LMFDB - Embedded newform 546.2.bw.a.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.73001 + 0.0839781i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.83225 + 0.758898i) q^{5} +(-0.528877 - 1.64933i) q^{6} +(-2.04314 + 1.68095i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98590 - 0.290567i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.73001 + 0.0839781i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.83225 + 0.758898i) q^{5} +(-0.528877 - 1.64933i) q^{6} +(-2.04314 + 1.68095i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98590 - 0.290567i) q^{9} +2.93216i q^{10} +(-0.0946467 - 0.0946467i) q^{11} +(1.45625 - 0.937734i) q^{12} +(1.73700 + 3.15956i) q^{13} +(-2.15247 - 1.53846i) q^{14} +(-4.96355 - 1.07506i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.08009 + 1.87078i) q^{17} +(1.05347 + 2.80895i) q^{18} +(-2.23830 - 2.23830i) q^{19} +(-2.83225 + 0.758898i) q^{20} +(3.39350 - 3.07964i) q^{21} +(0.0669254 - 0.115918i) q^{22} +(-3.38136 + 5.85668i) q^{23} +(1.28269 + 1.16392i) q^{24} +(3.11556 + 1.79877i) q^{25} +(-2.60233 + 2.49557i) q^{26} +(-5.14124 + 0.753434i) q^{27} +(0.928939 - 2.47731i) q^{28} +(-5.12781 + 2.96054i) q^{29} +(-0.246237 - 5.07267i) q^{30} +(2.47109 - 0.662128i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.171688 + 0.155792i) q^{33} +(-1.52748 + 1.52748i) q^{34} +(-7.06234 + 3.21031i) q^{35} +(-2.44058 + 1.74459i) q^{36} +(2.44342 + 9.11897i) q^{37} +(1.58272 - 2.74135i) q^{38} +(-3.27038 - 5.32021i) q^{39} +(-1.46608 - 2.53932i) q^{40} +(-8.14459 - 2.18234i) q^{41} +(3.85300 + 2.48080i) q^{42} +(2.46872 + 1.42532i) q^{43} +(0.129290 + 0.0346431i) q^{44} +(8.67730 + 1.44303i) q^{45} +(-6.53228 - 1.75032i) q^{46} +(0.420550 - 1.56951i) q^{47} +(-0.792280 + 1.54022i) q^{48} +(1.34885 - 6.86881i) q^{49} +(-0.931112 + 3.47496i) q^{50} +(-2.02568 - 3.14576i) q^{51} +(-3.08407 - 1.86776i) q^{52} +(-5.19889 - 3.00158i) q^{53} +(-2.05841 - 4.77105i) q^{54} +(-0.196236 - 0.339890i) q^{55} +(2.63333 + 0.256111i) q^{56} +(4.06026 + 3.68432i) q^{57} +(-4.18684 - 4.18684i) q^{58} +(0.837676 - 3.12625i) q^{59} +(4.83609 - 1.55075i) q^{60} +3.62498 q^{61} +(1.27913 + 2.21552i) q^{62} +(-5.61218 + 5.61279i) q^{63} +1.00000i q^{64} +(2.52184 + 10.2669i) q^{65} +(-0.106047 + 0.206160i) q^{66} +(2.72663 + 2.72663i) q^{67} +(-1.87078 - 1.08009i) q^{68} +(5.35796 - 10.4161i) q^{69} +(-4.92879 - 5.99081i) q^{70} +(2.50530 + 9.34991i) q^{71} +(-2.31681 - 1.90589i) q^{72} +(0.235334 + 0.878279i) q^{73} +(-8.17585 + 4.72033i) q^{74} +(-5.54102 - 2.85026i) q^{75} +(3.05758 + 0.819275i) q^{76} +(0.352473 + 0.0342806i) q^{77} +(4.29249 - 4.53591i) q^{78} +(4.27906 + 7.41154i) q^{79} +(2.07335 - 2.07335i) q^{80} +(8.83114 - 1.73520i) q^{81} -8.43190i q^{82} +(11.9054 - 11.9054i) q^{83} +(-1.39904 + 4.36379i) q^{84} +(1.63936 + 6.11818i) q^{85} +(-0.737798 + 2.75350i) q^{86} +(8.62256 - 5.55240i) q^{87} +0.133851i q^{88} +(-10.6072 + 2.84220i) q^{89} +(0.851987 + 8.75511i) q^{90} +(-8.85999 - 3.53562i) q^{91} -6.76271i q^{92} +(-4.21942 + 1.35301i) q^{93} +1.62488 q^{94} +(-4.64078 - 8.03806i) q^{95} +(-1.69280 - 0.366644i) q^{96} +(8.60864 - 2.30668i) q^{97} +(6.98387 - 0.474894i) q^{98} +(-0.310106 - 0.255104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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
$3$	−1.73001	+	0.0839781i	−0.998824	+	0.0484848i
$3$	−1.73001	+	0.0839781i	−0.998824	+	0.0484848i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.83225	+	0.758898i	1.26662	+	0.339389i	0.828734	−	0.559642i	$-0.189061\pi$
$5$	2.83225	+	0.758898i	1.26662	+	0.339389i	0.437884	+	0.899031i	$0.355728\pi$
$6$	−0.528877	−	1.64933i	−0.215913	−	0.673336i
$7$	−2.04314	+	1.68095i	−0.772235	+	0.635338i
$7$	−2.04314	+	1.68095i	−0.772235	+	0.635338i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.98590	−	0.290567i	0.995298	−	0.0968555i
$10$			2.93216i			0.927229i
$11$	−0.0946467	−	0.0946467i	−0.0285371	−	0.0285371i	0.692694	−	0.721231i	$-0.256424\pi$
$11$	−0.0946467	−	0.0946467i	−0.0285371	−	0.0285371i	−0.721231	+	0.692694i	$0.756424\pi$
$12$	1.45625	−	0.937734i	0.420382	−	0.270701i
$13$	1.73700	+	3.15956i	0.481758	+	0.876304i
$13$	1.73700	+	3.15956i	0.481758	+	0.876304i
$14$	−2.15247	−	1.53846i	−0.575272	−	0.411171i
$15$	−4.96355	−	1.07506i	−1.28158	−	0.277579i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.08009	+	1.87078i	0.261961	+	0.453730i	0.966763	−	0.255674i	$-0.0822975\pi$
$17$	1.08009	+	1.87078i	0.261961	+	0.453730i	−0.704802	+	0.709404i	$0.748964\pi$
$18$	1.05347	+	2.80895i	0.248306	+	0.662076i
$19$	−2.23830	−	2.23830i	−0.513501	−	0.513501i	0.402096	−	0.915597i	$-0.368282\pi$
$19$	−2.23830	−	2.23830i	−0.513501	−	0.513501i	−0.915597	+	0.402096i	$0.868282\pi$
$20$	−2.83225	+	0.758898i	−0.633309	+	0.169695i
$21$	3.39350	−	3.07964i	0.740522	−	0.672032i
$22$	0.0669254	−	0.115918i	0.0142685	−	0.0247138i
$23$	−3.38136	+	5.85668i	−0.705062	+	1.22120i	0.261608	+	0.965174i	$0.415747\pi$
$23$	−3.38136	+	5.85668i	−0.705062	+	1.22120i	−0.966669	+	0.256028i	$0.917586\pi$
$24$	1.28269	+	1.16392i	0.261827	+	0.237585i
$25$	3.11556	+	1.79877i	0.623112	+	0.359754i
$26$	−2.60233	+	2.49557i	−0.510359	+	0.489422i
$27$	−5.14124	+	0.753434i	−0.989432	+	0.144998i
$28$	0.928939	−	2.47731i	0.175553	−	0.468168i
$29$	−5.12781	+	2.96054i	−0.952210	+	0.549759i	−0.893767	−	0.448532i	$-0.851947\pi$
$29$	−5.12781	+	2.96054i	−0.952210	+	0.549759i	−0.0584431	+	0.998291i	$0.518614\pi$
$30$	−0.246237	−	5.07267i	−0.0449565	−	0.926139i
$31$	2.47109	−	0.662128i	0.443822	−	0.118922i	−0.0299854	−	0.999550i	$-0.509546\pi$
$31$	2.47109	−	0.662128i	0.443822	−	0.118922i	0.473807	+	0.880629i	$0.342879\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	0.171688	+	0.155792i	0.0298871	+	0.0271199i
$34$	−1.52748	+	1.52748i	−0.261961	+	0.261961i
$35$	−7.06234	+	3.21031i	−1.19375	+	0.542642i
$36$	−2.44058	+	1.74459i	−0.406763	+	0.290764i
$37$	2.44342	+	9.11897i	0.401696	+	1.49915i	0.810069	+	0.586335i	$0.199430\pi$
$37$	2.44342	+	9.11897i	0.401696	+	1.49915i	−0.408373	+	0.912815i	$0.633904\pi$
$38$	1.58272	−	2.74135i	0.256751	−	0.444705i
$39$	−3.27038	−	5.32021i	−0.523679	−	0.851916i
$40$	−1.46608	−	2.53932i	−0.231807	−	0.401502i
$41$	−8.14459	−	2.18234i	−1.27197	−	0.340824i	−0.441186	−	0.897416i	$-0.645442\pi$
$41$	−8.14459	−	2.18234i	−1.27197	−	0.340824i	−0.830786	+	0.556592i	$0.812109\pi$
$42$	3.85300	+	2.48080i	0.594531	+	0.382796i
$43$	2.46872	+	1.42532i	0.376476	+	0.217359i	0.676284	−	0.736641i	$-0.263589\pi$
$43$	2.46872	+	1.42532i	0.376476	+	0.217359i	−0.299808	+	0.954000i	$0.596923\pi$
$44$	0.129290	+	0.0346431i	0.0194912	+	0.00522265i
$45$	8.67730	+	1.44303i	1.29354	+	0.215115i
$46$	−6.53228	−	1.75032i	−0.963132	−	0.258070i
$47$	0.420550	−	1.56951i	0.0613435	−	0.228937i	−0.928447	−	0.371464i	$-0.878856\pi$
$47$	0.420550	−	1.56951i	0.0613435	−	0.228937i	0.989791	+	0.142527i	$0.0455227\pi$
$48$	−0.792280	+	1.54022i	−0.114356	+	0.222312i
$49$	1.34885	−	6.86881i	0.192692	−	0.981259i
$50$	−0.931112	+	3.47496i	−0.131679	+	0.491433i
$51$	−2.02568	−	3.14576i	−0.283652	−	0.440495i
$52$	−3.08407	−	1.86776i	−0.427684	−	0.259011i
$53$	−5.19889	−	3.00158i	−0.714122	−	0.412299i	0.0984632	−	0.995141i	$-0.468607\pi$
$53$	−5.19889	−	3.00158i	−0.714122	−	0.412299i	−0.812586	+	0.582842i	$0.801941\pi$
$54$	−2.05841	−	4.77105i	−0.280114	−	0.649258i
$55$	−0.196236	−	0.339890i	−0.0264604	−	0.0458308i
$56$	2.63333	+	0.256111i	0.351893	+	0.0342242i
$57$	4.06026	+	3.68432i	0.537794	+	0.488000i
$58$	−4.18684	−	4.18684i	−0.549759	−	0.549759i
$59$	0.837676	−	3.12625i	0.109056	−	0.407003i	−0.889718	−	0.456511i	$-0.849099\pi$
$59$	0.837676	−	3.12625i	0.109056	−	0.407003i	0.998774	+	0.0495085i	$0.0157655\pi$
$60$	4.83609	−	1.55075i	0.624337	−	0.200201i
$61$	3.62498			0.464131			0.232065	−	0.972700i	$-0.425452\pi$
$61$	3.62498			0.464131			0.232065	+	0.972700i	$0.425452\pi$
$62$	1.27913	+	2.21552i	0.162450	+	0.281372i
$63$	−5.61218	+	5.61279i	−0.707068	+	0.707146i
$64$			1.00000i			0.125000i
$65$	2.52184	+	10.2669i	0.312796	+	1.27345i
$66$	−0.106047	+	0.206160i	−0.0130535	+	0.0253766i
$67$	2.72663	+	2.72663i	0.333111	+	0.333111i	0.853767	−	0.520655i	$-0.174312\pi$
$67$	2.72663	+	2.72663i	0.333111	+	0.333111i	−0.520655	+	0.853767i	$0.674312\pi$
$68$	−1.87078	−	1.08009i	−0.226865	−	0.130981i
$69$	5.35796	−	10.4161i	0.645023	−	1.25395i
$70$	−4.92879	−	5.99081i	−0.589104	−	0.716038i
$71$	2.50530	+	9.34991i	0.297325	+	1.10963i	0.939354	+	0.342950i	$0.111426\pi$
$71$	2.50530	+	9.34991i	0.297325	+	1.10963i	−0.642029	+	0.766680i	$0.721907\pi$
$72$	−2.31681	−	1.90589i	−0.273038	−	0.224611i
$73$	0.235334	+	0.878279i	0.0275438	+	0.102795i	0.978329	−	0.207055i	$-0.0663879\pi$
$73$	0.235334	+	0.878279i	0.0275438	+	0.102795i	−0.950786	+	0.309850i	$0.899721\pi$
$74$	−8.17585	+	4.72033i	−0.950423	+	0.548727i
$75$	−5.54102	−	2.85026i	−0.639822	−	0.329119i
$76$	3.05758	+	0.819275i	0.350728	+	0.0939773i
$77$	0.352473	+	0.0342806i	0.0401680	+	0.00390664i
$78$	4.29249	−	4.53591i	0.486029	−	0.513591i
$79$	4.27906	+	7.41154i	0.481431	+	0.833864i	0.999773	−	0.0213100i	$-0.00678371\pi$
$79$	4.27906	+	7.41154i	0.481431	+	0.833864i	−0.518341	+	0.855174i	$0.673450\pi$
$80$	2.07335	−	2.07335i	0.231807	−	0.231807i
$81$	8.83114	−	1.73520i	0.981238	−	0.192800i
$82$		−	8.43190i		−	0.931148i
$83$	11.9054	−	11.9054i	1.30678	−	1.30678i	0.383060	−	0.923724i	$-0.374870\pi$
$83$	11.9054	−	11.9054i	1.30678	−	1.30678i	0.923724	−	0.383060i	$-0.125130\pi$
$84$	−1.39904	+	4.36379i	−0.152647	+	0.476129i
$85$	1.63936	+	6.11818i	0.177814	+	0.663610i
$86$	−0.737798	+	2.75350i	−0.0795588	+	0.296918i
$87$	8.62256	−	5.55240i	0.924435	−	0.595280i
$88$			0.133851i			0.0142685i
$89$	−10.6072	+	2.84220i	−1.12436	+	0.301272i	−0.772648	−	0.634834i	$-0.781068\pi$
$89$	−10.6072	+	2.84220i	−1.12436	+	0.301272i	−0.351716	+	0.936107i	$0.614402\pi$
$90$	0.851987	+	8.75511i	0.0898073	+	0.922870i
$91$	−8.85999	−	3.53562i	−0.928779	−	0.370633i
$92$		−	6.76271i		−	0.705062i
$93$	−4.21942	+	1.35301i	−0.437534	+	0.140300i
$94$	1.62488			0.167594
$95$	−4.64078	−	8.03806i	−0.476133	−	0.824687i
$96$	−1.69280	−	0.366644i	−0.172771	−	0.0374204i
$97$	8.60864	−	2.30668i	0.874075	−	0.234208i	0.206226	−	0.978504i	$-0.433882\pi$
$97$	8.60864	−	2.30668i	0.874075	−	0.234208i	0.667849	+	0.744297i	$0.267215\pi$
$98$	6.98387	−	0.474894i	0.705478	−	0.0479716i
$99$	−0.310106	−	0.255104i	−0.0311669	−	0.0256389i
$100$	−3.59754			−0.359754
$101$	16.4193			1.63379			0.816893	−	0.576789i	$-0.195695\pi$
$101$	16.4193			1.63379			0.816893	+	0.576789i	$0.195695\pi$
$102$	2.51429	−	2.77084i	0.248952	−	0.274354i
$103$	16.1428	−	9.32005i	1.59060	−	0.918332i	0.597392	−	0.801949i	$-0.296203\pi$
$103$	16.1428	−	9.32005i	1.59060	−	0.918332i	0.993204	−	0.116382i	$-0.0371298\pi$
$104$	1.00590	−	3.46239i	0.0986364	−	0.339516i
$105$	11.9484	−	6.14697i	1.16604	−	0.599883i
$106$	1.55373	−	5.79861i	0.150912	−	0.563210i
$107$	6.91346	+	3.99149i	0.668349	+	0.385872i	0.795451	−	0.606018i	$-0.207234\pi$
$107$	6.91346	+	3.99149i	0.668349	+	0.385872i	−0.127102	+	0.991890i	$0.540567\pi$
$108$	4.07573	−	3.22311i	0.392187	−	0.310144i
$109$	8.92494	−	2.39143i	0.854855	−	0.229058i	0.195327	−	0.980738i	$-0.437423\pi$
$109$	8.92494	−	2.39143i	0.854855	−	0.229058i	0.659527	+	0.751681i	$0.270756\pi$
$110$	0.277519	−	0.277519i	0.0264604	−	0.0264604i
$111$	−4.99295	−	15.5708i	−0.473910	−	1.47791i
$112$	0.434171	+	2.60988i	0.0410253	+	0.246611i
$113$	4.23815	+	2.44689i	0.398691	+	0.230184i	0.685919	−	0.727678i	$-0.259400\pi$
$113$	4.23815	+	2.44689i	0.398691	+	0.230184i	−0.287228	+	0.957862i	$0.592734\pi$
$114$	−2.50791	+	4.87548i	−0.234887	+	0.456631i
$115$	−14.0215	+	14.0215i	−1.30751	+	1.30751i
$116$	2.96054	−	5.12781i	0.274879	−	0.476105i
$117$	6.10458	+	8.92940i	0.564368	+	0.825523i
$118$	3.23653			0.297947
$119$	−5.35146	−	2.00668i	−0.490567	−	0.183952i
$120$	2.74958	+	4.26994i	0.251001	+	0.389791i
$121$		−	10.9821i		−	0.998371i
$122$	0.938213	+	3.50146i	0.0849418	+	0.317007i
$123$	14.2735	+	3.09151i	1.28700	+	0.278752i
$124$	−1.80897	+	1.80897i	−0.162450	+	0.162450i
$125$	−2.90779	−	2.90779i	−0.260080	−	0.260080i
$126$	−6.87408	−	3.96825i	−0.612392	−	0.353520i
$127$	−0.102881	+	0.0593984i	−0.00912922	+	0.00527076i	−0.504558	−	0.863378i	$-0.668344\pi$
$127$	−0.102881	+	0.0593984i	−0.00912922	+	0.00527076i	0.495428	+	0.868649i	$0.335011\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−4.39062	−	2.25850i	−0.386572	−	0.198850i
$130$	−9.26432	+	5.09317i	−0.812535	+	0.446700i
$131$	4.03853	−	2.33165i	0.352848	−	0.203717i	−0.313091	−	0.949723i	$-0.601364\pi$
$131$	4.03853	−	2.33165i	0.352848	−	0.203717i	0.665939	+	0.746006i	$0.268031\pi$
$132$	−0.226583	−	0.0490755i	−0.0197215	−	0.00427148i
$133$	8.33562	+	0.810702i	0.722790	+	0.0702968i
$134$	−1.92802	+	3.33943i	−0.166556	+	0.288483i
$135$	−15.1330	−	1.76777i	−1.30244	−	0.152145i
$136$	0.559097	−	2.08658i	0.0479422	−	0.178923i
$137$	5.24383	−	19.5702i	0.448010	−	1.67200i	−0.259854	−	0.965648i	$-0.583674\pi$
$137$	5.24383	−	19.5702i	0.448010	−	1.67200i	0.707864	−	0.706349i	$-0.249659\pi$
$138$	11.4479	+	2.47951i	0.974512	+	0.211070i
$139$	1.13201	−	1.96070i	0.0960161	−	0.166305i	−0.814016	−	0.580842i	$-0.802723\pi$
$139$	1.13201	−	1.96070i	0.0960161	−	0.166305i	0.910032	+	0.414538i	$0.136057\pi$
$140$	4.51101	−	6.31138i	0.381250	−	0.533409i
$141$	−0.595752	+	2.75060i	−0.0501714	+	0.231642i
$142$	−8.38290	+	4.83987i	−0.703477	+	0.406153i
$143$	0.134640	−	0.463444i	0.0112592	−	0.0387551i
$144$	1.24131	−	2.73114i	0.103442	−	0.227595i
$145$	−16.7700	+	4.49350i	−1.39267	+	0.373164i
$146$	−0.787443	+	0.454631i	−0.0651693	+	0.0376255i
$147$	−1.75669	+	11.9964i	−0.144890	+	0.989448i
$148$	−6.67555	−	6.67555i	−0.548727	−	0.548727i
$149$	−11.8821	+	11.8821i	−0.973418	+	0.973418i	−0.999656	−	0.0262382i	$-0.991647\pi$
$149$	−11.8821	+	11.8821i	−0.973418	+	0.973418i	0.0262382	+	0.999656i	$0.491647\pi$
$150$	1.31902	−	6.08992i	0.107697	−	0.497240i
$151$	4.92861	+	18.3938i	0.401084	+	1.49687i	0.811165	+	0.584818i	$0.198834\pi$
$151$	4.92861	+	18.3938i	0.401084	+	1.49687i	−0.410081	+	0.912049i	$0.634499\pi$
$152$			3.16544i			0.256751i
$153$	3.76863	+	5.27210i	0.304676	+	0.426224i
$154$	0.0581141	+	0.349335i	0.00468297	+	0.0281502i
$155$	7.50123			0.602513
$156$	5.49233	+	2.97225i	0.439739	+	0.237970i
$157$	−1.91713	+	3.32057i	−0.153004	+	0.265010i	−0.932330	−	0.361608i	$-0.882228\pi$
$157$	−1.91713	+	3.32057i	−0.153004	+	0.265010i	0.779327	+	0.626618i	$0.215561\pi$
$158$	−6.05150	+	6.05150i	−0.481431	+	0.481431i
$159$	9.24622	+	4.75618i	0.733273	+	0.377190i
$160$	2.53932	+	1.46608i	0.200751	+	0.115904i
$161$	−2.93617	−	17.6499i	−0.231403	−	1.39101i
$162$	3.96174	+	8.08112i	0.311264	+	0.634913i
$163$	−8.74890	+	8.74890i	−0.685266	+	0.685266i	−0.961182	−	0.275915i	$-0.911019\pi$
$163$	−8.74890	+	8.74890i	−0.685266	+	0.685266i	0.275915	+	0.961182i	$0.411019\pi$
$164$	8.14459	−	2.18234i	0.635986	−	0.170412i
$165$	0.368034	+	0.571535i	0.0286514	+	0.0444939i
$166$	14.5810	+	8.41836i	1.13171	+	0.653392i
$167$	−4.23341	+	15.7993i	−0.327591	+	1.22259i	0.584089	+	0.811689i	$0.301452\pi$
$167$	−4.23341	+	15.7993i	−0.327591	+	1.22259i	−0.911681	+	0.410899i	$0.865215\pi$
$168$	−4.57720	−	0.221933i	−0.353139	−	0.0171225i
$169$	−6.96563	+	10.9763i	−0.535818	+	0.844334i
$170$	−5.48541	+	3.16700i	−0.420712	+	0.242898i
$171$	−7.33371	−	6.03296i	−0.560823	−	0.461352i
$172$	−2.85063			−0.217359
$173$	−11.1476			−0.847540			−0.423770	−	0.905770i	$-0.639293\pi$
$173$	−11.1476			−0.847540			−0.423770	+	0.905770i	$0.639293\pi$
$174$	7.59489	+	6.89168i	0.575767	+	0.522457i
$175$	−9.38916	+	1.56195i	−0.709754	+	0.118072i
$176$	−0.129290	+	0.0346431i	−0.00974559	+	0.00261132i
$177$	−1.18665	+	5.47880i	−0.0891944	+	0.411812i
$178$	−5.49071	−	9.51018i	−0.411546	−	0.712818i
$179$	−16.3041			−1.21863			−0.609314	−	0.792929i	$-0.708555\pi$
$179$	−16.3041			−1.21863			−0.609314	+	0.792929i	$0.708555\pi$
$180$	−8.23628	+	3.08895i	−0.613896	+	0.230236i
$181$		−	14.2891i		−	1.06210i	−0.847341	−	0.531050i	$-0.821798\pi$
$181$		−	14.2891i		−	1.06210i	0.847341	−	0.531050i	$-0.178202\pi$
$182$	1.12201	−	9.47318i	0.0831687	−	0.702199i
$183$	−6.27126	+	0.304419i	−0.463585	+	0.0225033i
$184$	6.53228	−	1.75032i	0.481566	−	0.129035i
$185$			27.6815i			2.03518i
$186$	−2.39897	−	3.72547i	−0.175901	−	0.273164i
$187$	0.0748356	−	0.279290i	0.00547252	−	0.0204237i
$188$	0.420550	+	1.56951i	0.0306718	+	0.114469i
$189$	9.23779	−	10.1815i	0.671951	−	0.740596i
$190$	6.56305	−	6.56305i	0.476133	−	0.476133i
$191$		−	7.24619i		−	0.524316i	−0.965025	−	0.262158i	$-0.915566\pi$
$191$		−	7.24619i		−	0.524316i	0.965025	−	0.262158i	$-0.0844341\pi$
$192$	−0.0839781	−	1.73001i	−0.00606060	−	0.124853i
$193$	14.0101	−	14.0101i	1.00847	−	1.00847i	0.00850345	−	0.999964i	$-0.497293\pi$
$193$	14.0101	−	14.0101i	1.00847	−	1.00847i	0.999964	−	0.00850345i	$-0.00270676\pi$
$194$	4.45616	+	7.71830i	0.319934	+	0.554141i
$195$	−5.22501	−	17.5500i	−0.374171	−	1.25678i
$196$	2.26627	+	6.62299i	0.161877	+	0.473071i
$197$	−9.39565	−	2.51756i	−0.669413	−	0.179369i	−0.0919223	−	0.995766i	$-0.529301\pi$
$197$	−9.39565	−	2.51756i	−0.669413	−	0.179369i	−0.577490	+	0.816398i	$0.695968\pi$
$198$	0.166150	−	0.365566i	0.0118078	−	0.0259796i
$199$	2.28348	−	1.31837i	0.161871	−	0.0934565i	−0.416876	−	0.908963i	$-0.636875\pi$
$199$	2.28348	−	1.31837i	0.161871	−	0.0934565i	0.578747	+	0.815507i	$0.303542\pi$
$200$	−0.931112	−	3.47496i	−0.0658395	−	0.245717i
$201$	−4.94609	−	4.48814i	−0.348870	−	0.316569i
$202$	4.24964	+	15.8599i	0.299004	+	1.11590i
$203$	5.50032	−	14.6684i	0.386047	−	1.02952i
$204$	3.32717	+	1.71147i	0.232949	+	0.119827i
$205$	−21.4113	−	12.3618i	−1.49543	−	0.863388i
$206$	13.1805	+	13.1805i	0.918332	+	0.918332i
$207$	−8.39462	+	18.4699i	−0.583467	+	1.28375i
$208$	3.60476	+	0.0754898i	0.249945	+	0.00523428i
$209$			0.423696i			0.0293076i
$210$	9.02998	+	9.95027i	0.623128	+	0.686634i
$211$	−10.9365	−	18.9426i	−0.752902	−	1.30406i	−0.946410	−	0.322966i	$-0.895320\pi$
$211$	−10.9365	−	18.9426i	−0.752902	−	1.30406i	0.193508	−	0.981099i	$-0.438013\pi$
$212$	6.00316			0.412299
$213$	−5.11939	−	15.9651i	−0.350775	−	1.09391i
$214$	−2.06615	+	7.71096i	−0.141239	+	0.527110i
$215$	5.91035	+	5.91035i	0.403083	+	0.403083i
$216$	4.16816	+	3.10265i	0.283608	+	0.211108i
$217$	−3.93579	+	5.50659i	−0.267179	+	0.373812i
$218$	4.61989	+	8.00189i	0.312899	+	0.541956i
$219$	−0.480887	−	1.49967i	−0.0324954	−	0.101338i
$220$	0.339890	+	0.196236i	0.0229154	+	0.0132302i
$221$	−4.03470	+	6.66217i	−0.271403	+	0.448146i
$222$	13.7479	−	8.85282i	0.922700	−	0.594163i
$223$	1.20790	−	4.50794i	0.0808868	−	0.301874i	−0.913617	−	0.406577i	$-0.866722\pi$
$223$	1.20790	−	4.50794i	0.0808868	−	0.301874i	0.994504	+	0.104703i	$0.0333891\pi$
$224$	−2.40858	+	1.09486i	−0.160930	+	0.0731537i
$225$	9.82540	+	4.46566i	0.655027	+	0.297711i
$226$	−1.26661	+	4.72704i	−0.0842534	+	0.314438i
$227$	23.9931	+	6.42892i	1.59248	+	0.426702i	0.942759	−	0.333474i	$-0.108221\pi$
$227$	23.9931	+	6.42892i	1.59248	+	0.426702i	0.649716	+	0.760177i	$0.274888\pi$
$228$	−5.35845	−	1.16059i	−0.354872	−	0.0768618i
$229$	−0.274618	−	0.0735838i	−0.0181473	−	0.00486255i	0.249734	−	0.968314i	$-0.419657\pi$
$229$	−0.274618	−	0.0735838i	−0.0181473	−	0.00486255i	−0.267881	+	0.963452i	$0.586323\pi$
$230$	−17.1727	−	9.91467i	−1.13233	−	0.653754i
$231$	−0.612661	−	0.0297060i	−0.0403102	−	0.00195451i
$232$	5.71932	+	1.53249i	0.375492	+	0.100613i
$233$	−4.54823	−	7.87777i	−0.297965	−	0.516090i	0.677705	−	0.735333i	$-0.262974\pi$
$233$	−4.54823	−	7.87777i	−0.297965	−	0.516090i	−0.975670	+	0.219243i	$0.929641\pi$
$234$	−7.04516	+	8.20767i	−0.460556	+	0.536552i
$235$	2.38220	−	4.12609i	0.155398	−	0.269157i
$236$	0.837676	+	3.12625i	0.0545280	+	0.203501i
$237$	−8.02523	−	12.4627i	−0.521295	−	0.809541i
$238$	0.553247	−	5.68848i	0.0358617	−	0.368729i
$239$	−2.39543	+	2.39543i	−0.154948	+	0.154948i	−0.780324	−	0.625376i	$-0.784946\pi$
$239$	−2.39543	+	2.39543i	−0.154948	+	0.154948i	0.625376	+	0.780324i	$0.284946\pi$
$240$	−3.41280	+	3.76104i	−0.220296	+	0.242774i
$241$	26.7847	+	7.17693i	1.72535	+	0.462307i	0.979104	−	0.203362i	$-0.0651867\pi$
$241$	26.7847	+	7.17693i	1.72535	+	0.462307i	0.746248	+	0.665668i	$0.231853\pi$
$242$	10.6079	−	2.84237i	0.681900	−	0.182715i
$243$	−15.1323	+	3.74355i	−0.970736	+	0.240149i
$244$	−3.13932	+	1.81249i	−0.200974	+	0.116033i
$245$	9.03299	−	18.4305i	0.577097	−	1.17748i
$246$	0.708095	+	14.5873i	0.0451465	+	0.930053i
$247$	3.18411	−	10.9600i	0.202600	−	0.697367i
$248$	−2.21552	−	1.27913i	−0.140686	−	0.0812250i
$249$	−19.5967	+	21.5962i	−1.24189	+	1.36861i
$250$	2.05612	−	3.56130i	0.130040	−	0.225236i
$251$	6.76043	−	11.7094i	0.426714	−	0.739091i	−0.569865	−	0.821739i	$-0.693004\pi$
$251$	6.76043	−	11.7094i	0.426714	−	0.739091i	0.996579	+	0.0826478i	$0.0263377\pi$
$252$	2.05389	−	7.66691i	0.129383	−	0.482970i
$253$	0.874350	−	0.234281i	0.0549699	−	0.0147292i
$254$	−0.0840020	−	0.0840020i	−0.00527076	−	0.00527076i
$255$	−3.34991	−	10.4469i	−0.209780	−	0.654208i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.7506	−	22.0848i	0.795363	−	1.37761i	−0.127245	−	0.991871i	$-0.540614\pi$
$257$	12.7506	−	22.0848i	0.795363	−	1.37761i	0.922608	−	0.385738i	$-0.126053\pi$
$258$	1.04517	−	4.82555i	0.0650693	−	0.300426i
$259$	−20.3207	−	14.5241i	−1.26267	−	0.902483i
$260$	−7.31741	−	7.63044i	−0.453806	−	0.473220i
$261$	−14.4509	+	10.3298i	−0.894486	+	0.639401i
$262$	3.29745	+	3.29745i	0.203717	+	0.203717i
$263$			10.8310i			0.667868i	0.942597	+	0.333934i	$0.108376\pi$
$263$			10.8310i			0.667868i	−0.942597	+	0.333934i	$0.891624\pi$
$264$	−0.0112405	−	0.231564i	−0.000691807	−	0.0142518i
$265$	−12.4466	−	12.4466i	−0.764591	−	0.764591i
$266$	1.37434	+	8.26142i	0.0842662	+	0.506540i
$267$	18.1120	−	5.80782i	1.10843	−	0.355433i
$268$	−3.72465	−	0.998017i	−0.227519	−	0.0609636i
$269$	−26.4125	+	15.2493i	−1.61040	+	0.929764i	−0.621121	+	0.783715i	$0.713322\pi$
$269$	−26.4125	+	15.2493i	−1.61040	+	0.929764i	−0.989277	+	0.146049i	$0.953344\pi$
$270$	−2.20919	−	15.0749i	−0.134447	−	0.917430i
$271$	−5.28896	−	19.7387i	−0.321282	−	1.19904i	−0.917997	−	0.396586i	$-0.870195\pi$
$271$	−5.28896	−	19.7387i	−0.321282	−	1.19904i	0.596716	−	0.802453i	$-0.296472\pi$
$272$	2.16019			0.130981
$273$	15.6248	+	5.37262i	0.945657	+	0.325166i
$274$	20.2606			1.22399
$275$	−0.124630	−	0.465125i	−0.00751547	−	0.0280481i
$276$	0.567920	+	11.6996i	0.0341848	+	0.704232i
$277$	−10.4225	+	6.01743i	−0.626227	+	0.361552i	−0.779289	−	0.626664i	$-0.784420\pi$
$277$	−10.4225	+	6.01743i	−0.626227	+	0.361552i	0.153063	+	0.988216i	$0.451086\pi$
$278$	2.18688	+	0.585973i	0.131160	+	0.0351443i
$279$	7.18604	−	2.69506i	0.430217	−	0.161349i
$280$	7.26386	+	2.72379i	0.434099	+	0.162778i
$281$	18.4836	+	18.4836i	1.10264	+	1.10264i	0.994091	+	0.108548i	$0.0346200\pi$
$281$	18.4836	+	18.4836i	1.10264	+	1.10264i	0.108548	+	0.994091i	$0.465380\pi$
$282$	−2.81107	+	0.136454i	−0.167396	+	0.00812574i
$283$		−	0.669831i		−	0.0398173i	−0.999802	−	0.0199087i	$-0.993662\pi$
$283$		−	0.669831i		−	0.0398173i	0.999802	−	0.0199087i	$-0.00633755\pi$
$284$	−6.84461	−	6.84461i	−0.406153	−	0.406153i
$285$	8.70363	+	13.5162i	0.515558	+	0.800632i
$286$	0.482500	+	0.0101044i	0.0285308	+	0.000597484i
$287$	20.3089	−	9.23179i	1.19880	−	0.544936i
$288$	2.95936	+	0.492141i	0.174382	+	0.0289997i
$289$	6.16680	−	10.6812i	0.362753	−	0.628306i
$290$	−8.68077	−	15.0355i	−0.509752	−	0.882917i
$291$	−14.6994	+	4.71352i	−0.861692	+	0.276312i
$292$	−0.642945	−	0.642945i	−0.0376255	−	0.0376255i
$293$	−27.8322	+	7.45762i	−1.62597	+	0.435679i	−0.952749	−	0.303758i	$-0.901758\pi$
$293$	−27.8322	+	7.45762i	−1.62597	+	0.435679i	−0.673226	+	0.739437i	$0.735092\pi$
$294$	−12.0423	+	1.40807i	−0.702322	+	0.0821201i
$295$	4.74501	−	8.21859i	0.276265	−	0.478505i
$296$	4.72033	−	8.17585i	0.274363	−	0.475212i
$297$	0.557912	+	0.415291i	0.0323733	+	0.0240977i
$298$	−14.5525	−	8.40190i	−0.843004	−	0.486709i
$299$	−24.3780	−	0.510516i	−1.40981	−	0.0295239i
$300$	6.22379	−	0.302115i	0.359331	−	0.0174426i
$301$	−7.43982	+	1.23766i	−0.428824	+	0.0713376i
$302$	−16.4914	+	9.52134i	−0.948976	+	0.547891i
$303$	−28.4057	+	1.37887i	−1.63186	+	0.0792138i
$304$	−3.05758	+	0.819275i	−0.175364	+	0.0469886i
$305$	10.2668	+	2.75099i	0.587877	+	0.157521i
$306$	−4.11707	+	5.00474i	−0.235357	+	0.286102i
$307$	−5.81650	+	5.81650i	−0.331965	+	0.331965i	−0.853332	−	0.521367i	$-0.825422\pi$
$307$	−5.81650	+	5.81650i	−0.331965	+	0.331965i	0.521367	+	0.853332i	$0.325422\pi$
$308$	−0.322391	+	0.146548i	−0.0183699	+	0.00835037i
$309$	−27.1446	+	17.4795i	−1.54420	+	0.994371i
$310$	1.94146	+	7.24563i	0.110268	+	0.411524i
$311$	−0.578361	+	1.00175i	−0.0327959	+	0.0568041i	−0.881957	−	0.471329i	$-0.843774\pi$
$311$	−0.578361	+	1.00175i	−0.0327959	+	0.0568041i	0.849162	+	0.528133i	$0.177108\pi$
$312$	−1.44945	+	6.07446i	−0.0820591	+	0.343899i
$313$	5.50680	+	9.53805i	0.311263	+	0.539123i	0.978636	−	0.205601i	$-0.0659148\pi$
$313$	5.50680	+	9.53805i	0.311263	+	0.539123i	−0.667373	+	0.744723i	$0.732581\pi$
$314$	−3.70361	−	0.992380i	−0.209007	−	0.0560032i
$315$	−20.1546	+	11.6377i	−1.13558	+	0.655712i
$316$	−7.41154	−	4.27906i	−0.416932	−	0.240716i
$317$	27.1211	+	7.26708i	1.52327	+	0.408160i	0.920818	−	0.389992i	$-0.127522\pi$
$317$	27.1211	+	7.26708i	1.52327	+	0.408160i	0.602456	+	0.798152i	$0.294189\pi$
$318$	−2.20102	+	10.1621i	−0.123427	+	0.569865i
$319$	0.765536	+	0.205125i	0.0428618	+	0.0114848i
$320$	−0.758898	+	2.83225i	−0.0424237	+	0.158327i
$321$	−12.2956	−	6.32475i	−0.686272	−	0.353013i
$322$	16.2886	−	7.40426i	0.907726	−	0.412623i
$323$	1.76979	−	6.60493i	0.0984736	−	0.367508i
$324$	−6.78039	+	5.91830i	−0.376688	+	0.328794i
$325$	−0.271578	+	12.9683i	−0.0150644	+	0.719350i
$326$	−10.7152	−	6.18640i	−0.593458	−	0.342633i
$327$	−15.2394	+	4.88671i	−0.842743	+	0.270236i
$328$	4.21595	+	7.30224i	0.232787	+	0.403199i
$329$	1.77902	+	3.91366i	0.0980808	+	0.215767i
$330$	−0.456806	+	0.503417i	−0.0251464	+	0.0277122i
$331$	19.9941	+	19.9941i	1.09898	+	1.09898i	0.994531	+	0.104445i	$0.0333066\pi$
$331$	19.9941	+	19.9941i	1.09898	+	1.09898i	0.104445	+	0.994531i	$0.466693\pi$
$332$	−4.35767	+	16.2630i	−0.239158	+	0.892550i
$333$	9.94547	+	26.5183i	0.545008	+	1.45320i
$334$	−16.3567			−0.894997
$335$	5.65326	+	9.79173i	0.308871	+	0.534980i
$336$	−0.970295	−	4.47867i	−0.0529339	−	0.244332i
$337$			13.7791i			0.750595i	0.926904	+	0.375298i	$0.122460\pi$
$337$			13.7791i			0.750595i	−0.926904	+	0.375298i	$0.877540\pi$
$338$	−12.4052	−	3.88740i	−0.674752	−	0.211447i
$339$	−7.53754	−	3.87725i	−0.409383	−	0.210583i
$340$	−4.47882	−	4.47882i	−0.242898	−	0.242898i
$341$	−0.296549	−	0.171213i	−0.0160590	−	0.00927169i
$342$	3.92929	−	8.64526i	0.212471	−	0.467482i
$343$	8.79022	+	16.3013i	0.474627	+	0.880187i
$344$	−0.737798	−	2.75350i	−0.0397794	−	0.148459i
$345$	23.0798	−	25.4348i	1.24258	−	1.36936i
$346$	−2.88522	−	10.7678i	−0.155111	−	0.578880i
$347$	−18.6970	+	10.7947i	−1.00371	+	0.579490i	−0.909343	−	0.416048i	$-0.863415\pi$
$347$	−18.6970	+	10.7947i	−1.00371	+	0.579490i	−0.0943635	+	0.995538i	$0.530082\pi$
$348$	−4.69115	+	9.11980i	−0.251472	+	0.488872i
$349$	4.14914	+	1.11176i	0.222098	+	0.0595111i	0.368152	−	0.929766i	$-0.379991\pi$
$349$	4.14914	+	1.11176i	0.222098	+	0.0595111i	−0.146054	+	0.989277i	$0.546657\pi$
$350$	−3.93882	−	8.66497i	−0.210539	−	0.463162i
$351$	−11.3109	−	14.9353i	−0.603730	−	0.797189i
$352$	−0.0669254	−	0.115918i	−0.00356713	−	0.00617846i
$353$	7.78716	−	7.78716i	0.414469	−	0.414469i	−0.468823	−	0.883292i	$-0.655322\pi$
$353$	7.78716	−	7.78716i	0.414469	−	0.414469i	0.883292	+	0.468823i	$0.155322\pi$
$354$	−5.59924	+	0.271798i	−0.297596	+	0.0144459i
$355$			28.3825i			1.50639i
$356$	7.76503	−	7.76503i	0.411546	−	0.411546i
$357$	9.42661	+	3.02218i	0.498909	+	0.159951i
$358$	−4.21982	−	15.7486i	−0.223024	−	0.832338i
$359$	3.00311	−	11.2078i	0.158498	−	0.591523i	−0.840282	−	0.542149i	$-0.817611\pi$
$359$	3.00311	−	11.2078i	0.158498	−	0.591523i	0.998780	−	0.0493737i	$-0.0157225\pi$
$360$	−5.11540	−	7.15616i	−0.269605	−	0.377163i
$361$		−	8.98002i		−	0.472633i
$362$	13.8022	−	3.69829i	0.725427	−	0.194378i
$363$	0.922255	+	18.9992i	0.0484058	+	0.997197i
$364$	9.44078	−	1.36806i	0.494832	−	0.0717060i
$365$			2.66610i			0.139550i
$366$	−1.91717	−	5.97878i	−0.100212	−	0.312516i
$367$	28.9124			1.50921			0.754607	−	0.656177i	$-0.227827\pi$
$367$	28.9124			1.50921			0.754607	+	0.656177i	$0.227827\pi$
$368$	3.38136	+	5.85668i	0.176265	+	0.305301i
$369$	−24.9530	−	4.14968i	−1.29900	−	0.216024i
$370$	−26.7383	+	7.16449i	−1.39006	+	0.372464i
$371$	15.6676	−	2.60640i	0.813419	−	0.135317i
$372$	2.97762	−	3.28145i	0.154383	−	0.170135i
$373$	7.60386			0.393713			0.196857	−	0.980432i	$-0.436927\pi$
$373$	7.60386			0.393713			0.196857	+	0.980432i	$0.436927\pi$
$374$	0.289143			0.0149512
$375$	5.27470	+	4.78632i	0.272385	+	0.247165i
$376$	−1.40719	+	0.812440i	−0.0725702	+	0.0418984i
$377$	−18.2610	−	11.0591i	−0.940491	−	0.569575i
$378$	12.2255	+	6.28785i	0.628812	+	0.323412i
$379$	6.21686	−	23.2016i	0.319339	−	1.19179i	−0.600543	−	0.799592i	$-0.705049\pi$
$379$	6.21686	−	23.2016i	0.319339	−	1.19179i	0.919882	−	0.392196i	$-0.128284\pi$
$380$	8.03806	+	4.64078i	0.412344	+	0.238067i
$381$	0.172998	−	0.111400i	0.00886293	−	0.00570719i
$382$	6.99928	−	1.87545i	0.358114	−	0.0959564i
$383$	1.46563	−	1.46563i	0.0748902	−	0.0748902i	−0.668670	−	0.743560i	$-0.733136\pi$
$383$	1.46563	−	1.46563i	0.0748902	−	0.0748902i	0.743560	+	0.668670i	$0.233136\pi$
$384$	1.64933	−	0.528877i	0.0841670	−	0.0269891i
$385$	0.972273	+	0.364582i	0.0495516	+	0.0185808i
$386$	17.1588	+	9.90662i	0.873358	+	0.504234i
$387$	7.78549	+	3.53852i	0.395759	+	0.179873i
$388$	−6.30196	+	6.30196i	−0.319934	+	0.319934i
$389$	15.3483	−	26.5841i	0.778190	−	1.34787i	−0.154793	−	0.987947i	$-0.549471\pi$
$389$	15.3483	−	26.5841i	0.778190	−	1.34787i	0.932984	−	0.359918i	$-0.117195\pi$
$390$	15.5997	−	9.58925i	0.789921	−	0.485571i
$391$	−14.6087			−0.738795
$392$	−5.81076	+	3.90321i	−0.293488	+	0.197142i
$393$	−6.79091	+	4.37293i	−0.342556	+	0.220585i
$394$		−	9.72710i		−	0.490044i
$395$	6.49473	+	24.2387i	0.326785	+	1.21958i
$396$	0.396112	+	0.0658734i	0.0199054	+	0.00331026i
$397$	−13.8982	+	13.8982i	−0.697532	+	0.697532i	−0.963878	−	0.266346i	$-0.914184\pi$
$397$	−13.8982	+	13.8982i	−0.697532	+	0.697532i	0.266346	+	0.963878i	$0.414184\pi$
$398$	1.86445	+	1.86445i	0.0934565	+	0.0934565i
$399$	−14.4888	−	0.702516i	−0.725348	−	0.0351698i
$400$	3.11556	−	1.79877i	0.155778	−	0.0899385i
$401$	30.9399	−	8.29033i	1.54507	−	0.413999i	0.617167	−	0.786832i	$-0.288280\pi$
$401$	30.9399	−	8.29033i	1.54507	−	0.413999i	0.927898	+	0.372833i	$0.121614\pi$
$402$	3.05506	−	5.93917i	0.152373	−	0.296219i
$403$	6.38433	+	6.65745i	0.318026	+	0.331631i
$404$	−14.2196	+	8.20967i	−0.707450	+	0.408447i
$405$	26.3288	+	1.78741i	1.30829	+	0.0888174i
$406$	15.5921	+	1.51645i	0.773825	+	0.0752603i
$407$	0.631819	−	1.09434i	0.0313181	−	0.0542446i
$408$	−0.792019	+	3.65676i	−0.0392108	+	0.181037i
$409$	0.794642	−	2.96564i	0.0392925	−	0.146642i	−0.943493	−	0.331393i	$-0.892481\pi$
$409$	0.794642	−	2.96564i	0.0392925	−	0.146642i	0.982785	+	0.184751i	$0.0591480\pi$
$410$	6.39895	−	23.8812i	0.316022	−	1.17941i
$411$	−7.42842	+	34.2971i	−0.366417	+	1.69175i
$412$	−9.32005	+	16.1428i	−0.459166	+	0.795298i
$413$	3.54356	+	7.79545i	0.174367	+	0.383589i
$414$	−20.0133	−	3.32821i	−0.983599	−	0.163572i
$415$	42.7539	−	24.6840i	2.09870	−	1.21169i
$416$	0.860063	+	3.50147i	0.0421681	+	0.171674i
$417$	−1.79374	+	3.48711i	−0.0878399	+	0.170764i
$418$	−0.409259	+	0.109661i	−0.0200175	+	0.00536367i
$419$	−20.3563	+	11.7527i	−0.994469	+	0.574157i	−0.906607	−	0.421975i	$-0.861337\pi$
$419$	−20.3563	+	11.7527i	−0.994469	+	0.574157i	−0.0878622	+	0.996133i	$0.528004\pi$
$420$	−7.27409	+	11.2976i	−0.354939	+	0.551267i
$421$	10.5113	+	10.5113i	0.512288	+	0.512288i	0.915227	−	0.402939i	$-0.132011\pi$
$421$	10.5113	+	10.5113i	0.512288	+	0.512288i	−0.402939	+	0.915227i	$0.632011\pi$
$422$	15.4666	−	15.4666i	0.752902	−	0.752902i
$423$	0.799670	−	4.80860i	0.0388813	−	0.233802i
$424$	1.55373	+	5.79861i	0.0754559	+	0.281605i
$425$			7.77136i			0.376966i
$426$	14.0961	−	9.07702i	0.682958	−	0.439783i
$427$	−7.40634	+	6.09339i	−0.358418	+	0.294880i
$428$	−7.98297			−0.385872
$429$	−0.194010	+	0.813071i	−0.00936691	+	0.0392554i
$430$	−4.17925	+	7.23867i	−0.201541	+	0.349080i
$431$	4.20199	−	4.20199i	0.202403	−	0.202403i	−0.598626	−	0.801029i	$-0.704286\pi$
$431$	4.20199	−	4.20199i	0.202403	−	0.202403i	0.801029	+	0.598626i	$0.204286\pi$
$432$	−1.91813	+	4.82916i	−0.0922859	+	0.232343i
$433$	12.2991	+	7.10087i	0.591056	+	0.341246i	0.765515	−	0.643418i	$-0.222484\pi$
$433$	12.2991	+	7.10087i	0.591056	+	0.341246i	−0.174459	+	0.984664i	$0.555818\pi$
$434$	−6.33762	−	2.37647i	−0.304215	−	0.114074i
$435$	28.6349	−	9.18212i	1.37294	−	0.440249i
$436$	−6.53351	+	6.53351i	−0.312899	+	0.312899i
$437$	20.6775	−	5.54052i	0.989139	−	0.265039i
$438$	1.32411	−	0.852645i	0.0632684	−	0.0407410i
$439$	16.1229	+	9.30855i	0.769503	+	0.444273i	0.832697	−	0.553729i	$-0.186795\pi$
$439$	16.1229	+	9.30855i	0.769503	+	0.444273i	−0.0631944	+	0.998001i	$0.520129\pi$
$440$	−0.101579	+	0.379098i	−0.00484259	+	0.0180728i
$441$	2.03167	−	20.9015i	0.0967461	−	0.995309i
$442$	−7.47942	−	2.17293i	−0.355760	−	0.103356i
$443$	−25.7503	+	14.8670i	−1.22343	+	0.706350i	−0.965649	−	0.259852i	$-0.916326\pi$
$443$	−25.7503	+	14.8670i	−1.22343	+	0.706350i	−0.257786	+	0.966202i	$0.582993\pi$
$444$	12.1094	+	10.9882i	0.574687	+	0.521477i
$445$	−32.1992			−1.52639
$446$	4.66696			0.220987
$447$	19.5583	−	21.5540i	0.925077	−	1.01947i
$448$	−1.68095	−	2.04314i	−0.0794172	−	0.0965293i
$449$	21.2445	−	5.69243i	1.00259	−	0.268643i	0.280058	−	0.959983i	$-0.409646\pi$
$449$	21.2445	−	5.69243i	1.00259	−	0.268643i	0.722529	+	0.691340i	$0.242979\pi$
$450$	−1.77050	+	10.6464i	−0.0834620	+	0.501876i
$451$	0.564308	+	0.977410i	0.0265722	+	0.0460245i
$452$	−4.89379			−0.230184
$453$	−10.0712	−	31.4076i	−0.473188	−	1.47566i
$454$			24.8394i			1.16577i
$455$	−22.4105	−	16.7376i	−1.05062	−	0.784669i
$456$	−0.265827	−	5.47625i	−0.0124485	−	0.256449i
$457$	−21.5981	+	5.78720i	−1.01032	+	0.270714i	−0.725762	−	0.687946i	$-0.758513\pi$
$457$	−21.5981	+	5.78720i	−1.01032	+	0.270714i	−0.284555	+	0.958660i	$0.591846\pi$
$458$		−	0.284306i		−	0.0132847i
$459$	−6.96252	−	8.80433i	−0.324983	−	0.410951i
$460$	5.13221	−	19.1537i	0.239290	−	0.893044i
$461$	2.65597	+	9.91222i	0.123701	+	0.461658i	0.999790	−	0.0204911i	$-0.00652299\pi$
$461$	2.65597	+	9.91222i	0.123701	+	0.461658i	−0.876089	+	0.482149i	$0.839856\pi$
$462$	−0.129875	−	0.599474i	−0.00604232	−	0.0278900i
$463$	−18.6992	+	18.6992i	−0.869024	+	0.869024i	−0.992364	−	0.123340i	$-0.960639\pi$
$463$	−18.6992	+	18.6992i	−0.869024	+	0.869024i	0.123340	+	0.992364i	$0.460639\pi$
$464$			5.92108i			0.274879i
$465$	−12.9772	+	0.629939i	−0.601805	+	0.0292127i
$466$	6.43217	−	6.43217i	0.297965	−	0.297965i
$467$	−16.0323	−	27.7688i	−0.741888	−	1.28499i	−0.951635	−	0.307231i	$-0.900597\pi$
$467$	−16.0323	−	27.7688i	−0.741888	−	1.28499i	0.209747	−	0.977756i	$-0.432736\pi$
$468$	−9.75142	−	4.68080i	−0.450759	−	0.216370i
$469$	−10.1542	−	0.987574i	−0.468878	−	0.0456019i
$470$	4.60206	+	1.23312i	0.212277	+	0.0568795i
$471$	3.03781	−	5.90563i	0.139975	−	0.272117i
$472$	−2.80292	+	1.61826i	−0.129015	+	0.0744867i
$473$	−0.0987548	−	0.368558i	−0.00454075	−	0.0169463i
$474$	9.96098	−	10.9774i	0.457523	−	0.504207i
$475$	−2.94737	−	10.9997i	−0.135235	−	0.504703i
$476$	5.63784	−	0.937890i	0.258410	−	0.0429881i
$477$	−16.3955	−	7.45178i	−0.750698	−	0.341194i
$478$	−2.93379	−	1.69383i	−0.134189	−	0.0774738i
$479$	−17.0888	−	17.0888i	−0.780806	−	0.780806i	0.199161	−	0.979967i	$-0.436178\pi$
$479$	−17.0888	−	17.0888i	−0.780806	−	0.780806i	−0.979967	+	0.199161i	$0.936178\pi$
$480$	−4.51618	−	2.32309i	−0.206134	−	0.106034i
$481$	−24.5677	+	23.5598i	−1.12019	+	1.07424i
$482$			27.7295i			1.26304i
$483$	6.56183	+	30.2880i	0.298573	+	1.37815i
$484$	5.49104	+	9.51076i	0.249593	+	0.432307i
$485$	26.1323			1.18661
$486$	−7.53251	−	13.6478i	−0.341682	−	0.619075i
$487$	8.99634	−	33.5748i	0.407663	−	1.52142i	−0.391428	−	0.920209i	$-0.628019\pi$
$487$	8.99634	−	33.5748i	0.407663	−	1.52142i	0.799091	−	0.601210i	$-0.205315\pi$
$488$	−2.56325	−	2.56325i	−0.116033	−	0.116033i
$489$	14.4010	−	15.8704i	0.651236	−	0.717686i
$490$	20.1404	+	3.95503i	0.909852	+	0.178670i
$491$	0.699204	+	1.21106i	0.0315546	+	0.0546542i	0.881371	−	0.472424i	$-0.156621\pi$
$491$	0.699204	+	1.21106i	0.0315546	+	0.0546542i	−0.849817	+	0.527078i	$0.823288\pi$
$492$	−13.9070	+	4.45944i	−0.626976	+	0.201047i
$493$	−11.0770	−	6.39532i	−0.498884	−	0.288031i
$494$	11.4106	+	0.238958i	0.513389	+	0.0107512i
$495$	−0.684700	−	0.957857i	−0.0307750	−	0.0430524i
$496$	0.662128	−	2.47109i	0.0297304	−	0.110955i
$497$	−20.8354	−	14.8919i	−0.934594	−	0.667993i
$498$	−25.9323	−	13.3394i	−1.16206	−	0.597753i
$499$	−5.90298	+	22.0302i	−0.264254	+	0.986208i	0.698452	+	0.715657i	$0.253873\pi$
$499$	−5.90298	+	22.0302i	−0.264254	+	0.986208i	−0.962706	+	0.270551i	$0.912794\pi$
$500$	3.97211	+	1.06432i	0.177638	+	0.0475980i
$501$	5.99707	−	27.6886i	0.267929	−	1.23703i
$502$	13.0601	+	3.49945i	0.582903	+	0.156188i
$503$	−2.18632	−	1.26227i	−0.0974832	−	0.0562819i	0.450466	−	0.892794i	$-0.351258\pi$
$503$	−2.18632	−	1.26227i	−0.0974832	−	0.0562819i	−0.547949	+	0.836512i	$0.684591\pi$
$504$	7.93725		0.000436475i	0.353553		1.94421e-5i
$505$	46.5036	+	12.4606i	2.06938	+	0.554490i
$506$	0.452597	+	0.783921i	0.0201204	+	0.0348495i
$507$	11.1289	−	19.5742i	0.494250	−	0.869320i
$508$	0.0593984	−	0.102881i	0.00263538	−	0.00456461i
$509$	−6.84126	−	25.5319i	−0.303234	−	1.13168i	−0.934455	−	0.356081i	$-0.884113\pi$
$509$	−6.84126	−	25.5319i	−0.303234	−	1.13168i	0.631222	−	0.775603i	$-0.282554\pi$
$510$	9.22387	−	5.93961i	0.408440	−	0.263010i
$511$	−1.95716	−	1.39886i	−0.0865796	−	0.0618821i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	13.1941	+	9.82123i	0.582532	+	0.433618i
$514$	24.6323	+	6.60022i	1.08649	+	0.291123i
$515$	52.7933	−	14.1459i	2.32635	−	0.623344i
$516$	4.93163	−	0.239391i	0.217103	−	0.0105386i
$517$	−0.188353	+	0.108746i	−0.00828376	+	0.00478263i
$518$	8.76979	−	23.3874i	0.385323	−	1.02759i
$519$	19.2856	−	0.936158i	0.846543	−	0.0410928i
$520$	5.47655	−	9.04297i	0.240163	−	0.396561i
$521$	−12.0545	−	6.95965i	−0.528116	−	0.304908i	0.212133	−	0.977241i	$-0.431959\pi$
$521$	−12.0545	−	6.95965i	−0.528116	−	0.304908i	−0.740249	+	0.672333i	$0.765292\pi$
$522$	−13.7180	−	11.2849i	−0.600421	−	0.493927i
$523$	−17.1801	+	29.7568i	−0.751233	+	1.30117i	0.195993	+	0.980605i	$0.437207\pi$
$523$	−17.1801	+	29.7568i	−0.751233	+	1.30117i	−0.947225	+	0.320568i	$0.896126\pi$
$524$	−2.33165	+	4.03853i	−0.101859	+	0.176424i
$525$	16.1122	−	3.49067i	0.703194	−	0.152346i
$526$	−10.4619	+	2.80327i	−0.456162	+	0.122228i
$527$	3.90771	+	3.90771i	0.170222	+	0.170222i
$528$	0.220764	−	0.0707906i	0.00960752	−	0.00308076i
$529$	−11.3672	−	19.6885i	−0.494224	−	0.856021i
$530$	8.80110	−	15.2440i	0.382295	−	0.662155i
$531$	1.59283	−	9.57805i	0.0691229	−	0.415652i
$532$	−7.62421	+	3.46572i	−0.330552	+	0.150258i
$533$	−7.25197	−	29.5241i	−0.314118	−	1.27883i
$534$	10.2976	+	15.9916i	0.445623	+	0.692026i
$535$	16.5515	+	16.5515i	0.715583	+	0.715583i
$536$		−	3.85604i		−	0.166556i
$537$	28.2064	−	1.36919i	1.21719	−	0.0590849i
$538$	−21.5657	−	21.5657i	−0.929764	−	0.929764i
$539$	−0.777775	+	0.522447i	−0.0335011	+	0.0225034i
$540$	13.9895	−	6.03559i	0.602011	−	0.259730i
$541$	−22.3902	−	5.99945i	−0.962632	−	0.257936i	−0.256918	−	0.966433i	$-0.582707\pi$
$541$	−22.3902	−	5.99945i	−0.962632	−	0.257936i	−0.705714	+	0.708497i	$0.749374\pi$
$542$	17.6972	−	10.2175i	0.760160	−	0.438879i
$543$	1.19997	+	24.7203i	0.0514956	+	1.06085i
$544$	0.559097	+	2.08658i	0.0239711	+	0.0894614i
$545$	27.0925			1.16051
$546$	−1.14555	+	16.4830i	−0.0490250	+	0.705405i
$547$	−27.9196			−1.19376			−0.596879	−	0.802332i	$-0.703593\pi$
$547$	−27.9196			−1.19376			−0.596879	+	0.802332i	$0.703593\pi$
$548$	5.24383	+	19.5702i	0.224005	+	0.835999i
$549$	10.8238	−	1.05330i	0.461949	−	0.0449536i
$550$	0.417020	−	0.240767i	0.0177818	−	0.0102663i
$551$	18.1042	+	4.85099i	0.771263	+	0.206659i
$552$	−11.1539	+	3.57664i	−0.474743	+	0.152232i
$553$	−21.2011	−	7.94996i	−0.901563	−	0.338067i
$554$	−8.50993	−	8.50993i	−0.361552	−	0.361552i
$555$	−2.32464	−	47.8893i	−0.0986754	−	2.03279i
$556$			2.26403i			0.0960161i
$557$	25.5455	+	25.5455i	1.08240	+	1.08240i	0.996285	+	0.0861143i	$0.0274450\pi$
$557$	25.5455	+	25.5455i	1.08240	+	1.08240i	0.0861143	+	0.996285i	$0.472555\pi$
$558$	4.46311	+	6.24365i	0.188939	+	0.264315i
$559$	−0.215194	+	10.2758i	−0.00910173	+	0.434622i
$560$	−0.750957	+	7.72132i	−0.0317337	+	0.326285i
$561$	−0.106012	+	0.489460i	−0.00447584	+	0.0206650i
$562$	−13.0699	+	22.6377i	−0.551319	+	0.954913i
$563$	−6.72689	−	11.6513i	−0.283505	−	0.491045i	0.688741	−	0.725008i	$-0.258164\pi$
$563$	−6.72689	−	11.6513i	−0.283505	−	0.491045i	−0.972245	+	0.233963i	$0.924831\pi$
$564$	−0.859362	−	2.67996i	−0.0361857	−	0.112847i
$565$	10.1465	+	10.1465i	0.426868	+	0.426868i
$566$	0.647007	−	0.173365i	0.0271957	−	0.00728708i
$567$	−15.1265	+	18.3899i	−0.635253	+	0.772304i
$568$	4.83987	−	8.38290i	0.203076	−	0.351739i
$569$	1.88081	−	3.25767i	0.0788479	−	0.136569i	−0.823905	−	0.566728i	$-0.808209\pi$
$569$	1.88081	−	3.25767i	0.0788479	−	0.136569i	0.902753	+	0.430159i	$0.141543\pi$
$570$	−10.8030	+	11.9053i	−0.452488	+	0.498659i
$571$	25.5416	+	14.7464i	1.06888	+	0.617119i	0.927875	−	0.372890i	$-0.121633\pi$
$571$	25.5416	+	14.7464i	1.06888	+	0.617119i	0.141005	+	0.990009i	$0.454967\pi$
$572$	0.115120	+	0.468674i	0.00481341	+	0.0195963i
$573$	0.608521	+	12.5360i	0.0254213	+	0.523699i
$574$	14.1736	+	17.2276i	0.591593	+	0.719065i
$575$	−21.0696	+	12.1646i	−0.878665	+	0.507297i
$576$	0.290567	+	2.98590i	0.0121069	+	0.124412i
$577$	5.85695	−	1.56936i	0.243828	−	0.0653335i	−0.134835	−	0.990868i	$-0.543051\pi$
$577$	5.85695	−	1.56936i	0.243828	−	0.0653335i	0.378663	+	0.925535i	$0.376384\pi$
$578$	11.9133	+	3.19217i	0.495529	+	0.132777i
$579$	−23.0611	+	25.4142i	−0.958386	+	1.05618i
$580$	12.2765	−	12.2765i	0.509752	−	0.509752i
$581$	−4.31207	+	44.3366i	−0.178895	+	1.83939i
$582$	−8.35739	−	12.9785i	−0.346425	−	0.537978i
$583$	0.207968	+	0.776148i	0.00861316	+	0.0321448i
$584$	0.454631	−	0.787443i	0.0188127	−	0.0325846i
$585$	10.5132	+	29.9230i	0.434665	+	1.23716i
$586$	−14.4070	−	24.9537i	−0.595148	−	1.03083i
$587$	13.2930	+	3.56184i	0.548659	+	0.147013i	0.522491	−	0.852645i	$-0.325003\pi$
$587$	13.2930	+	3.56184i	0.548659	+	0.147013i	0.0261682	+	0.999658i	$0.491669\pi$
$588$	−4.47687	−	11.2675i	−0.184623	−	0.464666i
$589$	−7.01309	−	4.04901i	−0.288969	−	0.166837i
$590$	9.16665	+	2.45620i	0.377385	+	0.101120i
$591$	16.4660	+	3.56638i	0.677322	+	0.146701i
$592$	9.11897	+	2.44342i	0.374788	+	0.100424i
$593$	−8.92433	+	33.3061i	−0.366478	+	1.36772i	0.498927	+	0.866644i	$0.333727\pi$
$593$	−8.92433	+	33.3061i	−0.366478	+	1.36772i	−0.865406	+	0.501072i	$0.832939\pi$
$594$	−0.256743	+	0.646387i	−0.0105343	+	0.0265216i
$595$	−13.6338	−	9.74462i	−0.558930	−	0.399491i
$596$	4.34914	−	16.2312i	0.178148	−	0.664857i
$597$	−3.83973	+	2.47255i	−0.157150	+	0.101195i
$598$	−5.81636	−	23.6794i	−0.237849	−	0.968324i
$599$	−23.2612	−	13.4299i	−0.950427	−	0.548729i	−0.0572133	−	0.998362i	$-0.518221\pi$
$599$	−23.2612	−	13.4299i	−0.950427	−	0.548729i	−0.893213	+	0.449633i	$0.851555\pi$
$600$	1.90266	+	5.93353i	0.0776756	+	0.242235i
$601$	−8.28214	−	14.3451i	−0.337835	−	0.585148i	0.646190	−	0.763177i	$-0.276361\pi$
$601$	−8.28214	−	14.3451i	−0.337835	−	0.585148i	−0.984025	+	0.178028i	$0.943028\pi$
$602$	−3.12106	−	6.86599i	−0.127205	−	0.279837i
$603$	8.93371	+	7.34918i	0.363809	+	0.299282i
$604$	−13.4652	−	13.4652i	−0.547891	−	0.547891i
$605$	8.33428	−	31.1040i	0.338837	−	1.26456i
$606$	−8.68382	−	27.0809i	−0.352756	−	1.10009i
$607$	42.3422			1.71862			0.859309	−	0.511457i	$-0.170894\pi$
$607$	42.3422			1.71862			0.859309	+	0.511457i	$0.170894\pi$
$608$	−1.58272	−	2.74135i	−0.0641877	−	0.111176i
$609$	−8.28381	+	25.8384i	−0.335677	+	1.04702i
$610$			10.6290i			0.430355i
$611$	5.68947	−	1.39750i	0.230171	−	0.0565368i
$612$	−5.89978	−	2.68146i	−0.238485	−	0.108392i
$613$	9.04276	+	9.04276i	0.365234	+	0.365234i	0.865735	−	0.500502i	$-0.166851\pi$
$613$	9.04276	+	9.04276i	0.365234	+	0.365234i	−0.500502	+	0.865735i	$0.666851\pi$
$614$	−7.12372	−	4.11288i	−0.287490	−	0.165983i
$615$	38.0800	+	19.5881i	1.53553	+	0.789866i
$616$	−0.224996	−	0.273476i	−0.00906534	−	0.0110187i
$617$	−0.689142	−	2.57191i	−0.0277438	−	0.103541i	0.950666	−	0.310218i	$-0.100402\pi$
$617$	−0.689142	−	2.57191i	−0.0277438	−	0.103541i	−0.978409	+	0.206676i	$0.933735\pi$
$618$	−23.9094	−	21.6956i	−0.961777	−	0.872726i
$619$	−11.7157	−	43.7236i	−0.470894	−	1.75740i	−0.636567	−	0.771221i	$-0.719646\pi$
$619$	−11.7157	−	43.7236i	−0.470894	−	1.75740i	0.165673	−	0.986181i	$-0.447020\pi$
$620$	−6.49626	+	3.75062i	−0.260896	+	0.150628i
$621$	12.9717	−	32.6582i	0.520538	−	1.31053i
$622$	−1.11731	−	0.299382i	−0.0448000	−	0.0120041i
$623$	16.8945	−	23.6372i	0.676863	−	0.947004i
$624$	−6.24263	+	0.172123i	−0.249905	+	0.00689042i
$625$	−15.0227	−	26.0201i	−0.600908	−	1.04080i
$626$	−7.78779	+	7.78779i	−0.311263	+	0.311263i
$627$	−0.0355812	−	0.733000i	−0.00142097	−	0.0292732i
$628$		−	3.83426i		−	0.153004i
$629$	−14.4204	+	14.4204i	−0.574981	+	0.574981i
$630$	−16.4576	−	16.4558i	−0.655686	−	0.655614i
$631$	−5.90872	−	22.0517i	−0.235223	−	0.877863i	−0.978048	−	0.208378i	$-0.933182\pi$
$631$	−5.90872	−	22.0517i	−0.235223	−	0.877863i	0.742826	−	0.669485i	$-0.233485\pi$
$632$	2.21500	−	8.26650i	0.0881081	−	0.328824i
$633$	20.5111	+	31.8526i	0.815244	+	1.26603i
$634$			28.0779i			1.11511i
$635$	−0.336462	+	0.0901547i	−0.0133521	+	0.00357768i
$636$	−10.3855	+	0.504134i	−0.411814	+	0.0199902i
$637$	24.0454	−	7.66940i	0.952713	−	0.303873i
$638$			0.792541i			0.0313770i
$639$	10.1973	+	27.1899i	0.403400	+	1.07562i
$640$	−2.93216			−0.115904
$641$	−11.8674	−	20.5549i	−0.468734	−	0.811871i	0.530627	−	0.847605i	$-0.321956\pi$
$641$	−11.8674	−	20.5549i	−0.468734	−	0.811871i	−0.999361	+	0.0357341i	$0.988623\pi$
$642$	2.92691	−	13.5136i	0.115516	−	0.533338i
$643$	8.21147	−	2.20026i	0.323829	−	0.0867696i	−0.0932426	−	0.995643i	$-0.529723\pi$
$643$	8.21147	−	2.20026i	0.323829	−	0.0867696i	0.417071	+	0.908874i	$0.363057\pi$
$644$	11.3678	+	13.8172i	0.447952	+	0.544473i
$645$	−10.7213	−	9.72865i	−0.422152	−	0.383065i
$646$	6.83793			0.269035
$647$	−3.38505			−0.133080			−0.0665400	−	0.997784i	$-0.521196\pi$
$647$	−3.38505			−0.133080			−0.0665400	+	0.997784i	$0.521196\pi$
$648$	−7.47153	−	5.01759i	−0.293510	−	0.197109i
$649$	−0.375172	+	0.216606i	−0.0147268	+	0.00850253i
$650$	−12.5967	+	3.09411i	−0.494082	+	0.121361i
$651$	6.34654	−	9.85700i	0.248741	−	0.386326i
$652$	3.20232	−	11.9512i	0.125412	−	0.468046i
$653$	22.1591	+	12.7936i	0.867153	+	0.500651i	0.866401	−	0.499349i	$-0.166427\pi$
$653$	22.1591	+	12.7936i	0.867153	+	0.500651i	0.000751918		1.00000i	$0.499761\pi$
$654$	−8.66446	−	13.4554i	−0.338807	−	0.526148i
$655$	13.2076	−	3.53897i	0.516064	−	0.138279i
$656$	−5.96226	+	5.96226i	−0.232787	+	0.232787i
$657$	0.957881	+	2.55407i	0.0373705	+	0.0996437i
$658$	−3.31986	+	2.73133i	−0.129422	+	0.106479i
$659$	2.83835	+	1.63872i	0.110567	+	0.0638356i	0.554263	−	0.832341i	$-0.313000\pi$
$659$	2.83835	+	1.63872i	0.110567	+	0.0638356i	−0.443697	+	0.896177i	$0.646333\pi$
$660$	−0.604494	−	0.310947i	−0.0235299	−	0.0121036i
$661$	−13.0829	+	13.0829i	−0.508867	+	0.508867i	−0.914178	−	0.405312i	$-0.867163\pi$
$661$	−13.0829	+	13.0829i	−0.508867	+	0.508867i	0.405312	+	0.914178i	$0.367163\pi$
$662$	−14.1380	+	24.4877i	−0.549488	+	0.951741i
$663$	6.42062	−	11.8645i	0.249356	−	0.460778i
$664$	−16.8367			−0.653392
$665$	22.9933	+	8.62199i	0.891642	+	0.334347i
$666$	−23.0407	+	16.4700i	−0.892807	+	0.638201i
$667$		−	40.0426i		−	1.55045i
$668$	−4.23341	−	15.7993i	−0.163796	−	0.611294i
$669$	−1.71111	+	7.90023i	−0.0661554	+	0.305440i
$670$	−7.99492	+	7.99492i	−0.308871	+	0.308871i
$671$	−0.343092	−	0.343092i	−0.0132449	−	0.0132449i
$672$	4.07494	−	2.09640i	0.157194	−	0.0808704i
$673$	−4.38737	+	2.53305i	−0.169121	+	0.0976418i	−0.582171	−	0.813066i	$-0.697797\pi$
$673$	−4.38737	+	2.53305i	−0.169121	+	0.0976418i	0.413051	+	0.910708i	$0.364463\pi$
$674$	−13.3096	+	3.56629i	−0.512666	+	0.137368i
$675$	−17.3731	−	6.90054i	−0.668691	−	0.265602i
$676$	0.544246	−	12.9886i	0.0209325	−	0.499562i
$677$	−10.7044	+	6.18020i	−0.411405	+	0.237525i	−0.691393	−	0.722479i	$-0.743003\pi$
$677$	−10.7044	+	6.18020i	−0.411405	+	0.237525i	0.279988	+	0.960003i	$0.409669\pi$
$678$	1.79428	−	8.28421i	0.0689088	−	0.318153i
$679$	−13.7113	+	19.1835i	−0.526190	+	0.736196i
$680$	3.16700	−	5.48541i	0.121449	−	0.210356i
$681$	−42.0482	−	9.10723i	−1.61129	−	0.348990i
$682$	0.0886263	−	0.330758i	0.00339368	−	0.0126654i
$683$	−5.89273	+	21.9920i	−0.225479	+	0.841499i	0.756733	+	0.653724i	$0.226794\pi$
$683$	−5.89273	+	21.9920i	−0.225479	+	0.841499i	−0.982212	+	0.187775i	$0.939872\pi$
$684$	9.36765	+	1.55784i	0.358181	+	0.0595655i
$685$	29.7036	−	51.4481i	1.13492	−	1.96573i
$686$	−13.4708	+	12.7098i	−0.514316	+	0.485262i
$687$	0.481273	+	0.104239i	0.0183617	+	0.00397697i
$688$	2.46872	−	1.42532i	0.0941191	−	0.0543397i
$689$	0.453178	−	21.6400i	0.0172647	−	0.824417i
$690$	30.5416	+	15.7104i	1.16270	+	0.598084i
$691$	33.4231	−	8.95570i	1.27148	−	0.340691i	0.440879	−	0.897566i	$-0.354667\pi$
$691$	33.4231	−	8.95570i	1.27148	−	0.340691i	0.830596	+	0.556876i	$0.188000\pi$
$692$	9.65414	−	5.57382i	0.366995	−	0.211885i
$693$	1.06241		5.84225e-5i	0.0403575		2.21929e-6i
$694$	−15.2660	−	15.2660i	−0.579490	−	0.579490i
$695$	4.69411	−	4.69411i	0.178058	−	0.178058i
$696$	−10.0232	−	2.17093i	−0.379929	−	0.0822888i
$697$	−4.71426	−	17.5938i	−0.178565	−	0.666414i
$698$			4.29551i			0.162587i
$699$	8.53007	+	13.2467i	0.322637	+	0.501036i
$700$	7.35028	−	6.04727i	0.277814	−	0.228565i
$701$	−47.0698			−1.77780			−0.888901	−	0.458099i	$-0.848530\pi$
$701$	−47.0698			−1.77780			−0.888901	+	0.458099i	$0.848530\pi$
$702$	11.4990	−	14.7910i	0.434000	−	0.558251i
$703$	14.9419	−	25.8801i	0.563544	−	0.976087i
$704$	0.0946467	−	0.0946467i	0.00356713	−	0.00356713i
$705$	−3.77474	+	7.33825i	−0.142165	+	0.276375i
$706$	9.53729	+	5.50635i	0.358940	+	0.207234i
$707$	−33.5470	+	27.6000i	−1.26167	+	1.03801i
$708$	−1.71173	−	5.33811i	−0.0643306	−	0.200618i
$709$	1.88292	−	1.88292i	0.0707147	−	0.0707147i	−0.670865	−	0.741580i	$-0.734077\pi$
$709$	1.88292	−	1.88292i	0.0707147	−	0.0707147i	0.741580	+	0.670865i	$0.234077\pi$
$710$	−27.4154	+	7.34593i	−1.02888	+	0.275688i
$711$	14.9304	+	20.8867i	0.559932	+	0.783314i
$712$	9.51018	+	5.49071i	0.356409	+	0.205773i
$713$	−4.47778	+	16.7113i	−0.167694	+	0.625843i
$714$	−0.479418	+	9.88760i	−0.0179418	+	0.370034i
$715$	0.733041	−	1.21041i	0.0274142	−	0.0452667i
$716$	14.1198	−	8.15206i	0.527681	−	0.304657i
$717$	3.94297	−	4.34529i	0.147253	−	0.162278i
$718$	11.6031			0.433025
$719$	7.23206			0.269710			0.134855	−	0.990865i	$-0.456943\pi$
$719$	7.23206			0.269710			0.134855	+	0.990865i	$0.456943\pi$
$720$	5.58835	−	6.79324i	0.208266	−	0.253169i
$721$	−17.3155	+	46.1773i	−0.644863	+	1.71973i
$722$	8.67403	−	2.32420i	0.322814	−	0.0864978i
$723$	−46.9405	−	10.1669i	−1.74574	−	0.378110i
$724$	7.14454	+	12.3747i	0.265525	+	0.459902i
$725$	−21.3013			−0.791111
$726$	−18.1131	+	5.80817i	−0.672239	+	0.215562i
$727$			7.79019i			0.288922i	0.989510	+	0.144461i	$0.0461448\pi$
$727$			7.79019i			0.288922i	−0.989510	+	0.144461i	$0.953855\pi$
$728$	3.76490	+	8.76502i	0.139537	+	0.324853i
$729$	25.8647	−	7.74717i	0.957951	−	0.286932i
$730$	−2.57525	+	0.690036i	−0.0953143	+	0.0255394i
$731$			6.15790i			0.227758i
$732$	5.27886	−	3.39926i	0.195112	−	0.125640i
$733$	−1.39605	+	5.21015i	−0.0515644	+	0.192441i	−0.986904	−	0.161311i	$-0.948428\pi$
$733$	−1.39605	+	5.21015i	−0.0515644	+	0.192441i	0.935339	+	0.353752i	$0.115094\pi$
$734$	7.48308	+	27.9272i	0.276205	+	1.03081i
$735$	−14.0794	+	32.6436i	−0.519328	+	1.20408i
$736$	−4.78196	+	4.78196i	−0.176265	+	0.176265i
$737$		−	0.516134i		−	0.0190120i
$738$	−2.45003	−	25.1768i	−0.0901868	−	0.926770i
$739$	−12.3831	+	12.3831i	−0.455519	+	0.455519i	−0.897181	−	0.441662i	$-0.854389\pi$
$739$	−12.3831	+	12.3831i	−0.455519	+	0.455519i	0.441662	+	0.897181i	$0.354389\pi$
$740$	−13.8407	−	23.9729i	−0.508796	−	0.881260i
$741$	−4.58815	+	19.2283i	−0.168550	+	0.706370i
$742$	6.57265	+	14.4591i	0.241289	+	0.530811i
$743$	−15.2513	−	4.08656i	−0.559514	−	0.149921i	−0.0320310	−	0.999487i	$-0.510198\pi$
$743$	−15.2513	−	4.08656i	−0.559514	−	0.149921i	−0.527483	+	0.849566i	$0.676864\pi$
$744$	3.94030	+	2.02686i	0.144459	+	0.0743083i
$745$	−42.6702	+	24.6357i	−1.56332	+	0.902581i
$746$	1.96802	+	7.34477i	0.0720545	+	0.268911i
$747$	32.0889	−	39.0075i	1.17407	−	1.42721i
$748$	0.0748356	+	0.279290i	0.00273626	+	0.0102119i
$749$	−20.8346	+	3.46597i	−0.761281	+	0.126644i
$750$	−3.25804	+	6.33376i	−0.118967	+	0.231276i
$751$	8.05891	+	4.65282i	0.294074	+	0.169784i	0.639778	−	0.768560i	$-0.279026\pi$
$751$	8.05891	+	4.65282i	0.294074	+	0.169784i	−0.345704	+	0.938344i	$0.612360\pi$
$752$	−1.14896	−	1.14896i	−0.0418984	−	0.0418984i
$753$	−10.7123	+	20.8252i	−0.390378	+	0.758911i
$754$	5.95601	−	20.5011i	0.216905	−	0.746606i
$755$			55.8361i			2.03208i
$756$	−2.90941	+	13.4363i	−0.105814	+	0.488675i
$757$	−18.8965	−	32.7296i	−0.686804	−	1.18958i	−0.972866	−	0.231368i	$-0.925680\pi$
$757$	−18.8965	−	32.7296i	−0.686804	−	1.18958i	0.286063	−	0.958211i	$-0.407653\pi$
$758$	24.0201			0.872449
$759$	−1.49296	+	0.478736i	−0.0541911	+	0.0173770i
$760$	−2.40224	+	8.96529i	−0.0871385	+	0.325205i
$761$	14.6244	+	14.6244i	0.530134	+	0.530134i	0.920612	−	0.390478i	$-0.127690\pi$
$761$	14.6244	+	14.6244i	0.530134	+	0.530134i	−0.390478	+	0.920612i	$0.627690\pi$
$762$	0.152379	+	0.138270i	0.00552011	+	0.00500901i
$763$	−14.2151	+	19.8884i	−0.514619	+	0.720007i
$764$	3.62309	+	6.27538i	0.131079	+	0.227035i
$765$	6.67270	+	17.7919i	0.241252	+	0.643267i
$766$	1.79502	+	1.03636i	0.0648569	+	0.0374451i
$767$	11.3326	−	2.78362i	0.409197	−	0.100511i
$768$	0.937734	+	1.45625i	0.0338376	+	0.0525478i
$769$	1.26785	−	4.73168i	0.0457198	−	0.170629i	−0.939291	−	0.343122i	$-0.888516\pi$
$769$	1.26785	−	4.73168i	0.0457198	−	0.170629i	0.985011	+	0.172493i	$0.0551823\pi$
$770$	−0.100516	+	1.03350i	−0.00362235	+	0.0372449i
$771$	−20.2041	+	39.2777i	−0.727635	+	1.41455i
$772$	−5.12804	+	19.1381i	−0.184562	+	0.688796i
$773$	−28.3583	−	7.59859i	−1.01998	−	0.273302i	−0.290185	−	0.956970i	$-0.593717\pi$
$773$	−28.3583	−	7.59859i	−1.01998	−	0.273302i	−0.729793	+	0.683668i	$0.760384\pi$
$774$	−1.40291	+	8.43604i	−0.0504267	+	0.303227i
$775$	8.88986	+	2.38203i	0.319333	+	0.0855651i
$776$	−7.71830	−	4.45616i	−0.277071	−	0.159967i
$777$	36.3749	+	23.4204i	1.30494	+	0.840201i
$778$	29.6507	+	7.94487i	1.06303	+	0.284837i
$779$	13.3453	+	23.1148i	0.478146	+	0.828173i
$780$	13.3000	+	12.5863i	0.476216	+	0.450660i
$781$	0.647820	−	1.12206i	0.0231808	−	0.0401504i
$782$	−3.78102	−	14.1109i	−0.135209	−	0.504606i
$783$	24.1327	−	19.0843i	0.862433	−	0.682018i
$784$	−5.27414	−	4.60254i	−0.188362	−	0.164377i
$785$	−7.94976	+	7.94976i	−0.283739	+	0.283739i
$786$	−5.98155	−	5.42772i	−0.213355	−	0.193600i
$787$	−16.7617	−	4.49128i	−0.597489	−	0.160097i	−0.0526155	−	0.998615i	$-0.516756\pi$
$787$	−16.7617	−	4.49128i	−0.597489	−	0.160097i	−0.544874	+	0.838518i	$0.683422\pi$
$788$	9.39565	−	2.51756i	0.334706	−	0.0896843i
$789$	−0.909566	−	18.7378i	−0.0323814	−	0.667082i
$790$	−21.7318	+	12.5469i	−0.773183	+	0.446397i
$791$	−12.7722	+	2.12474i	−0.454128	+	0.0755471i
$792$	0.0388925	+	0.399664i	0.00138199	+	0.0142014i
$793$	6.29660	+	11.4533i	0.223599	+	0.406720i
$794$	−17.0218	−	9.82753i	−0.604080	−	0.348766i
$795$	22.5781	+	20.4876i	0.800763	+	0.726621i
$796$	−1.31837	+	2.28348i	−0.0467283	+	0.0809357i
$797$	−5.87148	+	10.1697i	−0.207978	+	0.360229i	−0.951078	−	0.308952i	$-0.900022\pi$
$797$	−5.87148	+	10.1697i	−0.207978	+	0.360229i	0.743099	+	0.669181i	$0.233355\pi$
$798$	−3.07141	−	14.1770i	−0.108727	−	0.501859i
$799$	3.39044	−	0.908466i	0.119945	−	0.0321392i
$800$	2.54384	+	2.54384i	0.0899385	+	0.0899385i
$801$	−30.8462	+	11.5686i	−1.08990	+	0.408757i
$802$	16.0157	+	27.7400i	0.565533	+	0.979532i
$803$	0.0608526	−	0.105400i	0.00214744	−	0.00371948i
$804$	6.52751	+	1.41379i	0.230208	+	0.0498607i
$805$	5.07851	−	52.2171i	0.178994	−	1.84041i
$806$	−4.77822	+	7.88987i	−0.168305	+	0.277909i
$807$	44.4134	−	28.5995i	1.56342	−	1.00675i
$808$	−11.6102	−	11.6102i	−0.408447	−	0.408447i
$809$		−	24.1633i		−	0.849537i	−0.905302	−	0.424769i	$-0.860355\pi$
$809$		−	24.1633i		−	0.849537i	0.905302	−	0.424769i	$-0.139645\pi$
$810$	5.08789	+	25.8943i	0.178770	+	0.909833i
$811$	25.9393	+	25.9393i	0.910851	+	0.910851i	0.996339	−	0.0854880i	$-0.0272449\pi$
$811$	25.9393	+	25.9393i	0.910851	+	0.910851i	−0.0854880	+	0.996339i	$0.527245\pi$
$812$	2.57076	+	15.4533i	0.0902160	+	0.542306i
$813$	10.8076	+	33.7040i	0.379039	+	1.18205i
$814$	1.22058	+	0.327054i	0.0427813	+	0.0114632i
$815$	−31.4185	+	18.1395i	−1.10054	+	0.635399i
$816$	−3.73715	+	0.181408i	−0.130827	+	0.00635056i
$817$	−2.33545	−	8.71603i	−0.0817071	−	0.304935i
$818$	3.07026			0.107349
$819$	−27.4823	−	7.98256i	−0.960311	−	0.278933i
$820$	24.7237			0.863388
$821$	−1.36005	−	5.07579i	−0.0474662	−	0.177146i	0.938123	−	0.346302i	$-0.112563\pi$
$821$	−1.36005	−	5.07579i	−0.0474662	−	0.177146i	−0.985589	+	0.169155i	$0.945896\pi$
$822$	−35.0511	+	1.70145i	−1.22255	+	0.0593447i
$823$	10.2408	−	5.91253i	0.356972	−	0.206098i	−0.310780	−	0.950482i	$-0.600590\pi$
$823$	10.2408	−	5.91253i	0.356972	−	0.206098i	0.667752	+	0.744384i	$0.267257\pi$
$824$	−18.0049	−	4.82441i	−0.627232	−	0.168066i
$825$	0.254672	+	0.794207i	0.00886654	+	0.0276507i
$826$	−6.61269	+	5.44043i	−0.230085	+	0.189297i
$827$	−35.8194	−	35.8194i	−1.24556	−	1.24556i	−0.957659	−	0.287904i	$-0.907042\pi$
$827$	−35.8194	−	35.8194i	−1.24556	−	1.24556i	−0.287904	−	0.957659i	$-0.592958\pi$
$828$	−1.96502	−	20.1928i	−0.0682891	−	0.701747i
$829$			33.7978i			1.17384i	0.809643	+	0.586922i	$0.199661\pi$
$829$			33.7978i			1.17384i	−0.809643	+	0.586922i	$0.800339\pi$
$830$	34.9084	+	34.9084i	1.21169	+	1.21169i
$831$	17.5257	−	11.2855i	0.607960	−	0.391489i
$832$	−3.15956	+	1.73700i	−0.109538	+	0.0602198i
$833$	14.3069	−	4.89557i	0.495705	−	0.169621i
$834$	−3.83254	−	0.830091i	−0.132710	−	0.0287437i
$835$	−23.9801	+	41.5348i	−0.829867	+	1.43737i
$836$	−0.211848	−	0.366931i	−0.00732691	−	0.0126906i
$837$	−12.2056	+	5.26596i	−0.421888	+	0.182018i
$838$	−16.6208	−	16.6208i	−0.574157	−	0.574157i
$839$	−12.8582	+	3.44535i	−0.443916	+	0.118947i	−0.473851	−	0.880605i	$-0.657136\pi$
$839$	−12.8582	+	3.44535i	−0.443916	+	0.118947i	0.0299355	+	0.999552i	$0.490470\pi$
$840$	−12.7953	−	4.10220i	−0.441481	−	0.141539i
$841$	3.02960	−	5.24742i	0.104469	−	0.180945i
$842$	−7.43259	+	12.8736i	−0.256144	+	0.443654i
$843$	−33.5291	−	30.4247i	−1.15480	−	1.04788i
$844$	18.9426	+	10.9365i	0.652032	+	0.376451i
$845$	−28.0583	+	25.8015i	−0.965235	+	0.887598i
$846$	4.85172	−	0.472136i	0.166806	−	0.0162324i
$847$	18.4603	+	22.4379i	0.634303	+	0.770977i
$848$	−5.19889	+	3.00158i	−0.178531	+	0.103075i
$849$	0.0562512	+	1.15882i	0.00193054	+	0.0397705i
$850$	−7.50655	+	2.01138i	−0.257473	+	0.0689896i
$851$	−61.6690	−	16.5242i	−2.11399	−	0.566441i
$852$	12.4161	+	11.2665i	0.425367	+	0.385983i
$853$	33.2414	−	33.2414i	1.13816	−	1.13816i	0.149385	−	0.988779i	$-0.452271\pi$
$853$	33.2414	−	33.2414i	1.13816	−	1.13816i	0.988779	−	0.149385i	$-0.0477294\pi$
$854$	−7.80266	−	5.57689i	−0.267002	−	0.190837i
$855$	−16.1925	−	22.6523i	−0.553770	−	0.774694i
$856$	−2.06615	−	7.71096i	−0.0706194	−	0.263555i
$857$	−24.2792	+	42.0528i	−0.829362	+	1.43650i	0.0691766	+	0.997604i	$0.477963\pi$
$857$	−24.2792	+	42.0528i	−0.829362	+	1.43650i	−0.898539	+	0.438894i	$0.855371\pi$
$858$	−0.835580	+	0.0230387i	−0.0285262	+	0.000786529i
$859$	−23.5636	−	40.8133i	−0.803979	−	1.39253i	−0.916978	−	0.398938i	$-0.869379\pi$
$859$	−23.5636	−	40.8133i	−0.803979	−	1.39253i	0.112998	−	0.993595i	$-0.463954\pi$
$860$	−8.07369	−	2.16334i	−0.275311	−	0.0737693i
$861$	−34.3595	+	17.6766i	−1.17097	+	0.602418i
$862$	5.14636	+	2.97125i	0.175286	+	0.101201i
$863$	40.0344	+	10.7272i	1.36279	+	0.365158i	0.864839	−	0.502050i	$-0.167421\pi$
$863$	40.0344	+	10.7272i	1.36279	+	0.365158i	0.497948	+	0.867207i	$0.334087\pi$
$864$	−5.16106	−	0.602889i	−0.175583	−	0.0205107i
$865$	−31.5729	−	8.45992i	−1.07351	−	0.287646i
$866$	−3.67568	+	13.7178i	−0.124905	+	0.466151i
$867$	−9.77166	+	18.9965i	−0.331863	+	0.645155i
$868$	0.655199	−	6.73675i	0.0222389	−	0.228660i
$869$	0.296480	−	1.10648i	0.0100574	−	0.0375347i
$870$	16.2805	+	25.2827i	0.551961	+	0.857163i
$871$	−3.87879	+	13.3511i	−0.131428	+	0.452386i
$872$	−8.00189	−	4.61989i	−0.270978	−	0.156449i
$873$	25.0343	−	9.38888i	0.847281	−	0.317766i
$874$	10.7035	+	18.5389i	0.362050	+	0.627089i
$875$	10.8289	+	1.05319i	0.366082	+	0.0356042i
$876$	1.16630	+	1.05831i	0.0394055	+	0.0357570i
$877$	−4.04539	−	4.04539i	−0.136603	−	0.136603i	0.635499	−	0.772102i	$-0.280795\pi$
$877$	−4.04539	−	4.04539i	−0.136603	−	0.136603i	−0.772102	+	0.635499i	$0.780795\pi$
$878$	−4.81846	+	17.9827i	−0.162615	+	0.606888i
$879$	47.5238	−	15.2391i	1.60294	−	0.514001i
$880$	−0.392471			−0.0132302
$881$	−4.45775	−	7.72106i	−0.150186	−	0.260129i	0.781110	−	0.624393i	$-0.214654\pi$
$881$	−4.45775	−	7.72106i	−0.150186	−	0.260129i	−0.931296	+	0.364264i	$0.881320\pi$
$882$	20.7151	−	3.44726i	0.697515	−	0.116075i
$883$			27.8617i			0.937622i	0.883298	+	0.468811i	$0.155317\pi$
$883$			27.8617i			0.937622i	−0.883298	+	0.468811i	$0.844683\pi$
$884$	0.163072	−	7.78696i	0.00548471	−	0.261904i
$885$	−7.51874	+	14.6168i	−0.252740	+	0.491337i
$886$	−21.0250	−	21.0250i	−0.706350	−	0.706350i
$887$	29.2780	+	16.9036i	0.983057	+	0.567568i	0.903192	−	0.429237i	$-0.141218\pi$
$887$	29.2780	+	16.9036i	0.983057	+	0.567568i	0.0798656	+	0.996806i	$0.474551\pi$
$888$	−7.47964	+	14.5407i	−0.251000	+	0.487955i
$889$	0.110355	−	0.294297i	0.00370119	−	0.00987040i
$890$	−8.33377	−	31.1021i	−0.279349	−	1.04254i
$891$	−1.00007	−	0.671608i	−0.0335036	−	0.0224997i
$892$	1.20790	+	4.50794i	0.0404434	+	0.150937i
$893$	−4.45436	+	2.57173i	−0.149060	+	0.0860595i
$894$	25.8816	+	13.3133i	0.865611	+	0.445263i
$895$	−46.1773	−	12.3732i	−1.54354	−	0.413589i
$896$	1.53846	−	2.15247i	0.0513964	−	0.0719090i
$897$	42.2171	−	1.16402i	1.40959	−	0.0388653i
$898$	10.9969	+	19.0473i	0.366973	+	0.635615i
$899$	−10.7110	+	10.7110i	−0.357233	+	0.357233i
$900$	−10.7419	+	1.04532i	−0.358063	+	0.0348442i
$901$		−	12.9679i		−	0.432025i
$902$	−0.798052	+	0.798052i	−0.0265722	+	0.0265722i
$903$	12.7671	−	2.76595i	0.424861	−	0.0920452i
$904$	−1.26661	−	4.72704i	−0.0421267	−	0.157219i
$905$	10.8440	−	40.4702i	0.360465	−	1.34527i
$906$	27.7308	−	17.8570i	0.921295	−	0.593258i
$907$		−	10.6997i		−	0.355278i	−0.984096	−	0.177639i	$-0.943154\pi$
$907$		−	10.6997i		−	0.355278i	0.984096	−	0.177639i	$-0.0568459\pi$
$908$	−23.9931	+	6.42892i	−0.796238	+	0.213351i
$909$	49.0265	−	4.77091i	1.62610	−	0.158241i
$910$	10.3670	−	25.9789i	0.343662	−	0.861191i
$911$		−	43.5285i		−	1.44216i	−0.692850	−	0.721082i	$-0.743645\pi$
$911$		−	43.5285i		−	1.44216i	0.692850	−	0.721082i	$-0.256355\pi$
$912$	5.22085	−	1.67413i	0.172880	−	0.0554359i
$913$	−2.25361			−0.0745835
$914$	−11.1800	−	19.3643i	−0.369802	−	0.640516i
$915$	−17.9928	−	3.89706i	−0.594823	−	0.128833i
$916$	0.274618	−	0.0735838i	0.00907365	−	0.00243128i
$917$	−4.33192	+	11.5524i	−0.143053	+	0.381495i
$918$	6.70230	−	9.00401i	0.221209	−	0.297177i
$919$	37.7447			1.24508			0.622541	−	0.782587i	$-0.286100\pi$
$919$	37.7447			1.24508			0.622541	+	0.782587i	$0.286100\pi$
$920$	19.8293			0.653754
$921$	9.57416	−	10.5511i	0.315479	−	0.347670i
$922$	−8.88705	+	5.13094i	−0.292679	+	0.168979i
$923$	−25.1899	+	24.1565i	−0.829135	+	0.795120i
$924$	0.545433	−	0.280605i	0.0179434	−	0.00923121i
$925$	−8.79031	+	32.8059i	−0.289023	+	1.07865i
$926$	−22.9017	−	13.2223i	−0.752597	−	0.434512i
$927$	45.4926	−	32.5192i	1.49417	−	1.06807i
$928$	−5.71932	+	1.53249i	−0.187746	+	0.0503064i
$929$	−13.4736	+	13.4736i	−0.442056	+	0.442056i	−0.892702	−	0.450647i	$-0.851193\pi$
$929$	−13.4736	+	13.4736i	−0.442056	+	0.442056i	0.450647	+	0.892702i	$0.351193\pi$
$930$	−3.96723	−	12.3720i	−0.130091	−	0.405694i
$931$	−18.3936	+	12.3553i	−0.602826	+	0.404930i
$932$	7.87777	+	4.54823i	0.258045	+	0.148982i
$933$	0.916448	−	1.78161i	0.0300032	−	0.0583274i
$934$	22.6731	−	22.6731i	0.741888	−	0.741888i
$935$	0.423906	−	0.734226i	0.0138632	−	0.0240118i
$936$	1.99745	−	10.6306i	0.0652887	−	0.347473i
$937$	−36.6004			−1.19568			−0.597842	−	0.801614i	$-0.703975\pi$
$937$	−36.6004			−1.19568			−0.597842	+	0.801614i	$0.703975\pi$
$938$	−1.67418	−	10.0638i	−0.0546640	−	0.328596i
$939$	−10.3278	−	16.0385i	−0.337036	−	0.523397i
$940$			4.76440i			0.155398i
$941$	5.31857	+	19.8492i	0.173380	+	0.647064i	0.996822	+	0.0796631i	$0.0253844\pi$
$941$	5.31857	+	19.8492i	0.173380	+	0.647064i	−0.823441	+	0.567401i	$0.807949\pi$
$942$	6.49064	+	1.40581i	0.211476	+	0.0458037i
$943$	40.3210	−	40.3210i	1.31303	−	1.31303i
$944$	−2.28857	−	2.28857i	−0.0744867	−	0.0744867i
$945$	33.8904	−	21.8260i	1.10246	−	0.710000i
$946$	0.330440	−	0.190780i	0.0107435	−	0.00620278i
$947$	16.3711	−	4.38661i	0.531988	−	0.142546i	0.0171818	−	0.999852i	$-0.494531\pi$
$947$	16.3711	−	4.38661i	0.531988	−	0.142546i	0.514806	+	0.857307i	$0.327864\pi$
$948$	13.1814	+	6.78042i	0.428113	+	0.220218i
$949$	−2.36620	+	2.26913i	−0.0768100	+	0.0736590i
$950$	9.86211	−	5.69389i	0.319969	−	0.184734i
$951$	−47.5302	−	10.2946i	−1.54127	−	0.333824i
$952$	2.36511	+	5.20299i	0.0766537	+	0.168630i
$953$	−10.0098	+	17.3374i	−0.324248	+	0.561614i	−0.981360	−	0.192179i	$-0.938445\pi$
$953$	−10.0098	+	17.3374i	−0.324248	+	0.561614i	0.657112	+	0.753793i	$0.271778\pi$
$954$	2.95440	−	17.7655i	0.0956522	−	0.575179i
$955$	5.49911	−	20.5230i	0.177947	−	0.664108i
$956$	0.876789	−	3.27222i	0.0283574	−	0.105831i
$957$	−1.34161	−	0.290580i	−0.0433682	−	0.00939313i
$958$	12.0836	−	20.9294i	0.390403	−	0.676198i
$959$	22.1826	+	48.7993i	0.716313	+	1.57581i
$960$	1.07506	−	4.96355i	0.0346973	−	0.160198i
$961$	−21.1789	+	12.2276i	−0.683190	+	0.394440i
$962$	−29.1156	−	17.6328i	−0.938726	−	0.568506i
$963$	21.8027	+	9.90934i	0.702581	+	0.319324i
$964$	−26.7847	+	7.17693i	−0.862676	+	0.231153i
$965$	50.3122	−	29.0478i	1.61961	−	0.935080i
$966$	−27.5576	+	14.1773i	−0.886652	+	0.456149i
$967$	9.02589	+	9.02589i	0.290253	+	0.290253i	0.837180	−	0.546927i	$-0.184203\pi$
$967$	9.02589	+	9.02589i	0.290253	+	0.290253i	−0.546927	+	0.837180i	$0.684203\pi$
$968$	−7.76551	+	7.76551i	−0.249593	+	0.249593i
$969$	−2.50709	+	11.5752i	−0.0805392	+	0.371851i
$970$	6.76354	+	25.2419i	0.217164	+	0.810468i
$971$		−	6.47613i		−	0.207829i	−0.994586	−	0.103914i	$-0.966863\pi$
$971$		−	6.47613i		−	0.207829i	0.994586	−	0.103914i	$-0.0331368\pi$
$972$	11.2332	−	10.8081i	0.360304	−	0.346671i
$973$	0.982974	+	5.90885i	0.0315127	+	0.189429i
$974$	34.7592			1.11376
$975$	−0.619218	−	22.4581i	−0.0198308	−	0.719235i
$976$	1.81249	−	3.13932i	0.0580163	−	0.100487i
$977$	−1.95030	+	1.95030i	−0.0623955	+	0.0623955i	−0.737616	−	0.675220i	$-0.764048\pi$
$977$	−1.95030	+	1.95030i	−0.0623955	+	0.0623955i	0.675220	+	0.737616i	$0.264048\pi$
$978$	19.0569	+	9.80272i	0.609373	+	0.313457i
$979$	1.27294	+	0.734935i	0.0406835	+	0.0234886i
$980$	1.39246	+	20.4778i	0.0444806	+	0.654139i
$981$	25.9541	−	9.73385i	0.828650	−	0.310778i
$982$	−0.988823	+	0.988823i	−0.0315546	+	0.0315546i
$983$	−11.6414	+	3.11930i	−0.371303	+	0.0994902i	−0.439645	−	0.898172i	$-0.644896\pi$
$983$	−11.6414	+	3.11930i	−0.371303	+	0.0994902i	0.0683422	+	0.997662i	$0.478229\pi$
$984$	−7.90688	−	12.2789i	−0.252062	−	0.391438i
$985$	−24.7002	−	14.2607i	−0.787015	−	0.454383i
$986$	3.31046	−	12.3548i	0.105427	−	0.393457i
$987$	−3.40640	−	6.62128i	−0.108427	−	0.210758i
$988$	2.72247	+	11.0837i	0.0866134	+	0.352619i
$989$	−16.6953	+	9.63901i	−0.530878	+	0.306503i
$990$	0.748005	−	0.909281i	0.0237732	−	0.0288988i
$991$	7.34221			0.233233			0.116617	−	0.993177i	$-0.462795\pi$
$991$	7.34221			0.233233			0.116617	+	0.993177i	$0.462795\pi$
$992$	2.55827			0.0812250
$993$	−36.2692	−	32.9110i	−1.15097	−	1.04440i
$994$	8.99189	−	23.9797i	0.285205	−	0.760591i
$995$	7.46788	−	2.00101i	0.236748	−	0.0634363i
$996$	6.17308	−	28.5012i	0.195602	−	0.903095i
$997$	−23.0671	−	39.9534i	−0.730542	−	1.26534i	−0.956652	−	0.291234i	$-0.905934\pi$
$997$	−23.0671	−	39.9534i	−0.730542	−	1.26534i	0.226110	−	0.974102i	$-0.427399\pi$
$998$	−22.8074			−0.721955
$999$	−19.4328	−	45.0419i	−0.614825	−	1.42506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.20	yes	152
3.2	odd	2	inner	546.2.bw.a.11.1	✓	152
7.2	even	3		546.2.ch.a.401.32	yes	152
13.6	odd	12		546.2.ch.a.305.13	yes	152
21.2	odd	6		546.2.ch.a.401.13	yes	152
39.32	even	12		546.2.ch.a.305.32	yes	152
91.58	odd	12	inner	546.2.bw.a.149.1	yes	152
273.149	even	12	inner	546.2.bw.a.149.20	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.1	✓	152	3.2	odd	2	inner
546.2.bw.a.11.20	yes	152	1.1	even	1	trivial
546.2.bw.a.149.1	yes	152	91.58	odd	12	inner
546.2.bw.a.149.20	yes	152	273.149	even	12	inner
546.2.ch.a.305.13	yes	152	13.6	odd	12
546.2.ch.a.305.32	yes	152	39.32	even	12
546.2.ch.a.401.13	yes	152	21.2	odd	6
546.2.ch.a.401.32	yes	152	7.2	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.73001 + 0.0839781i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.83225 + 0.758898i) q^{5} +(-0.528877 - 1.64933i) q^{6} +(-2.04314 + 1.68095i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98590 - 0.290567i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.73001 + 0.0839781i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.83225 + 0.758898i) q^{5} +(-0.528877 - 1.64933i) q^{6} +(-2.04314 + 1.68095i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.98590 - 0.290567i) q^{9} +2.93216i q^{10} +(-0.0946467 - 0.0946467i) q^{11} +(1.45625 - 0.937734i) q^{12} +(1.73700 + 3.15956i) q^{13} +(-2.15247 - 1.53846i) q^{14} +(-4.96355 - 1.07506i) q^{15} +(0.500000 - 0.866025i) q^{16} +(1.08009 + 1.87078i) q^{17} +(1.05347 + 2.80895i) q^{18} +(-2.23830 - 2.23830i) q^{19} +(-2.83225 + 0.758898i) q^{20} +(3.39350 - 3.07964i) q^{21} +(0.0669254 - 0.115918i) q^{22} +(-3.38136 + 5.85668i) q^{23} +(1.28269 + 1.16392i) q^{24} +(3.11556 + 1.79877i) q^{25} +(-2.60233 + 2.49557i) q^{26} +(-5.14124 + 0.753434i) q^{27} +(0.928939 - 2.47731i) q^{28} +(-5.12781 + 2.96054i) q^{29} +(-0.246237 - 5.07267i) q^{30} +(2.47109 - 0.662128i) q^{31} +(0.965926 + 0.258819i) q^{32} +(0.171688 + 0.155792i) q^{33} +(-1.52748 + 1.52748i) q^{34} +(-7.06234 + 3.21031i) q^{35} +(-2.44058 + 1.74459i) q^{36} +(2.44342 + 9.11897i) q^{37} +(1.58272 - 2.74135i) q^{38} +(-3.27038 - 5.32021i) q^{39} +(-1.46608 - 2.53932i) q^{40} +(-8.14459 - 2.18234i) q^{41} +(3.85300 + 2.48080i) q^{42} +(2.46872 + 1.42532i) q^{43} +(0.129290 + 0.0346431i) q^{44} +(8.67730 + 1.44303i) q^{45} +(-6.53228 - 1.75032i) q^{46} +(0.420550 - 1.56951i) q^{47} +(-0.792280 + 1.54022i) q^{48} +(1.34885 - 6.86881i) q^{49} +(-0.931112 + 3.47496i) q^{50} +(-2.02568 - 3.14576i) q^{51} +(-3.08407 - 1.86776i) q^{52} +(-5.19889 - 3.00158i) q^{53} +(-2.05841 - 4.77105i) q^{54} +(-0.196236 - 0.339890i) q^{55} +(2.63333 + 0.256111i) q^{56} +(4.06026 + 3.68432i) q^{57} +(-4.18684 - 4.18684i) q^{58} +(0.837676 - 3.12625i) q^{59} +(4.83609 - 1.55075i) q^{60} +3.62498 q^{61} +(1.27913 + 2.21552i) q^{62} +(-5.61218 + 5.61279i) q^{63} +1.00000i q^{64} +(2.52184 + 10.2669i) q^{65} +(-0.106047 + 0.206160i) q^{66} +(2.72663 + 2.72663i) q^{67} +(-1.87078 - 1.08009i) q^{68} +(5.35796 - 10.4161i) q^{69} +(-4.92879 - 5.99081i) q^{70} +(2.50530 + 9.34991i) q^{71} +(-2.31681 - 1.90589i) q^{72} +(0.235334 + 0.878279i) q^{73} +(-8.17585 + 4.72033i) q^{74} +(-5.54102 - 2.85026i) q^{75} +(3.05758 + 0.819275i) q^{76} +(0.352473 + 0.0342806i) q^{77} +(4.29249 - 4.53591i) q^{78} +(4.27906 + 7.41154i) q^{79} +(2.07335 - 2.07335i) q^{80} +(8.83114 - 1.73520i) q^{81} -8.43190i q^{82} +(11.9054 - 11.9054i) q^{83} +(-1.39904 + 4.36379i) q^{84} +(1.63936 + 6.11818i) q^{85} +(-0.737798 + 2.75350i) q^{86} +(8.62256 - 5.55240i) q^{87} +0.133851i q^{88} +(-10.6072 + 2.84220i) q^{89} +(0.851987 + 8.75511i) q^{90} +(-8.85999 - 3.53562i) q^{91} -6.76271i q^{92} +(-4.21942 + 1.35301i) q^{93} +1.62488 q^{94} +(-4.64078 - 8.03806i) q^{95} +(-1.69280 - 0.366644i) q^{96} +(8.60864 - 2.30668i) q^{97} +(6.98387 - 0.474894i) q^{98} +(-0.310106 - 0.255104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

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