LMFDB - Embedded newform 350.2.r.a.13.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.12
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987688 - 0.156434i) q^{2} +(-1.66180 - 0.846728i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.499152 + 2.17964i) q^{5} +(-1.77380 - 0.576341i) q^{6} +(-0.737955 + 2.54075i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.281267 + 0.387131i) q^{9} +O(q^{10})$	\(q+(0.987688 - 0.156434i) q^{2} +(-1.66180 - 0.846728i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.499152 + 2.17964i) q^{5} +(-1.77380 - 0.576341i) q^{6} +(-0.737955 + 2.54075i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.281267 + 0.387131i) q^{9} +(-0.152036 + 2.23089i) q^{10} +(4.96002 + 3.60366i) q^{11} +(-1.84212 - 0.291763i) q^{12} +(-0.692430 + 4.37183i) q^{13} +(-0.331409 + 2.62491i) q^{14} +(2.67506 - 3.19948i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.52004 - 0.774499i) q^{17} +(0.338365 + 0.338365i) q^{18} +(1.94881 - 5.99783i) q^{19} +(0.198825 + 2.22721i) q^{20} +(3.37766 - 3.59737i) q^{21} +(5.46269 + 2.78338i) q^{22} +(0.284423 + 1.79578i) q^{23} -1.86508 q^{24} +(-4.50169 - 2.17595i) q^{25} +4.42632i q^{26} +(0.735674 + 4.64486i) q^{27} +(0.0832985 + 2.64444i) q^{28} +(-8.17286 + 2.65552i) q^{29} +(2.14161 - 3.57856i) q^{30} +(4.43176 + 1.43997i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.19122 - 10.1883i) q^{33} +(1.38017 - 1.00275i) q^{34} +(-5.16958 - 2.87670i) q^{35} +(0.387131 + 0.281267i) q^{36} +(-0.563587 + 3.55835i) q^{37} +(0.986553 - 6.22885i) q^{38} +(4.85243 - 6.67880i) q^{39} +(0.544789 + 2.16869i) q^{40} +(-0.248189 - 0.341603i) q^{41} +(2.77332 - 4.08146i) q^{42} +(0.714628 + 0.714628i) q^{43} +(5.83085 + 1.89456i) q^{44} +(-0.984204 + 0.419825i) q^{45} +(0.561843 + 1.72917i) q^{46} +(-0.635825 + 1.24788i) q^{47} +(-1.84212 + 0.291763i) q^{48} +(-5.91084 - 3.74992i) q^{49} +(-4.78666 - 1.44494i) q^{50} -3.18179 q^{51} +(0.692430 + 4.37183i) q^{52} +(4.87664 - 9.57095i) q^{53} +(1.45323 + 4.47259i) q^{54} +(-10.3305 + 9.01229i) q^{55} +(0.495954 + 2.59885i) q^{56} +(-8.31707 + 8.31707i) q^{57} +(-7.65682 + 3.90135i) q^{58} +(10.6106 - 7.70902i) q^{59} +(1.55544 - 3.86952i) q^{60} +(-0.203989 + 0.280767i) q^{61} +(4.60246 + 0.728958i) q^{62} +(-1.19117 + 0.428945i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-9.18340 - 3.69146i) q^{65} +(-6.72112 - 9.25083i) q^{66} +(0.457649 + 0.898186i) q^{67} +(1.20631 - 1.20631i) q^{68} +(1.04788 - 3.22505i) q^{69} +(-5.55595 - 2.03258i) q^{70} +(-2.47077 - 7.60425i) q^{71} +(0.426365 + 0.217244i) q^{72} +(-11.7002 + 1.85313i) q^{73} +3.60270i q^{74} +(5.63847 + 7.42770i) q^{75} -6.30649i q^{76} +(-12.8163 + 9.94283i) q^{77} +(3.74789 - 7.35566i) q^{78} +(2.27511 - 0.739227i) q^{79} +(0.877340 + 2.05676i) q^{80} +(3.15401 - 9.70703i) q^{81} +(-0.298572 - 0.298572i) q^{82} +(-3.48589 - 6.84144i) q^{83} +(2.10070 - 4.46506i) q^{84} +(0.929401 + 3.69974i) q^{85} +(0.817623 + 0.594038i) q^{86} +(15.8301 + 2.50725i) q^{87} +(6.05544 + 0.959087i) q^{88} +(2.13410 + 1.55051i) q^{89} +(-0.906412 + 0.568620i) q^{90} +(-10.5968 - 4.98551i) q^{91} +(0.825428 + 1.61999i) q^{92} +(-6.14543 - 6.14543i) q^{93} +(-0.432786 + 1.33198i) q^{94} +(12.1004 + 7.24155i) q^{95} +(-1.77380 + 0.576341i) q^{96} +(2.22965 - 4.37593i) q^{97} +(-6.42469 - 2.77910i) q^{98} +2.93377i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$2$	0.987688	−	0.156434i	0.698401	−	0.110616i
$3$	−1.66180	−	0.846728i	−0.959439	−	0.488859i	−0.0971473	−	0.995270i	$-0.530972\pi$
$3$	−1.66180	−	0.846728i	−0.959439	−	0.488859i	−0.862292	+	0.506411i	$0.830972\pi$
$4$	0.951057	−	0.309017i	0.475528	−	0.154508i
$5$	−0.499152	+	2.17964i	−0.223228	+	0.974766i
$5$	−0.499152	+	2.17964i	−0.223228	+	0.974766i
$6$	−1.77380	−	0.576341i	−0.724149	−	0.235290i
$7$	−0.737955	+	2.54075i	−0.278921	+	0.960314i
$7$	−0.737955	+	2.54075i	−0.278921	+	0.960314i
$8$	0.891007	−	0.453990i	0.315018	−	0.160510i
$9$	0.281267	+	0.387131i	0.0937558	+	0.129044i
$10$	−0.152036	+	2.23089i	−0.0480779	+	0.705470i
$11$	4.96002	+	3.60366i	1.49550	+	1.08655i	0.972130	+	0.234441i	$0.0753258\pi$
$11$	4.96002	+	3.60366i	1.49550	+	1.08655i	0.523371	+	0.852105i	$0.324674\pi$
$12$	−1.84212	−	0.291763i	−0.531773	−	0.0842246i
$13$	−0.692430	+	4.37183i	−0.192045	+	1.21253i	0.683703	+	0.729760i	$0.260368\pi$
$13$	−0.692430	+	4.37183i	−0.192045	+	1.21253i	−0.875749	+	0.482767i	$0.839632\pi$
$14$	−0.331409	+	2.62491i	−0.0885727	+	0.701538i
$15$	2.67506	−	3.19948i	0.690697	−	0.826102i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	1.52004	−	0.774499i	0.368664	−	0.187844i	−0.259837	−	0.965652i	$-0.583669\pi$
$17$	1.52004	−	0.774499i	0.368664	−	0.187844i	0.628501	+	0.777809i	$0.283669\pi$
$18$	0.338365	+	0.338365i	0.0797535	+	0.0797535i
$19$	1.94881	−	5.99783i	0.447089	−	1.37600i	−0.433088	−	0.901351i	$-0.642576\pi$
$19$	1.94881	−	5.99783i	0.447089	−	1.37600i	0.880177	−	0.474646i	$-0.157424\pi$
$20$	0.198825	+	2.22721i	0.0444586	+	0.498020i
$21$	3.37766	−	3.59737i	0.737066	−	0.785010i
$22$	5.46269	+	2.78338i	1.16465	+	0.593418i
$23$	0.284423	+	1.79578i	0.0593063	+	0.374445i	0.999435	+	0.0336244i	$0.0107050\pi$
$23$	0.284423	+	1.79578i	0.0593063	+	0.374445i	−0.940128	+	0.340821i	$0.889295\pi$
$24$	−1.86508			−0.380708
$25$	−4.50169	−	2.17595i	−0.900339	−	0.435190i
$26$			4.42632i			0.868074i
$27$	0.735674	+	4.64486i	0.141580	+	0.893904i
$28$	0.0832985	+	2.64444i	0.0157419	+	0.499752i
$29$	−8.17286	+	2.65552i	−1.51766	+	0.493118i	−0.945111	−	0.326751i	$-0.894046\pi$
$29$	−8.17286	+	2.65552i	−1.51766	+	0.493118i	−0.572551	+	0.819869i	$0.694046\pi$
$30$	2.14161	−	3.57856i	0.391003	−	0.653353i
$31$	4.43176	+	1.43997i	0.795968	+	0.258626i	0.678644	−	0.734468i	$-0.262568\pi$
$31$	4.43176	+	1.43997i	0.795968	+	0.258626i	0.117325	+	0.993094i	$0.462568\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.19122	−	10.1883i	−0.903676	−	1.77356i
$34$	1.38017	−	1.00275i	0.236697	−	0.171970i
$35$	−5.16958	−	2.87670i	−0.873819	−	0.486251i
$36$	0.387131	+	0.281267i	0.0645219	+	0.0468779i
$37$	−0.563587	+	3.55835i	−0.0926531	+	0.584989i	0.897058	+	0.441912i	$0.145700\pi$
$37$	−0.563587	+	3.55835i	−0.0926531	+	0.584989i	−0.989712	+	0.143077i	$0.954300\pi$
$38$	0.986553	−	6.22885i	0.160040	−	1.01045i
$39$	4.85243	−	6.67880i	0.777010	−	1.06946i
$40$	0.544789	+	2.16869i	0.0861388	+	0.342900i
$41$	−0.248189	−	0.341603i	−0.0387606	−	0.0533494i	0.789197	−	0.614140i	$-0.210497\pi$
$41$	−0.248189	−	0.341603i	−0.0387606	−	0.0533494i	−0.827957	+	0.560791i	$0.810497\pi$
$42$	2.77332	−	4.08146i	0.427933	−	0.629783i
$43$	0.714628	+	0.714628i	0.108980	+	0.108980i	0.759494	−	0.650514i	$-0.225447\pi$
$43$	0.714628	+	0.714628i	0.108980	+	0.108980i	−0.650514	+	0.759494i	$0.725447\pi$
$44$	5.83085	+	1.89456i	0.879034	+	0.285615i
$45$	−0.984204	+	0.419825i	−0.146716	+	0.0625838i
$46$	0.561843	+	1.72917i	0.0828392	+	0.254953i
$47$	−0.635825	+	1.24788i	−0.0927446	+	0.182022i	−0.932719	−	0.360605i	$-0.882570\pi$
$47$	−0.635825	+	1.24788i	−0.0927446	+	0.182022i	0.839974	+	0.542627i	$0.182570\pi$
$48$	−1.84212	+	0.291763i	−0.265887	+	0.0421123i
$49$	−5.91084	−	3.74992i	−0.844406	−	0.535703i
$50$	−4.78666	−	1.44494i	−0.676936	−	0.204345i
$51$	−3.18179			−0.445540
$52$	0.692430	+	4.37183i	0.0960227	+	0.606264i
$53$	4.87664	−	9.57095i	0.669858	−	1.31467i	−0.266571	−	0.963815i	$-0.585891\pi$
$53$	4.87664	−	9.57095i	0.669858	−	1.31467i	0.936429	−	0.350856i	$-0.114109\pi$
$54$	1.45323	+	4.47259i	0.197760	+	0.608642i
$55$	−10.3305	+	9.01229i	−1.39297	+	1.21522i
$56$	0.495954	+	2.59885i	0.0662747	+	0.347286i
$57$	−8.31707	+	8.31707i	−1.10162	+	1.10162i
$58$	−7.65682	+	3.90135i	−1.00539	+	0.512272i
$59$	10.6106	−	7.70902i	1.38138	−	1.00363i	0.384627	−	0.923072i	$-0.374330\pi$
$59$	10.6106	−	7.70902i	1.38138	−	1.00363i	0.996750	−	0.0805574i	$-0.0256700\pi$
$60$	1.55544	−	3.86952i	0.200806	−	0.499554i
$61$	−0.203989	+	0.280767i	−0.0261181	+	0.0359485i	−0.821876	−	0.569666i	$-0.807073\pi$
$61$	−0.203989	+	0.280767i	−0.0261181	+	0.0359485i	0.795758	+	0.605614i	$0.207073\pi$
$62$	4.60246	+	0.728958i	0.584513	+	0.0925778i
$63$	−1.19117	+	0.428945i	−0.150073	+	0.0540420i
$64$	0.587785	−	0.809017i	0.0734732	−	0.101127i
$65$	−9.18340	−	3.69146i	−1.13906	−	0.457869i
$66$	−6.72112	−	9.25083i	−0.827312	−	1.13870i
$67$	0.457649	+	0.898186i	0.0559107	+	0.109731i	0.917271	−	0.398264i	$-0.130387\pi$
$67$	0.457649	+	0.898186i	0.0559107	+	0.109731i	−0.861360	+	0.507994i	$0.830387\pi$
$68$	1.20631	−	1.20631i	0.146287	−	0.146287i
$69$	1.04788	−	3.22505i	0.126150	−	0.388250i
$70$	−5.55595	−	2.03258i	−0.664063	−	0.242940i
$71$	−2.47077	−	7.60425i	−0.293227	−	0.902459i	−0.983811	−	0.179207i	$-0.942647\pi$
$71$	−2.47077	−	7.60425i	−0.293227	−	0.902459i	0.690585	−	0.723251i	$-0.257353\pi$
$72$	0.426365	+	0.217244i	0.0502476	+	0.0256024i
$73$	−11.7002	+	1.85313i	−1.36940	+	0.216892i	−0.797445	−	0.603392i	$-0.793816\pi$
$73$	−11.7002	+	1.85313i	−1.36940	+	0.216892i	−0.571957	+	0.820284i	$0.693816\pi$
$74$			3.60270i			0.418806i
$75$	5.63847	+	7.42770i	0.651074	+	0.857677i
$76$		−	6.30649i		−	0.723405i
$77$	−12.8163	+	9.94283i	−1.46055	+	1.13309i
$78$	3.74789	−	7.35566i	0.424365	−	0.832864i
$79$	2.27511	−	0.739227i	0.255969	−	0.0831695i	−0.178221	−	0.983990i	$-0.557034\pi$
$79$	2.27511	−	0.739227i	0.255969	−	0.0831695i	0.434191	+	0.900821i	$0.357034\pi$
$80$	0.877340	+	2.05676i	0.0980895	+	0.229953i
$81$	3.15401	−	9.70703i	0.350445	−	1.07856i
$82$	−0.298572	−	0.298572i	−0.0329717	−	0.0329717i
$83$	−3.48589	−	6.84144i	−0.382626	−	0.750945i	0.616717	−	0.787185i	$-0.288462\pi$
$83$	−3.48589	−	6.84144i	−0.382626	−	0.750945i	−0.999343	+	0.0362394i	$0.988462\pi$
$84$	2.10070	−	4.46506i	0.229205	−	0.487177i
$85$	0.929401	+	3.69974i	0.100808	+	0.401293i
$86$	0.817623	+	0.594038i	0.0881665	+	0.0640567i
$87$	15.8301	+	2.50725i	1.69717	+	0.268805i
$88$	6.05544	+	0.959087i	0.645512	+	0.102239i
$89$	2.13410	+	1.55051i	0.226214	+	0.164354i	0.695119	−	0.718894i	$-0.255352\pi$
$89$	2.13410	+	1.55051i	0.226214	+	0.164354i	−0.468905	+	0.883248i	$0.655352\pi$
$90$	−0.906412	+	0.568620i	−0.0955442	+	0.0599378i
$91$	−10.5968	−	4.98551i	−1.11084	−	0.522623i
$92$	0.825428	+	1.61999i	0.0860568	+	0.168896i
$93$	−6.14543	−	6.14543i	−0.637252	−	0.637252i
$94$	−0.432786	+	1.33198i	−0.0446385	+	0.137383i
$95$	12.1004	+	7.24155i	1.24147	+	0.742968i
$96$	−1.77380	+	0.576341i	−0.181037	+	0.0588226i
$97$	2.22965	−	4.37593i	0.226386	−	0.444308i	−0.749674	−	0.661807i	$-0.769790\pi$
$97$	2.22965	−	4.37593i	0.226386	−	0.444308i	0.976061	+	0.217499i	$0.0697898\pi$
$98$	−6.42469	−	2.77910i	−0.648992	−	0.280731i
$99$			2.93377i			0.294855i
$100$	−4.95377	−	0.678351i	−0.495377	−	0.0678351i
$101$		−	8.14490i		−	0.810448i	−0.914218	−	0.405224i	$-0.867194\pi$
$101$		−	8.14490i		−	0.810448i	0.914218	−	0.405224i	$-0.132806\pi$
$102$	−3.14262	+	0.497742i	−0.311165	+	0.0492838i
$103$	1.83160	+	0.933247i	0.180473	+	0.0919555i	0.541893	−	0.840448i	$-0.317708\pi$
$103$	1.83160	+	0.933247i	0.180473	+	0.0919555i	−0.361420	+	0.932403i	$0.617708\pi$
$104$	1.36781	+	4.20968i	0.134125	+	0.412793i
$105$	6.15502	+	9.15773i	0.600668	+	0.893703i
$106$	3.31938	−	10.2160i	0.322406	−	0.992265i
$107$	10.6342	−	10.6342i	1.02805	−	1.02805i	0.0284554	−	0.999595i	$-0.490941\pi$
$107$	10.6342	−	10.6342i	1.02805	−	1.02805i	0.999595	−	0.0284554i	$-0.00905885\pi$
$108$	2.13501	+	4.19019i	0.205441	+	0.403201i
$109$	9.24081	+	12.7189i	0.885109	+	1.21825i	0.974979	+	0.222295i	$0.0713548\pi$
$109$	9.24081	+	12.7189i	0.885109	+	1.21825i	−0.0898702	+	0.995953i	$0.528645\pi$
$110$	−8.79349	+	10.5174i	−0.838426	+	1.00279i
$111$	3.94952	−	5.43605i	0.374872	−	0.515967i
$112$	0.896398	+	2.48927i	0.0847017	+	0.235214i
$113$	3.38646	+	0.536363i	0.318571	+	0.0504568i	0.313672	−	0.949531i	$-0.398441\pi$
$113$	3.38646	+	0.536363i	0.318571	+	0.0504568i	0.00489896	+	0.999988i	$0.498441\pi$
$114$	−6.91360	+	9.51575i	−0.647518	+	0.891232i
$115$	−4.05612	−	0.276425i	−0.378235	−	0.0257768i
$116$	−6.95225	+	5.05110i	−0.645500	+	0.468983i
$117$	−1.88723	+	0.961592i	−0.174474	+	0.0888992i
$118$	9.27397	−	9.27397i	0.853738	−	0.853738i
$119$	0.846089	+	4.43359i	0.0775608	+	0.406427i
$120$	0.930959	−	4.06521i	0.0849845	−	0.371101i
$121$	8.21619	+	25.2868i	0.746927	+	2.29880i
$122$	−0.157556	+	0.309221i	−0.0142645	+	0.0279956i
$123$	0.123195	+	0.777823i	0.0111081	+	0.0701340i
$124$	4.65983			0.418465
$125$	6.98983	−	8.72596i	0.625189	−	0.780473i
$126$	−1.10940	+	0.610004i	−0.0988333	+	0.0543435i
$127$	−4.24777	+	0.672781i	−0.376929	+	0.0596997i	−0.342025	−	0.939691i	$-0.611113\pi$
$127$	−4.24777	+	0.672781i	−0.376929	+	0.0596997i	−0.0349042	+	0.999391i	$0.511113\pi$
$128$	0.453990	−	0.891007i	0.0401275	−	0.0787546i
$129$	−0.582472	−	1.79266i	−0.0512838	−	0.157835i
$130$	−9.64781	−	2.20941i	−0.846169	−	0.193778i
$131$	13.5124	+	4.39044i	1.18058	+	0.383594i	0.832583	−	0.553900i	$-0.186861\pi$
$131$	13.5124	+	4.39044i	1.18058	+	0.383594i	0.347999	+	0.937495i	$0.386861\pi$
$132$	−8.08552	−	8.08552i	−0.703754	−	0.703754i
$133$	13.8009	+	9.37759i	1.19669	+	0.813140i
$134$	0.592522	+	0.815536i	0.0511861	+	0.0704516i
$135$	−10.4914	−	0.714987i	−0.902952	−	0.0615363i
$136$	1.00275	−	1.38017i	0.0859852	−	0.118348i
$137$	3.37772	−	21.3261i	0.288578	−	1.82201i	−0.237287	−	0.971440i	$-0.576258\pi$
$137$	3.37772	−	21.3261i	0.288578	−	1.82201i	0.525864	−	0.850568i	$-0.323742\pi$
$138$	0.530472	−	3.34927i	0.0451567	−	0.285108i
$139$	7.33490	+	5.32912i	0.622138	+	0.452010i	0.853668	−	0.520818i	$-0.174373\pi$
$139$	7.33490	+	5.32912i	0.622138	+	0.452010i	−0.231530	+	0.972828i	$0.574373\pi$
$140$	−5.80552	−	1.13842i	−0.490656	−	0.0962138i
$141$	2.11323	−	1.53535i	0.177966	−	0.129300i
$142$	−3.62992	−	7.12412i	−0.304616	−	0.597843i
$143$	−19.1891	+	19.1891i	−1.60467	+	1.60467i
$144$	0.455100	+	0.147871i	0.0379250	+	0.0123226i
$145$	−1.70859	−	19.1394i	−0.141891	−	1.58944i
$146$	−11.2662	+	3.66062i	−0.932400	+	0.302955i
$147$	6.64746	+	11.2365i	0.548273	+	0.926770i
$148$	0.563587	+	3.55835i	0.0463266	+	0.292494i
$149$		−	3.35094i		−	0.274520i	−0.990535	−	0.137260i	$-0.956170\pi$
$149$		−	3.35094i		−	0.274520i	0.990535	−	0.137260i	$-0.0438296\pi$
$150$	6.73100	+	6.45420i	0.549584	+	0.526983i
$151$	12.6061			1.02587			0.512937	−	0.858426i	$-0.328558\pi$
$151$	12.6061			1.02587			0.512937	+	0.858426i	$0.328558\pi$
$152$	−0.986553	−	6.22885i	−0.0800200	−	0.505227i
$153$	0.727371	+	0.370614i	0.0588044	+	0.0299624i
$154$	−11.1031	+	11.8253i	−0.894713	+	0.952912i
$155$	−5.35074	+	8.94090i	−0.429782	+	0.718151i
$156$	2.55107	−	7.85139i	0.204249	−	0.628615i
$157$	8.44248	+	8.44248i	0.673783	+	0.673783i	0.958586	−	0.284803i	$-0.0919282\pi$
$157$	8.44248	+	8.44248i	0.673783	+	0.673783i	−0.284803	+	0.958586i	$0.591928\pi$
$158$	2.13145	−	1.08603i	0.169569	−	0.0863999i
$159$	−16.2080	+	11.7758i	−1.28538	+	0.933881i
$160$	1.18829	+	1.89419i	0.0939423	+	0.149749i
$161$	−4.77251	−	0.602554i	−0.376127	−	0.0474879i
$162$	1.59666	−	10.0809i	0.125446	−	0.792032i
$163$	0.119618	+	0.0189456i	0.00936918	+	0.00148393i	0.161117	−	0.986935i	$-0.448490\pi$
$163$	0.119618	+	0.0189456i	0.00936918	+	0.00148393i	−0.151748	+	0.988419i	$0.548490\pi$
$164$	−0.341603	−	0.248189i	−0.0266747	−	0.0193803i
$165$	24.7982	−	6.22948i	1.93054	−	0.484964i
$166$	−4.51321	−	6.21189i	−0.350293	−	0.482137i
$167$	−19.2061	+	9.78600i	−1.48621	+	0.757264i	−0.993597	−	0.112983i	$-0.963960\pi$
$167$	−19.2061	+	9.78600i	−1.48621	+	0.757264i	−0.492617	+	0.870246i	$0.663960\pi$
$168$	1.37635	−	4.73870i	0.106187	−	0.365599i
$169$	−6.26969	−	2.03715i	−0.482284	−	0.156704i
$170$	1.49672	+	3.50880i	0.114794	+	0.269113i
$171$	2.87009	−	0.932548i	0.219481	−	0.0713137i
$172$	0.900484	+	0.458820i	0.0686613	+	0.0349847i
$173$	7.65324	−	1.21215i	0.581865	−	0.0921584i	0.141438	−	0.989947i	$-0.454827\pi$
$173$	7.65324	−	1.21215i	0.581865	−	0.0921584i	0.440426	+	0.897789i	$0.354827\pi$
$174$	16.0275			1.21504
$175$	8.85060	−	9.83194i	0.669042	−	0.743224i
$176$	6.13092			0.462135
$177$	−24.1601	+	3.82658i	−1.81598	+	0.287623i
$178$	2.35038	+	1.19758i	0.176168	+	0.0897622i
$179$	15.1862	−	4.93429i	1.13507	−	0.368806i	0.319568	−	0.947563i	$-0.396462\pi$
$179$	15.1862	−	4.93429i	1.13507	−	0.368806i	0.815500	+	0.578758i	$0.196462\pi$
$180$	−0.806300	+	0.703413i	−0.0600981	+	0.0524293i
$181$	−18.2862	−	5.94155i	−1.35920	−	0.441632i	−0.463426	−	0.886136i	$-0.653380\pi$
$181$	−18.2862	−	5.94155i	−1.35920	−	0.441632i	−0.895777	+	0.444504i	$0.853380\pi$
$182$	−11.2462	−	3.26643i	−0.833623	−	0.242124i
$183$	0.576722	−	0.293855i	0.0426325	−	0.0217224i
$184$	1.06869	+	1.47092i	0.0787847	+	0.108438i
$185$	−7.47461	−	3.00458i	−0.549545	−	0.220901i
$186$	−7.03113	−	5.10842i	−0.515548	−	0.374567i
$187$	10.3305	+	1.63618i	0.755438	+	0.119650i
$188$	−0.219090	+	1.38328i	−0.0159788	+	0.100886i
$189$	−12.3443	−	1.55853i	−0.897918	−	0.113367i
$190$	13.0842	+	5.25948i	0.949230	+	0.381563i
$191$	−17.7163	+	12.8716i	−1.28190	+	0.931358i	−0.999609	−	0.0279693i	$-0.991096\pi$
$191$	−17.7163	+	12.8716i	−1.28190	+	0.931358i	−0.282296	+	0.959327i	$0.591096\pi$
$192$	−1.66180	+	0.846728i	−0.119930	+	0.0611073i
$193$	−4.47070	−	4.47070i	−0.321808	−	0.321808i	0.527652	−	0.849460i	$-0.323072\pi$
$193$	−4.47070	−	4.47070i	−0.321808	−	0.321808i	−0.849460	+	0.527652i	$0.823072\pi$
$194$	1.51765	−	4.67085i	0.108961	−	0.335347i
$195$	12.1353	+	13.9103i	0.869026	+	0.996138i
$196$	−6.78034	−	1.73984i	−0.484310	−	0.124274i
$197$	5.39775	+	2.75029i	0.384573	+	0.195950i	0.635579	−	0.772036i	$-0.280761\pi$
$197$	5.39775	+	2.75029i	0.384573	+	0.195950i	−0.251006	+	0.967986i	$0.580761\pi$
$198$	0.458943	+	2.89765i	0.0326157	+	0.205927i
$199$	−23.9275			−1.69618			−0.848089	−	0.529853i	$-0.822247\pi$
$199$	−23.9275			−1.69618			−0.848089	+	0.529853i	$0.822247\pi$
$200$	−4.99890	+	0.104941i	−0.353476	+	0.00742047i
$201$		−	1.88011i		−	0.132613i
$202$	−1.27414	−	8.04462i	−0.0896484	−	0.566018i
$203$	−0.715822	−	22.7249i	−0.0502408	−	1.59497i
$204$	−3.02606	+	0.983227i	−0.211867	+	0.0688397i
$205$	0.868456	−	0.370452i	0.0606556	−	0.0258735i
$206$	1.95504	+	0.635231i	0.136214	+	0.0442587i
$207$	−0.615203	+	0.615203i	−0.0427595	+	0.0427595i
$208$	2.00951	+	3.94388i	0.139334	+	0.273459i
$209$	31.2803	−	22.7265i	2.16371	−	1.57202i
$210$	7.51182	+	8.08213i	0.518365	+	0.557720i
$211$	7.12534	+	5.17687i	0.490529	+	0.356390i	0.805388	−	0.592748i	$-0.201957\pi$
$211$	7.12534	+	5.17687i	0.490529	+	0.356390i	−0.314859	+	0.949139i	$0.601957\pi$
$212$	1.68038	−	10.6095i	0.115409	−	0.728662i
$213$	−2.33281	+	14.7288i	−0.159842	+	1.00920i
$214$	8.83975	−	12.1669i	0.604273	−	0.831710i
$215$	−1.91434	+	1.20093i	−0.130557	+	0.0819025i
$216$	2.76421	+	3.80461i	0.188081	+	0.258871i
$217$	−6.92904	+	10.1974i	−0.470374	+	0.692243i
$218$	11.1167	+	11.1167i	0.752919	+	0.752919i
$219$	21.0124	+	6.82735i	1.41989	+	0.461350i
$220$	−7.03994	+	11.7635i	−0.474633	+	0.793095i
$221$	2.33346	+	7.18164i	0.156965	+	0.483090i
$222$	3.05051	−	5.98696i	0.204737	−	0.401819i
$223$	4.10776	−	0.650605i	0.275076	−	0.0435678i	−0.0173723	−	0.999849i	$-0.505530\pi$
$223$	4.10776	−	0.650605i	0.275076	−	0.0435678i	0.292448	+	0.956281i	$0.405530\pi$
$224$	1.27477	+	2.31840i	0.0851742	+	0.154904i
$225$	−0.423802	−	2.35477i	−0.0282534	−	0.156985i
$226$	3.42867			0.228072
$227$	−0.0954184	−	0.602448i	−0.00633314	−	0.0399859i	0.984319	−	0.176395i	$-0.0564437\pi$
$227$	−0.0954184	−	0.602448i	−0.00633314	−	0.0399859i	−0.990653	+	0.136409i	$0.956444\pi$
$228$	−5.33989	+	10.4801i	−0.353643	+	0.694063i
$229$	4.69597	+	14.4527i	0.310318	+	0.955061i	0.977639	+	0.210291i	$0.0674410\pi$
$229$	4.69597	+	14.4527i	0.310318	+	0.955061i	−0.667321	+	0.744770i	$0.732559\pi$
$230$	−4.04943	+	0.361495i	−0.267011	+	0.0238363i
$231$	29.7170	−	5.67107i	1.95523	−	0.373129i
$232$	−6.07649	+	6.07649i	−0.398941	+	0.398941i
$233$	−19.5303	+	9.95120i	−1.27947	+	0.651925i	−0.955737	−	0.294223i	$-0.904939\pi$
$233$	−19.5303	+	9.95120i	−1.27947	+	0.651925i	−0.323737	+	0.946147i	$0.604939\pi$
$234$	−1.71357	+	1.24498i	−0.112020	+	0.0813869i
$235$	−2.40255	−	2.00875i	−0.156725	−	0.131037i
$236$	7.70902	−	10.6106i	0.501815	−	0.690689i
$237$	−4.40669	−	0.697951i	−0.286245	−	0.0453368i
$238$	1.52924	+	4.24665i	0.0991258	+	0.275269i
$239$	5.97166	−	8.21928i	0.386274	−	0.531661i	−0.570959	−	0.820979i	$-0.693428\pi$
$239$	5.97166	−	8.21928i	0.386274	−	0.531661i	0.957233	+	0.289318i	$0.0934284\pi$
$240$	0.283559	−	4.16079i	0.0183036	−	0.268578i
$241$	−2.20037	−	3.02855i	−0.141738	−	0.195086i	0.732246	−	0.681040i	$-0.238472\pi$
$241$	−2.20037	−	3.02855i	−0.141738	−	0.195086i	−0.873984	+	0.485954i	$0.838472\pi$
$242$	12.0708	+	23.6902i	0.775939	+	1.52287i
$243$	−3.48448	+	3.48448i	−0.223530	+	0.223530i
$244$	−0.107243	+	0.330061i	−0.00686556	+	0.0211300i
$245$	11.1239	−	11.0118i	0.710680	−	0.703515i
$246$	0.243357	+	0.748975i	0.0155159	+	0.0477529i
$247$	24.8721	+	12.6730i	1.58257	+	0.806361i
$248$	4.60246	−	0.728958i	0.292257	−	0.0462889i
$249$			14.3207i			0.907536i
$250$	5.53873	−	9.71198i	0.350300	−	0.614239i
$251$			14.9758i			0.945262i	0.881260	+	0.472631i	$0.156696\pi$
$251$			14.9758i			0.945262i	−0.881260	+	0.472631i	$0.843304\pi$
$252$	−1.00032	+	0.776042i	−0.0630140	+	0.0488861i
$253$	−5.06063	+	9.93205i	−0.318159	+	0.624422i
$254$	−4.09023	+	1.32900i	−0.256644	+	0.0833886i
$255$	1.58820	−	6.93517i	0.0994568	−	0.434297i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−6.37903	−	6.37903i	−0.397913	−	0.397913i	0.479583	−	0.877496i	$-0.340788\pi$
$257$	−6.37903	−	6.37903i	−0.397913	−	0.397913i	−0.877496	+	0.479583i	$0.840788\pi$
$258$	−0.855735	−	1.67947i	−0.0532757	−	0.104560i
$259$	−8.62498	−	4.05784i	−0.535930	−	0.252142i
$260$	−9.87466	−	0.672959i	−0.612400	−	0.0417352i
$261$	−3.32680	−	2.41706i	−0.205923	−	0.149612i
$262$	14.0328	+	2.22258i	0.866952	+	0.137312i
$263$	−18.5311	−	2.93504i	−1.14268	−	0.180982i	−0.443734	−	0.896159i	$-0.646346\pi$
$263$	−18.5311	−	2.93504i	−1.14268	−	0.180982i	−0.698944	+	0.715176i	$0.746346\pi$
$264$	−9.25083	−	6.72112i	−0.569349	−	0.413656i
$265$	18.4271	+	15.4067i	1.13197	+	0.946426i
$266$	15.0979	+	7.10320i	0.925714	+	0.435525i
$267$	−2.23358	−	4.38364i	−0.136693	−	0.268274i
$268$	0.712805	+	0.712805i	0.0435415	+	0.0435415i
$269$	3.33497	−	10.2640i	0.203337	−	0.625806i	−0.796441	−	0.604716i	$-0.793286\pi$
$269$	3.33497	−	10.2640i	0.203337	−	0.625806i	0.999778	−	0.0210896i	$-0.00671354\pi$
$270$	−10.4740	+	0.935025i	−0.637430	+	0.0569038i
$271$	−5.93627	+	1.92881i	−0.360603	+	0.117167i	−0.483714	−	0.875226i	$-0.660713\pi$
$271$	−5.93627	+	1.92881i	−0.360603	+	0.117167i	0.123112	+	0.992393i	$0.460713\pi$
$272$	0.774499	−	1.52004i	0.0469609	−	0.0921660i
$273$	13.3883	+	17.2575i	0.810296	+	1.04447i
$274$		−	21.5919i		−	1.30441i
$275$	−14.4871	−	27.0153i	−0.873604	−	1.62909i
$276$		−	3.39101i		−	0.204115i
$277$	5.65608	−	0.895835i	0.339841	−	0.0538255i	0.0158183	−	0.999875i	$-0.494965\pi$
$277$	5.65608	−	0.895835i	0.339841	−	0.0538255i	0.324022	+	0.946049i	$0.394965\pi$
$278$	8.07825	+	4.11607i	0.484501	+	0.246866i
$279$	0.689054	+	2.12069i	0.0412526	+	0.126962i
$280$	−5.91213	−	0.216219i	−0.353317	−	0.0129216i
$281$	3.13542	−	9.64984i	0.187044	−	0.575661i	−0.812934	−	0.582356i	$-0.802131\pi$
$281$	3.13542	−	9.64984i	0.187044	−	0.575661i	0.999978	+	0.00669464i	$0.00213099\pi$
$282$	1.84703	−	1.84703i	0.109989	−	0.109989i
$283$	−10.4151	−	20.4407i	−0.619112	−	1.21508i	−0.961315	−	0.275450i	$-0.911173\pi$
$283$	−10.4151	−	20.4407i	−0.619112	−	1.21508i	0.342203	−	0.939626i	$-0.388827\pi$
$284$	−4.69969	−	6.46856i	−0.278875	−	0.383839i
$285$	−13.9768	−	22.2797i	−0.827912	−	1.31974i
$286$	−15.9510	+	21.9546i	−0.943201	+	1.29821i
$287$	1.05108	−	0.378499i	0.0620433	−	0.0223421i
$288$	0.472629	+	0.0748571i	0.0278500	+	0.00441100i
$289$	−8.28168	+	11.3987i	−0.487157	+	0.670515i
$290$	−4.68162	−	18.6365i	−0.274914	−	1.09437i
$291$	−7.41044	+	5.38400i	−0.434408	+	0.315616i
$292$	−10.5549	+	5.37798i	−0.617678	+	0.314723i
$293$	11.7397	−	11.7397i	0.685838	−	0.685838i	−0.275471	−	0.961309i	$-0.588834\pi$
$293$	11.7397	−	11.7397i	0.685838	−	0.685838i	0.961309	+	0.275471i	$0.0888339\pi$
$294$	8.32340	+	10.0583i	0.485430	+	0.586610i
$295$	11.5066	+	26.9752i	0.669942	+	1.57056i
$296$	1.11330	+	3.42637i	0.0647090	+	0.199154i
$297$	−13.0896	+	25.6897i	−0.759533	+	1.49067i
$298$	−0.524203	−	3.30969i	−0.0303663	−	0.191725i
$299$	−8.04777			−0.465415
$300$	7.65779	+	5.32178i	0.442122	+	0.307253i
$301$	−2.34306	+	1.28833i	−0.135052	+	0.0742581i
$302$	12.4509	−	1.97204i	0.716471	−	0.113478i
$303$	−6.89652	+	13.5352i	−0.396194	+	0.777575i
$304$	−1.94881	−	5.99783i	−0.111772	−	0.343999i
$305$	−0.510150	−	0.584769i	−0.0292111	−	0.0334838i
$306$	0.776392	+	0.252265i	0.0443834	+	0.0144210i
$307$	−11.9796	−	11.9796i	−0.683711	−	0.683711i	0.277123	−	0.960834i	$-0.410619\pi$
$307$	−11.9796	−	11.9796i	−0.683711	−	0.683711i	−0.960834	+	0.277123i	$0.910619\pi$
$308$	−9.11651	+	13.4166i	−0.519461	+	0.764484i
$309$	−2.25354	−	3.10173i	−0.128200	−	0.176451i
$310$	−3.88620	+	9.66787i	−0.220721	+	0.549098i
$311$	9.79100	−	13.4762i	0.555196	−	0.764162i	−0.435509	−	0.900184i	$-0.643432\pi$
$311$	9.79100	−	13.4762i	0.555196	−	0.764162i	0.990706	+	0.136022i	$0.0434317\pi$
$312$	1.29144	−	8.15381i	0.0731132	−	0.461618i
$313$	−1.64667	+	10.3967i	−0.0930754	+	0.587655i	0.896433	+	0.443179i	$0.146149\pi$
$313$	−1.64667	+	10.3967i	−0.0930754	+	0.587655i	−0.989508	+	0.144475i	$0.953851\pi$
$314$	9.65923	+	7.01784i	0.545102	+	0.396040i
$315$	−0.340373	−	2.81043i	−0.0191779	−	0.158350i
$316$	1.93532	−	1.40609i	0.108870	−	0.0790989i
$317$	−9.22405	−	18.1032i	−0.518074	−	1.01678i	−0.990770	−	0.135553i	$-0.956719\pi$
$317$	−9.22405	−	18.1032i	−0.518074	−	1.01678i	0.472696	−	0.881226i	$-0.343281\pi$
$318$	−14.1663	+	14.1663i	−0.794407	+	0.794407i
$319$	−50.1071	−	16.2808i	−2.80546	−	0.911549i
$320$	1.46997	+	1.68499i	0.0821741	+	0.0941935i
$321$	−26.6763	+	8.66764i	−1.48892	+	0.483781i
$322$	−4.80802	+	0.151450i	−0.267940	+	0.00843998i
$323$	−1.68304	−	10.6263i	−0.0936469	−	0.591263i
$324$		−	10.2066i		−	0.567032i
$325$	12.6300	−	18.1739i	0.700585	−	1.00811i
$326$	0.121109			0.00670759
$327$	−4.58692	−	28.9607i	−0.253657	−	1.60153i
$328$	−0.376222	−	0.191695i	−0.0207734	−	0.0105846i
$329$	−2.70134	−	2.53635i	−0.148929	−	0.139834i
$330$	23.5184	−	10.0321i	1.29464	−	0.552247i
$331$	2.85199	−	8.77753i	0.156760	−	0.482457i	−0.841575	−	0.540140i	$-0.818371\pi$
$331$	2.85199	−	8.77753i	0.156760	−	0.482457i	0.998335	+	0.0576832i	$0.0183713\pi$
$332$	−5.42940	−	5.42940i	−0.297977	−	0.297977i
$333$	−1.53607	+	0.782665i	−0.0841759	+	0.0428898i
$334$	−17.4388	+	12.6700i	−0.954208	+	0.693273i
$335$	−2.18616	+	0.549179i	−0.119443	+	0.0300049i
$336$	0.618103	−	4.89567i	0.0337203	−	0.267081i
$337$	0.660276	−	4.16882i	0.0359675	−	0.227090i	−0.963156	−	0.268942i	$-0.913326\pi$
$337$	0.660276	−	4.16882i	0.0359675	−	0.227090i	0.999124	+	0.0418524i	$0.0133259\pi$
$338$	−6.51118	−	1.03127i	−0.354162	−	0.0560937i
$339$	−5.17346	−	3.75874i	−0.280984	−	0.204147i
$340$	2.02719	+	3.23146i	0.109940	+	0.175251i
$341$	16.7925	+	23.1128i	0.909363	+	1.25163i
$342$	2.68887	−	1.37005i	0.145397	−	0.0740837i
$343$	13.8896	−	12.2507i	0.749966	−	0.661476i
$344$	0.961173	+	0.312304i	0.0518230	+	0.0168383i
$345$	6.50640	+	3.89380i	0.350293	+	0.209635i
$346$	7.36939	−	2.39446i	0.396181	−	0.128727i
$347$	11.8280	+	6.02666i	0.634960	+	0.323528i	0.741673	−	0.670762i	$-0.234033\pi$
$347$	11.8280	+	6.02666i	0.634960	+	0.323528i	−0.106713	+	0.994290i	$0.534033\pi$
$348$	15.8301	−	2.50725i	0.848585	−	0.134403i
$349$	−17.7099			−0.947991			−0.473996	−	0.880527i	$-0.657189\pi$
$349$	−17.7099			−0.947991			−0.473996	+	0.880527i	$0.657189\pi$
$350$	7.20358	−	11.0954i	0.385047	−	0.593075i
$351$	−20.8159			−1.11107
$352$	6.05544	−	0.959087i	0.322756	−	0.0511195i
$353$	31.7514	+	16.1782i	1.68996	+	0.861076i	0.989008	+	0.147865i	$0.0472402\pi$
$353$	31.7514	+	16.1782i	1.68996	+	0.861076i	0.700949	+	0.713211i	$0.252760\pi$
$354$	−23.2640	+	7.55893i	−1.23647	+	0.401753i
$355$	17.8079	−	1.58972i	0.945143	−	0.0843736i
$356$	2.50878	+	0.815153i	0.132965	+	0.0432030i
$357$	2.34802	−	8.08414i	0.124270	−	0.427858i
$358$	14.2273	−	7.24918i	0.751937	−	0.383131i
$359$	−16.1766	−	22.2652i	−0.853768	−	1.17511i	−0.983020	−	0.183499i	$-0.941258\pi$
$359$	−16.1766	−	22.2652i	−0.853768	−	1.17511i	0.129252	−	0.991612i	$-0.458742\pi$
$360$	−0.686335	+	0.820886i	−0.0361731	+	0.0432645i
$361$	−16.8048	−	12.2094i	−0.884463	−	0.642600i
$362$	−18.9905	−	3.00780i	−0.998120	−	0.158087i
$363$	7.75743	−	48.9785i	0.407160	−	2.57070i
$364$	−11.6187	−	1.46692i	−0.608986	−	0.0768876i
$365$	1.80102	−	26.4272i	0.0942696	−	1.38326i
$366$	0.523653	−	0.380456i	0.0273718	−	0.0198867i
$367$	30.9022	−	15.7455i	1.61308	−	0.821907i	0.613604	−	0.789614i	$-0.289719\pi$
$367$	30.9022	−	15.7455i	1.61308	−	0.821907i	0.999478	−	0.0322928i	$-0.0102809\pi$
$368$	1.28563	+	1.28563i	0.0670183	+	0.0670183i
$369$	0.0624377	−	0.192163i	0.00325038	−	0.0100036i
$370$	−7.85261	−	1.79830i	−0.408238	−	0.0934891i
$371$	20.7187	+	19.4533i	1.07566	+	1.00996i
$372$	−7.74370	−	3.94561i	−0.401492	−	0.204570i
$373$	0.0783049	+	0.494398i	0.00405447	+	0.0255989i	0.989633	−	0.143622i	$-0.0458749\pi$
$373$	0.0783049	+	0.494398i	0.00405447	+	0.0255989i	−0.985578	+	0.169221i	$0.945875\pi$
$374$	10.4592			0.540834
$375$	−19.0042	+	8.58229i	−0.981372	+	0.443188i
$376$			1.40052i			0.0722266i
$377$	−5.95036	−	37.5691i	−0.306459	−	1.93491i
$378$	−12.4362	+	0.391733i	−0.639647	+	0.0201486i
$379$	−5.90413	+	1.91837i	−0.303275	+	0.0985400i	−0.456701	−	0.889620i	$-0.650969\pi$
$379$	−5.90413	+	1.91837i	−0.303275	+	0.0985400i	0.153426	+	0.988160i	$0.450969\pi$
$380$	13.7459	+	3.14790i	0.705150	+	0.161484i
$381$	7.62860	+	2.47868i	0.390825	+	0.126987i
$382$	−15.4846	+	15.4846i	−0.792261	+	0.792261i
$383$	0.615146	+	1.20729i	0.0314325	+	0.0616898i	0.906189	−	0.422873i	$-0.138979\pi$
$383$	0.615146	+	1.20729i	0.0314325	+	0.0616898i	−0.874756	+	0.484563i	$0.838979\pi$
$384$	−1.50888	+	1.09627i	−0.0769998	+	0.0559436i
$385$	−15.2746	−	32.8979i	−0.778463	−	1.67663i
$386$	−5.11503	−	3.71629i	−0.260348	−	0.189154i
$387$	−0.0756534	+	0.477657i	−0.00384568	+	0.0242807i
$388$	0.768284	−	4.85075i	0.0390037	−	0.246260i
$389$	−1.72881	+	2.37950i	−0.0876541	+	0.120645i	−0.850592	−	0.525826i	$-0.823756\pi$
$389$	−1.72881	+	2.37950i	−0.0876541	+	0.120645i	0.762938	+	0.646472i	$0.223756\pi$
$390$	14.1619	+	11.8407i	0.717118	+	0.599575i
$391$	1.82316	+	2.50937i	0.0922013	+	0.126904i
$392$	−6.96903	−	0.657739i	−0.351989	−	0.0332208i
$393$	−18.7373	−	18.7373i	−0.945174	−	0.945174i
$394$	5.76153	+	1.87203i	0.290262	+	0.0943117i
$395$	0.475626	+	5.32791i	0.0239313	+	0.268076i
$396$	0.906585	+	2.79018i	0.0455576	+	0.140212i
$397$	−11.2318	+	22.0437i	−0.563709	+	1.10634i	0.416640	+	0.909072i	$0.363208\pi$
$397$	−11.2318	+	22.0437i	−0.563709	+	1.10634i	−0.980349	+	0.197270i	$0.936792\pi$
$398$	−23.6330	+	3.74309i	−1.18461	+	0.187624i
$399$	−14.9940	−	27.2692i	−0.750638	−	1.36517i
$400$	−4.92094	+	0.885649i	−0.246047	+	0.0442825i
$401$	−9.79598			−0.489188			−0.244594	−	0.969626i	$-0.578655\pi$
$401$	−9.79598			−0.489188			−0.244594	+	0.969626i	$0.578655\pi$
$402$	−0.294114	−	1.85696i	−0.0146691	−	0.0926168i
$403$	−9.36398	+	18.3778i	−0.466453	+	0.915465i
$404$	−2.51691	−	7.74626i	−0.125221	−	0.385391i
$405$	19.5835	+	11.7199i	0.973114	+	0.582367i
$406$	−4.26196	−	22.3331i	−0.211518	−	1.10837i
$407$	−15.6185	+	15.6185i	−0.774180	+	0.774180i
$408$	−2.83500	+	1.44450i	−0.140353	+	0.0715135i
$409$	−22.1737	+	16.1101i	−1.09642	+	0.796593i	−0.980471	−	0.196662i	$-0.936990\pi$
$409$	−22.1737	+	16.1101i	−1.09642	+	0.796593i	−0.115945	+	0.993256i	$0.536990\pi$
$410$	0.799813	−	0.501747i	0.0394999	−	0.0247795i
$411$	−23.6705	+	32.5796i	−1.16758	+	1.60703i
$412$	2.03034	+	0.321575i	0.100028	+	0.0158429i
$413$	11.7566	+	32.6477i	0.578504	+	1.60649i
$414$	−0.511389	+	0.703867i	−0.0251334	+	0.0345932i
$415$	16.6519	−	4.18307i	0.817409	−	0.205339i
$416$	2.60173	+	3.58097i	0.127560	+	0.175572i
$417$	−7.67680	−	15.0666i	−0.375935	−	0.737813i
$418$	27.3400	−	27.3400i	1.33724	−	1.33724i
$419$	−7.43017	+	22.8677i	−0.362988	+	1.11716i	0.588244	+	0.808684i	$0.299819\pi$
$419$	−7.43017	+	22.8677i	−0.362988	+	1.11716i	−0.951232	+	0.308478i	$0.900181\pi$
$420$	8.68366	+	6.80751i	0.423719	+	0.332173i
$421$	4.02786	+	12.3965i	0.196306	+	0.604167i	0.999959	+	0.00906922i	$0.00288686\pi$
$421$	4.02786	+	12.3965i	0.196306	+	0.604167i	−0.803653	+	0.595098i	$0.797113\pi$
$422$	7.84746	+	3.99848i	0.382008	+	0.194643i
$423$	−0.661929	+	0.104839i	−0.0321841	+	0.00509746i
$424$		−	10.7417i		−	0.521664i
$425$	−8.52803	+	0.179028i	−0.413670	+	0.00868412i
$426$			14.9124i			0.722508i
$427$	−0.562824	−	0.725479i	−0.0272370	−	0.0351084i
$428$	6.82760	−	13.3999i	0.330025	−	0.647710i
$429$	48.1363	−	15.6404i	2.32404	−	0.755127i
$430$	−1.70291	+	1.48561i	−0.0821216	+	0.0716425i
$431$	−2.78822	+	8.58125i	−0.134304	+	0.413344i	−0.995481	−	0.0949603i	$-0.969728\pi$
$431$	−2.78822	+	8.58125i	−0.134304	+	0.413344i	0.861177	+	0.508305i	$0.169728\pi$
$432$	3.32535	+	3.32535i	0.159991	+	0.159991i
$433$	5.56256	+	10.9171i	0.267319	+	0.524644i	0.985176	−	0.171547i	$-0.0548766\pi$
$433$	5.56256	+	10.9171i	0.267319	+	0.524644i	−0.717856	+	0.696191i	$0.754877\pi$
$434$	−5.24851	+	11.1558i	−0.251937	+	0.535494i
$435$	−13.3666	+	33.2526i	−0.640878	+	1.59434i
$436$	12.7189	+	9.24081i	0.609124	+	0.442555i
$437$	11.3251	+	1.79371i	0.541751	+	0.0858049i
$438$	21.8218	+	3.45623i	1.04268	+	0.165145i
$439$	22.0087	+	15.9903i	1.05042	+	0.763175i	0.972292	−	0.233768i	$-0.0751058\pi$
$439$	22.0087	+	15.9903i	1.05042	+	0.763175i	0.0781278	+	0.996943i	$0.475106\pi$
$440$	−5.11305	+	12.7200i	−0.243755	+	0.606400i
$441$	−0.210815	−	3.34300i	−0.0100388	−	0.159191i
$442$	3.42818	+	6.72819i	0.163062	+	0.320027i
$443$	1.77414	+	1.77414i	0.0842921	+	0.0842921i	0.747996	−	0.663704i	$-0.231016\pi$
$443$	1.77414	+	1.77414i	0.0842921	+	0.0842921i	−0.663704	+	0.747996i	$0.731016\pi$
$444$	2.07639	−	6.39046i	0.0985409	−	0.303278i
$445$	−4.44480	+	3.87763i	−0.210704	+	0.183817i
$446$	3.95541	−	1.28519i	0.187294	−	0.0608555i
$447$	−2.83734	+	5.56859i	−0.134201	+	0.263385i
$448$	1.62175	+	2.09044i	0.0766206	+	0.0987638i
$449$			24.0657i			1.13573i	0.823122	+	0.567865i	$0.192230\pi$
$449$			24.0657i			1.13573i	−0.823122	+	0.567865i	$0.807770\pi$
$450$	−0.786951	−	2.25948i	−0.0370972	−	0.106513i
$451$		−	2.58874i		−	0.121899i
$452$	3.38646	−	0.536363i	0.159286	−	0.0252284i
$453$	−20.9489	−	10.6740i	−0.984263	−	0.501507i
$454$	−0.188487	−	0.580104i	−0.00884615	−	0.0272256i
$455$	16.1560	−	20.6086i	0.757406	−	0.966147i
$456$	−3.63469	+	11.1864i	−0.170210	+	0.523853i
$457$	−6.97210	+	6.97210i	−0.326141	+	0.326141i	−0.851117	−	0.524976i	$-0.824074\pi$
$457$	−6.97210	+	6.97210i	−0.326141	+	0.326141i	0.524976	+	0.851117i	$0.324074\pi$
$458$	6.89905	+	13.5401i	0.322371	+	0.632690i
$459$	4.71569	+	6.49060i	0.220110	+	0.302955i
$460$	−3.94302	+	0.990515i	−0.183844	+	0.0461830i
$461$	−7.59138	+	10.4486i	−0.353566	+	0.486642i	−0.948342	−	0.317250i	$-0.897241\pi$
$461$	−7.59138	+	10.4486i	−0.353566	+	0.486642i	0.594776	+	0.803891i	$0.297241\pi$
$462$	28.4639	−	10.2500i	1.32426	−	0.476873i
$463$	10.8637	+	1.72063i	0.504877	+	0.0799647i	0.403677	−	0.914901i	$-0.367732\pi$
$463$	10.8637	+	1.72063i	0.504877	+	0.0799647i	0.101200	+	0.994866i	$0.467732\pi$
$464$	−5.05110	+	6.95225i	−0.234492	+	0.322750i
$465$	16.4624	−	10.3273i	0.763424	−	0.478919i
$466$	−17.7332	+	12.8839i	−0.821473	+	0.596835i
$467$	35.5703	−	18.1240i	1.64600	−	0.838677i	0.649037	−	0.760757i	$-0.275172\pi$
$467$	35.5703	−	18.1240i	1.64600	−	0.838677i	0.996960	−	0.0779201i	$-0.0248279\pi$
$468$	−1.49771	+	1.49771i	−0.0692319	+	0.0692319i
$469$	−2.61979	+	0.499951i	−0.120971	+	0.0230856i
$470$	−2.68721	−	1.60818i	−0.123952	−	0.0741798i
$471$	−6.88120	−	21.1782i	−0.317069	−	0.975839i
$472$	5.95426	−	11.6859i	0.274067	−	0.537886i
$473$	0.969289	+	6.11985i	0.0445680	+	0.281391i
$474$	−4.46162			−0.204929
$475$	−21.8239	+	22.7599i	−1.00135	+	1.04430i
$476$	2.17473	+	3.95514i	0.0996788	+	0.181284i
$477$	5.07686	−	0.804095i	0.232453	−	0.0368170i
$478$	4.61236	−	9.05226i	0.210964	−	0.414041i
$479$	−12.3260	−	37.9355i	−0.563189	−	1.73332i	−0.673272	−	0.739395i	$-0.735112\pi$
$479$	−12.3260	−	37.9355i	−0.563189	−	1.73332i	0.110083	−	0.993922i	$-0.464888\pi$
$480$	−0.370824	−	4.15393i	−0.0169257	−	0.189600i
$481$	−15.1662	−	4.92781i	−0.691521	−	0.224689i
$482$	−2.64705	−	2.64705i	−0.120570	−	0.120570i
$483$	7.42075	+	5.04235i	0.337656	+	0.229435i
$484$	15.6281	+	21.5103i	0.710370	+	0.977740i
$485$	8.42503	+	7.04409i	0.382561	+	0.319856i
$486$	−2.89649	+	3.98668i	−0.131387	+	0.180839i
$487$	2.62512	−	16.5744i	0.118956	−	0.751056i	−0.854036	−	0.520214i	$-0.825852\pi$
$487$	2.62512	−	16.5744i	0.118956	−	0.751056i	0.972991	−	0.230842i	$-0.0741479\pi$
$488$	−0.0542901	+	0.342774i	−0.00245760	+	0.0155167i
$489$	−0.182739	−	0.132767i	−0.00826372	−	0.00600395i
$490$	9.26434	−	12.6163i	0.418520	−	0.569948i
$491$	−24.7943	+	18.0141i	−1.11895	+	0.812967i	−0.984050	−	0.177892i	$-0.943072\pi$
$491$	−24.7943	+	18.0141i	−1.11895	+	0.812967i	−0.134903	+	0.990859i	$0.543072\pi$
$492$	0.357526	+	0.701684i	0.0161185	+	0.0316344i
$493$	−10.3664	+	10.3664i	−0.466878	+	0.466878i
$494$	26.5484	+	8.62608i	1.19447	+	0.388106i
$495$	−6.39458	−	1.46440i	−0.287415	−	0.0658199i
$496$	4.43176	−	1.43997i	0.198992	−	0.0646564i
$497$	21.1438	−	0.666020i	0.948431	−	0.0298751i
$498$	2.24025	+	14.1444i	0.100388	+	0.633824i
$499$			11.4072i			0.510657i	0.966854	+	0.255328i	$0.0821836\pi$
$499$			11.4072i			0.510657i	−0.966854	+	0.255328i	$0.917816\pi$
$500$	3.95125	−	10.4589i	0.176705	−	0.467734i
$501$	40.2028			1.79613
$502$	2.34273	+	14.7914i	0.104561	+	0.660172i
$503$	15.3344	+	7.81329i	0.683729	+	0.348377i	0.761109	−	0.648624i	$-0.224655\pi$
$503$	15.3344	+	7.81329i	0.683729	+	0.348377i	−0.0773798	+	0.997002i	$0.524655\pi$
$504$	−0.866601	+	0.922972i	−0.0386015	+	0.0411124i
$505$	17.7530	+	4.06555i	0.789997	+	0.180914i
$506$	−3.44461	+	10.6014i	−0.153132	+	0.471291i
$507$	8.69405	+	8.69405i	0.386116	+	0.386116i
$508$	−3.83197	+	1.95249i	−0.170016	+	0.0866276i
$509$	4.87441	−	3.54146i	0.216054	−	0.156973i	−0.474494	−	0.880258i	$-0.657369\pi$
$509$	4.87441	−	3.54146i	0.216054	−	0.156973i	0.690549	+	0.723286i	$0.257369\pi$
$510$	0.483746	−	7.09823i	0.0214206	−	0.314315i
$511$	3.92587	−	31.0948i	0.173670	−	1.37555i
$512$	0.156434	−	0.987688i	0.00691349	−	0.0436501i
$513$	29.2928	+	4.63952i	1.29331	+	0.204840i
$514$	−7.29839	−	5.30259i	−0.321918	−	0.233887i
$515$	−2.94839	+	3.52640i	−0.129922	+	0.155392i
$516$	−1.10793	−	1.52493i	−0.0487738	−	0.0671314i
$517$	−7.65063	+	3.89819i	−0.336474	+	0.171442i
$518$	−9.15358	−	2.65863i	−0.402185	−	0.116814i
$519$	−13.7445	−	4.46586i	−0.603317	−	0.196029i
$520$	−9.85836	+	0.880063i	−0.432318	+	0.0385933i
$521$	−8.06292	+	2.61980i	−0.353243	+	0.114776i	−0.480263	−	0.877125i	$-0.659459\pi$
$521$	−8.06292	+	2.61980i	−0.353243	+	0.114776i	0.127020	+	0.991900i	$0.459459\pi$
$522$	−3.66395	−	1.86687i	−0.160367	−	0.0817109i
$523$	1.67206	−	0.264828i	0.0731140	−	0.0115801i	−0.119770	−	0.992802i	$-0.538216\pi$
$523$	1.67206	−	0.264828i	0.0731140	−	0.0115801i	0.192884	+	0.981222i	$0.438216\pi$
$524$	14.2078			0.620669
$525$	−23.0329	+	8.84464i	−1.00524	+	0.386012i
$526$	−18.7621			−0.818067
$527$	7.85171	−	1.24359i	0.342026	−	0.0541716i
$528$	−10.1883	−	5.19122i	−0.443391	−	0.225919i
$529$	18.7304	−	6.08587i	0.814364	−	0.264603i
$530$	20.6103	+	12.3344i	0.895256	+	0.535772i
$531$	5.96881	+	1.93938i	0.259024	+	0.0841621i
$532$	16.0232	+	4.65391i	0.694696	+	0.201773i
$533$	1.66528	−	0.848503i	0.0721314	−	0.0367528i
$534$	−2.89183	−	3.98026i	−0.125142	−	0.172243i
$535$	17.8707	+	28.4870i	0.772620	+	1.23160i
$536$	0.815536	+	0.592522i	0.0352258	+	0.0255930i
$537$	−29.4143	−	4.65877i	−1.26932	−	0.201041i
$538$	1.68827	−	10.6593i	0.0727865	−	0.459556i
$539$	−15.8044	−	39.9004i	−0.680745	−	1.71863i
$540$	−10.1988	+	2.56201i	−0.438887	+	0.110251i
$541$	8.34102	−	6.06011i	0.358609	−	0.260544i	−0.393863	−	0.919169i	$-0.628862\pi$
$541$	8.34102	−	6.06011i	0.358609	−	0.260544i	0.752471	+	0.658625i	$0.228862\pi$
$542$	−5.56145	+	2.83370i	−0.238885	+	0.121718i
$543$	25.3571	+	25.3571i	1.08818	+	1.08818i
$544$	0.527177	−	1.62248i	0.0226025	−	0.0695634i
$545$	−32.3352	+	13.7930i	−1.38509	+	0.590828i
$546$	15.9231	+	14.9506i	0.681447	+	0.639827i
$547$	4.29719	+	2.18953i	0.183735	+	0.0936175i	0.543438	−	0.839449i	$-0.317122\pi$
$547$	4.29719	+	2.18953i	0.183735	+	0.0936175i	−0.359704	+	0.933067i	$0.617122\pi$
$548$	−3.37772	−	21.3261i	−0.144289	−	0.911004i
$549$	−0.166069			−0.00708766
$550$	−18.5349	−	24.4165i	−0.790329	−	1.04112i
$551$			54.1946i			2.30877i
$552$	−0.530472	−	3.34927i	−0.0225784	−	0.142554i
$553$	0.199266	+	6.32600i	0.00847363	+	0.269009i
$554$	5.44630	−	1.76961i	0.231391	−	0.0751836i
$555$	9.87724	+	11.3220i	0.419265	+	0.480591i
$556$	8.62269	+	2.80168i	0.365683	+	0.118818i
$557$	−0.352800	+	0.352800i	−0.0149486	+	0.0149486i	−0.714542	−	0.699593i	$-0.753365\pi$
$557$	−0.352800	+	0.352800i	−0.0149486	+	0.0149486i	0.699593	+	0.714542i	$0.253365\pi$
$558$	1.01232	+	1.98679i	0.0428549	+	0.0841075i
$559$	−3.61906	+	2.62940i	−0.153070	+	0.111212i
$560$	−5.87316	+	0.711303i	−0.248186	+	0.0300581i
$561$	−15.7817	−	11.4661i	−0.666305	−	0.484099i
$562$	1.58725	−	10.0215i	0.0669543	−	0.422733i
$563$	−2.39584	+	15.1267i	−0.100973	+	0.637516i	0.884351	+	0.466822i	$0.154601\pi$
$563$	−2.39584	+	15.1267i	−0.100973	+	0.637516i	−0.985324	+	0.170694i	$0.945399\pi$
$564$	1.53535	−	2.11323i	0.0646498	−	0.0889828i
$565$	−2.85944	+	7.11355i	−0.120298	+	0.299269i
$566$	−13.4845	−	18.5598i	−0.566795	−	0.780127i
$567$	22.3357	+	15.1769i	0.938009	+	0.637370i
$568$	−5.65373	−	5.65373i	−0.237225	−	0.237225i
$569$	−22.8803	−	7.43428i	−0.959194	−	0.311661i	−0.212748	−	0.977107i	$-0.568241\pi$
$569$	−22.8803	−	7.43428i	−0.959194	−	0.311661i	−0.746446	+	0.665446i	$0.768241\pi$
$570$	−17.2900	−	19.8190i	−0.724199	−	0.830126i
$571$	−8.97857	−	27.6332i	−0.375742	−	1.15641i	−0.942977	−	0.332858i	$-0.891987\pi$
$571$	−8.97857	−	27.6332i	−0.375742	−	1.15641i	0.567235	−	0.823556i	$-0.308013\pi$
$572$	−12.3201	+	24.1796i	−0.515131	+	1.01100i
$573$	40.3396	−	6.38917i	1.68521	−	0.266911i
$574$	0.978929	−	0.538264i	0.0408597	−	0.0224667i
$575$	2.62713	−	8.70293i	0.109559	−	0.362937i
$576$	0.478521			0.0199384
$577$	1.62615	+	10.2671i	0.0676974	+	0.427424i	0.998139	+	0.0609836i	$0.0194237\pi$
$577$	1.62615	+	10.2671i	0.0676974	+	0.427424i	−0.930441	+	0.366441i	$0.880576\pi$
$578$	−6.39656	+	12.5540i	−0.266062	+	0.522176i
$579$	3.64393	+	11.2149i	0.151437	+	0.466074i
$580$	−7.53938	−	17.6747i	−0.313056	−	0.733902i
$581$	19.9548	−	3.80810i	0.827866	−	0.157987i
$582$	−6.47696	+	6.47696i	−0.268479	+	0.268479i
$583$	58.6787	−	29.8983i	2.43022	−	1.23826i
$584$	−9.58363	+	6.96292i	−0.396573	+	0.288128i
$585$	−1.15391	−	4.59347i	−0.0477084	−	0.189917i
$586$	9.75863	−	13.4316i	0.403125	−	0.554855i
$587$	−15.4093	−	2.44059i	−0.636009	−	0.100734i	−0.169900	−	0.985461i	$-0.554344\pi$
$587$	−15.4093	−	2.44059i	−0.636009	−	0.100734i	−0.466109	+	0.884727i	$0.654344\pi$
$588$	9.79438	+	8.63236i	0.403913	+	0.355993i
$589$	17.2734	−	23.7748i	0.711737	−	0.979622i
$590$	15.5848	+	24.8431i	0.641617	+	1.02277i
$591$	−6.64121	−	9.14085i	−0.273183	−	0.376004i
$592$	1.63559	+	3.21003i	0.0672225	+	0.131932i
$593$	16.9557	−	16.9557i	0.696289	−	0.696289i	−0.267319	−	0.963608i	$-0.586138\pi$
$593$	16.9557	−	16.9557i	0.696289	−	0.696289i	0.963608	+	0.267319i	$0.0861378\pi$
$594$	−8.90965	+	27.4211i	−0.365567	+	1.12510i
$595$	−10.0860	−	0.368866i	−0.413485	−	0.0151220i
$596$	−1.03550	−	3.18694i	−0.0424157	−	0.130542i
$597$	39.7627	+	20.2601i	1.62738	+	0.829192i
$598$	−7.94869	+	1.25895i	−0.325046	+	0.0514822i
$599$			34.9994i			1.43004i	0.699106	+	0.715018i	$0.253582\pi$
$599$			34.9994i			1.43004i	−0.699106	+	0.715018i	$0.746418\pi$
$600$	8.39602	+	4.05832i	0.342766	+	0.165680i
$601$		−	4.05530i		−	0.165419i	−0.996574	−	0.0827095i	$-0.973643\pi$
$601$		−	4.05530i		−	0.165419i	0.996574	−	0.0827095i	$-0.0263574\pi$
$602$	−2.11267	+	1.63900i	−0.0861061	+	0.0668008i
$603$	−0.218994	+	0.429801i	−0.00891814	+	0.0175028i
$604$	11.9892	−	3.89551i	0.487832	−	0.158506i
$605$	−59.2174	+	5.28638i	−2.40753	+	0.214922i
$606$	−4.69424	+	14.4474i	−0.190690	+	0.586885i
$607$	−25.3446	−	25.3446i	−1.02871	−	1.02871i	−0.999576	−	0.0291317i	$-0.990726\pi$
$607$	−25.3446	−	25.3446i	−1.02871	−	1.02871i	−0.0291317	−	0.999576i	$-0.509274\pi$
$608$	−2.86309	−	5.61913i	−0.116114	−	0.227886i
$609$	−18.0522	+	38.3702i	−0.731514	+	1.55484i
$610$	−0.595347	−	0.497765i	−0.0241049	−	0.0201539i
$611$	−5.01524	−	3.64378i	−0.202895	−	0.147412i
$612$	0.806297	+	0.127705i	0.0325926	+	0.00516216i
$613$	−31.1665	−	4.93629i	−1.25880	−	0.199375i	−0.508844	−	0.860859i	$-0.669927\pi$
$613$	−31.1665	−	4.93629i	−1.25880	−	0.199375i	−0.749959	+	0.661484i	$0.769927\pi$
$614$	−13.7061	−	9.95807i	−0.553134	−	0.401875i
$615$	−1.75687	−	0.119731i	−0.0708439	−	0.00482802i
$616$	−6.90544	+	14.6776i	−0.278228	+	0.591377i
$617$	−9.49572	−	18.6364i	−0.382283	−	0.750273i	0.617045	−	0.786928i	$-0.288330\pi$
$617$	−9.49572	−	18.6364i	−0.382283	−	0.750273i	−0.999328	+	0.0366548i	$0.988330\pi$
$618$	−2.71102	−	2.71102i	−0.109053	−	0.109053i
$619$	−10.8099	+	33.2696i	−0.434488	+	1.33722i	0.459122	+	0.888373i	$0.348164\pi$
$619$	−10.8099	+	33.2696i	−0.434488	+	1.33722i	−0.893610	+	0.448844i	$0.851836\pi$
$620$	−2.32597	+	10.1568i	−0.0934131	+	0.407906i
$621$	−8.13189	+	2.64221i	−0.326321	+	0.106028i
$622$	7.56232	−	14.8419i	0.303221	−	0.595105i
$623$	−5.51434	+	4.27800i	−0.220927	+	0.171395i
$624$		−	8.25544i		−	0.330482i
$625$	15.5305	+	19.5909i	0.621220	+	0.783637i
$626$			10.5263i			0.420714i
$627$	−71.2247	+	11.2809i	−2.84444	+	0.450515i
$628$	10.6381	+	5.42040i	0.424508	+	0.216298i
$629$	1.89926	+	5.84533i	0.0757286	+	0.233069i
$630$	−0.775831	−	2.72258i	−0.0309098	−	0.108470i
$631$	−3.16479	+	9.74023i	−0.125988	+	0.387752i	−0.994080	−	0.108652i	$-0.965347\pi$
$631$	−3.16479	+	9.74023i	−0.125988	+	0.387752i	0.868091	+	0.496404i	$0.165347\pi$
$632$	1.69153	−	1.69153i	0.0672855	−	0.0672855i
$633$	−7.45748	−	14.6361i	−0.296408	−	0.581734i
$634$	−11.9425	−	16.4374i	−0.474296	−	0.652812i
$635$	0.653863	−	9.59445i	0.0259478	−	0.380744i
$636$	−11.7758	+	16.2080i	−0.466941	+	0.642689i
$637$	20.4869	−	23.2446i	0.811719	−	0.920986i
$638$	−52.0371	−	8.24187i	−2.06017	−	0.326299i
$639$	2.24890	−	3.09534i	0.0889650	−	0.122450i
$640$	1.71547	+	1.43429i	0.0678098	+	0.0566951i
$641$	−10.5421	+	7.65925i	−0.416386	+	0.302522i	−0.776182	−	0.630509i	$-0.782846\pi$
$641$	−10.5421	+	7.65925i	−0.416386	+	0.302522i	0.359796	+	0.933031i	$0.382846\pi$
$642$	−24.9919	+	12.7340i	−0.986352	+	0.502572i
$643$	7.03626	−	7.03626i	0.277483	−	0.277483i	−0.554620	−	0.832104i	$-0.687136\pi$
$643$	7.03626	−	7.03626i	0.277483	−	0.277483i	0.832104	+	0.554620i	$0.187136\pi$
$644$	−4.72513	+	0.901725i	−0.186196	+	0.0355329i
$645$	4.19811	−	0.374768i	0.165300	−	0.0147565i
$646$	−3.32464	−	10.2322i	−0.130806	−	0.402580i
$647$	1.18471	−	2.32512i	0.0465756	−	0.0914098i	−0.866546	−	0.499098i	$-0.833665\pi$
$647$	1.18471	−	2.32512i	0.0465756	−	0.0914098i	0.913121	+	0.407688i	$0.133665\pi$
$648$	−1.59666	−	10.0809i	−0.0627228	−	0.396016i
$649$	80.4093			3.15634
$650$	9.63146	−	19.9260i	0.377777	−	0.781560i
$651$	20.1491	−	11.0790i	0.789705	−	0.434219i
$652$	0.119618	−	0.0189456i	0.00468459	−	0.000741966i
$653$	4.63189	−	9.09061i	0.181260	−	0.355743i	−0.782442	−	0.622724i	$-0.786026\pi$
$653$	4.63189	−	9.09061i	0.181260	−	0.355743i	0.963702	+	0.266981i	$0.0860261\pi$
$654$	−9.06090	−	27.8866i	−0.354309	−	1.09045i
$655$	−16.3143	+	27.2607i	−0.637454	+	1.06516i
$656$	−0.401578	−	0.130481i	−0.0156790	−	0.00509441i
$657$	−4.00828	−	4.00828i	−0.156378	−	0.156378i
$658$	−3.06485	−	2.08254i	−0.119480	−	0.0811860i
$659$	8.65705	+	11.9154i	0.337231	+	0.464158i	0.943630	−	0.331002i	$-0.107387\pi$
$659$	8.65705	+	11.9154i	0.337231	+	0.464158i	−0.606399	+	0.795160i	$0.707387\pi$
$660$	21.6595	−	13.5876i	0.843093	−	0.528898i
$661$	16.0922	−	22.1490i	0.625913	−	0.861496i	−0.371853	−	0.928292i	$-0.621278\pi$
$661$	16.0922	−	22.1490i	0.625913	−	0.861496i	0.997767	+	0.0667956i	$0.0212775\pi$
$662$	1.44377	−	9.11561i	0.0561138	−	0.354288i
$663$	2.20317	−	13.9102i	0.0855639	−	0.540229i
$664$	−6.21189	−	4.51321i	−0.241068	−	0.175146i
$665$	−27.3285	+	25.4001i	−1.05976	+	0.984975i
$666$	−1.39472	+	1.01332i	−0.0540443	+	0.0392655i
$667$	−7.09327	−	13.9213i	−0.274653	−	0.539036i
$668$	−15.2421	+	15.2421i	−0.589733	+	0.589733i
$669$	−7.37715	−	2.39698i	−0.285217	−	0.0926727i
$670$	−2.07334	+	0.884409i	−0.0801000	+	0.0341677i
$671$	−2.02358	+	0.657501i	−0.0781194	+	0.0253825i
$672$	−0.155358	−	4.93209i	−0.00599308	−	0.190259i
$673$	2.95387	+	18.6500i	0.113863	+	0.718904i	0.976890	+	0.213745i	$0.0685661\pi$
$673$	2.95387	+	18.6500i	0.113863	+	0.718904i	−0.863026	+	0.505159i	$0.831434\pi$
$674$		−	4.22078i		−	0.162578i
$675$	6.79520	−	22.5105i	0.261547	−	0.866431i
$676$	−6.59234			−0.253552
$677$	−4.03034	−	25.4465i	−0.154898	−	0.977990i	−0.935594	−	0.353078i	$-0.885135\pi$
$677$	−4.03034	−	25.4465i	−0.154898	−	0.977990i	0.780695	−	0.624912i	$-0.214865\pi$
$678$	−5.69776	−	2.90315i	−0.218821	−	0.111495i
$679$	9.47277	+	8.89422i	0.363531	+	0.341329i
$680$	2.50775	+	2.87455i	0.0961678	+	0.110234i
$681$	−0.351544	+	1.08194i	−0.0134712	+	0.0414601i
$682$	20.2014	+	20.2014i	0.773550	+	0.773550i
$683$	−21.4150	+	10.9115i	−0.819423	+	0.417517i	−0.812858	−	0.582462i	$-0.802090\pi$
$683$	−21.4150	+	10.9115i	−0.819423	+	0.417517i	−0.00656454	+	0.999978i	$0.502090\pi$
$684$	2.44144	−	1.77381i	0.0933509	−	0.0678234i
$685$	44.7972	+	18.0072i	1.71161	+	0.688019i
$686$	11.8021	−	14.2727i	0.450607	−	0.544934i
$687$	4.43376	−	27.9937i	0.169159	−	1.06803i
$688$	0.998195	+	0.158098i	0.0380558	+	0.00602745i
$689$	38.4658	+	27.9471i	1.46543	+	1.06470i
$690$	7.03542	+	2.82803i	0.267834	+	0.107661i
$691$	−26.6693	−	36.7072i	−1.01455	−	1.39641i	−0.915955	−	0.401280i	$-0.868565\pi$
$691$	−26.6693	−	36.7072i	−1.01455	−	1.39641i	−0.0985942	−	0.995128i	$-0.531435\pi$
$692$	6.90409	−	3.51781i	0.262454	−	0.133727i
$693$	−7.45399	−	2.16499i	−0.283154	−	0.0822413i
$694$	12.6252	+	4.10216i	0.479244	+	0.155716i
$695$	−15.2768	+	13.3274i	−0.579482	+	0.505538i
$696$	15.2430	−	4.95276i	0.577786	−	0.187734i
$697$	−0.641828	−	0.327028i	−0.0243110	−	0.0123871i
$698$	−17.4919	+	2.77045i	−0.662078	+	0.104863i
$699$	40.8814			1.54628
$700$	5.37918	−	12.0857i	0.203314	−	0.456797i
$701$	32.1665			1.21491			0.607456	−	0.794354i	$-0.292190\pi$
$701$	32.1665			1.21491			0.607456	+	0.794354i	$0.292190\pi$
$702$	−20.5597	+	3.25633i	−0.775974	+	0.122902i
$703$	20.2440	+	10.3149i	0.763519	+	0.389032i
$704$	5.83085	−	1.89456i	0.219758	−	0.0714038i
$705$	2.29169	+	5.37245i	0.0863100	+	0.202338i
$706$	33.8913	+	11.0120i	1.27552	+	0.414440i
$707$	20.6942	+	6.01057i	0.778284	+	0.226051i
$708$	−21.7951	+	11.1052i	−0.819110	+	0.417357i
$709$	−12.8972	−	17.7515i	−0.484364	−	0.666670i	0.494972	−	0.868909i	$-0.335178\pi$
$709$	−12.8972	−	17.7515i	−0.484364	−	0.666670i	−0.979336	+	0.202239i	$0.935178\pi$
$710$	17.3399	−	4.35591i	0.650756	−	0.163474i
$711$	0.926091	+	0.672844i	0.0347311	+	0.0252336i
$712$	2.60541	+	0.412657i	0.0976420	+	0.0154650i
$713$	−1.32536	+	8.36802i	−0.0496353	+	0.313385i
$714$	1.05447	−	8.35192i	0.0394626	−	0.312563i
$715$	−32.2471	−	51.4036i	−1.20597	−	1.92239i
$716$	12.9181	−	9.38557i	0.482773	−	0.350755i
$717$	−16.8832	+	8.60241i	−0.630514	+	0.321263i
$718$	−19.4605	−	19.4605i	−0.726258	−	0.726258i
$719$	14.0620	−	43.2783i	0.524423	−	1.61401i	−0.241030	−	0.970518i	$-0.577485\pi$
$719$	14.0620	−	43.2783i	0.524423	−	1.61401i	0.765454	−	0.643491i	$-0.222515\pi$
$720$	−0.549471	+	0.918146i	−0.0204776	+	0.0342173i
$721$	−3.72279	+	3.96495i	−0.138644	+	0.147662i
$722$	−18.5079	−	9.43023i	−0.688792	−	0.350957i
$723$	1.09221	+	6.89596i	0.0406198	+	0.256463i
$724$	−19.2272			−0.714575
$725$	42.5700	+	5.82938i	1.58101	+	0.216498i
$726$		−	49.5890i		−	1.84042i
$727$	−1.93560	−	12.2209i	−0.0717875	−	0.453248i	−0.997231	−	0.0743633i	$-0.976308\pi$
$727$	−1.93560	−	12.2209i	−0.0717875	−	0.453248i	0.925444	−	0.378885i	$-0.123692\pi$
$728$	−11.7051	+	0.368706i	−0.433822	+	0.0136652i
$729$	−20.3802	+	6.62192i	−0.754822	+	0.245256i
$730$	−2.35528	−	26.3836i	−0.0871729	−	0.976500i
$731$	1.63974	+	0.532785i	0.0606481	+	0.0197058i
$732$	0.457689	−	0.457689i	0.0169167	−	0.0169167i
$733$	17.5711	+	34.4852i	0.649003	+	1.27374i	0.947630	+	0.319371i	$0.103472\pi$
$733$	17.5711	+	34.4852i	0.649003	+	1.27374i	−0.298627	+	0.954370i	$0.596528\pi$
$734$	28.0586	−	20.3858i	1.03566	−	0.752453i
$735$	−27.8096	+	8.88038i	−1.02577	+	0.327558i
$736$	1.47092	+	1.06869i	0.0542189	+	0.0393924i
$737$	−0.966815	+	6.10423i	−0.0356131	+	0.224852i
$738$	0.0316080	−	0.199565i	0.00116351	−	0.00734609i
$739$	−27.9688	+	38.4957i	−1.02885	+	1.41609i	−0.123039	+	0.992402i	$0.539264\pi$
$739$	−27.9688	+	38.4957i	−1.02885	+	1.41609i	−0.905809	+	0.423686i	$0.860736\pi$
$740$	−8.03725	−	0.547739i	−0.295455	−	0.0201353i
$741$	−30.6018	−	42.1198i	−1.12419	−	1.54731i
$742$	23.5068	+	15.9727i	0.862960	+	0.586375i
$743$	2.66404	+	2.66404i	0.0977343	+	0.0977343i	0.754283	−	0.656549i	$-0.227985\pi$
$743$	2.66404	+	2.66404i	0.0977343	+	0.0977343i	−0.656549	+	0.754283i	$0.727985\pi$
$744$	−8.26559	−	2.68565i	−0.303031	−	0.0984608i
$745$	7.30386	+	1.67263i	0.267593	+	0.0612805i
$746$	0.154682	+	0.476061i	0.00566330	+	0.0174298i
$747$	1.66807	−	3.27377i	0.0610314	−	0.119781i
$748$	10.3305	−	1.63618i	0.377719	−	0.0598248i
$749$	19.1714	+	34.8666i	0.700507	+	1.27400i
$750$	−17.4277	+	11.4495i	−0.636368	+	0.418078i
$751$	30.3951			1.10913			0.554566	−	0.832140i	$-0.312884\pi$
$751$	30.3951			1.10913			0.554566	+	0.832140i	$0.312884\pi$
$752$	0.219090	+	1.38328i	0.00798940	+	0.0504431i
$753$	12.6804	−	24.8867i	0.462100	−	0.906922i
$754$	−11.7542	−	36.1757i	−0.428063	−	1.31744i
$755$	−6.29239	+	27.4769i	−0.229003	+	0.999987i
$756$	−12.2218	+	2.33235i	−0.444502	+	0.0848269i
$757$	3.94438	−	3.94438i	0.143361	−	0.143361i	−0.631784	−	0.775145i	$-0.717677\pi$
$757$	3.94438	−	3.94438i	0.143361	−	0.143361i	0.775145	+	0.631784i	$0.217677\pi$
$758$	−5.53134	+	2.81836i	−0.200907	+	0.102367i
$759$	16.8195	−	12.2201i	0.610509	−	0.443561i
$760$	14.0691	+	0.958812i	0.510341	+	0.0347798i
$761$	−2.16387	+	2.97831i	−0.0784402	+	0.107964i	−0.846434	−	0.532493i	$-0.821255\pi$
$761$	−2.16387	+	2.97831i	−0.0784402	+	0.107964i	0.767994	+	0.640457i	$0.221255\pi$
$762$	7.92243	+	1.25479i	0.286999	+	0.0454562i
$763$	−39.1348	+	14.0926i	−1.41678	+	0.510188i
$764$	−12.8716	+	17.7163i	−0.465679	+	0.640952i
$765$	−1.17088	+	1.40042i	−0.0423331	+	0.0506322i
$766$	0.796435	+	1.09620i	0.0287764	+	0.0396073i
$767$	26.3555	+	51.7255i	0.951641	+	1.86770i
$768$	−1.31881	+	1.31881i	−0.0475885	+	0.0475885i
$769$	14.6129	−	44.9739i	0.526955	−	1.62180i	−0.233462	−	0.972366i	$-0.575005\pi$
$769$	14.6129	−	44.9739i	0.526955	−	1.62180i	0.760417	−	0.649435i	$-0.224995\pi$
$770$	−20.2329	−	30.1034i	−0.729142	−	1.08485i
$771$	5.19935	+	16.0020i	0.187250	+	0.576297i
$772$	−5.63341	−	2.87037i	−0.202751	−	0.103307i
$773$	−43.6549	+	6.91426i	−1.57016	+	0.248689i	−0.880002	−	0.474971i	$-0.842459\pi$
$773$	−43.6549	+	6.91426i	−1.57016	+	0.248689i	−0.690157	+	0.723660i	$0.742459\pi$
$774$			0.483611i			0.0173830i
$775$	−16.8171	−	16.1256i	−0.604090	−	0.579248i
$776$		−	4.91122i		−	0.176302i
$777$	10.8971	+	14.0463i	0.390931	+	0.503909i
$778$	−1.33529	+	2.62065i	−0.0478724	+	0.0939548i
$779$	−2.53255	+	0.822875i	−0.0907380	+	0.0294826i
$780$	15.8399	+	9.47947i	0.567158	+	0.339420i
$781$	15.1481	−	46.6210i	0.542042	−	1.66823i
$782$	2.19327	+	2.19327i	0.0784311	+	0.0784311i
$783$	−18.3471	−	36.0082i	−0.655671	−	1.28683i
$784$	−6.98612	+	0.440556i	−0.249504	+	0.0157341i
$785$	−22.6157	+	14.1875i	−0.807188	+	0.506374i
$786$	−21.4378	−	15.5755i	−0.764662	−	0.555559i
$787$	−11.4657	−	1.81599i	−0.408708	−	0.0647330i	−0.0513044	−	0.998683i	$-0.516338\pi$
$787$	−11.4657	−	1.81599i	−0.408708	−	0.0647330i	−0.357403	+	0.933950i	$0.616338\pi$
$788$	5.98345	+	0.947685i	0.213151	+	0.0337599i
$789$	28.3098	+	20.5683i	1.00786	+	0.732250i
$790$	1.30324	+	5.18791i	0.0463671	+	0.184577i
$791$	−3.86182	+	8.20835i	−0.137311	+	0.291855i
$792$	1.33190	+	2.61401i	0.0473272	+	0.0928848i
$793$	−1.08622	−	1.08622i	−0.0385727	−	0.0385727i
$794$	−7.64515	+	23.5294i	−0.271316	+	0.835025i
$795$	−17.5768	−	41.2056i	−0.623384	−	1.46141i
$796$	−22.7564	+	7.39402i	−0.806581	+	0.262074i
$797$	−5.74783	+	11.2808i	−0.203599	+	0.399585i	−0.970117	−	0.242638i	$-0.921987\pi$
$797$	−5.74783	+	11.2808i	−0.203599	+	0.399585i	0.766518	+	0.642222i	$0.221987\pi$
$798$	−19.0752	−	24.5879i	−0.675256	−	0.870403i
$799$			2.38927i			0.0845263i
$800$	−4.72181	+	1.64455i	−0.166941	+	0.0581436i
$801$			1.26228i			0.0446006i
$802$	−9.67538	+	1.53243i	−0.341649	+	0.0541120i
$803$	−64.7111	−	32.9720i	−2.28361	−	1.16356i
$804$	−0.580985	−	1.78809i	−0.0204898	−	0.0630610i
$805$	3.69557	−	10.1016i	0.130252	−	0.356035i
$806$	−6.37376	+	19.6164i	−0.224506	+	0.690959i
$807$	−14.2328	+	14.2328i	−0.501020	+	0.501020i
$808$	−3.69771	−	7.25716i	−0.130085	−	0.255306i
$809$	−18.4510	−	25.3956i	−0.648702	−	0.892861i	0.350340	−	0.936622i	$-0.386066\pi$
$809$	−18.4510	−	25.3956i	−0.648702	−	0.892861i	−0.999042	+	0.0437611i	$0.986066\pi$
$810$	21.1758	+	8.51207i	0.744043	+	0.299084i
$811$	17.3198	−	23.8386i	0.608180	−	0.837088i	−0.388247	−	0.921556i	$-0.626919\pi$
$811$	17.3198	−	23.8386i	0.608180	−	0.837088i	0.996426	+	0.0844680i	$0.0269191\pi$
$812$	−7.70316	−	21.3914i	−0.270328	−	0.750692i
$813$	11.4981	+	1.82111i	0.403254	+	0.0638692i
$814$	−12.9829	+	17.8695i	−0.455051	+	0.626325i
$815$	−0.101002	+	0.251267i	−0.00353795	+	0.00880150i
$816$	−2.57412	+	1.87021i	−0.0901123	+	0.0654704i
$817$	5.67890	−	2.89354i	0.198680	−	0.101232i
$818$	−19.3805	+	19.3805i	−0.677623	+	0.677623i
$819$	−1.05048	−	5.50460i	−0.0367066	−	0.192346i
$820$	0.711475	−	0.620688i	0.0248458	−	0.0216754i
$821$	1.02319	+	3.14906i	0.0357097	+	0.109903i	0.967322	−	0.253549i	$-0.0815980\pi$
$821$	1.02319	+	3.14906i	0.0357097	+	0.109903i	−0.931613	+	0.363452i	$0.881598\pi$
$822$	−18.2825	+	35.8814i	−0.637674	+	1.25151i
$823$	−5.12978	−	32.3881i	−0.178813	−	1.12898i	−0.899887	−	0.436122i	$-0.856352\pi$
$823$	−5.12978	−	32.3881i	−0.178813	−	1.12898i	0.721075	−	0.692857i	$-0.243648\pi$
$824$	2.05565			0.0716120
$825$	1.19997	+	57.1607i	0.0417775	+	1.99008i
$826$	16.7191	+	30.4066i	0.581731	+	1.05798i
$827$	18.6812	−	2.95881i	0.649608	−	0.102888i	0.177070	−	0.984198i	$-0.443338\pi$
$827$	18.6812	−	2.95881i	0.649608	−	0.102888i	0.472538	+	0.881310i	$0.343338\pi$
$828$	−0.394984	+	0.775200i	−0.0137267	+	0.0269401i
$829$	−0.981655	−	3.02122i	−0.0340943	−	0.104931i	0.932561	−	0.361012i	$-0.117569\pi$
$829$	−0.981655	−	3.02122i	−0.0340943	−	0.104931i	−0.966655	+	0.256081i	$0.917569\pi$
$830$	15.7925	−	6.73650i	0.548166	−	0.233827i
$831$	−10.1578	−	3.30046i	−0.352370	−	0.114492i
$832$	3.12988	+	3.12988i	0.108509	+	0.108509i
$833$	−11.8890	−	1.12209i	−0.411931	−	0.0388781i
$834$	−9.93922	−	13.6802i	−0.344167	−	0.473705i
$835$	−11.7432	−	46.7472i	−0.406391	−	1.61775i
$836$	22.7265	−	31.2803i	0.786012	−	1.08185i
$837$	−3.42812	+	21.6443i	−0.118493	+	0.748135i
$838$	−3.76140	+	23.7485i	−0.129935	+	0.820379i
$839$	4.45592	+	3.23742i	0.153835	+	0.111768i	0.662040	−	0.749468i	$-0.269691\pi$
$839$	4.45592	+	3.23742i	0.153835	+	0.111768i	−0.508205	+	0.861236i	$0.669691\pi$
$840$	9.64168	+	5.36528i	0.332670	+	0.185120i
$841$	36.2823	−	26.3607i	1.25111	−	0.908988i
$842$	5.91751	+	11.6138i	0.203931	+	0.400237i
$843$	−13.3812	+	13.3812i	−0.460874	+	0.460874i
$844$	8.37634	+	2.72164i	0.288326	+	0.0936827i
$845$	7.56978	−	12.6488i	0.260408	−	0.435134i
$846$	−0.637379	+	0.207097i	−0.0219135	+	0.00712014i
$847$	−70.3108	+	2.21475i	−2.41591	+	0.0760998i
$848$	−1.68038	−	10.6095i	−0.0577044	−	0.364331i
$849$			42.7871i			1.46845i
$850$	−8.39503	+	1.51090i	−0.287947	+	0.0518235i
$851$	−6.55029			−0.224541
$852$	2.33281	+	14.7288i	0.0799209	+	0.504600i
$853$	−20.3444	−	10.3660i	−0.696581	−	0.354926i	0.0695785	−	0.997576i	$-0.477835\pi$
$853$	−20.3444	−	10.3660i	−0.696581	−	0.354926i	−0.766159	+	0.642651i	$0.777835\pi$
$854$	−0.669385	−	0.628502i	−0.0229059	−	0.0215069i
$855$	0.600011	+	6.72125i	0.0205199	+	0.229862i
$856$	4.64733	−	14.3030i	0.158843	−	0.488867i
$857$	8.76401	+	8.76401i	0.299373	+	0.299373i	0.840768	−	0.541395i	$-0.182104\pi$
$857$	8.76401	+	8.76401i	0.299373	+	0.299373i	−0.541395	+	0.840768i	$0.682104\pi$
$858$	45.0969	−	22.9780i	1.53958	−	0.784457i
$859$	−13.9558	+	10.1394i	−0.476164	+	0.345953i	−0.799839	−	0.600215i	$-0.795082\pi$
$859$	−13.9558	+	10.1394i	−0.476164	+	0.345953i	0.323675	+	0.946168i	$0.395082\pi$
$860$	−1.44954	+	1.73371i	−0.0494290	+	0.0591192i
$861$	−2.06717	−	0.260990i	−0.0704489	−	0.00889453i
$862$	−1.41149	+	8.91177i	−0.0480754	+	0.303536i
$863$	22.6440	+	3.58645i	0.770810	+	0.122084i	0.529438	−	0.848348i	$-0.322403\pi$
$863$	22.6440	+	3.58645i	0.770810	+	0.122084i	0.241372	+	0.970433i	$0.422403\pi$
$864$	3.80461	+	2.76421i	0.129436	+	0.0940404i
$865$	−1.17807	+	17.2864i	−0.0400556	+	0.587755i
$866$	7.20189	+	9.91255i	0.244730	+	0.336842i
$867$	23.4141	−	11.9301i	0.795185	−	0.405167i
$868$	−3.43875	+	11.8395i	−0.116719	+	0.401858i
$869$	13.9485	+	4.53214i	0.473170	+	0.153742i
$870$	−8.00015	+	34.9342i	−0.271231	+	1.18438i
$871$	−4.24361	+	1.37883i	−0.143789	+	0.0467199i
$872$	14.0079	+	7.13737i	0.474367	+	0.241702i
$873$	2.32119	−	0.367640i	0.0785602	−	0.0124427i
$874$	11.4662			0.387851
$875$	17.0123	+	24.1988i	0.575121	+	0.818068i
$876$	22.0938			0.746479
$877$	−40.7073	+	6.44740i	−1.37459	+	0.217713i	−0.799641	−	0.600478i	$-0.794977\pi$
$877$	−40.7073	+	6.44740i	−1.37459	+	0.217713i	−0.574946	+	0.818191i	$0.694977\pi$
$878$	24.2392	+	12.3505i	0.818034	+	0.416809i
$879$	−29.4492	+	9.56864i	−0.993298	+	0.322742i
$880$	−3.06026	+	13.3632i	−0.103161	+	0.450474i
$881$	−38.9731	−	12.6631i	−1.31304	−	0.426632i	−0.432939	−	0.901423i	$-0.642523\pi$
$881$	−38.9731	−	12.6631i	−1.31304	−	0.426632i	−0.880098	+	0.474792i	$0.842523\pi$
$882$	−0.731181	−	3.26887i	−0.0246201	−	0.110069i
$883$	−13.9051	+	7.08500i	−0.467944	+	0.238429i	−0.672030	−	0.740523i	$-0.734578\pi$
$883$	−13.9051	+	7.08500i	−0.467944	+	0.238429i	0.204086	+	0.978953i	$0.434578\pi$
$884$	4.43850	+	6.10907i	0.149283	+	0.205470i
$885$	3.71898	−	54.5704i	0.125012	−	1.83436i
$886$	2.02984	+	1.47476i	0.0681937	+	0.0495456i
$887$	25.3945	+	4.02209i	0.852663	+	0.135049i	0.567442	−	0.823413i	$-0.307933\pi$
$887$	25.3945	+	4.02209i	0.852663	+	0.135049i	0.285221	+	0.958462i	$0.407933\pi$
$888$	1.05113	−	6.63660i	0.0352738	−	0.222710i
$889$	1.42530	−	11.2890i	0.0478029	−	0.378622i
$890$	−3.78349	+	4.52521i	−0.126823	+	0.151685i
$891$	50.6248	−	36.7811i	1.69600	−	1.23221i
$892$	3.70566	−	1.88813i	0.124075	−	0.0632193i
$893$	6.24545	+	6.24545i	0.208996	+	0.208996i
$894$	−1.93129	+	5.94389i	−0.0645919	+	0.198793i
$895$	3.17477	+	35.5634i	0.106121	+	1.18875i
$896$	1.92880	+	1.81100i	0.0644368	+	0.0605013i
$897$	13.3738	+	6.81427i	0.446537	+	0.227522i
$898$	3.76470	+	23.7694i	0.125630	+	0.793195i
$899$	−40.0440			−1.33554
$900$	−1.13072	−	2.10856i	−0.0376908	−	0.0702853i
$901$		−	18.3252i		−	0.610500i
$902$	−0.404969	−	2.55687i	−0.0134840	−	0.0851346i
$903$	4.98455	−	0.157011i	0.165876	−	0.00522499i
$904$	3.26086	−	1.05952i	0.108455	−	0.0352391i
$905$	22.0781	−	36.8917i	0.733899	−	1.22632i
$906$	−22.3607	−	7.26544i	−0.742885	−	0.241378i
$907$	27.9077	−	27.9077i	0.926659	−	0.926659i	−0.0708297	−	0.997488i	$-0.522565\pi$
$907$	27.9077	−	27.9077i	0.926659	−	0.926659i	0.997488	+	0.0708297i	$0.0225647\pi$
$908$	−0.276915	−	0.543476i	−0.00918975	−	0.0180359i
$909$	3.15315	−	2.29089i	0.104583	−	0.0759842i
$910$	12.7332	−	22.8822i	0.422102	−	0.758539i
$911$	19.6281	+	14.2606i	0.650308	+	0.472476i	0.863376	−	0.504561i	$-0.168346\pi$
$911$	19.6281	+	14.2606i	0.650308	+	0.472476i	−0.213068	+	0.977037i	$0.568346\pi$
$912$	−1.84000	+	11.6173i	−0.0609285	+	0.384687i
$913$	7.36418	−	46.4956i	0.243719	−	1.53878i
$914$	−5.79558	+	7.97693i	−0.191701	+	0.263854i
$915$	0.352626	+	1.40373i	0.0116575	+	0.0464058i
$916$	8.93226	+	12.2942i	0.295130	+	0.406212i
$917$	−21.1266	+	31.0917i	−0.697660	+	1.02674i
$918$	5.67299	+	5.67299i	0.187237	+	0.187237i
$919$	−39.0215	−	12.6789i	−1.28720	−	0.418237i	−0.416090	−	0.909323i	$-0.636600\pi$
$919$	−39.0215	−	12.6789i	−1.28720	−	0.418237i	−0.871111	+	0.491086i	$0.836600\pi$
$920$	−3.73953	+	1.59514i	−0.123289	+	0.0525904i
$921$	9.76419	+	30.0511i	0.321741	+	0.990217i
$922$	−5.86339	+	11.5076i	−0.193101	+	0.378981i
$923$	34.9553	−	5.53638i	1.15057	−	0.182232i
$924$	26.5100	−	14.5765i	0.872117	−	0.479533i
$925$	10.2799	−	14.7923i	0.338000	−	0.486366i
$926$	10.9991			0.361452
$927$	0.153880	+	0.971562i	0.00505409	+	0.0319103i
$928$	−3.90135	+	7.65682i	−0.128068	+	0.251348i
$929$	3.20383	+	9.86038i	0.105114	+	0.323509i	0.989757	−	0.142760i	$-0.0455978\pi$
$929$	3.20383	+	9.86038i	0.105114	+	0.323509i	−0.884643	+	0.466269i	$0.845598\pi$
$930$	14.6441	−	12.7755i	0.480200	−	0.418925i
$931$	−34.0105	+	28.1444i	−1.11465	+	0.922394i
$932$	−15.4994	+	15.4994i	−0.507698	+	0.507698i
$933$	−27.6813	+	14.1043i	−0.906245	+	0.461755i
$934$	32.2971	−	23.4652i	1.05679	−	0.767806i
$935$	−8.72277	+	21.7000i	−0.285265	+	0.709667i
$936$	−1.24498	+	1.71357i	−0.0406935	+	0.0560098i
$937$	−34.1963	−	5.41616i	−1.11714	−	0.176938i	−0.429557	−	0.903040i	$-0.641330\pi$
$937$	−34.1963	−	5.41616i	−1.11714	−	0.176938i	−0.687587	+	0.726102i	$0.741330\pi$
$938$	−2.50933	+	0.903622i	−0.0819325	+	0.0295043i
$939$	11.5396	−	15.8829i	0.376580	−	0.518318i
$940$	−2.90570	−	1.16801i	−0.0947736	−	0.0380962i
$941$	13.5381	+	18.6336i	0.441328	+	0.607436i	0.970507	−	0.241074i	$-0.0774997\pi$
$941$	13.5381	+	18.6336i	0.441328	+	0.607436i	−0.529178	+	0.848511i	$0.677500\pi$
$942$	−10.1095	−	19.8410i	−0.329385	−	0.646454i
$943$	0.542851	−	0.542851i	0.0176777	−	0.0176777i
$944$	4.05287	−	12.4735i	0.131910	−	0.405977i
$945$	9.55875	−	26.1283i	0.310946	−	0.849954i
$946$	1.91471	+	5.89287i	0.0622526	+	0.191594i
$947$	2.36280	+	1.20391i	0.0767808	+	0.0391218i	0.491959	−	0.870618i	$-0.336281\pi$
$947$	2.36280	+	1.20391i	0.0767808	+	0.0391218i	−0.415179	+	0.909740i	$0.636281\pi$
$948$	−4.40669	+	0.697951i	−0.143123	+	0.0226684i
$949$		−	52.4343i		−	1.70209i
$950$	−17.9948	+	25.8937i	−0.583829	+	0.840102i
$951$			37.8942i			1.22880i
$952$	2.76668	+	3.56624i	0.0896686	+	0.115583i
$953$	−26.7032	+	52.4079i	−0.865000	+	1.69766i	−0.161609	+	0.986855i	$0.551668\pi$
$953$	−26.7032	+	52.4079i	−0.865000	+	1.69766i	−0.703391	+	0.710803i	$0.748332\pi$
$954$	4.88856	−	1.58839i	0.158273	−	0.0514260i
$955$	−19.2124	−	45.0401i	−0.621700	−	1.45746i
$956$	3.13949	−	9.66235i	0.101538	−	0.312503i
$957$	69.4825	+	69.4825i	2.24605	+	2.24605i
$958$	−18.1087	−	35.5402i	−0.585064	−	1.14825i
$959$	51.6916	+	24.3196i	1.66921	+	0.785321i
$960$	−1.01608	−	4.04477i	−0.0327937	−	0.130545i
$961$	−7.51250	−	5.45815i	−0.242339	−	0.176069i
$962$	−15.7504	−	2.49462i	−0.507813	−	0.0804297i
$963$	7.10791	+	1.12578i	0.229049	+	0.0362778i
$964$	−3.02855	−	2.20037i	−0.0975431	−	0.0708692i
$965$	11.9761	−	7.51298i	0.385524	−	0.241851i
$966$	8.11819	+	3.81940i	0.261198	+	0.122887i
$967$	−2.38395	−	4.67876i	−0.0766625	−	0.150459i	0.849494	−	0.527599i	$-0.176908\pi$
$967$	−2.38395	−	4.67876i	−0.0766625	−	0.150459i	−0.926156	+	0.377140i	$0.876908\pi$
$968$	18.8007	+	18.8007i	0.604276	+	0.604276i
$969$	−6.20072	+	19.0838i	−0.199196	+	0.613061i
$970$	9.42324	+	5.63940i	0.302562	+	0.181070i
$971$	9.31119	−	3.02539i	0.298810	−	0.0970893i	−0.155775	−	0.987793i	$-0.549787\pi$
$971$	9.31119	−	3.02539i	0.298810	−	0.0970893i	0.454585	+	0.890703i	$0.349787\pi$
$972$	−2.23718	+	4.39071i	−0.0717575	+	0.140832i
$973$	−18.9528	+	14.7035i	−0.607598	+	0.471373i
$974$		−	16.7810i		−	0.537697i
$975$	−36.3769	+	19.5073i	−1.16499	+	0.624732i
$976$			0.347047i			0.0111087i
$977$	4.07447	−	0.645332i	0.130354	−	0.0206460i	−0.0909166	−	0.995859i	$-0.528980\pi$
$977$	4.07447	−	0.645332i	0.130354	−	0.0206460i	0.221270	+	0.975213i	$0.428980\pi$
$978$	−0.201258	−	0.102546i	−0.00643553	−	0.00327906i
$979$	4.99763	+	15.3811i	0.159725	+	0.491583i
$980$	7.17665	−	13.9103i	0.229250	−	0.444347i
$981$	−2.32474	+	7.15482i	−0.0742233	+	0.228436i
$982$	−21.6711	+	21.6711i	−0.691551	+	0.691551i
$983$	5.87689	+	11.5341i	0.187444	+	0.367879i	0.965535	−	0.260272i	$-0.0838121\pi$
$983$	5.87689	+	11.5341i	0.187444	+	0.367879i	−0.778092	+	0.628151i	$0.783812\pi$
$984$	0.462892	+	0.637116i	0.0147565	+	0.0203105i
$985$	−8.68895	+	10.3923i	−0.276853	+	0.331128i
$986$	−8.61709	+	11.8604i	−0.274424	+	0.377712i
$987$	2.34147	+	6.50220i	0.0745299	+	0.206967i
$988$	27.5709	+	4.36680i	0.877148	+	0.138927i
$989$	−1.08006	+	1.48657i	−0.0343438	+	0.0472702i
$990$	−6.54493	−	0.446038i	−0.208012	−	0.0141760i
$991$	−20.9604	+	15.2287i	−0.665830	+	0.483754i	−0.868627	−	0.495467i	$-0.834997\pi$
$991$	−20.9604	+	15.2287i	−0.665830	+	0.483754i	0.202796	+	0.979221i	$0.434997\pi$
$992$	4.15194	−	2.11552i	0.131824	−	0.0671678i
$993$	−12.1716	+	12.1716i	−0.386255	+	0.386255i
$994$	20.7793	−	3.96545i	0.659080	−	0.125776i
$995$	11.9435	−	52.1535i	0.378634	−	1.65338i
$996$	4.42533	+	13.6198i	0.140222	+	0.431559i
$997$	7.75926	−	15.2284i	0.245738	−	0.482289i	−0.734885	−	0.678192i	$-0.762764\pi$
$997$	7.75926	−	15.2284i	0.245738	−	0.482289i	0.980623	+	0.195903i	$0.0627639\pi$
$998$	1.78448	+	11.2668i	0.0564867	+	0.356643i
$999$	−16.9426			−0.536042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.13.12	✓	160
7.6	odd	2	inner	350.2.r.a.13.19	yes	160
25.2	odd	20	inner	350.2.r.a.27.19	yes	160
175.27	even	20	inner	350.2.r.a.27.12	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.12	✓	160	1.1	even	1	trivial
350.2.r.a.13.19	yes	160	7.6	odd	2	inner
350.2.r.a.27.12	yes	160	175.27	even	20	inner
350.2.r.a.27.19	yes	160	25.2	odd	20	inner

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.66180 - 0.846728i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.499152 + 2.17964i) q^{5} +(-1.77380 - 0.576341i) q^{6} +(-0.737955 + 2.54075i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.281267 + 0.387131i) q^{9} +O(q^{10})\)	\(q+(0.987688 - 0.156434i) q^{2} +(-1.66180 - 0.846728i) q^{3} +(0.951057 - 0.309017i) q^{4} +(-0.499152 + 2.17964i) q^{5} +(-1.77380 - 0.576341i) q^{6} +(-0.737955 + 2.54075i) q^{7} +(0.891007 - 0.453990i) q^{8} +(0.281267 + 0.387131i) q^{9} +(-0.152036 + 2.23089i) q^{10} +(4.96002 + 3.60366i) q^{11} +(-1.84212 - 0.291763i) q^{12} +(-0.692430 + 4.37183i) q^{13} +(-0.331409 + 2.62491i) q^{14} +(2.67506 - 3.19948i) q^{15} +(0.809017 - 0.587785i) q^{16} +(1.52004 - 0.774499i) q^{17} +(0.338365 + 0.338365i) q^{18} +(1.94881 - 5.99783i) q^{19} +(0.198825 + 2.22721i) q^{20} +(3.37766 - 3.59737i) q^{21} +(5.46269 + 2.78338i) q^{22} +(0.284423 + 1.79578i) q^{23} -1.86508 q^{24} +(-4.50169 - 2.17595i) q^{25} +4.42632i q^{26} +(0.735674 + 4.64486i) q^{27} +(0.0832985 + 2.64444i) q^{28} +(-8.17286 + 2.65552i) q^{29} +(2.14161 - 3.57856i) q^{30} +(4.43176 + 1.43997i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.19122 - 10.1883i) q^{33} +(1.38017 - 1.00275i) q^{34} +(-5.16958 - 2.87670i) q^{35} +(0.387131 + 0.281267i) q^{36} +(-0.563587 + 3.55835i) q^{37} +(0.986553 - 6.22885i) q^{38} +(4.85243 - 6.67880i) q^{39} +(0.544789 + 2.16869i) q^{40} +(-0.248189 - 0.341603i) q^{41} +(2.77332 - 4.08146i) q^{42} +(0.714628 + 0.714628i) q^{43} +(5.83085 + 1.89456i) q^{44} +(-0.984204 + 0.419825i) q^{45} +(0.561843 + 1.72917i) q^{46} +(-0.635825 + 1.24788i) q^{47} +(-1.84212 + 0.291763i) q^{48} +(-5.91084 - 3.74992i) q^{49} +(-4.78666 - 1.44494i) q^{50} -3.18179 q^{51} +(0.692430 + 4.37183i) q^{52} +(4.87664 - 9.57095i) q^{53} +(1.45323 + 4.47259i) q^{54} +(-10.3305 + 9.01229i) q^{55} +(0.495954 + 2.59885i) q^{56} +(-8.31707 + 8.31707i) q^{57} +(-7.65682 + 3.90135i) q^{58} +(10.6106 - 7.70902i) q^{59} +(1.55544 - 3.86952i) q^{60} +(-0.203989 + 0.280767i) q^{61} +(4.60246 + 0.728958i) q^{62} +(-1.19117 + 0.428945i) q^{63} +(0.587785 - 0.809017i) q^{64} +(-9.18340 - 3.69146i) q^{65} +(-6.72112 - 9.25083i) q^{66} +(0.457649 + 0.898186i) q^{67} +(1.20631 - 1.20631i) q^{68} +(1.04788 - 3.22505i) q^{69} +(-5.55595 - 2.03258i) q^{70} +(-2.47077 - 7.60425i) q^{71} +(0.426365 + 0.217244i) q^{72} +(-11.7002 + 1.85313i) q^{73} +3.60270i q^{74} +(5.63847 + 7.42770i) q^{75} -6.30649i q^{76} +(-12.8163 + 9.94283i) q^{77} +(3.74789 - 7.35566i) q^{78} +(2.27511 - 0.739227i) q^{79} +(0.877340 + 2.05676i) q^{80} +(3.15401 - 9.70703i) q^{81} +(-0.298572 - 0.298572i) q^{82} +(-3.48589 - 6.84144i) q^{83} +(2.10070 - 4.46506i) q^{84} +(0.929401 + 3.69974i) q^{85} +(0.817623 + 0.594038i) q^{86} +(15.8301 + 2.50725i) q^{87} +(6.05544 + 0.959087i) q^{88} +(2.13410 + 1.55051i) q^{89} +(-0.906412 + 0.568620i) q^{90} +(-10.5968 - 4.98551i) q^{91} +(0.825428 + 1.61999i) q^{92} +(-6.14543 - 6.14543i) q^{93} +(-0.432786 + 1.33198i) q^{94} +(12.1004 + 7.24155i) q^{95} +(-1.77380 + 0.576341i) q^{96} +(2.22965 - 4.37593i) q^{97} +(-6.42469 - 2.77910i) q^{98} +2.93377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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