LMFDB - Embedded newform 931.2.w.a.883.1

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			883.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	931.883
Dual form			931.2.w.a.834.1

$q$-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 $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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	−0.948618	−	0.316423i	$-0.897518\pi$
$2$	−0.233956	−	1.32683i	−0.165432	−	0.938209i	0.783187	−	0.621786i	$-0.213593\pi$
$3$	2.20574	−	1.85083i	1.27348	−	1.06858i	0.279375	−	0.960182i	$-0.409873\pi$
$3$	2.20574	−	1.85083i	1.27348	−	1.06858i	0.994108	−	0.108397i	$-0.0345718\pi$
$4$	0.173648	−	0.0632028i	0.0868241	−	0.0316014i
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	0.520121	−	0.854093i	$-0.325887\pi$
$5$	0.826352	+	0.300767i	0.369556	+	0.134507i	−0.150565	+	0.988600i	$0.548109\pi$
$6$	−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	0.983616	−	0.180276i	$-0.0576989\pi$
$11$	1.11334	+	1.92836i	0.335685	+	0.581423i	−0.647931	+	0.761699i	$0.724366\pi$
$12$	0.266044	−	0.460802i	0.0768004	−	0.133022i
$13$	−1.97178	−	1.65452i	−0.546874	−	0.458882i	0.327007	−	0.945022i	$-0.393960\pi$
$13$	−1.97178	−	1.65452i	−0.546874	−	0.458882i	−0.873881	+	0.486140i	$0.838404\pi$
$14$		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	0.973368	−	0.229249i	$-0.0736270\pi$
$17$	−0.0812519	−	0.460802i	−0.0197065	−	0.111761i	−0.993074	+	0.117488i	$0.962516\pi$
$18$	−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	−0.0642578	−	0.997933i	$-0.520468\pi$
$23$	2.53209	−	0.921605i	0.527977	−	0.192168i	0.592235	+	0.805765i	$0.298246\pi$
$24$	−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	0.646822	+	0.762641i	$0.276097\pi$
$29$	−1.19459	+	6.77487i	−0.221830	+	1.25806i	−0.868653	+	0.495421i	$0.835014\pi$
$30$	−1.70574	−	2.95442i	−0.311424	−	0.539401i
$31$	−3.55303	+	6.15403i	−0.638144	+	1.10530i	0.347696	+	0.937607i	$0.386964\pi$
$31$	−3.55303	+	6.15403i	−0.638144	+	1.10530i	−0.985840	+	0.167690i	$0.946369\pi$
$32$	−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	−0.778751	−	0.627333i	$-0.784146\pi$
$41$	−1.89646	+	1.59132i	−0.296177	+	0.248522i	0.482574	+	0.875855i	$0.339702\pi$
$42$		0			0
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	0.0469757	−	0.998896i	$-0.485042\pi$
$43$	−3.66637	−	1.33445i	−0.559117	−	0.203502i	−0.606093	+	0.795394i	$0.707264\pi$
$44$	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	−0.741705	−	0.670726i	$-0.765983\pi$
$47$	1.26604	−	7.18009i	0.184672	−	1.04732i	0.926377	−	0.376598i	$-0.122906\pi$
$48$	−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	−0.152335	−	0.988329i	$-0.548679\pi$
$53$	2.66637	−	0.970481i	0.366255	−	0.133306i	0.518590	+	0.855023i	$0.326457\pi$
$54$	−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	0.969304	+	0.245864i	$0.0790718\pi$
$59$	1.09492	+	6.20961i	0.142547	+	0.808423i	−0.826757	+	0.562559i	$0.809817\pi$
$60$	0.358441	−	0.300767i	0.0462745	−	0.0388289i
$61$	8.57785	−	3.12208i	1.09828	−	0.399742i	0.271599	−	0.962411i	$-0.412448\pi$
$61$	8.57785	−	3.12208i	1.09828	−	0.399742i	0.826682	+	0.562669i	$0.190225\pi$
$62$	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	−0.788461	−	0.615084i	$-0.789122\pi$
$67$	1.33275	−	7.55839i	0.162821	−	0.923405i	0.951283	−	0.308320i	$-0.0997669\pi$
$68$	−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	0.804026	−	0.594594i	$-0.202687\pi$
$71$	8.74422	+	3.18264i	1.03775	+	0.377709i	0.233722	+	0.972303i	$0.424909\pi$
$72$	−14.6348	+	5.32661i	−1.72472	+	0.627748i
$73$	−1.06418	+	0.892951i	−0.124553	+	0.104512i	−0.702936	−	0.711253i	$-0.748128\pi$
$73$	−1.06418	+	0.892951i	−0.124553	+	0.104512i	0.578384	+	0.815765i	$0.303684\pi$
$74$	−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	−0.989741	−	0.142876i	$-0.954365\pi$
$79$	−9.07398	+	7.61397i	−1.02090	+	0.856639i	−0.0311616	+	0.999514i	$0.509921\pi$
$80$	−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	0.0961469	+	0.995367i	$0.469348\pi$
$83$	−7.41534	+	12.8438i	−0.813940	+	1.40979i	−0.910087	+	0.414418i	$0.863985\pi$
$84$		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	0.956575	−	0.291487i	$-0.0941501\pi$
$89$	7.88326	+	6.61484i	0.835623	+	0.701171i	−0.120951	+	0.992658i	$0.538594\pi$
$90$	−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	−0.947320	−	0.320287i	$-0.896221\pi$
$97$	−1.64156	−	9.30975i	−0.166675	−	0.945261i	0.780645	−	0.624974i	$-0.214891\pi$
$98$		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	0.923190	−	0.384343i	$-0.125572\pi$
$101$	7.08512	+	5.94512i	0.704996	+	0.591562i	−0.218194	+	0.975905i	$0.570017\pi$
$102$	−0.907604	+	1.57202i	−0.0898662	+	0.155653i
$103$	−2.75490	−	4.77163i	−0.271448	−	0.470162i	0.697785	−	0.716308i	$-0.254169\pi$
$103$	−2.75490	−	4.77163i	−0.271448	−	0.470162i	−0.969233	+	0.246145i	$0.920836\pi$
$104$	−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	−0.999981	−	0.00610974i	$-0.998055\pi$
$107$	−5.11721	+	8.86327i	−0.494699	+	0.856845i	0.505282	+	0.862954i	$0.331389\pi$
$108$	−0.933763	−	0.783520i	−0.0898514	−	0.0753943i
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	0.422753	−	0.906245i	$-0.361064\pi$
$109$	1.71301	+	0.623485i	0.164077	+	0.0597190i	−0.258676	+	0.965964i	$0.583286\pi$
$110$	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	0.945445	−	0.325782i	$-0.105627\pi$
$127$	8.88919	+	7.45891i	0.788788	+	0.661871i	−0.156657	+	0.987653i	$0.550072\pi$
$128$	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	0.967605	−	0.252468i	$-0.0812422\pi$
$131$	−0.320422	−	1.81720i	−0.0279954	−	0.158770i	−0.995601	+	0.0936982i	$0.970131\pi$
$132$	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	−0.352267	−	0.935900i	$-0.614589\pi$
$137$	−0.240352	+	0.0874810i	−0.0205347	+	0.00747401i	0.331732	+	0.943374i	$0.392367\pi$
$138$	−9.82295	−	3.57526i	−0.836185	−	0.304346i
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	0.493682	−	0.869643i	$-0.335651\pi$
$139$	−3.26604	−	2.74054i	−0.277022	−	0.232449i	−0.770704	+	0.637193i	$0.780095\pi$
$140$		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	0.0472981	−	0.998881i	$-0.484939\pi$
$149$	12.6853	−	10.6442i	1.03922	−	0.872007i	0.991919	+	0.126874i	$0.0404945\pi$
$150$	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	−0.0448510	−	0.998994i	$-0.514281\pi$
$157$	−9.03849	−	3.28974i	−0.721350	−	0.262550i	−0.676499	+	0.736444i	$0.736504\pi$
$158$	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	0.654748	−	0.755847i	$-0.272775\pi$
$163$	−4.17752	−	7.23567i	−0.327209	−	0.566742i	−0.981957	+	0.189105i	$0.939441\pi$
$164$	−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	−0.191120	−	0.981567i	$-0.561212\pi$
$167$	3.79174	−	1.38008i	0.293413	−	0.106794i	0.484533	+	0.874773i	$0.338990\pi$
$168$		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	0.766335	+	0.642441i	$0.222078\pi$
$173$	3.49794	+	19.8378i	0.265943	+	1.50824i	−0.500391	+	0.865799i	$0.666811\pi$
$174$	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	0.996894	−	0.0787564i	$-0.0250949\pi$
$179$	5.75624	+	9.97011i	0.430242	+	0.745201i	−0.566652	+	0.823957i	$0.691762\pi$
$180$	0.149300	−	0.846723i	0.0111282	−	0.0631110i
$181$	−1.48246	+	8.40744i	−0.110190	+	0.624920i	0.878829	+	0.477136i	$0.158325\pi$
$181$	−1.48246	+	8.40744i	−0.110190	+	0.624920i	−0.989020	+	0.147784i	$0.952786\pi$
$182$		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	−0.634544	−	0.772887i	$-0.718812\pi$
$193$	0.228026	−	0.191336i	0.0164137	−	0.0137727i	0.650958	+	0.759114i	$0.274368\pi$
$194$	−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	−0.999337	−	0.0364128i	$-0.988407\pi$
$197$	−6.57057	+	11.3806i	−0.468134	+	0.810832i	0.531203	+	0.847245i	$0.321740\pi$
$198$	−7.93629	−	13.7461i	−0.564008	−	0.976890i
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	−0.983187	−	0.182602i	$-0.941548\pi$
$199$	0.0445774	−	0.252811i	0.00316001	−	0.0179213i	0.986347	+	0.164680i	$0.0526593\pi$
$200$	−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	0.995938	−	0.0900364i	$-0.0286983\pi$
$211$	0.425145	+	2.41112i	0.0292682	+	0.165988i	−0.966670	+	0.256024i	$0.917587\pi$
$212$	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	0.0600971	−	0.998193i	$-0.480859\pi$
$223$	−7.99660	−	2.91052i	−0.535492	−	0.194903i	−0.595589	+	0.803289i	$0.703081\pi$
$224$		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	−0.264249	−	0.964454i	$-0.585124\pi$
$233$	−16.5865	−	6.03698i	−1.08662	−	0.395496i	−0.822366	+	0.568959i	$0.807346\pi$
$234$	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	0.825475	−	0.564438i	$-0.190907\pi$
$239$	−1.17617	−	2.03719i	−0.0760804	−	0.131775i	−0.901556	+	0.432663i	$0.857574\pi$
$240$	−4.55303	+	7.88609i	−0.293897	+	0.509045i
$241$	−10.5719	−	8.87089i	−0.680997	−	0.571424i	0.235300	−	0.971923i	$-0.424393\pi$
$241$	−10.5719	−	8.87089i	−0.680997	−	0.571424i	−0.916298	+	0.400498i	$0.868837\pi$
$242$	−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	−0.462577	−	0.886579i	$-0.653075\pi$
$251$	−3.91400	+	1.42458i	−0.247050	+	0.0899187i	0.215528	+	0.976498i	$0.430853\pi$
$252$		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	−0.988208	−	0.153116i	$-0.951069\pi$
$257$	−0.115867	+	0.657115i	−0.00722759	+	0.0409897i	0.980981	+	0.194105i	$0.0621804\pi$
$258$	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	−0.332540	−	0.943089i	$-0.607906\pi$
$263$	8.73261	−	7.32753i	0.538476	−	0.451835i	0.871016	+	0.491254i	$0.163461\pi$
$264$	−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	−0.971286	−	0.237916i	$-0.923536\pi$
$269$	−14.8537	+	12.4637i	−0.905646	+	0.759927i	0.0656400	+	0.997843i	$0.479091\pi$
$270$	−7.34389	+	2.67296i	−0.446935	+	0.162671i
$271$	−12.5865	−	4.58110i	−0.764573	−	0.278282i	−0.0698486	−	0.997558i	$-0.522252\pi$
$271$	−12.5865	−	4.58110i	−0.764573	−	0.278282i	−0.694725	+	0.719276i	$0.744474\pi$
$272$	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	−0.999250	−	0.0387161i	$-0.987673\pi$
$277$	−8.87346	−	15.3693i	−0.533154	−	0.923450i	0.466096	−	0.884734i	$-0.345660\pi$
$278$	−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	−0.799050	−	0.601265i	$-0.794664\pi$
$281$	−17.1766	+	6.25179i	−1.02467	+	0.372950i	−0.225622	+	0.974215i	$0.572442\pi$
$282$	−21.6668	+	18.1806i	−1.29024	+	1.08264i
$283$	−1.33497	−	7.57099i	−0.0793557	−	0.450049i	−0.998432	−	0.0559700i	$-0.982175\pi$
$283$	−1.33497	−	7.57099i	−0.0793557	−	0.450049i	0.919077	−	0.394079i	$-0.128936\pi$
$284$	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	0.670864	−	0.741581i	$-0.265924\pi$
$293$	−5.25150	−	9.09586i	−0.306796	−	0.531386i	−0.977660	+	0.210195i	$0.932590\pi$
$294$		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	−0.350264	−	0.936651i	$-0.613908\pi$
$307$	8.95929	−	7.51774i	0.511334	−	0.429060i	0.861598	+	0.507591i	$0.169464\pi$
$308$		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	−0.545881	−	0.837863i	$-0.683805\pi$
$311$	7.98293	−	13.8268i	0.452670	−	0.784048i	0.998551	+	0.0538151i	$0.0171382\pi$
$312$	10.9081	+	18.8933i	0.617548	+	1.06962i
$313$	4.62402	−	26.2241i	0.261365	−	1.48227i	−0.517825	−	0.855487i	$-0.673258\pi$
$313$	4.62402	−	26.2241i	0.261365	−	1.48227i	0.779190	−	0.626788i	$-0.215631\pi$
$314$	−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	0.994465	+	0.105073i	$0.0335077\pi$
$317$	22.6229	+	18.9829i	1.27063	+	1.06618i	0.276164	+	0.961111i	$0.410937\pi$
$318$	−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	−0.942687	−	0.333677i	$-0.891710\pi$
$331$	−13.8327	−	23.9590i	−0.760317	−	1.31691i	0.182371	−	0.983230i	$-0.441623\pi$
$332$	−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	−0.158279	−	0.987394i	$-0.550594\pi$
$337$	−16.7827	−	6.10841i	−0.914212	−	0.332746i	−0.755934	+	0.654648i	$0.772817\pi$
$338$	−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	0.484157	−	0.874981i	$-0.339126\pi$
$347$	5.45084	+	1.98394i	0.292616	+	0.106504i	−0.191541	+	0.981485i	$0.561348\pi$
$348$	2.80406	+	2.35289i	0.150314	+	0.126128i
$349$	2.68614	−	4.65253i	0.143786	−	0.249044i	−0.785134	−	0.619326i	$-0.787406\pi$
$349$	2.68614	−	4.65253i	0.143786	−	0.249044i	0.928919	+	0.370282i	$0.120739\pi$
$350$		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	−0.977466	−	0.211095i	$-0.932297\pi$
$353$	−12.6172	−	21.8537i	−0.671546	−	1.16315i	0.305919	−	0.952057i	$-0.401036\pi$
$354$	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	0.999996	+	0.00285518i	$0.000908833\pi$
$359$	1.16116	+	6.58526i	0.0612837	+	0.347557i	−0.938712	+	0.344702i	$0.887980\pi$
$360$	−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	0.465865	−	0.884856i	$-0.345743\pi$
$367$	−6.21941	−	5.21870i	−0.324650	−	0.272414i	−0.790516	+	0.612441i	$0.790188\pi$
$368$	−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	−0.0804968	+	0.996755i	$0.525651\pi$
$373$	−17.4488	+	30.2222i	−0.903463	+	1.56484i	−0.822967	+	0.568090i	$0.807683\pi$
$374$	−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	−0.698453	−	0.715656i	$-0.746128\pi$
$383$	−2.24969	+	1.88771i	−0.114954	+	0.0964575i	0.583499	+	0.812114i	$0.301683\pi$
$384$	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	0.662344	+	0.749199i	$0.269562\pi$
$389$	−4.26604	+	24.1939i	−0.216297	+	1.22668i	−0.878642	+	0.477482i	$0.841550\pi$
$390$	−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	0.731059	+	0.682314i	$0.239026\pi$
$397$	5.52822	+	31.3521i	0.277453	+	1.57352i	−0.453606	+	0.891202i	$0.649863\pi$
$398$	−0.345866			−0.0173367
$399$		0			0
$400$	15.2003			0.760014
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	0.984431	−	0.175774i	$-0.0562428\pi$
$401$	−0.0150147	−	0.0851529i	−0.000749801	−	0.00425233i	−0.985180	+	0.171522i	$0.945132\pi$
$402$	−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	0.770019	+	0.638021i	$0.220247\pi$
$409$	−3.47400	+	19.7021i	−0.171778	+	0.974204i	−0.941797	+	0.336182i	$0.890864\pi$
$410$	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	−0.557565	−	0.830134i	$-0.688264\pi$
$421$	3.34730	−	2.80872i	0.163137	−	0.136888i	0.720702	+	0.693245i	$0.243820\pi$
$422$	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	−0.954732	−	0.297468i	$-0.903858\pi$
$431$	−29.3444	−	24.6228i	−1.41347	−	1.18604i	−0.458736	−	0.888572i	$-0.651698\pi$
$432$	22.2913	+	8.11338i	1.07249	+	0.390355i
$433$	−17.0376	+	6.20118i	−0.818775	+	0.298010i	−0.717244	−	0.696823i	$-0.754597\pi$
$433$	−17.0376	+	6.20118i	−0.818775	+	0.298010i	−0.101532	+	0.994832i	$0.532374\pi$
$434$		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	0.999589	−	0.0286685i	$-0.00912670\pi$
$439$	1.05762	+	5.99806i	0.0504774	+	0.286272i	−0.949112	+	0.314940i	$0.898016\pi$
$440$	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	−0.0914266	−	0.995812i	$-0.529143\pi$
$443$	−22.8995	−	19.2149i	−1.08799	−	0.912928i	−0.996559	+	0.0828833i	$0.973587\pi$
$444$	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	−0.702226	−	0.711955i	$-0.747810\pi$
$449$	5.62495	−	9.74270i	0.265458	−	0.459787i	0.967683	+	0.252168i	$0.0811435\pi$
$450$	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	−0.622853	−	0.782339i	$-0.714026\pi$
$461$	−34.4149	−	12.5260i	−1.60286	−	0.583395i	−0.980011	+	0.198945i	$0.936249\pi$
$462$		0			0
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.458340	−	0.888777i	$-0.348444\pi$
$463$	21.4932	−	37.2273i	0.998873	−	1.73010i	0.540534	−	0.841322i	$-0.318222\pi$
$464$	−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	0.993932	+	0.109998i	$0.0350845\pi$
$467$	12.7981	+	22.1670i	0.592227	+	1.02577i	−0.401705	+	0.915769i	$0.631582\pi$
$468$	−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	0.652236	−	0.758016i	$-0.273831\pi$
$479$	35.8739	−	13.0570i	1.63912	−	0.596591i	0.986885	+	0.161424i	$0.0516088\pi$
$480$	−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	−0.940475	−	0.339864i	$-0.889619\pi$
$487$	−3.88191	+	6.72367i	−0.175906	+	0.304678i	0.764568	+	0.644543i	$0.222952\pi$
$488$	−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	−0.274954	+	0.961457i	$0.588663\pi$
$491$	−28.1313	+	23.6050i	−1.26955	+	1.06528i	−0.994596	+	0.103822i	$0.966893\pi$
$492$	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	0.236318	−	0.971676i	$-0.424059\pi$
$499$	−4.62923	−	1.68490i	−0.207233	−	0.0754266i	−0.443551	+	0.896249i	$0.646281\pi$
$500$	−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	0.540663	+	0.841239i	$0.318173\pi$
$503$	−5.72163	+	32.4490i	−0.255115	+	1.44683i	−0.795778	+	0.605589i	$0.792938\pi$
$504$		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	−0.965657	−	0.259819i	$-0.916337\pi$
$509$	−34.7075	+	12.6325i	−1.53839	+	0.559926i	−0.572728	+	0.819746i	$0.694115\pi$
$510$	−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	0.949667	−	0.313262i	$-0.101422\pi$
$521$	4.64590	+	8.04693i	0.203540	+	0.352542i	−0.746126	+	0.665804i	$0.768088\pi$
$522$	8.51548	−	48.2937i	0.372713	−	2.11376i
$523$	4.93423	−	27.9834i	0.215759	−	1.22363i	−0.663826	−	0.747887i	$-0.731068\pi$
$523$	4.93423	−	27.9834i	0.215759	−	1.22363i	0.879585	−	0.475742i	$-0.157820\pi$
$524$	−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	−0.876372	−	0.481635i	$-0.840043\pi$
$541$	2.60220	−	14.7578i	0.111877	−	0.634487i	0.988249	−	0.152852i	$-0.0488458\pi$
$542$	−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	−0.262748	−	0.964864i	$-0.584629\pi$
$547$	3.65270	−	1.32948i	0.156178	−	0.0568443i	0.418926	+	0.908020i	$0.362407\pi$
$548$	−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	0.831420	−	0.555644i	$-0.187528\pi$
$557$	10.1152	+	8.48762i	0.428593	+	0.359632i	−0.402828	+	0.915276i	$0.631973\pi$
$558$	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	−0.730798	−	0.682594i	$-0.760852\pi$
$563$	5.35638	−	9.27752i	0.225745	−	0.391001i	0.956543	+	0.291593i	$0.0941852\pi$
$564$	−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	−0.954714	−	0.297526i	$-0.903839\pi$
$577$	−5.27719	+	9.14036i	−0.219692	+	0.380518i	0.735022	+	0.678044i	$0.237172\pi$
$578$	−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	0.973240	+	0.229791i	$0.0738041\pi$
$587$	3.32619	+	18.8638i	0.137287	+	0.778591i	−0.835954	+	0.548800i	$0.815085\pi$
$588$		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	−0.504282	−	0.863539i	$-0.668243\pi$
$593$	−8.17024	+	2.97373i	−0.335512	+	0.122116i	0.168770	+	0.985655i	$0.446020\pi$
$594$	−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	−0.830008	−	0.557752i	$-0.811664\pi$
$599$	3.44373	−	19.5303i	0.140707	−	0.797988i	0.970715	−	0.240236i	$-0.0772248\pi$
$600$	17.9119	+	31.0244i	0.731252	+	1.26657i
$601$	−16.8807	+	29.2383i	−0.688579	+	1.19265i	0.283718	+	0.958908i	$0.408432\pi$
$601$	−16.8807	+	29.2383i	−0.688579	+	1.19265i	−0.972298	+	0.233747i	$0.924901\pi$
$602$		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	−0.0328044	−	0.999462i	$-0.510444\pi$
$613$	−17.3405	−	6.31142i	−0.700376	−	0.254916i	−0.667571	+	0.744546i	$0.732666\pi$
$614$	−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	0.560408	+	0.828217i	$0.310644\pi$
$617$	−6.19671	+	35.1433i	−0.249470	+	1.41482i	−0.809878	+	0.586598i	$0.800467\pi$
$618$	−3.71167	+	21.0499i	−0.149305	+	0.846752i
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	0.900452	−	0.434955i	$-0.143236\pi$
$619$	1.82976	+	3.16923i	0.0735441	+	0.127382i	−0.826908	+	0.562337i	$0.809902\pi$
$620$	−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	−0.327129	−	0.944980i	$-0.606081\pi$
$631$	0.745977	−	0.271514i	0.0296969	−	0.0108088i	0.356826	+	0.934171i	$0.383859\pi$
$632$	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	−0.266723	−	0.963773i	$-0.585941\pi$
$641$	−27.6104	−	10.0494i	−1.09055	−	0.396926i	−0.823823	+	0.566847i	$0.808163\pi$
$642$	37.3089	−	13.5793i	1.47246	−	0.535933i
$643$	−17.0168	+	14.2788i	−0.671078	+	0.563101i	−0.913384	−	0.407098i	$-0.866541\pi$
$643$	−17.0168	+	14.2788i	−0.671078	+	0.563101i	0.242306	+	0.970200i	$0.422096\pi$
$644$		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	0.471160	+	0.882048i	$0.343835\pi$
$653$	−13.5000	+	23.3827i	−0.528296	+	0.915035i	−0.999456	+	0.0329874i	$0.989498\pi$
$654$	−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	0.956732	−	0.290970i	$-0.0939781\pi$
$659$	21.4691	+	18.0147i	0.836317	+	0.701753i	−0.120415	+	0.992724i	$0.538423\pi$
$660$	0.979055	+	0.356347i	0.0381097	+	0.0138708i
$661$	10.6823	−	3.88803i	0.415492	−	0.151227i	−0.125811	−	0.992054i	$-0.540153\pi$
$661$	10.6823	−	3.88803i	0.415492	−	0.151227i	0.541303	+	0.840827i	$0.317931\pi$
$662$	−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	0.980344	−	0.197296i	$-0.0632160\pi$
$673$	8.28359	+	14.3476i	0.319309	+	0.553059i	−0.661035	+	0.750355i	$0.729883\pi$
$674$	−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	−0.939781	−	0.341777i	$-0.888971\pi$
$677$	−4.52481	+	7.83721i	−0.173903	+	0.301208i	0.765878	+	0.642986i	$0.222305\pi$
$678$	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	−0.320099	−	0.947384i	$-0.603716\pi$
$691$	17.3601	−	30.0686i	0.660409	−	1.14386i	0.980508	−	0.196478i	$-0.0629504\pi$
$692$	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	0.786905	+	0.617074i	$0.211682\pi$
$701$	6.84436	+	38.8163i	0.258508	+	1.46607i	−0.528397	+	0.848997i	$0.677207\pi$
$702$	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	−0.999954	−	0.00959399i	$-0.996946\pi$
$709$	−31.5009	−	26.4324i	−1.18304	−	0.992690i	−0.183088	−	0.983096i	$-0.558609\pi$
$710$	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	0.211943	−	0.977282i	$-0.432021\pi$
$719$	32.4768	−	27.2513i	1.21118	−	1.01630i	0.999238	−	0.0390200i	$-0.0124236\pi$
$720$	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	0.998324	+	0.0578805i	$0.0184342\pi$
$727$	48.5411	+	17.6675i	1.80029	+	0.655251i	0.801965	+	0.597371i	$0.203788\pi$
$728$		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	0.573037	−	0.819530i	$-0.305765\pi$
$733$	−11.4581	−	19.8460i	−0.423215	−	0.733030i	−0.996252	+	0.0864997i	$0.972432\pi$
$734$	−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	0.932619	+	0.360862i	$0.117517\pi$
$739$	4.88413	+	27.6993i	0.179666	+	1.01894i	−0.752954	+	0.658074i	$0.771372\pi$
$740$	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	0.998091	−	0.0617657i	$-0.0196731\pi$
$743$	1.06489	+	6.03931i	0.0390671	+	0.221561i	−0.959024	+	0.283326i	$0.908562\pi$
$744$	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	−0.961707	−	0.274081i	$-0.911626\pi$
$751$	0.979522	−	5.55515i	0.0357433	−	0.202710i	0.997450	+	0.0713710i	$0.0227374\pi$
$752$	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	−0.397648	−	0.917538i	$-0.630173\pi$
$757$	12.0207	−	10.0866i	0.436900	−	0.366602i	0.834548	+	0.550936i	$0.185729\pi$
$758$	−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	0.829327	+	0.558764i	$0.188724\pi$
$769$	−3.91266	+	22.1898i	−0.141094	+	0.800184i	−0.970421	+	0.241420i	$0.922387\pi$
$770$		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	0.929660	−	0.368418i	$-0.120100\pi$
$773$	20.2481	+	16.9902i	0.728273	+	0.611094i	−0.201387	+	0.979512i	$0.564545\pi$
$774$	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	0.693424	−	0.720530i	$-0.256101\pi$
$787$	−7.77884	−	13.4733i	−0.277286	−	0.480273i	−0.970709	+	0.240257i	$0.922768\pi$
$788$	−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	−0.959880	−	0.280412i	$-0.909529\pi$
$809$	−20.5581	−	35.6076i	−0.722784	−	1.25190i	0.237096	−	0.971486i	$-0.423804\pi$
$810$	−1.84864	+	3.20194i	−0.0649546	+	0.112505i
$811$	−12.7836	−	10.7267i	−0.448892	−	0.376665i	0.390132	−	0.920759i	$-0.372429\pi$
$811$	−12.7836	−	10.7267i	−0.448892	−	0.376665i	−0.839025	+	0.544093i	$0.816874\pi$
$812$		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	0.228581	−	0.973525i	$-0.426591\pi$
$821$	29.4971	−	10.7361i	1.02945	−	0.374691i	0.800873	+	0.598834i	$0.204369\pi$
$822$	0.932419	+	0.339373i	0.0325218	+	0.0118370i
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.997751	+	0.0670347i	$0.0213538\pi$
$823$	35.4877	+	29.7777i	1.23702	+	1.03799i	0.239274	+	0.970952i	$0.423091\pi$
$824$	−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	−0.571773	−	0.820412i	$-0.693744\pi$
$827$	7.07769	−	40.1396i	0.246115	−	1.39579i	0.817888	−	0.575377i	$-0.195145\pi$
$828$	−1.31727	−	2.28157i	−0.0457782	−	0.0792901i
$829$	−17.7417	+	30.7295i	−0.616195	+	1.06728i	0.373979	+	0.927437i	$0.377993\pi$
$829$	−17.7417	+	30.7295i	−0.616195	+	1.06728i	−0.990174	+	0.139843i	$0.955340\pi$
$830$	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	0.0219545	−	0.999759i	$-0.493011\pi$
$839$	29.2649	−	24.5562i	1.01034	−	0.847774i	0.988383	+	0.151985i	$0.0485667\pi$
$840$		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	0.961286	+	0.275552i	$0.0888608\pi$
$853$	4.44568	+	25.2127i	0.152217	+	0.863266i	−0.809069	+	0.587714i	$0.800028\pi$
$854$		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	0.981261	+	0.192683i	$0.0617189\pi$
$857$	3.66163	+	20.7661i	0.125079	+	0.709357i	−0.856182	+	0.516674i	$0.827170\pi$
$858$	−17.0326	+	14.2920i	−0.581482	+	0.487921i
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	−0.636082	−	0.771621i	$-0.719446\pi$
$859$	−18.3871	+	6.69237i	−0.627361	+	0.228341i	0.00872148	+	0.999962i	$0.497224\pi$
$860$	−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	0.820832	−	0.571170i	$-0.193510\pi$
$863$	−2.47447	−	4.28591i	−0.0842319	−	0.145894i	−0.905064	+	0.425276i	$0.860177\pi$
$864$	−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	−0.626874	−	0.779121i	$-0.715666\pi$
$877$	0.934478	−	0.784120i	0.0315551	−	0.0264779i	0.658429	+	0.752643i	$0.271221\pi$
$878$	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	−0.146609	−	0.989194i	$-0.546836\pi$
$881$	23.2515	−	40.2728i	0.783363	−	1.35682i	0.929972	−	0.367630i	$-0.119831\pi$
$882$		0			0
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	−0.923472	−	0.383667i	$-0.874661\pi$
$883$	2.24438	−	12.7285i	0.0755296	−	0.428349i	0.999001	−	0.0446828i	$-0.0142277\pi$
$884$	−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	0.890595	−	0.454796i	$-0.150288\pi$
$887$	17.7909	+	14.9283i	0.597359	+	0.501243i	−0.293237	+	0.956040i	$0.594732\pi$
$888$	−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	0.879719	−	0.475495i	$-0.157731\pi$
$907$	37.5847	+	13.6797i	1.24798	+	0.454228i	0.368261	+	0.929722i	$0.379953\pi$
$908$	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	0.324436	+	0.945908i	$0.394825\pi$
$919$	−19.9158	+	34.4952i	−0.656962	+	1.13789i	−0.981398	+	0.191984i	$0.938508\pi$
$920$	−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	−0.960088	−	0.279698i	$-0.909766\pi$
$929$	−4.68051	−	26.5445i	−0.153563	−	0.870897i	0.806526	−	0.591199i	$-0.201345\pi$
$930$	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	0.609368	−	0.792887i	$-0.291423\pi$
$937$	−2.00980	−	1.68642i	−0.0656573	−	0.0550930i	−0.675026	+	0.737794i	$0.735867\pi$
$938$		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	−0.885260	−	0.465096i	$-0.846020\pi$
$941$	3.24194	−	18.3860i	0.105684	−	0.599366i	0.990945	−	0.134270i	$-0.0428690\pi$
$942$	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	−0.532227	−	0.846602i	$-0.678645\pi$
$947$	6.43448	−	5.39917i	0.209092	−	0.175449i	0.741320	+	0.671152i	$0.234200\pi$
$948$	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	−0.120602	−	0.992701i	$-0.538483\pi$
$953$	25.8102	−	21.6573i	0.836075	−	0.701550i	0.956677	+	0.291151i	$0.0940382\pi$
$954$	−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	0.999881	+	0.0154262i	$0.00491051\pi$
$967$	2.03920	+	11.5649i	0.0655763	+	0.371902i	−0.934305	+	0.356475i	$0.883978\pi$
$968$	−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	−0.999473	−	0.0324723i	$-0.989662\pi$
$971$	−2.22432	−	12.6147i	−0.0713817	−	0.404826i	0.928091	−	0.372354i	$-0.121449\pi$
$972$	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	0.726121	−	0.687567i	$-0.241321\pi$
$977$	−7.26382	−	12.5813i	−0.232390	−	0.402512i	−0.958511	+	0.285055i	$0.907988\pi$
$978$	−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	−0.279293	−	0.960206i	$-0.590100\pi$
$983$	−34.8158	−	12.6719i	−1.11045	−	0.404172i	−0.831159	+	0.556034i	$0.812322\pi$
$984$	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	−0.600082	−	0.799938i	$-0.704865\pi$
$991$	2.62860	−	2.20566i	0.0835004	−	0.0700651i	0.683582	+	0.729873i	$0.260421\pi$
$992$	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	0.929313	+	0.369294i	$0.120400\pi$
$997$	−2.21853	+	12.5819i	−0.0702616	+	0.398473i	−0.999574	+	0.0291792i	$0.990711\pi$
$998$	−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.883.1		6
7.2	even	3		931.2.x.b.655.1		6
7.3	odd	6		931.2.v.b.275.1		6
7.4	even	3		931.2.v.a.275.1		6
7.5	odd	6		931.2.x.a.655.1		6
7.6	odd	2		19.2.e.a.9.1	✓	6
19.17	even	9	inner	931.2.w.a.834.1		6
21.20	even	2		171.2.u.c.28.1		6
28.27	even	2		304.2.u.b.161.1		6
35.13	even	4		475.2.u.a.199.1		12
35.27	even	4		475.2.u.a.199.2		12
35.34	odd	2		475.2.l.a.351.1		6
133.6	odd	18		361.2.a.g.1.2		3
133.13	even	18		361.2.a.h.1.2		3
133.17	odd	18		931.2.x.a.226.1		6
133.27	even	6		361.2.e.a.234.1		6
133.34	even	18		361.2.c.h.68.2		6
133.41	even	18		361.2.e.b.62.1		6
133.48	even	18		361.2.c.h.292.2		6
133.55	odd	18		19.2.e.a.17.1	yes	6
133.62	odd	18		361.2.e.g.54.1		6
133.69	even	6		361.2.e.b.99.1		6
133.74	even	9		931.2.x.b.226.1		6
133.83	odd	6		361.2.e.f.99.1		6
133.90	even	18		361.2.e.a.54.1		6
133.93	even	9		931.2.v.a.606.1		6
133.97	even	18		361.2.e.h.245.1		6
133.104	odd	18		361.2.c.i.292.2		6
133.111	odd	18		361.2.e.f.62.1		6
133.118	odd	18		361.2.c.i.68.2		6
133.125	odd	6		361.2.e.g.234.1		6
133.131	odd	18		931.2.v.b.606.1		6
133.132	even	2		361.2.e.h.28.1		6
399.146	odd	18		3249.2.a.s.1.2		3
399.188	even	18		171.2.u.c.55.1		6
399.272	even	18		3249.2.a.z.1.2		3
532.55	even	18		304.2.u.b.17.1		6
532.139	even	18		5776.2.a.br.1.3		3
532.279	odd	18		5776.2.a.bi.1.1		3
665.139	odd	18		9025.2.a.bd.1.2		3
665.188	even	36		475.2.u.a.74.2		12
665.279	even	18		9025.2.a.x.1.2		3
665.454	odd	18		475.2.l.a.226.1		6
665.587	even	36		475.2.u.a.74.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	7.6	odd	2
19.2.e.a.17.1	yes	6	133.55	odd	18
171.2.u.c.28.1		6	21.20	even	2
171.2.u.c.55.1		6	399.188	even	18
304.2.u.b.17.1		6	532.55	even	18
304.2.u.b.161.1		6	28.27	even	2
361.2.a.g.1.2		3	133.6	odd	18
361.2.a.h.1.2		3	133.13	even	18
361.2.c.h.68.2		6	133.34	even	18
361.2.c.h.292.2		6	133.48	even	18
361.2.c.i.68.2		6	133.118	odd	18
361.2.c.i.292.2		6	133.104	odd	18
361.2.e.a.54.1		6	133.90	even	18
361.2.e.a.234.1		6	133.27	even	6
361.2.e.b.62.1		6	133.41	even	18
361.2.e.b.99.1		6	133.69	even	6
361.2.e.f.62.1		6	133.111	odd	18
361.2.e.f.99.1		6	133.83	odd	6
361.2.e.g.54.1		6	133.62	odd	18
361.2.e.g.234.1		6	133.125	odd	6
361.2.e.h.28.1		6	133.132	even	2
361.2.e.h.245.1		6	133.97	even	18
475.2.l.a.226.1		6	665.454	odd	18
475.2.l.a.351.1		6	35.34	odd	2
475.2.u.a.74.1		12	665.587	even	36
475.2.u.a.74.2		12	665.188	even	36
475.2.u.a.199.1		12	35.13	even	4
475.2.u.a.199.2		12	35.27	even	4
931.2.v.a.275.1		6	7.4	even	3
931.2.v.a.606.1		6	133.93	even	9
931.2.v.b.275.1		6	7.3	odd	6
931.2.v.b.606.1		6	133.131	odd	18
931.2.w.a.834.1		6	19.17	even	9	inner
931.2.w.a.883.1		6	1.1	even	1	trivial
931.2.x.a.226.1		6	133.17	odd	18
931.2.x.a.655.1		6	7.5	odd	6
931.2.x.b.226.1		6	133.74	even	9
931.2.x.b.655.1		6	7.2	even	3
3249.2.a.s.1.2		3	399.146	odd	18
3249.2.a.z.1.2		3	399.272	even	18
5776.2.a.bi.1.1		3	532.279	odd	18
5776.2.a.br.1.3		3	532.139	even	18
9025.2.a.x.1.2		3	665.279	even	18
9025.2.a.bd.1.2		3	665.139	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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