LMFDB - Embedded newform 21.6.e.b.4.2

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			4.2
Root			$-3.69493 - 2.71062i$ of defining polynomial
Character	$\chi$	$=$	21.4
Dual form			21.6.e.b.16.2

$q$-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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.69493	+	8.13186i	0.829955	+	1.43752i	0.898073	+	0.439847i	$0.144967\pi$
$2$	4.69493	+	8.13186i	0.829955	+	1.43752i	−0.0681181	+	0.997677i	$0.521699\pi$
$3$	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	0.985084	+	0.172076i	$0.0550476\pi$
$5$	35.8645	+	62.1192i	0.641564	+	1.11122i	−0.343519	+	0.939146i	$0.611619\pi$
$6$	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	−0.270524	−	0.962713i	$-0.587197\pi$
$11$	280.305	−	485.503i	0.698472	−	1.20979i	0.968996	−	0.247076i	$-0.0794698\pi$
$12$	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	−0.996135	−	0.0878311i	$-0.972006\pi$
$17$	−502.850	+	870.962i	−0.422004	+	0.730932i	0.574132	+	0.818763i	$0.305340\pi$
$18$	380.290	−	658.681i	0.276652	−	0.479175i
$19$	−684.263	−	1185.18i	−0.434850	−	0.753182i	0.562434	−	0.826842i	$-0.309865\pi$
$19$	−684.263	−	1185.18i	−0.434850	−	0.753182i	−0.997283	+	0.0736606i	$0.976532\pi$
$20$	−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	−0.986259	−	0.165205i	$-0.947171\pi$
$23$	−1614.04	−	2795.60i	−0.636201	−	1.10193i	0.350058	−	0.936728i	$-0.386162\pi$
$24$	−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	0.172389	+	0.985029i	$0.444852\pi$
$31$	−4103.21	+	7106.97i	−0.766866	+	1.32825i	−0.939254	+	0.343222i	$0.888482\pi$
$32$	−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	0.937943	−	0.346791i	$-0.112729\pi$
$37$	1404.33	+	2432.37i	0.168642	+	0.292096i	−0.769301	+	0.638887i	$0.779395\pi$
$38$	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	0.998922	+	0.0464219i	$0.0147819\pi$
$47$	8172.74	+	14155.6i	0.539663	+	0.934725i	−0.459258	+	0.888303i	$0.651885\pi$
$48$	−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	−0.234340	−	0.972155i	$-0.575293\pi$
$53$	14820.8	−	25670.4i	0.724741	−	1.25529i	0.959081	−	0.283133i	$-0.0913739\pi$
$54$	−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	−0.752801	−	0.658248i	$-0.771298\pi$
$59$	5178.05	−	8968.65i	0.193659	−	0.335426i	0.946460	+	0.322821i	$0.104631\pi$
$60$	−18130.5	+	31402.9i	−0.650176	+	1.12614i
$61$	−477.089	−	826.343i	−0.0164163	−	0.0284339i	0.857701	−	0.514150i	$-0.171892\pi$
$61$	−477.089	−	826.343i	−0.0164163	−	0.0284339i	−0.874117	+	0.485716i	$0.838559\pi$
$62$	−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	−0.699130	−	0.714994i	$-0.746429\pi$
$67$	9907.60	−	17160.5i	0.269638	−	0.467027i	0.968768	+	0.247967i	$0.0797626\pi$
$68$	−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	−0.975611	−	0.219509i	$-0.929555\pi$
$73$	−13554.8	+	23477.6i	−0.297705	+	0.515641i	0.677905	+	0.735149i	$0.262888\pi$
$74$	−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	0.591265	−	0.806477i	$-0.298629\pi$
$79$	−22343.7	−	38700.4i	−0.402798	−	0.697666i	−0.994062	+	0.108812i	$0.965295\pi$
$80$	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	0.816796	−	0.576926i	$-0.195748\pi$
$89$	−6817.66	−	11808.5i	−0.0912347	−	0.158023i	−0.908031	+	0.418903i	$0.862415\pi$
$90$	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	−0.920802	−	0.390029i	$-0.872465\pi$
$101$	−12571.5	+	21774.4i	−0.122626	+	0.212394i	0.798177	+	0.602424i	$0.205798\pi$
$102$	−42495.3	+	73604.0i	−0.404427	+	0.700488i
$103$	80376.6	+	139216.i	0.746511	+	1.29300i	0.949485	+	0.313811i	$0.101606\pi$
$103$	80376.6	+	139216.i	0.746511	+	1.29300i	−0.202974	+	0.979184i	$0.565061\pi$
$104$	−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	0.993534	−	0.113531i	$-0.0362162\pi$
$107$	47187.8	+	81731.6i	0.398446	+	0.690129i	−0.595088	+	0.803661i	$0.702883\pi$
$108$	20473.8	−	35461.7i	0.168904	−	0.292550i
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	−0.647553	−	0.762020i	$-0.724208\pi$
$109$	41696.7	−	72220.9i	0.336152	−	0.582233i	0.983705	+	0.179788i	$0.0575410\pi$
$110$	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	0.791764	−	0.610827i	$-0.209163\pi$
$131$	−26144.9	−	45284.3i	−0.133110	−	0.230553i	−0.924874	+	0.380274i	$0.875830\pi$
$132$	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	−0.876535	−	0.481337i	$-0.840151\pi$
$137$	−4705.05	+	8149.39i	−0.0214172	+	0.0370957i	0.855118	+	0.518433i	$0.173484\pi$
$138$	−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	0.977952	−	0.208830i	$-0.0669657\pi$
$149$	83500.8	+	144628.i	0.308123	+	0.533685i	−0.669828	+	0.742516i	$0.733632\pi$
$150$	−85356.4	+	147842.i	−0.309748	+	0.536499i
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	0.306029	+	0.952022i	$0.401000\pi$
$151$	−188132.	+	325855.i	−0.671461	+	1.16300i	−0.977490	+	0.210982i	$0.932334\pi$
$152$	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	−0.895920	−	0.444215i	$-0.853483\pi$
$157$	−19537.5	+	33840.0i	−0.0632587	+	0.109567i	0.832662	+	0.553782i	$0.186816\pi$
$158$	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	0.966887	+	0.255206i	$0.0821433\pi$
$163$	238959.	+	413890.i	0.704458	+	1.22016i	−0.262428	+	0.964951i	$0.584523\pi$
$164$	−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	0.833693	−	0.552228i	$-0.186222\pi$
$173$	−24169.1	−	41862.1i	−0.0613968	−	0.106342i	−0.895090	+	0.445886i	$0.852889\pi$
$174$	−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	−0.770566	−	0.637360i	$-0.780026\pi$
$179$	71455.3	−	123764.i	0.166687	−	0.288711i	0.937253	+	0.348650i	$0.113360\pi$
$180$	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	0.699010	−	0.715112i	$-0.253624\pi$
$191$	−136027.	−	235606.i	−0.269800	−	0.467307i	−0.968810	+	0.247805i	$0.920291\pi$
$192$	−222546.	+	385462.i	−0.435680	+	0.754620i
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	−0.858175	−	0.513357i	$-0.828402\pi$
$193$	8016.89	−	13885.7i	0.0154922	−	0.0268333i	0.873668	+	0.486523i	$0.161735\pi$
$194$	−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	−0.137290	−	0.990531i	$-0.543839\pi$
$199$	440868.	−	763606.i	0.789180	−	1.36690i	0.926470	−	0.376369i	$-0.122827\pi$
$200$	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	−0.987319	−	0.158748i	$-0.949254\pi$
$227$	−276524.	+	478954.i	−0.356179	+	0.616921i	0.631140	+	0.775669i	$0.282587\pi$
$228$	345913.	−	599139.i	0.440687	−	0.763292i
$229$	−261512.	−	452952.i	−0.329536	−	0.570773i	0.652884	−	0.757458i	$-0.273559\pi$
$229$	−261512.	−	452952.i	−0.329536	−	0.570773i	−0.982420	+	0.186685i	$0.940226\pi$
$230$	2.17420e6			2.71006
$231$	−197246.	+	623658.i	−0.243209	+	0.768983i
$232$	170996.			0.208577
$233$	182090.	+	315390.i	0.219734	+	0.380590i	0.954727	−	0.297485i	$-0.0961477\pi$
$233$	182090.	+	315390.i	0.219734	+	0.380590i	−0.734993	+	0.678075i	$0.762814\pi$
$234$	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	0.201678	−	0.979452i	$-0.435360\pi$
$241$	855737.	−	1.48218e6i	0.949069	−	1.64384i	0.747391	−	0.664384i	$-0.231306\pi$
$242$	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	0.930212	−	0.367023i	$-0.119623\pi$
$257$	155920.	+	270061.i	0.147254	+	0.255052i	−0.782957	+	0.622075i	$0.786290\pi$
$258$	−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	−0.991783	−	0.127928i	$-0.959167\pi$
$263$	−431983.	+	748216.i	−0.385103	+	0.667018i	0.606681	+	0.794946i	$0.292501\pi$
$264$	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	−0.527347	−	0.849650i	$-0.676813\pi$
$269$	560346.	−	970548.i	0.472145	−	0.817779i	0.999492	+	0.0318707i	$0.0101465\pi$
$270$	245500.	−	425219.i	0.204948	−	0.354980i
$271$	−570058.	−	987369.i	−0.471515	−	0.816688i	0.527954	−	0.849273i	$-0.322959\pi$
$271$	−570058.	−	987369.i	−0.471515	−	0.816688i	−0.999469	+	0.0325848i	$0.989626\pi$
$272$	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	−0.154502	−	0.987992i	$-0.549377\pi$
$277$	994005.	−	1.72167e6i	0.778375	−	1.34819i	0.932878	−	0.360193i	$-0.117289\pi$
$278$	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	−0.291087	+	0.956697i	$0.594017\pi$
$283$	−1.31237e6	+	2.27308e6i	−0.974067	+	1.68713i	−0.682980	+	0.730437i	$0.739316\pi$
$284$	−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	0.300813	−	0.953683i	$-0.402742\pi$
$311$	1.66530e6	−	2.88439e6i	0.976320	−	1.69104i	0.675507	−	0.737353i	$-0.263925\pi$
$312$	−544858.	+	943721.i	−0.316881	+	0.548854i
$313$	1.41835e6	+	2.45666e6i	0.818320	+	1.41737i	0.906919	+	0.421305i	$0.138428\pi$
$313$	1.41835e6	+	2.45666e6i	0.818320	+	1.41737i	−0.0885991	+	0.996067i	$0.528239\pi$
$314$	−366909.			−0.210007
$315$	−735516.	+	162376.i	−0.417653	+	0.0922032i
$316$	2.51007e6			1.41406
$317$	544195.	+	942574.i	0.304163	+	0.526826i	0.977075	−	0.212897i	$-0.0682899\pi$
$317$	544195.	+	942574.i	0.304163	+	0.526826i	−0.672912	+	0.739723i	$0.734957\pi$
$318$	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	0.654527	−	0.756039i	$-0.272868\pi$
$331$	−652773.	−	1.13064e6i	−0.327485	−	0.567221i	−0.982012	+	0.188817i	$0.939535\pi$
$332$	−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	−0.608911	−	0.793239i	$-0.708393\pi$
$347$	857958.	−	1.48603e6i	0.382510	−	0.662526i	0.991420	+	0.130713i	$0.0417265\pi$
$348$	−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	0.111119	+	0.993807i	$0.464557\pi$
$353$	−1.88490e6	+	3.26474e6i	−0.805103	+	1.39448i	−0.916222	+	0.400672i	$0.868777\pi$
$354$	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	0.597970	−	0.801518i	$-0.295974\pi$
$359$	−964935.	−	1.67132e6i	−0.395150	−	0.684420i	−0.993120	+	0.117099i	$0.962641\pi$
$360$	−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	−0.998895	−	0.0469885i	$-0.985038\pi$
$367$	−1.18371e6	+	2.05025e6i	−0.458754	+	0.794586i	0.540141	+	0.841575i	$0.318371\pi$
$368$	−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	−0.981029	−	0.193860i	$-0.937899\pi$
$373$	−1.76914e6	−	3.06425e6i	−0.658402	−	1.14039i	0.322627	−	0.946526i	$-0.395434\pi$
$374$	−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	0.544385	−	0.838836i	$-0.316763\pi$
$383$	−1.30407e6	−	2.25872e6i	−0.454261	−	0.786802i	−0.998645	+	0.0520333i	$0.983430\pi$
$384$	−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	−0.525455	−	0.850821i	$-0.676105\pi$
$389$	1.41498e6	−	2.45081e6i	0.474106	−	0.821175i	0.999560	+	0.0296466i	$0.00943818\pi$
$390$	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	0.992044	−	0.125888i	$-0.0401781\pi$
$397$	1.21531e6	+	2.10498e6i	0.387000	+	0.670303i	−0.605045	+	0.796191i	$0.706845\pi$
$398$	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	0.990714	−	0.135962i	$-0.0434124\pi$
$401$	1.21592e6	+	2.10604e6i	0.377611	+	0.654041i	−0.613103	+	0.790003i	$0.710079\pi$
$402$	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	−0.260774	−	0.965400i	$-0.583978\pi$
$409$	2.38733e6	−	4.13497e6i	0.705674	−	1.22226i	0.966448	−	0.256863i	$-0.0826889\pi$
$410$	−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	−0.559034	−	0.829145i	$-0.688828\pi$
$431$	1.69124e6	−	2.92932e6i	0.438544	−	0.759580i	0.997577	+	0.0695651i	$0.0221612\pi$
$432$	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	−0.998963	−	0.0455294i	$-0.985503\pi$
$439$	−2.17610e6	−	3.76911e6i	−0.538911	−	0.933421i	0.460052	−	0.887892i	$-0.347831\pi$
$440$	−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	0.989845	+	0.142148i	$0.0454010\pi$
$443$	2.55280e6	+	4.42158e6i	0.618027	+	1.07045i	−0.371819	+	0.928305i	$0.621266\pi$
$444$	−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	0.947014	−	0.321192i	$-0.104083\pi$
$457$	872162.	+	1.51063e6i	0.195347	+	0.338351i	−0.751667	+	0.659542i	$0.770750\pi$
$458$	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	0.999872	−	0.0160029i	$-0.00509409\pi$
$467$	2.29085e6	+	3.96788e6i	0.486077	+	0.841910i	−0.513795	+	0.857913i	$0.671761\pi$
$468$	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	−0.851304	−	0.524673i	$-0.824188\pi$
$479$	144261.	−	249868.i	0.0287284	−	0.0497590i	0.880032	+	0.474914i	$0.157521\pi$
$480$	−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	−0.202613	−	0.979259i	$-0.564943\pi$
$487$	3.90842e6	−	6.76959e6i	0.746757	−	1.29342i	0.949369	−	0.314162i	$-0.101723\pi$
$488$	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	−0.992118	−	0.125305i	$-0.960009\pi$
$499$	−3.36281e6	−	5.82456e6i	−0.604577	−	1.04716i	0.387541	−	0.921852i	$-0.373324\pi$
$500$	−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	0.944911	+	0.327328i	$0.106148\pi$
$509$	4.41851e6	+	7.65308e6i	0.755930	+	1.30931i	−0.188981	+	0.981981i	$0.560519\pi$
$510$	−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	−0.892705	−	0.450641i	$-0.851195\pi$
$521$	−347492.	+	601874.i	−0.0560855	+	0.0971430i	0.836619	+	0.547784i	$0.184529\pi$
$522$	−286531.	+	496287.i	−0.0460252	+	0.0797181i
$523$	−1.79105e6	−	3.10219e6i	−0.286321	−	0.495923i	0.686607	−	0.727028i	$-0.259099\pi$
$523$	−1.79105e6	−	3.10219e6i	−0.286321	−	0.495923i	−0.972929	+	0.231105i	$0.925766\pi$
$524$	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	0.991005	−	0.133821i	$-0.0427248\pi$
$541$	2.58423e6	+	4.47602e6i	0.379610	+	0.657504i	−0.611395	+	0.791325i	$0.709391\pi$
$542$	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	−0.252619	−	0.967566i	$-0.581292\pi$
$557$	5.21063e6	−	9.02508e6i	0.711627	−	1.23257i	0.964246	−	0.265009i	$-0.0853748\pi$
$558$	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	−0.518396	−	0.855141i	$-0.673471\pi$
$563$	3.62039e6	−	6.27069e6i	0.481375	−	0.833767i	0.999772	+	0.0213739i	$0.00680405\pi$
$564$	−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	0.834830	−	0.550508i	$-0.185566\pi$
$569$	−458268.	−	793743.i	−0.0593388	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$570$	4.14782e6	−	7.18424e6i	0.534728	−	0.926177i
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	0.337685	+	0.941259i	$0.390356\pi$
$571$	−5.03538e6	+	8.72154e6i	−0.646312	+	1.11944i	−0.983997	+	0.178186i	$0.942977\pi$
$572$	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	0.224760	+	0.974414i	$0.427840\pi$
$577$	−5.84987e6	+	1.01323e7i	−0.731488	+	1.26697i	−0.956247	+	0.292560i	$0.905493\pi$
$578$	−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	−0.797548	−	0.603255i	$-0.793870\pi$
$593$	−7.88850e6	−	1.36633e7i	−0.921208	−	1.59558i	−0.123660	−	0.992325i	$-0.539463\pi$
$594$	−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	0.0985183	+	0.995135i	$0.468590\pi$
$599$	−7.13541e6	+	1.23589e7i	−0.812553	+	1.40738i	−0.911072	+	0.412248i	$0.864744\pi$
$600$	−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	0.947262	−	0.320459i	$-0.103837\pi$
$607$	1.78017e6	+	3.08335e6i	0.196106	+	0.339665i	−0.751157	+	0.660124i	$0.770504\pi$
$608$	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	−0.215683	−	0.976463i	$-0.569198\pi$
$613$	6.86420e6	−	1.18891e7i	0.737800	−	1.27791i	0.953484	−	0.301445i	$-0.0974688\pi$
$614$	−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	−0.999167	−	0.0408136i	$-0.987005\pi$
$619$	−4.42555e6	+	7.66527e6i	−0.464238	+	0.804083i	0.534929	+	0.844897i	$0.320338\pi$
$620$	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	−0.117610	−	0.993060i	$-0.537523\pi$
$641$	8.33473e6	−	1.44362e7i	0.801210	−	1.38774i	0.918820	−	0.394677i	$-0.129144\pi$
$642$	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	−0.460217	−	0.887806i	$-0.652228\pi$
$647$	5.73656e6	−	9.93601e6i	0.538754	−	0.933150i	0.998971	−	0.0453435i	$-0.0144382\pi$
$648$	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	0.992084	+	0.125573i	$0.0400768\pi$
$653$	6.59005e6	+	1.14143e7i	0.604791	+	1.04753i	−0.387293	+	0.921957i	$0.626590\pi$
$654$	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	−0.910884	−	0.412662i	$-0.864599\pi$
$661$	−1.10160e6	+	1.90802e6i	−0.0980661	+	0.169856i	0.812818	+	0.582518i	$0.197932\pi$
$662$	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	0.902855	+	0.429945i	$0.141467\pi$
$677$	9.82377e6	+	1.70153e7i	0.823771	+	1.42681i	−0.0790842	+	0.996868i	$0.525200\pi$
$678$	−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	0.311363	+	0.950291i	$0.399215\pi$
$683$	−8.13523e6	+	1.40906e7i	−0.667295	+	1.15579i	−0.978658	+	0.205498i	$0.934119\pi$
$684$	−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	−0.934976	−	0.354712i	$-0.884579\pi$
$691$	−9.72335e6	−	1.68413e7i	−0.774677	−	1.34178i	0.160299	−	0.987069i	$-0.448754\pi$
$692$	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	0.834873	−	0.550442i	$-0.185541\pi$
$709$	−793193.	−	1.37385e6i	−0.0592603	−	0.102642i	−0.894134	+	0.447800i	$0.852208\pi$
$710$	−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	0.981817	+	0.189829i	$0.0607932\pi$
$719$	9.08376e6	+	1.57335e7i	0.655305	+	1.13502i	−0.326512	+	0.945193i	$0.605873\pi$
$720$	−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	0.914568	−	0.404432i	$-0.132531\pi$
$733$	1.55701e6	+	2.69681e6i	0.107036	+	0.185392i	−0.807532	+	0.589824i	$0.799197\pi$
$734$	−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	−0.977582	−	0.210555i	$-0.932473\pi$
$739$	−4.54950e6	+	7.87996e6i	−0.306445	+	0.530778i	0.671137	+	0.741333i	$0.265806\pi$
$740$	−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	0.815790	+	0.578349i	$0.196303\pi$
$751$	1.40459e7	+	2.43282e7i	0.908759	+	1.57402i	0.0929698	+	0.995669i	$0.470364\pi$
$752$	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	0.872113	−	0.489305i	$-0.162750\pi$
$761$	196591.	+	340506.i	0.0123056	+	0.0213139i	−0.859807	+	0.510619i	$0.829416\pi$
$762$	−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	−0.906166	−	0.422923i	$-0.861004\pi$
$773$	−1.44236e6	+	2.49824e6i	−0.0868210	+	0.150378i	0.819345	+	0.573301i	$0.194337\pi$
$774$	−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	−0.0174963	−	0.999847i	$-0.505570\pi$
$787$	1.48933e7	−	2.57960e7i	0.857145	−	1.48462i	0.874641	−	0.484771i	$-0.161097\pi$
$788$	−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	−0.867520	−	0.497402i	$-0.834287\pi$
$809$	−55798.5	+	96645.8i	−0.00299744	+	0.00519173i	0.864523	+	0.502594i	$0.167621\pi$
$810$	−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	0.763695	−	0.645577i	$-0.223383\pi$
$821$	−3.42307e6	−	5.92893e6i	−0.177238	−	0.306986i	−0.940934	+	0.338591i	$0.890050\pi$
$822$	−397618.	+	688695.i	−0.0205252	+	0.0355506i
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	−0.784743	−	0.619821i	$-0.787205\pi$
$823$	2.80605e6	−	4.86022e6i	0.144409	−	0.250125i	0.929152	+	0.369697i	$0.120538\pi$
$824$	−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	−0.999875	−	0.0158177i	$-0.994965\pi$
$829$	−9.62135e6	+	1.66647e7i	−0.486239	+	0.842190i	0.513636	+	0.858008i	$0.328298\pi$
$830$	−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	−0.826076	−	0.563558i	$-0.809432\pi$
$857$	1.61293e6	−	2.79367e6i	0.0750175	−	0.129934i	0.901094	+	0.433624i	$0.142765\pi$
$858$	1.26379e7	−	2.18895e7i	0.586079	−	1.01512i
$859$	−1.32335e7	−	2.29212e7i	−0.611918	−	1.05987i	−0.990917	−	0.134476i	$-0.957065\pi$
$859$	−1.32335e7	−	2.29212e7i	−0.611918	−	1.05987i	0.378999	−	0.925397i	$-0.376268\pi$
$860$	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	0.626086	−	0.779754i	$-0.284656\pi$
$863$	−7.92552e6	−	1.37274e7i	−0.362243	−	0.627424i	−0.988330	+	0.152330i	$0.951322\pi$
$864$	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	0.981989	−	0.188936i	$-0.0605037\pi$
$877$	7.45659e6	+	1.29152e7i	0.327372	+	0.567024i	−0.654618	+	0.755960i	$0.727170\pi$
$878$	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	0.611030	−	0.791608i	$-0.290756\pi$
$887$	−8.90504e6	−	1.54240e7i	−0.380038	−	0.658245i	−0.991067	+	0.133363i	$0.957422\pi$
$888$	−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	−0.853985	−	0.520298i	$-0.825821\pi$
$907$	584680.	−	1.01270e6i	0.0235993	−	0.0408753i	0.877584	+	0.479423i	$0.159154\pi$
$908$	−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	0.738103	−	0.674688i	$-0.235722\pi$
$919$	−5.51091e6	−	9.54518e6i	−0.215246	−	0.372817i	−0.953349	+	0.301872i	$0.902389\pi$
$920$	−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	0.822798	−	0.568334i	$-0.192412\pi$
$929$	−2.12526e6	−	3.68105e6i	−0.0807927	−	0.139937i	−0.903591	+	0.428397i	$0.859079\pi$
$930$	−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	−0.922306	−	0.386461i	$-0.873697\pi$
$941$	−3.43521e6	+	5.94997e6i	−0.126468	+	0.219049i	0.795838	+	0.605510i	$0.207031\pi$
$942$	−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	0.995776	−	0.0918172i	$-0.0292676\pi$
$947$	1.15462e7	+	1.99985e7i	0.418372	+	0.724641i	−0.577404	+	0.816459i	$0.695934\pi$
$948$	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	0.703671	−	0.710526i	$-0.251543\pi$
$971$	−7.74150e6	−	1.34087e7i	−0.263498	−	0.456391i	−0.967169	+	0.254134i	$0.918209\pi$
$972$	−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	−0.524609	−	0.851343i	$-0.675788\pi$
$977$	1.41714e7	−	2.45455e7i	0.474980	−	0.822690i	0.999589	+	0.0286531i	$0.00912183\pi$
$978$	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	−0.996340	−	0.0854834i	$-0.972757\pi$
$983$	−1.28497e7	+	2.22563e7i	−0.424139	+	0.734630i	0.572201	+	0.820114i	$0.306090\pi$
$984$	−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	0.238250	+	0.971204i	$0.423426\pi$
$991$	−2.23202e7	+	3.86598e7i	−0.721962	+	1.25048i	−0.960212	+	0.279271i	$0.909907\pi$
$992$	−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	−0.989140	−	0.146975i	$-0.953046\pi$
$997$	−1.15277e7	+	1.99665e7i	−0.367286	+	0.636158i	0.621854	+	0.783133i	$0.286380\pi$
$998$	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.4.2	✓	4
3.2	odd	2		63.6.e.c.46.1		4
4.3	odd	2		336.6.q.e.193.2		4
7.2	even	3	inner	21.6.e.b.16.2	yes	4
7.3	odd	6		147.6.a.k.1.1		2
7.4	even	3		147.6.a.i.1.1		2
7.5	odd	6		147.6.e.l.79.2		4
7.6	odd	2		147.6.e.l.67.2		4
21.2	odd	6		63.6.e.c.37.1		4
21.11	odd	6		441.6.a.t.1.2		2
21.17	even	6		441.6.a.s.1.2		2
28.23	odd	6		336.6.q.e.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	1.1	even	1	trivial
21.6.e.b.16.2	yes	4	7.2	even	3	inner
63.6.e.c.37.1		4	21.2	odd	6
63.6.e.c.46.1		4	3.2	odd	2
147.6.a.i.1.1		2	7.4	even	3
147.6.a.k.1.1		2	7.3	odd	6
147.6.e.l.67.2		4	7.6	odd	2
147.6.e.l.79.2		4	7.5	odd	6
336.6.q.e.193.2		4	4.3	odd	2
336.6.q.e.289.2		4	28.23	odd	6
441.6.a.s.1.2		2	21.17	even	6
441.6.a.t.1.2		2	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.69493 + 8.13186i) q^{2} +(4.50000 - 7.79423i) q^{3} +(-28.0848 + 48.6443i) q^{4} +(35.8645 + 62.1192i) q^{5} +84.5088 q^{6} +(-87.5000 - 95.6596i) q^{7} -226.949 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\)	\(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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