LMFDB - Embedded newform 150.11.b.a.149.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,11,Mod(149,150)]

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, 1]))

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

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	150.b (of order $2$, degree $1$, not 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:	$8$
Coefficient field:	8.0.3421020160000.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 967x^{4} + 194481 $ x^8 + 967*x^4 + 194481
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{8} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.2
Root			$-3.61315 + 3.61315i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.11.b.a.149.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +O(q^{10})$	\(q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +62442.7i q^{11} +(-70465.2 + 102538. i) q^{12} +170161. i q^{13} +525556. i q^{14} +262144. q^{16} +2.66626e6 q^{17} +(478941. + 1.24734e6i) q^{18} -766825. q^{19} +(4.65156e6 + 3.19661e6i) q^{21} -1.41292e6i q^{22} +1.40327e6 q^{23} +(1.59445e6 - 2.32016e6i) q^{24} -3.85029e6i q^{26} +(1.39529e7 + 3.34774e6i) q^{27} -1.18920e7i q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} -5.93164e6 q^{32} +(-1.25053e7 - 8.59382e6i) q^{33} -6.03306e7 q^{34} +(-1.08372e7 - 2.82240e7i) q^{36} +5.01619e7i q^{37} +1.73513e7 q^{38} +(-3.40779e7 - 2.34188e7i) q^{39} -1.49239e8i q^{41} +(-1.05253e8 - 7.23310e7i) q^{42} +1.98719e8i q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +1.55059e8 q^{47} +(-3.60782e7 + 5.24993e7i) q^{48} -2.56996e8 q^{49} +(-3.66951e8 + 5.33970e8i) q^{51} +8.71222e7i q^{52} +4.21541e7 q^{53} +(-3.15718e8 - 7.57507e7i) q^{54} +2.69085e8i q^{56} +(1.05536e8 - 1.53571e8i) q^{57} +1.09346e8i q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} +9.46499e8 q^{62} +(-1.28036e9 + 4.91622e8i) q^{63} +1.34218e8 q^{64} +(2.82963e8 + 1.94456e8i) q^{66} +5.22093e8i q^{67} +1.36513e9 q^{68} +(-1.93128e8 + 2.81031e8i) q^{69} +5.71364e8i q^{71} +(2.45218e8 + 6.38636e8i) q^{72} -2.18588e9i q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} +1.45033e9 q^{77} +(7.71095e8 + 5.29906e8i) q^{78} -1.96592e9 q^{79} +(-2.59075e9 + 2.33360e9i) q^{81} +3.37689e9i q^{82} -2.18558e9 q^{83} +(2.38160e9 + 1.63666e9i) q^{84} -4.49650e9i q^{86} +(9.67791e8 + 6.65078e8i) q^{87} -7.23413e8i q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +7.18473e8 q^{92} +(5.75692e9 - 8.37720e9i) q^{93} -3.50858e9 q^{94} +(8.16356e8 - 1.18792e9i) q^{96} -8.84112e9i q^{97} +5.81517e9 q^{98} +(3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9}+O(q^{10}) $ 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9	$ 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99}+O(q^{100}) $ 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9 + 2097152 * q^16 + 3137456 * q^19 + 19256016 * q^21 + 5505024 * q^24 - 43571696 * q^31 - 302174208 * q^34 - 162828288 * q^36 - 434574480 * q^39 + 377628672 * q^46 + 100116840 * q^49 - 1417153536 * q^51 - 963325440 * q^54 - 2368077488 * q^61 + 1073741824 * q^64 + 6246890496 * q^66 - 1192536576 * q^69 + 1606377472 * q^76 - 398565136 * q^79 + 2917929096 * q^81 + 9859080192 * q^84 + 16634464160 * q^91 - 17010954240 * q^94 + 2818572288 * q^96 + 5253825024 * 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 $

$2$	−22.6274			−0.707107
$2$	−22.6274			−0.707107
$3$	−137.627	+	200.269i	−0.566368	+	0.824153i
$3$	−137.627	+	200.269i	−0.566368	+	0.824153i
$4$	512.000			0.500000
$5$		0			0
$5$		0			0
$6$	3114.15	−	4531.57i	0.400483	−	0.582764i
$7$		−	23226.5i		−	1.38196i	−0.722876	−	0.690978i	$-0.757180\pi$
$7$		−	23226.5i		−	1.38196i	0.722876	−	0.690978i	$-0.242820\pi$
$8$	−11585.2			−0.353553
$9$	−21166.4	−	55125.0i	−0.358455	−	0.933547i
$10$		0			0
$11$			62442.7i			0.387720i	0.981029	+	0.193860i	$0.0621007\pi$
$11$			62442.7i			0.387720i	−0.981029	+	0.193860i	$0.937899\pi$
$12$	−70465.2	+	102538.i	−0.283184	+	0.412076i
$13$			170161.i			0.458292i	0.973392	+	0.229146i	$0.0735933\pi$
$13$			170161.i			0.458292i	−0.973392	+	0.229146i	$0.926407\pi$
$14$			525556.i			0.977190i
$15$		0			0
$16$	262144.			0.250000
$17$	2.66626e6			1.87784			0.938919	−	0.344139i	$-0.111829\pi$
$17$	2.66626e6			1.87784			0.938919	+	0.344139i	$0.111829\pi$
$18$	478941.	+	1.24734e6i	0.253466	+	0.660117i
$19$	−766825.			−0.309691			−0.154845	−	0.987939i	$-0.549488\pi$
$19$	−766825.			−0.309691			−0.154845	+	0.987939i	$0.549488\pi$
$20$		0			0
$21$	4.65156e6	+	3.19661e6i	1.13894	+	0.782695i
$22$		−	1.41292e6i		−	0.274159i
$23$	1.40327e6			0.218022			0.109011	−	0.994041i	$-0.465232\pi$
$23$	1.40327e6			0.218022			0.109011	+	0.994041i	$0.465232\pi$
$24$	1.59445e6	−	2.32016e6i	0.200241	−	0.291382i
$25$		0			0
$26$		−	3.85029e6i		−	0.324061i
$27$	1.39529e7	+	3.34774e6i	0.972402	+	0.233310i
$28$		−	1.18920e7i		−	0.690978i
$29$		−	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	$0.760734\pi$
$32$	−5.93164e6			−0.176777
$33$	−1.25053e7	−	8.59382e6i	−0.319540	−	0.219592i
$34$	−6.03306e7			−1.32783
$35$		0			0
$36$	−1.08372e7	−	2.82240e7i	−0.179227	−	0.466774i
$37$			5.01619e7i			0.723378i	0.932299	+	0.361689i	$0.117800\pi$
$37$			5.01619e7i			0.723378i	−0.932299	+	0.361689i	$0.882200\pi$
$38$	1.73513e7			0.218985
$39$	−3.40779e7	−	2.34188e7i	−0.377702	−	0.259562i
$40$		0			0
$41$		−	1.49239e8i		−	1.28814i	−0.764967	−	0.644069i	$-0.777245\pi$
$41$		−	1.49239e8i		−	1.28814i	0.764967	−	0.644069i	$-0.222755\pi$
$42$	−1.05253e8	−	7.23310e7i	−0.805354	−	0.553449i
$43$			1.98719e8i			1.35175i	0.737015	+	0.675876i	$0.236235\pi$
$43$			1.98719e8i			1.35175i	−0.737015	+	0.675876i	$0.763765\pi$
$44$			3.19706e7i			0.193860i
$45$		0			0
$46$	−3.17523e7			−0.154165
$47$	1.55059e8			0.676093			0.338047	−	0.941129i	$-0.390234\pi$
$47$	1.55059e8			0.676093			0.338047	+	0.941129i	$0.390234\pi$
$48$	−3.60782e7	+	5.24993e7i	−0.141592	+	0.206038i
$49$	−2.56996e8			−0.909802
$50$		0			0
$51$	−3.66951e8	+	5.33970e8i	−1.06355	+	1.54762i
$52$			8.71222e7i			0.229146i
$53$	4.21541e7			0.100800			0.0503999	−	0.998729i	$-0.483950\pi$
$53$	4.21541e7			0.100800			0.0503999	+	0.998729i	$0.483950\pi$
$54$	−3.15718e8	−	7.57507e7i	−0.687592	−	0.164975i
$55$		0			0
$56$			2.69085e8i			0.488595i
$57$	1.05536e8	−	1.53571e8i	0.175399	−	0.255233i
$58$			1.09346e8i			0.166595i
$59$		−	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	$0.601733\pi$
$62$	9.46499e8			1.03315
$63$	−1.28036e9	+	4.91622e8i	−1.29012	+	0.495369i
$64$	1.34218e8			0.125000
$65$		0			0
$66$	2.82963e8	+	1.94456e8i	0.225949	+	0.155275i
$67$			5.22093e8i			0.386700i	0.981130	+	0.193350i	$0.0619353\pi$
$67$			5.22093e8i			0.386700i	−0.981130	+	0.193350i	$0.938065\pi$
$68$	1.36513e9			0.938919
$69$	−1.93128e8	+	2.81031e8i	−0.123481	+	0.179684i
$70$		0			0
$71$			5.71364e8i			0.316681i	0.987385	+	0.158340i	$0.0506143\pi$
$71$			5.71364e8i			0.316681i	−0.987385	+	0.158340i	$0.949386\pi$
$72$	2.45218e8	+	6.38636e8i	0.126733	+	0.330059i
$73$		−	2.18588e9i		−	1.05441i	−0.849737	−	0.527207i	$-0.823239\pi$
$73$		−	2.18588e9i		−	1.05441i	0.849737	−	0.527207i	$-0.176761\pi$
$74$		−	1.13503e9i		−	0.511506i
$75$		0			0
$76$	−3.92615e8			−0.154845
$77$	1.45033e9			0.535812
$78$	7.71095e8	+	5.29906e8i	0.267076	+	0.183538i
$79$	−1.96592e9			−0.638897			−0.319449	−	0.947604i	$-0.603498\pi$
$79$	−1.96592e9			−0.638897			−0.319449	+	0.947604i	$0.603498\pi$
$80$		0			0
$81$	−2.59075e9	+	2.33360e9i	−0.743020	+	0.669269i
$82$			3.37689e9i			0.910851i
$83$	−2.18558e9			−0.554850			−0.277425	−	0.960747i	$-0.589481\pi$
$83$	−2.18558e9			−0.554850			−0.277425	+	0.960747i	$0.589481\pi$
$84$	2.38160e9	+	1.63666e9i	0.569471	+	0.391348i
$85$		0			0
$86$		−	4.49650e9i		−	0.955833i
$87$	9.67791e8	+	6.65078e8i	0.194171	+	0.133437i
$88$		−	7.23413e8i		−	0.137080i
$89$			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
$92$	7.18473e8			0.109011
$93$	5.75692e9	−	8.37720e9i	0.827514	−	1.20416i
$94$	−3.50858e9			−0.478070
$95$		0			0
$96$	8.16356e8	−	1.18792e9i	0.100121	−	0.145691i
$97$		−	8.84112e9i		−	1.02955i	−0.857324	−	0.514776i	$-0.827875\pi$
$97$		−	8.84112e9i		−	1.02955i	0.857324	−	0.514776i	$-0.172125\pi$
$98$	5.81517e9			0.643327
$99$	3.44215e9	−	1.32169e9i	0.361955	−	0.138980i
$100$		0			0
$101$			1.67928e10i			1.59778i	0.601477	+	0.798890i	$0.294579\pi$
$101$			1.67928e10i			1.59778i	−0.601477	+	0.798890i	$0.705421\pi$
$102$	8.30314e9	−	1.20824e10i	0.752041	−	1.09434i
$103$		−	8.36865e9i		−	0.721887i	−0.932588	−	0.360944i	$-0.882455\pi$
$103$		−	8.36865e9i		−	0.721887i	0.932588	−	0.360944i	$-0.117545\pi$
$104$		−	1.97135e9i		−	0.162031i
$105$		0			0
$106$	−9.53837e8			−0.0712763
$107$	1.43555e10			1.02353			0.511764	−	0.859126i	$-0.328992\pi$
$107$	1.43555e10			1.02353			0.511764	+	0.859126i	$0.328992\pi$
$108$	7.14389e9	+	1.71404e9i	0.486201	+	0.116655i
$109$	4.72564e9			0.307134			0.153567	−	0.988138i	$-0.450924\pi$
$109$	4.72564e9			0.307134			0.153567	+	0.988138i	$0.450924\pi$
$110$		0			0
$111$	−1.00459e10	−	6.90365e9i	−0.596174	−	0.409698i
$112$		−	6.08870e9i		−	0.345489i
$113$	−1.32158e10			−0.717303			−0.358651	−	0.933472i	$-0.616763\pi$
$113$	−1.32158e10			−0.717303			−0.358651	+	0.933472i	$0.616763\pi$
$114$	−2.38801e9	+	3.47492e9i	−0.124026	+	0.180477i
$115$		0			0
$116$		−	2.47422e9i		−	0.117801i
$117$	9.38011e9	−	3.60169e9i	0.427837	−	0.164277i
$118$			6.60779e9i			0.288833i
$119$		−	6.19280e10i		−	2.59509i
$120$		0			0
$121$	2.20383e10			0.849673
$122$	1.20090e10			0.444331
$123$	2.98879e10	+	2.05393e10i	1.06162	+	0.729560i
$124$	−2.14168e10			−0.730544
$125$		0			0
$126$	2.89713e10	−	1.11241e10i	0.912253	−	0.350279i
$127$		−	3.17814e10i		−	0.961953i	−0.876733	−	0.480976i	$-0.840282\pi$
$127$		−	3.17814e10i		−	0.961953i	0.876733	−	0.480976i	$-0.159718\pi$
$128$	−3.03700e9			−0.0883883
$129$	−3.97973e10	−	2.73492e10i	−1.11405	−	0.765589i
$130$		0			0
$131$		−	5.01094e10i		−	1.29886i	−0.760421	−	0.649430i	$-0.775007\pi$
$131$		−	5.01094e10i		−	1.29886i	0.760421	−	0.649430i	$-0.224993\pi$
$132$	−6.40273e9	−	4.40004e9i	−0.159770	−	0.109796i
$133$			1.78107e10i			0.427979i
$134$		−	1.18136e10i		−	0.273438i
$135$		0			0
$136$	−3.08893e10			−0.663916
$137$	2.74744e10			0.569279			0.284639	−	0.958635i	$-0.408126\pi$
$137$	2.74744e10			0.569279			0.284639	+	0.958635i	$0.408126\pi$
$138$	4.36999e9	−	6.35900e9i	0.0873142	−	0.127056i
$139$	−6.32488e10			−1.21893			−0.609464	−	0.792814i	$-0.708615\pi$
$139$	−6.32488e10			−1.21893			−0.609464	+	0.792814i	$0.708615\pi$
$140$		0			0
$141$	−2.13403e10	+	3.10534e10i	−0.382917	+	0.557204i
$142$		−	1.29285e10i		−	0.223927i
$143$	−1.06253e10			−0.177689
$144$	−5.54864e9	−	1.44507e10i	−0.0896137	−	0.233387i
$145$		0			0
$146$			4.94607e10i			0.745583i
$147$	3.53697e10	−	5.14684e10i	0.515282	−	0.749815i
$148$			2.56829e10i			0.361689i
$149$		−	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	$0.215472\pi$
$152$	8.88385e9			0.109492
$153$	−5.64351e10	−	1.46978e11i	−0.673120	−	1.75305i
$154$	−3.28171e10			−0.378876
$155$		0			0
$156$	−1.74479e10	−	1.19904e10i	−0.188851	−	0.129781i
$157$		−	1.58971e11i		−	1.66656i	−0.552853	−	0.833279i	$-0.686461\pi$
$157$		−	1.58971e11i		−	1.66656i	0.552853	−	0.833279i	$-0.313539\pi$
$158$	4.44838e10			0.451769
$159$	−5.80155e9	+	8.44215e9i	−0.0570898	+	0.0830745i
$160$		0			0
$161$		−	3.25930e10i		−	0.301297i
$162$	5.86220e10	−	5.28033e10i	0.525395	−	0.473245i
$163$			9.20831e10i			0.800280i	0.916454	+	0.400140i	$0.131038\pi$
$163$			9.20831e10i			0.800280i	−0.916454	+	0.400140i	$0.868962\pi$
$164$		−	7.64102e10i		−	0.644069i
$165$		0			0
$166$	4.94540e10			0.392338
$167$	2.12416e11			1.63533			0.817663	−	0.575697i	$-0.195269\pi$
$167$	2.12416e11			1.63533			0.817663	+	0.575697i	$0.195269\pi$
$168$	−5.38894e10	−	3.70334e10i	−0.402677	−	0.276725i
$169$	1.08904e11			0.789968
$170$		0			0
$171$	1.62309e10	+	4.22713e10i	0.111010	+	0.289111i
$172$			1.01744e11i			0.675876i
$173$	3.04132e11			1.96260			0.981300	−	0.192482i	$-0.0616538\pi$
$173$	3.04132e11			1.96260			0.981300	+	0.192482i	$0.0616538\pi$
$174$	−2.18986e10	−	1.50490e10i	−0.137300	−	0.0943542i
$175$		0			0
$176$			1.63690e10i			0.0969300i
$177$	5.84837e10	+	4.01908e10i	0.336642	+	0.231345i
$178$		−	5.40212e9i		−	0.0302318i
$179$		−	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	$0.606263\pi$
$182$	−8.94290e10			−0.447838
$183$	7.30425e10	−	1.06288e11i	0.355894	−	0.517880i
$184$	−1.62572e10			−0.0770825
$185$		0			0
$186$	−1.30264e11	+	1.89554e11i	−0.585141	+	0.851470i
$187$			1.66488e11i			0.728075i
$188$	7.93900e10			0.338047
$189$	7.77563e10	−	3.24078e11i	0.322424	−	1.34382i
$190$		0			0
$191$		−	2.06460e11i		−	0.812209i	−0.913827	−	0.406105i	$-0.866887\pi$
$191$		−	2.06460e11i		−	0.812209i	0.913827	−	0.406105i	$-0.133113\pi$
$192$	−1.84720e10	+	2.68797e10i	−0.0707960	+	0.103019i
$193$		−	3.11606e11i		−	1.16364i	−0.813317	−	0.581821i	$-0.802340\pi$
$193$		−	3.11606e11i		−	1.16364i	0.813317	−	0.581821i	$-0.197660\pi$
$194$			2.00052e11i			0.728004i
$195$		0			0
$196$	−1.31582e11			−0.454901
$197$	1.51694e11			0.511255			0.255628	−	0.966775i	$-0.417718\pi$
$197$	1.51694e11			0.511255			0.255628	+	0.966775i	$0.417718\pi$
$198$	−7.78870e10	+	2.99063e10i	−0.255941	+	0.0982737i
$199$	1.11692e11			0.357895			0.178947	−	0.983859i	$-0.442731\pi$
$199$	1.11692e11			0.357895			0.178947	+	0.983859i	$0.442731\pi$
$200$		0			0
$201$	−1.04559e11	−	7.18543e10i	−0.318700	−	0.219014i
$202$		−	3.79978e11i		−	1.12980i
$203$	−1.12241e11			−0.325591
$204$	−1.87879e11	+	2.73392e11i	−0.531773	+	0.773812i
$205$		0			0
$206$			1.89361e11i			0.510451i
$207$	−2.97021e10	−	7.73551e10i	−0.0781512	−	0.203534i
$208$			4.46066e10i			0.114573i
$209$		−	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	$0.441421\pi$
$212$	2.15829e10			0.0503999
$213$	−1.14427e11	−	7.86354e10i	−0.260993	−	0.179358i
$214$	−3.24828e11			−0.723744
$215$		0			0
$216$	−1.61648e11	−	3.87843e10i	−0.343796	−	0.0824874i
$217$			9.71560e11i			2.01916i
$218$	−1.06929e11			−0.217177
$219$	4.37763e11	+	3.00836e11i	0.868998	+	0.597186i
$220$		0			0
$221$			4.53693e11i			0.860598i
$222$	2.27312e11	+	1.56212e11i	0.421559	+	0.289700i
$223$			6.05759e11i			1.09844i	0.835678	+	0.549219i	$0.185075\pi$
$223$			6.05759e11i			1.09844i	−0.835678	+	0.549219i	$0.814925\pi$
$224$			1.37771e11i			0.244298i
$225$		0			0
$226$	2.99040e11			0.507210
$227$	−6.70588e11			−1.11257			−0.556284	−	0.830992i	$-0.687773\pi$
$227$	−6.70588e11			−1.11257			−0.556284	+	0.830992i	$0.687773\pi$
$228$	5.40345e10	−	7.86286e10i	0.0876995	−	0.127616i
$229$	−3.53356e11			−0.561094			−0.280547	−	0.959840i	$-0.590516\pi$
$229$	−3.53356e11			−0.561094			−0.280547	+	0.959840i	$0.590516\pi$
$230$		0			0
$231$	−1.99605e11	+	2.90456e11i	−0.303467	+	0.441591i
$232$			5.59851e10i			0.0832976i
$233$	−1.12390e12			−1.63662			−0.818309	−	0.574779i	$-0.805088\pi$
$233$	−1.12390e12			−1.63662			−0.818309	+	0.574779i	$0.805088\pi$
$234$	−2.12248e11	+	8.14969e10i	−0.302527	+	0.116161i
$235$		0			0
$236$		−	1.49517e11i		−	0.204236i
$237$	2.70565e11	−	3.93714e11i	0.361851	−	0.526549i
$238$			1.40127e12i			1.83500i
$239$			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	$0.316387\pi$
$242$	−4.98671e11			−0.600810
$243$	−1.10789e11	−	8.40014e11i	−0.130757	−	0.991414i
$244$	−2.71732e11			−0.314190
$245$		0			0
$246$	−6.76286e11	−	4.64752e11i	−0.750680	−	0.515877i
$247$		−	1.30483e11i		−	0.141929i
$248$	4.84607e11			0.516573
$249$	3.00795e11	−	4.37704e11i	0.314249	−	0.457281i
$250$		0			0
$251$		−	8.59494e11i		−	0.862729i	−0.902178	−	0.431364i	$-0.858032\pi$
$251$		−	8.59494e11i		−	0.862729i	0.902178	−	0.431364i	$-0.141968\pi$
$252$	−6.55546e11	+	2.51710e11i	−0.645060	+	0.247684i
$253$			8.76237e10i			0.0845316i
$254$			7.19130e11i			0.680203i
$255$		0			0
$256$	6.87195e10			0.0625000
$257$	−2.17900e12			−1.94353			−0.971764	−	0.235954i	$-0.924179\pi$
$257$	−2.17900e12			−1.94353			−0.971764	+	0.235954i	$0.924179\pi$
$258$	9.00510e11	+	6.18841e11i	0.787753	+	0.541353i
$259$	1.16509e12			0.999677
$260$		0			0
$261$	−2.66389e11	+	1.02286e11i	−0.219945	+	0.0844524i
$262$			1.13385e12i			0.918433i
$263$	−1.37942e12			−1.09627			−0.548134	−	0.836391i	$-0.684661\pi$
$263$	−1.37942e12			−1.09627			−0.548134	+	0.836391i	$0.684661\pi$
$264$	1.44877e11	+	9.95615e10i	0.112975	+	0.0776375i
$265$		0			0
$266$		−	4.03010e11i		−	0.302627i
$267$	−4.78126e10	−	3.28574e10i	−0.0352360	−	0.0242146i
$268$			2.67312e11i			0.193350i
$269$		−	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	$0.661765\pi$
$272$	6.98944e11			0.469459
$273$	−5.43937e11	+	7.91511e11i	−0.358703	+	0.521968i
$274$	−6.21674e11			−0.402541
$275$		0			0
$276$	−9.88815e10	+	1.43888e11i	−0.0617404	+	0.0898418i
$277$			5.29960e11i			0.324971i	0.986711	+	0.162485i	$0.0519510\pi$
$277$			5.29960e11i			0.324971i	−0.986711	+	0.162485i	$0.948049\pi$
$278$	1.43116e12			0.861913
$279$	8.85385e11	+	2.30587e12i	0.523734	+	1.36400i
$280$		0			0
$281$		−	2.28441e12i		−	1.30389i	−0.758265	−	0.651946i	$-0.773953\pi$
$281$		−	2.28441e12i		−	1.30389i	0.758265	−	0.651946i	$-0.226047\pi$
$282$	4.82876e11	−	7.02659e11i	0.270764	−	0.394003i
$283$		−	2.31274e12i		−	1.27408i	−0.770833	−	0.637038i	$-0.780160\pi$
$283$		−	2.31274e12i		−	1.27408i	0.770833	−	0.637038i	$-0.219840\pi$
$284$			2.92539e11i			0.158340i
$285$		0			0
$286$	2.40423e11			0.125645
$287$	−3.46630e12			−1.78015
$288$	1.25551e11	+	3.26982e11i	0.0633665	+	0.165029i
$289$	5.09295e12			2.52627
$290$		0			0
$291$	1.77060e12	+	1.21678e12i	0.848509	+	0.583106i
$292$		−	1.11917e12i		−	0.527207i
$293$	1.05989e12			0.490822			0.245411	−	0.969419i	$-0.421077\pi$
$293$	1.05989e12			0.490822			0.245411	+	0.969419i	$0.421077\pi$
$294$	−8.00326e11	+	1.16460e12i	−0.364360	+	0.530199i
$295$		0			0
$296$		−	5.81138e11i		−	0.255753i
$297$	−2.09042e11	+	8.71257e11i	−0.0904588	+	0.377020i
$298$			7.65890e11i			0.325900i
$299$			2.38781e11i			0.0999179i
$300$		0			0
$301$	4.61555e12			1.86806
$302$	−2.76928e12			−1.10238
$303$	−3.36308e12	−	2.31115e12i	−1.31681	−	0.904931i
$304$	−2.01019e11			−0.0774227
$305$		0			0
$306$	1.27698e12	+	3.32573e12i	0.475968	+	1.23959i
$307$			6.89209e11i			0.252731i	0.991984	+	0.126366i	$0.0403313\pi$
$307$			6.89209e11i			0.252731i	−0.991984	+	0.126366i	$0.959669\pi$
$308$	7.42567e11			0.267906
$309$	1.67598e12	+	1.15176e12i	0.594945	+	0.408854i
$310$		0			0
$311$		−	1.95674e12i		−	0.672559i	−0.941762	−	0.336280i	$-0.890831\pi$
$311$		−	1.95674e12i		−	0.672559i	0.941762	−	0.336280i	$-0.109169\pi$
$312$	3.94801e11	+	2.71312e11i	0.133538	+	0.0917690i
$313$			2.48821e11i			0.0828256i	0.999142	+	0.0414128i	$0.0131859\pi$
$313$			2.48821e11i			0.0828256i	−0.999142	+	0.0414128i	$0.986814\pi$
$314$			3.59711e12i			1.17843i
$315$		0			0
$316$	−1.00655e12			−0.319449
$317$	4.63675e12			1.44850			0.724249	−	0.689539i	$-0.242187\pi$
$317$	4.63675e12			1.44850			0.724249	+	0.689539i	$0.242187\pi$
$318$	1.31274e11	−	1.91024e11i	0.0403686	−	0.0587425i
$319$	3.01751e11			0.0913473
$320$		0			0
$321$	−1.97571e12	+	2.87497e12i	−0.579694	+	0.843544i
$322$			7.37496e11i			0.213049i
$323$	−2.04456e12			−0.581549
$324$	−1.32646e12	+	1.19480e12i	−0.371510	+	0.334634i
$325$		0			0
$326$		−	2.08360e12i		−	0.565883i
$327$	−6.50378e11	+	9.46400e11i	−0.173951	+	0.253125i
$328$			1.72897e12i			0.455426i
$329$		−	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	$0.556962\pi$
$332$	−1.11902e12			−0.277425
$333$	2.76518e12	−	1.06175e12i	0.675308	−	0.259298i
$334$	−4.80642e12			−1.15635
$335$		0			0
$336$	1.21938e12	+	8.37971e11i	0.284736	+	0.195674i
$337$			8.67755e11i			0.199640i	0.995006	+	0.0998201i	$0.0318267\pi$
$337$			8.67755e11i			0.199640i	−0.995006	+	0.0998201i	$0.968173\pi$
$338$	−2.46421e12			−0.558592
$339$	1.81886e12	−	2.64672e12i	0.406257	−	0.591167i
$340$		0			0
$341$		−	2.61196e12i		−	0.566493i
$342$	−3.67264e11	−	9.56490e11i	−0.0784961	−	0.204432i
$343$		−	5.91785e11i		−	0.124650i
$344$		−	2.30221e12i		−	0.477917i
$345$		0			0
$346$	−6.88173e12			−1.38777
$347$	−5.20712e12			−1.03502			−0.517512	−	0.855676i	$-0.673142\pi$
$347$	−5.20712e12			−1.03502			−0.517512	+	0.855676i	$0.673142\pi$
$348$	4.95509e11	+	3.40520e11i	0.0970857	+	0.0667185i
$349$	−1.11953e12			−0.216226			−0.108113	−	0.994139i	$-0.534481\pi$
$349$	−1.11953e12			−0.216226			−0.108113	+	0.994139i	$0.534481\pi$
$350$		0			0
$351$	−5.69653e11	+	2.37424e12i	−0.106924	+	0.445644i
$352$		−	3.70388e11i		−	0.0685398i
$353$	3.73952e12			0.682248			0.341124	−	0.940018i	$-0.389192\pi$
$353$	3.73952e12			0.682248			0.341124	+	0.940018i	$0.389192\pi$
$354$	−1.32334e12	−	9.09413e11i	−0.238042	−	0.163586i
$355$		0			0
$356$			1.22236e11i			0.0213771i
$357$	1.24023e13	+	8.52299e12i	2.13875	+	1.46977i
$358$			1.60002e11i			0.0272088i
$359$		−	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
$362$	2.88066e12			0.463393
$363$	−3.03308e12	+	4.41360e12i	−0.481228	+	0.700260i
$364$	2.02355e12			0.316670
$365$		0			0
$366$	−1.65276e12	+	2.40503e12i	−0.251655	+	0.366197i
$367$		−	1.01161e13i		−	1.51944i	−0.650248	−	0.759722i	$-0.725335\pi$
$367$		−	1.01161e13i		−	1.51944i	0.650248	−	0.759722i	$-0.274665\pi$
$368$	3.67858e11			0.0545056
$369$	−8.22679e12	+	3.15885e12i	−1.20254	+	0.461739i
$370$		0			0
$371$		−	9.79093e11i		−	0.139301i
$372$	2.94754e12	−	4.28913e12i	0.413757	−	0.602080i
$373$		−	3.81055e12i		−	0.527769i	−0.964554	−	0.263885i	$-0.914996\pi$
$373$		−	3.81055e12i		−	0.527769i	0.964554	−	0.263885i	$-0.0850038\pi$
$374$		−	3.76720e12i		−	0.514827i
$375$		0			0
$376$	−1.79639e12			−0.239035
$377$	8.22293e11			0.107974
$378$	−1.75943e12	+	7.33304e12i	−0.227988	+	0.950222i
$379$	−1.11052e13			−1.42014			−0.710069	−	0.704132i	$-0.751336\pi$
$379$	−1.11052e13			−1.42014			−0.710069	+	0.704132i	$0.751336\pi$
$380$		0			0
$381$	6.36482e12	+	4.37399e12i	0.792796	+	0.544819i
$382$			4.67165e12i			0.574319i
$383$	4.29169e12			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$383$	4.29169e12			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$384$	4.17974e11	−	6.08217e11i	0.0500603	−	0.0728455i
$385$		0			0
$386$			7.05084e12i			0.822820i
$387$	1.09544e13	−	4.20617e12i	1.26192	−	0.484542i
$388$		−	4.52665e12i		−	0.514776i
$389$		−	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
$392$	2.97736e12			0.321663
$393$	1.00354e13	+	6.89642e12i	1.07046	+	0.735633i
$394$	−3.43245e12			−0.361512
$395$		0			0
$396$	1.76238e12	−	6.76703e11i	0.180977	−	0.0694900i
$397$		−	1.11669e13i		−	1.13235i	−0.824286	−	0.566174i	$-0.808423\pi$
$397$		−	1.11669e13i		−	1.13235i	0.824286	−	0.566174i	$-0.191577\pi$
$398$	−2.52729e12			−0.253070
$399$	−3.56693e12	−	2.45124e12i	−0.352720	−	0.242394i
$400$		0			0
$401$		−	1.15685e13i		−	1.11572i	−0.829935	−	0.557861i	$-0.811622\pi$
$401$		−	1.15685e13i		−	1.11572i	0.829935	−	0.557861i	$-0.188378\pi$
$402$	2.36590e12	+	1.62588e12i	0.225355	+	0.154867i
$403$		−	7.11777e12i		−	0.669605i
$404$			8.59793e12i			0.798890i
$405$		0			0
$406$	2.53973e12			0.230227
$407$	−3.13224e12			−0.280468
$408$	4.25121e12	−	6.18616e12i	0.376021	−	0.547168i
$409$	1.07411e13			0.938498			0.469249	−	0.883066i	$-0.344525\pi$
$409$	1.07411e13			0.938498			0.469249	+	0.883066i	$0.344525\pi$
$410$		0			0
$411$	−3.78123e12	+	5.50227e12i	−0.322421	+	0.469172i
$412$		−	4.28475e12i		−	0.360944i
$413$	−6.78275e12			−0.564489
$414$	6.72082e11	+	1.75035e12i	0.0552612	+	0.143920i
$415$		0			0
$416$		−	1.00933e12i		−	0.0810153i
$417$	8.70477e12	−	1.26668e13i	0.690362	−	1.00458i
$418$			1.08346e12i			0.0849047i
$419$			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	$0.569104\pi$
$422$	−3.46348e12			−0.258792
$423$	−3.28203e12	−	8.54761e12i	−0.242349	−	0.631165i
$424$	−4.88365e11			−0.0356381
$425$		0			0
$426$	2.58918e12	+	1.77932e12i	0.184550	+	0.126825i
$427$			1.23269e13i			0.868392i
$428$	7.35003e12			0.511764
$429$	1.46233e12	−	2.12792e12i	0.100637	−	0.146443i
$430$		0			0
$431$		−	1.80323e13i		−	1.21245i	−0.795293	−	0.606226i	$-0.792683\pi$
$431$		−	1.80323e13i		−	1.21245i	0.795293	−	0.606226i	$-0.207317\pi$
$432$	3.65767e12	+	8.77590e11i	0.243101	+	0.0583274i
$433$		−	2.06339e13i		−	1.35563i	−0.735232	−	0.677816i	$-0.762927\pi$
$433$		−	2.06339e13i		−	1.35563i	0.735232	−	0.677816i	$-0.237073\pi$
$434$		−	2.19839e13i		−	1.42776i
$435$		0			0
$436$	2.41953e12			0.153567
$437$	−1.07606e12			−0.0675195
$438$	−9.90545e12	−	6.80715e12i	−0.614474	−	0.422275i
$439$	−1.95313e13			−1.19787			−0.598935	−	0.800798i	$-0.704409\pi$
$439$	−1.95313e13			−1.19787			−0.598935	+	0.800798i	$0.704409\pi$
$440$		0			0
$441$	5.43969e12	+	1.41669e13i	0.326123	+	0.849343i
$442$		−	1.02659e13i		−	0.608535i
$443$	2.97469e13			1.74351			0.871753	−	0.489946i	$-0.162984\pi$
$443$	2.97469e13			1.74351			0.871753	+	0.489946i	$0.162984\pi$
$444$	−5.14349e12	−	3.53467e12i	−0.298087	−	0.204849i
$445$		0			0
$446$		−	1.37068e13i		−	0.776713i
$447$	6.77868e12	+	4.65839e12i	0.379846	+	0.261035i
$448$		−	3.11741e12i		−	0.172744i
$449$		−	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
$452$	−6.76651e12			−0.358651
$453$	−1.68437e13	+	2.45102e13i	−0.882971	+	1.28486i
$454$	1.51737e13			0.786704
$455$		0			0
$456$	−1.22266e12	+	1.77916e12i	−0.0620129	+	0.0902383i
$457$			4.10224e11i			0.0205798i	0.999947	+	0.0102899i	$0.00327543\pi$
$457$			4.10224e11i			0.0205798i	−0.999947	+	0.0102899i	$0.996725\pi$
$458$	7.99554e12			0.396753
$459$	3.72021e13	+	8.92594e12i	1.82601	+	0.438118i
$460$		0			0
$461$			2.10914e11i			0.0101298i	0.999987	+	0.00506490i	$0.00161221\pi$
$461$			2.10914e11i			0.0101298i	−0.999987	+	0.00506490i	$0.998388\pi$
$462$	4.51654e12	−	6.57226e12i	0.214583	−	0.312252i
$463$			1.96738e13i			0.924660i	0.886708	+	0.462330i	$0.152987\pi$
$463$			1.96738e13i			0.924660i	−0.886708	+	0.462330i	$0.847013\pi$
$464$		−	1.26680e12i		−	0.0589003i
$465$		0			0
$466$	2.54309e13			1.15726
$467$	−1.21902e13			−0.548815			−0.274407	−	0.961614i	$-0.588482\pi$
$467$	−1.21902e13			−0.548815			−0.274407	+	0.961614i	$0.588482\pi$
$468$	4.80261e12	−	1.84406e12i	0.213919	−	0.0821385i
$469$	1.21264e13			0.534402
$470$		0			0
$471$	3.18370e13	+	2.18788e13i	1.37350	+	0.943885i
$472$			3.38319e12i			0.144416i
$473$	−1.24085e13			−0.524101
$474$	−6.12218e12	+	8.90872e12i	−0.255867	+	0.372326i
$475$		0			0
$476$		−	3.17071e13i		−	1.29754i
$477$	−8.92250e11	−	2.32374e12i	−0.0361322	−	0.0941014i
$478$		−	5.98729e12i		−	0.239933i
$479$			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
$482$	−2.00653e13			−0.771276
$483$	6.52737e12	+	4.48569e12i	0.248315	+	0.170645i
$484$	1.12836e13			0.424837
$485$		0			0
$486$	2.50686e12	+	1.90074e13i	0.0924590	+	0.701036i
$487$		−	4.17000e13i		−	1.52227i	−0.648595	−	0.761134i	$-0.724643\pi$
$487$		−	4.17000e13i		−	1.52227i	0.648595	−	0.761134i	$-0.275357\pi$
$488$	6.14859e12			0.222166
$489$	−1.84414e13	−	1.26732e13i	−0.659553	−	0.453253i
$490$		0			0
$491$			2.10340e12i			0.0737081i	0.999321	+	0.0368540i	$0.0117337\pi$
$491$			2.10340e12i			0.0737081i	−0.999321	+	0.0368540i	$0.988266\pi$
$492$	1.53026e13	+	1.05161e13i	0.530811	+	0.364780i
$493$		−	1.28846e13i		−	0.442421i
$494$			2.95250e12i			0.100359i
$495$		0			0
$496$	−1.09654e13			−0.365272
$497$	1.32708e13			0.437639
$498$	−6.80622e12	+	9.90410e12i	−0.222208	+	0.323347i
$499$	−2.74482e13			−0.887179			−0.443589	−	0.896230i	$-0.646295\pi$
$499$	−2.74482e13			−0.887179			−0.443589	+	0.896230i	$0.646295\pi$
$500$		0			0
$501$	−2.92342e13	+	4.25403e13i	−0.926197	+	1.34776i
$502$			1.94481e13i			0.610041i
$503$	−2.26985e13			−0.704949			−0.352474	−	0.935822i	$-0.614660\pi$
$503$	−2.26985e13			−0.704949			−0.352474	+	0.935822i	$0.614660\pi$
$504$	1.48333e13	−	5.69556e12i	0.456127	−	0.175139i
$505$		0			0
$506$		−	1.98270e12i		−	0.0597729i
$507$	−1.49882e13	+	2.18101e13i	−0.447413	+	0.651055i
$508$		−	1.62721e13i		−	0.480976i
$509$			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
$512$	−1.55494e12			−0.0441942
$513$	−1.06994e13	−	2.56713e12i	−0.301144	−	0.0722539i
$514$	4.93051e13			1.37428
$515$		0			0
$516$	−2.03762e13	−	1.40028e13i	−0.557025	−	0.382795i
$517$			9.68227e12i			0.262135i
$518$	−2.63629e13			−0.706878
$519$	−4.18569e13	+	6.09083e13i	−1.11155	+	1.61748i
$520$		0			0
$521$		−	6.54420e13i		−	1.70478i	−0.522907	−	0.852390i	$-0.675152\pi$
$521$		−	6.54420e13i		−	1.70478i	0.522907	−	0.852390i	$-0.324848\pi$
$522$	6.02770e12	−	2.31446e12i	0.155525	−	0.0597169i
$523$			6.14531e13i			1.57049i	0.619185	+	0.785245i	$0.287463\pi$
$523$			6.14531e13i			1.57049i	−0.619185	+	0.785245i	$0.712537\pi$
$524$		−	2.56560e13i		−	0.649430i
$525$		0			0
$526$	3.12126e13			0.775178
$527$	−1.11529e14			−2.74369
$528$	−3.27820e12	−	2.25282e12i	−0.0798851	−	0.0548980i
$529$	−3.94574e13			−0.952466
$530$		0			0
$531$	−1.60979e13	+	6.18114e12i	−0.381327	+	0.146418i
$532$			9.11907e12i			0.213990i
$533$	2.53946e13			0.590343
$534$	1.08188e12	+	7.43479e11i	0.0249156	+	0.0171223i
$535$		0			0
$536$		−	6.04857e12i		−	0.136719i
$537$	1.41613e12	+	9.73183e11i	0.0317126	+	0.0217933i
$538$			2.67296e13i			0.593036i
$539$		−	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	$0.448187\pi$
$542$	3.21877e13			0.688166
$543$	1.75211e13	−	2.54960e13i	0.371162	−	0.540098i
$544$	−1.58153e13			−0.331958
$545$		0			0
$546$	1.23079e13	−	1.79099e13i	0.253641	−	0.369087i
$547$			7.15097e13i			1.46025i	0.683312	+	0.730127i	$0.260539\pi$
$547$			7.15097e13i			1.46025i	−0.683312	+	0.730127i	$0.739461\pi$
$548$	1.40669e13			0.284639
$549$	1.12336e13	+	2.92563e13i	0.225245	+	0.586621i
$550$		0			0
$551$			3.70565e12i			0.0729636i
$552$	2.23743e12	−	3.25581e12i	0.0436571	−	0.0635278i
$553$			4.56616e13i			0.882928i
$554$		−	1.19916e13i		−	0.229789i
$555$		0			0
$556$	−3.23834e13			−0.609464
$557$	−7.34107e13			−1.36925			−0.684626	−	0.728895i	$-0.740034\pi$
$557$	−7.34107e13			−1.36925			−0.684626	+	0.728895i	$0.740034\pi$
$558$	−2.00340e13	−	5.21758e13i	−0.370336	−	0.964490i
$559$	−3.38141e13			−0.619497
$560$		0			0
$561$	−3.33425e13	−	2.29134e13i	−0.600045	−	0.412358i
$562$			5.16902e13i			0.921991i
$563$	−4.77347e13			−0.843902			−0.421951	−	0.906619i	$-0.638655\pi$
$563$	−4.77347e13			−0.843902			−0.421951	+	0.906619i	$0.638655\pi$
$564$	−1.09262e13	+	1.58994e13i	−0.191459	+	0.278602i
$565$		0			0
$566$			5.23314e13i			0.900907i
$567$	5.42013e13	+	6.01742e13i	0.924900	+	1.02682i
$568$		−	6.61939e12i		−	0.111963i
$569$			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	$0.555194\pi$
$572$	−5.44014e12			−0.0888444
$573$	4.13475e13	+	2.84145e13i	0.669385	+	0.460009i
$574$	7.84334e13			1.25876
$575$		0			0
$576$	−2.84091e12	−	7.39876e12i	−0.0448069	−	0.116693i
$577$			3.56688e13i			0.557711i	0.960333	+	0.278855i	$0.0899550\pi$
$577$			3.56688e13i			0.557711i	−0.960333	+	0.278855i	$0.910045\pi$
$578$	−1.15240e14			−1.78635
$579$	6.24051e13	+	4.28856e13i	0.959019	+	0.659050i
$580$		0			0
$581$			5.07634e13i			0.766778i
$582$	−4.00642e13	−	2.75326e13i	−0.599986	−	0.412318i
$583$			2.63221e12i			0.0390821i
$584$			2.53239e13i			0.372792i
$585$		0			0
$586$	−2.39826e13			−0.347064
$587$	1.29418e14			1.85697			0.928483	−	0.371375i	$-0.121114\pi$
$587$	1.29418e14			1.85697			0.928483	+	0.371375i	$0.121114\pi$
$588$	1.81093e13	−	2.63518e13i	0.257641	−	0.374908i
$589$	3.20761e13			0.452486
$590$		0			0
$591$	−2.08773e13	+	3.03797e13i	−0.289559	+	0.421352i
$592$			1.31496e13i			0.180845i
$593$	3.96596e13			0.540848			0.270424	−	0.962741i	$-0.412836\pi$
$593$	3.96596e13			0.540848			0.270424	+	0.962741i	$0.412836\pi$
$594$	4.73007e12	−	1.97143e13i	0.0639640	−	0.266593i
$595$		0			0
$596$		−	1.73301e13i		−	0.230446i
$597$	−1.53718e13	+	2.23684e13i	−0.202700	+	0.294960i
$598$		−	5.40299e12i		−	0.0706526i
$599$			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	$0.263650\pi$
$602$	−1.04438e14			−1.32092
$603$	2.87804e13	−	1.10508e13i	0.361003	−	0.138614i
$604$	6.26617e13			0.779503
$605$		0			0
$606$	7.60979e13	+	5.22954e13i	0.931128	+	0.639883i
$607$		−	9.55067e13i		−	1.15902i	−0.814966	−	0.579509i	$-0.803244\pi$
$607$		−	9.55067e13i		−	1.15902i	0.814966	−	0.579509i	$-0.196756\pi$
$608$	4.54853e12			0.0547461
$609$	1.54475e13	−	2.24784e13i	0.184404	−	0.268336i
$610$		0			0
$611$			2.63849e13i			0.309848i
$612$	−2.88948e13	−	7.52526e13i	−0.336560	−	0.876525i
$613$			5.18411e13i			0.598924i	0.954108	+	0.299462i	$0.0968072\pi$
$613$			5.18411e13i			0.598924i	−0.954108	+	0.299462i	$0.903193\pi$
$614$		−	1.55950e13i		−	0.178708i
$615$		0			0
$616$	−1.68024e13			−0.189438
$617$	−8.05443e13			−0.900760			−0.450380	−	0.892837i	$-0.648711\pi$
$617$	−8.05443e13			−0.900760			−0.450380	+	0.892837i	$0.648711\pi$
$618$	−3.79231e13	−	2.60612e13i	−0.420690	−	0.289103i
$619$	5.14946e13			0.566642			0.283321	−	0.959025i	$-0.408564\pi$
$619$	5.14946e13			0.566642			0.283321	+	0.959025i	$0.408564\pi$
$620$		0			0
$621$	1.95797e13	+	4.69777e12i	0.212005	+	0.0508667i
$622$			4.42759e13i			0.475571i
$623$	5.54515e12			0.0590844
$624$	−8.93332e12	−	6.13909e12i	−0.0944256	−	0.0648905i
$625$		0			0
$626$		−	5.63017e12i		−	0.0585665i
$627$	9.58941e12	+	6.58996e12i	0.0989587	+	0.0680057i
$628$		−	8.13933e13i		−	0.833279i
$629$			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	$0.516382\pi$
$632$	2.27757e13			0.225884
$633$	−2.10660e13	+	3.06543e13i	−0.207283	+	0.301629i
$634$	−1.04918e14			−1.02424
$635$		0			0
$636$	−2.97040e12	+	4.32238e12i	−0.0285449	+	0.0415372i
$637$		−	4.37307e13i		−	0.416955i
$638$	−6.82785e12			−0.0645923
$639$	3.14965e13	−	1.20937e13i	0.295636	−	0.113516i
$640$		0			0
$641$		−	4.62451e13i		−	0.427342i	−0.976906	−	0.213671i	$-0.931458\pi$
$641$		−	4.62451e13i		−	0.427342i	0.976906	−	0.213671i	$-0.0685420\pi$
$642$	4.47053e13	−	6.50531e13i	0.409906	−	0.596476i
$643$		−	2.73102e13i		−	0.248468i	−0.992253	−	0.124234i	$-0.960353\pi$
$643$		−	2.73102e13i		−	0.248468i	0.992253	−	0.124234i	$-0.0396474\pi$
$644$		−	1.66876e13i		−	0.150649i
$645$		0			0
$646$	4.62630e13			0.411217
$647$	−1.34984e13			−0.119059			−0.0595293	−	0.998227i	$-0.518960\pi$
$647$	−1.34984e13			−0.119059			−0.0595293	+	0.998227i	$0.518960\pi$
$648$	3.00145e13	−	2.70353e13i	0.262697	−	0.236622i
$649$	1.82349e13			0.158372
$650$		0			0
$651$	−1.94573e14	−	1.33713e14i	−1.66410	−	1.14359i
$652$			4.71466e13i			0.400140i
$653$	8.41840e13			0.709029			0.354514	−	0.935051i	$-0.384646\pi$
$653$	8.41840e13			0.709029			0.354514	+	0.935051i	$0.384646\pi$
$654$	1.47164e13	−	2.14146e13i	0.123002	−	0.178987i
$655$		0			0
$656$		−	3.91220e13i		−	0.322034i
$657$	−1.20496e14	+	4.62671e13i	−0.984345	+	0.377960i
$658$			8.14920e13i			0.660672i
$659$		−	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	$0.205284\pi$
$662$	3.20050e13			0.251726
$663$	−9.08606e13	−	6.24405e13i	−0.709264	−	0.487415i
$664$	2.53204e13			0.196169
$665$		0			0
$666$	−6.25688e13	+	2.40246e13i	−0.477515	+	0.183352i
$667$		−	6.78122e12i		−	0.0513664i
$668$	1.08757e14			0.817663
$669$	−1.21315e14	−	8.33691e13i	−0.905281	−	0.622120i
$670$		0			0
$671$		−	3.31400e13i		−	0.243635i
$672$	−2.75914e13	−	1.89611e13i	−0.201338	−	0.138362i
$673$		−	6.04368e12i		−	0.0437750i	−0.999760	−	0.0218875i	$-0.993032\pi$
$673$		−	6.04368e12i		−	0.0437750i	0.999760	−	0.0218875i	$-0.00696757\pi$
$674$		−	1.96351e13i		−	0.141167i
$675$		0			0
$676$	5.57588e13			0.394984
$677$	1.21474e14			0.854164			0.427082	−	0.904213i	$-0.359542\pi$
$677$	1.21474e14			0.854164			0.427082	+	0.904213i	$0.359542\pi$
$678$	−4.11561e13	+	5.98885e13i	−0.287267	+	0.418018i
$679$	−2.05349e14			−1.42280
$680$		0			0
$681$	9.22913e13	−	1.34298e14i	0.630123	−	0.916926i
$682$			5.91019e13i			0.400571i
$683$	1.51629e14			1.02019			0.510094	−	0.860119i	$-0.329611\pi$
$683$	1.51629e14			1.02019			0.510094	+	0.860119i	$0.329611\pi$
$684$	8.31024e12	+	2.16429e13i	0.0555051	+	0.144556i
$685$		0			0
$686$			1.33906e13i			0.0881410i
$687$	4.86315e13	−	7.07663e13i	0.317785	−	0.462427i
$688$			5.20930e13i			0.337938i
$689$			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	$0.432593\pi$
$692$	1.55716e14			0.981300
$693$	−3.06982e13	−	7.99493e13i	−0.192064	−	0.500205i
$694$	1.17824e14			0.731873
$695$		0			0
$696$	−1.12121e13	−	7.70509e12i	−0.0686500	−	0.0471771i
$697$		−	3.97909e14i		−	2.41891i
$698$	2.53321e13			0.152895
$699$	1.54679e14	−	2.25082e14i	0.926928	−	1.34882i
$700$		0			0
$701$		−	5.78990e13i		−	0.342043i	−0.985267	−	0.171022i	$-0.945293\pi$
$701$		−	5.78990e13i		−	0.342043i	0.985267	−	0.171022i	$-0.0547068\pi$
$702$	1.28898e13	−	5.37228e13i	0.0756066	−	0.315118i
$703$		−	3.84654e13i		−	0.224024i
$704$			8.38091e12i			0.0484650i
$705$		0			0
$706$	−8.46157e13			−0.482422
$707$	3.90039e14			2.20806
$708$	2.99437e13	+	2.05777e13i	0.168321	+	0.115672i
$709$	−2.70077e14			−1.50750			−0.753750	−	0.657162i	$-0.771757\pi$
$709$	−2.70077e14			−1.50750			−0.753750	+	0.657162i	$0.771757\pi$
$710$		0			0
$711$	4.16115e13	+	1.08372e14i	0.229016	+	0.596441i
$712$		−	2.76588e12i		−	0.0151159i
$713$	−5.86983e13			−0.318550
$714$	−2.80631e14	−	1.92853e14i	−1.51232	−	1.03929i
$715$		0			0
$716$		−	3.62043e12i		−	0.0192395i
$717$	−5.29918e13	−	3.64166e13i	−0.279649	−	0.192178i
$718$			8.02117e13i			0.420354i
$719$		−	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
$722$	1.25425e14			0.639289
$723$	−1.22044e14	+	1.77592e14i	−0.617765	+	0.898944i
$724$	−6.51820e13			−0.327669
$725$		0			0
$726$	6.86307e13	−	9.98683e13i	0.340279	−	0.495159i
$727$			5.21602e13i			0.256842i	0.991720	+	0.128421i	$0.0409910\pi$
$727$			5.21602e13i			0.256842i	−0.991720	+	0.128421i	$0.959009\pi$
$728$	−4.57876e13			−0.223919
$729$	1.83476e14	+	9.34214e13i	0.891133	+	0.453742i
$730$		0			0
$731$			5.29837e14i			2.53837i
$732$	3.73978e13	−	5.44195e13i	0.177947	−	0.258940i
$733$		−	3.21782e14i		−	1.52069i	−0.649518	−	0.760346i	$-0.725029\pi$
$733$		−	3.21782e14i		−	1.52069i	0.649518	−	0.760346i	$-0.274971\pi$
$734$			2.28902e14i			1.07441i
$735$		0			0
$736$	−8.32367e12			−0.0385413
$737$	−3.26009e13			−0.149931
$738$	1.86151e14	−	7.14765e13i	0.850322	−	0.326499i
$739$	−1.66542e14			−0.755617			−0.377809	−	0.925884i	$-0.623322\pi$
$739$	−1.66542e14			−0.755617			−0.377809	+	0.925884i	$0.623322\pi$
$740$		0			0
$741$	2.61318e13	+	1.79581e13i	0.116971	+	0.0803839i
$742$			2.21543e13i			0.0985007i
$743$	−1.13631e14			−0.501825			−0.250912	−	0.968010i	$-0.580731\pi$
$743$	−1.13631e14			−0.501825			−0.250912	+	0.968010i	$0.580731\pi$
$744$	−6.66953e13	+	9.70519e13i	−0.292570	+	0.425735i
$745$		0			0
$746$			8.62230e13i			0.373189i
$747$	4.62608e13	+	1.20480e14i	0.198889	+	0.517979i
$748$			8.52421e13i			0.364037i
$749$		−	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	$0.612207\pi$
$752$	4.06477e13			0.169023
$753$	1.72130e14	+	1.18290e14i	0.711020	+	0.488622i
$754$	−1.86064e13			−0.0763493
$755$		0			0
$756$	3.98112e13	−	1.65928e14i	0.161212	−	0.671909i
$757$		−	2.67990e14i		−	1.07805i	−0.842289	−	0.539026i	$-0.818793\pi$
$757$		−	2.67990e14i		−	1.07805i	0.842289	−	0.539026i	$-0.181207\pi$
$758$	2.51282e14			1.00419
$759$	−1.75483e13	−	1.20594e13i	−0.0696669	−	0.0478760i
$760$		0			0
$761$			1.29795e14i			0.508550i	0.967132	+	0.254275i	$0.0818368\pi$
$761$			1.29795e14i			0.508550i	−0.967132	+	0.254275i	$0.918163\pi$
$762$	−1.44020e14	−	9.89720e13i	−0.560591	−	0.385245i
$763$		−	1.09760e14i		−	0.424446i
$764$		−	1.05707e14i		−	0.406105i
$765$		0			0
$766$	−9.71099e13			−0.368230
$767$	4.96913e13			0.187199
$768$	−9.45768e12	+	1.37624e13i	−0.0353980	+	0.0515095i
$769$	2.19185e14			0.815041			0.407521	−	0.913196i	$-0.366393\pi$
$769$	2.19185e14			0.815041			0.407521	+	0.913196i	$0.366393\pi$
$770$		0			0
$771$	2.99890e14	−	4.36386e14i	1.10075	−	1.60176i
$772$		−	1.59542e14i		−	0.581821i
$773$	−4.05042e14			−1.46758			−0.733792	−	0.679374i	$-0.762251\pi$
$773$	−4.05042e14			−1.46758			−0.733792	+	0.679374i	$0.762251\pi$
$774$	−2.47870e14	+	9.51747e13i	−0.892315	+	0.342623i
$775$		0			0
$776$			1.02426e14i			0.364002i
$777$	−1.60348e14	+	2.33331e14i	−0.566185	+	0.823886i
$778$			3.40665e14i			1.19517i
$779$			1.14440e14i			0.398925i
$780$		0			0
$781$	−3.56775e13			−0.122783
$782$	−8.46599e13			−0.289497
$783$	1.61778e13	−	6.74268e13i	0.0549681	−	0.229099i
$784$	−6.73701e13			−0.227450
$785$		0			0
$786$	−2.27074e14	−	1.56048e14i	−0.756929	−	0.520171i
$787$			4.98729e14i			1.65193i	0.563724	+	0.825963i	$0.309368\pi$
$787$			4.98729e14i			1.65193i	−0.563724	+	0.825963i	$0.690632\pi$
$788$	7.76674e13			0.255628
$789$	1.89845e14	−	2.76254e14i	0.620890	−	0.903491i
$790$		0			0
$791$			3.06958e14i			0.991280i
$792$	−3.98782e13	+	1.53121e13i	−0.127970	+	0.0491369i
$793$		−	9.03088e13i		−	0.287981i
$794$			2.52678e14i			0.800690i
$795$		0			0
$796$	5.71861e13			0.178947
$797$	1.48672e14			0.462314			0.231157	−	0.972917i	$-0.425749\pi$
$797$	1.48672e14			0.462314			0.231157	+	0.972917i	$0.425749\pi$
$798$	8.07104e13	+	5.54652e13i	0.249411	+	0.171398i
$799$	4.13427e14			1.26959
$800$		0			0
$801$	1.31607e13	−	5.05331e12i	0.0399131	−	0.0153255i
$802$			2.61766e14i			0.788934i
$803$	1.36492e14			0.408817
$804$	−5.35343e13	−	3.67894e13i	−0.159350	−	0.109507i
$805$		0			0
$806$			1.61057e14i			0.473482i
$807$	2.36576e14	+	1.62578e14i	0.691200	+	0.475001i
$808$		−	1.94549e14i		−	0.564901i
$809$			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	$0.679718\pi$
$812$	−5.74675e13			−0.162795
$813$	1.95776e14	−	2.84884e14i	0.551197	−	0.802076i
$814$	7.08746e13			0.198321
$815$		0			0
$816$	−9.61939e13	+	1.39977e14i	−0.265887	+	0.386906i
$817$		−	1.52383e14i		−	0.418625i
$818$	−2.43044e14			−0.663618
$819$	−8.36547e13	−	2.17867e14i	−0.227023	−	0.591252i
$820$		0			0
$821$		−	4.64480e12i		−	0.0124524i	−0.999981	−	0.00622618i	$-0.998018\pi$
$821$		−	4.64480e12i		−	0.0124524i	0.999981	−	0.00622618i	$-0.00198187\pi$
$822$	8.55594e13	−	1.24502e14i	0.227986	−	0.331755i
$823$		−	6.38146e14i		−	1.69013i	−0.534661	−	0.845067i	$-0.679561\pi$
$823$		−	6.38146e14i		−	1.69013i	0.534661	−	0.845067i	$-0.320439\pi$
$824$			9.69528e13i			0.255226i
$825$		0			0
$826$	1.53476e14			0.399154
$827$	5.33624e14			1.37946			0.689728	−	0.724068i	$-0.257730\pi$
$827$	5.33624e14			1.37946			0.689728	+	0.724068i	$0.257730\pi$
$828$	−1.52075e13	−	3.96058e13i	−0.0390756	−	0.101767i
$829$	8.63626e13			0.220573			0.110287	−	0.993900i	$-0.464823\pi$
$829$	8.63626e13			0.220573			0.110287	+	0.993900i	$0.464823\pi$
$830$		0			0
$831$	−1.06135e14	−	7.29370e13i	−0.267825	−	0.184053i
$832$			2.28386e13i			0.0572865i
$833$	−6.85220e14			−1.70846
$834$	−1.96966e14	+	2.86616e14i	−0.488160	+	0.710347i
$835$		0			0
$836$		−	2.45159e13i		−	0.0600367i
$837$	−5.83647e14	−	1.40035e14i	−1.42077	−	0.340886i
$838$		−	1.99510e14i		−	0.482774i
$839$			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
$842$	1.28918e14			0.304616
$843$	4.57496e14	+	3.14397e14i	1.07461	+	0.738483i
$844$	7.83697e13			0.182994
$845$		0			0
$846$	7.42639e13	+	1.93410e14i	0.171367	+	0.446301i
$847$		−	5.11874e14i		−	1.17421i
$848$	1.10504e13			0.0252000
$849$	4.63171e14	+	3.18297e14i	1.05003	+	0.721595i
$850$		0			0
$851$			7.03905e13i			0.157713i
$852$	−5.85864e13	−	4.02613e13i	−0.130497	−	0.0896789i
$853$			8.99493e10i			0.000199183i	1.00000		9.95916e-5i	$3.17010e-5\pi$
$853$			8.99493e10i			0.000199183i	−1.00000		9.95916e-5i	$0.999968\pi$
$854$		−	2.78927e14i		−	0.614046i
$855$		0			0
$856$	−1.66312e14			−0.361872
$857$	1.45265e14			0.314238			0.157119	−	0.987580i	$-0.449779\pi$
$857$	1.45265e14			0.314238			0.157119	+	0.987580i	$0.449779\pi$
$858$	−3.30887e13	+	4.81492e13i	−0.0711613	+	0.103551i
$859$	3.53555e14			0.755947			0.377974	−	0.925816i	$-0.376621\pi$
$859$	3.53555e14			0.755947			0.377974	+	0.925816i	$0.376621\pi$
$860$		0			0
$861$	4.77058e14	−	6.94192e14i	1.00822	−	1.46711i
$862$			4.08024e14i			0.857333i
$863$	5.16372e14			1.07872			0.539360	−	0.842075i	$-0.318666\pi$
$863$	5.16372e14			1.07872			0.539360	+	0.842075i	$0.318666\pi$
$864$	−8.27637e13	−	1.98576e13i	−0.171898	−	0.0412437i
$865$		0			0
$866$			4.66892e14i			0.958576i
$867$	−7.00930e14	+	1.01996e15i	−1.43080	+	2.08204i
$868$			4.97439e14i			1.00958i
$869$		−	1.22757e14i		−	0.247713i
$870$		0			0
$871$	−8.88397e13			−0.177221
$872$	−5.47477e13			−0.108588
$873$	−4.87367e14	+	1.87135e14i	−0.961136	+	0.369048i
$874$	2.43485e13			0.0477435
$875$		0			0
$876$	2.24135e14	+	1.54028e14i	0.434499	+	0.298593i
$877$			3.23487e13i			0.0623532i	0.999514	+	0.0311766i	$0.00992543\pi$
$877$			3.23487e13i			0.0623532i	−0.999514	+	0.0311766i	$0.990075\pi$
$878$	4.41944e14			0.847022
$879$	−1.45870e14	+	2.12264e14i	−0.277986	+	0.404512i
$880$		0			0
$881$		−	3.45484e14i		−	0.650950i	−0.945551	−	0.325475i	$-0.894476\pi$
$881$		−	3.45484e14i		−	0.650950i	0.945551	−	0.325475i	$-0.105524\pi$
$882$	−1.23086e14	−	3.20561e14i	−0.230604	−	0.600576i
$883$			1.94069e14i			0.361537i	0.983526	+	0.180769i	$0.0578585\pi$
$883$			1.94069e14i			0.361537i	−0.983526	+	0.180769i	$0.942141\pi$
$884$			2.32291e14i			0.430299i
$885$		0			0
$886$	−6.73096e14			−1.23284
$887$	−2.06383e14			−0.375885			−0.187943	−	0.982180i	$-0.560182\pi$
$887$	−2.06383e14			−0.375885			−0.187943	+	0.982180i	$0.560182\pi$
$888$	1.16384e14	+	7.99804e13i	0.210779	+	0.144850i
$889$	−7.38171e14			−1.32938
$890$		0			0
$891$	−1.45716e14	−	1.61773e14i	−0.259489	−	0.288084i
$892$			3.10149e14i			0.549219i
$893$	−1.18903e14			−0.209380
$894$	−1.53384e14	−	1.05407e14i	−0.268592	−	0.184579i
$895$		0			0
$896$			7.05390e13i			0.122149i
$897$	−4.78204e13	−	3.28628e13i	−0.0823476	−	0.0565903i
$898$			3.11139e14i			0.532811i
$899$			2.02140e14i			0.344234i
$900$		0			0
$901$	1.12394e14			0.189286
$902$	−2.10862e14			−0.353155
$903$	−6.35227e14	+	9.24353e14i	−1.05801	+	1.53957i
$904$	1.53109e14			0.253605
$905$		0			0
$906$	3.81129e14	−	5.54602e14i	0.624354	−	0.908532i
$907$		−	3.53646e14i		−	0.576145i	−0.957609	−	0.288073i	$-0.906986\pi$
$907$		−	3.53646e14i		−	0.576145i	0.957609	−	0.288073i	$-0.0930144\pi$
$908$	−3.43341e14			−0.556284
$909$	9.25705e14	−	3.55444e14i	1.49160	−	0.572732i
$910$		0			0
$911$		−	4.57044e14i		−	0.728394i	−0.931322	−	0.364197i	$-0.881344\pi$
$911$		−	4.57044e14i		−	0.728394i	0.931322	−	0.364197i	$-0.118656\pi$
$912$	2.76657e13	−	4.02578e13i	0.0438497	−	0.0638081i
$913$		−	1.36473e14i		−	0.215126i
$914$		−	9.28232e12i		−	0.0145521i
$915$		0			0
$916$	−1.80918e14			−0.280547
$917$	−1.16387e15			−1.79497
$918$	−8.41788e14	−	2.01971e14i	−1.29119	−	0.309796i
$919$	−4.85254e14			−0.740273			−0.370136	−	0.928977i	$-0.620689\pi$
$919$	−4.85254e14			−0.740273			−0.370136	+	0.928977i	$0.620689\pi$
$920$		0			0
$921$	−1.38027e14	−	9.48541e13i	−0.208289	−	0.143139i
$922$		−	4.77244e12i		−	0.00716285i
$923$	−9.72237e13			−0.145132
$924$	−1.02198e14	+	1.48713e14i	−0.151733	+	0.220795i
$925$		0			0
$926$		−	4.45166e14i		−	0.653834i
$927$	−4.61322e14	+	1.77134e14i	−0.673916	+	0.258764i
$928$			2.86644e13i			0.0416488i
$929$			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
$932$	−5.75436e14			−0.818309
$933$	3.91874e14	+	2.69301e14i	0.554292	+	0.380916i
$934$	2.75832e14			0.388071
$935$		0			0
$936$	−1.08671e14	+	4.17264e13i	−0.151263	+	0.0580807i
$937$		−	6.90133e14i		−	0.955510i	−0.878493	−	0.477755i	$-0.841451\pi$
$937$		−	6.90133e14i		−	0.955510i	0.878493	−	0.477755i	$-0.158549\pi$
$938$	−2.74389e14			−0.377879
$939$	−4.98311e13	−	3.42445e13i	−0.0682609	−	0.0469098i
$940$		0			0
$941$		−	1.26481e14i		−	0.171426i	−0.996320	−	0.0857129i	$-0.972683\pi$
$941$		−	1.26481e14i		−	0.171426i	0.996320	−	0.0857129i	$-0.0273168\pi$
$942$	−7.20390e14	−	4.95061e14i	−0.971210	−	0.667428i
$943$		−	2.09422e14i		−	0.280843i
$944$		−	7.65528e13i		−	0.102118i
$945$		0			0
$946$	2.80773e14			0.370596
$947$	−3.05743e14			−0.401427			−0.200713	−	0.979650i	$-0.564326\pi$
$947$	−3.05743e14			−0.401427			−0.200713	+	0.979650i	$0.564326\pi$
$948$	1.38529e14	−	2.01581e14i	0.180925	−	0.263274i
$949$	3.71950e14			0.483230
$950$		0			0
$951$	−6.38144e14	+	9.28598e14i	−0.820382	+	1.19378i
$952$			7.17450e14i			0.917502i
$953$	7.71039e14			0.980870			0.490435	−	0.871478i	$-0.336838\pi$
$953$	7.71039e14			0.980870			0.490435	+	0.871478i	$0.336838\pi$
$954$	2.01893e13	+	5.25803e13i	0.0255493	+	0.0665398i
$955$		0			0
$956$			1.35477e14i			0.169658i
$957$	−4.15292e13	+	6.04315e13i	−0.0517362	+	0.0752841i
$958$		−	1.13338e14i		−	0.140458i
$959$		−	6.38134e14i		−	0.786718i
$960$		0			0
$961$	9.30098e14			1.13478
$962$	1.93138e14			0.234419
$963$	−3.03855e14	−	7.91348e14i	−0.366889	−	0.955512i
$964$	4.54025e14			0.545375
$965$		0			0
$966$	−1.47698e14	−	1.01500e14i	−0.175585	−	0.120664i
$967$			1.27364e15i			1.50631i	0.657845	+	0.753154i	$0.271468\pi$
$967$			1.27364e15i			1.50631i	−0.657845	+	0.753154i	$0.728532\pi$
$968$	−2.55319e14			−0.300405
$969$	2.81387e14	−	4.09461e14i	0.329371	−	0.479285i
$970$		0			0
$971$			4.71364e14i			0.546085i	0.962002	+	0.273043i	$0.0880300\pi$
$971$			4.71364e14i			0.546085i	−0.962002	+	0.273043i	$0.911970\pi$
$972$	−5.67238e13	−	4.30087e14i	−0.0653784	−	0.495707i
$973$			1.46905e15i			1.68451i
$974$			9.43563e14i			1.07641i
$975$		0			0
$976$	−1.39127e14			−0.157095
$977$	1.09733e15			1.23272			0.616360	−	0.787465i	$-0.288607\pi$
$977$	1.09733e15			1.23272			0.616360	+	0.787465i	$0.288607\pi$
$978$	4.17281e14	+	2.86761e14i	0.466374	+	0.320498i
$979$	−1.49077e13			−0.0165767
$980$		0			0
$981$	−1.00025e14	−	2.60501e14i	−0.110094	−	0.286724i
$982$		−	4.75946e13i		−	0.0521195i
$983$	−1.52240e15			−1.65867			−0.829336	−	0.558751i	$-0.811281\pi$
$983$	−1.52240e15			−1.65867			−0.829336	+	0.558751i	$0.811281\pi$
$984$	−3.46258e14	−	2.37953e14i	−0.375340	−	0.257938i
$985$		0			0
$986$			2.91545e14i			0.312839i
$987$	7.21264e14	+	4.95661e14i	0.770031	+	0.529175i
$988$		−	6.68075e13i		−	0.0709644i
$989$			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	$0.436392\pi$
$992$	2.48119e14			0.258286
$993$	1.94665e14	−	2.83267e14i	0.201623	−	0.293393i
$994$	−3.00284e14			−0.309457
$995$		0			0
$996$	1.54007e14	−	2.24104e14i	0.157125	−	0.228641i
$997$			3.25337e13i			0.0330262i	0.999864	+	0.0165131i	$0.00525652\pi$
$997$			3.25337e13i			0.0330262i	−0.999864	+	0.0165131i	$0.994743\pi$
$998$	6.21082e14			0.627330
$999$	−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.b.a.149.2		8
3.2	odd	2	inner	150.11.b.a.149.8		8
5.2	odd	4		150.11.d.a.101.2		4
5.3	odd	4		6.11.b.a.5.3	yes	4
5.4	even	2	inner	150.11.b.a.149.7		8
15.2	even	4		150.11.d.a.101.4		4
15.8	even	4		6.11.b.a.5.1	✓	4
15.14	odd	2	inner	150.11.b.a.149.1		8
20.3	even	4		48.11.e.d.17.4		4
40.3	even	4		192.11.e.h.65.1		4
40.13	odd	4		192.11.e.g.65.4		4
45.13	odd	12		162.11.d.d.107.1		8
45.23	even	12		162.11.d.d.107.4		8
45.38	even	12		162.11.d.d.53.1		8
45.43	odd	12		162.11.d.d.53.4		8
60.23	odd	4		48.11.e.d.17.3		4
120.53	even	4		192.11.e.g.65.3		4
120.83	odd	4		192.11.e.h.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.11.b.a.5.1	✓	4	15.8	even	4
6.11.b.a.5.3	yes	4	5.3	odd	4
48.11.e.d.17.3		4	60.23	odd	4
48.11.e.d.17.4		4	20.3	even	4
150.11.b.a.149.1		8	15.14	odd	2	inner
150.11.b.a.149.2		8	1.1	even	1	trivial
150.11.b.a.149.7		8	5.4	even	2	inner
150.11.b.a.149.8		8	3.2	odd	2	inner
150.11.d.a.101.2		4	5.2	odd	4
150.11.d.a.101.4		4	15.2	even	4
162.11.d.d.53.1		8	45.38	even	12
162.11.d.d.53.4		8	45.43	odd	12
162.11.d.d.107.1		8	45.13	odd	12
162.11.d.d.107.4		8	45.23	even	12
192.11.e.g.65.3		4	120.53	even	4
192.11.e.g.65.4		4	40.13	odd	4
192.11.e.h.65.1		4	40.3	even	4
192.11.e.h.65.2		4	120.83	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +O(q^{10})\)	\(q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +62442.7i q^{11} +(-70465.2 + 102538. i) q^{12} +170161. i q^{13} +525556. i q^{14} +262144. q^{16} +2.66626e6 q^{17} +(478941. + 1.24734e6i) q^{18} -766825. q^{19} +(4.65156e6 + 3.19661e6i) q^{21} -1.41292e6i q^{22} +1.40327e6 q^{23} +(1.59445e6 - 2.32016e6i) q^{24} -3.85029e6i q^{26} +(1.39529e7 + 3.34774e6i) q^{27} -1.18920e7i q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} -5.93164e6 q^{32} +(-1.25053e7 - 8.59382e6i) q^{33} -6.03306e7 q^{34} +(-1.08372e7 - 2.82240e7i) q^{36} +5.01619e7i q^{37} +1.73513e7 q^{38} +(-3.40779e7 - 2.34188e7i) q^{39} -1.49239e8i q^{41} +(-1.05253e8 - 7.23310e7i) q^{42} +1.98719e8i q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +1.55059e8 q^{47} +(-3.60782e7 + 5.24993e7i) q^{48} -2.56996e8 q^{49} +(-3.66951e8 + 5.33970e8i) q^{51} +8.71222e7i q^{52} +4.21541e7 q^{53} +(-3.15718e8 - 7.57507e7i) q^{54} +2.69085e8i q^{56} +(1.05536e8 - 1.53571e8i) q^{57} +1.09346e8i q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} +9.46499e8 q^{62} +(-1.28036e9 + 4.91622e8i) q^{63} +1.34218e8 q^{64} +(2.82963e8 + 1.94456e8i) q^{66} +5.22093e8i q^{67} +1.36513e9 q^{68} +(-1.93128e8 + 2.81031e8i) q^{69} +5.71364e8i q^{71} +(2.45218e8 + 6.38636e8i) q^{72} -2.18588e9i q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} +1.45033e9 q^{77} +(7.71095e8 + 5.29906e8i) q^{78} -1.96592e9 q^{79} +(-2.59075e9 + 2.33360e9i) q^{81} +3.37689e9i q^{82} -2.18558e9 q^{83} +(2.38160e9 + 1.63666e9i) q^{84} -4.49650e9i q^{86} +(9.67791e8 + 6.65078e8i) q^{87} -7.23413e8i q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +7.18473e8 q^{92} +(5.75692e9 - 8.37720e9i) q^{93} -3.50858e9 q^{94} +(8.16356e8 - 1.18792e9i) q^{96} -8.84112e9i q^{97} +5.81517e9 q^{98} +(3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9}+O(q^{10}) \) 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9	\( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99}+O(q^{100}) \) 8 * q + 4096 * q^4 + 10752 * q^6 - 318024 * q^9 + 2097152 * q^16 + 3137456 * q^19 + 19256016 * q^21 + 5505024 * q^24 - 43571696 * q^31 - 302174208 * q^34 - 162828288 * q^36 - 434574480 * q^39 + 377628672 * q^46 + 100116840 * q^49 - 1417153536 * q^51 - 963325440 * q^54 - 2368077488 * q^61 + 1073741824 * q^64 + 6246890496 * q^66 - 1192536576 * q^69 + 1606377472 * q^76 - 398565136 * q^79 + 2917929096 * q^81 + 9859080192 * q^84 + 16634464160 * q^91 - 17010954240 * q^94 + 2818572288 * q^96 + 5253825024 * q^99

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