	73344.5i	0.0123652	−	0.0214172i
$412$	−9.02944e6			−2.62070
$413$	−1.31102e6	−	289427.i	−0.378210	−	0.0834956i
$414$	−2.45521e6			−0.704024
$415$	559725.	−	969472.i	0.159534	−	0.276322i
$416$	−1.10168e6	−	1.90817e6i	−0.312121	−	0.540609i
$417$	823924.	+	1.42708e6i	0.232032	+	0.401890i
$418$	−3.60200e6	+	6.23884e6i	−1.00833	+	1.74648i
$419$	−457181.			−0.127219			−0.0636097	−	0.997975i	$-0.520261\pi$
$419$	−457181.			−0.127219			−0.0636097	+	0.997975i	$0.520261\pi$
$420$	4.59040e6	+	1.01340e6i	1.26978	+	0.280322i
$421$	−1.82396e6			−0.501545			−0.250773	−	0.968046i	$-0.580685\pi$
$421$	−1.82396e6			−0.501545			−0.250773	+	0.968046i	$0.580685\pi$
$422$	−1.75033e6	+	3.03166e6i	−0.478453	+	0.828704i
$423$	661992.	+	1.14660e6i	0.179888	+	0.311575i
$424$	−3.36358e6	−	5.82589e6i	−0.908629	−	1.57379i
$425$	−1.01579e6	+	1.75939e6i	−0.272791	+	0.472488i
$426$	5.25014e6			1.40167
$427$	−37302.3	−	117943.i	−0.00990069	−	0.0313042i
$428$	−5.30104e6			−1.39879
$429$	−1.34591e6	+	2.33118e6i	−0.353079	+	0.611551i
$430$	5.89487e6	+	1.02102e7i	1.53746	+	2.66295i
$431$	1.69124e6	+	2.92932e6i	0.438544	+	0.759580i	0.997577	−	0.0695651i	$-0.0221612\pi$
$431$	1.69124e6	+	2.92932e6i	0.438544	+	0.759580i	−0.559034	+	0.829145i	$0.688828\pi$
$432$	121596.	−	210611.i	0.0313480	−	0.0542964i
$433$	−285266.			−0.0731190			−0.0365595	−	0.999331i	$-0.511640\pi$
$433$	−285266.			−0.0731190			−0.0365595	+	0.999331i	$0.511640\pi$
$434$	6.74250e6	−	7.37125e6i	1.71829	−	1.87853i
$435$	−486402.			−0.123246
$436$	2.34209e6	−	4.05662e6i	0.590048	−	1.02199i
$437$	−2.20886e6	−	3.82585e6i	−0.553304	−	0.958351i
$438$	−1.14550e6	−	1.98407e6i	−0.285306	−	0.494164i
$439$	−2.17610e6	+	3.76911e6i	−0.538911	+	0.933421i	0.460052	+	0.887892i	$0.347831\pi$
$439$	−2.17610e6	+	3.76911e6i	−0.538911	+	0.933421i	−0.998963	+	0.0455294i	$0.985503\pi$
$440$	−9.12610e6			−2.24726
$441$	1.23484e6	+	573151.i	0.302352	+	0.140337i
$442$	−5.03813e6			−1.22663
$443$	2.55280e6	−	4.42158e6i	0.618027	−	1.07045i	−0.371819	−	0.928305i	$-0.621266\pi$
$443$	2.55280e6	−	4.42158e6i	0.618027	−	1.07045i	0.989845	−	0.142148i	$-0.0454010\pi$
$444$	−709927.	−	1.22963e6i	−0.170906	−	0.296017i
$445$	489024.	+	847015.i	0.117066	+	0.202764i
$446$	−5.08014e6	+	8.79906e6i	−1.20931	+	2.09459i
$447$	1.50301e6			0.355790
$448$	4.32729e6	−	4.73082e6i	1.01864	−	1.11363i
$449$	3.04163e6			0.712016			0.356008	−	0.934483i	$-0.384138\pi$
$449$	3.04163e6			0.712016			0.356008	+	0.934483i	$0.384138\pi$
$450$	768208.	−	1.33057e6i	0.178833	−	0.309748i
$451$	68906.7	+	119350.i	0.0159522	+	0.0276300i
$452$	5.03430e6	+	8.71966e6i	1.15903	+	2.00749i
$453$	1.69319e6	−	2.93269e6i	0.387668	−	0.671461i
$454$	−5.19305e6			−1.18245
$455$	1.49604e6	+	4.73020e6i	0.338777	+	1.07115i
$456$	2.79528e6			0.629524
$457$	872162.	−	1.51063e6i	0.195347	−	0.338351i	−0.751667	−	0.659542i	$-0.770750\pi$
$457$	872162.	−	1.51063e6i	0.195347	−	0.338351i	0.947014	+	0.321192i	$0.104083\pi$
$458$	2.45556e6	+	4.25316e6i	0.547000	+	0.947432i
$459$	366578.	+	634931.i	0.0812147	+	0.140668i
$460$	6.50295e6	−	1.12634e7i	1.43290	−	2.48186i
$461$	−6.85701e6			−1.50273			−0.751367	−	0.659884i	$-0.770605\pi$
$461$	−6.85701e6			−1.50273			−0.751367	+	0.659884i	$0.770605\pi$
$462$	−5.99756e6	−	1.32405e6i	−1.30728	−	0.288602i
$463$	5.13844e6			1.11398			0.556992	−	0.830518i	$-0.311955\pi$
$463$	5.13844e6			1.11398			0.556992	+	0.830518i	$0.311955\pi$
$464$	125675.	−	217676.i	0.0270991	−	0.0469370i
$465$	−2.64887e6	−	4.58798e6i	−0.568105	−	0.983987i
$466$	−1.70980e6	−	2.96147e6i	−0.364738	−	0.631746i
$467$	2.29085e6	−	3.96788e6i	0.486077	−	0.841910i	−0.513795	−	0.857913i	$-0.671761\pi$
$467$	2.29085e6	−	3.96788e6i	0.486077	−	0.841910i	0.999872	+	0.0160029i	$0.00509409\pi$
$468$	2.42733e6			0.512287
$469$	−2.50848e6	−	553784.i	−0.526597	−	0.116254i
$470$	−1.10091e7			−2.29883
$471$	175838.	−	304560.i	0.0365224	−	0.0632587i
$472$	−1.17516e6	−	2.03543e6i	−0.242795	−	0.420534i
$473$	−4.90660e6	−	8.49848e6i	−1.00839	−	1.74658i
$474$	−1.88824e6	+	3.27052e6i	−0.386021	+	0.668608i
$475$	2.76450e6			0.562190
$476$	−2.20839e6	−	6.98253e6i	−0.446743	−	1.41252i
$477$	−2.40097e6			−0.483161
$478$	1.74577e6	−	3.02376e6i	0.349476	−	0.605310i
$479$	144261.	+	249868.i	0.0287284	+	0.0497590i	0.880032	−	0.474914i	$-0.157521\pi$
$479$	144261.	+	249868.i	0.0287284	+	0.0497590i	−0.851304	+	0.524673i	$0.824188\pi$
$480$	−1.33307e6	−	2.30894e6i	−0.264088	−	0.457414i
$481$	749223.	−	1.29769e6i	0.147655	−	0.255746i
$482$	1.60705e7			3.15074
$483$	2.54211e6	−	2.77917e6i	0.495823	−	0.542060i
$484$	8.60702e6			1.67009
$485$	−463352.	+	802549.i	−0.0894451	+	0.154923i
$486$	−277231.	−	480178.i	−0.0532416	−	0.0922172i
$487$	3.90842e6	+	6.76959e6i	0.746757	+	1.29342i	0.949369	+	0.314162i	$0.101723\pi$
$487$	3.90842e6	+	6.76959e6i	0.746757	+	1.29342i	−0.202613	+	0.979259i	$0.564943\pi$
$488$	108275.	−	187538.i	0.0205816	−	0.0356484i
$489$	4.30127e6			0.813438
$490$	−9.26124e6	+	6.50929e6i	−1.74253	+	1.22474i
$491$	3.14467e6			0.588669			0.294335	−	0.955702i	$-0.404902\pi$
$491$	3.14467e6			0.588669			0.294335	+	0.955702i	$0.404902\pi$
$492$	62136.1	−	107623.i	0.0115726	−	0.0200444i
$493$	378875.	+	656232.i	0.0702068	+	0.121602i
$494$	3.42787e6	+	5.93724e6i	0.631985	+	1.09463i
$495$	−1.62859e6	+	2.82080e6i	−0.298743	+	0.517439i
$496$	2.73763e6			0.499656
$497$	−5.43597e6	+	5.94289e6i	−0.987157	+	1.07921i
$498$	1.31890e6			0.238308
$499$	−3.36281e6	+	5.82456e6i	−0.604577	+	1.04716i	0.387541	+	0.921852i	$0.373324\pi$
$499$	−3.36281e6	+	5.82456e6i	−0.604577	+	1.04716i	−0.992118	+	0.125305i	$0.960009\pi$
$500$	−2.22590e6	−	3.85537e6i	−0.398181	−	0.689670i
$501$	179070.	+	310159.i	0.0318734	+	0.0552064i
$502$	272936.	−	472738.i	0.0483394	−	0.0837262i
$503$	−9.45056e6			−1.66547			−0.832737	−	0.553669i	$-0.813227\pi$
$503$	−9.45056e6			−1.66547			−0.832737	+	0.553669i	$0.813227\pi$
$504$	718654.	+	2.27225e6i	0.126021	+	0.398456i
$505$	−1.80348e6			−0.314690
$506$	−8.49639e6	+	1.47162e7i	−1.47522	+	2.55516i
$507$	−389976.	−	675458.i	−0.0673780	−	0.116702i
$508$	4.03506e6	+	6.98892e6i	0.693730	+	1.20158i
$509$	4.41851e6	−	7.65308e6i	0.755930	−	1.30931i	−0.188981	−	0.981981i	$-0.560519\pi$
$509$	4.41851e6	−	7.65308e6i	0.755930	−	1.30931i	0.944911	−	0.327328i	$-0.106148\pi$
$510$	−6.09629e6			−1.03786
$511$	3.43191e6	+	757645.i	0.581411	+	0.128355i
$512$	3.80044e6			0.640707
$513$	498828.	−	863995.i	0.0836869	−	0.144950i
$514$	−1.46406e6	−	2.53583e6i	−0.244429	−	0.423363i
$515$	−5.76534e6	−	9.98585e6i	−0.957870	−	1.65908i
$516$	−4.42449e6	+	7.66345e6i	−0.731542	+	1.26707i
$517$	9.16344e6			1.50776
$518$	3.33865e6	+	737057.i	0.546697	+	0.120692i
$519$	−435044.			−0.0708949
$520$	−4.34246e6	+	7.52136e6i	−0.704251	+	1.21980i
$521$	−347492.	−	601874.i	−0.0560855	−	0.0971430i	0.836619	−	0.547784i	$-0.184529\pi$
$521$	−347492.	−	601874.i	−0.0560855	−	0.0971430i	−0.892705	+	0.450641i	$0.851195\pi$
$522$	−286531.	−	496287.i	−0.0460252	−	0.0797181i
$523$	−1.79105e6	+	3.10219e6i	−0.286321	+	0.495923i	−0.972929	−	0.231105i	$-0.925766\pi$
$523$	−1.79105e6	+	3.10219e6i	−0.286321	+	0.495923i	0.686607	+	0.727028i	$0.259099\pi$
$524$	2.93710e6			0.467294
$525$	710743.	+	2.24724e6i	0.112542	+	0.355837i
$526$	−8.11252e6			−1.27847
$527$	−4.12660e6	+	7.14748e6i	−0.647240	+	1.12105i
$528$	−841580.	−	1.45766e6i	−0.131374	−	0.227547i
$529$	−1.99208e6	−	3.45038e6i	−0.309504	−	0.536077i
$530$	9.98222e6	−	1.72897e7i	1.54361	−	2.67361i
$531$	−838845.			−0.129106
$532$	−6.72609e6	+	7.35331e6i	−1.03035	+	1.12643i
$533$	131151.			0.0199965
$534$	−576152.	+	997925.i	−0.0874347	+	0.151441i
$535$	−3.38473e6	−	5.86253e6i	−0.511258	−	0.885525i
$536$	−2.24852e6	−	3.89456e6i	−0.338053	−	0.585526i
$537$	−643098.	+	1.11388e6i	−0.0962368	+	0.166687i
$538$	1.05231e7			1.56744
$539$	7.70860e6	−	5.41801e6i	1.14289	−	0.803282i
$540$	2.93714e6			0.433451
$541$	2.58423e6	−	4.47602e6i	0.379610	−	0.657504i	−0.611395	−	0.791325i	$-0.709391\pi$
$541$	2.58423e6	−	4.47602e6i	0.379610	−	0.657504i	0.991005	+	0.133821i	$0.0427248\pi$
$542$	5.35277e6	+	9.27126e6i	0.782673	+	1.35563i
$543$	−347604.	−	602068.i	−0.0505924	−	0.0876285i
$544$	−2.07675e6	+	3.59703e6i	−0.300875	+	0.521131i
$545$	5.98174e6			0.862653
$546$	−3.94504e6	+	4.31292e6i	−0.566331	+	0.619142i
$547$	8.47489e6			1.21106			0.605530	−	0.795822i	$-0.292961\pi$
$547$	8.47489e6			1.21106			0.605530	+	0.795822i	$0.292961\pi$
$548$	−264281.	+	457748.i	−0.0375936	+	0.0651141i
$549$	−38644.2	−	66933.8i	−0.00547210	−	0.00947795i
$550$	−5.31685e6	−	9.20906e6i	−0.749459	−	1.29810i
$551$	515562.	−	892980.i	0.0723439	−	0.125303i
$552$	6.59349e6			0.921018
$553$	−1.74699e6	−	5.52367e6i	−0.242928	−	0.768095i
$554$	1.86671e7			2.58407
$555$	906583.	−	1.57025e6i	0.124932	−	0.216389i
$556$	−5.14217e6	−	8.90649e6i	−0.705438	−	1.22186i
$557$	5.21063e6	+	9.02508e6i	0.711627	+	1.23257i	0.964246	+	0.265009i	$0.0853748\pi$
$557$	5.21063e6	+	9.02508e6i	0.711627	+	1.23257i	−0.252619	+	0.967566i	$0.581292\pi$
$558$	3.12082e6	−	5.40541e6i	0.424309	−	0.734925i
$559$	−9.33880e6			−1.26404
$560$	−3.02921e6	−	668743.i	−0.408187	−	0.0901134i
$561$	5.07425e6			0.680714
$562$	2.49921e6	−	4.32876e6i	0.333781	−	0.578126i
$563$	3.62039e6	+	6.27069e6i	0.481375	+	0.833767i	0.999772	−	0.0213739i	$-0.00680405\pi$
$563$	3.62039e6	+	6.27069e6i	0.481375	+	0.833767i	−0.518396	+	0.855141i	$0.673471\pi$
$564$	−4.13154e6	−	7.15603e6i	−0.546907	−	0.947271i
$565$	−6.42885e6	+	1.11351e7i	−0.847251	+	1.46748i
$566$	−2.46459e7			−3.23373
$567$	830581.	+	183363.i	0.108499	+	0.0239527i
$568$	−1.40993e7			−1.83369
$569$	−458268.	+	793743.i	−0.0593388	+	0.102778i	−0.894169	−	0.447730i	$-0.852233\pi$
$569$	−458268.	+	793743.i	−0.0593388	+	0.102778i	0.834830	+	0.550508i	$0.185566\pi$
$570$	4.14782e6	+	7.18424e6i	0.534728	+	0.926177i
$571$	−5.03538e6	−	8.72154e6i	−0.646312	−	1.11944i	−0.983997	−	0.178186i	$-0.942977\pi$
$571$	−5.03538e6	−	8.72154e6i	−0.646312	−	1.11944i	0.337685	−	0.941259i	$-0.390356\pi$
$572$	8.39990e6	−	1.45490e7i	1.07345	−	1.85928i
$573$	−2.44849e6			−0.311538
$574$	90239.2	+	285320.i	0.0114318	+	0.0361454i
$575$	6.52091e6			0.822505
$576$	2.00292e6	−	3.46916e6i	0.251540	−	0.435680i
$577$	−5.84987e6	−	1.01323e7i	−0.731488	−	1.26697i	−0.956247	−	0.292560i	$-0.905493\pi$
$577$	−5.84987e6	−	1.01323e7i	−0.731488	−	1.26697i	0.224760	−	0.974414i	$-0.427840\pi$
$578$	−1.91752e6	−	3.32125e6i	−0.238738	−	0.413506i
$579$	−72152.0	+	124971.i	−0.00894442	+	0.0154922i
$580$	3.03567e6			0.374701
$581$	−1.36558e6	+	1.49292e6i	−0.167833	+	0.183484i
$582$	−1.09181e6			−0.133610
$583$	−8.30871e6	+	1.43911e7i	−1.01242	+	1.75357i
$584$	3.07626e6	+	5.32823e6i	0.373242	+	0.646474i
$585$	1.54986e6	+	2.68443e6i	0.187242	+	0.324312i
$586$	2.86373e6	−	4.96013e6i	0.344499	−	0.596690i
$587$	−6.92367e6			−0.829357			−0.414678	−	0.909968i	$-0.636106\pi$
$587$	−6.92367e6			−0.829357			−0.414678	+	0.909968i	$0.636106\pi$
$588$	−7.70669e6	−	3.57707e6i	−0.919231	−	0.426662i
$589$	1.12307e7			1.33389
$590$	3.48756e6	−	6.04062e6i	0.412469	−	0.714417i
$591$	4.64527e6	+	8.04584e6i	0.547069	+	0.947552i
$592$	468481.	+	811432.i	0.0549398	+	0.0951586i
$593$	−7.88850e6	+	1.36633e7i	−0.921208	+	1.59558i	−0.123660	+	0.992325i	$0.539463\pi$
$593$	−7.88850e6	+	1.36633e7i	−0.921208	+	1.59558i	−0.797548	+	0.603255i	$0.793870\pi$
$594$	−3.83750e6			−0.446254
$595$	6.31207e6	−	6.90068e6i	0.730936	−	0.799097i
$596$	−9.38041e6			−1.08170
$597$	−3.96781e6	+	6.87245e6i	−0.455633	+	0.789180i
$598$	8.08565e6	+	1.40048e7i	0.924618	+	1.60148i
$599$	−7.13541e6	−	1.23589e7i	−0.812553	−	1.40738i	−0.911072	−	0.412248i	$-0.864744\pi$
$599$	−7.13541e6	−	1.23589e7i	−0.812553	−	1.40738i	0.0985183	−	0.995135i	$-0.468590\pi$
$600$	−2.06303e6	+	3.57327e6i	−0.233952	+	0.405217i
$601$	7.63222e6			0.861916			0.430958	−	0.902372i	$-0.358176\pi$
$601$	7.63222e6			0.861916			0.430958	+	0.902372i	$0.358176\pi$
$602$	−6.42562e6	−	2.03167e7i	−0.722643	−	2.28487i
$603$	−1.60503e6			−0.179759
$604$	−1.05673e7	+	1.83031e7i	−1.17862	+	2.04142i
$605$	5.49562e6	+	9.51869e6i	0.610419	+	1.05728i
$606$	−1.06240e6	−	1.84013e6i	−0.117518	−	0.203548i
$607$	1.78017e6	−	3.08335e6i	0.196106	−	0.339665i	−0.751157	−	0.660124i	$-0.770504\pi$
$607$	1.78017e6	−	3.08335e6i	0.196106	−	0.339665i	0.947262	+	0.320459i	$0.103837\pi$
$608$	5.65194e6			0.620067
$609$	858444.	+	189515.i	0.0937927	+	0.0207061i
$610$	642664.			0.0699294
$611$	4.36023e6	−	7.55214e6i	0.472505	−	0.818402i
$612$	−2.28784e6	−	3.96265e6i	−0.246914	−	0.427668i
$613$	6.86420e6	+	1.18891e7i	0.737800	+	1.27791i	0.953484	+	0.301445i	$0.0974688\pi$
$613$	6.86420e6	+	1.18891e7i	0.737800	+	1.27791i	−0.215683	+	0.976463i	$0.569198\pi$
$614$	−6.33080e6	+	1.09653e7i	−0.677700	+	1.17381i
$615$	158697.			0.0169192
$616$	1.61065e7	+	3.55576e6i	1.71021	+	0.377555i
$617$	−6.51173e6			−0.688626			−0.344313	−	0.938855i	$-0.611888\pi$
$617$	−6.51173e6			−0.688626			−0.344313	+	0.938855i	$0.611888\pi$
$618$	6.79253e6	−	1.17650e7i	0.715419	−	1.23914i
$619$	−4.42555e6	−	7.66527e6i	−0.464238	−	0.804083i	0.534929	−	0.844897i	$-0.320338\pi$
$619$	−4.42555e6	−	7.66527e6i	−0.464238	−	0.804083i	−0.999167	+	0.0408136i	$0.987005\pi$
$620$	1.65318e7	+	2.86339e7i	1.72719	+	2.99159i
$621$	1.17663e6	−	2.03799e6i	0.122437	−	0.212067i
$622$	3.12739e7			3.24121
$623$	−533054.	−	1.68542e6i	−0.0550238	−	0.173976i
$624$	−1.60179e6			−0.164681
$625$	5.99884e6	−	1.03903e7i	0.614281	−	1.06397i
$626$	−1.33181e7	−	2.30677e7i	−1.35834	−	2.35271i
$627$	−3.45244e6	−	5.97981e6i	−0.350718	−	0.607461i
$628$	−1.09741e6	+	1.90078e6i	−0.111038	+	0.192323i
$629$	−2.82467e6			−0.284670
$630$	−4.77362e6	+	5.21877e6i	−0.479177	+	0.523862i
$631$	−6.89663e6			−0.689546			−0.344773	−	0.938686i	$-0.612044\pi$
$631$	−6.89663e6			−0.689546			−0.344773	+	0.938686i	$0.612044\pi$
$632$	5.07088e6	−	8.78303e6i	0.504999	−	0.874685i
$633$	−1.67766e6	−	2.90579e6i	−0.166416	−	0.288240i
$634$	−5.10992e6	−	8.85064e6i	−0.504883	−	0.874483i
$635$	−5.15280e6	+	8.92492e6i	−0.507118	+	0.878355i
$636$	1.49846e7			1.46894
$637$	−797329.	−	8.93116e6i	−0.0778554	−	0.872086i
$638$	−3.96623e6			−0.385768
$639$	−2.51608e6	+	4.35797e6i	−0.243765	+	0.422214i
$640$	1.19147e7	+	2.06369e7i	1.14983	+	1.99157i
$641$	8.33473e6	+	1.44362e7i	0.801210	+	1.38774i	0.918820	+	0.394677i	$0.129144\pi$
$641$	8.33473e6	+	1.44362e7i	0.801210	+	1.38774i	−0.117610	+	0.993060i	$0.537523\pi$
$642$	3.98778e6	−	6.90704e6i	0.381851	−	0.661385i
$643$	−1.28697e7			−1.22756			−0.613779	−	0.789478i	$-0.710351\pi$
$643$	−1.28697e7			−1.22756			−0.613779	+	0.789478i	$0.710351\pi$
$644$	−1.58655e7	+	1.73450e7i	−1.50744	+	1.64801i
$645$	−1.13002e7			−1.06952
$646$	6.46177e6	−	1.11921e7i	0.609214	−	1.05519i
$647$	5.73656e6	+	9.93601e6i	0.538754	+	0.933150i	0.998971	+	0.0453435i	$0.0144382\pi$
$647$	5.73656e6	+	9.93601e6i	0.538754	+	0.933150i	−0.460217	+	0.887806i	$0.652228\pi$
$648$	744507.	+	1.28952e6i	0.0696517	+	0.120640i
$649$	−2.90287e6	+	5.02792e6i	−0.270530	+	0.468572i
$650$	−1.01196e7			−0.939467
$651$	2.88737e6	+	9.12934e6i	0.267023	+	0.844280i
$652$	−2.68445e7			−2.47307
$653$	6.59005e6	−	1.14143e7i	0.604791	−	1.04753i	−0.387293	−	0.921957i	$-0.626590\pi$
$653$	6.59005e6	−	1.14143e7i	0.604791	−	1.04753i	0.992084	−	0.125573i	$-0.0400768\pi$
$654$	3.52374e6	+	6.10330e6i	0.322151	+	0.557982i
$655$	1.87535e6	+	3.24820e6i	0.170797	+	0.295829i
$656$	−41003.6	+	71020.4i	−0.00372017	+	0.00644352i
$657$	2.19588e6			0.198470
$658$	1.94298e7	+	4.28943e6i	1.74946	+	0.386220i
$659$	−1.13068e7			−1.01421			−0.507104	−	0.861885i	$-0.669284\pi$
$659$	−1.13068e7			−1.01421			−0.507104	+	0.861885i	$0.669284\pi$
$660$	1.01641e7	−	1.76048e7i	0.908260	−	1.57315i
$661$	−1.10160e6	−	1.90802e6i	−0.0980661	−	0.169856i	0.812818	−	0.582518i	$-0.197932\pi$
$661$	−1.10160e6	−	1.90802e6i	−0.0980661	−	0.169856i	−0.910884	+	0.412662i	$0.864599\pi$
$662$	6.12945e6	+	1.06165e7i	0.543596	+	0.941536i
$663$	2.41447e6	−	4.18199e6i	0.213324	−	0.369487i
$664$	−3.54192e6			−0.311758
$665$	−1.24268e7	−	2.74341e6i	−1.08970	−	0.240567i
$666$	2.13621e6			0.186620
$667$	1.21611e6	−	2.10636e6i	0.105842	−	0.183323i
$668$	−1.11759e6	−	1.93572e6i	−0.0969038	−	0.167842i
$669$	−4.86921e6	−	8.43372e6i	−0.420623	−	0.728541i
$670$	6.67303e6	−	1.15580e7i	0.574296	−	0.994710i
$671$	−534922.			−0.0458653
$672$	1.45309e6	+	4.59442e6i	0.124128	+	0.392471i
$673$	−1.89787e7			−1.61521			−0.807606	−	0.589723i	$-0.799237\pi$
$673$	−1.89787e7			−1.61521			−0.807606	+	0.589723i	$0.799237\pi$
$674$	−1.48837e7	+	2.57793e7i	−1.26200	+	2.18586i
$675$	736312.	+	1.27533e6i	0.0622017	+	0.107736i
$676$	2.43387e6	+	4.21558e6i	0.204847	+	0.354806i
$677$	9.82377e6	−	1.70153e7i	0.823771	−	1.42681i	−0.0790842	−	0.996868i	$-0.525200\pi$
$677$	9.82377e6	−	1.70153e7i	0.823771	−	1.42681i	0.902855	−	0.429945i	$-0.141467\pi$
$678$	−1.51485e7			−1.26560
$679$	1.13046e6	−	1.23587e6i	0.0940977	−	0.102873i
$680$	1.63717e7			1.35775
$681$	2.48872e6	−	4.31059e6i	0.205640	−	0.356179i
$682$	−2.15995e7	−	3.74115e7i	−1.77821	−	3.07995i
$683$	−8.13523e6	−	1.40906e7i	−0.667295	−	1.15579i	−0.978658	−	0.205498i	$-0.934119\pi$
$683$	−8.13523e6	−	1.40906e7i	−0.667295	−	1.15579i	0.311363	−	0.950291i	$-0.399215\pi$
$684$	−3.11322e6	+	5.39225e6i	−0.254431	+	0.440687i
$685$	−674978.			−0.0549621
$686$	1.88812e7	−	7.87973e6i	1.53186	−	0.639295i
$687$	−4.70722e6			−0.380515
$688$	2.91972e6	−	5.05711e6i	0.235164	−	0.407316i
$689$	7.90704e6	+	1.36954e7i	0.634550	+	1.09907i
$690$	9.78388e6	+	1.69462e7i	0.782327	+	1.35503i
$691$	−9.72335e6	+	1.68413e7i	−0.774677	+	1.34178i	0.160299	+	0.987069i	$0.448754\pi$
$691$	−9.72335e6	+	1.68413e7i	−0.774677	+	1.34178i	−0.934976	+	0.354712i	$0.884579\pi$
$692$	2.71514e6			0.215539
$693$	3.97332e6	−	4.34384e6i	0.314283	−	0.343591i
$694$	1.61122e7			1.26986
$695$	6.56659e6	−	1.13737e7i	0.515677	−	0.893179i
$696$	769484.	+	1.33278e6i	0.0602111	+	0.104289i
$697$	−123614.	−	214106.i	−0.00963800	−	0.0166935i
$698$	−1.38886e7	+	2.40558e7i	−1.07900	+	1.86888i
$699$	3.27763e6			0.253727
$700$	−4.43579e6	−	1.40252e7i	−0.342157	−	1.08184i
$701$	1.49625e7			1.15003			0.575014	−	0.818144i	$-0.304997\pi$
$701$	1.49625e7			1.15003			0.575014	+	0.818144i	$0.304997\pi$
$702$	−1.82599e6	+	3.16271e6i	−0.139848	+	0.242224i
$703$	1.92187e6	+	3.32877e6i	0.146668	+	0.254036i
$704$	−1.38624e7	−	2.40104e7i	−1.05416	−	1.82586i
$705$	5.27601e6	−	9.13831e6i	0.399791	−	0.692458i
$706$	−3.53979e7			−2.67280
$707$	3.18293e6	+	702680.i	0.239485	+	0.0528700i
$708$	5.23529e6			0.392516
$709$	−793193.	+	1.37385e6i	−0.0592603	+	0.102642i	−0.894134	−	0.447800i	$-0.852208\pi$
$709$	−793193.	+	1.37385e6i	−0.0592603	+	0.102642i	0.834873	+	0.550442i	$0.185541\pi$
$710$	−2.09215e7	−	3.62372e7i	−1.55757	−	2.69779i
$711$	−1.80984e6	−	3.13473e6i	−0.134266	−	0.232555i
$712$	1.54726e6	−	2.67994e6i	0.114384	−	0.198118i
$713$	2.64910e7			1.95152
$714$	1.07593e7	+	2.37527e6i	0.789836	+	0.174368i
$715$	2.14535e7			1.56940
$716$	4.01362e6	−	6.95179e6i	0.292586	−	0.506774i
$717$	1.67329e6	+	2.89822e6i	0.121555	+	0.210539i
$718$	9.06061e6	+	1.56934e7i	0.655913	+	1.13607i
$719$	9.08376e6	−	1.57335e7i	0.655305	−	1.13502i	−0.326512	−	0.945193i	$-0.605873\pi$
$719$	9.08376e6	−	1.57335e7i	0.655305	−	1.13502i	0.981817	−	0.189829i	$-0.0607932\pi$
$720$	−1.93822e6			−0.139338
$721$	6.28442e6	+	1.98702e7i	0.450222	+	1.42352i
$722$	5.66429e6			0.404392
$723$	−7.70164e6	+	1.33396e7i	−0.547945	+	0.949069i
$724$	2.16942e6	+	3.75754e6i	0.153814	+	0.266414i
$725$	761013.	+	1.31811e6i	0.0537709	+	0.0931339i
$726$	−6.47476e6	+	1.12146e7i	−0.455913	+	0.789664i
$727$	1.26903e7			0.890506			0.445253	−	0.895405i	$-0.353114\pi$
$727$	1.26903e7			0.890506			0.445253	+	0.895405i	$0.353114\pi$
$728$	1.05945e7	−	1.15824e7i	0.740884	−	0.809973i
$729$	531441.			0.0370370
$730$	−9.12953e6	+	1.58128e7i	−0.634076	+	1.09825i
$731$	8.80214e6	+	1.52458e7i	0.609249	+	1.05525i
$732$	241181.	+	417738.i	0.0166366	+	0.0288155i
$733$	1.55701e6	−	2.69681e6i	0.107036	−	0.185392i	−0.807532	−	0.589824i	$-0.799197\pi$
$733$	1.55701e6	−	2.69681e6i	0.107036	−	0.185392i	0.914568	+	0.404432i	$0.132531\pi$
$734$	−2.22298e7			−1.52298
$735$	−964792.	−	1.08070e7i	−0.0658742	−	0.737880i
$736$	1.33318e7			0.907182
$737$	−5.55430e6	+	9.62033e6i	−0.376670	+	0.652411i
$738$	93485.6	+	161922.i	0.00631835	+	0.0109437i
$739$	−4.54950e6	−	7.87996e6i	−0.306445	−	0.530778i	0.671137	−	0.741333i	$-0.265806\pi$
$739$	−4.54950e6	−	7.87996e6i	−0.306445	−	0.530778i	−0.977582	+	0.210555i	$0.932473\pi$
$740$	−5.65804e6	+	9.80002e6i	−0.379828	+	0.657881i
$741$	−6.57109e6			−0.439634
$742$	−2.43540e7	+	2.66250e7i	−1.62390	+	1.77534i
$743$	−8.79218e6			−0.584285			−0.292142	−	0.956375i	$-0.594368\pi$
$743$	−8.79218e6			−0.584285			−0.292142	+	0.956375i	$0.594368\pi$
$744$	−8.38098e6	+	1.45163e7i	−0.555089	+	0.961443i
$745$	−5.98943e6	−	1.03740e7i	−0.395362	−	0.684787i
$746$	1.66120e7	+	2.87729e7i	1.09289	+	1.89294i
$747$	−632069.	+	1.09478e6i	−0.0414441	+	0.0717833i
$748$	−3.16687e7			−2.06955
$749$	3.68948e6	+	1.16655e7i	0.240304	+	0.759798i
$750$	6.69786e6			0.434793
$751$	1.40459e7	−	2.43282e7i	0.908759	−	1.57402i	0.0929698	−	0.995669i	$-0.470364\pi$
$751$	1.40459e7	−	2.43282e7i	0.908759	−	1.57402i	0.815790	−	0.578349i	$-0.196303\pi$
$752$	2.72640e6	+	4.72226e6i	0.175811	+	0.304513i
$753$	261603.	+	453110.i	0.0168134	+	0.0291217i
$754$	−1.88725e6	+	3.26881e6i	−0.120893	+	0.209393i
$755$	−2.69891e7			−1.72314
$756$	−5.18371e6	−	1.14438e6i	−0.329865	−	0.0728227i
$757$	−4.18815e6			−0.265634			−0.132817	−	0.991141i	$-0.542402\pi$
$757$	−4.18815e6			−0.265634			−0.132817	+	0.991141i	$0.542402\pi$
$758$	8.44369e6	−	1.46249e7i	0.533776	−	0.924527i
$759$	−8.14362e6	−	1.41052e7i	−0.513113	−	0.888738i
$760$	−1.11390e7	−	1.92934e7i	−0.699541	−	1.21164i
$761$	196591.	−	340506.i	0.0123056	−	0.0213139i	−0.859807	−	0.510619i	$-0.829416\pi$
$761$	196591.	−	340506.i	0.0123056	−	0.0213139i	0.872113	+	0.489305i	$0.162750\pi$
$762$	−1.21417e7			−0.757518
$763$	−1.05571e7	−	2.33063e6i	−0.656497	−	0.144932i
$764$	1.52812e7			0.947159
$765$	2.92159e6	−	5.06034e6i	0.180495	−	0.312627i
$766$	1.22451e7	+	2.12091e7i	0.754031	+	1.30602i
$767$	2.76254e6	+	4.78486e6i	0.169559	+	0.293684i
$768$	−6.91607e6	+	1.19790e7i	−0.423113	+	0.732853i
$769$	1.57517e7			0.960530			0.480265	−	0.877124i	$-0.340541\pi$
$769$	1.57517e7			0.960530			0.480265	+	0.877124i	$0.340541\pi$
$770$	1.47612e7	+	4.66722e7i	0.897211	+	2.83682i
$771$	2.80655e6			0.170035
$772$	450306.	−	779952.i	0.0271934	−	0.0471004i
$773$	−1.44236e6	−	2.49824e6i	−0.0868210	−	0.150378i	0.819345	−	0.573301i	$-0.194337\pi$
$773$	−1.44236e6	−	2.49824e6i	−0.0868210	−	0.150378i	−0.906166	+	0.422923i	$0.861004\pi$
$774$	−6.65678e6	−	1.15299e7i	−0.399403	−	0.691787i
$775$	−8.28873e6	+	1.43565e7i	−0.495717	+	0.858606i
$776$	2.93207e6			0.174791
$777$	−2.21182e6	+	2.41808e6i	−0.131431	+	0.143687i
$778$	2.65729e7			1.57394
$779$	−168211.	+	291349.i	−0.00993139	+	0.0172017i
$780$	−9.67276e6	−	1.67537e7i	−0.569265	−	0.985995i
$781$	1.74141e7	+	3.01620e7i	1.02158	+	1.76943i
$782$	1.52420e7	−	2.63999e7i	0.891303	−	1.54378i
$783$	549269.			0.0320170
$784$	5.08564e6	+	2.36051e6i	0.295499	+	0.137156i
$785$	−2.80281e6			−0.162338
$786$	−2.20948e6	+	3.82693e6i	−0.127565	+	0.220950i
$787$	1.48933e7	+	2.57960e7i	0.857145	+	1.48462i	0.874641	+	0.484771i	$0.161097\pi$
$787$	1.48933e7	+	2.57960e7i	0.857145	+	1.48462i	−0.0174963	+	0.999847i	$0.505570\pi$
$788$	−2.89914e7	−	5.02146e7i	−1.66324	−	2.88081i
$789$	3.88784e6	−	6.73394e6i	0.222339	−	0.385103i
$790$	3.00981e7			1.71582
$791$	1.56847e7	−	1.71473e7i	0.891322	−	0.974440i
$792$	1.03056e7			0.583797
$793$	−254531.	+	440861.i	−0.0143734	+	0.0248954i
$794$	−1.14116e7	−	1.97655e7i	−0.642385	−	1.11264i
$795$	9.56776e6	+	1.65718e7i	0.536899	+	0.929936i
$796$	2.47634e7	−	4.28914e7i	1.38525	−	2.39932i
$797$	8.11321e6			0.452425			0.226213	−	0.974078i	$-0.427366\pi$
$797$	8.11321e6			0.452425			0.226213	+	0.974078i	$0.427366\pi$
$798$	−4.52127e6	−	1.42955e7i	−0.251335	−	0.794678i
$799$	−1.64387e7			−0.910960
$800$	−4.17137e6	+	7.22503e6i	−0.230438	+	0.399130i
$801$	−552230.	−	956491.i	−0.0304116	−	0.0526744i
$802$	−1.14173e7	−	1.97754e7i	−0.626800	−	1.08565i
$803$	7.59897e6	−	1.31618e7i	0.415878	−	0.720321i
$804$	1.00171e7			0.546515
$805$	−2.93124e7	−	6.47115e6i	−1.59427	−	0.351959i
$806$	−4.11107e7			−2.22904
$807$	−5.04311e6	+	8.73493e6i	−0.272593	+	0.472145i
$808$	2.85308e6	+	4.94169e6i	0.153740	+	0.266285i
$809$	−55798.5	−	96645.8i	−0.00299744	−	0.00519173i	0.864523	−	0.502594i	$-0.167621\pi$
$809$	−55798.5	−	96645.8i	−0.00299744	−	0.00519173i	−0.867520	+	0.497402i	$0.834287\pi$
$810$	−2.20950e6	+	3.82697e6i	−0.118327	+	0.204948i
$811$	−209250.			−0.0111716			−0.00558578	−	0.999984i	$-0.501778\pi$
$811$	−209250.			−0.0111716			−0.00558578	+	0.999984i	$0.501778\pi$
$812$	−5.35761e6	−	1.18277e6i	−0.285155	−	0.0629523i
$813$	−1.02610e7			−0.544459
$814$	7.39248e6	−	1.28042e7i	0.391047	−	0.677314i
$815$	−1.71403e7	−	2.96879e7i	−0.903910	−	1.56562i
$816$	1.50974e6	+	2.61495e6i	0.0793739	+	0.137480i
$817$	1.19777e7	−	2.07460e7i	0.627795	−	1.08737i
$818$	4.48334e7			2.34271
$819$	−1.68940e6	−	5.34158e6i	−0.0880081	−	0.278266i
$820$	−990437.			−0.0514390
$821$	−3.42307e6	+	5.92893e6i	−0.177238	+	0.306986i	−0.940934	−	0.338591i	$-0.890050\pi$
$821$	−3.42307e6	+	5.92893e6i	−0.177238	+	0.306986i	0.763695	+	0.645577i	$0.223383\pi$
$822$	−397618.	−	688695.i	−0.0205252	−	0.0355506i
$823$	2.80605e6	+	4.86022e6i	0.144409	+	0.250125i	0.929152	−	0.369697i	$-0.120538\pi$
$823$	2.80605e6	+	4.86022e6i	0.144409	+	0.250125i	−0.784743	+	0.619821i	$0.787205\pi$
$824$	−1.82414e7	+	3.15950e7i	−0.935923	+	1.62107i
$825$	1.01922e7			0.521354
$826$	−8.50872e6	+	9.30217e6i	−0.433924	+	0.474389i
$827$	−2.15868e7			−1.09755			−0.548776	−	0.835969i	$-0.684906\pi$
$827$	−2.15868e7			−1.09755			−0.548776	+	0.835969i	$0.684906\pi$
$828$	−7.34346e6	+	1.27192e7i	−0.372241	+	0.644741i
$829$	−9.62135e6	−	1.66647e7i	−0.486239	−	0.842190i	0.513636	−	0.858008i	$-0.328298\pi$
$829$	−9.62135e6	−	1.66647e7i	−0.486239	−	0.842190i	−0.999875	+	0.0158177i	$0.994965\pi$
$830$	−5.25574e6	−	9.10321e6i	−0.264813	−	0.458669i
$831$	−8.94604e6	+	1.54950e7i	−0.449395	+	0.778375i
$832$	−2.63846e7			−1.32142
$833$	−1.38288e7	+	9.71958e6i	−0.690511	+	0.485327i
$834$	1.54731e7			0.770303
$835$	1.42717e6	−	2.47193e6i	0.0708369	−	0.122693i
$836$	2.15469e7	+	3.73204e7i	1.06628	+	1.84684i
$837$	2.99124e6	+	5.18098e6i	0.147583	+	0.255622i
$838$	−2.14644e6	+	3.71774e6i	−0.105586	+	0.182881i
$839$	2.47678e7			1.21474			0.607369	−	0.794420i	$-0.292225\pi$
$839$	2.47678e7			1.21474			0.607369	+	0.794420i	$0.292225\pi$
$840$	1.28196e7	−	1.40151e7i	0.626869	−	0.685325i
$841$	−1.99435e7			−0.972323
$842$	−8.56337e6	+	1.48322e7i	−0.416260	+	0.720983i
$843$	2.39544e6	+	4.14903e6i	0.116096	+	0.201084i
$844$	1.04704e7	+	1.81352e7i	0.505948	+	0.876328i
$845$	−3.10807e6	+	5.38333e6i	−0.149744	+	0.259364i
$846$	1.24320e7			0.597195
$847$	−5.99042e6	−	1.89406e7i	−0.286912	−	0.907165i
$848$	−9.88836e6			−0.472210
$849$	1.18113e7	−	2.04578e7i	0.562378	−	0.974067i
$850$	9.53811e6	+	1.65205e7i	0.452809	+	0.784288i
$851$	4.53329e6	+	7.85190e6i	0.214580	+	0.371664i
$852$	1.57030e7	−	2.71984e7i	0.741112	−	1.28364i
$853$	−2.91267e7			−1.37062			−0.685312	−	0.728250i	$-0.740334\pi$
$853$	−2.91267e7			−1.37062			−0.685312	+	0.728250i	$0.740334\pi$
$854$	−1.13423e6	−	250398.i	−0.0532177	−	0.0117486i
$855$	−7.95121e6			−0.371979
$856$	−1.07092e7	+	1.85489e7i	−0.499544	+	0.865236i
$857$	1.61293e6	+	2.79367e6i	0.0750175	+	0.129934i	0.901094	−	0.433624i	$-0.142765\pi$
$857$	1.61293e6	+	2.79367e6i	0.0750175	+	0.129934i	−0.826076	+	0.563558i	$0.809432\pi$
$858$	1.26379e7	+	2.18895e7i	0.586079	+	1.01512i
$859$	−1.32335e7	+	2.29212e7i	−0.611918	+	1.05987i	0.378999	+	0.925397i	$0.376268\pi$
$859$	−1.32335e7	+	2.29212e7i	−0.611918	+	1.05987i	−0.990917	+	0.134476i	$0.957065\pi$
$860$	7.05255e7			3.25162
$861$	−280082.	−	61832.2i	−0.0128759	−	0.00284254i
$862$	3.17611e7			1.45589
$863$	−7.92552e6	+	1.37274e7i	−0.362243	+	0.627424i	−0.988330	−	0.152330i	$-0.951322\pi$
$863$	−7.92552e6	+	1.37274e7i	−0.362243	+	0.627424i	0.626086	+	0.779754i	$0.284656\pi$
$864$	1.50537e6	+	2.60737e6i	0.0686053	+	0.118828i
$865$	1.73363e6	+	3.00273e6i	0.0787799	+	0.136451i
$866$	−1.33930e6	+	2.31974e6i	−0.0606854	+	0.105110i
$867$	3.67582e6			0.166076
$868$	−1.80202e7	−	5.69768e7i	−0.811823	−	2.56684i
$869$	−2.50522e7			−1.12537
$870$	−2.28363e6	+	3.95536e6i	−0.102289	+	0.177169i
$871$	5.28579e6	+	9.15526e6i	0.236083	+	0.408908i
$872$	−9.46305e6	−	1.63905e7i	−0.421444	−	0.729962i
$873$	523240.	−	906277.i	0.0232362	−	0.0402463i
$874$	−4.14817e7			−1.83687
$875$	−6.93493e6	+	7.58163e6i	−0.306212	+	0.334767i
$876$	−1.37046e7			−0.603403
$877$	7.45659e6	−	1.29152e7i	0.327372	−	0.567024i	−0.654618	−	0.755960i	$-0.727170\pi$
$877$	7.45659e6	−	1.29152e7i	0.327372	−	0.567024i	0.981989	+	0.188936i	$0.0605037\pi$
$878$	2.04333e7	+	3.53915e7i	0.894544	+	1.54940i
$879$	2.74483e6	+	4.75419e6i	0.119824	+	0.207541i
$880$	−6.70730e6	+	1.16174e7i	−0.291972	+	0.505711i
$881$	−3.70679e7			−1.60901			−0.804504	−	0.593947i	$-0.797569\pi$
$881$	−3.70679e7			−1.60901			−0.804504	+	0.593947i	$0.797569\pi$
$882$	1.04583e7	−	7.35061e6i	0.452676	−	0.318165i
$883$	1.50440e7			0.649325			0.324663	−	0.945830i	$-0.394749\pi$
$883$	1.50440e7			0.649325			0.324663	+	0.945830i	$0.394749\pi$
$884$	−1.50689e7	+	2.61001e7i	−0.648561	+	1.12334i
$885$	3.34275e6	+	5.78982e6i	0.143465	+	0.248489i
$886$	−2.39704e7	−	4.15180e7i	−1.02587	−	1.77686i
$887$	−8.90504e6	+	1.54240e7i	−0.380038	+	0.658245i	−0.991067	−	0.133363i	$-0.957422\pi$
$887$	−8.90504e6	+	1.54240e7i	−0.380038	+	0.658245i	0.611030	+	0.791608i	$0.290756\pi$
$888$	−5.73682e6			−0.244140
$889$	1.25715e7	−	1.37438e7i	0.533497	−	0.583247i
$890$	9.18375e6			0.388638
$891$	1.83908e6	−	3.18538e6i	0.0776080	−	0.134421i
$892$	3.03891e7	+	5.26354e7i	1.27881	+	2.21496i
$893$	1.11846e7	+	1.93723e7i	0.469345	+	0.812929i
$894$	7.05655e6	−	1.22223e7i	0.295290	−	0.511457i
$895$	1.02508e7			0.427762
$896$	−1.29875e7	−	4.10641e7i	−0.540450	−	1.70881i
$897$	−1.54999e7			−0.643202
$898$	1.42802e7	−	2.47341e7i	0.590941	−	1.02354i
$899$	3.09159e6	+	5.35479e6i	0.127580	+	0.220975i
$900$	−4.59537e6	−	7.95941e6i	−0.189110	−	0.327548i
$901$	1.49053e7	−	2.58168e7i	0.611687	−	1.05947i
$902$	1.29405e6			0.0529583
$903$	1.99436e7	+	4.40285e6i	0.813925	+	0.179686i
$904$	4.06815e7			1.65568
$905$	−2.77037e6	+	4.79842e6i	−0.112439	+	0.194750i
$906$	−1.58988e7	−	2.75376e7i	−0.643494	−	1.11456i
$907$	584680.	+	1.01270e6i	0.0235993	+	0.0408753i	0.877584	−	0.479423i	$-0.159154\pi$
$907$	584680.	+	1.01270e6i	0.0235993	+	0.0408753i	−0.853985	+	0.520298i	$0.825821\pi$
$908$	−1.55323e7	+	2.69027e7i	−0.625202	+	1.08288i
$909$	2.03658e6			0.0817506
$910$	4.54892e7	+	1.00424e7i	1.82098	+	0.402008i
$911$	2.74389e7			1.09539			0.547697	−	0.836677i	$-0.315505\pi$
$911$	2.74389e7			1.09539			0.547697	+	0.836677i	$0.315505\pi$
$912$	2.05441e6	−	3.55835e6i	0.0817901	−	0.141665i
$913$	4.37462e6	+	7.57707e6i	0.173685	+	0.300832i
$914$	−8.18948e6	−	1.41846e7i	−0.324258	−	0.561632i
$915$	−307991.	+	533455.i	−0.0121614	+	0.0210642i
$916$	2.93781e7			1.15687
$917$	−2.04420e6	−	6.46339e6i	−0.0802786	−	0.253827i
$918$	6.88423e6			0.269618
$919$	−5.51091e6	+	9.54518e6i	−0.215246	+	0.372817i	−0.953349	−	0.301872i	$-0.902389\pi$
$919$	−5.51091e6	+	9.54518e6i	−0.215246	+	0.372817i	0.738103	+	0.674688i	$0.235722\pi$
$920$	−2.62747e7	−	4.55092e7i	−1.02345	−	1.77268i
$921$	−6.06794e6	−	1.05100e7i	−0.235718	−	0.408275i
$922$	−3.21932e7	+	5.57602e7i	−1.24720	+	2.16022i
$923$	3.31444e7			1.28058
$924$	−2.47978e7	+	2.71102e7i	−0.955505	+	1.04461i
$925$	−5.67367e6			−0.218027
$926$	2.41246e7	−	4.17851e7i	0.924557	−	1.60138i
$927$	6.51050e6	+	1.12765e7i	0.248837	+	0.430998i
$928$	1.55587e6	+	2.69484e6i	0.0593065	+	0.102722i
$929$	−2.12526e6	+	3.68105e6i	−0.0807927	+	0.139937i	−0.903591	−	0.428397i	$-0.859079\pi$
$929$	−2.12526e6	+	3.68105e6i	−0.0807927	+	0.139937i	0.822798	+	0.568334i	$0.192412\pi$
$930$	−4.97452e7			−1.88601
$931$	2.08630e7	+	9.68361e6i	0.788866	+	0.366153i
$932$	−2.04559e7			−0.771398
$933$	−1.49877e7	+	2.59595e7i	−0.563679	+	0.976320i
$934$	−2.15108e7	−	3.72578e7i	−0.806844	−	1.39749i
$935$	−2.02206e7	−	3.50232e7i	−0.756425	−	1.31017i
$936$	4.90372e6	−	8.49349e6i	0.182951	−	0.316881i
$937$	3.75738e7			1.39809			0.699046	−	0.715077i	$-0.253608\pi$
$937$	3.75738e7			1.39809			0.699046	+	0.715077i	$0.253608\pi$
$938$	−1.62804e7	+	1.77986e7i	−0.604169	+	0.660509i
$939$	2.55303e7			0.944915
$940$	−3.29279e7	+	5.70328e7i	−1.21547	+	2.10526i
$941$	−3.43521e6	−	5.94997e6i	−0.126468	−	0.219049i	0.795838	−	0.605510i	$-0.207031\pi$
$941$	−3.43521e6	−	5.94997e6i	−0.126468	−	0.219049i	−0.922306	+	0.386461i	$0.873697\pi$
$942$	−1.65109e6	−	2.85977e6i	−0.0606239	−	0.105004i
$943$	−396775.	+	687235.i	−0.0145300	+	0.0251667i
$944$	−3.45476e6			−0.126179
$945$	−2.04422e6	−	6.46347e6i	−0.0744644	−	0.235443i
$946$	−9.21446e7			−3.34767
$947$	1.15462e7	−	1.99985e7i	0.418372	−	0.724641i	−0.577404	−	0.816459i	$-0.695934\pi$
$947$	1.15462e7	−	1.99985e7i	0.418372	−	0.724641i	0.995776	+	0.0918172i	$0.0292676\pi$
$948$	1.12953e7	+	1.95641e7i	0.408204	+	0.707031i
$949$	−7.23161e6	−	1.25255e7i	−0.260657	−	0.451471i
$950$	1.29792e7	−	2.24806e7i	0.466592	−	0.808162i
$951$	9.79551e6			0.351217
$952$	−2.88941e7	−	6.37881e6i	−1.03328	−	0.228112i
$953$	−2.95399e7			−1.05360			−0.526802	−	0.849988i	$-0.676609\pi$
$953$	−2.95399e7			−1.05360			−0.526802	+	0.849988i	$0.676609\pi$
$954$	−1.12724e7	+	1.95244e7i	−0.401002	+	0.694555i
$955$	9.75709e6	+	1.68998e7i	0.346188	+	0.599615i
$956$	−1.04431e7	−	1.80880e7i	−0.369559	−	0.640096i
$957$	1.90078e6	−	3.29224e6i	0.0670890	−	0.116202i
$958$	2.70919e6			0.0953730
$959$	1.19126e6	+	262988.i	0.0418273	+	0.00923400i
$960$	−3.19261e7			−1.11807
$961$	−1.93581e7	+	3.35292e7i	−0.676166	+	1.17115i
$962$	−7.03511e6	−	1.21852e7i	−0.245094	−	0.424516i
$963$	3.82221e6	+	6.62026e6i	0.132815	+	0.230043i
$964$	4.80664e7	−	8.32535e7i	1.66590	−	2.88543i
$965$	1.15009e6			0.0397569
$966$	−1.06648e7	−	3.37201e7i	−0.367713	−	1.16264i
$967$	1.49151e7			0.512931			0.256466	−	0.966553i	$-0.417442\pi$
$967$	1.49151e7			0.512931			0.256466	+	0.966553i	$0.417442\pi$
$968$	1.73880e7	−	3.01170e7i	0.596434	−	1.03305i
$969$	6.19347e6	+	1.07274e7i	0.211897	+	0.367016i
$970$	4.35081e6	+	7.53582e6i	0.148471	+	0.257159i
$971$	−7.74150e6	+	1.34087e7i	−0.263498	+	0.456391i	−0.967169	−	0.254134i	$-0.918209\pi$
$971$	−7.74150e6	+	1.34087e7i	−0.263498	+	0.456391i	0.703671	+	0.710526i	$0.251543\pi$
$972$	−3.31676e6			−0.112603
$973$	−1.60207e7	+	1.75147e7i	−0.542501	+	0.593091i
$974$	7.33992e7			2.47910
$975$	4.84974e6	−	8.39999e6i	0.163383	−	0.282988i
$976$	−159155.	−	275665.i	−0.00534807	−	0.00926313i
$977$	1.41714e7	+	2.45455e7i	0.474980	+	0.822690i	0.999589	−	0.0286531i	$-0.00912183\pi$
$977$	1.41714e7	+	2.45455e7i	0.474980	+	0.822690i	−0.524609	+	0.851343i	$0.675788\pi$
$978$	2.01942e7	−	3.49773e7i	0.675117	−	1.16934i
$979$	−7.64410e6			−0.254900
$980$	6.02133e6	+	6.74470e7i	0.200275	+	2.24335i
$981$	−6.75487e6			−0.224101
$982$	1.47640e7	−	2.55720e7i	0.488569	−	0.846226i
$983$	−1.28497e7	−	2.22563e7i	−0.424139	−	0.734630i	0.572201	−	0.820114i	$-0.306090\pi$
$983$	−1.28497e7	−	2.22563e7i	−0.424139	−	0.734630i	−0.996340	+	0.0854834i	$0.972757\pi$
$984$	−251057.	−	434843.i	−0.00826578	−	0.0143168i
$985$	3.70223e7	−	6.41245e7i	1.21583	−	2.10588i
$986$	7.11518e6			0.233074
$987$	−1.28721e7	+	1.40724e7i	−0.420587	+	0.459807i
$988$	4.10106e7			1.33661
$989$	2.82530e7	−	4.89355e7i	0.918487	−	1.59087i
$990$	1.52922e7	+	2.64869e7i	0.495887	+	0.858901i
$991$	−2.23202e7	−	3.86598e7i	−0.721962	−	1.25048i	−0.960212	−	0.279271i	$-0.909907\pi$
$991$	−2.23202e7	−	3.86598e7i	−0.721962	−	1.25048i	0.238250	−	0.971204i	$-0.423426\pi$
$992$	−1.69460e7	+	2.93514e7i	−0.546750	+	0.947000i
$993$	−1.17499e7			−0.378148
$994$	2.28052e7	+	7.21060e7i	0.732096	+	2.31476i
$995$	6.32461e7			2.02524
$996$	3.94479e6	−	6.83257e6i	0.126001	−	0.218241i
$997$	−1.15277e7	−	1.99665e7i	−0.367286	−	0.636158i	0.621854	−	0.783133i	$-0.286380\pi$
$997$	−1.15277e7	−	1.99665e7i	−0.367286	−	0.636158i	−0.989140	+	0.146975i	$0.953046\pi$
$998$	3.15764e7	+	5.46919e7i	1.00354	+	1.73819i
$999$	−1.02376e6	+	1.77320e6i	−0.0324551	+	0.0562140i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.e.b.16.2	yes	4
3.2	odd	2		63.6.e.c.37.1		4
4.3	odd	2		336.6.q.e.289.2		4
7.2	even	3		147.6.a.i.1.1		2
7.3	odd	6		147.6.e.l.67.2		4
7.4	even	3	inner	21.6.e.b.4.2	✓	4
7.5	odd	6		147.6.a.k.1.1		2
7.6	odd	2		147.6.e.l.79.2		4
21.2	odd	6		441.6.a.t.1.2		2
21.5	even	6		441.6.a.s.1.2		2
21.11	odd	6		63.6.e.c.46.1		4
28.11	odd	6		336.6.q.e.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	7.4	even	3	inner
21.6.e.b.16.2	yes	4	1.1	even	1	trivial
63.6.e.c.37.1		4	3.2	odd	2
63.6.e.c.46.1		4	21.11	odd	6
147.6.a.i.1.1		2	7.2	even	3
147.6.a.k.1.1		2	7.5	odd	6
147.6.e.l.67.2		4	7.3	odd	6
147.6.e.l.79.2		4	7.6	odd	2
336.6.q.e.193.2		4	28.11	odd	6
336.6.q.e.289.2		4	4.3	odd	2
441.6.a.s.1.2		2	21.5	even	6
441.6.a.t.1.2		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)

\(f(q)\)	\(=\)	\(q+(4.69493 - 8.13186i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(35.8645 - 62.1192i) q^{5} +84.5088 q^{6} +(-87.5000 + 95.6596i) q^{7} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\)	\(q+(4.69493 - 8.13186i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(35.8645 - 62.1192i) q^{5} +84.5088 q^{6} +(-87.5000 + 95.6596i) q^{7} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-336.763 - 583.291i) q^{10} +(280.305 + 485.503i) q^{11} +(252.763 - 437.799i) q^{12} +533.509 q^{13} +(367.084 + 1160.65i) q^{14} +645.562 q^{15} +(-166.798 + 288.903i) q^{16} +(-502.850 - 870.962i) q^{17} +(380.290 + 658.681i) q^{18} +(-684.263 + 1185.18i) q^{19} -4028.99 q^{20} +(-1139.34 - 251.527i) q^{21} +5264.05 q^{22} +(-1614.04 + 2795.60i) q^{23} +(-1021.27 - 1768.90i) q^{24} +(-1010.03 - 1749.42i) q^{25} +(2504.79 - 4338.42i) q^{26} -729.000 q^{27} +(7110.71 + 1569.80i) q^{28} -753.456 q^{29} +(3030.87 - 5249.62i) q^{30} +(-4103.21 - 7106.97i) q^{31} +(-2064.97 - 3576.64i) q^{32} +(-2522.75 + 4369.52i) q^{33} -9443.39 q^{34} +(2804.15 + 8866.21i) q^{35} +4549.74 q^{36} +(1404.33 - 2432.37i) q^{37} +(6425.14 + 11128.7i) q^{38} +(2400.79 + 4158.29i) q^{39} +(-8139.43 + 14097.9i) q^{40} +245.827 q^{41} +(-7394.52 + 8084.07i) q^{42} -17504.5 q^{43} +(15744.6 - 27270.5i) q^{44} +(2905.03 + 5031.65i) q^{45} +(15155.6 + 26250.3i) q^{46} +(8172.74 - 14155.6i) q^{47} -3002.37 q^{48} +(-1494.50 - 16740.4i) q^{49} -18968.1 q^{50} +(4525.65 - 7838.66i) q^{51} +(-14983.5 - 25952.2i) q^{52} +(14820.8 + 25670.4i) q^{53} +(-3422.61 + 5928.13i) q^{54} +40212.0 q^{55} +(19858.1 - 21709.9i) q^{56} -12316.7 q^{57} +(-3537.43 + 6127.00i) q^{58} +(5178.05 + 8968.65i) q^{59} +(-18130.5 - 31402.9i) q^{60} +(-477.089 + 826.343i) q^{61} -77057.2 q^{62} +(-3166.58 - 10012.2i) q^{63} -49454.8 q^{64} +(19134.0 - 33141.1i) q^{65} +(23688.2 + 41029.2i) q^{66} +(9907.60 + 17160.5i) q^{67} +(-28244.9 + 48921.6i) q^{68} -29052.7 q^{69} +(85264.1 + 18823.3i) q^{70} +62125.4 q^{71} +(9191.45 - 15920.1i) q^{72} +(-13554.8 - 23477.6i) q^{73} +(-13186.5 - 22839.7i) q^{74} +(9090.27 - 15744.8i) q^{75} +76869.6 q^{76} +(-70969.7 - 15667.6i) q^{77} +45086.2 q^{78} +(-22343.7 + 38700.4i) q^{79} +(11964.3 + 20722.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(1154.14 - 1999.03i) q^{82} +15606.6 q^{83} +(19762.8 + 62486.6i) q^{84} -72137.9 q^{85} +(-82182.5 + 142344. i) q^{86} +(-3390.55 - 5872.61i) q^{87} +(-63615.0 - 110184. i) q^{88} +(-6817.66 + 11808.5i) q^{89} +54555.6 q^{90} +(-46682.0 + 51035.2i) q^{91} +181320. q^{92} +(36928.9 - 63962.7i) q^{93} +(-76740.9 - 132919. i) q^{94} +(49081.6 + 85011.8i) q^{95} +(18584.8 - 32189.8i) q^{96} -12919.5 q^{97} +(-143147. - 66442.1i) q^{98} -45409.4 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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