LMFDB - Embedded newform 300.9.k.e.193.1

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			193.1
Root			$-2402.08 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.0681 - 33.0681i) q^{3} +(-2666.08 + 2666.08i) q^{7} +2187.00i q^{9} +O(q^{10})$	$q+(-33.0681 - 33.0681i) q^{3} +(-2666.08 + 2666.08i) q^{7} +2187.00i q^{9} -4230.00 q^{11} +(33060.9 + 33060.9i) q^{13} +(-27668.9 + 27668.9i) q^{17} +35751.5i q^{19} +176324. q^{21} +(143767. + 143767. i) q^{23} +(72320.0 - 72320.0i) q^{27} +41593.0i q^{29} +1.33575e6 q^{31} +(139878. + 139878. i) q^{33} +(-205126. + 205126. i) q^{37} -2.18653e6i q^{39} +681555. q^{41} +(1.31868e6 + 1.31868e6i) q^{43} +(-5.69795e6 + 5.69795e6i) q^{47} -8.45116e6i q^{49} +1.82991e6 q^{51} +(-8.35358e6 - 8.35358e6i) q^{53} +(1.18223e6 - 1.18223e6i) q^{57} +8.05809e6i q^{59} -8.53592e6 q^{61} +(-5.83072e6 - 5.83072e6i) q^{63} +(2.55140e7 - 2.55140e7i) q^{67} -9.50818e6i q^{69} +1.98155e7 q^{71} +(-1.32128e7 - 1.32128e7i) q^{73} +(1.12775e7 - 1.12775e7i) q^{77} +2.86194e7i q^{79} -4.78297e6 q^{81} +(4.35915e7 + 4.35915e7i) q^{83} +(1.37540e6 - 1.37540e6i) q^{87} +1.06483e8i q^{89} -1.76286e8 q^{91} +(-4.41708e7 - 4.41708e7i) q^{93} +(8.59422e7 - 8.59422e7i) q^{97} -9.25101e6i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2666.08	+	2666.08i	−1.11040	+	1.11040i	−0.117308	+	0.993096i	$0.537427\pi$
$7$	−2666.08	+	2666.08i	−1.11040	+	1.11040i	−0.993096	+	0.117308i	$0.962573\pi$
$8$		0			0
$9$			2187.00i			0.333333i
$10$		0			0
$11$	−4230.00			−0.288915			−0.144457	−	0.989511i	$-0.546144\pi$
$11$	−4230.00			−0.288915			−0.144457	+	0.989511i	$0.546144\pi$
$12$		0			0
$13$	33060.9	+	33060.9i	1.15756	+	1.15756i	0.985000	+	0.172555i	$0.0552024\pi$
$13$	33060.9	+	33060.9i	1.15756	+	1.15756i	0.172555	+	0.985000i	$0.444798\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−27668.9	+	27668.9i	−0.331280	+	0.331280i	−0.853073	−	0.521792i	$-0.825264\pi$
$17$	−27668.9	+	27668.9i	−0.331280	+	0.331280i	0.521792	+	0.853073i	$0.325264\pi$
$18$		0			0
$19$			35751.5i			0.274334i	0.990548	+	0.137167i	$0.0437997\pi$
$19$			35751.5i			0.274334i	−0.990548	+	0.137167i	$0.956200\pi$
$20$		0			0
$21$	176324.			0.906641
$22$		0			0
$23$	143767.	+	143767.i	0.513744	+	0.513744i	0.915671	−	0.401928i	$-0.131660\pi$
$23$	143767.	+	143767.i	0.513744	+	0.513744i	−0.401928	+	0.915671i	$0.631660\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$		0			0
$29$			41593.0i			0.0588069i	0.999568	+	0.0294035i	$0.00936076\pi$
$29$			41593.0i			0.0588069i	−0.999568	+	0.0294035i	$0.990639\pi$
$30$		0			0
$31$	1.33575e6			1.44637			0.723185	−	0.690654i	$-0.242677\pi$
$31$	1.33575e6			1.44637			0.723185	+	0.690654i	$0.242677\pi$
$32$		0			0
$33$	139878.	+	139878.i	0.117949	+	0.117949i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−205126.	+	205126.i	−0.109450	+	0.109450i	−0.759711	−	0.650261i	$-0.774659\pi$
$37$	−205126.	+	205126.i	−0.109450	+	0.109450i	0.650261	+	0.759711i	$0.274659\pi$
$38$		0			0
$39$		−	2.18653e6i		−	0.945140i
$40$		0			0
$41$	681555.			0.241193			0.120597	−	0.992702i	$-0.461519\pi$
$41$	681555.			0.241193			0.120597	+	0.992702i	$0.461519\pi$
$42$		0			0
$43$	1.31868e6	+	1.31868e6i	0.385713	+	0.385713i	0.873155	−	0.487442i	$-0.162070\pi$
$43$	1.31868e6	+	1.31868e6i	0.385713	+	0.385713i	−0.487442	+	0.873155i	$0.662070\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.69795e6	+	5.69795e6i	−1.16769	+	1.16769i	−0.184938	+	0.982750i	$0.559208\pi$
$47$	−5.69795e6	+	5.69795e6i	−1.16769	+	1.16769i	−0.982750	+	0.184938i	$0.940792\pi$
$48$		0			0
$49$		−	8.45116e6i		−	1.46599i
$50$		0			0
$51$	1.82991e6			0.270489
$52$		0			0
$53$	−8.35358e6	−	8.35358e6i	−1.05869	−	1.05869i	−0.998167	−	0.0605244i	$-0.980723\pi$
$53$	−8.35358e6	−	8.35358e6i	−1.05869	−	1.05869i	−0.0605244	−	0.998167i	$-0.519277\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.18223e6	−	1.18223e6i	0.111996	−	0.111996i
$58$		0			0
$59$			8.05809e6i			0.665004i	0.943103	+	0.332502i	$0.107893\pi$
$59$			8.05809e6i			0.665004i	−0.943103	+	0.332502i	$0.892107\pi$
$60$		0			0
$61$	−8.53592e6			−0.616497			−0.308249	−	0.951306i	$-0.599743\pi$
$61$	−8.53592e6			−0.616497			−0.308249	+	0.951306i	$0.599743\pi$
$62$		0			0
$63$	−5.83072e6	−	5.83072e6i	−0.370135	−	0.370135i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.55140e7	−	2.55140e7i	1.26613	−	1.26613i	0.318064	−	0.948069i	$-0.396967\pi$
$67$	2.55140e7	−	2.55140e7i	1.26613	−	1.26613i	0.948069	−	0.318064i	$-0.103033\pi$
$68$		0			0
$69$		−	9.50818e6i		−	0.419470i
$70$		0			0
$71$	1.98155e7			0.779779			0.389890	−	0.920862i	$-0.372513\pi$
$71$	1.98155e7			0.779779			0.389890	+	0.920862i	$0.372513\pi$
$72$		0			0
$73$	−1.32128e7	−	1.32128e7i	−0.465268	−	0.465268i	0.435110	−	0.900377i	$-0.356710\pi$
$73$	−1.32128e7	−	1.32128e7i	−0.465268	−	0.465268i	−0.900377	+	0.435110i	$0.856710\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.12775e7	−	1.12775e7i	0.320812	−	0.320812i
$78$		0			0
$79$			2.86194e7i			0.734770i	0.930069	+	0.367385i	$0.119747\pi$
$79$			2.86194e7i			0.734770i	−0.930069	+	0.367385i	$0.880253\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	4.35915e7	+	4.35915e7i	0.918521	+	0.918521i	0.996922	−	0.0784009i	$-0.0249814\pi$
$83$	4.35915e7	+	4.35915e7i	0.918521	+	0.918521i	−0.0784009	+	0.996922i	$0.524981\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1.37540e6	−	1.37540e6i	0.0240078	−	0.0240078i
$88$		0			0
$89$			1.06483e8i			1.69716i	0.529069	+	0.848579i	$0.322541\pi$
$89$			1.06483e8i			1.69716i	−0.529069	+	0.848579i	$0.677459\pi$
$90$		0			0
$91$	−1.76286e8			−2.57071
$92$		0			0
$93$	−4.41708e7	−	4.41708e7i	−0.590478	−	0.590478i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	8.59422e7	−	8.59422e7i	0.970777	−	0.970777i	−0.0288082	−	0.999585i	$-0.509171\pi$
$97$	8.59422e7	−	8.59422e7i	0.970777	−	0.970777i	0.999585	+	0.0288082i	$0.00917122\pi$
$98$		0			0
$99$		−	9.25101e6i		−	0.0963049i
$100$		0			0
$101$	1.77652e8			1.70720			0.853601	−	0.520927i	$-0.174414\pi$
$101$	1.77652e8			1.70720			0.853601	+	0.520927i	$0.174414\pi$
$102$		0			0
$103$	7.11485e7	+	7.11485e7i	0.632146	+	0.632146i	0.948606	−	0.316460i	$-0.102494\pi$
$103$	7.11485e7	+	7.11485e7i	0.632146	+	0.632146i	−0.316460	+	0.948606i	$0.602494\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.52765e8	+	1.52765e8i	−1.16544	+	1.16544i	−0.182171	+	0.983267i	$0.558313\pi$
$107$	−1.52765e8	+	1.52765e8i	−1.16544	+	1.16544i	−0.983267	+	0.182171i	$0.941687\pi$
$108$		0			0
$109$		−	4.50898e7i		−	0.319428i	−0.987163	−	0.159714i	$-0.948943\pi$
$109$		−	4.50898e7i		−	0.319428i	0.987163	−	0.159714i	$-0.0510571\pi$
$110$		0			0
$111$	1.35663e7			0.0893653
$112$		0			0
$113$	−1.61001e8	−	1.61001e8i	−0.987451	−	0.987451i	0.0124717	−	0.999922i	$-0.496030\pi$
$113$	−1.61001e8	−	1.61001e8i	−0.987451	−	0.987451i	−0.999922	+	0.0124717i	$0.996030\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.23043e7	+	7.23043e7i	−0.385852	+	0.385852i
$118$		0			0
$119$		−	1.47535e8i		−	0.735710i
$120$		0			0
$121$	−1.96466e8			−0.916528
$122$		0			0
$123$	−2.25377e7	−	2.25377e7i	−0.0984668	−	0.0984668i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.24633e8	+	2.24633e8i	−0.863494	+	0.863494i	−0.991742	−	0.128248i	$-0.959065\pi$
$127$	−2.24633e8	+	2.24633e8i	−0.863494	+	0.863494i	0.128248	+	0.991742i	$0.459065\pi$
$128$		0			0
$129$		−	8.72122e7i		−	0.314933i
$130$		0			0
$131$	−4.72583e8			−1.60470			−0.802348	−	0.596857i	$-0.796416\pi$
$131$	−4.72583e8			−1.60470			−0.802348	+	0.596857i	$0.796416\pi$
$132$		0			0
$133$	−9.53163e7	−	9.53163e7i	−0.304622	−	0.304622i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.18904e8	+	4.18904e8i	−1.18914	+	1.18914i	−0.211833	+	0.977306i	$0.567943\pi$
$137$	−4.18904e8	+	4.18904e8i	−1.18914	+	1.18914i	−0.977306	+	0.211833i	$0.932057\pi$
$138$		0			0
$139$			1.69916e8i			0.455171i	0.973758	+	0.227585i	$0.0730831\pi$
$139$			1.69916e8i			0.455171i	−0.973758	+	0.227585i	$0.926917\pi$
$140$		0			0
$141$	3.76841e8			0.953413
$142$		0			0
$143$	−1.39848e8	−	1.39848e8i	−0.334435	−	0.334435i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−2.79464e8	+	2.79464e8i	−0.598489	+	0.598489i
$148$		0			0
$149$			4.38300e8i			0.889256i	0.895715	+	0.444628i	$0.146664\pi$
$149$			4.38300e8i			0.889256i	−0.895715	+	0.444628i	$0.853336\pi$
$150$		0			0
$151$	−8.13079e8			−1.56396			−0.781978	−	0.623305i	$-0.785789\pi$
$151$	−8.13079e8			−1.56396			−0.781978	+	0.623305i	$0.785789\pi$
$152$		0			0
$153$	−6.05118e7	−	6.05118e7i	−0.110427	−	0.110427i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.03454e8	−	3.03454e8i	0.499452	−	0.499452i	−0.411815	−	0.911267i	$-0.635105\pi$
$157$	3.03454e8	−	3.03454e8i	0.499452	−	0.499452i	0.911267	+	0.411815i	$0.135105\pi$
$158$		0			0
$159$			5.52474e8i			0.864418i
$160$		0			0
$161$	−7.66586e8			−1.14093
$162$		0			0
$163$	5.03451e8	+	5.03451e8i	0.713193	+	0.713193i	0.967202	−	0.254009i	$-0.0817493\pi$
$163$	5.03451e8	+	5.03451e8i	0.713193	+	0.713193i	−0.254009	+	0.967202i	$0.581749\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.20759e8	−	9.20759e8i	1.18380	−	1.18380i	0.205054	−	0.978751i	$-0.434263\pi$
$167$	9.20759e8	−	9.20759e8i	1.18380	−	1.18380i	0.978751	−	0.205054i	$-0.0657370\pi$
$168$		0			0
$169$			1.37032e9i			1.67987i
$170$		0			0
$171$	−7.81885e7			−0.0914447
$172$		0			0
$173$	−9.97910e8	−	9.97910e8i	−1.11406	−	1.11406i	−0.992596	−	0.121459i	$-0.961243\pi$
$173$	−9.97910e8	−	9.97910e8i	−1.11406	−	1.11406i	−0.121459	−	0.992596i	$-0.538757\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	2.66466e8	−	2.66466e8i	0.271487	−	0.271487i
$178$		0			0
$179$		−	3.38819e8i		−	0.330031i	−0.986291	−	0.165016i	$-0.947233\pi$
$179$		−	3.38819e8i		−	0.330031i	0.986291	−	0.165016i	$-0.0527675\pi$
$180$		0			0
$181$	−3.01131e8			−0.280570			−0.140285	−	0.990111i	$-0.544802\pi$
$181$	−3.01131e8			−0.280570			−0.140285	+	0.990111i	$0.544802\pi$
$182$		0			0
$183$	2.82267e8	+	2.82267e8i	0.251684	+	0.251684i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.17039e8	−	1.17039e8i	0.0957117	−	0.0957117i
$188$		0			0
$189$			3.85622e8i			0.302214i
$190$		0			0
$191$	−1.39831e9			−1.05068			−0.525341	−	0.850892i	$-0.676062\pi$
$191$	−1.39831e9			−1.05068			−0.525341	+	0.850892i	$0.676062\pi$
$192$		0			0
$193$	−1.65905e9	−	1.65905e9i	−1.19572	−	1.19572i	−0.975434	−	0.220290i	$-0.929300\pi$
$193$	−1.65905e9	−	1.65905e9i	−1.19572	−	1.19572i	−0.220290	−	0.975434i	$-0.570700\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.80824e8	+	3.80824e8i	−0.252848	+	0.252848i	−0.822137	−	0.569289i	$-0.807218\pi$
$197$	−3.80824e8	+	3.80824e8i	−0.252848	+	0.252848i	0.569289	+	0.822137i	$0.307218\pi$
$198$		0			0
$199$			1.26259e9i			0.805099i	0.915398	+	0.402550i	$0.131876\pi$
$199$			1.26259e9i			0.805099i	−0.915398	+	0.402550i	$0.868124\pi$
$200$		0			0
$201$	−1.68740e9			−1.03379
$202$		0			0
$203$	−1.10890e8	−	1.10890e8i	−0.0652994	−	0.0652994i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−3.14417e8	+	3.14417e8i	−0.171248	+	0.171248i
$208$		0			0
$209$		−	1.51229e8i		−	0.0792591i
$210$		0			0
$211$	2.74217e8			0.138346			0.0691728	−	0.997605i	$-0.477964\pi$
$211$	2.74217e8			0.138346			0.0691728	+	0.997605i	$0.477964\pi$
$212$		0			0
$213$	−6.55261e8	−	6.55261e8i	−0.318344	−	0.318344i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.56123e9	+	3.56123e9i	−1.60606	+	1.60606i
$218$		0			0
$219$			8.73843e8i			0.379889i
$220$		0			0
$221$	−1.82952e9			−0.766950
$222$		0			0
$223$	−2.56079e9	−	2.56079e9i	−1.03551	−	1.03551i	−0.999346	−	0.0361645i	$-0.988486\pi$
$223$	−2.56079e9	−	2.56079e9i	−1.03551	−	1.03551i	−0.0361645	−	0.999346i	$-0.511514\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.53659e8	−	2.53659e8i	0.0955316	−	0.0955316i	−0.657726	−	0.753257i	$-0.728481\pi$
$227$	2.53659e8	−	2.53659e8i	0.0955316	−	0.0955316i	0.753257	+	0.657726i	$0.228481\pi$
$228$		0			0
$229$		−	2.39918e9i		−	0.872411i	−0.899847	−	0.436205i	$-0.856322\pi$
$229$		−	2.39918e9i		−	0.872411i	0.899847	−	0.436205i	$-0.143678\pi$
$230$		0			0
$231$	−7.45852e8			−0.261942
$232$		0			0
$233$	−4.74015e8	−	4.74015e8i	−0.160831	−	0.160831i	0.622104	−	0.782935i	$-0.286278\pi$
$233$	−4.74015e8	−	4.74015e8i	−0.160831	−	0.160831i	−0.782935	+	0.622104i	$0.786278\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	9.46388e8	−	9.46388e8i	0.299969	−	0.299969i
$238$		0			0
$239$		−	2.18086e8i		−	0.0668399i	−0.999441	−	0.0334199i	$-0.989360\pi$
$239$		−	2.18086e8i		−	0.0668399i	0.999441	−	0.0334199i	$-0.0106399\pi$
$240$		0			0
$241$	8.11831e8			0.240657			0.120328	−	0.992734i	$-0.461605\pi$
$241$	8.11831e8			0.240657			0.120328	+	0.992734i	$0.461605\pi$
$242$		0			0
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.18198e9	+	1.18198e9i	−0.317557	+	0.317557i
$248$		0			0
$249$		−	2.88297e9i		−	0.749969i
$250$		0			0
$251$	1.44794e9			0.364801			0.182400	−	0.983224i	$-0.441613\pi$
$251$	1.44794e9			0.364801			0.182400	+	0.983224i	$0.441613\pi$
$252$		0			0
$253$	−6.08133e8	−	6.08133e8i	−0.148428	−	0.148428i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.29500e9	+	4.29500e9i	−0.984535	+	0.984535i	−0.999882	−	0.0153473i	$-0.995115\pi$
$257$	−4.29500e9	+	4.29500e9i	−0.984535	+	0.984535i	0.0153473	+	0.999882i	$0.495115\pi$
$258$		0			0
$259$		−	1.09377e9i		−	0.243067i
$260$		0			0
$261$	−9.09639e7			−0.0196023
$262$		0			0
$263$	4.09078e7	+	4.09078e7i	0.00855034	+	0.00855034i	0.711369	−	0.702819i	$-0.248075\pi$
$263$	4.09078e7	+	4.09078e7i	0.00855034	+	0.00855034i	−0.702819	+	0.711369i	$0.748075\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	3.52121e9	−	3.52121e9i	0.692862	−	0.692862i
$268$		0			0
$269$			8.80640e9i			1.68186i	0.541146	+	0.840929i	$0.317991\pi$
$269$			8.80640e9i			1.68186i	−0.541146	+	0.840929i	$0.682009\pi$
$270$		0			0
$271$	3.69563e9			0.685190			0.342595	−	0.939483i	$-0.388694\pi$
$271$	3.69563e9			0.685190			0.342595	+	0.939483i	$0.388694\pi$
$272$		0			0
$273$	5.82945e9	+	5.82945e9i	1.04949	+	1.04949i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.10353e9	−	4.10353e9i	0.697009	−	0.697009i	−0.266755	−	0.963764i	$-0.585951\pi$
$277$	4.10353e9	−	4.10353e9i	0.697009	−	0.697009i	0.963764	+	0.266755i	$0.0859514\pi$
$278$		0			0
$279$			2.92129e9i			0.482124i
$280$		0			0
$281$	−1.13263e10			−1.81661			−0.908305	−	0.418308i	$-0.862623\pi$
$281$	−1.13263e10			−1.81661			−0.908305	+	0.418308i	$0.862623\pi$
$282$		0			0
$283$	2.08509e9	+	2.08509e9i	0.325071	+	0.325071i	0.850709	−	0.525637i	$-0.176173\pi$
$283$	2.08509e9	+	2.08509e9i	0.325071	+	0.325071i	−0.525637	+	0.850709i	$0.676173\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.81708e9	+	1.81708e9i	−0.267822	+	0.267822i
$288$		0			0
$289$			5.44463e9i			0.780507i
$290$		0			0
$291$	−5.68389e9			−0.792636
$292$		0			0
$293$	−1.08347e9	−	1.08347e9i	−0.147009	−	0.147009i	0.629771	−	0.776781i	$-0.283149\pi$
$293$	−1.08347e9	−	1.08347e9i	−0.147009	−	0.147009i	−0.776781	+	0.629771i	$0.783149\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−3.05913e8	+	3.05913e8i	−0.0393163	+	0.0393163i
$298$		0			0
$299$			9.50611e9i			1.18937i
$300$		0			0
$301$	−7.03139e9			−0.856594
$302$		0			0
$303$	−5.87462e9	−	5.87462e9i	−0.696962	−	0.696962i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.72563e9	+	1.72563e9i	−0.194265	+	0.194265i	−0.797536	−	0.603271i	$-0.793864\pi$
$307$	−1.72563e9	+	1.72563e9i	−0.194265	+	0.194265i	0.603271	+	0.797536i	$0.293864\pi$
$308$		0			0
$309$		−	4.70550e9i		−	0.516145i
$310$		0			0
$311$	9.04637e9			0.967014			0.483507	−	0.875341i	$-0.339363\pi$
$311$	9.04637e9			0.967014			0.483507	+	0.875341i	$0.339363\pi$
$312$		0			0
$313$	2.77154e9	+	2.77154e9i	0.288764	+	0.288764i	0.836591	−	0.547827i	$-0.184545\pi$
$313$	2.77154e9	+	2.77154e9i	0.288764	+	0.288764i	−0.547827	+	0.836591i	$0.684545\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.22842e9	−	2.22842e9i	0.220679	−	0.220679i	−0.588106	−	0.808784i	$-0.700126\pi$
$317$	2.22842e9	−	2.22842e9i	0.220679	−	0.220679i	0.808784	+	0.588106i	$0.200126\pi$
$318$		0			0
$319$		−	1.75938e8i		−	0.0169902i
$320$		0			0
$321$	1.01033e10			0.951576
$322$		0			0
$323$	−9.89203e8	−	9.89203e8i	−0.0908814	−	0.0908814i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.49104e9	+	1.49104e9i	−0.130406	+	0.130406i
$328$		0			0
$329$		−	3.03824e10i		−	2.59321i
$330$		0			0
$331$	−1.95554e9			−0.162913			−0.0814564	−	0.996677i	$-0.525957\pi$
$331$	−1.95554e9			−0.162913			−0.0814564	+	0.996677i	$0.525957\pi$
$332$		0			0
$333$	−4.48611e8	−	4.48611e8i	−0.0364832	−	0.0364832i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.12125e10	−	1.12125e10i	0.869326	−	0.869326i	−0.123072	−	0.992398i	$-0.539275\pi$
$337$	1.12125e10	−	1.12125e10i	0.869326	−	0.869326i	0.992398	+	0.123072i	$0.0392746\pi$
$338$		0			0
$339$			1.06480e10i			0.806250i
$340$		0			0
$341$	−5.65024e9			−0.417878
$342$		0			0
$343$	7.16205e9	+	7.16205e9i	0.517441	+	0.517441i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.55202e8	+	8.55202e8i	−0.0589863	+	0.0589863i	−0.735985	−	0.676998i	$-0.763280\pi$
$347$	−8.55202e8	+	8.55202e8i	−0.0589863	+	0.0589863i	0.676998	+	0.735985i	$0.263280\pi$
$348$		0			0
$349$		−	4.10410e9i		−	0.276641i	−0.990388	−	0.138320i	$-0.955830\pi$
$349$		−	4.10410e9i		−	0.276641i	0.990388	−	0.138320i	$-0.0441703\pi$
$350$		0			0
$351$	4.78193e9			0.315047
$352$		0			0
$353$	−8.83814e9	−	8.83814e9i	−0.569196	−	0.569196i	0.362707	−	0.931903i	$-0.381853\pi$
$353$	−8.83814e9	−	8.83814e9i	−0.569196	−	0.569196i	−0.931903	+	0.362707i	$0.881853\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−4.87870e9	+	4.87870e9i	−0.300352	+	0.300352i
$358$		0			0
$359$		−	2.36100e10i		−	1.42141i	−0.703493	−	0.710703i	$-0.748377\pi$
$359$		−	2.36100e10i		−	1.42141i	0.703493	−	0.710703i	$-0.251623\pi$
$360$		0			0
$361$	1.57054e10			0.924741
$362$		0			0
$363$	6.49676e9	+	6.49676e9i	0.374171	+	0.374171i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.46072e9	+	4.46072e9i	−0.245890	+	0.245890i	−0.819281	−	0.573392i	$-0.805627\pi$
$367$	−4.46072e9	+	4.46072e9i	−0.245890	+	0.245890i	0.573392	+	0.819281i	$0.305627\pi$
$368$		0			0
$369$			1.49056e9i			0.0803978i
$370$		0			0
$371$	4.45426e10			2.35115
$372$		0			0
$373$	1.15162e10	+	1.15162e10i	0.594942	+	0.594942i	0.938962	−	0.344020i	$-0.111789\pi$
$373$	1.15162e10	+	1.15162e10i	0.594942	+	0.594942i	−0.344020	+	0.938962i	$0.611789\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1.37510e9	+	1.37510e9i	−0.0680723	+	0.0680723i
$378$		0			0
$379$			1.85132e10i			0.897275i	0.893714	+	0.448638i	$0.148091\pi$
$379$			1.85132e10i			0.897275i	−0.893714	+	0.448638i	$0.851909\pi$
$380$		0			0
$381$	1.48564e10			0.705040
$382$		0			0
$383$	2.14648e9	+	2.14648e9i	0.0997542	+	0.0997542i	0.755223	−	0.655468i	$-0.227529\pi$
$383$	2.14648e9	+	2.14648e9i	0.0997542	+	0.0997542i	−0.655468	+	0.755223i	$0.727529\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.88394e9	+	2.88394e9i	−0.128571	+	0.128571i
$388$		0			0
$389$		−	4.35233e10i		−	1.90074i	−0.311119	−	0.950371i	$-0.600704\pi$
$389$		−	4.35233e10i		−	1.90074i	0.311119	−	0.950371i	$-0.399296\pi$
$390$		0			0
$391$	−7.95571e9			−0.340386
$392$		0			0
$393$	1.56274e10	+	1.56274e10i	0.655114	+	0.655114i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	2.30783e10	−	2.30783e10i	0.929058	−	0.929058i	−0.0685875	−	0.997645i	$-0.521849\pi$
$397$	2.30783e10	−	2.30783e10i	0.929058	−	0.929058i	0.997645	+	0.0685875i	$0.0218492\pi$
$398$		0			0
$399$			6.30386e9i			0.248722i
$400$		0			0
$401$	6.74663e9			0.260921			0.130461	−	0.991453i	$-0.458354\pi$
$401$	6.74663e9			0.260921			0.130461	+	0.991453i	$0.458354\pi$
$402$		0			0
$403$	4.41613e10	+	4.41613e10i	1.67425	+	1.67425i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	8.67684e8	−	8.67684e8i	0.0316216	−	0.0316216i
$408$		0			0
$409$		−	1.92106e10i		−	0.686510i	−0.939242	−	0.343255i	$-0.888471\pi$
$409$		−	1.92106e10i		−	0.686510i	0.939242	−	0.343255i	$-0.111529\pi$
$410$		0			0
$411$	2.77048e10			0.970928
$412$		0			0
$413$	−2.14835e10	−	2.14835e10i	−0.738423	−	0.738423i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	5.61879e9	−	5.61879e9i	0.185823	−	0.185823i
$418$		0			0
$419$			1.63752e10i			0.531289i	0.964071	+	0.265644i	$0.0855847\pi$
$419$			1.63752e10i			0.531289i	−0.964071	+	0.265644i	$0.914415\pi$
$420$		0			0
$421$	5.44735e10			1.73403			0.867016	−	0.498281i	$-0.166035\pi$
$421$	5.44735e10			1.73403			0.867016	+	0.498281i	$0.166035\pi$
$422$		0			0
$423$	−1.24614e10	−	1.24614e10i	−0.389229	−	0.389229i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	2.27575e10	−	2.27575e10i	0.684561	−	0.684561i
$428$		0			0
$429$			9.24900e9i			0.273065i
$430$		0			0
$431$	−2.04805e10			−0.593515			−0.296757	−	0.954953i	$-0.595905\pi$
$431$	−2.04805e10			−0.593515			−0.296757	+	0.954953i	$0.595905\pi$
$432$		0			0
$433$	−3.15184e9	−	3.15184e9i	−0.0896629	−	0.0896629i	0.660853	−	0.750516i	$-0.270195\pi$
$433$	−3.15184e9	−	3.15184e9i	−0.0896629	−	0.0896629i	−0.750516	+	0.660853i	$0.770195\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.13987e9	+	5.13987e9i	−0.140937	+	0.140937i
$438$		0			0
$439$		−	5.90316e10i		−	1.58937i	−0.607019	−	0.794687i	$-0.707635\pi$
$439$		−	5.90316e10i		−	1.58937i	0.607019	−	0.794687i	$-0.292365\pi$
$440$		0			0
$441$	1.84827e10			0.488665
$442$		0			0
$443$	−1.85479e10	−	1.85479e10i	−0.481593	−	0.481593i	0.424047	−	0.905640i	$-0.360609\pi$
$443$	−1.85479e10	−	1.85479e10i	−0.481593	−	0.481593i	−0.905640	+	0.424047i	$0.860609\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	1.44938e10	−	1.44938e10i	0.363037	−	0.363037i
$448$		0			0
$449$		−	1.37680e10i		−	0.338754i	−0.985551	−	0.169377i	$-0.945824\pi$
$449$		−	1.37680e10i		−	0.338754i	0.985551	−	0.169377i	$-0.0541756\pi$
$450$		0			0
$451$	−2.88298e9			−0.0696843
$452$		0			0
$453$	2.68870e10	+	2.68870e10i	0.638483	+	0.638483i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.79885e10	−	2.79885e10i	0.641674	−	0.641674i	−0.309293	−	0.950967i	$-0.600092\pi$
$457$	2.79885e10	−	2.79885e10i	0.641674	−	0.641674i	0.950967	+	0.309293i	$0.100092\pi$
$458$		0			0
$459$			4.00202e9i			0.0901631i
$460$		0			0
$461$	−6.13060e10			−1.35737			−0.678687	−	0.734428i	$-0.737451\pi$
$461$	−6.13060e10			−1.35737			−0.678687	+	0.734428i	$0.737451\pi$
$462$		0			0
$463$	−1.44760e10	−	1.44760e10i	−0.315011	−	0.315011i	0.531836	−	0.846847i	$-0.321502\pi$
$463$	−1.44760e10	−	1.44760e10i	−0.315011	−	0.315011i	−0.846847	+	0.531836i	$0.821502\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.87433e9	+	4.87433e9i	−0.102482	+	0.102482i	−0.756489	−	0.654007i	$-0.773087\pi$
$467$	−4.87433e9	+	4.87433e9i	−0.102482	+	0.102482i	0.654007	+	0.756489i	$0.273087\pi$
$468$		0			0
$469$			1.36045e11i			2.81184i
$470$		0			0
$471$	−2.00693e10			−0.407801
$472$		0			0
$473$	−5.57800e9	−	5.57800e9i	−0.111438	−	0.111438i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.82693e10	−	1.82693e10i	0.352897	−	0.352897i
$478$		0			0
$479$		−	3.31779e10i		−	0.630242i	−0.949051	−	0.315121i	$-0.897955\pi$
$479$		−	3.31779e10i		−	0.630242i	0.949051	−	0.315121i	$-0.102045\pi$
$480$		0			0
$481$	−1.35633e10			−0.253388
$482$		0			0
$483$	2.53496e10	+	2.53496e10i	0.465781	+	0.465781i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−6.64774e10	+	6.64774e10i	−1.18184	+	1.18184i	−0.202571	+	0.979268i	$0.564930\pi$
$487$	−6.64774e10	+	6.64774e10i	−1.18184	+	1.18184i	−0.979268	+	0.202571i	$0.935070\pi$
$488$		0			0
$489$		−	3.32964e10i		−	0.582319i
$490$		0			0
$491$	−1.96715e10			−0.338464			−0.169232	−	0.985576i	$-0.554129\pi$
$491$	−1.96715e10			−0.338464			−0.169232	+	0.985576i	$0.554129\pi$
$492$		0			0
$493$	−1.15083e9	−	1.15083e9i	−0.0194816	−	0.0194816i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.28297e10	+	5.28297e10i	−0.865870	+	0.865870i
$498$		0			0
$499$		−	5.48770e10i		−	0.885092i	−0.896746	−	0.442546i	$-0.854075\pi$
$499$		−	5.48770e10i		−	0.885092i	0.896746	−	0.442546i	$-0.145925\pi$
$500$		0			0
$501$	−6.08955e10			−0.966572
$502$		0			0
$503$	−2.22290e10	−	2.22290e10i	−0.347254	−	0.347254i	0.511832	−	0.859086i	$-0.328967\pi$
$503$	−2.22290e10	−	2.22290e10i	−0.347254	−	0.347254i	−0.859086	+	0.511832i	$0.828967\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.53139e10	−	4.53139e10i	0.685803	−	0.685803i
$508$		0			0
$509$			1.54866e10i			0.230720i	0.993324	+	0.115360i	$0.0368021\pi$
$509$			1.54866e10i			0.230720i	−0.993324	+	0.115360i	$0.963198\pi$
$510$		0			0
$511$	7.04527e10			1.03327
$512$		0			0
$513$	2.58555e9	+	2.58555e9i	0.0373321	+	0.0373321i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	2.41023e10	−	2.41023e10i	0.337362	−	0.337362i
$518$		0			0
$519$			6.59980e10i			0.909623i
$520$		0			0
$521$	9.00392e10			1.22203			0.611013	−	0.791620i	$-0.290762\pi$
$521$	9.00392e10			1.22203			0.611013	+	0.791620i	$0.290762\pi$
$522$		0			0
$523$	6.40325e10	+	6.40325e10i	0.855843	+	0.855843i	0.990845	−	0.135003i	$-0.0431043\pi$
$523$	6.40325e10	+	6.40325e10i	0.855843	+	0.855843i	−0.135003	+	0.990845i	$0.543104\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.69588e10	+	3.69588e10i	−0.479154	+	0.479154i
$528$		0			0
$529$		−	3.69733e10i		−	0.472135i
$530$		0			0
$531$	−1.76230e10			−0.221668
$532$		0			0
$533$	2.25328e10	+	2.25328e10i	0.279195	+	0.279195i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−1.12041e10	+	1.12041e10i	−0.134735	+	0.134735i
$538$		0			0
$539$			3.57484e10i			0.423547i
$540$		0			0
$541$	−2.91080e10			−0.339800			−0.169900	−	0.985461i	$-0.554345\pi$
$541$	−2.91080e10			−0.339800			−0.169900	+	0.985461i	$0.554345\pi$
$542$		0			0
$543$	9.95785e9	+	9.95785e9i	0.114542	+	0.114542i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−2.49355e10	+	2.49355e10i	−0.278528	+	0.278528i	−0.832521	−	0.553993i	$-0.813103\pi$
$547$	−2.49355e10	+	2.49355e10i	−0.278528	+	0.278528i	0.553993	+	0.832521i	$0.313103\pi$
$548$		0			0
$549$		−	1.86681e10i		−	0.205499i
$550$		0			0
$551$	−1.48701e9			−0.0161327
$552$		0			0
$553$	−7.63015e10	−	7.63015e10i	−0.815892	−	0.815892i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.90039e10	+	1.90039e10i	−0.197434	+	0.197434i	−0.798899	−	0.601465i	$-0.794584\pi$
$557$	−1.90039e10	+	1.90039e10i	−0.197434	+	0.197434i	0.601465	+	0.798899i	$0.294584\pi$
$558$		0			0
$559$			8.71933e10i			0.892968i
$560$		0			0
$561$	−7.74054e9			−0.0781483
$562$		0			0
$563$	−3.91441e10	−	3.91441e10i	−0.389612	−	0.389612i	0.484937	−	0.874549i	$-0.338843\pi$
$563$	−3.91441e10	−	3.91441e10i	−0.389612	−	0.389612i	−0.874549	+	0.484937i	$0.838843\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.27518e10	−	1.27518e10i	0.123378	−	0.123378i
$568$		0			0
$569$		−	8.30756e10i		−	0.792545i	−0.918133	−	0.396273i	$-0.870303\pi$
$569$		−	8.30756e10i		−	0.792545i	0.918133	−	0.396273i	$-0.129697\pi$
$570$		0			0
$571$	9.13683e10			0.859510			0.429755	−	0.902946i	$-0.358600\pi$
$571$	9.13683e10			0.859510			0.429755	+	0.902946i	$0.358600\pi$
$572$		0			0
$573$	4.62396e10	+	4.62396e10i	0.428939	+	0.428939i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−7.70957e10	+	7.70957e10i	−0.695548	+	0.695548i	−0.963447	−	0.267899i	$-0.913671\pi$
$577$	−7.70957e10	+	7.70957e10i	−0.695548	+	0.695548i	0.267899	+	0.963447i	$0.413671\pi$
$578$		0			0
$579$			1.09724e11i			0.976305i
$580$		0			0
$581$	−2.32437e11			−2.03986
$582$		0			0
$583$	3.53357e10	+	3.53357e10i	0.305871	+	0.305871i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.11623e10	+	7.11623e10i	−0.599373	+	0.599373i	−0.940146	−	0.340773i	$-0.889311\pi$
$587$	−7.11623e10	+	7.11623e10i	−0.599373	+	0.599373i	0.340773	+	0.940146i	$0.389311\pi$
$588$		0			0
$589$			4.77552e10i			0.396789i
$590$		0			0
$591$	2.51863e10			0.206450
$592$		0			0
$593$	−1.26100e11	−	1.26100e11i	−1.01976	−	1.01976i	−0.999801	−	0.0199543i	$-0.993648\pi$
$593$	−1.26100e11	−	1.26100e11i	−1.01976	−	1.01976i	−0.0199543	−	0.999801i	$-0.506352\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	4.17514e10	−	4.17514e10i	0.328680	−	0.328680i
$598$		0			0
$599$		−	1.79664e11i		−	1.39558i	−0.716304	−	0.697789i	$-0.754167\pi$
$599$		−	1.79664e11i		−	1.39558i	0.716304	−	0.697789i	$-0.245833\pi$
$600$		0			0
$601$	5.73524e10			0.439596			0.219798	−	0.975545i	$-0.429460\pi$
$601$	5.73524e10			0.439596			0.219798	+	0.975545i	$0.429460\pi$
$602$		0			0
$603$	5.57991e10	+	5.57991e10i	0.422044	+	0.422044i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.24845e10	+	4.24845e10i	−0.312951	+	0.312951i	−0.846052	−	0.533101i	$-0.821027\pi$
$607$	−4.24845e10	+	4.24845e10i	−0.312951	+	0.312951i	0.533101	+	0.846052i	$0.321027\pi$
$608$		0			0
$609$			7.33387e9i			0.0533168i
$610$		0			0
$611$	−3.76759e11			−2.70333
$612$		0			0
$613$	−1.55504e11	−	1.55504e11i	−1.10129	−	1.10129i	−0.994256	−	0.107031i	$-0.965866\pi$
$613$	−1.55504e11	−	1.55504e11i	−1.10129	−	1.10129i	−0.107031	−	0.994256i	$-0.534134\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.63850e10	+	5.63850e10i	−0.389066	+	0.389066i	−0.874354	−	0.485288i	$-0.838715\pi$
$617$	−5.63850e10	+	5.63850e10i	−0.389066	+	0.389066i	0.485288	+	0.874354i	$0.338715\pi$
$618$		0			0
$619$			1.28081e11i			0.872412i	0.899847	+	0.436206i	$0.143678\pi$
$619$			1.28081e11i			0.872412i	−0.899847	+	0.436206i	$0.856322\pi$
$620$		0			0
$621$	2.07944e10			0.139823
$622$		0			0
$623$	−2.83893e11	−	2.83893e11i	−1.88453	−	1.88453i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−5.00085e9	+	5.00085e9i	−0.0323574	+	0.0323574i
$628$		0			0
$629$		−	1.13512e10i		−	0.0725170i
$630$		0			0
$631$	−2.12376e11			−1.33964			−0.669819	−	0.742524i	$-0.733629\pi$
$631$	−2.12376e11			−1.33964			−0.669819	+	0.742524i	$0.733629\pi$
$632$		0			0
$633$	−9.06785e9	−	9.06785e9i	−0.0564793	−	0.0564793i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	2.79403e11	−	2.79403e11i	1.69697	−	1.69697i
$638$		0			0
$639$			4.33365e10i			0.259926i
$640$		0			0
$641$	−3.62819e10			−0.214911			−0.107455	−	0.994210i	$-0.534270\pi$
$641$	−3.62819e10			−0.214911			−0.107455	+	0.994210i	$0.534270\pi$
$642$		0			0
$643$	9.94083e10	+	9.94083e10i	0.581539	+	0.581539i	0.935326	−	0.353787i	$-0.115106\pi$
$643$	9.94083e10	+	9.94083e10i	0.581539	+	0.581539i	−0.353787	+	0.935326i	$0.615106\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.32385e10	−	3.32385e10i	0.189681	−	0.189681i	−0.605877	−	0.795558i	$-0.707178\pi$
$647$	3.32385e10	−	3.32385e10i	0.189681	−	0.189681i	0.795558	+	0.605877i	$0.207178\pi$
$648$		0			0
$649$		−	3.40857e10i		−	0.192129i
$650$		0			0
$651$	2.35526e11			1.31134
$652$		0			0
$653$	−1.65291e11	−	1.65291e11i	−0.909066	−	0.909066i	0.0871306	−	0.996197i	$-0.472230\pi$
$653$	−1.65291e11	−	1.65291e11i	−0.909066	−	0.909066i	−0.996197	+	0.0871306i	$0.972230\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.88963e10	−	2.88963e10i	0.155089	−	0.155089i
$658$		0			0
$659$			2.33254e11i			1.23676i	0.785878	+	0.618382i	$0.212212\pi$
$659$			2.33254e11i			1.23676i	−0.785878	+	0.618382i	$0.787788\pi$
$660$		0			0
$661$	−3.45654e11			−1.81065			−0.905327	−	0.424716i	$-0.860374\pi$
$661$	−3.45654e11			−1.81065			−0.905327	+	0.424716i	$0.860374\pi$
$662$		0			0
$663$	6.04987e10	+	6.04987e10i	0.313106	+	0.313106i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.97968e9	+	5.97968e9i	−0.0302117	+	0.0302117i
$668$		0			0
$669$			1.69361e11i			0.845491i
$670$		0			0
$671$	3.61070e10			0.178115
$672$		0			0
$673$	2.40046e11	+	2.40046e11i	1.17013	+	1.17013i	0.982178	+	0.187953i	$0.0601852\pi$
$673$	2.40046e11	+	2.40046e11i	1.17013	+	1.17013i	0.187953	+	0.982178i	$0.439815\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.31348e11	−	2.31348e11i	1.10132	−	1.10132i	0.107063	−	0.994252i	$-0.465855\pi$
$677$	2.31348e11	−	2.31348e11i	1.10132	−	1.10132i	0.994252	−	0.107063i	$-0.0341446\pi$
$678$		0			0
$679$			4.58257e11i			2.15591i
$680$		0			0
$681$	−1.67761e10			−0.0780012
$682$		0			0
$683$	−2.41273e11	−	2.41273e11i	−1.10873	−	1.10873i	−0.993317	−	0.115414i	$-0.963181\pi$
$683$	−2.41273e11	−	2.41273e11i	−1.10873	−	1.10873i	−0.115414	−	0.993317i	$-0.536819\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−7.93364e10	+	7.93364e10i	−0.356160	+	0.356160i
$688$		0			0
$689$		−	5.52354e11i		−	2.45099i
$690$		0			0
$691$	3.01264e11			1.32140			0.660700	−	0.750650i	$-0.270259\pi$
$691$	3.01264e11			1.32140			0.660700	+	0.750650i	$0.270259\pi$
$692$		0			0
$693$	2.46639e10	+	2.46639e10i	0.106937	+	0.106937i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.88579e10	+	1.88579e10i	−0.0799026	+	0.0799026i
$698$		0			0
$699$			3.13496e10i			0.131318i
$700$		0			0
$701$	1.75215e10			0.0725604			0.0362802	−	0.999342i	$-0.488449\pi$
$701$	1.75215e10			0.0725604			0.0362802	+	0.999342i	$0.488449\pi$
$702$		0			0
$703$	−7.33357e9	−	7.33357e9i	−0.0300258	−	0.0300258i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.73635e11	+	4.73635e11i	−1.89568	+	1.89568i
$708$		0			0
$709$			1.02260e11i			0.404688i	0.979314	+	0.202344i	$0.0648560\pi$
$709$			1.02260e11i			0.404688i	−0.979314	+	0.202344i	$0.935144\pi$
$710$		0			0
$711$	−6.25905e10			−0.244923
$712$		0			0
$713$	1.92037e11	+	1.92037e11i	0.743064	+	0.743064i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−7.21168e9	+	7.21168e9i	−0.0272873	+	0.0272873i
$718$		0			0
$719$			4.23327e11i			1.58402i	0.610509	+	0.792009i	$0.290965\pi$
$719$			4.23327e11i			1.58402i	−0.610509	+	0.792009i	$0.709035\pi$
$720$		0			0
$721$	−3.79375e11			−1.40387
$722$		0			0
$723$	−2.68457e10	−	2.68457e10i	−0.0982476	−	0.0982476i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.55192e10	−	4.55192e10i	0.162951	−	0.162951i	−0.620922	−	0.783873i	$-0.713242\pi$
$727$	4.55192e10	−	4.55192e10i	0.162951	−	0.162951i	0.783873	+	0.620922i	$0.213242\pi$
$728$		0			0
$729$		−	1.04604e10i		−	0.0370370i
$730$		0			0
$731$	−7.29725e10			−0.255558
$732$		0			0
$733$	1.61922e11	+	1.61922e11i	0.560907	+	0.560907i	0.929565	−	0.368658i	$-0.120183\pi$
$733$	1.61922e11	+	1.61922e11i	0.560907	+	0.560907i	−0.368658	+	0.929565i	$0.620183\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.07924e11	+	1.07924e11i	−0.365805	+	0.365805i
$738$		0			0
$739$		−	1.28406e11i		−	0.430534i	−0.976555	−	0.215267i	$-0.930938\pi$
$739$		−	1.28406e11i		−	0.430534i	0.976555	−	0.215267i	$-0.0690622\pi$
$740$		0			0
$741$	7.81715e10			0.259284
$742$		0			0
$743$	1.98948e11	+	1.98948e11i	0.652805	+	0.652805i	0.953667	−	0.300863i	$-0.0972746\pi$
$743$	1.98948e11	+	1.98948e11i	0.652805	+	0.652805i	−0.300863	+	0.953667i	$0.597275\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−9.53345e10	+	9.53345e10i	−0.306174	+	0.306174i
$748$		0			0
$749$		−	8.14568e11i		−	2.58821i
$750$		0			0
$751$	1.67795e11			0.527497			0.263749	−	0.964591i	$-0.415041\pi$
$751$	1.67795e11			0.527497			0.263749	+	0.964591i	$0.415041\pi$
$752$		0			0
$753$	−4.78806e10	−	4.78806e10i	−0.148929	−	0.148929i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1.41853e11	−	1.41853e11i	0.431971	−	0.431971i	−0.457328	−	0.889298i	$-0.651193\pi$
$757$	1.41853e11	−	1.41853e11i	0.431971	−	0.431971i	0.889298	+	0.457328i	$0.151193\pi$
$758$		0			0
$759$			4.02196e10i			0.121191i
$760$		0			0
$761$	9.15535e10			0.272983			0.136492	−	0.990641i	$-0.456417\pi$
$761$	9.15535e10			0.272983			0.136492	+	0.990641i	$0.456417\pi$
$762$		0			0
$763$	1.20213e11	+	1.20213e11i	0.354694	+	0.354694i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.66408e11	+	2.66408e11i	−0.769778	+	0.769778i
$768$		0			0
$769$		−	2.72533e11i		−	0.779316i	−0.920960	−	0.389658i	$-0.872593\pi$
$769$		−	2.72533e11i		−	0.779316i	0.920960	−	0.389658i	$-0.127407\pi$
$770$		0			0
$771$	2.84055e11			0.803869
$772$		0			0
$773$	−4.06178e11	−	4.06178e11i	−1.13762	−	1.13762i	−0.988875	−	0.148749i	$-0.952475\pi$
$773$	−4.06178e11	−	4.06178e11i	−1.13762	−	1.13762i	−0.148749	−	0.988875i	$-0.547525\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.61688e10	+	3.61688e10i	−0.0992315	+	0.0992315i
$778$		0			0
$779$			2.43666e10i			0.0661676i
$780$		0			0
$781$	−8.38196e10			−0.225290
$782$		0			0
$783$	3.00801e9	+	3.00801e9i	0.00800261	+	0.00800261i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.39167e11	+	1.39167e11i	−0.362776	+	0.362776i	−0.864834	−	0.502058i	$-0.832576\pi$
$787$	−1.39167e11	+	1.39167e11i	−0.362776	+	0.362776i	0.502058	+	0.864834i	$0.332576\pi$
$788$		0			0
$789$		−	2.70549e9i		−	0.00698132i
$790$		0			0
$791$	8.58484e11			2.19294
$792$		0			0
$793$	−2.82206e11	−	2.82206e11i	−0.713630	−	0.713630i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.50760e10	+	4.50760e10i	−0.111715	+	0.111715i	−0.760755	−	0.649040i	$-0.775171\pi$
$797$	−4.50760e10	+	4.50760e10i	−0.111715	+	0.111715i	0.649040	+	0.760755i	$0.275171\pi$
$798$		0			0
$799$		−	3.15311e11i		−	0.773664i
$800$		0			0
$801$	−2.32879e11			−0.565719
$802$		0			0
$803$	5.58901e10	+	5.58901e10i	0.134423	+	0.134423i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.91211e11	−	2.91211e11i	0.686615	−	0.686615i
$808$		0			0
$809$			5.41595e11i			1.26439i	0.774810	+	0.632194i	$0.217846\pi$
$809$			5.41595e11i			1.26439i	−0.774810	+	0.632194i	$0.782154\pi$
$810$		0			0
$811$	−4.69699e11			−1.08577			−0.542883	−	0.839808i	$-0.682667\pi$
$811$	−4.69699e11			−1.08577			−0.542883	+	0.839808i	$0.682667\pi$
$812$		0			0
$813$	−1.22208e11	−	1.22208e11i	−0.279728	−	0.279728i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.71446e10	+	4.71446e10i	−0.105814	+	0.105814i
$818$		0			0
$819$		−	3.85538e11i		−	0.856903i
$820$		0			0
$821$	−3.07080e11			−0.675894			−0.337947	−	0.941165i	$-0.609733\pi$
$821$	−3.07080e11			−0.675894			−0.337947	+	0.941165i	$0.609733\pi$
$822$		0			0
$823$	1.37347e11	+	1.37347e11i	0.299378	+	0.299378i	0.840770	−	0.541392i	$-0.182103\pi$
$823$	1.37347e11	+	1.37347e11i	0.299378	+	0.299378i	−0.541392	+	0.840770i	$0.682103\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.84135e11	−	1.84135e11i	0.393654	−	0.393654i	−0.482334	−	0.875988i	$-0.660211\pi$
$827$	1.84135e11	−	1.84135e11i	0.393654	−	0.393654i	0.875988	+	0.482334i	$0.160211\pi$
$828$		0			0
$829$		−	2.55668e11i		−	0.541324i	−0.962674	−	0.270662i	$-0.912757\pi$
$829$		−	2.55668e11i		−	0.541324i	0.962674	−	0.270662i	$-0.0872426\pi$
$830$		0			0
$831$	−2.71392e11			−0.569106
$832$		0			0
$833$	2.33834e11	+	2.33834e11i	0.485655	+	0.485655i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	9.66016e10	−	9.66016e10i	0.196826	−	0.196826i
$838$		0			0
$839$			3.31981e11i			0.669984i	0.942221	+	0.334992i	$0.108734\pi$
$839$			3.31981e11i			0.669984i	−0.942221	+	0.334992i	$0.891266\pi$
$840$		0			0
$841$	4.98516e11			0.996542
$842$		0			0
$843$	3.74538e11	+	3.74538e11i	0.741628	+	0.741628i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.23794e11	−	5.23794e11i	1.01772	−	1.01772i
$848$		0			0
$849$		−	1.37900e11i		−	0.265420i
$850$		0			0
$851$	−5.89806e10			−0.112458
$852$		0			0
$853$	4.02307e11	+	4.02307e11i	0.759909	+	0.759909i	0.976305	−	0.216397i	$-0.0694305\pi$
$853$	4.02307e11	+	4.02307e11i	0.759909	+	0.759909i	−0.216397	+	0.976305i	$0.569431\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.04678e11	+	2.04678e11i	−0.379443	+	0.379443i	−0.870901	−	0.491458i	$-0.836464\pi$
$857$	−2.04678e11	+	2.04678e11i	−0.379443	+	0.379443i	0.491458	+	0.870901i	$0.336464\pi$
$858$		0			0
$859$			9.74402e11i			1.78964i	0.446428	+	0.894820i	$0.352696\pi$
$859$			9.74402e11i			1.78964i	−0.446428	+	0.894820i	$0.647304\pi$
$860$		0			0
$861$	1.20175e11			0.218676
$862$		0			0
$863$	4.32807e11	+	4.32807e11i	0.780281	+	0.780281i	0.979878	−	0.199597i	$-0.0639633\pi$
$863$	4.32807e11	+	4.32807e11i	0.780281	+	0.780281i	−0.199597	+	0.979878i	$0.563963\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.80044e11	−	1.80044e11i	0.318641	−	0.318641i
$868$		0			0
$869$		−	1.21060e11i		−	0.212286i
$870$		0			0
$871$	1.68703e12			2.93124
$872$		0			0
$873$	1.87956e11	+	1.87956e11i	0.323592	+	0.323592i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.84945e11	+	1.84945e11i	−0.312639	+	0.312639i	−0.845931	−	0.533292i	$-0.820955\pi$
$877$	−1.84945e11	+	1.84945e11i	−0.312639	+	0.312639i	0.533292	+	0.845931i	$0.320955\pi$
$878$		0			0
$879$			7.16563e10i			0.120033i
$880$		0			0
$881$	−4.48810e11			−0.745005			−0.372503	−	0.928031i	$-0.621500\pi$
$881$	−4.48810e11			−0.745005			−0.372503	+	0.928031i	$0.621500\pi$
$882$		0			0
$883$	−2.24906e11	−	2.24906e11i	−0.369963	−	0.369963i	0.497500	−	0.867464i	$-0.334251\pi$
$883$	−2.24906e11	−	2.24906e11i	−0.369963	−	0.369963i	−0.867464	+	0.497500i	$0.834251\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.96651e11	−	6.96651e11i	1.12544	−	1.12544i	0.134526	−	0.990910i	$-0.457049\pi$
$887$	6.96651e11	−	6.96651e11i	1.12544	−	1.12544i	0.990910	−	0.134526i	$-0.0429511\pi$
$888$		0			0
$889$		−	1.19778e12i		−	1.91765i
$890$		0			0
$891$	2.02320e10			0.0321016
$892$		0			0
$893$	−2.03710e11	−	2.03710e11i	−0.320337	−	0.320337i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	3.14349e11	−	3.14349e11i	0.485560	−	0.485560i
$898$		0			0
$899$			5.55580e10i			0.0850566i
$900$		0			0
$901$	4.62268e11			0.701447
$902$		0			0
$903$	2.32515e11	+	2.32515e11i	0.349703	+	0.349703i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	2.77022e11	−	2.77022e11i	0.409340	−	0.409340i	−0.472168	−	0.881509i	$-0.656528\pi$
$907$	2.77022e11	−	2.77022e11i	0.409340	−	0.409340i	0.881509	+	0.472168i	$0.156528\pi$
$908$		0			0
$909$			3.88525e11i			0.569067i
$910$		0			0
$911$	5.90840e11			0.857821			0.428911	−	0.903347i	$-0.358898\pi$
$911$	5.90840e11			0.857821			0.428911	+	0.903347i	$0.358898\pi$
$912$		0			0
$913$	−1.84392e11	−	1.84392e11i	−0.265374	−	0.265374i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.25994e12	−	1.25994e12i	1.78186	−	1.78186i
$918$		0			0
$919$			4.54155e11i			0.636710i	0.947972	+	0.318355i	$0.103130\pi$
$919$			4.54155e11i			0.636710i	−0.947972	+	0.318355i	$0.896870\pi$
$920$		0			0
$921$	1.14126e11			0.158616
$922$		0			0
$923$	6.55119e11	+	6.55119e11i	0.902638	+	0.902638i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.55602e11	+	1.55602e11i	−0.210715	+	0.210715i
$928$		0			0
$929$			1.96626e10i			0.0263985i	0.999913	+	0.0131992i	$0.00420157\pi$
$929$			1.96626e10i			0.0263985i	−0.999913	+	0.0131992i	$0.995798\pi$
$930$		0			0
$931$	3.02142e11			0.402172
$932$		0			0
$933$	−2.99146e11	−	2.99146e11i	−0.394782	−	0.394782i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.45064e11	+	2.45064e11i	−0.317923	+	0.317923i	−0.847969	−	0.530046i	$-0.822175\pi$
$937$	−2.45064e11	+	2.45064e11i	−0.317923	+	0.317923i	0.530046	+	0.847969i	$0.322175\pi$
$938$		0			0
$939$		−	1.83299e11i		−	0.235775i
$940$		0			0
$941$	−1.11899e11			−0.142715			−0.0713575	−	0.997451i	$-0.522733\pi$
$941$	−1.11899e11			−0.142715			−0.0713575	+	0.997451i	$0.522733\pi$
$942$		0			0
$943$	9.79848e10	+	9.79848e10i	0.123912	+	0.123912i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.14945e11	+	4.14945e11i	−0.515930	+	0.515930i	−0.916337	−	0.400408i	$-0.868869\pi$
$947$	−4.14945e11	+	4.14945e11i	−0.515930	+	0.515930i	0.400408	+	0.916337i	$0.368869\pi$
$948$		0			0
$949$		−	8.73654e11i		−	1.07715i
$950$		0			0
$951$	−1.47379e11			−0.180183
$952$		0			0
$953$	−6.28336e11	−	6.28336e11i	−0.761764	−	0.761764i	0.214877	−	0.976641i	$-0.431065\pi$
$953$	−6.28336e11	−	6.28336e11i	−0.761764	−	0.761764i	−0.976641	+	0.214877i	$0.931065\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−5.81795e9	+	5.81795e9i	−0.00693621	+	0.00693621i
$958$		0			0
$959$		−	2.23367e12i		−	2.64085i
$960$		0			0
$961$	9.31347e11			1.09199
$962$		0			0
$963$	−3.34097e11	−	3.34097e11i	−0.388479	−	0.388479i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−8.01745e11	+	8.01745e11i	−0.916918	+	0.916918i	−0.996804	−	0.0798861i	$-0.974544\pi$
$967$	−8.01745e11	+	8.01745e11i	−0.916918	+	0.916918i	0.0798861	+	0.996804i	$0.474544\pi$
$968$		0			0
$969$			6.54221e10i			0.0742044i
$970$		0			0
$971$	5.32550e11			0.599078			0.299539	−	0.954084i	$-0.403167\pi$
$971$	5.32550e11			0.599078			0.299539	+	0.954084i	$0.403167\pi$
$972$		0			0
$973$	−4.53009e11	−	4.53009e11i	−0.505423	−	0.505423i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.23340e11	+	2.23340e11i	−0.245125	+	0.245125i	−0.818966	−	0.573841i	$-0.805453\pi$
$977$	−2.23340e11	+	2.23340e11i	−0.245125	+	0.245125i	0.573841	+	0.818966i	$0.305453\pi$
$978$		0			0
$979$		−	4.50425e11i		−	0.490334i
$980$		0			0
$981$	9.86114e10			0.106476
$982$		0			0
$983$	1.07084e12	+	1.07084e12i	1.14686	+	1.14686i	0.987166	+	0.159695i	$0.0510512\pi$
$983$	1.07084e12	+	1.07084e12i	1.14686	+	1.14686i	0.159695	+	0.987166i	$0.448949\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.00469e12	+	1.00469e12i	−1.05867	+	1.05867i
$988$		0			0
$989$			3.79163e11i			0.396315i
$990$		0			0
$991$	−9.20259e11			−0.954147			−0.477074	−	0.878863i	$-0.658303\pi$
$991$	−9.20259e11			−0.954147			−0.477074	+	0.878863i	$0.658303\pi$
$992$		0			0
$993$	6.46661e10	+	6.46661e10i	0.0665088	+	0.0665088i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.57090e11	+	8.57090e11i	−0.867453	+	0.867453i	−0.992190	−	0.124737i	$-0.960191\pi$
$997$	−8.57090e11	+	8.57090e11i	−0.867453	+	0.867453i	0.124737	+	0.992190i	$0.460191\pi$
$998$		0			0
$999$			2.96694e10i			0.0297884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.193.1		16
5.2	odd	4	inner	300.9.k.e.157.1		16
5.3	odd	4		60.9.k.a.37.8	yes	16
5.4	even	2		60.9.k.a.13.8	✓	16
15.8	even	4		180.9.l.c.37.1		16
15.14	odd	2		180.9.l.c.73.1		16
20.3	even	4		240.9.bg.c.97.4		16
20.19	odd	2		240.9.bg.c.193.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.8	✓	16	5.4	even	2
60.9.k.a.37.8	yes	16	5.3	odd	4
180.9.l.c.37.1		16	15.8	even	4
180.9.l.c.73.1		16	15.14	odd	2
240.9.bg.c.97.4		16	20.3	even	4
240.9.bg.c.193.4		16	20.19	odd	2
300.9.k.e.157.1		16	5.2	odd	4	inner
300.9.k.e.193.1		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)

\(f(q)\)	\(=\)	\(q+(-33.0681 - 33.0681i) q^{3} +(-2666.08 + 2666.08i) q^{7} +2187.00i q^{9} +O(q^{10})\)	\(q+(-33.0681 - 33.0681i) q^{3} +(-2666.08 + 2666.08i) q^{7} +2187.00i q^{9} -4230.00 q^{11} +(33060.9 + 33060.9i) q^{13} +(-27668.9 + 27668.9i) q^{17} +35751.5i q^{19} +176324. q^{21} +(143767. + 143767. i) q^{23} +(72320.0 - 72320.0i) q^{27} +41593.0i q^{29} +1.33575e6 q^{31} +(139878. + 139878. i) q^{33} +(-205126. + 205126. i) q^{37} -2.18653e6i q^{39} +681555. q^{41} +(1.31868e6 + 1.31868e6i) q^{43} +(-5.69795e6 + 5.69795e6i) q^{47} -8.45116e6i q^{49} +1.82991e6 q^{51} +(-8.35358e6 - 8.35358e6i) q^{53} +(1.18223e6 - 1.18223e6i) q^{57} +8.05809e6i q^{59} -8.53592e6 q^{61} +(-5.83072e6 - 5.83072e6i) q^{63} +(2.55140e7 - 2.55140e7i) q^{67} -9.50818e6i q^{69} +1.98155e7 q^{71} +(-1.32128e7 - 1.32128e7i) q^{73} +(1.12775e7 - 1.12775e7i) q^{77} +2.86194e7i q^{79} -4.78297e6 q^{81} +(4.35915e7 + 4.35915e7i) q^{83} +(1.37540e6 - 1.37540e6i) q^{87} +1.06483e8i q^{89} -1.76286e8 q^{91} +(-4.41708e7 - 4.41708e7i) q^{93} +(8.59422e7 - 8.59422e7i) q^{97} -9.25101e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 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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