LMFDB - Embedded newform 30.12.c.b.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,12,Mod(19,30)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 12, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30.19"); S:= CuspForms(chi, 12); N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	30.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$23.0502954168$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 350078x^{4} + 30638651521x^{2} + 173683668788100 $ x^6 + 350078x^4 + 30638651521x^2 + 173683668788100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2}\cdot 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.1
Root			$78.0027i$ of defining polynomial
Character	$\chi$	$=$	30.19
Dual form			30.12.c.b.19.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-32.0000i q^{2} -243.000i q^{3} -1024.00 q^{4} +(-6709.81 - 1951.05i) q^{5} -7776.00 q^{6} +52907.3i q^{7} +32768.0i q^{8} -59049.0 q^{9} +(-62433.8 + 214714. i) q^{10} +531122. q^{11} +248832. i q^{12} -373795. i q^{13} +1.69303e6 q^{14} +(-474106. + 1.63048e6i) q^{15} +1.04858e6 q^{16} +4.81399e6i q^{17} +1.88957e6i q^{18} -5.80222e6 q^{19} +(6.87084e6 + 1.99788e6i) q^{20} +1.28565e7 q^{21} -1.69959e7i q^{22} -3.32148e7i q^{23} +7.96262e6 q^{24} +(4.12149e7 + 2.61824e7i) q^{25} -1.19614e7 q^{26} +1.43489e7i q^{27} -5.41770e7i q^{28} +1.30307e8 q^{29} +(5.21755e7 + 1.51714e7i) q^{30} +6.18143e7 q^{31} -3.35544e7i q^{32} -1.29063e8i q^{33} +1.54048e8 q^{34} +(1.03225e8 - 3.54997e8i) q^{35} +6.04662e7 q^{36} +1.37358e8i q^{37} +1.85671e8i q^{38} -9.08322e7 q^{39} +(6.39322e7 - 2.19867e8i) q^{40} +1.46886e9 q^{41} -4.11407e8i q^{42} +5.30160e8i q^{43} -5.43869e8 q^{44} +(3.96207e8 + 1.15208e8i) q^{45} -1.06287e9 q^{46} +1.34319e9i q^{47} -2.54804e8i q^{48} -8.21851e8 q^{49} +(8.37837e8 - 1.31888e9i) q^{50} +1.16980e9 q^{51} +3.82766e8i q^{52} +4.74535e9i q^{53} +4.59165e8 q^{54} +(-3.56372e9 - 1.03625e9i) q^{55} -1.73366e9 q^{56} +1.40994e9i q^{57} -4.16982e9i q^{58} -4.37861e9 q^{59} +(4.85485e8 - 1.66961e9i) q^{60} -7.78414e9 q^{61} -1.97806e9i q^{62} -3.12412e9i q^{63} -1.07374e9 q^{64} +(-7.29295e8 + 2.50809e9i) q^{65} -4.13000e9 q^{66} +4.98481e9i q^{67} -4.92953e9i q^{68} -8.07119e9 q^{69} +(-1.13599e10 - 3.30320e9i) q^{70} +9.09417e9 q^{71} -1.93492e9i q^{72} +1.88613e10i q^{73} +4.39545e9 q^{74} +(6.36232e9 - 1.00152e10i) q^{75} +5.94148e9 q^{76} +2.81002e10i q^{77} +2.90663e9i q^{78} +4.50312e10 q^{79} +(-7.03574e9 - 2.04583e9i) q^{80} +3.48678e9 q^{81} -4.70035e10i q^{82} +6.88856e10i q^{83} -1.31650e10 q^{84} +(9.39236e9 - 3.23009e10i) q^{85} +1.69651e10 q^{86} -3.16645e10i q^{87} +1.74038e10i q^{88} +3.49597e9 q^{89} +(3.68665e9 - 1.26786e10i) q^{90} +1.97765e10 q^{91} +3.40119e10i q^{92} -1.50209e10i q^{93} +4.29820e10 q^{94} +(3.89318e10 + 1.13205e10i) q^{95} -8.15373e9 q^{96} -1.62848e11i q^{97} +2.62992e10i q^{98} -3.13622e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6144 q^{4} - 9926 q^{5} - 46656 q^{6} - 354294 q^{9} + 72576 q^{10} + 1753400 q^{11} - 4312576 q^{14} + 551124 q^{15} + 6291456 q^{16} - 4069824 q^{19} + 10164224 q^{20} - 32748624 q^{21} + 47775744 q^{24}+ \cdots - 103536516600 q^{99}+O(q^{100}) $ 6 * q - 6144 * q^4 - 9926 * q^5 - 46656 * q^6 - 354294 * q^9 + 72576 * q^10 + 1753400 * q^11 - 4312576 * q^14 + 551124 * q^15 + 6291456 * q^16 - 4069824 * q^19 + 10164224 * q^20 - 32748624 * q^21 + 47775744 * q^24 + 169978326 * q^25 + 20172288 * q^26 + 71715564 * q^29 + 77184576 * q^30 - 122243352 * q^31 - 183956736 * q^34 + 825571904 * q^35 + 362797056 * q^36 + 153183312 * q^39 - 74317824 * q^40 + 2006768564 * q^41 - 1795481600 * q^44 + 586120374 * q^45 + 3191443200 * q^46 - 9590905446 * q^49 - 2993989376 * q^50 - 1396921464 * q^51 + 2754990144 * q^54 + 9162341400 * q^55 + 4416077824 * q^56 - 4069460200 * q^59 - 564350976 * q^60 - 12386466660 * q^61 - 6442450944 * q^64 - 30310342152 * q^65 - 13634438400 * q^66 + 24235021800 * q^69 - 15427048704 * q^70 + 13703505600 * q^71 + 59877797888 * q^74 - 22735606824 * q^75 + 4167499776 * q^76 - 13438327752 * q^79 - 10408165376 * q^80 + 20920706406 * q^81 + 33534590976 * q^84 + 50595843144 * q^85 - 62741662976 * q^86 - 127436589092 * q^89 - 4285540224 * q^90 + 271843383552 * q^91 + 140200608000 * q^94 - 87931077696 * q^95 - 48922361856 * q^96 - 103536516600 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

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

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 $

$2$		−	32.0000i		−	0.707107i
$2$		−	32.0000i		−	0.707107i
$3$		−	243.000i		−	0.577350i
$3$		−	243.000i		−	0.577350i
$4$	−1024.00			−0.500000
$5$	−6709.81	−	1951.05i	−0.960229	−	0.279212i
$5$	−6709.81	−	1951.05i	−0.960229	−	0.279212i
$6$	−7776.00			−0.408248
$7$			52907.3i			1.18981i	0.803798	+	0.594903i	$0.202809\pi$
$7$			52907.3i			1.18981i	−0.803798	+	0.594903i	$0.797191\pi$
$8$			32768.0i			0.353553i
$9$	−59049.0			−0.333333
$10$	−62433.8	+	214714.i	−0.197433	+	0.678985i
$11$	531122.			0.994339			0.497169	−	0.867654i	$-0.334373\pi$
$11$	531122.			0.994339			0.497169	+	0.867654i	$0.334373\pi$
$12$			248832.i			0.288675i
$13$		−	373795.i		−	0.279219i	−0.990207	−	0.139610i	$-0.955415\pi$
$13$		−	373795.i		−	0.279219i	0.990207	−	0.139610i	$-0.0445848\pi$
$14$	1.69303e6			0.841320
$15$	−474106.	+	1.63048e6i	−0.161203	+	0.554389i
$16$	1.04858e6			0.250000
$17$			4.81399e6i			0.822311i	0.911565	+	0.411156i	$0.134875\pi$
$17$			4.81399e6i			0.822311i	−0.911565	+	0.411156i	$0.865125\pi$
$18$			1.88957e6i			0.235702i
$19$	−5.80222e6			−0.537588			−0.268794	−	0.963198i	$-0.586625\pi$
$19$	−5.80222e6			−0.537588			−0.268794	+	0.963198i	$0.586625\pi$
$20$	6.87084e6	+	1.99788e6i	0.480115	+	0.139606i
$21$	1.28565e7			0.686935
$22$		−	1.69959e7i		−	0.703104i
$23$		−	3.32148e7i		−	1.07604i	−0.842932	−	0.538020i	$-0.819173\pi$
$23$		−	3.32148e7i		−	1.07604i	0.842932	−	0.538020i	$-0.180827\pi$
$24$	7.96262e6			0.204124
$25$	4.12149e7	+	2.61824e7i	0.844081	+	0.536216i
$26$	−1.19614e7			−0.197438
$27$			1.43489e7i			0.192450i
$28$		−	5.41770e7i		−	0.594903i
$29$	1.30307e8			1.17972			0.589859	−	0.807507i	$-0.299184\pi$
$29$	1.30307e8			1.17972			0.589859	+	0.807507i	$0.299184\pi$
$30$	5.21755e7	+	1.51714e7i	0.392012	+	0.113988i
$31$	6.18143e7			0.387793			0.193896	−	0.981022i	$-0.437887\pi$
$31$	6.18143e7			0.387793			0.193896	+	0.981022i	$0.437887\pi$
$32$		−	3.35544e7i		−	0.176777i
$33$		−	1.29063e8i		−	0.574082i
$34$	1.54048e8			0.581462
$35$	1.03225e8	−	3.54997e8i	0.332208	−	1.14249i
$36$	6.04662e7			0.166667
$37$			1.37358e8i			0.325645i	0.986655	+	0.162822i	$0.0520598\pi$
$37$			1.37358e8i			0.325645i	−0.986655	+	0.162822i	$0.947940\pi$
$38$			1.85671e8i			0.380132i
$39$	−9.08322e7			−0.161207
$40$	6.39322e7	−	2.19867e8i	0.0987164	−	0.339492i
$41$	1.46886e9			1.98002			0.990009	−	0.141003i	$-0.0450326\pi$
$41$	1.46886e9			1.98002			0.990009	+	0.141003i	$0.0450326\pi$
$42$		−	4.11407e8i		−	0.485736i
$43$			5.30160e8i			0.549960i	0.961450	+	0.274980i	$0.0886712\pi$
$43$			5.30160e8i			0.549960i	−0.961450	+	0.274980i	$0.911329\pi$
$44$	−5.43869e8			−0.497169
$45$	3.96207e8	+	1.15208e8i	0.320076	+	0.0930708i
$46$	−1.06287e9			−0.760875
$47$			1.34319e9i			0.854277i	0.904186	+	0.427138i	$0.140478\pi$
$47$			1.34319e9i			0.854277i	−0.904186	+	0.427138i	$0.859522\pi$
$48$		−	2.54804e8i		−	0.144338i
$49$	−8.21851e8			−0.415637
$50$	8.37837e8	−	1.31888e9i	0.379162	−	0.596855i
$51$	1.16980e9			0.474762
$52$			3.82766e8i			0.139610i
$53$			4.74535e9i			1.55866i	0.626615	+	0.779329i	$0.284440\pi$
$53$			4.74535e9i			1.55866i	−0.626615	+	0.779329i	$0.715560\pi$
$54$	4.59165e8			0.136083
$55$	−3.56372e9	−	1.03625e9i	−0.954793	−	0.277632i
$56$	−1.73366e9			−0.420660
$57$			1.40994e9i			0.310377i
$58$		−	4.16982e9i		−	0.834186i
$59$	−4.37861e9			−0.797352			−0.398676	−	0.917092i	$-0.630530\pi$
$59$	−4.37861e9			−0.797352			−0.398676	+	0.917092i	$0.630530\pi$
$60$	4.85485e8	−	1.66961e9i	0.0806016	−	0.277194i
$61$	−7.78414e9			−1.18004			−0.590020	−	0.807389i	$-0.700880\pi$
$61$	−7.78414e9			−1.18004			−0.590020	+	0.807389i	$0.700880\pi$
$62$		−	1.97806e9i		−	0.274211i
$63$		−	3.12412e9i		−	0.396602i
$64$	−1.07374e9			−0.125000
$65$	−7.29295e8	+	2.50809e9i	−0.0779614	+	0.268114i
$66$	−4.13000e9			−0.405937
$67$			4.98481e9i			0.451063i	0.974236	+	0.225531i	$0.0724118\pi$
$67$			4.98481e9i			0.451063i	−0.974236	+	0.225531i	$0.927588\pi$
$68$		−	4.92953e9i		−	0.411156i
$69$	−8.07119e9			−0.621252
$70$	−1.13599e10	−	3.30320e9i	−0.807860	−	0.234907i
$71$	9.09417e9			0.598194			0.299097	−	0.954223i	$-0.403315\pi$
$71$	9.09417e9			0.598194			0.299097	+	0.954223i	$0.403315\pi$
$72$		−	1.93492e9i		−	0.117851i
$73$			1.88613e10i			1.06487i	0.846471	+	0.532435i	$0.178723\pi$
$73$			1.88613e10i			1.06487i	−0.846471	+	0.532435i	$0.821277\pi$
$74$	4.39545e9			0.230266
$75$	6.36232e9	−	1.00152e10i	0.309584	−	0.487330i
$76$	5.94148e9			0.268794
$77$			2.81002e10i			1.18307i
$78$			2.90663e9i			0.113991i
$79$	4.50312e10			1.64651			0.823255	−	0.567672i	$-0.192156\pi$
$79$	4.50312e10			1.64651			0.823255	+	0.567672i	$0.192156\pi$
$80$	−7.03574e9	−	2.04583e9i	−0.240057	−	0.0698031i
$81$	3.48678e9			0.111111
$82$		−	4.70035e10i		−	1.40008i
$83$			6.88856e10i			1.91955i	0.280773	+	0.959774i	$0.409409\pi$
$83$			6.88856e10i			1.91955i	−0.280773	+	0.959774i	$0.590591\pi$
$84$	−1.31650e10			−0.343467
$85$	9.39236e9	−	3.23009e10i	0.229599	−	0.789607i
$86$	1.69651e10			0.388880
$87$		−	3.16645e10i		−	0.681110i
$88$			1.74038e10i			0.351552i
$89$	3.49597e9			0.0663624			0.0331812	−	0.999449i	$-0.489436\pi$
$89$	3.49597e9			0.0663624			0.0331812	+	0.999449i	$0.489436\pi$
$90$	3.68665e9	−	1.26786e10i	0.0658110	−	0.226328i
$91$	1.97765e10			0.332217
$92$			3.40119e10i			0.538020i
$93$		−	1.50209e10i		−	0.223892i
$94$	4.29820e10			0.604065
$95$	3.89318e10	+	1.13205e10i	0.516208	+	0.150101i
$96$	−8.15373e9			−0.102062
$97$		−	1.62848e11i		−	1.92548i	−0.270437	−	0.962738i	$-0.587168\pi$
$97$		−	1.62848e11i		−	1.92548i	0.270437	−	0.962738i	$-0.412832\pi$
$98$			2.62992e10i			0.293900i
$99$	−3.13622e10			−0.331446
$100$	−4.22041e10	−	2.68108e10i	−0.422041	−	0.268108i
$101$	1.33281e11			1.26183			0.630915	−	0.775852i	$-0.282680\pi$
$101$	1.33281e11			1.26183			0.630915	+	0.775852i	$0.282680\pi$
$102$		−	3.74336e10i		−	0.335707i
$103$		−	8.49052e10i		−	0.721655i	−0.932633	−	0.360827i	$-0.882494\pi$
$103$		−	8.49052e10i		−	0.721655i	0.932633	−	0.360827i	$-0.117506\pi$
$104$	1.22485e10			0.0987189
$105$	−8.62644e10	−	2.50837e10i	−0.659615	−	0.191801i
$106$	1.51851e11			1.10214
$107$			4.19151e10i			0.288908i	0.989512	+	0.144454i	$0.0461425\pi$
$107$			4.19151e10i			0.288908i	−0.989512	+	0.144454i	$0.953857\pi$
$108$		−	1.46933e10i		−	0.0962250i
$109$	−2.67212e11			−1.66345			−0.831727	−	0.555185i	$-0.812647\pi$
$109$	−2.67212e11			−1.66345			−0.831727	+	0.555185i	$0.812647\pi$
$110$	−3.31599e10	+	1.14039e11i	−0.196315	+	0.675141i
$111$	3.33780e10			0.188011
$112$			5.54773e10i			0.297451i
$113$			2.37749e11i			1.21391i	0.794735	+	0.606957i	$0.207610\pi$
$113$			2.37749e11i			1.21391i	−0.794735	+	0.606957i	$0.792390\pi$
$114$	4.51181e10			0.219469
$115$	−6.48038e10	+	2.22865e11i	−0.300443	+	1.03324i
$116$	−1.33434e11			−0.589859
$117$			2.20722e10i			0.0930731i
$118$			1.40116e11i			0.563813i
$119$	−2.54695e11			−0.978390
$120$	−5.34277e10	−	1.55355e10i	−0.196006	−	0.0569940i
$121$	−3.22132e9			−0.0112905
$122$			2.49093e11i			0.834414i
$123$		−	3.56933e11i		−	1.14316i
$124$	−6.32978e10			−0.193896
$125$	−2.25461e11	−	2.56091e11i	−0.660793	−	0.750568i
$126$	−9.99719e10			−0.280440
$127$		−	7.15504e10i		−	0.192173i	−0.995373	−	0.0960863i	$-0.969368\pi$
$127$		−	7.15504e10i		−	0.192173i	0.995373	−	0.0960863i	$-0.0306325\pi$
$128$			3.43597e10i			0.0883883i
$129$	1.28829e11			0.317519
$130$	8.02590e10	+	2.33374e10i	0.189586	+	0.0551271i
$131$	4.56783e11			1.03447			0.517235	−	0.855844i	$-0.326961\pi$
$131$	4.56783e11			1.03447			0.517235	+	0.855844i	$0.326961\pi$
$132$			1.32160e11i			0.287041i
$133$		−	3.06980e11i		−	0.639626i
$134$	1.59514e11			0.318949
$135$	2.79955e10	−	9.62784e10i	0.0537344	−	0.184796i
$136$	−1.57745e11			−0.290731
$137$			2.86655e10i			0.0507454i	0.999678	+	0.0253727i	$0.00807725\pi$
$137$			2.86655e10i			0.0507454i	−0.999678	+	0.0253727i	$0.991923\pi$
$138$			2.58278e11i			0.439291i
$139$	−1.20093e12			−1.96307			−0.981536	−	0.191280i	$-0.938736\pi$
$139$	−1.20093e12			−1.96307			−0.981536	+	0.191280i	$0.938736\pi$
$140$	−1.05702e11	+	3.63517e11i	−0.166104	+	0.571243i
$141$	3.26395e11			0.493217
$142$		−	2.91014e11i		−	0.422987i
$143$		−	1.98531e11i		−	0.277638i
$144$	−6.19174e10			−0.0833333
$145$	−8.74333e11	−	2.54236e11i	−1.13280	−	0.329391i
$146$	6.03563e11			0.752977
$147$			1.99710e11i			0.239968i
$148$		−	1.40655e11i		−	0.162822i
$149$	6.64637e11			0.741412			0.370706	−	0.928750i	$-0.379116\pi$
$149$	6.64637e11			0.741412			0.370706	+	0.928750i	$0.379116\pi$
$150$	−3.20487e11	−	2.03594e11i	−0.344595	−	0.218909i
$151$	1.70963e12			1.77226			0.886130	−	0.463436i	$-0.153384\pi$
$151$	1.70963e12			1.77226			0.886130	+	0.463436i	$0.153384\pi$
$152$		−	1.90127e11i		−	0.190066i
$153$		−	2.84261e11i		−	0.274104i
$154$	8.99206e11			0.836557
$155$	−4.14762e11	−	1.20603e11i	−0.372370	−	0.108276i
$156$	9.30122e10			0.0806036
$157$			9.96231e11i			0.833512i	0.909018	+	0.416756i	$0.136833\pi$
$157$			9.96231e11i			0.833512i	−0.909018	+	0.416756i	$0.863167\pi$
$158$		−	1.44100e12i		−	1.16426i
$159$	1.15312e12			0.899892
$160$	−6.54665e10	+	2.25144e11i	−0.0493582	+	0.169746i
$161$	1.75730e12			1.28028
$162$		−	1.11577e11i		−	0.0785674i
$163$			2.56482e11i			0.174592i	0.996182	+	0.0872960i	$0.0278226\pi$
$163$			2.56482e11i			0.174592i	−0.996182	+	0.0872960i	$0.972177\pi$
$164$	−1.50411e12			−0.990009
$165$	−2.51808e11	+	8.65985e11i	−0.160291	+	0.551250i
$166$	2.20434e12			1.35733
$167$			1.02735e12i			0.612040i	0.952025	+	0.306020i	$0.0989974\pi$
$167$			1.02735e12i			0.612040i	−0.952025	+	0.306020i	$0.901003\pi$
$168$			4.21281e11i			0.242868i
$169$	1.65244e12			0.922037
$170$	−1.03363e12	−	3.00556e11i	−0.558337	−	0.162351i
$171$	3.42616e11			0.179196
$172$		−	5.42884e11i		−	0.274980i
$173$		−	3.51424e12i		−	1.72416i	−0.506769	−	0.862082i	$-0.669160\pi$
$173$		−	3.51424e12i		−	1.72416i	0.506769	−	0.862082i	$-0.330840\pi$
$174$	−1.01327e12			−0.481617
$175$	−1.38524e12	+	2.18057e12i	−0.637992	+	1.00429i
$176$	5.56922e11			0.248585
$177$			1.06400e12i			0.460352i
$178$		−	1.11871e11i		−	0.0469253i
$179$	−4.59480e12			−1.86885			−0.934427	−	0.356156i	$-0.884087\pi$
$179$	−4.59480e12			−1.86885			−0.934427	+	0.356156i	$0.884087\pi$
$180$	−4.05716e11	−	1.17973e11i	−0.160038	−	0.0465354i
$181$	−9.54953e11			−0.365384			−0.182692	−	0.983170i	$-0.558481\pi$
$181$	−9.54953e11			−0.365384			−0.182692	+	0.983170i	$0.558481\pi$
$182$		−	6.32847e11i		−	0.234913i
$183$			1.89155e12i			0.681297i
$184$	1.08838e12			0.380437
$185$	2.67993e11	−	9.21645e11i	0.0909240	−	0.312694i
$186$	−4.80668e11			−0.158316
$187$			2.55682e12i			0.817656i
$188$		−	1.37542e12i		−	0.427138i
$189$	−7.59161e11			−0.228978
$190$	3.62255e11	−	1.24582e12i	0.106138	−	0.365014i
$191$	4.18247e12			1.19055			0.595277	−	0.803520i	$-0.297042\pi$
$191$	4.18247e12			1.19055			0.595277	+	0.803520i	$0.297042\pi$
$192$			2.60919e11i			0.0721688i
$193$			3.35128e12i			0.900836i	0.892818	+	0.450418i	$0.148725\pi$
$193$			3.35128e12i			0.900836i	−0.892818	+	0.450418i	$0.851275\pi$
$194$	−5.21114e12			−1.36152
$195$	6.09467e11	+	1.77219e11i	0.154796	+	0.0450110i
$196$	8.41575e11			0.207819
$197$		−	7.22875e12i		−	1.73580i	−0.496742	−	0.867899i	$-0.665470\pi$
$197$		−	7.22875e12i		−	1.73580i	0.496742	−	0.867899i	$-0.334530\pi$
$198$			1.00359e12i			0.234368i
$199$	−1.05138e12			−0.238818			−0.119409	−	0.992845i	$-0.538100\pi$
$199$	−1.05138e12			−0.238818			−0.119409	+	0.992845i	$0.538100\pi$
$200$	−8.57945e11	+	1.35053e12i	−0.189581	+	0.298428i
$201$	1.21131e12			0.260421
$202$		−	4.26499e12i		−	0.892248i
$203$			6.89417e12i			1.40363i
$204$	−1.19787e12			−0.237381
$205$	−9.85577e12	−	2.86583e12i	−1.90127	−	0.552845i
$206$	−2.71697e12			−0.510287
$207$			1.96130e12i			0.358680i
$208$		−	3.91953e11i		−	0.0698048i
$209$	−3.08169e12			−0.534545
$210$	−8.02677e11	+	2.76046e12i	−0.135623	+	0.466418i
$211$	3.80994e11			0.0627141			0.0313570	−	0.999508i	$-0.490017\pi$
$211$	3.80994e11			0.0627141			0.0313570	+	0.999508i	$0.490017\pi$
$212$		−	4.85924e12i		−	0.779329i
$213$		−	2.20988e12i		−	0.345368i
$214$	1.34128e12			0.204289
$215$	1.03437e12	−	3.55727e12i	0.153555	−	0.528087i
$216$	−4.70185e11			−0.0680414
$217$			3.27042e12i			0.461398i
$218$			8.55079e12i			1.17624i
$219$	4.58331e12			0.614803
$220$	3.64925e12	+	1.06112e12i	0.477397	+	0.138816i
$221$	1.79945e12			0.229605
$222$		−	1.06810e12i		−	0.132944i
$223$			3.50569e12i			0.425693i	0.977086	+	0.212846i	$0.0682734\pi$
$223$			3.50569e12i			0.425693i	−0.977086	+	0.212846i	$0.931727\pi$
$224$	1.77527e12			0.210330
$225$	−2.43370e12	−	1.54604e12i	−0.281360	−	0.178739i
$226$	7.60798e12			0.858367
$227$			4.84938e12i			0.534003i	0.963696	+	0.267002i	$0.0860329\pi$
$227$			4.84938e12i			0.534003i	−0.963696	+	0.267002i	$0.913967\pi$
$228$		−	1.44378e12i		−	0.155188i
$229$	−1.41260e12			−0.148225			−0.0741127	−	0.997250i	$-0.523612\pi$
$229$	−1.41260e12			−0.148225			−0.0741127	+	0.997250i	$0.523612\pi$
$230$	7.13167e12	+	2.07372e12i	0.730614	+	0.212446i
$231$	6.82835e12			0.683046
$232$			4.26989e12i			0.417093i
$233$		−	9.88438e12i		−	0.942957i	−0.881878	−	0.471478i	$-0.843721\pi$
$233$		−	9.88438e12i		−	0.942957i	0.881878	−	0.471478i	$-0.156279\pi$
$234$	7.06311e11			0.0658126
$235$	2.62063e12	−	9.01253e12i	0.238525	−	0.820302i
$236$	4.48370e12			0.398676
$237$		−	1.09426e13i		−	0.950613i
$238$			8.15024e12i			0.691826i
$239$	5.87747e12			0.487531			0.243765	−	0.969834i	$-0.421617\pi$
$239$	5.87747e12			0.487531			0.243765	+	0.969834i	$0.421617\pi$
$240$	−4.97137e11	+	1.70969e12i	−0.0403008	+	0.138597i
$241$	−9.32982e12			−0.739230			−0.369615	−	0.929185i	$-0.620510\pi$
$241$	−9.32982e12			−0.739230			−0.369615	+	0.929185i	$0.620510\pi$
$242$			1.03082e11i			0.00798360i
$243$		−	8.47289e11i		−	0.0641500i
$244$	7.97096e12			0.590020
$245$	5.51446e12	+	1.60348e12i	0.399107	+	0.116051i
$246$	−1.14219e13			−0.808339
$247$			2.16884e12i			0.150105i
$248$			2.02553e12i			0.137105i
$249$	1.67392e13			1.10825
$250$	−8.19492e12	+	7.21474e12i	−0.530732	+	0.467252i
$251$	1.76150e13			1.11603			0.558016	−	0.829830i	$-0.311563\pi$
$251$	1.76150e13			1.11603			0.558016	+	0.829830i	$0.311563\pi$
$252$			3.19910e12i			0.198301i
$253$		−	1.76411e13i		−	1.06995i
$254$	−2.28961e12			−0.135887
$255$	−7.84913e12	−	2.28234e12i	−0.455880	−	0.132559i
$256$	1.09951e12			0.0625000
$257$			1.61047e13i			0.896023i	0.894028	+	0.448012i	$0.147868\pi$
$257$			1.61047e13i			0.896023i	−0.894028	+	0.448012i	$0.852132\pi$
$258$		−	4.12253e12i		−	0.224520i
$259$	−7.26723e12			−0.387454
$260$	7.46798e11	−	2.56829e12i	0.0389807	−	0.134057i
$261$	−7.69448e12			−0.393239
$262$		−	1.46171e13i		−	0.731480i
$263$		−	8.60423e12i		−	0.421653i	−0.977524	−	0.210826i	$-0.932384\pi$
$263$		−	8.60423e12i		−	0.421653i	0.977524	−	0.210826i	$-0.0676155\pi$
$264$	4.22912e12			0.202969
$265$	9.25844e12	−	3.18404e13i	0.435196	−	1.49667i
$266$	−9.82335e12			−0.452284
$267$		−	8.49520e11i		−	0.0383144i
$268$		−	5.10444e12i		−	0.225531i
$269$	−1.03462e13			−0.447861			−0.223931	−	0.974605i	$-0.571889\pi$
$269$	−1.03462e13			−0.447861			−0.223931	+	0.974605i	$0.571889\pi$
$270$	−3.08091e12	−	8.95856e11i	−0.130671	−	0.0379960i
$271$	−3.19603e13			−1.32825			−0.664124	−	0.747622i	$-0.731196\pi$
$271$	−3.19603e13			−1.32825			−0.664124	+	0.747622i	$0.731196\pi$
$272$			5.04783e12i			0.205578i
$273$		−	4.80568e12i		−	0.191805i
$274$	9.17297e11			0.0358824
$275$	2.18901e13	+	1.39060e13i	0.839302	+	0.533180i
$276$	8.26490e12			0.310626
$277$		−	7.21606e12i		−	0.265865i	−0.991125	−	0.132933i	$-0.957561\pi$
$277$		−	7.21606e12i		−	0.265865i	0.991125	−	0.132933i	$-0.0424394\pi$
$278$			3.84297e13i			1.38810i
$279$	−3.65007e12			−0.129264
$280$	1.16326e13	+	3.38248e12i	0.403930	+	0.117453i
$281$	−4.86472e13			−1.65643			−0.828216	−	0.560409i	$-0.810644\pi$
$281$	−4.86472e13			−1.65643			−0.828216	+	0.560409i	$0.810644\pi$
$282$		−	1.04446e13i		−	0.348757i
$283$			4.50061e13i			1.47382i	0.675988	+	0.736912i	$0.263717\pi$
$283$			4.50061e13i			1.47382i	−0.675988	+	0.736912i	$0.736283\pi$
$284$	−9.31243e12			−0.299097
$285$	2.75087e12	−	9.46043e12i	0.0866610	−	0.298033i
$286$	−6.35298e12			−0.196320
$287$			7.77134e13i			2.35584i
$288$			1.98136e12i			0.0589256i
$289$	1.10974e13			0.323804
$290$	−8.13554e12	+	2.79787e13i	−0.232915	+	0.801010i
$291$	−3.95721e13			−1.11167
$292$		−	1.93140e13i		−	0.532435i
$293$		−	1.55228e13i		−	0.419949i	−0.977707	−	0.209975i	$-0.932662\pi$
$293$		−	1.55228e13i		−	0.419949i	0.977707	−	0.209975i	$-0.0673382\pi$
$294$	6.39071e12			0.169683
$295$	2.93796e13	+	8.54291e12i	0.765641	+	0.222631i
$296$	−4.50094e12			−0.115133
$297$			7.62102e12i			0.191361i
$298$		−	2.12684e13i		−	0.524258i
$299$	−1.24155e13			−0.300451
$300$	−6.51502e12	+	1.02556e13i	−0.154792	+	0.243665i
$301$	−2.80493e13			−0.654345
$302$		−	5.47080e13i		−	1.25318i
$303$		−	3.23873e13i		−	0.728518i
$304$	−6.08407e12			−0.134397
$305$	5.22301e13	+	1.51873e13i	1.13311	+	0.329482i
$306$	−9.09636e12			−0.193821
$307$			5.15314e13i			1.07848i	0.842153	+	0.539239i	$0.181288\pi$
$307$			5.15314e13i			1.07848i	−0.842153	+	0.539239i	$0.818712\pi$
$308$		−	2.87746e13i		−	0.591535i
$309$	−2.06320e13			−0.416648
$310$	−3.85930e12	+	1.32724e13i	−0.0765630	+	0.263305i
$311$	−1.21704e13			−0.237204			−0.118602	−	0.992942i	$-0.537841\pi$
$311$	−1.21704e13			−0.237204			−0.118602	+	0.992942i	$0.537841\pi$
$312$		−	2.97639e12i		−	0.0569954i
$313$		−	4.90592e13i		−	0.923053i	−0.887126	−	0.461527i	$-0.847302\pi$
$313$		−	4.90592e13i		−	0.923053i	0.887126	−	0.461527i	$-0.152698\pi$
$314$	3.18794e13			0.589382
$315$	−6.09533e12	+	2.09622e13i	−0.110736	+	0.380829i
$316$	−4.61119e13			−0.823255
$317$		−	2.65586e12i		−	0.0465992i	−0.999729	−	0.0232996i	$-0.992583\pi$
$317$		−	2.65586e12i		−	0.0465992i	0.999729	−	0.0232996i	$-0.00741717\pi$
$318$		−	3.68998e13i		−	0.636320i
$319$	6.92087e13			1.17304
$320$	7.20460e12	+	2.09493e12i	0.120029	+	0.0349015i
$321$	1.01854e13			0.166801
$322$		−	5.62337e13i		−	0.905293i
$323$		−	2.79319e13i		−	0.442065i
$324$	−3.57047e12			−0.0555556
$325$	9.78686e12	−	1.54059e13i	0.149722	−	0.235684i
$326$	8.20741e12			0.123455
$327$			6.49326e13i			0.960395i
$328$			4.81316e13i			0.700042i
$329$	−7.10644e13			−1.01642
$330$	2.77115e13	+	8.05786e12i	0.389793	+	0.113343i
$331$	8.86699e13			1.22665			0.613327	−	0.789829i	$-0.289831\pi$
$331$	8.86699e13			1.22665			0.613327	+	0.789829i	$0.289831\pi$
$332$		−	7.05389e13i		−	0.959774i
$333$		−	8.11085e12i		−	0.108548i
$334$	3.28753e13			0.432777
$335$	9.72563e12	−	3.34471e13i	0.125942	−	0.433124i
$336$	1.34810e13			0.171734
$337$		−	5.28648e13i		−	0.662525i	−0.943539	−	0.331262i	$-0.892525\pi$
$337$		−	5.28648e13i		−	0.662525i	0.943539	−	0.331262i	$-0.107475\pi$
$338$		−	5.28780e13i		−	0.651978i
$339$	5.77731e13			0.700853
$340$	−9.61778e12	+	3.30762e13i	−0.114800	+	0.394804i
$341$	3.28309e13			0.385597
$342$		−	1.09637e13i		−	0.126711i
$343$			6.11331e13i			0.695278i
$344$	−1.73723e13			−0.194440
$345$	5.41561e13	+	1.57473e13i	0.596544	+	0.173461i
$346$	−1.12456e14			−1.21917
$347$			2.14116e13i			0.228474i	0.993454	+	0.114237i	$0.0364424\pi$
$347$			2.14116e13i			0.228474i	−0.993454	+	0.114237i	$0.963558\pi$
$348$			3.24245e13i			0.340555i
$349$	1.29282e14			1.33659			0.668295	−	0.743896i	$-0.267024\pi$
$349$	1.29282e14			1.33659			0.668295	+	0.743896i	$0.267024\pi$
$350$	6.97781e13	+	4.43277e13i	0.710142	+	0.451129i
$351$	5.36355e12			0.0537358
$352$		−	1.78215e13i		−	0.175776i
$353$		−	3.24173e13i		−	0.314786i	−0.987536	−	0.157393i	$-0.949691\pi$
$353$		−	3.24173e13i		−	0.314786i	0.987536	−	0.157393i	$-0.0503090\pi$
$354$	3.40481e13			0.325518
$355$	−6.10201e13	−	1.77432e13i	−0.574404	−	0.167023i
$356$	−3.57987e12			−0.0331812
$357$			6.18909e13i			0.564874i
$358$			1.47034e14i			1.32148i
$359$	1.01176e14			0.895483			0.447741	−	0.894163i	$-0.352229\pi$
$359$	1.01176e14			0.895483			0.447741	+	0.894163i	$0.352229\pi$
$360$	−3.77513e12	+	1.29829e13i	−0.0329055	+	0.113164i
$361$	−8.28244e13			−0.710999
$362$			3.05585e13i			0.258366i
$363$			7.82780e11i			0.00651858i
$364$	−2.02511e13			−0.166108
$365$	3.67995e13	−	1.26556e14i	0.297325	−	1.02252i
$366$	6.05295e13			0.481749
$367$		−	6.19096e12i		−	0.0485395i	−0.999705	−	0.0242697i	$-0.992274\pi$
$367$		−	6.19096e12i		−	0.0485395i	0.999705	−	0.0242697i	$-0.00772605\pi$
$368$		−	3.48282e13i		−	0.269010i
$369$	−8.67347e13			−0.660006
$370$	−2.94926e13	−	8.57577e12i	−0.221108	−	0.0642930i
$371$	−2.51063e14			−1.85450
$372$			1.53814e13i			0.111946i
$373$			2.17159e14i			1.55733i	0.627442	+	0.778664i	$0.284102\pi$
$373$			2.17159e14i			1.55733i	−0.627442	+	0.778664i	$0.715898\pi$
$374$	8.18181e13			0.578170
$375$	−6.22302e13	+	5.47869e13i	−0.433341	+	0.381509i
$376$	−4.40136e13			−0.302033
$377$		−	4.87080e13i		−	0.329400i
$378$			2.42932e13i			0.161912i
$379$	−1.35854e14			−0.892397			−0.446199	−	0.894934i	$-0.647222\pi$
$379$	−1.35854e14			−0.892397			−0.446199	+	0.894934i	$0.647222\pi$
$380$	−3.98662e13	−	1.15922e13i	−0.258104	−	0.0750506i
$381$	−1.73867e13			−0.110951
$382$		−	1.33839e14i		−	0.841849i
$383$		−	1.53210e14i		−	0.949932i	−0.880004	−	0.474966i	$-0.842460\pi$
$383$		−	1.53210e14i		−	0.949932i	0.880004	−	0.474966i	$-0.157540\pi$
$384$	8.34942e12			0.0510310
$385$	5.48250e13	−	1.88547e14i	0.330328	−	1.13602i
$386$	1.07241e14			0.636988
$387$		−	3.13054e13i		−	0.183320i
$388$			1.66756e14i			0.962738i
$389$	−6.34461e13			−0.361145			−0.180573	−	0.983562i	$-0.557795\pi$
$389$	−6.34461e13			−0.361145			−0.180573	+	0.983562i	$0.557795\pi$
$390$	5.67100e12	−	1.95029e13i	0.0318276	−	0.109457i
$391$	1.59896e14			0.884839
$392$		−	2.69304e13i		−	0.146950i
$393$		−	1.10998e14i		−	0.597251i
$394$	−2.31320e14			−1.22739
$395$	−3.02151e14	−	8.78583e13i	−1.58103	−	0.459726i
$396$	3.21149e13			0.165723
$397$			2.82212e14i			1.43624i	0.695918	+	0.718121i	$0.254998\pi$
$397$			2.82212e14i			1.43624i	−0.695918	+	0.718121i	$0.745002\pi$
$398$			3.36442e13i			0.168870i
$399$	−7.45961e13			−0.369288
$400$	4.32169e13	+	2.74542e13i	0.211020	+	0.134054i
$401$	−4.11588e13			−0.198230			−0.0991149	−	0.995076i	$-0.531601\pi$
$401$	−4.11588e13			−0.198230			−0.0991149	+	0.995076i	$0.531601\pi$
$402$		−	3.87619e13i		−	0.184146i
$403$		−	2.31059e13i		−	0.108279i
$404$	−1.36480e14			−0.630915
$405$	−2.33957e13	−	6.80291e12i	−0.106692	−	0.0310236i
$406$	2.20613e14			0.992519
$407$			7.29538e13i			0.323801i
$408$			3.83320e13i			0.167854i
$409$	−7.28620e13			−0.314792			−0.157396	−	0.987536i	$-0.550310\pi$
$409$	−7.28620e13			−0.314792			−0.157396	+	0.987536i	$0.550310\pi$
$410$	−9.17065e13	+	3.15385e14i	−0.390921	+	1.34440i
$411$	6.96573e12			0.0292979
$412$			8.69429e13i			0.360827i
$413$		−	2.31660e14i		−	0.948694i
$414$	6.27616e13			0.253625
$415$	1.34400e14	−	4.62209e14i	0.535961	−	1.84321i
$416$	−1.25425e13			−0.0493594
$417$			2.91826e14i			1.13338i
$418$			9.86140e13i			0.377980i
$419$	4.44807e13			0.168265			0.0841326	−	0.996455i	$-0.473188\pi$
$419$	4.44807e13			0.168265			0.0841326	+	0.996455i	$0.473188\pi$
$420$	8.83347e13	+	2.56857e13i	0.329807	+	0.0959003i
$421$	4.08282e13			0.150456			0.0752279	−	0.997166i	$-0.476032\pi$
$421$	4.08282e13			0.150456			0.0752279	+	0.997166i	$0.476032\pi$
$422$		−	1.21918e13i		−	0.0443455i
$423$		−	7.93139e13i		−	0.284759i
$424$	−1.55496e14			−0.551069
$425$	−1.26042e14	+	1.98408e14i	−0.440936	+	0.694097i
$426$	−7.07163e13			−0.244212
$427$		−	4.11838e14i		−	1.40402i
$428$		−	4.29210e13i		−	0.144454i
$429$	−4.82430e13			−0.160295
$430$	−1.13833e14	−	3.30999e13i	−0.373414	−	0.108580i
$431$	5.01831e14			1.62530			0.812648	−	0.582754i	$-0.198025\pi$
$431$	5.01831e14			1.62530			0.812648	+	0.582754i	$0.198025\pi$
$432$			1.50459e13i			0.0481125i
$433$			3.09744e14i			0.977957i	0.872296	+	0.488979i	$0.162630\pi$
$433$			3.09744e14i			0.977957i	−0.872296	+	0.488979i	$0.837370\pi$
$434$	1.04654e14			0.326258
$435$	−6.17793e13	+	2.12463e14i	−0.190174	+	0.654022i
$436$	2.73625e14			0.831727
$437$			1.92720e14i			0.578466i
$438$		−	1.46666e14i		−	0.434732i
$439$	1.08027e13			0.0316213			0.0158106	−	0.999875i	$-0.494967\pi$
$439$	1.08027e13			0.0316213			0.0158106	+	0.999875i	$0.494967\pi$
$440$	3.39558e13	−	1.16776e14i	0.0981576	−	0.337570i
$441$	4.85295e13			0.138546
$442$		−	5.75823e13i		−	0.162355i
$443$			3.45097e14i			0.960993i	0.876997	+	0.480497i	$0.159544\pi$
$443$			3.45097e14i			0.960993i	−0.876997	+	0.480497i	$0.840456\pi$
$444$	−3.41790e13			−0.0940056
$445$	−2.34573e13	−	6.82082e12i	−0.0637232	−	0.0185292i
$446$	1.12182e14			0.301010
$447$		−	1.61507e14i		−	0.428055i
$448$		−	5.68087e13i		−	0.148726i
$449$	5.12768e14			1.32607			0.663035	−	0.748589i	$-0.269268\pi$
$449$	5.12768e14			1.32607			0.663035	+	0.748589i	$0.269268\pi$
$450$	−4.94734e13	+	7.78783e13i	−0.126387	+	0.198952i
$451$	7.80144e14			1.96881
$452$		−	2.43455e14i		−	0.606957i
$453$		−	4.15439e14i		−	1.02322i
$454$	1.55180e14			0.377597
$455$	−1.32696e14	−	3.85850e13i	−0.319004	−	0.0927589i
$456$	−4.62009e13			−0.109735
$457$		−	2.33364e14i		−	0.547640i	−0.961781	−	0.273820i	$-0.911713\pi$
$457$		−	2.33364e14i		−	0.547640i	0.961781	−	0.273820i	$-0.0882873\pi$
$458$			4.52030e13i			0.104811i
$459$	−6.90755e13			−0.158254
$460$	6.63591e13	−	2.28213e14i	0.150222	−	0.516622i
$461$	1.62814e14			0.364197			0.182098	−	0.983280i	$-0.441711\pi$
$461$	1.62814e14			0.364197			0.182098	+	0.983280i	$0.441711\pi$
$462$		−	2.18507e14i		−	0.482986i
$463$			2.48926e14i			0.543718i	0.962337	+	0.271859i	$0.0876385\pi$
$463$			2.48926e14i			0.543718i	−0.962337	+	0.271859i	$0.912361\pi$
$464$	1.36637e14			0.294929
$465$	−2.93065e13	+	1.00787e14i	−0.0625134	+	0.214988i
$466$	−3.16300e14			−0.666771
$467$			3.50158e14i			0.729494i	0.931107	+	0.364747i	$0.118845\pi$
$467$			3.50158e14i			0.729494i	−0.931107	+	0.364747i	$0.881155\pi$
$468$		−	2.26020e13i		−	0.0465365i
$469$	−2.63732e14			−0.536677
$470$	−2.88401e14	−	8.38603e13i	−0.580041	−	0.168662i
$471$	2.42084e14			0.481228
$472$		−	1.43478e14i		−	0.281907i
$473$			2.81580e14i			0.546846i
$474$	−3.50162e14			−0.672185
$475$	−2.39138e14	−	1.51916e14i	−0.453768	−	0.288263i
$476$	2.60808e14			0.489195
$477$		−	2.80208e14i		−	0.519553i
$478$		−	1.88079e14i		−	0.344736i
$479$	−4.41157e14			−0.799370			−0.399685	−	0.916653i	$-0.630881\pi$
$479$	−4.41157e14			−0.799370			−0.399685	+	0.916653i	$0.630881\pi$
$480$	5.47099e13	+	1.59084e13i	0.0980030	+	0.0284970i
$481$	5.13437e13			0.0909263
$482$			2.98554e14i			0.522715i
$483$		−	4.27024e14i		−	0.739169i
$484$	3.29863e12			0.00564526
$485$	−3.17725e14	+	1.09268e15i	−0.537616	+	1.84890i
$486$	−2.71132e13			−0.0453609
$487$		−	4.35803e12i		−	0.00720909i	−0.999994	−	0.00360455i	$-0.998853\pi$
$487$		−	4.35803e12i		−	0.00720909i	0.999994	−	0.00360455i	$-0.00114736\pi$
$488$		−	2.55071e14i		−	0.417207i
$489$	6.23250e13			0.100801
$490$	5.13112e13	−	1.76463e14i	0.0820605	−	0.282211i
$491$	−6.73844e13			−0.106564			−0.0532821	−	0.998580i	$-0.516968\pi$
$491$	−6.73844e13			−0.106564			−0.0532821	+	0.998580i	$0.516968\pi$
$492$			3.65499e14i			0.571582i
$493$			6.27295e14i			0.970094i
$494$	6.94030e13			0.106140
$495$	2.10434e14	+	6.11894e13i	0.318264	+	0.0925439i
$496$	6.48170e13			0.0969481
$497$			4.81148e14i			0.711735i
$498$		−	5.35655e14i		−	0.783652i
$499$	−8.06287e14			−1.16664			−0.583320	−	0.812243i	$-0.698247\pi$
$499$	−8.06287e14			−1.16664			−0.583320	+	0.812243i	$0.698247\pi$
$500$	2.30872e14	+	2.62238e14i	0.330397	+	0.375284i
$501$	2.49647e14			0.353361
$502$		−	5.63680e14i		−	0.789154i
$503$		−	1.30287e15i		−	1.80416i	−0.431565	−	0.902082i	$-0.642038\pi$
$503$		−	1.30287e15i		−	1.80416i	0.431565	−	0.902082i	$-0.357962\pi$
$504$	1.02371e14			0.140220
$505$	−8.94290e14	−	2.60039e14i	−1.21165	−	0.352318i
$506$	−5.64515e14			−0.756567
$507$		−	4.01542e14i		−	0.532338i
$508$			7.32676e13i			0.0960863i
$509$	1.09216e15			1.41690			0.708450	−	0.705761i	$-0.249395\pi$
$509$	1.09216e15			1.41690			0.708450	+	0.705761i	$0.249395\pi$
$510$	−7.30350e13	+	2.51172e14i	−0.0937335	+	0.322356i
$511$	−9.97902e14			−1.26699
$512$		−	3.51844e13i		−	0.0441942i
$513$		−	8.32556e13i		−	0.103459i
$514$	5.15349e14			0.633584
$515$	−1.65655e14	+	5.69697e14i	−0.201495	+	0.692954i
$516$	−1.31921e14			−0.158760
$517$			7.13397e14i			0.849441i
$518$			2.32551e14i			0.273971i
$519$	−8.53961e14			−0.995446
$520$	−8.21852e13	−	2.38975e13i	−0.0947928	−	0.0275635i
$521$	5.50995e14			0.628840			0.314420	−	0.949284i	$-0.398190\pi$
$521$	5.50995e14			0.628840			0.314420	+	0.949284i	$0.398190\pi$
$522$			2.46223e14i			0.278062i
$523$			4.43612e14i			0.495729i	0.968795	+	0.247865i	$0.0797288\pi$
$523$			4.43612e14i			0.495729i	−0.968795	+	0.247865i	$0.920271\pi$
$524$	−4.67746e14			−0.517235
$525$	5.29878e14	+	3.36613e14i	0.579828	+	0.368345i
$526$	−2.75335e14			−0.298154
$527$			2.97573e14i			0.318886i
$528$		−	1.35332e14i		−	0.143520i
$529$	−1.50411e14			−0.157861
$530$	−1.01889e15	−	2.96270e14i	−1.05831	−	0.307730i
$531$	2.58553e14			0.265784
$532$			3.14347e14i			0.319813i
$533$		−	5.49053e14i		−	0.552859i
$534$	−2.71846e13			−0.0270923
$535$	8.17786e13	−	2.81242e14i	0.0806666	−	0.277418i
$536$	−1.63342e14			−0.159475
$537$			1.11654e15i			1.07898i
$538$			3.31078e14i			0.316686i
$539$	−4.36503e14			−0.413284
$540$	−2.86674e13	+	9.85891e13i	−0.0268672	+	0.0923981i
$541$	−7.37013e14			−0.683739			−0.341869	−	0.939747i	$-0.611060\pi$
$541$	−7.37013e14			−0.683739			−0.341869	+	0.939747i	$0.611060\pi$
$542$			1.02273e15i			0.939214i
$543$			2.32054e14i			0.210955i
$544$	1.61531e14			0.145365
$545$	1.79294e15	+	5.21346e14i	1.59730	+	0.464457i
$546$	−1.53782e14			−0.135627
$547$		−	2.04180e15i		−	1.78272i	−0.453299	−	0.891358i	$-0.649753\pi$
$547$		−	2.04180e15i		−	1.78272i	0.453299	−	0.891358i	$-0.350247\pi$
$548$		−	2.93535e13i		−	0.0253727i
$549$	4.59646e14			0.393347
$550$	4.44993e14	−	7.00484e14i	0.377015	−	0.593476i
$551$	−7.56069e14			−0.634202
$552$		−	2.64477e14i		−	0.219646i
$553$			2.38248e15i			1.95903i
$554$	−2.30914e14			−0.187995
$555$	−2.23960e14	−	6.51223e13i	−0.180534	−	0.0524950i
$556$	1.22975e15			0.981536
$557$		−	2.16374e15i		−	1.71002i	−0.518611	−	0.855011i	$-0.673551\pi$
$557$		−	2.16374e15i		−	1.71002i	0.518611	−	0.855011i	$-0.326449\pi$
$558$			1.16802e14i			0.0914036i
$559$	1.98171e14			0.153559
$560$	1.08239e14	−	3.72242e14i	0.0830521	−	0.285622i
$561$	6.21306e14			0.472074
$562$			1.55671e15i			1.17127i
$563$		−	2.38895e15i		−	1.77996i	−0.455995	−	0.889982i	$-0.650717\pi$
$563$		−	2.38895e15i		−	1.77996i	0.455995	−	0.889982i	$-0.349283\pi$
$564$	−3.34228e14			−0.246609
$565$	4.63862e14	−	1.59525e15i	0.338940	−	1.16564i
$566$	1.44019e15			1.04215
$567$			1.84476e14i			0.132201i
$568$			2.97998e14i			0.211494i
$569$	−8.76463e13			−0.0616050			−0.0308025	−	0.999525i	$-0.509806\pi$
$569$	−8.76463e13			−0.0616050			−0.0308025	+	0.999525i	$0.509806\pi$
$570$	−3.02734e14	−	8.80279e13i	−0.210741	−	0.0612786i
$571$	1.74097e15			1.20031			0.600155	−	0.799884i	$-0.295106\pi$
$571$	1.74097e15			1.20031			0.600155	+	0.799884i	$0.295106\pi$
$572$			2.03296e14i			0.138819i
$573$		−	1.01634e15i		−	0.687367i
$574$	2.48683e15			1.66583
$575$	8.69643e14	−	1.36894e15i	0.576989	−	0.908264i
$576$	6.34034e13			0.0416667
$577$		−	1.81953e15i		−	1.18438i	−0.805797	−	0.592192i	$-0.798263\pi$
$577$		−	1.81953e15i		−	1.18438i	0.805797	−	0.592192i	$-0.201737\pi$
$578$		−	3.55117e14i		−	0.228964i
$579$	8.14362e14			0.520098
$580$	8.95317e14	+	2.60337e14i	0.566400	+	0.164696i
$581$	−3.64455e15			−2.28389
$582$			1.26631e15i			0.786072i
$583$			2.52036e15i			1.54983i
$584$	−6.18048e14			−0.376489
$585$	4.30641e13	−	1.48100e14i	0.0259871	−	0.0893715i
$586$	−4.96728e14			−0.296949
$587$		−	7.68456e14i		−	0.455103i	−0.973766	−	0.227551i	$-0.926928\pi$
$587$		−	7.68456e14i		−	0.455103i	0.973766	−	0.227551i	$-0.0730719\pi$
$588$		−	2.04503e14i		−	0.119984i
$589$	−3.58660e14			−0.208473
$590$	2.73373e14	−	9.40148e14i	0.157424	−	0.541390i
$591$	−1.75659e15			−1.00216
$592$			1.44030e14i			0.0814112i
$593$			1.21221e15i			0.678855i	0.940632	+	0.339427i	$0.110233\pi$
$593$			1.21221e15i			0.678855i	−0.940632	+	0.339427i	$0.889767\pi$
$594$	2.43873e14			0.135312
$595$	1.70895e15	+	4.96924e14i	0.939479	+	0.273179i
$596$	−6.80588e14			−0.370706
$597$			2.55485e14i			0.137882i
$598$			3.97297e14i			0.212451i
$599$	1.29651e15			0.686954			0.343477	−	0.939161i	$-0.388395\pi$
$599$	1.29651e15			0.686954			0.343477	+	0.939161i	$0.388395\pi$
$600$	3.28179e14	+	2.08481e14i	0.172297	+	0.109455i
$601$	−1.83742e15			−0.955871			−0.477935	−	0.878395i	$-0.658615\pi$
$601$	−1.83742e15			−0.955871			−0.477935	+	0.878395i	$0.658615\pi$
$602$			8.97579e14i			0.462692i
$603$		−	2.94348e14i		−	0.150354i
$604$	−1.75066e15			−0.886130
$605$	2.16144e13	+	6.28497e12i	0.0108415	+	0.00315245i
$606$	−1.03639e15			−0.515140
$607$		−	9.38310e14i		−	0.462177i	−0.972933	−	0.231089i	$-0.925771\pi$
$607$		−	9.38310e14i		−	0.462177i	0.972933	−	0.231089i	$-0.0742287\pi$
$608$			1.94690e14i			0.0950331i
$609$	1.67528e15			0.810388
$610$	4.85993e14	−	1.67136e15i	0.232979	−	0.801229i
$611$	5.02077e14			0.238531
$612$			2.91084e14i			0.137052i
$613$		−	8.45726e13i		−	0.0394636i	−0.999805	−	0.0197318i	$-0.993719\pi$
$613$		−	8.45726e13i		−	0.0394636i	0.999805	−	0.0197318i	$-0.00628124\pi$
$614$	1.64901e15			0.762599
$615$	−6.96396e14	+	2.39495e15i	−0.319185	+	1.09770i
$616$	−9.20787e14			−0.418278
$617$		−	1.30490e15i		−	0.587501i	−0.955882	−	0.293750i	$-0.905097\pi$
$617$		−	1.30490e15i		−	0.587501i	0.955882	−	0.293750i	$-0.0949034\pi$
$618$			6.60223e14i			0.294614i
$619$	1.79372e15			0.793335			0.396668	−	0.917962i	$-0.370167\pi$
$619$	1.79372e15			0.793335			0.396668	+	0.917962i	$0.370167\pi$
$620$	4.24716e14	+	1.23498e14i	0.186185	+	0.0541382i
$621$	4.76596e14			0.207084
$622$			3.89453e14i			0.167729i
$623$			1.84962e14i			0.0789584i
$624$	−9.52445e13			−0.0403018
$625$	1.01315e15	+	2.15821e15i	0.424946	+	0.905219i
$626$	−1.56990e15			−0.652697
$627$			7.48850e14i			0.308620i
$628$		−	1.02014e15i		−	0.416756i
$629$	−6.61240e14			−0.267781
$630$	6.70792e14	+	1.95051e14i	0.269287	+	0.0783023i
$631$	−1.89462e15			−0.753981			−0.376991	−	0.926217i	$-0.623041\pi$
$631$	−1.89462e15			−0.753981			−0.376991	+	0.926217i	$0.623041\pi$
$632$			1.47558e15i			0.582129i
$633$		−	9.25816e13i		−	0.0362080i
$634$	−8.49874e13			−0.0329506
$635$	−1.39599e14	+	4.80089e14i	−0.0536570	+	0.184530i
$636$	−1.18079e15			−0.449946
$637$			3.07204e14i			0.116054i
$638$		−	2.21468e15i		−	0.829463i
$639$	−5.37002e14			−0.199398
$640$	6.70377e13	−	2.30547e14i	0.0246791	−	0.0848731i
$641$	−2.48785e14			−0.0908040			−0.0454020	−	0.998969i	$-0.514457\pi$
$641$	−2.48785e14			−0.0908040			−0.0454020	+	0.998969i	$0.514457\pi$
$642$		−	3.25931e14i		−	0.117946i
$643$			4.34116e15i			1.55756i	0.627297	+	0.778780i	$0.284161\pi$
$643$			4.34116e15i			1.55756i	−0.627297	+	0.778780i	$0.715839\pi$
$644$	−1.79948e15			−0.640139
$645$	−8.64418e14	−	2.51352e14i	−0.304891	−	0.0886553i
$646$	−8.93819e14			−0.312587
$647$			1.76476e15i			0.611944i	0.952041	+	0.305972i	$0.0989814\pi$
$647$			1.76476e15i			0.611944i	−0.952041	+	0.305972i	$0.901019\pi$
$648$			1.14255e14i			0.0392837i
$649$	−2.32558e15			−0.792838
$650$	−4.92990e14	−	3.13179e14i	−0.166653	−	0.105869i
$651$	7.94713e14			0.266388
$652$		−	2.62637e14i		−	0.0872960i
$653$		−	8.57218e14i		−	0.282533i	−0.989972	−	0.141266i	$-0.954883\pi$
$653$		−	8.57218e14i		−	0.282533i	0.989972	−	0.141266i	$-0.0451174\pi$
$654$	2.07784e15			0.679102
$655$	−3.06493e15	−	8.91209e14i	−0.993328	−	0.288837i
$656$	1.54021e15			0.495005
$657$		−	1.11374e15i		−	0.354957i
$658$			2.27406e15i			0.718720i
$659$	−2.32789e15			−0.729613			−0.364807	−	0.931083i	$-0.618865\pi$
$659$	−2.32789e15			−0.729613			−0.364807	+	0.931083i	$0.618865\pi$
$660$	2.57852e14	−	8.86769e14i	0.0801453	−	0.275625i
$661$	−3.06684e15			−0.945328			−0.472664	−	0.881243i	$-0.656708\pi$
$661$	−3.06684e15			−0.945328			−0.472664	+	0.881243i	$0.656708\pi$
$662$		−	2.83744e15i		−	0.867375i
$663$		−	4.37266e14i		−	0.132563i
$664$	−2.25724e15			−0.678663
$665$	−5.98934e14	+	2.05978e15i	−0.178591	+	0.614187i
$666$	−2.59547e14			−0.0767552
$667$		−	4.32811e15i		−	1.26942i
$668$		−	1.05201e15i		−	0.306020i
$669$	8.51882e14			0.245774
$670$	−1.07031e15	−	3.11220e14i	−0.306265	−	0.0890546i
$671$	−4.13433e15			−1.17336
$672$		−	4.31391e14i		−	0.121434i
$673$		−	2.69617e15i		−	0.752775i	−0.926462	−	0.376387i	$-0.877166\pi$
$673$		−	2.69617e15i		−	0.752775i	0.926462	−	0.376387i	$-0.122834\pi$
$674$	−1.69167e15			−0.468476
$675$	−3.75689e14	+	5.91389e14i	−0.103195	+	0.162443i
$676$	−1.69210e15			−0.461018
$677$		−	5.36073e15i		−	1.44872i	−0.689419	−	0.724362i	$-0.742134\pi$
$677$		−	5.36073e15i		−	1.44872i	0.689419	−	0.724362i	$-0.257866\pi$
$678$		−	1.84874e15i		−	0.495578i
$679$	8.61584e15			2.29094
$680$	1.05844e15	+	3.07769e14i	0.279168	+	0.0811756i
$681$	1.17840e15			0.308307
$682$		−	1.05059e15i		−	0.272658i
$683$			7.26562e15i			1.87050i	0.353981	+	0.935252i	$0.384828\pi$
$683$			7.26562e15i			1.87050i	−0.353981	+	0.935252i	$0.615172\pi$
$684$	−3.50838e14			−0.0895980
$685$	5.59280e13	−	1.92340e14i	0.0141687	−	0.0487273i
$686$	1.95626e15			0.491636
$687$			3.43261e14i			0.0855780i
$688$			5.55913e14i			0.137490i
$689$	1.77379e15			0.435207
$690$	5.03915e14	−	1.73300e15i	0.122656	−	0.421820i
$691$	2.83285e15			0.684061			0.342030	−	0.939689i	$-0.388885\pi$
$691$	2.83285e15			0.684061			0.342030	+	0.939689i	$0.388885\pi$
$692$			3.59859e15i			0.862082i
$693$		−	1.65929e15i		−	0.394357i
$694$	6.85171e14			0.161556
$695$	8.05800e15	+	2.34308e15i	1.88500	+	0.548114i
$696$	1.03758e15			0.240809
$697$			7.07108e15i			1.62819i
$698$		−	4.13703e15i		−	0.945112i
$699$	−2.40190e15			−0.544416
$700$	1.41848e15	−	2.23290e15i	0.318996	−	0.502146i
$701$	6.35487e15			1.41794			0.708969	−	0.705239i	$-0.249161\pi$
$701$	6.35487e15			1.41794			0.708969	+	0.705239i	$0.249161\pi$
$702$		−	1.71634e14i		−	0.0379969i
$703$		−	7.96982e14i		−	0.175063i
$704$	−5.70288e14			−0.124292
$705$	−2.19005e15	−	6.36814e14i	−0.473601	−	0.137712i
$706$	−1.03735e15			−0.222587
$707$			7.05153e15i			1.50133i
$708$		−	1.08954e15i		−	0.230176i
$709$	−5.55781e15			−1.16506			−0.582531	−	0.812808i	$-0.697938\pi$
$709$	−5.55781e15			−1.16506			−0.582531	+	0.812808i	$0.697938\pi$
$710$	−5.67783e14	+	1.95264e15i	−0.118103	+	0.406165i
$711$	−2.65905e15			−0.548837
$712$			1.14556e14i			0.0234627i
$713$		−	2.05315e15i		−	0.417280i
$714$	1.98051e15			0.399426
$715$	−3.87344e14	+	1.33210e15i	−0.0775201	+	0.266597i
$716$	4.70508e15			0.934427
$717$		−	1.42823e15i		−	0.281476i
$718$		−	3.23763e15i		−	0.633202i
$719$	−1.05266e15			−0.204305			−0.102153	−	0.994769i	$-0.532573\pi$
$719$	−1.05266e15			−0.204305			−0.102153	+	0.994769i	$0.532573\pi$
$720$	4.15454e14	+	1.20804e14i	0.0800191	+	0.0232677i
$721$	4.49210e15			0.858629
$722$			2.65038e15i			0.502752i
$723$			2.26715e15i			0.426795i
$724$	9.77872e14			0.182692
$725$	5.37058e15	+	3.41174e15i	0.995777	+	0.632583i
$726$	2.50490e13			0.00460934
$727$		−	3.83121e15i		−	0.699675i	−0.936810	−	0.349838i	$-0.886237\pi$
$727$		−	3.83121e15i		−	0.699675i	0.936810	−	0.349838i	$-0.113763\pi$
$728$			6.48036e14i			0.117456i
$729$	−2.05891e14			−0.0370370
$730$	−4.04979e15	−	1.17758e15i	−0.723031	−	0.210240i
$731$	−2.55219e15			−0.452238
$732$		−	1.93694e15i		−	0.340648i
$733$		−	7.31689e15i		−	1.27719i	−0.769544	−	0.638594i	$-0.779517\pi$
$733$		−	7.31689e15i		−	1.27719i	0.769544	−	0.638594i	$-0.220483\pi$
$734$	−1.98111e14			−0.0343226
$735$	3.89645e14	−	1.34001e15i	0.0670021	−	0.230425i
$736$	−1.11450e15			−0.190219
$737$			2.64754e15i			0.448509i
$738$			2.77551e15i			0.466695i
$739$	1.04805e16			1.74920			0.874598	−	0.484848i	$-0.161125\pi$
$739$	1.04805e16			1.74920			0.874598	+	0.484848i	$0.161125\pi$
$740$	−2.74425e14	+	9.43765e14i	−0.0454620	+	0.156347i
$741$	5.27029e14			0.0866631
$742$			8.03403e15i			1.31133i
$743$			3.28089e15i			0.531561i	0.964034	+	0.265780i	$0.0856296\pi$
$743$			3.28089e15i			0.531561i	−0.964034	+	0.265780i	$0.914370\pi$
$744$	4.92204e14			0.0791578
$745$	−4.45958e15	−	1.29674e15i	−0.711926	−	0.207011i
$746$	6.94910e15			1.10120
$747$		−	4.06763e15i		−	0.639850i
$748$		−	2.61818e15i		−	0.408828i
$749$	−2.21761e15			−0.343744
$750$	1.75318e15	+	1.99137e15i	0.269768	+	0.306418i
$751$	9.30704e15			1.42165			0.710824	−	0.703370i	$-0.248322\pi$
$751$	9.30704e15			1.42165			0.710824	+	0.703370i	$0.248322\pi$
$752$			1.40843e15i			0.213569i
$753$		−	4.28044e15i		−	0.644342i
$754$	−1.55866e15			−0.232921
$755$	−1.14713e16	−	3.33557e15i	−1.70178	−	0.494837i
$756$	7.77381e14			0.114489
$757$		−	6.20592e15i		−	0.907359i	−0.891165	−	0.453680i	$-0.850111\pi$
$757$		−	6.20592e15i		−	0.907359i	0.891165	−	0.453680i	$-0.149889\pi$
$758$			4.34734e15i			0.631020i
$759$	−4.28678e15			−0.617735
$760$	−3.70949e14	+	1.27572e15i	−0.0530688	+	0.182507i
$761$	−6.29521e14			−0.0894118			−0.0447059	−	0.999000i	$-0.514235\pi$
$761$	−6.29521e14			−0.0894118			−0.0447059	+	0.999000i	$0.514235\pi$
$762$			5.56376e14i			0.0784542i
$763$		−	1.41375e16i		−	1.97919i
$764$	−4.28285e15			−0.595277
$765$	−5.54609e14	+	1.90734e15i	−0.0765331	+	0.263202i
$766$	−4.90271e15			−0.671703
$767$			1.63670e15i			0.222636i
$768$		−	2.67181e14i		−	0.0360844i
$769$	−4.37850e15			−0.587126			−0.293563	−	0.955940i	$-0.594841\pi$
$769$	−4.37850e15			−0.587126			−0.293563	+	0.955940i	$0.594841\pi$
$770$	−6.03350e15	−	1.75440e15i	−0.803286	−	0.233577i
$771$	3.91343e15			0.517319
$772$		−	3.43171e15i		−	0.450418i
$773$		−	6.24169e15i		−	0.813420i	−0.913557	−	0.406710i	$-0.866676\pi$
$773$		−	6.24169e15i		−	0.813420i	0.913557	−	0.406710i	$-0.133324\pi$
$774$	−1.00177e15			−0.129627
$775$	2.54767e15	+	1.61845e15i	0.327328	+	0.207940i
$776$	5.33620e15			0.680758
$777$			1.76594e15i			0.223697i
$778$			2.03027e15i			0.255368i
$779$	−8.52266e15			−1.06443
$780$	−6.24094e14	−	1.81472e14i	−0.0773980	−	0.0225055i
$781$	4.83011e15			0.594808
$782$		−	5.11666e15i		−	0.625676i
$783$			1.86976e15i			0.227037i
$784$	−8.61773e14			−0.103909
$785$	1.94370e15	−	6.68452e15i	0.232727	−	0.800363i
$786$	−3.55194e15			−0.422320
$787$			1.67198e16i			1.97411i	0.160397	+	0.987053i	$0.448722\pi$
$787$			1.67198e16i			1.97411i	−0.160397	+	0.987053i	$0.551278\pi$
$788$			7.40224e15i			0.867899i
$789$	−2.09083e15			−0.243441
$790$	−2.81147e15	+	9.66882e15i	−0.325075	+	1.11796i
$791$	−1.25787e16			−1.44432
$792$		−	1.02768e15i		−	0.117184i
$793$			2.90968e15i			0.329490i
$794$	9.03078e15			1.01558
$795$	−7.73721e15	−	2.24980e15i	−0.864102	−	0.251261i
$796$	1.07661e15			0.119409
$797$		−	4.36301e15i		−	0.480580i	−0.970701	−	0.240290i	$-0.922758\pi$
$797$		−	4.36301e15i		−	0.480580i	0.970701	−	0.240290i	$-0.0772425\pi$
$798$			2.38707e15i			0.261126i
$799$	−6.46610e15			−0.702481
$800$	8.78536e14	−	1.38294e15i	0.0947904	−	0.149214i
$801$	−2.06433e14			−0.0221208
$802$			1.31708e15i			0.140170i
$803$			1.00177e16i			1.05884i
$804$	−1.24038e15			−0.130211
$805$	−1.17912e16	−	3.42859e15i	−1.22936	−	0.357469i
$806$	−7.39388e14			−0.0765649
$807$			2.51413e15i			0.258573i
$808$			4.36735e15i			0.446124i
$809$	−3.55238e15			−0.360415			−0.180208	−	0.983629i	$-0.557677\pi$
$809$	−3.55238e15			−0.360415			−0.180208	+	0.983629i	$0.557677\pi$
$810$	−2.17693e14	+	7.48661e14i	−0.0219370	+	0.0754427i
$811$	1.38794e16			1.38917			0.694585	−	0.719411i	$-0.255588\pi$
$811$	1.38794e16			1.38917			0.694585	+	0.719411i	$0.255588\pi$
$812$		−	7.05963e15i		−	0.701817i
$813$			7.76635e15i			0.766865i
$814$	2.33452e15			0.228962
$815$	5.00410e14	−	1.72094e15i	0.0487482	−	0.167648i
$816$	1.22662e15			0.118690
$817$		−	3.07611e15i		−	0.295652i
$818$			2.33158e15i			0.222591i
$819$	−1.16778e15			−0.110739
$820$	1.00923e16	+	2.93461e15i	0.950636	+	0.276423i
$821$	9.65670e15			0.903528			0.451764	−	0.892138i	$-0.350795\pi$
$821$	9.65670e15			0.903528			0.451764	+	0.892138i	$0.350795\pi$
$822$		−	2.22903e14i		−	0.0207167i
$823$			1.62599e16i			1.50114i	0.660793	+	0.750568i	$0.270220\pi$
$823$			1.62599e16i			1.50114i	−0.660793	+	0.750568i	$0.729780\pi$
$824$	2.78217e15			0.255144
$825$	3.37917e15	−	5.31930e15i	0.307832	−	0.484571i
$826$	−7.41313e15			−0.670828
$827$		−	9.52899e15i		−	0.856578i	−0.903642	−	0.428289i	$-0.859117\pi$
$827$		−	9.52899e15i		−	0.856578i	0.903642	−	0.428289i	$-0.140883\pi$
$828$		−	2.00837e15i		−	0.179340i
$829$	−1.66053e16			−1.47298			−0.736492	−	0.676446i	$-0.763519\pi$
$829$	−1.66053e16			−1.47298			−0.736492	+	0.676446i	$0.763519\pi$
$830$	−1.47907e16	−	4.30079e15i	−1.30334	−	0.378982i
$831$	−1.75350e15			−0.153497
$832$			4.01360e14i			0.0349024i
$833$		−	3.95638e15i		−	0.341783i
$834$	9.33843e15			0.801420
$835$	2.00442e15	−	6.89335e15i	0.170889	−	0.587699i
$836$	3.15565e15			0.267272
$837$			8.86967e14i			0.0746307i
$838$		−	1.42338e15i		−	0.118981i
$839$	1.01371e16			0.841827			0.420913	−	0.907101i	$-0.361710\pi$
$839$	1.01371e16			0.841827			0.420913	+	0.907101i	$0.361710\pi$
$840$	8.21942e14	−	2.82671e15i	0.0678117	−	0.233209i
$841$	4.77933e15			0.391732
$842$		−	1.30650e15i		−	0.106388i
$843$			1.18213e16i			0.956341i
$844$	−3.90138e14			−0.0313570
$845$	−1.10875e16	−	3.22400e15i	−0.885367	−	0.257444i
$846$	−2.53805e15			−0.201355
$847$		−	1.70431e14i		−	0.0134335i
$848$			4.97586e15i			0.389665i
$849$	1.09365e16			0.850913
$850$	6.34906e15	+	4.03334e15i	0.490801	+	0.311789i
$851$	4.56231e15			0.350407
$852$			2.26292e15i			0.172684i
$853$		−	2.03075e16i		−	1.53970i	−0.638224	−	0.769851i	$-0.720331\pi$
$853$		−	2.03075e16i		−	1.53970i	0.638224	−	0.769851i	$-0.279669\pi$
$854$	−1.31788e16			−0.992791
$855$	−2.29888e15	−	6.68462e14i	−0.172069	−	0.0500337i
$856$	−1.37347e15			−0.102144
$857$			4.99342e15i			0.368981i	0.982834	+	0.184490i	$0.0590635\pi$
$857$			4.99342e15i			0.368981i	−0.982834	+	0.184490i	$0.940937\pi$
$858$			1.54378e15i			0.113345i
$859$	−5.27939e15			−0.385142			−0.192571	−	0.981283i	$-0.561683\pi$
$859$	−5.27939e15			−0.385142			−0.192571	+	0.981283i	$0.561683\pi$
$860$	−1.05920e15	+	3.64265e15i	−0.0767777	+	0.264044i
$861$	1.88843e16			1.36014
$862$		−	1.60586e16i		−	1.14926i
$863$		−	6.94499e15i		−	0.493869i	−0.969032	−	0.246935i	$-0.920577\pi$
$863$		−	6.94499e15i		−	0.493869i	0.969032	−	0.246935i	$-0.0794233\pi$
$864$	4.81469e14			0.0340207
$865$	−6.85648e15	+	2.35799e16i	−0.481408	+	1.65559i
$866$	9.91182e15			0.691520
$867$		−	2.69667e15i		−	0.186949i
$868$		−	3.34891e15i		−	0.230699i
$869$	2.39170e16			1.63719
$870$	6.79881e15	+	1.97694e15i	0.462463	+	0.134474i
$871$	1.86330e15			0.125945
$872$		−	8.75601e15i		−	0.588120i
$873$			9.61601e15i			0.641825i
$874$	6.16703e15			0.409037
$875$	1.35491e16	−	1.19285e16i	0.893030	−	0.786216i
$876$	−4.69330e15			−0.307402
$877$			1.66689e16i			1.08495i	0.840073	+	0.542473i	$0.182512\pi$
$877$			1.66689e16i			1.08495i	−0.840073	+	0.542473i	$0.817488\pi$
$878$		−	3.45688e14i		−	0.0223596i
$879$	−3.77203e15			−0.242458
$880$	−3.73684e15	−	1.08658e15i	−0.238698	−	0.0694079i
$881$	−7.30716e15			−0.463854			−0.231927	−	0.972733i	$-0.574503\pi$
$881$	−7.30716e15			−0.463854			−0.231927	+	0.972733i	$0.574503\pi$
$882$		−	1.55294e15i		−	0.0979667i
$883$		−	1.41660e16i		−	0.888100i	−0.896002	−	0.444050i	$-0.853541\pi$
$883$		−	1.41660e16i		−	0.888100i	0.896002	−	0.444050i	$-0.146459\pi$
$884$	−1.84263e15			−0.114803
$885$	2.07593e15	−	7.13925e15i	0.128536	−	0.442043i
$886$	1.10431e16			0.679525
$887$		−	1.48432e16i		−	0.907713i	−0.891075	−	0.453857i	$-0.850048\pi$
$887$		−	1.48432e16i		−	0.907713i	0.891075	−	0.453857i	$-0.149952\pi$
$888$			1.09373e15i			0.0664720i
$889$	3.78554e15			0.228648
$890$	−2.18266e14	+	7.50632e14i	−0.0131021	+	0.0450591i
$891$	1.85191e15			0.110482
$892$		−	3.58982e15i		−	0.212846i
$893$		−	7.79348e15i		−	0.459249i
$894$	−5.16822e15			−0.302680
$895$	3.08302e16	+	8.96471e15i	1.79453	+	0.521807i
$896$	−1.81788e15			−0.105165
$897$			3.01697e15i			0.173465i
$898$		−	1.64086e16i		−	0.937673i
$899$	8.05482e15			0.457486
$900$	2.49211e15	+	1.58315e15i	0.140680	+	0.0893693i
$901$	−2.28441e16			−1.28170
$902$		−	2.49646e16i		−	1.39216i
$903$			6.81599e15i			0.377786i
$904$	−7.79057e15			−0.429183
$905$	6.40755e15	+	1.86317e15i	0.350853	+	0.102020i
$906$	−1.32940e16			−0.723522
$907$			1.13330e16i			0.613061i	0.951861	+	0.306530i	$0.0991681\pi$
$907$			1.13330e16i			0.613061i	−0.951861	+	0.306530i	$0.900832\pi$
$908$		−	4.96577e15i		−	0.267002i
$909$	−7.87011e15			−0.420610
$910$	−1.23472e15	+	4.24628e15i	−0.0655905	+	0.225570i
$911$	−1.91130e16			−1.00920			−0.504602	−	0.863352i	$-0.668361\pi$
$911$	−1.91130e16			−1.00920			−0.504602	+	0.863352i	$0.668361\pi$
$912$			1.47843e15i			0.0775942i
$913$			3.65867e16i			1.90868i
$914$	−7.46766e15			−0.387240
$915$	3.69051e15	−	1.26919e16i	0.190226	−	0.654201i
$916$	1.44650e15			0.0741127
$917$			2.41671e16i			1.23082i
$918$			2.21042e15i			0.111902i
$919$	−7.09706e15			−0.357144			−0.178572	−	0.983927i	$-0.557148\pi$
$919$	−7.09706e15			−0.357144			−0.178572	+	0.983927i	$0.557148\pi$
$920$	−7.30283e15	−	2.12349e15i	−0.365307	−	0.106223i
$921$	1.25221e16			0.622660
$922$		−	5.21004e15i		−	0.257526i
$923$		−	3.39936e15i		−	0.167027i
$924$	−6.99223e15			−0.341523
$925$	−3.59636e15	+	5.66119e15i	−0.174616	+	0.274871i
$926$	7.96562e15			0.384467
$927$			5.01357e15i			0.240552i
$928$		−	4.37237e15i		−	0.208546i
$929$	1.87622e16			0.889604			0.444802	−	0.895629i	$-0.353274\pi$
$929$	1.87622e16			0.889604			0.444802	+	0.895629i	$0.353274\pi$
$930$	3.22519e15	+	9.37809e14i	0.152019	+	0.0442037i
$931$	4.76856e15			0.223442
$932$			1.01216e16i			0.471478i
$933$			2.95741e15i			0.136950i
$934$	1.12051e16			0.515830
$935$	4.98849e15	−	1.71557e16i	0.228300	−	0.785137i
$936$	−7.23263e14			−0.0329063
$937$			3.08165e16i			1.39385i	0.717145	+	0.696924i	$0.245448\pi$
$937$			3.08165e16i			1.39385i	−0.717145	+	0.696924i	$0.754552\pi$
$938$			8.43944e15i			0.379488i
$939$	−1.19214e16			−0.532925
$940$	−2.68353e15	+	9.22883e15i	−0.119262	+	0.410151i
$941$	−4.26974e16			−1.88651			−0.943255	−	0.332070i	$-0.892253\pi$
$941$	−4.26974e16			−1.88651			−0.943255	+	0.332070i	$0.892253\pi$
$942$		−	7.74669e15i		−	0.340280i
$943$		−	4.87879e16i		−	2.13058i
$944$	−4.59131e15			−0.199338
$945$	5.09383e15	+	1.48117e15i	0.219872	+	0.0639335i
$946$	9.01055e15			0.386679
$947$			1.63317e16i			0.696799i	0.937346	+	0.348399i	$0.113275\pi$
$947$			1.63317e16i			0.696799i	−0.937346	+	0.348399i	$0.886725\pi$
$948$			1.12052e16i			0.475306i
$949$	7.05028e15			0.297332
$950$	−4.86132e15	+	7.65242e15i	−0.203833	+	0.320862i
$951$	−6.45373e14			−0.0269041
$952$		−	8.34585e15i		−	0.345913i
$953$			2.78821e16i			1.14899i	0.818509	+	0.574494i	$0.194801\pi$
$953$			2.78821e16i			1.14899i	−0.818509	+	0.574494i	$0.805199\pi$
$954$	−8.96666e15			−0.367379
$955$	−2.80636e16	−	8.16023e15i	−1.14321	−	0.332417i
$956$	−6.01853e15			−0.243765
$957$		−	1.68177e16i		−	0.677254i
$958$			1.41170e16i			0.565240i
$959$	−1.51662e15			−0.0603772
$960$	5.09068e14	−	1.75072e15i	0.0201504	−	0.0692986i
$961$	−2.15875e16			−0.849617
$962$		−	1.64300e15i		−	0.0642946i
$963$		−	2.47504e15i		−	0.0963026i
$964$	9.55374e15			0.369615
$965$	6.53854e15	−	2.24865e16i	0.251525	−	0.865010i
$966$	−1.36648e16			−0.522671
$967$		−	7.21160e15i		−	0.274275i	−0.990552	−	0.137137i	$-0.956210\pi$
$967$		−	7.21160e15i		−	0.274275i	0.990552	−	0.137137i	$-0.0437902\pi$
$968$		−	1.05556e14i		−	0.00399180i
$969$	−6.78744e15			−0.255226
$970$	3.49657e16	+	1.01672e16i	1.30737	+	0.380152i
$971$	−4.56053e16			−1.69555			−0.847773	−	0.530359i	$-0.822057\pi$
$971$	−4.56053e16			−1.69555			−0.847773	+	0.530359i	$0.822057\pi$
$972$			8.67624e14i			0.0320750i
$973$		−	6.35379e16i		−	2.33567i
$974$	−1.39457e14			−0.00509760
$975$	−3.74364e15	−	2.37821e15i	−0.136072	−	0.0864419i
$976$	−8.16227e15			−0.295010
$977$			4.85178e16i			1.74374i	0.489740	+	0.871868i	$0.337092\pi$
$977$			4.85178e16i			1.74374i	−0.489740	+	0.871868i	$0.662908\pi$
$978$		−	1.99440e15i		−	0.0712769i
$979$	1.85678e15			0.0659867
$980$	−5.64681e15	−	1.64196e15i	−0.199554	−	0.0580255i
$981$	1.57786e16			0.554485
$982$			2.15630e15i			0.0753522i
$983$			4.37954e16i			1.52189i	0.648814	+	0.760947i	$0.275265\pi$
$983$			4.37954e16i			1.52189i	−0.648814	+	0.760947i	$0.724735\pi$
$984$	1.16960e16			0.404170
$985$	−1.41037e16	+	4.85035e16i	−0.484656	+	1.66676i
$986$	2.00735e16			0.685960
$987$			1.72687e16i			0.586832i
$988$		−	2.22090e15i		−	0.0750525i
$989$	1.76092e16			0.591778
$990$	1.95806e15	−	6.73390e15i	0.0654384	−	0.225047i
$991$	−2.55075e16			−0.847740			−0.423870	−	0.905723i	$-0.639329\pi$
$991$	−2.55075e16			−0.847740			−0.423870	+	0.905723i	$0.639329\pi$
$992$		−	2.07414e15i		−	0.0685527i
$993$		−	2.15468e16i		−	0.708209i
$994$	1.53967e16			0.503273
$995$	7.05456e15	+	2.05130e15i	0.229321	+	0.0666810i
$996$	−1.71409e16			−0.554126
$997$		−	8.08618e15i		−	0.259968i	−0.991516	−	0.129984i	$-0.958507\pi$
$997$		−	8.08618e15i		−	0.259968i	0.991516	−	0.129984i	$-0.0414926\pi$
$998$			2.58012e16i			0.824939i
$999$	−1.97094e15			−0.0626704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.12.c.b.19.1	✓	6
3.2	odd	2		90.12.c.c.19.6		6
4.3	odd	2		240.12.f.b.49.4		6
5.2	odd	4		150.12.a.u.1.1		3
5.3	odd	4		150.12.a.t.1.3		3
5.4	even	2	inner	30.12.c.b.19.4	yes	6
15.14	odd	2		90.12.c.c.19.3		6
20.19	odd	2		240.12.f.b.49.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.c.b.19.1	✓	6	1.1	even	1	trivial
30.12.c.b.19.4	yes	6	5.4	even	2	inner
90.12.c.c.19.3		6	15.14	odd	2
90.12.c.c.19.6		6	3.2	odd	2
150.12.a.t.1.3		3	5.3	odd	4
150.12.a.u.1.1		3	5.2	odd	4
240.12.f.b.49.1		6	20.19	odd	2
240.12.f.b.49.4		6	4.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-32.0000i q^{2} -243.000i q^{3} -1024.00 q^{4} +(-6709.81 - 1951.05i) q^{5} -7776.00 q^{6} +52907.3i q^{7} +32768.0i q^{8} -59049.0 q^{9} +(-62433.8 + 214714. i) q^{10} +531122. q^{11} +248832. i q^{12} -373795. i q^{13} +1.69303e6 q^{14} +(-474106. + 1.63048e6i) q^{15} +1.04858e6 q^{16} +4.81399e6i q^{17} +1.88957e6i q^{18} -5.80222e6 q^{19} +(6.87084e6 + 1.99788e6i) q^{20} +1.28565e7 q^{21} -1.69959e7i q^{22} -3.32148e7i q^{23} +7.96262e6 q^{24} +(4.12149e7 + 2.61824e7i) q^{25} -1.19614e7 q^{26} +1.43489e7i q^{27} -5.41770e7i q^{28} +1.30307e8 q^{29} +(5.21755e7 + 1.51714e7i) q^{30} +6.18143e7 q^{31} -3.35544e7i q^{32} -1.29063e8i q^{33} +1.54048e8 q^{34} +(1.03225e8 - 3.54997e8i) q^{35} +6.04662e7 q^{36} +1.37358e8i q^{37} +1.85671e8i q^{38} -9.08322e7 q^{39} +(6.39322e7 - 2.19867e8i) q^{40} +1.46886e9 q^{41} -4.11407e8i q^{42} +5.30160e8i q^{43} -5.43869e8 q^{44} +(3.96207e8 + 1.15208e8i) q^{45} -1.06287e9 q^{46} +1.34319e9i q^{47} -2.54804e8i q^{48} -8.21851e8 q^{49} +(8.37837e8 - 1.31888e9i) q^{50} +1.16980e9 q^{51} +3.82766e8i q^{52} +4.74535e9i q^{53} +4.59165e8 q^{54} +(-3.56372e9 - 1.03625e9i) q^{55} -1.73366e9 q^{56} +1.40994e9i q^{57} -4.16982e9i q^{58} -4.37861e9 q^{59} +(4.85485e8 - 1.66961e9i) q^{60} -7.78414e9 q^{61} -1.97806e9i q^{62} -3.12412e9i q^{63} -1.07374e9 q^{64} +(-7.29295e8 + 2.50809e9i) q^{65} -4.13000e9 q^{66} +4.98481e9i q^{67} -4.92953e9i q^{68} -8.07119e9 q^{69} +(-1.13599e10 - 3.30320e9i) q^{70} +9.09417e9 q^{71} -1.93492e9i q^{72} +1.88613e10i q^{73} +4.39545e9 q^{74} +(6.36232e9 - 1.00152e10i) q^{75} +5.94148e9 q^{76} +2.81002e10i q^{77} +2.90663e9i q^{78} +4.50312e10 q^{79} +(-7.03574e9 - 2.04583e9i) q^{80} +3.48678e9 q^{81} -4.70035e10i q^{82} +6.88856e10i q^{83} -1.31650e10 q^{84} +(9.39236e9 - 3.23009e10i) q^{85} +1.69651e10 q^{86} -3.16645e10i q^{87} +1.74038e10i q^{88} +3.49597e9 q^{89} +(3.68665e9 - 1.26786e10i) q^{90} +1.97765e10 q^{91} +3.40119e10i q^{92} -1.50209e10i q^{93} +4.29820e10 q^{94} +(3.89318e10 + 1.13205e10i) q^{95} -8.15373e9 q^{96} -1.62848e11i q^{97} +2.62992e10i q^{98} -3.13622e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6144 q^{4} - 9926 q^{5} - 46656 q^{6} - 354294 q^{9} + 72576 q^{10} + 1753400 q^{11} - 4312576 q^{14} + 551124 q^{15} + 6291456 q^{16} - 4069824 q^{19} + 10164224 q^{20} - 32748624 q^{21} + 47775744 q^{24}+ \cdots - 103536516600 q^{99}+O(q^{100}) \) 6 * q - 6144 * q^4 - 9926 * q^5 - 46656 * q^6 - 354294 * q^9 + 72576 * q^10 + 1753400 * q^11 - 4312576 * q^14 + 551124 * q^15 + 6291456 * q^16 - 4069824 * q^19 + 10164224 * q^20 - 32748624 * q^21 + 47775744 * q^24 + 169978326 * q^25 + 20172288 * q^26 + 71715564 * q^29 + 77184576 * q^30 - 122243352 * q^31 - 183956736 * q^34 + 825571904 * q^35 + 362797056 * q^36 + 153183312 * q^39 - 74317824 * q^40 + 2006768564 * q^41 - 1795481600 * q^44 + 586120374 * q^45 + 3191443200 * q^46 - 9590905446 * q^49 - 2993989376 * q^50 - 1396921464 * q^51 + 2754990144 * q^54 + 9162341400 * q^55 + 4416077824 * q^56 - 4069460200 * q^59 - 564350976 * q^60 - 12386466660 * q^61 - 6442450944 * q^64 - 30310342152 * q^65 - 13634438400 * q^66 + 24235021800 * q^69 - 15427048704 * q^70 + 13703505600 * q^71 + 59877797888 * q^74 - 22735606824 * q^75 + 4167499776 * q^76 - 13438327752 * q^79 - 10408165376 * q^80 + 20920706406 * q^81 + 33534590976 * q^84 + 50595843144 * q^85 - 62741662976 * q^86 - 127436589092 * q^89 - 4285540224 * q^90 + 271843383552 * q^91 + 140200608000 * q^94 - 87931077696 * q^95 - 48922361856 * q^96 - 103536516600 * q^99

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