LMFDB - Embedded newform 150.9.b.a.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,9,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, 9, names="a")

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

chi := DirichletCharacter("150.149");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
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:	$61.1067915092$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 6)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			149.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	150.149
Dual form			150.9.b.a.149.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.3137 q^{2} +(50.9117 - 63.0000i) q^{3} +128.000 q^{4} +(-576.000 + 712.764i) q^{6} -2786.00i q^{7} -1448.15 q^{8} +(-1377.00 - 6414.87i) q^{9} +O(q^{10})$	\(q-11.3137 q^{2} +(50.9117 - 63.0000i) q^{3} +128.000 q^{4} +(-576.000 + 712.764i) q^{6} -2786.00i q^{7} -1448.15 q^{8} +(-1377.00 - 6414.87i) q^{9} -22435.1i q^{11} +(6516.70 - 8064.00i) q^{12} -13150.0i q^{13} +31520.0i q^{14} +16384.0 q^{16} +66388.8 q^{17} +(15579.0 + 72576.0i) q^{18} -144002. q^{19} +(-175518. - 141840. i) q^{21} +253824. i q^{22} +49350.4 q^{23} +(-73728.0 + 91233.7i) q^{24} +148775. i q^{26} +(-474242. - 239841. i) q^{27} -356608. i q^{28} -627402. i q^{29} +728738. q^{31} -185364. q^{32} +(-1.41341e6 - 1.14221e6i) q^{33} -751104. q^{34} +(-176256. - 821104. i) q^{36} +1.96445e6i q^{37} +1.62920e6 q^{38} +(-828450. - 669489. i) q^{39} -986125. i q^{41} +(1.98576e6 + 1.60474e6i) q^{42} -78142.0i q^{43} -2.87169e6i q^{44} -558336. q^{46} +3.51969e6 q^{47} +(834137. - 1.03219e6i) q^{48} -1.99700e6 q^{49} +(3.37997e6 - 4.18250e6i) q^{51} -1.68320e6i q^{52} +522048. q^{53} +(5.36544e6 + 2.71349e6i) q^{54} +4.03456e6i q^{56} +(-7.33138e6 + 9.07213e6i) q^{57} +7.09824e6i q^{58} -5.00425e6i q^{59} +1.75783e7 q^{61} -8.24473e6 q^{62} +(-1.78718e7 + 3.83632e6i) q^{63} +2.09715e6 q^{64} +(1.59909e7 + 1.29226e7i) q^{66} +1.71368e7i q^{67} +8.49777e6 q^{68} +(2.51251e6 - 3.10907e6i) q^{69} -2.58906e7i q^{71} +(1.99411e6 + 9.28973e6i) q^{72} +2.81393e7i q^{73} -2.22252e7i q^{74} -1.84323e7 q^{76} -6.25041e7 q^{77} +(9.37284e6 + 7.57440e6i) q^{78} -9.18250e6 q^{79} +(-3.92545e7 + 1.76666e7i) q^{81} +1.11567e7i q^{82} -8.71084e7 q^{83} +(-2.24663e7 - 1.81555e7i) q^{84} +884076. i q^{86} +(-3.95263e7 - 3.19421e7i) q^{87} +3.24895e7i q^{88} -8.12528e7i q^{89} -3.66359e7 q^{91} +6.31685e6 q^{92} +(3.71013e7 - 4.59105e7i) q^{93} -3.98208e7 q^{94} +(-9.43718e6 + 1.16779e7i) q^{96} +1.28723e8i q^{97} +2.25934e7 q^{98} +(-1.43918e8 + 3.08931e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 512 q^{4} - 2304 q^{6} - 5508 q^{9}+O(q^{10}) $ 4 * q + 512 * q^4 - 2304 * q^6 - 5508 * q^9	$ 4 q + 512 q^{4} - 2304 q^{6} - 5508 q^{9} + 65536 q^{16} - 576008 q^{19} - 702072 q^{21} - 294912 q^{24} + 2914952 q^{31} - 3004416 q^{34} - 705024 q^{36} - 3313800 q^{39} - 2233344 q^{46} - 7987980 q^{49} + 13519872 q^{51} + 21461760 q^{54} + 70313096 q^{61} + 8388608 q^{64} + 63963648 q^{66} + 10050048 q^{69} - 73729024 q^{76} - 36729992 q^{79} - 157017852 q^{81} - 89865216 q^{84} - 146543600 q^{91} - 159283200 q^{94} - 37748736 q^{96} - 575672832 q^{99}+O(q^{100}) $ 4 * q + 512 * q^4 - 2304 * q^6 - 5508 * q^9 + 65536 * q^16 - 576008 * q^19 - 702072 * q^21 - 294912 * q^24 + 2914952 * q^31 - 3004416 * q^34 - 705024 * q^36 - 3313800 * q^39 - 2233344 * q^46 - 7987980 * q^49 + 13519872 * q^51 + 21461760 * q^54 + 70313096 * q^61 + 8388608 * q^64 + 63963648 * q^66 + 10050048 * q^69 - 73729024 * q^76 - 36729992 * q^79 - 157017852 * q^81 - 89865216 * q^84 - 146543600 * q^91 - 159283200 * q^94 - 37748736 * q^96 - 575672832 * 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 $

$2$	−11.3137			−0.707107
$2$	−11.3137			−0.707107
$3$	50.9117	−	63.0000i	0.628539	−	0.777778i
$3$	50.9117	−	63.0000i	0.628539	−	0.777778i
$4$	128.000			0.500000
$5$		0			0
$5$		0			0
$6$	−576.000	+	712.764i	−0.444444	+	0.549972i
$7$		−	2786.00i		−	1.16035i	−0.814492	−	0.580175i	$-0.802984\pi$
$7$		−	2786.00i		−	1.16035i	0.814492	−	0.580175i	$-0.197016\pi$
$8$	−1448.15			−0.353553
$9$	−1377.00	−	6414.87i	−0.209877	−	0.977728i
$10$		0			0
$11$		−	22435.1i		−	1.53235i	−0.642634	−	0.766173i	$-0.722158\pi$
$11$		−	22435.1i		−	1.53235i	0.642634	−	0.766173i	$-0.277842\pi$
$12$	6516.70	−	8064.00i	0.314270	−	0.388889i
$13$		−	13150.0i		−	0.460418i	−0.973141	−	0.230209i	$-0.926059\pi$
$13$		−	13150.0i		−	0.460418i	0.973141	−	0.230209i	$-0.0739410\pi$
$14$			31520.0i			0.820491i
$15$		0			0
$16$	16384.0			0.250000
$17$	66388.8			0.794876			0.397438	−	0.917629i	$-0.369899\pi$
$17$	66388.8			0.794876			0.397438	+	0.917629i	$0.369899\pi$
$18$	15579.0	+	72576.0i	0.148405	+	0.691358i
$19$	−144002.			−1.10498			−0.552490	−	0.833520i	$-0.686322\pi$
$19$	−144002.			−1.10498			−0.552490	+	0.833520i	$0.686322\pi$
$20$		0			0
$21$	−175518.	−	141840.i	−0.902494	−	0.729326i
$22$			253824.i			1.08353i
$23$	49350.4			0.176352			0.0881758	−	0.996105i	$-0.471896\pi$
$23$	49350.4			0.176352			0.0881758	+	0.996105i	$0.471896\pi$
$24$	−73728.0	+	91233.7i	−0.222222	+	0.274986i
$25$		0			0
$26$			148775.i			0.325565i
$27$	−474242.	−	239841.i	−0.892371	−	0.451303i
$28$		−	356608.i		−	0.580175i
$29$		−	627402.i		−	0.887061i	−0.896259	−	0.443531i	$-0.853726\pi$
$29$		−	627402.i		−	0.887061i	0.896259	−	0.443531i	$-0.146274\pi$
$30$		0			0
$31$	728738.			0.789087			0.394543	−	0.918877i	$-0.370903\pi$
$31$	728738.			0.789087			0.394543	+	0.918877i	$0.370903\pi$
$32$	−185364.			−0.176777
$33$	−1.41341e6	−	1.14221e6i	−1.19182	−	0.963140i
$34$	−751104.			−0.562062
$35$		0			0
$36$	−176256.	−	821104.i	−0.104938	−	0.488864i
$37$			1.96445e6i			1.04817i	0.851665	+	0.524087i	$0.175593\pi$
$37$			1.96445e6i			1.04817i	−0.851665	+	0.524087i	$0.824407\pi$
$38$	1.62920e6			0.781338
$39$	−828450.	−	669489.i	−0.358103	−	0.289391i
$40$		0			0
$41$		−	986125.i		−	0.348977i	−0.984659	−	0.174488i	$-0.944173\pi$
$41$		−	986125.i		−	0.348977i	0.984659	−	0.174488i	$-0.0558272\pi$
$42$	1.98576e6	+	1.60474e6i	0.638160	+	0.515711i
$43$		−	78142.0i		−	0.0228566i	−0.999935	−	0.0114283i	$-0.996362\pi$
$43$		−	78142.0i		−	0.0228566i	0.999935	−	0.0114283i	$-0.00363781\pi$
$44$		−	2.87169e6i		−	0.766173i
$45$		0			0
$46$	−558336.			−0.124699
$47$	3.51969e6			0.721296			0.360648	−	0.932702i	$-0.382556\pi$
$47$	3.51969e6			0.721296			0.360648	+	0.932702i	$0.382556\pi$
$48$	834137.	−	1.03219e6i	0.157135	−	0.194444i
$49$	−1.99700e6			−0.346412
$50$		0			0
$51$	3.37997e6	−	4.18250e6i	0.499611	−	0.618237i
$52$		−	1.68320e6i		−	0.230209i
$53$	522048.			0.0661618			0.0330809	−	0.999453i	$-0.489468\pi$
$53$	522048.			0.0661618			0.0330809	+	0.999453i	$0.489468\pi$
$54$	5.36544e6	+	2.71349e6i	0.631001	+	0.319120i
$55$		0			0
$56$			4.03456e6i			0.410246i
$57$	−7.33138e6	+	9.07213e6i	−0.694523	+	0.859428i
$58$			7.09824e6i			0.627247i
$59$		−	5.00425e6i		−	0.412981i	−0.978449	−	0.206491i	$-0.933796\pi$
$59$		−	5.00425e6i		−	0.412981i	0.978449	−	0.206491i	$-0.0662043\pi$
$60$		0			0
$61$	1.75783e7			1.26957			0.634785	−	0.772689i	$-0.281089\pi$
$61$	1.75783e7			1.26957			0.634785	+	0.772689i	$0.281089\pi$
$62$	−8.24473e6			−0.557968
$63$	−1.78718e7	+	3.83632e6i	−1.13451	+	0.243530i
$64$	2.09715e6			0.125000
$65$		0			0
$66$	1.59909e7	+	1.29226e7i	0.842748	+	0.681043i
$67$			1.71368e7i			0.850413i	0.905096	+	0.425206i	$0.139798\pi$
$67$			1.71368e7i			0.850413i	−0.905096	+	0.425206i	$0.860202\pi$
$68$	8.49777e6			0.397438
$69$	2.51251e6	−	3.10907e6i	0.110844	−	0.137162i
$70$		0			0
$71$		−	2.58906e7i		−	1.01885i	−0.860516	−	0.509424i	$-0.829859\pi$
$71$		−	2.58906e7i		−	1.01885i	0.860516	−	0.509424i	$-0.170141\pi$
$72$	1.99411e6	+	9.28973e6i	0.0742026	+	0.345679i
$73$			2.81393e7i			0.990883i	0.868641	+	0.495441i	$0.164994\pi$
$73$			2.81393e7i			0.990883i	−0.868641	+	0.495441i	$0.835006\pi$
$74$		−	2.22252e7i		−	0.741171i
$75$		0			0
$76$	−1.84323e7			−0.552490
$77$	−6.25041e7			−1.77806
$78$	9.37284e6	+	7.57440e6i	0.253217	+	0.204630i
$79$	−9.18250e6			−0.235750			−0.117875	−	0.993028i	$-0.537608\pi$
$79$	−9.18250e6			−0.235750			−0.117875	+	0.993028i	$0.537608\pi$
$80$		0			0
$81$	−3.92545e7	+	1.76666e7i	−0.911904	+	0.410404i
$82$			1.11567e7i			0.246764i
$83$	−8.71084e7			−1.83547			−0.917736	−	0.397190i	$-0.869985\pi$
$83$	−8.71084e7			−1.83547			−0.917736	+	0.397190i	$0.869985\pi$
$84$	−2.24663e7	−	1.81555e7i	−0.451247	−	0.364663i
$85$		0			0
$86$			884076.i			0.0161620i
$87$	−3.95263e7	−	3.19421e7i	−0.689937	−	0.557553i
$88$			3.24895e7i			0.541766i
$89$		−	8.12528e7i		−	1.29503i	−0.762055	−	0.647513i	$-0.775809\pi$
$89$		−	8.12528e7i		−	1.29503i	0.762055	−	0.647513i	$-0.224191\pi$
$90$		0			0
$91$	−3.66359e7			−0.534246
$92$	6.31685e6			0.0881758
$93$	3.71013e7	−	4.59105e7i	0.495972	−	0.613734i
$94$	−3.98208e7			−0.510033
$95$		0			0
$96$	−9.43718e6	+	1.16779e7i	−0.111111	+	0.137493i
$97$			1.28723e8i			1.45401i	0.686632	+	0.727006i	$0.259089\pi$
$97$			1.28723e8i			1.45401i	−0.686632	+	0.727006i	$0.740911\pi$
$98$	2.25934e7			0.244950
$99$	−1.43918e8	+	3.08931e7i	−1.49822	+	0.321604i
$100$		0			0
$101$			9.37809e7i			0.901216i	0.892722	+	0.450608i	$0.148793\pi$
$101$			9.37809e7i			0.901216i	−0.892722	+	0.450608i	$0.851207\pi$
$102$	−3.82400e7	+	4.73196e7i	−0.353278	+	0.437160i
$103$		−	5.30322e7i		−	0.471184i	−0.971852	−	0.235592i	$-0.924297\pi$
$103$		−	5.30322e7i		−	0.471184i	0.971852	−	0.235592i	$-0.0757030\pi$
$104$			1.90432e7i			0.162782i
$105$		0			0
$106$	−5.90630e6			−0.0467835
$107$	−1.90801e8			−1.45561			−0.727804	−	0.685785i	$-0.759459\pi$
$107$	−1.90801e8			−1.45561			−0.727804	+	0.685785i	$0.759459\pi$
$108$	−6.07030e7	−	3.06996e7i	−0.446185	−	0.225652i
$109$	−2.71959e8			−1.92662			−0.963312	−	0.268384i	$-0.913510\pi$
$109$	−2.71959e8			−1.92662			−0.963312	+	0.268384i	$0.913510\pi$
$110$		0			0
$111$	1.23760e8	+	1.00013e8i	0.815246	+	0.658818i
$112$		−	4.56458e7i		−	0.290087i
$113$	7.69189e7			0.471758			0.235879	−	0.971782i	$-0.424203\pi$
$113$	7.69189e7			0.471758			0.235879	+	0.971782i	$0.424203\pi$
$114$	8.29452e7	−	1.02639e8i	0.491102	−	0.607708i
$115$		0			0
$116$		−	8.03074e7i		−	0.443531i
$117$	−8.43556e7	+	1.81076e7i	−0.450164	+	0.0966309i
$118$			5.66166e7i			0.292022i
$119$		−	1.84959e8i		−	0.922334i
$120$		0			0
$121$	−2.88974e8			−1.34809
$122$	−1.98875e8			−0.897722
$123$	−6.21259e7	−	5.02053e7i	−0.271427	−	0.219346i
$124$	9.32785e7			0.394543
$125$		0			0
$126$	2.02197e8	−	4.34030e7i	0.802217	−	0.172202i
$127$			1.25417e8i			0.482104i	0.970512	+	0.241052i	$0.0774925\pi$
$127$			1.25417e8i			0.482104i	−0.970512	+	0.241052i	$0.922508\pi$
$128$	−2.37266e7			−0.0883883
$129$	−4.92295e6	−	3.97834e6i	−0.0177773	−	0.0143662i
$130$		0			0
$131$			1.24051e8i			0.421225i	0.977570	+	0.210612i	$0.0675458\pi$
$131$			1.24051e8i			0.421225i	−0.977570	+	0.210612i	$0.932454\pi$
$132$	−1.80917e8	−	1.46203e8i	−0.595912	−	0.481570i
$133$			4.01190e8i			1.28216i
$134$		−	1.93880e8i		−	0.601332i
$135$		0			0
$136$	−9.61413e7			−0.281031
$137$	5.50746e8			1.56340			0.781699	−	0.623656i	$-0.214353\pi$
$137$	5.50746e8			1.56340			0.781699	+	0.623656i	$0.214353\pi$
$138$	−2.84258e7	+	3.51752e7i	−0.0783785	+	0.0969884i
$139$	7.59262e7			0.203391			0.101696	−	0.994816i	$-0.467573\pi$
$139$	7.59262e7			0.203391			0.101696	+	0.994816i	$0.467573\pi$
$140$		0			0
$141$	1.79194e8	−	2.21741e8i	0.453363	−	0.561008i
$142$			2.92919e8i			0.720434i
$143$	−2.95021e8			−0.705520
$144$	−2.25608e7	−	1.05101e8i	−0.0524691	−	0.244432i
$145$		0			0
$146$		−	3.18360e8i		−	0.700660i
$147$	−1.01670e8	+	1.25811e8i	−0.217733	+	0.269431i
$148$			2.51449e8i			0.524087i
$149$			7.35143e8i			1.49151i	0.666219	+	0.745756i	$0.267912\pi$
$149$			7.35143e8i			1.49151i	−0.666219	+	0.745756i	$0.732088\pi$
$150$		0			0
$151$	3.01637e8			0.580198			0.290099	−	0.956997i	$-0.406312\pi$
$151$	3.01637e8			0.580198			0.290099	+	0.956997i	$0.406312\pi$
$152$	2.08537e8			0.390669
$153$	−9.14174e7	−	4.25876e8i	−0.166826	−	0.777172i
$154$	7.07154e8			1.25728
$155$		0			0
$156$	−1.06042e8	−	8.56946e7i	−0.179051	−	0.144695i
$157$			1.61241e8i			0.265386i	0.991157	+	0.132693i	$0.0423624\pi$
$157$			1.61241e8i			0.265386i	−0.991157	+	0.132693i	$0.957638\pi$
$158$	1.03888e8			0.166701
$159$	2.65784e7	−	3.28891e7i	0.0415853	−	0.0514592i
$160$		0			0
$161$		−	1.37490e8i		−	0.204630i
$162$	4.44114e8	−	1.99874e8i	0.644813	−	0.290200i
$163$		−	2.21232e8i		−	0.313399i	−0.987646	−	0.156700i	$-0.949915\pi$
$163$		−	2.21232e8i		−	0.313399i	0.987646	−	0.156700i	$-0.0500855\pi$
$164$		−	1.26224e8i		−	0.174488i
$165$		0			0
$166$	9.85519e8			1.29787
$167$	4.01854e8			0.516657			0.258328	−	0.966057i	$-0.416828\pi$
$167$	4.01854e8			0.516657			0.258328	+	0.966057i	$0.416828\pi$
$168$	2.54177e8	+	2.05406e8i	0.319080	+	0.257856i
$169$	6.42808e8			0.788015
$170$		0			0
$171$	1.98291e8	+	9.23755e8i	0.231909	+	1.08037i
$172$		−	1.00022e7i		−	0.0114283i
$173$	−1.08224e7			−0.0120820			−0.00604099	−	0.999982i	$-0.501923\pi$
$173$	−1.08224e7			−0.0120820			−0.00604099	+	0.999982i	$0.501923\pi$
$174$	4.47189e8	+	3.61383e8i	0.487859	+	0.394250i
$175$		0			0
$176$		−	3.67576e8i		−	0.383087i
$177$	−3.15267e8	−	2.54775e8i	−0.321208	−	0.259575i
$178$			9.19271e8i			0.915721i
$179$			2.24822e8i			0.218991i	0.993987	+	0.109495i	$0.0349235\pi$
$179$			2.24822e8i			0.218991i	−0.993987	+	0.109495i	$0.965076\pi$
$180$		0			0
$181$	−1.31026e9			−1.22080			−0.610398	−	0.792095i	$-0.708990\pi$
$181$	−1.31026e9			−1.22080			−0.610398	+	0.792095i	$0.708990\pi$
$182$	4.14488e8			0.377769
$183$	8.94940e8	−	1.10743e9i	0.797975	−	0.987444i
$184$	−7.14670e7			−0.0623497
$185$		0			0
$186$	−4.19753e8	+	5.19418e8i	−0.350705	+	0.433975i
$187$		−	1.48944e9i		−	1.21803i
$188$	4.50521e8			0.360648
$189$	−6.68197e8	+	1.32124e9i	−0.523670	+	1.03546i
$190$		0			0
$191$		−	2.18984e9i		−	1.64543i	−0.568454	−	0.822715i	$-0.692458\pi$
$191$		−	2.18984e9i		−	1.64543i	0.568454	−	0.822715i	$-0.307542\pi$
$192$	1.06770e8	−	1.32121e8i	0.0785674	−	0.0972222i
$193$		−	1.71183e9i		−	1.23376i	−0.787057	−	0.616881i	$-0.788396\pi$
$193$		−	1.71183e9i		−	1.23376i	0.787057	−	0.616881i	$-0.211604\pi$
$194$		−	1.45633e9i		−	1.02814i
$195$		0			0
$196$	−2.55615e8			−0.173206
$197$	2.63287e9			1.74810			0.874048	−	0.485840i	$-0.161486\pi$
$197$	2.63287e9			1.74810			0.874048	+	0.485840i	$0.161486\pi$
$198$	1.62825e9	−	3.49516e8i	1.05940	−	0.227408i
$199$	−2.95243e9			−1.88264			−0.941319	−	0.337517i	$-0.890413\pi$
$199$	−2.95243e9			−1.88264			−0.941319	+	0.337517i	$0.890413\pi$
$200$		0			0
$201$	1.07962e9	+	8.72462e8i	0.661432	+	0.534518i
$202$		−	1.06101e9i		−	0.637256i
$203$	−1.74794e9			−1.02930
$204$	4.32636e8	−	5.35360e8i	0.249805	−	0.309118i
$205$		0			0
$206$			5.99991e8i			0.333178i
$207$	−6.79555e7	−	3.16577e8i	−0.0370121	−	0.172424i
$208$		−	2.15450e8i		−	0.115105i
$209$			3.23070e9i			1.69321i
$210$		0			0
$211$	−2.66349e9			−1.34376			−0.671880	−	0.740660i	$-0.734513\pi$
$211$	−2.66349e9			−1.34376			−0.671880	+	0.740660i	$0.734513\pi$
$212$	6.68222e7			0.0330809
$213$	−1.63111e9	−	1.31814e9i	−0.792437	−	0.640386i
$214$	2.15866e9			1.02927
$215$		0			0
$216$	6.86776e8	+	3.47327e8i	0.315501	+	0.159560i
$217$		−	2.03026e9i		−	0.915616i
$218$	3.07686e9			1.36233
$219$	1.77278e9	+	1.43262e9i	0.770687	+	0.622809i
$220$		0			0
$221$		−	8.73013e8i		−	0.365975i
$222$	−1.40019e9	−	1.13152e9i	−0.576466	−	0.465855i
$223$		−	2.04266e8i		−	0.0825993i	−0.999147	−	0.0412996i	$-0.986850\pi$
$223$		−	2.04266e8i		−	0.0825993i	0.999147	−	0.0412996i	$-0.0131498\pi$
$224$			5.16424e8i			0.205123i
$225$		0			0
$226$	−8.70238e8			−0.333583
$227$	4.26163e8			0.160499			0.0802495	−	0.996775i	$-0.474428\pi$
$227$	4.26163e8			0.160499			0.0802495	+	0.996775i	$0.474428\pi$
$228$	−9.38417e8	+	1.16123e9i	−0.347261	+	0.429714i
$229$	3.05784e8			0.111192			0.0555960	−	0.998453i	$-0.482294\pi$
$229$	3.05784e8			0.111192			0.0555960	+	0.998453i	$0.482294\pi$
$230$		0			0
$231$	−3.18219e9	+	3.93776e9i	−1.11758	+	1.38293i
$232$			9.08575e8i			0.313624i
$233$	1.40915e9			0.478117			0.239059	−	0.971005i	$-0.423161\pi$
$233$	1.40915e9			0.478117			0.239059	+	0.971005i	$0.423161\pi$
$234$	9.54374e8	−	2.04864e8i	0.318314	−	0.0683284i
$235$		0			0
$236$		−	6.40543e8i		−	0.206491i
$237$	−4.67496e8	+	5.78497e8i	−0.148178	+	0.183361i
$238$			2.09258e9i			0.652189i
$239$		−	2.28759e9i		−	0.701109i	−0.936542	−	0.350555i	$-0.885993\pi$
$239$		−	2.28759e9i		−	0.701109i	0.936542	−	0.350555i	$-0.114007\pi$
$240$		0			0
$241$	4.37370e9			1.29653			0.648263	−	0.761417i	$-0.275496\pi$
$241$	4.37370e9			1.29653			0.648263	+	0.761417i	$0.275496\pi$
$242$	3.26937e9			0.953240
$243$	−8.85518e8	+	3.37247e9i	−0.253964	+	0.967214i
$244$	2.25002e9			0.634785
$245$		0			0
$246$	7.02874e8	+	5.68008e8i	0.191928	+	0.155101i
$247$			1.89363e9i			0.508752i
$248$	−1.05533e9			−0.278984
$249$	−4.43484e9	+	5.48783e9i	−1.15367	+	1.42759i
$250$		0			0
$251$		−	1.78995e9i		−	0.450969i	−0.974247	−	0.225484i	$-0.927604\pi$
$251$		−	1.78995e9i		−	0.450969i	0.974247	−	0.225484i	$-0.0723965\pi$
$252$	−2.28759e9	+	4.91049e8i	−0.567253	+	0.121765i
$253$		−	1.10718e9i		−	0.270232i
$254$		−	1.41893e9i		−	0.340899i
$255$		0			0
$256$	2.68435e8			0.0625000
$257$	2.20683e9			0.505867			0.252933	−	0.967484i	$-0.418605\pi$
$257$	2.20683e9			0.505867			0.252933	+	0.967484i	$0.418605\pi$
$258$	5.56968e7	+	4.50098e7i	0.0125705	+	0.0101585i
$259$	5.47295e9			1.21625
$260$		0			0
$261$	−4.02470e9	+	8.63932e8i	−0.867305	+	0.186173i
$262$		−	1.40347e9i		−	0.297851i
$263$	−1.77804e9			−0.371636			−0.185818	−	0.982584i	$-0.559494\pi$
$263$	−1.77804e9			−0.371636			−0.185818	+	0.982584i	$0.559494\pi$
$264$	2.04684e9	+	1.65409e9i	0.421374	+	0.340521i
$265$		0			0
$266$		−	4.53894e9i		−	0.906626i
$267$	−5.11893e9	−	4.13672e9i	−1.00724	−	0.813975i
$268$			2.19351e9i			0.425206i
$269$		−	5.97276e9i		−	1.14069i	−0.821406	−	0.570343i	$-0.806810\pi$
$269$		−	5.97276e9i		−	1.14069i	0.821406	−	0.570343i	$-0.193190\pi$
$270$		0			0
$271$	3.24555e9			0.601744			0.300872	−	0.953665i	$-0.402722\pi$
$271$	3.24555e9			0.601744			0.300872	+	0.953665i	$0.402722\pi$
$272$	1.08771e9			0.198719
$273$	−1.86520e9	+	2.30806e9i	−0.335795	+	0.415525i
$274$	−6.23098e9			−1.10549
$275$		0			0
$276$	3.21602e8	−	3.97962e8i	0.0554219	−	0.0685812i
$277$			1.34137e9i			0.227841i	0.993490	+	0.113920i	$0.0363408\pi$
$277$			1.34137e9i			0.227841i	−0.993490	+	0.113920i	$0.963659\pi$
$278$	−8.59007e8			−0.143819
$279$	−1.00347e9	−	4.67476e9i	−0.165611	−	0.771512i
$280$		0			0
$281$		−	1.89253e9i		−	0.303541i	−0.988416	−	0.151771i	$-0.951502\pi$
$281$		−	1.89253e9i		−	0.303541i	0.988416	−	0.151771i	$-0.0484975\pi$
$282$	−2.02734e9	+	2.50871e9i	−0.320576	+	0.396693i
$283$		−	6.88292e9i		−	1.07307i	−0.843879	−	0.536534i	$-0.819733\pi$
$283$		−	6.88292e9i		−	1.07307i	0.843879	−	0.536534i	$-0.180267\pi$
$284$		−	3.31400e9i		−	0.509424i
$285$		0			0
$286$	3.33779e9			0.498878
$287$	−2.74735e9			−0.404935
$288$	2.55246e8	+	1.18909e9i	0.0371013	+	0.172840i
$289$	−2.56828e9			−0.368172
$290$		0			0
$291$	8.10952e9	+	6.55348e9i	1.13090	+	0.913903i
$292$			3.60183e9i			0.495441i
$293$	4.31371e9			0.585302			0.292651	−	0.956219i	$-0.405463\pi$
$293$	4.31371e9			0.585302			0.292651	+	0.956219i	$0.405463\pi$
$294$	1.15027e9	−	1.42339e9i	0.153961	−	0.190517i
$295$		0			0
$296$		−	2.84482e9i		−	0.370585i
$297$	−5.38085e9	+	1.06397e10i	−0.691553	+	1.36742i
$298$		−	8.31719e9i		−	1.05466i
$299$		−	6.48958e8i		−	0.0811954i
$300$		0			0
$301$	−2.17704e8			−0.0265216
$302$	−3.41263e9			−0.410262
$303$	5.90820e9	+	4.77455e9i	0.700946	+	0.566450i
$304$	−2.35933e9			−0.276245
$305$		0			0
$306$	1.03427e9	+	4.81824e9i	0.117964	+	0.549544i
$307$			8.32155e9i			0.936809i	0.883514	+	0.468404i	$0.155171\pi$
$307$			8.32155e9i			0.936809i	−0.883514	+	0.468404i	$0.844829\pi$
$308$	−8.00053e9			−0.889029
$309$	−3.34103e9	−	2.69996e9i	−0.366477	−	0.296158i
$310$		0			0
$311$		−	1.09184e10i		−	1.16712i	−0.812069	−	0.583561i	$-0.801659\pi$
$311$		−	1.09184e10i		−	1.16712i	0.812069	−	0.583561i	$-0.198341\pi$
$312$	1.19972e9	+	9.69523e8i	0.126609	+	0.102315i
$313$			6.19953e9i			0.645924i	0.946412	+	0.322962i	$0.104679\pi$
$313$			6.19953e9i			0.645924i	−0.946412	+	0.322962i	$0.895321\pi$
$314$		−	1.82424e9i		−	0.187656i
$315$		0			0
$316$	−1.17536e9			−0.117875
$317$	1.86870e10			1.85056			0.925278	−	0.379289i	$-0.123831\pi$
$317$	1.86870e10			1.85056			0.925278	+	0.379289i	$0.123831\pi$
$318$	−3.00700e8	+	3.72097e8i	−0.0294052	+	0.0363871i
$319$	−1.40758e10			−1.35929
$320$		0			0
$321$	−9.71398e9	+	1.20204e10i	−0.914907	+	1.13214i
$322$			1.55552e9i			0.144695i
$323$	−9.56013e9			−0.878322
$324$	−5.02457e9	+	2.26132e9i	−0.455952	+	0.205202i
$325$		0			0
$326$			2.50296e9i			0.221607i
$327$	−1.38459e10	+	1.71334e10i	−1.21096	+	1.49849i
$328$			1.42806e9i			0.123382i
$329$		−	9.80587e9i		−	0.836956i
$330$		0			0
$331$	3.24478e9			0.270317			0.135158	−	0.990824i	$-0.456846\pi$
$331$	3.24478e9			0.270317			0.135158	+	0.990824i	$0.456846\pi$
$332$	−1.11499e10			−0.917736
$333$	1.26017e10	−	2.70504e9i	1.02483	−	0.219987i
$334$	−4.54645e9			−0.365331
$335$		0			0
$336$	−2.87569e9	−	2.32391e9i	−0.225624	−	0.182331i
$337$		−	4.89137e9i		−	0.379237i	−0.981858	−	0.189619i	$-0.939275\pi$
$337$		−	4.89137e9i		−	0.379237i	0.981858	−	0.189619i	$-0.0607251\pi$
$338$	−7.27254e9			−0.557211
$339$	3.91607e9	−	4.84589e9i	0.296518	−	0.366923i
$340$		0			0
$341$		−	1.63493e10i		−	1.20915i
$342$	−2.24340e9	−	1.04511e10i	−0.163985	−	0.763936i
$343$		−	1.04971e10i		−	0.758391i
$344$			1.13162e8i			0.00808101i
$345$		0			0
$346$	1.22441e8			0.00854324
$347$	−1.44263e10			−0.995030			−0.497515	−	0.867455i	$-0.665754\pi$
$347$	−1.44263e10			−0.995030			−0.497515	+	0.867455i	$0.665754\pi$
$348$	−5.05937e9	−	4.08859e9i	−0.344968	−	0.278777i
$349$	5.34169e9			0.360062			0.180031	−	0.983661i	$-0.442380\pi$
$349$	5.34169e9			0.360062			0.180031	+	0.983661i	$0.442380\pi$
$350$		0			0
$351$	−3.15391e9	+	6.23629e9i	−0.207788	+	0.410864i
$352$			4.15865e9i			0.270883i
$353$	−7.82366e9			−0.503861			−0.251931	−	0.967745i	$-0.581065\pi$
$353$	−7.82366e9			−0.503861			−0.251931	+	0.967745i	$0.581065\pi$
$354$	3.56684e9	+	2.88245e9i	0.227128	+	0.183547i
$355$		0			0
$356$		−	1.04004e10i		−	0.647513i
$357$	−1.16524e10	−	9.41659e9i	−0.717371	−	0.579723i
$358$		−	2.54357e9i		−	0.154850i
$359$		−	1.66718e10i		−	1.00370i	−0.864955	−	0.501850i	$-0.832653\pi$
$359$		−	1.66718e10i		−	1.00370i	0.864955	−	0.501850i	$-0.167347\pi$
$360$		0			0
$361$	3.75301e9			0.220979
$362$	1.48239e10			0.863233
$363$	−1.47122e10	+	1.82054e10i	−0.847325	+	1.04851i
$364$	−4.68940e9			−0.267123
$365$		0			0
$366$	−1.01251e10	+	1.25292e10i	−0.564254	+	0.698228i
$367$		−	1.86456e10i		−	1.02781i	−0.857847	−	0.513905i	$-0.828198\pi$
$367$		−	1.86456e10i		−	1.02781i	0.857847	−	0.513905i	$-0.171802\pi$
$368$	8.08557e8			0.0440879
$369$	−6.32587e9	+	1.35789e9i	−0.341205	+	0.0732421i
$370$		0			0
$371$		−	1.45443e9i		−	0.0767708i
$372$	4.74896e9	−	5.87654e9i	0.247986	−	0.306867i
$373$			3.38390e10i			1.74817i	0.485776	+	0.874083i	$0.338537\pi$
$373$			3.38390e10i			1.74817i	−0.485776	+	0.874083i	$0.661463\pi$
$374$			1.68511e10i			0.861274i
$375$		0			0
$376$	−5.09706e9			−0.255017
$377$	−8.25033e9			−0.408419
$378$	7.55979e9	−	1.49481e10i	0.370290	−	0.732182i
$379$	2.82088e10			1.36719			0.683594	−	0.729863i	$-0.260416\pi$
$379$	2.82088e10			1.36719			0.683594	+	0.729863i	$0.260416\pi$
$380$		0			0
$381$	7.90126e9	+	6.38518e9i	0.374970	+	0.303021i
$382$			2.47752e10i			1.16349i
$383$	1.82405e10			0.847698			0.423849	−	0.905733i	$-0.360679\pi$
$383$	1.82405e10			0.847698			0.423849	+	0.905733i	$0.360679\pi$
$384$	−1.20796e9	+	1.49477e9i	−0.0555556	+	0.0687465i
$385$		0			0
$386$			1.93671e10i			0.872401i
$387$	−5.01271e8	+	1.07602e8i	−0.0223475	+	0.00479705i
$388$			1.64765e10i			0.727006i
$389$			1.94375e10i			0.848871i	0.905458	+	0.424435i	$0.139527\pi$
$389$			1.94375e10i			0.848871i	−0.905458	+	0.424435i	$0.860473\pi$
$390$		0			0
$391$	3.27632e9			0.140178
$392$	2.89196e9			0.122475
$393$	7.81519e9	+	6.31563e9i	0.327619	+	0.264756i
$394$	−2.97876e10			−1.23609
$395$		0			0
$396$	−1.84215e10	+	3.95432e9i	−0.749109	+	0.160802i
$397$		−	1.66719e10i		−	0.671157i	−0.942012	−	0.335578i	$-0.891068\pi$
$397$		−	1.66719e10i		−	0.671157i	0.942012	−	0.335578i	$-0.108932\pi$
$398$	3.34029e10			1.33123
$399$	2.52749e10	+	2.04252e10i	0.997238	+	0.805890i
$400$		0			0
$401$			3.30836e10i			1.27949i	0.768589	+	0.639743i	$0.220959\pi$
$401$			3.30836e10i			1.27949i	−0.768589	+	0.639743i	$0.779041\pi$
$402$	−1.22145e10	−	9.87078e9i	−0.467703	−	0.377961i
$403$		−	9.58290e9i		−	0.363310i
$404$			1.20040e10i			0.450608i
$405$		0			0
$406$	1.97757e10			0.727826
$407$	4.40725e10			1.60616
$408$	−4.89472e9	+	6.05690e9i	−0.176639	+	0.218580i
$409$	5.03326e10			1.79869			0.899345	−	0.437240i	$-0.144044\pi$
$409$	5.03326e10			1.79869			0.899345	+	0.437240i	$0.144044\pi$
$410$		0			0
$411$	2.80394e10	−	3.46970e10i	0.982657	−	1.21598i
$412$		−	6.78812e9i		−	0.235592i
$413$	−1.39418e10			−0.479203
$414$	7.68829e8	+	3.58165e9i	0.0261715	+	0.121922i
$415$		0			0
$416$			2.43753e9i			0.0813912i
$417$	3.86553e9	−	4.78335e9i	0.127839	−	0.158193i
$418$		−	3.65512e10i		−	1.19728i
$419$		−	2.94280e10i		−	0.954782i	−0.878691	−	0.477391i	$-0.841582\pi$
$419$		−	2.94280e10i		−	0.954782i	0.878691	−	0.477391i	$-0.158418\pi$
$420$		0			0
$421$	−3.33243e10			−1.06080			−0.530399	−	0.847748i	$-0.677958\pi$
$421$	−3.33243e10			−1.06080			−0.530399	+	0.847748i	$0.677958\pi$
$422$	3.01340e10			0.950181
$423$	−4.84662e9	−	2.25784e10i	−0.151383	−	0.705231i
$424$	−7.56007e8			−0.0233917
$425$		0			0
$426$	1.84539e10	+	1.49130e10i	0.560338	+	0.452821i
$427$		−	4.89731e10i		−	1.47315i
$428$	−2.44225e10			−0.727804
$429$	−1.50200e10	+	1.85863e10i	−0.443447	+	0.548738i
$430$		0			0
$431$		−	5.62271e10i		−	1.62943i	−0.579860	−	0.814716i	$-0.696893\pi$
$431$		−	5.62271e10i		−	1.62943i	0.579860	−	0.814716i	$-0.303107\pi$
$432$	−7.76999e9	−	3.92955e9i	−0.223093	−	0.112826i
$433$		−	2.18807e10i		−	0.622457i	−0.950335	−	0.311229i	$-0.899260\pi$
$433$		−	2.18807e10i		−	0.622457i	0.950335	−	0.311229i	$-0.100740\pi$
$434$			2.29698e10i			0.647439i
$435$		0			0
$436$	−3.48107e10			−0.963312
$437$	−7.10656e9			−0.194865
$438$	−2.00567e10	−	1.62083e10i	−0.544958	−	0.440392i
$439$	−1.87990e10			−0.506146			−0.253073	−	0.967447i	$-0.581441\pi$
$439$	−1.87990e10			−0.506146			−0.253073	+	0.967447i	$0.581441\pi$
$440$		0			0
$441$	2.74986e9	+	1.28105e10i	0.0727037	+	0.338696i
$442$			9.87702e9i			0.258784i
$443$	6.53593e10			1.69704			0.848520	−	0.529163i	$-0.177494\pi$
$443$	6.53593e10			1.69704			0.848520	+	0.529163i	$0.177494\pi$
$444$	1.58413e10	+	1.28017e10i	0.407623	+	0.329409i
$445$		0			0
$446$			2.31100e9i			0.0584065i
$447$	4.63140e10	+	3.74274e10i	1.16006	+	0.937474i
$448$		−	5.84267e9i		−	0.145044i
$449$		−	1.58084e10i		−	0.388959i	−0.980907	−	0.194479i	$-0.937698\pi$
$449$		−	1.58084e10i		−	0.388959i	0.980907	−	0.194479i	$-0.0623017\pi$
$450$		0			0
$451$	−2.21238e10			−0.534754
$452$	9.84562e9			0.235879
$453$	1.53568e10	−	1.90031e10i	0.364677	−	0.451265i
$454$	−4.82148e9			−0.113490
$455$		0			0
$456$	1.06170e10	−	1.31378e10i	0.245551	−	0.303854i
$457$		−	3.30400e9i		−	0.0757486i	−0.999283	−	0.0378743i	$-0.987941\pi$
$457$		−	3.30400e9i		−	0.0757486i	0.999283	−	0.0378743i	$-0.0120587\pi$
$458$	−3.45956e9			−0.0786246
$459$	−3.14844e10	−	1.59228e10i	−0.709324	−	0.358730i
$460$		0			0
$461$		−	3.30139e10i		−	0.730960i	−0.930819	−	0.365480i	$-0.880905\pi$
$461$		−	3.30139e10i		−	0.730960i	0.930819	−	0.365480i	$-0.119095\pi$
$462$	3.60024e10	−	4.45507e10i	0.790248	−	0.977882i
$463$			5.63117e10i			1.22539i	0.790319	+	0.612696i	$0.209915\pi$
$463$			5.63117e10i			1.22539i	−0.790319	+	0.612696i	$0.790085\pi$
$464$		−	1.02793e10i		−	0.221765i
$465$		0			0
$466$	−1.59428e10			−0.338080
$467$	5.38175e10			1.13150			0.565752	−	0.824576i	$-0.308586\pi$
$467$	5.38175e10			1.13150			0.565752	+	0.824576i	$0.308586\pi$
$468$	−1.07975e10	+	2.31777e9i	−0.225082	+	0.0483155i
$469$	4.77430e10			0.986776
$470$		0			0
$471$	1.01582e10	+	8.20907e9i	0.206411	+	0.166805i
$472$			7.24692e9i			0.146011i
$473$	−1.75312e9			−0.0350242
$474$	5.28912e9	−	6.54495e9i	0.104778	−	0.129656i
$475$		0			0
$476$		−	2.36748e10i		−	0.461167i
$477$	−7.18861e8	−	3.34887e9i	−0.0138858	−	0.0646882i
$478$			2.58811e10i			0.495759i
$479$			8.02692e10i			1.52478i	0.647119	+	0.762389i	$0.275974\pi$
$479$			8.02692e10i			1.52478i	−0.647119	+	0.762389i	$0.724026\pi$
$480$		0			0
$481$	2.58325e10			0.482598
$482$	−4.94828e10			−0.916782
$483$	−8.66188e9	−	6.99986e9i	−0.159156	−	0.128618i
$484$	−3.69887e10			−0.674043
$485$		0			0
$486$	1.00185e10	−	3.81551e10i	0.179580	−	0.683923i
$487$			7.07093e10i			1.25707i	0.777780	+	0.628537i	$0.216346\pi$
$487$			7.07093e10i			1.25707i	−0.777780	+	0.628537i	$0.783654\pi$
$488$	−2.54561e10			−0.448861
$489$	−1.39376e10	−	1.12633e10i	−0.243755	−	0.196984i
$490$		0			0
$491$			6.06876e10i			1.04418i	0.852892	+	0.522088i	$0.174847\pi$
$491$			6.06876e10i			1.04418i	−0.852892	+	0.522088i	$0.825153\pi$
$492$	−7.95212e9	−	6.42628e9i	−0.135713	−	0.109673i
$493$		−	4.16525e10i		−	0.705104i
$494$		−	2.14239e10i		−	0.359742i
$495$		0			0
$496$	1.19396e10			0.197272
$497$	−7.21313e10			−1.18222
$498$	5.01745e10	−	6.20877e10i	0.815766	−	1.00946i
$499$	1.04926e11			1.69232			0.846158	−	0.532932i	$-0.178910\pi$
$499$	1.04926e11			1.69232			0.846158	+	0.532932i	$0.178910\pi$
$500$		0			0
$501$	2.04590e10	−	2.53168e10i	0.324739	−	0.401844i
$502$			2.02510e10i			0.318883i
$503$	−4.73262e9			−0.0739315			−0.0369657	−	0.999317i	$-0.511769\pi$
$503$	−4.73262e9			−0.0739315			−0.0369657	+	0.999317i	$0.511769\pi$
$504$	2.58812e10	−	5.55559e9i	0.401109	−	0.0861009i
$505$		0			0
$506$			1.25263e10i			0.191083i
$507$	3.27265e10	−	4.04969e10i	0.495299	−	0.612901i
$508$			1.60534e10i			0.241052i
$509$		−	8.34402e7i		−	0.00124309i	−1.00000		0.000621547i	$-0.999802\pi$
$509$		−	8.34402e7i		−	0.00124309i	1.00000		0.000621547i	$-0.000197845\pi$
$510$		0			0
$511$	7.83962e10			1.14977
$512$	−3.03700e9			−0.0441942
$513$	6.82919e10	+	3.45376e10i	0.986051	+	0.498681i
$514$	−2.49674e10			−0.357702
$515$		0			0
$516$	−6.30137e8	−	5.09228e8i	−0.00888866	−	0.00718312i
$517$		−	7.89646e10i		−	1.10528i
$518$	−6.19193e10			−0.860017
$519$	−5.50985e8	+	6.81809e8i	−0.00759399	+	0.00939709i
$520$		0			0
$521$			3.30179e10i			0.448124i	0.974575	+	0.224062i	$0.0719318\pi$
$521$			3.30179e10i			0.448124i	−0.974575	+	0.224062i	$0.928068\pi$
$522$	4.55343e10	−	9.77428e9i	0.613277	−	0.131644i
$523$		−	7.60491e9i		−	0.101645i	−0.998708	−	0.0508227i	$-0.983816\pi$
$523$		−	7.60491e9i		−	0.101645i	0.998708	−	0.0508227i	$-0.0161843\pi$
$524$			1.58785e10i			0.210612i
$525$		0			0
$526$	2.01162e10			0.262786
$527$	4.83801e10			0.627226
$528$	−2.31573e10	−	1.87139e10i	−0.297956	−	0.240785i
$529$	−7.58755e10			−0.968900
$530$		0			0
$531$	−3.21016e10	+	6.89085e9i	−0.403784	+	0.0866751i
$532$			5.13523e10i			0.641081i
$533$	−1.29675e10			−0.160675
$534$	5.79141e10	+	4.68016e10i	0.712228	+	0.575567i
$535$		0			0
$536$		−	2.48167e10i		−	0.300666i
$537$	1.41638e10	+	1.14460e10i	0.170326	+	0.137644i
$538$			6.75741e10i			0.806587i
$539$			4.48028e10i			0.530823i
$540$		0			0
$541$	−1.18116e11			−1.37885			−0.689427	−	0.724355i	$-0.742138\pi$
$541$	−1.18116e11			−1.37885			−0.689427	+	0.724355i	$0.742138\pi$
$542$	−3.67192e10			−0.425497
$543$	−6.67075e10	+	8.25464e10i	−0.767318	+	0.949508i
$544$	−1.23061e10			−0.140516
$545$		0			0
$546$	2.11023e10	−	2.61127e10i	0.237443	−	0.293820i
$547$			6.60454e10i			0.737723i	0.929484	+	0.368862i	$0.120252\pi$
$547$			6.60454e10i			0.737723i	−0.929484	+	0.368862i	$0.879748\pi$
$548$	7.04955e10			0.781699
$549$	−2.42053e10	−	1.12762e11i	−0.266453	−	1.24129i
$550$		0			0
$551$			9.03471e10i			0.980184i
$552$	−3.63851e9	+	4.50242e9i	−0.0391892	+	0.0484942i
$553$			2.55824e10i			0.273553i
$554$		−	1.51759e10i		−	0.161108i
$555$		0			0
$556$	9.71855e9			0.101696
$557$	−1.38850e11			−1.44253			−0.721265	−	0.692659i	$-0.756439\pi$
$557$	−1.38850e11			−1.44253			−0.721265	+	0.692659i	$0.756439\pi$
$558$	1.13530e10	+	5.28889e10i	0.117104	+	0.545541i
$559$	−1.02757e9			−0.0105236
$560$		0			0
$561$	−9.38347e10	−	7.58299e10i	−0.947353	−	0.765577i
$562$			2.14115e10i			0.214636i
$563$	3.29834e10			0.328294			0.164147	−	0.986436i	$-0.447513\pi$
$563$	3.29834e10			0.328294			0.164147	+	0.986436i	$0.447513\pi$
$564$	2.29368e10	−	2.83828e10i	0.226681	−	0.280504i
$565$		0			0
$566$			7.78713e10i			0.758773i
$567$	4.92190e10	+	1.09363e11i	0.476213	+	1.05813i
$568$			3.74936e10i			0.360217i
$569$		−	7.16018e10i		−	0.683085i	−0.939866	−	0.341543i	$-0.889051\pi$
$569$		−	7.16018e10i		−	0.683085i	0.939866	−	0.341543i	$-0.110949\pi$
$570$		0			0
$571$	4.20250e10			0.395333			0.197667	−	0.980269i	$-0.436664\pi$
$571$	4.20250e10			0.395333			0.197667	+	0.980269i	$0.436664\pi$
$572$	−3.77627e10			−0.352760
$573$	−1.37960e11	−	1.11489e11i	−1.27978	−	1.03422i
$574$	3.10827e10			0.286333
$575$		0			0
$576$	−2.88778e9	−	1.34530e10i	−0.0262346	−	0.122216i
$577$		−	2.19502e11i		−	1.98032i	−0.139927	−	0.990162i	$-0.544687\pi$
$577$		−	2.19502e11i		−	1.98032i	0.139927	−	0.990162i	$-0.455313\pi$
$578$	2.90568e10			0.260337
$579$	−1.07845e11	−	8.71521e10i	−0.959592	−	0.775468i
$580$		0			0
$581$			2.42684e11i			2.12979i
$582$	−9.17488e10	−	7.41442e10i	−0.799665	−	0.646227i
$583$		−	1.17122e10i		−	0.101383i
$584$		−	4.07501e10i		−	0.350330i
$585$		0			0
$586$	−4.88040e10			−0.413871
$587$	−2.05299e11			−1.72916			−0.864580	−	0.502496i	$-0.832415\pi$
$587$	−2.05299e11			−1.72916			−0.864580	+	0.502496i	$0.832415\pi$
$588$	−1.30138e10	+	1.61038e10i	−0.108867	+	0.134716i
$589$	−1.04940e11			−0.871924
$590$		0			0
$591$	1.34044e11	−	1.65871e11i	1.09875	−	1.35963i
$592$			3.21855e10i			0.262043i
$593$	−1.01405e11			−0.820052			−0.410026	−	0.912074i	$-0.634480\pi$
$593$	−1.01405e11			−0.820052			−0.410026	+	0.912074i	$0.634480\pi$
$594$	6.08774e10	−	1.20374e11i	0.489002	−	0.966913i
$595$		0			0
$596$			9.40983e10i			0.745756i
$597$	−1.50313e11	+	1.86003e11i	−1.18331	+	1.46427i
$598$			7.34212e9i			0.0574138i
$599$			9.27543e10i			0.720488i	0.932858	+	0.360244i	$0.117307\pi$
$599$			9.27543e10i			0.720488i	−0.932858	+	0.360244i	$0.882693\pi$
$600$		0			0
$601$	−1.18263e11			−0.906464			−0.453232	−	0.891393i	$-0.649729\pi$
$601$	−1.18263e11			−0.906464			−0.453232	+	0.891393i	$0.649729\pi$
$602$	2.46304e9			0.0187536
$603$	1.09930e11	−	2.35973e10i	0.831472	−	0.178482i
$604$	3.86095e10			0.290099
$605$		0			0
$606$	−6.68436e10	−	5.40178e10i	−0.495644	−	0.400541i
$607$			7.78725e10i			0.573627i	0.957986	+	0.286813i	$0.0925960\pi$
$607$			7.78725e10i			0.573627i	−0.957986	+	0.286813i	$0.907404\pi$
$608$	2.66928e10			0.195335
$609$	−8.89906e10	+	1.10120e11i	−0.646957	+	0.800568i
$610$		0			0
$611$		−	4.62840e10i		−	0.332098i
$612$	−1.17014e10	−	5.45121e10i	−0.0834129	−	0.388586i
$613$		−	6.04009e10i		−	0.427761i	−0.976860	−	0.213881i	$-0.931390\pi$
$613$		−	6.04009e10i		−	0.427761i	0.976860	−	0.213881i	$-0.0686104\pi$
$614$		−	9.41476e10i		−	0.662424i
$615$		0			0
$616$	9.05157e10			0.628638
$617$	−1.86030e11			−1.28364			−0.641819	−	0.766856i	$-0.721820\pi$
$617$	−1.86030e11			−1.28364			−0.641819	+	0.766856i	$0.721820\pi$
$618$	3.77994e10	+	3.05466e10i	0.259138	+	0.209415i
$619$	−1.54130e11			−1.04984			−0.524922	−	0.851151i	$-0.675905\pi$
$619$	−1.54130e11			−1.04984			−0.524922	+	0.851151i	$0.675905\pi$
$620$		0			0
$621$	−2.34040e10	−	1.18362e10i	−0.157371	−	0.0795880i
$622$			1.23527e11i			0.825281i
$623$	−2.26370e11			−1.50268
$624$	−1.35733e10	−	1.09689e10i	−0.0895257	−	0.0723477i
$625$		0			0
$626$		−	7.01397e10i		−	0.456737i
$627$	2.03534e11	+	1.64480e11i	1.31694	+	1.06425i
$628$			2.06389e10i			0.132693i
$629$			1.30417e11i			0.833168i
$630$		0			0
$631$	4.35140e10			0.274480			0.137240	−	0.990538i	$-0.456177\pi$
$631$	4.35140e10			0.274480			0.137240	+	0.990538i	$0.456177\pi$
$632$	1.32977e10			0.0833504
$633$	−1.35603e11	+	1.67800e11i	−0.844606	+	1.04515i
$634$	−2.11419e11			−1.30854
$635$		0			0
$636$	3.40203e9	−	4.20980e9i	0.0207926	−	0.0257296i
$637$			2.62605e10i			0.159494i
$638$	1.59250e11			0.961160
$639$	−1.66085e11	+	3.56514e10i	−0.996156	+	0.213832i
$640$		0			0
$641$			1.74736e11i			1.03502i	0.855676	+	0.517512i	$0.173142\pi$
$641$			1.74736e11i			1.03502i	−0.855676	+	0.517512i	$0.826858\pi$
$642$	1.09901e11	−	1.35996e11i	0.646937	−	0.800544i
$643$		−	2.46091e11i		−	1.43963i	−0.694164	−	0.719817i	$-0.744226\pi$
$643$		−	2.46091e11i		−	1.43963i	0.694164	−	0.719817i	$-0.255774\pi$
$644$		−	1.75987e10i		−	0.102315i
$645$		0			0
$646$	1.08160e11			0.621067
$647$	1.89739e10			0.108278			0.0541390	−	0.998533i	$-0.482759\pi$
$647$	1.89739e10			0.108278			0.0541390	+	0.998533i	$0.482759\pi$
$648$	5.68465e10	−	2.55839e10i	0.322407	−	0.145100i
$649$	−1.12271e11			−0.632831
$650$		0			0
$651$	−1.27907e11	−	1.03364e11i	−0.712146	−	0.575501i
$652$		−	2.83177e10i		−	0.156700i
$653$	1.53366e11			0.843484			0.421742	−	0.906716i	$-0.361419\pi$
$653$	1.53366e11			0.843484			0.421742	+	0.906716i	$0.361419\pi$
$654$	1.56648e11	−	1.93842e11i	0.856277	−	1.05959i
$655$		0			0
$656$		−	1.61567e10i		−	0.0872442i
$657$	1.80510e11	−	3.87479e10i	0.968814	−	0.207963i
$658$			1.10941e11i			0.591817i
$659$		−	1.47234e11i		−	0.780667i	−0.920674	−	0.390333i	$-0.872360\pi$
$659$		−	1.47234e11i		−	0.780667i	0.920674	−	0.390333i	$-0.127640\pi$
$660$		0			0
$661$	−6.61159e10			−0.346338			−0.173169	−	0.984892i	$-0.555401\pi$
$661$	−6.61159e10			−0.346338			−0.173169	+	0.984892i	$0.555401\pi$
$662$	−3.67105e10			−0.191143
$663$	−5.49998e10	−	4.44466e10i	−0.284647	−	0.230030i
$664$	1.26146e11			0.648937
$665$		0			0
$666$	−1.42572e11	+	3.06041e10i	−0.724663	+	0.155554i
$667$		−	3.09625e10i		−	0.156435i
$668$	5.14373e10			0.258328
$669$	−1.28687e10	−	1.03995e10i	−0.0642439	−	0.0519169i
$670$		0			0
$671$		−	3.94370e11i		−	1.94542i
$672$	3.25347e10	+	2.62920e10i	0.159540	+	0.128928i
$673$		−	1.67142e11i		−	0.814753i	−0.913260	−	0.407377i	$-0.866444\pi$
$673$		−	1.67142e11i		−	0.814753i	0.913260	−	0.407377i	$-0.133556\pi$
$674$			5.53395e10i			0.268161i
$675$		0			0
$676$	8.22795e10			0.394008
$677$	−7.82435e10			−0.372472			−0.186236	−	0.982505i	$-0.559629\pi$
$677$	−7.82435e10			−0.372472			−0.186236	+	0.982505i	$0.559629\pi$
$678$	−4.43053e10	+	5.48250e10i	−0.209670	+	0.259454i
$679$	3.58621e11			1.68716
$680$		0			0
$681$	2.16967e10	−	2.68483e10i	0.100880	−	0.124832i
$682$			1.84971e11i			0.855001i
$683$	−1.21724e11			−0.559361			−0.279681	−	0.960093i	$-0.590229\pi$
$683$	−1.21724e11			−0.559361			−0.279681	+	0.960093i	$0.590229\pi$
$684$	2.53812e10	+	1.18241e11i	0.115955	+	0.540185i
$685$		0			0
$686$			1.18761e11i			0.536263i
$687$	1.55680e10	−	1.92644e10i	0.0698885	−	0.0864827i
$688$		−	1.28028e9i		−	0.00571414i
$689$		−	6.86494e9i		−	0.0304621i
$690$		0			0
$691$	3.71272e11			1.62847			0.814236	−	0.580535i	$-0.197156\pi$
$691$	3.71272e11			1.62847			0.814236	+	0.580535i	$0.197156\pi$
$692$	−1.38526e9			−0.00604099
$693$	8.60682e10	+	4.00956e11i	0.373173	+	1.73846i
$694$	1.63215e11			0.703592
$695$		0			0
$696$	5.72402e10	+	4.62571e10i	0.243929	+	0.197125i
$697$		−	6.54677e10i		−	0.277393i
$698$	−6.04343e10			−0.254602
$699$	7.17424e10	−	8.87767e10i	0.300516	−	0.371869i
$700$		0			0
$701$			2.35914e11i			0.976970i	0.872572	+	0.488485i	$0.162450\pi$
$701$			2.35914e11i			0.976970i	−0.872572	+	0.488485i	$0.837550\pi$
$702$	3.56824e10	−	7.05555e10i	0.146928	−	0.290524i
$703$		−	2.82884e11i		−	1.15821i
$704$		−	4.70498e10i		−	0.191543i
$705$		0			0
$706$	8.85146e10			0.356284
$707$	2.61274e11			1.04573
$708$	−4.03542e10	−	3.26111e10i	−0.160604	−	0.129788i
$709$	1.51154e11			0.598184			0.299092	−	0.954224i	$-0.403316\pi$
$709$	1.51154e11			0.598184			0.299092	+	0.954224i	$0.403316\pi$
$710$		0			0
$711$	1.26443e10	+	5.89046e10i	0.0494785	+	0.230500i
$712$			1.17667e11i			0.457861i
$713$	3.59635e10			0.139157
$714$	1.31832e11	+	1.06537e11i	0.507258	+	0.409926i
$715$		0			0
$716$			2.87772e10i			0.109495i
$717$	−1.44118e11	−	1.16465e11i	−0.545307	−	0.440675i
$718$			1.88619e11i			0.709723i
$719$			1.57719e10i			0.0590158i	0.999565	+	0.0295079i	$0.00939402\pi$
$719$			1.57719e10i			0.0590158i	−0.999565	+	0.0295079i	$0.990606\pi$
$720$		0			0
$721$	−1.47748e11			−0.546739
$722$	−4.24605e10			−0.156256
$723$	2.22673e11	−	2.75543e11i	0.814918	−	1.00841i
$724$	−1.67713e11			−0.610398
$725$		0			0
$726$	1.66449e11	−	2.05970e11i	0.599149	−	0.741409i
$727$		−	3.61913e11i		−	1.29559i	−0.761816	−	0.647794i	$-0.775692\pi$
$727$		−	3.61913e11i		−	1.29559i	0.761816	−	0.647794i	$-0.224308\pi$
$728$	5.30545e10			0.188884
$729$	1.67382e11	+	2.27486e11i	0.592651	+	0.805459i
$730$		0			0
$731$		−	5.18776e9i		−	0.0181681i
$732$	1.14552e11	−	1.41751e11i	0.398988	−	0.493722i
$733$			5.75659e10i			0.199411i	0.995017	+	0.0997056i	$0.0317901\pi$
$733$			5.75659e10i			0.199411i	−0.995017	+	0.0997056i	$0.968210\pi$
$734$			2.10951e11i			0.726772i
$735$		0			0
$736$	−9.14778e9			−0.0311748
$737$	3.84465e11			1.30313
$738$	7.15690e10	−	1.53628e10i	0.241268	−	0.0517900i
$739$	2.30778e11			0.773780			0.386890	−	0.922126i	$-0.373549\pi$
$739$	2.30778e11			0.773780			0.386890	+	0.922126i	$0.373549\pi$
$740$		0			0
$741$	1.19298e11	+	9.64077e10i	0.395696	+	0.319771i
$742$			1.64550e10i			0.0542852i
$743$	−4.84430e10			−0.158956			−0.0794778	−	0.996837i	$-0.525325\pi$
$743$	−4.84430e10			−0.158956			−0.0794778	+	0.996837i	$0.525325\pi$
$744$	−5.37284e10	+	6.64855e10i	−0.175353	+	0.216988i
$745$		0			0
$746$		−	3.82845e11i		−	1.23614i
$747$	1.19948e11	+	5.58790e11i	0.385223	+	1.79459i
$748$		−	1.90648e11i		−	0.609013i
$749$			5.31571e11i			1.68902i
$750$		0			0
$751$	1.03467e11			0.325269			0.162635	−	0.986686i	$-0.448001\pi$
$751$	1.03467e11			0.325269			0.162635	+	0.986686i	$0.448001\pi$
$752$	5.76667e10			0.180324
$753$	−1.12767e11	−	9.11295e10i	−0.350753	−	0.283452i
$754$	9.33419e10			0.288796
$755$		0			0
$756$	−8.55292e10	+	1.69119e11i	−0.261835	+	0.517731i
$757$		−	3.09395e11i		−	0.942170i	−0.882088	−	0.471085i	$-0.843863\pi$
$757$		−	3.09395e11i		−	0.942170i	0.882088	−	0.471085i	$-0.156137\pi$
$758$	−3.19146e11			−0.966748
$759$	−6.97524e10	−	5.63684e10i	−0.210180	−	0.169851i
$760$		0			0
$761$			3.57736e11i			1.06665i	0.845909	+	0.533327i	$0.179059\pi$
$761$			3.57736e11i			1.06665i	−0.845909	+	0.533327i	$0.820941\pi$
$762$	−8.93925e10	−	7.22401e10i	−0.265144	−	0.214268i
$763$			7.57677e11i			2.23556i
$764$		−	2.80300e11i		−	0.822715i
$765$		0			0
$766$	−2.06367e11			−0.599413
$767$	−6.58058e10			−0.190144
$768$	1.36665e10	−	1.69114e10i	0.0392837	−	0.0486111i
$769$	−6.91156e10			−0.197638			−0.0988190	−	0.995105i	$-0.531506\pi$
$769$	−6.91156e10			−0.197638			−0.0988190	+	0.995105i	$0.531506\pi$
$770$		0			0
$771$	1.12353e11	−	1.39030e11i	0.317957	−	0.393452i
$772$		−	2.19114e11i		−	0.616881i
$773$	4.96225e11			1.38983			0.694914	−	0.719093i	$-0.255443\pi$
$773$	4.96225e11			1.38983			0.694914	+	0.719093i	$0.255443\pi$
$774$	5.67123e9	−	1.21737e9i	0.0158021	−	0.00339203i
$775$		0			0
$776$		−	1.86410e11i		−	0.514071i
$777$	2.78637e11	−	3.44796e11i	0.764460	−	0.945971i
$778$		−	2.19910e11i		−	0.600242i
$779$			1.42004e11i			0.385612i
$780$		0			0
$781$	−5.80858e11			−1.56123
$782$	−3.70673e10			−0.0991206
$783$	−1.50477e11	+	2.97540e11i	−0.400334	+	0.791588i
$784$	−3.27188e10			−0.0866029
$785$		0			0
$786$	−8.84188e10	−	7.14532e10i	−0.231662	−	0.187211i
$787$		−	1.30010e11i		−	0.338906i	−0.985538	−	0.169453i	$-0.945800\pi$
$787$		−	1.30010e11i		−	0.338906i	0.985538	−	0.169453i	$-0.0542000\pi$
$788$	3.37008e11			0.874048
$789$	−9.05229e10	+	1.12016e11i	−0.233588	+	0.289050i
$790$		0			0
$791$		−	2.14296e11i		−	0.547404i
$792$	2.08416e11	−	4.47380e10i	0.529700	−	0.113704i
$793$		−	2.31154e11i		−	0.584533i
$794$			1.88621e11i			0.474580i
$795$		0			0
$796$	−3.77911e11			−0.941319
$797$	4.08242e11			1.01178			0.505888	−	0.862599i	$-0.331165\pi$
$797$	4.08242e11			1.01178			0.505888	+	0.862599i	$0.331165\pi$
$798$	−2.85953e11	−	2.31085e11i	−0.705153	−	0.569850i
$799$	2.33668e11			0.573341
$800$		0			0
$801$	−5.21226e11	+	1.11885e11i	−1.26618	+	0.271796i
$802$		−	3.74299e11i		−	0.904734i
$803$	6.31308e11			1.51838
$804$	1.38191e11	+	1.11675e11i	0.330716	+	0.267259i
$805$		0			0
$806$			1.08418e11i			0.256899i
$807$	−3.76284e11	−	3.04084e11i	−0.887201	−	0.716966i
$808$		−	1.35809e11i		−	0.318628i
$809$		−	2.23269e11i		−	0.521235i	−0.965442	−	0.260618i	$-0.916074\pi$
$809$		−	2.23269e11i		−	0.521235i	0.965442	−	0.260618i	$-0.0839262\pi$
$810$		0			0
$811$	1.75526e11			0.405750			0.202875	−	0.979205i	$-0.434972\pi$
$811$	1.75526e11			0.405750			0.202875	+	0.979205i	$0.434972\pi$
$812$	−2.23736e11			−0.514651
$813$	1.65237e11	−	2.04470e11i	0.378220	−	0.468023i
$814$	−4.98624e11			−1.13573
$815$		0			0
$816$	5.53774e10	−	6.85260e10i	0.124903	−	0.154559i
$817$			1.12526e10i			0.0252560i
$818$	−5.69449e11			−1.27187
$819$	5.04476e10	+	2.35015e11i	0.112126	+	0.522347i
$820$		0			0
$821$		−	8.37441e10i		−	0.184324i	−0.995744	−	0.0921619i	$-0.970622\pi$
$821$		−	8.37441e10i		−	0.184324i	0.995744	−	0.0921619i	$-0.0293777\pi$
$822$	−3.17230e11	+	3.92552e11i	−0.694843	+	0.859825i
$823$		−	5.41972e11i		−	1.18135i	−0.806911	−	0.590673i	$-0.798862\pi$
$823$		−	5.41972e11i		−	1.18135i	0.806911	−	0.590673i	$-0.201138\pi$
$824$			7.67989e10i			0.166589i
$825$		0			0
$826$	1.57734e11			0.338848
$827$	5.30564e11			1.13427			0.567134	−	0.823626i	$-0.308052\pi$
$827$	5.30564e11			1.13427			0.567134	+	0.823626i	$0.308052\pi$
$828$	−8.69830e9	−	4.05218e10i	−0.0185060	−	0.0862119i
$829$	−4.65551e11			−0.985710			−0.492855	−	0.870111i	$-0.664047\pi$
$829$	−4.65551e11			−0.985710			−0.492855	+	0.870111i	$0.664047\pi$
$830$		0			0
$831$	8.45066e10	+	6.82916e10i	0.177209	+	0.143207i
$832$		−	2.75775e10i		−	0.0575523i
$833$	−1.32578e11			−0.275354
$834$	−4.37335e10	+	5.41174e10i	−0.0903962	+	0.111860i
$835$		0			0
$836$			4.13529e11i			0.846605i
$837$	−3.45598e11	−	1.74781e11i	−0.704158	−	0.356117i
$838$			3.32940e11i			0.675133i
$839$		−	7.93304e11i		−	1.60100i	−0.599332	−	0.800501i	$-0.704567\pi$
$839$		−	7.93304e11i		−	1.60100i	0.599332	−	0.800501i	$-0.295433\pi$
$840$		0			0
$841$	1.06614e11			0.213122
$842$	3.77021e11			0.750097
$843$	−1.19229e11	−	9.63520e10i	−0.236088	−	0.190788i
$844$	−3.40927e11			−0.671880
$845$		0			0
$846$	5.48332e10	+	2.55445e11i	0.107044	+	0.498674i
$847$			8.05082e11i			1.56425i
$848$	8.55324e9			0.0165405
$849$	−4.33624e11	−	3.50421e11i	−0.834608	−	0.674465i
$850$		0			0
$851$			9.69462e10i			0.184847i
$852$	−2.08782e11	−	1.68721e11i	−0.396219	−	0.320193i
$853$			4.55056e10i			0.0859545i	0.999076	+	0.0429772i	$0.0136843\pi$
$853$			4.55056e10i			0.0859545i	−0.999076	+	0.0429772i	$0.986316\pi$
$854$			5.54067e11i			1.04167i
$855$		0			0
$856$	2.76309e11			0.514635
$857$	−8.48487e11			−1.57297			−0.786487	−	0.617606i	$-0.788102\pi$
$857$	−8.48487e11			−1.57297			−0.786487	+	0.617606i	$0.788102\pi$
$858$	1.69932e11	−	2.10280e11i	0.313564	−	0.388016i
$859$	7.64741e11			1.40456			0.702282	−	0.711899i	$-0.252164\pi$
$859$	7.64741e11			1.40456			0.702282	+	0.711899i	$0.252164\pi$
$860$		0			0
$861$	−1.39872e11	+	1.73083e11i	−0.254518	+	0.314950i
$862$			6.36137e11i			1.15218i
$863$	−4.55374e11			−0.820966			−0.410483	−	0.911868i	$-0.634640\pi$
$863$	−4.55374e11			−0.820966			−0.410483	+	0.911868i	$0.634640\pi$
$864$	8.79074e10	+	4.44578e10i	0.157750	+	0.0797799i
$865$		0			0
$866$			2.47552e11i			0.440144i
$867$	−1.30755e11	+	1.61802e11i	−0.231411	+	0.286356i
$868$		−	2.59874e11i		−	0.457808i
$869$			2.06010e11i			0.361251i
$870$		0			0
$871$	2.25348e11			0.391545
$872$	3.93838e11			0.681164
$873$	8.25739e11	−	1.77251e11i	1.42163	−	0.305163i
$874$	8.04015e10			0.137790
$875$		0			0
$876$	2.26916e11	+	1.83375e11i	0.385343	+	0.311404i
$877$		−	8.42742e11i		−	1.42461i	−0.701869	−	0.712306i	$-0.747651\pi$
$877$		−	8.42742e11i		−	1.42461i	0.701869	−	0.712306i	$-0.252349\pi$
$878$	2.12686e11			0.357899
$879$	2.19618e11	−	2.71764e11i	0.367886	−	0.455235i
$880$		0			0
$881$		−	1.12314e12i		−	1.86436i	−0.361994	−	0.932181i	$-0.617904\pi$
$881$		−	1.12314e12i		−	1.86436i	0.361994	−	0.932181i	$-0.382096\pi$
$882$	−3.11111e10	−	1.44934e11i	−0.0514093	−	0.239495i
$883$			6.25330e11i			1.02865i	0.857596	+	0.514323i	$0.171957\pi$
$883$			6.25330e11i			1.02865i	−0.857596	+	0.514323i	$0.828043\pi$
$884$		−	1.11746e11i		−	0.182988i
$885$		0			0
$886$	−7.39456e11			−1.19999
$887$	−4.73224e11			−0.764491			−0.382246	−	0.924061i	$-0.624849\pi$
$887$	−4.73224e11			−0.764491			−0.382246	+	0.924061i	$0.624849\pi$
$888$	−1.79224e11	−	1.44835e11i	−0.288233	−	0.232927i
$889$	3.49411e11			0.559409
$890$		0			0
$891$	3.96351e11	+	8.80677e11i	0.628882	+	1.39735i
$892$		−	2.61460e10i		−	0.0412996i
$893$	−5.06843e11			−0.797017
$894$	−5.23983e11	−	4.23442e11i	−0.820290	−	0.662894i
$895$		0			0
$896$			6.61022e10i			0.102561i
$897$	−4.08843e10	−	3.30395e10i	−0.0631520	−	0.0510345i
$898$			1.78852e11i			0.275035i
$899$		−	4.57211e11i		−	0.699968i
$900$		0			0
$901$	3.46582e10			0.0525904
$902$	2.50302e11			0.378128
$903$	−1.10837e10	+	1.37153e10i	−0.0166699	+	0.0206279i
$904$	−1.11390e11			−0.166792
$905$		0			0
$906$	−1.73743e11	+	2.14996e11i	−0.257866	+	0.319093i
$907$			9.14524e11i			1.35134i	0.737202	+	0.675672i	$0.236147\pi$
$907$			9.14524e11i			1.35134i	−0.737202	+	0.675672i	$0.763853\pi$
$908$	5.45488e10			0.0802495
$909$	6.01593e11	−	1.29136e11i	0.881144	−	0.189144i
$910$		0			0
$911$		−	8.57040e11i		−	1.24431i	−0.782895	−	0.622154i	$-0.786258\pi$
$911$		−	8.57040e11i		−	1.24431i	0.782895	−	0.622154i	$-0.213742\pi$
$912$	−1.20117e11	+	1.48638e11i	−0.173631	+	0.214857i
$913$			1.95429e12i			2.81258i
$914$			3.73805e10i			0.0535624i
$915$		0			0
$916$	3.91404e10			0.0555960
$917$	3.45605e11			0.488768
$918$	3.56205e11	+	1.80146e11i	0.501568	+	0.253660i
$919$	−9.47490e10			−0.132835			−0.0664175	−	0.997792i	$-0.521157\pi$
$919$	−9.47490e10			−0.132835			−0.0664175	+	0.997792i	$0.521157\pi$
$920$		0			0
$921$	5.24258e11	+	4.23664e11i	0.728629	+	0.588821i
$922$			3.73510e11i			0.516867i
$923$	−3.40462e11			−0.469096
$924$	−4.07321e11	+	5.04033e11i	−0.558790	+	0.691467i
$925$		0			0
$926$		−	6.37095e11i		−	0.866483i
$927$	−3.40195e11	+	7.30254e10i	−0.460690	+	0.0988906i
$928$			1.16298e11i			0.156812i
$929$		−	2.06406e11i		−	0.277115i	−0.990354	−	0.138557i	$-0.955753\pi$
$929$		−	2.06406e11i		−	0.277115i	0.990354	−	0.138557i	$-0.0442466\pi$
$930$		0			0
$931$	2.87571e11			0.382778
$932$	1.80372e11			0.239059
$933$	−6.87858e11	−	5.55873e11i	−0.907762	−	0.733583i
$934$	−6.08875e11			−0.800094
$935$		0			0
$936$	1.22160e11	−	2.62225e10i	0.159157	−	0.0341642i
$937$			2.99452e11i			0.388480i	0.980954	+	0.194240i	$0.0622241\pi$
$937$			2.99452e11i			0.388480i	−0.980954	+	0.194240i	$0.937776\pi$
$938$	−5.40151e11			−0.697756
$939$	3.90571e11	+	3.15629e11i	0.502386	+	0.405989i
$940$		0			0
$941$		−	9.75658e11i		−	1.24434i	−0.782882	−	0.622170i	$-0.786251\pi$
$941$		−	9.75658e11i		−	1.24434i	0.782882	−	0.622170i	$-0.213749\pi$
$942$	−1.14927e11	−	9.28750e10i	−0.145955	−	0.117949i
$943$		−	4.86657e10i		−	0.0615426i
$944$		−	8.19896e10i		−	0.103245i
$945$		0			0
$946$	1.98343e10			0.0247658
$947$	6.85570e11			0.852416			0.426208	−	0.904625i	$-0.359849\pi$
$947$	6.85570e11			0.852416			0.426208	+	0.904625i	$0.359849\pi$
$948$	−5.98395e10	+	7.40477e10i	−0.0740892	+	0.0916807i
$949$	3.70032e11			0.456220
$950$		0			0
$951$	9.51386e11	−	1.17728e12i	1.16315	−	1.43932i
$952$			2.67850e11i			0.326094i
$953$	−1.81880e11			−0.220502			−0.110251	−	0.993904i	$-0.535165\pi$
$953$	−1.81880e11			−0.220502			−0.110251	+	0.993904i	$0.535165\pi$
$954$	8.13298e9	+	3.78882e10i	0.00981875	+	0.0457415i
$955$		0			0
$956$		−	2.92811e11i		−	0.350555i
$957$	−7.16623e11	+	8.86776e11i	−0.854364	+	1.05722i
$958$		−	9.08142e11i		−	1.07818i
$959$		−	1.53438e12i		−	1.81409i
$960$		0			0
$961$	−3.21832e11			−0.377342
$962$	−2.92261e11			−0.341248
$963$	2.62732e11	+	1.22396e12i	0.305498	+	1.42319i
$964$	5.59834e11			0.648263
$965$		0			0
$966$	9.79980e10	+	7.91944e10i	0.112540	+	0.0909464i
$967$			1.51799e11i			0.173605i	0.996226	+	0.0868024i	$0.0276649\pi$
$967$			1.51799e11i			0.173605i	−0.996226	+	0.0868024i	$0.972335\pi$
$968$	4.18479e11			0.476620
$969$	−4.86722e11	+	6.02288e11i	−0.552060	+	0.683139i
$970$		0			0
$971$			2.30877e11i			0.259718i	0.991532	+	0.129859i	$0.0414525\pi$
$971$			2.30877e11i			0.259718i	−0.991532	+	0.129859i	$0.958547\pi$
$972$	−1.13346e11	+	4.31676e11i	−0.126982	+	0.483607i
$973$		−	2.11530e11i		−	0.236005i
$974$		−	7.99985e11i		−	0.888886i
$975$		0			0
$976$	2.88002e11			0.317393
$977$	−1.10823e12			−1.21633			−0.608163	−	0.793812i	$-0.708093\pi$
$977$	−1.10823e12			−1.21633			−0.608163	+	0.793812i	$0.708093\pi$
$978$	1.57686e11	+	1.27430e11i	0.172361	+	0.139289i
$979$	−1.82291e12			−1.98443
$980$		0			0
$981$	3.74487e11	+	1.74458e12i	0.404353	+	1.88371i
$982$		−	6.86602e11i		−	0.738344i
$983$	−3.64534e11			−0.390413			−0.195207	−	0.980762i	$-0.562538\pi$
$983$	−3.64534e11			−0.390413			−0.195207	+	0.980762i	$0.562538\pi$
$984$	8.99679e10	+	7.27051e10i	0.0959638	+	0.0775504i
$985$		0			0
$986$			4.71244e11i			0.498584i
$987$	−6.17770e11	−	4.99233e11i	−0.650966	−	0.526060i
$988$			2.42384e11i			0.254376i
$989$		−	3.85634e9i		−	0.00403079i
$990$		0			0
$991$	1.27281e10			0.0131968			0.00659842	−	0.999978i	$-0.497900\pi$
$991$	1.27281e10			0.0131968			0.00659842	+	0.999978i	$0.497900\pi$
$992$	−1.35082e11			−0.139492
$993$	1.65197e11	−	2.04421e11i	0.169905	−	0.210247i
$994$	8.16072e11			0.835956
$995$		0			0
$996$	−5.67659e11	+	7.02442e11i	−0.576833	+	0.713795i
$997$			1.56439e12i			1.58330i	0.610973	+	0.791651i	$0.290778\pi$
$997$			1.56439e12i			1.58330i	−0.610973	+	0.791651i	$0.709222\pi$
$998$	−1.18710e12			−1.19665
$999$	4.71155e11	−	9.31624e11i	0.473044	−	0.935359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.9.b.a.149.1		4
3.2	odd	2	inner	150.9.b.a.149.3		4
5.2	odd	4		6.9.b.a.5.1	✓	2
5.3	odd	4		150.9.d.a.101.2		2
5.4	even	2	inner	150.9.b.a.149.4		4
15.2	even	4		6.9.b.a.5.2	yes	2
15.8	even	4		150.9.d.a.101.1		2
15.14	odd	2	inner	150.9.b.a.149.2		4
20.7	even	4		48.9.e.d.17.2		2
40.27	even	4		192.9.e.c.65.1		2
40.37	odd	4		192.9.e.h.65.2		2
45.2	even	12		162.9.d.a.53.2		4
45.7	odd	12		162.9.d.a.53.1		4
45.22	odd	12		162.9.d.a.107.2		4
45.32	even	12		162.9.d.a.107.1		4
60.47	odd	4		48.9.e.d.17.1		2
120.77	even	4		192.9.e.h.65.1		2
120.107	odd	4		192.9.e.c.65.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.9.b.a.5.1	✓	2	5.2	odd	4
6.9.b.a.5.2	yes	2	15.2	even	4
48.9.e.d.17.1		2	60.47	odd	4
48.9.e.d.17.2		2	20.7	even	4
150.9.b.a.149.1		4	1.1	even	1	trivial
150.9.b.a.149.2		4	15.14	odd	2	inner
150.9.b.a.149.3		4	3.2	odd	2	inner
150.9.b.a.149.4		4	5.4	even	2	inner
150.9.d.a.101.1		2	15.8	even	4
150.9.d.a.101.2		2	5.3	odd	4
162.9.d.a.53.1		4	45.7	odd	12
162.9.d.a.53.2		4	45.2	even	12
162.9.d.a.107.1		4	45.32	even	12
162.9.d.a.107.2		4	45.22	odd	12
192.9.e.c.65.1		2	40.27	even	4
192.9.e.c.65.2		2	120.107	odd	4
192.9.e.h.65.1		2	120.77	even	4
192.9.e.h.65.2		2	40.37	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	150.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-11.3137 q^{2} +(50.9117 - 63.0000i) q^{3} +128.000 q^{4} +(-576.000 + 712.764i) q^{6} -2786.00i q^{7} -1448.15 q^{8} +(-1377.00 - 6414.87i) q^{9} +O(q^{10})\)	\(q-11.3137 q^{2} +(50.9117 - 63.0000i) q^{3} +128.000 q^{4} +(-576.000 + 712.764i) q^{6} -2786.00i q^{7} -1448.15 q^{8} +(-1377.00 - 6414.87i) q^{9} -22435.1i q^{11} +(6516.70 - 8064.00i) q^{12} -13150.0i q^{13} +31520.0i q^{14} +16384.0 q^{16} +66388.8 q^{17} +(15579.0 + 72576.0i) q^{18} -144002. q^{19} +(-175518. - 141840. i) q^{21} +253824. i q^{22} +49350.4 q^{23} +(-73728.0 + 91233.7i) q^{24} +148775. i q^{26} +(-474242. - 239841. i) q^{27} -356608. i q^{28} -627402. i q^{29} +728738. q^{31} -185364. q^{32} +(-1.41341e6 - 1.14221e6i) q^{33} -751104. q^{34} +(-176256. - 821104. i) q^{36} +1.96445e6i q^{37} +1.62920e6 q^{38} +(-828450. - 669489. i) q^{39} -986125. i q^{41} +(1.98576e6 + 1.60474e6i) q^{42} -78142.0i q^{43} -2.87169e6i q^{44} -558336. q^{46} +3.51969e6 q^{47} +(834137. - 1.03219e6i) q^{48} -1.99700e6 q^{49} +(3.37997e6 - 4.18250e6i) q^{51} -1.68320e6i q^{52} +522048. q^{53} +(5.36544e6 + 2.71349e6i) q^{54} +4.03456e6i q^{56} +(-7.33138e6 + 9.07213e6i) q^{57} +7.09824e6i q^{58} -5.00425e6i q^{59} +1.75783e7 q^{61} -8.24473e6 q^{62} +(-1.78718e7 + 3.83632e6i) q^{63} +2.09715e6 q^{64} +(1.59909e7 + 1.29226e7i) q^{66} +1.71368e7i q^{67} +8.49777e6 q^{68} +(2.51251e6 - 3.10907e6i) q^{69} -2.58906e7i q^{71} +(1.99411e6 + 9.28973e6i) q^{72} +2.81393e7i q^{73} -2.22252e7i q^{74} -1.84323e7 q^{76} -6.25041e7 q^{77} +(9.37284e6 + 7.57440e6i) q^{78} -9.18250e6 q^{79} +(-3.92545e7 + 1.76666e7i) q^{81} +1.11567e7i q^{82} -8.71084e7 q^{83} +(-2.24663e7 - 1.81555e7i) q^{84} +884076. i q^{86} +(-3.95263e7 - 3.19421e7i) q^{87} +3.24895e7i q^{88} -8.12528e7i q^{89} -3.66359e7 q^{91} +6.31685e6 q^{92} +(3.71013e7 - 4.59105e7i) q^{93} -3.98208e7 q^{94} +(-9.43718e6 + 1.16779e7i) q^{96} +1.28723e8i q^{97} +2.25934e7 q^{98} +(-1.43918e8 + 3.08931e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 512 q^{4} - 2304 q^{6} - 5508 q^{9}+O(q^{10}) \) 4 * q + 512 * q^4 - 2304 * q^6 - 5508 * q^9	\( 4 q + 512 q^{4} - 2304 q^{6} - 5508 q^{9} + 65536 q^{16} - 576008 q^{19} - 702072 q^{21} - 294912 q^{24} + 2914952 q^{31} - 3004416 q^{34} - 705024 q^{36} - 3313800 q^{39} - 2233344 q^{46} - 7987980 q^{49} + 13519872 q^{51} + 21461760 q^{54} + 70313096 q^{61} + 8388608 q^{64} + 63963648 q^{66} + 10050048 q^{69} - 73729024 q^{76} - 36729992 q^{79} - 157017852 q^{81} - 89865216 q^{84} - 146543600 q^{91} - 159283200 q^{94} - 37748736 q^{96} - 575672832 q^{99}+O(q^{100}) \) 4 * q + 512 * q^4 - 2304 * q^6 - 5508 * q^9 + 65536 * q^16 - 576008 * q^19 - 702072 * q^21 - 294912 * q^24 + 2914952 * q^31 - 3004416 * q^34 - 705024 * q^36 - 3313800 * q^39 - 2233344 * q^46 - 7987980 * q^49 + 13519872 * q^51 + 21461760 * q^54 + 70313096 * q^61 + 8388608 * q^64 + 63963648 * q^66 + 10050048 * q^69 - 73729024 * q^76 - 36729992 * q^79 - 157017852 * q^81 - 89865216 * q^84 - 146543600 * q^91 - 159283200 * q^94 - 37748736 * q^96 - 575672832 * q^99

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