LMFDB - Embedded newform 931.2.w.a.834.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(99,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("931.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.w (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			834.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	931.834
Dual form			931.2.w.a.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.233956 + 1.32683i) q^{2} +(2.20574 + 1.85083i) q^{3} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-2.97178 + 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(0.918748 + 5.21048i) q^{9} +O(q^{10})$	\(q+(-0.233956 + 1.32683i) q^{2} +(2.20574 + 1.85083i) q^{3} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-2.97178 + 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(0.918748 + 5.21048i) q^{9} +(0.205737 + 1.16679i) q^{10} +(1.11334 - 1.92836i) q^{11} +(0.266044 + 0.460802i) q^{12} +(-1.97178 + 1.65452i) q^{13} +(2.37939 + 0.866025i) q^{15} +(-2.75490 - 2.31164i) q^{16} +(-0.0812519 + 0.460802i) q^{17} -7.12836 q^{18} +(4.29813 - 0.725293i) q^{19} +0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(2.53209 + 0.921605i) q^{23} +(-7.96451 + 2.89884i) q^{24} +(-3.23783 + 2.71686i) q^{25} +(-1.73396 - 3.00330i) q^{26} +(-3.29813 + 5.71253i) q^{27} +(-1.19459 - 6.77487i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(-3.55303 - 6.15403i) q^{31} +(-0.798133 + 0.669713i) q^{32} +(6.02481 - 2.19285i) q^{33} +(-0.592396 - 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} +4.94356 q^{37} +(-0.0432332 + 5.87257i) q^{38} -7.41147 q^{39} +(-0.449493 + 2.54920i) q^{40} +(-1.89646 - 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(0.315207 - 0.264490i) q^{44} +(2.32635 + 4.02936i) q^{45} +(-1.81521 + 3.14403i) q^{46} +(1.26604 + 7.18009i) q^{47} +(-1.79813 - 10.1977i) q^{48} +(-2.84730 - 4.93166i) q^{50} +(-1.03209 + 0.866025i) q^{51} +(-0.446967 + 0.162683i) q^{52} +(2.66637 + 0.970481i) q^{53} +(-6.80793 - 5.71253i) q^{54} +(0.340022 - 1.92836i) q^{55} +(10.8229 + 6.35532i) q^{57} +9.26857 q^{58} +(1.09492 - 6.20961i) q^{59} +(0.358441 + 0.300767i) q^{60} +(8.57785 + 3.12208i) q^{61} +(8.99660 - 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-1.13176 + 1.96026i) q^{65} +(1.50000 + 8.50692i) q^{66} +(1.33275 + 7.55839i) q^{67} +(-0.0432332 + 0.0748822i) q^{68} +(3.87939 + 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(-14.6348 - 5.32661i) q^{72} +(-1.06418 - 0.892951i) q^{73} +(-1.15657 + 6.55926i) q^{74} -12.1702 q^{75} +(0.792204 + 0.145708i) q^{76} +(1.73396 - 9.83375i) q^{78} +(-9.07398 - 7.61397i) q^{79} +(-2.97178 - 1.08164i) q^{80} +(-2.93242 + 1.06731i) q^{81} +(2.55509 - 2.14398i) q^{82} +(-7.41534 - 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(-0.912818 - 5.17685i) q^{86} +(9.90420 - 17.1546i) q^{87} +(3.27719 + 5.67626i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-5.89053 + 2.14398i) q^{90} +(0.381445 + 0.320070i) q^{92} +(3.55303 - 20.1503i) q^{93} -9.82295 q^{94} +(3.33363 - 1.89209i) q^{95} -3.00000 q^{96} +(-1.64156 + 9.30975i) q^{97} +(11.0706 + 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{5} - 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^5 - 3 * q^6 + 6 * q^8 + 3 * q^9	$ 6 q - 6 q^{2} + 3 q^{3} + 6 q^{5} - 3 q^{6} + 6 q^{8} + 3 q^{9} - 9 q^{10} - 3 q^{12} + 3 q^{13} + 3 q^{15} - 18 q^{16} - 3 q^{17} - 6 q^{18} + 12 q^{19} + 6 q^{20} + 6 q^{23} - 15 q^{24} - 15 q^{26} - 6 q^{27} - 3 q^{29} - 9 q^{31} + 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} - 21 q^{41} - 3 q^{43} + 9 q^{44} + 15 q^{45} - 18 q^{46} + 3 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 15 q^{52} - 3 q^{53} - 30 q^{54} - 18 q^{55} + 24 q^{57} + 36 q^{58} - 12 q^{59} - 6 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} - 12 q^{65} + 9 q^{66} - 30 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{71} - 12 q^{72} + 12 q^{73} + 15 q^{74} - 30 q^{75} - 36 q^{76} + 15 q^{78} - 39 q^{79} - 3 q^{80} + 6 q^{81} + 54 q^{82} + 24 q^{86} + 21 q^{87} + 9 q^{88} + 12 q^{89} - 18 q^{90} + 42 q^{92} + 9 q^{93} - 18 q^{94} + 39 q^{95} - 18 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^5 - 3 * q^6 + 6 * q^8 + 3 * q^9 - 9 * q^10 - 3 * q^12 + 3 * q^13 + 3 * q^15 - 18 * q^16 - 3 * q^17 - 6 * q^18 + 12 * q^19 + 6 * q^20 + 6 * q^23 - 15 * q^24 - 15 * q^26 - 6 * q^27 - 3 * q^29 - 9 * q^31 + 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 - 21 * q^41 - 3 * q^43 + 9 * q^44 + 15 * q^45 - 18 * q^46 + 3 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 15 * q^52 - 3 * q^53 - 30 * q^54 - 18 * q^55 + 24 * q^57 + 36 * q^58 - 12 * q^59 - 6 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 - 12 * q^65 + 9 * q^66 - 30 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^71 - 12 * q^72 + 12 * q^73 + 15 * q^74 - 30 * q^75 - 36 * q^76 + 15 * q^78 - 39 * q^79 - 3 * q^80 + 6 * q^81 + 54 * q^82 + 24 * q^86 + 21 * q^87 + 9 * q^88 + 12 * q^89 - 18 * q^90 + 42 * q^92 + 9 * q^93 - 18 * q^94 + 39 * q^95 - 18 * q^96 - 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.233956	+	1.32683i	−0.165432	+	0.938209i	0.783187	+	0.621786i	$0.213593\pi$
$2$	−0.233956	+	1.32683i	−0.165432	+	0.938209i	−0.948618	+	0.316423i	$0.897518\pi$
$3$	2.20574	+	1.85083i	1.27348	+	1.06858i	0.994108	+	0.108397i	$0.0345718\pi$
$3$	2.20574	+	1.85083i	1.27348	+	1.06858i	0.279375	+	0.960182i	$0.409873\pi$
$4$	0.173648	+	0.0632028i	0.0868241	+	0.0316014i
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	−0.150565	−	0.988600i	$-0.548109\pi$
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	0.520121	+	0.854093i	$0.325887\pi$
$6$	−2.97178	+	2.49362i	−1.21322	+	1.01802i
$7$		0			0
$7$		0			0
$8$	−1.47178	+	2.54920i	−0.520353	+	0.901278i
$9$	0.918748	+	5.21048i	0.306249	+	1.73683i
$10$	0.205737	+	1.16679i	0.0650598	+	0.368972i
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	−0.647931	−	0.761699i	$-0.724366\pi$
$11$	1.11334	−	1.92836i	0.335685	−	0.581423i	0.983616	+	0.180276i	$0.0576989\pi$
$12$	0.266044	+	0.460802i	0.0768004	+	0.133022i
$13$	−1.97178	+	1.65452i	−0.546874	+	0.458882i	−0.873881	−	0.486140i	$-0.838404\pi$
$13$	−1.97178	+	1.65452i	−0.546874	+	0.458882i	0.327007	+	0.945022i	$0.393960\pi$
$14$		0			0
$15$	2.37939	+	0.866025i	0.614355	+	0.223607i
$16$	−2.75490	−	2.31164i	−0.688725	−	0.577909i
$17$	−0.0812519	+	0.460802i	−0.0197065	+	0.111761i	−0.993074	−	0.117488i	$-0.962516\pi$
$17$	−0.0812519	+	0.460802i	−0.0197065	+	0.111761i	0.973368	+	0.229249i	$0.0736270\pi$
$18$	−7.12836			−1.68017
$19$	4.29813	−	0.725293i	0.986059	−	0.166394i
$19$	4.29813	−	0.725293i	0.986059	−	0.166394i
$20$	0.162504			0.0363370
$21$		0			0
$22$	2.29813	+	1.92836i	0.489964	+	0.411128i
$23$	2.53209	+	0.921605i	0.527977	+	0.192168i	0.592235	−	0.805765i	$-0.298246\pi$
$23$	2.53209	+	0.921605i	0.527977	+	0.192168i	−0.0642578	+	0.997933i	$0.520468\pi$
$24$	−7.96451	+	2.89884i	−1.62575	+	0.591724i
$25$	−3.23783	+	2.71686i	−0.647565	+	0.543372i
$26$	−1.73396	−	3.00330i	−0.340057	−	0.588995i
$27$	−3.29813	+	5.71253i	−0.634726	+	1.09938i
$28$		0			0
$29$	−1.19459	−	6.77487i	−0.221830	−	1.25806i	−0.868653	−	0.495421i	$-0.835014\pi$
$29$	−1.19459	−	6.77487i	−0.221830	−	1.25806i	0.646822	−	0.762641i	$-0.276097\pi$
$30$	−1.70574	+	2.95442i	−0.311424	+	0.539401i
$31$	−3.55303	−	6.15403i	−0.638144	−	1.10530i	−0.985840	−	0.167690i	$-0.946369\pi$
$31$	−3.55303	−	6.15403i	−0.638144	−	1.10530i	0.347696	−	0.937607i	$-0.386964\pi$
$32$	−0.798133	+	0.669713i	−0.141091	+	0.118390i
$33$	6.02481	−	2.19285i	1.04879	−	0.381727i
$34$	−0.592396	−	0.215615i	−0.101595	−	0.0369776i
$35$		0			0
$36$	−0.169778	+	0.962858i	−0.0282963	+	0.160476i
$37$	4.94356			0.812717			0.406358	−	0.913714i	$-0.366798\pi$
$37$	4.94356			0.812717			0.406358	+	0.913714i	$0.366798\pi$
$38$	−0.0432332	+	5.87257i	−0.00701336	+	0.952657i
$39$	−7.41147			−1.18679
$40$	−0.449493	+	2.54920i	−0.0710711	+	0.403064i
$41$	−1.89646	−	1.59132i	−0.296177	−	0.248522i	0.482574	−	0.875855i	$-0.339702\pi$
$41$	−1.89646	−	1.59132i	−0.296177	−	0.248522i	−0.778751	+	0.627333i	$0.784146\pi$
$42$		0			0
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	−0.606093	−	0.795394i	$-0.707264\pi$
$43$	−3.66637	+	1.33445i	−0.559117	+	0.203502i	0.0469757	+	0.998896i	$0.485042\pi$
$44$	0.315207	−	0.264490i	0.0475193	−	0.0398734i
$45$	2.32635	+	4.02936i	0.346792	+	0.600661i
$46$	−1.81521	+	3.14403i	−0.267638	+	0.463562i
$47$	1.26604	+	7.18009i	0.184672	+	1.04732i	0.926377	+	0.376598i	$0.122906\pi$
$47$	1.26604	+	7.18009i	0.184672	+	1.04732i	−0.741705	+	0.670726i	$0.765983\pi$
$48$	−1.79813	−	10.1977i	−0.259538	−	1.47191i
$49$		0			0
$50$	−2.84730	−	4.93166i	−0.402669	−	0.697442i
$51$	−1.03209	+	0.866025i	−0.144521	+	0.121268i
$52$	−0.446967	+	0.162683i	−0.0619831	+	0.0225600i
$53$	2.66637	+	0.970481i	0.366255	+	0.133306i	0.518590	−	0.855023i	$-0.326457\pi$
$53$	2.66637	+	0.970481i	0.366255	+	0.133306i	−0.152335	+	0.988329i	$0.548679\pi$
$54$	−6.80793	−	5.71253i	−0.926442	−	0.777377i
$55$	0.340022	−	1.92836i	0.0458486	−	0.260020i
$56$		0			0
$57$	10.8229	+	6.35532i	1.43353	+	0.841783i
$58$	9.26857			1.21702
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	−0.826757	−	0.562559i	$-0.809817\pi$
$59$	1.09492	−	6.20961i	0.142547	−	0.808423i	0.969304	−	0.245864i	$-0.0790718\pi$
$60$	0.358441	+	0.300767i	0.0462745	+	0.0388289i
$61$	8.57785	+	3.12208i	1.09828	+	0.399742i	0.826682	−	0.562669i	$-0.190225\pi$
$61$	8.57785	+	3.12208i	1.09828	+	0.399742i	0.271599	+	0.962411i	$0.412448\pi$
$62$	8.99660	−	3.27449i	1.14257	−	0.415861i
$63$		0			0
$64$	−4.29813	−	7.44459i	−0.537267	−	0.930573i
$65$	−1.13176	+	1.96026i	−0.140377	+	0.243141i
$66$	1.50000	+	8.50692i	0.184637	+	1.04713i
$67$	1.33275	+	7.55839i	0.162821	+	0.923405i	0.951283	+	0.308320i	$0.0997669\pi$
$67$	1.33275	+	7.55839i	0.162821	+	0.923405i	−0.788461	+	0.615084i	$0.789122\pi$
$68$	−0.0432332	+	0.0748822i	−0.00524280	+	0.00908080i
$69$	3.87939	+	6.71929i	0.467023	+	0.808908i
$70$		0			0
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.233722	−	0.972303i	$-0.424909\pi$
$71$	8.74422	−	3.18264i	1.03775	−	0.377709i	0.804026	+	0.594594i	$0.202687\pi$
$72$	−14.6348	−	5.32661i	−1.72472	−	0.627748i
$73$	−1.06418	−	0.892951i	−0.124553	−	0.104512i	0.578384	−	0.815765i	$-0.303684\pi$
$73$	−1.06418	−	0.892951i	−0.124553	−	0.104512i	−0.702936	+	0.711253i	$0.748128\pi$
$74$	−1.15657	+	6.55926i	−0.134449	+	0.762498i
$75$	−12.1702			−1.40530
$76$	0.792204	+	0.145708i	0.0908720	+	0.0167139i
$77$		0			0
$78$	1.73396	−	9.83375i	0.196332	−	1.11345i
$79$	−9.07398	−	7.61397i	−1.02090	−	0.856639i	−0.0311616	−	0.999514i	$-0.509921\pi$
$79$	−9.07398	−	7.61397i	−1.02090	−	0.856639i	−0.989741	+	0.142876i	$0.954365\pi$
$80$	−2.97178	−	1.08164i	−0.332255	−	0.120931i
$81$	−2.93242	+	1.06731i	−0.325824	+	0.118590i
$82$	2.55509	−	2.14398i	0.282163	−	0.236763i
$83$	−7.41534	−	12.8438i	−0.813940	−	1.40979i	−0.910087	−	0.414418i	$-0.863985\pi$
$83$	−7.41534	−	12.8438i	−0.813940	−	1.40979i	0.0961469	−	0.995367i	$-0.469348\pi$
$84$		0			0
$85$	0.0714517	+	0.405223i	0.00775003	+	0.0439526i
$86$	−0.912818	−	5.17685i	−0.0984317	−	0.558234i
$87$	9.90420	−	17.1546i	1.06184	−	1.83916i
$88$	3.27719	+	5.67626i	0.349349	+	0.605091i
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	−0.120951	−	0.992658i	$-0.538594\pi$
$89$	7.88326	−	6.61484i	0.835623	−	0.701171i	0.956575	+	0.291487i	$0.0941501\pi$
$90$	−5.89053	+	2.14398i	−0.620916	+	0.225995i
$91$		0			0
$92$	0.381445	+	0.320070i	0.0397684	+	0.0333696i
$93$	3.55303	−	20.1503i	0.368432	−	2.08948i
$94$	−9.82295			−1.01316
$95$	3.33363	−	1.89209i	0.342023	−	0.194124i
$96$	−3.00000			−0.306186
$97$	−1.64156	+	9.30975i	−0.166675	+	0.945261i	0.780645	+	0.624974i	$0.214891\pi$
$97$	−1.64156	+	9.30975i	−0.166675	+	0.945261i	−0.947320	+	0.320287i	$0.896221\pi$
$98$		0			0
$99$	11.0706	+	4.02936i	1.11263	+	0.404966i
$100$	−0.733956	+	0.267138i	−0.0733956	+	0.0267138i
$101$	7.08512	−	5.94512i	0.704996	−	0.591562i	−0.218194	−	0.975905i	$-0.570017\pi$
$101$	7.08512	−	5.94512i	0.704996	−	0.591562i	0.923190	+	0.384343i	$0.125572\pi$
$102$	−0.907604	−	1.57202i	−0.0898662	−	0.155653i
$103$	−2.75490	+	4.77163i	−0.271448	+	0.470162i	−0.969233	−	0.246145i	$-0.920836\pi$
$103$	−2.75490	+	4.77163i	−0.271448	+	0.470162i	0.697785	+	0.716308i	$0.254169\pi$
$104$	−1.31567	−	7.46156i	−0.129012	−	0.731666i
$105$		0			0
$106$	−1.91147	+	3.31077i	−0.185659	+	0.321570i
$107$	−5.11721	−	8.86327i	−0.494699	−	0.856845i	0.505282	−	0.862954i	$-0.331389\pi$
$107$	−5.11721	−	8.86327i	−0.494699	−	0.856845i	−0.999981	+	0.00610974i	$0.998055\pi$
$108$	−0.933763	+	0.783520i	−0.0898514	+	0.0753943i
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	−0.258676	−	0.965964i	$-0.583286\pi$
$109$	1.71301	−	0.623485i	0.164077	−	0.0597190i	0.422753	+	0.906245i	$0.361064\pi$
$110$	2.47906	+	0.902302i	0.236369	+	0.0860312i
$111$	10.9042	+	9.14971i	1.03498	+	0.868452i
$112$		0			0
$113$	−17.6878			−1.66393			−0.831963	−	0.554830i	$-0.812783\pi$
$113$	−17.6878			−1.66393			−0.831963	+	0.554830i	$0.812783\pi$
$114$	−10.9645	+	12.8733i	−1.02692	+	1.20570i
$115$	2.36959			0.220965
$116$	0.220752	−	1.25195i	0.0204963	−	0.116240i
$117$	−10.4324	−	8.75384i	−0.964477	−	0.809293i
$118$	7.98293	+	2.90555i	0.734888	+	0.267477i
$119$		0			0
$120$	−5.70961	+	4.79093i	−0.521213	+	0.437350i
$121$	3.02094	+	5.23243i	0.274631	+	0.475675i
$122$	−6.14930	+	10.6509i	−0.556731	+	0.964287i
$123$	−1.23783	−	7.02006i	−0.111611	−	0.632977i
$124$	−0.228026	−	1.29320i	−0.0204773	−	0.116133i
$125$	−4.05690	+	7.02676i	−0.362861	+	0.628493i
$126$		0			0
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	−0.156657	−	0.987653i	$-0.550072\pi$
$127$	8.88919	−	7.45891i	0.788788	−	0.661871i	0.945445	+	0.325782i	$0.105627\pi$
$128$	8.92514	−	3.24849i	0.788879	−	0.287128i
$129$	−10.5569	−	3.84240i	−0.929484	−	0.338304i
$130$	−2.33615	−	1.96026i	−0.204894	−	0.171927i
$131$	−0.320422	+	1.81720i	−0.0279954	+	0.158770i	−0.995601	−	0.0936982i	$-0.970131\pi$
$131$	−0.320422	+	1.81720i	−0.0279954	+	0.158770i	0.967605	+	0.252468i	$0.0812422\pi$
$132$	1.18479			0.103123
$133$		0			0
$134$	−10.3405			−0.893282
$135$	−1.00727	+	5.71253i	−0.0866923	+	0.491657i
$136$	−1.05509	−	0.885328i	−0.0904735	−	0.0759162i
$137$	−0.240352	−	0.0874810i	−0.0205347	−	0.00747401i	0.331732	−	0.943374i	$-0.392367\pi$
$137$	−0.240352	−	0.0874810i	−0.0205347	−	0.00747401i	−0.352267	+	0.935900i	$0.614589\pi$
$138$	−9.82295	+	3.57526i	−0.836185	+	0.304346i
$139$	−3.26604	+	2.74054i	−0.277022	+	0.232449i	−0.770704	−	0.637193i	$-0.780095\pi$
$139$	−3.26604	+	2.74054i	−0.277022	+	0.232449i	0.493682	+	0.869643i	$0.335651\pi$
$140$		0			0
$141$	−10.4966	+	18.1806i	−0.883973	+	1.53109i
$142$	2.17705	+	12.3467i	0.182694	+	1.03611i
$143$	0.995252	+	5.64436i	0.0832272	+	0.472005i
$144$	9.51367	−	16.4782i	0.792806	−	1.37318i
$145$	−3.02481	−	5.23913i	−0.251197	−	0.435086i
$146$	1.43376	−	1.20307i	0.118659	−	0.0995668i
$147$		0			0
$148$	0.858441	+	0.312447i	0.0705634	+	0.0256830i
$149$	12.6853	+	10.6442i	1.03922	+	0.872007i	0.991919	−	0.126874i	$-0.0404945\pi$
$149$	12.6853	+	10.6442i	1.03922	+	0.872007i	0.0472981	+	0.998881i	$0.484939\pi$
$150$	2.84730	−	16.1478i	0.232481	−	1.31846i
$151$	−4.36184			−0.354962			−0.177481	−	0.984124i	$-0.556795\pi$
$151$	−4.36184			−0.354962			−0.177481	+	0.984124i	$0.556795\pi$
$152$	−4.47700	+	12.0243i	−0.363132	+	0.975298i
$153$	−2.47565			−0.200145
$154$		0			0
$155$	−4.78699	−	4.01676i	−0.384500	−	0.322634i
$156$	−1.28699	−	0.468426i	−0.103042	−	0.0375041i
$157$	−9.03849	+	3.28974i	−0.721350	+	0.262550i	−0.676499	−	0.736444i	$-0.736504\pi$
$157$	−9.03849	+	3.28974i	−0.721350	+	0.262550i	−0.0448510	+	0.998994i	$0.514281\pi$
$158$	12.2253	−	10.2583i	0.972596	−	0.816105i
$159$	4.08512	+	7.07564i	0.323971	+	0.561135i
$160$	−0.458111	+	0.793471i	−0.0362168	+	0.0627294i
$161$		0			0
$162$	−0.730085	−	4.14052i	−0.0573609	−	0.325310i
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	−0.981957	−	0.189105i	$-0.939441\pi$
$163$	−4.17752	+	7.23567i	−0.327209	+	0.566742i	0.654748	+	0.755847i	$0.272775\pi$
$164$	−0.228741	−	0.396191i	−0.0178617	−	0.0309373i
$165$	4.31908	−	3.62414i	0.336240	−	0.282139i
$166$	18.7763	−	6.83402i	1.45732	−	0.530423i
$167$	3.79174	+	1.38008i	0.293413	+	0.106794i	0.484533	−	0.874773i	$-0.338990\pi$
$167$	3.79174	+	1.38008i	0.293413	+	0.106794i	−0.191120	+	0.981567i	$0.561212\pi$
$168$		0			0
$169$	−1.10694	+	6.27779i	−0.0851496	+	0.482907i
$170$	−0.554378			−0.0425188
$171$	7.72803	+	21.7290i	0.590977	+	1.66166i
$172$	−0.721000			−0.0549758
$173$	3.49794	−	19.8378i	0.265943	−	1.50824i	−0.500391	−	0.865799i	$-0.666811\pi$
$173$	3.49794	−	19.8378i	0.265943	−	1.50824i	0.766335	−	0.642441i	$-0.222078\pi$
$174$	20.4440	+	17.1546i	1.54986	+	1.30049i
$175$		0			0
$176$	−7.52481	+	2.73881i	−0.567204	+	0.206445i
$177$	13.9081	−	11.6703i	1.04539	−	0.877190i
$178$	6.93242	+	12.0073i	0.519607	+	0.899985i
$179$	5.75624	−	9.97011i	0.430242	−	0.745201i	−0.566652	−	0.823957i	$-0.691762\pi$
$179$	5.75624	−	9.97011i	0.430242	−	0.745201i	0.996894	+	0.0787564i	$0.0250949\pi$
$180$	0.149300	+	0.846723i	0.0111282	+	0.0631110i
$181$	−1.48246	−	8.40744i	−0.110190	−	0.624920i	−0.989020	−	0.147784i	$-0.952786\pi$
$181$	−1.48246	−	8.40744i	−0.110190	−	0.624920i	0.878829	−	0.477136i	$-0.158325\pi$
$182$		0			0
$183$	13.1420	+	22.7627i	0.971487	+	1.68266i
$184$	−6.07604	+	5.09840i	−0.447931	+	0.375859i
$185$	4.08512	−	1.48686i	0.300344	−	0.109316i
$186$	25.9047	+	9.42853i	1.89942	+	0.691333i
$187$	0.798133	+	0.669713i	0.0583653	+	0.0489743i
$188$	−0.233956	+	1.32683i	−0.0170630	+	0.0967689i
$189$		0			0
$190$	1.73055	+	4.86581i	0.125547	+	0.353003i
$191$	18.3354			1.32671			0.663353	−	0.748307i	$-0.269133\pi$
$191$	18.3354			1.32671			0.663353	+	0.748307i	$0.269133\pi$
$192$	4.29813	−	24.3759i	0.310191	−	1.75918i
$193$	0.228026	+	0.191336i	0.0164137	+	0.0137727i	0.650958	−	0.759114i	$-0.274368\pi$
$193$	0.228026	+	0.191336i	0.0164137	+	0.0137727i	−0.634544	+	0.772887i	$0.718812\pi$
$194$	−11.9684	−	4.35613i	−0.859279	−	0.312752i
$195$	−6.12449	+	2.22913i	−0.438583	+	0.159631i
$196$		0			0
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	0.531203	−	0.847245i	$-0.321740\pi$
$197$	−6.57057	−	11.3806i	−0.468134	−	0.810832i	−0.999337	+	0.0364128i	$0.988407\pi$
$198$	−7.93629	+	13.7461i	−0.564008	+	0.976890i
$199$	0.0445774	+	0.252811i	0.00316001	+	0.0179213i	0.986347	−	0.164680i	$-0.0526593\pi$
$199$	0.0445774	+	0.252811i	0.00316001	+	0.0179213i	−0.983187	+	0.182602i	$0.941548\pi$
$200$	−2.16044	−	12.2525i	−0.152766	−	0.866382i
$201$	−11.0496	+	19.1385i	−0.779381	+	1.34993i
$202$	6.23055	+	10.7916i	0.438380	+	0.759297i
$203$		0			0
$204$	−0.233956	+	0.0851529i	−0.0163802	+	0.00596189i
$205$	−2.04576	−	0.744596i	−0.142882	−	0.0520048i
$206$	−5.68660	−	4.77163i	−0.396204	−	0.332455i
$207$	−2.47565	+	14.0401i	−0.172070	+	0.975856i
$208$	9.25671			0.641837
$209$	3.38666	−	9.09586i	0.234260	−	0.629174i
$210$		0			0
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	−0.966670	−	0.256024i	$-0.917587\pi$
$211$	0.425145	−	2.41112i	0.0292682	−	0.165988i	0.995938	+	0.0900364i	$0.0286983\pi$
$212$	0.401674	+	0.337044i	0.0275871	+	0.0231483i
$213$	25.1780	+	9.16404i	1.72517	+	0.627909i
$214$	12.9572	−	4.71605i	0.885738	−	0.322382i
$215$	−2.62836	+	2.20545i	−0.179252	+	0.150411i
$216$	−9.70826	−	16.8152i	−0.660564	−	1.14413i
$217$		0			0
$218$	0.426489	+	2.41874i	0.0288855	+	0.163818i
$219$	−0.694593	−	3.93923i	−0.0469362	−	0.266189i
$220$	0.180922	−	0.313366i	0.0121978	−	0.0211272i
$221$	−0.602196	−	1.04303i	−0.0405081	−	0.0701621i
$222$	−14.6912	+	12.3274i	−0.986008	+	0.827359i
$223$	−7.99660	+	2.91052i	−0.535492	+	0.194903i	−0.595589	−	0.803289i	$-0.703081\pi$
$223$	−7.99660	+	2.91052i	−0.535492	+	0.194903i	0.0600971	+	0.998193i	$0.480859\pi$
$224$		0			0
$225$	−17.1309	−	14.3745i	−1.14206	−	0.958301i
$226$	4.13816	−	23.4686i	0.275266	−	1.56111i
$227$	14.1506			0.939211			0.469606	−	0.882876i	$-0.344396\pi$
$227$	14.1506			0.939211			0.469606	+	0.882876i	$0.344396\pi$
$228$	1.47771	+	1.78763i	0.0978638	+	0.118389i
$229$	20.5330			1.35686			0.678430	−	0.734665i	$-0.262661\pi$
$229$	20.5330			1.35686			0.678430	+	0.734665i	$0.262661\pi$
$230$	−0.554378	+	3.14403i	−0.0365546	+	0.207311i
$231$		0			0
$232$	19.0287	+	6.92588i	1.24929	+	0.454706i
$233$	−16.5865	+	6.03698i	−1.08662	+	0.395496i	−0.822366	−	0.568959i	$-0.807346\pi$
$233$	−16.5865	+	6.03698i	−1.08662	+	0.395496i	−0.264249	+	0.964454i	$0.585124\pi$
$234$	14.0556	−	11.7940i	0.918841	−	0.770999i
$235$	3.20574	+	5.55250i	0.209119	+	0.362205i
$236$	0.582596	−	1.00909i	0.0379238	−	0.0656859i
$237$	−5.92262	−	33.5888i	−0.384715	−	2.18183i
$238$		0			0
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	−0.901556	−	0.432663i	$-0.857574\pi$
$239$	−1.17617	+	2.03719i	−0.0760804	+	0.131775i	0.825475	+	0.564438i	$0.190907\pi$
$240$	−4.55303	−	7.88609i	−0.293897	−	0.509045i
$241$	−10.5719	+	8.87089i	−0.680997	+	0.571424i	−0.916298	−	0.400498i	$-0.868837\pi$
$241$	−10.5719	+	8.87089i	−0.680997	+	0.571424i	0.235300	+	0.971923i	$0.424393\pi$
$242$	−7.64930	+	2.78412i	−0.491716	+	0.178970i
$243$	10.1518	+	3.69496i	0.651240	+	0.237032i
$244$	1.29220	+	1.08429i	0.0827249	+	0.0694144i
$245$		0			0
$246$	9.60401			0.612329
$247$	−7.27497	+	8.54147i	−0.462895	+	0.543481i
$248$	20.9172			1.32824
$249$	7.41534	−	42.0545i	0.469928	−	2.66510i
$250$	−8.37417	−	7.02676i	−0.529629	−	0.444412i
$251$	−3.91400	−	1.42458i	−0.247050	−	0.0899187i	0.215528	−	0.976498i	$-0.430853\pi$
$251$	−3.91400	−	1.42458i	−0.247050	−	0.0899187i	−0.462577	+	0.886579i	$0.653075\pi$
$252$		0			0
$253$	4.59627	−	3.85673i	0.288965	−	0.242470i
$254$	7.81702	+	13.5395i	0.490483	+	0.849542i
$255$	−0.592396	+	1.02606i	−0.0370973	+	0.0642544i
$256$	−0.763356	−	4.32921i	−0.0477098	−	0.270575i
$257$	−0.115867	−	0.657115i	−0.00722759	−	0.0409897i	0.980981	−	0.194105i	$-0.0621804\pi$
$257$	−0.115867	−	0.657115i	−0.00722759	−	0.0409897i	−0.988208	+	0.153116i	$0.951069\pi$
$258$	7.56805	−	13.1082i	0.471166	−	0.816084i
$259$		0			0
$260$	−0.320422	+	0.268866i	−0.0198717	+	0.0166744i
$261$	34.2028	−	12.4488i	2.11710	−	0.770561i
$262$	−2.33615	−	0.850290i	−0.144328	−	0.0525311i
$263$	8.73261	+	7.32753i	0.538476	+	0.451835i	0.871016	−	0.491254i	$-0.163461\pi$
$263$	8.73261	+	7.32753i	0.538476	+	0.451835i	−0.332540	+	0.943089i	$0.607906\pi$
$264$	−3.27719	+	18.5859i	−0.201697	+	1.14388i
$265$	2.49525			0.153282
$266$		0			0
$267$	29.6313			1.81341
$268$	−0.246282	+	1.39673i	−0.0150441	+	0.0853191i
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	0.0656400	−	0.997843i	$-0.479091\pi$
$269$	−14.8537	−	12.4637i	−0.905646	−	0.759927i	−0.971286	+	0.237916i	$0.923536\pi$
$270$	−7.34389	−	2.67296i	−0.446935	−	0.162671i
$271$	−12.5865	+	4.58110i	−0.764573	+	0.278282i	−0.694725	−	0.719276i	$-0.744474\pi$
$271$	−12.5865	+	4.58110i	−0.764573	+	0.278282i	−0.0698486	+	0.997558i	$0.522252\pi$
$272$	1.28905	−	1.08164i	0.0781600	−	0.0655841i
$273$		0			0
$274$	0.172304	−	0.298439i	0.0104093	−	0.0180294i
$275$	1.63429	+	9.26849i	0.0985511	+	0.558911i
$276$	0.248970	+	1.41198i	0.0149863	+	0.0849913i
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	0.466096	+	0.884734i	$0.345660\pi$
$277$	−8.87346	+	15.3693i	−0.533154	+	0.923450i	−0.999250	+	0.0387161i	$0.987673\pi$
$278$	−2.87211	−	4.97464i	−0.172258	−	0.298359i
$279$	28.8011	−	24.1670i	1.72428	−	1.44684i
$280$		0			0
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.225622	−	0.974215i	$-0.572442\pi$
$281$	−17.1766	−	6.25179i	−1.02467	−	0.372950i	−0.799050	+	0.601265i	$0.794664\pi$
$282$	−21.6668	−	18.1806i	−1.29024	−	1.08264i
$283$	−1.33497	+	7.57099i	−0.0793557	+	0.450049i	0.919077	+	0.394079i	$0.128936\pi$
$283$	−1.33497	+	7.57099i	−0.0793557	+	0.450049i	−0.998432	+	0.0559700i	$0.982175\pi$
$284$	1.71957			0.102038
$285$	10.8550	+	1.99654i	0.642997	+	0.118265i
$286$	−7.72193			−0.456608
$287$		0			0
$288$	−4.22281	−	3.54336i	−0.248832	−	0.208794i
$289$	15.7690	+	5.73946i	0.927590	+	0.337615i
$290$	7.65910	−	2.78768i	0.449758	−	0.163698i
$291$	−20.8516	+	17.4966i	−1.22234	+	1.02567i
$292$	−0.128356	−	0.222318i	−0.00751144	−	0.0130102i
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	−0.977660	−	0.210195i	$-0.932590\pi$
$293$	−5.25150	+	9.09586i	−0.306796	+	0.531386i	0.670864	+	0.741581i	$0.265924\pi$
$294$		0			0
$295$	−0.962859	−	5.46064i	−0.0560598	−	0.317931i
$296$	−7.27584	+	12.6021i	−0.422900	+	0.732484i
$297$	7.34389	+	12.7200i	0.426136	+	0.738089i
$298$	−17.0908	+	14.3409i	−0.990044	+	0.830745i
$299$	−6.51754	+	2.37219i	−0.376919	+	0.137187i
$300$	−2.11334	−	0.769193i	−0.122014	−	0.0444094i
$301$		0			0
$302$	1.02048	−	5.78742i	0.0587219	−	0.333028i
$303$	26.6313			1.52993
$304$	−13.5175	−	7.93761i	−0.775284	−	0.455253i
$305$	8.02734			0.459644
$306$	0.579193	−	3.28476i	0.0331102	−	0.187777i
$307$	8.95929	+	7.51774i	0.511334	+	0.429060i	0.861598	−	0.507591i	$-0.169464\pi$
$307$	8.95929	+	7.51774i	0.511334	+	0.429060i	−0.350264	+	0.936651i	$0.613908\pi$
$308$		0			0
$309$	−14.9081	+	5.42609i	−0.848091	+	0.308680i
$310$	6.44949	−	5.41177i	0.366307	−	0.307368i
$311$	7.98293	+	13.8268i	0.452670	+	0.784048i	0.998551	−	0.0538151i	$-0.0171382\pi$
$311$	7.98293	+	13.8268i	0.452670	+	0.784048i	−0.545881	+	0.837863i	$0.683805\pi$
$312$	10.9081	−	18.8933i	0.617548	−	1.06962i
$313$	4.62402	+	26.2241i	0.261365	+	1.48227i	0.779190	+	0.626788i	$0.215631\pi$
$313$	4.62402	+	26.2241i	0.261365	+	1.48227i	−0.517825	+	0.855487i	$0.673258\pi$
$314$	−2.25031	−	12.7622i	−0.126993	−	0.720211i
$315$		0			0
$316$	−1.09446	−	1.89565i	−0.0615679	−	0.106639i
$317$	22.6229	−	18.9829i	1.27063	−	1.06618i	0.276164	−	0.961111i	$-0.410937\pi$
$317$	22.6229	−	18.9829i	1.27063	−	1.06618i	0.994465	−	0.105073i	$-0.0335077\pi$
$318$	−10.3439	+	3.76487i	−0.580057	+	0.211123i
$319$	−14.3944	−	5.23913i	−0.805932	−	0.293335i
$320$	−5.79086	−	4.85911i	−0.323719	−	0.271632i
$321$	5.11721	−	29.0211i	0.285615	−	1.61980i
$322$		0			0
$323$	−0.0150147	+	2.03952i	−0.000835443	+	0.113482i
$324$	−0.576666			−0.0320370
$325$	1.88919	−	10.7141i	0.104793	−	0.594311i
$326$	−8.62314	−	7.23567i	−0.477592	−	0.400747i
$327$	4.93242	+	1.79525i	0.272763	+	0.0992777i
$328$	6.84776	−	2.49238i	0.378104	−	0.137619i
$329$		0			0
$330$	3.79813	+	6.57856i	0.209080	+	0.362138i
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	0.182371	+	0.983230i	$0.441623\pi$
$331$	−13.8327	+	23.9590i	−0.760317	+	1.31691i	−0.942687	+	0.333677i	$0.891710\pi$
$332$	−0.475900	−	2.69896i	−0.0261184	−	0.148125i
$333$	4.54189	+	25.7583i	0.248894	+	1.41155i
$334$	−2.71823	+	4.70810i	−0.148735	+	0.257616i
$335$	3.37464	+	5.84504i	0.184376	+	0.319349i
$336$		0			0
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.755934	−	0.654648i	$-0.772817\pi$
$337$	−16.7827	+	6.10841i	−0.914212	+	0.332746i	−0.158279	+	0.987394i	$0.550594\pi$
$338$	−8.07057	−	2.93745i	−0.438981	−	0.159776i
$339$	−39.0146	−	32.7371i	−2.11898	−	1.77804i
$340$	−0.0132037	+	0.0748822i	−0.000716074	+	0.00406106i
$341$	−15.8229			−0.856861
$342$	−30.6386	+	5.17015i	−1.65675	+	0.279569i
$343$		0			0
$344$	1.99432	−	11.3103i	0.107526	−	0.609813i
$345$	5.22668	+	4.38571i	0.281395	+	0.236119i
$346$	25.5030	+	9.28233i	1.37105	+	0.499021i
$347$	5.45084	−	1.98394i	0.292616	−	0.106504i	−0.191541	−	0.981485i	$-0.561348\pi$
$347$	5.45084	−	1.98394i	0.292616	−	0.106504i	0.484157	+	0.874981i	$0.339126\pi$
$348$	2.80406	−	2.35289i	0.150314	−	0.126128i
$349$	2.68614	+	4.65253i	0.143786	+	0.249044i	0.928919	−	0.370282i	$-0.120739\pi$
$349$	2.68614	+	4.65253i	0.143786	+	0.249044i	−0.785134	+	0.619326i	$0.787406\pi$
$350$		0			0
$351$	−2.94831	−	16.7207i	−0.157369	−	0.892485i
$352$	0.402856	+	2.28471i	0.0214723	+	0.121775i
$353$	−12.6172	+	21.8537i	−0.671546	+	1.16315i	0.305919	+	0.952057i	$0.401036\pi$
$353$	−12.6172	+	21.8537i	−0.671546	+	1.16315i	−0.977466	+	0.211095i	$0.932297\pi$
$354$	12.2306	+	21.1839i	0.650047	+	1.12591i
$355$	6.26857	−	5.25996i	0.332701	−	0.279169i
$356$	1.78699	−	0.650411i	0.0947102	−	0.0344717i
$357$		0			0
$358$	11.8819	+	9.97011i	0.627979	+	0.526937i
$359$	1.16116	−	6.58526i	0.0612837	−	0.347557i	−0.938712	−	0.344702i	$-0.887980\pi$
$359$	1.16116	−	6.58526i	0.0612837	−	0.347557i	0.999996	−	0.00285518i	$-0.000908833\pi$
$360$	−13.6955			−0.721818
$361$	17.9479	−	6.23481i	0.944626	−	0.328148i
$362$	11.5021			0.604535
$363$	−3.02094	+	17.1326i	−0.158558	+	0.899230i
$364$		0			0
$365$	−1.14796	−	0.417822i	−0.0600868	−	0.0218698i
$366$	−33.2768	+	12.1118i	−1.73941	+	0.633092i
$367$	−6.21941	+	5.21870i	−0.324650	+	0.272414i	−0.790516	−	0.612441i	$-0.790188\pi$
$367$	−6.21941	+	5.21870i	−0.324650	+	0.272414i	0.465865	+	0.884856i	$0.345743\pi$
$368$	−4.84524	−	8.39220i	−0.252575	−	0.437473i
$369$	6.54916	−	11.3435i	0.340936	−	0.590518i
$370$	1.01707	+	5.76811i	0.0528752	+	0.299870i
$371$		0			0
$372$	1.89053	−	3.27449i	0.0980194	−	0.169775i
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.822967	−	0.568090i	$-0.807683\pi$
$373$	−17.4488	−	30.2222i	−0.903463	−	1.56484i	−0.0804968	−	0.996755i	$-0.525651\pi$
$374$	−1.07532	+	0.902302i	−0.0556036	+	0.0466569i
$375$	−21.9538	+	7.99054i	−1.13369	+	0.412630i
$376$	−20.1668	−	7.34013i	−1.04003	−	0.378538i
$377$	13.5646	+	11.3821i	0.698615	+	0.586207i
$378$		0			0
$379$	1.70140			0.0873950			0.0436975	−	0.999045i	$-0.486086\pi$
$379$	1.70140			0.0873950			0.0436975	+	0.999045i	$0.486086\pi$
$380$	0.698463	−	0.117863i	0.0358304	−	0.00604624i
$381$	33.4124			1.71177
$382$	−4.28968	+	24.3280i	−0.219479	+	1.24473i
$383$	−2.24969	−	1.88771i	−0.114954	−	0.0964575i	0.583499	−	0.812114i	$-0.301683\pi$
$383$	−2.24969	−	1.88771i	−0.114954	−	0.0964575i	−0.698453	+	0.715656i	$0.746128\pi$
$384$	25.6989	+	9.35365i	1.31144	+	0.477326i
$385$		0			0
$386$	−0.307218	+	0.257787i	−0.0156370	+	0.0131210i
$387$	−10.3216	−	17.8775i	−0.524677	−	0.908767i
$388$	−0.873455	+	1.51287i	−0.0443430	+	0.0768043i
$389$	−4.26604	−	24.1939i	−0.216297	−	1.22668i	−0.878642	−	0.477482i	$-0.841550\pi$
$389$	−4.26604	−	24.1939i	−0.216297	−	1.22668i	0.662344	−	0.749199i	$-0.269562\pi$
$390$	−1.52481	−	8.64766i	−0.0772120	−	0.437891i
$391$	−0.630415	+	1.09191i	−0.0318815	+	0.0552203i
$392$		0			0
$393$	−4.07011	+	3.41523i	−0.205310	+	0.172275i
$394$	16.6373	−	6.05547i	0.838174	−	0.305070i
$395$	−9.78833	−	3.56266i	−0.492504	−	0.179257i
$396$	1.66772	+	1.39938i	0.0838060	+	0.0703216i
$397$	5.52822	−	31.3521i	0.277453	−	1.57352i	−0.453606	−	0.891202i	$-0.649863\pi$
$397$	5.52822	−	31.3521i	0.277453	−	1.57352i	0.731059	−	0.682314i	$-0.239026\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	−0.0150147	+	0.0851529i	−0.000749801	+	0.00425233i	−0.985180	−	0.171522i	$-0.945132\pi$
$401$	−0.0150147	+	0.0851529i	−0.000749801	+	0.00425233i	0.984431	+	0.175774i	$0.0562428\pi$
$402$	−22.8084	−	19.1385i	−1.13758	−	0.954543i
$403$	17.1878	+	6.25584i	0.856185	+	0.311626i
$404$	1.60607	−	0.584561i	0.0799048	−	0.0290830i
$405$	−2.10220	+	1.76395i	−0.104459	+	0.0876515i
$406$		0			0
$407$	5.50387	−	9.53298i	0.272817	−	0.472532i
$408$	−0.688663	−	3.90560i	−0.0340939	−	0.193356i
$409$	−3.47400	−	19.7021i	−0.171778	−	0.974204i	−0.941797	−	0.336182i	$-0.890864\pi$
$409$	−3.47400	−	19.7021i	−0.171778	−	0.974204i	0.770019	−	0.638021i	$-0.220247\pi$
$410$	1.46657	−	2.54017i	0.0724286	−	0.125450i
$411$	−0.368241	−	0.637812i	−0.0181640	−	0.0314609i
$412$	−0.779963	+	0.654467i	−0.0384260	+	0.0322433i
$413$		0			0
$414$	−18.0496	−	6.56953i	−0.887091	−	0.322875i
$415$	−9.99067	−	8.38316i	−0.490423	−	0.411513i
$416$	0.465690	−	2.64106i	0.0228323	−	0.129488i
$417$	−12.2763			−0.601174
$418$	11.2763	+	6.62154i	0.551542	+	0.323870i
$419$	−25.4097			−1.24135			−0.620673	−	0.784070i	$-0.713141\pi$
$419$	−25.4097			−1.24135			−0.620673	+	0.784070i	$0.713141\pi$
$420$		0			0
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	0.720702	−	0.693245i	$-0.243820\pi$
$421$	3.34730	+	2.80872i	0.163137	+	0.136888i	−0.557565	+	0.830134i	$0.688264\pi$
$422$	3.09967	+	1.12819i	0.150890	+	0.0549193i
$423$	−36.2486	+	13.1934i	−1.76247	+	0.641485i
$424$	−6.39827	+	5.36879i	−0.310727	+	0.260731i
$425$	−0.988856	−	1.71275i	−0.0479665	−	0.0830805i
$426$	−18.0496	+	31.2629i	−0.874507	+	1.51469i
$427$		0			0
$428$	−0.328411	−	1.86251i	−0.0158744	−	0.0900279i
$429$	−8.25150	+	14.2920i	−0.398386	+	0.690025i
$430$	−2.31134	−	4.00335i	−0.111463	−	0.193059i
$431$	−29.3444	+	24.6228i	−1.41347	+	1.18604i	−0.458736	+	0.888572i	$0.651698\pi$
$431$	−29.3444	+	24.6228i	−1.41347	+	1.18604i	−0.954732	+	0.297468i	$0.903858\pi$
$432$	22.2913	−	8.11338i	1.07249	−	0.390355i
$433$	−17.0376	−	6.20118i	−0.818775	−	0.298010i	−0.101532	−	0.994832i	$-0.532374\pi$
$433$	−17.0376	−	6.20118i	−0.818775	−	0.298010i	−0.717244	+	0.696823i	$0.754597\pi$
$434$		0			0
$435$	3.02481	−	17.1546i	0.145029	−	0.822499i
$436$	0.336867			0.0161330
$437$	11.5517	+	2.12467i	0.552592	+	0.101637i
$438$	5.38919			0.257505
$439$	1.05762	−	5.99806i	0.0504774	−	0.286272i	−0.949112	−	0.314940i	$-0.898016\pi$
$439$	1.05762	−	5.99806i	0.0504774	−	0.286272i	0.999589	+	0.0286685i	$0.00912670\pi$
$440$	4.41534	+	3.70491i	0.210493	+	0.176625i
$441$		0			0
$442$	1.52481	−	0.554987i	0.0725280	−	0.0263981i
$443$	−22.8995	+	19.2149i	−1.08799	+	0.912928i	−0.996559	−	0.0828833i	$-0.973587\pi$
$443$	−22.8995	+	19.2149i	−1.08799	+	0.912928i	−0.0914266	+	0.995812i	$0.529143\pi$
$444$	1.31521	+	2.27801i	0.0624170	+	0.108109i
$445$	4.52481	−	7.83721i	0.214497	−	0.371519i
$446$	−1.99092	−	11.2910i	−0.0942726	−	0.534646i
$447$	8.27972	+	46.9566i	0.391617	+	2.22097i
$448$		0			0
$449$	5.62495	+	9.74270i	0.265458	+	0.459787i	0.967683	−	0.252168i	$-0.0811435\pi$
$449$	5.62495	+	9.74270i	0.265458	+	0.459787i	−0.702226	+	0.711955i	$0.747810\pi$
$450$	23.0804	−	19.3667i	1.08802	−	0.912957i
$451$	−5.18004	+	1.88538i	−0.243919	+	0.0887792i
$452$	−3.07145	−	1.11792i	−0.144469	−	0.0525824i
$453$	−9.62108	−	8.07305i	−0.452038	−	0.379305i
$454$	−3.31062	+	18.7755i	−0.155375	+	0.881176i
$455$		0			0
$456$	−32.1300	+	18.2362i	−1.50463	+	0.853989i
$457$	−23.3901			−1.09414			−0.547072	−	0.837086i	$-0.684258\pi$
$457$	−23.3901			−1.09414			−0.547072	+	0.837086i	$0.684258\pi$
$458$	−4.80381	+	27.2438i	−0.224468	+	1.27302i
$459$	−2.36437	−	1.98394i	−0.110359	−	0.0926025i
$460$	0.411474	+	0.149764i	0.0191851	+	0.00698280i
$461$	−34.4149	+	12.5260i	−1.60286	+	0.583395i	−0.980011	−	0.198945i	$-0.936249\pi$
$461$	−34.4149	+	12.5260i	−1.60286	+	0.583395i	−0.622853	+	0.782339i	$0.714026\pi$
$462$		0			0
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.540534	+	0.841322i	$0.318222\pi$
$463$	21.4932	+	37.2273i	0.998873	+	1.73010i	0.458340	+	0.888777i	$0.348444\pi$
$464$	−12.3701	+	21.4256i	−0.574265	+	0.994657i
$465$	−3.12449	−	17.7198i	−0.144895	−	0.821738i
$466$	−4.12954	−	23.4198i	−0.191297	−	1.08490i
$467$	12.7981	−	22.1670i	0.592227	−	1.02577i	−0.401705	−	0.915769i	$-0.631582\pi$
$467$	12.7981	−	22.1670i	0.592227	−	1.02577i	0.993932	−	0.109998i	$-0.0350845\pi$
$468$	−1.25830	−	2.17945i	−0.0581651	−	0.100745i
$469$		0			0
$470$	−8.11721	+	2.95442i	−0.374419	+	0.136277i
$471$	−26.0253	−	9.47243i	−1.19918	−	0.436466i
$472$	14.2181	+	11.9304i	0.654439	+	0.549140i
$473$	−1.50862	+	8.55580i	−0.0693663	+	0.393396i
$474$	45.9522			2.11066
$475$	−11.9461	+	14.0258i	−0.548124	+	0.643548i
$476$		0			0
$477$	−2.60694	+	14.7847i	−0.119364	+	0.676946i
$478$	−2.42783	−	2.03719i	−0.111046	−	0.0931791i
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.986885	−	0.161424i	$-0.0516088\pi$
$479$	35.8739	+	13.0570i	1.63912	+	0.596591i	0.652236	+	0.758016i	$0.273831\pi$
$480$	−2.47906	+	0.902302i	−0.113153	+	0.0411843i
$481$	−9.74763	+	8.17923i	−0.444453	+	0.372941i
$482$	−9.29679	−	16.1025i	−0.423457	−	0.733449i
$483$		0			0
$484$	0.193877	+	1.09953i	0.00881261	+	0.0499788i
$485$	1.44356	+	8.18685i	0.0655488	+	0.371746i
$486$	−7.27766	+	12.6053i	−0.330121	+	0.571787i
$487$	−3.88191	−	6.72367i	−0.175906	−	0.304678i	0.764568	−	0.644543i	$-0.222952\pi$
$487$	−3.88191	−	6.72367i	−0.175906	−	0.304678i	−0.940475	+	0.339864i	$0.889619\pi$
$488$	−20.5835	+	17.2716i	−0.931773	+	0.781850i
$489$	−22.6065	+	8.22811i	−1.02230	+	0.372088i
$490$		0			0
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.994596	−	0.103822i	$-0.966893\pi$
$491$	−28.1313	−	23.6050i	−1.26955	−	1.06528i	−0.274954	−	0.961457i	$-0.588663\pi$
$492$	0.228741	−	1.29725i	0.0103124	−	0.0584848i
$493$	3.21894			0.144974
$494$	−9.63104	−	11.6510i	−0.433321	−	0.524201i
$495$	10.3601			0.465651
$496$	−4.43763	+	25.1671i	−0.199256	+	1.13003i
$497$		0			0
$498$	54.0642	+	19.6778i	2.42268	+	0.881782i
$499$	−4.62923	+	1.68490i	−0.207233	+	0.0754266i	−0.443551	−	0.896249i	$-0.646281\pi$
$499$	−4.62923	+	1.68490i	−0.207233	+	0.0754266i	0.236318	+	0.971676i	$0.424059\pi$
$500$	−1.14858	+	0.963777i	−0.0513663	+	0.0431014i
$501$	5.80928	+	10.0620i	0.259539	+	0.449535i
$502$	2.80587	−	4.85992i	0.125232	−	0.216909i
$503$	−5.72163	−	32.4490i	−0.255115	−	1.44683i	−0.795778	−	0.605589i	$-0.792938\pi$
$503$	−5.72163	−	32.4490i	−0.255115	−	1.44683i	0.540663	−	0.841239i	$-0.318173\pi$
$504$		0			0
$505$	4.06670	−	7.04374i	0.180966	−	0.313442i
$506$	4.04189	+	7.00076i	0.179684	+	0.311222i
$507$	−14.0608	+	11.7984i	−0.624461	+	0.523985i
$508$	2.01501	−	0.733405i	0.0894018	−	0.0325396i
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.572728	−	0.819746i	$-0.694115\pi$
$509$	−34.7075	−	12.6325i	−1.53839	−	0.559926i	−0.965657	+	0.259819i	$0.916337\pi$
$510$	−1.22281	−	1.02606i	−0.0541470	−	0.0454347i
$511$		0			0
$512$	24.9186			1.10126
$513$	−10.0326	+	26.9453i	−0.442948	+	1.18967i
$514$	0.898986			0.0396526
$515$	−0.841367	+	4.77163i	−0.0370750	+	0.210263i
$516$	−1.59034	−	1.33445i	−0.0700107	−	0.0587459i
$517$	15.2554	+	5.55250i	0.670930	+	0.244199i
$518$		0			0
$519$	44.4320	−	37.2829i	1.95035	−	1.63654i
$520$	−3.33140	−	5.77016i	−0.146092	−	0.253038i
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	−0.746126	−	0.665804i	$-0.768088\pi$
$521$	4.64590	−	8.04693i	0.203540	−	0.352542i	0.949667	+	0.313262i	$0.101422\pi$
$522$	8.51548	+	48.2937i	0.372713	+	2.11376i
$523$	4.93423	+	27.9834i	0.215759	+	1.22363i	0.879585	+	0.475742i	$0.157820\pi$
$523$	4.93423	+	27.9834i	0.215759	+	1.22363i	−0.663826	+	0.747887i	$0.731068\pi$
$524$	−0.170493	+	0.295303i	−0.00744802	+	0.0129004i
$525$		0			0
$526$	−11.7654	+	9.87236i	−0.512996	+	0.430455i
$527$	3.12449	−	1.13722i	0.136105	−	0.0495381i
$528$	−21.6668	−	7.88609i	−0.942928	−	0.343198i
$529$	−12.0569	−	10.1169i	−0.524213	−	0.439867i
$530$	−0.583778	+	3.31077i	−0.0253577	+	0.143811i
$531$	33.3610			1.44775
$532$		0			0
$533$	6.37227			0.276014
$534$	−6.93242	+	39.3157i	−0.299995	+	1.70136i
$535$	−6.89440	−	5.78509i	−0.298071	−	0.250111i
$536$	−21.2294	−	7.72686i	−0.916969	−	0.333749i
$537$	31.1498	−	11.3376i	1.34421	−	0.489253i
$538$	20.0123	−	16.7923i	0.862793	−	0.723969i
$539$		0			0
$540$	−0.535959	+	0.928309i	−0.0230640	+	0.0399480i
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	0.988249	+	0.152852i	$0.0488458\pi$
$541$	2.60220	+	14.7578i	0.111877	+	0.634487i	−0.876372	+	0.481635i	$0.840043\pi$
$542$	−3.13366	−	17.7718i	−0.134602	−	0.763366i
$543$	12.2909	−	21.2884i	0.527451	−	0.913572i
$544$	−0.243756	−	0.422197i	−0.0104509	−	0.0181016i
$545$	1.22803	−	1.03044i	0.0526028	−	0.0441390i
$546$		0			0
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	0.418926	−	0.908020i	$-0.362407\pi$
$547$	3.65270	+	1.32948i	0.156178	+	0.0568443i	−0.262748	+	0.964864i	$0.584629\pi$
$548$	−0.0362077	−	0.0303818i	−0.00154672	−	0.00129785i
$549$	−8.38666	+	47.5631i	−0.357934	+	2.02994i
$550$	−12.6800			−0.540679
$551$	−10.0483	−	28.2529i	−0.428071	−	1.20361i
$552$	−22.8384			−0.972068
$553$		0			0
$554$	−18.3164	−	15.3693i	−0.778189	−	0.652978i
$555$	11.7626	+	4.28125i	0.499296	+	0.181729i
$556$	−0.740352	+	0.269466i	−0.0313979	+	0.0114279i
$557$	10.1152	−	8.48762i	0.428593	−	0.359632i	−0.402828	−	0.915276i	$-0.631973\pi$
$557$	10.1152	−	8.48762i	0.428593	−	0.359632i	0.831420	+	0.555644i	$0.187528\pi$
$558$	25.3273	+	43.8681i	1.07219	+	1.85709i
$559$	5.02141	−	8.69734i	0.212383	−	0.367858i
$560$		0			0
$561$	0.520945	+	2.95442i	0.0219943	+	0.124736i
$562$	12.3136	−	21.3278i	0.519418	−	0.899659i
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	0.956543	−	0.291593i	$-0.0941852\pi$
$563$	5.35638	+	9.27752i	0.225745	+	0.391001i	−0.730798	+	0.682594i	$0.760852\pi$
$564$	−2.97178	+	2.49362i	−0.125135	+	0.105000i
$565$	−14.6163	+	5.31991i	−0.614914	+	0.223810i
$566$	−9.73308	−	3.54255i	−0.409112	−	0.148905i
$567$		0			0
$568$	−4.75641	+	26.9749i	−0.199574	+	1.13184i
$569$	−13.4706			−0.564717			−0.282358	−	0.959309i	$-0.591117\pi$
$569$	−13.4706			−0.564717			−0.282358	+	0.959309i	$0.591117\pi$
$570$	−5.18866	+	13.9357i	−0.217329	+	0.583701i
$571$	12.6655			0.530035			0.265017	−	0.964244i	$-0.414622\pi$
$571$	12.6655			0.530035			0.265017	+	0.964244i	$0.414622\pi$
$572$	−0.183915	+	1.04303i	−0.00768988	+	0.0436115i
$573$	40.4432	+	33.9358i	1.68954	+	1.41769i
$574$		0			0
$575$	−10.7023	+	3.89533i	−0.446318	+	0.162447i
$576$	34.8410	−	29.2350i	1.45171	−	1.21813i
$577$	−5.27719	−	9.14036i	−0.219692	−	0.380518i	0.735022	−	0.678044i	$-0.237172\pi$
$577$	−5.27719	−	9.14036i	−0.219692	−	0.380518i	−0.954714	+	0.297526i	$0.903839\pi$
$578$	−11.3045	+	19.5800i	−0.470206	+	0.814421i
$579$	0.148833	+	0.844075i	0.00618530	+	0.0350786i
$580$	−0.194126	−	1.10094i	−0.00806064	−	0.0457142i
$581$		0			0
$582$	−18.3366	−	31.7600i	−0.760077	−	1.31649i
$583$	4.84002	−	4.06126i	0.200453	−	0.168200i
$584$	3.84255	−	1.39857i	0.159006	−	0.0578734i
$585$	−11.2537	−	4.09602i	−0.465284	−	0.169350i
$586$	−10.8400	−	9.09586i	−0.447797	−	0.375746i
$587$	3.32619	−	18.8638i	0.137287	−	0.778591i	−0.835954	−	0.548800i	$-0.815085\pi$
$587$	3.32619	−	18.8638i	0.137287	−	0.778591i	0.973240	−	0.229791i	$-0.0738041\pi$
$588$		0			0
$589$	−19.7349	−	23.8739i	−0.813162	−	0.983706i
$590$	7.47060			0.307560
$591$	6.57057	−	37.2636i	0.270277	−	1.53282i
$592$	−13.6190	−	11.4277i	−0.559738	−	0.469676i
$593$	−8.17024	−	2.97373i	−0.335512	−	0.122116i	0.168770	−	0.985655i	$-0.446020\pi$
$593$	−8.17024	−	2.97373i	−0.335512	−	0.122116i	−0.504282	+	0.863539i	$0.668243\pi$
$594$	−18.5954	+	6.76817i	−0.762978	+	0.277701i
$595$		0			0
$596$	1.53003	+	2.65009i	0.0626724	+	0.108552i
$597$	−0.369585	+	0.640140i	−0.0151261	+	0.0261992i
$598$	−1.62267	−	9.20264i	−0.0663561	−	0.376324i
$599$	3.44373	+	19.5303i	0.140707	+	0.797988i	0.970715	+	0.240236i	$0.0772248\pi$
$599$	3.44373	+	19.5303i	0.140707	+	0.797988i	−0.830008	+	0.557752i	$0.811664\pi$
$600$	17.9119	−	31.0244i	0.731252	−	1.26657i
$601$	−16.8807	−	29.2383i	−0.688579	−	1.19265i	−0.972298	−	0.233747i	$-0.924901\pi$
$601$	−16.8807	−	29.2383i	−0.688579	−	1.19265i	0.283718	−	0.958908i	$-0.408432\pi$
$602$		0			0
$603$	−38.1584	+	13.8885i	−1.55393	+	0.565584i
$604$	−0.757426	−	0.275681i	−0.0308192	−	0.0112173i
$605$	4.07011	+	3.41523i	0.165473	+	0.138849i
$606$	−6.23055	+	35.3352i	−0.253099	+	1.43540i
$607$	−35.2850			−1.43217			−0.716087	−	0.698011i	$-0.754068\pi$
$607$	−35.2850			−1.43217			−0.716087	+	0.698011i	$0.754068\pi$
$608$	−2.94475	+	3.45740i	−0.119425	+	0.140216i
$609$		0			0
$610$	−1.87804	+	10.6509i	−0.0760397	+	0.431242i
$611$	−14.3760	−	12.0629i	−0.581590	−	0.488012i
$612$	−0.429892	−	0.156468i	−0.0173774	−	0.00632485i
$613$	−17.3405	+	6.31142i	−0.700376	+	0.254916i	−0.667571	−	0.744546i	$-0.732666\pi$
$613$	−17.3405	+	6.31142i	−0.700376	+	0.254916i	−0.0328044	+	0.999462i	$0.510444\pi$
$614$	−12.0708	+	10.1286i	−0.487139	+	0.408758i
$615$	−3.13429	−	5.42874i	−0.126387	−	0.218908i
$616$		0			0
$617$	−6.19671	−	35.1433i	−0.249470	−	1.41482i	−0.809878	−	0.586598i	$-0.800467\pi$
$617$	−6.19671	−	35.1433i	−0.249470	−	1.41482i	0.560408	−	0.828217i	$-0.310644\pi$
$618$	−3.71167	−	21.0499i	−0.149305	−	0.846752i
$619$	1.82976	−	3.16923i	0.0735441	−	0.127382i	−0.826908	−	0.562337i	$-0.809902\pi$
$619$	1.82976	−	3.16923i	0.0735441	−	0.127382i	0.900452	+	0.434955i	$0.143236\pi$
$620$	−0.577382	−	1.00005i	−0.0231882	−	0.0401631i
$621$	−13.6159	+	11.4251i	−0.546386	+	0.458472i
$622$	−20.2135	+	7.35710i	−0.810487	+	0.294993i
$623$		0			0
$624$	20.4179	+	17.1326i	0.817369	+	0.685854i
$625$	2.43077	−	13.7856i	0.0972308	−	0.551423i
$626$	−35.8767			−1.43392
$627$	24.3050	−	13.7949i	0.970648	−	0.550917i
$628$	−1.77744			−0.0709275
$629$	−0.401674	+	2.27801i	−0.0160158	+	0.0908301i
$630$		0			0
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	0.356826	−	0.934171i	$-0.383859\pi$
$631$	0.745977	+	0.271514i	0.0296969	+	0.0108088i	−0.327129	+	0.944980i	$0.606081\pi$
$632$	32.7645	−	11.9253i	1.30330	−	0.474362i
$633$	5.40033	−	4.53141i	0.214644	−	0.180108i
$634$	19.8942	+	34.4578i	0.790101	+	1.36850i
$635$	5.10220	−	8.83726i	0.202474	−	0.350696i
$636$	0.262174	+	1.48686i	0.0103959	+	0.0589579i
$637$		0			0
$638$	10.3191	−	17.8732i	0.408536	−	0.707605i
$639$	24.6168	+	42.6375i	0.973826	+	1.68672i
$640$	6.39827	−	5.36879i	0.252914	−	0.212220i
$641$	−27.6104	+	10.0494i	−1.09055	+	0.396926i	−0.823823	−	0.566847i	$-0.808163\pi$
$641$	−27.6104	+	10.0494i	−1.09055	+	0.396926i	−0.266723	+	0.963773i	$0.585941\pi$
$642$	37.3089	+	13.5793i	1.47246	+	0.535933i
$643$	−17.0168	−	14.2788i	−0.671078	−	0.563101i	0.242306	−	0.970200i	$-0.422096\pi$
$643$	−17.0168	−	14.2788i	−0.671078	−	0.563101i	−0.913384	+	0.407098i	$0.866541\pi$
$644$		0			0
$645$	−9.87939			−0.389000
$646$	−2.70258	−	0.497079i	−0.106332	−	0.0195573i
$647$	−11.2591			−0.442640			−0.221320	−	0.975201i	$-0.571037\pi$
$647$	−11.2591			−0.442640			−0.221320	+	0.975201i	$0.571037\pi$
$648$	1.59508	−	9.04617i	0.0626608	−	0.355367i
$649$	−10.7554	−	9.02482i	−0.422185	−	0.354255i
$650$	13.7738	+	5.01325i	0.540252	+	0.196636i
$651$		0			0
$652$	−1.18273	+	0.992431i	−0.0463194	+	0.0388666i
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	−3.53596	+	6.12446i	−0.138267	+	0.239485i
$655$	0.281774	+	1.59802i	0.0110098	+	0.0624399i
$656$	1.54601	+	8.76785i	0.0603615	+	0.342327i
$657$	3.67499	−	6.36527i	0.143375	−	0.248333i
$658$		0			0
$659$	21.4691	−	18.0147i	0.836317	−	0.701753i	−0.120415	−	0.992724i	$-0.538423\pi$
$659$	21.4691	−	18.0147i	0.836317	−	0.701753i	0.956732	+	0.290970i	$0.0939781\pi$
$660$	0.979055	−	0.356347i	0.0381097	−	0.0138708i
$661$	10.6823	+	3.88803i	0.415492	+	0.151227i	0.541303	−	0.840827i	$-0.317931\pi$
$661$	10.6823	+	3.88803i	0.415492	+	0.151227i	−0.125811	+	0.992054i	$0.540153\pi$
$662$	−28.5533	−	23.9590i	−1.10975	−	0.931194i
$663$	0.602196	−	3.41523i	0.0233874	−	0.132636i
$664$	43.6551			1.69415
$665$		0			0
$666$	−35.2395			−1.36550
$667$	3.21894	−	18.2555i	0.124638	−	0.706857i
$668$	0.571203	+	0.479297i	0.0221005	+	0.0185445i
$669$	−23.0253	−	8.38052i	−0.890209	−	0.324010i
$670$	−8.54488	+	3.11008i	−0.330118	+	0.120153i
$671$	15.5706	−	13.0653i	0.601095	−	0.504379i
$672$		0			0
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	−0.661035	−	0.750355i	$-0.729883\pi$
$673$	8.28359	−	14.3476i	0.319309	−	0.553059i	0.980344	+	0.197296i	$0.0632160\pi$
$674$	−4.17840	−	23.6969i	−0.160946	−	0.912769i
$675$	−4.84137	−	27.4568i	−0.186344	−	1.05681i
$676$	−0.588993	+	1.02017i	−0.0226536	+	0.0392371i
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	0.765878	−	0.642986i	$-0.222305\pi$
$677$	−4.52481	−	7.83721i	−0.173903	−	0.301208i	−0.939781	+	0.341777i	$0.888971\pi$
$678$	52.5642	−	44.1066i	2.01872	−	1.69390i
$679$		0			0
$680$	−1.13816	−	0.414255i	−0.0436463	−	0.0158859i
$681$	31.2126	+	26.1905i	1.19607	+	1.00362i
$682$	3.70187	−	20.9943i	0.141752	−	0.803914i
$683$	8.73143			0.334099			0.167049	−	0.985949i	$-0.446576\pi$
$683$	8.73143			0.334099			0.167049	+	0.985949i	$0.446576\pi$
$684$	−0.0313737	+	4.26163i	−0.00119960	+	0.162947i
$685$	−0.224927			−0.00859402
$686$		0			0
$687$	45.2904	+	38.0032i	1.72794	+	1.44991i
$688$	13.1853	+	4.79904i	0.502683	+	0.182962i
$689$	−6.86319	+	2.49800i	−0.261467	+	0.0951661i
$690$	−7.04189	+	5.90885i	−0.268080	+	0.224946i
$691$	17.3601	+	30.0686i	0.660409	+	1.14386i	0.980508	+	0.196478i	$0.0629504\pi$
$691$	17.3601	+	30.0686i	0.660409	+	1.14386i	−0.320099	+	0.947384i	$0.603716\pi$
$692$	1.86122	−	3.22372i	0.0707528	−	0.122547i
$693$		0			0
$694$	1.35710	+	7.69648i	0.0515147	+	0.292154i
$695$	−1.87464	+	3.24697i	−0.0711091	+	0.123164i
$696$	29.1536	+	50.4956i	1.10507	+	1.91403i
$697$	0.887374	−	0.744596i	0.0336117	−	0.0282036i
$698$	−6.80154	+	2.47556i	−0.257442	+	0.0937012i
$699$	−47.7588	−	17.3828i	−1.80640	−	0.657478i
$700$		0			0
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	−0.528397	−	0.848997i	$-0.677207\pi$
$701$	6.84436	−	38.8163i	0.258508	−	1.46607i	0.786905	−	0.617074i	$-0.211682\pi$
$702$	22.8753			0.863371
$703$	21.2481	−	3.58553i	0.801387	−	0.135231i
$704$	−19.1411			−0.721409
$705$	−3.20574	+	18.1806i	−0.120735	+	0.684722i
$706$	−26.0442	−	21.8537i	−0.980185	−	0.822473i
$707$		0			0
$708$	3.15270	−	1.14749i	0.118486	−	0.0431253i
$709$	−31.5009	+	26.4324i	−1.18304	+	0.992690i	−0.183088	+	0.983096i	$0.558609\pi$
$709$	−31.5009	+	26.4324i	−1.18304	+	0.992690i	−0.999954	+	0.00959399i	$0.996946\pi$
$710$	5.51249	+	9.54791i	0.206880	+	0.358327i
$711$	31.3357	−	54.2751i	1.17518	−	2.03548i
$712$	5.26011	+	29.8316i	0.197131	+	1.11799i
$713$	−3.32501	−	18.8571i	−0.124523	−	0.706202i
$714$		0			0
$715$	2.52007	+	4.36488i	0.0942452	+	0.163237i
$716$	1.62970	−	1.36748i	0.0609047	−	0.0511051i
$717$	−6.36484	+	2.31661i	−0.237699	+	0.0865154i
$718$	8.46585	+	3.08132i	0.315943	+	0.114994i
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.999238	+	0.0390200i	$0.0124236\pi$
$719$	32.4768	+	27.2513i	1.21118	+	1.01630i	0.211943	+	0.977282i	$0.432021\pi$
$720$	2.90554	−	16.4782i	0.108283	−	0.614105i
$721$		0			0
$722$	4.07351	+	25.2724i	0.151600	+	0.940543i
$723$	−39.7374			−1.47785
$724$	0.273947	−	1.55363i	0.0101812	−	0.0577403i
$725$	22.2743	+	18.6903i	0.827245	+	0.694141i
$726$	−22.0253	−	8.01655i	−0.817435	−	0.297522i
$727$	48.5411	−	17.6675i	1.80029	−	0.655251i	0.801965	−	0.597371i	$-0.203788\pi$
$727$	48.5411	−	17.6675i	1.80029	−	0.655251i	0.998324	−	0.0578805i	$-0.0184342\pi$
$728$		0			0
$729$	20.2344	+	35.0470i	0.749423	+	1.29804i
$730$	0.822948	−	1.42539i	0.0304587	−	0.0527560i
$731$	−0.317018	−	1.79790i	−0.0117254	−	0.0664978i
$732$	0.843426	+	4.78331i	0.0311739	+	0.176796i
$733$	−11.4581	+	19.8460i	−0.423215	+	0.733030i	−0.996252	−	0.0864997i	$-0.972432\pi$
$733$	−11.4581	+	19.8460i	−0.423215	+	0.733030i	0.573037	+	0.819530i	$0.305765\pi$
$734$	−5.46926	−	9.47303i	−0.201874	−	0.349656i
$735$		0			0
$736$	−2.63816	+	0.960210i	−0.0972437	+	0.0353938i
$737$	16.0591	+	5.84504i	0.591545	+	0.215305i
$738$	13.5186	+	11.3435i	0.497628	+	0.417559i
$739$	4.88413	−	27.6993i	0.179666	−	1.01894i	−0.752954	−	0.658074i	$-0.771372\pi$
$739$	4.88413	−	27.6993i	0.179666	−	1.01894i	0.932619	−	0.360862i	$-0.117517\pi$
$740$	0.803348			0.0295317
$741$	−31.8555	+	5.37549i	−1.17024	+	0.197474i
$742$		0			0
$743$	1.06489	−	6.03931i	0.0390671	−	0.221561i	−0.959024	−	0.283326i	$-0.908562\pi$
$743$	1.06489	−	6.03931i	0.0390671	−	0.221561i	0.998091	+	0.0617657i	$0.0196731\pi$
$744$	46.1377	+	38.7142i	1.69149	+	1.41933i
$745$	13.6839	+	4.98054i	0.501340	+	0.182473i
$746$	44.1819	−	16.0809i	1.61761	−	0.588763i
$747$	60.1093	−	50.4377i	2.19928	−	1.84542i
$748$	0.0962667	+	0.166739i	0.00351986	+	0.00609657i
$749$		0			0
$750$	−5.46585	−	30.9984i	−0.199585	−	1.13190i
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	0.997450	−	0.0713710i	$-0.0227374\pi$
$751$	0.979522	+	5.55515i	0.0357433	+	0.202710i	−0.961707	+	0.274081i	$0.911626\pi$
$752$	13.1099	−	22.7071i	0.478070	−	0.828042i
$753$	−5.99660	−	10.3864i	−0.218528	−	0.378502i
$754$	−18.2756	+	15.3350i	−0.665558	+	0.558469i
$755$	−3.60442	+	1.31190i	−0.131178	+	0.0477450i
$756$		0			0
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	0.834548	−	0.550936i	$-0.185729\pi$
$757$	12.0207	+	10.0866i	0.436900	+	0.366602i	−0.397648	+	0.917538i	$0.630173\pi$
$758$	−0.398052	+	2.25746i	−0.0144579	+	0.0819948i
$759$	17.2763			0.627090
$760$	−0.0830629	+	11.2828i	−0.00301301	+	0.409271i
$761$	−4.86484			−0.176350			−0.0881751	−	0.996105i	$-0.528104\pi$
$761$	−4.86484			−0.176350			−0.0881751	+	0.996105i	$0.528104\pi$
$762$	−7.81702	+	44.3325i	−0.283181	+	1.60600i
$763$		0			0
$764$	3.18392	+	1.15885i	0.115190	+	0.0419257i
$765$	−2.04576	+	0.744596i	−0.0739646	+	0.0269209i
$766$	3.03099	−	2.54331i	0.109514	−	0.0918934i
$767$	8.11499	+	14.0556i	0.293015	+	0.507517i
$768$	6.32888	−	10.9619i	0.228374	−	0.395555i
$769$	−3.91266	−	22.1898i	−0.141094	−	0.800184i	−0.970421	−	0.241420i	$-0.922387\pi$
$769$	−3.91266	−	22.1898i	−0.141094	−	0.800184i	0.829327	−	0.558764i	$-0.188724\pi$
$770$		0			0
$771$	0.960637	−	1.66387i	0.0345965	−	0.0599229i
$772$	0.0275033	+	0.0476371i	0.000989864	+	0.00171450i
$773$	20.2481	−	16.9902i	0.728273	−	0.611094i	−0.201387	−	0.979512i	$-0.564545\pi$
$773$	20.2481	−	16.9902i	0.728273	−	0.611094i	0.929660	+	0.368418i	$0.120100\pi$
$774$	26.1352	−	9.51244i	0.939411	−	0.341918i
$775$	28.2237	+	10.2726i	1.01383	+	0.369003i
$776$	−21.3164	−	17.8866i	−0.765214	−	0.642091i
$777$		0			0
$778$	33.0993			1.18667
$779$	−9.30541	−	5.46421i	−0.333401	−	0.195776i
$780$	−1.20439			−0.0431242
$781$	3.59802	−	20.4054i	0.128747	−	0.730162i
$782$	−1.30129	−	1.09191i	−0.0465340	−	0.0390466i
$783$	42.6416	+	15.5203i	1.52389	+	0.554650i
$784$		0			0
$785$	−6.47952	+	5.43696i	−0.231264	+	0.194054i
$786$	−3.57919	−	6.19934i	−0.127666	−	0.221123i
$787$	−7.77884	+	13.4733i	−0.277286	+	0.480273i	−0.970709	−	0.240257i	$-0.922768\pi$
$787$	−7.77884	+	13.4733i	−0.277286	+	0.480273i	0.693424	+	0.720530i	$0.256101\pi$
$788$	−0.421685	−	2.39149i	−0.0150219	−	0.0851934i
$789$	5.69981	+	32.3252i	0.202919	+	1.15081i
$790$	7.01707	−	12.1539i	0.249656	−	0.432417i
$791$		0			0
$792$	−26.5651	+	22.2908i	−0.943950	+	0.792068i
$793$	−22.0792	+	8.03617i	−0.784055	+	0.285373i
$794$	40.3055	+	14.6700i	1.43039	+	0.520618i
$795$	5.50387	+	4.61830i	0.195202	+	0.163794i
$796$	−0.00823757	+	0.0467176i	−0.000291973	+	0.00165586i
$797$	−33.4935			−1.18640			−0.593200	−	0.805055i	$-0.702136\pi$
$797$	−33.4935			−1.18640			−0.593200	+	0.805055i	$0.702136\pi$
$798$		0			0
$799$	−3.41147			−0.120689
$800$	0.764700	−	4.33683i	0.0270362	−	0.153330i
$801$	41.7092	+	34.9982i	1.47372	+	1.23660i
$802$	−0.109470	−	0.0398440i	−0.00386553	−	0.00140694i
$803$	−2.90673	+	1.05796i	−0.102576	+	0.0373347i
$804$	−3.12836	+	2.62500i	−0.110329	+	0.0925767i
$805$		0			0
$806$	−12.3216	+	21.3416i	−0.434010	+	0.751727i
$807$	−9.69506	−	54.9834i	−0.341282	−	1.93551i
$808$	4.72756	+	26.8113i	0.166315	+	0.943219i
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	0.237096	+	0.971486i	$0.423804\pi$
$809$	−20.5581	+	35.6076i	−0.722784	+	1.25190i	−0.959880	+	0.280412i	$0.909529\pi$
$810$	−1.84864	−	3.20194i	−0.0649546	−	0.112505i
$811$	−12.7836	+	10.7267i	−0.448892	+	0.376665i	−0.839025	−	0.544093i	$-0.816874\pi$
$811$	−12.7836	+	10.7267i	−0.448892	+	0.376665i	0.390132	+	0.920759i	$0.372429\pi$
$812$		0			0
$813$	−36.2413	−	13.1907i	−1.27104	−	0.462620i
$814$	11.3610	+	9.53298i	0.398202	+	0.334131i
$815$	−1.27584	+	7.23567i	−0.0446909	+	0.253455i
$816$	4.84524			0.169617
$817$	−14.7907	+	8.39484i	−0.517461	+	0.293698i
$818$	26.9540			0.942424
$819$		0			0
$820$	−0.308182	−	0.258595i	−0.0107622	−	0.00903054i
$821$	29.4971	+	10.7361i	1.02945	+	0.374691i	0.800873	−	0.598834i	$-0.204369\pi$
$821$	29.4971	+	10.7361i	1.02945	+	0.374691i	0.228581	+	0.973525i	$0.426591\pi$
$822$	0.932419	−	0.339373i	0.0325218	−	0.0118370i
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.239274	−	0.970952i	$-0.423091\pi$
$823$	35.4877	−	29.7777i	1.23702	−	1.03799i	0.997751	−	0.0670347i	$-0.0213538\pi$
$824$	−8.10922	−	14.0456i	−0.282498	−	0.489301i
$825$	−13.5496	+	23.4686i	−0.471738	+	0.817073i
$826$		0			0
$827$	7.07769	+	40.1396i	0.246115	+	1.39579i	0.817888	+	0.575377i	$0.195145\pi$
$827$	7.07769	+	40.1396i	0.246115	+	1.39579i	−0.571773	+	0.820412i	$0.693744\pi$
$828$	−1.31727	+	2.28157i	−0.0457782	+	0.0792901i
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	−0.990174	−	0.139843i	$-0.955340\pi$
$829$	−17.7417	−	30.7295i	−0.616195	−	1.06728i	0.373979	−	0.927437i	$-0.377993\pi$
$830$	13.4604	−	11.2946i	0.467217	−	0.392042i
$831$	−48.0185	+	17.4773i	−1.66574	+	0.606281i
$832$	20.7922	+	7.56774i	0.720840	+	0.262364i
$833$		0			0
$834$	2.87211	−	16.2886i	0.0994531	−	0.564026i
$835$	3.54839			0.122797
$836$	1.16297	−	1.36543i	0.0402222	−	0.0472245i
$837$	46.8735			1.62019
$838$	5.94475	−	33.7143i	0.205358	−	1.16464i
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.988383	−	0.151985i	$-0.0485667\pi$
$839$	29.2649	+	24.5562i	1.01034	+	0.847774i	0.0219545	+	0.999759i	$0.493011\pi$
$840$		0			0
$841$	−17.2208	+	6.26784i	−0.593819	+	0.216132i
$842$	−4.50980	+	3.78417i	−0.155418	+	0.130411i
$843$	−26.3161	−	45.5809i	−0.906376	−	1.56989i
$844$	0.226215	−	0.391815i	0.00778663	−	0.0134868i
$845$	0.973430	+	5.52060i	0.0334870	+	0.189914i
$846$	−9.02481	−	51.1823i	−0.310280	−	1.75968i
$847$		0			0
$848$	−5.10220	−	8.83726i	−0.175210	−	0.303473i
$849$	−16.9572	+	14.2288i	−0.581971	+	0.488331i
$850$	2.50387	−	0.911334i	0.0858820	−	0.0312585i
$851$	12.5175	+	4.55601i	0.429096	+	0.156178i
$852$	3.79292	+	3.18264i	0.129943	+	0.109035i
$853$	4.44568	−	25.2127i	0.152217	−	0.863266i	−0.809069	−	0.587714i	$-0.800028\pi$
$853$	4.44568	−	25.2127i	0.152217	−	0.863266i	0.961286	−	0.275552i	$-0.0888608\pi$
$854$		0			0
$855$	12.9214	+	15.6314i	0.441904	+	0.534584i
$856$	30.1257			1.02967
$857$	3.66163	−	20.7661i	0.125079	−	0.709357i	−0.856182	−	0.516674i	$-0.827170\pi$
$857$	3.66163	−	20.7661i	0.125079	−	0.709357i	0.981261	−	0.192683i	$-0.0617189\pi$
$858$	−17.0326	−	14.2920i	−0.581482	−	0.487921i
$859$	−18.3871	−	6.69237i	−0.627361	−	0.228341i	0.00872148	−	0.999962i	$-0.497224\pi$
$859$	−18.3871	−	6.69237i	−0.627361	−	0.228341i	−0.636082	+	0.771621i	$0.719446\pi$
$860$	−0.595800	+	0.216853i	−0.0203166	+	0.00739464i
$861$		0			0
$862$	−25.8050	−	44.6956i	−0.878922	−	1.52234i
$863$	−2.47447	+	4.28591i	−0.0842319	+	0.145894i	−0.905064	−	0.425276i	$-0.860177\pi$
$863$	−2.47447	+	4.28591i	−0.0842319	+	0.145894i	0.820832	+	0.571170i	$0.193510\pi$
$864$	−1.19341	−	6.76817i	−0.0406007	−	0.230258i
$865$	−3.07604	−	17.4451i	−0.104588	−	0.593150i
$866$	12.2139	−	21.1552i	0.415047	−	0.718882i
$867$	24.1596	+	41.8456i	0.820502	+	1.42115i
$868$		0			0
$869$	−24.7849	+	9.02098i	−0.840771	+	0.306016i
$870$	22.0535	+	8.02682i	0.747684	+	0.272135i
$871$	−15.1334	−	12.6984i	−0.512776	−	0.430270i
$872$	−0.931790	+	5.28444i	−0.0315544	+	0.178954i
$873$	−50.0164			−1.69280
$874$	−5.52166	+	14.8300i	−0.186773	+	0.501633i
$875$		0			0
$876$	0.128356	−	0.727940i	0.00433673	−	0.0245948i
$877$	0.934478	+	0.784120i	0.0315551	+	0.0264779i	0.658429	−	0.752643i	$-0.271221\pi$
$877$	0.934478	+	0.784120i	0.0315551	+	0.0264779i	−0.626874	+	0.779121i	$0.715666\pi$
$878$	7.71095	+	2.80656i	0.260232	+	0.0947167i
$879$	−28.4183	+	10.3434i	−0.958527	+	0.348875i
$880$	−5.39440	+	4.52644i	−0.181845	+	0.152586i
$881$	23.2515	+	40.2728i	0.783363	+	1.35682i	0.929972	+	0.367630i	$0.119831\pi$
$881$	23.2515	+	40.2728i	0.783363	+	1.35682i	−0.146609	+	0.989194i	$0.546836\pi$
$882$		0			0
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	0.999001	+	0.0446828i	$0.0142277\pi$
$883$	2.24438	+	12.7285i	0.0755296	+	0.428349i	−0.923472	+	0.383667i	$0.874661\pi$
$884$	−0.0386476	−	0.219182i	−0.00129986	−	0.00737187i
$885$	7.98293	−	13.8268i	0.268343	−	0.464784i
$886$	−20.1374	−	34.8791i	−0.676531	−	1.17179i
$887$	17.7909	−	14.9283i	0.597359	−	0.501243i	−0.293237	−	0.956040i	$-0.594732\pi$
$887$	17.7909	−	14.9283i	0.597359	−	0.501243i	0.890595	+	0.454796i	$0.150288\pi$
$888$	−39.3730	+	14.3306i	−1.32127	+	0.480904i
$889$		0			0
$890$	9.34002	+	7.83721i	0.313078	+	0.262704i
$891$	−1.20661	+	6.84305i	−0.0404231	+	0.229251i
$892$	−1.57255			−0.0526528
$893$	10.6493	+	29.9428i	0.356365	+	1.00200i
$894$	−64.2404			−2.14852
$895$	1.75800	−	9.97011i	0.0587634	−	0.333264i
$896$		0			0
$897$	−18.7665	−	6.83045i	−0.626596	−	0.228062i
$898$	−14.2429	+	5.18398i	−0.475291	+	0.172992i
$899$	−37.4484	+	31.4229i	−1.24897	+	1.04801i
$900$	−2.06624	−	3.57883i	−0.0688746	−	0.119294i
$901$	−0.663848	+	1.14982i	−0.0221160	+	0.0383060i
$902$	−1.28968	−	7.31412i	−0.0429416	−	0.243534i
$903$		0			0
$904$	26.0326	−	45.0897i	0.865830	−	1.49966i
$905$	−3.75372	−	6.50163i	−0.124778	−	0.216122i
$906$	12.9624	−	10.8768i	0.430648	−	0.361357i
$907$	37.5847	−	13.6797i	1.24798	−	0.454228i	0.368261	−	0.929722i	$-0.379953\pi$
$907$	37.5847	−	13.6797i	1.24798	−	0.454228i	0.879719	+	0.475495i	$0.157731\pi$
$908$	2.45723	+	0.894360i	0.0815462	+	0.0296804i
$909$	37.4864	+	31.4548i	1.24334	+	1.04329i
$910$		0			0
$911$	−18.7997			−0.622863			−0.311431	−	0.950269i	$-0.600808\pi$
$911$	−18.7997			−0.622863			−0.311431	+	0.950269i	$0.600808\pi$
$912$	−15.1250	−	42.5270i	−0.500837	−	1.40821i
$913$	−33.0232			−1.09291
$914$	5.47225	−	31.0347i	0.181006	−	1.02654i
$915$	17.7062	+	14.8573i	0.585349	+	0.491166i
$916$	3.56552	+	1.29774i	0.117808	+	0.0428787i
$917$		0			0
$918$	3.18551	−	2.67296i	0.105137	−	0.0882208i
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	−0.981398	−	0.191984i	$-0.938508\pi$
$919$	−19.9158	−	34.4952i	−0.656962	−	1.13789i	0.324436	−	0.945908i	$-0.394825\pi$
$920$	−3.48751	+	6.04055i	−0.114980	+	0.199151i
$921$	5.84776	+	33.1643i	0.192690	+	1.09280i
$922$	−8.56830	−	48.5932i	−0.282182	−	1.60033i
$923$	−11.9760	+	20.7430i	−0.394193	+	0.682763i
$924$		0			0
$925$	−16.0064	+	13.4310i	−0.526287	+	0.441607i
$926$	−54.4227	+	19.8082i	−1.78844	+	0.650939i
$927$	−27.3935	−	9.97043i	−0.899721	−	0.327472i
$928$	5.49067	+	4.60722i	0.180240	+	0.151239i
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	0.806526	+	0.591199i	$0.201345\pi$
$929$	−4.68051	+	26.5445i	−0.153563	+	0.870897i	−0.960088	+	0.279698i	$0.909766\pi$
$930$	24.2422			0.794932
$931$		0			0
$932$	−3.26176			−0.106843
$933$	−7.98293	+	45.2734i	−0.261349	+	1.48219i
$934$	26.4176	+	22.1670i	0.864411	+	0.725327i
$935$	0.860967	+	0.313366i	0.0281566	+	0.0102482i
$936$	37.6695	−	13.7106i	1.23127	−	0.448145i
$937$	−2.00980	+	1.68642i	−0.0656573	+	0.0550930i	−0.675026	−	0.737794i	$-0.735867\pi$
$937$	−2.00980	+	1.68642i	−0.0656573	+	0.0550930i	0.609368	+	0.792887i	$0.291423\pi$
$938$		0			0
$939$	−38.3371	+	66.4018i	−1.25108	+	2.16694i
$940$	0.205737	+	1.16679i	0.00671040	+	0.0380566i
$941$	3.24194	+	18.3860i	0.105684	+	0.599366i	0.990945	+	0.134270i	$0.0428690\pi$
$941$	3.24194	+	18.3860i	0.105684	+	0.599366i	−0.885260	+	0.465096i	$0.846020\pi$
$942$	18.6570	−	32.3149i	0.607879	−	1.05288i
$943$	−3.33544	−	5.77715i	−0.108617	−	0.188130i
$944$	−17.3708	+	14.5758i	−0.565370	+	0.474402i
$945$		0			0
$946$	−10.9991	−	4.00335i	−0.357612	−	0.130160i
$947$	6.43448	+	5.39917i	0.209092	+	0.175449i	0.741320	−	0.671152i	$-0.234200\pi$
$947$	6.43448	+	5.39917i	0.209092	+	0.175449i	−0.532227	+	0.846602i	$0.678645\pi$
$948$	1.09446	−	6.20697i	0.0355463	−	0.201593i
$949$	3.57573			0.116073
$950$	−15.8150	−	19.1318i	−0.513105	−	0.620718i
$951$	85.0343			2.75742
$952$		0			0
$953$	25.8102	+	21.6573i	0.836075	+	0.701550i	0.956677	−	0.291151i	$-0.0940382\pi$
$953$	25.8102	+	21.6573i	0.836075	+	0.701550i	−0.120602	+	0.992701i	$0.538483\pi$
$954$	−19.0069	−	6.91793i	−0.615370	−	0.223976i
$955$	15.1515	−	5.51470i	0.490292	−	0.178452i
$956$	−0.332997	+	0.279418i	−0.0107699	+	0.00903701i
$957$	−22.0535	−	38.1978i	−0.712888	−	1.23476i
$958$	−25.7173	+	44.5438i	−0.830890	+	1.43914i
$959$		0			0
$960$	−3.77972	−	21.4358i	−0.121990	−	0.691838i
$961$	−9.74809	+	16.8842i	−0.314455	+	0.544651i
$962$	−8.57192	−	14.8470i	−0.276370	−	0.478686i
$963$	41.4805	−	34.8062i	1.33669	−	1.12162i
$964$	−2.39646	+	0.872240i	−0.0771848	+	0.0280930i
$965$	0.245977	+	0.0895284i	0.00791829	+	0.00288202i
$966$		0			0
$967$	2.03920	−	11.5649i	0.0655763	−	0.371902i	−0.934305	−	0.356475i	$-0.883978\pi$
$967$	2.03920	−	11.5649i	0.0655763	−	0.371902i	0.999881	−	0.0154262i	$-0.00491051\pi$
$968$	−17.7847			−0.571621
$969$	−3.80793	+	4.47086i	−0.122328	+	0.143625i
$970$	−11.2003			−0.359619
$971$	−2.22432	+	12.6147i	−0.0713817	+	0.404826i	0.928091	+	0.372354i	$0.121449\pi$
$971$	−2.22432	+	12.6147i	−0.0713817	+	0.404826i	−0.999473	+	0.0324723i	$0.989662\pi$
$972$	1.52931	+	1.28325i	0.0490528	+	0.0411602i
$973$		0			0
$974$	9.82934	−	3.57759i	0.314953	−	0.114633i
$975$	23.9971	−	20.1359i	0.768521	−	0.644866i
$976$	−16.4140	−	28.4299i	−0.525399	−	0.910018i
$977$	−7.26382	+	12.5813i	−0.232390	+	0.402512i	−0.958511	−	0.285055i	$-0.907988\pi$
$977$	−7.26382	+	12.5813i	−0.232390	+	0.402512i	0.726121	+	0.687567i	$0.241321\pi$
$978$	−5.62836	−	31.9200i	−0.179975	−	1.02069i
$979$	−3.97906	−	22.5663i	−0.127171	−	0.721224i
$980$		0			0
$981$	4.82248	+	8.35278i	0.153970	+	0.266684i
$982$	37.9013	−	31.8029i	1.20948	−	1.01487i
$983$	−34.8158	+	12.6719i	−1.11045	+	0.404172i	−0.831159	−	0.556034i	$-0.812322\pi$
$983$	−34.8158	+	12.6719i	−1.11045	+	0.404172i	−0.279293	+	0.960206i	$0.590100\pi$
$984$	19.7173	+	7.17653i	0.628566	+	0.228779i
$985$	−8.85251	−	7.42814i	−0.282064	−	0.236680i
$986$	−0.753089	+	4.27098i	−0.0239832	+	0.136016i
$987$		0			0
$988$	−1.80313	+	1.02341i	−0.0573652	+	0.0325591i
$989$	−10.5134			−0.334307
$990$	−2.42380	+	13.7461i	−0.0770334	+	0.436878i
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	0.683582	−	0.729873i	$-0.260421\pi$
$991$	2.62860	+	2.20566i	0.0835004	+	0.0700651i	−0.600082	+	0.799938i	$0.704865\pi$
$992$	6.95723	+	2.53223i	0.220892	+	0.0803983i
$993$	−74.8556	+	27.2452i	−2.37547	+	0.864600i
$994$		0			0
$995$	0.112874	+	0.195503i	0.00357835	+	0.00619788i
$996$	3.94562	−	6.83402i	0.125022	−	0.216544i
$997$	−2.21853	−	12.5819i	−0.0702616	−	0.398473i	−0.999574	−	0.0291792i	$-0.990711\pi$
$997$	−2.21853	−	12.5819i	−0.0702616	−	0.398473i	0.929313	−	0.369294i	$-0.120400\pi$
$998$	−1.15254	−	6.53639i	−0.0364831	−	0.206906i
$999$	−16.3045	+	28.2403i	−0.515852	+	0.893483i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.w.a.834.1		6
7.2	even	3		931.2.v.a.606.1		6
7.3	odd	6		931.2.x.a.226.1		6
7.4	even	3		931.2.x.b.226.1		6
7.5	odd	6		931.2.v.b.606.1		6
7.6	odd	2		19.2.e.a.17.1	yes	6
19.9	even	9	inner	931.2.w.a.883.1		6
21.20	even	2		171.2.u.c.55.1		6
28.27	even	2		304.2.u.b.17.1		6
35.13	even	4		475.2.u.a.74.2		12
35.27	even	4		475.2.u.a.74.1		12
35.34	odd	2		475.2.l.a.226.1		6
133.6	odd	18		361.2.e.f.99.1		6
133.9	even	9		931.2.x.b.655.1		6
133.13	even	18		361.2.e.b.99.1		6
133.27	even	6		361.2.e.b.62.1		6
133.34	even	18		361.2.e.a.234.1		6
133.41	even	18		361.2.a.h.1.2		3
133.47	odd	18		931.2.x.a.655.1		6
133.48	even	18		361.2.e.h.28.1		6
133.55	odd	18		361.2.c.i.68.2		6
133.62	odd	18		361.2.c.i.292.2		6
133.66	odd	18		931.2.v.b.275.1		6
133.69	even	6		361.2.e.a.54.1		6
133.83	odd	6		361.2.e.g.54.1		6
133.90	even	18		361.2.c.h.292.2		6
133.97	even	18		361.2.c.h.68.2		6
133.104	odd	18		19.2.e.a.9.1	✓	6
133.111	odd	18		361.2.a.g.1.2		3
133.118	odd	18		361.2.e.g.234.1		6
133.123	even	9		931.2.v.a.275.1		6
133.125	odd	6		361.2.e.f.62.1		6
133.132	even	2		361.2.e.h.245.1		6
399.41	odd	18		3249.2.a.s.1.2		3
399.104	even	18		171.2.u.c.28.1		6
399.377	even	18		3249.2.a.z.1.2		3
532.111	even	18		5776.2.a.br.1.3		3
532.307	odd	18		5776.2.a.bi.1.1		3
532.503	even	18		304.2.u.b.161.1		6
665.104	odd	18		475.2.l.a.351.1		6
665.174	even	18		9025.2.a.x.1.2		3
665.237	even	36		475.2.u.a.199.2		12
665.244	odd	18		9025.2.a.bd.1.2		3
665.503	even	36		475.2.u.a.199.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	133.104	odd	18
19.2.e.a.17.1	yes	6	7.6	odd	2
171.2.u.c.28.1		6	399.104	even	18
171.2.u.c.55.1		6	21.20	even	2
304.2.u.b.17.1		6	28.27	even	2
304.2.u.b.161.1		6	532.503	even	18
361.2.a.g.1.2		3	133.111	odd	18
361.2.a.h.1.2		3	133.41	even	18
361.2.c.h.68.2		6	133.97	even	18
361.2.c.h.292.2		6	133.90	even	18
361.2.c.i.68.2		6	133.55	odd	18
361.2.c.i.292.2		6	133.62	odd	18
361.2.e.a.54.1		6	133.69	even	6
361.2.e.a.234.1		6	133.34	even	18
361.2.e.b.62.1		6	133.27	even	6
361.2.e.b.99.1		6	133.13	even	18
361.2.e.f.62.1		6	133.125	odd	6
361.2.e.f.99.1		6	133.6	odd	18
361.2.e.g.54.1		6	133.83	odd	6
361.2.e.g.234.1		6	133.118	odd	18
361.2.e.h.28.1		6	133.48	even	18
361.2.e.h.245.1		6	133.132	even	2
475.2.l.a.226.1		6	35.34	odd	2
475.2.l.a.351.1		6	665.104	odd	18
475.2.u.a.74.1		12	35.27	even	4
475.2.u.a.74.2		12	35.13	even	4
475.2.u.a.199.1		12	665.503	even	36
475.2.u.a.199.2		12	665.237	even	36
931.2.v.a.275.1		6	133.123	even	9
931.2.v.a.606.1		6	7.2	even	3
931.2.v.b.275.1		6	133.66	odd	18
931.2.v.b.606.1		6	7.5	odd	6
931.2.w.a.834.1		6	1.1	even	1	trivial
931.2.w.a.883.1		6	19.9	even	9	inner
931.2.x.a.226.1		6	7.3	odd	6
931.2.x.a.655.1		6	133.47	odd	18
931.2.x.b.226.1		6	7.4	even	3
931.2.x.b.655.1		6	133.9	even	9
3249.2.a.s.1.2		3	399.41	odd	18
3249.2.a.z.1.2		3	399.377	even	18
5776.2.a.bi.1.1		3	532.307	odd	18
5776.2.a.br.1.3		3	532.111	even	18
9025.2.a.x.1.2		3	665.174	even	18
9025.2.a.bd.1.2		3	665.244	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.233956 + 1.32683i) q^{2} +(2.20574 + 1.85083i) q^{3} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-2.97178 + 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(0.918748 + 5.21048i) q^{9} +O(q^{10})\)	\(q+(-0.233956 + 1.32683i) q^{2} +(2.20574 + 1.85083i) q^{3} +(0.173648 + 0.0632028i) q^{4} +(0.826352 - 0.300767i) q^{5} +(-2.97178 + 2.49362i) q^{6} +(-1.47178 + 2.54920i) q^{8} +(0.918748 + 5.21048i) q^{9} +(0.205737 + 1.16679i) q^{10} +(1.11334 - 1.92836i) q^{11} +(0.266044 + 0.460802i) q^{12} +(-1.97178 + 1.65452i) q^{13} +(2.37939 + 0.866025i) q^{15} +(-2.75490 - 2.31164i) q^{16} +(-0.0812519 + 0.460802i) q^{17} -7.12836 q^{18} +(4.29813 - 0.725293i) q^{19} +0.162504 q^{20} +(2.29813 + 1.92836i) q^{22} +(2.53209 + 0.921605i) q^{23} +(-7.96451 + 2.89884i) q^{24} +(-3.23783 + 2.71686i) q^{25} +(-1.73396 - 3.00330i) q^{26} +(-3.29813 + 5.71253i) q^{27} +(-1.19459 - 6.77487i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(-3.55303 - 6.15403i) q^{31} +(-0.798133 + 0.669713i) q^{32} +(6.02481 - 2.19285i) q^{33} +(-0.592396 - 0.215615i) q^{34} +(-0.169778 + 0.962858i) q^{36} +4.94356 q^{37} +(-0.0432332 + 5.87257i) q^{38} -7.41147 q^{39} +(-0.449493 + 2.54920i) q^{40} +(-1.89646 - 1.59132i) q^{41} +(-3.66637 + 1.33445i) q^{43} +(0.315207 - 0.264490i) q^{44} +(2.32635 + 4.02936i) q^{45} +(-1.81521 + 3.14403i) q^{46} +(1.26604 + 7.18009i) q^{47} +(-1.79813 - 10.1977i) q^{48} +(-2.84730 - 4.93166i) q^{50} +(-1.03209 + 0.866025i) q^{51} +(-0.446967 + 0.162683i) q^{52} +(2.66637 + 0.970481i) q^{53} +(-6.80793 - 5.71253i) q^{54} +(0.340022 - 1.92836i) q^{55} +(10.8229 + 6.35532i) q^{57} +9.26857 q^{58} +(1.09492 - 6.20961i) q^{59} +(0.358441 + 0.300767i) q^{60} +(8.57785 + 3.12208i) q^{61} +(8.99660 - 3.27449i) q^{62} +(-4.29813 - 7.44459i) q^{64} +(-1.13176 + 1.96026i) q^{65} +(1.50000 + 8.50692i) q^{66} +(1.33275 + 7.55839i) q^{67} +(-0.0432332 + 0.0748822i) q^{68} +(3.87939 + 6.71929i) q^{69} +(8.74422 - 3.18264i) q^{71} +(-14.6348 - 5.32661i) q^{72} +(-1.06418 - 0.892951i) q^{73} +(-1.15657 + 6.55926i) q^{74} -12.1702 q^{75} +(0.792204 + 0.145708i) q^{76} +(1.73396 - 9.83375i) q^{78} +(-9.07398 - 7.61397i) q^{79} +(-2.97178 - 1.08164i) q^{80} +(-2.93242 + 1.06731i) q^{81} +(2.55509 - 2.14398i) q^{82} +(-7.41534 - 12.8438i) q^{83} +(0.0714517 + 0.405223i) q^{85} +(-0.912818 - 5.17685i) q^{86} +(9.90420 - 17.1546i) q^{87} +(3.27719 + 5.67626i) q^{88} +(7.88326 - 6.61484i) q^{89} +(-5.89053 + 2.14398i) q^{90} +(0.381445 + 0.320070i) q^{92} +(3.55303 - 20.1503i) q^{93} -9.82295 q^{94} +(3.33363 - 1.89209i) q^{95} -3.00000 q^{96} +(-1.64156 + 9.30975i) q^{97} +(11.0706 + 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{5} - 3 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^5 - 3 * q^6 + 6 * q^8 + 3 * q^9	\( 6 q - 6 q^{2} + 3 q^{3} + 6 q^{5} - 3 q^{6} + 6 q^{8} + 3 q^{9} - 9 q^{10} - 3 q^{12} + 3 q^{13} + 3 q^{15} - 18 q^{16} - 3 q^{17} - 6 q^{18} + 12 q^{19} + 6 q^{20} + 6 q^{23} - 15 q^{24} - 15 q^{26} - 6 q^{27} - 3 q^{29} - 9 q^{31} + 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} - 21 q^{41} - 3 q^{43} + 9 q^{44} + 15 q^{45} - 18 q^{46} + 3 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 15 q^{52} - 3 q^{53} - 30 q^{54} - 18 q^{55} + 24 q^{57} + 36 q^{58} - 12 q^{59} - 6 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} - 12 q^{65} + 9 q^{66} - 30 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{71} - 12 q^{72} + 12 q^{73} + 15 q^{74} - 30 q^{75} - 36 q^{76} + 15 q^{78} - 39 q^{79} - 3 q^{80} + 6 q^{81} + 54 q^{82} + 24 q^{86} + 21 q^{87} + 9 q^{88} + 12 q^{89} - 18 q^{90} + 42 q^{92} + 9 q^{93} - 18 q^{94} + 39 q^{95} - 18 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 3 * q^3 + 6 * q^5 - 3 * q^6 + 6 * q^8 + 3 * q^9 - 9 * q^10 - 3 * q^12 + 3 * q^13 + 3 * q^15 - 18 * q^16 - 3 * q^17 - 6 * q^18 + 12 * q^19 + 6 * q^20 + 6 * q^23 - 15 * q^24 - 15 * q^26 - 6 * q^27 - 3 * q^29 - 9 * q^31 + 9 * q^32 + 9 * q^33 - 24 * q^36 + 15 * q^38 - 24 * q^39 - 21 * q^41 - 3 * q^43 + 9 * q^44 + 15 * q^45 - 18 * q^46 + 3 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 15 * q^52 - 3 * q^53 - 30 * q^54 - 18 * q^55 + 24 * q^57 + 36 * q^58 - 12 * q^59 - 6 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 - 12 * q^65 + 9 * q^66 - 30 * q^67 + 15 * q^68 + 12 * q^69 - 6 * q^71 - 12 * q^72 + 12 * q^73 + 15 * q^74 - 30 * q^75 - 36 * q^76 + 15 * q^78 - 39 * q^79 - 3 * q^80 + 6 * q^81 + 54 * q^82 + 24 * q^86 + 21 * q^87 + 9 * q^88 + 12 * q^89 - 18 * q^90 + 42 * q^92 + 9 * q^93 - 18 * q^94 + 39 * q^95 - 18 * q^96 - 18 * q^97 + 9 * q^99

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