LMFDB - Embedded newform 240.9.c.c.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,9,Mod(209,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("240.209");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	240.c (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:	$97.7708664147$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 2096 x^{10} + 1966565 x^{8} + 942732880 x^{6} + 407378811520 x^{4} + 58185108489824 x^{2} + 32\!\cdots\!64 $ x^12 + 2096x^10 + 1966565x^8 + 942732880x^6 + 407378811520x^4 + 58185108489824*x^2 + 3250133486843364
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{18}\cdot 5^{7} $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.3
Root			$2.83292 + 10.0603i$ of defining polynomial
Character	$\chi$	$=$	240.209
Dual form			240.9.c.c.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-35.3550 - 72.8768i) q^{3} +(-531.836 + 328.291i) q^{5} +1674.62i q^{7} +(-4061.05 + 5153.12i) q^{9} +O(q^{10})$	\(q+(-35.3550 - 72.8768i) q^{3} +(-531.836 + 328.291i) q^{5} +1674.62i q^{7} +(-4061.05 + 5153.12i) q^{9} -21417.9i q^{11} +5980.82i q^{13} +(42727.9 + 27151.8i) q^{15} +69210.3 q^{17} +18044.8 q^{19} +(122041. - 59206.3i) q^{21} -91800.0 q^{23} +(175075. - 349194. i) q^{25} +(519121. + 113768. i) q^{27} +1.12754e6i q^{29} +1.27927e6 q^{31} +(-1.56087e6 + 757230. i) q^{33} +(-549764. - 890626. i) q^{35} -2.19804e6i q^{37} +(435863. - 211452. i) q^{39} -29007.4i q^{41} -6.78169e6i q^{43} +(468092. - 4.07382e6i) q^{45} -1.96089e6 q^{47} +2.96044e6 q^{49} +(-2.44693e6 - 5.04382e6i) q^{51} -1.23039e7 q^{53} +(7.03131e6 + 1.13908e7i) q^{55} +(-637973. - 1.31504e6i) q^{57} -5.58621e6i q^{59} +312034. q^{61} +(-8.62953e6 - 6.80073e6i) q^{63} +(-1.96345e6 - 3.18082e6i) q^{65} +853503. i q^{67} +(3.24559e6 + 6.69009e6i) q^{69} +3.18282e7i q^{71} +2.36800e6i q^{73} +(-3.16379e7 - 413140. i) q^{75} +3.58669e7 q^{77} -2.92328e7 q^{79} +(-1.00625e7 - 4.18541e7i) q^{81} -6.73076e7 q^{83} +(-3.68086e7 + 2.27211e7i) q^{85} +(8.21715e7 - 3.98642e7i) q^{87} +4.90240e7i q^{89} -1.00156e7 q^{91} +(-4.52287e7 - 9.32293e7i) q^{93} +(-9.59686e6 + 5.92394e6i) q^{95} +7.18400e7i q^{97} +(1.10369e8 + 8.69792e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 22824 q^{9}+O(q^{10}) $ 12 * q - 22824 * q^9	$ 12 q - 22824 q^{9} + 95520 q^{15} - 276192 q^{19} - 604044 q^{21} - 2036220 q^{25} + 279216 q^{31} - 3780864 q^{39} + 9523980 q^{45} - 6222300 q^{49} - 3931248 q^{51} + 16903440 q^{55} - 91958256 q^{61} + 8138748 q^{69} - 15031440 q^{75} - 420402672 q^{79} + 98480772 q^{81} - 117091440 q^{85} + 100211328 q^{91} + 640360080 q^{99}+O(q^{100}) $ 12 * q - 22824 * q^9 + 95520 * q^15 - 276192 * q^19 - 604044 * q^21 - 2036220 * q^25 + 279216 * q^31 - 3780864 * q^39 + 9523980 * q^45 - 6222300 * q^49 - 3931248 * q^51 + 16903440 * q^55 - 91958256 * q^61 + 8138748 * q^69 - 15031440 * q^75 - 420402672 * q^79 + 98480772 * q^81 - 117091440 * q^85 + 100211328 * q^91 + 640360080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−35.3550	−	72.8768i	−0.436481	−	0.899713i
$3$	−35.3550	−	72.8768i	−0.436481	−	0.899713i
$4$		0			0
$5$	−531.836	+	328.291i	−0.850938	+	0.525266i
$5$	−531.836	+	328.291i	−0.850938	+	0.525266i
$6$		0			0
$7$			1674.62i			0.697469i	0.937222	+	0.348734i	$0.113388\pi$
$7$			1674.62i			0.697469i	−0.937222	+	0.348734i	$0.886612\pi$
$8$		0			0
$9$	−4061.05	+	5153.12i	−0.618968	+	0.785416i
$10$		0			0
$11$		−	21417.9i		−	1.46287i	−0.681910	−	0.731436i	$-0.738850\pi$
$11$		−	21417.9i		−	1.46287i	0.681910	−	0.731436i	$-0.261150\pi$
$12$		0			0
$13$			5980.82i			0.209405i	0.994504	+	0.104703i	$0.0333890\pi$
$13$			5980.82i			0.209405i	−0.994504	+	0.104703i	$0.966611\pi$
$14$		0			0
$15$	42727.9	+	27151.8i	0.844007	+	0.536332i
$16$		0			0
$17$	69210.3			0.828657			0.414329	−	0.910127i	$-0.364016\pi$
$17$	69210.3			0.828657			0.414329	+	0.910127i	$0.364016\pi$
$18$		0			0
$19$	18044.8			0.138464			0.0692320	−	0.997601i	$-0.477945\pi$
$19$	18044.8			0.138464			0.0692320	+	0.997601i	$0.477945\pi$
$20$		0			0
$21$	122041.	−	59206.3i	0.627522	−	0.304432i
$22$		0			0
$23$	−91800.0			−0.328043			−0.164022	−	0.986457i	$-0.552447\pi$
$23$	−91800.0			−0.328043			−0.164022	+	0.986457i	$0.552447\pi$
$24$		0			0
$25$	175075.	−	349194.i	0.448192	−	0.893937i
$26$		0			0
$27$	519121.	+	113768.i	0.976817	+	0.214074i
$28$		0			0
$29$			1.12754e6i			1.59419i	0.603854	+	0.797095i	$0.293631\pi$
$29$			1.12754e6i			1.59419i	−0.603854	+	0.797095i	$0.706369\pi$
$30$		0			0
$31$	1.27927e6			1.38521			0.692607	−	0.721316i	$-0.256462\pi$
$31$	1.27927e6			1.38521			0.692607	+	0.721316i	$0.256462\pi$
$32$		0			0
$33$	−1.56087e6	+	757230.i	−1.31617	+	0.638517i
$34$		0			0
$35$	−549764.	−	890626.i	−0.366356	−	0.593503i
$36$		0			0
$37$		−	2.19804e6i		−	1.17281i	−0.810018	−	0.586405i	$-0.800543\pi$
$37$		−	2.19804e6i		−	1.17281i	0.810018	−	0.586405i	$-0.199457\pi$
$38$		0			0
$39$	435863.	−	211452.i	0.188404	−	0.0914014i
$40$		0			0
$41$		−	29007.4i		−	0.0102653i	−0.999987	−	0.00513267i	$-0.998366\pi$
$41$		−	29007.4i		−	0.0102653i	0.999987	−	0.00513267i	$-0.00163379\pi$
$42$		0			0
$43$		−	6.78169e6i		−	1.98365i	−0.127625	−	0.991823i	$-0.540735\pi$
$43$		−	6.78169e6i		−	1.98365i	0.127625	−	0.991823i	$-0.459265\pi$
$44$		0			0
$45$	468092.	−	4.07382e6i	0.114151	−	0.993463i
$46$		0			0
$47$	−1.96089e6			−0.401847			−0.200924	−	0.979607i	$-0.564394\pi$
$47$	−1.96089e6			−0.401847			−0.200924	+	0.979607i	$0.564394\pi$
$48$		0			0
$49$	2.96044e6			0.513537
$50$		0			0
$51$	−2.44693e6	−	5.04382e6i	−0.361694	−	0.745554i
$52$		0			0
$53$	−1.23039e7			−1.55933			−0.779664	−	0.626198i	$-0.784610\pi$
$53$	−1.23039e7			−1.55933			−0.779664	+	0.626198i	$0.784610\pi$
$54$		0			0
$55$	7.03131e6	+	1.13908e7i	0.768397	+	1.24481i
$56$		0			0
$57$	−637973.	−	1.31504e6i	−0.0604370	−	0.124578i
$58$		0			0
$59$		−	5.58621e6i		−	0.461009i	−0.973071	−	0.230504i	$-0.925962\pi$
$59$		−	5.58621e6i		−	0.461009i	0.973071	−	0.230504i	$-0.0740376\pi$
$60$		0			0
$61$	312034.			0.0225363			0.0112681	−	0.999937i	$-0.496413\pi$
$61$	312034.			0.0225363			0.0112681	+	0.999937i	$0.496413\pi$
$62$		0			0
$63$	−8.62953e6	−	6.80073e6i	−0.547803	−	0.431711i
$64$		0			0
$65$	−1.96345e6	−	3.18082e6i	−0.109993	−	0.178191i
$66$		0			0
$67$			853503.i			0.0423551i	0.999776	+	0.0211775i	$0.00674153\pi$
$67$			853503.i			0.0423551i	−0.999776	+	0.0211775i	$0.993258\pi$
$68$		0			0
$69$	3.24559e6	+	6.69009e6i	0.143185	+	0.295145i
$70$		0			0
$71$			3.18282e7i			1.25250i	0.779621	+	0.626252i	$0.215412\pi$
$71$			3.18282e7i			1.25250i	−0.779621	+	0.626252i	$0.784588\pi$
$72$		0			0
$73$			2.36800e6i			0.0833855i	0.999130	+	0.0416927i	$0.0132751\pi$
$73$			2.36800e6i			0.0833855i	−0.999130	+	0.0416927i	$0.986725\pi$
$74$		0			0
$75$	−3.16379e7	−	413140.i	−0.999915	−	0.0130573i
$76$		0			0
$77$	3.58669e7			1.02031
$78$		0			0
$79$	−2.92328e7			−0.750520			−0.375260	−	0.926920i	$-0.622447\pi$
$79$	−2.92328e7			−0.750520			−0.375260	+	0.926920i	$0.622447\pi$
$80$		0			0
$81$	−1.00625e7	−	4.18541e7i	−0.233757	−	0.972295i
$82$		0			0
$83$	−6.73076e7			−1.41825			−0.709124	−	0.705084i	$-0.750909\pi$
$83$	−6.73076e7			−1.41825			−0.709124	+	0.705084i	$0.750909\pi$
$84$		0			0
$85$	−3.68086e7	+	2.27211e7i	−0.705136	+	0.435265i
$86$		0			0
$87$	8.21715e7	−	3.98642e7i	1.43431	−	0.695834i
$88$		0			0
$89$			4.90240e7i			0.781355i	0.920528	+	0.390678i	$0.127759\pi$
$89$			4.90240e7i			0.781355i	−0.920528	+	0.390678i	$0.872241\pi$
$90$		0			0
$91$	−1.00156e7			−0.146054
$92$		0			0
$93$	−4.52287e7	−	9.32293e7i	−0.604620	−	1.24629i
$94$		0			0
$95$	−9.59686e6	+	5.92394e6i	−0.117824	+	0.0727304i
$96$		0			0
$97$			7.18400e7i			0.811483i	0.913988	+	0.405741i	$0.132987\pi$
$97$			7.18400e7i			0.811483i	−0.913988	+	0.405741i	$0.867013\pi$
$98$		0			0
$99$	1.10369e8	+	8.69792e7i	1.14896	+	0.905471i
$100$		0			0
$101$			1.12197e8i			1.07819i	0.842244	+	0.539097i	$0.181234\pi$
$101$			1.12197e8i			1.07819i	−0.842244	+	0.539097i	$0.818766\pi$
$102$		0			0
$103$			1.33889e8i			1.18959i	0.803877	+	0.594795i	$0.202767\pi$
$103$			1.33889e8i			1.18959i	−0.803877	+	0.594795i	$0.797233\pi$
$104$		0			0
$105$	−4.54690e7	+	7.15531e7i	−0.374075	+	0.588669i
$106$		0			0
$107$	−3.67153e7			−0.280100			−0.140050	−	0.990144i	$-0.544726\pi$
$107$	−3.67153e7			−0.280100			−0.140050	+	0.990144i	$0.544726\pi$
$108$		0			0
$109$	1.68006e8			1.19020			0.595099	−	0.803652i	$-0.297113\pi$
$109$	1.68006e8			1.19020			0.595099	+	0.803652i	$0.297113\pi$
$110$		0			0
$111$	−1.60186e8	+	7.77115e7i	−1.05519	+	0.511910i
$112$		0			0
$113$	9.78362e7			0.600048			0.300024	−	0.953932i	$-0.403005\pi$
$113$	9.78362e7			0.600048			0.300024	+	0.953932i	$0.403005\pi$
$114$		0			0
$115$	4.88226e7	−	3.01371e7i	0.279145	−	0.172310i
$116$		0			0
$117$	−3.08198e7	−	2.42884e7i	−0.164470	−	0.129615i
$118$		0			0
$119$			1.15901e8i			0.577963i
$120$		0			0
$121$	−2.44368e8			−1.14000
$122$		0			0
$123$	−2.11397e6	+	1.02556e6i	−0.00923586	+	0.00448063i
$124$		0			0
$125$	2.15261e7	+	2.43190e8i	0.0881709	+	0.996105i
$126$		0			0
$127$		−	1.37799e8i		−	0.529701i	−0.964289	−	0.264851i	$-0.914677\pi$
$127$		−	1.37799e8i		−	0.529701i	0.964289	−	0.264851i	$-0.0853227\pi$
$128$		0			0
$129$	−4.94228e8	+	2.39767e8i	−1.78471	+	0.865824i
$130$		0			0
$131$		−	7.11572e7i		−	0.241620i	−0.992676	−	0.120810i	$-0.961451\pi$
$131$		−	7.11572e7i		−	0.241620i	0.992676	−	0.120810i	$-0.0385492\pi$
$132$		0			0
$133$			3.02182e7i			0.0965743i
$134$		0			0
$135$	−3.13436e8	+	1.09917e8i	−0.943657	+	0.330925i
$136$		0			0
$137$	−5.04740e8			−1.43280			−0.716400	−	0.697689i	$-0.754212\pi$
$137$	−5.04740e8			−1.43280			−0.716400	+	0.697689i	$0.754212\pi$
$138$		0			0
$139$	−2.09113e8			−0.560171			−0.280086	−	0.959975i	$-0.590363\pi$
$139$	−2.09113e8			−0.560171			−0.280086	+	0.959975i	$0.590363\pi$
$140$		0			0
$141$	6.93271e7	+	1.42903e8i	0.175399	+	0.361547i
$142$		0			0
$143$	1.28097e8			0.306333
$144$		0			0
$145$	−3.70161e8	−	5.99667e8i	−0.837373	−	1.35656i
$146$		0			0
$147$	−1.04666e8	−	2.15747e8i	−0.224149	−	0.462036i
$148$		0			0
$149$			2.19726e8i			0.445796i	0.974842	+	0.222898i	$0.0715517\pi$
$149$			2.19726e8i			0.445796i	−0.974842	+	0.222898i	$0.928448\pi$
$150$		0			0
$151$	−3.50620e8			−0.674418			−0.337209	−	0.941430i	$-0.609483\pi$
$151$	−3.50620e8			−0.674418			−0.337209	+	0.941430i	$0.609483\pi$
$152$		0			0
$153$	−2.81066e8	+	3.56649e8i	−0.512912	+	0.650841i
$154$		0			0
$155$	−6.80364e8	+	4.19974e8i	−1.17873	+	0.727605i
$156$		0			0
$157$			7.08761e7i			0.116654i	0.998298	+	0.0583272i	$0.0185767\pi$
$157$			7.08761e7i			0.116654i	−0.998298	+	0.0583272i	$0.981423\pi$
$158$		0			0
$159$	4.35003e8	+	8.96665e8i	0.680618	+	1.40295i
$160$		0			0
$161$		−	1.53730e8i		−	0.228800i
$162$		0			0
$163$		−	7.30934e8i		−	1.03545i	−0.855548	−	0.517724i	$-0.826780\pi$
$163$		−	7.30934e8i		−	1.03545i	0.855548	−	0.517724i	$-0.173220\pi$
$164$		0			0
$165$	5.81535e8	−	9.15142e8i	0.784585	−	1.23468i
$166$		0			0
$167$	−1.02725e9			−1.32072			−0.660361	−	0.750948i	$-0.729597\pi$
$167$	−1.02725e9			−1.32072			−0.660361	+	0.750948i	$0.729597\pi$
$168$		0			0
$169$	7.79961e8			0.956150
$170$		0			0
$171$	−7.32807e7	+	9.29868e7i	−0.0857048	+	0.108752i
$172$		0			0
$173$	−1.07140e8			−0.119610			−0.0598050	−	0.998210i	$-0.519048\pi$
$173$	−1.07140e8			−0.119610			−0.0598050	+	0.998210i	$0.519048\pi$
$174$		0			0
$175$	5.84769e8	+	2.93185e8i	0.623494	+	0.312600i
$176$		0			0
$177$	−4.07105e8	+	1.97500e8i	−0.414776	+	0.201222i
$178$		0			0
$179$			1.76590e8i			0.172010i	0.996295	+	0.0860051i	$0.0274101\pi$
$179$			1.76590e8i			0.172010i	−0.996295	+	0.0860051i	$0.972590\pi$
$180$		0			0
$181$	−1.03775e9			−0.966896			−0.483448	−	0.875373i	$-0.660616\pi$
$181$	−1.03775e9			−0.966896			−0.483448	+	0.875373i	$0.660616\pi$
$182$		0			0
$183$	−1.10319e7	−	2.27400e7i	−0.00983666	−	0.0202762i
$184$		0			0
$185$	7.21595e8	+	1.16900e9i	0.616037	+	0.997989i
$186$		0			0
$187$		−	1.48234e9i		−	1.21222i
$188$		0			0
$189$	−1.90518e8	+	8.69332e8i	−0.149310	+	0.681300i
$190$		0			0
$191$			4.41653e8i			0.331854i	0.986138	+	0.165927i	$0.0530617\pi$
$191$			4.41653e8i			0.331854i	−0.986138	+	0.165927i	$0.946938\pi$
$192$		0			0
$193$		−	1.80470e9i		−	1.30070i	−0.759635	−	0.650349i	$-0.774623\pi$
$193$		−	1.80470e9i		−	1.30070i	0.759635	−	0.650349i	$-0.225377\pi$
$194$		0			0
$195$	−1.62390e8	+	2.55548e8i	−0.112311	+	0.176739i
$196$		0			0
$197$	−1.84458e9			−1.22471			−0.612355	−	0.790583i	$-0.709778\pi$
$197$	−1.84458e9			−1.22471			−0.612355	+	0.790583i	$0.709778\pi$
$198$		0			0
$199$	−1.80610e9			−1.15167			−0.575837	−	0.817564i	$-0.695324\pi$
$199$	−1.80610e9			−1.15167			−0.575837	+	0.817564i	$0.695324\pi$
$200$		0			0
$201$	6.22005e7	−	3.01756e7i	0.0381074	−	0.0184872i
$202$		0			0
$203$	−1.88820e9			−1.11190
$204$		0			0
$205$	9.52287e6	+	1.54272e7i	0.00539203	+	0.00873517i
$206$		0			0
$207$	3.72804e8	−	4.73056e8i	0.203048	−	0.257651i
$208$		0			0
$209$		−	3.86481e8i		−	0.202555i
$210$		0			0
$211$	−2.94285e8			−0.148470			−0.0742350	−	0.997241i	$-0.523651\pi$
$211$	−2.94285e8			−0.148470			−0.0742350	+	0.997241i	$0.523651\pi$
$212$		0			0
$213$	2.31954e9	−	1.12529e9i	1.12689	−	0.546695i
$214$		0			0
$215$	2.22637e9	+	3.60675e9i	1.04194	+	1.68796i
$216$		0			0
$217$			2.14230e9i			0.966143i
$218$		0			0
$219$	1.72572e8	−	8.37207e7i	0.0750230	−	0.0363962i
$220$		0			0
$221$			4.13934e8i			0.173525i
$222$		0			0
$223$			3.54930e9i			1.43523i	0.696438	+	0.717617i	$0.254767\pi$
$223$			3.54930e9i			1.43523i	−0.696438	+	0.717617i	$0.745233\pi$
$224$		0			0
$225$	1.08845e9	+	2.32028e9i	0.424696	+	0.905336i
$226$		0			0
$227$	3.07376e9			1.15762			0.578811	−	0.815461i	$-0.303517\pi$
$227$	3.07376e9			1.15762			0.578811	+	0.815461i	$0.303517\pi$
$228$		0			0
$229$	−2.58716e9			−0.940767			−0.470383	−	0.882462i	$-0.655884\pi$
$229$	−2.58716e9			−0.940767			−0.470383	+	0.882462i	$0.655884\pi$
$230$		0			0
$231$	−1.26808e9	−	2.61387e9i	−0.445346	−	0.917985i
$232$		0			0
$233$	−4.46492e9			−1.51492			−0.757460	−	0.652882i	$-0.773560\pi$
$233$	−4.46492e9			−1.51492			−0.757460	+	0.652882i	$0.773560\pi$
$234$		0			0
$235$	1.04287e9	−	6.43741e8i	0.341947	−	0.211077i
$236$		0			0
$237$	1.03353e9	+	2.13039e9i	0.327588	+	0.675253i
$238$		0			0
$239$		−	2.49405e9i		−	0.764388i	−0.924082	−	0.382194i	$-0.875169\pi$
$239$		−	2.49405e9i		−	0.764388i	0.924082	−	0.382194i	$-0.124831\pi$
$240$		0			0
$241$	−1.06935e9			−0.316993			−0.158497	−	0.987360i	$-0.550665\pi$
$241$	−1.06935e9			−0.316993			−0.158497	+	0.987360i	$0.550665\pi$
$242$		0			0
$243$	−2.69443e9	+	2.21307e9i	−0.772756	+	0.634703i
$244$		0			0
$245$	−1.57447e9	+	9.71886e8i	−0.436988	+	0.269743i
$246$		0			0
$247$			1.07922e8i			0.0289951i
$248$		0			0
$249$	2.37966e9	+	4.90516e9i	0.619039	+	1.27602i
$250$		0			0
$251$		−	2.58790e9i		−	0.652007i	−0.945369	−	0.326003i	$-0.894298\pi$
$251$		−	2.58790e9i		−	0.652007i	0.945369	−	0.326003i	$-0.105702\pi$
$252$		0			0
$253$			1.96617e9i			0.479886i
$254$		0			0
$255$	2.95721e9	+	1.87918e9i	0.699393	+	0.444435i
$256$		0			0
$257$	3.99995e9			0.916900			0.458450	−	0.888720i	$-0.348405\pi$
$257$	3.99995e9			0.916900			0.458450	+	0.888720i	$0.348405\pi$
$258$		0			0
$259$	3.68088e9			0.817999
$260$		0			0
$261$	−5.81035e9	−	4.57900e9i	−1.25210	−	0.986753i
$262$		0			0
$263$	2.61772e9			0.547142			0.273571	−	0.961852i	$-0.411795\pi$
$263$	2.61772e9			0.547142			0.273571	+	0.961852i	$0.411795\pi$
$264$		0			0
$265$	6.54364e9	−	4.03925e9i	1.32689	−	0.819062i
$266$		0			0
$267$	3.57271e9	−	1.73324e9i	0.702996	−	0.341047i
$268$		0			0
$269$		−	6.21608e9i		−	1.18715i	−0.804777	−	0.593577i	$-0.797715\pi$
$269$		−	6.21608e9i		−	1.18715i	0.804777	−	0.593577i	$-0.202285\pi$
$270$		0			0
$271$	−5.31021e9			−0.984543			−0.492271	−	0.870442i	$-0.663833\pi$
$271$	−5.31021e9			−0.984543			−0.492271	+	0.870442i	$0.663833\pi$
$272$		0			0
$273$	3.54102e8	+	7.29906e8i	0.0637496	+	0.131406i
$274$		0			0
$275$	−7.47902e9	−	3.74974e9i	−1.30772	−	0.655648i
$276$		0			0
$277$			2.24918e9i			0.382037i	0.981586	+	0.191018i	$0.0611790\pi$
$277$			2.24918e9i			0.382037i	−0.981586	+	0.191018i	$0.938821\pi$
$278$		0			0
$279$	−5.19519e9	+	6.59224e9i	−0.857403	+	1.08797i
$280$		0			0
$281$		−	7.68684e9i		−	1.23289i	−0.787400	−	0.616443i	$-0.788573\pi$
$281$		−	7.68684e9i		−	1.23289i	0.787400	−	0.616443i	$-0.211427\pi$
$282$		0			0
$283$		−	7.20498e9i		−	1.12328i	−0.827382	−	0.561639i	$-0.810171\pi$
$283$		−	7.20498e9i		−	1.12328i	0.827382	−	0.561639i	$-0.189829\pi$
$284$		0			0
$285$	7.71014e8	+	4.89948e8i	0.116865	+	0.0742626i
$286$		0			0
$287$	4.85765e7			0.00715976
$288$		0			0
$289$	−2.18569e9			−0.313327
$290$		0			0
$291$	5.23547e9	−	2.53990e9i	0.730102	−	0.354197i
$292$		0			0
$293$	3.98677e9			0.540942			0.270471	−	0.962728i	$-0.412821\pi$
$293$	3.98677e9			0.540942			0.270471	+	0.962728i	$0.412821\pi$
$294$		0			0
$295$	1.83390e9	+	2.97095e9i	0.242152	+	0.392290i
$296$		0			0
$297$	2.43667e9	−	1.11185e10i	0.313163	−	1.42896i
$298$		0			0
$299$		−	5.49039e8i		−	0.0686940i
$300$		0			0
$301$	1.13568e10			1.38353
$302$		0			0
$303$	8.17658e9	−	3.96674e9i	0.970066	−	0.470612i
$304$		0			0
$305$	−1.65951e8	+	1.02438e8i	−0.0191770	+	0.0118375i
$306$		0			0
$307$			9.29130e9i			1.04598i	0.852339	+	0.522990i	$0.175183\pi$
$307$			9.29130e9i			1.04598i	−0.852339	+	0.522990i	$0.824817\pi$
$308$		0			0
$309$	9.75743e9	−	4.73366e9i	1.07029	−	0.519234i
$310$		0			0
$311$		−	1.12048e10i		−	1.19774i	−0.800847	−	0.598869i	$-0.795617\pi$
$311$		−	1.12048e10i		−	1.19774i	0.800847	−	0.598869i	$-0.204383\pi$
$312$		0			0
$313$			9.45147e9i			0.984741i	0.870386	+	0.492371i	$0.163870\pi$
$313$			9.45147e9i			0.984741i	−0.870386	+	0.492371i	$0.836130\pi$
$314$		0			0
$315$	6.82211e9	+	7.83878e8i	0.692910	+	0.0796170i
$316$		0			0
$317$	−8.48385e8			−0.0840148			−0.0420074	−	0.999117i	$-0.513375\pi$
$317$	−8.48385e8			−0.0840148			−0.0420074	+	0.999117i	$0.513375\pi$
$318$		0			0
$319$	2.41496e10			2.33210
$320$		0			0
$321$	1.29807e9	+	2.67570e9i	0.122258	+	0.252009i
$322$		0			0
$323$	1.24888e9			0.114739
$324$		0			0
$325$	2.08847e9	+	1.04709e9i	0.187195	+	0.0938537i
$326$		0			0
$327$	−5.93986e9	−	1.22437e10i	−0.519499	−	1.07084i
$328$		0			0
$329$		−	3.28374e9i		−	0.280276i
$330$		0			0
$331$	−4.71539e9			−0.392831			−0.196415	−	0.980521i	$-0.562930\pi$
$331$	−4.71539e9			−0.392831			−0.196415	+	0.980521i	$0.562930\pi$
$332$		0			0
$333$	1.13267e10	+	8.92633e9i	0.921144	+	0.725932i
$334$		0			0
$335$	−2.80197e8	−	4.53924e8i	−0.0222477	−	0.0360416i
$336$		0			0
$337$		−	3.45801e8i		−	0.0268106i	−0.999910	−	0.0134053i	$-0.995733\pi$
$337$		−	3.45801e8i		−	0.0268106i	0.999910	−	0.0134053i	$-0.00426716\pi$
$338$		0			0
$339$	−3.45900e9	−	7.12999e9i	−0.261910	−	0.539871i
$340$		0			0
$341$		−	2.73994e10i		−	2.02639i
$342$		0			0
$343$			1.46115e10i			1.05565i
$344$		0			0
$345$	−3.92242e9	−	2.49254e9i	−0.276871	−	0.175940i
$346$		0			0
$347$	−3.52962e9			−0.243450			−0.121725	−	0.992564i	$-0.538843\pi$
$347$	−3.52962e9			−0.243450			−0.121725	+	0.992564i	$0.538843\pi$
$348$		0			0
$349$	8.25013e9			0.556108			0.278054	−	0.960565i	$-0.410311\pi$
$349$	8.25013e9			0.556108			0.278054	+	0.960565i	$0.410311\pi$
$350$		0			0
$351$	−6.80424e8	+	3.10477e9i	−0.0448282	+	0.204550i
$352$		0			0
$353$	−1.08036e10			−0.695776			−0.347888	−	0.937536i	$-0.613101\pi$
$353$	−1.08036e10			−0.695776			−0.347888	+	0.937536i	$0.613101\pi$
$354$		0			0
$355$	−1.04489e10	−	1.69274e10i	−0.657897	−	1.06580i
$356$		0			0
$357$	8.44650e9	−	4.09768e9i	0.520001	−	0.252270i
$358$		0			0
$359$		−	1.78116e10i		−	1.07232i	−0.844115	−	0.536162i	$-0.819874\pi$
$359$		−	1.78116e10i		−	1.07232i	0.844115	−	0.536162i	$-0.180126\pi$
$360$		0			0
$361$	−1.66579e10			−0.980828
$362$		0			0
$363$	8.63965e9	+	1.78088e10i	0.497587	+	1.02567i
$364$		0			0
$365$	−7.77394e8	−	1.25939e9i	−0.0437995	−	0.0709559i
$366$		0			0
$367$			7.25059e9i			0.399677i	0.979829	+	0.199839i	$0.0640418\pi$
$367$			7.25059e9i			0.399677i	−0.979829	+	0.199839i	$0.935958\pi$
$368$		0			0
$369$	1.49478e8	+	1.17800e8i	0.00806256	+	0.00635392i
$370$		0			0
$371$		−	2.06043e10i		−	1.08758i
$372$		0			0
$373$		−	1.40594e10i		−	0.726325i	−0.931726	−	0.363163i	$-0.881697\pi$
$373$		−	1.40594e10i		−	0.726325i	0.931726	−	0.363163i	$-0.118303\pi$
$374$		0			0
$375$	1.69618e10	−	1.01667e10i	0.857724	−	0.514110i
$376$		0			0
$377$	−6.74361e9			−0.333831
$378$		0			0
$379$	−9.41156e9			−0.456147			−0.228073	−	0.973644i	$-0.573243\pi$
$379$	−9.41156e9			−0.456147			−0.228073	+	0.973644i	$0.573243\pi$
$380$		0			0
$381$	−1.00423e10	+	4.87188e9i	−0.476579	+	0.231205i
$382$		0			0
$383$	−2.22515e10			−1.03410			−0.517052	−	0.855954i	$-0.672971\pi$
$383$	−2.22515e10			−1.03410			−0.517052	+	0.855954i	$0.672971\pi$
$384$		0			0
$385$	−1.90753e10	+	1.17748e10i	−0.868219	+	0.535933i
$386$		0			0
$387$	3.49468e10	+	2.75408e10i	1.55799	+	1.22781i
$388$		0			0
$389$			1.67518e10i			0.731582i	0.930697	+	0.365791i	$0.119202\pi$
$389$			1.67518e10i			0.731582i	−0.930697	+	0.365791i	$0.880798\pi$
$390$		0			0
$391$	−6.35351e9			−0.271836
$392$		0			0
$393$	−5.18570e9	+	2.51576e9i	−0.217389	+	0.105463i
$394$		0			0
$395$	1.55471e10	−	9.59687e9i	0.638646	−	0.394223i
$396$		0			0
$397$		−	3.88428e9i		−	0.156368i	−0.996939	−	0.0781840i	$-0.975088\pi$
$397$		−	3.88428e9i		−	0.156368i	0.996939	−	0.0781840i	$-0.0249122\pi$
$398$		0			0
$399$	2.20220e9	−	1.06836e9i	0.0868892	−	0.0421529i
$400$		0			0
$401$			3.28950e10i			1.27219i	0.771610	+	0.636096i	$0.219452\pi$
$401$			3.28950e10i			1.27219i	−0.771610	+	0.636096i	$0.780548\pi$
$402$		0			0
$403$			7.65110e9i			0.290071i
$404$		0			0
$405$	1.90919e10	+	1.89561e10i	0.709626	+	0.704578i
$406$		0			0
$407$	−4.70774e10			−1.71567
$408$		0			0
$409$	−1.08495e9			−0.0387718			−0.0193859	−	0.999812i	$-0.506171\pi$
$409$	−1.08495e9			−0.0387718			−0.0193859	+	0.999812i	$0.506171\pi$
$410$		0			0
$411$	1.78451e10	+	3.67838e10i	0.625391	+	1.28911i
$412$		0			0
$413$	9.35479e9			0.321539
$414$		0			0
$415$	3.57967e10	−	2.20965e10i	1.20684	−	0.744957i
$416$		0			0
$417$	7.39317e9	+	1.52395e10i	0.244504	+	0.503994i
$418$		0			0
$419$			3.39202e10i			1.10053i	0.834990	+	0.550266i	$0.185474\pi$
$419$			3.39202e10i			1.10053i	−0.834990	+	0.550266i	$0.814526\pi$
$420$		0			0
$421$	2.88554e10			0.918542			0.459271	−	0.888296i	$-0.348111\pi$
$421$	2.88554e10			0.918542			0.459271	+	0.888296i	$0.348111\pi$
$422$		0			0
$423$	7.96325e9	−	1.01047e10i	0.248731	−	0.315617i
$424$		0			0
$425$	1.21170e10	−	2.41678e10i	0.371398	−	0.740768i
$426$		0			0
$427$			5.22539e8i			0.0157183i
$428$		0			0
$429$	−4.52886e9	−	9.33527e9i	−0.133709	−	0.275612i
$430$		0			0
$431$			7.99799e8i			0.0231778i	0.999933	+	0.0115889i	$0.00368894\pi$
$431$			7.99799e8i			0.0231778i	−0.999933	+	0.0115889i	$0.996311\pi$
$432$		0			0
$433$			2.02420e10i			0.575839i	0.957655	+	0.287920i	$0.0929636\pi$
$433$			2.02420e10i			0.575839i	−0.957655	+	0.287920i	$0.907036\pi$
$434$		0			0
$435$	−3.06147e10	+	4.81774e10i	−0.855015	+	1.34551i
$436$		0			0
$437$	−1.65651e9			−0.0454222
$438$		0			0
$439$	−4.16160e10			−1.12048			−0.560238	−	0.828332i	$-0.689290\pi$
$439$	−4.16160e10			−1.12048			−0.560238	+	0.828332i	$0.689290\pi$
$440$		0			0
$441$	−1.20225e10	+	1.52555e10i	−0.317863	+	0.403340i
$442$		0			0
$443$	−1.00330e10			−0.260504			−0.130252	−	0.991481i	$-0.541579\pi$
$443$	−1.00330e10			−0.260504			−0.130252	+	0.991481i	$0.541579\pi$
$444$		0			0
$445$	−1.60941e10	−	2.60727e10i	−0.410419	−	0.664885i
$446$		0			0
$447$	1.60129e10	−	7.76841e9i	0.401088	−	0.194582i
$448$		0			0
$449$			2.59211e10i			0.637775i	0.947793	+	0.318888i	$0.103309\pi$
$449$			2.59211e10i			0.637775i	−0.947793	+	0.318888i	$0.896691\pi$
$450$		0			0
$451$	−6.21278e8			−0.0150169
$452$		0			0
$453$	1.23962e10	+	2.55521e10i	0.294371	+	0.606783i
$454$		0			0
$455$	5.32667e9	−	3.28804e9i	0.124283	−	0.0767169i
$456$		0			0
$457$		−	5.83258e10i		−	1.33720i	−0.743623	−	0.668599i	$-0.766894\pi$
$457$		−	5.83258e10i		−	1.33720i	0.743623	−	0.668599i	$-0.233106\pi$
$458$		0			0
$459$	3.59285e10	+	7.87390e9i	0.809447	+	0.177394i
$460$		0			0
$461$		−	2.73170e10i		−	0.604825i	−0.953177	−	0.302412i	$-0.902208\pi$
$461$		−	2.73170e10i		−	0.604825i	0.953177	−	0.302412i	$-0.0977920\pi$
$462$		0			0
$463$		−	5.50831e10i		−	1.19866i	−0.800504	−	0.599328i	$-0.795435\pi$
$463$		−	5.50831e10i		−	1.19866i	0.800504	−	0.599328i	$-0.204565\pi$
$464$		0			0
$465$	5.46606e10	+	3.47346e10i	1.16913	+	0.742934i
$466$		0			0
$467$	−4.06476e10			−0.854610			−0.427305	−	0.904108i	$-0.640537\pi$
$467$	−4.06476e10			−0.854610			−0.427305	+	0.904108i	$0.640537\pi$
$468$		0			0
$469$	−1.42929e9			−0.0295414
$470$		0			0
$471$	5.16522e9	−	2.50582e9i	0.104956	−	0.0509175i
$472$		0			0
$473$	−1.45250e11			−2.90182
$474$		0			0
$475$	3.15919e9	−	6.30113e9i	0.0620585	−	0.123778i
$476$		0			0
$477$	4.99666e10	−	6.34032e10i	0.965175	−	1.22472i
$478$		0			0
$479$			1.08547e10i			0.206194i	0.994671	+	0.103097i	$0.0328752\pi$
$479$			1.08547e10i			0.206194i	−0.994671	+	0.103097i	$0.967125\pi$
$480$		0			0
$481$	1.31460e10			0.245592
$482$		0			0
$483$	−1.12034e10	+	5.43514e9i	−0.205855	+	0.0998670i
$484$		0			0
$485$	−2.35844e10	−	3.82071e10i	−0.426244	−	0.690522i
$486$		0			0
$487$			1.77991e10i			0.316433i	0.987404	+	0.158216i	$0.0505743\pi$
$487$			1.77991e10i			0.316433i	−0.987404	+	0.158216i	$0.949426\pi$
$488$		0			0
$489$	−5.32681e10	+	2.58422e10i	−0.931606	+	0.451953i
$490$		0			0
$491$			7.93615e10i			1.36547i	0.730664	+	0.682737i	$0.239211\pi$
$491$			7.93615e10i			1.36547i	−0.730664	+	0.682737i	$0.760789\pi$
$492$		0			0
$493$			7.80374e10i			1.32104i
$494$		0			0
$495$	−8.72528e10	−	1.00256e10i	−1.45331	−	0.166989i
$496$		0			0
$497$	−5.33003e10			−0.873582
$498$		0			0
$499$	−6.54034e10			−1.05487			−0.527434	−	0.849596i	$-0.676846\pi$
$499$	−6.54034e10			−1.05487			−0.527434	+	0.849596i	$0.676846\pi$
$500$		0			0
$501$	3.63185e10	+	7.48629e10i	0.576471	+	1.18827i
$502$		0			0
$503$	−1.01074e11			−1.57894			−0.789471	−	0.613788i	$-0.789645\pi$
$503$	−1.01074e11			−1.57894			−0.789471	+	0.613788i	$0.789645\pi$
$504$		0			0
$505$	−3.68334e10	−	5.96706e10i	−0.566339	−	0.917477i
$506$		0			0
$507$	−2.75755e10	−	5.68410e10i	−0.417341	−	0.860260i
$508$		0			0
$509$		−	1.19907e11i		−	1.78638i	−0.449681	−	0.893189i	$-0.648462\pi$
$509$		−	1.19907e11i		−	1.78638i	0.449681	−	0.893189i	$-0.351538\pi$
$510$		0			0
$511$	−3.96551e9			−0.0581588
$512$		0			0
$513$	9.36741e9	+	2.05291e9i	0.135254	+	0.0296416i
$514$		0			0
$515$	−4.39547e10	−	7.12073e10i	−0.624851	−	1.01227i
$516$		0			0
$517$			4.19981e10i			0.587851i
$518$		0			0
$519$	3.78794e9	+	7.80802e9i	0.0522076	+	0.107615i
$520$		0			0
$521$			1.21461e11i			1.64849i	0.566230	+	0.824247i	$0.308401\pi$
$521$			1.21461e11i			1.64849i	−0.566230	+	0.824247i	$0.691599\pi$
$522$		0			0
$523$			8.02894e10i			1.07313i	0.843860	+	0.536564i	$0.180278\pi$
$523$			8.02894e10i			1.07313i	−0.843860	+	0.536564i	$0.819722\pi$
$524$		0			0
$525$	6.91853e8	−	5.29816e10i	0.00910703	−	0.697409i
$526$		0			0
$527$	8.85389e10			1.14787
$528$		0			0
$529$	−6.98837e10			−0.892387
$530$		0			0
$531$	2.87864e10	+	2.26859e10i	0.362084	+	0.285350i
$532$		0			0
$533$	1.73488e8			0.00214961
$534$		0			0
$535$	1.95266e10	−	1.20533e10i	0.238347	−	0.147127i
$536$		0			0
$537$	1.28693e10	−	6.24334e9i	0.154760	−	0.0750793i
$538$		0			0
$539$		−	6.34064e10i		−	0.751239i
$540$		0			0
$541$	2.31499e10			0.270246			0.135123	−	0.990829i	$-0.456857\pi$
$541$	2.31499e10			0.270246			0.135123	+	0.990829i	$0.456857\pi$
$542$		0			0
$543$	3.66897e10	+	7.56281e10i	0.422032	+	0.869929i
$544$		0			0
$545$	−8.93518e10	+	5.51549e10i	−1.01279	+	0.625170i
$546$		0			0
$547$		−	1.06905e11i		−	1.19412i	−0.802196	−	0.597061i	$-0.796335\pi$
$547$		−	1.06905e11i		−	1.19412i	0.802196	−	0.597061i	$-0.203665\pi$
$548$		0			0
$549$	−1.26718e9	+	1.60794e9i	−0.0139492	+	0.0177003i
$550$		0			0
$551$			2.03462e10i			0.220738i
$552$		0			0
$553$		−	4.89540e10i		−	0.523465i
$554$		0			0
$555$	5.96806e10	−	9.39174e10i	0.629016	−	0.989861i
$556$		0			0
$557$	−3.49063e10			−0.362646			−0.181323	−	0.983424i	$-0.558038\pi$
$557$	−3.49063e10			−0.362646			−0.181323	+	0.983424i	$0.558038\pi$
$558$		0			0
$559$	4.05600e10			0.415385
$560$		0			0
$561$	−1.08028e11	+	5.24081e10i	−1.09065	+	0.529112i
$562$		0			0
$563$	−1.11294e10			−0.110775			−0.0553873	−	0.998465i	$-0.517639\pi$
$563$	−1.11294e10			−0.110775			−0.0553873	+	0.998465i	$0.517639\pi$
$564$		0			0
$565$	−5.20329e10	+	3.21188e10i	−0.510604	+	0.315185i
$566$		0			0
$567$	7.00899e10	−	1.68509e10i	0.678146	−	0.163038i
$568$		0			0
$569$			1.10613e11i			1.05526i	0.849475	+	0.527629i	$0.176919\pi$
$569$			1.10613e11i			1.05526i	−0.849475	+	0.527629i	$0.823081\pi$
$570$		0			0
$571$	3.15777e10			0.297055			0.148527	−	0.988908i	$-0.452547\pi$
$571$	3.15777e10			0.297055			0.148527	+	0.988908i	$0.452547\pi$
$572$		0			0
$573$	3.21862e10	−	1.56146e10i	0.298574	−	0.144848i
$574$		0			0
$575$	−1.60719e10	+	3.20560e10i	−0.147026	+	0.293250i
$576$		0			0
$577$		−	3.66049e10i		−	0.330245i	−0.986273	−	0.165123i	$-0.947198\pi$
$577$		−	3.66049e10i		−	0.330245i	0.986273	−	0.165123i	$-0.0528020\pi$
$578$		0			0
$579$	−1.31521e11	+	6.38053e10i	−1.17026	+	0.567731i
$580$		0			0
$581$		−	1.12715e11i		−	0.989184i
$582$		0			0
$583$			2.63523e11i			2.28110i
$584$		0			0
$585$	2.43648e10	+	2.79957e9i	0.208036	+	0.0239039i
$586$		0			0
$587$	−5.45783e10			−0.459693			−0.229846	−	0.973227i	$-0.573822\pi$
$587$	−5.45783e10			−0.459693			−0.229846	+	0.973227i	$0.573822\pi$
$588$		0			0
$589$	2.30842e10			0.191802
$590$		0			0
$591$	6.52152e10	+	1.34427e11i	0.534563	+	1.10189i
$592$		0			0
$593$	8.35997e10			0.676061			0.338031	−	0.941135i	$-0.390239\pi$
$593$	8.35997e10			0.676061			0.338031	+	0.941135i	$0.390239\pi$
$594$		0			0
$595$	−3.80493e10	−	6.16405e10i	−0.303584	−	0.491811i
$596$		0			0
$597$	6.38547e10	+	1.31623e11i	0.502684	+	1.03618i
$598$		0			0
$599$		−	1.39529e10i		−	0.108382i	−0.998531	−	0.0541909i	$-0.982742\pi$
$599$		−	1.39529e10i		−	0.108382i	0.998531	−	0.0541909i	$-0.0172579\pi$
$600$		0			0
$601$	2.42138e11			1.85595			0.927974	−	0.372645i	$-0.121549\pi$
$601$	2.42138e11			1.85595			0.927974	+	0.372645i	$0.121549\pi$
$602$		0			0
$603$	−4.39820e9	−	3.46612e9i	−0.0332664	−	0.0262164i
$604$		0			0
$605$	1.29964e11	−	8.02240e10i	0.970067	−	0.598801i
$606$		0			0
$607$		−	1.24176e11i		−	0.914712i	−0.889284	−	0.457356i	$-0.848797\pi$
$607$		−	1.24176e11i		−	0.914712i	0.889284	−	0.457356i	$-0.151203\pi$
$608$		0			0
$609$	6.67575e10	+	1.37606e11i	0.485323	+	1.00039i
$610$		0			0
$611$		−	1.17277e10i		−	0.0841488i
$612$		0			0
$613$			1.73317e11i			1.22743i	0.789526	+	0.613717i	$0.210327\pi$
$613$			1.73317e11i			1.22743i	−0.789526	+	0.613717i	$0.789673\pi$
$614$		0			0
$615$	7.87603e8	−	1.23942e9i	0.00550563	−	0.00866402i
$616$		0			0
$617$	−1.52659e11			−1.05337			−0.526687	−	0.850060i	$-0.676566\pi$
$617$	−1.52659e11			−1.05337			−0.526687	+	0.850060i	$0.676566\pi$
$618$		0			0
$619$	2.41342e11			1.64388			0.821942	−	0.569571i	$-0.192891\pi$
$619$	2.41342e11			1.64388			0.821942	+	0.569571i	$0.192891\pi$
$620$		0			0
$621$	−4.76553e10	−	1.04439e10i	−0.320439	−	0.0702256i
$622$		0			0
$623$	−8.20967e10			−0.544971
$624$		0			0
$625$	−9.12854e10	−	1.22270e11i	−0.598248	−	0.801311i
$626$		0			0
$627$	−2.81655e10	+	1.36640e10i	−0.182242	+	0.0884116i
$628$		0			0
$629$		−	1.52127e11i		−	0.971858i
$630$		0			0
$631$	−1.68033e11			−1.05993			−0.529966	−	0.848019i	$-0.677795\pi$
$631$	−1.68033e11			−1.05993			−0.529966	+	0.848019i	$0.677795\pi$
$632$		0			0
$633$	1.04045e10	+	2.14466e10i	0.0648044	+	0.133580i
$634$		0			0
$635$	4.52382e10	+	7.32865e10i	0.278234	+	0.450743i
$636$		0			0
$637$			1.77058e10i			0.107537i
$638$		0			0
$639$	−1.64015e11	−	1.29256e11i	−0.983737	−	0.775260i
$640$		0			0
$641$			1.07087e11i			0.634313i	0.948373	+	0.317156i	$0.102728\pi$
$641$			1.07087e11i			0.634313i	−0.948373	+	0.317156i	$0.897272\pi$
$642$		0			0
$643$			1.21734e11i			0.712142i	0.934459	+	0.356071i	$0.115884\pi$
$643$			1.21734e11i			0.712142i	−0.934459	+	0.356071i	$0.884116\pi$
$644$		0			0
$645$	1.84135e11	−	2.89767e11i	1.06389	−	1.67421i
$646$		0			0
$647$	1.91646e11			1.09366			0.546829	−	0.837244i	$-0.315835\pi$
$647$	1.91646e11			1.09366			0.546829	+	0.837244i	$0.315835\pi$
$648$		0			0
$649$	−1.19645e11			−0.674397
$650$		0			0
$651$	1.56124e11	−	7.57410e10i	0.869252	−	0.421704i
$652$		0			0
$653$	−1.71426e11			−0.942811			−0.471406	−	0.881917i	$-0.656253\pi$
$653$	−1.71426e11			−0.942811			−0.471406	+	0.881917i	$0.656253\pi$
$654$		0			0
$655$	2.33603e10	+	3.78440e10i	0.126915	+	0.205604i
$656$		0			0
$657$	−1.22026e10	−	9.61657e9i	−0.0654923	−	0.0516129i
$658$		0			0
$659$		−	6.16692e10i		−	0.326984i	−0.986545	−	0.163492i	$-0.947724\pi$
$659$		−	6.16692e10i		−	0.326984i	0.986545	−	0.163492i	$-0.0522758\pi$
$660$		0			0
$661$	2.25974e10			0.118373			0.0591864	−	0.998247i	$-0.481149\pi$
$661$	2.25974e10			0.118373			0.0591864	+	0.998247i	$0.481149\pi$
$662$		0			0
$663$	3.01662e10	−	1.46346e10i	0.156123	−	0.0757404i
$664$		0			0
$665$	−9.92036e9	−	1.60711e10i	−0.0507272	−	0.0821788i
$666$		0			0
$667$		−	1.03508e11i		−	0.522964i
$668$		0			0
$669$	2.58661e11	−	1.25485e11i	1.29130	−	0.626453i
$670$		0			0
$671$		−	6.68311e9i		−	0.0329677i
$672$		0			0
$673$			3.18816e11i			1.55410i	0.629437	+	0.777051i	$0.283285\pi$
$673$			3.18816e11i			1.55410i	−0.629437	+	0.777051i	$0.716715\pi$
$674$		0			0
$675$	1.30612e11	−	1.61356e11i	0.629171	−	0.777267i
$676$		0			0
$677$	3.75454e11			1.78732			0.893660	−	0.448745i	$-0.148129\pi$
$677$	3.75454e11			1.78732			0.893660	+	0.448745i	$0.148129\pi$
$678$		0			0
$679$	−1.20305e11			−0.565984
$680$		0			0
$681$	−1.08673e11	−	2.24006e11i	−0.505281	−	1.04153i
$682$		0			0
$683$	−1.83700e11			−0.844162			−0.422081	−	0.906558i	$-0.638700\pi$
$683$	−1.83700e11			−0.844162			−0.422081	+	0.906558i	$0.638700\pi$
$684$		0			0
$685$	2.68439e11	−	1.65702e11i	1.21922	−	0.752601i
$686$		0			0
$687$	9.14692e10	+	1.88544e11i	0.410627	+	0.846420i
$688$		0			0
$689$		−	7.35871e10i		−	0.326531i
$690$		0			0
$691$	−1.46577e11			−0.642916			−0.321458	−	0.946924i	$-0.604173\pi$
$691$	−1.46577e11			−0.642916			−0.321458	+	0.946924i	$0.604173\pi$
$692$		0			0
$693$	−1.45657e11	+	1.84827e11i	−0.631538	+	0.801367i
$694$		0			0
$695$	1.11214e11	−	6.86498e10i	0.476671	−	0.294239i
$696$		0			0
$697$		−	2.00761e9i		−	0.00850645i
$698$		0			0
$699$	1.57857e11	+	3.25389e11i	0.661234	+	1.36299i
$700$		0			0
$701$		−	3.90726e11i		−	1.61808i	−0.587753	−	0.809041i	$-0.699987\pi$
$701$		−	3.90726e11i		−	1.61808i	0.587753	−	0.809041i	$-0.300013\pi$
$702$		0			0
$703$		−	3.96630e10i		−	0.162392i
$704$		0			0
$705$	−8.37845e10	−	5.32416e10i	−0.339162	−	0.215523i
$706$		0			0
$707$	−1.87888e11			−0.752007
$708$		0			0
$709$	−3.36760e10			−0.133271			−0.0666354	−	0.997777i	$-0.521226\pi$
$709$	−3.36760e10			−0.133271			−0.0666354	+	0.997777i	$0.521226\pi$
$710$		0			0
$711$	1.18716e11	−	1.50640e11i	0.464548	−	0.589471i
$712$		0			0
$713$	−1.17437e11			−0.454410
$714$		0			0
$715$	−6.81265e10	+	4.20530e10i	−0.260670	+	0.160906i
$716$		0			0
$717$	−1.81758e11	+	8.81772e10i	−0.687730	+	0.333641i
$718$		0			0
$719$		−	3.34576e11i		−	1.25193i	−0.779852	−	0.625964i	$-0.784706\pi$
$719$		−	3.34576e11i		−	1.25193i	0.779852	−	0.625964i	$-0.215294\pi$
$720$		0			0
$721$	−2.24214e11			−0.829703
$722$		0			0
$723$	3.78067e10	+	7.79305e10i	0.138362	+	0.285203i
$724$		0			0
$725$	3.93731e11	+	1.97404e11i	1.42511	+	0.714503i
$726$		0			0
$727$		−	7.75537e10i		−	0.277629i	−0.990318	−	0.138815i	$-0.955671\pi$
$727$		−	7.75537e10i		−	0.277629i	0.990318	−	0.138815i	$-0.0443292\pi$
$728$		0			0
$729$	2.56543e11	+	1.18118e11i	0.908345	+	0.418223i
$730$		0			0
$731$		−	4.69363e11i		−	1.64376i
$732$		0			0
$733$		−	1.83371e10i		−	0.0635205i	−0.999496	−	0.0317603i	$-0.989889\pi$
$733$		−	1.83371e10i		−	0.0635205i	0.999496	−	0.0317603i	$-0.0101113\pi$
$734$		0			0
$735$	1.26493e11	+	8.03812e10i	0.433429	+	0.275426i
$736$		0			0
$737$	1.82803e10			0.0619601
$738$		0			0
$739$	4.44324e11			1.48978			0.744890	−	0.667187i	$-0.232502\pi$
$739$	4.44324e11			1.48978			0.744890	+	0.667187i	$0.232502\pi$
$740$		0			0
$741$	7.86504e9	−	3.81560e9i	0.0260872	−	0.0126558i
$742$		0			0
$743$	−5.92783e10			−0.194509			−0.0972547	−	0.995260i	$-0.531006\pi$
$743$	−5.92783e10			−0.194509			−0.0972547	+	0.995260i	$0.531006\pi$
$744$		0			0
$745$	−7.21340e10	−	1.16858e11i	−0.234161	−	0.379345i
$746$		0			0
$747$	2.73340e11	−	3.46844e11i	0.877850	−	1.11391i
$748$		0			0
$749$		−	6.14843e10i		−	0.195361i
$750$		0			0
$751$	1.35059e11			0.424585			0.212292	−	0.977206i	$-0.431907\pi$
$751$	1.35059e11			0.424585			0.212292	+	0.977206i	$0.431907\pi$
$752$		0			0
$753$	−1.88598e11	+	9.14950e10i	−0.586619	+	0.284589i
$754$		0			0
$755$	1.86473e11	−	1.15105e11i	0.573888	−	0.354249i
$756$		0			0
$757$		−	3.52798e11i		−	1.07434i	−0.843473	−	0.537171i	$-0.819493\pi$
$757$		−	3.52798e11i		−	1.07434i	0.843473	−	0.537171i	$-0.180507\pi$
$758$		0			0
$759$	1.43288e11	−	6.95138e10i	0.431760	−	0.209461i
$760$		0			0
$761$			4.67185e11i			1.39300i	0.717558	+	0.696499i	$0.245260\pi$
$761$			4.67185e11i			1.39300i	−0.717558	+	0.696499i	$0.754740\pi$
$762$		0			0
$763$			2.81347e11i			0.830126i
$764$		0			0
$765$	3.23968e10	−	2.81950e11i	0.0945924	−	0.823241i
$766$		0			0
$767$	3.34101e10			0.0965375
$768$		0			0
$769$	−1.44792e11			−0.414038			−0.207019	−	0.978337i	$-0.566376\pi$
$769$	−1.44792e11			−0.414038			−0.207019	+	0.978337i	$0.566376\pi$
$770$		0			0
$771$	−1.41418e11	−	2.91503e11i	−0.400210	−	0.824947i
$772$		0			0
$773$	1.13132e11			0.316860			0.158430	−	0.987370i	$-0.449357\pi$
$773$	1.13132e11			0.316860			0.158430	+	0.987370i	$0.449357\pi$
$774$		0			0
$775$	2.23969e11	−	4.46715e11i	0.620841	−	1.23829i
$776$		0			0
$777$	−1.30138e11	−	2.68251e11i	−0.357041	−	0.735964i
$778$		0			0
$779$		−	5.23432e8i		−	0.00142138i
$780$		0			0
$781$	6.81694e11			1.83225
$782$		0			0
$783$	−1.28278e11	+	5.85330e11i	−0.341275	+	1.55723i
$784$		0			0
$785$	−2.32680e10	−	3.76945e10i	−0.0612746	−	0.0992657i
$786$		0			0
$787$		−	4.10788e10i		−	0.107083i	−0.998566	−	0.0535413i	$-0.982949\pi$
$787$		−	4.10788e10i		−	0.107083i	0.998566	−	0.0535413i	$-0.0170509\pi$
$788$		0			0
$789$	−9.25494e10	−	1.90771e11i	−0.238817	−	0.492271i
$790$		0			0
$791$			1.63839e11i			0.418515i
$792$		0			0
$793$			1.86622e9i			0.00471921i
$794$		0			0
$795$	−5.25717e11	−	3.34072e11i	−1.31608	−	0.836318i
$796$		0			0
$797$	1.01477e11			0.251498			0.125749	−	0.992062i	$-0.459867\pi$
$797$	1.01477e11			0.251498			0.125749	+	0.992062i	$0.459867\pi$
$798$		0			0
$799$	−1.35713e11			−0.332994
$800$		0			0
$801$	−2.52626e11	−	1.99089e11i	−0.613689	−	0.483634i
$802$		0			0
$803$	5.07177e10			0.121982
$804$		0			0
$805$	5.04683e10	+	8.17594e10i	0.120181	+	0.194695i
$806$		0			0
$807$	−4.53008e11	+	2.19769e11i	−1.06810	+	0.518171i
$808$		0			0
$809$		−	2.81290e11i		−	0.656689i	−0.944558	−	0.328344i	$-0.893509\pi$
$809$		−	2.81290e11i		−	0.656689i	0.944558	−	0.328344i	$-0.106491\pi$
$810$		0			0
$811$	−3.06605e11			−0.708754			−0.354377	−	0.935103i	$-0.615307\pi$
$811$	−3.06605e11			−0.708754			−0.354377	+	0.935103i	$0.615307\pi$
$812$		0			0
$813$	1.87742e11	+	3.86991e11i	0.429735	+	0.885806i
$814$		0			0
$815$	2.39959e11	+	3.88738e11i	0.543885	+	0.881102i
$816$		0			0
$817$		−	1.22374e11i		−	0.274663i
$818$		0			0
$819$	4.06739e10	−	5.16116e10i	0.0904024	−	0.114713i
$820$		0			0
$821$		−	5.33533e11i		−	1.17433i	−0.809469	−	0.587163i	$-0.800245\pi$
$821$		−	5.33533e11i		−	1.17433i	0.809469	−	0.587163i	$-0.199755\pi$
$822$		0			0
$823$			5.45096e11i			1.18816i	0.804407	+	0.594078i	$0.202483\pi$
$823$			5.45096e11i			1.18816i	−0.804407	+	0.594078i	$0.797517\pi$
$824$		0			0
$825$	−8.84859e9	+	6.77619e11i	−0.0191011	+	1.46275i
$826$		0			0
$827$	7.10494e11			1.51893			0.759466	−	0.650547i	$-0.225460\pi$
$827$	7.10494e11			1.51893			0.759466	+	0.650547i	$0.225460\pi$
$828$		0			0
$829$	3.64341e11			0.771419			0.385710	−	0.922620i	$-0.373957\pi$
$829$	3.64341e11			0.771419			0.385710	+	0.922620i	$0.373957\pi$
$830$		0			0
$831$	1.63913e11	−	7.95198e10i	0.343724	−	0.166752i
$832$		0			0
$833$	2.04893e11			0.425546
$834$		0			0
$835$	5.46331e11	−	3.37238e11i	1.12385	−	0.693730i
$836$		0			0
$837$	6.64098e11	+	1.45540e11i	1.35310	+	0.296538i
$838$		0			0
$839$			3.80877e11i			0.768665i	0.923195	+	0.384333i	$0.125568\pi$
$839$			3.80877e11i			0.768665i	−0.923195	+	0.384333i	$0.874432\pi$
$840$		0			0
$841$	−7.71101e11			−1.54144
$842$		0			0
$843$	−5.60192e11	+	2.71768e11i	−1.10924	+	0.538132i
$844$		0			0
$845$	−4.14811e11	+	2.56054e11i	−0.813624	+	0.502233i
$846$		0			0
$847$		−	4.09225e11i		−	0.795112i
$848$		0			0
$849$	−5.25076e11	+	2.54732e11i	−1.01063	+	0.490290i
$850$		0			0
$851$			2.01780e11i			0.384733i
$852$		0			0
$853$			8.33398e11i			1.57419i	0.616834	+	0.787093i	$0.288415\pi$
$853$			8.33398e11i			1.57419i	−0.616834	+	0.787093i	$0.711585\pi$
$854$		0			0
$855$	8.44661e9	−	7.35111e10i	0.0158059	−	0.137559i
$856$		0			0
$857$	2.81549e11			0.521952			0.260976	−	0.965345i	$-0.415956\pi$
$857$	2.81549e11			0.521952			0.260976	+	0.965345i	$0.415956\pi$
$858$		0			0
$859$	−6.11769e11			−1.12361			−0.561804	−	0.827271i	$-0.689892\pi$
$859$	−6.11769e11			−1.12361			−0.561804	+	0.827271i	$0.689892\pi$
$860$		0			0
$861$	−1.71742e9	−	3.54010e9i	−0.00312510	−	0.00644173i
$862$		0			0
$863$	4.91320e11			0.885771			0.442886	−	0.896578i	$-0.353955\pi$
$863$	4.91320e11			0.885771			0.442886	+	0.896578i	$0.353955\pi$
$864$		0			0
$865$	5.69810e10	−	3.51731e10i	0.101781	−	0.0628270i
$866$		0			0
$867$	7.72752e10	+	1.59286e11i	0.136761	+	0.281904i
$868$		0			0
$869$			6.26106e11i			1.09792i
$870$		0			0
$871$	−5.10464e9			−0.00886937
$872$		0			0
$873$	−3.70200e11	−	2.91746e11i	−0.637352	−	0.502282i
$874$		0			0
$875$	−4.07251e11	+	3.60481e10i	−0.694753	+	0.0614964i
$876$		0			0
$877$		−	2.91940e11i		−	0.493509i	−0.969078	−	0.246755i	$-0.920636\pi$
$877$		−	2.91940e11i		−	0.493509i	0.969078	−	0.246755i	$-0.0793641\pi$
$878$		0			0
$879$	−1.40952e11	−	2.90543e11i	−0.236111	−	0.486693i
$880$		0			0
$881$			3.04364e11i			0.505230i	0.967567	+	0.252615i	$0.0812906\pi$
$881$			3.04364e11i			0.505230i	−0.967567	+	0.252615i	$0.918709\pi$
$882$		0			0
$883$			4.35514e11i			0.716407i	0.933644	+	0.358203i	$0.116611\pi$
$883$			4.35514e11i			0.716407i	−0.933644	+	0.358203i	$0.883389\pi$
$884$		0			0
$885$	1.51676e11	−	2.38687e11i	0.247254	−	0.389095i
$886$		0			0
$887$	−1.80753e11			−0.292006			−0.146003	−	0.989284i	$-0.546641\pi$
$887$	−1.80753e11			−0.292006			−0.146003	+	0.989284i	$0.546641\pi$
$888$		0			0
$889$	2.30761e11			0.369450
$890$		0			0
$891$	−8.96428e11	+	2.15518e11i	−1.42234	+	0.341957i
$892$		0			0
$893$	−3.53837e10			−0.0556414
$894$		0			0
$895$	−5.79730e10	−	9.39171e10i	−0.0903511	−	0.146370i
$896$		0			0
$897$	−4.00122e10	+	1.94113e10i	−0.0618049	+	0.0299836i
$898$		0			0
$899$			1.44243e12i			2.20829i
$900$		0			0
$901$	−8.51553e11			−1.29215
$902$		0			0
$903$	−4.01519e11	−	8.27645e11i	−0.603885	−	1.24478i
$904$		0			0
$905$	5.51915e11	−	3.40685e11i	0.822769	−	0.507877i
$906$		0			0
$907$			1.24264e12i			1.83618i	0.396374	+	0.918089i	$0.370268\pi$
$907$			1.24264e12i			1.83618i	−0.396374	+	0.918089i	$0.629732\pi$
$908$		0			0
$909$	−5.78166e11	−	4.55639e11i	−0.846832	−	0.667368i
$910$		0			0
$911$			3.34146e10i			0.0485135i	0.999706	+	0.0242568i	$0.00772193\pi$
$911$			3.34146e10i			0.0485135i	−0.999706	+	0.0242568i	$0.992278\pi$
$912$		0			0
$913$			1.44159e12i			2.07472i
$914$		0			0
$915$	1.33325e10	+	8.47227e9i	0.0190208	+	0.0120869i
$916$		0			0
$917$	1.19161e11			0.168523
$918$		0			0
$919$	−1.22601e12			−1.71882			−0.859412	−	0.511283i	$-0.829170\pi$
$919$	−1.22601e12			−1.71882			−0.859412	+	0.511283i	$0.829170\pi$
$920$		0			0
$921$	6.77120e11	−	3.28494e11i	0.941081	−	0.456550i
$922$		0			0
$923$	−1.90359e11			−0.262281
$924$		0			0
$925$	−7.67541e11	−	3.84821e11i	−1.04842	−	0.525644i
$926$		0			0
$927$	−6.89948e11	−	5.43732e11i	−0.934324	−	0.736319i
$928$		0			0
$929$			1.46087e12i			1.96133i	0.195701	+	0.980664i	$0.437302\pi$
$929$			1.46087e12i			1.96133i	−0.195701	+	0.980664i	$0.562698\pi$
$930$		0			0
$931$	5.34204e10			0.0711064
$932$		0			0
$933$	−8.16568e11	+	3.96145e11i	−1.07762	+	0.522790i
$934$		0			0
$935$	4.86639e11	+	7.88363e11i	0.636738	+	1.03152i
$936$		0			0
$937$		−	1.02495e12i		−	1.32968i	−0.746987	−	0.664838i	$-0.768500\pi$
$937$		−	1.02495e12i		−	1.32968i	0.746987	−	0.664838i	$-0.231500\pi$
$938$		0			0
$939$	6.88793e11	−	3.34157e11i	0.885985	−	0.429821i
$940$		0			0
$941$		−	1.83735e11i		−	0.234333i	−0.993112	−	0.117166i	$-0.962619\pi$
$941$		−	1.83735e11i		−	0.234333i	0.993112	−	0.117166i	$-0.0373811\pi$
$942$		0			0
$943$			2.66288e9i			0.00336748i
$944$		0			0
$945$	−1.84069e11	−	5.24888e11i	−0.230810	−	0.658172i
$946$		0			0
$947$	−2.26053e11			−0.281067			−0.140533	−	0.990076i	$-0.544882\pi$
$947$	−2.26053e11			−0.281067			−0.140533	+	0.990076i	$0.544882\pi$
$948$		0			0
$949$	−1.41626e10			−0.0174613
$950$		0			0
$951$	2.99946e10	+	6.18276e10i	0.0366709	+	0.0755893i
$952$		0			0
$953$	−1.49255e12			−1.80949			−0.904745	−	0.425953i	$-0.859939\pi$
$953$	−1.49255e12			−1.80949			−0.904745	+	0.425953i	$0.859939\pi$
$954$		0			0
$955$	−1.44991e11	−	2.34887e11i	−0.174312	−	0.282388i
$956$		0			0
$957$	−8.53808e11	−	1.75994e12i	−1.01792	−	2.09822i
$958$		0			0
$959$		−	8.45250e11i		−	0.999334i
$960$		0			0
$961$	7.83650e11			0.918816
$962$		0			0
$963$	1.49103e11	−	1.89198e11i	0.173373	−	0.219995i
$964$		0			0
$965$	5.92468e11	+	9.59807e11i	0.683212	+	1.10681i
$966$		0			0
$967$		−	7.94256e11i		−	0.908352i	−0.890912	−	0.454176i	$-0.849934\pi$
$967$		−	7.94256e11i		−	0.908352i	0.890912	−	0.454176i	$-0.150066\pi$
$968$		0			0
$969$	−4.41543e10	−	9.10146e10i	−0.0500815	−	0.103232i
$970$		0			0
$971$		−	7.55855e10i		−	0.0850279i	−0.999096	−	0.0425139i	$-0.986463\pi$
$971$		−	7.55855e10i		−	0.0850279i	0.999096	−	0.0425139i	$-0.0135367\pi$
$972$		0			0
$973$		−	3.50185e11i		−	0.390702i
$974$		0			0
$975$	2.47091e9	−	1.89221e11i	0.00273425	−	0.209387i
$976$		0			0
$977$	1.31247e11			0.144049			0.0720244	−	0.997403i	$-0.477054\pi$
$977$	1.31247e11			0.144049			0.0720244	+	0.997403i	$0.477054\pi$
$978$		0			0
$979$	1.04999e12			1.14302
$980$		0			0
$981$	−6.82281e11	+	8.65755e11i	−0.736694	+	0.934801i
$982$		0			0
$983$	−2.55150e11			−0.273264			−0.136632	−	0.990622i	$-0.543628\pi$
$983$	−2.55150e11			−0.273264			−0.136632	+	0.990622i	$0.543628\pi$
$984$		0			0
$985$	9.81017e11	−	6.05560e11i	1.04215	−	0.643298i
$986$		0			0
$987$	−2.39309e11	+	1.16097e11i	−0.252168	+	0.122335i
$988$		0			0
$989$			6.22559e11i			0.650722i
$990$		0			0
$991$	1.00441e12			1.04139			0.520697	−	0.853742i	$-0.325672\pi$
$991$	1.00441e12			1.04139			0.520697	+	0.853742i	$0.325672\pi$
$992$		0			0
$993$	1.66713e11	+	3.43642e11i	0.171463	+	0.353435i
$994$		0			0
$995$	9.60550e11	−	5.92927e11i	0.980004	−	0.604935i
$996$		0			0
$997$			1.22258e12i			1.23737i	0.785641	+	0.618683i	$0.212333\pi$
$997$			1.22258e12i			1.23737i	−0.785641	+	0.618683i	$0.787667\pi$
$998$		0			0
$999$	2.50066e11	−	1.14105e12i	0.251068	−	1.14562i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.9.c.c.209.3		12
3.2	odd	2	inner	240.9.c.c.209.9		12
4.3	odd	2		15.9.d.c.14.8	yes	12
5.4	even	2	inner	240.9.c.c.209.10		12
12.11	even	2		15.9.d.c.14.6	yes	12
15.14	odd	2	inner	240.9.c.c.209.4		12
20.3	even	4		75.9.c.h.26.5		12
20.7	even	4		75.9.c.h.26.8		12
20.19	odd	2		15.9.d.c.14.5	✓	12
60.23	odd	4		75.9.c.h.26.7		12
60.47	odd	4		75.9.c.h.26.6		12
60.59	even	2		15.9.d.c.14.7	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.9.d.c.14.5	✓	12	20.19	odd	2
15.9.d.c.14.6	yes	12	12.11	even	2
15.9.d.c.14.7	yes	12	60.59	even	2
15.9.d.c.14.8	yes	12	4.3	odd	2
75.9.c.h.26.5		12	20.3	even	4
75.9.c.h.26.6		12	60.47	odd	4
75.9.c.h.26.7		12	60.23	odd	4
75.9.c.h.26.8		12	20.7	even	4
240.9.c.c.209.3		12	1.1	even	1	trivial
240.9.c.c.209.4		12	15.14	odd	2	inner
240.9.c.c.209.9		12	3.2	odd	2	inner
240.9.c.c.209.10		12	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-35.3550 - 72.8768i) q^{3} +(-531.836 + 328.291i) q^{5} +1674.62i q^{7} +(-4061.05 + 5153.12i) q^{9} +O(q^{10})\)	\(q+(-35.3550 - 72.8768i) q^{3} +(-531.836 + 328.291i) q^{5} +1674.62i q^{7} +(-4061.05 + 5153.12i) q^{9} -21417.9i q^{11} +5980.82i q^{13} +(42727.9 + 27151.8i) q^{15} +69210.3 q^{17} +18044.8 q^{19} +(122041. - 59206.3i) q^{21} -91800.0 q^{23} +(175075. - 349194. i) q^{25} +(519121. + 113768. i) q^{27} +1.12754e6i q^{29} +1.27927e6 q^{31} +(-1.56087e6 + 757230. i) q^{33} +(-549764. - 890626. i) q^{35} -2.19804e6i q^{37} +(435863. - 211452. i) q^{39} -29007.4i q^{41} -6.78169e6i q^{43} +(468092. - 4.07382e6i) q^{45} -1.96089e6 q^{47} +2.96044e6 q^{49} +(-2.44693e6 - 5.04382e6i) q^{51} -1.23039e7 q^{53} +(7.03131e6 + 1.13908e7i) q^{55} +(-637973. - 1.31504e6i) q^{57} -5.58621e6i q^{59} +312034. q^{61} +(-8.62953e6 - 6.80073e6i) q^{63} +(-1.96345e6 - 3.18082e6i) q^{65} +853503. i q^{67} +(3.24559e6 + 6.69009e6i) q^{69} +3.18282e7i q^{71} +2.36800e6i q^{73} +(-3.16379e7 - 413140. i) q^{75} +3.58669e7 q^{77} -2.92328e7 q^{79} +(-1.00625e7 - 4.18541e7i) q^{81} -6.73076e7 q^{83} +(-3.68086e7 + 2.27211e7i) q^{85} +(8.21715e7 - 3.98642e7i) q^{87} +4.90240e7i q^{89} -1.00156e7 q^{91} +(-4.52287e7 - 9.32293e7i) q^{93} +(-9.59686e6 + 5.92394e6i) q^{95} +7.18400e7i q^{97} +(1.10369e8 + 8.69792e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 22824 q^{9}+O(q^{10}) \) 12 * q - 22824 * q^9	\( 12 q - 22824 q^{9} + 95520 q^{15} - 276192 q^{19} - 604044 q^{21} - 2036220 q^{25} + 279216 q^{31} - 3780864 q^{39} + 9523980 q^{45} - 6222300 q^{49} - 3931248 q^{51} + 16903440 q^{55} - 91958256 q^{61} + 8138748 q^{69} - 15031440 q^{75} - 420402672 q^{79} + 98480772 q^{81} - 117091440 q^{85} + 100211328 q^{91} + 640360080 q^{99}+O(q^{100}) \) 12 * q - 22824 * q^9 + 95520 * q^15 - 276192 * q^19 - 604044 * q^21 - 2036220 * q^25 + 279216 * q^31 - 3780864 * q^39 + 9523980 * q^45 - 6222300 * q^49 - 3931248 * q^51 + 16903440 * q^55 - 91958256 * q^61 + 8138748 * q^69 - 15031440 * q^75 - 420402672 * q^79 + 98480772 * q^81 - 117091440 * q^85 + 100211328 * q^91 + 640360080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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