LMFDB - Embedded newform 8.11.d.b.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,11,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$5.08285802139$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 $ x^8 - 3x^7 + 5x^6 - 51x^5 + 30855x^4 - 121569x^3 + 12144527x^2 + 279415575*x + 3348211684
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.5
Root			$-8.43092 + 11.1953i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.11.d.b.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(22.8618 - 22.3905i) q^{2} +352.099 q^{3} +(21.3279 - 1023.78i) q^{4} +3773.58i q^{5} +(8049.62 - 7883.68i) q^{6} -15618.2i q^{7} +(-22435.3 - 23883.0i) q^{8} +64924.4 q^{9} +(84492.5 + 86271.1i) q^{10} -115158. q^{11} +(7509.52 - 360471. i) q^{12} +546374. i q^{13} +(-349700. - 357061. i) q^{14} +1.32867e6i q^{15} +(-1.04767e6 - 43670.1i) q^{16} -1.50100e6 q^{17} +(1.48429e6 - 1.45369e6i) q^{18} +3.45753e6 q^{19} +(3.86331e6 + 80482.6i) q^{20} -5.49914e6i q^{21} +(-2.63273e6 + 2.57846e6i) q^{22} +3.90931e6i q^{23} +(-7.89945e6 - 8.40917e6i) q^{24} -4.47430e6 q^{25} +(1.22336e7 + 1.24911e7i) q^{26} +2.06872e6 q^{27} +(-1.59896e7 - 333103. i) q^{28} -1.57435e7i q^{29} +(2.97497e7 + 3.03759e7i) q^{30} -1.36335e7i q^{31} +(-2.49294e7 + 2.24594e7i) q^{32} -4.05471e7 q^{33} +(-3.43155e7 + 3.36081e7i) q^{34} +5.89365e7 q^{35} +(1.38470e6 - 6.64682e7i) q^{36} -7.96225e7i q^{37} +(7.90455e7 - 7.74159e7i) q^{38} +1.92377e8i q^{39} +(9.01244e7 - 8.46616e7i) q^{40} -1.01409e7 q^{41} +(-1.23129e8 - 1.25721e8i) q^{42} +4.09302e7 q^{43} +(-2.45608e6 + 1.17897e8i) q^{44} +2.44998e8i q^{45} +(8.75315e7 + 8.93740e7i) q^{46} -2.36040e8i q^{47} +(-3.68882e8 - 1.53762e7i) q^{48} +3.85474e7 q^{49} +(-1.02291e8 + 1.00182e8i) q^{50} -5.28499e8 q^{51} +(5.59365e8 + 1.16530e7i) q^{52} +3.09768e8i q^{53} +(4.72948e7 - 4.63198e7i) q^{54} -4.34559e8i q^{55} +(-3.73009e8 + 3.50399e8i) q^{56} +1.21739e9 q^{57} +(-3.52505e8 - 3.59925e8i) q^{58} -6.26191e7 q^{59} +(1.36027e9 + 2.83378e7i) q^{60} -1.02129e9i q^{61} +(-3.05262e8 - 3.11688e8i) q^{62} -1.01400e9i q^{63} +(-6.70530e7 + 1.07165e9i) q^{64} -2.06179e9 q^{65} +(-9.26981e8 + 9.07871e8i) q^{66} +6.25414e8 q^{67} +(-3.20131e7 + 1.53669e9i) q^{68} +1.37646e9i q^{69} +(1.34740e9 - 1.31962e9i) q^{70} +2.05543e9i q^{71} +(-1.45660e9 - 1.55059e9i) q^{72} +2.44117e9 q^{73} +(-1.78279e9 - 1.82032e9i) q^{74} -1.57539e9 q^{75} +(7.37418e7 - 3.53974e9i) q^{76} +1.79856e9i q^{77} +(4.30743e9 + 4.39810e9i) q^{78} +3.04489e9i q^{79} +(1.64793e8 - 3.95346e9i) q^{80} -3.10533e9 q^{81} +(-2.31839e8 + 2.27059e8i) q^{82} +2.75511e9 q^{83} +(-5.62990e9 - 1.17285e8i) q^{84} -5.66413e9i q^{85} +(9.35741e8 - 9.16450e8i) q^{86} -5.54325e9i q^{87} +(2.58362e9 + 2.75032e9i) q^{88} +2.51922e8 q^{89} +(5.48563e9 + 5.60110e9i) q^{90} +8.53337e9 q^{91} +(4.00226e9 + 8.33773e7i) q^{92} -4.80035e9i q^{93} +(-5.28506e9 - 5.39630e9i) q^{94} +1.30473e10i q^{95} +(-8.77760e9 + 7.90793e9i) q^{96} -1.56384e10 q^{97} +(8.81265e8 - 8.63097e8i) q^{98} -7.47658e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19}+ \cdots - 13646747232 q^{99}+O(q^{100}) $ 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	22.8618	−	22.3905i	0.714433	−	0.699704i
$2$	22.8618	−	22.3905i	0.714433	−	0.699704i
$3$	352.099			1.44897			0.724483	−	0.689293i	$-0.242079\pi$
$3$	352.099			1.44897			0.724483	+	0.689293i	$0.242079\pi$
$4$	21.3279	−	1023.78i	0.0208280	−	0.999783i
$5$			3773.58i			1.20755i	0.797156	+	0.603773i	$0.206337\pi$
$5$			3773.58i			1.20755i	−0.797156	+	0.603773i	$0.793663\pi$
$6$	8049.62	−	7883.68i	1.03519	−	1.01385i
$7$		−	15618.2i		−	0.929267i	−0.885503	−	0.464633i	$-0.846186\pi$
$7$		−	15618.2i		−	0.929267i	0.885503	−	0.464633i	$-0.153814\pi$
$8$	−22435.3	−	23883.0i	−0.684672	−	0.728851i
$9$	64924.4			1.09950
$10$	84492.5	+	86271.1i	0.844925	+	0.862711i
$11$	−115158.			−0.715042			−0.357521	−	0.933905i	$-0.616378\pi$
$11$	−115158.			−0.715042			−0.357521	+	0.933905i	$0.616378\pi$
$12$	7509.52	−	360471.i	0.0301791	−	1.44865i
$13$			546374.i			1.47154i	0.677230	+	0.735772i	$0.263180\pi$
$13$			546374.i			1.47154i	−0.677230	+	0.735772i	$0.736820\pi$
$14$	−349700.	−	357061.i	−0.650212	−	0.663899i
$15$			1.32867e6i			1.74969i
$16$	−1.04767e6	−	43670.1i	−0.999132	−	0.0416470i
$17$	−1.50100e6			−1.05715			−0.528573	−	0.848888i	$-0.677273\pi$
$17$	−1.50100e6			−1.05715			−0.528573	+	0.848888i	$0.677273\pi$
$18$	1.48429e6	−	1.45369e6i	0.785519	−	0.769325i
$19$	3.45753e6			1.39636			0.698180	−	0.715922i	$-0.253993\pi$
$19$	3.45753e6			1.39636			0.698180	+	0.715922i	$0.253993\pi$
$20$	3.86331e6	+	80482.6i	1.20728	+	0.0251508i
$21$		−	5.49914e6i		−	1.34648i
$22$	−2.63273e6	+	2.57846e6i	−0.510850	+	0.500318i
$23$			3.90931e6i			0.607380i	0.952771	+	0.303690i	$0.0982188\pi$
$23$			3.90931e6i			0.607380i	−0.952771	+	0.303690i	$0.901781\pi$
$24$	−7.89945e6	−	8.40917e6i	−0.992066	−	1.05608i
$25$	−4.47430e6			−0.458168
$26$	1.22336e7	+	1.24911e7i	1.02965	+	1.05132i
$27$	2.06872e6			0.144173
$28$	−1.59896e7	−	333103.i	−0.929065	−	0.0193548i
$29$		−	1.57435e7i		−	0.767557i	−0.923425	−	0.383778i	$-0.874623\pi$
$29$		−	1.57435e7i		−	0.767557i	0.923425	−	0.383778i	$-0.125377\pi$
$30$	2.97497e7	+	3.03759e7i	1.22427	+	1.25004i
$31$		−	1.36335e7i		−	0.476212i	−0.971239	−	0.238106i	$-0.923473\pi$
$31$		−	1.36335e7i		−	0.476212i	0.971239	−	0.238106i	$-0.0765265\pi$
$32$	−2.49294e7	+	2.24594e7i	−0.742953	+	0.669343i
$33$	−4.05471e7			−1.03607
$34$	−3.43155e7	+	3.36081e7i	−0.755260	+	0.739690i
$35$	5.89365e7			1.12213
$36$	1.38470e6	−	6.64682e7i	0.0229004	−	1.09926i
$37$		−	7.96225e7i		−	1.14823i	−0.818776	−	0.574113i	$-0.805347\pi$
$37$		−	7.96225e7i		−	1.14823i	0.818776	−	0.574113i	$-0.194653\pi$
$38$	7.90455e7	−	7.74159e7i	0.997606	−	0.977040i
$39$			1.92377e8i			2.13222i
$40$	9.01244e7	−	8.46616e7i	0.880122	−	0.826773i
$41$	−1.01409e7			−0.0875298			−0.0437649	−	0.999042i	$-0.513935\pi$
$41$	−1.01409e7			−0.0875298			−0.0437649	+	0.999042i	$0.513935\pi$
$42$	−1.23129e8	−	1.25721e8i	−0.942135	−	0.961966i
$43$	4.09302e7			0.278421			0.139210	−	0.990263i	$-0.455544\pi$
$43$	4.09302e7			0.278421			0.139210	+	0.990263i	$0.455544\pi$
$44$	−2.45608e6	+	1.17897e8i	−0.0148929	+	0.714887i
$45$			2.44998e8i			1.32770i
$46$	8.75315e7	+	8.93740e7i	0.424987	+	0.433932i
$47$		−	2.36040e8i		−	1.02919i	−0.857433	−	0.514595i	$-0.827942\pi$
$47$		−	2.36040e8i		−	1.02919i	0.857433	−	0.514595i	$-0.172058\pi$
$48$	−3.68882e8	−	1.53762e7i	−1.44771	−	0.0603451i
$49$	3.85474e7			0.136463
$50$	−1.02291e8	+	1.00182e8i	−0.327330	+	0.320582i
$51$	−5.28499e8			−1.53177
$52$	5.59365e8	+	1.16530e7i	1.47122	+	0.0306493i
$53$			3.09768e8i			0.740725i	0.928887	+	0.370362i	$0.120766\pi$
$53$			3.09768e8i			0.740725i	−0.928887	+	0.370362i	$0.879234\pi$
$54$	4.72948e7	−	4.63198e7i	0.103002	−	0.100878i
$55$		−	4.34559e8i		−	0.863447i
$56$	−3.73009e8	+	3.50399e8i	−0.677297	+	0.636243i
$57$	1.21739e9			2.02328
$58$	−3.52505e8	−	3.59925e8i	−0.537063	−	0.548368i
$59$	−6.26191e7			−0.0875885			−0.0437942	−	0.999041i	$-0.513945\pi$
$59$	−6.26191e7			−0.0875885			−0.0437942	+	0.999041i	$0.513945\pi$
$60$	1.36027e9	+	2.83378e7i	1.74931	+	0.0364426i
$61$		−	1.02129e9i		−	1.20921i	−0.796527	−	0.604603i	$-0.793332\pi$
$61$		−	1.02129e9i		−	1.20921i	0.796527	−	0.604603i	$-0.206668\pi$
$62$	−3.05262e8	−	3.11688e8i	−0.333207	−	0.340221i
$63$		−	1.01400e9i		−	1.02173i
$64$	−6.70530e7	+	1.07165e9i	−0.0624479	+	0.998048i
$65$	−2.06179e9			−1.77696
$66$	−9.26981e8	+	9.07871e8i	−0.740203	+	0.724944i
$67$	6.25414e8			0.463227			0.231613	−	0.972808i	$-0.425600\pi$
$67$	6.25414e8			0.463227			0.231613	+	0.972808i	$0.425600\pi$
$68$	−3.20131e7	+	1.53669e9i	−0.0220183	+	1.05692i
$69$			1.37646e9i			0.880073i
$70$	1.34740e9	−	1.31962e9i	0.801688	−	0.785161i
$71$			2.05543e9i			1.13923i	0.821913	+	0.569614i	$0.192907\pi$
$71$			2.05543e9i			1.13923i	−0.821913	+	0.569614i	$0.807093\pi$
$72$	−1.45660e9	−	1.55059e9i	−0.752797	−	0.801372i
$73$	2.44117e9			1.17756			0.588781	−	0.808292i	$-0.299608\pi$
$73$	2.44117e9			1.17756			0.588781	+	0.808292i	$0.299608\pi$
$74$	−1.78279e9	−	1.82032e9i	−0.803418	−	0.820330i
$75$	−1.57539e9			−0.663870
$76$	7.37418e7	−	3.53974e9i	0.0290834	−	1.39606i
$77$			1.79856e9i			0.664465i
$78$	4.30743e9	+	4.39810e9i	1.49192	+	1.52332i
$79$			3.04489e9i			0.989548i	0.869022	+	0.494774i	$0.164749\pi$
$79$			3.04489e9i			0.989548i	−0.869022	+	0.494774i	$0.835251\pi$
$80$	1.64793e8	−	3.95346e9i	0.0502907	−	1.20650i
$81$	−3.10533e9			−0.890599
$82$	−2.31839e8	+	2.27059e8i	−0.0625341	+	0.0612450i
$83$	2.75511e9			0.699438			0.349719	−	0.936855i	$-0.386277\pi$
$83$	2.75511e9			0.699438			0.349719	+	0.936855i	$0.386277\pi$
$84$	−5.62990e9	−	1.17285e8i	−1.34618	−	0.0280444i
$85$		−	5.66413e9i		−	1.27655i
$86$	9.35741e8	−	9.16450e8i	0.198913	−	0.194812i
$87$		−	5.54325e9i		−	1.11216i
$88$	2.58362e9	+	2.75032e9i	0.489570	+	0.521159i
$89$	2.51922e8			0.0451145			0.0225573	−	0.999746i	$-0.492819\pi$
$89$	2.51922e8			0.0451145			0.0225573	+	0.999746i	$0.492819\pi$
$90$	5.48563e9	+	5.60110e9i	0.928996	+	0.948551i
$91$	8.53337e9			1.36746
$92$	4.00226e9	+	8.33773e7i	0.607249	+	0.0126505i
$93$		−	4.80035e9i		−	0.690014i
$94$	−5.28506e9	−	5.39630e9i	−0.720129	−	0.735287i
$95$			1.30473e10i			1.68617i
$96$	−8.77760e9	+	7.90793e9i	−1.07651	+	0.969855i
$97$	−1.56384e10			−1.82110			−0.910549	−	0.413401i	$-0.864341\pi$
$97$	−1.56384e10			−1.82110			−0.910549	+	0.413401i	$0.864341\pi$
$98$	8.81265e8	−	8.63097e8i	0.0974936	−	0.0954837i
$99$	−7.47658e9			−0.786189
$100$	−9.54274e7	+	4.58069e9i	−0.00954274	+	0.458069i
$101$		−	3.85788e9i		−	0.367064i	−0.983014	−	0.183532i	$-0.941247\pi$
$101$		−	3.85788e9i		−	0.367064i	0.983014	−	0.183532i	$-0.0587532\pi$
$102$	−1.20825e10	+	1.18334e10i	−1.09435	+	1.07178i
$103$		−	9.28145e9i		−	0.800626i	−0.916378	−	0.400313i	$-0.868901\pi$
$103$		−	9.28145e9i		−	0.800626i	0.916378	−	0.400313i	$-0.131099\pi$
$104$	1.30490e10	−	1.22581e10i	1.07254	−	1.00752i
$105$	2.07515e10			1.62593
$106$	6.93586e9	+	7.08186e9i	0.518288	+	0.529198i
$107$	−3.91137e9			−0.278875			−0.139438	−	0.990231i	$-0.544529\pi$
$107$	−3.91137e9			−0.278875			−0.139438	+	0.990231i	$0.544529\pi$
$108$	4.41215e7	−	2.11791e9i	0.00300283	−	0.144142i
$109$			1.09799e10i			0.713619i	0.934177	+	0.356809i	$0.116135\pi$
$109$			1.09799e10i			0.713619i	−0.934177	+	0.356809i	$0.883865\pi$
$110$	−9.73002e9	−	9.93483e9i	−0.604157	−	0.616875i
$111$		−	2.80350e10i		−	1.66374i
$112$	−6.82047e8	+	1.63626e10i	−0.0387012	+	0.928461i
$113$	2.02898e10			1.10125			0.550624	−	0.834753i	$-0.314390\pi$
$113$	2.02898e10			1.10125			0.550624	+	0.834753i	$0.314390\pi$
$114$	2.78318e10	−	2.72580e10i	1.44550	−	1.41570i
$115$	−1.47521e10			−0.733440
$116$	−1.61178e10	−	3.35775e8i	−0.767390	−	0.0159867i
$117$			3.54730e10i			1.61796i
$118$	−1.43159e9	+	1.40208e9i	−0.0625761	+	0.0612860i
$119$			2.34428e10i			0.982371i
$120$	3.17327e10	−	2.98092e10i	1.27527	−	1.19797i
$121$	−1.26760e10			−0.488714
$122$	−2.28673e10	−	2.33486e10i	−0.846087	−	0.863896i
$123$	−3.57058e9			−0.126828
$124$	−1.39577e10	−	2.90775e8i	−0.476108	−	0.00991855i
$125$			1.99672e10i			0.654287i
$126$	−2.27040e10	−	2.31819e10i	−0.714908	−	0.729957i
$127$			6.26328e9i			0.189576i	0.995497	+	0.0947880i	$0.0302173\pi$
$127$			6.26328e9i			0.189576i	−0.995497	+	0.0947880i	$0.969783\pi$
$128$	2.24618e10	+	2.60012e10i	0.653724	+	0.756733i
$129$	1.44115e10			0.403422
$130$	−4.71362e10	+	4.61645e10i	−1.26952	+	1.24334i
$131$	−4.99170e9			−0.129387			−0.0646937	−	0.997905i	$-0.520607\pi$
$131$	−4.99170e9			−0.129387			−0.0646937	+	0.997905i	$0.520607\pi$
$132$	−8.64784e8	+	4.15112e10i	−0.0215793	+	1.03585i
$133$		−	5.40003e10i		−	1.29759i
$134$	1.42981e10	−	1.40034e10i	0.330944	−	0.324122i
$135$			7.80649e9i			0.174095i
$136$	3.36754e10	+	3.58483e10i	0.723798	+	0.770502i
$137$	−5.31439e10			−1.10116			−0.550580	−	0.834782i	$-0.685594\pi$
$137$	−5.31439e10			−1.10116			−0.550580	+	0.834782i	$0.685594\pi$
$138$	3.08197e10	+	3.14685e10i	0.615791	+	0.628753i
$139$	3.24537e10			0.625446			0.312723	−	0.949844i	$-0.398759\pi$
$139$	3.24537e10			0.625446			0.312723	+	0.949844i	$0.398759\pi$
$140$	1.25699e9	−	6.03379e10i	0.0233718	−	1.12189i
$141$		−	8.31093e10i		−	1.49126i
$142$	4.60221e10	+	4.69909e10i	0.797122	+	0.813901i
$143$		−	6.29195e10i		−	1.05222i
$144$	−6.80191e10	−	2.83525e9i	−1.09855	−	0.0457909i
$145$	5.94093e10			0.926860
$146$	5.58097e10	−	5.46591e10i	0.841289	−	0.823946i
$147$	1.35725e10			0.197730
$148$	−8.15157e10	−	1.69818e9i	−1.14798	−	0.0239153i
$149$			9.33485e10i			1.27109i	0.772064	+	0.635544i	$0.219224\pi$
$149$			9.33485e10i			1.27109i	−0.772064	+	0.635544i	$0.780776\pi$
$150$	−3.60164e10	+	3.52739e10i	−0.474290	+	0.464513i
$151$		−	1.79317e8i		−	0.00228422i	−0.999999	−	0.00114211i	$-0.999636\pi$
$151$		−	1.79317e8i		−	0.00228422i	0.999999	−	0.00114211i	$-0.000363545\pi$
$152$	−7.75708e10	−	8.25761e10i	−0.956049	−	1.01774i
$153$	−9.74513e10			−1.16233
$154$	4.02708e10	+	4.11185e10i	0.464929	+	0.474716i
$155$	5.14473e10			0.575048
$156$	1.96952e11	+	4.10301e9i	2.13175	+	0.0444098i
$157$		−	4.41399e10i		−	0.462736i	−0.972866	−	0.231368i	$-0.925680\pi$
$157$		−	4.41399e10i		−	0.462736i	0.972866	−	0.231368i	$-0.0743201\pi$
$158$	6.81768e10	+	6.96119e10i	0.692391	+	0.706965i
$159$			1.09069e11i			1.07328i
$160$	−8.47525e10	−	9.40731e10i	−0.808263	−	0.897151i
$161$	6.10563e10			0.564419
$162$	−7.09935e10	+	6.95299e10i	−0.636273	+	0.623156i
$163$	−1.06005e11			−0.921272			−0.460636	−	0.887589i	$-0.652379\pi$
$163$	−1.06005e11			−0.921272			−0.460636	+	0.887589i	$0.652379\pi$
$164$	−2.16283e8	+	1.03820e10i	−0.00182307	+	0.0875108i
$165$		−	1.53008e11i		−	1.25110i
$166$	6.29870e10	−	6.16885e10i	0.499701	−	0.489400i
$167$			1.65219e11i			1.27198i	0.771699	+	0.635988i	$0.219407\pi$
$167$			1.65219e11i			1.27198i	−0.771699	+	0.635988i	$0.780593\pi$
$168$	−1.31336e11	+	1.23375e11i	−0.981380	+	0.921894i
$169$	−1.60666e11			−1.16544
$170$	−1.26823e11	−	1.29493e11i	−0.893209	−	0.912011i
$171$	2.24478e11			1.53530
$172$	8.72956e8	−	4.19035e10i	0.00579896	−	0.278361i
$173$			2.73295e11i			1.76361i	0.471617	+	0.881803i	$0.343670\pi$
$173$			2.73295e11i			1.76361i	−0.471617	+	0.881803i	$0.656330\pi$
$174$	−1.24116e11	−	1.26729e11i	−0.778185	−	0.794566i
$175$			6.98805e10i			0.425761i
$176$	1.20647e11	+	5.02897e9i	0.714422	+	0.0297794i
$177$	−2.20481e10			−0.126913
$178$	5.75941e9	−	5.64067e9i	0.0322313	−	0.0315668i
$179$	−1.55618e11			−0.846824			−0.423412	−	0.905937i	$-0.639168\pi$
$179$	−1.55618e11			−0.846824			−0.423412	+	0.905937i	$0.639168\pi$
$180$	2.50823e11	+	5.22528e9i	1.32741	+	0.0276533i
$181$		−	1.55132e10i		−	0.0798562i	−0.999203	−	0.0399281i	$-0.987287\pi$
$181$		−	1.55132e10i		−	0.0798562i	0.999203	−	0.0399281i	$-0.0127129\pi$
$182$	1.95089e11	−	1.91067e11i	0.976956	−	0.956815i
$183$		−	3.59595e11i		−	1.75210i
$184$	9.33660e10	−	8.77067e10i	0.442690	−	0.415856i
$185$	3.00462e11			1.38654
$186$	−1.07482e11	−	1.09745e11i	−0.482806	−	0.492969i
$187$	1.72852e11			0.755904
$188$	−2.41652e11	−	5.03423e9i	−1.02897	−	0.0214360i
$189$		−	3.23097e10i		−	0.133975i
$190$	2.92135e11	+	2.98285e11i	1.17982	+	1.20466i
$191$		−	2.19148e11i		−	0.862127i	−0.902322	−	0.431063i	$-0.858139\pi$
$191$		−	2.19148e11i		−	0.862127i	0.902322	−	0.431063i	$-0.141861\pi$
$192$	−2.36093e10	+	3.77325e11i	−0.0904849	+	1.44614i
$193$	1.83821e11			0.686451			0.343225	−	0.939253i	$-0.388481\pi$
$193$	1.83821e11			0.686451			0.343225	+	0.939253i	$0.388481\pi$
$194$	−3.57522e11	+	3.50152e11i	−1.30105	+	1.27423i
$195$	−7.25952e11			−2.57475
$196$	8.22135e8	−	3.94640e10i	0.00284225	−	0.136433i
$197$			2.89571e10i			0.0975943i	0.998809	+	0.0487971i	$0.0155388\pi$
$197$			2.89571e10i			0.0975943i	−0.998809	+	0.0487971i	$0.984461\pi$
$198$	−1.70928e11	+	1.67405e11i	−0.561679	+	0.550100i
$199$		−	3.25273e11i		−	1.04228i	−0.853473	−	0.521138i	$-0.825508\pi$
$199$		−	3.25273e11i		−	1.04228i	0.853473	−	0.521138i	$-0.174492\pi$
$200$	1.00382e11	+	1.06860e11i	0.313695	+	0.333937i
$201$	2.20207e11			0.671199
$202$	−8.63801e10	−	8.81983e10i	−0.256836	−	0.262243i
$203$	−2.45884e11			−0.713265
$204$	−1.12718e10	+	5.41065e11i	−0.0319037	+	1.53144i
$205$		−	3.82674e10i		−	0.105696i
$206$	−2.07817e11	−	2.12191e11i	−0.560201	−	0.571993i
$207$			2.53810e11i			0.667815i
$208$	2.38602e10	−	5.72417e11i	0.0612854	−	1.47027i
$209$	−3.98163e11			−0.998457
$210$	4.74417e11	−	4.64636e11i	1.16162	−	1.13767i
$211$	6.20459e11			1.48354			0.741772	−	0.670652i	$-0.233986\pi$
$211$	6.20459e11			1.48354			0.741772	+	0.670652i	$0.233986\pi$
$212$	3.17133e11	+	6.60669e9i	0.740564	+	0.0154278i
$213$			7.23713e11i			1.65070i
$214$	−8.94211e10	+	8.75776e10i	−0.199237	+	0.195130i
$215$			1.54454e11i			0.336206i
$216$	−4.64125e10	−	4.94073e10i	−0.0987111	−	0.105080i
$217$	−2.12931e11			−0.442528
$218$	2.45846e11	+	2.51021e11i	0.499322	+	0.509832i
$219$	8.59533e11			1.70625
$220$	−4.44892e11	−	9.26824e9i	−0.863260	−	0.0179839i
$221$		−	8.20105e11i		−	1.55564i
$222$	−6.27718e11	−	6.40931e11i	−1.16412	−	1.18863i
$223$			5.25673e11i			0.953217i	0.879116	+	0.476608i	$0.158134\pi$
$223$			5.25673e11i			0.953217i	−0.879116	+	0.476608i	$0.841866\pi$
$224$	3.50776e11	+	3.89352e11i	0.621998	+	0.690402i
$225$	−2.90491e11			−0.503756
$226$	4.63862e11	−	4.54299e11i	0.786768	−	0.770548i
$227$	−8.73761e11			−1.44965			−0.724825	−	0.688933i	$-0.758079\pi$
$227$	−8.73761e11			−1.44965			−0.724825	+	0.688933i	$0.758079\pi$
$228$	2.59644e10	−	1.24634e12i	0.0421409	−	2.02284i
$229$		−	8.30219e11i		−	1.31830i	−0.752010	−	0.659151i	$-0.770916\pi$
$229$		−	8.30219e11i		−	1.31830i	0.752010	−	0.659151i	$-0.229084\pi$
$230$	−3.37260e11	+	3.30307e11i	−0.523994	+	0.513191i
$231$			6.33272e11i			0.962787i
$232$	−3.76001e11	+	3.53210e11i	−0.559435	+	0.525525i
$233$	8.33377e11			1.21356			0.606781	−	0.794869i	$-0.292460\pi$
$233$	8.33377e11			1.21356			0.606781	+	0.794869i	$0.292460\pi$
$234$	7.94259e11	+	8.10978e11i	1.13210	+	1.15593i
$235$	8.90716e11			1.24280
$236$	−1.33553e9	+	6.41081e10i	−0.00182429	+	0.0875695i
$237$			1.07210e12i			1.43382i
$238$	5.24898e11	+	5.35947e11i	0.687369	+	0.701838i
$239$		−	9.19325e11i		−	1.17891i	−0.807802	−	0.589454i	$-0.799343\pi$
$239$		−	9.19325e11i		−	1.17891i	0.807802	−	0.589454i	$-0.200657\pi$
$240$	5.80232e10	−	1.39201e12i	0.0728695	−	1.74817i
$241$	−1.56744e12			−1.92799			−0.963997	−	0.265912i	$-0.914327\pi$
$241$	−1.56744e12			−1.92799			−0.963997	+	0.265912i	$0.914327\pi$
$242$	−2.89797e11	+	2.83822e11i	−0.349153	+	0.341955i
$243$	−1.21554e12			−1.43462
$244$	−1.04558e12	−	2.17820e10i	−1.20894	−	0.0251854i
$245$			1.45462e11i			0.164785i
$246$	−8.16302e10	+	7.99473e10i	−0.0906098	+	0.0887418i
$247$			1.88910e12i			2.05481i
$248$	−3.25610e11	+	3.05873e11i	−0.347087	+	0.326049i
$249$	9.70072e11			1.01346
$250$	4.47077e11	+	4.56488e11i	0.457807	+	0.467444i
$251$	1.83947e12			1.84639			0.923195	−	0.384331i	$-0.125568\pi$
$251$	1.83947e12			1.84639			0.923195	+	0.384331i	$0.125568\pi$
$252$	−1.03811e12	−	2.16265e10i	−1.02151	−	0.0212806i
$253$		−	4.50189e11i		−	0.434303i
$254$	1.40238e11	+	1.43190e11i	0.132647	+	0.135439i
$255$		−	1.99433e12i		−	1.84968i
$256$	1.09570e12	+	9.15033e10i	0.996531	+	0.0832218i
$257$	−4.69431e11			−0.418703			−0.209352	−	0.977840i	$-0.567135\pi$
$257$	−4.69431e11			−0.418703			−0.209352	+	0.977840i	$0.567135\pi$
$258$	3.29473e11	−	3.22681e11i	0.288218	−	0.282276i
$259$	−1.24356e12			−1.06701
$260$	−4.39736e10	+	2.11081e12i	−0.0370105	+	1.77657i
$261$		−	1.02214e12i		−	0.843929i
$262$	−1.14119e11	+	1.11767e11i	−0.0924386	+	0.0905329i
$263$		−	2.02740e12i		−	1.61124i	−0.592433	−	0.805619i	$-0.701833\pi$
$263$		−	2.02740e12i		−	1.61124i	0.592433	−	0.805619i	$-0.298167\pi$
$264$	9.09687e11	+	9.68385e11i	0.709369	+	0.755142i
$265$	−1.16893e12			−0.894459
$266$	−1.20910e12	−	1.23455e12i	−0.907931	−	0.927042i
$267$	8.87015e10			0.0653694
$268$	1.33388e10	−	6.40285e11i	0.00964810	−	0.463126i
$269$		−	1.54905e12i		−	1.09977i	−0.835239	−	0.549886i	$-0.814671\pi$
$269$		−	1.54905e12i		−	1.09977i	0.835239	−	0.549886i	$-0.185329\pi$
$270$	1.74792e11	+	1.78471e11i	0.121815	+	0.124379i
$271$			2.74756e12i			1.87975i	0.341514	+	0.939877i	$0.389060\pi$
$271$			2.74756e12i			1.87975i	−0.341514	+	0.939877i	$0.610940\pi$
$272$	1.57254e12	+	6.55486e10i	1.05623	+	0.0440270i
$273$	3.00459e12			1.98140
$274$	−1.21497e12	+	1.18992e12i	−0.786705	+	0.770487i
$275$	5.15253e11			0.327610
$276$	1.40919e12	+	2.93570e10i	0.879882	+	0.0183302i
$277$			3.44260e11i			0.211100i	0.994414	+	0.105550i	$0.0336603\pi$
$277$			3.44260e11i			0.211100i	−0.994414	+	0.105550i	$0.966340\pi$
$278$	7.41951e11	−	7.26655e11i	0.446839	−	0.437627i
$279$		−	8.85149e11i		−	0.523595i
$280$	−1.32226e12	−	1.40758e12i	−0.768293	−	0.817868i
$281$	−5.16881e11			−0.295025			−0.147513	−	0.989060i	$-0.547127\pi$
$281$	−5.16881e11			−0.295025			−0.147513	+	0.989060i	$0.547127\pi$
$282$	−1.86086e12	−	1.90003e12i	−1.04344	−	1.06541i
$283$	9.80974e11			0.540413			0.270206	−	0.962802i	$-0.412908\pi$
$283$	9.80974e11			0.540413			0.270206	+	0.962802i	$0.412908\pi$
$284$	2.10430e12	+	4.38379e10i	1.13898	+	0.0237279i
$285$			4.59392e12i			2.44320i
$286$	−1.40880e12	−	1.43846e12i	−0.736240	−	0.751737i
$287$			1.58382e11i			0.0813385i
$288$	−1.61853e12	+	1.45817e12i	−0.816878	+	0.735943i
$289$	2.36996e11			0.117558
$290$	1.35821e12	−	1.33021e12i	0.662179	−	0.648528i
$291$	−5.50625e12			−2.63871
$292$	5.20651e10	−	2.49922e12i	0.0245263	−	1.17731i
$293$			3.78962e12i			1.75492i	0.479648	+	0.877461i	$0.340764\pi$
$293$			3.78962e12i			1.75492i	−0.479648	+	0.877461i	$0.659236\pi$
$294$	3.10292e11	−	3.03895e11i	0.141265	−	0.138353i
$295$		−	2.36298e11i		−	0.105767i
$296$	−1.90162e12	+	1.78636e12i	−0.836885	+	0.786158i
$297$	−2.38230e11			−0.103090
$298$	2.09012e12	+	2.13412e12i	0.889386	+	0.908107i
$299$	−2.13594e12			−0.893787
$300$	−3.35999e10	+	1.61285e12i	−0.0138271	+	0.663726i
$301$		−	6.39256e11i		−	0.258727i
$302$	−4.01501e9	−	4.09952e9i	−0.00159828	−	0.00163192i
$303$		−	1.35836e12i		−	0.531864i
$304$	−3.62234e12	−	1.50990e11i	−1.39515	−	0.0581543i
$305$	3.85393e12			1.46017
$306$	−2.22792e12	+	2.18199e12i	−0.830408	+	0.813289i
$307$	4.74199e12			1.73888			0.869438	−	0.494041i	$-0.164481\pi$
$307$	4.74199e12			1.73888			0.869438	+	0.494041i	$0.164481\pi$
$308$	1.84133e12	+	3.83596e10i	0.664321	+	0.0138395i
$309$		−	3.26798e12i		−	1.16008i
$310$	1.17618e12	−	1.15193e12i	0.410833	−	0.402363i
$311$		−	1.77863e12i		−	0.611340i	−0.952138	−	0.305670i	$-0.901120\pi$
$311$		−	1.77863e12i		−	0.611340i	0.952138	−	0.305670i	$-0.0988804\pi$
$312$	4.59455e12	−	4.31605e12i	1.55407	−	1.45987i
$313$	−2.19482e12			−0.730595			−0.365297	−	0.930891i	$-0.619033\pi$
$313$	−2.19482e12			−0.730595			−0.365297	+	0.930891i	$0.619033\pi$
$314$	−9.88316e11	−	1.00912e12i	−0.323778	−	0.330594i
$315$	3.82642e12			1.23379
$316$	3.11730e12	+	6.49412e10i	0.989333	+	0.0206103i
$317$		−	2.30472e12i		−	0.719981i	−0.932956	−	0.359991i	$-0.882780\pi$
$317$		−	2.30472e12i		−	0.719981i	0.932956	−	0.359991i	$-0.117220\pi$
$318$	2.44211e12	+	2.49351e12i	0.750981	+	0.766789i
$319$			1.81299e12i			0.548836i
$320$	−4.04395e12	−	2.53030e11i	−1.20519	−	0.0754088i
$321$	−1.37719e12			−0.404080
$322$	1.39586e12	−	1.36708e12i	0.403239	−	0.394926i
$323$	−5.18974e12			−1.47616
$324$	−6.62301e10	+	3.17917e12i	−0.0185494	+	0.890406i
$325$		−	2.44464e12i		−	0.674215i
$326$	−2.42347e12	+	2.37351e12i	−0.658187	+	0.644618i
$327$			3.86601e12i			1.03401i
$328$	2.27514e11	+	2.42194e11i	0.0599292	+	0.0637962i
$329$	−3.68651e12			−0.956393
$330$	−3.42592e12	−	3.49804e12i	−0.875403	−	0.893830i
$331$	3.59393e12			0.904544			0.452272	−	0.891880i	$-0.350614\pi$
$331$	3.59393e12			0.904544			0.452272	+	0.891880i	$0.350614\pi$
$332$	5.87608e10	−	2.82062e12i	0.0145679	−	0.699286i
$333$		−	5.16944e12i		−	1.26247i
$334$	3.69935e12	+	3.77722e12i	0.890006	+	0.908740i
$335$			2.36005e12i			0.559368i
$336$	−2.40148e11	+	5.76127e12i	−0.0560767	+	1.34531i
$337$	−1.56362e12			−0.359734			−0.179867	−	0.983691i	$-0.557567\pi$
$337$	−1.56362e12			−0.359734			−0.179867	+	0.983691i	$0.557567\pi$
$338$	−3.67312e12	+	3.59739e12i	−0.832629	+	0.815464i
$339$	7.14401e12			1.59567
$340$	−5.79881e12	−	1.20804e11i	−1.27628	−	0.0265881i
$341$			1.57001e12i			0.340512i
$342$	5.13198e12	−	5.02618e12i	1.09687	−	1.07426i
$343$		−	5.01379e12i		−	1.05608i
$344$	−9.18284e11	−	9.77537e11i	−0.190627	−	0.202927i
$345$	−5.19419e12			−1.06273
$346$	6.11923e12	+	6.24804e12i	1.23400	+	1.25998i
$347$	−1.77379e10			−0.00352578			−0.00176289	−	0.999998i	$-0.500561\pi$
$347$	−1.77379e10			−0.00352578			−0.00176289	+	0.999998i	$0.500561\pi$
$348$	−5.67506e12	−	1.18226e11i	−1.11192	−	0.0231642i
$349$		−	1.94015e12i		−	0.374722i	−0.982291	−	0.187361i	$-0.940007\pi$
$349$		−	1.94015e12i		−	0.374722i	0.982291	−	0.187361i	$-0.0599934\pi$
$350$	1.56466e12	+	1.59760e12i	0.297907	+	0.304177i
$351$			1.13030e12i			0.212157i
$352$	2.87082e12	−	2.58639e12i	0.531243	−	0.478609i
$353$	4.41804e12			0.806038			0.403019	−	0.915192i	$-0.367961\pi$
$353$	4.41804e12			0.806038			0.403019	+	0.915192i	$0.367961\pi$
$354$	−5.04060e11	+	4.93669e11i	−0.0906705	+	0.0888013i
$355$	−7.75633e12			−1.37567
$356$	5.37297e9	−	2.57912e11i	0.000939647	−	0.0451047i
$357$			8.25419e12i			1.42342i
$358$	−3.55770e12	+	3.48436e12i	−0.604999	+	0.592527i
$359$			4.43076e12i			0.743029i	0.928427	+	0.371515i	$0.121161\pi$
$359$			4.43076e12i			0.743029i	−0.928427	+	0.371515i	$0.878839\pi$
$360$	5.85128e12	−	5.49660e12i	0.967694	−	0.909038i
$361$	5.82343e12			0.949824
$362$	−3.47349e11	−	3.54660e11i	−0.0558757	−	0.0570519i
$363$	−4.46320e12			−0.708130
$364$	1.81999e11	−	8.73627e12i	0.0284814	−	1.36716i
$365$			9.21196e12i			1.42196i
$366$	−8.05153e12	−	8.22101e12i	−1.22595	−	1.25176i
$367$		−	2.67602e12i		−	0.401939i	−0.979598	−	0.200969i	$-0.935591\pi$
$367$		−	2.67602e12i		−	0.401939i	0.979598	−	0.200969i	$-0.0644092\pi$
$368$	1.70720e11	−	4.09565e12i	0.0252956	−	0.606853i
$369$	−6.58390e11			−0.0962390
$370$	6.86912e12	−	6.72751e12i	0.990586	−	0.970165i
$371$	4.83801e12			0.688331
$372$	−4.91449e12	−	1.02381e11i	−0.689865	−	0.0143716i
$373$		−	9.92009e12i		−	1.37395i	−0.726680	−	0.686976i	$-0.758938\pi$
$373$		−	9.92009e12i		−	1.37395i	0.726680	−	0.686976i	$-0.241062\pi$
$374$	3.95172e12	−	3.87025e12i	0.540043	−	0.528909i
$375$			7.03044e12i			0.948039i
$376$	−5.63734e12	+	5.29563e12i	−0.750127	+	0.704658i
$377$	8.60182e12			1.12949
$378$	−7.23431e11	−	7.38659e11i	−0.0937429	−	0.0957161i
$379$	6.20132e11			0.0793028			0.0396514	−	0.999214i	$-0.487375\pi$
$379$	6.20132e11			0.0793028			0.0396514	+	0.999214i	$0.487375\pi$
$380$	1.33575e13	+	2.78271e11i	1.68580	+	0.0351196i
$381$			2.20529e12i			0.274689i
$382$	−4.90685e12	−	5.01013e12i	−0.603234	−	0.615931i
$383$		−	5.18547e12i		−	0.629207i	−0.949223	−	0.314604i	$-0.898128\pi$
$383$		−	5.18547e12i		−	0.629207i	0.949223	−	0.314604i	$-0.101872\pi$
$384$	7.90876e12	+	9.15497e12i	0.947223	+	1.09648i
$385$	−6.78703e12			−0.802373
$386$	4.20250e12	−	4.11586e12i	0.490423	−	0.480313i
$387$	2.65737e12			0.306124
$388$	−3.33534e11	+	1.60102e13i	−0.0379299	+	1.82070i
$389$			1.84987e12i			0.207679i	0.994594	+	0.103840i	$0.0331129\pi$
$389$			1.84987e12i			0.207679i	−0.994594	+	0.103840i	$0.966887\pi$
$390$	−1.65966e13	+	1.62545e13i	−1.83948	+	1.80156i
$391$		−	5.86786e12i		−	0.642090i
$392$	−8.64824e11	−	9.20628e11i	−0.0934324	−	0.0994612i
$393$	−1.75757e12			−0.187478
$394$	6.48366e11	+	6.62013e11i	0.0682871	+	0.0697245i
$395$	−1.14902e13			−1.19493
$396$	−1.59460e11	+	7.65436e12i	−0.0163748	+	0.786019i
$397$			6.84533e12i			0.694132i	0.937841	+	0.347066i	$0.112822\pi$
$397$			6.84533e12i			0.694132i	−0.937841	+	0.347066i	$0.887178\pi$
$398$	−7.28303e12	−	7.43634e12i	−0.729285	−	0.744636i
$399$		−	1.90134e13i		−	1.88017i
$400$	4.68757e12	+	1.95393e11i	0.457771	+	0.0190813i
$401$	−1.07383e13			−1.03565			−0.517825	−	0.855486i	$-0.673258\pi$
$401$	−1.07383e13			−1.03565			−0.517825	+	0.855486i	$0.673258\pi$
$402$	5.03435e12	−	4.93056e12i	0.479527	−	0.469641i
$403$	7.44901e12			0.700766
$404$	−3.94962e12	−	8.22805e10i	−0.366985	−	0.00764523i
$405$		−	1.17182e13i		−	1.07544i
$406$	−5.62137e12	+	5.50548e12i	−0.509580	+	0.499075i
$407$			9.16919e12i			0.821030i
$408$	1.18570e13	+	1.26221e13i	1.04876	+	1.11643i
$409$	1.79443e13			1.56787			0.783936	−	0.620841i	$-0.213209\pi$
$409$	1.79443e13			1.56787			0.783936	+	0.620841i	$0.213209\pi$
$410$	−8.56828e11	−	8.74863e11i	−0.0739561	−	0.0755129i
$411$	−1.87119e13			−1.59554
$412$	−9.50214e12	−	1.97954e11i	−0.800452	−	0.0166755i
$413$			9.77997e11i			0.0813931i
$414$	5.68293e12	+	5.80255e12i	0.467273	+	0.477109i
$415$			1.03967e13i			0.844604i
$416$	−1.22712e13	−	1.36208e13i	−0.984968	−	1.09329i
$417$	1.14269e13			0.906250
$418$	−9.10274e12	+	8.91508e12i	−0.713330	+	0.698625i
$419$	1.01675e13			0.787303			0.393652	−	0.919260i	$-0.371212\pi$
$419$	1.01675e13			0.787303			0.393652	+	0.919260i	$0.371212\pi$
$420$	4.42585e11	−	2.12449e13i	0.0338649	−	1.62558i
$421$			1.38694e13i			1.04869i	0.851505	+	0.524346i	$0.175690\pi$
$421$			1.38694e13i			1.04869i	−0.851505	+	0.524346i	$0.824310\pi$
$422$	1.41848e13	−	1.38924e13i	1.05989	−	1.03804i
$423$		−	1.53247e13i		−	1.13160i
$424$	7.39818e12	−	6.94974e12i	0.539878	−	0.507153i
$425$	6.71591e12			0.484351
$426$	1.62043e13	+	1.65454e13i	1.15500	+	1.17931i
$427$	−1.59507e13			−1.12368
$428$	−8.34212e10	+	4.00437e12i	−0.00580842	+	0.278815i
$429$		−	2.21539e13i		−	1.52462i
$430$	3.45830e12	+	3.53109e12i	0.235245	+	0.240197i
$431$		−	3.51756e11i		−	0.0236513i	−0.999930	−	0.0118257i	$-0.996236\pi$
$431$		−	3.51756e11i		−	0.0236513i	0.999930	−	0.0118257i	$-0.00376431\pi$
$432$	−2.16733e12	−	9.03412e10i	−0.144048	−	0.00600437i
$433$	−1.73769e13			−1.14165			−0.570823	−	0.821073i	$-0.693376\pi$
$433$	−1.73769e13			−1.14165			−0.570823	+	0.821073i	$0.693376\pi$
$434$	−4.86800e12	+	4.76764e12i	−0.316156	+	0.309639i
$435$	2.09179e13			1.34299
$436$	1.12410e13	+	2.34178e11i	0.713464	+	0.0148633i
$437$			1.35165e13i			0.848122i
$438$	1.96505e13	−	1.92454e13i	1.21900	−	1.19387i
$439$		−	1.05808e13i		−	0.648928i	−0.945898	−	0.324464i	$-0.894816\pi$
$439$		−	1.05808e13i		−	0.648928i	0.945898	−	0.324464i	$-0.105184\pi$
$440$	−1.03786e13	+	9.74949e12i	−0.629324	+	0.591178i
$441$	2.50267e12			0.150041
$442$	−1.83626e13	−	1.87491e13i	−1.08849	−	1.11140i
$443$	2.18951e13			1.28330			0.641651	−	0.766996i	$-0.278250\pi$
$443$	2.18951e13			1.28330			0.641651	+	0.766996i	$0.278250\pi$
$444$	−2.87016e13	−	5.97927e11i	−1.66338	−	0.0346524i
$445$			9.50649e11i			0.0544779i
$446$	1.17701e13	+	1.20179e13i	0.666970	+	0.681009i
$447$			3.28679e13i			1.84176i
$448$	1.67372e13	+	1.04725e12i	0.927453	+	0.0580308i
$449$	−3.53942e13			−1.93954			−0.969772	−	0.244011i	$-0.921537\pi$
$449$	−3.53942e13			−1.93954			−0.969772	+	0.244011i	$0.921537\pi$
$450$	−6.64117e12	+	6.50426e12i	−0.359900	+	0.352480i
$451$	1.16780e12			0.0625875
$452$	4.32739e11	−	2.07722e13i	0.0229368	−	1.10101i
$453$		−	6.31374e10i		−	0.00330975i
$454$	−1.99758e13	+	1.95640e13i	−1.03568	+	1.01433i
$455$			3.22014e13i			1.65127i
$456$	−2.73126e13	−	2.90749e13i	−1.38528	−	1.47467i
$457$	−1.93883e13			−0.972653			−0.486326	−	0.873777i	$-0.661663\pi$
$457$	−1.93883e13			−0.972653			−0.486326	+	0.873777i	$0.661663\pi$
$458$	−1.85890e13	−	1.89803e13i	−0.922422	−	0.941839i
$459$	−3.10514e12			−0.152412
$460$	−3.14631e11	+	1.51029e13i	−0.0152761	+	0.733281i
$461$		−	1.69421e13i		−	0.813696i	−0.913496	−	0.406848i	$-0.866628\pi$
$461$		−	1.69421e13i		−	0.813696i	0.913496	−	0.406848i	$-0.133372\pi$
$462$	1.41793e13	+	1.44778e13i	0.673666	+	0.687847i
$463$			4.19900e13i			1.97352i	0.162198	+	0.986758i	$0.448142\pi$
$463$			4.19900e13i			1.97352i	−0.162198	+	0.986758i	$0.551858\pi$
$464$	−6.87518e11	+	1.64939e13i	−0.0319664	+	0.766891i
$465$	1.81145e13			0.833224
$466$	1.90525e13	−	1.86598e13i	0.867009	−	0.849135i
$467$	9.55773e12			0.430299			0.215150	−	0.976581i	$-0.430976\pi$
$467$	9.55773e12			0.430299			0.215150	+	0.976581i	$0.430976\pi$
$468$	3.63165e13	+	7.56564e11i	1.61761	+	0.0336990i
$469$		−	9.76783e12i		−	0.430461i
$470$	2.03634e13	−	1.99436e13i	0.887894	−	0.869589i
$471$		−	1.55416e13i		−	0.670488i
$472$	1.40488e12	+	1.49553e12i	0.0599694	+	0.0638390i
$473$	−4.71346e12			−0.199083
$474$	2.40050e13	+	2.45103e13i	1.00325	+	1.02437i
$475$	−1.54700e13			−0.639768
$476$	2.40003e13	+	4.99987e11i	0.982158	+	0.0204608i
$477$			2.01115e13i			0.814427i
$478$	−2.05842e13	−	2.10175e13i	−0.824886	−	0.842250i
$479$		−	4.05634e13i		−	1.60863i	−0.594201	−	0.804317i	$-0.702532\pi$
$479$		−	4.05634e13i		−	1.60863i	0.594201	−	0.804317i	$-0.297468\pi$
$480$	−2.98412e13	−	3.31230e13i	−1.17114	−	1.29994i
$481$	4.35036e13			1.68966
$482$	−3.58346e13	+	3.50958e13i	−1.37742	+	1.34903i
$483$	2.14978e13			0.817823
$484$	−2.70352e11	+	1.29774e13i	−0.0101790	+	0.488608i
$485$		−	5.90127e13i		−	2.19906i
$486$	−2.77894e13	+	2.72165e13i	−1.02494	+	1.00381i
$487$		−	5.27934e13i		−	1.92723i	−0.267286	−	0.963617i	$-0.586127\pi$
$487$		−	5.27934e13i		−	1.92723i	0.267286	−	0.963617i	$-0.413873\pi$
$488$	−2.43915e13	+	2.29130e13i	−0.881331	+	0.827910i
$489$	−3.73242e13			−1.33489
$490$	3.25697e12	+	3.32553e12i	0.115301	+	0.117728i
$491$	−2.41468e13			−0.846158			−0.423079	−	0.906093i	$-0.639051\pi$
$491$	−2.41468e13			−0.846158			−0.423079	+	0.906093i	$0.639051\pi$
$492$	−7.61531e10	+	3.65549e12i	−0.00264157	+	0.126800i
$493$			2.36309e13i			0.811419i
$494$	4.22980e13	+	4.31884e13i	1.43776	+	1.46802i
$495$		−	2.82135e13i		−	0.949360i
$496$	−5.95377e11	+	1.42834e13i	−0.0198328	+	0.475799i
$497$	3.21021e13			1.05865
$498$	2.21776e13	−	2.17204e13i	0.724050	−	0.709123i
$499$	2.21286e11			0.00715238			0.00357619	−	0.999994i	$-0.498862\pi$
$499$	2.21286e11			0.00715238			0.00357619	+	0.999994i	$0.498862\pi$
$500$	2.04420e13	+	4.25859e11i	0.654145	+	0.0136275i
$501$			5.81735e13i			1.84305i
$502$	4.20536e13	−	4.11867e13i	1.31912	−	1.29193i
$503$			9.04543e12i			0.280924i	0.990086	+	0.140462i	$0.0448588\pi$
$503$			9.04543e12i			0.280924i	−0.990086	+	0.140462i	$0.955141\pi$
$504$	−2.42174e13	+	2.27495e13i	−0.744689	+	0.699550i
$505$	1.45580e13			0.443247
$506$	−1.00800e13	−	1.02922e13i	−0.303883	−	0.310280i
$507$	−5.65702e13			−1.68868
$508$	6.41221e12	+	1.33583e11i	0.189535	+	0.00394849i
$509$		−	2.24139e13i		−	0.656036i	−0.944671	−	0.328018i	$-0.893619\pi$
$509$		−	2.24139e13i		−	0.656036i	0.944671	−	0.328018i	$-0.106381\pi$
$510$	−4.46542e13	−	4.55941e13i	−1.29423	−	1.32147i
$511$		−	3.81267e13i		−	1.09427i
$512$	2.70985e13	−	2.24413e13i	0.770185	−	0.637821i
$513$	7.15266e12			0.201317
$514$	−1.07321e13	+	1.05108e13i	−0.299135	+	0.292968i
$515$	3.50243e13			0.966793
$516$	3.07367e11	−	1.47542e13i	0.00840249	−	0.403335i
$517$			2.71819e13i			0.735915i
$518$	−2.84301e13	+	2.78440e13i	−0.762305	+	0.746590i
$519$			9.62269e13i			2.55540i
$520$	4.62569e13	+	4.92416e13i	1.21663	+	1.29514i
$521$	2.19502e12			0.0571807			0.0285904	−	0.999591i	$-0.490898\pi$
$521$	2.19502e12			0.0571807			0.0285904	+	0.999591i	$0.490898\pi$
$522$	−2.28862e13	−	2.33679e13i	−0.590501	−	0.602930i
$523$	−2.91933e13			−0.746062			−0.373031	−	0.927819i	$-0.621681\pi$
$523$	−2.91933e13			−0.746062			−0.373031	+	0.927819i	$0.621681\pi$
$524$	−1.06462e11	+	5.11039e12i	−0.00269488	+	0.129359i
$525$			2.46048e13i			0.616913i
$526$	−4.53945e13	−	4.63500e13i	−1.12739	−	1.15112i
$527$			2.04639e13i			0.503425i
$528$	4.24798e13	+	1.77069e12i	1.03517	+	0.0431493i
$529$	2.61438e13			0.631089
$530$	−2.67240e13	+	2.61731e13i	−0.639031	+	0.625857i
$531$	−4.06551e12			−0.0963036
$532$	−5.52843e13	−	1.15171e12i	−1.29731	−	0.0270263i
$533$		−	5.54070e12i		−	0.128804i
$534$	2.02788e12	−	1.98607e12i	0.0467020	−	0.0457392i
$535$		−	1.47599e13i		−	0.336755i
$536$	−1.40314e13	−	1.49368e13i	−0.317158	−	0.337623i
$537$	−5.47927e13			−1.22702
$538$	−3.46840e13	−	3.54141e13i	−0.769516	−	0.785714i
$539$	−4.43905e12			−0.0975768
$540$	7.99211e12	+	1.66496e11i	0.174058	+	0.00362606i
$541$			4.86387e12i			0.104953i	0.998622	+	0.0524766i	$0.0167115\pi$
$541$			4.86387e12i			0.104953i	−0.998622	+	0.0524766i	$0.983288\pi$
$542$	6.15194e13	+	6.28143e13i	1.31527	+	1.34296i
$543$		−	5.46218e12i		−	0.115709i
$544$	3.74189e13	−	3.37115e13i	0.785410	−	0.707593i
$545$	−4.14336e13			−0.861728
$546$	6.86904e13	−	6.72743e13i	1.41557	−	1.38639i
$547$	3.29297e13			0.672436			0.336218	−	0.941784i	$-0.390852\pi$
$547$	3.29297e13			0.672436			0.336218	+	0.941784i	$0.390852\pi$
$548$	−1.13345e12	+	5.44076e13i	−0.0229350	+	1.10092i
$549$		−	6.63067e13i		−	1.32952i
$550$	1.17796e13	−	1.15368e13i	0.234055	−	0.229230i
$551$		−	5.44335e13i		−	1.07179i
$552$	3.28740e13	−	3.08814e13i	0.641442	−	0.602562i
$553$	4.75557e13			0.919554
$554$	7.70817e12	+	7.87043e12i	0.147708	+	0.150817i
$555$	1.05792e14			2.00904
$556$	6.92169e11	−	3.32254e13i	0.0130268	−	0.625311i
$557$			4.29354e13i			0.800828i	0.916334	+	0.400414i	$0.131134\pi$
$557$			4.29354e13i			0.800828i	−0.916334	+	0.400414i	$0.868866\pi$
$558$	−1.98190e13	−	2.02361e13i	−0.366362	−	0.374073i
$559$			2.23632e13i			0.409709i
$560$	−6.17458e13	−	2.57376e12i	−1.12116	−	0.0467335i
$561$	6.08610e13			1.09528
$562$	−1.18169e13	+	1.15732e13i	−0.210776	+	0.206430i
$563$	−1.01247e14			−1.78994			−0.894970	−	0.446126i	$-0.852803\pi$
$563$	−1.01247e14			−1.78994			−0.894970	+	0.446126i	$0.852803\pi$
$564$	−8.50854e13	−	1.77255e12i	−1.49094	−	0.0310600i
$565$			7.65652e13i			1.32981i
$566$	2.24269e13	−	2.19645e13i	0.386088	−	0.378129i
$567$			4.84996e13i			0.827604i
$568$	4.90898e13	−	4.61142e13i	0.830327	−	0.779997i
$569$	−3.75395e12			−0.0629401			−0.0314701	−	0.999505i	$-0.510019\pi$
$569$	−3.75395e12			−0.0629401			−0.0314701	+	0.999505i	$0.510019\pi$
$570$	1.02860e14	+	1.05026e14i	1.70952	+	1.74550i
$571$	−4.82773e13			−0.795358			−0.397679	−	0.917525i	$-0.630184\pi$
$571$	−4.82773e13			−0.795358			−0.397679	+	0.917525i	$0.630184\pi$
$572$	−6.44156e13	−	1.34194e12i	−1.05199	−	0.0219156i
$573$		−	7.71618e13i		−	1.24919i
$574$	3.54626e12	+	3.62090e12i	0.0569129	+	0.0581109i
$575$		−	1.74914e13i		−	0.278283i
$576$	−4.35337e12	+	6.95760e13i	−0.0686615	+	1.09735i
$577$	−3.01929e13			−0.472091			−0.236046	−	0.971742i	$-0.575851\pi$
$577$	−3.01929e13			−0.472091			−0.236046	+	0.971742i	$0.575851\pi$
$578$	5.41816e12	−	5.30646e12i	0.0839871	−	0.0822556i
$579$	6.47232e13			0.994644
$580$	1.26707e12	−	6.08219e13i	0.0193047	−	0.926659i
$581$		−	4.30299e13i		−	0.649964i
$582$	−1.25883e14	+	1.23288e14i	−1.88518	+	1.84631i
$583$		−	3.56723e13i		−	0.529649i
$584$	−5.47685e13	−	5.83025e13i	−0.806244	−	0.858268i
$585$	−1.33860e14			−1.95377
$586$	8.48516e13	+	8.66377e13i	1.22793	+	1.25377i
$587$	5.82710e13			0.836107			0.418053	−	0.908422i	$-0.362712\pi$
$587$	5.82710e13			0.836107			0.418053	+	0.908422i	$0.362712\pi$
$588$	2.89473e11	−	1.38952e13i	0.00411833	−	0.197687i
$589$		−	4.71383e13i		−	0.664963i
$590$	−5.29085e12	−	5.40222e12i	−0.0740057	−	0.0755635i
$591$			1.01958e13i			0.141411i
$592$	−3.47712e12	+	8.34178e13i	−0.0478202	+	1.14723i
$593$	−3.13152e13			−0.427052			−0.213526	−	0.976937i	$-0.568495\pi$
$593$	−3.13152e13			−0.427052			−0.213526	+	0.976937i	$0.568495\pi$
$594$	−5.44639e12	+	5.33411e12i	−0.0736506	+	0.0721323i
$595$	−8.84635e13			−1.18626
$596$	9.55681e13	+	1.99093e12i	1.27081	+	0.0264743i
$597$		−	1.14528e14i		−	1.51022i
$598$	−4.88316e13	+	4.78249e13i	−0.638550	+	0.625386i
$599$			7.34955e13i			0.953074i	0.879154	+	0.476537i	$0.158108\pi$
$599$			7.34955e13i			0.953074i	−0.879154	+	0.476537i	$0.841892\pi$
$600$	3.53445e13	+	3.76251e13i	0.454533	+	0.483862i
$601$	1.07112e14			1.36605			0.683024	−	0.730396i	$-0.260665\pi$
$601$	1.07112e14			1.36605			0.683024	+	0.730396i	$0.260665\pi$
$602$	−1.43133e13	−	1.46146e13i	−0.181033	−	0.184843i
$603$	4.06046e13			0.509318
$604$	−1.83581e11	−	3.82446e9i	−0.00228372	−	4.75757e-5i
$605$		−	4.78339e13i		−	0.590145i
$606$	−3.04143e13	−	3.10545e13i	−0.372147	−	0.379981i
$607$			1.36295e13i			0.165401i	0.996574	+	0.0827004i	$0.0263545\pi$
$607$			1.36295e13i			0.165401i	−0.996574	+	0.0827004i	$0.973646\pi$
$608$	−8.61940e13	+	7.76541e13i	−1.03743	+	0.934645i
$609$	−8.65756e13			−1.03350
$610$	8.81079e13	−	8.62915e13i	1.04319	−	1.02169i
$611$	1.28966e14			1.51450
$612$	−2.07843e12	+	9.97685e13i	−0.0242091	+	1.16208i
$613$			1.16805e14i			1.34946i	0.738066	+	0.674729i	$0.235739\pi$
$613$			1.16805e14i			1.34946i	−0.738066	+	0.674729i	$0.764261\pi$
$614$	1.08411e14	−	1.06176e14i	1.24231	−	1.21670i
$615$		−	1.34739e13i		−	0.153150i
$616$	4.29551e13	−	4.03514e13i	0.484296	−	0.454941i
$617$	4.22466e13			0.472461			0.236230	−	0.971697i	$-0.424088\pi$
$617$	4.22466e13			0.472461			0.236230	+	0.971697i	$0.424088\pi$
$618$	−7.31719e13	−	7.47122e13i	−0.811712	−	0.828798i
$619$	1.04957e14			1.15493			0.577466	−	0.816415i	$-0.304042\pi$
$619$	1.04957e14			1.15493			0.577466	+	0.816415i	$0.304042\pi$
$620$	1.09726e12	−	5.26706e13i	0.0119771	−	0.574923i
$621$			8.08727e12i			0.0875677i
$622$	−3.98244e13	−	4.06627e13i	−0.427757	−	0.436761i
$623$		−	3.93457e12i		−	0.0419234i
$624$	8.40113e12	−	2.01547e14i	0.0888004	−	2.13037i
$625$	−1.19042e14			−1.24825
$626$	−5.01776e13	+	4.91431e13i	−0.521961	+	0.511200i
$627$	−1.40193e14			−1.44673
$628$	−4.51895e13	−	9.41411e11i	−0.462635	−	0.00963787i
$629$			1.19513e14i			1.21384i
$630$	8.74790e13	−	8.56756e13i	0.881457	−	0.863285i
$631$		−	2.87613e12i		−	0.0287516i	−0.999897	−	0.0143758i	$-0.995424\pi$
$631$		−	2.87613e12i		−	0.0287516i	0.999897	−	0.0143758i	$-0.00457612\pi$
$632$	7.27212e13	−	6.83133e13i	0.721233	−	0.677516i
$633$	2.18463e14			2.14960
$634$	−5.16038e13	−	5.26901e13i	−0.503774	−	0.514378i
$635$	−2.36350e13			−0.228922
$636$	1.11662e14	+	2.32621e12i	1.07305	+	0.0223544i
$637$			2.10613e13i			0.200811i
$638$	4.05938e13	+	4.14483e13i	0.384023	+	0.392106i
$639$			1.33447e14i			1.25258i
$640$	−9.81175e13	+	8.47614e13i	−0.913791	+	0.789402i
$641$	−3.00941e13			−0.278094			−0.139047	−	0.990286i	$-0.544404\pi$
$641$	−3.00941e13			−0.278094			−0.139047	+	0.990286i	$0.544404\pi$
$642$	−3.14850e13	+	3.08359e13i	−0.288688	+	0.282737i
$643$	−1.66359e14			−1.51353			−0.756764	−	0.653689i	$-0.773221\pi$
$643$	−1.66359e14			−1.51353			−0.756764	+	0.653689i	$0.773221\pi$
$644$	1.30220e12	−	6.25081e13i	0.0117557	−	0.564296i
$645$			5.43829e13i			0.487151i
$646$	−1.18647e14	+	1.16201e14i	−1.05461	+	1.03287i
$647$		−	1.73339e14i		−	1.52889i	−0.644690	−	0.764444i	$-0.723013\pi$
$647$		−	1.73339e14i		−	1.52889i	0.644690	−	0.764444i	$-0.276987\pi$
$648$	6.96691e13	+	7.41645e13i	0.609768	+	0.649114i
$649$	7.21111e12			0.0626295
$650$	−5.47368e13	−	5.58890e13i	−0.471751	−	0.481681i
$651$	−7.49728e13			−0.641207
$652$	−2.26086e12	+	1.08525e14i	−0.0191883	+	0.921072i
$653$			1.89861e14i			1.59908i	0.600612	+	0.799541i	$0.294924\pi$
$653$			1.89861e14i			1.59908i	−0.600612	+	0.799541i	$0.705076\pi$
$654$	8.65620e13	+	8.83841e13i	0.723500	+	0.738730i
$655$		−	1.88366e13i		−	0.156241i
$656$	1.06242e13	+	4.42852e11i	0.0874538	+	0.00364535i
$657$	1.58492e14			1.29473
$658$	−8.42805e13	+	8.25430e13i	−0.683278	+	0.669192i
$659$	−9.80342e13			−0.788771			−0.394385	−	0.918945i	$-0.629042\pi$
$659$	−9.80342e13			−0.788771			−0.394385	+	0.918945i	$0.629042\pi$
$660$	−1.56646e14	−	3.26333e12i	−1.25083	−	0.0260580i
$661$		−	1.54197e14i		−	1.22199i	−0.791634	−	0.610996i	$-0.790769\pi$
$661$		−	1.54197e14i		−	1.22199i	0.791634	−	0.610996i	$-0.209231\pi$
$662$	8.21638e13	−	8.04700e13i	0.646236	−	0.632913i
$663$		−	2.88758e14i		−	2.25406i
$664$	−6.18119e13	−	6.58004e13i	−0.478886	−	0.509786i
$665$	2.03775e14			1.56690
$666$	−1.15747e14	−	1.18183e14i	−0.883359	−	0.901953i
$667$	6.15461e13			0.466199
$668$	1.69148e14	+	3.52378e12i	1.27170	+	0.0264927i
$669$			1.85089e14i			1.38118i
$670$	5.28428e13	+	5.39551e13i	0.391392	+	0.399631i
$671$			1.17610e14i			0.864634i
$672$	1.23508e14	+	1.37090e14i	0.901254	+	1.00037i
$673$	−6.70067e13			−0.485336			−0.242668	−	0.970109i	$-0.578023\pi$
$673$	−6.70067e13			−0.485336			−0.242668	+	0.970109i	$0.578023\pi$
$674$	−3.57472e13	+	3.50103e13i	−0.257006	+	0.251707i
$675$	−9.25608e12			−0.0660554
$676$	−3.42666e12	+	1.64486e14i	−0.0242738	+	1.16519i
$677$		−	1.71430e14i		−	1.20543i	−0.797956	−	0.602715i	$-0.794085\pi$
$677$		−	1.71430e14i		−	1.20543i	0.797956	−	0.602715i	$-0.205915\pi$
$678$	1.63325e14	−	1.59958e14i	1.14000	−	1.11650i
$679$			2.44243e14i			1.69229i
$680$	−1.35276e14	+	1.27077e14i	−0.930417	+	0.874020i
$681$	−3.07650e14			−2.10049
$682$	3.51535e13	+	3.58934e13i	0.238257	+	0.243273i
$683$	5.05521e13			0.340123			0.170061	−	0.985433i	$-0.445603\pi$
$683$	5.05521e13			0.340123			0.170061	+	0.985433i	$0.445603\pi$
$684$	4.78764e12	−	2.29816e14i	0.0319773	−	1.53497i
$685$		−	2.00543e14i		−	1.32970i
$686$	−1.12262e14	−	1.14625e14i	−0.738942	−	0.754496i
$687$		−	2.92319e14i		−	1.91017i
$688$	−4.28812e13	−	1.78743e12i	−0.278179	−	0.0115954i
$689$	−1.69249e14			−1.09001
$690$	−1.18749e14	+	1.16301e14i	−0.759248	+	0.743596i
$691$	5.33777e13			0.338821			0.169410	−	0.985546i	$-0.445814\pi$
$691$	5.33777e13			0.338821			0.169410	+	0.985546i	$0.445814\pi$
$692$	2.79794e14	+	5.82881e12i	1.76322	+	0.0367324i
$693$			1.16771e14i			0.730580i
$694$	−4.05521e11	+	3.97161e11i	−0.00251893	+	0.00246700i
$695$			1.22467e14i			0.755256i
$696$	−1.32389e14	+	1.24365e14i	−0.810601	+	0.761467i
$697$	1.52214e13			0.0925317
$698$	−4.34411e13	−	4.43555e13i	−0.262195	−	0.267714i
$699$	2.93431e14			1.75841
$700$	7.15421e13	+	1.49040e12i	0.425668	+	0.00886775i
$701$		−	3.55178e13i		−	0.209824i	−0.994481	−	0.104912i	$-0.966544\pi$
$701$		−	3.55178e13i		−	0.209824i	0.994481	−	0.104912i	$-0.0334561\pi$
$702$	2.53079e13	+	2.58406e13i	0.148447	+	0.151572i
$703$		−	2.75297e14i		−	1.60334i
$704$	7.72170e12	−	1.23409e14i	0.0446529	−	0.713647i
$705$	3.13620e14			1.80077
$706$	1.01004e14	−	9.89222e13i	0.575860	−	0.563988i
$707$	−6.02531e13			−0.341101
$708$	−4.70240e11	+	2.25724e13i	−0.00264334	+	0.126885i
$709$		−	2.13491e14i		−	1.19165i	−0.803115	−	0.595824i	$-0.796826\pi$
$709$		−	2.13491e14i		−	1.19165i	0.803115	−	0.595824i	$-0.203174\pi$
$710$	−1.77324e14	+	1.73668e14i	−0.982824	+	0.962562i
$711$			1.97688e14i			1.08801i
$712$	−5.65196e12	−	6.01666e12i	−0.0308887	−	0.0328818i
$713$	5.32977e13			0.289242
$714$	1.84816e14	+	1.88706e14i	0.995974	+	1.01694i
$715$	2.37432e14			1.27060
$716$	−3.31899e12	+	1.59318e14i	−0.0176377	+	0.846641i
$717$		−	3.23693e14i		−	1.70820i
$718$	9.92071e13	+	1.01295e14i	0.519901	+	0.530844i
$719$			2.65916e14i			1.38389i	0.721952	+	0.691943i	$0.243245\pi$
$719$			2.65916e14i			1.38389i	−0.721952	+	0.691943i	$0.756755\pi$
$720$	1.06991e13	−	2.56676e14i	0.0552947	−	1.32655i
$721$	−1.44959e14			−0.743995
$722$	1.33134e14	−	1.30390e14i	0.678585	−	0.664596i
$723$	−5.51893e14			−2.79360
$724$	−1.58821e13	−	3.30864e11i	−0.0798389	−	0.00166325i
$725$			7.04410e13i			0.351670i
$726$	−1.02037e14	+	9.99334e13i	−0.505911	+	0.495482i
$727$			1.56999e14i			0.773082i	0.922272	+	0.386541i	$0.126330\pi$
$727$			1.56999e14i			0.773082i	−0.922272	+	0.386541i	$0.873670\pi$
$728$	−1.91449e14	−	2.03802e14i	−0.936260	−	0.996672i
$729$	−2.44622e14			−1.18812
$730$	2.06261e14	+	2.10602e14i	0.994953	+	1.01590i
$731$	−6.14361e13			−0.294332
$732$	−3.68146e14	−	7.66941e12i	−1.75172	−	0.0364927i
$733$			2.64144e14i			1.24831i	0.781302	+	0.624153i	$0.214556\pi$
$733$			2.64144e14i			1.24831i	−0.781302	+	0.624153i	$0.785444\pi$
$734$	−5.99176e13	−	6.11789e13i	−0.281238	−	0.287158i
$735$			5.12169e13i			0.238768i
$736$	−8.78008e13	−	9.74566e13i	−0.406546	−	0.451255i
$737$	−7.20216e13			−0.331227
$738$	−1.50520e13	+	1.47417e13i	−0.0687563	+	0.0673389i
$739$	2.68052e14			1.21618			0.608089	−	0.793869i	$-0.291936\pi$
$739$	2.68052e14			1.21618			0.608089	+	0.793869i	$0.291936\pi$
$740$	6.40822e12	−	3.07606e14i	0.0288788	−	1.38623i
$741$			6.65150e14i			2.97734i
$742$	1.10606e14	−	1.08326e14i	0.491766	−	0.481628i
$743$			9.68880e13i			0.427884i	0.976846	+	0.213942i	$0.0686303\pi$
$743$			9.68880e13i			0.427884i	−0.976846	+	0.213942i	$0.931370\pi$
$744$	−1.14647e14	+	1.07697e14i	−0.502918	+	0.472434i
$745$	−3.52258e14			−1.53490
$746$	−2.22116e14	−	2.26792e14i	−0.961360	−	0.981596i
$747$	1.78874e14			0.769032
$748$	3.68657e12	−	1.76962e14i	0.0157440	−	0.755740i
$749$			6.10885e13i			0.259149i
$750$	1.57415e14	+	1.60729e14i	0.663347	+	0.677310i
$751$		−	2.13814e13i		−	0.0895026i	−0.998998	−	0.0447513i	$-0.985750\pi$
$751$		−	2.13814e13i		−	0.0895026i	0.998998	−	0.0447513i	$-0.0142495\pi$
$752$	−1.03079e13	+	2.47291e14i	−0.0428627	+	1.02830i
$753$	6.47674e14			2.67536
$754$	1.96653e14	−	1.92599e14i	0.806947	−	0.790311i
$755$	6.76669e11			0.00275830
$756$	−3.30779e13	−	6.89098e11i	−0.133946	−	0.00279043i
$757$		−	3.45330e14i		−	1.38917i	−0.719412	−	0.694584i	$-0.755589\pi$
$757$		−	3.45330e14i		−	1.38917i	0.719412	−	0.694584i	$-0.244411\pi$
$758$	1.41774e13	−	1.38851e13i	0.0566565	−	0.0554885i
$759$		−	1.58511e14i		−	0.629290i
$760$	3.11608e14	−	2.92720e14i	1.22897	−	1.15447i
$761$	1.01279e14			0.396822			0.198411	−	0.980119i	$-0.436422\pi$
$761$	1.01279e14			0.396822			0.198411	+	0.980119i	$0.436422\pi$
$762$	4.93777e13	+	5.04170e13i	0.192201	+	0.196247i
$763$	1.71486e14			0.663142
$764$	−2.24359e14	−	4.67397e12i	−0.861940	−	0.0179564i
$765$		−	3.67740e14i		−	1.40357i
$766$	−1.16105e14	−	1.18549e14i	−0.440259	−	0.449526i
$767$		−	3.42135e13i		−	0.128890i
$768$	3.85794e14	+	3.22182e13i	1.44394	+	0.120585i
$769$	−2.20211e14			−0.818854			−0.409427	−	0.912343i	$-0.634271\pi$
$769$	−2.20211e14			−0.818854			−0.409427	+	0.912343i	$0.634271\pi$
$770$	−1.55164e14	+	1.51965e14i	−0.573241	+	0.561424i
$771$	−1.65286e14			−0.606687
$772$	3.92052e12	−	1.88192e14i	0.0142974	−	0.686302i
$773$			1.15285e14i			0.417709i	0.977947	+	0.208855i	$0.0669735\pi$
$773$			1.15285e14i			0.417709i	−0.977947	+	0.208855i	$0.933026\pi$
$774$	6.07524e13	−	5.95000e13i	0.218705	−	0.214196i
$775$			6.10005e13i			0.218185i
$776$	3.50853e14	+	3.73492e14i	1.24686	+	1.32731i
$777$	−4.37855e14			−1.54606
$778$	4.14196e13	+	4.22915e13i	0.145314	+	0.148373i
$779$	−3.50623e13			−0.122223
$780$	−1.54830e13	+	7.43214e14i	−0.0536269	+	2.57419i
$781$		−	2.36700e14i		−	0.814596i
$782$	−1.31384e14	−	1.34150e14i	−0.449273	−	0.458730i
$783$		−	3.25689e13i		−	0.110661i
$784$	−4.03848e13	−	1.68337e12i	−0.136345	−	0.00568328i
$785$	1.66566e14			0.558775
$786$	−4.01813e13	+	3.93529e13i	−0.133940	+	0.131179i
$787$	2.91930e14			0.966953			0.483476	−	0.875357i	$-0.339374\pi$
$787$	2.91930e14			0.966953			0.483476	+	0.875357i	$0.339374\pi$
$788$	2.96457e13	+	6.17595e11i	0.0975731	+	0.00203270i
$789$		−	7.13843e14i		−	2.33463i
$790$	−2.62686e14	+	2.57271e14i	−0.853694	+	0.836094i
$791$		−	3.16890e14i		−	1.02335i
$792$	1.67740e14	+	1.78563e14i	0.538282	+	0.573015i
$793$	5.58007e14			1.77940
$794$	1.53271e14	+	1.56497e14i	0.485687	+	0.495910i
$795$	−4.11580e14			−1.29604
$796$	−3.33007e14	−	6.93739e12i	−1.04205	−	0.0217085i
$797$			3.56212e14i			1.10769i	0.832621	+	0.553843i	$0.186839\pi$
$797$			3.56212e14i			1.10769i	−0.832621	+	0.553843i	$0.813161\pi$
$798$	−4.25721e14	−	4.34682e14i	−1.31556	−	1.34325i
$799$			3.54295e14i			1.08800i
$800$	1.11542e14	−	1.00490e14i	0.340398	−	0.306672i
$801$	1.63559e13			0.0496035
$802$	−2.45497e14	+	2.40436e14i	−0.739903	+	0.724649i
$803$	−2.81121e14			−0.842007
$804$	4.69656e12	−	2.25443e14i	0.0139798	−	0.671054i
$805$			2.30401e14i			0.681562i
$806$	1.70298e14	−	1.66787e14i	0.500650	−	0.490329i
$807$		−	5.45417e14i		−	1.59353i
$808$	−9.21378e13	+	8.65529e13i	−0.267535	+	0.251319i
$809$	−2.42201e14			−0.698930			−0.349465	−	0.936949i	$-0.613637\pi$
$809$	−2.42201e14			−0.698930			−0.349465	+	0.936949i	$0.613637\pi$
$810$	−2.62377e14	−	2.67900e14i	−0.752490	−	0.768329i
$811$	−4.06752e14			−1.15938			−0.579689	−	0.814838i	$-0.696826\pi$
$811$	−4.06752e14			−1.15938			−0.579689	+	0.814838i	$0.696826\pi$
$812$	−5.24420e12	+	2.51731e14i	−0.0148559	+	0.713110i
$813$			9.67412e14i			2.72370i
$814$	2.05303e14	+	2.09625e14i	0.574478	+	0.586570i
$815$		−	4.00018e14i		−	1.11248i
$816$	5.53690e14	+	2.30796e13i	1.53044	+	0.0637936i
$817$	1.41517e14			0.388776
$818$	4.10241e14	−	4.01783e14i	1.12014	−	1.09705i
$819$	5.54024e14			1.50352
$820$	−3.91773e13	−	8.16163e11i	−0.105673	−	0.00220144i
$821$			4.04166e14i			1.08354i	0.840528	+	0.541768i	$0.182245\pi$
$821$			4.04166e14i			1.08354i	−0.840528	+	0.541768i	$0.817755\pi$
$822$	−4.27788e14	+	4.18969e14i	−1.13991	+	1.11641i
$823$			1.42442e14i			0.377259i	0.982048	+	0.188630i	$0.0604045\pi$
$823$			1.42442e14i			0.377259i	−0.982048	+	0.188630i	$0.939595\pi$
$824$	−2.21669e14	+	2.08232e14i	−0.583537	+	0.548166i
$825$	1.81420e14			0.474695
$826$	2.18979e13	+	2.23588e13i	0.0569511	+	0.0581499i
$827$	−3.85554e13			−0.0996684			−0.0498342	−	0.998758i	$-0.515869\pi$
$827$	−3.85554e13			−0.0996684			−0.0498342	+	0.998758i	$0.515869\pi$
$828$	2.59845e14	+	5.41322e12i	0.667670	+	0.0139093i
$829$		−	2.35400e14i		−	0.601221i	−0.953747	−	0.300610i	$-0.902810\pi$
$829$		−	2.35400e14i		−	0.601221i	0.953747	−	0.300610i	$-0.0971904\pi$
$830$	2.32787e14	+	2.37687e14i	0.590973	+	0.603412i
$831$			1.21214e14i			0.305877i
$832$	−5.85519e14	−	3.66360e13i	−1.46867	−	0.0918949i
$833$	−5.78595e13			−0.144261
$834$	2.61240e14	−	2.55854e14i	0.647455	−	0.634107i
$835$	−6.23469e14			−1.53597
$836$	−8.49198e12	+	4.07630e14i	−0.0207959	+	0.998241i
$837$		−	2.82040e13i		−	0.0686568i
$838$	2.32447e14	−	2.27655e14i	0.562475	−	0.550879i
$839$		−	5.54263e14i		−	1.33323i	−0.745401	−	0.666616i	$-0.767742\pi$
$839$		−	5.54263e14i		−	1.33323i	0.745401	−	0.666616i	$-0.232258\pi$
$840$	−4.65566e14	−	4.95607e14i	−1.11323	−	1.18506i
$841$	1.72850e14			0.410857
$842$	3.10544e14	+	3.17081e14i	0.733774	+	0.749220i
$843$	−1.81993e14			−0.427481
$844$	1.32331e13	−	6.35212e14i	0.0308993	−	1.48322i
$845$		−	6.06286e14i		−	1.40732i
$846$	−3.43129e14	−	3.50352e14i	−0.791782	−	0.808449i
$847$			1.97976e14i			0.454146i
$848$	1.35276e13	−	3.24533e14i	0.0308490	−	0.740082i
$849$	3.45400e14			0.783039
$850$	1.53538e14	−	1.50373e14i	0.346036	−	0.338902i
$851$	3.11269e14			0.697410
$852$	7.40921e14	+	1.54353e13i	1.65034	+	0.0343808i
$853$			2.17078e14i			0.480696i	0.970687	+	0.240348i	$0.0772615\pi$
$853$			2.17078e14i			0.480696i	−0.970687	+	0.240348i	$0.922738\pi$
$854$	−3.64663e14	+	3.57145e14i	−0.802790	+	0.786240i
$855$			8.47086e14i			1.85395i
$856$	8.77528e13	+	9.34151e13i	0.190938	+	0.203258i
$857$	7.39171e14			1.59897			0.799485	−	0.600685i	$-0.205106\pi$
$857$	7.39171e14			1.59897			0.799485	+	0.600685i	$0.205106\pi$
$858$	−4.96037e14	−	5.06478e14i	−1.06679	−	1.08924i
$859$	3.16235e14			0.676152			0.338076	−	0.941119i	$-0.390224\pi$
$859$	3.16235e14			0.676152			0.338076	+	0.941119i	$0.390224\pi$
$860$	1.58126e14	+	3.29417e12i	0.336133	+	0.00700251i
$861$			5.57661e13i			0.117857i
$862$	−7.87601e12	−	8.04180e12i	−0.0165489	−	0.0168973i
$863$		−	3.17121e14i		−	0.662478i	−0.943547	−	0.331239i	$-0.892533\pi$
$863$		−	3.17121e14i		−	0.662478i	0.943547	−	0.331239i	$-0.107467\pi$
$864$	−5.15720e13	+	4.64623e13i	−0.107114	+	0.0965011i
$865$	−1.03130e15			−2.12964
$866$	−3.97267e14	+	3.89077e14i	−0.815630	+	0.798815i
$867$	8.34458e13			0.170337
$868$	−4.54137e12	+	2.17994e14i	−0.00921698	+	0.442432i
$869$		−	3.50645e14i		−	0.707569i
$870$	4.78222e14	−	4.68363e14i	0.959475	−	0.939695i
$871$			3.41710e14i			0.681658i
$872$	2.62233e14	−	2.46338e14i	0.520122	−	0.488595i
$873$	−1.01531e15			−2.00230
$874$	3.02643e14	+	3.09013e14i	0.593435	+	0.605926i
$875$	3.11852e14			0.608007
$876$	1.83320e13	−	8.79971e14i	0.0355378	−	1.70588i
$877$			5.34325e14i			1.02993i	0.857211	+	0.514965i	$0.172195\pi$
$877$			5.34325e14i			1.02993i	−0.857211	+	0.514965i	$0.827805\pi$
$878$	−2.36910e14	−	2.41897e14i	−0.454058	−	0.463616i
$879$			1.33432e15i			2.54282i
$880$	−1.89772e13	+	4.55273e14i	−0.0359600	+	0.862698i
$881$	−1.20104e13			−0.0226297			−0.0113148	−	0.999936i	$-0.503602\pi$
$881$	−1.20104e13			−0.0226297			−0.0113148	+	0.999936i	$0.503602\pi$
$882$	5.72156e13	−	5.60361e13i	0.107194	−	0.104984i
$883$	6.89886e14			1.28521			0.642605	−	0.766198i	$-0.277854\pi$
$883$	6.89886e14			1.28521			0.642605	+	0.766198i	$0.277854\pi$
$884$	−8.39605e14	−	1.74911e13i	−1.55530	−	0.0324008i
$885$		−	8.32003e13i		−	0.153253i
$886$	5.00563e14	−	4.90244e14i	0.916833	−	0.897932i
$887$			7.40300e13i			0.134831i	0.997725	+	0.0674154i	$0.0214753\pi$
$887$			7.40300e13i			0.134831i	−0.997725	+	0.0674154i	$0.978525\pi$
$888$	−6.69559e14	+	6.28974e14i	−1.21262	+	1.13912i
$889$	9.78211e13			0.176167
$890$	2.12855e13	+	2.17336e13i	0.0381184	+	0.0389208i
$891$	3.57604e14			0.636816
$892$	5.38173e14	+	1.12115e13i	0.953010	+	0.0198536i
$893$		−	8.16114e14i		−	1.43712i
$894$	7.35929e14	+	7.51420e14i	1.28869	+	1.31582i
$895$		−	5.87236e14i		−	1.02258i
$896$	4.06091e14	−	3.50812e14i	0.703207	−	0.607484i
$897$	−7.52063e14			−1.29507
$898$	−8.09176e14	+	7.92494e14i	−1.38567	+	1.35711i
$899$	−2.14639e14			−0.365519
$900$	−6.19557e12	+	2.97399e14i	−0.0104922	+	0.503647i
$901$		−	4.64960e14i		−	0.783054i
$902$	2.66982e13	−	2.61478e13i	0.0447146	−	0.0437927i
$903$		−	2.25081e14i		−	0.374887i
$904$	−4.55208e14	−	4.84581e14i	−0.753994	−	0.802646i
$905$	5.85404e13			0.0964301
$906$	−1.41368e12	−	1.44344e12i	−0.00231585	−	0.00236459i
$907$	−1.10129e15			−1.79418			−0.897088	−	0.441852i	$-0.854322\pi$
$907$	−1.10129e15			−1.79418			−0.897088	+	0.441852i	$0.854322\pi$
$908$	−1.86355e13	+	8.94537e14i	−0.0301933	+	1.44934i
$909$		−	2.50471e14i		−	0.403587i
$910$	7.21006e14	+	7.36183e14i	1.15540	+	1.17972i
$911$		−	5.75678e14i		−	0.917461i	−0.888575	−	0.458730i	$-0.848304\pi$
$911$		−	5.75678e14i		−	0.917461i	0.888575	−	0.458730i	$-0.151696\pi$
$912$	−1.27542e15	−	5.31635e13i	−2.02152	−	0.0842635i
$913$	−3.17274e14			−0.500128
$914$	−4.43251e14	+	4.34114e14i	−0.694895	+	0.680569i
$915$	1.35696e15			2.11574
$916$	−8.49960e14	−	1.77068e13i	−1.31802	−	0.0274576i
$917$			7.79613e13i			0.120235i
$918$	−7.09893e13	+	6.95258e13i	−0.108888	+	0.106643i
$919$		−	2.49831e14i		−	0.381126i	−0.981675	−	0.190563i	$-0.938969\pi$
$919$		−	2.49831e14i		−	0.381126i	0.981675	−	0.190563i	$-0.0610314\pi$
$920$	3.30968e14	+	3.52324e14i	0.502166	+	0.534569i
$921$	1.66965e15			2.51957
$922$	−3.79342e14	−	3.87327e14i	−0.569346	−	0.581331i
$923$	−1.12303e15			−1.67642
$924$	6.48330e14	+	1.35064e13i	0.962578	+	0.0200530i
$925$			3.56255e14i			0.526081i
$926$	9.40178e14	+	9.59968e14i	1.38088	+	1.40994i
$927$		−	6.02593e14i		−	0.880289i
$928$	3.53589e14	+	3.92475e14i	0.513759	+	0.570259i
$929$	−5.75740e14			−0.832046			−0.416023	−	0.909354i	$-0.636576\pi$
$929$	−5.75740e14			−0.832046			−0.416023	+	0.909354i	$0.636576\pi$
$930$	4.14131e14	−	4.05594e14i	0.595283	−	0.583011i
$931$	1.33279e14			0.190552
$932$	1.77742e13	−	8.53193e14i	0.0252761	−	1.21330i
$933$		−	6.26252e14i		−	0.885811i
$934$	2.18507e14	−	2.14003e14i	0.307420	−	0.301082i
$935$			6.52272e14i			0.912789i
$936$	8.47201e14	−	7.95849e14i	1.17925	−	1.10777i
$937$	4.19947e14			0.581428			0.290714	−	0.956810i	$-0.406107\pi$
$937$	4.19947e14			0.581428			0.290714	+	0.956810i	$0.406107\pi$
$938$	−2.18707e14	−	2.23311e14i	−0.301196	−	0.307536i
$939$	−7.72792e14			−1.05861
$940$	1.89971e13	−	9.11895e14i	0.0258850	−	1.24253i
$941$		−	4.76423e14i		−	0.645721i	−0.946447	−	0.322860i	$-0.895356\pi$
$941$		−	4.76423e14i		−	0.645721i	0.946447	−	0.322860i	$-0.104644\pi$
$942$	−3.47985e14	−	3.55310e14i	−0.469143	−	0.479019i
$943$		−	3.96438e13i		−	0.0531639i
$944$	6.56039e13	+	2.73458e12i	0.0875125	+	0.00364780i
$945$	1.21923e14			0.161781
$946$	−1.07758e14	+	1.05537e14i	−0.142231	+	0.139299i
$947$	7.31112e14			0.959918			0.479959	−	0.877291i	$-0.340652\pi$
$947$	7.31112e14			0.959918			0.479959	+	0.877291i	$0.340652\pi$
$948$	1.09760e15	+	2.28657e13i	1.43351	+	0.0298637i
$949$			1.33379e15i			1.73283i
$950$	−3.53673e14	+	3.46382e14i	−0.457071	+	0.447649i
$951$		−	8.11488e14i		−	1.04323i
$952$	5.59885e14	−	5.25948e14i	0.716002	−	0.672602i
$953$	4.33318e14			0.551242			0.275621	−	0.961266i	$-0.411116\pi$
$953$	4.33318e14			0.551242			0.275621	+	0.961266i	$0.411116\pi$
$954$	4.50307e14	+	4.59786e14i	0.569858	+	0.581853i
$955$	8.26974e14			1.04106
$956$	−9.41185e14	−	1.96073e13i	−1.17865	−	0.0245543i
$957$			6.38352e14i			0.795244i
$958$	−9.08237e14	−	9.27355e14i	−1.12557	−	1.14926i
$959$			8.30012e14i			1.02327i
$960$	−1.42387e15	−	8.90915e13i	−1.74628	−	0.109265i
$961$	6.33755e14			0.773222
$962$	9.94573e14	−	9.74070e14i	1.20715	−	1.18226i
$963$	−2.53943e14			−0.306623
$964$	−3.34302e13	+	1.60471e15i	−0.0401563	+	1.92758i
$965$			6.93665e14i			0.828921i
$966$	4.91480e14	−	4.81348e14i	0.584279	−	0.572234i
$967$			1.28203e15i			1.51623i	0.652120	+	0.758115i	$0.273880\pi$
$967$			1.28203e15i			1.51623i	−0.652120	+	0.758115i	$0.726120\pi$
$968$	2.84390e14	+	3.02741e14i	0.334609	+	0.356200i
$969$	−1.82730e15			−2.13890
$970$	−1.32133e15	−	1.34914e15i	−1.53869	−	1.57108i
$971$	−1.03910e15			−1.20381			−0.601907	−	0.798566i	$-0.705592\pi$
$971$	−1.03910e15			−1.20381			−0.601907	+	0.798566i	$0.705592\pi$
$972$	−2.59249e13	+	1.24444e15i	−0.0298803	+	1.43431i
$973$		−	5.06868e14i		−	0.581207i
$974$	−1.18207e15	−	1.20695e15i	−1.34849	−	1.37688i
$975$		−	8.60755e14i		−	0.976914i
$976$	−4.45998e13	+	1.06997e15i	−0.0503598	+	1.20816i
$977$	−8.98564e13			−0.100943			−0.0504715	−	0.998726i	$-0.516072\pi$
$977$	−8.98564e13			−0.100943			−0.0504715	+	0.998726i	$0.516072\pi$
$978$	−8.53299e14	+	8.35708e14i	−0.953690	+	0.934029i
$979$	−2.90109e13			−0.0322588
$980$	1.48921e14	+	3.10240e12i	0.164750	+	0.00343215i
$981$			7.12864e14i			0.784624i
$982$	−5.52040e14	+	5.40659e14i	−0.604523	+	0.592060i
$983$			5.65525e14i			0.616147i	0.951363	+	0.308073i	$0.0996842\pi$
$983$			5.65525e14i			0.616147i	−0.951363	+	0.308073i	$0.900316\pi$
$984$	8.01073e13	+	8.52763e13i	0.0868353	+	0.0924384i
$985$	−1.09272e14			−0.117850
$986$	5.29108e14	+	5.40246e14i	0.567754	+	0.579705i
$987$	−1.29802e15			−1.38578
$988$	1.93402e15	+	4.02906e13i	2.05436	+	0.0427975i
$989$			1.60009e14i			0.169107i
$990$	−6.31716e14	−	6.45013e14i	−0.664271	−	0.678254i
$991$		−	1.22093e15i		−	1.27739i	−0.769461	−	0.638693i	$-0.779475\pi$
$991$		−	1.22093e15i		−	1.27739i	0.769461	−	0.638693i	$-0.220525\pi$
$992$	3.06201e14	+	3.39876e14i	0.318749	+	0.353803i
$993$	1.26542e15			1.31065
$994$	7.33912e14	−	7.18782e14i	0.756332	−	0.740739i
$995$	1.22744e15			1.25860
$996$	2.06896e13	−	9.93138e14i	0.0211084	−	1.01324i
$997$		−	4.49639e14i		−	0.456445i	−0.973609	−	0.228222i	$-0.926709\pi$
$997$		−	4.49639e14i		−	0.456445i	0.973609	−	0.228222i	$-0.0732913\pi$
$998$	5.05900e12	−	4.95470e12i	0.00510989	−	0.00500455i
$999$		−	1.64717e14i		−	0.165543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.11.d.b.3.5	✓	8
3.2	odd	2		72.11.b.b.19.4		8
4.3	odd	2		32.11.d.b.15.2		8
8.3	odd	2	inner	8.11.d.b.3.6	yes	8
8.5	even	2		32.11.d.b.15.1		8
12.11	even	2		288.11.b.b.271.2		8
16.3	odd	4		256.11.c.m.255.2		16
16.5	even	4		256.11.c.m.255.1		16
16.11	odd	4		256.11.c.m.255.15		16
16.13	even	4		256.11.c.m.255.16		16
24.5	odd	2		288.11.b.b.271.7		8
24.11	even	2		72.11.b.b.19.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.11.d.b.3.5	✓	8	1.1	even	1	trivial
8.11.d.b.3.6	yes	8	8.3	odd	2	inner
32.11.d.b.15.1		8	8.5	even	2
32.11.d.b.15.2		8	4.3	odd	2
72.11.b.b.19.3		8	24.11	even	2
72.11.b.b.19.4		8	3.2	odd	2
256.11.c.m.255.1		16	16.5	even	4
256.11.c.m.255.2		16	16.3	odd	4
256.11.c.m.255.15		16	16.11	odd	4
256.11.c.m.255.16		16	16.13	even	4
288.11.b.b.271.2		8	12.11	even	2
288.11.b.b.271.7		8	24.5	odd	2

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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(22.8618 - 22.3905i) q^{2} +352.099 q^{3} +(21.3279 - 1023.78i) q^{4} +3773.58i q^{5} +(8049.62 - 7883.68i) q^{6} -15618.2i q^{7} +(-22435.3 - 23883.0i) q^{8} +64924.4 q^{9} +(84492.5 + 86271.1i) q^{10} -115158. q^{11} +(7509.52 - 360471. i) q^{12} +546374. i q^{13} +(-349700. - 357061. i) q^{14} +1.32867e6i q^{15} +(-1.04767e6 - 43670.1i) q^{16} -1.50100e6 q^{17} +(1.48429e6 - 1.45369e6i) q^{18} +3.45753e6 q^{19} +(3.86331e6 + 80482.6i) q^{20} -5.49914e6i q^{21} +(-2.63273e6 + 2.57846e6i) q^{22} +3.90931e6i q^{23} +(-7.89945e6 - 8.40917e6i) q^{24} -4.47430e6 q^{25} +(1.22336e7 + 1.24911e7i) q^{26} +2.06872e6 q^{27} +(-1.59896e7 - 333103. i) q^{28} -1.57435e7i q^{29} +(2.97497e7 + 3.03759e7i) q^{30} -1.36335e7i q^{31} +(-2.49294e7 + 2.24594e7i) q^{32} -4.05471e7 q^{33} +(-3.43155e7 + 3.36081e7i) q^{34} +5.89365e7 q^{35} +(1.38470e6 - 6.64682e7i) q^{36} -7.96225e7i q^{37} +(7.90455e7 - 7.74159e7i) q^{38} +1.92377e8i q^{39} +(9.01244e7 - 8.46616e7i) q^{40} -1.01409e7 q^{41} +(-1.23129e8 - 1.25721e8i) q^{42} +4.09302e7 q^{43} +(-2.45608e6 + 1.17897e8i) q^{44} +2.44998e8i q^{45} +(8.75315e7 + 8.93740e7i) q^{46} -2.36040e8i q^{47} +(-3.68882e8 - 1.53762e7i) q^{48} +3.85474e7 q^{49} +(-1.02291e8 + 1.00182e8i) q^{50} -5.28499e8 q^{51} +(5.59365e8 + 1.16530e7i) q^{52} +3.09768e8i q^{53} +(4.72948e7 - 4.63198e7i) q^{54} -4.34559e8i q^{55} +(-3.73009e8 + 3.50399e8i) q^{56} +1.21739e9 q^{57} +(-3.52505e8 - 3.59925e8i) q^{58} -6.26191e7 q^{59} +(1.36027e9 + 2.83378e7i) q^{60} -1.02129e9i q^{61} +(-3.05262e8 - 3.11688e8i) q^{62} -1.01400e9i q^{63} +(-6.70530e7 + 1.07165e9i) q^{64} -2.06179e9 q^{65} +(-9.26981e8 + 9.07871e8i) q^{66} +6.25414e8 q^{67} +(-3.20131e7 + 1.53669e9i) q^{68} +1.37646e9i q^{69} +(1.34740e9 - 1.31962e9i) q^{70} +2.05543e9i q^{71} +(-1.45660e9 - 1.55059e9i) q^{72} +2.44117e9 q^{73} +(-1.78279e9 - 1.82032e9i) q^{74} -1.57539e9 q^{75} +(7.37418e7 - 3.53974e9i) q^{76} +1.79856e9i q^{77} +(4.30743e9 + 4.39810e9i) q^{78} +3.04489e9i q^{79} +(1.64793e8 - 3.95346e9i) q^{80} -3.10533e9 q^{81} +(-2.31839e8 + 2.27059e8i) q^{82} +2.75511e9 q^{83} +(-5.62990e9 - 1.17285e8i) q^{84} -5.66413e9i q^{85} +(9.35741e8 - 9.16450e8i) q^{86} -5.54325e9i q^{87} +(2.58362e9 + 2.75032e9i) q^{88} +2.51922e8 q^{89} +(5.48563e9 + 5.60110e9i) q^{90} +8.53337e9 q^{91} +(4.00226e9 + 8.33773e7i) q^{92} -4.80035e9i q^{93} +(-5.28506e9 - 5.39630e9i) q^{94} +1.30473e10i q^{95} +(-8.77760e9 + 7.90793e9i) q^{96} -1.56384e10 q^{97} +(8.81265e8 - 8.63097e8i) q^{98} -7.47658e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19}+ \cdots - 13646747232 q^{99}+O(q^{100}) \) 8 * q + 42 * q^2 + 480 * q^3 + 212 * q^4 - 5412 * q^6 - 72 * q^8 - 35496 * q^9 + 9120 * q^10 + 143328 * q^11 + 180120 * q^12 - 400320 * q^14 - 1987312 * q^16 - 370800 * q^17 + 3067758 * q^18 + 1753312 * q^19 + 2557440 * q^20 + 1549180 * q^22 - 19794288 * q^24 - 18792760 * q^25 + 1891680 * q^26 + 28949184 * q^27 + 18286080 * q^28 + 67026240 * q^30 - 64016928 * q^32 - 74308704 * q^33 - 115705388 * q^34 + 53736960 * q^35 + 50631516 * q^36 + 375128220 * q^38 - 357584640 * q^40 + 92669328 * q^41 - 576155520 * q^42 - 10190624 * q^43 + 727831512 * q^44 + 851947200 * q^46 - 1142760480 * q^48 - 80432248 * q^49 - 1669361190 * q^50 - 276714816 * q^51 + 2420759040 * q^52 + 1749768696 * q^54 - 2928529920 * q^56 + 1400712864 * q^57 - 3245264160 * q^58 - 965642016 * q^59 + 5250055680 * q^60 + 4060980480 * q^62 - 5804705728 * q^64 - 839028480 * q^65 - 5970262296 * q^66 - 1225582880 * q^67 + 5258111400 * q^68 + 7723829760 * q^70 - 4343608728 * q^72 + 2800072720 * q^73 - 7669373280 * q^74 + 4485554400 * q^75 + 3753451288 * q^76 + 7176312000 * q^78 - 6408629760 * q^80 - 11909065176 * q^81 - 3638778380 * q^82 + 1853422560 * q^83 - 2916218880 * q^84 + 3022180476 * q^86 + 5815578640 * q^88 + 6162596112 * q^89 + 12545940960 * q^90 + 7645985280 * q^91 - 8903892480 * q^92 - 14182177920 * q^94 + 7877525568 * q^96 - 9697863536 * q^97 + 34759868298 * q^98 - 13646747232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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