LMFDB - Embedded newform 475.2.l.a.351.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (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:	$3.79289409601$
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			351.1
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	475.351
Dual form			475.2.l.a.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +O(q^{10})$	\(q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +(1.11334 + 1.92836i) q^{11} +(0.266044 - 0.460802i) q^{12} +(-1.97178 - 1.65452i) q^{13} +(0.439693 + 0.160035i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-0.0812519 - 0.460802i) q^{17} +7.12836 q^{18} +(-4.29813 - 0.725293i) q^{19} +(-0.173648 - 0.984808i) q^{21} +(-2.29813 + 1.92836i) q^{22} +(-2.53209 + 0.921605i) q^{23} +(7.96451 + 2.89884i) q^{24} +(1.73396 - 3.00330i) q^{26} +(-3.29813 - 5.71253i) q^{27} +(0.0111444 - 0.0632028i) q^{28} +(-1.19459 + 6.77487i) q^{29} +(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} +(1.89646 - 1.59132i) q^{41} +(1.26604 - 0.460802i) q^{42} +(3.66637 + 1.33445i) q^{43} +(0.315207 + 0.264490i) q^{44} +(-1.81521 - 3.14403i) q^{46} +(1.26604 - 7.18009i) q^{47} +(-1.79813 + 10.1977i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-1.03209 - 0.866025i) q^{51} +(-0.446967 - 0.162683i) q^{52} +(-2.66637 + 0.970481i) q^{53} +(6.80793 - 5.71253i) q^{54} +1.02229 q^{56} +(-10.8229 + 6.35532i) q^{57} -9.26857 q^{58} +(-1.09492 - 6.20961i) q^{59} +(-8.57785 + 3.12208i) q^{61} +(8.99660 + 3.27449i) q^{62} +(-1.40760 - 1.18112i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-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} +(-0.792204 + 0.145708i) q^{76} +0.773318 q^{77} +(-1.73396 - 9.83375i) q^{78} +(-9.07398 + 7.61397i) q^{79} +(-2.93242 - 1.06731i) q^{81} +(2.55509 + 2.14398i) q^{82} +(-7.41534 + 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(-0.912818 + 5.17685i) q^{86} +(9.90420 + 17.1546i) q^{87} +(-3.27719 + 5.67626i) q^{88} +(-7.88326 - 6.61484i) q^{89} +(-0.840022 + 0.305743i) q^{91} +(-0.381445 + 0.320070i) q^{92} +(-3.55303 - 20.1503i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-1.64156 - 9.30975i) q^{97} +(-7.10014 + 5.95772i) q^{98} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	$ 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 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^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 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^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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	$0.102482\pi$
$2$	0.233956	+	1.32683i	0.165432	+	0.938209i	−0.783187	+	0.621786i	$0.786407\pi$
$3$	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			0
$5$		0			0
$6$	2.97178	+	2.49362i	1.21322	+	1.01802i
$7$	0.173648	−	0.300767i	0.0656328	−	0.113679i	−0.831342	−	0.555762i	$-0.812427\pi$
$7$	0.173648	−	0.300767i	0.0656328	−	0.113679i	0.896975	+	0.442082i	$0.145760\pi$
$8$	1.47178	+	2.54920i	0.520353	+	0.901278i
$9$	0.918748	−	5.21048i	0.306249	−	1.73683i
$10$		0			0
$11$	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	$0.838404\pi$
$14$	0.439693	+	0.160035i	0.117513	+	0.0427712i
$15$		0			0
$16$	−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			0
$21$	−0.173648	−	0.984808i	−0.0378931	−	0.214903i
$22$	−2.29813	+	1.92836i	−0.489964	+	0.411128i
$23$	−2.53209	+	0.921605i	−0.527977	+	0.192168i	−0.592235	−	0.805765i	$-0.701754\pi$
$23$	−2.53209	+	0.921605i	−0.527977	+	0.192168i	0.0642578	+	0.997933i	$0.479532\pi$
$24$	7.96451	+	2.89884i	1.62575	+	0.591724i
$25$		0			0
$26$	1.73396	−	3.00330i	0.340057	−	0.588995i
$27$	−3.29813	−	5.71253i	−0.634726	−	1.09938i
$28$	0.0111444	−	0.0632028i	0.00210608	−	0.0119442i
$29$	−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	$0.835014\pi$
$30$		0			0
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	−0.347696	−	0.937607i	$-0.613036\pi$
$31$	3.55303	−	6.15403i	0.638144	−	1.10530i	0.985840	−	0.167690i	$-0.0536307\pi$
$32$	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	$-0.633202\pi$
$37$	−4.94356			−0.812717			−0.406358	+	0.913714i	$0.633202\pi$
$38$	−0.0432332	−	5.87257i	−0.00701336	−	0.952657i
$39$	−7.41147			−1.18679
$40$		0			0
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	−0.482574	−	0.875855i	$-0.660298\pi$
$41$	1.89646	−	1.59132i	0.296177	−	0.248522i	0.778751	+	0.627333i	$0.215854\pi$
$42$	1.26604	−	0.460802i	0.195355	−	0.0711034i
$43$	3.66637	+	1.33445i	0.559117	+	0.203502i	0.606093	−	0.795394i	$-0.292736\pi$
$43$	3.66637	+	1.33445i	0.559117	+	0.203502i	−0.0469757	+	0.998896i	$0.514958\pi$
$44$	0.315207	+	0.264490i	0.0475193	+	0.0398734i
$45$		0			0
$46$	−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
$49$	3.43969	+	5.95772i	0.491385	+	0.851103i
$50$		0			0
$51$	−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	$-0.673543\pi$
$53$	−2.66637	+	0.970481i	−0.366255	+	0.133306i	0.152335	+	0.988329i	$0.451321\pi$
$54$	6.80793	−	5.71253i	0.926442	−	0.777377i
$55$		0			0
$56$	1.02229			0.136609
$57$	−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	$-0.920928\pi$
$59$	−1.09492	−	6.20961i	−0.142547	−	0.808423i	0.826757	−	0.562559i	$-0.190183\pi$
$60$		0			0
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.826682	−	0.562669i	$-0.809775\pi$
$61$	−8.57785	+	3.12208i	−1.09828	+	0.399742i	−0.271599	+	0.962411i	$0.587552\pi$
$62$	8.99660	+	3.27449i	1.14257	+	0.415861i
$63$	−1.40760	−	1.18112i	−0.177341	−	0.148807i
$64$	−4.29813	+	7.44459i	−0.537267	+	0.930573i
$65$		0			0
$66$	−1.50000	+	8.50692i	−0.184637	+	1.04713i
$67$	−1.33275	+	7.55839i	−0.162821	+	0.923405i	0.788461	+	0.615084i	$0.210878\pi$
$67$	−1.33275	+	7.55839i	−0.162821	+	0.923405i	−0.951283	+	0.308320i	$0.900233\pi$
$68$	−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
$75$		0			0
$76$	−0.792204	+	0.145708i	−0.0908720	+	0.0167139i
$77$	0.773318			0.0881278
$78$	−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	$0.509921\pi$
$80$		0			0
$81$	−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	$0.863985\pi$
$84$	−0.0923963	−	0.160035i	−0.0100813	−	0.0174613i
$85$		0			0
$86$	−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	$-0.461406\pi$
$89$	−7.88326	−	6.61484i	−0.835623	−	0.701171i	−0.956575	+	0.291487i	$0.905850\pi$
$90$		0			0
$91$	−0.840022	+	0.305743i	−0.0880583	+	0.0320506i
$92$	−0.381445	+	0.320070i	−0.0397684	+	0.0333696i
$93$	−3.55303	−	20.1503i	−0.368432	−	2.08948i
$94$	9.82295			1.01316
$95$		0			0
$96$	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	$-0.214891\pi$
$98$	−7.10014	+	5.95772i	−0.717222	+	0.601821i
$99$	11.0706	−	4.02936i	1.11263	−	0.404966i
$100$		0			0
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	0.218194	−	0.975905i	$-0.429983\pi$
$101$	−7.08512	−	5.94512i	−0.704996	−	0.591562i	−0.923190	+	0.384343i	$0.874428\pi$
$102$	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	−0.505282	−	0.862954i	$-0.668611\pi$
$107$	5.11721	−	8.86327i	0.494699	−	0.856845i	0.999981	+	0.00610974i	$0.00194480\pi$
$108$	−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	$0.583286\pi$
$110$		0			0
$111$	−10.9042	+	9.14971i	−1.03498	+	0.868452i
$112$	0.216881	+	1.23000i	0.0204934	+	0.116224i
$113$	17.6878			1.66393			0.831963	−	0.554830i	$-0.187217\pi$
$113$	17.6878			1.66393			0.831963	+	0.554830i	$0.187217\pi$
$114$	−10.9645	−	12.8733i	−1.02692	−	1.20570i
$115$		0			0
$116$	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
$119$	−0.152704	−	0.0555796i	−0.0139983	−	0.00509497i
$120$		0			0
$121$	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
$125$		0			0
$126$	1.23783	−	2.14398i	0.110274	−	0.191001i
$127$	−8.88919	−	7.45891i	−0.788788	−	0.661871i	0.156657	−	0.987653i	$-0.449928\pi$
$127$	−8.88919	−	7.45891i	−0.788788	−	0.661871i	−0.945445	+	0.325782i	$0.894373\pi$
$128$	−8.92514	−	3.24849i	−0.788879	−	0.287128i
$129$	10.5569	−	3.84240i	0.929484	−	0.338304i
$130$		0			0
$131$	0.320422	+	1.81720i	0.0279954	+	0.158770i	0.995601	−	0.0936982i	$-0.0298689\pi$
$131$	0.320422	+	1.81720i	0.0279954	+	0.158770i	−0.967605	+	0.252468i	$0.918758\pi$
$132$	1.18479			0.103123
$133$	−0.964508	+	1.16679i	−0.0836334	+	0.101174i
$134$	−10.3405			−0.893282
$135$		0			0
$136$	1.05509	−	0.885328i	0.0904735	−	0.0759162i
$137$	0.240352	−	0.0874810i	0.0205347	−	0.00747401i	−0.331732	−	0.943374i	$-0.607633\pi$
$137$	0.240352	−	0.0874810i	0.0205347	−	0.00747401i	0.352267	+	0.935900i	$0.385411\pi$
$138$	−9.82295	−	3.57526i	−0.836185	−	0.304346i
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	0.770704	−	0.637193i	$-0.219905\pi$
$139$	3.26604	+	2.74054i	0.277022	+	0.232449i	−0.493682	+	0.869643i	$0.664349\pi$
$140$		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
$145$		0			0
$146$	−1.43376	−	1.20307i	−0.118659	−	0.0995668i
$147$	18.6138	+	6.77487i	1.53524	+	0.558782i
$148$	−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	$0.0404945\pi$
$150$		0			0
$151$	−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
$154$	0.180922	+	1.02606i	0.0145791	+	0.0826823i
$155$		0			0
$156$	−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			0
$161$	−0.162504	+	0.921605i	−0.0128071	+	0.0726326i
$162$	0.730085	−	4.14052i	0.0573609	−	0.325310i
$163$	4.17752	+	7.23567i	0.327209	+	0.566742i	0.981957	−	0.189105i	$-0.0605587\pi$
$163$	4.17752	+	7.23567i	0.327209	+	0.566742i	−0.654748	+	0.755847i	$0.727225\pi$
$164$	0.228741	−	0.396191i	0.0178617	−	0.0309373i
$165$		0			0
$166$	−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	$0.338990\pi$
$168$	2.25490	−	1.89209i	0.173969	−	0.145978i
$169$	−1.10694	−	6.27779i	−0.0851496	−	0.482907i
$170$		0			0
$171$	−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			0
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	−0.878829	−	0.477136i	$-0.841675\pi$
$181$	1.48246	−	8.40744i	0.110190	−	0.624920i	0.989020	−	0.147784i	$-0.0472141\pi$
$182$	−0.602196	−	1.04303i	−0.0446378	−	0.0773149i
$183$	−13.1420	+	22.7627i	−0.971487	+	1.68266i
$184$	−6.07604	−	5.09840i	−0.447931	−	0.375859i
$185$		0			0
$186$	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
$189$	−2.29086			−0.166635
$190$		0			0
$191$	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	$-0.725632\pi$
$193$	−0.228026	+	0.191336i	−0.0164137	+	0.0137727i	0.634544	+	0.772887i	$0.281188\pi$
$194$	11.9684	−	4.35613i	0.859279	−	0.312752i
$195$		0			0
$196$	0.973841	+	0.817150i	0.0695601	+	0.0583678i
$197$	6.57057	−	11.3806i	0.468134	−	0.810832i	−0.531203	−	0.847245i	$-0.678260\pi$
$197$	6.57057	−	11.3806i	0.468134	−	0.810832i	0.999337	+	0.0364128i	$0.0115931\pi$
$198$	7.93629	+	13.7461i	0.564008	+	0.976890i
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	−0.986347	−	0.164680i	$-0.947341\pi$
$199$	−0.0445774	+	0.252811i	−0.00316001	+	0.0179213i	0.983187	+	0.182602i	$0.0584519\pi$
$200$		0			0
$201$	11.0496	+	19.1385i	0.779381	+	1.34993i
$202$	6.23055	−	10.7916i	0.438380	−	0.759297i
$203$	1.83022	+	1.53574i	0.128456	+	0.107788i
$204$	−0.233956	−	0.0851529i	−0.0163802	−	0.00596189i
$205$		0			0
$206$	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
$215$		0			0
$216$	9.70826	−	16.8152i	0.660564	−	1.14413i
$217$	−1.23396	−	2.13727i	−0.0837664	−	0.145088i
$218$	−0.426489	+	2.41874i	−0.0288855	+	0.163818i
$219$	−0.694593	+	3.93923i	−0.0469362	+	0.266189i
$220$		0			0
$221$	−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	$0.703081\pi$
$224$	0.340022	−	0.123758i	0.0227187	−	0.00826893i
$225$		0			0
$226$	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	$-0.737339\pi$
$229$	−20.5330			−1.35686			−0.678430	+	0.734665i	$0.737339\pi$
$230$		0			0
$231$	1.70574	−	1.43128i	0.112229	−	0.0941715i
$232$	−19.0287	+	6.92588i	−1.24929	+	0.454706i
$233$	16.5865	+	6.03698i	1.08662	+	0.395496i	0.822366	−	0.568959i	$-0.192654\pi$
$233$	16.5865	+	6.03698i	1.08662	+	0.395496i	0.264249	+	0.964454i	$0.414876\pi$
$234$	−14.0556	−	11.7940i	−0.918841	−	0.770999i
$235$		0			0
$236$	−0.582596	−	1.00909i	−0.0379238	−	0.0656859i
$237$	−5.92262	+	33.5888i	−0.384715	+	2.18183i
$238$	0.0380187	−	0.215615i	0.00246438	−	0.0139762i
$239$	−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	$0.857574\pi$
$240$		0			0
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	0.916298	−	0.400498i	$-0.131163\pi$
$241$	10.5719	+	8.87089i	0.680997	+	0.571424i	−0.235300	+	0.971923i	$0.575607\pi$
$242$	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
$250$		0			0
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	−0.215528	−	0.976498i	$-0.569147\pi$
$251$	3.91400	−	1.42458i	0.247050	−	0.0899187i	0.462577	+	0.886579i	$0.346925\pi$
$252$	−0.319078	−	0.116135i	−0.0201000	−	0.00731581i
$253$	−4.59627	−	3.85673i	−0.288965	−	0.242470i
$254$	7.81702	−	13.5395i	0.490483	−	0.849542i
$255$		0			0
$256$	−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
$259$	−0.858441	+	1.48686i	−0.0533409	+	0.0923892i
$260$		0			0
$261$	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	$-0.836539\pi$
$263$	−8.73261	+	7.32753i	−0.538476	+	0.451835i	0.332540	+	0.943089i	$0.392094\pi$
$264$	3.27719	+	18.5859i	0.201697	+	1.14388i
$265$		0			0
$266$	−1.77379	−	1.00676i	−0.108758	−	0.0617283i
$267$	−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	$-0.520909\pi$
$269$	14.8537	−	12.4637i	0.905646	−	0.759927i	0.971286	+	0.237916i	$0.0764644\pi$
$270$		0			0
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.694725	−	0.719276i	$-0.255526\pi$
$271$	12.5865	+	4.58110i	0.764573	+	0.278282i	0.0698486	+	0.997558i	$0.477748\pi$
$272$	1.28905	+	1.08164i	0.0781600	+	0.0655841i
$273$	−1.28699	+	2.22913i	−0.0778921	+	0.134913i
$274$	0.172304	+	0.298439i	0.0104093	+	0.0180294i
$275$		0			0
$276$	−0.248970	+	1.41198i	−0.0149863	+	0.0849913i
$277$	8.87346	+	15.3693i	0.533154	+	0.923450i	0.999250	+	0.0387161i	$0.0123268\pi$
$277$	8.87346	+	15.3693i	0.533154	+	0.923450i	−0.466096	+	0.884734i	$0.654340\pi$
$278$	−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
$285$		0			0
$286$	7.72193			0.456608
$287$	−0.149300	−	0.846723i	−0.00881290	−	0.0499805i
$288$	4.22281	−	3.54336i	0.248832	−	0.208794i
$289$	15.7690	−	5.73946i	0.927590	−	0.337615i
$290$		0			0
$291$	−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	$0.932590\pi$
$294$	−4.63429	+	26.2823i	−0.270277	+	1.53282i
$295$		0			0
$296$	−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
$300$		0			0
$301$	1.03802	−	0.871001i	0.0598304	−	0.0502037i
$302$	−1.02048	−	5.78742i	−0.0587219	−	0.333028i
$303$	−26.6313			−1.52993
$304$	13.5175	−	7.93761i	0.775284	−	0.455253i
$305$		0			0
$306$	−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	$0.169464\pi$
$308$	0.134285	−	0.0488759i	0.00765162	−	0.00278496i
$309$	−14.9081	−	5.42609i	−0.848091	−	0.308680i
$310$		0			0
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	−0.998551	−	0.0538151i	$-0.982862\pi$
$311$	−7.98293	+	13.8268i	−0.452670	+	0.784048i	0.545881	+	0.837863i	$0.316195\pi$
$312$	−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	$-0.966492\pi$
$317$	−22.6229	−	18.9829i	−1.27063	−	1.06618i	−0.276164	−	0.961111i	$-0.589063\pi$
$318$	−10.3439	−	3.76487i	−0.580057	−	0.211123i
$319$	−14.3944	+	5.23913i	−0.805932	+	0.293335i
$320$		0			0
$321$	−5.11721	−	29.0211i	−0.285615	−	1.61980i
$322$	−1.26083			−0.0702633
$323$	0.0150147	+	2.03952i	0.000835443	+	0.113482i
$324$	−0.576666			−0.0320370
$325$		0			0
$326$	−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
$329$	−1.93969	−	1.62760i	−0.106939	−	0.0897322i
$330$		0			0
$331$	−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
$335$		0			0
$336$	2.75490	+	2.31164i	0.150292	+	0.126110i
$337$	16.7827	+	6.10841i	0.914212	+	0.332746i	0.755934	−	0.654648i	$-0.227183\pi$
$337$	16.7827	+	6.10841i	0.914212	+	0.332746i	0.158279	+	0.987394i	$0.449406\pi$
$338$	8.07057	−	2.93745i	0.438981	−	0.159776i
$339$	39.0146	−	32.7371i	2.11898	−	1.77804i
$340$		0			0
$341$	15.8229			0.856861
$342$	−30.6386	−	5.17015i	−1.65675	−	0.279569i
$343$	4.82026			0.260270
$344$	1.99432	+	11.3103i	0.107526	+	0.609813i
$345$		0			0
$346$	−25.5030	+	9.28233i	−1.37105	+	0.499021i
$347$	−5.45084	−	1.98394i	−0.292616	−	0.106504i	0.191541	−	0.981485i	$-0.438652\pi$
$347$	−5.45084	−	1.98394i	−0.292616	−	0.106504i	−0.484157	+	0.874981i	$0.660874\pi$
$348$	2.80406	+	2.35289i	0.150314	+	0.126128i
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	−0.928919	−	0.370282i	$-0.879261\pi$
$349$	−2.68614	+	4.65253i	−0.143786	+	0.249044i	0.785134	+	0.619326i	$0.212594\pi$
$350$		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
$355$		0			0
$356$	−1.78699	−	0.650411i	−0.0947102	−	0.0344717i
$357$	−0.439693	+	0.160035i	−0.0232710	+	0.00846995i
$358$	−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	$0.887980\pi$
$360$		0			0
$361$	17.9479	+	6.23481i	0.944626	+	0.328148i
$362$	11.5021			0.604535
$363$	−3.02094	−	17.1326i	−0.158558	−	0.899230i
$364$	−0.126545	+	0.106183i	−0.00663274	+	0.00556553i
$365$		0			0
$366$	−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
$370$		0			0
$371$	−0.171122	+	0.970481i	−0.00888421	+	0.0503849i
$372$	−1.89053	−	3.27449i	−0.0980194	−	0.169775i
$373$	17.4488	−	30.2222i	0.903463	−	1.56484i	0.0804968	−	0.996755i	$-0.474349\pi$
$373$	17.4488	−	30.2222i	0.903463	−	1.56484i	0.822967	−	0.568090i	$-0.192317\pi$
$374$	1.07532	+	0.902302i	0.0556036	+	0.0466569i
$375$		0			0
$376$	20.1668	−	7.34013i	1.04003	−	0.378538i
$377$	13.5646	−	11.3821i	0.698615	−	0.586207i
$378$	−0.535959	−	3.03958i	−0.0275668	−	0.156339i
$379$	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			0
$381$	−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	$0.841550\pi$
$390$		0			0
$391$	0.630415	+	1.09191i	0.0318815	+	0.0552203i
$392$	−10.1250	+	17.5369i	−0.511387	+	0.885749i
$393$	4.07011	+	3.41523i	0.205310	+	0.172275i
$394$	16.6373	+	6.05547i	0.838174	+	0.305070i
$395$		0			0
$396$	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
$399$	0.0320889	+	4.35878i	0.00160645	+	0.218212i
$400$		0			0
$401$	−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
$405$		0			0
$406$	−1.60947	+	2.78768i	−0.0798767	+	0.138350i
$407$	−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	$-0.779753\pi$
$409$	3.47400	−	19.7021i	0.171778	−	0.974204i	0.941797	−	0.336182i	$-0.109136\pi$
$410$		0			0
$411$	0.368241	−	0.637812i	0.0181640	−	0.0314609i
$412$	−0.779963	−	0.654467i	−0.0384260	−	0.0322433i
$413$	−2.05778	−	0.748971i	−0.101257	−	0.0368545i
$414$	−18.0496	+	6.56953i	−0.887091	+	0.322875i
$415$		0			0
$416$	−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	$-0.286859\pi$
$419$	25.4097			1.24135			0.620673	+	0.784070i	$0.286859\pi$
$420$		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			0
$426$	18.0496	+	31.2629i	0.874507	+	1.51469i
$427$	−0.550507	+	3.12208i	−0.0266409	+	0.151088i
$428$	0.328411	−	1.86251i	0.0158744	−	0.0900279i
$429$	−8.25150	−	14.2920i	−0.398386	−	0.690025i
$430$		0			0
$431$	−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	$0.532374\pi$
$434$	2.54710	−	2.13727i	0.122265	−	0.102592i
$435$		0			0
$436$	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	$-0.101984\pi$
$439$	−1.05762	−	5.99806i	−0.0504774	−	0.286272i	−0.999589	+	0.0286685i	$0.990873\pi$
$440$		0			0
$441$	34.2028	−	12.4488i	1.62870	−	0.592800i
$442$	−1.52481	−	0.554987i	−0.0725280	−	0.0263981i
$443$	22.8995	+	19.2149i	1.08799	+	0.912928i	0.996559	−	0.0828833i	$-0.0264129\pi$
$443$	22.8995	+	19.2149i	1.08799	+	0.912928i	0.0914266	+	0.995812i	$0.470857\pi$
$444$	−1.31521	+	2.27801i	−0.0624170	+	0.108109i
$445$		0			0
$446$	1.99092	−	11.2910i	0.0942726	−	0.534646i
$447$	8.27972	−	46.9566i	0.391617	−	2.22097i
$448$	1.49273	+	2.58548i	0.0705247	+	0.122152i
$449$	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	$0.0811435\pi$
$450$		0			0
$451$	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	$-0.315742\pi$
$457$	23.3901			1.09414			0.547072	+	0.837086i	$0.315742\pi$
$458$	−4.80381	−	27.2438i	−0.224468	−	1.27302i
$459$	−2.36437	+	1.98394i	−0.110359	+	0.0926025i
$460$		0			0
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.980011	−	0.198945i	$-0.0637514\pi$
$461$	34.4149	+	12.5260i	1.60286	+	0.583395i	0.622853	+	0.782339i	$0.285974\pi$
$462$	2.29813	+	1.92836i	0.106919	+	0.0897156i
$463$	−21.4932	+	37.2273i	−0.998873	+	1.73010i	−0.458340	+	0.888777i	$0.651556\pi$
$463$	−21.4932	+	37.2273i	−0.998873	+	1.73010i	−0.540534	+	0.841322i	$0.681778\pi$
$464$	−12.3701	−	21.4256i	−0.574265	−	0.994657i
$465$		0			0
$466$	−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
$469$	2.04189	+	1.71335i	0.0942857	+	0.0791151i
$470$		0			0
$471$	−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
$475$		0			0
$476$	−0.0300295			−0.00137640
$477$	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	$-0.948391\pi$
$479$	−35.8739	+	13.0570i	−1.63912	+	0.596591i	−0.652236	+	0.758016i	$0.726169\pi$
$480$		0			0
$481$	9.74763	+	8.17923i	0.444453	+	0.372941i
$482$	−9.29679	+	16.1025i	−0.423457	+	0.733449i
$483$	1.34730	+	2.33359i	0.0613041	+	0.106182i
$484$	0.193877	−	1.09953i	0.00881261	−	0.0499788i
$485$		0			0
$486$	7.27766	+	12.6053i	0.330121	+	0.571787i
$487$	3.88191	−	6.72367i	0.175906	−	0.304678i	−0.764568	−	0.644543i	$-0.777048\pi$
$487$	3.88191	−	6.72367i	0.175906	−	0.304678i	0.940475	+	0.339864i	$0.110381\pi$
$488$	−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
$495$		0			0
$496$	4.43763	+	25.1671i	0.199256	+	1.13003i
$497$	2.47565	−	2.07732i	0.111048	−	0.0931805i
$498$	−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	$0.646281\pi$
$500$		0			0
$501$	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	$0.792938\pi$
$504$	0.939226	−	5.32661i	0.0418364	−	0.237266i
$505$		0			0
$506$	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	$-0.305885\pi$
$509$	34.7075	−	12.6325i	1.53839	−	0.559926i	0.965657	+	0.259819i	$0.0836630\pi$
$510$		0			0
$511$	0.0837781	+	0.475129i	0.00370613	+	0.0210185i
$512$	−24.9186			−1.10126
$513$	10.0326	+	26.9453i	0.442948	+	1.18967i
$514$	−0.898986			−0.0396526
$515$		0			0
$516$	1.59034	−	1.33445i	0.0700107	−	0.0587459i
$517$	15.2554	−	5.55250i	0.670930	−	0.244199i
$518$	−2.17365	−	0.791143i	−0.0955046	−	0.0347608i
$519$	44.4320	+	37.2829i	1.95035	+	1.63654i
$520$		0			0
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	0.746126	−	0.665804i	$-0.231912\pi$
$521$	−4.64590	−	8.04693i	−0.203540	−	0.352542i	−0.949667	+	0.313262i	$0.898578\pi$
$522$	−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			0
$531$	−33.3610			−1.44775
$532$	−0.0937404	+	0.263571i	−0.00406416	+	0.0114273i
$533$	−6.37227			−0.276014
$534$	−6.93242	−	39.3157i	−0.299995	−	1.70136i
$535$		0			0
$536$	−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
$539$	−7.65910	+	13.2660i	−0.329901	+	0.571405i
$540$		0			0
$541$	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
$545$		0			0
$546$	−3.25877	−	1.18610i	−0.139463	−	0.0507602i
$547$	−3.65270	+	1.32948i	−0.156178	+	0.0568443i	−0.418926	−	0.908020i	$-0.637593\pi$
$547$	−3.65270	+	1.32948i	−0.156178	+	0.0568443i	0.262748	+	0.964864i	$0.415371\pi$
$548$	0.0362077	−	0.0303818i	0.00154672	−	0.00129785i
$549$	8.38666	+	47.5631i	0.357934	+	2.02994i
$550$		0			0
$551$	10.0483	−	28.2529i	0.428071	−	1.20361i
$552$	−22.8384			−0.972068
$553$	0.714355	+	4.05131i	0.0303775	+	0.172279i
$554$	−18.3164	+	15.3693i	−0.778189	+	0.652978i
$555$		0			0
$556$	0.740352	+	0.269466i	0.0313979	+	0.0114279i
$557$	−10.1152	−	8.48762i	−0.428593	−	0.359632i	0.402828	−	0.915276i	$-0.368027\pi$
$557$	−10.1152	−	8.48762i	−0.428593	−	0.359632i	−0.831420	+	0.555644i	$0.812472\pi$
$558$	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
$565$		0			0
$566$	9.73308	−	3.54255i	0.409112	−	0.148905i
$567$	−0.830222	+	0.696639i	−0.0348661	+	0.0292561i
$568$	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	$0.591117\pi$
$570$		0			0
$571$	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
$574$	1.08853	−	0.396191i	0.0454342	−	0.0165367i
$575$		0			0
$576$	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			0
$581$	2.57532	+	4.46059i	0.106842	+	0.185056i
$582$	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
$585$		0			0
$586$	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	$0.815085\pi$
$588$	3.66044			0.150954
$589$	−19.7349	+	23.8739i	−0.813162	+	0.983706i
$590$		0			0
$591$	−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	$-0.0772248\pi$
$600$		0			0
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	−0.283718	−	0.958908i	$-0.591568\pi$
$601$	16.8807	−	29.2383i	0.688579	−	1.19265i	0.972298	−	0.233747i	$-0.0750986\pi$
$602$	1.39852	+	1.17350i	0.0569994	+	0.0478282i
$603$	38.1584	+	13.8885i	1.55393	+	0.565584i
$604$	−0.757426	+	0.275681i	−0.0308192	+	0.0112173i
$605$		0			0
$606$	−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
$609$	6.87939			0.278767
$610$		0			0
$611$	−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	$-0.267334\pi$
$613$	17.3405	+	6.31142i	0.700376	+	0.254916i	0.0328044	+	0.999462i	$0.489556\pi$
$614$	12.0708	+	10.1286i	0.487139	+	0.408758i
$615$		0			0
$616$	1.13816	+	1.97134i	0.0458576	+	0.0794277i
$617$	6.19671	−	35.1433i	0.249470	−	1.41482i	−0.560408	−	0.828217i	$-0.689356\pi$
$617$	6.19671	−	35.1433i	0.249470	−	1.41482i	0.809878	−	0.586598i	$-0.199533\pi$
$618$	3.71167	−	21.0499i	0.149305	−	0.846752i
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	0.826908	−	0.562337i	$-0.190098\pi$
$619$	−1.82976	−	3.16923i	−0.0735441	−	0.127382i	−0.900452	+	0.434955i	$0.856764\pi$
$620$		0			0
$621$	13.6159	+	11.4251i	0.546386	+	0.458472i
$622$	−20.2135	−	7.35710i	−0.810487	−	0.294993i
$623$	−3.35844	+	1.22237i	−0.134553	+	0.0489733i
$624$	20.4179	−	17.1326i	0.817369	−	0.685854i
$625$		0			0
$626$	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
$635$		0			0
$636$	−0.262174	+	1.48686i	−0.0103959	+	0.0589579i
$637$	3.07486	−	17.4384i	0.121830	−	0.690933i
$638$	−10.3191	−	17.8732i	−0.408536	−	0.707605i
$639$	24.6168	−	42.6375i	0.973826	−	1.68672i
$640$		0			0
$641$	−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	$0.422096\pi$
$644$	0.0300295	+	0.170306i	0.00118333	+	0.00671099i
$645$		0			0
$646$	−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
$650$		0			0
$651$	−6.67752	−	2.43042i	−0.261713	−	0.0952556i
$652$	1.18273	+	0.992431i	0.0463194	+	0.0388666i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$	3.53596	+	6.12446i	0.138267	+	0.239485i
$655$		0			0
$656$	−1.54601	+	8.76785i	−0.0603615	+	0.342327i
$657$	3.67499	+	6.36527i	0.143375	+	0.248333i
$658$	1.70574	−	2.95442i	0.0664966	−	0.115175i
$659$	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			0
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	−0.541303	−	0.840827i	$-0.682069\pi$
$661$	−10.6823	+	3.88803i	−0.415492	+	0.151227i	0.125811	+	0.992054i	$0.459847\pi$
$662$	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
$670$		0			0
$671$	−15.5706	−	13.0653i	−0.601095	−	0.504379i
$672$	0.520945	−	0.902302i	0.0200959	−	0.0348071i
$673$	−8.28359	−	14.3476i	−0.319309	−	0.553059i	0.661035	−	0.750355i	$-0.270117\pi$
$673$	−8.28359	−	14.3476i	−0.319309	−	0.553059i	−0.980344	+	0.197296i	$0.936784\pi$
$674$	−4.17840	+	23.6969i	−0.160946	+	0.912769i
$675$		0			0
$676$	−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
$679$	−3.08512	−	1.12289i	−0.118396	−	0.0430927i
$680$		0			0
$681$	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	$-0.553424\pi$
$683$	−8.73143			−0.334099			−0.167049	+	0.985949i	$0.553424\pi$
$684$	0.0313737	+	4.26163i	0.00119960	+	0.162947i
$685$		0			0
$686$	1.12773	+	6.39566i	0.0430568	+	0.244187i
$687$	−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
$690$		0			0
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	0.320099	+	0.947384i	$0.396284\pi$
$691$	−17.3601	+	30.0686i	−0.660409	+	1.14386i	−0.980508	+	0.196478i	$0.937050\pi$
$692$	1.86122	+	3.22372i	0.0707528	+	0.122547i
$693$	0.710485	−	4.02936i	0.0269891	−	0.153063i
$694$	1.35710	−	7.69648i	0.0515147	−	0.292154i
$695$		0			0
$696$	−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
$705$		0			0
$706$	26.0442	−	21.8537i	0.980185	−	0.822473i
$707$	−3.01842	+	1.09861i	−0.113519	+	0.0413176i
$708$	−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	$-0.558609\pi$
$710$		0			0
$711$	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
$714$	−0.315207	−	0.545955i	−0.0117963	−	0.0204319i
$715$		0			0
$716$	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	$0.567979\pi$
$719$	−32.4768	+	27.2513i	−1.21118	+	1.01630i	−0.999238	+	0.0390200i	$0.987576\pi$
$720$		0			0
$721$	−1.91353			−0.0712637
$722$	−4.07351	+	25.2724i	−0.151600	+	0.940543i
$723$	39.7374			1.47785
$724$	−0.273947	−	1.55363i	−0.0101812	−	0.0577403i
$725$		0			0
$726$	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	$0.203788\pi$
$728$	−2.01573	−	1.69140i	−0.0747079	−	0.0626874i
$729$	20.2344	−	35.0470i	0.749423	−	1.29804i
$730$		0			0
$731$	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			0
$741$	31.8555	+	5.37549i	1.17024	+	0.197474i
$742$	−1.32770			−0.0487413
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	0.959024	−	0.283326i	$-0.0914380\pi$
$743$	−1.06489	−	6.03931i	−0.0390671	−	0.221561i	−0.998091	+	0.0617657i	$0.980327\pi$
$744$	46.1377	−	38.7142i	1.69149	−	1.41933i
$745$		0			0
$746$	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
$749$	−1.77719	−	3.07818i	−0.0649371	−	0.112474i
$750$		0			0
$751$	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
$755$		0			0
$756$	−0.397804	+	0.144789i	−0.0144680	+	0.00526591i
$757$	−12.0207	+	10.0866i	−0.436900	+	0.366602i	−0.834548	−	0.550936i	$-0.814271\pi$
$757$	−12.0207	+	10.0866i	−0.436900	+	0.366602i	0.397648	+	0.917538i	$0.369827\pi$
$758$	0.398052	+	2.25746i	0.0144579	+	0.0819948i
$759$	−17.2763			−0.627090
$760$		0			0
$761$	4.86484			0.176350			0.0881751	−	0.996105i	$-0.471896\pi$
$761$	4.86484			0.176350			0.0881751	+	0.996105i	$0.471896\pi$
$762$	−7.81702	−	44.3325i	−0.283181	−	1.60600i
$763$	0.484985	−	0.406951i	0.0175576	−	0.0147326i
$764$	3.18392	−	1.15885i	0.115190	−	0.0419257i
$765$		0			0
$766$	−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	$-0.811276\pi$
$769$	3.91266	−	22.1898i	0.141094	−	0.800184i	0.970421	−	0.241420i	$-0.0776131\pi$
$770$		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
$775$		0			0
$776$	21.3164	−	17.8866i	0.765214	−	0.642091i
$777$	0.858441	+	4.86846i	0.0307964	+	0.174655i
$778$	−33.0993			−1.18667
$779$	−9.30541	+	5.46421i	−0.333401	+	0.195776i
$780$		0			0
$781$	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
$784$	−23.2481	−	8.46161i	−0.830289	−	0.302200i
$785$		0			0
$786$	−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
$790$		0			0
$791$	3.07145	−	5.31991i	0.109208	−	0.189154i
$792$	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
$795$		0			0
$796$	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	$0.702136\pi$
$798$	−5.77584	+	1.06234i	−0.204463	+	0.0376063i
$799$	−3.41147			−0.120689
$800$		0			0
$801$	−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	$-0.423804\pi$
$810$		0			0
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	0.839025	−	0.544093i	$-0.183126\pi$
$811$	12.7836	+	10.7267i	0.448892	+	0.376665i	−0.390132	+	0.920759i	$0.627571\pi$
$812$	0.414878	+	0.151003i	0.0145594	+	0.00529917i
$813$	36.2413	−	13.1907i	1.27104	−	0.462620i
$814$	11.3610	−	9.53298i	0.398202	−	0.334131i
$815$		0			0
$816$	4.84524			0.169617
$817$	−14.7907	−	8.39484i	−0.517461	−	0.293698i
$818$	26.9540			0.942424
$819$	0.821299	+	4.65782i	0.0286985	+	0.162757i
$820$		0			0
$821$	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	$-0.978646\pi$
$823$	−35.4877	−	29.7777i	−1.23702	−	1.03799i	−0.239274	−	0.970952i	$-0.576909\pi$
$824$	8.10922	−	14.0456i	0.282498	−	0.489301i
$825$		0			0
$826$	0.512326	−	2.90555i	0.0178261	−	0.101097i
$827$	−7.07769	+	40.1396i	−0.246115	+	1.39579i	0.571773	+	0.820412i	$0.306256\pi$
$827$	−7.07769	+	40.1396i	−0.246115	+	1.39579i	−0.817888	+	0.575377i	$0.804855\pi$
$828$	1.31727	+	2.28157i	0.0457782	+	0.0792901i
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	−0.373979	−	0.927437i	$-0.622007\pi$
$829$	17.7417	−	30.7295i	0.616195	−	1.06728i	0.990174	−	0.139843i	$-0.0446598\pi$
$830$		0			0
$831$	48.0185	+	17.4773i	1.66574	+	0.606281i
$832$	20.7922	−	7.56774i	0.720840	−	0.262364i
$833$	2.46585	−	2.06910i	0.0854367	−	0.0716899i
$834$	2.87211	+	16.2886i	0.0994531	+	0.564026i
$835$		0			0
$836$	−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	$-0.951433\pi$
$839$	−29.2649	+	24.5562i	−1.01034	+	0.847774i	−0.0219545	+	0.999759i	$0.506989\pi$
$840$		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			0
$846$	9.02481	−	51.1823i	0.310280	−	1.75968i
$847$	−1.04916	−	1.81720i	−0.0360497	−	0.0624399i
$848$	5.10220	−	8.83726i	0.175210	−	0.303473i
$849$	−16.9572	−	14.2288i	−0.581971	−	0.488331i
$850$		0			0
$851$	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	$0.800028\pi$
$854$	−4.27126			−0.146159
$855$		0			0
$856$	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	−0.00872148	−	0.999962i	$-0.502776\pi$
$859$	18.3871	−	6.69237i	0.627361	−	0.228341i	0.636082	+	0.771621i	$0.280554\pi$
$860$		0			0
$861$	−1.89646	−	1.59132i	−0.0646312	−	0.0542320i
$862$	25.8050	−	44.6956i	0.878922	−	1.52234i
$863$	2.47447	+	4.28591i	0.0842319	+	0.145894i	0.905064	−	0.425276i	$-0.139823\pi$
$863$	2.47447	+	4.28591i	0.0842319	+	0.145894i	−0.820832	+	0.571170i	$0.806490\pi$
$864$	1.19341	−	6.76817i	0.0406007	−	0.230258i
$865$		0			0
$866$	−12.2139	−	21.1552i	−0.415047	−	0.718882i
$867$	24.1596	−	41.8456i	0.820502	−	1.42115i
$868$	−0.349356	−	0.293144i	−0.0118579	−	0.00994997i
$869$	−24.7849	−	9.02098i	−0.840771	−	0.306016i
$870$		0			0
$871$	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	$-0.728779\pi$
$877$	−0.934478	+	0.784120i	−0.0315551	+	0.0264779i	0.626874	+	0.779121i	$0.284334\pi$
$878$	7.71095	−	2.80656i	0.260232	−	0.0947167i
$879$	−28.4183	−	10.3434i	−0.958527	−	0.348875i
$880$		0			0
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	0.146609	+	0.989194i	$0.453164\pi$
$881$	−23.2515	+	40.2728i	−0.783363	+	1.35682i	−0.929972	+	0.367630i	$0.880169\pi$
$882$	24.5194	+	42.4688i	0.825610	+	1.43000i
$883$	−2.24438	+	12.7285i	−0.0755296	+	0.428349i	0.923472	+	0.383667i	$0.125339\pi$
$883$	−2.24438	+	12.7285i	−0.0755296	+	0.428349i	−0.999001	+	0.0446828i	$0.985772\pi$
$884$	−0.0386476	+	0.219182i	−0.00129986	+	0.00737187i
$885$		0			0
$886$	−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
$889$	−3.78699	+	1.37835i	−0.127012	+	0.0462284i
$890$		0			0
$891$	−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
$895$		0			0
$896$	−2.52687	+	2.12030i	−0.0844169	+	0.0708342i
$897$	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
$900$		0			0
$901$	0.663848	+	1.14982i	0.0221160	+	0.0383060i
$902$	−1.28968	+	7.31412i	−0.0429416	+	0.243534i
$903$	0.677519	−	3.84240i	0.0225464	−	0.127867i
$904$	26.0326	+	45.0897i	0.865830	+	1.49966i
$905$		0			0
$906$	−12.9624	−	10.8768i	−0.430648	−	0.361357i
$907$	−37.5847	−	13.6797i	−1.24798	−	0.454228i	−0.368261	−	0.929722i	$-0.620047\pi$
$907$	−37.5847	−	13.6797i	−1.24798	−	0.454228i	−0.879719	+	0.475495i	$0.842269\pi$
$908$	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
$915$		0			0
$916$	−3.56552	+	1.29774i	−0.117808	+	0.0428787i
$917$	0.602196	+	0.219182i	0.0198863	+	0.00723801i
$918$	−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	$0.938508\pi$
$920$		0			0
$921$	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
$924$	0.205737	−	0.356347i	0.00676825	−	0.0117230i
$925$		0			0
$926$	−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	$0.0902342\pi$
$929$	4.68051	+	26.5445i	0.153563	+	0.870897i	−0.806526	+	0.591199i	$0.798655\pi$
$930$		0			0
$931$	−10.4632	−	28.1019i	−0.342916	−	0.921002i
$932$	3.26176			0.106843
$933$	7.98293	+	45.2734i	0.261349	+	1.48219i
$934$	−26.4176	+	22.1670i	−0.864411	+	0.725327i
$935$		0			0
$936$	−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	$0.735867\pi$
$938$	−1.79561	+	3.11008i	−0.0586287	+	0.101548i
$939$	−38.3371	−	66.4018i	−1.25108	−	2.16694i
$940$		0			0
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	0.885260	+	0.465096i	$0.153980\pi$
$941$	−3.24194	+	18.3860i	−0.105684	+	0.599366i	−0.990945	+	0.134270i	$0.957131\pi$
$942$	−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	$-0.765800\pi$
$947$	−6.43448	+	5.39917i	−0.209092	+	0.175449i	0.532227	+	0.846602i	$0.321355\pi$
$948$	1.09446	+	6.20697i	0.0355463	+	0.201593i
$949$	3.57573			0.116073
$950$		0			0
$951$	−85.0343			−2.75742
$952$	−0.0830629	−	0.471073i	−0.00269208	−	0.0152676i
$953$	−25.8102	+	21.6573i	−0.836075	+	0.701550i	−0.956677	−	0.291151i	$-0.905962\pi$
$953$	−25.8102	+	21.6573i	−0.836075	+	0.701550i	0.120602	+	0.992701i	$0.461517\pi$
$954$	−19.0069	+	6.91793i	−0.615370	+	0.223976i
$955$		0			0
$956$	−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
$959$	0.0154253	−	0.0874810i	0.000498108	−	0.00282491i
$960$		0			0
$961$	−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			0
$966$	−2.78106	+	2.33359i	−0.0894791	+	0.0750819i
$967$	−2.03920	−	11.5649i	−0.0655763	−	0.371902i	−0.999881	−	0.0154262i	$-0.995089\pi$
$967$	−2.03920	−	11.5649i	−0.0655763	−	0.371902i	0.934305	−	0.356475i	$-0.116022\pi$
$968$	17.7847			0.571621
$969$	3.80793	+	4.47086i	0.122328	+	0.143625i
$970$		0			0
$971$	2.22432	+	12.6147i	0.0713817	+	0.404826i	0.999473	+	0.0324723i	$0.0103381\pi$
$971$	2.22432	+	12.6147i	0.0713817	+	0.404826i	−0.928091	+	0.372354i	$0.878551\pi$
$972$	1.52931	−	1.28325i	0.0490528	−	0.0411602i
$973$	1.39141	−	0.506431i	0.0446065	−	0.0162354i
$974$	9.82934	+	3.57759i	0.314953	+	0.114633i
$975$		0			0
$976$	16.4140	−	28.4299i	0.525399	−	0.910018i
$977$	7.26382	+	12.5813i	0.232390	+	0.402512i	0.958511	−	0.285055i	$-0.0920120\pi$
$977$	7.26382	+	12.5813i	0.232390	+	0.402512i	−0.726121	+	0.687567i	$0.758679\pi$
$978$	−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
$985$		0			0
$986$	0.753089	+	4.27098i	0.0239832	+	0.136016i
$987$	−7.29086			−0.232071
$988$	1.80313	+	1.02341i	0.0573652	+	0.0325591i
$989$	−10.5134			−0.334307
$990$		0			0
$991$	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
$994$	3.33544	+	2.79876i	0.105794	+	0.0887714i
$995$		0			0
$996$	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	475.2.l.a.351.1		6
5.2	odd	4		475.2.u.a.199.1		12
5.3	odd	4		475.2.u.a.199.2		12
5.4	even	2		19.2.e.a.9.1	✓	6
15.14	odd	2		171.2.u.c.28.1		6
19.6	even	9		9025.2.a.bd.1.2		3
19.13	odd	18		9025.2.a.x.1.2		3
19.17	even	9	inner	475.2.l.a.226.1		6
20.19	odd	2		304.2.u.b.161.1		6
35.4	even	6		931.2.v.b.275.1		6
35.9	even	6		931.2.x.a.655.1		6
35.19	odd	6		931.2.x.b.655.1		6
35.24	odd	6		931.2.v.a.275.1		6
35.34	odd	2		931.2.w.a.883.1		6
95.4	even	18		361.2.c.i.68.2		6
95.9	even	18		361.2.c.i.292.2		6
95.14	odd	18		361.2.e.a.54.1		6
95.17	odd	36		475.2.u.a.74.2		12
95.24	even	18		361.2.e.g.54.1		6
95.29	odd	18		361.2.c.h.292.2		6
95.34	odd	18		361.2.c.h.68.2		6
95.44	even	18		361.2.a.g.1.2		3
95.49	even	6		361.2.e.g.234.1		6
95.54	even	18		361.2.e.f.62.1		6
95.59	odd	18		361.2.e.h.245.1		6
95.64	even	6		361.2.e.f.99.1		6
95.69	odd	6		361.2.e.b.99.1		6
95.74	even	18		19.2.e.a.17.1	yes	6
95.79	odd	18		361.2.e.b.62.1		6
95.84	odd	6		361.2.e.a.234.1		6
95.89	odd	18		361.2.a.h.1.2		3
95.93	odd	36		475.2.u.a.74.1		12
95.94	odd	2		361.2.e.h.28.1		6
285.44	odd	18		3249.2.a.z.1.2		3
285.74	odd	18		171.2.u.c.55.1		6
285.89	even	18		3249.2.a.s.1.2		3
380.139	odd	18		5776.2.a.br.1.3		3
380.279	even	18		5776.2.a.bi.1.1		3
380.359	odd	18		304.2.u.b.17.1		6
665.74	even	18		931.2.x.a.226.1		6
665.264	odd	18		931.2.v.a.606.1		6
665.359	even	18		931.2.v.b.606.1		6
665.454	odd	18		931.2.w.a.834.1		6
665.549	odd	18		931.2.x.b.226.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.9.1	✓	6	5.4	even	2
19.2.e.a.17.1	yes	6	95.74	even	18
171.2.u.c.28.1		6	15.14	odd	2
171.2.u.c.55.1		6	285.74	odd	18
304.2.u.b.17.1		6	380.359	odd	18
304.2.u.b.161.1		6	20.19	odd	2
361.2.a.g.1.2		3	95.44	even	18
361.2.a.h.1.2		3	95.89	odd	18
361.2.c.h.68.2		6	95.34	odd	18
361.2.c.h.292.2		6	95.29	odd	18
361.2.c.i.68.2		6	95.4	even	18
361.2.c.i.292.2		6	95.9	even	18
361.2.e.a.54.1		6	95.14	odd	18
361.2.e.a.234.1		6	95.84	odd	6
361.2.e.b.62.1		6	95.79	odd	18
361.2.e.b.99.1		6	95.69	odd	6
361.2.e.f.62.1		6	95.54	even	18
361.2.e.f.99.1		6	95.64	even	6
361.2.e.g.54.1		6	95.24	even	18
361.2.e.g.234.1		6	95.49	even	6
361.2.e.h.28.1		6	95.94	odd	2
361.2.e.h.245.1		6	95.59	odd	18
475.2.l.a.226.1		6	19.17	even	9	inner
475.2.l.a.351.1		6	1.1	even	1	trivial
475.2.u.a.74.1		12	95.93	odd	36
475.2.u.a.74.2		12	95.17	odd	36
475.2.u.a.199.1		12	5.2	odd	4
475.2.u.a.199.2		12	5.3	odd	4
931.2.v.a.275.1		6	35.24	odd	6
931.2.v.a.606.1		6	665.264	odd	18
931.2.v.b.275.1		6	35.4	even	6
931.2.v.b.606.1		6	665.359	even	18
931.2.w.a.834.1		6	665.454	odd	18
931.2.w.a.883.1		6	35.34	odd	2
931.2.x.a.226.1		6	665.74	even	18
931.2.x.a.655.1		6	35.9	even	6
931.2.x.b.226.1		6	665.549	odd	18
931.2.x.b.655.1		6	35.19	odd	6
3249.2.a.s.1.2		3	285.89	even	18
3249.2.a.z.1.2		3	285.44	odd	18
5776.2.a.bi.1.1		3	380.279	even	18
5776.2.a.br.1.3		3	380.139	odd	18
9025.2.a.x.1.2		3	19.13	odd	18
9025.2.a.bd.1.2		3	19.6	even	9

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +O(q^{10})\)	\(q+(0.233956 + 1.32683i) q^{2} +(2.20574 - 1.85083i) q^{3} +(0.173648 - 0.0632028i) q^{4} +(2.97178 + 2.49362i) q^{6} +(0.173648 - 0.300767i) q^{7} +(1.47178 + 2.54920i) q^{8} +(0.918748 - 5.21048i) q^{9} +(1.11334 + 1.92836i) q^{11} +(0.266044 - 0.460802i) q^{12} +(-1.97178 - 1.65452i) q^{13} +(0.439693 + 0.160035i) q^{14} +(-2.75490 + 2.31164i) q^{16} +(-0.0812519 - 0.460802i) q^{17} +7.12836 q^{18} +(-4.29813 - 0.725293i) q^{19} +(-0.173648 - 0.984808i) q^{21} +(-2.29813 + 1.92836i) q^{22} +(-2.53209 + 0.921605i) q^{23} +(7.96451 + 2.89884i) q^{24} +(1.73396 - 3.00330i) q^{26} +(-3.29813 - 5.71253i) q^{27} +(0.0111444 - 0.0632028i) q^{28} +(-1.19459 + 6.77487i) q^{29} +(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} +(1.89646 - 1.59132i) q^{41} +(1.26604 - 0.460802i) q^{42} +(3.66637 + 1.33445i) q^{43} +(0.315207 + 0.264490i) q^{44} +(-1.81521 - 3.14403i) q^{46} +(1.26604 - 7.18009i) q^{47} +(-1.79813 + 10.1977i) q^{48} +(3.43969 + 5.95772i) q^{49} +(-1.03209 - 0.866025i) q^{51} +(-0.446967 - 0.162683i) q^{52} +(-2.66637 + 0.970481i) q^{53} +(6.80793 - 5.71253i) q^{54} +1.02229 q^{56} +(-10.8229 + 6.35532i) q^{57} -9.26857 q^{58} +(-1.09492 - 6.20961i) q^{59} +(-8.57785 + 3.12208i) q^{61} +(8.99660 + 3.27449i) q^{62} +(-1.40760 - 1.18112i) q^{63} +(-4.29813 + 7.44459i) q^{64} +(-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} +(-0.792204 + 0.145708i) q^{76} +0.773318 q^{77} +(-1.73396 - 9.83375i) q^{78} +(-9.07398 + 7.61397i) q^{79} +(-2.93242 - 1.06731i) q^{81} +(2.55509 + 2.14398i) q^{82} +(-7.41534 + 12.8438i) q^{83} +(-0.0923963 - 0.160035i) q^{84} +(-0.912818 + 5.17685i) q^{86} +(9.90420 + 17.1546i) q^{87} +(-3.27719 + 5.67626i) q^{88} +(-7.88326 - 6.61484i) q^{89} +(-0.840022 + 0.305743i) q^{91} +(-0.381445 + 0.320070i) q^{92} +(-3.55303 - 20.1503i) q^{93} +9.82295 q^{94} +3.00000 q^{96} +(-1.64156 - 9.30975i) q^{97} +(-7.10014 + 5.95772i) q^{98} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9	\( 6 q + 6 q^{2} + 3 q^{3} + 3 q^{6} - 6 q^{8} + 3 q^{9} - 3 q^{12} + 3 q^{13} - 3 q^{14} - 18 q^{16} - 3 q^{17} + 6 q^{18} - 12 q^{19} - 6 q^{23} + 15 q^{24} + 15 q^{26} - 6 q^{27} - 6 q^{28} - 3 q^{29} + 9 q^{31} - 9 q^{32} + 9 q^{33} - 24 q^{36} + 15 q^{38} - 24 q^{39} + 21 q^{41} + 3 q^{42} + 3 q^{43} + 9 q^{44} - 18 q^{46} + 3 q^{47} + 3 q^{48} + 15 q^{49} + 3 q^{51} - 15 q^{52} + 3 q^{53} + 30 q^{54} - 6 q^{56} - 24 q^{57} - 36 q^{58} + 12 q^{59} - 12 q^{61} + 12 q^{62} - 12 q^{63} - 12 q^{64} - 9 q^{66} + 30 q^{67} + 15 q^{68} - 12 q^{69} - 6 q^{71} + 12 q^{72} + 12 q^{73} + 15 q^{74} + 36 q^{76} + 18 q^{77} - 15 q^{78} - 39 q^{79} + 6 q^{81} + 54 q^{82} + 3 q^{84} + 24 q^{86} + 21 q^{87} - 9 q^{88} - 12 q^{89} + 15 q^{91} - 42 q^{92} - 9 q^{93} + 18 q^{94} + 18 q^{96} - 18 q^{97} + 9 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 3 * q^3 + 3 * q^6 - 6 * q^8 + 3 * q^9 - 3 * q^12 + 3 * q^13 - 3 * q^14 - 18 * q^16 - 3 * q^17 + 6 * q^18 - 12 * q^19 - 6 * q^23 + 15 * q^24 + 15 * q^26 - 6 * q^27 - 6 * q^28 - 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^42 + 3 * q^43 + 9 * q^44 - 18 * q^46 + 3 * q^47 + 3 * q^48 + 15 * q^49 + 3 * q^51 - 15 * q^52 + 3 * q^53 + 30 * q^54 - 6 * q^56 - 24 * q^57 - 36 * q^58 + 12 * q^59 - 12 * q^61 + 12 * q^62 - 12 * q^63 - 12 * q^64 - 9 * q^66 + 30 * q^67 + 15 * q^68 - 12 * q^69 - 6 * q^71 + 12 * q^72 + 12 * q^73 + 15 * q^74 + 36 * q^76 + 18 * q^77 - 15 * q^78 - 39 * q^79 + 6 * q^81 + 54 * q^82 + 3 * q^84 + 24 * q^86 + 21 * q^87 - 9 * q^88 - 12 * q^89 + 15 * q^91 - 42 * q^92 - 9 * q^93 + 18 * q^94 + 18 * q^96 - 18 * q^97 + 9 * q^98 + 9 * q^99

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