LMFDB - Embedded newform 390.2.bl.a.263.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(107,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 4]))

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

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

chi := DirichletCharacter("390.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bl (of order $12$, degree $4$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			263.26
Character	$\chi$	$=$	390.263
Dual form			390.2.bl.a.347.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(1.49587 - 0.873148i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00792 + 0.984002i) q^{5} +(-0.456238 - 1.67088i) q^{6} +(1.14260 + 4.26423i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47523 - 2.61222i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(1.49587 - 0.873148i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00792 + 0.984002i) q^{5} +(-0.456238 - 1.67088i) q^{6} +(1.14260 + 4.26423i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47523 - 2.61222i) q^{9} +(1.47016 - 1.68482i) q^{10} +(-0.825330 + 0.476504i) q^{11} +(-1.73203 + 0.00823552i) q^{12} +(2.69900 - 2.39069i) q^{13} +4.41465 q^{14} +(3.86276 - 0.281275i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.33990 + 0.894923i) q^{17} +(-2.14140 - 2.10105i) q^{18} +(1.54728 + 0.893324i) q^{19} +(-1.24691 - 1.85613i) q^{20} +(5.43247 + 5.38106i) q^{21} +(0.246657 + 0.920535i) q^{22} +(-8.08195 - 2.16555i) q^{23} +(-0.440328 + 1.67515i) q^{24} +(3.06348 + 3.95159i) q^{25} +(-1.61068 - 3.22579i) q^{26} +(-0.0741174 - 5.19562i) q^{27} +(1.14260 - 4.26423i) q^{28} +(-4.88895 - 8.46790i) q^{29} +(0.728064 - 3.80394i) q^{30} -6.82211 q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.818523 + 1.43342i) q^{33} +3.45772i q^{34} +(-1.90177 + 9.68655i) q^{35} +(-2.58369 + 1.52464i) q^{36} +(-6.67357 - 1.78818i) q^{37} +(1.26335 - 1.26335i) q^{38} +(1.94991 - 5.93278i) q^{39} +(-2.11561 + 0.724018i) q^{40} +(2.64130 - 1.52496i) q^{41} +(6.60373 - 3.85465i) q^{42} +(9.09289 - 2.43643i) q^{43} +0.953008 q^{44} +(5.53257 - 3.79351i) q^{45} +(-4.18353 + 7.24608i) q^{46} +(3.36827 + 3.36827i) q^{47} +(1.50410 + 0.858883i) q^{48} +(-10.8159 + 6.24459i) q^{49} +(4.60983 - 1.93635i) q^{50} +(-4.21464 + 4.25491i) q^{51} +(-3.53275 + 0.720901i) q^{52} +(2.82578 - 2.82578i) q^{53} +(-5.03777 - 1.27313i) q^{54} +(-2.12608 + 0.144656i) q^{55} +(-3.82320 - 2.20733i) q^{56} +(3.09453 - 0.0147140i) q^{57} +(-9.44472 + 2.53070i) q^{58} +(-1.06950 + 1.85244i) q^{59} +(-3.48588 - 1.68779i) q^{60} +(-1.86312 + 3.22701i) q^{61} +(-1.76569 + 6.58965i) q^{62} +(12.8247 + 3.30598i) q^{63} -1.00000i q^{64} +(7.77182 - 2.14450i) q^{65} +(1.17273 + 1.16163i) q^{66} +(13.5079 + 3.61943i) q^{67} +(3.33990 + 0.894923i) q^{68} +(-13.9804 + 3.81736i) q^{69} +(8.86427 + 4.34403i) q^{70} +(-4.99166 - 2.88194i) q^{71} +(0.803978 + 2.89026i) q^{72} +(-3.85570 - 3.85570i) q^{73} +(-3.45450 + 5.98336i) q^{74} +(8.03288 + 3.23618i) q^{75} +(-0.893324 - 1.54728i) q^{76} +(-2.97494 - 2.97494i) q^{77} +(-5.22595 - 3.41898i) q^{78} +5.02131i q^{79} +(0.151789 + 2.23091i) q^{80} +(-4.64742 - 7.70724i) q^{81} +(-0.789375 - 2.94599i) q^{82} +(0.528913 - 0.528913i) q^{83} +(-2.01413 - 7.37637i) q^{84} +(-7.58685 - 1.48953i) q^{85} -9.41365i q^{86} +(-14.7069 - 8.39807i) q^{87} +(0.246657 - 0.920535i) q^{88} +(1.40316 + 2.43034i) q^{89} +(-2.23231 - 6.32588i) q^{90} +(13.2783 + 8.77755i) q^{91} +(5.91640 + 5.91640i) q^{92} +(-10.2050 + 5.95671i) q^{93} +(4.12528 - 2.38173i) q^{94} +(2.22779 + 3.31625i) q^{95} +(1.21891 - 1.23055i) q^{96} +(1.91208 + 7.13599i) q^{97} +(3.23244 + 12.0636i) q^{98} +(0.0271878 + 2.85890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) $ 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	1.49587	−	0.873148i	0.863638	−	0.504112i
$3$	1.49587	−	0.873148i	0.863638	−	0.504112i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.00792	+	0.984002i	0.897969	+	0.440059i
$5$	2.00792	+	0.984002i	0.897969	+	0.440059i
$6$	−0.456238	−	1.67088i	−0.186258	−	0.682135i
$7$	1.14260	+	4.26423i	0.431861	+	1.61173i	0.748468	+	0.663170i	$0.230790\pi$
$7$	1.14260	+	4.26423i	0.431861	+	1.61173i	−0.316607	+	0.948557i	$0.602544\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.47523	−	2.61222i	0.491742	−	0.870741i
$10$	1.47016	−	1.68482i	0.464906	−	0.532788i
$11$	−0.825330	+	0.476504i	−0.248846	+	0.143671i	−0.619236	−	0.785205i	$-0.712558\pi$
$11$	−0.825330	+	0.476504i	−0.248846	+	0.143671i	0.370390	+	0.928876i	$0.379224\pi$
$12$	−1.73203	+	0.00823552i	−0.499994	+	0.00237739i
$13$	2.69900	−	2.39069i	0.748567	−	0.663059i
$13$	2.69900	−	2.39069i	0.748567	−	0.663059i
$14$	4.41465			1.17987
$15$	3.86276	−	0.281275i	0.997359	−	0.0726249i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.33990	+	0.894923i	−0.810044	+	0.217051i	−0.639989	−	0.768384i	$-0.721061\pi$
$17$	−3.33990	+	0.894923i	−0.810044	+	0.217051i	−0.170055	+	0.985435i	$0.554394\pi$
$18$	−2.14140	−	2.10105i	−0.504732	−	0.495223i
$19$	1.54728	+	0.893324i	0.354971	+	0.204943i	0.666873	−	0.745172i	$-0.267633\pi$
$19$	1.54728	+	0.893324i	0.354971	+	0.204943i	−0.311901	+	0.950114i	$0.600966\pi$
$20$	−1.24691	−	1.85613i	−0.278817	−	0.415043i
$21$	5.43247	+	5.38106i	1.18546	+	1.17424i
$22$	0.246657	+	0.920535i	0.0525874	+	0.196259i
$23$	−8.08195	−	2.16555i	−1.68520	−	0.451549i	−0.716058	−	0.698040i	$-0.754056\pi$
$23$	−8.08195	−	2.16555i	−1.68520	−	0.451549i	−0.969145	+	0.246491i	$0.920722\pi$
$24$	−0.440328	+	1.67515i	−0.0898815	+	0.341938i
$25$	3.06348	+	3.95159i	0.612696	+	0.790319i
$26$	−1.61068	−	3.22579i	−0.315880	−	0.632629i
$27$	−0.0741174	−	5.19562i	−0.0142639	−	0.999898i
$28$	1.14260	−	4.26423i	0.215930	−	0.805864i
$29$	−4.88895	−	8.46790i	−0.907855	−	1.57245i	−0.817039	−	0.576583i	$-0.804386\pi$
$29$	−4.88895	−	8.46790i	−0.907855	−	1.57245i	−0.0908157	−	0.995868i	$-0.528947\pi$
$30$	0.728064	−	3.80394i	0.132926	−	0.694500i
$31$	−6.82211			−1.22529			−0.612644	−	0.790359i	$-0.709894\pi$
$31$	−6.82211			−1.22529			−0.612644	+	0.790359i	$0.709894\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	−0.818523	+	1.43342i	−0.142487	+	0.249527i
$34$			3.45772i			0.592993i
$35$	−1.90177	+	9.68655i	−0.321458	+	1.63733i
$36$	−2.58369	+	1.52464i	−0.430616	+	0.254106i
$37$	−6.67357	−	1.78818i	−1.09713	−	0.293975i	−0.335534	−	0.942028i	$-0.608917\pi$
$37$	−6.67357	−	1.78818i	−1.09713	−	0.293975i	−0.761595	+	0.648053i	$0.775583\pi$
$38$	1.26335	−	1.26335i	0.204943	−	0.204943i
$39$	1.94991	−	5.93278i	0.312235	−	0.950005i
$40$	−2.11561	+	0.724018i	−0.334507	+	0.114477i
$41$	2.64130	−	1.52496i	0.412502	−	0.238158i	−0.279362	−	0.960186i	$-0.590123\pi$
$41$	2.64130	−	1.52496i	0.412502	−	0.238158i	0.691864	+	0.722028i	$0.256790\pi$
$42$	6.60373	−	3.85465i	1.01898	−	0.594785i
$43$	9.09289	−	2.43643i	1.38665	−	0.371552i	0.513120	−	0.858317i	$-0.328490\pi$
$43$	9.09289	−	2.43643i	1.38665	−	0.371552i	0.873533	+	0.486765i	$0.161823\pi$
$44$	0.953008			0.143671
$45$	5.53257	−	3.79351i	0.824747	−	0.565503i
$46$	−4.18353	+	7.24608i	−0.616827	+	1.06838i
$47$	3.36827	+	3.36827i	0.491313	+	0.491313i	0.908720	−	0.417407i	$-0.137061\pi$
$47$	3.36827	+	3.36827i	0.491313	+	0.491313i	−0.417407	+	0.908720i	$0.637061\pi$
$48$	1.50410	+	0.858883i	0.217098	+	0.123969i
$49$	−10.8159	+	6.24459i	−1.54514	+	0.892084i
$50$	4.60983	−	1.93635i	0.651929	−	0.273841i
$51$	−4.21464	+	4.25491i	−0.590167	+	0.595806i
$52$	−3.53275	+	0.720901i	−0.489904	+	0.0999710i
$53$	2.82578	−	2.82578i	0.388151	−	0.388151i	−0.485877	−	0.874027i	$-0.661500\pi$
$53$	2.82578	−	2.82578i	0.388151	−	0.388151i	0.874027	+	0.485877i	$0.161500\pi$
$54$	−5.03777	−	1.27313i	−0.685554	−	0.173252i
$55$	−2.12608	+	0.144656i	−0.286680	+	0.0195054i
$56$	−3.82320	−	2.20733i	−0.510897	−	0.294967i
$57$	3.09453	−	0.0147140i	0.409881	−	0.00194891i
$58$	−9.44472	+	2.53070i	−1.24015	+	0.332298i
$59$	−1.06950	+	1.85244i	−0.139238	+	0.241167i	−0.927208	−	0.374546i	$-0.877799\pi$
$59$	−1.06950	+	1.85244i	−0.139238	+	0.241167i	0.787971	+	0.615713i	$0.211132\pi$
$60$	−3.48588	−	1.68779i	−0.450025	−	0.217892i
$61$	−1.86312	+	3.22701i	−0.238548	+	0.413177i	−0.960298	−	0.278977i	$-0.910005\pi$
$61$	−1.86312	+	3.22701i	−0.238548	+	0.413177i	0.721750	+	0.692154i	$0.243338\pi$
$62$	−1.76569	+	6.58965i	−0.224243	+	0.836887i
$63$	12.8247	+	3.30598i	1.61576	+	0.416515i
$64$		−	1.00000i		−	0.125000i
$65$	7.77182	−	2.14450i	0.963975	−	0.265992i
$66$	1.17273	+	1.16163i	0.144353	+	0.142987i
$67$	13.5079	+	3.61943i	1.65025	+	0.442183i	0.959683	−	0.281085i	$-0.0906941\pi$
$67$	13.5079	+	3.61943i	1.65025	+	0.442183i	0.690568	+	0.723268i	$0.257361\pi$
$68$	3.33990	+	0.894923i	0.405022	+	0.108525i
$69$	−13.9804	+	3.81736i	−1.68304	+	0.459557i
$70$	8.86427	+	4.34403i	1.05948	+	0.519211i
$71$	−4.99166	−	2.88194i	−0.592401	−	0.342023i	0.173645	−	0.984808i	$-0.444445\pi$
$71$	−4.99166	−	2.88194i	−0.592401	−	0.342023i	−0.766046	+	0.642785i	$0.777779\pi$
$72$	0.803978	+	2.89026i	0.0947498	+	0.340621i
$73$	−3.85570	−	3.85570i	−0.451276	−	0.451276i	0.444502	−	0.895778i	$-0.353381\pi$
$73$	−3.85570	−	3.85570i	−0.451276	−	0.451276i	−0.895778	+	0.444502i	$0.853381\pi$
$74$	−3.45450	+	5.98336i	−0.401577	+	0.695552i
$75$	8.03288	+	3.23618i	0.927557	+	0.373682i
$76$	−0.893324	−	1.54728i	−0.102471	−	0.177486i
$77$	−2.97494	−	2.97494i	−0.339026	−	0.339026i
$78$	−5.22595	−	3.41898i	−0.591722	−	0.387124i
$79$			5.02131i			0.564942i	0.959276	+	0.282471i	$0.0911540\pi$
$79$			5.02131i			0.564942i	−0.959276	+	0.282471i	$0.908846\pi$
$80$	0.151789	+	2.23091i	0.0169705	+	0.249423i
$81$	−4.64742	−	7.70724i	−0.516380	−	0.856360i
$82$	−0.789375	−	2.94599i	−0.0871719	−	0.325330i
$83$	0.528913	−	0.528913i	0.0580558	−	0.0580558i	−0.677483	−	0.735539i	$-0.736929\pi$
$83$	0.528913	−	0.528913i	0.0580558	−	0.0580558i	0.735539	+	0.677483i	$0.236929\pi$
$84$	−2.01413	−	7.37637i	−0.219760	−	0.804828i
$85$	−7.58685	−	1.48953i	−0.822909	−	0.161563i
$86$		−	9.41365i		−	1.01510i
$87$	−14.7069	−	8.39807i	−1.57675	−	0.900368i
$88$	0.246657	−	0.920535i	0.0262937	−	0.0981294i
$89$	1.40316	+	2.43034i	0.148734	+	0.257615i	0.930760	−	0.365631i	$-0.119147\pi$
$89$	1.40316	+	2.43034i	0.148734	+	0.257615i	−0.782026	+	0.623246i	$0.785813\pi$
$90$	−2.23231	−	6.32588i	−0.235306	−	0.666807i
$91$	13.2783	+	8.77755i	1.39195	+	0.920137i
$92$	5.91640	+	5.91640i	0.616827	+	0.616827i
$93$	−10.2050	+	5.95671i	−1.05820	+	0.617682i
$94$	4.12528	−	2.38173i	0.425490	−	0.245657i
$95$	2.22779	+	3.31625i	0.228566	+	0.340240i
$96$	1.21891	−	1.23055i	0.124404	−	0.125593i
$97$	1.91208	+	7.13599i	0.194143	+	0.724550i	0.992487	+	0.122349i	$0.0390427\pi$
$97$	1.91208	+	7.13599i	0.194143	+	0.724550i	−0.798345	+	0.602201i	$0.794291\pi$
$98$	3.23244	+	12.0636i	0.326525	+	1.21861i
$99$	0.0271878	+	2.85890i	0.00273247	+	0.287330i
$100$	−0.677253	−	4.95392i	−0.0677253	−	0.495392i
$101$	1.66880	−	0.963481i	0.166052	−	0.0958700i	−0.414671	−	0.909971i	$-0.636103\pi$
$101$	1.66880	−	0.963481i	0.166052	−	0.0958700i	0.580723	+	0.814101i	$0.302770\pi$
$102$	3.01910	+	5.17228i	0.298935	+	0.512132i
$103$	4.91538	+	4.91538i	0.484327	+	0.484327i	0.906510	−	0.422184i	$-0.138736\pi$
$103$	4.91538	+	4.91538i	0.484327	+	0.484327i	−0.422184	+	0.906510i	$0.638736\pi$
$104$	−0.218005	+	3.59895i	−0.0213772	+	0.352907i
$105$	5.61299	+	16.1503i	0.547772	+	1.57611i
$106$	−1.99813	−	3.46086i	−0.194075	−	0.336148i
$107$	−0.751993	+	2.80647i	−0.0726979	+	0.271312i	−0.992701	−	0.120598i	$-0.961519\pi$
$107$	−0.751993	+	2.80647i	−0.0726979	+	0.271312i	0.920004	+	0.391910i	$0.128186\pi$
$108$	−2.53362	+	4.53660i	−0.243798	+	0.436535i
$109$		−	9.66610i		−	0.925844i	−0.886399	−	0.462922i	$-0.846801\pi$
$109$		−	9.66610i		−	0.925844i	0.886399	−	0.462922i	$-0.153199\pi$
$110$	−0.410542	+	2.09107i	−0.0391437	+	0.199376i
$111$	−11.5441	+	3.15214i	−1.09572	+	0.299188i
$112$	−3.12163	+	3.12163i	−0.294967	+	0.294967i
$113$	1.02785	+	3.83597i	0.0966916	+	0.360858i	0.997271	−	0.0738345i	$-0.0235237\pi$
$113$	1.02785	+	3.83597i	0.0966916	+	0.360858i	−0.900579	+	0.434693i	$0.856857\pi$
$114$	0.786711	−	2.99290i	0.0736822	−	0.280310i
$115$	−14.0970	−	12.3009i	−1.31455	−	1.14707i
$116$			9.77789i			0.907855i
$117$	−2.26339	−	10.5772i	−0.209250	−	0.977862i
$118$	1.51251	+	1.51251i	0.139238	+	0.139238i
$119$	−7.63231	−	13.2195i	−0.699653	−	1.21183i
$120$	−2.53249	+	2.93027i	−0.231184	+	0.267496i
$121$	−5.04589	+	8.73973i	−0.458717	+	0.794521i
$122$	2.63485	+	2.63485i	0.238548	+	0.238548i
$123$	2.61952	−	4.58737i	0.236194	−	0.413630i
$124$	5.90812	+	3.41105i	0.530565	+	0.306322i
$125$	2.26284	+	10.9490i	0.202394	+	0.979304i
$126$	6.51261	−	11.5321i	0.580190	−	1.02736i
$127$	7.36020	+	1.97216i	0.653112	+	0.175001i	0.570135	−	0.821551i	$-0.306891\pi$
$127$	7.36020	+	1.97216i	0.653112	+	0.175001i	0.0829765	+	0.996552i	$0.473557\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	11.4744	−	11.5840i	1.01026	−	1.01992i
$130$	−0.0599299	−	8.06204i	−0.00525620	−	0.707087i
$131$			22.1031i			1.93115i	0.260117	+	0.965577i	$0.416239\pi$
$131$			22.1031i			1.93115i	−0.260117	+	0.965577i	$0.583761\pi$
$132$	1.42557	−	0.832117i	0.124080	−	0.0724265i
$133$	−2.04142	+	7.61868i	−0.177013	+	0.660623i
$134$	6.99220	−	12.1108i	0.604034	−	1.04622i
$135$	4.96368	−	10.5053i	0.427206	−	0.904154i
$136$	1.72886	−	2.99447i	0.148248	−	0.256774i
$137$	2.36675	−	0.634169i	0.202205	−	0.0541808i	−0.156295	−	0.987710i	$-0.549955\pi$
$137$	2.36675	−	0.634169i	0.202205	−	0.0541808i	0.358500	+	0.933530i	$0.383288\pi$
$138$	0.0689070	+	14.4920i	0.00586575	+	1.23364i
$139$	−12.4638	−	7.19598i	−1.05717	−	0.610355i	−0.132519	−	0.991180i	$-0.542307\pi$
$139$	−12.4638	−	7.19598i	−1.05717	−	0.610355i	−0.924647	+	0.380826i	$0.875640\pi$
$140$	6.49025	−	7.43791i	0.548527	−	0.628618i
$141$	7.97949	+	2.09748i	0.671994	+	0.176640i
$142$	−4.07567	+	4.07567i	−0.342023	+	0.342023i
$143$	−1.08839	+	3.25919i	−0.0910156	+	0.272547i
$144$	2.99986	−	0.0285284i	0.249989	−	0.00237736i
$145$	−1.48417	−	21.8136i	−0.123254	−	1.81152i
$146$	−4.72225	+	2.72639i	−0.390817	+	0.225638i
$147$	−10.7267	+	18.7850i	−0.884727	+	1.54936i
$148$	4.88539	+	4.88539i	0.401577	+	0.401577i
$149$	2.42714	−	4.20393i	0.198839	−	0.344399i	−0.749313	−	0.662216i	$-0.769616\pi$
$149$	2.42714	−	4.20393i	0.198839	−	0.344399i	0.948152	+	0.317816i	$0.102950\pi$
$150$	5.20497	−	6.92158i	0.424984	−	0.565144i
$151$	−16.2684			−1.32390			−0.661951	−	0.749547i	$-0.730271\pi$
$151$	−16.2684			−1.32390			−0.661951	+	0.749547i	$0.730271\pi$
$152$	−1.72577	+	0.462419i	−0.139978	+	0.0375071i
$153$	−2.58936	+	10.0448i	−0.209338	+	0.812071i
$154$	−3.64355	+	2.10360i	−0.293605	+	0.169513i
$155$	−13.6982	−	6.71297i	−1.10027	−	0.539199i
$156$	−4.65506	+	4.16298i	−0.372703	+	0.333305i
$157$	1.88409	−	1.88409i	0.150367	−	0.150367i	−0.627915	−	0.778282i	$-0.716091\pi$
$157$	1.88409	−	1.88409i	0.150367	−	0.150367i	0.778282	+	0.627915i	$0.216091\pi$
$158$	4.85021	+	1.29961i	0.385862	+	0.103391i
$159$	1.75966	−	6.69431i	0.139550	−	0.530893i
$160$	2.19418	+	0.430786i	0.173465	+	0.0340566i
$161$		−	36.9376i		−	2.91109i
$162$	−8.64746	+	2.49428i	−0.679409	+	0.195969i
$163$	15.2773	−	4.09354i	1.19661	−	0.320631i	0.395115	−	0.918631i	$-0.370705\pi$
$163$	15.2773	−	4.09354i	1.19661	−	0.320631i	0.801496	+	0.598001i	$0.204038\pi$
$164$	−3.04991			−0.238158
$165$	−3.05402	+	2.07276i	−0.237755	+	0.161364i
$166$	−0.373998	−	0.647784i	−0.0290279	−	0.0502778i
$167$	−3.04474	+	11.3631i	−0.235609	+	0.879305i	0.742264	+	0.670107i	$0.233752\pi$
$167$	−3.04474	+	11.3631i	−0.235609	+	0.879305i	−0.977873	+	0.209197i	$0.932915\pi$
$168$	−7.64632	+	0.0363570i	−0.589926	+	0.00280500i
$169$	1.56918	−	12.9049i	0.120706	−	0.992688i
$170$	−3.40240	+	6.94281i	−0.260952	+	0.532489i
$171$	4.61615	−	2.72399i	0.353006	−	0.208309i
$172$	−9.09289	−	2.43643i	−0.693326	−	0.185776i
$173$	−1.05005	−	3.91883i	−0.0798337	−	0.297943i	0.914452	−	0.404694i	$-0.132622\pi$
$173$	−1.05005	−	3.91883i	−0.0798337	−	0.297943i	−0.994286	+	0.106751i	$0.965955\pi$
$174$	−11.9183	+	12.0322i	−0.903528	+	0.912161i
$175$	−13.3502	+	17.5785i	−1.00918	+	1.32881i
$176$	−0.825330	−	0.476504i	−0.0622116	−	0.0359179i
$177$	0.0176158	+	3.70483i	0.00132409	+	0.278472i
$178$	2.71069	−	0.726327i	0.203175	−	0.0544405i
$179$	5.38795	+	9.33221i	0.402715	+	0.697522i	0.994053	−	0.108902i	$-0.0347334\pi$
$179$	5.38795	+	9.33221i	0.402715	+	0.697522i	−0.591338	+	0.806424i	$0.701400\pi$
$180$	−6.68810	+	0.518989i	−0.498501	+	0.0386832i
$181$	6.27828			0.466661			0.233330	−	0.972398i	$-0.425038\pi$
$181$	6.27828			0.466661			0.233330	+	0.972398i	$0.425038\pi$
$182$	11.9151	−	10.5541i	0.883209	−	0.782321i
$183$	0.0306875	+	6.45396i	0.00226848	+	0.477090i
$184$	7.24608	−	4.18353i	0.534188	−	0.308414i
$185$	−11.6404	−	10.1573i	−0.855821	−	0.746782i
$186$	3.11250	+	11.3989i	0.228220	+	0.835811i
$187$	2.33008	−	2.33008i	0.170392	−	0.170392i
$188$	−1.23287	−	4.60115i	−0.0899166	−	0.335573i
$189$	22.0706	−	6.25256i	1.60540	−	0.454807i
$190$	3.77985	−	1.29357i	0.274219	−	0.0938452i
$191$	−7.59842	−	4.38695i	−0.549802	−	0.317429i	0.199240	−	0.979951i	$-0.436153\pi$
$191$	−7.59842	−	4.38695i	−0.549802	−	0.317429i	−0.749042	+	0.662522i	$0.769486\pi$
$192$	−0.873148	−	1.49587i	−0.0630140	−	0.107955i
$193$	2.08054	−	7.76467i	0.149760	−	0.558913i	−0.849737	−	0.527207i	$-0.823239\pi$
$193$	2.08054	−	7.76467i	0.149760	−	0.558913i	0.999497	−	0.0317062i	$-0.0100941\pi$
$194$	7.38772			0.530407
$195$	9.75313	−	9.99382i	0.698436	−	0.715672i
$196$	12.4892			0.892084
$197$	5.11654	−	19.0952i	0.364538	−	1.36048i	−0.503507	−	0.863991i	$-0.667957\pi$
$197$	5.11654	−	19.0952i	0.364538	−	1.36048i	0.868045	−	0.496485i	$-0.165376\pi$
$198$	2.76852	+	0.713675i	0.196750	+	0.0507187i
$199$	13.2265	+	7.63633i	0.937603	+	0.541325i	0.889208	−	0.457503i	$-0.151256\pi$
$199$	13.2265	+	7.63633i	0.937603	+	0.541325i	0.0483946	+	0.998828i	$0.484589\pi$
$200$	−4.96041	−	0.627993i	−0.350754	−	0.0444058i
$201$	23.3663	−	6.38020i	1.64813	−	0.450025i
$202$	−0.498735	−	1.86130i	−0.0350908	−	0.130961i
$203$	30.5230	−	30.5230i	2.14229	−	2.14229i
$204$	5.77744	−	1.57754i	0.404501	−	0.110450i
$205$	6.80408	−	0.462941i	0.475217	−	0.0323332i
$206$	6.02008	−	3.47570i	0.419439	−	0.242163i
$207$	−17.5796	+	17.9172i	−1.22187	+	1.24533i
$208$	3.41990	+	1.14205i	0.237127	+	0.0791873i
$209$	−1.70269			−0.117778
$210$	17.0527	−	1.24173i	1.17675	−	0.0856877i
$211$	−3.09256	−	5.35648i	−0.212901	−	0.368755i	0.739720	−	0.672915i	$-0.234958\pi$
$211$	−3.09256	−	5.35648i	−0.212901	−	0.368755i	−0.952621	+	0.304159i	$0.901624\pi$
$212$	−3.86009	+	1.03431i	−0.265112	+	0.0710365i
$213$	−9.98320	+	0.0474685i	−0.684038	+	0.00325249i
$214$	2.51622	+	1.45274i	0.172005	+	0.0993071i
$215$	20.6552	+	4.05527i	1.40868	+	0.276567i
$216$	3.72627	+	3.62145i	0.253541	+	0.246409i
$217$	−7.79492	−	29.0910i	−0.529154	−	1.97483i
$218$	−9.33673	−	2.50177i	−0.632363	−	0.169441i
$219$	−9.13422	−	2.40101i	−0.617233	−	0.162246i
$220$	1.91356	+	0.937763i	0.129012	+	0.0632239i
$221$	−6.87489	+	10.4001i	−0.462455	+	0.699584i
$222$	0.0568991	+	11.9666i	0.00381882	+	0.803145i
$223$	−0.972948	+	3.63109i	−0.0651534	+	0.243156i	−0.990821	−	0.135183i	$-0.956838\pi$
$223$	−0.972948	+	3.63109i	−0.0651534	+	0.243156i	0.925667	+	0.378339i	$0.123505\pi$
$224$	2.20733	+	3.82320i	0.147483	+	0.255449i
$225$	14.8418	−	2.17299i	0.989451	−	0.144866i
$226$	3.97129			0.264166
$227$	8.67677	−	2.32493i	0.575898	−	0.154311i	0.0408976	−	0.999163i	$-0.486978\pi$
$227$	8.67677	−	2.32493i	0.575898	−	0.154311i	0.535000	+	0.844852i	$0.320312\pi$
$228$	−2.68730	−	1.53452i	−0.177971	−	0.101626i
$229$			15.7837i			1.04302i	0.853245	+	0.521510i	$0.174631\pi$
$229$			15.7837i			1.04302i	−0.853245	+	0.521510i	$0.825369\pi$
$230$	−15.5303	+	10.4329i	−1.02404	+	0.687928i
$231$	−7.04768	−	1.85255i	−0.463703	−	0.121889i
$232$	9.44472	+	2.53070i	0.620076	+	0.166149i
$233$	8.90583	−	8.90583i	0.583440	−	0.583440i	−0.352407	−	0.935847i	$-0.614637\pi$
$233$	8.90583	−	8.90583i	0.583440	−	0.583440i	0.935847	+	0.352407i	$0.114637\pi$
$234$	−10.8026	−	0.551314i	−0.706188	−	0.0360405i
$235$	3.44883	+	10.0776i	0.224977	+	0.657391i
$236$	1.85244	−	1.06950i	0.120583	−	0.0696188i
$237$	4.38435	+	7.51120i	0.284794	+	0.487905i
$238$	−14.7445	+	3.95077i	−0.955743	+	0.256091i
$239$	−13.0202			−0.842209			−0.421104	−	0.907012i	$-0.638357\pi$
$239$	−13.0202			−0.842209			−0.421104	+	0.907012i	$0.638357\pi$
$240$	2.17497	+	3.20461i	0.140394	+	0.206857i
$241$	1.64758	−	2.85369i	0.106130	−	0.183822i	−0.808069	−	0.589087i	$-0.799487\pi$
$241$	1.64758	−	2.85369i	0.106130	−	0.183822i	0.914199	+	0.405265i	$0.132821\pi$
$242$	7.13596	+	7.13596i	0.458717	+	0.458717i
$243$	−13.6815	−	7.47111i	−0.877667	−	0.479272i
$244$	3.22701	−	1.86312i	0.206588	−	0.119274i
$245$	−27.8622	+	1.89571i	−1.78005	+	0.121113i
$246$	−3.75308	−	3.71756i	−0.239288	−	0.237023i
$247$	6.31178	−	1.28800i	0.401609	−	0.0819533i
$248$	4.82396	−	4.82396i	0.306322	−	0.306322i
$249$	0.329363	−	1.25300i	0.0208726	−	0.0794058i
$250$	11.1615	+	0.648063i	0.705918	+	0.0409871i
$251$	−13.0422	−	7.52991i	−0.823216	−	0.475284i	0.0283083	−	0.999599i	$-0.490988\pi$
$251$	−13.0422	−	7.52991i	−0.823216	−	0.475284i	−0.851524	+	0.524315i	$0.824321\pi$
$252$	−9.45353	−	9.27542i	−0.595516	−	0.584296i
$253$	7.70217	−	2.06379i	0.484231	−	0.129749i
$254$	3.80992	−	6.59897i	0.239056	−	0.414056i
$255$	−12.6495	+	4.39630i	−0.792142	+	0.275307i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.15454	+	8.04084i	−0.134396	+	0.501574i	0.865603	+	0.500730i	$0.166935\pi$
$257$	−2.15454	+	8.04084i	−0.134396	+	0.501574i	−1.00000		0.000843410i	$0.999732\pi$
$258$	−8.21951	−	14.0816i	−0.511724	−	0.876679i
$259$		−	30.5008i		−	1.89523i
$260$	−7.80284	−	2.02872i	−0.483912	−	0.125816i
$261$	−29.3324	+	0.278947i	−1.81563	+	0.0172664i
$262$	21.3499	+	5.72070i	1.31900	+	0.353426i
$263$	0.135419	+	0.0362854i	0.00835028	+	0.00223745i	0.262992	−	0.964798i	$-0.415291\pi$
$263$	0.135419	+	0.0362854i	0.00835028	+	0.00223745i	−0.254641	+	0.967036i	$0.581957\pi$
$264$	−0.434798	−	1.59236i	−0.0267600	−	0.0980033i
$265$	8.45451	−	2.89336i	0.519356	−	0.177738i
$266$	6.83072	+	3.94372i	0.418818	+	0.241805i
$267$	4.22098	+	2.41029i	0.258319	+	0.147508i
$268$	−9.88846	−	9.88846i	−0.604034	−	0.604034i
$269$	−3.92128	+	6.79185i	−0.239085	+	0.414107i	−0.960452	−	0.278446i	$-0.910181\pi$
$269$	−3.92128	+	6.79185i	−0.239085	+	0.414107i	0.721367	+	0.692553i	$0.243514\pi$
$270$	−8.86267	−	7.51353i	−0.539365	−	0.457259i
$271$	0.513464	+	0.889345i	0.0311907	+	0.0540239i	0.881199	−	0.472745i	$-0.156737\pi$
$271$	0.513464	+	0.889345i	0.0311907	+	0.0540239i	−0.850009	+	0.526769i	$0.823403\pi$
$272$	−2.44497	−	2.44497i	−0.148248	−	0.148248i
$273$	27.5267	+	1.53609i	1.66599	+	0.0929684i
$274$		−	2.45024i		−	0.148025i
$275$	−4.41133	−	1.80161i	−0.266013	−	0.108641i
$276$	14.0160	+	3.68425i	0.843666	+	0.221766i
$277$	−8.04688	−	30.0314i	−0.483490	−	1.80441i	−0.586765	−	0.809757i	$-0.699599\pi$
$277$	−8.04688	−	30.0314i	−0.483490	−	1.80441i	0.103275	−	0.994653i	$-0.467068\pi$
$278$	−10.1767	+	10.1767i	−0.610355	+	0.610355i
$279$	−10.0642	+	17.8209i	−0.602525	+	1.06691i
$280$	−5.50467	−	8.19418i	−0.328967	−	0.489696i
$281$			12.8591i			0.767112i	0.923518	+	0.383556i	$0.125301\pi$
$281$			12.8591i			0.767112i	−0.923518	+	0.383556i	$0.874699\pi$
$282$	4.09126	−	7.16472i	0.243631	−	0.426653i
$283$	−3.85039	+	14.3699i	−0.228882	+	0.854199i	0.751930	+	0.659243i	$0.229123\pi$
$283$	−3.85039	+	14.3699i	−0.228882	+	0.854199i	−0.980812	+	0.194956i	$0.937544\pi$
$284$	2.88194	+	4.99166i	0.171011	+	0.296200i
$285$	6.22805	+	3.01548i	0.368918	+	0.178622i
$286$	2.86644	+	1.89484i	0.169496	+	0.112044i
$287$	9.52070	+	9.52070i	0.561989	+	0.561989i
$288$	0.748866	−	2.90503i	0.0441273	−	0.171181i
$289$	−4.36841	+	2.52210i	−0.256965	+	0.148359i
$290$	−21.4545	−	4.21218i	−1.25985	−	0.247347i
$291$	9.09099	+	9.00495i	0.532923	+	0.527879i
$292$	1.41129	+	5.26699i	0.0825893	+	0.308227i
$293$	−2.80896	−	10.4832i	−0.164101	−	0.612434i	−0.998153	−	0.0607479i	$-0.980651\pi$
$293$	−2.80896	−	10.4832i	−0.164101	−	0.612434i	0.834052	−	0.551686i	$-0.186015\pi$
$294$	15.3686	+	15.2232i	0.896316	+	0.887832i
$295$	−3.97028	+	2.66715i	−0.231159	+	0.155287i
$296$	5.98336	−	3.45450i	0.347776	−	0.200788i
$297$	2.53691	+	4.25278i	0.147206	+	0.246772i
$298$	−3.43250	−	3.43250i	−0.198839	−	0.198839i
$299$	−26.9903	+	13.4766i	−1.56089	+	0.779374i
$300$	−5.33858	−	6.81906i	−0.308223	−	0.393698i
$301$	20.7790	+	35.9903i	1.19768	+	2.07445i
$302$	−4.21057	+	15.7141i	−0.242291	+	0.904242i
$303$	1.65504	−	2.89835i	0.0950793	−	0.166506i
$304$			1.78665i			0.102471i
$305$	−6.91638	+	4.64627i	−0.396031	+	0.266045i
$306$	9.03232	+	5.10091i	0.516344	+	0.291600i
$307$	−2.77335	+	2.77335i	−0.158283	+	0.158283i	−0.781806	−	0.623522i	$-0.785701\pi$
$307$	−2.77335	+	2.77335i	−0.158283	+	0.158283i	0.623522	+	0.781806i	$0.285701\pi$
$308$	1.08890	+	4.06385i	0.0620461	+	0.231559i
$309$	11.6446	+	3.06089i	0.662438	+	0.174128i
$310$	−10.0296	+	11.4940i	−0.569643	+	0.652818i
$311$		−	3.21754i		−	0.182450i	−0.995830	−	0.0912249i	$-0.970922\pi$
$311$		−	3.21754i		−	0.182450i	0.995830	−	0.0912249i	$-0.0290782\pi$
$312$	2.81631	+	5.57390i	0.159442	+	0.315560i
$313$	−9.33105	−	9.33105i	−0.527422	−	0.527422i	0.392381	−	0.919803i	$-0.371652\pi$
$313$	−9.33105	−	9.33105i	−0.527422	−	0.527422i	−0.919803	+	0.392381i	$0.871652\pi$
$314$	−1.33226	−	2.30753i	−0.0751835	−	0.130222i
$315$	22.4979	+	19.2577i	1.26761	+	1.08505i
$316$	2.51066	−	4.34858i	0.141235	−	0.244627i
$317$	22.4314	+	22.4314i	1.25987	+	1.25987i	0.951153	+	0.308721i	$0.0999010\pi$
$317$	22.4314	+	22.4314i	1.25987	+	1.25987i	0.308721	+	0.951153i	$0.400099\pi$
$318$	−6.01077	−	3.43232i	−0.337067	−	0.192475i
$319$	8.06998	+	4.65921i	0.451832	+	0.260866i
$320$	0.984002	−	2.00792i	0.0550074	−	0.112246i
$321$	1.32559	+	4.85471i	0.0739871	+	0.270963i
$322$	−35.6790	−	9.56017i	−1.98831	−	0.532767i
$323$	−5.96722	−	1.59891i	−0.332025	−	0.0889659i
$324$	0.171162	+	8.99837i	0.00950902	+	0.499910i
$325$	17.7154	+	3.34151i	0.982672	+	0.185354i
$326$		−	15.8162i		−	0.875980i
$327$	−8.43993	−	14.4592i	−0.466729	−	0.799595i
$328$	−0.789375	+	2.94599i	−0.0435859	+	0.162665i
$329$	−10.5145	+	18.2117i	−0.579684	+	1.00404i
$330$	1.21170	+	3.48643i	0.0667018	+	0.191921i
$331$	10.6052	−	18.3687i	0.582912	−	1.00963i	−0.412220	−	0.911084i	$-0.635247\pi$
$331$	10.6052	−	18.3687i	0.582912	−	1.00963i	0.995132	−	0.0985487i	$-0.0314200\pi$
$332$	−0.722509	+	0.193596i	−0.0396528	+	0.0106249i
$333$	−14.5161	+	14.7949i	−0.795480	+	0.810755i
$334$	10.1879	+	5.88198i	0.557457	+	0.321848i
$335$	23.5612	+	20.5593i	1.28729	+	1.12327i
$336$	−1.94390	+	7.39519i	−0.106048	+	0.403441i
$337$	−13.0004	+	13.0004i	−0.708174	+	0.708174i	−0.966151	−	0.257977i	$-0.916944\pi$
$337$	−13.0004	+	13.0004i	−0.708174	+	0.708174i	0.257977	+	0.966151i	$0.416944\pi$
$338$	−12.0591	−	4.85576i	−0.655928	−	0.264118i
$339$	4.88689	+	4.84064i	0.265420	+	0.262907i
$340$	5.82564	+	5.08340i	0.315939	+	0.275686i
$341$	5.63049	−	3.25076i	0.304908	−	0.176039i
$342$	−1.43643	−	5.16388i	−0.0776731	−	0.279231i
$343$	−17.1352	−	17.1352i	−0.925214	−	0.925214i
$344$	−4.70683	+	8.15246i	−0.253775	+	0.439551i
$345$	−31.8277	−	6.09175i	−1.71355	−	0.327969i
$346$	−4.05708			−0.218110
$347$	26.3854	−	7.06994i	1.41644	−	0.379534i	0.532222	−	0.846605i	$-0.321357\pi$
$347$	26.3854	−	7.06994i	1.41644	−	0.379534i	0.884220	+	0.467071i	$0.154691\pi$
$348$	8.53755	+	14.6264i	0.457660	+	0.784058i
$349$	1.00584	−	0.580720i	0.0538412	−	0.0310852i	−0.472838	−	0.881150i	$-0.656770\pi$
$349$	1.00584	−	0.580720i	0.0538412	−	0.0310852i	0.526679	+	0.850064i	$0.323437\pi$
$350$	13.5242	+	17.4449i	0.722899	+	0.932471i
$351$	−12.6212	−	13.8458i	−0.673669	−	0.739033i
$352$	−0.673879	+	0.673879i	−0.0359179	+	0.0359179i
$353$	10.0427	+	2.69094i	0.534521	+	0.143224i	0.515975	−	0.856604i	$-0.327430\pi$
$353$	10.0427	+	2.69094i	0.534521	+	0.143224i	0.0185456	+	0.999828i	$0.494096\pi$
$354$	3.58315	+	0.941865i	0.190442	+	0.0500595i
$355$	−7.18701	−	10.6985i	−0.381447	−	0.567817i
$356$		−	2.80631i		−	0.148734i
$357$	−22.9595	−	13.1105i	−1.21515	−	0.693883i
$358$	10.4087	−	2.78901i	0.550118	−	0.147404i
$359$	6.56646			0.346565			0.173282	−	0.984872i	$-0.444563\pi$
$359$	6.56646			0.346565			0.173282	+	0.984872i	$0.444563\pi$
$360$	−1.22970	+	6.59453i	−0.0648110	+	0.347562i
$361$	−7.90394	−	13.6900i	−0.415997	−	0.720528i
$362$	1.62494	−	6.06435i	0.0854048	−	0.318735i
$363$	0.0831110	+	17.4793i	0.00436220	+	0.917424i
$364$	−7.11059	−	14.2407i	−0.372696	−	0.746418i
$365$	−3.94792	−	11.5360i	−0.206644	−	0.603820i
$366$	6.24199	+	1.64076i	0.326274	+	0.0857642i
$367$	2.64871	+	0.709720i	0.138262	+	0.0370471i	0.327286	−	0.944925i	$-0.393866\pi$
$367$	2.64871	+	0.709720i	0.138262	+	0.0370471i	−0.189025	+	0.981972i	$0.560533\pi$
$368$	−2.16555	−	8.08195i	−0.112887	−	0.421301i
$369$	−0.0870089	−	9.14932i	−0.00452950	−	0.476295i
$370$	−12.8240	+	8.61487i	−0.666687	+	0.447866i
$371$	15.2785	+	8.82104i	0.793220	+	0.457966i
$372$	11.8161	−	0.0561836i	0.612637	−	0.00291298i
$373$	−12.6386	+	3.38650i	−0.654402	+	0.175347i	−0.570718	−	0.821146i	$-0.693335\pi$
$373$	−12.6386	+	3.38650i	−0.654402	+	0.175347i	−0.0836837	+	0.996492i	$0.526669\pi$
$374$	−1.64762	−	2.85375i	−0.0851962	−	0.147564i
$375$	12.9450	+	14.4024i	0.668475	+	0.743735i
$376$	−4.76346			−0.245657
$377$	−33.4394	−	11.1669i	−1.72222	−	0.575124i
$378$	−0.327203	−	22.9369i	−0.0168295	−	1.17975i
$379$	−27.0729	+	15.6306i	−1.39064	+	0.802888i	−0.993386	−	0.114819i	$-0.963371\pi$
$379$	−27.0729	+	15.6306i	−1.39064	+	0.802888i	−0.397257	+	0.917707i	$0.630038\pi$
$380$	−0.271193	−	3.98585i	−0.0139119	−	0.204470i
$381$	12.7319	−	3.47646i	0.652272	−	0.178104i
$382$	−6.20408	+	6.20408i	−0.317429	+	0.317429i
$383$	8.23494	+	30.7332i	0.420786	+	1.57039i	0.772957	+	0.634459i	$0.218777\pi$
$383$	8.23494	+	30.7332i	0.420786	+	1.57039i	−0.352171	+	0.935936i	$0.614556\pi$
$384$	−1.67088	+	0.456238i	−0.0852668	+	0.0232823i
$385$	−3.04609	−	8.90079i	−0.155243	−	0.453626i
$386$	−6.96161	−	4.01929i	−0.354337	−	0.204576i
$387$	7.04956	−	27.3469i	0.358349	−	1.39012i
$388$	1.91208	−	7.13599i	0.0970713	−	0.362275i
$389$	1.18528			0.0600960			0.0300480	−	0.999548i	$-0.490434\pi$
$389$	1.18528			0.0600960			0.0300480	+	0.999548i	$0.490434\pi$
$390$	−7.12899	−	12.0074i	−0.360991	−	0.608018i
$391$	28.9309			1.46310
$392$	3.23244	−	12.0636i	0.163263	−	0.609305i
$393$	19.2992	+	33.0632i	0.973518	+	1.66782i
$394$	−17.1203	−	9.88440i	−0.862507	−	0.497969i
$395$	−4.94098	+	10.0824i	−0.248608	+	0.507300i
$396$	1.40590	−	2.48947i	0.0706493	−	0.125101i
$397$	−1.77108	−	6.60977i	−0.0888880	−	0.331735i	0.907134	−	0.420842i	$-0.138265\pi$
$397$	−1.77108	−	6.60977i	−0.0888880	−	0.331735i	−0.996022	+	0.0891072i	$0.971599\pi$
$398$	10.7994	−	10.7994i	0.541325	−	0.541325i
$399$	3.59854	+	13.1790i	0.180153	+	0.659774i
$400$	−1.89044	+	4.62885i	−0.0945221	+	0.231442i
$401$	15.6065	−	9.01040i	0.779350	−	0.449958i	−0.0568499	−	0.998383i	$-0.518106\pi$
$401$	15.6065	−	9.01040i	0.779350	−	0.449958i	0.836200	+	0.548425i	$0.184772\pi$
$402$	−0.115169	−	24.2214i	−0.00574409	−	1.20805i
$403$	−18.4129	+	16.3096i	−0.917210	+	0.812437i
$404$	−1.92696			−0.0958700
$405$	−1.74770	−	20.0486i	−0.0868438	−	0.996222i
$406$	−21.5830	−	37.3829i	−1.07115	−	1.85528i
$407$	6.35997	−	1.70415i	0.315252	−	0.0844715i
$408$	−0.0284761	−	5.98887i	−0.00140978	−	0.296493i
$409$	4.77164	+	2.75491i	0.235943	+	0.136222i	0.613310	−	0.789842i	$-0.289837\pi$
$409$	4.77164	+	2.75491i	0.235943	+	0.136222i	−0.377368	+	0.926063i	$0.623171\pi$
$410$	1.31386	−	6.69205i	0.0648868	−	0.330497i
$411$	2.98662	−	3.01516i	0.147319	−	0.148727i
$412$	−1.79915	−	6.71453i	−0.0886379	−	0.330801i
$413$	−9.12122	−	2.44402i	−0.448826	−	0.120263i
$414$	12.7567	+	21.6179i	0.626959	+	1.06246i
$415$	1.58247	−	0.541563i	0.0776802	−	0.0265843i
$416$	1.98828	−	3.00778i	0.0974832	−	0.147469i
$417$	−24.9273	+	0.118525i	−1.22070	+	0.00580421i
$418$	−0.440689	+	1.64467i	−0.0215548	+	0.0804436i
$419$	10.8963	+	18.8729i	0.532319	+	0.922003i	0.999288	+	0.0377297i	$0.0120126\pi$
$419$	10.8963	+	18.8729i	0.532319	+	0.922003i	−0.466969	+	0.884274i	$0.654654\pi$
$420$	3.21415	−	16.7931i	0.156835	−	0.819417i
$421$	−7.06034			−0.344100			−0.172050	−	0.985088i	$-0.555039\pi$
$421$	−7.06034			−0.344100			−0.172050	+	0.985088i	$0.555039\pi$
$422$	−5.97438	+	1.60083i	−0.290828	+	0.0779272i
$423$	13.7676	−	3.82972i	0.669406	−	0.186207i
$424$			3.99626i			0.194075i
$425$	−13.7681	−	10.4563i	−0.667850	−	0.507207i
$426$	−2.53799	+	9.65532i	−0.122966	+	0.467802i
$427$	−15.8895	−	4.25758i	−0.768948	−	0.206039i
$428$	2.05448	−	2.05448i	0.0993071	−	0.0993071i
$429$	1.21768	+	5.82564i	0.0587899	+	0.281264i
$430$	9.26306	−	18.9019i	0.446704	−	0.911528i
$431$	−3.61799	+	2.08885i	−0.174273	+	0.100616i	−0.584599	−	0.811322i	$-0.698748\pi$
$431$	−3.61799	+	2.08885i	−0.174273	+	0.100616i	0.410326	+	0.911939i	$0.365415\pi$
$432$	4.46248	−	2.66200i	0.214701	−	0.128076i
$433$	21.5187	−	5.76593i	1.03412	−	0.277093i	0.298448	−	0.954426i	$-0.403531\pi$
$433$	21.5187	−	5.76593i	1.03412	−	0.277093i	0.735676	+	0.677333i	$0.236864\pi$
$434$	−30.1173			−1.44567
$435$	−21.2666	−	31.3343i	−1.01966	−	1.50237i
$436$	−4.83305	+	8.37109i	−0.231461	+	0.400902i
$437$	−10.5705	−	10.5705i	−0.505657	−	0.505657i
$438$	−4.68331	+	8.20155i	−0.223777	+	0.391885i
$439$	6.75510	−	3.90006i	0.322403	−	0.186140i	−0.330060	−	0.943960i	$-0.607069\pi$
$439$	6.75510	−	3.90006i	0.322403	−	0.186140i	0.652463	+	0.757820i	$0.273736\pi$
$440$	1.40108	−	1.60565i	0.0667937	−	0.0765464i
$441$	0.356296	+	37.4658i	0.0169665	+	1.78409i
$442$	8.26633	+	9.33237i	0.393189	+	0.443895i
$443$	−17.8260	+	17.8260i	−0.846941	+	0.846941i	−0.989750	−	0.142810i	$-0.954386\pi$
$443$	−17.8260	+	17.8260i	−0.846941	+	0.846941i	0.142810	+	0.989750i	$0.454386\pi$
$444$	11.5736	+	3.04222i	0.549257	+	0.144377i
$445$	0.425966	+	6.26063i	0.0201927	+	0.296782i
$446$	3.25555	+	1.87959i	0.154155	+	0.0890012i
$447$	−0.0399775	−	8.40777i	−0.00189087	−	0.397674i
$448$	4.26423	−	1.14260i	0.201466	−	0.0539826i
$449$	3.92730	−	6.80229i	0.185341	−	0.321020i	−0.758350	−	0.651847i	$-0.773994\pi$
$449$	3.92730	−	6.80229i	0.185341	−	0.321020i	0.943691	+	0.330827i	$0.107328\pi$
$450$	1.74238	−	14.8985i	0.0821366	−	0.702320i
$451$	−1.45330	+	2.51718i	−0.0684330	+	0.118529i
$452$	1.02785	−	3.83597i	0.0483458	−	0.180429i
$453$	−24.3353	+	14.2047i	−1.14337	+	0.667395i
$454$		−	8.98286i		−	0.421586i
$455$	18.0247	+	30.6905i	0.845010	+	1.43879i
$456$	−2.17776	+	2.19857i	−0.101983	+	0.102957i
$457$	26.0290	+	6.97446i	1.21759	+	0.326251i	0.809734	−	0.586796i	$-0.199611\pi$
$457$	26.0290	+	6.97446i	1.21759	+	0.326251i	0.407852	+	0.913048i	$0.366278\pi$
$458$	15.2459	+	4.08513i	0.712395	+	0.190886i
$459$	4.89723	+	17.2865i	0.228583	+	0.806866i
$460$	6.05790	+	17.7014i	0.282451	+	0.825332i
$461$	−2.96932	−	1.71434i	−0.138295	−	0.0798446i	0.429256	−	0.903183i	$-0.358776\pi$
$461$	−2.96932	−	1.71434i	−0.138295	−	0.0798446i	−0.567551	+	0.823338i	$0.692109\pi$
$462$	−3.61350	+	6.32806i	−0.168115	+	0.294408i
$463$	−5.13341	−	5.13341i	−0.238570	−	0.238570i	0.577688	−	0.816258i	$-0.303955\pi$
$463$	−5.13341	−	5.13341i	−0.238570	−	0.238570i	−0.816258	+	0.577688i	$0.803955\pi$
$464$	4.88895	−	8.46790i	0.226964	−	0.393113i
$465$	−26.3521	+	1.91889i	−1.22205	+	0.0889864i
$466$	−6.29737	−	10.9074i	−0.291720	−	0.505274i
$467$	13.5078	+	13.5078i	0.625068	+	0.625068i	0.946823	−	0.321755i	$-0.104273\pi$
$467$	13.5078	+	13.5078i	0.625068	+	0.625068i	−0.321755	+	0.946823i	$0.604273\pi$
$468$	−3.32845	+	10.2918i	−0.153857	+	0.475739i
$469$			61.7363i			2.85072i
$470$	10.6268	−	0.723038i	0.490180	−	0.0333513i
$471$	1.17326	−	4.46344i	0.0540609	−	0.205665i
$472$	−0.553616	−	2.06612i	−0.0254822	−	0.0951010i
$473$	−6.34366	+	6.34366i	−0.291682	+	0.291682i
$474$	8.39002	−	2.29091i	0.385366	−	0.105225i
$475$	1.21001	+	8.85091i	0.0555192	+	0.406108i
$476$			15.2646i			0.699653i
$477$	−3.21290	−	11.5502i	−0.147109	−	0.528849i
$478$	−3.36988	+	12.5766i	−0.154135	+	0.575239i
$479$	−6.77236	−	11.7301i	−0.309437	−	0.535961i	0.668802	−	0.743440i	$-0.266807\pi$
$479$	−6.77236	−	11.7301i	−0.309437	−	0.535961i	−0.978239	+	0.207480i	$0.933474\pi$
$480$	3.65834	−	1.27145i	0.166979	−	0.0580333i
$481$	−22.2869	+	11.1282i	−1.01620	+	0.507401i
$482$	−2.33002	−	2.33002i	−0.106130	−	0.106130i
$483$	−32.2520	−	55.2537i	−1.46752	−	2.51413i
$484$	8.73973	−	5.04589i	0.397261	−	0.229359i
$485$	−3.18252	+	16.2100i	−0.144511	+	0.736057i
$486$	−10.7576	+	11.2816i	−0.487973	+	0.511745i
$487$	7.77342	+	29.0108i	0.352247	+	1.31460i	0.883913	+	0.467650i	$0.154899\pi$
$487$	7.77342	+	29.0108i	0.352247	+	1.31460i	−0.531666	+	0.846954i	$0.678434\pi$
$488$	−0.964421	−	3.59927i	−0.0436573	−	0.162931i
$489$	19.2785	−	19.4627i	0.871805	−	0.880135i
$490$	−5.38016	+	27.4035i	−0.243051	+	1.23796i
$491$	0.281170	−	0.162334i	0.0126890	−	0.00732601i	−0.493642	−	0.869665i	$-0.664335\pi$
$491$	0.281170	−	0.162334i	0.0126890	−	0.00732601i	0.506331	+	0.862339i	$0.331001\pi$
$492$	−4.56226	+	2.66302i	−0.205682	+	0.120058i
$493$	23.9067	+	23.9067i	1.07670	+	1.07670i
$494$	0.389499	−	6.43007i	0.0175244	−	0.289302i
$495$	−2.75857	+	5.76719i	−0.123988	+	0.259216i
$496$	−3.41105	−	5.90812i	−0.153161	−	0.265282i
$497$	6.58578	−	24.5785i	0.295413	−	1.10249i
$498$	−1.12506	−	0.642441i	−0.0504152	−	0.0287885i
$499$		−	6.59704i		−	0.295324i	−0.989038	−	0.147662i	$-0.952825\pi$
$499$		−	6.59704i		−	0.295324i	0.989038	−	0.147662i	$-0.0471748\pi$
$500$	3.51480	−	10.6135i	0.157187	−	0.474650i
$501$	5.36716	+	19.6562i	0.239787	+	0.878174i
$502$	−10.6489	+	10.6489i	−0.475284	+	0.475284i
$503$	−10.6595	−	39.7817i	−0.475283	−	1.77378i	−0.620316	−	0.784352i	$-0.712996\pi$
$503$	−10.6595	−	39.7817i	−0.475283	−	1.77378i	0.145033	−	0.989427i	$-0.453671\pi$
$504$	−11.4061	+	6.73075i	−0.508069	+	0.299812i
$505$	4.29888	−	0.292491i	0.191298	−	0.0130157i
$506$		−	7.97387i		−	0.354482i
$507$	−8.92064	−	20.6742i	−0.396180	−	0.918173i
$508$	−5.38804	−	5.38804i	−0.239056	−	0.239056i
$509$	8.76469	+	15.1809i	0.388488	+	0.672881i	0.992246	−	0.124286i	$-0.0396641\pi$
$509$	8.76469	+	15.1809i	0.388488	+	0.672881i	−0.603758	+	0.797167i	$0.706331\pi$
$510$	0.972569	+	13.3563i	0.0430661	+	0.591427i
$511$	12.0361	−	20.8471i	0.532445	−	0.922223i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	4.52670	−	8.10531i	0.199859	−	0.357858i
$514$	7.20922	+	4.16224i	0.317985	+	0.183589i
$515$	5.03294	+	14.7064i	0.221778	+	0.648042i
$516$	−15.7291	+	4.29486i	−0.692435	+	0.189071i
$517$	−4.38493	−	1.17494i	−0.192849	−	0.0516738i
$518$	−29.4615	−	7.89419i	−1.29446	−	0.346851i
$519$	−4.99245	−	4.94520i	−0.219144	−	0.217070i
$520$	−3.97912	+	7.01189i	−0.174496	+	0.307492i
$521$		−	23.9936i		−	1.05118i	−0.850738	−	0.525589i	$-0.823845\pi$
$521$		−	23.9936i		−	1.05118i	0.850738	−	0.525589i	$-0.176155\pi$
$522$	−7.32233	+	28.4051i	−0.320490	+	1.24326i
$523$	8.41970	−	31.4228i	0.368168	−	1.37402i	−0.494907	−	0.868946i	$-0.664798\pi$
$523$	8.41970	−	31.4228i	0.368168	−	1.37402i	0.863075	−	0.505075i	$-0.168535\pi$
$524$	11.0515	−	19.1418i	0.482789	−	0.836214i
$525$	−4.62149	+	37.9517i	−0.201698	+	1.65635i
$526$	0.0700979	−	0.121413i	0.00305642	−	0.00529387i
$527$	22.7851	−	6.10526i	0.992536	−	0.265949i
$528$	−1.65064	+	0.00784852i	−0.0718349	+	0.000341563i
$529$	40.7097	+	23.5038i	1.76999	+	1.02190i
$530$	−0.606586	−	8.91529i	−0.0263484	−	0.387255i
$531$	3.26121	+	5.52654i	0.141525	+	0.239832i
$532$	5.57726	−	5.57726i	0.241805	−	0.241805i
$533$	3.48317	−	10.4304i	0.150873	−	0.451790i
$534$	3.42063	−	3.45332i	0.148025	−	0.149440i
$535$	−4.27152	+	4.89521i	−0.184674	+	0.211638i
$536$	−12.1108	+	6.99220i	−0.523108	+	0.302017i
$537$	16.2081	+	9.25525i	0.699429	+	0.399393i
$538$	5.54552	+	5.54552i	0.239085	+	0.239085i
$539$	5.95115	−	10.3077i	0.256334	−	0.443984i
$540$	−9.55134	+	6.61604i	−0.411024	+	0.284709i
$541$	7.10909			0.305644			0.152822	−	0.988254i	$-0.451164\pi$
$541$	7.10909			0.305644			0.152822	+	0.988254i	$0.451164\pi$
$542$	0.991936	−	0.265788i	0.0426073	−	0.0114166i
$543$	9.39146	−	5.48186i	0.403026	−	0.235249i
$544$	−2.99447	+	1.72886i	−0.128387	+	0.0741242i
$545$	9.51146	−	19.4087i	0.407426	−	0.831379i
$546$	8.60818	−	26.1912i	0.368396	−	1.12088i
$547$	24.3663	−	24.3663i	1.04183	−	1.04183i	0.0427396	−	0.999086i	$-0.486391\pi$
$547$	24.3663	−	24.3663i	1.04183	−	1.04183i	0.999086	−	0.0427396i	$-0.0136086\pi$
$548$	−2.36675	−	0.634169i	−0.101103	−	0.0270904i
$549$	5.68116	+	9.62745i	0.242466	+	0.410890i
$550$	−2.88196	+	3.79473i	−0.122887	+	0.161808i
$551$		−	17.4697i		−	0.744232i
$552$	7.18632	−	12.5849i	0.305870	−	0.535648i
$553$	−21.4120	+	5.73733i	−0.910532	+	0.243976i
$554$	−31.0908			−1.32092
$555$	−26.2814	−	5.03019i	−1.11558	−	0.213520i
$556$	7.19598	+	12.4638i	0.305177	+	0.528583i
$557$	−7.18238	+	26.8050i	−0.304327	+	1.13577i	0.629195	+	0.777247i	$0.283385\pi$
$557$	−7.18238	+	26.8050i	−0.304327	+	1.13577i	−0.933523	+	0.358518i	$0.883282\pi$
$558$	14.6088	+	14.3336i	0.618442	+	0.606790i
$559$	18.7169	−	28.3142i	0.791642	−	1.19756i
$560$	−9.33968	+	3.19629i	−0.394673	+	0.135068i
$561$	1.45098	−	5.51999i	0.0612605	−	0.233054i
$562$	12.4210	+	3.32819i	0.523947	+	0.140391i
$563$	1.60491	+	5.98962i	0.0676390	+	0.252432i	0.991464	−	0.130384i	$-0.0416210\pi$
$563$	1.60491	+	5.98962i	0.0676390	+	0.252432i	−0.923825	+	0.382816i	$0.874954\pi$
$564$	−5.86170	−	5.80622i	−0.246822	−	0.244486i
$565$	−1.71078	+	8.71373i	−0.0719729	+	0.366589i
$566$	12.8837	+	7.43838i	0.541540	+	0.312659i
$567$	27.5553	−	28.6239i	1.15721	−	1.20209i
$568$	5.56747	−	1.49180i	0.233606	−	0.0625945i
$569$	16.5135	+	28.6022i	0.692280	+	1.19906i	0.971089	+	0.238718i	$0.0767272\pi$
$569$	16.5135	+	28.6022i	0.692280	+	1.19906i	−0.278808	+	0.960347i	$0.589939\pi$
$570$	4.52467	−	5.23537i	0.189518	−	0.219285i
$571$	−29.0119			−1.21411			−0.607056	−	0.794659i	$-0.707650\pi$
$571$	−29.0119			−1.21411			−0.607056	+	0.794659i	$0.707650\pi$
$572$	2.57217	−	2.27835i	0.107548	−	0.0952626i
$573$	−15.1967	+	0.0722576i	−0.634850	+	0.00301861i
$574$	11.6604	−	6.73215i	0.486697	−	0.280995i
$575$	−16.2015	−	38.5707i	−0.675649	−	1.60851i
$576$	−2.61222	−	1.47523i	−0.108843	−	0.0614677i
$577$	30.0883	−	30.0883i	1.25259	−	1.25259i	0.298037	−	0.954554i	$-0.403668\pi$
$577$	30.0883	−	30.0883i	1.25259	−	1.25259i	0.954554	−	0.298037i	$-0.0963319\pi$
$578$	1.30554	+	4.87233i	0.0543031	+	0.202662i
$579$	−3.66750	−	13.4315i	−0.152416	−	0.558195i
$580$	−9.62147	+	19.6332i	−0.399510	+	0.815225i
$581$	2.85974	+	1.65107i	0.118642	+	0.0684980i
$582$	11.0510	−	6.45057i	0.458080	−	0.267385i
$583$	−0.985703	+	3.67869i	−0.0408237	+	0.152356i
$584$	5.45279			0.225638
$585$	5.86328	−	23.4653i	0.242417	−	0.970172i
$586$	−10.8530			−0.448333
$587$	−1.06155	+	3.96176i	−0.0438148	+	0.163519i	−0.984367	−	0.176131i	$-0.943642\pi$
$587$	−1.06155	+	3.96176i	−0.0438148	+	0.163519i	0.940552	+	0.339650i	$0.110309\pi$
$588$	18.6821	−	10.9049i	0.770438	−	0.449710i
$589$	−10.5557	−	6.09436i	−0.434941	−	0.251114i
$590$	1.54868	+	4.52530i	0.0637582	+	0.186304i
$591$	−9.01927	−	33.0313i	−0.371003	−	1.35873i
$592$	−1.78818	−	6.67357i	−0.0734937	−	0.274282i
$593$	2.31460	−	2.31460i	0.0950491	−	0.0950491i	−0.657983	−	0.753032i	$-0.728590\pi$
$593$	2.31460	−	2.31460i	0.0950491	−	0.0950491i	0.753032	+	0.657983i	$0.228590\pi$
$594$	4.76447	−	1.34976i	0.195489	−	0.0553815i
$595$	−2.31699	−	34.0540i	−0.0949875	−	1.39608i
$596$	−4.20393	+	2.42714i	−0.172200	+	0.0994196i
$597$	26.4527	−	0.125778i	1.08264	−	0.00514776i
$598$	6.03182	+	29.5587i	0.246659	+	1.20874i
$599$	2.95273			0.120645			0.0603226	−	0.998179i	$-0.480787\pi$
$599$	2.95273			0.120645			0.0603226	+	0.998179i	$0.480787\pi$
$600$	−7.96843	+	3.39177i	−0.325310	+	0.138469i
$601$	−22.1321	−	38.3340i	−0.902789	−	1.56368i	−0.823858	−	0.566796i	$-0.808183\pi$
$601$	−22.1321	−	38.3340i	−0.902789	−	1.56368i	−0.0789311	−	0.996880i	$-0.525151\pi$
$602$	40.1420	−	10.7560i	1.63606	−	0.438382i
$603$	29.3819	−	29.9461i	1.19652	−	1.21950i
$604$	14.0888	+	8.13419i	0.573267	+	0.330976i
$605$	−18.7317	+	12.5835i	−0.761550	+	0.511593i
$606$	−2.37123	−	2.34879i	−0.0963247	−	0.0954130i
$607$	−4.38820	−	16.3770i	−0.178112	−	0.664722i	−0.996001	−	0.0893457i	$-0.971522\pi$
$607$	−4.38820	−	16.3770i	−0.178112	−	0.664722i	0.817889	−	0.575376i	$-0.195144\pi$
$608$	1.72577	+	0.462419i	0.0699892	+	0.0187536i
$609$	19.0072	−	72.3094i	0.770211	−	2.93012i
$610$	2.69786	+	7.88325i	0.109233	+	0.319184i
$611$	17.1435	+	1.03846i	0.693551	+	0.0420116i
$612$	7.26484	−	7.40434i	0.293664	−	0.299303i
$613$	−7.19641	+	26.8574i	−0.290660	+	1.08476i	0.653943	+	0.756544i	$0.273114\pi$
$613$	−7.19641	+	26.8574i	−0.290660	+	1.08476i	−0.944603	+	0.328215i	$0.893553\pi$
$614$	1.96105	+	3.39665i	0.0791417	+	0.137077i
$615$	9.77377	−	6.63346i	0.394116	−	0.267487i
$616$	4.20720			0.169513
$617$	−11.2681	+	3.01928i	−0.453636	+	0.121551i	−0.478400	−	0.878142i	$-0.658783\pi$
$617$	−11.2681	+	3.01928i	−0.453636	+	0.121551i	0.0247640	+	0.999693i	$0.492117\pi$
$618$	5.97044	−	10.4556i	0.240166	−	0.420586i
$619$			23.1085i			0.928809i	0.885623	+	0.464404i	$0.153732\pi$
$619$			23.1085i			0.928809i	−0.885623	+	0.464404i	$0.846268\pi$
$620$	8.50654	+	12.6627i	0.341631	+	0.508547i
$621$	−10.6524	+	42.1513i	−0.427465	+	1.69147i
$622$	−3.10790	−	0.832760i	−0.124616	−	0.0333906i
$623$	−8.76027	+	8.76027i	−0.350973	+	0.350973i
$624$	6.11289	−	1.27772i	0.244711	−	0.0511496i
$625$	−6.23020	+	24.2113i	−0.249208	+	0.968450i
$626$	−11.4282	+	6.59805i	−0.456761	+	0.263711i
$627$	−2.54700	+	1.48670i	−0.101717	+	0.0593731i
$628$	−2.57372	+	0.689626i	−0.102703	+	0.0275191i
$629$	23.8893			0.952530
$630$	24.4244	−	16.7470i	0.973091	−	0.667217i
$631$	24.2019	−	41.9189i	0.963463	−	1.66877i	0.249772	−	0.968305i	$-0.419644\pi$
$631$	24.2019	−	41.9189i	0.963463	−	1.66877i	0.713690	−	0.700462i	$-0.247022\pi$
$632$	−3.55060	−	3.55060i	−0.141235	−	0.141235i
$633$	−9.30306	−	5.31231i	−0.369763	−	0.211145i
$634$	27.4728	−	15.8614i	1.09108	−	0.629937i
$635$	12.8381	+	11.2024i	0.509463	+	0.444553i
$636$	−4.87107	+	4.91761i	−0.193150	+	0.194996i
$637$	−14.2633	+	42.7117i	−0.565134	+	1.69230i
$638$	6.58911	−	6.58911i	0.260866	−	0.260866i
$639$	−14.8921	+	8.78782i	−0.589122	+	0.347641i
$640$	−1.68482	−	1.47016i	−0.0665985	−	0.0581132i
$641$	35.3939	+	20.4347i	1.39798	+	0.807122i	0.994181	−	0.107726i	$-0.0343571\pi$
$641$	35.3939	+	20.4347i	1.39798	+	0.807122i	0.403796	+	0.914849i	$0.367690\pi$
$642$	5.03238	−	0.0239281i	0.198612	−	0.000944367i
$643$	−31.1138	+	8.33691i	−1.22701	+	0.328775i	−0.813413	−	0.581686i	$-0.802393\pi$
$643$	−31.1138	+	8.33691i	−1.22701	+	0.328775i	−0.413593	+	0.910462i	$0.635727\pi$
$644$	−18.4688	+	31.9889i	−0.727774	+	1.26054i
$645$	34.4383	−	11.9689i	1.35601	−	0.471277i
$646$	−3.08886	+	5.35006i	−0.121530	+	0.210495i
$647$	11.2494	−	41.9835i	0.442261	−	1.65054i	−0.280807	−	0.959764i	$-0.590602\pi$
$647$	11.2494	−	41.9835i	0.442261	−	1.65054i	0.723068	−	0.690777i	$-0.242731\pi$
$648$	8.73606	+	2.16362i	0.343185	+	0.0849950i
$649$		−	2.03849i		−	0.0800178i
$650$	7.81273	−	16.2469i	0.306440	−	0.637255i
$651$	−37.0609	−	36.7102i	−1.45253	−	1.43878i
$652$	−15.2773	−	4.09354i	−0.598306	−	0.160315i
$653$	−28.7633	−	7.70710i	−1.12559	−	0.301602i	−0.352449	−	0.935831i	$-0.614651\pi$
$653$	−28.7633	−	7.70710i	−1.12559	−	0.301602i	−0.773145	+	0.634229i	$0.781318\pi$
$654$	−16.1509	+	4.41004i	−0.631551	+	0.172446i
$655$	−21.7495	+	44.3812i	−0.849822	+	1.73412i
$656$	2.64130	+	1.52496i	0.103125	+	0.0595395i
$657$	−15.7600	+	4.38392i	−0.614856	+	0.171033i
$658$	14.8698	+	14.8698i	0.579684	+	0.579684i
$659$	−1.31198	+	2.27241i	−0.0511073	+	0.0885205i	−0.890447	−	0.455086i	$-0.849608\pi$
$659$	−1.31198	+	2.27241i	−0.0511073	+	0.0885205i	0.839340	+	0.543607i	$0.182942\pi$
$660$	3.68124	−	0.268058i	0.143292	−	0.0104341i
$661$	6.78774	+	11.7567i	0.264013	+	0.457283i	0.967304	−	0.253618i	$-0.0816206\pi$
$661$	6.78774	+	11.7567i	0.264013	+	0.457283i	−0.703292	+	0.710901i	$0.748287\pi$
$662$	−14.9979	−	14.9979i	−0.582912	−	0.582912i
$663$	−1.20312	+	21.5599i	−0.0467254	+	0.837316i
$664$			0.747996i			0.0290279i
$665$	−11.5958	+	13.2889i	−0.449666	+	0.515323i
$666$	10.5337	+	17.8507i	0.408173	+	0.691701i
$667$	21.1745	+	79.0245i	0.819881	+	3.05984i
$668$	8.31838	−	8.31838i	0.321848	−	0.321848i
$669$	1.71508	+	6.28115i	0.0663088	+	0.242843i
$670$	25.9569	−	17.4372i	1.00280	−	0.673660i
$671$		−	3.55113i		−	0.137090i
$672$	6.64009	+	3.79167i	0.256147	+	0.146267i
$673$	4.58858	−	17.1248i	0.176877	−	0.660113i	−0.819348	−	0.573297i	$-0.805664\pi$
$673$	4.58858	−	17.1248i	0.176877	−	0.660113i	0.996224	−	0.0868159i	$-0.0276692\pi$
$674$	9.19264	+	15.9221i	0.354087	+	0.613297i
$675$	20.3039	−	16.2096i	0.781499	−	0.623906i
$676$	−7.81142	+	10.3914i	−0.300439	+	0.399670i
$677$	32.2838	+	32.2838i	1.24077	+	1.24077i	0.959682	+	0.281087i	$0.0906948\pi$
$677$	32.2838	+	32.2838i	1.24077	+	1.24077i	0.281087	+	0.959682i	$0.409305\pi$
$678$	5.94052	−	3.46753i	0.228144	−	0.133170i
$679$	−28.2448	+	16.3071i	−1.08393	+	0.625810i
$680$	6.41797	−	4.31145i	0.246118	−	0.165337i
$681$	10.9493	−	11.0539i	0.419577	−	0.423586i
$682$	−1.68272	−	6.27999i	−0.0644347	−	0.240473i
$683$	−2.97648	−	11.1084i	−0.113892	−	0.425050i	0.885310	−	0.465001i	$-0.153946\pi$
$683$	−2.97648	−	11.1084i	−0.113892	−	0.425050i	−0.999202	+	0.0399518i	$0.987280\pi$
$684$	−5.35970	+	0.0509701i	−0.204933	+	0.00194889i
$685$	5.37627	+	1.05553i	0.205417	+	0.0403297i
$686$	−20.9862	+	12.1164i	−0.801259	+	0.462607i
$687$	13.7815	+	23.6104i	0.525799	+	0.900791i
$688$	6.65646	+	6.65646i	0.253775	+	0.253775i
$689$	0.871204	−	14.3823i	0.0331902	−	0.547924i
$690$	−14.1218	+	29.1666i	−0.537608	+	1.11035i
$691$	2.98020	+	5.16186i	0.113372	+	0.196366i	0.917128	−	0.398593i	$-0.130501\pi$
$691$	2.98020	+	5.16186i	0.113372	+	0.196366i	−0.803756	+	0.594960i	$0.797168\pi$
$692$	−1.05005	+	3.91883i	−0.0399169	+	0.148972i
$693$	−12.1599	+	3.38250i	−0.461917	+	0.128491i
$694$		−	27.3162i		−	1.03691i
$695$	−17.9454	−	26.7134i	−0.680710	−	1.01330i
$696$	16.3377	−	4.46104i	0.619279	−	0.169095i
$697$	−7.45695	+	7.45695i	−0.282452	+	0.282452i
$698$	−0.300603	−	1.12187i	−0.0113780	−	0.0424632i
$699$	5.54582	−	21.0980i	0.209762	−	0.798001i
$700$	20.3508	−	8.54830i	0.769189	−	0.323095i
$701$		−	18.4252i		−	0.695912i	−0.937511	−	0.347956i	$-0.886876\pi$
$701$		−	18.4252i		−	0.695912i	0.937511	−	0.347956i	$-0.113124\pi$
$702$	−16.6406	+	8.60757i	−0.628059	+	0.324872i
$703$	−8.72848	−	8.72848i	−0.329201	−	0.329201i
$704$	0.476504	+	0.825330i	0.0179589	+	0.0311058i
$705$	13.9582	+	12.0634i	0.525697	+	0.454334i
$706$	5.19850	−	9.00407i	0.195648	−	0.338872i
$707$	6.01527	+	6.01527i	0.226227	+	0.226227i
$708$	1.83716	−	3.21728i	0.0690447	−	0.120913i
$709$	−22.1328	−	12.7784i	−0.831216	−	0.479903i	0.0230525	−	0.999734i	$-0.492661\pi$
$709$	−22.1328	−	12.7784i	−0.831216	−	0.479903i	−0.854269	+	0.519831i	$0.825995\pi$
$710$	−12.1941	+	4.17315i	−0.457636	+	0.156615i
$711$	13.1168	+	7.40757i	0.491918	+	0.277805i
$712$	−2.71069	−	0.726327i	−0.101587	−	0.0272202i
$713$	55.1360	+	14.7736i	2.06486	+	0.553277i
$714$	−18.6062	+	18.7839i	−0.696318	+	0.702972i
$715$	−5.39245	+	5.47322i	−0.201666	+	0.204687i
$716$		−	10.7759i		−	0.402715i
$717$	−19.4765	+	11.3686i	−0.727363	+	0.424568i
$718$	1.69953	−	6.34272i	0.0634257	−	0.236708i
$719$	13.2462	−	22.9431i	0.494000	−	0.855634i	−0.505976	−	0.862548i	$-0.668867\pi$
$719$	13.2462	−	22.9431i	0.494000	−	0.855634i	0.999976	+	0.00691392i	$0.00220079\pi$
$720$	6.05156	+	2.89459i	0.225528	+	0.107875i
$721$	−15.3440	+	26.5766i	−0.571441	+	0.989764i
$722$	−15.2692	+	4.09138i	−0.568263	+	0.152265i
$723$	−0.0271373	−	5.70731i	−0.00100925	−	0.212257i
$724$	−5.43715	−	3.13914i	−0.202070	−	0.116665i
$725$	18.4845	−	45.2604i	0.686499	−	1.68093i
$726$	16.9052	+	4.44369i	0.627410	+	0.164921i
$727$	−6.01950	+	6.01950i	−0.223251	+	0.223251i	−0.809866	−	0.586615i	$-0.800460\pi$
$727$	−6.01950	+	6.01950i	−0.223251	+	0.223251i	0.586615	+	0.809866i	$0.300460\pi$
$728$	−15.5959	+	3.18253i	−0.578021	+	0.117952i
$729$	−26.9890	+	0.770173i	−0.999593	+	0.0285249i
$730$	−12.1647	+	0.827671i	−0.450235	+	0.0306335i
$731$	−28.1889	+	16.2749i	−1.04260	+	0.601948i
$732$	3.20040	−	5.60463i	0.118290	−	0.207153i
$733$	−23.3956	−	23.3956i	−0.864138	−	0.864138i	0.127678	−	0.991816i	$-0.459248\pi$
$733$	−23.3956	−	23.3956i	−0.864138	−	0.864138i	−0.991816	+	0.127678i	$0.959248\pi$
$734$	1.37107	−	2.37477i	0.0506073	−	0.0876543i
$735$	−40.0229	+	27.1636i	−1.47627	+	1.00194i
$736$	−8.36705			−0.308414
$737$	−12.8731	+	3.44934i	−0.474188	+	0.127058i
$738$	−8.86008	−	2.28397i	−0.326144	−	0.0840742i
$739$	−33.6755	+	19.4426i	−1.23877	+	0.715206i	−0.968843	−	0.247674i	$-0.920334\pi$
$739$	−33.6755	+	19.4426i	−1.23877	+	0.715206i	−0.269930	+	0.962880i	$0.587000\pi$
$740$	5.00224	+	14.6167i	0.183886	+	0.537321i
$741$	8.31696	−	7.43778i	0.305531	−	0.273234i
$742$	12.4748	−	12.4748i	0.457966	−	0.457966i
$743$	−7.40811	−	1.98500i	−0.271777	−	0.0728225i	0.120356	−	0.992731i	$-0.461596\pi$
$743$	−7.40811	−	1.98500i	−0.271777	−	0.0728225i	−0.392134	+	0.919908i	$0.628263\pi$
$744$	3.00396	−	11.4280i	0.110131	−	0.418972i
$745$	9.01018	−	6.05284i	0.330107	−	0.221759i
$746$			13.0844i			0.479056i
$747$	−0.601373	−	2.16191i	−0.0220031	−	0.0791000i
$748$	−3.18295	+	0.852869i	−0.116380	+	0.0311840i
$749$	−12.8267			−0.468677
$750$	17.2620	−	8.77626i	0.630320	−	0.320464i
$751$	2.85664	+	4.94785i	0.104240	+	0.180549i	0.913428	−	0.407001i	$-0.133426\pi$
$751$	2.85664	+	4.94785i	0.104240	+	0.180549i	−0.809187	+	0.587551i	$0.800092\pi$
$752$	−1.23287	+	4.60115i	−0.0449583	+	0.167787i
$753$	−26.0841	+	0.124025i	−0.950557	+	0.00451974i
$754$	−19.4411	+	29.4098i	−0.708005	+	1.07104i
$755$	−32.6656	−	16.0081i	−1.18882	−	0.582596i
$756$	−22.2400	−	5.62045i	−0.808862	−	0.204414i
$757$	−24.6421	−	6.60283i	−0.895632	−	0.239984i	−0.218492	−	0.975839i	$-0.570114\pi$
$757$	−24.6421	−	6.60283i	−0.895632	−	0.239984i	−0.677139	+	0.735855i	$0.736781\pi$
$758$	8.09098	+	30.1959i	0.293878	+	1.09677i
$759$	9.71941	−	9.81228i	0.352792	−	0.356163i
$760$	−3.92023	−	0.769662i	−0.142202	−	0.0279186i
$761$	5.30759	+	3.06434i	0.192400	+	0.111082i	0.593106	−	0.805125i	$-0.297902\pi$
$761$	5.30759	+	3.06434i	0.192400	+	0.111082i	−0.400706	+	0.916207i	$0.631235\pi$
$762$	−0.0627533	−	13.1978i	−0.00227331	−	0.478106i
$763$	41.2185	−	11.0445i	1.49221	−	0.399836i
$764$	4.38695	+	7.59842i	0.158714	+	0.274901i
$765$	−15.0833	+	17.6211i	−0.545338	+	0.637094i
$766$	31.8174			1.14961
$767$	1.54201	+	7.55657i	0.0556789	+	0.272852i
$768$	0.00823552	+	1.73203i	0.000297174	+	0.0624993i
$769$	11.2286	−	6.48284i	0.404914	−	0.233777i	−0.283688	−	0.958917i	$-0.591558\pi$
$769$	11.2286	−	6.48284i	0.404914	−	0.233777i	0.688602	+	0.725139i	$0.258225\pi$
$770$	−9.38589	+	0.638605i	−0.338244	+	0.0230137i
$771$	3.79794	+	13.9092i	0.136780	+	0.500929i
$772$	−5.68413	+	5.68413i	−0.204576	+	0.204576i
$773$	9.04811	+	33.7680i	0.325438	+	1.21455i	0.913871	+	0.406005i	$0.133078\pi$
$773$	9.04811	+	33.7680i	0.325438	+	1.21455i	−0.588433	+	0.808546i	$0.700255\pi$
$774$	−24.5906	−	13.8873i	−0.883889	−	0.499167i
$775$	−20.8994	−	26.9582i	−0.750728	−	0.968367i
$776$	−6.39795	−	3.69386i	−0.229673	−	0.132602i
$777$	−26.6317	−	45.6251i	−0.955407	−	1.63679i
$778$	0.306772	−	1.14489i	0.0109983	−	0.0410463i
$779$	5.44912			0.195235
$780$	−13.4434	+	3.77834i	−0.481350	+	0.135286i
$781$	5.49302			0.196556
$782$	7.48786	−	27.9451i	0.267765	−	0.999314i
$783$	−43.6337	+	26.0287i	−1.55934	+	0.930192i
$784$	−10.8159	−	6.24459i	−0.386284	−	0.223021i
$785$	5.63706	−	1.92916i	0.201195	−	0.0688545i
$786$	36.9316	−	10.0843i	1.31731	−	0.359693i
$787$	−1.23030	−	4.59153i	−0.0438554	−	0.163671i	0.940525	−	0.339724i	$-0.110334\pi$
$787$	−1.23030	−	4.59153i	−0.0438554	−	0.163671i	−0.984381	+	0.176053i	$0.943667\pi$
$788$	−13.9786	+	13.9786i	−0.497969	+	0.497969i
$789$	0.234251	−	0.0639626i	0.00833955	−	0.00227713i
$790$	8.46002	+	7.38214i	0.300994	+	0.262645i
$791$	−15.1831	+	8.76594i	−0.539847	+	0.311681i
$792$	−2.04077	−	2.00232i	−0.0725156	−	0.0711493i
$793$	2.68625	+	13.1638i	0.0953914	+	0.467462i
$794$	−6.84293			−0.242847
$795$	10.1205	−	11.7101i	0.358936	−	0.415315i
$796$	−7.63633	−	13.2265i	−0.270663	−	0.468801i
$797$	−49.8892	+	13.3678i	−1.76717	+	0.473511i	−0.988150	−	0.153492i	$-0.950948\pi$
$797$	−49.8892	+	13.3678i	−1.76717	+	0.473511i	−0.779017	+	0.627003i	$0.784281\pi$
$798$	13.6613	−	0.0649571i	0.483604	−	0.00229946i
$799$	−14.2640	−	8.23534i	−0.504625	−	0.291345i
$800$	3.98184	+	3.02406i	0.140779	+	0.106917i
$801$	8.41855	−	0.0800594i	0.297455	−	0.00282876i
$802$	−4.66413	−	17.4068i	−0.164696	−	0.614654i
$803$	5.01949	+	1.34497i	0.177134	+	0.0474629i
$804$	−23.4259	−	6.15772i	−0.826167	−	0.217166i
$805$	36.3467	−	74.1678i	1.28105	−	2.61407i
$806$	10.9882	+	22.0067i	0.387044	+	0.775152i
$807$	0.0645875	+	13.5836i	0.00227359	+	0.478164i
$808$	−0.498735	+	1.86130i	−0.0175454	+	0.0654804i
$809$	−7.29175	−	12.6297i	−0.256364	−	0.444036i	0.708901	−	0.705308i	$-0.249191\pi$
$809$	−7.29175	−	12.6297i	−0.256364	−	0.444036i	−0.965265	+	0.261272i	$0.915858\pi$
$810$	−19.8178	−	3.50081i	−0.696326	−	0.123006i
$811$	36.2063			1.27138			0.635688	−	0.771946i	$-0.280717\pi$
$811$	36.2063			1.27138			0.635688	+	0.771946i	$0.280717\pi$
$812$	−41.6952	+	11.1722i	−1.46321	+	0.392067i
$813$	1.54460	+	0.882011i	0.0541716	+	0.0309335i
$814$		−	6.58433i		−	0.230781i
$815$	34.7037	+	6.81341i	1.21562	+	0.238663i
$816$	−5.79218	−	1.52253i	−0.202767	−	0.0532991i
$817$	16.2458	+	4.35305i	0.568369	+	0.152294i
$818$	3.89603	−	3.89603i	0.136222	−	0.136222i
$819$	42.5174	−	21.7371i	1.48568	−	0.759555i
$820$	−6.12397	−	3.00112i	−0.213858	−	0.104804i
$821$	−48.2569	+	27.8611i	−1.68418	+	0.972360i	−0.725346	+	0.688385i	$0.758320\pi$
$821$	−48.2569	+	27.8611i	−1.68418	+	0.972360i	−0.958832	+	0.283975i	$0.908347\pi$
$822$	−2.13942	−	3.66523i	−0.0746210	−	0.127840i
$823$	−16.2640	+	4.35793i	−0.566928	+	0.151908i	−0.530887	−	0.847442i	$-0.678141\pi$
$823$	−16.2640	+	4.35793i	−0.566928	+	0.151908i	−0.0360408	+	0.999350i	$0.511475\pi$
$824$	−6.95139			−0.242163
$825$	−8.17183	+	1.15678i	−0.284506	+	0.0402740i
$826$	−4.72149	+	8.17786i	−0.164282	+	0.284544i
$827$	−16.1654	−	16.1654i	−0.562127	−	0.562127i	0.367784	−	0.929911i	$-0.380117\pi$
$827$	−16.1654	−	16.1654i	−0.562127	−	0.562127i	−0.929911	+	0.367784i	$0.880117\pi$
$828$	24.1830	−	6.72693i	0.840417	−	0.233777i
$829$	2.40846	−	1.39053i	0.0836494	−	0.0482950i	−0.457592	−	0.889162i	$-0.651288\pi$
$829$	2.40846	−	1.39053i	0.0836494	−	0.0482950i	0.541241	+	0.840867i	$0.317955\pi$
$830$	−0.113537	−	1.66871i	−0.00394093	−	0.0579218i
$831$	−38.2589	−	37.8968i	−1.32719	−	1.31462i
$832$	−2.39069	−	2.69900i	−0.0828823	−	0.0935709i
$833$	30.5357	−	30.5357i	1.05800	−	1.05800i
$834$	−6.33718	+	24.1086i	−0.219439	+	0.834813i
$835$	−17.2949	+	19.8202i	−0.598516	+	0.685906i
$836$	1.47457	+	0.851346i	0.0509992	+	0.0294444i
$837$	0.505637	+	35.4451i	0.0174774	+	1.22516i
$838$	21.0500	−	5.64034i	0.727161	−	0.194842i
$839$	17.8628	−	30.9393i	0.616694	−	1.06814i	−0.373391	−	0.927674i	$-0.621805\pi$
$839$	17.8628	−	30.9393i	0.616694	−	1.06814i	0.990085	−	0.140471i	$-0.0448616\pi$
$840$	−15.3890	−	7.45100i	−0.530970	−	0.257084i
$841$	−33.3036	+	57.6835i	−1.14840	+	1.98909i
$842$	−1.82735	+	6.81976i	−0.0629746	+	0.235024i
$843$	11.2279	+	19.2355i	0.386710	+	0.662507i
$844$			6.18513i			0.212901i
$845$	15.8493	−	24.3680i	0.545232	−	0.838285i
$846$	−0.135894	−	14.2897i	−0.00467212	−	0.491291i
$847$	−43.0336	−	11.5308i	−1.47865	−	0.396204i
$848$	3.86009	+	1.03431i	0.132556	+	0.0355182i
$849$	6.78734	+	24.8573i	0.232941	+	0.853101i
$850$	−13.6635	+	10.5926i	−0.468654	+	0.363324i
$851$	50.0631	+	28.9039i	1.71614	+	0.990814i
$852$	8.66944	+	4.95049i	0.297010	+	0.169601i
$853$	−6.16440	−	6.16440i	−0.211065	−	0.211065i	0.593655	−	0.804720i	$-0.297684\pi$
$853$	−6.16440	−	6.16440i	−0.211065	−	0.211065i	−0.804720	+	0.593655i	$0.797684\pi$
$854$	−8.22502	+	14.2462i	−0.281454	+	0.487493i
$855$	11.9493	−	0.927251i	0.408657	−	0.0317113i
$856$	−1.45274	−	2.51622i	−0.0496536	−	0.0860025i
$857$	−12.5624	−	12.5624i	−0.429122	−	0.429122i	0.459207	−	0.888329i	$-0.348134\pi$
$857$	−12.5624	−	12.5624i	−0.429122	−	0.429122i	−0.888329	+	0.459207i	$0.848134\pi$
$858$	5.94229	+	0.331602i	0.202866	+	0.0113207i
$859$		−	47.0383i		−	1.60493i	−0.596701	−	0.802464i	$-0.703522\pi$
$859$		−	47.0383i		−	1.60493i	0.596701	−	0.802464i	$-0.296478\pi$
$860$	−15.8603	−	13.8396i	−0.540833	−	0.471926i
$861$	22.5547	+	5.92871i	0.768661	+	0.202050i
$862$	1.08127	+	4.03535i	0.0368281	+	0.137444i
$863$	−12.6661	+	12.6661i	−0.431160	+	0.431160i	−0.889023	−	0.457863i	$-0.848615\pi$
$863$	−12.6661	+	12.6661i	−0.431160	+	0.431160i	0.457863	+	0.889023i	$0.348615\pi$
$864$	−1.41632	−	4.99940i	−0.0481841	−	0.170083i
$865$	1.74773	−	8.90195i	0.0594246	−	0.302675i
$866$		−	22.2778i		−	0.757031i
$867$	−4.33238	+	7.58699i	−0.147135	+	0.257668i
$868$	−7.79492	+	29.0910i	−0.264577	+	0.987414i
$869$	−2.39268	−	4.14424i	−0.0811660	−	0.140584i
$870$	−35.7708	+	12.4321i	−1.21274	+	0.421486i
$871$	45.1107	−	22.5244i	1.52852	−	0.763209i
$872$	6.83496	+	6.83496i	0.231461	+	0.231461i
$873$	21.4615	+	5.53241i	0.726363	+	0.187244i
$874$	−12.9462	+	7.47449i	−0.437912	+	0.252828i
$875$	−44.1033	+	22.1595i	−1.49096	+	0.749128i
$876$	6.70995	+	6.64645i	0.226708	+	0.224563i
$877$	13.6622	+	50.9881i	0.461341	+	1.72175i	0.668745	+	0.743492i	$0.266832\pi$
$877$	13.6622	+	50.9881i	0.461341	+	1.72175i	−0.207404	+	0.978255i	$0.566502\pi$
$878$	−2.01882	−	7.53433i	−0.0681318	−	0.254271i
$879$	−13.3552	−	13.2288i	−0.450459	−	0.446196i
$880$	−1.18831	−	1.76891i	−0.0400580	−	0.0596299i
$881$	−21.3667	+	12.3361i	−0.719863	+	0.415613i	−0.814702	−	0.579880i	$-0.803100\pi$
$881$	−21.3667	+	12.3361i	−0.719863	+	0.415613i	0.0948394	+	0.995493i	$0.469766\pi$
$882$	36.2814	+	9.35272i	1.22166	+	0.314922i
$883$	4.86578	+	4.86578i	0.163747	+	0.163747i	0.784224	−	0.620478i	$-0.213061\pi$
$883$	4.86578	+	4.86578i	0.163747	+	0.163747i	−0.620478	+	0.784224i	$0.713061\pi$
$884$	11.1539	−	5.56927i	0.375145	−	0.187315i
$885$	−3.61019	+	7.45633i	−0.121355	+	0.250642i
$886$	12.6049	+	21.8323i	0.423470	+	0.733472i
$887$	−9.38974	+	35.0430i	−0.315276	+	1.17663i	0.608455	+	0.793588i	$0.291789\pi$
$887$	−9.38974	+	35.0430i	−0.315276	+	1.17663i	−0.923732	+	0.383040i	$0.874877\pi$
$888$	5.93402	−	10.3918i	0.199133	−	0.348727i
$889$			33.6390i			1.12821i
$890$	6.15755	+	1.20892i	0.206402	+	0.0405230i
$891$	7.50818	+	4.14650i	0.251534	+	0.138913i
$892$	2.65814	−	2.65814i	0.0890012	−	0.0890012i
$893$	2.20271	+	8.22063i	0.0737110	+	0.275093i
$894$	−8.13163	−	2.13748i	−0.271962	−	0.0714879i
$895$	1.63566	+	24.0401i	0.0546741	+	0.803571i
$896$		−	4.41465i		−	0.147483i
$897$	−28.6068	+	43.7258i	−0.955154	+	1.45996i
$898$	−5.55405	−	5.55405i	−0.185341	−	0.185341i
$899$	33.3529	+	57.7690i	1.11238	+	1.92670i
$900$	−13.9398	−	5.53902i	−0.464662	−	0.184634i
$901$	−6.90896	+	11.9667i	−0.230171	+	0.398667i
$902$	2.05527	+	2.05527i	0.0684330	+	0.0684330i
$903$	62.5075	+	35.6935i	2.08012	+	1.18781i
$904$	−3.43924	−	1.98565i	−0.114387	−	0.0660416i
$905$	12.6063	+	6.17784i	0.419047	+	0.205358i
$906$	7.42225	+	27.1826i	0.246588	+	0.903080i
$907$	−29.1710	−	7.81634i	−0.968606	−	0.259537i	−0.260367	−	0.965510i	$-0.583844\pi$
$907$	−29.1710	−	7.81634i	−0.968606	−	0.259537i	−0.708239	+	0.705972i	$0.750510\pi$
$908$	−8.67677	−	2.32493i	−0.287949	−	0.0771557i
$909$	−0.0549731	−	5.78063i	−0.00182334	−	0.191731i
$910$	34.3099	−	9.46721i	1.13736	−	0.313835i
$911$		−	9.47315i		−	0.313859i	−0.987610	−	0.156930i	$-0.949840\pi$
$911$		−	9.47315i		−	0.313859i	0.987610	−	0.156930i	$-0.0501596\pi$
$912$	1.56001	+	2.67259i	0.0516570	+	0.0884981i
$913$	−0.184498	+	0.688557i	−0.00610600	+	0.0227879i
$914$	13.4736	−	23.3370i	0.445668	−	0.771919i
$915$	−6.28909	+	12.9892i	−0.207911	+	0.429410i
$916$	7.89187	−	13.6691i	0.260755	−	0.451640i
$917$	−94.2525	+	25.2549i	−3.11249	+	0.833990i
$918$	17.9650	−	0.256277i	0.592933	−	0.00845840i
$919$	−33.2844	−	19.2168i	−1.09795	−	0.633902i	−0.162269	−	0.986747i	$-0.551881\pi$
$919$	−33.2844	−	19.2168i	−1.09795	−	0.633902i	−0.935682	+	0.352844i	$0.885214\pi$
$920$	18.6661	−	1.27002i	0.615404	−	0.0418714i
$921$	−1.72701	+	6.57010i	−0.0569070	+	0.216492i
$922$	−2.42444	+	2.42444i	−0.0798446	+	0.0798446i
$923$	−20.3623	+	4.15518i	−0.670233	+	0.136769i
$924$	5.17719	+	5.12819i	0.170317	+	0.168705i
$925$	−13.3782	−	31.8493i	−0.439872	−	1.04720i
$926$	−6.28712	+	3.62987i	−0.206608	+	0.119285i
$927$	20.0914	−	5.58877i	0.659887	−	0.183559i
$928$	−6.91401	−	6.91401i	−0.226964	−	0.226964i
$929$	28.2306	−	48.8968i	0.926215	−	1.60425i	0.136620	−	0.990624i	$-0.456376\pi$
$929$	28.2306	−	48.8968i	0.926215	−	1.60425i	0.789595	−	0.613628i	$-0.210290\pi$
$930$	−4.96693	+	25.9509i	−0.162872	+	0.850962i
$931$	−22.3138			−0.731304
$932$	−12.1656	+	3.25976i	−0.398497	+	0.106777i
$933$	−2.80939	−	4.81300i	−0.0919752	−	0.157571i
$934$	16.5436	−	9.55148i	0.541325	−	0.312534i
$935$	6.97142	−	2.38581i	0.227990	−	0.0780243i
$936$	9.07966	+	5.87875i	0.296778	+	0.192153i
$937$	29.6775	−	29.6775i	0.969522	−	0.969522i	−0.0300273	−	0.999549i	$-0.509559\pi$
$937$	29.6775	−	29.6775i	0.969522	−	0.969522i	0.999549	+	0.0300273i	$0.00955941\pi$
$938$	59.6326	+	15.9785i	1.94707	+	0.521717i
$939$	−22.1054	−	5.81061i	−0.721382	−	0.189622i
$940$	2.05203	−	10.4519i	0.0669298	−	0.340903i
$941$		−	41.0420i		−	1.33793i	−0.743293	−	0.668966i	$-0.766737\pi$
$941$		−	41.0420i		−	1.33793i	0.743293	−	0.668966i	$-0.233263\pi$
$942$	−4.00769	−	2.28850i	−0.130578	−	0.0745635i
$943$	−24.6492	+	6.60474i	−0.802690	+	0.215080i
$944$	−2.13901			−0.0696188
$945$	50.4686	+	9.16294i	1.64174	+	0.298070i
$946$	4.48565	+	7.76937i	0.145841	+	0.252604i
$947$	11.8703	−	44.3006i	0.385733	−	1.43958i	−0.451275	−	0.892385i	$-0.649030\pi$
$947$	11.8703	−	44.3006i	0.385733	−	1.43958i	0.837008	−	0.547191i	$-0.184303\pi$
$948$	−0.0413531	−	8.69707i	−0.00134309	−	0.282468i
$949$	−19.6243	−	1.18874i	−0.637033	−	0.0385880i
$950$	8.86250	+	1.12200i	0.287538	+	0.0364026i
$951$	53.1403	+	13.9684i	1.72319	+	0.452958i
$952$	14.7445	+	3.95077i	0.477872	+	0.128045i
$953$	−0.673945	−	2.51520i	−0.0218312	−	0.0814752i	0.954151	−	0.299326i	$-0.0967619\pi$
$953$	−0.673945	−	2.51520i	−0.0218312	−	0.0814752i	−0.975982	+	0.217851i	$0.930095\pi$
$954$	−11.9882	+	0.114007i	−0.388133	+	0.00369110i
$955$	−10.9402	−	16.2855i	−0.354018	−	0.526987i
$956$	11.2758	+	6.51011i	0.364687	+	0.210552i
$957$	16.1398	−	0.0767420i	0.521725	−	0.00248072i
$958$	−13.0832	+	3.50563i	−0.422699	+	0.113262i
$959$	5.40849	+	9.36778i	0.174649	+	0.302501i
$960$	−0.281275	−	3.86276i	−0.00907812	−	0.124670i
$961$	15.5412			0.501328
$962$	4.98070	+	24.4077i	0.160584	+	0.786936i
$963$	6.22178	+	6.10456i	0.200494	+	0.196717i
$964$	−2.85369	+	1.64758i	−0.0919110	+	0.0530649i
$965$	11.8180	−	13.5436i	0.380435	−	0.435983i
$966$	−61.7185	+	16.8523i	−1.98576	+	0.542215i
$967$	8.05593	−	8.05593i	0.259061	−	0.259061i	−0.565611	−	0.824672i	$-0.691360\pi$
$967$	8.05593	−	8.05593i	0.259061	−	0.259061i	0.824672	+	0.565611i	$0.191360\pi$
$968$	−2.61194	−	9.74791i	−0.0839510	−	0.313310i
$969$	−10.3222	+	2.81851i	−0.331598	+	0.0905436i
$970$	14.8339	+	7.26953i	0.476289	+	0.233411i
$971$	−10.7906	−	6.22993i	−0.346286	−	0.199928i	0.316763	−	0.948505i	$-0.397404\pi$
$971$	−10.7906	−	6.22993i	−0.346286	−	0.199928i	−0.663048	+	0.748577i	$0.730738\pi$
$972$	8.11294	+	13.3109i	0.260223	+	0.426947i
$973$	16.4442	−	61.3706i	0.527177	−	1.96745i
$974$	30.0342			0.962357
$975$	29.4174	−	10.4697i	0.942112	−	0.335298i
$976$	−3.72624			−0.119274
$977$	−6.50283	+	24.2689i	−0.208044	+	0.776430i	0.780456	+	0.625210i	$0.214987\pi$
$977$	−6.50283	+	24.2689i	−0.208044	+	0.776430i	−0.988500	+	0.151220i	$0.951680\pi$
$978$	−13.8099	−	23.6590i	−0.441592	−	0.756530i
$979$	−2.31613	−	1.33722i	−0.0740239	−	0.0427377i
$980$	25.0773	+	12.2894i	0.801064	+	0.392570i
$981$	−25.2500	−	14.2597i	−0.806171	−	0.455277i
$982$	−0.0840301	−	0.313604i	−0.00268151	−	0.0100075i
$983$	−10.7567	+	10.7567i	−0.343087	+	0.343087i	−0.857527	−	0.514440i	$-0.828000\pi$
$983$	−10.7567	+	10.7567i	−0.343087	+	0.343087i	0.514440	+	0.857527i	$0.328000\pi$
$984$	1.39148	+	5.09604i	0.0443589	+	0.162456i
$985$	29.0633	−	33.3069i	0.926034	−	1.06125i
$986$	29.2796	−	16.9046i	0.932452	−	0.538352i
$987$	0.173185	+	36.4229i	0.00551254	+	1.15935i
$988$	−6.11016	−	2.04045i	−0.194390	−	0.0649154i
$989$	−78.7645			−2.50457
$990$	4.85670	+	4.15723i	0.154356	+	0.132125i
$991$	20.5646	+	35.6190i	0.653257	+	1.13148i	0.982328	+	0.187170i	$0.0599314\pi$
$991$	20.5646	+	35.6190i	0.653257	+	1.13148i	−0.329070	+	0.944305i	$0.606735\pi$
$992$	−6.58965	+	1.76569i	−0.209222	+	0.0560608i
$993$	−0.174678	−	36.7369i	−0.00554323	−	1.16581i
$994$	−22.0364	−	12.7227i	−0.698954	−	0.403541i
$995$	19.0436	+	28.3481i	0.603723	+	0.898694i
$996$	−0.911738	+	0.920450i	−0.0288895	+	0.0291656i
$997$	7.10168	+	26.5038i	0.224913	+	0.839385i	0.982440	+	0.186581i	$0.0597408\pi$
$997$	7.10168	+	26.5038i	0.224913	+	0.839385i	−0.757527	+	0.652804i	$0.773593\pi$
$998$	−6.37225	−	1.70744i	−0.201710	−	0.0540481i
$999$	−8.79607	+	34.8059i	−0.278295	+	1.10121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bl.a.263.26	yes	112
3.2	odd	2	inner	390.2.bl.a.263.5	yes	112
5.2	odd	4	inner	390.2.bl.a.107.19	yes	112
13.9	even	3	inner	390.2.bl.a.113.3	yes	112
15.2	even	4	inner	390.2.bl.a.107.3	✓	112
39.35	odd	6	inner	390.2.bl.a.113.19	yes	112
65.22	odd	12	inner	390.2.bl.a.347.5	yes	112
195.152	even	12	inner	390.2.bl.a.347.26	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bl.a.107.3	✓	112	15.2	even	4	inner
390.2.bl.a.107.19	yes	112	5.2	odd	4	inner
390.2.bl.a.113.3	yes	112	13.9	even	3	inner
390.2.bl.a.113.19	yes	112	39.35	odd	6	inner
390.2.bl.a.263.5	yes	112	3.2	odd	2	inner
390.2.bl.a.263.26	yes	112	1.1	even	1	trivial
390.2.bl.a.347.5	yes	112	65.22	odd	12	inner
390.2.bl.a.347.26	yes	112	195.152	even	12	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bl (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.49587 - 0.873148i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00792 + 0.984002i) q^{5} +(-0.456238 - 1.67088i) q^{6} +(1.14260 + 4.26423i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47523 - 2.61222i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(1.49587 - 0.873148i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.00792 + 0.984002i) q^{5} +(-0.456238 - 1.67088i) q^{6} +(1.14260 + 4.26423i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.47523 - 2.61222i) q^{9} +(1.47016 - 1.68482i) q^{10} +(-0.825330 + 0.476504i) q^{11} +(-1.73203 + 0.00823552i) q^{12} +(2.69900 - 2.39069i) q^{13} +4.41465 q^{14} +(3.86276 - 0.281275i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.33990 + 0.894923i) q^{17} +(-2.14140 - 2.10105i) q^{18} +(1.54728 + 0.893324i) q^{19} +(-1.24691 - 1.85613i) q^{20} +(5.43247 + 5.38106i) q^{21} +(0.246657 + 0.920535i) q^{22} +(-8.08195 - 2.16555i) q^{23} +(-0.440328 + 1.67515i) q^{24} +(3.06348 + 3.95159i) q^{25} +(-1.61068 - 3.22579i) q^{26} +(-0.0741174 - 5.19562i) q^{27} +(1.14260 - 4.26423i) q^{28} +(-4.88895 - 8.46790i) q^{29} +(0.728064 - 3.80394i) q^{30} -6.82211 q^{31} +(0.965926 - 0.258819i) q^{32} +(-0.818523 + 1.43342i) q^{33} +3.45772i q^{34} +(-1.90177 + 9.68655i) q^{35} +(-2.58369 + 1.52464i) q^{36} +(-6.67357 - 1.78818i) q^{37} +(1.26335 - 1.26335i) q^{38} +(1.94991 - 5.93278i) q^{39} +(-2.11561 + 0.724018i) q^{40} +(2.64130 - 1.52496i) q^{41} +(6.60373 - 3.85465i) q^{42} +(9.09289 - 2.43643i) q^{43} +0.953008 q^{44} +(5.53257 - 3.79351i) q^{45} +(-4.18353 + 7.24608i) q^{46} +(3.36827 + 3.36827i) q^{47} +(1.50410 + 0.858883i) q^{48} +(-10.8159 + 6.24459i) q^{49} +(4.60983 - 1.93635i) q^{50} +(-4.21464 + 4.25491i) q^{51} +(-3.53275 + 0.720901i) q^{52} +(2.82578 - 2.82578i) q^{53} +(-5.03777 - 1.27313i) q^{54} +(-2.12608 + 0.144656i) q^{55} +(-3.82320 - 2.20733i) q^{56} +(3.09453 - 0.0147140i) q^{57} +(-9.44472 + 2.53070i) q^{58} +(-1.06950 + 1.85244i) q^{59} +(-3.48588 - 1.68779i) q^{60} +(-1.86312 + 3.22701i) q^{61} +(-1.76569 + 6.58965i) q^{62} +(12.8247 + 3.30598i) q^{63} -1.00000i q^{64} +(7.77182 - 2.14450i) q^{65} +(1.17273 + 1.16163i) q^{66} +(13.5079 + 3.61943i) q^{67} +(3.33990 + 0.894923i) q^{68} +(-13.9804 + 3.81736i) q^{69} +(8.86427 + 4.34403i) q^{70} +(-4.99166 - 2.88194i) q^{71} +(0.803978 + 2.89026i) q^{72} +(-3.85570 - 3.85570i) q^{73} +(-3.45450 + 5.98336i) q^{74} +(8.03288 + 3.23618i) q^{75} +(-0.893324 - 1.54728i) q^{76} +(-2.97494 - 2.97494i) q^{77} +(-5.22595 - 3.41898i) q^{78} +5.02131i q^{79} +(0.151789 + 2.23091i) q^{80} +(-4.64742 - 7.70724i) q^{81} +(-0.789375 - 2.94599i) q^{82} +(0.528913 - 0.528913i) q^{83} +(-2.01413 - 7.37637i) q^{84} +(-7.58685 - 1.48953i) q^{85} -9.41365i q^{86} +(-14.7069 - 8.39807i) q^{87} +(0.246657 - 0.920535i) q^{88} +(1.40316 + 2.43034i) q^{89} +(-2.23231 - 6.32588i) q^{90} +(13.2783 + 8.77755i) q^{91} +(5.91640 + 5.91640i) q^{92} +(-10.2050 + 5.95671i) q^{93} +(4.12528 - 2.38173i) q^{94} +(2.22779 + 3.31625i) q^{95} +(1.21891 - 1.23055i) q^{96} +(1.91208 + 7.13599i) q^{97} +(3.23244 + 12.0636i) q^{98} +(0.0271878 + 2.85890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q + 24 q^{13} + 56 q^{16} - 16 q^{18} - 16 q^{21} + 24 q^{27} + 12 q^{30} - 80 q^{31} + 52 q^{33} - 8 q^{36} - 8 q^{37} - 16 q^{40} + 12 q^{42} - 8 q^{43} + 20 q^{45} - 8 q^{46} - 80 q^{51} + 24 q^{52} + 8 q^{55} - 96 q^{57} + 8 q^{58} - 32 q^{60} - 16 q^{61} - 16 q^{63} - 32 q^{66} + 40 q^{67} - 32 q^{70} - 8 q^{72} - 80 q^{73} - 64 q^{75} + 16 q^{76} - 36 q^{78} + 8 q^{81} - 16 q^{82} + 96 q^{85} - 8 q^{87} + 24 q^{90} - 32 q^{91} - 68 q^{93} - 40 q^{97}+O(q^{100}) \) 112 * q + 24 * q^13 + 56 * q^16 - 16 * q^18 - 16 * q^21 + 24 * q^27 + 12 * q^30 - 80 * q^31 + 52 * q^33 - 8 * q^36 - 8 * q^37 - 16 * q^40 + 12 * q^42 - 8 * q^43 + 20 * q^45 - 8 * q^46 - 80 * q^51 + 24 * q^52 + 8 * q^55 - 96 * q^57 + 8 * q^58 - 32 * q^60 - 16 * q^61 - 16 * q^63 - 32 * q^66 + 40 * q^67 - 32 * q^70 - 8 * q^72 - 80 * q^73 - 64 * q^75 + 16 * q^76 - 36 * q^78 + 8 * q^81 - 16 * q^82 + 96 * q^85 - 8 * q^87 + 24 * q^90 - 32 * q^91 - 68 * q^93 - 40 * q^97

Introduction

L-functions

Modular forms

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