LMFDB - Embedded newform 300.9.k.e.193.4

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			193.4
Root			$1773.40 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.0681 - 33.0681i) q^{3} +(1509.40 - 1509.40i) q^{7} +2187.00i q^{9} +O(q^{10})$	$q+(-33.0681 - 33.0681i) q^{3} +(1509.40 - 1509.40i) q^{7} +2187.00i q^{9} +12339.2 q^{11} +(-9649.16 - 9649.16i) q^{13} +(-66498.2 + 66498.2i) q^{17} +32035.7i q^{19} -99826.3 q^{21} +(-350810. - 350810. i) q^{23} +(72320.0 - 72320.0i) q^{27} -2971.46i q^{29} +1.18827e6 q^{31} +(-408035. - 408035. i) q^{33} +(-1.22202e6 + 1.22202e6i) q^{37} +638159. i q^{39} +2.94527e6 q^{41} +(-3.78041e6 - 3.78041e6i) q^{43} +(4.13260e6 - 4.13260e6i) q^{47} +1.20820e6i q^{49} +4.39794e6 q^{51} +(-1.33150e6 - 1.33150e6i) q^{53} +(1.05936e6 - 1.05936e6i) q^{57} -1.96892e6i q^{59} -6.15612e6 q^{61} +(3.30107e6 + 3.30107e6i) q^{63} +(1.46848e6 - 1.46848e6i) q^{67} +2.32013e7i q^{69} -8.71644e6 q^{71} +(2.57421e7 + 2.57421e7i) q^{73} +(1.86249e7 - 1.86249e7i) q^{77} -7.60852e7i q^{79} -4.78297e6 q^{81} +(-2.55396e7 - 2.55396e7i) q^{83} +(-98260.5 + 98260.5i) q^{87} -1.45631e7i q^{89} -2.91290e7 q^{91} +(-3.92940e7 - 3.92940e7i) q^{93} +(-4.66894e7 + 4.66894e7i) q^{97} +2.69859e7i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1509.40	−	1509.40i	0.628656	−	0.628656i	−0.319074	−	0.947730i	$-0.603372\pi$
$7$	1509.40	−	1509.40i	0.628656	−	0.628656i	0.947730	+	0.319074i	$0.103372\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	12339.2			0.842787			0.421393	−	0.906878i	$-0.361541\pi$
$11$	12339.2			0.842787			0.421393	+	0.906878i	$0.361541\pi$
$12$		0			0
$13$	−9649.16	−	9649.16i	−0.337844	−	0.337844i	0.517711	−	0.855555i	$-0.326784\pi$
$13$	−9649.16	−	9649.16i	−0.337844	−	0.337844i	−0.855555	+	0.517711i	$0.826784\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−66498.2	+	66498.2i	−0.796185	+	0.796185i	−0.982492	−	0.186307i	$-0.940348\pi$
$17$	−66498.2	+	66498.2i	−0.796185	+	0.796185i	0.186307	+	0.982492i	$0.440348\pi$
$18$		0			0
$19$			32035.7i			0.245821i	0.992418	+	0.122911i	$0.0392229\pi$
$19$			32035.7i			0.245821i	−0.992418	+	0.122911i	$0.960777\pi$
$20$		0			0
$21$	−99826.3			−0.513296
$22$		0			0
$23$	−350810.	−	350810.i	−1.25361	−	1.25361i	−0.954092	−	0.299514i	$-0.903175\pi$
$23$	−350810.	−	350810.i	−1.25361	−	1.25361i	−0.299514	−	0.954092i	$-0.596825\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$		0			0
$29$		−	2971.46i		−	0.00420124i	−0.999998	−	0.00210062i	$-0.999331\pi$
$29$		−	2971.46i		−	0.00420124i	0.999998	−	0.00210062i	$-0.000668648\pi$
$30$		0			0
$31$	1.18827e6			1.28668			0.643339	−	0.765582i	$-0.277549\pi$
$31$	1.18827e6			1.28668			0.643339	+	0.765582i	$0.277549\pi$
$32$		0			0
$33$	−408035.	−	408035.i	−0.344066	−	0.344066i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.22202e6	+	1.22202e6i	−0.652035	+	0.652035i	−0.953483	−	0.301448i	$-0.902530\pi$
$37$	−1.22202e6	+	1.22202e6i	−0.652035	+	0.652035i	0.301448	+	0.953483i	$0.402530\pi$
$38$		0			0
$39$			638159.i			0.275848i
$40$		0			0
$41$	2.94527e6			1.04229			0.521147	−	0.853467i	$-0.325504\pi$
$41$	2.94527e6			1.04229			0.521147	+	0.853467i	$0.325504\pi$
$42$		0			0
$43$	−3.78041e6	−	3.78041e6i	−1.10577	−	1.10577i	−0.993700	−	0.112071i	$-0.964252\pi$
$43$	−3.78041e6	−	3.78041e6i	−1.10577	−	1.10577i	−0.112071	−	0.993700i	$-0.535748\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.13260e6	−	4.13260e6i	0.846899	−	0.846899i	−0.142846	−	0.989745i	$-0.545625\pi$
$47$	4.13260e6	−	4.13260e6i	0.846899	−	0.846899i	0.989745	+	0.142846i	$0.0456253\pi$
$48$		0			0
$49$			1.20820e6i			0.209582i
$50$		0			0
$51$	4.39794e6			0.650082
$52$		0			0
$53$	−1.33150e6	−	1.33150e6i	−0.168748	−	0.168748i	0.617681	−	0.786429i	$-0.288072\pi$
$53$	−1.33150e6	−	1.33150e6i	−0.168748	−	0.168748i	−0.786429	+	0.617681i	$0.788072\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.05936e6	−	1.05936e6i	0.100356	−	0.100356i
$58$		0			0
$59$		−	1.96892e6i		−	0.162488i	−0.996694	−	0.0812438i	$-0.974111\pi$
$59$		−	1.96892e6i		−	0.162488i	0.996694	−	0.0812438i	$-0.0258892\pi$
$60$		0			0
$61$	−6.15612e6			−0.444619			−0.222309	−	0.974976i	$-0.571360\pi$
$61$	−6.15612e6			−0.444619			−0.222309	+	0.974976i	$0.571360\pi$
$62$		0			0
$63$	3.30107e6	+	3.30107e6i	0.209552	+	0.209552i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.46848e6	−	1.46848e6i	0.0728734	−	0.0728734i	−0.669731	−	0.742604i	$-0.733590\pi$
$67$	1.46848e6	−	1.46848e6i	0.0728734	−	0.0728734i	0.742604	+	0.669731i	$0.233590\pi$
$68$		0			0
$69$			2.32013e7i			1.02357i
$70$		0			0
$71$	−8.71644e6			−0.343009			−0.171505	−	0.985183i	$-0.554863\pi$
$71$	−8.71644e6			−0.343009			−0.171505	+	0.985183i	$0.554863\pi$
$72$		0			0
$73$	2.57421e7	+	2.57421e7i	0.906468	+	0.906468i	0.995985	−	0.0895169i	$-0.0285323\pi$
$73$	2.57421e7	+	2.57421e7i	0.906468	+	0.906468i	−0.0895169	+	0.995985i	$0.528532\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.86249e7	−	1.86249e7i	0.529823	−	0.529823i
$78$		0			0
$79$		−	7.60852e7i		−	1.95340i	−0.214602	−	0.976701i	$-0.568846\pi$
$79$		−	7.60852e7i		−	1.95340i	0.214602	−	0.976701i	$-0.431154\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	−2.55396e7	−	2.55396e7i	−0.538148	−	0.538148i	0.384837	−	0.922985i	$-0.374258\pi$
$83$	−2.55396e7	−	2.55396e7i	−0.538148	−	0.538148i	−0.922985	+	0.384837i	$0.874258\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−98260.5	+	98260.5i	−0.00171515	+	0.00171515i
$88$		0			0
$89$		−	1.45631e7i		−	0.232110i	−0.993243	−	0.116055i	$-0.962975\pi$
$89$		−	1.45631e7i		−	0.232110i	0.993243	−	0.116055i	$-0.0370249\pi$
$90$		0			0
$91$	−2.91290e7			−0.424776
$92$		0			0
$93$	−3.92940e7	−	3.92940e7i	−0.525284	−	0.525284i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.66894e7	+	4.66894e7i	−0.527390	+	0.527390i	−0.919793	−	0.392404i	$-0.871644\pi$
$97$	−4.66894e7	+	4.66894e7i	−0.527390	+	0.527390i	0.392404	+	0.919793i	$0.371644\pi$
$98$		0			0
$99$			2.69859e7i			0.280929i
$100$		0			0
$101$	−1.63015e8			−1.56654			−0.783270	−	0.621682i	$-0.786450\pi$
$101$	−1.63015e8			−1.56654			−0.783270	+	0.621682i	$0.786450\pi$
$102$		0			0
$103$	7.80625e7	+	7.80625e7i	0.693575	+	0.693575i	0.963017	−	0.269442i	$-0.0868391\pi$
$103$	7.80625e7	+	7.80625e7i	0.693575	+	0.693575i	−0.269442	+	0.963017i	$0.586839\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.56350e6	−	4.56350e6i	0.0348147	−	0.0348147i	−0.689485	−	0.724300i	$-0.742163\pi$
$107$	4.56350e6	−	4.56350e6i	0.0348147	−	0.0348147i	0.724300	+	0.689485i	$0.242163\pi$
$108$		0			0
$109$			1.35090e8i			0.957012i	0.878084	+	0.478506i	$0.158822\pi$
$109$			1.35090e8i			0.957012i	−0.878084	+	0.478506i	$0.841178\pi$
$110$		0			0
$111$	8.08197e7			0.532384
$112$		0			0
$113$	−1.73094e8	−	1.73094e8i	−1.06162	−	1.06162i	−0.997973	−	0.0636451i	$-0.979727\pi$
$113$	−1.73094e8	−	1.73094e8i	−1.06162	−	1.06162i	−0.0636451	−	0.997973i	$-0.520273\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.11027e7	−	2.11027e7i	0.112615	−	0.112615i
$118$		0			0
$119$			2.00745e8i			1.00105i
$120$		0			0
$121$	−6.21020e7			−0.289711
$122$		0			0
$123$	−9.73947e7	−	9.73947e7i	−0.425515	−	0.425515i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.03817e8	+	3.03817e8i	−1.16788	+	1.16788i	−0.185172	+	0.982706i	$0.559284\pi$
$127$	−3.03817e8	+	3.03817e8i	−1.16788	+	1.16788i	−0.982706	+	0.185172i	$0.940716\pi$
$128$		0			0
$129$			2.50022e8i			0.902858i
$130$		0			0
$131$	3.12029e8			1.05952			0.529760	−	0.848147i	$-0.322282\pi$
$131$	3.12029e8			1.05952			0.529760	+	0.848147i	$0.322282\pi$
$132$		0			0
$133$	4.83548e7	+	4.83548e7i	0.154537	+	0.154537i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.25779e8	+	1.25779e8i	−0.357048	+	0.357048i	−0.862724	−	0.505676i	$-0.831243\pi$
$137$	−1.25779e8	+	1.25779e8i	−0.357048	+	0.357048i	0.505676	+	0.862724i	$0.331243\pi$
$138$		0			0
$139$		−	2.89643e8i		−	0.775898i	−0.921681	−	0.387949i	$-0.873184\pi$
$139$		−	2.89643e8i		−	0.775898i	0.921681	−	0.387949i	$-0.126816\pi$
$140$		0			0
$141$	−2.73314e8			−0.691490
$142$		0			0
$143$	−1.19063e8	−	1.19063e8i	−0.284730	−	0.284730i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.99529e7	−	3.99529e7i	0.0855616	−	0.0855616i
$148$		0			0
$149$			8.34677e8i			1.69345i	0.532027	+	0.846727i	$0.321431\pi$
$149$			8.34677e8i			1.69345i	−0.532027	+	0.846727i	$0.678569\pi$
$150$		0			0
$151$	−8.21066e8			−1.57932			−0.789660	−	0.613545i	$-0.789743\pi$
$151$	−8.21066e8			−1.57932			−0.789660	+	0.613545i	$0.789743\pi$
$152$		0			0
$153$	−1.45432e8	−	1.45432e8i	−0.265395	−	0.265395i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.06191e8	−	2.06191e8i	0.339368	−	0.339368i	−0.516761	−	0.856129i	$-0.672863\pi$
$157$	2.06191e8	−	2.06191e8i	0.339368	−	0.339368i	0.856129	+	0.516761i	$0.172863\pi$
$158$		0			0
$159$			8.80605e7i			0.137782i
$160$		0			0
$161$	−1.05903e9			−1.57618
$162$		0			0
$163$	−2.10696e8	−	2.10696e8i	−0.298474	−	0.298474i	0.541942	−	0.840416i	$-0.317689\pi$
$163$	−2.10696e8	−	2.10696e8i	−0.298474	−	0.298474i	−0.840416	+	0.541942i	$0.817689\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.28106e8	+	5.28106e8i	−0.678977	+	0.678977i	−0.959769	−	0.280792i	$-0.909403\pi$
$167$	−5.28106e8	+	5.28106e8i	−0.678977	+	0.678977i	0.280792	+	0.959769i	$0.409403\pi$
$168$		0			0
$169$		−	6.29518e8i		−	0.771723i
$170$		0			0
$171$	−7.00620e7			−0.0819404
$172$		0			0
$173$	−8.39513e7	−	8.39513e7i	−0.0937223	−	0.0937223i	0.658691	−	0.752413i	$-0.271110\pi$
$173$	−8.39513e7	−	8.39513e7i	−0.0937223	−	0.0937223i	−0.752413	+	0.658691i	$0.771110\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.51085e7	+	6.51085e7i	−0.0663352	+	0.0663352i
$178$		0			0
$179$		−	1.11615e8i		−	0.108720i	−0.998521	−	0.0543599i	$-0.982688\pi$
$179$		−	1.11615e8i		−	0.108720i	0.998521	−	0.0543599i	$-0.0173118\pi$
$180$		0			0
$181$	−1.72587e9			−1.60803			−0.804013	−	0.594612i	$-0.797306\pi$
$181$	−1.72587e9			−1.60803			−0.804013	+	0.594612i	$0.797306\pi$
$182$		0			0
$183$	2.03571e8	+	2.03571e8i	0.181515	+	0.181515i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.20537e8	+	8.20537e8i	−0.671014	+	0.671014i
$188$		0			0
$189$		−	2.18320e8i		−	0.171099i
$190$		0			0
$191$	−1.60883e9			−1.20886			−0.604431	−	0.796658i	$-0.706599\pi$
$191$	−1.60883e9			−1.20886			−0.604431	+	0.796658i	$0.706599\pi$
$192$		0			0
$193$	−1.38400e9	−	1.38400e9i	−0.997484	−	0.997484i	0.00251271	−	0.999997i	$-0.499200\pi$
$193$	−1.38400e9	−	1.38400e9i	−0.997484	−	0.997484i	−0.999997	+	0.00251271i	$0.999200\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	3.83726e8	−	3.83726e8i	0.254775	−	0.254775i	−0.568150	−	0.822925i	$-0.692341\pi$
$197$	3.83726e8	−	3.83726e8i	0.254775	−	0.254775i	0.822925	+	0.568150i	$0.192341\pi$
$198$		0			0
$199$			2.59309e9i			1.65351i	0.562566	+	0.826753i	$0.309814\pi$
$199$			2.59309e9i			1.65351i	−0.562566	+	0.826753i	$0.690186\pi$
$200$		0			0
$201$	−9.71198e7			−0.0595009
$202$		0			0
$203$	−4.48513e6	−	4.48513e6i	−0.00264114	−	0.00264114i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	7.67222e8	−	7.67222e8i	0.417869	−	0.417869i
$208$		0			0
$209$			3.95296e8i			0.207175i
$210$		0			0
$211$	1.37062e9			0.691490			0.345745	−	0.938329i	$-0.387626\pi$
$211$	1.37062e9			0.691490			0.345745	+	0.938329i	$0.387626\pi$
$212$		0			0
$213$	2.88236e8	+	2.88236e8i	0.140033	+	0.140033i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.79359e9	−	1.79359e9i	0.808878	−	0.808878i
$218$		0			0
$219$		−	1.70249e9i		−	0.740128i
$220$		0			0
$221$	1.28330e9			0.537973
$222$		0			0
$223$	−7.66316e8	−	7.66316e8i	−0.309876	−	0.309876i	0.534985	−	0.844861i	$-0.320317\pi$
$223$	−7.66316e8	−	7.66316e8i	−0.309876	−	0.309876i	−0.844861	+	0.534985i	$0.820317\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.69145e9	+	1.69145e9i	−0.637022	+	0.637022i	−0.949820	−	0.312798i	$-0.898734\pi$
$227$	−1.69145e9	+	1.69145e9i	−0.637022	+	0.637022i	0.312798	+	0.949820i	$0.398734\pi$
$228$		0			0
$229$			5.10522e9i			1.85641i	0.372075	+	0.928203i	$0.378646\pi$
$229$			5.10522e9i			1.85641i	−0.372075	+	0.928203i	$0.621354\pi$
$230$		0			0
$231$	−1.23178e9			−0.432599
$232$		0			0
$233$	−3.59010e9	−	3.59010e9i	−1.21810	−	1.21810i	−0.968297	−	0.249801i	$-0.919635\pi$
$233$	−3.59010e9	−	3.59010e9i	−1.21810	−	1.21810i	−0.249801	−	0.968297i	$-0.580365\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−2.51599e9	+	2.51599e9i	−0.797473	+	0.797473i
$238$		0			0
$239$			4.97073e8i			0.152345i	0.997095	+	0.0761726i	$0.0242700\pi$
$239$			4.97073e8i			0.152345i	−0.997095	+	0.0761726i	$0.975730\pi$
$240$		0			0
$241$	2.85491e8			0.0846301			0.0423151	−	0.999104i	$-0.486527\pi$
$241$	2.85491e8			0.0846301			0.0423151	+	0.999104i	$0.486527\pi$
$242$		0			0
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.09117e8	−	3.09117e8i	0.0830492	−	0.0830492i
$248$		0			0
$249$			1.68909e9i			0.439396i
$250$		0			0
$251$	−5.50872e9			−1.38789			−0.693946	−	0.720027i	$-0.744129\pi$
$251$	−5.50872e9			−1.38789			−0.693946	+	0.720027i	$0.744129\pi$
$252$		0			0
$253$	−4.32873e9	−	4.32873e9i	−1.05652	−	1.05652i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.43723e9	+	2.43723e9i	−0.558680	+	0.558680i	−0.928932	−	0.370252i	$-0.879271\pi$
$257$	−2.43723e9	+	2.43723e9i	−0.558680	+	0.558680i	0.370252	+	0.928932i	$0.379271\pi$
$258$		0			0
$259$			3.68904e9i			0.819812i
$260$		0			0
$261$	6.49858e6			0.00140041
$262$		0			0
$263$	−1.70523e9	−	1.70523e9i	−0.356419	−	0.356419i	0.506072	−	0.862491i	$-0.331097\pi$
$263$	−1.70523e9	−	1.70523e9i	−0.356419	−	0.356419i	−0.862491	+	0.506072i	$0.831097\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−4.81574e8	+	4.81574e8i	−0.0947584	+	0.0947584i
$268$		0			0
$269$		−	1.03662e10i		−	1.97975i	−0.141947	−	0.989874i	$-0.545336\pi$
$269$		−	1.03662e10i		−	1.97975i	0.141947	−	0.989874i	$-0.454664\pi$
$270$		0			0
$271$	7.08826e8			0.131420			0.0657102	−	0.997839i	$-0.479069\pi$
$271$	7.08826e8			0.131420			0.0657102	+	0.997839i	$0.479069\pi$
$272$		0			0
$273$	9.63240e8	+	9.63240e8i	0.173414	+	0.173414i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.07841e9	+	2.07841e9i	−0.353031	+	0.353031i	−0.861236	−	0.508205i	$-0.830309\pi$
$277$	−2.07841e9	+	2.07841e9i	−0.353031	+	0.353031i	0.508205	+	0.861236i	$0.330309\pi$
$278$		0			0
$279$			2.59875e9i			0.428892i
$280$		0			0
$281$	−4.63183e9			−0.742895			−0.371447	−	0.928454i	$-0.621138\pi$
$281$	−4.63183e9			−0.742895			−0.371447	+	0.928454i	$0.621138\pi$
$282$		0			0
$283$	2.47157e9	+	2.47157e9i	0.385325	+	0.385325i	0.873016	−	0.487691i	$-0.162161\pi$
$283$	2.47157e9	+	2.47157e9i	0.385325	+	0.385325i	−0.487691	+	0.873016i	$0.662161\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.44561e9	−	4.44561e9i	0.655245	−	0.655245i
$288$		0			0
$289$		−	1.86826e9i		−	0.267821i
$290$		0			0
$291$	3.08786e9			0.430612
$292$		0			0
$293$	7.72996e9	+	7.72996e9i	1.04883	+	1.04883i	0.998745	+	0.0500898i	$0.0159507\pi$
$293$	7.72996e9	+	7.72996e9i	1.04883	+	1.04883i	0.0500898	+	0.998745i	$0.484049\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	8.92373e8	−	8.92373e8i	0.114689	−	0.114689i
$298$		0			0
$299$			6.77005e9i			0.847046i
$300$		0			0
$301$	−1.14123e10			−1.39030
$302$		0			0
$303$	5.39059e9	+	5.39059e9i	0.639537	+	0.639537i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	1.56509e9	−	1.56509e9i	0.176192	−	0.176192i	−0.613501	−	0.789694i	$-0.710240\pi$
$307$	1.56509e9	−	1.56509e9i	0.176192	−	0.176192i	0.789694	+	0.613501i	$0.210240\pi$
$308$		0			0
$309$		−	5.16276e9i		−	0.566302i
$310$		0			0
$311$	−9.92911e7			−0.0106137			−0.00530687	−	0.999986i	$-0.501689\pi$
$311$	−9.92911e7			−0.0106137			−0.00530687	+	0.999986i	$0.501689\pi$
$312$		0			0
$313$	6.74111e9	+	6.74111e9i	0.702350	+	0.702350i	0.964915	−	0.262564i	$-0.0845682\pi$
$313$	6.74111e9	+	6.74111e9i	0.702350	+	0.702350i	−0.262564	+	0.964915i	$0.584568\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.75686e9	+	7.75686e9i	−0.768155	+	0.768155i	−0.977782	−	0.209627i	$-0.932775\pi$
$317$	−7.75686e9	+	7.75686e9i	−0.768155	+	0.768155i	0.209627	+	0.977782i	$0.432775\pi$
$318$		0			0
$319$		−	3.66655e7i		−	0.00354075i
$320$		0			0
$321$	−3.01813e8			−0.0284261
$322$		0			0
$323$	−2.13031e9	−	2.13031e9i	−0.195719	−	0.195719i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.46717e9	−	4.46717e9i	0.390699	−	0.390699i
$328$		0			0
$329$		−	1.24755e10i		−	1.06482i
$330$		0			0
$331$	1.07836e10			0.898363			0.449181	−	0.893441i	$-0.351716\pi$
$331$	1.07836e10			0.898363			0.449181	+	0.893441i	$0.351716\pi$
$332$		0			0
$333$	−2.67255e9	−	2.67255e9i	−0.217345	−	0.217345i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−2.60122e9	+	2.60122e9i	−0.201678	+	0.201678i	−0.800719	−	0.599041i	$-0.795549\pi$
$337$	−2.60122e9	+	2.60122e9i	−0.201678	+	0.201678i	0.599041	+	0.800719i	$0.295549\pi$
$338$		0			0
$339$			1.14478e10i			0.866807i
$340$		0			0
$341$	1.46624e10			1.08439
$342$		0			0
$343$	1.05251e10	+	1.05251e10i	0.760412	+	0.760412i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.46136e9	−	6.46136e9i	0.445663	−	0.445663i	−0.448247	−	0.893910i	$-0.647952\pi$
$347$	6.46136e9	−	6.46136e9i	0.445663	−	0.445663i	0.893910	+	0.448247i	$0.147952\pi$
$348$		0			0
$349$		−	1.23067e10i		−	0.829543i	−0.909926	−	0.414772i	$-0.863861\pi$
$349$		−	1.23067e10i		−	0.829543i	0.909926	−	0.414772i	$-0.136139\pi$
$350$		0			0
$351$	−1.39565e9			−0.0919495
$352$		0			0
$353$	−1.37220e10	−	1.37220e10i	−0.883728	−	0.883728i	0.110184	−	0.993911i	$-0.464856\pi$
$353$	−1.37220e10	−	1.37220e10i	−0.883728	−	0.883728i	−0.993911	+	0.110184i	$0.964856\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.63827e9	−	6.63827e9i	0.408678	−	0.408678i
$358$		0			0
$359$			1.28125e10i			0.771359i	0.922633	+	0.385680i	$0.126033\pi$
$359$			1.28125e10i			0.771359i	−0.922633	+	0.385680i	$0.873967\pi$
$360$		0			0
$361$	1.59573e10			0.939572
$362$		0			0
$363$	2.05360e9	+	2.05360e9i	0.118274	+	0.118274i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	3.21919e9	−	3.21919e9i	0.177453	−	0.177453i	−0.612792	−	0.790244i	$-0.709954\pi$
$367$	3.21919e9	−	3.21919e9i	0.177453	−	0.177453i	0.790244	+	0.612792i	$0.209954\pi$
$368$		0			0
$369$			6.44131e9i			0.347431i
$370$		0			0
$371$	−4.01955e9			−0.212169
$372$		0			0
$373$	1.68933e10	+	1.68933e10i	0.872726	+	0.872726i	0.992769	−	0.120043i	$-0.0383031\pi$
$373$	1.68933e10	+	1.68933e10i	0.872726	+	0.872726i	−0.120043	+	0.992769i	$0.538303\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.86721e7	+	2.86721e7i	−0.00141936	+	0.00141936i
$378$		0			0
$379$		−	3.73678e10i		−	1.81109i	−0.424250	−	0.905545i	$-0.639462\pi$
$379$		−	3.73678e10i		−	1.81109i	0.424250	−	0.905545i	$-0.360538\pi$
$380$		0			0
$381$	2.00933e10			0.953569
$382$		0			0
$383$	−1.45621e10	−	1.45621e10i	−0.676752	−	0.676752i	0.282511	−	0.959264i	$-0.408832\pi$
$383$	−1.45621e10	−	1.45621e10i	−0.676752	−	0.676752i	−0.959264	+	0.282511i	$0.908832\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.26776e9	−	8.26776e9i	0.368590	−	0.368590i
$388$		0			0
$389$		−	3.10520e9i		−	0.135610i	−0.997699	−	0.0678048i	$-0.978400\pi$
$389$		−	3.10520e9i		−	0.135610i	0.997699	−	0.0678048i	$-0.0215995\pi$
$390$		0			0
$391$	4.66565e10			1.99620
$392$		0			0
$393$	−1.03182e10	−	1.03182e10i	−0.432547	−	0.432547i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.98539e10	−	1.98539e10i	0.799254	−	0.799254i	−0.183724	−	0.982978i	$-0.558815\pi$
$397$	1.98539e10	−	1.98539e10i	0.799254	−	0.799254i	0.982978	+	0.183724i	$0.0588153\pi$
$398$		0			0
$399$		−	3.19800e9i		−	0.126179i
$400$		0			0
$401$	5.08877e10			1.96805			0.984023	−	0.178040i	$-0.0569756\pi$
$401$	5.08877e10			1.96805			0.984023	+	0.178040i	$0.0569756\pi$
$402$		0			0
$403$	−1.14658e10	−	1.14658e10i	−0.434696	−	0.434696i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.50788e10	+	1.50788e10i	−0.549526	+	0.549526i
$408$		0			0
$409$		−	1.04498e10i		−	0.373433i	−0.982414	−	0.186717i	$-0.940215\pi$
$409$		−	1.04498e10i		−	0.373433i	0.982414	−	0.186717i	$-0.0597846\pi$
$410$		0			0
$411$	8.31856e9			0.291529
$412$		0			0
$413$	−2.97190e9	−	2.97190e9i	−0.102149	−	0.102149i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.57796e9	+	9.57796e9i	−0.316759	+	0.316759i
$418$		0			0
$419$		−	3.94794e10i		−	1.28090i	−0.768001	−	0.640449i	$-0.778748\pi$
$419$		−	3.94794e10i		−	1.28090i	0.768001	−	0.640449i	$-0.221252\pi$
$420$		0			0
$421$	−5.05344e10			−1.60864			−0.804320	−	0.594197i	$-0.797470\pi$
$421$	−5.05344e10			−1.60864			−0.804320	+	0.594197i	$0.797470\pi$
$422$		0			0
$423$	9.03799e9	+	9.03799e9i	0.282300	+	0.282300i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−9.29208e9	+	9.29208e9i	−0.279513	+	0.279513i
$428$		0			0
$429$			7.87440e9i			0.232481i
$430$		0			0
$431$	4.84805e9			0.140494			0.0702470	−	0.997530i	$-0.477621\pi$
$431$	4.84805e9			0.140494			0.0702470	+	0.997530i	$0.477621\pi$
$432$		0			0
$433$	4.55541e10	+	4.55541e10i	1.29591	+	1.29591i	0.931068	+	0.364845i	$0.118878\pi$
$433$	4.55541e10	+	4.55541e10i	1.29591	+	1.29591i	0.364845	+	0.931068i	$0.381122\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.12384e10	−	1.12384e10i	0.308163	−	0.308163i
$438$		0			0
$439$			3.81807e10i			1.02798i	0.857795	+	0.513992i	$0.171834\pi$
$439$			3.81807e10i			1.02798i	−0.857795	+	0.513992i	$0.828166\pi$
$440$		0			0
$441$	−2.64233e9			−0.0698607
$442$		0			0
$443$	2.30055e10	+	2.30055e10i	0.597334	+	0.597334i	0.939602	−	0.342268i	$-0.111195\pi$
$443$	2.30055e10	+	2.30055e10i	0.597334	+	0.597334i	−0.342268	+	0.939602i	$0.611195\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.76012e10	−	2.76012e10i	0.691350	−	0.691350i
$448$		0			0
$449$		−	2.72340e10i		−	0.670080i	−0.942204	−	0.335040i	$-0.891250\pi$
$449$		−	2.72340e10i		−	0.670080i	0.942204	−	0.335040i	$-0.108750\pi$
$450$		0			0
$451$	3.63424e10			0.878432
$452$		0			0
$453$	2.71511e10	+	2.71511e10i	0.644755	+	0.644755i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	5.11382e10	−	5.11382e10i	1.17241	−	1.17241i	0.190782	−	0.981633i	$-0.438898\pi$
$457$	5.11382e10	−	5.11382e10i	1.17241	−	1.17241i	0.981633	−	0.190782i	$-0.0611022\pi$
$458$		0			0
$459$			9.61829e9i			0.216694i
$460$		0			0
$461$	−5.15221e10			−1.14075			−0.570374	−	0.821385i	$-0.693202\pi$
$461$	−5.15221e10			−1.14075			−0.570374	+	0.821385i	$0.693202\pi$
$462$		0			0
$463$	4.19946e10	+	4.19946e10i	0.913838	+	0.913838i	0.996572	−	0.0827336i	$-0.0263651\pi$
$463$	4.19946e10	+	4.19946e10i	0.913838	+	0.913838i	−0.0827336	+	0.996572i	$0.526365\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.15193e10	+	1.15193e10i	−0.242191	+	0.242191i	−0.817756	−	0.575565i	$-0.804782\pi$
$467$	−1.15193e10	+	1.15193e10i	−0.242191	+	0.242191i	0.575565	+	0.817756i	$0.304782\pi$
$468$		0			0
$469$		−	4.43306e9i		−	0.0916247i
$470$		0			0
$471$	−1.36367e10			−0.277093
$472$		0			0
$473$	−4.66474e10	−	4.66474e10i	−0.931929	−	0.931929i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.91200e9	−	2.91200e9i	0.0562493	−	0.0562493i
$478$		0			0
$479$		−	6.52577e10i		−	1.23962i	−0.784751	−	0.619812i	$-0.787209\pi$
$479$		−	6.52577e10i		−	1.23962i	0.784751	−	0.619812i	$-0.212791\pi$
$480$		0			0
$481$	2.35829e10			0.440572
$482$		0			0
$483$	3.50201e10	+	3.50201e10i	0.643471	+	0.643471i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−4.30732e10	+	4.30732e10i	−0.765758	+	0.765758i	−0.977357	−	0.211599i	$-0.932133\pi$
$487$	−4.30732e10	+	4.30732e10i	−0.765758	+	0.765758i	0.211599	+	0.977357i	$0.432133\pi$
$488$		0			0
$489$			1.39347e10i			0.243703i
$490$		0			0
$491$	−6.38071e10			−1.09785			−0.548925	−	0.835872i	$-0.684963\pi$
$491$	−6.38071e10			−1.09785			−0.548925	+	0.835872i	$0.684963\pi$
$492$		0			0
$493$	1.97596e8	+	1.97596e8i	0.00334496	+	0.00334496i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.31566e10	+	1.31566e10i	−0.215635	+	0.215635i
$498$		0			0
$499$			3.75610e10i			0.605808i	0.953021	+	0.302904i	$0.0979561\pi$
$499$			3.75610e10i			0.605808i	−0.953021	+	0.302904i	$0.902044\pi$
$500$		0			0
$501$	3.49269e10			0.554382
$502$		0			0
$503$	−8.16846e9	−	8.16846e9i	−0.127605	−	0.127605i	0.640420	−	0.768025i	$-0.278760\pi$
$503$	−8.16846e9	−	8.16846e9i	−0.127605	−	0.127605i	−0.768025	+	0.640420i	$0.778760\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.08170e10	+	2.08170e10i	−0.315055	+	0.315055i
$508$		0			0
$509$		−	7.69060e10i		−	1.14575i	−0.819643	−	0.572874i	$-0.805828\pi$
$509$		−	7.69060e10i		−	1.14575i	0.819643	−	0.572874i	$-0.194172\pi$
$510$		0			0
$511$	7.77105e10			1.13971
$512$		0			0
$513$	2.31682e9	+	2.31682e9i	0.0334520	+	0.0334520i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	5.09931e10	−	5.09931e10i	0.713755	−	0.713755i
$518$		0			0
$519$			5.55222e9i			0.0765239i
$520$		0			0
$521$	−5.42570e10			−0.736384			−0.368192	−	0.929750i	$-0.620023\pi$
$521$	−5.42570e10			−0.736384			−0.368192	+	0.929750i	$0.620023\pi$
$522$		0			0
$523$	−5.99678e10	−	5.99678e10i	−0.801514	−	0.801514i	0.181818	−	0.983332i	$-0.441802\pi$
$523$	−5.99678e10	−	5.99678e10i	−0.801514	−	0.801514i	−0.983332	+	0.181818i	$0.941802\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.90180e10	+	7.90180e10i	−1.02443	+	1.02443i
$528$		0			0
$529$			1.67825e11i			2.14306i
$530$		0			0
$531$	4.30603e9			0.0541625
$532$		0			0
$533$	−2.84194e10	−	2.84194e10i	−0.352133	−	0.352133i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−3.69088e9	+	3.69088e9i	−0.0443847	+	0.0443847i
$538$		0			0
$539$			1.49083e10i			0.176633i
$540$		0			0
$541$	−8.04080e10			−0.938664			−0.469332	−	0.883022i	$-0.655505\pi$
$541$	−8.04080e10			−0.938664			−0.469332	+	0.883022i	$0.655505\pi$
$542$		0			0
$543$	5.70712e10	+	5.70712e10i	0.656474	+	0.656474i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−9.30602e10	+	9.30602e10i	−1.03948	+	1.03948i	−0.0402890	+	0.999188i	$0.512828\pi$
$547$	−9.30602e10	+	9.30602e10i	−1.03948	+	1.03948i	−0.999188	+	0.0402890i	$0.987172\pi$
$548$		0			0
$549$		−	1.34634e10i		−	0.148206i
$550$		0			0
$551$	9.51926e7			0.00103275
$552$		0			0
$553$	−1.14843e11	−	1.14843e11i	−1.22802	−	1.22802i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5.80982e9	−	5.80982e9i	0.0603590	−	0.0603590i	−0.676283	−	0.736642i	$-0.736410\pi$
$557$	5.80982e9	−	5.80982e9i	0.0603590	−	0.0603590i	0.736642	+	0.676283i	$0.236410\pi$
$558$		0			0
$559$			7.29556e10i			0.747156i
$560$		0			0
$561$	5.42672e10			0.547881
$562$		0			0
$563$	−1.31583e11	−	1.31583e11i	−1.30968	−	1.30968i	−0.921643	−	0.388038i	$-0.873153\pi$
$563$	−1.31583e11	−	1.31583e11i	−1.30968	−	1.30968i	−0.388038	−	0.921643i	$-0.626847\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.21943e9	+	7.21943e9i	−0.0698507	+	0.0698507i
$568$		0			0
$569$		−	6.24859e10i		−	0.596119i	−0.954547	−	0.298059i	$-0.903661\pi$
$569$		−	6.24859e10i		−	0.596119i	0.954547	−	0.298059i	$-0.0963393\pi$
$570$		0			0
$571$	−1.78190e10			−0.167625			−0.0838124	−	0.996482i	$-0.526710\pi$
$571$	−1.78190e10			−0.167625			−0.0838124	+	0.996482i	$0.526710\pi$
$572$		0			0
$573$	5.32010e10	+	5.32010e10i	0.493516	+	0.493516i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.19205e11	−	1.19205e11i	1.07545	−	1.07545i	0.0785399	−	0.996911i	$-0.474974\pi$
$577$	1.19205e11	−	1.19205e11i	1.07545	−	1.07545i	0.996911	−	0.0785399i	$-0.0250258\pi$
$578$		0			0
$579$			9.15324e10i			0.814442i
$580$		0			0
$581$	−7.70991e10			−0.676620
$582$		0			0
$583$	−1.64297e10	−	1.64297e10i	−0.142219	−	0.142219i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.24866e11	+	1.24866e11i	−1.05170	+	1.05170i	−0.0531141	+	0.998588i	$0.516915\pi$
$587$	−1.24866e11	+	1.24866e11i	−1.05170	+	1.05170i	−0.998588	+	0.0531141i	$0.983085\pi$
$588$		0			0
$589$			3.80672e10i			0.316293i
$590$		0			0
$591$	−2.53782e10			−0.208023
$592$		0			0
$593$	−1.22611e11	−	1.22611e11i	−0.991545	−	0.991545i	0.00841977	−	0.999965i	$-0.497320\pi$
$593$	−1.22611e11	−	1.22611e11i	−0.991545	−	0.991545i	−0.999965	+	0.00841977i	$0.997320\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.57487e10	−	8.57487e10i	0.675041	−	0.675041i
$598$		0			0
$599$			5.95747e10i			0.462759i	0.972864	+	0.231379i	$0.0743238\pi$
$599$			5.95747e10i			0.462759i	−0.972864	+	0.231379i	$0.925676\pi$
$600$		0			0
$601$	−8.67695e10			−0.665073			−0.332536	−	0.943090i	$-0.607904\pi$
$601$	−8.67695e10			−0.665073			−0.332536	+	0.943090i	$0.607904\pi$
$602$		0			0
$603$	3.21157e9	+	3.21157e9i	0.0242911	+	0.0242911i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	6.51578e10	−	6.51578e10i	0.479968	−	0.479968i	−0.425154	−	0.905121i	$-0.639780\pi$
$607$	6.51578e10	−	6.51578e10i	0.479968	−	0.479968i	0.905121	+	0.425154i	$0.139780\pi$
$608$		0			0
$609$			2.96629e8i			0.00215648i
$610$		0			0
$611$	−7.97522e10			−0.572240
$612$		0			0
$613$	1.65174e11	+	1.65174e11i	1.16977	+	1.16977i	0.982264	+	0.187503i	$0.0600395\pi$
$613$	1.65174e11	+	1.65174e11i	1.16977	+	1.16977i	0.187503	+	0.982264i	$0.439961\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.35459e11	+	1.35459e11i	−0.934691	+	0.934691i	−0.997994	−	0.0633031i	$-0.979837\pi$
$617$	−1.35459e11	+	1.35459e11i	−0.934691	+	0.934691i	0.0633031	+	0.997994i	$0.479837\pi$
$618$		0			0
$619$			2.06046e10i			0.140347i	0.997535	+	0.0701733i	$0.0223552\pi$
$619$			2.06046e10i			0.140347i	−0.997535	+	0.0701733i	$0.977645\pi$
$620$		0			0
$621$	−5.07412e10			−0.341188
$622$		0			0
$623$	−2.19816e10	−	2.19816e10i	−0.145917	−	0.145917i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.30717e10	−	1.30717e10i	0.0845788	−	0.0845788i
$628$		0			0
$629$		−	1.62524e11i		−	1.03828i
$630$		0			0
$631$	1.25415e11			0.791101			0.395551	−	0.918444i	$-0.370554\pi$
$631$	1.25415e11			0.791101			0.395551	+	0.918444i	$0.370554\pi$
$632$		0			0
$633$	−4.53237e10	−	4.53237e10i	−0.282300	−	0.282300i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.16581e10	−	1.16581e10i	0.0708061	−	0.0708061i
$638$		0			0
$639$		−	1.90629e10i		−	0.114336i
$640$		0			0
$641$	−1.44561e11			−0.856285			−0.428142	−	0.903711i	$-0.640832\pi$
$641$	−1.44561e11			−0.856285			−0.428142	+	0.903711i	$0.640832\pi$
$642$		0			0
$643$	1.23710e11	+	1.23710e11i	0.723704	+	0.723704i	0.969358	−	0.245654i	$-0.0790026\pi$
$643$	1.23710e11	+	1.23710e11i	0.723704	+	0.723704i	−0.245654	+	0.969358i	$0.579003\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.90077e11	−	1.90077e11i	1.08471	−	1.08471i	0.0886448	−	0.996063i	$-0.471746\pi$
$647$	1.90077e11	−	1.90077e11i	1.08471	−	1.08471i	0.996063	−	0.0886448i	$-0.0282536\pi$
$648$		0			0
$649$		−	2.42950e10i		−	0.136942i
$650$		0			0
$651$	−1.18621e11			−0.660446
$652$		0			0
$653$	−5.23962e10	−	5.23962e10i	−0.288169	−	0.288169i	0.548187	−	0.836356i	$-0.315318\pi$
$653$	−5.23962e10	−	5.23962e10i	−0.288169	−	0.288169i	−0.836356	+	0.548187i	$0.815318\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.62980e10	+	5.62980e10i	−0.302156	+	0.302156i
$658$		0			0
$659$			9.85777e10i			0.522682i	0.965247	+	0.261341i	$0.0841646\pi$
$659$			9.85777e10i			0.522682i	−0.965247	+	0.261341i	$0.915835\pi$
$660$		0			0
$661$	−1.48386e11			−0.777298			−0.388649	−	0.921386i	$-0.627058\pi$
$661$	−1.48386e11			−0.777298			−0.388649	+	0.921386i	$0.627058\pi$
$662$		0			0
$663$	−4.24364e10	−	4.24364e10i	−0.219626	−	0.219626i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.04242e9	+	1.04242e9i	−0.00526670	+	0.00526670i
$668$		0			0
$669$			5.06813e10i			0.253013i
$670$		0			0
$671$	−7.59619e10			−0.374719
$672$		0			0
$673$	1.60959e10	+	1.60959e10i	0.0784611	+	0.0784611i	0.745248	−	0.666787i	$-0.232331\pi$
$673$	1.60959e10	+	1.60959e10i	0.0784611	+	0.0784611i	−0.666787	+	0.745248i	$0.732331\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.83915e10	+	9.83915e10i	−0.468385	+	0.468385i	−0.901391	−	0.433006i	$-0.857453\pi$
$677$	−9.83915e10	+	9.83915e10i	−0.468385	+	0.468385i	0.433006	+	0.901391i	$0.357453\pi$
$678$		0			0
$679$			1.40946e11i			0.663094i
$680$		0			0
$681$	1.11866e11			0.520126
$682$		0			0
$683$	−6.40210e10	−	6.40210e10i	−0.294198	−	0.294198i	0.544538	−	0.838736i	$-0.316705\pi$
$683$	−6.40210e10	−	6.40210e10i	−0.294198	−	0.294198i	−0.838736	+	0.544538i	$0.816705\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	1.68820e11	−	1.68820e11i	0.757874	−	0.757874i
$688$		0			0
$689$			2.56958e10i			0.114021i
$690$		0			0
$691$	−3.65971e11			−1.60522			−0.802611	−	0.596503i	$-0.796556\pi$
$691$	−3.65971e11			−1.60522			−0.802611	+	0.596503i	$0.796556\pi$
$692$		0			0
$693$	4.07327e10	+	4.07327e10i	0.176608	+	0.176608i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.95855e11	+	1.95855e11i	−0.829859	+	0.829859i
$698$		0			0
$699$			2.37435e11i			0.994573i
$700$		0			0
$701$	−4.33157e11			−1.79380			−0.896898	−	0.442238i	$-0.854185\pi$
$701$	−4.33157e11			−1.79380			−0.896898	+	0.442238i	$0.854185\pi$
$702$		0			0
$703$	−3.91482e10	−	3.91482e10i	−0.160284	−	0.160284i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.46055e11	+	2.46055e11i	−0.984815	+	0.984815i
$708$		0			0
$709$		−	4.87998e11i		−	1.93123i	−0.259982	−	0.965613i	$-0.583717\pi$
$709$		−	4.87998e11i		−	1.93123i	0.259982	−	0.965613i	$-0.416283\pi$
$710$		0			0
$711$	1.66398e11			0.651134
$712$		0			0
$713$	−4.16859e11	−	4.16859e11i	−1.61299	−	1.61299i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.64373e10	−	1.64373e10i	0.0621947	−	0.0621947i
$718$		0			0
$719$			5.77284e10i			0.216010i	0.994150	+	0.108005i	$0.0344462\pi$
$719$			5.77284e10i			0.216010i	−0.994150	+	0.108005i	$0.965554\pi$
$720$		0			0
$721$	2.35656e11			0.872041
$722$		0			0
$723$	−9.44066e9	−	9.44066e9i	−0.0345501	−	0.0345501i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−1.49059e11	+	1.49059e11i	−0.533607	+	0.533607i	−0.921644	−	0.388037i	$-0.873153\pi$
$727$	−1.49059e11	+	1.49059e11i	−0.533607	+	0.533607i	0.388037	+	0.921644i	$0.373153\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	5.02781e11			1.76080
$732$		0			0
$733$	7.67146e9	+	7.67146e9i	0.0265743	+	0.0265743i	0.720269	−	0.693695i	$-0.244018\pi$
$733$	7.67146e9	+	7.67146e9i	0.0265743	+	0.0265743i	−0.693695	+	0.720269i	$0.744018\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.81199e10	−	1.81199e10i	0.0614168	−	0.0614168i
$738$		0			0
$739$			3.14430e11i			1.05426i	0.849785	+	0.527129i	$0.176731\pi$
$739$			3.14430e11i			1.05426i	−0.849785	+	0.527129i	$0.823269\pi$
$740$		0			0
$741$	−2.04439e10			−0.0678094
$742$		0			0
$743$	−2.13161e11	−	2.13161e11i	−0.699445	−	0.699445i	0.264846	−	0.964291i	$-0.414679\pi$
$743$	−2.13161e11	−	2.13161e11i	−0.699445	−	0.699445i	−0.964291	+	0.264846i	$0.914679\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.58551e10	−	5.58551e10i	0.179383	−	0.179383i
$748$		0			0
$749$		−	1.37763e10i		−	0.0437730i
$750$		0			0
$751$	7.04931e10			0.221609			0.110804	−	0.993842i	$-0.464657\pi$
$751$	7.04931e10			0.221609			0.110804	+	0.993842i	$0.464657\pi$
$752$		0			0
$753$	1.82163e11	+	1.82163e11i	0.566604	+	0.566604i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.39659e11	−	1.39659e11i	0.425290	−	0.425290i	−0.461731	−	0.887020i	$-0.652771\pi$
$757$	1.39659e11	−	1.39659e11i	0.425290	−	0.425290i	0.887020	+	0.461731i	$0.152771\pi$
$758$		0			0
$759$			2.86286e11i			0.862647i
$760$		0			0
$761$	4.07660e11			1.21551			0.607756	−	0.794124i	$-0.292070\pi$
$761$	4.07660e11			1.21551			0.607756	+	0.794124i	$0.292070\pi$
$762$		0			0
$763$	2.03905e11	+	2.03905e11i	0.601632	+	0.601632i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.89984e10	+	1.89984e10i	−0.0548954	+	0.0548954i
$768$		0			0
$769$		−	4.09403e11i		−	1.17070i	−0.810781	−	0.585350i	$-0.800957\pi$
$769$		−	4.09403e11i		−	1.17070i	0.810781	−	0.585350i	$-0.199043\pi$
$770$		0			0
$771$	1.61189e11			0.456160
$772$		0			0
$773$	1.17530e11	+	1.17530e11i	0.329177	+	0.329177i	0.852273	−	0.523097i	$-0.175223\pi$
$773$	1.17530e11	+	1.17530e11i	0.329177	+	0.329177i	−0.523097	+	0.852273i	$0.675223\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.21990e11	−	1.21990e11i	0.334687	−	0.334687i
$778$		0			0
$779$			9.43539e10i			0.256218i
$780$		0			0
$781$	−1.07554e11			−0.289084
$782$		0			0
$783$	−2.14896e8	−	2.14896e8i	−0.000571716	−	0.000571716i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5.24505e10	−	5.24505e10i	0.136726	−	0.136726i	−0.635431	−	0.772157i	$-0.719178\pi$
$787$	5.24505e10	−	5.24505e10i	0.136726	−	0.136726i	0.772157	+	0.635431i	$0.219178\pi$
$788$		0			0
$789$			1.12778e11i			0.291015i
$790$		0			0
$791$	−5.22537e11			−1.33479
$792$		0			0
$793$	5.94014e10	+	5.94014e10i	0.150212	+	0.150212i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.22486e10	+	9.22486e10i	−0.228626	+	0.228626i	−0.812119	−	0.583492i	$-0.801686\pi$
$797$	−9.22486e10	+	9.22486e10i	−0.228626	+	0.228626i	0.583492	+	0.812119i	$0.301686\pi$
$798$		0			0
$799$			5.49620e11i			1.34858i
$800$		0			0
$801$	3.18495e10			0.0773699
$802$		0			0
$803$	3.17638e11	+	3.17638e11i	0.763960	+	0.763960i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.42790e11	+	3.42790e11i	−0.808229	+	0.808229i
$808$		0			0
$809$		−	3.52896e11i		−	0.823860i	−0.911216	−	0.411930i	$-0.864855\pi$
$809$		−	3.52896e11i		−	0.823860i	0.911216	−	0.411930i	$-0.135145\pi$
$810$		0			0
$811$	5.24524e11			1.21250			0.606251	−	0.795274i	$-0.292673\pi$
$811$	5.24524e11			1.21250			0.606251	+	0.795274i	$0.292673\pi$
$812$		0			0
$813$	−2.34395e10	−	2.34395e10i	−0.0536521	−	0.0536521i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.21108e11	−	1.21108e11i	0.271822	−	0.271822i
$818$		0			0
$819$		−	6.37051e10i		−	0.141592i
$820$		0			0
$821$	−5.23177e11			−1.15153			−0.575766	−	0.817615i	$-0.695296\pi$
$821$	−5.23177e11			−1.15153			−0.575766	+	0.817615i	$0.695296\pi$
$822$		0			0
$823$	3.88354e11	+	3.88354e11i	0.846502	+	0.846502i	0.989695	−	0.143193i	$-0.0457369\pi$
$823$	3.88354e11	+	3.88354e11i	0.846502	+	0.846502i	−0.143193	+	0.989695i	$0.545737\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.30441e11	−	3.30441e11i	0.706435	−	0.706435i	−0.259348	−	0.965784i	$-0.583508\pi$
$827$	3.30441e11	−	3.30441e11i	0.706435	−	0.706435i	0.965784	+	0.259348i	$0.0835078\pi$
$828$		0			0
$829$		−	5.39953e11i		−	1.14324i	−0.820518	−	0.571621i	$-0.806315\pi$
$829$		−	5.39953e11i		−	1.14324i	0.820518	−	0.571621i	$-0.193685\pi$
$830$		0			0
$831$	1.37458e11			0.288249
$832$		0			0
$833$	−8.03431e10	−	8.03431e10i	−0.166866	−	0.166866i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.59359e10	−	8.59359e10i	0.175095	−	0.175095i
$838$		0			0
$839$		−	5.21298e11i		−	1.05205i	−0.850468	−	0.526027i	$-0.823681\pi$
$839$		−	5.21298e11i		−	1.05205i	0.850468	−	0.526027i	$-0.176319\pi$
$840$		0			0
$841$	5.00238e11			0.999982
$842$		0			0
$843$	1.53166e11	+	1.53166e11i	0.303286	+	0.303286i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−9.37371e10	+	9.37371e10i	−0.182128	+	0.182128i
$848$		0			0
$849$		−	1.63460e11i		−	0.314616i
$850$		0			0
$851$	8.57393e11			1.63479
$852$		0			0
$853$	−3.97277e11	−	3.97277e11i	−0.750407	−	0.750407i	0.224148	−	0.974555i	$-0.428040\pi$
$853$	−3.97277e11	−	3.97277e11i	−0.750407	−	0.750407i	−0.974555	+	0.224148i	$0.928040\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.57661e11	−	4.57661e11i	0.848439	−	0.848439i	−0.141499	−	0.989938i	$-0.545192\pi$
$857$	4.57661e11	−	4.57661e11i	0.848439	−	0.848439i	0.989938	+	0.141499i	$0.0451923\pi$
$858$		0			0
$859$			3.08466e11i			0.566546i	0.959039	+	0.283273i	$0.0914203\pi$
$859$			3.08466e11i			0.566546i	−0.959039	+	0.283273i	$0.908580\pi$
$860$		0			0
$861$	−2.94016e11			−0.535005
$862$		0			0
$863$	3.85991e11	+	3.85991e11i	0.695879	+	0.695879i	0.963519	−	0.267640i	$-0.0862437\pi$
$863$	3.85991e11	+	3.85991e11i	0.695879	+	0.695879i	−0.267640	+	0.963519i	$0.586244\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.17797e10	+	6.17797e10i	−0.109338	+	0.109338i
$868$		0			0
$869$		−	9.38834e11i		−	1.64630i
$870$		0			0
$871$	−2.83392e10			−0.0492397
$872$		0			0
$873$	−1.02110e11	−	1.02110e11i	−0.175797	−	0.175797i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.67562e11	−	3.67562e11i	0.621344	−	0.621344i	−0.324531	−	0.945875i	$-0.605207\pi$
$877$	3.67562e11	−	3.67562e11i	0.621344	−	0.621344i	0.945875	+	0.324531i	$0.105207\pi$
$878$		0			0
$879$		−	5.11231e11i		−	0.856370i
$880$		0			0
$881$	−7.40283e11			−1.22884			−0.614418	−	0.788981i	$-0.710609\pi$
$881$	−7.40283e11			−1.22884			−0.614418	+	0.788981i	$0.710609\pi$
$882$		0			0
$883$	6.93329e11	+	6.93329e11i	1.14050	+	1.14050i	0.988358	+	0.152144i	$0.0486179\pi$
$883$	6.93329e11	+	6.93329e11i	1.14050	+	1.14050i	0.152144	+	0.988358i	$0.451382\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.57281e11	+	5.57281e11i	−0.900285	+	0.900285i	−0.995460	−	0.0951758i	$-0.969659\pi$
$887$	−5.57281e11	+	5.57281e11i	−0.900285	+	0.900285i	0.0951758	+	0.995460i	$0.469659\pi$
$888$		0			0
$889$			9.17166e11i			1.46839i
$890$		0			0
$891$	−5.90182e10			−0.0936430
$892$		0			0
$893$	1.32391e11	+	1.32391e11i	0.208186	+	0.208186i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.23873e11	−	2.23873e11i	0.345805	−	0.345805i
$898$		0			0
$899$		−	3.53090e9i		−	0.00540564i
$900$		0			0
$901$	1.77085e11			0.268709
$902$		0			0
$903$	3.77384e11	+	3.77384e11i	0.567588	+	0.567588i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.85513e11	−	1.85513e11i	0.274123	−	0.274123i	−0.556635	−	0.830757i	$-0.687908\pi$
$907$	1.85513e11	−	1.85513e11i	0.274123	−	0.274123i	0.830757	+	0.556635i	$0.187908\pi$
$908$		0			0
$909$		−	3.56513e11i		−	0.522180i
$910$		0			0
$911$	1.32949e12			1.93024			0.965122	−	0.261802i	$-0.0843166\pi$
$911$	1.32949e12			1.93024			0.965122	+	0.261802i	$0.0843166\pi$
$912$		0			0
$913$	−3.15139e11	−	3.15139e11i	−0.453544	−	0.453544i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.70977e11	−	4.70977e11i	0.666074	−	0.666074i
$918$		0			0
$919$		−	3.07104e11i		−	0.430550i	−0.976553	−	0.215275i	$-0.930935\pi$
$919$		−	3.07104e11i		−	0.430550i	0.976553	−	0.215275i	$-0.0690648\pi$
$920$		0			0
$921$	−1.03509e11			−0.143860
$922$		0			0
$923$	8.41064e10	+	8.41064e10i	0.115884	+	0.115884i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.70723e11	+	1.70723e11i	−0.231192	+	0.231192i
$928$		0			0
$929$		−	7.57157e11i		−	1.01654i	−0.861199	−	0.508269i	$-0.830286\pi$
$929$		−	7.57157e11i		−	1.01654i	0.861199	−	0.508269i	$-0.169714\pi$
$930$		0			0
$931$	−3.87055e10			−0.0515198
$932$		0			0
$933$	3.28337e9	+	3.28337e9i	0.00433304	+	0.00433304i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3.99093e11	−	3.99093e11i	0.517744	−	0.517744i	−0.399144	−	0.916888i	$-0.630693\pi$
$937$	3.99093e11	−	3.99093e11i	0.517744	−	0.517744i	0.916888	+	0.399144i	$0.130693\pi$
$938$		0			0
$939$		−	4.45831e11i		−	0.573467i
$940$		0			0
$941$	1.43321e12			1.82790			0.913951	−	0.405826i	$-0.133016\pi$
$941$	1.43321e12			1.82790			0.913951	+	0.405826i	$0.133016\pi$
$942$		0			0
$943$	−1.03323e12	−	1.03323e12i	−1.30663	−	1.30663i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.60275e11	+	3.60275e11i	−0.447954	+	0.447954i	−0.894674	−	0.446720i	$-0.852592\pi$
$947$	−3.60275e11	+	3.60275e11i	−0.447954	+	0.447954i	0.446720	+	0.894674i	$0.352592\pi$
$948$		0			0
$949$		−	4.96780e11i		−	0.612490i
$950$		0			0
$951$	5.13009e11			0.627196
$952$		0			0
$953$	7.87578e11	+	7.87578e11i	0.954821	+	0.954821i	0.999023	−	0.0442019i	$-0.0140745\pi$
$953$	7.87578e11	+	7.87578e11i	0.954821	+	0.954821i	−0.0442019	+	0.999023i	$0.514074\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.21246e9	+	1.21246e9i	−0.00144550	+	0.00144550i
$958$		0			0
$959$			3.79703e11i			0.448921i
$960$		0			0
$961$	5.59103e11			0.655539
$962$		0			0
$963$	9.98038e9	+	9.98038e9i	0.0116049	+	0.0116049i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	7.93429e11	−	7.93429e11i	0.907407	−	0.907407i	−0.0886553	−	0.996062i	$-0.528257\pi$
$967$	7.93429e11	−	7.93429e11i	0.907407	−	0.907407i	0.996062	+	0.0886553i	$0.0282570\pi$
$968$		0			0
$969$			1.40891e11i			0.159804i
$970$		0			0
$971$	−4.07428e11			−0.458326			−0.229163	−	0.973388i	$-0.573599\pi$
$971$	−4.07428e11			−0.458326			−0.229163	+	0.973388i	$0.573599\pi$
$972$		0			0
$973$	−4.37189e11	−	4.37189e11i	−0.487773	−	0.487773i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.19282e11	−	2.19282e11i	0.240672	−	0.240672i	−0.576456	−	0.817128i	$-0.695565\pi$
$977$	2.19282e11	−	2.19282e11i	0.240672	−	0.240672i	0.817128	+	0.576456i	$0.195565\pi$
$978$		0			0
$979$		−	1.79697e11i		−	0.195619i
$980$		0			0
$981$	−2.95442e11			−0.319004
$982$		0			0
$983$	−2.97471e11	−	2.97471e11i	−0.318589	−	0.318589i	0.529636	−	0.848225i	$-0.322328\pi$
$983$	−2.97471e11	−	2.97471e11i	−0.318589	−	0.318589i	−0.848225	+	0.529636i	$0.822328\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−4.12542e11	+	4.12542e11i	−0.434710	+	0.434710i
$988$		0			0
$989$			2.65241e12i			2.77240i
$990$		0			0
$991$	9.32631e11			0.966975			0.483488	−	0.875351i	$-0.339370\pi$
$991$	9.32631e11			0.966975			0.483488	+	0.875351i	$0.339370\pi$
$992$		0			0
$993$	−3.56593e11	−	3.56593e11i	−0.366755	−	0.366755i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−5.81581e11	+	5.81581e11i	−0.588613	+	0.588613i	−0.937256	−	0.348643i	$-0.886643\pi$
$997$	−5.81581e11	+	5.81581e11i	−0.588613	+	0.588613i	0.348643	+	0.937256i	$0.386643\pi$
$998$		0			0
$999$			1.76753e11i			0.177461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.193.4		16
5.2	odd	4	inner	300.9.k.e.157.4		16
5.3	odd	4		60.9.k.a.37.6	yes	16
5.4	even	2		60.9.k.a.13.6	✓	16
15.8	even	4		180.9.l.c.37.5		16
15.14	odd	2		180.9.l.c.73.5		16
20.3	even	4		240.9.bg.c.97.2		16
20.19	odd	2		240.9.bg.c.193.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.6	✓	16	5.4	even	2
60.9.k.a.37.6	yes	16	5.3	odd	4
180.9.l.c.37.5		16	15.8	even	4
180.9.l.c.73.5		16	15.14	odd	2
240.9.bg.c.97.2		16	20.3	even	4
240.9.bg.c.193.2		16	20.19	odd	2
300.9.k.e.157.4		16	5.2	odd	4	inner
300.9.k.e.193.4		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)

\(f(q)\)	\(=\)	\(q+(-33.0681 - 33.0681i) q^{3} +(1509.40 - 1509.40i) q^{7} +2187.00i q^{9} +O(q^{10})\)	\(q+(-33.0681 - 33.0681i) q^{3} +(1509.40 - 1509.40i) q^{7} +2187.00i q^{9} +12339.2 q^{11} +(-9649.16 - 9649.16i) q^{13} +(-66498.2 + 66498.2i) q^{17} +32035.7i q^{19} -99826.3 q^{21} +(-350810. - 350810. i) q^{23} +(72320.0 - 72320.0i) q^{27} -2971.46i q^{29} +1.18827e6 q^{31} +(-408035. - 408035. i) q^{33} +(-1.22202e6 + 1.22202e6i) q^{37} +638159. i q^{39} +2.94527e6 q^{41} +(-3.78041e6 - 3.78041e6i) q^{43} +(4.13260e6 - 4.13260e6i) q^{47} +1.20820e6i q^{49} +4.39794e6 q^{51} +(-1.33150e6 - 1.33150e6i) q^{53} +(1.05936e6 - 1.05936e6i) q^{57} -1.96892e6i q^{59} -6.15612e6 q^{61} +(3.30107e6 + 3.30107e6i) q^{63} +(1.46848e6 - 1.46848e6i) q^{67} +2.32013e7i q^{69} -8.71644e6 q^{71} +(2.57421e7 + 2.57421e7i) q^{73} +(1.86249e7 - 1.86249e7i) q^{77} -7.60852e7i q^{79} -4.78297e6 q^{81} +(-2.55396e7 - 2.55396e7i) q^{83} +(-98260.5 + 98260.5i) q^{87} -1.45631e7i q^{89} -2.91290e7 q^{91} +(-3.92940e7 - 3.92940e7i) q^{93} +(-4.66894e7 + 4.66894e7i) q^{97} +2.69859e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 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

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