LMFDB - Embedded newform 240.9.c.e.209.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,9,Mod(209,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.209"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	240.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,21928] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$97.7708664147$
Analytic rank:	$0$
Dimension:	$16$
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} + 11030 x^{14} + 49274731 x^{12} + 114127354194 x^{10} + 145952808215673 x^{8} + \cdots + 37\!\cdots\!00 $ x^16 + 11030x^14 + 49274731x^12 + 114127354194x^10 + 145952808215673x^8 + 102178334474381688x^6 + 37133934963356085616x^4 + 6178447219085671000280*x^2 + 379932896280343584768100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{44}\cdot 3^{20}\cdot 5^{10} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.11
Root			$-1.41421 + 26.0340i$ of defining polynomial
Character	$\chi$	$=$	240.209
Dual form			240.9.c.e.209.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(59.7326 - 54.7084i) q^{3} +(-556.269 + 284.937i) q^{5} +2732.68i q^{7} +(574.975 - 6535.76i) q^{9} +138.973i q^{11} -39979.9i q^{13} +(-17639.0 + 47452.7i) q^{15} -90959.5 q^{17} -23974.1 q^{19} +(149501. + 163230. i) q^{21} +435843. q^{23} +(228247. - 317004. i) q^{25} +(-323216. - 421854. i) q^{27} -631532. i q^{29} +603686. q^{31} +(7603.01 + 8301.24i) q^{33} +(-778644. - 1.52011e6i) q^{35} +3.25530e6i q^{37} +(-2.18724e6 - 2.38810e6i) q^{39} +2.45798e6i q^{41} +3.58077e6i q^{43} +(1.54244e6 + 3.79947e6i) q^{45} -1.43490e6 q^{47} -1.70276e6 q^{49} +(-5.43325e6 + 4.97625e6i) q^{51} -3.71194e6 q^{53} +(-39598.7 - 77306.6i) q^{55} +(-1.43203e6 + 1.31158e6i) q^{57} +4.19381e6i q^{59} -1.96341e7 q^{61} +(1.78602e7 + 1.57122e6i) q^{63} +(1.13918e7 + 2.22396e7i) q^{65} +3.59493e7i q^{67} +(2.60341e7 - 2.38443e7i) q^{69} +3.72539e7i q^{71} +9.08762e6i q^{73} +(-3.70902e6 - 3.14225e7i) q^{75} -379770. q^{77} +4.51811e7 q^{79} +(-4.23855e7 - 7.51579e6i) q^{81} -6.35482e7 q^{83} +(5.05980e7 - 2.59177e7i) q^{85} +(-3.45501e7 - 3.77230e7i) q^{87} +3.28534e7i q^{89} +1.09252e8 q^{91} +(3.60597e7 - 3.30267e7i) q^{93} +(1.33360e7 - 6.83110e6i) q^{95} +9.60947e7i q^{97} +(908296. + 79906.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 21928 q^{9} + 62920 q^{15} - 96048 q^{19} + 667112 q^{21} + 1292160 q^{25} + 5127152 q^{31} + 5420160 q^{39} - 8741480 q^{45} - 21439680 q^{49} - 3556688 q^{51} - 27329120 q^{55} + 67157264 q^{61}+ \cdots - 754526432 q^{99}+O(q^{100}) $ 16 * q + 21928 * q^9 + 62920 * q^15 - 96048 * q^19 + 667112 * q^21 + 1292160 * q^25 + 5127152 * q^31 + 5420160 * q^39 - 8741480 * q^45 - 21439680 * q^49 - 3556688 * q^51 - 27329120 * q^55 + 67157264 * q^61 + 97106152 * q^69 - 17107360 * q^75 + 296926128 * q^79 - 214283008 * q^81 + 190319120 * q^85 - 143834880 * q^91 - 754526432 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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
$3$	59.7326	−	54.7084i	0.737440	−	0.675413i
$3$	59.7326	−	54.7084i	0.737440	−	0.675413i
$4$		0			0
$5$	−556.269	+	284.937i	−0.890031	+	0.455900i
$5$	−556.269	+	284.937i	−0.890031	+	0.455900i
$6$		0			0
$7$			2732.68i			1.13814i	0.822288	+	0.569072i	$0.192698\pi$
$7$			2732.68i			1.13814i	−0.822288	+	0.569072i	$0.807302\pi$
$8$		0			0
$9$	574.975	−	6535.76i	0.0876352	−	0.996153i
$10$		0			0
$11$			138.973i			0.00949206i	0.999989	+	0.00474603i	$0.00151071\pi$
$11$			138.973i			0.00949206i	−0.999989	+	0.00474603i	$0.998489\pi$
$12$		0			0
$13$		−	39979.9i		−	1.39981i	−0.714238	−	0.699903i	$-0.753227\pi$
$13$		−	39979.9i		−	1.39981i	0.714238	−	0.699903i	$-0.246773\pi$
$14$		0			0
$15$	−17639.0	+	47452.7i	−0.348424	+	0.937337i
$16$		0			0
$17$	−90959.5			−1.08906			−0.544531	−	0.838741i	$-0.683292\pi$
$17$	−90959.5			−1.08906			−0.544531	+	0.838741i	$0.683292\pi$
$18$		0			0
$19$	−23974.1			−0.183962			−0.0919808	−	0.995761i	$-0.529320\pi$
$19$	−23974.1			−0.183962			−0.0919808	+	0.995761i	$0.529320\pi$
$20$		0			0
$21$	149501.	+	163230.i	0.768717	+	0.839313i
$22$		0			0
$23$	435843.			1.55747			0.778734	−	0.627354i	$-0.215862\pi$
$23$	435843.			1.55747			0.778734	+	0.627354i	$0.215862\pi$
$24$		0			0
$25$	228247.	−	317004.i	0.584311	−	0.811530i
$26$		0			0
$27$	−323216.	−	421854.i	−0.608188	−	0.793793i
$28$		0			0
$29$		−	631532.i		−	0.892900i	−0.894808	−	0.446450i	$-0.852688\pi$
$29$		−	631532.i		−	0.892900i	0.894808	−	0.446450i	$-0.147312\pi$
$30$		0			0
$31$	603686.			0.653678			0.326839	−	0.945080i	$-0.394016\pi$
$31$	603686.			0.653678			0.326839	+	0.945080i	$0.394016\pi$
$32$		0			0
$33$	7603.01	+	8301.24i	0.00641106	+	0.00699983i
$34$		0			0
$35$	−778644.	−	1.52011e6i	−0.518880	−	1.01298i
$36$		0			0
$37$			3.25530e6i			1.73694i	0.495743	+	0.868469i	$0.334896\pi$
$37$			3.25530e6i			1.73694i	−0.495743	+	0.868469i	$0.665104\pi$
$38$		0			0
$39$	−2.18724e6	−	2.38810e6i	−0.945447	−	1.03227i
$40$		0			0
$41$			2.45798e6i			0.869848i	0.900467	+	0.434924i	$0.143225\pi$
$41$			2.45798e6i			0.869848i	−0.900467	+	0.434924i	$0.856775\pi$
$42$		0			0
$43$			3.58077e6i			1.04738i	0.851910	+	0.523688i	$0.175444\pi$
$43$			3.58077e6i			1.04738i	−0.851910	+	0.523688i	$0.824556\pi$
$44$		0			0
$45$	1.54244e6	+	3.79947e6i	0.376148	+	0.926560i
$46$		0			0
$47$	−1.43490e6			−0.294057			−0.147029	−	0.989132i	$-0.546971\pi$
$47$	−1.43490e6			−0.294057			−0.147029	+	0.989132i	$0.546971\pi$
$48$		0			0
$49$	−1.70276e6			−0.295373
$50$		0			0
$51$	−5.43325e6	+	4.97625e6i	−0.803117	+	0.735566i
$52$		0			0
$53$	−3.71194e6			−0.470432			−0.235216	−	0.971943i	$-0.575580\pi$
$53$	−3.71194e6			−0.470432			−0.235216	+	0.971943i	$0.575580\pi$
$54$		0			0
$55$	−39598.7	−	77306.6i	−0.00432743	−	0.00844823i
$56$		0			0
$57$	−1.43203e6	+	1.31158e6i	−0.135661	+	0.124250i
$58$		0			0
$59$			4.19381e6i			0.346099i	0.984913	+	0.173050i	$0.0553621\pi$
$59$			4.19381e6i			0.346099i	−0.984913	+	0.173050i	$0.944638\pi$
$60$		0			0
$61$	−1.96341e7			−1.41805			−0.709026	−	0.705183i	$-0.750865\pi$
$61$	−1.96341e7			−1.41805			−0.709026	+	0.705183i	$0.750865\pi$
$62$		0			0
$63$	1.78602e7	+	1.57122e6i	1.13377	+	0.0997416i
$64$		0			0
$65$	1.13918e7	+	2.22396e7i	0.638171	+	1.24587i
$66$		0			0
$67$			3.59493e7i			1.78399i	0.452049	+	0.891993i	$0.350693\pi$
$67$			3.59493e7i			1.78399i	−0.452049	+	0.891993i	$0.649307\pi$
$68$		0			0
$69$	2.60341e7	−	2.38443e7i	1.14854	−	1.05193i
$70$		0			0
$71$			3.72539e7i			1.46602i	0.680220	+	0.733008i	$0.261884\pi$
$71$			3.72539e7i			1.46602i	−0.680220	+	0.733008i	$0.738116\pi$
$72$		0			0
$73$			9.08762e6i			0.320006i	0.987116	+	0.160003i	$0.0511505\pi$
$73$			9.08762e6i			0.320006i	−0.987116	+	0.160003i	$0.948850\pi$
$74$		0			0
$75$	−3.70902e6	−	3.14225e7i	−0.117223	−	0.993106i
$76$		0			0
$77$	−379770.			−0.0108033
$78$		0			0
$79$	4.51811e7			1.15997			0.579987	−	0.814626i	$-0.303058\pi$
$79$	4.51811e7			1.15997			0.579987	+	0.814626i	$0.303058\pi$
$80$		0			0
$81$	−4.23855e7	−	7.51579e6i	−0.984640	−	0.174596i
$82$		0			0
$83$	−6.35482e7			−1.33903			−0.669516	−	0.742797i	$-0.733499\pi$
$83$	−6.35482e7			−1.33903			−0.669516	+	0.742797i	$0.733499\pi$
$84$		0			0
$85$	5.05980e7	−	2.59177e7i	0.969299	−	0.496503i
$86$		0			0
$87$	−3.45501e7	−	3.77230e7i	−0.603076	−	0.658460i
$88$		0			0
$89$			3.28534e7i			0.523625i	0.965119	+	0.261813i	$0.0843203\pi$
$89$			3.28534e7i			0.523625i	−0.965119	+	0.261813i	$0.915680\pi$
$90$		0			0
$91$	1.09252e8			1.59318
$92$		0			0
$93$	3.60597e7	−	3.30267e7i	0.482048	−	0.441503i
$94$		0			0
$95$	1.33360e7	−	6.83110e6i	0.163732	−	0.0838680i
$96$		0			0
$97$			9.60947e7i			1.08546i	0.839908	+	0.542728i	$0.182609\pi$
$97$			9.60947e7i			1.08546i	−0.839908	+	0.542728i	$0.817391\pi$
$98$		0			0
$99$	908296.	+	79906.1i	0.00945554	+	0.000831839i
$100$		0			0
$101$		−	3.67333e7i		−	0.353000i	−0.984301	−	0.176500i	$-0.943522\pi$
$101$		−	3.67333e7i		−	0.353000i	0.984301	−	0.176500i	$-0.0564775\pi$
$102$		0			0
$103$		−	9.43652e7i		−	0.838423i	−0.907889	−	0.419211i	$-0.862307\pi$
$103$		−	9.43652e7i		−	0.838423i	0.907889	−	0.419211i	$-0.137693\pi$
$104$		0			0
$105$	−1.29673e8	−	4.82017e7i	−1.06682	−	0.396557i
$106$		0			0
$107$	−8.69727e7			−0.663511			−0.331755	−	0.943365i	$-0.607641\pi$
$107$	−8.69727e7			−0.663511			−0.331755	+	0.943365i	$0.607641\pi$
$108$		0			0
$109$	2.38438e8			1.68915			0.844577	−	0.535434i	$-0.179852\pi$
$109$	2.38438e8			1.68915			0.844577	+	0.535434i	$0.179852\pi$
$110$		0			0
$111$	1.78093e8	+	1.94448e8i	1.17315	+	1.28089i
$112$		0			0
$113$	−8.57304e7			−0.525801			−0.262900	−	0.964823i	$-0.584679\pi$
$113$	−8.57304e7			−0.525801			−0.262900	+	0.964823i	$0.584679\pi$
$114$		0			0
$115$	−2.42446e8	+	1.24188e8i	−1.38620	+	0.710049i
$116$		0			0
$117$	−2.61299e8	−	2.29874e7i	−1.39442	−	0.122672i
$118$		0			0
$119$		−	2.48564e8i		−	1.23951i
$120$		0			0
$121$	2.14340e8			0.999910
$122$		0			0
$123$	1.34472e8	+	1.46822e8i	0.587507	+	0.641461i
$124$		0			0
$125$	−3.66404e7	+	2.41375e8i	−0.150079	+	0.988674i
$126$		0			0
$127$		−	7.43701e7i		−	0.285880i	−0.989731	−	0.142940i	$-0.954344\pi$
$127$		−	7.43701e7i		−	0.285880i	0.989731	−	0.142940i	$-0.0456556\pi$
$128$		0			0
$129$	1.95898e8	+	2.13889e8i	0.707412	+	0.772378i
$130$		0			0
$131$			2.87710e8i			0.976944i	0.872580	+	0.488472i	$0.162446\pi$
$131$			2.87710e8i			0.976944i	−0.872580	+	0.488472i	$0.837554\pi$
$132$		0			0
$133$		−	6.55135e7i		−	0.209375i
$134$		0			0
$135$	2.99997e8	+	1.42568e8i	0.903196	+	0.429227i
$136$		0			0
$137$	5.65629e8			1.60564			0.802822	−	0.596219i	$-0.203331\pi$
$137$	5.65629e8			1.60564			0.802822	+	0.596219i	$0.203331\pi$
$138$		0			0
$139$	4.25011e8			1.13852			0.569261	−	0.822157i	$-0.307230\pi$
$139$	4.25011e8			1.13852			0.569261	+	0.822157i	$0.307230\pi$
$140$		0			0
$141$	−8.57106e7	+	7.85014e7i	−0.216849	+	0.198610i
$142$		0			0
$143$	5.55613e6			0.0132870
$144$		0			0
$145$	1.79947e8	+	3.51302e8i	0.407073	+	0.794709i
$146$		0			0
$147$	−1.01711e8	+	9.31556e7i	−0.217820	+	0.199498i
$148$		0			0
$149$			3.05645e7i			0.0620116i	0.999519	+	0.0310058i	$0.00987103\pi$
$149$			3.05645e7i			0.0620116i	−0.999519	+	0.0310058i	$0.990129\pi$
$150$		0			0
$151$	4.93529e7			0.0949302			0.0474651	−	0.998873i	$-0.484886\pi$
$151$	4.93529e7			0.0949302			0.0474651	+	0.998873i	$0.484886\pi$
$152$		0			0
$153$	−5.22994e7	+	5.94489e8i	−0.0954401	+	1.08487i
$154$		0			0
$155$	−3.35812e8	+	1.72013e8i	−0.581794	+	0.298012i
$156$		0			0
$157$			6.00890e8i			0.989001i	0.869177	+	0.494500i	$0.164649\pi$
$157$			6.00890e8i			0.989001i	−0.869177	+	0.494500i	$0.835351\pi$
$158$		0			0
$159$	−2.21724e8	+	2.03074e8i	−0.346915	+	0.317736i
$160$		0			0
$161$			1.19102e9i			1.77262i
$162$		0			0
$163$			7.84714e8i			1.11163i	0.831305	+	0.555816i	$0.187594\pi$
$163$			7.84714e8i			1.11163i	−0.831305	+	0.555816i	$0.812406\pi$
$164$		0			0
$165$	−6.59466e6	−	2.45135e6i	−0.00889726	−	0.00330726i
$166$		0			0
$167$	−7.21668e8			−0.927836			−0.463918	−	0.885878i	$-0.653557\pi$
$167$	−7.21668e8			−0.927836			−0.463918	+	0.885878i	$0.653557\pi$
$168$		0			0
$169$	−7.82658e8			−0.959456
$170$		0			0
$171$	−1.37845e7	+	1.56689e8i	−0.0161215	+	0.183254i
$172$		0			0
$173$	−1.34867e9			−1.50564			−0.752821	−	0.658225i	$-0.771308\pi$
$173$	−1.34867e9			−1.50564			−0.752821	+	0.658225i	$0.771308\pi$
$174$		0			0
$175$	8.66272e8	+	6.23726e8i	0.923638	+	0.665030i
$176$		0			0
$177$	2.29437e8	+	2.50507e8i	0.233760	+	0.255228i
$178$		0			0
$179$			9.68358e8i			0.943244i	0.881801	+	0.471622i	$0.156331\pi$
$179$			9.68358e8i			0.943244i	−0.881801	+	0.471622i	$0.843669\pi$
$180$		0			0
$181$	5.79390e8			0.539829			0.269915	−	0.962884i	$-0.413005\pi$
$181$	5.79390e8			0.539829			0.269915	+	0.962884i	$0.413005\pi$
$182$		0			0
$183$	−1.17280e9	+	1.07415e9i	−1.04573	+	0.957770i
$184$		0			0
$185$	−9.27557e8	−	1.81083e9i	−0.791870	−	1.54593i
$186$		0			0
$187$		−	1.26409e7i		−	0.0103374i
$188$		0			0
$189$	1.15279e9	−	8.83248e8i	0.903451	−	0.692206i
$190$		0			0
$191$			1.13330e9i			0.851553i	0.904828	+	0.425777i	$0.139999\pi$
$191$			1.13330e9i			0.851553i	−0.904828	+	0.425777i	$0.860001\pi$
$192$		0			0
$193$		−	1.62798e9i		−	1.17333i	−0.809831	−	0.586663i	$-0.800441\pi$
$193$		−	1.62798e9i		−	1.17333i	0.809831	−	0.586663i	$-0.199559\pi$
$194$		0			0
$195$	1.89715e9	+	7.05203e8i	1.31209	+	0.487726i
$196$		0			0
$197$	5.30676e8			0.352342			0.176171	−	0.984360i	$-0.443629\pi$
$197$	5.30676e8			0.352342			0.176171	+	0.984360i	$0.443629\pi$
$198$		0			0
$199$	1.73556e9			1.10669			0.553346	−	0.832951i	$-0.313351\pi$
$199$	1.73556e9			1.10669			0.553346	+	0.832951i	$0.313351\pi$
$200$		0			0
$201$	1.96673e9	+	2.14735e9i	1.20493	+	1.31558i
$202$		0			0
$203$	1.72578e9			1.01625
$204$		0			0
$205$	−7.00371e8	−	1.36730e9i	−0.396563	−	0.774192i
$206$		0			0
$207$	2.50599e8	−	2.84857e9i	0.136489	−	1.55148i
$208$		0			0
$209$		−	3.33175e6i		−	0.00174618i
$210$		0			0
$211$	−1.24909e9			−0.630178			−0.315089	−	0.949062i	$-0.602034\pi$
$211$	−1.24909e9			−0.630178			−0.315089	+	0.949062i	$0.602034\pi$
$212$		0			0
$213$	2.03810e9	+	2.22528e9i	0.990166	+	1.08110i
$214$		0			0
$215$	−1.02030e9	−	1.99187e9i	−0.477499	−	0.932198i
$216$		0			0
$217$			1.64968e9i			0.743980i
$218$		0			0
$219$	4.97169e8	+	5.42827e8i	0.216136	+	0.235985i
$220$		0			0
$221$			3.63655e9i			1.52447i
$222$		0			0
$223$		−	3.79992e9i		−	1.53658i	−0.640103	−	0.768289i	$-0.721108\pi$
$223$		−	3.79992e9i		−	1.53658i	0.640103	−	0.768289i	$-0.278892\pi$
$224$		0			0
$225$	−1.94062e9	−	1.67403e9i	−0.757201	−	0.653182i
$226$		0			0
$227$	−2.14940e9			−0.809493			−0.404746	−	0.914429i	$-0.632640\pi$
$227$	−2.14940e9			−0.809493			−0.404746	+	0.914429i	$0.632640\pi$
$228$		0			0
$229$	−2.61527e8			−0.0950989			−0.0475494	−	0.998869i	$-0.515141\pi$
$229$	−2.61527e8			−0.0950989			−0.0475494	+	0.998869i	$0.515141\pi$
$230$		0			0
$231$	−2.26847e7	+	2.07766e7i	−0.00796681	+	0.00729671i
$232$		0			0
$233$	−1.11109e9			−0.376986			−0.188493	−	0.982074i	$-0.560360\pi$
$233$	−1.11109e9			−0.376986			−0.188493	+	0.982074i	$0.560360\pi$
$234$		0			0
$235$	7.98194e8	−	4.08858e8i	0.261720	−	0.134061i
$236$		0			0
$237$	2.69878e9	−	2.47179e9i	0.855411	−	0.783461i
$238$		0			0
$239$			1.68005e9i			0.514908i	0.966291	+	0.257454i	$0.0828836\pi$
$239$			1.68005e9i			0.514908i	−0.966291	+	0.257454i	$0.917116\pi$
$240$		0			0
$241$	3.35727e9			0.995217			0.497608	−	0.867402i	$-0.334212\pi$
$241$	3.35727e9			0.995217			0.497608	+	0.867402i	$0.334212\pi$
$242$		0			0
$243$	−2.94298e9	+	1.86991e9i	−0.844037	+	0.536284i
$244$		0			0
$245$	9.47196e8	−	4.85181e8i	0.262891	−	0.134660i
$246$		0			0
$247$			9.58479e8i			0.257510i
$248$		0			0
$249$	−3.79590e9	+	3.47662e9i	−0.987456	+	0.904400i
$250$		0			0
$251$		−	7.51224e8i		−	0.189267i	−0.995512	−	0.0946334i	$-0.969832\pi$
$251$		−	7.51224e8i		−	0.189267i	0.995512	−	0.0946334i	$-0.0301679\pi$
$252$		0			0
$253$			6.05706e7i			0.0147836i
$254$		0			0
$255$	1.60443e9	−	4.31627e9i	0.379455	−	1.02082i
$256$		0			0
$257$	−4.57720e9			−1.04922			−0.524612	−	0.851342i	$-0.675789\pi$
$257$	−4.57720e9			−1.04922			−0.524612	+	0.851342i	$0.675789\pi$
$258$		0			0
$259$	−8.89572e9			−1.97689
$260$		0			0
$261$	−4.12754e9	−	3.63115e8i	−0.889465	−	0.0782495i
$262$		0			0
$263$	7.25043e9			1.51545			0.757723	−	0.652576i	$-0.226312\pi$
$263$	7.25043e9			1.51545			0.757723	+	0.652576i	$0.226312\pi$
$264$		0			0
$265$	2.06484e9	−	1.05767e9i	0.418699	−	0.214470i
$266$		0			0
$267$	1.79736e9	+	1.96242e9i	0.353663	+	0.386142i
$268$		0			0
$269$		−	4.13659e9i		−	0.790012i	−0.918678	−	0.395006i	$-0.870742\pi$
$269$		−	4.13659e9i		−	0.790012i	0.918678	−	0.395006i	$-0.129258\pi$
$270$		0			0
$271$	2.06046e9			0.382020			0.191010	−	0.981588i	$-0.438824\pi$
$271$	2.06046e9			0.382020			0.191010	+	0.981588i	$0.438824\pi$
$272$		0			0
$273$	6.52593e9	−	5.97702e9i	1.17488	−	1.07605i
$274$		0			0
$275$	4.40551e7	+	3.17202e7i	0.00770309	+	0.00554632i
$276$		0			0
$277$			4.00090e9i			0.679577i	0.940502	+	0.339789i	$0.110356\pi$
$277$			4.00090e9i			0.679577i	−0.940502	+	0.339789i	$0.889644\pi$
$278$		0			0
$279$	3.47104e8	−	3.94554e9i	0.0572852	−	0.651163i
$280$		0			0
$281$		−	9.28447e9i		−	1.48913i	−0.667552	−	0.744563i	$-0.732658\pi$
$281$		−	9.28447e9i		−	1.48913i	0.667552	−	0.744563i	$-0.267342\pi$
$282$		0			0
$283$			2.65616e9i			0.414103i	0.978330	+	0.207051i	$0.0663867\pi$
$283$			2.65616e9i			0.414103i	−0.978330	+	0.207051i	$0.933613\pi$
$284$		0			0
$285$	4.22878e8	−	1.13763e9i	0.0640966	−	0.172434i
$286$		0			0
$287$	−6.71689e9			−0.990013
$288$		0			0
$289$	1.29787e9			0.186055
$290$		0			0
$291$	5.25719e9	+	5.73999e9i	0.733131	+	0.800459i
$292$		0			0
$293$	−1.31400e10			−1.78290			−0.891448	−	0.453122i	$-0.850310\pi$
$293$	−1.31400e10			−1.78290			−0.891448	+	0.453122i	$0.850310\pi$
$294$		0			0
$295$	−1.19497e9	−	2.33289e9i	−0.157787	−	0.308039i
$296$		0			0
$297$	5.86264e7	−	4.49184e7i	0.00753473	−	0.00577296i
$298$		0			0
$299$		−	1.74250e10i		−	2.18015i
$300$		0			0
$301$	−9.78512e9			−1.19207
$302$		0			0
$303$	−2.00962e9	−	2.19418e9i	−0.238421	−	0.260316i
$304$		0			0
$305$	1.09219e10	−	5.59449e9i	1.26211	−	0.646489i
$306$		0			0
$307$			1.07169e9i			0.120647i	0.998179	+	0.0603236i	$0.0192133\pi$
$307$			1.07169e9i			0.120647i	−0.998179	+	0.0603236i	$0.980787\pi$
$308$		0			0
$309$	−5.16257e9	−	5.63668e9i	−0.566281	−	0.618286i
$310$		0			0
$311$			1.10247e10i			1.17849i	0.807954	+	0.589245i	$0.200575\pi$
$311$			1.10247e10i			1.17849i	−0.807954	+	0.589245i	$0.799425\pi$
$312$		0			0
$313$			2.37337e9i			0.247279i	0.992327	+	0.123640i	$0.0394567\pi$
$313$			2.37337e9i			0.247279i	−0.992327	+	0.123640i	$0.960543\pi$
$314$		0			0
$315$	−1.03828e10	+	4.21500e9i	−1.05456	+	0.428110i
$316$		0			0
$317$	1.16552e10			1.15421			0.577103	−	0.816672i	$-0.304183\pi$
$317$	1.16552e10			1.15421			0.577103	+	0.816672i	$0.304183\pi$
$318$		0			0
$319$	8.77660e7			0.00847547
$320$		0			0
$321$	−5.19511e9	+	4.75814e9i	−0.489299	+	0.448144i
$322$		0			0
$323$	2.18067e9			0.200345
$324$		0			0
$325$	−1.26738e10	−	9.12526e9i	−1.13598	−	0.817922i
$326$		0			0
$327$	1.42425e10	−	1.30446e10i	1.24565	−	1.14088i
$328$		0			0
$329$		−	3.92114e9i		−	0.334679i
$330$		0			0
$331$	3.25495e9			0.271164			0.135582	−	0.990766i	$-0.456710\pi$
$331$	3.25495e9			0.271164			0.135582	+	0.990766i	$0.456710\pi$
$332$		0			0
$333$	2.12759e10	+	1.87172e9i	1.73026	+	0.152217i
$334$		0			0
$335$	−1.02433e10	−	1.99975e10i	−0.813319	−	1.58780i
$336$		0			0
$337$			1.06140e9i			0.0822921i	0.999153	+	0.0411461i	$0.0131009\pi$
$337$			1.06140e9i			0.0822921i	−0.999153	+	0.0411461i	$0.986899\pi$
$338$		0			0
$339$	−5.12090e9	+	4.69018e9i	−0.387746	+	0.355133i
$340$		0			0
$341$			8.38962e7i			0.00620476i
$342$		0			0
$343$			1.11003e10i			0.801968i
$344$		0			0
$345$	−7.68783e9	+	2.06819e10i	−0.542659	+	1.45987i
$346$		0			0
$347$	−2.72743e9			−0.188120			−0.0940600	−	0.995567i	$-0.529985\pi$
$347$	−2.72743e9			−0.188120			−0.0940600	+	0.995567i	$0.529985\pi$
$348$		0			0
$349$	1.33281e9			0.0898394			0.0449197	−	0.998991i	$-0.485697\pi$
$349$	1.33281e9			0.0898394			0.0449197	+	0.998991i	$0.485697\pi$
$350$		0			0
$351$	−1.68657e10	+	1.29221e10i	−1.11116	+	0.851346i
$352$		0			0
$353$	4.09481e9			0.263715			0.131857	−	0.991269i	$-0.457906\pi$
$353$	4.09481e9			0.263715			0.131857	+	0.991269i	$0.457906\pi$
$354$		0			0
$355$	−1.06150e10	−	2.07232e10i	−0.668356	−	1.30480i
$356$		0			0
$357$	−1.35985e10	−	1.48474e10i	−0.837180	−	0.914063i
$358$		0			0
$359$		−	1.26490e10i		−	0.761517i	−0.924674	−	0.380759i	$-0.875663\pi$
$359$		−	1.26490e10i		−	0.761517i	0.924674	−	0.380759i	$-0.124337\pi$
$360$		0			0
$361$	−1.64088e10			−0.966158
$362$		0			0
$363$	1.28031e10	−	1.17262e10i	0.737373	−	0.675352i
$364$		0			0
$365$	−2.58940e9	−	5.05516e9i	−0.145891	−	0.284816i
$366$		0			0
$367$			2.60644e10i			1.43676i	0.695651	+	0.718380i	$0.255116\pi$
$367$			2.60644e10i			1.43676i	−0.695651	+	0.718380i	$0.744884\pi$
$368$		0			0
$369$	1.60648e10	+	1.41328e9i	0.866502	+	0.0762293i
$370$		0			0
$371$		−	1.01435e10i		−	0.535420i
$372$		0			0
$373$			1.06671e10i			0.551074i	0.961290	+	0.275537i	$0.0888557\pi$
$373$			1.06671e10i			0.551074i	−0.961290	+	0.275537i	$0.911144\pi$
$374$		0			0
$375$	1.10166e10	+	1.64225e10i	0.557089	+	0.830453i
$376$		0			0
$377$	−2.52485e10			−1.24989
$378$		0			0
$379$	1.58507e10			0.768231			0.384116	−	0.923285i	$-0.374506\pi$
$379$	1.58507e10			0.768231			0.384116	+	0.923285i	$0.374506\pi$
$380$		0			0
$381$	−4.06867e9	−	4.44232e9i	−0.193087	−	0.210819i
$382$		0			0
$383$	−7.03804e9			−0.327082			−0.163541	−	0.986537i	$-0.552292\pi$
$383$	−7.03804e9			−0.327082			−0.163541	+	0.986537i	$0.552292\pi$
$384$		0			0
$385$	2.11255e8	−	1.08211e8i	0.00961531	−	0.00492524i
$386$		0			0
$387$	2.34031e10	+	2.05885e9i	1.04335	+	0.0917871i
$388$		0			0
$389$		−	2.67699e10i		−	1.16909i	−0.811360	−	0.584546i	$-0.801273\pi$
$389$		−	2.67699e10i		−	1.16909i	0.811360	−	0.584546i	$-0.198727\pi$
$390$		0			0
$391$	−3.96441e10			−1.69618
$392$		0			0
$393$	1.57402e10	+	1.71857e10i	0.659840	+	0.720438i
$394$		0			0
$395$	−2.51329e10	+	1.28738e10i	−1.03241	+	0.528832i
$396$		0			0
$397$		−	3.89022e10i		−	1.56607i	−0.621975	−	0.783037i	$-0.713669\pi$
$397$		−	3.89022e10i		−	1.56607i	0.621975	−	0.783037i	$-0.286331\pi$
$398$		0			0
$399$	−3.58414e9	−	3.91330e9i	−0.141414	−	0.154401i
$400$		0			0
$401$			3.78185e10i			1.46261i	0.682053	+	0.731303i	$0.261087\pi$
$401$			3.78185e10i			1.46261i	−0.682053	+	0.731303i	$0.738913\pi$
$402$		0			0
$403$		−	2.41353e10i		−	0.915023i
$404$		0			0
$405$	2.57193e10	−	7.89641e9i	0.955959	−	0.293501i
$406$		0			0
$407$	−4.52400e8			−0.0164871
$408$		0			0
$409$	3.18590e9			0.113852			0.0569258	−	0.998378i	$-0.481870\pi$
$409$	3.18590e9			0.113852			0.0569258	+	0.998378i	$0.481870\pi$
$410$		0			0
$411$	3.37865e10	−	3.09447e10i	1.18407	−	1.08447i
$412$		0			0
$413$	−1.14604e10			−0.393911
$414$		0			0
$415$	3.53500e10	−	1.81073e10i	1.19178	−	0.610465i
$416$		0			0
$417$	2.53870e10	−	2.32517e10i	0.839591	−	0.768972i
$418$		0			0
$419$			2.70655e10i			0.878131i	0.898455	+	0.439065i	$0.144690\pi$
$419$			2.70655e10i			0.878131i	−0.898455	+	0.439065i	$0.855310\pi$
$420$		0			0
$421$	5.67845e10			1.80760			0.903798	−	0.427959i	$-0.140767\pi$
$421$	5.67845e10			1.80760			0.903798	+	0.427959i	$0.140767\pi$
$422$		0			0
$423$	−8.25034e8	+	9.37819e9i	−0.0257698	+	0.292926i
$424$		0			0
$425$	−2.07612e10	+	2.88345e10i	−0.636351	+	0.883806i
$426$		0			0
$427$		−	5.36538e10i		−	1.61395i
$428$		0			0
$429$	3.31882e8	−	3.03967e8i	0.00979840	−	0.00897424i
$430$		0			0
$431$		−	2.71837e10i		−	0.787769i	−0.919160	−	0.393884i	$-0.871131\pi$
$431$		−	2.71837e10i		−	0.787769i	0.919160	−	0.393884i	$-0.128869\pi$
$432$		0			0
$433$		−	6.53469e9i		−	0.185897i	−0.995671	−	0.0929487i	$-0.970371\pi$
$433$		−	6.53469e9i		−	0.185897i	0.995671	−	0.0929487i	$-0.0296293\pi$
$434$		0			0
$435$	2.99679e10	+	1.11396e10i	0.836949	+	0.311108i
$436$		0			0
$437$	−1.04489e10			−0.286514
$438$		0			0
$439$	9.86558e9			0.265622			0.132811	−	0.991141i	$-0.457600\pi$
$439$	9.86558e9			0.265622			0.132811	+	0.991141i	$0.457600\pi$
$440$		0			0
$441$	−9.79047e8	+	1.11289e10i	−0.0258851	+	0.294236i
$442$		0			0
$443$	−3.59381e10			−0.933127			−0.466563	−	0.884488i	$-0.654508\pi$
$443$	−3.59381e10			−0.933127			−0.466563	+	0.884488i	$0.654508\pi$
$444$		0			0
$445$	−9.36117e9	−	1.82754e10i	−0.238721	−	0.466043i
$446$		0			0
$447$	1.67214e9	+	1.82570e9i	0.0418834	+	0.0457298i
$448$		0			0
$449$			2.10210e10i			0.517212i	0.965983	+	0.258606i	$0.0832632\pi$
$449$			2.10210e10i			0.517212i	−0.965983	+	0.258606i	$0.916737\pi$
$450$		0			0
$451$	−3.41594e8			−0.00825665
$452$		0			0
$453$	2.94798e9	−	2.70002e9i	0.0700053	−	0.0641171i
$454$		0			0
$455$	−6.07737e10	+	3.11301e10i	−1.41798	+	0.726331i
$456$		0			0
$457$			4.53613e10i			1.03997i	0.854176	+	0.519985i	$0.174062\pi$
$457$			4.53613e10i			1.03997i	−0.854176	+	0.519985i	$0.825938\pi$
$458$		0			0
$459$	2.93996e10	+	3.83716e10i	0.662355	+	0.864489i
$460$		0			0
$461$		−	7.50697e10i		−	1.66211i	−0.556187	−	0.831057i	$-0.687736\pi$
$461$		−	7.50697e10i		−	1.66211i	0.556187	−	0.831057i	$-0.312264\pi$
$462$		0			0
$463$			5.77718e10i			1.25716i	0.777743	+	0.628582i	$0.216364\pi$
$463$			5.77718e10i			1.25716i	−0.777743	+	0.628582i	$0.783636\pi$
$464$		0			0
$465$	−1.06484e10	+	2.86465e10i	−0.227757	+	0.612717i
$466$		0			0
$467$	−1.87315e10			−0.393826			−0.196913	−	0.980421i	$-0.563092\pi$
$467$	−1.87315e10			−0.393826			−0.196913	+	0.980421i	$0.563092\pi$
$468$		0			0
$469$	−9.82382e10			−2.03043
$470$		0			0
$471$	3.28738e10	+	3.58928e10i	0.667984	+	0.729329i
$472$		0			0
$473$	−4.97632e8			−0.00994177
$474$		0			0
$475$	−5.47199e9	+	7.59987e9i	−0.107491	+	0.149290i
$476$		0			0
$477$	−2.13427e9	+	2.42603e10i	−0.0412264	+	0.468622i
$478$		0			0
$479$			1.66308e10i			0.315916i	0.987446	+	0.157958i	$0.0504910\pi$
$479$			1.66308e10i			0.315916i	−0.987446	+	0.157958i	$0.949509\pi$
$480$		0			0
$481$	1.30147e11			2.43138
$482$		0			0
$483$	6.51590e10	+	7.11429e10i	1.19725	+	1.30720i
$484$		0			0
$485$	−2.73810e10	−	5.34546e10i	−0.494859	−	0.966091i
$486$		0			0
$487$			7.82184e10i			1.39057i	0.718734	+	0.695285i	$0.244722\pi$
$487$			7.82184e10i			1.39057i	−0.718734	+	0.695285i	$0.755278\pi$
$488$		0			0
$489$	4.29305e10	+	4.68730e10i	0.750810	+	0.819762i
$490$		0			0
$491$		−	7.12593e10i		−	1.22607i	−0.790056	−	0.613035i	$-0.789948\pi$
$491$		−	7.12593e10i		−	1.22607i	0.790056	−	0.613035i	$-0.210052\pi$
$492$		0			0
$493$			5.74438e10i			0.972423i
$494$		0			0
$495$	−5.28026e8	+	2.14358e8i	−0.00879496	+	0.00357042i
$496$		0			0
$497$	−1.01803e11			−1.66854
$498$		0			0
$499$	−7.30983e9			−0.117898			−0.0589488	−	0.998261i	$-0.518775\pi$
$499$	−7.30983e9			−0.117898			−0.0589488	+	0.998261i	$0.518775\pi$
$500$		0			0
$501$	−4.31071e10	+	3.94813e10i	−0.684224	+	0.626673i
$502$		0			0
$503$	6.85791e10			1.07132			0.535661	−	0.844433i	$-0.320063\pi$
$503$	6.85791e10			1.07132			0.535661	+	0.844433i	$0.320063\pi$
$504$		0			0
$505$	1.04667e10	+	2.04336e10i	0.160933	+	0.314181i
$506$		0			0
$507$	−4.67502e10	+	4.28180e10i	−0.707541	+	0.648029i
$508$		0			0
$509$			6.50774e10i			0.969525i	0.874646	+	0.484762i	$0.161094\pi$
$509$			6.50774e10i			0.969525i	−0.874646	+	0.484762i	$0.838906\pi$
$510$		0			0
$511$	−2.48336e10			−0.364213
$512$		0			0
$513$	7.74881e9	+	1.01136e10i	0.111883	+	0.146027i
$514$		0			0
$515$	2.68882e10	+	5.24925e10i	0.382237	+	0.746222i
$516$		0			0
$517$		−	1.99413e8i		−	0.00279121i
$518$		0			0
$519$	−8.05597e10	+	7.37837e10i	−1.11032	+	1.01693i
$520$		0			0
$521$		−	3.04885e10i		−	0.413795i	−0.978363	−	0.206898i	$-0.933663\pi$
$521$		−	3.04885e10i		−	0.413795i	0.978363	−	0.206898i	$-0.0663367\pi$
$522$		0			0
$523$			1.41009e10i			0.188469i	0.995550	+	0.0942345i	$0.0300403\pi$
$523$			1.41009e10i			0.188469i	−0.995550	+	0.0942345i	$0.969960\pi$
$524$		0			0
$525$	8.58677e10	−	1.01356e10i	1.13030	−	0.133417i
$526$		0			0
$527$	−5.49109e10			−0.711896
$528$		0			0
$529$	1.11649e11			1.42571
$530$		0			0
$531$	2.74097e10	+	2.41134e9i	0.344768	+	0.0303305i
$532$		0			0
$533$	9.82698e10			1.21762
$534$		0			0
$535$	4.83803e10	−	2.47818e10i	0.590545	−	0.302494i
$536$		0			0
$537$	5.29774e10	+	5.78426e10i	0.637079	+	0.695586i
$538$		0			0
$539$		−	2.36639e8i		−	0.00280370i
$540$		0			0
$541$	−1.48883e11			−1.73802			−0.869010	−	0.494794i	$-0.835243\pi$
$541$	−1.48883e11			−1.73802			−0.869010	+	0.494794i	$0.835243\pi$
$542$		0			0
$543$	3.46085e10	−	3.16975e10i	0.398092	−	0.364608i
$544$		0			0
$545$	−1.32636e11	+	6.79399e10i	−1.50340	+	0.770085i
$546$		0			0
$547$			3.44145e10i			0.384408i	0.981355	+	0.192204i	$0.0615635\pi$
$547$			3.44145e10i			0.384408i	−0.981355	+	0.192204i	$0.938436\pi$
$548$		0			0
$549$	−1.12891e10	+	1.28324e11i	−0.124271	+	1.41260i
$550$		0			0
$551$			1.51404e10i			0.164259i
$552$		0			0
$553$			1.23466e11i			1.32022i
$554$		0			0
$555$	−1.54473e11	−	5.74202e10i	−1.62810	−	0.605191i
$556$		0			0
$557$	−4.19800e10			−0.436136			−0.218068	−	0.975934i	$-0.569975\pi$
$557$	−4.19800e10			−0.436136			−0.218068	+	0.975934i	$0.569975\pi$
$558$		0			0
$559$	1.43159e11			1.46612
$560$		0			0
$561$	−6.91566e8	−	7.55077e8i	−0.00698204	−	0.00762324i
$562$		0			0
$563$	−1.00579e11			−1.00109			−0.500547	−	0.865710i	$-0.666868\pi$
$563$	−1.00579e11			−1.00109			−0.500547	+	0.865710i	$0.666868\pi$
$564$		0			0
$565$	4.76892e10	−	2.44278e10i	0.467979	−	0.239712i
$566$		0			0
$567$	2.05383e10	−	1.15826e11i	0.198716	−	1.12066i
$568$		0			0
$569$			5.71322e10i			0.545045i	0.962149	+	0.272522i	$0.0878579\pi$
$569$			5.71322e10i			0.545045i	−0.962149	+	0.272522i	$0.912142\pi$
$570$		0			0
$571$	4.61293e10			0.433942			0.216971	−	0.976178i	$-0.430382\pi$
$571$	4.61293e10			0.433942			0.216971	+	0.976178i	$0.430382\pi$
$572$		0			0
$573$	6.20011e10	+	6.76951e10i	0.575150	+	0.627969i
$574$		0			0
$575$	9.94797e10	−	1.38164e11i	0.910046	−	1.26393i
$576$		0			0
$577$		−	3.38834e10i		−	0.305691i	−0.988250	−	0.152846i	$-0.951156\pi$
$577$		−	3.38834e10i		−	0.305691i	0.988250	−	0.152846i	$-0.0488437\pi$
$578$		0			0
$579$	−8.90641e10	−	9.72433e10i	−0.792480	−	0.865258i
$580$		0			0
$581$		−	1.73657e11i		−	1.52401i
$582$		0			0
$583$		−	5.15860e8i		−	0.00446537i
$584$		0			0
$585$	1.51902e11	−	6.16665e10i	1.29700	−	0.526533i
$586$		0			0
$587$	−6.45108e10			−0.543350			−0.271675	−	0.962389i	$-0.587578\pi$
$587$	−6.45108e10			−0.543350			−0.271675	+	0.962389i	$0.587578\pi$
$588$		0			0
$589$	−1.44728e10			−0.120252
$590$		0			0
$591$	3.16987e10	−	2.90325e10i	0.259831	−	0.237976i
$592$		0			0
$593$	−3.86595e10			−0.312635			−0.156317	−	0.987707i	$-0.549962\pi$
$593$	−3.86595e10			−0.312635			−0.156317	+	0.987707i	$0.549962\pi$
$594$		0			0
$595$	7.08250e10	+	1.38268e11i	0.565092	+	1.10320i
$596$		0			0
$597$	1.03669e11	−	9.49497e10i	0.816119	−	0.747474i
$598$		0			0
$599$			1.01190e11i			0.786016i	0.919535	+	0.393008i	$0.128566\pi$
$599$			1.01190e11i			0.786016i	−0.919535	+	0.393008i	$0.871434\pi$
$600$		0			0
$601$	8.63507e10			0.661863			0.330932	−	0.943655i	$-0.392637\pi$
$601$	8.63507e10			0.661863			0.330932	+	0.943655i	$0.392637\pi$
$602$		0			0
$603$	2.34956e11	+	2.06700e10i	1.77712	+	0.156340i
$604$		0			0
$605$	−1.19231e11	+	6.10733e10i	−0.889951	+	0.455859i
$606$		0			0
$607$		−	2.18211e11i		−	1.60739i	−0.595040	−	0.803696i	$-0.702864\pi$
$607$		−	2.18211e11i		−	1.60739i	0.595040	−	0.803696i	$-0.297136\pi$
$608$		0			0
$609$	1.03085e11	−	9.44145e10i	0.749423	−	0.686388i
$610$		0			0
$611$			5.73673e10i			0.411623i
$612$		0			0
$613$		−	2.62660e11i		−	1.86016i	−0.367352	−	0.930082i	$-0.619736\pi$
$613$		−	2.62660e11i		−	1.86016i	0.367352	−	0.930082i	$-0.380264\pi$
$614$		0			0
$615$	−1.16638e11	−	4.33563e10i	−0.815341	−	0.303076i
$616$		0			0
$617$	−1.06035e11			−0.731658			−0.365829	−	0.930682i	$-0.619215\pi$
$617$	−1.06035e11			−0.731658			−0.365829	+	0.930682i	$0.619215\pi$
$618$		0			0
$619$	−7.46029e10			−0.508152			−0.254076	−	0.967184i	$-0.581771\pi$
$619$	−7.46029e10			−0.508152			−0.254076	+	0.967184i	$0.581771\pi$
$620$		0			0
$621$	−1.40872e11	−	1.83862e11i	−0.947234	−	1.23631i
$622$		0			0
$623$	−8.97781e10			−0.595961
$624$		0			0
$625$	−4.83950e10	−	1.44710e11i	−0.317161	−	0.948372i
$626$		0			0
$627$	−1.82275e8	−	1.99014e8i	−0.00117939	−	0.00128770i
$628$		0			0
$629$		−	2.96101e11i		−	1.89163i
$630$		0			0
$631$	−1.57908e10			−0.0996063			−0.0498032	−	0.998759i	$-0.515859\pi$
$631$	−1.57908e10			−0.0996063			−0.0498032	+	0.998759i	$0.515859\pi$
$632$		0			0
$633$	−7.46113e10	+	6.83356e10i	−0.464718	+	0.425630i
$634$		0			0
$635$	2.11908e10	+	4.13698e10i	0.130333	+	0.254442i
$636$		0			0
$637$			6.80763e10i			0.413464i
$638$		0			0
$639$	2.43483e11	+	2.14201e10i	1.46038	+	0.128475i
$640$		0			0
$641$			1.75340e11i			1.03860i	0.854591	+	0.519301i	$0.173808\pi$
$641$			1.75340e11i			1.03860i	−0.854591	+	0.519301i	$0.826192\pi$
$642$		0			0
$643$			2.52429e11i			1.47671i	0.674413	+	0.738354i	$0.264397\pi$
$643$			2.52429e11i			1.47671i	−0.674413	+	0.738354i	$0.735603\pi$
$644$		0			0
$645$	−1.69917e11	−	6.31612e10i	−0.981745	−	0.364931i
$646$		0			0
$647$	−1.72802e11			−0.986124			−0.493062	−	0.869994i	$-0.664122\pi$
$647$	−1.72802e11			−0.986124			−0.493062	+	0.869994i	$0.664122\pi$
$648$		0			0
$649$	−5.82828e8			−0.00328520
$650$		0			0
$651$	9.02515e10	+	9.85399e10i	0.502494	+	0.548641i
$652$		0			0
$653$	2.59647e11			1.42801			0.714003	−	0.700143i	$-0.246880\pi$
$653$	2.59647e11			1.42801			0.714003	+	0.700143i	$0.246880\pi$
$654$		0			0
$655$	−8.19793e10	−	1.60044e11i	−0.445388	−	0.869511i
$656$		0			0
$657$	5.93945e10	+	5.22515e9i	0.318775	+	0.0280438i
$658$		0			0
$659$		−	3.06755e11i		−	1.62649i	−0.581925	−	0.813243i	$-0.697700\pi$
$659$		−	3.06755e11i		−	1.62649i	0.581925	−	0.813243i	$-0.302300\pi$
$660$		0			0
$661$	−7.89336e10			−0.413481			−0.206741	−	0.978396i	$-0.566286\pi$
$661$	−7.89336e10			−0.413481			−0.206741	+	0.978396i	$0.566286\pi$
$662$		0			0
$663$	1.98950e11	+	2.17221e11i	1.02965	+	1.12421i
$664$		0			0
$665$	1.86672e10	+	3.64432e10i	0.0954539	+	0.186350i
$666$		0			0
$667$		−	2.75249e11i		−	1.39066i
$668$		0			0
$669$	−2.07888e11	−	2.26979e11i	−1.03782	−	1.13313i
$670$		0			0
$671$		−	2.72862e9i		−	0.0134602i
$672$		0			0
$673$			3.07460e11i			1.49875i	0.662146	+	0.749375i	$0.269646\pi$
$673$			3.07460e11i			1.49875i	−0.662146	+	0.749375i	$0.730354\pi$
$674$		0			0
$675$	−2.07502e11	+	6.17411e9i	−0.999558	+	0.0297412i
$676$		0			0
$677$	2.14869e11			1.02287			0.511433	−	0.859323i	$-0.329115\pi$
$677$	2.14869e11			1.02287			0.511433	+	0.859323i	$0.329115\pi$
$678$		0			0
$679$	−2.62597e11			−1.23541
$680$		0			0
$681$	−1.28389e11	+	1.17590e11i	−0.596952	+	0.546742i
$682$		0			0
$683$	1.86313e11			0.856170			0.428085	−	0.903738i	$-0.359188\pi$
$683$	1.86313e11			0.856170			0.428085	+	0.903738i	$0.359188\pi$
$684$		0			0
$685$	−3.14642e11	+	1.61169e11i	−1.42907	+	0.732012i
$686$		0			0
$687$	−1.56217e10	+	1.43078e10i	−0.0701297	+	0.0642310i
$688$		0			0
$689$			1.48403e11i			0.658514i
$690$		0			0
$691$	−2.15983e11			−0.947343			−0.473672	−	0.880702i	$-0.657072\pi$
$691$	−2.15983e11			−0.947343			−0.473672	+	0.880702i	$0.657072\pi$
$692$		0			0
$693$	−2.18358e8	+	2.48209e9i	−0.000946753	+	0.0107618i
$694$		0			0
$695$	−2.36421e11	+	1.21102e11i	−1.01332	+	0.519051i
$696$		0			0
$697$		−	2.23577e11i		−	0.947318i
$698$		0			0
$699$	−6.63684e10	+	6.07860e10i	−0.278005	+	0.254621i
$700$		0			0
$701$		−	1.11048e11i		−	0.459876i	−0.973205	−	0.229938i	$-0.926148\pi$
$701$		−	1.11048e11i		−	0.459876i	0.973205	−	0.229938i	$-0.0738523\pi$
$702$		0			0
$703$		−	7.80428e10i		−	0.319530i
$704$		0			0
$705$	2.53102e10	−	6.80901e10i	0.102457	−	0.275631i
$706$		0			0
$707$	1.00381e11			0.401765
$708$		0			0
$709$	−1.92847e10			−0.0763181			−0.0381590	−	0.999272i	$-0.512149\pi$
$709$	−1.92847e10			−0.0763181			−0.0381590	+	0.999272i	$0.512149\pi$
$710$		0			0
$711$	2.59780e10	−	2.95293e11i	0.101655	−	1.15551i
$712$		0			0
$713$	2.63112e11			1.01808
$714$		0			0
$715$	−3.09071e9	+	1.58315e9i	−0.0118259	+	0.00605756i
$716$		0			0
$717$	9.19127e10	+	1.00354e11i	0.347775	+	0.379714i
$718$		0			0
$719$		−	8.08348e10i		−	0.302470i	−0.988498	−	0.151235i	$-0.951675\pi$
$719$		−	8.08348e10i		−	0.302470i	0.988498	−	0.151235i	$-0.0483251\pi$
$720$		0			0
$721$	2.57870e11			0.954246
$722$		0			0
$723$	2.00538e11	−	1.83671e11i	0.733912	−	0.672182i
$724$		0			0
$725$	−2.00198e11	−	1.44145e11i	−0.724615	−	0.521732i
$726$		0			0
$727$		−	8.16014e10i		−	0.292119i	−0.989276	−	0.146060i	$-0.953341\pi$
$727$		−	8.16014e10i		−	0.292119i	0.989276	−	0.146060i	$-0.0466591\pi$
$728$		0			0
$729$	−7.34920e10	+	2.72700e11i	−0.260214	+	0.965551i
$730$		0			0
$731$		−	3.25705e11i		−	1.14066i
$732$		0			0
$733$			1.18380e11i			0.410073i	0.978754	+	0.205036i	$0.0657313\pi$
$733$			1.18380e11i			0.410073i	−0.978754	+	0.205036i	$0.934269\pi$
$734$		0			0
$735$	3.00350e10	−	8.08008e10i	0.102915	−	0.276864i
$736$		0			0
$737$	−4.99600e9			−0.0169337
$738$		0			0
$739$	−3.41688e7			−0.000114565			−5.72826e−5	−	1.00000i	$-0.500018\pi$
$739$	−3.41688e7			−0.000114565			−5.72826e−5		1.00000i	$0.500018\pi$
$740$		0			0
$741$	5.24369e10	+	5.72525e10i	0.173926	+	0.189899i
$742$		0			0
$743$	4.64134e11			1.52296			0.761479	−	0.648190i	$-0.224474\pi$
$743$	4.64134e11			1.52296			0.761479	+	0.648190i	$0.224474\pi$
$744$		0			0
$745$	−8.70898e9	−	1.70021e10i	−0.0282711	−	0.0551922i
$746$		0			0
$747$	−3.65386e10	+	4.15336e11i	−0.117346	+	1.33388i
$748$		0			0
$749$		−	2.37669e11i		−	0.755171i
$750$		0			0
$751$	−5.06216e11			−1.59139			−0.795693	−	0.605699i	$-0.792893\pi$
$751$	−5.06216e11			−1.59139			−0.795693	+	0.605699i	$0.792893\pi$
$752$		0			0
$753$	−4.10983e10	−	4.48726e10i	−0.127833	−	0.139573i
$754$		0			0
$755$	−2.74535e10	+	1.40625e10i	−0.0844909	+	0.0432787i
$756$		0			0
$757$		−	5.78541e11i		−	1.76178i	−0.473325	−	0.880888i	$-0.656946\pi$
$757$		−	5.78541e11i		−	1.76178i	0.473325	−	0.880888i	$-0.343054\pi$
$758$		0			0
$759$	3.31372e9	+	3.61804e9i	0.00998502	+	0.0109020i
$760$		0			0
$761$			1.05017e11i			0.313128i	0.987668	+	0.156564i	$0.0500417\pi$
$761$			1.05017e11i			0.313128i	−0.987668	+	0.156564i	$0.949958\pi$
$762$		0			0
$763$			6.51576e11i			1.92250i
$764$		0			0
$765$	−1.40300e11	−	3.45598e11i	−0.409648	−	1.00908i
$766$		0			0
$767$	1.67668e11			0.484472
$768$		0			0
$769$	−2.55088e11			−0.729432			−0.364716	−	0.931119i	$-0.618834\pi$
$769$	−2.55088e11			−0.729432			−0.364716	+	0.931119i	$0.618834\pi$
$770$		0			0
$771$	−2.73408e11	+	2.50412e11i	−0.773739	+	0.708659i
$772$		0			0
$773$	5.12267e11			1.43476			0.717379	−	0.696684i	$-0.245342\pi$
$773$	5.12267e11			1.43476			0.717379	+	0.696684i	$0.245342\pi$
$774$		0			0
$775$	1.37789e11	−	1.91371e11i	0.381951	−	0.530479i
$776$		0			0
$777$	−5.31365e11	+	4.86671e11i	−1.45784	+	1.33521i
$778$		0			0
$779$		−	5.89278e10i		−	0.160019i
$780$		0			0
$781$	−5.17730e9			−0.0139155
$782$		0			0
$783$	−2.66414e11	+	2.04121e11i	−0.708778	+	0.543052i
$784$		0			0
$785$	−1.71216e11	−	3.34257e11i	−0.450885	−	0.880241i
$786$		0			0
$787$		−	4.20303e11i		−	1.09563i	−0.836600	−	0.547814i	$-0.815460\pi$
$787$		−	4.20303e11i		−	1.09563i	0.836600	−	0.547814i	$-0.184540\pi$
$788$		0			0
$789$	4.33087e11	−	3.96660e11i	1.11755	−	1.02355i
$790$		0			0
$791$		−	2.34274e11i		−	0.598437i
$792$		0			0
$793$			7.84969e11i			1.98500i
$794$		0			0
$795$	6.54747e10	−	1.76141e11i	0.163910	−	0.440953i
$796$		0			0
$797$	−4.85908e11			−1.20426			−0.602130	−	0.798398i	$-0.705681\pi$
$797$	−4.85908e11			−1.20426			−0.602130	+	0.798398i	$0.705681\pi$
$798$		0			0
$799$	1.30518e11			0.320246
$800$		0			0
$801$	2.14722e11	+	1.88899e10i	0.521611	+	0.0458880i
$802$		0			0
$803$	−1.26294e9			−0.00303752
$804$		0			0
$805$	−3.39367e11	−	6.62530e11i	−0.808139	−	1.57769i
$806$		0			0
$807$	−2.26307e11	−	2.47090e11i	−0.533584	−	0.582587i
$808$		0			0
$809$			1.86200e11i			0.434695i	0.976094	+	0.217348i	$0.0697405\pi$
$809$			1.86200e11i			0.434695i	−0.976094	+	0.217348i	$0.930259\pi$
$810$		0			0
$811$	−1.47774e11			−0.341598			−0.170799	−	0.985306i	$-0.554635\pi$
$811$	−1.47774e11			−0.341598			−0.170799	+	0.985306i	$0.554635\pi$
$812$		0			0
$813$	1.23076e11	−	1.12724e11i	0.281717	−	0.258021i
$814$		0			0
$815$	−2.23594e11	−	4.36513e11i	−0.506793	−	0.989387i
$816$		0			0
$817$		−	8.58457e10i		−	0.192677i
$818$		0			0
$819$	6.28173e10	−	7.14047e11i	0.139619	−	1.58705i
$820$		0			0
$821$			7.04918e11i			1.55155i	0.631009	+	0.775776i	$0.282641\pi$
$821$			7.04918e11i			1.55155i	−0.631009	+	0.775776i	$0.717359\pi$
$822$		0			0
$823$		−	1.75927e11i		−	0.383473i	−0.981446	−	0.191736i	$-0.938588\pi$
$823$		−	1.75927e11i		−	0.383473i	0.981446	−	0.191736i	$-0.0614118\pi$
$824$		0			0
$825$	4.36689e9	−	5.15455e8i	0.00942662	−	0.00111269i
$826$		0			0
$827$	−3.58495e11			−0.766410			−0.383205	−	0.923663i	$-0.625180\pi$
$827$	−3.58495e11			−0.766410			−0.383205	+	0.923663i	$0.625180\pi$
$828$		0			0
$829$	−5.08041e11			−1.07567			−0.537837	−	0.843049i	$-0.680758\pi$
$829$	−5.08041e11			−1.07567			−0.537837	+	0.843049i	$0.680758\pi$
$830$		0			0
$831$	2.18883e11	+	2.38984e11i	0.458995	+	0.501147i
$832$		0			0
$833$	1.54883e11			0.321679
$834$		0			0
$835$	4.01442e11	−	2.05630e11i	0.825803	−	0.423000i
$836$		0			0
$837$	−1.95121e11	−	2.54667e11i	−0.397560	−	0.518885i
$838$		0			0
$839$			5.88276e11i			1.18723i	0.804751	+	0.593613i	$0.202299\pi$
$839$			5.88276e11i			1.18723i	−0.804751	+	0.593613i	$0.797701\pi$
$840$		0			0
$841$	1.01414e11			0.202729
$842$		0			0
$843$	−5.07939e11	−	5.54586e11i	−1.00578	−	1.09814i
$844$		0			0
$845$	4.35369e11	−	2.23008e11i	0.853946	−	0.437416i
$846$		0			0
$847$			5.85722e11i			1.13804i
$848$		0			0
$849$	1.45314e11	+	1.58659e11i	0.279690	+	0.305376i
$850$		0			0
$851$			1.41880e12i			2.70523i
$852$		0			0
$853$			2.11606e10i			0.0399698i	0.999800	+	0.0199849i	$0.00636181\pi$
$853$			2.11606e10i			0.0399698i	−0.999800	+	0.0199849i	$0.993638\pi$
$854$		0			0
$855$	−3.69785e10	−	9.10888e10i	−0.0691967	−	0.170451i
$856$		0			0
$857$	8.17007e11			1.51462			0.757308	−	0.653058i	$-0.226514\pi$
$857$	8.17007e11			1.51462			0.757308	+	0.653058i	$0.226514\pi$
$858$		0			0
$859$	5.49220e11			1.00873			0.504364	−	0.863491i	$-0.331727\pi$
$859$	5.49220e11			1.00873			0.504364	+	0.863491i	$0.331727\pi$
$860$		0			0
$861$	−4.01218e11	+	3.67471e11i	−0.730075	+	0.668667i
$862$		0			0
$863$	1.06081e12			1.91247			0.956234	−	0.292604i	$-0.0945217\pi$
$863$	1.06081e12			1.91247			0.956234	+	0.292604i	$0.0945217\pi$
$864$		0			0
$865$	7.50225e11	−	3.84287e11i	1.34007	−	0.686422i
$866$		0			0
$867$	7.75253e10	−	7.10045e10i	0.137204	−	0.125664i
$868$		0			0
$869$			6.27896e9i			0.0110105i
$870$		0			0
$871$	1.43725e12			2.49723
$872$		0			0
$873$	6.28052e11	+	5.52520e10i	1.08128	+	0.0951243i
$874$		0			0
$875$	−6.59603e11	−	1.00127e11i	−1.12525	−	0.170811i
$876$		0			0
$877$			4.00990e11i			0.677852i	0.940813	+	0.338926i	$0.110064\pi$
$877$			4.00990e11i			0.677852i	−0.940813	+	0.338926i	$0.889936\pi$
$878$		0			0
$879$	−7.84889e11	+	7.18871e11i	−1.31478	+	1.20419i
$880$		0			0
$881$			1.61379e10i			0.0267883i	0.999910	+	0.0133941i	$0.00426361\pi$
$881$			1.61379e10i			0.0267883i	−0.999910	+	0.0133941i	$0.995736\pi$
$882$		0			0
$883$			2.73511e11i			0.449916i	0.974368	+	0.224958i	$0.0722245\pi$
$883$			2.73511e11i			0.449916i	−0.974368	+	0.224958i	$0.927776\pi$
$884$		0			0
$885$	−1.99008e11	−	7.39745e10i	−0.324412	−	0.120589i
$886$		0			0
$887$	5.67434e11			0.916687			0.458343	−	0.888775i	$-0.348443\pi$
$887$	5.67434e11			0.916687			0.458343	+	0.888775i	$0.348443\pi$
$888$		0			0
$889$	2.03230e11			0.325373
$890$		0			0
$891$	1.04449e9	−	5.89046e9i	0.00165728	−	0.00934627i
$892$		0			0
$893$	3.44005e10			0.0540952
$894$		0			0
$895$	−2.75921e11	−	5.38668e11i	−0.430025	−	0.839517i
$896$		0			0
$897$	−9.53292e11	−	1.04084e12i	−1.47250	−	1.60773i
$898$		0			0
$899$		−	3.81246e11i		−	0.583670i
$900$		0			0
$901$	3.37636e11			0.512329
$902$		0			0
$903$	−5.84491e11	+	5.35329e11i	−0.879077	+	0.805137i
$904$		0			0
$905$	−3.22297e11	+	1.65090e11i	−0.480465	+	0.246108i
$906$		0			0
$907$			6.34471e11i			0.937525i	0.883324	+	0.468762i	$0.155300\pi$
$907$			6.34471e11i			0.937525i	−0.883324	+	0.468762i	$0.844700\pi$
$908$		0			0
$909$	−2.40080e11	−	2.11207e10i	−0.351642	−	0.0309352i
$910$		0			0
$911$			2.98891e11i			0.433949i	0.976177	+	0.216975i	$0.0696189\pi$
$911$			2.98891e11i			0.433949i	−0.976177	+	0.216975i	$0.930381\pi$
$912$		0			0
$913$		−	8.83151e9i		−	0.0127102i
$914$		0			0
$915$	3.46325e11	−	9.31691e11i	0.494083	−	1.32919i
$916$		0			0
$917$	−7.86221e11			−1.11190
$918$		0			0
$919$	−5.56887e11			−0.780737			−0.390369	−	0.920659i	$-0.627652\pi$
$919$	−5.56887e11			−0.780737			−0.390369	+	0.920659i	$0.627652\pi$
$920$		0			0
$921$	5.86307e10	+	6.40151e10i	0.0814867	+	0.0889701i
$922$		0			0
$923$	1.48941e12			2.05214
$924$		0			0
$925$	1.03194e12	+	7.43011e11i	1.40958	+	1.01491i
$926$		0			0
$927$	−6.16748e11	−	5.42576e10i	−0.835197	−	0.0734754i
$928$		0			0
$929$			7.18845e10i			0.0965101i	0.998835	+	0.0482550i	$0.0153660\pi$
$929$			7.18845e10i			0.0965101i	−0.998835	+	0.0482550i	$0.984634\pi$
$930$		0			0
$931$	4.08222e10			0.0543372
$932$		0			0
$933$	6.03145e11	+	6.58536e11i	0.795967	+	0.869066i
$934$		0			0
$935$	3.60188e9	+	7.03177e9i	0.00471284	+	0.00920064i
$936$		0			0
$937$		−	1.88285e11i		−	0.244262i	−0.992514	−	0.122131i	$-0.961027\pi$
$937$		−	1.88285e11i		−	0.244262i	0.992514	−	0.122131i	$-0.0389729\pi$
$938$		0			0
$939$	1.29843e11	+	1.41767e11i	0.167016	+	0.182354i
$940$		0			0
$941$			1.83977e11i			0.234642i	0.993094	+	0.117321i	$0.0374306\pi$
$941$			1.83977e11i			0.234642i	−0.993094	+	0.117321i	$0.962569\pi$
$942$		0			0
$943$			1.07130e12i			1.35476i
$944$		0			0
$945$	−3.89594e11	+	8.19798e11i	−0.488523	+	1.02797i
$946$		0			0
$947$	6.05359e10			0.0752685			0.0376343	−	0.999292i	$-0.488018\pi$
$947$	6.05359e10			0.0752685			0.0376343	+	0.999292i	$0.488018\pi$
$948$		0			0
$949$	3.63322e11			0.447947
$950$		0			0
$951$	6.96196e11	−	6.37638e11i	0.851157	−	0.779565i
$952$		0			0
$953$	−7.22112e11			−0.875454			−0.437727	−	0.899108i	$-0.644216\pi$
$953$	−7.22112e11			−0.875454			−0.437727	+	0.899108i	$0.644216\pi$
$954$		0			0
$955$	−3.22920e11	−	6.30421e11i	−0.388223	−	0.757909i
$956$		0			0
$957$	5.24250e9	−	4.80154e9i	0.00625015	−	0.00572444i
$958$		0			0
$959$			1.54568e12i			1.82745i
$960$		0			0
$961$	−4.88455e11			−0.572705
$962$		0			0
$963$	−5.00071e10	+	5.68433e11i	−0.0581469	+	0.660958i
$964$		0			0
$965$	4.63871e11	+	9.05594e11i	0.534919	+	1.04430i
$966$		0			0
$967$			3.69045e11i			0.422059i	0.977480	+	0.211030i	$0.0676816\pi$
$967$			3.69045e11i			0.422059i	−0.977480	+	0.211030i	$0.932318\pi$
$968$		0			0
$969$	1.30257e11	−	1.19301e11i	0.147743	−	0.135316i
$970$		0			0
$971$			1.13835e12i			1.28056i	0.768143	+	0.640278i	$0.221181\pi$
$971$			1.13835e12i			1.28056i	−0.768143	+	0.640278i	$0.778819\pi$
$972$		0			0
$973$			1.16142e12i			1.29580i
$974$		0			0
$975$	−1.25627e12	+	1.48286e11i	−1.39015	+	0.164090i
$976$		0			0
$977$	−2.96676e11			−0.325615			−0.162807	−	0.986658i	$-0.552055\pi$
$977$	−2.96676e11			−0.325615			−0.162807	+	0.986658i	$0.552055\pi$
$978$		0			0
$979$	−4.56575e9			−0.00497029
$980$		0			0
$981$	1.37096e11	−	1.55837e12i	0.148029	−	1.68266i
$982$		0			0
$983$	−3.62593e11			−0.388334			−0.194167	−	0.980968i	$-0.562200\pi$
$983$	−3.62593e11			−0.388334			−0.194167	+	0.980968i	$0.562200\pi$
$984$		0			0
$985$	−2.95199e11	+	1.51209e11i	−0.313596	+	0.160633i
$986$		0			0
$987$	−2.14520e11	−	2.34220e11i	−0.226047	−	0.246806i
$988$		0			0
$989$			1.56066e12i			1.63126i
$990$		0			0
$991$	−6.08713e11			−0.631129			−0.315565	−	0.948904i	$-0.602194\pi$
$991$	−6.08713e11			−0.631129			−0.315565	+	0.948904i	$0.602194\pi$
$992$		0			0
$993$	1.94427e11	−	1.78073e11i	0.199967	−	0.183148i
$994$		0			0
$995$	−9.65438e11	+	4.94525e11i	−0.984991	+	0.504541i
$996$		0			0
$997$			3.95370e11i			0.400150i	0.979781	+	0.200075i	$0.0641186\pi$
$997$			3.95370e11i			0.400150i	−0.979781	+	0.200075i	$0.935881\pi$
$998$		0			0
$999$	1.37326e12	−	1.05217e12i	1.37877	−	1.05639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.9.c.e.209.11		16
3.2	odd	2	inner	240.9.c.e.209.5		16
4.3	odd	2		30.9.b.a.29.12	yes	16
5.4	even	2	inner	240.9.c.e.209.6		16
12.11	even	2		30.9.b.a.29.6	yes	16
15.14	odd	2	inner	240.9.c.e.209.12		16
20.3	even	4		150.9.d.e.101.2		16
20.7	even	4		150.9.d.e.101.15		16
20.19	odd	2		30.9.b.a.29.5	✓	16
60.23	odd	4		150.9.d.e.101.10		16
60.47	odd	4		150.9.d.e.101.7		16
60.59	even	2		30.9.b.a.29.11	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.9.b.a.29.5	✓	16	20.19	odd	2
30.9.b.a.29.6	yes	16	12.11	even	2
30.9.b.a.29.11	yes	16	60.59	even	2
30.9.b.a.29.12	yes	16	4.3	odd	2
150.9.d.e.101.2		16	20.3	even	4
150.9.d.e.101.7		16	60.47	odd	4
150.9.d.e.101.10		16	60.23	odd	4
150.9.d.e.101.15		16	20.7	even	4
240.9.c.e.209.5		16	3.2	odd	2	inner
240.9.c.e.209.6		16	5.4	even	2	inner
240.9.c.e.209.11		16	1.1	even	1	trivial
240.9.c.e.209.12		16	15.14	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(59.7326 - 54.7084i) q^{3} +(-556.269 + 284.937i) q^{5} +2732.68i q^{7} +(574.975 - 6535.76i) q^{9} +138.973i q^{11} -39979.9i q^{13} +(-17639.0 + 47452.7i) q^{15} -90959.5 q^{17} -23974.1 q^{19} +(149501. + 163230. i) q^{21} +435843. q^{23} +(228247. - 317004. i) q^{25} +(-323216. - 421854. i) q^{27} -631532. i q^{29} +603686. q^{31} +(7603.01 + 8301.24i) q^{33} +(-778644. - 1.52011e6i) q^{35} +3.25530e6i q^{37} +(-2.18724e6 - 2.38810e6i) q^{39} +2.45798e6i q^{41} +3.58077e6i q^{43} +(1.54244e6 + 3.79947e6i) q^{45} -1.43490e6 q^{47} -1.70276e6 q^{49} +(-5.43325e6 + 4.97625e6i) q^{51} -3.71194e6 q^{53} +(-39598.7 - 77306.6i) q^{55} +(-1.43203e6 + 1.31158e6i) q^{57} +4.19381e6i q^{59} -1.96341e7 q^{61} +(1.78602e7 + 1.57122e6i) q^{63} +(1.13918e7 + 2.22396e7i) q^{65} +3.59493e7i q^{67} +(2.60341e7 - 2.38443e7i) q^{69} +3.72539e7i q^{71} +9.08762e6i q^{73} +(-3.70902e6 - 3.14225e7i) q^{75} -379770. q^{77} +4.51811e7 q^{79} +(-4.23855e7 - 7.51579e6i) q^{81} -6.35482e7 q^{83} +(5.05980e7 - 2.59177e7i) q^{85} +(-3.45501e7 - 3.77230e7i) q^{87} +3.28534e7i q^{89} +1.09252e8 q^{91} +(3.60597e7 - 3.30267e7i) q^{93} +(1.33360e7 - 6.83110e6i) q^{95} +9.60947e7i q^{97} +(908296. + 79906.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 21928 q^{9} + 62920 q^{15} - 96048 q^{19} + 667112 q^{21} + 1292160 q^{25} + 5127152 q^{31} + 5420160 q^{39} - 8741480 q^{45} - 21439680 q^{49} - 3556688 q^{51} - 27329120 q^{55} + 67157264 q^{61}+ \cdots - 754526432 q^{99}+O(q^{100}) \) 16 * q + 21928 * q^9 + 62920 * q^15 - 96048 * q^19 + 667112 * q^21 + 1292160 * q^25 + 5127152 * q^31 + 5420160 * q^39 - 8741480 * q^45 - 21439680 * q^49 - 3556688 * q^51 - 27329120 * q^55 + 67157264 * q^61 + 97106152 * q^69 - 17107360 * q^75 + 296926128 * q^79 - 214283008 * q^81 + 190319120 * q^85 - 143834880 * q^91 - 754526432 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more