LMFDB - Embedded newform 1338.2.e.h.1075.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(931,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.931"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,-14,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} + 21 x^{12} - 26 x^{11} + 217 x^{10} - 335 x^{9} + 1058 x^{8} - 1539 x^{7} + 3657 x^{6} + \cdots + 64 $ x^14 - 3x^13 + 21x^12 - 26x^11 + 217x^10 - 335x^9 + 1058x^8 - 1539x^7 + 3657x^6 - 4850x^5 + 6077x^4 - 4079x^3 + 2145x^2 - 424*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1075.6
Root			$0.379092 - 0.656607i$ of defining polynomial
Character	$\chi$	$=$	1338.1075
Dual form			1338.2.e.h.931.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.652613 - 1.13036i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.36767 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.652613 + 1.13036i) q^{10} +(-0.271475 + 0.470208i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.71940 q^{13} -3.36767 q^{14} -1.30523 q^{15} +1.00000 q^{16} +1.55840 q^{17} +(0.500000 - 0.866025i) q^{18} +(3.69076 + 6.39259i) q^{19} +(0.652613 - 1.13036i) q^{20} +(-1.68384 - 2.91649i) q^{21} +(0.271475 - 0.470208i) q^{22} +(1.97801 + 3.42601i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.64819 + 2.85475i) q^{25} -1.71940 q^{26} +1.00000 q^{27} +3.36767 q^{28} +(2.60664 - 4.51483i) q^{29} +1.30523 q^{30} +(-0.119344 - 0.206710i) q^{31} -1.00000 q^{32} +0.542949 q^{33} -1.55840 q^{34} +(2.19779 - 3.80668i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.09940 + 3.63626i) q^{37} +(-3.69076 - 6.39259i) q^{38} +(-0.859702 - 1.48905i) q^{39} +(-0.652613 + 1.13036i) q^{40} -3.87207 q^{41} +(1.68384 + 2.91649i) q^{42} +(1.01702 + 1.76152i) q^{43} +(-0.271475 + 0.470208i) q^{44} +(0.652613 + 1.13036i) q^{45} +(-1.97801 - 3.42601i) q^{46} +(-3.55440 + 6.15641i) q^{47} +(-0.500000 - 0.866025i) q^{48} +4.34121 q^{49} +(-1.64819 - 2.85475i) q^{50} +(-0.779202 - 1.34962i) q^{51} +1.71940 q^{52} +(-2.96526 + 5.13598i) q^{53} -1.00000 q^{54} +(0.354336 + 0.613727i) q^{55} -3.36767 q^{56} +(3.69076 - 6.39259i) q^{57} +(-2.60664 + 4.51483i) q^{58} +0.705752 q^{59} -1.30523 q^{60} +(1.93180 + 3.34597i) q^{61} +(0.119344 + 0.206710i) q^{62} +(-1.68384 + 2.91649i) q^{63} +1.00000 q^{64} +(1.12211 - 1.94354i) q^{65} -0.542949 q^{66} +(-3.32588 - 5.76059i) q^{67} +1.55840 q^{68} +(1.97801 - 3.42601i) q^{69} +(-2.19779 + 3.80668i) q^{70} +(-0.295931 - 0.512568i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.65303 - 2.86313i) q^{73} +(2.09940 - 3.63626i) q^{74} +(1.64819 - 2.85475i) q^{75} +(3.69076 + 6.39259i) q^{76} +(-0.914237 + 1.58350i) q^{77} +(0.859702 + 1.48905i) q^{78} +(6.83269 - 11.8346i) q^{79} +(0.652613 - 1.13036i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.87207 q^{82} +(5.59413 - 9.68933i) q^{83} +(-1.68384 - 2.91649i) q^{84} +(1.01703 - 1.76156i) q^{85} +(-1.01702 - 1.76152i) q^{86} -5.21328 q^{87} +(0.271475 - 0.470208i) q^{88} +(2.23576 + 3.87245i) q^{89} +(-0.652613 - 1.13036i) q^{90} +5.79039 q^{91} +(1.97801 + 3.42601i) q^{92} +(-0.119344 + 0.206710i) q^{93} +(3.55440 - 6.15641i) q^{94} +9.63456 q^{95} +(0.500000 + 0.866025i) q^{96} +(-2.08092 + 3.60426i) q^{97} -4.34121 q^{98} +(-0.271475 - 0.470208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) $ 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1338\mathbb{Z}\right)^\times$.

$n$	$893$	$895$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.652613	−	1.13036i	0.291857	−	0.505512i	−0.682392	−	0.730987i	$-0.739060\pi$
$5$	0.652613	−	1.13036i	0.291857	−	0.505512i	0.974249	+	0.225475i	$0.0723934\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	3.36767			1.27286			0.636430	−	0.771334i	$-0.280410\pi$
$7$	3.36767			1.27286			0.636430	+	0.771334i	$0.280410\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.652613	+	1.13036i	−0.206374	+	0.357451i
$11$	−0.271475	+	0.470208i	−0.0818526	+	0.141773i	−0.904046	−	0.427436i	$-0.859417\pi$
$11$	−0.271475	+	0.470208i	−0.0818526	+	0.141773i	0.822193	+	0.569209i	$0.192750\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.71940			0.476877			0.238439	−	0.971158i	$-0.423364\pi$
$13$	1.71940			0.476877			0.238439	+	0.971158i	$0.423364\pi$
$14$	−3.36767			−0.900048
$15$	−1.30523			−0.337008
$16$	1.00000			0.250000
$17$	1.55840			0.377969			0.188984	−	0.981980i	$-0.439480\pi$
$17$	1.55840			0.377969			0.188984	+	0.981980i	$0.439480\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	3.69076	+	6.39259i	0.846719	+	1.46656i	0.884120	+	0.467260i	$0.154759\pi$
$19$	3.69076	+	6.39259i	0.846719	+	1.46656i	−0.0374007	+	0.999300i	$0.511908\pi$
$20$	0.652613	−	1.13036i	0.145929	−	0.252756i
$21$	−1.68384	−	2.91649i	−0.367443	−	0.636430i
$22$	0.271475	−	0.470208i	0.0578786	−	0.100249i
$23$	1.97801	+	3.42601i	0.412443	+	0.714372i	0.995156	−	0.0983055i	$-0.0313422\pi$
$23$	1.97801	+	3.42601i	0.412443	+	0.714372i	−0.582713	+	0.812678i	$0.698009\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	1.64819	+	2.85475i	0.329639	+	0.570951i
$26$	−1.71940			−0.337203
$27$	1.00000			0.192450
$28$	3.36767			0.636430
$29$	2.60664	−	4.51483i	0.484041	−	0.838384i	−0.515791	−	0.856714i	$-0.672502\pi$
$29$	2.60664	−	4.51483i	0.484041	−	0.838384i	0.999832	+	0.0183309i	$0.00583522\pi$
$30$	1.30523			0.238301
$31$	−0.119344	−	0.206710i	−0.0214348	−	0.0371262i	0.855109	−	0.518448i	$-0.173490\pi$
$31$	−0.119344	−	0.206710i	−0.0214348	−	0.0371262i	−0.876544	+	0.481322i	$0.840157\pi$
$32$	−1.00000			−0.176777
$33$	0.542949			0.0945153
$34$	−1.55840			−0.267264
$35$	2.19779	−	3.80668i	0.371494	−	0.643446i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.09940	+	3.63626i	−0.345139	+	0.597798i	−0.985379	−	0.170377i	$-0.945502\pi$
$37$	−2.09940	+	3.63626i	−0.345139	+	0.597798i	0.640240	+	0.768175i	$0.278835\pi$
$38$	−3.69076	−	6.39259i	−0.598721	−	1.03701i
$39$	−0.859702	−	1.48905i	−0.137663	−	0.238439i
$40$	−0.652613	+	1.13036i	−0.103187	+	0.178725i
$41$	−3.87207			−0.604716			−0.302358	−	0.953194i	$-0.597774\pi$
$41$	−3.87207			−0.604716			−0.302358	+	0.953194i	$0.597774\pi$
$42$	1.68384	+	2.91649i	0.259821	+	0.450024i
$43$	1.01702	+	1.76152i	0.155094	+	0.268630i	0.933093	−	0.359635i	$-0.117099\pi$
$43$	1.01702	+	1.76152i	0.155094	+	0.268630i	−0.778000	+	0.628265i	$0.783765\pi$
$44$	−0.271475	+	0.470208i	−0.0409263	+	0.0708865i
$45$	0.652613	+	1.13036i	0.0972858	+	0.168504i
$46$	−1.97801	−	3.42601i	−0.291641	−	0.505138i
$47$	−3.55440	+	6.15641i	−0.518463	+	0.898004i	0.481307	+	0.876552i	$0.340162\pi$
$47$	−3.55440	+	6.15641i	−0.518463	+	0.898004i	−0.999770	+	0.0214520i	$0.993171\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	4.34121			0.620173
$50$	−1.64819	−	2.85475i	−0.233090	−	0.403723i
$51$	−0.779202	−	1.34962i	−0.109110	−	0.188984i
$52$	1.71940			0.238439
$53$	−2.96526	+	5.13598i	−0.407310	+	0.705481i	−0.994587	−	0.103905i	$-0.966866\pi$
$53$	−2.96526	+	5.13598i	−0.407310	+	0.705481i	0.587278	+	0.809386i	$0.300200\pi$
$54$	−1.00000			−0.136083
$55$	0.354336	+	0.613727i	0.0477786	+	0.0827549i
$56$	−3.36767			−0.450024
$57$	3.69076	−	6.39259i	0.488854	−	0.846719i
$58$	−2.60664	+	4.51483i	−0.342269	+	0.592827i
$59$	0.705752			0.0918810			0.0459405	−	0.998944i	$-0.485372\pi$
$59$	0.705752			0.0918810			0.0459405	+	0.998944i	$0.485372\pi$
$60$	−1.30523			−0.168504
$61$	1.93180	+	3.34597i	0.247342	+	0.428408i	0.962787	−	0.270260i	$-0.0871097\pi$
$61$	1.93180	+	3.34597i	0.247342	+	0.428408i	−0.715446	+	0.698668i	$0.753776\pi$
$62$	0.119344	+	0.206710i	0.0151567	+	0.0262522i
$63$	−1.68384	+	2.91649i	−0.212143	+	0.367443i
$64$	1.00000			0.125000
$65$	1.12211	−	1.94354i	0.139180	−	0.241067i
$66$	−0.542949			−0.0668324
$67$	−3.32588	−	5.76059i	−0.406321	−	0.703768i	0.588154	−	0.808749i	$-0.299855\pi$
$67$	−3.32588	−	5.76059i	−0.406321	−	0.703768i	−0.994474	+	0.104981i	$0.966522\pi$
$68$	1.55840			0.188984
$69$	1.97801	−	3.42601i	0.238124	−	0.412443i
$70$	−2.19779	+	3.80668i	−0.262686	+	0.454985i
$71$	−0.295931	−	0.512568i	−0.0351206	−	0.0608307i	0.847931	−	0.530107i	$-0.177848\pi$
$71$	−0.295931	−	0.512568i	−0.0351206	−	0.0608307i	−0.883051	+	0.469276i	$0.844515\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	1.65303	−	2.86313i	0.193473	−	0.335105i	−0.752926	−	0.658105i	$-0.771358\pi$
$73$	1.65303	−	2.86313i	0.193473	−	0.335105i	0.946399	+	0.323001i	$0.104692\pi$
$74$	2.09940	−	3.63626i	0.244050	−	0.422707i
$75$	1.64819	−	2.85475i	0.190317	−	0.329639i
$76$	3.69076	+	6.39259i	0.423360	+	0.733280i
$77$	−0.914237	+	1.58350i	−0.104187	+	0.180457i
$78$	0.859702	+	1.48905i	0.0973421	+	0.168601i
$79$	6.83269	−	11.8346i	0.768737	−	1.33149i	−0.169510	−	0.985528i	$-0.554219\pi$
$79$	6.83269	−	11.8346i	0.768737	−	1.33149i	0.938248	−	0.345964i	$-0.112448\pi$
$80$	0.652613	−	1.13036i	0.0729643	−	0.126378i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	3.87207			0.427599
$83$	5.59413	−	9.68933i	0.614036	−	1.06354i	−0.376517	−	0.926410i	$-0.622878\pi$
$83$	5.59413	−	9.68933i	0.614036	−	1.06354i	0.990553	−	0.137132i	$-0.0437884\pi$
$84$	−1.68384	−	2.91649i	−0.183722	−	0.318215i
$85$	1.01703	−	1.76156i	0.110313	−	0.191068i
$86$	−1.01702	−	1.76152i	−0.109668	−	0.189950i
$87$	−5.21328			−0.558922
$88$	0.271475	−	0.470208i	0.0289393	−	0.0501243i
$89$	2.23576	+	3.87245i	0.236990	+	0.410479i	0.959849	−	0.280517i	$-0.0905058\pi$
$89$	2.23576	+	3.87245i	0.236990	+	0.410479i	−0.722859	+	0.690995i	$0.757173\pi$
$90$	−0.652613	−	1.13036i	−0.0687914	−	0.119150i
$91$	5.79039			0.606998
$92$	1.97801	+	3.42601i	0.206222	+	0.357186i
$93$	−0.119344	+	0.206710i	−0.0123754	+	0.0214348i
$94$	3.55440	−	6.15641i	0.366609	−	0.634985i
$95$	9.63456			0.988485
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−2.08092	+	3.60426i	−0.211285	+	0.365957i	−0.952117	−	0.305734i	$-0.901098\pi$
$97$	−2.08092	+	3.60426i	−0.211285	+	0.365957i	0.740832	+	0.671691i	$0.234432\pi$
$98$	−4.34121			−0.438528
$99$	−0.271475	−	0.470208i	−0.0272842	−	0.0472576i
$100$	1.64819	+	2.85475i	0.164819	+	0.285475i
$101$	−3.97843	−	6.89084i	−0.395868	−	0.685664i	0.597343	−	0.801986i	$-0.296223\pi$
$101$	−3.97843	−	6.89084i	−0.395868	−	0.685664i	−0.993212	+	0.116322i	$0.962890\pi$
$102$	0.779202	+	1.34962i	0.0771525	+	0.133632i
$103$	6.41415			0.632005			0.316002	−	0.948758i	$-0.397659\pi$
$103$	6.41415			0.632005			0.316002	+	0.948758i	$0.397659\pi$
$104$	−1.71940			−0.168601
$105$	−4.39557			−0.428964
$106$	2.96526	−	5.13598i	0.288011	−	0.498850i
$107$	6.81559	−	11.8049i	0.658888	−	1.14123i	−0.322016	−	0.946734i	$-0.604361\pi$
$107$	6.81559	−	11.8049i	0.658888	−	1.14123i	0.980904	−	0.194493i	$-0.0623060\pi$
$108$	1.00000			0.0962250
$109$	0.665484	−	1.15265i	0.0637418	−	0.110404i	−0.832393	−	0.554185i	$-0.813030\pi$
$109$	0.665484	−	1.15265i	0.0637418	−	0.110404i	0.896135	+	0.443781i	$0.146363\pi$
$110$	−0.354336	−	0.613727i	−0.0337846	−	0.0585166i
$111$	4.19880			0.398532
$112$	3.36767			0.318215
$113$	−0.992514	−	1.71908i	−0.0933678	−	0.161718i	0.815558	−	0.578675i	$-0.196430\pi$
$113$	−0.992514	−	1.71908i	−0.0933678	−	0.161718i	−0.908926	+	0.416957i	$0.863097\pi$
$114$	−3.69076	+	6.39259i	−0.345672	+	0.598721i
$115$	5.16349			0.481498
$116$	2.60664	−	4.51483i	0.242020	−	0.419192i
$117$	−0.859702	+	1.48905i	−0.0794795	+	0.137663i
$118$	−0.705752			−0.0649697
$119$	5.24819			0.481101
$120$	1.30523			0.119150
$121$	5.35260	+	9.27098i	0.486600	+	0.842816i
$122$	−1.93180	−	3.34597i	−0.174897	−	0.302930i
$123$	1.93604	+	3.35331i	0.174567	+	0.302358i
$124$	−0.119344	−	0.206710i	−0.0107174	−	0.0185631i
$125$	10.8287			0.968544
$126$	1.68384	−	2.91649i	0.150008	−	0.259821i
$127$	6.09999	+	10.5655i	0.541287	+	0.937536i	0.998830	+	0.0483493i	$0.0153960\pi$
$127$	6.09999	+	10.5655i	0.541287	+	0.937536i	−0.457544	+	0.889187i	$0.651271\pi$
$128$	−1.00000			−0.0883883
$129$	1.01702	−	1.76152i	0.0895433	−	0.155094i
$130$	−1.12211	+	1.94354i	−0.0984152	+	0.170460i
$131$	1.18727	+	2.05640i	0.103732	+	0.179669i	0.913219	−	0.407468i	$-0.133588\pi$
$131$	1.18727	+	2.05640i	0.103732	+	0.179669i	−0.809488	+	0.587137i	$0.800255\pi$
$132$	0.542949			0.0472576
$133$	12.4293	+	21.5281i	1.07775	+	1.86673i
$134$	3.32588	+	5.76059i	0.287312	+	0.497639i
$135$	0.652613	−	1.13036i	0.0561680	−	0.0972858i
$136$	−1.55840			−0.133632
$137$	−7.69606	−	13.3300i	−0.657518	−	1.13886i	−0.981256	−	0.192708i	$-0.938273\pi$
$137$	−7.69606	−	13.3300i	−0.657518	−	1.13886i	0.323738	−	0.946147i	$-0.395060\pi$
$138$	−1.97801	+	3.42601i	−0.168379	+	0.291641i
$139$	−7.88789	−	13.6622i	−0.669042	−	1.15881i	−0.978172	−	0.207795i	$-0.933371\pi$
$139$	−7.88789	−	13.6622i	−0.669042	−	1.15881i	0.309130	−	0.951020i	$-0.399962\pi$
$140$	2.19779	−	3.80668i	0.185747	−	0.321723i
$141$	7.10881			0.598669
$142$	0.295931	+	0.512568i	0.0248340	+	0.0430138i
$143$	−0.466775	+	0.808477i	−0.0390336	+	0.0676083i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.40225	−	5.89288i	−0.282542	−	0.489377i
$146$	−1.65303	+	2.86313i	−0.136806	+	0.236955i
$147$	−2.17060	−	3.75960i	−0.179028	−	0.310086i
$148$	−2.09940	+	3.63626i	−0.172569	+	0.298899i
$149$	2.03745	−	3.52896i	0.166914	−	0.289104i	−0.770419	−	0.637538i	$-0.779953\pi$
$149$	2.03745	−	3.52896i	0.166914	−	0.289104i	0.937333	+	0.348434i	$0.113286\pi$
$150$	−1.64819	+	2.85475i	−0.134574	+	0.233090i
$151$	5.52311	−	9.56630i	0.449464	−	0.778495i	−0.548887	−	0.835896i	$-0.684948\pi$
$151$	5.52311	−	9.56630i	0.449464	−	0.778495i	0.998351	+	0.0574019i	$0.0182817\pi$
$152$	−3.69076	−	6.39259i	−0.299360	−	0.518507i
$153$	−0.779202	+	1.34962i	−0.0629948	+	0.109110i
$154$	0.914237	−	1.58350i	0.0736713	−	0.127602i
$155$	−0.311542			−0.0250237
$156$	−0.859702	−	1.48905i	−0.0688313	−	0.119219i
$157$	14.7840			1.17989			0.589945	−	0.807443i	$-0.299149\pi$
$157$	14.7840			1.17989			0.589945	+	0.807443i	$0.299149\pi$
$158$	−6.83269	+	11.8346i	−0.543579	+	0.941507i
$159$	5.93052			0.470321
$160$	−0.652613	+	1.13036i	−0.0515936	+	0.0893627i
$161$	6.66128	+	11.5377i	0.524982	+	0.909296i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−5.37708			−0.421165			−0.210583	−	0.977576i	$-0.567536\pi$
$163$	−5.37708			−0.421165			−0.210583	+	0.977576i	$0.567536\pi$
$164$	−3.87207			−0.302358
$165$	0.354336	−	0.613727i	0.0275850	−	0.0477786i
$166$	−5.59413	+	9.68933i	−0.434189	+	0.752038i
$167$	−18.1137			−1.40168			−0.700841	−	0.713318i	$-0.747192\pi$
$167$	−18.1137			−1.40168			−0.700841	+	0.713318i	$0.747192\pi$
$168$	1.68384	+	2.91649i	0.129911	+	0.225012i
$169$	−10.0436			−0.772588
$170$	−1.01703	+	1.76156i	−0.0780030	+	0.135105i
$171$	−7.38153			−0.564479
$172$	1.01702	+	1.76152i	0.0775468	+	0.134315i
$173$	−2.41732	−	4.18691i	−0.183785	−	0.318325i	0.759381	−	0.650646i	$-0.225502\pi$
$173$	−2.41732	−	4.18691i	−0.183785	−	0.318325i	−0.943166	+	0.332321i	$0.892168\pi$
$174$	5.21328			0.395218
$175$	5.55057	+	9.61387i	0.419584	+	0.726740i
$176$	−0.271475	+	0.470208i	−0.0204632	+	0.0354432i
$177$	−0.352876	−	0.611199i	−0.0265238	−	0.0459405i
$178$	−2.23576	−	3.87245i	−0.167577	−	0.290252i
$179$	2.12325	−	3.67758i	0.158699	−	0.274875i	−0.775701	−	0.631101i	$-0.782603\pi$
$179$	2.12325	−	3.67758i	0.158699	−	0.274875i	0.934400	+	0.356226i	$0.115937\pi$
$180$	0.652613	+	1.13036i	0.0486429	+	0.0842520i
$181$	−3.64457	−	6.31258i	−0.270899	−	0.469210i	0.698193	−	0.715909i	$-0.253988\pi$
$181$	−3.64457	−	6.31258i	−0.270899	−	0.469210i	−0.969092	+	0.246699i	$0.920654\pi$
$182$	−5.79039			−0.429212
$183$	1.93180	−	3.34597i	0.142803	−	0.247342i
$184$	−1.97801	−	3.42601i	−0.145821	−	0.252569i
$185$	2.74019	+	4.74614i	0.201463	+	0.348944i
$186$	0.119344	−	0.206710i	0.00875074	−	0.0151567i
$187$	−0.423067	+	0.732774i	−0.0309377	+	0.0535857i
$188$	−3.55440	+	6.15641i	−0.259231	+	0.449002i
$189$	3.36767			0.244962
$190$	−9.63456			−0.698964
$191$	12.8931			0.932909			0.466455	−	0.884545i	$-0.345531\pi$
$191$	12.8931			0.932909			0.466455	+	0.884545i	$0.345531\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−6.52539			−0.469708			−0.234854	−	0.972031i	$-0.575461\pi$
$193$	−6.52539			−0.469708			−0.234854	+	0.972031i	$0.575461\pi$
$194$	2.08092	−	3.60426i	0.149401	−	0.258771i
$195$	−2.24421			−0.160711
$196$	4.34121			0.310086
$197$	−17.7001			−1.26108			−0.630541	−	0.776156i	$-0.717167\pi$
$197$	−17.7001			−1.26108			−0.630541	+	0.776156i	$0.717167\pi$
$198$	0.271475	+	0.470208i	0.0192929	+	0.0334162i
$199$	3.51636	+	6.09051i	0.249268	+	0.431745i	0.963323	−	0.268345i	$-0.0864766\pi$
$199$	3.51636	+	6.09051i	0.249268	+	0.431745i	−0.714055	+	0.700090i	$0.753143\pi$
$200$	−1.64819	−	2.85475i	−0.116545	−	0.201862i
$201$	−3.32588	+	5.76059i	−0.234589	+	0.406321i
$202$	3.97843	+	6.89084i	0.279921	+	0.484838i
$203$	8.77831	−	15.2045i	0.616116	−	1.06714i
$204$	−0.779202	−	1.34962i	−0.0545551	−	0.0944921i
$205$	−2.52696	+	4.37683i	−0.176491	+	0.305691i
$206$	−6.41415			−0.446895
$207$	−3.95602			−0.274962
$208$	1.71940			0.119219
$209$	−4.00779			−0.277225
$210$	4.39557			0.303323
$211$	2.51652	+	4.35875i	0.173245	+	0.300069i	0.939552	−	0.342405i	$-0.111242\pi$
$211$	2.51652	+	4.35875i	0.173245	+	0.300069i	−0.766308	+	0.642474i	$0.777908\pi$
$212$	−2.96526	+	5.13598i	−0.203655	+	0.352740i
$213$	−0.295931	+	0.512568i	−0.0202769	+	0.0351206i
$214$	−6.81559	+	11.8049i	−0.465904	+	0.806969i
$215$	2.65487			0.181061
$216$	−1.00000			−0.0680414
$217$	−0.401912	−	0.696132i	−0.0272836	−	0.0472565i
$218$	−0.665484	+	1.15265i	−0.0450723	+	0.0780675i
$219$	−3.30606			−0.223403
$220$	0.354336	+	0.613727i	0.0238893	+	0.0413775i
$221$	2.67953			0.180244
$222$	−4.19880			−0.281805
$223$	−2.19702	−	14.7707i	−0.147123	−	0.989118i
$223$	−2.19702	−	14.7707i	−0.147123	−	0.989118i
$224$	−3.36767			−0.225012
$225$	−3.29639			−0.219759
$226$	0.992514	+	1.71908i	0.0660210	+	0.114352i
$227$	0.167753			0.0111342			0.00556709	−	0.999985i	$-0.498228\pi$
$227$	0.167753			0.0111342			0.00556709	+	0.999985i	$0.498228\pi$
$228$	3.69076	−	6.39259i	0.244427	−	0.423360i
$229$	−1.13208	−	1.96081i	−0.0748097	−	0.129574i	0.826194	−	0.563386i	$-0.190502\pi$
$229$	−1.13208	−	1.96081i	−0.0748097	−	0.129574i	−0.901003	+	0.433812i	$0.857168\pi$
$230$	−5.16349			−0.340471
$231$	1.82847			0.120305
$232$	−2.60664	+	4.51483i	−0.171134	+	0.296413i
$233$	1.40286	−	2.42982i	0.0919042	−	0.159183i	−0.816408	−	0.577475i	$-0.804038\pi$
$233$	1.40286	−	2.42982i	0.0919042	−	0.159183i	0.908312	+	0.418293i	$0.137371\pi$
$234$	0.859702	−	1.48905i	0.0562005	−	0.0973421i
$235$	4.63930	+	8.03550i	0.302634	+	0.524178i
$236$	0.705752			0.0459405
$237$	−13.6654			−0.887662
$238$	−5.24819			−0.340190
$239$	16.7388			1.08274			0.541372	−	0.840783i	$-0.317905\pi$
$239$	16.7388			1.08274			0.541372	+	0.840783i	$0.317905\pi$
$240$	−1.30523			−0.0842520
$241$	0.0507932	−	0.0879765i	0.00327188	−	0.00566706i	−0.864385	−	0.502831i	$-0.832292\pi$
$241$	0.0507932	−	0.0879765i	0.00327188	−	0.00566706i	0.867657	+	0.497164i	$0.165625\pi$
$242$	−5.35260	−	9.27098i	−0.344078	−	0.595961i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	1.93180	+	3.34597i	0.123671	+	0.214204i
$245$	2.83313	−	4.90712i	0.181002	−	0.313504i
$246$	−1.93604	−	3.35331i	−0.123437	−	0.213799i
$247$	6.34591	+	10.9914i	0.403781	+	0.699369i
$248$	0.119344	+	0.206710i	0.00757836	+	0.0131261i
$249$	−11.1883			−0.709028
$250$	−10.8287			−0.684864
$251$	10.8626			0.685643			0.342821	−	0.939401i	$-0.388617\pi$
$251$	10.8626			0.685643			0.342821	+	0.939401i	$0.388617\pi$
$252$	−1.68384	+	2.91649i	−0.106072	+	0.183722i
$253$	−2.14791			−0.135038
$254$	−6.09999	−	10.5655i	−0.382748	−	0.662938i
$255$	−2.03407			−0.127378
$256$	1.00000			0.0625000
$257$	−29.6495			−1.84948			−0.924742	−	0.380594i	$-0.875720\pi$
$257$	−29.6495			−1.84948			−0.924742	+	0.380594i	$0.875720\pi$
$258$	−1.01702	+	1.76152i	−0.0633167	+	0.109668i
$259$	−7.07008	+	12.2457i	−0.439313	+	0.760913i
$260$	1.12211	−	1.94354i	0.0695900	−	0.120533i
$261$	2.60664	+	4.51483i	0.161347	+	0.279461i
$262$	−1.18727	−	2.05640i	−0.0733495	−	0.127045i
$263$	−15.0614	+	26.0870i	−0.928723	+	1.60860i	−0.143263	+	0.989685i	$0.545759\pi$
$263$	−15.0614	+	26.0870i	−0.928723	+	1.60860i	−0.785461	+	0.618912i	$0.787574\pi$
$264$	−0.542949			−0.0334162
$265$	3.87033	+	6.70361i	0.237753	+	0.411800i
$266$	−12.4293	−	21.5281i	−0.762088	−	1.31997i
$267$	2.23576	−	3.87245i	0.136826	−	0.236990i
$268$	−3.32588	−	5.76059i	−0.203160	−	0.351884i
$269$	1.56533	+	2.71123i	0.0954398	+	0.165307i	0.909792	−	0.415064i	$-0.136241\pi$
$269$	1.56533	+	2.71123i	0.0954398	+	0.165307i	−0.814352	+	0.580371i	$0.802908\pi$
$270$	−0.652613	+	1.13036i	−0.0397168	+	0.0687914i
$271$	−1.83828	−	3.18399i	−0.111667	−	0.193414i	0.804775	−	0.593580i	$-0.202286\pi$
$271$	−1.83828	−	3.18399i	−0.111667	−	0.193414i	−0.916443	+	0.400166i	$0.868952\pi$
$272$	1.55840			0.0944921
$273$	−2.89519	−	5.01462i	−0.175225	−	0.303499i
$274$	7.69606	+	13.3300i	0.464936	+	0.805292i
$275$	−1.78977			−0.107927
$276$	1.97801	−	3.42601i	0.119062	−	0.206222i
$277$	−14.2648			−0.857091			−0.428545	−	0.903520i	$-0.640974\pi$
$277$	−14.2648			−0.857091			−0.428545	+	0.903520i	$0.640974\pi$
$278$	7.88789	+	13.6622i	0.473084	+	0.819406i
$279$	0.238688			0.0142899
$280$	−2.19779	+	3.80668i	−0.131343	+	0.227492i
$281$	−5.23430	+	9.06607i	−0.312252	+	0.540836i	−0.978850	−	0.204581i	$-0.934417\pi$
$281$	−5.23430	+	9.06607i	−0.312252	+	0.540836i	0.666598	+	0.745418i	$0.267750\pi$
$282$	−7.10881			−0.423323
$283$	7.04563			0.418819			0.209410	−	0.977828i	$-0.432846\pi$
$283$	7.04563			0.418819			0.209410	+	0.977828i	$0.432846\pi$
$284$	−0.295931	−	0.512568i	−0.0175603	−	0.0304153i
$285$	−4.81728	−	8.34377i	−0.285351	−	0.494242i
$286$	0.466775	−	0.808477i	0.0276010	−	0.0478063i
$287$	−13.0399			−0.769719
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−14.5714			−0.857140
$290$	3.40225	+	5.89288i	0.199787	+	0.346042i
$291$	4.16184			0.243971
$292$	1.65303	−	2.86313i	0.0967363	−	0.167552i
$293$	0.195843	−	0.339210i	0.0114413	−	0.0198168i	−0.860248	−	0.509876i	$-0.829691\pi$
$293$	0.195843	−	0.339210i	0.0114413	−	0.0198168i	0.871689	+	0.490059i	$0.163025\pi$
$294$	2.17060	+	3.75960i	0.126592	+	0.219264i
$295$	0.460583	−	0.797752i	0.0268162	−	0.0464469i
$296$	2.09940	−	3.63626i	0.122025	−	0.211354i
$297$	−0.271475	+	0.470208i	−0.0157525	+	0.0272842i
$298$	−2.03745	+	3.52896i	−0.118026	+	0.204427i
$299$	3.40100	+	5.89070i	0.196685	+	0.340668i
$300$	1.64819	−	2.85475i	0.0951585	−	0.164819i
$301$	3.42498	+	5.93223i	0.197412	+	0.341928i
$302$	−5.52311	+	9.56630i	−0.317819	+	0.550479i
$303$	−3.97843	+	6.89084i	−0.228555	+	0.395868i
$304$	3.69076	+	6.39259i	0.211680	+	0.366640i
$305$	5.04287			0.288754
$306$	0.779202	−	1.34962i	0.0445440	−	0.0771525i
$307$	−6.86335	−	11.8877i	−0.391712	−	0.678465i	0.600964	−	0.799276i	$-0.294784\pi$
$307$	−6.86335	−	11.8877i	−0.391712	−	0.678465i	−0.992675	+	0.120811i	$0.961450\pi$
$308$	−0.914237	+	1.58350i	−0.0520935	+	0.0902286i
$309$	−3.20707	−	5.55482i	−0.182444	−	0.316002i
$310$	0.311542			0.0176944
$311$	−4.96301	+	8.59618i	−0.281426	+	0.487445i	−0.971736	−	0.236069i	$-0.924141\pi$
$311$	−4.96301	+	8.59618i	−0.281426	+	0.487445i	0.690310	+	0.723514i	$0.257474\pi$
$312$	0.859702	+	1.48905i	0.0486711	+	0.0843007i
$313$	−14.3231	−	24.8083i	−0.809589	−	1.40225i	−0.913149	−	0.407626i	$-0.866357\pi$
$313$	−14.3231	−	24.8083i	−0.809589	−	1.40225i	0.103559	−	0.994623i	$-0.466977\pi$
$314$	−14.7840			−0.834308
$315$	2.19779	+	3.80668i	0.123831	+	0.214482i
$316$	6.83269	−	11.8346i	0.384369	−	0.665746i
$317$	3.51918	−	6.09540i	0.197657	−	0.342352i	−0.750111	−	0.661312i	$-0.770000\pi$
$317$	3.51918	−	6.09540i	0.197657	−	0.342352i	0.947768	+	0.318960i	$0.103333\pi$
$318$	−5.93052			−0.332567
$319$	1.41527	+	2.45132i	0.0792401	+	0.137248i
$320$	0.652613	−	1.13036i	0.0364822	−	0.0631890i
$321$	−13.6312			−0.760818
$322$	−6.66128	−	11.5377i	−0.371219	−	0.642969i
$323$	5.75170	+	9.96224i	0.320033	+	0.554314i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	2.83391	+	4.90848i	0.157197	+	0.272273i
$326$	5.37708			0.297809
$327$	−1.33097			−0.0736027
$328$	3.87207			0.213799
$329$	−11.9701	+	20.7328i	−0.659931	+	1.14303i
$330$	−0.354336	+	0.613727i	−0.0195055	+	0.0337846i
$331$	25.7320			1.41436			0.707179	−	0.707035i	$-0.249968\pi$
$331$	25.7320			1.41436			0.707179	+	0.707035i	$0.249968\pi$
$332$	5.59413	−	9.68933i	0.307018	−	0.531771i
$333$	−2.09940	−	3.63626i	−0.115046	−	0.199266i
$334$	18.1137			0.991139
$335$	−8.68204			−0.474351
$336$	−1.68384	−	2.91649i	−0.0918608	−	0.159107i
$337$	0.810305	−	1.40349i	0.0441401	−	0.0764530i	−0.843111	−	0.537739i	$-0.819279\pi$
$337$	0.810305	−	1.40349i	0.0441401	−	0.0764530i	0.887251	+	0.461286i	$0.152612\pi$
$338$	10.0436			0.546302
$339$	−0.992514	+	1.71908i	−0.0539059	+	0.0933678i
$340$	1.01703	−	1.76156i	0.0551564	−	0.0955338i
$341$	0.129596			0.00701800
$342$	7.38153			0.399147
$343$	−8.95394			−0.483467
$344$	−1.01702	−	1.76152i	−0.0548338	−	0.0949750i
$345$	−2.58175	−	4.47172i	−0.138997	−	0.240749i
$346$	2.41732	+	4.18691i	0.129956	+	0.225090i
$347$	−2.15834	−	3.73835i	−0.115866	−	0.200685i	0.802260	−	0.596975i	$-0.203631\pi$
$347$	−2.15834	−	3.73835i	−0.115866	−	0.200685i	−0.918125	+	0.396290i	$0.870298\pi$
$348$	−5.21328			−0.279461
$349$	−11.2092	+	19.4149i	−0.600013	+	1.03925i	0.392805	+	0.919622i	$0.371505\pi$
$349$	−11.2092	+	19.4149i	−0.600013	+	1.03925i	−0.992818	+	0.119632i	$0.961829\pi$
$350$	−5.55057	−	9.61387i	−0.296691	−	0.513883i
$351$	1.71940			0.0917750
$352$	0.271475	−	0.470208i	0.0144696	−	0.0250622i
$353$	−12.0903	+	20.9410i	−0.643503	+	1.11458i	0.341142	+	0.940012i	$0.389186\pi$
$353$	−12.0903	+	20.9410i	−0.643503	+	1.11458i	−0.984645	+	0.174568i	$0.944147\pi$
$354$	0.352876	+	0.611199i	0.0187551	+	0.0324849i
$355$	−0.772515			−0.0410008
$356$	2.23576	+	3.87245i	0.118495	+	0.205239i
$357$	−2.62410	−	4.54507i	−0.138882	−	0.240550i
$358$	−2.12325	+	3.67758i	−0.112217	+	0.194366i
$359$	−9.52104			−0.502502			−0.251251	−	0.967922i	$-0.580842\pi$
$359$	−9.52104			−0.502502			−0.251251	+	0.967922i	$0.580842\pi$
$360$	−0.652613	−	1.13036i	−0.0343957	−	0.0595751i
$361$	−17.7435	+	30.7326i	−0.933867	+	1.61750i
$362$	3.64457	+	6.31258i	0.191554	+	0.331782i
$363$	5.35260	−	9.27098i	0.280939	−	0.486600i
$364$	5.79039			0.303499
$365$	−2.15758	−	3.73704i	−0.112933	−	0.195605i
$366$	−1.93180	+	3.34597i	−0.100977	+	0.174897i
$367$	8.63445	−	14.9553i	0.450715	−	0.780661i	−0.547716	−	0.836664i	$-0.684502\pi$
$367$	8.63445	−	14.9553i	0.450715	−	0.780661i	0.998431	+	0.0560035i	$0.0178358\pi$
$368$	1.97801	+	3.42601i	0.103111	+	0.178593i
$369$	1.93604	−	3.35331i	0.100786	−	0.174567i
$370$	−2.74019	−	4.74614i	−0.142456	−	0.246740i
$371$	−9.98602	+	17.2963i	−0.518448	+	0.897978i
$372$	−0.119344	+	0.206710i	−0.00618771	+	0.0107174i
$373$	6.69532	−	11.5966i	0.346670	−	0.600451i	−0.638985	−	0.769219i	$-0.720646\pi$
$373$	6.69532	−	11.5966i	0.346670	−	0.600451i	0.985656	+	0.168768i	$0.0539789\pi$
$374$	0.423067	−	0.732774i	0.0218763	−	0.0378908i
$375$	−5.41433	−	9.37789i	−0.279595	−	0.484272i
$376$	3.55440	−	6.15641i	0.183304	−	0.317492i
$377$	4.48187	−	7.76283i	0.230828	−	0.399806i
$378$	−3.36767			−0.173214
$379$	−5.17288	−	8.95968i	−0.265713	−	0.460228i	0.702037	−	0.712140i	$-0.252274\pi$
$379$	−5.17288	−	8.95968i	−0.265713	−	0.460228i	−0.967750	+	0.251912i	$0.918941\pi$
$380$	9.63456			0.494242
$381$	6.09999	−	10.5655i	0.312512	−	0.541287i
$382$	−12.8931			−0.659666
$383$	9.37495	−	16.2379i	0.479038	−	0.829718i	−0.520673	−	0.853756i	$-0.674319\pi$
$383$	9.37495	−	16.2379i	0.479038	−	0.829718i	0.999711	+	0.0240384i	$0.00765239\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	1.19329	+	2.06683i	0.0608155	+	0.105335i
$386$	6.52539			0.332133
$387$	−2.03403			−0.103396
$388$	−2.08092	+	3.60426i	−0.105643	+	0.182978i
$389$	−8.34766	+	14.4586i	−0.423243	+	0.733079i	−0.996255	−	0.0864685i	$-0.972442\pi$
$389$	−8.34766	+	14.4586i	−0.423243	+	0.733079i	0.573011	+	0.819548i	$0.305775\pi$
$390$	2.24421			0.113640
$391$	3.08254	+	5.33911i	0.155891	+	0.270010i
$392$	−4.34121			−0.219264
$393$	1.18727	−	2.05640i	0.0598896	−	0.103732i
$394$	17.7001			0.891720
$395$	−8.91820	−	15.4468i	−0.448723	−	0.777212i
$396$	−0.271475	−	0.470208i	−0.0136421	−	0.0236288i
$397$	−29.1796			−1.46448			−0.732242	−	0.681045i	$-0.761526\pi$
$397$	−29.1796			−1.46448			−0.732242	+	0.681045i	$0.761526\pi$
$398$	−3.51636	−	6.09051i	−0.176259	−	0.305290i
$399$	12.4293	−	21.5281i	0.622242	−	1.07775i
$400$	1.64819	+	2.85475i	0.0824096	+	0.142738i
$401$	−2.60047	−	4.50415i	−0.129861	−	0.224927i	0.793761	−	0.608229i	$-0.208120\pi$
$401$	−2.60047	−	4.50415i	−0.129861	−	0.224927i	−0.923623	+	0.383303i	$0.874787\pi$
$402$	3.32588	−	5.76059i	0.165880	−	0.287312i
$403$	−0.205201	−	0.355418i	−0.0102218	−	0.0177047i
$404$	−3.97843	−	6.89084i	−0.197934	−	0.342832i
$405$	−1.30523			−0.0648572
$406$	−8.77831	+	15.2045i	−0.435660	+	0.754585i
$407$	−1.13987	−	1.97431i	−0.0565011	−	0.0978627i
$408$	0.779202	+	1.34962i	0.0385762	+	0.0668160i
$409$	−11.8825	+	20.5811i	−0.587551	+	1.01767i	0.407001	+	0.913428i	$0.366575\pi$
$409$	−11.8825	+	20.5811i	−0.587551	+	1.01767i	−0.994552	+	0.104241i	$0.966759\pi$
$410$	2.52696	−	4.37683i	0.124798	−	0.216156i
$411$	−7.69606	+	13.3300i	−0.379618	+	0.657518i
$412$	6.41415			0.316002
$413$	2.37674			0.116952
$414$	3.95602			0.194428
$415$	−7.30161	−	12.6468i	−0.358422	−	0.620805i
$416$	−1.71940			−0.0843007
$417$	−7.88789	+	13.6622i	−0.386272	+	0.669042i
$418$	4.00779			0.196028
$419$	−7.60407			−0.371483			−0.185742	−	0.982599i	$-0.559469\pi$
$419$	−7.60407			−0.371483			−0.185742	+	0.982599i	$0.559469\pi$
$420$	−4.39557			−0.214482
$421$	−11.9689	−	20.7308i	−0.583329	−	1.01036i	−0.995081	−	0.0990597i	$-0.968417\pi$
$421$	−11.9689	−	20.7308i	−0.583329	−	1.01036i	0.411753	−	0.911296i	$-0.364917\pi$
$422$	−2.51652	−	4.35875i	−0.122502	−	0.212180i
$423$	−3.55440	−	6.15641i	−0.172821	−	0.299335i
$424$	2.96526	−	5.13598i	0.144006	−	0.249425i
$425$	2.56855	+	4.44886i	0.124593	+	0.215801i
$426$	0.295931	−	0.512568i	0.0143379	−	0.0248340i
$427$	6.50566	+	11.2681i	0.314831	+	0.545304i
$428$	6.81559	−	11.8049i	0.329444	−	0.570613i
$429$	0.933549			0.0450722
$430$	−2.65487			−0.128029
$431$	−4.07084			−0.196085			−0.0980427	−	0.995182i	$-0.531258\pi$
$431$	−4.07084			−0.196085			−0.0980427	+	0.995182i	$0.531258\pi$
$432$	1.00000			0.0481125
$433$	−12.5158			−0.601473			−0.300736	−	0.953707i	$-0.597232\pi$
$433$	−12.5158			−0.601473			−0.300736	+	0.953707i	$0.597232\pi$
$434$	0.401912	+	0.696132i	0.0192924	+	0.0334154i
$435$	−3.40225	+	5.89288i	−0.163126	+	0.282542i
$436$	0.665484	−	1.15265i	0.0318709	−	0.0552020i
$437$	−14.6007	+	25.2892i	−0.698447	+	1.20975i
$438$	3.30606			0.157970
$439$	−16.8005			−0.801844			−0.400922	−	0.916112i	$-0.631310\pi$
$439$	−16.8005			−0.801844			−0.400922	+	0.916112i	$0.631310\pi$
$440$	−0.354336	−	0.613727i	−0.0168923	−	0.0292583i
$441$	−2.17060	+	3.75960i	−0.103362	+	0.179028i
$442$	−2.67953			−0.127452
$443$	−2.36304	−	4.09291i	−0.112271	−	0.194460i	0.804414	−	0.594069i	$-0.202479\pi$
$443$	−2.36304	−	4.09291i	−0.112271	−	0.194460i	−0.916686	+	0.399609i	$0.869146\pi$
$444$	4.19880			0.199266
$445$	5.83634			0.276669
$446$	2.19702	+	14.7707i	0.104032	+	0.699412i
$447$	−4.07489			−0.192736
$448$	3.36767			0.159107
$449$	6.15229	+	10.6561i	0.290344	+	0.502891i	0.973891	−	0.227015i	$-0.0728968\pi$
$449$	6.15229	+	10.6561i	0.290344	+	0.502891i	−0.683547	+	0.729907i	$0.739563\pi$
$450$	3.29639			0.155393
$451$	1.05117	−	1.82068i	0.0494976	−	0.0857324i
$452$	−0.992514	−	1.71908i	−0.0466839	−	0.0808589i
$453$	−11.0462			−0.518996
$454$	−0.167753			−0.00787305
$455$	3.77888	−	6.54522i	0.177157	−	0.306844i
$456$	−3.69076	+	6.39259i	−0.172836	+	0.299360i
$457$	−3.66778	+	6.35277i	−0.171571	+	0.297170i	−0.938969	−	0.344001i	$-0.888218\pi$
$457$	−3.66778	+	6.35277i	−0.171571	+	0.297170i	0.767398	+	0.641171i	$0.221551\pi$
$458$	1.13208	+	1.96081i	0.0528984	+	0.0916227i
$459$	1.55840			0.0727401
$460$	5.16349			0.240749
$461$	25.8860			1.20563			0.602815	−	0.797881i	$-0.294046\pi$
$461$	25.8860			1.20563			0.602815	+	0.797881i	$0.294046\pi$
$462$	−1.82847			−0.0850683
$463$	28.0018			1.30135			0.650676	−	0.759355i	$-0.274485\pi$
$463$	28.0018			1.30135			0.650676	+	0.759355i	$0.274485\pi$
$464$	2.60664	−	4.51483i	0.121010	−	0.209596i
$465$	0.155771	+	0.269803i	0.00722371	+	0.0125118i
$466$	−1.40286	+	2.42982i	−0.0649861	+	0.112559i
$467$	5.07482	+	8.78984i	0.234835	+	0.406745i	0.959225	−	0.282645i	$-0.0912118\pi$
$467$	5.07482	+	8.78984i	0.234835	+	0.406745i	−0.724390	+	0.689390i	$0.757878\pi$
$468$	−0.859702	+	1.48905i	−0.0397398	+	0.0688313i
$469$	−11.2005	−	19.3998i	−0.517189	−	0.895798i
$470$	−4.63930	−	8.03550i	−0.213995	−	0.370650i
$471$	−7.39199	−	12.8033i	−0.340605	−	0.589945i
$472$	−0.705752			−0.0324849
$473$	−1.10438			−0.0507793
$474$	13.6654			0.627672
$475$	−12.1662	+	21.0724i	−0.558223	+	0.966870i
$476$	5.24819			0.240550
$477$	−2.96526	−	5.13598i	−0.135770	−	0.235160i
$478$	−16.7388			−0.765615
$479$	21.2551			0.971169			0.485584	−	0.874190i	$-0.338607\pi$
$479$	21.2551			0.971169			0.485584	+	0.874190i	$0.338607\pi$
$480$	1.30523			0.0595751
$481$	−3.60971	+	6.25221i	−0.164589	+	0.285076i
$482$	−0.0507932	+	0.0879765i	−0.00231357	+	0.00400722i
$483$	6.66128	−	11.5377i	0.303099	−	0.524982i
$484$	5.35260	+	9.27098i	0.243300	+	0.421408i
$485$	2.71607	+	4.70437i	0.123330	+	0.213614i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−25.0729			−1.13616			−0.568081	−	0.822973i	$-0.692314\pi$
$487$	−25.0729			−1.13616			−0.568081	+	0.822973i	$0.692314\pi$
$488$	−1.93180	−	3.34597i	−0.0874485	−	0.151465i
$489$	2.68854	+	4.65669i	0.121580	+	0.210583i
$490$	−2.83313	+	4.90712i	−0.127988	+	0.221681i
$491$	19.3019	+	33.4318i	0.871081	+	1.50876i	0.860879	+	0.508809i	$0.169914\pi$
$491$	19.3019	+	33.4318i	0.871081	+	1.50876i	0.0102018	+	0.999948i	$0.496753\pi$
$492$	1.93604	+	3.35331i	0.0872833	+	0.151179i
$493$	4.06220	−	7.03594i	0.182952	−	0.316883i
$494$	−6.34591	−	10.9914i	−0.285516	−	0.494529i
$495$	−0.708671			−0.0318524
$496$	−0.119344	−	0.206710i	−0.00535871	−	0.00928156i
$497$	−0.996600	−	1.72616i	−0.0447036	−	0.0774289i
$498$	11.1883			0.501358
$499$	13.7728	−	23.8552i	0.616556	−	1.06791i	−0.373553	−	0.927609i	$-0.621861\pi$
$499$	13.7728	−	23.8552i	0.616556	−	1.06791i	0.990109	−	0.140298i	$-0.0448060\pi$
$500$	10.8287			0.484272
$501$	9.05686	+	15.6869i	0.404631	+	0.700841i
$502$	−10.8626			−0.484823
$503$	2.79892	−	4.84786i	0.124797	−	0.216156i	−0.796856	−	0.604169i	$-0.793505\pi$
$503$	2.79892	−	4.84786i	0.124797	−	0.216156i	0.921654	+	0.388013i	$0.126839\pi$
$504$	1.68384	−	2.91649i	0.0750040	−	0.129911i
$505$	−10.3855			−0.462148
$506$	2.14791			0.0954865
$507$	5.02182	+	8.69805i	0.223027	+	0.386294i
$508$	6.09999	+	10.5655i	0.270643	+	0.468768i
$509$	−5.66444	+	9.81110i	−0.251072	+	0.434869i	−0.963821	−	0.266550i	$-0.914116\pi$
$509$	−5.66444	+	9.81110i	−0.251072	+	0.434869i	0.712749	+	0.701419i	$0.247450\pi$
$510$	2.03407			0.0900701
$511$	5.56687	−	9.64209i	0.246264	−	0.426541i
$512$	−1.00000			−0.0441942
$513$	3.69076	+	6.39259i	0.162951	+	0.282240i
$514$	29.6495			1.30778
$515$	4.18596	−	7.25029i	0.184455	−	0.319486i
$516$	1.01702	−	1.76152i	0.0447716	−	0.0775468i
$517$	−1.92986	−	3.34261i	−0.0848751	−	0.147008i
$518$	7.07008	−	12.2457i	0.310642	−	0.538047i
$519$	−2.41732	+	4.18691i	−0.106108	+	0.183785i
$520$	−1.12211	+	1.94354i	−0.0492076	+	0.0852300i
$521$	−19.6072	+	33.9606i	−0.859005	+	1.48784i	0.0138742	+	0.999904i	$0.495584\pi$
$521$	−19.6072	+	33.9606i	−0.859005	+	1.48784i	−0.872879	+	0.487936i	$0.837750\pi$
$522$	−2.60664	−	4.51483i	−0.114090	−	0.197609i
$523$	18.3659	−	31.8106i	0.803083	−	1.39098i	−0.114495	−	0.993424i	$-0.536525\pi$
$523$	18.3659	−	31.8106i	0.803083	−	1.39098i	0.917578	−	0.397557i	$-0.130142\pi$
$524$	1.18727	+	2.05640i	0.0518659	+	0.0898344i
$525$	5.55057	−	9.61387i	0.242247	−	0.419584i
$526$	15.0614	−	26.0870i	0.656707	−	1.13745i
$527$	−0.185986	−	0.322138i	−0.00810170	−	0.0140325i
$528$	0.542949			0.0236288
$529$	3.67497	−	6.36524i	0.159781	−	0.276749i
$530$	−3.87033	−	6.70361i	−0.168116	−	0.291186i
$531$	−0.352876	+	0.611199i	−0.0153135	+	0.0265238i
$532$	12.4293	+	21.5281i	0.538877	+	0.933363i
$533$	−6.65766			−0.288375
$534$	−2.23576	+	3.87245i	−0.0967507	+	0.167577i
$535$	−8.89588	−	15.4081i	−0.384602	−	0.666151i
$536$	3.32588	+	5.76059i	0.143656	+	0.248820i
$537$	−4.24650			−0.183250
$538$	−1.56533	−	2.71123i	−0.0674861	−	0.116889i
$539$	−1.17853	+	2.04127i	−0.0507628	+	0.0879237i
$540$	0.652613	−	1.13036i	0.0280840	−	0.0486429i
$541$	14.2029			0.610629			0.305314	−	0.952252i	$-0.401238\pi$
$541$	14.2029			0.610629			0.305314	+	0.952252i	$0.401238\pi$
$542$	1.83828	+	3.18399i	0.0789608	+	0.136764i
$543$	−3.64457	+	6.31258i	−0.156403	+	0.270899i
$544$	−1.55840			−0.0668160
$545$	−0.868607	−	1.50447i	−0.0372070	−	0.0644445i
$546$	2.89519	+	5.01462i	0.123903	+	0.214606i
$547$	−0.545315	−	0.944514i	−0.0233160	−	0.0403845i	0.854132	−	0.520056i	$-0.174089\pi$
$547$	−0.545315	−	0.944514i	−0.0233160	−	0.0403845i	−0.877448	+	0.479672i	$0.840756\pi$
$548$	−7.69606	−	13.3300i	−0.328759	−	0.569428i
$549$	−3.86360			−0.164894
$550$	1.78977			0.0763160
$551$	38.4820			1.63939
$552$	−1.97801	+	3.42601i	−0.0841896	+	0.145821i
$553$	23.0102	−	39.8549i	0.978495	−	1.69480i
$554$	14.2648			0.606055
$555$	2.74019	−	4.74614i	0.116315	−	0.201463i
$556$	−7.88789	−	13.6622i	−0.334521	−	0.579407i
$557$	43.5769			1.84641			0.923206	−	0.384305i	$-0.125559\pi$
$557$	43.5769			1.84641			0.923206	+	0.384305i	$0.125559\pi$
$558$	−0.238688			−0.0101045
$559$	1.74866	+	3.02877i	0.0739605	+	0.128103i
$560$	2.19779	−	3.80668i	0.0928734	−	0.160861i
$561$	0.846134			0.0357238
$562$	5.23430	−	9.06607i	0.220796	−	0.382429i
$563$	14.1395	−	24.4904i	0.595910	−	1.03215i	−0.397508	−	0.917599i	$-0.630125\pi$
$563$	14.1395	−	24.4904i	0.595910	−	1.03215i	0.993418	−	0.114547i	$-0.0365417\pi$
$564$	7.10881			0.299335
$565$	−2.59091			−0.109000
$566$	−7.04563			−0.296150
$567$	−1.68384	−	2.91649i	−0.0707144	−	0.122481i
$568$	0.295931	+	0.512568i	0.0124170	+	0.0215069i
$569$	11.1000	+	19.2258i	0.465337	+	0.805988i	0.999217	−	0.0395727i	$-0.0125997\pi$
$569$	11.1000	+	19.2258i	0.465337	+	0.805988i	−0.533879	+	0.845561i	$0.679266\pi$
$570$	4.81728	+	8.34377i	0.201774	+	0.349482i
$571$	−4.67982			−0.195845			−0.0979223	−	0.995194i	$-0.531220\pi$
$571$	−4.67982			−0.195845			−0.0979223	+	0.995194i	$0.531220\pi$
$572$	−0.466775	+	0.808477i	−0.0195168	+	0.0338041i
$573$	−6.44653	−	11.1657i	−0.269308	−	0.466455i
$574$	13.0399			0.544274
$575$	−6.52028	+	11.2935i	−0.271914	+	0.470969i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.61190	+	4.52395i	0.108735	+	0.188334i	0.915258	−	0.402868i	$-0.131987\pi$
$577$	2.61190	+	4.52395i	0.108735	+	0.188334i	−0.806523	+	0.591203i	$0.798653\pi$
$578$	14.5714			0.606089
$579$	3.26269	+	5.65115i	0.135593	+	0.234854i
$580$	−3.40225	−	5.89288i	−0.141271	−	0.244688i
$581$	18.8392	−	32.6305i	0.781582	−	1.35374i
$582$	−4.16184			−0.172514
$583$	−1.60998	−	2.78857i	−0.0666787	−	0.115491i
$584$	−1.65303	+	2.86313i	−0.0684029	+	0.118477i
$585$	1.12211	+	1.94354i	0.0463934	+	0.0803556i
$586$	−0.195843	+	0.339210i	−0.00809019	+	0.0140126i
$587$	6.73233			0.277873			0.138936	−	0.990301i	$-0.455632\pi$
$587$	6.73233			0.277873			0.138936	+	0.990301i	$0.455632\pi$
$588$	−2.17060	−	3.75960i	−0.0895142	−	0.155043i
$589$	0.880942	−	1.52584i	0.0362986	−	0.0628710i
$590$	−0.460583	+	0.797752i	−0.0189619	+	0.0328429i
$591$	8.85006	+	15.3288i	0.364043	+	0.630541i
$592$	−2.09940	+	3.63626i	−0.0862847	+	0.149450i
$593$	1.65855	+	2.87268i	0.0681083	+	0.117967i	0.898069	−	0.439855i	$-0.144970\pi$
$593$	1.65855	+	2.87268i	0.0681083	+	0.117967i	−0.829960	+	0.557822i	$0.811637\pi$
$594$	0.271475	−	0.470208i	0.0111387	−	0.0192929i
$595$	3.42504	−	5.93234i	0.140413	−	0.243202i
$596$	2.03745	−	3.52896i	0.0834571	−	0.144552i
$597$	3.51636	−	6.09051i	0.143915	−	0.249268i
$598$	−3.40100	−	5.89070i	−0.139077	−	0.240889i
$599$	0.604589	−	1.04718i	0.0247028	−	0.0427866i	−0.853410	−	0.521241i	$-0.825469\pi$
$599$	0.604589	−	1.04718i	0.0247028	−	0.0427866i	0.878113	+	0.478454i	$0.158803\pi$
$600$	−1.64819	+	2.85475i	−0.0672872	+	0.116545i
$601$	−7.01994			−0.286349			−0.143175	−	0.989697i	$-0.545731\pi$
$601$	−7.01994			−0.286349			−0.143175	+	0.989697i	$0.545731\pi$
$602$	−3.42498	−	5.93223i	−0.139592	−	0.241780i
$603$	6.65175			0.270880
$604$	5.52311	−	9.56630i	0.224732	−	0.389247i
$605$	13.9727			0.568071
$606$	3.97843	−	6.89084i	0.161613	−	0.279921i
$607$	−12.5670	−	21.7667i	−0.510079	−	0.883483i	−0.999932	−	0.0116775i	$-0.996283\pi$
$607$	−12.5670	−	21.7667i	−0.510079	−	0.883483i	0.489853	−	0.871805i	$-0.337050\pi$
$608$	−3.69076	−	6.39259i	−0.149680	−	0.259254i
$609$	−17.5566			−0.711430
$610$	−5.04287			−0.204180
$611$	−6.11146	+	10.5854i	−0.247243	+	0.428238i
$612$	−0.779202	+	1.34962i	−0.0314974	+	0.0545551i
$613$	−39.7122			−1.60396			−0.801980	−	0.597351i	$-0.796220\pi$
$613$	−39.7122			−1.60396			−0.801980	+	0.597351i	$0.796220\pi$
$614$	6.86335	+	11.8877i	0.276982	+	0.479747i
$615$	5.05393			0.203794
$616$	0.914237	−	1.58350i	0.0368357	−	0.0638012i
$617$	27.8438			1.12095			0.560474	−	0.828172i	$-0.310619\pi$
$617$	27.8438			1.12095			0.560474	+	0.828172i	$0.310619\pi$
$618$	3.20707	+	5.55482i	0.129007	+	0.223447i
$619$	0.787646	+	1.36424i	0.0316582	+	0.0548335i	0.881420	−	0.472333i	$-0.156588\pi$
$619$	0.787646	+	1.36424i	0.0316582	+	0.0548335i	−0.849762	+	0.527166i	$0.823255\pi$
$620$	−0.311542			−0.0125118
$621$	1.97801	+	3.42601i	0.0793747	+	0.137481i
$622$	4.96301	−	8.59618i	0.198998	−	0.344675i
$623$	7.52930	+	13.0411i	0.301655	+	0.522482i
$624$	−0.859702	−	1.48905i	−0.0344156	−	0.0596096i
$625$	−1.17405	+	2.03351i	−0.0469618	+	0.0813402i
$626$	14.3231	+	24.8083i	0.572466	+	0.991540i
$627$	2.00390	+	3.47085i	0.0800279	+	0.138612i
$628$	14.7840			0.589945
$629$	−3.27171	+	5.66677i	−0.130452	+	0.225949i
$630$	−2.19779	−	3.80668i	−0.0875619	−	0.151662i
$631$	23.3723	+	40.4820i	0.930437	+	1.61156i	0.782575	+	0.622556i	$0.213906\pi$
$631$	23.3723	+	40.4820i	0.930437	+	1.61156i	0.147862	+	0.989008i	$0.452761\pi$
$632$	−6.83269	+	11.8346i	−0.271790	+	0.470754i
$633$	2.51652	−	4.35875i	0.100023	−	0.173245i
$634$	−3.51918	+	6.09540i	−0.139765	+	0.242079i
$635$	15.9237			0.631914
$636$	5.93052			0.235160
$637$	7.46429			0.295746
$638$	−1.41527	−	2.45132i	−0.0560312	−	0.0970489i
$639$	0.591863			0.0234137
$640$	−0.652613	+	1.13036i	−0.0257968	+	0.0446813i
$641$	19.2549			0.760522			0.380261	−	0.924879i	$-0.375834\pi$
$641$	19.2549			0.760522			0.380261	+	0.924879i	$0.375834\pi$
$642$	13.6312			0.537979
$643$	−6.08078			−0.239803			−0.119901	−	0.992786i	$-0.538258\pi$
$643$	−6.08078			−0.239803			−0.119901	+	0.992786i	$0.538258\pi$
$644$	6.66128	+	11.5377i	0.262491	+	0.454648i
$645$	−1.32744	−	2.29919i	−0.0522677	−	0.0905304i
$646$	−5.75170	−	9.96224i	−0.226298	−	0.391959i
$647$	−15.4462	+	26.7536i	−0.607252	+	1.05179i	0.384439	+	0.923150i	$0.374395\pi$
$647$	−15.4462	+	26.7536i	−0.607252	+	1.05179i	−0.991691	+	0.128641i	$0.958939\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−0.191594	+	0.331850i	−0.00752071	+	0.0130262i
$650$	−2.83391	−	4.90848i	−0.111155	−	0.192526i
$651$	−0.401912	+	0.696132i	−0.0157522	+	0.0272836i
$652$	−5.37708			−0.210583
$653$	−15.7699			−0.617122			−0.308561	−	0.951205i	$-0.599847\pi$
$653$	−15.7699			−0.617122			−0.308561	+	0.951205i	$0.599847\pi$
$654$	1.33097			0.0520450
$655$	3.09930			0.121100
$656$	−3.87207			−0.151179
$657$	1.65303	+	2.86313i	0.0644909	+	0.111702i
$658$	11.9701	−	20.7328i	0.466641	−	0.808247i
$659$	16.7094	−	28.9415i	0.650904	−	1.12740i	−0.332000	−	0.943280i	$-0.607723\pi$
$659$	16.7094	−	28.9415i	0.650904	−	1.12740i	0.982904	−	0.184120i	$-0.0589434\pi$
$660$	0.354336	−	0.613727i	0.0137925	−	0.0238893i
$661$	5.21464			0.202826			0.101413	−	0.994844i	$-0.467664\pi$
$661$	5.21464			0.202826			0.101413	+	0.994844i	$0.467664\pi$
$662$	−25.7320			−1.00010
$663$	−1.33976	−	2.32054i	−0.0520321	−	0.0901222i
$664$	−5.59413	+	9.68933i	−0.217095	+	0.376019i
$665$	32.4460			1.25820
$666$	2.09940	+	3.63626i	0.0813500	+	0.140902i
$667$	20.6238			0.798558
$668$	−18.1137			−0.700841
$669$	−11.6933	+	9.28802i	−0.452088	+	0.359095i
$670$	8.68204			0.335417
$671$	−2.09774			−0.0809823
$672$	1.68384	+	2.91649i	0.0649554	+	0.112506i
$673$	−14.6188			−0.563512			−0.281756	−	0.959486i	$-0.590917\pi$
$673$	−14.6188			−0.563512			−0.281756	+	0.959486i	$0.590917\pi$
$674$	−0.810305	+	1.40349i	−0.0312118	+	0.0540604i
$675$	1.64819	+	2.85475i	0.0634390	+	0.109880i
$676$	−10.0436			−0.386294
$677$	30.3183			1.16523			0.582614	−	0.812749i	$-0.302030\pi$
$677$	30.3183			1.16523			0.582614	+	0.812749i	$0.302030\pi$
$678$	0.992514	−	1.71908i	0.0381173	−	0.0660210i
$679$	−7.00785	+	12.1380i	−0.268937	+	0.465812i
$680$	−1.01703	+	1.76156i	−0.0390015	+	0.0675526i
$681$	−0.0838767	−	0.145279i	−0.00321416	−	0.00556709i
$682$	−0.129596			−0.00496247
$683$	−34.1573			−1.30699			−0.653496	−	0.756930i	$-0.726698\pi$
$683$	−34.1573			−1.30699			−0.653496	+	0.756930i	$0.726698\pi$
$684$	−7.38153			−0.282240
$685$	−20.0902			−0.767606
$686$	8.95394			0.341863
$687$	−1.13208	+	1.96081i	−0.0431914	+	0.0748097i
$688$	1.01702	+	1.76152i	0.0387734	+	0.0671575i
$689$	−5.09848	+	8.83082i	−0.194237	+	0.336428i
$690$	2.58175	+	4.47172i	0.0982854	+	0.170235i
$691$	26.2137	−	45.4035i	0.997218	−	1.72723i	0.434053	−	0.900887i	$-0.357083\pi$
$691$	26.2137	−	45.4035i	0.997218	−	1.72723i	0.563165	−	0.826345i	$-0.309584\pi$
$692$	−2.41732	−	4.18691i	−0.0918926	−	0.159163i
$693$	−0.914237	−	1.58350i	−0.0347290	−	0.0601524i
$694$	2.15834	+	3.73835i	0.0819295	+	0.141906i
$695$	−20.5909			−0.781059
$696$	5.21328			0.197609
$697$	−6.03425			−0.228564
$698$	11.2092	−	19.4149i	0.424274	−	0.734863i
$699$	−2.80571			−0.106122
$700$	5.55057	+	9.61387i	0.209792	+	0.363370i
$701$	−21.7141			−0.820131			−0.410066	−	0.912056i	$-0.634494\pi$
$701$	−21.7141			−0.820131			−0.410066	+	0.912056i	$0.634494\pi$
$702$	−1.71940			−0.0648947
$703$	−30.9935			−1.16894
$704$	−0.271475	+	0.470208i	−0.0102316	+	0.0177216i
$705$	4.63930	−	8.03550i	0.174726	−	0.302634i
$706$	12.0903	−	20.9410i	0.455025	−	0.788127i
$707$	−13.3980	−	23.2061i	−0.503885	−	0.872754i
$708$	−0.352876	−	0.611199i	−0.0132619	−	0.0229703i
$709$	−1.77390	+	3.07248i	−0.0666202	+	0.115390i	−0.897412	−	0.441194i	$-0.854555\pi$
$709$	−1.77390	+	3.07248i	−0.0666202	+	0.115390i	0.830791	+	0.556584i	$0.187888\pi$
$710$	0.772515			0.0289920
$711$	6.83269	+	11.8346i	0.256246	+	0.443831i
$712$	−2.23576	−	3.87245i	−0.0837886	−	0.145126i
$713$	0.472127	−	0.817749i	0.0176813	−	0.0306249i
$714$	2.62410	+	4.54507i	0.0982043	+	0.170095i
$715$	0.609246	+	1.05525i	0.0227845	+	0.0394639i
$716$	2.12325	−	3.67758i	0.0793496	−	0.137438i
$717$	−8.36941	−	14.4962i	−0.312561	−	0.541372i
$718$	9.52104			0.355322
$719$	−2.38961	−	4.13892i	−0.0891172	−	0.154356i	0.818021	−	0.575188i	$-0.195071\pi$
$719$	−2.38961	−	4.13892i	−0.0891172	−	0.154356i	−0.907138	+	0.420833i	$0.861738\pi$
$720$	0.652613	+	1.13036i	0.0243214	+	0.0421260i
$721$	21.6007			0.804454
$722$	17.7435	−	30.7326i	0.660343	−	1.14375i
$723$	−0.101586			−0.00377804
$724$	−3.64457	−	6.31258i	−0.135449	−	0.234605i
$725$	17.1850			0.638234
$726$	−5.35260	+	9.27098i	−0.198654	+	0.344078i
$727$	−11.3542	+	19.6660i	−0.421103	+	0.729372i	−0.996048	−	0.0888203i	$-0.971690\pi$
$727$	−11.3542	+	19.6660i	−0.421103	+	0.729372i	0.574944	+	0.818192i	$0.305024\pi$
$728$	−5.79039			−0.214606
$729$	1.00000			0.0370370
$730$	2.15758	+	3.73704i	0.0798556	+	0.138314i
$731$	1.58492	+	2.74517i	0.0586205	+	0.101534i
$732$	1.93180	−	3.34597i	0.0714014	−	0.123671i
$733$	24.0027			0.886558			0.443279	−	0.896384i	$-0.353815\pi$
$733$	24.0027			0.886558			0.443279	+	0.896384i	$0.353815\pi$
$734$	−8.63445	+	14.9553i	−0.318703	+	0.552011i
$735$	−5.66626			−0.209003
$736$	−1.97801	−	3.42601i	−0.0729103	−	0.126284i
$737$	3.61156			0.133034
$738$	−1.93604	+	3.35331i	−0.0712665	+	0.123437i
$739$	−21.2137	+	36.7433i	−0.780360	+	1.35162i	0.151373	+	0.988477i	$0.451631\pi$
$739$	−21.2137	+	36.7433i	−0.780360	+	1.35162i	−0.931732	+	0.363146i	$0.881703\pi$
$740$	2.74019	+	4.74614i	0.100731	+	0.174472i
$741$	6.34591	−	10.9914i	0.233123	−	0.403781i
$742$	9.98602	−	17.2963i	0.366598	−	0.634967i
$743$	−22.4166	+	38.8267i	−0.822386	+	1.42441i	0.0815155	+	0.996672i	$0.474024\pi$
$743$	−22.4166	+	38.8267i	−0.822386	+	1.42441i	−0.903901	+	0.427742i	$0.859309\pi$
$744$	0.119344	−	0.206710i	0.00437537	−	0.00757836i
$745$	−2.65933	−	4.60609i	−0.0974303	−	0.168754i
$746$	−6.69532	+	11.5966i	−0.245133	+	0.424583i
$747$	5.59413	+	9.68933i	0.204679	+	0.354514i
$748$	−0.423067	+	0.732774i	−0.0154689	+	0.0267929i
$749$	22.9526	−	39.7552i	0.838672	−	1.45262i
$750$	5.41433	+	9.37789i	0.197703	+	0.342432i
$751$	22.6446			0.826315			0.413157	−	0.910660i	$-0.364426\pi$
$751$	22.6446			0.826315			0.413157	+	0.910660i	$0.364426\pi$
$752$	−3.55440	+	6.15641i	−0.129616	+	0.224501i
$753$	−5.43131	−	9.40731i	−0.197928	−	0.342821i
$754$	−4.48187	+	7.76283i	−0.163220	+	0.282705i
$755$	−7.20890	−	12.4862i	−0.262359	−	0.454419i
$756$	3.36767			0.122481
$757$	7.99883	−	13.8544i	0.290722	−	0.503546i	−0.683258	−	0.730177i	$-0.739438\pi$
$757$	7.99883	−	13.8544i	0.290722	−	0.503546i	0.973981	+	0.226631i	$0.0727711\pi$
$758$	5.17288	+	8.95968i	0.187887	+	0.325430i
$759$	1.07396	+	1.86015i	0.0389822	+	0.0675191i
$760$	−9.63456			−0.349482
$761$	9.67408	+	16.7560i	0.350685	+	0.607405i	0.986370	−	0.164544i	$-0.0526154\pi$
$761$	9.67408	+	16.7560i	0.350685	+	0.607405i	−0.635684	+	0.771949i	$0.719282\pi$
$762$	−6.09999	+	10.5655i	−0.220979	+	0.382748i
$763$	2.24113	−	3.88175i	0.0811344	−	0.140529i
$764$	12.8931			0.466455
$765$	1.01703	+	1.76156i	0.0367710	+	0.0636892i
$766$	−9.37495	+	16.2379i	−0.338731	+	0.586699i
$767$	1.21347			0.0438160
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−24.7281	−	42.8303i	−0.891718	−	1.54450i	−0.837814	−	0.545955i	$-0.816167\pi$
$769$	−24.7281	−	42.8303i	−0.891718	−	1.54450i	−0.0539040	−	0.998546i	$-0.517167\pi$
$770$	−1.19329	−	2.06683i	−0.0430030	−	0.0744834i
$771$	14.8247	+	25.6772i	0.533900	+	0.924742i
$772$	−6.52539			−0.234854
$773$	−50.5886			−1.81955			−0.909773	−	0.415106i	$-0.863745\pi$
$773$	−50.5886			−1.81955			−0.909773	+	0.415106i	$0.863745\pi$
$774$	2.03403			0.0731118
$775$	0.393404	−	0.681396i	0.0141315	−	0.0244765i
$776$	2.08092	−	3.60426i	0.0747006	−	0.129385i
$777$	14.1402			0.507276
$778$	8.34766	−	14.4586i	0.299278	−	0.518365i
$779$	−14.2909	−	24.7526i	−0.512025	−	0.886853i
$780$	−2.24421			−0.0803556
$781$	0.321351			0.0114989
$782$	−3.08254	−	5.33911i	−0.110231	−	0.190926i
$783$	2.60664	−	4.51483i	0.0931537	−	0.161347i
$784$	4.34121			0.155043
$785$	9.64822	−	16.7112i	0.344360	−	0.596448i
$786$	−1.18727	+	2.05640i	−0.0423483	+	0.0733495i
$787$	−21.2319			−0.756836			−0.378418	−	0.925635i	$-0.623532\pi$
$787$	−21.2319			−0.756836			−0.378418	+	0.925635i	$0.623532\pi$
$788$	−17.7001			−0.630541
$789$	30.1227			1.07240
$790$	8.91820	+	15.4468i	0.317295	+	0.549572i
$791$	−3.34246	−	5.78931i	−0.118844	−	0.205844i
$792$	0.271475	+	0.470208i	0.00964643	+	0.0167081i
$793$	3.32154	+	5.75308i	0.117952	+	0.204298i
$794$	29.1796			1.03555
$795$	3.87033	−	6.70361i	0.137267	−	0.237753i
$796$	3.51636	+	6.09051i	0.124634	+	0.215873i
$797$	17.4821			0.619246			0.309623	−	0.950859i	$-0.399797\pi$
$797$	17.4821			0.619246			0.309623	+	0.950859i	$0.399797\pi$
$798$	−12.4293	+	21.5281i	−0.439992	+	0.762088i
$799$	−5.53920	+	9.59417i	−0.195963	+	0.339417i
$800$	−1.64819	−	2.85475i	−0.0582724	−	0.100931i
$801$	−4.47152			−0.157993
$802$	2.60047	+	4.50415i	0.0918259	+	0.159047i
$803$	0.897512	+	1.55454i	0.0316725	+	0.0548584i
$804$	−3.32588	+	5.76059i	−0.117295	+	0.203160i
$805$	17.3889			0.612880
$806$	0.205201	+	0.355418i	0.00722789	+	0.0125191i
$807$	1.56533	−	2.71123i	0.0551022	−	0.0954398i
$808$	3.97843	+	6.89084i	0.139961	+	0.242419i
$809$	−2.37815	+	4.11908i	−0.0836114	+	0.144819i	−0.904799	−	0.425840i	$-0.859979\pi$
$809$	−2.37815	+	4.11908i	−0.0836114	+	0.144819i	0.821187	+	0.570659i	$0.193312\pi$
$810$	1.30523			0.0458610
$811$	−4.65010	−	8.05421i	−0.163287	−	0.282822i	0.772759	−	0.634700i	$-0.218876\pi$
$811$	−4.65010	−	8.05421i	−0.163287	−	0.282822i	−0.936046	+	0.351878i	$0.885543\pi$
$812$	8.77831	−	15.2045i	0.308058	−	0.533572i
$813$	−1.83828	+	3.18399i	−0.0644713	+	0.111667i
$814$	1.13987	+	1.97431i	0.0399523	+	0.0691994i
$815$	−3.50915	+	6.07803i	−0.122920	+	0.212904i
$816$	−0.779202	−	1.34962i	−0.0272775	−	0.0472461i
$817$	−7.50713	+	13.0027i	−0.262641	+	0.454908i
$818$	11.8825	−	20.5811i	0.415461	−	0.719600i
$819$	−2.89519	+	5.01462i	−0.101166	+	0.175225i
$820$	−2.52696	+	4.37683i	−0.0882454	+	0.152846i
$821$	16.6969	+	28.9198i	0.582725	+	1.00931i	0.995155	+	0.0983202i	$0.0313469\pi$
$821$	16.6969	+	28.9198i	0.582725	+	1.00931i	−0.412430	+	0.910989i	$0.635320\pi$
$822$	7.69606	−	13.3300i	0.268431	−	0.464936i
$823$	−18.2336	+	31.5816i	−0.635585	+	1.10086i	0.350806	+	0.936448i	$0.385908\pi$
$823$	−18.2336	+	31.5816i	−0.635585	+	1.10086i	−0.986391	+	0.164417i	$0.947426\pi$
$824$	−6.41415			−0.223447
$825$	0.894885	+	1.54999i	0.0311559	+	0.0539636i
$826$	−2.37674			−0.0826973
$827$	6.47297	−	11.2115i	0.225087	−	0.389862i	−0.731259	−	0.682100i	$-0.761067\pi$
$827$	6.47297	−	11.2115i	0.225087	−	0.389862i	0.956346	+	0.292238i	$0.0944000\pi$
$828$	−3.95602			−0.137481
$829$	3.80114	−	6.58376i	0.132019	−	0.228664i	−0.792436	−	0.609955i	$-0.791187\pi$
$829$	3.80114	−	6.58376i	0.132019	−	0.228664i	0.924455	+	0.381292i	$0.124521\pi$
$830$	7.30161	+	12.6468i	0.253443	+	0.438975i
$831$	7.13242	+	12.3537i	0.247421	+	0.428545i
$832$	1.71940			0.0596096
$833$	6.76536			0.234406
$834$	7.88789	−	13.6622i	0.273135	−	0.473084i
$835$	−11.8212	+	20.4750i	−0.409091	+	0.708567i
$836$	−4.00779			−0.138612
$837$	−0.119344	−	0.206710i	−0.00412514	−	0.00714495i
$838$	7.60407			0.262678
$839$	10.0374	−	17.3853i	0.346530	−	0.600208i	−0.639100	−	0.769123i	$-0.720693\pi$
$839$	10.0374	−	17.3853i	0.346530	−	0.600208i	0.985631	+	0.168915i	$0.0540265\pi$
$840$	4.39557			0.151662
$841$	0.910850	+	1.57764i	0.0314086	+	0.0544013i
$842$	11.9689	+	20.7308i	0.412476	+	0.714429i
$843$	10.4686			0.360558
$844$	2.51652	+	4.35875i	0.0866223	+	0.150034i
$845$	−6.55461	+	11.3529i	−0.225486	+	0.390552i
$846$	3.55440	+	6.15641i	0.122203	+	0.211662i
$847$	18.0258	+	31.2216i	0.619374	+	1.07279i
$848$	−2.96526	+	5.13598i	−0.101827	+	0.176370i
$849$	−3.52281	−	6.10169i	−0.120903	−	0.209410i
$850$	−2.56855	−	4.44886i	−0.0881006	−	0.152595i
$851$	−16.6105			−0.569401
$852$	−0.295931	+	0.512568i	−0.0101384	+	0.0175603i
$853$	−17.7958	−	30.8233i	−0.609317	−	1.05537i	−0.991353	−	0.131221i	$-0.958110\pi$
$853$	−17.7958	−	30.8233i	−0.609317	−	1.05537i	0.382036	−	0.924147i	$-0.375223\pi$
$854$	−6.50566	−	11.2681i	−0.222619	−	0.385588i
$855$	−4.81728	+	8.34377i	−0.164747	+	0.285351i
$856$	−6.81559	+	11.8049i	−0.232952	+	0.403485i
$857$	22.5785	−	39.1071i	0.771266	−	1.33587i	−0.165603	−	0.986192i	$-0.552957\pi$
$857$	22.5785	−	39.1071i	0.771266	−	1.33587i	0.936869	−	0.349680i	$-0.113710\pi$
$858$	−0.933549			−0.0318708
$859$	37.7268			1.28722			0.643611	−	0.765353i	$-0.277435\pi$
$859$	37.7268			1.28722			0.643611	+	0.765353i	$0.277435\pi$
$860$	2.65487			0.0905304
$861$	6.51993	+	11.2929i	0.222199	+	0.384860i
$862$	4.07084			0.138653
$863$	−3.60265	+	6.23998i	−0.122636	+	0.212411i	−0.920806	−	0.390020i	$-0.872468\pi$
$863$	−3.60265	+	6.23998i	−0.122636	+	0.212411i	0.798171	+	0.602432i	$0.205801\pi$
$864$	−1.00000			−0.0340207
$865$	−6.31029			−0.214556
$866$	12.5158			0.425306
$867$	7.28569	+	12.6192i	0.247435	+	0.428570i
$868$	−0.401912	−	0.696132i	−0.0136418	−	0.0236283i
$869$	3.70980	+	6.42556i	0.125846	+	0.217972i
$870$	3.40225	−	5.89288i	0.115347	−	0.199787i
$871$	−5.71853	−	9.90478i	−0.193765	−	0.335611i
$872$	−0.665484	+	1.15265i	−0.0225361	+	0.0390337i
$873$	−2.08092	−	3.60426i	−0.0704284	−	0.121986i
$874$	14.6007	−	25.2892i	0.493877	−	0.855419i
$875$	36.4674			1.23282
$876$	−3.30606			−0.111702
$877$	−8.86093			−0.299212			−0.149606	−	0.988746i	$-0.547801\pi$
$877$	−8.86093			−0.299212			−0.149606	+	0.988746i	$0.547801\pi$
$878$	16.8005			0.566990
$879$	−0.391686			−0.0132112
$880$	0.354336	+	0.613727i	0.0119446	+	0.0206887i
$881$	−13.8805	+	24.0417i	−0.467645	+	0.809984i	−0.999317	−	0.0369662i	$-0.988231\pi$
$881$	−13.8805	+	24.0417i	−0.467645	+	0.809984i	0.531672	+	0.846950i	$0.321564\pi$
$882$	2.17060	−	3.75960i	0.0730880	−	0.126592i
$883$	−13.8866	+	24.0524i	−0.467323	+	0.809427i	−0.999303	−	0.0373301i	$-0.988115\pi$
$883$	−13.8866	+	24.0524i	−0.467323	+	0.809427i	0.531980	+	0.846757i	$0.321448\pi$
$884$	2.67953			0.0901222
$885$	−0.921165			−0.0309646
$886$	2.36304	+	4.09291i	0.0793879	+	0.137504i
$887$	2.56904	−	4.44970i	0.0862598	−	0.149406i	−0.819668	−	0.572840i	$-0.805842\pi$
$887$	2.56904	−	4.44970i	0.0862598	−	0.149406i	0.905927	+	0.423433i	$0.139175\pi$
$888$	−4.19880			−0.140902
$889$	20.5428	+	35.5811i	0.688982	+	1.19335i
$890$	−5.83634			−0.195634
$891$	0.542949			0.0181895
$892$	−2.19702	−	14.7707i	−0.0735616	−	0.494559i
$893$	−52.4738			−1.75597
$894$	4.07489			0.136285
$895$	−2.77132	−	4.80007i	−0.0926351	−	0.160449i
$896$	−3.36767			−0.112506
$897$	3.40100	−	5.89070i	0.113556	−	0.196685i
$898$	−6.15229	−	10.6561i	−0.205305	−	0.355598i
$899$	−1.24435			−0.0415014
$900$	−3.29639			−0.109880
$901$	−4.62107	+	8.00393i	−0.153950	+	0.266650i
$902$	−1.05117	+	1.82068i	−0.0350001	+	0.0606220i
$903$	3.42498	−	5.93223i	0.113976	−	0.197412i
$904$	0.992514	+	1.71908i	0.0330105	+	0.0571759i
$905$	−9.51397			−0.316255
$906$	11.0462			0.366986
$907$	−5.59114			−0.185651			−0.0928254	−	0.995682i	$-0.529590\pi$
$907$	−5.59114			−0.185651			−0.0928254	+	0.995682i	$0.529590\pi$
$908$	0.167753			0.00556709
$909$	7.95685			0.263912
$910$	−3.77888	+	6.54522i	−0.125269	+	0.216972i
$911$	−7.90330	−	13.6889i	−0.261848	−	0.453534i	0.704885	−	0.709322i	$-0.250999\pi$
$911$	−7.90330	−	13.6889i	−0.261848	−	0.453534i	−0.966733	+	0.255788i	$0.917665\pi$
$912$	3.69076	−	6.39259i	0.122213	−	0.211680i
$913$	3.03733	+	5.26081i	0.100521	+	0.174107i
$914$	3.66778	−	6.35277i	0.121319	−	0.210131i
$915$	−2.52143	−	4.36725i	−0.0833560	−	0.144377i
$916$	−1.13208	−	1.96081i	−0.0374048	−	0.0647871i
$917$	3.99832	+	6.92529i	0.132036	+	0.228693i
$918$	−1.55840			−0.0514350
$919$	−38.5677			−1.27223			−0.636115	−	0.771594i	$-0.719460\pi$
$919$	−38.5677			−1.27223			−0.636115	+	0.771594i	$0.719460\pi$
$920$	−5.16349			−0.170235
$921$	−6.86335	+	11.8877i	−0.226155	+	0.391712i
$922$	−25.8860			−0.852509
$923$	−0.508826	−	0.881312i	−0.0167482	−	0.0290087i
$924$	1.82847			0.0601524
$925$	−13.8409			−0.455084
$926$	−28.0018			−0.920195
$927$	−3.20707	+	5.55482i	−0.105334	+	0.182444i
$928$	−2.60664	+	4.51483i	−0.0855672	+	0.148207i
$929$	1.12212	−	1.94356i	0.0368155	−	0.0637662i	−0.847031	−	0.531544i	$-0.821612\pi$
$929$	1.12212	−	1.94356i	0.0368155	−	0.0637662i	0.883846	+	0.467778i	$0.154945\pi$
$930$	−0.155771	−	0.269803i	−0.00510793	−	0.00884720i
$931$	16.0224	+	27.7516i	0.525112	+	0.909521i
$932$	1.40286	−	2.42982i	0.0459521	−	0.0795914i
$933$	9.92601			0.324963
$934$	−5.07482	−	8.78984i	−0.166053	−	0.287612i
$935$	0.552198	+	0.956435i	0.0180588	+	0.0312788i
$936$	0.859702	−	1.48905i	0.0281002	−	0.0486711i
$937$	−12.0307	−	20.8378i	−0.393026	−	0.680741i	0.599821	−	0.800134i	$-0.295238\pi$
$937$	−12.0307	−	20.8378i	−0.393026	−	0.680741i	−0.992847	+	0.119393i	$0.961905\pi$
$938$	11.2005	+	19.3998i	0.365708	+	0.633425i
$939$	−14.3231	+	24.8083i	−0.467417	+	0.809589i
$940$	4.63930	+	8.03550i	0.151317	+	0.262089i
$941$	17.8762			0.582746			0.291373	−	0.956610i	$-0.405888\pi$
$941$	17.8762			0.582746			0.291373	+	0.956610i	$0.405888\pi$
$942$	7.39199	+	12.8033i	0.240844	+	0.417154i
$943$	−7.65899	−	13.2658i	−0.249411	−	0.431993i
$944$	0.705752			0.0229703
$945$	2.19779	−	3.80668i	0.0714940	−	0.123831i
$946$	1.10438			0.0359064
$947$	−17.5511	−	30.3995i	−0.570336	−	0.987850i	−0.996531	−	0.0832192i	$-0.973480\pi$
$947$	−17.5511	−	30.3995i	−0.570336	−	0.987850i	0.426196	−	0.904631i	$-0.359854\pi$
$948$	−13.6654			−0.443831
$949$	2.84223	−	4.92289i	0.0922627	−	0.159804i
$950$	12.1662	−	21.0724i	0.394723	−	0.683680i
$951$	−7.03836			−0.228235
$952$	−5.24819			−0.170095
$953$	−4.74893	−	8.22538i	−0.153833	−	0.266446i	0.778801	−	0.627272i	$-0.215828\pi$
$953$	−4.74893	−	8.22538i	−0.153833	−	0.266446i	−0.932633	+	0.360825i	$0.882495\pi$
$954$	2.96526	+	5.13598i	0.0960038	+	0.166283i
$955$	8.41418	−	14.5738i	0.272276	−	0.471597i
$956$	16.7388			0.541372
$957$	1.41527	−	2.45132i	0.0457493	−	0.0792401i
$958$	−21.2551			−0.686720
$959$	−25.9178	−	44.8909i	−0.836929	−	1.44960i
$960$	−1.30523			−0.0421260
$961$	15.4715	−	26.7974i	0.499081	−	0.864434i
$962$	3.60971	−	6.25221i	0.116382	−	0.201579i
$963$	6.81559	+	11.8049i	0.219629	+	0.380409i
$964$	0.0507932	−	0.0879765i	0.00163594	−	0.00283353i
$965$	−4.25855	+	7.37603i	−0.137088	+	0.237443i
$966$	−6.66128	+	11.5377i	−0.214323	+	0.371219i
$967$	13.7083	−	23.7434i	0.440829	−	0.763537i	−0.556923	−	0.830564i	$-0.688018\pi$
$967$	13.7083	−	23.7434i	0.440829	−	0.763537i	0.997751	+	0.0670269i	$0.0213513\pi$
$968$	−5.35260	−	9.27098i	−0.172039	−	0.297981i
$969$	5.75170	−	9.96224i	0.184771	−	0.320033i
$970$	−2.71607	−	4.70437i	−0.0872077	−	0.151048i
$971$	3.62547	−	6.27951i	0.116347	−	0.201519i	−0.801970	−	0.597364i	$-0.796215\pi$
$971$	3.62547	−	6.27951i	0.116347	−	0.201519i	0.918317	+	0.395845i	$0.129548\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−26.5638	−	46.0099i	−0.851597	−	1.47501i
$974$	25.0729			0.803388
$975$	2.83391	−	4.90848i	0.0907578	−	0.157197i
$976$	1.93180	+	3.34597i	0.0618354	+	0.107102i
$977$	−5.26830	+	9.12496i	−0.168548	+	0.291933i	−0.937909	−	0.346880i	$-0.887241\pi$
$977$	−5.26830	+	9.12496i	−0.168548	+	0.291933i	0.769362	+	0.638813i	$0.220574\pi$
$978$	−2.68854	−	4.65669i	−0.0859700	−	0.148904i
$979$	−2.42781			−0.0775930
$980$	2.83313	−	4.90712i	0.0905010	−	0.156752i
$981$	0.665484	+	1.15265i	0.0212473	+	0.0368014i
$982$	−19.3019	−	33.4318i	−0.615947	−	1.06685i
$983$	33.8130			1.07847			0.539233	−	0.842156i	$-0.318714\pi$
$983$	33.8130			1.07847			0.539233	+	0.842156i	$0.318714\pi$
$984$	−1.93604	−	3.35331i	−0.0617186	−	0.106900i
$985$	−11.5513	+	20.0075i	−0.368056	+	0.637492i
$986$	−4.06220	+	7.03594i	−0.129367	+	0.224070i
$987$	23.9401			0.762022
$988$	6.34591	+	10.9914i	0.201890	+	0.349685i
$989$	−4.02333	+	6.96861i	−0.127935	+	0.221589i
$990$	0.708671			0.0225230
$991$	8.94486	+	15.4929i	0.284143	+	0.492150i	0.972401	−	0.233316i	$-0.0749577\pi$
$991$	8.94486	+	15.4929i	0.284143	+	0.492150i	−0.688258	+	0.725466i	$0.741624\pi$
$992$	0.119344	+	0.206710i	0.00378918	+	0.00656305i
$993$	−12.8660	−	22.2846i	−0.408290	−	0.707179i
$994$	0.996600	+	1.72616i	0.0316102	+	0.0547505i
$995$	9.17929			0.291003
$996$	−11.1883			−0.354514
$997$	29.5477			0.935785			0.467893	−	0.883785i	$-0.345013\pi$
$997$	29.5477			0.935785			0.467893	+	0.883785i	$0.345013\pi$
$998$	−13.7728	+	23.8552i	−0.435971	+	0.755124i
$999$	−2.09940	+	3.63626i	−0.0664220	+	0.115046i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.e.h.1075.6	yes	14
223.39	even	3	inner	1338.2.e.h.931.6	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.e.h.931.6	✓	14	223.39	even	3	inner
1338.2.e.h.1075.6	yes	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.652613 - 1.13036i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.36767 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.652613 + 1.13036i) q^{10} +(-0.271475 + 0.470208i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.71940 q^{13} -3.36767 q^{14} -1.30523 q^{15} +1.00000 q^{16} +1.55840 q^{17} +(0.500000 - 0.866025i) q^{18} +(3.69076 + 6.39259i) q^{19} +(0.652613 - 1.13036i) q^{20} +(-1.68384 - 2.91649i) q^{21} +(0.271475 - 0.470208i) q^{22} +(1.97801 + 3.42601i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.64819 + 2.85475i) q^{25} -1.71940 q^{26} +1.00000 q^{27} +3.36767 q^{28} +(2.60664 - 4.51483i) q^{29} +1.30523 q^{30} +(-0.119344 - 0.206710i) q^{31} -1.00000 q^{32} +0.542949 q^{33} -1.55840 q^{34} +(2.19779 - 3.80668i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.09940 + 3.63626i) q^{37} +(-3.69076 - 6.39259i) q^{38} +(-0.859702 - 1.48905i) q^{39} +(-0.652613 + 1.13036i) q^{40} -3.87207 q^{41} +(1.68384 + 2.91649i) q^{42} +(1.01702 + 1.76152i) q^{43} +(-0.271475 + 0.470208i) q^{44} +(0.652613 + 1.13036i) q^{45} +(-1.97801 - 3.42601i) q^{46} +(-3.55440 + 6.15641i) q^{47} +(-0.500000 - 0.866025i) q^{48} +4.34121 q^{49} +(-1.64819 - 2.85475i) q^{50} +(-0.779202 - 1.34962i) q^{51} +1.71940 q^{52} +(-2.96526 + 5.13598i) q^{53} -1.00000 q^{54} +(0.354336 + 0.613727i) q^{55} -3.36767 q^{56} +(3.69076 - 6.39259i) q^{57} +(-2.60664 + 4.51483i) q^{58} +0.705752 q^{59} -1.30523 q^{60} +(1.93180 + 3.34597i) q^{61} +(0.119344 + 0.206710i) q^{62} +(-1.68384 + 2.91649i) q^{63} +1.00000 q^{64} +(1.12211 - 1.94354i) q^{65} -0.542949 q^{66} +(-3.32588 - 5.76059i) q^{67} +1.55840 q^{68} +(1.97801 - 3.42601i) q^{69} +(-2.19779 + 3.80668i) q^{70} +(-0.295931 - 0.512568i) q^{71} +(0.500000 - 0.866025i) q^{72} +(1.65303 - 2.86313i) q^{73} +(2.09940 - 3.63626i) q^{74} +(1.64819 - 2.85475i) q^{75} +(3.69076 + 6.39259i) q^{76} +(-0.914237 + 1.58350i) q^{77} +(0.859702 + 1.48905i) q^{78} +(6.83269 - 11.8346i) q^{79} +(0.652613 - 1.13036i) q^{80} +(-0.500000 - 0.866025i) q^{81} +3.87207 q^{82} +(5.59413 - 9.68933i) q^{83} +(-1.68384 - 2.91649i) q^{84} +(1.01703 - 1.76156i) q^{85} +(-1.01702 - 1.76152i) q^{86} -5.21328 q^{87} +(0.271475 - 0.470208i) q^{88} +(2.23576 + 3.87245i) q^{89} +(-0.652613 - 1.13036i) q^{90} +5.79039 q^{91} +(1.97801 + 3.42601i) q^{92} +(-0.119344 + 0.206710i) q^{93} +(3.55440 - 6.15641i) q^{94} +9.63456 q^{95} +(0.500000 + 0.866025i) q^{96} +(-2.08092 + 3.60426i) q^{97} -4.34121 q^{98} +(-0.271475 - 0.470208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 7 q^{3} + 14 q^{4} - 4 q^{5} + 7 q^{6} + 12 q^{7} - 14 q^{8} - 7 q^{9} + 4 q^{10} - 10 q^{11} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 8 q^{15} + 14 q^{16} + 8 q^{17} + 7 q^{18} - 8 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 7 * q^3 + 14 * q^4 - 4 * q^5 + 7 * q^6 + 12 * q^7 - 14 * q^8 - 7 * q^9 + 4 * q^10 - 10 * q^11 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 8 * q^15 + 14 * q^16 + 8 * q^17 + 7 * q^18 - 8 * q^19 - 4 * q^20 - 6 * q^21 + 10 * q^22 - 8 * q^23 + 7 * q^24 - 13 * q^25 + 4 * q^26 + 14 * q^27 + 12 * q^28 - 6 * q^29 - 8 * q^30 - 10 * q^31 - 14 * q^32 + 20 * q^33 - 8 * q^34 + 18 * q^35 - 7 * q^36 + 15 * q^37 + 8 * q^38 + 2 * q^39 + 4 * q^40 + 24 * q^41 + 6 * q^42 - 14 * q^43 - 10 * q^44 - 4 * q^45 + 8 * q^46 - 10 * q^47 - 7 * q^48 + 54 * q^49 + 13 * q^50 - 4 * q^51 - 4 * q^52 - 9 * q^53 - 14 * q^54 + 13 * q^55 - 12 * q^56 - 8 * q^57 + 6 * q^58 - 20 * q^59 + 8 * q^60 - 20 * q^61 + 10 * q^62 - 6 * q^63 + 14 * q^64 + 7 * q^65 - 20 * q^66 - 13 * q^67 + 8 * q^68 - 8 * q^69 - 18 * q^70 - 26 * q^71 + 7 * q^72 + 7 * q^73 - 15 * q^74 - 13 * q^75 - 8 * q^76 - 13 * q^77 - 2 * q^78 + 36 * q^79 - 4 * q^80 - 7 * q^81 - 24 * q^82 + 27 * q^83 - 6 * q^84 + 27 * q^85 + 14 * q^86 + 12 * q^87 + 10 * q^88 - 33 * q^89 + 4 * q^90 - 14 * q^91 - 8 * q^92 - 10 * q^93 + 10 * q^94 - 40 * q^95 + 7 * q^96 - 19 * q^97 - 54 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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