LMFDB - Embedded newform 845.2.t.f.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,-2,6,0,4] 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			657.4
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	845.657
Dual form			845.2.t.f.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+(0.885613 + 0.511309i) q^{2} +(-0.721300 - 2.69193i) q^{3} +(-0.477126 - 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(0.737614 - 2.75281i) q^{6} +(-0.481787 - 0.834479i) q^{7} -3.02107i q^{8} +(-4.12812 + 2.38337i) q^{9} +(-0.423625 - 2.24706i) q^{10} +(-0.430490 - 1.60661i) q^{11} +(-1.88048 + 1.88048i) q^{12} -0.985368i q^{14} +(-3.51384 + 5.14652i) q^{15} +(0.590448 - 1.02269i) q^{16} +(7.00342 + 1.87656i) q^{17} -4.87456 q^{18} +(-2.64041 - 0.707496i) q^{19} +(-0.706075 + 2.01357i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(0.440226 - 1.64295i) q^{22} +(3.72214 - 0.997344i) q^{23} +(-8.13250 + 2.17910i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.459747 + 0.796304i) q^{28} +(0.253107 + 0.146132i) q^{29} +(-5.74336 + 2.76117i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(-4.18683 + 2.41727i) q^{32} +(-4.01436 + 2.31769i) q^{33} +(5.24282 + 5.24282i) q^{34} +(-0.712972 + 2.03323i) q^{35} +(3.93927 + 2.27434i) q^{36} +(2.04061 - 3.53443i) q^{37} +(-1.97663 - 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(6.69071 - 1.79277i) q^{41} +(-2.65254 + 0.710745i) q^{42} +(-2.05706 + 7.67707i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(10.0583 + 3.52703i) q^{45} +(3.80633 + 1.01990i) q^{46} -7.84582 q^{47} +(-3.17888 - 0.851780i) q^{48} +(3.03576 - 5.25810i) q^{49} +(-3.19325 + 3.99335i) q^{50} -20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(1.30317 + 4.86351i) q^{54} +(-2.09714 + 3.07157i) q^{55} +(-2.52102 + 1.45551i) q^{56} +7.61811i q^{57} +(0.149437 + 0.258832i) q^{58} +(1.30739 - 4.87924i) q^{59} +(5.92967 + 0.448318i) q^{60} +(-1.04169 - 1.80425i) q^{61} +(-0.0470311 - 0.175522i) q^{62} +(3.97775 + 2.29655i) q^{63} -7.30568 q^{64} -4.74023 q^{66} +(-6.32050 - 3.64915i) q^{67} +(-1.79071 - 6.68304i) q^{68} +(-5.36956 - 9.30034i) q^{69} +(-1.67103 + 1.43611i) q^{70} +(-3.37837 + 12.6082i) q^{71} +(7.20034 + 12.4713i) q^{72} -3.22747i q^{73} +(3.61437 - 2.08676i) q^{74} +(13.8489 - 1.54181i) q^{75} +(0.675130 + 2.51962i) q^{76} +(-1.13328 + 1.13328i) q^{77} -13.5845i q^{79} +(-2.59485 + 0.489192i) q^{80} +(-0.289196 + 0.500902i) q^{81} +(6.84204 + 1.83332i) q^{82} -8.56854 q^{83} +(2.47521 + 0.663230i) q^{84} +(-7.02469 - 14.6117i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.210809 - 0.786751i) q^{87} +(-4.85368 + 1.30054i) q^{88} +(0.500868 - 0.134207i) q^{89} +(7.10435 + 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.247608 + 0.428870i) q^{93} +(-6.94836 - 4.01164i) q^{94} +(2.64843 + 5.50885i) q^{95} +(9.52707 + 9.52707i) q^{96} +(6.50662 - 3.75660i) q^{97} +(5.37702 - 3.10442i) q^{98} +(5.60626 + 5.60626i) 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.885613	+	0.511309i	0.626223	+	0.361550i	0.779288	−	0.626666i	$-0.215581\pi$
$2$	0.885613	+	0.511309i	0.626223	+	0.361550i	−0.153065	+	0.988216i	$0.548914\pi$
$3$	−0.721300	−	2.69193i	−0.416443	−	1.55418i	−0.781929	−	0.623368i	$-0.785764\pi$
$3$	−0.721300	−	2.69193i	−0.416443	−	1.55418i	0.365486	−	0.930817i	$-0.380903\pi$
$4$	−0.477126	−	0.826407i	−0.238563	−	0.413204i
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$5$	−1.45744	−	1.69584i	−0.651785	−	0.758404i
$6$	0.737614	−	2.75281i	0.301130	−	1.12383i
$7$	−0.481787	−	0.834479i	−0.182098	−	0.315404i	0.760497	−	0.649342i	$-0.224956\pi$
$7$	−0.481787	−	0.834479i	−0.182098	−	0.315404i	−0.942595	+	0.333938i	$0.891622\pi$
$8$		−	3.02107i		−	1.06811i
$9$	−4.12812	+	2.38337i	−1.37604	+	0.794457i
$10$	−0.423625	−	2.24706i	−0.133962	−	0.710583i
$11$	−0.430490	−	1.60661i	−0.129797	−	0.484411i	0.870168	−	0.492756i	$-0.164010\pi$
$11$	−0.430490	−	1.60661i	−0.129797	−	0.484411i	−0.999965	+	0.00834492i	$0.997344\pi$
$12$	−1.88048	+	1.88048i	−0.542847	+	0.542847i
$13$		0			0
$13$		0			0
$14$		−	0.985368i		−	0.263351i
$15$	−3.51384	+	5.14652i	−0.907268	+	1.32883i
$16$	0.590448	−	1.02269i	0.147612	−	0.255671i
$17$	7.00342	+	1.87656i	1.69858	+	0.455133i	0.972581	−	0.232564i	$-0.0747114\pi$
$17$	7.00342	+	1.87656i	1.69858	+	0.455133i	0.725998	+	0.687697i	$0.241378\pi$
$18$	−4.87456			−1.14894
$19$	−2.64041	−	0.707496i	−0.605752	−	0.162311i	−0.0571095	−	0.998368i	$-0.518188\pi$
$19$	−2.64041	−	0.707496i	−0.605752	−	0.162311i	−0.548642	+	0.836057i	$0.684855\pi$
$20$	−0.706075	+	2.01357i	−0.157883	+	0.450247i
$21$	−1.89884	+	1.89884i	−0.414362	+	0.414362i
$22$	0.440226	−	1.64295i	0.0938565	−	0.350277i
$23$	3.72214	−	0.997344i	0.776120	−	0.207961i	0.151046	−	0.988527i	$-0.451736\pi$
$23$	3.72214	−	0.997344i	0.776120	−	0.207961i	0.625073	+	0.780566i	$0.285069\pi$
$24$	−8.13250	+	2.17910i	−1.66004	+	0.444806i
$25$	−0.751762	+	4.94316i	−0.150352	+	0.988632i
$26$		0			0
$27$	3.48159	+	3.48159i	0.670033	+	0.670033i
$28$	−0.459747	+	0.796304i	−0.0868839	+	0.150487i
$29$	0.253107	+	0.146132i	0.0470008	+	0.0271360i	0.523316	−	0.852139i	$-0.324695\pi$
$29$	0.253107	+	0.146132i	0.0470008	+	0.0271360i	−0.476315	+	0.879274i	$0.658028\pi$
$30$	−5.74336	+	2.76117i	−1.04859	+	0.504118i
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$	−4.18683	+	2.41727i	−0.740134	+	0.427317i
$33$	−4.01436	+	2.31769i	−0.698811	+	0.403458i
$34$	5.24282	+	5.24282i	0.899136	+	0.899136i
$35$	−0.712972	+	2.03323i	−0.120514	+	0.343679i
$36$	3.93927	+	2.27434i	0.656545	+	0.379057i
$37$	2.04061	−	3.53443i	0.335474	−	0.581057i	−0.648102	−	0.761553i	$-0.724437\pi$
$37$	2.04061	−	3.53443i	0.335474	−	0.581057i	0.983576	+	0.180496i	$0.0577703\pi$
$38$	−1.97663	−	1.97663i	−0.320652	−	0.320652i
$39$		0			0
$40$	−5.12326	+	4.40302i	−0.810059	+	0.696178i
$41$	6.69071	−	1.79277i	1.04491	−	0.279984i	0.304765	−	0.952427i	$-0.401422\pi$
$41$	6.69071	−	1.79277i	1.04491	−	0.279984i	0.740148	+	0.672444i	$0.234755\pi$
$42$	−2.65254	+	0.710745i	−0.409295	+	0.109670i
$43$	−2.05706	+	7.67707i	−0.313699	+	1.17074i	0.611495	+	0.791248i	$0.290568\pi$
$43$	−2.05706	+	7.67707i	−0.313699	+	1.17074i	−0.925194	+	0.379494i	$0.876098\pi$
$44$	−1.12232	+	1.12232i	−0.169195	+	0.169195i
$45$	10.0583	+	3.52703i	1.49940	+	0.525779i
$46$	3.80633	+	1.01990i	0.561212	+	0.150376i
$47$	−7.84582			−1.14443			−0.572215	−	0.820103i	$-0.693916\pi$
$47$	−7.84582			−1.14443			−0.572215	+	0.820103i	$0.693916\pi$
$48$	−3.17888	−	0.851780i	−0.458832	−	0.122944i
$49$	3.03576	−	5.25810i	0.433680	−	0.751156i
$50$	−3.19325	+	3.99335i	−0.451594	+	0.564744i
$51$		−	20.2063i		−	2.82944i
$52$		0			0
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	−0.830918	−	0.556395i	$-0.812184\pi$
$53$	−1.99855	+	1.99855i	−0.274522	+	0.274522i	0.556395	+	0.830918i	$0.312184\pi$
$54$	1.30317	+	4.86351i	0.177339	+	0.661840i
$55$	−2.09714	+	3.07157i	−0.282779	+	0.414171i
$56$	−2.52102	+	1.45551i	−0.336886	+	0.194501i
$57$			7.61811i			1.00904i
$58$	0.149437	+	0.258832i	0.0196220	+	0.0339863i
$59$	1.30739	−	4.87924i	0.170207	−	0.635223i	−0.827111	−	0.562039i	$-0.810017\pi$
$59$	1.30739	−	4.87924i	0.170207	−	0.635223i	0.997318	−	0.0731843i	$-0.0233161\pi$
$60$	5.92967	+	0.448318i	0.765517	+	0.0578776i
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	0.791601	−	0.611038i	$-0.209248\pi$
$61$	−1.04169	−	1.80425i	−0.133374	−	0.231011i	−0.924975	+	0.380027i	$0.875915\pi$
$62$	−0.0470311	−	0.175522i	−0.00597296	−	0.0222914i
$63$	3.97775	+	2.29655i	0.501149	+	0.289339i
$64$	−7.30568			−0.913209
$65$		0			0
$66$	−4.74023			−0.583482
$67$	−6.32050	−	3.64915i	−0.772173	−	0.445814i	0.0614765	−	0.998109i	$-0.480419\pi$
$67$	−6.32050	−	3.64915i	−0.772173	−	0.445814i	−0.833649	+	0.552294i	$0.813752\pi$
$68$	−1.79071	−	6.68304i	−0.217156	−	0.810437i
$69$	−5.36956	−	9.30034i	−0.646419	−	1.11963i
$70$	−1.67103	+	1.43611i	−0.199726	+	0.171648i
$71$	−3.37837	+	12.6082i	−0.400939	+	1.49632i	0.410486	+	0.911867i	$0.365359\pi$
$71$	−3.37837	+	12.6082i	−0.400939	+	1.49632i	−0.811425	+	0.584457i	$0.801308\pi$
$72$	7.20034	+	12.4713i	0.848568	+	1.46976i
$73$		−	3.22747i		−	0.377746i	−0.982001	−	0.188873i	$-0.939517\pi$
$73$		−	3.22747i		−	0.377746i	0.982001	−	0.188873i	$-0.0604835\pi$
$74$	3.61437	−	2.08676i	0.420163	−	0.242581i
$75$	13.8489	−	1.54181i	1.59913	−	0.178033i
$76$	0.675130	+	2.51962i	0.0774427	+	0.289020i
$77$	−1.13328	+	1.13328i	−0.129149	+	0.129149i
$78$		0			0
$79$		−	13.5845i		−	1.52838i	−0.644992	−	0.764190i	$-0.723139\pi$
$79$		−	13.5845i		−	1.52838i	0.644992	−	0.764190i	$-0.276861\pi$
$80$	−2.59485	+	0.489192i	−0.290113	+	0.0546934i
$81$	−0.289196	+	0.500902i	−0.0321329	+	0.0556558i
$82$	6.84204	+	1.83332i	0.755577	+	0.202456i
$83$	−8.56854			−0.940519			−0.470260	−	0.882528i	$-0.655840\pi$
$83$	−8.56854			−0.940519			−0.470260	+	0.882528i	$0.655840\pi$
$84$	2.47521	+	0.663230i	0.270067	+	0.0723643i
$85$	−7.02469	−	14.6117i	−0.761934	−	1.58486i
$86$	−5.74712	+	5.74712i	−0.619728	+	0.619728i
$87$	0.210809	−	0.786751i	0.0226011	−	0.0843486i
$88$	−4.85368	+	1.30054i	−0.517404	+	0.138638i
$89$	0.500868	−	0.134207i	0.0530919	−	0.0142259i	−0.232175	−	0.972674i	$-0.574584\pi$
$89$	0.500868	−	0.134207i	0.0530919	−	0.0142259i	0.285267	+	0.958448i	$0.407918\pi$
$90$	7.10435	+	8.26648i	0.748864	+	0.871363i
$91$		0			0
$92$	−2.60014	−	2.60014i	−0.271084	−	0.271084i
$93$	−0.247608	+	0.428870i	−0.0256758	+	0.0444718i
$94$	−6.94836	−	4.01164i	−0.716669	−	0.413769i
$95$	2.64843	+	5.50885i	0.271723	+	0.565196i
$96$	9.52707	+	9.52707i	0.972353	+	0.972353i
$97$	6.50662	−	3.75660i	0.660648	−	0.381425i	−0.131876	−	0.991266i	$-0.542100\pi$
$97$	6.50662	−	3.75660i	0.660648	−	0.381425i	0.792524	+	0.609841i	$0.208767\pi$
$98$	5.37702	−	3.10442i	0.543161	−	0.313594i
$99$	5.60626	+	5.60626i	0.563450	+	0.563450i
$100$	4.44375	−	1.73725i	0.444375	−	0.173725i
$101$	−8.44685	−	4.87679i	−0.840493	−	0.485259i	0.0169388	−	0.999857i	$-0.494608\pi$
$101$	−8.44685	−	4.87679i	−0.840493	−	0.485259i	−0.857432	+	0.514598i	$0.827941\pi$
$102$	10.3316	−	17.8949i	1.02298	−	1.77186i
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	0.820404	−	0.571784i	$-0.193749\pi$
$103$	2.52321	+	2.52321i	0.248619	+	0.248619i	−0.571784	+	0.820404i	$0.693749\pi$
$104$		0			0
$105$	5.98759	+	0.452697i	0.584329	+	0.0441787i
$106$	−2.79182	+	0.748066i	−0.271166	+	0.0726586i
$107$	0.429359	−	0.115046i	0.0415077	−	0.0111220i	−0.238005	−	0.971264i	$-0.576494\pi$
$107$	0.429359	−	0.115046i	0.0415077	−	0.0111220i	0.279513	+	0.960142i	$0.409827\pi$
$108$	1.21605	−	4.53837i	0.117015	−	0.436705i
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	−0.329206	−	0.944258i	$-0.606781\pi$
$109$	6.42134	−	6.42134i	0.615053	−	0.615053i	0.944258	+	0.329206i	$0.106781\pi$
$110$	−3.42778	+	1.64793i	−0.326826	+	0.157124i
$111$	−10.9863	−	2.94378i	−1.04278	−	0.279411i
$112$	−1.13788			−0.107520
$113$	−1.86865	−	0.500704i	−0.175788	−	0.0471023i	0.169851	−	0.985470i	$-0.445671\pi$
$113$	−1.86865	−	0.500704i	−0.175788	−	0.0471023i	−0.345639	+	0.938367i	$0.612338\pi$
$114$	−3.89521	+	6.74670i	−0.364820	+	0.631886i
$115$	−7.11612	−	4.85860i	−0.663581	−	0.453066i
$116$		−	0.278893i		−	0.0258946i
$117$		0			0
$118$	3.65264	−	3.65264i	0.336253	−	0.336253i
$119$	−1.80821	−	6.74831i	−0.165758	−	0.618617i
$120$	15.5480	+	10.6155i	1.41933	+	0.969062i
$121$	7.13041	−	4.11674i	0.648219	−	0.374249i
$122$		−	2.13050i		−	0.192886i
$123$	−9.65202	−	16.7178i	−0.870293	−	1.50739i
$124$	−0.0438869	+	0.163788i	−0.00394116	+	0.0147086i
$125$	9.47847	−	5.92947i	0.847780	−	0.530348i
$126$	2.34850	+	4.06772i	0.209221	+	0.362381i
$127$	0.562967	+	2.10102i	0.0499553	+	0.186436i	0.986395	−	0.164393i	$-0.0525666\pi$
$127$	0.562967	+	2.10102i	0.0499553	+	0.186436i	−0.936440	+	0.350829i	$0.885900\pi$
$128$	1.90366	+	1.09908i	0.168262	+	0.0971460i
$129$	22.1499			1.95019
$130$		0			0
$131$	−0.0622493			−0.00543874			−0.00271937	−	0.999996i	$-0.500866\pi$
$131$	−0.0622493			−0.00543874			−0.00271937	+	0.999996i	$0.500866\pi$
$132$	3.83072	+	2.21166i	0.333421	+	0.192501i
$133$	0.681725	+	2.54423i	0.0591130	+	0.220613i
$134$	−3.73168	−	6.46346i	−0.322368	−	0.558358i
$135$	0.830034	−	10.9784i	0.0714380	−	0.944872i
$136$	5.66923	−	21.1578i	0.486132	−	1.81427i
$137$	2.20873	+	3.82564i	0.188705	+	0.326846i	0.944819	−	0.327594i	$-0.106238\pi$
$137$	2.20873	+	3.82564i	0.188705	+	0.326846i	−0.756114	+	0.654440i	$0.772904\pi$
$138$		−	10.9820i		−	0.934850i
$139$	11.9066	−	6.87430i	1.00991	−	0.583070i	0.0987430	−	0.995113i	$-0.468518\pi$
$139$	11.9066	−	6.87430i	1.00991	−	0.583070i	0.911165	+	0.412043i	$0.135184\pi$
$140$	2.02046	−	0.380905i	0.170760	−	0.0321923i
$141$	5.65919	+	21.1204i	0.476590	+	1.77866i
$142$	−9.43864	+	9.43864i	−0.792073	+	0.792073i
$143$		0			0
$144$			5.62903i			0.469085i
$145$	−0.121072	−	0.642207i	−0.0100544	−	0.0533324i
$146$	1.65023	−	2.85829i	0.136574	−	0.236553i
$147$	−16.3441	−	4.37939i	−1.34804	−	0.361206i
$148$	−3.89451			−0.320127
$149$	−4.18471	−	1.12129i	−0.342825	−	0.0918596i	0.0832987	−	0.996525i	$-0.473454\pi$
$149$	−4.18471	−	1.12129i	−0.342825	−	0.0918596i	−0.426124	+	0.904665i	$0.640121\pi$
$150$	13.0531	+	5.71560i	1.06578	+	0.466677i
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	−2.13740	+	7.97687i	−0.173366	+	0.647010i
$153$	−33.3835	+	8.94508i	−2.69890	+	0.723167i
$154$	−1.58310	+	0.424190i	−0.127570	+	0.0341822i
$155$	−0.0299556	+	0.396208i	−0.00240610	+	0.0318242i
$156$		0			0
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.985920	+	0.167218i	$0.0534784\pi$
$157$	14.4488	+	14.4488i	1.15314	+	1.15314i	0.167218	+	0.985920i	$0.446522\pi$
$158$	6.94589	−	12.0306i	0.552586	−	0.957106i
$159$	6.82151	+	3.93840i	0.540981	+	0.312336i
$160$	10.2013	+	3.57719i	0.806487	+	0.282802i
$161$	−2.62554	−	2.62554i	−0.206922	−	0.206922i
$162$	−0.512231	+	0.295737i	−0.0402447	+	0.0232353i
$163$	−18.5201	+	10.6926i	−1.45061	+	0.837508i	−0.998516	−	0.0544633i	$-0.982655\pi$
$163$	−18.5201	+	10.6926i	−1.45061	+	0.837508i	−0.452091	+	0.891972i	$0.649322\pi$
$164$	−4.67387	−	4.67387i	−0.364968	−	0.364968i
$165$	9.78111	+	3.42984i	0.761459	+	0.267012i
$166$	−7.58841	−	4.38117i	−0.588975	−	0.340045i
$167$	0.857220	−	1.48475i	0.0663337	−	0.114893i	−0.830951	−	0.556345i	$-0.812203\pi$
$167$	0.857220	−	1.48475i	0.0663337	−	0.114893i	0.897285	+	0.441452i	$0.145536\pi$
$168$	5.73655	+	5.73655i	0.442584	+	0.442584i
$169$		0			0
$170$	1.24992	−	16.5321i	0.0958646	−	1.26795i
$171$	12.5862	−	3.37245i	0.962488	−	0.257898i
$172$	7.32587	−	1.96296i	0.558592	−	0.149674i
$173$	3.92804	−	14.6596i	0.298643	−	1.11455i	−0.639638	−	0.768677i	$-0.720916\pi$
$173$	3.92804	−	14.6596i	0.298643	−	1.11455i	0.938281	−	0.345875i	$-0.112418\pi$
$174$	0.588968	−	0.588968i	0.0446496	−	0.0446496i
$175$	4.48716	−	1.75422i	0.339197	−	0.132607i
$176$	−1.89724	−	0.508363i	−0.143010	−	0.0383193i
$177$	−14.0776			−1.05814
$178$	0.512196	+	0.137243i	0.0383907	+	0.0102868i
$179$	−1.37961	+	2.38956i	−0.103117	+	0.178604i	−0.912967	−	0.408033i	$-0.866215\pi$
$179$	−1.37961	+	2.38956i	−0.103117	+	0.178604i	0.809850	+	0.586637i	$0.199548\pi$
$180$	−1.88431	−	9.99508i	−0.140448	−	0.744990i
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$		0			0
$183$	−4.10555	+	4.10555i	−0.303491	+	0.303491i
$184$	−3.01305	−	11.2449i	−0.222125	−	0.828981i
$185$	−8.96789	+	1.69066i	−0.659333	+	0.124300i
$186$	−0.438570	+	0.253209i	−0.0321575	+	0.0185662i
$187$		−	12.0596i		−	0.881885i
$188$	3.74345	+	6.48384i	0.273019	+	0.472883i
$189$	1.22793	−	4.58270i	0.0893188	−	0.333342i
$190$	−0.471242	+	6.23287i	−0.0341875	+	0.452180i
$191$	−9.28983	−	16.0905i	−0.672189	−	1.16427i	−0.977282	−	0.211943i	$-0.932021\pi$
$191$	−9.28983	−	16.0905i	−0.672189	−	1.16427i	0.305093	−	0.952322i	$-0.401312\pi$
$192$	5.26958	+	19.6663i	0.380299	+	1.41930i
$193$	10.8872	+	6.28576i	0.783681	+	0.452459i	0.837733	−	0.546079i	$-0.183880\pi$
$193$	10.8872	+	6.28576i	0.783681	+	0.452459i	−0.0540520	+	0.998538i	$0.517214\pi$
$194$	7.68313			0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	−12.3722	−	7.14308i	−0.881481	−	0.508924i	−0.0103349	−	0.999947i	$-0.503290\pi$
$197$	−12.3722	−	7.14308i	−0.881481	−	0.508924i	−0.871147	+	0.491023i	$0.836623\pi$
$198$	2.09845	+	7.83150i	0.149130	+	0.556561i
$199$	7.36781	+	12.7614i	0.522291	+	0.904634i	0.999664	+	0.0259331i	$0.00825568\pi$
$199$	7.36781	+	12.7614i	0.522291	+	0.904634i	−0.477373	+	0.878701i	$0.658411\pi$
$200$	14.9336	+	2.27113i	1.05597	+	0.160593i
$201$	−5.26425	+	19.6465i	−0.371312	+	1.38575i
$202$	−4.98709	−	8.63790i	−0.350891	−	0.607760i
$203$		−	0.281617i		−	0.0197656i
$204$	−16.6986	+	9.64094i	−1.16914	+	0.675001i
$205$	−12.7915	−	8.73354i	−0.893400	−	0.609977i
$206$	0.944449	+	3.52473i	0.0658029	+	0.245580i
$207$	−12.9884	+	12.9884i	−0.902756	+	0.902756i
$208$		0			0
$209$			4.54668i			0.314500i
$210$	5.07122	+	3.46242i	0.349947	+	0.238930i
$211$	4.26604	−	7.38900i	0.293686	−	0.508680i	−0.680992	−	0.732291i	$-0.738451\pi$
$211$	4.26604	−	7.38900i	0.293686	−	0.508680i	0.974678	+	0.223611i	$0.0717845\pi$
$212$	2.60518	+	0.698056i	0.178925	+	0.0479427i
$213$	36.3773			2.49253
$214$	0.439070	+	0.117649i	0.0300142	+	0.00804229i
$215$	16.0171	−	7.70038i	1.09236	−	0.525161i
$216$	10.5181	−	10.5181i	0.715669	−	0.715669i
$217$	−0.0443156	+	0.165388i	−0.00300834	+	0.0112273i
$218$	8.97011	−	2.40353i	0.607532	−	0.162788i
$219$	−8.68810	+	2.32797i	−0.587087	+	0.157310i
$220$	3.53897	+	0.267567i	0.238597	+	0.0180394i
$221$		0			0
$222$	−8.22445	−	8.22445i	−0.551989	−	0.551989i
$223$	−3.53040	+	6.11483i	−0.236413	+	0.409479i	−0.959682	−	0.281087i	$-0.909305\pi$
$223$	−3.53040	+	6.11483i	−0.236413	+	0.409479i	0.723269	+	0.690566i	$0.242638\pi$
$224$	4.03432	+	2.32922i	0.269555	+	0.155627i
$225$	−8.67803	−	22.1977i	−0.578535	−	1.47985i
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$	−14.8744	+	8.58775i	−0.987249	+	0.569989i	−0.904451	−	0.426578i	$-0.859719\pi$
$227$	−14.8744	+	8.58775i	−0.987249	+	0.569989i	−0.0827985	+	0.996566i	$0.526386\pi$
$228$	6.29566	−	3.63480i	0.416940	−	0.240721i
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	0.348684	−	0.937240i	$-0.386629\pi$
$229$	−8.90647	−	8.90647i	−0.588556	−	0.588556i	−0.937240	+	0.348684i	$0.886629\pi$
$230$	−3.81788	−	7.94137i	−0.251744	−	0.523638i
$231$	3.86813	+	2.23327i	0.254504	+	0.146938i
$232$	0.441474	−	0.764655i	0.0289842	−	0.0502021i
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.986182	−	0.165666i	$-0.947023\pi$
$233$	−17.5822	−	17.5822i	−1.15185	−	1.15185i	−0.165666	−	0.986182i	$-0.552977\pi$
$234$		0			0
$235$	11.4348	+	13.3053i	0.745923	+	0.867940i
$236$	−4.65603	+	1.24758i	−0.303082	+	0.0812105i
$237$	−36.5686	+	9.79852i	−2.37538	+	0.636482i
$238$	1.84910	−	6.90095i	0.119860	−	0.447322i
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	−0.775684	−	0.631122i	$-0.782595\pi$
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	0.631122	+	0.775684i	$0.282595\pi$
$240$	3.18854	+	6.63230i	0.205819	+	0.428113i
$241$	17.4048	+	4.66361i	1.12114	+	0.300409i	0.771346	−	0.636416i	$-0.219584\pi$
$241$	17.4048	+	4.66361i	1.12114	+	0.300409i	0.349797	+	0.936825i	$0.386250\pi$
$242$	8.41971			0.541239
$243$	15.8248	+	4.24025i	1.01516	+	0.272012i
$244$	−0.994033	+	1.72172i	−0.0636364	+	0.110222i
$245$	−13.3413	+	2.51516i	−0.852346	+	0.160688i
$246$		−	19.7406i		−	1.25862i
$247$		0			0
$248$	−0.379596	+	0.379596i	−0.0241044	+	0.0241044i
$249$	6.18048	+	23.0659i	0.391672	+	1.46174i
$250$	11.4260	−	0.404792i	0.722647	−	0.0256013i
$251$	−12.1009	+	6.98644i	−0.763800	+	0.440980i	−0.830658	−	0.556782i	$-0.812036\pi$
$251$	−12.1009	+	6.98644i	−0.763800	+	0.440980i	0.0668586	+	0.997762i	$0.478702\pi$
$252$		−	4.38299i		−	0.276102i
$253$	−3.20468	−	5.55068i	−0.201477	−	0.348968i
$254$	−0.575700	+	2.14854i	−0.0361227	+	0.134812i
$255$	−34.2666	+	29.4493i	−2.14586	+	1.84419i
$256$	8.42962	+	14.6005i	0.526851	+	0.912533i
$257$	5.99887	+	22.3881i	0.374199	+	1.39653i	0.854511	+	0.519433i	$0.173857\pi$
$257$	5.99887	+	22.3881i	0.374199	+	1.39653i	−0.480312	+	0.877098i	$0.659476\pi$
$258$	19.6162	+	11.3254i	1.22125	+	0.705090i
$259$	−3.93255			−0.244357
$260$		0			0
$261$	−1.39314			−0.0862334
$262$	−0.0551288	−	0.0318286i	−0.00340587	−	0.00196638i
$263$	0.336737	+	1.25672i	0.0207641	+	0.0774926i	0.975530	−	0.219864i	$-0.0705615\pi$
$263$	0.336737	+	1.25672i	0.0207641	+	0.0774926i	−0.954766	+	0.297357i	$0.903895\pi$
$264$	7.00191	+	12.1277i	0.430938	+	0.746407i
$265$	6.30199	+	0.476468i	0.387128	+	0.0292692i
$266$	−0.697144	+	2.60178i	−0.0427446	+	0.159525i
$267$	−0.722551	−	1.25150i	−0.0442194	−	0.0765903i
$268$			6.96441i			0.425419i
$269$	6.87429	−	3.96887i	0.419133	−	0.241986i	−0.275574	−	0.961280i	$-0.588868\pi$
$269$	6.87429	−	3.96887i	0.419133	−	0.241986i	0.694706	+	0.719294i	$0.255534\pi$
$270$	6.34846	−	9.29823i	0.386355	−	0.565872i
$271$	0.231787	+	0.865041i	0.0140801	+	0.0525475i	0.972608	−	0.232450i	$-0.0746741\pi$
$271$	0.231787	+	0.865041i	0.0140801	+	0.0525475i	−0.958528	+	0.284997i	$0.908007\pi$
$272$	6.05429	−	6.05429i	0.367095	−	0.367095i
$273$		0			0
$274$			4.51738i			0.272905i
$275$	8.26535	−	0.920192i	0.498420	−	0.0554897i
$276$	−5.12391	+	8.87488i	−0.308423	+	0.534205i
$277$	−9.22930	−	2.47298i	−0.554535	−	0.148587i	−0.0293404	−	0.999569i	$-0.509341\pi$
$277$	−9.22930	−	2.47298i	−0.554535	−	0.148587i	−0.525194	+	0.850982i	$0.676007\pi$
$278$	14.0596			0.843236
$279$	0.818165	+	0.219227i	0.0489823	+	0.0131248i
$280$	6.14255	+	2.15394i	0.367087	+	0.128723i
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	−0.520651	−	0.853769i	$-0.674311\pi$
$281$	5.58408	−	5.58408i	0.333118	−	0.333118i	0.853769	+	0.520651i	$0.174311\pi$
$282$	−5.78719	+	21.5981i	−0.344622	+	1.28615i
$283$	20.3851	−	5.46218i	1.21177	−	0.324693i	0.404314	−	0.914620i	$-0.367510\pi$
$283$	20.3851	−	5.46218i	1.21177	−	0.324693i	0.807457	+	0.589927i	$0.200843\pi$
$284$	12.0315	−	3.22382i	0.713936	−	0.191298i
$285$	12.9191	−	11.1029i	0.765262	−	0.657679i
$286$		0			0
$287$	−4.71953	−	4.71953i	−0.278585	−	0.278585i
$288$	11.5225	−	19.9576i	0.678970	−	1.17601i
$289$	30.8040	+	17.7847i	1.81200	+	1.04616i
$290$	0.221144	−	0.630652i	0.0129860	−	0.0370332i
$291$	−14.8057	−	14.8057i	−0.867927	−	0.867927i
$292$	−2.66720	+	1.53991i	−0.156086	+	0.0901164i
$293$	−3.48280	+	2.01079i	−0.203467	+	0.117472i	−0.598272	−	0.801293i	$-0.704146\pi$
$293$	−3.48280	+	2.01079i	−0.203467	+	0.117472i	0.394805	+	0.918765i	$0.370812\pi$
$294$	−12.2353	−	12.2353i	−0.713579	−	0.713579i
$295$	−10.1799	+	4.89405i	−0.592694	+	0.284943i
$296$	−10.6778	−	6.16482i	−0.620633	−	0.358323i
$297$	4.09477	−	7.09234i	0.237602	−	0.411539i
$298$	−3.13271	−	3.13271i	−0.181473	−	0.181473i
$299$		0			0
$300$	−7.88183	−	10.7092i	−0.455058	−	0.618294i
$301$	7.39742	−	1.98213i	0.426380	−	0.114248i
$302$	6.63524	−	1.77791i	0.381815	−	0.102307i
$303$	−7.03525	+	26.2559i	−0.404165	+	1.50836i
$304$	−2.28257	+	2.28257i	−0.130914	+	0.130914i
$305$	−1.54154	+	4.39612i	−0.0882683	+	0.251721i
$306$	−34.1386	−	9.14740i	−1.95157	−	0.522922i
$307$	24.2191			1.38226			0.691128	−	0.722732i	$-0.257114\pi$
$307$	24.2191			1.38226			0.691128	+	0.722732i	$0.257114\pi$
$308$	1.47727	+	0.395832i	0.0841750	+	0.0225546i
$309$	4.97231	−	8.61229i	0.282865	−	0.489936i
$310$	−0.229114	+	0.335570i	−0.0130128	+	0.0190591i
$311$		−	7.87243i		−	0.446405i	−0.974772	−	0.223202i	$-0.928349\pi$
$311$		−	7.87243i		−	0.446405i	0.974772	−	0.223202i	$-0.0716511\pi$
$312$		0			0
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	−0.604740	−	0.796423i	$-0.706723\pi$
$313$	3.39121	−	3.39121i	0.191683	−	0.191683i	0.796423	+	0.604740i	$0.206723\pi$
$314$	5.40824	+	20.1838i	0.305204	+	1.13904i
$315$	−1.90272	−	10.0927i	−0.107206	−	0.568660i
$316$	−11.2264	+	6.48154i	−0.631532	+	0.364615i
$317$			22.9255i			1.28762i	0.765184	+	0.643812i	$0.222648\pi$
$317$			22.9255i			1.28762i	−0.765184	+	0.643812i	$0.777352\pi$
$318$	4.02748	+	6.97580i	0.225850	+	0.391183i
$319$	0.125816	−	0.469553i	0.00704436	−	0.0262899i
$320$	10.6476	+	12.3893i	0.595216	+	0.692581i
$321$	−0.619393	−	1.07282i	−0.0345712	−	0.0598790i
$322$	−0.982751	−	3.66768i	−0.0547666	−	0.204392i
$323$	−17.1643	−	9.90979i	−0.955044	−	0.551395i
$324$	0.551932			0.0306629
$325$		0			0
$326$	−21.8689			−1.21120
$327$	−21.9175	−	12.6541i	−1.21204	−	0.699771i
$328$	−5.41609	−	20.2131i	−0.299053	−	1.11608i
$329$	3.78001	+	6.54718i	0.208399	+	0.360958i
$330$	6.90858	+	8.03868i	0.380305	+	0.442515i
$331$	8.68470	−	32.4118i	0.477354	−	1.78151i	−0.134910	−	0.990858i	$-0.543075\pi$
$331$	8.68470	−	32.4118i	0.477354	−	1.78151i	0.612264	−	0.790653i	$-0.290259\pi$
$332$	4.08828	+	7.08110i	0.224373	+	0.388626i
$333$			19.4541i			1.06608i
$334$	1.51833	−	0.876609i	0.0830794	−	0.0479659i
$335$	3.02336	+	16.0370i	0.165184	+	0.876194i
$336$	0.820752	+	3.06309i	0.0447757	+	0.167105i
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	−0.981953	−	0.189126i	$-0.939434\pi$
$337$	−14.5544	+	14.5544i	−0.792826	+	0.792826i	0.189126	+	0.981953i	$0.439434\pi$
$338$		0			0
$339$			5.39143i			0.292822i
$340$	−8.72352	+	12.7769i	−0.473099	+	0.692923i
$341$	−0.147779	+	0.255960i	−0.00800267	+	0.0138610i
$342$	12.8708	+	3.44873i	0.695975	+	0.186486i
$343$	−12.5954			−0.680087
$344$	23.1930	+	6.21454i	1.25048	+	0.335065i
$345$	−7.94613	+	22.6606i	−0.427805	+	1.22000i
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	5.90442	−	22.0356i	0.316966	−	1.18293i	−0.605179	−	0.796089i	$-0.706899\pi$
$347$	5.90442	−	22.0356i	0.316966	−	1.18293i	0.922145	−	0.386844i	$-0.126435\pi$
$348$	−0.750759	+	0.201165i	−0.0402449	+	0.0107836i
$349$	10.0317	−	2.68798i	0.536983	−	0.143884i	0.0198718	−	0.999803i	$-0.493674\pi$
$349$	10.0317	−	2.68798i	0.536983	−	0.143884i	0.517111	+	0.855918i	$0.327008\pi$
$350$	4.87083	+	0.740762i	0.260357	+	0.0395954i
$351$		0			0
$352$	5.68599	+	5.68599i	0.303064	+	0.303064i
$353$	−2.15017	+	3.72420i	−0.114442	+	0.198219i	−0.917556	−	0.397605i	$-0.869841\pi$
$353$	−2.15017	+	3.72420i	−0.114442	+	0.198219i	0.803115	+	0.595825i	$0.203175\pi$
$354$	−12.4673	−	7.19799i	−0.662629	−	0.382569i
$355$	26.3054	−	12.6465i	1.39614	−	0.671208i
$356$	−0.349887	−	0.349887i	−0.0185440	−	0.0185440i
$357$	−16.8617	+	9.73511i	−0.892416	+	0.515237i
$358$	−2.44361	+	1.41082i	−0.129149	+	0.0745640i
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	0.376204	−	0.926537i	$-0.377229\pi$
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$360$	10.6554	−	30.3868i	0.561589	−	1.60153i
$361$	−9.98326	−	5.76384i	−0.525435	−	0.303360i
$362$	−5.29555	+	9.17216i	−0.278328	+	0.482078i
$363$	−16.2251	−	16.2251i	−0.851599	−	0.851599i
$364$		0			0
$365$	−5.47327	+	4.70382i	−0.286484	+	0.246209i
$366$	−5.73514	+	1.53673i	−0.299780	+	0.0803259i
$367$	−11.0341	+	2.95657i	−0.575973	+	0.154331i	−0.535034	−	0.844830i	$-0.679701\pi$
$367$	−11.0341	+	2.95657i	−0.575973	+	0.154331i	−0.0409383	+	0.999162i	$0.513035\pi$
$368$	1.17776	−	4.39546i	0.0613950	−	0.229129i
$369$	−23.3472	+	23.3472i	−1.21541	+	1.21541i
$370$	−8.80653	−	3.08809i	−0.457830	−	0.160542i
$371$	2.63063	+	0.704874i	0.136575	+	0.0365953i
$372$	0.472562			0.0245012
$373$	−27.1975	−	7.28755i	−1.40823	−	0.377335i	−0.526939	−	0.849903i	$-0.676661\pi$
$373$	−27.1975	−	7.28755i	−1.40823	−	0.377335i	−0.881294	+	0.472568i	$0.843327\pi$
$374$	6.16618	−	10.6801i	0.318846	−	0.552257i
$375$	−22.7985	−	21.2384i	−1.17731	−	1.09675i
$376$			23.7028i			1.22238i
$377$		0			0
$378$	3.43065	−	3.43065i	0.176453	−	0.176453i
$379$	−4.38232	−	16.3551i	−0.225105	−	0.840103i	−0.982362	−	0.186987i	$-0.940128\pi$
$379$	−4.38232	−	16.3551i	−0.225105	−	0.840103i	0.757258	−	0.653116i	$-0.226539\pi$
$380$	3.28892	−	4.81710i	0.168718	−	0.247112i
$381$	5.24973	−	3.03093i	0.268952	−	0.155279i
$382$		−	18.9999i		−	0.972119i
$383$	−3.30197	−	5.71918i	−0.168723	−	0.292236i	0.769248	−	0.638950i	$-0.220631\pi$
$383$	−3.30197	−	5.71918i	−0.168723	−	0.292236i	−0.937971	+	0.346714i	$0.887298\pi$
$384$	1.58553	−	5.91729i	0.0809114	−	0.301966i
$385$	3.57354	+	0.270181i	0.182124	+	0.0137697i
$386$	6.42793	+	11.1335i	0.327173	+	0.566680i
$387$	−9.80550	−	36.5946i	−0.498441	−	1.86021i
$388$	−6.20897	−	3.58475i	−0.315212	−	0.181988i
$389$	33.6949			1.70840			0.854199	−	0.519946i	$-0.174048\pi$
$389$	33.6949			1.70840			0.854199	+	0.519946i	$0.174048\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	−15.8851	−	9.17126i	−0.802318	−	0.463218i
$393$	0.0449004	+	0.167570i	0.00226492	+	0.00845281i
$394$	−7.30464	−	12.6520i	−0.368003	−	0.637399i
$395$	−23.0372	+	19.7986i	−1.15913	+	0.996175i
$396$	1.95816	−	7.30795i	0.0984012	−	0.367238i
$397$	−2.91045	−	5.04104i	−0.146071	−	0.253002i	0.783701	−	0.621138i	$-0.213329\pi$
$397$	−2.91045	−	5.04104i	−0.146071	−	0.253002i	−0.929772	+	0.368136i	$0.879996\pi$
$398$			15.0689i			0.755337i
$399$	6.35716	−	3.67031i	0.318256	−	0.183745i
$400$	4.61142	+	3.68750i	0.230571	+	0.184375i
$401$	−0.0683280	−	0.255004i	−0.00341214	−	0.0127343i	0.964199	−	0.265181i	$-0.0854316\pi$
$401$	−0.0683280	−	0.255004i	−0.00341214	−	0.0127343i	−0.967611	+	0.252446i	$0.918765\pi$
$402$	−14.7075	+	14.7075i	−0.733544	+	0.733544i
$403$		0			0
$404$			9.30738i			0.463060i
$405$	1.27094	−	0.239602i	0.0631533	−	0.0119059i
$406$	0.143993	−	0.249404i	0.00714627	−	0.0123777i
$407$	−6.55691	−	1.75692i	−0.325014	−	0.0870872i
$408$	−61.0446			−3.02216
$409$	35.8975	+	9.61872i	1.77502	+	0.475615i	0.989661	−	0.143427i	$-0.0458121\pi$
$409$	35.8975	+	9.61872i	1.77502	+	0.475615i	0.785358	+	0.619042i	$0.212479\pi$
$410$	−6.86281	−	14.2750i	−0.338930	−	0.704990i
$411$	8.70518	−	8.70518i	0.429395	−	0.429395i
$412$	0.881310	−	3.28909i	0.0434190	−	0.162042i
$413$	−4.70151	+	1.25977i	−0.231346	+	0.0619890i
$414$	−18.1438	+	4.86161i	−0.891718	+	0.238935i
$415$	12.4881	+	14.5309i	0.613016	+	0.713293i
$416$		0			0
$417$	−27.0934	−	27.0934i	−1.32677	−	1.32677i
$418$	−2.32476	+	4.02660i	−0.113708	+	0.196947i
$419$	−29.3721	−	16.9580i	−1.43492	−	0.828451i	−0.437428	−	0.899253i	$-0.644111\pi$
$419$	−29.3721	−	16.9580i	−1.43492	−	0.828451i	−0.997490	+	0.0708027i	$0.977444\pi$
$420$	−2.48272	−	5.16418i	−0.121145	−	0.251986i
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$	7.55613	−	4.36253i	0.367826	−	0.212365i
$423$	32.3885	−	18.6995i	1.57478	−	0.909201i
$424$	6.03777	+	6.03777i	0.293220	+	0.293220i
$425$	−14.5411	+	33.2083i	−0.705345	+	1.61084i
$426$	32.2162	+	18.6000i	1.56088	+	0.901175i
$427$	−1.00374	+	1.73853i	−0.0485745	+	0.0841335i
$428$	−0.299934	−	0.299934i	−0.0144979	−	0.0144979i
$429$		0			0
$430$	18.1223	+	1.37015i	0.873933	+	0.0660745i
$431$	−4.44167	+	1.19014i	−0.213948	+	0.0573271i	−0.364201	−	0.931320i	$-0.618658\pi$
$431$	−4.44167	+	1.19014i	−0.213948	+	0.0573271i	0.150253	+	0.988648i	$0.451991\pi$
$432$	5.61627	−	1.50488i	0.270213	−	0.0724033i
$433$	1.03596	−	3.86627i	0.0497853	−	0.185801i	−0.936555	−	0.350520i	$-0.886005\pi$
$433$	1.03596	−	3.86627i	0.0497853	−	0.185801i	0.986341	+	0.164719i	$0.0526716\pi$
$434$	−0.123811	+	0.123811i	−0.00594311	+	0.00594311i
$435$	−1.64145	+	0.789140i	−0.0787013	+	0.0378364i
$436$	−8.37043	−	2.24285i	−0.400871	−	0.107413i
$437$	−10.5336			−0.503890
$438$	−8.88461	−	2.38062i	−0.424523	−	0.113751i
$439$	11.3618	−	19.6793i	0.542271	−	0.939242i	−0.456502	−	0.889723i	$-0.650898\pi$
$439$	11.3618	−	19.6793i	0.542271	−	0.939242i	0.998773	−	0.0495192i	$-0.0157689\pi$
$440$	9.27944	+	6.33562i	0.442380	+	0.302039i
$441$			28.9414i			1.37816i
$442$		0			0
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	−0.661824	−	0.749660i	$-0.730217\pi$
$443$	1.84874	−	1.84874i	0.0878361	−	0.0878361i	0.749660	+	0.661824i	$0.230217\pi$
$444$	2.80911	+	10.4837i	0.133314	+	0.497536i
$445$	−0.957576	−	0.653794i	−0.0453935	−	0.0309928i
$446$	−6.25313	+	3.61025i	−0.296094	+	0.170950i
$447$			12.0737i			0.571067i
$448$	3.51978	+	6.09644i	0.166294	+	0.288030i
$449$	−8.32705	+	31.0770i	−0.392978	+	1.46661i	0.432219	+	0.901769i	$0.357731\pi$
$449$	−8.32705	+	31.0770i	−0.392978	+	1.46661i	−0.825197	+	0.564845i	$0.808936\pi$
$450$	3.66451	−	24.0957i	0.172746	−	1.13588i
$451$	−5.76056	−	9.97759i	−0.271254	−	0.469826i
$452$	0.477798	+	1.78317i	0.0224737	+	0.0838731i
$453$	−16.2125	−	9.36029i	−0.761729	−	0.439785i
$454$	−17.5640			−0.824318
$455$		0			0
$456$	23.0149			1.07777
$457$	24.5669	+	14.1837i	1.14919	+	0.663486i	0.948690	−	0.316208i	$-0.102410\pi$
$457$	24.5669	+	14.1837i	1.14919	+	0.663486i	0.200501	+	0.979693i	$0.435743\pi$
$458$	−3.33373	−	12.4416i	−0.155775	−	0.581360i
$459$	17.8496	+	30.9165i	0.833149	+	1.44306i
$460$	−0.619891	+	8.19898i	−0.0289026	+	0.382279i
$461$	2.97890	−	11.1174i	0.138741	−	0.517790i	−0.861213	−	0.508244i	$-0.830295\pi$
$461$	2.97890	−	11.1174i	0.138741	−	0.517790i	0.999954	−	0.00954570i	$-0.00303854\pi$
$462$	2.28378	+	3.95562i	0.106251	+	0.184032i
$463$		−	29.9456i		−	1.39169i	−0.718192	−	0.695845i	$-0.755030\pi$
$463$		−	29.9456i		−	1.39169i	0.718192	−	0.695845i	$-0.244970\pi$
$464$	0.298893	−	0.172566i	0.0138758	−	0.00801118i
$465$	1.08817	−	0.205146i	0.0504626	−	0.00951342i
$466$	−6.58109	−	24.5609i	−0.304863	−	1.13776i
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	−0.227274	−	0.973831i	$-0.572981\pi$
$467$	16.1332	−	16.1332i	0.746557	−	0.746557i	0.973831	+	0.227274i	$0.0729812\pi$
$468$		0			0
$469$			7.03244i			0.324728i
$470$	3.32368	+	17.6300i	0.153310	+	0.813213i
$471$	28.4732	−	49.3170i	1.31197	−	2.27241i
$472$	−14.7405	−	3.94971i	−0.678488	−	0.181800i
$473$	13.2196			0.607837
$474$	−37.3957	−	10.0201i	−1.71764	−	0.460240i
$475$	5.48223	−	12.5201i	0.251542	−	0.574462i
$476$	−4.71411	+	4.71411i	−0.216071	+	0.216071i
$477$	3.48697	−	13.0136i	0.159657	−	0.595850i
$478$	−3.12195	+	0.836524i	−0.142795	+	0.0382617i
$479$	37.5043	−	10.0493i	1.71362	−	0.459162i	0.737309	−	0.675555i	$-0.236096\pi$
$479$	37.5043	−	10.0493i	1.71362	−	0.459162i	0.976306	+	0.216393i	$0.0694293\pi$
$480$	2.27132	−	30.0415i	0.103671	−	1.37120i
$481$		0			0
$482$	13.0294	+	13.0294i	0.593473	+	0.593473i
$483$	−5.17396	+	8.96157i	−0.235424	+	0.407765i
$484$	−6.80421	−	3.92841i	−0.309282	−	0.178564i
$485$	−15.8536	−	5.55920i	−0.719874	−	0.252430i
$486$	11.8466	+	11.8466i	0.537372	+	0.537372i
$487$	25.0660	−	14.4718i	1.13585	−	0.655782i	0.190448	−	0.981697i	$-0.439006\pi$
$487$	25.0660	−	14.4718i	1.13585	−	0.655782i	0.945399	+	0.325916i	$0.105673\pi$
$488$	−5.45078	+	3.14701i	−0.246745	+	0.142458i
$489$	42.1422	+	42.1422i	1.90574	+	1.90574i
$490$	−13.1013	−	4.59408i	−0.591855	−	0.207539i
$491$	−6.30003	−	3.63733i	−0.284317	−	0.164150i	0.351059	−	0.936353i	$-0.385822\pi$
$491$	−6.30003	−	3.63733i	−0.284317	−	0.164150i	−0.635376	+	0.772203i	$0.719155\pi$
$492$	−9.21046	+	15.9530i	−0.415240	+	0.719216i
$493$	1.49839	+	1.49839i	0.0674842	+	0.0674842i
$494$		0			0
$495$	1.33657	−	17.6781i	0.0600743	−	0.794571i
$496$	−0.202689	+	0.0543104i	−0.00910102	+	0.00243861i
$497$	12.1490	−	3.25531i	0.544956	−	0.146021i
$498$	−6.32027	+	23.5876i	−0.283218	+	1.05698i
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	−0.605754	−	0.795652i	$-0.707128\pi$
$499$	4.24201	−	4.24201i	0.189899	−	0.189899i	0.795652	+	0.605754i	$0.207128\pi$
$500$	−9.42259	−	5.00397i	−0.421391	−	0.223784i
$501$	−4.61515	−	1.23663i	−0.206190	−	0.0552483i
$502$	−14.2889			−0.637745
$503$	−3.50677	−	0.939636i	−0.156359	−	0.0418963i	0.179790	−	0.983705i	$-0.442458\pi$
$503$	−3.50677	−	0.939636i	−0.156359	−	0.0418963i	−0.336149	+	0.941809i	$0.609125\pi$
$504$	6.93805	−	12.0171i	0.309046	−	0.535283i
$505$	4.04047	+	21.4321i	0.179799	+	0.953717i
$506$		−	6.55433i		−	0.291376i
$507$		0			0
$508$	1.46769	−	1.46769i	0.0651184	−	0.0651184i
$509$	6.02986	+	22.5037i	0.267269	+	0.997460i	0.960847	+	0.277079i	$0.0893664\pi$
$509$	6.02986	+	22.5037i	0.267269	+	0.997460i	−0.693578	+	0.720381i	$0.743967\pi$
$510$	−45.4047	+	8.55987i	−2.01055	+	0.379038i
$511$	−2.69325	+	1.55495i	−0.119143	+	0.0687870i
$512$			12.8442i			0.567640i
$513$	−6.72962	−	11.6560i	−0.297120	−	0.514627i
$514$	−6.13455	+	22.8945i	−0.270584	+	1.00983i
$515$	0.601550	−	7.95639i	0.0265075	−	0.350600i
$516$	−10.5683	−	18.3048i	−0.465243	−	0.805824i
$517$	3.37754	+	12.6052i	0.148544	+	0.554375i
$518$	−3.48272	−	2.01075i	−0.153022	−	0.0883472i
$519$	−42.2960			−1.85659
$520$		0			0
$521$	−13.0530			−0.571862			−0.285931	−	0.958250i	$-0.592303\pi$
$521$	−13.0530			−0.571862			−0.285931	+	0.958250i	$0.592303\pi$
$522$	−1.23379	−	0.712327i	−0.0540013	−	0.0311777i
$523$	4.40520	+	16.4404i	0.192626	+	0.718890i	0.992869	+	0.119214i	$0.0380374\pi$
$523$	4.40520	+	16.4404i	0.192626	+	0.718890i	−0.800243	+	0.599677i	$0.795296\pi$
$524$	0.0297008	+	0.0514432i	0.00129748	+	0.00224731i
$525$	−7.95882	−	10.8138i	−0.347351	−	0.471952i
$526$	−0.344353	+	1.28514i	−0.0150145	+	0.0560349i
$527$	−0.644187	−	1.11577i	−0.0280612	−	0.0486035i
$528$			5.47391i			0.238221i
$529$	−7.05896	+	4.07549i	−0.306911	+	0.177195i
$530$	5.33750	+	3.64423i	0.231846	+	0.158295i
$531$	6.23198	+	23.2581i	0.270445	+	1.00931i
$532$	1.77730	−	1.77730i	0.0770558	−	0.0770558i
$533$		0			0
$534$		−	1.47779i		−	0.0639501i
$535$	−0.820864	−	0.560453i	−0.0354891	−	0.0242305i
$536$	−11.0243	+	19.0947i	−0.476178	+	0.824765i
$537$	7.42764	+	1.99023i	0.320526	+	0.0858847i
$538$	8.11728			0.349961
$539$	−9.75457	−	2.61373i	−0.420159	−	0.112581i
$540$	−9.46868	+	4.55215i	−0.407467	+	0.195893i
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	−0.237029	+	0.884606i	−0.0101813	+	0.0379971i
$543$	27.8799	−	7.47039i	1.19644	−	0.320585i
$544$	−33.8583	+	9.07231i	−1.45166	+	0.388972i
$545$	−20.2483	−	1.53089i	−0.867340	−	0.0655761i
$546$		0			0
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	0.118756	−	0.992923i	$-0.462109\pi$
$547$	−20.4450	−	20.4450i	−0.874167	−	0.874167i	−0.992923	+	0.118756i	$0.962109\pi$
$548$	2.10769	−	3.65063i	0.0900361	−	0.155947i
$549$	8.60042	+	4.96545i	0.367057	+	0.211920i
$550$	7.79041	+	3.41121i	0.332184	+	0.145455i
$551$	−0.564920	−	0.564920i	−0.0240664	−	0.0240664i
$552$	−28.0970	+	16.2218i	−1.19589	+	0.690446i
$553$	−11.3360	+	6.54485i	−0.482056	+	0.278315i
$554$	−6.90913	−	6.90913i	−0.293541	−	0.293541i
$555$	11.0197	+	22.9214i	0.467759	+	0.972961i
$556$	−11.3619	−	6.55982i	−0.481854	−	0.278198i
$557$	6.79015	−	11.7609i	0.287708	−	0.498324i	−0.685555	−	0.728021i	$-0.740440\pi$
$557$	6.79015	−	11.7609i	0.287708	−	0.498324i	0.973262	+	0.229697i	$0.0737735\pi$
$558$	0.612485	+	0.612485i	0.0259286	+	0.0259286i
$559$		0			0
$560$	1.65839	+	1.92967i	0.0700797	+	0.0815432i
$561$	−32.4636	+	8.69858i	−1.37061	+	0.367254i
$562$	7.80052	−	2.09014i	0.329045	−	0.0881673i
$563$	−1.25538	+	4.68514i	−0.0529080	+	0.197455i	−0.987321	−	0.158736i	$-0.949258\pi$
$563$	−1.25538	+	4.68514i	−0.0529080	+	0.197455i	0.934413	+	0.356191i	$0.115925\pi$
$564$	14.7539	−	14.7539i	0.621251	−	0.621251i
$565$	1.87433	+	3.89868i	0.0788535	+	0.164019i
$566$	20.8462	+	5.58573i	0.876232	+	0.234786i
$567$	0.557323			0.0234054
$568$	38.0904	+	10.2063i	1.59824	+	0.428247i
$569$	0.124396	−	0.215461i	0.00521497	−	0.00903259i	−0.863406	−	0.504509i	$-0.831673\pi$
$569$	0.124396	−	0.215461i	0.00521497	−	0.00903259i	0.868621	+	0.495477i	$0.165007\pi$
$570$	17.1183	−	3.22722i	0.717009	−	0.135173i
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$		0			0
$573$	−36.6136	+	36.6136i	−1.52955	+	1.52955i
$574$	−1.76654	−	6.59281i	−0.0737339	−	0.275179i
$575$	2.13187	+	19.1489i	0.0889052	+	0.798565i
$576$	30.1587	−	17.4121i	1.25661	−	0.725506i
$577$		−	12.1339i		−	0.505141i	−0.967578	−	0.252570i	$-0.918724\pi$
$577$		−	12.1339i		−	0.505141i	0.967578	−	0.252570i	$-0.0812760\pi$
$578$	18.1869	+	31.5007i	0.756477	+	1.31026i
$579$	9.06783	−	33.8416i	0.376846	−	1.40641i
$580$	−0.472958	+	0.406469i	−0.0196385	+	0.0168777i
$581$	4.12821	+	7.15027i	0.171267	+	0.296643i
$582$	−5.54184	−	20.6824i	−0.229717	−	0.857315i
$583$	4.07125	+	2.35054i	0.168614	+	0.0973492i
$584$	−9.75040			−0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	31.6354	+	18.2647i	1.30573	+	0.753865i	0.981381	−	0.192072i	$-0.0615207\pi$
$587$	31.6354	+	18.2647i	1.30573	+	0.753865i	0.324351	+	0.945937i	$0.394854\pi$
$588$	4.17904	+	15.5964i	0.172341	+	0.643185i
$589$	0.242870	+	0.420663i	0.0100073	+	0.0173331i
$590$	−11.5178	−	0.870813i	−0.474180	−	0.0358508i
$591$	−10.3046	+	38.4573i	−0.423875	+	1.58192i
$592$	−2.40974	−	4.17380i	−0.0990398	−	0.171542i
$593$			16.6936i			0.685525i	0.939422	+	0.342762i	$0.111363\pi$
$593$			16.6936i			0.685525i	−0.939422	+	0.342762i	$0.888637\pi$
$594$	7.25276	−	4.18738i	0.297584	−	0.171810i
$595$	−8.80873	+	12.9017i	−0.361123	+	0.528917i
$596$	1.06999	+	3.99327i	0.0438287	+	0.163571i
$597$	29.0384	−	29.0384i	1.18846	−	1.18846i
$598$		0			0
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$	−4.65793	−	41.8384i	−0.190159	−	1.70805i
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	−0.876958	−	0.480566i	$-0.840431\pi$
$601$	−0.546605	+	0.946748i	−0.0222965	+	0.0386187i	0.854662	+	0.519185i	$0.173764\pi$
$602$	7.56474	+	2.02696i	0.308316	+	0.0826129i
$603$	34.7891			1.41672
$604$	−6.19166	−	1.65905i	−0.251935	−	0.0675058i
$605$	−17.3735	−	6.09216i	−0.706332	−	0.247682i
$606$	−19.6554	+	19.6554i	−0.798446	+	0.798446i
$607$	−10.8348	+	40.4361i	−0.439771	+	1.64125i	0.289612	+	0.957144i	$0.406474\pi$
$607$	−10.8348	+	40.4361i	−0.439771	+	1.64125i	−0.729384	+	0.684105i	$0.760193\pi$
$608$	12.7652	−	3.42042i	0.517696	−	0.138716i
$609$	−0.758093	+	0.203130i	−0.0307195	+	0.00823126i
$610$	−3.61298	+	3.10506i	−0.146285	+	0.125720i
$611$		0			0
$612$	23.3204	+	23.3204i	0.942673	+	0.942673i
$613$	−13.9548	+	24.1705i	−0.563630	+	0.976235i	0.433546	+	0.901131i	$0.357262\pi$
$613$	−13.9548	+	24.1705i	−0.563630	+	0.976235i	−0.997176	+	0.0751039i	$0.976071\pi$
$614$	21.4487	+	12.3834i	0.865601	+	0.499755i
$615$	−14.2835	+	40.7334i	−0.575967	+	1.64253i
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$	3.79548	−	2.19132i	0.152800	−	0.0882193i	−0.421650	−	0.906758i	$-0.638549\pi$
$617$	3.79548	−	2.19132i	0.152800	−	0.0882193i	0.574451	+	0.818539i	$0.305216\pi$
$618$	8.80708	−	5.08477i	0.354273	−	0.204540i
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	0.859582	−	0.510998i	$-0.170724\pi$
$619$	8.67268	+	8.67268i	0.348584	+	0.348584i	−0.510998	+	0.859582i	$0.670724\pi$
$620$	0.341722	−	0.164286i	0.0137239	−	0.00659787i
$621$	16.4313	+	9.48662i	0.659366	+	0.380685i
$622$	4.02525	−	6.97193i	0.161398	−	0.279549i
$623$	−0.353304	−	0.353304i	−0.0141548	−	0.0141548i
$624$		0			0
$625$	−23.8697	−	7.43216i	−0.954788	−	0.297287i
$626$	4.73726	−	1.26934i	0.189339	−	0.0507332i
$627$	12.2393	−	3.27952i	0.488791	−	0.130971i
$628$	5.04668	−	18.8345i	0.201385	−	0.751577i
$629$	20.9238	−	20.9238i	0.834287	−	0.834287i
$630$	3.47542	−	9.91112i	0.138464	−	0.394868i
$631$	24.4748	+	6.55800i	0.974326	+	0.261070i	0.710653	−	0.703542i	$-0.248399\pi$
$631$	24.4748	+	6.55800i	0.974326	+	0.261070i	0.263673	+	0.964612i	$0.415066\pi$
$632$	−41.0398			−1.63248
$633$	−22.9677	−	6.15419i	−0.912886	−	0.244607i
$634$	−11.7220	+	20.3031i	−0.465540	+	0.806340i
$635$	2.74251	−	4.01681i	0.108833	−	0.159402i
$636$		−	7.51646i		−	0.298047i
$637$		0			0
$638$	0.351511	−	0.351511i	0.0139164	−	0.0139164i
$639$	−16.1038	−	60.1003i	−0.637057	−	2.37753i
$640$	−0.910600	−	4.83016i	−0.0359946	−	0.190929i
$641$	1.41675	−	0.817961i	0.0559582	−	0.0323075i	−0.471760	−	0.881727i	$-0.656381\pi$
$641$	1.41675	−	0.817961i	0.0559582	−	0.0323075i	0.527718	+	0.849420i	$0.323048\pi$
$642$		−	1.26681i		−	0.0499968i
$643$	19.8344	+	34.3541i	0.782191	+	1.35479i	0.930663	+	0.365878i	$0.119231\pi$
$643$	19.8344	+	34.3541i	0.782191	+	1.35479i	−0.148472	+	0.988917i	$0.547435\pi$
$644$	−0.917051	+	3.42248i	−0.0361369	+	0.134865i
$645$	−32.2820	−	37.5627i	−1.27110	−	1.47903i
$646$	−10.1339	−	17.5525i	−0.398714	−	0.690593i
$647$	3.84742	+	14.3588i	0.151258	+	0.564501i	0.999397	+	0.0347277i	$0.0110564\pi$
$647$	3.84742	+	14.3588i	0.151258	+	0.564501i	−0.848139	+	0.529773i	$0.822277\pi$
$648$	1.51326	+	0.873682i	0.0594465	+	0.0343215i
$649$	−8.40185			−0.329801
$650$		0			0
$651$	0.477178			0.0187021
$652$	17.6729	+	10.2034i	0.692123	+	0.399597i
$653$	3.32718	+	12.4172i	0.130203	+	0.485922i	0.999972	−	0.00753655i	$-0.00239898\pi$
$653$	3.32718	+	12.4172i	0.130203	+	0.485922i	−0.869769	+	0.493459i	$0.835732\pi$
$654$	−12.9403	−	22.4132i	−0.506005	−	0.876426i
$655$	0.0907243	+	0.105565i	0.00354489	+	0.00412476i
$656$	2.11708	−	7.90103i	0.0826579	−	0.308483i
$657$	7.69225	+	13.3234i	0.300103	+	0.519794i
$658$			7.73102i			0.301387i
$659$	−20.8742	+	12.0517i	−0.813144	+	0.469469i	−0.848047	−	0.529922i	$-0.822221\pi$
$659$	−20.8742	+	12.0517i	−0.813144	+	0.469469i	0.0349025	+	0.999391i	$0.488888\pi$
$660$	−1.83239	−	9.71965i	−0.0713256	−	0.378337i
$661$	−10.1325	−	37.8150i	−0.394108	−	1.47083i	−0.823293	−	0.567616i	$-0.807866\pi$
$661$	−10.1325	−	37.8150i	−0.394108	−	1.47083i	0.429185	−	0.903217i	$-0.358801\pi$
$662$	24.2637	−	24.2637i	0.943036	−	0.943036i
$663$		0			0
$664$			25.8862i			1.00458i
$665$	3.32104	−	4.86415i	0.128785	−	0.188624i
$666$	−9.94705	+	17.2288i	−0.385440	+	0.667602i
$667$	1.08784	+	0.291487i	0.0421215	+	0.0112864i
$668$	−1.63601			−0.0632991
$669$	19.0071	+	5.09295i	0.734858	+	0.196905i
$670$	−5.52232	+	15.7484i	−0.213346	+	0.608415i
$671$	−2.45030	+	2.45030i	−0.0945926	+	0.0945926i
$672$	3.36013	−	12.5402i	0.129620	−	0.483747i
$673$	9.87723	−	2.64660i	0.380739	−	0.102019i	−0.0633730	−	0.997990i	$-0.520186\pi$
$673$	9.87723	−	2.64660i	0.380739	−	0.102019i	0.444112	+	0.895971i	$0.353519\pi$
$674$	−20.3313	+	5.44776i	−0.783132	+	0.209840i
$675$	−19.8274	+	14.5927i	−0.763157	+	0.561675i
$676$		0			0
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.986771	+	0.162121i	$0.0518333\pi$
$677$	29.8933	+	29.8933i	1.14889	+	1.14889i	0.162121	+	0.986771i	$0.448167\pi$
$678$	−2.75669	+	4.77472i	−0.105870	+	0.183372i
$679$	−6.26961	−	3.61976i	−0.240606	−	0.138914i
$680$	−44.1429	+	21.2221i	−1.69280	+	0.813829i
$681$	33.8465	+	33.8465i	1.29700	+	1.29700i
$682$	−0.261750	+	0.151121i	−0.0100229	+	0.00578673i
$683$	−17.3384	+	10.0103i	−0.663436	+	0.383035i	−0.793585	−	0.608459i	$-0.791788\pi$
$683$	−17.3384	+	10.0103i	−0.663436	+	0.383035i	0.130149	+	0.991494i	$0.458455\pi$
$684$	−8.79221	−	8.79221i	−0.336178	−	0.336178i
$685$	3.26859	−	9.32129i	0.124886	−	0.356148i
$686$	−11.1546	−	6.44013i	−0.425886	−	0.245885i
$687$	−17.5513	+	30.3998i	−0.669625	+	1.15983i
$688$	6.63664	+	6.63664i	0.253019	+	0.253019i
$689$		0			0
$690$	−18.6238	+	16.0056i	−0.708994	+	0.609322i
$691$	34.1813	−	9.15886i	1.30032	−	0.348420i	0.458749	−	0.888566i	$-0.348298\pi$
$691$	34.1813	−	9.15886i	1.30032	−	0.348420i	0.841571	+	0.540147i	$0.181631\pi$
$692$	−13.9890	+	3.74834i	−0.531782	+	0.142491i
$693$	1.97729	−	7.37933i	0.0751109	−	0.280318i
$694$	16.4960	−	16.4960i	0.626181	−	0.626181i
$695$	−29.0109	−	10.1729i	−1.10045	−	0.385881i
$696$	−2.37683	−	0.636870i	−0.0900935	−	0.0241405i
$697$	50.2221			1.90230
$698$	10.2586	+	2.74877i	0.388292	+	0.104043i
$699$	−34.6479	+	60.0120i	−1.31051	+	2.26986i
$700$	−3.59064	−	2.87123i	−0.135714	−	0.108522i
$701$			37.1781i			1.40420i	0.712080	+	0.702098i	$0.247753\pi$
$701$			37.1781i			1.40420i	−0.712080	+	0.702098i	$0.752247\pi$
$702$		0			0
$703$	−7.88864	+	7.88864i	−0.297526	+	0.297526i
$704$	3.14502	+	11.7374i	0.118532	+	0.442368i
$705$	27.5689	−	40.3787i	1.03831	−	1.52075i
$706$	−3.80843	+	2.19880i	−0.143332	+	0.0827529i
$707$			9.39830i			0.353459i
$708$	6.71678	+	11.6338i	0.252432	+	0.437225i
$709$	12.4732	−	46.5506i	0.468440	−	1.74824i	−0.176783	−	0.984250i	$-0.556569\pi$
$709$	12.4732	−	46.5506i	0.468440	−	1.74824i	0.645224	−	0.763994i	$-0.276764\pi$
$710$	29.7626	+	2.25023i	1.11697	+	0.0844497i
$711$	32.3770	+	56.0786i	1.21423	+	2.10311i
$712$	−0.405449	−	1.51316i	−0.0151948	−	0.0567079i
$713$	−0.593001	−	0.342369i	−0.0222080	−	0.0128218i
$714$	−19.9106			−0.745135
$715$		0			0
$716$	2.63300			0.0983998
$717$	7.62814	+	4.40411i	0.284878	+	0.164474i
$718$	−3.90299	−	14.5662i	−0.145658	−	0.543604i
$719$	−16.6992	−	28.9239i	−0.622777	−	1.07868i	−0.988966	−	0.148141i	$-0.952671\pi$
$719$	−16.6992	−	28.9239i	−0.622777	−	1.07868i	0.366190	−	0.930540i	$-0.380662\pi$
$720$	9.54594	−	8.20394i	0.355756	−	0.305743i
$721$	0.889918	−	3.32122i	0.0331423	−	0.123689i
$722$	−5.89421	−	10.2091i	−0.219360	−	0.379942i
$723$		−	50.2164i		−	1.86757i
$724$	8.55897	−	4.94153i	0.318092	−	0.183650i
$725$	−0.912629	+	1.14129i	−0.0338942	+	0.0423866i
$726$	−6.07313	−	22.6652i	−0.225395	−	0.841186i
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	−0.116149	−	0.993232i	$-0.537055\pi$
$727$	23.6487	−	23.6487i	0.877083	−	0.877083i	0.993232	+	0.116149i	$0.0370549\pi$
$728$		0			0
$729$		−	43.9226i		−	1.62676i
$730$	−7.25231	+	1.36723i	−0.268420	+	0.0506036i
$731$	−28.8130	+	49.9055i	−1.06569	+	1.84582i
$732$	5.35173	+	1.43399i	0.197806	+	0.0530018i
$733$	−14.7049			−0.543138			−0.271569	−	0.962419i	$-0.587542\pi$
$733$	−14.7049			−0.543138			−0.271569	+	0.962419i	$0.587542\pi$
$734$	−11.2836	−	3.02344i	−0.416486	−	0.111597i
$735$	16.3937	+	34.0997i	0.604692	+	1.25779i
$736$	−13.1731	+	13.1731i	−0.485568	+	0.485568i
$737$	−3.14184	+	11.7255i	−0.115731	+	0.431914i
$738$	−32.6142	+	8.73896i	−1.20055	+	0.321686i
$739$	19.8706	−	5.32432i	0.730953	−	0.195858i	0.125900	−	0.992043i	$-0.459818\pi$
$739$	19.8706	−	5.32432i	0.730953	−	0.195858i	0.605054	+	0.796185i	$0.293152\pi$
$740$	5.67600	+	6.60447i	0.208654	+	0.242785i
$741$		0			0
$742$	1.96931	+	1.96931i	0.0722956	+	0.0722956i
$743$	22.3204	−	38.6601i	0.818856	−	1.41830i	−0.0876692	−	0.996150i	$-0.527942\pi$
$743$	22.3204	−	38.6601i	0.818856	−	1.41830i	0.906526	−	0.422151i	$-0.138725\pi$
$744$	1.29565	+	0.748042i	0.0475007	+	0.0274246i
$745$	4.19742	+	8.73082i	0.153781	+	0.319872i
$746$	−20.3603	−	20.3603i	−0.745443	−	0.745443i
$747$	35.3720	−	20.4220i	1.29419	−	0.747202i
$748$	−9.96614	+	5.75395i	−0.364398	+	0.210385i
$749$	−0.302864	−	0.302864i	−0.0110664	−	0.0110664i
$750$	−9.33127	−	30.4661i	−0.340730	−	1.11246i
$751$	−15.2247	−	8.78996i	−0.555555	−	0.320750i	0.195804	−	0.980643i	$-0.437268\pi$
$751$	−15.2247	−	8.78996i	−0.555555	−	0.320750i	−0.751360	+	0.659893i	$0.770602\pi$
$752$	−4.63255	+	8.02381i	−0.168932	+	0.292598i
$753$	27.5353	+	27.5353i	1.00344	+	1.00344i
$754$		0			0
$755$	−14.9778	−	1.13241i	−0.545097	−	0.0412125i
$756$	−4.37306	+	1.17176i	−0.159047	+	0.0426164i
$757$	33.9933	−	9.10848i	1.23551	−	0.331053i	0.418786	−	0.908085i	$-0.362456\pi$
$757$	33.9933	−	9.10848i	1.23551	−	0.331053i	0.816722	+	0.577032i	$0.195789\pi$
$758$	4.48144	−	16.7250i	0.162773	−	0.607478i
$759$	−12.6305	+	12.6305i	−0.458457	+	0.458457i
$760$	16.6426	−	8.00109i	0.603692	−	0.290230i
$761$	11.3127	+	3.03122i	0.410084	+	0.109882i	0.457962	−	0.888972i	$-0.348579\pi$
$761$	11.3127	+	3.03122i	0.410084	+	0.109882i	−0.0478787	+	0.998853i	$0.515246\pi$
$762$	6.19897			0.224565
$763$	−8.45219	−	2.26476i	−0.305990	−	0.0819897i
$764$	−8.86485	+	15.3544i	−0.320719	+	0.555502i
$765$	63.8238	+	43.5763i	2.30755	+	1.57550i
$766$		−	6.75331i		−	0.244007i
$767$		0			0
$768$	33.2233	−	33.2233i	1.19884	−	1.19884i
$769$	−4.90954	−	18.3227i	−0.177043	−	0.660732i	−0.996195	−	0.0871555i	$-0.972222\pi$
$769$	−4.90954	−	18.3227i	−0.177043	−	0.660732i	0.819152	−	0.573576i	$-0.194444\pi$
$770$	3.02663	+	2.06646i	0.109072	+	0.0744700i
$771$	55.9401	−	32.2971i	2.01463	−	1.16315i
$772$		−	11.9964i		−	0.431760i
$773$	−8.20497	−	14.2114i	−0.295112	−	0.511149i	0.679899	−	0.733306i	$-0.262024\pi$
$773$	−8.20497	−	14.2114i	−0.295112	−	0.511149i	−0.975011	+	0.222157i	$0.928690\pi$
$774$	10.0273	−	37.4223i	0.360423	−	1.34512i
$775$	0.715564	−	0.526647i	0.0257038	−	0.0189177i
$776$	−11.3490	−	19.6570i	−0.407404	−	0.705644i
$777$	2.83655	+	10.5861i	0.101761	+	0.379775i
$778$	29.8406	+	17.2285i	1.06984	+	0.617671i
$779$	−18.9346			−0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	24.7434	+	14.2856i	0.884822	+	0.510852i
$783$	0.372446	+	1.38999i	0.0133101	+	0.0496741i
$784$	−3.58492	−	6.20926i	−0.128033	−	0.221759i
$785$	3.44468	−	45.5610i	0.122946	−	1.62614i
$786$	−0.0459159	+	0.171361i	−0.00163777	+	0.00611223i
$787$	6.80008	+	11.7781i	0.242397	+	0.419844i	0.961396	−	0.275167i	$-0.0887331\pi$
$787$	6.80008	+	11.7781i	0.242397	+	0.419844i	−0.719000	+	0.695010i	$0.755400\pi$
$788$			13.6326i			0.485642i
$789$	3.14011	−	1.81294i	0.111791	−	0.0645424i
$790$	−30.5253	+	5.75474i	−1.08604	+	0.204745i
$791$	0.482465	+	1.80058i	0.0171545	+	0.0640214i
$792$	16.9369	−	16.9369i	0.601827	−	0.601827i
$793$		0			0
$794$		−	5.95255i		−	0.211248i
$795$	−3.26301	−	17.3082i	−0.115727	−	0.613858i
$796$	7.03076	−	12.1776i	0.249199	−	0.431625i
$797$	28.9148	+	7.74769i	1.02421	+	0.274437i	0.731557	−	0.681780i	$-0.238794\pi$
$797$	28.9148	+	7.74769i	1.02421	+	0.274437i	0.292657	+	0.956218i	$0.405461\pi$
$798$	7.50664			0.265732
$799$	−54.9476	−	14.7232i	−1.94391	−	0.520868i
$800$	−8.80145	−	22.5134i	−0.311178	−	0.795969i
$801$	−1.74778	+	1.74778i	−0.0617546	+	0.0617546i
$802$	0.0698734	−	0.260771i	0.00246732	−	0.00920815i
$803$	−5.18527	+	1.38939i	−0.182984	+	0.0490305i
$804$	18.7477	−	5.02343i	0.661180	−	0.177163i
$805$	−0.625946	+	8.27906i	−0.0220617	+	0.291799i
$806$		0			0
$807$	−15.6423	−	15.6423i	−0.550636	−	0.550636i
$808$	−14.7331	+	25.5185i	−0.518310	+	0.897739i
$809$	2.54661	+	1.47029i	0.0895342	+	0.0516926i	0.544099	−	0.839021i	$-0.316872\pi$
$809$	2.54661	+	1.47029i	0.0895342	+	0.0516926i	−0.454564	+	0.890714i	$0.650205\pi$
$810$	1.24807	+	0.437646i	0.0438526	+	0.0153773i
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$	−0.232730	+	0.134367i	−0.00816724	+	0.00471536i
$813$	2.16144	−	1.24791i	0.0758050	−	0.0437660i
$814$	−4.90856	−	4.90856i	−0.172045	−	0.172045i
$815$	45.1248	+	15.8234i	1.58065	+	0.554270i
$816$	−20.6647	−	11.9307i	−0.723408	−	0.417660i
$817$	10.8630	−	18.8153i	0.380048	−	0.658262i
$818$	26.8732	+	26.8732i	0.939599	+	0.939599i
$819$		0			0
$820$	−1.11428	+	14.7380i	−0.0389124	+	0.514674i
$821$	−44.3125	+	11.8735i	−1.54652	+	0.414388i	−0.928364	−	0.371672i	$-0.878785\pi$
$821$	−44.3125	+	11.8735i	−1.54652	+	0.414388i	−0.618151	+	0.786059i	$0.712118\pi$
$822$	12.1605	−	3.25838i	0.424145	−	0.113649i
$823$	4.58752	−	17.1209i	0.159911	−	0.596796i	−0.838724	−	0.544557i	$-0.816698\pi$
$823$	4.58752	−	17.1209i	0.159911	−	0.596796i	0.998635	−	0.0522385i	$-0.0166356\pi$
$824$	7.62280	−	7.62280i	0.265553	−	0.265553i
$825$	−8.43889	−	21.5860i	−0.293804	−	0.751528i
$826$	−4.80785	−	1.28826i	−0.167286	−	0.0448242i
$827$	5.79276			0.201434			0.100717	−	0.994915i	$-0.467886\pi$
$827$	5.79276			0.201434			0.100717	+	0.994915i	$0.467886\pi$
$828$	16.9308	+	4.53660i	0.588387	+	0.157658i
$829$	16.8799	−	29.2368i	0.586262	−	1.01544i	−0.408454	−	0.912779i	$-0.633932\pi$
$829$	16.8799	−	29.2368i	0.586262	−	1.01544i	0.994717	−	0.102657i	$-0.0327346\pi$
$830$	3.62985	+	19.2540i	0.125994	+	0.668317i
$831$			26.6284i			0.923727i
$832$		0			0
$833$	31.1279	−	31.1279i	1.07852	−	1.07852i
$834$	−10.1412	−	37.8473i	−0.351160	−	1.31055i
$835$	−3.76724	+	0.710216i	−0.130371	+	0.0245780i
$836$	3.75741	−	2.16934i	0.129953	−	0.0750282i
$837$		−	0.874920i		−	0.0302417i
$838$	−17.3415	−	30.0364i	−0.599053	−	1.03759i
$839$	−10.1452	+	37.8626i	−0.350253	+	1.30716i	0.536101	+	0.844154i	$0.319897\pi$
$839$	−10.1452	+	37.8626i	−0.350253	+	1.30716i	−0.886354	+	0.463008i	$0.846770\pi$
$840$	1.36763	−	18.0889i	0.0471877	−	0.624127i
$841$	−14.4573	−	25.0408i	−0.498527	−	0.863475i
$842$	−8.06995	−	30.1175i	−0.278109	−	1.03792i
$843$	−19.0597	−	11.0041i	−0.656451	−	0.379002i
$844$	−8.14177			−0.280251
$845$		0			0
$846$	38.2449			1.31489
$847$	−6.87068	−	3.96679i	−0.236079	−	0.136300i
$848$	0.863850	+	3.22393i	0.0296647	+	0.110710i
$849$	−29.4076	−	50.9354i	−1.00927	−	1.74810i
$850$	−29.8575	+	21.9748i	−1.02410	+	0.753728i
$851$	4.07037	−	15.1908i	0.139531	−	0.520735i
$852$	−17.3566	−	30.0625i	−0.594626	−	1.02992i
$853$		−	40.6417i		−	1.39154i	−0.718262	−	0.695772i	$-0.755062\pi$
$853$		−	40.6417i		−	1.39154i	0.718262	−	0.695772i	$-0.244938\pi$
$854$	−1.77785	+	1.02644i	−0.0608369	+	0.0351242i
$855$	−24.0627	−	16.4290i	−0.822926	−	0.561860i
$856$	−0.347564	−	1.29713i	−0.0118795	−	0.0443348i
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	−0.997721	−	0.0674695i	$-0.978507\pi$
$857$	−27.2327	+	27.2327i	−0.930252	+	0.930252i	0.0674695	+	0.997721i	$0.478507\pi$
$858$		0			0
$859$		−	44.5502i		−	1.52003i	−0.649904	−	0.760016i	$-0.725191\pi$
$859$		−	44.5502i		−	1.52003i	0.649904	−	0.760016i	$-0.274809\pi$
$860$	−14.0058	−	9.56262i	−0.477595	−	0.326083i
$861$	−9.30043	+	16.1088i	−0.316958	+	0.548987i
$862$	−4.54213	−	1.21706i	−0.154706	−	0.0414532i
$863$	55.4497			1.88753			0.943766	−	0.330615i	$-0.107256\pi$
$863$	55.4497			1.88753			0.943766	+	0.330615i	$0.107256\pi$
$864$	−22.9928	−	6.16090i	−0.782230	−	0.209598i
$865$	−30.5853	+	14.7041i	−1.03993	+	0.499956i
$866$	2.89432	−	2.89432i	0.0983531	−	0.0983531i
$867$	25.6562	−	95.7502i	0.871330	−	3.25185i
$868$	0.157822	−	0.0422883i	0.00535683	−	0.00143536i
$869$	−21.8250	+	5.84800i	−0.740363	+	0.198380i
$870$	−1.85718	−	0.140414i	−0.0629643	−	0.00476048i
$871$		0			0
$872$	−19.3993	−	19.3993i	−0.656944	−	0.656944i
$873$	−17.9068	+	31.0154i	−0.606052	+	1.04971i
$874$	−9.32869	−	5.38592i	−0.315548	−	0.182181i
$875$	−9.51462	−	5.05285i	−0.321653	−	0.170817i
$876$	6.06917	+	6.06917i	0.205058	+	0.205058i
$877$	4.65661	−	2.68849i	0.157242	−	0.0907839i	−0.419314	−	0.907841i	$-0.637729\pi$
$877$	4.65661	−	2.68849i	0.157242	−	0.0907839i	0.576557	+	0.817057i	$0.304396\pi$
$878$	20.1244	−	11.6188i	0.679166	−	0.392116i
$879$	7.92505	+	7.92505i	0.267305	+	0.267305i
$880$	1.90300	+	3.95832i	0.0641500	+	0.133435i
$881$	37.0890	+	21.4133i	1.24956	+	0.721434i	0.971022	−	0.238992i	$-0.0768169\pi$
$881$	37.0890	+	21.4133i	1.24956	+	0.721434i	0.278538	+	0.960425i	$0.410150\pi$
$882$	−14.7980	+	25.6309i	−0.498274	+	0.863037i
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.993271	+	0.115813i	$0.0369473\pi$
$883$	32.9568	+	32.9568i	1.10908	+	1.10908i	0.115813	+	0.993271i	$0.463053\pi$
$884$		0			0
$885$	20.5172	+	23.8733i	0.689677	+	0.802494i
$886$	2.58254	−	0.691990i	0.0867622	−	0.0232478i
$887$	20.4194	−	5.47136i	0.685616	−	0.183710i	0.100837	−	0.994903i	$-0.467848\pi$
$887$	20.4194	−	5.47136i	0.685616	−	0.183710i	0.584779	+	0.811193i	$0.301181\pi$
$888$	−8.89336	+	33.1905i	−0.298442	+	1.11380i
$889$	1.48203	−	1.48203i	0.0497057	−	0.0497057i
$890$	−0.513751	−	1.06863i	−0.0172210	−	0.0358204i
$891$	0.929249	+	0.248992i	0.0311310	+	0.00834153i
$892$	6.73778			0.225598
$893$	20.7162	+	5.55089i	0.693241	+	0.185753i
$894$	−6.17340	+	10.6926i	−0.206469	+	0.357616i
$895$	6.06302	−	1.14302i	0.202664	−	0.0382071i
$896$		−	2.11809i		−	0.0707605i
$897$		0			0
$898$	−23.2645	+	23.2645i	−0.776346	+	0.776346i
$899$	−0.0134414	−	0.0501642i	−0.000448297	−	0.00167307i
$900$	−14.2038	+	17.7627i	−0.473461	+	0.592090i
$901$	−17.7471	+	10.2463i	−0.591242	+	0.341354i
$902$		−	11.7817i		−	0.392288i
$903$	−10.6715	−	18.4836i	−0.355126	−	0.615096i
$904$	−1.51266	+	5.64533i	−0.0503104	+	0.187761i
$905$	17.5636	−	15.0944i	0.583833	−	0.501756i
$906$	−9.57200	−	16.5792i	−0.318008	−	0.550807i
$907$	−2.86355	−	10.6869i	−0.0950825	−	0.354853i	0.901949	−	0.431842i	$-0.142136\pi$
$907$	−2.86355	−	10.6869i	−0.0950825	−	0.354853i	−0.997032	+	0.0769889i	$0.975469\pi$
$908$	14.1940	+	8.19488i	0.471043	+	0.271957i
$909$	46.4928			1.54207
$910$		0			0
$911$	−15.0479			−0.498560			−0.249280	−	0.968431i	$-0.580194\pi$
$911$	−15.0479			−0.498560			−0.249280	+	0.968431i	$0.580194\pi$
$912$	7.79093	+	4.49810i	0.257983	+	0.148947i
$913$	3.68867	+	13.7663i	0.122077	+	0.455598i
$914$	14.5045	+	25.1226i	0.479767	+	0.830980i
$915$	12.9459	+	0.978791i	0.427980	+	0.0323578i
$916$	−3.11086	+	11.6099i	−0.102786	+	0.383602i
$917$	0.0299909	+	0.0519457i	0.000990386	+	0.00171540i
$918$			36.5067i			1.20490i
$919$	10.8342	−	6.25513i	0.357388	−	0.206338i	−0.310547	−	0.950558i	$-0.600512\pi$
$919$	10.8342	−	6.25513i	0.357388	−	0.206338i	0.667934	+	0.744220i	$0.267179\pi$
$920$	−14.6782	+	21.4983i	−0.483925	+	0.708778i
$921$	−17.4692	−	65.1960i	−0.575630	−	2.14828i
$922$	8.32259	−	8.32259i	0.274090	−	0.274090i
$923$		0			0
$924$		−	4.26220i		−	0.140216i
$925$	15.9372	+	12.7441i	0.524013	+	0.419023i
$926$	15.3114	−	26.5202i	0.503165	−	0.871508i
$927$	−16.4299	−	4.40237i	−0.539628	−	0.144593i
$928$	−1.41296			−0.0463826
$929$	47.0874	+	12.6170i	1.54489	+	0.413952i	0.927841	−	0.372975i	$-0.121662\pi$
$929$	47.0874	+	12.6170i	1.54489	+	0.413952i	0.617047	+	0.786926i	$0.288329\pi$
$930$	1.06859	+	0.374711i	0.0350404	+	0.0122872i
$931$	−11.7357	+	11.7357i	−0.384623	+	0.384623i
$932$	−6.14112	+	22.9190i	−0.201159	+	0.750736i
$933$	−21.1920	+	5.67838i	−0.693795	+	0.185902i
$934$	22.5369	−	6.03874i	0.737429	−	0.197594i
$935$	−20.4512	+	17.5761i	−0.668825	+	0.574800i
$936$		0			0
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	0.817306	−	0.576203i	$-0.195466\pi$
$937$	7.38027	+	7.38027i	0.241103	+	0.241103i	−0.576203	+	0.817306i	$0.695466\pi$
$938$	−3.59575	+	6.22802i	−0.117405	+	0.203352i
$939$	−11.5750	−	6.68281i	−0.377735	−	0.218085i
$940$	5.53974	−	15.7981i	0.180686	−	0.515277i
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	0.681491	−	0.731827i	$-0.261332\pi$
$941$	−1.54410	−	1.54410i	−0.0503363	−	0.0503363i	−0.731827	+	0.681491i	$0.761332\pi$
$942$	50.4324	−	29.1172i	1.64318	−	0.948688i
$943$	23.1158	−	13.3459i	0.752753	−	0.434602i
$944$	−4.21798	−	4.21798i	−0.137284	−	0.137284i
$945$	−9.56117	+	4.59662i	−0.311025	+	0.149528i
$946$	11.7074	+	6.75929i	0.380642	+	0.219764i
$947$	3.35827	−	5.81670i	0.109129	−	0.189017i	−0.806289	−	0.591522i	$-0.798527\pi$
$947$	3.35827	−	5.81670i	0.109129	−	0.189017i	0.915418	+	0.402505i	$0.131860\pi$
$948$	25.5454	+	25.5454i	0.829676	+	0.829676i
$949$		0			0
$950$	11.2568	−	8.28486i	0.365218	−	0.268796i
$951$	61.7137	−	16.5361i	2.00121	−	0.536221i
$952$	−20.3871	+	5.46272i	−0.660751	+	0.177048i
$953$	4.67309	−	17.4402i	0.151376	−	0.564944i	−0.848012	−	0.529977i	$-0.822201\pi$
$953$	4.67309	−	17.4402i	0.151376	−	0.564944i	0.999388	−	0.0349673i	$-0.0111327\pi$
$954$	9.74205	−	9.74205i	0.315411	−	0.315411i
$955$	−13.7476	+	39.2049i	−0.444860	+	1.26864i
$956$	2.91324	+	0.780600i	0.0942208	+	0.0252464i
$957$	−1.35475			−0.0437929
$958$	38.3526	+	10.2765i	1.23912	+	0.332020i
$959$	2.12828	−	3.68629i	0.0687257	−	0.119036i
$960$	25.6709	−	37.5988i	0.828526	−	1.21350i
$961$		−	30.9684i		−	0.998981i
$962$		0			0
$963$	−1.49825	+	1.49825i	−0.0482804	+	0.0482804i
$964$	−4.45026	−	16.6086i	−0.143333	−	0.534927i
$965$	−5.20782	−	27.6241i	−0.167646	−	0.889253i
$966$	−9.16426	+	5.29099i	−0.294855	+	0.170235i
$967$			60.0570i			1.93130i	0.259841	+	0.965651i	$0.416330\pi$
$967$			60.0570i			1.93130i	−0.259841	+	0.965651i	$0.583670\pi$
$968$	−12.4370	−	21.5415i	−0.399740	−	0.692369i
$969$	−14.2958	+	53.3528i	−0.459249	+	1.71394i
$970$	−11.1977	−	13.0294i	−0.359536	−	0.418348i
$971$	20.4589	+	35.4359i	0.656558	+	1.13719i	0.981501	+	0.191459i	$0.0613218\pi$
$971$	20.4589	+	35.4359i	0.656558	+	1.13719i	−0.324942	+	0.945734i	$0.605345\pi$
$972$	−4.04627	−	15.1009i	−0.129784	−	0.484361i
$973$	−11.4729	−	6.62390i	−0.367805	−	0.212352i
$974$	29.5983			0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	−32.4724	−	18.7479i	−1.03888	−	0.599800i	−0.119367	−	0.992850i	$-0.538087\pi$
$977$	−32.4724	−	18.7479i	−1.03888	−	0.599800i	−0.919517	+	0.393050i	$0.871420\pi$
$978$	15.7740	+	58.8694i	0.504397	+	1.88244i
$979$	−0.431236	−	0.746923i	−0.0137824	−	0.0238718i
$980$	8.44405	+	9.82532i	0.269735	+	0.313858i
$981$	−11.2036	+	41.8125i	−0.357704	+	1.33497i
$982$	−3.71959	−	6.44253i	−0.118697	−	0.205589i
$983$			46.1176i			1.47092i	0.677567	+	0.735461i	$0.263034\pi$
$983$			46.1176i			1.47092i	−0.677567	+	0.735461i	$0.736966\pi$
$984$	−50.5056	+	29.1594i	−1.61006	+	0.929569i
$985$	5.91812	+	31.3919i	0.188567	+	1.00023i
$986$	0.560854	+	2.09314i	0.0178612	+	0.0666591i
$987$	14.8980	−	14.8980i	0.474208	−	0.474208i
$988$		0			0
$989$			30.6267i			0.973873i
$990$	10.2226	−	14.9725i	0.324897	−	0.475859i
$991$	−0.401099	+	0.694724i	−0.0127413	+	0.0220686i	−0.872326	−	0.488925i	$-0.837389\pi$
$991$	−0.401099	+	0.694724i	−0.0127413	+	0.0220686i	0.859584	+	0.510994i	$0.170722\pi$
$992$	0.829802	+	0.222345i	0.0263462	+	0.00705945i
$993$	−93.5143			−2.96759
$994$	12.4238	+	3.32894i	0.394058	+	0.105587i
$995$	10.9033	−	31.0936i	0.345656	−	0.985734i
$996$	16.1129	−	16.1129i	0.510558	−	0.510558i
$997$	4.04012	−	15.0779i	0.127952	−	0.477522i	−0.871976	−	0.489549i	$-0.837162\pi$
$997$	4.04012	−	15.0779i	0.127952	−	0.477522i	0.999928	+	0.0120264i	$0.00382820\pi$
$998$	5.92576	−	1.58780i	0.187577	−	0.0502610i
$999$	19.4100	−	5.20090i	0.614106	−	0.164549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.f.657.4		20
5.3	odd	4		845.2.o.e.488.4		20
13.2	odd	12		845.2.o.e.587.4		20
13.3	even	3		65.2.t.a.37.2	yes	20
13.4	even	6		845.2.f.d.437.8		20
13.5	odd	4		65.2.o.a.32.4	✓	20
13.6	odd	12		845.2.k.e.577.3		20
13.7	odd	12		845.2.k.d.577.8		20
13.8	odd	4		845.2.o.g.357.2		20
13.9	even	3		845.2.f.e.437.3		20
13.10	even	6		845.2.t.g.427.4		20
13.11	odd	12		845.2.o.f.587.2		20
13.12	even	2		845.2.t.e.657.2		20
39.5	even	4		585.2.cf.a.487.2		20
39.29	odd	6		585.2.dp.a.37.4		20
65.3	odd	12		65.2.o.a.63.4	yes	20
65.8	even	4		845.2.t.g.188.4		20
65.18	even	4		65.2.t.a.58.2	yes	20
65.23	odd	12		845.2.o.g.258.2		20
65.28	even	12	inner	845.2.t.f.418.4		20
65.29	even	6		325.2.x.b.232.4		20
65.33	even	12		845.2.f.d.408.3		20
65.38	odd	4		845.2.o.f.488.2		20
65.42	odd	12		325.2.s.b.193.2		20
65.43	odd	12		845.2.k.d.268.8		20
65.44	odd	4		325.2.s.b.32.2		20
65.48	odd	12		845.2.k.e.268.3		20
65.57	even	4		325.2.x.b.318.4		20
65.58	even	12		845.2.f.e.408.8		20
65.63	even	12		845.2.t.e.418.2		20
195.68	even	12		585.2.cf.a.388.2		20
195.83	odd	4		585.2.dp.a.253.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	13.5	odd	4
65.2.o.a.63.4	yes	20	65.3	odd	12
65.2.t.a.37.2	yes	20	13.3	even	3
65.2.t.a.58.2	yes	20	65.18	even	4
325.2.s.b.32.2		20	65.44	odd	4
325.2.s.b.193.2		20	65.42	odd	12
325.2.x.b.232.4		20	65.29	even	6
325.2.x.b.318.4		20	65.57	even	4
585.2.cf.a.388.2		20	195.68	even	12
585.2.cf.a.487.2		20	39.5	even	4
585.2.dp.a.37.4		20	39.29	odd	6
585.2.dp.a.253.4		20	195.83	odd	4
845.2.f.d.408.3		20	65.33	even	12
845.2.f.d.437.8		20	13.4	even	6
845.2.f.e.408.8		20	65.58	even	12
845.2.f.e.437.3		20	13.9	even	3
845.2.k.d.268.8		20	65.43	odd	12
845.2.k.d.577.8		20	13.7	odd	12
845.2.k.e.268.3		20	65.48	odd	12
845.2.k.e.577.3		20	13.6	odd	12
845.2.o.e.488.4		20	5.3	odd	4
845.2.o.e.587.4		20	13.2	odd	12
845.2.o.f.488.2		20	65.38	odd	4
845.2.o.f.587.2		20	13.11	odd	12
845.2.o.g.258.2		20	65.23	odd	12
845.2.o.g.357.2		20	13.8	odd	4
845.2.t.e.418.2		20	65.63	even	12
845.2.t.e.657.2		20	13.12	even	2
845.2.t.f.418.4		20	65.28	even	12	inner
845.2.t.f.657.4		20	1.1	even	1	trivial
845.2.t.g.188.4		20	65.8	even	4
845.2.t.g.427.4		20	13.10	even	6

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+(0.885613 + 0.511309i) q^{2} +(-0.721300 - 2.69193i) q^{3} +(-0.477126 - 0.826407i) q^{4} +(-1.45744 - 1.69584i) q^{5} +(0.737614 - 2.75281i) q^{6} +(-0.481787 - 0.834479i) q^{7} -3.02107i q^{8} +(-4.12812 + 2.38337i) q^{9} +(-0.423625 - 2.24706i) q^{10} +(-0.430490 - 1.60661i) q^{11} +(-1.88048 + 1.88048i) q^{12} -0.985368i q^{14} +(-3.51384 + 5.14652i) q^{15} +(0.590448 - 1.02269i) q^{16} +(7.00342 + 1.87656i) q^{17} -4.87456 q^{18} +(-2.64041 - 0.707496i) q^{19} +(-0.706075 + 2.01357i) q^{20} +(-1.89884 + 1.89884i) q^{21} +(0.440226 - 1.64295i) q^{22} +(3.72214 - 0.997344i) q^{23} +(-8.13250 + 2.17910i) q^{24} +(-0.751762 + 4.94316i) q^{25} +(3.48159 + 3.48159i) q^{27} +(-0.459747 + 0.796304i) q^{28} +(0.253107 + 0.146132i) q^{29} +(-5.74336 + 2.76117i) q^{30} +(-0.125649 - 0.125649i) q^{31} +(-4.18683 + 2.41727i) q^{32} +(-4.01436 + 2.31769i) q^{33} +(5.24282 + 5.24282i) q^{34} +(-0.712972 + 2.03323i) q^{35} +(3.93927 + 2.27434i) q^{36} +(2.04061 - 3.53443i) q^{37} +(-1.97663 - 1.97663i) q^{38} +(-5.12326 + 4.40302i) q^{40} +(6.69071 - 1.79277i) q^{41} +(-2.65254 + 0.710745i) q^{42} +(-2.05706 + 7.67707i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(10.0583 + 3.52703i) q^{45} +(3.80633 + 1.01990i) q^{46} -7.84582 q^{47} +(-3.17888 - 0.851780i) q^{48} +(3.03576 - 5.25810i) q^{49} +(-3.19325 + 3.99335i) q^{50} -20.2063i q^{51} +(-1.99855 + 1.99855i) q^{53} +(1.30317 + 4.86351i) q^{54} +(-2.09714 + 3.07157i) q^{55} +(-2.52102 + 1.45551i) q^{56} +7.61811i q^{57} +(0.149437 + 0.258832i) q^{58} +(1.30739 - 4.87924i) q^{59} +(5.92967 + 0.448318i) q^{60} +(-1.04169 - 1.80425i) q^{61} +(-0.0470311 - 0.175522i) q^{62} +(3.97775 + 2.29655i) q^{63} -7.30568 q^{64} -4.74023 q^{66} +(-6.32050 - 3.64915i) q^{67} +(-1.79071 - 6.68304i) q^{68} +(-5.36956 - 9.30034i) q^{69} +(-1.67103 + 1.43611i) q^{70} +(-3.37837 + 12.6082i) q^{71} +(7.20034 + 12.4713i) q^{72} -3.22747i q^{73} +(3.61437 - 2.08676i) q^{74} +(13.8489 - 1.54181i) q^{75} +(0.675130 + 2.51962i) q^{76} +(-1.13328 + 1.13328i) q^{77} -13.5845i q^{79} +(-2.59485 + 0.489192i) q^{80} +(-0.289196 + 0.500902i) q^{81} +(6.84204 + 1.83332i) q^{82} -8.56854 q^{83} +(2.47521 + 0.663230i) q^{84} +(-7.02469 - 14.6117i) q^{85} +(-5.74712 + 5.74712i) q^{86} +(0.210809 - 0.786751i) q^{87} +(-4.85368 + 1.30054i) q^{88} +(0.500868 - 0.134207i) q^{89} +(7.10435 + 8.26648i) q^{90} +(-2.60014 - 2.60014i) q^{92} +(-0.247608 + 0.428870i) q^{93} +(-6.94836 - 4.01164i) q^{94} +(2.64843 + 5.50885i) q^{95} +(9.52707 + 9.52707i) q^{96} +(6.50662 - 3.75660i) q^{97} +(5.37702 - 3.10442i) q^{98} +(5.60626 + 5.60626i) 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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