LMFDB - Embedded newform 429.2.j.a.122.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.11
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28581 - 1.28581i) q^{2} +(0.911426 + 1.47286i) q^{3} +1.30661i q^{4} +(-1.56311 - 1.56311i) q^{5} +(0.721891 - 3.06573i) q^{6} +(-0.788371 - 0.788371i) q^{7} +(-0.891573 + 0.891573i) q^{8} +(-1.33861 + 2.68480i) q^{9} +O(q^{10})$	\(q+(-1.28581 - 1.28581i) q^{2} +(0.911426 + 1.47286i) q^{3} +1.30661i q^{4} +(-1.56311 - 1.56311i) q^{5} +(0.721891 - 3.06573i) q^{6} +(-0.788371 - 0.788371i) q^{7} +(-0.891573 + 0.891573i) q^{8} +(-1.33861 + 2.68480i) q^{9} +4.01973i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-1.92444 + 1.19087i) q^{12} +(-0.313323 + 3.59191i) q^{13} +2.02739i q^{14} +(0.877579 - 3.72690i) q^{15} +4.90599 q^{16} -0.522034 q^{17} +(5.17332 - 1.73094i) q^{18} +(-2.83758 + 2.83758i) q^{19} +(2.04237 - 2.04237i) q^{20} +(0.442615 - 1.87970i) q^{21} +1.81841 q^{22} +1.33838 q^{23} +(-2.12576 - 0.500556i) q^{24} -0.113347i q^{25} +(5.02138 - 4.21564i) q^{26} +(-5.17436 + 0.475417i) q^{27} +(1.03009 - 1.03009i) q^{28} +9.04928i q^{29} +(-5.92048 + 3.66369i) q^{30} +(-6.68703 + 6.68703i) q^{31} +(-4.52502 - 4.52502i) q^{32} +(-1.68594 - 0.396991i) q^{33} +(0.671235 + 0.671235i) q^{34} +2.46463i q^{35} +(-3.50797 - 1.74903i) q^{36} +(-0.119561 - 0.119561i) q^{37} +7.29717 q^{38} +(-5.57594 + 2.81228i) q^{39} +2.78726 q^{40} +(-5.69017 - 5.69017i) q^{41} +(-2.98605 + 1.84781i) q^{42} +9.38452i q^{43} +(-0.923909 - 0.923909i) q^{44} +(6.28904 - 2.10425i) q^{45} +(-1.72089 - 1.72089i) q^{46} +(5.82272 - 5.82272i) q^{47} +(4.47145 + 7.22582i) q^{48} -5.75694i q^{49} +(-0.145742 + 0.145742i) q^{50} +(-0.475795 - 0.768880i) q^{51} +(-4.69321 - 0.409390i) q^{52} +8.31755i q^{53} +(7.26453 + 6.04194i) q^{54} +2.21058 q^{55} +1.40578 q^{56} +(-6.76559 - 1.59310i) q^{57} +(11.6356 - 11.6356i) q^{58} +(3.09303 - 3.09303i) q^{59} +(4.86959 + 1.14665i) q^{60} -9.64192 q^{61} +17.1965 q^{62} +(3.17194 - 1.06130i) q^{63} +1.82463i q^{64} +(6.10433 - 5.12481i) q^{65} +(1.65734 + 2.67825i) q^{66} +(2.44408 - 2.44408i) q^{67} -0.682092i q^{68} +(1.21983 + 1.97123i) q^{69} +(3.16904 - 3.16904i) q^{70} +(6.93216 + 6.93216i) q^{71} +(-1.20023 - 3.58716i) q^{72} +(0.0568680 + 0.0568680i) q^{73} +0.307464i q^{74} +(0.166944 - 0.103307i) q^{75} +(-3.70760 - 3.70760i) q^{76} +1.11493 q^{77} +(10.7856 + 3.55353i) q^{78} -4.05593 q^{79} +(-7.66863 - 7.66863i) q^{80} +(-5.41626 - 7.18777i) q^{81} +14.6329i q^{82} +(-1.21562 - 1.21562i) q^{83} +(2.45602 + 0.578323i) q^{84} +(0.815998 + 0.815998i) q^{85} +(12.0667 - 12.0667i) q^{86} +(-13.3283 + 8.24774i) q^{87} -1.26087i q^{88} +(-6.40992 + 6.40992i) q^{89} +(-10.7922 - 5.38084i) q^{90} +(3.07878 - 2.58474i) q^{91} +1.74873i q^{92} +(-15.9438 - 3.75430i) q^{93} -14.9738 q^{94} +8.87093 q^{95} +(2.54048 - 10.7889i) q^{96} +(4.46187 - 4.46187i) q^{97} +(-7.40232 + 7.40232i) q^{98} +(-0.951900 - 2.84498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.28581	−	1.28581i	−0.909204	−	0.909204i	0.0870043	−	0.996208i	$-0.472271\pi$
$2$	−1.28581	−	1.28581i	−0.909204	−	0.909204i	−0.996208	+	0.0870043i	$0.972271\pi$
$3$	0.911426	+	1.47286i	0.526212	+	0.850354i
$3$	0.911426	+	1.47286i	0.526212	+	0.850354i
$4$			1.30661i			0.653303i
$5$	−1.56311	−	1.56311i	−0.699046	−	0.699046i	0.265159	−	0.964205i	$-0.414576\pi$
$5$	−1.56311	−	1.56311i	−0.699046	−	0.699046i	−0.964205	+	0.265159i	$0.914576\pi$
$6$	0.721891	−	3.06573i	0.294711	−	1.25158i
$7$	−0.788371	−	0.788371i	−0.297976	−	0.297976i	0.542244	−	0.840221i	$-0.317575\pi$
$7$	−0.788371	−	0.788371i	−0.297976	−	0.297976i	−0.840221	+	0.542244i	$0.817575\pi$
$8$	−0.891573	+	0.891573i	−0.315219	+	0.315219i
$9$	−1.33861	+	2.68480i	−0.446202	+	0.894932i
$10$			4.01973i			1.27115i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	−1.92444	+	1.19087i	−0.555538	+	0.343776i
$13$	−0.313323	+	3.59191i	−0.0869003	+	0.996217i
$13$	−0.313323	+	3.59191i	−0.0869003	+	0.996217i
$14$			2.02739i			0.541842i
$15$	0.877579	−	3.72690i	0.226590	−	0.962282i
$16$	4.90599			1.22650
$17$	−0.522034			−0.126612			−0.0633059	−	0.997994i	$-0.520164\pi$
$17$	−0.522034			−0.126612			−0.0633059	+	0.997994i	$0.520164\pi$
$18$	5.17332	−	1.73094i	1.21936	−	0.407987i
$19$	−2.83758	+	2.83758i	−0.650986	+	0.650986i	−0.953230	−	0.302245i	$-0.902264\pi$
$19$	−2.83758	+	2.83758i	−0.650986	+	0.650986i	0.302245	+	0.953230i	$0.402264\pi$
$20$	2.04237	−	2.04237i	0.456689	−	0.456689i
$21$	0.442615	−	1.87970i	0.0965866	−	0.410184i
$22$	1.81841			0.387686
$23$	1.33838			0.279071			0.139535	−	0.990217i	$-0.455439\pi$
$23$	1.33838			0.279071			0.139535	+	0.990217i	$0.455439\pi$
$24$	−2.12576	−	0.500556i	−0.433919	−	0.102175i
$25$		−	0.113347i		−	0.0226694i
$26$	5.02138	−	4.21564i	0.984774	−	0.826754i
$27$	−5.17436	+	0.475417i	−0.995806	+	0.0914941i
$28$	1.03009	−	1.03009i	0.194669	−	0.194669i
$29$			9.04928i			1.68041i	0.542270	+	0.840204i	$0.317565\pi$
$29$			9.04928i			1.68041i	−0.542270	+	0.840204i	$0.682435\pi$
$30$	−5.92048	+	3.66369i	−1.08093	+	0.668894i
$31$	−6.68703	+	6.68703i	−1.20103	+	1.20103i	−0.227171	+	0.973855i	$0.572948\pi$
$31$	−6.68703	+	6.68703i	−1.20103	+	1.20103i	−0.973855	+	0.227171i	$0.927052\pi$
$32$	−4.52502	−	4.52502i	−0.799918	−	0.799918i
$33$	−1.68594	−	0.396991i	−0.293485	−	0.0691073i
$34$	0.671235	+	0.671235i	0.115116	+	0.115116i
$35$			2.46463i			0.416598i
$36$	−3.50797	−	1.74903i	−0.584662	−	0.291505i
$37$	−0.119561	−	0.119561i	−0.0196556	−	0.0196556i	0.697211	−	0.716866i	$-0.254424\pi$
$37$	−0.119561	−	0.119561i	−0.0196556	−	0.0196556i	−0.716866	+	0.697211i	$0.754424\pi$
$38$	7.29717			1.18376
$39$	−5.57594	+	2.81228i	−0.892865	+	0.450325i
$40$	2.78726			0.440704
$41$	−5.69017	−	5.69017i	−0.888655	−	0.888655i	0.105739	−	0.994394i	$-0.466279\pi$
$41$	−5.69017	−	5.69017i	−0.888655	−	0.888655i	−0.994394	+	0.105739i	$0.966279\pi$
$42$	−2.98605	+	1.84781i	−0.460758	+	0.285124i
$43$			9.38452i			1.43113i	0.698548	+	0.715563i	$0.253830\pi$
$43$			9.38452i			1.43113i	−0.698548	+	0.715563i	$0.746170\pi$
$44$	−0.923909	−	0.923909i	−0.139285	−	0.139285i
$45$	6.28904	−	2.10425i	0.937515	−	0.313683i
$46$	−1.72089	−	1.72089i	−0.253732	−	0.253732i
$47$	5.82272	−	5.82272i	0.849331	−	0.849331i	−0.140719	−	0.990050i	$-0.544941\pi$
$47$	5.82272	−	5.82272i	0.849331	−	0.849331i	0.990050	+	0.140719i	$0.0449414\pi$
$48$	4.47145	+	7.22582i	0.645398	+	1.04296i
$49$		−	5.75694i		−	0.822420i
$50$	−0.145742	+	0.145742i	−0.0206111	+	0.0206111i
$51$	−0.475795	−	0.768880i	−0.0666246	−	0.107665i
$52$	−4.69321	−	0.409390i	−0.650831	−	0.0567722i
$53$			8.31755i			1.14250i	0.820775	+	0.571252i	$0.193542\pi$
$53$			8.31755i			1.14250i	−0.820775	+	0.571252i	$0.806458\pi$
$54$	7.26453	+	6.04194i	0.988577	+	0.822203i
$55$	2.21058			0.298074
$56$	1.40578			0.187855
$57$	−6.76559	−	1.59310i	−0.896124	−	0.211012i
$58$	11.6356	−	11.6356i	1.52783	−	1.52783i
$59$	3.09303	−	3.09303i	0.402678	−	0.402678i	−0.476498	−	0.879176i	$-0.658094\pi$
$59$	3.09303	−	3.09303i	0.402678	−	0.402678i	0.879176	+	0.476498i	$0.158094\pi$
$60$	4.86959	+	1.14665i	0.628662	+	0.148032i
$61$	−9.64192			−1.23452			−0.617260	−	0.786759i	$-0.711758\pi$
$61$	−9.64192			−1.23452			−0.617260	+	0.786759i	$0.711758\pi$
$62$	17.1965			2.18395
$63$	3.17194	−	1.06130i	0.399626	−	0.133711i
$64$			1.82463i			0.228079i
$65$	6.10433	−	5.12481i	0.757149	−	0.635654i
$66$	1.65734	+	2.67825i	0.204005	+	0.329670i
$67$	2.44408	−	2.44408i	0.298592	−	0.298592i	−0.541870	−	0.840462i	$-0.682284\pi$
$67$	2.44408	−	2.44408i	0.298592	−	0.298592i	0.840462	+	0.541870i	$0.182284\pi$
$68$		−	0.682092i		−	0.0827158i
$69$	1.21983	+	1.97123i	0.146850	+	0.237309i
$70$	3.16904	−	3.16904i	0.378773	−	0.378773i
$71$	6.93216	+	6.93216i	0.822696	+	0.822696i	0.986494	−	0.163798i	$-0.0523745\pi$
$71$	6.93216	+	6.93216i	0.822696	+	0.822696i	−0.163798	+	0.986494i	$0.552375\pi$
$72$	−1.20023	−	3.58716i	−0.141448	−	0.422750i
$73$	0.0568680	+	0.0568680i	0.00665589	+	0.00665589i	0.710427	−	0.703771i	$-0.248502\pi$
$73$	0.0568680	+	0.0568680i	0.00665589	+	0.00665589i	−0.703771	+	0.710427i	$0.748502\pi$
$74$			0.307464i			0.0357420i
$75$	0.166944	−	0.103307i	0.0192770	−	0.0119289i
$76$	−3.70760	−	3.70760i	−0.425291	−	0.425291i
$77$	1.11493			0.127058
$78$	10.7856	+	3.55353i	1.22123	+	0.402358i
$79$	−4.05593			−0.456328			−0.228164	−	0.973623i	$-0.573272\pi$
$79$	−4.05593			−0.456328			−0.228164	+	0.973623i	$0.573272\pi$
$80$	−7.66863	−	7.66863i	−0.857379	−	0.857379i
$81$	−5.41626	−	7.18777i	−0.601807	−	0.798642i
$82$			14.6329i			1.61594i
$83$	−1.21562	−	1.21562i	−0.133432	−	0.133432i	0.637236	−	0.770668i	$-0.280077\pi$
$83$	−1.21562	−	1.21562i	−0.133432	−	0.133432i	−0.770668	+	0.637236i	$0.780077\pi$
$84$	2.45602	+	0.578323i	0.267974	+	0.0631003i
$85$	0.815998	+	0.815998i	0.0885075	+	0.0885075i
$86$	12.0667	−	12.0667i	1.30119	−	1.30119i
$87$	−13.3283	+	8.24774i	−1.42894	+	0.884251i
$88$		−	1.26087i		−	0.134410i
$89$	−6.40992	+	6.40992i	−0.679451	+	0.679451i	−0.959876	−	0.280425i	$-0.909524\pi$
$89$	−6.40992	+	6.40992i	−0.679451	+	0.679451i	0.280425	+	0.959876i	$0.409524\pi$
$90$	−10.7922	−	5.38084i	−1.13759	−	0.567190i
$91$	3.07878	−	2.58474i	0.322743	−	0.270955i
$92$			1.74873i			0.182318i
$93$	−15.9438	−	3.75430i	−1.65329	−	0.389303i
$94$	−14.9738			−1.54443
$95$	8.87093			0.910138
$96$	2.54048	−	10.7889i	0.259287	−	1.10114i
$97$	4.46187	−	4.46187i	0.453034	−	0.453034i	−0.443326	−	0.896360i	$-0.646202\pi$
$97$	4.46187	−	4.46187i	0.453034	−	0.453034i	0.896360	+	0.443326i	$0.146202\pi$
$98$	−7.40232	+	7.40232i	−0.747747	+	0.747747i
$99$	−0.951900	−	2.84498i	−0.0956695	−	0.285931i
$100$	0.148100			0.0148100
$101$	−9.54064			−0.949329			−0.474665	−	0.880167i	$-0.657431\pi$
$101$	−9.54064			−0.949329			−0.474665	+	0.880167i	$0.657431\pi$
$102$	−0.376852	+	1.60041i	−0.0373139	+	0.158465i
$103$		−	18.5066i		−	1.82351i	−0.410735	−	0.911755i	$-0.634728\pi$
$103$		−	18.5066i		−	1.82351i	0.410735	−	0.911755i	$-0.365272\pi$
$104$	−2.92310	−	3.48180i	−0.286633	−	0.341419i
$105$	−3.63004	+	2.24633i	−0.354256	+	0.219219i
$106$	10.6948	−	10.6948i	1.03877	−	1.03877i
$107$		−	11.7702i		−	1.13787i	−0.822383	−	0.568935i	$-0.807356\pi$
$107$		−	11.7702i		−	1.13787i	0.822383	−	0.568935i	$-0.192644\pi$
$108$	−0.621183	−	6.76084i	−0.0597733	−	0.650562i
$109$	−1.56360	+	1.56360i	−0.149766	+	0.149766i	−0.778014	−	0.628247i	$-0.783773\pi$
$109$	−1.56360	+	1.56360i	−0.149766	+	0.149766i	0.628247	+	0.778014i	$0.283773\pi$
$110$	−2.84238	−	2.84238i	−0.271010	−	0.271010i
$111$	0.0671249	−	0.285066i	0.00637122	−	0.0270573i
$112$	−3.86774	−	3.86774i	−0.365467	−	0.365467i
$113$			2.24991i			0.211654i	0.994385	+	0.105827i	$0.0337489\pi$
$113$			2.24991i			0.211654i	−0.994385	+	0.105827i	$0.966251\pi$
$114$	6.65083	+	10.7477i	0.622907	+	1.00661i
$115$	−2.09203	−	2.09203i	−0.195083	−	0.195083i
$116$	−11.8238			−1.09782
$117$	−9.22413	−	5.64937i	−0.852772	−	0.522284i
$118$	−7.95408			−0.732232
$119$	0.411556	+	0.411556i	0.0377273	+	0.0377273i
$120$	2.54038	+	4.10523i	0.231904	+	0.374755i
$121$		−	1.00000i		−	0.0909091i
$122$	12.3977	+	12.3977i	1.12243	+	1.12243i
$123$	3.19463	−	13.5670i	0.288050	−	1.22329i
$124$	−8.73731	−	8.73731i	−0.784633	−	0.784633i
$125$	−7.99275	+	7.99275i	−0.714893	+	0.714893i
$126$	−5.44313	−	2.71388i	−0.484912	−	0.241771i
$127$			7.41582i			0.658048i	0.944322	+	0.329024i	$0.106720\pi$
$127$			7.41582i			0.658048i	−0.944322	+	0.329024i	$0.893280\pi$
$128$	−6.70392	+	6.70392i	−0.592548	+	0.592548i
$129$	−13.8220	+	8.55329i	−1.21696	+	0.753076i
$130$	−14.4385	−	1.25948i	−1.26634	−	0.110463i
$131$		−	19.0740i		−	1.66650i	−0.552893	−	0.833252i	$-0.686476\pi$
$131$		−	19.0740i		−	1.66650i	0.552893	−	0.833252i	$-0.313524\pi$
$132$	0.518710	−	2.20286i	0.0451480	−	0.191734i
$133$	4.47413			0.387957
$134$	−6.28524			−0.542962
$135$	8.83124	+	7.34498i	0.760073	+	0.632155i
$136$	0.465431	−	0.465431i	0.0399104	−	0.0399104i
$137$	0.495241	−	0.495241i	0.0423113	−	0.0423113i	−0.685635	−	0.727946i	$-0.740475\pi$
$137$	0.495241	−	0.495241i	0.0423113	−	0.0423113i	0.727946	+	0.685635i	$0.240475\pi$
$138$	0.966161	−	4.10309i	0.0822451	−	0.349279i
$139$	20.6917			1.75505			0.877525	−	0.479530i	$-0.159193\pi$
$139$	20.6917			1.75505			0.877525	+	0.479530i	$0.159193\pi$
$140$	−3.22030			−0.272165
$141$	13.8830	+	3.26905i	1.16916	+	0.275303i
$142$		−	17.8269i		−	1.49600i
$143$	−2.31831	−	2.76142i	−0.193867	−	0.230921i
$144$	−6.56720	+	13.1716i	−0.547266	+	1.09763i
$145$	14.1451	−	14.1451i	1.17468	−	1.17468i
$146$		−	0.146243i		−	0.0121031i
$147$	8.47914	−	5.24702i	0.699348	−	0.432767i
$148$	0.156219	−	0.156219i	0.0128411	−	0.0128411i
$149$	1.37065	+	1.37065i	0.112288	+	0.112288i	0.761018	−	0.648730i	$-0.224700\pi$
$149$	1.37065	+	1.37065i	0.112288	+	0.112288i	−0.648730	+	0.761018i	$0.724700\pi$
$150$	−0.347491	−	0.0818241i	−0.0283725	−	0.00668091i
$151$	−4.03296	−	4.03296i	−0.328198	−	0.328198i	0.523703	−	0.851901i	$-0.324550\pi$
$151$	−4.03296	−	4.03296i	−0.328198	−	0.328198i	−0.851901	+	0.523703i	$0.824550\pi$
$152$		−	5.05982i		−	0.410405i
$153$	0.698798	−	1.40155i	0.0564945	−	0.113309i
$154$	−1.43358	−	1.43358i	−0.115521	−	0.115521i
$155$	20.9052			1.67914
$156$	−3.67454	−	7.28555i	−0.294199	−	0.583311i
$157$	4.24959			0.339154			0.169577	−	0.985517i	$-0.445760\pi$
$157$	4.24959			0.339154			0.169577	+	0.985517i	$0.445760\pi$
$158$	5.21515	+	5.21515i	0.414895	+	0.414895i
$159$	−12.2506	+	7.58083i	−0.971532	+	0.601199i
$160$			14.1463i			1.11836i
$161$	−1.05514	−	1.05514i	−0.0831564	−	0.0831564i
$162$	−2.27782	+	16.2064i	−0.178963	+	1.27329i
$163$	12.1475	+	12.1475i	0.951464	+	0.951464i	0.998875	−	0.0474113i	$-0.0150971\pi$
$163$	12.1475	+	12.1475i	0.951464	+	0.951464i	−0.0474113	+	0.998875i	$0.515097\pi$
$164$	7.43480	−	7.43480i	0.580561	−	0.580561i
$165$	2.01478	+	3.25586i	0.156850	+	0.253468i
$166$			3.12612i			0.242634i
$167$	−8.21630	+	8.21630i	−0.635796	+	0.635796i	−0.949516	−	0.313719i	$-0.898425\pi$
$167$	−8.21630	+	8.21630i	−0.635796	+	0.635796i	0.313719	+	0.949516i	$0.398425\pi$
$168$	1.28126	+	2.07051i	0.0988517	+	0.159743i
$169$	−12.8037	−	2.25086i	−0.984897	−	0.173143i
$170$		−	2.09843i		−	0.160943i
$171$	−3.81992	−	11.4167i	−0.292117	−	0.873059i
$172$	−12.2619			−0.934959
$173$	19.1677			1.45729			0.728646	−	0.684891i	$-0.240150\pi$
$173$	19.1677			1.45729			0.728646	+	0.684891i	$0.240150\pi$
$174$	27.7426	+	6.53259i	2.10316	+	0.495235i
$175$	−0.0893594	+	0.0893594i	−0.00675494	+	0.00675494i
$176$	−3.46906	+	3.46906i	−0.261490	+	0.261490i
$177$	7.37465	+	1.73652i	0.554312	+	0.130525i
$178$	16.4839			1.23552
$179$	−19.3441			−1.44585			−0.722923	−	0.690928i	$-0.757202\pi$
$179$	−19.3441			−1.44585			−0.722923	+	0.690928i	$0.757202\pi$
$180$	2.74942	+	8.21729i	0.204930	+	0.612481i
$181$			4.92714i			0.366232i	0.983091	+	0.183116i	$0.0586184\pi$
$181$			4.92714i			0.366232i	−0.983091	+	0.183116i	$0.941382\pi$
$182$	−7.28220	−	0.635228i	−0.539793	−	0.0470862i
$183$	−8.78789	−	14.2012i	−0.649619	−	1.04978i
$184$	−1.19326	+	1.19326i	−0.0879682	+	0.0879682i
$185$			0.373774i			0.0274804i
$186$	15.6733	+	25.3279i	1.14922	+	1.85713i
$187$	0.369134	−	0.369134i	0.0269937	−	0.0269937i
$188$	7.60799	+	7.60799i	0.554870	+	0.554870i
$189$	4.45412	+	3.70451i	0.323990	+	0.269463i
$190$	−11.4063	−	11.4063i	−0.827501	−	0.827501i
$191$			7.12670i			0.515670i	0.966189	+	0.257835i	$0.0830090\pi$
$191$			7.12670i			0.515670i	−0.966189	+	0.257835i	$0.916991\pi$
$192$	−2.68742	+	1.66302i	−0.193948	+	0.120018i
$193$	7.89768	+	7.89768i	0.568488	+	0.568488i	0.931705	−	0.363217i	$-0.118322\pi$
$193$	7.89768	+	7.89768i	0.568488	+	0.568488i	−0.363217	+	0.931705i	$0.618322\pi$
$194$	−11.4742			−0.823801
$195$	13.1117	+	4.31991i	0.938951	+	0.309355i
$196$	7.52205			0.537289
$197$	−11.0826	−	11.0826i	−0.789603	−	0.789603i	0.191826	−	0.981429i	$-0.438559\pi$
$197$	−11.0826	−	11.0826i	−0.789603	−	0.789603i	−0.981429	+	0.191826i	$0.938559\pi$
$198$	−2.43413	+	4.88205i	−0.172986	+	0.346952i
$199$			18.5889i			1.31773i	0.752259	+	0.658867i	$0.228964\pi$
$199$			18.5889i			1.31773i	−0.752259	+	0.658867i	$0.771036\pi$
$200$	0.101057	+	0.101057i	0.00714581	+	0.00714581i
$201$	5.82738	+	1.37218i	0.411032	+	0.0967862i
$202$	12.2674	+	12.2674i	0.863134	+	0.863134i
$203$	7.13419	−	7.13419i	0.500722	−	0.500722i
$204$	1.00462	−	0.621676i	0.0703377	−	0.0435260i
$205$			17.7888i			1.24242i
$206$	−23.7959	+	23.7959i	−1.65794	+	1.65794i
$207$	−1.79156	+	3.59327i	−0.124522	+	0.249749i
$208$	−1.53716	+	17.6219i	−0.106583	+	1.22186i
$209$		−	4.01294i		−	0.277581i
$210$	7.55588	+	1.77919i	0.521405	+	0.122776i
$211$	4.01932			0.276702			0.138351	−	0.990383i	$-0.455820\pi$
$211$	4.01932			0.276702			0.138351	+	0.990383i	$0.455820\pi$
$212$	−10.8678			−0.746401
$213$	−3.89192	+	16.5282i	−0.266670	+	1.13249i
$214$	−15.1342	+	15.1342i	−1.03455	+	1.03455i
$215$	14.6691	−	14.6691i	1.00042	−	1.00042i
$216$	4.18945	−	5.03718i	0.285056	−	0.342737i
$217$	10.5437			0.715755
$218$	4.02099			0.272336
$219$	−0.0319274	+	0.135589i	−0.00215745	+	0.00916227i
$220$			2.88835i			0.194733i
$221$	0.163565	−	1.87510i	0.0110026	−	0.126133i
$222$	−0.452850	+	0.280231i	−0.0303933	+	0.0188078i
$223$	6.50769	−	6.50769i	0.435787	−	0.435787i	−0.454804	−	0.890591i	$-0.650291\pi$
$223$	6.50769	−	6.50769i	0.435787	−	0.435787i	0.890591	+	0.454804i	$0.150291\pi$
$224$			7.13479i			0.476713i
$225$	0.304313	+	0.151727i	0.0202875	+	0.0101151i
$226$	2.89295	−	2.89295i	0.192436	−	0.192436i
$227$	12.2419	+	12.2419i	0.812521	+	0.812521i	0.985011	−	0.172490i	$-0.0551814\pi$
$227$	12.2419	+	12.2419i	0.812521	+	0.812521i	−0.172490	+	0.985011i	$0.555181\pi$
$228$	2.08156	−	8.83996i	0.137854	−	0.585440i
$229$	−1.06230	−	1.06230i	−0.0701987	−	0.0701987i	0.671136	−	0.741334i	$-0.265807\pi$
$229$	−1.06230	−	1.06230i	−0.0701987	−	0.0701987i	−0.741334	+	0.671136i	$0.765807\pi$
$230$			5.37991i			0.354741i
$231$	1.01617	+	1.64212i	0.0668592	+	0.108044i
$232$	−8.06809	−	8.06809i	−0.529696	−	0.529696i
$233$	−11.7901			−0.772397			−0.386199	−	0.922416i	$-0.626212\pi$
$233$	−11.7901			−0.772397			−0.386199	+	0.922416i	$0.626212\pi$
$234$	4.59646	+	19.1245i	0.300480	+	1.25021i
$235$	−18.2031			−1.18744
$236$	4.04137	+	4.04137i	0.263070	+	0.263070i
$237$	−3.69668	−	5.97380i	−0.240125	−	0.388040i
$238$		−	1.05837i		−	0.0686036i
$239$	4.27371	+	4.27371i	0.276443	+	0.276443i	0.831687	−	0.555244i	$-0.187375\pi$
$239$	4.27371	+	4.27371i	0.276443	+	0.276443i	−0.555244	+	0.831687i	$0.687375\pi$
$240$	4.30540	−	18.2842i	0.277912	−	1.18024i
$241$	7.72376	+	7.72376i	0.497531	+	0.497531i	0.910669	−	0.413137i	$-0.135567\pi$
$241$	7.72376	+	7.72376i	0.497531	+	0.497531i	−0.413137	+	0.910669i	$0.635567\pi$
$242$	−1.28581	+	1.28581i	−0.0826549	+	0.0826549i
$243$	5.65003	−	14.5285i	0.362450	−	0.932003i
$244$		−	12.5982i		−	0.806516i
$245$	−8.99876	+	8.99876i	−0.574910	+	0.574910i
$246$	−21.5522	+	13.3368i	−1.37412	+	0.850325i
$247$	−9.30326	−	11.0814i	−0.591952	−	0.705094i
$248$		−	11.9239i		−	0.757171i
$249$	0.682488	−	2.89839i	0.0432509	−	0.183678i
$250$	20.5543			1.29997
$251$	−9.72404			−0.613776			−0.306888	−	0.951746i	$-0.599288\pi$
$251$	−9.72404			−0.613776			−0.306888	+	0.951746i	$0.599288\pi$
$252$	1.38670	+	4.14447i	0.0873537	+	0.261077i
$253$	−0.946374	+	0.946374i	−0.0594980	+	0.0594980i
$254$	9.53532	−	9.53532i	0.598299	−	0.598299i
$255$	−0.458126	+	1.94557i	−0.0286890	+	0.121836i
$256$	20.8892			1.30557
$257$	23.0178			1.43581			0.717905	−	0.696141i	$-0.245101\pi$
$257$	23.0178			1.43581			0.717905	+	0.696141i	$0.245101\pi$
$258$	28.7704	+	6.77461i	1.79117	+	0.421768i
$259$			0.188516i			0.0117138i
$260$	6.69610	+	7.97595i	0.415275	+	0.494647i
$261$	−24.2955	−	12.1134i	−1.50385	−	0.749802i
$262$	−24.5255	+	24.5255i	−1.51519	+	1.51519i
$263$		−	0.485462i		−	0.0299349i	−0.999888	−	0.0149674i	$-0.995236\pi$
$263$		−	0.485462i		−	0.0299349i	0.999888	−	0.0149674i	$-0.00476446\pi$
$264$	1.85709	−	1.14919i	0.114296	−	0.0707279i
$265$	13.0013	−	13.0013i	0.798663	−	0.798663i
$266$	−5.75288	−	5.75288i	−0.352732	−	0.352732i
$267$	−15.2831	−	3.59872i	−0.935308	−	0.220238i
$268$	3.19345	+	3.19345i	0.195071	+	0.195071i
$269$			28.8275i			1.75765i	0.477148	+	0.878823i	$0.341670\pi$
$269$			28.8275i			1.75765i	−0.477148	+	0.878823i	$0.658330\pi$
$270$	−1.91105	−	20.7995i	−0.116303	−	1.26582i
$271$	11.7058	+	11.7058i	0.711078	+	0.711078i	0.966761	−	0.255683i	$-0.0823003\pi$
$271$	11.7058	+	11.7058i	0.711078	+	0.711078i	−0.255683	+	0.966761i	$0.582300\pi$
$272$	−2.56109			−0.155289
$273$	6.61303	+	2.17879i	0.400239	+	0.131866i
$274$	−1.27357			−0.0769392
$275$	0.0801483	+	0.0801483i	0.00483313	+	0.00483313i
$276$	−2.57562	+	1.59384i	−0.155034	+	0.0959376i
$277$			2.93623i			0.176421i	0.996102	+	0.0882106i	$0.0281148\pi$
$277$			2.93623i			0.176421i	−0.996102	+	0.0882106i	$0.971885\pi$
$278$	−26.6056	−	26.6056i	−1.59570	−	1.59570i
$279$	−9.00201	−	26.9046i	−0.538936	−	1.61074i
$280$	−2.19740	−	2.19740i	−0.131320	−	0.131320i
$281$	−13.7091	+	13.7091i	−0.817817	+	0.817817i	−0.985791	−	0.167974i	$-0.946277\pi$
$281$	−13.7091	+	13.7091i	−0.817817	+	0.817817i	0.167974	+	0.985791i	$0.446277\pi$
$282$	−13.6475	−	22.0542i	−0.812697	−	1.31331i
$283$		−	30.1280i		−	1.79092i	−0.445139	−	0.895462i	$-0.646846\pi$
$283$		−	30.1280i		−	1.79092i	0.445139	−	0.895462i	$-0.353154\pi$
$284$	−9.05759	+	9.05759i	−0.537469	+	0.537469i
$285$	8.08519	+	13.0656i	0.478925	+	0.773939i
$286$	−0.569750	+	6.53156i	−0.0336900	+	0.386219i
$287$			8.97193i			0.529596i
$288$	18.2060	−	6.09154i	1.07280	−	0.358947i
$289$	−16.7275			−0.983969
$290$	−36.3757			−2.13605
$291$	10.6384	+	2.50503i	0.623631	+	0.146847i
$292$	−0.0743040	+	0.0743040i	−0.00434831	+	0.00434831i
$293$	−11.6786	+	11.6786i	−0.682269	+	0.682269i	−0.960511	−	0.278242i	$-0.910248\pi$
$293$	−11.6786	+	11.6786i	−0.682269	+	0.682269i	0.278242	+	0.960511i	$0.410248\pi$
$294$	−17.6492	−	4.15589i	−1.02932	−	0.242376i
$295$	−9.66951			−0.562981
$296$	0.213194			0.0123916
$297$	3.32265	−	3.99499i	0.192800	−	0.231813i
$298$		−	3.52478i		−	0.204185i
$299$	−0.419344	+	4.80733i	−0.0242513	+	0.278015i
$300$	0.134982	+	0.218129i	0.00779318	+	0.0125937i
$301$	7.39849	−	7.39849i	0.426442	−	0.426442i
$302$			10.3712i			0.596797i
$303$	−8.69558	−	14.0520i	−0.499548	−	0.807265i
$304$	−13.9212	+	13.9212i	−0.798433	+	0.798433i
$305$	15.0714	+	15.0714i	0.862987	+	0.862987i
$306$	−2.70065	+	0.903610i	−0.154386	+	0.0516559i
$307$	3.69414	+	3.69414i	0.210836	+	0.210836i	0.804622	−	0.593787i	$-0.202368\pi$
$307$	3.69414	+	3.69414i	0.210836	+	0.210836i	−0.593787	+	0.804622i	$0.702368\pi$
$308$			1.45677i			0.0830070i
$309$	27.2576	−	16.8674i	1.55063	−	0.959552i
$310$	−26.8801	−	26.8801i	−1.52668	−	1.52668i
$311$	1.06828			0.0605764			0.0302882	−	0.999541i	$-0.490357\pi$
$311$	1.06828			0.0605764			0.0302882	+	0.999541i	$0.490357\pi$
$312$	2.46400	−	7.47871i	0.139497	−	0.423398i
$313$	19.8857			1.12401			0.562003	−	0.827135i	$-0.310031\pi$
$313$	19.8857			1.12401			0.562003	+	0.827135i	$0.310031\pi$
$314$	−5.46416	−	5.46416i	−0.308360	−	0.308360i
$315$	−6.61703	−	3.29917i	−0.372827	−	0.185887i
$316$		−	5.29950i		−	0.298120i
$317$	2.40550	+	2.40550i	0.135106	+	0.135106i	0.771426	−	0.636319i	$-0.219544\pi$
$317$	2.40550	+	2.40550i	0.135106	+	0.135106i	−0.636319	+	0.771426i	$0.719544\pi$
$318$	25.4994	+	6.00437i	1.42993	+	0.336708i
$319$	−6.39880	−	6.39880i	−0.358264	−	0.358264i
$320$	2.85211	−	2.85211i	0.159438	−	0.159438i
$321$	17.3358	−	10.7277i	0.967591	−	0.598760i
$322$			2.71341i			0.151212i
$323$	1.48131	−	1.48131i	0.0824224	−	0.0824224i
$324$	9.39158	−	7.07692i	0.521755	−	0.393162i
$325$	0.407132	+	0.0355142i	0.0225836	+	0.00196997i
$326$		−	31.2387i		−	1.73015i
$327$	−3.72807	−	0.877854i	−0.206163	−	0.0485454i
$328$	10.1464			0.560241
$329$	−9.18093			−0.506161
$330$	1.59580	−	6.77703i	0.0878457	−	0.373063i
$331$	−12.7084	+	12.7084i	−0.698515	+	0.698515i	−0.964090	−	0.265576i	$-0.914438\pi$
$331$	−12.7084	+	12.7084i	−0.698515	+	0.698515i	0.265576	+	0.964090i	$0.414438\pi$
$332$	1.58834	−	1.58834i	0.0871715	−	0.0871715i
$333$	0.481041	−	0.160951i	0.0263609	−	0.00882007i
$334$	21.1292			1.15614
$335$	−7.64076			−0.417459
$336$	2.17147	−	9.22179i	0.118463	−	0.503090i
$337$			21.0686i			1.14768i	0.818967	+	0.573840i	$0.194547\pi$
$337$			21.0686i			1.14768i	−0.818967	+	0.573840i	$0.805453\pi$
$338$	13.5689	+	19.3572i	0.738049	+	1.05289i
$339$	−3.31379	+	2.05063i	−0.179980	+	0.111375i
$340$	−1.06619	+	1.06619i	−0.0578222	+	0.0578222i
$341$		−	9.45689i		−	0.512119i
$342$	−9.76804	+	19.5914i	−0.528195	+	1.05938i
$343$	−10.0572	+	10.0572i	−0.543038	+	0.543038i
$344$	−8.36698	−	8.36698i	−0.451118	−	0.451118i
$345$	1.17453	−	4.98800i	0.0632346	−	0.268545i
$346$	−24.6460	−	24.6460i	−1.32497	−	1.32497i
$347$			19.3338i			1.03789i	0.854807	+	0.518946i	$0.173675\pi$
$347$			19.3338i			1.03789i	−0.854807	+	0.518946i	$0.826325\pi$
$348$	−10.7765	−	17.4148i	−0.577683	−	0.933531i
$349$	2.16448	+	2.16448i	0.115862	+	0.115862i	0.762661	−	0.646799i	$-0.223893\pi$
$349$	2.16448	+	2.16448i	0.115862	+	0.115862i	−0.646799	+	0.762661i	$0.723893\pi$
$350$	0.229798			0.0122832
$351$	−0.0864098	−	18.7348i	−0.00461222	−	0.999989i
$352$	6.39935			0.341086
$353$	4.82745	+	4.82745i	0.256939	+	0.256939i	0.823808	−	0.566869i	$-0.191845\pi$
$353$	4.82745	+	4.82745i	0.256939	+	0.256939i	−0.566869	+	0.823808i	$0.691845\pi$
$354$	−7.24955	−	11.7152i	−0.385309	−	0.622656i
$355$		−	21.6715i		−	1.15020i
$356$	−8.37524	−	8.37524i	−0.443887	−	0.443887i
$357$	−0.231060	+	0.981266i	−0.0122290	+	0.0519341i
$358$	24.8728	+	24.8728i	1.31457	+	1.31457i
$359$	−12.2591	+	12.2591i	−0.647011	+	0.647011i	−0.952270	−	0.305258i	$-0.901257\pi$
$359$	−12.2591	+	12.2591i	−0.647011	+	0.647011i	0.305258	+	0.952270i	$0.401257\pi$
$360$	−3.73105	+	7.48323i	−0.196643	+	0.394401i
$361$			2.89627i			0.152435i
$362$	6.33536	−	6.33536i	0.332979	−	0.332979i
$363$	1.47286	−	0.911426i	0.0773049	−	0.0478374i
$364$	3.37724	+	4.02274i	0.177016	+	0.210849i
$365$		−	0.177782i		−	0.00930555i
$366$	−6.96042	+	29.5595i	−0.363827	+	1.54510i
$367$	−26.5238			−1.38453			−0.692266	−	0.721643i	$-0.743387\pi$
$367$	−26.5238			−1.38453			−0.692266	+	0.721643i	$0.743387\pi$
$368$	6.56606			0.342280
$369$	22.8938	−	7.66004i	1.19181	−	0.398766i
$370$	0.480601	−	0.480601i	0.0249853	−	0.0249853i
$371$	6.55732	−	6.55732i	0.340439	−	0.340439i
$372$	4.90539	−	20.8322i	0.254332	−	1.08010i
$373$	−11.5598			−0.598542			−0.299271	−	0.954168i	$-0.596743\pi$
$373$	−11.5598			−0.598542			−0.299271	+	0.954168i	$0.596743\pi$
$374$	−0.949270			−0.0490856
$375$	−19.0570	−	4.48737i	−0.984097	−	0.231727i
$376$			10.3827i			0.535449i
$377$	−32.5042	−	2.83535i	−1.67405	−	0.146028i
$378$	−0.963856	−	10.4904i	−0.0495754	−	0.539570i
$379$	12.9934	−	12.9934i	0.667429	−	0.667429i	−0.289691	−	0.957120i	$-0.593553\pi$
$379$	12.9934	−	12.9934i	0.667429	−	0.667429i	0.957120	+	0.289691i	$0.0935527\pi$
$380$			11.5908i			0.594595i
$381$	−10.9224	+	6.75897i	−0.559573	+	0.346272i
$382$	9.16356	−	9.16356i	0.468849	−	0.468849i
$383$	−7.71881	−	7.71881i	−0.394413	−	0.394413i	0.481844	−	0.876257i	$-0.339967\pi$
$383$	−7.71881	−	7.71881i	−0.394413	−	0.394413i	−0.876257	+	0.481844i	$0.839967\pi$
$384$	−15.9840	−	3.76378i	−0.815681	−	0.192070i
$385$	−1.74276	−	1.74276i	−0.0888191	−	0.0888191i
$386$		−	20.3098i		−	1.03374i
$387$	−25.1955	−	12.5622i	−1.28076	−	0.638572i
$388$	5.82990	+	5.82990i	0.295969	+	0.295969i
$389$	14.7044			0.745545			0.372773	−	0.927923i	$-0.378407\pi$
$389$	14.7044			0.745545			0.372773	+	0.927923i	$0.378407\pi$
$390$	−11.3046	−	22.4138i	−0.572431	−	1.13497i
$391$	−0.698677			−0.0353336
$392$	5.13273	+	5.13273i	0.259242	+	0.259242i
$393$	28.0933	−	17.3845i	1.41712	−	0.876935i
$394$			28.5002i			1.43582i
$395$	6.33989	+	6.33989i	0.318994	+	0.318994i
$396$	3.71726	−	1.24376i	0.186799	−	0.0625011i
$397$	23.3139	+	23.3139i	1.17009	+	1.17009i	0.982188	+	0.187903i	$0.0601690\pi$
$397$	23.3139	+	23.3139i	1.17009	+	1.17009i	0.187903	+	0.982188i	$0.439831\pi$
$398$	23.9018	−	23.9018i	1.19809	−	1.19809i
$399$	4.07784	+	6.58975i	0.204147	+	0.329900i
$400$		−	0.556079i		−	0.0278039i
$401$	3.03111	−	3.03111i	0.151367	−	0.151367i	−0.627362	−	0.778728i	$-0.715865\pi$
$401$	3.03111	−	3.03111i	0.151367	−	0.151367i	0.778728	+	0.627362i	$0.215865\pi$
$402$	−5.72853	−	9.25726i	−0.285713	−	0.461710i
$403$	−21.9240	−	26.1144i	−1.09211	−	1.30085i
$404$		−	12.4659i		−	0.620199i
$405$	−2.76907	+	19.7016i	−0.137596	+	0.978978i
$406$	−18.3464			−0.910516
$407$	0.169084			0.00838120
$408$	1.10972	+	0.261307i	0.0549392	+	0.0129366i
$409$	−23.2813	+	23.2813i	−1.15119	+	1.15119i	−0.164873	+	0.986315i	$0.552722\pi$
$409$	−23.2813	+	23.2813i	−1.15119	+	1.15119i	−0.986315	+	0.164873i	$0.947278\pi$
$410$	22.8729	−	22.8729i	1.12961	−	1.12961i
$411$	1.18079	+	0.278043i	0.0582443	+	0.0137149i
$412$	24.1808			1.19130
$413$	−4.87691			−0.239977
$414$	6.92385	−	2.31665i	0.340289	−	0.113857i
$415$			3.80032i			0.186550i
$416$	17.6713	−	14.8357i	0.866405	−	0.727379i
$417$	18.8590	+	30.4759i	0.923528	+	1.49241i
$418$	−5.15988	+	5.15988i	−0.252378	+	0.252378i
$419$		−	10.6393i		−	0.519766i	−0.965640	−	0.259883i	$-0.916316\pi$
$419$		−	10.6393i		−	0.519766i	0.965640	−	0.259883i	$-0.0836840\pi$
$420$	−2.93506	−	4.74303i	−0.143216	−	0.231436i
$421$	−23.9839	+	23.9839i	−1.16890	+	1.16890i	−0.186436	+	0.982467i	$0.559694\pi$
$421$	−23.9839	+	23.9839i	−1.16890	+	1.16890i	−0.982467	+	0.186436i	$0.940306\pi$
$422$	−5.16808	−	5.16808i	−0.251578	−	0.251578i
$423$	7.83848	+	23.4271i	0.381120	+	1.13907i
$424$	−7.41570	−	7.41570i	−0.360138	−	0.360138i
$425$			0.0591709i			0.00287021i
$426$	26.2564	−	16.2478i	1.27213	−	0.787211i
$427$	7.60141	+	7.60141i	0.367858	+	0.367858i
$428$	15.3790			0.743373
$429$	1.95420	−	5.93137i	0.0943497	−	0.286369i
$430$	−37.7233			−1.81918
$431$	22.0268	+	22.0268i	1.06099	+	1.06099i	0.998015	+	0.0629781i	$0.0200598\pi$
$431$	22.0268	+	22.0268i	1.06099	+	1.06099i	0.0629781	+	0.998015i	$0.479940\pi$
$432$	−25.3854	+	2.33239i	−1.22135	+	0.112217i
$433$		−	12.1560i		−	0.584182i	−0.956390	−	0.292091i	$-0.905649\pi$
$433$		−	12.1560i		−	0.584182i	0.956390	−	0.292091i	$-0.0943511\pi$
$434$	−13.5572	−	13.5572i	−0.650767	−	0.650767i
$435$	33.7258	+	7.94146i	1.61703	+	0.380764i
$436$	−2.04301	−	2.04301i	−0.0978426	−	0.0978426i
$437$	−3.79775	+	3.79775i	−0.181671	+	0.181671i
$438$	0.215394	−	0.133289i	0.0102919	−	0.00636881i
$439$		−	13.6026i		−	0.649217i	−0.945849	−	0.324608i	$-0.894768\pi$
$439$		−	13.6026i		−	0.649217i	0.945849	−	0.324608i	$-0.105232\pi$
$440$	−1.97089	+	1.97089i	−0.0939585	+	0.0939585i
$441$	15.4562	+	7.70628i	0.736010	+	0.366966i
$442$	−2.62133	+	2.20070i	−0.124684	+	0.104677i
$443$			5.89339i			0.280003i	0.990151	+	0.140002i	$0.0447108\pi$
$443$			5.89339i			0.280003i	−0.990151	+	0.140002i	$0.955289\pi$
$444$	0.372469	+	0.0877058i	0.0176766	+	0.00416233i
$445$	20.0389			0.949934
$446$	−16.7353			−0.792439
$447$	−0.769524	+	3.26801i	−0.0363972	+	0.154572i
$448$	1.43849	−	1.43849i	0.0679621	−	0.0679621i
$449$	4.97669	−	4.97669i	0.234865	−	0.234865i	−0.579855	−	0.814720i	$-0.696891\pi$
$449$	4.97669	−	4.97669i	0.234865	−	0.234865i	0.814720	+	0.579855i	$0.196891\pi$
$450$	−0.196197	−	0.586380i	−0.00924880	−	0.0276422i
$451$	8.04711			0.378924
$452$	−2.93974			−0.138274
$453$	2.26422	−	9.61571i	0.106383	−	0.451785i
$454$		−	31.4814i		−	1.47749i
$455$	−8.85273	−	0.772226i	−0.415022	−	0.0362025i
$456$	7.45238	−	4.61165i	0.348990	−	0.215960i
$457$	16.3346	−	16.3346i	0.764099	−	0.764099i	−0.212962	−	0.977061i	$-0.568311\pi$
$457$	16.3346	−	16.3346i	0.764099	−	0.764099i	0.977061	+	0.212962i	$0.0683110\pi$
$458$			2.73183i			0.127650i
$459$	2.70119	−	0.248184i	0.126081	−	0.0115842i
$460$	2.73346	−	2.73346i	0.127448	−	0.127448i
$461$	15.1463	+	15.1463i	0.705434	+	0.705434i	0.965572	−	0.260137i	$-0.0837679\pi$
$461$	15.1463	+	15.1463i	0.705434	+	0.705434i	−0.260137	+	0.965572i	$0.583768\pi$
$462$	0.804855	−	3.41806i	0.0374452	−	0.159022i
$463$	−21.2839	−	21.2839i	−0.989147	−	0.989147i	0.0107951	−	0.999942i	$-0.496564\pi$
$463$	−21.2839	−	21.2839i	−0.989147	−	0.989147i	−0.999942	+	0.0107951i	$0.996564\pi$
$464$			44.3957i			2.06102i
$465$	19.0535	+	30.7903i	0.883586	+	1.42787i
$466$	15.1599	+	15.1599i	0.702267	+	0.702267i
$467$	39.2631			1.81688			0.908440	−	0.418015i	$-0.137274\pi$
$467$	39.2631			1.81688			0.908440	+	0.418015i	$0.137274\pi$
$468$	7.38149	−	12.0523i	0.341210	−	0.557118i
$469$	−3.85369			−0.177947
$470$	23.4058	+	23.4058i	1.07963	+	1.07963i
$471$	3.87319	+	6.25903i	0.178467	+	0.288401i
$472$			5.51532i			0.253863i
$473$	−6.63586	−	6.63586i	−0.305117	−	0.305117i
$474$	−2.92794	+	12.4344i	−0.134485	+	0.571130i
$475$	0.321631	+	0.321631i	0.0147574	+	0.0147574i
$476$	−0.537742	+	0.537742i	−0.0246474	+	0.0246474i
$477$	−22.3309	−	11.1339i	−1.02246	−	0.509788i
$478$		−	10.9903i		−	0.502686i
$479$	26.0711	−	26.0711i	1.19122	−	1.19122i	0.214496	−	0.976725i	$-0.431189\pi$
$479$	26.0711	−	26.0711i	1.19122	−	1.19122i	0.976725	−	0.214496i	$-0.0688110\pi$
$480$	−20.8354	+	12.8933i	−0.951001	+	0.588494i
$481$	0.466912	−	0.391990i	0.0212894	−	0.0178732i
$482$		−	19.8625i		−	0.904714i
$483$	0.592385	−	2.51574i	0.0269545	−	0.114470i
$484$	1.30661			0.0593911
$485$	−13.9488			−0.633384
$486$	−25.9457	+	11.4160i	−1.17692	+	0.517840i
$487$	23.1645	−	23.1645i	1.04968	−	1.04968i	0.0509838	−	0.998699i	$-0.483764\pi$
$487$	23.1645	−	23.1645i	1.04968	−	1.04968i	0.998699	−	0.0509838i	$-0.0162357\pi$
$488$	8.59647	−	8.59647i	0.389144	−	0.389144i
$489$	−6.81996	+	28.9630i	−0.308409	+	1.30975i
$490$	23.1414			1.04542
$491$	18.7218			0.844904			0.422452	−	0.906385i	$-0.361170\pi$
$491$	18.7218			0.844904			0.422452	+	0.906385i	$0.361170\pi$
$492$	17.7267	+	4.17412i	0.799180	+	0.188184i
$493$		−	4.72403i		−	0.212759i
$494$	−2.28637	+	26.2108i	−0.102869	+	1.17928i
$495$	−2.95909	+	5.93495i	−0.133001	+	0.266756i
$496$	−32.8065	+	32.8065i	−1.47306	+	1.47306i
$497$		−	10.9302i		−	0.490288i
$498$	−4.60432	+	2.84922i	−0.206324	+	0.127677i
$499$	5.49591	−	5.49591i	0.246031	−	0.246031i	−0.573309	−	0.819339i	$-0.694340\pi$
$499$	5.49591	−	5.49591i	0.246031	−	0.246031i	0.819339	+	0.573309i	$0.194340\pi$
$500$	−10.4434	−	10.4434i	−0.467041	−	0.467041i
$501$	−19.5900	−	4.61288i	−0.875215	−	0.206088i
$502$	12.5032	+	12.5032i	0.558047	+	0.558047i
$503$		−	14.1757i		−	0.632064i	−0.948749	−	0.316032i	$-0.897649\pi$
$503$		−	14.1757i		−	0.632064i	0.948749	−	0.316032i	$-0.102351\pi$
$504$	−1.88179	+	3.77423i	−0.0838215	+	0.168118i
$505$	14.9131	+	14.9131i	0.663625	+	0.663625i
$506$	2.43371			0.108192
$507$	−8.35439	−	20.9094i	−0.371031	−	0.928620i
$508$	−9.68955			−0.429904
$509$	−8.45999	−	8.45999i	−0.374983	−	0.374983i	0.494306	−	0.869288i	$-0.335422\pi$
$509$	−8.45999	−	8.45999i	−0.374983	−	0.374983i	−0.869288	+	0.494306i	$0.835422\pi$
$510$	3.09069	−	1.91257i	0.136858	−	0.0846899i
$511$		−	0.0896662i		−	0.00396660i
$512$	−13.4516	−	13.4516i	−0.594483	−	0.594483i
$513$	13.3336	−	16.0317i	0.588694	−	0.707816i
$514$	−29.5965	−	29.5965i	−1.30544	−	1.30544i
$515$	−28.9279	+	28.9279i	−1.27472	+	1.27472i
$516$	−11.1758	−	18.0600i	−0.491986	−	0.795045i
$517$			8.23457i			0.362156i
$518$	0.242396	−	0.242396i	0.0106503	−	0.0106503i
$519$	17.4699	+	28.2312i	0.766844	+	1.23921i
$520$	−0.873314	+	10.0116i	−0.0382973	+	0.439037i
$521$			28.0324i			1.22812i	0.789259	+	0.614061i	$0.210465\pi$
$521$			28.0324i			1.22812i	−0.789259	+	0.614061i	$0.789535\pi$
$522$	15.6638	+	46.8148i	0.685584	+	2.04903i
$523$	−8.33350			−0.364398			−0.182199	−	0.983262i	$-0.558322\pi$
$523$	−8.33350			−0.364398			−0.182199	+	0.983262i	$0.558322\pi$
$524$	24.9222			1.08873
$525$	−0.213058	−	0.0501691i	−0.00929861	−	0.00218956i
$526$	−0.624211	+	0.624211i	−0.0272169	+	0.0272169i
$527$	3.49085	−	3.49085i	0.152064	−	0.152064i
$528$	−8.27122	−	1.94763i	−0.359959	−	0.0847599i
$529$	−21.2088			−0.922120
$530$	−33.4343			−1.45229
$531$	4.16380	+	12.4445i	0.180694	+	0.540045i
$532$			5.84593i			0.253453i
$533$	22.2214	−	18.6557i	0.962517	−	0.808069i
$534$	15.0238	+	24.2784i	0.650144	+	1.05063i
$535$	−18.3982	+	18.3982i	−0.795423	+	0.795423i
$536$			4.35816i			0.188244i
$537$	−17.6307	−	28.4911i	−0.760821	−	1.22948i
$538$	37.0667	−	37.0667i	1.59806	−	1.59806i
$539$	4.07077	+	4.07077i	0.175341	+	0.175341i
$540$	−9.59699	+	11.5390i	−0.412989	+	0.496557i
$541$	−8.70523	−	8.70523i	−0.374267	−	0.374267i	0.494762	−	0.869029i	$-0.335255\pi$
$541$	−8.70523	−	8.70523i	−0.374267	−	0.374267i	−0.869029	+	0.494762i	$0.835255\pi$
$542$		−	30.1029i		−	1.29303i
$543$	−7.25697	+	4.49073i	−0.311426	+	0.192715i
$544$	2.36221	+	2.36221i	0.101279	+	0.101279i
$545$	4.88818			0.209387
$546$	−5.70158	−	11.3046i	−0.244005	−	0.483792i
$547$	27.2480			1.16504			0.582520	−	0.812816i	$-0.302067\pi$
$547$	27.2480			1.16504			0.582520	+	0.812816i	$0.302067\pi$
$548$	0.647085	+	0.647085i	0.0276421	+	0.0276421i
$549$	12.9067	−	25.8866i	0.550846	−	1.10481i
$550$		−	0.206111i		−	0.00878859i
$551$	−25.6781	−	25.6781i	−1.09392	−	1.09392i
$552$	−2.84506	−	0.669931i	−0.121094	−	0.0285142i
$553$	3.19758	+	3.19758i	0.135975	+	0.135975i
$554$	3.77543	−	3.77543i	0.160403	−	0.160403i
$555$	−0.550515	+	0.340667i	−0.0233681	+	0.0144605i
$556$			27.0359i			1.14658i
$557$	−14.3619	+	14.3619i	−0.608533	+	0.608533i	−0.942563	−	0.334029i	$-0.891592\pi$
$557$	−14.3619	+	14.3619i	−0.608533	+	0.608533i	0.334029	+	0.942563i	$0.391592\pi$
$558$	−23.0193	+	46.1690i	−0.974486	+	1.95449i
$559$	−33.7084	−	2.94039i	−1.42571	−	0.124365i
$560$			12.0915i			0.510957i
$561$	0.880118	+	0.207243i	0.0371586	+	0.00874979i
$562$	35.2546			1.48712
$563$	19.0237			0.801752			0.400876	−	0.916132i	$-0.368706\pi$
$563$	19.0237			0.801752			0.400876	+	0.916132i	$0.368706\pi$
$564$	−4.27136	+	18.1396i	−0.179856	+	0.763815i
$565$	3.51687	−	3.51687i	0.147956	−	0.147956i
$566$	−38.7388	+	38.7388i	−1.62831	+	1.62831i
$567$	−1.39661	+	9.93666i	−0.0586520	+	0.417301i
$568$	−12.3610			−0.518658
$569$	−11.5701			−0.485043			−0.242521	−	0.970146i	$-0.577974\pi$
$569$	−11.5701			−0.485043			−0.242521	+	0.970146i	$0.577974\pi$
$570$	6.40384	−	27.1958i	0.268228	−	1.13911i
$571$		−	35.1071i		−	1.46919i	−0.678508	−	0.734593i	$-0.737373\pi$
$571$		−	35.1071i		−	1.46919i	0.678508	−	0.734593i	$-0.262627\pi$
$572$	3.60808	−	3.02912i	0.150862	−	0.126654i
$573$	−10.4966	+	6.49545i	−0.438502	+	0.271351i
$574$	11.5362	−	11.5362i	0.481511	−	0.481511i
$575$		−	0.151701i		−	0.00632635i
$576$	−4.89876	−	2.44246i	−0.204115	−	0.101769i
$577$	4.12501	−	4.12501i	0.171726	−	0.171726i	−0.616011	−	0.787738i	$-0.711252\pi$
$577$	4.12501	−	4.12501i	0.171726	−	0.171726i	0.787738	+	0.616011i	$0.211252\pi$
$578$	21.5083	+	21.5083i	0.894629	+	0.894629i
$579$	−4.43400	+	18.8303i	−0.184271	+	0.782560i
$580$	18.4820	+	18.4820i	0.767423	+	0.767423i
$581$			1.91673i			0.0795192i
$582$	−10.4579	−	16.8999i	−0.433494	−	0.700522i
$583$	−5.88140	−	5.88140i	−0.243583	−	0.243583i
$584$	−0.101404			−0.00419612
$585$	5.58777	+	23.2490i	0.231026	+	0.961227i
$586$	30.0328			1.24064
$587$	−2.22893	−	2.22893i	−0.0919977	−	0.0919977i	0.659610	−	0.751608i	$-0.270721\pi$
$587$	−2.22893	−	2.22893i	−0.0919977	−	0.0919977i	−0.751608	+	0.659610i	$0.770721\pi$
$588$	6.85579	+	11.0789i	0.282728	+	0.456886i
$589$		−	37.9500i		−	1.56370i
$590$	12.4331	+	12.4331i	0.511864	+	0.511864i
$591$	6.22211	−	26.4241i	0.255943	−	1.08694i
$592$	−0.586564	−	0.586564i	−0.0241076	−	0.0241076i
$593$	13.8061	−	13.8061i	0.566949	−	0.566949i	−0.364324	−	0.931272i	$-0.618700\pi$
$593$	13.8061	−	13.8061i	0.566949	−	0.566949i	0.931272	+	0.364324i	$0.118700\pi$
$594$	−9.40909	+	0.864502i	−0.386060	+	0.0354710i
$595$		−	1.28662i		−	0.0527463i
$596$	−1.79090	+	1.79090i	−0.0733580	+	0.0733580i
$597$	−27.3788	+	16.9424i	−1.12054	+	0.693407i
$598$	6.72049	−	5.64210i	0.274821	−	0.230723i
$599$		−	15.8311i		−	0.646840i	−0.946256	−	0.323420i	$-0.895167\pi$
$599$		−	15.8311i		−	0.646840i	0.946256	−	0.323420i	$-0.104833\pi$
$600$	−0.0567364	+	0.240948i	−0.00231625	+	0.00983667i
$601$	−44.1901			−1.80255			−0.901276	−	0.433246i	$-0.857368\pi$
$601$	−44.1901			−1.80255			−0.901276	+	0.433246i	$0.857368\pi$
$602$	−19.0261			−0.775445
$603$	3.29020	+	9.83353i	0.133987	+	0.400452i
$604$	5.26949	−	5.26949i	0.214412	−	0.214412i
$605$	−1.56311	+	1.56311i	−0.0635496	+	0.0635496i
$606$	−6.88731	+	29.2490i	−0.279778	+	1.18816i
$607$	42.3343			1.71830			0.859149	−	0.511725i	$-0.170993\pi$
$607$	42.3343			1.71830			0.859149	+	0.511725i	$0.170993\pi$
$608$	25.6802			1.04147
$609$	17.0099	+	4.00535i	0.689276	+	0.162305i
$610$		−	38.7579i		−	1.56926i
$611$	19.0903	+	22.7391i	0.772310	+	0.919925i
$612$	1.83128	+	0.913053i	0.0740250	+	0.0369080i
$613$	8.84377	−	8.84377i	0.357196	−	0.357196i	−0.505582	−	0.862779i	$-0.668722\pi$
$613$	8.84377	−	8.84377i	0.357196	−	0.357196i	0.862779	+	0.505582i	$0.168722\pi$
$614$		−	9.49991i		−	0.383385i
$615$	−26.2003	+	16.2131i	−1.05650	+	0.653777i
$616$	−0.994037	+	0.994037i	−0.0400509	+	0.0400509i
$617$	−26.3372	−	26.3372i	−1.06030	−	1.06030i	−0.998061	−	0.0622362i	$-0.980177\pi$
$617$	−26.3372	−	26.3372i	−1.06030	−	1.06030i	−0.0622362	−	0.998061i	$-0.519823\pi$
$618$	−56.7362	−	13.3598i	−2.28227	−	0.537408i
$619$	−31.8343	−	31.8343i	−1.27953	−	1.27953i	−0.940932	−	0.338595i	$-0.890048\pi$
$619$	−31.8343	−	31.8343i	−1.27953	−	1.27953i	−0.338595	−	0.940932i	$-0.609952\pi$
$620$			27.3148i			1.09699i
$621$	−6.92523	+	0.636287i	−0.277900	+	0.0255333i
$622$	−1.37360	−	1.37360i	−0.0550762	−	0.0550762i
$623$	10.1068			0.404920
$624$	−27.3555	+	13.7970i	−1.09510	+	0.552323i
$625$	24.4204			0.976817
$626$	−25.5692	−	25.5692i	−1.02195	−	1.02195i
$627$	5.91049	−	3.65750i	0.236042	−	0.146067i
$628$			5.55254i			0.221570i
$629$	0.0624147	+	0.0624147i	0.00248864	+	0.00248864i
$630$	4.26613	+	12.7503i	0.169967	+	0.507985i
$631$	−18.9788	−	18.9788i	−0.755536	−	0.755536i	0.219971	−	0.975506i	$-0.429404\pi$
$631$	−18.9788	−	18.9788i	−0.755536	−	0.755536i	−0.975506	+	0.219971i	$0.929404\pi$
$632$	3.61616	−	3.61616i	0.143843	−	0.143843i
$633$	3.66332	+	5.91988i	0.145604	+	0.235294i
$634$		−	6.18603i		−	0.245679i
$635$	11.5918	−	11.5918i	0.460006	−	0.460006i
$636$	−9.90515	−	16.0066i	−0.392765	−	0.634704i
$637$	20.6784	+	1.80378i	0.819309	+	0.0714685i
$638$			16.4553i			0.651470i
$639$	−27.8909	+	9.33200i	−1.10335	+	0.369168i
$640$	20.9580			0.828437
$641$	−8.13142			−0.321172			−0.160586	−	0.987022i	$-0.551338\pi$
$641$	−8.13142			−0.321172			−0.160586	+	0.987022i	$0.551338\pi$
$642$	−36.0843	−	8.49681i	−1.42413	−	0.335342i
$643$	6.51430	−	6.51430i	0.256899	−	0.256899i	−0.566893	−	0.823792i	$-0.691855\pi$
$643$	6.51430	−	6.51430i	0.256899	−	0.256899i	0.823792	+	0.566893i	$0.191855\pi$
$644$	1.37865	−	1.37865i	0.0543263	−	0.0543263i
$645$	34.9752	+	8.23566i	1.37715	+	0.324279i
$646$	−3.80937			−0.149878
$647$	−27.0333			−1.06279			−0.531394	−	0.847125i	$-0.678332\pi$
$647$	−27.0333			−1.06279			−0.531394	+	0.847125i	$0.678332\pi$
$648$	11.2374	+	1.57943i	0.441447	+	0.0620459i
$649$			4.37420i			0.171702i
$650$	−0.477829	−	0.569158i	−0.0187420	−	0.0223242i
$651$	9.60982	+	15.5294i	0.376639	+	0.608644i
$652$	−15.8720	+	15.8720i	−0.621594	+	0.621594i
$653$			17.2211i			0.673913i	0.941520	+	0.336956i	$0.109398\pi$
$653$			17.2211i			0.673913i	−0.941520	+	0.336956i	$0.890602\pi$
$654$	3.66483	+	5.92234i	0.143306	+	0.231582i
$655$	−29.8149	+	29.8149i	−1.16496	+	1.16496i
$656$	−27.9159	−	27.9159i	−1.08993	−	1.08993i
$657$	−0.228803	+	0.0765551i	−0.00892645	+	0.00298670i
$658$	11.8049	+	11.8049i	0.460203	+	0.460203i
$659$		−	26.9054i		−	1.04809i	−0.851692	−	0.524043i	$-0.824423\pi$
$659$		−	26.9054i		−	1.04809i	0.851692	−	0.524043i	$-0.175577\pi$
$660$	−4.25413	+	2.63252i	−0.165592	+	0.102471i
$661$	3.96884	+	3.96884i	0.154370	+	0.154370i	0.780067	−	0.625697i	$-0.215185\pi$
$661$	3.96884	+	3.96884i	0.154370	+	0.154370i	−0.625697	+	0.780067i	$0.715185\pi$
$662$	32.6810			1.27018
$663$	2.91083	−	1.46810i	0.113047	−	0.0570165i
$664$	2.16763			0.0841205
$665$	−6.99358	−	6.99358i	−0.271200	−	0.271200i
$666$	−0.825478	−	0.411574i	−0.0319866	−	0.0159481i
$667$			12.1113i			0.468952i
$668$	−10.7355	−	10.7355i	−0.415367	−	0.415367i
$669$	15.5162	+	3.65361i	0.599889	+	0.141257i
$670$	9.82456	+	9.82456i	0.379556	+	0.379556i
$671$	6.81786	−	6.81786i	0.263201	−	0.263201i
$672$	−10.5085	+	6.50283i	−0.405375	+	0.250852i
$673$			18.7746i			0.723709i	0.932235	+	0.361854i	$0.117856\pi$
$673$			18.7746i			0.723709i	−0.932235	+	0.361854i	$0.882144\pi$
$674$	27.0902	−	27.0902i	1.04348	−	1.04348i
$675$	0.0538871	+	0.586497i	0.00207411	+	0.0225743i
$676$	2.94099	−	16.7293i	0.113115	−	0.643436i
$677$		−	15.5408i		−	0.597283i	−0.954365	−	0.298641i	$-0.903467\pi$
$677$		−	15.5408i		−	0.597283i	0.954365	−	0.298641i	$-0.0965335\pi$
$678$	6.89761	+	1.62419i	0.264901	+	0.0623766i
$679$	−7.03522			−0.269987
$680$	−1.45504			−0.0557984
$681$	−6.87295	+	29.1880i	−0.263372	+	1.11849i
$682$	−12.1597	+	12.1597i	−0.465621	+	0.465621i
$683$	−12.7370	+	12.7370i	−0.487367	+	0.487367i	−0.907474	−	0.420107i	$-0.861992\pi$
$683$	−12.7370	+	12.7370i	−0.487367	+	0.487367i	0.420107	+	0.907474i	$0.361992\pi$
$684$	14.9172	−	4.99113i	0.570372	−	0.190841i
$685$	−1.54824			−0.0591551
$686$	25.8633			0.987464
$687$	0.596407	−	2.53282i	0.0227543	−	0.0966331i
$688$			46.0404i			1.75527i
$689$	−29.8759	−	2.60608i	−1.13818	−	0.0992839i
$690$	−7.92383	+	4.90339i	−0.301655	+	0.186669i
$691$	−10.0654	+	10.0654i	−0.382904	+	0.382904i	−0.872148	−	0.489243i	$-0.837273\pi$
$691$	−10.0654	+	10.0654i	−0.382904	+	0.382904i	0.489243	+	0.872148i	$0.337273\pi$
$692$			25.0446i			0.952052i
$693$	−1.49245	+	2.99335i	−0.0566934	+	0.113708i
$694$	24.8595	−	24.8595i	0.943655	−	0.943655i
$695$	−32.3436	−	32.3436i	−1.22686	−	1.22686i
$696$	4.52967	−	19.2366i	0.171697	−	0.729161i
$697$	2.97046	+	2.97046i	0.112514	+	0.112514i
$698$		−	5.56621i		−	0.210684i
$699$	−10.7458	−	17.3652i	−0.406445	−	0.656811i
$700$	−0.116757	−	0.116757i	−0.00441302	−	0.00441302i
$701$	16.1680			0.610658			0.305329	−	0.952247i	$-0.401233\pi$
$701$	16.1680			0.610658			0.305329	+	0.952247i	$0.401233\pi$
$702$	−23.9782	+	24.2005i	−0.905001	+	0.913387i
$703$	0.678526			0.0255911
$704$	−1.29021	−	1.29021i	−0.0486266	−	0.0486266i
$705$	−16.5908	−	26.8106i	−0.624846	−	1.00975i
$706$		−	12.4143i		−	0.467220i
$707$	7.52157	+	7.52157i	0.282878	+	0.282878i
$708$	−2.26894	+	9.63575i	−0.0852721	+	0.362134i
$709$	23.5513	+	23.5513i	0.884488	+	0.884488i	0.993987	−	0.109499i	$-0.0349246\pi$
$709$	23.5513	+	23.5513i	0.884488	+	0.884488i	−0.109499	+	0.993987i	$0.534925\pi$
$710$	−27.8654	+	27.8654i	−1.04577	+	1.04577i
$711$	5.42930	−	10.8894i	0.203615	−	0.408383i
$712$		−	11.4298i		−	0.428351i
$713$	−8.94976	+	8.94976i	−0.335171	+	0.335171i
$714$	1.55882	−	0.964621i	0.0583373	−	0.0361000i
$715$	−0.692626	+	7.94020i	−0.0259027	+	0.296947i
$716$		−	25.2751i		−	0.944575i
$717$	−2.39939	+	10.1897i	−0.0896067	+	0.380542i
$718$	31.5257			1.17653
$719$	0.204240			0.00761686			0.00380843	−	0.999993i	$-0.498788\pi$
$719$	0.204240			0.00761686			0.00380843	+	0.999993i	$0.498788\pi$
$720$	30.8540	−	10.3234i	1.14986	−	0.384731i
$721$	−14.5901	+	14.5901i	−0.543363	+	0.543363i
$722$	3.72405	−	3.72405i	0.138595	−	0.138595i
$723$	−4.33635	+	18.4156i	−0.161271	+	0.684884i
$724$	−6.43783			−0.239260
$725$	1.02571			0.0380938
$726$	−3.06573	−	0.721891i	−0.113780	−	0.0267919i
$727$			8.07388i			0.299444i	0.988728	+	0.149722i	$0.0478378\pi$
$727$			8.07388i			0.299444i	−0.988728	+	0.149722i	$0.952162\pi$
$728$	−0.440464	+	5.04944i	−0.0163247	+	0.187145i
$729$	26.5480	−	4.91996i	0.983258	−	0.182221i
$730$	−0.228594	+	0.228594i	−0.00846064	+	0.00846064i
$731$		−	4.89904i		−	0.181197i
$732$	18.5553	−	11.4823i	0.685824	−	0.424398i
$733$	18.9941	−	18.9941i	0.701561	−	0.701561i	−0.263184	−	0.964746i	$-0.584773\pi$
$733$	18.9941	−	18.9941i	0.701561	−	0.701561i	0.964746	+	0.263184i	$0.0847727\pi$
$734$	34.1045	+	34.1045i	1.25882	+	1.25882i
$735$	−21.4556	−	5.05217i	−0.791401	−	0.186352i
$736$	−6.05618	−	6.05618i	−0.223234	−	0.223234i
$737$			3.45646i			0.127320i
$738$	−39.2864	−	19.5877i	−1.44615	−	0.721035i
$739$	22.3374	+	22.3374i	0.821693	+	0.821693i	0.986351	−	0.164657i	$-0.0526519\pi$
$739$	22.3374	+	22.3374i	0.821693	+	0.821693i	−0.164657	+	0.986351i	$0.552652\pi$
$740$	−0.488375			−0.0179530
$741$	7.84210	−	23.8022i	0.288087	−	0.874397i
$742$	−16.8629			−0.619057
$743$	30.6813	+	30.6813i	1.12559	+	1.12559i	0.990886	+	0.134701i	$0.0430074\pi$
$743$	30.6813	+	30.6813i	1.12559	+	1.12559i	0.134701	+	0.990886i	$0.456993\pi$
$744$	17.5622	−	10.8678i	0.643863	−	0.398432i
$745$		−	4.28496i		−	0.156989i
$746$	14.8636	+	14.8636i	0.544196	+	0.544196i
$747$	4.89094	−	1.63646i	0.178950	−	0.0598749i
$748$	0.482312	+	0.482312i	0.0176351	+	0.0176351i
$749$	−9.27930	+	9.27930i	−0.339058	+	0.339058i
$750$	18.7337	+	30.2735i	0.684058	+	1.10543i
$751$			40.6665i			1.48394i	0.670433	+	0.741970i	$0.266109\pi$
$751$			40.6665i			1.48394i	−0.670433	+	0.741970i	$0.733891\pi$
$752$	28.5662	−	28.5662i	1.04170	−	1.04170i
$753$	−8.86274	−	14.3221i	−0.322976	−	0.521926i
$754$	38.1484	+	45.4399i	1.38928	+	1.65482i
$755$			12.6080i			0.458850i
$756$	−4.84033	+	5.81978i	−0.176041	+	0.211663i
$757$	20.4689			0.743956			0.371978	−	0.928242i	$-0.378680\pi$
$757$	20.4689			0.743956			0.371978	+	0.928242i	$0.378680\pi$
$758$	−33.4142			−1.21366
$759$	−2.25642	−	0.531323i	−0.0819029	−	0.0192858i
$760$	−7.90907	+	7.90907i	−0.286892	+	0.286892i
$761$	6.16551	−	6.16551i	0.223500	−	0.223500i	−0.586471	−	0.809970i	$-0.699483\pi$
$761$	6.16551	−	6.16551i	0.223500	−	0.223500i	0.809970	+	0.586471i	$0.199483\pi$
$762$	22.7349	+	5.35342i	0.823598	+	0.193934i
$763$	2.46540			0.0892535
$764$	−9.31178			−0.336888
$765$	−3.28309	+	1.09849i	−0.118700	+	0.0397159i
$766$			19.8498i			0.717203i
$767$	10.1408	+	12.0790i	0.366162	+	0.436147i
$768$	19.0389	+	30.7667i	0.687008	+	1.11020i
$769$	−12.2760	+	12.2760i	−0.442686	+	0.442686i	−0.892914	−	0.450228i	$-0.851343\pi$
$769$	−12.2760	+	12.2760i	−0.442686	+	0.442686i	0.450228	+	0.892914i	$0.351343\pi$
$770$			4.48170i			0.161509i
$771$	20.9790	+	33.9019i	0.755540	+	1.22095i
$772$	−10.3192	+	10.3192i	−0.371394	+	0.371394i
$773$	20.3279	+	20.3279i	0.731143	+	0.731143i	0.970846	−	0.239703i	$-0.0770501\pi$
$773$	20.3279	+	20.3279i	0.731143	+	0.731143i	−0.239703	+	0.970846i	$0.577050\pi$
$774$	16.2441	+	48.5492i	0.583881	+	1.74506i
$775$	0.757954	+	0.757954i	0.0272265	+	0.0272265i
$776$			7.95616i			0.285610i
$777$	−0.277657	+	0.171819i	−0.00996090	+	0.00616396i
$778$	−18.9071	−	18.9071i	−0.677852	−	0.677852i
$779$	32.2926			1.15700
$780$	−5.64442	+	17.1319i	−0.202103	+	0.613419i
$781$	−9.80355			−0.350799
$782$	0.898365	+	0.898365i	0.0321255	+	0.0321255i
$783$	−4.30218	−	46.8242i	−0.153747	−	1.67336i
$784$		−	28.2435i		−	1.00870i
$785$	−6.64260	−	6.64260i	−0.237084	−	0.237084i
$786$	−58.4758	−	13.7694i	−2.08576	−	0.491137i
$787$	−23.2166	−	23.2166i	−0.827583	−	0.827583i	0.159599	−	0.987182i	$-0.448980\pi$
$787$	−23.2166	−	23.2166i	−0.827583	−	0.827583i	−0.987182	+	0.159599i	$0.948980\pi$
$788$	14.4806	−	14.4806i	0.515850	−	0.515850i
$789$	0.715015	−	0.442462i	0.0254552	−	0.0157521i
$790$		−	16.3038i		−	0.580062i
$791$	1.77376	−	1.77376i	0.0630678	−	0.0630678i
$792$	3.38519	+	1.68781i	0.120287	+	0.0599739i
$793$	3.02104	−	34.6329i	0.107280	−	1.22985i
$794$		−	59.9544i		−	2.12770i
$795$	30.9987	+	7.29931i	1.09941	+	0.258880i
$796$	−24.2884			−0.860879
$797$	−53.2547			−1.88638			−0.943189	−	0.332257i	$-0.892190\pi$
$797$	−53.2547			−1.88638			−0.943189	+	0.332257i	$0.892190\pi$
$798$	3.22984	−	13.7165i	0.114335	−	0.485558i
$799$	−3.03965	+	3.03965i	−0.107535	+	0.107535i
$800$	−0.512897	+	0.512897i	−0.0181336	+	0.0181336i
$801$	−8.62897	−	25.7897i	−0.304890	−	0.911234i
$802$	−7.79486			−0.275246
$803$	−0.0804235			−0.00283808
$804$	−1.79290	+	7.61409i	−0.0632307	+	0.268528i
$805$			3.29860i			0.116260i
$806$	−5.38806	+	61.7682i	−0.189786	+	2.17569i
$807$	−42.4588	+	26.2741i	−1.49462	+	0.924894i
$808$	8.50617	−	8.50617i	0.299246	−	0.299246i
$809$		−	44.0038i		−	1.54709i	−0.633740	−	0.773546i	$-0.718481\pi$
$809$		−	44.0038i		−	1.54709i	0.633740	−	0.773546i	$-0.281519\pi$
$810$	28.8929	−	21.7719i	1.01519	−	0.764987i
$811$	3.62785	−	3.62785i	0.127391	−	0.127391i	−0.640537	−	0.767928i	$-0.721288\pi$
$811$	3.62785	−	3.62785i	0.127391	−	0.127391i	0.767928	+	0.640537i	$0.221288\pi$
$812$	9.32157	+	9.32157i	0.327123	+	0.327123i
$813$	−6.57200	+	27.9100i	−0.230490	+	0.978845i
$814$	−0.217410	−	0.217410i	−0.00762021	−	0.00762021i
$815$		−	37.9758i		−	1.33023i
$816$	−2.33425	−	3.77212i	−0.0817150	−	0.132051i
$817$	−26.6293	−	26.6293i	−0.931643	−	0.931643i
$818$	59.8707			2.09333
$819$	2.81824	+	11.7258i	0.0984774	+	0.409734i
$820$	−23.2429			−0.811677
$821$	17.1645	+	17.1645i	0.599046	+	0.599046i	0.940059	−	0.341012i	$-0.110770\pi$
$821$	17.1645	+	17.1645i	0.599046	+	0.599046i	−0.341012	+	0.940059i	$0.610770\pi$
$822$	−1.16077	−	1.87579i	−0.0404863	−	0.0654256i
$823$			19.0812i			0.665129i	0.943081	+	0.332564i	$0.107914\pi$
$823$			19.0812i			0.665129i	−0.943081	+	0.332564i	$0.892086\pi$
$824$	16.5000	+	16.5000i	0.574804	+	0.574804i
$825$	−0.0449977	+	0.191096i	−0.00156662	+	0.00665311i
$826$	6.27077	+	6.27077i	0.218188	+	0.218188i
$827$	13.2207	−	13.2207i	0.459730	−	0.459730i	−0.438837	−	0.898567i	$-0.644609\pi$
$827$	13.2207	−	13.2207i	0.459730	−	0.459730i	0.898567	+	0.438837i	$0.144609\pi$
$828$	−4.69498	−	2.34086i	−0.163162	−	0.0813505i
$829$			46.8711i			1.62790i	0.580935	+	0.813950i	$0.302687\pi$
$829$			46.8711i			1.62790i	−0.580935	+	0.813950i	$0.697313\pi$
$830$	4.88648	−	4.88648i	0.169612	−	0.169612i
$831$	−4.32465	+	2.67616i	−0.150020	+	0.0928349i
$832$	−6.55391	−	0.571700i	−0.227216	−	0.0198201i
$833$			3.00532i			0.104128i
$834$	14.9372	−	63.4353i	0.517233	−	2.19658i
$835$	25.6860			0.888902
$836$	5.24333			0.181345
$837$	31.4220	−	37.7802i	1.08610	−	1.30588i
$838$	−13.6802	+	13.6802i	−0.472573	+	0.472573i
$839$	33.1942	−	33.1942i	1.14599	−	1.14599i	0.158657	−	0.987334i	$-0.449283\pi$
$839$	33.1942	−	33.1942i	1.14599	−	1.14599i	0.987334	−	0.158657i	$-0.0507166\pi$
$840$	1.23368	−	5.23921i	0.0425661	−	0.180770i
$841$	−52.8894			−1.82377
$842$	61.6774			2.12554
$843$	−32.6864	−	7.69671i	−1.12578	−	0.265089i
$844$			5.25167i			0.180770i
$845$	16.4952	+	23.5319i	0.567453	+	0.809523i
$846$	20.0440	−	40.2016i	0.689128	−	1.38216i
$847$	−0.788371	+	0.788371i	−0.0270888	+	0.0270888i
$848$			40.8059i			1.40128i
$849$	44.3742	−	27.4594i	1.52292	−	0.942405i
$850$	0.0760824	−	0.0760824i	0.00260960	−	0.00260960i
$851$	−0.160017	−	0.160017i	−0.00548531	−	0.00548531i
$852$	−21.5959	−	5.08521i	−0.739862	−	0.174216i
$853$	−29.7377	−	29.7377i	−1.01820	−	1.01820i	−0.999831	−	0.0183675i	$-0.994153\pi$
$853$	−29.7377	−	29.7377i	−1.01820	−	1.01820i	−0.0183675	−	0.999831i	$-0.505847\pi$
$854$		−	19.5479i		−	0.668916i
$855$	−11.8747	+	23.8166i	−0.406106	+	0.814512i
$856$	10.4940	+	10.4940i	0.358677	+	0.358677i
$857$	5.60247			0.191377			0.0956884	−	0.995411i	$-0.469495\pi$
$857$	5.60247			0.191377			0.0956884	+	0.995411i	$0.469495\pi$
$858$	−10.1393	+	5.11387i	−0.346151	+	0.174585i
$859$	20.1831			0.688640			0.344320	−	0.938852i	$-0.388110\pi$
$859$	20.1831			0.688640			0.344320	+	0.938852i	$0.388110\pi$
$860$	19.1667	+	19.1667i	0.653579	+	0.653579i
$861$	−13.2144	+	8.17725i	−0.450344	+	0.278680i
$862$		−	56.6444i		−	1.92932i
$863$	22.3112	+	22.3112i	0.759481	+	0.759481i	0.976228	−	0.216747i	$-0.0695446\pi$
$863$	22.3112	+	22.3112i	0.759481	+	0.759481i	−0.216747	+	0.976228i	$0.569545\pi$
$864$	25.5654	+	21.2628i	0.869751	+	0.723375i
$865$	−29.9613	−	29.9613i	−1.01871	−	1.01871i
$866$	−15.6303	+	15.6303i	−0.531141	+	0.531141i
$867$	−15.2459	−	24.6372i	−0.517776	−	0.836722i
$868$			13.7765i			0.467604i
$869$	2.86798	−	2.86798i	0.0972895	−	0.0972895i
$870$	−33.1537	−	53.5761i	−1.12402	−	1.81640i
$871$	8.01314	+	9.54472i	0.271515	+	0.323410i
$872$		−	2.78813i		−	0.0944181i
$873$	6.00652	+	17.9519i	0.203290	+	0.607580i
$874$	9.76635			0.330352
$875$	12.6025			0.426042
$876$	−0.177162	−	0.0417165i	−0.00598574	−	0.00140947i
$877$	−38.1554	+	38.1554i	−1.28842	+	1.28842i	−0.352669	+	0.935748i	$0.614726\pi$
$877$	−38.1554	+	38.1554i	−1.28842	+	1.28842i	−0.935748	+	0.352669i	$0.885274\pi$
$878$	−17.4903	+	17.4903i	−0.590270	+	0.590270i
$879$	−27.8450	−	6.55669i	−0.939187	−	0.221152i
$880$	10.8451			0.365588
$881$	44.7297			1.50698			0.753491	−	0.657459i	$-0.228369\pi$
$881$	44.7297			1.50698			0.753491	+	0.657459i	$0.228369\pi$
$882$	−9.96493	−	29.7825i	−0.335537	−	1.00283i
$883$			22.7761i			0.766476i	0.923650	+	0.383238i	$0.125191\pi$
$883$			22.7761i			0.766476i	−0.923650	+	0.383238i	$0.874809\pi$
$884$	2.45001	+	0.213715i	0.0824029	+	0.00718803i
$885$	−8.81304	−	14.2418i	−0.296247	−	0.478733i
$886$	7.57777	−	7.57777i	0.254580	−	0.254580i
$887$		−	24.6390i		−	0.827296i	−0.910437	−	0.413648i	$-0.864254\pi$
$887$		−	24.6390i		−	0.827296i	0.910437	−	0.413648i	$-0.135746\pi$
$888$	0.194310	+	0.314004i	0.00652063	+	0.0105373i
$889$	5.84642	−	5.84642i	0.196083	−	0.196083i
$890$	−25.7662	−	25.7662i	−0.863684	−	0.863684i
$891$	8.91240	+	1.25265i	0.298577	+	0.0419653i
$892$	8.50298	+	8.50298i	0.284701	+	0.284701i
$893$			33.0449i			1.10580i
$894$	5.19150	−	3.21258i	0.173630	−	0.107445i
$895$	30.2371	+	30.2371i	1.01071	+	1.01071i
$896$	10.5703			0.353131
$897$	−7.46270	+	3.76389i	−0.249172	+	0.125672i
$898$	−12.7981			−0.427080
$899$	−60.5128	−	60.5128i	−2.01821	−	2.01821i
$900$	−0.198247	+	0.397617i	−0.00660824	+	0.0132539i
$901$		−	4.34204i		−	0.144654i
$902$	−10.3470	−	10.3470i	−0.344519	−	0.344519i
$903$	17.6401	+	4.15373i	0.587025	+	0.138228i
$904$	−2.00596	−	2.00596i	−0.0667172	−	0.0667172i
$905$	7.70169	−	7.70169i	0.256013	−	0.256013i
$906$	−15.2753	+	9.45260i	−0.507488	+	0.314042i
$907$			26.1756i			0.869147i	0.900636	+	0.434573i	$0.143101\pi$
$907$			26.1756i			0.869147i	−0.900636	+	0.434573i	$0.856899\pi$
$908$	−15.9953	+	15.9953i	−0.530822	+	0.530822i
$909$	12.7712	−	25.6147i	0.423593	−	0.849585i
$910$	10.3900	+	12.3758i	0.344424	+	0.410255i
$911$		−	53.7586i		−	1.78110i	−0.454884	−	0.890551i	$-0.650319\pi$
$911$		−	53.7586i		−	1.78110i	0.454884	−	0.890551i	$-0.349681\pi$
$912$	−33.1919	−	7.81575i	−1.09909	−	0.258805i
$913$	1.71915			0.0568956
$914$	−42.0062			−1.38944
$915$	−8.46155	+	35.9345i	−0.279730	+	1.18796i
$916$	1.38801	−	1.38801i	0.0458610	−	0.0458610i
$917$	−15.0374	+	15.0374i	−0.496579	+	0.496579i
$918$	−3.79233	−	3.15409i	−0.125165	−	0.104101i
$919$	−22.0970			−0.728913			−0.364457	−	0.931220i	$-0.618745\pi$
$919$	−22.0970			−0.728913			−0.364457	+	0.931220i	$0.618745\pi$
$920$	3.73040			0.122988
$921$	−2.07400	+	8.80787i	−0.0683407	+	0.290229i
$922$		−	38.9505i		−	1.28277i
$923$	−27.0717	+	22.7277i	−0.891076	+	0.748091i
$924$	−2.14561	+	1.32773i	−0.0705853	+	0.0436793i
$925$	−0.0135518	+	0.0135518i	−0.000445581	+	0.000445581i
$926$			54.7340i			1.79867i
$927$	49.6865	+	24.7731i	1.63192	+	0.813654i
$928$	40.9482	−	40.9482i	1.34419	−	1.34419i
$929$	−28.8285	−	28.8285i	−0.945833	−	0.945833i	0.0527731	−	0.998607i	$-0.483194\pi$
$929$	−28.8285	−	28.8285i	−0.945833	−	0.945833i	−0.998607	+	0.0527731i	$0.983194\pi$
$930$	15.0913	−	64.0896i	0.494862	−	2.10158i
$931$	16.3358	+	16.3358i	0.535384	+	0.535384i
$932$		−	15.4051i		−	0.504609i
$933$	0.973654	+	1.57342i	0.0318760	+	0.0515113i
$934$	−50.4848	−	50.4848i	−1.65191	−	1.65191i
$935$	−1.15400			−0.0377397
$936$	13.2608	−	3.18716i	0.433443	−	0.104176i
$937$	38.7966			1.26743			0.633715	−	0.773567i	$-0.281529\pi$
$937$	38.7966			1.26743			0.633715	+	0.773567i	$0.281529\pi$
$938$	4.95511	+	4.95511i	0.161790	+	0.161790i
$939$	18.1243	+	29.2888i	0.591465	+	0.955803i
$940$		−	23.7843i		−	0.775759i
$941$	−27.6505	−	27.6505i	−0.901382	−	0.901382i	0.0941737	−	0.995556i	$-0.469979\pi$
$941$	−27.6505	−	27.6505i	−0.901382	−	0.901382i	−0.995556	+	0.0941737i	$0.969979\pi$
$942$	3.06774	−	13.0281i	0.0999525	−	0.424478i
$943$	−7.61558	−	7.61558i	−0.247997	−	0.247997i
$944$	15.1744	−	15.1744i	0.493884	−	0.493884i
$945$	−1.17173	−	12.7529i	−0.0381163	−	0.414851i
$946$			17.0649i			0.554827i
$947$	−39.1653	+	39.1653i	−1.27270	+	1.27270i	−0.328038	+	0.944664i	$0.606388\pi$
$947$	−39.1653	+	39.1653i	−1.27270	+	1.27270i	−0.944664	+	0.328038i	$0.893612\pi$
$948$	7.80540	−	4.83010i	0.253508	−	0.156874i
$949$	−0.222083	+	0.186447i	−0.00720911	+	0.00605232i
$950$		−	0.827111i		−	0.0268350i
$951$	−1.35052	+	5.73539i	−0.0437936	+	0.185983i
$952$	−0.733865			−0.0237847
$953$	−31.5484			−1.02195			−0.510976	−	0.859595i	$-0.670716\pi$
$953$	−31.5484			−1.02195			−0.510976	+	0.859595i	$0.670716\pi$
$954$	14.3972	+	43.0294i	0.466126	+	1.39313i
$955$	11.1398	−	11.1398i	0.360477	−	0.360477i
$956$	−5.58405	+	5.58405i	−0.180601	+	0.180601i
$957$	3.59248	−	15.2565i	0.116128	−	0.493174i
$958$	−67.0450			−2.16613
$959$	−0.780868			−0.0252156
$960$	6.80023	+	1.60126i	0.219476	+	0.0516804i
$961$		−	58.4327i		−	1.88493i
$962$	−1.10438	−	0.0963357i	−0.0356068	−	0.00310599i
$963$	31.6006	+	15.7557i	1.01832	+	0.507720i
$964$	−10.0919	+	10.0919i	−0.325038	+	0.325038i
$965$		−	24.6900i		−	0.794798i
$966$	−3.99646	+	2.47307i	−0.128584	+	0.0795697i
$967$	−16.6633	+	16.6633i	−0.535857	+	0.535857i	−0.922309	−	0.386452i	$-0.873700\pi$
$967$	−16.6633	+	16.6633i	−0.535857	+	0.535857i	0.386452	+	0.922309i	$0.373700\pi$
$968$	0.891573	+	0.891573i	0.0286562	+	0.0286562i
$969$	3.53187	+	0.831653i	0.113460	+	0.0267166i
$970$	17.9355	+	17.9355i	0.575875	+	0.575875i
$971$			23.1535i			0.743032i	0.928426	+	0.371516i	$0.121162\pi$
$971$			23.1535i			0.743032i	−0.928426	+	0.371516i	$0.878838\pi$
$972$	18.9830	+	7.38236i	0.608880	+	0.236789i
$973$	−16.3128	−	16.3128i	−0.522964	−	0.522964i
$974$	−59.5702			−1.90875
$975$	0.318763	+	0.632015i	0.0102086	+	0.0202407i
$976$	−47.3032			−1.51414
$977$	−6.15179	−	6.15179i	−0.196813	−	0.196813i	0.601819	−	0.798632i	$-0.294443\pi$
$977$	−6.15179	−	6.15179i	−0.196813	−	0.196813i	−0.798632	+	0.601819i	$0.794443\pi$
$978$	46.0100	−	28.4717i	1.47124	−	0.910425i
$979$		−	9.06500i		−	0.289719i
$980$	−11.7578	−	11.7578i	−0.375590	−	0.375590i
$981$	−2.10491	−	6.29101i	−0.0672045	−	0.200856i
$982$	−24.0727	−	24.0727i	−0.768190	−	0.768190i
$983$	1.16495	−	1.16495i	0.0371563	−	0.0371563i	−0.688285	−	0.725441i	$-0.741636\pi$
$983$	1.16495	−	1.16495i	0.0371563	−	0.0371563i	0.725441	+	0.688285i	$0.241636\pi$
$984$	9.24768	+	14.9442i	0.294805	+	0.476403i
$985$			34.6468i			1.10394i
$986$	−6.07419	+	6.07419i	−0.193442	+	0.193442i
$987$	−8.36773	−	13.5222i	−0.266348	−	0.430416i
$988$	14.4790	−	12.1557i	0.460640	−	0.386724i
$989$			12.5600i			0.399385i
$990$	11.4360	−	3.82638i	0.363461	−	0.121610i
$991$	43.9819			1.39713			0.698565	−	0.715546i	$-0.253822\pi$
$991$	43.9819			1.39713			0.698565	+	0.715546i	$0.253822\pi$
$992$	60.5179			1.92145
$993$	−30.3003	−	7.13485i	−0.961551	−	0.226418i
$994$	−14.0542	+	14.0542i	−0.445771	+	0.445771i
$995$	29.0566	−	29.0566i	0.921157	−	0.921157i
$996$	3.78705	+	0.891742i	0.119997	+	0.0282559i
$997$	−11.4532			−0.362727			−0.181363	−	0.983416i	$-0.558051\pi$
$997$	−11.4532			−0.362727			−0.181363	+	0.983416i	$0.558051\pi$
$998$	−14.1334			−0.447384
$999$	0.675491	+	0.561808i	0.0213716	+	0.0177748i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.11	✓	96
3.2	odd	2	inner	429.2.j.a.122.38	yes	96
13.8	odd	4	inner	429.2.j.a.320.38	yes	96
39.8	even	4	inner	429.2.j.a.320.11	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.11	✓	96	1.1	even	1	trivial
429.2.j.a.122.38	yes	96	3.2	odd	2	inner
429.2.j.a.320.11	yes	96	39.8	even	4	inner
429.2.j.a.320.38	yes	96	13.8	odd	4	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28581 - 1.28581i) q^{2} +(0.911426 + 1.47286i) q^{3} +1.30661i q^{4} +(-1.56311 - 1.56311i) q^{5} +(0.721891 - 3.06573i) q^{6} +(-0.788371 - 0.788371i) q^{7} +(-0.891573 + 0.891573i) q^{8} +(-1.33861 + 2.68480i) q^{9} +O(q^{10})\)	\(q+(-1.28581 - 1.28581i) q^{2} +(0.911426 + 1.47286i) q^{3} +1.30661i q^{4} +(-1.56311 - 1.56311i) q^{5} +(0.721891 - 3.06573i) q^{6} +(-0.788371 - 0.788371i) q^{7} +(-0.891573 + 0.891573i) q^{8} +(-1.33861 + 2.68480i) q^{9} +4.01973i q^{10} +(-0.707107 + 0.707107i) q^{11} +(-1.92444 + 1.19087i) q^{12} +(-0.313323 + 3.59191i) q^{13} +2.02739i q^{14} +(0.877579 - 3.72690i) q^{15} +4.90599 q^{16} -0.522034 q^{17} +(5.17332 - 1.73094i) q^{18} +(-2.83758 + 2.83758i) q^{19} +(2.04237 - 2.04237i) q^{20} +(0.442615 - 1.87970i) q^{21} +1.81841 q^{22} +1.33838 q^{23} +(-2.12576 - 0.500556i) q^{24} -0.113347i q^{25} +(5.02138 - 4.21564i) q^{26} +(-5.17436 + 0.475417i) q^{27} +(1.03009 - 1.03009i) q^{28} +9.04928i q^{29} +(-5.92048 + 3.66369i) q^{30} +(-6.68703 + 6.68703i) q^{31} +(-4.52502 - 4.52502i) q^{32} +(-1.68594 - 0.396991i) q^{33} +(0.671235 + 0.671235i) q^{34} +2.46463i q^{35} +(-3.50797 - 1.74903i) q^{36} +(-0.119561 - 0.119561i) q^{37} +7.29717 q^{38} +(-5.57594 + 2.81228i) q^{39} +2.78726 q^{40} +(-5.69017 - 5.69017i) q^{41} +(-2.98605 + 1.84781i) q^{42} +9.38452i q^{43} +(-0.923909 - 0.923909i) q^{44} +(6.28904 - 2.10425i) q^{45} +(-1.72089 - 1.72089i) q^{46} +(5.82272 - 5.82272i) q^{47} +(4.47145 + 7.22582i) q^{48} -5.75694i q^{49} +(-0.145742 + 0.145742i) q^{50} +(-0.475795 - 0.768880i) q^{51} +(-4.69321 - 0.409390i) q^{52} +8.31755i q^{53} +(7.26453 + 6.04194i) q^{54} +2.21058 q^{55} +1.40578 q^{56} +(-6.76559 - 1.59310i) q^{57} +(11.6356 - 11.6356i) q^{58} +(3.09303 - 3.09303i) q^{59} +(4.86959 + 1.14665i) q^{60} -9.64192 q^{61} +17.1965 q^{62} +(3.17194 - 1.06130i) q^{63} +1.82463i q^{64} +(6.10433 - 5.12481i) q^{65} +(1.65734 + 2.67825i) q^{66} +(2.44408 - 2.44408i) q^{67} -0.682092i q^{68} +(1.21983 + 1.97123i) q^{69} +(3.16904 - 3.16904i) q^{70} +(6.93216 + 6.93216i) q^{71} +(-1.20023 - 3.58716i) q^{72} +(0.0568680 + 0.0568680i) q^{73} +0.307464i q^{74} +(0.166944 - 0.103307i) q^{75} +(-3.70760 - 3.70760i) q^{76} +1.11493 q^{77} +(10.7856 + 3.55353i) q^{78} -4.05593 q^{79} +(-7.66863 - 7.66863i) q^{80} +(-5.41626 - 7.18777i) q^{81} +14.6329i q^{82} +(-1.21562 - 1.21562i) q^{83} +(2.45602 + 0.578323i) q^{84} +(0.815998 + 0.815998i) q^{85} +(12.0667 - 12.0667i) q^{86} +(-13.3283 + 8.24774i) q^{87} -1.26087i q^{88} +(-6.40992 + 6.40992i) q^{89} +(-10.7922 - 5.38084i) q^{90} +(3.07878 - 2.58474i) q^{91} +1.74873i q^{92} +(-15.9438 - 3.75430i) q^{93} -14.9738 q^{94} +8.87093 q^{95} +(2.54048 - 10.7889i) q^{96} +(4.46187 - 4.46187i) q^{97} +(-7.40232 + 7.40232i) q^{98} +(-0.951900 - 2.84498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

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