LMFDB - Embedded newform 845.2.t.g.657.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] 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("845.188"); 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, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [20,6,-2,6,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.74735897080$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			657.4
Root			$1.83163i$ of defining polynomial
Character	$\chi$	$=$	845.657
Dual form			845.2.t.g.418.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.58624	+	0.915816i	1.12164	+	0.647580i	0.941819	−	0.336119i	$-0.109115\pi$
$2$	1.58624	+	0.915816i	1.12164	+	0.647580i	0.179822	+	0.983699i	$0.442448\pi$
$3$	−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
$5$	1.69810	−	1.45480i	0.759414	−	0.650608i
$5$	1.69810	−	1.45480i	0.759414	−	0.650608i
$6$	0.939520	−	3.50634i	0.383558	−	1.43146i
$7$	1.76945	+	3.06478i	0.668790	+	1.15838i	0.978243	+	0.207464i	$0.0665209\pi$
$7$	1.76945	+	3.06478i	0.668790	+	1.15838i	−0.309453	+	0.950915i	$0.600146\pi$
$8$		−	1.18163i		−	0.417769i
$9$	−0.803451	+	0.463873i	−0.267817	+	0.154624i
$10$	4.02593	−	0.752519i	1.27311	−	0.237967i
$11$	1.00269	+	3.74209i	0.302323	+	1.12828i	0.935226	+	0.354053i	$0.115197\pi$
$11$	1.00269	+	3.74209i	0.302323	+	1.12828i	−0.632903	+	0.774231i	$0.718137\pi$
$12$	1.89870	−	1.89870i	0.548108	−	0.548108i
$13$		0			0
$13$		0			0
$14$			6.48197i			1.73238i
$15$	−3.65599	−	2.50449i	−0.943973	−	0.646656i
$16$	2.43703	−	4.22106i	0.609258	−	1.05527i
$17$	1.95684	+	0.524334i	0.474603	+	0.127170i	0.488189	−	0.872738i	$-0.337658\pi$
$17$	1.95684	+	0.524334i	0.474603	+	0.127170i	−0.0135853	+	0.999908i	$0.504324\pi$
$18$	−1.69929			−0.400526
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	0.198797	−	0.980041i	$-0.436296\pi$
$19$	−0.518968	−	0.139057i	−0.119059	−	0.0319019i	−0.317857	+	0.948139i	$0.602963\pi$
$20$	2.85736	+	1.00694i	0.638926	+	0.225159i
$21$	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	−0.228027	−	0.973655i	$-0.573227\pi$
$23$	0.294095	−	0.0788026i	0.0613231	−	0.0164315i	0.289350	+	0.957223i	$0.406561\pi$
$24$	−2.26202	+	0.606106i	−0.461733	+	0.123721i
$25$	0.767094	−	4.94081i	0.153419	−	0.988161i
$26$		0			0
$27$	−2.90402	−	2.90402i	−0.558879	−	0.558879i
$28$	−2.39739	+	4.15240i	−0.453064	+	0.784730i
$29$	−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	0.230331	−	0.973112i	$-0.426019\pi$
$31$	−4.13563	−	4.13563i	−0.742781	−	0.742781i	−0.973112	+	0.230331i	$0.926019\pi$
$32$	5.68479	−	3.28212i	1.00494	−	0.580202i
$33$	6.64926	−	3.83895i	1.15749	−	0.668276i
$34$	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
$37$	2.70887	−	4.69189i	0.445335	−	0.771342i	−0.552741	−	0.833353i	$-0.686418\pi$
$37$	2.70887	−	4.69189i	0.445335	−	0.771342i	0.998075	+	0.0620109i	$0.0197514\pi$
$38$	−0.695857	−	0.695857i	−0.112883	−	0.112883i
$39$		0			0
$40$	−1.71904	−	2.00652i	−0.271803	−	0.317259i
$41$	−0.649884	+	0.174136i	−0.101495	+	0.0271955i	−0.309209	−	0.950994i	$-0.600064\pi$
$41$	−0.649884	+	0.174136i	−0.101495	+	0.0271955i	0.207714	+	0.978190i	$0.433398\pi$
$42$	12.4086	−	3.32487i	1.91469	−	0.513039i
$43$	−2.28069	+	8.51164i	−0.347802	+	1.29801i	0.541504	+	0.840698i	$0.317855\pi$
$43$	−2.28069	+	8.51164i	−0.347802	+	1.29801i	−0.889305	+	0.457314i	$0.848811\pi$
$44$	−3.71155	+	3.71155i	−0.559538	+	0.559538i
$45$	−0.689498	+	1.95657i	−0.102784	+	0.291668i
$46$	0.538675	+	0.144337i	0.0794232	+	0.0212814i
$47$	−9.75201			−1.42248			−0.711238	−	0.702951i	$-0.751865\pi$
$47$	−9.75201			−1.42248			−0.711238	+	0.702951i	$0.751865\pi$
$48$	−9.33053	−	2.50011i	−1.34675	−	0.360860i
$49$	−2.76192	+	4.78379i	−0.394561	+	0.683399i
$50$	5.74167	−	7.13479i	0.811994	−	1.00901i
$51$		−	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	$0.150617\pi$
$54$	−1.94693	−	7.26602i	−0.264943	−	0.988781i
$55$	7.14668	+	4.89574i	0.963658	+	0.660141i
$56$	3.62143	−	2.09083i	0.483934	−	0.279399i
$57$			1.06480i			0.141036i
$58$	−1.81120	−	3.13709i	−0.237822	−	0.411919i
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	0.385495	+	0.922710i	$0.374031\pi$
$59$	−3.14703	+	11.7449i	−0.409708	+	1.52905i	−0.795203	+	0.606343i	$0.792636\pi$
$60$	0.461950	−	5.98642i	0.0596374	−	0.772844i
$61$	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
$63$	−2.84334	−	1.64160i	−0.358227	−	0.206822i
$64$	2.27514			0.284392
$65$		0			0
$66$	14.0631			1.73105
$67$	1.98310	+	1.14494i	0.242274	+	0.139877i	0.616222	−	0.787573i	$-0.288663\pi$
$67$	1.98310	+	1.14494i	0.242274	+	0.139877i	−0.373947	+	0.927450i	$0.621996\pi$
$68$	0.710408	+	2.65128i	0.0861496	+	0.321515i
$69$	−0.301707	−	0.522573i	−0.0363213	−	0.0629104i
$70$	9.43000	+	11.0070i	1.12710	+	1.31559i
$71$	1.19607	−	4.46378i	0.141947	−	0.529753i	−0.857925	−	0.513774i	$-0.828247\pi$
$71$	1.19607	−	4.46378i	0.141947	−	0.529753i	0.999872	−	0.0159789i	$-0.00508645\pi$
$72$	0.548125	+	0.949380i	0.0645972	+	0.111886i
$73$			14.7546i			1.72690i	0.504436	+	0.863449i	$0.331701\pi$
$73$			14.7546i			1.72690i	−0.504436	+	0.863449i	$0.668299\pi$
$74$	8.59382	−	4.96165i	0.999011	−	0.576780i
$75$	−9.85178	+	1.06588i	−1.13759	+	0.123077i
$76$	−0.188405	−	0.703137i	−0.0216115	−	0.0806554i
$77$	−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	$0.971362\pi$
$80$	−2.00249	−	10.7132i	−0.223885	−	1.19777i
$81$	−5.46126	+	9.45918i	−0.606807	+	1.05102i
$82$	−1.19035	−	0.318953i	−0.131452	−	0.0352225i
$83$	7.57341			0.831290			0.415645	−	0.909527i	$-0.363556\pi$
$83$	7.57341			0.831290			0.415645	+	0.909527i	$0.363556\pi$
$84$	9.17877	+	2.45944i	1.00149	+	0.268347i
$85$	4.08571	−	1.95645i	0.443158	−	0.212206i
$86$	−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
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	−0.491488	−	0.870884i	$-0.663547\pi$
$89$	−4.54423	+	1.21762i	−0.481687	+	0.129068i	0.00980081	+	0.999952i	$0.496880\pi$
$90$	−2.88556	+	2.47213i	−0.304165	+	0.260586i
$91$		0			0
$92$	0.291695	+	0.291695i	0.0304113	+	0.0304113i
$93$	−5.79560	+	10.0383i	−0.600976	+	1.04092i
$94$	−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
$97$	−15.4372	+	8.91268i	−1.56741	+	0.904945i	−0.570942	+	0.820991i	$0.693422\pi$
$97$	−15.4372	+	8.91268i	−1.56741	+	0.904945i	−0.996470	+	0.0839547i	$0.973245\pi$
$98$	−8.76215	+	5.05883i	−0.885111	+	0.511019i
$99$	−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	0.290787	−	0.956788i	$-0.406083\pi$
$101$	−3.94379	−	2.27695i	−0.392421	−	0.226565i	−0.683209	+	0.730223i	$0.739416\pi$
$102$	3.67698	−	6.36872i	0.364075	−	0.630597i
$103$	9.79285	+	9.79285i	0.964918	+	0.964918i	0.999405	−	0.0344872i	$-0.0109798\pi$
$103$	9.79285	+	9.79285i	0.964918	+	0.964918i	−0.0344872	+	0.999405i	$0.510980\pi$
$104$		0			0
$105$	1.20660	−	15.6364i	0.117752	−	1.52596i
$106$	7.91286	−	2.12024i	0.768565	−	0.205936i
$107$	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	$-0.516283\pi$
$109$	9.89281	−	9.89281i	0.947560	−	0.947560i	0.998692	+	0.0511324i	$0.0162830\pi$
$110$	6.85276	+	14.3109i	0.653385	+	1.36449i
$111$	−10.3713	−	2.77898i	−0.984399	−	0.263769i
$112$	17.2488			1.62986
$113$	−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
$115$	0.384761	−	0.561666i	0.0358792	−	0.0523756i
$116$		−	2.67952i		−	0.248787i
$117$		0			0
$118$	−15.7481	+	15.7481i	−1.44973	+	1.44973i
$119$	1.85557	+	6.92507i	0.170099	+	0.634820i
$120$	−2.95937	+	4.32002i	−0.270152	+	0.394362i
$121$	−3.47160	+	2.00433i	−0.315600	+	0.182212i
$122$			5.28668i			0.478633i
$123$	0.666705	+	1.15477i	0.0601148	+	0.104122i
$124$	2.05094	−	7.65421i	0.184180	−	0.687368i
$125$	−5.88530	−	9.50596i	−0.526397	−	0.850239i
$126$	−3.00681	−	5.20795i	−0.267868	−	0.463961i
$127$	−0.332860	−	1.24225i	−0.0295366	−	0.110232i	0.949584	−	0.313513i	$-0.101506\pi$
$127$	−0.332860	−	1.24225i	−0.0295366	−	0.110232i	−0.979120	+	0.203281i	$0.934839\pi$
$128$	−7.76067	−	4.48062i	−0.685953	−	0.396035i
$129$	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	$0.578588\pi$
$132$	9.00893	+	5.20131i	0.784127	+	0.452716i
$133$	−0.492109	−	1.83658i	−0.0426713	−	0.159251i
$134$	2.09712	+	3.63231i	0.181163	+	0.313784i
$135$	−9.15610	−	0.706541i	−0.788032	−	0.0608094i
$136$	0.619567	−	2.31226i	0.0531274	−	0.198274i
$137$	−7.14509	−	12.3757i	−0.610446	−	1.05732i	−0.991165	−	0.132633i	$-0.957657\pi$
$137$	−7.14509	−	12.3757i	−0.610446	−	1.05732i	0.380719	−	0.924691i	$-0.375676\pi$
$138$		−	1.10523i		−	0.0940838i
$139$	−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
$141$	5.00221	+	18.6685i	0.421262	+	1.57217i
$142$	5.98525	−	5.98525i	0.502271	−	0.502271i
$143$		0			0
$144$			4.52189i			0.376824i
$145$	−4.34696	+	0.812525i	−0.360995	+	0.0674765i
$146$	−13.5125	+	23.4044i	−1.11830	+	1.93696i
$147$	10.5744	+	2.83341i	0.872165	+	0.233696i
$148$	7.34036			0.603374
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.301308	−	0.953527i	$-0.597423\pi$
$149$	−12.6828	−	3.39833i	−1.03901	−	0.278402i	−0.737704	+	0.675124i	$0.764090\pi$
$150$	−16.6034	−	7.33168i	−1.35566	−	0.598629i
$151$	−0.765191	+	0.765191i	−0.0622704	+	0.0622704i	−0.737556	−	0.675286i	$-0.764020\pi$
$151$	−0.765191	+	0.765191i	−0.0622704	+	0.0622704i	0.675286	+	0.737556i	$0.264020\pi$
$152$	−0.164314	+	0.613227i	−0.0133276	+	0.0497392i
$153$	−1.81545	+	0.486448i	−0.146770	+	0.0393270i
$154$	−24.2562	+	6.49942i	−1.95462	+	0.523738i
$155$	−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	$0.695215\pi$
$158$	−1.46272	+	2.53350i	−0.116368	+	0.201555i
$159$	−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
$162$	−17.3257	+	10.0030i	−1.36124	+	0.785912i
$163$	1.96032	−	1.13179i	0.153544	−	0.0886486i	−0.421260	−	0.906940i	$-0.638412\pi$
$163$	1.96032	−	1.13179i	0.153544	−	0.0886486i	0.574803	+	0.818292i	$0.305079\pi$
$164$	−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
$167$	−0.309785	+	0.536563i	−0.0239719	+	0.0415205i	−0.877762	−	0.479096i	$-0.840965\pi$
$167$	−0.309785	+	0.536563i	−0.0239719	+	0.0415205i	0.853791	+	0.520617i	$0.174298\pi$
$168$	−5.86012	−	5.86012i	−0.452118	−	0.452118i
$169$		0			0
$170$	8.27267	+	0.638370i	0.634485	+	0.0489608i
$171$	0.481470	−	0.129009i	0.0368189	−	0.00986560i
$172$	−11.5322	+	3.09005i	−0.879324	+	0.235614i
$173$	−1.71382	+	6.39606i	−0.130299	+	0.486283i	−0.999973	−	0.00734343i	$-0.997662\pi$
$173$	−1.71382	+	6.39606i	−0.130299	+	0.486283i	0.869674	+	0.493627i	$0.164329\pi$
$174$	−5.07636	+	5.07636i	−0.384838	+	0.384838i
$175$	16.4998	−	6.39155i	1.24727	−	0.483155i
$176$	18.2392	+	4.88718i	1.37483	+	0.368385i
$177$	24.0977			1.81130
$178$	−8.32336	−	2.23024i	−0.623862	−	0.167163i
$179$	−1.09512	+	1.89680i	−0.0818528	+	0.141773i	−0.904046	−	0.427436i	$-0.859417\pi$
$179$	−1.09512	+	1.89680i	−0.0818528	+	0.141773i	0.822193	+	0.569209i	$0.192750\pi$
$180$	−2.76285	+	0.516426i	−0.205930	+	0.0384921i
$181$			9.59255i			0.713009i	0.934294	+	0.356504i	$0.116031\pi$
$181$			9.59255i			0.713009i	−0.934294	+	0.356504i	$0.883969\pi$
$182$		0			0
$183$	4.04484	−	4.04484i	0.299003	−	0.299003i
$184$	−0.0931154	−	0.347511i	−0.00686456	−	0.0256189i
$185$	−2.22585	−	11.9082i	−0.163648	−	0.875506i
$186$	−18.3864	+	10.6154i	−1.34816	+	0.778359i
$187$			7.84842i			0.573933i
$188$	−6.60639	−	11.4426i	−0.481820	−	0.834537i
$189$	3.76166	−	14.0387i	0.273621	−	1.02117i
$190$	−2.19397	−	0.169300i	−0.159167	−	0.0122823i
$191$	−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
$193$	−0.246025	−	0.142043i	−0.0177093	−	0.0102245i	0.491119	−	0.871092i	$-0.336588\pi$
$193$	−0.246025	−	0.142043i	−0.0177093	−	0.0102245i	−0.508829	+	0.860868i	$0.669921\pi$
$194$	−32.6495			−2.34410
$195$		0			0
$196$	−7.48414			−0.534581
$197$	22.3860	+	12.9246i	1.59494	+	0.920838i	0.992442	+	0.122716i	$0.0391604\pi$
$197$	22.3860	+	12.9246i	1.59494	+	0.920838i	0.602496	+	0.798122i	$0.294173\pi$
$198$	−1.70386	−	6.35890i	−0.121088	−	0.451907i
$199$	−2.87625	−	4.98181i	−0.203892	−	0.353151i	0.745887	−	0.666072i	$-0.232026\pi$
$199$	−2.87625	−	4.98181i	−0.203892	−	0.353151i	−0.949779	+	0.312921i	$0.898692\pi$
$200$	−5.83819	−	0.906420i	−0.412823	−	0.0640936i
$201$	1.17458	−	4.38359i	0.0828484	−	0.309194i
$202$	−4.17053	−	7.22357i	−0.293437	−	0.508248i
$203$		−	6.99884i		−	0.491223i
$204$	4.71101	−	2.71990i	0.329836	−	0.190431i
$205$	−0.850235	+	1.24115i	−0.0593830	+	0.0866859i
$206$	6.56536	+	24.5023i	0.457430	+	1.70715i
$207$	−0.199737	+	0.199737i	−0.0138827	+	0.0138827i
$208$		0			0
$209$		−	2.08146i		−	0.143977i
$210$	16.2340	−	23.6980i	1.12025	−	1.63532i
$211$	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
$213$	−9.15863			−0.627539
$214$	12.5088	+	3.35173i	0.855085	+	0.229119i
$215$	8.50993	+	17.7716i	0.580372	+	1.21201i
$216$	−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
$219$	28.2451	−	7.56826i	1.90863	−	0.511416i
$220$	−0.903013	+	11.7022i	−0.0608811	+	0.788961i
$221$		0			0
$222$	−13.9063	−	13.9063i	−0.933331	−	0.933331i
$223$	−3.70762	+	6.42178i	−0.248280	+	0.430034i	−0.963049	−	0.269327i	$-0.913199\pi$
$223$	−3.70762	+	6.42178i	−0.248280	+	0.430034i	0.714768	+	0.699361i	$0.246532\pi$
$224$	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
$227$	3.37949	−	1.95115i	0.224305	−	0.129502i	−0.383637	−	0.923484i	$-0.625329\pi$
$227$	3.37949	−	1.95115i	0.224305	−	0.129502i	0.607942	+	0.793981i	$0.291995\pi$
$228$	−1.24939	+	0.721337i	−0.0827430	+	0.0477717i
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	0.166912	−	0.985972i	$-0.446621\pi$
$229$	−12.3946	−	12.3946i	−0.819060	−	0.819060i	−0.985972	+	0.166912i	$0.946621\pi$
$230$	1.12471	−	0.538566i	0.0741609	−	0.0355120i
$231$	23.5311	+	13.5857i	1.54823	+	0.893872i
$232$	−1.16844	+	2.02381i	−0.0767121	+	0.132869i
$233$	2.88962	+	2.88962i	0.189305	+	0.189305i	0.795396	−	0.606090i	$-0.207263\pi$
$233$	2.88962	+	2.88962i	0.189305	+	0.189305i	−0.606090	+	0.795396i	$0.707263\pi$
$234$		0			0
$235$	−16.5599	+	14.1873i	−1.08025	+	0.925474i
$236$	−15.9129	+	4.26384i	−1.03584	+	0.277552i
$237$	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	$-0.615384\pi$
$239$	8.97299	−	8.97299i	0.580415	−	0.580415i	0.935017	+	0.354602i	$0.115384\pi$
$240$	−19.4814	+	9.32866i	−1.25752	+	0.602162i
$241$	−16.9497	−	4.54165i	−1.09183	−	0.292554i	−0.332394	−	0.943141i	$-0.607856\pi$
$241$	−16.9497	−	4.54165i	−1.09183	−	0.292554i	−0.759432	+	0.650587i	$0.774523\pi$
$242$	−7.34239			−0.471986
$243$	9.00835	+	2.41378i	0.577886	+	0.154844i
$244$	−1.95530	+	3.38669i	−0.125176	+	0.216810i
$245$	2.26945	+	12.1414i	0.144990	+	0.775687i
$246$			2.44232i			0.155716i
$247$		0			0
$248$	−4.88677	+	4.88677i	−0.310311	+	0.310311i
$249$	−3.88472	−	14.4980i	−0.246184	−	0.918771i
$250$	−0.629785	−	20.4686i	−0.0398311	−	1.29455i
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.231659	−	0.972797i	$-0.425585\pi$
$251$	18.8524	−	10.8845i	1.18996	−	0.687021i	0.958296	+	0.285776i	$0.0922513\pi$
$252$		−	4.44834i		−	0.280219i
$253$	0.589774	+	1.02152i	0.0370787	+	0.0642223i
$254$	0.609678	−	2.27535i	0.0382546	−	0.142768i
$255$	−5.84100	−	6.81784i	−0.365778	−	0.426950i
$256$	−10.4820	−	18.1554i	−0.655125	−	1.13471i
$257$	3.31629	+	12.3766i	0.206864	+	0.772029i	0.988873	+	0.148761i	$0.0475286\pi$
$257$	3.31629	+	12.3766i	0.206864	+	0.772029i	−0.782009	+	0.623268i	$0.785805\pi$
$258$	27.7019	+	15.9937i	1.72465	+	0.995725i
$259$	19.1728			1.19134
$260$		0			0
$261$	1.83479			0.113571
$262$	−8.87405	−	5.12344i	−0.548241	−	0.316527i
$263$	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
$265$	0.769439	−	9.97120i	0.0472663	−	0.612526i
$266$	0.901363	−	3.36393i	0.0552661	−	0.206256i
$267$	4.66185	+	8.07456i	0.285301	+	0.494155i
$268$			3.10252i			0.189516i
$269$	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
$271$	−4.52218	−	16.8770i	−0.274703	−	1.02521i	−0.956040	−	0.293236i	$-0.905268\pi$
$271$	−4.52218	−	16.8770i	−0.274703	−	1.02521i	0.681337	−	0.731970i	$-0.261399\pi$
$272$	6.98212	−	6.98212i	0.423353	−	0.423353i
$273$		0			0
$274$		−	26.1743i		−	1.58125i
$275$	19.2581	−	2.08356i	1.16131	−	0.125644i
$276$	0.408777	−	0.708022i	0.0246055	−	0.0426179i
$277$	−2.96961	−	0.795705i	−0.178427	−	0.0478093i	0.168499	−	0.985702i	$-0.446108\pi$
$277$	−2.96961	−	0.795705i	−0.178427	−	0.0478093i	−0.346926	+	0.937892i	$0.612775\pi$
$278$	−31.9008			−1.91328
$279$	5.24118	+	1.40437i	0.313781	+	0.0840775i
$280$	3.10780	−	8.81892i	0.185727	−	0.527031i
$281$	18.6757	−	18.6757i	1.11410	−	1.11410i	0.121508	−	0.992590i	$-0.461227\pi$
$281$	18.6757	−	18.6757i	1.11410	−	1.11410i	0.992590	−	0.121508i	$-0.0387731\pi$
$282$	−9.16221	+	34.1938i	−0.545602	+	2.03621i
$283$	−14.8164	+	3.97005i	−0.880745	+	0.235995i	−0.670728	−	0.741703i	$-0.734018\pi$
$283$	−14.8164	+	3.97005i	−0.880745	+	0.235995i	−0.210016	+	0.977698i	$0.567352\pi$
$284$	6.04787	−	1.62052i	0.358875	−	0.0961603i
$285$	1.54907	+	1.80814i	0.0917593	+	0.107105i
$286$		0			0
$287$	−1.68363	−	1.68363i	−0.0993814	−	0.0993814i
$288$	−3.04497	+	5.27404i	−0.179427	+	0.310776i
$289$	−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
$292$	−17.3125	+	9.99535i	−1.01314	+	0.584934i
$293$	−8.98649	+	5.18835i	−0.524996	+	0.303107i	−0.738976	−	0.673731i	$-0.764691\pi$
$293$	−8.98649	+	5.18835i	−0.524996	+	0.303107i	0.213980	+	0.976838i	$0.431357\pi$
$294$	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
$297$	7.95528	−	13.7790i	0.461612	−	0.799536i
$298$	−17.0057	−	17.0057i	−0.985111	−	0.985111i
$299$		0			0
$300$	−7.92463	−	10.8376i	−0.457529	−	0.625709i
$301$	−30.1219	+	8.07113i	−1.73620	+	0.465212i
$302$	−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
$305$	6.08710	+	2.14510i	0.348546	+	0.122828i
$306$	−3.32524	−	0.890994i	−0.190091	−	0.0509347i
$307$	−2.13935			−0.122099			−0.0610496	−	0.998135i	$-0.519445\pi$
$307$	−2.13935			−0.122099			−0.0610496	+	0.998135i	$0.519445\pi$
$308$	−17.9425	−	4.80768i	−1.02237	−	0.273943i
$309$	13.7235	−	23.7698i	0.780704	−	1.35222i
$310$	−19.7619	−	13.5376i	−1.12240	−	0.768884i
$311$		−	3.82084i		−	0.216660i	−0.994115	−	0.108330i	$-0.965450\pi$
$311$		−	3.82084i		−	0.216660i	0.994115	−	0.108330i	$-0.0345503\pi$
$312$		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	$0.211161\pi$
$314$	2.03461	+	7.59327i	0.114820	+	0.428513i
$315$	−7.21648	+	1.34889i	−0.406603	+	0.0760014i
$316$	−1.87406	+	1.08199i	−0.105424	+	0.0608666i
$317$			23.1127i			1.29814i	0.760730	+	0.649068i	$0.224841\pi$
$317$			23.1127i			1.29814i	−0.760730	+	0.649068i	$0.775159\pi$
$318$	−8.11767	−	14.0602i	−0.455216	−	0.788458i
$319$	1.98301	−	7.40069i	0.111027	−	0.414359i
$320$	3.86342	−	3.30988i	0.215972	−	0.185028i
$321$	−7.00609	−	12.1349i	−0.391042	−	0.677305i
$322$	0.510796	+	1.90632i	0.0284656	+	0.106235i
$323$	−0.942624	−	0.544224i	−0.0524490	−	0.0302814i
$324$	−14.7987			−0.822149
$325$		0			0
$326$	4.14604			0.229628
$327$	−24.0125	−	13.8636i	−1.32789	−	0.766660i
$328$	0.205764	+	0.767921i	0.0113614	+	0.0424013i
$329$	−17.2557	−	29.8878i	−0.951338	−	1.64777i
$330$	23.8806	−	20.4590i	1.31458	−	1.12623i
$331$	−0.516858	+	1.92894i	−0.0284091	+	0.106024i	−0.978675	−	0.205417i	$-0.934145\pi$
$331$	−0.516858	+	1.92894i	−0.0284091	+	0.106024i	0.950265	+	0.311441i	$0.100812\pi$
$332$	5.13052	+	8.88632i	0.281574	+	0.487700i
$333$			5.02628i			0.275438i
$334$	−0.982786	+	0.567412i	−0.0537756	+	0.0310474i
$335$	5.03317	−	0.940791i	0.274992	−	0.0514009i
$336$	−8.84765	−	33.0199i	−0.482679	−	1.80138i
$337$	6.12727	−	6.12727i	0.333773	−	0.333773i	−0.520244	−	0.854018i	$-0.674159\pi$
$337$	6.12727	−	6.12727i	0.333773	−	0.333773i	0.854018	+	0.520244i	$0.174159\pi$
$338$		0			0
$339$			4.54338i			0.246763i
$340$	5.06343	+	3.46863i	0.274603	+	0.188113i
$341$	11.3292	−	19.6227i	0.613508	−	1.06263i
$342$	0.881876	+	0.236298i	0.0476864	+	0.0127775i
$343$	5.22396			0.282067
$344$	10.0576	+	2.69492i	0.542269	+	0.145301i
$345$	−1.27257	−	0.448456i	−0.0685129	−	0.0241441i
$346$	−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
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	−0.430418	−	0.902630i	$-0.641634\pi$
$349$	−6.57321	+	1.76129i	−0.351856	+	0.0942795i	0.0785620	+	0.996909i	$0.474967\pi$
$350$	32.0262	+	4.97228i	1.71187	+	0.265780i
$351$		0			0
$352$	17.9821	+	17.9821i	0.958448	+	0.958448i
$353$	13.6631	−	23.6652i	0.727213	−	1.25957i	−0.230843	−	0.972991i	$-0.574148\pi$
$353$	13.6631	−	23.6652i	0.727213	−	1.25957i	0.958057	−	0.286579i	$-0.0925182\pi$
$354$	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
$357$	12.3050	−	7.10431i	0.651251	−	0.376000i
$358$	−3.47423	+	2.00585i	−0.183619	+	0.106012i
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	0.596699	−	0.802465i	$-0.296479\pi$
$359$	−3.89871	−	3.89871i	−0.205766	−	0.205766i	−0.802465	+	0.596699i	$0.796479\pi$
$360$	2.31193	+	0.814730i	0.121850	+	0.0429400i
$361$	−16.2045	−	9.35567i	−0.852868	−	0.492404i
$362$	−8.78501	+	15.2161i	−0.461730	+	0.799740i
$363$	5.61766	+	5.61766i	0.294851	+	0.294851i
$364$		0			0
$365$	21.4651	+	25.0548i	1.12353	+	1.31143i
$366$	10.1204	−	2.71176i	0.529003	−	0.141746i
$367$	−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
$370$	7.37496	−	20.9277i	0.383406	−	1.08798i
$371$	15.2885	+	4.09653i	0.793738	+	0.212681i
$372$	−15.7046			−0.814248
$373$	−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
$375$	−15.1787	+	16.1424i	−0.783823	+	0.833588i
$376$			11.5232i			0.594266i
$377$		0			0
$378$	18.8238	−	18.8238i	0.968191	−	0.968191i
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	0.949515	+	0.313722i	$0.101576\pi$
$379$	5.53029	+	20.6393i	0.284072	+	1.06017i	−0.665443	+	0.746449i	$0.731757\pi$
$380$	−1.34286	−	0.919906i	−0.0688871	−	0.0471902i
$381$	−2.20733	+	1.27440i	−0.113085	+	0.0652897i
$382$		−	6.83407i		−	0.349661i
$383$	9.70362	+	16.8072i	0.495832	+	0.858806i	0.999988	−	0.00480620i	$-0.00152987\pi$
$383$	9.70362	+	16.8072i	0.495832	+	0.858806i	−0.504157	+	0.863612i	$0.668197\pi$
$384$	−4.59660	+	17.1547i	−0.234569	+	0.875424i
$385$	−2.35865	+	30.5658i	−0.120208	+	1.55778i
$386$	−0.260170	−	0.450628i	−0.0132423	−	0.0229364i
$387$	−2.11590	−	7.89664i	−0.107557	−	0.401409i
$388$	−20.9155	−	12.0756i	−1.06182	−	0.613045i
$389$	−14.8591			−0.753387			−0.376693	−	0.926338i	$-0.622939\pi$
$389$	−14.8591			−0.753387			−0.376693	+	0.926338i	$0.622939\pi$
$390$		0			0
$391$	0.616816			0.0311937
$392$	5.65266	+	3.26357i	0.285503	+	0.164835i
$393$	2.86960	+	10.7095i	0.144752	+	0.540222i
$394$	23.6731	+	41.0030i	1.19263	+	2.06570i
$395$	2.32358	+	2.71217i	0.116912	+	0.136464i
$396$	1.26036	−	4.70374i	0.0633357	−	0.236372i
$397$	2.63889	+	4.57070i	0.132442	+	0.229397i	0.924617	−	0.380897i	$-0.124385\pi$
$397$	2.63889	+	4.57070i	0.132442	+	0.229397i	−0.792175	+	0.610294i	$0.791051\pi$
$398$		−	10.5365i		−	0.528145i
$399$	−3.26338	+	1.88411i	−0.163373	+	0.0943236i
$400$	−18.9860	−	15.2789i	−0.949301	−	0.763943i
$401$	−7.21557	−	26.9289i	−0.360328	−	1.34476i	−0.873645	−	0.486564i	$-0.838250\pi$
$401$	−7.21557	−	26.9289i	−0.360328	−	1.34476i	0.513317	−	0.858199i	$-0.328417\pi$
$402$	5.87772	−	5.87772i	0.293154	−	0.293154i
$403$		0			0
$404$		−	6.16996i		−	0.306967i
$405$	4.48748	+	24.0077i	0.222985	+	1.19295i
$406$	6.40965	−	11.1018i	0.318106	−	0.550975i
$407$	20.2737	+	5.43231i	1.00493	+	0.269270i
$408$	−4.74421			−0.234873
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	0.195340	−	0.980736i	$-0.437419\pi$
$409$	−2.54532	−	0.682016i	−0.125858	−	0.0337235i	−0.321198	+	0.947012i	$0.604086\pi$
$410$	−2.48535	+	1.19011i	−0.122742	+	0.0587753i
$411$	−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
$414$	−0.499753	+	0.133908i	−0.0245615	+	0.00658124i
$415$	12.8604	−	11.0178i	0.631293	−	0.540844i
$416$		0			0
$417$	24.4073	+	24.4073i	1.19523	+	1.19523i
$418$	1.90623	−	3.30169i	0.0932368	−	0.161491i
$419$	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	0.405256	−	0.914203i	$-0.367183\pi$
$421$	−10.4427	−	10.4427i	−0.508948	−	0.508948i	−0.914203	+	0.405256i	$0.867183\pi$
$422$	5.11948	−	2.95573i	0.249212	−	0.143883i
$423$	7.83526	−	4.52369i	0.380964	−	0.219949i
$424$	−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
$427$	−5.10721	+	8.84594i	−0.247155	+	0.428085i
$428$	6.77359	+	6.77359i	0.327414	+	0.327414i
$429$		0			0
$430$	−2.77671	+	35.9835i	−0.133905	+	1.73528i
$431$	−16.5486	+	4.43419i	−0.797119	+	0.213587i	−0.634319	−	0.773072i	$-0.718719\pi$
$431$	−16.5486	+	4.43419i	−0.797119	+	0.213587i	−0.162800	+	0.986659i	$0.552053\pi$
$432$	−19.3352	+	5.18086i	−0.930267	+	0.249264i
$433$	2.90826	−	10.8538i	0.139762	−	0.521599i	−0.860171	−	0.510006i	$-0.829643\pi$
$433$	2.90826	−	10.8538i	0.139762	−	0.521599i	0.999933	−	0.0115927i	$-0.00369014\pi$
$434$	26.8070	−	26.8070i	1.28678	−	1.28678i
$435$	3.78517	+	7.90470i	0.181485	+	0.379002i
$436$	18.3096	+	4.90604i	0.876870	+	0.234957i
$437$	−0.163584			−0.00782528
$438$	51.7347	+	13.8623i	2.47198	+	0.662365i
$439$	2.12218	−	3.67572i	0.101286	−	0.175432i	−0.810929	−	0.585145i	$-0.801038\pi$
$439$	2.12218	−	3.67572i	0.101286	−	0.175432i	0.912215	+	0.409712i	$0.134371\pi$
$440$	5.78494	−	8.44472i	0.275786	−	0.402586i
$441$		−	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	$0.0799392\pi$
$444$	−3.76518	−	14.0518i	−0.178687	−	0.666870i
$445$	−5.94516	+	8.67861i	−0.281828	+	0.411405i
$446$	−11.7623	+	6.79099i	−0.556963	+	0.321563i
$447$			26.0221i			1.23080i
$448$	4.02575	+	6.97281i	0.190199	+	0.329434i
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	−0.818385	−	0.574671i	$-0.805130\pi$
$449$	3.76524	−	14.0521i	0.177693	−	0.663158i	0.996077	−	0.0884873i	$-0.0282033\pi$
$450$	−1.30351	+	8.39586i	−0.0614483	+	0.395785i
$451$	−1.30327	−	2.25732i	−0.0613684	−	0.106293i
$452$	−0.803904	−	3.00021i	−0.0378124	−	0.141118i
$453$	1.85732	+	1.07233i	0.0872646	+	0.0503822i
$454$	7.14758			0.335453
$455$		0			0
$456$	1.25820			0.0589205
$457$	26.2365	+	15.1476i	1.22729	+	0.708576i	0.966462	−	0.256809i	$-0.0826711\pi$
$457$	26.2365	+	15.1476i	1.22729	+	0.708576i	0.260828	+	0.965385i	$0.416004\pi$
$458$	−8.30966	−	31.0121i	−0.388285	−	1.44910i
$459$	−4.16003	−	7.20538i	−0.194173	−	0.336318i
$460$	0.919687	+	0.0709688i	0.0428806	+	0.00330894i
$461$	−1.79565	+	6.70146i	−0.0836318	+	0.312118i	−0.995052	−	0.0993596i	$-0.968321\pi$
$461$	−1.79565	+	6.70146i	−0.0836318	+	0.312118i	0.911420	+	0.411478i	$0.134987\pi$
$462$	24.8840	+	43.1003i	1.15771	+	2.00521i
$463$			31.4463i			1.46143i	0.682680	+	0.730717i	$0.260814\pi$
$463$			31.4463i			1.46143i	−0.682680	+	0.730717i	$0.739186\pi$
$464$	−8.34794	+	4.81968i	−0.387543	+	0.223748i
$465$	4.76220	+	25.4775i	0.220842	+	1.18149i
$466$	1.93727	+	7.22999i	0.0897423	+	0.334923i
$467$	−3.69622	+	3.69622i	−0.171041	+	0.171041i	−0.787436	−	0.616396i	$-0.788592\pi$
$467$	−3.69622	+	3.69622i	−0.171041	+	0.171041i	0.616396	+	0.787436i	$0.288592\pi$
$468$		0			0
$469$			8.10369i			0.374194i
$470$	−39.2609	+	7.33857i	−1.81097	+	0.338503i
$471$	4.25293	−	7.36630i	0.195965	−	0.339421i
$472$	13.8781	+	3.71862i	0.638790	+	0.171163i
$473$	−34.1382			−1.56968
$474$	5.60024	+	1.50058i	0.257227	+	0.0689239i
$475$	−1.08515	+	2.45745i	−0.0497901	+	0.112755i
$476$	−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
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.194928	−	0.980818i	$-0.437553\pi$
$479$	18.6940	−	5.00904i	0.854150	−	0.228869i	0.659222	+	0.751949i	$0.270886\pi$
$480$	−29.0036	−	2.23810i	−1.32383	−	0.102155i
$481$		0			0
$482$	−22.7270	−	22.7270i	−1.03518	−	1.03518i
$483$	1.06771	−	1.84934i	0.0485827	−	0.0841477i
$484$	−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
$487$	20.2327	−	11.6813i	0.916830	−	0.529332i	0.0342077	−	0.999415i	$-0.489109\pi$
$487$	20.2327	−	11.6813i	0.916830	−	0.529332i	0.882622	+	0.470083i	$0.155776\pi$
$488$	2.95363	−	1.70528i	0.133704	−	0.0771943i
$489$	−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	0.854946	−	0.518716i	$-0.173590\pi$
$491$	18.4624	+	10.6593i	0.833198	+	0.481047i	−0.0217482	+	0.999763i	$0.506923\pi$
$492$	−0.903303	+	1.56457i	−0.0407241	+	0.0705362i
$493$	−2.83305	−	2.83305i	−0.127594	−	0.127594i
$494$		0			0
$495$	−8.01301	−	0.618334i	−0.360158	−	0.0277920i
$496$	−27.5354	+	7.37809i	−1.23638	+	0.331286i
$497$	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	−0.0318687	+	0.999492i	$0.510146\pi$
$499$	−23.0389	+	23.0389i	−1.03136	+	1.03136i	−0.999492	+	0.0318687i	$0.989854\pi$
$500$	7.16697	−	13.3453i	0.320516	−	0.596818i
$501$	1.18606	+	0.317803i	0.0529891	+	0.0141984i
$502$	39.8727			1.77960
$503$	−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
$505$	−10.0095	+	1.87095i	−0.445415	+	0.0832561i
$506$			2.16050i			0.0960458i
$507$		0			0
$508$	1.23211	−	1.23211i	0.0546662	−	0.0546662i
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	−0.864050	−	0.503405i	$-0.832080\pi$
$509$	−8.29035	−	30.9400i	−0.367463	−	1.37139i	0.496587	−	0.867987i	$-0.334586\pi$
$510$	−3.02135	−	16.1640i	−0.133787	−	0.715754i
$511$	−45.2197	+	26.1076i	−2.00040	+	1.15493i
$512$		−	20.4758i		−	0.904912i
$513$	1.10327	+	1.91092i	0.0487105	+	0.0843690i
$514$	−6.07422	+	22.6693i	−0.267923	+	0.999901i
$515$	30.8759	+	2.38258i	1.36056	+	0.104989i
$516$	11.8307	+	20.4914i	0.520818	+	0.902084i
$517$	−9.77825	−	36.4929i	−0.430047	−	1.60496i
$518$	30.4127	+	17.5588i	1.33626	+	0.771489i
$519$	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	$0.671919\pi$
$522$	2.91042	+	1.68033i	0.127386	+	0.0735461i
$523$	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
$525$	−20.6989	−	28.3075i	−0.903376	−	1.23544i
$526$	−7.82436	+	29.2009i	−0.341158	+	1.27322i
$527$	−5.92431	−	10.2612i	−0.258067	−	0.446985i
$528$		−	37.4226i		−	1.62861i
$529$	−19.8383	+	11.4536i	−0.862535	+	0.497985i
$530$	10.3523	−	15.1120i	0.449675	−	0.656425i
$531$	−2.91964	−	10.8963i	−0.126702	−	0.472857i
$532$	1.82159	−	1.82159i	0.0789759	−	0.0789759i
$533$		0			0
$534$			17.0776i			0.739019i
$535$	8.93473	−	13.0427i	0.386282	−	0.563885i
$536$	1.35290	−	2.34329i	0.0584363	−	0.101215i
$537$	4.19281	+	1.12346i	0.180933	+	0.0484809i
$538$	59.1745			2.55119
$539$	−20.6708	−	5.53871i	−0.890353	−	0.238569i
$540$	−5.37367	−	11.2220i	−0.231246	−	0.482919i
$541$	27.6908	−	27.6908i	1.19052	−	1.19052i	0.213597	−	0.976922i	$-0.431482\pi$
$541$	27.6908	−	27.6908i	1.19052	−	1.19052i	0.976922	−	0.213597i	$-0.0685180\pi$
$542$	8.28297	−	30.9125i	0.355784	−	1.32780i
$543$	18.3632	−	4.92042i	0.788042	−	0.211155i
$544$	12.8452	−	3.44185i	0.550731	−	0.147568i
$545$	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	$0.686652\pi$
$548$	9.68071	−	16.7675i	0.413540	−	0.716272i
$549$	−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
$552$	−0.617486	+	0.356506i	−0.0262820	+	0.0151739i
$553$	−4.89500	+	2.82613i	−0.208156	+	0.120179i
$554$	−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
$557$	8.12429	−	14.0717i	0.344237	−	0.596237i	−0.640978	−	0.767560i	$-0.721471\pi$
$557$	8.12429	−	14.0717i	0.344237	−	0.596237i	0.985215	+	0.171323i	$0.0548042\pi$
$558$	7.02763	+	7.02763i	0.297503	+	0.297503i
$559$		0			0
$560$	29.2903	−	25.0937i	1.23774	−	1.06040i
$561$	15.0244	−	4.02578i	0.634332	−	0.169969i
$562$	46.7277	−	12.5206i	1.97109	−	0.528151i
$563$	8.41827	−	31.4174i	0.354788	−	1.32409i	−0.525964	−	0.850507i	$-0.676295\pi$
$563$	8.41827	−	31.4174i	0.354788	−	1.32409i	0.880751	−	0.473579i	$-0.157038\pi$
$564$	−18.5161	+	18.5161i	−0.779670	+	0.779670i
$565$	−4.62343	+	2.21393i	−0.194509	+	0.0931408i
$566$	−27.1382	−	7.27167i	−1.14071	−	0.305651i
$567$	−38.6538			−1.62331
$568$	−5.27453	−	1.41331i	−0.221314	−	0.0593010i
$569$	16.4164	−	28.4341i	0.688212	−	1.19202i	−0.284203	−	0.958764i	$-0.591729\pi$
$569$	16.4164	−	28.4341i	0.688212	−	1.19202i	0.972416	−	0.233255i	$-0.0749376\pi$
$570$	0.801283	+	4.28681i	0.0335620	+	0.179555i
$571$		−	31.7967i		−	1.33065i	−0.746554	−	0.665325i	$-0.768293\pi$
$571$		−	31.7967i		−	1.33065i	0.746554	−	0.665325i	$-0.231707\pi$
$572$		0			0
$573$	−5.22875	+	5.22875i	−0.218434	+	0.218434i
$574$	−1.12874	−	4.21253i	−0.0471129	−	0.175828i
$575$	−0.163750	−	1.51352i	−0.00682883	−	0.0631180i
$576$	−1.82796	+	1.05538i	−0.0761652	+	0.0439740i
$577$		−	39.9389i		−	1.66268i	−0.555767	−	0.831338i	$-0.687575\pi$
$577$		−	39.9389i		−	1.66268i	0.555767	−	0.831338i	$-0.312425\pi$
$578$	−11.8102	−	20.4559i	−0.491241	−	0.850854i
$579$	−0.145719	+	0.543832i	−0.00605589	+	0.0226009i
$580$	−3.89818	−	4.55010i	−0.161863	−	0.188933i
$581$	13.4008	+	23.2109i	0.555959	+	0.962949i
$582$	16.7473	+	62.5017i	0.694197	+	2.59078i
$583$	15.0056	+	8.66348i	0.621468	+	0.358805i
$584$	17.4345			0.721444
$585$		0			0
$586$	−19.0063			−0.785143
$587$	−16.1561	−	9.32773i	−0.666834	−	0.384997i	0.128042	−	0.991769i	$-0.459131\pi$
$587$	−16.1561	−	9.32773i	−0.666834	−	0.384997i	−0.794876	+	0.606772i	$0.792464\pi$
$588$	3.83892	+	14.3271i	0.158315	+	0.590838i
$589$	1.57117	+	2.72135i	0.0647389	+	0.112131i
$590$	−3.83147	+	49.6522i	−0.157739	+	2.04415i
$591$	13.2591	−	49.4837i	0.545407	−	2.03549i
$592$	−13.2032	−	22.8686i	−0.542647	−	0.939893i
$593$			8.65172i			0.355284i	0.984095	+	0.177642i	$0.0568468\pi$
$593$			8.65172i			0.355284i	−0.984095	+	0.177642i	$0.943153\pi$
$594$	25.2380	−	14.5712i	1.03553	−	0.597862i
$595$	13.2256	+	9.05998i	0.542195	+	0.371423i
$596$	−4.60433	−	17.1836i	−0.188601	−	0.703867i
$597$	−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	$-0.255247\pi$
$600$	1.25947	+	11.6411i	0.0514177	+	0.475247i
$601$	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
$603$	−2.12443			−0.0865136
$604$	−1.41621	−	0.379473i	−0.0576249	−	0.0154405i
$605$	−2.97922	+	8.45405i	−0.121123	+	0.343706i
$606$	−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
$609$	−13.3981	+	3.59000i	−0.542917	+	0.145474i
$610$	7.69108	+	8.97731i	0.311403	+	0.363481i
$611$		0			0
$612$	−1.80063	−	1.80063i	−0.0727863	−	0.0727863i
$613$	−10.1397	+	17.5625i	−0.409540	+	0.709344i	−0.994838	−	0.101474i	$-0.967644\pi$
$613$	−10.1397	+	17.5625i	−0.409540	+	0.709344i	0.585298	+	0.810818i	$0.300978\pi$
$614$	−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
$617$	−7.50891	+	4.33527i	−0.302297	+	0.174531i	−0.643474	−	0.765468i	$-0.722508\pi$
$617$	−7.50891	+	4.33527i	−0.302297	+	0.174531i	0.341177	+	0.939999i	$0.389174\pi$
$618$	43.5376	−	25.1365i	1.75134	−	1.01114i
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	0.134638	−	0.990895i	$-0.457013\pi$
$619$	−21.3034	−	21.3034i	−0.856257	−	0.856257i	−0.990895	+	0.134638i	$0.957013\pi$
$620$	−7.65267	−	15.9813i	−0.307339	−	0.641826i
$621$	−1.08290	−	0.625215i	−0.0434554	−	0.0250890i
$622$	3.49919	−	6.06077i	0.140305	−	0.243015i
$623$	−11.7725	−	11.7725i	−0.471657	−	0.471657i
$624$		0			0
$625$	−23.8231	−	7.58013i	−0.952925	−	0.303205i
$626$	7.61954	−	2.04165i	0.304538	−	0.0816007i
$627$	−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
$630$	−12.6824	−	4.46931i	−0.505279	−	0.178061i
$631$	27.4324	+	7.35050i	1.09207	+	0.292619i	0.759531	−	0.650472i	$-0.225429\pi$
$631$	27.4324	+	7.35050i	1.09207	+	0.292619i	0.332537	+	0.943090i	$0.392095\pi$
$632$	1.88727			0.0750715
$633$	−6.17835	−	1.65548i	−0.245567	−	0.0657996i
$634$	−21.1670	+	36.6622i	−0.840647	+	1.45604i
$635$	−2.37246	−	1.62522i	−0.0941483	−	0.0644950i
$636$		−	12.0094i		−	0.476206i
$637$		0			0
$638$	9.92320	−	9.92320i	0.392863	−	0.392863i
$639$	1.10965	+	4.14125i	0.0438969	+	0.163825i
$640$	−19.6968	+	3.68169i	−0.778585	+	0.145532i
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	−0.193204	−	0.981159i	$-0.561888\pi$
$641$	14.1756	−	8.18429i	0.559903	−	0.323260i	0.753107	+	0.657899i	$0.228554\pi$
$642$		−	25.6652i		−	1.01292i
$643$	−20.5258	−	35.5518i	−0.809460	−	1.40203i	−0.913239	−	0.407425i	$-0.866427\pi$
$643$	−20.5258	−	35.5518i	−0.809460	−	1.40203i	0.103779	−	0.994600i	$-0.466907\pi$
$644$	−0.377841	+	1.41012i	−0.0148890	+	0.0555666i
$645$	29.6555	−	25.4065i	1.16768	−	1.00038i
$646$	−0.996819	−	1.72654i	−0.0392193	−	0.0679298i
$647$	0.733807	+	2.73861i	0.0288489	+	0.107666i	0.978849	−	0.204584i	$-0.0655841\pi$
$647$	0.733807	+	2.73861i	0.0288489	+	0.107666i	−0.950000	+	0.312250i	$0.898917\pi$
$648$	11.1772	+	6.45318i	0.439083	+	0.253505i
$649$	−47.1059			−1.84907
$650$		0			0
$651$	−41.0201			−1.60771
$652$	2.65599	+	1.53344i	0.104017	+	0.0600540i
$653$	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
$655$	−9.49985	+	8.13874i	−0.371190	+	0.318007i
$656$	−0.848749	+	3.16758i	−0.0331381	+	0.123673i
$657$	−6.84427	−	11.8546i	−0.267020	−	0.462493i
$658$		−	63.2122i		−	2.46427i
$659$	−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
$661$	6.64415	+	24.7963i	0.258427	+	0.964464i	0.966152	+	0.257975i	$0.0830553\pi$
$661$	6.64415	+	24.7963i	0.258427	+	0.964464i	−0.707724	+	0.706489i	$0.750278\pi$
$662$	−2.58641	+	2.58641i	−0.100524	+	0.100524i
$663$		0			0
$664$		−	8.94896i		−	0.347287i
$665$	−3.50751	−	2.40277i	−0.136015	−	0.0931755i
$666$	−4.60315	+	7.97288i	−0.178368	+	0.308943i
$667$	−0.581628	−	0.155847i	−0.0225207	−	0.00603441i
$668$	−0.839440			−0.0324789
$669$	14.1952	+	3.80358i	0.548817	+	0.147055i
$670$	8.84541	+	3.11714i	0.341728	+	0.120426i
$671$	−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	0.613098	−	0.790007i	$-0.289923\pi$
$673$	39.9267	−	10.6983i	1.53906	−	0.412390i	0.925962	+	0.377617i	$0.123256\pi$
$674$	15.3308	−	4.10787i	0.590519	−	0.158229i
$675$	−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	$0.611290\pi$
$678$	−4.16090	+	7.20690i	−0.159799	+	0.276779i
$679$	−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
$682$	35.9415	−	20.7508i	1.37627	−	0.794591i
$683$	−5.76170	+	3.32652i	−0.220465	+	0.127286i	−0.606166	−	0.795338i	$-0.707293\pi$
$683$	−5.76170	+	3.32652i	−0.220465	+	0.127286i	0.385700	+	0.922624i	$0.373960\pi$
$684$	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
$687$	−17.3696	+	30.0851i	−0.662692	+	1.14782i
$688$	30.3701	+	30.3701i	1.15785	+	1.15785i
$689$		0			0
$690$	−1.60790	−	1.87680i	−0.0612117	−	0.0714485i
$691$	36.3445	−	9.73848i	1.38261	−	0.370469i	0.510542	−	0.859853i	$-0.329445\pi$
$691$	36.3445	−	9.73848i	1.38261	−	0.370469i	0.872069	+	0.489384i	$0.162778\pi$
$692$	−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
$695$	−12.9440	+	36.7307i	−0.490993	+	1.39327i
$696$	4.47356	+	1.19869i	0.169570	+	0.0454361i
$697$	−1.36302			−0.0516282
$698$	−12.0397	−	3.22603i	−0.455710	−	0.122107i
$699$	4.04946	−	7.01387i	0.153165	−	0.265289i
$700$	18.6772	+	15.0303i	0.705931	+	0.568093i
$701$			40.3398i			1.52361i	0.647804	+	0.761807i	$0.275688\pi$
$701$			40.3398i			1.52361i	−0.647804	+	0.761807i	$0.724312\pi$
$702$		0			0
$703$	−2.05825	+	2.05825i	−0.0776285	+	0.0776285i
$704$	2.28126	+	8.51379i	0.0859783	+	0.320875i
$705$	35.6533	+	24.4238i	1.34278	+	0.919852i
$706$	43.3459	−	25.0258i	1.63134	−	0.941857i
$707$		−	16.1158i		−	0.606097i
$708$	16.3247	+	28.2753i	0.613521	+	1.06265i
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	0.311304	+	0.950311i	$0.399234\pi$
$709$	−11.5415	+	43.0733i	−0.433449	+	1.61765i	−0.744752	+	0.667341i	$0.767432\pi$
$710$	1.45620	−	18.8709i	0.0546501	−	0.708213i
$711$	−0.740887	−	1.28325i	−0.0277854	−	0.0481258i
$712$	1.43878	+	5.36959i	0.0539204	+	0.201234i
$713$	−1.54217	−	0.890371i	−0.0577546	−	0.0333447i
$714$	26.0250			0.973960
$715$		0			0
$716$	−2.96749			−0.110900
$717$	−21.7798	−	12.5746i	−0.813383	−	0.469607i
$718$	−2.61379	−	9.75479i	−0.0975457	−	0.364045i
$719$	13.7825	+	23.8720i	0.514001	+	0.890276i	0.999868	+	0.0162430i	$0.00517055\pi$
$719$	13.7825	+	23.8720i	0.514001	+	0.890276i	−0.485867	+	0.874033i	$0.661496\pi$
$720$	6.57846	+	7.67863i	0.245165	+	0.286166i
$721$	−12.6850	+	47.3409i	−0.472413	+	1.76307i
$722$	−17.1361	−	29.6807i	−0.637741	−	1.10460i
$723$			34.7768i			1.29336i
$724$	−11.2555	+	6.49836i	−0.418307	+	0.241510i
$725$	−6.19951	+	7.70371i	−0.230244	+	0.286109i
$726$	3.76622	+	14.0557i	0.139777	+	0.521656i
$727$	−29.4624	+	29.4624i	−1.09270	+	1.09270i	−0.0974593	+	0.995240i	$0.531072\pi$
$727$	−29.4624	+	29.4624i	−1.09270	+	1.09270i	−0.995240	+	0.0974593i	$0.968928\pi$
$728$		0			0
$729$			14.2845i			0.529057i
$730$	11.1031	+	59.4011i	0.410946	+	2.19853i
$731$	−8.92588	+	15.4601i	−0.330135	+	0.571811i
$732$	7.48617	+	2.00591i	0.276697	+	0.0741407i
$733$	23.3958			0.864144			0.432072	−	0.901839i	$-0.357783\pi$
$733$	23.3958			0.864144			0.432072	+	0.901839i	$0.357783\pi$
$734$	−31.9794	−	8.56885i	−1.18038	−	0.316282i
$735$	22.0785	−	10.5723i	0.814378	−	0.389965i
$736$	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
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.532581	−	0.846379i	$-0.678778\pi$
$739$	−15.5120	+	4.15644i	−0.570620	+	0.152897i	−0.0380389	+	0.999276i	$0.512111\pi$
$740$	12.4647	−	10.6788i	0.458210	−	0.392560i
$741$		0			0
$742$	20.4995	+	20.4995i	0.752561	+	0.752561i
$743$	26.1400	−	45.2759i	0.958985	−	1.66101i	0.234011	−	0.972234i	$-0.424815\pi$
$743$	26.1400	−	45.2759i	0.958985	−	1.66101i	0.724973	−	0.688777i	$-0.241852\pi$
$744$	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
$747$	−6.08487	+	3.51310i	−0.222634	+	0.128538i
$748$	−9.20901	+	5.31682i	−0.336715	+	0.194402i
$749$	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	0.866354	−	0.499431i	$-0.166458\pi$
$751$	23.7599	+	13.7178i	0.867010	+	0.500569i	0.000656703		1.00000i	$0.499791\pi$
$752$	−23.7659	+	41.1638i	−0.866655	+	1.50109i
$753$	−30.5066	−	30.5066i	−1.11172	−	1.11172i
$754$		0			0
$755$	−0.186169	+	2.41257i	−0.00677539	+	0.0878026i
$756$	19.0207	−	5.09659i	0.691777	−	0.185361i
$757$	−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
$760$	0.613103	+	1.28036i	0.0222396	+	0.0464437i
$761$	−2.35997	−	0.632352i	−0.0855488	−	0.0229227i	0.215791	−	0.976440i	$-0.430767\pi$
$761$	−2.35997	−	0.632352i	−0.0855488	−	0.0229227i	−0.301340	+	0.953517i	$0.597434\pi$
$762$	−4.66848			−0.169121
$763$	47.8242	+	12.8144i	1.73135	+	0.463914i
$764$	2.52761	−	4.37796i	0.0914459	−	0.158389i
$765$	−2.37513	+	3.46716i	−0.0858730	+	0.125355i
$766$			35.5469i			1.28436i
$767$		0			0
$768$	−29.3786	+	29.3786i	−1.06011	+	1.06011i
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	0.873365	−	0.487066i	$-0.161933\pi$
$769$	−3.50862	−	13.0944i	−0.126524	−	0.472195i	−0.999889	+	0.0148712i	$0.995266\pi$
$770$	−31.7340	+	46.3246i	−1.14361	+	1.66942i
$771$	21.9917	−	12.6969i	0.792011	−	0.457268i
$772$		−	0.384901i		−	0.0138529i
$773$	11.2222	+	19.4375i	0.403636	+	0.699118i	0.994162	−	0.107901i	$-0.0344128\pi$
$773$	11.2222	+	19.4375i	0.403636	+	0.699118i	−0.590525	+	0.807019i	$0.701079\pi$
$774$	3.87555	−	14.4637i	0.139304	−	0.519888i
$775$	−23.6058	+	17.2609i	−0.847944	+	0.620031i
$776$	10.5315	+	18.2410i	0.378058	+	0.654815i
$777$	−9.83454	−	36.7030i	−0.352812	−	1.31671i
$778$	−23.5701	−	13.6082i	−0.845030	−	0.487878i
$779$	0.361484			0.0129515
$780$		0			0
$781$	17.9032			0.640626
$782$	0.978419	+	0.564890i	0.0349882	+	0.0202004i
$783$	2.10217	+	7.84541i	0.0751255	+	0.280372i
$784$	13.4618	+	23.3165i	0.480778	+	0.832732i
$785$	9.56847	+	0.738363i	0.341513	+	0.0263533i
$786$	−5.25605	+	19.6158i	−0.187477	+	0.699674i
$787$	−6.74791	−	11.6877i	−0.240537	−	0.416622i	0.720330	−	0.693631i	$-0.243990\pi$
$787$	−6.74791	−	11.6877i	−0.240537	−	0.416622i	−0.960867	+	0.277009i	$0.910657\pi$
$788$			35.0224i			1.24762i
$789$	28.3280	−	16.3552i	1.00850	−	0.582260i
$790$	1.20191	+	6.43012i	0.0427619	+	0.228773i
$791$	−2.09978	−	7.83647i	−0.0746594	−	0.278633i
$792$	−3.00307	+	3.00307i	−0.106709	+	0.106709i
$793$		0			0
$794$			9.66696i			0.343068i
$795$	−19.4828	+	3.64168i	−0.690983	+	0.129157i
$796$	3.89696	−	6.74974i	0.138124	−	0.239238i
$797$	−6.06076	−	1.62398i	−0.214683	−	0.0575242i	0.149874	−	0.988705i	$-0.452113\pi$
$797$	−6.06076	−	1.62398i	−0.214683	−	0.0575242i	−0.364558	+	0.931181i	$0.618780\pi$
$798$	−6.90201			−0.244328
$799$	−19.0831	−	5.11330i	−0.675112	−	0.180896i
$800$	−11.8555	−	30.6052i	−0.419156	−	1.08206i
$801$	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
$804$	5.93922	−	1.59141i	0.209460	−	0.0561247i
$805$	2.40220	+	0.185369i	0.0846664	+	0.00653339i
$806$		0			0
$807$	−45.2744	−	45.2744i	−1.59374	−	1.59374i
$808$	−2.69050	+	4.66009i	−0.0946516	+	0.163941i
$809$	−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	0.190035	−	0.981777i	$-0.439140\pi$
$811$	−22.5473	−	22.5473i	−0.791743	−	0.791743i	−0.981777	+	0.190035i	$0.939140\pi$
$812$	8.21215	−	4.74129i	0.288190	−	0.166387i
$813$	−29.9885	+	17.3138i	−1.05174	+	0.607223i
$814$	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
$817$	2.36721	−	4.10012i	0.0828180	−	0.143445i
$818$	−3.41289	−	3.41289i	−0.119329	−	0.119329i
$819$		0			0
$820$	−2.03230	−	0.156825i	−0.0709710	−	0.00547656i
$821$	17.3216	−	4.64130i	0.604526	−	0.161982i	0.0564427	−	0.998406i	$-0.482024\pi$
$821$	17.3216	−	4.64130i	0.604526	−	0.161982i	0.548084	+	0.836423i	$0.315358\pi$
$822$	−50.1062	+	13.4259i	−1.74765	+	0.468282i
$823$	0.298185	−	1.11284i	0.0103941	−	0.0387913i	−0.960534	−	0.278162i	$-0.910275\pi$
$823$	0.298185	−	1.11284i	0.0103941	−	0.0387913i	0.970928	+	0.239371i	$0.0769413\pi$
$824$	11.5715	−	11.5715i	0.403112	−	0.403112i
$825$	−13.8669	−	35.7975i	−0.482784	−	1.24631i
$826$	−76.1300	−	20.3990i	−2.64890	−	0.709771i
$827$	4.45029			0.154752			0.0773759	−	0.997002i	$-0.475346\pi$
$827$	4.45029			0.154752			0.0773759	+	0.997002i	$0.475346\pi$
$828$	−0.369672	−	0.0990534i	−0.0128470	−	0.00344234i
$829$	−14.5637	+	25.2251i	−0.505819	+	0.876103i	0.494159	+	0.869372i	$0.335476\pi$
$829$	−14.5637	+	25.2251i	−0.505819	+	0.876103i	−0.999977	+	0.00673181i	$0.997857\pi$
$830$	30.4900	−	5.69914i	1.05832	−	0.197820i
$831$			6.09295i			0.211362i
$832$		0			0
$833$	−7.91294	+	7.91294i	−0.274167	+	0.274167i
$834$	16.3633	+	61.0685i	0.566613	+	2.11463i
$835$	0.254548	+	1.36181i	0.00880899	+	0.0471275i
$836$	2.44229	−	1.41006i	0.0844685	−	0.0487679i
$837$			24.0199i			0.830249i
$838$	18.0142	+	31.2015i	0.622291	+	1.07784i
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	−0.657099	−	0.753804i	$-0.728217\pi$
$839$	8.36719	−	31.2268i	0.288867	−	1.07807i	0.945967	−	0.324264i	$-0.105117\pi$
$840$	−18.4764	−	1.42575i	−0.637496	−	0.0491931i
$841$	−12.5444	−	21.7275i	−0.432565	−	0.749224i
$842$	−7.00106	−	26.1283i	−0.241273	−	0.900441i
$843$	−45.3309	−	26.1718i	−1.56128	−	0.901405i
$844$	4.37277			0.150517
$845$		0			0
$846$	16.5715			0.569739
$847$	−12.2857	−	7.09313i	−0.422140	−	0.243723i
$848$	−5.64207	−	21.0565i	−0.193750	−	0.723083i
$849$	15.1999	+	26.3270i	0.521660	+	0.903541i
$850$	14.9765	−	10.9511i	0.513691	−	0.375619i
$851$	0.426931	−	1.59333i	0.0146350	−	0.0546186i
$852$	−6.20441	−	10.7464i	−0.212560	−	0.368164i
$853$			9.24230i			0.316450i	0.987403	+	0.158225i	$0.0505772\pi$
$853$			9.24230i			0.316450i	−0.987403	+	0.158225i	$0.949423\pi$
$854$	−16.2025	+	9.35453i	−0.554439	+	0.320105i
$855$	0.629901	−	0.919515i	0.0215422	−	0.0314468i
$856$	−2.16228	−	8.06972i	−0.0739051	−	0.275817i
$857$	37.7913	−	37.7913i	1.29093	−	1.29093i	0.356713	−	0.934214i	$-0.383897\pi$
$857$	37.7913	−	37.7913i	1.29093	−	1.29093i	0.934214	−	0.356713i	$-0.116103\pi$
$858$		0			0
$859$			6.16263i			0.210266i	0.994458	+	0.105133i	$0.0335269\pi$
$859$			6.16263i			0.210266i	−0.994458	+	0.105133i	$0.966473\pi$
$860$	−15.0875	+	22.0243i	−0.514478	+	0.751024i
$861$	−2.35941	+	4.08661i	−0.0804083	+	0.139271i
$862$	−30.3110	−	8.12181i	−1.03240	−	0.276630i
$863$	33.7740			1.14968			0.574840	−	0.818266i	$-0.305064\pi$
$863$	33.7740			1.14968			0.574840	+	0.818266i	$0.305064\pi$
$864$	−26.0401	−	6.97742i	−0.885902	−	0.237377i
$865$	6.39477	+	13.3544i	0.217429	+	0.454064i
$866$	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
$869$	−5.97678	+	1.60147i	−0.202748	+	0.0543263i
$870$	−1.23507	+	16.0053i	−0.0418727	+	0.542630i
$871$		0			0
$872$	−11.6896	−	11.6896i	−0.395861	−	0.395861i
$873$	8.26870	−	14.3218i	0.279853	−	0.484720i
$874$	−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
$877$	−19.6563	+	11.3486i	−0.663747	+	0.383214i	−0.793703	−	0.608305i	$-0.791850\pi$
$877$	−19.6563	+	11.3486i	−0.663747	+	0.383214i	0.129956	+	0.991520i	$0.458516\pi$
$878$	6.73256	−	3.88705i	0.227213	−	0.131181i
$879$	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	0.381364	−	0.924425i	$-0.375454\pi$
$881$	−6.78312	−	3.91623i	−0.228529	−	0.131941i	−0.609893	+	0.792484i	$0.708788\pi$
$882$	4.69331	−	8.12905i	0.158032	−	0.273719i
$883$	−18.9296	−	18.9296i	−0.637032	−	0.637032i	0.312790	−	0.949822i	$-0.398736\pi$
$883$	−18.9296	−	18.9296i	−0.637032	−	0.637032i	−0.949822	+	0.312790i	$0.898736\pi$
$884$		0			0
$885$	40.9204	−	35.0575i	1.37552	−	1.17844i
$886$	37.9234	−	10.1615i	1.27406	−	0.341384i
$887$	−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
$890$	−17.3785	+	8.32168i	−0.582527	+	0.278943i
$891$	−40.8731	−	10.9519i	−1.36930	−	0.366903i
$892$	−10.0467			−0.336389
$893$	5.06098	+	1.35608i	0.169359	+	0.0453796i
$894$	−23.8314	+	41.2772i	−0.797042	+	1.38052i
$895$	0.899848	+	4.81413i	0.0300786	+	0.160919i
$896$		−	31.7130i		−	1.05946i
$897$		0			0
$898$	18.8417	−	18.8417i	0.628755	−	0.628755i
$899$	2.99371	+	11.1727i	0.0998459	+	0.372630i
$900$	−3.94029	+	4.89634i	−0.131343	+	0.163211i
$901$	7.84682	−	4.53036i	0.261415	−	0.150928i
$902$		−	4.77421i		−	0.158964i
$903$	30.9015	+	53.5230i	1.02834	+	1.78113i
$904$	−0.701108	+	2.61657i	−0.0233185	+	0.0870258i
$905$	13.9553	+	16.2891i	0.463889	+	0.541469i
$906$	1.96411	+	3.40193i	0.0652530	+	0.113022i
$907$	12.0355	+	44.9172i	0.399633	+	1.49145i	0.813743	+	0.581225i	$0.197426\pi$
$907$	12.0355	+	44.9172i	0.399633	+	1.49145i	−0.414109	+	0.910227i	$0.635907\pi$
$908$	4.57880	+	2.64357i	0.151953	+	0.0877300i
$909$	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	$0.405096\pi$
$912$	4.49459	+	2.59495i	0.148831	+	0.0859274i
$913$	7.59379	+	28.3404i	0.251318	+	0.937931i
$914$	27.7449	+	48.0556i	0.917720	+	1.58954i
$915$	0.984100	−	12.7530i	0.0325333	−	0.421601i
$916$	6.14674	−	22.9399i	0.203094	−	0.757957i
$917$	−9.89902	−	17.1456i	−0.326894	−	0.566198i
$918$		−	15.2393i		−	0.502971i
$919$	−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
$921$	1.09736	+	4.09541i	0.0361593	+	0.134948i
$922$	−8.98564	+	8.98564i	−0.295926	+	0.295926i
$923$		0			0
$924$			36.8139i			1.21109i
$925$	−21.1038	−	16.9831i	−0.693888	−	0.558401i
$926$	−28.7990	+	49.8814i	−0.946395	+	1.63920i
$927$	−12.4107	−	3.32544i	−0.407621	−	0.109222i
$928$	−12.9820			−0.426155
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	0.419620	−	0.907700i	$-0.362163\pi$
$929$	10.0330	+	2.68833i	0.329171	+	0.0882012i	−0.0904485	+	0.995901i	$0.528830\pi$
$930$	−15.7787	+	44.7747i	−0.517403	+	1.46822i
$931$	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
$934$	−9.24814	+	2.47803i	−0.302608	+	0.0810837i
$935$	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	$0.710794\pi$
$938$	−7.42149	+	12.8544i	−0.242320	+	0.419711i
$939$	−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	0.946911	+	0.321497i	$0.104186\pi$
$941$	38.9093	+	38.9093i	1.26841	+	1.26841i	0.321497	+	0.946911i	$0.395814\pi$
$942$	13.4923	−	7.78981i	0.439604	−	0.253806i
$943$	−0.177406	+	0.102425i	−0.00577712	+	0.00333542i
$944$	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
$947$	16.8759	−	29.2298i	0.548392	−	0.949842i	−0.449993	−	0.893032i	$-0.648574\pi$
$947$	16.8759	−	29.2298i	0.548392	−	0.949842i	0.998385	−	0.0568101i	$-0.0180930\pi$
$948$	3.03256	+	3.03256i	0.0984930	+	0.0984930i
$949$		0			0
$950$	−3.97188	+	2.90431i	−0.128865	+	0.0942281i
$951$	44.2451	−	11.8554i	1.43475	−	0.384439i
$952$	8.18285	−	2.19259i	0.265208	−	0.0710622i
$953$	1.14302	−	4.26581i	0.0370260	−	0.138183i	−0.944939	−	0.327248i	$-0.893879\pi$
$953$	1.14302	−	4.26581i	0.0370260	−	0.138183i	0.981965	+	0.189065i	$0.0605455\pi$
$954$	−5.37407	+	5.37407i	−0.173992	+	0.173992i
$955$	−7.86877	−	2.77297i	−0.254627	−	0.0897311i
$956$	16.6072	+	4.44988i	0.537115	+	0.143919i
$957$	−15.1845			−0.490845
$958$	34.2405	+	9.17471i	1.10626	+	0.296422i
$959$	25.2858	−	43.7963i	0.816520	−	1.41425i
$960$	−8.31789	−	5.69806i	−0.268459	−	0.183904i
$961$			3.20686i			0.103447i
$962$		0			0
$963$	−4.63819	+	4.63819i	−0.149463	+	0.149463i
$964$	−6.15338	−	22.9647i	−0.198187	−	0.739645i
$965$	−0.624420	+	0.116715i	−0.0201008	+	0.00375720i
$966$	3.38730	−	1.95566i	0.108985	−	0.0629223i
$967$		−	16.2803i		−	0.523540i	−0.965130	−	0.261770i	$-0.915694\pi$
$967$		−	16.2803i		−	0.523540i	0.965130	−	0.261770i	$-0.0843061\pi$
$968$	2.36837	+	4.10214i	0.0761223	+	0.131848i
$969$	−0.558310	+	2.08364i	−0.0179355	+	0.0669363i
$970$	−55.4421	+	47.4986i	−1.78014	+	1.52509i
$971$	−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
$973$	−53.3781	−	30.8179i	−1.71122	−	0.987975i
$974$	42.7918			1.37114
$975$		0			0
$976$	14.0681			0.450309
$977$	−13.8986	−	8.02436i	−0.444655	−	0.256722i	0.260915	−	0.965362i	$-0.415976\pi$
$977$	−13.8986	−	8.02436i	−0.444655	−	0.256722i	−0.705570	+	0.708640i	$0.749309\pi$
$978$	−2.12668	−	7.93687i	−0.0680037	−	0.253793i
$979$	−9.11292	−	15.7840i	−0.291250	−	0.504460i
$980$	−12.7088	+	10.8879i	−0.405968	+	0.347803i
$981$	−3.35939	+	12.5374i	−0.107257	+	0.400288i
$982$	19.5239	+	33.8164i	0.623033	+	1.07912i
$983$		−	34.3036i		−	1.09411i	−0.837096	−	0.547057i	$-0.815748\pi$
$983$		−	34.3036i		−	1.09411i	0.837096	−	0.547057i	$-0.184252\pi$
$984$	1.36450	−	0.787797i	0.0434988	−	0.0251141i
$985$	56.8164	−	10.6200i	1.81032	−	0.338382i
$986$	−1.89934	−	7.08844i	−0.0604874	−	0.225742i
$987$	−48.3637	+	48.3637i	−1.53943	+	1.53943i
$988$		0			0
$989$			2.68296i			0.0853131i
$990$	−12.1443	−	8.31927i	−0.385971	−	0.264404i
$991$	−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
$993$	3.95773			0.125595
$994$	28.9341	+	7.75287i	0.917734	+	0.245906i
$995$	−12.1317	−	4.27524i	−0.384601	−	0.135534i
$996$	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
$999$	−21.4920	+	5.75875i	−0.679975	+	0.182199i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	13.11	odd	12
65.2.o.a.33.2	yes	20	65.38	odd	4
65.2.t.a.7.2	yes	20	13.12	even	2
65.2.t.a.28.2	yes	20	65.63	even	12
325.2.s.b.132.4		20	65.24	odd	12
325.2.s.b.293.4		20	65.12	odd	4
325.2.x.b.7.4		20	65.64	even	2
325.2.x.b.93.4		20	65.37	even	12
585.2.cf.a.163.4		20	195.38	even	4
585.2.cf.a.262.4		20	39.11	even	12
585.2.dp.a.28.4		20	195.128	odd	12
585.2.dp.a.397.4		20	39.38	odd	2
845.2.f.d.408.8		20	65.58	even	12
845.2.f.d.437.3		20	13.9	even	3
845.2.f.e.408.3		20	65.33	even	12
845.2.f.e.437.8		20	13.4	even	6
845.2.k.d.268.3		20	65.48	odd	12
845.2.k.d.577.3		20	13.6	odd	12
845.2.k.e.268.8		20	65.43	odd	12
845.2.k.e.577.8		20	13.7	odd	12
845.2.o.e.258.2		20	65.23	odd	12
845.2.o.e.357.2		20	13.8	odd	4
845.2.o.f.258.4		20	65.3	odd	12
845.2.o.f.357.4		20	13.5	odd	4
845.2.o.g.488.4		20	5.3	odd	4
845.2.o.g.587.4		20	13.2	odd	12
845.2.t.e.188.2		20	65.18	even	4
845.2.t.e.427.2		20	13.3	even	3
845.2.t.f.188.4		20	65.8	even	4
845.2.t.f.427.4		20	13.10	even	6
845.2.t.g.418.4		20	65.28	even	12	inner
845.2.t.g.657.4		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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