LMFDB - Embedded newform 150.11.d.a.101.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,11,Mod(101,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("150.101");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	150.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$95.3035879011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{85})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 37x^{2} + 38x + 531 $ x^4 - 2x^3 - 37x^2 + 38*x + 531
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.4
Root			$5.10977 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	150.101
Dual form			150.11.d.a.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274i q^{2} +(200.269 - 137.627i) q^{3} -512.000 q^{4} +(3114.15 + 4531.57i) q^{6} +23226.5 q^{7} -11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +O(q^{10})$	\(q+22.6274i q^{2} +(200.269 - 137.627i) q^{3} -512.000 q^{4} +(3114.15 + 4531.57i) q^{6} +23226.5 q^{7} -11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} -62442.7i q^{11} +(-102538. + 70465.2i) q^{12} +170161. q^{13} +525556. i q^{14} +262144. q^{16} -2.66626e6i q^{17} +(1.24734e6 + 478941. i) q^{18} +766825. q^{19} +(4.65156e6 - 3.19661e6i) q^{21} +1.41292e6 q^{22} +1.40327e6i q^{23} +(-1.59445e6 - 2.32016e6i) q^{24} +3.85029e6i q^{26} +(-3.34774e6 - 1.39529e7i) q^{27} -1.18920e7 q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} +5.93164e6i q^{32} +(-8.59382e6 - 1.25053e7i) q^{33} +6.03306e7 q^{34} +(-1.08372e7 + 2.82240e7i) q^{36} -5.01619e7 q^{37} +1.73513e7i q^{38} +(3.40779e7 - 2.34188e7i) q^{39} +1.49239e8i q^{41} +(7.23310e7 + 1.05253e8i) q^{42} +1.98719e8 q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} -1.55059e8i q^{47} +(5.24993e7 - 3.60782e7i) q^{48} +2.56996e8 q^{49} +(-3.66951e8 - 5.33970e8i) q^{51} -8.71222e7 q^{52} +4.21541e7i q^{53} +(3.15718e8 - 7.57507e7i) q^{54} -2.69085e8i q^{56} +(1.53571e8 - 1.05536e8i) q^{57} +1.09346e8 q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} -9.46499e8i q^{62} +(4.91622e8 - 1.28036e9i) q^{63} -1.34218e8 q^{64} +(2.82963e8 - 1.94456e8i) q^{66} -5.22093e8 q^{67} +1.36513e9i q^{68} +(1.93128e8 + 2.81031e8i) q^{69} -5.71364e8i q^{71} +(-6.38636e8 - 2.45218e8i) q^{72} -2.18588e9 q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} -1.45033e9i q^{77} +(5.29906e8 + 7.71095e8i) q^{78} +1.96592e9 q^{79} +(-2.59075e9 - 2.33360e9i) q^{81} -3.37689e9 q^{82} -2.18558e9i q^{83} +(-2.38160e9 + 1.63666e9i) q^{84} +4.49650e9i q^{86} +(-6.65078e8 - 9.67791e8i) q^{87} -7.23413e8 q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} -7.18473e8i q^{92} +(-8.37720e9 + 5.75692e9i) q^{93} +3.50858e9 q^{94} +(8.16356e8 + 1.18792e9i) q^{96} +8.84112e9 q^{97} +5.81517e9i q^{98} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 84 q^{3} - 2048 q^{4} + 5376 q^{6} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) $ 4 * q - 84 * q^3 - 2048 * q^4 + 5376 * q^6 + 45112 * q^7 + 159012 * q^9	$ 4 q - 84 q^{3} - 2048 q^{4} + 5376 q^{6} + 45112 q^{7} + 159012 q^{9} + 43008 q^{12} - 275240 q^{13} + 1048576 q^{16} + 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} - 7730688 q^{22} - 2752512 q^{24} - 34619508 q^{27} - 23097344 q^{28} - 21785848 q^{31} - 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} + 71014168 q^{37} + 217287240 q^{39} + 145233408 q^{42} + 470688664 q^{43} + 188814336 q^{46} - 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} + 140922880 q^{52} + 481662720 q^{54} + 1058753208 q^{57} + 1564177920 q^{58} - 1184038744 q^{61} + 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} + 297365848 q^{67} + 596268288 q^{69} - 1488715776 q^{72} - 6534269000 q^{73} + 803188736 q^{76} + 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} - 8378668032 q^{82} - 4929540096 q^{84} - 210268800 q^{87} + 3958112256 q^{88} + 8317232080 q^{91} - 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} + 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) $ 4 * q - 84 * q^3 - 2048 * q^4 + 5376 * q^6 + 45112 * q^7 + 159012 * q^9 + 43008 * q^12 - 275240 * q^13 + 1048576 * q^16 + 2907648 * q^18 - 1568728 * q^19 + 9628008 * q^21 - 7730688 * q^22 - 2752512 * q^24 - 34619508 * q^27 - 23097344 * q^28 - 21785848 * q^31 - 25974144 * q^33 + 151087104 * q^34 - 81414144 * q^36 + 71014168 * q^37 + 217287240 * q^39 + 145233408 * q^42 + 470688664 * q^43 + 188814336 * q^46 - 22020096 * q^48 - 50058420 * q^49 - 708576768 * q^51 + 140922880 * q^52 + 481662720 * q^54 + 1058753208 * q^57 + 1564177920 * q^58 - 1184038744 * q^61 + 905007096 * q^63 - 536870912 * q^64 + 3123445248 * q^66 + 297365848 * q^67 + 596268288 * q^69 - 1488715776 * q^72 - 6534269000 * q^73 + 803188736 * q^76 + 1322135040 * q^78 + 199282568 * q^79 + 1458964548 * q^81 - 8378668032 * q^82 - 4929540096 * q^84 - 210268800 * q^87 + 3958112256 * q^88 + 8317232080 * q^91 - 31744468392 * q^93 + 8505477120 * q^94 + 1409286144 * q^96 + 39176355064 * q^97 - 2626912512 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			22.6274i			0.707107i
$2$			22.6274i			0.707107i
$3$	200.269	−	137.627i	0.824153	−	0.566368i
$3$	200.269	−	137.627i	0.824153	−	0.566368i
$4$	−512.000			−0.500000
$5$		0			0
$5$		0			0
$6$	3114.15	+	4531.57i	0.400483	+	0.582764i
$7$	23226.5			1.38196			0.690978	−	0.722876i	$-0.257180\pi$
$7$	23226.5			1.38196			0.690978	+	0.722876i	$0.257180\pi$
$8$		−	11585.2i		−	0.353553i
$9$	21166.4	−	55125.0i	0.358455	−	0.933547i
$10$		0			0
$11$		−	62442.7i		−	0.387720i	−0.981029	−	0.193860i	$-0.937899\pi$
$11$		−	62442.7i		−	0.387720i	0.981029	−	0.193860i	$-0.0621007\pi$
$12$	−102538.	+	70465.2i	−0.412076	+	0.283184i
$13$	170161.			0.458292			0.229146	−	0.973392i	$-0.426407\pi$
$13$	170161.			0.458292			0.229146	+	0.973392i	$0.426407\pi$
$14$			525556.i			0.977190i
$15$		0			0
$16$	262144.			0.250000
$17$		−	2.66626e6i		−	1.87784i	−0.344139	−	0.938919i	$-0.611829\pi$
$17$		−	2.66626e6i		−	1.87784i	0.344139	−	0.938919i	$-0.388171\pi$
$18$	1.24734e6	+	478941.i	0.660117	+	0.253466i
$19$	766825.			0.309691			0.154845	−	0.987939i	$-0.450512\pi$
$19$	766825.			0.309691			0.154845	+	0.987939i	$0.450512\pi$
$20$		0			0
$21$	4.65156e6	−	3.19661e6i	1.13894	−	0.782695i
$22$	1.41292e6			0.274159
$23$			1.40327e6i			0.218022i	0.994041	+	0.109011i	$0.0347684\pi$
$23$			1.40327e6i			0.218022i	−0.994041	+	0.109011i	$0.965232\pi$
$24$	−1.59445e6	−	2.32016e6i	−0.200241	−	0.291382i
$25$		0			0
$26$			3.85029e6i			0.324061i
$27$	−3.34774e6	−	1.39529e7i	−0.233310	−	0.972402i
$28$	−1.18920e7			−0.690978
$29$		−	4.83245e6i		−	0.235601i	−0.993037	−	0.117801i	$-0.962416\pi$
$29$		−	4.83245e6i		−	0.235601i	0.993037	−	0.117801i	$-0.0375844\pi$
$30$		0			0
$31$	−4.18297e7			−1.46109			−0.730544	−	0.682865i	$-0.760734\pi$
$31$	−4.18297e7			−1.46109			−0.730544	+	0.682865i	$0.760734\pi$
$32$			5.93164e6i			0.176777i
$33$	−8.59382e6	−	1.25053e7i	−0.219592	−	0.319540i
$34$	6.03306e7			1.32783
$35$		0			0
$36$	−1.08372e7	+	2.82240e7i	−0.179227	+	0.466774i
$37$	−5.01619e7			−0.723378			−0.361689	−	0.932299i	$-0.617800\pi$
$37$	−5.01619e7			−0.723378			−0.361689	+	0.932299i	$0.617800\pi$
$38$			1.73513e7i			0.218985i
$39$	3.40779e7	−	2.34188e7i	0.377702	−	0.259562i
$40$		0			0
$41$			1.49239e8i			1.28814i	0.764967	+	0.644069i	$0.222755\pi$
$41$			1.49239e8i			1.28814i	−0.764967	+	0.644069i	$0.777245\pi$
$42$	7.23310e7	+	1.05253e8i	0.553449	+	0.805354i
$43$	1.98719e8			1.35175			0.675876	−	0.737015i	$-0.263765\pi$
$43$	1.98719e8			1.35175			0.675876	+	0.737015i	$0.263765\pi$
$44$			3.19706e7i			0.193860i
$45$		0			0
$46$	−3.17523e7			−0.154165
$47$		−	1.55059e8i		−	0.676093i	−0.941129	−	0.338047i	$-0.890234\pi$
$47$		−	1.55059e8i		−	0.676093i	0.941129	−	0.338047i	$-0.109766\pi$
$48$	5.24993e7	−	3.60782e7i	0.206038	−	0.141592i
$49$	2.56996e8			0.909802
$50$		0			0
$51$	−3.66951e8	−	5.33970e8i	−1.06355	−	1.54762i
$52$	−8.71222e7			−0.229146
$53$			4.21541e7i			0.100800i	0.998729	+	0.0503999i	$0.0160496\pi$
$53$			4.21541e7i			0.100800i	−0.998729	+	0.0503999i	$0.983950\pi$
$54$	3.15718e8	−	7.57507e7i	0.687592	−	0.164975i
$55$		0			0
$56$		−	2.69085e8i		−	0.488595i
$57$	1.53571e8	−	1.05536e8i	0.255233	−	0.175399i
$58$	1.09346e8			0.166595
$59$		−	2.92026e8i		−	0.408471i	−0.978922	−	0.204236i	$-0.934529\pi$
$59$		−	2.92026e8i		−	0.408471i	0.978922	−	0.204236i	$-0.0654708\pi$
$60$		0			0
$61$	−5.30727e8			−0.628379			−0.314190	−	0.949360i	$-0.601733\pi$
$61$	−5.30727e8			−0.628379			−0.314190	+	0.949360i	$0.601733\pi$
$62$		−	9.46499e8i		−	1.03315i
$63$	4.91622e8	−	1.28036e9i	0.495369	−	1.29012i
$64$	−1.34218e8			−0.125000
$65$		0			0
$66$	2.82963e8	−	1.94456e8i	0.225949	−	0.155275i
$67$	−5.22093e8			−0.386700			−0.193350	−	0.981130i	$-0.561935\pi$
$67$	−5.22093e8			−0.386700			−0.193350	+	0.981130i	$0.561935\pi$
$68$			1.36513e9i			0.938919i
$69$	1.93128e8	+	2.81031e8i	0.123481	+	0.179684i
$70$		0			0
$71$		−	5.71364e8i		−	0.316681i	−0.987385	−	0.158340i	$-0.949386\pi$
$71$		−	5.71364e8i		−	0.316681i	0.987385	−	0.158340i	$-0.0506143\pi$
$72$	−6.38636e8	−	2.45218e8i	−0.330059	−	0.126733i
$73$	−2.18588e9			−1.05441			−0.527207	−	0.849737i	$-0.676761\pi$
$73$	−2.18588e9			−1.05441			−0.527207	+	0.849737i	$0.676761\pi$
$74$		−	1.13503e9i		−	0.511506i
$75$		0			0
$76$	−3.92615e8			−0.154845
$77$		−	1.45033e9i		−	0.535812i
$78$	5.29906e8	+	7.71095e8i	0.183538	+	0.267076i
$79$	1.96592e9			0.638897			0.319449	−	0.947604i	$-0.396502\pi$
$79$	1.96592e9			0.638897			0.319449	+	0.947604i	$0.396502\pi$
$80$		0			0
$81$	−2.59075e9	−	2.33360e9i	−0.743020	−	0.669269i
$82$	−3.37689e9			−0.910851
$83$		−	2.18558e9i		−	0.554850i	−0.960747	−	0.277425i	$-0.910519\pi$
$83$		−	2.18558e9i		−	0.554850i	0.960747	−	0.277425i	$-0.0894810\pi$
$84$	−2.38160e9	+	1.63666e9i	−0.569471	+	0.391348i
$85$		0			0
$86$			4.49650e9i			0.955833i
$87$	−6.65078e8	−	9.67791e8i	−0.133437	−	0.194171i
$88$	−7.23413e8			−0.137080
$89$			2.38742e8i			0.0427542i	0.999771	+	0.0213771i	$0.00680506\pi$
$89$			2.38742e8i			0.0427542i	−0.999771	+	0.0213771i	$0.993195\pi$
$90$		0			0
$91$	3.95224e9			0.633339
$92$		−	7.18473e8i		−	0.109011i
$93$	−8.37720e9	+	5.75692e9i	−1.20416	+	0.827514i
$94$	3.50858e9			0.478070
$95$		0			0
$96$	8.16356e8	+	1.18792e9i	0.100121	+	0.145691i
$97$	8.84112e9			1.02955			0.514776	−	0.857324i	$-0.327875\pi$
$97$	8.84112e9			1.02955			0.514776	+	0.857324i	$0.327875\pi$
$98$			5.81517e9i			0.643327i
$99$	−3.44215e9	−	1.32169e9i	−0.361955	−	0.138980i
$100$		0			0
$101$		−	1.67928e10i		−	1.59778i	−0.601477	−	0.798890i	$-0.705421\pi$
$101$		−	1.67928e10i		−	1.59778i	0.601477	−	0.798890i	$-0.294579\pi$
$102$	1.20824e10	−	8.30314e9i	1.09434	−	0.752041i
$103$	−8.36865e9			−0.721887			−0.360944	−	0.932588i	$-0.617545\pi$
$103$	−8.36865e9			−0.721887			−0.360944	+	0.932588i	$0.617545\pi$
$104$		−	1.97135e9i		−	0.162031i
$105$		0			0
$106$	−9.53837e8			−0.0712763
$107$		−	1.43555e10i		−	1.02353i	−0.859126	−	0.511764i	$-0.828992\pi$
$107$		−	1.43555e10i		−	1.02353i	0.859126	−	0.511764i	$-0.171008\pi$
$108$	1.71404e9	+	7.14389e9i	0.116655	+	0.486201i
$109$	−4.72564e9			−0.307134			−0.153567	−	0.988138i	$-0.549076\pi$
$109$	−4.72564e9			−0.307134			−0.153567	+	0.988138i	$0.549076\pi$
$110$		0			0
$111$	−1.00459e10	+	6.90365e9i	−0.596174	+	0.409698i
$112$	6.08870e9			0.345489
$113$		−	1.32158e10i		−	0.717303i	−0.933472	−	0.358651i	$-0.883237\pi$
$113$		−	1.32158e10i		−	0.717303i	0.933472	−	0.358651i	$-0.116763\pi$
$114$	2.38801e9	+	3.47492e9i	0.124026	+	0.180477i
$115$		0			0
$116$			2.47422e9i			0.117801i
$117$	3.60169e9	−	9.38011e9i	0.164277	−	0.427837i
$118$	6.60779e9			0.288833
$119$		−	6.19280e10i		−	2.59509i
$120$		0			0
$121$	2.20383e10			0.849673
$122$		−	1.20090e10i		−	0.444331i
$123$	2.05393e10	+	2.98879e10i	0.729560	+	1.06162i
$124$	2.14168e10			0.730544
$125$		0			0
$126$	2.89713e10	+	1.11241e10i	0.912253	+	0.350279i
$127$	3.17814e10			0.961953			0.480976	−	0.876733i	$-0.340282\pi$
$127$	3.17814e10			0.961953			0.480976	+	0.876733i	$0.340282\pi$
$128$		−	3.03700e9i		−	0.0883883i
$129$	3.97973e10	−	2.73492e10i	1.11405	−	0.765589i
$130$		0			0
$131$			5.01094e10i			1.29886i	0.760421	+	0.649430i	$0.224993\pi$
$131$			5.01094e10i			1.29886i	−0.760421	+	0.649430i	$0.775007\pi$
$132$	4.40004e9	+	6.40273e9i	0.109796	+	0.159770i
$133$	1.78107e10			0.427979
$134$		−	1.18136e10i		−	0.273438i
$135$		0			0
$136$	−3.08893e10			−0.663916
$137$		−	2.74744e10i		−	0.569279i	−0.958635	−	0.284639i	$-0.908126\pi$
$137$		−	2.74744e10i		−	0.569279i	0.958635	−	0.284639i	$-0.0918738\pi$
$138$	−6.35900e9	+	4.36999e9i	−0.127056	+	0.0873142i
$139$	6.32488e10			1.21893			0.609464	−	0.792814i	$-0.291385\pi$
$139$	6.32488e10			1.21893			0.609464	+	0.792814i	$0.291385\pi$
$140$		0			0
$141$	−2.13403e10	−	3.10534e10i	−0.382917	−	0.557204i
$142$	1.29285e10			0.223927
$143$		−	1.06253e10i		−	0.177689i
$144$	5.54864e9	−	1.44507e10i	0.0896137	−	0.233387i
$145$		0			0
$146$		−	4.94607e10i		−	0.745583i
$147$	5.14684e10	−	3.53697e10i	0.749815	−	0.515282i
$148$	2.56829e10			0.361689
$149$		−	3.38479e10i		−	0.460893i	−0.973085	−	0.230446i	$-0.925981\pi$
$149$		−	3.38479e10i		−	0.460893i	0.973085	−	0.230446i	$-0.0740186\pi$
$150$		0			0
$151$	1.22386e11			1.55901			0.779503	−	0.626399i	$-0.215472\pi$
$151$	1.22386e11			1.55901			0.779503	+	0.626399i	$0.215472\pi$
$152$		−	8.88385e9i		−	0.109492i
$153$	−1.46978e11	−	5.64351e10i	−1.75305	−	0.673120i
$154$	3.28171e10			0.378876
$155$		0			0
$156$	−1.74479e10	+	1.19904e10i	−0.188851	+	0.129781i
$157$	1.58971e11			1.66656			0.833279	−	0.552853i	$-0.186461\pi$
$157$	1.58971e11			1.66656			0.833279	+	0.552853i	$0.186461\pi$
$158$			4.44838e10i			0.451769i
$159$	5.80155e9	+	8.44215e9i	0.0570898	+	0.0830745i
$160$		0			0
$161$			3.25930e10i			0.301297i
$162$	5.28033e10	−	5.86220e10i	0.473245	−	0.525395i
$163$	9.20831e10			0.800280			0.400140	−	0.916454i	$-0.368962\pi$
$163$	9.20831e10			0.800280			0.400140	+	0.916454i	$0.368962\pi$
$164$		−	7.64102e10i		−	0.644069i
$165$		0			0
$166$	4.94540e10			0.392338
$167$		−	2.12416e11i		−	1.63533i	−0.575697	−	0.817663i	$-0.695269\pi$
$167$		−	2.12416e11i		−	1.63533i	0.575697	−	0.817663i	$-0.304731\pi$
$168$	−3.70334e10	−	5.38894e10i	−0.276725	−	0.402677i
$169$	−1.08904e11			−0.789968
$170$		0			0
$171$	1.62309e10	−	4.22713e10i	0.111010	−	0.289111i
$172$	−1.01744e11			−0.675876
$173$			3.04132e11i			1.96260i	0.192482	+	0.981300i	$0.438346\pi$
$173$			3.04132e11i			1.96260i	−0.192482	+	0.981300i	$0.561654\pi$
$174$	2.18986e10	−	1.50490e10i	0.137300	−	0.0943542i
$175$		0			0
$176$		−	1.63690e10i		−	0.0969300i
$177$	−4.01908e10	−	5.84837e10i	−0.231345	−	0.336642i
$178$	−5.40212e9			−0.0302318
$179$		−	7.07114e9i		−	0.0384791i	−0.999815	−	0.0192395i	$-0.993875\pi$
$179$		−	7.07114e9i		−	0.0384791i	0.999815	−	0.0192395i	$-0.00612451\pi$
$180$		0			0
$181$	−1.27309e11			−0.655337			−0.327669	−	0.944793i	$-0.606263\pi$
$181$	−1.27309e11			−0.655337			−0.327669	+	0.944793i	$0.606263\pi$
$182$			8.94290e10i			0.447838i
$183$	−1.06288e11	+	7.30425e10i	−0.517880	+	0.355894i
$184$	1.62572e10			0.0770825
$185$		0			0
$186$	−1.30264e11	−	1.89554e11i	−0.585141	−	0.851470i
$187$	−1.66488e11			−0.728075
$188$			7.93900e10i			0.338047i
$189$	−7.77563e10	−	3.24078e11i	−0.322424	−	1.34382i
$190$		0			0
$191$			2.06460e11i			0.812209i	0.913827	+	0.406105i	$0.133113\pi$
$191$			2.06460e11i			0.812209i	−0.913827	+	0.406105i	$0.866887\pi$
$192$	−2.68797e10	+	1.84720e10i	−0.103019	+	0.0707960i
$193$	−3.11606e11			−1.16364			−0.581821	−	0.813317i	$-0.697660\pi$
$193$	−3.11606e11			−1.16364			−0.581821	+	0.813317i	$0.697660\pi$
$194$			2.00052e11i			0.728004i
$195$		0			0
$196$	−1.31582e11			−0.454901
$197$		−	1.51694e11i		−	0.511255i	−0.966775	−	0.255628i	$-0.917718\pi$
$197$		−	1.51694e11i		−	0.511255i	0.966775	−	0.255628i	$-0.0822821\pi$
$198$	2.99063e10	−	7.78870e10i	0.0982737	−	0.255941i
$199$	−1.11692e11			−0.357895			−0.178947	−	0.983859i	$-0.557269\pi$
$199$	−1.11692e11			−0.357895			−0.178947	+	0.983859i	$0.557269\pi$
$200$		0			0
$201$	−1.04559e11	+	7.18543e10i	−0.318700	+	0.219014i
$202$	3.79978e11			1.12980
$203$		−	1.12241e11i		−	0.325591i
$204$	1.87879e11	+	2.73392e11i	0.531773	+	0.773812i
$205$		0			0
$206$		−	1.89361e11i		−	0.510451i
$207$	7.73551e10	+	2.97021e10i	0.203534	+	0.0781512i
$208$	4.46066e10			0.114573
$209$		−	4.78826e10i		−	0.120073i
$210$		0			0
$211$	1.53066e11			0.365987			0.182994	−	0.983114i	$-0.441421\pi$
$211$	1.53066e11			0.365987			0.182994	+	0.983114i	$0.441421\pi$
$212$		−	2.15829e10i		−	0.0503999i
$213$	−7.86354e10	−	1.14427e11i	−0.179358	−	0.260993i
$214$	3.24828e11			0.723744
$215$		0			0
$216$	−1.61648e11	+	3.87843e10i	−0.343796	+	0.0824874i
$217$	−9.71560e11			−2.01916
$218$		−	1.06929e11i		−	0.217177i
$219$	−4.37763e11	+	3.00836e11i	−0.868998	+	0.597186i
$220$		0			0
$221$		−	4.53693e11i		−	0.860598i
$222$	−1.56212e11	−	2.27312e11i	−0.289700	−	0.421559i
$223$	6.05759e11			1.09844			0.549219	−	0.835678i	$-0.314925\pi$
$223$	6.05759e11			1.09844			0.549219	+	0.835678i	$0.314925\pi$
$224$			1.37771e11i			0.244298i
$225$		0			0
$226$	2.99040e11			0.507210
$227$			6.70588e11i			1.11257i	0.830992	+	0.556284i	$0.187773\pi$
$227$			6.70588e11i			1.11257i	−0.830992	+	0.556284i	$0.812227\pi$
$228$	−7.86286e10	+	5.40345e10i	−0.127616	+	0.0876995i
$229$	3.53356e11			0.561094			0.280547	−	0.959840i	$-0.409484\pi$
$229$	3.53356e11			0.561094			0.280547	+	0.959840i	$0.409484\pi$
$230$		0			0
$231$	−1.99605e11	−	2.90456e11i	−0.303467	−	0.441591i
$232$	−5.59851e10			−0.0832976
$233$		−	1.12390e12i		−	1.63662i	−0.574779	−	0.818309i	$-0.694912\pi$
$233$		−	1.12390e12i		−	1.63662i	0.574779	−	0.818309i	$-0.305088\pi$
$234$	2.12248e11	+	8.14969e10i	0.302527	+	0.116161i
$235$		0			0
$236$			1.49517e11i			0.204236i
$237$	3.93714e11	−	2.70565e11i	0.526549	−	0.361851i
$238$	1.40127e12			1.83500
$239$			2.64603e11i			0.339317i	0.985503	+	0.169658i	$0.0542665\pi$
$239$			2.64603e11i			0.339317i	−0.985503	+	0.169658i	$0.945734\pi$
$240$		0			0
$241$	8.86768e11			1.09075			0.545375	−	0.838192i	$-0.316387\pi$
$241$	8.86768e11			1.09075			0.545375	+	0.838192i	$0.316387\pi$
$242$			4.98671e11i			0.600810i
$243$	−8.40014e11	−	1.10789e11i	−0.991414	−	0.130757i
$244$	2.71732e11			0.314190
$245$		0			0
$246$	−6.76286e11	+	4.64752e11i	−0.750680	+	0.515877i
$247$	1.30483e11			0.141929
$248$			4.84607e11i			0.516573i
$249$	−3.00795e11	−	4.37704e11i	−0.314249	−	0.457281i
$250$		0			0
$251$			8.59494e11i			0.862729i	0.902178	+	0.431364i	$0.141968\pi$
$251$			8.59494e11i			0.862729i	−0.902178	+	0.431364i	$0.858032\pi$
$252$	−2.51710e11	+	6.55546e11i	−0.247684	+	0.645060i
$253$	8.76237e10			0.0845316
$254$			7.19130e11i			0.680203i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$			2.17900e12i			1.94353i	0.235954	+	0.971764i	$0.424179\pi$
$257$			2.17900e12i			1.94353i	−0.235954	+	0.971764i	$0.575821\pi$
$258$	6.18841e11	+	9.00510e11i	0.541353	+	0.787753i
$259$	−1.16509e12			−0.999677
$260$		0			0
$261$	−2.66389e11	−	1.02286e11i	−0.219945	−	0.0844524i
$262$	−1.13385e12			−0.918433
$263$		−	1.37942e12i		−	1.09627i	−0.836391	−	0.548134i	$-0.815339\pi$
$263$		−	1.37942e12i		−	1.09627i	0.836391	−	0.548134i	$-0.184661\pi$
$264$	−1.44877e11	+	9.95615e10i	−0.112975	+	0.0776375i
$265$		0			0
$266$			4.03010e11i			0.302627i
$267$	3.28574e10	+	4.78126e10i	0.0242146	+	0.0352360i
$268$	2.67312e11			0.193350
$269$		−	1.18129e12i		−	0.838680i	−0.907829	−	0.419340i	$-0.862262\pi$
$269$		−	1.18129e12i		−	0.838680i	0.907829	−	0.419340i	$-0.137738\pi$
$270$		0			0
$271$	−1.42251e12			−0.973213			−0.486606	−	0.873621i	$-0.661765\pi$
$271$	−1.42251e12			−0.973213			−0.486606	+	0.873621i	$0.661765\pi$
$272$		−	6.98944e11i		−	0.469459i
$273$	7.91511e11	−	5.43937e11i	0.521968	−	0.358703i
$274$	6.21674e11			0.402541
$275$		0			0
$276$	−9.88815e10	−	1.43888e11i	−0.0617404	−	0.0898418i
$277$	−5.29960e11			−0.324971			−0.162485	−	0.986711i	$-0.551951\pi$
$277$	−5.29960e11			−0.324971			−0.162485	+	0.986711i	$0.551951\pi$
$278$			1.43116e12i			0.861913i
$279$	−8.85385e11	+	2.30587e12i	−0.523734	+	1.36400i
$280$		0			0
$281$			2.28441e12i			1.30389i	0.758265	+	0.651946i	$0.226047\pi$
$281$			2.28441e12i			1.30389i	−0.758265	+	0.651946i	$0.773953\pi$
$282$	7.02659e11	−	4.82876e11i	0.394003	−	0.270764i
$283$	−2.31274e12			−1.27408			−0.637038	−	0.770833i	$-0.719840\pi$
$283$	−2.31274e12			−1.27408			−0.637038	+	0.770833i	$0.719840\pi$
$284$			2.92539e11i			0.158340i
$285$		0			0
$286$	2.40423e11			0.125645
$287$			3.46630e12i			1.78015i
$288$	3.26982e11	+	1.25551e11i	0.165029	+	0.0633665i
$289$	−5.09295e12			−2.52627
$290$		0			0
$291$	1.77060e12	−	1.21678e12i	0.848509	−	0.583106i
$292$	1.11917e12			0.527207
$293$			1.05989e12i			0.490822i	0.969419	+	0.245411i	$0.0789229\pi$
$293$			1.05989e12i			0.490822i	−0.969419	+	0.245411i	$0.921077\pi$
$294$	8.00326e11	+	1.16460e12i	0.364360	+	0.530199i
$295$		0			0
$296$			5.81138e11i			0.255753i
$297$	−8.71257e11	+	2.09042e11i	−0.377020	+	0.0904588i
$298$	7.65890e11			0.325900
$299$			2.38781e11i			0.0999179i
$300$		0			0
$301$	4.61555e12			1.86806
$302$			2.76928e12i			1.10238i
$303$	−2.31115e12	−	3.36308e12i	−0.904931	−	1.31681i
$304$	2.01019e11			0.0774227
$305$		0			0
$306$	1.27698e12	−	3.32573e12i	0.475968	−	1.23959i
$307$	−6.89209e11			−0.252731			−0.126366	−	0.991984i	$-0.540331\pi$
$307$	−6.89209e11			−0.252731			−0.126366	+	0.991984i	$0.540331\pi$
$308$			7.42567e11i			0.267906i
$309$	−1.67598e12	+	1.15176e12i	−0.594945	+	0.408854i
$310$		0			0
$311$			1.95674e12i			0.672559i	0.941762	+	0.336280i	$0.109169\pi$
$311$			1.95674e12i			0.672559i	−0.941762	+	0.336280i	$0.890831\pi$
$312$	−2.71312e11	−	3.94801e11i	−0.0917690	−	0.133538i
$313$	2.48821e11			0.0828256			0.0414128	−	0.999142i	$-0.486814\pi$
$313$	2.48821e11			0.0828256			0.0414128	+	0.999142i	$0.486814\pi$
$314$			3.59711e12i			1.17843i
$315$		0			0
$316$	−1.00655e12			−0.319449
$317$		−	4.63675e12i		−	1.44850i	−0.689539	−	0.724249i	$-0.742187\pi$
$317$		−	4.63675e12i		−	1.44850i	0.689539	−	0.724249i	$-0.257813\pi$
$318$	−1.91024e11	+	1.31274e11i	−0.0587425	+	0.0403686i
$319$	−3.01751e11			−0.0913473
$320$		0			0
$321$	−1.97571e12	−	2.87497e12i	−0.579694	−	0.843544i
$322$	−7.37496e11			−0.213049
$323$		−	2.04456e12i		−	0.581549i
$324$	1.32646e12	+	1.19480e12i	0.371510	+	0.334634i
$325$		0			0
$326$			2.08360e12i			0.565883i
$327$	−9.46400e11	+	6.50378e11i	−0.253125	+	0.173951i
$328$	1.72897e12			0.455426
$329$		−	3.60147e12i		−	0.934331i
$330$		0			0
$331$	−1.41443e12			−0.355994			−0.177997	−	0.984031i	$-0.556962\pi$
$331$	−1.41443e12			−0.355994			−0.177997	+	0.984031i	$0.556962\pi$
$332$			1.11902e12i			0.277425i
$333$	−1.06175e12	+	2.76518e12i	−0.259298	+	0.675308i
$334$	4.80642e12			1.15635
$335$		0			0
$336$	1.21938e12	−	8.37971e11i	0.284736	−	0.195674i
$337$	−8.67755e11			−0.199640			−0.0998201	−	0.995006i	$-0.531827\pi$
$337$	−8.67755e11			−0.199640			−0.0998201	+	0.995006i	$0.531827\pi$
$338$		−	2.46421e12i		−	0.558592i
$339$	−1.81886e12	−	2.64672e12i	−0.406257	−	0.591167i
$340$		0			0
$341$			2.61196e12i			0.566493i
$342$	9.56490e11	+	3.67264e11i	0.204432	+	0.0784961i
$343$	−5.91785e11			−0.124650
$344$		−	2.30221e12i		−	0.477917i
$345$		0			0
$346$	−6.88173e12			−1.38777
$347$			5.20712e12i			1.03502i	0.855676	+	0.517512i	$0.173142\pi$
$347$			5.20712e12i			1.03502i	−0.855676	+	0.517512i	$0.826858\pi$
$348$	3.40520e11	+	4.95509e11i	0.0667185	+	0.0970857i
$349$	1.11953e12			0.216226			0.108113	−	0.994139i	$-0.465519\pi$
$349$	1.11953e12			0.216226			0.108113	+	0.994139i	$0.465519\pi$
$350$		0			0
$351$	−5.69653e11	−	2.37424e12i	−0.106924	−	0.445644i
$352$	3.70388e11			0.0685398
$353$			3.73952e12i			0.682248i	0.940018	+	0.341124i	$0.110808\pi$
$353$			3.73952e12i			0.682248i	−0.940018	+	0.341124i	$0.889192\pi$
$354$	1.32334e12	−	9.09413e11i	0.238042	−	0.163586i
$355$		0			0
$356$		−	1.22236e11i		−	0.0213771i
$357$	−8.52299e12	−	1.24023e13i	−1.46977	−	2.13875i
$358$	1.60002e11			0.0272088
$359$		−	3.54489e12i		−	0.594471i	−0.954804	−	0.297235i	$-0.903935\pi$
$359$		−	3.54489e12i		−	0.594471i	0.954804	−	0.297235i	$-0.0960646\pi$
$360$		0			0
$361$	−5.54305e12			−0.904092
$362$		−	2.88066e12i		−	0.463393i
$363$	4.41360e12	−	3.03308e12i	0.700260	−	0.481228i
$364$	−2.02355e12			−0.316670
$365$		0			0
$366$	−1.65276e12	−	2.40503e12i	−0.251655	−	0.366197i
$367$	1.01161e13			1.51944			0.759722	−	0.650248i	$-0.225335\pi$
$367$	1.01161e13			1.51944			0.759722	+	0.650248i	$0.225335\pi$
$368$			3.67858e11i			0.0545056i
$369$	8.22679e12	+	3.15885e12i	1.20254	+	0.461739i
$370$		0			0
$371$			9.79093e11i			0.139301i
$372$	4.28913e12	−	2.94754e12i	0.602080	−	0.413757i
$373$	−3.81055e12			−0.527769			−0.263885	−	0.964554i	$-0.585004\pi$
$373$	−3.81055e12			−0.527769			−0.263885	+	0.964554i	$0.585004\pi$
$374$		−	3.76720e12i		−	0.514827i
$375$		0			0
$376$	−1.79639e12			−0.239035
$377$		−	8.22293e11i		−	0.107974i
$378$	7.33304e12	−	1.75943e12i	0.950222	−	0.227988i
$379$	1.11052e13			1.42014			0.710069	−	0.704132i	$-0.248664\pi$
$379$	1.11052e13			1.42014			0.710069	+	0.704132i	$0.248664\pi$
$380$		0			0
$381$	6.36482e12	−	4.37399e12i	0.792796	−	0.544819i
$382$	−4.67165e12			−0.574319
$383$			4.29169e12i			0.520756i	0.965507	+	0.260378i	$0.0838472\pi$
$383$			4.29169e12i			0.520756i	−0.965507	+	0.260378i	$0.916153\pi$
$384$	−4.17974e11	−	6.08217e11i	−0.0500603	−	0.0728455i
$385$		0			0
$386$		−	7.05084e12i		−	0.822820i
$387$	4.20617e12	−	1.09544e13i	0.484542	−	1.26192i
$388$	−4.52665e12			−0.514776
$389$		−	1.50554e13i		−	1.69023i	−0.534588	−	0.845113i	$-0.679533\pi$
$389$		−	1.50554e13i		−	1.69023i	0.534588	−	0.845113i	$-0.320467\pi$
$390$		0			0
$391$	3.74148e12			0.409411
$392$		−	2.97736e12i		−	0.321663i
$393$	6.89642e12	+	1.00354e13i	0.735633	+	1.07046i
$394$	3.43245e12			0.361512
$395$		0			0
$396$	1.76238e12	+	6.76703e11i	0.180977	+	0.0694900i
$397$	1.11669e13			1.13235			0.566174	−	0.824286i	$-0.308423\pi$
$397$	1.11669e13			1.13235			0.566174	+	0.824286i	$0.308423\pi$
$398$		−	2.52729e12i		−	0.253070i
$399$	3.56693e12	−	2.45124e12i	0.352720	−	0.242394i
$400$		0			0
$401$			1.15685e13i			1.11572i	0.829935	+	0.557861i	$0.188378\pi$
$401$			1.15685e13i			1.11572i	−0.829935	+	0.557861i	$0.811622\pi$
$402$	−1.62588e12	−	2.36590e12i	−0.154867	−	0.225355i
$403$	−7.11777e12			−0.669605
$404$			8.59793e12i			0.798890i
$405$		0			0
$406$	2.53973e12			0.230227
$407$			3.13224e12i			0.280468i
$408$	−6.18616e12	+	4.25121e12i	−0.547168	+	0.376021i
$409$	−1.07411e13			−0.938498			−0.469249	−	0.883066i	$-0.655475\pi$
$409$	−1.07411e13			−0.938498			−0.469249	+	0.883066i	$0.655475\pi$
$410$		0			0
$411$	−3.78123e12	−	5.50227e12i	−0.322421	−	0.469172i
$412$	4.28475e12			0.360944
$413$		−	6.78275e12i		−	0.564489i
$414$	−6.72082e11	+	1.75035e12i	−0.0552612	+	0.143920i
$415$		0			0
$416$			1.00933e12i			0.0810153i
$417$	1.26668e13	−	8.70477e12i	1.00458	−	0.690362i
$418$	1.08346e12			0.0849047
$419$			8.81717e12i			0.682746i	0.939928	+	0.341373i	$0.110892\pi$
$419$			8.81717e12i			0.682746i	−0.939928	+	0.341373i	$0.889108\pi$
$420$		0			0
$421$	−5.69741e12			−0.430792			−0.215396	−	0.976527i	$-0.569104\pi$
$421$	−5.69741e12			−0.430792			−0.215396	+	0.976527i	$0.569104\pi$
$422$			3.46348e12i			0.258792i
$423$	−8.54761e12	−	3.28203e12i	−0.631165	−	0.242349i
$424$	4.88365e11			0.0356381
$425$		0			0
$426$	2.58918e12	−	1.77932e12i	0.184550	−	0.126825i
$427$	−1.23269e13			−0.868392
$428$			7.35003e12i			0.511764i
$429$	−1.46233e12	−	2.12792e12i	−0.100637	−	0.146443i
$430$		0			0
$431$			1.80323e13i			1.21245i	0.795293	+	0.606226i	$0.207317\pi$
$431$			1.80323e13i			1.21245i	−0.795293	+	0.606226i	$0.792683\pi$
$432$	−8.77590e11	−	3.65767e12i	−0.0583274	−	0.243101i
$433$	−2.06339e13			−1.35563			−0.677816	−	0.735232i	$-0.737073\pi$
$433$	−2.06339e13			−1.35563			−0.677816	+	0.735232i	$0.737073\pi$
$434$		−	2.19839e13i		−	1.42776i
$435$		0			0
$436$	2.41953e12			0.153567
$437$			1.07606e12i			0.0675195i
$438$	−6.80715e12	−	9.90545e12i	−0.422275	−	0.614474i
$439$	1.95313e13			1.19787			0.598935	−	0.800798i	$-0.295591\pi$
$439$	1.95313e13			1.19787			0.598935	+	0.800798i	$0.295591\pi$
$440$		0			0
$441$	5.43969e12	−	1.41669e13i	0.326123	−	0.849343i
$442$	1.02659e13			0.608535
$443$			2.97469e13i			1.74351i	0.489946	+	0.871753i	$0.337016\pi$
$443$			2.97469e13i			1.74351i	−0.489946	+	0.871753i	$0.662984\pi$
$444$	5.14349e12	−	3.53467e12i	0.298087	−	0.204849i
$445$		0			0
$446$			1.37068e13i			0.776713i
$447$	−4.65839e12	−	6.77868e12i	−0.261035	−	0.379846i
$448$	−3.11741e12			−0.172744
$449$		−	1.37505e13i		−	0.753509i	−0.926313	−	0.376754i	$-0.877040\pi$
$449$		−	1.37505e13i		−	0.753509i	0.926313	−	0.376754i	$-0.122960\pi$
$450$		0			0
$451$	9.31887e12			0.499437
$452$			6.76651e12i			0.358651i
$453$	2.45102e13	−	1.68437e13i	1.28486	−	0.882971i
$454$	−1.51737e13			−0.786704
$455$		0			0
$456$	−1.22266e12	−	1.77916e12i	−0.0620129	−	0.0902383i
$457$	−4.10224e11			−0.0205798			−0.0102899	−	0.999947i	$-0.503275\pi$
$457$	−4.10224e11			−0.0205798			−0.0102899	+	0.999947i	$0.503275\pi$
$458$			7.99554e12i			0.396753i
$459$	−3.72021e13	+	8.92594e12i	−1.82601	+	0.438118i
$460$		0			0
$461$		−	2.10914e11i		−	0.0101298i	−0.999987	−	0.00506490i	$-0.998388\pi$
$461$		−	2.10914e11i		−	0.0101298i	0.999987	−	0.00506490i	$-0.00161221\pi$
$462$	6.57226e12	−	4.51654e12i	0.312252	−	0.214583i
$463$	1.96738e13			0.924660			0.462330	−	0.886708i	$-0.347013\pi$
$463$	1.96738e13			0.924660			0.462330	+	0.886708i	$0.347013\pi$
$464$		−	1.26680e12i		−	0.0589003i
$465$		0			0
$466$	2.54309e13			1.15726
$467$			1.21902e13i			0.548815i	0.961614	+	0.274407i	$0.0884817\pi$
$467$			1.21902e13i			0.548815i	−0.961614	+	0.274407i	$0.911518\pi$
$468$	−1.84406e12	+	4.80261e12i	−0.0821385	+	0.213919i
$469$	−1.21264e13			−0.534402
$470$		0			0
$471$	3.18370e13	−	2.18788e13i	1.37350	−	0.943885i
$472$	−3.38319e12			−0.144416
$473$		−	1.24085e13i		−	0.524101i
$474$	6.12218e12	+	8.90872e12i	0.255867	+	0.372326i
$475$		0			0
$476$			3.17071e13i			1.29754i
$477$	2.32374e12	+	8.92250e11i	0.0941014	+	0.0361322i
$478$	−5.98729e12			−0.239933
$479$			5.00886e12i			0.198637i	0.995056	+	0.0993187i	$0.0316663\pi$
$479$			5.00886e12i			0.198637i	−0.995056	+	0.0993187i	$0.968334\pi$
$480$		0			0
$481$	−8.53558e12			−0.331518
$482$			2.00653e13i			0.771276i
$483$	4.48569e12	+	6.52737e12i	0.170645	+	0.248315i
$484$	−1.12836e13			−0.424837
$485$		0			0
$486$	2.50686e12	−	1.90074e13i	0.0924590	−	0.701036i
$487$	4.17000e13			1.52227			0.761134	−	0.648595i	$-0.224643\pi$
$487$	4.17000e13			1.52227			0.761134	+	0.648595i	$0.224643\pi$
$488$			6.14859e12i			0.222166i
$489$	1.84414e13	−	1.26732e13i	0.659553	−	0.453253i
$490$		0			0
$491$		−	2.10340e12i		−	0.0737081i	−0.999321	−	0.0368540i	$-0.988266\pi$
$491$		−	2.10340e12i		−	0.0737081i	0.999321	−	0.0368540i	$-0.0117337\pi$
$492$	−1.05161e13	−	1.53026e13i	−0.364780	−	0.530811i
$493$	−1.28846e13			−0.442421
$494$			2.95250e12i			0.100359i
$495$		0			0
$496$	−1.09654e13			−0.365272
$497$		−	1.32708e13i		−	0.437639i
$498$	9.90410e12	−	6.80622e12i	0.323347	−	0.222208i
$499$	2.74482e13			0.887179			0.443589	−	0.896230i	$-0.353705\pi$
$499$	2.74482e13			0.887179			0.443589	+	0.896230i	$0.353705\pi$
$500$		0			0
$501$	−2.92342e13	−	4.25403e13i	−0.926197	−	1.34776i
$502$	−1.94481e13			−0.610041
$503$		−	2.26985e13i		−	0.704949i	−0.935822	−	0.352474i	$-0.885340\pi$
$503$		−	2.26985e13i		−	0.704949i	0.935822	−	0.352474i	$-0.114660\pi$
$504$	−1.48333e13	−	5.69556e12i	−0.456127	−	0.175139i
$505$		0			0
$506$			1.98270e12i			0.0597729i
$507$	−2.18101e13	+	1.49882e13i	−0.651055	+	0.447413i
$508$	−1.62721e13			−0.480976
$509$			4.21460e13i			1.23358i	0.787127	+	0.616791i	$0.211567\pi$
$509$			4.21460e13i			1.23358i	−0.787127	+	0.616791i	$0.788433\pi$
$510$		0			0
$511$	−5.07703e13			−1.45715
$512$			1.55494e12i			0.0441942i
$513$	−2.56713e12	−	1.06994e13i	−0.0722539	−	0.301144i
$514$	−4.93051e13			−1.37428
$515$		0			0
$516$	−2.03762e13	+	1.40028e13i	−0.557025	+	0.382795i
$517$	−9.68227e12			−0.262135
$518$		−	2.63629e13i		−	0.706878i
$519$	4.18569e13	+	6.09083e13i	1.11155	+	1.61748i
$520$		0			0
$521$			6.54420e13i			1.70478i	0.522907	+	0.852390i	$0.324848\pi$
$521$			6.54420e13i			1.70478i	−0.522907	+	0.852390i	$0.675152\pi$
$522$	2.31446e12	−	6.02770e12i	0.0597169	−	0.155525i
$523$	6.14531e13			1.57049			0.785245	−	0.619185i	$-0.212537\pi$
$523$	6.14531e13			1.57049			0.785245	+	0.619185i	$0.212537\pi$
$524$		−	2.56560e13i		−	0.649430i
$525$		0			0
$526$	3.12126e13			0.775178
$527$			1.11529e14i			2.74369i
$528$	−2.25282e12	−	3.27820e12i	−0.0548980	−	0.0798851i
$529$	3.94574e13			0.952466
$530$		0			0
$531$	−1.60979e13	−	6.18114e12i	−0.381327	−	0.146418i
$532$	−9.11907e12			−0.213990
$533$			2.53946e13i			0.590343i
$534$	−1.08188e12	+	7.43479e11i	−0.0249156	+	0.0171223i
$535$		0			0
$536$			6.04857e12i			0.136719i
$537$	−9.73183e11	−	1.41613e12i	−0.0217933	−	0.0317126i
$538$	2.67296e13			0.593036
$539$		−	1.60475e13i		−	0.352748i
$540$		0			0
$541$	1.50207e13			0.324118			0.162059	−	0.986781i	$-0.448187\pi$
$541$	1.50207e13			0.324118			0.162059	+	0.986781i	$0.448187\pi$
$542$		−	3.21877e13i		−	0.688166i
$543$	−2.54960e13	+	1.75211e13i	−0.540098	+	0.371162i
$544$	1.58153e13			0.331958
$545$		0			0
$546$	1.23079e13	+	1.79099e13i	0.253641	+	0.369087i
$547$	−7.15097e13			−1.46025			−0.730127	−	0.683312i	$-0.760539\pi$
$547$	−7.15097e13			−1.46025			−0.730127	+	0.683312i	$0.760539\pi$
$548$			1.40669e13i			0.284639i
$549$	−1.12336e13	+	2.92563e13i	−0.225245	+	0.586621i
$550$		0			0
$551$		−	3.70565e12i		−	0.0729636i
$552$	3.25581e12	−	2.23743e12i	0.0635278	−	0.0436571i
$553$	4.56616e13			0.882928
$554$		−	1.19916e13i		−	0.229789i
$555$		0			0
$556$	−3.23834e13			−0.609464
$557$			7.34107e13i			1.36925i	0.728895	+	0.684626i	$0.240034\pi$
$557$			7.34107e13i			1.36925i	−0.728895	+	0.684626i	$0.759966\pi$
$558$	−5.21758e13	−	2.00340e13i	−0.964490	−	0.370336i
$559$	3.38141e13			0.619497
$560$		0			0
$561$	−3.33425e13	+	2.29134e13i	−0.600045	+	0.412358i
$562$	−5.16902e13			−0.921991
$563$		−	4.77347e13i		−	0.843902i	−0.906619	−	0.421951i	$-0.861345\pi$
$563$		−	4.77347e13i		−	0.843902i	0.906619	−	0.421951i	$-0.138655\pi$
$564$	1.09262e13	+	1.58994e13i	0.191459	+	0.278602i
$565$		0			0
$566$		−	5.23314e13i		−	0.900907i
$567$	−6.01742e13	−	5.42013e13i	−1.02682	−	0.924900i
$568$	−6.61939e12			−0.111963
$569$			1.90951e13i			0.320156i	0.987104	+	0.160078i	$0.0511745\pi$
$569$			1.90951e13i			0.320156i	−0.987104	+	0.160078i	$0.948825\pi$
$570$		0			0
$571$	−2.09448e13			−0.345060			−0.172530	−	0.985004i	$-0.555194\pi$
$571$	−2.09448e13			−0.345060			−0.172530	+	0.985004i	$0.555194\pi$
$572$			5.44014e12i			0.0888444i
$573$	2.84145e13	+	4.13475e13i	0.460009	+	0.669385i
$574$	−7.84334e13			−1.25876
$575$		0			0
$576$	−2.84091e12	+	7.39876e12i	−0.0448069	+	0.116693i
$577$	−3.56688e13			−0.557711			−0.278855	−	0.960333i	$-0.589955\pi$
$577$	−3.56688e13			−0.557711			−0.278855	+	0.960333i	$0.589955\pi$
$578$		−	1.15240e14i		−	1.78635i
$579$	−6.24051e13	+	4.28856e13i	−0.959019	+	0.659050i
$580$		0			0
$581$		−	5.07634e13i		−	0.766778i
$582$	2.75326e13	+	4.00642e13i	0.412318	+	0.599986i
$583$	2.63221e12			0.0390821
$584$			2.53239e13i			0.372792i
$585$		0			0
$586$	−2.39826e13			−0.347064
$587$		−	1.29418e14i		−	1.85697i	−0.371375	−	0.928483i	$-0.621114\pi$
$587$		−	1.29418e14i		−	1.85697i	0.371375	−	0.928483i	$-0.378886\pi$
$588$	−2.63518e13	+	1.81093e13i	−0.374908	+	0.257641i
$589$	−3.20761e13			−0.452486
$590$		0			0
$591$	−2.08773e13	−	3.03797e13i	−0.289559	−	0.421352i
$592$	−1.31496e13			−0.180845
$593$			3.96596e13i			0.540848i	0.962741	+	0.270424i	$0.0871639\pi$
$593$			3.96596e13i			0.540848i	−0.962741	+	0.270424i	$0.912836\pi$
$594$	−4.73007e12	−	1.97143e13i	−0.0639640	−	0.266593i
$595$		0			0
$596$			1.73301e13i			0.230446i
$597$	−2.23684e13	+	1.53718e13i	−0.294960	+	0.202700i
$598$	−5.40299e12			−0.0706526
$599$			4.57555e13i			0.593347i	0.954979	+	0.296674i	$0.0958774\pi$
$599$			4.57555e13i			0.593347i	−0.954979	+	0.296674i	$0.904123\pi$
$600$		0			0
$601$	1.06033e14			1.35229			0.676143	−	0.736770i	$-0.263650\pi$
$601$	1.06033e14			1.35229			0.676143	+	0.736770i	$0.263650\pi$
$602$			1.04438e14i			1.32092i
$603$	−1.10508e13	+	2.87804e13i	−0.138614	+	0.361003i
$604$	−6.26617e13			−0.779503
$605$		0			0
$606$	7.60979e13	−	5.22954e13i	0.931128	−	0.639883i
$607$	9.55067e13			1.15902			0.579509	−	0.814966i	$-0.303244\pi$
$607$	9.55067e13			1.15902			0.579509	+	0.814966i	$0.303244\pi$
$608$			4.54853e12i			0.0547461i
$609$	−1.54475e13	−	2.24784e13i	−0.184404	−	0.268336i
$610$		0			0
$611$		−	2.63849e13i		−	0.309848i
$612$	7.52526e13	+	2.88948e13i	0.876525	+	0.336560i
$613$	5.18411e13			0.598924			0.299462	−	0.954108i	$-0.403193\pi$
$613$	5.18411e13			0.598924			0.299462	+	0.954108i	$0.403193\pi$
$614$		−	1.55950e13i		−	0.178708i
$615$		0			0
$616$	−1.68024e13			−0.189438
$617$			8.05443e13i			0.900760i	0.892837	+	0.450380i	$0.148711\pi$
$617$			8.05443e13i			0.900760i	−0.892837	+	0.450380i	$0.851289\pi$
$618$	−2.60612e13	−	3.79231e13i	−0.289103	−	0.420690i
$619$	−5.14946e13			−0.566642			−0.283321	−	0.959025i	$-0.591436\pi$
$619$	−5.14946e13			−0.566642			−0.283321	+	0.959025i	$0.591436\pi$
$620$		0			0
$621$	1.95797e13	−	4.69777e12i	0.212005	−	0.0508667i
$622$	−4.42759e13			−0.475571
$623$			5.54515e12i			0.0590844i
$624$	8.93332e12	−	6.13909e12i	0.0944256	−	0.0648905i
$625$		0			0
$626$			5.63017e12i			0.0585665i
$627$	−6.58996e12	−	9.58941e12i	−0.0680057	−	0.0989587i
$628$	−8.13933e13			−0.833279
$629$			1.33745e14i			1.35839i
$630$		0			0
$631$	−1.02922e13			−0.102887			−0.0514435	−	0.998676i	$-0.516382\pi$
$631$	−1.02922e13			−0.102887			−0.0514435	+	0.998676i	$0.516382\pi$
$632$		−	2.27757e13i		−	0.225884i
$633$	3.06543e13	−	2.10660e13i	0.301629	−	0.207283i
$634$	1.04918e14			1.02424
$635$		0			0
$636$	−2.97040e12	−	4.32238e12i	−0.0285449	−	0.0415372i
$637$	4.37307e13			0.416955
$638$		−	6.82785e12i		−	0.0645923i
$639$	−3.14965e13	−	1.20937e13i	−0.295636	−	0.113516i
$640$		0			0
$641$			4.62451e13i			0.427342i	0.976906	+	0.213671i	$0.0685420\pi$
$641$			4.62451e13i			0.427342i	−0.976906	+	0.213671i	$0.931458\pi$
$642$	6.50531e13	−	4.47053e13i	0.596476	−	0.409906i
$643$	−2.73102e13			−0.248468			−0.124234	−	0.992253i	$-0.539647\pi$
$643$	−2.73102e13			−0.248468			−0.124234	+	0.992253i	$0.539647\pi$
$644$		−	1.66876e13i		−	0.150649i
$645$		0			0
$646$	4.62630e13			0.411217
$647$			1.34984e13i			0.119059i	0.998227	+	0.0595293i	$0.0189600\pi$
$647$			1.34984e13i			0.119059i	−0.998227	+	0.0595293i	$0.981040\pi$
$648$	−2.70353e13	+	3.00145e13i	−0.236622	+	0.262697i
$649$	−1.82349e13			−0.158372
$650$		0			0
$651$	−1.94573e14	+	1.33713e14i	−1.66410	+	1.14359i
$652$	−4.71466e13			−0.400140
$653$			8.41840e13i			0.709029i	0.935051	+	0.354514i	$0.115354\pi$
$653$			8.41840e13i			0.709029i	−0.935051	+	0.354514i	$0.884646\pi$
$654$	−1.47164e13	−	2.14146e13i	−0.123002	−	0.178987i
$655$		0			0
$656$			3.91220e13i			0.322034i
$657$	−4.62671e13	+	1.20496e14i	−0.377960	+	0.984345i
$658$	8.14920e13			0.660672
$659$		−	1.65464e14i		−	1.33130i	−0.746264	−	0.665650i	$-0.768154\pi$
$659$		−	1.65464e14i		−	1.33130i	0.746264	−	0.665650i	$-0.231846\pi$
$660$		0			0
$661$	2.01681e14			1.59830			0.799148	−	0.601135i	$-0.205284\pi$
$661$	2.01681e14			1.59830			0.799148	+	0.601135i	$0.205284\pi$
$662$		−	3.20050e13i		−	0.251726i
$663$	−6.24405e13	−	9.08606e13i	−0.487415	−	0.709264i
$664$	−2.53204e13			−0.196169
$665$		0			0
$666$	−6.25688e13	−	2.40246e13i	−0.477515	−	0.183352i
$667$	6.78122e12			0.0513664
$668$			1.08757e14i			0.817663i
$669$	1.21315e14	−	8.33691e13i	0.905281	−	0.622120i
$670$		0			0
$671$			3.31400e13i			0.243635i
$672$	1.89611e13	+	2.75914e13i	0.138362	+	0.201338i
$673$	−6.04368e12			−0.0437750			−0.0218875	−	0.999760i	$-0.506968\pi$
$673$	−6.04368e12			−0.0437750			−0.0218875	+	0.999760i	$0.506968\pi$
$674$		−	1.96351e13i		−	0.141167i
$675$		0			0
$676$	5.57588e13			0.394984
$677$		−	1.21474e14i		−	0.854164i	−0.904213	−	0.427082i	$-0.859542\pi$
$677$		−	1.21474e14i		−	0.854164i	0.904213	−	0.427082i	$-0.140458\pi$
$678$	5.98885e13	−	4.11561e13i	0.418018	−	0.287267i
$679$	2.05349e14			1.42280
$680$		0			0
$681$	9.22913e13	+	1.34298e14i	0.630123	+	0.916926i
$682$	−5.91019e13			−0.400571
$683$			1.51629e14i			1.02019i	0.860119	+	0.510094i	$0.170389\pi$
$683$			1.51629e14i			1.02019i	−0.860119	+	0.510094i	$0.829611\pi$
$684$	−8.31024e12	+	2.16429e13i	−0.0555051	+	0.144556i
$685$		0			0
$686$		−	1.33906e13i		−	0.0881410i
$687$	7.07663e13	−	4.86315e13i	0.462427	−	0.317785i
$688$	5.20930e13			0.337938
$689$			7.17296e12i			0.0461958i
$690$		0			0
$691$	6.62249e13			0.420369			0.210185	−	0.977662i	$-0.432593\pi$
$691$	6.62249e13			0.420369			0.210185	+	0.977662i	$0.432593\pi$
$692$		−	1.55716e14i		−	0.981300i
$693$	−7.99493e13	−	3.06982e13i	−0.500205	−	0.192064i
$694$	−1.17824e14			−0.731873
$695$		0			0
$696$	−1.12121e13	+	7.70509e12i	−0.0686500	+	0.0471771i
$697$	3.97909e14			2.41891
$698$			2.53321e13i			0.152895i
$699$	−1.54679e14	−	2.25082e14i	−0.926928	−	1.34882i
$700$		0			0
$701$			5.78990e13i			0.342043i	0.985267	+	0.171022i	$0.0547068\pi$
$701$			5.78990e13i			0.342043i	−0.985267	+	0.171022i	$0.945293\pi$
$702$	5.37228e13	−	1.28898e13i	0.315118	−	0.0756066i
$703$	−3.84654e13			−0.224024
$704$			8.38091e12i			0.0484650i
$705$		0			0
$706$	−8.46157e13			−0.482422
$707$		−	3.90039e14i		−	2.20806i
$708$	2.05777e13	+	2.99437e13i	0.115672	+	0.168321i
$709$	2.70077e14			1.50750			0.753750	−	0.657162i	$-0.228243\pi$
$709$	2.70077e14			1.50750			0.753750	+	0.657162i	$0.228243\pi$
$710$		0			0
$711$	4.16115e13	−	1.08372e14i	0.229016	−	0.596441i
$712$	2.76588e12			0.0151159
$713$		−	5.86983e13i		−	0.318550i
$714$	2.80631e14	−	1.92853e14i	1.51232	−	1.03929i
$715$		0			0
$716$			3.62043e12i			0.0192395i
$717$	3.64166e13	+	5.29918e13i	0.192178	+	0.279649i
$718$	8.02117e13			0.420354
$719$		−	1.48102e14i		−	0.770755i	−0.922759	−	0.385377i	$-0.874071\pi$
$719$		−	1.48102e14i		−	0.770755i	0.922759	−	0.385377i	$-0.125929\pi$
$720$		0			0
$721$	−1.94375e14			−0.997616
$722$		−	1.25425e14i		−	0.639289i
$723$	1.77592e14	−	1.22044e14i	0.898944	−	0.617765i
$724$	6.51820e13			0.327669
$725$		0			0
$726$	6.86307e13	+	9.98683e13i	0.340279	+	0.495159i
$727$	−5.21602e13			−0.256842			−0.128421	−	0.991720i	$-0.540991\pi$
$727$	−5.21602e13			−0.256842			−0.128421	+	0.991720i	$0.540991\pi$
$728$		−	4.57876e13i		−	0.223919i
$729$	−1.83476e14	+	9.34214e13i	−0.891133	+	0.453742i
$730$		0			0
$731$		−	5.29837e14i		−	2.53837i
$732$	5.44195e13	−	3.73978e13i	0.258940	−	0.177947i
$733$	−3.21782e14			−1.52069			−0.760346	−	0.649518i	$-0.774971\pi$
$733$	−3.21782e14			−1.52069			−0.760346	+	0.649518i	$0.774971\pi$
$734$			2.28902e14i			1.07441i
$735$		0			0
$736$	−8.32367e12			−0.0385413
$737$			3.26009e13i			0.149931i
$738$	−7.14765e13	+	1.86151e14i	−0.326499	+	0.850322i
$739$	1.66542e14			0.755617			0.377809	−	0.925884i	$-0.376678\pi$
$739$	1.66542e14			0.755617			0.377809	+	0.925884i	$0.376678\pi$
$740$		0			0
$741$	2.61318e13	−	1.79581e13i	0.116971	−	0.0803839i
$742$	−2.21543e13			−0.0985007
$743$		−	1.13631e14i		−	0.501825i	−0.968010	−	0.250912i	$-0.919269\pi$
$743$		−	1.13631e14i		−	0.501825i	0.968010	−	0.250912i	$-0.0807306\pi$
$744$	6.66953e13	+	9.70519e13i	0.292570	+	0.425735i
$745$		0			0
$746$		−	8.62230e13i		−	0.373189i
$747$	−1.20480e14	−	4.62608e13i	−0.517979	−	0.198889i
$748$	8.52421e13			0.364037
$749$		−	3.33429e14i		−	1.41447i
$750$		0			0
$751$	−1.64956e14			−0.690508			−0.345254	−	0.938509i	$-0.612207\pi$
$751$	−1.64956e14			−0.690508			−0.345254	+	0.938509i	$0.612207\pi$
$752$		−	4.06477e13i		−	0.169023i
$753$	1.18290e14	+	1.72130e14i	0.488622	+	0.711020i
$754$	1.86064e13			0.0763493
$755$		0			0
$756$	3.98112e13	+	1.65928e14i	0.161212	+	0.671909i
$757$	2.67990e14			1.07805			0.539026	−	0.842289i	$-0.318793\pi$
$757$	2.67990e14			1.07805			0.539026	+	0.842289i	$0.318793\pi$
$758$			2.51282e14i			1.00419i
$759$	1.75483e13	−	1.20594e13i	0.0696669	−	0.0478760i
$760$		0			0
$761$		−	1.29795e14i		−	0.508550i	−0.967132	−	0.254275i	$-0.918163\pi$
$761$		−	1.29795e14i		−	0.508550i	0.967132	−	0.254275i	$-0.0818368\pi$
$762$	9.89720e13	+	1.44020e14i	0.385245	+	0.560591i
$763$	−1.09760e14			−0.424446
$764$		−	1.05707e14i		−	0.406105i
$765$		0			0
$766$	−9.71099e13			−0.368230
$767$		−	4.96913e13i		−	0.187199i
$768$	1.37624e13	−	9.45768e12i	0.0515095	−	0.0353980i
$769$	−2.19185e14			−0.815041			−0.407521	−	0.913196i	$-0.633607\pi$
$769$	−2.19185e14			−0.815041			−0.407521	+	0.913196i	$0.633607\pi$
$770$		0			0
$771$	2.99890e14	+	4.36386e14i	1.10075	+	1.60176i
$772$	1.59542e14			0.581821
$773$		−	4.05042e14i		−	1.46758i	−0.679374	−	0.733792i	$-0.737749\pi$
$773$		−	4.05042e14i		−	1.46758i	0.679374	−	0.733792i	$-0.262251\pi$
$774$	2.47870e14	+	9.51747e13i	0.892315	+	0.342623i
$775$		0			0
$776$		−	1.02426e14i		−	0.364002i
$777$	−2.33331e14	+	1.60348e14i	−0.823886	+	0.566185i
$778$	3.40665e14			1.19517
$779$			1.14440e14i			0.398925i
$780$		0			0
$781$	−3.56775e13			−0.122783
$782$			8.46599e13i			0.289497i
$783$	−6.74268e13	+	1.61778e13i	−0.229099	+	0.0549681i
$784$	6.73701e13			0.227450
$785$		0			0
$786$	−2.27074e14	+	1.56048e14i	−0.756929	+	0.520171i
$787$	−4.98729e14			−1.65193			−0.825963	−	0.563724i	$-0.809368\pi$
$787$	−4.98729e14			−1.65193			−0.825963	+	0.563724i	$0.809368\pi$
$788$			7.76674e13i			0.255628i
$789$	−1.89845e14	−	2.76254e14i	−0.620890	−	0.903491i
$790$		0			0
$791$		−	3.06958e14i		−	0.991280i
$792$	−1.53121e13	+	3.98782e13i	−0.0491369	+	0.127970i
$793$	−9.03088e13			−0.287981
$794$			2.52678e14i			0.800690i
$795$		0			0
$796$	5.71861e13			0.178947
$797$		−	1.48672e14i		−	0.462314i	−0.972917	−	0.231157i	$-0.925749\pi$
$797$		−	1.48672e14i		−	0.462314i	0.972917	−	0.231157i	$-0.0742510\pi$
$798$	5.54652e13	+	8.07104e13i	0.171398	+	0.249411i
$799$	−4.13427e14			−1.26959
$800$		0			0
$801$	1.31607e13	+	5.05331e12i	0.0399131	+	0.0153255i
$802$	−2.61766e14			−0.788934
$803$			1.36492e14i			0.408817i
$804$	5.35343e13	−	3.67894e13i	0.159350	−	0.109507i
$805$		0			0
$806$		−	1.61057e14i		−	0.473482i
$807$	−1.62578e14	−	2.36576e14i	−0.475001	−	0.691200i
$808$	−1.94549e14			−0.564901
$809$			1.32296e14i			0.381772i	0.981612	+	0.190886i	$0.0611361\pi$
$809$			1.32296e14i			0.381772i	−0.981612	+	0.190886i	$0.938864\pi$
$810$		0			0
$811$	−3.75449e14			−1.07016			−0.535078	−	0.844803i	$-0.679718\pi$
$811$	−3.75449e14			−1.07016			−0.535078	+	0.844803i	$0.679718\pi$
$812$			5.74675e13i			0.162795i
$813$	−2.84884e14	+	1.95776e14i	−0.802076	+	0.551197i
$814$	−7.08746e13			−0.198321
$815$		0			0
$816$	−9.61939e13	−	1.39977e14i	−0.265887	−	0.386906i
$817$	1.52383e14			0.418625
$818$		−	2.43044e14i		−	0.663618i
$819$	8.36547e13	−	2.17867e14i	0.227023	−	0.591252i
$820$		0			0
$821$			4.64480e12i			0.0124524i	0.999981	+	0.00622618i	$0.00198187\pi$
$821$			4.64480e12i			0.0124524i	−0.999981	+	0.00622618i	$0.998018\pi$
$822$	1.24502e14	−	8.55594e13i	0.331755	−	0.227986i
$823$	−6.38146e14			−1.69013			−0.845067	−	0.534661i	$-0.820439\pi$
$823$	−6.38146e14			−1.69013			−0.845067	+	0.534661i	$0.820439\pi$
$824$			9.69528e13i			0.255226i
$825$		0			0
$826$	1.53476e14			0.399154
$827$		−	5.33624e14i		−	1.37946i	−0.724068	−	0.689728i	$-0.757730\pi$
$827$		−	5.33624e14i		−	1.37946i	0.724068	−	0.689728i	$-0.242270\pi$
$828$	−3.96058e13	−	1.52075e13i	−0.101767	−	0.0390756i
$829$	−8.63626e13			−0.220573			−0.110287	−	0.993900i	$-0.535177\pi$
$829$	−8.63626e13			−0.220573			−0.110287	+	0.993900i	$0.535177\pi$
$830$		0			0
$831$	−1.06135e14	+	7.29370e13i	−0.267825	+	0.184053i
$832$	−2.28386e13			−0.0572865
$833$		−	6.85220e14i		−	1.70846i
$834$	1.96966e14	+	2.86616e14i	0.488160	+	0.710347i
$835$		0			0
$836$			2.45159e13i			0.0600367i
$837$	1.40035e14	+	5.83647e14i	0.340886	+	1.42077i
$838$	−1.99510e14			−0.482774
$839$			4.28770e14i			1.03137i	0.856778	+	0.515685i	$0.172462\pi$
$839$			4.28770e14i			1.03137i	−0.856778	+	0.515685i	$0.827538\pi$
$840$		0			0
$841$	3.97355e14			0.944492
$842$		−	1.28918e14i		−	0.304616i
$843$	3.14397e14	+	4.57496e14i	0.738483	+	1.07461i
$844$	−7.83697e13			−0.182994
$845$		0			0
$846$	7.42639e13	−	1.93410e14i	0.171367	−	0.446301i
$847$	5.11874e14			1.17421
$848$			1.10504e13i			0.0252000i
$849$	−4.63171e14	+	3.18297e14i	−1.05003	+	0.721595i
$850$		0			0
$851$		−	7.03905e13i		−	0.157713i
$852$	4.02613e13	+	5.85864e13i	0.0896789	+	0.130497i
$853$	8.99493e10			0.000199183			9.95916e−5	−	1.00000i	$-0.499968\pi$
$853$	8.99493e10			0.000199183			9.95916e−5		1.00000i	$0.499968\pi$
$854$		−	2.78927e14i		−	0.614046i
$855$		0			0
$856$	−1.66312e14			−0.361872
$857$		−	1.45265e14i		−	0.314238i	−0.987580	−	0.157119i	$-0.949779\pi$
$857$		−	1.45265e14i		−	0.314238i	0.987580	−	0.157119i	$-0.0502205\pi$
$858$	4.81492e13	−	3.30887e13i	0.103551	−	0.0711613i
$859$	−3.53555e14			−0.755947			−0.377974	−	0.925816i	$-0.623379\pi$
$859$	−3.53555e14			−0.755947			−0.377974	+	0.925816i	$0.623379\pi$
$860$		0			0
$861$	4.77058e14	+	6.94192e14i	1.00822	+	1.46711i
$862$	−4.08024e14			−0.857333
$863$			5.16372e14i			1.07872i	0.842075	+	0.539360i	$0.181334\pi$
$863$			5.16372e14i			1.07872i	−0.842075	+	0.539360i	$0.818666\pi$
$864$	8.27637e13	−	1.98576e13i	0.171898	−	0.0412437i
$865$		0			0
$866$		−	4.66892e14i		−	0.958576i
$867$	−1.01996e15	+	7.00930e14i	−2.08204	+	1.43080i
$868$	4.97439e14			1.00958
$869$		−	1.22757e14i		−	0.247713i
$870$		0			0
$871$	−8.88397e13			−0.177221
$872$			5.47477e13i			0.108588i
$873$	1.87135e14	−	4.87367e14i	0.369048	−	0.961136i
$874$	−2.43485e13			−0.0477435
$875$		0			0
$876$	2.24135e14	−	1.54028e14i	0.434499	−	0.298593i
$877$	−3.23487e13			−0.0623532			−0.0311766	−	0.999514i	$-0.509925\pi$
$877$	−3.23487e13			−0.0623532			−0.0311766	+	0.999514i	$0.509925\pi$
$878$			4.41944e14i			0.847022i
$879$	1.45870e14	+	2.12264e14i	0.277986	+	0.404512i
$880$		0			0
$881$			3.45484e14i			0.650950i	0.945551	+	0.325475i	$0.105524\pi$
$881$			3.45484e14i			0.650950i	−0.945551	+	0.325475i	$0.894476\pi$
$882$	3.20561e14	+	1.23086e14i	0.600576	+	0.230604i
$883$	1.94069e14			0.361537			0.180769	−	0.983526i	$-0.442141\pi$
$883$	1.94069e14			0.361537			0.180769	+	0.983526i	$0.442141\pi$
$884$			2.32291e14i			0.430299i
$885$		0			0
$886$	−6.73096e14			−1.23284
$887$			2.06383e14i			0.375885i	0.982180	+	0.187943i	$0.0601819\pi$
$887$			2.06383e14i			0.375885i	−0.982180	+	0.187943i	$0.939818\pi$
$888$	7.99804e13	+	1.16384e14i	0.144850	+	0.210779i
$889$	7.38171e14			1.32938
$890$		0			0
$891$	−1.45716e14	+	1.61773e14i	−0.259489	+	0.288084i
$892$	−3.10149e14			−0.549219
$893$		−	1.18903e14i		−	0.209380i
$894$	1.53384e14	−	1.05407e14i	0.268592	−	0.184579i
$895$		0			0
$896$		−	7.05390e13i		−	0.122149i
$897$	3.28628e13	+	4.78204e13i	0.0565903	+	0.0823476i
$898$	3.11139e14			0.532811
$899$			2.02140e14i			0.344234i
$900$		0			0
$901$	1.12394e14			0.189286
$902$			2.10862e14i			0.353155i
$903$	9.24353e14	−	6.35227e14i	1.53957	−	1.05801i
$904$	−1.53109e14			−0.253605
$905$		0			0
$906$	3.81129e14	+	5.54602e14i	0.624354	+	0.908532i
$907$	3.53646e14			0.576145			0.288073	−	0.957609i	$-0.406986\pi$
$907$	3.53646e14			0.576145			0.288073	+	0.957609i	$0.406986\pi$
$908$		−	3.43341e14i		−	0.556284i
$909$	−9.25705e14	−	3.55444e14i	−1.49160	−	0.572732i
$910$		0			0
$911$			4.57044e14i			0.728394i	0.931322	+	0.364197i	$0.118656\pi$
$911$			4.57044e14i			0.728394i	−0.931322	+	0.364197i	$0.881344\pi$
$912$	4.02578e13	−	2.76657e13i	0.0638081	−	0.0438497i
$913$	−1.36473e14			−0.215126
$914$		−	9.28232e12i		−	0.0145521i
$915$		0			0
$916$	−1.80918e14			−0.280547
$917$			1.16387e15i			1.79497i
$918$	−2.01971e14	−	8.41788e14i	−0.309796	−	1.29119i
$919$	4.85254e14			0.740273			0.370136	−	0.928977i	$-0.379311\pi$
$919$	4.85254e14			0.740273			0.370136	+	0.928977i	$0.379311\pi$
$920$		0			0
$921$	−1.38027e14	+	9.48541e13i	−0.208289	+	0.143139i
$922$	4.77244e12			0.00716285
$923$		−	9.72237e13i		−	0.145132i
$924$	1.02198e14	+	1.48713e14i	0.151733	+	0.220795i
$925$		0			0
$926$			4.45166e14i			0.653834i
$927$	−1.77134e14	+	4.61322e14i	−0.258764	+	0.673916i
$928$	2.86644e13			0.0416488
$929$			8.16207e14i			1.17957i	0.807562	+	0.589783i	$0.200787\pi$
$929$			8.16207e14i			1.17957i	−0.807562	+	0.589783i	$0.799213\pi$
$930$		0			0
$931$	1.97071e14			0.281757
$932$			5.75436e14i			0.818309i
$933$	2.69301e14	+	3.91874e14i	0.380916	+	0.554292i
$934$	−2.75832e14			−0.388071
$935$		0			0
$936$	−1.08671e14	−	4.17264e13i	−0.151263	−	0.0580807i
$937$	6.90133e14			0.955510			0.477755	−	0.878493i	$-0.341451\pi$
$937$	6.90133e14			0.955510			0.477755	+	0.878493i	$0.341451\pi$
$938$		−	2.74389e14i		−	0.377879i
$939$	4.98311e13	−	3.42445e13i	0.0682609	−	0.0469098i
$940$		0			0
$941$			1.26481e14i			0.171426i	0.996320	+	0.0857129i	$0.0273168\pi$
$941$			1.26481e14i			0.171426i	−0.996320	+	0.0857129i	$0.972683\pi$
$942$	4.95061e14	+	7.20390e14i	0.667428	+	0.971210i
$943$	−2.09422e14			−0.280843
$944$		−	7.65528e13i		−	0.102118i
$945$		0			0
$946$	2.80773e14			0.370596
$947$			3.05743e14i			0.401427i	0.979650	+	0.200713i	$0.0643260\pi$
$947$			3.05743e14i			0.401427i	−0.979650	+	0.200713i	$0.935674\pi$
$948$	−2.01581e14	+	1.38529e14i	−0.263274	+	0.180925i
$949$	−3.71950e14			−0.483230
$950$		0			0
$951$	−6.38144e14	−	9.28598e14i	−0.820382	−	1.19378i
$952$	−7.17450e14			−0.917502
$953$			7.71039e14i			0.980870i	0.871478	+	0.490435i	$0.163162\pi$
$953$			7.71039e14i			0.980870i	−0.871478	+	0.490435i	$0.836838\pi$
$954$	−2.01893e13	+	5.25803e13i	−0.0255493	+	0.0665398i
$955$		0			0
$956$		−	1.35477e14i		−	0.169658i
$957$	−6.04315e13	+	4.15292e13i	−0.0752841	+	0.0517362i
$958$	−1.13338e14			−0.140458
$959$		−	6.38134e14i		−	0.786718i
$960$		0			0
$961$	9.30098e14			1.13478
$962$		−	1.93138e14i		−	0.234419i
$963$	−7.91348e14	−	3.03855e14i	−0.955512	−	0.366889i
$964$	−4.54025e14			−0.545375
$965$		0			0
$966$	−1.47698e14	+	1.01500e14i	−0.175585	+	0.120664i
$967$	−1.27364e15			−1.50631			−0.753154	−	0.657845i	$-0.771468\pi$
$967$	−1.27364e15			−1.50631			−0.753154	+	0.657845i	$0.771468\pi$
$968$		−	2.55319e14i		−	0.300405i
$969$	−2.81387e14	−	4.09461e14i	−0.329371	−	0.479285i
$970$		0			0
$971$		−	4.71364e14i		−	0.546085i	−0.962002	−	0.273043i	$-0.911970\pi$
$971$		−	4.71364e14i		−	0.546085i	0.962002	−	0.273043i	$-0.0880300\pi$
$972$	4.30087e14	+	5.67238e13i	0.495707	+	0.0653784i
$973$	1.46905e15			1.68451
$974$			9.43563e14i			1.07641i
$975$		0			0
$976$	−1.39127e14			−0.157095
$977$		−	1.09733e15i		−	1.23272i	−0.787465	−	0.616360i	$-0.788607\pi$
$977$		−	1.09733e15i		−	1.23272i	0.787465	−	0.616360i	$-0.211393\pi$
$978$	2.86761e14	+	4.17281e14i	0.320498	+	0.466374i
$979$	1.49077e13			0.0165767
$980$		0			0
$981$	−1.00025e14	+	2.60501e14i	−0.110094	+	0.286724i
$982$	4.75946e13			0.0521195
$983$		−	1.52240e15i		−	1.65867i	−0.558751	−	0.829336i	$-0.688719\pi$
$983$		−	1.52240e15i		−	1.65867i	0.558751	−	0.829336i	$-0.311281\pi$
$984$	3.46258e14	−	2.37953e14i	0.375340	−	0.257938i
$985$		0			0
$986$		−	2.91545e14i		−	0.312839i
$987$	−4.95661e14	−	7.21264e14i	−0.529175	−	0.770031i
$988$	−6.68075e13			−0.0709644
$989$			2.78856e14i			0.294712i
$990$		0			0
$991$	3.79461e14			0.397008			0.198504	−	0.980100i	$-0.436392\pi$
$991$	3.79461e14			0.397008			0.198504	+	0.980100i	$0.436392\pi$
$992$		−	2.48119e14i		−	0.258286i
$993$	−2.83267e14	+	1.94665e14i	−0.293393	+	0.201623i
$994$	3.00284e14			0.309457
$995$		0			0
$996$	1.54007e14	+	2.24104e14i	0.157125	+	0.228641i
$997$	−3.25337e13			−0.0330262			−0.0165131	−	0.999864i	$-0.505257\pi$
$997$	−3.25337e13			−0.0330262			−0.0165131	+	0.999864i	$0.505257\pi$
$998$			6.21082e14i			0.627330i
$999$	1.67929e14	+	6.99905e14i	0.168771	+	0.703415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.11.d.a.101.4		4
3.2	odd	2	inner	150.11.d.a.101.2		4
5.2	odd	4		150.11.b.a.149.1		8
5.3	odd	4		150.11.b.a.149.8		8
5.4	even	2		6.11.b.a.5.1	✓	4
15.2	even	4		150.11.b.a.149.7		8
15.8	even	4		150.11.b.a.149.2		8
15.14	odd	2		6.11.b.a.5.3	yes	4
20.19	odd	2		48.11.e.d.17.3		4
40.19	odd	2		192.11.e.h.65.2		4
40.29	even	2		192.11.e.g.65.3		4
45.4	even	6		162.11.d.d.107.4		8
45.14	odd	6		162.11.d.d.107.1		8
45.29	odd	6		162.11.d.d.53.4		8
45.34	even	6		162.11.d.d.53.1		8
60.59	even	2		48.11.e.d.17.4		4
120.29	odd	2		192.11.e.g.65.4		4
120.59	even	2		192.11.e.h.65.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.1	✓	4	5.4	even	2
6.11.b.a.5.3	yes	4	15.14	odd	2
48.11.e.d.17.3		4	20.19	odd	2
48.11.e.d.17.4		4	60.59	even	2
150.11.b.a.149.1		8	5.2	odd	4
150.11.b.a.149.2		8	15.8	even	4
150.11.b.a.149.7		8	15.2	even	4
150.11.b.a.149.8		8	5.3	odd	4
150.11.d.a.101.2		4	3.2	odd	2	inner
150.11.d.a.101.4		4	1.1	even	1	trivial
162.11.d.d.53.1		8	45.34	even	6
162.11.d.d.53.4		8	45.29	odd	6
162.11.d.d.107.1		8	45.14	odd	6
162.11.d.d.107.4		8	45.4	even	6
192.11.e.g.65.3		4	40.29	even	2
192.11.e.g.65.4		4	120.29	odd	2
192.11.e.h.65.1		4	120.59	even	2
192.11.e.h.65.2		4	40.19	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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274i q^{2} +(200.269 - 137.627i) q^{3} -512.000 q^{4} +(3114.15 + 4531.57i) q^{6} +23226.5 q^{7} -11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +O(q^{10})\)	\(q+22.6274i q^{2} +(200.269 - 137.627i) q^{3} -512.000 q^{4} +(3114.15 + 4531.57i) q^{6} +23226.5 q^{7} -11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} -62442.7i q^{11} +(-102538. + 70465.2i) q^{12} +170161. q^{13} +525556. i q^{14} +262144. q^{16} -2.66626e6i q^{17} +(1.24734e6 + 478941. i) q^{18} +766825. q^{19} +(4.65156e6 - 3.19661e6i) q^{21} +1.41292e6 q^{22} +1.40327e6i q^{23} +(-1.59445e6 - 2.32016e6i) q^{24} +3.85029e6i q^{26} +(-3.34774e6 - 1.39529e7i) q^{27} -1.18920e7 q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} +5.93164e6i q^{32} +(-8.59382e6 - 1.25053e7i) q^{33} +6.03306e7 q^{34} +(-1.08372e7 + 2.82240e7i) q^{36} -5.01619e7 q^{37} +1.73513e7i q^{38} +(3.40779e7 - 2.34188e7i) q^{39} +1.49239e8i q^{41} +(7.23310e7 + 1.05253e8i) q^{42} +1.98719e8 q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} -1.55059e8i q^{47} +(5.24993e7 - 3.60782e7i) q^{48} +2.56996e8 q^{49} +(-3.66951e8 - 5.33970e8i) q^{51} -8.71222e7 q^{52} +4.21541e7i q^{53} +(3.15718e8 - 7.57507e7i) q^{54} -2.69085e8i q^{56} +(1.53571e8 - 1.05536e8i) q^{57} +1.09346e8 q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} -9.46499e8i q^{62} +(4.91622e8 - 1.28036e9i) q^{63} -1.34218e8 q^{64} +(2.82963e8 - 1.94456e8i) q^{66} -5.22093e8 q^{67} +1.36513e9i q^{68} +(1.93128e8 + 2.81031e8i) q^{69} -5.71364e8i q^{71} +(-6.38636e8 - 2.45218e8i) q^{72} -2.18588e9 q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} -1.45033e9i q^{77} +(5.29906e8 + 7.71095e8i) q^{78} +1.96592e9 q^{79} +(-2.59075e9 - 2.33360e9i) q^{81} -3.37689e9 q^{82} -2.18558e9i q^{83} +(-2.38160e9 + 1.63666e9i) q^{84} +4.49650e9i q^{86} +(-6.65078e8 - 9.67791e8i) q^{87} -7.23413e8 q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} -7.18473e8i q^{92} +(-8.37720e9 + 5.75692e9i) q^{93} +3.50858e9 q^{94} +(8.16356e8 + 1.18792e9i) q^{96} +8.84112e9 q^{97} +5.81517e9i q^{98} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 84 q^{3} - 2048 q^{4} + 5376 q^{6} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) \) 4 * q - 84 * q^3 - 2048 * q^4 + 5376 * q^6 + 45112 * q^7 + 159012 * q^9	\( 4 q - 84 q^{3} - 2048 q^{4} + 5376 q^{6} + 45112 q^{7} + 159012 q^{9} + 43008 q^{12} - 275240 q^{13} + 1048576 q^{16} + 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} - 7730688 q^{22} - 2752512 q^{24} - 34619508 q^{27} - 23097344 q^{28} - 21785848 q^{31} - 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} + 71014168 q^{37} + 217287240 q^{39} + 145233408 q^{42} + 470688664 q^{43} + 188814336 q^{46} - 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} + 140922880 q^{52} + 481662720 q^{54} + 1058753208 q^{57} + 1564177920 q^{58} - 1184038744 q^{61} + 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} + 297365848 q^{67} + 596268288 q^{69} - 1488715776 q^{72} - 6534269000 q^{73} + 803188736 q^{76} + 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} - 8378668032 q^{82} - 4929540096 q^{84} - 210268800 q^{87} + 3958112256 q^{88} + 8317232080 q^{91} - 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} + 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) \) 4 * q - 84 * q^3 - 2048 * q^4 + 5376 * q^6 + 45112 * q^7 + 159012 * q^9 + 43008 * q^12 - 275240 * q^13 + 1048576 * q^16 + 2907648 * q^18 - 1568728 * q^19 + 9628008 * q^21 - 7730688 * q^22 - 2752512 * q^24 - 34619508 * q^27 - 23097344 * q^28 - 21785848 * q^31 - 25974144 * q^33 + 151087104 * q^34 - 81414144 * q^36 + 71014168 * q^37 + 217287240 * q^39 + 145233408 * q^42 + 470688664 * q^43 + 188814336 * q^46 - 22020096 * q^48 - 50058420 * q^49 - 708576768 * q^51 + 140922880 * q^52 + 481662720 * q^54 + 1058753208 * q^57 + 1564177920 * q^58 - 1184038744 * q^61 + 905007096 * q^63 - 536870912 * q^64 + 3123445248 * q^66 + 297365848 * q^67 + 596268288 * q^69 - 1488715776 * q^72 - 6534269000 * q^73 + 803188736 * q^76 + 1322135040 * q^78 + 199282568 * q^79 + 1458964548 * q^81 - 8378668032 * q^82 - 4929540096 * q^84 - 210268800 * q^87 + 3958112256 * q^88 + 8317232080 * q^91 - 31744468392 * q^93 + 8505477120 * q^94 + 1409286144 * q^96 + 39176355064 * q^97 - 2626912512 * q^99

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