LMFDB - Embedded newform 845.2.o.f.357.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,4,-2,-6,6,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			357.4
Root			$-1.83163i$ of defining polynomial
Character	$\chi$	$=$	845.357
Dual form			845.2.o.f.258.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.915816 - 1.58624i) q^{2} +(-0.512942 - 1.91432i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(-1.45480 - 1.69810i) q^{5} +(-3.50634 - 0.939520i) q^{6} +(-3.06478 + 1.76945i) q^{7} +1.18163 q^{8} +(-0.803451 + 0.463873i) q^{9} +(-4.02593 + 0.752519i) q^{10} +(-3.74209 + 1.00269i) q^{11} +(-1.89870 + 1.89870i) q^{12} +6.48197i q^{14} +(-2.50449 + 3.65599i) q^{15} +(2.43703 - 4.22106i) q^{16} +(-1.95684 - 0.524334i) q^{17} +1.69929i q^{18} +(-0.139057 + 0.518968i) q^{19} +(-1.00694 + 2.85736i) q^{20} +(4.95936 + 4.95936i) q^{21} +(-1.83656 + 6.85414i) q^{22} +(-0.294095 + 0.0788026i) q^{23} +(-0.606106 - 2.26202i) q^{24} +(-0.767094 + 4.94081i) q^{25} +(-2.90402 - 2.90402i) q^{27} +(4.15240 + 2.39739i) q^{28} +(-1.71273 - 0.988843i) q^{29} +(3.50563 + 7.32093i) q^{30} +(-4.13563 + 4.13563i) q^{31} +(-3.28212 - 5.68479i) q^{32} +(3.83895 + 6.64926i) q^{33} +(-2.62382 + 2.62382i) q^{34} +(7.46336 + 2.63010i) q^{35} +(1.08858 + 0.628491i) q^{36} +(4.69189 + 2.70887i) q^{37} +(0.695857 + 0.695857i) q^{38} +(-1.71904 - 2.00652i) q^{40} +(0.174136 + 0.649884i) q^{41} +(12.4086 - 3.32487i) q^{42} +(2.28069 - 8.51164i) q^{43} +(3.71155 + 3.71155i) q^{44} +(1.95657 + 0.689498i) q^{45} +(-0.144337 + 0.538675i) q^{46} -9.75201i q^{47} +(-9.33053 - 2.50011i) q^{48} +(2.76192 - 4.78379i) q^{49} +(7.13479 + 5.74167i) q^{50} +4.01498i q^{51} +(3.16254 - 3.16254i) q^{53} +(-7.26602 + 1.94693i) q^{54} +(7.14668 + 4.89574i) q^{55} +(-3.62143 + 2.09083i) q^{56} +1.06480 q^{57} +(-3.13709 + 1.81120i) q^{58} +(-11.7449 - 3.14703i) q^{59} +(5.98642 + 0.461950i) q^{60} +(1.44316 + 2.49963i) q^{61} +(2.77263 + 10.3476i) q^{62} +(1.64160 - 2.84334i) q^{63} -2.27514 q^{64} +14.0631 q^{66} +(1.14494 - 1.98310i) q^{67} +(0.710408 + 2.65128i) q^{68} +(0.301707 + 0.522573i) q^{69} +(11.0070 - 9.43000i) q^{70} +(-4.46378 - 1.19607i) q^{71} +(-0.949380 + 0.548125i) q^{72} -14.7546 q^{73} +(8.59382 - 4.96165i) q^{74} +(9.85178 - 1.06588i) q^{75} +(0.703137 - 0.188405i) q^{76} +(9.69449 - 9.69449i) q^{77} +1.59718i q^{79} +(-10.7132 + 2.00249i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(1.19035 + 0.318953i) q^{82} -7.57341i q^{83} +(2.45944 - 9.17877i) q^{84} +(1.95645 + 4.08571i) q^{85} +(-11.4128 - 11.4128i) q^{86} +(-1.01444 + 3.78593i) q^{87} +(-4.42176 + 1.18481i) q^{88} +(-1.21762 - 4.54423i) q^{89} +(2.88556 - 2.47213i) q^{90} +(0.291695 + 0.291695i) q^{92} +(10.0383 + 5.79560i) q^{93} +(-15.4690 - 8.93105i) q^{94} +(1.08356 - 0.518863i) q^{95} +(-9.19900 + 9.19900i) q^{96} +(8.91268 + 15.4372i) q^{97} +(-5.05883 - 8.76215i) q^{98} +(2.54147 - 2.54147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.915816	−	1.58624i	0.647580	−	1.12164i	−0.336119	−	0.941819i	$-0.609115\pi$
$2$	0.915816	−	1.58624i	0.647580	−	1.12164i	0.983699	−	0.179822i	$-0.0575521\pi$
$3$	−0.512942	−	1.91432i	−0.296147	−	1.10524i	−0.940302	−	0.340341i	$-0.889458\pi$
$3$	−0.512942	−	1.91432i	−0.296147	−	1.10524i	0.644155	−	0.764895i	$-0.277209\pi$
$4$	−0.677439	−	1.17336i	−0.338719	−	0.586679i
$5$	−1.45480	−	1.69810i	−0.650608	−	0.759414i
$5$	−1.45480	−	1.69810i	−0.650608	−	0.759414i
$6$	−3.50634	−	0.939520i	−1.43146	−	0.383558i
$7$	−3.06478	+	1.76945i	−1.15838	+	0.668790i	−0.950915	−	0.309453i	$-0.899854\pi$
$7$	−3.06478	+	1.76945i	−1.15838	+	0.668790i	−0.207464	+	0.978243i	$0.566521\pi$
$8$	1.18163			0.417769
$9$	−0.803451	+	0.463873i	−0.267817	+	0.154624i
$10$	−4.02593	+	0.752519i	−1.27311	+	0.237967i
$11$	−3.74209	+	1.00269i	−1.12828	+	0.302323i	−0.774231	−	0.632903i	$-0.781863\pi$
$11$	−3.74209	+	1.00269i	−1.12828	+	0.302323i	−0.354053	+	0.935226i	$0.615197\pi$
$12$	−1.89870	+	1.89870i	−0.548108	+	0.548108i
$13$		0			0
$13$		0			0
$14$			6.48197i			1.73238i
$15$	−2.50449	+	3.65599i	−0.646656	+	0.943973i
$16$	2.43703	−	4.22106i	0.609258	−	1.05527i
$17$	−1.95684	−	0.524334i	−0.474603	−	0.127170i	0.0135853	−	0.999908i	$-0.495676\pi$
$17$	−1.95684	−	0.524334i	−0.474603	−	0.127170i	−0.488189	+	0.872738i	$0.662342\pi$
$18$			1.69929i			0.400526i
$19$	−0.139057	+	0.518968i	−0.0319019	+	0.119059i	−0.980041	−	0.198797i	$-0.936296\pi$
$19$	−0.139057	+	0.518968i	−0.0319019	+	0.119059i	0.948139	+	0.317857i	$0.102963\pi$
$20$	−1.00694	+	2.85736i	−0.225159	+	0.638926i
$21$	4.95936	+	4.95936i	1.08222	+	1.08222i
$22$	−1.83656	+	6.85414i	−0.391556	+	1.46131i
$23$	−0.294095	+	0.0788026i	−0.0613231	+	0.0164315i	−0.289350	−	0.957223i	$-0.593439\pi$
$23$	−0.294095	+	0.0788026i	−0.0613231	+	0.0164315i	0.228027	+	0.973655i	$0.426773\pi$
$24$	−0.606106	−	2.26202i	−0.123721	−	0.461733i
$25$	−0.767094	+	4.94081i	−0.153419	+	0.988161i
$26$		0			0
$27$	−2.90402	−	2.90402i	−0.558879	−	0.558879i
$28$	4.15240	+	2.39739i	0.784730	+	0.453064i
$29$	−1.71273	−	0.988843i	−0.318045	−	0.183624i	0.332476	−	0.943112i	$-0.392116\pi$
$29$	−1.71273	−	0.988843i	−0.318045	−	0.183624i	−0.650521	+	0.759488i	$0.725449\pi$
$30$	3.50563	+	7.32093i	0.640038	+	1.33661i
$31$	−4.13563	+	4.13563i	−0.742781	+	0.742781i	−0.973112	−	0.230331i	$-0.926019\pi$
$31$	−4.13563	+	4.13563i	−0.742781	+	0.742781i	0.230331	+	0.973112i	$0.426019\pi$
$32$	−3.28212	−	5.68479i	−0.580202	−	1.00494i
$33$	3.83895	+	6.64926i	0.668276	+	1.15749i
$34$	−2.62382	+	2.62382i	−0.449982	+	0.449982i
$35$	7.46336	+	2.63010i	1.26154	+	0.444569i
$36$	1.08858	+	0.628491i	0.181430	+	0.104748i
$37$	4.69189	+	2.70887i	0.771342	+	0.445335i	0.833353	−	0.552741i	$-0.186418\pi$
$37$	4.69189	+	2.70887i	0.771342	+	0.445335i	−0.0620109	+	0.998075i	$0.519751\pi$
$38$	0.695857	+	0.695857i	0.112883	+	0.112883i
$39$		0			0
$40$	−1.71904	−	2.00652i	−0.271803	−	0.317259i
$41$	0.174136	+	0.649884i	0.0271955	+	0.101495i	0.978190	−	0.207714i	$-0.0666024\pi$
$41$	0.174136	+	0.649884i	0.0271955	+	0.101495i	−0.950994	+	0.309209i	$0.899936\pi$
$42$	12.4086	−	3.32487i	1.91469	−	0.513039i
$43$	2.28069	−	8.51164i	0.347802	−	1.29801i	−0.541504	−	0.840698i	$-0.682145\pi$
$43$	2.28069	−	8.51164i	0.347802	−	1.29801i	0.889305	−	0.457314i	$-0.151189\pi$
$44$	3.71155	+	3.71155i	0.559538	+	0.559538i
$45$	1.95657	+	0.689498i	0.291668	+	0.102784i
$46$	−0.144337	+	0.538675i	−0.0212814	+	0.0794232i
$47$		−	9.75201i		−	1.42248i	−0.702951	−	0.711238i	$-0.748135\pi$
$47$		−	9.75201i		−	1.42248i	0.702951	−	0.711238i	$-0.251865\pi$
$48$	−9.33053	−	2.50011i	−1.34675	−	0.360860i
$49$	2.76192	−	4.78379i	0.394561	−	0.683399i
$50$	7.13479	+	5.74167i	1.00901	+	0.811994i
$51$			4.01498i			0.562209i
$52$		0			0
$53$	3.16254	−	3.16254i	0.434409	−	0.434409i	−0.455716	−	0.890125i	$-0.650617\pi$
$53$	3.16254	−	3.16254i	0.434409	−	0.434409i	0.890125	+	0.455716i	$0.150617\pi$
$54$	−7.26602	+	1.94693i	−0.988781	+	0.264943i
$55$	7.14668	+	4.89574i	0.963658	+	0.660141i
$56$	−3.62143	+	2.09083i	−0.483934	+	0.279399i
$57$	1.06480			0.141036
$58$	−3.13709	+	1.81120i	−0.411919	+	0.237822i
$59$	−11.7449	−	3.14703i	−1.52905	−	0.409708i	−0.606343	−	0.795203i	$-0.707364\pi$
$59$	−11.7449	−	3.14703i	−1.52905	−	0.409708i	−0.922710	+	0.385495i	$0.874031\pi$
$60$	5.98642	+	0.461950i	0.772844	+	0.0596374i
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	0.943502	−	0.331368i	$-0.107510\pi$
$61$	1.44316	+	2.49963i	0.184778	+	0.320044i	−0.758724	+	0.651412i	$0.774177\pi$
$62$	2.77263	+	10.3476i	0.352124	+	1.31414i
$63$	1.64160	−	2.84334i	0.206822	−	0.358227i
$64$	−2.27514			−0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$	1.14494	−	1.98310i	0.139877	−	0.242274i	−0.787573	−	0.616222i	$-0.788663\pi$
$67$	1.14494	−	1.98310i	0.139877	−	0.242274i	0.927450	+	0.373947i	$0.121996\pi$
$68$	0.710408	+	2.65128i	0.0861496	+	0.321515i
$69$	0.301707	+	0.522573i	0.0363213	+	0.0629104i
$70$	11.0070	−	9.43000i	1.31559	−	1.12710i
$71$	−4.46378	−	1.19607i	−0.529753	−	0.141947i	−0.0159789	−	0.999872i	$-0.505086\pi$
$71$	−4.46378	−	1.19607i	−0.529753	−	0.141947i	−0.513774	+	0.857925i	$0.671753\pi$
$72$	−0.949380	+	0.548125i	−0.111886	+	0.0645972i
$73$	−14.7546			−1.72690			−0.863449	−	0.504436i	$-0.831701\pi$
$73$	−14.7546			−1.72690			−0.863449	+	0.504436i	$0.831701\pi$
$74$	8.59382	−	4.96165i	0.999011	−	0.576780i
$75$	9.85178	−	1.06588i	1.13759	−	0.123077i
$76$	0.703137	−	0.188405i	0.0806554	−	0.0216115i
$77$	9.69449	−	9.69449i	1.10479	−	1.10479i
$78$		0			0
$79$			1.59718i			0.179696i	0.995955	+	0.0898482i	$0.0286382\pi$
$79$			1.59718i			0.179696i	−0.995955	+	0.0898482i	$0.971362\pi$
$80$	−10.7132	+	2.00249i	−1.19777	+	0.223885i
$81$	−5.46126	+	9.45918i	−0.606807	+	1.05102i
$82$	1.19035	+	0.318953i	0.131452	+	0.0352225i
$83$		−	7.57341i		−	0.831290i	−0.909527	−	0.415645i	$-0.863556\pi$
$83$		−	7.57341i		−	0.831290i	0.909527	−	0.415645i	$-0.136444\pi$
$84$	2.45944	−	9.17877i	0.268347	−	1.00149i
$85$	1.95645	+	4.08571i	0.212206	+	0.443158i
$86$	−11.4128	−	11.4128i	−1.23068	−	1.23068i
$87$	−1.01444	+	3.78593i	−0.108759	+	0.405895i
$88$	−4.42176	+	1.18481i	−0.471361	+	0.126301i
$89$	−1.21762	−	4.54423i	−0.129068	−	0.481687i	0.870884	−	0.491488i	$-0.163547\pi$
$89$	−1.21762	−	4.54423i	−0.129068	−	0.481687i	−0.999952	+	0.00980081i	$0.996880\pi$
$90$	2.88556	−	2.47213i	0.304165	−	0.260586i
$91$		0			0
$92$	0.291695	+	0.291695i	0.0304113	+	0.0304113i
$93$	10.0383	+	5.79560i	1.04092	+	0.600976i
$94$	−15.4690	−	8.93105i	−1.59551	−	0.921167i
$95$	1.08356	−	0.518863i	0.111171	−	0.0532342i
$96$	−9.19900	+	9.19900i	−0.938869	+	0.938869i
$97$	8.91268	+	15.4372i	0.904945	+	1.56741i	0.820991	+	0.570942i	$0.193422\pi$
$97$	8.91268	+	15.4372i	0.904945	+	1.56741i	0.0839547	+	0.996470i	$0.473245\pi$
$98$	−5.05883	−	8.76215i	−0.511019	−	0.885111i
$99$	2.54147	−	2.54147i	0.255427	−	0.255427i
$100$	6.31699	−	2.44702i	0.631699	−	0.244702i
$101$	3.94379	+	2.27695i	0.392421	+	0.226565i	0.683209	−	0.730223i	$-0.260584\pi$
$101$	3.94379	+	2.27695i	0.392421	+	0.226565i	−0.290787	+	0.956788i	$0.593917\pi$
$102$	6.36872	+	3.67698i	0.630597	+	0.364075i
$103$	−9.79285	−	9.79285i	−0.964918	−	0.964918i	0.0344872	−	0.999405i	$-0.489020\pi$
$103$	−9.79285	−	9.79285i	−0.964918	−	0.964918i	−0.999405	+	0.0344872i	$0.989020\pi$
$104$		0			0
$105$	1.20660	−	15.6364i	0.117752	−	1.52596i
$106$	−2.12024	−	7.91286i	−0.205936	−	0.768565i
$107$	6.82933	−	1.82991i	0.660216	−	0.176904i	0.0868725	−	0.996219i	$-0.472313\pi$
$107$	6.82933	−	1.82991i	0.660216	−	0.176904i	0.573344	+	0.819315i	$0.305646\pi$
$108$	−1.44016	+	5.37475i	−0.138580	+	0.517186i
$109$	−9.89281	−	9.89281i	−0.947560	−	0.947560i	0.0511324	−	0.998692i	$-0.483717\pi$
$109$	−9.89281	−	9.89281i	−0.947560	−	0.947560i	−0.998692	+	0.0511324i	$0.983717\pi$
$110$	14.3109	−	6.85276i	1.36449	−	0.653385i
$111$	2.77898	−	10.3713i	0.263769	−	0.984399i
$112$			17.2488i			1.62986i
$113$	−2.21438	−	0.593341i	−0.208311	−	0.0558168i	0.153154	−	0.988202i	$-0.451057\pi$
$113$	−2.21438	−	0.593341i	−0.208311	−	0.0558168i	−0.361466	+	0.932385i	$0.617723\pi$
$114$	0.975161	−	1.68903i	0.0913322	−	0.158192i
$115$	0.561666	+	0.384761i	0.0523756	+	0.0358792i
$116$			2.67952i			0.248787i
$117$		0			0
$118$	−15.7481	+	15.7481i	−1.44973	+	1.44973i
$119$	6.92507	−	1.85557i	0.634820	−	0.170099i
$120$	−2.95937	+	4.32002i	−0.270152	+	0.394362i
$121$	3.47160	−	2.00433i	0.315600	−	0.182212i
$122$	5.28668			0.478633
$123$	1.15477	−	0.666705i	0.104122	−	0.0601148i
$124$	7.65421	+	2.05094i	0.687368	+	0.184180i
$125$	9.50596	−	5.88530i	0.850239	−	0.526397i
$126$	−3.00681	−	5.20795i	−0.267868	−	0.463961i
$127$	0.332860	+	1.24225i	0.0295366	+	0.110232i	0.979120	−	0.203281i	$-0.0651606\pi$
$127$	0.332860	+	1.24225i	0.0295366	+	0.110232i	−0.949584	+	0.313513i	$0.898494\pi$
$128$	4.48062	−	7.76067i	0.396035	−	0.685953i
$129$	−17.4639			−1.53761
$130$		0			0
$131$	−5.59439			−0.488785			−0.244392	−	0.969676i	$-0.578588\pi$
$131$	−5.59439			−0.488785			−0.244392	+	0.969676i	$0.578588\pi$
$132$	5.20131	−	9.00893i	0.452716	−	0.784127i
$133$	−0.492109	−	1.83658i	−0.0426713	−	0.159251i
$134$	−2.09712	−	3.63231i	−0.181163	−	0.313784i
$135$	−0.706541	+	9.15610i	−0.0608094	+	0.788032i
$136$	−2.31226	−	0.619567i	−0.198274	−	0.0531274i
$137$	12.3757	−	7.14509i	1.05732	−	0.610446i	0.132633	−	0.991165i	$-0.457657\pi$
$137$	12.3757	−	7.14509i	1.05732	−	0.610446i	0.924691	+	0.380719i	$0.124324\pi$
$138$	1.10523			0.0940838
$139$	−15.0832	+	8.70830i	−1.27934	+	0.738629i	−0.976727	−	0.214484i	$-0.931193\pi$
$139$	−15.0832	+	8.70830i	−1.27934	+	0.738629i	−0.302615	+	0.953113i	$0.597860\pi$
$140$	−1.96992	−	10.5389i	−0.166488	−	0.890702i
$141$	−18.6685	+	5.00221i	−1.57217	+	0.421262i
$142$	−5.98525	+	5.98525i	−0.502271	+	0.502271i
$143$		0			0
$144$			4.52189i			0.376824i
$145$	0.812525	+	4.34696i	0.0674765	+	0.360995i
$146$	−13.5125	+	23.4044i	−1.11830	+	1.93696i
$147$	−10.5744	−	2.83341i	−0.872165	−	0.233696i
$148$		−	7.34036i		−	0.603374i
$149$	−3.39833	+	12.6828i	−0.278402	+	1.03901i	0.675124	+	0.737704i	$0.264090\pi$
$149$	−3.39833	+	12.6828i	−0.278402	+	1.03901i	−0.953527	+	0.301308i	$0.902577\pi$
$150$	7.33168	−	16.6034i	0.598629	−	1.35566i
$151$	−0.765191	−	0.765191i	−0.0622704	−	0.0622704i	0.675286	−	0.737556i	$-0.264020\pi$
$151$	−0.765191	−	0.765191i	−0.0622704	−	0.0622704i	−0.737556	+	0.675286i	$0.764020\pi$
$152$	−0.164314	+	0.613227i	−0.0133276	+	0.0497392i
$153$	1.81545	−	0.486448i	0.146770	−	0.0393270i
$154$	−6.49942	−	24.2562i	−0.523738	−	1.95462i
$155$	13.0392	+	1.00619i	1.04734	+	0.0808190i
$156$		0			0
$157$	3.03481	+	3.03481i	0.242204	+	0.242204i	0.817762	−	0.575557i	$-0.195215\pi$
$157$	3.03481	+	3.03481i	0.242204	+	0.242204i	−0.575557	+	0.817762i	$0.695215\pi$
$158$	2.53350	+	1.46272i	0.201555	+	0.116368i
$159$	−7.67633	−	4.43193i	−0.608773	−	0.351475i
$160$	−4.87852	+	13.8436i	−0.385681	+	1.09443i
$161$	0.761901	−	0.761901i	0.0600462	−	0.0600462i
$162$	10.0030	+	17.3257i	0.785912	+	1.36124i
$163$	1.13179	+	1.96032i	0.0886486	+	0.153544i	0.906940	−	0.421260i	$-0.138412\pi$
$163$	1.13179	+	1.96032i	0.0886486	+	0.153544i	−0.818292	+	0.574803i	$0.805079\pi$
$164$	0.644580	−	0.644580i	0.0503333	−	0.0503333i
$165$	5.70619	−	16.1923i	0.444227	−	1.26057i
$166$	−12.0133	−	6.93585i	−0.932409	−	0.538327i
$167$	−0.536563	−	0.309785i	−0.0415205	−	0.0239719i	0.479096	−	0.877762i	$-0.340965\pi$
$167$	−0.536563	−	0.309785i	−0.0415205	−	0.0239719i	−0.520617	+	0.853791i	$0.674298\pi$
$168$	5.86012	+	5.86012i	0.452118	+	0.452118i
$169$		0			0
$170$	8.27267	+	0.638370i	0.634485	+	0.0489608i
$171$	−0.129009	−	0.481470i	−0.00986560	−	0.0368189i
$172$	−11.5322	+	3.09005i	−0.879324	+	0.235614i
$173$	1.71382	−	6.39606i	0.130299	−	0.486283i	−0.869674	−	0.493627i	$-0.835671\pi$
$173$	1.71382	−	6.39606i	0.130299	−	0.486283i	0.999973	+	0.00734343i	$0.00233751\pi$
$174$	5.07636	+	5.07636i	0.384838	+	0.384838i
$175$	−6.39155	−	16.4998i	−0.483155	−	1.24727i
$176$	−4.88718	+	18.2392i	−0.368385	+	1.37483i
$177$			24.0977i			1.81130i
$178$	−8.32336	−	2.23024i	−0.623862	−	0.167163i
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	−0.822193	−	0.569209i	$-0.807250\pi$
$179$	1.09512	−	1.89680i	0.0818528	−	0.141773i	0.904046	+	0.427436i	$0.140583\pi$
$180$	−0.516426	−	2.76285i	−0.0384921	−	0.205930i
$181$		−	9.59255i		−	0.713009i	−0.934294	−	0.356504i	$-0.883969\pi$
$181$		−	9.59255i		−	0.713009i	0.934294	−	0.356504i	$-0.116031\pi$
$182$		0			0
$183$	4.04484	−	4.04484i	0.299003	−	0.299003i
$184$	−0.347511	+	0.0931154i	−0.0256189	+	0.00686456i
$185$	−2.22585	−	11.9082i	−0.163648	−	0.875506i
$186$	18.3864	−	10.6154i	1.34816	−	0.778359i
$187$	7.84842			0.573933
$188$	−11.4426	+	6.60639i	−0.834537	+	0.481820i
$189$	14.0387	+	3.76166i	1.02117	+	0.273621i
$190$	0.169300	−	2.19397i	0.0122823	−	0.159167i
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	0.790605	−	0.612326i	$-0.209766\pi$
$191$	−1.86557	−	3.23126i	−0.134988	−	0.233806i	−0.925593	+	0.378521i	$0.876433\pi$
$192$	1.16701	+	4.35536i	0.0842220	+	0.314321i
$193$	0.142043	−	0.246025i	0.0102245	−	0.0177093i	−0.860868	−	0.508829i	$-0.830079\pi$
$193$	0.142043	−	0.246025i	0.0102245	−	0.0177093i	0.871092	+	0.491119i	$0.163412\pi$
$194$	32.6495			2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$	12.9246	−	22.3860i	0.920838	−	1.59494i	0.122716	−	0.992442i	$-0.460840\pi$
$197$	12.9246	−	22.3860i	0.920838	−	1.59494i	0.798122	−	0.602496i	$-0.205827\pi$
$198$	−1.70386	−	6.35890i	−0.121088	−	0.451907i
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	0.949779	−	0.312921i	$-0.101308\pi$
$199$	2.87625	+	4.98181i	0.203892	+	0.353151i	−0.745887	+	0.666072i	$0.767974\pi$
$200$	−0.906420	+	5.83819i	−0.0640936	+	0.412823i
$201$	−4.38359	−	1.17458i	−0.309194	−	0.0828484i
$202$	7.22357	−	4.17053i	0.508248	−	0.293437i
$203$	6.99884			0.491223
$204$	4.71101	−	2.71990i	0.329836	−	0.190431i
$205$	0.850235	−	1.24115i	0.0593830	−	0.0866859i
$206$	−24.5023	+	6.56536i	−1.70715	+	0.457430i
$207$	0.199737	−	0.199737i	0.0138827	−	0.0138827i
$208$		0			0
$209$		−	2.08146i		−	0.143977i
$210$	−23.6980	−	16.2340i	−1.63532	−	1.12025i
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	−0.805118	−	0.593114i	$-0.797898\pi$
$211$	1.61372	−	2.79504i	0.111093	−	0.192418i	0.916211	+	0.400696i	$0.131232\pi$
$212$	−5.85322	−	1.56837i	−0.402001	−	0.107716i
$213$			9.15863i			0.627539i
$214$	3.35173	−	12.5088i	0.229119	−	0.855085i
$215$	−17.7716	+	8.50993i	−1.21201	+	0.580372i
$216$	−3.43147	−	3.43147i	−0.233482	−	0.233482i
$217$	5.35700	−	19.9926i	0.363657	−	1.35719i
$218$	−24.7524	+	6.63238i	−1.67644	+	0.449201i
$219$	7.56826	+	28.2451i	0.511416	+	1.90863i
$220$	0.903013	−	11.7022i	0.0608811	−	0.788961i
$221$		0			0
$222$	−13.9063	−	13.9063i	−0.933331	−	0.933331i
$223$	6.42178	+	3.70762i	0.430034	+	0.248280i	0.699361	−	0.714768i	$-0.253468\pi$
$223$	6.42178	+	3.70762i	0.430034	+	0.248280i	−0.269327	+	0.963049i	$0.586801\pi$
$224$	20.1179	+	11.6151i	1.34419	+	0.776067i
$225$	−1.67558	−	4.32553i	−0.111706	−	0.288369i
$226$	−2.96914	+	2.96914i	−0.197504	+	0.197504i
$227$	−1.95115	−	3.37949i	−0.129502	−	0.224305i	0.793981	−	0.607942i	$-0.208005\pi$
$227$	−1.95115	−	3.37949i	−0.129502	−	0.224305i	−0.923484	+	0.383637i	$0.874671\pi$
$228$	−0.721337	−	1.24939i	−0.0477717	−	0.0827430i
$229$	12.3946	−	12.3946i	0.819060	−	0.819060i	−0.166912	−	0.985972i	$-0.553379\pi$
$229$	12.3946	−	12.3946i	0.819060	−	0.819060i	0.985972	+	0.166912i	$0.0533795\pi$
$230$	1.12471	−	0.538566i	0.0741609	−	0.0355120i
$231$	−23.5311	−	13.5857i	−1.54823	−	0.893872i
$232$	−2.02381	−	1.16844i	−0.132869	−	0.0767121i
$233$	−2.88962	−	2.88962i	−0.189305	−	0.189305i	0.606090	−	0.795396i	$-0.292737\pi$
$233$	−2.88962	−	2.88962i	−0.189305	−	0.189305i	−0.795396	+	0.606090i	$0.792737\pi$
$234$		0			0
$235$	−16.5599	+	14.1873i	−1.08025	+	0.925474i
$236$	4.26384	+	15.9129i	0.277552	+	1.03584i
$237$	3.05751	−	0.819258i	0.198607	−	0.0532165i
$238$	3.39872	−	12.6842i	0.220306	−	0.822193i
$239$	−8.97299	−	8.97299i	−0.580415	−	0.580415i	0.354602	−	0.935017i	$-0.384616\pi$
$239$	−8.97299	−	8.97299i	−0.580415	−	0.580415i	−0.935017	+	0.354602i	$0.884616\pi$
$240$	9.32866	+	19.4814i	0.602162	+	1.25752i
$241$	4.54165	−	16.9497i	0.292554	−	1.09183i	−0.650587	−	0.759432i	$-0.725477\pi$
$241$	4.54165	−	16.9497i	0.292554	−	1.09183i	0.943141	−	0.332394i	$-0.107856\pi$
$242$		−	7.34239i		−	0.471986i
$243$	9.00835	+	2.41378i	0.577886	+	0.154844i
$244$	1.95530	−	3.38669i	0.125176	−	0.216810i
$245$	−12.1414	+	2.26945i	−0.775687	+	0.144990i
$246$		−	2.44232i		−	0.155716i
$247$		0			0
$248$	−4.88677	+	4.88677i	−0.310311	+	0.310311i
$249$	−14.4980	+	3.88472i	−0.918771	+	0.246184i
$250$	−0.629785	−	20.4686i	−0.0398311	−	1.29455i
$251$	−18.8524	+	10.8845i	−1.18996	+	0.687021i	−0.958296	−	0.285776i	$-0.907749\pi$
$251$	−18.8524	+	10.8845i	−1.18996	+	0.687021i	−0.231659	+	0.972797i	$0.574415\pi$
$252$	−4.44834			−0.280219
$253$	1.02152	−	0.589774i	0.0642223	−	0.0370787i
$254$	2.27535	+	0.609678i	0.142768	+	0.0382546i
$255$	6.81784	−	5.84100i	0.426950	−	0.365778i
$256$	−10.4820	−	18.1554i	−0.655125	−	1.13471i
$257$	−3.31629	−	12.3766i	−0.206864	−	0.772029i	−0.988873	−	0.148761i	$-0.952471\pi$
$257$	−3.31629	−	12.3766i	−0.206864	−	0.772029i	0.782009	−	0.623268i	$-0.214195\pi$
$258$	−15.9937	+	27.7019i	−0.995725	+	1.72465i
$259$	−19.1728			−1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$	−5.12344	+	8.87405i	−0.316527	+	0.548241i
$263$	4.27179	+	15.9426i	0.263410	+	0.983060i	0.963216	+	0.268727i	$0.0866030\pi$
$263$	4.27179	+	15.9426i	0.263410	+	0.983060i	−0.699806	+	0.714333i	$0.746730\pi$
$264$	4.53621	+	7.85695i	0.279185	+	0.483562i
$265$	−9.97120	−	0.769439i	−0.612526	−	0.0472663i
$266$	−3.36393	−	0.901363i	−0.206256	−	0.0552661i
$267$	−8.07456	+	4.66185i	−0.494155	+	0.285301i
$268$	−3.10252			−0.189516
$269$	27.9787	−	16.1535i	1.70589	−	0.984895i	0.766370	−	0.642400i	$-0.222061\pi$
$269$	27.9787	−	16.1535i	1.70589	−	0.984895i	0.939519	−	0.342495i	$-0.111272\pi$
$270$	13.8767	+	9.50605i	0.844510	+	0.578520i
$271$	16.8770	−	4.52218i	1.02521	−	0.274703i	0.293236	−	0.956040i	$-0.405268\pi$
$271$	16.8770	−	4.52218i	1.02521	−	0.274703i	0.731970	+	0.681337i	$0.238601\pi$
$272$	−6.98212	+	6.98212i	−0.423353	+	0.423353i
$273$		0			0
$274$		−	26.1743i		−	1.58125i
$275$	−2.08356	−	19.2581i	−0.125644	−	1.16131i
$276$	0.408777	−	0.708022i	0.0246055	−	0.0426179i
$277$	2.96961	+	0.795705i	0.178427	+	0.0478093i	0.346926	−	0.937892i	$-0.387225\pi$
$277$	2.96961	+	0.795705i	0.178427	+	0.0478093i	−0.168499	+	0.985702i	$0.553892\pi$
$278$			31.9008i			1.91328i
$279$	1.40437	−	5.24118i	0.0840775	−	0.313781i
$280$	8.81892	+	3.10780i	0.527031	+	0.185727i
$281$	18.6757	+	18.6757i	1.11410	+	1.11410i	0.992590	+	0.121508i	$0.0387731\pi$
$281$	18.6757	+	18.6757i	1.11410	+	1.11410i	0.121508	+	0.992590i	$0.461227\pi$
$282$	−9.16221	+	34.1938i	−0.545602	+	2.03621i
$283$	14.8164	−	3.97005i	0.880745	−	0.235995i	0.210016	−	0.977698i	$-0.432648\pi$
$283$	14.8164	−	3.97005i	0.880745	−	0.235995i	0.670728	+	0.741703i	$0.265982\pi$
$284$	1.62052	+	6.04787i	0.0961603	+	0.358875i
$285$	−1.54907	−	1.80814i	−0.0917593	−	0.107105i
$286$		0			0
$287$	−1.68363	−	1.68363i	−0.0993814	−	0.0993814i
$288$	5.27404	+	3.04497i	0.310776	+	0.179427i
$289$	−11.1681	−	6.44793i	−0.656949	−	0.379290i
$290$	7.63944	+	2.69215i	0.448603	+	0.158089i
$291$	24.9801	−	24.9801i	1.46436	−	1.46436i
$292$	9.99535	+	17.3125i	0.584934	+	1.01314i
$293$	−5.18835	−	8.98649i	−0.303107	−	0.524996i	0.673731	−	0.738976i	$-0.264691\pi$
$293$	−5.18835	−	8.98649i	−0.303107	−	0.524996i	−0.976838	+	0.213980i	$0.931357\pi$
$294$	−14.1787	+	14.1787i	−0.826919	+	0.826919i
$295$	11.7425	+	24.5223i	0.683675	+	1.42774i
$296$	5.54407	+	3.20087i	0.322243	+	0.186047i
$297$	13.7790	+	7.95528i	0.799536	+	0.461612i
$298$	17.0057	+	17.0057i	0.985111	+	0.985111i
$299$		0			0
$300$	−7.92463	−	10.8376i	−0.457529	−	0.625709i
$301$	8.07113	+	30.1219i	0.465212	+	1.73620i
$302$	−1.91455	+	0.513002i	−0.110170	+	0.0295200i
$303$	2.33588	−	8.71763i	0.134193	−	0.500814i
$304$	1.85171	+	1.85171i	0.106203	+	0.106203i
$305$	2.14510	−	6.08710i	0.122828	−	0.348546i
$306$	0.890994	−	3.32524i	0.0509347	−	0.190091i
$307$		−	2.13935i		−	0.122099i	−0.998135	−	0.0610496i	$-0.980555\pi$
$307$		−	2.13935i		−	0.122099i	0.998135	−	0.0610496i	$-0.0194448\pi$
$308$	−17.9425	−	4.80768i	−1.02237	−	0.273943i
$309$	−13.7235	+	23.7698i	−0.780704	+	1.35222i
$310$	13.5376	−	19.7619i	0.768884	−	1.12240i
$311$			3.82084i			0.216660i	0.994115	+	0.108330i	$0.0345503\pi$
$311$			3.82084i			0.216660i	−0.994115	+	0.108330i	$0.965450\pi$
$312$		0			0
$313$	3.04531	−	3.04531i	0.172131	−	0.172131i	−0.615784	−	0.787915i	$-0.711161\pi$
$313$	3.04531	−	3.04531i	0.172131	−	0.172131i	0.787915	+	0.615784i	$0.211161\pi$
$314$	7.59327	−	2.03461i	0.428513	−	0.114820i
$315$	−7.21648	+	1.34889i	−0.406603	+	0.0760014i
$316$	1.87406	−	1.08199i	0.105424	−	0.0608666i
$317$	23.1127			1.29814			0.649068	−	0.760730i	$-0.275159\pi$
$317$	23.1127			1.29814			0.649068	+	0.760730i	$0.275159\pi$
$318$	−14.0602	+	8.11767i	−0.788458	+	0.455216i
$319$	7.40069	+	1.98301i	0.414359	+	0.111027i
$320$	3.30988	+	3.86342i	0.185028	+	0.215972i
$321$	−7.00609	−	12.1349i	−0.391042	−	0.677305i
$322$	−0.510796	−	1.90632i	−0.0284656	−	0.106235i
$323$	0.544224	−	0.942624i	0.0302814	−	0.0524490i
$324$	14.7987			0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$	−13.8636	+	24.0125i	−0.766660	+	1.32789i
$328$	0.205764	+	0.767921i	0.0113614	+	0.0424013i
$329$	17.2557	+	29.8878i	0.951338	+	1.64777i
$330$	−20.4590	−	23.8806i	−1.12623	−	1.31458i
$331$	1.92894	+	0.516858i	0.106024	+	0.0284091i	0.311441	−	0.950265i	$-0.399188\pi$
$331$	1.92894	+	0.516858i	0.106024	+	0.0284091i	−0.205417	+	0.978675i	$0.565855\pi$
$332$	−8.88632	+	5.13052i	−0.487700	+	0.281574i
$333$	−5.02628			−0.275438
$334$	−0.982786	+	0.567412i	−0.0537756	+	0.0310474i
$335$	−5.03317	+	0.940791i	−0.274992	+	0.0514009i
$336$	33.0199	−	8.84765i	1.80138	−	0.482679i
$337$	−6.12727	+	6.12727i	−0.333773	+	0.333773i	−0.854018	−	0.520244i	$-0.825841\pi$
$337$	−6.12727	+	6.12727i	−0.333773	+	0.333773i	0.520244	+	0.854018i	$0.325841\pi$
$338$		0			0
$339$			4.54338i			0.246763i
$340$	3.46863	−	5.06343i	0.188113	−	0.274603i
$341$	11.3292	−	19.6227i	0.613508	−	1.06263i
$342$	−0.881876	−	0.236298i	−0.0476864	−	0.0127775i
$343$		−	5.22396i		−	0.282067i
$344$	2.69492	−	10.0576i	0.145301	−	0.542269i
$345$	0.448456	−	1.27257i	0.0241441	−	0.0685129i
$346$	−8.57614	−	8.57614i	−0.461056	−	0.461056i
$347$	−8.41384	+	31.4009i	−0.451679	+	1.68569i	0.245994	+	0.969271i	$0.420886\pi$
$347$	−8.41384	+	31.4009i	−0.451679	+	1.68569i	−0.697673	+	0.716417i	$0.745781\pi$
$348$	5.12947	−	1.37444i	0.274969	−	0.0736776i
$349$	−1.76129	−	6.57321i	−0.0942795	−	0.351856i	0.902630	−	0.430418i	$-0.141634\pi$
$349$	−1.76129	−	6.57321i	−0.0942795	−	0.351856i	−0.996909	+	0.0785620i	$0.974967\pi$
$350$	−32.0262	−	4.97228i	−1.71187	−	0.265780i
$351$		0			0
$352$	17.9821	+	17.9821i	0.958448	+	0.958448i
$353$	−23.6652	−	13.6631i	−1.25957	−	0.727213i	−0.286579	−	0.958057i	$-0.592518\pi$
$353$	−23.6652	−	13.6631i	−1.25957	−	0.727213i	−0.972991	+	0.230843i	$0.925852\pi$
$354$	38.2248	+	22.0691i	2.03163	+	1.17296i
$355$	4.46288	+	9.31999i	0.236865	+	0.494654i
$356$	−4.50714	+	4.50714i	−0.238878	+	0.238878i
$357$	−7.10431	−	12.3050i	−0.376000	−	0.651251i
$358$	−2.00585	−	3.47423i	−0.106012	−	0.183619i
$359$	3.89871	−	3.89871i	0.205766	−	0.205766i	−0.596699	−	0.802465i	$-0.703521\pi$
$359$	3.89871	−	3.89871i	0.205766	−	0.205766i	0.802465	+	0.596699i	$0.203521\pi$
$360$	2.31193	+	0.814730i	0.121850	+	0.0429400i
$361$	16.2045	+	9.35567i	0.852868	+	0.492404i
$362$	−15.2161	−	8.78501i	−0.799740	−	0.461730i
$363$	−5.61766	−	5.61766i	−0.294851	−	0.294851i
$364$		0			0
$365$	21.4651	+	25.0548i	1.12353	+	1.31143i
$366$	−2.71176	−	10.1204i	−0.141746	−	0.529003i
$367$	−17.4595	+	4.67826i	−0.911378	+	0.244203i	−0.683896	−	0.729579i	$-0.739716\pi$
$367$	−17.4595	+	4.67826i	−0.911378	+	0.244203i	−0.227482	+	0.973782i	$0.573049\pi$
$368$	−0.384089	+	1.43344i	−0.0200220	+	0.0747232i
$369$	−0.441373	−	0.441373i	−0.0229770	−	0.0229770i
$370$	−20.9277	−	7.37496i	−1.08798	−	0.383406i
$371$	−4.09653	+	15.2885i	−0.212681	+	0.793738i
$372$		−	15.7046i		−	0.814248i
$373$	−14.9855	−	4.01536i	−0.775921	−	0.207907i	−0.150936	−	0.988544i	$-0.548229\pi$
$373$	−14.9855	−	4.01536i	−0.775921	−	0.207907i	−0.624986	+	0.780636i	$0.714895\pi$
$374$	7.18771	−	12.4495i	0.371668	−	0.643747i
$375$	−16.1424	−	15.1787i	−0.833588	−	0.783823i
$376$		−	11.5232i		−	0.594266i
$377$		0			0
$378$	18.8238	−	18.8238i	0.968191	−	0.968191i
$379$	20.6393	−	5.53029i	1.06017	−	0.284072i	0.313722	−	0.949515i	$-0.398424\pi$
$379$	20.6393	−	5.53029i	1.06017	−	0.284072i	0.746449	+	0.665443i	$0.231757\pi$
$380$	−1.34286	−	0.919906i	−0.0688871	−	0.0471902i
$381$	2.20733	−	1.27440i	0.113085	−	0.0652897i
$382$	−6.83407			−0.349661
$383$	16.8072	−	9.70362i	0.858806	−	0.495832i	−0.00480620	−	0.999988i	$-0.501530\pi$
$383$	16.8072	−	9.70362i	0.858806	−	0.495832i	0.863612	+	0.504157i	$0.168197\pi$
$384$	−17.1547	−	4.59660i	−0.875424	−	0.234569i
$385$	−30.5658	−	2.35865i	−1.55778	−	0.120208i
$386$	−0.260170	−	0.450628i	−0.0132423	−	0.0229364i
$387$	2.11590	+	7.89664i	0.107557	+	0.401409i
$388$	12.0756	−	20.9155i	0.613045	−	1.06182i
$389$	14.8591			0.753387			0.376693	−	0.926338i	$-0.377061\pi$
$389$	14.8591			0.753387			0.376693	+	0.926338i	$0.377061\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$	3.26357	−	5.65266i	0.164835	−	0.285503i
$393$	2.86960	+	10.7095i	0.144752	+	0.540222i
$394$	−23.6731	−	41.0030i	−1.19263	−	2.06570i
$395$	2.71217	−	2.32358i	0.136464	−	0.116912i
$396$	−4.70374	−	1.26036i	−0.236372	−	0.0633357i
$397$	−4.57070	+	2.63889i	−0.229397	+	0.132442i	−0.610294	−	0.792175i	$-0.708949\pi$
$397$	−4.57070	+	2.63889i	−0.229397	+	0.132442i	0.380897	+	0.924617i	$0.375615\pi$
$398$	10.5365			0.528145
$399$	−3.26338	+	1.88411i	−0.163373	+	0.0943236i
$400$	18.9860	+	15.2789i	0.949301	+	0.763943i
$401$	26.9289	−	7.21557i	1.34476	−	0.360328i	0.486564	−	0.873645i	$-0.338250\pi$
$401$	26.9289	−	7.21557i	1.34476	−	0.360328i	0.858199	+	0.513317i	$0.171583\pi$
$402$	−5.87772	+	5.87772i	−0.293154	+	0.293154i
$403$		0			0
$404$		−	6.16996i		−	0.306967i
$405$	24.0077	−	4.48748i	1.19295	−	0.222985i
$406$	6.40965	−	11.1018i	0.318106	−	0.550975i
$407$	−20.2737	−	5.43231i	−1.00493	−	0.269270i
$408$			4.74421i			0.234873i
$409$	−0.682016	+	2.54532i	−0.0337235	+	0.125858i	−0.980736	−	0.195340i	$-0.937419\pi$
$409$	−0.682016	+	2.54532i	−0.0337235	+	0.125858i	0.947012	+	0.321198i	$0.104086\pi$
$410$	−1.19011	−	2.48535i	−0.0587753	−	0.122742i
$411$	−20.0260	−	20.0260i	−0.987810	−	0.987810i
$412$	−4.85646	+	18.1246i	−0.239261	+	0.892933i
$413$	41.5640	−	11.1370i	2.04523	−	0.548018i
$414$	−0.133908	−	0.499753i	−0.00658124	−	0.0245615i
$415$	−12.8604	+	11.0178i	−0.631293	+	0.540844i
$416$		0			0
$417$	24.4073	+	24.4073i	1.19523	+	1.19523i
$418$	−3.30169	−	1.90623i	−0.161491	−	0.0932368i
$419$	17.0348	+	9.83506i	0.832205	+	0.480474i	0.854607	−	0.519275i	$-0.173798\pi$
$419$	17.0348	+	9.83506i	0.832205	+	0.480474i	−0.0224018	+	0.999749i	$0.507131\pi$
$420$	−19.1645	+	9.17692i	−0.935131	+	0.447788i
$421$	−10.4427	+	10.4427i	−0.508948	+	0.508948i	−0.914203	−	0.405256i	$-0.867183\pi$
$421$	−10.4427	+	10.4427i	−0.508948	+	0.508948i	0.405256	+	0.914203i	$0.367183\pi$
$422$	−2.95573	−	5.11948i	−0.143883	−	0.249212i
$423$	4.52369	+	7.83526i	0.219949	+	0.380964i
$424$	3.73695	−	3.73695i	0.181482	−	0.181482i
$425$	4.09171	−	9.26615i	0.198477	−	0.449474i
$426$	14.5278	+	8.38762i	0.703874	+	0.406382i
$427$	−8.84594	−	5.10721i	−0.428085	−	0.247155i
$428$	−6.77359	−	6.77359i	−0.327414	−	0.327414i
$429$		0			0
$430$	−2.77671	+	35.9835i	−0.133905	+	1.73528i
$431$	4.43419	+	16.5486i	0.213587	+	0.797119i	0.986659	+	0.162800i	$0.0520526\pi$
$431$	4.43419	+	16.5486i	0.213587	+	0.797119i	−0.773072	+	0.634319i	$0.781281\pi$
$432$	−19.3352	+	5.18086i	−0.930267	+	0.249264i
$433$	−2.90826	+	10.8538i	−0.139762	+	0.521599i	0.860171	+	0.510006i	$0.170357\pi$
$433$	−2.90826	+	10.8538i	−0.139762	+	0.521599i	−0.999933	+	0.0115927i	$0.996310\pi$
$434$	−26.8070	−	26.8070i	−1.28678	−	1.28678i
$435$	7.90470	−	3.78517i	0.379002	−	0.181485i
$436$	−4.90604	+	18.3096i	−0.234957	+	0.876870i
$437$		−	0.163584i		−	0.00782528i
$438$	51.7347	+	13.8623i	2.47198	+	0.662365i
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	−0.912215	−	0.409712i	$-0.865629\pi$
$439$	−2.12218	+	3.67572i	−0.101286	+	0.175432i	0.810929	+	0.585145i	$0.198962\pi$
$440$	8.44472	+	5.78494i	0.402586	+	0.275786i
$441$			5.12473i			0.244035i
$442$		0			0
$443$	15.1569	−	15.1569i	0.720126	−	0.720126i	−0.248505	−	0.968631i	$-0.579939\pi$
$443$	15.1569	−	15.1569i	0.720126	−	0.720126i	0.968631	+	0.248505i	$0.0799392\pi$
$444$	−14.0518	+	3.76518i	−0.666870	+	0.178687i
$445$	−5.94516	+	8.67861i	−0.281828	+	0.411405i
$446$	11.7623	−	6.79099i	0.556963	−	0.321563i
$447$	26.0221			1.23080
$448$	6.97281	−	4.02575i	0.329434	−	0.190199i
$449$	14.0521	+	3.76524i	0.663158	+	0.177693i	0.574671	−	0.818385i	$-0.305130\pi$
$449$	14.0521	+	3.76524i	0.663158	+	0.177693i	0.0884873	+	0.996077i	$0.471797\pi$
$450$	−8.39586	−	1.30351i	−0.395785	−	0.0614483i
$451$	−1.30327	−	2.25732i	−0.0613684	−	0.106293i
$452$	0.803904	+	3.00021i	0.0378124	+	0.141118i
$453$	−1.07233	+	1.85732i	−0.0503822	+	0.0872646i
$454$	−7.14758			−0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$	15.1476	−	26.2365i	0.708576	−	1.22729i	−0.256809	−	0.966462i	$-0.582671\pi$
$457$	15.1476	−	26.2365i	0.708576	−	1.22729i	0.965385	−	0.260828i	$-0.0839956\pi$
$458$	−8.30966	−	31.0121i	−0.388285	−	1.44910i
$459$	4.16003	+	7.20538i	0.194173	+	0.336318i
$460$	0.0709688	−	0.919687i	0.00330894	−	0.0428806i
$461$	6.70146	+	1.79565i	0.312118	+	0.0836318i	0.411478	−	0.911420i	$-0.365013\pi$
$461$	6.70146	+	1.79565i	0.312118	+	0.0836318i	−0.0993596	+	0.995052i	$0.531679\pi$
$462$	−43.1003	+	24.8840i	−2.00521	+	1.15771i
$463$	−31.4463			−1.46143			−0.730717	−	0.682680i	$-0.760814\pi$
$463$	−31.4463			−1.46143			−0.730717	+	0.682680i	$0.760814\pi$
$464$	−8.34794	+	4.81968i	−0.387543	+	0.223748i
$465$	−4.76220	−	25.4775i	−0.220842	−	1.18149i
$466$	−7.22999	+	1.93727i	−0.334923	+	0.0897423i
$467$	3.69622	−	3.69622i	0.171041	−	0.171041i	−0.616396	−	0.787436i	$-0.711408\pi$
$467$	3.69622	−	3.69622i	0.171041	−	0.171041i	0.787436	+	0.616396i	$0.211408\pi$
$468$		0			0
$469$			8.10369i			0.374194i
$470$	7.33857	+	39.2609i	0.338503	+	1.81097i
$471$	4.25293	−	7.36630i	0.195965	−	0.339421i
$472$	−13.8781	−	3.71862i	−0.638790	−	0.171163i
$473$			34.1382i			1.56968i
$474$	1.50058	−	5.60024i	0.0689239	−	0.257227i
$475$	−2.45745	−	1.08515i	−0.112755	−	0.0497901i
$476$	−6.86855	−	6.86855i	−0.314820	−	0.314820i
$477$	−1.07393	+	4.00797i	−0.0491720	+	0.183512i
$478$	−22.4509	+	6.01571i	−1.02688	+	0.275152i
$479$	5.00904	+	18.6940i	0.228869	+	0.854150i	0.980818	+	0.194928i	$0.0624474\pi$
$479$	5.00904	+	18.6940i	0.228869	+	0.854150i	−0.751949	+	0.659222i	$0.770886\pi$
$480$	29.0036	+	2.23810i	1.32383	+	0.102155i
$481$		0			0
$482$	−22.7270	−	22.7270i	−1.03518	−	1.03518i
$483$	−1.84934	−	1.06771i	−0.0841477	−	0.0485827i
$484$	−4.70359	−	2.71562i	−0.213800	−	0.123437i
$485$	13.2477	−	37.5927i	0.601549	−	1.70700i
$486$	12.0788	−	12.0788i	0.547907	−	0.547907i
$487$	−11.6813	−	20.2327i	−0.529332	−	0.916830i	−0.999415	−	0.0342077i	$-0.989109\pi$
$487$	−11.6813	−	20.2327i	−0.529332	−	0.916830i	0.470083	−	0.882622i	$-0.344224\pi$
$488$	1.70528	+	2.95363i	0.0771943	+	0.133704i
$489$	3.17214	−	3.17214i	0.143449	−	0.143449i
$490$	−7.51941	+	21.3376i	−0.339692	+	0.963935i
$491$	−18.4624	−	10.6593i	−0.833198	−	0.481047i	0.0217482	−	0.999763i	$-0.493077\pi$
$491$	−18.4624	−	10.6593i	−0.833198	−	0.481047i	−0.854946	+	0.518716i	$0.826410\pi$
$492$	−1.56457	−	0.903303i	−0.0705362	−	0.0407241i
$493$	2.83305	+	2.83305i	0.127594	+	0.127594i
$494$		0			0
$495$	−8.01301	−	0.618334i	−0.360158	−	0.0277920i
$496$	7.37809	+	27.5354i	0.331286	+	1.23638i
$497$	15.7969	−	4.23276i	0.708587	−	0.189865i
$498$	−7.11538	+	26.5549i	−0.318848	+	1.18996i
$499$	23.0389	+	23.0389i	1.03136	+	1.03136i	0.999492	+	0.0318687i	$0.0101459\pi$
$499$	23.0389	+	23.0389i	1.03136	+	1.03136i	0.0318687	+	0.999492i	$0.489854\pi$
$500$	−13.3453	−	7.16697i	−0.596818	−	0.320516i
$501$	−0.317803	+	1.18606i	−0.0141984	+	0.0529891i
$502$			39.8727i			1.77960i
$503$	−0.634433	−	0.169996i	−0.0282879	−	0.00757973i	0.244647	−	0.969612i	$-0.421328\pi$
$503$	−0.634433	−	0.169996i	−0.0282879	−	0.00757973i	−0.272935	+	0.962032i	$0.587994\pi$
$504$	1.93976	−	3.35977i	0.0864039	−	0.149656i
$505$	−1.87095	−	10.0095i	−0.0832561	−	0.445415i
$506$		−	2.16050i		−	0.0960458i
$507$		0			0
$508$	1.23211	−	1.23211i	0.0546662	−	0.0546662i
$509$	−30.9400	+	8.29035i	−1.37139	+	0.367463i	−0.867987	−	0.496587i	$-0.834586\pi$
$509$	−30.9400	+	8.29035i	−1.37139	+	0.367463i	−0.503405	+	0.864050i	$0.667920\pi$
$510$	−3.02135	−	16.1640i	−0.133787	−	0.715754i
$511$	45.2197	−	26.1076i	2.00040	−	1.15493i
$512$	−20.4758			−0.904912
$513$	1.91092	−	1.10327i	0.0843690	−	0.0487105i
$514$	−22.6693	−	6.07422i	−0.999901	−	0.267923i
$515$	−2.38258	+	30.8759i	−0.104989	+	1.36056i
$516$	11.8307	+	20.4914i	0.520818	+	0.902084i
$517$	9.77825	+	36.4929i	0.430047	+	1.60496i
$518$	−17.5588	+	30.4127i	−0.771489	+	1.33626i
$519$	−13.1232			−0.576046
$520$		0			0
$521$	−23.4746			−1.02844			−0.514220	−	0.857658i	$-0.671919\pi$
$521$	−23.4746			−1.02844			−0.514220	+	0.857658i	$0.671919\pi$
$522$	1.68033	−	2.91042i	0.0735461	−	0.127386i
$523$	6.40400	+	23.9001i	0.280027	+	1.04508i	0.952397	+	0.304861i	$0.0986099\pi$
$523$	6.40400	+	23.9001i	0.280027	+	1.04508i	−0.672370	+	0.740216i	$0.734723\pi$
$524$	3.78986	+	6.56423i	0.165561	+	0.286760i
$525$	−28.3075	+	20.6989i	−1.23544	+	0.903376i
$526$	29.2009	+	7.82436i	1.27322	+	0.341158i
$527$	10.2612	−	5.92431i	0.446985	−	0.258067i
$528$	37.4226			1.62861
$529$	−19.8383	+	11.4536i	−0.862535	+	0.497985i
$530$	−10.3523	+	15.1120i	−0.449675	+	0.656425i
$531$	10.8963	−	2.91964i	0.472857	−	0.126702i
$532$	−1.82159	+	1.82159i	−0.0789759	+	0.0789759i
$533$		0			0
$534$			17.0776i			0.739019i
$535$	−13.0427	−	8.93473i	−0.563885	−	0.386282i
$536$	1.35290	−	2.34329i	0.0584363	−	0.101215i
$537$	−4.19281	−	1.12346i	−0.180933	−	0.0484809i
$538$		−	59.1745i		−	2.55119i
$539$	−5.53871	+	20.6708i	−0.238569	+	0.890353i
$540$	11.2220	−	5.37367i	0.482919	−	0.231246i
$541$	27.6908	+	27.6908i	1.19052	+	1.19052i	0.976922	+	0.213597i	$0.0685180\pi$
$541$	27.6908	+	27.6908i	1.19052	+	1.19052i	0.213597	+	0.976922i	$0.431482\pi$
$542$	8.28297	−	30.9125i	0.355784	−	1.32780i
$543$	−18.3632	+	4.92042i	−0.788042	+	0.211155i
$544$	3.44185	+	12.8452i	0.147568	+	0.550731i
$545$	−2.40690	+	31.1911i	−0.103100	+	1.33608i
$546$		0			0
$547$	6.53914	+	6.53914i	0.279593	+	0.279593i	0.832947	−	0.553353i	$-0.186652\pi$
$547$	6.53914	+	6.53914i	0.279593	+	0.279593i	−0.553353	+	0.832947i	$0.686652\pi$
$548$	−16.7675	−	9.68071i	−0.716272	−	0.413540i
$549$	−2.31902	−	1.33889i	−0.0989733	−	0.0571422i
$550$	−32.4562	−	14.3319i	−1.38394	−	0.611113i
$551$	0.751344	−	0.751344i	0.0320083	−	0.0320083i
$552$	0.356506	+	0.617486i	0.0151739	+	0.0262820i
$553$	−2.82613	−	4.89500i	−0.120179	−	0.208156i
$554$	3.98180	−	3.98180i	0.169170	−	0.169170i
$555$	−21.6544	+	10.3692i	−0.919177	+	0.440148i
$556$	20.4359	+	11.7987i	0.866676	+	0.500375i
$557$	14.0717	+	8.12429i	0.596237	+	0.344237i	0.767560	−	0.640978i	$-0.221471\pi$
$557$	14.0717	+	8.12429i	0.596237	+	0.344237i	−0.171323	+	0.985215i	$0.554804\pi$
$558$	−7.02763	−	7.02763i	−0.297503	−	0.297503i
$559$		0			0
$560$	29.2903	−	25.0937i	1.23774	−	1.06040i
$561$	−4.02578	−	15.0244i	−0.169969	−	0.634332i
$562$	46.7277	−	12.5206i	1.97109	−	0.528151i
$563$	−8.41827	+	31.4174i	−0.354788	+	1.32409i	0.525964	+	0.850507i	$0.323705\pi$
$563$	−8.41827	+	31.4174i	−0.354788	+	1.32409i	−0.880751	+	0.473579i	$0.842962\pi$
$564$	18.5161	+	18.5161i	0.779670	+	0.779670i
$565$	2.21393	+	4.62343i	0.0931408	+	0.194509i
$566$	7.27167	−	27.1382i	0.305651	−	1.14071i
$567$		−	38.6538i		−	1.62331i
$568$	−5.27453	−	1.41331i	−0.221314	−	0.0593010i
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	0.284203	+	0.958764i	$0.408271\pi$
$569$	−16.4164	+	28.4341i	−0.688212	+	1.19202i	−0.972416	+	0.233255i	$0.925062\pi$
$570$	−4.28681	+	0.801283i	−0.179555	+	0.0335620i
$571$			31.7967i			1.33065i	0.746554	+	0.665325i	$0.231707\pi$
$571$			31.7967i			1.33065i	−0.746554	+	0.665325i	$0.768293\pi$
$572$		0			0
$573$	−5.22875	+	5.22875i	−0.218434	+	0.218434i
$574$	−4.21253	+	1.12874i	−0.175828	+	0.0471129i
$575$	−0.163750	−	1.51352i	−0.00682883	−	0.0631180i
$576$	1.82796	−	1.05538i	0.0761652	−	0.0439740i
$577$	−39.9389			−1.66268			−0.831338	−	0.555767i	$-0.812425\pi$
$577$	−39.9389			−1.66268			−0.831338	+	0.555767i	$0.812425\pi$
$578$	−20.4559	+	11.8102i	−0.850854	+	0.491241i
$579$	−0.543832	−	0.145719i	−0.0226009	−	0.00605589i
$580$	4.55010	−	3.89818i	0.188933	−	0.161863i
$581$	13.4008	+	23.2109i	0.555959	+	0.962949i
$582$	−16.7473	−	62.5017i	−0.694197	−	2.59078i
$583$	−8.66348	+	15.0056i	−0.358805	+	0.621468i
$584$	−17.4345			−0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$	−9.32773	+	16.1561i	−0.384997	+	0.666834i	−0.991769	−	0.128042i	$-0.959131\pi$
$587$	−9.32773	+	16.1561i	−0.384997	+	0.666834i	0.606772	+	0.794876i	$0.292464\pi$
$588$	3.83892	+	14.3271i	0.158315	+	0.590838i
$589$	−1.57117	−	2.72135i	−0.0647389	−	0.112131i
$590$	49.6522	+	3.83147i	2.04415	+	0.157739i
$591$	−49.4837	−	13.2591i	−2.03549	−	0.545407i
$592$	22.8686	−	13.2032i	0.939893	−	0.542647i
$593$	−8.65172			−0.355284			−0.177642	−	0.984095i	$-0.556847\pi$
$593$	−8.65172			−0.355284			−0.177642	+	0.984095i	$0.556847\pi$
$594$	25.2380	−	14.5712i	1.03553	−	0.597862i
$595$	−13.2256	−	9.05998i	−0.542195	−	0.371423i
$596$	17.1836	−	4.60433i	0.703867	−	0.188601i
$597$	8.06145	−	8.06145i	0.329933	−	0.329933i
$598$		0			0
$599$		−	35.1779i		−	1.43733i	−0.695356	−	0.718666i	$-0.744753\pi$
$599$		−	35.1779i		−	1.43733i	0.695356	−	0.718666i	$-0.255247\pi$
$600$	11.6411	−	1.25947i	0.475247	−	0.0514177i
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	−0.0902170	−	0.995922i	$-0.528756\pi$
$601$	20.0384	−	34.7076i	0.817385	−	1.41575i	0.907602	−	0.419831i	$-0.137911\pi$
$602$	55.1722	+	14.7834i	2.24865	+	0.602524i
$603$			2.12443i			0.0865136i
$604$	−0.379473	+	1.41621i	−0.0154405	+	0.0576249i
$605$	−8.45405	−	2.97922i	−0.343706	−	0.121123i
$606$	−11.6890	−	11.6890i	−0.474834	−	0.474834i
$607$	11.1449	−	41.5934i	0.452358	−	1.68822i	−0.243384	−	0.969930i	$-0.578258\pi$
$607$	11.1449	−	41.5934i	0.452358	−	1.68822i	0.695742	−	0.718292i	$-0.255076\pi$
$608$	3.40662	−	0.912802i	0.138157	−	0.0370190i
$609$	−3.59000	−	13.3981i	−0.145474	−	0.542917i
$610$	−7.69108	−	8.97731i	−0.311403	−	0.363481i
$611$		0			0
$612$	−1.80063	−	1.80063i	−0.0727863	−	0.0727863i
$613$	17.5625	+	10.1397i	0.709344	+	0.409540i	0.810818	−	0.585298i	$-0.199022\pi$
$613$	17.5625	+	10.1397i	0.709344	+	0.409540i	−0.101474	+	0.994838i	$0.532356\pi$
$614$	−3.39352	−	1.95925i	−0.136952	−	0.0790690i
$615$	−2.81209	−	0.990986i	−0.113394	−	0.0399604i
$616$	11.4553	−	11.4553i	0.461546	−	0.461546i
$617$	4.33527	+	7.50891i	0.174531	+	0.302297i	0.939999	−	0.341177i	$-0.110826\pi$
$617$	4.33527	+	7.50891i	0.174531	+	0.302297i	−0.765468	+	0.643474i	$0.777492\pi$
$618$	25.1365	+	43.5376i	1.01114	+	1.75134i
$619$	21.3034	−	21.3034i	0.856257	−	0.856257i	−0.134638	−	0.990895i	$-0.542987\pi$
$619$	21.3034	−	21.3034i	0.856257	−	0.856257i	0.990895	+	0.134638i	$0.0429871\pi$
$620$	−7.65267	−	15.9813i	−0.307339	−	0.641826i
$621$	1.08290	+	0.625215i	0.0434554	+	0.0250890i
$622$	6.06077	+	3.49919i	0.243015	+	0.140305i
$623$	11.7725	+	11.7725i	0.471657	+	0.471657i
$624$		0			0
$625$	−23.8231	−	7.58013i	−0.952925	−	0.303205i
$626$	−2.04165	−	7.61954i	−0.0816007	−	0.304538i
$627$	−3.98458	+	1.06767i	−0.159129	+	0.0426385i
$628$	1.50502	−	5.61682i	0.0600569	−	0.224136i
$629$	−7.76093	−	7.76093i	−0.309449	−	0.309449i
$630$	−4.46931	+	12.6824i	−0.178061	+	0.505279i
$631$	−7.35050	+	27.4324i	−0.292619	+	1.09207i	0.650472	+	0.759531i	$0.274571\pi$
$631$	−7.35050	+	27.4324i	−0.292619	+	1.09207i	−0.943090	+	0.332537i	$0.892095\pi$
$632$			1.88727i			0.0750715i
$633$	−6.17835	−	1.65548i	−0.245567	−	0.0657996i
$634$	21.1670	−	36.6622i	0.840647	−	1.45604i
$635$	1.62522	−	2.37246i	0.0644950	−	0.0941483i
$636$			12.0094i			0.476206i
$637$		0			0
$638$	9.92320	−	9.92320i	0.392863	−	0.392863i
$639$	4.14125	−	1.10965i	0.163825	−	0.0438969i
$640$	−19.6968	+	3.68169i	−0.778585	+	0.145532i
$641$	−14.1756	+	8.18429i	−0.559903	+	0.323260i	−0.753107	−	0.657899i	$-0.771446\pi$
$641$	−14.1756	+	8.18429i	−0.559903	+	0.323260i	0.193204	+	0.981159i	$0.438112\pi$
$642$	−25.6652			−1.01292
$643$	−35.5518	+	20.5258i	−1.40203	+	0.809460i	−0.994600	−	0.103779i	$-0.966907\pi$
$643$	−35.5518	+	20.5258i	−1.40203	+	0.809460i	−0.407425	+	0.913239i	$0.633573\pi$
$644$	−1.41012	−	0.377841i	−0.0555666	−	0.0148890i
$645$	25.4065	+	29.6555i	1.00038	+	1.16768i
$646$	−0.996819	−	1.72654i	−0.0392193	−	0.0679298i
$647$	−0.733807	−	2.73861i	−0.0288489	−	0.107666i	0.950000	−	0.312250i	$-0.101083\pi$
$647$	−0.733807	−	2.73861i	−0.0288489	−	0.107666i	−0.978849	+	0.204584i	$0.934416\pi$
$648$	−6.45318	+	11.1772i	−0.253505	+	0.439083i
$649$	47.1059			1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$	1.53344	−	2.65599i	0.0600540	−	0.104017i
$653$	0.324978	+	1.21283i	0.0127174	+	0.0474619i	0.971993	−	0.235010i	$-0.0755123\pi$
$653$	0.324978	+	1.21283i	0.0127174	+	0.0474619i	−0.959276	+	0.282472i	$0.908846\pi$
$654$	25.3930	+	43.9820i	0.992947	+	1.71983i
$655$	8.13874	+	9.49985i	0.318007	+	0.371190i
$656$	3.16758	+	0.848749i	0.123673	+	0.0331381i
$657$	11.8546	−	6.84427i	0.462493	−	0.267020i
$658$	63.2122			2.46427
$659$	−8.09916	+	4.67605i	−0.315498	+	0.182153i	−0.649384	−	0.760460i	$-0.724973\pi$
$659$	−8.09916	+	4.67605i	−0.315498	+	0.182153i	0.333886	+	0.942613i	$0.391640\pi$
$660$	−22.8650	+	4.27387i	−0.890017	+	0.166360i
$661$	−24.7963	+	6.64415i	−0.964464	+	0.258427i	−0.706489	−	0.707724i	$-0.749722\pi$
$661$	−24.7963	+	6.64415i	−0.964464	+	0.258427i	−0.257975	+	0.966152i	$0.583055\pi$
$662$	2.58641	−	2.58641i	0.100524	−	0.100524i
$663$		0			0
$664$		−	8.94896i		−	0.347287i
$665$	−2.40277	+	3.50751i	−0.0931755	+	0.136015i
$666$	−4.60315	+	7.97288i	−0.178368	+	0.308943i
$667$	0.581628	+	0.155847i	0.0225207	+	0.00603441i
$668$			0.839440i			0.0324789i
$669$	3.80358	−	14.1952i	0.147055	−	0.548817i
$670$	−3.11714	+	8.84541i	−0.120426	+	0.341728i
$671$	−7.90679	−	7.90679i	−0.305238	−	0.305238i
$672$	11.9157	−	44.4701i	0.459660	−	1.71547i
$673$	−39.9267	+	10.6983i	−1.53906	+	0.412390i	−0.925962	−	0.377617i	$-0.876744\pi$
$673$	−39.9267	+	10.6983i	−1.53906	+	0.412390i	−0.613098	+	0.790007i	$0.710077\pi$
$674$	4.10787	+	15.3308i	0.158229	+	0.590519i
$675$	16.5759	−	12.1205i	0.638005	−	0.466520i
$676$		0			0
$677$	15.5322	+	15.5322i	0.596950	+	0.596950i	0.939500	−	0.342549i	$-0.111290\pi$
$677$	15.5322	+	15.5322i	0.596950	+	0.596950i	−0.342549	+	0.939500i	$0.611290\pi$
$678$	7.20690	+	4.16090i	0.276779	+	0.159799i
$679$	−54.6308	−	31.5411i	−2.09654	−	1.21044i
$680$	2.31179	+	4.82779i	0.0886531	+	0.185137i
$681$	−5.46862	+	5.46862i	−0.209558	+	0.209558i
$682$	−20.7508	−	35.9415i	−0.794591	−	1.37627i
$683$	−3.32652	−	5.76170i	−0.127286	−	0.220465i	0.795338	−	0.606166i	$-0.207293\pi$
$683$	−3.32652	−	5.76170i	−0.127286	−	0.220465i	−0.922624	+	0.385700i	$0.873960\pi$
$684$	−0.477541	+	0.477541i	−0.0182592	+	0.0182592i
$685$	−30.1372	−	10.6204i	−1.15148	−	0.405785i
$686$	−8.28646	−	4.78419i	−0.316378	−	0.182661i
$687$	−30.0851	−	17.3696i	−1.14782	−	0.662692i
$688$	−30.3701	−	30.3701i	−1.15785	−	1.15785i
$689$		0			0
$690$	−1.60790	−	1.87680i	−0.0612117	−	0.0714485i
$691$	−9.73848	−	36.3445i	−0.370469	−	1.38261i	−0.859853	−	0.510542i	$-0.829445\pi$
$691$	−9.73848	−	36.3445i	−0.370469	−	1.38261i	0.489384	−	0.872069i	$-0.337222\pi$
$692$	−8.66588	+	2.32201i	−0.329427	+	0.0882698i
$693$	−3.29204	+	12.2861i	−0.125054	+	0.466709i
$694$	42.1038	+	42.1038i	1.59824	+	1.59824i
$695$	36.7307	+	12.9440i	1.39327	+	0.490993i
$696$	−1.19869	+	4.47356i	−0.0454361	+	0.169570i
$697$		−	1.36302i		−	0.0516282i
$698$	−12.0397	−	3.22603i	−0.455710	−	0.122107i
$699$	−4.04946	+	7.01387i	−0.153165	+	0.265289i
$700$	−15.0303	+	18.6772i	−0.568093	+	0.705931i
$701$		−	40.3398i		−	1.52361i	−0.647804	−	0.761807i	$-0.724312\pi$
$701$		−	40.3398i		−	1.52361i	0.647804	−	0.761807i	$-0.275688\pi$
$702$		0			0
$703$	−2.05825	+	2.05825i	−0.0776285	+	0.0776285i
$704$	8.51379	−	2.28126i	0.320875	−	0.0859783i
$705$	35.6533	+	24.4238i	1.34278	+	0.919852i
$706$	−43.3459	+	25.0258i	−1.63134	+	0.941857i
$707$	−16.1158			−0.606097
$708$	28.2753	−	16.3247i	1.06265	−	0.613521i
$709$	−43.0733	−	11.5415i	−1.61765	−	0.433449i	−0.667341	−	0.744752i	$-0.732568\pi$
$709$	−43.0733	−	11.5415i	−1.61765	−	0.433449i	−0.950311	+	0.311304i	$0.899234\pi$
$710$	18.8709	+	1.45620i	0.708213	+	0.0546501i
$711$	−0.740887	−	1.28325i	−0.0277854	−	0.0481258i
$712$	−1.43878	−	5.36959i	−0.0539204	−	0.201234i
$713$	0.890371	−	1.54217i	0.0333447	−	0.0577546i
$714$	−26.0250			−0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$	−12.5746	+	21.7798i	−0.469607	+	0.813383i
$718$	−2.61379	−	9.75479i	−0.0975457	−	0.364045i
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	−0.999868	−	0.0162430i	$-0.994829\pi$
$719$	−13.7825	−	23.8720i	−0.514001	−	0.890276i	0.485867	−	0.874033i	$-0.338504\pi$
$720$	7.67863	−	6.57846i	0.286166	−	0.245165i
$721$	47.3409	+	12.6850i	1.76307	+	0.472413i
$722$	29.6807	−	17.1361i	1.10460	−	0.637741i
$723$	−34.7768			−1.29336
$724$	−11.2555	+	6.49836i	−0.418307	+	0.241510i
$725$	6.19951	−	7.70371i	0.230244	−	0.286109i
$726$	−14.0557	+	3.76622i	−0.521656	+	0.139777i
$727$	29.4624	−	29.4624i	1.09270	−	1.09270i	0.0974593	−	0.995240i	$-0.468928\pi$
$727$	29.4624	−	29.4624i	1.09270	−	1.09270i	0.995240	−	0.0974593i	$-0.0310716\pi$
$728$		0			0
$729$			14.2845i			0.529057i
$730$	59.4011	−	11.1031i	2.19853	−	0.410946i
$731$	−8.92588	+	15.4601i	−0.330135	+	0.571811i
$732$	−7.48617	−	2.00591i	−0.276697	−	0.0741407i
$733$		−	23.3958i		−	0.864144i	−0.901839	−	0.432072i	$-0.857783\pi$
$733$		−	23.3958i		−	0.864144i	0.901839	−	0.432072i	$-0.142217\pi$
$734$	−8.56885	+	31.9794i	−0.316282	+	1.18038i
$735$	10.5723	+	22.0785i	0.389965	+	0.814378i
$736$	1.41323	+	1.41323i	0.0520924	+	0.0520924i
$737$	−2.29605	+	8.56897i	−0.0845761	+	0.315642i
$738$	−1.10434	+	0.295907i	−0.0406513	+	0.0108925i
$739$	−4.15644	−	15.5120i	−0.152897	−	0.570620i	−0.999276	−	0.0380389i	$-0.987889\pi$
$739$	−4.15644	−	15.5120i	−0.152897	−	0.570620i	0.846379	−	0.532581i	$-0.178778\pi$
$740$	−12.4647	+	10.6788i	−0.458210	+	0.392560i
$741$		0			0
$742$	20.4995	+	20.4995i	0.752561	+	0.752561i
$743$	−45.2759	−	26.1400i	−1.66101	−	0.958985i	−0.972234	−	0.234011i	$-0.924815\pi$
$743$	−45.2759	−	26.1400i	−1.66101	−	0.958985i	−0.688777	−	0.724973i	$-0.741852\pi$
$744$	11.8615	+	6.84824i	0.434864	+	0.251069i
$745$	26.4805	−	12.6802i	0.970171	−	0.464567i
$746$	−20.0933	+	20.0933i	−0.735669	+	0.735669i
$747$	3.51310	+	6.08487i	0.128538	+	0.222634i
$748$	−5.31682	−	9.20901i	−0.194402	−	0.336715i
$749$	−17.6925	+	17.6925i	−0.646468	+	0.646468i
$750$	−38.8605	+	11.7048i	−1.41898	+	0.427399i
$751$	−23.7599	−	13.7178i	−0.867010	−	0.500569i	−0.000656703	−	1.00000i	$-0.500209\pi$
$751$	−23.7599	−	13.7178i	−0.867010	−	0.500569i	−0.866354	+	0.499431i	$0.833542\pi$
$752$	−41.1638	−	23.7659i	−1.50109	−	0.866655i
$753$	30.5066	+	30.5066i	1.11172	+	1.11172i
$754$		0			0
$755$	−0.186169	+	2.41257i	−0.00677539	+	0.0878026i
$756$	−5.09659	−	19.0207i	−0.185361	−	0.691777i
$757$	−2.32441	+	0.622824i	−0.0844821	+	0.0226369i	−0.300813	−	0.953683i	$-0.597258\pi$
$757$	−2.32441	+	0.622824i	−0.0844821	+	0.0226369i	0.216330	+	0.976320i	$0.430591\pi$
$758$	10.1295	−	37.8037i	0.367919	−	1.37309i
$759$	−1.65300	−	1.65300i	−0.0600000	−	0.0600000i
$760$	1.28036	−	0.613103i	0.0464437	−	0.0222396i
$761$	0.632352	−	2.35997i	0.0229227	−	0.0855488i	−0.953517	−	0.301340i	$-0.902566\pi$
$761$	0.632352	−	2.35997i	0.0229227	−	0.0855488i	0.976440	+	0.215791i	$0.0692329\pi$
$762$		−	4.66848i		−	0.169121i
$763$	47.8242	+	12.8144i	1.73135	+	0.463914i
$764$	−2.52761	+	4.37796i	−0.0914459	+	0.158389i
$765$	−3.46716	−	2.37513i	−0.125355	−	0.0858730i
$766$		−	35.5469i		−	1.28436i
$767$		0			0
$768$	−29.3786	+	29.3786i	−1.06011	+	1.06011i
$769$	−13.0944	+	3.50862i	−0.472195	+	0.126524i	−0.487066	−	0.873365i	$-0.661933\pi$
$769$	−13.0944	+	3.50862i	−0.472195	+	0.126524i	0.0148712	+	0.999889i	$0.495266\pi$
$770$	−31.7340	+	46.3246i	−1.14361	+	1.66942i
$771$	−21.9917	+	12.6969i	−0.792011	+	0.457268i
$772$	−0.384901			−0.0138529
$773$	19.4375	−	11.2222i	0.699118	−	0.403636i	−0.107901	−	0.994162i	$-0.534413\pi$
$773$	19.4375	−	11.2222i	0.699118	−	0.403636i	0.807019	+	0.590525i	$0.201079\pi$
$774$	14.4637	+	3.87555i	0.519888	+	0.139304i
$775$	−17.2609	−	23.6058i	−0.620031	−	0.847944i
$776$	10.5315	+	18.2410i	0.378058	+	0.654815i
$777$	9.83454	+	36.7030i	0.352812	+	1.31671i
$778$	13.6082	−	23.5701i	0.487878	−	0.845030i
$779$	−0.361484			−0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$	0.564890	−	0.978419i	0.0202004	−	0.0349882i
$783$	2.10217	+	7.84541i	0.0751255	+	0.280372i
$784$	−13.4618	−	23.3165i	−0.480778	−	0.832732i
$785$	0.738363	−	9.56847i	0.0263533	−	0.341513i
$786$	19.6158	+	5.25605i	0.699674	+	0.187477i
$787$	11.6877	−	6.74791i	0.416622	−	0.240537i	−0.277009	−	0.960867i	$-0.589343\pi$
$787$	11.6877	−	6.74791i	0.416622	−	0.240537i	0.693631	+	0.720330i	$0.256010\pi$
$788$	−35.0224			−1.24762
$789$	28.3280	−	16.3552i	1.00850	−	0.582260i
$790$	−1.20191	−	6.43012i	−0.0427619	−	0.228773i
$791$	7.83647	−	2.09978i	0.278633	−	0.0746594i
$792$	3.00307	−	3.00307i	0.106709	−	0.106709i
$793$		0			0
$794$			9.66696i			0.343068i
$795$	3.64168	+	19.4828i	0.129157	+	0.690983i
$796$	3.89696	−	6.74974i	0.138124	−	0.239238i
$797$	6.06076	+	1.62398i	0.214683	+	0.0575242i	0.364558	−	0.931181i	$-0.381220\pi$
$797$	6.06076	+	1.62398i	0.214683	+	0.0575242i	−0.149874	+	0.988705i	$0.547887\pi$
$798$			6.90201i			0.244328i
$799$	−5.11330	+	19.0831i	−0.180896	+	0.675112i
$800$	30.6052	−	11.8555i	1.08206	−	0.419156i
$801$	3.08625	+	3.08625i	0.109047	+	0.109047i
$802$	13.2163	−	49.3238i	0.466683	−	1.74168i
$803$	55.2132	−	14.7943i	1.94843	−	0.522081i
$804$	1.59141	+	5.93922i	0.0561247	+	0.209460i
$805$	−2.40220	−	0.185369i	−0.0846664	−	0.00653339i
$806$		0			0
$807$	−45.2744	−	45.2744i	−1.59374	−	1.59374i
$808$	4.66009	+	2.69050i	0.163941	+	0.0946516i
$809$	−18.6872	−	10.7890i	−0.657006	−	0.379322i	0.134130	−	0.990964i	$-0.457176\pi$
$809$	−18.6872	−	10.7890i	−0.657006	−	0.379322i	−0.791135	+	0.611641i	$0.790510\pi$
$810$	14.8684	−	42.1917i	0.522424	−	1.48247i
$811$	−22.5473	+	22.5473i	−0.791743	+	0.791743i	−0.981777	−	0.190035i	$-0.939140\pi$
$811$	−22.5473	+	22.5473i	−0.791743	+	0.791743i	0.190035	+	0.981777i	$0.439140\pi$
$812$	−4.74129	−	8.21215i	−0.166387	−	0.288190i
$813$	−17.3138	−	29.9885i	−0.607223	−	1.05174i
$814$	−27.1839	+	27.1839i	−0.952795	+	0.952795i
$815$	1.68229	−	4.77377i	0.0589279	−	0.167218i
$816$	16.9475	+	9.78462i	0.593280	+	0.342530i
$817$	4.10012	+	2.36721i	0.143445	+	0.0828180i
$818$	3.41289	+	3.41289i	0.119329	+	0.119329i
$819$		0			0
$820$	−2.03230	−	0.156825i	−0.0709710	−	0.00547656i
$821$	−4.64130	−	17.3216i	−0.161982	−	0.604526i	−0.998406	−	0.0564427i	$-0.982024\pi$
$821$	−4.64130	−	17.3216i	−0.161982	−	0.604526i	0.836423	−	0.548084i	$-0.184642\pi$
$822$	−50.1062	+	13.4259i	−1.74765	+	0.468282i
$823$	−0.298185	+	1.11284i	−0.0103941	+	0.0387913i	−0.970928	−	0.239371i	$-0.923059\pi$
$823$	−0.298185	+	1.11284i	−0.0103941	+	0.0387913i	0.960534	+	0.278162i	$0.0897254\pi$
$824$	−11.5715	−	11.5715i	−0.403112	−	0.403112i
$825$	−35.7975	+	13.8669i	−1.24631	+	0.482784i
$826$	20.3990	−	76.1300i	0.709771	−	2.64890i
$827$			4.45029i			0.154752i	0.997002	+	0.0773759i	$0.0246542\pi$
$827$			4.45029i			0.154752i	−0.997002	+	0.0773759i	$0.975346\pi$
$828$	−0.369672	−	0.0990534i	−0.0128470	−	0.00344234i
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	−0.494159	−	0.869372i	$-0.664524\pi$
$829$	14.5637	−	25.2251i	0.505819	−	0.876103i	0.999977	−	0.00673181i	$-0.00214282\pi$
$830$	5.69914	+	30.4900i	0.197820	+	1.05832i
$831$		−	6.09295i		−	0.211362i
$832$		0			0
$833$	−7.91294	+	7.91294i	−0.274167	+	0.274167i
$834$	61.0685	−	16.3633i	2.11463	−	0.566613i
$835$	0.254548	+	1.36181i	0.00880899	+	0.0471275i
$836$	−2.44229	+	1.41006i	−0.0844685	+	0.0487679i
$837$	24.0199			0.830249
$838$	31.2015	−	18.0142i	1.07784	−	0.622291i
$839$	31.2268	+	8.36719i	1.07807	+	0.288867i	0.753804	−	0.657099i	$-0.228217\pi$
$839$	31.2268	+	8.36719i	1.07807	+	0.288867i	0.324264	+	0.945967i	$0.394883\pi$
$840$	1.42575	−	18.4764i	0.0491931	−	0.637496i
$841$	−12.5444	−	21.7275i	−0.432565	−	0.749224i
$842$	7.00106	+	26.1283i	0.241273	+	0.900441i
$843$	26.1718	−	45.3309i	0.901405	−	1.56128i
$844$	−4.37277			−0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$	−7.09313	+	12.2857i	−0.243723	+	0.422140i
$848$	−5.64207	−	21.0565i	−0.193750	−	0.723083i
$849$	−15.1999	−	26.3270i	−0.521660	−	0.903541i
$850$	−10.9511	−	14.9765i	−0.375619	−	0.513691i
$851$	−1.59333	−	0.426931i	−0.0546186	−	0.0146350i
$852$	10.7464	−	6.20441i	0.368164	−	0.212560i
$853$	−9.24230			−0.316450			−0.158225	−	0.987403i	$-0.550577\pi$
$853$	−9.24230			−0.316450			−0.158225	+	0.987403i	$0.550577\pi$
$854$	−16.2025	+	9.35453i	−0.554439	+	0.320105i
$855$	−0.629901	+	0.919515i	−0.0215422	+	0.0314468i
$856$	8.06972	−	2.16228i	0.275817	−	0.0739051i
$857$	−37.7913	+	37.7913i	−1.29093	+	1.29093i	−0.356713	+	0.934214i	$0.616103\pi$
$857$	−37.7913	+	37.7913i	−1.29093	+	1.29093i	−0.934214	+	0.356713i	$0.883897\pi$
$858$		0			0
$859$			6.16263i			0.210266i	0.994458	+	0.105133i	$0.0335269\pi$
$859$			6.16263i			0.210266i	−0.994458	+	0.105133i	$0.966473\pi$
$860$	22.0243	+	15.0875i	0.751024	+	0.514478i
$861$	−2.35941	+	4.08661i	−0.0804083	+	0.139271i
$862$	30.3110	+	8.12181i	1.03240	+	0.276630i
$863$		−	33.7740i		−	1.14968i	−0.818266	−	0.574840i	$-0.805064\pi$
$863$		−	33.7740i		−	1.14968i	0.818266	−	0.574840i	$-0.194936\pi$
$864$	−6.97742	+	26.0401i	−0.237377	+	0.885902i
$865$	−13.3544	+	6.39477i	−0.454064	+	0.217429i
$866$	14.5532	+	14.5532i	0.494539	+	0.494539i
$867$	−6.61482	+	24.6868i	−0.224651	+	0.838409i
$868$	−27.0875	+	7.25808i	−0.919410	+	0.246355i
$869$	−1.60147	−	5.97678i	−0.0543263	−	0.202748i
$870$	1.23507	−	16.0053i	0.0418727	−	0.542630i
$871$		0			0
$872$	−11.6896	−	11.6896i	−0.395861	−	0.395861i
$873$	−14.3218	−	8.26870i	−0.484720	−	0.279853i
$874$	−0.259484	−	0.149813i	−0.00877716	−	0.00506750i
$875$	−18.7199	+	34.8575i	−0.632849	+	1.17840i
$876$	28.0146	−	28.0146i	0.946527	−	0.946527i
$877$	11.3486	+	19.6563i	0.383214	+	0.663747i	0.991520	−	0.129956i	$-0.0414837\pi$
$877$	11.3486	+	19.6563i	0.383214	+	0.663747i	−0.608305	+	0.793703i	$0.708150\pi$
$878$	3.88705	+	6.73256i	0.131181	+	0.227213i
$879$	−14.5417	+	14.5417i	−0.490480	+	0.490480i
$880$	38.0819	−	18.2355i	1.28374	−	0.614719i
$881$	6.78312	+	3.91623i	0.228529	+	0.131941i	0.609893	−	0.792484i	$-0.291212\pi$
$881$	6.78312	+	3.91623i	0.228529	+	0.131941i	−0.381364	+	0.924425i	$0.624546\pi$
$882$	8.12905	+	4.69331i	0.273719	+	0.158032i
$883$	18.9296	+	18.9296i	0.637032	+	0.637032i	0.949822	−	0.312790i	$-0.101264\pi$
$883$	18.9296	+	18.9296i	0.637032	+	0.637032i	−0.312790	+	0.949822i	$0.601264\pi$
$884$		0			0
$885$	40.9204	−	35.0575i	1.37552	−	1.17844i
$886$	−10.1615	−	37.9234i	−0.341384	−	1.27406i
$887$	−34.3248	+	9.19729i	−1.15251	+	0.308815i	−0.783972	−	0.620797i	$-0.786809\pi$
$887$	−34.3248	+	9.19729i	−1.15251	+	0.308815i	−0.368541	+	0.929612i	$0.620143\pi$
$888$	3.28372	−	12.2550i	0.110194	−	0.411251i
$889$	−3.21825	−	3.21825i	−0.107937	−	0.107937i
$890$	8.32168	+	17.3785i	0.278943	+	0.582527i
$891$	10.9519	−	40.8731i	0.366903	−	1.36930i
$892$		−	10.0467i		−	0.336389i
$893$	5.06098	+	1.35608i	0.169359	+	0.0453796i
$894$	23.8314	−	41.2772i	0.797042	−	1.38052i
$895$	−4.81413	+	0.899848i	−0.160919	+	0.0300786i
$896$			31.7130i			1.05946i
$897$		0			0
$898$	18.8417	−	18.8417i	0.628755	−	0.628755i
$899$	11.1727	−	2.99371i	0.372630	−	0.0998459i
$900$	−3.94029	+	4.89634i	−0.131343	+	0.163211i
$901$	−7.84682	+	4.53036i	−0.261415	+	0.150928i
$902$	−4.77421			−0.158964
$903$	53.5230	−	30.9015i	1.78113	−	1.02834i
$904$	−2.61657	−	0.701108i	−0.0870258	−	0.0233185i
$905$	−16.2891	+	13.9553i	−0.541469	+	0.463889i
$906$	1.96411	+	3.40193i	0.0652530	+	0.113022i
$907$	−12.0355	−	44.9172i	−0.399633	−	1.49145i	−0.813743	−	0.581225i	$-0.802574\pi$
$907$	−12.0355	−	44.9172i	−0.399633	−	1.49145i	0.414109	−	0.910227i	$-0.364093\pi$
$908$	−2.64357	+	4.57880i	−0.0877300	+	0.151953i
$909$	−4.22485			−0.140130
$910$		0			0
$911$	17.7325			0.587504			0.293752	−	0.955882i	$-0.405096\pi$
$911$	17.7325			0.587504			0.293752	+	0.955882i	$0.405096\pi$
$912$	2.59495	−	4.49459i	0.0859274	−	0.148831i
$913$	7.59379	+	28.3404i	0.251318	+	0.937931i
$914$	−27.7449	−	48.0556i	−0.917720	−	1.58954i
$915$	−12.7530	−	0.984100i	−0.421601	−	0.0325333i
$916$	−22.9399	−	6.14674i	−0.757957	−	0.203094i
$917$	17.1456	−	9.89902i	0.566198	−	0.326894i
$918$	15.2393			0.502971
$919$	−42.2580	+	24.3977i	−1.39396	+	0.804806i	−0.993751	−	0.111617i	$-0.964397\pi$
$919$	−42.2580	+	24.3977i	−1.39396	+	0.804806i	−0.400213	+	0.916422i	$0.631064\pi$
$920$	0.663680	+	0.454645i	0.0218809	+	0.0149892i
$921$	−4.09541	+	1.09736i	−0.134948	+	0.0361593i
$922$	8.98564	−	8.98564i	0.295926	−	0.295926i
$923$		0			0
$924$			36.8139i			1.21109i
$925$	−16.9831	+	21.1038i	−0.558401	+	0.693888i
$926$	−28.7990	+	49.8814i	−0.946395	+	1.63920i
$927$	12.4107	+	3.32544i	0.407621	+	0.109222i
$928$			12.9820i			0.426155i
$929$	2.68833	−	10.0330i	0.0882012	−	0.329171i	−0.907700	−	0.419620i	$-0.862163\pi$
$929$	2.68833	−	10.0330i	0.0882012	−	0.329171i	0.995901	+	0.0904485i	$0.0288300\pi$
$930$	−44.7747	−	15.7787i	−1.46822	−	0.517403i
$931$	2.09857	+	2.09857i	0.0687778	+	0.0687778i
$932$	−1.43302	+	5.34810i	−0.0469401	+	0.175183i
$933$	7.31433	−	1.95987i	0.239460	−	0.0641632i
$934$	−2.47803	−	9.24814i	−0.0810837	−	0.302608i
$935$	−11.4179	−	13.3274i	−0.373406	−	0.435853i
$936$		0			0
$937$	5.31856	+	5.31856i	0.173750	+	0.173750i	0.788625	−	0.614875i	$-0.210794\pi$
$937$	5.31856	+	5.31856i	0.173750	+	0.173750i	−0.614875	+	0.788625i	$0.710794\pi$
$938$	12.8544	+	7.42149i	0.419711	+	0.242320i
$939$	−7.39178	−	4.26764i	−0.241221	−	0.139269i
$940$	27.8650	+	9.81969i	0.908857	+	0.320283i
$941$	38.9093	−	38.9093i	1.26841	−	1.26841i	0.321497	−	0.946911i	$-0.395814\pi$
$941$	38.9093	−	38.9093i	1.26841	−	1.26841i	0.946911	−	0.321497i	$-0.104186\pi$
$942$	−7.78981	−	13.4923i	−0.253806	−	0.439604i
$943$	−0.102425	−	0.177406i	−0.00333542	−	0.00577712i
$944$	−41.9064	+	41.9064i	−1.36394	+	1.36394i
$945$	−14.0359	−	29.3116i	−0.456587	−	0.953508i
$946$	54.1514	+	31.2643i	1.76061	+	1.01649i
$947$	29.2298	+	16.8759i	0.949842	+	0.548392i	0.893032	−	0.449993i	$-0.148574\pi$
$947$	29.2298	+	16.8759i	0.949842	+	0.548392i	0.0568101	+	0.998385i	$0.481907\pi$
$948$	−3.03256	−	3.03256i	−0.0984930	−	0.0984930i
$949$		0			0
$950$	−3.97188	+	2.90431i	−0.128865	+	0.0942281i
$951$	−11.8554	−	44.2451i	−0.384439	−	1.43475i
$952$	8.18285	−	2.19259i	0.265208	−	0.0710622i
$953$	−1.14302	+	4.26581i	−0.0370260	+	0.138183i	−0.981965	−	0.189065i	$-0.939454\pi$
$953$	−1.14302	+	4.26581i	−0.0370260	+	0.138183i	0.944939	+	0.327248i	$0.106121\pi$
$954$	5.37407	+	5.37407i	0.173992	+	0.173992i
$955$	−2.77297	+	7.86877i	−0.0897311	+	0.254627i
$956$	−4.44988	+	16.6072i	−0.143919	+	0.537115i
$957$		−	15.1845i		−	0.490845i
$958$	34.2405	+	9.17471i	1.10626	+	0.296422i
$959$	−25.2858	+	43.7963i	−0.816520	+	1.41425i
$960$	5.69806	−	8.31789i	0.183904	−	0.268459i
$961$		−	3.20686i		−	0.103447i
$962$		0			0
$963$	−4.63819	+	4.63819i	−0.149463	+	0.149463i
$964$	−22.9647	+	6.15338i	−0.739645	+	0.198187i
$965$	−0.624420	+	0.116715i	−0.0201008	+	0.00375720i
$966$	−3.38730	+	1.95566i	−0.108985	+	0.0629223i
$967$	−16.2803			−0.523540			−0.261770	−	0.965130i	$-0.584306\pi$
$967$	−16.2803			−0.523540			−0.261770	+	0.965130i	$0.584306\pi$
$968$	4.10214	−	2.36837i	0.131848	−	0.0761223i
$969$	−2.08364	−	0.558310i	−0.0669363	−	0.0179355i
$970$	−47.4986	−	55.4421i	−1.52509	−	1.78014i
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	0.744838	−	0.667245i	$-0.232527\pi$
$971$	−6.40146	−	11.0877i	−0.205433	−	0.355820i	−0.950270	+	0.311426i	$0.899193\pi$
$972$	−3.27038	−	12.2052i	−0.104897	−	0.391482i
$973$	30.8179	−	53.3781i	0.987975	−	1.71122i
$974$	−42.7918			−1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$	−8.02436	+	13.8986i	−0.256722	+	0.444655i	−0.965362	−	0.260915i	$-0.915976\pi$
$977$	−8.02436	+	13.8986i	−0.256722	+	0.444655i	0.708640	+	0.705570i	$0.249309\pi$
$978$	−2.12668	−	7.93687i	−0.0680037	−	0.253793i
$979$	9.11292	+	15.7840i	0.291250	+	0.504460i
$980$	10.8879	+	12.7088i	0.347803	+	0.405968i
$981$	12.5374	+	3.35939i	0.400288	+	0.107257i
$982$	−33.8164	+	19.5239i	−1.07912	+	0.623033i
$983$	34.3036			1.09411			0.547057	−	0.837096i	$-0.315748\pi$
$983$	34.3036			1.09411			0.547057	+	0.837096i	$0.315748\pi$
$984$	1.36450	−	0.787797i	0.0434988	−	0.0251141i
$985$	−56.8164	+	10.6200i	−1.81032	+	0.338382i
$986$	7.08844	−	1.89934i	0.225742	−	0.0604874i
$987$	48.3637	−	48.3637i	1.53943	−	1.53943i
$988$		0			0
$989$			2.68296i			0.0853131i
$990$	−8.31927	+	12.1443i	−0.264404	+	0.385971i
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	−0.987128	−	0.159934i	$-0.948872\pi$
$991$	−11.1772	+	19.3596i	−0.355057	+	0.614977i	0.632071	+	0.774911i	$0.282205\pi$
$992$	37.0838	+	9.93658i	1.17741	+	0.315487i
$993$		−	3.95773i		−	0.125595i
$994$	7.75287	−	28.9341i	0.245906	−	0.917734i
$995$	4.27524	−	12.1317i	0.135534	−	0.384601i
$996$	14.3796	+	14.3796i	0.455637	+	0.455637i
$997$	3.08118	−	11.4991i	0.0975820	−	0.364181i	−0.899816	−	0.436269i	$-0.856300\pi$
$997$	3.08118	−	11.4991i	0.0975820	−	0.364181i	0.997398	+	0.0720881i	$0.0229663\pi$
$998$	57.6445	−	15.4458i	1.82471	−	0.488928i
$999$	−5.75875	−	21.4920i	−0.182199	−	0.679975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.f.357.4		20
5.3	odd	4		845.2.t.e.188.2		20
13.2	odd	12		845.2.t.f.427.4		20
13.3	even	3		845.2.o.g.587.4		20
13.4	even	6		845.2.k.e.577.8		20
13.5	odd	4		65.2.t.a.7.2	yes	20
13.6	odd	12		845.2.f.e.437.8		20
13.7	odd	12		845.2.f.d.437.3		20
13.8	odd	4		845.2.t.g.657.4		20
13.9	even	3		845.2.k.d.577.3		20
13.10	even	6		65.2.o.a.2.2	✓	20
13.11	odd	12		845.2.t.e.427.2		20
13.12	even	2		845.2.o.e.357.2		20
39.5	even	4		585.2.dp.a.397.4		20
39.23	odd	6		585.2.cf.a.262.4		20
65.3	odd	12		845.2.t.g.418.4		20
65.8	even	4		845.2.o.g.488.4		20
65.18	even	4		65.2.o.a.33.2	yes	20
65.23	odd	12		65.2.t.a.28.2	yes	20
65.28	even	12		845.2.o.e.258.2		20
65.33	even	12		845.2.k.d.268.3		20
65.38	odd	4		845.2.t.f.188.4		20
65.43	odd	12		845.2.f.e.408.3		20
65.44	odd	4		325.2.x.b.7.4		20
65.48	odd	12		845.2.f.d.408.8		20
65.49	even	6		325.2.s.b.132.4		20
65.57	even	4		325.2.s.b.293.4		20
65.58	even	12		845.2.k.e.268.8		20
65.62	odd	12		325.2.x.b.93.4		20
65.63	even	12	inner	845.2.o.f.258.4		20
195.23	even	12		585.2.dp.a.28.4		20
195.83	odd	4		585.2.cf.a.163.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	13.10	even	6
65.2.o.a.33.2	yes	20	65.18	even	4
65.2.t.a.7.2	yes	20	13.5	odd	4
65.2.t.a.28.2	yes	20	65.23	odd	12
325.2.s.b.132.4		20	65.49	even	6
325.2.s.b.293.4		20	65.57	even	4
325.2.x.b.7.4		20	65.44	odd	4
325.2.x.b.93.4		20	65.62	odd	12
585.2.cf.a.163.4		20	195.83	odd	4
585.2.cf.a.262.4		20	39.23	odd	6
585.2.dp.a.28.4		20	195.23	even	12
585.2.dp.a.397.4		20	39.5	even	4
845.2.f.d.408.8		20	65.48	odd	12
845.2.f.d.437.3		20	13.7	odd	12
845.2.f.e.408.3		20	65.43	odd	12
845.2.f.e.437.8		20	13.6	odd	12
845.2.k.d.268.3		20	65.33	even	12
845.2.k.d.577.3		20	13.9	even	3
845.2.k.e.268.8		20	65.58	even	12
845.2.k.e.577.8		20	13.4	even	6
845.2.o.e.258.2		20	65.28	even	12
845.2.o.e.357.2		20	13.12	even	2
845.2.o.f.258.4		20	65.63	even	12	inner
845.2.o.f.357.4		20	1.1	even	1	trivial
845.2.o.g.488.4		20	65.8	even	4
845.2.o.g.587.4		20	13.3	even	3
845.2.t.e.188.2		20	5.3	odd	4
845.2.t.e.427.2		20	13.11	odd	12
845.2.t.f.188.4		20	65.38	odd	4
845.2.t.f.427.4		20	13.2	odd	12
845.2.t.g.418.4		20	65.3	odd	12
845.2.t.g.657.4		20	13.8	odd	4

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.915816 - 1.58624i) q^{2} +(-0.512942 - 1.91432i) q^{3} +(-0.677439 - 1.17336i) q^{4} +(-1.45480 - 1.69810i) q^{5} +(-3.50634 - 0.939520i) q^{6} +(-3.06478 + 1.76945i) q^{7} +1.18163 q^{8} +(-0.803451 + 0.463873i) q^{9} +(-4.02593 + 0.752519i) q^{10} +(-3.74209 + 1.00269i) q^{11} +(-1.89870 + 1.89870i) q^{12} +6.48197i q^{14} +(-2.50449 + 3.65599i) q^{15} +(2.43703 - 4.22106i) q^{16} +(-1.95684 - 0.524334i) q^{17} +1.69929i q^{18} +(-0.139057 + 0.518968i) q^{19} +(-1.00694 + 2.85736i) q^{20} +(4.95936 + 4.95936i) q^{21} +(-1.83656 + 6.85414i) q^{22} +(-0.294095 + 0.0788026i) q^{23} +(-0.606106 - 2.26202i) q^{24} +(-0.767094 + 4.94081i) q^{25} +(-2.90402 - 2.90402i) q^{27} +(4.15240 + 2.39739i) q^{28} +(-1.71273 - 0.988843i) q^{29} +(3.50563 + 7.32093i) q^{30} +(-4.13563 + 4.13563i) q^{31} +(-3.28212 - 5.68479i) q^{32} +(3.83895 + 6.64926i) q^{33} +(-2.62382 + 2.62382i) q^{34} +(7.46336 + 2.63010i) q^{35} +(1.08858 + 0.628491i) q^{36} +(4.69189 + 2.70887i) q^{37} +(0.695857 + 0.695857i) q^{38} +(-1.71904 - 2.00652i) q^{40} +(0.174136 + 0.649884i) q^{41} +(12.4086 - 3.32487i) q^{42} +(2.28069 - 8.51164i) q^{43} +(3.71155 + 3.71155i) q^{44} +(1.95657 + 0.689498i) q^{45} +(-0.144337 + 0.538675i) q^{46} -9.75201i q^{47} +(-9.33053 - 2.50011i) q^{48} +(2.76192 - 4.78379i) q^{49} +(7.13479 + 5.74167i) q^{50} +4.01498i q^{51} +(3.16254 - 3.16254i) q^{53} +(-7.26602 + 1.94693i) q^{54} +(7.14668 + 4.89574i) q^{55} +(-3.62143 + 2.09083i) q^{56} +1.06480 q^{57} +(-3.13709 + 1.81120i) q^{58} +(-11.7449 - 3.14703i) q^{59} +(5.98642 + 0.461950i) q^{60} +(1.44316 + 2.49963i) q^{61} +(2.77263 + 10.3476i) q^{62} +(1.64160 - 2.84334i) q^{63} -2.27514 q^{64} +14.0631 q^{66} +(1.14494 - 1.98310i) q^{67} +(0.710408 + 2.65128i) q^{68} +(0.301707 + 0.522573i) q^{69} +(11.0070 - 9.43000i) q^{70} +(-4.46378 - 1.19607i) q^{71} +(-0.949380 + 0.548125i) q^{72} -14.7546 q^{73} +(8.59382 - 4.96165i) q^{74} +(9.85178 - 1.06588i) q^{75} +(0.703137 - 0.188405i) q^{76} +(9.69449 - 9.69449i) q^{77} +1.59718i q^{79} +(-10.7132 + 2.00249i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(1.19035 + 0.318953i) q^{82} -7.57341i q^{83} +(2.45944 - 9.17877i) q^{84} +(1.95645 + 4.08571i) q^{85} +(-11.4128 - 11.4128i) q^{86} +(-1.01444 + 3.78593i) q^{87} +(-4.42176 + 1.18481i) q^{88} +(-1.21762 - 4.54423i) q^{89} +(2.88556 - 2.47213i) q^{90} +(0.291695 + 0.291695i) q^{92} +(10.0383 + 5.79560i) q^{93} +(-15.4690 - 8.93105i) q^{94} +(1.08356 - 0.518863i) q^{95} +(-9.19900 + 9.19900i) q^{96} +(8.91268 + 15.4372i) q^{97} +(-5.05883 - 8.76215i) q^{98} +(2.54147 - 2.54147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 12 q^{8} + 12 q^{9} + 2 q^{10} - 8 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 4 q^{17} + 16 q^{19} - 8 q^{20} - 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 12 * q^8 + 12 * q^9 + 2 * q^10 - 8 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 4 * q^17 + 16 * q^19 - 8 * q^20 - 4 * q^21 + 16 * q^22 + 10 * q^23 - 28 * q^24 - 18 * q^25 + 4 * q^27 + 6 * q^28 + 26 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 + 40 * q^35 - 36 * q^36 + 42 * q^37 + 8 * q^38 - 16 * q^40 - 28 * q^41 + 40 * q^42 - 10 * q^43 - 36 * q^44 + 32 * q^45 + 8 * q^46 - 56 * q^48 - 18 * q^49 - 8 * q^50 - 10 * q^53 + 12 * q^54 - 10 * q^55 + 12 * q^57 - 90 * q^58 + 8 * q^59 + 92 * q^60 - 16 * q^61 + 44 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 22 * q^68 + 16 * q^69 - 32 * q^70 - 56 * q^71 - 66 * q^72 - 72 * q^73 + 18 * q^74 + 38 * q^75 - 80 * q^76 + 28 * q^77 - 68 * q^80 - 14 * q^81 - 56 * q^82 + 32 * q^84 - 6 * q^85 - 60 * q^86 - 34 * q^87 - 82 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 + 48 * q^93 - 48 * q^94 + 26 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

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