LMFDB - Embedded newform 1008.2.cc.b.545.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(209,1008)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1008.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.cc (of order $6$, degree $2$, not 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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
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} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			545.4
Root			$-0.0967785 - 1.72934i$ of defining polynomial
Character	$\chi$	$=$	1008.545
Dual form			1008.2.cc.b.209.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0967785 + 1.72934i) q^{3} +(0.183299 - 0.317483i) q^{5} +(0.624224 - 2.57106i) q^{7} +(-2.98127 - 0.334727i) q^{9} +O(q^{10})$	\(q+(-0.0967785 + 1.72934i) q^{3} +(0.183299 - 0.317483i) q^{5} +(0.624224 - 2.57106i) q^{7} +(-2.98127 - 0.334727i) q^{9} +(-0.579764 + 0.334727i) q^{11} +(0.867380 + 0.500782i) q^{13} +(0.531299 + 0.347713i) q^{15} +4.98906 q^{17} -6.35722i q^{19} +(4.38584 + 1.32832i) q^{21} +(6.66371 + 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(0.867380 - 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(5.47837 + 3.16294i) q^{31} +(-0.522749 - 1.03501i) q^{33} +(-0.701849 - 0.669453i) q^{35} -5.16789 q^{37} +(-0.949969 + 1.45154i) q^{39} +(2.15928 - 3.73998i) q^{41} +(-2.24922 - 3.89576i) q^{43} +(-0.652734 + 0.885148i) q^{45} +(4.16450 + 7.21313i) q^{47} +(-6.22069 - 3.20983i) q^{49} +(-0.482834 + 8.62781i) q^{51} +0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} +(4.36348 - 7.55776i) q^{59} +(4.29351 - 2.47886i) q^{61} +(-2.72158 + 7.45607i) q^{63} +(0.317980 - 0.183586i) q^{65} +(-5.44537 + 9.43166i) q^{67} +(-7.29820 + 11.1515i) q^{69} -5.49843i q^{71} -4.07314i q^{73} +(-7.52245 + 3.79936i) q^{75} +(0.498700 + 1.69955i) q^{77} +(4.17784 + 7.23623i) q^{79} +(8.77592 + 1.99582i) q^{81} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} +(1.42818 + 2.82769i) q^{87} -10.7113 q^{89} +(1.82898 - 1.91749i) q^{91} +(-6.00000 + 9.16789i) q^{93} +(-2.01831 - 1.16527i) q^{95} +(14.9093 - 8.60787i) q^{97} +(1.84047 - 0.803848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q - 2 * q^7 + 12 * q^9	$ 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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
$3$	−0.0967785	+	1.72934i	−0.0558751	+	0.998438i
$3$	−0.0967785	+	1.72934i	−0.0558751	+	0.998438i
$4$		0			0
$5$	0.183299	−	0.317483i	0.0819738	−	0.141983i	−0.822124	−	0.569309i	$-0.807211\pi$
$5$	0.183299	−	0.317483i	0.0819738	−	0.141983i	0.904098	+	0.427326i	$0.140544\pi$
$6$		0			0
$7$	0.624224	−	2.57106i	0.235935	−	0.971769i
$7$	0.624224	−	2.57106i	0.235935	−	0.971769i
$8$		0			0
$9$	−2.98127	−	0.334727i	−0.993756	−	0.111576i
$10$		0			0
$11$	−0.579764	+	0.334727i	−0.174805	+	0.100924i	−0.584850	−	0.811142i	$-0.698847\pi$
$11$	−0.579764	+	0.334727i	−0.174805	+	0.100924i	0.410044	+	0.912066i	$0.365513\pi$
$12$		0			0
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	0.615438	−	0.788185i	$-0.288979\pi$
$13$	0.867380	+	0.500782i	0.240568	+	0.138892i	−0.374870	+	0.927077i	$0.622313\pi$
$14$		0			0
$15$	0.531299	+	0.347713i	0.137181	+	0.0897791i
$16$		0			0
$17$	4.98906			1.21003			0.605013	−	0.796216i	$-0.293168\pi$
$17$	4.98906			1.21003			0.605013	+	0.796216i	$0.293168\pi$
$18$		0			0
$19$		−	6.35722i		−	1.45845i	−0.684275	−	0.729224i	$-0.739881\pi$
$19$		−	6.35722i		−	1.45845i	0.684275	−	0.729224i	$-0.260119\pi$
$20$		0			0
$21$	4.38584	+	1.32832i	0.957068	+	0.289864i
$22$		0			0
$23$	6.66371	+	3.84729i	1.38948	+	0.802216i	0.993256	−	0.115938i	$-0.0369875\pi$
$23$	6.66371	+	3.84729i	1.38948	+	0.802216i	0.396223	+	0.918154i	$0.370321\pi$
$24$		0			0
$25$	2.43280	+	4.21374i	0.486561	+	0.842748i
$26$		0			0
$27$	0.867380	−	5.12325i	0.166927	−	0.985969i
$28$		0			0
$29$	1.58394	−	0.914490i	0.294131	−	0.169817i	−0.345672	−	0.938355i	$-0.612349\pi$
$29$	1.58394	−	0.914490i	0.294131	−	0.169817i	0.639803	+	0.768539i	$0.279016\pi$
$30$		0			0
$31$	5.47837	+	3.16294i	0.983944	+	0.568081i	0.903459	−	0.428675i	$-0.141020\pi$
$31$	5.47837	+	3.16294i	0.983944	+	0.568081i	0.0804857	+	0.996756i	$0.474353\pi$
$32$		0			0
$33$	−0.522749	−	1.03501i	−0.0909990	−	0.180171i
$34$		0			0
$35$	−0.701849	−	0.669453i	−0.118634	−	0.113158i
$36$		0			0
$37$	−5.16789			−0.849595			−0.424798	−	0.905288i	$-0.639655\pi$
$37$	−5.16789			−0.849595			−0.424798	+	0.905288i	$0.639655\pi$
$38$		0			0
$39$	−0.949969	+	1.45154i	−0.152117	+	0.232432i
$40$		0			0
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	−0.646686	−	0.762756i	$-0.723846\pi$
$41$	2.15928	−	3.73998i	0.337223	−	0.584087i	0.983909	+	0.178669i	$0.0571790\pi$
$42$		0			0
$43$	−2.24922	−	3.89576i	−0.343002	−	0.594098i	0.641986	−	0.766716i	$-0.278111\pi$
$43$	−2.24922	−	3.89576i	−0.343002	−	0.594098i	−0.984989	+	0.172618i	$0.944777\pi$
$44$		0			0
$45$	−0.652734	+	0.885148i	−0.0973038	+	0.131950i
$46$		0			0
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	0.991658	+	0.128895i	$0.0411429\pi$
$47$	4.16450	+	7.21313i	0.607455	+	1.05214i	−0.384203	+	0.923249i	$0.625524\pi$
$48$		0			0
$49$	−6.22069	−	3.20983i	−0.888670	−	0.458548i
$50$		0			0
$51$	−0.482834	+	8.62781i	−0.0676102	+	1.20813i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			0.245420i			0.0330925i
$56$		0			0
$57$	10.9938	+	0.615242i	1.45617	+	0.0814909i
$58$		0			0
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	−0.428680	−	0.903456i	$-0.641021\pi$
$59$	4.36348	−	7.55776i	0.568076	−	0.983937i	0.996756	−	0.0804804i	$-0.0256455\pi$
$60$		0			0
$61$	4.29351	−	2.47886i	0.549727	−	0.317385i	−0.199285	−	0.979942i	$-0.563862\pi$
$61$	4.29351	−	2.47886i	0.549727	−	0.317385i	0.749012	+	0.662556i	$0.230529\pi$
$62$		0			0
$63$	−2.72158	+	7.45607i	−0.342887	+	0.939377i
$64$		0			0
$65$	0.317980	−	0.183586i	0.0394406	−	0.0227710i
$66$		0			0
$67$	−5.44537	+	9.43166i	−0.665258	+	1.15226i	0.313958	+	0.949437i	$0.398345\pi$
$67$	−5.44537	+	9.43166i	−0.665258	+	1.15226i	−0.979215	+	0.202823i	$0.934988\pi$
$68$		0			0
$69$	−7.29820	+	11.1515i	−0.878600	+	1.34248i
$70$		0			0
$71$		−	5.49843i		−	0.652544i	−0.945276	−	0.326272i	$-0.894207\pi$
$71$		−	5.49843i		−	0.652544i	0.945276	−	0.326272i	$-0.105793\pi$
$72$		0			0
$73$		−	4.07314i		−	0.476725i	−0.971176	−	0.238363i	$-0.923389\pi$
$73$		−	4.07314i		−	0.476725i	0.971176	−	0.238363i	$-0.0766106\pi$
$74$		0			0
$75$	−7.52245	+	3.79936i	−0.868618	+	0.438712i
$76$		0			0
$77$	0.498700	+	1.69955i	0.0568321	+	0.193682i
$78$		0			0
$79$	4.17784	+	7.23623i	0.470044	+	0.814140i	0.999413	−	0.0342518i	$-0.0109048\pi$
$79$	4.17784	+	7.23623i	0.470044	+	0.814140i	−0.529370	+	0.848391i	$0.677571\pi$
$80$		0			0
$81$	8.77592	+	1.99582i	0.975102	+	0.221758i
$82$		0			0
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.776798	+	0.629750i	$0.216842\pi$
$83$	8.50712	+	14.7348i	0.933778	+	1.61735i	0.156980	+	0.987602i	$0.449824\pi$
$84$		0			0
$85$	0.914490	−	1.58394i	0.0991904	−	0.171803i
$86$		0			0
$87$	1.42818	+	2.82769i	0.153117	+	0.303160i
$88$		0			0
$89$	−10.7113			−1.13540			−0.567699	−	0.823236i	$-0.692166\pi$
$89$	−10.7113			−1.13540			−0.567699	+	0.823236i	$0.692166\pi$
$90$		0			0
$91$	1.82898	−	1.91749i	0.191729	−	0.201007i
$92$		0			0
$93$	−6.00000	+	9.16789i	−0.622171	+	0.950666i
$94$		0			0
$95$	−2.01831	−	1.16527i	−0.207074	−	0.119555i
$96$		0			0
$97$	14.9093	−	8.60787i	1.51381	−	0.873997i	0.513937	−	0.857828i	$-0.328186\pi$
$97$	14.9093	−	8.60787i	1.51381	−	0.873997i	0.999869	−	0.0161687i	$-0.00514689\pi$
$98$		0			0
$99$	1.84047	−	0.803848i	0.184974	−	0.0807897i
$100$		0			0
$101$	7.86586	+	13.6241i	0.782683	+	1.35565i	0.930374	+	0.366613i	$0.119483\pi$
$101$	7.86586	+	13.6241i	0.782683	+	1.35565i	−0.147691	+	0.989034i	$0.547184\pi$
$102$		0			0
$103$	−9.91124	−	5.72226i	−0.976584	−	0.563831i	−0.0753467	−	0.997157i	$-0.524006\pi$
$103$	−9.91124	−	5.72226i	−0.976584	−	0.563831i	−0.901237	+	0.433327i	$0.857340\pi$
$104$		0			0
$105$	1.22564	−	1.14895i	0.119610	−	0.112126i
$106$		0			0
$107$		−	11.0618i		−	1.06938i	−0.845048	−	0.534690i	$-0.820428\pi$
$107$		−	11.0618i		−	1.06938i	0.845048	−	0.534690i	$-0.179572\pi$
$108$		0			0
$109$	−10.5633			−1.01178			−0.505891	−	0.862597i	$-0.668836\pi$
$109$	−10.5633			−1.01178			−0.505891	+	0.862597i	$0.668836\pi$
$110$		0			0
$111$	0.500140	−	8.93706i	0.0474712	−	0.848268i
$112$		0			0
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	0.659773	−	0.751465i	$-0.270652\pi$
$113$	3.60226	+	2.07976i	0.338872	+	0.195648i	−0.320901	+	0.947113i	$0.603986\pi$
$114$		0			0
$115$	2.44290	−	1.41041i	0.227802	−	0.131521i
$116$		0			0
$117$	−2.41827	−	1.78330i	−0.223569	−	0.164866i
$118$		0			0
$119$	3.11429	−	12.8272i	0.285487	−	1.17586i
$120$		0			0
$121$	−5.27592	+	9.13815i	−0.479629	+	0.830741i
$122$		0			0
$123$	6.25875	+	4.09609i	0.564332	+	0.369332i
$124$		0			0
$125$	3.61671			0.323489
$126$		0			0
$127$	1.66945			0.148140			0.0740700	−	0.997253i	$-0.476401\pi$
$127$	1.66945			0.148140			0.0740700	+	0.997253i	$0.476401\pi$
$128$		0			0
$129$	6.95479	−	3.51265i	0.612335	−	0.309271i
$130$		0			0
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	−0.402923	−	0.915234i	$-0.632006\pi$
$131$	6.76607	−	11.7192i	0.591154	−	1.02391i	0.994077	−	0.108675i	$-0.0346609\pi$
$132$		0			0
$133$	−16.3448	−	3.96833i	−1.41727	−	0.344098i
$134$		0			0
$135$	−1.46755	−	1.21446i	−0.126307	−	0.104525i
$136$		0			0
$137$	7.78428	−	4.49425i	0.665056	−	0.383970i	−0.129145	−	0.991626i	$-0.541223\pi$
$137$	7.78428	−	4.49425i	0.665056	−	0.383970i	0.794201	+	0.607656i	$0.207890\pi$
$138$		0			0
$139$	−8.05336	−	4.64961i	−0.683077	−	0.394375i	0.117936	−	0.993021i	$-0.462372\pi$
$139$	−8.05336	−	4.64961i	−0.683077	−	0.394375i	−0.801014	+	0.598646i	$0.795706\pi$
$140$		0			0
$141$	−12.8770	+	6.50379i	−1.08444	+	0.547718i
$142$		0			0
$143$	−0.670501			−0.0560701
$144$		0			0
$145$		−	0.670501i		−	0.0556821i
$146$		0			0
$147$	6.15294	−	10.4471i	0.507486	−	0.861660i
$148$		0			0
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	0.396158	−	0.918182i	$-0.370343\pi$
$149$	−2.45268	−	1.41606i	−0.200931	−	0.116008i	−0.597090	+	0.802174i	$0.703676\pi$
$150$		0			0
$151$	−8.27592	−	14.3343i	−0.673484	−	1.16651i	−0.976909	−	0.213654i	$-0.931463\pi$
$151$	−8.27592	−	14.3343i	−0.673484	−	1.16651i	0.303425	−	0.952855i	$-0.401870\pi$
$152$		0			0
$153$	−14.8737	−	1.66997i	−1.20247	−	0.135009i
$154$		0			0
$155$	2.00836	−	1.15953i	0.161315	−	0.0931355i
$156$		0			0
$157$	−2.45480	−	1.41728i	−0.195914	−	0.113111i	0.398834	−	0.917023i	$-0.369415\pi$
$157$	−2.45480	−	1.41728i	−0.195914	−	0.113111i	−0.594748	+	0.803912i	$0.702748\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	14.0513	−	14.7312i	1.10739	−	1.16098i
$162$		0			0
$163$	−24.7281			−1.93685			−0.968426	−	0.249300i	$-0.919800\pi$
$163$	−24.7281			−1.93685			−0.968426	+	0.249300i	$0.919800\pi$
$164$		0			0
$165$	−0.424416	−	0.0237514i	−0.0330408	−	0.00184904i
$166$		0			0
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	0.199874	+	0.979822i	$0.435947\pi$
$167$	−9.67422	+	16.7562i	−0.748614	+	1.29664i	−0.948487	+	0.316815i	$0.897386\pi$
$168$		0			0
$169$	−5.99843	−	10.3896i	−0.461418	−	0.799199i
$170$		0			0
$171$	−2.12793	+	18.9526i	−0.162727	+	1.44934i
$172$		0			0
$173$	2.41827	+	4.18856i	0.183858	+	0.318451i	0.943191	−	0.332251i	$-0.107808\pi$
$173$	2.41827	+	4.18856i	0.183858	+	0.318451i	−0.759333	+	0.650702i	$0.774475\pi$
$174$		0			0
$175$	12.3524	−	3.62456i	0.933752	−	0.273991i
$176$		0			0
$177$	12.6477	+	8.27738i	0.950658	+	0.622166i
$178$		0			0
$179$		−	3.65796i		−	0.273409i	−0.990612	−	0.136704i	$-0.956349\pi$
$179$		−	3.65796i		−	0.273409i	0.990612	−	0.136704i	$-0.0436511\pi$
$180$		0			0
$181$		−	5.66796i		−	0.421296i	−0.977562	−	0.210648i	$-0.932443\pi$
$181$		−	5.66796i		−	0.421296i	0.977562	−	0.210648i	$-0.0675574\pi$
$182$		0			0
$183$	3.87128	+	7.66485i	0.286173	+	0.566602i
$184$		0			0
$185$	−0.947269	+	1.64072i	−0.0696446	+	0.120628i
$186$		0			0
$187$	−2.89248	+	1.66997i	−0.211519	+	0.122120i
$188$		0			0
$189$	−12.6307	−	5.42814i	−0.918750	−	0.394839i
$190$		0			0
$191$	−23.7098	+	13.6888i	−1.71558	+	0.990490i	−0.788996	+	0.614398i	$0.789399\pi$
$191$	−23.7098	+	13.6888i	−1.71558	+	0.990490i	−0.926583	+	0.376091i	$0.877268\pi$
$192$		0			0
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	−0.627188	−	0.778868i	$-0.715794\pi$
$193$	5.01413	−	8.68473i	0.360925	−	0.625141i	0.988113	+	0.153727i	$0.0491276\pi$
$194$		0			0
$195$	0.286710	+	0.567664i	0.0205317	+	0.0406513i
$196$		0			0
$197$		−	18.8258i		−	1.34129i	−0.741780	−	0.670643i	$-0.766018\pi$
$197$		−	18.8258i		−	1.34129i	0.741780	−	0.670643i	$-0.233982\pi$
$198$		0			0
$199$		−	5.36406i		−	0.380248i	−0.981760	−	0.190124i	$-0.939111\pi$
$199$		−	5.36406i		−	0.380248i	0.981760	−	0.190124i	$-0.0608890\pi$
$200$		0			0
$201$	−15.7836	−	10.3297i	−1.11329	−	0.728601i
$202$		0			0
$203$	−1.36247	−	4.64326i	−0.0956268	−	0.325893i
$204$		0			0
$205$	−0.791588	−	1.37107i	−0.0552869	−	0.0957597i
$206$		0			0
$207$	−18.5785	−	13.7003i	−1.29130	−	0.952239i
$208$		0			0
$209$	2.12793	+	3.68569i	0.147192	+	0.254944i
$210$		0			0
$211$	0.828981	−	1.43584i	0.0570694	−	0.0988471i	−0.836079	−	0.548609i	$-0.815158\pi$
$211$	0.828981	−	1.43584i	0.0570694	−	0.0988471i	0.893149	+	0.449762i	$0.148491\pi$
$212$		0			0
$213$	9.50869	+	0.532130i	0.651525	+	0.0364609i
$214$		0			0
$215$	−1.64912			−0.112469
$216$		0			0
$217$	11.5518	−	12.1108i	0.784189	−	0.822137i
$218$		0			0
$219$	7.04387	+	0.394192i	0.475980	+	0.0266370i
$220$		0			0
$221$	4.32741	+	2.49843i	0.291093	+	0.168063i
$222$		0			0
$223$	14.7546	−	8.51860i	0.988044	−	0.570448i	0.0833551	−	0.996520i	$-0.473436\pi$
$223$	14.7546	−	8.51860i	0.988044	−	0.570448i	0.904689	+	0.426072i	$0.140103\pi$
$224$		0			0
$225$	−5.84239	−	13.3766i	−0.389492	−	0.891774i
$226$		0			0
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	0.938276	−	0.345889i	$-0.112423\pi$
$227$	2.55512	+	4.42560i	0.169589	+	0.293737i	−0.768686	+	0.639626i	$0.779089\pi$
$228$		0			0
$229$	13.2215	+	7.63345i	0.873703	+	0.504433i	0.868577	−	0.495554i	$-0.165035\pi$
$229$	13.2215	+	7.63345i	0.873703	+	0.504433i	0.00512595	+	0.999987i	$0.498368\pi$
$230$		0			0
$231$	−2.98737	+	0.697944i	−0.196555	+	0.0459213i
$232$		0			0
$233$			10.1930i			0.667767i	0.942614	+	0.333883i	$0.108359\pi$
$233$			10.1930i			0.667767i	−0.942614	+	0.333883i	$0.891641\pi$
$234$		0			0
$235$	3.05340			0.199182
$236$		0			0
$237$	−12.9183	+	6.52461i	−0.839131	+	0.423819i
$238$		0			0
$239$	16.6117	+	9.59076i	1.07452	+	0.620375i	0.929413	−	0.369041i	$-0.120314\pi$
$239$	16.6117	+	9.59076i	1.07452	+	0.620375i	0.145108	+	0.989416i	$0.453647\pi$
$240$		0			0
$241$	−17.9140	+	10.3426i	−1.15394	+	0.666227i	−0.949844	−	0.312724i	$-0.898759\pi$
$241$	−17.9140	+	10.3426i	−1.15394	+	0.666227i	−0.204095	+	0.978951i	$0.565425\pi$
$242$		0			0
$243$	−4.30078	+	14.9834i	−0.275895	+	0.961188i
$244$		0			0
$245$	−2.15931	+	1.38661i	−0.137954	+	0.0885869i
$246$		0			0
$247$	3.18359	−	5.51413i	0.202567	−	0.350856i
$248$		0			0
$249$	−26.3048	+	13.2857i	−1.66700	+	0.841950i
$250$		0			0
$251$	−1.81200			−0.114373			−0.0571864	−	0.998364i	$-0.518213\pi$
$251$	−1.81200			−0.114373			−0.0571864	+	0.998364i	$0.518213\pi$
$252$		0			0
$253$	−5.15117			−0.323851
$254$		0			0
$255$	2.65068	+	1.73476i	0.165992	+	0.108635i
$256$		0			0
$257$	−3.22773	+	5.59059i	−0.201340	+	0.348731i	−0.948960	−	0.315395i	$-0.897863\pi$
$257$	−3.22773	+	5.59059i	−0.201340	+	0.348731i	0.747620	+	0.664126i	$0.231196\pi$
$258$		0			0
$259$	−3.22592	+	13.2869i	−0.200449	+	0.825611i
$260$		0			0
$261$	−5.02826	+	2.19615i	−0.311242	+	0.135938i
$262$		0			0
$263$	7.63888	−	4.41031i	0.471034	−	0.271951i	−0.245639	−	0.969361i	$-0.578998\pi$
$263$	7.63888	−	4.41031i	0.471034	−	0.271951i	0.716672	+	0.697410i	$0.245664\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.03663	−	18.5236i	0.0634404	−	1.13362i
$268$		0			0
$269$	−14.2653			−0.869773			−0.434886	−	0.900485i	$-0.643212\pi$
$269$	−14.2653			−0.869773			−0.434886	+	0.900485i	$0.643212\pi$
$270$		0			0
$271$			3.05281i			0.185445i	0.995692	+	0.0927226i	$0.0295570\pi$
$271$			3.05281i			0.185445i	−0.995692	+	0.0927226i	$0.970443\pi$
$272$		0			0
$273$	3.13899	+	3.34851i	0.189980	+	0.202661i
$274$		0			0
$275$	−2.82090	−	1.62865i	−0.170107	−	0.0982112i
$276$		0			0
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	0.846388	−	0.532567i	$-0.178773\pi$
$277$	−0.632828	−	1.09609i	−0.0380230	−	0.0658577i	−0.884411	+	0.466710i	$0.845439\pi$
$278$		0			0
$279$	−15.2738	−	11.2633i	−0.914417	−	0.674318i
$280$		0			0
$281$	9.11639	−	5.26335i	0.543838	−	0.313985i	−0.202795	−	0.979221i	$-0.565002\pi$
$281$	9.11639	−	5.26335i	0.543838	−	0.313985i	0.746633	+	0.665236i	$0.231669\pi$
$282$		0			0
$283$	−17.2094	−	9.93588i	−1.02300	−	0.590627i	−0.108025	−	0.994148i	$-0.534453\pi$
$283$	−17.2094	−	9.93588i	−1.02300	−	0.590627i	−0.914970	+	0.403522i	$0.867786\pi$
$284$		0			0
$285$	2.21049	−	3.37759i	0.130938	−	0.200071i
$286$		0			0
$287$	−8.26784	−	7.88623i	−0.488035	−	0.465509i
$288$		0			0
$289$	7.89074			0.464161
$290$		0			0
$291$	13.4431	+	26.6163i	0.788047	+	1.56028i
$292$		0			0
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	−0.992683	−	0.120747i	$-0.961471\pi$
$293$	−6.70606	+	11.6152i	−0.391772	+	0.678569i	0.600911	+	0.799316i	$0.294804\pi$
$294$		0			0
$295$	−1.59964	−	2.77066i	−0.0931348	−	0.161314i
$296$		0			0
$297$	1.21201	+	3.26061i	0.0703280	+	0.189200i
$298$		0			0
$299$	3.85331	+	6.67413i	0.222843	+	0.385975i
$300$		0			0
$301$	−11.4202	+	3.35104i	−0.658252	+	0.193151i
$302$		0			0
$303$	−24.3220	+	12.2843i	−1.39726	+	0.705713i
$304$		0			0
$305$		−	1.81749i		−	0.104069i
$306$		0			0
$307$			0.653728i			0.0373102i	0.999826	+	0.0186551i	$0.00593845\pi$
$307$			0.653728i			0.0373102i	−0.999826	+	0.0186551i	$0.994062\pi$
$308$		0			0
$309$	10.8550	−	16.5862i	0.617517	−	0.943554i
$310$		0			0
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	−0.704688	−	0.709517i	$-0.748913\pi$
$311$	4.62246	−	8.00634i	0.262116	−	0.453998i	0.966804	+	0.255519i	$0.0822464\pi$
$312$		0			0
$313$	5.33830	−	3.08207i	0.301739	−	0.174209i	−0.341485	−	0.939887i	$-0.610930\pi$
$313$	5.33830	−	3.08207i	0.301739	−	0.174209i	0.643224	+	0.765678i	$0.277597\pi$
$314$		0			0
$315$	1.86831	+	2.23075i	0.105268	+	0.125688i
$316$		0			0
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.909626	−	0.415428i	$-0.863632\pi$
$317$	−17.8876	+	10.3274i	−1.00467	+	0.580045i	−0.0950420	+	0.995473i	$0.530299\pi$
$318$		0			0
$319$	−0.612209	+	1.06038i	−0.0342771	+	0.0593697i
$320$		0			0
$321$	19.1296	+	1.07054i	1.06771	+	0.0597517i
$322$		0			0
$323$		−	31.7166i		−	1.76476i
$324$		0			0
$325$			4.87322i			0.270318i
$326$		0			0
$327$	1.02230	−	18.2676i	0.0565334	−	1.01020i
$328$		0			0
$329$	21.1450	−	6.20457i	1.16576	−	0.342069i
$330$		0			0
$331$	5.35568	+	9.27631i	0.294375	+	0.509872i	0.974839	−	0.222909i	$-0.0715553\pi$
$331$	5.35568	+	9.27631i	0.294375	+	0.509872i	−0.680464	+	0.732781i	$0.738222\pi$
$332$		0			0
$333$	15.4069	+	1.72983i	0.844291	+	0.0947941i
$334$		0			0
$335$	1.99626	+	3.45763i	0.109067	+	0.188910i
$336$		0			0
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	−0.744664	−	0.667439i	$-0.767390\pi$
$337$	3.77592	−	6.54008i	0.205687	−	0.356261i	0.950351	+	0.311179i	$0.100724\pi$
$338$		0			0
$339$	−3.94525	+	6.02827i	−0.214277	+	0.327411i
$340$		0			0
$341$	−4.23488			−0.229332
$342$		0			0
$343$	−12.1358	+	13.9901i	−0.655270	+	0.755394i
$344$		0			0
$345$	2.20267	+	4.36112i	0.118588	+	0.234795i
$346$		0			0
$347$	9.46737	+	5.46599i	0.508235	+	0.293430i	0.732108	−	0.681189i	$-0.238537\pi$
$347$	9.46737	+	5.46599i	0.508235	+	0.293430i	−0.223873	+	0.974618i	$0.571870\pi$
$348$		0			0
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	−0.527199	−	0.849742i	$-0.676758\pi$
$349$	−1.02562	+	0.592145i	−0.0549004	+	0.0316968i	0.472299	+	0.881439i	$0.343424\pi$
$350$		0			0
$351$	3.31798	−	4.00943i	0.177101	−	0.214008i
$352$		0			0
$353$	−16.7912	−	29.0832i	−0.893706	−	1.54794i	−0.835398	−	0.549646i	$-0.814763\pi$
$353$	−16.7912	−	29.0832i	−0.893706	−	1.54794i	−0.0583086	−	0.998299i	$-0.518571\pi$
$354$		0			0
$355$	−1.74566	−	1.00786i	−0.0926501	−	0.0534915i
$356$		0			0
$357$	21.8812	+	6.62708i	1.15808	+	0.350742i
$358$		0			0
$359$			10.1281i			0.534542i	0.963621	+	0.267271i	$0.0861219\pi$
$359$			10.1281i			0.534542i	−0.963621	+	0.267271i	$0.913878\pi$
$360$		0			0
$361$	−21.4143			−1.12707
$362$		0			0
$363$	−15.2924	−	10.0083i	−0.802644	−	0.525297i
$364$		0			0
$365$	−1.29315	−	0.746603i	−0.0676868	−	0.0390790i
$366$		0			0
$367$	−15.5903	+	9.00104i	−0.813805	+	0.469850i	−0.848275	−	0.529555i	$-0.822359\pi$
$367$	−15.5903	+	9.00104i	−0.813805	+	0.469850i	0.0344706	+	0.999406i	$0.489025\pi$
$368$		0			0
$369$	−7.68927	+	10.4271i	−0.400287	+	0.542814i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	−0.996403	−	0.0847411i	$-0.972994\pi$
$373$	−8.20451	+	14.2106i	−0.424814	+	0.735799i	0.571589	+	0.820540i	$0.306327\pi$
$374$		0			0
$375$	−0.350020	+	6.25454i	−0.0180749	+	0.322983i
$376$		0			0
$377$	1.83184			0.0943447
$378$		0			0
$379$	2.91372			0.149668			0.0748339	−	0.997196i	$-0.476157\pi$
$379$	2.91372			0.149668			0.0748339	+	0.997196i	$0.476157\pi$
$380$		0			0
$381$	−0.161567	+	2.88706i	−0.00827734	+	0.147909i
$382$		0			0
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	−0.954523	−	0.298138i	$-0.903634\pi$
$383$	−4.28721	+	7.42567i	−0.219066	+	0.379434i	0.735456	+	0.677572i	$0.236968\pi$
$384$		0			0
$385$	0.630990	+	0.153197i	0.0321582	+	0.00780766i
$386$		0			0
$387$	5.40150	+	12.3672i	0.274574	+	0.628659i
$388$		0			0
$389$	−30.7906	+	17.7770i	−1.56115	+	0.901328i	−0.564004	+	0.825772i	$0.690740\pi$
$389$	−30.7906	+	17.7770i	−1.56115	+	0.901328i	−0.997142	+	0.0755559i	$0.975927\pi$
$390$		0			0
$391$	33.2456	+	19.1944i	1.68130	+	0.970702i
$392$		0			0
$393$	19.6117	+	12.8350i	0.989279	+	0.647442i
$394$		0			0
$395$	3.06318			0.154125
$396$		0			0
$397$			3.58034i			0.179692i	0.995956	+	0.0898460i	$0.0286375\pi$
$397$			3.58034i			0.179692i	−0.995956	+	0.0898460i	$0.971363\pi$
$398$		0			0
$399$	8.44444	−	27.8817i	0.422751	−	1.39583i
$400$		0			0
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	0.504122	−	0.863633i	$-0.331816\pi$
$401$	0.165300	+	0.0954357i	0.00825467	+	0.00476583i	−0.495867	+	0.868398i	$0.665150\pi$
$402$		0			0
$403$	3.16789	+	5.48694i	0.157804	+	0.273324i
$404$		0			0
$405$	2.24226	−	2.42037i	0.111419	−	0.120269i
$406$		0			0
$407$	2.99615	−	1.72983i	0.148514	−	0.0857445i
$408$		0			0
$409$	3.00832	+	1.73685i	0.148752	+	0.0858819i	0.572529	−	0.819885i	$-0.305963\pi$
$409$	3.00832	+	1.73685i	0.148752	+	0.0858819i	−0.423777	+	0.905767i	$0.639296\pi$
$410$		0			0
$411$	7.01877	+	13.8966i	0.346210	+	0.685471i
$412$		0			0
$413$	−16.7077	−	15.9365i	−0.822130	−	0.784183i
$414$		0			0
$415$	6.23739			0.306182
$416$		0			0
$417$	8.82017	−	13.4771i	0.431926	−	0.659975i
$418$		0			0
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	−0.848318	−	0.529487i	$-0.822384\pi$
$419$	0.703955	−	1.21929i	0.0343905	−	0.0595660i	0.882708	+	0.469921i	$0.155718\pi$
$420$		0			0
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	0.952285	+	0.305211i	$0.0987268\pi$
$421$	15.1930	+	26.3151i	0.740463	+	1.28252i	−0.211822	+	0.977308i	$0.567940\pi$
$422$		0			0
$423$	−10.0011	−	22.8982i	−0.486269	−	1.11335i
$424$		0			0
$425$	12.1374	+	21.0226i	0.588751	+	1.01975i
$426$		0			0
$427$	−3.69318	−	12.5862i	−0.178725	−	0.609090i
$428$		0			0
$429$	0.0648900	−	1.15953i	0.00313292	−	0.0559825i
$430$		0			0
$431$			27.2747i			1.31378i	0.753988	+	0.656888i	$0.228127\pi$
$431$			27.2747i			1.31378i	−0.753988	+	0.656888i	$0.771873\pi$
$432$		0			0
$433$		−	8.15047i		−	0.391686i	−0.980635	−	0.195843i	$-0.937256\pi$
$433$		−	8.15047i		−	0.391686i	0.980635	−	0.195843i	$-0.0627444\pi$
$434$		0			0
$435$	1.15953	+	0.0648900i	0.0555951	+	0.00311124i
$436$		0			0
$437$	24.4581	−	42.3627i	1.16999	−	2.02648i
$438$		0			0
$439$	10.6005	−	6.12020i	0.505934	−	0.292101i	−0.225226	−	0.974306i	$-0.572312\pi$
$439$	10.6005	−	6.12020i	0.505934	−	0.292101i	0.731161	+	0.682205i	$0.238979\pi$
$440$		0			0
$441$	17.4711	+	11.6516i	0.831958	+	0.554838i
$442$		0			0
$443$	−6.93544	+	4.00418i	−0.329513	+	0.190244i	−0.655625	−	0.755087i	$-0.727595\pi$
$443$	−6.93544	+	4.00418i	−0.329513	+	0.190244i	0.326112	+	0.945331i	$0.394261\pi$
$444$		0			0
$445$	−1.96337	+	3.40067i	−0.0930729	+	0.161207i
$446$		0			0
$447$	2.68622	−	4.10449i	0.127054	−	0.194136i
$448$		0			0
$449$			14.5183i			0.685163i	0.939488	+	0.342581i	$0.111301\pi$
$449$			14.5183i			0.685163i	−0.939488	+	0.342581i	$0.888699\pi$
$450$		0			0
$451$			2.89108i			0.136135i
$452$		0			0
$453$	25.5899	−	12.9247i	1.20232	−	0.607254i
$454$		0			0
$455$	−0.273519	−	0.932144i	−0.0128228	−	0.0436996i
$456$		0			0
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	0.725804	−	0.687901i	$-0.241468\pi$
$457$	−4.97751	−	8.62130i	−0.232838	−	0.403287i	−0.958642	+	0.284614i	$0.908135\pi$
$458$		0			0
$459$	4.32741	−	25.5602i	0.201986	−	1.19305i
$460$		0			0
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	0.946456	+	0.322834i	$0.104636\pi$
$461$	16.1635	+	27.9960i	0.752810	+	1.30391i	−0.193645	+	0.981072i	$0.562031\pi$
$462$		0			0
$463$	4.72516	−	8.18421i	0.219597	−	0.380353i	−0.735088	−	0.677972i	$-0.762859\pi$
$463$	4.72516	−	8.18421i	0.219597	−	0.380353i	0.954685	+	0.297619i	$0.0961925\pi$
$464$		0			0
$465$	1.81086	+	3.58536i	0.0839765	+	0.166267i
$466$		0			0
$467$	20.6623			0.956138			0.478069	−	0.878322i	$-0.341337\pi$
$467$	20.6623			0.956138			0.478069	+	0.878322i	$0.341337\pi$
$468$		0			0
$469$	20.8502	+	19.8878i	0.962773	+	0.918335i
$470$		0			0
$471$	2.68853	−	4.10803i	0.123881	−	0.189288i
$472$		0			0
$473$	2.60803	+	1.50575i	0.119917	+	0.0692343i
$474$		0			0
$475$	26.7877	−	15.4659i	1.22910	−	0.709623i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	0.726304	−	0.687373i	$-0.241236\pi$
$479$	−5.08042	−	8.79955i	−0.232131	−	0.402062i	−0.958435	+	0.285311i	$0.907903\pi$
$480$		0			0
$481$	−4.48252	−	2.58799i	−0.204386	−	0.118002i
$482$		0			0
$483$	24.1155	+	25.7251i	1.09729	+	1.17053i
$484$		0			0
$485$		−	6.31126i		−	0.286579i
$486$		0			0
$487$	31.2296			1.41515			0.707575	−	0.706638i	$-0.249789\pi$
$487$	31.2296			1.41515			0.707575	+	0.706638i	$0.249789\pi$
$488$		0			0
$489$	2.39315	−	42.7634i	0.108222	−	1.93383i
$490$		0			0
$491$	−17.8314	−	10.2950i	−0.804720	−	0.464605i	0.0403987	−	0.999184i	$-0.487137\pi$
$491$	−17.8314	−	10.2950i	−0.804720	−	0.464605i	−0.845119	+	0.534578i	$0.820471\pi$
$492$		0			0
$493$	7.90239	−	4.56245i	0.355906	−	0.205482i
$494$		0			0
$495$	0.0821487	−	0.731664i	0.00369231	−	0.0328858i
$496$		0			0
$497$	−14.1368	−	3.43226i	−0.634122	−	0.153958i
$498$		0			0
$499$	−12.5766	+	21.7834i	−0.563007	+	0.975157i	0.434225	+	0.900805i	$0.357022\pi$
$499$	−12.5766	+	21.7834i	−0.563007	+	0.975157i	−0.997232	+	0.0743527i	$0.976311\pi$
$500$		0			0
$501$	−28.0411	−	18.3517i	−1.25278	−	0.819894i
$502$		0			0
$503$	−31.1553			−1.38915			−0.694574	−	0.719421i	$-0.744407\pi$
$503$	−31.1553			−1.38915			−0.694574	+	0.719421i	$0.744407\pi$
$504$		0			0
$505$	5.76722			0.256638
$506$		0			0
$507$	18.5477	−	9.36787i	0.823733	−	0.416042i
$508$		0			0
$509$	2.41674	−	4.18591i	0.107120	−	0.185537i	−0.807482	−	0.589892i	$-0.799170\pi$
$509$	2.41674	−	4.18591i	0.107120	−	0.185537i	0.914602	+	0.404354i	$0.132504\pi$
$510$		0			0
$511$	−10.4723	−	2.54255i	−0.463267	−	0.112476i
$512$		0			0
$513$	−32.5696	−	5.51413i	−1.43798	−	0.243455i
$514$		0			0
$515$	−3.63344	+	2.09777i	−0.160109	+	0.0924387i
$516$		0			0
$517$	−4.82886	−	2.78794i	−0.212373	−	0.122613i
$518$		0			0
$519$	−7.47751	+	3.77666i	−0.328226	+	0.165777i
$520$		0			0
$521$	−17.5322			−0.768101			−0.384050	−	0.923312i	$-0.625471\pi$
$521$	−17.5322			−0.768101			−0.384050	+	0.923312i	$0.625471\pi$
$522$		0			0
$523$		−	19.1019i		−	0.835267i	−0.908616	−	0.417633i	$-0.862860\pi$
$523$		−	19.1019i		−	0.835267i	0.908616	−	0.417633i	$-0.137140\pi$
$524$		0			0
$525$	5.07267	+	21.7123i	0.221390	+	0.947603i
$526$		0			0
$527$	27.3319	+	15.7801i	1.19060	+	0.687392i
$528$		0			0
$529$	18.1033	+	31.3559i	0.787101	+	1.36330i
$530$		0			0
$531$	−15.5385	+	21.0711i	−0.674312	+	0.914410i
$532$		0			0
$533$	3.74584	−	2.16266i	0.162250	−	0.0936752i
$534$		0			0
$535$	−3.51192	−	2.02761i	−0.151834	−	0.0876612i
$536$		0			0
$537$	6.32588	+	0.354012i	0.272982	+	0.0152767i
$538$		0			0
$539$	4.68095	−	0.221286i	0.201623	−	0.00953144i
$540$		0			0
$541$	13.6642			0.587471			0.293735	−	0.955887i	$-0.405102\pi$
$541$	13.6642			0.587471			0.293735	+	0.955887i	$0.405102\pi$
$542$		0			0
$543$	9.80186	+	0.548537i	0.420638	+	0.0235400i
$544$		0			0
$545$	−1.93625	+	3.35368i	−0.0829397	+	0.143656i
$546$		0			0
$547$	−4.94380	−	8.56292i	−0.211382	−	0.366124i	0.740765	−	0.671764i	$-0.234463\pi$
$547$	−4.94380	−	8.56292i	−0.211382	−	0.366124i	−0.952147	+	0.305640i	$0.901130\pi$
$548$		0			0
$549$	−13.6298	+	5.95299i	−0.581707	+	0.254067i
$550$		0			0
$551$	−5.81362	−	10.0695i	−0.247669	−	0.428975i
$552$		0			0
$553$	21.2127	−	6.22444i	0.902055	−	0.264690i
$554$		0			0
$555$	−2.74569	−	1.79694i	−0.116548	−	0.0762759i
$556$		0			0
$557$		−	12.5800i		−	0.533034i	−0.963830	−	0.266517i	$-0.914127\pi$
$557$		−	12.5800i		−	0.533034i	0.963830	−	0.266517i	$-0.0858728\pi$
$558$		0			0
$559$		−	4.50547i		−	0.190561i
$560$		0			0
$561$	−2.60803	−	5.16371i	−0.110111	−	0.218012i
$562$		0			0
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	−0.487127	−	0.873331i	$-0.661955\pi$
$563$	12.1666	−	21.0732i	0.512763	−	0.888132i	0.999890	−	0.0148007i	$-0.00471137\pi$
$564$		0			0
$565$	1.32058	−	0.762437i	0.0555572	−	0.0320760i
$566$		0			0
$567$	10.6095	−	21.3176i	0.445557	−	0.895253i
$568$		0			0
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	−0.661702	−	0.749767i	$-0.730166\pi$
$569$	−8.18746	+	4.72703i	−0.343236	+	0.198167i	0.318466	+	0.947934i	$0.396832\pi$
$570$		0			0
$571$	−15.7843	+	27.3392i	−0.660551	+	1.14411i	0.319920	+	0.947445i	$0.396344\pi$
$571$	−15.7843	+	27.3392i	−0.660551	+	1.14411i	−0.980471	+	0.196664i	$0.936989\pi$
$572$		0			0
$573$	−21.3781	−	42.3272i	−0.893084	−	1.76824i
$574$		0			0
$575$			37.4388i			1.56131i
$576$		0			0
$577$			33.5794i			1.39793i	0.715157	+	0.698964i	$0.246355\pi$
$577$			33.5794i			1.39793i	−0.715157	+	0.698964i	$0.753645\pi$
$578$		0			0
$579$	14.5336	+	9.51166i	0.603997	+	0.395291i
$580$		0			0
$581$	43.1943	−	12.6745i	1.79200	−	0.525828i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−1.00943	+	0.440882i	−0.0417350	+	0.0182282i
$586$		0			0
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	0.594909	−	0.803793i	$-0.297188\pi$
$587$	−9.65855	−	16.7291i	−0.398651	−	0.690484i	−0.993560	+	0.113310i	$0.963855\pi$
$588$		0			0
$589$	20.1075	−	34.8272i	0.828516	−	1.43503i
$590$		0			0
$591$	32.5564	+	1.82194i	1.33919	+	0.0749445i
$592$		0			0
$593$	−0.733196			−0.0301088			−0.0150544	−	0.999887i	$-0.504792\pi$
$593$	−0.733196			−0.0301088			−0.0150544	+	0.999887i	$0.504792\pi$
$594$		0			0
$595$	−3.50157	−	3.33994i	−0.143550	−	0.136924i
$596$		0			0
$597$	9.27631	+	0.519125i	0.379654	+	0.0212464i
$598$		0			0
$599$	−26.6548	−	15.3892i	−1.08909	−	0.628785i	−0.155754	−	0.987796i	$-0.549781\pi$
$599$	−26.6548	−	15.3892i	−1.08909	−	0.628785i	−0.933333	+	0.359011i	$0.883114\pi$
$600$		0			0
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	−0.483864	−	0.875143i	$-0.660767\pi$
$601$	0.786931	−	0.454335i	0.0320996	−	0.0185327i	0.515964	+	0.856610i	$0.327434\pi$
$602$		0			0
$603$	19.3911	−	26.2956i	0.789668	−	1.07084i
$604$		0			0
$605$	1.93414	+	3.35003i	0.0786340	+	0.136198i
$606$		0			0
$607$	38.7783	+	22.3887i	1.57396	+	0.908728i	0.995676	+	0.0928949i	$0.0296121\pi$
$607$	38.7783	+	22.3887i	1.57396	+	0.908728i	0.578287	+	0.815833i	$0.303721\pi$
$608$		0			0
$609$	8.16166	−	1.90682i	0.330727	−	0.0772682i
$610$		0			0
$611$			8.34204i			0.337483i
$612$		0			0
$613$	18.1480			0.732992			0.366496	−	0.930420i	$-0.380557\pi$
$613$	18.1480			0.732992			0.366496	+	0.930420i	$0.380557\pi$
$614$		0			0
$615$	2.44766	−	1.23624i	0.0986993	−	0.0498500i
$616$		0			0
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	0.0469315	−	0.998898i	$-0.485056\pi$
$617$	−19.7393	−	11.3965i	−0.794674	−	0.458805i	−0.841605	+	0.540093i	$0.818389\pi$
$618$		0			0
$619$	−38.4228	+	22.1834i	−1.54434	+	0.891626i	−0.545785	+	0.837925i	$0.683768\pi$
$619$	−38.4228	+	22.1834i	−1.54434	+	0.891626i	−0.998557	+	0.0537011i	$0.982898\pi$
$620$		0			0
$621$	25.4906	−	30.8027i	1.02290	−	1.23607i
$622$		0			0
$623$	−6.68626	+	27.5394i	−0.267880	+	1.10334i
$624$		0			0
$625$	−11.5011	+	19.9204i	−0.460043	+	0.796818i
$626$		0			0
$627$	−6.57976	+	3.32323i	−0.262770	+	0.132717i
$628$		0			0
$629$	−25.7829			−1.02803
$630$		0			0
$631$	32.5707			1.29662			0.648310	−	0.761377i	$-0.275476\pi$
$631$	32.5707			1.29662			0.648310	+	0.761377i	$0.275476\pi$
$632$		0			0
$633$	2.40283	+	1.57255i	0.0955039	+	0.0625033i
$634$		0			0
$635$	0.306009	−	0.530024i	0.0121436	−	0.0210333i
$636$		0			0
$637$	−3.78828	−	5.89936i	−0.150097	−	0.233741i
$638$		0			0
$639$	−1.84047	+	16.3923i	−0.0728080	+	0.648470i
$640$		0			0
$641$	−10.2270	+	5.90456i	−0.403942	+	0.233216i	−0.688184	−	0.725537i	$-0.741592\pi$
$641$	−10.2270	+	5.90456i	−0.403942	+	0.233216i	0.284241	+	0.958753i	$0.408258\pi$
$642$		0			0
$643$	25.3714	+	14.6482i	1.00055	+	0.577668i	0.908411	−	0.418078i	$-0.137296\pi$
$643$	25.3714	+	14.6482i	1.00055	+	0.577668i	0.0921392	+	0.995746i	$0.470630\pi$
$644$		0			0
$645$	0.159599	−	2.85189i	0.00628421	−	0.112293i
$646$		0			0
$647$	−28.1683			−1.10741			−0.553705	−	0.832713i	$-0.686786\pi$
$647$	−28.1683			−1.10741			−0.553705	+	0.832713i	$0.686786\pi$
$648$		0			0
$649$			5.84229i			0.229330i
$650$		0			0
$651$	19.8258	+	21.1492i	0.777036	+	0.828901i
$652$		0			0
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.999431	+	0.0337326i	$0.0107394\pi$
$653$	39.0555	+	22.5487i	1.52836	+	0.882399i	0.528929	+	0.848666i	$0.322594\pi$
$654$		0			0
$655$	−2.48043	−	4.29623i	−0.0969184	−	0.167868i
$656$		0			0
$657$	−1.36339	+	12.1431i	−0.0531909	+	0.473748i
$658$		0			0
$659$	−27.5435	+	15.9022i	−1.07294	+	0.619463i	−0.928984	−	0.370121i	$-0.879316\pi$
$659$	−27.5435	+	15.9022i	−1.07294	+	0.619463i	−0.143958	+	0.989584i	$0.545983\pi$
$660$		0			0
$661$	−17.1234	−	9.88619i	−0.666022	−	0.384528i	0.128546	−	0.991704i	$-0.458969\pi$
$661$	−17.1234	−	9.88619i	−0.666022	−	0.384528i	−0.794568	+	0.607175i	$0.792302\pi$
$662$		0			0
$663$	−4.73945	+	7.24180i	−0.184065	+	0.281248i
$664$		0			0
$665$	−4.25587	+	4.46181i	−0.165035	+	0.173022i
$666$		0			0
$667$	14.0733			0.544918
$668$		0			0
$669$	13.3037	+	26.3403i	0.514349	+	1.01837i
$670$		0			0
$671$	−1.65948	+	2.87430i	−0.0640635	+	0.110961i
$672$		0			0
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	0.847230	−	0.531227i	$-0.178269\pi$
$673$	−0.945369	−	1.63743i	−0.0364413	−	0.0631182i	−0.883671	+	0.468109i	$0.844936\pi$
$674$		0			0
$675$	23.6982	−	8.80893i	0.912144	−	0.339056i
$676$		0			0
$677$	−10.5661	−	18.3010i	−0.406088	−	0.703364i	0.588360	−	0.808599i	$-0.299774\pi$
$677$	−10.5661	−	18.3010i	−0.406088	−	0.703364i	−0.994447	+	0.105235i	$0.966441\pi$
$678$		0			0
$679$	−12.8246	−	43.7058i	−0.492164	−	1.67728i
$680$		0			0
$681$	−7.90067	+	3.99038i	−0.302754	+	0.152912i
$682$		0			0
$683$			8.71972i			0.333651i	0.985986	+	0.166825i	$0.0533516\pi$
$683$			8.71972i			0.333651i	−0.985986	+	0.166825i	$0.946648\pi$
$684$		0			0
$685$		−	3.29517i		−	0.125902i
$686$		0			0
$687$	−14.4804	+	22.1258i	−0.552463	+	0.844153i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−15.7071	+	9.06850i	−0.597526	+	0.344982i	−0.768068	−	0.640369i	$-0.778782\pi$
$691$	−15.7071	+	9.06850i	−0.597526	+	0.344982i	0.170542	+	0.985350i	$0.445448\pi$
$692$		0			0
$693$	−0.917872	−	5.23374i	−0.0348671	−	0.198814i
$694$		0			0
$695$	−2.95235	+	1.70454i	−0.111989	+	0.0646568i
$696$		0			0
$697$	10.7728	−	18.6590i	0.408048	−	0.706760i
$698$		0			0
$699$	−17.6272	−	0.986465i	−0.666724	−	0.0373115i
$700$		0			0
$701$			35.6167i			1.34523i	0.739995	+	0.672613i	$0.234828\pi$
$701$			35.6167i			1.34523i	−0.739995	+	0.672613i	$0.765172\pi$
$702$		0			0
$703$			32.8534i			1.23909i
$704$		0			0
$705$	−0.295503	+	5.28038i	−0.0111293	+	0.198871i
$706$		0			0
$707$	39.9384	−	11.7191i	1.50204	−	0.440743i
$708$		0			0
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$		0			0
$711$	−10.0331	−	22.9716i	−0.376271	−	0.861501i
$712$		0			0
$713$	24.3375	+	42.1538i	0.911447	+	1.57867i
$714$		0			0
$715$	−0.122902	+	0.212873i	−0.00459628	+	0.00796099i
$716$		0			0
$717$	−18.1934	+	27.7992i	−0.679445	+	1.03818i
$718$		0			0
$719$	−25.7829			−0.961540			−0.480770	−	0.876847i	$-0.659643\pi$
$719$	−25.7829			−0.961540			−0.480770	+	0.876847i	$0.659643\pi$
$720$		0			0
$721$	−20.8991	+	21.9104i	−0.778323	+	0.815987i
$722$		0			0
$723$	−16.1523	−	31.9804i	−0.600710	−	1.18936i
$724$		0			0
$725$	7.70685	+	4.44955i	0.286225	+	0.165252i
$726$		0			0
$727$	1.32423	−	0.764544i	0.0491129	−	0.0283554i	−0.475242	−	0.879855i	$-0.657640\pi$
$727$	1.32423	−	0.764544i	0.0491129	−	0.0283554i	0.524355	+	0.851499i	$0.324306\pi$
$728$		0			0
$729$	−25.4953	−	8.88761i	−0.944270	−	0.329171i
$730$		0			0
$731$	−11.2215	−	19.4362i	−0.415042	−	0.718873i
$732$		0			0
$733$	17.9908	+	10.3870i	0.664504	+	0.383651i	0.793991	−	0.607930i	$-0.208000\pi$
$733$	17.9908	+	10.3870i	0.664504	+	0.383651i	−0.129487	+	0.991581i	$0.541333\pi$
$734$		0			0
$735$	−2.18894	−	3.86839i	−0.0807404	−	0.142688i
$736$		0			0
$737$		−	7.29084i		−	0.268562i
$738$		0			0
$739$	11.8709			0.436678			0.218339	−	0.975873i	$-0.429936\pi$
$739$	11.8709			0.436678			0.218339	+	0.975873i	$0.429936\pi$
$740$		0			0
$741$	9.22773	+	6.03917i	0.338989	+	0.221854i
$742$		0			0
$743$	37.5906	+	21.7029i	1.37907	+	0.796204i	0.992047	−	0.125868i	$-0.0401716\pi$
$743$	37.5906	+	21.7029i	1.37907	+	0.796204i	0.387019	+	0.922072i	$0.373505\pi$
$744$		0			0
$745$	−0.899148	+	0.519124i	−0.0329422	+	0.0190192i
$746$		0			0
$747$	−20.4299	−	46.7759i	−0.747491	−	1.71144i
$748$		0			0
$749$	−28.4404	−	6.90502i	−1.03919	−	0.252304i
$750$		0			0
$751$	1.15691	−	2.00383i	0.0422164	−	0.0731209i	−0.844145	−	0.536115i	$-0.819891\pi$
$751$	1.15691	−	2.00383i	0.0422164	−	0.0731209i	0.886362	+	0.462994i	$0.153225\pi$
$752$		0			0
$753$	0.175363	−	3.13358i	0.00639058	−	0.114194i
$754$		0			0
$755$	−6.06787			−0.220832
$756$		0			0
$757$	−15.0946			−0.548624			−0.274312	−	0.961641i	$-0.588450\pi$
$757$	−15.0946			−0.548624			−0.274312	+	0.961641i	$0.588450\pi$
$758$		0			0
$759$	0.498522	−	8.90814i	0.0180952	−	0.323345i
$760$		0			0
$761$	−11.6690	+	20.2112i	−0.422999	+	0.732656i	−0.996231	−	0.0867370i	$-0.972356\pi$
$761$	−11.6690	+	20.2112i	−0.422999	+	0.732656i	0.573232	+	0.819393i	$0.305689\pi$
$762$		0			0
$763$	−6.59388	+	27.1589i	−0.238715	+	0.983219i
$764$		0			0
$765$	−3.25653	+	4.41606i	−0.117740	+	0.159663i
$766$		0			0
$767$	7.56959	−	4.37030i	0.273322	−	0.157803i
$768$		0			0
$769$	15.8266	+	9.13748i	0.570721	+	0.329506i	0.757437	−	0.652908i	$-0.226451\pi$
$769$	15.8266	+	9.13748i	0.570721	+	0.329506i	−0.186716	+	0.982414i	$0.559784\pi$
$770$		0			0
$771$	−9.35568	−	6.12290i	−0.336937	−	0.220511i
$772$		0			0
$773$	0.438507			0.0157720			0.00788600	−	0.999969i	$-0.497490\pi$
$773$	0.438507			0.0157720			0.00788600	+	0.999969i	$0.497490\pi$
$774$		0			0
$775$			30.7792i			1.10562i
$776$		0			0
$777$	−22.6655	−	6.86462i	−0.813121	−	0.246267i
$778$		0			0
$779$	−23.7759	−	13.7270i	−0.851861	−	0.491822i
$780$		0			0
$781$	1.84047	+	3.18779i	0.0658573	+	0.114068i
$782$		0			0
$783$	−3.31128	−	8.90814i	−0.118335	−	0.318351i
$784$		0			0
$785$	−0.899924	+	0.519571i	−0.0321197	+	0.0185443i
$786$		0			0
$787$	−33.1317	−	19.1286i	−1.18102	−	0.681861i	−0.224769	−	0.974412i	$-0.572163\pi$
$787$	−33.1317	−	19.1286i	−1.18102	−	0.681861i	−0.956250	+	0.292551i	$0.905496\pi$
$788$		0			0
$789$	6.88767	+	13.6371i	0.245207	+	0.485493i
$790$		0			0
$791$	7.59581	−	7.96337i	0.270076	−	0.283145i
$792$		0			0
$793$	4.96547			0.176329
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	0.362832	+	0.931855i	$0.381810\pi$
$797$	−17.6613	+	30.5902i	−0.625594	+	1.08356i	−0.988426	+	0.151706i	$0.951523\pi$
$798$		0			0
$799$	20.7770	+	35.9868i	0.735036	+	1.27312i
$800$		0			0
$801$	31.9333	+	3.58536i	1.12831	+	0.126683i
$802$		0			0
$803$	1.36339	+	2.36146i	0.0481130	+	0.0833341i
$804$		0			0
$805$	−2.10133	−	7.16126i	−0.0740621	−	0.252401i
$806$		0			0
$807$	1.38058	−	24.6697i	0.0485986	−	0.868414i
$808$		0			0
$809$			21.7669i			0.765282i	0.923897	+	0.382641i	$0.124985\pi$
$809$			21.7669i			0.765282i	−0.923897	+	0.382641i	$0.875015\pi$
$810$		0			0
$811$		−	17.0184i		−	0.597598i	−0.954316	−	0.298799i	$-0.903414\pi$
$811$		−	17.0184i		−	0.597598i	0.954316	−	0.298799i	$-0.0965860\pi$
$812$		0			0
$813$	−5.27937	−	0.295447i	−0.185156	−	0.0103618i
$814$		0			0
$815$	−4.53263	+	7.85075i	−0.158771	+	0.275000i
$816$		0			0
$817$	−24.7662	+	14.2988i	−0.866460	+	0.500251i
$818$		0			0
$819$	−6.09452	+	5.10433i	−0.212960	+	0.178360i
$820$		0			0
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	−0.825552	−	0.564326i	$-0.809136\pi$
$821$	−21.4786	+	12.4007i	−0.749608	+	0.432786i	0.0759445	+	0.997112i	$0.475803\pi$
$822$		0			0
$823$	10.6572	−	18.4588i	0.371486	−	0.643433i	−0.618308	−	0.785936i	$-0.712182\pi$
$823$	10.6572	−	18.4588i	0.371486	−	0.643433i	0.989794	+	0.142503i	$0.0455149\pi$
$824$		0			0
$825$	3.08950	−	4.72069i	0.107562	−	0.164353i
$826$		0			0
$827$		−	49.7585i		−	1.73027i	−0.501537	−	0.865136i	$-0.667232\pi$
$827$		−	49.7585i		−	1.73027i	0.501537	−	0.865136i	$-0.332768\pi$
$828$		0			0
$829$		−	43.1190i		−	1.49759i	−0.662804	−	0.748793i	$-0.730634\pi$
$829$		−	43.1190i		−	1.49759i	0.662804	−	0.748793i	$-0.269366\pi$
$830$		0			0
$831$	1.95676	−	0.988300i	0.0678794	−	0.0342838i
$832$		0			0
$833$	−31.0354	−	16.0141i	−1.07531	−	0.554854i
$834$		0			0
$835$	3.54655	+	6.14281i	0.122733	+	0.212581i
$836$		0			0
$837$	20.9563	−	25.3236i	0.724357	−	0.875311i
$838$		0			0
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	0.999786	+	0.0206851i	$0.00658476\pi$
$839$	14.9985	+	25.9782i	0.517807	+	0.896868i	−0.481979	+	0.876183i	$0.660082\pi$
$840$		0			0
$841$	−12.8274	+	22.2177i	−0.442325	+	0.766129i
$842$		0			0
$843$	8.21988	+	16.2748i	0.283108	+	0.560532i
$844$		0			0
$845$	−4.39803			−0.151297
$846$		0			0
$847$	20.2014	+	19.2689i	0.694128	+	0.662089i
$848$		0			0
$849$	18.8481	−	28.7995i	0.646864	−	0.988396i
$850$		0			0
$851$	−34.4373	−	19.8824i	−1.18050	−	0.681559i
$852$		0			0
$853$	25.7693	−	14.8779i	0.882325	−	0.509411i	0.0109007	−	0.999941i	$-0.496530\pi$
$853$	25.7693	−	14.8779i	0.882325	−	0.509411i	0.871424	+	0.490530i	$0.163197\pi$
$854$		0			0
$855$	5.62708	+	4.14957i	0.192442	+	0.141912i
$856$		0			0
$857$	−22.9296	−	39.7152i	−0.783260	−	1.35665i	−0.930033	−	0.367476i	$-0.880222\pi$
$857$	−22.9296	−	39.7152i	−0.783260	−	1.35665i	0.146773	−	0.989170i	$-0.453111\pi$
$858$		0			0
$859$	−3.24073	−	1.87104i	−0.110572	−	0.0638390i	0.443694	−	0.896178i	$-0.353668\pi$
$859$	−3.24073	−	1.87104i	−0.110572	−	0.0638390i	−0.554266	+	0.832339i	$0.687001\pi$
$860$		0			0
$861$	14.4382	−	13.5347i	0.492051	−	0.461263i
$862$		0			0
$863$		−	31.3944i		−	1.06868i	−0.845270	−	0.534339i	$-0.820561\pi$
$863$		−	31.3944i		−	1.06868i	0.845270	−	0.534339i	$-0.179439\pi$
$864$		0			0
$865$	1.77307			0.0602860
$866$		0			0
$867$	−0.763654	+	13.6458i	−0.0259350	+	0.463436i
$868$		0			0
$869$	−4.84432	−	2.79687i	−0.164332	−	0.0948773i
$870$		0			0
$871$	−9.44641	+	5.45389i	−0.320080	+	0.184798i
$872$		0			0
$873$	−47.3298	+	20.6718i	−1.60187	+	0.699635i
$874$		0			0
$875$	2.25764	−	9.29878i	0.0763221	−	0.314356i
$876$		0			0
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$		0			0
$879$	−19.4377	−	12.7212i	−0.655619	−	0.429075i
$880$		0			0
$881$	−21.2010			−0.714280			−0.357140	−	0.934051i	$-0.616248\pi$
$881$	−21.2010			−0.714280			−0.357140	+	0.934051i	$0.616248\pi$
$882$		0			0
$883$	−38.6157			−1.29952			−0.649761	−	0.760139i	$-0.725131\pi$
$883$	−38.6157			−1.29952			−0.649761	+	0.760139i	$0.725131\pi$
$884$		0			0
$885$	4.94624	−	2.49819i	0.166266	−	0.0839758i
$886$		0			0
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	−0.913311	−	0.407263i	$-0.866483\pi$
$887$	−3.09606	+	5.36253i	−0.103955	+	0.180056i	0.809356	+	0.587319i	$0.199817\pi$
$888$		0			0
$889$	1.04211	−	4.29226i	0.0349513	−	0.143958i
$890$		0			0
$891$	−5.75601	+	1.78043i	−0.192834	+	0.0596466i
$892$		0			0
$893$	45.8555	−	26.4747i	1.53450	−	0.885941i
$894$		0			0
$895$	−1.16134	−	0.670501i	−0.0388194	−	0.0224124i
$896$		0			0
$897$	−11.9148	+	6.01779i	−0.397824	+	0.200928i
$898$		0			0
$899$	11.5699			0.385878
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−4.68988	−	20.0738i	−0.156069	−	0.668016i
$904$		0			0
$905$	−1.79948	−	1.03893i	−0.0598168	−	0.0345353i
$906$		0			0
$907$	−0.0645566	−	0.111815i	−0.00214357	−	0.00371277i	0.864952	−	0.501855i	$-0.167349\pi$
$907$	−0.0645566	−	0.111815i	−0.00214357	−	0.00371277i	−0.867095	+	0.498142i	$0.834016\pi$
$908$		0			0
$909$	−18.8899	−	43.2499i	−0.626539	−	1.43451i
$910$		0			0
$911$	−29.6682	+	17.1290i	−0.982952	+	0.567508i	−0.903160	−	0.429304i	$-0.858759\pi$
$911$	−29.6682	+	17.1290i	−0.982952	+	0.567508i	−0.0797919	+	0.996812i	$0.525426\pi$
$912$		0			0
$913$	−9.86424	−	5.69512i	−0.326459	−	0.188481i
$914$		0			0
$915$	3.14306	+	0.175894i	0.103907	+	0.00581487i
$916$		0			0
$917$	−25.9072	−	24.7114i	−0.855530	−	0.816041i
$918$		0			0
$919$	−14.3054			−0.471892			−0.235946	−	0.971766i	$-0.575819\pi$
$919$	−14.3054			−0.471892			−0.235946	+	0.971766i	$0.575819\pi$
$920$		0			0
$921$	−1.13052	−	0.0632668i	−0.0372519	−	0.00208471i
$922$		0			0
$923$	2.75352	−	4.76923i	0.0906332	−	0.156981i
$924$		0			0
$925$	−12.5725	−	21.7761i	−0.413380	−	0.715995i
$926$		0			0
$927$	27.6327	+	20.3771i	0.907576	+	0.669273i
$928$		0			0
$929$	−5.87364	−	10.1734i	−0.192708	−	0.333780i	0.753439	−	0.657518i	$-0.228394\pi$
$929$	−5.87364	−	10.1734i	−0.192708	−	0.333780i	−0.946147	+	0.323738i	$0.895060\pi$
$930$		0			0
$931$	−20.4056	+	39.5463i	−0.668768	+	1.29608i
$932$		0			0
$933$	13.3984	+	8.76868i	0.438643	+	0.287074i
$934$		0			0
$935$			1.22442i			0.0400427i
$936$		0			0
$937$		−	2.63611i		−	0.0861179i	−0.999073	−	0.0430589i	$-0.986290\pi$
$937$		−	2.63611i		−	0.0861179i	0.999073	−	0.0430589i	$-0.0137103\pi$
$938$		0			0
$939$	4.81333	+	9.53004i	0.157077	+	0.311001i
$940$		0			0
$941$	5.96557	−	10.3327i	0.194472	−	0.336836i	−0.752255	−	0.658872i	$-0.771034\pi$
$941$	5.96557	−	10.3327i	0.194472	−	0.336836i	0.946727	+	0.322036i	$0.104367\pi$
$942$		0			0
$943$	28.7776	−	16.6148i	0.937128	−	0.541051i
$944$		0			0
$945$	−4.03854	+	3.01507i	−0.131374	+	0.0980803i
$946$		0			0
$947$	−6.70267	+	3.86979i	−0.217807	+	0.125751i	−0.604935	−	0.796275i	$-0.706801\pi$
$947$	−6.70267	+	3.86979i	−0.217807	+	0.125751i	0.387127	+	0.922026i	$0.373467\pi$
$948$		0			0
$949$	2.03976	−	3.53296i	0.0662133	−	0.114685i
$950$		0			0
$951$	−16.1285	−	31.9333i	−0.523003	−	1.03551i
$952$		0			0
$953$			3.76685i			0.122020i	0.998137	+	0.0610102i	$0.0194322\pi$
$953$			3.76685i			0.122020i	−0.998137	+	0.0610102i	$0.980568\pi$
$954$		0			0
$955$			10.0366i			0.324777i
$956$		0			0
$957$	−1.77451	−	1.16134i	−0.0573617	−	0.0375408i
$958$		0			0
$959$	−6.69586	−	22.8193i	−0.216221	−	0.736872i
$960$		0			0
$961$	4.50836	+	7.80871i	0.145431	+	0.251894i
$962$		0			0
$963$	−3.70267	+	32.9781i	−0.119317	+	1.06270i
$964$		0			0
$965$	−1.83817	−	3.18381i	−0.0591728	−	0.102490i
$966$		0			0
$967$	2.28741	−	3.96191i	0.0735581	−	0.127406i	−0.826900	−	0.562349i	$-0.809898\pi$
$967$	2.28741	−	3.96191i	0.0735581	−	0.127406i	0.900458	+	0.434942i	$0.143231\pi$
$968$		0			0
$969$	54.8489	+	3.06948i	1.76200	+	0.0986060i
$970$		0			0
$971$	−25.8445			−0.829388			−0.414694	−	0.909961i	$-0.636111\pi$
$971$	−25.8445			−0.829388			−0.414694	+	0.909961i	$0.636111\pi$
$972$		0			0
$973$	−16.9815	+	17.8033i	−0.544403	+	0.570747i
$974$		0			0
$975$	−8.42748	−	0.471623i	−0.269895	−	0.0151040i
$976$		0			0
$977$	−26.0950	−	15.0659i	−0.834852	−	0.482002i	0.0206590	−	0.999787i	$-0.493424\pi$
$977$	−26.0950	−	15.0659i	−0.834852	−	0.482002i	−0.855511	+	0.517785i	$0.826757\pi$
$978$		0			0
$979$	6.21003	−	3.58536i	0.198474	−	0.114589i
$980$		0			0
$981$	31.4921	+	3.53583i	1.00547	+	0.112890i
$982$		0			0
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	0.747829	−	0.663891i	$-0.231096\pi$
$983$	−6.30293	−	10.9170i	−0.201032	−	0.348198i	−0.948861	+	0.315693i	$0.897763\pi$
$984$		0			0
$985$	−5.97689	−	3.45076i	−0.190440	−	0.109950i
$986$		0			0
$987$	8.68347	+	37.1674i	0.276398	+	1.18305i
$988$		0			0
$989$		−	34.6136i		−	1.10065i
$990$		0			0
$991$	−51.6852			−1.64184			−0.820918	−	0.571046i	$-0.806538\pi$
$991$	−51.6852			−1.64184			−0.820918	+	0.571046i	$0.806538\pi$
$992$		0			0
$993$	−16.5603	+	8.36407i	−0.525524	+	0.265426i
$994$		0			0
$995$	−1.70300	−	0.983227i	−0.0539887	−	0.0311704i
$996$		0			0
$997$	−35.1469	+	20.2921i	−1.11311	+	0.642656i	−0.939634	−	0.342181i	$-0.888834\pi$
$997$	−35.1469	+	20.2921i	−1.11311	+	0.642656i	−0.173479	+	0.984837i	$0.555501\pi$
$998$		0			0
$999$	−4.48252	+	26.4764i	−0.141821	+	0.837675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.cc.b.545.4		16
3.2	odd	2		3024.2.cc.b.881.4		16
4.3	odd	2		126.2.m.a.41.7	yes	16
7.6	odd	2	inner	1008.2.cc.b.545.5		16
9.2	odd	6	inner	1008.2.cc.b.209.5		16
9.7	even	3		3024.2.cc.b.2897.5		16
12.11	even	2		378.2.m.a.125.2		16
21.20	even	2		3024.2.cc.b.881.5		16
28.3	even	6		882.2.l.a.509.8		16
28.11	odd	6		882.2.l.a.509.5		16
28.19	even	6		882.2.t.b.815.1		16
28.23	odd	6		882.2.t.b.815.4		16
28.27	even	2		126.2.m.a.41.6	✓	16
36.7	odd	6		378.2.m.a.251.3		16
36.11	even	6		126.2.m.a.83.6	yes	16
36.23	even	6		1134.2.d.a.1133.5		16
36.31	odd	6		1134.2.d.a.1133.12		16
63.20	even	6	inner	1008.2.cc.b.209.4		16
63.34	odd	6		3024.2.cc.b.2897.4		16
84.11	even	6		2646.2.l.b.1097.2		16
84.23	even	6		2646.2.t.a.2285.7		16
84.47	odd	6		2646.2.t.a.2285.6		16
84.59	odd	6		2646.2.l.b.1097.3		16
84.83	odd	2		378.2.m.a.125.3		16
252.11	even	6		882.2.t.b.803.1		16
252.47	odd	6		882.2.l.a.227.1		16
252.79	odd	6		2646.2.l.b.521.7		16
252.83	odd	6		126.2.m.a.83.7	yes	16
252.115	even	6		2646.2.t.a.1979.7		16
252.139	even	6		1134.2.d.a.1133.13		16
252.151	odd	6		2646.2.t.a.1979.6		16
252.167	odd	6		1134.2.d.a.1133.4		16
252.187	even	6		2646.2.l.b.521.6		16
252.191	even	6		882.2.l.a.227.4		16
252.223	even	6		378.2.m.a.251.2		16
252.227	odd	6		882.2.t.b.803.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.6	✓	16	28.27	even	2
126.2.m.a.41.7	yes	16	4.3	odd	2
126.2.m.a.83.6	yes	16	36.11	even	6
126.2.m.a.83.7	yes	16	252.83	odd	6
378.2.m.a.125.2		16	12.11	even	2
378.2.m.a.125.3		16	84.83	odd	2
378.2.m.a.251.2		16	252.223	even	6
378.2.m.a.251.3		16	36.7	odd	6
882.2.l.a.227.1		16	252.47	odd	6
882.2.l.a.227.4		16	252.191	even	6
882.2.l.a.509.5		16	28.11	odd	6
882.2.l.a.509.8		16	28.3	even	6
882.2.t.b.803.1		16	252.11	even	6
882.2.t.b.803.4		16	252.227	odd	6
882.2.t.b.815.1		16	28.19	even	6
882.2.t.b.815.4		16	28.23	odd	6
1008.2.cc.b.209.4		16	63.20	even	6	inner
1008.2.cc.b.209.5		16	9.2	odd	6	inner
1008.2.cc.b.545.4		16	1.1	even	1	trivial
1008.2.cc.b.545.5		16	7.6	odd	2	inner
1134.2.d.a.1133.4		16	252.167	odd	6
1134.2.d.a.1133.5		16	36.23	even	6
1134.2.d.a.1133.12		16	36.31	odd	6
1134.2.d.a.1133.13		16	252.139	even	6
2646.2.l.b.521.6		16	252.187	even	6
2646.2.l.b.521.7		16	252.79	odd	6
2646.2.l.b.1097.2		16	84.11	even	6
2646.2.l.b.1097.3		16	84.59	odd	6
2646.2.t.a.1979.6		16	252.151	odd	6
2646.2.t.a.1979.7		16	252.115	even	6
2646.2.t.a.2285.6		16	84.47	odd	6
2646.2.t.a.2285.7		16	84.23	even	6
3024.2.cc.b.881.4		16	3.2	odd	2
3024.2.cc.b.881.5		16	21.20	even	2
3024.2.cc.b.2897.4		16	63.34	odd	6
3024.2.cc.b.2897.5		16	9.7	even	3

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0967785 + 1.72934i) q^{3} +(0.183299 - 0.317483i) q^{5} +(0.624224 - 2.57106i) q^{7} +(-2.98127 - 0.334727i) q^{9} +O(q^{10})\)	\(q+(-0.0967785 + 1.72934i) q^{3} +(0.183299 - 0.317483i) q^{5} +(0.624224 - 2.57106i) q^{7} +(-2.98127 - 0.334727i) q^{9} +(-0.579764 + 0.334727i) q^{11} +(0.867380 + 0.500782i) q^{13} +(0.531299 + 0.347713i) q^{15} +4.98906 q^{17} -6.35722i q^{19} +(4.38584 + 1.32832i) q^{21} +(6.66371 + 3.84729i) q^{23} +(2.43280 + 4.21374i) q^{25} +(0.867380 - 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(5.47837 + 3.16294i) q^{31} +(-0.522749 - 1.03501i) q^{33} +(-0.701849 - 0.669453i) q^{35} -5.16789 q^{37} +(-0.949969 + 1.45154i) q^{39} +(2.15928 - 3.73998i) q^{41} +(-2.24922 - 3.89576i) q^{43} +(-0.652734 + 0.885148i) q^{45} +(4.16450 + 7.21313i) q^{47} +(-6.22069 - 3.20983i) q^{49} +(-0.482834 + 8.62781i) q^{51} +0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} +(4.36348 - 7.55776i) q^{59} +(4.29351 - 2.47886i) q^{61} +(-2.72158 + 7.45607i) q^{63} +(0.317980 - 0.183586i) q^{65} +(-5.44537 + 9.43166i) q^{67} +(-7.29820 + 11.1515i) q^{69} -5.49843i q^{71} -4.07314i q^{73} +(-7.52245 + 3.79936i) q^{75} +(0.498700 + 1.69955i) q^{77} +(4.17784 + 7.23623i) q^{79} +(8.77592 + 1.99582i) q^{81} +(8.50712 + 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} +(1.42818 + 2.82769i) q^{87} -10.7113 q^{89} +(1.82898 - 1.91749i) q^{91} +(-6.00000 + 9.16789i) q^{93} +(-2.01831 - 1.16527i) q^{95} +(14.9093 - 8.60787i) q^{97} +(1.84047 - 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q - 2 * q^7 + 12 * q^9	\( 16 q - 2 q^{7} + 12 q^{9} + 12 q^{11} + 18 q^{21} + 48 q^{23} - 8 q^{25} - 12 q^{29} - 8 q^{37} + 36 q^{39} - 4 q^{43} - 8 q^{49} - 12 q^{51} + 48 q^{57} - 24 q^{63} + 84 q^{65} + 28 q^{67} + 78 q^{77} + 4 q^{79} + 36 q^{81} - 12 q^{85} - 24 q^{91} - 96 q^{93} - 12 q^{95} + 72 q^{99}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^9 + 12 * q^11 + 18 * q^21 + 48 * q^23 - 8 * q^25 - 12 * q^29 - 8 * q^37 + 36 * q^39 - 4 * q^43 - 8 * q^49 - 12 * q^51 + 48 * q^57 - 24 * q^63 + 84 * q^65 + 28 * q^67 + 78 * q^77 + 4 * q^79 + 36 * q^81 - 12 * q^85 - 24 * q^91 - 96 * q^93 - 12 * q^95 + 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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