LMFDB - Embedded newform 775.2.ck.a.474.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(49,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([15, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.ck (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			474.3
Character	$\chi$	$=$	775.474
Dual form			775.2.ck.a.224.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17187 + 0.380762i) q^{2} +(-0.431412 + 2.02963i) q^{3} +(-0.389745 - 0.283166i) q^{4} +(-1.27836 + 2.21419i) q^{6} +(-1.54713 - 3.47491i) q^{7} +(-1.79742 - 2.47393i) q^{8} +(-1.19265 - 0.531003i) q^{9} +(0.393186 - 3.74092i) q^{11} +(0.742864 - 0.668878i) q^{12} +(1.95823 + 1.76320i) q^{13} +(-0.489913 - 4.66121i) q^{14} +(-0.866611 - 2.66715i) q^{16} +(3.75366 - 0.394526i) q^{17} +(-1.19544 - 1.07638i) q^{18} +(-4.08057 - 4.53193i) q^{19} +(7.72023 - 1.64099i) q^{21} +(1.88516 - 4.23414i) q^{22} +(0.534795 + 0.736082i) q^{23} +(5.79659 - 2.58081i) q^{24} +(1.62343 + 2.81186i) q^{26} +(-2.06665 + 2.84451i) q^{27} +(-0.380991 + 1.79242i) q^{28} +(2.10397 - 6.47535i) q^{29} +(-3.88819 - 3.98522i) q^{31} +2.66037i q^{32} +(7.42306 + 2.41190i) q^{33} +(4.54901 + 0.966922i) q^{34} +(0.314468 + 0.544675i) q^{36} +(1.57103 + 0.907032i) q^{37} +(-3.05629 - 6.86454i) q^{38} +(-4.42345 + 3.21383i) q^{39} +(-0.329777 + 0.0700963i) q^{41} +(9.67189 + 1.01656i) q^{42} +(2.88637 - 2.59890i) q^{43} +(-1.21255 + 1.34667i) q^{44} +(0.346435 + 1.06622i) q^{46} +(1.13095 - 0.367467i) q^{47} +(5.78721 - 0.608260i) q^{48} +(-4.99745 + 5.55023i) q^{49} +(-0.818631 + 7.78876i) q^{51} +(-0.263933 - 1.24171i) q^{52} +(-0.953442 + 2.14147i) q^{53} +(-3.50492 + 2.54647i) q^{54} +(-5.81584 + 10.0733i) q^{56} +(10.9586 - 6.32692i) q^{57} +(4.93114 - 6.78713i) q^{58} +(7.60885 + 1.61731i) q^{59} -2.72343 q^{61} +(-3.03901 - 6.15062i) q^{62} +4.96588i q^{63} +(-2.74619 + 8.45191i) q^{64} +(7.78047 + 5.65284i) q^{66} +(-6.42693 + 3.71059i) q^{67} +(-1.57469 - 0.909147i) q^{68} +(-1.72469 + 0.767882i) q^{69} +(-4.65742 - 2.07362i) q^{71} +(0.830027 + 3.90497i) q^{72} +(5.36221 + 0.563591i) q^{73} +(1.49567 + 1.66111i) q^{74} +(0.307091 + 2.92178i) q^{76} +(-13.6076 + 4.42139i) q^{77} +(-6.40740 + 2.08189i) q^{78} +(-1.01782 - 9.68388i) q^{79} +(-7.50241 - 8.33227i) q^{81} +(-0.413145 - 0.0434232i) q^{82} +(-1.74545 - 8.21169i) q^{83} +(-3.47359 - 1.54654i) q^{84} +(4.37200 - 1.94654i) q^{86} +(12.2349 + 7.06383i) q^{87} +(-9.96149 + 5.75127i) q^{88} +(4.12243 + 2.99512i) q^{89} +(3.09732 - 9.53258i) q^{91} -0.438320i q^{92} +(9.76595 - 6.17231i) q^{93} +1.46523 q^{94} +(-5.39957 - 1.14771i) q^{96} +(6.41522 - 8.82979i) q^{97} +(-7.96966 + 4.60129i) q^{98} +(-2.45537 + 4.25283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) $ 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{1}{15}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.17187	+	0.380762i	0.828634	+	0.269240i	0.692470	−	0.721447i	$-0.256523\pi$
$2$	1.17187	+	0.380762i	0.828634	+	0.269240i	0.136164	+	0.990686i	$0.456523\pi$
$3$	−0.431412	+	2.02963i	−0.249076	+	1.17181i	0.658718	+	0.752390i	$0.271099\pi$
$3$	−0.431412	+	2.02963i	−0.249076	+	1.17181i	−0.907793	+	0.419418i	$0.862234\pi$
$4$	−0.389745	−	0.283166i	−0.194873	−	0.141583i
$5$		0			0
$5$		0			0
$6$	−1.27836	+	2.21419i	−0.521890	+	0.903939i
$7$	−1.54713	−	3.47491i	−0.584759	−	1.31339i	−0.927452	−	0.373943i	$-0.878005\pi$
$7$	−1.54713	−	3.47491i	−0.584759	−	1.31339i	0.342692	−	0.939448i	$-0.388661\pi$
$8$	−1.79742	−	2.47393i	−0.635482	−	0.874666i
$9$	−1.19265	−	0.531003i	−0.397551	−	0.177001i
$10$		0			0
$11$	0.393186	−	3.74092i	0.118550	−	1.12793i	−0.759882	−	0.650061i	$-0.774743\pi$
$11$	0.393186	−	3.74092i	0.118550	−	1.12793i	0.878432	−	0.477868i	$-0.158590\pi$
$12$	0.742864	−	0.668878i	0.214446	−	0.193088i
$13$	1.95823	+	1.76320i	0.543116	+	0.489024i	0.894414	−	0.447240i	$-0.147593\pi$
$13$	1.95823	+	1.76320i	0.543116	+	0.489024i	−0.351298	+	0.936264i	$0.614260\pi$
$14$	−0.489913	−	4.66121i	−0.130935	−	1.24576i
$15$		0			0
$16$	−0.866611	−	2.66715i	−0.216653	−	0.666789i
$17$	3.75366	−	0.394526i	0.910397	−	0.0956866i	0.362262	−	0.932076i	$-0.382005\pi$
$17$	3.75366	−	0.394526i	0.910397	−	0.0956866i	0.548135	+	0.836390i	$0.315338\pi$
$18$	−1.19544	−	1.07638i	−0.281768	−	0.253705i
$19$	−4.08057	−	4.53193i	−0.936147	−	1.03970i	−0.999131	−	0.0416817i	$-0.986728\pi$
$19$	−4.08057	−	4.53193i	−0.936147	−	1.03970i	0.0629842	−	0.998015i	$-0.479938\pi$
$20$		0			0
$21$	7.72023	−	1.64099i	1.68469	−	0.358092i
$22$	1.88516	−	4.23414i	0.401918	−	0.902722i
$23$	0.534795	+	0.736082i	0.111512	+	0.153484i	0.861125	−	0.508393i	$-0.169760\pi$
$23$	0.534795	+	0.736082i	0.111512	+	0.153484i	−0.749613	+	0.661877i	$0.769760\pi$
$24$	5.79659	−	2.58081i	1.18322	−	0.526805i
$25$		0			0
$26$	1.62343	+	2.81186i	0.318380	+	0.551450i
$27$	−2.06665	+	2.84451i	−0.397728	+	0.547425i
$28$	−0.380991	+	1.79242i	−0.0720006	+	0.338736i
$29$	2.10397	−	6.47535i	0.390697	−	1.20244i	−0.541565	−	0.840659i	$-0.682168\pi$
$29$	2.10397	−	6.47535i	0.390697	−	1.20244i	0.932262	−	0.361784i	$-0.117832\pi$
$30$		0			0
$31$	−3.88819	−	3.98522i	−0.698339	−	0.715767i
$31$	−3.88819	−	3.98522i	−0.698339	−	0.715767i
$32$			2.66037i			0.470292i
$33$	7.42306	+	2.41190i	1.29219	+	0.419858i
$34$	4.54901	+	0.966922i	0.780149	+	0.165826i
$35$		0			0
$36$	0.314468	+	0.544675i	0.0524114	+	0.0907792i
$37$	1.57103	+	0.907032i	0.258275	+	0.149115i	0.623547	−	0.781786i	$-0.285691\pi$
$37$	1.57103	+	0.907032i	0.258275	+	0.149115i	−0.365272	+	0.930901i	$0.619024\pi$
$38$	−3.05629	−	6.86454i	−0.495796	−	1.11358i
$39$	−4.42345	+	3.21383i	−0.708320	+	0.514624i
$40$		0			0
$41$	−0.329777	+	0.0700963i	−0.0515026	+	0.0109472i	−0.233591	−	0.972335i	$-0.575048\pi$
$41$	−0.329777	+	0.0700963i	−0.0515026	+	0.0109472i	0.182088	+	0.983282i	$0.441714\pi$
$42$	9.67189	+	1.01656i	1.49241	+	0.156858i
$43$	2.88637	−	2.59890i	0.440167	−	0.396329i	−0.419030	−	0.907972i	$-0.637630\pi$
$43$	2.88637	−	2.59890i	0.440167	−	0.396329i	0.859198	+	0.511644i	$0.170963\pi$
$44$	−1.21255	+	1.34667i	−0.182798	+	0.203018i
$45$		0			0
$46$	0.346435	+	1.06622i	0.0510791	+	0.157205i
$47$	1.13095	−	0.367467i	0.164965	−	0.0536005i	−0.225370	−	0.974273i	$-0.572359\pi$
$47$	1.13095	−	0.367467i	0.164965	−	0.0536005i	0.390335	+	0.920673i	$0.372359\pi$
$48$	5.78721	−	0.608260i	0.835311	−	0.0877948i
$49$	−4.99745	+	5.55023i	−0.713922	+	0.792890i
$50$		0			0
$51$	−0.818631	+	7.78876i	−0.114631	+	1.09064i
$52$	−0.263933	−	1.24171i	−0.0366009	−	0.172194i
$53$	−0.953442	+	2.14147i	−0.130965	+	0.294153i	−0.967111	−	0.254354i	$-0.918137\pi$
$53$	−0.953442	+	2.14147i	−0.130965	+	0.294153i	0.836146	+	0.548507i	$0.184804\pi$
$54$	−3.50492	+	2.54647i	−0.476959	+	0.346531i
$55$		0			0
$56$	−5.81584	+	10.0733i	−0.777175	+	1.34611i
$57$	10.9586	−	6.32692i	1.45150	−	0.838022i
$58$	4.93114	−	6.78713i	0.647490	−	0.891194i
$59$	7.60885	+	1.61731i	0.990587	+	0.210556i	0.674581	−	0.738201i	$-0.264324\pi$
$59$	7.60885	+	1.61731i	0.990587	+	0.210556i	0.316007	+	0.948757i	$0.397658\pi$
$60$		0			0
$61$	−2.72343			−0.348700			−0.174350	−	0.984684i	$-0.555782\pi$
$61$	−2.72343			−0.348700			−0.174350	+	0.984684i	$0.555782\pi$
$62$	−3.03901	−	6.15062i	−0.385954	−	0.781130i
$63$			4.96588i			0.625642i
$64$	−2.74619	+	8.45191i	−0.343274	+	1.05649i
$65$		0			0
$66$	7.78047	+	5.65284i	0.957709	+	0.695817i
$67$	−6.42693	+	3.71059i	−0.785175	+	0.453321i	−0.838261	−	0.545269i	$-0.816427\pi$
$67$	−6.42693	+	3.71059i	−0.785175	+	0.453321i	0.0530864	+	0.998590i	$0.483094\pi$
$68$	−1.57469	−	0.909147i	−0.190959	−	0.110250i
$69$	−1.72469	+	0.767882i	−0.207628	+	0.0924421i
$70$		0			0
$71$	−4.65742	−	2.07362i	−0.552734	−	0.246093i	0.111311	−	0.993786i	$-0.464495\pi$
$71$	−4.65742	−	2.07362i	−0.552734	−	0.246093i	−0.664045	+	0.747693i	$0.731162\pi$
$72$	0.830027	+	3.90497i	0.0978196	+	0.460205i
$73$	5.36221	+	0.563591i	0.627599	+	0.0659633i	0.412988	−	0.910736i	$-0.364485\pi$
$73$	5.36221	+	0.563591i	0.627599	+	0.0659633i	0.214611	+	0.976700i	$0.431152\pi$
$74$	1.49567	+	1.66111i	0.173868	+	0.193100i
$75$		0			0
$76$	0.307091	+	2.92178i	0.0352258	+	0.335151i
$77$	−13.6076	+	4.42139i	−1.55074	+	0.503865i
$78$	−6.40740	+	2.08189i	−0.725495	+	0.235728i
$79$	−1.01782	−	9.68388i	−0.114513	−	1.08952i	−0.889308	−	0.457309i	$-0.848813\pi$
$79$	−1.01782	−	9.68388i	−0.114513	−	1.08952i	0.774795	−	0.632213i	$-0.217853\pi$
$80$		0			0
$81$	−7.50241	−	8.33227i	−0.833601	−	0.925808i
$82$	−0.413145	−	0.0434232i	−0.0456242	−	0.00479530i
$83$	−1.74545	−	8.21169i	−0.191588	−	0.901350i	−0.963933	−	0.266147i	$-0.914249\pi$
$83$	−1.74545	−	8.21169i	−0.191588	−	0.901350i	0.772345	−	0.635204i	$-0.219084\pi$
$84$	−3.47359	−	1.54654i	−0.379000	−	0.168742i
$85$		0			0
$86$	4.37200	−	1.94654i	0.471445	−	0.209901i
$87$	12.2349	+	7.06383i	1.31172	+	0.757322i
$88$	−9.96149	+	5.75127i	−1.06190	+	0.613087i
$89$	4.12243	+	2.99512i	0.436976	+	0.317482i	0.784432	−	0.620214i	$-0.212954\pi$
$89$	4.12243	+	2.99512i	0.436976	+	0.317482i	−0.347456	+	0.937696i	$0.612954\pi$
$90$		0			0
$91$	3.09732	−	9.53258i	0.324688	−	0.999285i
$92$		−	0.438320i		−	0.0456980i
$93$	9.76595	−	6.17231i	1.01268	−	0.640039i
$94$	1.46523			0.151127
$95$		0			0
$96$	−5.39957	−	1.14771i	−0.551092	−	0.117138i
$97$	6.41522	−	8.82979i	0.651367	−	0.896530i	−0.347791	−	0.937572i	$-0.613068\pi$
$97$	6.41522	−	8.82979i	0.651367	−	0.896530i	0.999157	+	0.0410427i	$0.0130680\pi$
$98$	−7.96966	+	4.60129i	−0.805057	+	0.464800i
$99$	−2.45537	+	4.25283i	−0.246774	+	0.427426i
$100$		0			0
$101$	0.322577	−	0.234366i	0.0320976	−	0.0233203i	−0.571621	−	0.820518i	$-0.693685\pi$
$101$	0.322577	−	0.234366i	0.0320976	−	0.0233203i	0.603718	+	0.797198i	$0.293685\pi$
$102$	−3.92499	+	8.81567i	−0.388632	+	0.872881i
$103$	0.681286	+	3.20520i	0.0671291	+	0.315817i	0.998882	−	0.0472758i	$-0.0150540\pi$
$103$	0.681286	+	3.20520i	0.0671291	+	0.315817i	−0.931753	+	0.363093i	$0.881721\pi$
$104$	0.842278	−	8.01374i	0.0825921	−	0.785812i
$105$		0			0
$106$	−1.93269	+	2.14647i	−0.187720	+	0.208484i
$107$	3.13955	−	0.329980i	0.303512	−	0.0319004i	0.0484517	−	0.998826i	$-0.484571\pi$
$107$	3.13955	−	0.329980i	0.303512	−	0.0319004i	0.255060	+	0.966925i	$0.417905\pi$
$108$	1.61094	−	0.523425i	0.155013	−	0.0503666i
$109$	−2.14959	−	6.61576i	−0.205893	−	0.633675i	−0.999676	−	0.0254724i	$-0.991891\pi$
$109$	−2.14959	−	6.61576i	−0.205893	−	0.633675i	0.793782	−	0.608202i	$-0.208109\pi$
$110$		0			0
$111$	−2.51870	+	2.79730i	−0.239064	+	0.265508i
$112$	−7.92735	+	7.13782i	−0.749064	+	0.674461i
$113$	−15.1633	−	1.59372i	−1.42644	−	0.149925i	−0.640372	−	0.768065i	$-0.721220\pi$
$113$	−15.1633	−	1.59372i	−1.42644	−	0.149925i	−0.786068	+	0.618140i	$0.787886\pi$
$114$	15.2510	−	3.24170i	1.42839	−	0.303613i
$115$		0			0
$116$	−2.65362	+	1.92796i	−0.246382	+	0.179007i
$117$	−1.39923	−	3.14271i	−0.129359	−	0.290544i
$118$	8.30073	+	4.79243i	0.764144	+	0.441179i
$119$	−7.17834	−	12.4332i	−0.658037	−	1.13975i
$120$		0			0
$121$	−3.08025	−	0.654727i	−0.280023	−	0.0595207i
$122$	−3.19150	−	1.03698i	−0.288945	−	0.0938838i
$123$		−	0.699567i		−	0.0630778i
$124$	0.386920	+	2.65423i	0.0347464	+	0.238357i
$125$		0			0
$126$	−1.89082	+	5.81935i	−0.168448	+	0.518429i
$127$	−4.20530	+	19.7844i	−0.373160	+	1.75558i	0.244996	+	0.969524i	$0.421213\pi$
$127$	−4.20530	+	19.7844i	−0.373160	+	1.75558i	−0.618156	+	0.786055i	$0.712120\pi$
$128$	−3.30888	+	4.55428i	−0.292466	+	0.402545i
$129$	4.02960	+	6.97946i	0.354786	+	0.614508i
$130$		0			0
$131$	11.5575	−	5.14574i	1.00979	−	0.449585i	0.165919	−	0.986139i	$-0.446941\pi$
$131$	11.5575	−	5.14574i	1.00979	−	0.449585i	0.843866	+	0.536554i	$0.180274\pi$
$132$	−2.21013	−	3.04199i	−0.192367	−	0.264771i
$133$	−9.43487	+	21.1911i	−0.818107	+	1.83750i
$134$	−8.94435	+	1.90118i	−0.772674	+	0.164237i
$135$		0			0
$136$	−7.72292	−	8.57717i	−0.662235	−	0.735486i
$137$	−7.34079	−	6.60968i	−0.627166	−	0.564703i	0.293058	−	0.956095i	$-0.405327\pi$
$137$	−7.34079	−	6.60968i	−0.627166	−	0.564703i	−0.920224	+	0.391392i	$0.871994\pi$
$138$	−2.31349	+	0.243157i	−0.196937	+	0.0206989i
$139$	4.78945	+	14.7404i	0.406236	+	1.25026i	0.919859	+	0.392249i	$0.128303\pi$
$139$	4.78945	+	14.7404i	0.406236	+	1.25026i	−0.513623	+	0.858016i	$0.671697\pi$
$140$		0			0
$141$	0.257919	+	2.45393i	0.0217207	+	0.206658i
$142$	−4.66831	−	4.20337i	−0.391756	−	0.352739i
$143$	7.36594	−	6.63233i	0.615971	−	0.554623i
$144$	−0.382701	+	3.64116i	−0.0318918	+	0.303430i
$145$		0			0
$146$	6.06919	+	2.70218i	0.502290	+	0.223634i
$147$	−9.10897	−	12.5374i	−0.751295	−	1.03407i
$148$	−0.355459	−	0.798373i	−0.0292185	−	0.0656259i
$149$	−7.62162	+	13.2010i	−0.624388	+	1.08147i	0.364271	+	0.931293i	$0.381318\pi$
$149$	−7.62162	+	13.2010i	−0.624388	+	1.08147i	−0.988659	+	0.150178i	$0.952015\pi$
$150$		0			0
$151$	0.211823	+	0.153899i	0.0172379	+	0.0125241i	0.596371	−	0.802709i	$-0.296609\pi$
$151$	0.211823	+	0.153899i	0.0172379	+	0.0125241i	−0.579133	+	0.815233i	$0.696609\pi$
$152$	−3.87720	+	18.2408i	−0.314483	+	1.47952i
$153$	−4.68631	−	1.52267i	−0.378866	−	0.123101i
$154$	−17.6298			−1.42065
$155$		0			0
$156$	2.63407			0.210894
$157$	15.1470	+	4.92157i	1.20886	+	0.392784i	0.843015	−	0.537890i	$-0.180778\pi$
$157$	15.1470	+	4.92157i	1.20886	+	0.392784i	0.365850	+	0.930674i	$0.380778\pi$
$158$	2.49451	−	11.7358i	0.198453	−	0.933647i
$159$	−3.93506	−	2.85899i	−0.312071	−	0.226733i
$160$		0			0
$161$	1.73042	−	2.99717i	0.136376	−	0.236210i
$162$	−5.61920	−	12.6209i	−0.441486	−	0.991594i
$163$	−0.0782785	−	0.107741i	−0.00613125	−	0.00843894i	0.805940	−	0.591997i	$-0.201660\pi$
$163$	−0.0782785	−	0.107741i	−0.00613125	−	0.00843894i	−0.812072	+	0.583558i	$0.801660\pi$
$164$	0.148378	+	0.0660621i	0.0115864	+	0.00515859i
$165$		0			0
$166$	1.08127	−	10.2876i	0.0839228	−	0.798472i
$167$	2.93451	−	2.64225i	0.227080	−	0.204463i	−0.547735	−	0.836652i	$-0.684510\pi$
$167$	2.93451	−	2.64225i	0.227080	−	0.204463i	0.774815	+	0.632188i	$0.217843\pi$
$168$	−17.9361	−	16.1498i	−1.38380	−	1.24598i
$169$	−0.633070	−	6.02326i	−0.0486977	−	0.463328i
$170$		0			0
$171$	2.46023	+	7.57181i	0.188139	+	0.579031i
$172$	−1.86087	+	0.195585i	−0.141890	+	0.0149132i
$173$	10.7436	+	9.67358i	0.816821	+	0.735469i	0.967434	−	0.253124i	$-0.0814581\pi$
$173$	10.7436	+	9.67358i	0.816821	+	0.735469i	−0.150613	+	0.988593i	$0.548125\pi$
$174$	11.6480	+	12.9364i	0.883035	+	0.980709i
$175$		0			0
$176$	−10.3183	+	2.19323i	−0.777775	+	0.165321i
$177$	−6.56509	+	14.7454i	−0.493462	+	1.10833i
$178$	3.69050	+	5.07954i	0.276615	+	0.380727i
$179$	16.1879	−	7.20733i	1.20994	−	0.538701i	0.300201	−	0.953876i	$-0.402946\pi$
$179$	16.1879	−	7.20733i	1.20994	−	0.538701i	0.909741	+	0.415175i	$0.136280\pi$
$180$		0			0
$181$	6.02958	+	10.4435i	0.448175	+	0.776262i	0.998267	−	0.0588418i	$-0.0187408\pi$
$181$	6.02958	+	10.4435i	0.448175	+	0.776262i	−0.550092	+	0.835104i	$0.685407\pi$
$182$	7.25929	−	9.99155i	0.538094	−	0.740623i
$183$	1.17492	−	5.52757i	0.0868526	−	0.408609i
$184$	0.859766	−	2.64609i	0.0633828	−	0.195072i
$185$		0			0
$186$	13.7946	−	3.51462i	1.01147	−	0.257704i
$187$		−	14.1973i		−	1.03821i
$188$	−0.544835	−	0.177028i	−0.0397362	−	0.0129111i
$189$	13.0818	+	2.78062i	0.951559	+	0.202260i
$190$		0			0
$191$	−2.53576	−	4.39207i	−0.183481	−	0.317799i	0.759583	−	0.650411i	$-0.225403\pi$
$191$	−2.53576	−	4.39207i	−0.183481	−	0.317799i	−0.943064	+	0.332612i	$0.892070\pi$
$192$	−15.9695	−	9.22001i	−1.15250	−	0.665397i
$193$	8.15171	+	18.3090i	0.586773	+	1.31791i	0.926112	+	0.377250i	$0.123130\pi$
$193$	8.15171	+	18.3090i	0.586773	+	1.31791i	−0.339339	+	0.940664i	$0.610203\pi$
$194$	10.8798	−	7.90466i	0.781126	−	0.567521i
$195$		0			0
$196$	3.51937	−	0.748066i	0.251384	−	0.0534333i
$197$	−21.5894	−	2.26914i	−1.53818	−	0.161670i	−0.702820	−	0.711367i	$-0.748076\pi$
$197$	−21.5894	−	2.26914i	−1.53818	−	0.161670i	−0.835364	+	0.549698i	$0.814743\pi$
$198$	−4.49668	+	4.04883i	−0.319565	+	0.287738i
$199$	−10.1477	+	11.2702i	−0.719352	+	0.798921i	−0.986330	−	0.164781i	$-0.947308\pi$
$199$	−10.1477	+	11.2702i	−0.719352	+	0.798921i	0.266978	+	0.963703i	$0.413975\pi$
$200$		0			0
$201$	−4.75848	−	14.6451i	−0.335637	−	1.03299i
$202$	0.467255	−	0.151820i	0.0328759	−	0.0106820i
$203$	−25.7564	+	2.70710i	−1.80774	+	0.190001i
$204$	2.52457	−	2.80382i	0.176755	−	0.196307i
$205$		0			0
$206$	−0.422043	+	4.01547i	−0.0294051	+	0.279771i
$207$	−0.246962	−	1.16187i	−0.0171651	−	0.0807553i
$208$	3.00570	−	6.75092i	0.208408	−	0.468092i
$209$	−18.5580	+	13.4832i	−1.28368	+	0.932651i
$210$		0			0
$211$	−3.15220	+	5.45978i	−0.217007	+	0.375867i	−0.953891	−	0.300152i	$-0.902963\pi$
$211$	−3.15220	+	5.45978i	−0.217007	+	0.375867i	0.736885	+	0.676018i	$0.236296\pi$
$212$	0.977990	−	0.564643i	0.0671687	−	0.0387798i
$213$	6.21794	−	8.55826i	0.426046	−	0.586403i
$214$	3.80478	+	0.808730i	0.260089	+	0.0552837i
$215$		0			0
$216$	10.7517			0.731564
$217$	−7.83276	+	19.6767i	−0.531722	+	1.33574i
$218$		−	8.57126i		−	0.580519i
$219$	−3.45720	+	10.6402i	−0.233616	+	0.718996i
$220$		0			0
$221$	8.04618	+	5.84589i	0.541245	+	0.393237i
$222$	−4.01668	+	2.31903i	−0.269582	+	0.155643i
$223$	6.39915	+	3.69455i	0.428519	+	0.247406i	0.698716	−	0.715400i	$-0.253755\pi$
$223$	6.39915	+	3.69455i	0.428519	+	0.247406i	−0.270196	+	0.962805i	$0.587089\pi$
$224$	9.24454	−	4.11594i	0.617677	−	0.275007i
$225$		0			0
$226$	−17.1625	−	7.64123i	−1.14163	−	0.508287i
$227$	−4.00018	−	18.8193i	−0.265501	−	1.24908i	−0.885559	−	0.464528i	$-0.846224\pi$
$227$	−4.00018	−	18.8193i	−0.265501	−	1.24908i	0.620058	−	0.784556i	$-0.287109\pi$
$228$	−6.06262	−	0.637207i	−0.401507	−	0.0422000i
$229$	4.07307	+	4.52360i	0.269156	+	0.298928i	0.862537	−	0.505994i	$-0.168874\pi$
$229$	4.07307	+	4.52360i	0.269156	+	0.298928i	−0.593381	+	0.804921i	$0.702207\pi$
$230$		0			0
$231$	−3.10330	−	29.5260i	−0.204182	−	1.94267i
$232$	−19.8013	+	6.43383i	−1.30002	+	0.422401i
$233$	16.6702	−	5.41646i	1.09210	−	0.354844i	0.293042	−	0.956100i	$-0.405333\pi$
$233$	16.6702	−	5.41646i	1.09210	−	0.354844i	0.799057	+	0.601255i	$0.205333\pi$
$234$	−0.443078	−	4.21561i	−0.0289649	−	0.275583i
$235$		0			0
$236$	−2.50754	−	2.78491i	−0.163227	−	0.181282i
$237$	20.0938	+	2.11195i	1.30523	+	0.137186i
$238$	−3.67794	−	17.3033i	−0.238405	−	1.12161i
$239$	25.4989	+	11.3529i	1.64939	+	0.734355i	0.999667	−	0.0258176i	$-0.00821891\pi$
$239$	25.4989	+	11.3529i	1.64939	+	0.734355i	0.649721	+	0.760172i	$0.274886\pi$
$240$		0			0
$241$	20.7829	−	9.25315i	1.33875	−	0.596048i	0.392576	−	0.919720i	$-0.371584\pi$
$241$	20.7829	−	9.25315i	1.33875	−	0.596048i	0.946169	+	0.323672i	$0.104917\pi$
$242$	−3.36034	−	1.94010i	−0.216011	−	0.124714i
$243$	11.0132	−	6.35849i	0.706499	−	0.407897i
$244$	1.06144	+	0.771185i	0.0679520	+	0.0493701i
$245$		0			0
$246$	0.266369	−	0.819798i	0.0169830	−	0.0522684i
$247$		−	16.0694i		−	1.02247i
$248$	−2.87048	+	16.7822i	−0.182276	+	1.06567i
$249$	17.4197			1.10393
$250$		0			0
$251$	15.8797	+	3.37534i	1.00232	+	0.213050i	0.679709	−	0.733482i	$-0.262106\pi$
$251$	15.8797	+	3.37534i	1.00232	+	0.213050i	0.322611	+	0.946532i	$0.395439\pi$
$252$	1.40617	−	1.93543i	0.0885805	−	0.121921i
$253$	2.96390	−	1.71121i	0.186339	−	0.107583i
$254$	−12.4612	+	21.5834i	−0.781884	+	1.35426i
$255$		0			0
$256$	8.76759	−	6.37002i	0.547974	−	0.398126i
$257$	−9.49816	+	21.3332i	−0.592479	+	1.33073i	0.329744	+	0.944070i	$0.393037\pi$
$257$	−9.49816	+	21.3332i	−0.592479	+	1.33073i	−0.922223	+	0.386659i	$0.873629\pi$
$258$	2.06463	+	9.71331i	0.128538	+	0.604724i
$259$	0.721274	−	6.86246i	0.0448178	−	0.426412i
$260$		0			0
$261$	−5.94774	+	6.60563i	−0.368156	+	0.408878i
$262$	15.5032	−	1.62945i	0.957789	−	0.100668i
$263$	−9.88562	+	3.21203i	−0.609574	+	0.198062i	−0.597506	−	0.801865i	$-0.703841\pi$
$263$	−9.88562	+	3.21203i	−0.609574	+	0.198062i	−0.0120680	+	0.999927i	$0.503841\pi$
$264$	−7.37545	−	22.6993i	−0.453928	−	1.39705i
$265$		0			0
$266$	−19.1252	+	21.2406i	−1.17264	+	1.30235i
$267$	−7.85745	+	7.07488i	−0.480868	+	0.432975i
$268$	3.55558	+	0.373707i	0.217192	+	0.0228278i
$269$	−4.32150	+	0.918563i	−0.263487	+	0.0560058i	−0.337761	−	0.941232i	$-0.609669\pi$
$269$	−4.32150	+	0.918563i	−0.263487	+	0.0560058i	0.0742740	+	0.997238i	$0.476336\pi$
$270$		0			0
$271$	−4.97777	+	3.61656i	−0.302378	+	0.219691i	−0.728619	−	0.684919i	$-0.759838\pi$
$271$	−4.97777	+	3.61656i	−0.302378	+	0.219691i	0.426241	+	0.904610i	$0.359838\pi$
$272$	−4.30523	−	9.66970i	−0.261043	−	0.586312i
$273$	18.0114	+	10.3989i	1.09010	+	0.629369i
$274$	−6.08571	−	10.5408i	−0.367651	−	0.636790i
$275$		0			0
$276$	0.889629	+	0.189096i	0.0535493	+	0.0113823i
$277$	20.9683	+	6.81302i	1.25987	+	0.409355i	0.861446	−	0.507849i	$-0.169559\pi$
$277$	20.9683	+	6.81302i	1.25987	+	0.409355i	0.398419	+	0.917204i	$0.369559\pi$
$278$			19.0974i			1.14539i
$279$	2.52109	+	6.81762i	0.150933	+	0.408160i
$280$		0			0
$281$	−9.50955	+	29.2674i	−0.567292	+	1.74595i	0.0937474	+	0.995596i	$0.470115\pi$
$281$	−9.50955	+	29.2674i	−0.567292	+	1.74595i	−0.661040	+	0.750351i	$0.729885\pi$
$282$	−0.632119	+	2.97389i	−0.0376421	+	0.177092i
$283$	12.5464	−	17.2687i	0.745807	−	1.02652i	−0.252456	−	0.967608i	$-0.581238\pi$
$283$	12.5464	−	17.2687i	0.745807	−	1.02652i	0.998263	−	0.0589075i	$-0.0187617\pi$
$284$	1.22803	+	2.12701i	0.0728701	+	0.126215i
$285$		0			0
$286$	11.1572	−	4.96752i	0.659741	−	0.293736i
$287$	0.753786	+	1.03750i	0.0444946	+	0.0612415i
$288$	1.41267	−	3.17290i	0.0832421	−	0.186965i
$289$	−2.69417	+	0.572664i	−0.158481	+	0.0336861i
$290$		0			0
$291$	15.1536	+	16.8298i	0.888321	+	0.986581i
$292$	−1.93030	−	1.73805i	−0.112963	−	0.101712i
$293$	1.78917	−	0.188050i	0.104525	−	0.0109860i	−0.0521218	−	0.998641i	$-0.516598\pi$
$293$	1.78917	−	0.188050i	0.104525	−	0.0109860i	0.156646	+	0.987655i	$0.449932\pi$
$294$	−5.90071	−	18.1605i	−0.344136	−	1.05914i
$295$		0			0
$296$	−0.579852	−	5.51692i	−0.0337032	−	0.320664i
$297$	9.82848	+	8.84961i	0.570306	+	0.513506i
$298$	−13.9580	+	12.5678i	−0.808564	+	0.728034i
$299$	−0.250607	+	2.38437i	−0.0144930	+	0.137892i
$300$		0			0
$301$	−13.4965	−	6.00904i	−0.777926	−	0.346355i
$302$	0.189630	+	0.261003i	0.0109120	+	0.0150190i
$303$	0.336513	+	0.755821i	0.0193322	+	0.0434208i
$304$	−8.55109	+	14.8109i	−0.490439	+	0.849465i
$305$		0			0
$306$	−4.91195	−	3.56874i	−0.280797	−	0.204011i
$307$	5.56567	−	26.1844i	0.317650	−	1.49442i	−0.472402	−	0.881383i	$-0.656613\pi$
$307$	5.56567	−	26.1844i	0.317650	−	1.49442i	0.790051	−	0.613041i	$-0.210054\pi$
$308$	6.55551	+	2.13001i	0.373535	+	0.121369i
$309$	−6.79928			−0.386798
$310$		0			0
$311$	4.18114			0.237090			0.118545	−	0.992949i	$-0.462177\pi$
$311$	4.18114			0.237090			0.118545	+	0.992949i	$0.462177\pi$
$312$	15.9016	+	5.16673i	0.900249	+	0.292509i
$313$	2.35831	−	11.0950i	0.133299	−	0.627124i	−0.859877	−	0.510501i	$-0.829460\pi$
$313$	2.35831	−	11.0950i	0.133299	−	0.627124i	0.993176	−	0.116623i	$-0.0372069\pi$
$314$	15.8763	+	11.5348i	0.895953	+	0.650948i
$315$		0			0
$316$	−2.34546	+	4.06246i	−0.131943	+	0.228531i
$317$	10.5269	+	23.6438i	0.591249	+	1.32797i	0.923073	+	0.384626i	$0.125669\pi$
$317$	10.5269	+	23.6438i	0.591249	+	1.32797i	−0.331824	+	0.943341i	$0.607664\pi$
$318$	−3.52277	−	4.84867i	−0.197547	−	0.271900i
$319$	−23.3965	−	10.4168i	−1.30995	−	0.583229i
$320$		0			0
$321$	−0.684701	+	6.51449i	−0.0382163	+	0.363604i
$322$	3.16903	−	2.85341i	0.176603	−	0.159014i
$323$	−17.1050	−	15.4015i	−0.951750	−	0.856960i
$324$	0.564609	+	5.37189i	0.0313672	+	0.298439i
$325$		0			0
$326$	−0.0507081	−	0.156064i	−0.00280846	−	0.00864356i
$327$	14.3549	−	1.50876i	0.793828	−	0.0834347i
$328$	0.766160	+	0.689854i	0.0423041	+	0.0380908i
$329$	−3.02663	−	3.36141i	−0.166864	−	0.185321i
$330$		0			0
$331$	−0.749053	+	0.159216i	−0.0411717	+	0.00875131i	−0.228451	−	0.973555i	$-0.573366\pi$
$331$	−0.749053	+	0.159216i	−0.0411717	+	0.00875131i	0.187280	+	0.982307i	$0.440033\pi$
$332$	−1.64500	+	3.69472i	−0.0902808	+	0.202774i
$333$	−1.39205	−	1.91599i	−0.0762839	−	0.104996i
$334$	4.44493	−	1.97901i	0.243215	−	0.108287i
$335$		0			0
$336$	−11.0672	−	19.1689i	−0.603765	−	1.04575i
$337$	1.40736	−	1.93706i	0.0766637	−	0.105519i	−0.768963	−	0.639293i	$-0.779227\pi$
$337$	1.40736	−	1.93706i	0.0766637	−	0.105519i	0.845627	+	0.533775i	$0.179227\pi$
$338$	1.55156	−	7.29950i	0.0843936	−	0.397041i
$339$	9.77628	−	30.0883i	0.530974	−	1.63417i
$340$		0			0
$341$	−16.4372	+	12.9784i	−0.890123	+	0.702822i
$342$			9.80991i			0.530459i
$343$	1.69511	+	0.550776i	0.0915276	+	0.0297391i
$344$	−11.6175	−	2.46938i	−0.626374	−	0.133140i
$345$		0			0
$346$	8.90672	+	15.4269i	0.478828	+	0.829355i
$347$	−4.89980	−	2.82890i	−0.263035	−	0.151863i	0.362683	−	0.931912i	$-0.381861\pi$
$347$	−4.89980	−	2.82890i	−0.263035	−	0.151863i	−0.625718	+	0.780049i	$0.715194\pi$
$348$	−2.76826	−	6.21761i	−0.148394	−	0.333299i
$349$	23.5162	−	17.0855i	1.25879	−	0.914566i	0.260095	−	0.965583i	$-0.416246\pi$
$349$	23.5162	−	17.0855i	1.25879	−	0.914566i	0.998698	+	0.0510167i	$0.0162462\pi$
$350$		0			0
$351$	−9.06243	+	1.92628i	−0.483717	+	0.102817i
$352$	9.95223	+	1.04602i	0.530456	+	0.0557532i
$353$	−14.3243	+	12.8976i	−0.762404	+	0.686471i	−0.955593	−	0.294690i	$-0.904784\pi$
$353$	−14.3243	+	12.8976i	−0.762404	+	0.686471i	0.193189	+	0.981162i	$0.438117\pi$
$354$	−13.3079	+	14.7799i	−0.707307	+	0.785544i
$355$		0			0
$356$	−0.758579	−	2.33467i	−0.0402046	−	0.123737i
$357$	28.3317	−	9.20553i	1.49947	−	0.487209i
$358$	21.7143	−	2.28227i	1.14764	−	0.120622i
$359$	−6.92167	+	7.68729i	−0.365312	+	0.405720i	−0.897577	−	0.440858i	$-0.854674\pi$
$359$	−6.92167	+	7.68729i	−0.365312	+	0.405720i	0.532265	+	0.846578i	$0.321341\pi$
$360$		0			0
$361$	−1.90131	+	18.0898i	−0.100069	+	0.952095i
$362$	3.08935	+	14.5343i	0.162373	+	0.763904i
$363$	2.65771	−	5.96932i	0.139494	−	0.313308i
$364$	−3.90647	+	2.83822i	−0.204755	+	0.148763i
$365$		0			0
$366$	3.48154	−	6.03020i	0.181983	−	0.315203i
$367$	−0.118268	+	0.0682819i	−0.00617352	+	0.00356428i	−0.503084	−	0.864238i	$-0.667801\pi$
$367$	−0.118268	+	0.0682819i	−0.00617352	+	0.00356428i	0.496910	+	0.867802i	$0.334468\pi$
$368$	1.49978	−	2.06428i	0.0781817	−	0.107608i
$369$	0.430531	+	0.0915122i	0.0224125	+	0.00476393i
$370$		0			0
$371$	8.91649			0.462921
$372$	−5.55402	−	0.359759i	−0.287963	−	0.0186527i
$373$			7.36393i			0.381290i	0.981659	+	0.190645i	$0.0610579\pi$
$373$			7.36393i			0.381290i	−0.981659	+	0.190645i	$0.938942\pi$
$374$	5.40578	−	16.6373i	0.279526	−	0.860294i
$375$		0			0
$376$	−2.94187	−	2.13739i	−0.151715	−	0.110228i
$377$	15.5374	−	8.97053i	0.800218	−	0.462006i
$378$	14.2713	+	8.23955i	0.734038	+	0.423797i
$379$	4.20974	−	1.87430i	0.216240	−	0.0962762i	−0.295758	−	0.955263i	$-0.595572\pi$
$379$	4.20974	−	1.87430i	0.216240	−	0.0962762i	0.511998	+	0.858987i	$0.328906\pi$
$380$		0			0
$381$	−38.3408	−	17.0704i	−1.96426	−	0.874544i
$382$	−1.29924	−	6.11243i	−0.0664748	−	0.312739i
$383$	−32.1179	−	3.37572i	−1.64115	−	0.172491i	−0.761515	−	0.648147i	$-0.775544\pi$
$383$	−32.1179	−	3.37572i	−1.64115	−	0.172491i	−0.879631	+	0.475656i	$0.842211\pi$
$384$	−7.81602	−	8.68057i	−0.398860	−	0.442979i
$385$		0			0
$386$	2.58132	+	24.5596i	0.131386	+	1.25005i
$387$	−4.82246	+	1.56691i	−0.245139	+	0.0796506i
$388$	−5.00060	+	1.62479i	−0.253867	+	0.0824864i
$389$	−3.68685	−	35.0781i	−0.186931	−	1.77853i	−0.538756	−	0.842462i	$-0.681105\pi$
$389$	−3.68685	−	35.0781i	−0.186931	−	1.77853i	0.351825	−	0.936066i	$-0.385561\pi$
$390$		0			0
$391$	2.29784	+	2.55201i	0.116207	+	0.129061i
$392$	22.7134	+	2.38727i	1.14720	+	0.120575i
$393$	5.45791	+	25.6774i	0.275315	+	1.29526i
$394$	−24.4359	−	10.8796i	−1.23106	−	0.548105i
$395$		0			0
$396$	2.16123	−	0.962241i	0.108606	−	0.0483544i
$397$	3.49356	+	2.01701i	0.175337	+	0.101231i	0.585100	−	0.810961i	$-0.301055\pi$
$397$	3.49356	+	2.01701i	0.175337	+	0.101231i	−0.409763	+	0.912192i	$0.634389\pi$
$398$	−16.1830	+	9.34326i	−0.811181	+	0.468335i
$399$	−38.9398	−	28.2914i	−1.94943	−	1.41634i
$400$		0			0
$401$	7.68933	−	23.6653i	0.383987	−	1.18179i	−0.553225	−	0.833032i	$-0.686603\pi$
$401$	7.68933	−	23.6653i	0.383987	−	1.18179i	0.937212	−	0.348759i	$-0.113397\pi$
$402$		−	18.9739i		−	0.946334i
$403$	−0.587221	−	14.6597i	−0.0292516	−	0.730249i
$404$	−0.192087			−0.00955671
$405$		0			0
$406$	−31.2137	−	6.63469i	−1.54911	−	0.329274i
$407$	4.01084	−	5.52044i	0.198810	−	0.273638i
$408$	20.7403	−	11.9744i	1.02680	−	0.592821i
$409$	1.75361	−	3.03734i	0.0867105	−	0.150187i	−0.819408	−	0.573210i	$-0.805698\pi$
$409$	1.75361	−	3.03734i	0.0867105	−	0.150187i	0.906119	+	0.423023i	$0.139031\pi$
$410$		0			0
$411$	16.5821	−	12.0476i	0.817936	−	0.594265i
$412$	0.642076	−	1.44213i	0.0316328	−	0.0710485i
$413$	−6.15186	−	28.9422i	−0.302713	−	1.42415i
$414$	0.152988	−	1.45559i	0.00751896	−	0.0715381i
$415$		0			0
$416$	−4.69077	+	5.20963i	−0.229984	+	0.255423i
$417$	−31.9838	+	3.36163i	−1.56625	+	0.164620i
$418$	−26.8814	+	8.73429i	−1.31481	+	0.427208i
$419$	−1.27325	−	3.91865i	−0.0622022	−	0.191439i	0.915126	−	0.403167i	$-0.132091\pi$
$419$	−1.27325	−	3.91865i	−0.0622022	−	0.191439i	−0.977328	+	0.211729i	$0.932091\pi$
$420$		0			0
$421$	18.4689	−	20.5118i	0.900121	−	0.999686i	−0.0998679	−	0.995001i	$-0.531842\pi$
$421$	18.4689	−	20.5118i	0.900121	−	0.999686i	0.999989	−	0.00468505i	$-0.00149130\pi$
$422$	−5.77283	+	5.19788i	−0.281017	+	0.253029i
$423$	−1.54395	−	0.162276i	−0.0750695	−	0.00789012i
$424$	7.01157	−	1.49035i	0.340512	−	0.0723780i
$425$		0			0
$426$	10.5453	−	7.66158i	0.510919	−	0.371205i
$427$	4.21350	+	9.46367i	0.203905	+	0.457979i
$428$	−1.31706	−	0.760408i	−0.0636627	−	0.0367557i
$429$	10.2834	+	17.8114i	0.496488	+	0.859943i
$430$		0			0
$431$	14.5489	+	3.09247i	0.700796	+	0.148959i	0.544512	−	0.838753i	$-0.316715\pi$
$431$	14.5489	+	3.09247i	0.700796	+	0.148959i	0.156284	+	0.987712i	$0.450048\pi$
$432$	9.37772	+	3.04701i	0.451186	+	0.146599i
$433$		−	9.26195i		−	0.445101i	−0.974921	−	0.222550i	$-0.928562\pi$
$433$		−	9.26195i		−	0.445101i	0.974921	−	0.222550i	$-0.0714382\pi$
$434$	−16.6711	+	20.0761i	−0.800238	+	0.963682i
$435$		0			0
$436$	−1.03557	+	3.18715i	−0.0495947	+	0.152637i
$437$	1.15361	−	5.42728i	0.0551844	−	0.259622i
$438$	−8.10275	+	11.1525i	−0.387164	+	0.532886i
$439$	8.85909	+	15.3444i	0.422821	+	0.732348i	0.996214	−	0.0869324i	$-0.0277064\pi$
$439$	8.85909	+	15.3444i	0.422821	+	0.732348i	−0.573393	+	0.819281i	$0.694373\pi$
$440$		0			0
$441$	8.90741	−	3.96584i	0.424163	−	0.188849i
$442$	7.20314	+	9.91428i	0.342619	+	0.471574i
$443$	−7.50439	+	16.8551i	−0.356544	+	0.800811i	0.642850	+	0.765993i	$0.277752\pi$
$443$	−7.50439	+	16.8551i	−0.356544	+	0.800811i	−0.999394	+	0.0348187i	$0.988915\pi$
$444$	1.77375	−	0.377023i	0.0841785	−	0.0178927i
$445$		0			0
$446$	6.09220	+	6.76608i	0.288474	+	0.320383i
$447$	−23.5052	−	21.1642i	−1.11176	−	1.00103i
$448$	33.6183	−	3.53342i	1.58831	−	0.166939i
$449$	−7.01784	−	21.5987i	−0.331192	−	1.01931i	−0.968567	−	0.248752i	$-0.919980\pi$
$449$	−7.01784	−	21.5987i	−0.331192	−	1.01931i	0.637375	−	0.770554i	$-0.280020\pi$
$450$		0			0
$451$	0.132561	+	1.26123i	0.00624204	+	0.0593890i
$452$	5.45852	+	4.91487i	0.256747	+	0.231176i
$453$	−0.403740	+	0.363530i	−0.0189694	+	0.0170801i
$454$	2.47803	−	23.5769i	0.116300	−	1.10652i
$455$		0			0
$456$	−35.3494	−	15.7386i	−1.65539	−	0.737027i
$457$	9.49970	+	13.0752i	0.444377	+	0.611633i	0.971178	−	0.238356i	$-0.0766085\pi$
$457$	9.49970	+	13.0752i	0.444377	+	0.611633i	−0.526800	+	0.849989i	$0.676608\pi$
$458$	3.05067	+	6.85192i	0.142549	+	0.320169i
$459$	−6.63529	+	11.4927i	−0.309709	+	0.536432i
$460$		0			0
$461$	−17.4252	−	12.6602i	−0.811573	−	0.589642i	0.102713	−	0.994711i	$-0.467248\pi$
$461$	−17.4252	−	12.6602i	−0.811573	−	0.589642i	−0.914286	+	0.405069i	$0.867248\pi$
$462$	7.60571	−	35.7821i	0.353850	−	1.66473i
$463$	16.6528	+	5.41083i	0.773922	+	0.251462i	0.669243	−	0.743044i	$-0.266619\pi$
$463$	16.6528	+	5.41083i	0.773922	+	0.251462i	0.104679	+	0.994506i	$0.466619\pi$
$464$	−19.0941			−0.886421
$465$		0			0
$466$	21.5976			1.00049
$467$	−11.2288	−	3.64845i	−0.519605	−	0.168830i	0.0374608	−	0.999298i	$-0.488073\pi$
$467$	−11.2288	−	3.64845i	−0.519605	−	0.168830i	−0.557066	+	0.830468i	$0.688073\pi$
$468$	−0.344569	+	1.62107i	−0.0159277	+	0.0749341i
$469$	22.8372	+	16.5922i	1.05453	+	0.766158i
$470$		0			0
$471$	−16.5236	+	28.6197i	−0.761366	+	1.31872i
$472$	−9.67514	−	21.7307i	−0.445335	−	1.00024i
$473$	−8.58739	−	11.8195i	−0.394849	−	0.543463i
$474$	22.7431	+	10.1259i	1.04463	+	0.465097i
$475$		0			0
$476$	−0.722955	+	6.87846i	−0.0331366	+	0.315274i
$477$	2.27425	−	2.04774i	0.104131	−	0.0937597i
$478$	25.5586	+	23.0130i	1.16902	+	1.05259i
$479$	−1.65246	−	15.7221i	−0.0755029	−	0.718362i	−0.965147	−	0.261708i	$-0.915714\pi$
$479$	−1.65246	−	15.7221i	−0.0755029	−	0.718362i	0.889644	−	0.456654i	$-0.150952\pi$
$480$		0			0
$481$	1.47715	+	4.54621i	0.0673525	+	0.207290i
$482$	27.8780	−	2.93010i	1.26981	−	0.133462i
$483$	5.33664	+	4.80513i	0.242825	+	0.218641i
$484$	1.01512	+	1.12740i	0.0461416	+	0.0512455i
$485$		0			0
$486$	15.3271	−	3.25787i	0.695251	−	0.147780i
$487$	−5.20283	+	11.6857i	−0.235763	+	0.529532i	−0.992218	−	0.124514i	$-0.960263\pi$
$487$	−5.20283	+	11.6857i	−0.235763	+	0.529532i	0.756455	+	0.654046i	$0.226930\pi$
$488$	4.89514	+	6.73758i	0.221593	+	0.304996i
$489$	0.252445	−	0.112396i	0.0114160	−	0.00508271i
$490$		0			0
$491$	9.26410	+	16.0459i	0.418083	+	0.724141i	0.995747	−	0.0921341i	$-0.0293688\pi$
$491$	9.26410	+	16.0459i	0.418083	+	0.724141i	−0.577664	+	0.816275i	$0.696036\pi$
$492$	−0.198094	+	0.272653i	−0.00893076	+	0.0122921i
$493$	5.34290	−	25.1364i	0.240632	−	1.13209i
$494$	6.11864	−	18.8312i	0.275290	−	0.847257i
$495$		0			0
$496$	−7.25967	+	13.8240i	−0.325969	+	0.620717i
$497$			19.3922i			0.869861i
$498$	20.4136	+	6.63277i	0.914754	+	0.297221i
$499$	39.9938	+	8.50094i	1.79037	+	0.380554i	0.978980	−	0.203955i	$-0.0653797\pi$
$499$	39.9938	+	8.50094i	1.79037	+	0.380554i	0.811387	+	0.584510i	$0.198713\pi$
$500$		0			0
$501$	4.09681	+	7.09588i	0.183032	+	0.317021i
$502$	17.3237	+	10.0018i	0.773195	+	0.446404i
$503$	−8.16609	−	18.3413i	−0.364108	−	0.817800i	−0.998979	−	0.0451817i	$-0.985613\pi$
$503$	−8.16609	−	18.3413i	−0.364108	−	0.817800i	0.634871	−	0.772618i	$-0.281053\pi$
$504$	12.2852	−	8.92575i	0.547228	−	0.397585i
$505$		0			0
$506$	4.12485	−	0.876764i	0.183372	−	0.0389769i
$507$	12.4981	+	1.31361i	0.555061	+	0.0583393i
$508$	7.24127	−	6.52007i	0.321279	−	0.289281i
$509$	21.3528	−	23.7147i	0.946445	−	1.05113i	−0.0521763	−	0.998638i	$-0.516616\pi$
$509$	21.3528	−	23.7147i	0.946445	−	1.05113i	0.998621	−	0.0524956i	$-0.0167176\pi$
$510$		0			0
$511$	−6.33760	−	19.5051i	−0.280359	−	0.862855i
$512$	23.4076	−	7.60561i	1.03448	−	0.336123i
$513$	21.3242	−	2.24127i	0.941488	−	0.0989544i
$514$	−19.2534	+	21.3831i	−0.849233	+	0.943169i
$515$		0			0
$516$	0.405835	−	3.86126i	0.0178659	−	0.169982i
$517$	−0.929990	−	4.37526i	−0.0409009	−	0.192424i
$518$	3.45820	−	7.76725i	0.151945	−	0.341273i
$519$	−24.2687	+	17.6323i	−1.06528	+	0.773970i
$520$		0			0
$521$	−1.05378	+	1.82520i	−0.0461670	+	0.0799635i	−0.888185	−	0.459485i	$-0.848034\pi$
$521$	−1.05378	+	1.82520i	−0.0461670	+	0.0799635i	0.842019	+	0.539449i	$0.181367\pi$
$522$	−9.48512	+	5.47624i	−0.415152	+	0.239688i
$523$	−2.88471	+	3.97047i	−0.126140	+	0.173616i	−0.867416	−	0.497584i	$-0.834221\pi$
$523$	−2.88471	+	3.97047i	−0.126140	+	0.173616i	0.741276	+	0.671200i	$0.234221\pi$
$524$	−5.96159	−	1.26717i	−0.260433	−	0.0553568i
$525$		0			0
$526$	−12.8076			−0.558440
$527$	−16.1672	−	13.4252i	−0.704255	−	0.584811i
$528$		−	21.8886i		−	0.952580i
$529$	6.85158	−	21.0870i	0.297895	−	0.916826i
$530$		0			0
$531$	−8.21591	−	5.96921i	−0.356540	−	0.259042i
$532$	9.67780	−	5.58748i	0.419586	−	0.242248i
$533$	−0.769375	−	0.444199i	−0.0333253	−	0.0192404i
$534$	−11.9017	+	5.29898i	−0.515038	+	0.229310i
$535$		0			0
$536$	20.7316	+	9.23030i	0.895469	+	0.398688i
$537$	7.64456	+	35.9648i	0.329887	+	1.55200i
$538$	−5.41397	−	0.569031i	−0.233413	−	0.0245327i
$539$	18.7980	+	20.8773i	0.809689	+	0.899251i
$540$		0			0
$541$	1.30002	+	12.3689i	0.0558923	+	0.531780i	0.986266	+	0.165167i	$0.0528162\pi$
$541$	1.30002	+	12.3689i	0.0558923	+	0.531780i	−0.930373	+	0.366613i	$0.880517\pi$
$542$	−7.21033	+	2.34278i	−0.309710	+	0.100631i
$543$	−23.7978	+	7.73236i	−1.02126	+	0.331827i
$544$	1.04959	+	9.98614i	0.0450006	+	0.428152i
$545$		0			0
$546$	17.1474	+	19.0442i	0.733842	+	0.815014i
$547$	13.8885	+	1.45974i	0.593830	+	0.0624140i	0.396676	−	0.917959i	$-0.370164\pi$
$547$	13.8885	+	1.45974i	0.593830	+	0.0624140i	0.197154	+	0.980373i	$0.436830\pi$
$548$	0.989399	+	4.65476i	0.0422650	+	0.198841i
$549$	3.24811	+	1.44615i	0.138626	+	0.0617202i
$550$		0			0
$551$	−37.9313	+	16.8881i	−1.61593	+	0.719456i
$552$	4.99967	+	2.88656i	0.212800	+	0.122860i
$553$	−32.0759	+	18.5190i	−1.36401	+	0.787509i
$554$	21.9779	+	15.9679i	0.933752	+	0.678411i
$555$		0			0
$556$	2.30732	−	7.10121i	0.0978523	−	0.301159i
$557$		−	37.2207i		−	1.57709i	−0.614976	−	0.788546i	$-0.710834\pi$
$557$		−	37.2207i		−	1.57709i	0.614976	−	0.788546i	$-0.289166\pi$
$558$	0.358481	+	8.94927i	0.0151757	+	0.378853i
$559$	10.2346			0.432876
$560$		0			0
$561$	28.8152	+	6.12487i	1.21658	+	0.258592i
$562$	−22.2878	+	30.6766i	−0.940156	+	1.29401i
$563$	26.0039	−	15.0134i	1.09593	−	0.632738i	0.160784	−	0.986990i	$-0.448598\pi$
$563$	26.0039	−	15.0134i	1.09593	−	0.632738i	0.935150	+	0.354252i	$0.115264\pi$
$564$	0.594349	−	1.02944i	0.0250266	−	0.0433474i
$565$		0			0
$566$	21.2780	−	15.4594i	0.894380	−	0.649805i
$567$	−17.3467	+	38.9613i	−0.728492	+	1.63622i
$568$	3.24133	+	15.2493i	0.136003	+	0.639846i
$569$	−4.21995	+	40.1502i	−0.176910	+	1.68318i	0.441449	+	0.897286i	$0.354464\pi$
$569$	−4.21995	+	40.1502i	−0.176910	+	1.68318i	−0.618359	+	0.785896i	$0.712202\pi$
$570$		0			0
$571$	28.5060	−	31.6591i	1.19294	−	1.32489i	0.259677	−	0.965696i	$-0.416384\pi$
$571$	28.5060	−	31.6591i	1.19294	−	1.32489i	0.933262	−	0.359197i	$-0.116949\pi$
$572$	−4.74889	+	0.499129i	−0.198561	+	0.0208696i
$573$	10.0082	−	3.25187i	0.418100	−	0.135849i
$574$	0.488296	+	1.50282i	0.0203811	+	0.0627265i
$575$		0			0
$576$	7.76324	−	8.62195i	0.323468	−	0.359248i
$577$	4.85851	−	4.37462i	0.202262	−	0.182118i	−0.561775	−	0.827290i	$-0.689881\pi$
$577$	4.85851	−	4.37462i	0.202262	−	0.182118i	0.764037	+	0.645173i	$0.223215\pi$
$578$	−3.37526	−	0.354754i	−0.140392	−	0.0147558i
$579$	−40.6774	+	8.64624i	−1.69049	+	0.359325i
$580$		0			0
$581$	−25.8344	+	18.7698i	−1.07179	+	0.778703i
$582$	11.3499	+	25.4922i	0.470467	+	1.05669i
$583$	7.63617	+	4.40874i	0.316258	+	0.182591i
$584$	−8.24383	−	14.2787i	−0.341132	−	0.590858i
$585$		0			0
$586$	2.16827	+	0.460880i	0.0895704	+	0.0190388i
$587$	−20.3314	−	6.60607i	−0.839167	−	0.272662i	−0.142265	−	0.989829i	$-0.545439\pi$
$587$	−20.3314	−	6.60607i	−0.839167	−	0.272662i	−0.696902	+	0.717167i	$0.745439\pi$
$588$			7.46576i			0.307883i
$589$	−2.19476	+	33.8830i	−0.0904333	+	1.39612i
$590$		0			0
$591$	13.9195	−	42.8397i	0.572570	−	1.76219i
$592$	1.05773	−	4.97621i	0.0434723	−	0.204521i
$593$	−15.2769	+	21.0268i	−0.627347	+	0.863468i	−0.997862	−	0.0653579i	$-0.979181\pi$
$593$	−15.2769	+	21.0268i	−0.627347	+	0.863468i	0.370515	+	0.928826i	$0.379181\pi$
$594$	8.14807	+	14.1129i	0.334319	+	0.579058i
$595$		0			0
$596$	6.70858	−	2.98685i	0.274794	−	0.122346i
$597$	−18.4965	−	25.4582i	−0.757010	−	1.04193i
$598$	−1.20156	+	2.69874i	−0.0491353	+	0.110360i
$599$	−8.98718	+	1.91028i	−0.367206	+	0.0780521i	−0.387819	−	0.921735i	$-0.626772\pi$
$599$	−8.98718	+	1.91028i	−0.367206	+	0.0780521i	0.0206131	+	0.999788i	$0.493438\pi$
$600$		0			0
$601$	22.2948	+	24.7609i	0.909423	+	1.01002i	0.999900	+	0.0141185i	$0.00449419\pi$
$601$	22.2948	+	24.7609i	0.909423	+	1.01002i	−0.0904769	+	0.995899i	$0.528839\pi$
$602$	−13.5281	−	12.1807i	−0.551364	−	0.496450i
$603$	9.63543	−	1.01272i	0.392385	−	0.0412413i
$604$	−0.0389782	−	0.119962i	−0.00158600	−	0.00488120i
$605$		0			0
$606$	0.106560	+	1.01385i	0.00432871	+	0.0411849i
$607$	−36.1917	−	32.5872i	−1.46898	−	1.32267i	−0.836322	−	0.548238i	$-0.815299\pi$
$607$	−36.1917	−	32.5872i	−1.46898	−	1.32267i	−0.632654	−	0.774434i	$-0.718035\pi$
$608$	12.0566	−	10.8558i	0.488961	−	0.440262i
$609$	5.61717	−	53.4438i	0.227619	−	2.16565i
$610$		0			0
$611$	2.86257	+	1.27450i	0.115807	+	0.0515608i
$612$	1.39530	+	1.92046i	0.0564015	+	0.0776300i
$613$	−8.50649	−	19.1059i	−0.343574	−	0.771680i	−0.999853	−	0.0171613i	$-0.994537\pi$
$613$	−8.50649	−	19.1059i	−0.343574	−	0.771680i	0.656279	−	0.754519i	$-0.272130\pi$
$614$	16.4923	−	28.5654i	0.665573	−	1.15281i
$615$		0			0
$616$	35.3968	+	25.7173i	1.42618	+	1.03618i
$617$	9.43586	−	44.3922i	0.379873	−	1.78716i	−0.207913	−	0.978147i	$-0.566667\pi$
$617$	9.43586	−	44.3922i	0.379873	−	1.78716i	0.587787	−	0.809016i	$-0.299999\pi$
$618$	−7.96784	−	2.58891i	−0.320514	−	0.104141i
$619$	10.2462			0.411832			0.205916	−	0.978570i	$-0.433983\pi$
$619$	10.2462			0.411832			0.205916	+	0.978570i	$0.433983\pi$
$620$		0			0
$621$	−3.19902			−0.128372
$622$	4.89973	+	1.59202i	0.196461	+	0.0638341i
$623$	4.02983	−	18.9589i	0.161452	−	0.759571i
$624$	12.4052	+	9.01290i	0.496605	+	0.360805i
$625$		0			0
$626$	6.98816	−	12.1038i	0.279303	−	0.483767i
$627$	−19.3598	−	43.4827i	−0.773154	−	1.73653i
$628$	−4.50986	−	6.20729i	−0.179963	−	0.247698i
$629$	6.25495	+	2.78488i	0.249401	+	0.111041i
$630$		0			0
$631$	1.11605	−	10.6185i	0.0444291	−	0.422715i	−0.949589	−	0.313498i	$-0.898499\pi$
$631$	1.11605	−	10.6185i	0.0444291	−	0.422715i	0.994018	−	0.109217i	$-0.0348343\pi$
$632$	−22.1278	+	19.9240i	−0.880197	+	0.792533i
$633$	−9.72144	−	8.75322i	−0.386392	−	0.347909i
$634$	3.33344	+	31.7156i	0.132388	+	1.25959i
$635$		0			0
$636$	0.724101	+	2.22855i	0.0287125	+	0.0883679i
$637$	−19.5724	+	2.05714i	−0.775485	+	0.0815068i
$638$	−23.4512	−	21.1156i	−0.928444	−	0.835975i
$639$	4.45358	+	4.94621i	0.176181	+	0.195669i
$640$		0			0
$641$	−23.3407	+	4.96121i	−0.921900	+	0.195956i	−0.644328	−	0.764749i	$-0.722863\pi$
$641$	−23.3407	+	4.96121i	−0.921900	+	0.195956i	−0.277572	+	0.960705i	$0.589530\pi$
$642$	−3.28285	+	7.37340i	−0.129564	+	0.291005i
$643$	−4.66658	−	6.42300i	−0.184032	−	0.253298i	0.707026	−	0.707187i	$-0.250036\pi$
$643$	−4.66658	−	6.42300i	−0.184032	−	0.253298i	−0.891058	+	0.453889i	$0.850036\pi$
$644$	−1.52312	+	0.678137i	−0.0600194	+	0.0267224i
$645$		0			0
$646$	−14.1805	−	24.5614i	−0.557925	−	0.966355i
$647$	1.45630	−	2.00443i	0.0572532	−	0.0788023i	−0.779430	−	0.626489i	$-0.784491\pi$
$647$	1.45630	−	2.00443i	0.0572532	−	0.0788023i	0.836684	+	0.547687i	$0.184491\pi$
$648$	−7.12851	+	33.5370i	−0.280034	+	1.31746i
$649$	9.04192	−	27.8282i	0.354926	−	1.09235i
$650$		0			0
$651$	−36.5574	−	24.3864i	−1.43280	−	0.955778i
$652$			0.0641574i			0.00251260i
$653$	−21.3931	−	6.95104i	−0.837177	−	0.272015i	−0.141112	−	0.989994i	$-0.545068\pi$
$653$	−21.3931	−	6.95104i	−0.837177	−	0.272015i	−0.696065	+	0.717978i	$0.745068\pi$
$654$	17.3965	+	3.69774i	0.680257	+	0.144593i
$655$		0			0
$656$	0.472746	+	0.818821i	0.0184576	+	0.0319696i
$657$	−6.09598	−	3.51952i	−0.237827	−	0.137309i
$658$	−2.26690	−	5.09155i	−0.0883731	−	0.198489i
$659$	−9.67555	+	7.02970i	−0.376906	+	0.273838i	−0.760069	−	0.649843i	$-0.774835\pi$
$659$	−9.67555	+	7.02970i	−0.376906	+	0.273838i	0.383163	+	0.923681i	$0.374835\pi$
$660$		0			0
$661$	−23.3151	+	4.95578i	−0.906852	+	0.192757i	−0.637650	−	0.770326i	$-0.720093\pi$
$661$	−23.3151	+	4.95578i	−0.906852	+	0.192757i	−0.269202	+	0.963084i	$0.586760\pi$
$662$	−0.938413	−	0.0986312i	−0.0364725	−	0.00383341i
$663$	−15.3362	+	13.8088i	−0.595609	+	0.536289i
$664$	−17.1779	+	19.0779i	−0.666630	+	0.740368i
$665$		0			0
$666$	−0.901758	−	2.77533i	−0.0349424	−	0.107542i
$667$	5.89158	−	1.91429i	0.228123	−	0.0741216i
$668$	−1.89191	+	0.198848i	−0.0732002	+	0.00769365i
$669$	−10.2593	+	11.3941i	−0.396646	+	0.440520i
$670$		0			0
$671$	−1.07082	+	10.1881i	−0.0413384	+	0.393309i
$672$	4.36563	+	20.5387i	0.168408	+	0.792297i
$673$	1.42119	−	3.19204i	0.0547827	−	0.123044i	−0.884080	−	0.467335i	$-0.845214\pi$
$673$	1.42119	−	3.19204i	0.0547827	−	0.123044i	0.938863	+	0.344291i	$0.111881\pi$
$674$	2.38679	−	1.73411i	0.0919359	−	0.0667953i
$675$		0			0
$676$	−1.45885	+	2.52680i	−0.0561096	+	0.0971847i
$677$	−16.6673	+	9.62287i	−0.640576	+	0.369837i	−0.784836	−	0.619703i	$-0.787253\pi$
$677$	−16.6673	+	9.62287i	−0.640576	+	0.369837i	0.144260	+	0.989540i	$0.453920\pi$
$678$	22.9130	−	31.5370i	0.879967	−	1.21117i
$679$	−40.6079	−	8.63147i	−1.55839	−	0.331245i
$680$		0			0
$681$	39.9221			1.52982
$682$	−24.2039	+	8.95034i	−0.926814	+	0.342726i
$683$			39.8738i			1.52573i	0.646558	+	0.762865i	$0.276208\pi$
$683$			39.8738i			1.52573i	−0.646558	+	0.762865i	$0.723792\pi$
$684$	1.18522	−	3.64773i	0.0453180	−	0.139475i
$685$		0			0
$686$	1.77673	+	1.29087i	0.0678359	+	0.0492857i
$687$	−10.9384	+	6.31529i	−0.417326	+	0.240944i
$688$	−9.43303	−	5.44616i	−0.359631	−	0.207633i
$689$	−5.64290	+	2.51238i	−0.214977	+	0.0957140i
$690$		0			0
$691$	35.0897	+	15.6229i	1.33487	+	0.594325i	0.945159	−	0.326611i	$-0.105907\pi$
$691$	35.0897	+	15.6229i	1.33487	+	0.594325i	0.389716	+	0.920935i	$0.372573\pi$
$692$	−1.44803	−	6.81246i	−0.0550459	−	0.258971i
$693$	18.5770	+	1.95252i	0.705680	+	0.0741700i
$694$	−4.66477	−	5.18075i	−0.177072	−	0.196659i
$695$		0			0
$696$	−4.51580	−	42.9649i	−0.171171	−	1.62858i
$697$	−1.21022	+	0.393224i	−0.0458403	+	0.0148944i
$698$	34.0633	−	11.0678i	1.28932	−	0.418924i
$699$	3.80173	+	36.1710i	0.143795	+	1.36811i
$700$		0			0
$701$	−23.7043	−	26.3263i	−0.895298	−	0.994329i	0.104702	−	0.994504i	$-0.466611\pi$
$701$	−23.7043	−	26.3263i	−0.895298	−	0.994329i	−1.00000		0.000174860i	$0.999944\pi$
$702$	−11.3534	−	1.19329i	−0.428507	−	0.0450379i
$703$	−2.30007	−	10.8210i	−0.0867488	−	0.408121i
$704$	30.5381	+	13.5965i	1.15095	+	0.512436i
$705$		0			0
$706$	−21.6970	+	9.66015i	−0.816579	+	0.363564i
$707$	−1.31347	−	0.758331i	−0.0493980	−	0.0285200i
$708$	6.73412	−	3.88795i	0.253084	−	0.146118i
$709$	−20.8801	−	15.1703i	−0.784170	−	0.569733i	0.122057	−	0.992523i	$-0.461051\pi$
$709$	−20.8801	−	15.1703i	−0.784170	−	0.569733i	−0.906228	+	0.422790i	$0.861051\pi$
$710$		0			0
$711$	−3.92827	+	12.0900i	−0.147322	+	0.453409i
$712$		−	15.5821i		−	0.583962i
$713$	0.854070	−	4.99330i	0.0319852	−	0.187001i
$714$	36.7061			1.37369
$715$		0			0
$716$	−8.35004	−	1.77486i	−0.312056	−	0.0663295i
$717$	−34.0426	+	46.8557i	−1.27135	+	1.74986i
$718$	−11.0383	+	6.37296i	−0.411945	+	0.237837i
$719$	−19.5234	+	33.8155i	−0.728099	+	1.26110i	0.229587	+	0.973288i	$0.426262\pi$
$719$	−19.5234	+	33.8155i	−0.728099	+	1.26110i	−0.957686	+	0.287816i	$0.907071\pi$
$720$		0			0
$721$	10.0837	−	7.32625i	0.375537	−	0.272844i
$722$	−9.11599	+	20.4749i	−0.339262	+	0.761995i
$723$	9.81450	+	46.1736i	0.365005	+	1.71721i
$724$	0.607260	−	5.77769i	0.0225686	−	0.214726i
$725$		0			0
$726$	5.38737	−	5.98328i	0.199944	−	0.222060i
$727$	24.8468	−	2.61150i	0.921516	−	0.0968552i	0.368124	−	0.929777i	$-0.380000\pi$
$727$	24.8468	−	2.61150i	0.921516	−	0.0968552i	0.553391	+	0.832921i	$0.313333\pi$
$728$	−29.1501	+	9.47144i	−1.08037	+	0.351035i
$729$	−2.24010	−	6.89433i	−0.0829668	−	0.255345i
$730$		0			0
$731$	9.80913	−	10.8941i	0.362804	−	0.402934i
$732$	−2.02314	+	1.82164i	−0.0747774	+	0.0673299i
$733$	−16.8562	−	1.77166i	−0.622598	−	0.0654377i	−0.212023	−	0.977265i	$-0.568005\pi$
$733$	−16.8562	−	1.77166i	−0.622598	−	0.0654377i	−0.410575	+	0.911827i	$0.634672\pi$
$734$	−0.164593	+	0.0349853i	−0.00607524	+	0.00129133i
$735$		0			0
$736$	−1.95825	+	1.42275i	−0.0721821	+	0.0524434i
$737$	11.3540	+	25.5016i	0.418231	+	0.939363i
$738$	0.469680	+	0.271170i	0.0172892	+	0.00998190i
$739$	7.19107	+	12.4553i	0.264528	+	0.458175i	0.967440	−	0.253101i	$-0.0814506\pi$
$739$	7.19107	+	12.4553i	0.264528	+	0.458175i	−0.702912	+	0.711277i	$0.748117\pi$
$740$		0			0
$741$	32.6151	+	6.93254i	1.19814	+	0.254673i
$742$	10.4489	+	3.39506i	0.383592	+	0.124637i
$743$			27.7705i			1.01880i	0.860530	+	0.509400i	$0.170133\pi$
$743$			27.7705i			1.01880i	−0.860530	+	0.509400i	$0.829867\pi$
$744$	−32.8233	−	13.0661i	−1.20336	−	0.479025i
$745$		0			0
$746$	−2.80390	+	8.62953i	−0.102658	+	0.315950i
$747$	−2.27872	+	10.7205i	−0.0833740	+	0.392244i
$748$	−4.02019	+	5.53332i	−0.146993	+	0.202318i
$749$	−6.00394	−	10.3991i	−0.219379	−	0.379976i
$750$		0			0
$751$	−39.8034	+	17.7216i	−1.45245	+	0.646670i	−0.972980	−	0.230891i	$-0.925836\pi$
$751$	−39.8034	+	17.7216i	−1.45245	+	0.646670i	−0.479465	+	0.877561i	$0.659169\pi$
$752$	−1.96018	−	2.69796i	−0.0714804	−	0.0983844i
$753$	−13.7014	+	30.7739i	−0.499307	+	1.12146i
$754$	21.6234	−	4.59620i	0.787478	−	0.167384i
$755$		0			0
$756$	−4.31118	−	4.78805i	−0.156796	−	0.174140i
$757$	18.7400	+	16.8735i	0.681115	+	0.613279i	0.935291	−	0.353879i	$-0.115138\pi$
$757$	18.7400	+	16.8735i	0.681115	+	0.613279i	−0.254176	+	0.967158i	$0.581804\pi$
$758$	5.64691	−	0.593514i	0.205105	−	0.0215574i
$759$	2.19446	+	6.75385i	0.0796538	+	0.245149i
$760$		0			0
$761$	0.273439	+	2.60160i	0.00991216	+	0.0943079i	0.998359	−	0.0572569i	$-0.0182354\pi$
$761$	0.273439	+	2.60160i	0.00991216	+	0.0943079i	−0.988447	+	0.151565i	$0.951569\pi$
$762$	−38.4305	−	34.6029i	−1.39219	−	1.25353i
$763$	−19.6634	+	17.7050i	−0.711864	+	0.640966i
$764$	−0.255385	+	2.42983i	−0.00923952	+	0.0879081i
$765$		0			0
$766$	−36.3525	−	16.1852i	−1.31347	−	0.584794i
$767$	12.0483	+	16.5830i	0.435037	+	0.598777i
$768$	9.14636	+	20.5431i	0.330041	+	0.741284i
$769$	5.67534	−	9.82998i	0.204658	−	0.354478i	−0.745366	−	0.666656i	$-0.767725\pi$
$769$	5.67534	−	9.82998i	0.204658	−	0.354478i	0.950024	+	0.312178i	$0.101058\pi$
$770$		0			0
$771$	−39.2009	−	28.4811i	−1.41179	−	1.02572i
$772$	2.00742	−	9.44415i	0.0722485	−	0.339903i
$773$	10.8586	+	3.52816i	0.390556	+	0.126899i	0.497711	−	0.867343i	$-0.334174\pi$
$773$	10.8586	+	3.52816i	0.390556	+	0.126899i	−0.107155	+	0.994242i	$0.534174\pi$
$774$	−6.24789			−0.224576
$775$		0			0
$776$	−33.3751			−1.19810
$777$	13.6171	+	4.42446i	0.488511	+	0.158727i
$778$	9.03590	−	42.5106i	0.323953	−	1.52408i
$779$	1.66335	+	1.20849i	0.0595957	+	0.0432988i
$780$		0			0
$781$	−9.58846	+	16.6077i	−0.343102	+	0.594270i
$782$	1.72105	+	3.86555i	0.0615447	+	0.138232i
$783$	14.0710	+	19.3671i	0.502857	+	0.692123i
$784$	19.1342	+	8.51909i	0.683364	+	0.304253i
$785$		0			0
$786$	−3.38106	+	32.1687i	−0.120599	+	1.14742i
$787$	20.1312	−	18.1262i	0.717600	−	0.646130i	−0.227173	−	0.973854i	$-0.572948\pi$
$787$	20.1312	−	18.1262i	0.717600	−	0.646130i	0.944773	+	0.327724i	$0.106282\pi$
$788$	7.77184	+	6.99779i	0.276860	+	0.249286i
$789$	−2.25447	−	21.4499i	−0.0802614	−	0.763636i
$790$		0			0
$791$	17.9215	+	55.1566i	0.637214	+	1.96114i
$792$	14.9345	−	1.56968i	0.530675	−	0.0557762i
$793$	−5.33312	−	4.80196i	−0.189385	−	0.170523i
$794$	3.32598	+	3.69388i	0.118035	+	0.131091i
$795$		0			0
$796$	7.14635	−	1.51900i	0.253296	−	0.0538397i
$797$	−19.7901	+	44.4493i	−0.701002	+	1.57448i	0.112988	+	0.993596i	$0.463958\pi$
$797$	−19.7901	+	44.4493i	−0.701002	+	1.57448i	−0.813990	+	0.580879i	$0.802709\pi$
$798$	−34.8599	−	47.9805i	−1.23403	−	1.69849i
$799$	4.10022	−	1.82553i	0.145055	−	0.0645827i
$800$		0			0
$801$	−3.32620	−	5.76115i	−0.117526	−	0.203560i
$802$	18.0217	−	24.8048i	0.636369	−	0.875887i
$803$	4.21669	−	19.8380i	0.148804	−	0.700067i
$804$	−2.29240	+	7.05530i	−0.0808469	+	0.248821i
$805$		0			0
$806$	4.89370	−	17.4027i	0.172373	−	0.612985i
$807$		−	9.16733i		−	0.322705i
$808$	−1.15961	−	0.376780i	−0.0407949	−	0.0132551i
$809$	−18.3981	−	3.91064i	−0.646843	−	0.137491i	−0.127204	−	0.991877i	$-0.540600\pi$
$809$	−18.3981	−	3.91064i	−0.646843	−	0.137491i	−0.519639	+	0.854386i	$0.673934\pi$
$810$		0			0
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	0.970452	+	0.241294i	$0.0775720\pi$
$811$	19.7693	+	34.2414i	0.694193	+	1.20238i	−0.276259	+	0.961083i	$0.589095\pi$
$812$	10.8050	+	6.23826i	0.379180	+	0.218920i
$813$	−5.19282	−	11.6633i	−0.182120	−	0.409049i
$814$	6.80214	−	4.94204i	0.238415	−	0.173219i
$815$		0			0
$816$	21.4833	−	4.56641i	0.752064	−	0.159856i
$817$	−23.5561	−	2.47584i	−0.824123	−	0.0866188i
$818$	3.21150	−	2.89165i	0.112288	−	0.101104i
$819$	−8.75585	+	9.72436i	−0.305954	+	0.339797i
$820$		0			0
$821$	−4.52299	−	13.9203i	−0.157854	−	0.485823i	0.840585	−	0.541679i	$-0.182211\pi$
$821$	−4.52299	−	13.9203i	−0.157854	−	0.485823i	−0.998439	+	0.0558559i	$0.982211\pi$
$822$	24.0193	−	7.80434i	0.837769	−	0.272208i
$823$	−41.5578	+	4.36790i	−1.44861	+	0.152255i	−0.795936	−	0.605381i	$-0.793021\pi$
$823$	−41.5578	+	4.36790i	−1.44861	+	0.152255i	−0.652677	+	0.757636i	$0.726354\pi$
$824$	6.70488	−	7.44652i	0.233575	−	0.259412i
$825$		0			0
$826$	3.81095	−	36.2588i	0.132600	−	1.26160i
$827$	1.95564	+	9.20058i	0.0680044	+	0.319936i	0.998980	−	0.0451446i	$-0.0143749\pi$
$827$	1.95564	+	9.20058i	0.0680044	+	0.319936i	−0.930976	+	0.365080i	$0.881042\pi$
$828$	−0.232749	+	0.522764i	−0.00808860	+	0.0181673i
$829$	32.6283	−	23.7058i	1.13323	−	0.823337i	0.147065	−	0.989127i	$-0.453017\pi$
$829$	32.6283	−	23.7058i	1.13323	−	0.823337i	0.986161	+	0.165790i	$0.0530173\pi$
$830$		0			0
$831$	−22.8739	+	39.6188i	−0.793487	+	1.37436i
$832$	−20.2801	+	11.7087i	−0.703086	+	0.405927i
$833$	−16.5690	+	22.8053i	−0.574083	+	0.790158i
$834$	−38.7607	−	8.23884i	−1.34217	−	0.285288i
$835$		0			0
$836$	11.0509			0.382203
$837$	19.3715	−	2.82388i	0.669578	−	0.0976077i
$838$		−	5.07693i		−	0.175380i
$839$	−2.20936	+	6.79972i	−0.0762757	+	0.234752i	−0.981923	−	0.189278i	$-0.939385\pi$
$839$	−2.20936	+	6.79972i	−0.0762757	+	0.234752i	0.905648	+	0.424031i	$0.139385\pi$
$840$		0			0
$841$	−14.0420	−	10.2021i	−0.484208	−	0.351798i
$842$	29.4532	−	17.0048i	1.01503	−	0.586025i
$843$	−55.2995	−	31.9272i	−1.90462	−	1.09963i
$844$	2.77458	−	1.23532i	0.0955050	−	0.0425216i
$845$		0			0
$846$	−1.74751	−	0.778044i	−0.0600808	−	0.0267497i
$847$	2.49042	+	11.7165i	0.0855720	+	0.402585i
$848$	6.53788	+	0.687159i	0.224512	+	0.0235971i
$849$	29.6364	+	32.9145i	1.01712	+	1.12962i
$850$		0			0
$851$	0.172526	+	1.64148i	0.00591413	+	0.0562692i
$852$	−4.84683	+	1.57483i	−0.166050	+	0.0539528i
$853$	1.07153	−	0.348160i	0.0366884	−	0.0119208i	−0.290615	−	0.956840i	$-0.593860\pi$
$853$	1.07153	−	0.348160i	0.0366884	−	0.0119208i	0.327304	+	0.944919i	$0.393860\pi$
$854$	1.33424	+	12.6945i	0.0456569	+	0.434397i
$855$		0			0
$856$	−6.45943	−	7.17392i	−0.220779	−	0.245200i
$857$	23.7234	+	2.49343i	0.810374	+	0.0851738i	0.500647	−	0.865652i	$-0.333096\pi$
$857$	23.7234	+	2.49343i	0.810374	+	0.0851738i	0.309727	+	0.950825i	$0.399762\pi$
$858$	5.26888	+	24.7881i	0.179877	+	0.846252i
$859$	−29.6589	−	13.2050i	−1.01195	−	0.450548i	−0.167320	−	0.985903i	$-0.553511\pi$
$859$	−29.6589	−	13.2050i	−1.01195	−	0.450548i	−0.844628	+	0.535354i	$0.820178\pi$
$860$		0			0
$861$	−2.43093	+	1.08232i	−0.0828458	+	0.0368853i
$862$	15.8719	+	9.16363i	0.540598	+	0.312114i
$863$	20.6476	−	11.9209i	0.702853	−	0.405793i	−0.105556	−	0.994413i	$-0.533662\pi$
$863$	20.6476	−	11.9209i	0.702853	−	0.405793i	0.808409	+	0.588621i	$0.200329\pi$
$864$	−7.56744	−	5.49807i	−0.257450	−	0.187048i
$865$		0			0
$866$	3.52660	−	10.8538i	0.119839	−	0.368826i
$867$		−	5.71523i		−	0.194099i
$868$	8.62457	−	5.45094i	0.292737	−	0.185017i
$869$	−36.6268			−1.24248
$870$		0			0
$871$	−19.1280	−	4.06577i	−0.648126	−	0.137763i
$872$	−12.5032	+	17.2092i	−0.423412	+	0.582777i
$873$	−12.3398	+	7.12437i	−0.417638	+	0.241123i
$874$	3.41837	−	5.92080i	0.115628	−	0.200274i
$875$		0			0
$876$	4.36037	−	3.16799i	0.147323	−	0.107036i
$877$	−11.9071	+	26.7437i	−0.402073	+	0.903071i	0.593118	+	0.805116i	$0.297897\pi$
$877$	−11.9071	+	26.7437i	−0.402073	+	0.903071i	−0.995191	+	0.0979552i	$0.968770\pi$
$878$	4.53910	+	21.3548i	0.153187	+	0.720689i
$879$	−0.390198	+	3.71249i	−0.0131611	+	0.125219i
$880$		0			0
$881$	6.04230	−	6.71066i	0.203570	−	0.226088i	−0.632711	−	0.774388i	$-0.718058\pi$
$881$	6.04230	−	6.71066i	0.203570	−	0.226088i	0.836282	+	0.548300i	$0.184725\pi$
$882$	11.9483	−	1.25582i	0.402321	−	0.0422857i
$883$	20.3598	−	6.61531i	0.685162	−	0.222623i	0.0543083	−	0.998524i	$-0.482705\pi$
$883$	20.3598	−	6.61531i	0.685162	−	0.222623i	0.630854	+	0.775901i	$0.282705\pi$
$884$	−1.48060	−	4.55682i	−0.0497979	−	0.153262i
$885$		0			0
$886$	−15.2119	+	16.8946i	−0.511055	+	0.567584i
$887$	−18.2777	+	16.4573i	−0.613704	+	0.552581i	−0.916277	−	0.400545i	$-0.868821\pi$
$887$	−18.2777	+	16.4573i	−0.613704	+	0.552581i	0.302574	+	0.953126i	$0.402154\pi$
$888$	11.4475	+	1.20318i	0.384152	+	0.0403760i
$889$	75.2550	−	15.9959i	2.52397	−	0.536487i
$890$		0			0
$891$	−34.1202	+	24.7898i	−1.14307	+	0.830489i
$892$	−1.44787	−	3.25196i	−0.0484781	−	0.108884i
$893$	−6.28024	−	3.62590i	−0.210160	−	0.121336i
$894$	−19.4864	−	33.7514i	−0.651723	−	1.12882i
$895$		0			0
$896$	20.9450	+	4.45199i	0.699722	+	0.148730i
$897$	−4.73128	−	1.53729i	−0.157973	−	0.0513285i
$898$		−	27.9829i		−	0.933801i
$899$	−33.9864	+	16.7926i	−1.13351	+	0.560064i
$900$		0			0
$901$	−2.73404	+	8.41450i	−0.0910839	+	0.280328i
$902$	−0.324886	+	1.52847i	−0.0108175	+	0.0508924i
$903$	18.0187	−	24.8006i	0.599624	−	0.825312i
$904$	23.3119	+	40.3774i	0.775343	+	1.34293i
$905$		0			0
$906$	−0.611548	+	0.272279i	−0.0203173	+	0.00904585i
$907$	11.6183	+	15.9913i	0.385781	+	0.530981i	0.957104	−	0.289743i	$-0.0935700\pi$
$907$	11.6183	+	15.9913i	0.385781	+	0.530981i	−0.571324	+	0.820725i	$0.693570\pi$
$908$	−3.76996	+	8.46747i	−0.125110	+	0.281003i
$909$	−0.509171	+	0.108228i	−0.0168881	+	0.00358969i
$910$		0			0
$911$	−23.8355	−	26.4720i	−0.789705	−	0.877056i	0.205112	−	0.978739i	$-0.434244\pi$
$911$	−23.8355	−	26.4720i	−0.789705	−	0.877056i	−0.994817	+	0.101682i	$0.967578\pi$
$912$	−26.3717	−	23.7452i	−0.873254	−	0.786281i
$913$	−31.4056	+	3.30086i	−1.03937	+	0.109242i
$914$	6.15383	+	18.9395i	0.203550	+	0.626464i
$915$		0			0
$916$	−0.306527	−	2.91641i	−0.0101279	−	0.0963608i
$917$	−35.7619	−	32.2002i	−1.18096	−	1.06334i
$918$	−12.1516	+	10.9414i	−0.401064	+	0.361120i
$919$	−1.79332	+	17.0623i	−0.0591563	+	0.562835i	0.924297	+	0.381674i	$0.124652\pi$
$919$	−1.79332	+	17.0623i	−0.0591563	+	0.562835i	−0.983453	+	0.181161i	$0.942014\pi$
$920$		0			0
$921$	50.7436	+	22.5925i	1.67206	+	0.744449i
$922$	−15.5995	−	21.4709i	−0.513742	−	0.707105i
$923$	−5.46411	−	12.2726i	−0.179853	−	0.403957i
$924$	−7.15126	+	12.3863i	−0.235259	+	0.407481i
$925$		0			0
$926$	17.4546	+	12.6815i	0.573594	+	0.416741i
$927$	0.889432	−	4.18445i	0.0292128	−	0.137435i
$928$	17.2268	+	5.59734i	0.565499	+	0.183742i
$929$	−45.5222			−1.49353			−0.746767	−	0.665086i	$-0.768395\pi$
$929$	−45.5222			−1.49353			−0.746767	+	0.665086i	$0.768395\pi$
$930$		0			0
$931$	45.5457			1.49270
$932$	−8.03088	−	2.60939i	−0.263060	−	0.0854734i
$933$	−1.80379	+	8.48617i	−0.0590534	+	0.277825i
$934$	−11.7694	−	8.55098i	−0.385107	−	0.279797i
$935$		0			0
$936$	−5.25986	+	9.11035i	−0.171924	+	0.297781i
$937$	10.4196	+	23.4027i	0.340392	+	0.764534i	0.999917	+	0.0128513i	$0.00409081\pi$
$937$	10.4196	+	23.4027i	0.340392	+	0.764534i	−0.659525	+	0.751683i	$0.729243\pi$
$938$	20.4445	+	28.1394i	0.667536	+	0.918784i
$939$	21.5013	+	9.57299i	0.701668	+	0.312403i
$940$		0			0
$941$	−1.26729	+	12.0574i	−0.0413123	+	0.393061i	0.954254	+	0.298998i	$0.0966522\pi$
$941$	−1.26729	+	12.0574i	−0.0413123	+	0.393061i	−0.995566	+	0.0940632i	$0.970014\pi$
$942$	−30.2607	+	27.2469i	−0.985947	+	0.887750i
$943$	−0.227960	−	0.205256i	−0.00742339	−	0.00668405i
$944$	−2.28029	−	21.6955i	−0.0742172	−	0.706130i
$945$		0			0
$946$	−5.56284	−	17.1207i	−0.180863	−	0.556640i
$947$	−27.0521	+	2.84329i	−0.879074	+	0.0923944i	−0.533303	−	0.845925i	$-0.679049\pi$
$947$	−27.0521	+	2.84329i	−0.879074	+	0.0923944i	−0.345771	+	0.938319i	$0.612383\pi$
$948$	−7.23344	−	6.51302i	−0.234931	−	0.211533i
$949$	9.50673	+	10.5583i	0.308602	+	0.342737i
$950$		0			0
$951$	−52.5296	+	11.1655i	−1.70339	+	0.362066i
$952$	−17.8565	+	40.1064i	−0.578733	+	1.29986i
$953$	14.6316	+	20.1386i	0.473962	+	0.652353i	0.977331	−	0.211719i	$-0.0679061\pi$
$953$	14.6316	+	20.1386i	0.473962	+	0.652353i	−0.503368	+	0.864072i	$0.667906\pi$
$954$	3.44482	−	1.53373i	0.111530	−	0.0496564i
$955$		0			0
$956$	−6.72333	−	11.6452i	−0.217448	−	0.376631i
$957$	31.2358	−	42.9924i	1.00971	−	1.38975i
$958$	4.04993	−	19.0534i	0.130847	−	0.615587i
$959$	−11.6109	+	35.7346i	−0.374935	+	1.15393i
$960$		0			0
$961$	−0.764031	+	30.9906i	−0.0246462	+	0.999696i
$962$			5.89000i			0.189901i
$963$	−3.91961	−	1.27356i	−0.126308	−	0.0410399i
$964$	−10.7202	−	2.27865i	−0.345275	−	0.0733905i
$965$		0			0
$966$	4.42421	+	7.66295i	0.142347	+	0.246551i
$967$	−45.2064	−	26.0999i	−1.45374	−	0.839316i	−0.455048	−	0.890467i	$-0.650378\pi$
$967$	−45.2064	−	26.0999i	−1.45374	−	0.839316i	−0.998691	+	0.0511507i	$0.983711\pi$
$968$	3.91674	+	8.79714i	0.125889	+	0.282751i
$969$	38.6386	−	28.0726i	1.24125	−	0.901821i
$970$		0			0
$971$	19.5246	−	4.15009i	0.626576	−	0.133183i	0.116329	−	0.993211i	$-0.462887\pi$
$971$	19.5246	−	4.15009i	0.626576	−	0.133183i	0.510247	+	0.860028i	$0.329554\pi$
$972$	−6.09286	−	0.640386i	−0.195429	−	0.0205404i
$973$	43.8116	−	39.4482i	1.40454	−	1.26465i
$974$	−10.5465	+	11.7131i	−0.337932	+	0.375311i
$975$		0			0
$976$	2.36016	+	7.26382i	0.0755468	+	0.232509i
$977$	57.3017	−	18.6185i	1.83324	−	0.595657i	0.834224	−	0.551426i	$-0.185916\pi$
$977$	57.3017	−	18.6185i	1.83324	−	0.595657i	0.999021	−	0.0442310i	$-0.0140838\pi$
$978$	0.338628	−	0.0355912i	0.0108281	−	0.00113808i
$979$	12.8254	−	14.2440i	0.409901	−	0.455241i
$980$		0			0
$981$	−0.949273	+	9.03173i	−0.0303080	+	0.288361i
$982$	4.74661	+	22.3310i	0.151470	+	0.712612i
$983$	−4.69322	+	10.5411i	−0.149691	+	0.336210i	−0.972791	−	0.231686i	$-0.925576\pi$
$983$	−4.69322	+	10.5411i	−0.149691	+	0.336210i	0.823100	+	0.567896i	$0.192243\pi$
$984$	−1.73068	+	1.25741i	−0.0551720	+	0.0400848i
$985$		0			0
$986$	15.8321	−	27.4221i	0.504198	−	0.873297i
$987$	8.12816	−	4.69279i	0.258722	−	0.149373i
$988$	−4.55033	+	6.26299i	−0.144765	+	0.199252i
$989$	3.45662	+	0.734727i	0.109914	+	0.0233630i
$990$		0			0
$991$	37.3423			1.18622			0.593109	−	0.805122i	$-0.297900\pi$
$991$	37.3423			1.18622			0.593109	+	0.805122i	$0.297900\pi$
$992$	10.6022	−	10.3440i	0.336620	−	0.328423i
$993$		−	1.58899i		−	0.0504251i
$994$	−7.38383	+	22.7251i	−0.234201	+	0.720796i
$995$		0			0
$996$	−6.78925	−	4.93268i	−0.215126	−	0.156298i
$997$	18.0154	−	10.4012i	0.570555	−	0.329410i	−0.186816	−	0.982395i	$-0.559817\pi$
$997$	18.0154	−	10.4012i	0.570555	−	0.329410i	0.757371	+	0.652985i	$0.226484\pi$
$998$	43.6305	+	25.1901i	1.38110	+	0.797378i
$999$	−5.82682	+	2.59427i	−0.184353	+	0.0820790i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.ck.a.474.3		32
5.2	odd	4		775.2.bl.a.226.1		16
5.3	odd	4		31.2.g.a.9.2	yes	16
5.4	even	2	inner	775.2.ck.a.474.2		32
15.8	even	4		279.2.y.c.226.1		16
20.3	even	4		496.2.bg.c.257.2		16
31.7	even	15	inner	775.2.ck.a.224.2		32
155.3	even	60		961.2.g.n.732.1		16
155.7	odd	60		775.2.bl.a.751.1		16
155.8	odd	20		961.2.g.t.235.1		16
155.13	even	60		961.2.d.q.374.2		16
155.18	odd	60		961.2.d.p.374.2		16
155.23	even	20		961.2.g.n.235.1		16
155.28	odd	60		961.2.g.t.732.1		16
155.33	odd	20		961.2.c.j.439.5		16
155.38	odd	60		31.2.g.a.7.2	✓	16
155.43	even	60		961.2.c.i.521.5		16
155.48	even	60		961.2.g.m.338.1		16
155.53	even	60		961.2.d.q.388.2		16
155.58	even	20		961.2.g.j.547.2		16
155.68	even	12		961.2.g.j.448.2		16
155.69	even	30	inner	775.2.ck.a.224.3		32
155.73	even	60		961.2.d.n.531.3		16
155.78	odd	20		961.2.g.s.816.1		16
155.83	even	60		961.2.a.j.1.5		8
155.88	even	12		961.2.d.n.628.3		16
155.98	odd	12		961.2.d.o.628.3		16
155.103	odd	60		961.2.a.i.1.5		8
155.108	even	20		961.2.g.m.816.1		16
155.113	odd	60		961.2.d.o.531.3		16
155.118	odd	12		961.2.g.k.448.2		16
155.123	even	4		961.2.g.l.846.2		16
155.128	odd	20		961.2.g.k.547.2		16
155.133	odd	60		961.2.d.p.388.2		16
155.138	odd	60		961.2.g.s.338.1		16
155.143	odd	60		961.2.c.j.521.5		16
155.148	even	60		961.2.g.l.844.2		16
155.153	even	20		961.2.c.i.439.5		16
465.38	even	60		279.2.y.c.100.1		16
465.83	odd	60		8649.2.a.be.1.4		8
465.413	even	60		8649.2.a.bf.1.4		8
620.503	even	60		496.2.bg.c.193.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.7.2	✓	16	155.38	odd	60
31.2.g.a.9.2	yes	16	5.3	odd	4
279.2.y.c.100.1		16	465.38	even	60
279.2.y.c.226.1		16	15.8	even	4
496.2.bg.c.193.2		16	620.503	even	60
496.2.bg.c.257.2		16	20.3	even	4
775.2.bl.a.226.1		16	5.2	odd	4
775.2.bl.a.751.1		16	155.7	odd	60
775.2.ck.a.224.2		32	31.7	even	15	inner
775.2.ck.a.224.3		32	155.69	even	30	inner
775.2.ck.a.474.2		32	5.4	even	2	inner
775.2.ck.a.474.3		32	1.1	even	1	trivial
961.2.a.i.1.5		8	155.103	odd	60
961.2.a.j.1.5		8	155.83	even	60
961.2.c.i.439.5		16	155.153	even	20
961.2.c.i.521.5		16	155.43	even	60
961.2.c.j.439.5		16	155.33	odd	20
961.2.c.j.521.5		16	155.143	odd	60
961.2.d.n.531.3		16	155.73	even	60
961.2.d.n.628.3		16	155.88	even	12
961.2.d.o.531.3		16	155.113	odd	60
961.2.d.o.628.3		16	155.98	odd	12
961.2.d.p.374.2		16	155.18	odd	60
961.2.d.p.388.2		16	155.133	odd	60
961.2.d.q.374.2		16	155.13	even	60
961.2.d.q.388.2		16	155.53	even	60
961.2.g.j.448.2		16	155.68	even	12
961.2.g.j.547.2		16	155.58	even	20
961.2.g.k.448.2		16	155.118	odd	12
961.2.g.k.547.2		16	155.128	odd	20
961.2.g.l.844.2		16	155.148	even	60
961.2.g.l.846.2		16	155.123	even	4
961.2.g.m.338.1		16	155.48	even	60
961.2.g.m.816.1		16	155.108	even	20
961.2.g.n.235.1		16	155.23	even	20
961.2.g.n.732.1		16	155.3	even	60
961.2.g.s.338.1		16	155.138	odd	60
961.2.g.s.816.1		16	155.78	odd	20
961.2.g.t.235.1		16	155.8	odd	20
961.2.g.t.732.1		16	155.28	odd	60
8649.2.a.be.1.4		8	465.83	odd	60
8649.2.a.bf.1.4		8	465.413	even	60

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.ck (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.17187 + 0.380762i) q^{2} +(-0.431412 + 2.02963i) q^{3} +(-0.389745 - 0.283166i) q^{4} +(-1.27836 + 2.21419i) q^{6} +(-1.54713 - 3.47491i) q^{7} +(-1.79742 - 2.47393i) q^{8} +(-1.19265 - 0.531003i) q^{9} +(0.393186 - 3.74092i) q^{11} +(0.742864 - 0.668878i) q^{12} +(1.95823 + 1.76320i) q^{13} +(-0.489913 - 4.66121i) q^{14} +(-0.866611 - 2.66715i) q^{16} +(3.75366 - 0.394526i) q^{17} +(-1.19544 - 1.07638i) q^{18} +(-4.08057 - 4.53193i) q^{19} +(7.72023 - 1.64099i) q^{21} +(1.88516 - 4.23414i) q^{22} +(0.534795 + 0.736082i) q^{23} +(5.79659 - 2.58081i) q^{24} +(1.62343 + 2.81186i) q^{26} +(-2.06665 + 2.84451i) q^{27} +(-0.380991 + 1.79242i) q^{28} +(2.10397 - 6.47535i) q^{29} +(-3.88819 - 3.98522i) q^{31} +2.66037i q^{32} +(7.42306 + 2.41190i) q^{33} +(4.54901 + 0.966922i) q^{34} +(0.314468 + 0.544675i) q^{36} +(1.57103 + 0.907032i) q^{37} +(-3.05629 - 6.86454i) q^{38} +(-4.42345 + 3.21383i) q^{39} +(-0.329777 + 0.0700963i) q^{41} +(9.67189 + 1.01656i) q^{42} +(2.88637 - 2.59890i) q^{43} +(-1.21255 + 1.34667i) q^{44} +(0.346435 + 1.06622i) q^{46} +(1.13095 - 0.367467i) q^{47} +(5.78721 - 0.608260i) q^{48} +(-4.99745 + 5.55023i) q^{49} +(-0.818631 + 7.78876i) q^{51} +(-0.263933 - 1.24171i) q^{52} +(-0.953442 + 2.14147i) q^{53} +(-3.50492 + 2.54647i) q^{54} +(-5.81584 + 10.0733i) q^{56} +(10.9586 - 6.32692i) q^{57} +(4.93114 - 6.78713i) q^{58} +(7.60885 + 1.61731i) q^{59} -2.72343 q^{61} +(-3.03901 - 6.15062i) q^{62} +4.96588i q^{63} +(-2.74619 + 8.45191i) q^{64} +(7.78047 + 5.65284i) q^{66} +(-6.42693 + 3.71059i) q^{67} +(-1.57469 - 0.909147i) q^{68} +(-1.72469 + 0.767882i) q^{69} +(-4.65742 - 2.07362i) q^{71} +(0.830027 + 3.90497i) q^{72} +(5.36221 + 0.563591i) q^{73} +(1.49567 + 1.66111i) q^{74} +(0.307091 + 2.92178i) q^{76} +(-13.6076 + 4.42139i) q^{77} +(-6.40740 + 2.08189i) q^{78} +(-1.01782 - 9.68388i) q^{79} +(-7.50241 - 8.33227i) q^{81} +(-0.413145 - 0.0434232i) q^{82} +(-1.74545 - 8.21169i) q^{83} +(-3.47359 - 1.54654i) q^{84} +(4.37200 - 1.94654i) q^{86} +(12.2349 + 7.06383i) q^{87} +(-9.96149 + 5.75127i) q^{88} +(4.12243 + 2.99512i) q^{89} +(3.09732 - 9.53258i) q^{91} -0.438320i q^{92} +(9.76595 - 6.17231i) q^{93} +1.46523 q^{94} +(-5.39957 - 1.14771i) q^{96} +(6.41522 - 8.82979i) q^{97} +(-7.96966 + 4.60129i) q^{98} +(-2.45537 + 4.25283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 28 q^{4} + 22 q^{6} + 20 q^{9} - 14 q^{11} + 12 q^{14} - 4 q^{16} - 32 q^{19} + 18 q^{21} + 40 q^{24} + 18 q^{26} + 28 q^{29} + 30 q^{31} + 64 q^{34} + 2 q^{36} + 6 q^{39} - 16 q^{41} - 78 q^{44}+ \cdots - 12 q^{99}+O(q^{100}) \) 32 * q + 28 * q^4 + 22 * q^6 + 20 * q^9 - 14 * q^11 + 12 * q^14 - 4 * q^16 - 32 * q^19 + 18 * q^21 + 40 * q^24 + 18 * q^26 + 28 * q^29 + 30 * q^31 + 64 * q^34 + 2 * q^36 + 6 * q^39 - 16 * q^41 - 78 * q^44 + 68 * q^46 - 4 * q^49 - 84 * q^51 + 92 * q^54 - 60 * q^56 - 8 * q^59 - 120 * q^61 - 46 * q^64 - 60 * q^66 - 76 * q^69 - 28 * q^71 - 26 * q^74 - 24 * q^76 - 36 * q^79 + 46 * q^81 - 16 * q^84 - 52 * q^86 - 2 * q^89 + 16 * q^91 - 88 * q^94 + 16 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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