LMFDB - Embedded newform 15.11.d.c.14.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(14,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, 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("15.14");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 17880 x^{14} + 140656106 x^{12} + 568287997200 x^{10} + \cdots + 16\!\cdots\!76 $ x^16 + 17880x^14 + 140656106x^12 + 568287997200x^10 + 2185320263599761x^8 + 14044998488243281560x^6 + 65358313992126025248056x^4 + 158088257382003622736619360*x^2 + 166976847233168897062137442576
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{32}\cdot 5^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			14.7
Root			$61.4341 + 30.7435i$ of defining polynomial
Character	$\chi$	$=$	15.14
Dual form			15.11.d.c.14.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.37421 q^{2} +(-224.817 - 92.2305i) q^{3} -1012.61 q^{4} +(862.380 - 3003.65i) q^{5} +(758.580 + 311.205i) q^{6} +16006.0i q^{7} +6871.97 q^{8} +(42036.1 + 41469.9i) q^{9} +O(q^{10})$	\(q-3.37421 q^{2} +(-224.817 - 92.2305i) q^{3} -1012.61 q^{4} +(862.380 - 3003.65i) q^{5} +(758.580 + 311.205i) q^{6} +16006.0i q^{7} +6871.97 q^{8} +(42036.1 + 41469.9i) q^{9} +(-2909.86 + 10135.0i) q^{10} -109087. i q^{11} +(227653. + 93393.9i) q^{12} +572716. i q^{13} -54007.6i q^{14} +(-470906. + 595733. i) q^{15} +1.01373e6 q^{16} +1.54275e6 q^{17} +(-141839. - 139928. i) q^{18} -720399. q^{19} +(-873259. + 3.04154e6i) q^{20} +(1.47624e6 - 3.59841e6i) q^{21} +368084. i q^{22} -2.49708e6 q^{23} +(-1.54493e6 - 633805. i) q^{24} +(-8.27823e6 - 5.18058e6i) q^{25} -1.93247e6i q^{26} +(-5.62563e6 - 1.32001e7i) q^{27} -1.62079e7i q^{28} +1.79908e7i q^{29} +(1.58894e6 - 2.01013e6i) q^{30} +1.83900e7 q^{31} -1.04574e7 q^{32} +(-1.00612e7 + 2.45246e7i) q^{33} -5.20558e6 q^{34} +(4.80764e7 + 1.38032e7i) q^{35} +(-4.25664e7 - 4.19930e7i) q^{36} +6.73581e7i q^{37} +2.43078e6 q^{38} +(5.28219e7 - 1.28756e8i) q^{39} +(5.92625e6 - 2.06410e7i) q^{40} +1.78223e8i q^{41} +(-4.98115e6 + 1.21418e7i) q^{42} +1.66496e8i q^{43} +1.10463e8i q^{44} +(1.60812e8 - 9.04990e7i) q^{45} +8.42568e6 q^{46} +2.99761e8 q^{47} +(-2.27903e8 - 9.34968e7i) q^{48} +2.62835e7 q^{49} +(2.79325e7 + 1.74804e7i) q^{50} +(-3.46837e8 - 1.42289e8i) q^{51} -5.79941e8i q^{52} -6.37040e8 q^{53} +(1.89821e7 + 4.45401e7i) q^{54} +(-3.27660e8 - 9.40747e7i) q^{55} +1.09993e8i q^{56} +(1.61958e8 + 6.64428e7i) q^{57} -6.07047e7i q^{58} -3.05843e7i q^{59} +(4.76846e8 - 6.03248e8i) q^{60} +9.80370e8 q^{61} -6.20518e7 q^{62} +(-6.63767e8 + 6.72829e8i) q^{63} -1.00277e9 q^{64} +(1.72024e9 + 4.93899e8i) q^{65} +(3.39485e7 - 8.27514e7i) q^{66} +6.91391e8i q^{67} -1.56222e9 q^{68} +(5.61385e8 + 2.30307e8i) q^{69} +(-1.62220e8 - 4.65751e7i) q^{70} -2.10199e9i q^{71} +(2.88871e8 + 2.84980e8i) q^{72} +2.47490e9i q^{73} -2.27281e8i q^{74} +(1.38328e9 + 1.92819e9i) q^{75} +7.29487e8 q^{76} +1.74605e9 q^{77} +(-1.78232e8 + 4.34451e8i) q^{78} +1.45740e9 q^{79} +(8.74220e8 - 3.04489e9i) q^{80} +(4.72803e7 + 3.48646e9i) q^{81} -6.01364e8i q^{82} -6.85447e9 q^{83} +(-1.49486e9 + 3.64381e9i) q^{84} +(1.33044e9 - 4.63390e9i) q^{85} -5.61794e8i q^{86} +(1.65930e9 - 4.04462e9i) q^{87} -7.49645e8i q^{88} -5.45554e9i q^{89} +(-5.42615e8 + 3.05363e8i) q^{90} -9.16689e9 q^{91} +2.52858e9 q^{92} +(-4.13438e9 - 1.69612e9i) q^{93} -1.01146e9 q^{94} +(-6.21258e8 + 2.16383e9i) q^{95} +(2.35101e9 + 9.64495e8i) q^{96} -3.04168e9i q^{97} -8.86862e7 q^{98} +(4.52384e9 - 4.58560e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	$ 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) $ 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−3.37421			−0.105444			−0.0527221	−	0.998609i	$-0.516790\pi$
$2$	−3.37421			−0.105444			−0.0527221	+	0.998609i	$0.516790\pi$
$3$	−224.817	−	92.2305i	−0.925172	−	0.379549i
$3$	−224.817	−	92.2305i	−0.925172	−	0.379549i
$4$	−1012.61			−0.988882
$5$	862.380	−	3003.65i	0.275962	−	0.961169i
$5$	862.380	−	3003.65i	0.275962	−	0.961169i
$6$	758.580	+	311.205i	0.0975540	+	0.0400213i
$7$			16006.0i			0.952341i	0.879353	+	0.476170i	$0.157975\pi$
$7$			16006.0i			0.952341i	−0.879353	+	0.476170i	$0.842025\pi$
$8$	6871.97			0.209716
$9$	42036.1	+	41469.9i	0.711885	+	0.702296i
$10$	−2909.86	+	10135.0i	−0.0290986	+	0.101350i
$11$		−	109087.i		−	0.677346i	−0.940904	−	0.338673i	$-0.890022\pi$
$11$		−	109087.i		−	0.677346i	0.940904	−	0.338673i	$-0.109978\pi$
$12$	227653.	+	93393.9i	0.914885	+	0.375329i
$13$			572716.i			1.54249i	0.636538	+	0.771245i	$0.280366\pi$
$13$			572716.i			1.54249i	−0.636538	+	0.771245i	$0.719634\pi$
$14$		−	54007.6i		−	0.100419i
$15$	−470906.	+	595733.i	−0.620123	+	0.784505i
$16$	1.01373e6			0.966768
$17$	1.54275e6			1.08656			0.543278	−	0.839553i	$-0.317183\pi$
$17$	1.54275e6			1.08656			0.543278	+	0.839553i	$0.317183\pi$
$18$	−141839.	−	139928.i	−0.0750641	−	0.0740531i
$19$	−720399.			−0.290941			−0.145471	−	0.989363i	$-0.546470\pi$
$19$	−720399.			−0.290941			−0.145471	+	0.989363i	$0.546470\pi$
$20$	−873259.	+	3.04154e6i	−0.272893	+	0.950482i
$21$	1.47624e6	−	3.59841e6i	0.361460	−	0.881079i
$22$			368084.i			0.0714222i
$23$	−2.49708e6			−0.387965			−0.193983	−	0.981005i	$-0.562141\pi$
$23$	−2.49708e6			−0.387965			−0.193983	+	0.981005i	$0.562141\pi$
$24$	−1.54493e6	−	633805.i	−0.194023	−	0.0795976i
$25$	−8.27823e6	−	5.18058e6i	−0.847690	−	0.530491i
$26$		−	1.93247e6i		−	0.162647i
$27$	−5.62563e6	−	1.32001e7i	−0.392060	−	0.919940i
$28$		−	1.62079e7i		−	0.941752i
$29$			1.79908e7i			0.877121i	0.898702	+	0.438561i	$0.144512\pi$
$29$			1.79908e7i			0.877121i	−0.898702	+	0.438561i	$0.855488\pi$
$30$	1.58894e6	−	2.01013e6i	0.0653883	−	0.0827215i
$31$	1.83900e7			0.642352			0.321176	−	0.947020i	$-0.395922\pi$
$31$	1.83900e7			0.642352			0.321176	+	0.947020i	$0.395922\pi$
$32$	−1.04574e7			−0.311656
$33$	−1.00612e7	+	2.45246e7i	−0.257086	+	0.626661i
$34$	−5.20558e6			−0.114571
$35$	4.80764e7	+	1.38032e7i	0.915360	+	0.262809i
$36$	−4.25664e7	−	4.19930e7i	−0.703970	−	0.694488i
$37$			6.73581e7i			0.971362i	0.874136	+	0.485681i	$0.161428\pi$
$37$			6.73581e7i			0.971362i	−0.874136	+	0.485681i	$0.838572\pi$
$38$	2.43078e6			0.0306781
$39$	5.28219e7	−	1.28756e8i	0.585451	−	1.42707i
$40$	5.92625e6	−	2.06410e7i	0.0578736	−	0.201572i
$41$			1.78223e8i			1.53832i	0.639058	+	0.769158i	$0.279324\pi$
$41$			1.78223e8i			1.53832i	−0.639058	+	0.769158i	$0.720676\pi$
$42$	−4.98115e6	+	1.21418e7i	−0.0381139	+	0.0929046i
$43$			1.66496e8i			1.13256i	0.824212	+	0.566281i	$0.191618\pi$
$43$			1.66496e8i			1.13256i	−0.824212	+	0.566281i	$0.808382\pi$
$44$			1.10463e8i			0.669815i
$45$	1.60812e8	−	9.04990e7i	0.871478	−	0.490435i
$46$	8.42568e6			0.0409087
$47$	2.99761e8			1.30703			0.653514	−	0.756914i	$-0.273294\pi$
$47$	2.99761e8			1.30703			0.653514	+	0.756914i	$0.273294\pi$
$48$	−2.27903e8	−	9.34968e7i	−0.894426	−	0.366936i
$49$	2.62835e7			0.0930472
$50$	2.79325e7	+	1.74804e7i	0.0893840	+	0.0559372i
$51$	−3.46837e8	−	1.42289e8i	−1.00525	−	0.412402i
$52$		−	5.79941e8i		−	1.52534i
$53$	−6.37040e8			−1.52331			−0.761653	−	0.647985i	$-0.775612\pi$
$53$	−6.37040e8			−1.52331			−0.761653	+	0.647985i	$0.775612\pi$
$54$	1.89821e7	+	4.45401e7i	0.0413404	+	0.0970023i
$55$	−3.27660e8	−	9.40747e7i	−0.651044	−	0.186922i
$56$			1.09993e8i			0.199721i
$57$	1.61958e8	+	6.64428e7i	0.269171	+	0.110427i
$58$		−	6.07047e7i		−	0.0924873i
$59$		−	3.05843e7i		−	0.0427798i	−0.999771	−	0.0213899i	$-0.993191\pi$
$59$		−	3.05843e7i		−	0.0427798i	0.999771	−	0.0213899i	$-0.00680914\pi$
$60$	4.76846e8	−	6.03248e8i	0.613228	−	0.775782i
$61$	9.80370e8			1.16076			0.580378	−	0.814347i	$-0.302905\pi$
$61$	9.80370e8			1.16076			0.580378	+	0.814347i	$0.302905\pi$
$62$	−6.20518e7			−0.0677323
$63$	−6.63767e8	+	6.72829e8i	−0.668825	+	0.677957i
$64$	−1.00277e9			−0.933906
$65$	1.72024e9	+	4.93899e8i	1.48259	+	0.425668i
$66$	3.39485e7	−	8.27514e7i	0.0271083	−	0.0660778i
$67$			6.91391e8i			0.512094i	0.966664	+	0.256047i	$0.0824203\pi$
$67$			6.91391e8i			0.512094i	−0.966664	+	0.256047i	$0.917580\pi$
$68$	−1.56222e9			−1.07448
$69$	5.61385e8	+	2.30307e8i	0.358935	+	0.147252i
$70$	−1.62220e8	−	4.65751e7i	−0.0965194	−	0.0277117i
$71$		−	2.10199e9i		−	1.16503i	−0.812819	−	0.582516i	$-0.802068\pi$
$71$		−	2.10199e9i		−	1.16503i	0.812819	−	0.582516i	$-0.197932\pi$
$72$	2.88871e8	+	2.84980e8i	0.149294	+	0.147283i
$73$			2.47490e9i			1.19383i	0.802304	+	0.596916i	$0.203607\pi$
$73$			2.47490e9i			1.19383i	−0.802304	+	0.596916i	$0.796393\pi$
$74$		−	2.27281e8i		−	0.102424i
$75$	1.38328e9	+	1.92819e9i	0.582911	+	0.812536i
$76$	7.29487e8			0.287706
$77$	1.74605e9			0.645064
$78$	−1.78232e8	+	4.34451e8i	−0.0617324	+	0.150476i
$79$	1.45740e9			0.473635			0.236818	−	0.971554i	$-0.423896\pi$
$79$	1.45740e9			0.473635			0.236818	+	0.971554i	$0.423896\pi$
$80$	8.74220e8	−	3.04489e9i	0.266791	−	0.929227i
$81$	4.72803e7	+	3.48646e9i	0.0135599	+	0.999908i
$82$		−	6.01364e8i		−	0.162207i
$83$	−6.85447e9			−1.74014			−0.870068	−	0.492931i	$-0.835925\pi$
$83$	−6.85447e9			−1.74014			−0.870068	+	0.492931i	$0.835925\pi$
$84$	−1.49486e9	+	3.64381e9i	−0.357441	+	0.871282i
$85$	1.33044e9	−	4.63390e9i	0.299848	−	1.04436i
$86$		−	5.61794e8i		−	0.119422i
$87$	1.65930e9	−	4.04462e9i	0.332911	−	0.811487i
$88$		−	7.49645e8i		−	0.142050i
$89$		−	5.45554e9i		−	0.976985i	−0.872568	−	0.488493i	$-0.837547\pi$
$89$		−	5.45554e9i		−	0.976985i	0.872568	−	0.488493i	$-0.162453\pi$
$90$	−5.42615e8	+	3.05363e8i	−0.0918923	+	0.0517135i
$91$	−9.16689e9			−1.46898
$92$	2.52858e9			0.383652
$93$	−4.13438e9	−	1.69612e9i	−0.594286	−	0.243804i
$94$	−1.01146e9			−0.137819
$95$	−6.21258e8	+	2.16383e9i	−0.0802886	+	0.279644i
$96$	2.35101e9	+	9.64495e8i	0.288335	+	0.118289i
$97$		−	3.04168e9i		−	0.354205i	−0.984192	−	0.177103i	$-0.943328\pi$
$97$		−	3.04168e9i		−	0.354205i	0.984192	−	0.177103i	$-0.0566725\pi$
$98$	−8.86862e7			−0.00981129
$99$	4.52384e9	−	4.58560e9i	0.475698	−	0.482192i
$100$	8.38265e9	+	5.24593e9i	0.838265	+	0.524593i
$101$			1.00889e10i			0.959920i	0.877290	+	0.479960i	$0.159349\pi$
$101$			1.00889e10i			0.959920i	−0.877290	+	0.479960i	$0.840651\pi$
$102$	1.17030e9	+	4.80113e8i	0.105998	+	0.0434854i
$103$		−	2.12524e9i		−	0.183325i	−0.995790	−	0.0916626i	$-0.970782\pi$
$103$		−	2.12524e9i		−	0.183325i	0.995790	−	0.0916626i	$-0.0292181\pi$
$104$			3.93569e9i			0.323485i
$105$	−9.53530e9	−	7.53731e9i	−0.747116	−	0.590568i
$106$	2.14951e9			0.160624
$107$	−4.65164e9			−0.331656			−0.165828	−	0.986155i	$-0.553030\pi$
$107$	−4.65164e9			−0.331656			−0.165828	+	0.986155i	$0.553030\pi$
$108$	5.69659e9	+	1.33666e10i	0.387700	+	0.909712i
$109$	1.40621e9			0.0913940			0.0456970	−	0.998955i	$-0.485449\pi$
$109$	1.40621e9			0.0913940			0.0456970	+	0.998955i	$0.485449\pi$
$110$	1.10560e9	+	3.17428e8i	0.0686488	+	0.0197098i
$111$	6.21246e9	−	1.51432e10i	0.368680	−	0.898676i
$112$			1.62258e10i			0.920693i
$113$	2.64325e10			1.43465			0.717324	−	0.696739i	$-0.245367\pi$
$113$	2.64325e10			1.43465			0.717324	+	0.696739i	$0.245367\pi$
$114$	−5.46480e8	−	2.24192e8i	−0.0283825	−	0.0116438i
$115$	−2.15343e9	+	7.50036e9i	−0.107064	+	0.372900i
$116$		−	1.82177e10i		−	0.867369i
$117$	−2.37505e10	+	2.40747e10i	−1.08329	+	1.09808i
$118$			1.03198e8i			0.00451089i
$119$			2.46933e10i			1.03477i
$120$	−3.23605e9	+	4.09386e9i	−0.130050	+	0.164523i
$121$	1.40374e10			0.541202
$122$	−3.30798e9			−0.122395
$123$	1.64376e10	−	4.00676e10i	0.583867	−	1.42321i
$124$	−1.86220e10			−0.635210
$125$	−2.26996e10	+	2.03973e10i	−0.743822	+	0.668378i
$126$	2.23969e9	−	2.27027e9i	0.0705238	−	0.0714866i
$127$		−	3.50550e10i		−	1.06104i	−0.847673	−	0.530519i	$-0.821997\pi$
$127$		−	3.50550e10i		−	1.06104i	0.847673	−	0.530519i	$-0.178003\pi$
$128$	1.40920e10			0.410131
$129$	1.53560e10	−	3.74311e10i	0.429863	−	1.04781i
$130$	−5.80446e9	−	1.66652e9i	−0.156331	−	0.0448842i
$131$			3.84731e10i			0.997243i	0.866820	+	0.498621i	$0.166160\pi$
$131$			3.84731e10i			0.997243i	−0.866820	+	0.498621i	$0.833840\pi$
$132$	1.01881e10	−	2.48340e10i	0.254228	−	0.619694i
$133$		−	1.15307e10i		−	0.277075i
$134$		−	2.33290e9i		−	0.0539974i
$135$	−4.45000e10	+	5.51389e9i	−0.992411	+	0.122967i
$136$	1.06018e10			0.227868
$137$	−7.23598e9			−0.149932			−0.0749660	−	0.997186i	$-0.523885\pi$
$137$	−7.23598e9			−0.149932			−0.0749660	+	0.997186i	$0.523885\pi$
$138$	−1.89423e9	−	7.77104e8i	−0.0378476	−	0.0155269i
$139$	−5.23987e10			−1.00983			−0.504913	−	0.863170i	$-0.668475\pi$
$139$	−5.23987e10			−1.00983			−0.504913	+	0.863170i	$0.668475\pi$
$140$	−4.86829e10	−	1.39774e10i	−0.905183	−	0.259887i
$141$	−6.73912e10	−	2.76471e10i	−1.20923	−	0.496082i
$142$			7.09255e9i			0.122846i
$143$	6.24760e10			1.04480
$144$	4.26132e10	+	4.20393e10i	0.688228	+	0.678958i
$145$	5.40380e10	+	1.55149e10i	0.843061	+	0.242052i
$146$		−	8.35084e9i		−	0.125883i
$147$	−5.90897e9	−	2.42414e9i	−0.0860846	−	0.0353160i
$148$		−	6.82078e10i		−	0.960562i
$149$		−	1.02267e10i		−	0.139253i	−0.997573	−	0.0696265i	$-0.977819\pi$
$149$		−	1.02267e10i		−	0.139253i	0.997573	−	0.0696265i	$-0.0221808\pi$
$150$	−4.66747e9	−	6.50611e9i	−0.0614646	−	0.0856772i
$151$	4.69180e10			0.597661			0.298831	−	0.954306i	$-0.403403\pi$
$151$	4.69180e10			0.597661			0.298831	+	0.954306i	$0.403403\pi$
$152$	−4.95057e9			−0.0610150
$153$	6.48514e10	+	6.39779e10i	0.773503	+	0.763084i
$154$	−5.89155e9			−0.0680183
$155$	1.58592e10	−	5.52371e10i	0.177265	−	0.617409i
$156$	−5.34882e10	+	1.30380e11i	−0.578942	+	1.41120i
$157$			1.72513e11i			1.80853i	0.426976	+	0.904263i	$0.359579\pi$
$157$			1.72513e11i			1.80853i	−0.426976	+	0.904263i	$0.640421\pi$
$158$	−4.91759e9			−0.0499421
$159$	1.43217e11	+	5.87545e10i	1.40932	+	0.578169i
$160$	−9.01829e9	+	3.14105e10i	−0.0860051	+	0.299554i
$161$		−	3.99682e10i		−	0.369475i
$162$	−1.59534e8	−	1.17641e10i	−0.00142981	−	0.105435i
$163$			6.40750e10i			0.556866i	0.960456	+	0.278433i	$0.0898151\pi$
$163$			6.40750e10i			0.556866i	−0.960456	+	0.278433i	$0.910185\pi$
$164$		−	1.80472e11i		−	1.52121i
$165$	6.49869e10	+	5.13698e10i	0.531381	+	0.420038i
$166$	2.31284e10			0.183487
$167$	−7.67116e10			−0.590580			−0.295290	−	0.955408i	$-0.595416\pi$
$167$	−7.67116e10			−0.590580			−0.295290	+	0.955408i	$0.595416\pi$
$168$	1.01447e10	−	2.47282e10i	0.0758040	−	0.184776i
$169$	−1.90145e11			−1.37928
$170$	−4.48919e9	+	1.56358e10i	−0.0316172	+	0.110122i
$171$	−3.02828e10	−	2.98749e10i	−0.207117	−	0.204327i
$172$		−	1.68596e11i		−	1.11997i
$173$	−2.57821e10			−0.166375			−0.0831874	−	0.996534i	$-0.526510\pi$
$173$	−2.57821e10			−0.166375			−0.0831874	+	0.996534i	$0.526510\pi$
$174$	−5.59882e9	+	1.36474e10i	−0.0351035	+	0.0855666i
$175$	8.29203e10	−	1.32501e11i	0.505208	−	0.807290i
$176$		−	1.10585e11i		−	0.654837i
$177$	−2.82081e9	+	6.87587e9i	−0.0162371	+	0.0395787i
$178$			1.84082e10i			0.103017i
$179$			1.90863e11i			1.03862i	0.854586	+	0.519309i	$0.173811\pi$
$179$			1.90863e11i			1.03862i	−0.854586	+	0.519309i	$0.826189\pi$
$180$	−1.62841e11	+	9.16406e10i	−0.861789	+	0.484982i
$181$	1.39429e11			0.717729			0.358864	−	0.933390i	$-0.383164\pi$
$181$	1.39429e11			0.717729			0.358864	+	0.933390i	$0.383164\pi$
$182$	3.09310e10			0.154895
$183$	−2.20403e11	−	9.04200e10i	−1.07390	−	0.440564i
$184$	−1.71599e10			−0.0813626
$185$	2.02320e11	+	5.80882e10i	0.933642	+	0.268059i
$186$	1.39503e10	+	5.72306e9i	0.0626640	+	0.0257077i
$187$		−	1.68295e11i		−	0.735975i
$188$	−3.03542e11			−1.29250
$189$	2.11281e11	−	9.00437e10i	0.876096	−	0.373374i
$190$	2.09626e9	−	7.30122e9i	0.00846597	−	0.0294868i
$191$			1.29311e10i			0.0508709i	0.999676	+	0.0254354i	$0.00809722\pi$
$191$			1.29311e10i			0.0508709i	−0.999676	+	0.0254354i	$0.991903\pi$
$192$	2.25440e11	+	9.24863e10i	0.864023	+	0.354463i
$193$			2.61082e10i			0.0974969i	0.998811	+	0.0487484i	$0.0155233\pi$
$193$			2.61082e10i			0.0974969i	−0.998811	+	0.0487484i	$0.984477\pi$
$194$			1.02633e10i			0.0373489i
$195$	−3.41186e11	−	2.69695e11i	−1.21009	−	0.956533i
$196$	−2.66151e10			−0.0920126
$197$	1.49535e11			0.503977			0.251989	−	0.967730i	$-0.418915\pi$
$197$	1.49535e11			0.503977			0.251989	+	0.967730i	$0.418915\pi$
$198$	−1.52644e10	+	1.54728e10i	−0.0501596	+	0.0508444i
$199$	−4.65959e11			−1.49308			−0.746539	−	0.665341i	$-0.768286\pi$
$199$	−4.65959e11			−1.49308			−0.746539	+	0.665341i	$0.768286\pi$
$200$	−5.68878e10	−	3.56008e10i	−0.177774	−	0.111253i
$201$	6.37674e10	−	1.55436e11i	0.194365	−	0.473775i
$202$		−	3.40419e10i		−	0.101218i
$203$	−2.87960e11			−0.835318
$204$	3.51212e11	+	1.44084e11i	0.994074	+	0.407816i
$205$	5.35321e11	+	1.53696e11i	1.47858	+	0.424516i
$206$			7.17102e9i			0.0193306i
$207$	−1.04967e11	−	1.03554e11i	−0.276187	−	0.272467i
$208$			5.80579e11i			1.49123i
$209$			7.85864e10i			0.197068i
$210$	3.21742e10	+	2.54325e10i	0.0787790	+	0.0622720i
$211$	−1.29382e11			−0.309359			−0.154679	−	0.987965i	$-0.549434\pi$
$211$	−1.29382e11			−0.309359			−0.154679	+	0.987965i	$0.549434\pi$
$212$	6.45076e11			1.50637
$213$	−1.93867e11	+	4.72561e11i	−0.442187	+	1.07785i
$214$	1.56956e10			0.0349712
$215$	5.00097e11	+	1.43583e11i	1.08858	+	0.312544i
$216$	−3.86592e10	−	9.07110e10i	−0.0822212	−	0.192926i
$217$			2.94350e11i			0.611738i
$218$	−4.74485e9			−0.00963697
$219$	2.28261e11	−	5.56399e11i	0.453118	−	1.10450i
$220$	3.31794e11	+	9.52614e10i	0.643805	+	0.184843i
$221$			8.83560e11i			1.67600i
$222$	−2.09622e10	+	5.10965e10i	−0.0388751	+	0.0947602i
$223$		−	6.06435e11i		−	1.09966i	−0.835275	−	0.549832i	$-0.814692\pi$
$223$		−	6.06435e11i		−	1.09966i	0.835275	−	0.549832i	$-0.185308\pi$
$224$		−	1.67382e11i		−	0.296803i
$225$	−1.33146e11	−	5.61068e11i	−0.230896	−	0.972978i
$226$	−8.91888e10			−0.151275
$227$	−8.79312e11			−1.45886			−0.729431	−	0.684055i	$-0.760215\pi$
$227$	−8.79312e11			−1.45886			−0.729431	+	0.684055i	$0.760215\pi$
$228$	−1.64001e11	−	6.72809e10i	−0.266178	−	0.109199i
$229$	−2.98404e11			−0.473835			−0.236918	−	0.971530i	$-0.576137\pi$
$229$	−2.98404e11			−0.473835			−0.236918	+	0.971530i	$0.576137\pi$
$230$	7.26614e9	−	2.53078e10i	0.0112892	−	0.0393202i
$231$	−3.92541e11	−	1.61039e11i	−0.596795	−	0.244834i
$232$			1.23632e11i			0.183946i
$233$	1.62068e11			0.236003			0.118001	−	0.993013i	$-0.462351\pi$
$233$	1.62068e11			0.236003			0.118001	+	0.993013i	$0.462351\pi$
$234$	8.01392e10	−	8.12333e10i	0.114226	−	0.115786i
$235$	2.58507e11	−	9.00376e11i	0.360690	−	1.25628i
$236$			3.09702e10i			0.0423042i
$237$	−3.27648e11	−	1.34417e11i	−0.438194	−	0.179768i
$238$		−	8.33205e10i		−	0.109111i
$239$			6.75549e11i			0.866298i	0.901322	+	0.433149i	$0.142598\pi$
$239$			6.75549e11i			0.866298i	−0.901322	+	0.433149i	$0.857402\pi$
$240$	−4.77371e11	+	6.03913e11i	−0.599515	+	0.758434i
$241$	2.09769e11			0.258022			0.129011	−	0.991643i	$-0.458820\pi$
$241$	2.09769e11			0.258022			0.129011	+	0.991643i	$0.458820\pi$
$242$	−4.73652e10			−0.0570666
$243$	3.10929e11	−	7.88176e11i	0.366969	−	0.930233i
$244$	−9.92737e11			−1.14785
$245$	2.26664e10	−	7.89466e10i	0.0256774	−	0.0894340i
$246$	−5.54641e10	+	1.35197e11i	−0.0615654	+	0.150069i
$247$		−	4.12584e11i		−	0.448774i
$248$	1.26376e11			0.134712
$249$	1.54100e12	+	6.32191e11i	1.60992	+	0.660467i
$250$	7.65934e10	−	6.88248e10i	0.0784317	−	0.0704766i
$251$		−	1.53797e12i		−	1.54376i	−0.635769	−	0.771880i	$-0.719317\pi$
$251$		−	1.53797e12i		−	1.54376i	0.635769	−	0.771880i	$-0.280683\pi$
$252$	6.72140e11	−	6.81317e11i	0.661389	−	0.670419i
$253$			2.72400e11i			0.262787i
$254$			1.18283e11i			0.111880i
$255$	−7.26492e11	+	9.19070e11i	−0.673798	+	0.852409i
$256$	9.79291e11			0.890660
$257$	−3.09044e11			−0.275648			−0.137824	−	0.990457i	$-0.544011\pi$
$257$	−3.09044e11			−0.275648			−0.137824	+	0.990457i	$0.544011\pi$
$258$	−5.18145e10	+	1.26301e11i	−0.0453266	+	0.110486i
$259$	−1.07813e12			−0.925067
$260$	−1.74194e12	−	5.00129e11i	−1.46611	−	0.420935i
$261$	−7.46075e11	+	7.56261e11i	−0.615999	+	0.624409i
$262$		−	1.29817e11i		−	0.105153i
$263$	1.27422e12			1.01267			0.506333	−	0.862338i	$-0.331001\pi$
$263$	1.27422e12			1.01267			0.506333	+	0.862338i	$0.331001\pi$
$264$	−6.91401e10	+	1.68533e11i	−0.0539151	+	0.131421i
$265$	−5.49370e11	+	1.91345e12i	−0.420374	+	1.46415i
$266$			3.89071e10i			0.0292160i
$267$	−5.03167e11	+	1.22650e12i	−0.370814	+	0.903879i
$268$		−	7.00113e11i		−	0.506401i
$269$		−	2.76933e12i		−	1.96613i	−0.183253	−	0.983066i	$-0.558663\pi$
$269$		−	2.76933e12i		−	1.96613i	0.183253	−	0.983066i	$-0.441337\pi$
$270$	1.50153e11	−	1.86051e10i	0.104644	−	0.0129662i
$271$	1.98616e12			1.35884			0.679421	−	0.733749i	$-0.262231\pi$
$271$	1.98616e12			1.35884			0.679421	+	0.733749i	$0.262231\pi$
$272$	1.56394e12			1.05045
$273$	2.06087e12	+	8.45466e11i	1.35906	+	0.557549i
$274$	2.44157e10			0.0158095
$275$	−5.65135e11	+	9.03049e11i	−0.359326	+	0.574180i
$276$	−5.68467e11	−	2.33212e11i	−0.354944	−	0.145615i
$277$			2.22799e12i			1.36620i	0.730324	+	0.683101i	$0.239369\pi$
$277$			2.22799e12i			1.36620i	−0.730324	+	0.683101i	$0.760631\pi$
$278$	1.76804e11			0.106480
$279$	7.73043e11	+	7.62631e11i	0.457281	+	0.451121i
$280$	3.30380e11	+	9.48556e10i	0.191966	+	0.0551154i
$281$		−	9.00059e11i		−	0.513735i	−0.966447	−	0.256868i	$-0.917310\pi$
$281$		−	9.00059e11i		−	0.513735i	0.966447	−	0.256868i	$-0.0826905\pi$
$282$	2.27392e11	+	9.32871e10i	0.127506	+	0.0523089i
$283$		−	4.14490e11i		−	0.228340i	−0.993461	−	0.114170i	$-0.963579\pi$
$283$		−	4.14490e11i		−	0.228340i	0.993461	−	0.114170i	$-0.0364208\pi$
$284$			2.12850e12i			1.15208i
$285$	3.39240e11	−	4.29166e11i	0.180419	−	0.228245i
$286$	−2.10807e11			−0.110168
$287$	−2.85264e12			−1.46500
$288$	−4.39590e11	−	4.33669e11i	−0.221863	−	0.218875i
$289$	3.64097e11			0.180604
$290$	−1.82336e11	−	5.23505e10i	−0.0888959	−	0.0255230i
$291$	−2.80536e11	+	6.83821e11i	−0.134438	+	0.327701i
$292$		−	2.50612e12i		−	1.18056i
$293$	2.76959e12			1.28256			0.641280	−	0.767307i	$-0.278404\pi$
$293$	2.76959e12			1.28256			0.641280	+	0.767307i	$0.278404\pi$
$294$	1.99381e10	+	8.17957e9i	0.00907712	+	0.00372387i
$295$	−9.18647e10	−	2.63753e10i	−0.0411186	−	0.0118056i
$296$			4.62883e11i			0.203710i
$297$	−1.43997e12	+	6.13684e11i	−0.623118	+	0.265560i
$298$			3.45071e10i			0.0146834i
$299$		−	1.43012e12i		−	0.598433i
$300$	−1.40073e12	−	1.95251e12i	−0.576430	−	0.803502i
$301$	−2.66494e12			−1.07858
$302$	−1.58312e11			−0.0630199
$303$	9.30499e11	−	2.26814e12i	0.364337	−	0.888090i
$304$	−7.30290e11			−0.281273
$305$	8.45451e11	−	2.94469e12i	0.320324	−	1.11568i
$306$	−2.18822e11	−	2.15875e11i	−0.0815614	−	0.0804628i
$307$		−	4.47551e11i		−	0.164116i	−0.996628	−	0.0820579i	$-0.973851\pi$
$307$		−	4.47551e11i		−	0.164116i	0.996628	−	0.0820579i	$-0.0261492\pi$
$308$	−1.76808e12			−0.637892
$309$	−1.96012e11	+	4.77790e11i	−0.0695810	+	0.169607i
$310$	−5.35122e10	+	1.86382e11i	−0.0186915	+	0.0651022i
$311$			3.35727e12i			1.15394i	0.816765	+	0.576971i	$0.195765\pi$
$311$			3.35727e12i			1.15394i	−0.816765	+	0.576971i	$0.804235\pi$
$312$	3.62990e11	−	8.84809e11i	0.122778	−	0.299279i
$313$		−	1.38448e12i		−	0.460857i	−0.973089	−	0.230428i	$-0.925987\pi$
$313$		−	1.38448e12i		−	0.460857i	0.973089	−	0.230428i	$-0.0740127\pi$
$314$		−	5.82097e11i		−	0.190699i
$315$	1.44853e12	+	2.57396e12i	0.467061	+	0.829944i
$316$	−1.47579e12			−0.468369
$317$	−1.97509e12			−0.617008			−0.308504	−	0.951223i	$-0.599828\pi$
$317$	−1.97509e12			−0.617008			−0.308504	+	0.951223i	$0.599828\pi$
$318$	−4.83245e11	−	1.98250e11i	−0.148605	−	0.0609646i
$319$	1.96256e12			0.594115
$320$	−8.64772e11	+	3.01198e12i	−0.257722	+	0.897641i
$321$	1.04577e12	+	4.29023e11i	0.306838	+	0.125880i
$322$			1.34861e11i			0.0389590i
$323$	−1.11140e12			−0.316124
$324$	−4.78767e10	−	3.53044e12i	−0.0134091	−	0.988791i
$325$	2.96700e12	−	4.74107e12i	0.818278	−	1.30755i
$326$		−	2.16203e11i		−	0.0587183i
$327$	−3.16139e11	−	1.29695e11i	−0.0845551	−	0.0346885i
$328$			1.22475e12i			0.322610i
$329$			4.79796e12i			1.24474i
$330$	−2.19280e11	−	1.73333e11i	−0.0560311	−	0.0442905i
$331$	9.94662e11			0.250343			0.125171	−	0.992135i	$-0.460052\pi$
$331$	9.94662e11			0.250343			0.125171	+	0.992135i	$0.460052\pi$
$332$	6.94093e12			1.72079
$333$	−2.79333e12	+	2.83147e12i	−0.682184	+	0.691498i
$334$	2.58841e11			0.0622732
$335$	2.07670e12	+	5.96242e11i	0.492209	+	0.141318i
$336$	1.49651e12	−	3.64782e12i	0.349448	−	0.851799i
$337$			3.33420e12i			0.767083i	0.923524	+	0.383541i	$0.125296\pi$
$337$			3.33420e12i			0.767083i	−0.923524	+	0.383541i	$0.874704\pi$
$338$	6.41590e11			0.145437
$339$	−5.94246e12	−	2.43788e12i	−1.32730	−	0.544520i
$340$	−1.34722e12	+	4.69235e12i	−0.296514	+	1.03275i
$341$		−	2.00611e12i		−	0.435095i
$342$	1.02181e11	+	1.00804e11i	0.0218392	+	0.0215451i
$343$			4.94199e12i			1.04095i
$344$			1.14416e12i			0.237516i
$345$	1.17589e12	−	1.48759e12i	0.240586	−	0.304361i
$346$	8.69942e10			0.0175433
$347$	4.36427e12			0.867489			0.433745	−	0.901036i	$-0.357192\pi$
$347$	4.36427e12			0.867489			0.433745	+	0.901036i	$0.357192\pi$
$348$	−1.68023e12	+	4.09564e12i	−0.329209	+	0.802465i
$349$	2.40524e12			0.464548			0.232274	−	0.972650i	$-0.425383\pi$
$349$	2.40524e12			0.464548			0.232274	+	0.972650i	$0.425383\pi$
$350$	−2.79791e11	+	4.47087e11i	−0.0532713	+	0.0851241i
$351$	7.55993e12	−	3.22189e12i	1.41900	−	0.604748i
$352$			1.14077e12i			0.211099i
$353$	−7.89736e12			−1.44081			−0.720407	−	0.693551i	$-0.756045\pi$
$353$	−7.89736e12			−1.44081			−0.720407	+	0.693551i	$0.756045\pi$
$354$	9.51801e9	−	2.32007e10i	0.00171210	−	0.00417334i
$355$	−6.31363e12	−	1.81271e12i	−1.11979	−	0.321504i
$356$			5.52436e12i			0.966123i
$357$	2.27748e12	−	5.55147e12i	0.392747	−	0.957341i
$358$		−	6.44012e11i		−	0.109516i
$359$			2.29923e10i			0.00385576i	0.999998	+	0.00192788i	$0.000613664\pi$
$359$			2.29923e10i			0.00385576i	−0.999998	+	0.00192788i	$0.999386\pi$
$360$	1.10510e12	−	6.21907e11i	0.182763	−	0.102852i
$361$	−5.61209e12			−0.915353
$362$	−4.70463e11			−0.0756803
$363$	−3.15584e12	−	1.29468e12i	−0.500705	−	0.205413i
$364$	9.28252e12			1.45264
$365$	7.43374e12	+	2.13430e12i	1.14747	+	0.329452i
$366$	7.43689e11	+	3.05096e11i	0.113236	+	0.0464549i
$367$		−	5.32967e12i		−	0.800516i	−0.916403	−	0.400258i	$-0.868921\pi$
$367$		−	5.32967e12i		−	0.800516i	0.916403	−	0.400258i	$-0.131079\pi$
$368$	−2.53136e12			−0.375073
$369$	−7.39091e12	+	7.49182e12i	−1.08035	+	1.09510i
$370$	−6.82672e11	−	1.96002e11i	−0.0984472	−	0.0282652i
$371$		−	1.01964e13i		−	1.45071i
$372$	4.18653e12	+	1.71751e12i	0.587678	+	0.241093i
$373$		−	4.76124e12i		−	0.659441i	−0.944079	−	0.329720i	$-0.893046\pi$
$373$		−	4.76124e12i		−	0.659441i	0.944079	−	0.329720i	$-0.106954\pi$
$374$			5.67863e11i			0.0776043i
$375$	6.98451e12	−	2.49205e12i	0.941845	−	0.336048i
$376$	2.05995e12			0.274105
$377$	−1.03036e13			−1.35295
$378$	−7.12908e11	+	3.03827e11i	−0.0923793	+	0.0393701i
$379$	−1.90196e12			−0.243224			−0.121612	−	0.992578i	$-0.538806\pi$
$379$	−1.90196e12			−0.243224			−0.121612	+	0.992578i	$0.538806\pi$
$380$	6.29095e11	−	2.19112e12i	0.0793959	−	0.276534i
$381$	−3.23314e12	+	7.88095e12i	−0.402716	+	0.981643i
$382$		−	4.36323e10i		−	0.00536404i
$383$	−3.90047e12			−0.473285			−0.236643	−	0.971597i	$-0.576047\pi$
$383$	−3.90047e12			−0.473285			−0.236643	+	0.971597i	$0.576047\pi$
$384$	−3.16812e12	−	1.29971e12i	−0.379442	−	0.155665i
$385$	1.50576e12	−	5.24453e12i	0.178013	−	0.620016i
$386$		−	8.80947e10i		−	0.0102805i
$387$	−6.90458e12	+	6.99885e12i	−0.795394	+	0.806254i
$388$			3.08005e12i			0.350267i
$389$		−	1.17374e13i		−	1.31772i	−0.752265	−	0.658860i	$-0.771039\pi$
$389$		−	1.17374e13i		−	1.31772i	0.752265	−	0.658860i	$-0.228961\pi$
$390$	1.15123e12	+	9.10009e11i	0.127597	+	0.100861i
$391$	−3.85238e12			−0.421546
$392$	1.80620e11			0.0195135
$393$	3.54839e12	−	8.64940e12i	0.378503	−	0.922621i
$394$	−5.04562e11			−0.0531415
$395$	1.25683e12	−	4.37753e12i	0.130705	−	0.455243i
$396$	−4.58090e12	+	4.64345e12i	−0.470409	+	0.476831i
$397$		−	8.00409e12i		−	0.811632i	−0.913955	−	0.405816i	$-0.866987\pi$
$397$		−	8.00409e12i		−	0.811632i	0.913955	−	0.405816i	$-0.133013\pi$
$398$	1.57225e12			0.157437
$399$	−1.06348e12	+	2.59229e12i	−0.105164	+	0.256342i
$400$	−8.39189e12	−	5.25171e12i	−0.819520	−	0.512862i
$401$			1.05898e13i			1.02133i	0.859779	+	0.510667i	$0.170601\pi$
$401$			1.05898e13i			1.02133i	−0.859779	+	0.510667i	$0.829399\pi$
$402$	−2.15165e11	+	5.24476e11i	−0.0204947	+	0.0499568i
$403$			1.05322e13i			0.990822i
$404$		−	1.02161e13i		−	0.949247i
$405$	1.05129e13	+	2.86464e12i	0.964822	+	0.262903i
$406$	9.71639e11			0.0880794
$407$	7.34791e12			0.657948
$408$	−2.38345e12	−	9.77806e11i	−0.210817	−	0.0864872i
$409$	2.15103e13			1.87945			0.939723	−	0.341937i	$-0.111083\pi$
$409$	2.15103e13			1.87945			0.939723	+	0.341937i	$0.111083\pi$
$410$	−1.80629e12	−	5.18605e11i	−0.155908	−	0.0447628i
$411$	1.62677e12	+	6.67377e11i	0.138713	+	0.0569066i
$412$			2.15205e12i			0.181287i
$413$	4.89533e11			0.0407410
$414$	3.54183e11	+	3.49412e11i	0.0291223	+	0.0287300i
$415$	−5.91116e12	+	2.05884e13i	−0.480211	+	1.67256i
$416$		−	5.98914e12i		−	0.480727i
$417$	1.17801e13	+	4.83275e12i	0.934262	+	0.383279i
$418$		−	2.65167e11i		−	0.0207797i
$419$			2.02804e13i			1.57039i	0.619249	+	0.785194i	$0.287437\pi$
$419$			2.02804e13i			1.57039i	−0.619249	+	0.785194i	$0.712563\pi$
$420$	9.65559e12	+	7.63239e12i	0.738809	+	0.584002i
$421$	−2.48486e12			−0.187885			−0.0939425	−	0.995578i	$-0.529947\pi$
$421$	−2.48486e12			−0.187885			−0.0939425	+	0.995578i	$0.529947\pi$
$422$	4.36563e11			0.0326201
$423$	1.26008e13	+	1.24310e13i	0.930454	+	0.917921i
$424$	−4.37772e12			−0.319462
$425$	−1.27713e13	−	7.99236e12i	−0.921063	−	0.576409i
$426$	6.54149e11	−	1.59452e12i	0.0466261	−	0.113654i
$427$			1.56918e13i			1.10543i
$428$	4.71032e12			0.327968
$429$	−1.40457e13	−	5.76219e12i	−0.966619	−	0.396553i
$430$	−1.68743e12	−	4.84480e11i	−0.114785	−	0.0329559i
$431$		−	1.32401e13i		−	0.890234i	−0.895472	−	0.445117i	$-0.853162\pi$
$431$		−	1.32401e13i		−	0.890234i	0.895472	−	0.445117i	$-0.146838\pi$
$432$	−5.70286e12	−	1.33814e13i	−0.379031	−	0.889369i
$433$		−	1.35236e13i		−	0.888490i	−0.895905	−	0.444245i	$-0.853472\pi$
$433$		−	1.35236e13i		−	0.888490i	0.895905	−	0.444245i	$-0.146528\pi$
$434$		−	9.93200e11i		−	0.0645042i
$435$	−1.07177e13	−	8.47195e12i	−0.688106	−	0.543923i
$436$	−1.42395e12			−0.0903778
$437$	1.79889e12			0.112875
$438$	−7.70202e11	+	1.87741e12i	−0.0477787	+	0.116463i
$439$	8.77457e12			0.538150			0.269075	−	0.963119i	$-0.413282\pi$
$439$	8.77457e12			0.538150			0.269075	+	0.963119i	$0.413282\pi$
$440$	−2.25167e12	−	6.46479e11i	−0.136534	−	0.0392004i
$441$	1.10486e12	+	1.08997e12i	0.0662389	+	0.0653467i
$442$		−	2.98132e12i		−	0.176725i
$443$	2.84909e13			1.66989			0.834946	−	0.550333i	$-0.185499\pi$
$443$	2.84909e13			1.66989			0.834946	+	0.550333i	$0.185499\pi$
$444$	−6.29083e12	+	1.53342e13i	−0.364580	+	0.888684i
$445$	−1.63866e13	−	4.70475e12i	−0.939048	−	0.269610i
$446$			2.04624e12i			0.115953i
$447$	−9.43214e11	+	2.29914e12i	−0.0528534	+	0.128833i
$448$		−	1.60504e13i		−	0.889397i
$449$		−	1.57522e13i		−	0.863194i	−0.902066	−	0.431597i	$-0.857950\pi$
$449$		−	1.57522e13i		−	0.863194i	0.902066	−	0.431597i	$-0.142050\pi$
$450$	4.49264e11	+	1.89317e12i	0.0243466	+	0.102595i
$451$	1.94419e13			1.04197
$452$	−2.67659e13			−1.41870
$453$	−1.05480e13	−	4.32727e12i	−0.552939	−	0.226842i
$454$	2.96699e12			0.153828
$455$	−7.90534e12	+	2.75341e13i	−0.405381	+	1.41193i
$456$	1.11297e12	+	4.56593e11i	0.0564494	+	0.0231582i
$457$		−	8.92089e9i		−	0.000447535i	−1.00000		0.000223768i	$-0.999929\pi$
$457$		−	8.92089e9i		−	0.000447535i	1.00000		0.000223768i	$-7.12274e-5\pi$
$458$	1.00688e12			0.0499632
$459$	−8.67896e12	−	2.03646e13i	−0.425995	−	0.999566i
$460$	2.18060e12	−	7.59497e12i	0.105873	−	0.368754i
$461$			2.32159e13i			1.11502i	0.830172	+	0.557508i	$0.188242\pi$
$461$			2.32159e13i			1.11502i	−0.830172	+	0.557508i	$0.811758\pi$
$462$	1.32452e12	+	5.43380e11i	0.0629286	+	0.0258163i
$463$		−	8.54316e12i		−	0.401526i	−0.979640	−	0.200763i	$-0.935658\pi$
$463$		−	8.54316e12i		−	0.401526i	0.979640	−	0.200763i	$-0.0643421\pi$
$464$			1.82378e13i			0.847973i
$465$	−8.65995e12	+	1.09555e13i	−0.398337	+	0.503928i
$466$	−5.46852e11			−0.0248851
$467$	−3.80094e12			−0.171122			−0.0855611	−	0.996333i	$-0.527268\pi$
$467$	−3.80094e12			−0.171122			−0.0855611	+	0.996333i	$0.527268\pi$
$468$	2.40501e13	−	2.43784e13i	1.07124	−	1.08587i
$469$	−1.10664e13			−0.487688
$470$	−8.72260e11	+	3.03806e12i	−0.0380326	+	0.132467i
$471$	1.59110e13	−	3.87839e13i	0.686425	−	1.67320i
$472$		−	2.10175e11i		−	0.00897162i
$473$	1.81626e13			0.767136
$474$	1.10556e12	+	4.53551e11i	0.0462050	+	0.0189555i
$475$	5.96363e12	+	3.73209e12i	0.246628	+	0.154342i
$476$		−	2.50048e13i		−	1.02327i
$477$	−2.67786e13	−	2.64180e13i	−1.08442	−	1.06981i
$478$		−	2.27945e12i		−	0.0913461i
$479$			2.00941e13i			0.796878i	0.917195	+	0.398439i	$0.130448\pi$
$479$			2.00941e13i			0.796878i	−0.917195	+	0.398439i	$0.869552\pi$
$480$	4.92447e12	−	6.22985e12i	0.193265	−	0.244496i
$481$	−3.85770e13			−1.49832
$482$	−7.07807e11			−0.0272069
$483$	−3.68629e12	+	8.98552e12i	−0.140234	+	0.341828i
$484$	−1.42145e13			−0.535185
$485$	−9.13616e12	−	2.62309e12i	−0.340451	−	0.0977471i
$486$	−1.04914e12	+	2.65947e12i	−0.0386948	+	0.0980877i
$487$			1.06632e13i			0.389262i	0.980876	+	0.194631i	$0.0623510\pi$
$487$			1.06632e13i			0.389262i	−0.980876	+	0.194631i	$0.937649\pi$
$488$	6.73708e12			0.243429
$489$	5.90967e12	−	1.44051e13i	0.211358	−	0.515197i
$490$	−7.64813e10	+	2.66383e11i	−0.00270754	+	0.00943030i
$491$			4.81742e13i			1.68813i	0.536238	+	0.844067i	$0.319845\pi$
$491$			4.81742e13i			1.68813i	−0.536238	+	0.844067i	$0.680155\pi$
$492$	−1.66450e13	+	4.05731e13i	−0.577375	+	1.40738i
$493$			2.77553e13i			0.953041i
$494$			1.39215e12i			0.0473206i
$495$	−9.87228e12	−	1.75426e13i	−0.332194	−	0.590292i
$496$	1.86425e13			0.621006
$497$	3.36444e13			1.10951
$498$	−5.19966e12	−	2.13315e12i	−0.169757	−	0.0696425i
$499$	5.42436e13			1.75326			0.876629	−	0.481167i	$-0.159787\pi$
$499$	5.42436e13			1.75326			0.876629	+	0.481167i	$0.159787\pi$
$500$	2.29860e13	−	2.06546e13i	0.735551	−	0.660947i
$501$	1.72460e13	+	7.07514e12i	0.546388	+	0.224154i
$502$			5.18945e12i			0.162780i
$503$	−1.00719e13			−0.312804			−0.156402	−	0.987694i	$-0.549989\pi$
$503$	−1.00719e13			−0.312804			−0.156402	+	0.987694i	$0.549989\pi$
$504$	−4.56139e12	+	4.62366e12i	−0.140263	+	0.142178i
$505$	3.03034e13	+	8.70042e12i	0.922645	+	0.264901i
$506$		−	9.19134e11i		−	0.0277094i
$507$	4.27478e13	+	1.75372e13i	1.27607	+	0.523504i
$508$			3.54972e13i			1.04924i
$509$		−	4.99580e12i		−	0.146223i	−0.997324	−	0.0731116i	$-0.976707\pi$
$509$		−	4.99580e12i		−	0.146223i	0.997324	−	0.0731116i	$-0.0232929\pi$
$510$	2.45134e12	−	3.10114e12i	0.0710481	−	0.0898815i
$511$	−3.96132e13			−1.13694
$512$	−1.77345e13			−0.504046
$513$	4.05270e12	+	9.50936e12i	0.114066	+	0.267648i
$514$	1.04278e12			0.0290655
$515$	−6.38349e12	−	1.83277e12i	−0.176207	−	0.0505907i
$516$	−1.55497e13	+	3.79033e13i	−0.425084	+	1.03616i
$517$		−	3.27001e13i		−	0.885311i
$518$	3.63785e12			0.0975430
$519$	5.79624e12	+	2.37789e12i	0.153925	+	0.0631474i
$520$	1.18214e13	+	3.39406e12i	0.310924	+	0.0892694i
$521$		−	3.61057e13i		−	0.940562i	−0.882517	−	0.470281i	$-0.844153\pi$
$521$		−	3.61057e13i		−	0.940562i	0.882517	−	0.470281i	$-0.155847\pi$
$522$	2.51742e12	−	2.55179e12i	0.0649535	−	0.0658403i
$523$		−	5.28013e13i		−	1.34939i	−0.738098	−	0.674693i	$-0.764276\pi$
$523$		−	5.28013e13i		−	1.34939i	0.738098	−	0.674693i	$-0.235724\pi$
$524$		−	3.89585e13i		−	0.986155i
$525$	−3.08625e13	+	2.21407e13i	−0.773811	+	0.555130i
$526$	−4.29950e12			−0.106780
$527$	2.83712e13			0.697952
$528$	−1.01993e13	+	2.48614e13i	−0.248543	+	0.605836i
$529$	−3.51911e13			−0.849483
$530$	1.85369e12	−	6.45637e12i	0.0443260	−	0.154387i
$531$	1.26833e12	−	1.28565e12i	0.0300441	−	0.0304543i
$532$			1.16762e13i			0.273994i
$533$	−1.02071e14			−2.37284
$534$	1.69779e12	−	4.13847e12i	0.0391002	−	0.0953088i
$535$	−4.01148e12	+	1.39719e13i	−0.0915243	+	0.318777i
$536$			4.75122e12i			0.107394i
$537$	1.76034e13	−	4.29091e13i	0.394207	−	0.960900i
$538$			9.34430e12i			0.207317i
$539$		−	2.86720e12i		−	0.0630251i
$540$	4.50614e13	−	5.58345e12i	0.981377	−	0.121600i
$541$	6.31636e12			0.136295			0.0681476	−	0.997675i	$-0.478291\pi$
$541$	6.31636e12			0.136295			0.0681476	+	0.997675i	$0.478291\pi$
$542$	−6.70174e12			−0.143282
$543$	−3.13460e13	−	1.28596e13i	−0.664022	−	0.272413i
$544$	−1.61333e13			−0.338632
$545$	1.21269e12	−	4.22376e12i	0.0252212	−	0.0878450i
$546$	−6.95381e12	−	2.85278e12i	−0.143305	−	0.0587903i
$547$		−	6.04095e13i		−	1.23358i	−0.787126	−	0.616792i	$-0.788432\pi$
$547$		−	6.04095e13i		−	1.23358i	0.787126	−	0.616792i	$-0.211568\pi$
$548$	7.32726e12			0.148265
$549$	4.12109e13	+	4.06558e13i	0.826324	+	0.815194i
$550$	1.90689e12	−	3.04708e12i	0.0378889	−	0.0605439i
$551$		−	1.29605e13i		−	0.255191i
$552$	3.85782e12	+	1.58266e12i	0.0752743	+	0.0308811i
$553$			2.33272e13i			0.451062i
$554$		−	7.51772e12i		−	0.144058i
$555$	−4.01274e13	−	3.17193e13i	−0.762038	−	0.602363i
$556$	5.30597e13			0.998598
$557$	3.98198e13			0.742716			0.371358	−	0.928490i	$-0.378892\pi$
$557$	3.98198e13			0.742716			0.371358	+	0.928490i	$0.378892\pi$
$558$	−2.60841e12	−	2.57328e12i	−0.0482176	−	0.0475681i
$559$	−9.53550e13			−1.74697
$560$	4.87365e13	+	1.39928e13i	0.884941	+	0.254076i
$561$	−1.55219e13	+	3.78355e13i	−0.279339	+	0.680903i
$562$			3.03699e12i			0.0541704i
$563$	−4.77136e13			−0.843530			−0.421765	−	0.906705i	$-0.638589\pi$
$563$	−4.77136e13			−0.843530			−0.421765	+	0.906705i	$0.638589\pi$
$564$	6.82413e13	+	2.79958e13i	1.19578	+	0.490566i
$565$	2.27948e13	−	7.93940e13i	0.395908	−	1.37894i
$566$			1.39858e12i			0.0240771i
$567$	−5.58043e13	+	7.56768e11i	−0.952253	+	0.0129136i
$568$		−	1.44448e13i		−	0.244326i
$569$			7.89252e12i			0.132329i	0.997809	+	0.0661644i	$0.0210762\pi$
$569$			7.89252e12i			0.132329i	−0.997809	+	0.0661644i	$0.978924\pi$
$570$	−1.14467e12	+	1.44810e12i	−0.0190242	+	0.0240671i
$571$	6.59396e13			1.08634			0.543170	−	0.839623i	$-0.317224\pi$
$571$	6.59396e13			1.08634			0.543170	+	0.839623i	$0.317224\pi$
$572$	−6.32641e13			−1.03318
$573$	1.19264e12	−	2.90713e12i	0.0193080	−	0.0470643i
$574$	9.62543e12			0.154476
$575$	2.06714e13	+	1.29363e13i	0.328875	+	0.205812i
$576$	−4.21527e13	−	4.15849e13i	−0.664833	−	0.655879i
$577$			7.94344e13i			1.24202i	0.783802	+	0.621011i	$0.213278\pi$
$577$			7.94344e13i			1.24202i	−0.783802	+	0.621011i	$0.786722\pi$
$578$	−1.22854e12			−0.0190437
$579$	2.40797e12	−	5.86956e12i	0.0370049	−	0.0902014i
$580$	−5.47197e13	−	1.57106e13i	−0.833688	−	0.239361i
$581$		−	1.09713e14i		−	1.65720i
$582$	9.46588e11	−	2.30736e12i	0.0141758	−	0.0345541i
$583$			6.94929e13i			1.03181i
$584$			1.70074e13i			0.250366i
$585$	5.18302e13	+	9.20997e13i	0.756491	+	1.34425i
$586$	−9.34519e12			−0.135238
$587$	2.48653e13			0.356783			0.178391	−	0.983960i	$-0.442911\pi$
$587$	2.48653e13			0.356783			0.178391	+	0.983960i	$0.442911\pi$
$588$	5.98351e12	+	2.45472e12i	0.0851275	+	0.0349233i
$589$	−1.32481e13			−0.186887
$590$	3.09971e11	+	8.89960e10i	0.00433572	+	0.00124483i
$591$	−3.36179e13	−	1.37917e13i	−0.466266	−	0.191284i
$592$			6.82829e13i			0.939081i
$593$	−8.66034e11			−0.0118103			−0.00590516	−	0.999983i	$-0.501880\pi$
$593$	−8.66034e11			−0.0118103			−0.00590516	+	0.999983i	$0.501880\pi$
$594$	4.85876e12	−	2.07070e12i	0.0657042	−	0.0280018i
$595$	7.41701e13	+	2.12950e13i	0.994590	+	0.285557i
$596$			1.03557e13i			0.137705i
$597$	1.04755e14	+	4.29757e13i	1.38135	+	0.566697i
$598$			4.82552e12i			0.0631013i
$599$		−	4.91176e13i		−	0.636946i	−0.947932	−	0.318473i	$-0.896830\pi$
$599$		−	4.91176e13i		−	0.636946i	0.947932	−	0.318473i	$-0.103170\pi$
$600$	9.50584e12	+	1.32504e13i	0.122246	+	0.170402i
$601$	9.45088e13			1.20531			0.602656	−	0.798001i	$-0.294109\pi$
$601$	9.45088e13			1.20531			0.602656	+	0.798001i	$0.294109\pi$
$602$	8.99207e12			0.113731
$603$	−2.86719e13	+	2.90634e13i	−0.359642	+	0.364552i
$604$	−4.75099e13			−0.591016
$605$	1.21056e13	−	4.21634e13i	0.149351	−	0.520187i
$606$	−3.13970e12	+	7.65320e12i	−0.0384172	+	0.0936440i
$607$		−	8.45768e13i		−	1.02638i	−0.858275	−	0.513190i	$-0.828464\pi$
$607$		−	8.45768e13i		−	1.02638i	0.858275	−	0.513190i	$-0.171536\pi$
$608$	7.53353e12			0.0906736
$609$	6.47382e13	+	2.65587e13i	0.772813	+	0.317044i
$610$	−2.85273e12	+	9.93602e12i	−0.0337763	+	0.117642i
$611$			1.71678e14i			2.01608i
$612$	−6.56694e13	−	6.47849e13i	−0.764903	−	0.754600i
$613$			5.40212e13i			0.624111i	0.950064	+	0.312056i	$0.101018\pi$
$613$			5.40212e13i			0.624111i	−0.950064	+	0.312056i	$0.898982\pi$
$614$			1.51013e12i			0.0173051i
$615$	−1.06174e14	−	8.39264e13i	−1.20682	−	0.953945i
$616$	1.19988e13			0.135280
$617$	3.34524e13			0.374112			0.187056	−	0.982349i	$-0.440105\pi$
$617$	3.34524e13			0.374112			0.187056	+	0.982349i	$0.440105\pi$
$618$	6.61387e11	−	1.61217e12i	0.00733691	−	0.0178841i
$619$	−1.09079e14			−1.20030			−0.600148	−	0.799889i	$-0.704892\pi$
$619$	−1.09079e14			−1.20030			−0.600148	+	0.799889i	$0.704892\pi$
$620$	−1.60592e13	+	5.59339e13i	−0.175294	+	0.610544i
$621$	1.40476e13	+	3.29618e13i	0.152106	+	0.356905i
$622$		−	1.13281e13i		−	0.121676i
$623$	8.73214e13			0.930423
$624$	5.35471e13	−	1.30524e14i	0.565995	−	1.37964i
$625$	4.16906e13	+	8.57720e13i	0.437158	+	0.899385i
$626$			4.67154e12i			0.0485947i
$627$	7.24806e12	−	1.76675e13i	0.0747970	−	0.182322i
$628$		−	1.74690e14i		−	1.78842i
$629$			1.03917e14i			1.05544i
$630$	−4.88764e12	−	8.68509e12i	−0.0492488	−	0.0875128i
$631$	−1.15153e14			−1.15114			−0.575570	−	0.817752i	$-0.695220\pi$
$631$	−1.15153e14			−1.15114			−0.575570	+	0.817752i	$0.695220\pi$
$632$	1.00152e13			0.0993289
$633$	2.90873e13	+	1.19330e13i	0.286210	+	0.117417i
$634$	6.66438e12			0.0650599
$635$	−1.05293e14	−	3.02307e13i	−1.01984	−	0.292806i
$636$	−1.45024e14	−	5.94956e13i	−1.39365	−	0.571741i
$637$			1.50530e13i			0.143524i
$638$	−6.62211e12			−0.0626459
$639$	8.71691e13	−	8.83592e13i	0.818198	−	0.829369i
$640$	1.21527e13	−	4.23275e13i	0.113180	−	0.394205i
$641$		−	4.03480e13i		−	0.372848i	−0.982469	−	0.186424i	$-0.940310\pi$
$641$		−	4.03480e13i		−	0.372848i	0.982469	−	0.186424i	$-0.0596898\pi$
$642$	−3.52864e12	−	1.44762e12i	−0.0323543	−	0.0132733i
$643$		−	7.11482e13i		−	0.647305i	−0.946176	−	0.323652i	$-0.895089\pi$
$643$		−	7.11482e13i		−	0.647305i	0.946176	−	0.323652i	$-0.104911\pi$
$644$			4.04724e13i			0.365367i
$645$	−9.91873e13	−	7.84040e13i	−0.888500	−	0.702327i
$646$	3.75010e12			0.0333334
$647$	−4.65327e13			−0.410428			−0.205214	−	0.978717i	$-0.565789\pi$
$647$	−4.65327e13			−0.410428			−0.205214	+	0.978717i	$0.565789\pi$
$648$	3.24909e11	+	2.39589e13i	0.00284372	+	0.209697i
$649$	−3.33636e12			−0.0289768
$650$	−1.00113e13	+	1.59974e13i	−0.0862827	+	0.137874i
$651$	2.71480e13	−	6.61748e13i	0.232185	−	0.565963i
$652$		−	6.48833e13i		−	0.550675i
$653$	3.78141e13			0.318484			0.159242	−	0.987240i	$-0.449095\pi$
$653$	3.78141e13			0.318484			0.159242	+	0.987240i	$0.449095\pi$
$654$	1.06672e12	+	4.37620e11i	0.00891585	+	0.00365770i
$655$	1.15560e14	+	3.31785e13i	0.958519	+	0.275201i
$656$			1.80670e14i			1.48720i
$657$	−1.02634e14	+	1.04035e14i	−0.838424	+	0.849871i
$658$		−	1.61894e13i		−	0.131250i
$659$			7.78536e13i			0.626400i	0.949687	+	0.313200i	$0.101401\pi$
$659$			7.78536e13i			0.626400i	−0.949687	+	0.313200i	$0.898599\pi$
$660$	−6.58067e13	−	5.20178e13i	−0.525473	−	0.415368i
$661$	−5.57101e13			−0.441496			−0.220748	−	0.975331i	$-0.570850\pi$
$661$	−5.57101e13			−0.441496			−0.220748	+	0.975331i	$0.570850\pi$
$662$	−3.35620e12			−0.0263972
$663$	8.14911e13	−	1.98639e14i	0.636125	−	1.55059i
$664$	−4.71037e13			−0.364934
$665$	−3.46342e13	−	9.94385e12i	−0.266316	−	0.0764621i
$666$	9.42530e12	−	9.55398e12i	0.0719323	−	0.0729144i
$667$		−	4.49243e13i		−	0.340293i
$668$	7.76793e13			0.584013
$669$	−5.59318e13	+	1.36337e14i	−0.417377	+	1.01738i
$670$	−7.00723e12	−	2.01185e12i	−0.0519006	−	0.0149012i
$671$		−	1.06946e14i		−	0.786233i
$672$	−1.54377e13	+	3.76302e13i	−0.112651	+	0.274594i
$673$			5.51238e13i			0.399267i	0.979871	+	0.199634i	$0.0639752\pi$
$673$			5.51238e13i			0.399267i	−0.979871	+	0.199634i	$0.936025\pi$
$674$		−	1.12503e13i		−	0.0808844i
$675$	−2.18141e13	+	1.38418e14i	−0.155675	+	0.987808i
$676$	1.92544e14			1.36394
$677$	−1.36412e14			−0.959202			−0.479601	−	0.877487i	$-0.659219\pi$
$677$	−1.36412e14			−0.959202			−0.479601	+	0.877487i	$0.659219\pi$
$678$	2.00511e13	+	8.22593e12i	0.139956	+	0.0574165i
$679$	4.86851e13			0.337324
$680$	9.14275e12	−	3.18440e13i	0.0628829	−	0.219020i
$681$	1.97684e14	+	8.10994e13i	1.34970	+	0.553710i
$682$			6.76906e12i			0.0458782i
$683$	2.62727e14			1.76767			0.883836	−	0.467797i	$-0.154952\pi$
$683$	2.62727e14			1.76767			0.883836	+	0.467797i	$0.154952\pi$
$684$	3.06648e13	+	3.02517e13i	0.204814	+	0.202055i
$685$	−6.24016e12	+	2.17344e13i	−0.0413755	+	0.144110i
$686$		−	1.66753e13i		−	0.109762i
$687$	6.70863e13	+	2.75220e13i	0.438379	+	0.179844i
$688$			1.68782e14i			1.09492i
$689$		−	3.64843e14i		−	2.34968i
$690$	−3.96770e12	+	5.01946e12i	−0.0253684	+	0.0320931i
$691$	−1.92807e14			−1.22386			−0.611931	−	0.790911i	$-0.709607\pi$
$691$	−1.92807e14			−1.22386			−0.611931	+	0.790911i	$0.709607\pi$
$692$	2.61073e13			0.164525
$693$	7.33971e13	+	7.24085e13i	0.459211	+	0.453026i
$694$	−1.47260e13			−0.0914717
$695$	−4.51876e13	+	1.57387e14i	−0.278673	+	0.970613i
$696$	1.14026e13	−	2.77945e13i	0.0698167	−	0.170182i
$697$			2.74955e14i			1.67147i
$698$	−8.11579e12			−0.0489839
$699$	−3.64356e13	−	1.49476e13i	−0.218343	−	0.0895747i
$700$	−8.39663e13	+	1.34173e14i	−0.499591	+	0.798314i
$701$		−	2.04011e14i		−	1.20521i	−0.798038	−	0.602607i	$-0.794129\pi$
$701$		−	2.04011e14i		−	1.20521i	0.798038	−	0.602607i	$-0.205871\pi$
$702$	−2.55088e13	+	1.08713e13i	−0.149625	+	0.0637672i
$703$		−	4.85247e13i		−	0.282609i
$704$			1.09390e14i			0.632578i
$705$	−1.41159e14	+	1.78577e14i	−0.810518	+	1.02537i
$706$	2.66474e13			0.151926
$707$	−1.61482e14			−0.914171
$708$	2.85639e12	−	6.96261e12i	0.0160565	−	0.0391386i
$709$	1.13809e14			0.635250			0.317625	−	0.948216i	$-0.397115\pi$
$709$	1.13809e14			0.635250			0.317625	+	0.948216i	$0.397115\pi$
$710$	2.13036e13	+	6.11647e12i	0.118076	+	0.0339008i
$711$	6.12635e13	+	6.04383e13i	0.337174	+	0.332632i
$712$		−	3.74904e13i		−	0.204890i
$713$	−4.59213e13			−0.249210
$714$	−7.68469e12	+	1.87318e13i	−0.0414129	+	0.100946i
$715$	5.38781e13	−	1.87656e14i	0.288325	−	1.00423i
$716$		−	1.93270e14i		−	1.02707i
$717$	6.23062e13	−	1.51875e14i	0.328803	−	0.801474i
$718$		−	7.75810e10i		−	0.000406568i
$719$			7.96589e13i			0.414562i	0.978281	+	0.207281i	$0.0664615\pi$
$719$			7.96589e13i			0.414562i	−0.978281	+	0.207281i	$0.933539\pi$
$720$	1.63020e14	−	9.17415e13i	0.842517	−	0.474136i
$721$	3.40166e13			0.174588
$722$	1.89364e13			0.0965187
$723$	−4.71596e13	−	1.93471e13i	−0.238715	−	0.0979320i
$724$	−1.41188e14			−0.709748
$725$	9.32026e13	−	1.48932e14i	0.465305	−	0.743527i
$726$	1.06485e13	+	4.36851e12i	0.0527964	+	0.0216596i
$727$		−	2.03214e13i		−	0.100065i	−0.998748	−	0.0500323i	$-0.984068\pi$
$727$		−	2.03214e13i		−	0.100065i	0.998748	−	0.0500323i	$-0.0159324\pi$
$728$	−6.29946e13			−0.308068
$729$	−1.42596e14	+	1.48518e14i	−0.692579	+	0.721342i
$730$	−2.50830e13	−	7.20160e12i	−0.120994	−	0.0347388i
$731$			2.56863e14i			1.23059i
$732$	2.23184e14	+	9.15606e13i	1.06196	+	0.435665i
$733$		−	3.95830e14i		−	1.87063i	−0.353810	−	0.935317i	$-0.615114\pi$
$733$		−	3.95830e14i		−	1.87063i	0.353810	−	0.935317i	$-0.384886\pi$
$734$			1.79834e13i			0.0844098i
$735$	−1.23771e13	+	1.56580e13i	−0.0577007	+	0.0729960i
$736$	2.61131e13			0.120912
$737$	7.54220e13			0.346865
$738$	2.49385e13	−	2.52790e13i	0.113917	−	0.115472i
$739$	2.22171e14			1.00801			0.504006	−	0.863700i	$-0.331859\pi$
$739$	2.22171e14			1.00801			0.504006	+	0.863700i	$0.331859\pi$
$740$	−2.04872e14	−	5.88210e13i	−0.923262	−	0.265078i
$741$	−3.80528e13	+	9.27558e13i	−0.170332	+	0.415193i
$742$			3.44050e13i			0.152969i
$743$	−2.64190e14			−1.16673			−0.583367	−	0.812209i	$-0.698265\pi$
$743$	−2.64190e14			−1.16673			−0.583367	+	0.812209i	$0.698265\pi$
$744$	−2.84113e13	−	1.16557e13i	−0.124631	−	0.0511297i
$745$	−3.07175e13	−	8.81931e12i	−0.133846	−	0.0384285i
$746$			1.60654e13i			0.0695342i
$747$	−2.88135e14	−	2.84254e14i	−1.23878	−	1.22209i
$748$			1.70418e14i			0.727792i
$749$		−	7.44542e13i		−	0.315849i
$750$	−2.35672e13	+	8.40872e12i	−0.0993121	+	0.0354343i
$751$	−2.00121e14			−0.837708			−0.418854	−	0.908054i	$-0.637568\pi$
$751$	−2.00121e14			−0.837708			−0.418854	+	0.908054i	$0.637568\pi$
$752$	3.03876e14			1.26359
$753$	−1.41848e14	+	3.45762e14i	−0.585933	+	1.42824i
$754$	3.47665e13			0.142661
$755$	4.04612e13	−	1.40925e14i	0.164932	−	0.574453i
$756$	−2.13946e14	+	9.11796e13i	−0.866355	+	0.369223i
$757$		−	3.98484e14i		−	1.60299i	−0.598001	−	0.801496i	$-0.704038\pi$
$757$		−	3.98484e14i		−	1.60299i	0.598001	−	0.801496i	$-0.295962\pi$
$758$	6.41763e12			0.0256465
$759$	2.51235e13	−	6.12400e13i	0.0997406	−	0.243123i
$760$	−4.26927e12	+	1.48698e13i	−0.0168378	+	0.0586457i
$761$		−	1.37475e14i		−	0.538642i	−0.963050	−	0.269321i	$-0.913201\pi$
$761$		−	1.37475e14i		−	0.538642i	0.963050	−	0.269321i	$-0.0867993\pi$
$762$	1.09093e13	−	2.65920e13i	0.0424641	−	0.103509i
$763$			2.25078e13i			0.0870382i
$764$		−	1.30942e13i		−	0.0503053i
$765$	2.48094e14	−	1.39618e14i	0.946910	−	0.532885i
$766$	1.31610e13			0.0499052
$767$	1.75161e13			0.0659875
$768$	−2.20161e14	−	9.03205e13i	−0.824013	−	0.338049i
$769$	−4.46994e13			−0.166215			−0.0831074	−	0.996541i	$-0.526484\pi$
$769$	−4.46994e13			−0.166215			−0.0831074	+	0.996541i	$0.526484\pi$
$770$	−5.08075e12	+	1.76962e13i	−0.0187704	+	0.0653771i
$771$	6.94782e13	+	2.85033e13i	0.255022	+	0.104622i
$772$		−	2.64376e13i		−	0.0964129i
$773$	−3.88269e14			−1.40681			−0.703405	−	0.710790i	$-0.748338\pi$
$773$	−3.88269e14			−1.40681			−0.703405	+	0.710790i	$0.748338\pi$
$774$	2.32975e13	−	2.36156e13i	0.0838697	−	0.0850148i
$775$	−1.52237e14	−	9.52708e13i	−0.544516	−	0.340762i
$776$		−	2.09024e13i		−	0.0742826i
$777$	2.42382e14	+	9.94366e13i	0.855846	+	0.351109i
$778$			3.96044e13i			0.138946i
$779$		−	1.28392e14i		−	0.447560i
$780$	3.45490e14	+	2.73097e14i	1.19664	+	0.945898i
$781$	−2.29300e14			−0.789130
$782$	1.29988e13			0.0444496
$783$	2.37480e14	−	1.01209e14i	0.806899	−	0.343884i
$784$	2.66444e13			0.0899550
$785$	5.18170e14	+	1.48772e14i	1.73830	+	0.499084i
$786$	−1.19730e13	+	2.91849e13i	−0.0399109	+	0.0972850i
$787$			4.86473e14i			1.61133i	0.592371	+	0.805665i	$0.298192\pi$
$787$			4.86473e14i			1.61133i	−0.592371	+	0.805665i	$0.701808\pi$
$788$	−1.51421e14			−0.498374
$789$	−2.86466e14	−	1.17522e14i	−0.936890	−	0.384357i
$790$	−4.24083e12	+	1.47707e13i	−0.0137821	+	0.0480028i
$791$			4.23078e14i			1.36627i
$792$	3.10877e13	−	3.15121e13i	0.0997614	−	0.101123i
$793$			5.61473e14i			1.79045i
$794$			2.70075e13i			0.0855819i
$795$	2.99986e14	−	3.79506e14i	0.944636	−	1.19504i
$796$	4.71837e14			1.47648
$797$	−3.00706e14			−0.935084			−0.467542	−	0.883971i	$-0.654860\pi$
$797$	−3.00706e14			−0.935084			−0.467542	+	0.883971i	$0.654860\pi$
$798$	3.58842e12	−	8.74696e12i	0.0110889	−	0.0270298i
$799$	4.62457e14			1.42016
$800$	8.65691e13	+	5.41756e13i	0.264188	+	0.165331i
$801$	2.26241e14	−	2.29330e14i	0.686133	−	0.695501i
$802$		−	3.57324e13i		−	0.107694i
$803$	2.69980e14			0.808638
$804$	−6.45718e13	+	1.57397e14i	−0.192204	+	0.468507i
$805$	−1.20051e14	−	3.44678e13i	−0.355128	−	0.101961i
$806$		−	3.55380e13i		−	0.104476i
$807$	−2.55416e14	+	6.22590e14i	−0.746244	+	1.81901i
$808$			6.93303e13i			0.201311i
$809$			2.06102e14i			0.594756i	0.954760	+	0.297378i	$0.0961121\pi$
$809$			2.06102e14i			0.594756i	−0.954760	+	0.297378i	$0.903888\pi$
$810$	−3.54728e13	−	9.66592e12i	−0.101735	−	0.0277216i
$811$	−6.94199e13			−0.197870			−0.0989349	−	0.995094i	$-0.531544\pi$
$811$	−6.94199e13			−0.197870			−0.0989349	+	0.995094i	$0.531544\pi$
$812$	2.91592e14			0.826031
$813$	−4.46523e14	−	1.83185e14i	−1.25716	−	0.515747i
$814$	−2.47934e13			−0.0693768
$815$	1.92459e14	+	5.52570e13i	0.535242	+	0.153674i
$816$	−3.51599e14	−	1.44243e14i	−0.971845	−	0.398697i
$817$		−	1.19944e14i		−	0.329509i
$818$	−7.25803e13			−0.198177
$819$	−3.85340e14	−	3.80150e14i	−1.04574	−	1.03166i
$820$	−5.42074e14	−	1.55635e14i	−1.46214	−	0.419796i
$821$			9.32564e13i			0.250013i	0.992156	+	0.125007i	$0.0398952\pi$
$821$			9.32564e13i			0.250013i	−0.992156	+	0.125007i	$0.960105\pi$
$822$	−5.48907e12	−	2.25187e12i	−0.0146265	−	0.00600047i
$823$			6.30725e13i			0.167048i	0.996506	+	0.0835239i	$0.0266175\pi$
$823$			6.30725e13i			0.167048i	−0.996506	+	0.0835239i	$0.973382\pi$
$824$		−	1.46046e13i		−	0.0384462i
$825$	2.10340e14	−	1.50898e14i	0.550368	−	0.394833i
$826$	−1.65179e12			−0.00429590
$827$	9.76525e13			0.252439			0.126219	−	0.992002i	$-0.459716\pi$
$827$	9.76525e13			0.252439			0.126219	+	0.992002i	$0.459716\pi$
$828$	1.06292e14	+	1.04860e14i	0.273116	+	0.269437i
$829$	3.08315e14			0.787448			0.393724	−	0.919229i	$-0.371187\pi$
$829$	3.08315e14			0.787448			0.393724	+	0.919229i	$0.371187\pi$
$830$	1.99455e13	−	6.94698e13i	0.0506355	−	0.176362i
$831$	2.05489e14	−	5.00890e14i	0.518541	−	1.26397i
$832$		−	5.74305e14i		−	1.44054i
$833$	4.05490e13			0.101101
$834$	−3.97486e13	−	1.63068e13i	−0.0985125	−	0.0404145i
$835$	−6.61545e13	+	2.30415e14i	−0.162977	+	0.567647i
$836$		−	7.95777e13i		−	0.194877i
$837$	−1.03455e14	−	2.42750e14i	−0.251840	−	0.590925i
$838$		−	6.84305e13i		−	0.165588i
$839$			6.70121e14i			1.61192i	0.591971	+	0.805960i	$0.298350\pi$
$839$			6.70121e14i			1.61192i	−0.591971	+	0.805960i	$0.701650\pi$
$840$	−6.55264e13	−	5.17962e13i	−0.156682	−	0.123852i
$841$	9.70398e13			0.230659
$842$	8.38446e12			0.0198114
$843$	−8.30129e13	+	2.02348e14i	−0.194988	+	0.475293i
$844$	1.31014e14			0.305919
$845$	−1.63977e14	+	5.71130e14i	−0.380628	+	1.32572i
$846$	−4.25177e13	−	4.19450e13i	−0.0981110	−	0.0967895i
$847$			2.24682e14i			0.515409i
$848$	−6.45786e14			−1.47268
$849$	−3.82286e13	+	9.31842e13i	−0.0866662	+	0.211254i
$850$	4.30930e13	+	2.69679e13i	0.0971208	+	0.0607789i
$851$		−	1.68198e14i		−	0.376855i
$852$	1.96313e14	−	4.78523e14i	0.437271	−	1.06587i
$853$		−	4.95600e14i		−	1.09745i	−0.836002	−	0.548727i	$-0.815113\pi$
$853$		−	4.95600e14i		−	1.09745i	0.836002	−	0.548727i	$-0.184887\pi$
$854$		−	5.29475e13i		−	0.116562i
$855$	−1.15849e14	+	6.51954e13i	−0.253549	+	0.142688i
$856$	−3.19660e13			−0.0695535
$857$	1.74867e14			0.378272			0.189136	−	0.981951i	$-0.439431\pi$
$857$	1.74867e14			0.378272			0.189136	+	0.981951i	$0.439431\pi$
$858$	4.73930e13	+	1.94429e13i	0.101924	+	0.0418142i
$859$	−2.27200e14			−0.485784			−0.242892	−	0.970053i	$-0.578096\pi$
$859$	−2.27200e14			−0.485784			−0.242892	+	0.970053i	$0.578096\pi$
$860$	−5.06405e14	−	1.45394e14i	−1.07648	−	0.309069i
$861$	6.41322e14	+	2.63101e14i	1.35538	+	0.556040i
$862$			4.46749e13i			0.0938700i
$863$	7.42681e14			1.55149			0.775744	−	0.631047i	$-0.217375\pi$
$863$	7.42681e14			1.55149			0.775744	+	0.631047i	$0.217375\pi$
$864$	5.88297e13	+	1.38040e14i	0.122188	+	0.286705i
$865$	−2.22339e13	+	7.74404e13i	−0.0459130	+	0.159914i
$866$			4.56315e13i			0.0936861i
$867$	−8.18551e13	−	3.35808e13i	−0.167090	−	0.0685482i
$868$		−	2.98063e14i		−	0.604936i
$869$		−	1.58984e14i		−	0.320815i
$870$	3.61638e13	+	2.85862e13i	0.0725568	+	0.0573535i
$871$	−3.95971e14			−0.789901
$872$	9.66344e12			0.0191668
$873$	1.26138e14	−	1.27860e14i	0.248757	−	0.252153i
$874$	−6.06985e12			−0.0119020
$875$	−3.26479e14	−	3.63330e14i	−0.636524	−	0.708372i
$876$	−2.31141e14	+	5.63418e14i	−0.448080	+	1.09222i
$877$		−	2.63334e14i		−	0.507585i	−0.967259	−	0.253793i	$-0.918322\pi$
$877$		−	2.63334e14i		−	0.507585i	0.967259	−	0.253793i	$-0.0816781\pi$
$878$	−2.96073e13			−0.0567448
$879$	−6.22650e14	−	2.55441e14i	−1.18659	−	0.486794i
$880$	−3.32159e14	−	9.53663e13i	−0.629409	−	0.180710i
$881$		−	2.49117e14i		−	0.469380i	−0.972070	−	0.234690i	$-0.924593\pi$
$881$		−	2.49117e14i		−	0.469380i	0.972070	−	0.234690i	$-0.0754074\pi$
$882$	−3.72802e12	−	3.67781e12i	−0.00698450	−	0.00689043i
$883$		−	1.84295e14i		−	0.343328i	−0.985156	−	0.171664i	$-0.945086\pi$
$883$		−	1.84295e14i		−	0.343328i	0.985156	−	0.171664i	$-0.0549144\pi$
$884$		−	8.94706e14i		−	1.65737i
$885$	1.82201e13	+	1.44023e13i	0.0335610	+	0.0265287i
$886$	−9.61345e13			−0.176080
$887$	−1.97737e14			−0.360139			−0.180070	−	0.983654i	$-0.557632\pi$
$887$	−1.97737e14			−0.360139			−0.180070	+	0.983654i	$0.557632\pi$
$888$	4.26919e13	−	1.04064e14i	0.0773180	−	0.188467i
$889$	5.61090e14			1.01047
$890$	5.52918e13	+	1.58748e13i	0.0990171	+	0.0284289i
$891$	3.80329e14	−	5.15768e12i	0.677284	−	0.00918471i
$892$			6.14085e14i			1.08744i
$893$	−2.15947e14			−0.380269
$894$	3.18261e12	−	7.75778e12i	0.00557308	−	0.0135847i
$895$	5.73285e14	+	1.64596e14i	0.998287	+	0.286619i
$896$			2.25556e14i			0.390585i
$897$	−1.31900e14	+	3.21514e14i	−0.227135	+	0.553653i
$898$			5.31512e13i			0.0910188i
$899$			3.30850e14i			0.563420i
$900$	1.34826e14	+	5.68146e14i	0.228329	+	0.962160i
$901$	−9.82796e14			−1.65516
$902$	−6.56012e13			−0.109870
$903$	5.99122e14	+	2.45788e14i	0.997876	+	0.409376i
$904$	1.81643e14			0.300869
$905$	1.20241e14	−	4.18796e14i	0.198066	−	0.689858i
$906$	3.55911e13	+	1.46011e13i	0.0583042	+	0.0239192i
$907$			6.26076e14i			1.01998i	0.860181	+	0.509989i	$0.170350\pi$
$907$			6.26076e14i			1.01998i	−0.860181	+	0.509989i	$0.829650\pi$
$908$	8.90405e14			1.44264
$909$	−4.18384e14	+	4.24096e14i	−0.674148	+	0.683352i
$910$	2.66743e13	−	9.29061e13i	0.0427451	−	0.148880i
$911$		−	1.45847e14i		−	0.232437i	−0.993224	−	0.116219i	$-0.962923\pi$
$911$		−	1.45847e14i		−	0.232437i	0.993224	−	0.116219i	$-0.0370774\pi$
$912$	1.64181e14	+	6.73550e13i	0.260225	+	0.106757i
$913$			7.47735e14i			1.17867i
$914$			3.01010e10i			4.71900e-5i
$915$	−4.61662e14	+	5.84039e14i	−0.719811	+	0.910618i
$916$	3.02169e14			0.468567
$917$	−6.15800e14			−0.949715
$918$	2.92847e13	+	6.87144e13i	0.0449187	+	0.105398i
$919$	1.05040e15			1.60242			0.801210	−	0.598383i	$-0.204190\pi$
$919$	1.05040e15			1.60242			0.801210	+	0.598383i	$0.204190\pi$
$920$	−1.47983e13	+	5.15423e13i	−0.0224529	+	0.0782032i
$921$	−4.12778e13	+	1.00617e14i	−0.0622900	+	0.151835i
$922$		−	7.83355e13i		−	0.117572i
$923$	1.20384e15			1.79705
$924$	3.97493e14	+	1.63070e14i	0.590160	+	0.242111i
$925$	3.48954e14	−	5.57605e14i	0.515299	−	0.823414i
$926$			2.88265e13i			0.0423386i
$927$	8.81336e13	−	8.93369e13i	0.128749	−	0.130506i
$928$		−	1.88137e14i		−	0.273360i
$929$		−	3.64767e14i		−	0.527154i	−0.964638	−	0.263577i	$-0.915098\pi$
$929$		−	3.64767e14i		−	0.527154i	0.964638	−	0.263577i	$-0.0849022\pi$
$930$	2.92205e13	−	3.69663e13i	0.0420023	−	0.0531363i
$931$	−1.89346e13			−0.0270713
$932$	−1.64112e14			−0.233379
$933$	3.09642e14	−	7.54770e14i	0.437978	−	1.06759i
$934$	1.28252e13			0.0180438
$935$	−5.05499e14	−	1.45134e14i	−0.707396	−	0.203101i
$936$	−1.63213e14	+	1.65441e14i	−0.227182	+	0.230284i
$937$		−	2.49525e14i		−	0.345474i	−0.984968	−	0.172737i	$-0.944739\pi$
$937$		−	2.49525e14i		−	0.345474i	0.984968	−	0.172737i	$-0.0552611\pi$
$938$	3.73404e13			0.0514239
$939$	−1.27691e14	+	3.11255e14i	−0.174918	+	0.426372i
$940$	−2.61768e14	+	9.11734e14i	−0.356679	+	1.24231i
$941$			3.92974e14i			0.532618i	0.963888	+	0.266309i	$0.0858041\pi$
$941$			3.92974e14i			0.532618i	−0.963888	+	0.266309i	$0.914196\pi$
$942$	−5.36871e13	+	1.30865e14i	−0.0723795	+	0.176429i
$943$		−	4.45038e14i		−	0.596814i
$944$		−	3.10043e13i		−	0.0413582i
$945$	−8.82553e13	−	7.12267e14i	−0.117107	−	0.945113i
$946$	−6.12846e13			−0.0808901
$947$	−7.14752e14			−0.938438			−0.469219	−	0.883082i	$-0.655465\pi$
$947$	−7.14752e14			−0.938438			−0.469219	+	0.883082i	$0.655465\pi$
$948$	3.31781e14	+	1.36112e14i	0.433322	+	0.177769i
$949$	−1.41741e15			−1.84147
$950$	−2.01226e13	−	1.25929e13i	−0.0260055	−	0.0162744i
$951$	4.44033e14	+	1.82164e14i	0.570838	+	0.234185i
$952$			1.69692e14i			0.217008i
$953$	−9.88465e14			−1.25747			−0.628734	−	0.777621i	$-0.716426\pi$
$953$	−9.88465e14			−1.25747			−0.628734	+	0.777621i	$0.716426\pi$
$954$	9.03569e13	+	8.91399e13i	0.114346	+	0.112805i
$955$	3.88406e13	+	1.11515e13i	0.0488955	+	0.0140384i
$956$		−	6.84071e14i		−	0.856666i
$957$	−4.41217e14	−	1.81008e14i	−0.549658	−	0.225496i
$958$		−	6.78019e13i		−	0.0840261i
$959$		−	1.15819e14i		−	0.142786i
$960$	4.72212e14	−	5.97386e14i	0.579136	−	0.732654i
$961$	−4.81436e14			−0.587384
$962$	1.30167e14			0.157989
$963$	−1.95537e14	−	1.92903e14i	−0.236101	−	0.232921i
$964$	−2.12415e14			−0.255153
$965$	7.84200e13	+	2.25152e13i	0.0937110	+	0.0269054i
$966$	1.24383e13	−	3.03191e13i	0.0147869	−	0.0360438i
$967$		−	3.84406e14i		−	0.454629i	−0.973821	−	0.227315i	$-0.927005\pi$
$967$		−	3.84406e14i		−	0.454629i	0.973821	−	0.227315i	$-0.0729946\pi$
$968$	9.64646e13			0.113499
$969$	2.49861e14	+	1.02505e14i	0.292469	+	0.119985i
$970$	3.08274e13	+	8.85086e12i	0.0358986	+	0.0103069i
$971$		−	5.38955e14i		−	0.624391i	−0.950018	−	0.312195i	$-0.898936\pi$
$971$		−	5.38955e14i		−	0.624391i	0.950018	−	0.312195i	$-0.101064\pi$
$972$	−3.14851e14	+	7.98119e14i	−0.362889	+	0.919890i
$973$		−	8.38693e14i		−	0.961698i
$974$		−	3.59799e13i		−	0.0410455i
$975$	−1.10430e15	+	7.92224e14i	−1.25333	+	0.899135i
$976$	9.93830e14			1.12218
$977$	9.01098e14			1.01228			0.506138	−	0.862452i	$-0.331073\pi$
$977$	9.01098e14			1.01228			0.506138	+	0.862452i	$0.331073\pi$
$978$	−1.99405e13	+	4.86060e13i	−0.0222865	+	0.0543245i
$979$	−5.95131e14			−0.661757
$980$	−2.29523e13	+	7.99424e13i	−0.0253920	+	0.0884397i
$981$	5.91115e13	+	5.83154e13i	0.0650620	+	0.0641857i
$982$		−	1.62550e14i		−	0.178004i
$983$	4.97465e14			0.541995			0.270997	−	0.962580i	$-0.412647\pi$
$983$	4.97465e14			0.541995			0.270997	+	0.962580i	$0.412647\pi$
$984$	1.12959e14	−	2.75344e14i	0.122446	−	0.298469i
$985$	1.28956e14	−	4.49150e14i	0.139078	−	0.484407i
$986$		−	9.36524e13i		−	0.100493i
$987$	4.42518e14	−	1.07866e15i	0.472439	−	1.15159i
$988$			4.17789e14i			0.443784i
$989$		−	4.15754e14i		−	0.439395i
$990$	3.33112e13	+	5.91924e13i	0.0350279	+	0.0622429i
$991$	1.04277e15			1.09099			0.545497	−	0.838113i	$-0.316341\pi$
$991$	1.04277e15			1.09099			0.545497	+	0.838113i	$0.316341\pi$
$992$	−1.92312e14			−0.200193
$993$	−2.23617e14	−	9.17381e13i	−0.231610	−	0.0950175i
$994$	−1.13523e14			−0.116991
$995$	−4.01834e14	+	1.39958e15i	−0.412032	+	1.43510i
$996$	−1.56044e15	−	6.40166e14i	−1.59202	−	0.653124i
$997$		−	9.01890e14i		−	0.915541i	−0.889070	−	0.457770i	$-0.848648\pi$
$997$		−	9.01890e14i		−	0.915541i	0.889070	−	0.457770i	$-0.151352\pi$
$998$	−1.83030e14			−0.184871
$999$	8.89135e14	−	3.78931e14i	0.893594	−	0.380832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.d.c.14.7	✓	16
3.2	odd	2	inner	15.11.d.c.14.9	yes	16
5.2	odd	4		75.11.c.h.26.7		16
5.3	odd	4		75.11.c.h.26.10		16
5.4	even	2	inner	15.11.d.c.14.10	yes	16
15.2	even	4		75.11.c.h.26.9		16
15.8	even	4		75.11.c.h.26.8		16
15.14	odd	2	inner	15.11.d.c.14.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.d.c.14.7	✓	16	1.1	even	1	trivial
15.11.d.c.14.8	yes	16	15.14	odd	2	inner
15.11.d.c.14.9	yes	16	3.2	odd	2	inner
15.11.d.c.14.10	yes	16	5.4	even	2	inner
75.11.c.h.26.7		16	5.2	odd	4
75.11.c.h.26.8		16	15.8	even	4
75.11.c.h.26.9		16	15.2	even	4
75.11.c.h.26.10		16	5.3	odd	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.37421 q^{2} +(-224.817 - 92.2305i) q^{3} -1012.61 q^{4} +(862.380 - 3003.65i) q^{5} +(758.580 + 311.205i) q^{6} +16006.0i q^{7} +6871.97 q^{8} +(42036.1 + 41469.9i) q^{9} +O(q^{10})\)	\(q-3.37421 q^{2} +(-224.817 - 92.2305i) q^{3} -1012.61 q^{4} +(862.380 - 3003.65i) q^{5} +(758.580 + 311.205i) q^{6} +16006.0i q^{7} +6871.97 q^{8} +(42036.1 + 41469.9i) q^{9} +(-2909.86 + 10135.0i) q^{10} -109087. i q^{11} +(227653. + 93393.9i) q^{12} +572716. i q^{13} -54007.6i q^{14} +(-470906. + 595733. i) q^{15} +1.01373e6 q^{16} +1.54275e6 q^{17} +(-141839. - 139928. i) q^{18} -720399. q^{19} +(-873259. + 3.04154e6i) q^{20} +(1.47624e6 - 3.59841e6i) q^{21} +368084. i q^{22} -2.49708e6 q^{23} +(-1.54493e6 - 633805. i) q^{24} +(-8.27823e6 - 5.18058e6i) q^{25} -1.93247e6i q^{26} +(-5.62563e6 - 1.32001e7i) q^{27} -1.62079e7i q^{28} +1.79908e7i q^{29} +(1.58894e6 - 2.01013e6i) q^{30} +1.83900e7 q^{31} -1.04574e7 q^{32} +(-1.00612e7 + 2.45246e7i) q^{33} -5.20558e6 q^{34} +(4.80764e7 + 1.38032e7i) q^{35} +(-4.25664e7 - 4.19930e7i) q^{36} +6.73581e7i q^{37} +2.43078e6 q^{38} +(5.28219e7 - 1.28756e8i) q^{39} +(5.92625e6 - 2.06410e7i) q^{40} +1.78223e8i q^{41} +(-4.98115e6 + 1.21418e7i) q^{42} +1.66496e8i q^{43} +1.10463e8i q^{44} +(1.60812e8 - 9.04990e7i) q^{45} +8.42568e6 q^{46} +2.99761e8 q^{47} +(-2.27903e8 - 9.34968e7i) q^{48} +2.62835e7 q^{49} +(2.79325e7 + 1.74804e7i) q^{50} +(-3.46837e8 - 1.42289e8i) q^{51} -5.79941e8i q^{52} -6.37040e8 q^{53} +(1.89821e7 + 4.45401e7i) q^{54} +(-3.27660e8 - 9.40747e7i) q^{55} +1.09993e8i q^{56} +(1.61958e8 + 6.64428e7i) q^{57} -6.07047e7i q^{58} -3.05843e7i q^{59} +(4.76846e8 - 6.03248e8i) q^{60} +9.80370e8 q^{61} -6.20518e7 q^{62} +(-6.63767e8 + 6.72829e8i) q^{63} -1.00277e9 q^{64} +(1.72024e9 + 4.93899e8i) q^{65} +(3.39485e7 - 8.27514e7i) q^{66} +6.91391e8i q^{67} -1.56222e9 q^{68} +(5.61385e8 + 2.30307e8i) q^{69} +(-1.62220e8 - 4.65751e7i) q^{70} -2.10199e9i q^{71} +(2.88871e8 + 2.84980e8i) q^{72} +2.47490e9i q^{73} -2.27281e8i q^{74} +(1.38328e9 + 1.92819e9i) q^{75} +7.29487e8 q^{76} +1.74605e9 q^{77} +(-1.78232e8 + 4.34451e8i) q^{78} +1.45740e9 q^{79} +(8.74220e8 - 3.04489e9i) q^{80} +(4.72803e7 + 3.48646e9i) q^{81} -6.01364e8i q^{82} -6.85447e9 q^{83} +(-1.49486e9 + 3.64381e9i) q^{84} +(1.33044e9 - 4.63390e9i) q^{85} -5.61794e8i q^{86} +(1.65930e9 - 4.04462e9i) q^{87} -7.49645e8i q^{88} -5.45554e9i q^{89} +(-5.42615e8 + 3.05363e8i) q^{90} -9.16689e9 q^{91} +2.52858e9 q^{92} +(-4.13438e9 - 1.69612e9i) q^{93} -1.01146e9 q^{94} +(-6.21258e8 + 2.16383e9i) q^{95} +(2.35101e9 + 9.64495e8i) q^{96} -3.04168e9i q^{97} -8.86862e7 q^{98} +(4.52384e9 - 4.58560e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9}+O(q^{10}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9	\( 16 q + 2184 q^{4} + 21516 q^{6} - 63000 q^{9} - 221680 q^{10} + 731640 q^{15} - 4218352 q^{16} + 1487600 q^{19} + 2444616 q^{21} + 28021368 q^{24} - 9324800 q^{25} - 35678700 q^{30} - 77667568 q^{31} + 251882368 q^{34} - 22344768 q^{36} - 70953984 q^{39} - 179966240 q^{40} - 484245000 q^{45} - 72018968 q^{46} + 89098816 q^{49} + 686556816 q^{51} + 441096084 q^{54} + 1424671200 q^{55} + 610091280 q^{60} - 1671368368 q^{61} - 4172730848 q^{64} + 2368350000 q^{66} - 2906594616 q^{69} + 2838634200 q^{70} - 1285884000 q^{75} + 4079367264 q^{76} - 3904999600 q^{79} - 11376681984 q^{81} + 13119851016 q^{84} + 8097594320 q^{85} - 15222287520 q^{90} + 19275224832 q^{91} - 9366481832 q^{94} - 5999937552 q^{96} + 42957756000 q^{99}+O(q^{100}) \) 16 * q + 2184 * q^4 + 21516 * q^6 - 63000 * q^9 - 221680 * q^10 + 731640 * q^15 - 4218352 * q^16 + 1487600 * q^19 + 2444616 * q^21 + 28021368 * q^24 - 9324800 * q^25 - 35678700 * q^30 - 77667568 * q^31 + 251882368 * q^34 - 22344768 * q^36 - 70953984 * q^39 - 179966240 * q^40 - 484245000 * q^45 - 72018968 * q^46 + 89098816 * q^49 + 686556816 * q^51 + 441096084 * q^54 + 1424671200 * q^55 + 610091280 * q^60 - 1671368368 * q^61 - 4172730848 * q^64 + 2368350000 * q^66 - 2906594616 * q^69 + 2838634200 * q^70 - 1285884000 * q^75 + 4079367264 * q^76 - 3904999600 * q^79 - 11376681984 * q^81 + 13119851016 * q^84 + 8097594320 * q^85 - 15222287520 * q^90 + 19275224832 * q^91 - 9366481832 * q^94 - 5999937552 * q^96 + 42957756000 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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