LMFDB - Embedded newform 1050.2.bc.h.157.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(157,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1050.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.bc (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.3
Root			$0.339278 - 0.0446668i$ of defining polynomial
Character	$\chi$	$=$	1050.157
Dual form			1050.2.bc.h.943.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.52756 + 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.52756 + 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.31272 + 2.27370i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-1.21865 - 1.21865i) q^{13} +(0.101115 + 2.64382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.95935 - 7.31238i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-2.32616 - 4.02903i) q^{19} +(-2.23906 + 1.40948i) q^{21} +(1.85647 + 1.85647i) q^{22} +(-4.95766 - 1.32840i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.49254 + 0.861717i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.57990 + 0.586601i) q^{28} -5.99410i q^{29} +(-8.66177 - 5.00088i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.679515 + 2.53598i) q^{33} -7.57033 q^{34} -1.00000 q^{36} +(-1.02429 + 3.82271i) q^{37} +(-4.49380 + 1.20411i) q^{38} +(-1.49254 - 0.861717i) q^{39} +5.59423i q^{41} +(0.781940 + 2.52756i) q^{42} +(0.545731 - 0.545731i) q^{43} +(2.27370 - 1.31272i) q^{44} +(-2.56627 + 4.44492i) q^{46} +(6.12372 + 1.64085i) q^{47} +(0.707107 + 0.707107i) q^{48} +(5.77714 - 3.95280i) q^{49} +(-3.78517 - 6.55610i) q^{51} +(0.446058 + 1.66471i) q^{52} +(2.22057 + 8.28728i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.23434 - 2.34017i) q^{56} +(-3.28969 - 3.28969i) q^{57} +(-5.78985 - 1.55139i) q^{58} +(-3.86022 + 6.68609i) q^{59} +(4.16543 - 2.40491i) q^{61} +(-7.07231 + 7.07231i) q^{62} +(-1.79796 + 1.94096i) q^{63} -1.00000i q^{64} +(2.27370 + 1.31272i) q^{66} +(-2.47605 + 0.663456i) q^{67} +(-1.95935 + 7.31238i) q^{68} -5.13255 q^{69} -8.36973 q^{71} +(-0.258819 + 0.965926i) q^{72} +(13.1877 - 3.53363i) q^{73} +(3.42734 + 1.97878i) q^{74} +4.65232i q^{76} +(1.54009 - 6.77339i) q^{77} +(-1.21865 + 1.21865i) q^{78} +(7.78980 - 4.49744i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.40361 + 1.44789i) q^{82} +(7.99504 + 7.99504i) q^{83} +(2.64382 - 0.101115i) q^{84} +(-0.385890 - 0.668382i) q^{86} +(-1.55139 - 5.78985i) q^{87} +(-0.679515 - 2.53598i) q^{88} +(-0.0812661 - 0.140757i) q^{89} +(4.03313 + 2.12731i) q^{91} +(3.62926 + 3.62926i) q^{92} +(-9.66095 - 2.58864i) q^{93} +(3.16987 - 5.49038i) q^{94} +(0.866025 - 0.500000i) q^{96} +(4.35278 - 4.35278i) q^{97} +(-2.32288 - 6.60335i) q^{98} +2.62544i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		−	1.00000i		−	0.408248i
$7$	−2.52756	+	0.781940i	−0.955329	+	0.295546i
$7$	−2.52756	+	0.781940i	−0.955329	+	0.295546i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	−1.31272	+	2.27370i	−0.395800	+	0.685546i	−0.993203	−	0.116395i	$-0.962866\pi$
$11$	−1.31272	+	2.27370i	−0.395800	+	0.685546i	0.597403	+	0.801942i	$0.296199\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−1.21865	−	1.21865i	−0.337993	−	0.337993i	0.517618	−	0.855612i	$-0.326819\pi$
$13$	−1.21865	−	1.21865i	−0.337993	−	0.337993i	−0.855612	+	0.517618i	$0.826819\pi$
$14$	0.101115	+	2.64382i	0.0270242	+	0.706590i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.95935	−	7.31238i	−0.475211	−	1.77351i	−0.620589	−	0.784136i	$-0.713106\pi$
$17$	−1.95935	−	7.31238i	−0.475211	−	1.77351i	0.145377	−	0.989376i	$-0.453560\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−2.32616	−	4.02903i	−0.533658	−	0.924322i	−0.999227	−	0.0393108i	$-0.987484\pi$
$19$	−2.32616	−	4.02903i	−0.533658	−	0.924322i	0.465569	−	0.885011i	$-0.345850\pi$
$20$		0			0
$21$	−2.23906	+	1.40948i	−0.488602	+	0.307573i
$22$	1.85647	+	1.85647i	0.395800	+	0.395800i
$23$	−4.95766	−	1.32840i	−1.03374	−	0.276991i	−0.298225	−	0.954496i	$-0.596395\pi$
$23$	−4.95766	−	1.32840i	−1.03374	−	0.276991i	−0.735518	+	0.677505i	$0.763061\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−1.49254	+	0.861717i	−0.292711	+	0.168997i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.57990	+	0.586601i	0.487556	+	0.110857i
$29$		−	5.99410i		−	1.11308i	−0.830822	−	0.556538i	$-0.812129\pi$
$29$		−	5.99410i		−	1.11308i	0.830822	−	0.556538i	$-0.187871\pi$
$30$		0			0
$31$	−8.66177	−	5.00088i	−1.55570	−	0.898184i	−0.997660	−	0.0683700i	$-0.978220\pi$
$31$	−8.66177	−	5.00088i	−1.55570	−	0.898184i	−0.558040	−	0.829814i	$-0.688447\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.679515	+	2.53598i	−0.118288	+	0.441458i
$34$	−7.57033			−1.29830
$35$		0			0
$36$	−1.00000			−0.166667
$37$	−1.02429	+	3.82271i	−0.168392	+	0.628449i	0.829191	+	0.558966i	$0.188802\pi$
$37$	−1.02429	+	3.82271i	−0.168392	+	0.628449i	−0.997583	+	0.0694832i	$0.977865\pi$
$38$	−4.49380	+	1.20411i	−0.728990	+	0.195332i
$39$	−1.49254	−	0.861717i	−0.238997	−	0.137985i
$40$		0			0
$41$			5.59423i			0.873671i	0.899541	+	0.436836i	$0.143901\pi$
$41$			5.59423i			0.873671i	−0.899541	+	0.436836i	$0.856099\pi$
$42$	0.781940	+	2.52756i	0.120656	+	0.390011i
$43$	0.545731	−	0.545731i	0.0832233	−	0.0832233i	−0.664270	−	0.747493i	$-0.731257\pi$
$43$	0.545731	−	0.545731i	0.0832233	−	0.0832233i	0.747493	+	0.664270i	$0.231257\pi$
$44$	2.27370	−	1.31272i	0.342773	−	0.197900i
$45$		0			0
$46$	−2.56627	+	4.44492i	−0.378376	+	0.655367i
$47$	6.12372	+	1.64085i	0.893237	+	0.239342i	0.676109	−	0.736801i	$-0.263665\pi$
$47$	6.12372	+	1.64085i	0.893237	+	0.239342i	0.217127	+	0.976143i	$0.430331\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	5.77714	−	3.95280i	0.825306	−	0.564686i
$50$		0			0
$51$	−3.78517	−	6.55610i	−0.530029	−	0.918038i
$52$	0.446058	+	1.66471i	0.0618571	+	0.230854i
$53$	2.22057	+	8.28728i	0.305019	+	1.13835i	0.932929	+	0.360060i	$0.117244\pi$
$53$	2.22057	+	8.28728i	0.305019	+	1.13835i	−0.627910	+	0.778286i	$0.716089\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	1.23434	−	2.34017i	0.164946	−	0.312719i
$57$	−3.28969	−	3.28969i	−0.435730	−	0.435730i
$58$	−5.78985	−	1.55139i	−0.760245	−	0.203707i
$59$	−3.86022	+	6.68609i	−0.502557	+	0.870455i	0.497438	+	0.867499i	$0.334274\pi$
$59$	−3.86022	+	6.68609i	−0.502557	+	0.870455i	−0.999996	+	0.00295539i	$0.999059\pi$
$60$		0			0
$61$	4.16543	−	2.40491i	0.533328	−	0.307917i	−0.209042	−	0.977907i	$-0.567035\pi$
$61$	4.16543	−	2.40491i	0.533328	−	0.307917i	0.742371	+	0.669989i	$0.233701\pi$
$62$	−7.07231	+	7.07231i	−0.898184	+	0.898184i
$63$	−1.79796	+	1.94096i	−0.226522	+	0.244538i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	2.27370	+	1.31272i	0.279873	+	0.161585i
$67$	−2.47605	+	0.663456i	−0.302498	+	0.0810541i	−0.406875	−	0.913484i	$-0.633382\pi$
$67$	−2.47605	+	0.663456i	−0.302498	+	0.0810541i	0.104377	+	0.994538i	$0.466715\pi$
$68$	−1.95935	+	7.31238i	−0.237606	+	0.886756i
$69$	−5.13255			−0.617886
$70$		0			0
$71$	−8.36973			−0.993304			−0.496652	−	0.867950i	$-0.665437\pi$
$71$	−8.36973			−0.993304			−0.496652	+	0.867950i	$0.665437\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	13.1877	−	3.53363i	1.54350	−	0.413581i	0.616108	−	0.787662i	$-0.288709\pi$
$73$	13.1877	−	3.53363i	1.54350	−	0.413581i	0.927396	+	0.374081i	$0.122042\pi$
$74$	3.42734	+	1.97878i	0.398421	+	0.230028i
$75$		0			0
$76$			4.65232i			0.533658i
$77$	1.54009	−	6.77339i	0.175509	−	0.771899i
$78$	−1.21865	+	1.21865i	−0.137985	+	0.137985i
$79$	7.78980	−	4.49744i	0.876421	−	0.506002i	0.00694408	−	0.999976i	$-0.497790\pi$
$79$	7.78980	−	4.49744i	0.876421	−	0.506002i	0.869477	+	0.493974i	$0.164456\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	5.40361	+	1.44789i	0.596729	+	0.159893i
$83$	7.99504	+	7.99504i	0.877570	+	0.877570i	0.993283	−	0.115713i	$-0.0369152\pi$
$83$	7.99504	+	7.99504i	0.877570	+	0.877570i	−0.115713	+	0.993283i	$0.536915\pi$
$84$	2.64382	−	0.101115i	0.288464	−	0.0110326i
$85$		0			0
$86$	−0.385890	−	0.668382i	−0.0416116	−	0.0720734i
$87$	−1.55139	−	5.78985i	−0.166326	−	0.620738i
$88$	−0.679515	−	2.53598i	−0.0724365	−	0.270337i
$89$	−0.0812661	−	0.140757i	−0.00861419	−	0.0149202i	0.861686	−	0.507442i	$-0.169409\pi$
$89$	−0.0812661	−	0.140757i	−0.00861419	−	0.0149202i	−0.870300	+	0.492521i	$0.836075\pi$
$90$		0			0
$91$	4.03313	+	2.12731i	0.422787	+	0.223002i
$92$	3.62926	+	3.62926i	0.378376	+	0.378376i
$93$	−9.66095	−	2.58864i	−1.00179	−	0.268430i
$94$	3.16987	−	5.49038i	0.326947	−	0.566289i
$95$		0			0
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	4.35278	−	4.35278i	0.441958	−	0.441958i	−0.450711	−	0.892670i	$-0.648830\pi$
$97$	4.35278	−	4.35278i	0.441958	−	0.441958i	0.892670	+	0.450711i	$0.148830\pi$
$98$	−2.32288	−	6.60335i	−0.234647	−	0.667039i
$99$			2.62544i			0.263867i
$100$		0			0
$101$	−6.64586	−	3.83699i	−0.661287	−	0.381795i	0.131480	−	0.991319i	$-0.458027\pi$
$101$	−6.64586	−	3.83699i	−0.661287	−	0.381795i	−0.792767	+	0.609524i	$0.791360\pi$
$102$	−7.31238	+	1.95935i	−0.724033	+	0.194004i
$103$	1.05286	−	3.92931i	0.103741	−	0.387167i	−0.894458	−	0.447151i	$-0.852439\pi$
$103$	1.05286	−	3.92931i	0.103741	−	0.387167i	0.998199	+	0.0599847i	$0.0191052\pi$
$104$	1.72343			0.168997
$105$		0			0
$106$	8.57963			0.833327
$107$	0.729112	−	2.72108i	0.0704859	−	0.263057i	−0.921686	−	0.387937i	$-0.873188\pi$
$107$	0.729112	−	2.72108i	0.0704859	−	0.263057i	0.992172	+	0.124880i	$0.0398545\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−10.5314	−	6.08031i	−1.00872	−	0.582388i	−0.0979069	−	0.995196i	$-0.531215\pi$
$109$	−10.5314	−	6.08031i	−1.00872	−	0.582388i	−0.910818	+	0.412808i	$0.864548\pi$
$110$		0			0
$111$			3.95756i			0.375635i
$112$	−1.94096	−	1.79796i	−0.183404	−	0.169892i
$113$	−1.63875	+	1.63875i	−0.154161	+	0.154161i	−0.779973	−	0.625813i	$-0.784767\pi$
$113$	−1.63875	+	1.63875i	−0.154161	+	0.154161i	0.625813	+	0.779973i	$0.284767\pi$
$114$	−4.02903	+	2.32616i	−0.377353	+	0.217865i
$115$		0			0
$116$	−2.99705	+	5.19104i	−0.278269	+	0.481976i
$117$	−1.66471	−	0.446058i	−0.153902	−	0.0412380i
$118$	5.45917	+	5.45917i	0.502557	+	0.502557i
$119$	10.6702	+	16.9504i	0.978137	+	1.55384i
$120$		0			0
$121$	2.05352	+	3.55681i	0.186684	+	0.323346i
$122$	−1.24487	−	4.64593i	−0.112706	−	0.420623i
$123$	1.44789	+	5.40361i	0.130552	+	0.487227i
$124$	5.00088	+	8.66177i	0.449092	+	0.777850i
$125$		0			0
$126$	1.40948	+	2.23906i	0.125566	+	0.199471i
$127$	−6.79622	−	6.79622i	−0.603067	−	0.603067i	0.338058	−	0.941125i	$-0.390230\pi$
$127$	−6.79622	−	6.79622i	−0.603067	−	0.603067i	−0.941125	+	0.338058i	$0.890230\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	0.385890	−	0.668382i	0.0339757	−	0.0588477i
$130$		0			0
$131$	−3.66846	+	2.11799i	−0.320515	+	0.185050i	−0.651622	−	0.758544i	$-0.725911\pi$
$131$	−3.66846	+	2.11799i	−0.320515	+	0.185050i	0.331107	+	0.943593i	$0.392578\pi$
$132$	1.85647	−	1.85647i	0.161585	−	0.161585i
$133$	9.02997	+	8.36470i	0.782998	+	0.725311i
$134$			2.56340i			0.221444i
$135$		0			0
$136$	6.55610	+	3.78517i	0.562181	+	0.324575i
$137$	−7.98108	+	2.13852i	−0.681870	+	0.182706i	−0.583096	−	0.812403i	$-0.698159\pi$
$137$	−7.98108	+	2.13852i	−0.681870	+	0.182706i	−0.0987740	+	0.995110i	$0.531492\pi$
$138$	−1.32840	+	4.95766i	−0.113081	+	0.422024i
$139$	9.35059			0.793106			0.396553	−	0.918012i	$-0.370206\pi$
$139$	9.35059			0.793106			0.396553	+	0.918012i	$0.370206\pi$
$140$		0			0
$141$	6.33974			0.533903
$142$	−2.16624	+	8.08453i	−0.181787	+	0.678439i
$143$	4.37060	−	1.17110i	0.365488	−	0.0979322i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$		0			0
$146$		−	13.6529i		−	1.12992i
$147$	4.55723	−	5.31335i	0.375874	−	0.438238i
$148$	2.79841	−	2.79841i	0.230028	−	0.230028i
$149$	−4.12068	+	2.37908i	−0.337579	+	0.194902i	−0.659201	−	0.751967i	$-0.729105\pi$
$149$	−4.12068	+	2.37908i	−0.337579	+	0.194902i	0.321622	+	0.946868i	$0.395772\pi$
$150$		0			0
$151$	−1.07557	+	1.86294i	−0.0875286	+	0.151604i	−0.906466	−	0.422279i	$-0.861230\pi$
$151$	−1.07557	+	1.86294i	−0.0875286	+	0.151604i	0.818937	+	0.573883i	$0.194564\pi$
$152$	4.49380	+	1.20411i	0.364495	+	0.0976661i
$153$	−5.35303	−	5.35303i	−0.432767	−	0.432767i
$154$	−6.14399	−	3.24069i	−0.495097	−	0.261142i
$155$		0			0
$156$	0.861717	+	1.49254i	0.0689926	+	0.119499i
$157$	−0.984635	−	3.67471i	−0.0785824	−	0.293274i	0.915439	−	0.402456i	$-0.131843\pi$
$157$	−0.984635	−	3.67471i	−0.0785824	−	0.293274i	−0.994022	+	0.109182i	$0.965177\pi$
$158$	−2.32805	−	8.68839i	−0.185209	−	0.691211i
$159$	4.28981	+	7.43018i	0.340204	+	0.589251i
$160$		0			0
$161$	13.5695	−	0.518978i	1.06943	−	0.0409012i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	4.30925	+	1.15466i	0.337526	+	0.0904399i	0.423601	−	0.905849i	$-0.360766\pi$
$163$	4.30925	+	1.15466i	0.337526	+	0.0904399i	−0.0860750	+	0.996289i	$0.527432\pi$
$164$	2.79711	−	4.84474i	0.218418	−	0.378311i
$165$		0			0
$166$	9.79189	−	5.65335i	0.759998	−	0.438785i
$167$	−16.1327	+	16.1327i	−1.24839	+	1.24839i	−0.291956	+	0.956432i	$0.594306\pi$
$167$	−16.1327	+	16.1327i	−1.24839	+	1.24839i	−0.956432	+	0.291956i	$0.905694\pi$
$168$	0.586601	−	2.57990i	0.0452572	−	0.199044i
$169$		−	10.0298i		−	0.771521i
$170$		0			0
$171$	−4.02903	−	2.32616i	−0.308107	−	0.177886i
$172$	−0.745483	+	0.199752i	−0.0568425	+	0.0152309i
$173$	3.20476	−	11.9603i	0.243653	−	0.909327i	−0.730402	−	0.683017i	$-0.760667\pi$
$173$	3.20476	−	11.9603i	0.243653	−	0.909327i	0.974055	−	0.226309i	$-0.0726660\pi$
$174$	−5.99410			−0.454411
$175$		0			0
$176$	−2.62544			−0.197900
$177$	−1.99819	+	7.45736i	−0.150194	+	0.560530i
$178$	−0.156994	+	0.0420664i	−0.0117672	+	0.00315301i
$179$	−17.5544	−	10.1350i	−1.31208	−	0.757528i	−0.329637	−	0.944108i	$-0.606926\pi$
$179$	−17.5544	−	10.1350i	−1.31208	−	0.757528i	−0.982440	+	0.186580i	$0.940260\pi$
$180$		0			0
$181$		−	7.52637i		−	0.559431i	−0.960083	−	0.279715i	$-0.909760\pi$
$181$		−	7.52637i		−	0.559431i	0.960083	−	0.279715i	$-0.0902401\pi$
$182$	3.09867	−	3.34512i	0.229689	−	0.247957i
$183$	3.40106	−	3.40106i	0.251413	−	0.251413i
$184$	4.44492	−	2.56627i	0.327684	−	0.189188i
$185$		0			0
$186$	−5.00088	+	8.66177i	−0.366682	+	0.635112i
$187$	19.1982	+	5.14415i	1.40391	+	0.376178i
$188$	−4.48288	−	4.48288i	−0.326947	−	0.326947i
$189$	−1.23434	+	2.34017i	−0.0897851	+	0.170222i
$190$		0			0
$191$	−2.16395	−	3.74807i	−0.156578	−	0.271201i	0.777055	−	0.629433i	$-0.216713\pi$
$191$	−2.16395	−	3.74807i	−0.156578	−	0.271201i	−0.933632	+	0.358233i	$0.883379\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−5.50458	−	20.5434i	−0.396228	−	1.47874i	−0.819678	−	0.572825i	$-0.805847\pi$
$193$	−5.50458	−	20.5434i	−0.396228	−	1.47874i	0.423449	−	0.905920i	$-0.360819\pi$
$194$	−3.07788	−	5.33105i	−0.220979	−	0.382747i
$195$		0			0
$196$	−6.97955	+	0.534660i	−0.498539	+	0.0381900i
$197$	14.1314	+	14.1314i	1.00682	+	1.00682i	0.999977	+	0.00684089i	$0.00217754\pi$
$197$	14.1314	+	14.1314i	1.00682	+	1.00682i	0.00684089	+	0.999977i	$0.497822\pi$
$198$	2.53598	+	0.679515i	0.180224	+	0.0482910i
$199$	0.422034	−	0.730985i	0.0299172	−	0.0518182i	−0.850679	−	0.525685i	$-0.823809\pi$
$199$	0.422034	−	0.730985i	0.0299172	−	0.0518182i	0.880596	+	0.473867i	$0.157142\pi$
$200$		0			0
$201$	−2.21997	+	1.28170i	−0.156584	+	0.0904041i
$202$	−5.42632	+	5.42632i	−0.381795	+	0.381795i
$203$	4.68703	+	15.1505i	0.328965	+	1.06335i
$204$			7.57033i			0.530029i
$205$		0			0
$206$	−3.52293	−	2.03396i	−0.245454	−	0.141713i
$207$	−4.95766	+	1.32840i	−0.344581	+	0.0923302i
$208$	0.446058	−	1.66471i	0.0309285	−	0.115427i
$209$	12.2144			0.844888
$210$		0			0
$211$	22.1844			1.52724			0.763619	−	0.645667i	$-0.223421\pi$
$211$	22.1844			1.52724			0.763619	+	0.645667i	$0.223421\pi$
$212$	2.22057	−	8.28728i	0.152509	−	0.569173i
$213$	−8.08453	+	2.16624i	−0.553943	+	0.148429i
$214$	−2.43966	−	1.40854i	−0.166771	−	0.0962855i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	25.8036	+	5.86704i	1.75166	+	0.398280i
$218$	−8.59885	+	8.59885i	−0.582388	+	0.582388i
$219$	11.8238	−	6.82646i	0.798976	−	0.461289i
$220$		0			0
$221$	−6.52348	+	11.2990i	−0.438817	+	0.760053i
$222$	3.82271	+	1.02429i	0.256563	+	0.0687459i
$223$	−10.7632	−	10.7632i	−0.720757	−	0.720757i	0.248002	−	0.968759i	$-0.420226\pi$
$223$	−10.7632	−	10.7632i	−0.720757	−	0.720757i	−0.968759	+	0.248002i	$0.920226\pi$
$224$	−2.23906	+	1.40948i	−0.149603	+	0.0941747i
$225$		0			0
$226$	1.15877	+	2.00705i	0.0770804	+	0.133507i
$227$	−0.967615	−	3.61119i	−0.0642229	−	0.239683i	0.926351	−	0.376661i	$-0.122928\pi$
$227$	−0.967615	−	3.61119i	−0.0642229	−	0.239683i	−0.990574	+	0.136978i	$0.956261\pi$
$228$	1.20411	+	4.49380i	0.0797441	+	0.297609i
$229$	7.59088	+	13.1478i	0.501619	+	0.868830i	0.999998	+	0.00187073i	$0.000595471\pi$
$229$	7.59088	+	13.1478i	0.501619	+	0.868830i	−0.498379	+	0.866959i	$0.666071\pi$
$230$		0			0
$231$	−0.265472	−	6.94119i	−0.0174668	−	0.456697i
$232$	4.23847	+	4.23847i	0.278269	+	0.278269i
$233$	−1.17170	−	0.313957i	−0.0767607	−	0.0205680i	0.220234	−	0.975447i	$-0.429318\pi$
$233$	−1.17170	−	0.313957i	−0.0767607	−	0.0205680i	−0.296995	+	0.954879i	$0.595984\pi$
$234$	−0.861717	+	1.49254i	−0.0563322	+	0.0975702i
$235$		0			0
$236$	6.68609	−	3.86022i	0.435227	−	0.251279i
$237$	6.36034	−	6.36034i	0.413149	−	0.413149i
$238$	19.1345	−	5.91955i	1.24030	−	0.383707i
$239$			16.1593i			1.04526i	0.852560	+	0.522630i	$0.175049\pi$
$239$			16.1593i			1.04526i	−0.852560	+	0.522630i	$0.824951\pi$
$240$		0			0
$241$	−21.8384	−	12.6084i	−1.40674	−	0.812180i	−0.411665	−	0.911335i	$-0.635053\pi$
$241$	−21.8384	−	12.6084i	−1.40674	−	0.812180i	−0.995072	+	0.0991549i	$0.968386\pi$
$242$	3.96710	−	1.06298i	0.255015	−	0.0683311i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	−4.80982			−0.307917
$245$		0			0
$246$	5.59423			0.356675
$247$	−2.07520	+	7.74476i	−0.132042	+	0.492787i
$248$	9.66095	−	2.58864i	0.613471	−	0.164379i
$249$	9.79189	+	5.65335i	0.620536	+	0.358266i
$250$		0			0
$251$			2.07559i			0.131010i	0.997852	+	0.0655051i	$0.0208659\pi$
$251$			2.07559i			0.131010i	−0.997852	+	0.0655051i	$0.979134\pi$
$252$	2.52756	−	0.781940i	0.159221	−	0.0492576i
$253$	9.52841	−	9.52841i	0.599046	−	0.599046i
$254$	−8.32363	+	4.80565i	−0.522271	+	0.301533i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.34881	−	1.16526i	−0.271271	−	0.0726869i	0.120619	−	0.992699i	$-0.461512\pi$
$257$	−4.34881	−	1.16526i	−0.271271	−	0.0726869i	−0.391890	+	0.920012i	$0.628179\pi$
$258$	−0.545731	−	0.545731i	−0.0339757	−	0.0339757i
$259$	−0.400169	−	10.4631i	−0.0248653	−	0.650143i
$260$		0			0
$261$	−2.99705	−	5.19104i	−0.185513	−	0.321317i
$262$	1.09635	+	4.09164i	0.0677328	+	0.252782i
$263$	−5.79744	−	21.6364i	−0.357486	−	1.33415i	−0.877327	−	0.479892i	$-0.840676\pi$
$263$	−5.79744	−	21.6364i	−0.357486	−	1.33415i	0.519842	−	0.854263i	$-0.325991\pi$
$264$	−1.31272	−	2.27370i	−0.0807924	−	0.139937i
$265$		0			0
$266$	10.4168	−	6.55734i	0.638695	−	0.402056i
$267$	−0.114928	−	0.114928i	−0.00703346	−	0.00703346i
$268$	2.47605	+	0.663456i	0.151249	+	0.0405270i
$269$	5.86211	−	10.1535i	0.357419	−	0.619068i	−0.630110	−	0.776506i	$-0.716990\pi$
$269$	5.86211	−	10.1535i	0.357419	−	0.619068i	0.987529	+	0.157438i	$0.0503235\pi$
$270$		0			0
$271$	20.8254	−	12.0235i	1.26505	−	0.730377i	0.291004	−	0.956722i	$-0.406011\pi$
$271$	20.8254	−	12.0235i	1.26505	−	0.730377i	0.974047	+	0.226344i	$0.0726775\pi$
$272$	5.35303	−	5.35303i	0.324575	−	0.324575i
$273$	4.44629	+	1.01097i	0.269102	+	0.0611866i
$274$			8.26262i			0.499163i
$275$		0			0
$276$	4.44492	+	2.56627i	0.267552	+	0.154471i
$277$	−26.2705	+	7.03917i	−1.57844	+	0.422943i	−0.938444	−	0.345433i	$-0.887732\pi$
$277$	−26.2705	+	7.03917i	−1.57844	+	0.422943i	−0.640000	+	0.768375i	$0.721066\pi$
$278$	2.42011	−	9.03197i	0.145149	−	0.541702i
$279$	−10.0018			−0.598789
$280$		0			0
$281$	22.1913			1.32382			0.661910	−	0.749583i	$-0.269746\pi$
$281$	22.1913			1.32382			0.661910	+	0.749583i	$0.269746\pi$
$282$	1.64085	−	6.12372i	0.0977110	−	0.364662i
$283$	−10.7244	+	2.87361i	−0.637502	+	0.170818i	−0.563072	−	0.826408i	$-0.690380\pi$
$283$	−10.7244	+	2.87361i	−0.637502	+	0.170818i	−0.0744302	+	0.997226i	$0.523714\pi$
$284$	7.24840	+	4.18486i	0.430113	+	0.248326i
$285$		0			0
$286$		−	4.52478i		−	0.267556i
$287$	−4.37435	−	14.1398i	−0.258210	−	0.834643i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−34.9094	+	20.1550i	−2.05350	+	1.18559i
$290$		0			0
$291$	3.07788	−	5.33105i	0.180429	−	0.312512i
$292$	−13.1877	−	3.53363i	−0.771752	−	0.206790i
$293$	−6.51580	−	6.51580i	−0.380657	−	0.380657i	0.490682	−	0.871339i	$-0.336748\pi$
$293$	−6.51580	−	6.51580i	−0.380657	−	0.380657i	−0.871339	+	0.490682i	$0.836748\pi$
$294$	−3.95280	−	5.77714i	−0.230532	−	0.336930i
$295$		0			0
$296$	−1.97878	−	3.42734i	−0.115014	−	0.199210i
$297$	0.679515	+	2.53598i	0.0394294	+	0.147153i
$298$	1.23150	+	4.59602i	0.0713389	+	0.266240i
$299$	4.42280	+	7.66052i	0.255777	+	0.443019i
$300$		0			0
$301$	−0.952640	+	1.80610i	−0.0549093	+	0.104102i
$302$	1.52108	+	1.52108i	0.0875286	+	0.0875286i
$303$	−7.41249	−	1.98617i	−0.425836	−	0.114103i
$304$	2.32616	−	4.02903i	0.133414	−	0.231081i
$305$		0			0
$306$	−6.55610	+	3.78517i	−0.374787	+	0.216384i
$307$	20.6010	−	20.6010i	1.17576	−	1.17576i	0.194947	−	0.980814i	$-0.437546\pi$
$307$	20.6010	−	20.6010i	1.17576	−	1.17576i	0.980814	−	0.194947i	$-0.0624536\pi$
$308$	−4.72045	+	5.09588i	−0.268973	+	0.290365i
$309$		−	4.06792i		−	0.231416i
$310$		0			0
$311$	28.4631	+	16.4332i	1.61399	+	0.931840i	0.988432	+	0.151665i	$0.0484634\pi$
$311$	28.4631	+	16.4332i	1.61399	+	0.931840i	0.625562	+	0.780175i	$0.284870\pi$
$312$	1.66471	−	0.446058i	0.0942456	−	0.0252530i
$313$	5.74141	−	21.4272i	0.324523	−	1.21114i	−0.590267	−	0.807208i	$-0.700977\pi$
$313$	5.74141	−	21.4272i	0.324523	−	1.21114i	0.914790	−	0.403930i	$-0.132356\pi$
$314$	−3.80434			−0.214691
$315$		0			0
$316$	−8.99488			−0.506002
$317$	3.71781	−	13.8751i	0.208813	−	0.779301i	−0.779440	−	0.626476i	$-0.784496\pi$
$317$	3.71781	−	13.8751i	0.208813	−	0.779301i	0.988253	−	0.152824i	$-0.0488368\pi$
$318$	8.28728	−	2.22057i	0.464728	−	0.124523i
$319$	13.6288	+	7.86858i	0.763065	+	0.440556i
$320$		0			0
$321$		−	2.81707i		−	0.157234i
$322$	3.01076	−	13.2415i	0.167783	−	0.737918i
$323$	−24.9040	+	24.9040i	−1.38570	+	1.38570i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$		0			0
$326$	2.23063	−	3.86356i	0.123543	−	0.213983i
$327$	−11.7462	−	3.14740i	−0.649569	−	0.174051i
$328$	−3.95571	−	3.95571i	−0.218418	−	0.218418i
$329$	−16.7611	+	0.641044i	−0.924071	+	0.0353419i
$330$		0			0
$331$	1.44533	+	2.50339i	0.0794427	+	0.137599i	0.903010	−	0.429620i	$-0.141353\pi$
$331$	1.44533	+	2.50339i	0.0794427	+	0.137599i	−0.823567	+	0.567219i	$0.808019\pi$
$332$	−2.92639	−	10.9214i	−0.160606	−	0.599391i
$333$	1.02429	+	3.82271i	0.0561308	+	0.209483i
$334$	11.4076	+	19.7585i	0.624194	+	1.08114i
$335$		0			0
$336$	−2.34017	−	1.23434i	−0.127667	−	0.0673388i
$337$	23.4453	+	23.4453i	1.27715	+	1.27715i	0.942257	+	0.334891i	$0.108699\pi$
$337$	23.4453	+	23.4453i	1.27715	+	1.27715i	0.334891	+	0.942257i	$0.391301\pi$
$338$	−9.68802	−	2.59590i	−0.526959	−	0.141198i
$339$	−1.15877	+	2.00705i	−0.0629359	+	0.109008i
$340$		0			0
$341$	22.7410	−	13.1295i	1.23149	−	0.711003i
$342$	−3.28969	+	3.28969i	−0.177886	+	0.177886i
$343$	−11.5112	+	14.5083i	−0.621547	+	0.783377i
$344$			0.771781i			0.0416116i
$345$		0			0
$346$	−10.7233	−	6.19112i	−0.576490	−	0.332837i
$347$	−10.9516	+	2.93447i	−0.587912	+	0.157531i	−0.540499	−	0.841345i	$-0.681765\pi$
$347$	−10.9516	+	2.93447i	−0.587912	+	0.157531i	−0.0474135	+	0.998875i	$0.515098\pi$
$348$	−1.55139	+	5.78985i	−0.0831631	+	0.310369i
$349$	6.80786			0.364417			0.182208	−	0.983260i	$-0.441675\pi$
$349$	6.80786			0.364417			0.182208	+	0.983260i	$0.441675\pi$
$350$		0			0
$351$	−1.72343			−0.0919901
$352$	−0.679515	+	2.53598i	−0.0362183	+	0.135168i
$353$	26.8765	−	7.20154i	1.43049	−	0.383299i	0.541299	−	0.840830i	$-0.317933\pi$
$353$	26.8765	−	7.20154i	1.43049	−	0.383299i	0.889194	+	0.457531i	$0.151266\pi$
$354$	6.68609	+	3.86022i	0.355362	+	0.205168i
$355$		0			0
$356$			0.162532i			0.00861419i
$357$	14.6937	+	13.6112i	0.777674	+	0.720380i
$358$	−14.3331	+	14.3331i	−0.757528	+	0.757528i
$359$	−11.8979	+	6.86927i	−0.627948	+	0.362546i	−0.779957	−	0.625833i	$-0.784759\pi$
$359$	−11.8979	+	6.86927i	−0.627948	+	0.362546i	0.152009	+	0.988379i	$0.451426\pi$
$360$		0			0
$361$	−1.32204	+	2.28984i	−0.0695809	+	0.120518i
$362$	−7.26992	−	1.94797i	−0.382098	−	0.102383i
$363$	2.90412	+	2.90412i	0.152427	+	0.152427i
$364$	−2.42914	−	3.85887i	−0.127322	−	0.202260i
$365$		0			0
$366$	−2.40491	−	4.16543i	−0.125707	−	0.217730i
$367$	−6.52689	−	24.3587i	−0.340701	−	1.27151i	−0.897555	−	0.440903i	$-0.854658\pi$
$367$	−6.52689	−	24.3587i	−0.340701	−	1.27151i	0.556854	−	0.830610i	$-0.312008\pi$
$368$	−1.32840	−	4.95766i	−0.0692477	−	0.258436i
$369$	2.79711	+	4.84474i	0.145612	+	0.252207i
$370$		0			0
$371$	−12.0928	−	19.2103i	−0.627827	−	0.997348i
$372$	7.07231	+	7.07231i	0.366682	+	0.366682i
$373$	25.9391	+	6.95037i	1.34308	+	0.359876i	0.857575	−	0.514359i	$-0.171970\pi$
$373$	25.9391	+	6.95037i	1.34308	+	0.359876i	0.485502	+	0.874235i	$0.338637\pi$
$374$	9.93774	−	17.2127i	0.513868	−	0.890046i
$375$		0			0
$376$	−5.49038	+	3.16987i	−0.283145	+	0.163474i
$377$	−7.30472	+	7.30472i	−0.376212	+	0.376212i
$378$	1.94096	+	1.79796i	0.0998323	+	0.0924772i
$379$		−	3.51982i		−	0.180801i	−0.995905	−	0.0904005i	$-0.971185\pi$
$379$		−	3.51982i		−	0.180801i	0.995905	−	0.0904005i	$-0.0288147\pi$
$380$		0			0
$381$	−8.32363	−	4.80565i	−0.426433	−	0.246201i
$382$	−4.18042	+	1.12014i	−0.213889	+	0.0573114i
$383$	−2.31980	+	8.65762i	−0.118536	+	0.442384i	−0.999527	−	0.0307499i	$-0.990210\pi$
$383$	−2.31980	+	8.65762i	−0.118536	+	0.442384i	0.880991	+	0.473133i	$0.156877\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−21.2681			−1.08252
$387$	0.199752	−	0.745483i	0.0101539	−	0.0378950i
$388$	−5.94601	+	1.59323i	−0.301863	+	0.0808840i
$389$	−27.3119	−	15.7685i	−1.38477	−	0.799497i	−0.392049	−	0.919944i	$-0.628234\pi$
$389$	−27.3119	−	15.7685i	−1.38477	−	0.799497i	−0.992720	+	0.120447i	$0.961567\pi$
$390$		0			0
$391$			38.8551i			1.96499i
$392$	−1.29000	+	6.88011i	−0.0651548	+	0.347498i
$393$	−2.99529	+	2.99529i	−0.151092	+	0.151092i
$394$	17.3073	−	9.99238i	0.871930	−	0.503409i
$395$		0			0
$396$	1.31272	−	2.27370i	0.0659667	−	0.114258i
$397$	6.00656	+	1.60945i	0.301461	+	0.0807762i	0.406379	−	0.913705i	$-0.366791\pi$
$397$	6.00656	+	1.60945i	0.301461	+	0.0807762i	−0.104918	+	0.994481i	$0.533458\pi$
$398$	−0.596847	−	0.596847i	−0.0299172	−	0.0299172i
$399$	10.8872	+	5.74255i	0.545043	+	0.287487i
$400$		0			0
$401$	10.2570	+	17.7657i	0.512211	+	0.887176i	0.999900	+	0.0141584i	$0.00450691\pi$
$401$	10.2570	+	17.7657i	0.512211	+	0.887176i	−0.487688	+	0.873018i	$0.662160\pi$
$402$	0.663456	+	2.47605i	0.0330902	+	0.123494i
$403$	4.46136	+	16.6500i	0.222236	+	0.829396i
$404$	3.83699	+	6.64586i	0.190897	+	0.330644i
$405$		0			0
$406$	15.8473	−	0.606094i	0.786489	−	0.0300799i
$407$	−7.34708	−	7.34708i	−0.364181	−	0.364181i
$408$	7.31238	+	1.95935i	0.362017	+	0.0970021i
$409$	12.8256	−	22.2145i	0.634184	−	1.09844i	−0.352504	−	0.935810i	$-0.614670\pi$
$409$	12.8256	−	22.2145i	0.634184	−	1.09844i	0.986687	−	0.162628i	$-0.0519970\pi$
$410$		0			0
$411$	−7.15564	+	4.13131i	−0.352962	+	0.203783i
$412$	−2.87646	+	2.87646i	−0.141713	+	0.141713i
$413$	4.52881	−	19.9180i	0.222848	−	0.980099i
$414$			5.13255i			0.252251i
$415$		0			0
$416$	−1.49254	−	0.861717i	−0.0731777	−	0.0422492i
$417$	9.03197	−	2.42011i	0.442298	−	0.118513i
$418$	3.16132	−	11.7982i	0.154625	−	0.577069i
$419$	1.54146			0.0753054			0.0376527	−	0.999291i	$-0.488012\pi$
$419$	1.54146			0.0753054			0.0376527	+	0.999291i	$0.488012\pi$
$420$		0			0
$421$	−20.0850			−0.978884			−0.489442	−	0.872036i	$-0.662800\pi$
$421$	−20.0850			−0.978884			−0.489442	+	0.872036i	$0.662800\pi$
$422$	5.74175	−	21.4285i	0.279504	−	1.04312i
$423$	6.12372	−	1.64085i	0.297746	−	0.0797807i
$424$	−7.43018	−	4.28981i	−0.360841	−	0.208332i
$425$		0			0
$426$			8.36973i			0.405515i
$427$	−8.64788	+	9.33568i	−0.418500	+	0.451785i
$428$	−1.99197	+	1.99197i	−0.0962855	+	0.0962855i
$429$	3.91857	−	2.26239i	0.189190	−	0.109229i
$430$		0			0
$431$	−10.9503	+	18.9665i	−0.527457	+	0.913583i	0.472030	+	0.881582i	$0.343521\pi$
$431$	−10.9503	+	18.9665i	−0.527457	+	0.913583i	−0.999488	+	0.0320007i	$0.989812\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	5.51584	+	5.51584i	0.265074	+	0.265074i	0.827112	−	0.562038i	$-0.189982\pi$
$433$	5.51584	+	5.51584i	0.265074	+	0.265074i	−0.562038	+	0.827112i	$0.689982\pi$
$434$	12.3456	−	23.4058i	0.592606	−	1.12352i
$435$		0			0
$436$	6.08031	+	10.5314i	0.291194	+	0.504362i
$437$	6.18014	+	23.0646i	0.295636	+	1.10333i
$438$	−3.53363	−	13.1877i	−0.168844	−	0.630133i
$439$	2.62203	+	4.54150i	0.125143	+	0.216754i	0.921789	−	0.387692i	$-0.126728\pi$
$439$	2.62203	+	4.54150i	0.125143	+	0.216754i	−0.796646	+	0.604446i	$0.793394\pi$
$440$		0			0
$441$	3.02675	−	6.31180i	0.144131	−	0.300562i
$442$	9.22560	+	9.22560i	0.438817	+	0.438817i
$443$	1.25609	+	0.336567i	0.0596784	+	0.0159908i	0.288535	−	0.957469i	$-0.406832\pi$
$443$	1.25609	+	0.336567i	0.0596784	+	0.0159908i	−0.228856	+	0.973460i	$0.573499\pi$
$444$	1.97878	−	3.42734i	0.0939087	−	0.162655i
$445$		0			0
$446$	−13.1822	+	7.61073i	−0.624194	+	0.360378i
$447$	−3.36452	+	3.36452i	−0.159136	+	0.159136i
$448$	0.781940	+	2.52756i	0.0369432	+	0.119416i
$449$		−	22.3625i		−	1.05535i	−0.849445	−	0.527676i	$-0.823063\pi$
$449$		−	22.3625i		−	1.05535i	0.849445	−	0.527676i	$-0.176937\pi$
$450$		0			0
$451$	−12.7196	−	7.34366i	−0.598942	−	0.345799i
$452$	2.23858	−	0.599825i	0.105294	−	0.0282134i
$453$	−0.556756	+	2.07784i	−0.0261587	+	0.0976255i
$454$	−3.73858			−0.175460
$455$		0			0
$456$	4.65232			0.217865
$457$	−0.853971	+	3.18706i	−0.0399471	+	0.149085i	−0.983019	−	0.183505i	$-0.941256\pi$
$457$	−0.853971	+	3.18706i	−0.0399471	+	0.149085i	0.943072	+	0.332589i	$0.107922\pi$
$458$	14.6644	−	3.92933i	0.685225	−	0.183605i
$459$	−6.55610	−	3.78517i	−0.306013	−	0.176676i
$460$		0			0
$461$			6.97417i			0.324819i	0.986723	+	0.162410i	$0.0519266\pi$
$461$			6.97417i			0.324819i	−0.986723	+	0.162410i	$0.948073\pi$
$462$	−6.77339	−	1.54009i	−0.315127	−	0.0716513i
$463$	−16.6658	+	16.6658i	−0.774527	+	0.774527i	−0.978894	−	0.204367i	$-0.934486\pi$
$463$	−16.6658	+	16.6658i	−0.774527	+	0.774527i	0.204367	+	0.978894i	$0.434486\pi$
$464$	5.19104	−	2.99705i	0.240988	−	0.139135i
$465$		0			0
$466$	−0.606518	+	1.05052i	−0.0280964	+	0.0486644i
$467$	11.0696	+	2.96609i	0.512240	+	0.137254i	0.505675	−	0.862724i	$-0.331244\pi$
$467$	11.0696	+	2.96609i	0.512240	+	0.137254i	0.00656516	+	0.999978i	$0.497910\pi$
$468$	1.21865	+	1.21865i	0.0563322	+	0.0563322i
$469$	5.73959	−	3.61305i	0.265030	−	0.166835i
$470$		0			0
$471$	−1.90217	−	3.29465i	−0.0876473	−	0.151810i
$472$	−1.99819	−	7.45736i	−0.0919744	−	0.343253i
$473$	0.524436	+	1.95722i	0.0241136	+	0.0899932i
$474$	−4.49744	−	7.78980i	−0.206574	−	0.357797i
$475$		0			0
$476$	−0.765475	−	20.0146i	−0.0350855	−	0.917367i
$477$	6.06671	+	6.06671i	0.277776	+	0.277776i
$478$	15.6087	+	4.18234i	0.713926	+	0.191296i
$479$	−5.05860	+	8.76174i	−0.231133	+	0.400334i	−0.958142	−	0.286294i	$-0.907577\pi$
$479$	−5.05860	+	8.76174i	−0.231133	+	0.400334i	0.727009	+	0.686628i	$0.240910\pi$
$480$		0			0
$481$	5.90680	−	3.41029i	0.269327	−	0.155496i
$482$	−17.8310	+	17.8310i	−0.812180	+	0.812180i
$483$	12.9728	−	4.01334i	0.590284	−	0.182614i
$484$		−	4.10705i		−	0.186684i
$485$		0			0
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−35.6908	+	9.56331i	−1.61730	+	0.433355i	−0.950208	−	0.311617i	$-0.899129\pi$
$487$	−35.6908	+	9.56331i	−1.61730	+	0.433355i	−0.667095	+	0.744972i	$0.732463\pi$
$488$	−1.24487	+	4.64593i	−0.0563528	+	0.210311i
$489$	4.46126			0.201745
$490$		0			0
$491$	−8.00737			−0.361368			−0.180684	−	0.983541i	$-0.557831\pi$
$491$	−8.00737			−0.361368			−0.180684	+	0.983541i	$0.557831\pi$
$492$	1.44789	−	5.40361i	0.0652760	−	0.243613i
$493$	−43.8311	+	11.7445i	−1.97405	+	0.528946i
$494$	6.94376	+	4.00898i	0.312415	+	0.180373i
$495$		0			0
$496$		−	10.0018i		−	0.449092i
$497$	21.1550	−	6.54463i	0.948932	−	0.293567i
$498$	7.99504	−	7.99504i	0.358266	−	0.358266i
$499$	−10.3636	+	5.98341i	−0.463937	+	0.267854i	−0.713698	−	0.700453i	$-0.752981\pi$
$499$	−10.3636	+	5.98341i	−0.463937	+	0.267854i	0.249761	+	0.968307i	$0.419648\pi$
$500$		0			0
$501$	−11.4076	+	19.7585i	−0.509652	+	0.882744i
$502$	2.00487	+	0.537203i	0.0894816	+	0.0239765i
$503$	20.3121	+	20.3121i	0.905670	+	0.905670i	0.995919	−	0.0902493i	$-0.0287664\pi$
$503$	20.3121	+	20.3121i	0.905670	+	0.905670i	−0.0902493	+	0.995919i	$0.528766\pi$
$504$	−0.101115	−	2.64382i	−0.00450403	−	0.117765i
$505$		0			0
$506$	−6.73760	−	11.6699i	−0.299523	−	0.518789i
$507$	−2.59590	−	9.68802i	−0.115288	−	0.430260i
$508$	2.48759	+	9.28381i	0.110369	+	0.411902i
$509$	−14.7797	−	25.5992i	−0.655098	−	1.13466i	−0.981869	−	0.189559i	$-0.939294\pi$
$509$	−14.7797	−	25.5992i	−0.655098	−	1.13466i	0.326771	−	0.945103i	$-0.394039\pi$
$510$		0			0
$511$	−30.5696	+	19.2435i	−1.35232	+	0.851281i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.49380	−	1.20411i	−0.198406	−	0.0531627i
$514$	−2.25111	+	3.89904i	−0.0992922	+	0.171979i
$515$		0			0
$516$	−0.668382	+	0.385890i	−0.0294239	+	0.0169879i
$517$	−11.7695	+	11.7695i	−0.517624	+	0.517624i
$518$	−10.2101	−	2.32151i	−0.448607	−	0.102001i
$519$		−	12.3822i		−	0.543520i
$520$		0			0
$521$	−7.64664	−	4.41479i	−0.335005	−	0.193415i	0.323056	−	0.946380i	$-0.395290\pi$
$521$	−7.64664	−	4.41479i	−0.335005	−	0.193415i	−0.658061	+	0.752964i	$0.728623\pi$
$522$	−5.78985	+	1.55139i	−0.253415	+	0.0679024i
$523$	−10.6856	+	39.8792i	−0.467249	+	1.74380i	0.182076	+	0.983284i	$0.441718\pi$
$523$	−10.6856	+	39.8792i	−0.467249	+	1.74380i	−0.649325	+	0.760511i	$0.724948\pi$
$524$	4.23598			0.185050
$525$		0			0
$526$	−22.3996			−0.976669
$527$	−19.5969	+	73.1366i	−0.853654	+	3.18588i
$528$	−2.53598	+	0.679515i	−0.110365	+	0.0295721i
$529$	2.89515	+	1.67152i	0.125876	+	0.0726746i
$530$		0			0
$531$			7.72043i			0.335038i
$532$	−3.63784	−	11.7590i	−0.157720	−	0.509818i
$533$	6.81741	−	6.81741i	0.295295	−	0.295295i
$534$	−0.140757	+	0.0812661i	−0.00609115	+	0.00351673i
$535$		0			0
$536$	1.28170	−	2.21997i	0.0553610	−	0.0958880i
$537$	−19.5794	−	5.24628i	−0.844913	−	0.226394i
$538$	−8.29027	−	8.29027i	−0.357419	−	0.357419i
$539$	1.40372	+	18.3244i	0.0604625	+	0.789288i
$540$		0			0
$541$	12.7674	+	22.1137i	0.548911	+	0.950742i	0.998349	+	0.0574309i	$0.0182909\pi$
$541$	12.7674	+	22.1137i	0.548911	+	0.950742i	−0.449438	+	0.893311i	$0.648376\pi$
$542$	−6.22384	−	23.2277i	−0.267337	−	0.997714i
$543$	−1.94797	−	7.26992i	−0.0835953	−	0.311982i
$544$	−3.78517	−	6.55610i	−0.162288	−	0.281090i
$545$		0			0
$546$	2.12731	−	4.03313i	0.0910403	−	0.172602i
$547$	−22.6183	−	22.6183i	−0.967087	−	0.967087i	0.0323883	−	0.999475i	$-0.489689\pi$
$547$	−22.6183	−	22.6183i	−0.967087	−	0.967087i	−0.999475	+	0.0323883i	$0.989689\pi$
$548$	7.98108	+	2.13852i	0.340935	+	0.0913532i
$549$	2.40491	−	4.16543i	0.102639	−	0.177776i
$550$		0			0
$551$	−24.1504	+	13.9432i	−1.02884	+	0.594002i
$552$	3.62926	−	3.62926i	0.154471	−	0.154471i
$553$	−16.1725	+	17.4587i	−0.687723	+	0.742420i
$554$			27.1973i			1.15550i
$555$		0			0
$556$	−8.09784	−	4.67529i	−0.343425	−	0.198277i
$557$	−16.9420	+	4.53960i	−0.717856	+	0.192349i	−0.599215	−	0.800588i	$-0.704520\pi$
$557$	−16.9420	+	4.53960i	−0.717856	+	0.192349i	−0.118641	+	0.992937i	$0.537854\pi$
$558$	−2.58864	+	9.66095i	−0.109586	+	0.408981i
$559$	−1.33011			−0.0562578
$560$		0			0
$561$	19.8755			0.839143
$562$	5.74352	−	21.4351i	0.242276	−	0.904186i
$563$	−15.0854	+	4.04211i	−0.635772	+	0.170355i	−0.562288	−	0.826942i	$-0.690079\pi$
$563$	−15.0854	+	4.04211i	−0.635772	+	0.170355i	−0.0734847	+	0.997296i	$0.523412\pi$
$564$	−5.49038	−	3.16987i	−0.231187	−	0.133476i
$565$		0			0
$566$			11.1028i			0.466684i
$567$	−0.586601	+	2.57990i	−0.0246349	+	0.108346i
$568$	5.91829	−	5.91829i	0.248326	−	0.248326i
$569$	15.5107	−	8.95511i	0.650243	−	0.375418i	−0.138307	−	0.990389i	$-0.544166\pi$
$569$	15.5107	−	8.95511i	0.650243	−	0.375418i	0.788549	+	0.614972i	$0.210833\pi$
$570$		0			0
$571$	10.2340	−	17.7258i	0.428278	−	0.741800i	−0.568442	−	0.822723i	$-0.692454\pi$
$571$	10.2340	−	17.7258i	0.428278	−	0.741800i	0.996720	+	0.0809234i	$0.0257869\pi$
$572$	−4.37060	−	1.17110i	−0.182744	−	0.0489661i
$573$	−3.06028	−	3.06028i	−0.127845	−	0.127845i
$574$	−14.7901	+	0.565661i	−0.617327	+	0.0236102i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−6.62634	−	24.7298i	−0.275858	−	1.02952i	−0.955264	−	0.295754i	$-0.904429\pi$
$577$	−6.62634	−	24.7298i	−0.275858	−	1.02952i	0.679406	−	0.733763i	$-0.262238\pi$
$578$	10.4330	+	38.9364i	0.433955	+	1.61954i
$579$	−10.6340	−	18.4187i	−0.441935	−	0.765455i
$580$		0			0
$581$	−26.4596	−	13.9563i	−1.09773	−	0.579006i
$582$	−4.35278	−	4.35278i	−0.180429	−	0.180429i
$583$	−21.7578	−	5.82998i	−0.901116	−	0.241453i
$584$	−6.82646	+	11.8238i	−0.282481	+	0.489271i
$585$		0			0
$586$	−7.98019	+	4.60737i	−0.329659	+	0.190329i
$587$	26.2627	−	26.2627i	1.08398	−	1.08398i	0.0878438	−	0.996134i	$-0.472002\pi$
$587$	26.2627	−	26.2627i	1.08398	−	1.08398i	0.996134	−	0.0878438i	$-0.0279977\pi$
$588$	−6.60335	+	2.32288i	−0.272318	+	0.0957941i
$589$			46.5313i			1.91729i
$590$		0			0
$591$	17.3073	+	9.99238i	0.711927	+	0.411032i
$592$	−3.82271	+	1.02429i	−0.157112	+	0.0420981i
$593$	2.49114	−	9.29705i	0.102299	−	0.381784i	−0.895726	−	0.444606i	$-0.853344\pi$
$593$	2.49114	−	9.29705i	0.102299	−	0.381784i	0.998025	+	0.0628225i	$0.0200102\pi$
$594$	2.62544			0.107723
$595$		0			0
$596$	4.75815			0.194902
$597$	0.218461	−	0.815308i	0.00894102	−	0.0333683i
$598$	8.54420	−	2.28941i	0.349398	−	0.0936210i
$599$	3.36700	+	1.94394i	0.137572	+	0.0794273i	0.567206	−	0.823576i	$-0.308024\pi$
$599$	3.36700	+	1.94394i	0.137572	+	0.0794273i	−0.429634	+	0.903003i	$0.641358\pi$
$600$		0			0
$601$		−	36.4068i		−	1.48506i	−0.669811	−	0.742531i	$-0.733625\pi$
$601$		−	36.4068i		−	1.48506i	0.669811	−	0.742531i	$-0.266375\pi$
$602$	1.49800	+	1.38763i	0.0610538	+	0.0565557i
$603$	−1.81260	+	1.81260i	−0.0738146	+	0.0738146i
$604$	1.86294	−	1.07557i	0.0758020	−	0.0437643i
$605$		0			0
$606$	−3.83699	+	6.64586i	−0.155867	+	0.269969i
$607$	−6.68399	−	1.79097i	−0.271295	−	0.0726932i	0.120607	−	0.992700i	$-0.461516\pi$
$607$	−6.68399	−	1.79097i	−0.271295	−	0.0726932i	−0.391902	+	0.920007i	$0.628183\pi$
$608$	−3.28969	−	3.28969i	−0.133414	−	0.133414i
$609$	8.44855	+	13.4211i	0.342352	+	0.543851i
$610$		0			0
$611$	−5.46307	−	9.46231i	−0.221012	−	0.382804i
$612$	1.95935	+	7.31238i	0.0792019	+	0.295585i
$613$	−11.5346	−	43.0478i	−0.465880	−	1.73869i	−0.653957	−	0.756532i	$-0.726892\pi$
$613$	−11.5346	−	43.0478i	−0.465880	−	1.73869i	0.188077	−	0.982154i	$-0.439775\pi$
$614$	−14.5671	−	25.2310i	−0.587881	−	1.01824i
$615$		0			0
$616$	3.70050	+	5.87851i	0.149098	+	0.236852i
$617$	−8.27627	−	8.27627i	−0.333190	−	0.333190i	0.520607	−	0.853797i	$-0.325706\pi$
$617$	−8.27627	−	8.27627i	−0.333190	−	0.333190i	−0.853797	+	0.520607i	$0.825706\pi$
$618$	−3.92931	−	1.05286i	−0.158060	−	0.0423521i
$619$	−5.79761	+	10.0418i	−0.233026	+	0.403612i	−0.958697	−	0.284429i	$-0.908196\pi$
$619$	−5.79761	+	10.0418i	−0.233026	+	0.403612i	0.725671	+	0.688042i	$0.241529\pi$
$620$		0			0
$621$	−4.44492	+	2.56627i	−0.178368	+	0.102981i
$622$	23.2400	−	23.2400i	0.931840	−	0.931840i
$623$	0.315469	+	0.292227i	0.0126390	+	0.0117078i
$624$		−	1.72343i		−	0.0689926i
$625$		0			0
$626$	−19.2111	−	11.0915i	−0.767831	−	0.443307i
$627$	11.7982	−	3.16132i	0.471175	−	0.126251i
$628$	−0.984635	+	3.67471i	−0.0392912	+	0.146637i
$629$	29.9600			1.19458
$630$		0			0
$631$	2.25813			0.0898949			0.0449474	−	0.998989i	$-0.485688\pi$
$631$	2.25813			0.0898949			0.0449474	+	0.998989i	$0.485688\pi$
$632$	−2.32805	+	8.68839i	−0.0926047	+	0.345606i
$633$	21.4285	−	5.74175i	0.851706	−	0.228214i
$634$	−12.4400	−	7.18226i	−0.494057	−	0.285244i
$635$		0			0
$636$		−	8.57963i		−	0.340204i
$637$	−11.8574	−	2.22323i	−0.469808	−	0.0880875i
$638$	11.1279	−	11.1279i	0.440556	−	0.440556i
$639$	−7.24840	+	4.18486i	−0.286742	+	0.165551i
$640$		0			0
$641$	−9.61246	+	16.6493i	−0.379669	+	0.657607i	−0.991014	−	0.133758i	$-0.957296\pi$
$641$	−9.61246	+	16.6493i	−0.379669	+	0.657607i	0.611345	+	0.791364i	$0.290629\pi$
$642$	−2.72108	−	0.729112i	−0.107393	−	0.0287757i
$643$	−15.5634	−	15.5634i	−0.613760	−	0.613760i	0.330163	−	0.943924i	$-0.392896\pi$
$643$	−15.5634	−	15.5634i	−0.613760	−	0.613760i	−0.943924	+	0.330163i	$0.892896\pi$
$644$	−12.0110	−	6.33531i	−0.473301	−	0.249646i
$645$		0			0
$646$	17.6098	+	30.5011i	0.692848	+	1.20005i
$647$	2.55828	+	9.54764i	0.100577	+	0.375357i	0.997806	−	0.0662082i	$-0.0210902\pi$
$647$	2.55828	+	9.54764i	0.100577	+	0.375357i	−0.897229	+	0.441565i	$0.854423\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−10.1348	−	17.5539i	−0.397825	−	0.689053i
$650$		0			0
$651$	26.4428	−	1.01133i	1.03638	−	0.0396371i
$652$	−3.15459	−	3.15459i	−0.123543	−	0.123543i
$653$	−9.61337	−	2.57589i	−0.376200	−	0.100803i	0.0657640	−	0.997835i	$-0.479052\pi$
$653$	−9.61337	−	2.57589i	−0.376200	−	0.100803i	−0.441964	+	0.897033i	$0.645718\pi$
$654$	−6.08031	+	10.5314i	−0.237759	+	0.411810i
$655$		0			0
$656$	−4.84474	+	2.79711i	−0.189155	+	0.109209i
$657$	9.65407	−	9.65407i	0.376641	−	0.376641i
$658$	−3.71890	+	16.3559i	−0.144978	+	0.637620i
$659$			16.2333i			0.632360i	0.948699	+	0.316180i	$0.102400\pi$
$659$			16.2333i			0.632360i	−0.948699	+	0.316180i	$0.897600\pi$
$660$		0			0
$661$	−8.77097	−	5.06392i	−0.341151	−	0.196964i	0.319630	−	0.947543i	$-0.396441\pi$
$661$	−8.77097	−	5.06392i	−0.341151	−	0.196964i	−0.660781	+	0.750579i	$0.729775\pi$
$662$	2.79217	−	0.748160i	0.108521	−	0.0290780i
$663$	−3.37680	+	12.6024i	−0.131144	+	0.489437i
$664$	−11.3067			−0.438785
$665$		0			0
$666$	3.95756			0.153352
$667$	−7.96256	+	29.7167i	−0.308312	+	1.15064i
$668$	22.0377	−	5.90499i	0.852665	−	0.228471i
$669$	−13.1822	−	7.61073i	−0.509652	−	0.294248i
$670$		0			0
$671$			12.6279i			0.487495i
$672$	−1.79796	+	1.94096i	−0.0693579	+	0.0748742i
$673$	−15.2038	+	15.2038i	−0.586062	+	0.586062i	−0.936563	−	0.350501i	$-0.886011\pi$
$673$	−15.2038	+	15.2038i	−0.586062	+	0.586062i	0.350501	+	0.936563i	$0.386011\pi$
$674$	28.7145	−	16.5783i	1.10604	−	0.638574i
$675$		0			0
$676$	−5.01489	+	8.68604i	−0.192880	+	0.334078i
$677$	−11.6492	−	3.12140i	−0.447716	−	0.119965i	0.0279145	−	0.999610i	$-0.491113\pi$
$677$	−11.6492	−	3.12140i	−0.447716	−	0.119965i	−0.475630	+	0.879645i	$0.657780\pi$
$678$	1.63875	+	1.63875i	0.0629359	+	0.0629359i
$679$	−7.59832	+	14.4056i	−0.291597	+	0.552834i
$680$		0			0
$681$	−1.86929	−	3.23770i	−0.0716313	−	0.124069i
$682$	−6.79634	−	25.3643i	−0.260245	−	0.971248i
$683$	−3.03256	−	11.3177i	−0.116038	−	0.433058i	0.883325	−	0.468761i	$-0.155300\pi$
$683$	−3.03256	−	11.3177i	−0.116038	−	0.433058i	−0.999362	+	0.0357033i	$0.988633\pi$
$684$	2.32616	+	4.02903i	0.0889429	+	0.154054i
$685$		0			0
$686$	11.0347	+	14.8740i	0.421305	+	0.567893i
$687$	10.7351	+	10.7351i	0.409570	+	0.409570i
$688$	0.745483	+	0.199752i	0.0284213	+	0.00761546i
$689$	7.39321	−	12.8054i	0.281659	−	0.487848i
$690$		0			0
$691$	−24.8579	+	14.3517i	−0.945639	+	0.545965i	−0.891723	−	0.452581i	$-0.850503\pi$
$691$	−24.8579	+	14.3517i	−0.945639	+	0.545965i	−0.0539153	+	0.998546i	$0.517170\pi$
$692$	−8.75557	+	8.75557i	−0.332837	+	0.332837i
$693$	−2.05294	−	6.63597i	−0.0779847	−	0.252080i
$694$			11.3379i			0.430382i
$695$		0			0
$696$	5.19104	+	2.99705i	0.196766	+	0.113603i
$697$	40.9071	−	10.9610i	1.54947	−	0.415178i
$698$	1.76200	−	6.57589i	0.0666929	−	0.248901i
$699$	−1.21304			−0.0458812
$700$		0			0
$701$	47.8761			1.80825			0.904127	−	0.427264i	$-0.140523\pi$
$701$	47.8761			1.80825			0.904127	+	0.427264i	$0.140523\pi$
$702$	−0.446058	+	1.66471i	−0.0168354	+	0.0628304i
$703$	17.7844	−	4.76533i	0.670753	−	0.179728i
$704$	2.27370	+	1.31272i	0.0856933	+	0.0494751i
$705$		0			0
$706$		−	27.8246i		−	1.04719i
$707$	19.7981	+	4.50156i	0.744585	+	0.169299i
$708$	5.45917	−	5.45917i	0.205168	−	0.205168i
$709$	−22.0830	+	12.7496i	−0.829343	+	0.478822i	−0.853628	−	0.520883i	$-0.825603\pi$
$709$	−22.0830	+	12.7496i	−0.829343	+	0.478822i	0.0242844	+	0.999705i	$0.492269\pi$
$710$		0			0
$711$	4.49744	−	7.78980i	0.168667	−	0.292140i
$712$	0.156994	+	0.0420664i	0.00588360	+	0.00157651i
$713$	36.2989	+	36.2989i	1.35941	+	1.35941i
$714$	16.9504	−	10.6702i	0.634353	−	0.399323i
$715$		0			0
$716$	10.1350	+	17.5544i	0.378764	+	0.656038i
$717$	4.18234	+	15.6087i	0.156192	+	0.582918i
$718$	3.55579	+	13.2704i	0.132701	+	0.495247i
$719$	−16.0438	−	27.7887i	−0.598333	−	1.03634i	−0.993067	−	0.117548i	$-0.962497\pi$
$719$	−16.0438	−	27.7887i	−0.598333	−	1.03634i	0.394734	−	0.918795i	$-0.370837\pi$
$720$		0			0
$721$	0.411329	+	10.7549i	0.0153187	+	0.400532i
$722$	1.86964	+	1.86964i	0.0695809	+	0.0695809i
$723$	−24.3576	−	6.52660i	−0.905869	−	0.242727i
$724$	−3.76319	+	6.51803i	−0.139858	+	0.242241i
$725$		0			0
$726$	3.55681	−	2.05352i	0.132006	−	0.0762134i
$727$	−11.3772	+	11.3772i	−0.421956	+	0.421956i	−0.885877	−	0.463921i	$-0.846442\pi$
$727$	−11.3772	+	11.3772i	−0.421956	+	0.421956i	0.463921	+	0.885877i	$0.346442\pi$
$728$	−4.35609	+	1.34762i	−0.161447	+	0.0499462i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−5.05987	−	2.92132i	−0.187146	−	0.108049i
$732$	−4.64593	+	1.24487i	−0.171719	+	0.0460119i
$733$	−5.43607	+	20.2877i	−0.200786	+	0.749343i	0.789907	+	0.613226i	$0.210129\pi$
$733$	−5.43607	+	20.2877i	−0.200786	+	0.749343i	−0.990693	+	0.136116i	$0.956538\pi$
$734$	−25.2180			−0.930812
$735$		0			0
$736$	−5.13255			−0.189188
$737$	1.74187	−	6.50073i	0.0641625	−	0.239458i
$738$	5.40361	−	1.44789i	0.198910	−	0.0532976i
$739$	31.8347	+	18.3797i	1.17106	+	0.676110i	0.953929	−	0.300033i	$-0.0969977\pi$
$739$	31.8347	+	18.3797i	1.17106	+	0.676110i	0.217128	+	0.976143i	$0.430331\pi$
$740$		0			0
$741$			8.01797i			0.294547i
$742$	−21.6855	+	6.70876i	−0.796101	+	0.246286i
$743$	17.1637	−	17.1637i	0.629676	−	0.629676i	−0.318310	−	0.947987i	$-0.603115\pi$
$743$	17.1637	−	17.1637i	0.629676	−	0.629676i	0.947987	+	0.318310i	$0.103115\pi$
$744$	8.66177	−	5.00088i	0.317556	−	0.183341i
$745$		0			0
$746$	13.4271	−	23.2564i	0.491600	−	0.851477i
$747$	10.9214	+	2.92639i	0.399594	+	0.107071i
$748$	−14.0541	−	14.0541i	−0.513868	−	0.513868i
$749$	0.284849	+	7.44782i	0.0104081	+	0.272138i
$750$		0			0
$751$	−15.1318	−	26.2091i	−0.552168	−	0.956384i	−0.998118	−	0.0613255i	$-0.980467\pi$
$751$	−15.1318	−	26.2091i	−0.552168	−	0.956384i	0.445949	−	0.895058i	$-0.352866\pi$
$752$	1.64085	+	6.12372i	0.0598355	+	0.223309i
$753$	0.537203	+	2.00487i	0.0195768	+	0.0730615i
$754$	5.16522	+	8.94642i	0.188106	+	0.325809i
$755$		0			0
$756$	2.23906	−	1.40948i	0.0814337	−	0.0512622i
$757$	1.48321	+	1.48321i	0.0539082	+	0.0539082i	0.733547	−	0.679639i	$-0.237863\pi$
$757$	1.48321	+	1.48321i	0.0539082	+	0.0539082i	−0.679639	+	0.733547i	$0.737863\pi$
$758$	−3.39988	−	0.910996i	−0.123489	−	0.0330889i
$759$	6.73760	−	11.6699i	0.244560	−	0.423590i
$760$		0			0
$761$	5.99246	−	3.45975i	0.217226	−	0.125416i	−0.387439	−	0.921895i	$-0.626640\pi$
$761$	5.99246	−	3.45975i	0.217226	−	0.125416i	0.604665	+	0.796480i	$0.293307\pi$
$762$	−6.79622	+	6.79622i	−0.246201	+	0.246201i
$763$	31.3732	+	7.13342i	1.13579	+	0.258247i
$764$			4.32789i			0.156578i
$765$		0			0
$766$	7.76221	+	4.48151i	0.280460	+	0.161924i
$767$	12.8523	−	3.44376i	0.464069	−	0.124347i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	16.5757			0.597736			0.298868	−	0.954294i	$-0.403391\pi$
$769$	16.5757			0.597736			0.298868	+	0.954294i	$0.403391\pi$
$770$		0			0
$771$	−4.50222			−0.162143
$772$	−5.50458	+	20.5434i	−0.198114	+	0.739372i
$773$	6.48331	−	1.73720i	0.233189	−	0.0624827i	−0.140332	−	0.990104i	$-0.544817\pi$
$773$	6.48331	−	1.73720i	0.233189	−	0.0624827i	0.373521	+	0.927622i	$0.378150\pi$
$774$	−0.668382	−	0.385890i	−0.0240245	−	0.0138705i
$775$		0			0
$776$			6.15577i			0.220979i
$777$	−3.09457	−	10.0030i	−0.111017	−	0.358854i
$778$	−22.3001	+	22.3001i	−0.799497	+	0.799497i
$779$	22.5393	−	13.0131i	0.807554	−	0.466241i
$780$		0			0
$781$	10.9871	−	19.0303i	0.393150	−	0.680956i
$782$	37.5311	+	10.0564i	1.34211	+	0.359617i
$783$	−4.23847	−	4.23847i	−0.151470	−	0.151470i
$784$	6.31180	+	3.02675i	0.225421	+	0.108098i
$785$		0			0
$786$	2.11799	+	3.66846i	0.0755461	+	0.130850i
$787$	−3.88207	−	14.4881i	−0.138381	−	0.516444i	−0.999961	−	0.00882263i	$-0.997192\pi$
$787$	−3.88207	−	14.4881i	−0.138381	−	0.516444i	0.861580	−	0.507621i	$-0.169475\pi$
$788$	−5.17244	−	19.3038i	−0.184260	−	0.687669i
$789$	−11.1998	−	19.3986i	−0.398723	−	0.690609i
$790$		0			0
$791$	2.86064	−	5.42345i	0.101713	−	0.192836i
$792$	−1.85647	−	1.85647i	−0.0659667	−	0.0659667i
$793$	−8.00696	−	2.14546i	−0.284335	−	0.0761874i
$794$	3.10923	−	5.38534i	0.110342	−	0.191118i
$795$		0			0
$796$	−0.730985	+	0.422034i	−0.0259091	+	0.0149586i
$797$	29.9616	−	29.9616i	1.06130	−	1.06130i	0.0633012	−	0.997994i	$-0.479837\pi$
$797$	29.9616	−	29.9616i	1.06130	−	1.06130i	0.997994	−	0.0633012i	$-0.0201629\pi$
$798$	8.36470	−	9.02997i	0.296107	−	0.319658i
$799$		−	47.9940i		−	1.69790i
$800$		0			0
$801$	−0.140757	−	0.0812661i	−0.00497341	−	0.00287140i
$802$	19.8151	−	5.30943i	0.699694	−	0.187482i
$803$	−9.27735	+	34.6236i	−0.327391	+	1.22184i
$804$	2.56340			0.0904041
$805$		0			0
$806$	17.2374			0.607160
$807$	3.03445	−	11.3247i	0.106818	−	0.398649i
$808$	7.41249	−	1.98617i	0.260771	−	0.0698732i
$809$	7.51129	+	4.33664i	0.264083	+	0.152468i	0.626196	−	0.779666i	$-0.284611\pi$
$809$	7.51129	+	4.33664i	0.264083	+	0.152468i	−0.362113	+	0.932134i	$0.617944\pi$
$810$		0			0
$811$		−	21.4366i		−	0.752741i	−0.926469	−	0.376370i	$-0.877172\pi$
$811$		−	21.4366i		−	0.752741i	0.926469	−	0.376370i	$-0.122828\pi$
$812$	3.51614	−	15.4642i	0.123392	−	0.542687i
$813$	17.0038	−	17.0038i	0.596351	−	0.596351i
$814$	−8.99830	+	5.19517i	−0.315390	+	0.182091i
$815$		0			0
$816$	3.78517	−	6.55610i	0.132507	−	0.229509i
$817$	−3.46822	−	0.929308i	−0.121338	−	0.0325124i
$818$	−18.1381	−	18.1381i	−0.634184	−	0.634184i
$819$	4.55645	−	0.174265i	0.159215	−	0.00608932i
$820$		0			0
$821$	−9.59996	−	16.6276i	−0.335041	−	0.580308i	0.648452	−	0.761256i	$-0.275417\pi$
$821$	−9.59996	−	16.6276i	−0.335041	−	0.580308i	−0.983493	+	0.180948i	$0.942084\pi$
$822$	2.13852	+	7.98108i	0.0745896	+	0.278372i
$823$	−2.61193	−	9.74786i	−0.0910462	−	0.339789i	0.905344	−	0.424679i	$-0.139613\pi$
$823$	−2.61193	−	9.74786i	−0.0910462	−	0.339789i	−0.996390	+	0.0848897i	$0.972946\pi$
$824$	2.03396	+	3.52293i	0.0708564	+	0.122727i
$825$		0			0
$826$	−18.0671	−	9.52964i	−0.628636	−	0.331579i
$827$	2.93550	+	2.93550i	0.102077	+	0.102077i	0.756301	−	0.654224i	$-0.227005\pi$
$827$	2.93550	+	2.93550i	0.102077	+	0.102077i	−0.654224	+	0.756301i	$0.727005\pi$
$828$	4.95766	+	1.32840i	0.172291	+	0.0461651i
$829$	0.316112	−	0.547523i	0.0109790	−	0.0190162i	−0.860484	−	0.509478i	$-0.829839\pi$
$829$	0.316112	−	0.547523i	0.0109790	−	0.0190162i	0.871463	+	0.490462i	$0.163172\pi$
$830$		0			0
$831$	−23.5535	+	13.5986i	−0.817062	+	0.471731i
$832$	−1.21865	+	1.21865i	−0.0422492	+	0.0422492i
$833$	−40.2238	−	34.4997i	−1.39367	−	1.19534i
$834$		−	9.35059i		−	0.323784i
$835$		0			0
$836$	−10.5780	−	6.10720i	−0.365847	−	0.211222i
$837$	−9.66095	+	2.58864i	−0.333931	+	0.0894766i
$838$	0.398960	−	1.48894i	0.0137818	−	0.0514345i
$839$	−7.93406			−0.273914			−0.136957	−	0.990577i	$-0.543732\pi$
$839$	−7.93406			−0.273914			−0.136957	+	0.990577i	$0.543732\pi$
$840$		0			0
$841$	−6.92921			−0.238938
$842$	−5.19839	+	19.4006i	−0.179148	+	0.668590i
$843$	21.4351	−	5.74352i	0.738265	−	0.197817i
$844$	−19.2123	−	11.0922i	−0.661313	−	0.381809i
$845$		0			0
$846$		−	6.33974i		−	0.217965i
$847$	−7.97162	−	7.38432i	−0.273908	−	0.253728i
$848$	−6.06671	+	6.06671i	−0.208332	+	0.208332i
$849$	−9.61527	+	5.55138i	−0.329995	+	0.190523i
$850$		0			0
$851$	10.1562	−	17.5910i	0.348149	−	0.603012i
$852$	8.08453	+	2.16624i	0.276972	+	0.0742143i
$853$	13.0203	+	13.0203i	0.445806	+	0.445806i	0.893957	−	0.448152i	$-0.147918\pi$
$853$	13.0203	+	13.0203i	0.445806	+	0.445806i	−0.448152	+	0.893957i	$0.647918\pi$
$854$	6.77934	+	10.7695i	0.231984	+	0.368523i
$855$		0			0
$856$	1.40854	+	2.43966i	0.0481428	+	0.0833857i
$857$	2.95372	+	11.0234i	0.100897	+	0.376553i	0.997847	−	0.0655783i	$-0.0208892\pi$
$857$	2.95372	+	11.0234i	0.100897	+	0.376553i	−0.896950	+	0.442131i	$0.854223\pi$
$858$	−1.17110	−	4.37060i	−0.0399807	−	0.149210i
$859$	−6.44883	−	11.1697i	−0.220031	−	0.381106i	0.734786	−	0.678299i	$-0.237283\pi$
$859$	−6.44883	−	11.1697i	−0.220031	−	0.381106i	−0.954817	+	0.297194i	$0.903949\pi$
$860$		0			0
$861$	−7.88493	−	12.5258i	−0.268718	−	0.426878i
$862$	15.4861	+	15.4861i	0.527457	+	0.527457i
$863$	−12.2574	−	3.28437i	−0.417248	−	0.111801i	0.0440862	−	0.999028i	$-0.485962\pi$
$863$	−12.2574	−	3.28437i	−0.417248	−	0.111801i	−0.461334	+	0.887226i	$0.652629\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	6.75549	−	3.90028i	0.229561	−	0.132537i
$867$	−28.5034	+	28.5034i	−0.968027	+	0.968027i
$868$	−19.4130	−	17.9828i	−0.658921	−	0.610375i
$869$			23.6156i			0.801103i
$870$		0			0
$871$	3.82597	+	2.20892i	0.129638	+	0.0748465i
$872$	11.7462	−	3.14740i	0.397778	−	0.106584i
$873$	1.59323	−	5.94601i	0.0539227	−	0.201242i
$874$	23.8782			0.807694
$875$		0			0
$876$	−13.6529			−0.461289
$877$	6.75617	−	25.2144i	0.228140	−	0.851429i	−0.752983	−	0.658040i	$-0.771386\pi$
$877$	6.75617	−	25.2144i	0.228140	−	0.851429i	0.981122	−	0.193388i	$-0.0619478\pi$
$878$	5.06538	−	1.35726i	0.170948	−	0.0458055i
$879$	−7.98019	−	4.60737i	−0.269165	−	0.155403i
$880$		0			0
$881$			34.2689i			1.15455i	0.816551	+	0.577274i	$0.195884\pi$
$881$			34.2689i			1.15455i	−0.816551	+	0.577274i	$0.804116\pi$
$882$	−5.31335	−	4.55723i	−0.178910	−	0.153450i
$883$	33.0880	−	33.0880i	1.11350	−	1.11350i	0.120827	−	0.992674i	$-0.461445\pi$
$883$	33.0880	−	33.0880i	1.11350	−	1.11350i	0.992674	−	0.120827i	$-0.0385546\pi$
$884$	11.2990	−	6.52348i	0.380027	−	0.219409i
$885$		0			0
$886$	0.650198	−	1.12618i	0.0218438	−	0.0378346i
$887$	18.3463	+	4.91587i	0.616008	+	0.165059i	0.553312	−	0.832974i	$-0.313364\pi$
$887$	18.3463	+	4.91587i	0.616008	+	0.165059i	0.0626958	+	0.998033i	$0.480030\pi$
$888$	−2.79841	−	2.79841i	−0.0939087	−	0.0939087i
$889$	22.4921	+	11.8636i	0.754361	+	0.397893i
$890$		0			0
$891$	1.31272	+	2.27370i	0.0439778	+	0.0761718i
$892$	3.93960	+	14.7028i	0.131908	+	0.492286i
$893$	−7.63374	−	28.4895i	−0.255453	−	0.953365i
$894$	2.37908	+	4.12068i	0.0795682	+	0.137816i
$895$		0			0
$896$	2.64382	−	0.101115i	0.0883238	−	0.00337802i
$897$	6.25479	+	6.25479i	0.208841	+	0.208841i
$898$	−21.6005	−	5.78785i	−0.720819	−	0.193143i
$899$	−29.9757	+	51.9195i	−0.999747	+	1.73161i
$900$		0			0
$901$	56.2489	−	32.4753i	1.87392	−	1.08191i
$902$	−10.3855	+	10.3855i	−0.345799	+	0.345799i
$903$	−0.452727	+	1.99112i	−0.0150658	+	0.0662603i
$904$		−	2.31755i		−	0.0770804i
$905$		0			0
$906$	1.86294	+	1.07557i	0.0618921	+	0.0357334i
$907$	54.6185	−	14.6350i	1.81358	−	0.485947i	0.817620	−	0.575759i	$-0.195293\pi$
$907$	54.6185	−	14.6350i	1.81358	−	0.485947i	0.995959	+	0.0898120i	$0.0286266\pi$
$908$	−0.967615	+	3.61119i	−0.0321114	+	0.119842i
$909$	−7.67397			−0.254530
$910$		0			0
$911$	−18.6286			−0.617193			−0.308596	−	0.951193i	$-0.599859\pi$
$911$	−18.6286			−0.617193			−0.308596	+	0.951193i	$0.599859\pi$
$912$	1.20411	−	4.49380i	0.0398720	−	0.148804i
$913$	−28.6736	+	7.68307i	−0.948958	+	0.254272i
$914$	2.85744	+	1.64975i	0.0945158	+	0.0545687i
$915$		0			0
$916$		−	15.1818i		−	0.501619i
$917$	7.61613	−	8.22187i	0.251507	−	0.271510i
$918$	−5.35303	+	5.35303i	−0.176676	+	0.176676i
$919$	−38.3850	+	22.1616i	−1.26620	+	0.731043i	−0.974268	−	0.225395i	$-0.927633\pi$
$919$	−38.3850	+	22.1616i	−1.26620	+	0.731043i	−0.291936	+	0.956438i	$0.594300\pi$
$920$		0			0
$921$	14.5671	−	25.2310i	0.480002	−	0.831389i
$922$	6.73653	+	1.80505i	0.221856	+	0.0594461i
$923$	10.1998	+	10.1998i	0.335730	+	0.335730i
$924$	−3.24069	+	6.14399i	−0.106611	+	0.202122i
$925$		0			0
$926$	11.7845	+	20.4114i	0.387264	+	0.670760i
$927$	−1.05286	−	3.92931i	−0.0345803	−	0.129056i
$928$	−1.55139	−	5.78985i	−0.0509268	−	0.190061i
$929$	7.02379	+	12.1656i	0.230443	+	0.399139i	0.957939	−	0.286973i	$-0.0926491\pi$
$929$	7.02379	+	12.1656i	0.230443	+	0.399139i	−0.727496	+	0.686112i	$0.759316\pi$
$930$		0			0
$931$	−29.3645	−	14.0814i	−0.962383	−	0.461499i
$932$	0.857745	+	0.857745i	0.0280964	+	0.0280964i
$933$	31.7464	+	8.50643i	1.03933	+	0.278488i
$934$	5.73005	−	9.92473i	0.187493	−	0.324747i
$935$		0			0
$936$	1.49254	−	0.861717i	0.0487851	−	0.0281661i
$937$	−24.1561	+	24.1561i	−0.789145	+	0.789145i	−0.981354	−	0.192209i	$-0.938435\pi$
$937$	−24.1561	+	24.1561i	−0.789145	+	0.789145i	0.192209	+	0.981354i	$0.438435\pi$
$938$	−2.00442	−	6.47915i	−0.0654468	−	0.211552i
$939$		−	22.1831i		−	0.723918i
$940$		0			0
$941$	45.3271	+	26.1696i	1.47762	+	0.853106i	0.999680	−	0.0252856i	$-0.00804953\pi$
$941$	45.3271	+	26.1696i	1.47762	+	0.853106i	0.477942	+	0.878391i	$0.341383\pi$
$942$	−3.67471	+	0.984635i	−0.119728	+	0.0320811i
$943$	7.43137	−	27.7343i	0.241999	−	0.903152i
$944$	−7.72043			−0.251279
$945$		0			0
$946$	2.02627			0.0658796
$947$	10.0914	−	37.6614i	0.327925	−	1.22383i	−0.583414	−	0.812175i	$-0.698283\pi$
$947$	10.0914	−	37.6614i	0.327925	−	1.22383i	0.911339	−	0.411657i	$-0.135050\pi$
$948$	−8.68839	+	2.32805i	−0.282186	+	0.0756115i
$949$	−20.3775	−	11.7649i	−0.661481	−	0.381906i
$950$		0			0
$951$		−	14.3645i		−	0.465801i
$952$	−19.5307	−	4.44076i	−0.632994	−	0.143926i
$953$	−1.45944	+	1.45944i	−0.0472759	+	0.0472759i	−0.730350	−	0.683074i	$-0.760643\pi$
$953$	−1.45944	+	1.45944i	−0.0472759	+	0.0472759i	0.683074	+	0.730350i	$0.260643\pi$
$954$	7.43018	−	4.28981i	0.240561	−	0.138888i
$955$		0			0
$956$	8.07967	−	13.9944i	0.261315	−	0.452611i
$957$	15.2009	+	4.07308i	0.491376	+	0.131664i
$958$	7.15393	+	7.15393i	0.231133	+	0.231133i
$959$	18.5005	−	11.6460i	0.597412	−	0.376068i
$960$		0			0
$961$	34.5175	+	59.7861i	1.11347	+	1.92858i
$962$	−1.76530	−	6.58818i	−0.0569155	−	0.212411i
$963$	−0.729112	−	2.72108i	−0.0234953	−	0.0876856i
$964$	12.6084	+	21.8384i	0.406090	+	0.703369i
$965$		0			0
$966$	−0.518978	−	13.5695i	−0.0166978	−	0.436592i
$967$	−11.2656	−	11.2656i	−0.362279	−	0.362279i	0.502373	−	0.864651i	$-0.332461\pi$
$967$	−11.2656	−	11.2656i	−0.362279	−	0.362279i	−0.864651	+	0.502373i	$0.832461\pi$
$968$	−3.96710	−	1.06298i	−0.127508	−	0.0341655i
$969$	−17.6098	+	30.5011i	−0.565708	+	0.979836i
$970$		0			0
$971$	−8.48873	+	4.90097i	−0.272416	+	0.157280i	−0.629985	−	0.776607i	$-0.716939\pi$
$971$	−8.48873	+	4.90097i	−0.272416	+	0.157280i	0.357569	+	0.933887i	$0.383606\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−23.6342	+	7.31160i	−0.757677	+	0.234399i
$974$			36.9498i			1.18395i
$975$		0			0
$976$	4.16543	+	2.40491i	0.133332	+	0.0769793i
$977$	−47.6370	+	12.7643i	−1.52404	+	0.408366i	−0.921071	−	0.389395i	$-0.872684\pi$
$977$	−47.6370	+	12.7643i	−1.52404	+	0.408366i	−0.602973	+	0.797762i	$0.706017\pi$
$978$	1.15466	−	4.30925i	0.0369219	−	0.137794i
$979$	0.426719			0.0136380
$980$		0			0
$981$	−12.1606			−0.388258
$982$	−2.07246	+	7.73453i	−0.0661349	+	0.246819i
$983$	5.77152	−	1.54648i	0.184083	−	0.0493249i	−0.165600	−	0.986193i	$-0.552956\pi$
$983$	5.77152	−	1.54648i	0.184083	−	0.0493249i	0.349683	+	0.936868i	$0.386289\pi$
$984$	−4.84474	−	2.79711i	−0.154445	−	0.0891687i
$985$		0			0
$986$			45.3773i			1.44511i
$987$	−16.0241	+	4.95730i	−0.510053	+	0.157793i
$988$	5.66956	−	5.66956i	0.180373	−	0.180373i
$989$	−3.43050	+	1.98060i	−0.109084	+	0.0629794i
$990$		0			0
$991$	−6.52086	+	11.2945i	−0.207142	+	0.358780i	−0.950813	−	0.309765i	$-0.899749\pi$
$991$	−6.52086	+	11.2945i	−0.207142	+	0.358780i	0.743671	+	0.668546i	$0.233083\pi$
$992$	−9.66095	−	2.58864i	−0.306736	−	0.0821895i
$993$	2.04401	+	2.04401i	0.0648647	+	0.0648647i
$994$	−0.846306	−	22.1280i	−0.0268432	−	0.701859i
$995$		0			0
$996$	−5.65335	−	9.79189i	−0.179133	−	0.310268i
$997$	−5.49854	−	20.5208i	−0.174141	−	0.649901i	−0.996696	−	0.0812171i	$-0.974119\pi$
$997$	−5.49854	−	20.5208i	−0.174141	−	0.649901i	0.822556	−	0.568684i	$-0.192547\pi$
$998$	3.09724	+	11.5591i	0.0980414	+	0.365896i
$999$	1.97878	+	3.42734i	0.0626058	+	0.108436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.bc.h.157.3		16
5.2	odd	4		210.2.u.b.73.3	yes	16
5.3	odd	4		1050.2.bc.g.493.1		16
5.4	even	2		210.2.u.a.157.2	yes	16
7.5	odd	6		1050.2.bc.g.607.1		16
15.2	even	4		630.2.bv.b.73.2		16
15.14	odd	2		630.2.bv.a.577.3		16
35.4	even	6		1470.2.m.d.97.2		16
35.12	even	12		210.2.u.a.103.2	✓	16
35.17	even	12		1470.2.m.d.1273.2		16
35.19	odd	6		210.2.u.b.187.3	yes	16
35.24	odd	6		1470.2.m.e.97.3		16
35.32	odd	12		1470.2.m.e.1273.3		16
35.33	even	12	inner	1050.2.bc.h.943.3		16
105.47	odd	12		630.2.bv.a.523.3		16
105.89	even	6		630.2.bv.b.397.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.103.2	✓	16	35.12	even	12
210.2.u.a.157.2	yes	16	5.4	even	2
210.2.u.b.73.3	yes	16	5.2	odd	4
210.2.u.b.187.3	yes	16	35.19	odd	6
630.2.bv.a.523.3		16	105.47	odd	12
630.2.bv.a.577.3		16	15.14	odd	2
630.2.bv.b.73.2		16	15.2	even	4
630.2.bv.b.397.2		16	105.89	even	6
1050.2.bc.g.493.1		16	5.3	odd	4
1050.2.bc.g.607.1		16	7.5	odd	6
1050.2.bc.h.157.3		16	1.1	even	1	trivial
1050.2.bc.h.943.3		16	35.33	even	12	inner
1470.2.m.d.97.2		16	35.4	even	6
1470.2.m.d.1273.2		16	35.17	even	12
1470.2.m.e.97.3		16	35.24	odd	6
1470.2.m.e.1273.3		16	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.52756 + 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} -1.00000i q^{6} +(-2.52756 + 0.781940i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.31272 + 2.27370i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-1.21865 - 1.21865i) q^{13} +(0.101115 + 2.64382i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.95935 - 7.31238i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-2.32616 - 4.02903i) q^{19} +(-2.23906 + 1.40948i) q^{21} +(1.85647 + 1.85647i) q^{22} +(-4.95766 - 1.32840i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.49254 + 0.861717i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.57990 + 0.586601i) q^{28} -5.99410i q^{29} +(-8.66177 - 5.00088i) q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.679515 + 2.53598i) q^{33} -7.57033 q^{34} -1.00000 q^{36} +(-1.02429 + 3.82271i) q^{37} +(-4.49380 + 1.20411i) q^{38} +(-1.49254 - 0.861717i) q^{39} +5.59423i q^{41} +(0.781940 + 2.52756i) q^{42} +(0.545731 - 0.545731i) q^{43} +(2.27370 - 1.31272i) q^{44} +(-2.56627 + 4.44492i) q^{46} +(6.12372 + 1.64085i) q^{47} +(0.707107 + 0.707107i) q^{48} +(5.77714 - 3.95280i) q^{49} +(-3.78517 - 6.55610i) q^{51} +(0.446058 + 1.66471i) q^{52} +(2.22057 + 8.28728i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.23434 - 2.34017i) q^{56} +(-3.28969 - 3.28969i) q^{57} +(-5.78985 - 1.55139i) q^{58} +(-3.86022 + 6.68609i) q^{59} +(4.16543 - 2.40491i) q^{61} +(-7.07231 + 7.07231i) q^{62} +(-1.79796 + 1.94096i) q^{63} -1.00000i q^{64} +(2.27370 + 1.31272i) q^{66} +(-2.47605 + 0.663456i) q^{67} +(-1.95935 + 7.31238i) q^{68} -5.13255 q^{69} -8.36973 q^{71} +(-0.258819 + 0.965926i) q^{72} +(13.1877 - 3.53363i) q^{73} +(3.42734 + 1.97878i) q^{74} +4.65232i q^{76} +(1.54009 - 6.77339i) q^{77} +(-1.21865 + 1.21865i) q^{78} +(7.78980 - 4.49744i) q^{79} +(0.500000 - 0.866025i) q^{81} +(5.40361 + 1.44789i) q^{82} +(7.99504 + 7.99504i) q^{83} +(2.64382 - 0.101115i) q^{84} +(-0.385890 - 0.668382i) q^{86} +(-1.55139 - 5.78985i) q^{87} +(-0.679515 - 2.53598i) q^{88} +(-0.0812661 - 0.140757i) q^{89} +(4.03313 + 2.12731i) q^{91} +(3.62926 + 3.62926i) q^{92} +(-9.66095 - 2.58864i) q^{93} +(3.16987 - 5.49038i) q^{94} +(0.866025 - 0.500000i) q^{96} +(4.35278 - 4.35278i) q^{97} +(-2.32288 - 6.60335i) q^{98} +2.62544i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} + 4 q^{11} + 16 q^{13} + 16 q^{14} + 8 q^{16} + 12 q^{17} - 8 q^{19} + 8 q^{21} - 4 q^{22} - 32 q^{23} - 8 q^{24} - 12 q^{26} + 8 q^{28} - 24 q^{31} - 8 q^{33} + 16 q^{34} - 16 q^{36} + 8 q^{37} + 28 q^{38} - 12 q^{39} + 4 q^{42} + 24 q^{43} - 4 q^{46} + 24 q^{47} + 52 q^{49} + 8 q^{51} + 8 q^{52} - 44 q^{53} - 8 q^{54} + 8 q^{56} + 8 q^{57} - 48 q^{58} + 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} - 36 q^{67} + 12 q^{68} - 8 q^{69} - 32 q^{71} + 40 q^{73} - 24 q^{74} + 44 q^{77} + 16 q^{78} + 12 q^{79} + 8 q^{81} - 12 q^{82} + 16 q^{83} + 4 q^{84} - 8 q^{86} - 12 q^{87} - 8 q^{88} - 16 q^{89} + 8 q^{91} - 8 q^{92} - 40 q^{93} + 8 q^{94} - 44 q^{97} + 8 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 + 4 * q^11 + 16 * q^13 + 16 * q^14 + 8 * q^16 + 12 * q^17 - 8 * q^19 + 8 * q^21 - 4 * q^22 - 32 * q^23 - 8 * q^24 - 12 * q^26 + 8 * q^28 - 24 * q^31 - 8 * q^33 + 16 * q^34 - 16 * q^36 + 8 * q^37 + 28 * q^38 - 12 * q^39 + 4 * q^42 + 24 * q^43 - 4 * q^46 + 24 * q^47 + 52 * q^49 + 8 * q^51 + 8 * q^52 - 44 * q^53 - 8 * q^54 + 8 * q^56 + 8 * q^57 - 48 * q^58 + 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 - 36 * q^67 + 12 * q^68 - 8 * q^69 - 32 * q^71 + 40 * q^73 - 24 * q^74 + 44 * q^77 + 16 * q^78 + 12 * q^79 + 8 * q^81 - 12 * q^82 + 16 * q^83 + 4 * q^84 - 8 * q^86 - 12 * q^87 - 8 * q^88 - 16 * q^89 + 8 * q^91 - 8 * q^92 - 40 * q^93 + 8 * q^94 - 44 * q^97 + 8 * q^98

Introduction

L-functions

Modular forms

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Database

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