LMFDB - Embedded newform 300.9.k.e.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,9,Mod(157,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("300.157");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	300.k (of order $4$, degree $2$, 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:	$122.213583018$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 30946474 x^{14} - 8341419336 x^{13} + 380689791299777 x^{12} + \cdots + 57\!\cdots\!00 $ x^16 - 4x^15 - 30946474x^14 - 8341419336x^13 + 380689791299777x^12 + 172233390406399084x^11 - 2382137738311270416524x^10 - 1303628014982980229183568x^9 + 8170157809851151257627202984x^8 + 4722131342312473670415721362432x^7 - 15187994345395678935434992322703872x^6 - 8501142216286271666986373720765290240x^5 + 13719409820001055356751562088159234867776x^4 + 6705290345628598892954879974291445910470400x^3 - 4432537206418276871411586926292645523148742400x^2 - 1274737393430152937401280967045971687758547840000*x + 575975308456587940916620472287127145276670888000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{20}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.3
Root			$1685.41 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.0681 - 33.0681i) q^{3} +(1421.41 - 1421.41i) q^{7} +2187.00i q^{9} +O(q^{10})$	$q+(-33.0681 - 33.0681i) q^{3} +(1421.41 - 1421.41i) q^{7} +2187.00i q^{9} -6448.89 q^{11} +(14027.0 + 14027.0i) q^{13} +(-21937.7 + 21937.7i) q^{17} -33080.7i q^{19} -94007.0 q^{21} +(-23074.9 - 23074.9i) q^{23} +(72320.0 - 72320.0i) q^{27} -541792. i q^{29} -571128. q^{31} +(213253. + 213253. i) q^{33} +(945689. - 945689. i) q^{37} -927693. i q^{39} -4.61879e6 q^{41} +(2.14190e6 + 2.14190e6i) q^{43} +(3.75023e6 - 3.75023e6i) q^{47} +1.72396e6i q^{49} +1.45088e6 q^{51} +(184412. + 184412. i) q^{53} +(-1.09392e6 + 1.09392e6i) q^{57} -6.00168e6i q^{59} +1.56657e7 q^{61} +(3.10863e6 + 3.10863e6i) q^{63} +(9.12552e6 - 9.12552e6i) q^{67} +1.52609e6i q^{69} +1.50788e7 q^{71} +(-3.53089e7 - 3.53089e7i) q^{73} +(-9.16654e6 + 9.16654e6i) q^{77} +5.63479e7i q^{79} -4.78297e6 q^{81} +(-3.49654e7 - 3.49654e7i) q^{83} +(-1.79160e7 + 1.79160e7i) q^{87} -8.31741e7i q^{89} +3.98764e7 q^{91} +(1.88861e7 + 1.88861e7i) q^{93} +(-6.21559e7 + 6.21559e7i) q^{97} -1.41037e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4220 q^{7}+O(q^{10}) $ 16 * q - 4220 * q^7	$ 16 q - 4220 q^{7} + 23616 q^{11} + 18900 q^{13} + 44940 q^{17} + 163944 q^{21} - 196440 q^{23} + 3742624 q^{31} + 134460 q^{33} + 2141100 q^{37} + 16347000 q^{41} - 12080280 q^{43} + 14942400 q^{47} + 7693704 q^{51} - 23760300 q^{53} + 27530280 q^{57} + 85401912 q^{61} - 9229140 q^{63} + 99451240 q^{67} + 73302480 q^{71} - 124097320 q^{73} + 185945400 q^{77} - 76527504 q^{81} + 22058160 q^{83} + 110300940 q^{87} + 170997360 q^{91} - 9969480 q^{93} - 185269800 q^{97}+O(q^{100}) $ 16 * q - 4220 * q^7 + 23616 * q^11 + 18900 * q^13 + 44940 * q^17 + 163944 * q^21 - 196440 * q^23 + 3742624 * q^31 + 134460 * q^33 + 2141100 * q^37 + 16347000 * q^41 - 12080280 * q^43 + 14942400 * q^47 + 7693704 * q^51 - 23760300 * q^53 + 27530280 * q^57 + 85401912 * q^61 - 9229140 * q^63 + 99451240 * q^67 + 73302480 * q^71 - 124097320 * q^73 + 185945400 * q^77 - 76527504 * q^81 + 22058160 * q^83 + 110300940 * q^87 + 170997360 * q^91 - 9969480 * q^93 - 185269800 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1421.41	−	1421.41i	0.592009	−	0.592009i	−0.346165	−	0.938174i	$-0.612516\pi$
$7$	1421.41	−	1421.41i	0.592009	−	0.592009i	0.938174	+	0.346165i	$0.112516\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−6448.89			−0.440468			−0.220234	−	0.975447i	$-0.570682\pi$
$11$	−6448.89			−0.440468			−0.220234	+	0.975447i	$0.570682\pi$
$12$		0			0
$13$	14027.0	+	14027.0i	0.491125	+	0.491125i	0.908660	−	0.417536i	$-0.137106\pi$
$13$	14027.0	+	14027.0i	0.491125	+	0.491125i	−0.417536	+	0.908660i	$0.637106\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−21937.7	+	21937.7i	−0.262661	+	0.262661i	−0.826134	−	0.563473i	$-0.809465\pi$
$17$	−21937.7	+	21937.7i	−0.262661	+	0.262661i	0.563473	+	0.826134i	$0.309465\pi$
$18$		0			0
$19$		−	33080.7i		−	0.253840i	−0.991913	−	0.126920i	$-0.959491\pi$
$19$		−	33080.7i		−	0.253840i	0.991913	−	0.126920i	$-0.0405092\pi$
$20$		0			0
$21$	−94007.0			−0.483374
$22$		0			0
$23$	−23074.9	−	23074.9i	−0.0824572	−	0.0824572i	0.664675	−	0.747132i	$-0.268570\pi$
$23$	−23074.9	−	23074.9i	−0.0824572	−	0.0824572i	−0.747132	+	0.664675i	$0.768570\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$		0			0
$29$		−	541792.i		−	0.766021i	−0.923744	−	0.383010i	$-0.874887\pi$
$29$		−	541792.i		−	0.766021i	0.923744	−	0.383010i	$-0.125113\pi$
$30$		0			0
$31$	−571128.			−0.618424			−0.309212	−	0.950993i	$-0.600065\pi$
$31$	−571128.			−0.618424			−0.309212	+	0.950993i	$0.600065\pi$
$32$		0			0
$33$	213253.	+	213253.i	0.179820	+	0.179820i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	945689.	−	945689.i	0.504593	−	0.504593i	−0.408268	−	0.912862i	$-0.633867\pi$
$37$	945689.	−	945689.i	0.504593	−	0.504593i	0.912862	+	0.408268i	$0.133867\pi$
$38$		0			0
$39$		−	927693.i		−	0.401002i
$40$		0			0
$41$	−4.61879e6			−1.63453			−0.817265	−	0.576262i	$-0.804511\pi$
$41$	−4.61879e6			−1.63453			−0.817265	+	0.576262i	$0.804511\pi$
$42$		0			0
$43$	2.14190e6	+	2.14190e6i	0.626506	+	0.626506i	0.947187	−	0.320681i	$-0.103912\pi$
$43$	2.14190e6	+	2.14190e6i	0.626506	+	0.626506i	−0.320681	+	0.947187i	$0.603912\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.75023e6	−	3.75023e6i	0.768540	−	0.768540i	−0.209310	−	0.977849i	$-0.567122\pi$
$47$	3.75023e6	−	3.75023e6i	0.768540	−	0.768540i	0.977849	+	0.209310i	$0.0671216\pi$
$48$		0			0
$49$			1.72396e6i			0.299050i
$50$		0			0
$51$	1.45088e6			0.214462
$52$		0			0
$53$	184412.	+	184412.i	0.0233715	+	0.0233715i	0.718696	−	0.695324i	$-0.244739\pi$
$53$	184412.	+	184412.i	0.0233715	+	0.0233715i	−0.695324	+	0.718696i	$0.744739\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.09392e6	+	1.09392e6i	−0.103630	+	0.103630i
$58$		0			0
$59$		−	6.00168e6i		−	0.495296i	−0.968850	−	0.247648i	$-0.920342\pi$
$59$		−	6.00168e6i		−	0.495296i	0.968850	−	0.247648i	$-0.0796576\pi$
$60$		0			0
$61$	1.56657e7			1.13144			0.565718	−	0.824599i	$-0.308599\pi$
$61$	1.56657e7			1.13144			0.565718	+	0.824599i	$0.308599\pi$
$62$		0			0
$63$	3.10863e6	+	3.10863e6i	0.197336	+	0.197336i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	9.12552e6	−	9.12552e6i	0.452854	−	0.452854i	−0.443447	−	0.896301i	$-0.646244\pi$
$67$	9.12552e6	−	9.12552e6i	0.452854	−	0.452854i	0.896301	+	0.443447i	$0.146244\pi$
$68$		0			0
$69$			1.52609e6i			0.0673261i
$70$		0			0
$71$	1.50788e7			0.593379			0.296690	−	0.954974i	$-0.404117\pi$
$71$	1.50788e7			0.593379			0.296690	+	0.954974i	$0.404117\pi$
$72$		0			0
$73$	−3.53089e7	−	3.53089e7i	−1.24335	−	1.24335i	−0.958603	−	0.284745i	$-0.908091\pi$
$73$	−3.53089e7	−	3.53089e7i	−1.24335	−	1.24335i	−0.284745	−	0.958603i	$-0.591909\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.16654e6	+	9.16654e6i	−0.260761	+	0.260761i
$78$		0			0
$79$			5.63479e7i			1.44667i	0.690497	+	0.723335i	$0.257392\pi$
$79$			5.63479e7i			1.44667i	−0.690497	+	0.723335i	$0.742608\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−3.49654e7	−	3.49654e7i	−0.736759	−	0.736759i	0.235190	−	0.971949i	$-0.424429\pi$
$83$	−3.49654e7	−	3.49654e7i	−0.736759	−	0.736759i	−0.971949	+	0.235190i	$0.924429\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.79160e7	+	1.79160e7i	−0.312727	+	0.312727i
$88$		0			0
$89$		−	8.31741e7i		−	1.32565i	−0.748775	−	0.662824i	$-0.769358\pi$
$89$		−	8.31741e7i		−	1.32565i	0.748775	−	0.662824i	$-0.230642\pi$
$90$		0			0
$91$	3.98764e7			0.581501
$92$		0			0
$93$	1.88861e7	+	1.88861e7i	0.252471	+	0.252471i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.21559e7	+	6.21559e7i	−0.702094	+	0.702094i	−0.964860	−	0.262766i	$-0.915365\pi$
$97$	−6.21559e7	+	6.21559e7i	−0.702094	+	0.702094i	0.262766	+	0.964860i	$0.415365\pi$
$98$		0			0
$99$		−	1.41037e7i		−	0.146823i
$100$		0			0
$101$	−1.11957e8			−1.07588			−0.537942	−	0.842982i	$-0.680798\pi$
$101$	−1.11957e8			−1.07588			−0.537942	+	0.842982i	$0.680798\pi$
$102$		0			0
$103$	−1.22142e8	−	1.22142e8i	−1.08522	−	1.08522i	−0.996013	−	0.0892031i	$-0.971568\pi$
$103$	−1.22142e8	−	1.22142e8i	−1.08522	−	1.08522i	−0.0892031	−	0.996013i	$-0.528432\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.32675e7	−	7.32675e7i	0.558954	−	0.558954i	−0.370056	−	0.929010i	$-0.620661\pi$
$107$	7.32675e7	−	7.32675e7i	0.558954	−	0.558954i	0.929010	+	0.370056i	$0.120661\pi$
$108$		0			0
$109$			1.53228e8i			1.08551i	0.839893	+	0.542753i	$0.182618\pi$
$109$			1.53228e8i			1.08551i	−0.839893	+	0.542753i	$0.817382\pi$
$110$		0			0
$111$	−6.25443e7			−0.411999
$112$		0			0
$113$	1.74305e8	+	1.74305e8i	1.06905	+	1.06905i	0.997432	+	0.0716129i	$0.0228146\pi$
$113$	1.74305e8	+	1.74305e8i	1.06905	+	1.06905i	0.0716129	+	0.997432i	$0.477185\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.06771e7	+	3.06771e7i	−0.163708	+	0.163708i
$118$		0			0
$119$			6.23652e7i			0.310996i
$120$		0			0
$121$	−1.72771e8			−0.805988
$122$		0			0
$123$	1.52735e8	+	1.52735e8i	0.667294	+	0.667294i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1.59727e8	−	1.59727e8i	0.613992	−	0.613992i	−0.329992	−	0.943984i	$-0.607046\pi$
$127$	1.59727e8	−	1.59727e8i	0.613992	−	0.613992i	0.943984	+	0.329992i	$0.107046\pi$
$128$		0			0
$129$		−	1.41657e8i		−	0.511540i
$130$		0			0
$131$	−5.42246e8			−1.84124			−0.920621	−	0.390457i	$-0.872317\pi$
$131$	−5.42246e8			−1.84124			−0.920621	+	0.390457i	$0.872317\pi$
$132$		0			0
$133$	−4.70214e7	−	4.70214e7i	−0.150276	−	0.150276i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.29494e8	+	4.29494e8i	−1.21920	+	1.21920i	−0.251285	+	0.967913i	$0.580853\pi$
$137$	−4.29494e8	+	4.29494e8i	−1.21920	+	1.21920i	−0.967913	+	0.251285i	$0.919147\pi$
$138$		0			0
$139$			6.26846e8i			1.67920i	0.543208	+	0.839598i	$0.317210\pi$
$139$			6.26846e8i			1.67920i	−0.543208	+	0.839598i	$0.682790\pi$
$140$		0			0
$141$	−2.48026e8			−0.627510
$142$		0			0
$143$	−9.04586e7	−	9.04586e7i	−0.216325	−	0.216325i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.70082e7	−	5.70082e7i	0.122087	−	0.122087i
$148$		0			0
$149$			1.74241e8i			0.353512i	0.984255	+	0.176756i	$0.0565603\pi$
$149$			1.74241e8i			0.353512i	−0.984255	+	0.176756i	$0.943440\pi$
$150$		0			0
$151$	−3.11625e8			−0.599411			−0.299705	−	0.954032i	$-0.596888\pi$
$151$	−3.11625e8			−0.599411			−0.299705	+	0.954032i	$0.596888\pi$
$152$		0			0
$153$	−4.79778e7	−	4.79778e7i	−0.0875537	−	0.0875537i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.11154e8	+	4.11154e8i	−0.676715	+	0.676715i	−0.959255	−	0.282541i	$-0.908823\pi$
$157$	−4.11154e8	+	4.11154e8i	−0.676715	+	0.676715i	0.282541	+	0.959255i	$0.408823\pi$
$158$		0			0
$159$		−	1.21963e7i		−	0.0190827i
$160$		0			0
$161$	−6.55980e7			−0.0976309
$162$		0			0
$163$	−7.85601e8	−	7.85601e8i	−1.11289	−	1.11289i	−0.992758	−	0.120130i	$-0.961669\pi$
$163$	−7.85601e8	−	7.85601e8i	−1.11289	−	1.11289i	−0.120130	−	0.992758i	$-0.538331\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.74678e8	+	2.74678e8i	−0.353150	+	0.353150i	−0.861280	−	0.508131i	$-0.830337\pi$
$167$	−2.74678e8	+	2.74678e8i	−0.353150	+	0.353150i	0.508131	+	0.861280i	$0.330337\pi$
$168$		0			0
$169$		−	4.22217e8i		−	0.517593i
$170$		0			0
$171$	7.23475e7			0.0846134
$172$		0			0
$173$	−8.67848e8	−	8.67848e8i	−0.968856	−	0.968856i	0.0306738	−	0.999529i	$-0.490235\pi$
$173$	−8.67848e8	−	8.67848e8i	−0.968856	−	0.968856i	−0.999529	+	0.0306738i	$0.990235\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.98464e8	+	1.98464e8i	−0.202204	+	0.202204i
$178$		0			0
$179$			1.27625e9i			1.24315i	0.783354	+	0.621576i	$0.213507\pi$
$179$			1.27625e9i			1.24315i	−0.783354	+	0.621576i	$0.786493\pi$
$180$		0			0
$181$	−2.00964e8			−0.187243			−0.0936214	−	0.995608i	$-0.529844\pi$
$181$	−2.00964e8			−0.187243			−0.0936214	+	0.995608i	$0.529844\pi$
$182$		0			0
$183$	−5.18035e8	−	5.18035e8i	−0.461907	−	0.461907i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.41474e8	−	1.41474e8i	0.115694	−	0.115694i
$188$		0			0
$189$		−	2.05593e8i		−	0.161125i
$190$		0			0
$191$	−3.64201e8			−0.273658			−0.136829	−	0.990595i	$-0.543691\pi$
$191$	−3.64201e8			−0.273658			−0.136829	+	0.990595i	$0.543691\pi$
$192$		0			0
$193$	−6.34737e8	−	6.34737e8i	−0.457472	−	0.457472i	0.440353	−	0.897825i	$-0.354853\pi$
$193$	−6.34737e8	−	6.34737e8i	−0.457472	−	0.457472i	−0.897825	+	0.440353i	$0.854853\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.53965e8	+	2.53965e8i	−0.168620	+	0.168620i	−0.786373	−	0.617752i	$-0.788043\pi$
$197$	−2.53965e8	+	2.53965e8i	−0.168620	+	0.168620i	0.617752	+	0.786373i	$0.288043\pi$
$198$		0			0
$199$			1.61073e9i			1.02709i	0.858061	+	0.513547i	$0.171669\pi$
$199$			1.61073e9i			1.02709i	−0.858061	+	0.513547i	$0.828331\pi$
$200$		0			0
$201$	−6.03528e8			−0.369754
$202$		0			0
$203$	−7.70111e8	−	7.70111e8i	−0.453491	−	0.453491i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.04648e7	−	5.04648e7i	0.0274857	−	0.0274857i
$208$		0			0
$209$			2.13334e8i			0.111808i
$210$		0			0
$211$	−2.47780e9			−1.25007			−0.625037	−	0.780595i	$-0.714916\pi$
$211$	−2.47780e9			−1.25007			−0.625037	+	0.780595i	$0.714916\pi$
$212$		0			0
$213$	−4.98626e8	−	4.98626e8i	−0.242246	−	0.242246i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−8.11809e8	+	8.11809e8i	−0.366113	+	0.366113i
$218$		0			0
$219$			2.33520e9i			1.01519i
$220$		0			0
$221$	−6.15441e8			−0.257999
$222$		0			0
$223$	2.69279e9	+	2.69279e9i	1.08889	+	1.08889i	0.995643	+	0.0932435i	$0.0297235\pi$
$223$	2.69279e9	+	2.69279e9i	1.08889	+	1.08889i	0.0932435	+	0.995643i	$0.470276\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.35597e8	−	3.35597e8i	0.126390	−	0.126390i	−0.641082	−	0.767472i	$-0.721514\pi$
$227$	3.35597e8	−	3.35597e8i	0.126390	−	0.126390i	0.767472	+	0.641082i	$0.221514\pi$
$228$		0			0
$229$		−	2.57359e9i		−	0.935831i	−0.883773	−	0.467916i	$-0.845005\pi$
$229$		−	2.57359e9i		−	0.935831i	0.883773	−	0.467916i	$-0.154995\pi$
$230$		0			0
$231$	6.06241e8			0.212911
$232$		0			0
$233$	−1.24380e9	−	1.24380e9i	−0.422014	−	0.422014i	0.463883	−	0.885897i	$-0.346456\pi$
$233$	−1.24380e9	−	1.24380e9i	−0.422014	−	0.422014i	−0.885897	+	0.463883i	$0.846456\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.86332e9	−	1.86332e9i	0.590601	−	0.590601i
$238$		0			0
$239$			1.14216e9i			0.350056i	0.984563	+	0.175028i	$0.0560016\pi$
$239$			1.14216e9i			0.350056i	−0.984563	+	0.175028i	$0.943998\pi$
$240$		0			0
$241$	−5.71416e9			−1.69389			−0.846944	−	0.531682i	$-0.821560\pi$
$241$	−5.71416e9			−1.69389			−0.846944	+	0.531682i	$0.821560\pi$
$242$		0			0
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.64024e8	−	4.64024e8i	0.124667	−	0.124667i
$248$		0			0
$249$			2.31248e9i			0.601561i
$250$		0			0
$251$	−5.39492e9			−1.35922			−0.679610	−	0.733573i	$-0.737851\pi$
$251$	−5.39492e9			−1.35922			−0.679610	+	0.733573i	$0.737851\pi$
$252$		0			0
$253$	1.48808e8	+	1.48808e8i	0.0363198	+	0.0363198i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.45318e9	−	1.45318e9i	0.333110	−	0.333110i	−0.520657	−	0.853766i	$-0.674313\pi$
$257$	1.45318e9	−	1.45318e9i	0.333110	−	0.333110i	0.853766	+	0.520657i	$0.174313\pi$
$258$		0			0
$259$		−	2.68843e9i		−	0.597448i
$260$		0			0
$261$	1.18490e9			0.255340
$262$		0			0
$263$	−3.11720e9	−	3.11720e9i	−0.651542	−	0.651542i	0.301822	−	0.953364i	$-0.402405\pi$
$263$	−3.11720e9	−	3.11720e9i	−0.651542	−	0.651542i	−0.953364	+	0.301822i	$0.902405\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−2.75041e9	+	2.75041e9i	−0.541194	+	0.541194i
$268$		0			0
$269$		−	4.76521e8i		−	0.0910066i	−0.998964	−	0.0455033i	$-0.985511\pi$
$269$		−	4.76521e8i		−	0.0910066i	0.998964	−	0.0455033i	$-0.0144892\pi$
$270$		0			0
$271$	1.71931e9			0.318769			0.159384	−	0.987217i	$-0.449049\pi$
$271$	1.71931e9			0.318769			0.159384	+	0.987217i	$0.449049\pi$
$272$		0			0
$273$	−1.31864e9	−	1.31864e9i	−0.237397	−	0.237397i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−4.00956e9	+	4.00956e9i	−0.681049	+	0.681049i	−0.960236	−	0.279188i	$-0.909935\pi$
$277$	−4.00956e9	+	4.00956e9i	−0.681049	+	0.681049i	0.279188	+	0.960236i	$0.409935\pi$
$278$		0			0
$279$		−	1.24906e9i		−	0.206141i
$280$		0			0
$281$	−4.24302e9			−0.680533			−0.340267	−	0.940329i	$-0.610517\pi$
$281$	−4.24302e9			−0.680533			−0.340267	+	0.940329i	$0.610517\pi$
$282$		0			0
$283$	2.42645e9	+	2.42645e9i	0.378291	+	0.378291i	0.870485	−	0.492194i	$-0.163805\pi$
$283$	2.42645e9	+	2.42645e9i	0.378291	+	0.378291i	−0.492194	+	0.870485i	$0.663805\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.56521e9	+	6.56521e9i	−0.967657	+	0.967657i
$288$		0			0
$289$			6.01323e9i			0.862018i
$290$		0			0
$291$	4.11075e9			0.573257
$292$		0			0
$293$	−4.63530e9	−	4.63530e9i	−0.628937	−	0.628937i	0.318864	−	0.947801i	$-0.396699\pi$
$293$	−4.63530e9	−	4.63530e9i	−0.628937	−	0.628937i	−0.947801	+	0.318864i	$0.896699\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.66383e8	+	4.66383e8i	−0.0599401	+	0.0599401i
$298$		0			0
$299$		−	6.47344e8i		−	0.0809936i
$300$		0			0
$301$	6.08905e9			0.741795
$302$		0			0
$303$	3.70220e9	+	3.70220e9i	0.439227	+	0.439227i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.63497e8	+	1.63497e8i	−0.0184058	+	0.0184058i	−0.716250	−	0.697844i	$-0.754143\pi$
$307$	−1.63497e8	+	1.63497e8i	−0.0184058	+	0.0184058i	0.697844	+	0.716250i	$0.254143\pi$
$308$		0			0
$309$			8.07802e9i			0.886076i
$310$		0			0
$311$	1.05701e10			1.12989			0.564947	−	0.825127i	$-0.308897\pi$
$311$	1.05701e10			1.12989			0.564947	+	0.825127i	$0.308897\pi$
$312$		0			0
$313$	−3.04959e9	−	3.04959e9i	−0.317734	−	0.317734i	0.530162	−	0.847896i	$-0.322131\pi$
$313$	−3.04959e9	−	3.04959e9i	−0.317734	−	0.317734i	−0.847896	+	0.530162i	$0.822131\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.16854e9	−	2.16854e9i	0.214748	−	0.214748i	−0.591533	−	0.806281i	$-0.701477\pi$
$317$	2.16854e9	−	2.16854e9i	0.214748	−	0.214748i	0.806281	+	0.591533i	$0.201477\pi$
$318$		0			0
$319$			3.49396e9i			0.337407i
$320$		0			0
$321$	−4.84563e9			−0.456384
$322$		0			0
$323$	7.25716e8	+	7.25716e8i	0.0666740	+	0.0666740i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.06696e9	−	5.06696e9i	0.443156	−	0.443156i
$328$		0			0
$329$		−	1.06613e10i		−	0.909965i
$330$		0			0
$331$	7.51717e9			0.626242			0.313121	−	0.949713i	$-0.398625\pi$
$331$	7.51717e9			0.626242			0.313121	+	0.949713i	$0.398625\pi$
$332$		0			0
$333$	2.06822e9	+	2.06822e9i	0.168198	+	0.168198i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	6.42067e9	−	6.42067e9i	0.497807	−	0.497807i	−0.412948	−	0.910755i	$-0.635501\pi$
$337$	6.42067e9	−	6.42067e9i	0.497807	−	0.497807i	0.910755	+	0.412948i	$0.135501\pi$
$338$		0			0
$339$		−	1.15279e10i		−	0.872872i
$340$		0			0
$341$	3.68314e9			0.272396
$342$		0			0
$343$	1.06446e10	+	1.06446e10i	0.769050	+	0.769050i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−6.31275e9	+	6.31275e9i	−0.435412	+	0.435412i	−0.890465	−	0.455052i	$-0.849621\pi$
$347$	−6.31275e9	+	6.31275e9i	−0.435412	+	0.435412i	0.455052	+	0.890465i	$0.349621\pi$
$348$		0			0
$349$			9.24869e9i			0.623417i	0.950178	+	0.311708i	$0.100901\pi$
$349$			9.24869e9i			0.623417i	−0.950178	+	0.311708i	$0.899099\pi$
$350$		0			0
$351$	2.02887e9			0.133667
$352$		0			0
$353$	1.03273e10	+	1.03273e10i	0.665101	+	0.665101i	0.956578	−	0.291477i	$-0.0941466\pi$
$353$	1.03273e10	+	1.03273e10i	0.665101	+	0.665101i	−0.291477	+	0.956578i	$0.594147\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.06230e9	−	2.06230e9i	0.126963	−	0.126963i
$358$		0			0
$359$		−	1.74137e10i		−	1.04837i	−0.851605	−	0.524183i	$-0.824371\pi$
$359$		−	1.74137e10i		−	1.04837i	0.851605	−	0.524183i	$-0.175629\pi$
$360$		0			0
$361$	1.58892e10			0.935565
$362$		0			0
$363$	5.71320e9	+	5.71320e9i	0.329043	+	0.329043i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.11285e10	−	2.11285e10i	1.16467	−	1.16467i	0.181234	−	0.983440i	$-0.441991\pi$
$367$	2.11285e10	−	2.11285e10i	1.16467	−	1.16467i	0.983440	−	0.181234i	$-0.0580092\pi$
$368$		0			0
$369$		−	1.01013e10i		−	0.544843i
$370$		0			0
$371$	5.24252e8			0.0276722
$372$		0			0
$373$	−9.08745e9	−	9.08745e9i	−0.469469	−	0.469469i	0.432274	−	0.901742i	$-0.357711\pi$
$373$	−9.08745e9	−	9.08745e9i	−0.469469	−	0.469469i	−0.901742	+	0.432274i	$0.857711\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.59972e9	−	7.59972e9i	0.376212	−	0.376212i
$378$		0			0
$379$		−	1.13934e9i		−	0.0552198i	−0.999619	−	0.0276099i	$-0.991210\pi$
$379$		−	1.13934e9i		−	0.0552198i	0.999619	−	0.0276099i	$-0.00878962\pi$
$380$		0			0
$381$	−1.05637e10			−0.501322
$382$		0			0
$383$	1.13787e10	+	1.13787e10i	0.528806	+	0.528806i	0.920216	−	0.391411i	$-0.128013\pi$
$383$	1.13787e10	+	1.13787e10i	0.528806	+	0.528806i	−0.391411	+	0.920216i	$0.628013\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.68433e9	+	4.68433e9i	−0.208835	+	0.208835i
$388$		0			0
$389$		−	1.95425e10i		−	0.853458i	−0.904380	−	0.426729i	$-0.859666\pi$
$389$		−	1.95425e10i		−	0.853458i	0.904380	−	0.426729i	$-0.140334\pi$
$390$		0			0
$391$	1.01242e9			0.0433166
$392$		0			0
$393$	1.79310e10	+	1.79310e10i	0.751684	+	0.751684i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.65060e8	−	4.65060e8i	0.0187218	−	0.0187218i	−0.697684	−	0.716406i	$-0.745786\pi$
$397$	4.65060e8	−	4.65060e8i	0.0187218	−	0.0187218i	0.716406	+	0.697684i	$0.245786\pi$
$398$		0			0
$399$			3.10982e9i			0.122700i
$400$		0			0
$401$	−1.65388e10			−0.639627			−0.319814	−	0.947480i	$-0.603620\pi$
$401$	−1.65388e10			−0.639627			−0.319814	+	0.947480i	$0.603620\pi$
$402$		0			0
$403$	−8.01121e9	−	8.01121e9i	−0.303723	−	0.303723i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.09865e9	+	6.09865e9i	−0.222257	+	0.222257i
$408$		0			0
$409$		−	3.74228e10i		−	1.33734i	−0.743558	−	0.668672i	$-0.766863\pi$
$409$		−	3.74228e10i		−	1.33734i	0.743558	−	0.668672i	$-0.233137\pi$
$410$		0			0
$411$	2.84051e10			0.995471
$412$		0			0
$413$	−8.53087e9	−	8.53087e9i	−0.293220	−	0.293220i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.07286e10	−	2.07286e10i	0.685529	−	0.685529i
$418$		0			0
$419$		−	1.13279e10i		−	0.367530i	−0.982970	−	0.183765i	$-0.941171\pi$
$419$		−	1.13279e10i		−	0.367530i	0.982970	−	0.183765i	$-0.0588286\pi$
$420$		0			0
$421$	4.75545e10			1.51378			0.756890	−	0.653542i	$-0.226718\pi$
$421$	4.75545e10			1.51378			0.756890	+	0.653542i	$0.226718\pi$
$422$		0			0
$423$	8.20175e9	+	8.20175e9i	0.256180	+	0.256180i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.22674e10	−	2.22674e10i	0.669821	−	0.669821i
$428$		0			0
$429$			5.98259e9i			0.176628i
$430$		0			0
$431$	4.17289e10			1.20928			0.604642	−	0.796497i	$-0.293316\pi$
$431$	4.17289e10			1.20928			0.604642	+	0.796497i	$0.293316\pi$
$432$		0			0
$433$	2.61230e10	+	2.61230e10i	0.743142	+	0.743142i	0.973181	−	0.230039i	$-0.0738855\pi$
$433$	2.61230e10	+	2.61230e10i	0.743142	+	0.743142i	−0.230039	+	0.973181i	$0.573885\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.63335e8	+	7.63335e8i	−0.0209310	+	0.0209310i
$438$		0			0
$439$			5.87521e10i			1.58185i	0.611913	+	0.790925i	$0.290400\pi$
$439$			5.87521e10i			1.58185i	−0.611913	+	0.790925i	$0.709600\pi$
$440$		0			0
$441$	−3.77031e9			−0.0996833
$442$		0			0
$443$	−3.96928e10	−	3.96928e10i	−1.03062	−	1.03062i	−0.999516	−	0.0310989i	$-0.990099\pi$
$443$	−3.96928e10	−	3.96928e10i	−1.03062	−	1.03062i	−0.0310989	−	0.999516i	$-0.509901\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	5.76180e9	−	5.76180e9i	0.144321	−	0.144321i
$448$		0			0
$449$		−	3.44193e10i		−	0.846871i	−0.905926	−	0.423435i	$-0.860824\pi$
$449$		−	3.44193e10i		−	0.846871i	0.905926	−	0.423435i	$-0.139176\pi$
$450$		0			0
$451$	2.97861e10			0.719958
$452$		0			0
$453$	1.03049e10	+	1.03049e10i	0.244708	+	0.244708i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.06839e10	+	1.06839e10i	−0.244942	+	0.244942i	−0.818891	−	0.573949i	$-0.805411\pi$
$457$	−1.06839e10	+	1.06839e10i	−0.244942	+	0.244942i	0.573949	+	0.818891i	$0.305411\pi$
$458$		0			0
$459$			3.17307e9i			0.0714873i
$460$		0			0
$461$	3.58156e10			0.792990			0.396495	−	0.918037i	$-0.370226\pi$
$461$	3.58156e10			0.792990			0.396495	+	0.918037i	$0.370226\pi$
$462$		0			0
$463$	3.14487e10	+	3.14487e10i	0.684350	+	0.684350i	0.960977	−	0.276628i	$-0.0892168\pi$
$463$	3.14487e10	+	3.14487e10i	0.684350	+	0.684350i	−0.276628	+	0.960977i	$0.589217\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.26874e10	+	5.26874e10i	−1.10774	+	1.10774i	−0.114297	+	0.993447i	$0.536461\pi$
$467$	−5.26874e10	+	5.26874e10i	−1.10774	+	1.10774i	−0.993447	+	0.114297i	$0.963539\pi$
$468$		0			0
$469$		−	2.59423e10i		−	0.536188i
$470$		0			0
$471$	2.71922e10			0.552535
$472$		0			0
$473$	−1.38129e10	−	1.38129e10i	−0.275956	−	0.275956i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.03309e8	+	4.03309e8i	−0.00779049	+	0.00779049i
$478$		0			0
$479$		−	1.74792e10i		−	0.332032i	−0.986123	−	0.166016i	$-0.946910\pi$
$479$		−	1.74792e10i		−	0.332032i	0.986123	−	0.166016i	$-0.0530904\pi$
$480$		0			0
$481$	2.65304e10			0.495637
$482$		0			0
$483$	2.16920e9	+	2.16920e9i	0.0398576	+	0.0398576i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	8.49508e8	−	8.49508e8i	0.0151026	−	0.0151026i	−0.699515	−	0.714618i	$-0.746601\pi$
$487$	8.49508e8	−	8.49508e8i	0.0151026	−	0.0151026i	0.714618	+	0.699515i	$0.246601\pi$
$488$		0			0
$489$			5.19567e10i			0.908670i
$490$		0			0
$491$	−6.78803e10			−1.16793			−0.583967	−	0.811778i	$-0.698500\pi$
$491$	−6.78803e10			−1.16793			−0.583967	+	0.811778i	$0.698500\pi$
$492$		0			0
$493$	1.18857e10	+	1.18857e10i	0.201204	+	0.201204i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.14332e10	−	2.14332e10i	0.351286	−	0.351286i
$498$		0			0
$499$			4.24035e10i			0.683910i	0.939716	+	0.341955i	$0.111089\pi$
$499$			4.24035e10i			0.683910i	−0.939716	+	0.341955i	$0.888911\pi$
$500$		0			0
$501$	1.81662e10			0.288345
$502$		0			0
$503$	−4.93021e10	−	4.93021e10i	−0.770183	−	0.770183i	0.207956	−	0.978138i	$-0.433319\pi$
$503$	−4.93021e10	−	4.93021e10i	−0.770183	−	0.770183i	−0.978138	+	0.207956i	$0.933319\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.39619e10	+	1.39619e10i	−0.211307	+	0.211307i
$508$		0			0
$509$		−	3.71415e10i		−	0.553336i	−0.960966	−	0.276668i	$-0.910770\pi$
$509$		−	3.71415e10i		−	0.553336i	0.960966	−	0.276668i	$-0.0892302\pi$
$510$		0			0
$511$	−1.00377e11			−1.47215
$512$		0			0
$513$	−2.39240e9	−	2.39240e9i	−0.0345433	−	0.0345433i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.41848e10	+	2.41848e10i	−0.338517	+	0.338517i
$518$		0			0
$519$			5.73962e10i			0.791067i
$520$		0			0
$521$	−1.18507e11			−1.60839			−0.804196	−	0.594364i	$-0.797404\pi$
$521$	−1.18507e11			−1.60839			−0.804196	+	0.594364i	$0.797404\pi$
$522$		0			0
$523$	8.70334e10	+	8.70334e10i	1.16327	+	1.16327i	0.983756	+	0.179510i	$0.0574513\pi$
$523$	8.70334e10	+	8.70334e10i	1.16327	+	1.16327i	0.179510	+	0.983756i	$0.442549\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.25292e10	−	1.25292e10i	0.162436	−	0.162436i
$528$		0			0
$529$		−	7.72461e10i		−	0.986402i
$530$		0			0
$531$	1.31257e10			0.165099
$532$		0			0
$533$	−6.47878e10	−	6.47878e10i	−0.802758	−	0.802758i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.22033e10	−	4.22033e10i	0.507515	−	0.507515i
$538$		0			0
$539$		−	1.11177e10i		−	0.131722i
$540$		0			0
$541$	3.70912e9			0.0432994			0.0216497	−	0.999766i	$-0.493108\pi$
$541$	3.70912e9			0.0432994			0.0216497	+	0.999766i	$0.493108\pi$
$542$		0			0
$543$	6.64551e9	+	6.64551e9i	0.0764415	+	0.0764415i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.08248e10	+	1.08248e10i	−0.120913	+	0.120913i	−0.764974	−	0.644061i	$-0.777248\pi$
$547$	−1.08248e10	+	1.08248e10i	−0.120913	+	0.120913i	0.644061	+	0.764974i	$0.277248\pi$
$548$		0			0
$549$			3.42609e10i			0.377146i
$550$		0			0
$551$	−1.79229e10			−0.194447
$552$		0			0
$553$	8.00938e10	+	8.00938e10i	0.856443	+	0.856443i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.65637e10	+	8.65637e10i	−0.899321	+	0.899321i	−0.995376	−	0.0960548i	$-0.969378\pi$
$557$	−8.65637e10	+	8.65637e10i	−0.899321	+	0.899321i	0.0960548	+	0.995376i	$0.469378\pi$
$558$		0			0
$559$			6.00889e10i			0.615385i
$560$		0			0
$561$	−9.35655e9			−0.0944636
$562$		0			0
$563$	−7.64216e10	−	7.64216e10i	−0.760646	−	0.760646i	0.215793	−	0.976439i	$-0.430766\pi$
$563$	−7.64216e10	−	7.64216e10i	−0.760646	−	0.760646i	−0.976439	+	0.215793i	$0.930766\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−6.79858e9	+	6.79858e9i	−0.0657788	+	0.0657788i
$568$		0			0
$569$		−	8.67875e10i		−	0.827957i	−0.910287	−	0.413979i	$-0.864139\pi$
$569$		−	8.67875e10i		−	0.827957i	0.910287	−	0.413979i	$-0.135861\pi$
$570$		0			0
$571$	−1.29832e11			−1.22134			−0.610672	−	0.791883i	$-0.709101\pi$
$571$	−1.29832e11			−1.22134			−0.610672	+	0.791883i	$0.709101\pi$
$572$		0			0
$573$	1.20435e10	+	1.20435e10i	0.111720	+	0.111720i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	4.75002e10	−	4.75002e10i	0.428541	−	0.428541i	−0.459590	−	0.888131i	$-0.652004\pi$
$577$	4.75002e10	−	4.75002e10i	0.428541	−	0.428541i	0.888131	+	0.459590i	$0.152004\pi$
$578$		0			0
$579$			4.19791e10i			0.373525i
$580$		0			0
$581$	−9.94005e10			−0.872337
$582$		0			0
$583$	−1.18925e9	−	1.18925e9i	−0.0102944	−	0.0102944i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.03443e10	+	7.03443e10i	−0.592484	+	0.592484i	−0.938302	−	0.345818i	$-0.887601\pi$
$587$	−7.03443e10	+	7.03443e10i	−0.592484	+	0.592484i	0.345818	+	0.938302i	$0.387601\pi$
$588$		0			0
$589$			1.88933e10i			0.156981i
$590$		0			0
$591$	1.67963e10			0.137678
$592$		0			0
$593$	−6.33808e10	−	6.33808e10i	−0.512553	−	0.512553i	0.402755	−	0.915308i	$-0.368053\pi$
$593$	−6.33808e10	−	6.33808e10i	−0.512553	−	0.512553i	−0.915308	+	0.402755i	$0.868053\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	5.32638e10	−	5.32638e10i	0.419310	−	0.419310i
$598$		0			0
$599$			7.63320e10i			0.592924i	0.955045	+	0.296462i	$0.0958069\pi$
$599$			7.63320e10i			0.592924i	−0.955045	+	0.296462i	$0.904193\pi$
$600$		0			0
$601$	−1.53362e11			−1.17549			−0.587747	−	0.809045i	$-0.699985\pi$
$601$	−1.53362e11			−1.17549			−0.587747	+	0.809045i	$0.699985\pi$
$602$		0			0
$603$	1.99575e10	+	1.99575e10i	0.150951	+	0.150951i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.67091e10	−	3.67091e10i	0.270407	−	0.270407i	−0.558857	−	0.829264i	$-0.688760\pi$
$607$	3.67091e10	−	3.67091e10i	0.270407	−	0.270407i	0.829264	+	0.558857i	$0.188760\pi$
$608$		0			0
$609$			5.09322e10i			0.370274i
$610$		0			0
$611$	1.05209e11			0.754898
$612$		0			0
$613$	−9.91184e10	−	9.91184e10i	−0.701960	−	0.701960i	0.262871	−	0.964831i	$-0.415331\pi$
$613$	−9.91184e10	−	9.91184e10i	−0.701960	−	0.701960i	−0.964831	+	0.262871i	$0.915331\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.28925e10	−	3.28925e10i	0.226963	−	0.226963i	−0.584460	−	0.811423i	$-0.698693\pi$
$617$	3.28925e10	−	3.28925e10i	0.226963	−	0.226963i	0.811423	+	0.584460i	$0.198693\pi$
$618$		0			0
$619$			1.23785e11i			0.843152i	0.906793	+	0.421576i	$0.138523\pi$
$619$			1.23785e11i			0.843152i	−0.906793	+	0.421576i	$0.861477\pi$
$620$		0			0
$621$	−3.33755e9			−0.0224420
$622$		0			0
$623$	−1.18225e11	−	1.18225e11i	−0.784796	−	0.784796i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	7.05455e9	−	7.05455e9i	0.0456456	−	0.0456456i
$628$		0			0
$629$			4.14926e10i			0.265074i
$630$		0			0
$631$	2.41762e11			1.52500			0.762502	−	0.646986i	$-0.223971\pi$
$631$	2.41762e11			1.52500			0.762502	+	0.646986i	$0.223971\pi$
$632$		0			0
$633$	8.19361e10	+	8.19361e10i	0.510341	+	0.510341i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.41821e10	+	2.41821e10i	−0.146871	+	0.146871i
$638$		0			0
$639$			3.29773e10i			0.197793i
$640$		0			0
$641$	−2.70651e11			−1.60316			−0.801580	−	0.597887i	$-0.796007\pi$
$641$	−2.70651e11			−1.60316			−0.801580	+	0.597887i	$0.796007\pi$
$642$		0			0
$643$	−9.28116e10	−	9.28116e10i	−0.542948	−	0.542948i	0.381444	−	0.924392i	$-0.375427\pi$
$643$	−9.28116e10	−	9.28116e10i	−0.542948	−	0.542948i	−0.924392	+	0.381444i	$0.875427\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.06412e11	+	2.06412e11i	−1.17793	+	1.17793i	−0.197656	+	0.980271i	$0.563333\pi$
$647$	−2.06412e11	+	2.06412e11i	−1.17793	+	1.17793i	−0.980271	+	0.197656i	$0.936667\pi$
$648$		0			0
$649$			3.87042e10i			0.218162i
$650$		0			0
$651$	5.36900e10			0.298930
$652$		0			0
$653$	−2.37189e11	−	2.37189e11i	−1.30450	−	1.30450i	−0.925328	−	0.379168i	$-0.876210\pi$
$653$	−2.37189e11	−	2.37189e11i	−1.30450	−	1.30450i	−0.379168	−	0.925328i	$-0.623790\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	7.72206e10	−	7.72206e10i	0.414449	−	0.414449i
$658$		0			0
$659$		−	1.37158e10i		−	0.0727243i	−0.999339	−	0.0363621i	$-0.988423\pi$
$659$		−	1.37158e10i		−	0.0727243i	0.999339	−	0.0363621i	$-0.0115770\pi$
$660$		0			0
$661$	2.13787e11			1.11989			0.559945	−	0.828530i	$-0.310822\pi$
$661$	2.13787e11			1.11989			0.559945	+	0.828530i	$0.310822\pi$
$662$		0			0
$663$	2.03515e10	+	2.03515e10i	0.105328	+	0.105328i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.25018e10	+	1.25018e10i	−0.0631639	+	0.0631639i
$668$		0			0
$669$		−	1.78091e11i		−	0.889072i
$670$		0			0
$671$	−1.01026e11			−0.498361
$672$		0			0
$673$	−1.07603e11	−	1.07603e11i	−0.524523	−	0.524523i	0.394411	−	0.918934i	$-0.370949\pi$
$673$	−1.07603e11	−	1.07603e11i	−0.524523	−	0.524523i	−0.918934	+	0.394411i	$0.870949\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.29032e10	+	3.29032e10i	−0.156633	+	0.156633i	−0.781073	−	0.624440i	$-0.785327\pi$
$677$	−3.29032e10	+	3.29032e10i	−0.156633	+	0.156633i	0.624440	+	0.781073i	$0.285327\pi$
$678$		0			0
$679$			1.76698e11i			0.831292i
$680$		0			0
$681$	−2.21951e10			−0.103197
$682$		0			0
$683$	−2.68404e9	−	2.68404e9i	−0.0123341	−	0.0123341i	0.700913	−	0.713247i	$-0.252776\pi$
$683$	−2.68404e9	−	2.68404e9i	−0.0123341	−	0.0123341i	−0.713247	+	0.700913i	$0.752776\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−8.51038e10	+	8.51038e10i	−0.382052	+	0.382052i
$688$		0			0
$689$			5.17350e9i			0.0229566i
$690$		0			0
$691$	−9.53739e10			−0.418329			−0.209164	−	0.977881i	$-0.567074\pi$
$691$	−9.53739e10			−0.418329			−0.209164	+	0.977881i	$0.567074\pi$
$692$		0			0
$693$	−2.00472e10	−	2.00472e10i	−0.0869204	−	0.0869204i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.01326e11	−	1.01326e11i	0.429328	−	0.429328i
$698$		0			0
$699$			8.22602e10i			0.344573i
$700$		0			0
$701$	−6.76064e9			−0.0279973			−0.0139986	−	0.999902i	$-0.504456\pi$
$701$	−6.76064e9			−0.0279973			−0.0139986	+	0.999902i	$0.504456\pi$
$702$		0			0
$703$	−3.12841e10	−	3.12841e10i	−0.128086	−	0.128086i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.59137e11	+	1.59137e11i	−0.636933	+	0.636933i
$708$		0			0
$709$			2.53114e11i			1.00169i	0.865538	+	0.500843i	$0.166977\pi$
$709$			2.53114e11i			1.00169i	−0.865538	+	0.500843i	$0.833023\pi$
$710$		0			0
$711$	−1.23233e11			−0.482224
$712$		0			0
$713$	1.31787e10	+	1.31787e10i	0.0509935	+	0.0509935i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	3.77692e10	−	3.77692e10i	0.142910	−	0.142910i
$718$		0			0
$719$		−	4.82778e11i		−	1.80647i	−0.429141	−	0.903237i	$-0.641184\pi$
$719$		−	4.82778e11i		−	1.80647i	0.429141	−	0.903237i	$-0.358816\pi$
$720$		0			0
$721$	−3.47229e11			−1.28492
$722$		0			0
$723$	1.88957e11	+	1.88957e11i	0.691527	+	0.691527i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.03485e11	+	1.03485e11i	−0.370460	+	0.370460i	−0.867645	−	0.497184i	$-0.834367\pi$
$727$	−1.03485e11	+	1.03485e11i	−0.370460	+	0.370460i	0.497184	+	0.867645i	$0.334367\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−9.39768e10			−0.329118
$732$		0			0
$733$	−1.73151e10	−	1.73151e10i	−0.0599804	−	0.0599804i	0.676480	−	0.736461i	$-0.263504\pi$
$733$	−1.73151e10	−	1.73151e10i	−0.0599804	−	0.0599804i	−0.736461	+	0.676480i	$0.763504\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.88495e10	+	5.88495e10i	−0.199468	+	0.199468i
$738$		0			0
$739$			2.28072e11i			0.764704i	0.924017	+	0.382352i	$0.124886\pi$
$739$			2.28072e11i			0.764704i	−0.924017	+	0.382352i	$0.875114\pi$
$740$		0			0
$741$	−3.06888e10			−0.101790
$742$		0			0
$743$	2.73820e11	+	2.73820e11i	0.898483	+	0.898483i	0.995302	−	0.0968188i	$-0.0308667\pi$
$743$	2.73820e11	+	2.73820e11i	0.898483	+	0.898483i	−0.0968188	+	0.995302i	$0.530867\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.64692e10	−	7.64692e10i	0.245586	−	0.245586i
$748$		0			0
$749$		−	2.08287e11i		−	0.661812i
$750$		0			0
$751$	1.49831e11			0.471022			0.235511	−	0.971872i	$-0.424324\pi$
$751$	1.49831e11			0.471022			0.235511	+	0.971872i	$0.424324\pi$
$752$		0			0
$753$	1.78400e11	+	1.78400e11i	0.554900	+	0.554900i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	3.59186e11	−	3.59186e11i	1.09379	−	1.09379i	0.0986738	−	0.995120i	$-0.468540\pi$
$757$	3.59186e11	−	3.59186e11i	1.09379	−	1.09379i	0.995120	−	0.0986738i	$-0.0314600\pi$
$758$		0			0
$759$		−	9.84157e9i		−	0.0296550i
$760$		0			0
$761$	−5.72166e11			−1.70602			−0.853008	−	0.521897i	$-0.825224\pi$
$761$	−5.72166e11			−1.70602			−0.853008	+	0.521897i	$0.825224\pi$
$762$		0			0
$763$	2.17800e11	+	2.17800e11i	0.642629	+	0.642629i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.41856e10	−	8.41856e10i	0.243252	−	0.243252i
$768$		0			0
$769$		−	1.50923e10i		−	0.0431570i	−0.999767	−	0.0215785i	$-0.993131\pi$
$769$		−	1.50923e10i		−	0.0431570i	0.999767	−	0.0215785i	$-0.00686918\pi$
$770$		0			0
$771$	−9.61079e10			−0.271983
$772$		0			0
$773$	−3.06517e11	−	3.06517e11i	−0.858494	−	0.858494i	0.132667	−	0.991161i	$-0.457646\pi$
$773$	−3.06517e11	−	3.06517e11i	−0.858494	−	0.858494i	−0.991161	+	0.132667i	$0.957646\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−8.89014e10	+	8.89014e10i	−0.243907	+	0.243907i
$778$		0			0
$779$			1.52793e11i			0.414909i
$780$		0			0
$781$	−9.72413e10			−0.261365
$782$		0			0
$783$	−3.91824e10	−	3.91824e10i	−0.104242	−	0.104242i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.56130e11	+	1.56130e11i	−0.406994	+	0.406994i	−0.880689	−	0.473695i	$-0.842920\pi$
$787$	−1.56130e11	+	1.56130e11i	−0.406994	+	0.406994i	0.473695	+	0.880689i	$0.342920\pi$
$788$		0			0
$789$			2.06160e11i			0.531982i
$790$		0			0
$791$	4.95519e11			1.26577
$792$		0			0
$793$	2.19743e11	+	2.19743e11i	0.555676	+	0.555676i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.44366e11	−	2.44366e11i	0.605631	−	0.605631i	−0.336170	−	0.941801i	$-0.609132\pi$
$797$	2.44366e11	−	2.44366e11i	0.605631	−	0.605631i	0.941801	+	0.336170i	$0.109132\pi$
$798$		0			0
$799$			1.64543e11i			0.403731i
$800$		0			0
$801$	1.81902e11			0.441883
$802$		0			0
$803$	2.27703e11	+	2.27703e11i	0.547655	+	0.547655i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.57576e10	+	1.57576e10i	−0.0371533	+	0.0371533i
$808$		0			0
$809$		−	7.14315e11i		−	1.66762i	−0.552055	−	0.833808i	$-0.686156\pi$
$809$		−	7.14315e11i		−	1.66762i	0.552055	−	0.833808i	$-0.313844\pi$
$810$		0			0
$811$	7.76757e11			1.79557			0.897784	−	0.440436i	$-0.145176\pi$
$811$	7.76757e11			1.79557			0.897784	+	0.440436i	$0.145176\pi$
$812$		0			0
$813$	−5.68542e10	−	5.68542e10i	−0.130137	−	0.130137i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	7.08556e10	−	7.08556e10i	0.159032	−	0.159032i
$818$		0			0
$819$			8.72097e10i			0.193834i
$820$		0			0
$821$	6.27315e10			0.138074			0.0690372	−	0.997614i	$-0.478007\pi$
$821$	6.27315e10			0.138074			0.0690372	+	0.997614i	$0.478007\pi$
$822$		0			0
$823$	2.85916e11	+	2.85916e11i	0.623216	+	0.623216i	0.946352	−	0.323136i	$-0.104737\pi$
$823$	2.85916e11	+	2.85916e11i	0.623216	+	0.623216i	−0.323136	+	0.946352i	$0.604737\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2.65770e11	+	2.65770e11i	−0.568178	+	0.568178i	−0.931618	−	0.363439i	$-0.881602\pi$
$827$	−2.65770e11	+	2.65770e11i	−0.568178	+	0.568178i	0.363439	+	0.931618i	$0.381602\pi$
$828$		0			0
$829$		−	7.37374e11i		−	1.56124i	−0.625006	−	0.780620i	$-0.714904\pi$
$829$		−	7.37374e11i		−	1.56124i	0.625006	−	0.780620i	$-0.285096\pi$
$830$		0			0
$831$	2.65177e11			0.556074
$832$		0			0
$833$	−3.78198e10	−	3.78198e10i	−0.0785488	−	0.0785488i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−4.13039e10	+	4.13039e10i	−0.0841569	+	0.0841569i
$838$		0			0
$839$			6.12019e11i			1.23514i	0.786515	+	0.617571i	$0.211883\pi$
$839$			6.12019e11i			1.23514i	−0.786515	+	0.617571i	$0.788117\pi$
$840$		0			0
$841$	2.06708e11			0.413212
$842$		0			0
$843$	1.40309e11	+	1.40309e11i	0.277827	+	0.277827i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−2.45579e11	+	2.45579e11i	−0.477152	+	0.477152i
$848$		0			0
$849$		−	1.60477e11i		−	0.308874i
$850$		0			0
$851$	−4.36434e10			−0.0832148
$852$		0			0
$853$	−2.38921e11	−	2.38921e11i	−0.451293	−	0.451293i	0.444491	−	0.895783i	$-0.353385\pi$
$853$	−2.38921e11	−	2.38921e11i	−0.451293	−	0.451293i	−0.895783	+	0.444491i	$0.853385\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.58794e10	−	7.58794e10i	0.140670	−	0.140670i	−0.633265	−	0.773935i	$-0.718286\pi$
$857$	7.58794e10	−	7.58794e10i	0.140670	−	0.140670i	0.773935	+	0.633265i	$0.218286\pi$
$858$		0			0
$859$			2.11109e11i			0.387734i	0.981028	+	0.193867i	$0.0621030\pi$
$859$			2.11109e11i			0.387734i	−0.981028	+	0.193867i	$0.937897\pi$
$860$		0			0
$861$	4.34198e11			0.790088
$862$		0			0
$863$	−3.97826e11	−	3.97826e11i	−0.717216	−	0.717216i	0.250818	−	0.968034i	$-0.419300\pi$
$863$	−3.97826e11	−	3.97826e11i	−0.717216	−	0.717216i	−0.968034	+	0.250818i	$0.919300\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.98846e11	−	1.98846e11i	0.351917	−	0.351917i
$868$		0			0
$869$		−	3.63382e11i		−	0.637212i
$870$		0			0
$871$	2.56008e11			0.444816
$872$		0			0
$873$	−1.35935e11	−	1.35935e11i	−0.234031	−	0.234031i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1.18129e10	−	1.18129e10i	0.0199690	−	0.0199690i	−0.697052	−	0.717021i	$-0.745505\pi$
$877$	1.18129e10	−	1.18129e10i	0.0199690	−	0.0199690i	0.717021	+	0.697052i	$0.245505\pi$
$878$		0			0
$879$			3.06561e11i			0.513525i
$880$		0			0
$881$	1.04360e12			1.73232			0.866161	−	0.499766i	$-0.166581\pi$
$881$	1.04360e12			1.73232			0.866161	+	0.499766i	$0.166581\pi$
$882$		0			0
$883$	2.83994e11	+	2.83994e11i	0.467160	+	0.467160i	0.900993	−	0.433833i	$-0.142839\pi$
$883$	2.83994e11	+	2.83994e11i	0.467160	+	0.467160i	−0.433833	+	0.900993i	$0.642839\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.22502e11	−	8.22502e11i	1.32875	−	1.32875i	0.422284	−	0.906464i	$-0.361228\pi$
$887$	8.22502e11	−	8.22502e11i	1.32875	−	1.32875i	0.906464	−	0.422284i	$-0.138772\pi$
$888$		0			0
$889$		−	4.54075e11i		−	0.726977i
$890$		0			0
$891$	3.08448e10			0.0489409
$892$		0			0
$893$	−1.24060e11	−	1.24060e11i	−0.195086	−	0.195086i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.14064e10	+	2.14064e10i	−0.0330655	+	0.0330655i
$898$		0			0
$899$			3.09432e11i			0.473726i
$900$		0			0
$901$	−8.09116e9			−0.0122776
$902$		0			0
$903$	−2.01353e11	−	2.01353e11i	−0.302836	−	0.302836i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−9.42315e10	+	9.42315e10i	−0.139241	+	0.139241i	−0.773292	−	0.634051i	$-0.781391\pi$
$907$	−9.42315e10	+	9.42315e10i	−0.139241	+	0.139241i	0.634051	+	0.773292i	$0.281391\pi$
$908$		0			0
$909$		−	2.44850e11i		−	0.358628i
$910$		0			0
$911$	7.38012e11			1.07149			0.535747	−	0.844379i	$-0.320030\pi$
$911$	7.38012e11			1.07149			0.535747	+	0.844379i	$0.320030\pi$
$912$		0			0
$913$	2.25488e11	+	2.25488e11i	0.324519	+	0.324519i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−7.70756e11	+	7.70756e11i	−1.09003	+	1.09003i
$918$		0			0
$919$		−	1.32818e12i		−	1.86206i	−0.364937	−	0.931032i	$-0.618909\pi$
$919$		−	1.32818e12i		−	1.86206i	0.364937	−	0.931032i	$-0.381091\pi$
$920$		0			0
$921$	1.08131e10			0.0150283
$922$		0			0
$923$	2.11510e11	+	2.11510e11i	0.291423	+	0.291423i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.67125e11	−	2.67125e11i	0.361739	−	0.361739i
$928$		0			0
$929$		−	6.88510e11i		−	0.924373i	−0.886783	−	0.462186i	$-0.847065\pi$
$929$		−	6.88510e11i		−	0.924373i	0.886783	−	0.462186i	$-0.152935\pi$
$930$		0			0
$931$	5.70300e10			0.0759109
$932$		0			0
$933$	−3.49533e11	−	3.49533e11i	−0.461277	−	0.461277i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	6.13306e11	−	6.13306e11i	0.795644	−	0.795644i	−0.186762	−	0.982405i	$-0.559799\pi$
$937$	6.13306e11	−	6.13306e11i	0.795644	−	0.795644i	0.982405	+	0.186762i	$0.0597992\pi$
$938$		0			0
$939$			2.01688e11i			0.259429i
$940$		0			0
$941$	−7.60176e10			−0.0969517			−0.0484759	−	0.998824i	$-0.515436\pi$
$941$	−7.60176e10			−0.0969517			−0.0484759	+	0.998824i	$0.515436\pi$
$942$		0			0
$943$	1.06578e11	+	1.06578e11i	0.134779	+	0.134779i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.85179e11	−	1.85179e11i	0.230246	−	0.230246i	−0.582549	−	0.812795i	$-0.697945\pi$
$947$	1.85179e11	−	1.85179e11i	0.230246	−	0.230246i	0.812795	+	0.582549i	$0.197945\pi$
$948$		0			0
$949$		−	9.90557e11i		−	1.22128i
$950$		0			0
$951$	−1.43419e11			−0.175341
$952$		0			0
$953$	4.37139e11	+	4.37139e11i	0.529966	+	0.529966i	0.920562	−	0.390596i	$-0.127731\pi$
$953$	4.37139e11	+	4.37139e11i	0.529966	+	0.529966i	−0.390596	+	0.920562i	$0.627731\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.15539e11	−	1.15539e11i	0.137746	−	0.137746i
$958$		0			0
$959$			1.22098e12i			1.44355i
$960$		0			0
$961$	−5.26704e11			−0.617552
$962$		0			0
$963$	1.60236e11	+	1.60236e11i	0.186318	+	0.186318i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.33772e10	−	2.33772e10i	0.0267354	−	0.0267354i	−0.693613	−	0.720348i	$-0.743982\pi$
$967$	2.33772e10	−	2.33772e10i	0.0267354	−	0.0267354i	0.720348	+	0.693613i	$0.243982\pi$
$968$		0			0
$969$		−	4.79961e10i		−	0.0544391i
$970$		0			0
$971$	8.00428e11			0.900421			0.450210	−	0.892923i	$-0.351349\pi$
$971$	8.00428e11			0.900421			0.450210	+	0.892923i	$0.351349\pi$
$972$		0			0
$973$	8.91008e11	+	8.91008e11i	0.994100	+	0.994100i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.18067e12	−	1.18067e12i	1.29583	−	1.29583i	0.364711	−	0.931121i	$-0.381168\pi$
$977$	1.18067e12	−	1.18067e12i	1.29583	−	1.29583i	0.931121	−	0.364711i	$-0.118832\pi$
$978$		0			0
$979$			5.36381e11i			0.583905i
$980$		0			0
$981$	−3.35109e11			−0.361835
$982$		0			0
$983$	5.71368e11	+	5.71368e11i	0.611931	+	0.611931i	0.943449	−	0.331518i	$-0.107561\pi$
$983$	5.71368e11	+	5.71368e11i	0.611931	+	0.611931i	−0.331518	+	0.943449i	$0.607561\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−3.52548e11	+	3.52548e11i	−0.371492	+	0.371492i
$988$		0			0
$989$		−	9.88483e10i		−	0.103320i
$990$		0			0
$991$	−3.27743e11			−0.339812			−0.169906	−	0.985460i	$-0.554346\pi$
$991$	−3.27743e11			−0.339812			−0.169906	+	0.985460i	$0.554346\pi$
$992$		0			0
$993$	−2.48579e11	−	2.48579e11i	−0.255662	−	0.255662i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	5.12978e11	−	5.12978e11i	0.519180	−	0.519180i	−0.398143	−	0.917323i	$-0.630345\pi$
$997$	5.12978e11	−	5.12978e11i	0.519180	−	0.519180i	0.917323	+	0.398143i	$0.130345\pi$
$998$		0			0
$999$		−	1.36784e11i		−	0.137333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.193.3		16
5.2	odd	4	inner	300.9.k.e.157.3		16
5.3	odd	4		60.9.k.a.37.7	yes	16
5.4	even	2		60.9.k.a.13.7	✓	16
15.8	even	4		180.9.l.c.37.3		16
15.14	odd	2		180.9.l.c.73.3		16
20.3	even	4		240.9.bg.c.97.3		16
20.19	odd	2		240.9.bg.c.193.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.7	✓	16	5.4	even	2
60.9.k.a.37.7	yes	16	5.3	odd	4
180.9.l.c.37.3		16	15.8	even	4
180.9.l.c.73.3		16	15.14	odd	2
240.9.bg.c.97.3		16	20.3	even	4
240.9.bg.c.193.3		16	20.19	odd	2
300.9.k.e.157.3		16	5.2	odd	4	inner
300.9.k.e.193.3		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	300.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-33.0681 - 33.0681i) q^{3} +(1421.41 - 1421.41i) q^{7} +2187.00i q^{9} +O(q^{10})\)	\(q+(-33.0681 - 33.0681i) q^{3} +(1421.41 - 1421.41i) q^{7} +2187.00i q^{9} -6448.89 q^{11} +(14027.0 + 14027.0i) q^{13} +(-21937.7 + 21937.7i) q^{17} -33080.7i q^{19} -94007.0 q^{21} +(-23074.9 - 23074.9i) q^{23} +(72320.0 - 72320.0i) q^{27} -541792. i q^{29} -571128. q^{31} +(213253. + 213253. i) q^{33} +(945689. - 945689. i) q^{37} -927693. i q^{39} -4.61879e6 q^{41} +(2.14190e6 + 2.14190e6i) q^{43} +(3.75023e6 - 3.75023e6i) q^{47} +1.72396e6i q^{49} +1.45088e6 q^{51} +(184412. + 184412. i) q^{53} +(-1.09392e6 + 1.09392e6i) q^{57} -6.00168e6i q^{59} +1.56657e7 q^{61} +(3.10863e6 + 3.10863e6i) q^{63} +(9.12552e6 - 9.12552e6i) q^{67} +1.52609e6i q^{69} +1.50788e7 q^{71} +(-3.53089e7 - 3.53089e7i) q^{73} +(-9.16654e6 + 9.16654e6i) q^{77} +5.63479e7i q^{79} -4.78297e6 q^{81} +(-3.49654e7 - 3.49654e7i) q^{83} +(-1.79160e7 + 1.79160e7i) q^{87} -8.31741e7i q^{89} +3.98764e7 q^{91} +(1.88861e7 + 1.88861e7i) q^{93} +(-6.21559e7 + 6.21559e7i) q^{97} -1.41037e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 16 * q - 4220 * q^7	\( 16 q - 4220 q^{7} + 23616 q^{11} + 18900 q^{13} + 44940 q^{17} + 163944 q^{21} - 196440 q^{23} + 3742624 q^{31} + 134460 q^{33} + 2141100 q^{37} + 16347000 q^{41} - 12080280 q^{43} + 14942400 q^{47} + 7693704 q^{51} - 23760300 q^{53} + 27530280 q^{57} + 85401912 q^{61} - 9229140 q^{63} + 99451240 q^{67} + 73302480 q^{71} - 124097320 q^{73} + 185945400 q^{77} - 76527504 q^{81} + 22058160 q^{83} + 110300940 q^{87} + 170997360 q^{91} - 9969480 q^{93} - 185269800 q^{97}+O(q^{100}) \) 16 * q - 4220 * q^7 + 23616 * q^11 + 18900 * q^13 + 44940 * q^17 + 163944 * q^21 - 196440 * q^23 + 3742624 * q^31 + 134460 * q^33 + 2141100 * q^37 + 16347000 * q^41 - 12080280 * q^43 + 14942400 * q^47 + 7693704 * q^51 - 23760300 * q^53 + 27530280 * q^57 + 85401912 * q^61 - 9229140 * q^63 + 99451240 * q^67 + 73302480 * q^71 - 124097320 * q^73 + 185945400 * q^77 - 76527504 * q^81 + 22058160 * q^83 + 110300940 * q^87 + 170997360 * q^91 - 9969480 * q^93 - 185269800 * q^97

Introduction

L-functions

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Database

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