LMFDB - Embedded newform 30.12.c.b.19.3

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			19.3
Root			$-451.888i$ of defining polynomial
Character	$\chi$	$=$	30.19
Dual form			30.12.c.b.19.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-32.0000i q^{2} -243.000i q^{3} -1024.00 q^{4} +(6755.14 - 1787.80i) q^{5} -7776.00 q^{6} -41527.6i q^{7} +32768.0i q^{8} -59049.0 q^{9} +(-57209.7 - 216164. i) q^{10} +839520. q^{11} +248832. i q^{12} -1.66178e6i q^{13} -1.32888e6 q^{14} +(-434436. - 1.64150e6i) q^{15} +1.04858e6 q^{16} -3.23669e6i q^{17} +1.88957e6i q^{18} -5.44307e6 q^{19} +(-6.91726e6 + 1.83071e6i) q^{20} -1.00912e7 q^{21} -2.68646e7i q^{22} +2.97481e7i q^{23} +7.96262e6 q^{24} +(4.24356e7 - 2.41537e7i) q^{25} -5.31769e7 q^{26} +1.43489e7i q^{27} +4.25243e7i q^{28} -1.55089e8 q^{29} +(-5.25279e7 + 1.39020e7i) q^{30} -2.76977e8 q^{31} -3.35544e7i q^{32} -2.04003e8i q^{33} -1.03574e8 q^{34} +(-7.42432e7 - 2.80525e8i) q^{35} +6.04662e7 q^{36} +4.58098e8i q^{37} +1.74178e8i q^{38} -4.03812e8 q^{39} +(5.85827e7 + 2.21352e8i) q^{40} +1.42131e8 q^{41} +3.22919e8i q^{42} -1.09829e9i q^{43} -8.59668e8 q^{44} +(-3.98884e8 + 1.05568e8i) q^{45} +9.51939e8 q^{46} -1.89330e9i q^{47} -2.54804e8i q^{48} +2.52786e8 q^{49} +(-7.72919e8 - 1.35794e9i) q^{50} -7.86516e8 q^{51} +1.70166e9i q^{52} +1.28322e9i q^{53} +4.59165e8 q^{54} +(5.67107e9 - 1.50090e9i) q^{55} +1.36078e9 q^{56} +1.32267e9i q^{57} +4.96286e9i q^{58} +5.01298e9 q^{59} +(4.44863e8 + 1.68089e9i) q^{60} +7.45699e9 q^{61} +8.86325e9i q^{62} +2.45216e9i q^{63} -1.07374e9 q^{64} +(-2.97093e9 - 1.12255e10i) q^{65} -6.52811e9 q^{66} -1.14069e9i q^{67} +3.31437e9i q^{68} +7.22879e9 q^{69} +(-8.97679e9 + 2.37578e9i) q^{70} +8.23753e9 q^{71} -1.93492e9i q^{72} +1.90626e10i q^{73} +1.46591e10 q^{74} +(-5.86935e9 - 1.03119e10i) q^{75} +5.57371e9 q^{76} -3.48632e10i q^{77} +1.29220e10i q^{78} -2.39605e10 q^{79} +(7.08328e9 - 1.87465e9i) q^{80} +3.48678e9 q^{81} -4.54818e9i q^{82} -6.55948e10i q^{83} +1.03334e10 q^{84} +(-5.78657e9 - 2.18643e10i) q^{85} -3.51452e10 q^{86} +3.76867e10i q^{87} +2.75094e10i q^{88} -3.18476e10 q^{89} +(3.37818e9 + 1.27643e10i) q^{90} -6.90096e10 q^{91} -3.04621e10i q^{92} +6.73053e10i q^{93} -6.05855e10 q^{94} +(-3.67687e10 + 9.73114e9i) q^{95} -8.15373e9 q^{96} -4.42047e10i q^{97} -8.08914e9i q^{98} -4.95728e10 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
$5$	6755.14	−	1787.80i	0.966717	−	0.255850i
$5$	6755.14	−	1787.80i	0.966717	−	0.255850i
$6$	−7776.00			−0.408248
$7$		−	41527.6i		−	0.933894i	−0.884285	−	0.466947i	$-0.845354\pi$
$7$		−	41527.6i		−	0.933894i	0.884285	−	0.466947i	$-0.154646\pi$
$8$			32768.0i			0.353553i
$9$	−59049.0			−0.333333
$10$	−57209.7	−	216164.i	−0.180913	−	0.683572i
$11$	839520.			1.57171			0.785853	−	0.618414i	$-0.212224\pi$
$11$	839520.			1.57171			0.785853	+	0.618414i	$0.212224\pi$
$12$			248832.i			0.288675i
$13$		−	1.66178e6i		−	1.24132i	−0.784079	−	0.620661i	$-0.786864\pi$
$13$		−	1.66178e6i		−	1.24132i	0.784079	−	0.620661i	$-0.213136\pi$
$14$	−1.32888e6			−0.660363
$15$	−434436.	−	1.64150e6i	−0.147715	−	0.558134i
$16$	1.04858e6			0.250000
$17$		−	3.23669e6i		−	0.552882i	−0.961031	−	0.276441i	$-0.910845\pi$
$17$		−	3.23669e6i		−	0.552882i	0.961031	−	0.276441i	$-0.0891550\pi$
$18$			1.88957e6i			0.235702i
$19$	−5.44307e6			−0.504312			−0.252156	−	0.967687i	$-0.581140\pi$
$19$	−5.44307e6			−0.504312			−0.252156	+	0.967687i	$0.581140\pi$
$20$	−6.91726e6	+	1.83071e6i	−0.483358	+	0.127925i
$21$	−1.00912e7			−0.539184
$22$		−	2.68646e7i		−	1.11136i
$23$			2.97481e7i			0.963732i	0.876245	+	0.481866i	$0.160041\pi$
$23$			2.97481e7i			0.963732i	−0.876245	+	0.481866i	$0.839959\pi$
$24$	7.96262e6			0.204124
$25$	4.24356e7	−	2.41537e7i	0.869082	−	0.494668i
$26$	−5.31769e7			−0.877747
$27$			1.43489e7i			0.192450i
$28$			4.25243e7i			0.466947i
$29$	−1.55089e8			−1.40408			−0.702042	−	0.712136i	$-0.747728\pi$
$29$	−1.55089e8			−1.40408			−0.702042	+	0.712136i	$0.747728\pi$
$30$	−5.25279e7	+	1.39020e7i	−0.394660	+	0.104450i
$31$	−2.76977e8			−1.73762			−0.868808	−	0.495150i	$-0.835113\pi$
$31$	−2.76977e8			−1.73762			−0.868808	+	0.495150i	$0.835113\pi$
$32$		−	3.35544e7i		−	0.176777i
$33$		−	2.04003e8i		−	0.907425i
$34$	−1.03574e8			−0.390946
$35$	−7.42432e7	−	2.80525e8i	−0.238936	−	0.902811i
$36$	6.04662e7			0.166667
$37$			4.58098e8i			1.08605i	0.839718	+	0.543023i	$0.182720\pi$
$37$			4.58098e8i			1.08605i	−0.839718	+	0.543023i	$0.817280\pi$
$38$			1.74178e8i			0.356602i
$39$	−4.03812e8			−0.716678
$40$	5.85827e7	+	2.21352e8i	0.0904565	+	0.341786i
$41$	1.42131e8			0.191592			0.0957958	−	0.995401i	$-0.469460\pi$
$41$	1.42131e8			0.191592			0.0957958	+	0.995401i	$0.469460\pi$
$42$			3.22919e8i			0.381261i
$43$		−	1.09829e9i		−	1.13930i	−0.821886	−	0.569652i	$-0.807078\pi$
$43$		−	1.09829e9i		−	1.13930i	0.821886	−	0.569652i	$-0.192922\pi$
$44$	−8.59668e8			−0.785853
$45$	−3.98884e8	+	1.05568e8i	−0.322239	+	0.0852832i
$46$	9.51939e8			0.681461
$47$		−	1.89330e9i		−	1.20415i	−0.798440	−	0.602075i	$-0.794341\pi$
$47$		−	1.89330e9i		−	1.20415i	0.798440	−	0.602075i	$-0.205659\pi$
$48$		−	2.54804e8i		−	0.144338i
$49$	2.52786e8			0.127842
$50$	−7.72919e8	−	1.35794e9i	−0.349783	−	0.614534i
$51$	−7.86516e8			−0.319206
$52$			1.70166e9i			0.620661i
$53$			1.28322e9i			0.421487i	0.977541	+	0.210743i	$0.0675884\pi$
$53$			1.28322e9i			0.421487i	−0.977541	+	0.210743i	$0.932412\pi$
$54$	4.59165e8			0.136083
$55$	5.67107e9	−	1.50090e9i	1.51939	−	0.402120i
$56$	1.36078e9			0.330181
$57$			1.32267e9i			0.291165i
$58$			4.96286e9i			0.992837i
$59$	5.01298e9			0.912872			0.456436	−	0.889756i	$-0.349126\pi$
$59$	5.01298e9			0.912872			0.456436	+	0.889756i	$0.349126\pi$
$60$	4.44863e8	+	1.68089e9i	0.0738574	+	0.279067i
$61$	7.45699e9			1.13045			0.565223	−	0.824938i	$-0.308790\pi$
$61$	7.45699e9			1.13045			0.565223	+	0.824938i	$0.308790\pi$
$62$			8.86325e9i			1.22868i
$63$			2.45216e9i			0.311298i
$64$	−1.07374e9			−0.125000
$65$	−2.97093e9	−	1.12255e10i	−0.317592	−	1.20001i
$66$	−6.52811e9			−0.641646
$67$		−	1.14069e9i		−	0.103219i	−0.998667	−	0.0516093i	$-0.983565\pi$
$67$		−	1.14069e9i		−	0.103219i	0.998667	−	0.0516093i	$-0.0164351\pi$
$68$			3.31437e9i			0.276441i
$69$	7.22879e9			0.556411
$70$	−8.97679e9	+	2.37578e9i	−0.638384	+	0.168954i
$71$	8.23753e9			0.541847			0.270923	−	0.962601i	$-0.412671\pi$
$71$	8.23753e9			0.541847			0.270923	+	0.962601i	$0.412671\pi$
$72$		−	1.93492e9i		−	0.117851i
$73$			1.90626e10i			1.07623i	0.842871	+	0.538116i	$0.180864\pi$
$73$			1.90626e10i			1.07623i	−0.842871	+	0.538116i	$0.819136\pi$
$74$	1.46591e10			0.767951
$75$	−5.86935e9	−	1.03119e10i	−0.285597	−	0.501765i
$76$	5.57371e9			0.252156
$77$		−	3.48632e10i		−	1.46781i
$78$			1.29220e10i			0.506768i
$79$	−2.39605e10			−0.876085			−0.438042	−	0.898954i	$-0.644328\pi$
$79$	−2.39605e10			−0.876085			−0.438042	+	0.898954i	$0.644328\pi$
$80$	7.08328e9	−	1.87465e9i	0.241679	−	0.0639624i
$81$	3.48678e9			0.111111
$82$		−	4.54818e9i		−	0.135476i
$83$		−	6.55948e10i		−	1.82785i	−0.405885	−	0.913924i	$-0.633037\pi$
$83$		−	6.55948e10i		−	1.82785i	0.405885	−	0.913924i	$-0.366963\pi$
$84$	1.03334e10			0.269592
$85$	−5.78657e9	−	2.18643e10i	−0.141455	−	0.534480i
$86$	−3.51452e10			−0.805610
$87$			3.76867e10i			0.810648i
$88$			2.75094e10i			0.555682i
$89$	−3.18476e10			−0.604549			−0.302274	−	0.953221i	$-0.597746\pi$
$89$	−3.18476e10			−0.604549			−0.302274	+	0.953221i	$0.597746\pi$
$90$	3.37818e9	+	1.27643e10i	0.0603043	+	0.227857i
$91$	−6.90096e10			−1.15926
$92$		−	3.04621e10i		−	0.481866i
$93$			6.73053e10i			1.00321i
$94$	−6.05855e10			−0.851462
$95$	−3.67687e10	+	9.73114e9i	−0.487527	+	0.129028i
$96$	−8.15373e9			−0.102062
$97$		−	4.42047e10i		−	0.522665i	−0.965249	−	0.261333i	$-0.915838\pi$
$97$		−	4.42047e10i		−	0.522665i	0.965249	−	0.261333i	$-0.0841620\pi$
$98$		−	8.08914e9i		−	0.0903980i
$99$	−4.95728e10			−0.523902
$100$	−4.34541e10	+	2.47334e10i	−0.434541	+	0.247334i
$101$	1.88396e11			1.78362			0.891812	−	0.452407i	$-0.149435\pi$
$101$	1.88396e11			1.78362			0.891812	+	0.452407i	$0.149435\pi$
$102$			2.51685e10i			0.225713i
$103$			1.74933e11i			1.48685i	0.668820	+	0.743424i	$0.266800\pi$
$103$			1.74933e11i			1.48685i	−0.668820	+	0.743424i	$0.733200\pi$
$104$	5.44531e10			0.438874
$105$	−6.81675e10	+	1.80411e10i	−0.521238	+	0.137950i
$106$	4.10630e10			0.298036
$107$		−	1.75156e11i		−	1.20730i	−0.797249	−	0.603650i	$-0.793712\pi$
$107$		−	1.75156e11i		−	1.20730i	0.797249	−	0.603650i	$-0.206288\pi$
$108$		−	1.46933e10i		−	0.0962250i
$109$	−5.67974e10			−0.353576			−0.176788	−	0.984249i	$-0.556571\pi$
$109$	−5.67974e10			−0.353576			−0.176788	+	0.984249i	$0.556571\pi$
$110$	−4.80287e10	−	1.81474e11i	−0.284342	−	1.07437i
$111$	1.11318e11			0.627029
$112$		−	4.35448e10i		−	0.233473i
$113$			7.76853e10i			0.396650i	0.980136	+	0.198325i	$0.0635501\pi$
$113$			7.76853e10i			0.396650i	−0.980136	+	0.198325i	$0.936450\pi$
$114$	4.23253e10			0.205884
$115$	5.31838e10	+	2.00953e11i	0.246570	+	0.931655i
$116$	1.58811e11			0.702042
$117$			9.81263e10i			0.413774i
$118$		−	1.60415e11i		−	0.645498i
$119$	−1.34412e11			−0.516333
$120$	5.37886e10	−	1.42356e10i	0.197330	−	0.0522251i
$121$	4.19482e11			1.47026
$122$		−	2.38624e11i		−	0.799346i
$123$		−	3.45377e10i		−	0.110615i
$124$	2.83624e11			0.868808
$125$	2.43477e11	−	2.39028e11i	0.713595	−	0.700558i
$126$	7.84692e10			0.220121
$127$			2.44393e11i			0.656401i	0.944608	+	0.328200i	$0.106442\pi$
$127$			2.44393e11i			0.656401i	−0.944608	+	0.328200i	$0.893558\pi$
$128$			3.43597e10i			0.0883883i
$129$	−2.66884e11			−0.657778
$130$	−3.59217e11	+	9.50698e10i	−0.848533	+	0.224571i
$131$	3.21349e10			0.0727755			0.0363877	−	0.999338i	$-0.488415\pi$
$131$	3.21349e10			0.0727755			0.0363877	+	0.999338i	$0.488415\pi$
$132$			2.08899e11i			0.453712i
$133$			2.26038e11i			0.470974i
$134$	−3.65022e10			−0.0729866
$135$	2.56530e10	+	9.69288e10i	0.0492383	+	0.186045i
$136$	1.06060e11			0.195473
$137$			1.03419e12i			1.83079i	0.402557	+	0.915395i	$0.368122\pi$
$137$			1.03419e12i			1.83079i	−0.402557	+	0.915395i	$0.631878\pi$
$138$		−	2.31321e11i		−	0.393442i
$139$	6.51000e11			1.06414			0.532071	−	0.846700i	$-0.321414\pi$
$139$	6.51000e11			1.06414			0.532071	+	0.846700i	$0.321414\pi$
$140$	7.60250e10	+	2.87257e11i	0.119468	+	0.451405i
$141$	−4.60071e11			−0.695216
$142$		−	2.63601e11i		−	0.383143i
$143$		−	1.39510e12i		−	1.95099i
$144$	−6.19174e10			−0.0833333
$145$	−1.04765e12	+	2.77269e11i	−1.35735	+	0.359234i
$146$	6.10002e11			0.761011
$147$		−	6.14269e10i		−	0.0738097i
$148$		−	4.69092e11i		−	0.543023i
$149$	−1.48776e12			−1.65962			−0.829808	−	0.558049i	$-0.811550\pi$
$149$	−1.48776e12			−1.65962			−0.829808	+	0.558049i	$0.811550\pi$
$150$	−3.29980e11	+	1.87819e11i	−0.354801	+	0.201947i
$151$	1.69992e12			1.76220			0.881100	−	0.472929i	$-0.156803\pi$
$151$	1.69992e12			1.76220			0.881100	+	0.472929i	$0.156803\pi$
$152$		−	1.78359e11i		−	0.178301i
$153$			1.91123e11i			0.184294i
$154$	−1.11562e12			−1.03790
$155$	−1.87101e12	+	4.95180e11i	−1.67978	+	0.444568i
$156$	4.13503e11			0.358339
$157$		−	3.75740e11i		−	0.314369i	−0.987569	−	0.157184i	$-0.949758\pi$
$157$		−	3.75740e11i		−	0.314369i	0.987569	−	0.157184i	$-0.0502417\pi$
$158$			7.66735e11i			0.619485i
$159$	3.11822e11			0.243345
$160$	−5.99887e10	−	2.26665e11i	−0.0452282	−	0.170893i
$161$	1.23537e12			0.900023
$162$		−	1.11577e11i		−	0.0785674i
$163$		−	1.19182e12i		−	0.811296i	−0.914029	−	0.405648i	$-0.867046\pi$
$163$		−	1.19182e12i		−	0.811296i	0.914029	−	0.405648i	$-0.132954\pi$
$164$	−1.45542e11			−0.0957958
$165$	−3.64718e11	−	1.37807e12i	−0.232164	−	0.877222i
$166$	−2.09903e12			−1.29248
$167$			7.86209e11i			0.468379i	0.972191	+	0.234190i	$0.0752436\pi$
$167$			7.86209e11i			0.468379i	−0.972191	+	0.234190i	$0.924756\pi$
$168$		−	3.30669e11i		−	0.190630i
$169$	−9.69345e11			−0.540880
$170$	−6.99657e11	+	1.85170e11i	−0.377934	+	0.100023i
$171$	3.21408e11			0.168104
$172$			1.12465e12i			0.569652i
$173$		−	2.61407e11i		−	0.128252i	−0.997942	−	0.0641258i	$-0.979574\pi$
$173$		−	2.61407e11i		−	0.128252i	0.997942	−	0.0641258i	$-0.0204259\pi$
$174$	1.20597e12			0.573215
$175$	−1.00305e12	−	1.76225e12i	−0.461968	−	0.811630i
$176$	8.80300e11			0.392926
$177$		−	1.21815e12i		−	0.527047i
$178$			1.01912e12i			0.427481i
$179$	−1.08084e12			−0.439614			−0.219807	−	0.975543i	$-0.570543\pi$
$179$	−1.08084e12			−0.439614			−0.219807	+	0.975543i	$0.570543\pi$
$180$	4.08457e11	−	1.08102e11i	0.161119	−	0.0426416i
$181$	3.87701e12			1.48342			0.741711	−	0.670720i	$-0.234015\pi$
$181$	3.87701e12			1.48342			0.741711	+	0.670720i	$0.234015\pi$
$182$			2.20831e12i			0.819723i
$183$		−	1.81205e12i		−	0.652663i
$184$	−9.74786e11			−0.340731
$185$	8.18988e11	+	3.09451e12i	0.277865	+	1.04990i
$186$	2.15377e12			0.709378
$187$		−	2.71727e12i		−	0.868967i
$188$			1.93874e12i			0.602075i
$189$	5.95876e11			0.179728
$190$	3.11397e11	+	1.17660e12i	0.0912366	+	0.344733i
$191$	4.34227e12			1.23604			0.618021	−	0.786161i	$-0.287935\pi$
$191$	4.34227e12			1.23604			0.618021	+	0.786161i	$0.287935\pi$
$192$			2.60919e11i			0.0721688i
$193$		−	4.45221e11i		−	0.119677i	−0.998208	−	0.0598384i	$-0.980941\pi$
$193$		−	4.45221e11i		−	0.119677i	0.998208	−	0.0598384i	$-0.0190585\pi$
$194$	−1.41455e12			−0.369580
$195$	−2.72781e12	+	7.21936e11i	−0.692824	+	0.183362i
$196$	−2.58852e11			−0.0639210
$197$			1.92250e12i			0.461640i	0.972997	+	0.230820i	$0.0741408\pi$
$197$			1.92250e12i			0.461640i	−0.972997	+	0.230820i	$0.925859\pi$
$198$			1.58633e12i			0.370455i
$199$	2.52317e12			0.573131			0.286566	−	0.958061i	$-0.407486\pi$
$199$	2.52317e12			0.573131			0.286566	+	0.958061i	$0.407486\pi$
$200$	7.91469e11	+	1.39053e12i	0.174892	+	0.307267i
$201$	−2.77189e11			−0.0595933
$202$		−	6.02866e12i		−	1.26121i
$203$			6.44048e12i			1.31126i
$204$	8.05392e11			0.159603
$205$	9.60112e11	−	2.54102e11i	0.185215	−	0.0490186i
$206$	5.59785e12			1.05136
$207$		−	1.75660e12i		−	0.321244i
$208$		−	1.74250e12i		−	0.310331i
$209$	−4.56957e12			−0.792630
$210$	5.77315e11	+	2.18136e12i	0.0975454	+	0.368571i
$211$	7.60254e12			1.25143			0.625713	−	0.780053i	$-0.284808\pi$
$211$	7.60254e12			1.25143			0.625713	+	0.780053i	$0.284808\pi$
$212$		−	1.31402e12i		−	0.210743i
$213$		−	2.00172e12i		−	0.312835i
$214$	−5.60501e12			−0.853690
$215$	−1.96352e12	−	7.41909e12i	−0.291491	−	1.10138i
$216$	−4.70185e11			−0.0680414
$217$			1.15022e13i			1.62275i
$218$			1.81752e12i			0.250016i
$219$	4.63221e12			0.621363
$220$	−5.80718e12	+	1.53692e12i	−0.759697	+	0.201060i
$221$	−5.37866e12			−0.686304
$222$		−	3.56217e12i		−	0.443377i
$223$			2.46671e12i			0.299531i	0.988722	+	0.149765i	$0.0478518\pi$
$223$			2.46671e12i			0.299531i	−0.988722	+	0.149765i	$0.952148\pi$
$224$	−1.39343e12			−0.165091
$225$	−2.50578e12	+	1.42625e12i	−0.289694	+	0.164889i
$226$	2.48593e12			0.280474
$227$		−	1.11438e13i		−	1.22713i	−0.789642	−	0.613567i	$-0.789734\pi$
$227$		−	1.11438e13i		−	1.22713i	0.789642	−	0.613567i	$-0.210266\pi$
$228$		−	1.35441e12i		−	0.145582i
$229$	1.12840e13			1.18404			0.592021	−	0.805923i	$-0.298330\pi$
$229$	1.12840e13			1.18404			0.592021	+	0.805923i	$0.298330\pi$
$230$	6.43048e12	−	1.70188e12i	0.658780	−	0.174352i
$231$	−8.47177e12			−0.847438
$232$		−	5.08197e12i		−	0.496418i
$233$			3.66685e12i			0.349813i	0.984585	+	0.174906i	$0.0559623\pi$
$233$			3.66685e12i			0.349813i	−0.984585	+	0.174906i	$0.944038\pi$
$234$	3.14004e12			0.292582
$235$	−3.38484e12	−	1.27895e13i	−0.308081	−	1.16407i
$236$	−5.13329e12			−0.456436
$237$			5.82239e12i			0.505808i
$238$			4.30118e12i			0.365102i
$239$	−1.40189e13			−1.16285			−0.581427	−	0.813598i	$-0.697506\pi$
$239$	−1.40189e13			−1.16285			−0.581427	+	0.813598i	$0.697506\pi$
$240$	−4.55539e11	−	1.72124e12i	−0.0369287	−	0.139534i
$241$	−1.19865e13			−0.949723			−0.474862	−	0.880060i	$-0.657502\pi$
$241$	−1.19865e13			−0.949723			−0.474862	+	0.880060i	$0.657502\pi$
$242$		−	1.34234e13i		−	1.03963i
$243$		−	8.47289e11i		−	0.0641500i
$244$	−7.63596e12			−0.565223
$245$	1.70760e12	−	4.51931e11i	0.123587	−	0.0327083i
$246$	−1.10521e12			−0.0782169
$247$			9.04517e12i			0.626014i
$248$		−	9.07597e12i		−	0.614340i
$249$	−1.59395e13			−1.05531
$250$	−7.64890e12	−	7.79125e12i	−0.495369	−	0.504588i
$251$	−4.71793e12			−0.298914			−0.149457	−	0.988768i	$-0.547753\pi$
$251$	−4.71793e12			−0.298914			−0.149457	+	0.988768i	$0.547753\pi$
$252$		−	2.51101e12i		−	0.155649i
$253$			2.49741e13i			1.51470i
$254$	7.82059e12			0.464146
$255$	−5.31302e12	+	1.40614e12i	−0.308582	+	0.0816688i
$256$	1.09951e12			0.0625000
$257$			2.26178e13i			1.25840i	0.777244	+	0.629199i	$0.216617\pi$
$257$			2.26178e13i			1.25840i	−0.777244	+	0.629199i	$0.783383\pi$
$258$			8.54029e12i			0.465119i
$259$	1.90237e13			1.01425
$260$	3.04223e12	+	1.14949e13i	0.158796	+	0.600003i
$261$	9.15787e12			0.468028
$262$		−	1.02832e12i		−	0.0514600i
$263$		−	2.63896e13i		−	1.29323i	−0.762815	−	0.646617i	$-0.776183\pi$
$263$		−	2.63896e13i		−	1.29323i	0.762815	−	0.646617i	$-0.223817\pi$
$264$	6.68478e12			0.320823
$265$	2.29414e12	+	8.66832e12i	0.107837	+	0.407458i
$266$	7.23321e12			0.333029
$267$			7.73896e12i			0.349036i
$268$			1.16807e12i			0.0516093i
$269$	−1.82859e13			−0.791550			−0.395775	−	0.918347i	$-0.629524\pi$
$269$	−1.82859e13			−0.791550			−0.395775	+	0.918347i	$0.629524\pi$
$270$	3.10172e12	−	8.20897e11i	0.131553	−	0.0348167i
$271$	−2.37685e13			−0.987803			−0.493902	−	0.869518i	$-0.664430\pi$
$271$	−2.37685e13			−0.987803			−0.493902	+	0.869518i	$0.664430\pi$
$272$		−	3.39392e12i		−	0.138220i
$273$			1.67693e13i			0.669301i
$274$	3.30942e13			1.29456
$275$	3.56256e13	−	2.02775e13i	1.36594	−	0.777473i
$276$	−7.40228e12			−0.278205
$277$			2.00012e13i			0.736914i	0.929645	+	0.368457i	$0.120114\pi$
$277$			2.00012e13i			0.736914i	−0.929645	+	0.368457i	$0.879886\pi$
$278$		−	2.08320e13i		−	0.752462i
$279$	1.63552e13			0.579205
$280$	9.19223e12	−	2.43280e12i	0.319192	−	0.0844768i
$281$	2.16062e13			0.735689			0.367845	−	0.929887i	$-0.380096\pi$
$281$	2.16062e13			0.735689			0.367845	+	0.929887i	$0.380096\pi$
$282$			1.47223e13i			0.491592i
$283$		−	4.22652e13i		−	1.38407i	−0.721865	−	0.692034i	$-0.756715\pi$
$283$		−	4.22652e13i		−	1.38407i	0.721865	−	0.692034i	$-0.243285\pi$
$284$	−8.43523e12			−0.270923
$285$	2.36467e12	+	8.93479e12i	0.0744944	+	0.281474i
$286$	−4.46431e13			−1.37956
$287$		−	5.90234e12i		−	0.178926i
$288$			1.98136e12i			0.0589256i
$289$	2.37957e13			0.694322
$290$	8.87261e12	+	3.35248e13i	0.254017	+	0.959792i
$291$	−1.07417e13			−0.301761
$292$		−	1.95201e13i		−	0.538116i
$293$		−	5.66640e13i		−	1.53298i	−0.642259	−	0.766488i	$-0.722003\pi$
$293$		−	5.66640e13i		−	1.53298i	0.642259	−	0.766488i	$-0.277997\pi$
$294$	−1.96566e12			−0.0521913
$295$	3.38634e13	−	8.96222e12i	0.882488	−	0.233558i
$296$	−1.50109e13			−0.383975
$297$			1.20462e13i			0.302475i
$298$			4.76082e13i			1.17353i
$299$	4.94347e13			1.19630
$300$	6.01022e12	+	1.05593e13i	0.142798	+	0.250882i
$301$	−4.56093e13			−1.06399
$302$		−	5.43975e13i		−	1.24606i
$303$		−	4.57801e13i		−	1.02978i
$304$	−5.70747e12			−0.126078
$305$	5.03730e13	−	1.33316e13i	1.09282	−	0.289224i
$306$	6.11595e12			0.130315
$307$			1.99364e13i			0.417239i	0.977997	+	0.208619i	$0.0668970\pi$
$307$			1.99364e13i			0.417239i	−0.977997	+	0.208619i	$0.933103\pi$
$308$			3.57000e13i			0.733903i
$309$	4.25087e13			0.858433
$310$	1.58457e13	+	5.98725e13i	0.314357	+	1.18778i
$311$	1.05339e13			0.205309			0.102655	−	0.994717i	$-0.467266\pi$
$311$	1.05339e13			0.205309			0.102655	+	0.994717i	$0.467266\pi$
$312$		−	1.32321e13i		−	0.253384i
$313$			5.27355e13i			0.992224i	0.868259	+	0.496112i	$0.165239\pi$
$313$			5.27355e13i			0.992224i	−0.868259	+	0.496112i	$0.834761\pi$
$314$	−1.20237e13			−0.222292
$315$	4.38399e12	+	1.65647e13i	0.0796455	+	0.300937i
$316$	2.45355e13			0.438042
$317$			6.68311e13i			1.17261i	0.810091	+	0.586304i	$0.199417\pi$
$317$			6.68311e13i			1.17261i	−0.810091	+	0.586304i	$0.800583\pi$
$318$		−	9.97832e12i		−	0.172071i
$319$	−1.30201e14			−2.20681
$320$	−7.25327e12	+	1.91964e12i	−0.120840	+	0.0319812i
$321$	−4.25630e13			−0.697035
$322$		−	3.95317e13i		−	0.636412i
$323$			1.76175e13i			0.278825i
$324$	−3.57047e12			−0.0555556
$325$	−4.01381e13	−	7.05186e13i	−0.614042	−	1.07881i
$326$	−3.81383e13			−0.573673
$327$			1.38018e13i			0.204137i
$328$			4.65734e12i			0.0677379i
$329$	−7.86241e13			−1.12455
$330$	−4.40983e13	+	1.16710e13i	−0.620290	+	0.164165i
$331$	2.79590e13			0.386783			0.193392	−	0.981122i	$-0.438051\pi$
$331$	2.79590e13			0.386783			0.193392	+	0.981122i	$0.438051\pi$
$332$			6.71691e13i			0.913924i
$333$		−	2.70502e13i		−	0.362016i
$334$	2.51587e13			0.331194
$335$	−2.03934e12	−	7.70555e12i	−0.0264084	−	0.0997831i
$336$	−1.05814e13			−0.134796
$337$		−	1.16982e14i		−	1.46606i	−0.680194	−	0.733032i	$-0.738104\pi$
$337$		−	1.16982e14i		−	1.46606i	0.680194	−	0.733032i	$-0.261896\pi$
$338$			3.10190e13i			0.382460i
$339$	1.88775e13			0.229006
$340$	5.92545e12	+	2.23890e13i	0.0707273	+	0.267240i
$341$	−2.32527e14			−2.73102
$342$		−	1.02851e13i		−	0.118867i
$343$		−	9.26112e13i		−	1.05328i
$344$	3.59887e13			0.402805
$345$	4.88315e13	−	1.29237e13i	0.537891	−	0.142357i
$346$	−8.36501e12			−0.0906876
$347$			1.62553e12i			0.0173453i	0.999962	+	0.00867265i	$0.00276062\pi$
$347$			1.62553e12i			0.0173453i	−0.999962	+	0.00867265i	$0.997239\pi$
$348$		−	3.85912e13i		−	0.405324i
$349$	1.40028e14			1.44769			0.723843	−	0.689965i	$-0.242374\pi$
$349$	1.40028e14			1.44769			0.723843	+	0.689965i	$0.242374\pi$
$350$	−5.63920e13	+	3.20975e13i	−0.573909	+	0.326660i
$351$	2.38447e13			0.238893
$352$		−	2.81696e13i		−	0.277841i
$353$		−	1.07894e13i		−	0.104770i	−0.998627	−	0.0523850i	$-0.983318\pi$
$353$		−	1.07894e13i		−	0.104770i	0.998627	−	0.0523850i	$-0.0166823\pi$
$354$	−3.89809e13			−0.372678
$355$	5.56457e13	−	1.47271e13i	0.523812	−	0.138631i
$356$	3.26119e13			0.302274
$357$			3.26621e13i			0.298105i
$358$			3.45870e13i			0.310854i
$359$	8.36216e13			0.740114			0.370057	−	0.929009i	$-0.379338\pi$
$359$	8.36216e13			0.740114			0.370057	+	0.929009i	$0.379338\pi$
$360$	−3.45925e12	−	1.30706e13i	−0.0301522	−	0.113929i
$361$	−8.68632e13			−0.745669
$362$		−	1.24064e14i		−	1.04894i
$363$		−	1.01934e14i		−	0.848854i
$364$	7.06659e13			0.579632
$365$	3.40801e13	+	1.28770e14i	0.275353	+	1.04041i
$366$	−5.79856e13			−0.461502
$367$		−	1.00049e13i		−	0.0784420i	−0.999231	−	0.0392210i	$-0.987512\pi$
$367$		−	1.00049e13i		−	0.0784420i	0.999231	−	0.0392210i	$-0.0124876\pi$
$368$			3.11931e13i			0.240933i
$369$	−8.39267e12			−0.0638639
$370$	9.90244e13	−	2.62076e13i	0.742391	−	0.196480i
$371$	5.32890e13			0.393624
$372$		−	6.89206e13i		−	0.501606i
$373$			2.32365e14i			1.66637i	0.552993	+	0.833186i	$0.313486\pi$
$373$			2.32365e14i			1.66637i	−0.552993	+	0.833186i	$0.686514\pi$
$374$	−8.69525e13			−0.614453
$375$	−5.80839e13	−	5.91648e13i	−0.404467	−	0.411994i
$376$	6.20395e13			0.425731
$377$			2.57724e14i			1.74292i
$378$		−	1.90680e13i		−	0.127087i
$379$	−1.60902e14			−1.05693			−0.528465	−	0.848955i	$-0.677232\pi$
$379$	−1.60902e14			−1.05693			−0.528465	+	0.848955i	$0.677232\pi$
$380$	3.76511e13	−	9.96469e12i	0.243763	−	0.0645140i
$381$	5.93876e13			0.378973
$382$		−	1.38953e14i		−	0.874014i
$383$		−	3.41226e12i		−	0.0211568i	−0.999944	−	0.0105784i	$-0.996633\pi$
$383$		−	3.41226e12i		−	0.0211568i	0.999944	−	0.0105784i	$-0.00336727\pi$
$384$	8.34942e12			0.0510310
$385$	−6.23286e13	−	2.35506e14i	−0.375538	−	1.41895i
$386$	−1.42471e13			−0.0846243
$387$			6.48528e13i			0.379768i
$388$			4.52656e13i			0.261333i
$389$	2.49915e14			1.42255			0.711277	−	0.702912i	$-0.248117\pi$
$389$	2.49915e14			1.42255			0.711277	+	0.702912i	$0.248117\pi$
$390$	2.31020e13	+	8.72898e13i	0.129656	+	0.489901i
$391$	9.62854e13			0.532830
$392$			8.28328e12i			0.0451990i
$393$		−	7.80879e12i		−	0.0420169i
$394$	6.15201e13			0.326428
$395$	−1.61856e14	+	4.28366e13i	−0.846926	+	0.224146i
$396$	5.07626e13			0.261951
$397$			2.50976e14i			1.27727i	0.769508	+	0.638637i	$0.220502\pi$
$397$			2.50976e14i			1.27727i	−0.769508	+	0.638637i	$0.779498\pi$
$398$		−	8.07414e13i		−	0.405265i
$399$	5.49272e13			0.271917
$400$	4.44970e13	−	2.53270e13i	0.217270	−	0.123667i
$401$	3.56396e14			1.71648			0.858240	−	0.513248i	$-0.171558\pi$
$401$	3.56396e14			1.71648			0.858240	+	0.513248i	$0.171558\pi$
$402$			8.87004e12i			0.0421388i
$403$			4.60273e14i			2.15694i
$404$	−1.92917e14			−0.891812
$405$	2.35537e13	−	6.23369e12i	0.107413	−	0.0284277i
$406$	2.06096e14			0.927204
$407$			3.84582e14i			1.70695i
$408$		−	2.57726e13i		−	0.112857i
$409$	4.76849e13			0.206017			0.103008	−	0.994680i	$-0.467153\pi$
$409$	4.76849e13			0.206017			0.103008	+	0.994680i	$0.467153\pi$
$410$	−8.13125e12	−	3.07236e13i	−0.0346614	−	0.130967i
$411$	2.51309e14			1.05701
$412$		−	1.79131e14i		−	0.743424i
$413$		−	2.08177e14i		−	0.852525i
$414$	−5.62111e13			−0.227154
$415$	−1.17271e14	−	4.43102e14i	−0.467654	−	1.76701i
$416$	−5.57600e13			−0.219437
$417$		−	1.58193e14i		−	0.614382i
$418$			1.46226e14i			0.560474i
$419$	−2.26851e14			−0.858150			−0.429075	−	0.903269i	$-0.641160\pi$
$419$	−2.26851e14			−0.858150			−0.429075	+	0.903269i	$0.641160\pi$
$420$	6.98035e13	−	1.84741e13i	0.260619	−	0.0689750i
$421$	−1.36580e14			−0.503309			−0.251654	−	0.967817i	$-0.580975\pi$
$421$	−1.36580e14			−0.503309			−0.251654	+	0.967817i	$0.580975\pi$
$422$		−	2.43281e14i		−	0.884892i
$423$			1.11797e14i			0.401383i
$424$	−4.20485e13			−0.149018
$425$	−7.81781e13	−	1.37351e14i	−0.273493	−	0.480500i
$426$	−6.40551e13			−0.221208
$427$		−	3.09671e14i		−	1.05572i
$428$			1.79360e14i			0.603650i
$429$	−3.39008e14			−1.12641
$430$	−2.37411e14	+	6.28328e13i	−0.778797	+	0.206115i
$431$	1.21003e13			0.0391896			0.0195948	−	0.999808i	$-0.493762\pi$
$431$	1.21003e13			0.0391896			0.0195948	+	0.999808i	$0.493762\pi$
$432$			1.50459e13i			0.0481125i
$433$		−	3.05977e14i		−	0.966064i	−0.875603	−	0.483032i	$-0.839536\pi$
$433$		−	3.05977e14i		−	0.966064i	0.875603	−	0.483032i	$-0.160464\pi$
$434$	3.68069e14			1.14746
$435$	6.73764e13	+	2.54579e14i	0.207404	+	0.783667i
$436$	5.81606e13			0.176788
$437$		−	1.61921e14i		−	0.486021i
$438$		−	1.48231e14i		−	0.439370i
$439$	−3.68147e14			−1.07762			−0.538811	−	0.842427i	$-0.681126\pi$
$439$	−3.68147e14			−1.07762			−0.538811	+	0.842427i	$0.681126\pi$
$440$	4.91814e13	+	1.85830e14i	0.142171	+	0.537187i
$441$	−1.49267e13			−0.0426140
$442$			1.72117e14i			0.485290i
$443$		−	1.38978e13i		−	0.0387012i	−0.999813	−	0.0193506i	$-0.993840\pi$
$443$		−	1.38978e13i		−	0.0387012i	0.999813	−	0.0193506i	$-0.00615987\pi$
$444$	−1.13989e14			−0.313515
$445$	−2.15135e14	+	5.69372e13i	−0.584427	+	0.154674i
$446$	7.89347e13			0.211800
$447$			3.61525e14i			0.958179i
$448$			4.45899e13i			0.116737i
$449$	−3.92376e13			−0.101472			−0.0507362	−	0.998712i	$-0.516157\pi$
$449$	−3.92376e13			−0.101472			−0.0507362	+	0.998712i	$0.516157\pi$
$450$	4.56401e13	+	8.01850e13i	0.116594	+	0.204845i
$451$	1.19321e14			0.301126
$452$		−	7.95497e13i		−	0.198325i
$453$		−	4.13081e14i		−	1.01741i
$454$	−3.56602e14			−0.867715
$455$	−4.66170e14	+	1.23376e14i	−1.12068	+	0.296597i
$456$	−4.33411e13			−0.102942
$457$		−	1.37201e14i		−	0.321973i	−0.986957	−	0.160986i	$-0.948532\pi$
$457$		−	1.37201e14i		−	0.321973i	0.986957	−	0.160986i	$-0.0514675\pi$
$458$		−	3.61087e14i		−	0.837244i
$459$	4.64430e13			0.106402
$460$	−5.44602e13	−	2.05775e14i	−0.123285	−	0.465828i
$461$	2.48659e14			0.556223			0.278111	−	0.960549i	$-0.410292\pi$
$461$	2.48659e14			0.556223			0.278111	+	0.960549i	$0.410292\pi$
$462$			2.71097e14i			0.599229i
$463$			6.31268e14i			1.37885i	0.724355	+	0.689427i	$0.242138\pi$
$463$			6.31268e14i			1.37885i	−0.724355	+	0.689427i	$0.757862\pi$
$464$	−1.62623e14			−0.351021
$465$	1.20329e14	+	4.54657e14i	0.256672	+	0.969822i
$466$	1.17339e14			0.247355
$467$		−	8.60246e14i		−	1.79217i	−0.443880	−	0.896086i	$-0.646398\pi$
$467$		−	8.60246e14i		−	1.79217i	0.443880	−	0.896086i	$-0.353602\pi$
$468$		−	1.00481e14i		−	0.206887i
$469$	−4.73703e13			−0.0963952
$470$	−4.09263e14	+	1.08315e14i	−0.823123	+	0.217846i
$471$	−9.13048e13			−0.181501
$472$			1.64265e14i			0.322749i
$473$		−	9.22035e14i		−	1.79065i
$474$	1.86317e14			0.357660
$475$	−2.30980e14	+	1.31470e14i	−0.438288	+	0.249467i
$476$	1.37638e14			0.258166
$477$		−	7.57728e13i		−	0.140496i
$478$			4.48605e14i			0.822263i
$479$	5.71890e14			1.03626			0.518129	−	0.855303i	$-0.326629\pi$
$479$	5.71890e14			1.03626			0.518129	+	0.855303i	$0.326629\pi$
$480$	−5.50795e13	+	1.45773e13i	−0.0986651	+	0.0261125i
$481$	7.61256e14			1.34813
$482$			3.83567e14i			0.671556i
$483$		−	3.00194e14i		−	0.519629i
$484$	−4.29550e14			−0.735129
$485$	−7.90293e13	−	2.98609e14i	−0.133724	−	0.505269i
$486$	−2.71132e13			−0.0453609
$487$			7.95200e14i			1.31543i	0.753268	+	0.657714i	$0.228476\pi$
$487$			7.95200e14i			1.31543i	−0.753268	+	0.657714i	$0.771524\pi$
$488$			2.44351e14i			0.399673i
$489$	−2.89612e14			−0.468402
$490$	−1.44618e13	−	5.46432e13i	−0.0231283	−	0.0873893i
$491$	−5.04124e13			−0.0797240			−0.0398620	−	0.999205i	$-0.512692\pi$
$491$	−5.04124e13			−0.0797240			−0.0398620	+	0.999205i	$0.512692\pi$
$492$			3.53666e13i			0.0553077i
$493$			5.01976e14i			0.776292i
$494$	2.89446e14			0.442658
$495$	−3.34871e14	+	8.86264e13i	−0.506465	+	0.134040i
$496$	−2.90431e14			−0.434404
$497$		−	3.42085e14i		−	0.506027i
$498$			5.10065e14i			0.746216i
$499$	2.91835e14			0.422264			0.211132	−	0.977458i	$-0.432285\pi$
$499$	2.91835e14			0.422264			0.211132	+	0.977458i	$0.432285\pi$
$500$	−2.49320e14	+	2.44765e14i	−0.356798	+	0.350279i
$501$	1.91049e14			0.270419
$502$			1.50974e14i			0.211364i
$503$		−	7.29427e14i		−	1.01008i	−0.863095	−	0.505042i	$-0.831477\pi$
$503$		−	7.29427e14i		−	1.01008i	0.863095	−	0.505042i	$-0.168523\pi$
$504$	−8.03525e13			−0.110060
$505$	1.27264e15	−	3.36814e14i	1.72426	−	0.456339i
$506$	7.99172e14			1.07106
$507$			2.35551e14i			0.312277i
$508$		−	2.50259e14i		−	0.328200i
$509$	3.75076e14			0.486600			0.243300	−	0.969951i	$-0.421770\pi$
$509$	3.75076e14			0.486600			0.243300	+	0.969951i	$0.421770\pi$
$510$	4.49964e13	+	1.70017e14i	0.0577486	+	0.218201i
$511$	7.91623e14			1.00509
$512$		−	3.51844e13i		−	0.0441942i
$513$		−	7.81021e13i		−	0.0970549i
$514$	7.23769e14			0.889822
$515$	3.12746e14	+	1.18170e15i	0.380410	+	1.43736i
$516$	2.73289e14			0.328889
$517$		−	1.58946e15i		−	1.89257i
$518$		−	6.08758e14i		−	0.717185i
$519$	−6.35218e13			−0.0740461
$520$	3.67838e14	−	9.73515e13i	0.424266	−	0.112286i
$521$	−1.27745e15			−1.45793			−0.728967	−	0.684549i	$-0.759999\pi$
$521$	−1.27745e15			−1.45793			−0.728967	+	0.684549i	$0.759999\pi$
$522$		−	2.93052e14i		−	0.330946i
$523$			1.16147e15i			1.29792i	0.760824	+	0.648959i	$0.224795\pi$
$523$			1.16147e15i			1.29792i	−0.760824	+	0.648959i	$0.775205\pi$
$524$	−3.29062e13			−0.0363877
$525$	−4.28227e14	+	2.43740e14i	−0.468595	+	0.266717i
$526$	−8.44469e14			−0.914454
$527$			8.96487e14i			0.960696i
$528$		−	2.13913e14i		−	0.226856i
$529$	6.78604e13			0.0712213
$530$	2.77386e14	−	7.34126e13i	0.288116	−	0.0762524i
$531$	−2.96011e14			−0.304291
$532$		−	2.31463e14i		−	0.235487i
$533$		−	2.36190e14i		−	0.237827i
$534$	2.47647e14			0.246806
$535$	−3.13145e14	−	1.18321e15i	−0.308887	−	1.16712i
$536$	3.73783e13			0.0364933
$537$			2.62645e14i			0.253811i
$538$			5.85149e14i			0.559711i
$539$	2.12219e14			0.200930
$540$	−2.62687e13	−	9.92551e13i	−0.0246191	−	0.0930223i
$541$	1.14931e15			1.06623			0.533115	−	0.846043i	$-0.321021\pi$
$541$	1.14931e15			1.06623			0.533115	+	0.846043i	$0.321021\pi$
$542$			7.60592e14i			0.698482i
$543$		−	9.42113e14i		−	0.856454i
$544$	−1.08605e14			−0.0977366
$545$	−3.83675e14	+	1.01543e14i	−0.341808	+	0.0904623i
$546$	5.36619e14			0.473267
$547$			5.91724e13i			0.0516641i	0.999666	+	0.0258321i	$0.00822352\pi$
$547$			5.91724e13i			0.0516641i	−0.999666	+	0.0258321i	$0.991776\pi$
$548$		−	1.05901e15i		−	0.915395i
$549$	−4.40328e14			−0.376815
$550$	−6.48881e14	−	1.14002e15i	−0.549756	−	0.965866i
$551$	8.44162e14			0.708096
$552$			2.36873e14i			0.196721i
$553$			9.95020e14i			0.818170i
$554$	6.40037e14			0.521077
$555$	7.51966e14	−	1.99014e14i	0.606160	−	0.160425i
$556$	−6.66624e14			−0.532071
$557$			8.98701e14i			0.710251i	0.934819	+	0.355125i	$0.115562\pi$
$557$			8.98701e14i			0.710251i	−0.934819	+	0.355125i	$0.884438\pi$
$558$		−	5.23366e14i		−	0.409560i
$559$	−1.82511e15			−1.41424
$560$	−7.78496e13	−	2.94151e14i	−0.0597341	−	0.225703i
$561$	−6.60296e14			−0.501699
$562$		−	6.91400e14i		−	0.520211i
$563$			1.00499e15i			0.748799i	0.927268	+	0.374399i	$0.122151\pi$
$563$			1.00499e15i			0.748799i	−0.927268	+	0.374399i	$0.877849\pi$
$564$	4.71113e14			0.347608
$565$	1.38886e14	+	5.24775e14i	0.101483	+	0.383448i
$566$	−1.35249e15			−0.978684
$567$		−	1.44798e14i		−	0.103766i
$568$			2.69928e14i			0.191572i
$569$	−2.14457e15			−1.50738			−0.753691	−	0.657228i	$-0.771729\pi$
$569$	−2.14457e15			−1.50738			−0.753691	+	0.657228i	$0.771729\pi$
$570$	2.85913e14	−	7.56694e13i	0.199032	−	0.0526755i
$571$	−1.36068e15			−0.938119			−0.469060	−	0.883167i	$-0.655407\pi$
$571$	−1.36068e15			−0.938119			−0.469060	+	0.883167i	$0.655407\pi$
$572$			1.42858e15i			0.975496i
$573$		−	1.05517e15i		−	0.713629i
$574$	−1.88875e14			−0.126520
$575$	7.18527e14	+	1.26238e15i	0.476727	+	0.837562i
$576$	6.34034e13			0.0416667
$577$		−	9.41505e14i		−	0.612852i	−0.951894	−	0.306426i	$-0.900867\pi$
$577$		−	9.41505e14i		−	0.612852i	0.951894	−	0.306426i	$-0.0991332\pi$
$578$		−	7.61463e14i		−	0.490960i
$579$	−1.08189e14			−0.0690955
$580$	1.07279e15	−	2.83924e14i	0.678675	−	0.179617i
$581$	−2.72400e15			−1.70702
$582$			3.43736e14i			0.213377i
$583$			1.07729e15i			0.662453i
$584$	−6.24642e14			−0.380505
$585$	1.75431e14	+	6.62857e14i	0.105864	+	0.400002i
$586$	−1.81325e15			−1.08398
$587$		−	7.11947e14i		−	0.421636i	−0.977525	−	0.210818i	$-0.932387\pi$
$587$		−	7.11947e14i		−	0.421636i	0.977525	−	0.210818i	$-0.0676128\pi$
$588$			6.29011e13i			0.0369048i
$589$	1.50760e15			0.876300
$590$	−2.86791e14	−	1.08363e15i	−0.165150	−	0.624013i
$591$	4.67169e14			0.266528
$592$			4.80350e14i			0.271512i
$593$			2.44357e15i			1.36844i	0.729278	+	0.684218i	$0.239856\pi$
$593$			2.44357e15i			1.36844i	−0.729278	+	0.684218i	$0.760144\pi$
$594$	3.85478e14			0.213882
$595$	−9.07972e14	+	2.40302e14i	−0.499148	+	0.132104i
$596$	1.52346e15			0.829808
$597$		−	6.13130e14i		−	0.330898i
$598$		−	1.58191e15i		−	0.845913i
$599$	6.81013e14			0.360835			0.180417	−	0.983590i	$-0.442255\pi$
$599$	6.81013e14			0.360835			0.180417	+	0.983590i	$0.442255\pi$
$600$	3.37899e14	−	1.92327e14i	0.177401	−	0.100974i
$601$	−1.35124e15			−0.702947			−0.351474	−	0.936198i	$-0.614319\pi$
$601$	−1.35124e15			−0.702947			−0.351474	+	0.936198i	$0.614319\pi$
$602$			1.45950e15i			0.752354i
$603$			6.73569e13i			0.0344062i
$604$	−1.74072e15			−0.881100
$605$	2.83366e15	−	7.49951e14i	1.42132	−	0.376165i
$606$	−1.46496e15			−0.728161
$607$		−	2.98246e15i		−	1.46905i	−0.678582	−	0.734524i	$-0.737405\pi$
$607$		−	2.98246e15i		−	1.46905i	0.678582	−	0.734524i	$-0.262595\pi$
$608$			1.82639e14i			0.0891506i
$609$	1.56504e15			0.757059
$610$	−4.26612e14	−	1.61194e15i	−0.204512	−	0.772741i
$611$	−3.14624e15			−1.49474
$612$		−	1.95710e14i		−	0.0921470i
$613$			2.62361e15i			1.22424i	0.790766	+	0.612119i	$0.209683\pi$
$613$			2.62361e15i			1.22424i	−0.790766	+	0.612119i	$0.790317\pi$
$614$	6.37964e14			0.295032
$615$	−6.17467e13	−	2.33307e14i	−0.0283009	−	0.106934i
$616$	1.14240e15			0.518948
$617$		−	1.36222e15i		−	0.613310i	−0.951821	−	0.306655i	$-0.900790\pi$
$617$		−	1.36222e15i		−	0.613310i	0.951821	−	0.306655i	$-0.0992098\pi$
$618$		−	1.36028e15i		−	0.607003i
$619$	4.10602e15			1.81603			0.908013	−	0.418942i	$-0.137599\pi$
$619$	4.10602e15			1.81603			0.908013	+	0.418942i	$0.137599\pi$
$620$	1.91592e15	−	5.07064e14i	0.839891	−	0.222284i
$621$	−4.26853e14			−0.185470
$622$		−	3.37086e14i		−	0.145176i
$623$			1.32255e15i			0.564585i
$624$	−4.23428e14			−0.179169
$625$	1.21738e15	−	2.04996e15i	0.510607	−	0.859814i
$626$	1.68754e15			0.701608
$627$			1.11040e15i			0.457625i
$628$			3.84757e14i			0.157184i
$629$	1.48272e15			0.600455
$630$	5.30070e14	−	1.40288e14i	0.212795	−	0.0563178i
$631$	−3.07651e15			−1.22433			−0.612163	−	0.790731i	$-0.709700\pi$
$631$	−3.07651e15			−1.22433			−0.612163	+	0.790731i	$0.709700\pi$
$632$		−	7.85136e14i		−	0.309743i
$633$		−	1.84742e15i		−	0.722511i
$634$	2.13859e15			0.829159
$635$	4.36928e14	+	1.65091e15i	0.167940	+	0.634554i
$636$	−3.19306e14			−0.121673
$637$		−	4.20073e14i		−	0.158693i
$638$			4.16642e15i			1.56045i
$639$	−4.86418e14			−0.180616
$640$	6.14285e13	+	2.32105e14i	0.0226141	+	0.0854465i
$641$	−2.43456e14			−0.0888590			−0.0444295	−	0.999013i	$-0.514147\pi$
$641$	−2.43456e14			−0.0888590			−0.0444295	+	0.999013i	$0.514147\pi$
$642$			1.36202e15i			0.492878i
$643$		−	6.07705e14i		−	0.218038i	−0.994040	−	0.109019i	$-0.965229\pi$
$643$		−	6.07705e14i		−	0.218038i	0.994040	−	0.109019i	$-0.0347710\pi$
$644$	−1.26502e15			−0.450012
$645$	−1.80284e15	+	4.77136e14i	−0.635885	+	0.168292i
$646$	5.63761e14			0.197159
$647$		−	3.75432e14i		−	0.130184i	−0.997879	−	0.0650919i	$-0.979266\pi$
$647$		−	3.75432e14i		−	0.130184i	0.997879	−	0.0650919i	$-0.0207341\pi$
$648$			1.14255e14i			0.0392837i
$649$	4.20849e15			1.43477
$650$	−2.25660e15	+	1.28442e15i	−0.762834	+	0.434194i
$651$	2.79503e15			0.936894
$652$			1.22042e15i			0.405648i
$653$		−	2.76536e15i		−	0.911442i	−0.890123	−	0.455721i	$-0.849382\pi$
$653$		−	2.76536e15i		−	0.911442i	0.890123	−	0.455721i	$-0.150618\pi$
$654$	4.41657e14			0.144347
$655$	2.17076e14	−	5.74509e13i	0.0703533	−	0.0186196i
$656$	1.49035e14			0.0478979
$657$		−	1.12563e15i		−	0.358744i
$658$			2.51597e15i			0.795176i
$659$	−3.26634e15			−1.02374			−0.511872	−	0.859062i	$-0.671048\pi$
$659$	−3.26634e15			−1.02374			−0.511872	+	0.859062i	$0.671048\pi$
$660$	3.73471e14	+	1.41114e15i	0.116082	+	0.438611i
$661$	1.72112e15			0.530521			0.265260	−	0.964177i	$-0.414542\pi$
$661$	1.72112e15			0.530521			0.265260	+	0.964177i	$0.414542\pi$
$662$		−	8.94688e14i		−	0.273497i
$663$			1.30701e15i			0.396238i
$664$	2.14941e15			0.646242
$665$	4.04111e14	+	1.52692e15i	0.120498	+	0.455298i
$666$	−8.65606e14			−0.255984
$667$		−	4.61361e15i		−	1.35316i
$668$		−	8.05078e14i		−	0.234190i
$669$	5.99410e14			0.172934
$670$	−2.46578e14	+	6.52588e13i	−0.0705573	+	0.0186736i
$671$	6.26029e15			1.77673
$672$			3.38605e14i			0.0953152i
$673$			4.18650e15i			1.16888i	0.811438	+	0.584438i	$0.198685\pi$
$673$			4.18650e15i			1.16888i	−0.811438	+	0.584438i	$0.801315\pi$
$674$	−3.74341e15			−1.03666
$675$	3.46579e14	+	6.08905e14i	0.0951989	+	0.167255i
$676$	9.92609e14			0.270440
$677$			4.21054e15i			1.13789i	0.822376	+	0.568945i	$0.192648\pi$
$677$			4.21054e15i			1.13789i	−0.822376	+	0.568945i	$0.807352\pi$
$678$		−	6.04081e14i		−	0.161932i
$679$	−1.83571e15			−0.488114
$680$	7.16449e14	−	1.89614e14i	0.188967	−	0.0500117i
$681$	−2.70795e15			−0.708486
$682$			7.44087e15i			1.93112i
$683$		−	6.85825e15i		−	1.76563i	−0.469722	−	0.882814i	$-0.655646\pi$
$683$		−	6.85825e15i		−	1.76563i	0.469722	−	0.882814i	$-0.344354\pi$
$684$	−3.29122e14			−0.0840520
$685$	1.84893e15	+	6.98612e15i	0.468407	+	1.76986i
$686$	−2.96356e15			−0.744785
$687$		−	2.74201e15i		−	0.683607i
$688$		−	1.15164e15i		−	0.284826i
$689$	2.13243e15			0.523201
$690$	−4.13557e14	−	1.56261e15i	−0.100662	−	0.380347i
$691$	−7.01392e15			−1.69368			−0.846841	−	0.531847i	$-0.821498\pi$
$691$	−7.01392e15			−1.69368			−0.846841	+	0.531847i	$0.821498\pi$
$692$			2.67680e14i			0.0641258i
$693$			2.05864e15i			0.489269i
$694$	5.20168e13			0.0122650
$695$	4.39759e15	−	1.16386e15i	1.02872	−	0.272260i
$696$	−1.23492e15			−0.286607
$697$		−	4.60033e14i		−	0.105927i
$698$		−	4.48089e15i		−	1.02367i
$699$	8.91045e14			0.201965
$700$	1.02712e15	+	1.80454e15i	0.230984	+	0.405815i
$701$	−3.59916e15			−0.803067			−0.401533	−	0.915844i	$-0.631523\pi$
$701$	−3.59916e15			−0.803067			−0.401533	+	0.915844i	$0.631523\pi$
$702$		−	7.63030e14i		−	0.168923i
$703$		−	2.49346e15i		−	0.547706i
$704$	−9.01428e14			−0.196463
$705$	−3.10784e15	+	8.22517e14i	−0.672077	+	0.177871i
$706$	−3.45261e14			−0.0740836
$707$		−	7.82361e15i		−	1.66571i
$708$			1.24739e15i			0.263523i
$709$	−9.13743e15			−1.91544			−0.957722	−	0.287695i	$-0.907111\pi$
$709$	−9.13743e15			−1.91544			−0.957722	+	0.287695i	$0.907111\pi$
$710$	−4.71267e14	−	1.78066e15i	−0.0980271	−	0.370391i
$711$	1.41484e15			0.292028
$712$		−	1.04358e15i		−	0.213740i
$713$		−	8.23952e15i		−	1.67459i
$714$	1.04519e15			0.210792
$715$	−2.49416e15	−	9.42406e15i	−0.499161	−	1.88606i
$716$	1.10678e15			0.219807
$717$			3.40659e15i			0.671375i
$718$		−	2.67589e15i		−	0.523340i
$719$	4.61453e15			0.895609			0.447805	−	0.894131i	$-0.352206\pi$
$719$	4.61453e15			0.895609			0.447805	+	0.894131i	$0.352206\pi$
$720$	−4.18260e14	+	1.10696e14i	−0.0805597	+	0.0213208i
$721$	7.26454e15			1.38856
$722$			2.77962e15i			0.527268i
$723$			2.91271e15i			0.548323i
$724$	−3.97006e15			−0.741711
$725$	−6.58131e15	+	3.74598e15i	−1.22026	+	0.694555i
$726$	−3.26189e15			−0.600231
$727$			4.47421e15i			0.817104i	0.912735	+	0.408552i	$0.133966\pi$
$727$			4.47421e15i			0.817104i	−0.912735	+	0.408552i	$0.866034\pi$
$728$		−	2.26131e15i		−	0.409861i
$729$	−2.05891e14			−0.0370370
$730$	4.12065e15	−	1.09056e15i	0.735682	−	0.194704i
$731$	−3.55482e15			−0.629901
$732$			1.85554e15i			0.326332i
$733$		−	4.68168e15i		−	0.817203i	−0.912713	−	0.408601i	$-0.866017\pi$
$733$		−	4.68168e15i		−	0.817203i	0.912713	−	0.408601i	$-0.133983\pi$
$734$	−3.20156e14			−0.0554669
$735$	−1.09819e14	−	4.14947e14i	−0.0188842	−	0.0713530i
$736$	9.98181e14			0.170365
$737$		−	9.57636e14i		−	0.162229i
$738$			2.68565e14i			0.0451586i
$739$	−5.58278e15			−0.931764			−0.465882	−	0.884847i	$-0.654263\pi$
$739$	−5.58278e15			−0.931764			−0.465882	+	0.884847i	$0.654263\pi$
$740$	−8.38644e14	−	3.16878e15i	−0.138932	−	0.524950i
$741$	2.19798e15			0.361429
$742$		−	1.70525e15i		−	0.278334i
$743$			5.84984e15i			0.947776i	0.880585	+	0.473888i	$0.157150\pi$
$743$			5.84984e15i			0.947776i	−0.880585	+	0.473888i	$0.842850\pi$
$744$	−2.20546e15			−0.354689
$745$	−1.00500e16	+	2.65982e15i	−1.60438	+	0.424612i
$746$	7.43568e15			1.17830
$747$			3.87331e15i			0.609283i
$748$			2.78248e15i			0.434484i
$749$	−7.27383e15			−1.12749
$750$	−1.89327e15	+	1.85868e15i	−0.291324	+	0.286002i
$751$	6.23385e15			0.952218			0.476109	−	0.879386i	$-0.342047\pi$
$751$	6.23385e15			0.952218			0.476109	+	0.879386i	$0.342047\pi$
$752$		−	1.98527e15i		−	0.301037i
$753$			1.14646e15i			0.172578i
$754$	8.24716e15			1.23243
$755$	1.14832e16	−	3.03912e15i	1.70355	−	0.450858i
$756$	−6.10177e14			−0.0898640
$757$			1.20579e16i			1.76297i	0.472210	+	0.881486i	$0.343457\pi$
$757$			1.20579e16i			1.76297i	−0.472210	+	0.881486i	$0.656543\pi$
$758$			5.14887e15i			0.747362i
$759$	6.06871e15			0.874514
$760$	−3.18870e14	−	1.20484e15i	−0.0456183	−	0.172367i
$761$	5.06900e15			0.719957			0.359979	−	0.932961i	$-0.382784\pi$
$761$	5.06900e15			0.719957			0.359979	+	0.932961i	$0.382784\pi$
$762$		−	1.90040e15i		−	0.267975i
$763$			2.35866e15i			0.330203i
$764$	−4.44649e15			−0.618021
$765$	3.41691e14	+	1.29106e15i	0.0471515	+	0.178160i
$766$	−1.09192e14			−0.0149601
$767$		−	8.33045e15i		−	1.13317i
$768$		−	2.67181e14i		−	0.0360844i
$769$	−1.35439e15			−0.181614			−0.0908072	−	0.995868i	$-0.528945\pi$
$769$	−1.35439e15			−0.181614			−0.0908072	+	0.995868i	$0.528945\pi$
$770$	−7.53619e15	+	1.99452e15i	−1.00335	+	0.265545i
$771$	5.49612e15			0.726537
$772$			4.55906e14i			0.0598384i
$773$			8.61815e15i			1.12312i	0.827435	+	0.561561i	$0.189799\pi$
$773$			8.61815e15i			1.12312i	−0.827435	+	0.561561i	$0.810201\pi$
$774$	2.07529e15			0.268537
$775$	−1.17537e16	+	6.69001e15i	−1.51013	+	0.859543i
$776$	1.44850e15			0.184790
$777$		−	4.62276e15i		−	0.585579i
$778$		−	7.99727e15i		−	1.00590i
$779$	−7.73627e14			−0.0966219
$780$	2.79327e15	−	7.39263e14i	0.346412	−	0.0916808i
$781$	6.91557e15			0.851623
$782$		−	3.08113e15i		−	0.376767i
$783$		−	2.22536e15i		−	0.270216i
$784$	2.65065e14			0.0319605
$785$	−6.71749e14	−	2.53817e15i	−0.0804311	−	0.303905i
$786$	−2.49881e14			−0.0297105
$787$			4.95922e15i			0.585534i	0.956184	+	0.292767i	$0.0945761\pi$
$787$			4.95922e15i			0.585534i	−0.956184	+	0.292767i	$0.905424\pi$
$788$		−	1.96864e15i		−	0.230820i
$789$	−6.41268e15			−0.746649
$790$	1.37077e15	+	5.17940e15i	0.158495	+	0.598867i
$791$	3.22608e15			0.370429
$792$		−	1.62440e15i		−	0.185227i
$793$		−	1.23919e16i		−	1.40325i
$794$	8.03123e15			0.903170
$795$	2.10640e15	−	5.57477e14i	0.235246	−	0.0622598i
$796$	−2.58372e15			−0.286566
$797$			1.48779e16i			1.63878i	0.573235	+	0.819391i	$0.305688\pi$
$797$			1.48779e16i			1.63878i	−0.573235	+	0.819391i	$0.694312\pi$
$798$		−	1.75767e15i		−	0.192274i
$799$	−6.12802e15			−0.665752
$800$	−8.10464e14	−	1.42390e15i	−0.0874458	−	0.153633i
$801$	1.88057e15			0.201516
$802$		−	1.14047e16i		−	1.21374i
$803$			1.60034e16i			1.69152i
$804$	2.83841e14			0.0297966
$805$	8.34507e15	−	2.20859e15i	0.870067	−	0.230271i
$806$	1.47287e16			1.52519
$807$			4.44347e15i			0.457002i
$808$			6.17335e15i			0.630606i
$809$	1.18817e16			1.20549			0.602744	−	0.797935i	$-0.294074\pi$
$809$	1.18817e16			1.20549			0.602744	+	0.797935i	$0.294074\pi$
$810$	−1.99478e14	−	7.53719e14i	−0.0201014	−	0.0759524i
$811$	−7.07941e14			−0.0708569			−0.0354284	−	0.999372i	$-0.511280\pi$
$811$	−7.07941e14			−0.0708569			−0.0354284	+	0.999372i	$0.511280\pi$
$812$		−	6.59506e15i		−	0.655632i
$813$			5.77574e15i			0.570309i
$814$	1.23066e16			1.20699
$815$	−2.13074e15	−	8.05091e15i	−0.207570	−	0.784293i
$816$	−8.24722e14			−0.0798016
$817$			5.97806e15i			0.574565i
$818$		−	1.52592e15i		−	0.145676i
$819$	4.07495e15			0.386421
$820$	−9.83155e14	+	2.60200e14i	−0.0926074	+	0.0245093i
$821$	4.20085e15			0.393052			0.196526	−	0.980499i	$-0.437034\pi$
$821$	4.20085e15			0.393052			0.196526	+	0.980499i	$0.437034\pi$
$822$		−	8.04189e15i		−	0.747417i
$823$		−	1.76608e16i		−	1.63046i	−0.579135	−	0.815232i	$-0.696609\pi$
$823$		−	1.76608e16i		−	1.63046i	0.579135	−	0.815232i	$-0.303391\pi$
$824$	−5.73220e15			−0.525680
$825$	−4.92744e15	−	8.65701e15i	−0.448874	−	0.788626i
$826$	−6.66166e15			−0.602826
$827$			7.42500e15i			0.667446i	0.942671	+	0.333723i	$0.108305\pi$
$827$			7.42500e15i			0.667446i	−0.942671	+	0.333723i	$0.891695\pi$
$828$			1.79875e15i			0.160622i
$829$	1.02610e16			0.910208			0.455104	−	0.890438i	$-0.349602\pi$
$829$	1.02610e16			0.910208			0.455104	+	0.890438i	$0.349602\pi$
$830$	−1.41793e16	+	3.75266e15i	−1.24947	+	0.330682i
$831$	4.86028e15			0.425457
$832$			1.78432e15i			0.155165i
$833$		−	8.18189e14i		−	0.0706816i
$834$	−5.06217e15			−0.434434
$835$	1.40559e15	+	5.31095e15i	0.119835	+	0.452790i
$836$	4.67924e15			0.396315
$837$		−	3.97431e15i		−	0.334404i
$838$			7.25923e15i			0.606804i
$839$	−5.46116e15			−0.453518			−0.226759	−	0.973951i	$-0.572813\pi$
$839$	−5.46116e15			−0.453518			−0.226759	+	0.973951i	$0.572813\pi$
$840$	−5.91171e14	−	2.23371e15i	−0.0487727	−	0.184285i
$841$	1.18522e16			0.971449
$842$			4.37055e15i			0.355893i
$843$		−	5.25032e15i		−	0.424750i
$844$	−7.78500e15			−0.625713
$845$	−6.54806e15	+	1.73300e15i	−0.522878	+	0.138384i
$846$	3.57751e15			0.283821
$847$		−	1.74201e16i		−	1.37307i
$848$			1.34555e15i			0.105372i
$849$	−1.02704e16			−0.799092
$850$	−4.39523e15	+	2.50170e15i	−0.339764	+	0.193389i
$851$	−1.36275e16			−1.04666
$852$			2.04976e15i			0.156418i
$853$			1.38989e16i			1.05380i	0.849926	+	0.526902i	$0.176647\pi$
$853$			1.38989e16i			1.05380i	−0.849926	+	0.526902i	$0.823353\pi$
$854$	−9.90947e15			−0.746504
$855$	2.17115e15	−	5.74614e14i	0.162509	−	0.0430093i
$856$	5.73953e15			0.426845
$857$		−	1.35605e16i		−	1.00203i	−0.865437	−	0.501017i	$-0.832959\pi$
$857$		−	1.35605e16i		−	1.00203i	0.865437	−	0.501017i	$-0.167041\pi$
$858$			1.08483e16i			0.796490i
$859$	−4.45328e15			−0.324876			−0.162438	−	0.986719i	$-0.551936\pi$
$859$	−4.45328e15			−0.324876			−0.162438	+	0.986719i	$0.551936\pi$
$860$	2.01065e15	+	7.59715e15i	0.145745	+	0.550692i
$861$	−1.43427e15			−0.103303
$862$		−	3.87209e14i		−	0.0277112i
$863$			1.15395e16i			0.820593i	0.911952	+	0.410297i	$0.134575\pi$
$863$			1.15395e16i			0.820593i	−0.911952	+	0.410297i	$0.865425\pi$
$864$	4.81469e14			0.0340207
$865$	−4.67344e14	−	1.76584e15i	−0.0328131	−	0.123983i
$866$	−9.79127e15			−0.683110
$867$		−	5.78236e15i		−	0.400867i
$868$		−	1.17782e16i		−	0.811374i
$869$	−2.01153e16			−1.37695
$870$	8.14652e15	−	2.15604e15i	0.554136	−	0.146657i
$871$	−1.89558e15			−0.128128
$872$		−	1.86114e15i		−	0.125008i
$873$			2.61024e15i			0.174222i
$874$	−5.18147e15			−0.343669
$875$	−9.92627e15	−	1.01110e16i	−0.654247	−	0.666422i
$876$	−4.74338e15			−0.310681
$877$		−	1.61714e16i		−	1.05257i	−0.850308	−	0.526285i	$-0.823584\pi$
$877$		−	1.61714e16i		−	1.05257i	0.850308	−	0.526285i	$-0.176416\pi$
$878$			1.17807e16i			0.761994i
$879$	−1.37693e16			−0.885064
$880$	5.94655e15	−	1.57380e15i	0.379848	−	0.100530i
$881$	−2.06661e16			−1.31187			−0.655936	−	0.754817i	$-0.727726\pi$
$881$	−2.06661e16			−1.31187			−0.655936	+	0.754817i	$0.727726\pi$
$882$			4.77656e14i			0.0301327i
$883$		−	2.69113e15i		−	0.168714i	−0.996436	−	0.0843569i	$-0.973116\pi$
$883$		−	2.69113e15i		−	0.168714i	0.996436	−	0.0843569i	$-0.0268836\pi$
$884$	5.50775e15			0.343152
$885$	−2.17782e15	−	8.22880e15i	−0.134845	−	0.509505i
$886$	−4.44728e14			−0.0273659
$887$			2.20727e16i			1.34982i	0.737900	+	0.674911i	$0.235818\pi$
$887$			2.20727e16i			1.34982i	−0.737900	+	0.674911i	$0.764182\pi$
$888$			3.64766e15i			0.221688i
$889$	1.01491e16			0.613009
$890$	1.82199e15	+	6.88431e15i	0.109371	+	0.413253i
$891$	2.92722e15			0.174634
$892$		−	2.52591e15i		−	0.149765i
$893$			1.03053e16i			0.607267i
$894$	1.15688e16			0.677535
$895$	−7.30125e15	+	1.93234e15i	−0.424982	+	0.112475i
$896$	1.42688e15			0.0825453
$897$		−	1.20126e16i		−	0.690685i
$898$			1.25560e15i			0.0717518i
$899$	4.29561e16			2.43976
$900$	2.56592e15	−	1.46048e15i	0.144847	−	0.0824447i
$901$	4.15339e15			0.233032
$902$		−	3.81829e15i		−	0.212928i
$903$			1.10831e16i			0.614295i
$904$	−2.54559e15			−0.140237
$905$	2.61897e16	−	6.93133e15i	1.43405	−	0.379533i
$906$	−1.32186e16			−0.719416
$907$			2.50362e16i			1.35434i	0.735827	+	0.677170i	$0.236794\pi$
$907$			2.50362e16i			1.35434i	−0.735827	+	0.677170i	$0.763206\pi$
$908$			1.14113e16i			0.613567i
$909$	−1.11246e16			−0.594541
$910$	3.94802e15	+	1.49174e16i	0.209726	+	0.792440i
$911$	−1.34918e16			−0.712393			−0.356196	−	0.934411i	$-0.615927\pi$
$911$	−1.34918e16			−0.712393			−0.356196	+	0.934411i	$0.615927\pi$
$912$			1.38692e15i			0.0727912i
$913$		−	5.50682e16i		−	2.87284i
$914$	−4.39044e15			−0.227669
$915$	−3.23959e15	−	1.22406e16i	−0.166984	−	0.630940i
$916$	−1.15548e16			−0.592021
$917$		−	1.33449e15i		−	0.0679646i
$918$		−	1.48618e15i		−	0.0752377i
$919$	−1.86406e16			−0.938048			−0.469024	−	0.883185i	$-0.655394\pi$
$919$	−1.86406e16			−0.938048			−0.469024	+	0.883185i	$0.655394\pi$
$920$	−6.58481e15	+	1.74273e15i	−0.329390	+	0.0871758i
$921$	4.84454e15			0.240893
$922$		−	7.95708e15i		−	0.393309i
$923$		−	1.36889e16i		−	0.672606i
$924$	8.67509e15			0.423719
$925$	1.10648e16	+	1.94397e16i	0.537233	+	0.943864i
$926$	2.02006e16			0.974997
$927$		−	1.03296e16i		−	0.495616i
$928$			5.20393e15i			0.248209i
$929$	−1.26618e16			−0.600358			−0.300179	−	0.953883i	$-0.597046\pi$
$929$	−1.26618e16			−0.600358			−0.300179	+	0.953883i	$0.597046\pi$
$930$	1.45490e16	−	3.85052e15i	0.685768	−	0.181494i
$931$	−1.37593e15			−0.0644723
$932$		−	3.75486e15i		−	0.174906i
$933$		−	2.55975e15i		−	0.118535i
$934$	−2.75279e16			−1.26726
$935$	−4.85794e15	−	1.83555e16i	−0.222325	−	0.840045i
$936$	−3.21540e15			−0.146291
$937$			3.98788e16i			1.80374i	0.432006	+	0.901871i	$0.357806\pi$
$937$			3.98788e16i			1.80374i	−0.432006	+	0.901871i	$0.642194\pi$
$938$			1.51585e15i			0.0681617i
$939$	1.28147e16			0.572861
$940$	3.46608e15	+	1.30964e16i	0.154041	+	0.582036i
$941$	−2.35800e16			−1.04184			−0.520920	−	0.853606i	$-0.674411\pi$
$941$	−2.35800e16			−1.04184			−0.520920	+	0.853606i	$0.674411\pi$
$942$			2.92175e15i			0.128340i
$943$			4.22812e15i			0.184643i
$944$	5.25649e15			0.228218
$945$	4.02522e15	−	1.06531e15i	0.173746	−	0.0459833i
$946$	−2.95051e16			−1.26618
$947$			2.50128e16i			1.06718i	0.845743	+	0.533591i	$0.179158\pi$
$947$			2.50128e16i			1.06718i	−0.845743	+	0.533591i	$0.820842\pi$
$948$		−	5.96213e15i		−	0.252904i
$949$	3.16778e16			1.33595
$950$	4.20705e15	+	7.39137e15i	0.176400	+	0.309917i
$951$	1.62400e16			0.677005
$952$		−	4.40441e15i		−	0.182551i
$953$		−	3.78726e16i		−	1.56068i	−0.625355	−	0.780340i	$-0.715046\pi$
$953$		−	3.78726e16i		−	1.56068i	0.625355	−	0.780340i	$-0.284954\pi$
$954$	−2.42473e15			−0.0993453
$955$	2.93326e16	−	7.76313e15i	1.19490	−	0.316241i
$956$	1.43554e16			0.581427
$957$			3.16387e16i			1.27410i
$958$		−	1.83005e16i		−	0.732744i
$959$	4.29476e16			1.70976
$960$	4.66472e14	+	1.76255e15i	0.0184644	+	0.0697668i
$961$	5.13075e16			2.01931
$962$		−	2.43602e16i		−	0.953274i
$963$			1.03428e16i			0.402433i
$964$	1.22741e16			0.474862
$965$	−7.95967e14	−	3.00753e15i	−0.0306193	−	0.115694i
$966$	−9.60621e15			−0.367433
$967$		−	1.01035e16i		−	0.384262i	−0.981369	−	0.192131i	$-0.938460\pi$
$967$		−	1.01035e16i		−	0.384262i	0.981369	−	0.192131i	$-0.0615398\pi$
$968$			1.37456e16i			0.519815i
$969$	4.28106e15			0.160980
$970$	−9.55548e15	+	2.52894e15i	−0.357279	+	0.0945570i
$971$	−1.09869e16			−0.408478			−0.204239	−	0.978921i	$-0.565472\pi$
$971$	−1.09869e16			−0.408478			−0.204239	+	0.978921i	$0.565472\pi$
$972$			8.67624e14i			0.0320750i
$973$		−	2.70344e16i		−	0.993795i
$974$	2.54464e16			0.930148
$975$	−1.71360e16	+	9.75356e15i	−0.622852	+	0.354518i
$976$	7.81922e15			0.282611
$977$		−	2.52822e16i		−	0.908644i	−0.890837	−	0.454322i	$-0.849881\pi$
$977$		−	2.52822e16i		−	0.908644i	0.890837	−	0.454322i	$-0.150119\pi$
$978$			9.26760e15i			0.331210i
$979$	−2.67367e16			−0.950173
$980$	−1.74858e15	+	4.62777e14i	−0.0617935	+	0.0163542i
$981$	3.35383e15			0.117859
$982$			1.61320e15i			0.0563734i
$983$			4.29168e16i			1.49136i	0.666304	+	0.745680i	$0.267875\pi$
$983$			4.29168e16i			1.49136i	−0.666304	+	0.745680i	$0.732125\pi$
$984$	1.13173e15			0.0391085
$985$	3.43706e15	+	1.29868e16i	0.118110	+	0.446275i
$986$	1.60632e16			0.548921
$987$			1.91056e16i			0.649258i
$988$		−	9.26226e15i		−	0.313007i
$989$	3.26720e16			1.09798
$990$	2.83605e15	+	1.07159e16i	0.0947807	+	0.358125i
$991$	−5.20325e16			−1.72930			−0.864648	−	0.502377i	$-0.832459\pi$
$991$	−5.20325e16			−1.72930			−0.864648	+	0.502377i	$0.832459\pi$
$992$			9.29379e15i			0.307170i
$993$		−	6.79404e15i		−	0.223309i
$994$	−1.09467e16			−0.357815
$995$	1.70443e16	−	4.51093e15i	0.554056	−	0.146635i
$996$	1.63221e16			0.527654
$997$			5.42887e16i			1.74537i	0.488288	+	0.872683i	$0.337622\pi$
$997$			5.42887e16i			1.74537i	−0.488288	+	0.872683i	$0.662378\pi$
$998$		−	9.33872e15i		−	0.298586i
$999$	−6.57320e15			−0.209010

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.12.c.b.19.3	✓	6
3.2	odd	2		90.12.c.c.19.4		6
4.3	odd	2		240.12.f.b.49.6		6
5.2	odd	4		150.12.a.u.1.2		3
5.3	odd	4		150.12.a.t.1.2		3
5.4	even	2	inner	30.12.c.b.19.6	yes	6
15.14	odd	2		90.12.c.c.19.1		6
20.19	odd	2		240.12.f.b.49.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.c.b.19.3	✓	6	1.1	even	1	trivial
30.12.c.b.19.6	yes	6	5.4	even	2	inner
90.12.c.c.19.1		6	15.14	odd	2
90.12.c.c.19.4		6	3.2	odd	2
150.12.a.t.1.2		3	5.3	odd	4
150.12.a.u.1.2		3	5.2	odd	4
240.12.f.b.49.3		6	20.19	odd	2
240.12.f.b.49.6		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} +(6755.14 - 1787.80i) q^{5} -7776.00 q^{6} -41527.6i q^{7} +32768.0i q^{8} -59049.0 q^{9} +(-57209.7 - 216164. i) q^{10} +839520. q^{11} +248832. i q^{12} -1.66178e6i q^{13} -1.32888e6 q^{14} +(-434436. - 1.64150e6i) q^{15} +1.04858e6 q^{16} -3.23669e6i q^{17} +1.88957e6i q^{18} -5.44307e6 q^{19} +(-6.91726e6 + 1.83071e6i) q^{20} -1.00912e7 q^{21} -2.68646e7i q^{22} +2.97481e7i q^{23} +7.96262e6 q^{24} +(4.24356e7 - 2.41537e7i) q^{25} -5.31769e7 q^{26} +1.43489e7i q^{27} +4.25243e7i q^{28} -1.55089e8 q^{29} +(-5.25279e7 + 1.39020e7i) q^{30} -2.76977e8 q^{31} -3.35544e7i q^{32} -2.04003e8i q^{33} -1.03574e8 q^{34} +(-7.42432e7 - 2.80525e8i) q^{35} +6.04662e7 q^{36} +4.58098e8i q^{37} +1.74178e8i q^{38} -4.03812e8 q^{39} +(5.85827e7 + 2.21352e8i) q^{40} +1.42131e8 q^{41} +3.22919e8i q^{42} -1.09829e9i q^{43} -8.59668e8 q^{44} +(-3.98884e8 + 1.05568e8i) q^{45} +9.51939e8 q^{46} -1.89330e9i q^{47} -2.54804e8i q^{48} +2.52786e8 q^{49} +(-7.72919e8 - 1.35794e9i) q^{50} -7.86516e8 q^{51} +1.70166e9i q^{52} +1.28322e9i q^{53} +4.59165e8 q^{54} +(5.67107e9 - 1.50090e9i) q^{55} +1.36078e9 q^{56} +1.32267e9i q^{57} +4.96286e9i q^{58} +5.01298e9 q^{59} +(4.44863e8 + 1.68089e9i) q^{60} +7.45699e9 q^{61} +8.86325e9i q^{62} +2.45216e9i q^{63} -1.07374e9 q^{64} +(-2.97093e9 - 1.12255e10i) q^{65} -6.52811e9 q^{66} -1.14069e9i q^{67} +3.31437e9i q^{68} +7.22879e9 q^{69} +(-8.97679e9 + 2.37578e9i) q^{70} +8.23753e9 q^{71} -1.93492e9i q^{72} +1.90626e10i q^{73} +1.46591e10 q^{74} +(-5.86935e9 - 1.03119e10i) q^{75} +5.57371e9 q^{76} -3.48632e10i q^{77} +1.29220e10i q^{78} -2.39605e10 q^{79} +(7.08328e9 - 1.87465e9i) q^{80} +3.48678e9 q^{81} -4.54818e9i q^{82} -6.55948e10i q^{83} +1.03334e10 q^{84} +(-5.78657e9 - 2.18643e10i) q^{85} -3.51452e10 q^{86} +3.76867e10i q^{87} +2.75094e10i q^{88} -3.18476e10 q^{89} +(3.37818e9 + 1.27643e10i) q^{90} -6.90096e10 q^{91} -3.04621e10i q^{92} +6.73053e10i q^{93} -6.05855e10 q^{94} +(-3.67687e10 + 9.73114e9i) q^{95} -8.15373e9 q^{96} -4.42047e10i q^{97} -8.08914e9i q^{98} -4.95728e10 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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