LMFDB - Embedded newform 392.2.p.g.373.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(165,392)] 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("392.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,-2,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.3
Root			$-0.0950561 + 1.41102i$ of defining polynomial
Character	$\chi$	$=$	392.373
Dual form			392.2.p.g.165.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.453773 - 1.33944i) q^{2} +(-1.36456 + 0.787829i) q^{3} +(-1.58818 + 1.21560i) q^{4} +(-0.476087 - 0.274869i) q^{5} +(1.67445 + 1.47024i) q^{6} +(2.34889 + 1.57566i) q^{8} +(-0.258652 + 0.447998i) q^{9} +(-0.152134 + 0.762416i) q^{10} +(2.07045 - 1.19538i) q^{11} +(1.20948 - 2.90997i) q^{12} -3.96641i q^{13} +0.866198 q^{15} +(1.04463 - 3.86119i) q^{16} +(-2.10755 - 3.65038i) q^{17} +(0.717435 + 0.143158i) q^{18} +(5.75174 + 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(1.17445 - 2.03420i) q^{23} +(-4.44655 - 0.299552i) q^{24} +(-2.34889 - 4.06840i) q^{25} +(-5.31275 + 1.79985i) q^{26} -5.54207i q^{27} -8.21720i q^{29} +(-0.393058 - 1.16022i) q^{30} +(0.433099 + 0.750150i) q^{31} +(-5.64584 + 0.352893i) q^{32} +(-1.88350 + 3.26232i) q^{33} +(-3.93310 + 4.47937i) q^{34} +(-0.133802 - 1.02592i) q^{36} +(0.229805 + 0.132678i) q^{37} +(1.83797 - 9.21097i) q^{38} +(3.12485 + 5.41240i) q^{39} +(-0.685178 - 1.39579i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(-1.83515 + 4.41531i) q^{44} +(0.246282 - 0.142191i) q^{45} +(-3.25762 - 0.650030i) q^{46} +(1.29930 - 2.25045i) q^{47} +(1.61650 + 6.09180i) q^{48} +(-4.38350 + 4.99233i) q^{50} +(5.75174 + 3.32077i) q^{51} +(4.82157 + 6.29937i) q^{52} +(9.36933 - 5.40939i) q^{53} +(-7.42324 + 2.51484i) q^{54} -1.31429 q^{55} -10.4648 q^{57} +(-11.0064 + 3.72875i) q^{58} +(-3.26891 + 1.88730i) q^{59} +(-1.37568 + 1.05295i) q^{60} +(-6.18061 - 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(-1.09024 + 1.88835i) q^{65} +(5.22436 + 1.04248i) q^{66} +(-2.31673 + 1.33757i) q^{67} +(7.78456 + 3.23552i) q^{68} +3.70105i q^{69} +8.76700 q^{71} +(-1.31344 + 0.644754i) q^{72} +(2.33159 + 4.03843i) q^{73} +(0.0734343 - 0.368015i) q^{74} +(6.41041 + 3.70105i) q^{75} +(-13.1715 + 1.71785i) q^{76} +(5.83159 - 6.64154i) q^{78} +(-0.308249 + 0.533903i) q^{79} +(-1.55865 + 1.55112i) q^{80} +(3.59024 + 6.21848i) q^{81} +(-2.83595 - 8.37108i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(7.16634 - 2.42781i) q^{86} +(6.47374 + 11.2129i) q^{87} +(6.74677 + 0.454511i) q^{88} +(-3.19779 + 5.53873i) q^{89} +(-0.302212 - 0.265356i) q^{90} +(0.607546 + 4.65834i) q^{92} +(-1.18198 - 0.682416i) q^{93} +(-3.60392 - 0.719132i) q^{94} +(-1.82555 - 3.16195i) q^{95} +(7.42606 - 4.92949i) q^{96} -12.9475 q^{97} +1.23675i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32}+ \cdots - 40 q^{97}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.453773	−	1.33944i	−0.320866	−	0.947124i
$2$	−0.453773	−	1.33944i	−0.320866	−	0.947124i
$3$	−1.36456	+	0.787829i	−0.787829	+	0.454853i	−0.839198	−	0.543827i	$-0.816975\pi$
$3$	−1.36456	+	0.787829i	−0.787829	+	0.454853i	0.0513689	+	0.998680i	$0.483642\pi$
$4$	−1.58818	+	1.21560i	−0.794090	+	0.607801i
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	0.389752	−	0.920920i	$-0.372561\pi$
$5$	−0.476087	−	0.274869i	−0.212913	−	0.122925i	−0.602664	+	0.797995i	$0.705894\pi$
$6$	1.67445	+	1.47024i	0.683590	+	0.600225i
$7$		0			0
$7$		0			0
$8$	2.34889	+	1.57566i	0.830460	+	0.557079i
$9$	−0.258652	+	0.447998i	−0.0862173	+	0.149333i
$10$	−0.152134	+	0.762416i	−0.0481089	+	0.241097i
$11$	2.07045	−	1.19538i	0.624265	−	0.360419i	−0.154263	−	0.988030i	$-0.549300\pi$
$11$	2.07045	−	1.19538i	0.624265	−	0.360419i	0.778527	+	0.627611i	$0.215967\pi$
$12$	1.20948	−	2.90997i	0.349147	−	0.840037i
$13$		−	3.96641i		−	1.10008i	−0.835137	−	0.550042i	$-0.814612\pi$
$13$		−	3.96641i		−	1.10008i	0.835137	−	0.550042i	$-0.185388\pi$
$14$		0			0
$15$	0.866198			0.223651
$16$	1.04463	−	3.86119i	0.261157	−	0.965296i
$17$	−2.10755	−	3.65038i	−0.511155	−	0.885347i	−0.999916	−	0.0129290i	$-0.995884\pi$
$17$	−2.10755	−	3.65038i	−0.511155	−	0.885347i	0.488761	−	0.872418i	$-0.337449\pi$
$18$	0.717435	+	0.143158i	0.169101	+	0.0337427i
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.983655	−	0.180066i	$-0.0576310\pi$
$19$	5.75174	+	3.32077i	1.31954	+	0.761837i	0.335886	+	0.941903i	$0.390964\pi$
$20$	1.09024	−	0.142191i	0.243786	−	0.0317948i
$21$		0			0
$22$	−2.54065	−	2.23081i	−0.541667	−	0.475610i
$23$	1.17445	−	2.03420i	0.244889	−	0.424160i	−0.717211	−	0.696856i	$-0.754582\pi$
$23$	1.17445	−	2.03420i	0.244889	−	0.424160i	0.962100	+	0.272695i	$0.0879151\pi$
$24$	−4.44655	−	0.299552i	−0.907649	−	0.0611457i
$25$	−2.34889	−	4.06840i	−0.469779	−	0.813681i
$26$	−5.31275	+	1.79985i	−1.04192	+	0.352980i
$27$		−	5.54207i		−	1.06657i
$28$		0			0
$29$		−	8.21720i		−	1.52590i	−0.646460	−	0.762948i	$-0.723751\pi$
$29$		−	8.21720i		−	1.52590i	0.646460	−	0.762948i	$-0.276249\pi$
$30$	−0.393058	−	1.16022i	−0.0717622	−	0.211826i
$31$	0.433099	+	0.750150i	0.0777869	+	0.134731i	0.902295	−	0.431120i	$-0.141881\pi$
$31$	0.433099	+	0.750150i	0.0777869	+	0.134731i	−0.824508	+	0.565850i	$0.808548\pi$
$32$	−5.64584	+	0.352893i	−0.998052	+	0.0623832i
$33$	−1.88350	+	3.26232i	−0.327876	+	0.567897i
$34$	−3.93310	+	4.47937i	−0.674521	+	0.768205i
$35$		0			0
$36$	−0.133802	−	1.02592i	−0.0223003	−	0.170987i
$37$	0.229805	+	0.132678i	0.0377797	+	0.0218121i	0.518771	−	0.854913i	$-0.326390\pi$
$37$	0.229805	+	0.132678i	0.0377797	+	0.0218121i	−0.480991	+	0.876725i	$0.659723\pi$
$38$	1.83797	−	9.21097i	0.298158	−	1.49422i
$39$	3.12485	+	5.41240i	0.500377	+	0.866678i
$40$	−0.685178	−	1.39579i	−0.108336	−	0.220693i
$41$	6.24970			0.976039			0.488020	−	0.872833i	$-0.337719\pi$
$41$	6.24970			0.976039			0.488020	+	0.872833i	$0.337719\pi$
$42$		0			0
$43$			5.35027i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$43$			5.35027i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$44$	−1.83515	+	4.41531i	−0.276659	+	0.665634i
$45$	0.246282	−	0.142191i	0.0367135	−	0.0211965i
$46$	−3.25762	−	0.650030i	−0.480309	−	0.0958417i
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	−0.755569	−	0.655069i	$-0.772639\pi$
$47$	1.29930	−	2.25045i	0.189522	−	0.328262i	0.945091	+	0.326807i	$0.105973\pi$
$48$	1.61650	+	6.09180i	0.233321	+	0.879276i
$49$		0			0
$50$	−4.38350	+	4.99233i	−0.619921	+	0.706022i
$51$	5.75174	+	3.32077i	0.805405	+	0.465001i
$52$	4.82157	+	6.29937i	0.668632	+	0.873565i
$53$	9.36933	−	5.40939i	1.28698	−	0.743037i	0.308863	−	0.951107i	$-0.400052\pi$
$53$	9.36933	−	5.40939i	1.28698	−	0.743037i	0.978114	+	0.208070i	$0.0667182\pi$
$54$	−7.42324	+	2.51484i	−1.01018	+	0.342227i
$55$	−1.31429			−0.177218
$56$		0			0
$57$	−10.4648			−1.38610
$58$	−11.0064	+	3.72875i	−1.44521	+	0.489608i
$59$	−3.26891	+	1.88730i	−0.425575	+	0.245706i	−0.697460	−	0.716624i	$-0.745686\pi$
$59$	−3.26891	+	1.88730i	−0.425575	+	0.245706i	0.271884	+	0.962330i	$0.412353\pi$
$60$	−1.37568	+	1.05295i	−0.177599	+	0.135935i
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	0.0490905	−	0.998794i	$-0.484368\pi$
$61$	−6.18061	−	3.56837i	−0.791345	−	0.456884i	−0.840436	+	0.541911i	$0.817701\pi$
$62$	0.808249	−	0.920507i	0.102648	−	0.116904i
$63$		0			0
$64$	3.03461	+	7.40210i	0.379326	+	0.925263i
$65$	−1.09024	+	1.88835i	−0.135228	+	0.234222i
$66$	5.22436	+	1.04248i	0.643074	+	0.128320i
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	−0.634796	−	0.772680i	$-0.718916\pi$
$67$	−2.31673	+	1.33757i	−0.283034	+	0.163410i	0.351762	+	0.936089i	$0.385583\pi$
$68$	7.78456	+	3.23552i	0.944017	+	0.392364i
$69$			3.70105i			0.445554i
$70$		0			0
$71$	8.76700			1.04045			0.520226	−	0.854029i	$-0.325848\pi$
$71$	8.76700			1.04045			0.520226	+	0.854029i	$0.325848\pi$
$72$	−1.31344	+	0.644754i	−0.154790	+	0.0759850i
$73$	2.33159	+	4.03843i	0.272892	+	0.472663i	0.969601	−	0.244691i	$-0.0786865\pi$
$73$	2.33159	+	4.03843i	0.272892	+	0.472663i	−0.696709	+	0.717354i	$0.745353\pi$
$74$	0.0734343	−	0.368015i	0.00853657	−	0.0427809i
$75$	6.41041	+	3.70105i	0.740210	+	0.427361i
$76$	−13.1715	+	1.71785i	−1.51088	+	0.197051i
$77$		0			0
$78$	5.83159	−	6.64154i	0.660298	−	0.752006i
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	−0.882845	−	0.469665i	$-0.844375\pi$
$79$	−0.308249	+	0.533903i	−0.0346807	+	0.0600687i	0.848164	+	0.529734i	$0.177708\pi$
$80$	−1.55865	+	1.55112i	−0.174263	+	0.173421i
$81$	3.59024	+	6.21848i	0.398916	+	0.690942i
$82$	−2.83595	−	8.37108i	−0.313178	−	0.924431i
$83$		−	1.09948i		−	0.120683i	−0.998178	−	0.0603416i	$-0.980781\pi$
$83$		−	1.09948i		−	0.120683i	0.998178	−	0.0603416i	$-0.0192190\pi$
$84$		0			0
$85$			2.31720i			0.251335i
$86$	7.16634	−	2.42781i	0.772766	−	0.261797i
$87$	6.47374	+	11.2129i	0.694058	+	1.20214i
$88$	6.74677	+	0.454511i	0.719208	+	0.0484510i
$89$	−3.19779	+	5.53873i	−0.338965	+	0.587104i	−0.984238	−	0.176847i	$-0.943410\pi$
$89$	−3.19779	+	5.53873i	−0.338965	+	0.587104i	0.645273	+	0.763952i	$0.276743\pi$
$90$	−0.302212	−	0.265356i	−0.0318559	−	0.0279710i
$91$		0			0
$92$	0.607546	+	4.65834i	0.0633411	+	0.485665i
$93$	−1.18198	−	0.682416i	−0.122565	−	0.0707632i
$94$	−3.60392	−	0.719132i	−0.371716	−	0.0741728i
$95$	−1.82555	−	3.16195i	−0.187298	−	0.324409i
$96$	7.42606	−	4.92949i	0.757919	−	0.503114i
$97$	−12.9475			−1.31462			−0.657309	−	0.753621i	$-0.728305\pi$
$97$	−12.9475			−1.31462			−0.657309	+	0.753621i	$0.728305\pi$
$98$		0			0
$99$			1.23675i			0.124298i
$100$	8.67602	+	3.60604i	0.867602	+	0.360604i
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.378047	−	0.925787i	$-0.376596\pi$
$101$	13.7565	−	7.94233i	1.36882	−	0.790291i	0.990778	+	0.135495i	$0.0432625\pi$
$102$	1.83797	−	9.21097i	0.181986	−	0.912022i
$103$	9.38954	−	16.2632i	0.925179	−	1.60246i	0.133906	−	0.990994i	$-0.457248\pi$
$103$	9.38954	−	16.2632i	0.925179	−	1.60246i	0.791273	−	0.611463i	$-0.209419\pi$
$104$	6.24970	−	9.31667i	0.612834	−	0.913575i
$105$		0			0
$106$	−11.4971	−	10.0950i	−1.11670	−	0.980512i
$107$	−0.293506	−	0.169456i	−0.0283743	−	0.0163819i	0.485746	−	0.874100i	$-0.338548\pi$
$107$	−0.293506	−	0.169456i	−0.0283743	−	0.0163819i	−0.514120	+	0.857718i	$0.671881\pi$
$108$	6.73694	+	8.80179i	0.648263	+	0.846953i
$109$	−6.75910	+	3.90237i	−0.647404	+	0.373779i	−0.787461	−	0.616365i	$-0.788605\pi$
$109$	−6.75910	+	3.90237i	−0.647404	+	0.373779i	0.140057	+	0.990143i	$0.455271\pi$
$110$	0.596388	+	1.76040i	0.0568634	+	0.167848i
$111$	−0.418110			−0.0396853
$112$		0			0
$113$	2.51730			0.236808			0.118404	−	0.992966i	$-0.462222\pi$
$113$	2.51730			0.236808			0.118404	+	0.992966i	$0.462222\pi$
$114$	4.74865	+	14.0169i	0.444751	+	1.31281i
$115$	−1.11828	+	0.645638i	−0.104280	+	0.0602060i
$116$	9.98884	+	13.0504i	0.927440	+	1.21170i
$117$	1.77694	+	1.02592i	0.164279	+	0.0948463i
$118$	4.01127	+	3.52208i	0.369267	+	0.324234i
$119$		0			0
$120$	2.03461	+	1.36483i	0.185733	+	0.124592i
$121$	−2.64215	+	4.57635i	−0.240196	+	0.416031i
$122$	−1.97502	+	9.89776i	−0.178809	+	0.896101i
$123$	−8.52809	+	4.92369i	−0.768952	+	0.443954i
$124$	−1.59972	−	0.664896i	−0.143659	−	0.0597095i
$125$			5.33124i			0.476841i
$126$		0			0
$127$	−5.30221			−0.470495			−0.235248	−	0.971935i	$-0.575590\pi$
$127$	−5.30221			−0.470495			−0.235248	+	0.971935i	$0.575590\pi$
$128$	8.53762	−	7.42354i	0.754626	−	0.656155i
$129$	−4.21509	−	7.30075i	−0.371118	−	0.642796i
$130$	3.02405	+	0.603425i	0.265227	+	0.0529238i
$131$	−8.69419	−	5.01959i	−0.759615	−	0.438564i	0.0695425	−	0.997579i	$-0.477846\pi$
$131$	−8.69419	−	5.01959i	−0.759615	−	0.438564i	−0.829157	+	0.559015i	$0.811179\pi$
$132$	−0.974343	−	7.47074i	−0.0848057	−	0.650244i
$133$		0			0
$134$	2.84286	+	2.49616i	0.245585	+	0.215636i
$135$	−1.52334	+	2.63850i	−0.131108	+	0.227086i
$136$	0.801340	−	11.8951i	0.0687144	−	1.02000i
$137$	−1.62485	−	2.81432i	−0.138820	−	0.240444i	0.788230	−	0.615381i	$-0.210998\pi$
$137$	−1.62485	−	2.81432i	−0.138820	−	0.240444i	−0.927050	+	0.374937i	$0.877664\pi$
$138$	4.95732	−	1.67944i	0.421995	−	0.142963i
$139$			15.3349i			1.30069i	0.759639	+	0.650346i	$0.225376\pi$
$139$			15.3349i			1.30069i	−0.759639	+	0.650346i	$0.774624\pi$
$140$		0			0
$141$			4.09449i			0.344819i
$142$	−3.97823	−	11.7428i	−0.333846	−	0.985438i
$143$	−4.74135	−	8.21226i	−0.396491	−	0.686743i
$144$	1.45961	+	1.46669i	0.121634	+	0.122225i
$145$	−2.25865	+	3.91210i	−0.187571	+	0.324882i
$146$	4.35121	−	4.95555i	0.360109	−	0.410124i
$147$		0			0
$148$	−0.526255	+	0.0686349i	−0.0432579	+	0.00564175i
$149$	−6.39393	−	3.69154i	−0.523812	−	0.302423i	0.214681	−	0.976684i	$-0.431129\pi$
$149$	−6.39393	−	3.69154i	−0.523812	−	0.302423i	−0.738493	+	0.674261i	$0.764462\pi$
$150$	2.04845	−	10.2658i	0.167255	−	0.838197i
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	0.645259	−	0.763964i	$-0.276750\pi$
$151$	−4.16550	−	7.21485i	−0.338983	−	0.587136i	−0.984242	+	0.176828i	$0.943416\pi$
$152$	8.27784	+	16.8629i	0.671422	+	1.36776i
$153$	2.18048			0.176282
$154$		0			0
$155$		−	0.476182i		−	0.0382478i
$156$	−11.5421	−	4.79729i	−0.924111	−	0.384090i
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	−0.725928	−	0.687770i	$-0.758590\pi$
$157$	−6.18061	+	3.56837i	−0.493266	+	0.284787i	0.232662	+	0.972558i	$0.425256\pi$
$158$	0.855004	+	0.170609i	0.0680204	+	0.0135729i
$159$	−8.52334	+	14.7629i	−0.675945	+	1.17077i
$160$	2.78491	+	1.38386i	0.220166	+	0.109404i
$161$		0			0
$162$	6.70010	−	7.63068i	0.526410	−	0.599523i
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	0.231164	−	0.972915i	$-0.425746\pi$
$163$	−6.33023	−	3.65476i	−0.495822	−	0.286263i	−0.726987	+	0.686652i	$0.759080\pi$
$164$	−9.92564	+	7.59714i	−0.775063	+	0.593237i
$165$	1.79342	−	1.03543i	0.139618	−	0.0806083i
$166$	−1.47268	+	0.498913i	−0.114302	+	0.0387231i
$167$	−1.88873			−0.146154			−0.0730772	−	0.997326i	$-0.523282\pi$
$167$	−1.88873			−0.146154			−0.0730772	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	−2.73240			−0.210184
$170$	3.10374	−	1.05148i	0.238046	−	0.0806450i
$171$	−2.97540	+	1.71785i	−0.227535	+	0.131367i
$172$	−6.50379	−	8.49718i	−0.495909	−	0.647904i
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.156329	−	0.987705i	$-0.549966\pi$
$173$	−14.3350	−	8.27632i	−1.08987	−	0.629237i	−0.933542	+	0.358468i	$0.883299\pi$
$174$	12.0813	−	13.7593i	0.915880	−	1.04309i
$175$		0			0
$176$	−2.45272	−	9.24312i	−0.184881	−	0.696726i
$177$	2.97374	−	5.15068i	0.223520	−	0.387149i
$178$	8.86985	+	1.76990i	0.664823	+	0.132660i
$179$	−4.79957	+	2.77103i	−0.358737	+	0.207117i	−0.668526	−	0.743688i	$-0.733075\pi$
$179$	−4.79957	+	2.77103i	−0.358737	+	0.207117i	0.309790	+	0.950805i	$0.399741\pi$
$180$	−0.218292	+	0.525205i	−0.0162705	+	0.0391464i
$181$			9.98466i			0.742154i	0.928602	+	0.371077i	$0.121011\pi$
$181$			9.98466i			0.742154i	−0.928602	+	0.371077i	$0.878989\pi$
$182$		0			0
$183$	11.2451			0.831259
$184$	5.96386	−	2.92760i	0.439661	−	0.215825i
$185$	−0.0729381	−	0.126333i	−0.00536252	−	0.00928816i
$186$	−0.377702	+	1.89285i	−0.0276944	+	0.138790i
$187$	−8.72714	−	5.03862i	−0.638192	−	0.368460i
$188$	0.672132	+	5.15354i	0.0490202	+	0.375861i
$189$		0			0
$190$	−3.40684	+	3.88002i	−0.247158	+	0.281486i
$191$	−0.0842049	+	0.145847i	−0.00609285	+	0.0105531i	−0.869056	−	0.494714i	$-0.835273\pi$
$191$	−0.0842049	+	0.145847i	−0.00609285	+	0.0105531i	0.862963	+	0.505267i	$0.168606\pi$
$192$	−9.97249	−	7.70986i	−0.719703	−	0.556411i
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	0.698450	−	0.715659i	$-0.253873\pi$
$193$	−3.75865	−	6.51018i	−0.270554	−	0.468613i	−0.969004	+	0.247046i	$0.920540\pi$
$194$	5.87523	+	17.3423i	0.421817	+	1.24511i
$195$		−	3.43570i		−	0.246035i
$196$		0			0
$197$		−	1.34581i		−	0.0958847i	−0.998850	−	0.0479424i	$-0.984734\pi$
$197$		−	1.34581i		−	0.0958847i	0.998850	−	0.0479424i	$-0.0152664\pi$
$198$	1.65654	−	0.561202i	0.117725	−	0.0398829i
$199$	−6.38059	−	11.0515i	−0.452308	−	0.783420i	0.546221	−	0.837641i	$-0.316066\pi$
$199$	−6.38059	−	11.0515i	−0.452308	−	0.783420i	−0.998529	+	0.0542208i	$0.982733\pi$
$200$	0.893107	−	13.2573i	0.0631522	−	0.937433i
$201$	2.10755	−	3.65038i	0.148655	−	0.257478i
$202$	−16.8806	−	14.8220i	−1.18771	−	1.04287i
$203$		0			0
$204$	−13.1715	+	1.71785i	−0.922192	+	0.120273i
$205$	−2.97540	−	1.71785i	−0.207811	−	0.119980i
$206$	−26.0442	−	5.19690i	−1.81458	−	0.362085i
$207$	0.607546	+	1.05230i	0.0422274	+	0.0731400i
$208$	−15.3150	−	4.14342i	−1.06191	−	0.287294i
$209$	15.8783			1.09832
$210$		0			0
$211$			8.46353i			0.582653i	0.956624	+	0.291327i	$0.0940967\pi$
$211$			8.46353i			0.582653i	−0.956624	+	0.291327i	$0.905903\pi$
$212$	−8.30452	+	19.9805i	−0.570357	+	1.37226i
$213$	−11.9631	+	6.90690i	−0.819698	+	0.473253i
$214$	−0.0937901	+	0.470028i	−0.00641136	+	0.0321304i
$215$	1.47062	−	2.54719i	0.100296	−	0.173717i
$216$	8.73240	−	13.0177i	0.594164	−	0.885744i
$217$		0			0
$218$	8.29407	+	7.28259i	0.561745	+	0.493239i
$219$	−6.36319	−	3.67379i	−0.429984	−	0.248252i
$220$	2.08732	−	1.59765i	0.140727	−	0.107713i
$221$	−14.4789	+	8.35939i	−0.973955	+	0.562313i
$222$	0.189727	+	0.560032i	0.0127337	+	0.0375869i
$223$	5.80161			0.388505			0.194252	−	0.980952i	$-0.437772\pi$
$223$	5.80161			0.388505			0.194252	+	0.980952i	$0.437772\pi$
$224$		0			0
$225$	2.43018			0.162012
$226$	−1.14229	−	3.37177i	−0.0759837	−	0.224287i
$227$	9.89265	−	5.71152i	0.656598	−	0.379087i	−0.134382	−	0.990930i	$-0.542905\pi$
$227$	9.89265	−	5.71152i	0.656598	−	0.379087i	0.790980	+	0.611843i	$0.209571\pi$
$228$	16.6200	−	12.7210i	1.10068	−	0.842470i
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.925164	−	0.379568i	$-0.123928\pi$
$229$	16.0260	+	9.25263i	1.05903	+	0.611431i	0.133866	+	0.990999i	$0.457261\pi$
$230$	1.37224	+	1.20489i	0.0904825	+	0.0794480i
$231$		0			0
$232$	12.9475	−	19.3013i	0.850044	−	1.26719i
$233$	5.52566	−	9.57072i	0.361998	−	0.626999i	−0.626292	−	0.779589i	$-0.715428\pi$
$233$	5.52566	−	9.57072i	0.361998	−	0.626999i	0.988290	+	0.152590i	$0.0487615\pi$
$234$	0.567823	−	2.84564i	0.0371198	−	0.186025i
$235$	−1.23716	+	0.714273i	−0.0807032	+	0.0465940i
$236$	2.89740	−	6.97106i	0.188605	−	0.453778i
$237$		−	0.971389i		−	0.0630985i
$238$		0			0
$239$	−22.6107			−1.46256			−0.731281	−	0.682076i	$-0.761077\pi$
$239$	−22.6107			−1.46256			−0.731281	+	0.682076i	$0.761077\pi$
$240$	0.904854	−	3.34455i	0.0584081	−	0.215890i
$241$	6.96479	+	12.0634i	0.448642	+	0.777070i	0.998298	−	0.0583207i	$-0.0185746\pi$
$241$	6.96479	+	12.0634i	0.448642	+	0.777070i	−0.549656	+	0.835391i	$0.685241\pi$
$242$	7.32866	+	1.46237i	0.471104	+	0.0940049i
$243$	4.60051	+	2.65611i	0.295123	+	0.170389i
$244$	14.1536	−	1.84593i	0.906093	−	0.118174i
$245$		0			0
$246$	10.4648	+	9.18859i	0.667211	+	0.585843i
$247$	13.1715	−	22.8138i	0.838085	−	1.45161i
$248$	−0.164675	+	2.44444i	−0.0104569	+	0.155222i
$249$	0.866198	+	1.50030i	0.0548931	+	0.0950776i
$250$	7.14086	−	2.41918i	0.451627	−	0.153002i
$251$		−	0.706033i		−	0.0445644i	−0.999752	−	0.0222822i	$-0.992907\pi$
$251$		−	0.706033i		−	0.0445644i	0.999752	−	0.0222822i	$-0.00709323\pi$
$252$		0			0
$253$		−	5.61562i		−	0.353051i
$254$	2.40600	+	7.10197i	0.150966	+	0.445618i
$255$	−1.82555	−	3.16195i	−0.114321	−	0.198009i
$256$	−13.8175	−	8.06700i	−0.863594	−	0.504187i
$257$	10.3919	−	17.9992i	0.648226	−	1.12276i	−0.335320	−	0.942104i	$-0.608844\pi$
$257$	10.3919	−	17.9992i	0.648226	−	1.12276i	0.983546	−	0.180656i	$-0.0578222\pi$
$258$	−7.86620	+	8.95874i	−0.489728	+	0.557747i
$259$		0			0
$260$	−0.563987	−	4.32435i	−0.0349770	−	0.268185i
$261$	3.68129	+	2.12540i	0.227866	+	0.131559i
$262$	−2.77823	+	13.9231i	−0.171640	+	0.860170i
$263$	11.3895	+	19.7273i	0.702309	+	1.21644i	0.967654	+	0.252281i	$0.0811809\pi$
$263$	11.3895	+	19.7273i	0.702309	+	1.21644i	−0.265345	+	0.964154i	$0.585486\pi$
$264$	−9.56445	+	4.69509i	−0.588651	+	0.288963i
$265$	−5.94749			−0.365351
$266$		0			0
$267$		−	10.0772i		−	0.616717i
$268$	2.05344	−	4.94052i	0.125434	−	0.301790i
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	−0.418839	−	0.908060i	$-0.637563\pi$
$269$	2.59376	−	1.49751i	0.158145	−	0.0913048i	0.576984	+	0.816756i	$0.304230\pi$
$270$	4.22536	+	0.843135i	0.257147	+	0.0513116i
$271$	−12.5926	+	21.8109i	−0.764943	+	1.32492i	0.175333	+	0.984509i	$0.443900\pi$
$271$	−12.5926	+	21.8109i	−0.764943	+	1.32492i	−0.940277	+	0.340412i	$0.889434\pi$
$272$	−16.2964	+	4.32435i	−0.988113	+	0.262202i
$273$		0			0
$274$	−3.03229	+	3.45345i	−0.183188	+	0.208630i
$275$	−9.72654	−	5.61562i	−0.586533	−	0.338635i
$276$	−4.49900	−	5.87793i	−0.270808	−	0.353810i
$277$	−8.17940	+	4.72238i	−0.491453	+	0.283740i	−0.725177	−	0.688563i	$-0.758242\pi$
$277$	−8.17940	+	4.72238i	−0.491453	+	0.283740i	0.233724	+	0.972303i	$0.424909\pi$
$278$	20.5402	−	6.95858i	1.23192	−	0.417348i
$279$	−0.448088			−0.0268263
$280$		0			0
$281$	26.8425			1.60129			0.800644	−	0.599141i	$-0.204491\pi$
$281$	26.8425			1.60129			0.800644	+	0.599141i	$0.204491\pi$
$282$	5.48432	−	1.85797i	0.326586	−	0.110641i
$283$	11.2429	−	6.49111i	0.668323	−	0.385856i	−0.127118	−	0.991888i	$-0.540573\pi$
$283$	11.2429	−	6.49111i	0.668323	−	0.385856i	0.795441	+	0.606031i	$0.207239\pi$
$284$	−13.9236	+	10.6572i	−0.826212	+	0.632387i
$285$	4.98215	+	2.87645i	0.295117	+	0.170386i
$286$	−8.84830	+	10.0772i	−0.523211	+	0.595880i
$287$		0			0
$288$	1.30221	−	2.62060i	0.0767336	−	0.154420i
$289$	−0.383502	+	0.664245i	−0.0225590	+	0.0390733i
$290$	6.26493	+	1.25011i	0.367889	+	0.0734092i
$291$	17.6676	−	10.2004i	1.03569	−	0.597958i
$292$	−8.61211	−	3.57947i	−0.503985	−	0.209473i
$293$		−	9.56300i		−	0.558677i	−0.960193	−	0.279338i	$-0.909885\pi$
$293$		−	9.56300i		−	0.558677i	0.960193	−	0.279338i	$-0.0901151\pi$
$294$		0			0
$295$	2.07504			0.120814
$296$	0.330733	+	0.673741i	0.0192235	+	0.0391604i
$297$	−6.62485	−	11.4746i	−0.384413	−	0.665823i
$298$	−2.04318	+	10.2394i	−0.118358	+	0.593152i
$299$	−8.06848	−	4.65834i	−0.466612	−	0.269399i
$300$	−14.6799	+	1.91457i	−0.847544	+	0.110538i
$301$		0			0
$302$	−7.77364	+	8.85332i	−0.447323	+	0.509452i
$303$	−12.5144	+	21.6756i	−0.718933	+	1.24523i
$304$	18.8305	−	18.7396i	1.08001	−	1.07479i
$305$	1.96167	+	3.39771i	0.112325	+	0.194552i
$306$	−0.989446	−	2.92062i	−0.0565629	−	0.166961i
$307$			12.2217i			0.697527i	0.937211	+	0.348763i	$0.113398\pi$
$307$			12.2217i			0.697527i	−0.937211	+	0.348763i	$0.886602\pi$
$308$		0			0
$309$			29.5894i			1.68328i
$310$	−0.637815	+	0.216079i	−0.0362255	+	0.0122724i
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.822311	+	0.569038i	$0.192684\pi$
$311$	15.9415	+	27.6114i	0.903957	+	1.56570i	0.0816453	+	0.996661i	$0.473983\pi$
$312$	−1.18814	+	17.6368i	−0.0672654	+	0.998490i
$313$	10.7618	−	18.6399i	0.608291	−	1.05359i	−0.383230	−	0.923653i	$-0.625189\pi$
$313$	10.7618	−	18.6399i	0.608291	−	1.05359i	0.991522	−	0.129939i	$-0.0414782\pi$
$314$	7.58420	+	6.65929i	0.428001	+	0.375806i
$315$		0			0
$316$	−0.159458	−	1.22264i	−0.00897023	−	0.0687789i
$317$	20.0481	+	11.5747i	1.12601	+	0.650103i	0.942929	−	0.332995i	$-0.108059\pi$
$317$	20.0481	+	11.5747i	1.12601	+	0.650103i	0.183082	+	0.983098i	$0.441393\pi$
$318$	23.6416	+	4.71748i	1.32575	+	0.264543i
$319$	−9.82264	−	17.0133i	−0.549962	−	0.952562i
$320$	0.589871	−	4.35816i	0.0329748	−	0.243629i
$321$	0.534009			0.0298055
$322$		0			0
$323$		−	27.9947i		−	1.55767i
$324$	−13.2611	−	5.51176i	−0.736730	−	0.306209i
$325$	−16.1370	+	9.31667i	−0.895117	+	0.516796i
$326$	−2.02283	+	10.1374i	−0.112034	+	0.561457i
$327$	6.14879	−	10.6500i	0.340029	−	0.588947i
$328$	14.6799	+	9.84739i	0.810561	+	0.543731i
$329$		0			0
$330$	−2.20070	−	1.93232i	−0.121145	−	0.106371i
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.994899	−	0.100878i	$-0.0321652\pi$
$331$	25.5615	+	14.7579i	1.40499	+	0.811169i	0.410086	+	0.912047i	$0.365499\pi$
$332$	1.33652	+	1.74616i	0.0733513	+	0.0958332i
$333$	−0.118879	+	0.0686349i	−0.00651454	+	0.00376117i
$334$	0.857056	+	2.52984i	0.0468960	+	0.138426i
$335$	1.47062			0.0803486
$336$		0			0
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$	1.23989	+	3.65987i	0.0674411	+	0.199071i
$339$	−3.43501	+	1.98320i	−0.186564	+	0.107713i
$340$	−2.81679	−	3.68012i	−0.152762	−	0.199583i
$341$	1.79342	+	1.03543i	0.0971192	+	0.0560718i
$342$	3.65111	+	3.20585i	0.197429	+	0.173352i
$343$		0			0
$344$	−8.43018	+	12.5672i	−0.454525	+	0.677578i
$345$	1.01730	−	1.76202i	0.0547698	−	0.0948641i
$346$	−4.58076	+	22.9564i	−0.246263	+	1.23414i
$347$	27.4329	−	15.8384i	1.47267	−	0.850248i	0.473146	−	0.880984i	$-0.343118\pi$
$347$	27.4329	−	15.8384i	1.47267	−	0.850248i	0.999528	+	0.0307361i	$0.00978515\pi$
$348$	−23.9118	−	9.93853i	−1.28181	−	0.532761i
$349$		−	28.4807i		−	1.52454i	−0.647260	−	0.762269i	$-0.724085\pi$
$349$		−	28.4807i		−	1.52454i	0.647260	−	0.762269i	$-0.275915\pi$
$350$		0			0
$351$	−21.9821			−1.17332
$352$	−11.2676	+	7.47954i	−0.600565	+	0.398661i
$353$	10.1196	+	17.5277i	0.538613	+	0.932905i	0.998979	+	0.0451760i	$0.0143849\pi$
$353$	10.1196	+	17.5277i	0.538613	+	0.932905i	−0.460366	+	0.887729i	$0.652282\pi$
$354$	−8.24841	−	1.64590i	−0.438398	−	0.0874786i
$355$	−4.17386	−	2.40978i	−0.221525	−	0.127898i
$356$	−1.65423	−	12.6837i	−0.0876740	−	0.672237i
$357$		0			0
$358$	5.88954	+	5.17130i	0.311272	+	0.273312i
$359$	−12.5611	+	21.7564i	−0.662948	+	1.14826i	0.316889	+	0.948463i	$0.397362\pi$
$359$	−12.5611	+	21.7564i	−0.662948	+	1.14826i	−0.979837	+	0.199797i	$0.935972\pi$
$360$	0.802533	+	0.0540644i	0.0422972	+	0.00284944i
$361$	12.5550	+	21.7460i	0.660791	+	1.14452i
$362$	13.3738	−	4.53077i	0.702912	−	0.238132i
$363$		−	8.32626i		−	0.437015i
$364$		0			0
$365$		−	2.56353i		−	0.134181i
$366$	−5.10271	−	15.0621i	−0.266723	−	0.787306i
$367$	−15.1912	−	26.3118i	−0.792972	−	1.37347i	−0.924119	−	0.382104i	$-0.875199\pi$
$367$	−15.1912	−	26.3118i	−0.792972	−	1.37347i	0.131147	−	0.991363i	$-0.458134\pi$
$368$	−6.62757	−	6.65974i	−0.345486	−	0.347163i
$369$	−1.61650	+	2.79986i	−0.0841515	+	0.145755i
$370$	−0.136117	+	0.155022i	−0.00707639	+	0.00805923i
$371$		0			0
$372$	2.70674	−	0.353016i	0.140338	−	0.0183031i
$373$	−4.86327	−	2.80781i	−0.251811	−	0.145383i	0.368782	−	0.929516i	$-0.379775\pi$
$373$	−4.86327	−	2.80781i	−0.251811	−	0.145383i	−0.620593	+	0.784133i	$0.713108\pi$
$374$	−2.78876	+	13.9758i	−0.144203	+	0.722674i
$375$	−4.20010	−	7.27479i	−0.216892	−	0.375669i
$376$	6.59785	−	3.23882i	0.340258	−	0.167029i
$377$	−32.5928			−1.67861
$378$		0			0
$379$			8.07009i			0.414533i	0.978285	+	0.207266i	$0.0664566\pi$
$379$			8.07009i			0.414533i	−0.978285	+	0.207266i	$0.933543\pi$
$380$	6.74298	+	2.80260i	0.345907	+	0.143770i
$381$	7.23518	−	4.17723i	0.370670	−	0.214006i
$382$	0.233563	+	0.0466055i	0.0119501	+	0.00238455i
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	0.327022	+	0.945017i	$0.393955\pi$
$383$	−12.8166	+	22.1990i	−0.654898	+	1.13432i	−0.981919	+	0.189299i	$0.939378\pi$
$384$	−5.80161	+	16.8560i	−0.296062	+	0.860182i
$385$		0			0
$386$	−7.01439	+	7.98862i	−0.357023	+	0.406610i
$387$	−2.39691	−	1.38386i	−0.121842	−	0.0703454i
$388$	20.5629	−	15.7390i	1.04392	−	0.799026i
$389$	22.9905	−	13.2736i	1.16566	−	0.672997i	0.213010	−	0.977050i	$-0.431673\pi$
$389$	22.9905	−	13.2736i	1.16566	−	0.672997i	0.952655	+	0.304053i	$0.0983401\pi$
$390$	−4.60190	+	1.55903i	−0.233026	+	0.0789444i
$391$	−9.90081			−0.500705
$392$		0			0
$393$	15.8183			0.797929
$394$	−1.80262	+	0.610691i	−0.0908148	+	0.0307662i
$395$	0.293506	−	0.169456i	0.0147679	−	0.00852626i
$396$	−1.50339	−	1.96417i	−0.0755482	−	0.0987034i
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.999791	−	0.0204418i	$-0.00650729\pi$
$397$	29.5283	+	17.0482i	1.48198	+	0.855624i	0.482192	+	0.876065i	$0.339841\pi$
$398$	−11.9074	+	13.5613i	−0.596866	+	0.679765i
$399$		0			0
$400$	−18.1626	+	4.81955i	−0.908129	+	0.240978i
$401$	−9.17676	+	15.8946i	−0.458266	+	0.793739i	−0.998869	−	0.0475379i	$-0.984862\pi$
$401$	−9.17676	+	15.8946i	−0.458266	+	0.793739i	0.540604	+	0.841277i	$0.318196\pi$
$402$	−5.84580	−	1.16648i	−0.291562	−	0.0581787i
$403$	2.97540	−	1.71785i	0.148215	−	0.0855721i
$404$	−12.1931	+	29.3363i	−0.606630	+	1.45953i
$405$		−	3.94738i		−	0.196147i
$406$		0			0
$407$	0.634401			0.0314461
$408$	8.27784	+	16.8629i	0.409814	+	0.834839i
$409$	5.87455	+	10.1750i	0.290478	+	0.503122i	0.973923	−	0.226880i	$-0.0728524\pi$
$409$	5.87455	+	10.1750i	0.290478	+	0.503122i	−0.683445	+	0.730002i	$0.739519\pi$
$410$	−0.950790	+	4.76487i	−0.0469562	+	0.235320i
$411$	4.43441	+	2.56021i	0.218733	+	0.126286i
$412$	4.85725	+	37.2427i	0.239299	+	1.83482i
$413$		0			0
$414$	1.13380	−	1.29128i	0.0557233	−	0.0634627i
$415$	−0.302212	+	0.523446i	−0.0148350	+	0.0256949i
$416$	1.39972	+	22.3937i	0.0686268	+	1.09794i
$417$	−12.0813	−	20.9254i	−0.591623	−	1.02472i
$418$	−7.20514	−	21.2679i	−0.352415	−	1.04025i
$419$		−	11.0841i		−	0.541495i	−0.962650	−	0.270748i	$-0.912729\pi$
$419$		−	11.0841i		−	0.541495i	0.962650	−	0.270748i	$-0.0872709\pi$
$420$		0			0
$421$		−	0.137270i		−	0.00669012i	−0.999994	−	0.00334506i	$-0.998935\pi$
$421$		−	0.137270i		−	0.00669012i	0.999994	−	0.00334506i	$-0.00106477\pi$
$422$	11.3364	−	3.84053i	0.551845	−	0.186954i
$423$	0.672132	+	1.16417i	0.0326802	+	0.0566037i
$424$	30.5309	+	2.05678i	1.48271	+	0.0998861i
$425$	−9.90081	+	17.1487i	−0.480260	+	0.831834i
$426$	14.6799	+	12.8896i	0.711243	+	0.624505i
$427$		0			0
$428$	0.672132	−	0.0876603i	0.0324887	−	0.00423722i
$429$	12.9397	+	7.47074i	0.624735	+	0.360691i
$430$	−4.07913	−	0.813956i	−0.196713	−	0.0392524i
$431$	−6.23008	−	10.7908i	−0.300092	−	0.519775i	0.676064	−	0.736843i	$-0.263684\pi$
$431$	−6.23008	−	10.7908i	−0.300092	−	0.519775i	−0.976157	+	0.217067i	$0.930351\pi$
$432$	−21.3989	−	5.78939i	−1.02956	−	0.278542i
$433$	14.1563			0.680310			0.340155	−	0.940369i	$-0.389520\pi$
$433$	14.1563			0.680310			0.340155	+	0.940369i	$0.389520\pi$
$434$		0			0
$435$		−	7.11772i		−	0.341269i
$436$	5.99093	−	14.4140i	0.286914	−	0.690306i
$437$	13.5102	−	7.80014i	0.646282	−	0.373131i
$438$	−2.03336	+	10.1901i	−0.0971576	+	0.486904i
$439$	−2.72948	+	4.72760i	−0.130271	+	0.225636i	−0.923781	−	0.382921i	$-0.874918\pi$
$439$	−2.72948	+	4.72760i	−0.130271	+	0.225636i	0.793510	+	0.608557i	$0.208251\pi$
$440$	−3.08712	−	2.07086i	−0.147173	−	0.0987246i
$441$		0			0
$442$	17.7670	+	15.6003i	0.845090	+	0.742030i
$443$	−28.8691	−	16.6676i	−1.37161	−	0.791900i	−0.380480	−	0.924789i	$-0.624241\pi$
$443$	−28.8691	−	16.6676i	−1.37161	−	0.791900i	−0.991131	+	0.132889i	$0.957575\pi$
$444$	0.664034	−	0.508256i	0.0315137	−	0.0241207i
$445$	3.04485	−	1.75794i	0.144340	−	0.0833346i
$446$	−2.63262	−	7.77089i	−0.124658	−	0.367962i
$447$	11.6332			0.550232
$448$		0			0
$449$	−26.9716			−1.27287			−0.636435	−	0.771330i	$-0.719592\pi$
$449$	−26.9716			−1.27287			−0.636435	+	0.771330i	$0.719592\pi$
$450$	−1.10275	−	3.25508i	−0.0519843	−	0.153446i
$451$	12.9397	−	7.47074i	0.609307	−	0.351783i
$452$	−3.99793	+	3.06004i	−0.188047	+	0.143932i
$453$	11.3681	+	6.56339i	0.534121	+	0.308375i
$454$	−12.1392	−	10.6588i	−0.569723	−	0.500244i
$455$		0			0
$456$	−24.5807	−	16.4889i	−1.15110	−	0.772165i
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	−0.998160	−	0.0606278i	$-0.980690\pi$
$457$	−9.54668	+	16.5353i	−0.446575	+	0.773491i	0.551585	+	0.834118i	$0.314023\pi$
$458$	5.12112	−	25.6644i	0.239294	−	1.19922i
$459$	−20.2306	+	11.6802i	−0.944285	+	0.545183i
$460$	0.991187	−	2.38477i	0.0462143	−	0.111190i
$461$			18.9177i			0.881087i	0.897731	+	0.440543i	$0.145214\pi$
$461$			18.9177i			0.881087i	−0.897731	+	0.440543i	$0.854786\pi$
$462$		0			0
$463$	0.860370			0.0399848			0.0199924	−	0.999800i	$-0.493636\pi$
$463$	0.860370			0.0399848			0.0199924	+	0.999800i	$0.493636\pi$
$464$	−31.7281	−	8.58391i	−1.47294	−	0.398498i
$465$	0.375150	+	0.649778i	0.0173972	+	0.0301328i
$466$	−15.3268	−	3.05833i	−0.709999	−	0.141674i
$467$	−16.1842	−	9.34394i	−0.748914	−	0.432386i	0.0763871	−	0.997078i	$-0.475662\pi$
$467$	−16.1842	−	9.34394i	−0.748914	−	0.432386i	−0.825302	+	0.564692i	$0.808995\pi$
$468$	−4.06922	+	0.530712i	−0.188100	+	0.0245322i
$469$		0			0
$470$	1.51811	+	1.33297i	0.0700253	+	0.0614855i
$471$	5.62253	−	9.73852i	0.259073	−	0.448727i
$472$	−10.6521	−	0.717599i	−0.490301	−	0.0330302i
$473$	6.39558	+	11.0775i	0.294069	+	0.509342i
$474$	−1.30111	+	0.440791i	−0.0597621	+	0.0202462i
$475$		−	31.2006i		−	1.43158i
$476$		0			0
$477$			5.59660i			0.256251i
$478$	10.2601	+	30.2856i	0.469287	+	1.38523i
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	0.572577	−	0.819851i	$-0.305944\pi$
$479$	−9.27364	−	16.0624i	−0.423723	−	0.733911i	−0.996300	+	0.0859405i	$0.972610\pi$
$480$	−4.89041	+	0.305675i	−0.223216	+	0.0139521i
$481$	0.526255	−	0.911501i	0.0239952	−	0.0415609i
$482$	12.9977	−	14.8029i	0.592028	−	0.674255i
$483$		0			0
$484$	−1.36680	−	10.4799i	−0.0621271	−	0.476357i
$485$	6.16413	+	3.55886i	0.279899	+	0.161600i
$486$	1.47010	−	7.36737i	0.0666849	−	0.334190i
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	0.999750	+	0.0223676i	$0.00712041\pi$
$487$	11.4588	+	19.8471i	0.519246	+	0.899360i	−0.480504	+	0.876993i	$0.659546\pi$
$488$	−8.89505	−	18.1202i	−0.402660	−	0.820265i
$489$	11.5173			0.520830
$490$		0			0
$491$		−	24.7987i		−	1.11915i	−0.828780	−	0.559575i	$-0.810964\pi$
$491$		−	24.7987i		−	1.11915i	0.828780	−	0.559575i	$-0.189036\pi$
$492$	7.55888	−	18.1865i	0.340781	−	0.819909i
$493$	−29.9959	+	17.3181i	−1.35095	+	0.779969i
$494$	−36.5345	−	7.29015i	−1.64376	−	0.327999i
$495$	0.339943	−	0.588798i	0.0152793	−	0.0264645i
$496$	3.34889	−	0.888650i	0.150370	−	0.0399016i
$497$		0			0
$498$	1.61650	−	1.84101i	0.0724370	−	0.0824978i
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.999701	+	0.0244624i	$0.00778739\pi$
$499$	33.9707	+	19.6130i	1.52074	+	0.877997i	0.521035	+	0.853535i	$0.325546\pi$
$500$	−6.48066	−	8.46697i	−0.289824	−	0.378654i
$501$	2.57729	−	1.48800i	0.115145	−	0.0664788i
$502$	−0.945686	+	0.320379i	−0.0422080	+	0.0142992i
$503$	−7.59396			−0.338598			−0.169299	−	0.985565i	$-0.554150\pi$
$503$	−7.59396			−0.338598			−0.169299	+	0.985565i	$0.554150\pi$
$504$		0			0
$505$	−8.73240			−0.388587
$506$	−7.52177	+	2.54822i	−0.334383	+	0.113282i
$507$	3.72852	−	2.15266i	0.165589	−	0.0956030i
$508$	8.42086	−	6.44538i	0.373615	−	0.285967i
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	0.413596	−	0.910460i	$-0.364272\pi$
$509$	−3.79222	−	2.18944i	−0.168087	−	0.0970451i	−0.581684	+	0.813415i	$0.697606\pi$
$510$	−3.40684	+	3.88002i	−0.150858	+	0.171810i
$511$		0			0
$512$	−4.53521	+	22.1683i	−0.200430	+	0.979708i
$513$	18.4039	−	31.8765i	0.812553	−	1.40738i
$514$	−28.8244	−	5.75166i	−1.27139	−	0.253695i
$515$	−8.94047	+	5.16178i	−0.393964	+	0.227455i
$516$	15.5691	+	6.47103i	0.685393	+	0.284871i
$517$		−	6.21259i		−	0.273230i
$518$		0			0
$519$	26.0813			1.14484
$520$	−5.53626	+	2.71770i	−0.242781	+	0.119179i
$521$	−5.37827	−	9.31544i	−0.235626	−	0.408117i	0.723828	−	0.689980i	$-0.242381\pi$
$521$	−5.37827	−	9.31544i	−0.235626	−	0.408117i	−0.959455	+	0.281863i	$0.909048\pi$
$522$	1.17636	−	5.89530i	0.0514878	−	0.258030i
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	0.552305	−	0.833642i	$-0.313748\pi$
$523$	2.43561	+	1.40620i	0.106502	+	0.0614889i	−0.445803	+	0.895131i	$0.647082\pi$
$524$	19.9098	−	2.59666i	0.869762	−	0.113435i
$525$		0			0
$526$	21.2551	−	24.2073i	0.926768	−	1.05549i
$527$	1.82555	−	3.16195i	0.0795223	−	0.137737i
$528$	10.6289	+	10.6805i	0.462562	+	0.464807i
$529$	8.74135	+	15.1405i	0.380059	+	0.658281i
$530$	2.69881	+	7.96628i	0.117229	+	0.346033i
$531$		−	1.95262i		−	0.0847365i
$532$		0			0
$533$		−	24.7889i		−	1.07372i
$534$	−13.4978	+	4.57278i	−0.584108	+	0.197884i
$535$	0.0931564	+	0.161352i	0.00402750	+	0.00697584i
$536$	−7.54931	−	0.508575i	−0.326080	−	0.0219671i
$537$	4.36620	−	7.56248i	0.188415	−	0.326345i
$538$	−3.18280	−	2.79465i	−0.137220	−	0.120486i
$539$		0			0
$540$	−0.788031	−	6.04219i	−0.0339114	−	0.260015i
$541$	−27.0699	−	15.6288i	−1.16383	−	0.671935i	−0.211608	−	0.977355i	$-0.567870\pi$
$541$	−27.0699	−	15.6288i	−1.16383	−	0.671935i	−0.952218	+	0.305419i	$0.901203\pi$
$542$	34.9285	+	6.96970i	1.50031	+	0.299374i
$543$	−7.86620	−	13.6247i	−0.337571	−	0.584690i
$544$	13.1871	+	19.8657i	0.565390	+	0.851735i
$545$	4.29055			0.183787
$546$		0			0
$547$			29.4711i			1.26010i	0.776556	+	0.630048i	$0.216965\pi$
$547$			29.4711i			1.26010i	−0.776556	+	0.630048i	$0.783035\pi$
$548$	6.00165	+	2.49448i	0.256378	+	0.106559i
$549$	3.19725	−	1.84593i	0.136455	−	0.0787826i
$550$	−3.10812	+	15.5763i	−0.132531	+	0.664176i
$551$	27.2874	−	47.2632i	1.16248	−	2.01348i
$552$	−5.83159	+	8.69338i	−0.248209	+	0.370015i
$553$		0			0
$554$	10.0369	+	8.81290i	0.426428	+	0.374424i
$555$	0.199057	+	0.114926i	0.00844949	+	0.00487832i
$556$	−18.6412	−	24.3546i	−0.790561	−	1.03287i
$557$	19.3751	−	11.1862i	0.820950	−	0.473976i	−0.0297941	−	0.999556i	$-0.509485\pi$
$557$	19.3751	−	11.1862i	0.820950	−	0.473976i	0.850744	+	0.525580i	$0.176152\pi$
$558$	0.203330	+	0.600185i	0.00860766	+	0.0254079i
$559$	21.2213			0.897567
$560$		0			0
$561$	15.8783			0.670381
$562$	−12.1804	−	35.9538i	−0.513799	−	1.51662i
$563$	−28.0528	+	16.1963i	−1.18229	+	0.682593i	−0.956542	−	0.291594i	$-0.905814\pi$
$563$	−28.0528	+	16.1963i	−1.18229	+	0.682593i	−0.225743	+	0.974187i	$0.572481\pi$
$564$	−4.97727	−	6.50279i	−0.209581	−	0.273817i
$565$	−1.19846	−	0.691928i	−0.0504194	−	0.0291097i
$566$	−13.7962	−	12.1137i	−0.579896	−	0.509177i
$567$		0			0
$568$	20.5928	+	13.8138i	0.864053	+	0.579614i
$569$	18.5288	−	32.0928i	0.776767	−	1.34540i	−0.157029	−	0.987594i	$-0.550192\pi$
$569$	18.5288	−	32.0928i	0.776767	−	1.34540i	0.933796	−	0.357806i	$-0.116475\pi$
$570$	1.59205	−	7.97853i	0.0666836	−	0.334184i
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	−0.0349102	−	0.999390i	$-0.511115\pi$
$571$	19.4303	−	11.2181i	0.813132	−	0.469462i	0.848042	+	0.529928i	$0.177781\pi$
$572$	17.5129	+	7.27894i	0.732253	+	0.304348i
$573$		−	0.265356i		−	0.0110854i
$574$		0			0
$575$	−11.0346			−0.460175
$576$	−4.10104	−	0.555070i	−0.170877	−	0.0231279i
$577$	4.78431	+	8.28667i	0.199173	+	0.344978i	0.948261	−	0.317493i	$-0.102841\pi$
$577$	4.78431	+	8.28667i	0.199173	+	0.344978i	−0.749087	+	0.662471i	$0.769508\pi$
$578$	1.06374	+	0.212260i	0.0442457	+	0.00882885i
$579$	10.2578	+	5.92235i	0.426300	+	0.246124i
$580$	−1.16841	−	8.95874i	−0.0485156	−	0.371991i
$581$		0			0
$582$	−21.6799	−	19.0360i	−0.898660	−	0.789067i
$583$	12.9325	−	22.3997i	0.535609	−	0.927703i
$584$	−0.886527	+	13.1596i	−0.0366848	+	0.544550i
$585$	−0.563987	−	0.976854i	−0.0233180	−	0.0403879i
$586$	−12.8090	+	4.33944i	−0.529136	+	0.179261i
$587$			23.6894i			0.977766i	0.872349	+	0.488883i	$0.162595\pi$
$587$			23.6894i			0.977766i	−0.872349	+	0.488883i	$0.837405\pi$
$588$		0			0
$589$			5.75289i			0.237044i
$590$	−0.941600	−	2.77939i	−0.0387651	−	0.114426i
$591$	1.06026	+	1.83643i	0.0436135	+	0.0755407i
$592$	0.752355	−	0.748721i	0.0309216	−	0.0307723i
$593$	−3.72404	+	6.45023i	−0.152928	+	0.264879i	−0.932303	−	0.361679i	$-0.882204\pi$
$593$	−3.72404	+	6.45023i	−0.152928	+	0.264879i	0.779375	+	0.626558i	$0.215537\pi$
$594$	−12.3633	+	14.0804i	−0.507272	+	0.577727i
$595$		0			0
$596$	14.6422	−	1.90965i	0.599766	−	0.0782222i
$597$	17.4134	+	10.0536i	0.712682	+	0.411467i
$598$	−2.57829	+	12.9210i	−0.105434	+	0.528381i
$599$	−0.837627	−	1.45081i	−0.0342245	−	0.0592786i	0.848406	−	0.529346i	$-0.177563\pi$
$599$	−0.837627	−	1.45081i	−0.0342245	−	0.0592786i	−0.882630	+	0.470068i	$0.844229\pi$
$600$	9.22579	+	18.7940i	0.376641	+	0.767261i
$601$	8.27385			0.337497			0.168749	−	0.985659i	$-0.446027\pi$
$601$	8.27385			0.337497			0.168749	+	0.985659i	$0.446027\pi$
$602$		0			0
$603$		−	1.38386i		−	0.0563550i
$604$	15.3859	+	6.39489i	0.626045	+	0.260205i
$605$	2.51579	−	1.45249i	0.102281	−	0.0590522i
$606$	34.7117	+	6.92643i	1.41007	+	0.281367i
$607$	−13.2647	+	22.9751i	−0.538397	+	0.932531i	0.460593	+	0.887611i	$0.347637\pi$
$607$	−13.2647	+	22.9751i	−0.538397	+	0.932531i	−0.998991	+	0.0449200i	$0.985697\pi$
$608$	−33.6453	−	16.7188i	−1.36450	−	0.678036i
$609$		0			0
$610$	3.66087	−	4.16932i	0.148224	−	0.168811i
$611$	−8.92620	−	5.15354i	−0.361115	−	0.208490i
$612$	−3.46300	+	2.65060i	−0.139983	+	0.107144i
$613$	−27.3692	+	15.8016i	−1.10543	+	0.638220i	−0.937642	−	0.347603i	$-0.886996\pi$
$613$	−27.3692	+	15.8016i	−1.10543	+	0.638220i	−0.167788	+	0.985823i	$0.553662\pi$
$614$	16.3701	−	5.54586i	0.660645	−	0.223813i
$615$	5.41348			0.218293
$616$		0			0
$617$	10.1113			0.407064			0.203532	−	0.979068i	$-0.434758\pi$
$617$	10.1113			0.407064			0.203532	+	0.979068i	$0.434758\pi$
$618$	39.6331	−	13.4269i	1.59428	−	0.540108i
$619$	−4.79105	+	2.76611i	−0.192568	+	0.111179i	−0.593184	−	0.805067i	$-0.702129\pi$
$619$	−4.79105	+	2.76611i	−0.192568	+	0.111179i	0.400616	+	0.916246i	$0.368796\pi$
$620$	0.578847	+	0.756262i	0.0232471	+	0.0303722i
$621$	−11.2737	−	6.50886i	−0.452397	−	0.261192i
$622$	29.7499	−	33.8819i	1.19286	−	1.35854i
$623$		0			0
$624$	24.1626	−	6.41169i	0.967277	−	0.256673i
$625$	−10.2791	+	17.8039i	−0.411163	+	0.712155i
$626$	−29.8504	−	5.95640i	−1.19306	−	0.238066i
$627$	−21.6668	+	12.5094i	−0.865290	+	0.499576i
$628$	5.47819	−	13.1804i	0.218604	−	0.525954i
$629$		−	1.11850i		−	0.0445975i
$630$		0			0
$631$	35.5582			1.41555			0.707774	−	0.706439i	$-0.249700\pi$
$631$	35.5582			1.41555			0.707774	+	0.706439i	$0.249700\pi$
$632$	−1.56529	+	0.768386i	−0.0622640	+	0.0305648i
$633$	−6.66781	−	11.5490i	−0.265022	−	0.459031i
$634$	6.40636	−	32.1054i	0.254429	−	1.27507i
$635$	2.52431	+	1.45741i	0.100174	+	0.0578357i
$636$	−4.40916	−	33.8071i	−0.174835	−	1.34054i
$637$		0			0
$638$	−18.3310	+	20.8770i	−0.725731	+	0.826528i
$639$	−2.26760	+	3.92760i	−0.0897050	+	0.155374i
$640$	−6.10515	+	1.18752i	−0.241327	+	0.0469410i
$641$	−4.73300	−	8.19779i	−0.186942	−	0.323793i	0.757287	−	0.653082i	$-0.226524\pi$
$641$	−4.73300	−	8.19779i	−0.186942	−	0.323793i	−0.944229	+	0.329289i	$0.893191\pi$
$642$	−0.242319	−	0.715271i	−0.00956358	−	0.0282295i
$643$			13.0085i			0.513007i	0.966543	+	0.256503i	$0.0825705\pi$
$643$			13.0085i			0.513007i	−0.966543	+	0.256503i	$0.917430\pi$
$644$		0			0
$645$			4.63439i			0.182479i
$646$	−37.4971	+	12.7033i	−1.47530	+	0.499803i
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	0.998847	+	0.0480078i	$0.0152872\pi$
$647$	13.7610	+	23.8347i	0.540999	+	0.937039i	−0.457848	+	0.889031i	$0.651379\pi$
$648$	−1.36510	+	20.2635i	−0.0536261	+	0.796027i
$649$	−4.51207	+	7.81514i	−0.177114	+	0.306771i
$650$	19.8016	+	17.3868i	0.776683	+	0.681965i
$651$		0			0
$652$	14.4963	−	1.89062i	0.567718	−	0.0740425i
$653$	−30.4390	−	17.5740i	−1.19117	−	0.687723i	−0.232598	−	0.972573i	$-0.574723\pi$
$653$	−30.4390	−	17.5740i	−1.19117	−	0.687723i	−0.958572	+	0.284850i	$0.908056\pi$
$654$	−17.0552	−	3.40322i	−0.666910	−	0.133076i
$655$	2.75946	+	4.77952i	0.107821	+	0.186751i
$656$	6.52860	−	24.1313i	0.254899	−	0.942167i
$657$	−2.41228			−0.0941121
$658$		0			0
$659$			3.86719i			0.150644i	0.997159	+	0.0753222i	$0.0239985\pi$
$659$			3.86719i			0.150644i	−0.997159	+	0.0753222i	$0.976001\pi$
$660$	−1.58960	+	3.82454i	−0.0618752	+	0.148870i
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	−0.192403	−	0.981316i	$-0.561628\pi$
$661$	14.4295	−	8.33085i	0.561241	−	0.324033i	0.753643	+	0.657284i	$0.228295\pi$
$662$	8.16818	−	40.9347i	0.317465	−	1.59097i
$663$	13.1715	−	22.8138i	0.511540	−	0.886013i
$664$	1.73240	−	2.58255i	0.0672300	−	0.100222i
$665$		0			0
$666$	0.145876	+	0.128086i	0.00565259	+	0.00496325i
$667$	−16.7154	−	9.65067i	−0.647225	−	0.373675i
$668$	2.99964	−	2.29594i	0.116060	−	0.0888328i
$669$	−7.91664	+	4.57068i	−0.306075	+	0.176713i
$670$	−0.667329	−	1.96980i	−0.0257812	−	0.0761002i
$671$	−17.0622			−0.658679
$672$		0			0
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$	1.49033	+	4.39912i	0.0574055	+	0.169448i
$675$	−22.5474	+	13.0177i	−0.867848	+	0.501053i
$676$	4.33954	−	3.32150i	0.166905	−	0.127750i
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.380334	−	0.924849i	$-0.624191\pi$
$677$	−35.6839	−	20.6021i	−1.37144	−	0.791804i	−0.991110	+	0.133045i	$0.957524\pi$
$678$	4.21509	+	3.70105i	0.161880	+	0.142138i
$679$		0			0
$680$	−3.65111	+	5.44285i	−0.140014	+	0.208724i
$681$	−8.99940	+	15.5874i	−0.344858	+	0.597311i
$682$	0.573089	−	2.87203i	0.0219447	−	0.109976i
$683$	−28.6643	+	16.5493i	−1.09681	+	0.633242i	−0.935381	−	0.353642i	$-0.884943\pi$
$683$	−28.6643	+	16.5493i	−1.09681	+	0.633242i	−0.161427	+	0.986885i	$0.551610\pi$
$684$	2.63725	−	6.34515i	0.100838	−	0.242613i
$685$			1.78648i			0.0682580i
$686$		0			0
$687$	−29.1580			−1.11245
$688$	20.6584	+	5.58903i	0.787593	+	0.213080i
$689$	−21.4558	−	37.1626i	−0.817402	−	1.41578i
$690$	−2.82174	−	0.563055i	−0.107422	−	0.0214351i
$691$	12.9010	+	7.44840i	0.490777	+	0.283350i	0.724897	−	0.688857i	$-0.241887\pi$
$691$	12.9010	+	7.44840i	0.490777	+	0.283350i	−0.234120	+	0.972208i	$0.575221\pi$
$692$	32.8273	−	4.28137i	1.24791	−	0.162753i
$693$		0			0
$694$	−33.6628	−	29.5575i	−1.27782	−	1.12199i
$695$	4.21509	−	7.30075i	0.159888	−	0.276933i
$696$	−2.46147	+	36.5382i	−0.0933020	+	1.38498i
$697$	−13.1715	−	22.8138i	−0.498907	−	0.864133i
$698$	−38.1481	+	12.9238i	−1.44393	+	0.489173i
$699$			17.4131i			0.658623i
$700$		0			0
$701$			32.5746i			1.23032i	0.788401	+	0.615162i	$0.210910\pi$
$701$			32.5746i			1.23032i	−0.788401	+	0.615162i	$0.789090\pi$
$702$	9.97489	+	29.4436i	0.376478	+	1.11128i
$703$	0.881187	+	1.52626i	0.0332346	+	0.0575640i
$704$	15.1313	+	11.6982i	0.570282	+	0.440893i
$705$	1.12545	−	1.94934i	0.0423869	−	0.0734162i
$706$	18.8852	−	21.5082i	0.710755	−	0.809471i
$707$		0			0
$708$	1.53833	+	11.7951i	0.0578140	+	0.443286i
$709$	−9.95635	−	5.74830i	−0.373918	−	0.215882i	0.301251	−	0.953545i	$-0.402596\pi$
$709$	−9.95635	−	5.74830i	−0.373918	−	0.215882i	−0.675169	+	0.737663i	$0.735929\pi$
$710$	−1.33376	+	6.68411i	−0.0500550	+	0.250850i
$711$	−0.159458	−	0.276190i	−0.00598016	−	0.0103579i
$712$	−16.2384	+	7.97128i	−0.608560	+	0.298736i
$713$	2.03461			0.0761967
$714$		0			0
$715$			5.21300i			0.194955i
$716$	4.25411	−	10.2353i	0.158983	−	0.382510i
$717$	30.8536	−	17.8133i	1.15225	−	0.665251i
$718$	34.8412	+	6.95227i	1.30026	+	0.259456i
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	0.496949	+	0.867780i	$0.334454\pi$
$719$	−13.4887	+	23.3632i	−0.503045	+	0.871299i	−0.999994	+	0.00351948i	$0.998880\pi$
$720$	−0.291753	−	1.09948i	−0.0108730	−	0.0409750i
$721$		0			0
$722$	23.4302	−	26.6844i	0.871981	−	0.993091i
$723$	−19.0077	−	10.9741i	−0.706906	−	0.408132i
$724$	−12.1374	−	15.8574i	−0.451081	−	0.589337i
$725$	−33.4309	+	19.3013i	−1.24159	+	0.716833i
$726$	−11.1525	+	3.77824i	−0.413908	+	0.140223i
$727$	27.0230			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$727$	27.0230			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$728$		0			0
$729$	−29.9117			−1.10784
$730$	−3.43368	+	1.16326i	−0.127086	+	0.0430542i
$731$	19.5305	−	11.2759i	0.722361	−	0.417055i
$732$	−17.8592	+	13.6695i	−0.660095	+	0.505240i
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	0.131428	−	0.991326i	$-0.458044\pi$
$733$	−17.9059	−	10.3380i	−0.661371	−	0.381843i	−0.792799	+	0.609483i	$0.791377\pi$
$734$	−28.3497	+	32.2872i	−1.04641	+	1.19174i
$735$		0			0
$736$	−5.91288	+	11.8992i	−0.217952	+	0.438611i
$737$	−3.19779	+	5.53873i	−0.117792	+	0.204022i
$738$	4.48375	+	0.894695i	0.165049	+	0.0329342i
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	−0.318981	−	0.947761i	$-0.603341\pi$
$739$	9.30563	−	5.37261i	0.342313	−	0.197635i	0.661294	+	0.750126i	$0.270007\pi$
$740$	0.269409	+	0.111975i	0.00990367	+	0.00411629i
$741$			41.5076i			1.52482i
$742$		0			0
$743$	11.8708			0.435498			0.217749	−	0.976005i	$-0.430129\pi$
$743$	11.8708			0.435498			0.217749	+	0.976005i	$0.430129\pi$
$744$	−1.70109	−	3.46532i	−0.0623650	−	0.127045i
$745$	2.02938	+	3.51499i	0.0743507	+	0.128779i
$746$	−1.55406	+	7.78815i	−0.0568982	+	0.285145i
$747$	0.492563	+	0.284382i	0.0180219	+	0.0104050i
$748$	19.9852	−	2.60650i	0.730732	−	0.0953030i
$749$		0			0
$750$	−7.83823	+	8.92688i	−0.286212	+	0.325964i
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	−0.978654	−	0.205513i	$-0.934114\pi$
$751$	−8.53229	+	14.7784i	−0.311348	+	0.539270i	0.667307	+	0.744783i	$0.267447\pi$
$752$	−7.33212	−	7.36771i	−0.267375	−	0.268673i
$753$	0.556233	+	0.963424i	0.0202703	+	0.0351091i
$754$	14.7897	+	43.6559i	0.538610	+	1.58986i
$755$			4.57986i			0.166678i
$756$		0			0
$757$		−	46.3272i		−	1.68379i	−0.539641	−	0.841895i	$-0.681440\pi$
$757$		−	46.3272i		−	1.68379i	0.539641	−	0.841895i	$-0.318560\pi$
$758$	10.8094	−	3.66199i	0.392614	−	0.133010i
$759$	4.42415	+	7.66285i	0.160586	+	0.278144i
$760$	0.694120	−	10.3035i	0.0251784	−	0.373748i
$761$	−7.30474	+	12.6522i	−0.264796	+	0.458641i	−0.967510	−	0.252832i	$-0.918638\pi$
$761$	−7.30474	+	12.6522i	−0.264796	+	0.458641i	0.702714	+	0.711473i	$0.251971\pi$
$762$	−8.87827	−	7.79555i	−0.321626	−	0.282403i
$763$		0			0
$764$	−0.0435595	−	0.333991i	−0.00157593	−	0.0120834i
$765$	−1.03810	−	0.599347i	−0.0375326	−	0.0216694i
$766$	35.5500	+	7.09370i	1.28447	+	0.256306i
$767$	7.48582	+	12.9658i	0.270297	+	0.468169i
$768$	25.2102	+	0.122063i	0.909696	+	0.00440457i
$769$	−49.3177			−1.77844			−0.889221	−	0.457477i	$-0.848753\pi$
$769$	−49.3177			−1.77844			−0.889221	+	0.457477i	$0.848753\pi$
$770$		0			0
$771$			32.7480i			1.17939i
$772$	13.8832	+	5.77030i	0.499667	+	0.207678i
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	−0.516147	−	0.856500i	$-0.672634\pi$
$773$	−0.902744	+	0.521200i	−0.0324695	+	0.0187462i	0.483677	+	0.875246i	$0.339301\pi$
$774$	−0.765934	+	3.83847i	−0.0275309	+	0.137971i
$775$	2.03461	−	3.52404i	0.0730853	−	0.126587i
$776$	−30.4123	−	20.4008i	−1.09174	−	0.732346i
$777$		0			0
$778$	−28.2116	−	24.7711i	−1.01143	−	0.888087i
$779$	35.9467	+	20.7538i	1.28792	+	0.743583i
$780$	4.17644	+	5.45650i	0.149540	+	0.195374i
$781$	18.1517	−	10.4799i	0.649517	−	0.374999i
$782$	4.49272	+	13.2615i	0.160659	+	0.474230i
$783$	−45.5403			−1.62748
$784$		0			0
$785$	3.92334			0.140030
$786$	−7.17793	−	21.1876i	−0.256028	−	0.755738i
$787$	34.8899	−	20.1437i	1.24369	−	0.718045i	0.273847	−	0.961773i	$-0.411704\pi$
$787$	34.8899	−	20.1437i	1.24369	−	0.718045i	0.969844	+	0.243728i	$0.0783705\pi$
$788$	1.63596	+	2.13738i	0.0582788	+	0.0761411i
$789$	−31.0834	−	17.9460i	−1.10660	−	0.638895i
$790$	−0.360161	−	0.316239i	−0.0128140	−	0.0112513i
$791$		0			0
$792$	−1.94869	+	2.90498i	−0.0692436	+	0.103224i
$793$	−14.1536	+	24.5148i	−0.502610	+	0.870546i
$794$	9.43578	−	47.2873i	0.334863	−	1.67816i
$795$	8.11570	−	4.68560i	0.287834	−	0.166181i
$796$	23.5677	+	9.79552i	0.835336	+	0.347193i
$797$			32.2902i			1.14378i	0.820331	+	0.571889i	$0.193789\pi$
$797$			32.2902i			1.14378i	−0.820331	+	0.571889i	$0.806211\pi$
$798$		0			0
$799$	−10.9533			−0.387501
$800$	14.6972	+	22.1406i	0.519624	+	0.782790i
$801$	−1.65423	−	2.86521i	−0.0584493	−	0.101237i
$802$	25.4540	+	5.07913i	0.898812	+	0.179350i
$803$	9.65489	+	5.57425i	0.340714	+	0.196711i
$804$	1.09024	+	8.35939i	0.0384499	+	0.294813i
$805$		0			0
$806$	−3.65111	−	3.20585i	−0.128605	−	0.112921i
$807$	−2.35956	+	4.08688i	−0.0830605	+	0.143865i
$808$	44.8270	+	3.01987i	1.57701	+	0.106239i
$809$	−20.8131	−	36.0493i	−0.731749	−	1.26743i	−0.956135	−	0.292926i	$-0.905371\pi$
$809$	−20.8131	−	36.0493i	−0.731749	−	1.26743i	0.224386	−	0.974500i	$-0.427962\pi$
$810$	−5.28727	+	1.79122i	−0.185776	+	0.0629370i
$811$			18.7227i			0.657444i	0.944427	+	0.328722i	$0.106618\pi$
$811$			18.7227i			0.657444i	−0.944427	+	0.328722i	$0.893382\pi$
$812$		0			0
$813$		−	39.6831i		−	1.39175i
$814$	−0.287874	−	0.849739i	−0.0100900	−	0.0297833i
$815$	2.00916	+	3.47997i	0.0703778	+	0.121898i
$816$	18.8305	−	18.7396i	0.659201	−	0.656017i
$817$	−17.7670	+	30.7734i	−0.621589	+	1.07662i
$818$	10.9631	−	12.4857i	0.383315	−	0.436554i
$819$		0			0
$820$	6.81369	−	0.888650i	0.237944	−	0.0310330i
$821$	16.2308	+	9.37088i	0.566460	+	0.327046i	0.755734	−	0.654878i	$-0.227280\pi$
$821$	16.2308	+	9.37088i	0.566460	+	0.327046i	−0.189274	+	0.981924i	$0.560614\pi$
$822$	1.41702	−	7.10136i	0.0494242	−	0.247688i
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	0.987337	−	0.158636i	$-0.0507095\pi$
$823$	10.2211	+	17.7035i	0.356286	+	0.617106i	−0.631051	+	0.775741i	$0.717376\pi$
$824$	47.6802	−	23.4057i	1.66102	−	0.815378i
$825$	17.6966			0.616116
$826$		0			0
$827$			48.6254i			1.69087i	0.534079	+	0.845435i	$0.320659\pi$
$827$			48.6254i			1.69087i	−0.534079	+	0.845435i	$0.679341\pi$
$828$	−2.24407	−	0.932709i	−0.0779869	−	0.0324139i
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	−0.601559	−	0.798829i	$-0.705453\pi$
$829$	−6.06173	+	3.49974i	−0.210532	+	0.121551i	0.391026	+	0.920379i	$0.372120\pi$
$830$	0.838258	+	0.167267i	0.0290964	+	0.00580593i
$831$	7.44085	−	12.8879i	0.258120	−	0.447078i
$832$	29.3598	−	12.0365i	1.01787	−	0.417290i
$833$		0			0
$834$	−22.5461	+	25.6775i	−0.780707	+	0.889140i
$835$	0.899200	+	0.519154i	0.0311181	+	0.0179660i
$836$	−25.2175	+	19.3016i	−0.872167	+	0.667562i
$837$	4.15738	−	2.40026i	0.143700	−	0.0829653i
$838$	−14.8465	+	5.02968i	−0.512863	+	0.173748i
$839$	−40.1867			−1.38740			−0.693700	−	0.720264i	$-0.744021\pi$
$839$	−40.1867			−1.38740			−0.693700	+	0.720264i	$0.744021\pi$
$840$		0			0
$841$	−38.5224			−1.32836
$842$	−0.183864	+	0.0622894i	−0.00633638	+	0.00214663i
$843$	−36.6281	+	21.1473i	−1.26154	+	0.728350i
$844$	−10.2883	−	13.4416i	−0.354137	−	0.462679i
$845$	1.30086	+	0.751051i	0.0447509	+	0.0258369i
$846$	1.25433	−	1.42855i	0.0431248	−	0.0491144i
$847$		0			0
$848$	−11.0992	−	41.8275i	−0.381148	−	1.43636i
$849$	−10.2278	+	17.7150i	−0.351016	+	0.607978i
$850$	27.4623	+	5.47987i	0.941950	+	0.187958i
$851$	0.539788	−	0.311647i	0.0185037	−	0.0106831i
$852$	10.6035	−	25.5117i	0.363270	−	0.874018i
$853$		−	30.8071i		−	1.05482i	−0.849612	−	0.527408i	$-0.823164\pi$
$853$		−	30.8071i		−	1.05482i	0.849612	−	0.527408i	$-0.176836\pi$
$854$		0			0
$855$	1.88873			0.0645933
$856$	−0.422411	−	0.860500i	−0.0144377	−	0.0294113i
$857$	6.84889	+	11.8626i	0.233954	+	0.405220i	0.958968	−	0.283514i	$-0.0915002\pi$
$857$	6.84889	+	11.8626i	0.233954	+	0.405220i	−0.725014	+	0.688734i	$0.758167\pi$
$858$	4.13489	−	20.7219i	0.141163	−	0.707435i
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	0.622908	−	0.782295i	$-0.285951\pi$
$859$	7.52869	+	4.34669i	0.256876	+	0.148307i	−0.366033	+	0.930602i	$0.619284\pi$
$860$	0.760758	+	5.83309i	0.0259416	+	0.198907i
$861$		0			0
$862$	−11.6266	+	13.2414i	−0.396002	+	0.451003i
$863$	0.296174	−	0.512989i	0.0100819	−	0.0174623i	−0.860940	−	0.508706i	$-0.830124\pi$
$863$	0.296174	−	0.512989i	0.0100819	−	0.0174623i	0.871022	+	0.491243i	$0.163457\pi$
$864$	1.95575	+	31.2896i	0.0665361	+	1.06449i
$865$	4.54981	+	7.88049i	0.154698	+	0.267945i
$866$	−6.42377	−	18.9615i	−0.218289	−	0.644338i
$867$		−	1.20854i		−	0.0410440i
$868$		0			0
$869$			1.47389i			0.0499984i
$870$	−9.53374	+	3.22983i	−0.323224	+	0.109502i
$871$	5.30533	+	9.18911i	0.179764	+	0.311361i
$872$	−22.0252	−	1.48377i	−0.745867	−	0.0502469i
$873$	3.34889	−	5.80045i	0.113343	−	0.196316i
$874$	−16.5784	−	14.5566i	−0.560772	−	0.492385i
$875$		0			0
$876$	14.5717	−	1.90046i	0.492333	−	0.0642108i
$877$	13.2310	+	7.63892i	0.446779	+	0.257948i	0.706469	−	0.707744i	$-0.250287\pi$
$877$	13.2310	+	7.63892i	0.446779	+	0.257948i	−0.259690	+	0.965692i	$0.583620\pi$
$878$	7.57089	+	1.51071i	0.255505	+	0.0509839i
$879$	7.53401	+	13.0493i	0.254116	+	0.440142i
$880$	−1.37294	+	5.07470i	−0.0462817	+	0.171068i
$881$	43.1280			1.45302			0.726509	−	0.687157i	$-0.241141\pi$
$881$	43.1280			1.45302			0.726509	+	0.687157i	$0.241141\pi$
$882$		0			0
$883$		−	20.2255i		−	0.680642i	−0.940309	−	0.340321i	$-0.889464\pi$
$883$		−	20.2255i		−	0.680642i	0.940309	−	0.340321i	$-0.110536\pi$
$884$	12.8334	−	30.8768i	0.431633	−	1.03850i
$885$	−2.83152	+	1.63478i	−0.0951805	+	0.0549525i
$886$	−9.22512	+	46.2316i	−0.309924	+	1.55318i
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	−0.626270	−	0.779606i	$-0.715419\pi$
$887$	10.7820	−	18.6750i	0.362024	−	0.627044i	0.988294	+	0.152563i	$0.0487525\pi$
$888$	−0.982097	−	0.658799i	−0.0329570	−	0.0221078i
$889$		0			0
$890$	−3.73633	−	3.28067i	−0.125242	−	0.109968i
$891$	14.8668	+	8.58338i	0.498058	+	0.287554i
$892$	−9.21400	+	7.05245i	−0.308508	+	0.236133i
$893$	14.9465	−	8.62934i	0.500164	−	0.288770i
$894$	−5.27884	−	15.5819i	−0.176551	−	0.521138i
$895$	3.04668			0.101839
$896$		0			0
$897$	14.6799			0.490147
$898$	12.2390	+	36.1268i	0.408421	+	1.20557i
$899$	6.16413	−	3.55886i	0.205585	−	0.118695i
$900$	−3.85957	+	2.95414i	−0.128652	+	0.0984712i
$901$	−39.4926	−	22.8011i	−1.31569	−	0.759614i
$902$	−15.8783	−	13.9419i	−0.528689	−	0.464214i
$903$		0			0
$904$	5.91288	+	3.96641i	0.196659	+	0.131921i
$905$	2.74447	−	4.75356i	0.0912293	−	0.158014i
$906$	3.63269	−	18.2052i	0.120688	−	0.604827i
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.879709	−	0.475513i	$-0.842263\pi$
$907$	−27.3384	+	15.7838i	−0.907757	+	0.524094i	−0.0280482	+	0.999607i	$0.508929\pi$
$908$	−8.76836	+	21.0964i	−0.290988	+	0.700110i
$909$			8.21720i			0.272547i
$910$		0			0
$911$	15.6873			0.519744			0.259872	−	0.965643i	$-0.416320\pi$
$911$	15.6873			0.519744			0.259872	+	0.965643i	$0.416320\pi$
$912$	−10.9318	+	40.4065i	−0.361988	+	1.33799i
$913$	−1.31429	−	2.27641i	−0.0434965	−	0.0753382i
$914$	26.4801	+	5.28387i	0.875883	+	0.174775i
$915$	−5.35363	−	3.09092i	−0.176986	−	0.102183i
$916$	−36.6997	+	4.78642i	−1.21259	+	0.158148i
$917$		0			0
$918$	24.8250	+	21.7975i	0.819346	+	0.719425i
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	−0.965464	−	0.260535i	$-0.916101\pi$
$919$	−7.79407	+	13.4997i	−0.257103	+	0.445315i	0.708362	+	0.705849i	$0.249434\pi$
$920$	−3.64402	−	0.245487i	−0.120140	−	0.00809347i
$921$	−9.62857	−	16.6772i	−0.317272	−	0.549532i
$922$	25.3391	−	8.58436i	0.834499	−	0.282711i
$923$		−	34.7735i		−	1.14458i
$924$		0			0
$925$		−	1.24659i		−	0.0409875i
$926$	−0.390413	−	1.15241i	−0.0128298	−	0.0378706i
$927$	4.85725	+	8.41300i	0.159533	+	0.276319i
$928$	2.89979	+	46.3930i	0.0951903	+	1.52292i
$929$	20.6926	−	35.8406i	0.678901	−	1.17589i	−0.296411	−	0.955060i	$-0.595790\pi$
$929$	20.6926	−	35.8406i	0.678901	−	1.17589i	0.975312	−	0.220830i	$-0.0708767\pi$
$930$	0.700104	−	0.797341i	0.0229573	−	0.0261459i
$931$		0			0
$932$	2.85844	+	21.9170i	0.0936315	+	0.717916i
$933$	−43.5061	−	25.1183i	−1.42433	−	0.822335i
$934$	−5.17166	+	25.9177i	−0.169222	+	0.848053i
$935$	2.76992	+	4.79764i	0.0905860	+	0.156900i
$936$	2.55736	+	5.20963i	0.0835899	+	0.170282i
$937$	23.9308			0.781785			0.390892	−	0.920436i	$-0.372166\pi$
$937$	23.9308			0.781785			0.390892	+	0.920436i	$0.372166\pi$
$938$		0			0
$939$			33.9137i			1.10673i
$940$	1.09656	−	2.63828i	0.0357657	−	0.0860513i
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.153841	−	0.988096i	$-0.450836\pi$
$941$	33.3285	−	19.2422i	1.08648	−	0.627278i	0.932636	+	0.360818i	$0.117502\pi$
$942$	−15.5955	−	3.11195i	−0.508128	−	0.101393i
$943$	7.33994	−	12.7132i	0.239021	−	0.413997i
$944$	3.87244	+	14.5934i	0.126037	+	0.474974i
$945$		0			0
$946$	11.9354	−	13.5931i	0.388054	−	0.441951i
$947$	−8.36198	−	4.82779i	−0.271728	−	0.156882i	0.357945	−	0.933743i	$-0.383478\pi$
$947$	−8.36198	−	4.82779i	−0.271728	−	0.156882i	−0.629673	+	0.776861i	$0.716811\pi$
$948$	1.18082	+	1.54274i	0.0383513	+	0.0501059i
$949$	16.0181	−	9.24804i	0.519969	−	0.300204i
$950$	−41.7912	+	14.1580i	−1.35588	+	0.459346i
$951$	−36.4757			−1.18280
$952$		0			0
$953$	−19.3777			−0.627704			−0.313852	−	0.949472i	$-0.601620\pi$
$953$	−19.3777			−0.627704			−0.313852	+	0.949472i	$0.601620\pi$
$954$	7.49628	−	2.53959i	0.242701	−	0.0822222i
$955$	0.0801777	−	0.0462906i	0.00259449	−	0.00149793i
$956$	35.9098	−	27.4856i	1.16141	−	0.888947i
$957$	26.8071	+	15.4771i	0.866552	+	0.500304i
$958$	−17.3065	+	19.7101i	−0.559146	+	0.636806i
$959$		0			0
$960$	2.62857	+	6.41169i	0.0848368	+	0.206936i
$961$	15.1249	−	26.1970i	0.487898	−	0.845065i
$962$	−1.45970	−	0.291271i	−0.0470626	−	0.00939094i
$963$	0.151832	−	0.0876603i	0.00489272	−	0.00282481i
$964$	−25.7256	−	10.6924i	−0.828566	−	0.344379i
$965$			4.13255i			0.133031i
$966$		0			0
$967$	34.8845			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$967$	34.8845			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$968$	−13.4169	+	6.58622i	−0.431235	+	0.211689i
$969$	22.0550	+	38.2004i	0.708510	+	1.22717i
$970$	1.96975	−	9.87138i	0.0632449	−	0.316951i
$971$	38.4767	+	22.2146i	1.23478	+	0.712899i	0.968022	−	0.250865i	$-0.0807151\pi$
$971$	38.4767	+	22.2146i	1.23478	+	0.712899i	0.266755	+	0.963764i	$0.414048\pi$
$972$	−10.5352	+	1.37402i	−0.337917	+	0.0440716i
$973$		0			0
$974$	21.3843	−	24.3544i	0.685197	−	0.780365i
$975$	14.6799	−	25.4263i	0.470133	−	0.814294i
$976$	−20.2346	+	20.1368i	−0.647693	+	0.644565i
$977$	13.5436	+	23.4581i	0.433297	+	0.750492i	0.997155	−	0.0753795i	$-0.0240168\pi$
$977$	13.5436	+	23.4581i	0.433297	+	0.750492i	−0.563858	+	0.825872i	$0.690684\pi$
$978$	−5.22625	−	15.4267i	−0.167117	−	0.493291i
$979$			15.2902i			0.488678i
$980$		0			0
$981$		−	4.03742i		−	0.128905i
$982$	−33.2163	+	11.2530i	−1.05997	+	0.359098i
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	0.993738	−	0.111736i	$-0.0356410\pi$
$983$	12.5444	+	21.7275i	0.400103	+	0.692999i	−0.593635	+	0.804735i	$0.702308\pi$
$984$	−27.7896	−	1.87211i	−0.885901	−	0.0596806i
$985$	−0.369920	+	0.640721i	−0.0117866	+	0.0204151i
$986$	36.8079	+	32.3191i	1.17220	+	1.02925i
$987$		0			0
$988$	6.81369	+	52.2437i	0.216772	+	1.66209i
$989$	10.8835	+	6.28360i	0.346076	+	0.199807i
$990$	−0.942915	−	0.188151i	−0.0299678	−	0.00597982i
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	0.691258	−	0.722608i	$-0.257057\pi$
$991$	−8.81972	−	15.2762i	−0.280168	−	0.485265i	−0.971426	+	0.237343i	$0.923723\pi$
$992$	−2.70993	−	4.08238i	−0.0860403	−	0.129616i
$993$	−46.5068			−1.47585
$994$		0			0
$995$			7.01530i			0.222400i
$996$	−3.19944	−	1.32979i	−0.101378	−	0.0421361i
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	−0.857583	−	0.514345i	$-0.828035\pi$
$997$	−26.5529	+	15.3303i	−0.840939	+	0.485516i	0.0166442	+	0.999861i	$0.494702\pi$
$998$	10.8553	−	54.4014i	0.343620	−	1.72205i
$999$	0.735311	−	1.27360i	0.0232642	−	0.0402948i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.p.g.373.3		12
4.3	odd	2		1568.2.t.g.177.5		12
7.2	even	3		392.2.b.f.197.2		6
7.3	odd	6		56.2.p.a.53.6	yes	12
7.4	even	3	inner	392.2.p.g.165.6		12
7.5	odd	6		392.2.b.e.197.2		6
7.6	odd	2		56.2.p.a.37.3	✓	12
8.3	odd	2		1568.2.t.g.177.2		12
8.5	even	2	inner	392.2.p.g.373.6		12
21.17	even	6		504.2.cj.c.109.1		12
21.20	even	2		504.2.cj.c.37.4		12
28.3	even	6		224.2.t.a.81.5		12
28.11	odd	6		1568.2.t.g.753.2		12
28.19	even	6		1568.2.b.f.785.2		6
28.23	odd	6		1568.2.b.e.785.5		6
28.27	even	2		224.2.t.a.177.2		12
56.3	even	6		224.2.t.a.81.2		12
56.5	odd	6		392.2.b.e.197.1		6
56.11	odd	6		1568.2.t.g.753.5		12
56.13	odd	2		56.2.p.a.37.6	yes	12
56.19	even	6		1568.2.b.f.785.5		6
56.27	even	2		224.2.t.a.177.5		12
56.37	even	6		392.2.b.f.197.1		6
56.45	odd	6		56.2.p.a.53.3	yes	12
56.51	odd	6		1568.2.b.e.785.2		6
56.53	even	6	inner	392.2.p.g.165.3		12
84.59	odd	6		2016.2.cr.c.1873.4		12
84.83	odd	2		2016.2.cr.c.1297.3		12
168.59	odd	6		2016.2.cr.c.1873.3		12
168.83	odd	2		2016.2.cr.c.1297.4		12
168.101	even	6		504.2.cj.c.109.4		12
168.125	even	2		504.2.cj.c.37.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	7.6	odd	2
56.2.p.a.37.6	yes	12	56.13	odd	2
56.2.p.a.53.3	yes	12	56.45	odd	6
56.2.p.a.53.6	yes	12	7.3	odd	6
224.2.t.a.81.2		12	56.3	even	6
224.2.t.a.81.5		12	28.3	even	6
224.2.t.a.177.2		12	28.27	even	2
224.2.t.a.177.5		12	56.27	even	2
392.2.b.e.197.1		6	56.5	odd	6
392.2.b.e.197.2		6	7.5	odd	6
392.2.b.f.197.1		6	56.37	even	6
392.2.b.f.197.2		6	7.2	even	3
392.2.p.g.165.3		12	56.53	even	6	inner
392.2.p.g.165.6		12	7.4	even	3	inner
392.2.p.g.373.3		12	1.1	even	1	trivial
392.2.p.g.373.6		12	8.5	even	2	inner
504.2.cj.c.37.1		12	168.125	even	2
504.2.cj.c.37.4		12	21.20	even	2
504.2.cj.c.109.1		12	21.17	even	6
504.2.cj.c.109.4		12	168.101	even	6
1568.2.b.e.785.2		6	56.51	odd	6
1568.2.b.e.785.5		6	28.23	odd	6
1568.2.b.f.785.2		6	28.19	even	6
1568.2.b.f.785.5		6	56.19	even	6
1568.2.t.g.177.2		12	8.3	odd	2
1568.2.t.g.177.5		12	4.3	odd	2
1568.2.t.g.753.2		12	28.11	odd	6
1568.2.t.g.753.5		12	56.11	odd	6
2016.2.cr.c.1297.3		12	84.83	odd	2
2016.2.cr.c.1297.4		12	168.83	odd	2
2016.2.cr.c.1873.3		12	168.59	odd	6
2016.2.cr.c.1873.4		12	84.59	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.453773 - 1.33944i) q^{2} +(-1.36456 + 0.787829i) q^{3} +(-1.58818 + 1.21560i) q^{4} +(-0.476087 - 0.274869i) q^{5} +(1.67445 + 1.47024i) q^{6} +(2.34889 + 1.57566i) q^{8} +(-0.258652 + 0.447998i) q^{9} +(-0.152134 + 0.762416i) q^{10} +(2.07045 - 1.19538i) q^{11} +(1.20948 - 2.90997i) q^{12} -3.96641i q^{13} +0.866198 q^{15} +(1.04463 - 3.86119i) q^{16} +(-2.10755 - 3.65038i) q^{17} +(0.717435 + 0.143158i) q^{18} +(5.75174 + 3.32077i) q^{19} +(1.09024 - 0.142191i) q^{20} +(-2.54065 - 2.23081i) q^{22} +(1.17445 - 2.03420i) q^{23} +(-4.44655 - 0.299552i) q^{24} +(-2.34889 - 4.06840i) q^{25} +(-5.31275 + 1.79985i) q^{26} -5.54207i q^{27} -8.21720i q^{29} +(-0.393058 - 1.16022i) q^{30} +(0.433099 + 0.750150i) q^{31} +(-5.64584 + 0.352893i) q^{32} +(-1.88350 + 3.26232i) q^{33} +(-3.93310 + 4.47937i) q^{34} +(-0.133802 - 1.02592i) q^{36} +(0.229805 + 0.132678i) q^{37} +(1.83797 - 9.21097i) q^{38} +(3.12485 + 5.41240i) q^{39} +(-0.685178 - 1.39579i) q^{40} +6.24970 q^{41} +5.35027i q^{43} +(-1.83515 + 4.41531i) q^{44} +(0.246282 - 0.142191i) q^{45} +(-3.25762 - 0.650030i) q^{46} +(1.29930 - 2.25045i) q^{47} +(1.61650 + 6.09180i) q^{48} +(-4.38350 + 4.99233i) q^{50} +(5.75174 + 3.32077i) q^{51} +(4.82157 + 6.29937i) q^{52} +(9.36933 - 5.40939i) q^{53} +(-7.42324 + 2.51484i) q^{54} -1.31429 q^{55} -10.4648 q^{57} +(-11.0064 + 3.72875i) q^{58} +(-3.26891 + 1.88730i) q^{59} +(-1.37568 + 1.05295i) q^{60} +(-6.18061 - 3.56837i) q^{61} +(0.808249 - 0.920507i) q^{62} +(3.03461 + 7.40210i) q^{64} +(-1.09024 + 1.88835i) q^{65} +(5.22436 + 1.04248i) q^{66} +(-2.31673 + 1.33757i) q^{67} +(7.78456 + 3.23552i) q^{68} +3.70105i q^{69} +8.76700 q^{71} +(-1.31344 + 0.644754i) q^{72} +(2.33159 + 4.03843i) q^{73} +(0.0734343 - 0.368015i) q^{74} +(6.41041 + 3.70105i) q^{75} +(-13.1715 + 1.71785i) q^{76} +(5.83159 - 6.64154i) q^{78} +(-0.308249 + 0.533903i) q^{79} +(-1.55865 + 1.55112i) q^{80} +(3.59024 + 6.21848i) q^{81} +(-2.83595 - 8.37108i) q^{82} -1.09948i q^{83} +2.31720i q^{85} +(7.16634 - 2.42781i) q^{86} +(6.47374 + 11.2129i) q^{87} +(6.74677 + 0.454511i) q^{88} +(-3.19779 + 5.53873i) q^{89} +(-0.302212 - 0.265356i) q^{90} +(0.607546 + 4.65834i) q^{92} +(-1.18198 - 0.682416i) q^{93} +(-3.60392 - 0.719132i) q^{94} +(-1.82555 - 3.16195i) q^{95} +(7.42606 - 4.92949i) q^{96} -12.9475 q^{97} +1.23675i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32}+ \cdots - 40 q^{97}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more