LMFDB - Embedded newform 300.9.k.e.193.2

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			193.2
Root			$-1675.46 - 1.00000i$ of defining polynomial
Character	$\chi$	$=$	300.193
Dual form			300.9.k.e.157.2

$q$-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 $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

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

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
$7$	−1939.46	+	1939.46i	−0.807772	+	0.807772i	−0.984296	−	0.176525i	$-0.943514\pi$
$7$	−1939.46	+	1939.46i	−0.807772	+	0.807772i	0.176525	+	0.984296i	$0.443514\pi$
$8$		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	0.103516	−	0.994628i	$-0.466991\pi$
$13$	−25451.0	−	25451.0i	−0.891112	−	0.891112i	−0.994628	+	0.103516i	$0.966991\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	98257.0	−	98257.0i	1.17643	−	1.17643i	0.195788	−	0.980646i	$-0.437274\pi$
$17$	98257.0	−	98257.0i	1.17643	−	1.17643i	0.980646	−	0.195788i	$-0.0627264\pi$
$18$		0			0
$19$			108317.i			0.831153i	0.909558	+	0.415577i	$0.136420\pi$
$19$			108317.i			0.831153i	−0.909558	+	0.415577i	$0.863580\pi$
$20$		0			0
$21$	128269.			0.659543
$22$		0			0
$23$	278325.	+	278325.i	0.994581	+	0.994581i	0.999985	−	0.00540448i	$-0.00172031\pi$
$23$	278325.	+	278325.i	0.994581	+	0.994581i	−0.00540448	+	0.999985i	$0.501720\pi$
$24$		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	$0.279861\pi$
$29$			1.08954e6i			1.54047i	−0.637761	+	0.770234i	$0.720139\pi$
$30$		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	0.390578	−	0.920570i	$-0.372275\pi$
$37$	2.45730e6	−	2.45730e6i	1.31115	−	1.31115i	0.920570	−	0.390578i	$-0.127725\pi$
$38$		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	0.0412749	−	0.999148i	$-0.486858\pi$
$43$	−3.27478e6	−	3.27478e6i	−0.957873	−	0.957873i	−0.999148	+	0.0412749i	$0.986858\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.76469e6	−	2.76469e6i	0.566573	−	0.566573i	−0.364594	−	0.931167i	$-0.618792\pi$
$47$	2.76469e6	−	2.76469e6i	0.566573	−	0.566573i	0.931167	+	0.364594i	$0.118792\pi$
$48$		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	0.609741	−	0.792601i	$-0.291274\pi$
$53$	−1.44286e6	−	1.44286e6i	−0.182861	−	0.182861i	−0.792601	+	0.609741i	$0.791274\pi$
$54$		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	$0.00176867\pi$
$59$			134658.i			0.0111128i	−0.999985	+	0.00555641i	$0.998231\pi$
$60$		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	−0.0615409	+	0.998105i	$0.519601\pi$
$67$	−2.13530e7	+	2.13530e7i	−1.05965	+	1.05965i	−0.998105	+	0.0615409i	$0.980399\pi$
$68$		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	0.607461	−	0.794349i	$-0.292188\pi$
$73$	−5.30729e6	−	5.30729e6i	−0.186888	−	0.186888i	−0.794349	+	0.607461i	$0.792188\pi$
$74$		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	$-0.848350\pi$
$79$		−	3.57253e7i		−	0.917208i	0.888641	−	0.458604i	$-0.151650\pi$
$80$		0			0
$81$	−4.78297e6			−0.111111
$82$		0			0
$83$	2.00841e7	+	2.00841e7i	0.423195	+	0.423195i	0.886302	−	0.463107i	$-0.153266\pi$
$83$	2.00841e7	+	2.00841e7i	0.423195	+	0.423195i	−0.463107	+	0.886302i	$0.653266\pi$
$84$		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	$0.155236\pi$
$89$			5.88002e7i			0.937170i	−0.883418	+	0.468585i	$0.844764\pi$
$90$		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	−0.744016	−	0.668162i	$-0.767081\pi$
$97$	−6.71527e6	+	6.71527e6i	−0.0758537	+	0.0758537i	0.668162	+	0.744016i	$0.267081\pi$
$98$		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	0.360824	−	0.932634i	$-0.382495\pi$
$103$	−6.43577e7	−	6.43577e7i	−0.571809	−	0.571809i	−0.932634	+	0.360824i	$0.882495\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.45109e7	+	7.45109e7i	−0.568440	+	0.568440i	−0.931691	−	0.363251i	$-0.881667\pi$
$107$	−7.45109e7	+	7.45109e7i	−0.568440	+	0.568440i	0.363251	+	0.931691i	$0.381667\pi$
$108$		0			0
$109$		−	9.88845e7i		−	0.700522i	−0.936652	−	0.350261i	$-0.886093\pi$
$109$		−	9.88845e7i		−	0.700522i	0.936652	−	0.350261i	$-0.113907\pi$
$110$		0			0
$111$	−1.62517e8			−1.07055
$112$		0			0
$113$	−5.15033e7	−	5.15033e7i	−0.315879	−	0.315879i	0.531303	−	0.847182i	$-0.321703\pi$
$113$	−5.15033e7	−	5.15033e7i	−0.315879	−	0.315879i	−0.847182	+	0.531303i	$0.821703\pi$
$114$		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	−0.0193650	+	0.999812i	$0.506164\pi$
$127$	−2.65134e8	+	2.65134e8i	−1.01918	+	1.01918i	−0.999812	+	0.0193650i	$0.993836\pi$
$128$		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	0.0718560	−	0.997415i	$-0.477108\pi$
$137$	3.76678e8	−	3.76678e8i	1.06927	−	1.06927i	0.997415	−	0.0718560i	$-0.0228922\pi$
$138$		0			0
$139$			5.48769e8i			1.47004i	0.678043	+	0.735022i	$0.262828\pi$
$139$			5.48769e8i			1.47004i	−0.678043	+	0.735022i	$0.737172\pi$
$140$		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	$-0.762069\pi$
$149$		−	6.70120e8i		−	1.35959i	0.733403	−	0.679794i	$-0.237931\pi$
$150$		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	−0.321295	+	0.946979i	$0.604118\pi$
$157$	−7.70569e8	+	7.70569e8i	−1.26827	+	1.26827i	−0.946979	+	0.321295i	$0.895882\pi$
$158$		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	0.535631	−	0.844452i	$-0.320074\pi$
$163$	−2.18000e8	−	2.18000e8i	−0.308821	−	0.308821i	−0.844452	+	0.535631i	$0.820074\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.75803e8	+	3.75803e8i	−0.483164	+	0.483164i	−0.906141	−	0.422977i	$-0.860985\pi$
$167$	−3.75803e8	+	3.75803e8i	−0.483164	+	0.483164i	0.422977	+	0.906141i	$0.360985\pi$
$168$		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	0.600891	−	0.799331i	$-0.294812\pi$
$173$	−1.77751e8	−	1.77751e8i	−0.198439	−	0.198439i	−0.799331	+	0.600891i	$0.794812\pi$
$174$		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	$0.0728054\pi$
$179$			4.65545e8i			0.453471i	−0.973956	+	0.226736i	$0.927195\pi$
$180$		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	0.832542	−	0.553962i	$-0.186885\pi$
$193$	3.86526e8	+	3.86526e8i	0.278580	+	0.278580i	−0.553962	+	0.832542i	$0.686885\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.23809e9	+	1.23809e9i	−0.822029	+	0.822029i	−0.986399	−	0.164370i	$-0.947441\pi$
$197$	−1.23809e9	+	1.23809e9i	−0.822029	+	0.822029i	0.164370	+	0.986399i	$0.447441\pi$
$198$		0			0
$199$		−	7.12668e8i		−	0.454438i	−0.973844	−	0.227219i	$-0.927037\pi$
$199$		−	7.12668e8i		−	0.454438i	0.973844	−	0.227219i	$-0.0729634\pi$
$200$		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	0.0331881	−	0.999449i	$-0.489434\pi$
$223$	−2.38954e9	−	2.38954e9i	−0.966261	−	0.966261i	−0.999449	+	0.0331881i	$0.989434\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.06931e8	−	5.06931e8i	0.190917	−	0.190917i	−0.605175	−	0.796092i	$-0.706897\pi$
$227$	5.06931e8	−	5.06931e8i	0.190917	−	0.190917i	0.796092	+	0.605175i	$0.206897\pi$
$228$		0			0
$229$			2.80021e9i			1.01824i	0.860696	+	0.509119i	$0.170029\pi$
$229$			2.80021e9i			1.01824i	−0.860696	+	0.509119i	$0.829971\pi$
$230$		0			0
$231$	4.13937e8			0.145374
$232$		0			0
$233$	−2.82554e9	−	2.82554e9i	−0.958689	−	0.958689i	0.0404906	−	0.999180i	$-0.487108\pi$
$233$	−2.82554e9	−	2.82554e9i	−0.958689	−	0.958689i	−0.999180	+	0.0404906i	$0.987108\pi$
$234$		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	$0.105353\pi$
$239$			2.12060e9i			0.649931i	−0.945726	+	0.324965i	$0.894647\pi$
$240$		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	−0.921533	−	0.388301i	$-0.873062\pi$
$257$	−2.32621e9	+	2.32621e9i	−0.533232	+	0.533232i	0.388301	+	0.921533i	$0.373062\pi$
$258$		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	0.999160	+	0.0409722i	$0.0130455\pi$
$263$	4.97636e9	+	4.97636e9i	1.04013	+	1.04013i	0.0409722	+	0.999160i	$0.486954\pi$
$264$		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	$0.0969741\pi$
$269$			3.14127e9i			0.599924i	−0.953951	+	0.299962i	$0.903026\pi$
$270$		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	−0.840743	−	0.541434i	$-0.817882\pi$
$277$	−1.76213e9	+	1.76213e9i	−0.299309	+	0.299309i	0.541434	+	0.840743i	$0.317882\pi$
$278$		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	0.992185	−	0.124775i	$-0.0398209\pi$
$283$	5.56378e9	+	5.56378e9i	0.867410	+	0.867410i	−0.124775	+	0.992185i	$0.539821\pi$
$284$		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	0.0213631	−	0.999772i	$-0.493199\pi$
$293$	−7.21092e9	−	7.21092e9i	−0.978409	−	0.978409i	−0.999772	+	0.0213631i	$0.993199\pi$
$294$		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	−0.838481	−	0.544930i	$-0.816556\pi$
$307$	−2.60758e9	+	2.60758e9i	−0.293551	+	0.293551i	0.544930	+	0.838481i	$0.316556\pi$
$308$		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	0.702738	−	0.711449i	$-0.251961\pi$
$313$	−8.36083e7	−	8.36083e7i	−0.00871108	−	0.00871108i	−0.711449	+	0.702738i	$0.751961\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.92187e9	+	7.92187e9i	−0.784496	+	0.784496i	−0.980586	−	0.196090i	$-0.937175\pi$
$317$	−7.92187e9	+	7.92187e9i	−0.784496	+	0.784496i	0.196090	+	0.980586i	$0.437175\pi$
$318$		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	−0.757665	−	0.652644i	$-0.773660\pi$
$337$	−1.35456e9	+	1.35456e9i	−0.105021	+	0.105021i	0.652644	+	0.757665i	$0.273660\pi$
$338$		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	−0.244518	−	0.969645i	$-0.578630\pi$
$347$	1.05131e10	−	1.05131e10i	0.725127	−	0.725127i	0.969645	+	0.244518i	$0.0786298\pi$
$348$		0			0
$349$		−	2.70963e10i		−	1.82645i	−0.407455	−	0.913225i	$-0.633584\pi$
$349$		−	2.70963e10i		−	1.82645i	0.407455	−	0.913225i	$-0.366416\pi$
$350$		0			0
$351$	−3.68124e9			−0.242530
$352$		0			0
$353$	−1.50350e10	−	1.50350e10i	−0.968286	−	0.968286i	0.0312263	−	0.999512i	$-0.490059\pi$
$353$	−1.50350e10	−	1.50350e10i	−0.968286	−	0.968286i	−0.999512	+	0.0312263i	$0.990059\pi$
$354$		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	$-0.794580\pi$
$359$		−	1.99814e10i		−	1.20295i	0.798892	−	0.601475i	$-0.205420\pi$
$360$		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	−0.644464	−	0.764635i	$-0.722919\pi$
$367$	2.18005e9	−	2.18005e9i	0.120172	−	0.120172i	0.764635	+	0.644464i	$0.222919\pi$
$368$		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	0.986522	−	0.163629i	$-0.0523201\pi$
$373$	1.59286e10	+	1.59286e10i	0.822892	+	0.822892i	−0.163629	+	0.986522i	$0.552320\pi$
$374$		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	$0.283828\pi$
$379$			3.21096e10i			1.55624i	−0.628113	+	0.778122i	$0.716172\pi$
$380$		0			0
$381$	1.75349e10			0.832155
$382$		0			0
$383$	−8.82401e9	−	8.82401e9i	−0.410082	−	0.410082i	0.471685	−	0.881767i	$-0.343646\pi$
$383$	−8.82401e9	−	8.82401e9i	−0.410082	−	0.410082i	−0.881767	+	0.471685i	$0.843646\pi$
$384$		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	$-0.834907\pi$
$389$		−	2.27017e10i		−	0.991427i	0.868486	−	0.495713i	$-0.165093\pi$
$390$		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	−0.452816	−	0.891604i	$-0.649581\pi$
$397$	1.08997e10	−	1.08997e10i	0.438787	−	0.438787i	0.891604	+	0.452816i	$0.149581\pi$
$398$		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	$0.130039\pi$
$409$			2.22330e10i			0.794521i	−0.917706	+	0.397261i	$0.869961\pi$
$410$		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	$-0.874749\pi$
$419$		−	2.36348e10i		−	0.766825i	0.923577	−	0.383412i	$-0.125251\pi$
$420$		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	0.794839	−	0.606821i	$-0.207555\pi$
$433$	6.60923e9	+	6.60923e9i	0.188018	+	0.188018i	−0.606821	+	0.794839i	$0.707555\pi$
$434$		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	$-0.804355\pi$
$439$		−	4.28360e10i		−	1.15332i	0.816983	−	0.576661i	$-0.195645\pi$
$440$		0			0
$441$	3.84519e9			0.101663
$442$		0			0
$443$	9.02375e9	+	9.02375e9i	0.234300	+	0.234300i	0.814485	−	0.580185i	$-0.197020\pi$
$443$	9.02375e9	+	9.02375e9i	0.234300	+	0.234300i	−0.580185	+	0.814485i	$0.697020\pi$
$444$		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	$-0.680774\pi$
$449$		−	6.85258e10i		−	1.68604i	0.537879	−	0.843022i	$-0.319226\pi$
$450$		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	−0.656909	−	0.753970i	$-0.728136\pi$
$457$	4.23359e9	−	4.23359e9i	0.0970608	−	0.0970608i	0.753970	+	0.656909i	$0.228136\pi$
$458$		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	0.226719	−	0.973960i	$-0.427200\pi$
$463$	−3.43388e10	−	3.43388e10i	−0.747241	−	0.747241i	−0.973960	+	0.226719i	$0.927200\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.06656e10	+	5.06656e10i	−1.06524	+	1.06524i	−0.0675173	+	0.997718i	$0.521508\pi$
$467$	−5.06656e10	+	5.06656e10i	−1.06524	+	1.06524i	−0.997718	+	0.0675173i	$0.978492\pi$
$468$		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	$0.0279465\pi$
$479$			9.23191e9i			0.175368i	−0.996148	+	0.0876838i	$0.972053\pi$
$480$		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	−0.0698841	−	0.997555i	$-0.522263\pi$
$487$	5.21807e10	−	5.21807e10i	0.927671	−	0.927671i	0.997555	+	0.0698841i	$0.0222629\pi$
$488$		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	$0.328458\pi$
$499$			1.06428e11i			1.71653i	−0.513204	+	0.858266i	$0.671542\pi$
$500$		0			0
$501$	2.48542e10			0.394502
$502$		0			0
$503$	−6.06663e10	−	6.06663e10i	−0.947710	−	0.947710i	0.0509895	−	0.998699i	$-0.483763\pi$
$503$	−6.06663e10	−	6.06663e10i	−0.947710	−	0.947710i	−0.998699	+	0.0509895i	$0.983763\pi$
$504$		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	$0.0403695\pi$
$509$			1.69801e10i			0.252969i	−0.991969	+	0.126485i	$0.959631\pi$
$510$		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	0.466227	−	0.884665i	$-0.345613\pi$
$523$	−3.13068e10	−	3.13068e10i	−0.418439	−	0.418439i	−0.884665	+	0.466227i	$0.845613\pi$
$524$		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	−0.0310968	−	0.999516i	$-0.509900\pi$
$547$	8.66988e10	−	8.66988e10i	0.968420	−	0.968420i	0.999516	+	0.0310968i	$0.00990002\pi$
$548$		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	−0.715693	−	0.698415i	$-0.753889\pi$
$557$	−1.66310e9	+	1.66310e9i	−0.0172781	+	0.0172781i	0.698415	+	0.715693i	$0.253889\pi$
$558$		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	0.259375	−	0.965777i	$-0.416484\pi$
$563$	−7.09718e10	−	7.09718e10i	−0.706402	−	0.706402i	−0.965777	+	0.259375i	$0.916484\pi$
$564$		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	$0.152020\pi$
$569$			9.63590e10i			0.919271i	−0.888108	+	0.459635i	$0.847980\pi$
$570$		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	−0.270258	−	0.962788i	$-0.587109\pi$
$577$	7.67613e10	−	7.67613e10i	0.692530	−	0.692530i	0.962788	+	0.270258i	$0.0871089\pi$
$578$		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	−0.986584	−	0.163252i	$-0.947802\pi$
$587$	−9.77524e10	+	9.77524e10i	−0.823332	+	0.823332i	0.163252	+	0.986584i	$0.447802\pi$
$588$		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	0.0965002	−	0.995333i	$-0.469235\pi$
$593$	−1.11147e11	−	1.11147e11i	−0.898833	−	0.898833i	−0.995333	+	0.0965002i	$0.969235\pi$
$594$		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	$-0.873772\pi$
$599$		−	9.94488e10i		−	0.772489i	0.922396	−	0.386245i	$-0.126228\pi$
$600$		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	−0.974085	−	0.226180i	$-0.927376\pi$
$607$	−1.01532e11	+	1.01532e11i	−0.747905	+	0.747905i	0.226180	+	0.974085i	$0.427376\pi$
$608$		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	0.335089	−	0.942187i	$-0.391234\pi$
$613$	−8.57237e10	−	8.57237e10i	−0.607098	−	0.607098i	−0.942187	+	0.335089i	$0.891234\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.24386e11	−	1.24386e11i	0.858286	−	0.858286i	−0.132850	−	0.991136i	$-0.542413\pi$
$617$	1.24386e11	−	1.24386e11i	0.858286	−	0.858286i	0.991136	+	0.132850i	$0.0424129\pi$
$618$		0			0
$619$			1.87700e11i			1.27850i	0.768998	+	0.639251i	$0.220755\pi$
$619$			1.87700e11i			1.27850i	−0.768998	+	0.639251i	$0.779245\pi$
$620$		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	0.734023	−	0.679125i	$-0.237640\pi$
$643$	9.38432e9	+	9.38432e9i	0.0548983	+	0.0548983i	−0.679125	+	0.734023i	$0.737640\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.97482e11	+	1.97482e11i	−1.12697	+	1.12697i	−0.136298	+	0.990668i	$0.543521\pi$
$647$	−1.97482e11	+	1.97482e11i	−1.12697	+	1.12697i	−0.990668	+	0.136298i	$0.956479\pi$
$648$		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	0.0332472	−	0.999447i	$-0.489415\pi$
$653$	−1.75679e11	−	1.75679e11i	−0.966200	−	0.966200i	−0.999447	+	0.0332472i	$0.989415\pi$
$654$		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	$-0.990953\pi$
$659$		−	1.07195e10i		−	0.0568374i	0.999596	−	0.0284187i	$-0.00904717\pi$
$660$		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	0.455808	−	0.890078i	$-0.349350\pi$
$673$	−8.90882e10	−	8.90882e10i	−0.434270	−	0.434270i	−0.890078	+	0.455808i	$0.849350\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.03143e11	+	1.03143e11i	−0.491003	+	0.491003i	−0.908622	−	0.417619i	$-0.862865\pi$
$677$	−1.03143e11	+	1.03143e11i	−0.491003	+	0.491003i	0.417619	+	0.908622i	$0.362865\pi$
$678$		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	0.948777	−	0.315946i	$-0.102322\pi$
$683$	1.37712e11	+	1.37712e11i	0.632831	+	0.632831i	−0.315946	+	0.948777i	$0.602322\pi$
$684$		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	$-0.925303\pi$
$709$		−	1.17510e11i		−	0.465039i	0.972592	−	0.232519i	$-0.0746969\pi$
$710$		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	$0.293660\pi$
$719$			4.26075e11i			1.59430i	−0.603780	+	0.797151i	$0.706340\pi$
$720$		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	−0.273583	−	0.961848i	$-0.588209\pi$
$727$	1.92262e11	−	1.92262e11i	0.688265	−	0.688265i	0.961848	+	0.273583i	$0.0882088\pi$
$728$		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	0.270641	−	0.962680i	$-0.412764\pi$
$733$	−1.99778e11	−	1.99778e11i	−0.692040	−	0.692040i	−0.962680	+	0.270641i	$0.912764\pi$
$734$		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	$0.226536\pi$
$739$			3.89578e11i			1.30622i	−0.757263	+	0.653110i	$0.773464\pi$
$740$		0			0
$741$	−1.82323e11			−0.604738
$742$		0			0
$743$	−2.48047e11	−	2.48047e11i	−0.813915	−	0.813915i	0.171303	−	0.985218i	$-0.445202\pi$
$743$	−2.48047e11	−	2.48047e11i	−0.813915	−	0.813915i	−0.985218	+	0.171303i	$0.945202\pi$
$744$		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	−0.376492	+	0.926420i	$0.622870\pi$
$757$	−4.27857e11	+	4.27857e11i	−1.30291	+	1.30291i	−0.926420	+	0.376492i	$0.877130\pi$
$758$		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	$0.0616658\pi$
$769$			1.34651e11i			0.385039i	−0.981293	+	0.192519i	$0.938334\pi$
$770$		0			0
$771$	1.53847e11			0.435382
$772$		0			0
$773$	3.72163e11	+	3.72163e11i	1.04235	+	1.04235i	0.999062	+	0.0432912i	$0.0137843\pi$
$773$	3.72163e11	+	3.72163e11i	1.04235	+	1.04235i	0.0432912	+	0.999062i	$0.486216\pi$
$774$		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	−0.885246	−	0.465122i	$-0.846010\pi$
$787$	−1.61167e11	+	1.61167e11i	−0.420124	+	0.420124i	0.465122	+	0.885246i	$0.346010\pi$
$788$		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	−0.848993	−	0.528404i	$-0.822791\pi$
$797$	−1.29355e11	+	1.29355e11i	−0.320590	+	0.320590i	0.528404	+	0.848993i	$0.322791\pi$
$798$		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	$-0.832472\pi$
$809$		−	4.30352e11i		−	1.00468i	0.864669	−	0.502342i	$-0.167528\pi$
$810$		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	0.859511	−	0.511117i	$-0.170768\pi$
$823$	1.59834e11	+	1.59834e11i	0.348394	+	0.348394i	−0.511117	+	0.859511i	$0.670768\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.23113e11	+	5.23113e11i	−1.11834	+	1.11834i	−0.126354	+	0.991985i	$0.540327\pi$
$827$	−5.23113e11	+	5.23113e11i	−1.11834	+	1.11834i	−0.991985	+	0.126354i	$0.959673\pi$
$828$		0			0
$829$			1.84303e11i			0.390225i	0.980781	+	0.195113i	$0.0625072\pi$
$829$			1.84303e11i			0.390225i	−0.980781	+	0.195113i	$0.937493\pi$
$830$		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	$-0.987250\pi$
$839$		−	3.96833e10i		−	0.0800866i	0.999198	−	0.0400433i	$-0.0127496\pi$
$840$		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	0.946910	−	0.321499i	$-0.104187\pi$
$853$	3.31102e11	+	3.31102e11i	0.625410	+	0.625410i	−0.321499	+	0.946910i	$0.604187\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.25719e10	−	7.25719e10i	0.134538	−	0.134538i	−0.636631	−	0.771169i	$-0.719672\pi$
$857$	7.25719e10	−	7.25719e10i	0.134538	−	0.134538i	0.771169	+	0.636631i	$0.219672\pi$
$858$		0			0
$859$		−	5.24861e11i		−	0.963989i	−0.876174	−	0.481994i	$-0.839913\pi$
$859$		−	5.24861e11i		−	0.963989i	0.876174	−	0.481994i	$-0.160087\pi$
$860$		0			0
$861$	3.09871e11			0.563856
$862$		0			0
$863$	5.46528e11	+	5.46528e11i	0.985301	+	0.985301i	0.999894	−	0.0145925i	$-0.00464511\pi$
$863$	5.46528e11	+	5.46528e11i	0.985301	+	0.985301i	−0.0145925	+	0.999894i	$0.504645\pi$
$864$		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	0.0489992	−	0.998799i	$-0.484397\pi$
$877$	6.19835e11	−	6.19835e11i	1.04780	−	1.04780i	0.998799	−	0.0489992i	$-0.0156032\pi$
$878$		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	0.898519	−	0.438934i	$-0.144644\pi$
$883$	2.79389e11	+	2.79389e11i	0.459585	+	0.459585i	−0.438934	+	0.898519i	$0.644644\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.35648e11	−	1.35648e11i	0.219139	−	0.219139i	−0.588996	−	0.808136i	$-0.700477\pi$
$887$	1.35648e11	−	1.35648e11i	0.219139	−	0.219139i	0.808136	+	0.588996i	$0.200477\pi$
$888$		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	−0.893437	−	0.449189i	$-0.851713\pi$
$907$	−3.00645e11	+	3.00645e11i	−0.444248	+	0.444248i	0.449189	+	0.893437i	$0.351713\pi$
$908$		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	$0.283431\pi$
$919$			1.10893e12i			1.55468i	−0.629081	+	0.777340i	$0.716569\pi$
$920$		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	$-0.976527\pi$
$929$		−	1.09753e11i		−	0.147352i	0.997282	−	0.0736759i	$-0.0234730\pi$
$930$		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	−0.350643	−	0.936509i	$-0.614037\pi$
$937$	4.51603e11	−	4.51603e11i	0.585866	−	0.585866i	0.936509	+	0.350643i	$0.114037\pi$
$938$		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	−0.198803	−	0.980039i	$-0.563705\pi$
$947$	6.28322e11	−	6.28322e11i	0.781236	−	0.781236i	0.980039	+	0.198803i	$0.0637055\pi$
$948$		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	0.991838	−	0.127507i	$-0.0406976\pi$
$953$	7.12937e11	+	7.12937e11i	0.864330	+	0.864330i	−0.127507	+	0.991838i	$0.540698\pi$
$954$		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	−0.578439	−	0.815726i	$-0.696338\pi$
$967$	2.07482e11	−	2.07482e11i	0.237287	−	0.237287i	0.815726	+	0.578439i	$0.196338\pi$
$968$		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	−0.885418	−	0.464796i	$-0.846128\pi$
$977$	−3.83239e11	+	3.83239e11i	−0.420621	+	0.420621i	0.464796	+	0.885418i	$0.346128\pi$
$978$		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	0.0235283	−	0.999723i	$-0.492510\pi$
$983$	−9.11487e11	−	9.11487e11i	−0.976195	−	0.976195i	−0.999723	+	0.0235283i	$0.992510\pi$
$984$		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	−0.566325	−	0.824182i	$-0.691635\pi$
$997$	2.54776e11	−	2.54776e11i	0.257856	−	0.257856i	0.824182	+	0.566325i	$0.191635\pi$
$998$		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.193.2		16
5.2	odd	4	inner	300.9.k.e.157.2		16
5.3	odd	4		60.9.k.a.37.5	yes	16
5.4	even	2		60.9.k.a.13.5	✓	16
15.8	even	4		180.9.l.c.37.8		16
15.14	odd	2		180.9.l.c.73.8		16
20.3	even	4		240.9.bg.c.97.1		16
20.19	odd	2		240.9.bg.c.193.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.9.k.a.13.5	✓	16	5.4	even	2
60.9.k.a.37.5	yes	16	5.3	odd	4
180.9.l.c.37.8		16	15.8	even	4
180.9.l.c.73.8		16	15.14	odd	2
240.9.bg.c.97.1		16	20.3	even	4
240.9.bg.c.193.1		16	20.19	odd	2
300.9.k.e.157.2		16	5.2	odd	4	inner
300.9.k.e.193.2		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)

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