LMFDB - Embedded newform 300.9.k.e.157.2

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			157.2
Root			$-1675.46 + 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.157
Dual form			300.9.k.e.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-33.0681 + 33.0681i) q^{3} +(-1939.46 - 1939.46i) q^{7} -2187.00i q^{9} +O(q^{10})$	$q+(-33.0681 + 33.0681i) q^{3} +(-1939.46 - 1939.46i) q^{7} -2187.00i q^{9} +3227.11 q^{11} +(-25451.0 + 25451.0i) q^{13} +(98257.0 + 98257.0i) q^{17} -108317. i q^{19} +128269. q^{21} +(278325. - 278325. i) q^{23} +(72320.0 + 72320.0i) q^{27} -1.08954e6i q^{29} -941873. q^{31} +(-106714. + 106714. i) q^{33} +(2.45730e6 + 2.45730e6i) q^{37} -1.68324e6i q^{39} +2.41580e6 q^{41} +(-3.27478e6 + 3.27478e6i) q^{43} +(2.76469e6 + 2.76469e6i) q^{47} +1.75821e6i q^{49} -6.49834e6 q^{51} +(-1.44286e6 + 1.44286e6i) q^{53} +(3.58183e6 + 3.58183e6i) q^{57} -134658. i q^{59} +6.73996e6 q^{61} +(-4.24160e6 + 4.24160e6i) q^{63} +(-2.13530e7 - 2.13530e7i) q^{67} +1.84073e7i q^{69} +7.79714e6 q^{71} +(-5.30729e6 + 5.30729e6i) q^{73} +(-6.25885e6 - 6.25885e6i) q^{77} +3.57253e7i q^{79} -4.78297e6 q^{81} +(2.00841e7 - 2.00841e7i) q^{83} +(3.60292e7 + 3.60292e7i) q^{87} -5.88002e7i q^{89} +9.87225e7 q^{91} +(3.11460e7 - 3.11460e7i) q^{93} +(-6.71527e6 - 6.71527e6i) q^{97} -7.05769e6i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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
$7$	−1939.46	−	1939.46i	−0.807772	−	0.807772i	0.176525	−	0.984296i	$-0.443514\pi$
$7$	−1939.46	−	1939.46i	−0.807772	−	0.807772i	−0.984296	+	0.176525i	$0.943514\pi$
$8$		0			0
$9$		−	2187.00i		−	0.333333i
$10$		0			0
$11$	3227.11			0.220416			0.110208	−	0.993909i	$-0.464848\pi$
$11$	3227.11			0.220416			0.110208	+	0.993909i	$0.464848\pi$
$12$		0			0
$13$	−25451.0	+	25451.0i	−0.891112	+	0.891112i	−0.994628	−	0.103516i	$-0.966991\pi$
$13$	−25451.0	+	25451.0i	−0.891112	+	0.891112i	0.103516	+	0.994628i	$0.466991\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	98257.0	+	98257.0i	1.17643	+	1.17643i	0.980646	+	0.195788i	$0.0627264\pi$
$17$	98257.0	+	98257.0i	1.17643	+	1.17643i	0.195788	+	0.980646i	$0.437274\pi$
$18$		0			0
$19$		−	108317.i		−	0.831153i	−0.909558	−	0.415577i	$-0.863580\pi$
$19$		−	108317.i		−	0.831153i	0.909558	−	0.415577i	$-0.136420\pi$
$20$		0			0
$21$	128269.			0.659543
$22$		0			0
$23$	278325.	−	278325.i	0.994581	−	0.994581i	−0.00540448	−	0.999985i	$-0.501720\pi$
$23$	278325.	−	278325.i	0.994581	−	0.994581i	0.999985	+	0.00540448i	$0.00172031\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	72320.0	+	72320.0i	0.136083	+	0.136083i
$28$		0			0
$29$		−	1.08954e6i		−	1.54047i	−0.637761	−	0.770234i	$-0.720139\pi$
$29$		−	1.08954e6i		−	1.54047i	0.637761	−	0.770234i	$-0.279861\pi$
$30$		0			0
$31$	−941873.			−1.01987			−0.509936	−	0.860212i	$-0.670331\pi$
$31$	−941873.			−1.01987			−0.509936	+	0.860212i	$0.670331\pi$
$32$		0			0
$33$	−106714.	+	106714.i	−0.0899845	+	0.0899845i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.45730e6	+	2.45730e6i	1.31115	+	1.31115i	0.920570	+	0.390578i	$0.127725\pi$
$37$	2.45730e6	+	2.45730e6i	1.31115	+	1.31115i	0.390578	+	0.920570i	$0.372275\pi$
$38$		0			0
$39$		−	1.68324e6i		−	0.727590i
$40$		0			0
$41$	2.41580e6			0.854919			0.427459	−	0.904035i	$-0.359409\pi$
$41$	2.41580e6			0.854919			0.427459	+	0.904035i	$0.359409\pi$
$42$		0			0
$43$	−3.27478e6	+	3.27478e6i	−0.957873	+	0.957873i	−0.999148	−	0.0412749i	$-0.986858\pi$
$43$	−3.27478e6	+	3.27478e6i	−0.957873	+	0.957873i	0.0412749	+	0.999148i	$0.486858\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.76469e6	+	2.76469e6i	0.566573	+	0.566573i	0.931167	−	0.364594i	$-0.118792\pi$
$47$	2.76469e6	+	2.76469e6i	0.566573	+	0.566573i	−0.364594	+	0.931167i	$0.618792\pi$
$48$		0			0
$49$			1.75821e6i			0.304990i
$50$		0			0
$51$	−6.49834e6			−0.960555
$52$		0			0
$53$	−1.44286e6	+	1.44286e6i	−0.182861	+	0.182861i	−0.792601	−	0.609741i	$-0.791274\pi$
$53$	−1.44286e6	+	1.44286e6i	−0.182861	+	0.182861i	0.609741	+	0.792601i	$0.291274\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.58183e6	+	3.58183e6i	0.339317	+	0.339317i
$58$		0			0
$59$		−	134658.i		−	0.0111128i	−0.999985	−	0.00555641i	$-0.998231\pi$
$59$		−	134658.i		−	0.0111128i	0.999985	−	0.00555641i	$-0.00176867\pi$
$60$		0			0
$61$	6.73996e6			0.486786			0.243393	−	0.969928i	$-0.421740\pi$
$61$	6.73996e6			0.486786			0.243393	+	0.969928i	$0.421740\pi$
$62$		0			0
$63$	−4.24160e6	+	4.24160e6i	−0.269257	+	0.269257i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.13530e7	−	2.13530e7i	−1.05965	−	1.05965i	−0.998105	−	0.0615409i	$-0.980399\pi$
$67$	−2.13530e7	−	2.13530e7i	−1.05965	−	1.05965i	−0.0615409	−	0.998105i	$-0.519601\pi$
$68$		0			0
$69$			1.84073e7i			0.812072i
$70$		0			0
$71$	7.79714e6			0.306833			0.153416	−	0.988162i	$-0.450972\pi$
$71$	7.79714e6			0.306833			0.153416	+	0.988162i	$0.450972\pi$
$72$		0			0
$73$	−5.30729e6	+	5.30729e6i	−0.186888	+	0.186888i	−0.794349	−	0.607461i	$-0.792188\pi$
$73$	−5.30729e6	+	5.30729e6i	−0.186888	+	0.186888i	0.607461	+	0.794349i	$0.292188\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.25885e6	−	6.25885e6i	−0.178046	−	0.178046i
$78$		0			0
$79$			3.57253e7i			0.917208i	0.888641	+	0.458604i	$0.151650\pi$
$79$			3.57253e7i			0.917208i	−0.888641	+	0.458604i	$0.848350\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	2.00841e7	−	2.00841e7i	0.423195	−	0.423195i	−0.463107	−	0.886302i	$-0.653266\pi$
$83$	2.00841e7	−	2.00841e7i	0.423195	−	0.423195i	0.886302	+	0.463107i	$0.153266\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.60292e7	+	3.60292e7i	0.628894	+	0.628894i
$88$		0			0
$89$		−	5.88002e7i		−	0.937170i	−0.883418	−	0.468585i	$-0.844764\pi$
$89$		−	5.88002e7i		−	0.937170i	0.883418	−	0.468585i	$-0.155236\pi$
$90$		0			0
$91$	9.87225e7			1.43963
$92$		0			0
$93$	3.11460e7	−	3.11460e7i	0.416361	−	0.416361i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.71527e6	−	6.71527e6i	−0.0758537	−	0.0758537i	0.668162	−	0.744016i	$-0.267081\pi$
$97$	−6.71527e6	−	6.71527e6i	−0.0758537	−	0.0758537i	−0.744016	+	0.668162i	$0.767081\pi$
$98$		0			0
$99$		−	7.05769e6i		−	0.0734720i
$100$		0			0
$101$	−1.30900e8			−1.25792			−0.628959	−	0.777438i	$-0.716519\pi$
$101$	−1.30900e8			−1.25792			−0.628959	+	0.777438i	$0.716519\pi$
$102$		0			0
$103$	−6.43577e7	+	6.43577e7i	−0.571809	+	0.571809i	−0.932634	−	0.360824i	$-0.882495\pi$
$103$	−6.43577e7	+	6.43577e7i	−0.571809	+	0.571809i	0.360824	+	0.932634i	$0.382495\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.45109e7	−	7.45109e7i	−0.568440	−	0.568440i	0.363251	−	0.931691i	$-0.381667\pi$
$107$	−7.45109e7	−	7.45109e7i	−0.568440	−	0.568440i	−0.931691	+	0.363251i	$0.881667\pi$
$108$		0			0
$109$			9.88845e7i			0.700522i	0.936652	+	0.350261i	$0.113907\pi$
$109$			9.88845e7i			0.700522i	−0.936652	+	0.350261i	$0.886093\pi$
$110$		0			0
$111$	−1.62517e8			−1.07055
$112$		0			0
$113$	−5.15033e7	+	5.15033e7i	−0.315879	+	0.315879i	−0.847182	−	0.531303i	$-0.821703\pi$
$113$	−5.15033e7	+	5.15033e7i	−0.315879	+	0.315879i	0.531303	+	0.847182i	$0.321703\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.56614e7	+	5.56614e7i	0.297037	+	0.297037i
$118$		0			0
$119$		−	3.81131e8i		−	1.90058i
$120$		0			0
$121$	−2.03945e8			−0.951417
$122$		0			0
$123$	−7.98858e7	+	7.98858e7i	−0.349019	+	0.349019i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.65134e8	−	2.65134e8i	−1.01918	−	1.01918i	−0.999812	−	0.0193650i	$-0.993836\pi$
$127$	−2.65134e8	−	2.65134e8i	−1.01918	−	1.01918i	−0.0193650	−	0.999812i	$-0.506164\pi$
$128$		0			0
$129$		−	2.16581e8i		−	0.782100i
$130$		0			0
$131$	−2.94932e8			−1.00147			−0.500733	−	0.865602i	$-0.666936\pi$
$131$	−2.94932e8			−1.00147			−0.500733	+	0.865602i	$0.666936\pi$
$132$		0			0
$133$	−2.10076e8	+	2.10076e8i	−0.671382	+	0.671382i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.76678e8	+	3.76678e8i	1.06927	+	1.06927i	0.997415	+	0.0718560i	$0.0228922\pi$
$137$	3.76678e8	+	3.76678e8i	1.06927	+	1.06927i	0.0718560	+	0.997415i	$0.477108\pi$
$138$		0			0
$139$		−	5.48769e8i		−	1.47004i	−0.678043	−	0.735022i	$-0.737172\pi$
$139$		−	5.48769e8i		−	1.47004i	0.678043	−	0.735022i	$-0.262828\pi$
$140$		0			0
$141$	−1.82846e8			−0.462605
$142$		0			0
$143$	−8.21334e7	+	8.21334e7i	−0.196415	+	0.196415i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.81405e7	−	5.81405e7i	−0.124512	−	0.124512i
$148$		0			0
$149$			6.70120e8i			1.35959i	0.733403	+	0.679794i	$0.237931\pi$
$149$			6.70120e8i			1.35959i	−0.733403	+	0.679794i	$0.762069\pi$
$150$		0			0
$151$	2.68284e8			0.516045			0.258022	−	0.966139i	$-0.416929\pi$
$151$	2.68284e8			0.516045			0.258022	+	0.966139i	$0.416929\pi$
$152$		0			0
$153$	2.14888e8	−	2.14888e8i	0.392145	−	0.392145i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.70569e8	−	7.70569e8i	−1.26827	−	1.26827i	−0.946979	−	0.321295i	$-0.895882\pi$
$157$	−7.70569e8	−	7.70569e8i	−1.26827	−	1.26827i	−0.321295	−	0.946979i	$-0.604118\pi$
$158$		0			0
$159$		−	9.54251e7i		−	0.149305i
$160$		0			0
$161$	−1.07960e9			−1.60679
$162$		0			0
$163$	−2.18000e8	+	2.18000e8i	−0.308821	+	0.308821i	−0.844452	−	0.535631i	$-0.820074\pi$
$163$	−2.18000e8	+	2.18000e8i	−0.308821	+	0.308821i	0.535631	+	0.844452i	$0.320074\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.75803e8	−	3.75803e8i	−0.483164	−	0.483164i	0.422977	−	0.906141i	$-0.360985\pi$
$167$	−3.75803e8	−	3.75803e8i	−0.483164	−	0.483164i	−0.906141	+	0.422977i	$0.860985\pi$
$168$		0			0
$169$		−	4.79781e8i		−	0.588161i
$170$		0			0
$171$	−2.36889e8			−0.277051
$172$		0			0
$173$	−1.77751e8	+	1.77751e8i	−0.198439	+	0.198439i	−0.799331	−	0.600891i	$-0.794812\pi$
$173$	−1.77751e8	+	1.77751e8i	−0.198439	+	0.198439i	0.600891	+	0.799331i	$0.294812\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.45289e6	+	4.45289e6i	0.00453679	+	0.00453679i
$178$		0			0
$179$		−	4.65545e8i		−	0.453471i	−0.973956	−	0.226736i	$-0.927195\pi$
$179$		−	4.65545e8i		−	0.453471i	0.973956	−	0.226736i	$-0.0728054\pi$
$180$		0			0
$181$	−1.01894e9			−0.949368			−0.474684	−	0.880156i	$-0.657438\pi$
$181$	−1.01894e9			−0.949368			−0.474684	+	0.880156i	$0.657438\pi$
$182$		0			0
$183$	−2.22878e8	+	2.22878e8i	−0.198730	+	0.198730i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.17086e8	+	3.17086e8i	0.259305	+	0.259305i
$188$		0			0
$189$		−	2.80523e8i		−	0.219848i
$190$		0			0
$191$	3.73834e8			0.280896			0.140448	−	0.990088i	$-0.455146\pi$
$191$	3.73834e8			0.280896			0.140448	+	0.990088i	$0.455146\pi$
$192$		0			0
$193$	3.86526e8	−	3.86526e8i	0.278580	−	0.278580i	−0.553962	−	0.832542i	$-0.686885\pi$
$193$	3.86526e8	−	3.86526e8i	0.278580	−	0.278580i	0.832542	+	0.553962i	$0.186885\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.23809e9	−	1.23809e9i	−0.822029	−	0.822029i	0.164370	−	0.986399i	$-0.447441\pi$
$197$	−1.23809e9	−	1.23809e9i	−0.822029	−	0.822029i	−0.986399	+	0.164370i	$0.947441\pi$
$198$		0			0
$199$			7.12668e8i			0.454438i	0.973844	+	0.227219i	$0.0729634\pi$
$199$			7.12668e8i			0.454438i	−0.973844	+	0.227219i	$0.927037\pi$
$200$		0			0
$201$	1.41221e9			0.865197
$202$		0			0
$203$	−2.11313e9	+	2.11313e9i	−1.24435	+	1.24435i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.08696e8	−	6.08696e8i	−0.331527	−	0.331527i
$208$		0			0
$209$		−	3.49550e8i		−	0.183199i
$210$		0			0
$211$	−2.21875e9			−1.11938			−0.559692	−	0.828701i	$-0.689081\pi$
$211$	−2.21875e9			−1.11938			−0.559692	+	0.828701i	$0.689081\pi$
$212$		0			0
$213$	−2.57837e8	+	2.57837e8i	−0.125264	+	0.125264i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	1.82672e9	+	1.82672e9i	0.823823	+	0.823823i
$218$		0			0
$219$		−	3.51004e8i		−	0.152593i
$220$		0			0
$221$	−5.00148e9			−2.09667
$222$		0			0
$223$	−2.38954e9	+	2.38954e9i	−0.966261	+	0.966261i	−0.999449	−	0.0331881i	$-0.989434\pi$
$223$	−2.38954e9	+	2.38954e9i	−0.966261	+	0.966261i	0.0331881	+	0.999449i	$0.489434\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.06931e8	+	5.06931e8i	0.190917	+	0.190917i	0.796092	−	0.605175i	$-0.206897\pi$
$227$	5.06931e8	+	5.06931e8i	0.190917	+	0.190917i	−0.605175	+	0.796092i	$0.706897\pi$
$228$		0			0
$229$		−	2.80021e9i		−	1.01824i	−0.860696	−	0.509119i	$-0.829971\pi$
$229$		−	2.80021e9i		−	1.01824i	0.860696	−	0.509119i	$-0.170029\pi$
$230$		0			0
$231$	4.13937e8			0.145374
$232$		0			0
$233$	−2.82554e9	+	2.82554e9i	−0.958689	+	0.958689i	−0.999180	−	0.0404906i	$-0.987108\pi$
$233$	−2.82554e9	+	2.82554e9i	−0.958689	+	0.958689i	0.0404906	+	0.999180i	$0.487108\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.18137e9	−	1.18137e9i	−0.374448	−	0.374448i
$238$		0			0
$239$		−	2.12060e9i		−	0.649931i	−0.945726	−	0.324965i	$-0.894647\pi$
$239$		−	2.12060e9i		−	0.649931i	0.945726	−	0.324965i	$-0.105353\pi$
$240$		0			0
$241$	−4.72169e9			−1.39968			−0.699840	−	0.714299i	$-0.746745\pi$
$241$	−4.72169e9			−1.39968			−0.699840	+	0.714299i	$0.746745\pi$
$242$		0			0
$243$	1.58164e8	−	1.58164e8i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.75677e9	+	2.75677e9i	0.740650	+	0.740650i
$248$		0			0
$249$			1.32829e9i			0.345537i
$250$		0			0
$251$	5.60318e9			1.41169			0.705846	−	0.708365i	$-0.250567\pi$
$251$	5.60318e9			1.41169			0.705846	+	0.708365i	$0.250567\pi$
$252$		0			0
$253$	8.98184e8	−	8.98184e8i	0.219222	−	0.219222i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.32621e9	−	2.32621e9i	−0.533232	−	0.533232i	0.388301	−	0.921533i	$-0.373062\pi$
$257$	−2.32621e9	−	2.32621e9i	−0.533232	−	0.533232i	−0.921533	+	0.388301i	$0.873062\pi$
$258$		0			0
$259$		−	9.53167e9i		−	2.11822i
$260$		0			0
$261$	−2.38283e9			−0.513490
$262$		0			0
$263$	4.97636e9	−	4.97636e9i	1.04013	−	1.04013i	0.0409722	−	0.999160i	$-0.486954\pi$
$263$	4.97636e9	−	4.97636e9i	1.04013	−	1.04013i	0.999160	−	0.0409722i	$-0.0130455\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.94441e9	+	1.94441e9i	0.382598	+	0.382598i
$268$		0			0
$269$		−	3.14127e9i		−	0.599924i	−0.953951	−	0.299962i	$-0.903026\pi$
$269$		−	3.14127e9i		−	0.599924i	0.953951	−	0.299962i	$-0.0969741\pi$
$270$		0			0
$271$	−8.45844e9			−1.56824			−0.784121	−	0.620608i	$-0.786886\pi$
$271$	−8.45844e9			−1.56824			−0.784121	+	0.620608i	$0.786886\pi$
$272$		0			0
$273$	−3.26457e9	+	3.26457e9i	−0.587726	+	0.587726i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.76213e9	−	1.76213e9i	−0.299309	−	0.299309i	0.541434	−	0.840743i	$-0.317882\pi$
$277$	−1.76213e9	−	1.76213e9i	−0.299309	−	0.299309i	−0.840743	+	0.541434i	$0.817882\pi$
$278$		0			0
$279$			2.05988e9i			0.339957i
$280$		0			0
$281$	5.11370e9			0.820181			0.410091	−	0.912045i	$-0.365497\pi$
$281$	5.11370e9			0.820181			0.410091	+	0.912045i	$0.365497\pi$
$282$		0			0
$283$	5.56378e9	−	5.56378e9i	0.867410	−	0.867410i	−0.124775	−	0.992185i	$-0.539821\pi$
$283$	5.56378e9	−	5.56378e9i	0.867410	−	0.867410i	0.992185	+	0.124775i	$0.0398209\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.68534e9	−	4.68534e9i	−0.690579	−	0.690579i
$288$		0			0
$289$			1.23331e10i			1.76800i
$290$		0			0
$291$	4.44123e8			0.0619343
$292$		0			0
$293$	−7.21092e9	+	7.21092e9i	−0.978409	+	0.978409i	−0.999772	−	0.0213631i	$-0.993199\pi$
$293$	−7.21092e9	+	7.21092e9i	−0.978409	+	0.978409i	0.0213631	+	0.999772i	$0.493199\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.33385e8	+	2.33385e8i	0.0299948	+	0.0299948i
$298$		0			0
$299$			1.41673e10i			1.77257i
$300$		0			0
$301$	1.27026e10			1.54748
$302$		0			0
$303$	4.32860e9	−	4.32860e9i	0.513543	−	0.513543i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−2.60758e9	−	2.60758e9i	−0.293551	−	0.293551i	0.544930	−	0.838481i	$-0.316556\pi$
$307$	−2.60758e9	−	2.60758e9i	−0.293551	−	0.293551i	−0.838481	+	0.544930i	$0.816556\pi$
$308$		0			0
$309$		−	4.25637e9i		−	0.466880i
$310$		0			0
$311$	−1.22301e10			−1.30734			−0.653670	−	0.756780i	$-0.726772\pi$
$311$	−1.22301e10			−1.30734			−0.653670	+	0.756780i	$0.726772\pi$
$312$		0			0
$313$	−8.36083e7	+	8.36083e7i	−0.00871108	+	0.00871108i	−0.711449	−	0.702738i	$-0.751961\pi$
$313$	−8.36083e7	+	8.36083e7i	−0.00871108	+	0.00871108i	0.702738	+	0.711449i	$0.251961\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.92187e9	−	7.92187e9i	−0.784496	−	0.784496i	0.196090	−	0.980586i	$-0.437175\pi$
$317$	−7.92187e9	−	7.92187e9i	−0.784496	−	0.784496i	−0.980586	+	0.196090i	$0.937175\pi$
$318$		0			0
$319$		−	3.51608e9i		−	0.339544i
$320$		0			0
$321$	4.92787e9			0.464130
$322$		0			0
$323$	1.06429e10	−	1.06429e10i	0.977797	−	0.977797i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.26992e9	−	3.26992e9i	−0.285987	−	0.285987i
$328$		0			0
$329$		−	1.07240e10i		−	0.915322i
$330$		0			0
$331$	1.12398e10			0.936367			0.468183	−	0.883631i	$-0.344909\pi$
$331$	1.12398e10			0.936367			0.468183	+	0.883631i	$0.344909\pi$
$332$		0			0
$333$	5.37412e9	−	5.37412e9i	0.437049	−	0.437049i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.35456e9	−	1.35456e9i	−0.105021	−	0.105021i	0.652644	−	0.757665i	$-0.273660\pi$
$337$	−1.35456e9	−	1.35456e9i	−0.105021	−	0.105021i	−0.757665	+	0.652644i	$0.773660\pi$
$338$		0			0
$339$		−	3.40623e9i		−	0.257914i
$340$		0			0
$341$	−3.03953e9			−0.224796
$342$		0			0
$343$	−7.77063e9	+	7.77063e9i	−0.561410	+	0.561410i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.05131e10	+	1.05131e10i	0.725127	+	0.725127i	0.969645	−	0.244518i	$-0.0786298\pi$
$347$	1.05131e10	+	1.05131e10i	0.725127	+	0.725127i	−0.244518	+	0.969645i	$0.578630\pi$
$348$		0			0
$349$			2.70963e10i			1.82645i	0.407455	+	0.913225i	$0.366416\pi$
$349$			2.70963e10i			1.82645i	−0.407455	+	0.913225i	$0.633584\pi$
$350$		0			0
$351$	−3.68124e9			−0.242530
$352$		0			0
$353$	−1.50350e10	+	1.50350e10i	−0.968286	+	0.968286i	−0.999512	−	0.0312263i	$-0.990059\pi$
$353$	−1.50350e10	+	1.50350e10i	−0.968286	+	0.968286i	0.0312263	+	0.999512i	$0.490059\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.26033e10	+	1.26033e10i	0.775909	+	0.775909i
$358$		0			0
$359$			1.99814e10i			1.20295i	0.798892	+	0.601475i	$0.205420\pi$
$359$			1.99814e10i			1.20295i	−0.798892	+	0.601475i	$0.794580\pi$
$360$		0			0
$361$	5.25106e9			0.309185
$362$		0			0
$363$	6.74406e9	−	6.74406e9i	0.388414	−	0.388414i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.18005e9	+	2.18005e9i	0.120172	+	0.120172i	0.764635	−	0.644464i	$-0.222919\pi$
$367$	2.18005e9	+	2.18005e9i	0.120172	+	0.120172i	−0.644464	+	0.764635i	$0.722919\pi$
$368$		0			0
$369$		−	5.28335e9i		−	0.284973i
$370$		0			0
$371$	5.59673e9			0.295419
$372$		0			0
$373$	1.59286e10	−	1.59286e10i	0.822892	−	0.822892i	−0.163629	−	0.986522i	$-0.552320\pi$
$373$	1.59286e10	−	1.59286e10i	0.822892	−	0.822892i	0.986522	+	0.163629i	$0.0523201\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.77300e10	+	2.77300e10i	1.37273	+	1.37273i
$378$		0			0
$379$		−	3.21096e10i		−	1.55624i	−0.628113	−	0.778122i	$-0.716172\pi$
$379$		−	3.21096e10i		−	1.55624i	0.628113	−	0.778122i	$-0.283828\pi$
$380$		0			0
$381$	1.75349e10			0.832155
$382$		0			0
$383$	−8.82401e9	+	8.82401e9i	−0.410082	+	0.410082i	−0.881767	−	0.471685i	$-0.843646\pi$
$383$	−8.82401e9	+	8.82401e9i	−0.410082	+	0.410082i	0.471685	+	0.881767i	$0.343646\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.16194e9	+	7.16194e9i	0.319291	+	0.319291i
$388$		0			0
$389$			2.27017e10i			0.991427i	0.868486	+	0.495713i	$0.165093\pi$
$389$			2.27017e10i			0.991427i	−0.868486	+	0.495713i	$0.834907\pi$
$390$		0			0
$391$	5.46946e10			2.34012
$392$		0			0
$393$	9.75284e9	−	9.75284e9i	0.408847	−	0.408847i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	1.08997e10	+	1.08997e10i	0.438787	+	0.438787i	0.891604	−	0.452816i	$-0.149581\pi$
$397$	1.08997e10	+	1.08997e10i	0.438787	+	0.438787i	−0.452816	+	0.891604i	$0.649581\pi$
$398$		0			0
$399$		−	1.38936e10i		−	0.548181i
$400$		0			0
$401$	−1.82700e9			−0.0706581			−0.0353290	−	0.999376i	$-0.511248\pi$
$401$	−1.82700e9			−0.0706581			−0.0353290	+	0.999376i	$0.511248\pi$
$402$		0			0
$403$	2.39716e10	−	2.39716e10i	0.908820	−	0.908820i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	7.92999e9	+	7.92999e9i	0.288998	+	0.288998i
$408$		0			0
$409$		−	2.22330e10i		−	0.794521i	−0.917706	−	0.397261i	$-0.869961\pi$
$409$		−	2.22330e10i		−	0.794521i	0.917706	−	0.397261i	$-0.130039\pi$
$410$		0			0
$411$	−2.49120e10			−0.873056
$412$		0			0
$413$	−2.61164e8	+	2.61164e8i	−0.00897663	+	0.00897663i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.81468e10	+	1.81468e10i	0.600143	+	0.600143i
$418$		0			0
$419$			2.36348e10i			0.766825i	0.923577	+	0.383412i	$0.125251\pi$
$419$			2.36348e10i			0.766825i	−0.923577	+	0.383412i	$0.874749\pi$
$420$		0			0
$421$	5.18217e10			1.64962			0.824808	−	0.565412i	$-0.191283\pi$
$421$	5.18217e10			1.64962			0.824808	+	0.565412i	$0.191283\pi$
$422$		0			0
$423$	6.04638e9	−	6.04638e9i	0.188858	−	0.188858i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.30719e10	−	1.30719e10i	−0.393212	−	0.393212i
$428$		0			0
$429$		−	5.43199e9i		−	0.160372i
$430$		0			0
$431$	2.60735e9			0.0755598			0.0377799	−	0.999286i	$-0.487971\pi$
$431$	2.60735e9			0.0755598			0.0377799	+	0.999286i	$0.487971\pi$
$432$		0			0
$433$	6.60923e9	−	6.60923e9i	0.188018	−	0.188018i	−0.606821	−	0.794839i	$-0.707555\pi$
$433$	6.60923e9	−	6.60923e9i	0.188018	−	0.188018i	0.794839	+	0.606821i	$0.207555\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.01472e10	−	3.01472e10i	−0.826649	−	0.826649i
$438$		0			0
$439$			4.28360e10i			1.15332i	0.816983	+	0.576661i	$0.195645\pi$
$439$			4.28360e10i			1.15332i	−0.816983	+	0.576661i	$0.804355\pi$
$440$		0			0
$441$	3.84519e9			0.101663
$442$		0			0
$443$	9.02375e9	−	9.02375e9i	0.234300	−	0.234300i	−0.580185	−	0.814485i	$-0.697020\pi$
$443$	9.02375e9	−	9.02375e9i	0.234300	−	0.234300i	0.814485	+	0.580185i	$0.197020\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−2.21596e10	−	2.21596e10i	−0.555049	−	0.555049i
$448$		0			0
$449$			6.85258e10i			1.68604i	0.537879	+	0.843022i	$0.319226\pi$
$449$			6.85258e10i			1.68604i	−0.537879	+	0.843022i	$0.680774\pi$
$450$		0			0
$451$	7.79604e9			0.188438
$452$		0			0
$453$	−8.87166e9	+	8.87166e9i	−0.210674	+	0.210674i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	4.23359e9	+	4.23359e9i	0.0970608	+	0.0970608i	0.753970	−	0.656909i	$-0.228136\pi$
$457$	4.23359e9	+	4.23359e9i	0.0970608	+	0.0970608i	−0.656909	+	0.753970i	$0.728136\pi$
$458$		0			0
$459$			1.42119e10i			0.320185i
$460$		0			0
$461$	−3.08923e9			−0.0683985			−0.0341993	−	0.999415i	$-0.510888\pi$
$461$	−3.08923e9			−0.0683985			−0.0341993	+	0.999415i	$0.510888\pi$
$462$		0			0
$463$	−3.43388e10	+	3.43388e10i	−0.747241	+	0.747241i	−0.973960	−	0.226719i	$-0.927200\pi$
$463$	−3.43388e10	+	3.43388e10i	−0.747241	+	0.747241i	0.226719	+	0.973960i	$0.427200\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.06656e10	−	5.06656e10i	−1.06524	−	1.06524i	−0.997718	−	0.0675173i	$-0.978492\pi$
$467$	−5.06656e10	−	5.06656e10i	−1.06524	−	1.06524i	−0.0675173	−	0.997718i	$-0.521508\pi$
$468$		0			0
$469$			8.28267e10i			1.71190i
$470$		0			0
$471$	5.09625e10			1.03554
$472$		0			0
$473$	−1.05681e10	+	1.05681e10i	−0.211131	+	0.211131i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.15553e9	+	3.15553e9i	0.0609535	+	0.0609535i
$478$		0			0
$479$		−	9.23191e9i		−	0.175368i	−0.996148	−	0.0876838i	$-0.972053\pi$
$479$		−	9.23191e9i		−	0.175368i	0.996148	−	0.0876838i	$-0.0279465\pi$
$480$		0			0
$481$	−1.25082e11			−2.33676
$482$		0			0
$483$	3.57003e10	−	3.57003e10i	0.655969	−	0.655969i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	5.21807e10	+	5.21807e10i	0.927671	+	0.927671i	0.997555	−	0.0698841i	$-0.0222629\pi$
$487$	5.21807e10	+	5.21807e10i	0.927671	+	0.927671i	−0.0698841	+	0.997555i	$0.522263\pi$
$488$		0			0
$489$		−	1.44177e10i		−	0.252151i
$490$		0			0
$491$	9.23744e10			1.58937			0.794686	−	0.607021i	$-0.207635\pi$
$491$	9.23744e10			1.58937			0.794686	+	0.607021i	$0.207635\pi$
$492$		0			0
$493$	1.07055e11	−	1.07055e11i	1.81226	−	1.81226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.51222e10	−	1.51222e10i	−0.247851	−	0.247851i
$498$		0			0
$499$		−	1.06428e11i		−	1.71653i	−0.513204	−	0.858266i	$-0.671542\pi$
$499$		−	1.06428e11i		−	1.71653i	0.513204	−	0.858266i	$-0.328458\pi$
$500$		0			0
$501$	2.48542e10			0.394502
$502$		0			0
$503$	−6.06663e10	+	6.06663e10i	−0.947710	+	0.947710i	−0.998699	−	0.0509895i	$-0.983763\pi$
$503$	−6.06663e10	+	6.06663e10i	−0.947710	+	0.947710i	0.0509895	+	0.998699i	$0.483763\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.58654e10	+	1.58654e10i	0.240116	+	0.240116i
$508$		0			0
$509$		−	1.69801e10i		−	0.252969i	−0.991969	−	0.126485i	$-0.959631\pi$
$509$		−	1.69801e10i		−	0.252969i	0.991969	−	0.126485i	$-0.0403695\pi$
$510$		0			0
$511$	2.05866e10			0.301926
$512$		0			0
$513$	7.83346e9	−	7.83346e9i	0.113106	−	0.113106i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	8.92197e9	+	8.92197e9i	0.124882	+	0.124882i
$518$		0			0
$519$		−	1.17558e10i		−	0.162025i
$520$		0			0
$521$	−8.14423e10			−1.10535			−0.552674	−	0.833397i	$-0.686393\pi$
$521$	−8.14423e10			−1.10535			−0.552674	+	0.833397i	$0.686393\pi$
$522$		0			0
$523$	−3.13068e10	+	3.13068e10i	−0.418439	+	0.418439i	−0.884665	−	0.466227i	$-0.845613\pi$
$523$	−3.13068e10	+	3.13068e10i	−0.418439	+	0.418439i	0.466227	+	0.884665i	$0.345613\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−9.25456e10	−	9.25456e10i	−1.19981	−	1.19981i
$528$		0			0
$529$		−	7.66181e10i		−	0.978382i
$530$		0			0
$531$	−2.94497e8			−0.00370428
$532$		0			0
$533$	−6.14846e10	+	6.14846e10i	−0.761828	+	0.761828i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.53947e10	+	1.53947e10i	0.185129	+	0.185129i
$538$		0			0
$539$			5.67392e9i			0.0672246i
$540$		0			0
$541$	−1.18938e11			−1.38845			−0.694226	−	0.719757i	$-0.744253\pi$
$541$	−1.18938e11			−1.38845			−0.694226	+	0.719757i	$0.744253\pi$
$542$		0			0
$543$	3.36945e10	−	3.36945e10i	0.387578	−	0.387578i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.66988e10	+	8.66988e10i	0.968420	+	0.968420i	0.999516	−	0.0310968i	$-0.00990002\pi$
$547$	8.66988e10	+	8.66988e10i	0.968420	+	0.968420i	−0.0310968	+	0.999516i	$0.509900\pi$
$548$		0			0
$549$		−	1.47403e10i		−	0.162262i
$550$		0			0
$551$	−1.18016e11			−1.28037
$552$		0			0
$553$	6.92878e10	−	6.92878e10i	0.740894	−	0.740894i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.66310e9	−	1.66310e9i	−0.0172781	−	0.0172781i	0.698415	−	0.715693i	$-0.253889\pi$
$557$	−1.66310e9	−	1.66310e9i	−0.0172781	−	0.0172781i	−0.715693	+	0.698415i	$0.753889\pi$
$558$		0			0
$559$		−	1.66693e11i		−	1.70714i
$560$		0			0
$561$	−2.09709e10			−0.211722
$562$		0			0
$563$	−7.09718e10	+	7.09718e10i	−0.706402	+	0.706402i	−0.965777	−	0.259375i	$-0.916484\pi$
$563$	−7.09718e10	+	7.09718e10i	−0.706402	+	0.706402i	0.259375	+	0.965777i	$0.416484\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	9.27637e9	+	9.27637e9i	0.0897524	+	0.0897524i
$568$		0			0
$569$		−	9.63590e10i		−	0.919271i	−0.888108	−	0.459635i	$-0.847980\pi$
$569$		−	9.63590e10i		−	0.919271i	0.888108	−	0.459635i	$-0.152020\pi$
$570$		0			0
$571$	5.02252e10			0.472473			0.236237	−	0.971696i	$-0.424086\pi$
$571$	5.02252e10			0.472473			0.236237	+	0.971696i	$0.424086\pi$
$572$		0			0
$573$	−1.23620e10	+	1.23620e10i	−0.114675	+	0.114675i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	7.67613e10	+	7.67613e10i	0.692530	+	0.692530i	0.962788	−	0.270258i	$-0.0871089\pi$
$577$	7.67613e10	+	7.67613e10i	0.692530	+	0.692530i	−0.270258	+	0.962788i	$0.587109\pi$
$578$		0			0
$579$			2.55634e10i			0.227460i
$580$		0			0
$581$	−7.79046e10			−0.683689
$582$		0			0
$583$	−4.65626e9	+	4.65626e9i	−0.0403054	+	0.0403054i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.77524e10	−	9.77524e10i	−0.823332	−	0.823332i	0.163252	−	0.986584i	$-0.447802\pi$
$587$	−9.77524e10	−	9.77524e10i	−0.823332	−	0.823332i	−0.986584	+	0.163252i	$0.947802\pi$
$588$		0			0
$589$			1.02021e11i			0.847669i
$590$		0			0
$591$	8.18826e10			0.671184
$592$		0			0
$593$	−1.11147e11	+	1.11147e11i	−0.898833	+	0.898833i	−0.995333	−	0.0965002i	$-0.969235\pi$
$593$	−1.11147e11	+	1.11147e11i	−0.898833	+	0.898833i	0.0965002	+	0.995333i	$0.469235\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−2.35666e10	−	2.35666e10i	−0.185524	−	0.185524i
$598$		0			0
$599$			9.94488e10i			0.772489i	0.922396	+	0.386245i	$0.126228\pi$
$599$			9.94488e10i			0.772489i	−0.922396	+	0.386245i	$0.873772\pi$
$600$		0			0
$601$	4.25532e10			0.326163			0.163081	−	0.986613i	$-0.447857\pi$
$601$	4.25532e10			0.326163			0.163081	+	0.986613i	$0.447857\pi$
$602$		0			0
$603$	−4.66991e10	+	4.66991e10i	−0.353215	+	0.353215i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−1.01532e11	−	1.01532e11i	−0.747905	−	0.747905i	0.226180	−	0.974085i	$-0.427376\pi$
$607$	−1.01532e11	−	1.01532e11i	−0.747905	−	0.747905i	−0.974085	+	0.226180i	$0.927376\pi$
$608$		0			0
$609$		−	1.39754e11i		−	1.01600i
$610$		0			0
$611$	−1.40729e11			−1.00976
$612$		0			0
$613$	−8.57237e10	+	8.57237e10i	−0.607098	+	0.607098i	−0.942187	−	0.335089i	$-0.891234\pi$
$613$	−8.57237e10	+	8.57237e10i	−0.607098	+	0.607098i	0.335089	+	0.942187i	$0.391234\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.24386e11	+	1.24386e11i	0.858286	+	0.858286i	0.991136	−	0.132850i	$-0.0424129\pi$
$617$	1.24386e11	+	1.24386e11i	0.858286	+	0.858286i	−0.132850	+	0.991136i	$0.542413\pi$
$618$		0			0
$619$		−	1.87700e11i		−	1.27850i	−0.768998	−	0.639251i	$-0.779245\pi$
$619$		−	1.87700e11i		−	1.27850i	0.768998	−	0.639251i	$-0.220755\pi$
$620$		0			0
$621$	4.02568e10			0.270691
$622$		0			0
$623$	−1.14041e11	+	1.14041e11i	−0.757020	+	0.757020i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.15590e10	+	1.15590e10i	0.0747909	+	0.0747909i
$628$		0			0
$629$			4.82894e11i			3.08496i
$630$		0			0
$631$	−2.17862e11			−1.37424			−0.687121	−	0.726543i	$-0.741126\pi$
$631$	−2.17862e11			−1.37424			−0.687121	+	0.726543i	$0.741126\pi$
$632$		0			0
$633$	7.33700e10	−	7.33700e10i	0.456987	−	0.456987i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.47482e10	−	4.47482e10i	−0.271780	−	0.271780i
$638$		0			0
$639$		−	1.70523e10i		−	0.102278i
$640$		0			0
$641$	−2.58517e10			−0.153129			−0.0765644	−	0.997065i	$-0.524395\pi$
$641$	−2.58517e10			−0.153129			−0.0765644	+	0.997065i	$0.524395\pi$
$642$		0			0
$643$	9.38432e9	−	9.38432e9i	0.0548983	−	0.0548983i	−0.679125	−	0.734023i	$-0.737640\pi$
$643$	9.38432e9	−	9.38432e9i	0.0548983	−	0.0548983i	0.734023	+	0.679125i	$0.237640\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.97482e11	−	1.97482e11i	−1.12697	−	1.12697i	−0.990668	−	0.136298i	$-0.956479\pi$
$647$	−1.97482e11	−	1.97482e11i	−1.12697	−	1.12697i	−0.136298	−	0.990668i	$-0.543521\pi$
$648$		0			0
$649$		−	4.34557e8i		−	0.00244945i
$650$		0			0
$651$	−1.20813e11			−0.672649
$652$		0			0
$653$	−1.75679e11	+	1.75679e11i	−0.966200	+	0.966200i	−0.999447	−	0.0332472i	$-0.989415\pi$
$653$	−1.75679e11	+	1.75679e11i	−0.966200	+	0.966200i	0.0332472	+	0.999447i	$0.489415\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.16070e10	+	1.16070e10i	0.0622960	+	0.0622960i
$658$		0			0
$659$			1.07195e10i			0.0568374i	0.999596	+	0.0284187i	$0.00904717\pi$
$659$			1.07195e10i			0.0568374i	−0.999596	+	0.0284187i	$0.990953\pi$
$660$		0			0
$661$	1.43173e10			0.0749992			0.0374996	−	0.999297i	$-0.488061\pi$
$661$	1.43173e10			0.0749992			0.0374996	+	0.999297i	$0.488061\pi$
$662$		0			0
$663$	1.65390e11	−	1.65390e11i	0.855962	−	0.855962i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.03247e11	−	3.03247e11i	−1.53212	−	1.53212i
$668$		0			0
$669$		−	1.58035e11i		−	0.788949i
$670$		0			0
$671$	2.17506e10			0.107295
$672$		0			0
$673$	−8.90882e10	+	8.90882e10i	−0.434270	+	0.434270i	−0.890078	−	0.455808i	$-0.849350\pi$
$673$	−8.90882e10	+	8.90882e10i	−0.434270	+	0.434270i	0.455808	+	0.890078i	$0.349350\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.03143e11	−	1.03143e11i	−0.491003	−	0.491003i	0.417619	−	0.908622i	$-0.362865\pi$
$677$	−1.03143e11	−	1.03143e11i	−0.491003	−	0.491003i	−0.908622	+	0.417619i	$0.862865\pi$
$678$		0			0
$679$			2.60480e10i			0.122545i
$680$		0			0
$681$	−3.35265e10			−0.155883
$682$		0			0
$683$	1.37712e11	−	1.37712e11i	0.632831	−	0.632831i	−0.315946	−	0.948777i	$-0.602322\pi$
$683$	1.37712e11	−	1.37712e11i	0.632831	−	0.632831i	0.948777	+	0.315946i	$0.102322\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	9.25978e10	+	9.25978e10i	0.415694	+	0.415694i
$688$		0			0
$689$		−	7.34445e10i		−	0.325898i
$690$		0			0
$691$	3.00486e11			1.31799			0.658994	−	0.752148i	$-0.270982\pi$
$691$	3.00486e11			1.31799			0.658994	+	0.752148i	$0.270982\pi$
$692$		0			0
$693$	−1.36881e10	+	1.36881e10i	−0.0593486	+	0.0593486i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	2.37369e11	+	2.37369e11i	1.00576	+	1.00576i
$698$		0			0
$699$		−	1.86871e11i		−	0.782767i
$700$		0			0
$701$	−1.84792e11			−0.765262			−0.382631	−	0.923901i	$-0.624982\pi$
$701$	−1.84792e11			−0.765262			−0.382631	+	0.923901i	$0.624982\pi$
$702$		0			0
$703$	2.66167e11	−	2.66167e11i	1.08976	−	1.08976i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.53874e11	+	2.53874e11i	1.01611	+	1.01611i
$708$		0			0
$709$			1.17510e11i			0.465039i	0.972592	+	0.232519i	$0.0746969\pi$
$709$			1.17510e11i			0.465039i	−0.972592	+	0.232519i	$0.925303\pi$
$710$		0			0
$711$	7.81312e10			0.305736
$712$		0			0
$713$	−2.62146e11	+	2.62146e11i	−1.01434	+	1.01434i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	7.01242e10	+	7.01242e10i	0.265333	+	0.265333i
$718$		0			0
$719$		−	4.26075e11i		−	1.59430i	−0.603780	−	0.797151i	$-0.706340\pi$
$719$		−	4.26075e11i		−	1.59430i	0.603780	−	0.797151i	$-0.293660\pi$
$720$		0			0
$721$	2.49638e11			0.923783
$722$		0			0
$723$	1.56137e11	−	1.56137e11i	0.571417	−	0.571417i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	1.92262e11	+	1.92262e11i	0.688265	+	0.688265i	0.961848	−	0.273583i	$-0.0882088\pi$
$727$	1.92262e11	+	1.92262e11i	0.688265	+	0.688265i	−0.273583	+	0.961848i	$0.588209\pi$
$728$		0			0
$729$			1.04604e10i			0.0370370i
$730$		0			0
$731$	−6.43539e11			−2.25375
$732$		0			0
$733$	−1.99778e11	+	1.99778e11i	−0.692040	+	0.692040i	−0.962680	−	0.270641i	$-0.912764\pi$
$733$	−1.99778e11	+	1.99778e11i	−0.692040	+	0.692040i	0.270641	+	0.962680i	$0.412764\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.89087e10	−	6.89087e10i	−0.233563	−	0.233563i
$738$		0			0
$739$		−	3.89578e11i		−	1.30622i	−0.757263	−	0.653110i	$-0.773464\pi$
$739$		−	3.89578e11i		−	1.30622i	0.757263	−	0.653110i	$-0.226536\pi$
$740$		0			0
$741$	−1.82323e11			−0.604738
$742$		0			0
$743$	−2.48047e11	+	2.48047e11i	−0.813915	+	0.813915i	−0.985218	−	0.171303i	$-0.945202\pi$
$743$	−2.48047e11	+	2.48047e11i	−0.813915	+	0.813915i	0.171303	+	0.985218i	$0.445202\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.39240e10	−	4.39240e10i	−0.141065	−	0.141065i
$748$		0			0
$749$			2.89022e11i			0.918340i
$750$		0			0
$751$	1.18926e11			0.373867			0.186934	−	0.982373i	$-0.440145\pi$
$751$	1.18926e11			0.373867			0.186934	+	0.982373i	$0.440145\pi$
$752$		0			0
$753$	−1.85287e11	+	1.85287e11i	−0.576321	+	0.576321i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−4.27857e11	−	4.27857e11i	−1.30291	−	1.30291i	−0.926420	−	0.376492i	$-0.877130\pi$
$757$	−4.27857e11	−	4.27857e11i	−1.30291	−	1.30291i	−0.376492	−	0.926420i	$-0.622870\pi$
$758$		0			0
$759$			5.94025e10i			0.178994i
$760$		0			0
$761$	−2.22157e11			−0.662402			−0.331201	−	0.943560i	$-0.607454\pi$
$761$	−2.22157e11			−0.662402			−0.331201	+	0.943560i	$0.607454\pi$
$762$		0			0
$763$	1.91782e11	−	1.91782e11i	0.565862	−	0.565862i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.42719e9	+	3.42719e9i	0.00990277	+	0.00990277i
$768$		0			0
$769$		−	1.34651e11i		−	0.385039i	−0.981293	−	0.192519i	$-0.938334\pi$
$769$		−	1.34651e11i		−	0.385039i	0.981293	−	0.192519i	$-0.0616658\pi$
$770$		0			0
$771$	1.53847e11			0.435382
$772$		0			0
$773$	3.72163e11	−	3.72163e11i	1.04235	−	1.04235i	0.0432912	−	0.999062i	$-0.486216\pi$
$773$	3.72163e11	−	3.72163e11i	1.04235	−	1.04235i	0.999062	−	0.0432912i	$-0.0137843\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.15194e11	+	3.15194e11i	0.864758	+	0.864758i
$778$		0			0
$779$		−	2.61671e11i		−	0.710569i
$780$		0			0
$781$	2.51622e10			0.0676309
$782$		0			0
$783$	7.87958e10	−	7.87958e10i	0.209631	−	0.209631i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−1.61167e11	−	1.61167e11i	−0.420124	−	0.420124i	0.465122	−	0.885246i	$-0.346010\pi$
$787$	−1.61167e11	−	1.61167e11i	−0.420124	−	0.420124i	−0.885246	+	0.465122i	$0.846010\pi$
$788$		0			0
$789$			3.29118e11i			0.849265i
$790$		0			0
$791$	1.99777e11			0.510317
$792$		0			0
$793$	−1.71539e11	+	1.71539e11i	−0.433781	+	0.433781i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.29355e11	−	1.29355e11i	−0.320590	−	0.320590i	0.528404	−	0.848993i	$-0.322791\pi$
$797$	−1.29355e11	−	1.29355e11i	−0.320590	−	0.320590i	−0.848993	+	0.528404i	$0.822791\pi$
$798$		0			0
$799$			5.43301e11i			1.33307i
$800$		0			0
$801$	−1.28596e11			−0.312390
$802$		0			0
$803$	−1.71272e10	+	1.71272e10i	−0.0411931	+	0.0411931i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.03876e11	+	1.03876e11i	0.244918	+	0.244918i
$808$		0			0
$809$			4.30352e11i			1.00468i	0.864669	+	0.502342i	$0.167528\pi$
$809$			4.30352e11i			1.00468i	−0.864669	+	0.502342i	$0.832472\pi$
$810$		0			0
$811$	−1.07973e11			−0.249593			−0.124797	−	0.992182i	$-0.539828\pi$
$811$	−1.07973e11			−0.249593			−0.124797	+	0.992182i	$0.539828\pi$
$812$		0			0
$813$	2.79704e11	−	2.79704e11i	0.640232	−	0.640232i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.54713e11	+	3.54713e11i	0.796139	+	0.796139i
$818$		0			0
$819$		−	2.15906e11i		−	0.479877i
$820$		0			0
$821$	6.70163e11			1.47505			0.737526	−	0.675318i	$-0.235994\pi$
$821$	6.70163e11			1.47505			0.737526	+	0.675318i	$0.235994\pi$
$822$		0			0
$823$	1.59834e11	−	1.59834e11i	0.348394	−	0.348394i	−0.511117	−	0.859511i	$-0.670768\pi$
$823$	1.59834e11	−	1.59834e11i	0.348394	−	0.348394i	0.859511	+	0.511117i	$0.170768\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.23113e11	−	5.23113e11i	−1.11834	−	1.11834i	−0.991985	−	0.126354i	$-0.959673\pi$
$827$	−5.23113e11	−	5.23113e11i	−1.11834	−	1.11834i	−0.126354	−	0.991985i	$-0.540327\pi$
$828$		0			0
$829$		−	1.84303e11i		−	0.390225i	−0.980781	−	0.195113i	$-0.937493\pi$
$829$		−	1.84303e11i		−	0.390225i	0.980781	−	0.195113i	$-0.0625072\pi$
$830$		0			0
$831$	1.16541e11			0.244385
$832$		0			0
$833$	−1.72756e11	+	1.72756e11i	−0.358800	+	0.358800i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.81162e10	−	6.81162e10i	−0.138787	−	0.138787i
$838$		0			0
$839$			3.96833e10i			0.0800866i	0.999198	+	0.0400433i	$0.0127496\pi$
$839$			3.96833e10i			0.0800866i	−0.999198	+	0.0400433i	$0.987250\pi$
$840$		0			0
$841$	−6.86860e11			−1.37304
$842$		0			0
$843$	−1.69100e11	+	1.69100e11i	−0.334838	+	0.334838i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	3.95542e11	+	3.95542e11i	0.768527	+	0.768527i
$848$		0			0
$849$			3.67968e11i			0.708237i
$850$		0			0
$851$	1.36785e12			2.60808
$852$		0			0
$853$	3.31102e11	−	3.31102e11i	0.625410	−	0.625410i	−0.321499	−	0.946910i	$-0.604187\pi$
$853$	3.31102e11	−	3.31102e11i	0.625410	−	0.625410i	0.946910	+	0.321499i	$0.104187\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.25719e10	+	7.25719e10i	0.134538	+	0.134538i	0.771169	−	0.636631i	$-0.219672\pi$
$857$	7.25719e10	+	7.25719e10i	0.134538	+	0.134538i	−0.636631	+	0.771169i	$0.719672\pi$
$858$		0			0
$859$			5.24861e11i			0.963989i	0.876174	+	0.481994i	$0.160087\pi$
$859$			5.24861e11i			0.963989i	−0.876174	+	0.481994i	$0.839913\pi$
$860$		0			0
$861$	3.09871e11			0.563856
$862$		0			0
$863$	5.46528e11	−	5.46528e11i	0.985301	−	0.985301i	−0.0145925	−	0.999894i	$-0.504645\pi$
$863$	5.46528e11	−	5.46528e11i	0.985301	−	0.985301i	0.999894	+	0.0145925i	$0.00464511\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.07832e11	−	4.07832e11i	−0.721781	−	0.721781i
$868$		0			0
$869$			1.15290e11i			0.202167i
$870$		0			0
$871$	1.08691e12			1.88853
$872$		0			0
$873$	−1.46863e10	+	1.46863e10i	−0.0252846	+	0.0252846i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.19835e11	+	6.19835e11i	1.04780	+	1.04780i	0.998799	+	0.0489992i	$0.0156032\pi$
$877$	6.19835e11	+	6.19835e11i	1.04780	+	1.04780i	0.0489992	+	0.998799i	$0.484397\pi$
$878$		0			0
$879$		−	4.76903e11i		−	0.798867i
$880$		0			0
$881$	2.88385e10			0.0478707			0.0239353	−	0.999714i	$-0.492380\pi$
$881$	2.88385e10			0.0478707			0.0239353	+	0.999714i	$0.492380\pi$
$882$		0			0
$883$	2.79389e11	−	2.79389e11i	0.459585	−	0.459585i	−0.438934	−	0.898519i	$-0.644644\pi$
$883$	2.79389e11	−	2.79389e11i	0.459585	−	0.459585i	0.898519	+	0.438934i	$0.144644\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.35648e11	+	1.35648e11i	0.219139	+	0.219139i	0.808136	−	0.588996i	$-0.200477\pi$
$887$	1.35648e11	+	1.35648e11i	0.219139	+	0.219139i	−0.588996	+	0.808136i	$0.700477\pi$
$888$		0			0
$889$			1.02843e12i			1.64653i
$890$		0			0
$891$	−1.54352e10			−0.0244907
$892$		0			0
$893$	2.99462e11	−	2.99462e11i	0.470909	−	0.470909i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−4.68486e11	−	4.68486e11i	−0.723647	−	0.723647i
$898$		0			0
$899$			1.02621e12i			1.57108i
$900$		0			0
$901$	−2.83542e11			−0.430247
$902$		0			0
$903$	−4.20051e11	+	4.20051e11i	−0.631758	+	0.631758i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−3.00645e11	−	3.00645e11i	−0.444248	−	0.444248i	0.449189	−	0.893437i	$-0.351713\pi$
$907$	−3.00645e11	−	3.00645e11i	−0.444248	−	0.444248i	−0.893437	+	0.449189i	$0.851713\pi$
$908$		0			0
$909$			2.86277e11i			0.419306i
$910$		0			0
$911$	1.08131e12			1.56992			0.784959	−	0.619548i	$-0.212684\pi$
$911$	1.08131e12			1.56992			0.784959	+	0.619548i	$0.212684\pi$
$912$		0			0
$913$	6.48137e10	−	6.48137e10i	0.0932789	−	0.0932789i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.72008e11	+	5.72008e11i	0.808956	+	0.808956i
$918$		0			0
$919$		−	1.10893e12i		−	1.55468i	−0.629081	−	0.777340i	$-0.716569\pi$
$919$		−	1.10893e12i		−	1.55468i	0.629081	−	0.777340i	$-0.283431\pi$
$920$		0			0
$921$	1.72455e11			0.239683
$922$		0			0
$923$	−1.98445e11	+	1.98445e11i	−0.273422	+	0.273422i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.40750e11	+	1.40750e11i	0.190603	+	0.190603i
$928$		0			0
$929$			1.09753e11i			0.147352i	0.997282	+	0.0736759i	$0.0234730\pi$
$929$			1.09753e11i			0.147352i	−0.997282	+	0.0736759i	$0.976527\pi$
$930$		0			0
$931$	1.90443e11			0.253493
$932$		0			0
$933$	4.04426e11	−	4.04426e11i	0.533719	−	0.533719i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	4.51603e11	+	4.51603e11i	0.585866	+	0.585866i	0.936509	−	0.350643i	$-0.114037\pi$
$937$	4.51603e11	+	4.51603e11i	0.585866	+	0.585866i	−0.350643	+	0.936509i	$0.614037\pi$
$938$		0			0
$939$		−	5.52954e9i		−	0.00711257i
$940$		0			0
$941$	−1.07532e12			−1.37144			−0.685721	−	0.727864i	$-0.740513\pi$
$941$	−1.07532e12			−1.37144			−0.685721	+	0.727864i	$0.740513\pi$
$942$		0			0
$943$	6.72375e11	−	6.72375e11i	0.850286	−	0.850286i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.28322e11	+	6.28322e11i	0.781236	+	0.781236i	0.980039	−	0.198803i	$-0.0637055\pi$
$947$	6.28322e11	+	6.28322e11i	0.781236	+	0.781236i	−0.198803	+	0.980039i	$0.563705\pi$
$948$		0			0
$949$		−	2.70152e11i		−	0.333076i
$950$		0			0
$951$	5.23922e11			0.640538
$952$		0			0
$953$	7.12937e11	−	7.12937e11i	0.864330	−	0.864330i	−0.127507	−	0.991838i	$-0.540698\pi$
$953$	7.12937e11	−	7.12937e11i	0.864330	−	0.864330i	0.991838	+	0.127507i	$0.0406976\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.16270e11	+	1.16270e11i	0.138618	+	0.138618i
$958$		0			0
$959$		−	1.46110e12i		−	1.72745i
$960$		0			0
$961$	3.42332e10			0.0401379
$962$		0			0
$963$	−1.62955e11	+	1.62955e11i	−0.189480	+	0.189480i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	2.07482e11	+	2.07482e11i	0.237287	+	0.237287i	0.815726	−	0.578439i	$-0.196338\pi$
$967$	2.07482e11	+	2.07482e11i	0.237287	+	0.237287i	−0.578439	+	0.815726i	$0.696338\pi$
$968$		0			0
$969$			7.03879e11i			0.798368i
$970$		0			0
$971$	−2.98570e11			−0.335868			−0.167934	−	0.985798i	$-0.553710\pi$
$971$	−2.98570e11			−0.335868			−0.167934	+	0.985798i	$0.553710\pi$
$972$		0			0
$973$	−1.06432e12	+	1.06432e12i	−1.18746	+	1.18746i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.83239e11	−	3.83239e11i	−0.420621	−	0.420621i	0.464796	−	0.885418i	$-0.346128\pi$
$977$	−3.83239e11	−	3.83239e11i	−0.420621	−	0.420621i	−0.885418	+	0.464796i	$0.846128\pi$
$978$		0			0
$979$		−	1.89755e11i		−	0.206567i
$980$		0			0
$981$	2.16260e11			0.233507
$982$		0			0
$983$	−9.11487e11	+	9.11487e11i	−0.976195	+	0.976195i	−0.999723	−	0.0235283i	$-0.992510\pi$
$983$	−9.11487e11	+	9.11487e11i	−0.976195	+	0.976195i	0.0235283	+	0.999723i	$0.492510\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.54623e11	+	3.54623e11i	0.373679	+	0.373679i
$988$		0			0
$989$			1.82290e12i			1.90536i
$990$		0			0
$991$	−3.20901e11			−0.332718			−0.166359	−	0.986065i	$-0.553201\pi$
$991$	−3.20901e11			−0.332718			−0.166359	+	0.986065i	$0.553201\pi$
$992$		0			0
$993$	−3.71678e11	+	3.71678e11i	−0.382270	+	0.382270i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.54776e11	+	2.54776e11i	0.257856	+	0.257856i	0.824182	−	0.566325i	$-0.191635\pi$
$997$	2.54776e11	+	2.54776e11i	0.257856	+	0.257856i	−0.566325	+	0.824182i	$0.691635\pi$
$998$		0			0
$999$			3.55424e11i			0.356849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.9.k.e.157.2		16
5.2	odd	4		60.9.k.a.13.5	✓	16
5.3	odd	4	inner	300.9.k.e.193.2		16
5.4	even	2		60.9.k.a.37.5	yes	16
15.2	even	4		180.9.l.c.73.8		16
15.14	odd	2		180.9.l.c.37.8		16
20.7	even	4		240.9.bg.c.193.1		16
20.19	odd	2		240.9.bg.c.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.5	✓	16	5.2	odd	4
60.9.k.a.37.5	yes	16	5.4	even	2
180.9.l.c.37.8		16	15.14	odd	2
180.9.l.c.73.8		16	15.2	even	4
240.9.bg.c.97.1		16	20.19	odd	2
240.9.bg.c.193.1		16	20.7	even	4
300.9.k.e.157.2		16	1.1	even	1	trivial
300.9.k.e.193.2		16	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-33.0681 + 33.0681i) q^{3} +(-1939.46 - 1939.46i) q^{7} -2187.00i q^{9} +O(q^{10})\)	\(q+(-33.0681 + 33.0681i) q^{3} +(-1939.46 - 1939.46i) q^{7} -2187.00i q^{9} +3227.11 q^{11} +(-25451.0 + 25451.0i) q^{13} +(98257.0 + 98257.0i) q^{17} -108317. i q^{19} +128269. q^{21} +(278325. - 278325. i) q^{23} +(72320.0 + 72320.0i) q^{27} -1.08954e6i q^{29} -941873. q^{31} +(-106714. + 106714. i) q^{33} +(2.45730e6 + 2.45730e6i) q^{37} -1.68324e6i q^{39} +2.41580e6 q^{41} +(-3.27478e6 + 3.27478e6i) q^{43} +(2.76469e6 + 2.76469e6i) q^{47} +1.75821e6i q^{49} -6.49834e6 q^{51} +(-1.44286e6 + 1.44286e6i) q^{53} +(3.58183e6 + 3.58183e6i) q^{57} -134658. i q^{59} +6.73996e6 q^{61} +(-4.24160e6 + 4.24160e6i) q^{63} +(-2.13530e7 - 2.13530e7i) q^{67} +1.84073e7i q^{69} +7.79714e6 q^{71} +(-5.30729e6 + 5.30729e6i) q^{73} +(-6.25885e6 - 6.25885e6i) q^{77} +3.57253e7i q^{79} -4.78297e6 q^{81} +(2.00841e7 - 2.00841e7i) q^{83} +(3.60292e7 + 3.60292e7i) q^{87} -5.88002e7i q^{89} +9.87225e7 q^{91} +(3.11460e7 - 3.11460e7i) q^{93} +(-6.71527e6 - 6.71527e6i) q^{97} -7.05769e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4220 q^{7}+O(q^{10}) \) 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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