LMFDB - Embedded newform 180.2.q.a.131.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(11,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("180.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.q (of order $6$, 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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.23
Character	$\chi$	$=$	180.131
Dual form			180.2.q.a.11.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34972 - 0.422205i) q^{2} +(-0.561951 - 1.63836i) q^{3} +(1.64349 - 1.13972i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.45020 - 1.97406i) q^{6} +(-0.811773 + 0.468677i) q^{7} +(1.73705 - 2.23218i) q^{8} +(-2.36842 + 1.84135i) q^{9} +O(q^{10})$	\(q+(1.34972 - 0.422205i) q^{2} +(-0.561951 - 1.63836i) q^{3} +(1.64349 - 1.13972i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.45020 - 1.97406i) q^{6} +(-0.811773 + 0.468677i) q^{7} +(1.73705 - 2.23218i) q^{8} +(-2.36842 + 1.84135i) q^{9} +(1.37999 + 0.309220i) q^{10} +(-0.291916 - 0.505614i) q^{11} +(-2.79082 - 2.05215i) q^{12} +(-0.579651 + 1.00399i) q^{13} +(-0.897788 + 0.975317i) q^{14} +(0.332514 - 1.69983i) q^{15} +(1.40209 - 3.74622i) q^{16} -0.238281i q^{17} +(-2.41928 + 3.48527i) q^{18} +7.00703i q^{19} +(1.99316 - 0.165280i) q^{20} +(1.22404 + 1.06660i) q^{21} +(-0.607478 - 0.559189i) q^{22} +(2.53353 - 4.38821i) q^{23} +(-4.63325 - 1.59153i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.358479 + 1.59983i) q^{26} +(4.34773 + 2.84557i) q^{27} +(-0.799978 + 1.69546i) q^{28} +(-7.91811 + 4.57152i) q^{29} +(-0.268878 - 2.43469i) q^{30} +(5.43436 + 3.13753i) q^{31} +(0.310764 - 5.64831i) q^{32} +(-0.664333 + 0.762394i) q^{33} +(-0.100603 - 0.321612i) q^{34} -0.937354 q^{35} +(-1.79385 + 5.72557i) q^{36} +3.50937 q^{37} +(2.95840 + 9.45752i) q^{38} +(1.97062 + 0.385484i) q^{39} +(2.62042 - 1.06460i) q^{40} +(2.86111 + 1.65186i) q^{41} +(2.10243 + 0.922815i) q^{42} +(-9.35224 + 5.39952i) q^{43} +(-1.05602 - 0.498268i) q^{44} +(-2.97179 + 0.410448i) q^{45} +(1.56684 - 6.99252i) q^{46} +(-4.27542 - 7.40525i) q^{47} +(-6.92554 - 0.191938i) q^{48} +(-3.06068 + 5.30126i) q^{49} +(1.04050 + 0.957789i) q^{50} +(-0.390388 + 0.133902i) q^{51} +(0.191609 + 2.31067i) q^{52} -11.9037i q^{53} +(7.06963 + 2.00508i) q^{54} -0.583833i q^{55} +(-0.363917 + 2.62614i) q^{56} +(11.4800 - 3.93761i) q^{57} +(-8.75710 + 9.51333i) q^{58} +(4.94604 - 8.56680i) q^{59} +(-1.39085 - 3.17262i) q^{60} +(-3.33295 - 5.77283i) q^{61} +(8.65955 + 1.94037i) q^{62} +(1.05962 - 2.60479i) q^{63} +(-1.96530 - 7.75484i) q^{64} +(-1.00399 + 0.579651i) q^{65} +(-0.574777 + 1.30950i) q^{66} +(-7.69738 - 4.44408i) q^{67} +(-0.271572 - 0.391611i) q^{68} +(-8.61317 - 1.68487i) q^{69} +(-1.26517 + 0.395755i) q^{70} -8.95946 q^{71} +(-0.00383002 + 8.48528i) q^{72} +11.7312 q^{73} +(4.73666 - 1.48167i) q^{74} +(1.13788 - 1.30584i) q^{75} +(7.98602 + 11.5160i) q^{76} +(0.473940 + 0.273629i) q^{77} +(2.82254 - 0.311710i) q^{78} +(-4.37420 + 2.52545i) q^{79} +(3.08736 - 2.54327i) q^{80} +(2.21884 - 8.72220i) q^{81} +(4.55912 + 1.02158i) q^{82} +(2.36468 + 4.09575i) q^{83} +(3.22731 + 0.357886i) q^{84} +(0.119140 - 0.206357i) q^{85} +(-10.3432 + 11.2364i) q^{86} +(11.9394 + 10.4037i) q^{87} +(-1.63570 - 0.226667i) q^{88} -2.36345i q^{89} +(-3.83779 + 1.80869i) q^{90} -1.08668i q^{91} +(-0.837485 - 10.0995i) q^{92} +(2.08654 - 10.6666i) q^{93} +(-8.89715 - 8.18990i) q^{94} +(-3.50351 + 6.06826i) q^{95} +(-9.42858 + 2.66493i) q^{96} +(-2.26656 - 3.92579i) q^{97} +(-1.89285 + 8.44745i) q^{98} +(1.62240 + 0.659986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 48 * q + 6 * q^6 + 4 * q^9	$ 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42} - 8 q^{45} - 12 q^{46} - 12 q^{48} + 24 q^{49} - 18 q^{52} - 32 q^{54} - 42 q^{56} - 12 q^{57} - 18 q^{58} + 14 q^{60} - 48 q^{64} + 16 q^{66} + 48 q^{68} + 36 q^{69} + 60 q^{72} - 24 q^{73} + 84 q^{74} + 6 q^{76} + 48 q^{77} + 38 q^{78} - 36 q^{82} + 50 q^{84} - 54 q^{86} - 18 q^{90} + 60 q^{92} - 32 q^{93} + 18 q^{94} - 18 q^{96} - 12 q^{97}+O(q^{100}) $ 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.34972	−	0.422205i	0.954396	−	0.298544i
$2$	1.34972	−	0.422205i	0.954396	−	0.298544i
$3$	−0.561951	−	1.63836i	−0.324443	−	0.945905i
$3$	−0.561951	−	1.63836i	−0.324443	−	0.945905i
$4$	1.64349	−	1.13972i	0.821743	−	0.569858i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	−1.45020	−	1.97406i	−0.592041	−	0.805908i
$7$	−0.811773	+	0.468677i	−0.306821	+	0.177143i	−0.645503	−	0.763758i	$-0.723352\pi$
$7$	−0.811773	+	0.468677i	−0.306821	+	0.177143i	0.338682	+	0.940901i	$0.390019\pi$
$8$	1.73705	−	2.23218i	0.614141	−	0.789197i
$9$	−2.36842	+	1.84135i	−0.789474	+	0.613784i
$10$	1.37999	+	0.309220i	0.436392	+	0.0977839i
$11$	−0.291916	−	0.505614i	−0.0880161	−	0.152448i	0.818656	−	0.574284i	$-0.194719\pi$
$11$	−0.291916	−	0.505614i	−0.0880161	−	0.152448i	−0.906672	+	0.421835i	$0.861386\pi$
$12$	−2.79082	−	2.05215i	−0.805640	−	0.592405i
$13$	−0.579651	+	1.00399i	−0.160766	+	0.278455i	−0.935144	−	0.354269i	$-0.884730\pi$
$13$	−0.579651	+	1.00399i	−0.160766	+	0.278455i	0.774377	+	0.632724i	$0.218063\pi$
$14$	−0.897788	+	0.975317i	−0.239944	+	0.260664i
$15$	0.332514	−	1.69983i	0.0858547	−	0.438895i
$16$	1.40209	−	3.74622i	0.350524	−	0.936554i
$17$		−	0.238281i		−	0.0577915i	−0.999582	−	0.0288958i	$-0.990801\pi$
$17$		−	0.238281i		−	0.0577915i	0.999582	−	0.0288958i	$-0.00919909\pi$
$18$	−2.41928	+	3.48527i	−0.570229	+	0.821486i
$19$			7.00703i			1.60752i	0.594952	+	0.803761i	$0.297171\pi$
$19$			7.00703i			1.60752i	−0.594952	+	0.803761i	$0.702829\pi$
$20$	1.99316	−	0.165280i	0.445684	−	0.0369577i
$21$	1.22404	+	1.06660i	0.267107	+	0.232751i
$22$	−0.607478	−	0.559189i	−0.129515	−	0.119219i
$23$	2.53353	−	4.38821i	0.528278	−	0.915005i	−0.471178	−	0.882038i	$-0.656171\pi$
$23$	2.53353	−	4.38821i	0.528278	−	0.915005i	0.999456	−	0.0329667i	$-0.0104955\pi$
$24$	−4.63325	−	1.59153i	−0.945759	−	0.324870i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.358479	+	1.59983i	−0.0703036	+	0.313752i
$27$	4.34773	+	2.84557i	0.836721	+	0.547629i
$28$	−0.799978	+	1.69546i	−0.151182	+	0.320411i
$29$	−7.91811	+	4.57152i	−1.47036	+	0.848910i	−0.999446	−	0.0332718i	$-0.989407\pi$
$29$	−7.91811	+	4.57152i	−1.47036	+	0.848910i	−0.470909	+	0.882182i	$0.656074\pi$
$30$	−0.268878	−	2.43469i	−0.0490901	−	0.444511i
$31$	5.43436	+	3.13753i	0.976041	+	0.563517i	0.901072	−	0.433669i	$-0.142781\pi$
$31$	5.43436	+	3.13753i	0.976041	+	0.563517i	0.0749682	+	0.997186i	$0.476114\pi$
$32$	0.310764	−	5.64831i	0.0549359	−	0.998490i
$33$	−0.664333	+	0.762394i	−0.115646	+	0.132716i
$34$	−0.100603	−	0.321612i	−0.0172533	−	0.0551560i
$35$	−0.937354			−0.158442
$36$	−1.79385	+	5.72557i	−0.298975	+	0.954261i
$37$	3.50937			0.576936			0.288468	−	0.957489i	$-0.406854\pi$
$37$	3.50937			0.576936			0.288468	+	0.957489i	$0.406854\pi$
$38$	2.95840	+	9.45752i	0.479916	+	1.53421i
$39$	1.97062	+	0.385484i	0.315552	+	0.0617268i
$40$	2.62042	−	1.06460i	0.414325	−	0.168328i
$41$	2.86111	+	1.65186i	0.446831	+	0.257978i	0.706491	−	0.707722i	$-0.250277\pi$
$41$	2.86111	+	1.65186i	0.446831	+	0.257978i	−0.259660	+	0.965700i	$0.583611\pi$
$42$	2.10243	+	0.922815i	0.324412	+	0.142393i
$43$	−9.35224	+	5.39952i	−1.42620	+	0.823419i	−0.996819	−	0.0797035i	$-0.974603\pi$
$43$	−9.35224	+	5.39952i	−1.42620	+	0.823419i	−0.429384	+	0.903122i	$0.641269\pi$
$44$	−1.05602	−	0.498268i	−0.159201	−	0.0751167i
$45$	−2.97179	+	0.410448i	−0.443008	+	0.0611860i
$46$	1.56684	−	6.99252i	0.231018	−	1.03099i
$47$	−4.27542	−	7.40525i	−0.623634	−	1.08017i	−0.988803	−	0.149225i	$-0.952322\pi$
$47$	−4.27542	−	7.40525i	−0.623634	−	1.08017i	0.365169	−	0.930941i	$-0.381011\pi$
$48$	−6.92554	−	0.191938i	−0.999616	−	0.0277039i
$49$	−3.06068	+	5.30126i	−0.437240	+	0.757323i
$50$	1.04050	+	0.957789i	0.147149	+	0.135452i
$51$	−0.390388	+	0.133902i	−0.0546653	+	0.0187500i
$52$	0.191609	+	2.31067i	0.0265714	+	0.320433i
$53$		−	11.9037i		−	1.63510i	−0.575855	−	0.817552i	$-0.695331\pi$
$53$		−	11.9037i		−	1.63510i	0.575855	−	0.817552i	$-0.304669\pi$
$54$	7.06963	+	2.00508i	0.962055	+	0.272857i
$55$		−	0.583833i		−	0.0787240i
$56$	−0.363917	+	2.62614i	−0.0486305	+	0.350933i
$57$	11.4800	−	3.93761i	1.52056	−	0.521549i
$58$	−8.75710	+	9.51333i	−1.14986	+	1.24916i
$59$	4.94604	−	8.56680i	0.643920	−	1.11530i	−0.340630	−	0.940198i	$-0.610640\pi$
$59$	4.94604	−	8.56680i	0.643920	−	1.11530i	0.984550	−	0.175105i	$-0.0560264\pi$
$60$	−1.39085	−	3.17262i	−0.179557	−	0.409584i
$61$	−3.33295	−	5.77283i	−0.426740	−	0.739135i	0.569841	−	0.821755i	$-0.307005\pi$
$61$	−3.33295	−	5.77283i	−0.426740	−	0.739135i	−0.996581	+	0.0826196i	$0.973671\pi$
$62$	8.65955	+	1.94037i	1.09976	+	0.246428i
$63$	1.05962	−	2.60479i	0.133499	−	0.328172i
$64$	−1.96530	−	7.75484i	−0.245662	−	0.969355i
$65$	−1.00399	+	0.579651i	−0.124529	+	0.0718969i
$66$	−0.574777	+	1.30950i	−0.0707502	+	0.161189i
$67$	−7.69738	−	4.44408i	−0.940384	−	0.542931i	−0.0503037	−	0.998734i	$-0.516019\pi$
$67$	−7.69738	−	4.44408i	−0.940384	−	0.542931i	−0.890081	+	0.455803i	$0.849352\pi$
$68$	−0.271572	−	0.391611i	−0.0329330	−	0.0474898i
$69$	−8.61317	−	1.68487i	−1.03690	−	0.202834i
$70$	−1.26517	+	0.395755i	−0.151216	+	0.0473018i
$71$	−8.95946			−1.06329			−0.531646	−	0.846966i	$-0.678426\pi$
$71$	−8.95946			−1.06329			−0.531646	+	0.846966i	$0.678426\pi$
$72$	−0.00383002	+	8.48528i	−0.000451372	+	1.00000i
$73$	11.7312			1.37303			0.686517	−	0.727114i	$-0.259139\pi$
$73$	11.7312			1.37303			0.686517	+	0.727114i	$0.259139\pi$
$74$	4.73666	−	1.48167i	0.550626	−	0.172241i
$75$	1.13788	−	1.30584i	0.131391	−	0.150786i
$76$	7.98602	+	11.5160i	0.916059	+	1.32097i
$77$	0.473940	+	0.273629i	0.0540104	+	0.0311829i
$78$	2.82254	−	0.311710i	0.319590	−	0.0352942i
$79$	−4.37420	+	2.52545i	−0.492136	+	0.284135i	−0.725460	−	0.688264i	$-0.758373\pi$
$79$	−4.37420	+	2.52545i	−0.492136	+	0.284135i	0.233324	+	0.972399i	$0.425040\pi$
$80$	3.08736	−	2.54327i	0.345177	−	0.284346i
$81$	2.21884	−	8.72220i	0.246537	−	0.969133i
$82$	4.55912	+	1.02158i	0.503471	+	0.112814i
$83$	2.36468	+	4.09575i	0.259557	+	0.449567i	0.966123	−	0.258081i	$-0.0830900\pi$
$83$	2.36468	+	4.09575i	0.259557	+	0.449567i	−0.706566	+	0.707647i	$0.749757\pi$
$84$	3.22731	+	0.357886i	0.352128	+	0.0390486i
$85$	0.119140	−	0.206357i	0.0129226	−	0.0223826i
$86$	−10.3432	+	11.2364i	−1.11534	+	1.21165i
$87$	11.9394	+	10.4037i	1.28003	+	1.11539i
$88$	−1.63570	−	0.226667i	−0.174366	−	0.0241627i
$89$		−	2.36345i		−	0.250525i	−0.992124	−	0.125263i	$-0.960023\pi$
$89$		−	2.36345i		−	0.250525i	0.992124	−	0.125263i	$-0.0399774\pi$
$90$	−3.83779	+	1.80869i	−0.404539	+	0.190653i
$91$		−	1.08668i		−	0.113915i
$92$	−0.837485	−	10.0995i	−0.0873138	−	1.05294i
$93$	2.08654	−	10.6666i	0.216365	−	1.10607i
$94$	−8.89715	−	8.18990i	−0.917671	−	0.844724i
$95$	−3.50351	+	6.06826i	−0.359453	+	0.622591i
$96$	−9.42858	+	2.66493i	−0.962300	+	0.271989i
$97$	−2.26656	−	3.92579i	−0.230134	−	0.398604i	0.727713	−	0.685881i	$-0.240583\pi$
$97$	−2.26656	−	3.92579i	−0.230134	−	0.398604i	−0.957847	+	0.287278i	$0.907250\pi$
$98$	−1.89285	+	8.44745i	−0.191206	+	0.853321i
$99$	1.62240	+	0.659986i	0.163057	+	0.0663311i
$100$	1.80877	+	0.853443i	0.180877	+	0.0853443i
$101$	1.06647	−	0.615729i	0.106118	−	0.0612673i	−0.446002	−	0.895032i	$-0.647152\pi$
$101$	1.06647	−	0.615729i	0.106118	−	0.0612673i	0.552120	+	0.833765i	$0.313819\pi$
$102$	−0.470381	+	0.345554i	−0.0465746	+	0.0342150i
$103$	5.30854	+	3.06489i	0.523066	+	0.301992i	0.738188	−	0.674595i	$-0.235682\pi$
$103$	5.30854	+	3.06489i	0.523066	+	0.301992i	−0.215122	+	0.976587i	$0.569015\pi$
$104$	1.23420	+	3.03786i	0.121023	+	0.297887i
$105$	0.526748	+	1.53572i	0.0514053	+	0.149871i
$106$	−5.02581	−	16.0667i	−0.488150	−	1.56054i
$107$	−7.54970			−0.729858			−0.364929	−	0.931035i	$-0.618907\pi$
$107$	−7.54970			−0.729858			−0.364929	+	0.931035i	$0.618907\pi$
$108$	10.3886	−	0.278529i	0.999641	−	0.0268015i
$109$	−5.97087			−0.571905			−0.285953	−	0.958244i	$-0.592310\pi$
$109$	−5.97087			−0.571905			−0.285953	+	0.958244i	$0.592310\pi$
$110$	−0.246497	−	0.788011i	−0.0235026	−	0.0751339i
$111$	−1.97209	−	5.74959i	−0.187183	−	0.545727i
$112$	0.617584	+	3.69821i	0.0583562	+	0.349448i
$113$	13.3573	+	7.71185i	1.25655	+	0.725470i	0.972402	−	0.233310i	$-0.0749557\pi$
$113$	13.3573	+	7.71185i	1.25655	+	0.725470i	0.284149	+	0.958780i	$0.408289\pi$
$114$	13.8323	−	10.1616i	1.29551	−	0.951719i
$115$	4.38821	−	2.53353i	0.409203	−	0.236253i
$116$	−7.80306	+	16.5376i	−0.724496	+	1.53548i
$117$	−0.475833	−	3.44520i	−0.0439908	−	0.318509i
$118$	3.05883	−	13.6510i	0.281588	−	1.25668i
$119$	0.111677	+	0.193430i	0.0102374	+	0.0177317i
$120$	−3.21675	−	3.69493i	−0.293648	−	0.337300i
$121$	5.32957	−	9.23109i	0.484506	−	0.839190i
$122$	−6.93586	−	6.38452i	−0.627943	−	0.578027i
$123$	1.09854	−	5.61579i	0.0990516	−	0.506359i
$124$	12.5072	−	1.03714i	1.12318	−	0.0931381i
$125$			1.00000i			0.0894427i
$126$	0.330436	−	3.96311i	0.0294376	−	0.353062i
$127$		−	20.9805i		−	1.86172i	−0.365375	−	0.930860i	$-0.619059\pi$
$127$		−	20.9805i		−	1.86172i	0.365375	−	0.930860i	$-0.380941\pi$
$128$	−5.92674	−	9.63711i	−0.523854	−	0.851808i
$129$	14.1018	+	12.2880i	1.24160	+	1.08190i
$130$	−1.11037	+	1.20625i	−0.0973856	+	0.105795i
$131$	−6.00620	+	10.4030i	−0.524764	+	0.908917i	0.474820	+	0.880083i	$0.342513\pi$
$131$	−6.00620	+	10.4030i	−0.524764	+	0.908917i	−0.999584	+	0.0288347i	$0.990820\pi$
$132$	−0.222910	+	2.01014i	−0.0194018	+	0.174960i
$133$	−3.28403	−	5.68811i	−0.284762	−	0.493222i
$134$	−12.2656	−	2.74840i	−1.05959	−	0.237425i
$135$	2.34246	+	4.63820i	0.201607	+	0.399192i
$136$	−0.531886	−	0.413906i	−0.0456089	−	0.0354921i
$137$	−2.78141	+	1.60585i	−0.237632	+	0.137197i	−0.614088	−	0.789238i	$-0.710476\pi$
$137$	−2.78141	+	1.60585i	−0.237632	+	0.137197i	0.376456	+	0.926434i	$0.377143\pi$
$138$	−12.3367	+	1.36242i	−1.05017	+	0.115977i
$139$	0.962964	+	0.555968i	0.0816776	+	0.0471566i	0.540283	−	0.841484i	$-0.318317\pi$
$139$	0.962964	+	0.555968i	0.0816776	+	0.0471566i	−0.458605	+	0.888640i	$0.651651\pi$
$140$	−1.54053	+	1.06832i	−0.130198	+	0.0902893i
$141$	−9.72985	+	11.1661i	−0.819401	+	0.940351i
$142$	−12.0928	+	3.78273i	−1.01480	+	0.317440i
$143$	0.676839			0.0566001
$144$	3.57736	+	11.4544i	0.298113	+	0.954531i
$145$	−9.14304			−0.759288
$146$	15.8338	−	4.95297i	1.31042	−	0.409911i
$147$	10.4053	+	2.03544i	0.858215	+	0.167880i
$148$	5.76760	−	3.99968i	0.474093	−	0.328772i
$149$	−0.707421	−	0.408430i	−0.0579542	−	0.0334599i	0.470743	−	0.882270i	$-0.343986\pi$
$149$	−0.707421	−	0.408430i	−0.0579542	−	0.0334599i	−0.528697	+	0.848811i	$0.677319\pi$
$150$	0.984489	−	2.24294i	0.0803832	−	0.183135i
$151$	15.2722	−	8.81739i	1.24283	−	0.717549i	0.273161	−	0.961968i	$-0.411931\pi$
$151$	15.2722	−	8.81739i	1.24283	−	0.717549i	0.969670	+	0.244420i	$0.0785974\pi$
$152$	15.6410	+	12.1716i	1.26865	+	0.987245i
$153$	0.438759	+	0.564349i	0.0354715	+	0.0456249i
$154$	0.755213	+	0.169223i	0.0608568	+	0.0136364i
$155$	3.13753	+	5.43436i	0.252013	+	0.436499i
$156$	3.67803	−	1.61241i	0.294478	−	0.129096i
$157$	−10.3945	+	18.0039i	−0.829575	+	1.43687i	0.0687973	+	0.997631i	$0.478084\pi$
$157$	−10.3945	+	18.0039i	−0.829575	+	1.43687i	−0.898372	+	0.439235i	$0.855250\pi$
$158$	−4.83769	+	5.25545i	−0.384866	+	0.418102i
$159$	−19.5026	+	6.68932i	−1.54665	+	0.530498i
$160$	3.09329	−	4.73620i	0.244546	−	0.374429i
$161$			4.74964i			0.374324i
$162$	−0.687747	−	12.7093i	−0.0540345	−	0.998539i
$163$			3.22298i			0.252443i	0.992002	+	0.126222i	$0.0402850\pi$
$163$			3.22298i			0.252443i	−0.992002	+	0.126222i	$0.959715\pi$
$164$	6.58486	−	0.546040i	0.514191	−	0.0426386i
$165$	−0.956526	+	0.328086i	−0.0744655	+	0.0255414i
$166$	4.92090	+	4.52973i	0.381936	+	0.351575i
$167$	−6.85148	+	11.8671i	−0.530184	+	0.918305i	0.469196	+	0.883094i	$0.344544\pi$
$167$	−6.85148	+	11.8671i	−0.530184	+	0.918305i	−0.999380	+	0.0352112i	$0.988790\pi$
$168$	4.50706	−	0.879539i	0.347727	−	0.0678579i
$169$	5.82801	+	10.0944i	0.448308	+	0.776493i
$170$	0.0736811	−	0.328826i	0.00565108	−	0.0252198i
$171$	−12.9024	−	16.5956i	−0.986672	−	1.26910i
$172$	−9.21636	+	19.5329i	−0.702741	+	1.48937i
$173$	−10.8588	+	6.26935i	−0.825582	+	0.476650i	−0.852338	−	0.522992i	$-0.824816\pi$
$173$	−10.8588	+	6.26935i	−0.825582	+	0.476650i	0.0267554	+	0.999642i	$0.491482\pi$
$174$	20.5073	+	9.00122i	1.55465	+	0.682381i
$175$	−0.811773	−	0.468677i	−0.0613643	−	0.0354287i
$176$	−2.30343	+	0.384663i	−0.173628	+	0.0289951i
$177$	−16.8149	−	3.28926i	−1.26389	−	0.247236i
$178$	−0.997861	−	3.19000i	−0.0747928	−	0.239100i
$179$	23.1645			1.73140			0.865700	−	0.500564i	$-0.166874\pi$
$179$	23.1645			1.73140			0.865700	+	0.500564i	$0.166874\pi$
$180$	−4.41630	+	4.06156i	−0.329172	+	0.302731i
$181$	−3.42840			−0.254831			−0.127415	−	0.991849i	$-0.540668\pi$
$181$	−3.42840			−0.254831			−0.127415	+	0.991849i	$0.540668\pi$
$182$	−0.458800	−	1.46671i	−0.0340085	−	0.108720i
$183$	−7.58500	+	8.70460i	−0.560699	+	0.643463i
$184$	−5.39441	−	13.2779i	−0.397681	−	0.978857i
$185$	3.03920	+	1.75468i	0.223446	+	0.129007i
$186$	−1.68722	−	15.2778i	−0.123713	−	1.12022i
$187$	−0.120478	+	0.0695580i	−0.00881023	+	0.00508659i
$188$	−15.4665	−	7.29766i	−1.12801	−	0.532236i
$189$	−4.86302	−	0.272271i	−0.353733	−	0.0198048i
$190$	−2.16671	+	9.66965i	−0.157190	+	0.701510i
$191$	2.32053	+	4.01927i	0.167908	+	0.290824i	0.937684	−	0.347489i	$-0.112966\pi$
$191$	2.32053	+	4.01927i	0.167908	+	0.290824i	−0.769776	+	0.638314i	$0.779632\pi$
$192$	−11.6008	+	7.57771i	−0.837215	+	0.546874i
$193$	−0.00425487	+	0.00736966i	−0.000306273	+	0.000530480i	−0.866178	−	0.499735i	$-0.833431\pi$
$193$	−0.00425487	+	0.00736966i	−0.000306273	+	0.000530480i	0.865872	+	0.500265i	$0.166764\pi$
$194$	−4.71670	−	4.34177i	−0.338640	−	0.311721i
$195$	1.51387	+	1.31915i	0.108410	+	0.0944662i
$196$	1.01174	+	12.2009i	0.0722671	+	0.871490i
$197$			5.83271i			0.415564i	0.978175	+	0.207782i	$0.0666244\pi$
$197$			5.83271i			0.415564i	−0.978175	+	0.207782i	$0.933376\pi$
$198$	2.46843	+	0.205813i	0.175424	+	0.0146265i
$199$			8.61133i			0.610441i	0.952282	+	0.305220i	$0.0987302\pi$
$199$			8.61133i			0.610441i	−0.952282	+	0.305220i	$0.901270\pi$
$200$	2.80165	+	0.388239i	0.198107	+	0.0274526i
$201$	−2.95544	+	15.1084i	−0.208461	+	1.06566i
$202$	1.17948	−	1.28133i	0.0829877	−	0.0901541i
$203$	4.28513	−	7.42207i	0.300757	−	0.520927i
$204$	−0.488988	+	0.664998i	−0.0342360	+	0.0465592i
$205$	1.65186	+	2.86111i	0.115371	+	0.199829i
$206$	8.45905	+	1.89545i	0.589370	+	0.132062i
$207$	2.07977	+	15.0583i	0.144554	+	1.04662i
$208$	2.94842	+	3.57918i	0.204436	+	0.248171i
$209$	3.54285	−	2.04547i	0.245064	−	0.141488i
$210$	1.35935	+	1.85040i	0.0938041	+	0.127689i
$211$	−1.96971	−	1.13721i	−0.135601	−	0.0782891i	0.430665	−	0.902512i	$-0.358279\pi$
$211$	−1.96971	−	1.13721i	−0.135601	−	0.0782891i	−0.566266	+	0.824223i	$0.691612\pi$
$212$	−13.5669	−	19.5636i	−0.931777	−	1.34364i
$213$	5.03478	+	14.6788i	0.344978	+	1.00577i
$214$	−10.1900	+	3.18752i	−0.696573	+	0.217894i
$215$	−10.7990			−0.736488
$216$	13.9041	−	4.76204i	0.946052	−	0.324016i
$217$	−5.88196			−0.399293
$218$	−8.05900	+	2.52093i	−0.545824	+	0.170739i
$219$	−6.59237	−	19.2199i	−0.445471	−	1.29876i
$220$	−0.665404	−	0.959522i	−0.0448615	−	0.0646909i
$221$	0.239230	+	0.138120i	0.0160924	+	0.00929093i
$222$	−5.08928	−	6.92771i	−0.341570	−	0.464957i
$223$	10.3774	−	5.99142i	0.694925	−	0.401215i	−0.110529	−	0.993873i	$-0.535255\pi$
$223$	10.3774	−	5.99142i	0.694925	−	0.401215i	0.805454	+	0.592658i	$0.201921\pi$
$224$	2.39496	+	4.73079i	0.160020	+	0.316089i
$225$	−2.77887	−	1.13044i	−0.185258	−	0.0753624i
$226$	21.2846	+	4.76932i	1.41583	+	0.317250i
$227$	6.89338	+	11.9397i	0.457530	+	0.792464i	0.998830	−	0.0483650i	$-0.0154011\pi$
$227$	6.89338	+	11.9397i	0.457530	+	0.792464i	−0.541300	+	0.840829i	$0.682068\pi$
$228$	14.3795	−	19.5554i	0.952304	−	1.29508i
$229$	6.43779	−	11.1506i	0.425421	−	0.736851i	−0.571039	−	0.820923i	$-0.693459\pi$
$229$	6.43779	−	11.1506i	0.425421	−	0.736851i	0.996460	+	0.0840722i	$0.0267926\pi$
$230$	4.85318	−	5.27228i	0.320009	−	0.347644i
$231$	0.181971	−	0.930248i	0.0119728	−	0.0612058i
$232$	−3.54968	+	25.6156i	−0.233048	+	1.68175i
$233$		−	10.2353i		−	0.670535i	−0.942123	−	0.335268i	$-0.891173\pi$
$233$		−	10.2353i		−	0.670535i	0.942123	−	0.335268i	$-0.108827\pi$
$234$	−2.09682	−	4.44916i	−0.137074	−	0.290851i
$235$		−	8.55084i		−	0.557796i
$236$	−1.63496	−	19.7165i	−0.106427	−	1.28344i
$237$	6.59567	+	5.74732i	0.428435	+	0.373329i
$238$	0.232399	+	0.213925i	0.0150642	+	0.0138667i
$239$	8.53636	−	14.7854i	0.552171	−	0.956389i	−0.445946	−	0.895060i	$-0.647133\pi$
$239$	8.53636	−	14.7854i	0.552171	−	0.956389i	0.998118	−	0.0613289i	$-0.0195339\pi$
$240$	−5.90173	−	3.62900i	−0.380955	−	0.234251i
$241$	10.7574	+	18.6324i	0.692946	+	1.20022i	0.970868	+	0.239614i	$0.0770209\pi$
$241$	10.7574	+	18.6324i	0.692946	+	1.20022i	−0.277922	+	0.960604i	$0.589646\pi$
$242$	3.29602	−	14.7095i	0.211876	−	0.945565i
$243$	−15.5369	+	1.26621i	−0.996696	+	0.0812273i
$244$	−12.0570	−	5.68896i	−0.771873	−	0.364198i
$245$	−5.30126	+	3.06068i	−0.338685	+	0.195540i
$246$	−0.888298	−	8.04355i	−0.0566358	−	0.512838i
$247$	−7.03495	−	4.06163i	−0.447623	−	0.258435i
$248$	16.4433	−	6.68045i	1.04415	−	0.424209i
$249$	5.38146	−	6.17580i	0.341036	−	0.391375i
$250$	0.422205	+	1.34972i	0.0267026	+	0.0853638i
$251$	29.3692			1.85377			0.926884	−	0.375348i	$-0.122477\pi$
$251$	29.3692			1.85377			0.926884	+	0.375348i	$0.122477\pi$
$252$	−1.22725	−	5.48859i	−0.0773092	−	0.345749i
$253$	−2.95832			−0.185988
$254$	−8.85808	−	28.3178i	−0.555805	−	1.77682i
$255$	−0.405037	−	0.0792316i	−0.0253644	−	0.00496167i
$256$	−12.0683	−	10.5051i	−0.754266	−	0.656568i
$257$	−7.24613	−	4.18355i	−0.452001	−	0.260963i	0.256674	−	0.966498i	$-0.417373\pi$
$257$	−7.24613	−	4.18355i	−0.452001	−	0.260963i	−0.708675	+	0.705535i	$0.750707\pi$
$258$	24.2216	+	10.6315i	1.50797	+	0.661890i
$259$	−2.84881	+	1.64476i	−0.177016	+	0.102200i
$260$	−0.989398	+	2.09691i	−0.0613599	+	0.130045i
$261$	10.3356	−	25.4073i	0.639759	−	1.57267i
$262$	−3.71447	+	16.5770i	−0.229481	+	1.02413i
$263$	−0.202267	−	0.350337i	−0.0124723	−	0.0216027i	0.859722	−	0.510762i	$-0.170637\pi$
$263$	−0.202267	−	0.350337i	−0.0124723	−	0.0216027i	−0.872194	+	0.489160i	$0.837304\pi$
$264$	0.547823	+	2.80723i	0.0337161	+	0.172773i
$265$	5.95187	−	10.3089i	0.365620	−	0.633273i
$266$	−6.83407	−	6.29082i	−0.419024	−	0.385715i
$267$	−3.87218	+	1.32815i	−0.236973	+	0.0812812i
$268$	−17.7155	+	1.46904i	−1.08215	+	0.0897357i
$269$		−	18.7650i		−	1.14412i	−0.820211	−	0.572061i	$-0.806144\pi$
$269$		−	18.7650i		−	1.14412i	0.820211	−	0.572061i	$-0.193856\pi$
$270$	5.11994	+	5.27127i	0.311589	+	0.320799i
$271$			12.2886i			0.746476i	0.927736	+	0.373238i	$0.121753\pi$
$271$			12.2886i			0.746476i	−0.927736	+	0.373238i	$0.878247\pi$
$272$	−0.892650	−	0.334092i	−0.0541249	−	0.0202573i
$273$	−1.78036	+	0.610660i	−0.107753	+	0.0369588i
$274$	−3.07613	+	3.34177i	−0.185836	+	0.201884i
$275$	0.291916	−	0.505614i	0.0176032	−	0.0304897i
$276$	−16.0759	+	7.04751i	−0.967656	+	0.424210i
$277$	−6.94857	−	12.0353i	−0.417499	−	0.723130i	0.578188	−	0.815904i	$-0.303760\pi$
$277$	−6.94857	−	12.0353i	−0.417499	−	0.723130i	−0.995687	+	0.0927737i	$0.970427\pi$
$278$	1.53446	+	0.343832i	0.0920310	+	0.0206217i
$279$	−18.6482	+	2.57559i	−1.11644	+	0.154196i
$280$	−1.62823	+	2.09235i	−0.0973056	+	0.125042i
$281$	15.1656	−	8.75587i	0.904705	−	0.522332i	0.0259813	−	0.999662i	$-0.491729\pi$
$281$	15.1656	−	8.75587i	0.904705	−	0.522332i	0.878724	+	0.477331i	$0.158396\pi$
$282$	−8.41821	+	19.1790i	−0.501297	+	1.14209i
$283$	3.10992	+	1.79551i	0.184866	+	0.106732i	0.589577	−	0.807712i	$-0.299295\pi$
$283$	3.10992	+	1.79551i	0.184866	+	0.106732i	−0.404711	+	0.914445i	$0.632628\pi$
$284$	−14.7248	+	10.2112i	−0.873754	+	0.605926i
$285$	11.9108	+	2.32993i	0.705534	+	0.138013i
$286$	0.913543	−	0.285765i	0.0540189	−	0.0168976i
$287$	−3.09676			−0.182796
$288$	9.66452	+	13.9498i	0.569487	+	0.822000i
$289$	16.9432			0.996660
$290$	−12.3405	+	3.86024i	−0.724662	+	0.226681i
$291$	−5.15815	+	5.91953i	−0.302376	+	0.347009i
$292$	19.2801	−	13.3702i	1.12828	−	0.782434i
$293$	−0.688534	−	0.397525i	−0.0402246	−	0.0232237i	0.479753	−	0.877404i	$-0.340726\pi$
$293$	−0.688534	−	0.397525i	−0.0402246	−	0.0232237i	−0.519977	+	0.854180i	$0.674060\pi$
$294$	14.9036	−	1.64590i	0.869197	−	0.0959907i
$295$	8.56680	−	4.94604i	0.498778	−	0.287970i
$296$	6.09595	−	7.83356i	0.354320	−	0.455316i
$297$	0.169584	−	3.02894i	0.00984028	−	0.175757i
$298$	−1.12726	−	0.252589i	−0.0653005	−	0.0146321i
$299$	2.93713	+	5.08726i	0.169859	+	0.294204i
$300$	0.381804	−	3.44300i	0.0220435	−	0.198782i
$301$	5.06126	−	8.76636i	0.291726	−	0.505285i
$302$	16.8904	−	18.3490i	0.971933	−	1.05587i
$303$	−1.60809	−	1.40125i	−0.0923823	−	0.0804999i
$304$	26.2498	+	9.82451i	1.50553	+	0.563474i
$305$		−	6.66589i		−	0.381688i
$306$	0.830472	+	0.576466i	0.0474749	+	0.0329544i
$307$		−	10.0055i		−	0.571044i	−0.958372	−	0.285522i	$-0.907833\pi$
$307$		−	10.0055i		−	0.571044i	0.958372	−	0.285522i	$-0.0921669\pi$
$308$	1.09077	−	0.0904509i	0.0621526	−	0.00515392i
$309$	2.03823	−	10.4196i	0.115951	−	0.592750i
$310$	6.52920	+	6.01019i	0.370834	+	0.341356i
$311$	−0.865396	+	1.49891i	−0.0490721	+	0.0849954i	−0.889518	−	0.456900i	$-0.848960\pi$
$311$	−0.865396	+	1.49891i	−0.0490721	+	0.0849954i	0.840446	+	0.541895i	$0.182293\pi$
$312$	4.28354	−	3.72918i	0.242508	−	0.211124i
$313$	−1.55560	−	2.69438i	−0.0879277	−	0.152295i	0.818707	−	0.574211i	$-0.194691\pi$
$313$	−1.55560	−	2.69438i	−0.0879277	−	0.152295i	−0.906635	+	0.421916i	$0.861358\pi$
$314$	−6.42840	+	28.6888i	−0.362775	+	1.61900i
$315$	2.22005	−	1.72600i	0.125086	−	0.0972491i
$316$	−4.31065	+	9.13589i	−0.242493	+	0.513934i
$317$	3.24641	−	1.87431i	0.182336	−	0.105272i	−0.406054	−	0.913849i	$-0.633095\pi$
$317$	3.24641	−	1.87431i	0.182336	−	0.105272i	0.588390	+	0.808577i	$0.299762\pi$
$318$	−23.4987	+	17.2628i	−1.31774	+	0.968049i
$319$	4.62285	+	2.66900i	0.258830	+	0.149436i
$320$	2.17542	−	7.69854i	0.121610	−	0.430362i
$321$	4.24257	+	12.3691i	0.236797	+	0.690376i
$322$	2.00532	+	6.41068i	0.111752	+	0.357253i
$323$	1.66964			0.0929011
$324$	−6.29420	−	16.8637i	−0.349678	−	0.936870i
$325$	−1.15930			−0.0643065
$326$	1.36076	+	4.35012i	0.0753653	+	0.240931i
$327$	3.35534	+	9.78241i	0.185551	+	0.540968i
$328$	8.65717	−	3.51716i	0.478012	−	0.194203i
$329$	6.94134	+	4.00759i	0.382689	+	0.220945i
$330$	−1.15252	+	0.846674i	−0.0634443	+	0.0466079i
$331$	−18.4686	+	10.6629i	−1.01513	+	0.586083i	−0.912689	−	0.408656i	$-0.865998\pi$
$331$	−18.4686	+	10.6629i	−1.01513	+	0.586083i	−0.102438	+	0.994739i	$0.532664\pi$
$332$	8.55431	+	4.03624i	0.469479	+	0.221517i
$333$	−8.31166	+	6.46198i	−0.455476	+	0.354115i
$334$	−4.23723	+	18.9100i	−0.231851	+	1.03471i
$335$	−4.44408	−	7.69738i	−0.242806	−	0.420553i
$336$	5.71192	−	3.09003i	0.311611	−	0.168575i
$337$	0.493788	−	0.855267i	0.0268984	−	0.0465893i	−0.852263	−	0.523114i	$-0.824770\pi$
$337$	0.493788	−	0.855267i	0.0268984	−	0.0465893i	0.879161	+	0.476524i	$0.158104\pi$
$338$	12.1281	+	11.1640i	0.659681	+	0.607242i
$339$	5.12860	−	26.2177i	0.278547	−	1.42395i
$340$	−0.0393830	−	0.474931i	−0.00213584	−	0.0257567i
$341$		−	3.66359i		−	0.198394i
$342$	−24.4214	−	16.9519i	−1.32056	−	0.916655i
$343$		−	12.2994i		−	0.664104i
$344$	−4.19260	+	30.2552i	−0.226050	+	1.63125i
$345$	−6.61679	−	5.76573i	−0.356236	−	0.310416i
$346$	−12.0094	+	13.0465i	−0.645631	+	0.701386i
$347$	−8.96419	+	15.5264i	−0.481223	+	0.833503i	−0.999768	−	0.0215477i	$-0.993141\pi$
$347$	−8.96419	+	15.5264i	−0.481223	+	0.833503i	0.518545	+	0.855050i	$0.326474\pi$
$348$	31.4795	+	3.49085i	1.68748	+	0.187129i
$349$	−6.00147	−	10.3948i	−0.321251	−	0.556423i	0.659495	−	0.751709i	$-0.270770\pi$
$349$	−6.00147	−	10.3948i	−0.321251	−	0.556423i	−0.980746	+	0.195285i	$0.937437\pi$
$350$	−1.29354	−	0.289849i	−0.0691428	−	0.0154931i
$351$	−5.37707	+	2.71562i	−0.287007	+	0.144949i
$352$	−2.94658	+	1.49171i	−0.157053	+	0.0795083i
$353$	−23.7990	+	13.7404i	−1.26670	+	0.731327i	−0.974361	−	0.224989i	$-0.927765\pi$
$353$	−23.7990	+	13.7404i	−1.26670	+	0.731327i	−0.292334	+	0.956316i	$0.594432\pi$
$354$	−24.0841	+	2.65976i	−1.28006	+	0.141365i
$355$	−7.75912	−	4.47973i	−0.411812	−	0.237759i
$356$	−2.69366	−	3.88430i	−0.142764	−	0.205868i
$357$	0.254150	−	0.291664i	0.0134510	−	0.0154365i
$358$	31.2656	−	9.78018i	1.65244	−	0.516899i
$359$	−7.30964			−0.385788			−0.192894	−	0.981220i	$-0.561787\pi$
$359$	−7.30964			−0.385788			−0.192894	+	0.981220i	$0.561787\pi$
$360$	−4.24596	+	7.34655i	−0.223782	+	0.387197i
$361$	−30.0984			−1.58413
$362$	−4.62738	+	1.44749i	−0.243209	+	0.0760782i
$363$	−18.1188	−	3.54431i	−0.950988	−	0.186028i
$364$	−1.23850	−	1.78594i	−0.0649152	−	0.0936086i
$365$	10.1595	+	5.86560i	0.531774	+	0.307020i
$366$	−6.56250	+	14.9512i	−0.343027	+	0.781511i
$367$	14.8418	−	8.56890i	0.774734	−	0.447293i	−0.0598265	−	0.998209i	$-0.519055\pi$
$367$	14.8418	−	8.56890i	0.774734	−	0.447293i	0.834561	+	0.550916i	$0.185721\pi$
$368$	−12.8869	−	15.6438i	−0.671777	−	0.815492i
$369$	−9.81798	+	1.35601i	−0.511104	+	0.0705910i
$370$	4.84290	+	1.08517i	0.251771	+	0.0564151i
$371$	5.57901	+	9.66313i	0.289648	+	0.501685i
$372$	−8.72765	−	19.9084i	−0.452507	−	1.03220i
$373$	−7.98599	+	13.8321i	−0.413499	+	0.716201i	−0.995270	−	0.0971520i	$-0.969027\pi$
$373$	−7.98599	+	13.8321i	−0.413499	+	0.716201i	0.581771	+	0.813353i	$0.302360\pi$
$374$	−0.133244	+	0.144750i	−0.00688987	+	0.00748486i
$375$	1.63836	−	0.561951i	0.0846043	−	0.0290190i
$376$	−23.9565	−	3.31977i	−1.23546	−	0.171204i
$377$		−	10.5995i		−	0.545904i
$378$	−6.67867	+	1.68570i	−0.343514	+	0.0867031i
$379$			27.3396i			1.40434i	0.712010	+	0.702169i	$0.247785\pi$
$379$			27.3396i			1.40434i	−0.712010	+	0.702169i	$0.752215\pi$
$380$	1.15812	+	13.9661i	0.0594103	+	0.716447i
$381$	−34.3736	+	11.7900i	−1.76101	+	0.604022i
$382$	4.82902	+	4.44515i	0.247074	+	0.227434i
$383$	7.57245	−	13.1159i	0.386934	−	0.670190i	−0.605101	−	0.796149i	$-0.706867\pi$
$383$	7.57245	−	13.1159i	0.386934	−	0.670190i	0.992035	+	0.125959i	$0.0402007\pi$
$384$	−12.4585	+	15.1257i	−0.635769	+	0.771880i
$385$	0.273629	+	0.473940i	0.0139454	+	0.0241542i
$386$	−0.00263138	+	0.0117434i	−0.000133934	+	0.000597723i
$387$	12.2076	−	30.0091i	0.620548	−	1.52545i
$388$	−8.19934	−	3.86875i	−0.416259	−	0.196406i
$389$	17.9649	−	10.3720i	0.910856	−	0.525883i	0.0301495	−	0.999545i	$-0.490402\pi$
$389$	17.9649	−	10.3720i	0.910856	−	0.525883i	0.880706	+	0.473662i	$0.157068\pi$
$390$	2.60025	+	1.14132i	0.131669	+	0.0577930i
$391$	−1.04562	−	0.603692i	−0.0528795	−	0.0305300i
$392$	6.51682	+	16.0406i	0.329149	+	0.810171i
$393$	20.4191	+	3.99429i	1.03001	+	0.201485i
$394$	2.46260	+	7.87253i	0.124064	+	0.396612i
$395$	−5.05089			−0.254138
$396$	3.41858	−	0.764392i	0.171790	−	0.0384122i
$397$	32.0445			1.60827			0.804133	−	0.594449i	$-0.202630\pi$
$397$	32.0445			1.60827			0.804133	+	0.594449i	$0.202630\pi$
$398$	3.63574	+	11.6229i	0.182243	+	0.582602i
$399$	−7.47369	+	8.57686i	−0.374152	+	0.429380i
$400$	3.94537	−	0.658858i	0.197268	−	0.0329429i
$401$	−25.6868	−	14.8303i	−1.28274	−	0.740588i	−0.305388	−	0.952228i	$-0.598786\pi$
$401$	−25.6868	−	14.8303i	−1.28274	−	0.740588i	−0.977348	+	0.211640i	$0.932119\pi$
$402$	2.38983	+	21.6399i	0.119194	+	1.07930i
$403$	−6.30007	+	3.63735i	−0.313829	+	0.181189i
$404$	1.05098	−	2.22742i	0.0522881	−	0.110818i
$405$	6.28267	−	6.44423i	0.312188	−	0.320216i
$406$	2.65010	−	11.8269i	0.131522	−	0.586960i
$407$	−1.02444	−	1.77439i	−0.0507797	−	0.0879530i
$408$	−0.379231	+	1.10401i	−0.0187747	+	0.0546568i
$409$	11.3587	−	19.6739i	0.561652	−	0.972810i	−0.435700	−	0.900092i	$-0.643499\pi$
$409$	11.3587	−	19.6739i	0.561652	−	0.972810i	0.997353	−	0.0727182i	$-0.0231674\pi$
$410$	3.43753	+	3.16427i	0.169767	+	0.156272i
$411$	4.19397	+	3.65453i	0.206873	+	0.180265i
$412$	12.2176	−	1.01313i	0.601919	−	0.0499133i
$413$			9.27239i			0.456265i
$414$	9.16477	+	19.4463i	0.450424	+	0.955735i
$415$			4.72936i			0.232155i
$416$	5.49069	+	3.58605i	0.269203	+	0.175821i
$417$	0.369734	−	1.89010i	0.0181059	−	0.0925588i
$418$	3.91825	−	4.25662i	0.191648	−	0.208198i
$419$	−4.22987	+	7.32635i	−0.206643	+	0.357916i	−0.950655	−	0.310250i	$-0.899587\pi$
$419$	−4.22987	+	7.32635i	−0.206643	+	0.357916i	0.744012	+	0.668166i	$0.232920\pi$
$420$	2.61599	+	1.92359i	0.127647	+	0.0938617i
$421$	12.4517	+	21.5670i	0.606860	+	1.05111i	0.991755	+	0.128151i	$0.0409044\pi$
$421$	12.4517	+	21.5670i	0.606860	+	1.05111i	−0.384895	+	0.922960i	$0.625762\pi$
$422$	−3.13870	−	0.703299i	−0.152789	−	0.0342360i
$423$	23.7617	+	9.66618i	1.15533	+	0.469986i
$424$	−26.5713	−	20.6774i	−1.29042	−	1.00418i
$425$	0.206357	−	0.119140i	0.0100098	−	0.00577915i
$426$	12.9930	+	17.6865i	0.629513	+	0.856916i
$427$	5.41119	+	3.12415i	0.261866	+	0.151188i
$428$	−12.4078	+	8.60452i	−0.599755	+	0.415915i
$429$	−0.380351	−	1.10890i	−0.0183635	−	0.0535383i
$430$	−14.5757	+	4.55940i	−0.702901	+	0.219874i
$431$	−9.37049			−0.451360			−0.225680	−	0.974201i	$-0.572460\pi$
$431$	−9.37049			−0.451360			−0.225680	+	0.974201i	$0.572460\pi$
$432$	16.7560	−	12.2978i	0.806175	−	0.591677i
$433$	−28.2137			−1.35586			−0.677932	−	0.735125i	$-0.737124\pi$
$433$	−28.2137			−1.35586			−0.677932	+	0.735125i	$0.737124\pi$
$434$	−7.93899	+	2.48339i	−0.381084	+	0.119207i
$435$	5.13795	+	14.9796i	0.246346	+	0.718215i
$436$	−9.81304	+	6.80509i	−0.469959	+	0.325905i
$437$	30.7483	+	17.7525i	1.47089	+	0.849219i
$438$	−17.0126	−	23.1581i	−0.812892	−	1.10654i
$439$	8.29258	−	4.78773i	0.395783	−	0.228506i	−0.288880	−	0.957365i	$-0.593283\pi$
$439$	8.29258	−	4.78773i	0.395783	−	0.228506i	0.684663	+	0.728860i	$0.259949\pi$
$440$	−1.30322	−	1.01415i	−0.0621287	−	0.0483476i
$441$	−2.51250	−	18.1914i	−0.119643	−	0.866258i
$442$	0.381208	+	0.0854186i	0.0181322	+	0.00406295i
$443$	3.67613	+	6.36724i	0.174658	+	0.302517i	0.940043	−	0.341056i	$-0.110785\pi$
$443$	3.67613	+	6.36724i	0.174658	+	0.302517i	−0.765385	+	0.643573i	$0.777451\pi$
$444$	−9.79401	−	7.20175i	−0.464803	−	0.341780i
$445$	1.18173	−	2.04681i	0.0560192	−	0.0970281i
$446$	11.4770	−	12.4681i	0.543453	−	0.590384i
$447$	−0.271617	+	1.38852i	−0.0128470	+	0.0656750i
$448$	5.22989	+	5.37408i	0.247089	+	0.253901i
$449$			26.6328i			1.25688i	0.777858	+	0.628440i	$0.216306\pi$
$449$			26.6328i			1.25688i	−0.777858	+	0.628440i	$0.783694\pi$
$450$	−4.22797	−	0.352520i	−0.199308	−	0.0166180i
$451$		−	1.92883i		−	0.0908248i
$452$	30.7419	−	2.54923i	1.44598	−	0.119906i
$453$	−23.0282	−	20.0663i	−1.08196	−	0.942797i
$454$	14.3451	+	13.2048i	0.673250	+	0.619732i
$455$	0.543339	−	0.941090i	0.0254721	−	0.0441190i
$456$	11.1519	−	32.4653i	0.522235	−	1.52033i
$457$	−2.64232	−	4.57663i	−0.123602	−	0.214086i	0.797583	−	0.603209i	$-0.206111\pi$
$457$	−2.64232	−	4.57663i	−0.123602	−	0.214086i	−0.921186	+	0.389123i	$0.872778\pi$
$458$	3.98138	−	17.7682i	0.186038	−	0.830254i
$459$	0.678043	−	1.03598i	0.0316483	−	0.0483554i
$460$	4.32445	−	9.16514i	0.201629	−	0.427327i
$461$	−9.04956	+	5.22477i	−0.421480	+	0.243342i	−0.695710	−	0.718322i	$-0.744910\pi$
$461$	−9.04956	+	5.22477i	−0.421480	+	0.243342i	0.274230	+	0.961664i	$0.411577\pi$
$462$	−0.147145	−	1.33240i	−0.00684583	−	0.0619890i
$463$	10.0576	+	5.80678i	0.467418	+	0.269864i	0.715158	−	0.698963i	$-0.246355\pi$
$463$	10.0576	+	5.80678i	0.467418	+	0.269864i	−0.247740	+	0.968827i	$0.579688\pi$
$464$	6.02397	+	36.0726i	0.279656	+	1.67463i
$465$	7.14028	−	8.19424i	0.331123	−	0.379999i
$466$	−4.32138	−	13.8148i	−0.200184	−	0.639956i
$467$	−32.6615			−1.51139			−0.755697	−	0.654921i	$-0.772702\pi$
$467$	−32.6615			−1.51139			−0.755697	+	0.654921i	$0.772702\pi$
$468$	−4.70858	−	5.11983i	−0.217654	−	0.236664i
$469$	8.33136			0.384707
$470$	−3.61021	−	11.5412i	−0.166526	−	0.532358i
$471$	35.3380	+	6.91266i	1.62829	+	0.318518i
$472$	−10.5311	−	25.9215i	−0.484735	−	1.19313i
$473$	5.46014	+	3.15242i	0.251058	+	0.144948i
$474$	11.3289	+	4.97255i	0.520351	+	0.228397i
$475$	−6.06826	+	3.50351i	−0.278431	+	0.160752i
$476$	0.403994	+	0.190619i	0.0185170	+	0.00873702i
$477$	21.9190	+	28.1931i	1.00360	+	1.29087i
$478$	5.27922	−	23.5602i	0.241466	−	1.07762i
$479$	−7.45617	−	12.9145i	−0.340681	−	0.590077i	0.643878	−	0.765128i	$-0.277324\pi$
$479$	−7.45617	−	12.9145i	−0.340681	−	0.590077i	−0.984559	+	0.175051i	$0.943991\pi$
$480$	−9.49786	−	2.40639i	−0.433516	−	0.109836i
$481$	−2.03421	+	3.52335i	−0.0927519	+	0.160651i
$482$	22.3862	+	20.6067i	1.01966	+	0.938608i
$483$	7.78160	−	2.66907i	0.354075	−	0.121447i
$484$	−1.76174	−	21.2454i	−0.0800792	−	0.965698i
$485$		−	4.53311i		−	0.205838i
$486$	−20.4359	+	8.26880i	−0.926992	+	0.375080i
$487$		−	23.3946i		−	1.06011i	−0.847964	−	0.530054i	$-0.822171\pi$
$487$		−	23.3946i		−	1.06011i	0.847964	−	0.530054i	$-0.177829\pi$
$488$	−18.6755	−	2.58796i	−0.845401	−	0.117151i
$489$	5.28039	−	1.81116i	0.238787	−	0.0819034i
$490$	−5.86298	+	6.36928i	−0.264862	+	0.287735i
$491$	14.2196	−	24.6290i	0.641721	−	1.11149i	−0.343328	−	0.939216i	$-0.611554\pi$
$491$	14.2196	−	24.6290i	0.641721	−	1.11149i	0.985048	−	0.172278i	$-0.0551126\pi$
$492$	−4.59498	−	10.4815i	−0.207158	−	0.472542i
$493$	1.08930	+	1.88673i	0.0490598	+	0.0849741i
$494$	−11.2100	−	2.51187i	−0.504364	−	0.113015i
$495$	1.07504	+	1.38276i	0.0483196	+	0.0621505i
$496$	19.3734	−	15.9592i	0.869890	−	0.716589i
$497$	7.27305	−	4.19910i	0.326241	−	0.188355i
$498$	4.65600	−	10.6077i	0.208641	−	0.475341i
$499$	0.252258	+	0.145641i	0.0112926	+	0.00651981i	0.505636	−	0.862747i	$-0.331258\pi$
$499$	0.252258	+	0.145641i	0.0112926	+	0.00651981i	−0.494343	+	0.869267i	$0.664591\pi$
$500$	1.13972	+	1.64349i	0.0509697	+	0.0734989i
$501$	23.2928	+	4.55643i	1.04064	+	0.203566i
$502$	39.6402	−	12.3998i	1.76923	−	0.553431i
$503$	−15.1659			−0.676212			−0.338106	−	0.941108i	$-0.609786\pi$
$503$	−15.1659			−0.676212			−0.338106	+	0.941108i	$0.609786\pi$
$504$	−3.97375	−	6.88991i	−0.177005	−	0.306901i
$505$	1.23146			0.0547991
$506$	−3.99290	+	1.24902i	−0.177506	+	0.0555256i
$507$	13.2632	−	15.2209i	0.589038	−	0.675985i
$508$	−23.9118	−	34.4812i	−1.06092	−	1.52986i
$509$	−28.1837	−	16.2719i	−1.24922	−	0.721238i	−0.278266	−	0.960504i	$-0.589760\pi$
$509$	−28.1837	−	16.2719i	−1.24922	−	0.721238i	−0.970954	+	0.239266i	$0.923093\pi$
$510$	−0.580139	+	0.0640683i	−0.0256890	+	0.00283699i
$511$	−9.52307	+	5.49815i	−0.421276	+	0.243224i
$512$	−20.7241	−	9.08366i	−0.915883	−	0.401445i
$513$	−19.9390	+	30.4647i	−0.880326	+	1.34505i
$514$	−11.5466	−	2.58728i	−0.509297	−	0.114120i
$515$	3.06489	+	5.30854i	0.135055	+	0.233922i
$516$	37.1810	+	4.12312i	1.63680	+	0.181510i
$517$	−2.49613	+	4.32343i	−0.109780	+	0.190144i
$518$	−3.15067	+	3.42275i	−0.138432	+	0.150387i
$519$	16.3736	+	14.2676i	0.718720	+	0.626277i
$520$	−0.450086	+	3.24796i	−0.0197376	+	0.142433i
$521$			29.6176i			1.29757i	0.760971	+	0.648786i	$0.224723\pi$
$521$			29.6176i			1.29757i	−0.760971	+	0.648786i	$0.775277\pi$
$522$	3.22311	−	38.6565i	0.141072	−	1.69195i
$523$			33.5009i			1.46489i	0.680824	+	0.732447i	$0.261622\pi$
$523$			33.5009i			1.46489i	−0.680824	+	0.732447i	$0.738378\pi$
$524$	1.98541	+	23.9426i	0.0867329	+	1.04594i
$525$	−0.311683	+	1.59335i	−0.0136030	+	0.0695393i
$526$	−0.420918	−	0.387459i	−0.0183529	−	0.0168940i
$527$	0.747613	−	1.29490i	0.0325665	−	0.0564069i
$528$	1.92463	+	3.55768i	0.0837589	+	0.154828i
$529$	−1.33758	−	2.31676i	−0.0581558	−	0.100729i
$530$	3.68087	−	16.4271i	0.159887	−	0.713547i
$531$	4.06019	+	29.3972i	0.176197	+	1.27573i
$532$	−11.8801	−	5.60547i	−0.515068	−	0.243028i
$533$	−3.31689	+	1.91501i	−0.143671	+	0.0829483i
$534$	−4.66560	+	3.42748i	−0.201900	+	0.148321i
$535$	−6.53824	−	3.77485i	−0.282673	−	0.163201i
$536$	−23.2908	+	9.46237i	−1.00601	+	0.408712i
$537$	−13.0173	−	37.9518i	−0.561740	−	1.63774i
$538$	−7.92267	−	25.3275i	−0.341570	−	1.09194i
$539$	3.57386			0.153937
$540$	9.13603	+	4.95307i	0.393152	+	0.213146i
$541$	−15.6319			−0.672069			−0.336035	−	0.941850i	$-0.609086\pi$
$541$	−15.6319			−0.672069			−0.336035	+	0.941850i	$0.609086\pi$
$542$	5.18829	+	16.5861i	0.222856	+	0.712434i
$543$	1.92659	+	5.61694i	0.0826780	+	0.241046i
$544$	−1.34588	−	0.0740491i	−0.0577042	−	0.00317483i
$545$	−5.17092	−	2.98543i	−0.221498	−	0.127882i
$546$	−2.14517	+	1.57590i	−0.0918047	+	0.0674422i
$547$	−3.67329	+	2.12077i	−0.157058	+	0.0906777i	−0.576469	−	0.817119i	$-0.695570\pi$
$547$	−3.67329	+	2.12077i	−0.157058	+	0.0906777i	0.419411	+	0.907796i	$0.362237\pi$
$548$	−2.74100	+	5.80920i	−0.117090	+	0.248157i
$549$	18.5236	+	7.53536i	0.790570	+	0.321601i
$550$	0.180533	−	0.805686i	0.00769794	−	0.0343546i
$551$	−32.0328	−	55.4824i	−1.36464	−	2.36363i
$552$	−18.7225	+	16.2995i	−0.796881	+	0.693752i
$553$	2.36724	−	4.10018i	0.100665	−	0.174357i
$554$	−14.4600	−	13.3105i	−0.614345	−	0.565510i
$555$	1.16691	−	5.96534i	0.0495327	−	0.253215i
$556$	2.21626	−	0.183781i	0.0939905	−	0.00779403i
$557$			35.6028i			1.50854i	0.656565	+	0.754270i	$0.272009\pi$
$557$			35.6028i			1.50854i	−0.656565	+	0.754270i	$0.727991\pi$
$558$	−24.0824	+	11.3497i	−1.01949	+	0.480470i
$559$		−	12.5193i		−	0.529512i
$560$	−1.31426	+	3.51153i	−0.0555376	+	0.148389i
$561$	0.181664	+	0.158298i	0.00766984	+	0.00668333i
$562$	16.7726	−	18.2210i	0.707508	−	0.768605i
$563$	−10.2108	+	17.6857i	−0.430335	+	0.745361i	−0.996902	−	0.0786540i	$-0.974938\pi$
$563$	−10.2108	+	17.6857i	−0.430335	+	0.745361i	0.566567	+	0.824015i	$0.308271\pi$
$564$	−3.26475	+	29.4405i	−0.137471	+	1.23967i
$565$	7.71185	+	13.3573i	0.324440	+	0.561947i
$566$	4.95560	+	1.11042i	0.208299	+	0.0466743i
$567$	2.28671	+	8.12036i	0.0960326	+	0.341023i
$568$	−15.5631	+	19.9992i	−0.653011	+	0.839147i
$569$	2.79252	−	1.61226i	0.117068	−	0.0675895i	−0.440322	−	0.897840i	$-0.645136\pi$
$569$	2.79252	−	1.61226i	0.117068	−	0.0675895i	0.557391	+	0.830250i	$0.311803\pi$
$570$	17.0599	−	1.88403i	0.714561	−	0.0789134i
$571$	−34.2930	−	19.7991i	−1.43512	−	0.828566i	−0.437613	−	0.899164i	$-0.644176\pi$
$571$	−34.2930	−	19.7991i	−1.43512	−	0.828566i	−0.997505	+	0.0705979i	$0.977509\pi$
$572$	1.11238	−	0.771404i	0.0465108	−	0.0322540i
$573$	5.28097	−	6.06049i	0.220616	−	0.253180i
$574$	−4.17976	+	1.30747i	−0.174460	+	0.0545727i
$575$	5.06707			0.211311
$576$	18.9341	+	14.7479i	0.788919	+	0.614497i
$577$	−20.9763			−0.873254			−0.436627	−	0.899643i	$-0.643827\pi$
$577$	−20.9763			−0.873254			−0.436627	+	0.899643i	$0.643827\pi$
$578$	22.8686	−	7.15351i	0.951208	−	0.297547i
$579$	0.0144652	+	0.00282961i	0.000601152	+	0.000117595i
$580$	−15.0265	+	10.4205i	−0.623940	+	0.432686i
$581$	−3.83917	−	2.21654i	−0.159275	−	0.0919577i
$582$	−4.46280	+	10.1675i	−0.184989	+	0.421457i
$583$	−6.01870	+	3.47490i	−0.249269	+	0.143916i
$584$	20.3777	−	26.1862i	0.843236	−	1.08359i
$585$	1.31052	−	3.22155i	0.0541832	−	0.133195i
$586$	−1.09716	−	0.245845i	−0.0453234	−	0.0101558i
$587$	−3.59949	−	6.23450i	−0.148567	−	0.257325i	0.782131	−	0.623114i	$-0.214133\pi$
$587$	−3.59949	−	6.23450i	−0.148567	−	0.257325i	−0.930698	+	0.365789i	$0.880799\pi$
$588$	19.4208	−	8.51388i	0.800900	−	0.351106i
$589$	−21.9848	+	38.0787i	−0.905866	+	1.56901i
$590$	9.47453	−	10.2927i	0.390060	−	0.423744i
$591$	9.55606	−	3.27770i	0.393084	−	0.134827i
$592$	4.92046	−	13.1468i	0.202230	−	0.540332i
$593$		−	5.52785i		−	0.227002i	−0.993538	−	0.113501i	$-0.963794\pi$
$593$		−	5.52785i		−	0.227002i	0.993538	−	0.113501i	$-0.0362065\pi$
$594$	−1.04994	−	4.15982i	−0.0430796	−	0.170680i
$595$			0.223353i			0.00915659i
$596$	−1.62813	+	0.135010i	−0.0666908	+	0.00553024i
$597$	14.1084	−	4.83915i	0.577419	−	0.198053i
$598$	6.11217	+	5.62630i	0.249945	+	0.230077i
$599$	−8.25929	+	14.3055i	−0.337465	+	0.584507i	−0.983955	−	0.178416i	$-0.942903\pi$
$599$	−8.25929	+	14.3055i	−0.337465	+	0.584507i	0.646490	+	0.762922i	$0.276236\pi$
$600$	−0.938321	−	4.80828i	−0.0383068	−	0.196297i
$601$	9.59942	+	16.6267i	0.391568	+	0.678216i	0.992657	−	0.120966i	$-0.0385993\pi$
$601$	9.59942	+	16.6267i	0.391568	+	0.678216i	−0.601088	+	0.799183i	$0.705266\pi$
$602$	3.13008	−	13.9690i	0.127573	−	0.569335i
$603$	26.4138	−	3.64813i	1.07565	−	0.148563i
$604$	15.0503	−	31.8972i	0.612387	−	1.29788i
$605$	9.23109	−	5.32957i	0.375297	−	0.216678i
$606$	−2.76208	−	1.21236i	−0.112202	−	0.0492486i
$607$	8.75321	+	5.05367i	0.355282	+	0.205122i	0.667009	−	0.745050i	$-0.267574\pi$
$607$	8.75321	+	5.05367i	0.355282	+	0.205122i	−0.311727	+	0.950172i	$0.600908\pi$
$608$	39.5779	+	2.17753i	1.60509	+	0.0883106i
$609$	−14.5680	−	2.84973i	−0.590326	−	0.115477i
$610$	−2.81437	−	8.99708i	−0.113951	−	0.364281i
$611$	9.91301			0.401038
$612$	1.36429	+	0.427439i	0.0551482	+	0.0172782i
$613$	33.5309			1.35430			0.677151	−	0.735844i	$-0.263214\pi$
$613$	33.5309			1.35430			0.677151	+	0.735844i	$0.263214\pi$
$614$	−4.22437	−	13.5046i	−0.170482	−	0.545002i
$615$	3.75925	−	4.31415i	0.151588	−	0.173963i
$616$	1.43405	−	0.582613i	0.0577795	−	0.0234741i
$617$	−32.0259	−	18.4901i	−1.28931	−	0.744385i	−0.310781	−	0.950482i	$-0.600590\pi$
$617$	−32.0259	−	18.4901i	−1.28931	−	0.744385i	−0.978532	+	0.206097i	$0.933924\pi$
$618$	−1.64816	−	14.9241i	−0.0662987	−	0.600335i
$619$	−14.8494	+	8.57332i	−0.596849	+	0.344591i	−0.767801	−	0.640688i	$-0.778649\pi$
$619$	−14.8494	+	8.57332i	−0.596849	+	0.344591i	0.170952	+	0.985279i	$0.445316\pi$
$620$	11.3501	+	5.35541i	0.455832	+	0.215078i
$621$	23.5021	−	11.8694i	0.943105	−	0.476303i
$622$	−0.535195	+	2.38848i	−0.0214594	+	0.0957694i
$623$	1.10770	+	1.91859i	0.0443789	+	0.0768665i
$624$	4.20710	−	6.84189i	0.168419	−	0.273895i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.23720	−	2.97987i	−0.129385	−	0.119100i
$627$	−5.34211	−	4.65500i	−0.213343	−	0.185903i
$628$	3.43602	+	41.4360i	0.137112	+	1.65347i
$629$		−	0.836214i		−	0.0333420i
$630$	2.26772	−	3.26693i	0.0903481	−	0.130158i
$631$			3.80264i			0.151381i	0.997131	+	0.0756904i	$0.0241161\pi$
$631$			3.80264i			0.151381i	−0.997131	+	0.0756904i	$0.975884\pi$
$632$	−1.96095	+	14.1509i	−0.0780025	+	0.562891i
$633$	−0.756279	+	3.86615i	−0.0300594	+	0.153666i
$634$	3.59040	−	3.90045i	0.142593	−	0.154907i
$635$	10.4903	−	18.1697i	0.416293	−	0.721041i
$636$	−24.4283	+	33.2212i	−0.968643	+	1.31731i
$637$	−3.54826	−	6.14576i	−0.140587	−	0.243504i
$638$	7.36642	+	1.65062i	0.291639	+	0.0653486i
$639$	21.2198	−	16.4975i	0.839442	−	0.652633i
$640$	−0.314150	−	11.3093i	−0.0124179	−	0.447041i
$641$	1.03750	−	0.598999i	0.0409787	−	0.0236590i	−0.479371	−	0.877613i	$-0.659135\pi$
$641$	1.03750	−	0.598999i	0.0409787	−	0.0236590i	0.520349	+	0.853953i	$0.325802\pi$
$642$	10.9486	+	14.9036i	0.432106	+	0.588198i
$643$	−14.2050	−	8.20123i	−0.560189	−	0.323425i	0.193033	−	0.981192i	$-0.438168\pi$
$643$	−14.2050	−	8.20123i	−0.560189	−	0.323425i	−0.753221	+	0.657767i	$0.771501\pi$
$644$	5.41324	+	7.80596i	0.213311	+	0.307598i
$645$	6.06853	+	17.6927i	0.238948	+	0.696648i
$646$	2.25354	−	0.704929i	0.0886645	−	0.0277351i
$647$	−4.22993			−0.166296			−0.0831478	−	0.996537i	$-0.526497\pi$
$647$	−4.22993			−0.166296			−0.0831478	+	0.996537i	$0.526497\pi$
$648$	−15.6153	−	20.1038i	−0.613428	−	0.789751i
$649$	−5.77533			−0.226701
$650$	−1.56473	+	0.489463i	−0.0613739	+	0.0191983i
$651$	3.30538	+	9.63674i	0.129548	+	0.377694i
$652$	3.67328	+	5.29692i	0.143857	+	0.207443i
$653$	−4.27547	−	2.46844i	−0.167312	−	0.0965976i	0.414006	−	0.910274i	$-0.364129\pi$
$653$	−4.27547	−	2.46844i	−0.167312	−	0.0965976i	−0.581318	+	0.813677i	$0.697463\pi$
$654$	8.65894	+	11.7869i	0.338592	+	0.460903i
$655$	−10.4030	+	6.00620i	−0.406480	+	0.234681i
$656$	10.1998	−	8.40227i	0.398235	−	0.328054i
$657$	−27.7844	+	21.6013i	−1.08397	+	0.842746i
$658$	11.0609	+	2.47845i	0.431198	+	0.0966200i
$659$	−9.46707	−	16.3975i	−0.368785	−	0.638754i	0.620591	−	0.784134i	$-0.286893\pi$
$659$	−9.46707	−	16.3975i	−0.368785	−	0.638754i	−0.989376	+	0.145380i	$0.953559\pi$
$660$	−1.19811	+	1.62937i	−0.0466365	+	0.0634233i
$661$	13.0731	−	22.6432i	0.508483	−	0.880718i	−0.491469	−	0.870895i	$-0.663540\pi$
$661$	13.0731	−	22.6432i	0.508483	−	0.880718i	0.999952	−	0.00982323i	$-0.00312688\pi$
$662$	−20.4255	+	22.1894i	−0.793861	+	0.862415i
$663$	0.0918533	−	0.469561i	0.00356729	−	0.0182362i
$664$	13.2500	+	1.83612i	0.514201	+	0.0712553i
$665$		−	6.56807i		−	0.254699i
$666$	−8.49013	+	12.2311i	−0.328986	+	0.473945i
$667$			46.3284i			1.79384i
$668$	2.26483	+	27.3122i	0.0876287	+	1.05674i
$669$	−15.6477	−	13.6351i	−0.604975	−	0.527162i
$670$	−9.24814	−	8.51299i	−0.357287	−	0.328886i
$671$	−1.94588	+	3.37037i	−0.0751200	+	0.130112i
$672$	6.40487	−	6.58228i	0.247073	−	0.253917i
$673$	16.0569	+	27.8114i	0.618949	+	1.07205i	0.989678	+	0.143310i	$0.0457746\pi$
$673$	16.0569	+	27.8114i	0.618949	+	1.07205i	−0.370729	+	0.928741i	$0.620892\pi$
$674$	0.305378	−	1.36285i	0.0117627	−	0.0524950i
$675$	−0.290467	+	5.18803i	−0.0111801	+	0.199687i
$676$	21.0830	+	9.94775i	0.810885	+	0.382606i
$677$	11.7427	−	6.77964i	0.451308	−	0.260563i	−0.257075	−	0.966392i	$-0.582759\pi$
$677$	11.7427	−	6.77964i	0.451308	−	0.260563i	0.708382	+	0.705829i	$0.249425\pi$
$678$	−4.14709	−	37.5519i	−0.159268	−	1.44217i
$679$	3.67986	+	2.12457i	0.141220	+	0.0815334i
$680$	−0.253674	−	0.624396i	−0.00972796	−	0.0239445i
$681$	15.6877	−	18.0033i	0.601154	−	0.689889i
$682$	−1.54678	−	4.94482i	−0.0592294	−	0.189347i
$683$	20.9171			0.800369			0.400185	−	0.916435i	$-0.368946\pi$
$683$	20.9171			0.800369			0.400185	+	0.916435i	$0.368946\pi$
$684$	−40.1192	−	12.5695i	−1.53400	−	0.480608i
$685$	−3.21169			−0.122713
$686$	−5.19285	−	16.6007i	−0.198264	−	0.633818i
$687$	−21.8863	−	4.28131i	−0.835016	−	0.163342i
$688$	7.11503	+	42.6061i	0.271258	+	1.62434i
$689$	11.9512	+	6.90001i	0.455303	+	0.262870i
$690$	−11.3651	−	4.98847i	−0.432663	−	0.189908i
$691$	−0.882546	+	0.509538i	−0.0335736	+	0.0193837i	−0.516693	−	0.856171i	$-0.672837\pi$
$691$	−0.882546	+	0.509538i	−0.0335736	+	0.0193837i	0.483119	+	0.875555i	$0.339504\pi$
$692$	−10.7011	+	22.6796i	−0.406794	+	0.862149i
$693$	−1.62634	+	0.224621i	−0.0617794	+	0.00853265i
$694$	−5.54381	+	24.7411i	−0.210440	+	0.939158i
$695$	0.555968	+	0.962964i	0.0210891	+	0.0365273i
$696$	43.9623	−	8.57910i	1.66639	−	0.325190i
$697$	0.393607	−	0.681747i	0.0149089	−	0.0258230i
$698$	−12.4890	−	11.4963i	−0.472717	−	0.435140i
$699$	−16.7690	+	5.75173i	−0.634263	+	0.217550i
$700$	−1.86830	+	0.154926i	−0.0706150	+	0.00585565i
$701$			16.7130i			0.631241i	0.948885	+	0.315621i	$0.102213\pi$
$701$			16.7130i			0.631241i	−0.948885	+	0.315621i	$0.897787\pi$
$702$	−6.11099	+	5.93555i	−0.230645	+	0.224023i
$703$			24.5902i			0.927438i
$704$	−3.34726	+	3.25745i	−0.126154	+	0.122770i
$705$	−14.0093	+	4.80516i	−0.527622	+	0.180973i
$706$	−26.3208	+	28.5937i	−0.990596	+	1.07614i
$707$	−0.577156	+	0.999663i	−0.0217062	+	0.0375962i
$708$	−31.3839	+	13.7584i	−1.17948	+	0.517071i
$709$	−23.3023	−	40.3608i	−0.875136	−	1.51578i	−0.856618	−	0.515952i	$-0.827438\pi$
$709$	−23.3023	−	40.3608i	−0.875136	−	1.51578i	−0.0185184	−	0.999829i	$-0.505895\pi$
$710$	−12.3640	−	2.77044i	−0.464013	−	0.103973i
$711$	5.70971	−	14.0358i	0.214131	−	0.526383i
$712$	−5.27566	−	4.10544i	−0.197714	−	0.153858i
$713$	27.5363	−	15.8981i	1.03124	−	0.595388i
$714$	0.219889	−	0.500968i	0.00822914	−	0.0187483i
$715$	0.586160	+	0.338419i	0.0219211	+	0.0126562i
$716$	38.0706	−	26.4010i	1.42277	−	0.986652i
$717$	−29.0208	−	5.67691i	−1.08380	−	0.212008i
$718$	−9.86597	+	3.08617i	−0.368195	+	0.115175i
$719$	16.2028			0.604264			0.302132	−	0.953266i	$-0.402302\pi$
$719$	16.2028			0.604264			0.302132	+	0.953266i	$0.402302\pi$
$720$	−2.62910	+	11.7085i	−0.0979808	+	0.436348i
$721$	−5.74577			−0.213984
$722$	−40.6244	+	12.7077i	−1.51188	+	0.472931i
$723$	24.4813	−	28.0950i	0.910471	−	1.04486i
$724$	−5.63452	+	3.90740i	−0.209405	+	0.145217i
$725$	−7.91811	−	4.57152i	−0.294071	−	0.169782i
$726$	−25.9517	+	2.86600i	−0.963157	+	0.106367i
$727$	8.87834	−	5.12591i	0.329280	−	0.190110i	−0.326242	−	0.945286i	$-0.605782\pi$
$727$	8.87834	−	5.12591i	0.329280	−	0.190110i	0.655521	+	0.755177i	$0.272449\pi$
$728$	−2.42566	−	1.88761i	−0.0899011	−	0.0699597i
$729$	10.8055	+	24.7435i	0.400204	+	0.916426i
$730$	16.1890	+	3.62752i	0.599181	+	0.134261i
$731$	1.28660	+	2.22846i	0.0475866	+	0.0824224i
$732$	−2.54507	+	22.9506i	−0.0940683	+	0.848280i
$733$	7.26607	−	12.5852i	0.268379	−	0.464845i	−0.700065	−	0.714079i	$-0.746846\pi$
$733$	7.26607	−	12.5852i	0.268379	−	0.464845i	0.968443	+	0.249234i	$0.0801789\pi$
$734$	16.4144	−	17.8319i	0.605867	−	0.658187i
$735$	7.99354	+	6.96539i	0.294846	+	0.256922i
$736$	−23.9986	−	15.6739i	−0.884602	−	0.577747i
$737$			5.18921i			0.191147i
$738$	−12.6790	+	5.97543i	−0.466721	+	0.219959i
$739$		−	34.5703i		−	1.27169i	−0.771818	−	0.635844i	$-0.780652\pi$
$739$		−	34.5703i		−	1.27169i	0.771818	−	0.635844i	$-0.219348\pi$
$740$	6.99473	−	0.580028i	0.257131	−	0.0213223i
$741$	−2.70110	+	13.8082i	−0.0992272	+	0.507257i
$742$	11.6099	+	10.6870i	0.426213	+	0.392333i
$743$	0.231687	−	0.401294i	0.00849978	−	0.0147221i	−0.861744	−	0.507343i	$-0.830628\pi$
$743$	0.231687	−	0.401294i	0.00849978	−	0.0147221i	0.870244	+	0.492621i	$0.163961\pi$
$744$	−20.1853	−	23.1859i	−0.740029	−	0.850037i
$745$	−0.408430	−	0.707421i	−0.0149637	−	0.0259179i
$746$	−4.93885	+	22.0412i	−0.180824	+	0.806987i
$747$	−13.1423	−	5.34624i	−0.480851	−	0.195609i
$748$	−0.118728	+	0.251628i	−0.00434111	+	0.00920045i
$749$	6.12864	−	3.53837i	0.223936	−	0.129289i
$750$	1.97406	−	1.45020i	0.0720826	−	0.0529538i
$751$	28.2813	+	16.3282i	1.03200	+	0.595826i	0.917557	−	0.397604i	$-0.130158\pi$
$751$	28.2813	+	16.3282i	1.03200	+	0.595826i	0.114443	+	0.993430i	$0.463492\pi$
$752$	−33.7362	+	5.63380i	−1.23023	+	0.205443i
$753$	−16.5041	−	48.1172i	−0.601442	−	1.75349i
$754$	−4.47518	−	14.3064i	−0.162976	−	0.521009i
$755$	17.6348			0.641795
$756$	−8.30262	+	5.09499i	−0.301963	+	0.185303i
$757$	46.0622			1.67416			0.837080	−	0.547081i	$-0.184261\pi$
$757$	46.0622			1.67416			0.837080	+	0.547081i	$0.184261\pi$
$758$	11.5429	+	36.9007i	0.419257	+	1.34030i
$759$	1.66243	+	4.84678i	0.0603425	+	0.175927i
$760$	7.45970	+	18.3614i	0.270592	+	0.666037i
$761$	−29.8599	−	17.2396i	−1.08242	−	0.624935i	−0.150871	−	0.988553i	$-0.548208\pi$
$761$	−29.8599	−	17.2396i	−1.08242	−	0.624935i	−0.931548	+	0.363618i	$0.881541\pi$
$762$	−41.4169	+	30.4259i	−1.50038	+	1.10222i
$763$	4.84699	−	2.79841i	0.175473	−	0.101309i
$764$	8.39459	+	3.96088i	0.303705	+	0.143299i
$765$	0.0978018	+	0.708120i	0.00353603	+	0.0256021i
$766$	4.68310	−	20.8999i	0.169207	−	0.755143i
$767$	5.73396	+	9.93151i	0.207041	+	0.358606i
$768$	−10.4293	+	25.6755i	−0.376335	+	0.926484i
$769$	−12.8450	+	22.2482i	−0.463203	+	0.802291i	−0.999118	−	0.0419805i	$-0.986633\pi$
$769$	−12.8450	+	22.2482i	−0.463203	+	0.802291i	0.535915	+	0.844272i	$0.319967\pi$
$770$	0.569422	+	0.524158i	0.0205206	+	0.0188893i
$771$	−2.78218	+	14.2227i	−0.100198	+	0.512218i
$772$	0.00140649	+	0.0169613i	5.06207e−5	+	0.000610450i
$773$		−	2.14085i		−	0.0770009i	−0.999259	−	0.0385004i	$-0.987742\pi$
$773$		−	2.14085i		−	0.0770009i	0.999259	−	0.0385004i	$-0.0122581\pi$
$774$	3.80688	−	45.6580i	0.136835	−	1.64114i
$775$			6.27506i			0.225407i
$776$	−12.7002	−	1.75993i	−0.455911	−	0.0631778i
$777$	4.29559	+	3.74309i	0.154104	+	0.134282i
$778$	19.8684	−	21.5842i	0.712318	−	0.773831i
$779$	−11.5747	+	20.0479i	−0.414705	+	0.718290i
$780$	3.99147	+	0.442627i	0.142918	+	0.0158486i
$781$	2.61542	+	4.53003i	0.0935869	+	0.162097i
$782$	−1.66618	−	0.373347i	−0.0595825	−	0.0133509i
$783$	−47.4343	−	2.65575i	−1.69517	−	0.0949089i
$784$	15.5683	+	18.8988i	0.556010	+	0.674959i
$785$	−18.0039	+	10.3945i	−0.642586	+	0.370997i
$786$	29.2464	−	3.22986i	1.04319	−	0.115205i
$787$	42.4986	+	24.5366i	1.51491	+	0.874634i	0.999847	+	0.0174819i	$0.00556495\pi$
$787$	42.4986	+	24.5366i	1.51491	+	0.874634i	0.515063	+	0.857152i	$0.327768\pi$
$788$	6.64764	+	9.58598i	0.236812	+	0.341487i
$789$	−0.460313	+	0.528258i	−0.0163876	+	0.0188065i
$790$	−6.81729	+	2.13251i	−0.242548	+	0.0758714i
$791$	−14.4575			−0.514049
$792$	4.29140	−	2.47506i	0.152488	−	0.0879473i
$793$	7.72778			0.274422
$794$	43.2511	−	13.5293i	1.53492	−	0.480138i
$795$	−20.2344	−	3.95816i	−0.717639	−	0.140381i
$796$	9.81447	+	14.1526i	0.347865	+	0.501626i
$797$	−12.3026	−	7.10293i	−0.435781	−	0.251599i	0.266025	−	0.963966i	$-0.414290\pi$
$797$	−12.3026	−	7.10293i	−0.435781	−	0.251599i	−0.701807	+	0.712368i	$0.747623\pi$
$798$	−6.46619	+	14.7318i	−0.228901	+	0.521499i
$799$	−1.76453	+	1.01875i	−0.0624245	+	0.0360408i
$800$	5.04696	−	2.55503i	0.178437	−	0.0903338i
$801$	4.35195	+	5.59765i	0.153769	+	0.197783i
$802$	−40.9313	−	9.17162i	−1.44534	−	0.323861i
$803$	−3.42453	−	5.93146i	−0.120849	−	0.209317i
$804$	12.3621	+	28.1988i	0.435977	+	0.994496i
$805$	−2.37482	+	4.11331i	−0.0837014	+	0.144975i
$806$	−6.96762	+	7.56932i	−0.245424	+	0.266618i
$807$	−30.7437	+	10.5450i	−1.08223	+	0.371202i
$808$	0.478099	−	3.45012i	0.0168195	−	0.121375i
$809$			1.60355i			0.0563779i	0.999603	+	0.0281890i	$0.00897401\pi$
$809$			1.60355i			0.0563779i	−0.999603	+	0.0281890i	$0.991026\pi$
$810$	5.75906	−	11.3505i	0.202353	−	0.398815i
$811$		−	12.3766i		−	0.434601i	−0.976105	−	0.217301i	$-0.930275\pi$
$811$		−	12.3766i		−	0.434601i	0.976105	−	0.217301i	$-0.0697252\pi$
$812$	−1.41649	−	17.0819i	−0.0497092	−	0.599457i
$813$	20.1330	−	6.90557i	0.706096	−	0.242189i
$814$	−2.13186	−	1.96240i	−0.0747218	−	0.0687820i
$815$	−1.61149	+	2.79118i	−0.0564480	+	0.0977708i
$816$	−0.0457352	+	1.65022i	−0.00160105	+	0.0577693i
$817$	−37.8345	−	65.5314i	−1.32366	−	2.29265i
$818$	7.02468	−	31.3499i	0.245612	−	1.09612i
$819$	2.00096	+	2.57371i	0.0699191	+	0.0899327i
$820$	5.97567	+	2.81954i	0.208680	+	0.0984627i
$821$	30.9702	−	17.8807i	1.08087	−	0.624040i	0.149738	−	0.988726i	$-0.452157\pi$
$821$	30.9702	−	17.8807i	1.08087	−	0.624040i	0.931131	+	0.364686i	$0.118824\pi$
$822$	7.20364	+	3.16188i	0.251256	+	0.110283i
$823$	−25.3380	−	14.6289i	−0.883228	−	0.509932i	−0.0115066	−	0.999934i	$-0.503663\pi$
$823$	−25.3380	−	14.6289i	−0.883228	−	0.509932i	−0.871721	+	0.490002i	$0.836996\pi$
$824$	16.0626	−	6.52578i	0.559568	−	0.227336i
$825$	−0.992419	−	0.194133i	−0.0345516	−	0.00675883i
$826$	3.91485	+	12.5151i	0.136215	+	0.435457i
$827$	45.0397			1.56619			0.783093	−	0.621905i	$-0.213641\pi$
$827$	45.0397			1.56619			0.783093	+	0.621905i	$0.213641\pi$
$828$	20.5802	+	22.3777i	0.715212	+	0.777679i
$829$	43.0934			1.49670			0.748349	−	0.663306i	$-0.230847\pi$
$829$	43.0934			1.49670			0.748349	+	0.663306i	$0.230847\pi$
$830$	1.99676	+	6.38331i	0.0693085	+	0.221568i
$831$	−15.8133	+	18.1475i	−0.548558	+	0.629529i
$832$	8.92494	+	2.52197i	0.309416	+	0.0874337i
$833$	1.26319	+	0.729301i	0.0437668	+	0.0252688i
$834$	−0.298974	−	2.70722i	−0.0103526	−	0.0937432i
$835$	−11.8671	+	6.85148i	−0.410679	+	0.237105i
$836$	3.49138	−	7.39954i	0.120752	−	0.255918i
$837$	14.6991	+	29.1050i	0.508075	+	1.00602i
$838$	−2.61592	+	11.6744i	−0.0903654	+	0.403285i
$839$	10.6968	+	18.5275i	0.369296	+	0.639639i	0.989456	−	0.144836i	$-0.0462656\pi$
$839$	10.6968	+	18.5275i	0.369296	+	0.639639i	−0.620160	+	0.784475i	$0.712932\pi$
$840$	4.34300	+	1.49183i	0.149848	+	0.0514730i
$841$	27.2976	−	47.2808i	0.941296	−	1.63037i
$842$	25.9120	+	23.8522i	0.892987	+	0.822003i
$843$	−22.8676	−	19.9263i	−0.787601	−	0.686299i
$844$	−4.53330	+	0.375918i	−0.156043	+	0.0129396i
$845$			11.6560i			0.400979i
$846$	36.1527	+	3.01434i	1.24296	+	0.103635i
$847$			9.99139i			0.343308i
$848$	−44.5940	−	16.6902i	−1.53136	−	0.573142i
$849$	1.19407	−	6.10415i	0.0409802	−	0.209494i
$850$	0.228223	−	0.247931i	0.00782797	−	0.00850396i
$851$	8.89110	−	15.3998i	0.304783	−	0.527899i
$852$	25.0043	+	18.3862i	0.856632	+	0.629900i
$853$	−22.6590	−	39.2466i	−0.775831	−	1.34378i	−0.934326	−	0.356419i	$-0.883998\pi$
$853$	−22.6590	−	39.2466i	−0.775831	−	1.34378i	0.158495	−	0.987360i	$-0.449336\pi$
$854$	8.62262	+	1.93210i	0.295060	+	0.0661150i
$855$	−2.87602	−	20.8234i	−0.0983578	−	0.712145i
$856$	−13.1142	+	16.8523i	−0.448235	+	0.576001i
$857$	4.84419	−	2.79680i	0.165475	−	0.0955368i	−0.414976	−	0.909833i	$-0.636210\pi$
$857$	4.84419	−	2.79680i	0.165475	−	0.0955368i	0.580450	+	0.814296i	$0.302877\pi$
$858$	−0.981551	−	1.33612i	−0.0335096	−	0.0456145i
$859$	41.2590	+	23.8209i	1.40774	+	0.812759i	0.995170	−	0.0981677i	$-0.0312982\pi$
$859$	41.2590	+	23.8209i	1.40774	+	0.812759i	0.412569	+	0.910926i	$0.364631\pi$
$860$	−17.7481	+	12.3078i	−0.605204	+	0.419694i
$861$	1.74023	+	5.07360i	0.0593069	+	0.172908i
$862$	−12.6475	+	3.95626i	−0.430777	+	0.134751i
$863$	−13.3295			−0.453742			−0.226871	−	0.973925i	$-0.572850\pi$
$863$	−13.3295			−0.453742			−0.226871	+	0.973925i	$0.572850\pi$
$864$	17.4238	−	23.6730i	0.592768	−	0.805373i
$865$	−12.5387			−0.426329
$866$	−38.0806	+	11.9120i	−1.29403	+	0.404785i
$867$	−9.52127	−	27.7590i	−0.323359	−	0.942746i
$868$	−9.66692	+	6.70376i	−0.328117	+	0.227541i
$869$	2.55380	+	1.47444i	0.0866319	+	0.0500169i
$870$	13.2592	+	18.0489i	0.449530	+	0.611916i
$871$	8.92359	−	5.15204i	0.302364	−	0.174570i
$872$	−10.3717	+	13.3281i	−0.351230	+	0.451346i
$873$	12.5969	+	5.12440i	0.426341	+	0.173435i
$874$	48.9968	+	10.9789i	1.65734	+	0.371366i
$875$	−0.468677	−	0.811773i	−0.0158442	−	0.0274429i
$876$	−32.7397	−	24.0742i	−1.10617	−	0.813392i
$877$	−21.1554	+	36.6422i	−0.714367	+	1.23732i	0.248836	+	0.968546i	$0.419952\pi$
$877$	−21.1554	+	36.6422i	−0.714367	+	1.23732i	−0.963203	+	0.268775i	$0.913381\pi$
$878$	9.17126	−	9.96326i	0.309515	−	0.336244i
$879$	−0.264365	+	1.35145i	−0.00891681	+	0.0455834i
$880$	−2.18716	−	0.818589i	−0.0737293	−	0.0275946i
$881$		−	16.0135i		−	0.539507i	−0.962929	−	0.269754i	$-0.913058\pi$
$881$		−	16.0135i		−	0.539507i	0.962929	−	0.269754i	$-0.0869423\pi$
$882$	−11.0717	−	23.4925i	−0.372803	−	0.791034i
$883$		−	53.4024i		−	1.79713i	−0.438836	−	0.898567i	$-0.644609\pi$
$883$		−	53.4024i		−	1.79713i	0.438836	−	0.898567i	$-0.355391\pi$
$884$	0.550589	−	0.0456568i	0.0185183	−	0.00153560i
$885$	−12.9175	−	11.2560i	−0.434217	−	0.378367i
$886$	7.65002	+	7.04191i	0.257008	+	0.236578i
$887$	3.13350	−	5.42738i	0.105213	−	0.182234i	−0.808612	−	0.588342i	$-0.799781\pi$
$887$	3.13350	−	5.42738i	0.105213	−	0.182234i	0.913825	+	0.406108i	$0.133114\pi$
$888$	−16.2598	−	5.58526i	−0.545643	−	0.187429i
$889$	9.83310	+	17.0314i	0.329791	+	0.571216i
$890$	0.730826	−	3.26155i	0.0244973	−	0.109327i
$891$	−5.05778	+	1.42428i	−0.169442	+	0.0477151i
$892$	10.2267	−	21.6742i	0.342414	−	0.725704i
$893$	51.8888	−	29.9580i	1.73639	−	1.00251i
$894$	0.219635	+	1.98880i	0.00734570	+	0.0665153i
$895$	20.0611	+	11.5823i	0.670568	+	0.387153i
$896$	9.32785	+	5.04541i	0.311622	+	0.168555i
$897$	6.68422	−	7.67086i	0.223180	−	0.256123i
$898$	11.2445	+	35.9468i	0.375234	+	1.19956i
$899$	−57.3732			−1.91350
$900$	−5.85541	+	1.30927i	−0.195180	+	0.0436422i
$901$	−2.83643			−0.0944951
$902$	−0.814359	−	2.60337i	−0.0271152	−	0.0866829i
$903$	−17.2066	−	3.36588i	−0.572600	−	0.112009i
$904$	40.4167	−	16.4201i	1.34424	−	0.546125i
$905$	−2.96908	−	1.71420i	−0.0986955	−	0.0569819i
$906$	−39.5537	−	17.3612i	−1.31409	−	0.576789i
$907$	−19.6047	+	11.3188i	−0.650964	+	0.375834i	−0.788826	−	0.614617i	$-0.789310\pi$
$907$	−19.6047	+	11.3188i	−0.650964	+	0.375834i	0.137861	+	0.990452i	$0.455977\pi$
$908$	24.9370	+	11.7662i	0.827564	+	0.390475i
$909$	−1.39208	+	3.42206i	−0.0461725	+	0.113503i
$910$	0.336022	−	1.49961i	0.0111390	−	0.0497115i
$911$	10.1022	+	17.4976i	0.334702	+	0.579721i	0.983428	−	0.181301i	$-0.0580310\pi$
$911$	10.1022	+	17.4976i	0.334702	+	0.579721i	−0.648725	+	0.761023i	$0.724698\pi$
$912$	1.34492	−	48.5275i	0.0445347	−	1.60690i
$913$	1.38058	−	2.39123i	0.0456905	−	0.0791382i
$914$	−5.49866	−	5.06157i	−0.181880	−	0.167422i
$915$	−10.9211	+	3.74591i	−0.361040	+	0.123836i
$916$	−2.12808	−	25.6631i	−0.0703136	−	0.847932i
$917$		−	11.2599i		−	0.371834i
$918$	0.477772	−	1.68455i	0.0157688	−	0.0555986i
$919$		−	51.8610i		−	1.71074i	−0.518021	−	0.855368i	$-0.673331\pi$
$919$		−	51.8610i		−	1.71074i	0.518021	−	0.855368i	$-0.326669\pi$
$920$	1.96723	−	14.1962i	0.0648577	−	0.468034i
$921$	−16.3926	+	5.62260i	−0.540153	+	0.185271i
$922$	−10.0084	+	10.8727i	−0.329611	+	0.358075i
$923$	5.19336	−	8.99517i	0.170942	−	0.296080i
$924$	−0.761152	−	1.73625i	−0.0250401	−	0.0571183i
$925$	1.75468	+	3.03920i	0.0576936	+	0.0999283i
$926$	16.0266	+	3.59114i	0.526668	+	0.118012i
$927$	−18.2164	+	2.51595i	−0.598305	+	0.0826348i
$928$	23.3607	+	46.1446i	0.766853	+	1.51477i
$929$	−11.2445	+	6.49203i	−0.368921	+	0.212997i	−0.672987	−	0.739654i	$-0.734989\pi$
$929$	−11.2445	+	6.49203i	−0.368921	+	0.212997i	0.304066	+	0.952651i	$0.401656\pi$
$930$	6.17773	−	14.0746i	0.202576	−	0.461524i
$931$	−37.1461	−	21.4463i	−1.21741	−	0.702874i
$932$	−11.6653	−	16.8215i	−0.382110	−	0.551008i
$933$	2.94206	+	0.575512i	0.0963187	+	0.0188414i
$934$	−44.0839	+	13.7898i	−1.44247	+	0.451218i
$935$	−0.139116			−0.00454958
$936$	−8.51688	−	4.92235i	−0.278383	−	0.160892i
$937$	15.3666			0.502006			0.251003	−	0.967986i	$-0.419240\pi$
$937$	15.3666			0.502006			0.251003	+	0.967986i	$0.419240\pi$
$938$	11.2450	−	3.51754i	0.367162	−	0.114852i
$939$	−3.54018	+	4.06274i	−0.115529	+	0.132582i
$940$	−9.74553	−	14.0532i	−0.317864	−	0.458365i
$941$	3.99834	+	2.30844i	0.130342	+	0.0752531i	0.563753	−	0.825943i	$-0.309357\pi$
$941$	3.99834	+	2.30844i	0.130342	+	0.0752531i	−0.433411	+	0.901196i	$0.642690\pi$
$942$	50.6149	−	5.58972i	1.64912	−	0.182123i
$943$	14.4974	−	8.37011i	0.472102	−	0.272568i
$944$	−25.1583	−	30.5404i	−0.818832	−	0.994006i
$945$	−4.07536	−	2.66730i	−0.132572	−	0.0867674i
$946$	8.70063	+	1.94958i	0.282882	+	0.0633863i
$947$	−12.7798	−	22.1352i	−0.415286	−	0.719297i	0.580172	−	0.814494i	$-0.302985\pi$
$947$	−12.7798	−	22.1352i	−0.415286	−	0.719297i	−0.995458	+	0.0951971i	$0.969652\pi$
$948$	17.3902	+	1.92845i	0.564808	+	0.0626332i
$949$	−6.80000	+	11.7780i	−0.220737	+	0.382329i
$950$	−6.71125	+	7.29081i	−0.217742	+	0.236545i
$951$	−4.89512	−	4.26550i	−0.158735	−	0.138318i
$952$	0.625759	+	0.0867144i	0.0202810	+	0.00281043i
$953$			2.90773i			0.0941907i	0.998890	+	0.0470954i	$0.0149965\pi$
$953$			2.90773i			0.0941907i	−0.998890	+	0.0470954i	$0.985004\pi$
$954$	41.4877	+	28.7984i	1.34321	+	0.932383i
$955$			4.64106i			0.150181i
$956$	−2.82178	−	34.0286i	−0.0912628	−	1.10056i
$957$	1.77496	−	9.07373i	0.0573764	−	0.293312i
$958$	−15.5163	−	14.2829i	−0.501309	−	0.461459i
$959$	1.50525	−	2.60717i	0.0486070	−	0.0841898i
$960$	−13.8354	+	0.762090i	−0.446537	+	0.0245963i
$961$	4.18821	+	7.25419i	0.135103	+	0.234006i
$962$	−1.25803	+	5.61439i	−0.0405607	+	0.181015i
$963$	17.8809	−	13.9017i	0.576203	−	0.447975i
$964$	38.9153	+	18.3617i	1.25338	+	0.591390i
$965$	−0.00736966	+	0.00425487i	−0.000237238	+	0.000136969i
$966$	9.37608	−	6.88792i	0.301671	−	0.221615i
$967$	−5.95955	−	3.44075i	−0.191646	−	0.110647i	0.401107	−	0.916031i	$-0.368626\pi$
$967$	−5.95955	−	3.44075i	−0.191646	−	0.110647i	−0.592753	+	0.805384i	$0.701959\pi$
$968$	−11.3477	−	27.9315i	−0.364730	−	0.897751i
$969$	−0.938255	−	2.73546i	−0.0301411	−	0.0878757i
$970$	−1.91390	−	6.11843i	−0.0614517	−	0.196451i
$971$	37.7409			1.21116			0.605581	−	0.795784i	$-0.292941\pi$
$971$	37.7409			1.21116			0.605581	+	0.795784i	$0.292941\pi$
$972$	−24.0916	+	19.7887i	−0.772740	+	0.634723i
$973$	−1.04228			−0.0334139
$974$	−9.87730	−	31.5761i	−0.316489	−	1.01176i
$975$	0.651472	+	1.89935i	0.0208638	+	0.0608279i
$976$	−26.2994	+	4.39188i	−0.841822	+	0.140581i
$977$	−6.55683	−	3.78559i	−0.209772	−	0.121112i	0.391434	−	0.920206i	$-0.371979\pi$
$977$	−6.55683	−	3.78559i	−0.209772	−	0.121112i	−0.601205	+	0.799095i	$0.705313\pi$
$978$	6.36236	−	4.67396i	0.203446	−	0.149457i
$979$	−1.19499	+	0.689931i	−0.0381922	+	0.0220503i
$980$	−5.22424	+	11.0721i	−0.166882	+	0.353686i
$981$	14.1415	−	10.9945i	0.451504	−	0.351027i
$982$	8.79395	−	39.2459i	0.280626	−	1.25239i
$983$	6.28255	+	10.8817i	0.200382	+	0.347072i	0.948652	−	0.316323i	$-0.102448\pi$
$983$	6.28255	+	10.8817i	0.200382	+	0.347072i	−0.748269	+	0.663395i	$0.769115\pi$
$984$	−10.6273	−	12.2071i	−0.338785	−	0.389147i
$985$	−2.91636	+	5.05128i	−0.0929228	+	0.160947i
$986$	2.26684	+	2.08665i	0.0721910	+	0.0664524i
$987$	2.66515	−	13.6245i	0.0848328	−	0.433671i
$988$	−16.1909	+	1.34261i	−0.515103	+	0.0427142i
$989$			54.7194i			1.73998i
$990$	2.03482	+	1.41245i	0.0646707	+	0.0448907i
$991$			39.4015i			1.25163i	0.779972	+	0.625814i	$0.215233\pi$
$991$			39.4015i			1.25163i	−0.779972	+	0.625814i	$0.784767\pi$
$992$	19.4106	−	29.7199i	0.616286	−	0.943609i
$993$	27.8480	+	24.2661i	0.883730	+	0.770063i
$994$	8.04370	−	8.73832i	0.255131	−	0.277163i
$995$	−4.30566	+	7.45763i	−0.136499	+	0.236423i
$996$	1.80569	−	16.2832i	0.0572155	−	0.515952i
$997$	24.6340	+	42.6673i	0.780166	+	1.35129i	0.931845	+	0.362858i	$0.118199\pi$
$997$	24.6340	+	42.6673i	0.780166	+	1.35129i	−0.151678	+	0.988430i	$0.548468\pi$
$998$	0.401969	+	0.0900705i	0.0127241	+	0.00285113i
$999$	15.2578	+	9.98613i	0.482735	+	0.315947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.q.a.131.23	yes	48
3.2	odd	2		540.2.q.a.71.2		48
4.3	odd	2	inner	180.2.q.a.131.18	yes	48
5.2	odd	4		900.2.o.c.599.15		48
5.3	odd	4		900.2.o.b.599.10		48
5.4	even	2		900.2.r.f.851.2		48
9.2	odd	6	inner	180.2.q.a.11.18	✓	48
9.4	even	3		1620.2.e.b.971.22		48
9.5	odd	6		1620.2.e.b.971.27		48
9.7	even	3		540.2.q.a.251.7		48
12.11	even	2		540.2.q.a.71.7		48
20.3	even	4		900.2.o.b.599.7		48
20.7	even	4		900.2.o.c.599.18		48
20.19	odd	2		900.2.r.f.851.7		48
36.7	odd	6		540.2.q.a.251.2		48
36.11	even	6	inner	180.2.q.a.11.23	yes	48
36.23	even	6		1620.2.e.b.971.21		48
36.31	odd	6		1620.2.e.b.971.28		48
45.2	even	12		900.2.o.b.299.7		48
45.29	odd	6		900.2.r.f.551.7		48
45.38	even	12		900.2.o.c.299.18		48
180.47	odd	12		900.2.o.b.299.10		48
180.83	odd	12		900.2.o.c.299.15		48
180.119	even	6		900.2.r.f.551.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.q.a.11.18	✓	48	9.2	odd	6	inner
180.2.q.a.11.23	yes	48	36.11	even	6	inner
180.2.q.a.131.18	yes	48	4.3	odd	2	inner
180.2.q.a.131.23	yes	48	1.1	even	1	trivial
540.2.q.a.71.2		48	3.2	odd	2
540.2.q.a.71.7		48	12.11	even	2
540.2.q.a.251.2		48	36.7	odd	6
540.2.q.a.251.7		48	9.7	even	3
900.2.o.b.299.7		48	45.2	even	12
900.2.o.b.299.10		48	180.47	odd	12
900.2.o.b.599.7		48	20.3	even	4
900.2.o.b.599.10		48	5.3	odd	4
900.2.o.c.299.15		48	180.83	odd	12
900.2.o.c.299.18		48	45.38	even	12
900.2.o.c.599.15		48	5.2	odd	4
900.2.o.c.599.18		48	20.7	even	4
900.2.r.f.551.2		48	180.119	even	6
900.2.r.f.551.7		48	45.29	odd	6
900.2.r.f.851.2		48	5.4	even	2
900.2.r.f.851.7		48	20.19	odd	2
1620.2.e.b.971.21		48	36.23	even	6
1620.2.e.b.971.22		48	9.4	even	3
1620.2.e.b.971.27		48	9.5	odd	6
1620.2.e.b.971.28		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34972 - 0.422205i) q^{2} +(-0.561951 - 1.63836i) q^{3} +(1.64349 - 1.13972i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.45020 - 1.97406i) q^{6} +(-0.811773 + 0.468677i) q^{7} +(1.73705 - 2.23218i) q^{8} +(-2.36842 + 1.84135i) q^{9} +O(q^{10})\)	\(q+(1.34972 - 0.422205i) q^{2} +(-0.561951 - 1.63836i) q^{3} +(1.64349 - 1.13972i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.45020 - 1.97406i) q^{6} +(-0.811773 + 0.468677i) q^{7} +(1.73705 - 2.23218i) q^{8} +(-2.36842 + 1.84135i) q^{9} +(1.37999 + 0.309220i) q^{10} +(-0.291916 - 0.505614i) q^{11} +(-2.79082 - 2.05215i) q^{12} +(-0.579651 + 1.00399i) q^{13} +(-0.897788 + 0.975317i) q^{14} +(0.332514 - 1.69983i) q^{15} +(1.40209 - 3.74622i) q^{16} -0.238281i q^{17} +(-2.41928 + 3.48527i) q^{18} +7.00703i q^{19} +(1.99316 - 0.165280i) q^{20} +(1.22404 + 1.06660i) q^{21} +(-0.607478 - 0.559189i) q^{22} +(2.53353 - 4.38821i) q^{23} +(-4.63325 - 1.59153i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.358479 + 1.59983i) q^{26} +(4.34773 + 2.84557i) q^{27} +(-0.799978 + 1.69546i) q^{28} +(-7.91811 + 4.57152i) q^{29} +(-0.268878 - 2.43469i) q^{30} +(5.43436 + 3.13753i) q^{31} +(0.310764 - 5.64831i) q^{32} +(-0.664333 + 0.762394i) q^{33} +(-0.100603 - 0.321612i) q^{34} -0.937354 q^{35} +(-1.79385 + 5.72557i) q^{36} +3.50937 q^{37} +(2.95840 + 9.45752i) q^{38} +(1.97062 + 0.385484i) q^{39} +(2.62042 - 1.06460i) q^{40} +(2.86111 + 1.65186i) q^{41} +(2.10243 + 0.922815i) q^{42} +(-9.35224 + 5.39952i) q^{43} +(-1.05602 - 0.498268i) q^{44} +(-2.97179 + 0.410448i) q^{45} +(1.56684 - 6.99252i) q^{46} +(-4.27542 - 7.40525i) q^{47} +(-6.92554 - 0.191938i) q^{48} +(-3.06068 + 5.30126i) q^{49} +(1.04050 + 0.957789i) q^{50} +(-0.390388 + 0.133902i) q^{51} +(0.191609 + 2.31067i) q^{52} -11.9037i q^{53} +(7.06963 + 2.00508i) q^{54} -0.583833i q^{55} +(-0.363917 + 2.62614i) q^{56} +(11.4800 - 3.93761i) q^{57} +(-8.75710 + 9.51333i) q^{58} +(4.94604 - 8.56680i) q^{59} +(-1.39085 - 3.17262i) q^{60} +(-3.33295 - 5.77283i) q^{61} +(8.65955 + 1.94037i) q^{62} +(1.05962 - 2.60479i) q^{63} +(-1.96530 - 7.75484i) q^{64} +(-1.00399 + 0.579651i) q^{65} +(-0.574777 + 1.30950i) q^{66} +(-7.69738 - 4.44408i) q^{67} +(-0.271572 - 0.391611i) q^{68} +(-8.61317 - 1.68487i) q^{69} +(-1.26517 + 0.395755i) q^{70} -8.95946 q^{71} +(-0.00383002 + 8.48528i) q^{72} +11.7312 q^{73} +(4.73666 - 1.48167i) q^{74} +(1.13788 - 1.30584i) q^{75} +(7.98602 + 11.5160i) q^{76} +(0.473940 + 0.273629i) q^{77} +(2.82254 - 0.311710i) q^{78} +(-4.37420 + 2.52545i) q^{79} +(3.08736 - 2.54327i) q^{80} +(2.21884 - 8.72220i) q^{81} +(4.55912 + 1.02158i) q^{82} +(2.36468 + 4.09575i) q^{83} +(3.22731 + 0.357886i) q^{84} +(0.119140 - 0.206357i) q^{85} +(-10.3432 + 11.2364i) q^{86} +(11.9394 + 10.4037i) q^{87} +(-1.63570 - 0.226667i) q^{88} -2.36345i q^{89} +(-3.83779 + 1.80869i) q^{90} -1.08668i q^{91} +(-0.837485 - 10.0995i) q^{92} +(2.08654 - 10.6666i) q^{93} +(-8.89715 - 8.18990i) q^{94} +(-3.50351 + 6.06826i) q^{95} +(-9.42858 + 2.66493i) q^{96} +(-2.26656 - 3.92579i) q^{97} +(-1.89285 + 8.44745i) q^{98} +(1.62240 + 0.659986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 48 * q + 6 * q^6 + 4 * q^9	\( 48 q + 6 q^{6} + 4 q^{9} - 22 q^{12} - 30 q^{14} - 16 q^{18} - 4 q^{21} - 28 q^{24} + 24 q^{25} - 12 q^{29} + 16 q^{30} - 44 q^{33} - 6 q^{34} + 42 q^{36} + 60 q^{38} - 6 q^{40} - 60 q^{41} - 18 q^{42} - 8 q^{45} - 12 q^{46} - 12 q^{48} + 24 q^{49} - 18 q^{52} - 32 q^{54} - 42 q^{56} - 12 q^{57} - 18 q^{58} + 14 q^{60} - 48 q^{64} + 16 q^{66} + 48 q^{68} + 36 q^{69} + 60 q^{72} - 24 q^{73} + 84 q^{74} + 6 q^{76} + 48 q^{77} + 38 q^{78} - 36 q^{82} + 50 q^{84} - 54 q^{86} - 18 q^{90} + 60 q^{92} - 32 q^{93} + 18 q^{94} - 18 q^{96} - 12 q^{97}+O(q^{100}) \) 48 * q + 6 * q^6 + 4 * q^9 - 22 * q^12 - 30 * q^14 - 16 * q^18 - 4 * q^21 - 28 * q^24 + 24 * q^25 - 12 * q^29 + 16 * q^30 - 44 * q^33 - 6 * q^34 + 42 * q^36 + 60 * q^38 - 6 * q^40 - 60 * q^41 - 18 * q^42 - 8 * q^45 - 12 * q^46 - 12 * q^48 + 24 * q^49 - 18 * q^52 - 32 * q^54 - 42 * q^56 - 12 * q^57 - 18 * q^58 + 14 * q^60 - 48 * q^64 + 16 * q^66 + 48 * q^68 + 36 * q^69 + 60 * q^72 - 24 * q^73 + 84 * q^74 + 6 * q^76 + 48 * q^77 + 38 * q^78 - 36 * q^82 + 50 * q^84 - 54 * q^86 - 18 * q^90 + 60 * q^92 - 32 * q^93 + 18 * q^94 - 18 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more