LMFDB - Embedded newform 14.11.b.a.13.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,11,Mod(13,14)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.89500153743$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14130x^{6} + 61043589x^{4} + 87066375930x^{2} + 12363031798119 $ x^8 + 14130x^6 + 61043589x^4 + 87066375930*x^2 + 12363031798119
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{2}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.7
Root			$58.7309i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.11.b.a.13.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274 q^{2} +96.1268i q^{3} +512.000 q^{4} -5042.67i q^{5} +2175.10i q^{6} +(15326.2 + 6897.94i) q^{7} +11585.2 q^{8} +49808.6 q^{9} +O(q^{10})$	\(q+22.6274 q^{2} +96.1268i q^{3} +512.000 q^{4} -5042.67i q^{5} +2175.10i q^{6} +(15326.2 + 6897.94i) q^{7} +11585.2 q^{8} +49808.6 q^{9} -114102. i q^{10} +39488.6 q^{11} +49216.9i q^{12} -97801.9i q^{13} +(346793. + 156083. i) q^{14} +484735. q^{15} +262144. q^{16} -2.49682e6i q^{17} +1.12704e6 q^{18} +4.33604e6i q^{19} -2.58184e6i q^{20} +(-663077. + 1.47326e6i) q^{21} +893525. q^{22} -7.59420e6 q^{23} +1.11365e6i q^{24} -1.56628e7 q^{25} -2.21300e6i q^{26} +1.04641e7i q^{27} +(7.84704e6 + 3.53174e6i) q^{28} -1.43209e7 q^{29} +1.09683e7 q^{30} +1.71800e7i q^{31} +5.93164e6 q^{32} +3.79591e6i q^{33} -5.64966e7i q^{34} +(3.47840e7 - 7.72851e7i) q^{35} +2.55020e7 q^{36} +7.22320e7 q^{37} +9.81134e7i q^{38} +9.40139e6 q^{39} -5.84205e7i q^{40} +8.80529e7i q^{41} +(-1.50037e7 + 3.33361e7i) q^{42} -8.51402e7 q^{43} +2.02182e7 q^{44} -2.51168e8i q^{45} -1.71837e8 q^{46} +1.00540e8i q^{47} +2.51991e7i q^{48} +(1.87312e8 + 2.11439e8i) q^{49} -3.54410e8 q^{50} +2.40011e8 q^{51} -5.00746e7i q^{52} -2.82493e8 q^{53} +2.36776e8i q^{54} -1.99128e8i q^{55} +(1.77558e8 + 7.99143e7i) q^{56} -4.16810e8 q^{57} -3.24045e8 q^{58} -1.83928e8i q^{59} +2.48185e8 q^{60} -1.70972e8i q^{61} +3.88739e8i q^{62} +(7.63379e8 + 3.43577e8i) q^{63} +1.34218e8 q^{64} -4.93182e8 q^{65} +8.58917e7i q^{66} +1.83033e9 q^{67} -1.27837e9i q^{68} -7.30007e8i q^{69} +(7.87072e8 - 1.74876e9i) q^{70} -1.43321e9 q^{71} +5.77045e8 q^{72} +2.62693e9i q^{73} +1.63442e9 q^{74} -1.50562e9i q^{75} +2.22005e9i q^{76} +(6.05212e8 + 2.72390e8i) q^{77} +2.12729e8 q^{78} -3.22612e9 q^{79} -1.32190e9i q^{80} +1.93527e9 q^{81} +1.99241e9i q^{82} -4.12390e8i q^{83} +(-3.39495e8 + 7.54311e8i) q^{84} -1.25906e10 q^{85} -1.92650e9 q^{86} -1.37662e9i q^{87} +4.57485e8 q^{88} +8.95824e9i q^{89} -5.68329e9i q^{90} +(6.74632e8 - 1.49894e9i) q^{91} -3.88823e9 q^{92} -1.65146e9 q^{93} +2.27496e9i q^{94} +2.18652e10 q^{95} +5.70190e8i q^{96} +1.03188e9i q^{97} +(4.23839e9 + 4.78432e9i) q^{98} +1.96687e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9}+O(q^{10}) $ 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9	$ 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9} + 430800 q^{11} - 136704 q^{14} - 1896960 q^{15} + 2097152 q^{16} - 4512768 q^{18} + 5339136 q^{21} + 13228032 q^{22} + 6265488 q^{23} - 28719160 q^{25} + 9408512 q^{28} - 46431408 q^{29} + 28584960 q^{30} + 184450560 q^{35} - 126185472 q^{36} + 360932816 q^{37} - 836120064 q^{39} + 308382720 q^{42} + 32112848 q^{43} + 220569600 q^{44} - 769191936 q^{46} + 853888904 q^{49} - 53836800 q^{50} + 1737904128 q^{51} - 1132258608 q^{53} - 69992448 q^{56} - 2040889344 q^{57} + 352352256 q^{58} - 971243520 q^{60} + 2661283080 q^{63} + 1073741824 q^{64} - 143001600 q^{65} - 2254742192 q^{67} + 402662400 q^{70} + 2121911184 q^{71} - 2310537216 q^{72} + 4970207232 q^{74} - 17516185008 q^{77} + 1916728320 q^{78} - 5257367792 q^{79} + 24706423944 q^{81} + 2733637632 q^{84} + 4331212800 q^{85} - 14424637440 q^{86} + 6772752384 q^{88} - 8536548864 q^{91} + 3207929856 q^{92} - 20748386304 q^{93} + 30330078720 q^{95} - 802977792 q^{98} - 16331376816 q^{99}+O(q^{100}) $ 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9 + 430800 * q^11 - 136704 * q^14 - 1896960 * q^15 + 2097152 * q^16 - 4512768 * q^18 + 5339136 * q^21 + 13228032 * q^22 + 6265488 * q^23 - 28719160 * q^25 + 9408512 * q^28 - 46431408 * q^29 + 28584960 * q^30 + 184450560 * q^35 - 126185472 * q^36 + 360932816 * q^37 - 836120064 * q^39 + 308382720 * q^42 + 32112848 * q^43 + 220569600 * q^44 - 769191936 * q^46 + 853888904 * q^49 - 53836800 * q^50 + 1737904128 * q^51 - 1132258608 * q^53 - 69992448 * q^56 - 2040889344 * q^57 + 352352256 * q^58 - 971243520 * q^60 + 2661283080 * q^63 + 1073741824 * q^64 - 143001600 * q^65 - 2254742192 * q^67 + 402662400 * q^70 + 2121911184 * q^71 - 2310537216 * q^72 + 4970207232 * q^74 - 17516185008 * q^77 + 1916728320 * q^78 - 5257367792 * q^79 + 24706423944 * q^81 + 2733637632 * q^84 + 4331212800 * q^85 - 14424637440 * q^86 + 6772752384 * q^88 - 8536548864 * q^91 + 3207929856 * q^92 - 20748386304 * q^93 + 30330078720 * q^95 - 802977792 * q^98 - 16331376816 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	22.6274			0.707107
$2$	22.6274			0.707107
$3$			96.1268i			0.395584i	0.980244	+	0.197792i	$0.0633770\pi$
$3$			96.1268i			0.395584i	−0.980244	+	0.197792i	$0.936623\pi$
$4$	512.000			0.500000
$5$		−	5042.67i		−	1.61365i	−0.590789	−	0.806826i	$-0.701183\pi$
$5$		−	5042.67i		−	1.61365i	0.590789	−	0.806826i	$-0.298817\pi$
$6$			2175.10i			0.279720i
$7$	15326.2	+	6897.94i	0.911896	+	0.410421i
$7$	15326.2	+	6897.94i	0.911896	+	0.410421i
$8$	11585.2			0.353553
$9$	49808.6			0.843514
$10$		−	114102.i		−	1.14102i
$11$	39488.6			0.245193			0.122597	−	0.992457i	$-0.460878\pi$
$11$	39488.6			0.245193			0.122597	+	0.992457i	$0.460878\pi$
$12$			49216.9i			0.197792i
$13$		−	97801.9i		−	0.263409i	−0.991289	−	0.131704i	$-0.957955\pi$
$13$		−	97801.9i		−	0.263409i	0.991289	−	0.131704i	$-0.0420450\pi$
$14$	346793.	+	156083.i	0.644808	+	0.290211i
$15$	484735.			0.638335
$16$	262144.			0.250000
$17$		−	2.49682e6i		−	1.75850i	−0.476359	−	0.879251i	$-0.658044\pi$
$17$		−	2.49682e6i		−	1.75850i	0.476359	−	0.879251i	$-0.341956\pi$
$18$	1.12704e6			0.596454
$19$			4.33604e6i			1.75116i	0.483076	+	0.875579i	$0.339520\pi$
$19$			4.33604e6i			1.75116i	−0.483076	+	0.875579i	$0.660480\pi$
$20$		−	2.58184e6i		−	0.806826i
$21$	−663077.	+	1.47326e6i	−0.162356	+	0.360731i
$22$	893525.			0.173378
$23$	−7.59420e6			−1.17989			−0.589947	−	0.807442i	$-0.700851\pi$
$23$	−7.59420e6			−1.17989			−0.589947	+	0.807442i	$0.700851\pi$
$24$			1.11365e6i			0.139860i
$25$	−1.56628e7			−1.60388
$26$		−	2.21300e6i		−	0.186258i
$27$			1.04641e7i			0.729264i
$28$	7.84704e6	+	3.53174e6i	0.455948	+	0.205210i
$29$	−1.43209e7			−0.698201			−0.349100	−	0.937085i	$-0.613513\pi$
$29$	−1.43209e7			−0.698201			−0.349100	+	0.937085i	$0.613513\pi$
$30$	1.09683e7			0.451371
$31$			1.71800e7i			0.600088i	0.953925	+	0.300044i	$0.0970013\pi$
$31$			1.71800e7i			0.600088i	−0.953925	+	0.300044i	$0.902999\pi$
$32$	5.93164e6			0.176777
$33$			3.79591e6i			0.0969944i
$34$		−	5.64966e7i		−	1.24345i
$35$	3.47840e7	−	7.72851e7i	0.662276	−	1.47148i
$36$	2.55020e7			0.421757
$37$	7.22320e7			1.04165			0.520824	−	0.853664i	$-0.325625\pi$
$37$	7.22320e7			1.04165			0.520824	+	0.853664i	$0.325625\pi$
$38$			9.81134e7i			1.23826i
$39$	9.40139e6			0.104200
$40$		−	5.84205e7i		−	0.570512i
$41$			8.80529e7i			0.760019i	0.924983	+	0.380009i	$0.124079\pi$
$41$			8.80529e7i			0.760019i	−0.924983	+	0.380009i	$0.875921\pi$
$42$	−1.50037e7	+	3.33361e7i	−0.114803	+	0.255076i
$43$	−8.51402e7			−0.579151			−0.289576	−	0.957155i	$-0.593514\pi$
$43$	−8.51402e7			−0.579151			−0.289576	+	0.957155i	$0.593514\pi$
$44$	2.02182e7			0.122597
$45$		−	2.51168e8i		−	1.36114i
$46$	−1.71837e8			−0.834311
$47$			1.00540e8i			0.438379i	0.975682	+	0.219189i	$0.0703413\pi$
$47$			1.00540e8i			0.438379i	−0.975682	+	0.219189i	$0.929659\pi$
$48$			2.51991e7i			0.0988959i
$49$	1.87312e8	+	2.11439e8i	0.663110	+	0.748522i
$50$	−3.54410e8			−1.13411
$51$	2.40011e8			0.695634
$52$		−	5.00746e7i		−	0.131704i
$53$	−2.82493e8			−0.675505			−0.337752	−	0.941235i	$-0.609667\pi$
$53$	−2.82493e8			−0.675505			−0.337752	+	0.941235i	$0.609667\pi$
$54$			2.36776e8i			0.515667i
$55$		−	1.99128e8i		−	0.395656i
$56$	1.77558e8	+	7.99143e7i	0.322404	+	0.145106i
$57$	−4.16810e8			−0.692729
$58$	−3.24045e8			−0.493702
$59$		−	1.83928e8i		−	0.257269i	−0.991692	−	0.128635i	$-0.958941\pi$
$59$		−	1.83928e8i		−	0.257269i	0.991692	−	0.128635i	$-0.0410594\pi$
$60$	2.48185e8			0.319167
$61$		−	1.70972e8i		−	0.202430i	−0.994865	−	0.101215i	$-0.967727\pi$
$61$		−	1.70972e8i		−	0.202430i	0.994865	−	0.101215i	$-0.0322731\pi$
$62$			3.88739e8i			0.424326i
$63$	7.63379e8	+	3.43577e8i	0.769197	+	0.346195i
$64$	1.34218e8			0.125000
$65$	−4.93182e8			−0.425051
$66$			8.58917e7i			0.0685854i
$67$	1.83033e9			1.35567			0.677835	−	0.735214i	$-0.262918\pi$
$67$	1.83033e9			1.35567			0.677835	+	0.735214i	$0.262918\pi$
$68$		−	1.27837e9i		−	0.879251i
$69$		−	7.30007e8i		−	0.466747i
$70$	7.87072e8	−	1.74876e9i	0.468300	−	1.04050i
$71$	−1.43321e9			−0.794361			−0.397180	−	0.917741i	$-0.630011\pi$
$71$	−1.43321e9			−0.794361			−0.397180	+	0.917741i	$0.630011\pi$
$72$	5.77045e8			0.298227
$73$			2.62693e9i			1.26717i	0.773674	+	0.633584i	$0.218417\pi$
$73$			2.62693e9i			1.26717i	−0.773674	+	0.633584i	$0.781583\pi$
$74$	1.63442e9			0.736556
$75$		−	1.50562e9i		−	0.634467i
$76$			2.22005e9i			0.875579i
$77$	6.05212e8	+	2.72390e8i	0.223591	+	0.100632i
$78$	2.12729e8			0.0736807
$79$	−3.22612e9			−1.04844			−0.524221	−	0.851582i	$-0.675644\pi$
$79$	−3.22612e9			−1.04844			−0.524221	+	0.851582i	$0.675644\pi$
$80$		−	1.32190e9i		−	0.403413i
$81$	1.93527e9			0.555029
$82$			1.99241e9i			0.537415i
$83$		−	4.12390e8i		−	0.104693i	−0.998629	−	0.0523465i	$-0.983330\pi$
$83$		−	4.12390e8i		−	0.104693i	0.998629	−	0.0523465i	$-0.0166700\pi$
$84$	−3.39495e8	+	7.54311e8i	−0.0811778	+	0.180366i
$85$	−1.25906e10			−2.83761
$86$	−1.92650e9			−0.409522
$87$		−	1.37662e9i		−	0.276197i
$88$	4.57485e8			0.0866888
$89$			8.95824e9i			1.60425i	0.597154	+	0.802126i	$0.296298\pi$
$89$			8.95824e9i			1.60425i	−0.597154	+	0.802126i	$0.703702\pi$
$90$		−	5.68329e9i		−	0.962470i
$91$	6.74632e8	−	1.49894e9i	0.108108	−	0.240202i
$92$	−3.88823e9			−0.589947
$93$	−1.65146e9			−0.237385
$94$			2.27496e9i			0.309981i
$95$	2.18652e10			2.82576
$96$			5.70190e8i			0.0699300i
$97$			1.03188e9i			0.120163i	0.998193	+	0.0600815i	$0.0191361\pi$
$97$			1.03188e9i			0.120163i	−0.998193	+	0.0600815i	$0.980864\pi$
$98$	4.23839e9	+	4.78432e9i	0.468890	+	0.529285i
$99$	1.96687e9			0.206824
$100$	−8.01938e9			−0.801938
$101$		−	1.85809e10i		−	1.76790i	−0.467577	−	0.883952i	$-0.654873\pi$
$101$		−	1.85809e10i		−	1.76790i	0.467577	−	0.883952i	$-0.345127\pi$
$102$	5.43084e9			0.491888
$103$		−	1.09696e10i		−	0.946244i	−0.880997	−	0.473122i	$-0.843127\pi$
$103$		−	1.09696e10i		−	0.946244i	0.880997	−	0.473122i	$-0.156873\pi$
$104$		−	1.13306e9i		−	0.0931291i
$105$	7.42917e9	+	3.34368e9i	0.582095	+	0.261986i
$106$	−6.39209e9			−0.477654
$107$	1.70919e10			1.21863			0.609313	−	0.792930i	$-0.291445\pi$
$107$	1.70919e10			1.21863			0.609313	+	0.792930i	$0.291445\pi$
$108$			5.35764e9i			0.364632i
$109$	−2.59945e9			−0.168946			−0.0844731	−	0.996426i	$-0.526921\pi$
$109$	−2.59945e9			−0.168946			−0.0844731	+	0.996426i	$0.526921\pi$
$110$		−	4.50575e9i		−	0.279771i
$111$			6.94343e9i			0.412059i
$112$	4.01768e9	+	1.80825e9i	0.227974	+	0.102605i
$113$	−2.04111e10			−1.10783			−0.553916	−	0.832572i	$-0.686867\pi$
$113$	−2.04111e10			−1.10783			−0.553916	+	0.832572i	$0.686867\pi$
$114$	−9.43133e9			−0.489834
$115$			3.82950e10i			1.90394i
$116$	−7.33230e9			−0.349100
$117$		−	4.87138e9i		−	0.222189i
$118$		−	4.16182e9i		−	0.181917i
$119$	1.72229e10	−	3.82669e10i	0.721725	−	1.60357i
$120$	5.61578e9			0.225685
$121$	−2.43781e10			−0.939880
$122$		−	3.86865e9i		−	0.143140i
$123$	−8.46425e9			−0.300651
$124$			8.79616e9i			0.300044i
$125$			2.97377e10i			0.974446i
$126$	1.72733e10	+	7.77426e9i	0.543904	+	0.244797i
$127$	−4.47220e10			−1.35364			−0.676819	−	0.736150i	$-0.736642\pi$
$127$	−4.47220e10			−1.35364			−0.676819	+	0.736150i	$0.736642\pi$
$128$	3.03700e9			0.0883883
$129$		−	8.18425e9i		−	0.229103i
$130$	−1.11594e10			−0.300556
$131$		−	2.11188e10i		−	0.547410i	−0.961814	−	0.273705i	$-0.911751\pi$
$131$		−	2.11188e10i		−	0.547410i	0.961814	−	0.273705i	$-0.0882491\pi$
$132$			1.94351e9i			0.0484972i
$133$	−2.99097e10	+	6.64552e10i	−0.718711	+	1.59687i
$134$	4.14155e10			0.958604
$135$	5.27672e10			1.17678
$136$		−	2.89263e10i		−	0.621724i
$137$	−1.93382e10			−0.400694			−0.200347	−	0.979725i	$-0.564207\pi$
$137$	−1.93382e10			−0.400694			−0.200347	+	0.979725i	$0.564207\pi$
$138$		−	1.65182e10i		−	0.330040i
$139$		−	5.61255e10i		−	1.08165i	−0.841135	−	0.540825i	$-0.818112\pi$
$139$		−	5.61255e10i		−	1.08165i	0.841135	−	0.540825i	$-0.181888\pi$
$140$	1.78094e10	−	3.95700e10i	0.331138	−	0.735742i
$141$	−9.66459e9			−0.173415
$142$	−3.24298e10			−0.561698
$143$		−	3.86206e9i		−	0.0645860i
$144$	1.30570e10			0.210878
$145$			7.22155e10i			1.12665i
$146$			5.94407e10i			0.896024i
$147$	−2.03250e10	+	1.80057e10i	−0.296103	+	0.262315i
$148$	3.69828e10			0.520824
$149$	1.24417e11			1.69414			0.847071	−	0.531480i	$-0.178364\pi$
$149$	1.24417e11			1.69414			0.847071	+	0.531480i	$0.178364\pi$
$150$		−	3.40683e10i		−	0.448636i
$151$	−4.03799e10			−0.514375			−0.257188	−	0.966361i	$-0.582796\pi$
$151$	−4.03799e10			−0.514375			−0.257188	+	0.966361i	$0.582796\pi$
$152$			5.02340e10i			0.619128i
$153$		−	1.24363e11i		−	1.48332i
$154$	1.36944e10	+	6.16348e9i	0.158102	+	0.0711578i
$155$	8.66330e10			0.968333
$156$	4.81351e9			0.0521001
$157$		−	5.25863e10i		−	0.551282i	−0.961261	−	0.275641i	$-0.911110\pi$
$157$		−	5.25863e10i		−	0.551282i	0.961261	−	0.275641i	$-0.0888901\pi$
$158$	−7.29987e10			−0.741361
$159$		−	2.71552e10i		−	0.267219i
$160$		−	2.99113e10i		−	0.285256i
$161$	−1.16391e11	−	5.23844e10i	−1.07594	−	0.484253i
$162$	4.37901e10			0.392465
$163$	4.26249e10			0.370447			0.185223	−	0.982696i	$-0.440699\pi$
$163$	4.26249e10			0.370447			0.185223	+	0.982696i	$0.440699\pi$
$164$			4.50831e10i			0.380009i
$165$	1.91415e10			0.156515
$166$		−	9.33133e9i		−	0.0740292i
$167$			1.80191e11i			1.38724i	0.720341	+	0.693620i	$0.243985\pi$
$167$			1.80191e11i			1.38724i	−0.720341	+	0.693620i	$0.756015\pi$
$168$	−7.68190e9	+	1.70681e10i	−0.0574014	+	0.127538i
$169$	1.28293e11			0.930616
$170$	−2.84893e11			−2.00649
$171$			2.15972e11i			1.47712i
$172$	−4.35918e10			−0.289576
$173$		−	1.11027e10i		−	0.0716469i	−0.999358	−	0.0358234i	$-0.988595\pi$
$173$		−	1.11027e10i		−	0.0716469i	0.999358	−	0.0358234i	$-0.0114054\pi$
$174$		−	3.11494e10i		−	0.195301i
$175$	−2.40053e11	−	1.08041e11i	−1.46257	−	0.658264i
$176$	1.03517e10			0.0612983
$177$	1.76804e10			0.101772
$178$			2.02702e11i			1.13438i
$179$	−6.78324e10			−0.369124			−0.184562	−	0.982821i	$-0.559087\pi$
$179$	−6.78324e10			−0.369124			−0.184562	+	0.982821i	$0.559087\pi$
$180$		−	1.28598e11i		−	0.680569i
$181$			6.80794e10i			0.350448i	0.984529	+	0.175224i	$0.0560649\pi$
$181$			6.80794e10i			0.350448i	−0.984529	+	0.175224i	$0.943935\pi$
$182$	1.52652e10	−	3.39170e10i	0.0764442	−	0.169848i
$183$	1.64350e10			0.0800781
$184$	−8.79807e10			−0.417156
$185$		−	3.64242e11i		−	1.68086i
$186$	−3.73683e10			−0.167856
$187$		−	9.85959e10i		−	0.431172i
$188$			5.14765e10i			0.219189i
$189$	−7.21810e10	+	1.60376e11i	−0.299305	+	0.665013i
$190$	4.94753e11			1.99811
$191$	1.49074e11			0.586457			0.293229	−	0.956042i	$-0.405270\pi$
$191$	1.49074e11			0.586457			0.293229	+	0.956042i	$0.405270\pi$
$192$			1.29019e10i			0.0494480i
$193$	2.66294e11			0.994432			0.497216	−	0.867627i	$-0.334356\pi$
$193$	2.66294e11			0.994432			0.497216	+	0.867627i	$0.334356\pi$
$194$			2.33488e10i			0.0849681i
$195$		−	4.74081e10i		−	0.168143i
$196$	9.59038e10	+	1.08257e11i	0.331555	+	0.374261i
$197$	2.10936e11			0.710919			0.355460	−	0.934692i	$-0.384324\pi$
$197$	2.10936e11			0.710919			0.355460	+	0.934692i	$0.384324\pi$
$198$	4.45052e10			0.146246
$199$		−	4.03047e10i		−	0.129149i	−0.997913	−	0.0645744i	$-0.979431\pi$
$199$		−	4.03047e10i		−	0.129149i	0.997913	−	0.0645744i	$-0.0205690\pi$
$200$	−1.81458e11			−0.567056
$201$			1.75943e11i			0.536281i
$202$		−	4.20437e11i		−	1.25010i
$203$	−2.19486e11	−	9.87847e10i	−0.636687	−	0.286556i
$204$	1.22886e11			0.347817
$205$	4.44021e11			1.22641
$206$		−	2.48213e11i		−	0.669095i
$207$	−3.78257e11			−0.995257
$208$		−	2.56382e10i		−	0.0658522i
$209$			1.71224e11i			0.429372i
$210$	1.68103e11	+	7.56587e10i	0.411603	+	0.185252i
$211$	−4.75297e11			−1.13646			−0.568228	−	0.822871i	$-0.692371\pi$
$211$	−4.75297e11			−1.13646			−0.568228	+	0.822871i	$0.692371\pi$
$212$	−1.44636e11			−0.337752
$213$		−	1.37770e11i		−	0.314236i
$214$	3.86745e11			0.861699
$215$			4.29333e11i			0.934549i
$216$			1.21230e11i			0.257834i
$217$	−1.18507e11	+	2.63305e11i	−0.246288	+	0.547218i
$218$	−5.88187e10			−0.119463
$219$	−2.52519e11			−0.501271
$220$		−	1.01953e11i		−	0.197828i
$221$	−2.44194e11			−0.463205
$222$			1.57112e11i			0.291370i
$223$		−	1.06930e11i		−	0.193899i	−0.995289	−	0.0969496i	$-0.969091\pi$
$223$		−	1.06930e11i		−	0.193899i	0.995289	−	0.0969496i	$-0.0309086\pi$
$224$	9.09098e10	+	4.09161e10i	0.161202	+	0.0725528i
$225$	−7.80145e11			−1.35289
$226$	−4.61850e11			−0.783356
$227$			4.70031e11i			0.779825i	0.920852	+	0.389913i	$0.127495\pi$
$227$			4.70031e11i			0.779825i	−0.920852	+	0.389913i	$0.872505\pi$
$228$	−2.13407e11			−0.346365
$229$		−	1.16834e12i		−	1.85520i	−0.373573	−	0.927601i	$-0.621867\pi$
$229$		−	1.16834e12i		−	1.85520i	0.373573	−	0.927601i	$-0.378133\pi$
$230$			8.66518e11i			1.34629i
$231$	−2.61840e10	+	5.81771e10i	−0.0398085	+	0.0884488i
$232$	−1.65911e11			−0.246851
$233$	8.97263e11			1.30659			0.653296	−	0.757102i	$-0.273386\pi$
$233$	8.97263e11			1.30659			0.653296	+	0.757102i	$0.273386\pi$
$234$		−	1.10227e11i		−	0.157111i
$235$	5.06989e11			0.707391
$236$		−	9.41712e10i		−	0.128635i
$237$		−	3.10116e11i		−	0.414747i
$238$	3.89710e11	−	8.65880e11i	0.510337	−	1.13390i
$239$	−2.07777e11			−0.266445			−0.133222	−	0.991086i	$-0.542532\pi$
$239$	−2.07777e11			−0.266445			−0.133222	+	0.991086i	$0.542532\pi$
$240$	1.27070e11			0.159584
$241$			1.42283e12i			1.75012i	0.484015	+	0.875060i	$0.339178\pi$
$241$			1.42283e12i			1.75012i	−0.484015	+	0.875060i	$0.660822\pi$
$242$	−5.51613e11			−0.664596
$243$			8.03928e11i			0.948824i
$244$		−	8.75376e10i		−	0.101215i
$245$	1.06622e12	−	9.44552e11i	1.20785	−	1.07003i
$246$	−1.91524e11			−0.212592
$247$	4.24073e11			0.461271
$248$			1.99034e11i			0.212163i
$249$	3.96418e10			0.0414149
$250$			6.72888e11i			0.689037i
$251$		−	1.34718e12i		−	1.35225i	−0.736788	−	0.676124i	$-0.763658\pi$
$251$		−	1.34718e12i		−	1.35225i	0.736788	−	0.676124i	$-0.236342\pi$
$252$	3.90850e11	+	1.75911e11i	0.384598	+	0.173098i
$253$	−2.99884e11			−0.289302
$254$	−1.01194e12			−0.957166
$255$		−	1.21030e12i		−	1.12251i
$256$	6.87195e10			0.0625000
$257$		−	8.61095e11i		−	0.768043i	−0.923324	−	0.384022i	$-0.874539\pi$
$257$		−	8.61095e11i		−	0.768043i	0.923324	−	0.384022i	$-0.125461\pi$
$258$		−	1.85189e11i		−	0.162000i
$259$	1.10704e12	+	4.98252e11i	0.949875	+	0.427514i
$260$	−2.52509e11			−0.212525
$261$	−7.13304e11			−0.588942
$262$		−	4.77863e11i		−	0.387077i
$263$	1.81540e12			1.44276			0.721380	−	0.692540i	$-0.243508\pi$
$263$	1.81540e12			1.44276			0.721380	+	0.692540i	$0.243508\pi$
$264$			4.39765e10i			0.0342927i
$265$			1.42452e12i			1.09003i
$266$	−6.76780e11	+	1.50371e12i	−0.508205	+	1.12916i
$267$	−8.61128e11			−0.634616
$268$	9.37126e11			0.677835
$269$			5.43819e11i			0.386094i	0.981189	+	0.193047i	$0.0618370\pi$
$269$			5.43819e11i			0.386094i	−0.981189	+	0.193047i	$0.938163\pi$
$270$	1.19398e12			0.832108
$271$			5.87004e10i			0.0401601i	0.999798	+	0.0200800i	$0.00639210\pi$
$271$			5.87004e10i			0.0401601i	−0.999798	+	0.0200800i	$0.993608\pi$
$272$		−	6.54526e11i		−	0.439625i
$273$	1.44088e11	+	6.48502e10i	0.0950199	+	0.0427659i
$274$	−4.37573e11			−0.283333
$275$	−6.18504e11			−0.393259
$276$		−	3.73763e11i		−	0.233373i
$277$	9.73590e11			0.597004			0.298502	−	0.954409i	$-0.403513\pi$
$277$	9.73590e11			0.597004			0.298502	+	0.954409i	$0.403513\pi$
$278$		−	1.26998e12i		−	0.764842i
$279$			8.55712e11i			0.506182i
$280$	4.02981e11	−	8.95366e11i	0.234150	−	0.520248i
$281$	−1.99761e12			−1.14020			−0.570098	−	0.821576i	$-0.693095\pi$
$281$	−1.99761e12			−1.14020			−0.570098	+	0.821576i	$0.693095\pi$
$282$	−2.18685e11			−0.122623
$283$		−	3.24795e12i		−	1.78928i	−0.446790	−	0.894639i	$-0.647433\pi$
$283$		−	3.24795e12i		−	1.78928i	0.446790	−	0.894639i	$-0.352567\pi$
$284$	−7.33803e11			−0.397180
$285$			2.10183e12i			1.11782i
$286$		−	8.73884e10i		−	0.0456692i
$287$	−6.07384e11	+	1.34952e12i	−0.311927	+	0.693059i
$288$	2.95447e11			0.149114
$289$	−4.21812e12			−2.09233
$290$			1.63405e12i			0.796664i
$291$	−9.91915e10			−0.0475346
$292$			1.34499e12i			0.633584i
$293$		−	2.56632e11i		−	0.118843i	−0.998233	−	0.0594214i	$-0.981074\pi$
$293$		−	2.56632e11i		−	0.118843i	0.998233	−	0.0594214i	$-0.0189256\pi$
$294$	−4.59901e11	+	4.07423e11i	−0.209377	+	0.185485i
$295$	−9.27488e11			−0.415143
$296$	8.36825e11			0.368278
$297$			4.13214e11i			0.178810i
$298$	2.81524e12			1.19794
$299$			7.42728e11i			0.310795i
$300$		−	7.70878e11i		−	0.317234i
$301$	−1.30488e12	−	5.87292e11i	−0.528126	−	0.237696i
$302$	−9.13692e11			−0.363718
$303$	1.78612e12			0.699354
$304$			1.13667e12i			0.437789i
$305$	−8.62154e11			−0.326652
$306$		−	2.81402e12i		−	1.04887i
$307$			2.54361e12i			0.932735i	0.884591	+	0.466368i	$0.154438\pi$
$307$			2.54361e12i			0.932735i	−0.884591	+	0.466368i	$0.845562\pi$
$308$	3.09868e11	+	1.39464e11i	0.111795	+	0.0503161i
$309$	1.05447e12			0.374319
$310$	1.96028e12			0.684715
$311$			2.25597e12i			0.775410i	0.921784	+	0.387705i	$0.126732\pi$
$311$			2.25597e12i			0.775410i	−0.921784	+	0.387705i	$0.873268\pi$
$312$	1.08917e11			0.0368404
$313$		−	4.18452e12i		−	1.39291i	−0.717599	−	0.696457i	$-0.754759\pi$
$313$		−	4.18452e12i		−	1.39291i	0.717599	−	0.696457i	$-0.245241\pi$
$314$		−	1.18989e12i		−	0.389815i
$315$	1.73254e12	−	3.84947e12i	0.558639	−	1.24122i
$316$	−1.65177e12			−0.524221
$317$	1.98589e11			0.0620382			0.0310191	−	0.999519i	$-0.490125\pi$
$317$	1.98589e11			0.0620382			0.0310191	+	0.999519i	$0.490125\pi$
$318$		−	6.14451e11i		−	0.188952i
$319$	−5.65512e11			−0.171194
$320$		−	6.76815e11i		−	0.201707i
$321$			1.64299e12i			0.482069i
$322$	−2.63362e12	−	1.18532e12i	−0.760805	−	0.342418i
$323$	1.08263e13			3.07941
$324$	9.90856e11			0.277514
$325$			1.53186e12i			0.422475i
$326$	9.64492e11			0.261945
$327$		−	2.49876e11i		−	0.0668323i
$328$			1.02011e12i			0.268707i
$329$	−6.93519e11	+	1.54090e12i	−0.179920	+	0.399756i
$330$	4.33123e11			0.110673
$331$	−2.33599e12			−0.587937			−0.293969	−	0.955815i	$-0.594976\pi$
$331$	−2.33599e12			−0.587937			−0.293969	+	0.955815i	$0.594976\pi$
$332$		−	2.11144e11i		−	0.0523465i
$333$	3.59778e12			0.878644
$334$			4.07727e12i			0.980927i
$335$		−	9.22972e12i		−	2.18758i
$336$	−1.73822e11	+	3.86207e11i	−0.0405889	+	0.0901828i
$337$	−1.03795e12			−0.238796			−0.119398	−	0.992846i	$-0.538096\pi$
$337$	−1.03795e12			−0.238796			−0.119398	+	0.992846i	$0.538096\pi$
$338$	2.90295e12			0.658045
$339$		−	1.96205e12i		−	0.438240i
$340$	−6.44640e12			−1.41881
$341$			6.78414e11i			0.147137i
$342$			4.88689e12i			1.04448i
$343$	1.41230e12	+	4.53263e12i	0.297479	+	0.954728i
$344$	−9.86369e11			−0.204761
$345$	−3.68118e12			−0.753168
$346$		−	2.51225e11i		−	0.0506620i
$347$	−8.68534e12			−1.72639			−0.863196	−	0.504870i	$-0.831541\pi$
$347$	−8.68534e12			−1.72639			−0.863196	+	0.504870i	$0.831541\pi$
$348$		−	7.04831e11i		−	0.138098i
$349$		−	8.13667e11i		−	0.157152i	−0.996908	−	0.0785759i	$-0.974963\pi$
$349$		−	8.13667e11i		−	0.157152i	0.996908	−	0.0785759i	$-0.0250373\pi$
$350$	−5.43177e12	−	2.44470e12i	−1.03419	−	0.465463i
$351$	1.02341e12			0.192095
$352$	2.34232e11			0.0433444
$353$		−	2.87814e11i		−	0.0525095i	−0.999655	−	0.0262548i	$-0.991642\pi$
$353$		−	2.87814e11i		−	0.0525095i	0.999655	−	0.0262548i	$-0.00835811\pi$
$354$	4.00062e11			0.0719633
$355$			7.22720e12i			1.28182i
$356$			4.58662e12i			0.802126i
$357$	3.67847e12	+	1.65558e12i	0.634347	+	0.285503i
$358$	−1.53487e12			−0.261010
$359$	−9.62233e10			−0.0161365			−0.00806823	−	0.999967i	$-0.502568\pi$
$359$	−9.62233e10			−0.0161365			−0.00806823	+	0.999967i	$0.502568\pi$
$360$		−	2.90984e12i		−	0.481235i
$361$	−1.26702e13			−2.06655
$362$			1.54046e12i			0.247804i
$363$		−	2.34339e12i		−	0.371801i
$364$	3.45411e11	−	7.67455e11i	0.0540542	−	0.120101i
$365$	1.32467e13			2.04477
$366$	3.71881e11			0.0566238
$367$		−	8.07225e11i		−	0.121245i	−0.998161	−	0.0606226i	$-0.980691\pi$
$367$		−	8.07225e11i		−	0.121245i	0.998161	−	0.0606226i	$-0.0193086\pi$
$368$	−1.99078e12			−0.294974
$369$			4.38580e12i			0.641086i
$370$		−	8.24185e12i		−	1.18855i
$371$	−4.32956e12	−	1.94862e12i	−0.615990	−	0.277241i
$372$	−8.45547e11			−0.118692
$373$	9.10414e12			1.26094			0.630471	−	0.776213i	$-0.282862\pi$
$373$	9.10414e12			1.26094			0.630471	+	0.776213i	$0.282862\pi$
$374$		−	2.23097e12i		−	0.304885i
$375$	−2.85859e12			−0.385475
$376$			1.16478e12i			0.154990i
$377$			1.40061e12i			0.183912i
$378$	−1.63327e12	+	3.62889e12i	−0.211641	+	0.470235i
$379$	1.64205e12			0.209986			0.104993	−	0.994473i	$-0.466518\pi$
$379$	1.64205e12			0.209986			0.104993	+	0.994473i	$0.466518\pi$
$380$	1.11950e13			1.41288
$381$		−	4.29898e12i		−	0.535477i
$382$	3.37317e12			0.414688
$383$		−	1.35119e13i		−	1.63954i	−0.572690	−	0.819772i	$-0.694100\pi$
$383$		−	1.35119e13i		−	1.63954i	0.572690	−	0.819772i	$-0.305900\pi$
$384$			2.91937e11i			0.0349650i
$385$	1.37357e12	−	3.05188e12i	0.162386	−	0.360798i
$386$	6.02555e12			0.703169
$387$	−4.24071e12			−0.488522
$388$			5.28323e11i			0.0600815i
$389$	1.27779e12			0.143454			0.0717268	−	0.997424i	$-0.477149\pi$
$389$	1.27779e12			0.143454			0.0717268	+	0.997424i	$0.477149\pi$
$390$		−	1.07272e12i		−	0.118895i
$391$			1.89614e13i			2.07485i
$392$	2.17006e12	+	2.44957e12i	0.234445	+	0.264642i
$393$	2.03008e12			0.216546
$394$	4.77294e12			0.502696
$395$			1.62682e13i			1.69182i
$396$	1.00704e12			0.103412
$397$		−	1.15319e13i		−	1.16936i	−0.811264	−	0.584680i	$-0.801220\pi$
$397$		−	1.15319e13i		−	1.16936i	0.811264	−	0.584680i	$-0.198780\pi$
$398$		−	9.11991e11i		−	0.0913219i
$399$	−6.38813e12	−	2.87513e12i	−0.631697	−	0.284310i
$400$	−4.10592e12			−0.400969
$401$	−9.31976e12			−0.898841			−0.449420	−	0.893320i	$-0.648369\pi$
$401$	−9.31976e12			−0.898841			−0.449420	+	0.893320i	$0.648369\pi$
$402$			3.98114e12i			0.379208i
$403$	1.68024e12			0.158068
$404$		−	9.51340e12i		−	0.883952i
$405$		−	9.75889e12i		−	0.895624i
$406$	−4.96639e12	−	2.23524e12i	−0.450205	−	0.202626i
$407$	2.85234e12			0.255405
$408$	2.78059e12			0.245944
$409$		−	3.12572e12i		−	0.273107i	−0.990633	−	0.136554i	$-0.956397\pi$
$409$		−	3.12572e12i		−	0.273107i	0.990633	−	0.136554i	$-0.0436026\pi$
$410$	1.00471e13			0.867201
$411$		−	1.85892e12i		−	0.158508i
$412$		−	5.61641e12i		−	0.473122i
$413$	1.26872e12	−	2.81893e12i	0.105589	−	0.234603i
$414$	−8.55898e12			−0.703753
$415$	−2.07955e12			−0.168938
$416$		−	5.80126e11i		−	0.0465646i
$417$	5.39517e12			0.427883
$418$			3.87436e12i			0.303612i
$419$			8.88404e12i			0.687924i	0.938984	+	0.343962i	$0.111769\pi$
$419$			8.88404e12i			0.687924i	−0.938984	+	0.343962i	$0.888231\pi$
$420$	3.80374e12	+	1.71196e12i	0.291048	+	0.130993i
$421$	−7.26228e12			−0.549114			−0.274557	−	0.961571i	$-0.588531\pi$
$421$	−7.26228e12			−0.549114			−0.274557	+	0.961571i	$0.588531\pi$
$422$	−1.07547e13			−0.803595
$423$			5.00776e12i			0.369778i
$424$	−3.27275e12			−0.238827
$425$			3.91073e13i			2.82042i
$426$		−	3.11738e12i		−	0.222199i
$427$	1.17935e12	−	2.62036e12i	0.0830816	−	0.184595i
$428$	8.75104e12			0.609313
$429$	3.71247e11			0.0255492
$430$			9.71470e12i			0.660826i
$431$	−1.27855e13			−0.859668			−0.429834	−	0.902908i	$-0.641428\pi$
$431$	−1.27855e13			−0.859668			−0.429834	+	0.902908i	$0.641428\pi$
$432$			2.74311e12i			0.182316i
$433$		−	7.88938e12i		−	0.518327i	−0.965834	−	0.259163i	$-0.916553\pi$
$433$		−	7.88938e12i		−	0.518327i	0.965834	−	0.259163i	$-0.0834468\pi$
$434$	−2.68150e12	+	5.95791e12i	−0.174152	+	0.386941i
$435$	−6.94185e12			−0.445686
$436$	−1.33092e12			−0.0844731
$437$		−	3.29288e13i		−	2.06618i
$438$	−5.71384e12			−0.354452
$439$		−	2.34378e13i		−	1.43745i	−0.695293	−	0.718726i	$-0.744725\pi$
$439$		−	2.34378e13i		−	1.43745i	0.695293	−	0.718726i	$-0.255275\pi$
$440$		−	2.30694e12i		−	0.139886i
$441$	9.32976e12	+	1.05315e13i	0.559342	+	0.631388i
$442$	−5.52548e12			−0.327535
$443$	−1.82456e13			−1.06940			−0.534700	−	0.845042i	$-0.679575\pi$
$443$	−1.82456e13			−1.06940			−0.534700	+	0.845042i	$0.679575\pi$
$444$			3.55504e12i			0.206029i
$445$	4.51734e13			2.58871
$446$		−	2.41955e12i		−	0.137107i
$447$			1.19598e13i			0.670175i
$448$	2.05705e12	+	9.25826e11i	0.113987	+	0.0513026i
$449$	−2.08618e13			−1.14320			−0.571598	−	0.820534i	$-0.693676\pi$
$449$	−2.08618e13			−1.14320			−0.571598	+	0.820534i	$0.693676\pi$
$450$	−1.76527e13			−0.956638
$451$			3.47708e12i			0.186351i
$452$	−1.04505e13			−0.553916
$453$		−	3.88159e12i		−	0.203478i
$454$			1.06356e13i			0.551420i
$455$	−7.55863e12	−	3.40194e12i	−0.387602	−	0.174450i
$456$	−4.82884e12			−0.244917
$457$	1.33766e13			0.671065			0.335533	−	0.942029i	$-0.391084\pi$
$457$	1.33766e13			0.671065			0.335533	+	0.942029i	$0.391084\pi$
$458$		−	2.64365e13i		−	1.31183i
$459$	2.61271e13			1.28241
$460$			1.96071e13i			0.951970i
$461$		−	1.08265e12i		−	0.0519977i	−0.999662	−	0.0259989i	$-0.991723\pi$
$461$		−	1.08265e12i		−	0.0519977i	0.999662	−	0.0259989i	$-0.00827663\pi$
$462$	−5.92476e11	+	1.31640e12i	−0.0281488	+	0.0625427i
$463$	3.18938e12			0.149900			0.0749499	−	0.997187i	$-0.476120\pi$
$463$	3.18938e12			0.149900			0.0749499	+	0.997187i	$0.476120\pi$
$464$	−3.75414e12			−0.174550
$465$			8.32776e12i			0.383057i
$466$	2.03027e13			0.923901
$467$			1.95436e13i			0.879873i	0.898029	+	0.439937i	$0.144999\pi$
$467$			1.95436e13i			0.879873i	−0.898029	+	0.439937i	$0.855001\pi$
$468$		−	2.49415e12i		−	0.111095i
$469$	2.80520e13	+	1.26255e13i	1.23623	+	0.556395i
$470$	1.14719e13			0.500201
$471$	5.05495e12			0.218078
$472$		−	2.13085e12i		−	0.0909584i
$473$	−3.36206e12			−0.142004
$474$		−	7.01713e12i		−	0.293270i
$475$		−	6.79147e13i		−	2.80864i
$476$	8.81813e12	−	1.95926e13i	0.360863	−	0.801785i
$477$	−1.40706e13			−0.569798
$478$	−4.70145e12			−0.188405
$479$		−	1.01633e12i		−	0.0403049i	−0.999797	−	0.0201525i	$-0.993585\pi$
$479$		−	1.01633e12i		−	0.0403049i	0.999797	−	0.0201525i	$-0.00641516\pi$
$480$	2.87528e12			0.112843
$481$		−	7.06443e12i		−	0.274379i
$482$			3.21950e13i			1.23752i
$483$	5.03554e12	−	1.11883e13i	0.191563	−	0.425625i
$484$	−1.24816e13			−0.469940
$485$	5.20343e12			0.193901
$486$			1.81908e13i			0.670920i
$487$	1.20527e13			0.439988			0.219994	−	0.975501i	$-0.429396\pi$
$487$	1.20527e13			0.439988			0.219994	+	0.975501i	$0.429396\pi$
$488$		−	1.98075e12i		−	0.0715699i
$489$			4.09740e12i			0.146543i
$490$	2.41257e13	−	2.13728e13i	0.854082	−	0.756625i
$491$	−1.64611e13			−0.576836			−0.288418	−	0.957505i	$-0.593129\pi$
$491$	−1.64611e13			−0.576836			−0.288418	+	0.957505i	$0.593129\pi$
$492$	−4.33370e12			−0.150326
$493$			3.57567e13i			1.22779i
$494$	9.59567e12			0.326168
$495$		−	9.91828e12i		−	0.333742i
$496$			4.50363e12i			0.150022i
$497$	−2.19657e13	−	9.88619e12i	−0.724375	−	0.326022i
$498$	8.96991e11			0.0292847
$499$	5.70754e13			1.84479			0.922394	−	0.386250i	$-0.126230\pi$
$499$	5.70754e13			1.84479			0.922394	+	0.386250i	$0.126230\pi$
$500$			1.52257e13i			0.487223i
$501$	−1.73212e13			−0.548770
$502$		−	3.04832e13i		−	0.956184i
$503$			5.90671e13i			1.83445i	0.398371	+	0.917224i	$0.369576\pi$
$503$			5.90671e13i			1.83445i	−0.398371	+	0.917224i	$0.630424\pi$
$504$	8.84393e12	+	3.98042e12i	0.271952	+	0.122399i
$505$	−9.36970e13			−2.85278
$506$	−6.78561e12			−0.204567
$507$			1.23324e13i			0.368136i
$508$	−2.28977e13			−0.676819
$509$		−	2.35370e13i		−	0.688909i	−0.938803	−	0.344455i	$-0.888064\pi$
$509$		−	2.35370e13i		−	0.688909i	0.938803	−	0.344455i	$-0.111936\pi$
$510$		−	2.73859e13i		−	0.793736i
$511$	−1.81204e13	+	4.02610e13i	−0.520072	+	1.15553i
$512$	1.55494e12			0.0441942
$513$	−4.53729e13			−1.27706
$514$		−	1.94844e13i		−	0.543089i
$515$	−5.53158e13			−1.52691
$516$		−	4.19034e12i		−	0.114551i
$517$			3.97018e12i			0.107487i
$518$	2.50496e13	+	1.12741e13i	0.671663	+	0.302298i
$519$	1.06727e12			0.0283423
$520$	−5.71363e12			−0.150278
$521$			1.10415e13i			0.287633i	0.989604	+	0.143816i	$0.0459374\pi$
$521$			1.10415e13i			0.287633i	−0.989604	+	0.143816i	$0.954063\pi$
$522$	−1.61402e13			−0.416445
$523$			4.24447e13i			1.08471i	0.840148	+	0.542357i	$0.182468\pi$
$523$			4.24447e13i			1.08471i	−0.840148	+	0.542357i	$0.817532\pi$
$524$		−	1.08128e13i		−	0.273705i
$525$	1.03857e13	−	2.30755e13i	0.260398	−	0.578568i
$526$	4.10779e13			1.02019
$527$	4.28954e13			1.05525
$528$			9.95076e11i			0.0242486i
$529$	1.62454e13			0.392150
$530$			3.22332e13i			0.770768i
$531$		−	9.16120e12i		−	0.217010i
$532$	−1.53138e13	+	3.40251e13i	−0.359355	+	0.798437i
$533$	8.61174e12			0.200196
$534$	−1.94851e13			−0.448741
$535$		−	8.61886e13i		−	1.96644i
$536$	2.12048e13			0.479302
$537$		−	6.52052e12i		−	0.146019i
$538$			1.23052e13i			0.273010i
$539$	7.39669e12	+	8.34942e12i	0.162590	+	0.183532i
$540$	2.70168e13			0.588389
$541$	3.26395e13			0.704298			0.352149	−	0.935944i	$-0.385451\pi$
$541$	3.26395e13			0.704298			0.352149	+	0.935944i	$0.385451\pi$
$542$			1.32824e12i			0.0283975i
$543$	−6.54426e12			−0.138631
$544$		−	1.48102e13i		−	0.310862i
$545$			1.31081e13i			0.272620i
$546$	3.26034e12	+	1.46739e12i	0.0671892	+	0.0302401i
$547$	5.34548e13			1.09157			0.545783	−	0.837927i	$-0.316232\pi$
$547$	5.34548e13			1.09157			0.545783	+	0.837927i	$0.316232\pi$
$548$	−9.90115e12			−0.200347
$549$		−	8.51588e12i		−	0.170753i
$550$	−1.39951e13			−0.278076
$551$		−	6.20960e13i		−	1.22266i
$552$		−	8.45730e12i		−	0.165020i
$553$	−4.94443e13	−	2.22536e13i	−0.956071	−	0.430302i
$554$	2.20298e13			0.422145
$555$	3.50134e13			0.664920
$556$		−	2.87363e13i		−	0.540825i
$557$	4.96209e13			0.925525			0.462763	−	0.886482i	$-0.346858\pi$
$557$	4.96209e13			0.925525			0.462763	+	0.886482i	$0.346858\pi$
$558$			1.93626e13i			0.357925i
$559$			8.32687e12i			0.152554i
$560$	9.11842e12	−	2.02598e13i	0.165569	−	0.367871i
$561$	9.47771e12			0.170565
$562$	−4.52008e13			−0.806241
$563$		−	4.43474e13i		−	0.784019i	−0.919961	−	0.392009i	$-0.871780\pi$
$563$		−	4.43474e13i		−	0.784019i	0.919961	−	0.392009i	$-0.128220\pi$
$564$	−4.94827e12			−0.0867077
$565$			1.02926e14i			1.78766i
$566$		−	7.34928e13i		−	1.26521i
$567$	2.96603e13	+	1.33493e13i	0.506129	+	0.227795i
$568$	−1.66041e13			−0.280849
$569$	4.38072e12			0.0734486			0.0367243	−	0.999325i	$-0.488308\pi$
$569$	4.38072e12			0.0734486			0.0367243	+	0.999325i	$0.488308\pi$
$570$			4.75590e13i			0.790421i
$571$	−1.53631e13			−0.253104			−0.126552	−	0.991960i	$-0.540391\pi$
$571$	−1.53631e13			−0.253104			−0.126552	+	0.991960i	$0.540391\pi$
$572$		−	1.97737e12i		−	0.0322930i
$573$			1.43300e13i			0.231993i
$574$	−1.37435e13	+	3.05362e13i	−0.220566	+	0.490066i
$575$	1.18947e14			1.89240
$576$	6.68520e12			0.105439
$577$			3.53277e13i			0.552378i	0.961103	+	0.276189i	$0.0890715\pi$
$577$			3.53277e13i			0.552378i	−0.961103	+	0.276189i	$0.910928\pi$
$578$	−9.54451e13			−1.47950
$579$			2.55980e13i			0.393381i
$580$			3.69743e13i			0.563327i
$581$	2.84464e12	−	6.32039e12i	0.0429682	−	0.0954692i
$582$	−2.24445e12			−0.0336120
$583$	−1.11553e13			−0.165629
$584$			3.04336e13i			0.448012i
$585$	−2.45647e13			−0.358536
$586$		−	5.80692e12i		−	0.0840346i
$587$		−	6.02124e13i		−	0.863964i	−0.901882	−	0.431982i	$-0.857814\pi$
$587$		−	6.02124e13i		−	0.863964i	0.901882	−	0.431982i	$-0.142186\pi$
$588$	−1.04064e13	+	9.21893e12i	−0.148052	+	0.131158i
$589$	−7.44931e13			−1.05085
$590$	−2.09867e13			−0.293551
$591$			2.02766e13i			0.281228i
$592$	1.89352e13			0.260412
$593$		−	1.02677e14i		−	1.40023i	−0.714028	−	0.700117i	$-0.753131\pi$
$593$		−	1.02677e14i		−	1.40023i	0.714028	−	0.700117i	$-0.246869\pi$
$594$			9.34997e12i			0.126438i
$595$	−1.92967e14	−	8.68494e13i	−2.58761	−	1.16461i
$596$	6.37017e13			0.847071
$597$	3.87436e12			0.0510891
$598$			1.68060e13i			0.219765i
$599$	−3.82993e13			−0.496657			−0.248329	−	0.968676i	$-0.579881\pi$
$599$	−3.82993e13			−0.496657			−0.248329	+	0.968676i	$0.579881\pi$
$600$		−	1.74430e13i		−	0.224318i
$601$			6.01419e13i			0.767017i	0.923537	+	0.383508i	$0.125284\pi$
$601$			6.01419e13i			0.767017i	−0.923537	+	0.383508i	$0.874716\pi$
$602$	−2.95260e13	−	1.32889e13i	−0.373442	−	0.168076i
$603$	9.11660e13			1.14353
$604$	−2.06745e13			−0.257188
$605$			1.22930e14i			1.51664i
$606$	4.04152e13			0.494518
$607$		−	4.05317e13i		−	0.491872i	−0.969286	−	0.245936i	$-0.920905\pi$
$607$		−	4.05317e13i		−	0.491872i	0.969286	−	0.245936i	$-0.0790953\pi$
$608$			2.57198e13i			0.309564i
$609$	9.49586e12	−	2.10985e13i	0.113357	−	0.251863i
$610$	−1.95083e13			−0.230978
$611$	9.83300e12			0.115473
$612$		−	6.36740e13i		−	0.741660i
$613$	−2.41704e13			−0.279242			−0.139621	−	0.990205i	$-0.544588\pi$
$613$	−2.41704e13			−0.279242			−0.139621	+	0.990205i	$0.544588\pi$
$614$			5.75553e13i			0.659544i
$615$			4.26824e13i			0.485147i
$616$	7.01152e12	+	3.15570e12i	0.0790512	+	0.0355789i
$617$	6.61702e13			0.740008			0.370004	−	0.929030i	$-0.379356\pi$
$617$	6.61702e13			0.740008			0.370004	+	0.929030i	$0.379356\pi$
$618$	2.38599e13			0.264683
$619$			1.00883e14i			1.11010i	0.831816	+	0.555051i	$0.187301\pi$
$619$			1.00883e14i			1.11010i	−0.831816	+	0.555051i	$0.812699\pi$
$620$	4.43561e13			0.484167
$621$		−	7.94668e13i		−	0.860454i
$622$			5.10468e13i			0.548298i
$623$	−6.17934e13	+	1.37296e14i	−0.658418	+	1.46291i
$624$	2.46452e12			0.0260501
$625$	−3.00010e12			−0.0314583
$626$		−	9.46849e13i		−	0.984939i
$627$	−1.64592e13			−0.169852
$628$		−	2.69242e13i		−	0.275641i
$629$		−	1.80350e14i		−	1.83174i
$630$	3.92030e13	−	8.71035e13i	0.395017	−	0.877673i
$631$	1.85415e13			0.185353			0.0926763	−	0.995696i	$-0.470458\pi$
$631$	1.85415e13			0.185353			0.0926763	+	0.995696i	$0.470458\pi$
$632$	−3.73753e13			−0.370680
$633$		−	4.56888e13i		−	0.449563i
$634$	4.49356e12			0.0438676
$635$			2.25518e14i			2.18430i
$636$		−	1.39034e13i		−	0.133609i
$637$	2.06791e13	−	1.83195e13i	0.197167	−	0.174669i
$638$	−1.27961e13			−0.121052
$639$	−7.13862e13			−0.670054
$640$		−	1.53146e13i		−	0.142628i
$641$	9.19492e13			0.849685			0.424842	−	0.905267i	$-0.360330\pi$
$641$	9.19492e13			0.849685			0.424842	+	0.905267i	$0.360330\pi$
$642$			3.71766e13i			0.340874i
$643$		−	7.63688e13i		−	0.694802i	−0.937717	−	0.347401i	$-0.887064\pi$
$643$		−	7.63688e13i		−	0.694802i	0.937717	−	0.347401i	$-0.112936\pi$
$644$	−5.95920e13	−	2.68208e13i	−0.537971	−	0.242126i
$645$	−4.12705e13			−0.369693
$646$	2.44971e14			2.17747
$647$		−	1.03621e14i		−	0.913957i	−0.889478	−	0.456978i	$-0.848932\pi$
$647$		−	1.03621e14i		−	0.913957i	0.889478	−	0.456978i	$-0.151068\pi$
$648$	2.24205e13			0.196232
$649$		−	7.26306e12i		−	0.0630806i
$650$			3.46620e13i			0.298735i
$651$	−2.53107e13	−	1.13917e13i	−0.216470	−	0.0974276i
$652$	2.18240e13			0.185223
$653$	−5.38975e13			−0.453944			−0.226972	−	0.973901i	$-0.572883\pi$
$653$	−5.38975e13			−0.453944			−0.226972	+	0.973901i	$0.572883\pi$
$654$		−	5.65406e12i		−	0.0472576i
$655$	−1.06495e14			−0.883329
$656$			2.30825e13i			0.190005i
$657$			1.30844e14i			1.06887i
$658$	−1.56925e13	+	3.48666e13i	−0.127222	+	0.282670i
$659$	2.43899e13			0.196238			0.0981189	−	0.995175i	$-0.468717\pi$
$659$	2.43899e13			0.196238			0.0981189	+	0.995175i	$0.468717\pi$
$660$	9.80046e12			0.0782576
$661$		−	1.05621e14i		−	0.837032i	−0.908209	−	0.418516i	$-0.862550\pi$
$661$		−	1.05621e14i		−	0.837032i	0.908209	−	0.418516i	$-0.137450\pi$
$662$	−5.28574e13			−0.415734
$663$		−	2.34736e13i		−	0.183236i
$664$		−	4.77764e12i		−	0.0370146i
$665$	3.35111e14	+	1.50825e14i	2.57680	+	1.15975i
$666$	8.14084e13			0.621295
$667$	1.08756e14			0.823803
$668$			9.22580e13i			0.693620i
$669$	1.02789e13			0.0767033
$670$		−	2.08845e14i		−	1.54685i
$671$		−	6.75144e12i		−	0.0496345i
$672$	−3.93314e12	+	8.73887e12i	−0.0287007	+	0.0637689i
$673$	−1.32177e14			−0.957370			−0.478685	−	0.877987i	$-0.658886\pi$
$673$	−1.32177e14			−0.957370			−0.478685	+	0.877987i	$0.658886\pi$
$674$	−2.34862e13			−0.168854
$675$		−	1.63898e14i		−	1.16965i
$676$	6.56862e13			0.465308
$677$		−	1.37178e14i		−	0.964590i	−0.876009	−	0.482295i	$-0.839803\pi$
$677$		−	1.37178e14i		−	0.964590i	0.876009	−	0.482295i	$-0.160197\pi$
$678$		−	4.43962e13i		−	0.309883i
$679$	−7.11785e12	+	1.58149e13i	−0.0493174	+	0.109576i
$680$	−1.45865e14			−1.00325
$681$	−4.51826e13			−0.308486
$682$			1.53508e13i			0.104042i
$683$	−1.60627e14			−1.08073			−0.540363	−	0.841432i	$-0.681713\pi$
$683$	−1.60627e14			−1.08073			−0.540363	+	0.841432i	$0.681713\pi$
$684$			1.10578e14i			0.738562i
$685$			9.75160e13i			0.646581i
$686$	3.19567e13	+	1.02562e14i	0.210349	+	0.675095i
$687$	1.12309e14			0.733888
$688$	−2.23190e13			−0.144788
$689$			2.76284e13i			0.177934i
$690$	−8.32956e13			−0.532570
$691$			1.30063e14i			0.825591i	0.910824	+	0.412796i	$0.135448\pi$
$691$			1.30063e14i			0.825591i	−0.910824	+	0.412796i	$0.864552\pi$
$692$		−	5.68457e12i		−	0.0358234i
$693$	3.01448e13	+	1.35674e13i	0.188602	+	0.0848847i
$694$	−1.96527e14			−1.22074
$695$	−2.83022e14			−1.74541
$696$		−	1.59485e13i		−	0.0976503i
$697$	2.19852e14			1.33649
$698$		−	1.84112e13i		−	0.111123i
$699$			8.62511e13i			0.516867i
$700$	−1.22907e14	−	5.53172e13i	−0.731284	−	0.329132i
$701$	−1.86336e14			−1.10079			−0.550397	−	0.834903i	$-0.685524\pi$
$701$	−1.86336e14			−1.10079			−0.550397	+	0.834903i	$0.685524\pi$
$702$	2.31572e13			0.135831
$703$			3.13201e14i			1.82409i
$704$	5.30007e12			0.0306491
$705$			4.87353e13i			0.279832i
$706$		−	6.51248e12i		−	0.0371298i
$707$	1.28170e14	−	2.84775e14i	0.725584	−	1.61215i
$708$	9.05238e12			0.0508858
$709$	3.30040e13			0.184219			0.0921096	−	0.995749i	$-0.470639\pi$
$709$	3.30040e13			0.184219			0.0921096	+	0.995749i	$0.470639\pi$
$710$			1.63533e14i			0.906386i
$711$	−1.60688e14			−0.884376
$712$			1.03783e14i			0.567189i
$713$		−	1.30468e14i		−	0.708040i
$714$	8.32344e13	+	3.74616e13i	0.448551	+	0.201881i
$715$	−1.94751e13			−0.104219
$716$	−3.47302e13			−0.184562
$717$		−	1.99729e13i		−	0.105401i
$718$	−2.17728e12			−0.0114102
$719$		−	3.05955e14i		−	1.59226i	−0.605127	−	0.796129i	$-0.706877\pi$
$719$		−	3.05955e14i		−	1.59226i	0.605127	−	0.796129i	$-0.293123\pi$
$720$		−	6.58423e13i		−	0.340285i
$721$	7.56673e13	−	1.68122e14i	0.388358	−	0.862876i
$722$	−2.86693e14			−1.46127
$723$	−1.36772e14			−0.692319
$724$			3.48567e13i			0.175224i
$725$	2.24306e14			1.11983
$726$		−	5.30248e13i		−	0.262903i
$727$			2.35104e13i			0.115768i	0.998323	+	0.0578839i	$0.0184353\pi$
$727$			2.35104e13i			0.115768i	−0.998323	+	0.0578839i	$0.981565\pi$
$728$	7.81577e12	−	1.73655e13i	0.0382221	−	0.0849241i
$729$	3.69964e13			0.179689
$730$	2.99739e14			1.44587
$731$			2.12580e14i			1.01844i
$732$	8.41471e12			0.0400391
$733$			2.17768e14i			1.02914i	0.857449	+	0.514569i	$0.172048\pi$
$733$			2.17768e14i			1.02914i	−0.857449	+	0.514569i	$0.827952\pi$
$734$		−	1.82654e13i		−	0.0857332i
$735$	9.07968e13	+	1.02492e14i	0.423286	+	0.477808i
$736$	−4.50461e13			−0.208578
$737$	7.22769e13			0.332401
$738$			9.92392e13i			0.453316i
$739$	1.43784e14			0.652360			0.326180	−	0.945308i	$-0.394238\pi$
$739$	1.43784e14			0.652360			0.326180	+	0.945308i	$0.394238\pi$
$740$		−	1.86492e14i		−	0.840429i
$741$			4.07648e13i			0.182471i
$742$	−9.79667e13	−	4.40922e13i	−0.435571	−	0.196039i
$743$	1.11241e14			0.491272			0.245636	−	0.969362i	$-0.421003\pi$
$743$	1.11241e14			0.491272			0.245636	+	0.969362i	$0.421003\pi$
$744$	−1.91325e13			−0.0839282
$745$		−	6.27395e14i		−	2.73376i
$746$	2.06003e14			0.891620
$747$		−	2.05406e13i		−	0.0883100i
$748$		−	5.04811e13i		−	0.215586i
$749$	2.61954e14	+	1.17899e14i	1.11126	+	0.500149i
$750$	−6.46826e13			−0.272572
$751$	4.09610e14			1.71463			0.857316	−	0.514791i	$-0.172131\pi$
$751$	4.09610e14			1.71463			0.857316	+	0.514791i	$0.172131\pi$
$752$			2.63560e13i			0.109595i
$753$	1.29500e14			0.534927
$754$			3.16922e13i			0.130046i
$755$			2.03622e14i			0.830023i
$756$	−3.69567e13	+	8.21125e13i	−0.149652	+	0.332507i
$757$	−3.46638e14			−1.39443			−0.697215	−	0.716862i	$-0.745578\pi$
$757$	−3.46638e14			−1.39443			−0.697215	+	0.716862i	$0.745578\pi$
$758$	3.71553e13			0.148482
$759$		−	2.88269e13i		−	0.114443i
$760$	2.53313e14			0.999057
$761$			3.02067e14i			1.18353i	0.806109	+	0.591767i	$0.201569\pi$
$761$			3.02067e14i			1.18353i	−0.806109	+	0.591767i	$0.798431\pi$
$762$		−	9.72749e13i		−	0.378639i
$763$	−3.98397e13	−	1.79308e13i	−0.154061	−	0.0693390i
$764$	7.63261e13			0.293229
$765$	−6.27122e14			−2.39356
$766$		−	3.05740e14i		−	1.15933i
$767$	−1.79885e13			−0.0677670
$768$			6.60579e12i			0.0247240i
$769$		−	2.65421e14i		−	0.986968i	−0.869755	−	0.493484i	$-0.835723\pi$
$769$		−	2.65421e14i		−	0.986968i	0.869755	−	0.493484i	$-0.164277\pi$
$770$	3.10804e13	−	6.90561e13i	0.114824	−	0.255122i
$771$	8.27744e13			0.303825
$772$	1.36343e14			0.497216
$773$		−	2.73467e13i		−	0.0990848i	−0.998772	−	0.0495424i	$-0.984224\pi$
$773$		−	2.73467e13i		−	0.0990848i	0.998772	−	0.0495424i	$-0.0157763\pi$
$774$	−9.59564e13			−0.345437
$775$		−	2.69088e14i		−	0.962466i
$776$			1.19546e13i			0.0424841i
$777$	−4.78954e13	+	1.06417e14i	−0.169117	+	0.375755i
$778$	2.89131e13			0.101437
$779$	−3.81801e14			−1.33091
$780$		−	2.42729e13i		−	0.0840716i
$781$	−5.65954e13			−0.194772
$782$			4.29047e14i			1.46714i
$783$		−	1.49856e14i		−	0.509173i
$784$	4.91028e13	+	5.54275e13i	0.165777	+	0.187131i
$785$	−2.65175e14			−0.889578
$786$	4.59355e13			0.153121
$787$			3.56222e14i			1.17991i	0.807437	+	0.589953i	$0.200854\pi$
$787$			3.56222e14i			1.17991i	−0.807437	+	0.589953i	$0.799146\pi$
$788$	1.07999e14			0.355460
$789$			1.74509e14i			0.570732i
$790$			3.68108e14i			1.19630i
$791$	−3.12825e14	−	1.40794e14i	−1.01023	−	0.454677i
$792$	2.27867e13			0.0731232
$793$	−1.67214e13			−0.0533220
$794$		−	2.60937e14i		−	0.826863i
$795$	−1.36934e14			−0.431198
$796$		−	2.06360e13i		−	0.0645744i
$797$			2.34948e14i			0.730600i	0.930890	+	0.365300i	$0.119034\pi$
$797$			2.34948e14i			0.730600i	−0.930890	+	0.365300i	$0.880966\pi$
$798$	−1.44547e14	−	6.50567e13i	−0.446677	−	0.201038i
$799$	2.51030e14			0.770890
$800$	−9.29064e13			−0.283528
$801$			4.46198e14i			1.35321i
$802$	−2.10882e14			−0.635576
$803$			1.03734e14i			0.310701i
$804$			9.00830e13i			0.268141i
$805$	−2.64157e14	+	5.86919e14i	−0.781416	+	1.73620i
$806$	3.80194e13			0.111771
$807$	−5.22756e13			−0.152733
$808$		−	2.15264e14i		−	0.625049i
$809$	3.70512e14			1.06920			0.534601	−	0.845104i	$-0.320462\pi$
$809$	3.70512e14			1.06920			0.534601	+	0.845104i	$0.320462\pi$
$810$		−	2.20819e14i		−	0.633302i
$811$		−	5.40725e14i		−	1.54125i	−0.637291	−	0.770623i	$-0.719945\pi$
$811$		−	5.40725e14i		−	1.54125i	0.637291	−	0.770623i	$-0.280055\pi$
$812$	−1.12377e14	−	5.05778e13i	−0.318343	−	0.143278i
$813$	−5.64268e12			−0.0158867
$814$	6.45410e13			0.180598
$815$		−	2.14943e14i		−	0.597772i
$816$	6.29176e13			0.173909
$817$		−	3.69171e14i		−	1.01419i
$818$		−	7.07269e13i		−	0.193116i
$819$	3.36025e13	−	7.46599e13i	0.0911910	−	0.202613i
$820$	2.27339e14			0.613203
$821$	−5.34259e14			−1.43231			−0.716154	−	0.697942i	$-0.754099\pi$
$821$	−5.34259e14			−1.43231			−0.716154	+	0.697942i	$0.754099\pi$
$822$		−	4.20625e13i		−	0.112082i
$823$	−7.86815e13			−0.208388			−0.104194	−	0.994557i	$-0.533226\pi$
$823$	−7.86815e13			−0.208388			−0.104194	+	0.994557i	$0.533226\pi$
$824$		−	1.27085e14i		−	0.334548i
$825$		−	5.94548e13i		−	0.155567i
$826$	2.87080e13	−	6.37850e13i	0.0746624	−	0.165889i
$827$	5.43521e14			1.40504			0.702520	−	0.711664i	$-0.252058\pi$
$827$	5.43521e14			1.40504			0.702520	+	0.711664i	$0.252058\pi$
$828$	−1.93668e14			−0.497628
$829$			4.54306e14i			1.16031i	0.814504	+	0.580157i	$0.197009\pi$
$829$			4.54306e14i			1.16031i	−0.814504	+	0.580157i	$0.802991\pi$
$830$	−4.70547e13			−0.119457
$831$			9.35881e13i			0.236165i
$832$		−	1.31268e13i		−	0.0329261i
$833$	5.27925e14	−	4.67685e14i	1.31628	−	1.16608i
$834$	1.22079e14			0.302559
$835$	9.08645e14			2.23852
$836$			8.76667e13i			0.214686i
$837$	−1.79774e14			−0.437622
$838$			2.01023e14i			0.486436i
$839$			5.33758e14i			1.28391i	0.766742	+	0.641955i	$0.221877\pi$
$839$			5.33758e14i			1.28391i	−0.766742	+	0.641955i	$0.778123\pi$
$840$	8.60687e13	+	3.87373e13i	0.205802	+	0.0926259i
$841$	−2.15619e14			−0.512516
$842$	−1.64327e14			−0.388282
$843$		−	1.92024e14i		−	0.451043i
$844$	−2.43352e14			−0.568228
$845$		−	6.46940e14i		−	1.50169i
$846$			1.13313e14i			0.261473i
$847$	−3.73624e14	−	1.68158e14i	−0.857073	−	0.385746i
$848$	−7.40539e13			−0.168876
$849$	3.12216e14			0.707809
$850$			8.84898e14i			1.99434i
$851$	−5.48544e14			−1.22903
$852$		−	7.05382e13i		−	0.157118i
$853$			3.28172e14i			0.726703i	0.931652	+	0.363351i	$0.118368\pi$
$853$			3.28172e14i			0.726703i	−0.931652	+	0.363351i	$0.881632\pi$
$854$	2.66857e13	−	5.92919e13i	0.0587475	−	0.130529i
$855$	1.08908e15			2.38357
$856$	1.98013e14			0.430850
$857$		−	3.25327e14i		−	0.703747i	−0.936048	−	0.351873i	$-0.885545\pi$
$857$		−	3.25327e14i		−	0.703747i	0.936048	−	0.351873i	$-0.114455\pi$
$858$	8.40037e12			0.0180660
$859$		−	3.47684e14i		−	0.743394i	−0.928354	−	0.371697i	$-0.878776\pi$
$859$		−	3.47684e14i		−	0.743394i	0.928354	−	0.371697i	$-0.121224\pi$
$860$			2.19819e14i			0.467275i
$861$	−1.29725e14	−	5.83859e13i	−0.274163	−	0.123393i
$862$	−2.89302e14			−0.607877
$863$	2.68408e14			0.560713			0.280357	−	0.959896i	$-0.409547\pi$
$863$	2.68408e14			0.560713			0.280357	+	0.959896i	$0.409547\pi$
$864$			6.20695e13i			0.128917i
$865$	−5.59871e13			−0.115613
$866$		−	1.78516e14i		−	0.366512i
$867$		−	4.05474e14i		−	0.827690i
$868$	−6.06754e13	+	1.34812e14i	−0.123144	+	0.273609i
$869$	−1.27395e14			−0.257071
$870$	−1.57076e14			−0.315147
$871$		−	1.79009e14i		−	0.357096i
$872$	−3.01152e13			−0.0597315
$873$			5.13966e13i			0.101359i
$874$		−	7.45093e14i		−	1.46101i
$875$	−2.05129e14	+	4.55768e14i	−0.399933	+	0.888594i
$876$	−1.29290e14			−0.250636
$877$	6.53459e14			1.25957			0.629783	−	0.776771i	$-0.283144\pi$
$877$	6.53459e14			1.25957			0.629783	+	0.776771i	$0.283144\pi$
$878$		−	5.30336e14i		−	1.01643i
$879$	2.46692e13			0.0470123
$880$		−	5.22001e13i		−	0.0989141i
$881$			2.35821e14i			0.444327i	0.975009	+	0.222164i	$0.0713119\pi$
$881$			2.35821e14i			0.444327i	−0.975009	+	0.222164i	$0.928688\pi$
$882$	2.11108e14	+	2.38300e14i	0.395515	+	0.446459i
$883$	5.53102e14			1.03039			0.515195	−	0.857073i	$-0.327719\pi$
$883$	5.53102e14			1.03039			0.515195	+	0.857073i	$0.327719\pi$
$884$	−1.25027e14			−0.231603
$885$		−	8.91565e13i		−	0.164224i
$886$	−4.12851e14			−0.756180
$887$			1.05990e15i			1.93039i	0.261529	+	0.965196i	$0.415773\pi$
$887$			1.05990e15i			1.93039i	−0.261529	+	0.965196i	$0.584227\pi$
$888$			8.04413e13i			0.145685i
$889$	−6.85420e14	−	3.08489e14i	−1.23438	−	0.555561i
$890$	1.02216e15			1.83049
$891$	7.64209e13			0.136089
$892$		−	5.47482e13i		−	0.0969496i
$893$	−4.35945e14			−0.767670
$894$			2.70620e14i			0.473885i
$895$			3.42056e14i			0.595638i
$896$	4.65458e13	+	2.09490e13i	0.0806010	+	0.0362764i
$897$	−7.13961e13			−0.122945
$898$	−4.72049e14			−0.808361
$899$		−	2.46033e14i		−	0.418982i
$900$	−3.99434e14			−0.676445
$901$			7.05335e14i			1.18788i
$902$			7.86774e13i			0.131770i
$903$	5.64545e13	−	1.25434e14i	0.0940285	−	0.208918i
$904$	−2.36467e14			−0.391678
$905$	3.43302e14			0.565501
$906$		−	8.78303e13i		−	0.143881i
$907$	−3.85480e14			−0.628009			−0.314005	−	0.949421i	$-0.601671\pi$
$907$	−3.85480e14			−0.628009			−0.314005	+	0.949421i	$0.601671\pi$
$908$			2.40656e14i			0.389913i
$909$		−	9.25487e14i		−	1.49125i
$910$	−1.71032e14	−	7.69771e13i	−0.274076	−	0.123354i
$911$	−1.10046e15			−1.75381			−0.876905	−	0.480663i	$-0.840396\pi$
$911$	−1.10046e15			−1.75381			−0.876905	+	0.480663i	$0.840396\pi$
$912$	−1.09264e14			−0.173182
$913$		−	1.62847e13i		−	0.0256700i
$914$	3.02678e14			0.474515
$915$		−	8.28761e13i		−	0.129218i
$916$		−	5.98189e14i		−	0.927601i
$917$	1.45676e14	−	3.23672e14i	0.224668	−	0.499181i
$918$	5.91188e14			0.906802
$919$	5.88693e14			0.898072			0.449036	−	0.893514i	$-0.351767\pi$
$919$	5.88693e14			0.898072			0.449036	+	0.893514i	$0.351767\pi$
$920$			4.43657e14i			0.673144i
$921$	−2.44509e14			−0.368975
$922$		−	2.44976e13i		−	0.0367680i
$923$			1.40171e14i			0.209242i
$924$	−1.34062e13	+	2.97867e13i	−0.0199042	+	0.0442244i
$925$	−1.13136e15			−1.67067
$926$	7.21674e13			0.105995
$927$		−	5.46379e14i		−	0.798169i
$928$	−8.49464e13			−0.123426
$929$			5.13603e14i			0.742248i	0.928583	+	0.371124i	$0.121028\pi$
$929$			5.13603e14i			0.742248i	−0.928583	+	0.371124i	$0.878972\pi$
$930$			1.88436e14i			0.270862i
$931$	−9.16807e14	+	8.12193e14i	−1.31078	+	1.16121i
$932$	4.59399e14			0.653296
$933$	−2.16859e14			−0.306739
$934$			4.42221e14i			0.622164i
$935$	−4.97186e14			−0.695762
$936$		−	5.64361e13i		−	0.0785557i
$937$			1.14018e15i			1.57861i	0.614001	+	0.789305i	$0.289559\pi$
$937$			1.14018e15i			1.57861i	−0.614001	+	0.789305i	$0.710441\pi$
$938$	6.34744e14	+	2.85682e14i	0.874147	+	0.393431i
$939$	4.02245e14			0.551014
$940$	2.59579e14			0.353696
$941$			4.03021e14i			0.546235i	0.961981	+	0.273118i	$0.0880548\pi$
$941$			4.03021e14i			0.546235i	−0.961981	+	0.273118i	$0.911945\pi$
$942$	1.14380e14			0.154205
$943$		−	6.68692e14i		−	0.896742i
$944$		−	4.82156e13i		−	0.0643173i
$945$	8.08722e14	+	3.63985e14i	1.07310	+	0.482974i
$946$	−7.60748e13			−0.100412
$947$	−7.06243e14			−0.927266			−0.463633	−	0.886027i	$-0.653454\pi$
$947$	−7.06243e14			−0.927266			−0.463633	+	0.886027i	$0.653454\pi$
$948$		−	1.58780e14i		−	0.207373i
$949$	2.56919e14			0.333784
$950$		−	1.53673e15i		−	1.98601i
$951$			1.90897e13i			0.0245413i
$952$	1.99532e14	−	4.43331e14i	0.255168	−	0.566948i
$953$	1.01961e15			1.29709			0.648545	−	0.761176i	$-0.275378\pi$
$953$	1.01961e15			1.29709			0.648545	+	0.761176i	$0.275378\pi$
$954$	−3.18381e14			−0.402908
$955$		−	7.51732e14i		−	0.946338i
$956$	−1.06382e14			−0.133222
$957$		−	5.43609e13i		−	0.0677215i
$958$		−	2.29970e13i		−	0.0284999i
$959$	−2.96382e14	−	1.33394e14i	−0.365391	−	0.164453i
$960$	6.50601e13			0.0797918
$961$	5.24476e14			0.639895
$962$		−	1.59850e14i		−	0.194016i
$963$	8.51322e14			1.02793
$964$			7.28489e14i			0.875060i
$965$		−	1.34283e15i		−	1.60467i
$966$	1.13941e14	−	2.53161e14i	0.135455	−	0.300962i
$967$	−9.35888e14			−1.10686			−0.553428	−	0.832897i	$-0.686681\pi$
$967$	−9.35888e14			−1.10686			−0.553428	+	0.832897i	$0.686681\pi$
$968$	−2.82426e14			−0.332298
$969$			1.04070e15i			1.21817i
$970$	1.17740e14			0.137109
$971$		−	6.50229e14i		−	0.753304i	−0.926355	−	0.376652i	$-0.877075\pi$
$971$		−	6.50229e14i		−	0.753304i	0.926355	−	0.376652i	$-0.122925\pi$
$972$			4.11611e14i			0.474412i
$973$	3.87151e14	−	8.60194e14i	0.443931	−	0.986352i
$974$	2.72722e14			0.311118
$975$	−1.47253e14			−0.167124
$976$		−	4.48193e13i		−	0.0506076i
$977$	1.27020e15			1.42692			0.713459	−	0.700697i	$-0.247127\pi$
$977$	1.27020e15			1.42692			0.713459	+	0.700697i	$0.247127\pi$
$978$			9.27136e13i			0.103621i
$979$			3.53748e14i			0.393352i
$980$	5.45903e14	−	4.83611e14i	0.603927	−	0.535015i
$981$	−1.29475e14			−0.142508
$982$	−3.72473e14			−0.407885
$983$			1.35838e15i			1.47997i	0.672621	+	0.739987i	$0.265168\pi$
$983$			1.35838e15i			1.47997i	−0.672621	+	0.739987i	$0.734832\pi$
$984$	−9.80603e13			−0.106296
$985$		−	1.06368e15i		−	1.14718i
$986$			8.09082e14i			0.868176i
$987$	−1.48122e14	−	6.66657e13i	−0.158137	−	0.0711733i
$988$	2.17125e14			0.230635
$989$	6.46572e14			0.683337
$990$		−	2.24425e14i		−	0.235991i
$991$	1.11533e15			1.16690			0.583452	−	0.812147i	$-0.301702\pi$
$991$	1.11533e15			1.16690			0.583452	+	0.812147i	$0.301702\pi$
$992$			1.01906e14i			0.106082i
$993$		−	2.24551e14i		−	0.232578i
$994$	−4.97027e14	−	2.23699e14i	−0.512210	−	0.230532i
$995$	−2.03243e14			−0.208401
$996$	2.02966e13			0.0207074
$997$			7.69493e14i			0.781140i	0.920573	+	0.390570i	$0.127722\pi$
$997$			7.69493e14i			0.781140i	−0.920573	+	0.390570i	$0.872278\pi$
$998$	1.29147e15			1.30446
$999$			7.55846e14i			0.759636i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.11.b.a.13.7	yes	8
3.2	odd	2		126.11.c.a.55.4		8
4.3	odd	2		112.11.c.d.97.4		8
7.2	even	3		98.11.d.c.31.2		16
7.3	odd	6		98.11.d.c.19.2		16
7.4	even	3		98.11.d.c.19.3		16
7.5	odd	6		98.11.d.c.31.3		16
7.6	odd	2	inner	14.11.b.a.13.6	✓	8
21.20	even	2		126.11.c.a.55.1		8
28.27	even	2		112.11.c.d.97.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.11.b.a.13.6	✓	8	7.6	odd	2	inner
14.11.b.a.13.7	yes	8	1.1	even	1	trivial
98.11.d.c.19.2		16	7.3	odd	6
98.11.d.c.19.3		16	7.4	even	3
98.11.d.c.31.2		16	7.2	even	3
98.11.d.c.31.3		16	7.5	odd	6
112.11.c.d.97.4		8	4.3	odd	2
112.11.c.d.97.5		8	28.27	even	2
126.11.c.a.55.1		8	21.20	even	2
126.11.c.a.55.4		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274 q^{2} +96.1268i q^{3} +512.000 q^{4} -5042.67i q^{5} +2175.10i q^{6} +(15326.2 + 6897.94i) q^{7} +11585.2 q^{8} +49808.6 q^{9} +O(q^{10})\)	\(q+22.6274 q^{2} +96.1268i q^{3} +512.000 q^{4} -5042.67i q^{5} +2175.10i q^{6} +(15326.2 + 6897.94i) q^{7} +11585.2 q^{8} +49808.6 q^{9} -114102. i q^{10} +39488.6 q^{11} +49216.9i q^{12} -97801.9i q^{13} +(346793. + 156083. i) q^{14} +484735. q^{15} +262144. q^{16} -2.49682e6i q^{17} +1.12704e6 q^{18} +4.33604e6i q^{19} -2.58184e6i q^{20} +(-663077. + 1.47326e6i) q^{21} +893525. q^{22} -7.59420e6 q^{23} +1.11365e6i q^{24} -1.56628e7 q^{25} -2.21300e6i q^{26} +1.04641e7i q^{27} +(7.84704e6 + 3.53174e6i) q^{28} -1.43209e7 q^{29} +1.09683e7 q^{30} +1.71800e7i q^{31} +5.93164e6 q^{32} +3.79591e6i q^{33} -5.64966e7i q^{34} +(3.47840e7 - 7.72851e7i) q^{35} +2.55020e7 q^{36} +7.22320e7 q^{37} +9.81134e7i q^{38} +9.40139e6 q^{39} -5.84205e7i q^{40} +8.80529e7i q^{41} +(-1.50037e7 + 3.33361e7i) q^{42} -8.51402e7 q^{43} +2.02182e7 q^{44} -2.51168e8i q^{45} -1.71837e8 q^{46} +1.00540e8i q^{47} +2.51991e7i q^{48} +(1.87312e8 + 2.11439e8i) q^{49} -3.54410e8 q^{50} +2.40011e8 q^{51} -5.00746e7i q^{52} -2.82493e8 q^{53} +2.36776e8i q^{54} -1.99128e8i q^{55} +(1.77558e8 + 7.99143e7i) q^{56} -4.16810e8 q^{57} -3.24045e8 q^{58} -1.83928e8i q^{59} +2.48185e8 q^{60} -1.70972e8i q^{61} +3.88739e8i q^{62} +(7.63379e8 + 3.43577e8i) q^{63} +1.34218e8 q^{64} -4.93182e8 q^{65} +8.58917e7i q^{66} +1.83033e9 q^{67} -1.27837e9i q^{68} -7.30007e8i q^{69} +(7.87072e8 - 1.74876e9i) q^{70} -1.43321e9 q^{71} +5.77045e8 q^{72} +2.62693e9i q^{73} +1.63442e9 q^{74} -1.50562e9i q^{75} +2.22005e9i q^{76} +(6.05212e8 + 2.72390e8i) q^{77} +2.12729e8 q^{78} -3.22612e9 q^{79} -1.32190e9i q^{80} +1.93527e9 q^{81} +1.99241e9i q^{82} -4.12390e8i q^{83} +(-3.39495e8 + 7.54311e8i) q^{84} -1.25906e10 q^{85} -1.92650e9 q^{86} -1.37662e9i q^{87} +4.57485e8 q^{88} +8.95824e9i q^{89} -5.68329e9i q^{90} +(6.74632e8 - 1.49894e9i) q^{91} -3.88823e9 q^{92} -1.65146e9 q^{93} +2.27496e9i q^{94} +2.18652e10 q^{95} +5.70190e8i q^{96} +1.03188e9i q^{97} +(4.23839e9 + 4.78432e9i) q^{98} +1.96687e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9}+O(q^{10}) \) 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9	\( 8 q + 4096 q^{4} + 18376 q^{7} - 246456 q^{9} + 430800 q^{11} - 136704 q^{14} - 1896960 q^{15} + 2097152 q^{16} - 4512768 q^{18} + 5339136 q^{21} + 13228032 q^{22} + 6265488 q^{23} - 28719160 q^{25} + 9408512 q^{28} - 46431408 q^{29} + 28584960 q^{30} + 184450560 q^{35} - 126185472 q^{36} + 360932816 q^{37} - 836120064 q^{39} + 308382720 q^{42} + 32112848 q^{43} + 220569600 q^{44} - 769191936 q^{46} + 853888904 q^{49} - 53836800 q^{50} + 1737904128 q^{51} - 1132258608 q^{53} - 69992448 q^{56} - 2040889344 q^{57} + 352352256 q^{58} - 971243520 q^{60} + 2661283080 q^{63} + 1073741824 q^{64} - 143001600 q^{65} - 2254742192 q^{67} + 402662400 q^{70} + 2121911184 q^{71} - 2310537216 q^{72} + 4970207232 q^{74} - 17516185008 q^{77} + 1916728320 q^{78} - 5257367792 q^{79} + 24706423944 q^{81} + 2733637632 q^{84} + 4331212800 q^{85} - 14424637440 q^{86} + 6772752384 q^{88} - 8536548864 q^{91} + 3207929856 q^{92} - 20748386304 q^{93} + 30330078720 q^{95} - 802977792 q^{98} - 16331376816 q^{99}+O(q^{100}) \) 8 * q + 4096 * q^4 + 18376 * q^7 - 246456 * q^9 + 430800 * q^11 - 136704 * q^14 - 1896960 * q^15 + 2097152 * q^16 - 4512768 * q^18 + 5339136 * q^21 + 13228032 * q^22 + 6265488 * q^23 - 28719160 * q^25 + 9408512 * q^28 - 46431408 * q^29 + 28584960 * q^30 + 184450560 * q^35 - 126185472 * q^36 + 360932816 * q^37 - 836120064 * q^39 + 308382720 * q^42 + 32112848 * q^43 + 220569600 * q^44 - 769191936 * q^46 + 853888904 * q^49 - 53836800 * q^50 + 1737904128 * q^51 - 1132258608 * q^53 - 69992448 * q^56 - 2040889344 * q^57 + 352352256 * q^58 - 971243520 * q^60 + 2661283080 * q^63 + 1073741824 * q^64 - 143001600 * q^65 - 2254742192 * q^67 + 402662400 * q^70 + 2121911184 * q^71 - 2310537216 * q^72 + 4970207232 * q^74 - 17516185008 * q^77 + 1916728320 * q^78 - 5257367792 * q^79 + 24706423944 * q^81 + 2733637632 * q^84 + 4331212800 * q^85 - 14424637440 * q^86 + 6772752384 * q^88 - 8536548864 * q^91 + 3207929856 * q^92 - 20748386304 * q^93 + 30330078720 * q^95 - 802977792 * q^98 - 16331376816 * q^99

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