LMFDB - Embedded newform 845.2.t.f.188.4

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,-2,6,0,4] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.4
Root			$1.83163i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.f.427.4

$q$-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} +(1.91432 - 0.512942i) q^{3} +(0.677439 + 1.17336i) q^{4} +(-1.69810 - 1.45480i) q^{5} +(3.50634 + 0.939520i) q^{6} +(-1.76945 - 3.06478i) q^{7} -1.18163i q^{8} +(0.803451 - 0.463873i) q^{9} +(-1.36126 - 3.86282i) q^{10} +(3.74209 - 1.00269i) q^{11} +(1.89870 + 1.89870i) q^{12} -6.48197i q^{14} +(-3.99694 - 1.91394i) q^{15} +(2.43703 - 4.22106i) q^{16} +(-0.524334 + 1.95684i) q^{17} +1.69929 q^{18} +(-0.139057 + 0.518968i) q^{19} +(0.556646 - 2.97802i) q^{20} +(-4.95936 - 4.95936i) q^{21} +(6.85414 + 1.83656i) q^{22} +(-0.0788026 - 0.294095i) q^{23} +(-0.606106 - 2.26202i) 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} +(-4.58730 - 6.69643i) 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} +(-1.45395 + 7.77851i) 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} +(-0.174136 - 0.649884i) q^{41} +(-3.32487 - 12.4086i) q^{42} +(8.51164 + 2.28069i) q^{43} +(3.71155 + 3.71155i) q^{44} +(-2.03919 - 0.381161i) q^{45} +(0.144337 - 0.538675i) q^{46} +9.75201 q^{47} +(2.50011 - 9.33053i) q^{48} +(-2.76192 + 4.78379i) q^{49} +(-3.30807 + 8.53982i) q^{50} +4.01498i q^{51} +(3.16254 + 3.16254i) q^{53} +(-7.26602 + 1.94693i) q^{54} +(-7.81317 - 3.74134i) q^{55} +(-3.62143 + 2.09083i) q^{56} +1.06480i q^{57} +(1.81120 + 3.13709i) q^{58} +(-11.7449 - 3.14703i) q^{59} +(-0.461950 - 5.98642i) q^{60} +(1.44316 + 2.49963i) q^{61} +(10.3476 - 2.77263i) q^{62} +(-2.84334 - 1.64160i) q^{63} +2.27514 q^{64} +14.0631 q^{66} +(1.98310 + 1.14494i) q^{67} +(-2.65128 + 0.710408i) q^{68} +(-0.301707 - 0.522573i) q^{69} +(-9.43000 + 11.0070i) q^{70} +(4.46378 + 1.19607i) q^{71} +(-0.548125 - 0.949380i) q^{72} +14.7546i q^{73} +(-8.59382 + 4.96165i) q^{74} +(4.00281 + 9.06483i) q^{75} +(-0.703137 + 0.188405i) q^{76} +(-9.69449 - 9.69449i) q^{77} -1.59718i q^{79} +(-10.2791 + 3.62239i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(0.318953 - 1.19035i) q^{82} -7.57341 q^{83} +(2.45944 - 9.17877i) q^{84} +(3.73719 - 2.56011i) q^{85} +(11.4128 + 11.4128i) q^{86} +(3.78593 + 1.01444i) q^{87} +(-1.18481 - 4.42176i) q^{88} +(-1.21762 - 4.54423i) 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} +(0.991129 - 0.678959i) 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} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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	$0.442448\pi$
$3$	1.91432	−	0.512942i	1.10524	−	0.296147i	0.340341	−	0.940302i	$-0.389458\pi$
$3$	1.91432	−	0.512942i	1.10524	−	0.296147i	0.764895	+	0.644155i	$0.222791\pi$
$4$	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
$6$	3.50634	+	0.939520i	1.43146	+	0.383558i
$7$	−1.76945	−	3.06478i	−0.668790	−	1.15838i	−0.978243	−	0.207464i	$-0.933479\pi$
$7$	−1.76945	−	3.06478i	−0.668790	−	1.15838i	0.309453	−	0.950915i	$-0.399854\pi$
$8$		−	1.18163i		−	0.417769i
$9$	0.803451	−	0.463873i	0.267817	−	0.154624i
$10$	−1.36126	−	3.86282i	−0.430469	−	1.22153i
$11$	3.74209	−	1.00269i	1.12828	−	0.302323i	0.354053	−	0.935226i	$-0.384803\pi$
$11$	3.74209	−	1.00269i	1.12828	−	0.302323i	0.774231	+	0.632903i	$0.218137\pi$
$12$	1.89870	+	1.89870i	0.548108	+	0.548108i
$13$		0			0
$13$		0			0
$14$		−	6.48197i		−	1.73238i
$15$	−3.99694	−	1.91394i	−1.03201	−	0.494177i
$16$	2.43703	−	4.22106i	0.609258	−	1.05527i
$17$	−0.524334	+	1.95684i	−0.127170	+	0.474603i	−0.999908	−	0.0135853i	$-0.995676\pi$
$17$	−0.524334	+	1.95684i	−0.127170	+	0.474603i	0.872738	+	0.488189i	$0.162342\pi$
$18$	1.69929			0.400526
$19$	−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	$0.102963\pi$
$20$	0.556646	−	2.97802i	0.124470	−	0.665906i
$21$	−4.95936	−	4.95936i	−1.08222	−	1.08222i
$22$	6.85414	+	1.83656i	1.46131	+	0.391556i
$23$	−0.0788026	−	0.294095i	−0.0164315	−	0.0613231i	0.957223	−	0.289350i	$-0.0934392\pi$
$23$	−0.0788026	−	0.294095i	−0.0164315	−	0.0613231i	−0.973655	+	0.228027i	$0.926773\pi$
$24$	−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
$28$	2.39739	−	4.15240i	0.453064	−	0.784730i
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	0.650521	−	0.759488i	$-0.274551\pi$
$29$	1.71273	+	0.988843i	0.318045	+	0.183624i	−0.332476	+	0.943112i	$0.607884\pi$
$30$	−4.58730	−	6.69643i	−0.837522	−	1.22260i
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	−0.230331	−	0.973112i	$-0.573981\pi$
$31$	4.13563	−	4.13563i	0.742781	−	0.742781i	0.973112	+	0.230331i	$0.0739810\pi$
$32$	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
$35$	−1.45395	+	7.77851i	−0.245762	+	1.31481i
$36$	1.08858	+	0.628491i	0.181430	+	0.104748i
$37$	−2.70887	+	4.69189i	−0.445335	+	0.771342i	−0.998075	−	0.0620109i	$-0.980249\pi$
$37$	−2.70887	+	4.69189i	−0.445335	+	0.771342i	0.552741	+	0.833353i	$0.313582\pi$
$38$	−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	0.950994	−	0.309209i	$-0.100064\pi$
$41$	−0.174136	−	0.649884i	−0.0271955	−	0.101495i	−0.978190	+	0.207714i	$0.933398\pi$
$42$	−3.32487	−	12.4086i	−0.513039	−	1.91469i
$43$	8.51164	+	2.28069i	1.29801	+	0.347802i	0.840698	−	0.541504i	$-0.182145\pi$
$43$	8.51164	+	2.28069i	1.29801	+	0.347802i	0.457314	+	0.889305i	$0.348811\pi$
$44$	3.71155	+	3.71155i	0.559538	+	0.559538i
$45$	−2.03919	−	0.381161i	−0.303984	−	0.0568201i
$46$	0.144337	−	0.538675i	0.0212814	−	0.0794232i
$47$	9.75201			1.42248			0.711238	−	0.702951i	$-0.248135\pi$
$47$	9.75201			1.42248			0.711238	+	0.702951i	$0.248135\pi$
$48$	2.50011	−	9.33053i	0.360860	−	1.34675i
$49$	−2.76192	+	4.78379i	−0.394561	+	0.683399i
$50$	−3.30807	+	8.53982i	−0.467832	+	1.20771i
$51$			4.01498i			0.562209i
$52$		0			0
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	0.890125	−	0.455716i	$-0.150617\pi$
$53$	3.16254	+	3.16254i	0.434409	+	0.434409i	−0.455716	+	0.890125i	$0.650617\pi$
$54$	−7.26602	+	1.94693i	−0.988781	+	0.264943i
$55$	−7.81317	−	3.74134i	−1.05353	−	0.504482i
$56$	−3.62143	+	2.09083i	−0.483934	+	0.279399i
$57$			1.06480i			0.141036i
$58$	1.81120	+	3.13709i	0.237822	+	0.411919i
$59$	−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	$0.874031\pi$
$60$	−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	$0.774177\pi$
$62$	10.3476	−	2.77263i	1.31414	−	0.352124i
$63$	−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	$0.621996\pi$
$68$	−2.65128	+	0.710408i	−0.321515	+	0.0861496i
$69$	−0.301707	−	0.522573i	−0.0363213	−	0.0629104i
$70$	−9.43000	+	11.0070i	−1.12710	+	1.31559i
$71$	4.46378	+	1.19607i	0.529753	+	0.141947i	0.513774	−	0.857925i	$-0.328247\pi$
$71$	4.46378	+	1.19607i	0.529753	+	0.141947i	0.0159789	+	0.999872i	$0.494914\pi$
$72$	−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
$75$	4.00281	+	9.06483i	0.462205	+	1.04672i
$76$	−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	$-0.971362\pi$
$79$		−	1.59718i		−	0.179696i	0.995955	−	0.0898482i	$-0.0286382\pi$
$80$	−10.2791	+	3.62239i	−1.14924	+	0.404995i
$81$	−5.46126	+	9.45918i	−0.606807	+	1.05102i
$82$	0.318953	−	1.19035i	0.0352225	−	0.131452i
$83$	−7.57341			−0.831290			−0.415645	−	0.909527i	$-0.636444\pi$
$83$	−7.57341			−0.831290			−0.415645	+	0.909527i	$0.636444\pi$
$84$	2.45944	−	9.17877i	0.268347	−	1.00149i
$85$	3.73719	−	2.56011i	0.405355	−	0.277683i
$86$	11.4128	+	11.4128i	1.23068	+	1.23068i
$87$	3.78593	+	1.01444i	0.405895	+	0.108759i
$88$	−1.18481	−	4.42176i	−0.126301	−	0.471361i
$89$	−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
$93$	5.79560	−	10.0383i	0.600976	−	1.04092i
$94$	15.4690	+	8.93105i	1.59551	+	0.921167i
$95$	0.991129	−	0.678959i	0.101688	−	0.0696597i
$96$	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
$100$	−5.27768	+	4.24717i	−0.527768	+	0.424717i
$101$	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	$0.593917\pi$
$102$	−3.67698	+	6.36872i	−0.364075	+	0.630597i
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	−0.0344872	−	0.999405i	$-0.510980\pi$
$103$	9.79285	−	9.79285i	0.964918	−	0.964918i	0.999405	+	0.0344872i	$0.0109798\pi$
$104$		0			0
$105$	1.20660	+	15.6364i	0.117752	+	1.52596i
$106$	2.12024	+	7.91286i	0.205936	+	0.768565i
$107$	−1.82991	−	6.82933i	−0.176904	−	0.660216i	−0.996219	−	0.0868725i	$-0.972313\pi$
$107$	−1.82991	−	6.82933i	−0.176904	−	0.660216i	0.819315	−	0.573344i	$-0.194354\pi$
$108$	−5.37475	−	1.44016i	−0.517186	−	0.138580i
$109$	−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	$0.983717\pi$
$110$	−8.96719	−	13.0901i	−0.854988	−	1.24809i
$111$	−2.77898	+	10.3713i	−0.263769	+	0.984399i
$112$	−17.2488			−1.62986
$113$	0.593341	−	2.21438i	0.0558168	−	0.208311i	−0.932385	−	0.361466i	$-0.882277\pi$
$113$	0.593341	−	2.21438i	0.0558168	−	0.208311i	0.988202	+	0.153154i	$0.0489432\pi$
$114$	−0.975161	+	1.68903i	−0.0913322	+	0.158192i
$115$	−0.294036	+	0.614046i	−0.0274190	+	0.0572601i
$116$			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
$120$	−2.26156	+	4.72290i	−0.206452	+	0.431140i
$121$	3.47160	−	2.00433i	0.315600	−	0.182212i
$122$			5.28668i			0.478633i
$123$	−0.666705	−	1.15477i	−0.0601148	−	0.104122i
$124$	7.65421	+	2.05094i	0.687368	+	0.184180i
$125$	5.88530	−	9.50596i	0.526397	−	0.850239i
$126$	−3.00681	−	5.20795i	−0.267868	−	0.463961i
$127$	1.24225	−	0.332860i	0.110232	−	0.0295366i	−0.203281	−	0.979120i	$-0.565161\pi$
$127$	1.24225	−	0.332860i	0.110232	−	0.0295366i	0.313513	+	0.949584i	$0.398494\pi$
$128$	−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
$133$	1.83658	−	0.492109i	0.159251	−	0.0426713i
$134$	2.09712	+	3.63231i	0.181163	+	0.313784i
$135$	9.15610	−	0.706541i	0.788032	−	0.0608094i
$136$	2.31226	+	0.619567i	0.198274	+	0.0531274i
$137$	7.14509	+	12.3757i	0.610446	+	1.05732i	0.991165	+	0.132633i	$0.0423431\pi$
$137$	7.14509	+	12.3757i	0.610446	+	1.05732i	−0.380719	+	0.924691i	$0.624324\pi$
$138$		−	1.10523i		−	0.0940838i
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.302615	−	0.953113i	$-0.402140\pi$
$139$	15.0832	−	8.70830i	1.27934	−	0.738629i	0.976727	+	0.214484i	$0.0688071\pi$
$140$	−10.1119	+	3.56347i	−0.854615	+	0.301168i
$141$	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
$145$	−1.46981	−	4.17084i	−0.122061	−	0.346369i
$146$	−13.5125	+	23.4044i	−1.11830	+	1.93696i
$147$	−2.83341	+	10.5744i	−0.233696	+	0.872165i
$148$	−7.34036			−0.603374
$149$	−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	$0.902577\pi$
$150$	−1.95230	+	18.0448i	−0.159404	+	1.47335i
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	0.737556	−	0.675286i	$-0.235980\pi$
$151$	0.765191	+	0.765191i	0.0622704	+	0.0622704i	−0.675286	+	0.737556i	$0.735980\pi$
$152$	0.613227	+	0.164314i	0.0497392	+	0.0133276i
$153$	0.486448	+	1.81545i	0.0393270	+	0.146770i
$154$	−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	−0.575557	−	0.817762i	$-0.695215\pi$
$157$	3.03481	−	3.03481i	0.242204	−	0.242204i	0.817762	+	0.575557i	$0.195215\pi$
$158$	1.46272	−	2.53350i	0.116368	−	0.201555i
$159$	7.67633	+	4.43193i	0.608773	+	0.351475i
$160$	−14.4282	−	2.69689i	−1.14065	−	0.213208i
$161$	−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
$165$	−16.8760	−	3.15444i	−1.31380	−	0.245573i
$166$	−12.0133	−	6.93585i	−0.932409	−	0.538327i
$167$	0.309785	−	0.536563i	0.0239719	−	0.0415205i	−0.853791	−	0.520617i	$-0.825702\pi$
$167$	0.309785	−	0.536563i	0.0239719	−	0.0415205i	0.877762	+	0.479096i	$0.159035\pi$
$168$	−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
$172$	3.09005	+	11.5322i	0.235614	+	0.879324i
$173$	6.39606	+	1.71382i	0.486283	+	0.130299i	0.493627	−	0.869674i	$-0.335671\pi$
$173$	6.39606	+	1.71382i	0.486283	+	0.130299i	−0.00734343	+	0.999973i	$0.502338\pi$
$174$	5.07636	+	5.07636i	0.384838	+	0.384838i
$175$	13.7852	−	11.0935i	1.04206	−	0.838590i
$176$	4.88718	−	18.2392i	0.368385	−	1.37483i
$177$	−24.0977			−1.81130
$178$	2.23024	−	8.32336i	0.167163	−	0.623862i
$179$	−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	$0.192750\pi$
$180$	−0.934185	−	2.65091i	−0.0696300	−	0.197587i
$181$		−	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
$185$	11.4257	−	4.02644i	0.840035	−	0.296030i
$186$	18.3864	−	10.6154i	1.34816	−	0.778359i
$187$			7.84842i			0.573933i
$188$	6.60639	+	11.4426i	0.481820	+	0.834537i
$189$	14.0387	+	3.76166i	1.02117	+	0.273621i
$190$	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	$0.876433\pi$
$192$	4.35536	−	1.16701i	0.314321	−	0.0842220i
$193$	−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	$0.294173\pi$
$198$	6.35890	−	1.70386i	0.451907	−	0.121088i
$199$	−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
$201$	4.38359	+	1.17458i	0.309194	+	0.0828484i
$202$	4.17053	+	7.22357i	0.293437	+	0.508248i
$203$		−	6.99884i		−	0.491223i
$204$	−4.71101	+	2.71990i	−0.329836	+	0.190431i
$205$	−0.649753	+	1.35690i	−0.0453807	+	0.0947702i
$206$	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
$210$	−12.4061	+	25.9081i	−0.856102	+	1.78783i
$211$	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	$0.131232\pi$
$212$	−1.56837	+	5.85322i	−0.107716	+	0.402001i
$213$	9.15863			0.627539
$214$	3.35173	−	12.5088i	0.229119	−	0.855085i
$215$	−11.1357	−	16.2556i	−0.759447	−	1.10862i
$216$	3.43147	+	3.43147i	0.233482	+	0.233482i
$217$	−19.9926	−	5.35700i	−1.35719	−	0.363657i
$218$	−6.63238	−	24.7524i	−0.449201	−	1.67644i
$219$	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
$223$	3.70762	−	6.42178i	0.248280	−	0.430034i	−0.714768	−	0.699361i	$-0.753468\pi$
$223$	3.70762	−	6.42178i	0.248280	−	0.430034i	0.963049	+	0.269327i	$0.0868012\pi$
$224$	−20.1179	−	11.6151i	−1.34419	−	0.776067i
$225$	2.90823	+	3.61386i	0.193882	+	0.240924i
$226$	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	$-0.553379\pi$
$229$	12.3946	−	12.3946i	0.819060	−	0.819060i	0.985972	+	0.166912i	$0.0533795\pi$
$230$	−1.02877	+	0.704741i	−0.0678348	+	0.0464693i
$231$	−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	−0.606090	−	0.795396i	$-0.707263\pi$
$233$	2.88962	−	2.88962i	0.189305	−	0.189305i	0.795396	+	0.606090i	$0.207263\pi$
$234$		0			0
$235$	−16.5599	−	14.1873i	−1.08025	−	0.925474i
$236$	−4.26384	−	15.9129i	−0.277552	−	1.03584i
$237$	−0.819258	−	3.05751i	−0.0532165	−	0.198607i
$238$	12.6842	+	3.39872i	0.822193	+	0.220306i
$239$	−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	$0.884616\pi$
$240$	−17.8195	+	12.2070i	−1.15025	+	0.787960i
$241$	−4.54165	+	16.9497i	−0.292554	+	1.09183i	0.650587	+	0.759432i	$0.274523\pi$
$241$	−4.54165	+	16.9497i	−0.292554	+	1.09183i	−0.943141	+	0.332394i	$0.892144\pi$
$242$	7.34239			0.471986
$243$	−2.41378	+	9.00835i	−0.154844	+	0.577886i
$244$	−1.95530	+	3.38669i	−0.125176	+	0.216810i
$245$	11.6495	−	4.10531i	0.744260	−	0.262278i
$246$		−	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
$250$	18.0412	−	9.68888i	1.14103	−	0.612779i
$251$	−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	$0.574415\pi$
$252$		−	4.44834i		−	0.280219i
$253$	−0.589774	−	1.02152i	−0.0370787	−	0.0642223i
$254$	2.27535	+	0.609678i	0.142768	+	0.0382546i
$255$	5.84100	−	6.81784i	0.365778	−	0.426950i
$256$	−10.4820	−	18.1554i	−0.655125	−	1.13471i
$257$	−12.3766	+	3.31629i	−0.772029	+	0.206864i	−0.623268	−	0.782009i	$-0.714195\pi$
$257$	−12.3766	+	3.31629i	−0.772029	+	0.206864i	−0.148761	+	0.988873i	$0.547529\pi$
$258$	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
$263$	−15.9426	+	4.27179i	−0.983060	+	0.263410i	−0.714333	−	0.699806i	$-0.753270\pi$
$263$	−15.9426	+	4.27179i	−0.983060	+	0.263410i	−0.268727	+	0.963216i	$0.586603\pi$
$264$	−4.53621	−	7.85695i	−0.279185	−	0.483562i
$265$	−0.769439	−	9.97120i	−0.0472663	−	0.612526i
$266$	3.36393	+	0.901363i	0.206256	+	0.0552661i
$267$	−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	$0.777939\pi$
$269$	−27.9787	+	16.1535i	−1.70589	+	0.984895i	−0.939519	+	0.342495i	$0.888728\pi$
$270$	15.1708	+	7.26456i	0.923268	+	0.442107i
$271$	−16.8770	+	4.52218i	−1.02521	+	0.274703i	−0.731970	−	0.681337i	$-0.761399\pi$
$271$	−16.8770	+	4.52218i	−1.02521	+	0.274703i	−0.293236	+	0.956040i	$0.594732\pi$
$272$	6.98212	+	6.98212i	0.423353	+	0.423353i
$273$		0			0
$274$			26.1743i			1.58125i
$275$	7.82464	+	17.7198i	0.471844	+	1.06854i
$276$	0.408777	−	0.708022i	0.0246055	−	0.0426179i
$277$	0.795705	−	2.96961i	0.0478093	−	0.178427i	−0.937892	−	0.346926i	$-0.887225\pi$
$277$	0.795705	−	2.96961i	0.0478093	−	0.178427i	0.985702	+	0.168499i	$0.0538921\pi$
$278$	31.9008			1.91328
$279$	1.40437	−	5.24118i	0.0840775	−	0.313781i
$280$	9.19131	+	1.71802i	0.549286	+	0.102671i
$281$	−18.6757	−	18.6757i	−1.11410	−	1.11410i	−0.992590	−	0.121508i	$-0.961227\pi$
$281$	−18.6757	−	18.6757i	−1.11410	−	1.11410i	−0.121508	−	0.992590i	$-0.538773\pi$
$282$	34.1938	+	9.16221i	2.03621	+	0.545602i
$283$	3.97005	+	14.8164i	0.235995	+	0.880745i	0.977698	+	0.210016i	$0.0673517\pi$
$283$	3.97005	+	14.8164i	0.235995	+	0.880745i	−0.741703	+	0.670728i	$0.765982\pi$
$284$	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
$288$	3.04497	−	5.27404i	0.179427	−	0.310776i
$289$	11.1681	+	6.44793i	0.656949	+	0.379290i
$290$	1.48825	−	7.96202i	0.0873929	−	0.467546i
$291$	−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
$295$	15.3657	+	22.4305i	0.894624	+	1.30595i
$296$	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
$301$	−8.07113	−	30.1219i	−0.465212	−	1.73620i
$302$	0.513002	+	1.91455i	0.0295200	+	0.110170i
$303$	8.71763	+	2.33588i	0.500814	+	0.134193i
$304$	1.85171	+	1.85171i	0.106203	+	0.106203i
$305$	1.18583	−	6.34413i	0.0679006	−	0.363264i
$306$	−0.890994	+	3.32524i	−0.0509347	+	0.190091i
$307$	2.13935			0.122099			0.0610496	−	0.998135i	$-0.480555\pi$
$307$	2.13935			0.122099			0.0610496	+	0.998135i	$0.480555\pi$
$308$	4.80768	−	17.9425i	0.273943	−	1.02237i
$309$	13.7235	−	23.7698i	0.780704	−	1.35222i
$310$	−21.6049	−	10.3455i	−1.22707	−	0.587585i
$311$			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	0.787915	−	0.615784i	$-0.211161\pi$
$313$	3.04531	+	3.04531i	0.172131	+	0.172131i	−0.615784	+	0.787915i	$0.711161\pi$
$314$	7.59327	−	2.03461i	0.428513	−	0.114820i
$315$	2.44007	+	6.92410i	0.137482	+	0.390129i
$316$	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
$319$	7.40069	+	1.98301i	0.414359	+	0.111027i
$320$	−3.86342	−	3.30988i	−0.215972	−	0.185028i
$321$	−7.00609	−	12.1349i	−0.391042	−	0.677305i
$322$	−1.90632	+	0.510796i	−0.106235	+	0.0284656i
$323$	−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
$328$	−0.767921	+	0.205764i	−0.0424013	+	0.0113614i
$329$	−17.2557	−	29.8878i	−0.951338	−	1.64777i
$330$	−23.8806	−	20.4590i	−1.31458	−	1.12623i
$331$	−1.92894	−	0.516858i	−0.106024	−	0.0284091i	0.205417	−	0.978675i	$-0.434145\pi$
$331$	−1.92894	−	0.516858i	−0.106024	−	0.0284091i	−0.311441	+	0.950265i	$0.600812\pi$
$332$	−5.13052	−	8.88632i	−0.281574	−	0.487700i
$333$			5.02628i			0.275438i
$334$	0.982786	−	0.567412i	0.0537756	−	0.0310474i
$335$	−1.70184	−	4.82925i	−0.0929813	−	0.263850i
$336$	−33.0199	+	8.84765i	−1.80138	+	0.482679i
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	0.854018	−	0.520244i	$-0.174159\pi$
$337$	6.12727	+	6.12727i	0.333773	+	0.333773i	−0.520244	+	0.854018i	$0.674159\pi$
$338$		0			0
$339$		−	4.54338i		−	0.246763i
$340$	5.53564	+	2.65074i	0.300212	+	0.143757i
$341$	11.3292	−	19.6227i	0.613508	−	1.06263i
$342$	−0.236298	+	0.881876i	−0.0127775	+	0.0476864i
$343$	−5.22396			−0.282067
$344$	2.69492	−	10.0576i	0.145301	−	0.542269i
$345$	−0.247911	+	1.32631i	−0.0133471	+	0.0714059i
$346$	8.57614	+	8.57614i	0.461056	+	0.461056i
$347$	31.4009	+	8.41384i	1.68569	+	0.451679i	0.969271	−	0.245994i	$-0.0791144\pi$
$347$	31.4009	+	8.41384i	1.68569	+	0.451679i	0.716417	+	0.697673i	$0.245781\pi$
$348$	1.37444	+	5.12947i	0.0736776	+	0.274969i
$349$	−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
$353$	−13.6631	+	23.6652i	−0.727213	+	1.25957i	0.230843	+	0.972991i	$0.425852\pi$
$353$	−13.6631	+	23.6652i	−0.727213	+	1.25957i	−0.958057	+	0.286579i	$0.907482\pi$
$354$	−38.2248	−	22.0691i	−2.03163	−	1.17296i
$355$	−5.83991	−	8.52496i	−0.309950	−	0.452458i
$356$	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	$-0.703521\pi$
$359$	3.89871	−	3.89871i	0.205766	−	0.205766i	0.802465	+	0.596699i	$0.203521\pi$
$360$	−0.450390	+	2.40956i	−0.0237376	+	0.126995i
$361$	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
$366$	2.71176	+	10.1204i	0.141746	+	0.529003i
$367$	4.67826	+	17.4595i	0.244203	+	0.911378i	0.973782	+	0.227482i	$0.0730493\pi$
$367$	4.67826	+	17.4595i	0.244203	+	0.911378i	−0.729579	+	0.683896i	$0.760284\pi$
$368$	−1.43344	−	0.384089i	−0.0747232	−	0.0200220i
$369$	−0.441373	−	0.441373i	−0.0229770	−	0.0229770i
$370$	21.8114	+	4.07695i	1.13392	+	0.211950i
$371$	4.09653	−	15.2885i	0.212681	−	0.793738i
$372$	15.7046			0.814248
$373$	4.01536	−	14.9855i	0.207907	−	0.775921i	−0.780636	−	0.624986i	$-0.785105\pi$
$373$	4.01536	−	14.9855i	0.207907	−	0.775921i	0.988544	−	0.150936i	$-0.0482286\pi$
$374$	−7.18771	+	12.4495i	−0.371668	+	0.643747i
$375$	6.39037	−	21.2163i	0.329997	−	1.09561i
$376$		−	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	$0.231757\pi$
$380$	1.46809	+	0.702996i	0.0753115	+	0.0360629i
$381$	2.20733	−	1.27440i	0.113085	−	0.0652897i
$382$		−	6.83407i		−	0.349661i
$383$	−9.70362	−	16.8072i	−0.495832	−	0.858806i	0.504157	−	0.863612i	$-0.331803\pi$
$383$	−9.70362	−	16.8072i	−0.495832	−	0.858806i	−0.999988	+	0.00480620i	$0.998470\pi$
$384$	−17.1547	−	4.59660i	−0.875424	−	0.234569i
$385$	2.35865	+	30.5658i	0.120208	+	1.55778i
$386$	−0.260170	−	0.450628i	−0.0132423	−	0.0229364i
$387$	7.89664	−	2.11590i	0.401409	−	0.107557i
$388$	−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
$393$	−10.7095	+	2.86960i	−0.540222	+	0.144752i
$394$	23.6731	+	41.0030i	1.19263	+	2.06570i
$395$	−2.32358	+	2.71217i	−0.116912	+	0.136464i
$396$	4.70374	+	1.26036i	0.236372	+	0.0633357i
$397$	−2.63889	−	4.57070i	−0.132442	−	0.229397i	0.792175	−	0.610294i	$-0.208949\pi$
$397$	−2.63889	−	4.57070i	−0.132442	−	0.229397i	−0.924617	+	0.380897i	$0.875615\pi$
$398$		−	10.5365i		−	0.528145i
$399$	3.26338	−	1.88411i	0.163373	−	0.0943236i
$400$	22.7249	+	8.80295i	1.13624	+	0.440147i
$401$	−26.9289	+	7.21557i	−1.34476	+	0.360328i	−0.858199	−	0.513317i	$-0.828417\pi$
$401$	−26.9289	+	7.21557i	−1.34476	+	0.360328i	−0.486564	+	0.873645i	$0.661750\pi$
$402$	5.87772	+	5.87772i	0.293154	+	0.293154i
$403$		0			0
$404$			6.16996i			0.306967i
$405$	23.0350	−	8.11759i	1.14462	−	0.403366i
$406$	6.40965	−	11.1018i	0.318106	−	0.550975i
$407$	−5.43231	+	20.2737i	−0.269270	+	1.00493i
$408$	4.74421			0.234873
$409$	−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	$0.104086\pi$
$410$	−2.27334	+	1.55732i	−0.112272	+	0.0769105i
$411$	20.0260	+	20.0260i	0.987810	+	0.987810i
$412$	18.1246	+	4.85646i	0.892933	+	0.239261i
$413$	11.1370	+	41.5640i	0.548018	+	2.04523i
$414$	−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
$418$	−1.90623	+	3.30169i	−0.0932368	+	0.161491i
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	0.0224018	−	0.999749i	$-0.492869\pi$
$419$	−17.0348	−	9.83506i	−0.832205	−	0.480474i	−0.854607	+	0.519275i	$0.826202\pi$
$420$	−17.5297	+	12.0085i	−0.855361	+	0.585953i
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	−0.405256	−	0.914203i	$-0.632817\pi$
$421$	10.4427	−	10.4427i	0.508948	−	0.508948i	0.914203	+	0.405256i	$0.132817\pi$
$422$	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
$425$	−10.0706	−	1.08955i	−0.488495	−	0.0528509i
$426$	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
$431$	−4.43419	−	16.5486i	−0.213587	−	0.797119i	−0.986659	−	0.162800i	$-0.947947\pi$
$431$	−4.43419	−	16.5486i	−0.213587	−	0.797119i	0.773072	−	0.634319i	$-0.218719\pi$
$432$	5.18086	+	19.3352i	0.249264	+	0.930267i
$433$	−10.8538	−	2.90826i	−0.521599	−	0.139762i	−0.0115927	−	0.999933i	$-0.503690\pi$
$433$	−10.8538	−	2.90826i	−0.521599	−	0.139762i	−0.510006	+	0.860171i	$0.670357\pi$
$434$	−26.8070	−	26.8070i	−1.28678	−	1.28678i
$435$	−4.95309	−	7.23040i	−0.237482	−	0.346671i
$436$	4.90604	−	18.3096i	0.234957	−	0.876870i
$437$	0.163584			0.00782528
$438$	−13.8623	+	51.7347i	−0.662365	+	2.47198i
$439$	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	$0.134371\pi$
$440$	−4.42087	+	9.23226i	−0.210757	+	0.440131i
$441$			5.12473i			0.244035i
$442$		0			0
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	0.968631	−	0.248505i	$-0.0799392\pi$
$443$	15.1569	+	15.1569i	0.720126	+	0.720126i	−0.248505	+	0.968631i	$0.579939\pi$
$444$	−14.0518	+	3.76518i	−0.666870	+	0.178687i
$445$	−4.54331	+	9.48796i	−0.215374	+	0.449773i
$446$	11.7623	−	6.79099i	0.556963	−	0.321563i
$447$			26.0221i			1.23080i
$448$	−4.02575	−	6.97281i	−0.190199	−	0.329434i
$449$	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	$0.471797\pi$
$450$	1.30351	+	8.39586i	0.0614483	+	0.395785i
$451$	−1.30327	−	2.25732i	−0.0613684	−	0.106293i
$452$	3.00021	−	0.803904i	0.141118	−	0.0378124i
$453$	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	$0.416004\pi$
$458$	31.0121	−	8.30966i	1.44910	−	0.388285i
$459$	−4.16003	−	7.20538i	−0.194173	−	0.336318i
$460$	−0.919687	+	0.0709688i	−0.0428806	+	0.00330894i
$461$	−6.70146	−	1.79565i	−0.312118	−	0.0836318i	0.0993596	−	0.995052i	$-0.468321\pi$
$461$	−6.70146	−	1.79565i	−0.312118	−	0.0836318i	−0.411478	+	0.911420i	$0.634987\pi$
$462$	−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
$465$	−24.4452	+	8.61454i	−1.13362	+	0.399490i
$466$	7.22999	−	1.93727i	0.334923	−	0.0897423i
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	0.616396	−	0.787436i	$-0.288592\pi$
$467$	−3.69622	−	3.69622i	−0.171041	−	0.171041i	−0.787436	+	0.616396i	$0.788592\pi$
$468$		0			0
$469$		−	8.10369i		−	0.374194i
$470$	−13.2751	−	37.6702i	−0.612332	−	1.73760i
$471$	4.25293	−	7.36630i	0.195965	−	0.339421i
$472$	−3.71862	+	13.8781i	−0.171163	+	0.638790i
$473$	34.1382			1.56968
$474$	1.50058	−	5.60024i	0.0689239	−	0.257227i
$475$	−2.67079	−	0.288956i	−0.122544	−	0.0132582i
$476$	6.86855	+	6.86855i	0.314820	+	0.314820i
$477$	4.00797	+	1.07393i	0.183512	+	0.0491720i
$478$	−6.01571	−	22.4509i	−0.275152	−	1.02688i
$479$	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
$483$	−1.06771	+	1.84934i	−0.0485827	+	0.0841477i
$484$	4.70359	+	2.71562i	0.213800	+	0.123437i
$485$	39.1801	+	7.32348i	1.77908	+	0.332542i
$486$	−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
$490$	22.2386	+	4.15680i	1.00464	+	0.187785i
$491$	−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	$0.826410\pi$
$492$	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
$496$	−7.37809	−	27.5354i	−0.331286	−	1.23638i
$497$	−4.23276	−	15.7969i	−0.189865	−	0.708587i
$498$	−26.5549	−	7.11538i	−1.18996	−	0.318848i
$499$	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	$0.489854\pi$
$500$	15.1408	+	0.465858i	0.677118	+	0.0208338i
$501$	0.317803	−	1.18606i	0.0141984	−	0.0529891i
$502$	−39.8727			−1.77960
$503$	0.169996	−	0.634433i	0.00757973	−	0.0282879i	−0.962032	−	0.272935i	$-0.912006\pi$
$503$	0.169996	−	0.634433i	0.00757973	−	0.0282879i	0.969612	+	0.244647i	$0.0786722\pi$
$504$	−1.93976	+	3.35977i	−0.0864039	+	0.149656i
$505$	−3.38444	−	9.60392i	−0.150606	−	0.427369i
$506$		−	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	$0.667920\pi$
$510$	15.5091	−	5.46544i	0.686755	−	0.242014i
$511$	45.2197	−	26.1076i	2.00040	−	1.15493i
$512$		−	20.4758i		−	0.904912i
$513$	−1.10327	−	1.91092i	−0.0487105	−	0.0843690i
$514$	−22.6693	−	6.07422i	−0.999901	−	0.267923i
$515$	−30.8759	+	2.38258i	−1.36056	+	0.104989i
$516$	11.8307	+	20.4914i	0.520818	+	0.902084i
$517$	36.4929	−	9.77825i	1.60496	−	0.430047i
$518$	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
$523$	−23.9001	+	6.40400i	−1.04508	+	0.280027i	−0.740216	−	0.672370i	$-0.765277\pi$
$523$	−23.9001	+	6.40400i	−1.04508	+	0.280027i	−0.304861	+	0.952397i	$0.598610\pi$
$524$	−3.78986	−	6.56423i	−0.165561	−	0.286760i
$525$	20.6989	−	28.3075i	0.903376	−	1.23544i
$526$	−29.2009	−	7.82436i	−1.27322	−	0.341158i
$527$	5.92431	+	10.2612i	0.258067	+	0.446985i
$528$		−	37.4226i		−	1.62861i
$529$	19.8383	−	11.4536i	0.862535	−	0.497985i
$530$	7.91127	−	16.5214i	0.343643	−	0.717643i
$531$	−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
$535$	−6.82795	+	14.2591i	−0.295198	+	0.616473i
$536$	1.35290	−	2.34329i	0.0584363	−	0.101215i
$537$	−1.12346	+	4.19281i	−0.0484809	+	0.180933i
$538$	−59.1745			−2.55119
$539$	−5.53871	+	20.6708i	−0.238569	+	0.890353i
$540$	7.03172	+	10.2647i	0.302597	+	0.441724i
$541$	−27.6908	−	27.6908i	−1.19052	−	1.19052i	−0.976922	−	0.213597i	$-0.931482\pi$
$541$	−27.6908	−	27.6908i	−1.19052	−	1.19052i	−0.213597	−	0.976922i	$-0.568518\pi$
$542$	−30.9125	−	8.28297i	−1.32780	−	0.355784i
$543$	−4.92042	−	18.3632i	−0.211155	−	0.788042i
$544$	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	−0.553353	−	0.832947i	$-0.686652\pi$
$547$	6.53914	−	6.53914i	0.279593	−	0.279593i	0.832947	+	0.553353i	$0.186652\pi$
$548$	−9.68071	+	16.7675i	−0.413540	+	0.716272i
$549$	2.31902	+	1.33889i	0.0989733	+	0.0571422i
$550$	−3.81632	+	35.2738i	−0.162729	+	1.50408i
$551$	−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
$555$	19.8072	−	13.5686i	0.840768	−	0.575956i
$556$	20.4359	+	11.7987i	0.866676	+	0.500375i
$557$	−8.12429	+	14.0717i	−0.344237	+	0.596237i	−0.985215	−	0.171323i	$-0.945196\pi$
$557$	−8.12429	+	14.0717i	−0.344237	+	0.596237i	0.640978	+	0.767560i	$0.278529\pi$
$558$	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
$562$	−12.5206	−	46.7277i	−0.528151	−	1.97109i
$563$	−31.4174	−	8.41827i	−1.32409	−	0.354788i	−0.473579	−	0.880751i	$-0.657038\pi$
$563$	−31.4174	−	8.41827i	−1.32409	−	0.354788i	−0.850507	+	0.525964i	$0.823705\pi$
$564$	18.5161	+	18.5161i	0.779670	+	0.779670i
$565$	−4.22904	+	2.89704i	−0.177917	+	0.121879i
$566$	−7.27167	+	27.1382i	−0.305651	+	1.14071i
$567$	38.6538			1.62331
$568$	1.41331	−	5.27453i	0.0593010	−	0.221314i
$569$	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	$-0.0749376\pi$
$570$	4.11313	−	1.44947i	0.172280	−	0.0607118i
$571$			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
$575$	1.39262	−	0.614947i	0.0580762	−	0.0256451i
$576$	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
$579$	−0.543832	−	0.145719i	−0.0226009	−	0.00605589i
$580$	3.89818	−	4.55010i	0.161863	−	0.188933i
$581$	13.4008	+	23.2109i	0.555959	+	0.962949i
$582$	−62.5017	+	16.7473i	−2.59078	+	0.694197i
$583$	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	$0.792464\pi$
$588$	−14.3271	+	3.83892i	−0.590838	+	0.158315i
$589$	1.57117	+	2.72135i	0.0647389	+	0.112131i
$590$	3.83147	+	49.6522i	0.157739	+	2.04415i
$591$	49.4837	+	13.2591i	2.03549	+	0.545407i
$592$	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
$595$	−14.4590	−	6.92367i	−0.592759	−	0.283843i
$596$	−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	$0.255247\pi$
$599$			35.1779i			1.43733i	−0.695356	+	0.718666i	$0.744753\pi$
$600$	10.7113	−	4.72983i	0.437285	−	0.193095i
$601$	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	$-0.137911\pi$
$602$	14.7834	−	55.1722i	0.602524	−	2.24865i
$603$	2.12443			0.0865136
$604$	−0.379473	+	1.41621i	−0.0154405	+	0.0576249i
$605$	−8.81103	−	1.64694i	−0.358219	−	0.0669577i
$606$	11.6890	+	11.6890i	0.474834	+	0.474834i
$607$	−41.5934	−	11.1449i	−1.68822	−	0.452358i	−0.718292	−	0.695742i	$-0.755076\pi$
$607$	−41.5934	−	11.1449i	−1.68822	−	0.452358i	−0.969930	+	0.243384i	$0.921742\pi$
$608$	0.912802	+	3.40662i	0.0370190	+	0.138157i
$609$	−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
$613$	10.1397	−	17.5625i	0.409540	−	0.709344i	−0.585298	−	0.810818i	$-0.699022\pi$
$613$	10.1397	−	17.5625i	0.409540	−	0.709344i	0.994838	+	0.101474i	$0.0323558\pi$
$614$	3.39352	+	1.95925i	0.136952	+	0.0790690i
$615$	−0.547826	+	2.93084i	−0.0220905	+	0.118183i
$616$	−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	$-0.542987\pi$
$619$	21.3034	−	21.3034i	0.856257	−	0.856257i	0.990895	+	0.134638i	$0.0429871\pi$
$620$	−10.0139	−	14.6181i	−0.402168	−	0.587076i
$621$	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
$626$	2.04165	+	7.61954i	0.0816007	+	0.304538i
$627$	1.06767	+	3.98458i	0.0426385	+	0.159129i
$628$	5.61682	+	1.50502i	0.224136	+	0.0600569i
$629$	−7.76093	−	7.76093i	−0.309449	−	0.309449i
$630$	−2.47067	+	13.2179i	−0.0984340	+	0.526615i
$631$	7.35050	−	27.4324i	0.292619	−	1.09207i	−0.650472	−	0.759531i	$-0.725429\pi$
$631$	7.35050	−	27.4324i	0.292619	−	1.09207i	0.943090	−	0.332537i	$-0.107905\pi$
$632$	−1.88727			−0.0750715
$633$	1.65548	−	6.17835i	0.0657996	−	0.245567i
$634$	−21.1670	+	36.6622i	−0.840647	+	1.45604i
$635$	−2.59371	−	1.24200i	−0.102928	−	0.0492873i
$636$			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
$640$	6.65997	+	18.8988i	0.263259	+	0.747041i
$641$	−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	$0.438112\pi$
$642$		−	25.6652i		−	1.01292i
$643$	20.5258	+	35.5518i	0.809460	+	1.40203i	0.913239	+	0.407425i	$0.133573\pi$
$643$	20.5258	+	35.5518i	0.809460	+	1.40203i	−0.103779	+	0.994600i	$0.533093\pi$
$644$	−1.41012	−	0.377841i	−0.0555666	−	0.0148890i
$645$	−29.6555	−	25.4065i	−1.16768	−	1.00038i
$646$	−0.996819	−	1.72654i	−0.0392193	−	0.0679298i
$647$	−2.73861	+	0.733807i	−0.107666	+	0.0288489i	−0.312250	−	0.950000i	$-0.601083\pi$
$647$	−2.73861	+	0.733807i	−0.107666	+	0.0288489i	0.204584	+	0.978849i	$0.434416\pi$
$648$	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
$653$	−1.21283	+	0.324978i	−0.0474619	+	0.0127174i	−0.282472	−	0.959276i	$-0.591154\pi$
$653$	−1.21283	+	0.324978i	−0.0474619	+	0.0127174i	0.235010	+	0.971993i	$0.424488\pi$
$654$	−25.3930	−	43.9820i	−0.992947	−	1.71983i
$655$	9.49985	+	8.13874i	0.371190	+	0.318007i
$656$	−3.16758	−	0.848749i	−0.123673	−	0.0331381i
$657$	6.84427	+	11.8546i	0.267020	+	0.462493i
$658$		−	63.2122i		−	2.46427i
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	−0.333886	−	0.942613i	$-0.608360\pi$
$659$	8.09916	−	4.67605i	0.315498	−	0.182153i	0.649384	+	0.760460i	$0.275027\pi$
$660$	−7.73119	−	21.9386i	−0.300936	−	0.853958i
$661$	24.7963	−	6.64415i	0.964464	−	0.258427i	0.257975	−	0.966152i	$-0.416945\pi$
$661$	24.7963	−	6.64415i	0.964464	−	0.258427i	0.706489	+	0.707724i	$0.250278\pi$
$662$	−2.58641	−	2.58641i	−0.100524	−	0.100524i
$663$		0			0
$664$			8.94896i			0.347287i
$665$	−3.83462	−	1.83621i	−0.148700	−	0.0712051i
$666$	−4.60315	+	7.97288i	−0.178368	+	0.308943i
$667$	0.155847	−	0.581628i	0.00603441	−	0.0225207i
$668$	0.839440			0.0324789
$669$	3.80358	−	14.1952i	0.147055	−	0.548817i
$670$	1.72318	−	9.21892i	0.0665724	−	0.356158i
$671$	7.90679	+	7.90679i	0.305238	+	0.305238i
$672$	−44.4701	−	11.9157i	−1.71547	−	0.459660i
$673$	−10.6983	−	39.9267i	−0.412390	−	1.53906i	−0.790007	−	0.613098i	$-0.789923\pi$
$673$	−10.6983	−	39.9267i	−0.412390	−	1.53906i	0.377617	−	0.925962i	$-0.376744\pi$
$674$	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	−0.342549	−	0.939500i	$-0.611290\pi$
$677$	15.5322	−	15.5322i	0.596950	−	0.596950i	0.939500	+	0.342549i	$0.111290\pi$
$678$	4.16090	−	7.20690i	0.159799	−	0.276779i
$679$	54.6308	+	31.5411i	2.09654	+	1.21044i
$680$	−3.02510	−	4.41597i	−0.116007	−	0.169345i
$681$	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
$685$	5.87106	−	31.4098i	0.224322	−	1.20011i
$686$	−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
$691$	9.73848	+	36.3445i	0.370469	+	1.38261i	0.859853	+	0.510542i	$0.170555\pi$
$691$	9.73848	+	36.3445i	0.370469	+	1.38261i	−0.489384	+	0.872069i	$0.662778\pi$
$692$	2.32201	+	8.66588i	0.0882698	+	0.329427i
$693$	−12.2861	−	3.29204i	−0.466709	−	0.125054i
$694$	42.1038	+	42.1038i	1.59824	+	1.59824i
$695$	−38.2817	−	7.15555i	−1.45211	−	0.271425i
$696$	1.19869	−	4.47356i	0.0454361	−	0.169570i
$697$	1.36302			0.0516282
$698$	3.22603	−	12.0397i	0.122107	−	0.455710i
$699$	4.04946	−	7.01387i	0.153165	−	0.265289i
$700$	22.3552	+	8.65976i	0.844949	+	0.327308i
$701$		−	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
$705$	−38.9782	−	18.6647i	−1.46801	−	0.702955i
$706$	−43.3459	+	25.0258i	−1.63134	+	0.941857i
$707$		−	16.1158i		−	0.606097i
$708$	−16.3247	−	28.2753i	−0.613521	−	1.06265i
$709$	−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	$0.899234\pi$
$710$	−1.45620	−	18.8709i	−0.0546501	−	0.708213i
$711$	−0.740887	−	1.28325i	−0.0277854	−	0.0481258i
$712$	−5.36959	+	1.43878i	−0.201234	+	0.0539204i
$713$	−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
$718$	9.75479	−	2.61379i	0.364045	−	0.0975457i
$719$	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
$721$	−47.3409	−	12.6850i	−1.76307	−	0.472413i
$722$	17.1361	+	29.6807i	0.637741	+	1.10460i
$723$			34.7768i			1.29336i
$724$	11.2555	−	6.49836i	0.418307	−	0.241510i
$725$	−3.57186	+	9.22079i	−0.132656	+	0.342451i
$726$	14.0557	−	3.76622i	0.521656	−	0.139777i
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.995240	−	0.0974593i	$-0.968928\pi$
$727$	−29.4624	−	29.4624i	−1.09270	−	1.09270i	−0.0974593	−	0.995240i	$-0.531072\pi$
$728$		0			0
$729$		−	14.2845i		−	0.529057i
$730$	56.9944	−	20.0849i	2.10946	−	0.743377i
$731$	−8.92588	+	15.4601i	−0.330135	+	0.571811i
$732$	−2.00591	+	7.48617i	−0.0741407	+	0.276697i
$733$	−23.3958			−0.864144			−0.432072	−	0.901839i	$-0.642217\pi$
$733$	−23.3958			−0.864144			−0.432072	+	0.901839i	$0.642217\pi$
$734$	−8.56885	+	31.9794i	−0.316282	+	1.18038i
$735$	20.1951	−	13.8344i	0.744909	−	0.510290i
$736$	−1.41323	−	1.41323i	−0.0520924	−	0.0520924i
$737$	8.56897	+	2.29605i	0.315642	+	0.0845761i
$738$	−0.295907	−	1.10434i	−0.0108925	−	0.0406513i
$739$	−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
$743$	−26.1400	+	45.2759i	−0.958985	+	1.66101i	−0.234011	+	0.972234i	$0.575185\pi$
$743$	−26.1400	+	45.2759i	−0.958985	+	1.66101i	−0.724973	+	0.688777i	$0.758148\pi$
$744$	−11.8615	−	6.84824i	−0.434864	−	0.251069i
$745$	24.2216	−	16.5927i	0.887412	−	0.607909i
$746$	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
$750$	29.5669	−	27.8017i	1.07963	−	1.01518i
$751$	−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	$0.833542\pi$
$752$	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
$756$	5.09659	+	19.0207i	0.185361	+	0.691777i
$757$	0.622824	+	2.32441i	0.0226369	+	0.0844821i	0.976320	−	0.216330i	$-0.0694088\pi$
$757$	0.622824	+	2.32441i	0.0226369	+	0.0844821i	−0.953683	+	0.300813i	$0.902742\pi$
$758$	37.8037	+	10.1295i	1.37309	+	0.367919i
$759$	−1.65300	−	1.65300i	−0.0600000	−	0.0600000i
$760$	−0.802277	−	1.17115i	−0.0291016	−	0.0424819i
$761$	−0.632352	+	2.35997i	−0.0229227	+	0.0855488i	−0.976440	−	0.215791i	$-0.930767\pi$
$761$	−0.632352	+	2.35997i	−0.0229227	+	0.0855488i	0.953517	+	0.301340i	$0.0974338\pi$
$762$	4.66848			0.169121
$763$	−12.8144	+	47.8242i	−0.463914	+	1.73135i
$764$	2.52761	−	4.37796i	0.0914459	−	0.158389i
$765$	1.81508	−	3.79050i	0.0656245	−	0.137046i
$766$		−	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	$0.495266\pi$
$770$	−24.2513	+	50.6448i	−0.873955	+	1.82511i
$771$	−21.9917	+	12.6969i	−0.792011	+	0.457268i
$772$		−	0.384901i		−	0.0138529i
$773$	−11.2222	−	19.4375i	−0.403636	−	0.699118i	0.590525	−	0.807019i	$-0.298921\pi$
$773$	−11.2222	−	19.4375i	−0.403636	−	0.699118i	−0.994162	+	0.107901i	$0.965587\pi$
$774$	14.4637	+	3.87555i	0.519888	+	0.139304i
$775$	23.6058	+	17.2609i	0.847944	+	0.620031i
$776$	10.5315	+	18.2410i	0.378058	+	0.654815i
$777$	36.7030	−	9.83454i	1.31671	−	0.352812i
$778$	−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
$783$	−7.84541	+	2.10217i	−0.280372	+	0.0751255i
$784$	13.4618	+	23.3165i	0.480778	+	0.832732i
$785$	−9.56847	+	0.738363i	−0.341513	+	0.0263533i
$786$	−19.6158	−	5.25605i	−0.699674	−	0.187477i
$787$	6.74791	+	11.6877i	0.240537	+	0.416622i	0.960867	−	0.277009i	$-0.0893431\pi$
$787$	6.74791	+	11.6877i	0.240537	+	0.416622i	−0.720330	+	0.693631i	$0.756010\pi$
$788$			35.0224i			1.24762i
$789$	−28.3280	+	16.3552i	−1.00850	+	0.582260i
$790$	−6.16960	+	2.17418i	−0.219504	+	0.0773538i
$791$	−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
$795$	−6.58760	−	18.6934i	−0.233638	−	0.662987i
$796$	3.89696	−	6.74974i	0.138124	−	0.239238i
$797$	1.62398	−	6.06076i	0.0575242	−	0.214683i	−0.931181	−	0.364558i	$-0.881220\pi$
$797$	1.62398	−	6.06076i	0.0575242	−	0.214683i	0.988705	+	0.149874i	$0.0478869\pi$
$798$	6.90201			0.244328
$799$	−5.11330	+	19.0831i	−0.180896	+	0.675112i
$800$	20.5771	+	25.5698i	0.727510	+	0.904028i
$801$	−3.08625	−	3.08625i	−0.109047	−	0.109047i
$802$	−49.3238	−	13.2163i	−1.74168	−	0.466683i
$803$	14.7943	+	55.2132i	0.522081	+	1.94843i
$804$	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
$808$	2.69050	−	4.66009i	0.0946516	−	0.163941i
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	0.791135	−	0.611641i	$-0.209490\pi$
$809$	18.6872	+	10.7890i	0.657006	+	0.379322i	−0.134130	+	0.990964i	$0.542824\pi$
$810$	43.9733	+	8.21941i	1.54506	+	0.288801i
$811$	22.5473	−	22.5473i	0.791743	−	0.791743i	−0.190035	−	0.981777i	$-0.560860\pi$
$811$	22.5473	−	22.5473i	0.791743	−	0.791743i	0.981777	+	0.190035i	$0.0608601\pi$
$812$	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
$815$	−4.97535	−	0.929983i	−0.174279	−	0.0325759i
$816$	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
$821$	4.64130	+	17.3216i	0.161982	+	0.604526i	0.998406	+	0.0564427i	$0.0179758\pi$
$821$	4.64130	+	17.3216i	0.161982	+	0.604526i	−0.836423	+	0.548084i	$0.815358\pi$
$822$	13.4259	+	50.1062i	0.468282	+	1.74765i
$823$	−1.11284	−	0.298185i	−0.0387913	−	0.0103941i	0.239371	−	0.970928i	$-0.423059\pi$
$823$	−1.11284	−	0.298185i	−0.0387913	−	0.0103941i	−0.278162	+	0.960534i	$0.589725\pi$
$824$	−11.5715	−	11.5715i	−0.403112	−	0.403112i
$825$	24.0681	+	29.9079i	0.837944	+	1.04126i
$826$	−20.3990	+	76.1300i	−0.709771	+	2.64890i
$827$	−4.45029			−0.154752			−0.0773759	−	0.997002i	$-0.524654\pi$
$827$	−4.45029			−0.154752			−0.0773759	+	0.997002i	$0.524654\pi$
$828$	0.0990534	−	0.369672i	0.00344234	−	0.0128470i
$829$	−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	$0.997857\pi$
$830$	10.3094	+	29.2547i	0.357845	+	1.01545i
$831$		−	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
$835$	−1.30664	+	0.460462i	−0.0452181	+	0.0159349i
$836$	−2.44229	+	1.41006i	−0.0844685	+	0.0487679i
$837$			24.0199i			0.830249i
$838$	−18.0142	−	31.2015i	−0.622291	−	1.07784i
$839$	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	$0.394883\pi$
$840$	18.4764	−	1.42575i	0.637496	−	0.0491931i
$841$	−12.5444	−	21.7275i	−0.432565	−	0.749224i
$842$	26.1283	−	7.00106i	0.900441	−	0.241273i
$843$	−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
$848$	21.0565	−	5.64207i	0.723083	−	0.193750i
$849$	15.1999	+	26.3270i	0.521660	+	0.903541i
$850$	−14.9765	−	10.9511i	−0.513691	−	0.375619i
$851$	1.59333	+	0.426931i	0.0546186	+	0.0146350i
$852$	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
$855$	0.481373	−	1.00527i	0.0164626	−	0.0343794i
$856$	−8.06972	+	2.16228i	−0.275817	+	0.0739051i
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.934214	+	0.356713i	$0.116103\pi$
$857$	37.7913	+	37.7913i	1.29093	+	1.29093i	0.356713	+	0.934214i	$0.383897\pi$
$858$		0			0
$859$		−	6.16263i		−	0.210266i	−0.994458	−	0.105133i	$-0.966473\pi$
$859$		−	6.16263i		−	0.210266i	0.994458	−	0.105133i	$-0.0335269\pi$
$860$	11.5299	−	24.0783i	0.393166	−	0.821063i
$861$	−2.35941	+	4.08661i	−0.0804083	+	0.139271i
$862$	8.12181	−	30.3110i	0.276630	−	1.03240i
$863$	−33.7740			−1.14968			−0.574840	−	0.818266i	$-0.694936\pi$
$863$	−33.7740			−1.14968			−0.574840	+	0.818266i	$0.694936\pi$
$864$	−6.97742	+	26.0401i	−0.237377	+	0.885902i
$865$	−8.36789	−	12.2152i	−0.284517	−	0.415331i
$866$	−14.5532	−	14.5532i	−0.494539	−	0.494539i
$867$	24.6868	+	6.61482i	0.838409	+	0.224651i
$868$	−7.25808	−	27.0875i	−0.246355	−	0.919410i
$869$	−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
$873$	−8.26870	+	14.3218i	−0.279853	+	0.484720i
$874$	0.259484	+	0.149813i	0.00877716	+	0.00506750i
$875$	−39.5474	−	1.21681i	−1.33695	−	0.0411357i
$876$	−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
$880$	−34.8334	+	23.8621i	−1.17423	+	0.804392i
$881$	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	$0.624546\pi$
$882$	−4.69331	+	8.12905i	−0.158032	+	0.273719i
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	−0.949822	−	0.312790i	$-0.898736\pi$
$883$	−18.9296	+	18.9296i	−0.637032	+	0.637032i	0.312790	+	0.949822i	$0.398736\pi$
$884$		0			0
$885$	40.9204	+	35.0575i	1.37552	+	1.17844i
$886$	10.1615	+	37.9234i	0.341384	+	1.27406i
$887$	9.19729	+	34.3248i	0.308815	+	1.15251i	0.929612	+	0.368541i	$0.120143\pi$
$887$	9.19729	+	34.3248i	0.308815	+	1.15251i	−0.620797	+	0.783972i	$0.713191\pi$
$888$	12.2550	+	3.28372i	0.411251	+	0.110194i
$889$	−3.21825	−	3.21825i	−0.107937	−	0.107937i
$890$	−15.8960	+	10.8893i	−0.532836	+	0.365012i
$891$	−10.9519	+	40.8731i	−0.366903	+	1.36930i
$892$	10.0467			0.336389
$893$	−1.35608	+	5.06098i	−0.0453796	+	0.169359i
$894$	−23.8314	+	41.2772i	−0.797042	+	1.38052i
$895$	4.61908	−	1.62777i	0.154399	−	0.0544104i
$896$			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
$900$	−2.27021	+	5.86056i	−0.0756736	+	0.195352i
$901$	−7.84682	+	4.53036i	−0.261415	+	0.150928i
$902$		−	4.77421i		−	0.158964i
$903$	−30.9015	−	53.5230i	−1.02834	−	1.78113i
$904$	−2.61657	−	0.701108i	−0.0870258	−	0.0233185i
$905$	−13.9553	+	16.2891i	−0.463889	+	0.541469i
$906$	1.96411	+	3.40193i	0.0652530	+	0.113022i
$907$	−44.9172	+	12.0355i	−1.49145	+	0.399633i	−0.910227	−	0.414109i	$-0.864093\pi$
$907$	−44.9172	+	12.0355i	−1.49145	+	0.399633i	−0.581225	+	0.813743i	$0.697426\pi$
$908$	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
$913$	−28.3404	+	7.59379i	−0.937931	+	0.251318i
$914$	27.7449	+	48.0556i	0.917720	+	1.58954i
$915$	−0.984100	−	12.7530i	−0.0325333	−	0.421601i
$916$	22.9399	+	6.14674i	0.757957	+	0.203094i
$917$	9.89902	+	17.1456i	0.326894	+	0.566198i
$918$		−	15.2393i		−	0.502971i
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.400213	−	0.916422i	$-0.368936\pi$
$919$	42.2580	−	24.3977i	1.39396	−	0.804806i	0.993751	+	0.111617i	$0.0356029\pi$
$920$	0.725574	+	0.347441i	0.0239215	+	0.0114548i
$921$	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
$925$	−25.2597	−	9.78485i	−0.830533	−	0.321724i
$926$	−28.7990	+	49.8814i	−0.946395	+	1.63920i
$927$	3.32544	−	12.4107i	0.109222	−	0.407621i
$928$	12.9820			0.426155
$929$	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	$0.0288300\pi$
$930$	−46.6653	−	8.72260i	−1.53022	−	0.286025i
$931$	−2.09857	−	2.09857i	−0.0687778	−	0.0687778i
$932$	5.34810	+	1.43302i	0.175183	+	0.0469401i
$933$	1.95987	+	7.31433i	0.0641632	+	0.239460i
$934$	−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	−0.614875	−	0.788625i	$-0.710794\pi$
$937$	5.31856	−	5.31856i	0.173750	−	0.173750i	0.788625	+	0.614875i	$0.210794\pi$
$938$	7.42149	−	12.8544i	0.242320	−	0.419711i
$939$	7.39178	+	4.26764i	0.241221	+	0.139269i
$940$	5.42842	−	29.0417i	0.177055	−	0.947235i
$941$	−38.9093	+	38.9093i	−1.26841	+	1.26841i	−0.321497	+	0.946911i	$0.604186\pi$
$941$	−38.9093	+	38.9093i	−1.26841	+	1.26841i	−0.946911	+	0.321497i	$0.895814\pi$
$942$	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
$945$	−18.3667	−	26.8113i	−0.597468	−	0.872170i
$946$	54.1514	+	31.2643i	1.76061	+	1.01649i
$947$	−16.8759	+	29.2298i	−0.548392	+	0.949842i	0.449993	+	0.893032i	$0.351426\pi$
$947$	−16.8759	+	29.2298i	−0.548392	+	0.949842i	−0.998385	+	0.0568101i	$0.981907\pi$
$948$	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
$952$	−2.19259	−	8.18285i	−0.0710622	−	0.265208i
$953$	−4.26581	−	1.14302i	−0.138183	−	0.0370260i	0.189065	−	0.981965i	$-0.439454\pi$
$953$	−4.26581	−	1.14302i	−0.138183	−	0.0370260i	−0.327248	+	0.944939i	$0.606121\pi$
$954$	5.37407	+	5.37407i	0.173992	+	0.173992i
$955$	−1.53292	+	8.20103i	−0.0496042	+	0.265379i
$956$	4.44988	−	16.6072i	0.143919	−	0.537115i
$957$	15.1845			0.490845
$958$	−9.17471	+	34.2405i	−0.296422	+	1.10626i
$959$	25.2858	−	43.7963i	0.816520	−	1.41425i
$960$	−9.09361	−	4.35448i	−0.293495	−	0.140540i
$961$		−	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
$965$	0.211132	+	0.599122i	0.00679657	+	0.0192864i
$966$	−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
$969$	−2.08364	−	0.558310i	−0.0669363	−	0.0179355i
$970$	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	$0.899193\pi$
$972$	−12.2052	+	3.27038i	−0.391482	+	0.104897i
$973$	−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	$0.749309\pi$
$978$	7.93687	−	2.12668i	0.253793	−	0.0680037i
$979$	−9.11292	−	15.7840i	−0.291250	−	0.504460i
$980$	12.7088	+	10.8879i	0.405968	+	0.347803i
$981$	−12.5374	−	3.35939i	−0.400288	−	0.107257i
$982$	−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
$985$	−19.2110	−	54.5145i	−0.612114	−	1.73698i
$986$	−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
$990$	−13.2768	−	6.35762i	−0.421966	−	0.202058i
$991$	−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	$0.282205\pi$
$992$	9.93658	−	37.0838i	0.315487	−	1.17741i
$993$	−3.95773			−0.125595
$994$	7.75287	−	28.9341i	0.245906	−	0.917734i
$995$	−2.36339	+	12.6440i	−0.0749246	+	0.400842i
$996$	−14.3796	−	14.3796i	−0.455637	−	0.455637i
$997$	−11.4991	−	3.08118i	−0.364181	−	0.0975820i	0.0720881	−	0.997398i	$-0.477034\pi$
$997$	−11.4991	−	3.08118i	−0.364181	−	0.0975820i	−0.436269	+	0.899816i	$0.643700\pi$
$998$	15.4458	+	57.6445i	0.488928	+	1.82471i
$999$	−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.t.f.188.4		20
5.2	odd	4		845.2.o.e.357.2		20
13.2	odd	12		845.2.o.f.258.4		20
13.3	even	3		65.2.t.a.28.2	yes	20
13.4	even	6		845.2.f.d.408.8		20
13.5	odd	4		845.2.o.g.488.4		20
13.6	odd	12		845.2.k.d.268.3		20
13.7	odd	12		845.2.k.e.268.8		20
13.8	odd	4		65.2.o.a.33.2	yes	20
13.9	even	3		845.2.f.e.408.3		20
13.10	even	6		845.2.t.g.418.4		20
13.11	odd	12		845.2.o.e.258.2		20
13.12	even	2		845.2.t.e.188.2		20
39.8	even	4		585.2.cf.a.163.4		20
39.29	odd	6		585.2.dp.a.28.4		20
65.2	even	12		845.2.t.e.427.2		20
65.3	odd	12		325.2.s.b.132.4		20
65.7	even	12		845.2.f.e.437.8		20
65.8	even	4		325.2.x.b.7.4		20
65.12	odd	4		845.2.o.f.357.4		20
65.17	odd	12		845.2.k.d.577.3		20
65.22	odd	12		845.2.k.e.577.8		20
65.29	even	6		325.2.x.b.93.4		20
65.32	even	12		845.2.f.d.437.3		20
65.34	odd	4		325.2.s.b.293.4		20
65.37	even	12	inner	845.2.t.f.427.4		20
65.42	odd	12		65.2.o.a.2.2	✓	20
65.47	even	4		65.2.t.a.7.2	yes	20
65.57	even	4		845.2.t.g.657.4		20
65.62	odd	12		845.2.o.g.587.4		20
195.47	odd	4		585.2.dp.a.397.4		20
195.107	even	12		585.2.cf.a.262.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.2	✓	20	65.42	odd	12
65.2.o.a.33.2	yes	20	13.8	odd	4
65.2.t.a.7.2	yes	20	65.47	even	4
65.2.t.a.28.2	yes	20	13.3	even	3
325.2.s.b.132.4		20	65.3	odd	12
325.2.s.b.293.4		20	65.34	odd	4
325.2.x.b.7.4		20	65.8	even	4
325.2.x.b.93.4		20	65.29	even	6
585.2.cf.a.163.4		20	39.8	even	4
585.2.cf.a.262.4		20	195.107	even	12
585.2.dp.a.28.4		20	39.29	odd	6
585.2.dp.a.397.4		20	195.47	odd	4
845.2.f.d.408.8		20	13.4	even	6
845.2.f.d.437.3		20	65.32	even	12
845.2.f.e.408.3		20	13.9	even	3
845.2.f.e.437.8		20	65.7	even	12
845.2.k.d.268.3		20	13.6	odd	12
845.2.k.d.577.3		20	65.17	odd	12
845.2.k.e.268.8		20	13.7	odd	12
845.2.k.e.577.8		20	65.22	odd	12
845.2.o.e.258.2		20	13.11	odd	12
845.2.o.e.357.2		20	5.2	odd	4
845.2.o.f.258.4		20	13.2	odd	12
845.2.o.f.357.4		20	65.12	odd	4
845.2.o.g.488.4		20	13.5	odd	4
845.2.o.g.587.4		20	65.62	odd	12
845.2.t.e.188.2		20	13.12	even	2
845.2.t.e.427.2		20	65.2	even	12
845.2.t.f.188.4		20	1.1	even	1	trivial
845.2.t.f.427.4		20	65.37	even	12	inner
845.2.t.g.418.4		20	13.10	even	6
845.2.t.g.657.4		20	65.57	even	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.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58624 + 0.915816i) q^{2} +(1.91432 - 0.512942i) q^{3} +(0.677439 + 1.17336i) q^{4} +(-1.69810 - 1.45480i) q^{5} +(3.50634 + 0.939520i) q^{6} +(-1.76945 - 3.06478i) q^{7} -1.18163i q^{8} +(0.803451 - 0.463873i) q^{9} +(-1.36126 - 3.86282i) q^{10} +(3.74209 - 1.00269i) q^{11} +(1.89870 + 1.89870i) q^{12} -6.48197i q^{14} +(-3.99694 - 1.91394i) q^{15} +(2.43703 - 4.22106i) q^{16} +(-0.524334 + 1.95684i) q^{17} +1.69929 q^{18} +(-0.139057 + 0.518968i) q^{19} +(0.556646 - 2.97802i) q^{20} +(-4.95936 - 4.95936i) q^{21} +(6.85414 + 1.83656i) q^{22} +(-0.0788026 - 0.294095i) q^{23} +(-0.606106 - 2.26202i) 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} +(-4.58730 - 6.69643i) 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} +(-1.45395 + 7.77851i) 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} +(-0.174136 - 0.649884i) q^{41} +(-3.32487 - 12.4086i) q^{42} +(8.51164 + 2.28069i) q^{43} +(3.71155 + 3.71155i) q^{44} +(-2.03919 - 0.381161i) q^{45} +(0.144337 - 0.538675i) q^{46} +9.75201 q^{47} +(2.50011 - 9.33053i) q^{48} +(-2.76192 + 4.78379i) q^{49} +(-3.30807 + 8.53982i) q^{50} +4.01498i q^{51} +(3.16254 + 3.16254i) q^{53} +(-7.26602 + 1.94693i) q^{54} +(-7.81317 - 3.74134i) q^{55} +(-3.62143 + 2.09083i) q^{56} +1.06480i q^{57} +(1.81120 + 3.13709i) q^{58} +(-11.7449 - 3.14703i) q^{59} +(-0.461950 - 5.98642i) q^{60} +(1.44316 + 2.49963i) q^{61} +(10.3476 - 2.77263i) q^{62} +(-2.84334 - 1.64160i) q^{63} +2.27514 q^{64} +14.0631 q^{66} +(1.98310 + 1.14494i) q^{67} +(-2.65128 + 0.710408i) q^{68} +(-0.301707 - 0.522573i) q^{69} +(-9.43000 + 11.0070i) q^{70} +(4.46378 + 1.19607i) q^{71} +(-0.548125 - 0.949380i) q^{72} +14.7546i q^{73} +(-8.59382 + 4.96165i) q^{74} +(4.00281 + 9.06483i) q^{75} +(-0.703137 + 0.188405i) q^{76} +(-9.69449 - 9.69449i) q^{77} -1.59718i q^{79} +(-10.2791 + 3.62239i) q^{80} +(-5.46126 + 9.45918i) q^{81} +(0.318953 - 1.19035i) q^{82} -7.57341 q^{83} +(2.45944 - 9.17877i) q^{84} +(3.73719 - 2.56011i) q^{85} +(11.4128 + 11.4128i) q^{86} +(3.78593 + 1.01444i) q^{87} +(-1.18481 - 4.42176i) q^{88} +(-1.21762 - 4.54423i) 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} +(0.991129 - 0.678959i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

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