LMFDB - Embedded newform 84.6.e.a.71.49

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,6,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, 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:	$13.4722408643$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.49
Character	$\chi$	$=$	84.71
Dual form			84.6.e.a.71.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.40093 - 3.55413i) q^{2} +(-2.02884 + 15.4559i) q^{3} +(6.73637 - 31.2829i) q^{4} -44.2997i q^{5} +(46.0033 + 75.2309i) q^{6} -49.0000i q^{7} +(-81.5372 - 161.616i) q^{8} +(-234.768 - 62.7150i) q^{9} +(-157.447 - 194.960i) q^{10} +344.560 q^{11} +(469.838 + 167.584i) q^{12} -378.416 q^{13} +(-174.152 - 215.646i) q^{14} +(684.690 + 89.8770i) q^{15} +(-933.243 - 421.466i) q^{16} -1696.09i q^{17} +(-1256.09 + 558.389i) q^{18} -2579.78i q^{19} +(-1385.82 - 298.419i) q^{20} +(757.337 + 99.4133i) q^{21} +(1516.38 - 1224.61i) q^{22} +526.327 q^{23} +(2663.34 - 932.335i) q^{24} +1162.54 q^{25} +(-1665.38 + 1344.94i) q^{26} +(1445.62 - 3501.30i) q^{27} +(-1532.86 - 330.082i) q^{28} +6045.46i q^{29} +(3332.70 - 2037.93i) q^{30} -2887.35i q^{31} +(-5605.08 + 1462.02i) q^{32} +(-699.058 + 5325.47i) q^{33} +(-6028.11 - 7464.37i) q^{34} -2170.68 q^{35} +(-3543.39 + 6921.75i) q^{36} -3591.74 q^{37} +(-9168.85 - 11353.4i) q^{38} +(767.747 - 5848.75i) q^{39} +(-7159.53 + 3612.07i) q^{40} +12630.3i q^{41} +(3686.32 - 2254.16i) q^{42} +21579.3i q^{43} +(2321.08 - 10778.8i) q^{44} +(-2778.25 + 10400.1i) q^{45} +(2316.33 - 1870.63i) q^{46} +16221.6 q^{47} +(8407.53 - 13569.0i) q^{48} -2401.00 q^{49} +(5116.26 - 4131.82i) q^{50} +(26214.5 + 3441.10i) q^{51} +(-2549.15 + 11838.0i) q^{52} -21958.7i q^{53} +(-6081.98 - 20546.9i) q^{54} -15263.9i q^{55} +(-7919.18 + 3995.32i) q^{56} +(39872.7 + 5233.96i) q^{57} +(21486.3 + 26605.6i) q^{58} -7005.98 q^{59} +(7423.93 - 20813.6i) q^{60} +7136.98 q^{61} +(-10262.0 - 12707.0i) q^{62} +(-3073.04 + 11503.6i) q^{63} +(-19471.4 + 26355.4i) q^{64} +16763.7i q^{65} +(15850.9 + 25921.6i) q^{66} +18300.1i q^{67} +(-53058.6 - 11425.5i) q^{68} +(-1067.83 + 8134.83i) q^{69} +(-9553.02 + 7714.88i) q^{70} +77638.4 q^{71} +(9006.55 + 43055.8i) q^{72} -53127.5 q^{73} +(-15807.0 + 12765.5i) q^{74} +(-2358.61 + 17968.1i) q^{75} +(-80702.9 - 17378.3i) q^{76} -16883.4i q^{77} +(-17408.4 - 28468.6i) q^{78} -8353.39i q^{79} +(-18670.8 + 41342.3i) q^{80} +(51182.7 + 29446.9i) q^{81} +(44889.7 + 55585.1i) q^{82} +76137.1 q^{83} +(8211.64 - 23022.0i) q^{84} -75136.1 q^{85} +(76695.5 + 94968.9i) q^{86} +(-93437.8 - 12265.3i) q^{87} +(-28094.4 - 55686.3i) q^{88} +9040.37i q^{89} +(24736.5 + 55644.5i) q^{90} +18542.4i q^{91} +(3545.53 - 16465.0i) q^{92} +(44626.5 + 5857.98i) q^{93} +(71390.3 - 57653.7i) q^{94} -114283. q^{95} +(-11224.9 - 89597.6i) q^{96} -52693.1 q^{97} +(-10566.6 + 8533.46i) q^{98} +(-80891.5 - 21609.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) $ 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	4.40093	−	3.55413i	0.777982	−	0.628287i
$2$	4.40093	−	3.55413i	0.777982	−	0.628287i
$3$	−2.02884	+	15.4559i	−0.130150	+	0.991494i
$3$	−2.02884	+	15.4559i	−0.130150	+	0.991494i
$4$	6.73637	−	31.2829i	0.210511	−	0.977591i
$5$		−	44.2997i		−	0.792456i	−0.918152	−	0.396228i	$-0.870319\pi$
$5$		−	44.2997i		−	0.792456i	0.918152	−	0.396228i	$-0.129681\pi$
$6$	46.0033	+	75.2309i	0.521688	+	0.853136i
$7$		−	49.0000i		−	0.377964i
$7$		−	49.0000i		−	0.377964i
$8$	−81.5372	−	161.616i	−0.450434	−	0.892810i
$9$	−234.768	−	62.7150i	−0.966122	−	0.258087i
$10$	−157.447	−	194.960i	−0.497890	−	0.616517i
$11$	344.560			0.858584			0.429292	−	0.903166i	$-0.358763\pi$
$11$	344.560			0.858584			0.429292	+	0.903166i	$0.358763\pi$
$12$	469.838	+	167.584i	0.941878	+	0.335955i
$13$	−378.416			−0.621029			−0.310514	−	0.950569i	$-0.600501\pi$
$13$	−378.416			−0.621029			−0.310514	+	0.950569i	$0.600501\pi$
$14$	−174.152	−	215.646i	−0.237470	−	0.294049i
$15$	684.690	+	89.8770i	0.785716	+	0.103138i
$16$	−933.243	−	421.466i	−0.911370	−	0.411588i
$17$		−	1696.09i		−	1.42340i	−0.702485	−	0.711699i	$-0.747926\pi$
$17$		−	1696.09i		−	1.42340i	0.702485	−	0.711699i	$-0.252074\pi$
$18$	−1256.09	+	558.389i	−0.913778	+	0.406215i
$19$		−	2579.78i		−	1.63945i	−0.572758	−	0.819724i	$-0.694127\pi$
$19$		−	2579.78i		−	1.63945i	0.572758	−	0.819724i	$-0.305873\pi$
$20$	−1385.82	−	298.419i	−0.774698	−	0.166821i
$21$	757.337	+	99.4133i	0.374750	+	0.0491922i
$22$	1516.38	−	1224.61i	0.667963	−	0.539437i
$23$	526.327			0.207461			0.103730	−	0.994605i	$-0.466922\pi$
$23$	526.327			0.207461			0.103730	+	0.994605i	$0.466922\pi$
$24$	2663.34	−	932.335i	0.943840	−	0.330403i
$25$	1162.54			0.372013
$26$	−1665.38	+	1344.94i	−0.483149	+	0.390184i
$27$	1445.62	−	3501.30i	0.381632	−	0.924314i
$28$	−1532.86	−	330.082i	−0.369495	−	0.0795658i
$29$			6045.46i			1.33486i	0.744675	+	0.667428i	$0.232605\pi$
$29$			6045.46i			1.33486i	−0.744675	+	0.667428i	$0.767395\pi$
$30$	3332.70	−	2037.93i	0.676073	−	0.413415i
$31$		−	2887.35i		−	0.539629i	−0.962912	−	0.269815i	$-0.913038\pi$
$31$		−	2887.35i		−	0.539629i	0.962912	−	0.269815i	$-0.0869625\pi$
$32$	−5605.08	+	1462.02i	−0.967625	+	0.252393i
$33$	−699.058	+	5325.47i	−0.111745	+	0.851281i
$34$	−6028.11	−	7464.37i	−0.894302	−	1.10738i
$35$	−2170.68			−0.299520
$36$	−3543.39	+	6921.75i	−0.455683	+	0.890142i
$37$	−3591.74			−0.431321			−0.215660	−	0.976468i	$-0.569190\pi$
$37$	−3591.74			−0.431321			−0.215660	+	0.976468i	$0.569190\pi$
$38$	−9168.85	−	11353.4i	−1.03004	−	1.27546i
$39$	767.747	−	5848.75i	0.0808271	−	0.615746i
$40$	−7159.53	+	3612.07i	−0.707513	+	0.356949i
$41$			12630.3i			1.17342i	0.809796	+	0.586711i	$0.199578\pi$
$41$			12630.3i			1.17342i	−0.809796	+	0.586711i	$0.800422\pi$
$42$	3686.32	−	2254.16i	0.322455	−	0.197180i
$43$			21579.3i			1.77978i	0.456176	+	0.889889i	$0.349219\pi$
$43$			21579.3i			1.77978i	−0.456176	+	0.889889i	$0.650781\pi$
$44$	2321.08	−	10778.8i	0.180742	−	0.839345i
$45$	−2778.25	+	10400.1i	−0.204522	+	0.765609i
$46$	2316.33	−	1870.63i	0.161401	−	0.130345i
$47$	16221.6			1.07115			0.535575	−	0.844488i	$-0.320095\pi$
$47$	16221.6			1.07115			0.535575	+	0.844488i	$0.320095\pi$
$48$	8407.53	−	13569.0i	0.526702	−	0.850050i
$49$	−2401.00			−0.142857
$50$	5116.26	−	4131.82i	0.289419	−	0.233731i
$51$	26214.5	+	3441.10i	1.41129	+	0.185256i
$52$	−2549.15	+	11838.0i	−0.130734	+	0.607112i
$53$		−	21958.7i		−	1.07379i	−0.843650	−	0.536893i	$-0.819598\pi$
$53$		−	21958.7i		−	1.07379i	0.843650	−	0.536893i	$-0.180402\pi$
$54$	−6081.98	−	20546.9i	−0.283831	−	0.958874i
$55$		−	15263.9i		−	0.680391i
$56$	−7919.18	+	3995.32i	−0.337450	+	0.170248i
$57$	39872.7	+	5233.96i	1.62550	+	0.213375i
$58$	21486.3	+	26605.6i	0.838672	+	1.03849i
$59$	−7005.98			−0.262023			−0.131011	−	0.991381i	$-0.541822\pi$
$59$	−7005.98			−0.262023			−0.131011	+	0.991381i	$0.541822\pi$
$60$	7423.93	−	20813.6i	0.266229	−	0.746397i
$61$	7136.98			0.245578			0.122789	−	0.992433i	$-0.460816\pi$
$61$	7136.98			0.245578			0.122789	+	0.992433i	$0.460816\pi$
$62$	−10262.0	−	12707.0i	−0.339042	−	0.419822i
$63$	−3073.04	+	11503.6i	−0.0975475	+	0.365160i
$64$	−19471.4	+	26355.4i	−0.594219	+	0.804303i
$65$			16763.7i			0.492138i
$66$	15850.9	+	25921.6i	0.447913	+	0.732489i
$67$			18300.1i			0.498042i	0.968498	+	0.249021i	$0.0801088\pi$
$67$			18300.1i			0.498042i	−0.968498	+	0.249021i	$0.919891\pi$
$68$	−53058.6	−	11425.5i	−1.39150	−	0.299641i
$69$	−1067.83	+	8134.83i	−0.0270011	+	0.205696i
$70$	−9553.02	+	7714.88i	−0.233021	+	0.188185i
$71$	77638.4			1.82781			0.913904	−	0.405931i	$-0.133053\pi$
$71$	77638.4			1.82781			0.913904	+	0.405931i	$0.133053\pi$
$72$	9006.55	+	43055.8i	0.204752	+	0.978814i
$73$	−53127.5			−1.16684			−0.583422	−	0.812169i	$-0.698287\pi$
$73$	−53127.5			−1.16684			−0.583422	+	0.812169i	$0.698287\pi$
$74$	−15807.0	+	12765.5i	−0.335560	+	0.270993i
$75$	−2358.61	+	17968.1i	−0.0484176	+	0.368849i
$76$	−80702.9	−	17378.3i	−1.60271	−	0.345123i
$77$		−	16883.4i		−	0.324514i
$78$	−17408.4	−	28468.6i	−0.323983	−	0.529822i
$79$		−	8353.39i		−	0.150590i	−0.997161	−	0.0752948i	$-0.976010\pi$
$79$		−	8353.39i		−	0.150590i	0.997161	−	0.0752948i	$-0.0239898\pi$
$80$	−18670.8	+	41342.3i	−0.326166	+	0.722221i
$81$	51182.7	+	29446.9i	0.866783	+	0.498686i
$82$	44889.7	+	55585.1i	0.737246	+	0.912901i
$83$	76137.1			1.21311			0.606556	−	0.795041i	$-0.292551\pi$
$83$	76137.1			1.21311			0.606556	+	0.795041i	$0.292551\pi$
$84$	8211.64	−	23022.0i	0.126979	−	0.355996i
$85$	−75136.1			−1.12798
$86$	76695.5	+	94968.9i	1.11821	+	1.38464i
$87$	−93437.8	−	12265.3i	−1.32350	−	0.173732i
$88$	−28094.4	−	55686.3i	−0.386735	−	0.766553i
$89$			9040.37i			0.120979i	0.998169	+	0.0604897i	$0.0192662\pi$
$89$			9040.37i			0.120979i	−0.998169	+	0.0604897i	$0.980734\pi$
$90$	24736.5	+	55644.5i	0.321908	+	0.724129i
$91$			18542.4i			0.234727i
$92$	3545.53	−	16465.0i	0.0436728	−	0.202812i
$93$	44626.5	+	5857.98i	0.535039	+	0.0702329i
$94$	71390.3	−	57653.7i	0.833335	−	0.672989i
$95$	−114283.			−1.29919
$96$	−11224.9	−	89597.6i	−0.124310	−	0.992243i
$97$	−52693.1			−0.568623			−0.284311	−	0.958732i	$-0.591765\pi$
$97$	−52693.1			−0.568623			−0.284311	+	0.958732i	$0.591765\pi$
$98$	−10566.6	+	8533.46i	−0.111140	+	0.0897553i
$99$	−80891.5	−	21609.1i	−0.829497	−	0.221589i
$100$	7831.30	−	36367.7i	0.0783130	−	0.363677i
$101$		−	82630.2i		−	0.806000i	−0.915200	−	0.403000i	$-0.867967\pi$
$101$		−	82630.2i		−	0.806000i	0.915200	−	0.403000i	$-0.132033\pi$
$102$	127598.	−	78025.7i	1.21435	−	0.742570i
$103$		−	69948.5i		−	0.649659i	−0.945773	−	0.324829i	$-0.894693\pi$
$103$		−	69948.5i		−	0.649659i	0.945773	−	0.324829i	$-0.105307\pi$
$104$	30855.0	+	61158.1i	0.279732	+	0.554461i
$105$	4403.97	−	33549.8i	0.0389827	−	0.296973i
$106$	−78044.2	−	96638.9i	−0.674646	−	0.835386i
$107$	46494.7			0.392594			0.196297	−	0.980544i	$-0.437108\pi$
$107$	46494.7			0.392594			0.196297	+	0.980544i	$0.437108\pi$
$108$	−99792.6	−	68809.3i	−0.823264	−	0.567659i
$109$	122497.			0.987552			0.493776	−	0.869589i	$-0.335616\pi$
$109$	122497.			0.987552			0.493776	+	0.869589i	$0.335616\pi$
$110$	−54249.8	−	67175.3i	−0.427480	−	0.529331i
$111$	7287.07	−	55513.4i	0.0561365	−	0.427652i
$112$	−20651.9	+	45728.9i	−0.155566	+	0.344465i
$113$			58741.6i			0.432762i	0.976309	+	0.216381i	$0.0694254\pi$
$113$			58741.6i			0.432762i	−0.976309	+	0.216381i	$0.930575\pi$
$114$	194079.	−	118678.i	1.39867	−	0.855281i
$115$		−	23316.1i		−	0.164404i
$116$	189120.	+	40724.4i	1.30494	+	0.281002i
$117$	88839.9	+	23732.4i	0.599989	+	0.160279i
$118$	−30832.8	+	24900.1i	−0.203849	+	0.164625i
$119$	−83108.3			−0.537994
$120$	−41302.1	−	117985.i	−0.261830	−	0.747952i
$121$	−42329.5			−0.262833
$122$	31409.3	−	25365.7i	0.191055	−	0.154294i
$123$	−195212.	−	25624.9i	−1.16344	−	0.152721i
$124$	−90324.8	−	19450.3i	−0.527537	−	0.113598i
$125$		−	189937.i		−	1.08726i
$126$	27361.1	+	61548.6i	0.153535	+	0.345375i
$127$		−	125876.i		−	0.692520i	−0.938139	−	0.346260i	$-0.887451\pi$
$127$		−	125876.i		−	0.692520i	0.938139	−	0.346260i	$-0.112549\pi$
$128$	7978.36	+	185192.i	0.0430416	+	0.999073i
$129$	−333527.	−	43781.0i	−1.76464	−	0.231639i
$130$	59580.4	+	73775.9i	0.309204	+	0.382874i
$131$	74756.6			0.380602			0.190301	−	0.981726i	$-0.439054\pi$
$131$	74756.6			0.380602			0.190301	+	0.981726i	$0.439054\pi$
$132$	161887.	+	57742.9i	0.808682	+	0.288445i
$133$	−126409.			−0.619653
$134$	65040.8	+	80537.4i	0.312913	+	0.387468i
$135$	−155106.	−	64040.5i	−0.732479	−	0.302427i
$136$	−274115.	+	138294.i	−1.27082	+	0.641146i
$137$		−	368808.i		−	1.67880i	−0.543513	−	0.839401i	$-0.682906\pi$
$137$		−	368808.i		−	1.67880i	0.543513	−	0.839401i	$-0.317094\pi$
$138$	24212.8	+	39596.1i	0.108230	+	0.176992i
$139$			409405.i			1.79728i	0.438687	+	0.898640i	$0.355444\pi$
$139$			409405.i			1.79728i	−0.438687	+	0.898640i	$0.644556\pi$
$140$	−14622.5	+	67905.3i	−0.0630524	+	0.292808i
$141$	−32911.1	+	250719.i	−0.139410	+	1.06204i
$142$	341681.	−	275937.i	1.42200	−	1.14839i
$143$	−130387.			−0.533205
$144$	192663.	+	157475.i	0.774269	+	0.632857i
$145$	267812.			1.05781
$146$	−233811.	+	188822.i	−0.907783	+	0.733112i
$147$	4871.25	−	37109.5i	0.0185929	−	0.141642i
$148$	−24195.3	+	112360.i	−0.0907979	+	0.421655i
$149$		−	394571.i		−	1.45599i	−0.685580	−	0.727997i	$-0.740452\pi$
$149$		−	394571.i		−	1.45599i	0.685580	−	0.727997i	$-0.259548\pi$
$150$	53480.7	+	87459.0i	0.194075	+	0.317378i
$151$		−	8762.51i		−	0.0312742i	−0.999878	−	0.0156371i	$-0.995022\pi$
$151$		−	8762.51i		−	0.0312742i	0.999878	−	0.0156371i	$-0.00497765\pi$
$152$	−416933.	+	210348.i	−1.46372	+	0.738463i
$153$	−106370.	+	398187.i	−0.367360	+	1.37518i
$154$	−60005.9	−	74302.8i	−0.203888	−	0.252466i
$155$	−127909.			−0.427633
$156$	−177794.	−	63416.7i	−0.584933	−	0.208637i
$157$	413913.			1.34017			0.670085	−	0.742284i	$-0.266258\pi$
$157$	413913.			1.34017			0.670085	+	0.742284i	$0.266258\pi$
$158$	−29689.0	−	36762.7i	−0.0946135	−	0.117156i
$159$	339391.	+	44550.8i	1.06465	+	0.139754i
$160$	64766.9	+	248303.i	0.200011	+	0.766800i
$161$		−	25790.0i		−	0.0784128i
$162$	329909.	−	52315.8i	0.987659	−	0.156619i
$163$			156479.i			0.461304i	0.973036	+	0.230652i	$0.0740859\pi$
$163$			156479.i			0.461304i	−0.973036	+	0.230652i	$0.925914\pi$
$164$	395113.	+	85082.4i	1.14713	+	0.247019i
$165$	235917.	+	30968.0i	0.674603	+	0.0885530i
$166$	335074.	−	270601.i	0.943779	−	0.762182i
$167$	256467.			0.711607			0.355804	−	0.934561i	$-0.384207\pi$
$167$	256467.			0.711607			0.355804	+	0.934561i	$0.384207\pi$
$168$	−45684.4	−	130504.i	−0.124881	−	0.356738i
$169$	−228094.			−0.614323
$170$	−330669.	+	267043.i	−0.877548	+	0.708695i
$171$	−161791.	+	605648.i	−0.423120	+	1.58391i
$172$	675063.	+	145366.i	1.73990	+	0.374664i
$173$		−	40911.6i		−	0.103928i	−0.998649	−	0.0519638i	$-0.983452\pi$
$173$		−	40911.6i		−	0.103928i	0.998649	−	0.0519638i	$-0.0165480\pi$
$174$	−454805.	+	278111.i	−1.13881	+	0.696378i
$175$		−	56964.5i		−	0.140608i
$176$	−321558.	−	145220.i	−0.782488	−	0.353383i
$177$	14214.0	−	108283.i	0.0341023	−	0.259794i
$178$	32130.6	+	39786.0i	0.0760097	+	0.0941198i
$179$	380158.			0.886811			0.443406	−	0.896321i	$-0.353770\pi$
$179$	380158.			0.886811			0.443406	+	0.896321i	$0.353770\pi$
$180$	306631.	+	156971.i	0.705399	+	0.361109i
$181$	−658395.			−1.49379			−0.746896	−	0.664941i	$-0.768457\pi$
$181$	−658395.			−1.49379			−0.746896	+	0.664941i	$0.768457\pi$
$182$	65902.1	+	81603.8i	0.147476	+	0.182613i
$183$	−14479.8	+	110308.i	−0.0319621	+	0.243489i
$184$	−42915.2	−	85062.7i	−0.0934473	−	0.185223i
$185$			159113.i			0.341803i
$186$	217218.	−	132828.i	0.460377	−	0.281518i
$187$		−	584404.i		−	1.22211i
$188$	109275.	−	507460.i	0.225489	−	1.04715i
$189$	−171564.	−	70835.4i	−0.349358	−	0.144243i
$190$	−502952.	+	406177.i	−1.01075	+	0.816265i
$191$	−165125.			−0.327514			−0.163757	−	0.986501i	$-0.552361\pi$
$191$	−165125.			−0.327514			−0.163757	+	0.986501i	$0.552361\pi$
$192$	−367841.	−	354418.i	−0.720124	−	0.693845i
$193$	769958.			1.48790			0.743950	−	0.668235i	$-0.232950\pi$
$193$	769958.			1.48790			0.743950	+	0.668235i	$0.232950\pi$
$194$	−231899.	+	187278.i	−0.442378	+	0.357258i
$195$	−259098.	−	34010.9i	−0.487952	−	0.0640519i
$196$	−16174.0	+	75110.3i	−0.0300731	+	0.139656i
$197$			647382.i			1.18849i	0.804285	+	0.594244i	$0.202549\pi$
$197$			647382.i			1.18849i	−0.804285	+	0.594244i	$0.797451\pi$
$198$	−432799.	+	192399.i	−0.784555	+	0.348770i
$199$			129883.i			0.232499i	0.993220	+	0.116249i	$0.0370872\pi$
$199$			129883.i			0.232499i	−0.993220	+	0.116249i	$0.962913\pi$
$200$	−94790.3	−	187885.i	−0.167567	−	0.332137i
$201$	−282844.	−	37128.0i	−0.493806	−	0.0648203i
$202$	−293678.	−	363650.i	−0.506399	−	0.627054i
$203$	296227.			0.504528
$204$	284238.	−	796886.i	0.478197	−	1.34067i
$205$	559518.			0.929886
$206$	−248606.	−	307838.i	−0.408172	−	0.505423i
$207$	−123564.	−	33008.6i	−0.200432	−	0.0535428i
$208$	353154.	+	159490.i	0.565987	+	0.255608i
$209$		−	888887.i		−	1.40761i
$210$	−99858.6	−	163303.i	−0.156256	−	0.255532i
$211$			448543.i			0.693581i	0.937943	+	0.346791i	$0.112729\pi$
$211$			448543.i			0.693581i	−0.937943	+	0.346791i	$0.887271\pi$
$212$	−686934.	−	147922.i	−1.04972	−	0.226044i
$213$	−157516.	+	1.19997e6i	−0.237890	+	1.81226i
$214$	204620.	−	165248.i	0.305431	−	0.246662i
$215$	955955.			1.41040
$216$	−683737.	+	51850.7i	−0.997137	+	0.0756172i
$217$	−141480.			−0.203961
$218$	539101.	−	435370.i	0.768297	−	0.620466i
$219$	107787.	−	821132.i	0.151865	−	1.15692i
$220$	−477499.	−	102823.i	−0.665144	−	0.143230i
$221$			641828.i			0.883971i
$222$	−165232.	−	270210.i	−0.225015	−	0.367975i
$223$		−	1.18883e6i		−	1.60087i	−0.599420	−	0.800435i	$-0.704602\pi$
$223$		−	1.18883e6i		−	1.60087i	0.599420	−	0.800435i	$-0.295398\pi$
$224$	71638.9	+	274649.i	0.0953958	+	0.365728i
$225$	−272927.	−	72908.8i	−0.359410	−	0.0960115i
$226$	208775.	+	258518.i	0.271899	+	0.336681i
$227$	1.08067e6			1.39197			0.695983	−	0.718058i	$-0.254969\pi$
$227$	1.08067e6			1.39197			0.695983	+	0.718058i	$0.254969\pi$
$228$	432330.	−	1.21208e6i	0.550780	−	1.54416i
$229$	773995.			0.975325			0.487663	−	0.873032i	$-0.337850\pi$
$229$	773995.			0.975325			0.487663	+	0.873032i	$0.337850\pi$
$230$	−82868.3	−	102612.i	−0.103293	−	0.127903i
$231$	260948.	+	34253.8i	0.321754	+	0.0422356i
$232$	977042.	−	492930.i	1.19177	−	0.601264i
$233$			713125.i			0.860550i	0.902698	+	0.430275i	$0.141583\pi$
$233$			713125.i			0.860550i	−0.902698	+	0.430275i	$0.858417\pi$
$234$	475326.	−	211304.i	0.567482	−	0.252271i
$235$		−	718613.i		−	0.848839i
$236$	−47194.8	+	219168.i	−0.0551588	+	0.256151i
$237$	129109.	+	16947.7i	0.149309	+	0.0195993i
$238$	−365754.	+	295378.i	−0.418549	+	0.338014i
$239$	−1.44920e6			−1.64110			−0.820549	−	0.571577i	$-0.806332\pi$
$239$	−1.44920e6			−1.64110			−0.820549	+	0.571577i	$0.806332\pi$
$240$	−601101.	−	372451.i	−0.673627	−	0.417389i
$241$	−1.01525e6			−1.12598			−0.562988	−	0.826465i	$-0.690348\pi$
$241$	−1.01525e6			−1.12598			−0.562988	+	0.826465i	$0.690348\pi$
$242$	−186289.	+	150444.i	−0.204479	+	0.165135i
$243$	−558969.	+	731329.i	−0.607256	+	0.794506i
$244$	48077.3	−	223266.i	0.0516970	−	0.240075i
$245$			106363.i			0.113208i
$246$	−950190.	+	581036.i	−1.00109	+	0.612161i
$247$			976229.i			1.01814i
$248$	−466642.	+	235427.i	−0.481786	+	0.243067i
$249$	−154470.	+	1.17676e6i	−0.157887	+	1.20279i
$250$	−675059.	−	835897.i	−0.683111	−	0.845869i
$251$	708118.			0.709449			0.354724	−	0.934971i	$-0.384575\pi$
$251$	708118.			0.709449			0.354724	+	0.934971i	$0.384575\pi$
$252$	339166.	+	173626.i	0.336442	+	0.172232i
$253$	181351.			0.178122
$254$	−447378.	−	553970.i	−0.435101	−	0.538768i
$255$	152439.	−	1.16129e6i	0.146807	−	1.11839i
$256$	693308.	+	786661.i	0.661190	+	0.750218i
$257$		−	1.30567e6i		−	1.23310i	−0.787314	−	0.616552i	$-0.788529\pi$
$257$		−	1.30567e6i		−	1.23310i	0.787314	−	0.616552i	$-0.211471\pi$
$258$	−1.62343e6	+	992719.i	−1.51839	+	0.928490i
$259$			175995.i			0.163024i
$260$	524418.	+	112927.i	0.481110	+	0.103601i
$261$	379141.	−	1.41928e6i	0.344508	−	1.28963i
$262$	328999.	−	265695.i	0.296102	−	0.239127i
$263$	358891.			0.319943			0.159972	−	0.987122i	$-0.448860\pi$
$263$	358891.			0.319943			0.159972	+	0.987122i	$0.448860\pi$
$264$	917680.	−	321245.i	0.810366	−	0.283679i
$265$	−972765.			−0.850929
$266$	−556317.	+	449274.i	−0.482079	+	0.389320i
$267$	−139727.	−	18341.5i	−0.119950	−	0.0157455i
$268$	572480.	+	123276.i	0.486882	+	0.104844i
$269$			680424.i			0.573322i	0.958032	+	0.286661i	$0.0925454\pi$
$269$			680424.i			0.573322i	−0.958032	+	0.286661i	$0.907455\pi$
$270$	−910220.	+	269430.i	−0.759866	+	0.224924i
$271$			122132.i			0.101020i	0.998724	+	0.0505098i	$0.0160846\pi$
$271$			122132.i			0.101020i	−0.998724	+	0.0505098i	$0.983915\pi$
$272$	−714844.	+	1.58286e6i	−0.585854	+	1.29724i
$273$	−286589.	−	37619.6i	−0.232730	−	0.0305498i
$274$	−1.31079e6	−	1.62310e6i	−1.05477	−	1.30608i
$275$	400565.			0.319405
$276$	247288.	+	88204.2i	0.195403	+	0.0696974i
$277$	1.45307e6			1.13786			0.568928	−	0.822387i	$-0.307358\pi$
$277$	1.45307e6			1.13786			0.568928	+	0.822387i	$0.307358\pi$
$278$	1.45508e6	+	1.80176e6i	1.12921	+	1.39825i
$279$	−181080.	+	677857.i	−0.139271	+	0.521348i
$280$	176991.	+	350817.i	0.134914	+	0.267415i
$281$			2.25718e6i			1.70530i	0.522484	+	0.852649i	$0.325005\pi$
$281$			2.25718e6i			1.70530i	−0.522484	+	0.852649i	$0.674995\pi$
$282$	746249.	+	1.22037e6i	0.558806	+	0.913836i
$283$		−	568122.i		−	0.421672i	−0.977521	−	0.210836i	$-0.932381\pi$
$283$		−	568122.i		−	0.421672i	0.977521	−	0.210836i	$-0.0676187\pi$
$284$	523000.	−	2.42876e6i	0.384774	−	1.78685i
$285$	231862.	−	1.76635e6i	0.169090	−	1.28814i
$286$	−573825.	+	463412.i	−0.414824	+	0.335006i
$287$	618885.			0.443512
$288$	1.40758e6	+	8288.07i	0.999983	+	0.00588806i
$289$	−1.45686e6			−1.02606
$290$	1.17862e6	−	951837.i	0.822960	−	0.664611i
$291$	106906.	−	814417.i	0.0740064	−	0.563786i
$292$	−357887.	+	1.66199e6i	−0.245634	+	1.14070i
$293$		−	2.31878e6i		−	1.57794i	−0.614430	−	0.788972i	$-0.710614\pi$
$293$		−	2.31878e6i		−	1.57794i	0.614430	−	0.788972i	$-0.289386\pi$
$294$	−110454.	−	180629.i	−0.0745269	−	0.121877i
$295$			310362.i			0.207641i
$296$	292860.	+	580482.i	0.194281	+	0.385087i
$297$	498103.	−	1.20641e6i	0.327664	−	0.793602i
$298$	−1.40236e6	−	1.73648e6i	−0.914782	−	1.13274i
$299$	−199171.			−0.128839
$300$	546205.	+	194824.i	0.350391	+	0.124980i
$301$	1.05739e6			0.672693
$302$	−31143.1	−	38563.2i	−0.0196492	−	0.0243308i
$303$	1.27712e6	+	167644.i	0.799145	+	0.104901i
$304$	−1.08729e6	+	2.40756e6i	−0.674778	+	1.49414i
$305$		−	316166.i		−	0.194610i
$306$	947078.	+	2.13044e6i	0.578205	+	1.30067i
$307$			1.29505e6i			0.784224i	0.919917	+	0.392112i	$0.128256\pi$
$307$			1.29505e6i			0.784224i	−0.919917	+	0.392112i	$0.871744\pi$
$308$	−528163.	−	113733.i	−0.317242	−	0.0683140i
$309$	1.08111e6	+	141914.i	0.644133	+	0.0845532i
$310$	−562917.	+	454604.i	−0.332690	+	0.268676i
$311$	−2.90926e6			−1.70562			−0.852810	−	0.522221i	$-0.825103\pi$
$311$	−2.90926e6			−1.70562			−0.852810	+	0.522221i	$0.825103\pi$
$312$	−1.00785e6	+	352811.i	−0.586152	+	0.205190i
$313$	−1.86057e6			−1.07346			−0.536728	−	0.843755i	$-0.680340\pi$
$313$	−1.86057e6			−1.07346			−0.536728	+	0.843755i	$0.680340\pi$
$314$	1.82160e6	−	1.47110e6i	1.04263	−	0.842011i
$315$	509606.	+	136134.i	0.289373	+	0.0773022i
$316$	−261319.	−	56271.5i	−0.147215	−	0.0317008i
$317$		−	229634.i		−	0.128348i	−0.997939	−	0.0641738i	$-0.979559\pi$
$317$		−	229634.i		−	0.128348i	0.997939	−	0.0641738i	$-0.0204412\pi$
$318$	1.65198e6	−	1.01018e6i	0.916086	−	0.560182i
$319$			2.08302e6i			1.14609i
$320$	1.16754e6	+	862575.i	0.637375	+	0.470893i
$321$	−94330.4	+	718616.i	−0.0510963	+	0.389255i
$322$	−91661.0	−	113500.i	−0.0492657	−	0.0610037i
$323$	−4.37553e6			−2.33359
$324$	1.26597e6	−	1.40278e6i	0.669979	−	0.742380i
$325$	−439925.			−0.231031
$326$	556146.	+	688653.i	0.289831	+	0.358886i
$327$	−248527.	+	1.89330e6i	−0.128530	+	0.979152i
$328$	2.04126e6	−	1.02984e6i	1.04764	−	0.528549i
$329$		−	794860.i		−	0.404856i
$330$	1.14832e6	−	702189.i	0.580466	−	0.354952i
$331$			768951.i			0.385770i	0.981221	+	0.192885i	$0.0617845\pi$
$331$			768951.i			0.385770i	−0.981221	+	0.192885i	$0.938216\pi$
$332$	512887.	−	2.38179e6i	0.255374	−	1.18593i
$333$	843224.	+	225256.i	0.416708	+	0.111318i
$334$	1.12869e6	−	911516.i	0.553617	−	0.447093i
$335$	810687.			0.394677
$336$	−664880.	−	411969.i	−0.321289	−	0.199075i
$337$	−342359.			−0.164213			−0.0821064	−	0.996624i	$-0.526165\pi$
$337$	−342359.			−0.164213			−0.0821064	+	0.996624i	$0.526165\pi$
$338$	−1.00383e6	+	810675.i	−0.477932	+	0.385971i
$339$	−907902.	−	119177.i	−0.429081	−	0.0563241i
$340$	−506144.	+	2.35048e6i	−0.237453	+	1.10270i
$341$		−	994866.i		−	0.463317i
$342$	1.44052e6	+	3.24044e6i	0.665969	+	1.49809i
$343$			117649.i			0.0539949i
$344$	3.48756e6	−	1.75952e6i	1.58900	−	0.801672i
$345$	360370.	+	47304.7i	0.163005	+	0.0213972i
$346$	−145405.	−	180049.i	−0.0652964	−	0.0808538i
$347$	−3.46788e6			−1.54611			−0.773055	−	0.634339i	$-0.781272\pi$
$347$	−3.46788e6			−1.54611			−0.773055	+	0.634339i	$0.781272\pi$
$348$	−1.01312e6	+	2.84038e6i	−0.448451	+	1.25727i
$349$	2.86639e6			1.25971			0.629856	−	0.776712i	$-0.283114\pi$
$349$	2.86639e6			1.25971			0.629856	+	0.776712i	$0.283114\pi$
$350$	−202459.	−	250697.i	−0.0883420	−	0.109390i
$351$	−547047.	+	1.32495e6i	−0.237005	+	0.574026i
$352$	−1.93129e6	+	503753.i	−0.830787	+	0.216701i
$353$			3.99256e6i			1.70535i	0.522438	+	0.852677i	$0.325022\pi$
$353$			3.99256e6i			1.70535i	−0.522438	+	0.852677i	$0.674978\pi$
$354$	−322298.	−	527066.i	−0.136694	−	0.223541i
$355$		−	3.43935e6i		−	1.44846i
$356$	282809.	+	60899.3i	0.118268	+	0.0254675i
$357$	168614.	−	1.28451e6i	0.0700200	−	0.533418i
$358$	1.67305e6	−	1.35113e6i	0.689923	−	0.557172i
$359$	2.03633e6			0.833896			0.416948	−	0.908930i	$-0.363100\pi$
$359$	2.03633e6			0.833896			0.416948	+	0.908930i	$0.363100\pi$
$360$	1.90736e6	−	398987.i	0.775667	−	0.162257i
$361$	−4.17914e6			−1.68779
$362$	−2.89755e6	+	2.34002e6i	−1.16214	+	0.938529i
$363$	85879.9	−	654239.i	0.0342078	−	0.260597i
$364$	580061.	+	124908.i	0.229467	+	0.0494127i
$365$			2.35353e6i			0.924673i
$366$	328325.	+	536922.i	0.128115	+	0.209512i
$367$			2.00386e6i			0.776610i	0.921531	+	0.388305i	$0.126939\pi$
$367$			2.00386e6i			0.776610i	−0.921531	+	0.388305i	$0.873061\pi$
$368$	−491191.	−	221829.i	−0.189073	−	0.0853884i
$369$	792110.	−	2.96519e6i	0.302845	−	1.13367i
$370$	565507.	+	700244.i	0.214750	+	0.265916i
$371$	−1.07598e6			−0.405853
$372$	483876.	−	1.35659e6i	0.181291	−	0.508265i
$373$	−642838.			−0.239237			−0.119619	−	0.992820i	$-0.538167\pi$
$373$	−642838.			−0.239237			−0.119619	+	0.992820i	$0.538167\pi$
$374$	−2.07705e6	−	2.57192e6i	−0.767833	−	0.950777i
$375$	2.93563e6	+	385351.i	1.07801	+	0.141507i
$376$	−1.32267e6	−	2.62167e6i	−0.482482	−	0.956332i
$377$		−	2.28770e6i		−	0.828983i
$378$	−1.00680e6	+	298017.i	−0.362420	+	0.107278i
$379$		−	1.88523e6i		−	0.674167i	−0.941475	−	0.337083i	$-0.890560\pi$
$379$		−	1.88523e6i		−	0.674167i	0.941475	−	0.337083i	$-0.109440\pi$
$380$	−769853.	+	3.57511e6i	−0.273495	+	1.27008i
$381$	1.94552e6	+	255382.i	0.686630	+	0.0901317i
$382$	−726705.	+	586876.i	−0.254800	+	0.205773i
$383$	−3.44186e6			−1.19894			−0.599469	−	0.800398i	$-0.704622\pi$
$383$	−3.44186e6			−1.19894			−0.599469	+	0.800398i	$0.704622\pi$
$384$	−2.87849e6	−	252413.i	−0.996177	−	0.0873541i
$385$	−747930.			−0.257163
$386$	3.38853e6	−	2.73653e6i	1.15756	−	0.934829i
$387$	1.35335e6	−	5.06612e6i	0.459337	−	1.71948i
$388$	−354960.	+	1.64839e6i	−0.119702	+	0.555881i
$389$		−	125849.i		−	0.0421672i	−0.999778	−	0.0210836i	$-0.993288\pi$
$389$		−	125849.i		−	0.0421672i	0.999778	−	0.0210836i	$-0.00671162\pi$
$390$	−1.26115e6	+	771187.i	−0.419861	+	0.256743i
$391$		−	892696.i		−	0.295299i
$392$	195771.	+	388040.i	0.0643477	+	0.127544i
$393$	−151669.	+	1.15543e6i	−0.0495355	+	0.377365i
$394$	2.30088e6	+	2.84908e6i	0.746711	+	0.924622i
$395$	−370052.			−0.119336
$396$	−1.22091e6	+	2.38496e6i	−0.391242	+	0.764262i
$397$	−4.93089e6			−1.57018			−0.785090	−	0.619382i	$-0.787383\pi$
$397$	−4.93089e6			−1.57018			−0.785090	+	0.619382i	$0.787383\pi$
$398$	461622.	+	571607.i	0.146076	+	0.180880i
$399$	256464.	−	1.95376e6i	0.0806481	−	0.614383i
$400$	−1.08493e6	−	489972.i	−0.339041	−	0.153116i
$401$			862477.i			0.267847i	0.990992	+	0.133923i	$0.0427576\pi$
$401$			862477.i			0.267847i	−0.990992	+	0.133923i	$0.957242\pi$
$402$	−1.37673e6	+	841864.i	−0.424898	+	0.259823i
$403$			1.09262e6i			0.335125i
$404$	−2.58491e6	−	556627.i	−0.787939	−	0.169672i
$405$	1.30449e6	−	2.26737e6i	0.395187	−	0.686887i
$406$	1.30368e6	−	1.05283e6i	0.392513	−	0.316988i
$407$	−1.23757e6			−0.370325
$408$	−1.58132e6	−	4.51726e6i	−0.470295	−	1.34346i
$409$	2.19083e6			0.647592			0.323796	−	0.946127i	$-0.395041\pi$
$409$	2.19083e6			0.647592			0.323796	+	0.946127i	$0.395041\pi$
$410$	2.46240e6	−	1.98860e6i	0.723435	−	0.584235i
$411$	5.70025e6	+	748254.i	1.66452	+	0.218497i
$412$	−2.18819e6	−	471198.i	−0.635101	−	0.136761i
$413$			343293.i			0.0990352i
$414$	−661115.	+	293895.i	−0.189573	+	0.0842736i
$415$		−	3.37285e6i		−	0.961339i
$416$	2.12105e6	−	553252.i	0.600923	−	0.156744i
$417$	−6.32770e6	−	830617.i	−1.78199	−	0.233916i
$418$	−3.15922e6	−	3.91193e6i	−0.884380	−	1.09509i
$419$	3.66270e6			1.01921			0.509607	−	0.860407i	$-0.329791\pi$
$419$	3.66270e6			1.01921			0.509607	+	0.860407i	$0.329791\pi$
$420$	−1.01987e6	−	363773.i	−0.282112	−	0.100625i
$421$	6.00951e6			1.65247			0.826236	−	0.563325i	$-0.190478\pi$
$421$	6.00951e6			1.65247			0.826236	+	0.563325i	$0.190478\pi$
$422$	1.59418e6	+	1.97400e6i	0.435768	+	0.539594i
$423$	−3.80831e6	−	1.01734e6i	−1.03486	−	0.276449i
$424$	−3.54888e6	+	1.79045e6i	−0.958687	+	0.483670i
$425$		−	1.97177e6i		−	0.529522i
$426$	3.57162e6	+	5.84081e6i	0.953546	+	1.55937i
$427$		−	349712.i		−	0.0928198i
$428$	313205.	−	1.45449e6i	0.0826456	−	0.383797i
$429$	264535.	−	2.01525e6i	0.0693968	−	0.528670i
$430$	4.20709e6	−	3.39759e6i	1.09726	−	0.886134i
$431$	1.12043e6			0.290529			0.145265	−	0.989393i	$-0.453597\pi$
$431$	1.12043e6			0.290529			0.145265	+	0.989393i	$0.453597\pi$
$432$	−2.82480e6	+	2.65828e6i	−0.728245	+	0.685317i
$433$	543582.			0.139330			0.0696651	−	0.997570i	$-0.477807\pi$
$433$	543582.			0.139330			0.0696651	+	0.997570i	$0.477807\pi$
$434$	−622645.	+	502839.i	−0.158678	+	0.128146i
$435$	−543348.	+	4.13926e6i	−0.137675	+	1.04882i
$436$	825186.	−	3.83207e6i	0.207891	−	0.965422i
$437$		−	1.35780e6i		−	0.340121i
$438$	−2.44404e6	−	3.99684e6i	−0.608729	−	0.995476i
$439$		−	1.09494e6i		−	0.271163i	−0.990766	−	0.135582i	$-0.956710\pi$
$439$		−	1.09494e6i		−	0.271163i	0.990766	−	0.135582i	$-0.0432903\pi$
$440$	−2.46689e6	+	1.24457e6i	−0.607459	+	0.306471i
$441$	563677.	+	150579.i	0.138017	+	0.0368695i
$442$	2.28114e6	+	2.82464e6i	0.555387	+	0.687713i
$443$	3.16516e6			0.766278			0.383139	−	0.923691i	$-0.374843\pi$
$443$	3.16516e6			0.766278			0.383139	+	0.923691i	$0.374843\pi$
$444$	−1.68753e6	−	601919.i	−0.406252	−	0.144904i
$445$	400485.			0.0958709
$446$	−4.22524e6	−	5.23194e6i	−1.00581	−	1.24545i
$447$	6.09844e6	+	800522.i	1.44361	+	0.189498i
$448$	1.29142e6	+	954097.i	0.303998	+	0.224594i
$449$			7.74623e6i			1.81332i	0.421862	+	0.906660i	$0.361377\pi$
$449$			7.74623e6i			1.81332i	−0.421862	+	0.906660i	$0.638623\pi$
$450$	−1.46026e6	+	649150.i	−0.339937	+	0.151117i
$451$			4.35190e6i			1.00748i
$452$	1.83761e6	+	395705.i	0.423065	+	0.0911014i
$453$	135432.	+	17777.8i	0.0310082	+	0.00407035i
$454$	4.75595e6	−	3.84084e6i	1.08292	−	0.874554i
$455$	821422.			0.186011
$456$	−2.40522e6	−	6.87082e6i	−0.541679	−	1.54738i
$457$	−1.10785e6			−0.248135			−0.124068	−	0.992274i	$-0.539594\pi$
$457$	−1.10785e6			−0.248135			−0.124068	+	0.992274i	$0.539594\pi$
$458$	3.40630e6	−	2.75088e6i	0.758785	−	0.612784i
$459$	−5.93851e6	−	2.45190e6i	−1.31567	−	0.543214i
$460$	−729395.	−	157066.i	−0.160719	−	0.0346088i
$461$			2.76440e6i			0.605826i	0.953018	+	0.302913i	$0.0979592\pi$
$461$			2.76440e6i			0.605826i	−0.953018	+	0.302913i	$0.902041\pi$
$462$	1.27016e6	−	776694.i	0.276855	−	0.169295i
$463$		−	7.08557e6i		−	1.53611i	−0.640384	−	0.768055i	$-0.721225\pi$
$463$		−	7.08557e6i		−	1.53611i	0.640384	−	0.768055i	$-0.278775\pi$
$464$	2.54796e6	−	5.64188e6i	0.549411	−	1.21655i
$465$	259507.	−	1.97694e6i	0.0556565	−	0.423995i
$466$	2.53454e6	+	3.13841e6i	0.540672	+	0.669492i
$467$	7.00008e6			1.48529			0.742644	−	0.669686i	$-0.233571\pi$
$467$	7.00008e6			1.48529			0.742644	+	0.669686i	$0.233571\pi$
$468$	1.34088e6	−	2.61930e6i	0.282992	−	0.552804i
$469$	896704.			0.188242
$470$	−2.55404e6	−	3.16256e6i	−0.533314	−	0.660381i
$471$	−839764.	+	6.39739e6i	−0.174424	+	1.32877i
$472$	571248.	+	1.13228e6i	0.118024	+	0.233936i
$473$			7.43536e6i			1.52809i
$474$	628434.	−	384284.i	0.128473	−	0.0785608i
$475$		−	2.99909e6i		−	0.609896i
$476$	−559848.	+	2.59987e6i	−0.113254	+	0.525938i
$477$	−1.37714e6	+	5.15520e6i	−0.277130	+	1.03741i
$478$	−6.37784e6	+	5.15065e6i	−1.27674	+	1.03108i
$479$	2.35991e6			0.469956			0.234978	−	0.972001i	$-0.424498\pi$
$479$	2.35991e6			0.469956			0.234978	+	0.972001i	$0.424498\pi$
$480$	−3.96914e6	+	497261.i	−0.786310	+	0.0985103i
$481$	1.35917e6			0.267863
$482$	−4.46803e6	+	3.60831e6i	−0.875988	+	0.707435i
$483$	398607.	+	52323.8i	0.0777458	+	0.0102054i
$484$	−285147.	+	1.32419e6i	−0.0553294	+	0.256943i
$485$			2.33428e6i			0.450609i
$486$	139253.	+	5.20517e6i	0.0267432	+	0.999642i
$487$			7.32192e6i			1.39895i	0.714656	+	0.699476i	$0.246583\pi$
$487$			7.32192e6i			1.39895i	−0.714656	+	0.699476i	$0.753417\pi$
$488$	−581929.	−	1.15345e6i	−0.110617	−	0.219255i
$489$	−2.41852e6	−	317471.i	−0.457380	−	0.0600389i
$490$	378029.	+	468098.i	0.0711271	+	0.0880738i
$491$	−714702.			−0.133789			−0.0668947	−	0.997760i	$-0.521309\pi$
$491$	−714702.			−0.133789			−0.0668947	+	0.997760i	$0.521309\pi$
$492$	−2.11664e6	+	5.93420e6i	−0.394217	+	1.10522i
$493$	1.02536e7			1.90003
$494$	3.46964e6	+	4.29632e6i	0.639687	+	0.792098i
$495$	−957275.	+	3.58346e6i	−0.175600	+	0.657340i
$496$	−1.21692e6	+	2.69460e6i	−0.222105	+	0.491802i
$497$		−	3.80428e6i		−	0.690846i
$498$	3.50256e6	+	5.72786e6i	0.632866	+	1.03495i
$499$			1.06401e7i			1.91291i	0.291881	+	0.956455i	$0.405719\pi$
$499$			1.06401e7i			1.91291i	−0.291881	+	0.956455i	$0.594281\pi$
$500$	−5.94177e6	−	1.27948e6i	−1.06290	−	0.228881i
$501$	−520331.	+	3.96392e6i	−0.0926159	+	0.705554i
$502$	3.11638e6	−	2.51674e6i	0.551938	−	0.445737i
$503$	−3.63711e6			−0.640968			−0.320484	−	0.947254i	$-0.603845\pi$
$503$	−3.63711e6			−0.640968			−0.320484	+	0.947254i	$0.603845\pi$
$504$	2.10973e6	−	441321.i	0.369957	−	0.0773888i
$505$	−3.66049e6			−0.638720
$506$	798113.	−	644545.i	0.138576	−	0.111912i
$507$	462767.	−	3.52539e6i	0.0799544	−	0.609098i
$508$	−3.93776e6	−	847944.i	−0.677002	−	0.145783i
$509$			6.58725e6i			1.12696i	0.826129	+	0.563481i	$0.190538\pi$
$509$			6.58725e6i			1.12696i	−0.826129	+	0.563481i	$0.809462\pi$
$510$	−3.45651e6	−	5.65256e6i	−0.588454	−	0.962321i
$511$			2.60325e6i			0.441025i
$512$	5.84709e6	+	997935.i	0.985746	+	0.168239i
$513$	−9.03256e6	−	3.72938e6i	−1.51537	−	0.625667i
$514$	−4.64051e6	−	5.74615e6i	−0.774743	−	0.959333i
$515$	−3.09869e6			−0.514826
$516$	−3.61635e6	+	1.01388e7i	−0.597925	+	1.67633i
$517$	5.58932e6			0.919672
$518$	625509.	+	774542.i	0.102426	+	0.126830i
$519$	632324.	+	83003.1i	0.103044	+	0.0135262i
$520$	2.70928e6	−	1.36687e6i	0.439386	−	0.221676i
$521$			4.47912e6i			0.722934i	0.932385	+	0.361467i	$0.117724\pi$
$521$			4.47912e6i			0.722934i	−0.932385	+	0.361467i	$0.882276\pi$
$522$	−3.37572e6	−	7.59365e6i	−0.542238	−	1.21976i
$523$		−	3.99101e6i		−	0.638012i	−0.947753	−	0.319006i	$-0.896651\pi$
$523$		−	3.99101e6i		−	0.638012i	0.947753	−	0.319006i	$-0.103349\pi$
$524$	503588.	−	2.33861e6i	0.0801211	−	0.372074i
$525$	880436.	+	115572.i	0.139412	+	0.0183001i
$526$	1.57945e6	−	1.27554e6i	0.248910	−	0.201016i
$527$	−4.89721e6			−0.768107
$528$	2.89690e6	−	4.67533e6i	0.452218	−	0.729839i
$529$	−6.15932e6			−0.956960
$530$	−4.28107e6	+	3.45733e6i	−0.662007	+	0.534627i
$531$	1.64478e6	+	439380.i	0.253146	+	0.0676245i
$532$	−851537.	+	3.95444e6i	−0.130444	+	0.605768i
$533$		−	4.77952e6i		−	0.728729i
$534$	−680116.	+	415887.i	−0.103212	+	0.0631135i
$535$		−	2.05970e6i		−	0.311114i
$536$	2.95758e6	−	1.49214e6i	0.444657	−	0.224335i
$537$	−771280.	+	5.87567e6i	−0.115419	+	0.879268i
$538$	2.41831e6	+	2.99450e6i	0.360211	+	0.446034i
$539$	−827288.			−0.122655
$540$	−3.04823e6	+	4.42078e6i	−0.449845	+	0.652400i
$541$	1.18244e7			1.73694			0.868470	−	0.495742i	$-0.165104\pi$
$541$	1.18244e7			1.73694			0.868470	+	0.495742i	$0.165104\pi$
$542$	434072.	+	537493.i	0.0634692	+	0.0785914i
$543$	1.33578e6	−	1.01761e7i	0.194417	−	1.48109i
$544$	2.47971e6	+	9.50671e6i	0.359256	+	1.37731i
$545$		−	5.42658e6i		−	0.782592i
$546$	−1.39496e6	+	853012.i	−0.200254	+	0.122454i
$547$			5.03397e6i			0.719353i	0.933077	+	0.359677i	$0.117113\pi$
$547$			5.03397e6i			0.719353i	−0.933077	+	0.359677i	$0.882887\pi$
$548$	−1.15374e7	−	2.48443e6i	−1.64118	−	0.353407i
$549$	−1.67553e6	−	447596.i	−0.237258	−	0.0633804i
$550$	1.76286e6	−	1.42366e6i	0.248491	−	0.200678i
$551$	1.55959e7			2.18843
$552$	1.40179e6	−	490713.i	0.195810	−	0.0685456i
$553$	−409316.			−0.0569175
$554$	6.39486e6	−	5.16440e6i	0.885231	−	0.714900i
$555$	−2.45923e6	−	322815.i	−0.338896	−	0.0444857i
$556$	1.28074e7	+	2.75790e6i	1.75701	+	0.378348i
$557$		−	1.14297e7i		−	1.56098i	−0.625167	−	0.780491i	$-0.714969\pi$
$557$		−	1.14297e7i		−	1.56098i	0.625167	−	0.780491i	$-0.285031\pi$
$558$	1.61227e6	+	3.62678e6i	0.219206	+	0.493101i
$559$		−	8.16596e6i		−	1.10529i
$560$	2.02577e6	+	914870.i	0.272974	+	0.123279i
$561$	9.03247e6	+	1.18566e6i	1.21171	+	0.159058i
$562$	8.02230e6	+	9.93369e6i	1.07142	+	1.32669i
$563$	5.20508e6			0.692080			0.346040	−	0.938220i	$-0.387526\pi$
$563$	5.20508e6			0.692080			0.346040	+	0.938220i	$0.387526\pi$
$564$	7.62153e6	+	2.71849e6i	1.00889	+	0.359858i
$565$	2.60223e6			0.342945
$566$	−2.01918e6	−	2.50026e6i	−0.264931	−	0.328053i
$567$	1.44290e6	−	2.50795e6i	0.188486	−	0.327613i
$568$	−6.33042e6	−	1.25476e7i	−0.823306	−	1.63188i
$569$		−	1.36150e7i		−	1.76294i	−0.472243	−	0.881468i	$-0.656556\pi$
$569$		−	1.36150e7i		−	1.76294i	0.472243	−	0.881468i	$-0.343444\pi$
$570$	−5.25740e6	−	8.59763e6i	−0.677773	−	1.10839i
$571$			2.37109e6i			0.304340i	0.988354	+	0.152170i	$0.0486260\pi$
$571$			2.37109e6i			0.304340i	−0.988354	+	0.152170i	$0.951374\pi$
$572$	−878335.	+	4.07889e6i	−0.112246	+	0.521257i
$573$	335013.	−	2.55215e6i	0.0426261	−	0.324728i
$574$	2.72367e6	−	2.19960e6i	0.345044	−	0.278653i
$575$	611876.			0.0771781
$576$	6.22413e6	−	4.96625e6i	0.781668	−	0.623695i
$577$	−9.60114e6			−1.20056			−0.600279	−	0.799791i	$-0.704944\pi$
$577$	−9.60114e6			−1.20056			−0.600279	+	0.799791i	$0.704944\pi$
$578$	−6.41153e6	+	5.17786e6i	−0.798256	+	0.644660i
$579$	−1.56212e6	+	1.19004e7i	−0.193651	+	1.47525i
$580$	1.80408e6	−	8.37793e6i	0.222682	−	1.03411i
$581$		−	3.73072e6i		−	0.458513i
$582$	−2.42406e6	−	3.96415e6i	−0.296644	−	0.485113i
$583$		−	7.56610e6i		−	0.921936i
$584$	4.33187e6	+	8.58625e6i	0.525586	+	1.04177i
$585$	1.05134e6	−	3.93558e6i	0.127014	−	0.475465i
$586$	−8.24125e6	−	1.02048e7i	−0.991401	−	1.22761i
$587$	−9.44610e6			−1.13151			−0.565753	−	0.824575i	$-0.691415\pi$
$587$	−9.44610e6			−1.13151			−0.565753	+	0.824575i	$0.691415\pi$
$588$	−1.12808e6	−	402370.i	−0.134554	−	0.0479935i
$589$	−7.44872e6			−0.884695
$590$	1.10307e6	+	1.36588e6i	0.130458	+	0.161541i
$591$	−1.00058e7	−	1.31344e6i	−1.17838	−	0.154682i
$592$	3.35196e6	+	1.51380e6i	0.393093	+	0.177527i
$593$		−	2.55949e6i		−	0.298894i	−0.988770	−	0.149447i	$-0.952251\pi$
$593$		−	2.55949e6i		−	0.298894i	0.988770	−	0.149447i	$-0.0477493\pi$
$594$	−2.09561e6	−	7.07963e6i	−0.243693	−	0.823274i
$595$			3.68167e6i			0.426336i
$596$	−1.23433e7	−	2.65797e6i	−1.42337	−	0.306503i
$597$	−2.00746e6	−	263513.i	−0.230521	−	0.0302598i
$598$	−876536.	+	707878.i	−0.100234	+	0.0809479i
$599$	−6.35830e6			−0.724059			−0.362030	−	0.932167i	$-0.617916\pi$
$599$	−6.35830e6			−0.724059			−0.362030	+	0.932167i	$0.617916\pi$
$600$	3.09624e6	−	1.08388e6i	0.351121	−	0.122914i
$601$	−4.70528e6			−0.531373			−0.265687	−	0.964059i	$-0.585599\pi$
$601$	−4.70528e6			−0.531373			−0.265687	+	0.964059i	$0.585599\pi$
$602$	4.65348e6	−	3.75808e6i	0.523343	−	0.422644i
$603$	1.14769e6	−	4.29627e6i	0.128538	−	0.481169i
$604$	−274117.	−	59027.5i	−0.0305734	−	0.00658358i
$605$			1.87518e6i			0.208284i
$606$	6.21635e6	−	3.80126e6i	0.687628	−	0.420481i
$607$		−	1.14458e7i		−	1.26089i	−0.776236	−	0.630443i	$-0.782873\pi$
$607$		−	1.14458e7i		−	1.26089i	0.776236	−	0.630443i	$-0.217127\pi$
$608$	3.77168e6	+	1.44598e7i	0.413786	+	1.58637i
$609$	−600999.	+	4.57845e6i	−0.0656644	+	0.500236i
$610$	−1.12369e6	−	1.39142e6i	−0.122271	−	0.151403i
$611$	−6.13853e6			−0.665214
$612$	1.17399e7	+	6.00990e6i	1.26703	+	0.648618i
$613$	−5.56627e6			−0.598292			−0.299146	−	0.954207i	$-0.596702\pi$
$613$	−5.56627e6			−0.598292			−0.299146	+	0.954207i	$0.596702\pi$
$614$	4.60277e6	+	5.69942e6i	0.492718	+	0.610112i
$615$	−1.13517e6	+	8.64784e6i	−0.121025	+	0.921977i
$616$	−2.72863e6	+	1.37663e6i	−0.289730	+	0.146172i
$617$		−	9.77784e6i		−	1.03402i	−0.855979	−	0.517011i	$-0.827045\pi$
$617$		−	9.77784e6i		−	1.03402i	0.855979	−	0.517011i	$-0.172955\pi$
$618$	5.26229e6	−	3.21786e6i	0.554247	−	0.338919i
$619$		−	401672.i		−	0.0421352i	−0.999778	−	0.0210676i	$-0.993293\pi$
$619$		−	401672.i		−	0.0421352i	0.999778	−	0.0210676i	$-0.00670652\pi$
$620$	−861640.	+	4.00136e6i	−0.0900216	+	0.418050i
$621$	760869.	−	1.84283e6i	0.0791737	−	0.191759i
$622$	−1.28035e7	+	1.03399e7i	−1.32694	+	1.07162i
$623$	442978.			0.0457259
$624$	−3.18155e6	+	5.13473e6i	−0.327097	+	0.527905i
$625$	−4.78118e6			−0.489593
$626$	−8.18822e6	+	6.61269e6i	−0.835130	+	0.674439i
$627$	1.37385e7	+	1.80341e6i	1.39563	+	0.183200i
$628$	2.78827e6	−	1.29484e7i	0.282121	−	1.31014i
$629$			6.09190e6i			0.613941i
$630$	2.72658e6	−	1.21209e6i	0.273695	−	0.121670i
$631$		−	1.37179e6i		−	0.137155i	−0.997646	−	0.0685777i	$-0.978154\pi$
$631$		−	1.37179e6i		−	0.137155i	0.997646	−	0.0685777i	$-0.0218461\pi$
$632$	−1.35004e6	+	681112.i	−0.134448	+	0.0678307i
$633$	−6.93261e6	−	910022.i	−0.687682	−	0.0902698i
$634$	−816148.	−	1.01060e6i	−0.0806391	−	0.0998521i
$635$	−5.57625e6			−0.548792
$636$	3.67994e6	−	1.03170e7i	0.360744	−	1.01138i
$637$	908578.			0.0887184
$638$	7.40332e6	+	9.16723e6i	0.720070	+	0.891634i
$639$	−1.82270e7	−	4.86909e6i	−1.76588	−	0.471733i
$640$	8.20394e6	−	353439.i	0.791722	−	0.0341086i
$641$		−	5.19717e6i		−	0.499599i	−0.968298	−	0.249800i	$-0.919635\pi$
$641$		−	5.19717e6i		−	0.499599i	0.968298	−	0.249800i	$-0.0803647\pi$
$642$	2.13891e6	+	3.49784e6i	0.204812	+	0.334937i
$643$		−	406989.i		−	0.0388200i	−0.999812	−	0.0194100i	$-0.993821\pi$
$643$		−	406989.i		−	0.0388200i	0.999812	−	0.0194100i	$-0.00617878\pi$
$644$	−806787.	−	173731.i	−0.0766556	−	0.0165068i
$645$	−1.93948e6	+	1.47751e7i	−0.183564	+	1.39840i
$646$	−1.92564e7	+	1.55512e7i	−1.81549	+	1.46616i
$647$	−4.46242e6			−0.419092			−0.209546	−	0.977799i	$-0.567199\pi$
$647$	−4.46242e6			−0.419092			−0.209546	+	0.977799i	$0.567199\pi$
$648$	585797.	−	1.06729e7i	0.0548037	−	0.998497i
$649$	−2.41398e6			−0.224969
$650$	−1.93608e6	+	1.56355e6i	−0.179738	+	0.145154i
$651$	287041.	−	2.18670e6i	0.0265455	−	0.202226i
$652$	4.89512e6	+	1.05410e6i	0.450967	+	0.0971098i
$653$		−	1.37929e6i		−	0.126582i	−0.997995	−	0.0632909i	$-0.979840\pi$
$653$		−	1.37929e6i		−	0.126582i	0.997995	−	0.0632909i	$-0.0201596\pi$
$654$	5.63528e6	+	9.21558e6i	0.515194	+	0.842516i
$655$		−	3.31169e6i		−	0.301611i
$656$	5.32325e6	−	1.17871e7i	0.482967	−	1.06942i
$657$	1.24726e7	+	3.33190e6i	1.12731	+	0.301147i
$658$	−2.82503e6	−	3.49812e6i	−0.254366	−	0.314971i
$659$	−1.17955e7			−1.05804			−0.529022	−	0.848608i	$-0.677441\pi$
$659$	−1.17955e7			−1.05804			−0.529022	+	0.848608i	$0.677441\pi$
$660$	2.55799e6	−	7.17155e6i	0.228580	−	0.640845i
$661$	1.10195e6			0.0980980			0.0490490	−	0.998796i	$-0.484381\pi$
$661$	1.10195e6			0.0980980			0.0490490	+	0.998796i	$0.484381\pi$
$662$	2.73295e6	+	3.38410e6i	0.242374	+	0.300122i
$663$	−9.92000e6	−	1.30217e6i	−0.876452	−	0.115049i
$664$	−6.20801e6	−	1.23050e7i	−0.546427	−	1.08308i
$665$			5.59987e6i			0.491048i
$666$	4.51156e6	−	2.00559e6i	0.394131	−	0.175209i
$667$			3.18188e6i			0.276930i
$668$	1.72766e6	−	8.02304e6i	0.149801	−	0.695661i
$669$	1.83743e7	+	2.41194e6i	1.58725	+	0.208354i
$670$	3.56778e6	−	2.88129e6i	0.307051	−	0.247970i
$671$	2.45912e6			0.210850
$672$	−4.39028e6	+	550022.i	−0.375033	+	0.0469848i
$673$	1.37263e7			1.16820			0.584098	−	0.811683i	$-0.301448\pi$
$673$	1.37263e7			1.16820			0.584098	+	0.811683i	$0.301448\pi$
$674$	−1.50670e6	+	1.21679e6i	−0.127755	+	0.103173i
$675$	1.68059e6	−	4.07040e6i	0.141972	−	0.343857i
$676$	−1.53652e6	+	7.13545e6i	−0.129322	+	0.600557i
$677$		−	8.78449e6i		−	0.736622i	−0.929703	−	0.368311i	$-0.879936\pi$
$677$		−	8.78449e6i		−	0.736622i	0.929703	−	0.368311i	$-0.120064\pi$
$678$	−4.41918e6	+	2.70231e6i	−0.369205	+	0.225767i
$679$			2.58196e6i			0.214919i
$680$	6.12639e6	+	1.21432e7i	0.508080	+	1.00707i
$681$	−2.19251e6	+	1.67027e7i	−0.181165	+	1.38013i
$682$	−3.53588e6	−	4.37833e6i	−0.291096	−	0.360452i
$683$	2.47234e6			0.202795			0.101398	−	0.994846i	$-0.467669\pi$
$683$	2.47234e6			0.202795			0.101398	+	0.994846i	$0.467669\pi$
$684$	1.78565e7	+	9.14115e6i	1.45934	+	0.747069i
$685$	−1.63381e7			−1.33038
$686$	418139.	+	517765.i	0.0339243	+	0.0420071i
$687$	−1.57031e6	+	1.19628e7i	−0.126939	+	0.967029i
$688$	9.09495e6	−	2.01387e7i	0.732536	−	1.62204i
$689$			8.30955e6i			0.666852i
$690$	1.75409e6	−	1.07262e6i	0.140259	−	0.0857674i
$691$		−	1.79021e6i		−	0.142629i	−0.997454	−	0.0713146i	$-0.977281\pi$
$691$		−	1.79021e6i		−	0.142629i	0.997454	−	0.0713146i	$-0.0227194\pi$
$692$	−1.27983e6	−	275595.i	−0.101599	−	0.0218780i
$693$	−1.05884e6	+	3.96368e6i	−0.0837528	+	0.313520i
$694$	−1.52619e7	+	1.23253e7i	−1.20285	+	0.971400i
$695$	1.81365e7			1.42427
$696$	5.63639e6	+	1.61011e7i	0.441040	+	1.25989i
$697$	2.14221e7			1.67025
$698$	1.26148e7	−	1.01875e7i	0.980033	−	0.791460i
$699$	−1.10220e7	−	1.44682e6i	−0.853230	−	0.112001i
$700$	−1.78202e6	−	383734.i	−0.137457	−	0.0295995i
$701$		−	2.41968e7i		−	1.85979i	−0.367829	−	0.929894i	$-0.619899\pi$
$701$		−	2.41968e7i		−	1.85979i	0.367829	−	0.929894i	$-0.380101\pi$
$702$	2.30152e6	+	7.77528e6i	0.176267	+	0.595488i
$703$			9.26588e6i			0.707128i
$704$	−6.70905e6	+	9.08102e6i	−0.510187	+	0.690562i
$705$	1.11068e7	+	1.45795e6i	0.841619	+	0.110477i
$706$	1.41901e7	+	1.75710e7i	1.07145	+	1.32673i
$707$	−4.04888e6			−0.304639
$708$	−3.29167e6	−	1.17409e6i	−0.246793	−	0.0880277i
$709$	2.75535e6			0.205855			0.102928	−	0.994689i	$-0.467179\pi$
$709$	2.75535e6			0.205855			0.102928	+	0.994689i	$0.467179\pi$
$710$	−1.22239e7	−	1.51364e7i	−0.910047	−	1.12687i
$711$	−523883.	+	1.96111e6i	−0.0388652	+	0.145488i
$712$	1.46107e6	−	737127.i	0.108012	−	0.0544932i
$713$		−	1.51969e6i		−	0.111952i
$714$	−3.82326e6	−	6.25232e6i	−0.280665	−	0.458982i
$715$			5.77610e6i			0.422542i
$716$	2.56088e6	−	1.18924e7i	0.186684	−	0.866939i
$717$	2.94020e6	−	2.23987e7i	0.213589	−	1.62714i
$718$	8.96174e6	−	7.23737e6i	0.648756	−	0.523926i
$719$	−7.78137e6			−0.561350			−0.280675	−	0.959803i	$-0.590558\pi$
$719$	−7.78137e6			−0.561350			−0.280675	+	0.959803i	$0.590558\pi$
$720$	6.97609e6	−	8.53490e6i	0.501511	−	0.613574i
$721$	−3.42748e6			−0.245548
$722$	−1.83921e7	+	1.48532e7i	−1.31307	+	1.06042i
$723$	2.05977e6	−	1.56915e7i	0.146546	−	1.11640i
$724$	−4.43519e6	+	2.05965e7i	−0.314460	+	1.46032i
$725$			7.02809e6i			0.496583i
$726$	−1.94730e6	−	3.18449e6i	−0.137117	−	0.224232i
$727$			1.69934e7i			1.19246i	0.802812	+	0.596232i	$0.203336\pi$
$727$			1.69934e7i			1.19246i	−0.802812	+	0.596232i	$0.796664\pi$
$728$	2.99675e6	−	1.51190e6i	0.209566	−	0.105729i
$729$	−1.01693e7	−	1.01231e7i	−0.708714	−	0.705496i
$730$	8.36475e6	+	1.03577e7i	0.580960	+	0.719378i
$731$	3.66004e7			2.53333
$732$	3.35322e6	+	1.19605e6i	0.231305	+	0.0825031i
$733$	−1.94968e7			−1.34031			−0.670153	−	0.742223i	$-0.733772\pi$
$733$	−1.94968e7			−1.34031			−0.670153	+	0.742223i	$0.733772\pi$
$734$	7.12198e6	+	8.81886e6i	0.487934	+	0.604188i
$735$	−1.64394e6	−	215795.i	−0.112245	−	0.0147341i
$736$	−2.95010e6	+	769500.i	−0.200744	+	0.0523617i
$737$			6.30547e6i			0.427611i
$738$	−7.05263e6	−	1.58648e7i	−0.476662	−	1.07225i
$739$			2.33899e7i			1.57549i	0.616000	+	0.787747i	$0.288752\pi$
$739$			2.33899e7i			1.57549i	−0.616000	+	0.787747i	$0.711248\pi$
$740$	4.97751e6	+	1.07184e6i	0.334143	+	0.0719534i
$741$	−1.50885e7	−	1.98062e6i	−1.00948	−	0.132512i
$742$	−4.73531e6	+	3.82416e6i	−0.315746	+	0.254992i
$743$	2.36878e7			1.57417			0.787085	−	0.616844i	$-0.211589\pi$
$743$	2.36878e7			1.57417			0.787085	+	0.616844i	$0.211589\pi$
$744$	−2.69198e6	−	7.69000e6i	−0.178295	−	0.509324i
$745$	−1.74794e7			−1.15381
$746$	−2.82908e6	+	2.28473e6i	−0.186122	+	0.150310i
$747$	−1.78745e7	−	4.77494e6i	−1.17201	−	0.313088i
$748$	−1.82819e7	−	3.93676e6i	−1.19472	−	0.257267i
$749$		−	2.27824e6i		−	0.148387i
$750$	1.42891e7	−	8.73771e6i	0.927581	−	0.567211i
$751$			9.85141e6i			0.637380i	0.947859	+	0.318690i	$0.103243\pi$
$751$			9.85141e6i			0.637380i	−0.947859	+	0.318690i	$0.896757\pi$
$752$	−1.51387e7	−	6.83687e6i	−0.976213	−	0.440872i
$753$	−1.43666e6	+	1.09446e7i	−0.0923350	+	0.703415i
$754$	−8.13078e6	−	1.00680e7i	−0.520839	−	0.644934i
$755$	−388176.			−0.0247834
$756$	−3.37166e6	+	4.88984e6i	−0.214555	+	0.311164i
$757$	−1.86760e7			−1.18452			−0.592262	−	0.805745i	$-0.701765\pi$
$757$	−1.86760e7			−1.18452			−0.592262	+	0.805745i	$0.701765\pi$
$758$	−6.70036e6	−	8.29678e6i	−0.423570	−	0.524489i
$759$	−367933.	+	2.80294e6i	−0.0231827	+	0.176607i
$760$	9.31833e6	+	1.84700e7i	0.585200	+	1.15993i
$761$			3.39083e6i			0.212248i	0.994353	+	0.106124i	$0.0338441\pi$
$761$			3.39083e6i			0.212248i	−0.994353	+	0.106124i	$0.966156\pi$
$762$	9.46974e6	−	5.79070e6i	0.590814	−	0.361280i
$763$		−	6.00236e6i		−	0.373259i
$764$	−1.11234e6	+	5.16560e6i	−0.0689455	+	0.320175i
$765$	1.76395e7	+	4.71216e6i	1.08977	+	0.291116i
$766$	−1.51474e7	+	1.22328e7i	−0.932752	+	0.753277i
$767$	2.65118e6			0.162724
$768$	−1.35651e7	+	9.11967e6i	−0.829891	+	0.557925i
$769$	3.88330e6			0.236802			0.118401	−	0.992966i	$-0.462223\pi$
$769$	3.88330e6			0.236802			0.118401	+	0.992966i	$0.462223\pi$
$770$	−3.29159e6	+	2.65824e6i	−0.200068	+	0.161572i
$771$	2.01802e7	+	2.64899e6i	1.22262	+	0.160489i
$772$	5.18672e6	−	2.40866e7i	0.313220	−	1.45456i
$773$			4.33830e6i			0.261139i	0.991439	+	0.130569i	$0.0416805\pi$
$773$			4.33830e6i			0.261139i	−0.991439	+	0.130569i	$0.958320\pi$
$774$	−1.20496e7	−	2.71056e7i	−0.722973	−	1.62632i
$775$		−	3.35667e6i		−	0.200749i
$776$	4.29645e6	+	8.51604e6i	0.256127	+	0.507672i
$777$	−2.72016e6	−	357066.i	−0.161637	−	0.0212176i
$778$	−447282.	−	553851.i	−0.0264931	−	0.0328053i
$779$	3.25834e7			1.92377
$780$	−2.80934e6	+	7.87623e6i	−0.165336	+	0.463534i
$781$	2.67511e7			1.56933
$782$	−3.17276e6	−	3.92869e6i	−0.185532	−	0.229737i
$783$	2.11669e7	+	8.73944e6i	1.23383	+	0.509424i
$784$	2.24072e6	+	1.01194e6i	0.130196	+	0.0587983i
$785$		−	1.83362e7i		−	1.06203i
$786$	3.43905e6	+	5.62401e6i	0.198556	+	0.324706i
$787$		−	127599.i		−	0.00734365i	−0.999993	−	0.00367182i	$-0.998831\pi$
$787$		−	127599.i		−	0.00734365i	0.999993	−	0.00367182i	$-0.00116878\pi$
$788$	2.02520e7	+	4.36100e6i	1.16186	+	0.250190i
$789$	−728133.	+	5.54697e6i	−0.0416407	+	0.317222i
$790$	−1.62857e6	+	1.31521e6i	−0.0928410	+	0.0749771i
$791$	2.87834e6			0.163569
$792$	3.10330e6	+	1.48353e7i	0.175797	+	0.840394i
$793$	−2.70075e6			−0.152511
$794$	−2.17005e7	+	1.75250e7i	−1.22157	+	0.986523i
$795$	1.97359e6	−	1.50349e7i	0.110749	−	0.843691i
$796$	4.06313e6	+	874941.i	0.227289	+	0.0489436i
$797$			2.09099e7i			1.16602i	0.812464	+	0.583011i	$0.198126\pi$
$797$			2.09099e7i			1.16602i	−0.812464	+	0.583011i	$0.801874\pi$
$798$	−5.81523e6	−	9.50987e6i	−0.323266	−	0.528649i
$799$		−	2.75133e7i		−	1.52467i
$800$	−6.51613e6	+	1.69966e6i	−0.359969	+	0.0938937i
$801$	566967.	−	2.12239e6i	0.0312231	−	0.116881i
$802$	3.06535e6	+	3.79570e6i	0.168285	+	0.208380i
$803$	−1.83056e7			−1.00183
$804$	−3.06681e6	+	8.59807e6i	−0.167320	+	0.469095i
$805$	−1.14249e6			−0.0621387
$806$	3.88332e6	+	4.80855e6i	0.210555	+	0.260721i
$807$	−1.05165e7	−	1.38047e6i	−0.568446	−	0.0746180i
$808$	−1.33543e7	+	6.73743e6i	−0.719605	+	0.363050i
$809$			2.83460e6i			0.152272i	0.997097	+	0.0761361i	$0.0242584\pi$
$809$			2.83460e6i			0.152272i	−0.997097	+	0.0761361i	$0.975742\pi$
$810$	−2.31757e6	−	1.46149e7i	−0.124114	−	0.782677i
$811$			4.12579e6i			0.220270i	0.993917	+	0.110135i	$0.0351283\pi$
$811$			4.12579e6i			0.220270i	−0.993917	+	0.110135i	$0.964872\pi$
$812$	1.99550e6	−	9.26686e6i	0.106209	−	0.493222i
$813$	−1.88765e6	−	247786.i	−0.100160	−	0.0131477i
$814$	−5.44645e6	+	4.39848e6i	−0.288106	+	0.232670i
$815$	6.93197e6			0.365563
$816$	−2.30142e7	−	1.42599e7i	−1.20996	−	0.749707i
$817$	5.56697e7			2.91786
$818$	9.64171e6	−	7.78650e6i	0.503815	−	0.406873i
$819$	1.16289e6	−	4.35316e6i	0.0605798	−	0.226775i
$820$	3.76912e6	−	1.75034e7i	0.195752	−	0.909049i
$821$			3.09426e7i			1.60214i	0.598573	+	0.801068i	$0.295735\pi$
$821$			3.09426e7i			1.60214i	−0.598573	+	0.801068i	$0.704265\pi$
$822$	2.77458e7	−	1.69664e7i	1.43225	−	0.875811i
$823$		−	3.78985e7i		−	1.95039i	−0.221343	−	0.975196i	$-0.571044\pi$
$823$		−	3.78985e7i		−	1.95039i	0.221343	−	0.975196i	$-0.428956\pi$
$824$	−1.13048e7	+	5.70340e6i	−0.580022	+	0.292628i
$825$	−812683.	+	6.19108e6i	−0.0415706	+	0.316688i
$826$	1.22011e6	+	1.51081e6i	0.0622225	+	0.0770476i
$827$	−8.10586e6			−0.412131			−0.206066	−	0.978538i	$-0.566066\pi$
$827$	−8.10586e6			−0.412131			−0.206066	+	0.978538i	$0.566066\pi$
$828$	−1.86498e6	+	3.64310e6i	−0.0945363	+	0.184669i
$829$	−5.94605e6			−0.300498			−0.150249	−	0.988648i	$-0.548008\pi$
$829$	−5.94605e6			−0.300498			−0.150249	+	0.988648i	$0.548008\pi$
$830$	−1.19875e7	−	1.48437e7i	−0.603996	−	0.747904i
$831$	−2.94805e6	+	2.24585e7i	−0.148092	+	1.12818i
$832$	7.36829e6	−	9.97332e6i	0.369027	−	0.499495i
$833$			4.07231e6i			0.203342i
$834$	−3.07999e7	+	1.88340e7i	−1.53332	+	0.937620i
$835$		−	1.13614e7i		−	0.563918i
$836$	−2.78070e7	−	5.98787e6i	−1.37606	−	0.296317i
$837$	−1.01095e7	−	4.17402e6i	−0.498787	−	0.205940i
$838$	1.61193e7	−	1.30177e7i	0.792931	−	0.640359i
$839$	−1.52217e7			−0.746548			−0.373274	−	0.927721i	$-0.621765\pi$
$839$	−1.52217e7			−0.746548			−0.373274	+	0.927721i	$0.621765\pi$
$840$	−5.78126e6	+	2.02380e6i	−0.282699	+	0.0989624i
$841$	−1.60364e7			−0.781838
$842$	2.64474e7	−	2.13586e7i	1.28559	−	1.03823i
$843$	−3.48867e7	−	4.57946e6i	−1.69079	−	0.221945i
$844$	1.40317e7	+	3.02155e6i	0.678039	+	0.146007i
$845$			1.01045e7i			0.486824i
$846$	−2.03759e7	+	9.05799e6i	−0.978792	+	0.435117i
$847$			2.07415e6i			0.0993415i
$848$	−9.25487e6	+	2.04928e7i	−0.441958	+	0.978617i
$849$	8.78081e6	+	1.15263e6i	0.418086	+	0.0548808i
$850$	−7.00793e6	−	8.67763e6i	−0.332692	−	0.411959i
$851$	−1.89043e6			−0.0894821
$852$	3.64774e7	+	1.30110e7i	1.72157	+	0.614061i
$853$	−1.14805e7			−0.540240			−0.270120	−	0.962827i	$-0.587063\pi$
$853$	−1.14805e7			−0.540240			−0.270120	+	0.962827i	$0.587063\pi$
$854$	−1.24292e6	−	1.53906e6i	−0.0583175	−	0.0722121i
$855$	2.68300e7	+	7.16727e6i	1.25518	+	0.335304i
$856$	−3.79105e6	−	7.51428e6i	−0.176838	−	0.350512i
$857$		−	7.23435e6i		−	0.336471i	−0.985747	−	0.168236i	$-0.946193\pi$
$857$		−	7.23435e6i		−	0.336471i	0.985747	−	0.168236i	$-0.0538069\pi$
$858$	−5.99824e6	−	9.80915e6i	−0.278167	−	0.454897i
$859$			3.67531e6i			0.169946i	0.996383	+	0.0849729i	$0.0270804\pi$
$859$			3.67531e6i			0.169946i	−0.996383	+	0.0849729i	$0.972920\pi$
$860$	6.43966e6	−	2.99051e7i	0.296905	−	1.37879i
$861$	−1.25562e6	+	9.56541e6i	−0.0577232	+	0.439740i
$862$	4.93092e6	−	3.98214e6i	0.226027	−	0.182536i
$863$	−3.05585e6			−0.139670			−0.0698352	−	0.997559i	$-0.522247\pi$
$863$	−3.05585e6			−0.139670			−0.0698352	+	0.997559i	$0.522247\pi$
$864$	−2.98386e6	+	2.17386e7i	−0.135986	+	0.990711i
$865$	−1.81237e6			−0.0823581
$866$	2.39227e6	−	1.93196e6i	0.108396	−	0.0875394i
$867$	2.95574e6	−	2.25170e7i	0.133542	−	1.01733i
$868$	−953063.	+	4.42592e6i	−0.0429361	+	0.199390i
$869$		−	2.87824e6i		−	0.129294i
$870$	1.23202e7	+	2.01477e7i	0.551849	+	0.902460i
$871$		−	6.92505e6i		−	0.309298i
$872$	−9.98808e6	−	1.97975e7i	−0.444827	−	0.881696i
$873$	1.23706e7	+	3.30465e6i	0.549359	+	0.146754i
$874$	−4.82581e6	−	5.97560e6i	−0.213694	−	0.264608i
$875$	−9.30689e6			−0.410946
$876$	−2.49613e7	−	8.90335e6i	−1.09902	−	0.392007i
$877$	−2.33195e6			−0.102381			−0.0511906	−	0.998689i	$-0.516302\pi$
$877$	−2.33195e6			−0.102381			−0.0511906	+	0.998689i	$0.516302\pi$
$878$	−3.89157e6	−	4.81877e6i	−0.170368	−	0.210960i
$879$	3.58388e7	+	4.70445e6i	1.56452	+	0.205370i
$880$	−6.43321e6	+	1.42449e7i	−0.280041	+	0.620087i
$881$			2.44678e7i			1.06207i	0.847348	+	0.531037i	$0.178198\pi$
$881$			2.44678e7i			1.06207i	−0.847348	+	0.531037i	$0.821802\pi$
$882$	3.01588e6	−	1.34069e6i	0.130540	−	0.0580307i
$883$		−	1.21881e7i		−	0.526060i	−0.964788	−	0.263030i	$-0.915278\pi$
$883$		−	1.21881e7i		−	0.526060i	0.964788	−	0.263030i	$-0.0847218\pi$
$884$	2.00782e7	+	4.32359e6i	0.864162	+	0.186086i
$885$	−4.79692e6	−	629676.i	−0.205875	−	0.0270246i
$886$	1.39296e7	−	1.12494e7i	0.596150	−	0.481442i
$887$	−2.95279e7			−1.26015			−0.630077	−	0.776533i	$-0.716977\pi$
$887$	−2.95279e7			−1.26015			−0.630077	+	0.776533i	$0.716977\pi$
$888$	−9.56602e6	+	3.34870e6i	−0.407098	+	0.142510i
$889$	−6.16791e6			−0.261748
$890$	1.76251e6	−	1.42338e6i	0.0745858	−	0.0602344i
$891$	1.76355e7	+	1.01462e7i	0.744206	+	0.428164i
$892$	−3.71899e7	−	8.00836e6i	−1.56500	−	0.337001i
$893$		−	4.18482e7i		−	1.75609i
$894$	2.96839e7	−	1.81516e7i	1.24216	−	0.759575i
$895$		−	1.68409e7i		−	0.702759i
$896$	9.07441e6	−	390940.i	0.377614	−	0.0162682i
$897$	404086.	−	3.07836e6i	0.0167684	−	0.127743i
$898$	2.75311e7	+	3.40906e7i	1.13929	+	1.41073i
$899$	1.74554e7			0.720327
$900$	−4.11933e6	+	8.04681e6i	−0.169520	+	0.331144i
$901$	−3.72440e7			−1.52842
$902$	1.54672e7	+	1.91524e7i	0.632988	+	0.783803i
$903$	−2.14527e6	+	1.63428e7i	−0.0875512	+	0.666971i
$904$	9.49357e6	−	4.78962e6i	0.386374	−	0.194931i
$905$			2.91667e7i			1.18376i
$906$	659212.	−	403105.i	0.0266812	−	0.0163154i
$907$			185741.i			0.00749703i	0.999993	+	0.00374852i	$0.00119319\pi$
$907$			185741.i			0.00749703i	−0.999993	+	0.00374852i	$0.998807\pi$
$908$	7.27979e6	−	3.38065e7i	0.293025	−	1.36077i
$909$	−5.18215e6	+	1.93989e7i	−0.208018	+	0.778694i
$910$	3.61502e6	−	2.91944e6i	0.144713	−	0.116868i
$911$	6.75595e6			0.269706			0.134853	−	0.990866i	$-0.456944\pi$
$911$	6.75595e6			0.269706			0.134853	+	0.990866i	$0.456944\pi$
$912$	−3.50049e7	−	2.16895e7i	−1.39361	−	0.863502i
$913$	2.62338e7			1.04156
$914$	−4.87555e6	+	3.93742e6i	−0.193045	+	0.155900i
$915$	4.88661e6	+	641450.i	0.192955	+	0.0253285i
$916$	5.21391e6	−	2.42128e7i	0.205317	−	0.953469i
$917$		−	3.66308e6i		−	0.143854i
$918$	−3.48493e7	+	1.03156e7i	−1.36486	+	0.404005i
$919$			2.92608e7i			1.14287i	0.820647	+	0.571436i	$0.193613\pi$
$919$			2.92608e7i			1.14287i	−0.820647	+	0.571436i	$0.806387\pi$
$920$	−3.76825e6	+	1.90113e6i	−0.146781	+	0.0740529i
$921$	−2.00161e7	−	2.62745e6i	−0.777554	−	0.102067i
$922$	9.82502e6	+	1.21659e7i	0.380633	+	0.471322i
$923$	−2.93796e7			−1.13512
$924$	2.82940e6	−	7.93247e6i	0.109022	−	0.305653i
$925$	−4.17554e6			−0.160457
$926$	−2.51830e7	−	3.11831e7i	−0.965117	−	1.19507i
$927$	−4.38682e6	+	1.64216e7i	−0.167668	+	0.627649i
$928$	−8.83857e6	−	3.38853e7i	−0.336909	−	1.29164i
$929$			1.00655e7i			0.382644i	0.981527	+	0.191322i	$0.0612774\pi$
$929$			1.00655e7i			0.382644i	−0.981527	+	0.191322i	$0.938723\pi$
$930$	−5.88423e6	−	9.62269e6i	−0.223091	−	0.364829i
$931$			6.19404e6i			0.234207i
$932$	2.23086e7	+	4.80387e6i	0.841266	+	0.181156i
$933$	5.90244e6	−	4.49652e7i	0.221987	−	1.69111i
$934$	3.08069e7	−	2.48792e7i	1.15553	−	0.933187i
$935$	−2.58889e7			−0.968466
$936$	−3.40823e6	−	1.62930e7i	−0.127157	−	0.607872i
$937$	4.80624e6			0.178837			0.0894183	−	0.995994i	$-0.471499\pi$
$937$	4.80624e6			0.178837			0.0894183	+	0.995994i	$0.471499\pi$
$938$	3.94633e6	−	3.18700e6i	0.146449	−	0.118270i
$939$	3.77480e6	−	2.87567e7i	0.139711	−	1.06433i
$940$	−2.24803e7	−	4.84084e6i	−0.829818	−	0.178690i
$941$			1.75486e7i			0.646055i	0.946390	+	0.323028i	$0.104701\pi$
$941$			1.75486e7i			0.646055i	−0.946390	+	0.323028i	$0.895299\pi$
$942$	1.90414e7	+	3.11391e7i	0.699151	+	1.14335i
$943$			6.64767e6i			0.243439i
$944$	6.53828e6	+	2.95278e6i	0.238800	+	0.107845i
$945$	−3.13799e6	+	7.60021e6i	−0.114307	+	0.276851i
$946$	2.64262e7	+	3.27225e7i	0.960079	+	1.18883i
$947$	−3.50620e7			−1.27046			−0.635231	−	0.772322i	$-0.719095\pi$
$947$	−3.50620e7			−1.27046			−0.635231	+	0.772322i	$0.719095\pi$
$948$	1.39990e6	−	3.92474e6i	0.0505913	−	0.141837i
$949$	2.01043e7			0.724643
$950$	−1.06592e7	−	1.31988e7i	−0.383190	−	0.474488i
$951$	3.54919e6	+	465891.i	0.127256	+	0.0167045i
$952$	6.77642e6	+	1.34316e7i	0.242330	+	0.480326i
$953$		−	5.57491e7i		−	1.98841i	−0.107500	−	0.994205i	$-0.534284\pi$
$953$		−	5.57491e7i		−	1.98841i	0.107500	−	0.994205i	$-0.465716\pi$
$954$	1.22615e7	+	2.75822e7i	0.436188	+	0.981202i
$955$			7.31499e6i			0.259541i
$956$	−9.76236e6	+	4.53353e7i	−0.345470	+	1.60432i
$957$	−3.21949e7	−	4.22612e6i	−1.13634	−	0.149163i
$958$	1.03858e7	−	8.38742e6i	0.365617	−	0.295267i
$959$	−1.80716e7			−0.634527
$960$	−1.57006e7	+	1.62952e7i	−0.549842	+	0.570667i
$961$	2.02923e7			0.708800
$962$	5.98162e6	−	4.83067e6i	0.208392	−	0.168294i
$963$	−1.09155e7	−	2.91592e6i	−0.379294	−	0.101323i
$964$	−6.83907e6	+	3.17599e7i	−0.237031	+	1.10074i
$965$		−	3.41089e7i		−	1.17910i
$966$	1.94021e6	−	1.18643e6i	0.0668968	−	0.0409070i
$967$			2.91267e7i			1.00167i	0.865542	+	0.500836i	$0.166974\pi$
$967$			2.91267e7i			1.00167i	−0.865542	+	0.500836i	$0.833026\pi$
$968$	3.45143e6	+	6.84112e6i	0.118389	+	0.234660i
$969$	8.87725e6	−	6.76276e7i	0.303717	−	2.31374i
$970$	8.29634e6	+	1.02730e7i	0.283111	+	0.350565i
$971$	1.85833e7			0.632522			0.316261	−	0.948672i	$-0.397572\pi$
$971$	1.85833e7			0.632522			0.316261	+	0.948672i	$0.397572\pi$
$972$	1.91127e7	+	2.24127e7i	0.648868	+	0.760901i
$973$	2.00608e7			0.679308
$974$	2.60230e7	+	3.22233e7i	0.878943	+	1.08836i
$975$	892537.	−	6.79941e6i	0.0300687	−	0.229066i
$976$	−6.66053e6	−	3.00800e6i	−0.223813	−	0.101077i
$977$		−	2.11129e7i		−	0.707639i	−0.935314	−	0.353820i	$-0.884883\pi$
$977$		−	2.11129e7i		−	0.707639i	0.935314	−	0.353820i	$-0.115117\pi$
$978$	−1.17721e7	+	7.19856e6i	−0.393555	+	0.240657i
$979$			3.11495e6i			0.103871i
$980$	3.32736e6	+	716503.i	0.110671	+	0.0238316i
$981$	−2.87584e7	−	7.68241e6i	−0.954095	−	0.254874i
$982$	−3.14535e6	+	2.54014e6i	−0.104086	+	0.0840581i
$983$	3.96350e7			1.30826			0.654132	−	0.756380i	$-0.273034\pi$
$983$	3.96350e7			1.30826			0.654132	+	0.756380i	$0.273034\pi$
$984$	1.17757e7	+	3.36388e7i	0.387702	+	1.10752i
$985$	2.86788e7			0.941825
$986$	4.51255e7	−	3.64427e7i	1.47819	−	1.19376i
$987$	1.22853e7	+	1.61265e6i	0.401413	+	0.0526922i
$988$	3.05393e7	+	6.57624e6i	0.995330	+	0.214331i
$989$			1.13578e7i			0.369234i
$990$	8.52319e6	+	1.91729e7i	0.276385	+	0.621726i
$991$		−	9.73754e6i		−	0.314967i	−0.987522	−	0.157484i	$-0.949662\pi$
$991$		−	9.73754e6i		−	0.314967i	0.987522	−	0.157484i	$-0.0503381\pi$
$992$	4.22137e6	+	1.61838e7i	0.136199	+	0.522159i
$993$	−1.18848e7	−	1.56008e6i	−0.382489	−	0.0502081i
$994$	−1.35209e7	−	1.67424e7i	−0.434050	−	0.537466i
$995$	5.75379e6			0.184245
$996$	3.57721e7	+	1.27594e7i	1.14260	+	0.407551i
$997$	−2.00990e7			−0.640377			−0.320188	−	0.947354i	$-0.603746\pi$
$997$	−2.00990e7			−0.640377			−0.320188	+	0.947354i	$0.603746\pi$
$998$	3.78163e7	+	4.68263e7i	1.20186	+	1.48821i
$999$	−5.19229e6	+	1.25757e7i	−0.164606	+	0.398676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.6.e.a.71.49	yes	60
3.2	odd	2	inner	84.6.e.a.71.12	yes	60
4.3	odd	2	inner	84.6.e.a.71.11	✓	60
12.11	even	2	inner	84.6.e.a.71.50	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.6.e.a.71.11	✓	60	4.3	odd	2	inner
84.6.e.a.71.12	yes	60	3.2	odd	2	inner
84.6.e.a.71.49	yes	60	1.1	even	1	trivial
84.6.e.a.71.50	yes	60	12.11	even	2	inner

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.40093 - 3.55413i) q^{2} +(-2.02884 + 15.4559i) q^{3} +(6.73637 - 31.2829i) q^{4} -44.2997i q^{5} +(46.0033 + 75.2309i) q^{6} -49.0000i q^{7} +(-81.5372 - 161.616i) q^{8} +(-234.768 - 62.7150i) q^{9} +(-157.447 - 194.960i) q^{10} +344.560 q^{11} +(469.838 + 167.584i) q^{12} -378.416 q^{13} +(-174.152 - 215.646i) q^{14} +(684.690 + 89.8770i) q^{15} +(-933.243 - 421.466i) q^{16} -1696.09i q^{17} +(-1256.09 + 558.389i) q^{18} -2579.78i q^{19} +(-1385.82 - 298.419i) q^{20} +(757.337 + 99.4133i) q^{21} +(1516.38 - 1224.61i) q^{22} +526.327 q^{23} +(2663.34 - 932.335i) q^{24} +1162.54 q^{25} +(-1665.38 + 1344.94i) q^{26} +(1445.62 - 3501.30i) q^{27} +(-1532.86 - 330.082i) q^{28} +6045.46i q^{29} +(3332.70 - 2037.93i) q^{30} -2887.35i q^{31} +(-5605.08 + 1462.02i) q^{32} +(-699.058 + 5325.47i) q^{33} +(-6028.11 - 7464.37i) q^{34} -2170.68 q^{35} +(-3543.39 + 6921.75i) q^{36} -3591.74 q^{37} +(-9168.85 - 11353.4i) q^{38} +(767.747 - 5848.75i) q^{39} +(-7159.53 + 3612.07i) q^{40} +12630.3i q^{41} +(3686.32 - 2254.16i) q^{42} +21579.3i q^{43} +(2321.08 - 10778.8i) q^{44} +(-2778.25 + 10400.1i) q^{45} +(2316.33 - 1870.63i) q^{46} +16221.6 q^{47} +(8407.53 - 13569.0i) q^{48} -2401.00 q^{49} +(5116.26 - 4131.82i) q^{50} +(26214.5 + 3441.10i) q^{51} +(-2549.15 + 11838.0i) q^{52} -21958.7i q^{53} +(-6081.98 - 20546.9i) q^{54} -15263.9i q^{55} +(-7919.18 + 3995.32i) q^{56} +(39872.7 + 5233.96i) q^{57} +(21486.3 + 26605.6i) q^{58} -7005.98 q^{59} +(7423.93 - 20813.6i) q^{60} +7136.98 q^{61} +(-10262.0 - 12707.0i) q^{62} +(-3073.04 + 11503.6i) q^{63} +(-19471.4 + 26355.4i) q^{64} +16763.7i q^{65} +(15850.9 + 25921.6i) q^{66} +18300.1i q^{67} +(-53058.6 - 11425.5i) q^{68} +(-1067.83 + 8134.83i) q^{69} +(-9553.02 + 7714.88i) q^{70} +77638.4 q^{71} +(9006.55 + 43055.8i) q^{72} -53127.5 q^{73} +(-15807.0 + 12765.5i) q^{74} +(-2358.61 + 17968.1i) q^{75} +(-80702.9 - 17378.3i) q^{76} -16883.4i q^{77} +(-17408.4 - 28468.6i) q^{78} -8353.39i q^{79} +(-18670.8 + 41342.3i) q^{80} +(51182.7 + 29446.9i) q^{81} +(44889.7 + 55585.1i) q^{82} +76137.1 q^{83} +(8211.64 - 23022.0i) q^{84} -75136.1 q^{85} +(76695.5 + 94968.9i) q^{86} +(-93437.8 - 12265.3i) q^{87} +(-28094.4 - 55686.3i) q^{88} +9040.37i q^{89} +(24736.5 + 55644.5i) q^{90} +18542.4i q^{91} +(3545.53 - 16465.0i) q^{92} +(44626.5 + 5857.98i) q^{93} +(71390.3 - 57653.7i) q^{94} -114283. q^{95} +(-11224.9 - 89597.6i) q^{96} -52693.1 q^{97} +(-10566.6 + 8533.46i) q^{98} +(-80891.5 - 21609.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 20 q^{4} - 114 q^{6} + 44 q^{9} + 668 q^{10} + 786 q^{12} - 3004 q^{16} - 3320 q^{18} + 7120 q^{22} + 16466 q^{24} - 37500 q^{25} - 7448 q^{28} - 35236 q^{30} - 9424 q^{33} + 43360 q^{34} + 50524 q^{36}+ \cdots + 232584 q^{97}+O(q^{100}) \) 60 * q - 20 * q^4 - 114 * q^6 + 44 * q^9 + 668 * q^10 + 786 * q^12 - 3004 * q^16 - 3320 * q^18 + 7120 * q^22 + 16466 * q^24 - 37500 * q^25 - 7448 * q^28 - 35236 * q^30 - 9424 * q^33 + 43360 * q^34 + 50524 * q^36 - 15056 * q^37 - 35468 * q^40 - 20090 * q^42 + 36024 * q^45 + 124416 * q^46 + 88654 * q^48 - 144060 * q^49 - 140108 * q^52 + 19486 * q^54 - 65072 * q^57 + 115616 * q^58 + 164908 * q^60 - 169424 * q^61 + 20116 * q^64 - 98484 * q^66 + 142536 * q^69 + 35868 * q^70 + 121312 * q^72 + 107256 * q^73 + 214836 * q^76 + 263708 * q^78 - 114932 * q^81 - 479624 * q^82 + 40474 * q^84 - 383992 * q^85 - 107320 * q^88 + 423760 * q^90 + 545208 * q^93 - 448512 * q^94 - 751618 * q^96 + 232584 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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