LMFDB - Embedded newform 546.2.bu.b.323.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.8
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.b.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.69149 - 0.372632i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.11112 - 1.11112i) q^{5} +(-1.53741 - 0.797725i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.72229 + 1.26061i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.69149 - 0.372632i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.11112 - 1.11112i) q^{5} +(-1.53741 - 0.797725i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.72229 + 1.26061i) q^{9} +(1.36084 - 0.785680i) q^{10} +(1.03434 - 3.86021i) q^{11} +(-1.27856 - 1.16845i) q^{12} +(-1.97046 + 3.01949i) q^{13} +1.00000i q^{14} +(-2.29349 + 1.46541i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.65413 - 4.59709i) q^{17} +(2.30326 + 1.92223i) q^{18} +(5.14536 - 1.37869i) q^{19} +(1.51782 - 0.406698i) q^{20} +(-0.0778557 - 1.73030i) q^{21} +(1.99819 - 3.46097i) q^{22} +(1.44928 + 2.51022i) q^{23} +(-0.932575 - 1.45956i) q^{24} +2.53083i q^{25} +(-2.68482 + 2.40661i) q^{26} +(-4.13499 - 3.14672i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(7.12197 - 4.11187i) q^{29} +(-2.59462 + 0.821880i) q^{30} +(-3.52940 - 3.52940i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.18801 + 6.14408i) q^{33} +(3.75351 - 3.75351i) q^{34} +(1.36084 + 0.785680i) q^{35} +(1.72727 + 2.45286i) q^{36} +(9.27105 + 2.48417i) q^{37} +5.32686 q^{38} +(4.45817 - 4.37318i) q^{39} +1.57136 q^{40} +(-0.976286 - 0.261595i) q^{41} +(0.372632 - 1.69149i) q^{42} +(-0.645525 - 0.372694i) q^{43} +(2.82587 - 2.82587i) q^{44} +(4.42548 - 1.62410i) q^{45} +(0.750200 + 2.79979i) q^{46} +(-4.72278 - 4.72278i) q^{47} +(-0.523037 - 1.65119i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.655026 + 2.44459i) q^{50} +(-6.20247 + 6.78693i) q^{51} +(-3.21621 + 1.62972i) q^{52} +7.57938i q^{53} +(-3.17966 - 4.10971i) q^{54} +(-3.13988 - 5.43843i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-9.21707 + 0.414727i) q^{57} +(7.94353 - 2.12846i) q^{58} +(-9.73021 + 2.60720i) q^{59} +(-2.71892 + 0.122339i) q^{60} +(1.42106 - 2.46134i) q^{61} +(-2.49566 - 4.32262i) q^{62} +(-0.513072 + 2.95580i) q^{63} +1.00000i q^{64} +(1.16560 + 5.54442i) q^{65} +(-4.66959 + 5.10961i) q^{66} +(-4.21963 + 15.7479i) q^{67} +(4.59709 - 2.65413i) q^{68} +(-1.51605 - 4.78606i) q^{69} +(1.11112 + 1.11112i) q^{70} +(-3.21485 - 11.9980i) q^{71} +(1.03357 + 2.81633i) q^{72} +(-3.67841 + 3.67841i) q^{73} +(8.31219 + 4.79905i) q^{74} +(0.943067 - 4.28088i) q^{75} +(5.14536 + 1.37869i) q^{76} +3.99638 q^{77} +(5.43812 - 3.07031i) q^{78} -11.4102 q^{79} +(1.51782 + 0.406698i) q^{80} +(5.82174 + 6.86348i) q^{81} +(-0.875314 - 0.505363i) q^{82} +(2.04710 - 2.04710i) q^{83} +(0.797725 - 1.53741i) q^{84} +(-2.15886 - 8.05698i) q^{85} +(-0.527069 - 0.527069i) q^{86} +(-13.5790 + 4.30133i) q^{87} +(3.46097 - 1.99819i) q^{88} +(-4.10776 + 15.3304i) q^{89} +(4.69503 - 0.423368i) q^{90} +(-3.42659 - 1.12182i) q^{91} +2.89855i q^{92} +(4.65479 + 7.28512i) q^{93} +(-3.33951 - 5.78420i) q^{94} +(4.18521 - 7.24900i) q^{95} +(-0.0778557 - 1.73030i) q^{96} +(-7.62598 + 2.04337i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(7.68198 - 9.20471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.69149	−	0.372632i	−0.976583	−	0.215139i
$3$	−1.69149	−	0.372632i	−0.976583	−	0.215139i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.11112	−	1.11112i	0.496908	−	0.496908i	−0.413566	−	0.910474i	$-0.635717\pi$
$5$	1.11112	−	1.11112i	0.496908	−	0.496908i	0.910474	+	0.413566i	$0.135717\pi$
$6$	−1.53741	−	0.797725i	−0.627646	−	0.325670i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$7$	0.258819	+	0.965926i	0.0978244	+	0.365086i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.72229	+	1.26061i	0.907430	+	0.420202i
$10$	1.36084	−	0.785680i	0.430335	−	0.248454i
$11$	1.03434	−	3.86021i	0.311865	−	1.16390i	−0.615008	−	0.788521i	$-0.710847\pi$
$11$	1.03434	−	3.86021i	0.311865	−	1.16390i	0.926873	−	0.375375i	$-0.122486\pi$
$12$	−1.27856	−	1.16845i	−0.369088	−	0.337304i
$13$	−1.97046	+	3.01949i	−0.546507	+	0.837455i
$13$	−1.97046	+	3.01949i	−0.546507	+	0.837455i
$14$			1.00000i			0.267261i
$15$	−2.29349	+	1.46541i	−0.592176	+	0.378368i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.65413	−	4.59709i	0.643722	−	1.11496i	−0.340873	−	0.940109i	$-0.610723\pi$
$17$	2.65413	−	4.59709i	0.643722	−	1.11496i	0.984595	−	0.174850i	$-0.0559439\pi$
$18$	2.30326	+	1.92223i	0.542884	+	0.453075i
$19$	5.14536	−	1.37869i	1.18043	−	0.316294i	0.385330	−	0.922779i	$-0.374087\pi$
$19$	5.14536	−	1.37869i	1.18043	−	0.316294i	0.795095	+	0.606485i	$0.207421\pi$
$20$	1.51782	−	0.406698i	0.339394	−	0.0909404i
$21$	−0.0778557	−	1.73030i	−0.0169895	−	0.377582i
$22$	1.99819	−	3.46097i	0.426016	−	0.737881i
$23$	1.44928	+	2.51022i	0.302195	+	0.523417i	0.976633	−	0.214915i	$-0.0689473\pi$
$23$	1.44928	+	2.51022i	0.302195	+	0.523417i	−0.674438	+	0.738331i	$0.735614\pi$
$24$	−0.932575	−	1.45956i	−0.190361	−	0.297931i
$25$			2.53083i			0.506166i
$26$	−2.68482	+	2.40661i	−0.526536	+	0.471975i
$27$	−4.13499	−	3.14672i	−0.795780	−	0.605586i
$28$	−0.258819	+	0.965926i	−0.0489122	+	0.182543i
$29$	7.12197	−	4.11187i	1.32252	−	0.763555i	0.338387	−	0.941007i	$-0.390119\pi$
$29$	7.12197	−	4.11187i	1.32252	−	0.763555i	0.984130	+	0.177452i	$0.0567853\pi$
$30$	−2.59462	+	0.821880i	−0.473710	+	0.150054i
$31$	−3.52940	−	3.52940i	−0.633899	−	0.633899i	0.315145	−	0.949044i	$-0.397947\pi$
$31$	−3.52940	−	3.52940i	−0.633899	−	0.633899i	−0.949044	+	0.315145i	$0.897947\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−3.18801	+	6.14408i	−0.554962	+	1.06955i
$34$	3.75351	−	3.75351i	0.643722	−	0.643722i
$35$	1.36084	+	0.785680i	0.230024	+	0.132804i
$36$	1.72727	+	2.45286i	0.287878	+	0.408811i
$37$	9.27105	+	2.48417i	1.52415	+	0.408395i	0.921106	−	0.389312i	$-0.127287\pi$
$37$	9.27105	+	2.48417i	1.52415	+	0.408395i	0.603045	+	0.797707i	$0.293954\pi$
$38$	5.32686			0.864132
$39$	4.45817	−	4.37318i	0.713878	−	0.700270i
$40$	1.57136			0.248454
$41$	−0.976286	−	0.261595i	−0.152470	−	0.0408543i	0.181777	−	0.983340i	$-0.441815\pi$
$41$	−0.976286	−	0.261595i	−0.152470	−	0.0408543i	−0.334247	+	0.942486i	$0.608482\pi$
$42$	0.372632	−	1.69149i	0.0574983	−	0.261003i
$43$	−0.645525	−	0.372694i	−0.0984416	−	0.0568353i	0.449971	−	0.893043i	$-0.351434\pi$
$43$	−0.645525	−	0.372694i	−0.0984416	−	0.0568353i	−0.548413	+	0.836208i	$0.684768\pi$
$44$	2.82587	−	2.82587i	0.426016	−	0.426016i
$45$	4.42548	−	1.62410i	0.659711	−	0.242107i
$46$	0.750200	+	2.79979i	0.110611	+	0.412806i
$47$	−4.72278	−	4.72278i	−0.688888	−	0.688888i	0.273098	−	0.961986i	$-0.411952\pi$
$47$	−4.72278	−	4.72278i	−0.688888	−	0.688888i	−0.961986	+	0.273098i	$0.911952\pi$
$48$	−0.523037	−	1.65119i	−0.0754940	−	0.238329i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−0.655026	+	2.44459i	−0.0926347	+	0.345718i
$51$	−6.20247	+	6.78693i	−0.868519	+	0.950361i
$52$	−3.21621	+	1.62972i	−0.446008	+	0.226002i
$53$			7.57938i			1.04111i	0.853829	+	0.520554i	$0.174275\pi$
$53$			7.57938i			1.04111i	−0.853829	+	0.520554i	$0.825725\pi$
$54$	−3.17966	−	4.10971i	−0.432698	−	0.559261i
$55$	−3.13988	−	5.43843i	−0.423381	−	0.733317i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	−9.21707	+	0.414727i	−1.22083	+	0.0549319i
$58$	7.94353	−	2.12846i	1.04304	−	0.279481i
$59$	−9.73021	+	2.60720i	−1.26677	+	0.339429i	−0.828791	−	0.559559i	$-0.810971\pi$
$59$	−9.73021	+	2.60720i	−1.26677	+	0.339429i	−0.437974	+	0.898987i	$0.644304\pi$
$60$	−2.71892	+	0.122339i	−0.351012	+	0.0157939i
$61$	1.42106	−	2.46134i	0.181947	−	0.315142i	−0.760596	−	0.649225i	$-0.775093\pi$
$61$	1.42106	−	2.46134i	0.181947	−	0.315142i	0.942544	+	0.334083i	$0.108427\pi$
$62$	−2.49566	−	4.32262i	−0.316950	−	0.548973i
$63$	−0.513072	+	2.95580i	−0.0646410	+	0.372396i
$64$			1.00000i			0.125000i
$65$	1.16560	+	5.54442i	0.144574	+	0.687701i
$66$	−4.66959	+	5.10961i	−0.574787	+	0.628950i
$67$	−4.21963	+	15.7479i	−0.515510	+	1.92391i	−0.170249	+	0.985401i	$0.554457\pi$
$67$	−4.21963	+	15.7479i	−0.515510	+	1.92391i	−0.345261	+	0.938507i	$0.612209\pi$
$68$	4.59709	−	2.65413i	0.557479	−	0.321861i
$69$	−1.51605	−	4.78606i	−0.182511	−	0.576174i
$70$	1.11112	+	1.11112i	0.132804	+	0.132804i
$71$	−3.21485	−	11.9980i	−0.381533	−	1.42390i	−0.843561	−	0.537034i	$-0.819545\pi$
$71$	−3.21485	−	11.9980i	−0.381533	−	1.42390i	0.462028	−	0.886865i	$-0.347122\pi$
$72$	1.03357	+	2.81633i	0.121807	+	0.331908i
$73$	−3.67841	+	3.67841i	−0.430525	+	0.430525i	−0.888807	−	0.458282i	$-0.848465\pi$
$73$	−3.67841	+	3.67841i	−0.430525	+	0.430525i	0.458282	+	0.888807i	$0.348465\pi$
$74$	8.31219	+	4.79905i	0.966273	+	0.557878i
$75$	0.943067	−	4.28088i	0.108896	−	0.494313i
$76$	5.14536	+	1.37869i	0.590213	+	0.158147i
$77$	3.99638			0.455430
$78$	5.43812	−	3.07031i	0.615746	−	0.347644i
$79$	−11.4102			−1.28374			−0.641872	−	0.766812i	$-0.721842\pi$
$79$	−11.4102			−1.28374			−0.641872	+	0.766812i	$0.721842\pi$
$80$	1.51782	+	0.406698i	0.169697	+	0.0454702i
$81$	5.82174	+	6.86348i	0.646860	+	0.762609i
$82$	−0.875314	−	0.505363i	−0.0966623	−	0.0558080i
$83$	2.04710	−	2.04710i	0.224698	−	0.224698i	−0.585775	−	0.810473i	$-0.699210\pi$
$83$	2.04710	−	2.04710i	0.224698	−	0.224698i	0.810473	+	0.585775i	$0.199210\pi$
$84$	0.797725	−	1.53741i	0.0870389	−	0.167745i
$85$	−2.15886	−	8.05698i	−0.234161	−	0.873902i
$86$	−0.527069	−	0.527069i	−0.0568353	−	0.0568353i
$87$	−13.5790	+	4.30133i	−1.45582	+	0.461151i
$88$	3.46097	−	1.99819i	0.368940	−	0.213008i
$89$	−4.10776	+	15.3304i	−0.435422	+	1.62502i	0.304633	+	0.952470i	$0.401466\pi$
$89$	−4.10776	+	15.3304i	−0.435422	+	1.62502i	−0.740055	+	0.672546i	$0.765201\pi$
$90$	4.69503	−	0.423368i	0.494900	−	0.0446269i
$91$	−3.42659	−	1.12182i	−0.359204	−	0.117598i
$92$			2.89855i			0.302195i
$93$	4.65479	+	7.28512i	0.482679	+	0.755432i
$94$	−3.33951	−	5.78420i	−0.344444	−	0.596594i
$95$	4.18521	−	7.24900i	0.429394	−	0.743731i
$96$	−0.0778557	−	1.73030i	−0.00794612	−	0.176598i
$97$	−7.62598	+	2.04337i	−0.774301	+	0.207473i	−0.624271	−	0.781208i	$-0.714604\pi$
$97$	−7.62598	+	2.04337i	−0.774301	+	0.207473i	−0.150030	+	0.988681i	$0.547937\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	7.68198	−	9.20471i	0.772068	−	0.925109i
$100$	−1.26541	+	2.19176i	−0.126541	+	0.219176i
$101$	2.83502	+	4.91039i	0.282095	+	0.488602i	0.971900	−	0.235392i	$-0.0756374\pi$
$101$	2.83502	+	4.91039i	0.282095	+	0.488602i	−0.689806	+	0.723994i	$0.742304\pi$
$102$	−7.74771	+	4.95036i	−0.767138	+	0.490158i
$103$		−	8.09989i		−	0.798106i	−0.916928	−	0.399053i	$-0.869339\pi$
$103$		−	8.09989i		−	0.798106i	0.916928	−	0.399053i	$-0.130661\pi$
$104$	−3.52842	+	0.741775i	−0.345990	+	0.0727371i
$105$	−2.00908	−	1.83606i	−0.196066	−	0.179181i
$106$	−1.96169	+	7.32112i	−0.190536	+	0.711090i
$107$	0.0829210	−	0.0478745i	0.00801628	−	0.00462820i	−0.495987	−	0.868330i	$-0.665193\pi$
$107$	0.0829210	−	0.0478745i	0.00801628	−	0.00462820i	0.504003	+	0.863702i	$0.331860\pi$
$108$	−2.00765	−	4.79263i	−0.193186	−	0.461172i
$109$	−13.8425	−	13.8425i	−1.32587	−	1.32587i	−0.908940	−	0.416927i	$-0.863107\pi$
$109$	−13.8425	−	13.8425i	−1.32587	−	1.32587i	−0.416927	−	0.908940i	$-0.636893\pi$
$110$	−1.62532	−	6.06578i	−0.154968	−	0.578349i
$111$	−14.7562	−	7.65664i	−1.40060	−	0.726736i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$	−11.6098	−	6.70295i	−1.09216	−	0.630560i	−0.158011	−	0.987437i	$-0.550508\pi$
$113$	−11.6098	−	6.70295i	−1.09216	−	0.630560i	−0.934151	+	0.356877i	$0.883841\pi$
$114$	−9.01035	−	1.98496i	−0.843897	−	0.185908i
$115$	4.39947	+	1.17883i	0.410253	+	0.109927i
$116$	8.22374			0.763555
$117$	−9.17055	+	5.73595i	−0.847817	+	0.530289i
$118$	−10.0735			−0.927336
$119$	5.12739	+	1.37388i	0.470027	+	0.125943i
$120$	−2.65794	−	0.585539i	−0.242636	−	0.0534521i
$121$	−4.30507	−	2.48553i	−0.391370	−	0.225958i
$122$	2.00968	−	2.00968i	0.181947	−	0.181947i
$123$	1.55390	+	0.806281i	0.140111	+	0.0726999i
$124$	−1.29185	−	4.82125i	−0.116012	−	0.432961i
$125$	8.36765	+	8.36765i	0.748425	+	0.748425i
$126$	−1.26061	+	2.72229i	−0.112304	+	0.242521i
$127$	−5.82316	+	3.36200i	−0.516722	+	0.298330i	−0.735592	−	0.677424i	$-0.763096\pi$
$127$	−5.82316	+	3.36200i	−0.516722	+	0.298330i	0.218871	+	0.975754i	$0.429763\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	0.953023	+	0.870952i	0.0839090	+	0.0766831i
$130$	−0.309123	+	5.65718i	−0.0271119	+	0.496167i
$131$			10.1299i			0.885050i	0.896756	+	0.442525i	$0.145917\pi$
$131$			10.1299i			0.885050i	−0.896756	+	0.442525i	$0.854083\pi$
$132$	−5.83294	+	3.72693i	−0.507693	+	0.324387i
$133$	2.66343	+	4.61320i	0.230949	+	0.400015i
$134$	−8.15169	+	14.1191i	−0.704199	+	1.21971i
$135$	−8.09085	+	1.09809i	−0.696349	+	0.0945084i
$136$	5.12739	−	1.37388i	0.439670	−	0.117809i
$137$	6.68398	−	1.79097i	0.571051	−	0.153013i	0.0382722	−	0.999267i	$-0.487815\pi$
$137$	6.68398	−	1.79097i	0.571051	−	0.153013i	0.532778	+	0.846255i	$0.321148\pi$
$138$	−0.225669	−	5.01536i	−0.0192102	−	0.426936i
$139$	−1.67800	+	2.90638i	−0.142326	+	0.246516i	−0.928372	−	0.371652i	$-0.878791\pi$
$139$	−1.67800	+	2.90638i	−0.142326	+	0.246516i	0.786046	+	0.618168i	$0.212125\pi$
$140$	0.785680	+	1.36084i	0.0664021	+	0.115012i
$141$	6.22868	+	9.74840i	0.524550	+	0.820963i
$142$		−	12.4212i		−	1.04237i
$143$	9.61772	+	10.7296i	0.804274	+	0.897250i
$144$	0.269428	+	2.98788i	0.0224523	+	0.248990i
$145$	3.34458	−	12.4821i	0.277752	−	1.03659i
$146$	−4.50511	+	2.60103i	−0.372846	+	0.215263i
$147$	1.65119	−	0.523037i	0.136188	−	0.0431394i
$148$	6.78688	+	6.78688i	0.557878	+	0.557878i
$149$	1.57701	+	5.88548i	0.129194	+	0.482158i	0.999954	−	0.00954954i	$-0.00303976\pi$
$149$	1.57701	+	5.88548i	0.129194	+	0.482158i	−0.870761	+	0.491707i	$0.836373\pi$
$150$	2.01890	−	3.89092i	0.164843	−	0.317693i
$151$	3.25994	−	3.25994i	0.265290	−	0.265290i	−0.561909	−	0.827199i	$-0.689933\pi$
$151$	3.25994	−	3.25994i	0.265290	−	0.265290i	0.827199	+	0.561909i	$0.189933\pi$
$152$	4.61320	+	2.66343i	0.374180	+	0.216033i
$153$	13.0205	−	9.16881i	1.05264	−	0.741254i
$154$	3.86021	+	1.03434i	0.311064	+	0.0833495i
$155$	−7.84317			−0.629979
$156$	6.04748	−	1.55820i	0.484186	−	0.124756i
$157$	10.9582			0.874560			0.437280	−	0.899325i	$-0.355942\pi$
$157$	10.9582			0.874560			0.437280	+	0.899325i	$0.355942\pi$
$158$	−11.0214	−	2.95317i	−0.876813	−	0.234941i
$159$	2.82432	−	12.8205i	0.223983	−	1.01673i
$160$	1.36084	+	0.785680i	0.107584	+	0.0621135i
$161$	−2.04959	+	2.04959i	−0.161530	+	0.161530i
$162$	3.84697	+	8.13639i	0.302246	+	0.639255i
$163$	5.08086	+	18.9620i	0.397964	+	1.48522i	0.816673	+	0.577101i	$0.195816\pi$
$163$	5.08086	+	18.9620i	0.397964	+	1.48522i	−0.418709	+	0.908120i	$0.637517\pi$
$164$	−0.714691	−	0.714691i	−0.0558080	−	0.0558080i
$165$	3.28455	+	10.3691i	0.255702	+	0.807231i
$166$	2.50717	−	1.44752i	0.194594	−	0.112349i
$167$	2.10435	−	7.85354i	0.162839	−	0.607725i	−0.835466	−	0.549541i	$-0.814802\pi$
$167$	2.10435	−	7.85354i	0.162839	−	0.607725i	0.998306	−	0.0581836i	$-0.0185309\pi$
$168$	1.16845	−	1.27856i	0.0901482	−	0.0986430i
$169$	−5.23459	−	11.8995i	−0.402661	−	0.915349i
$170$		−	8.34120i		−	0.639741i
$171$	15.7451	+	2.73307i	1.20406	+	0.209003i
$172$	−0.372694	−	0.645525i	−0.0284177	−	0.0492208i
$173$	0.130518	−	0.226063i	0.00992307	−	0.0171873i	−0.861021	−	0.508569i	$-0.830175\pi$
$173$	0.130518	−	0.226063i	0.00992307	−	0.0171873i	0.870944	+	0.491382i	$0.163508\pi$
$174$	−14.2295	+	0.640266i	−1.07874	+	0.0485384i
$175$	−2.44459	+	0.655026i	−0.184794	+	0.0495153i
$176$	3.86021	−	1.03434i	0.290974	−	0.0779663i
$177$	17.4301	−	0.784276i	1.31013	−	0.0589498i
$178$	−7.93558	+	13.7448i	−0.594797	+	1.03022i
$179$	−8.54492	−	14.8002i	−0.638677	−	1.10622i	−0.985723	−	0.168374i	$-0.946149\pi$
$179$	−8.54492	−	14.8002i	−0.638677	−	1.10622i	0.347046	−	0.937848i	$-0.387185\pi$
$180$	4.64463	+	0.806221i	0.346190	+	0.0600922i
$181$		−	10.0519i		−	0.747154i	−0.927599	−	0.373577i	$-0.878131\pi$
$181$		−	10.0519i		−	0.747154i	0.927599	−	0.373577i	$-0.121869\pi$
$182$	−3.01949	−	1.97046i	−0.223819	−	0.146060i
$183$	−3.32088	+	3.63381i	−0.245486	+	0.268619i
$184$	−0.750200	+	2.79979i	−0.0553055	+	0.206403i
$185$	13.0614	−	7.54103i	0.960297	−	0.554428i
$186$	2.61065	+	8.24163i	0.191422	+	0.604306i
$187$	−15.0005	−	15.0005i	−1.09694	−	1.09694i
$188$	−1.72866	−	6.45143i	−0.126075	−	0.470519i
$189$	1.96928	−	4.80853i	0.143244	−	0.349769i
$190$	5.91878	−	5.91878i	0.429394	−	0.429394i
$191$	13.9352	+	8.04548i	1.00831	+	0.582151i	0.910698	−	0.413073i	$-0.135545\pi$
$191$	13.9352	+	8.04548i	1.00831	+	0.582151i	0.0976170	+	0.995224i	$0.468878\pi$
$192$	0.372632	−	1.69149i	0.0268924	−	0.122073i
$193$	1.36356	+	0.365365i	0.0981512	+	0.0262995i	0.307560	−	0.951529i	$-0.400487\pi$
$193$	1.36356	+	0.365365i	0.0981512	+	0.0262995i	−0.209409	+	0.977828i	$0.567154\pi$
$194$	−7.89499			−0.566827
$195$	0.0944313	−	9.81269i	0.00676236	−	0.702701i
$196$	−1.00000			−0.0714286
$197$	−0.874547	−	0.234334i	−0.0623089	−	0.0166956i	0.227530	−	0.973771i	$-0.426935\pi$
$197$	−0.874547	−	0.234334i	−0.0623089	−	0.0166956i	−0.289839	+	0.957075i	$0.593602\pi$
$198$	9.80258	−	6.90283i	0.696639	−	0.490563i
$199$	6.43378	+	3.71454i	0.456079	+	0.263317i	0.710394	−	0.703804i	$-0.248517\pi$
$199$	6.43378	+	3.71454i	0.456079	+	0.263317i	−0.254315	+	0.967121i	$0.581850\pi$
$200$	−1.78957	+	1.78957i	−0.126541	+	0.126541i
$201$	13.0056	−	25.0650i	0.917346	−	1.76795i
$202$	1.46751	+	5.47683i	0.103254	+	0.385349i
$203$	5.81506	+	5.81506i	0.408138	+	0.408138i
$204$	−8.76496	+	2.77642i	−0.613670	+	0.194388i
$205$	−1.37543	+	0.794107i	−0.0960644	+	0.0554628i
$206$	2.09641	−	7.82389i	0.146064	−	0.545116i
$207$	0.780950	+	8.66051i	0.0542797	+	0.601947i
$208$	−3.60018	−	0.196723i	−0.249628	−	0.0136403i
$209$		−	21.2882i		−	1.47253i
$210$	−1.46541	−	2.29349i	−0.101123	−	0.158266i
$211$	5.63900	+	9.76703i	0.388204	+	0.672390i	0.992208	−	0.124592i	$-0.0397621\pi$
$211$	5.63900	+	9.76703i	0.388204	+	0.672390i	−0.604004	+	0.796982i	$0.706429\pi$
$212$	−3.78969	+	6.56394i	−0.260277	+	0.450813i
$213$	0.967064	+	21.4925i	0.0662621	+	1.47264i
$214$	0.0924864	−	0.0247817i	0.00632224	−	0.00169404i
$215$	−1.13136	+	0.303148i	−0.0771583	+	0.0206745i
$216$	−0.698814	−	5.14895i	−0.0475483	−	0.350341i
$217$	2.49566	−	4.32262i	0.169417	−	0.293438i
$218$	−9.78809	−	16.9535i	−0.662933	−	1.14823i
$219$	7.59269	−	4.85131i	0.513067	−	0.327821i
$220$		−	6.27975i		−	0.423381i
$221$	8.65100	+	17.0725i	0.581929	+	1.14842i
$222$	−12.2717	−	11.2149i	−0.823625	−	0.752697i
$223$	−5.14752	+	19.2108i	−0.344703	+	1.28645i	0.548255	+	0.836311i	$0.315292\pi$
$223$	−5.14752	+	19.2108i	−0.344703	+	1.28645i	−0.892958	+	0.450139i	$0.851374\pi$
$224$	−0.866025	+	0.500000i	−0.0578638	+	0.0334077i
$225$	−3.19038	+	6.88965i	−0.212692	+	0.459310i
$226$	−9.47940	−	9.47940i	−0.630560	−	0.630560i
$227$	−1.25695	−	4.69102i	−0.0834270	−	0.311354i	0.911585	−	0.411112i	$-0.134860\pi$
$227$	−1.25695	−	4.69102i	−0.0834270	−	0.311354i	−0.995012	+	0.0997586i	$0.968193\pi$
$228$	−8.18958	−	4.24937i	−0.542368	−	0.281422i
$229$	7.12968	−	7.12968i	0.471142	−	0.471142i	−0.431142	−	0.902284i	$-0.641889\pi$
$229$	7.12968	−	7.12968i	0.471142	−	0.471142i	0.902284	+	0.431142i	$0.141889\pi$
$230$	3.94446	+	2.27733i	0.260090	+	0.150163i
$231$	−6.75985	−	1.48918i	−0.444765	−	0.0979808i
$232$	7.94353	+	2.12846i	0.521518	+	0.139740i
$233$	−7.76640			−0.508794			−0.254397	−	0.967100i	$-0.581877\pi$
$233$	−7.76640			−0.508794			−0.254397	+	0.967100i	$0.581877\pi$
$234$	−10.3426	+	3.16699i	−0.676119	+	0.207032i
$235$	−10.4951			−0.684627
$236$	−9.73021	−	2.60720i	−0.633383	−	0.169714i
$237$	19.3002	+	4.25179i	1.25368	+	0.276183i
$238$	4.59709	+	2.65413i	0.297985	+	0.172042i
$239$	1.73807	−	1.73807i	0.112427	−	0.112427i	−0.648656	−	0.761082i	$-0.724668\pi$
$239$	1.73807	−	1.73807i	0.112427	−	0.112427i	0.761082	+	0.648656i	$0.224668\pi$
$240$	−2.41583	−	1.25351i	−0.155941	−	0.0809139i
$241$	6.48524	+	24.2033i	0.417751	+	1.55907i	0.779261	+	0.626700i	$0.215595\pi$
$241$	6.48524	+	24.2033i	0.417751	+	1.55907i	−0.361509	+	0.932368i	$0.617738\pi$
$242$	−3.51507	−	3.51507i	−0.225958	−	0.225958i
$243$	−7.28987	−	13.7789i	−0.467646	−	0.883916i
$244$	2.46134	−	1.42106i	0.157571	−	0.0909737i
$245$	−0.406698	+	1.51782i	−0.0259830	+	0.0969698i
$246$	1.29227	+	1.18099i	0.0823923	+	0.0752970i
$247$	−5.97576	+	18.2530i	−0.380228	+	1.16141i
$248$		−	4.99133i		−	0.316950i
$249$	−4.22546	+	2.69984i	−0.267778	+	0.171095i
$250$	5.91682	+	10.2482i	0.374213	+	0.648155i
$251$	−12.6205	+	21.8593i	−0.796598	+	1.37975i	0.125222	+	0.992129i	$0.460036\pi$
$251$	−12.6205	+	21.8593i	−0.796598	+	1.37975i	−0.921820	+	0.387619i	$0.873298\pi$
$252$	−1.92223	+	2.30326i	−0.121089	+	0.145092i
$253$	11.1890	−	2.99809i	0.703447	−	0.188488i
$254$	−6.49489	+	1.74030i	−0.407526	+	0.109196i
$255$	0.649410	+	14.4328i	0.0406676	+	0.903815i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.61336	+	4.52647i	0.163017	+	0.282354i	0.935949	−	0.352135i	$-0.114544\pi$
$257$	2.61336	+	4.52647i	0.163017	+	0.282354i	−0.772932	+	0.634488i	$0.781211\pi$
$258$	0.695130	+	1.08794i	0.0432769	+	0.0677319i
$259$			9.59809i			0.596397i
$260$	−1.76278	+	5.38441i	−0.109323	+	0.333927i
$261$	24.5715	−	2.21570i	1.52094	−	0.137149i
$262$	−2.62180	+	9.78469i	−0.161975	+	0.604500i
$263$	10.8599	−	6.26995i	0.669648	−	0.386622i	−0.126295	−	0.991993i	$-0.540309\pi$
$263$	10.8599	−	6.26995i	0.669648	−	0.386622i	0.795943	+	0.605371i	$0.206975\pi$
$264$	−6.59879	+	2.09026i	−0.406127	+	0.128646i
$265$	8.42160	+	8.42160i	0.517335	+	0.517335i
$266$	1.37869	+	5.14536i	0.0845332	+	0.315482i
$267$	12.6608	−	24.4005i	0.774830	−	1.49329i
$268$	−11.5282	+	11.5282i	−0.704199	+	0.704199i
$269$	−1.87678	−	1.08356i	−0.114430	−	0.0660660i	0.441693	−	0.897166i	$-0.354378\pi$
$269$	−1.87678	−	1.08356i	−0.114430	−	0.0660660i	−0.556122	+	0.831100i	$0.687711\pi$
$270$	−8.09937	−	1.03339i	−0.492912	−	0.0628904i
$271$	−10.3036	−	2.76085i	−0.625900	−	0.167709i	−0.0680916	−	0.997679i	$-0.521691\pi$
$271$	−10.3036	−	2.76085i	−0.625900	−	0.167709i	−0.557809	+	0.829970i	$0.688358\pi$
$272$	5.30827			0.321861
$273$	5.37803	+	3.17440i	0.325493	+	0.192123i
$274$	6.91976			0.418038
$275$	9.76952	+	2.61774i	0.589124	+	0.157855i
$276$	1.08009	−	4.90288i	0.0650139	−	0.295118i
$277$	−28.0018	−	16.1669i	−1.68247	−	0.971373i	−0.960013	−	0.279954i	$-0.909681\pi$
$277$	−28.0018	−	16.1669i	−1.68247	−	0.971373i	−0.722454	−	0.691419i	$-0.756986\pi$
$278$	−2.37305	+	2.37305i	−0.142326	+	0.142326i
$279$	−5.15887	−	14.0572i	−0.308853	−	0.841585i
$280$	0.406698	+	1.51782i	0.0243048	+	0.0907069i
$281$	−22.5530	−	22.5530i	−1.34540	−	1.34540i	−0.890590	−	0.454807i	$-0.849708\pi$
$281$	−22.5530	−	22.5530i	−1.34540	−	1.34540i	−0.454807	−	0.890590i	$-0.650292\pi$
$282$	3.49338	+	11.0283i	0.208028	+	0.656728i
$283$	13.8757	−	8.01114i	0.824824	−	0.476213i	−0.0272529	−	0.999629i	$-0.508676\pi$
$283$	13.8757	−	8.01114i	0.824824	−	0.476213i	0.852077	+	0.523416i	$0.175343\pi$
$284$	3.21485	−	11.9980i	0.190766	−	0.711949i
$285$	−9.78046	+	10.7021i	−0.579344	+	0.633936i
$286$	6.51300	+	12.8532i	0.385121	+	0.760026i
$287$		−	1.01073i		−	0.0596612i
$288$	−0.513072	+	2.95580i	−0.0302331	+	0.174172i
$289$	−5.58884	−	9.68016i	−0.328755	−	0.569421i
$290$	6.46123	−	11.1912i	0.379416	−	0.657169i
$291$	13.6607	−	0.614670i	0.800805	−	0.0360326i
$292$	−5.02480	+	1.34639i	−0.294054	+	0.0787916i
$293$	−21.6857	+	5.81065i	−1.26689	+	0.339462i	−0.828838	−	0.559488i	$-0.810998\pi$
$293$	−21.6857	+	5.81065i	−1.26689	+	0.339462i	−0.438051	+	0.898950i	$0.644331\pi$
$294$	1.73030	−	0.0778557i	0.100913	−	0.00454064i
$295$	−7.91451	+	13.7083i	−0.460801	+	0.798130i
$296$	4.79905	+	8.31219i	0.278939	+	0.483136i
$297$	−16.4240	+	12.7072i	−0.953016	+	0.737344i
$298$			6.09310i			0.352964i
$299$	−10.4353	−	0.570212i	−0.603489	−	0.0329762i
$300$	2.95716	−	3.23581i	0.170732	−	0.186820i
$301$	0.192921	−	0.719990i	0.0111198	−	0.0414995i
$302$	3.99259	−	2.30513i	0.229748	−	0.132645i
$303$	−2.96564	−	9.36231i	−0.170372	−	0.537851i
$304$	3.76666	+	3.76666i	0.216033	+	0.216033i
$305$	−1.15588	−	4.31380i	−0.0661855	−	0.247008i
$306$	14.9499	−	5.48645i	0.854626	−	0.313639i
$307$	20.1181	−	20.1181i	1.14820	−	1.14820i	0.161296	−	0.986906i	$-0.448433\pi$
$307$	20.1181	−	20.1181i	1.14820	−	1.14820i	0.986906	−	0.161296i	$-0.0515672\pi$
$308$	3.46097	+	1.99819i	0.197207	+	0.113857i
$309$	−3.01828	+	13.7009i	−0.171704	+	0.779417i
$310$	−7.57592	−	2.02996i	−0.430283	−	0.115294i
$311$	−23.3812			−1.32582			−0.662912	−	0.748697i	$-0.730680\pi$
$311$	−23.3812			−1.32582			−0.662912	+	0.748697i	$0.730680\pi$
$312$	6.24471	+	0.0600952i	0.353537	+	0.00340222i
$313$	19.0557			1.07709			0.538547	−	0.842596i	$-0.318974\pi$
$313$	19.0557			1.07709			0.538547	+	0.842596i	$0.318974\pi$
$314$	10.5848	+	2.83619i	0.597335	+	0.160056i
$315$	2.71416	+	3.85433i	0.152926	+	0.217167i
$316$	−9.88149	−	5.70508i	−0.555877	−	0.320936i
$317$	14.2156	−	14.2156i	0.798427	−	0.798427i	−0.184420	−	0.982847i	$-0.559041\pi$
$317$	14.2156	−	14.2156i	0.798427	−	0.798427i	0.982847	+	0.184420i	$0.0590408\pi$
$318$	6.04626	−	11.6526i	0.339058	−	0.653447i
$319$	−8.50614	−	31.7454i	−0.476253	−	1.77740i
$320$	1.11112	+	1.11112i	0.0621135	+	0.0621135i
$321$	−0.158100	+	0.0500803i	−0.00882427	+	0.00279521i
$322$	−2.51022	+	1.44928i	−0.139889	+	0.0807650i
$323$	7.31847	−	27.3129i	0.407211	−	1.51973i
$324$	1.61003	+	8.85482i	0.0894463	+	0.491934i
$325$	−7.64180	−	4.98689i	−0.423891	−	0.276623i
$326$			19.6309i			1.08726i
$327$	18.2563	+	28.5725i	1.00957	+	1.58007i
$328$	−0.505363	−	0.875314i	−0.0279040	−	0.0483311i
$329$	3.33951	−	5.78420i	0.184113	−	0.318893i
$330$	0.488915	+	10.8659i	0.0269139	+	0.598146i
$331$	22.9655	−	6.15358i	1.26230	−	0.338231i	0.435222	−	0.900323i	$-0.356670\pi$
$331$	22.9655	−	6.15358i	1.26230	−	0.338231i	0.827075	+	0.562092i	$0.190003\pi$
$332$	2.79639	−	0.749290i	0.153472	−	0.0411226i
$333$	22.1069	+	18.4498i	1.21145	+	1.01104i
$334$	4.06529	−	7.04129i	0.222443	−	0.385282i
$335$	12.8092	+	22.1863i	0.699844	+	1.21217i
$336$	1.45956	−	0.932575i	0.0796253	−	0.0508761i
$337$			4.32839i			0.235783i	0.993027	+	0.117891i	$0.0376135\pi$
$337$			4.32839i			0.235783i	−0.993027	+	0.117891i	$0.962387\pi$
$338$	−1.97640	−	12.8489i	−0.107502	−	0.698887i
$339$	17.1402	+	15.6642i	0.930929	+	0.850761i
$340$	2.15886	−	8.05698i	0.117081	−	0.436951i
$341$	−17.2748	+	9.97362i	−0.935484	+	0.540102i
$342$	14.5013	+	6.71508i	0.784139	+	0.363110i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−0.192921	−	0.719990i	−0.0104016	−	0.0388192i
$345$	−7.00240	−	3.63337i	−0.376996	−	0.195614i
$346$	0.184580	−	0.184580i	0.00992307	−	0.00992307i
$347$	8.83048	+	5.09828i	0.474045	+	0.273690i	0.717931	−	0.696114i	$-0.245089\pi$
$347$	8.83048	+	5.09828i	0.474045	+	0.273690i	−0.243886	+	0.969804i	$0.578422\pi$
$348$	−13.9104	−	3.06443i	−0.745676	−	0.164271i
$349$	12.8081	+	3.43193i	0.685604	+	0.183707i	0.584774	−	0.811197i	$-0.301183\pi$
$349$	12.8081	+	3.43193i	0.685604	+	0.183707i	0.100831	+	0.994904i	$0.467850\pi$
$350$	−2.53083			−0.135278
$351$	17.6493	−	6.28507i	0.942050	−	0.335472i
$352$	3.99638			0.213008
$353$	−17.2129	−	4.61217i	−0.916148	−	0.245481i	−0.230210	−	0.973141i	$-0.573941\pi$
$353$	−17.2129	−	4.61217i	−0.916148	−	0.245481i	−0.685938	+	0.727660i	$0.740608\pi$
$354$	17.0392	+	3.75369i	0.905621	+	0.199506i
$355$	−16.9033	−	9.75911i	−0.897133	−	0.517960i
$356$	−11.2226	+	11.2226i	−0.594797	+	0.594797i
$357$	−8.16099	−	4.23454i	−0.431925	−	0.224115i
$358$	−4.42318	−	16.5075i	−0.233772	−	0.872450i
$359$	−18.1970	−	18.1970i	−0.960402	−	0.960402i	0.0388433	−	0.999245i	$-0.487633\pi$
$359$	−18.1970	−	18.1970i	−0.960402	−	0.960402i	−0.999245	+	0.0388433i	$0.987633\pi$
$360$	4.27770	+	1.98087i	0.225455	+	0.104401i
$361$	8.11941	−	4.68774i	0.427337	−	0.246723i
$362$	2.60163	−	9.70942i	0.136739	−	0.510316i
$363$	6.35580	+	5.80847i	0.333593	+	0.304865i
$364$	−2.40661	−	2.68482i	−0.126141	−	0.140723i
$365$			8.17430i			0.427863i
$366$	−4.14822	+	2.65048i	−0.216831	+	0.138543i
$367$	17.1515	+	29.7072i	0.895299	+	1.55070i	0.833434	+	0.552618i	$0.186371\pi$
$367$	17.1515	+	29.7072i	0.895299	+	1.55070i	0.0618644	+	0.998085i	$0.480295\pi$
$368$	−1.44928	+	2.51022i	−0.0755487	+	0.130854i
$369$	−2.32797	−	1.94285i	−0.121189	−	0.101141i
$370$	14.5682	−	3.90352i	0.757362	−	0.202935i
$371$	−7.32112	+	1.96169i	−0.380094	+	0.101846i
$372$	0.388603	+	8.63649i	0.0201481	+	0.447781i
$373$	−12.4609	+	21.5828i	−0.645198	+	1.11752i	0.339057	+	0.940766i	$0.389892\pi$
$373$	−12.4609	+	21.5828i	−0.645198	+	1.11752i	−0.984256	+	0.176751i	$0.943441\pi$
$374$	−10.6069	−	18.3717i	−0.548471	−	0.949980i
$375$	−11.0358	−	17.2719i	−0.569884	−	0.891915i
$376$		−	6.67902i		−	0.344444i
$377$	−1.61780	+	29.6070i	−0.0833209	+	1.52484i
$378$	3.14672	−	4.13499i	0.161850	−	0.212681i
$379$	4.21119	−	15.7164i	0.216314	−	0.807296i	−0.769385	−	0.638785i	$-0.779437\pi$
$379$	4.21119	−	15.7164i	0.216314	−	0.807296i	0.985700	−	0.168511i	$-0.0538959\pi$
$380$	7.24900	−	4.18521i	0.371866	−	0.214697i
$381$	11.1026	−	3.51691i	0.568804	−	0.180177i
$382$	11.3780	+	11.3780i	0.582151	+	0.582151i
$383$	−3.19097	−	11.9089i	−0.163051	−	0.608514i	−0.998281	−	0.0586132i	$-0.981332\pi$
$383$	−3.19097	−	11.9089i	−0.163051	−	0.608514i	0.835230	−	0.549901i	$-0.185335\pi$
$384$	0.797725	−	1.53741i	0.0407087	−	0.0784557i
$385$	4.44046	−	4.44046i	0.226307	−	0.226307i
$386$	1.22253	+	0.705830i	0.0622253	+	0.0359258i
$387$	−1.28749	−	1.82834i	−0.0654466	−	0.0929395i
$388$	−7.62598	−	2.04337i	−0.387150	−	0.103737i
$389$	−3.19617			−0.162052			−0.0810262	−	0.996712i	$-0.525820\pi$
$389$	−3.19617			−0.162052			−0.0810262	+	0.996712i	$0.525820\pi$
$390$	2.63092	−	9.45389i	0.133222	−	0.478716i
$391$	15.3863			0.778118
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	3.77471	−	17.1346i	0.190409	−	0.864325i
$394$	−0.784097	−	0.452699i	−0.0395022	−	0.0228066i
$395$	−12.6780	+	12.6780i	−0.637902	+	0.637902i
$396$	11.2551	−	4.13053i	0.565592	−	0.207567i
$397$	−1.65482	−	6.17587i	−0.0830530	−	0.309958i	0.911885	−	0.410445i	$-0.134627\pi$
$397$	−1.65482	−	6.17587i	−0.0830530	−	0.309958i	−0.994938	+	0.100487i	$0.967960\pi$
$398$	5.25316	+	5.25316i	0.263317	+	0.263317i
$399$	−2.78615	−	8.79567i	−0.139482	−	0.440334i
$400$	−2.19176	+	1.26541i	−0.109588	+	0.0632707i
$401$	−1.69247	+	6.31637i	−0.0845177	+	0.315424i	−0.995222	−	0.0976337i	$-0.968873\pi$
$401$	−1.69247	+	6.31637i	−0.0845177	+	0.315424i	0.910705	+	0.413058i	$0.135539\pi$
$402$	19.0498	−	20.8448i	0.950116	−	1.03965i
$403$	17.6115	−	3.70244i	0.877292	−	0.184432i
$404$			5.67003i			0.282095i
$405$	14.0948	+	1.15750i	0.700376	+	0.0575166i
$406$	4.11187	+	7.12197i	0.204069	+	0.353457i
$407$	19.1788	−	33.2187i	0.950659	−	1.64659i
$408$	−9.18489	+	0.413279i	−0.454720	+	0.0204604i
$409$	−1.01716	+	0.272547i	−0.0502953	+	0.0134766i	−0.283879	−	0.958860i	$-0.591621\pi$
$409$	−1.01716	+	0.272547i	−0.0502953	+	0.0134766i	0.233584	+	0.972337i	$0.424955\pi$
$410$	−1.53410	+	0.411060i	−0.0757636	+	0.0203008i
$411$	−11.9733	+	0.538743i	−0.590598	+	0.0265742i
$412$	4.04995	−	7.01471i	0.199526	−	0.345590i
$413$	−5.03673	−	8.72387i	−0.247841	−	0.429273i
$414$	−1.48717	+	8.56754i	−0.0730902	+	0.421072i
$415$		−	4.54914i		−	0.223308i
$416$	−3.42659	−	1.12182i	−0.168002	−	0.0550015i
$417$	3.92133	−	4.29084i	0.192028	−	0.210123i
$418$	5.50979	−	20.5628i	0.269493	−	1.00576i
$419$	−4.25679	+	2.45766i	−0.207958	+	0.120065i	−0.600362	−	0.799728i	$-0.704977\pi$
$419$	−4.25679	+	2.45766i	−0.207958	+	0.120065i	0.392404	+	0.919793i	$0.371644\pi$
$420$	−0.821880	−	2.59462i	−0.0401036	−	0.126604i
$421$	2.58462	+	2.58462i	0.125967	+	0.125967i	0.767280	−	0.641313i	$-0.221610\pi$
$421$	2.58462	+	2.58462i	0.125967	+	0.125967i	−0.641313	+	0.767280i	$0.721610\pi$
$422$	2.91896	+	10.8937i	0.142093	+	0.530297i
$423$	−6.90321	−	18.8103i	−0.335645	−	0.914590i
$424$	−5.35943	+	5.35943i	−0.260277	+	0.260277i
$425$	11.6345	+	6.71715i	0.564354	+	0.325830i
$426$	−4.62854	+	21.0104i	−0.224254	+	1.01796i
$427$	2.74527	+	0.735592i	0.132853	+	0.0355978i
$428$	0.0957490			0.00462820
$429$	−12.2701	−	21.7328i	−0.592408	−	1.04927i
$430$	−1.17127			−0.0564838
$431$	−23.6762	−	6.34401i	−1.14044	−	0.305580i	−0.361312	−	0.932445i	$-0.617671\pi$
$431$	−23.6762	−	6.34401i	−1.14044	−	0.305580i	−0.779128	+	0.626865i	$0.784338\pi$
$432$	0.657643	−	5.15437i	0.0316409	−	0.247990i
$433$	−12.6415	−	7.29859i	−0.607513	−	0.350748i	0.164478	−	0.986381i	$-0.447406\pi$
$433$	−12.6415	−	7.29859i	−0.607513	−	0.350748i	−0.771991	+	0.635633i	$0.780739\pi$
$434$	3.52940	−	3.52940i	0.169417	−	0.169417i
$435$	−10.3086	+	19.8671i	−0.494258	+	0.952557i
$436$	−5.06669	−	18.9091i	−0.242650	−	0.905584i
$437$	10.9179	+	10.9179i	0.522272	+	0.522272i
$438$	8.58959	−	2.72087i	0.410426	−	0.130008i
$439$	16.7352	−	9.66208i	0.798728	−	0.461146i	−0.0442980	−	0.999018i	$-0.514105\pi$
$439$	16.7352	−	9.66208i	0.798728	−	0.461146i	0.843026	+	0.537872i	$0.180772\pi$
$440$	1.62532	−	6.06578i	0.0774841	−	0.289175i
$441$	−2.98788	+	0.269428i	−0.142280	+	0.0128299i
$442$	3.93754	+	18.7298i	0.187290	+	0.890886i
$443$			24.5657i			1.16715i	0.812059	+	0.583575i	$0.198347\pi$
$443$			24.5657i			1.16715i	−0.812059	+	0.583575i	$0.801653\pi$
$444$	−8.95094	−	14.0090i	−0.424793	−	0.664836i
$445$	12.4697	+	21.5981i	0.591119	+	1.02385i
$446$	−9.94424	+	17.2239i	−0.470873	+	0.815577i
$447$	−0.474383	−	10.5429i	−0.0224375	−	0.498662i
$448$	−0.965926	+	0.258819i	−0.0456357	+	0.0122281i
$449$	−0.650620	+	0.174333i	−0.0307047	+	0.00822729i	−0.274139	−	0.961690i	$-0.588393\pi$
$449$	−0.650620	+	0.174333i	−0.0307047	+	0.00822729i	0.243434	+	0.969917i	$0.421726\pi$
$450$	−4.86484	+	5.82916i	−0.229331	+	0.274789i
$451$	−2.01962	+	3.49809i	−0.0951003	+	0.164719i
$452$	−6.70295	−	11.6098i	−0.315280	−	0.546081i
$453$	−6.72892	+	4.29940i	−0.316152	+	0.202004i
$454$		−	4.85650i		−	0.227927i
$455$	−5.05382	+	2.56088i	−0.236927	+	0.120056i
$456$	−6.81071	−	6.22420i	−0.318941	−	0.291475i
$457$	−1.47784	+	5.51537i	−0.0691304	+	0.257998i	−0.991838	−	0.127502i	$-0.959304\pi$
$457$	−1.47784	+	5.51537i	−0.0691304	+	0.257998i	0.922708	+	0.385500i	$0.125971\pi$
$458$	8.73204	−	5.04144i	0.408021	−	0.235571i
$459$	−25.4406	+	10.6571i	−1.18746	+	0.497432i
$460$	3.22064	+	3.22064i	0.150163	+	0.150163i
$461$	−0.767948	−	2.86602i	−0.0357669	−	0.133484i	0.945734	−	0.324942i	$-0.105345\pi$
$461$	−0.767948	−	2.86602i	−0.0357669	−	0.133484i	−0.981501	+	0.191458i	$0.938678\pi$
$462$	−6.14408	−	3.18801i	−0.285849	−	0.148320i
$463$	−10.0952	+	10.0952i	−0.469164	+	0.469164i	−0.901644	−	0.432479i	$-0.857639\pi$
$463$	−10.0952	+	10.0952i	−0.469164	+	0.469164i	0.432479	+	0.901644i	$0.357639\pi$
$464$	7.12197	+	4.11187i	0.330629	+	0.190889i
$465$	13.2667	+	2.92261i	0.615227	+	0.135533i
$466$	−7.50177	−	2.01009i	−0.347513	−	0.0931157i
$467$	−7.17468			−0.332004			−0.166002	−	0.986125i	$-0.553086\pi$
$467$	−7.17468			−0.332004			−0.166002	+	0.986125i	$0.553086\pi$
$468$	−10.8099	+	0.382204i	−0.499688	+	0.0176674i
$469$	−16.3034			−0.752821
$470$	−10.1375	−	2.71634i	−0.467609	−	0.125296i
$471$	−18.5357	−	4.08337i	−0.854081	−	0.188152i
$472$	−8.72387	−	5.03673i	−0.401548	−	0.231834i
$473$	−2.10637	+	2.10637i	−0.0968509	+	0.0968509i
$474$	17.5421	+	9.10217i	0.805736	+	0.418077i
$475$	3.48924	+	13.0220i	0.160097	+	0.597491i
$476$	3.75351	+	3.75351i	0.172042	+	0.172042i
$477$	−9.55463	+	20.6333i	−0.437476	+	0.944733i
$478$	2.12869	−	1.22900i	0.0973642	−	0.0562133i
$479$	5.40790	−	20.1825i	0.247093	−	0.922164i	−0.725227	−	0.688510i	$-0.758265\pi$
$479$	5.40790	−	20.1825i	0.247093	−	0.922164i	0.972320	−	0.233654i	$-0.0750682\pi$
$480$	−2.00908	−	1.83606i	−0.0917014	−	0.0838044i
$481$	−25.7691	+	23.0989i	−1.17497	+	1.05322i
$482$			25.0571i			1.14132i
$483$	4.23060	−	2.70312i	0.192499	−	0.122996i
$484$	−2.48553	−	4.30507i	−0.112979	−	0.195685i
$485$	−6.20294	+	10.7438i	−0.281661	+	0.487851i
$486$	−3.47524	−	15.1961i	−0.157640	−	0.689311i
$487$	−4.98694	+	1.33625i	−0.225980	+	0.0605511i	−0.370032	−	0.929019i	$-0.620653\pi$
$487$	−4.98694	+	1.33625i	−0.225980	+	0.0605511i	0.144052	+	0.989570i	$0.453987\pi$
$488$	2.74527	−	0.735592i	0.124272	−	0.0332987i
$489$	−1.52838	−	33.9674i	−0.0691158	−	1.53606i
$490$	−0.785680	+	1.36084i	−0.0354934	+	0.0614764i
$491$	5.19814	+	9.00345i	0.234589	+	0.406320i	0.959153	−	0.282887i	$-0.0912923\pi$
$491$	5.19814	+	9.00345i	0.234589	+	0.406320i	−0.724564	+	0.689207i	$0.757959\pi$
$492$	0.942577	+	1.47521i	0.0424947	+	0.0665076i
$493$		−	43.6538i		−	1.96607i
$494$	−10.4964	+	16.0844i	−0.472254	+	0.723671i
$495$	−1.69194	−	18.7631i	−0.0760470	−	0.843340i
$496$	1.29185	−	4.82125i	0.0580058	−	0.216481i
$497$	10.7571	−	6.21061i	0.482522	−	0.278584i
$498$	−4.78025	+	1.51421i	−0.214208	+	0.0678534i
$499$	−10.5815	−	10.5815i	−0.473694	−	0.473694i	0.429414	−	0.903108i	$-0.358720\pi$
$499$	−10.5815	−	10.5815i	−0.473694	−	0.473694i	−0.903108	+	0.429414i	$0.858720\pi$
$500$	3.06277	+	11.4304i	0.136971	+	0.511184i
$501$	−6.48597	+	12.5001i	−0.289772	+	0.558461i
$502$	−17.8481	+	17.8481i	−0.796598	+	0.796598i
$503$	15.2729	+	8.81781i	0.680985	+	0.393167i	0.800226	−	0.599699i	$-0.204713\pi$
$503$	15.2729	+	8.81781i	0.680985	+	0.393167i	−0.119241	+	0.992865i	$0.538046\pi$
$504$	−2.45286	+	1.72727i	−0.109259	+	0.0769387i
$505$	8.60607	+	2.30599i	0.382965	+	0.102615i
$506$	11.5837			0.514959
$507$	4.42013	+	22.0786i	0.196305	+	0.980543i
$508$	−6.72401			−0.298330
$509$	−0.543031	−	0.145505i	−0.0240694	−	0.00644939i	0.246764	−	0.969076i	$-0.420633\pi$
$509$	−0.543031	−	0.145505i	−0.0240694	−	0.00644939i	−0.270834	+	0.962626i	$0.587299\pi$
$510$	−3.10819	+	14.1091i	−0.137633	+	0.624760i
$511$	−4.50511	−	2.60103i	−0.199294	−	0.115063i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−25.6144	−	10.4901i	−1.13090	−	0.463149i
$514$	1.35278	+	5.04863i	0.0596684	+	0.222685i
$515$	−8.99994	−	8.99994i	−0.396585	−	0.396585i
$516$	0.389866	+	1.23078i	0.0171629	+	0.0541820i
$517$	−23.1159	+	13.3460i	−1.01663	+	0.586954i
$518$	−2.48417	+	9.27105i	−0.109148	+	0.407346i
$519$	−0.305008	+	0.333749i	−0.0133884	+	0.0146500i
$520$	−3.09630	+	4.74470i	−0.135782	+	0.208069i
$521$			20.5663i			0.901026i	0.892770	+	0.450513i	$0.148759\pi$
$521$			20.5663i			0.901026i	−0.892770	+	0.450513i	$0.851241\pi$
$522$	24.3077	+	4.21938i	1.06392	+	0.184677i
$523$	18.2060	+	31.5337i	0.796092	+	1.37887i	0.922143	+	0.386849i	$0.126436\pi$
$523$	18.2060	+	31.5337i	0.796092	+	1.37887i	−0.126051	+	0.992024i	$0.540230\pi$
$524$	−5.06493	+	8.77272i	−0.221262	+	0.383238i
$525$	4.37909	−	0.197039i	0.191119	−	0.00859951i
$526$	12.1126	−	3.24556i	0.528135	−	0.141513i
$527$	−25.5925	+	6.85748i	−1.11483	+	0.298717i
$528$	−6.91494	+	0.311141i	−0.300934	+	0.0135407i
$529$	7.29920	−	12.6426i	0.317357	−	0.549678i
$530$	5.95497	+	10.3143i	0.258667	+	0.448025i
$531$	−29.7751	−	5.16841i	−1.29213	−	0.224290i
$532$			5.32686i			0.230949i
$533$	2.71361	−	2.43242i	0.117540	−	0.105360i
$534$	18.5447	−	20.2922i	0.802509	−	0.878131i
$535$	0.0389409	−	0.145329i	0.00168356	−	0.00628314i
$536$	−14.1191	+	8.15169i	−0.609854	+	0.352100i
$537$	8.93863	+	28.2186i	0.385730	+	1.21772i
$538$	−1.53239	−	1.53239i	−0.0660660	−	0.0660660i
$539$	1.03434	+	3.86021i	0.0445522	+	0.166271i
$540$	−7.55593	−	3.09445i	−0.325155	−	0.133164i
$541$	8.45294	−	8.45294i	0.363420	−	0.363420i	−0.501650	−	0.865070i	$-0.667274\pi$
$541$	8.45294	−	8.45294i	0.363420	−	0.363420i	0.865070	+	0.501650i	$0.167274\pi$
$542$	−9.23797	−	5.33354i	−0.396805	−	0.229095i
$543$	−3.74567	+	17.0028i	−0.160742	+	0.729658i
$544$	5.12739	+	1.37388i	0.219835	+	0.0589046i
$545$	−30.7612			−1.31767
$546$	4.37318	+	4.45817i	0.187155	+	0.190792i
$547$	−7.76093			−0.331833			−0.165917	−	0.986140i	$-0.553058\pi$
$547$	−7.76093			−0.331833			−0.165917	+	0.986140i	$0.553058\pi$
$548$	6.68398	+	1.79097i	0.285525	+	0.0765063i
$549$	6.97131	−	4.90909i	0.297528	−	0.209515i
$550$	8.75911	+	5.05708i	0.373490	+	0.215634i
$551$	30.9761	−	30.9761i	1.31962	−	1.31962i
$552$	2.31225	−	4.45627i	0.0984158	−	0.189671i
$553$	−2.95317	−	11.0214i	−0.125581	−	0.468676i
$554$	−22.8634	−	22.8634i	−0.971373	−	0.971373i
$555$	−24.9034	+	7.88848i	−1.05709	+	0.334847i
$556$	−2.90638	+	1.67800i	−0.123258	+	0.0711629i
$557$	−0.804689	+	3.00314i	−0.0340958	+	0.127247i	−0.980876	−	0.194633i	$-0.937648\pi$
$557$	−0.804689	+	3.00314i	−0.0340958	+	0.127247i	0.946780	+	0.321881i	$0.104315\pi$
$558$	−1.34480	−	14.9135i	−0.0569300	−	0.631337i
$559$	2.39732	−	1.21478i	0.101396	−	0.0513796i
$560$			1.57136i			0.0664021i
$561$	19.7835	+	30.9628i	0.835261	+	1.30725i
$562$	−15.9474	−	27.6216i	−0.672699	−	1.16515i
$563$	−13.6658	+	23.6698i	−0.575943	+	0.997563i	0.419995	+	0.907526i	$0.362032\pi$
$563$	−13.6658	+	23.6698i	−0.575943	+	0.997563i	−0.995938	+	0.0900370i	$0.971301\pi$
$564$	0.520000	+	11.5567i	0.0218959	+	0.486625i
$565$	−20.3477	+	5.45215i	−0.856034	+	0.229374i
$566$	15.4763	−	4.14687i	0.650519	−	0.174306i
$567$	−5.12284	+	7.39977i	−0.215139	+	0.310761i
$568$	6.21061	−	10.7571i	0.260592	−	0.451358i
$569$	−15.9756	−	27.6705i	−0.669732	−	1.16001i	−0.977979	−	0.208703i	$-0.933076\pi$
$569$	−15.9756	−	27.6705i	−0.669732	−	1.16001i	0.308247	−	0.951306i	$-0.400258\pi$
$570$	−12.2171	+	7.80605i	−0.511718	+	0.326959i
$571$			25.3767i			1.06198i	0.847377	+	0.530992i	$0.178181\pi$
$571$			25.3767i			1.06198i	−0.847377	+	0.530992i	$0.821819\pi$
$572$	2.96442	+	14.1009i	0.123949	+	0.589589i
$573$	−20.5733	−	18.8016i	−0.859460	−	0.785447i
$574$	0.261595	−	0.976286i	0.0109188	−	0.0407494i
$575$	−6.35293	+	3.66787i	−0.264936	+	0.152961i
$576$	−1.26061	+	2.72229i	−0.0525253	+	0.113429i
$577$	−28.9938	−	28.9938i	−1.20703	−	1.20703i	−0.971985	−	0.235042i	$-0.924477\pi$
$577$	−28.9938	−	28.9938i	−1.20703	−	1.20703i	−0.235042	−	0.971985i	$-0.575523\pi$
$578$	−2.89300	−	10.7968i	−0.120333	−	0.449088i
$579$	−2.17030	−	1.12612i	−0.0901947	−	0.0467998i
$580$	9.13756	−	9.13756i	0.379416	−	0.379416i
$581$	2.50717	+	1.44752i	0.104015	+	0.0600531i
$582$	13.3543	+	2.94192i	0.553554	+	0.121947i
$583$	29.2580	+	7.83966i	1.21174	+	0.324685i
$584$	−5.20206			−0.215263
$585$	−3.81625	+	16.5629i	−0.157782	+	0.684791i
$586$	−22.4506			−0.927427
$587$	7.88933	+	2.11394i	0.325628	+	0.0872517i	0.417930	−	0.908479i	$-0.362756\pi$
$587$	7.88933	+	2.11394i	0.325628	+	0.0872517i	−0.0923020	+	0.995731i	$0.529423\pi$
$588$	1.69149	+	0.372632i	0.0697560	+	0.0153671i
$589$	−23.0260	−	13.2941i	−0.948769	−	0.547772i
$590$	−11.1928	+	11.1928i	−0.460801	+	0.460801i
$591$	1.39197	+	0.722258i	0.0572579	+	0.0297097i
$592$	2.48417	+	9.27105i	0.102099	+	0.381038i
$593$	22.7385	+	22.7385i	0.933760	+	0.933760i	0.997938	−	0.0641782i	$-0.0204426\pi$
$593$	22.7385	+	22.7385i	0.933760	+	0.933760i	−0.0641782	+	0.997938i	$0.520443\pi$
$594$	−19.1532	+	8.02333i	−0.785865	+	0.329201i
$595$	7.22369	−	4.17060i	0.296142	−	0.170978i
$596$	−1.57701	+	5.88548i	−0.0645969	+	0.241079i
$597$	−9.49853	−	8.68055i	−0.388749	−	0.355271i
$598$	−9.93215	−	3.25164i	−0.406156	−	0.132969i
$599$		−	3.61810i		−	0.147832i	−0.997264	−	0.0739158i	$-0.976450\pi$
$599$		−	3.61810i		−	0.147832i	0.997264	−	0.0739158i	$-0.0235496\pi$
$600$	3.69389	−	2.36019i	0.150802	−	0.0963542i
$601$	15.1258	+	26.1987i	0.616996	+	1.06867i	0.990031	+	0.140851i	$0.0449838\pi$
$601$	15.1258	+	26.1987i	0.616996	+	1.06867i	−0.373035	+	0.927817i	$0.621683\pi$
$602$	0.372694	−	0.645525i	0.0151899	−	0.0263096i
$603$	−31.3389	+	37.5510i	−1.27622	+	1.52919i
$604$	4.45316	−	1.19322i	0.181197	−	0.0485515i
$605$	−7.54517	+	2.02172i	−0.306755	+	0.0821947i
$606$	−0.441445	−	9.81086i	−0.0179325	−	0.398539i
$607$	−12.4211	+	21.5140i	−0.504158	+	0.873228i	0.495830	+	0.868419i	$0.334864\pi$
$607$	−12.4211	+	21.5140i	−0.504158	+	0.873228i	−0.999988	+	0.00480819i	$0.998470\pi$
$608$	2.66343	+	4.61320i	0.108016	+	0.187090i
$609$	−7.66926	−	12.0030i	−0.310774	−	0.486387i
$610$		−	4.46598i		−	0.180822i
$611$	23.5664	−	4.95433i	0.953394	−	0.200431i
$612$	15.8604	−	1.43019i	0.641120	−	0.0578121i
$613$	12.0279	−	44.8888i	0.485803	−	1.81304i	−0.0906138	−	0.995886i	$-0.528883\pi$
$613$	12.0279	−	44.8888i	0.485803	−	1.81304i	0.576417	−	0.817156i	$-0.304450\pi$
$614$	24.6396	−	14.2257i	0.994372	−	0.574101i
$615$	2.62244	−	0.830695i	0.105747	−	0.0334969i
$616$	2.82587	+	2.82587i	0.113857	+	0.113857i
$617$	−5.72544	−	21.3676i	−0.230497	−	0.860228i	−0.980127	−	0.198371i	$-0.936435\pi$
$617$	−5.72544	−	21.3676i	−0.230497	−	0.860228i	0.749630	−	0.661857i	$-0.230232\pi$
$618$	−6.46148	+	12.4529i	−0.259919	+	0.500928i
$619$	−24.2571	+	24.2571i	−0.974975	+	0.974975i	−0.999694	−	0.0247195i	$-0.992131\pi$
$619$	−24.2571	+	24.2571i	−0.974975	+	0.974975i	0.0247195	+	0.999694i	$0.492131\pi$
$620$	−6.79238	−	3.92159i	−0.272789	−	0.157495i
$621$	1.90621	−	14.9402i	0.0764937	−	0.599529i
$622$	−22.5845	−	6.05149i	−0.905554	−	0.242643i
$623$	−15.8712			−0.635865
$624$	6.01637	+	1.67430i	0.240848	+	0.0670255i
$625$	5.94077			0.237631
$626$	18.4064	+	4.93198i	0.735668	+	0.197122i
$627$	−7.93265	+	36.0088i	−0.316800	+	1.43805i
$628$	9.49008	+	5.47910i	0.378695	+	0.218640i
$629$	36.0266	−	36.0266i	1.43647	−	1.43647i
$630$	1.62410	+	4.42548i	0.0647059	+	0.176315i
$631$	−7.35156	−	27.4364i	−0.292661	−	1.09223i	−0.943057	−	0.332631i	$-0.892064\pi$
$631$	−7.35156	−	27.4364i	−0.292661	−	1.09223i	0.650396	−	0.759595i	$-0.274603\pi$
$632$	−8.06820	−	8.06820i	−0.320936	−	0.320936i
$633$	−5.89881	−	18.6221i	−0.234457	−	0.740163i
$634$	17.4105	−	10.0519i	0.691458	−	0.399214i
$635$	−2.73464	+	10.2058i	−0.108521	+	0.405005i
$636$	8.85617	−	9.69069i	0.351170	−	0.384261i
$637$	0.196723	−	3.60018i	0.00779445	−	0.142644i
$638$		−	32.8652i		−	1.30115i
$639$	6.37299	−	36.7147i	0.252112	−	1.45241i
$640$	0.785680	+	1.36084i	0.0310567	+	0.0537918i
$641$	12.7231	−	22.0370i	0.502532	−	0.870411i	−0.497464	−	0.867485i	$-0.665735\pi$
$641$	12.7231	−	22.0370i	0.502532	−	0.870411i	0.999996	−	0.00292593i	$-0.000931354\pi$
$642$	−0.165674	+	0.00745461i	−0.00653865	+	0.000294210i
$643$	−25.2271	+	6.75959i	−0.994860	+	0.266572i	−0.719291	−	0.694709i	$-0.755533\pi$
$643$	−25.2271	+	6.75959i	−0.994860	+	0.266572i	−0.275570	+	0.961281i	$0.588866\pi$
$644$	−2.79979	+	0.750200i	−0.110327	+	0.0295620i
$645$	2.02665	−	0.0911903i	0.0797994	−	0.00359061i
$646$	14.1382	−	24.4881i	0.556260	−	0.963471i
$647$	−8.70102	−	15.0706i	−0.342073	−	0.592487i	0.642745	−	0.766080i	$-0.277796\pi$
$647$	−8.70102	−	15.0706i	−0.342073	−	0.592487i	−0.984817	+	0.173593i	$0.944462\pi$
$648$	−0.736623	+	8.96980i	−0.0289373	+	0.352367i
$649$			40.2574i			1.58024i
$650$	−6.09071	−	6.79481i	−0.238897	−	0.266514i
$651$	−5.83214	+	6.38171i	−0.228580	+	0.250119i
$652$	−5.08086	+	18.9620i	−0.198982	+	0.742611i
$653$	−37.7870	+	21.8163i	−1.47872	+	0.853739i	−0.999710	−	0.0240717i	$-0.992337\pi$
$653$	−37.7870	+	21.8163i	−1.47872	+	0.853739i	−0.479008	+	0.877810i	$0.659004\pi$
$654$	10.2391	+	32.3240i	0.400380	+	1.26397i
$655$	11.2555	+	11.2555i	0.439788	+	0.439788i
$656$	−0.261595	−	0.976286i	−0.0102136	−	0.0381176i
$657$	−14.6507	+	5.37667i	−0.571579	+	0.209764i
$658$	4.72278	−	4.72278i	0.184113	−	0.184113i
$659$	23.8896	+	13.7927i	0.930608	+	0.537287i	0.887004	−	0.461762i	$-0.152783\pi$
$659$	23.8896	+	13.7927i	0.930608	+	0.537287i	0.0436042	+	0.999049i	$0.486116\pi$
$660$	−2.34004	+	10.6222i	−0.0910858	+	0.413467i
$661$	−14.3184	−	3.83659i	−0.556920	−	0.149226i	−0.0306290	−	0.999531i	$-0.509751\pi$
$661$	−14.3184	−	3.83659i	−0.556920	−	0.149226i	−0.526291	+	0.850305i	$0.676418\pi$
$662$	23.7756			0.924065
$663$	−8.27135	−	32.1016i	−0.321233	−	1.24672i
$664$	2.89503			0.112349
$665$	8.08521	+	2.16642i	0.313531	+	0.0840103i
$666$	16.5785	+	23.5428i	0.642404	+	0.912266i
$667$	20.6434	+	11.9185i	0.799315	+	0.461485i
$668$	5.74919	−	5.74919i	0.222443	−	0.222443i
$669$	15.8655	−	30.5768i	0.613397	−	1.18217i
$670$	6.63055	+	24.7456i	0.256161	+	0.956005i
$671$	−8.03143	−	8.03143i	−0.310050	−	0.310050i
$672$	1.65119	−	0.523037i	0.0636961	−	0.0201766i
$673$	−25.3872	+	14.6573i	−0.978605	+	0.564998i	−0.901849	−	0.432052i	$-0.857790\pi$
$673$	−25.3872	+	14.6573i	−0.978605	+	0.564998i	−0.0767560	+	0.997050i	$0.524456\pi$
$674$	−1.12027	+	4.18091i	−0.0431512	+	0.161043i
$675$	7.96381	−	10.4650i	0.306527	−	0.402796i
$676$	1.41648	−	12.9226i	0.0544799	−	0.497023i
$677$			25.7483i			0.989587i	0.869011	+	0.494794i	$0.164756\pi$
$677$			25.7483i			0.989587i	−0.869011	+	0.494794i	$0.835244\pi$
$678$	12.5020	+	19.5667i	0.480137	+	0.751453i
$679$	−3.94750	−	6.83726i	−0.151491	−	0.262390i
$680$	4.17060	−	7.22369i	0.159935	−	0.277016i
$681$	0.378106	+	8.40320i	0.0144891	+	0.322011i
$682$	−19.2676	+	5.16273i	−0.737793	+	0.197691i
$683$	−6.65558	+	1.78336i	−0.254669	+	0.0682383i	−0.383895	−	0.923377i	$-0.625417\pi$
$683$	−6.65558	+	1.78336i	−0.254669	+	0.0682383i	0.129226	+	0.991615i	$0.458751\pi$
$684$	12.2692	+	10.2395i	0.469123	+	0.391516i
$685$	5.43672	−	9.41667i	0.207726	−	0.359793i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−14.7165	+	9.40305i	−0.561471	+	0.358749i
$688$		−	0.745388i		−	0.0284177i
$689$	−22.8858	−	14.9349i	−0.871881	−	0.568973i
$690$	−5.82341	−	5.32192i	−0.221693	−	0.202602i
$691$	11.6304	−	43.4052i	0.442441	−	1.65121i	−0.280164	−	0.959952i	$-0.590389\pi$
$691$	11.6304	−	43.4052i	0.442441	−	1.65121i	0.722605	−	0.691261i	$-0.242945\pi$
$692$	0.226063	−	0.130518i	0.00859363	−	0.00496153i
$693$	10.8793	+	5.03787i	0.413271	+	0.191373i
$694$	7.21006	+	7.21006i	0.273690	+	0.273690i
$695$	1.36488	+	5.09378i	0.0517727	+	0.193218i
$696$	−12.6433	−	6.56029i	−0.479242	−	0.248667i
$697$	−3.79377	+	3.79377i	−0.143699	+	0.143699i
$698$	11.4835	+	6.62998i	0.434656	+	0.250949i
$699$	13.1368	+	2.89401i	0.496880	+	0.109461i
$700$	−2.44459	−	0.655026i	−0.0923969	−	0.0247577i
$701$	−2.97339			−0.112303			−0.0561516	−	0.998422i	$-0.517883\pi$
$701$	−2.97339			−0.112303			−0.0561516	+	0.998422i	$0.517883\pi$
$702$	18.6746	−	1.50294i	0.704828	−	0.0567248i
$703$	51.1278			1.92832
$704$	3.86021	+	1.03434i	0.145487	+	0.0389831i
$705$	17.7524	+	3.91082i	0.668596	+	0.147290i
$706$	−15.4326	−	8.91003i	−0.580814	−	0.335333i
$707$	−4.00932	+	4.00932i	−0.150786	+	0.150786i
$708$	15.4870	+	8.03584i	0.582039	+	0.302006i
$709$	2.22590	+	8.30716i	0.0835953	+	0.311982i	0.995044	−	0.0994307i	$-0.0317022\pi$
$709$	2.22590	+	8.30716i	0.0835953	+	0.311982i	−0.911449	+	0.411413i	$0.865035\pi$
$710$	−13.8015	−	13.8015i	−0.517960	−	0.517960i
$711$	−31.0618	−	14.3837i	−1.16491	−	0.539432i
$712$	−13.7448	+	7.93558i	−0.515109	+	0.297399i
$713$	3.74449	−	13.9746i	0.140232	−	0.523354i
$714$	−6.78693	−	6.20247i	−0.253995	−	0.232122i
$715$	22.6082	+	1.23537i	0.845501	+	0.0462003i
$716$		−	17.0898i		−	0.638677i
$717$	−3.58760	+	2.29227i	−0.133981	+	0.0856065i
$718$	−12.8672	−	22.2867i	−0.480201	−	0.831733i
$719$	−0.0484197	+	0.0838654i	−0.00180575	+	0.00312765i	−0.866927	−	0.498435i	$-0.833908\pi$
$719$	−0.0484197	+	0.0838654i	−0.00180575	+	0.00312765i	0.865121	+	0.501563i	$0.167241\pi$
$720$	3.61925	+	3.02052i	0.134882	+	0.112568i
$721$	7.82389	−	2.09641i	0.291377	−	0.0780742i
$722$	9.05602	−	2.42655i	0.337030	−	0.0903070i
$723$	−1.95083	−	43.3562i	−0.0725523	−	1.61244i
$724$	5.02597	−	8.70523i	0.186789	−	0.323527i
$725$	10.4064	+	18.0245i	0.386485	+	0.669412i
$726$	4.63589	+	7.25555i	0.172054	+	0.269279i
$727$		−	6.46092i		−	0.239622i	−0.992797	−	0.119811i	$-0.961771\pi$
$727$		−	6.46092i		−	0.239622i	0.992797	−	0.119811i	$-0.0382289\pi$
$728$	−1.62972	−	3.21621i	−0.0604016	−	0.119201i
$729$	7.19631	+	26.0233i	0.266530	+	0.963827i
$730$	−2.11567	+	7.89577i	−0.0783043	+	0.292236i
$731$	−3.42662	+	1.97836i	−0.126738	+	0.0731722i
$732$	−4.69287	+	1.48653i	−0.173453	+	0.0549437i
$733$	16.3697	+	16.3697i	0.604627	+	0.604627i	0.941537	−	0.336910i	$-0.109382\pi$
$733$	16.3697	+	16.3697i	0.604627	+	0.604627i	−0.336910	+	0.941537i	$0.609382\pi$
$734$	8.87825	+	33.1341i	0.327702	+	1.22300i
$735$	1.25351	−	2.41583i	0.0462365	−	0.0891091i
$736$	−2.04959	+	2.04959i	−0.0755487	+	0.0755487i
$737$	56.4255	+	32.5773i	2.07846	+	1.20000i
$738$	−1.74580	−	2.47917i	−0.0642636	−	0.0912596i
$739$	38.1176	+	10.2136i	1.40218	+	0.375713i	0.879127	−	0.476588i	$-0.158127\pi$
$739$	38.1176	+	10.2136i	1.40218	+	0.375713i	0.523052	+	0.852301i	$0.324793\pi$
$740$	15.0821			0.554428
$741$	16.9096	−	28.6480i	0.621189	−	1.05241i
$742$	−7.57938			−0.278248
$743$	9.97404	+	2.67254i	0.365912	+	0.0980458i	0.437090	−	0.899418i	$-0.356009\pi$
$743$	9.97404	+	2.67254i	0.365912	+	0.0980458i	−0.0711779	+	0.997464i	$0.522676\pi$
$744$	−1.85993	+	8.44279i	−0.0681882	+	0.309528i
$745$	8.29172	+	4.78723i	0.303785	+	0.175390i
$746$	−17.6223	+	17.6223i	−0.645198	+	0.645198i
$747$	8.15338	−	2.99221i	0.298317	−	0.109479i
$748$	−5.49055	−	20.4910i	−0.200754	−	0.749226i
$749$	0.0677047	+	0.0677047i	0.00247388	+	0.00247388i
$750$	−6.18944	−	19.5396i	−0.226006	−	0.713485i
$751$	−6.29890	+	3.63667i	−0.229850	+	0.132704i	−0.610503	−	0.792014i	$-0.709033\pi$
$751$	−6.29890	+	3.63667i	−0.229850	+	0.132704i	0.380653	+	0.924718i	$0.375699\pi$
$752$	1.72866	−	6.45143i	0.0630376	−	0.235260i
$753$	29.4929	−	32.2721i	1.07478	−	1.17606i
$754$	−9.22552	+	28.1794i	−0.335974	+	1.02623i
$755$		−	7.24436i		−	0.263649i
$756$	4.10971	−	3.17966i	0.149469	−	0.115643i
$757$	26.2728	+	45.5058i	0.954901	+	1.65394i	0.734594	+	0.678507i	$0.237373\pi$
$757$	26.2728	+	45.5058i	0.954901	+	1.65394i	0.220308	+	0.975430i	$0.429294\pi$
$758$	8.13540	−	14.0909i	0.295491	−	0.511805i
$759$	−20.0433	+	0.901859i	−0.727526	+	0.0327354i
$760$	8.08521	−	2.16642i	0.293281	−	0.0785845i
$761$	10.2974	−	2.75919i	0.373282	−	0.100021i	−0.0673005	−	0.997733i	$-0.521439\pi$
$761$	10.2974	−	2.75919i	0.373282	−	0.100021i	0.440582	+	0.897712i	$0.354772\pi$
$762$	11.6345	−	0.523502i	0.421475	−	0.0189645i
$763$	9.78809	−	16.9535i	0.354353	−	0.613757i
$764$	8.04548	+	13.9352i	0.291075	+	0.504157i
$765$	4.27964	−	24.6549i	0.154731	−	0.891400i
$766$		−	12.3290i		−	0.445463i
$767$	11.3006	−	34.5176i	0.408039	−	1.24636i
$768$	1.16845	−	1.27856i	0.0421630	−	0.0461360i
$769$	4.23085	−	15.7897i	0.152568	−	0.569393i	−0.846733	−	0.532018i	$-0.821434\pi$
$769$	4.23085	−	15.7897i	0.152568	−	0.569393i	0.999301	−	0.0373747i	$-0.0118995\pi$
$770$	5.43843	−	3.13988i	0.195987	−	0.113153i
$771$	−2.73377	−	8.63032i	−0.0984544	−	0.310813i
$772$	0.998195	+	0.998195i	0.0359258	+	0.0359258i
$773$	−9.31158	−	34.7513i	−0.334914	−	1.24992i	−0.903962	−	0.427613i	$-0.859355\pi$
$773$	−9.31158	−	34.7513i	−0.334914	−	1.24992i	0.569048	−	0.822304i	$-0.307312\pi$
$774$	−0.770408	−	2.09926i	−0.0276917	−	0.0754564i
$775$	8.93231	−	8.93231i	0.320858	−	0.320858i
$776$	−6.83726	−	3.94750i	−0.245443	−	0.141707i
$777$	3.57656	−	16.2351i	0.128308	−	0.582431i
$778$	−3.08727	−	0.827231i	−0.110684	−	0.0296577i
$779$	−5.38400			−0.192902
$780$	4.98812	−	8.45082i	0.178603	−	0.302588i
$781$	−49.6400			−1.77626
$782$	14.8620	+	3.98226i	0.531464	+	0.142405i
$783$	−42.3882	−	5.40829i	−1.51483	−	0.193276i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	12.1759	−	12.1759i	0.434575	−	0.434575i
$786$	8.08084	−	15.5738i	0.288234	−	0.555498i
$787$	10.6818	+	39.8652i	0.380767	+	1.42104i	0.844733	+	0.535188i	$0.179759\pi$
$787$	10.6818	+	39.8652i	0.380767	+	1.42104i	−0.463966	+	0.885853i	$0.653574\pi$
$788$	−0.640213	−	0.640213i	−0.0228066	−	0.0228066i
$789$	−20.7058	+	6.55884i	−0.737145	+	0.233501i
$790$	−15.5274	+	8.96473i	−0.552439	+	0.318951i
$791$	3.46970	−	12.9491i	0.123368	−	0.460417i
$792$	11.9407	−	1.07674i	0.424294	−	0.0382601i
$793$	4.63185	+	9.14082i	0.164482	+	0.324600i
$794$		−	6.39373i		−	0.226905i
$795$	−11.1069	−	17.3832i	−0.393922	−	0.616519i
$796$	3.71454	+	6.43378i	0.131659	+	0.228039i
$797$	4.98336	−	8.63143i	0.176520	−	0.305741i	−0.764167	−	0.645019i	$-0.776849\pi$
$797$	4.98336	−	8.63143i	0.176520	−	0.305741i	0.940686	+	0.339278i	$0.110183\pi$
$798$	−0.414727	−	9.21707i	−0.0146812	−	0.326281i
$799$	−34.2459	+	9.17617i	−1.21153	+	0.324630i
$800$	−2.44459	+	0.655026i	−0.0864294	+	0.0231587i
$801$	−30.5081	+	36.5555i	−1.07795	+	1.29162i
$802$	−3.26959	+	5.66310i	−0.115453	+	0.199971i
$803$	10.3947	+	18.0041i	0.366821	+	0.635353i
$804$	23.7957	−	15.2041i	0.839210	−	0.536209i
$805$			4.55467i			0.160531i
$806$	17.9697	+	0.981909i	0.632955	+	0.0345863i
$807$	2.77080	+	2.53219i	0.0975367	+	0.0891372i
$808$	−1.46751	+	5.47683i	−0.0516269	+	0.192674i
$809$	16.4239	−	9.48232i	0.577432	−	0.333381i	−0.182680	−	0.983172i	$-0.558477\pi$
$809$	16.4239	−	9.48232i	0.577432	−	0.333381i	0.760112	+	0.649792i	$0.225144\pi$
$810$	13.3149	+	4.76606i	0.467839	+	0.167462i
$811$	1.28685	+	1.28685i	0.0451873	+	0.0451873i	0.729339	−	0.684152i	$-0.239828\pi$
$811$	1.28685	+	1.28685i	0.0451873	+	0.0451873i	−0.684152	+	0.729339i	$0.739828\pi$
$812$	2.12846	+	7.94353i	0.0746943	+	0.278763i
$813$	16.3997	+	8.50940i	0.575163	+	0.298438i
$814$	27.1230	−	27.1230i	0.950659	−	0.950659i
$815$	26.7145	+	15.4236i	0.935769	+	0.540266i
$816$	−8.97889	−	1.97803i	−0.314324	−	0.0692448i
$817$	−3.83529	−	1.02766i	−0.134180	−	0.0359533i
$818$	−1.05304			−0.0368187
$819$	−7.91401	−	7.37349i	−0.276538	−	0.257651i
$820$	−1.58821			−0.0554628
$821$	21.4795	+	5.75541i	0.749639	+	0.200865i	0.613358	−	0.789805i	$-0.289818\pi$
$821$	21.4795	+	5.75541i	0.749639	+	0.200865i	0.136281	+	0.990670i	$0.456485\pi$
$822$	−11.7047	−	2.57852i	−0.408249	−	0.0899363i
$823$	15.5798	+	8.99501i	0.543078	+	0.313546i	0.746326	−	0.665581i	$-0.231816\pi$
$823$	15.5798	+	8.99501i	0.543078	+	0.313546i	−0.203247	+	0.979127i	$0.565150\pi$
$824$	5.72749	−	5.72749i	0.199526	−	0.199526i
$825$	−15.5496	−	8.06831i	−0.541368	−	0.280903i
$826$	−2.60720	−	9.73021i	−0.0907161	−	0.338557i
$827$	−10.6679	−	10.6679i	−0.370961	−	0.370961i	0.496866	−	0.867827i	$-0.334484\pi$
$827$	−10.6679	−	10.6679i	−0.370961	−	0.370961i	−0.867827	+	0.496866i	$0.834484\pi$
$828$	−3.65393	+	7.89070i	−0.126983	+	0.274221i
$829$	24.6079	−	14.2074i	0.854666	−	0.493442i	−0.00755635	−	0.999971i	$-0.502405\pi$
$829$	24.6079	−	14.2074i	0.854666	−	0.493442i	0.862223	+	0.506530i	$0.169072\pi$
$830$	1.17740	−	4.39413i	0.0408683	−	0.152522i
$831$	41.3406	+	37.7805i	1.43409	+	1.31059i
$832$	−3.01949	−	1.97046i	−0.104682	−	0.0683133i
$833$			5.30827i			0.183921i
$834$	4.89826	−	3.12972i	0.169613	−	0.108373i
$835$	−6.38803	−	11.0644i	−0.221067	−	0.382899i
$836$	10.6441	−	18.4361i	0.368134	−	0.637626i
$837$	3.48801	+	25.7001i	0.120563	+	0.888325i
$838$	−4.74784	+	1.27218i	−0.164011	+	0.0439467i
$839$	34.6493	−	9.28425i	1.19623	−	0.320528i	0.394883	−	0.918732i	$-0.370785\pi$
$839$	34.6493	−	9.28425i	1.19623	−	0.320528i	0.801344	+	0.598204i	$0.204119\pi$
$840$	−0.122339	−	2.71892i	−0.00422111	−	0.0938118i
$841$	19.3150	−	33.4545i	0.666034	−	1.15360i
$842$	1.82760	+	3.16550i	0.0629834	+	0.109090i
$843$	29.7442	+	46.5521i	1.02445	+	1.60334i
$844$			11.2780i			0.388204i
$845$	−19.0381	−	7.40555i	−0.654929	−	0.254759i
$846$	−1.79951	−	19.9561i	−0.0618685	−	0.686104i
$847$	1.28661	−	4.80168i	0.0442083	−	0.164988i
$848$	−6.56394	+	3.78969i	−0.225407	+	0.130139i
$849$	−26.4558	+	8.38025i	−0.907962	+	0.287609i
$850$	9.49949	+	9.49949i	0.325830	+	0.325830i
$851$	7.20049	+	26.8726i	0.246830	+	0.921181i
$852$	−9.90872	+	19.0965i	−0.339467	+	0.654237i
$853$	5.66683	−	5.66683i	0.194029	−	0.194029i	−0.603406	−	0.797434i	$-0.706190\pi$
$853$	5.66683	−	5.66683i	0.194029	−	0.194029i	0.797434	+	0.603406i	$0.206190\pi$
$854$	2.46134	+	1.42106i	0.0842253	+	0.0486275i
$855$	20.5315	−	14.4580i	0.702163	−	0.494452i
$856$	0.0924864	+	0.0247817i	0.00316112	+	0.000847019i
$857$	45.7136			1.56155			0.780773	−	0.624815i	$-0.214826\pi$
$857$	45.7136			1.56155			0.780773	+	0.624815i	$0.214826\pi$
$858$	−6.22717	−	24.1680i	−0.212592	−	0.825083i
$859$	0.774161			0.0264140			0.0132070	−	0.999913i	$-0.495796\pi$
$859$	0.774161			0.0264140			0.0132070	+	0.999913i	$0.495796\pi$
$860$	−1.13136	−	0.303148i	−0.0385791	−	0.0103373i
$861$	−0.376628	+	1.70963i	−0.0128355	+	0.0582642i
$862$	−21.2275	−	12.2557i	−0.723010	−	0.417430i
$863$	−25.5049	+	25.5049i	−0.868195	+	0.868195i	−0.992273	−	0.124077i	$-0.960403\pi$
$863$	−25.5049	+	25.5049i	−0.868195	+	0.868195i	0.124077	+	0.992273i	$0.460403\pi$
$864$	1.96928	−	4.80853i	0.0669964	−	0.163589i
$865$	−0.106162	−	0.396204i	−0.00360963	−	0.0134713i
$866$	−10.3218	−	10.3218i	−0.350748	−	0.350748i
$867$	5.84635	+	18.4565i	0.198552	+	0.626815i
$868$	4.32262	−	2.49566i	0.146719	−	0.0847083i
$869$	−11.8020	+	44.0456i	−0.400355	+	1.49414i
$870$	−15.0993	+	16.5221i	−0.511914	+	0.560153i
$871$	−39.2359	−	43.7716i	−1.32946	−	1.48314i
$872$		−	19.5762i		−	0.662933i
$873$	−23.3360	−	4.05070i	−0.789805	−	0.137096i
$874$	7.72009	+	13.3716i	0.261136	+	0.452301i
$875$	−5.91682	+	10.2482i	−0.200025	+	0.346454i
$876$	9.00112	−	0.405010i	0.304120	−	0.0136840i
$877$	−27.6975	+	7.42152i	−0.935278	+	0.250607i	−0.694104	−	0.719875i	$-0.744199\pi$
$877$	−27.6975	+	7.42152i	−0.935278	+	0.250607i	−0.241174	+	0.970482i	$0.577533\pi$
$878$	18.6657	−	5.00146i	0.629937	−	0.168791i
$879$	38.8463	−	1.74791i	1.31025	−	0.0589556i
$880$	3.13988	−	5.43843i	0.105845	−	0.183329i
$881$	13.7108	+	23.7478i	0.461928	+	0.800083i	0.999057	−	0.0434173i	$-0.0138245\pi$
$881$	13.7108	+	23.7478i	0.461928	+	0.800083i	−0.537129	+	0.843500i	$0.680491\pi$
$882$	−2.95580	−	0.513072i	−0.0995270	−	0.0172760i
$883$			12.7957i			0.430611i	0.976547	+	0.215306i	$0.0690747\pi$
$883$			12.7957i			0.430611i	−0.976547	+	0.215306i	$0.930925\pi$
$884$	−1.04426	+	19.1107i	−0.0351222	+	0.642763i
$885$	18.4955	−	20.2383i	0.621719	−	0.680304i
$886$	−6.35806	+	23.7286i	−0.213603	+	0.797178i
$887$	34.5838	−	19.9670i	1.16121	−	0.670425i	0.209617	−	0.977784i	$-0.432778\pi$
$887$	34.5838	−	19.9670i	1.16121	−	0.670425i	0.951594	+	0.307358i	$0.0994450\pi$
$888$	−5.02016	−	15.8483i	−0.168466	−	0.531834i
$889$	−4.75459	−	4.75459i	−0.159464	−	0.159464i
$890$	6.45477	+	24.0895i	0.216364	+	0.807483i
$891$	32.5161	−	15.3740i	1.08933	−	0.515047i
$892$	−14.0633	+	14.0633i	−0.470873	+	0.470873i
$893$	−30.8116	−	17.7891i	−1.03107	−	0.595290i
$894$	2.27048	−	10.3064i	0.0759363	−	0.344699i
$895$	−25.9393	−	6.95040i	−0.867054	−	0.232326i
$896$	−1.00000			−0.0334077
$897$	17.4388	+	4.85304i	0.582263	+	0.162038i
$898$	−0.673572			−0.0224774
$899$	−39.6487	−	10.6238i	−1.32236	−	0.354325i
$900$	−6.20778	+	4.37142i	−0.206926	+	0.145714i
$901$	34.8431	+	20.1167i	1.16079	+	0.670184i
$902$	−2.85618	+	2.85618i	−0.0951003	+	0.0951003i
$903$	−0.594615	+	1.14597i	−0.0197875	+	0.0381354i
$904$	−3.46970	−	12.9491i	−0.115401	−	0.430681i
$905$	−11.1689	−	11.1689i	−0.371267	−	0.371267i
$906$	−7.61240	+	2.41133i	−0.252905	+	0.0801112i
$907$	19.1805	−	11.0739i	0.636878	−	0.367702i	−0.146533	−	0.989206i	$-0.546811\pi$
$907$	19.1805	−	11.0739i	0.636878	−	0.367702i	0.783411	+	0.621504i	$0.213478\pi$
$908$	1.25695	−	4.69102i	0.0417135	−	0.155677i
$909$	1.52766	+	16.9414i	0.0506694	+	0.561910i
$910$	−5.54442	+	1.16560i	−0.183796	+	0.0386391i
$911$			8.96035i			0.296870i	0.988922	+	0.148435i	$0.0474235\pi$
$911$			8.96035i			0.296870i	−0.988922	+	0.148435i	$0.952576\pi$
$912$	−4.96770	−	7.77486i	−0.164497	−	0.257451i
$913$	−5.78483	−	10.0196i	−0.191450	−	0.331601i
$914$	−2.85497	+	4.94494i	−0.0944338	+	0.163564i
$915$	0.347702	+	7.72748i	0.0114947	+	0.255463i
$916$	9.73932	−	2.60964i	0.321796	−	0.0862250i
$917$	−9.78469	+	2.62180i	−0.323119	+	0.0865795i
$918$	−27.3320	+	3.70949i	−0.902090	+	0.122431i
$919$	−13.8466	+	23.9829i	−0.456756	+	0.791124i	−0.998787	−	0.0492339i	$-0.984322\pi$
$919$	−13.8466	+	23.9829i	−0.456756	+	0.791124i	0.542031	+	0.840358i	$0.317655\pi$
$920$	2.27733	+	3.94446i	0.0750815	+	0.130045i
$921$	−41.5263	+	26.5330i	−1.36834	+	0.874292i
$922$		−	2.96713i		−	0.0977171i
$923$	42.5625	+	13.9343i	1.40096	+	0.458654i
$924$	−5.10961	−	4.66959i	−0.168094	−	0.153618i
$925$	−6.28701	+	23.4634i	−0.206715	+	0.771473i
$926$	−12.3641	+	7.13839i	−0.406308	+	0.234582i
$927$	10.2108	−	22.0503i	0.335366	−	0.724226i
$928$	5.81506	+	5.81506i	0.190889	+	0.190889i
$929$	1.36103	+	5.07943i	0.0446539	+	0.166651i	0.984652	−	0.174529i	$-0.0558402\pi$
$929$	1.36103	+	5.07943i	0.0446539	+	0.166651i	−0.939998	+	0.341180i	$0.889174\pi$
$930$	12.0582	+	6.25669i	0.395403	+	0.205165i
$931$	−3.76666	+	3.76666i	−0.123447	+	0.123447i
$932$	−6.72590	−	3.88320i	−0.220314	−	0.127198i
$933$	39.5490	+	8.71256i	1.29478	+	0.285236i
$934$	−6.93021	−	1.85694i	−0.226763	−	0.0607610i
$935$	−33.3346			−1.09016
$936$	−10.5405	−	2.42863i	−0.344526	−	0.0793822i
$937$	−56.8673			−1.85777			−0.928887	−	0.370362i	$-0.879234\pi$
$937$	−56.8673			−1.85777			−0.928887	+	0.370362i	$0.879234\pi$
$938$	−15.7479	−	4.21963i	−0.514186	−	0.137776i
$939$	−32.2326	−	7.10077i	−1.05187	−	0.231725i
$940$	−9.08906	−	5.24757i	−0.296452	−	0.171157i
$941$	39.7069	−	39.7069i	1.29441	−	1.29441i	0.362374	−	0.932033i	$-0.381966\pi$
$941$	39.7069	−	39.7069i	1.29441	−	1.29441i	0.932033	−	0.362374i	$-0.118034\pi$
$942$	−16.8473	−	8.74163i	−0.548914	−	0.284818i
$943$	−0.758246	−	2.82981i	−0.0246919	−	0.0921514i
$944$	−7.12301	−	7.12301i	−0.231834	−	0.231834i
$945$	−3.15474	−	7.53095i	−0.102624	−	0.244982i
$946$	−2.57976	+	1.48943i	−0.0838754	+	0.0484255i
$947$	12.8157	−	47.8289i	0.416455	−	1.55423i	−0.365450	−	0.930831i	$-0.619085\pi$
$947$	12.8157	−	47.8289i	0.416455	−	1.55423i	0.781904	−	0.623399i	$-0.214249\pi$
$948$	14.5886	+	13.3323i	0.473815	+	0.433012i
$949$	−3.85876	−	18.3551i	−0.125261	−	0.595830i
$950$			13.4814i			0.437394i
$951$	−29.3427	+	18.7484i	−0.951504	+	0.607958i
$952$	2.65413	+	4.59709i	0.0860209	+	0.148993i
$953$	23.1302	−	40.0627i	0.749260	−	1.29776i	−0.198918	−	0.980016i	$-0.563743\pi$
$953$	23.1302	−	40.0627i	0.749260	−	1.29776i	0.948178	−	0.317740i	$-0.102924\pi$
$954$	−14.5694	+	17.4573i	−0.471700	+	0.565201i
$955$	24.4231	−	6.54416i	0.790315	−	0.211764i
$956$	2.37425	−	0.636178i	0.0767887	−	0.0205755i
$957$	2.55875	+	56.8667i	0.0827125	+	1.83824i
$958$	10.4473	−	18.0952i	0.337535	−	0.584628i
$959$	3.45988	+	5.99269i	0.111725	+	0.193514i
$960$	−1.46541	−	2.29349i	−0.0472959	−	0.0740220i
$961$		−	6.08666i		−	0.196344i
$962$	−30.8695	+	15.6422i	−0.995272	+	0.504326i
$963$	0.286086	−	0.0257974i	0.00921900	−	0.000831310i
$964$	−6.48524	+	24.2033i	−0.208876	+	0.779534i
$965$	1.92104	−	1.10911i	0.0618405	−	0.0357036i
$966$	4.78606	−	1.51605i	0.153989	−	0.0487781i
$967$	18.0661	+	18.0661i	0.580966	+	0.580966i	0.935169	−	0.354202i	$-0.115248\pi$
$967$	18.0661	+	18.0661i	0.580966	+	0.580966i	−0.354202	+	0.935169i	$0.615248\pi$
$968$	−1.28661	−	4.80168i	−0.0413531	−	0.154332i
$969$	−22.5568	+	43.4725i	−0.724629	+	1.39654i
$970$	−8.77228	+	8.77228i	−0.281661	+	0.281661i
$971$	21.8731	+	12.6285i	0.701942	+	0.405267i	0.808070	−	0.589086i	$-0.200512\pi$
$971$	21.8731	+	12.6285i	0.701942	+	0.405267i	−0.106128	+	0.994352i	$0.533845\pi$
$972$	0.576228	−	15.5778i	0.0184825	−	0.499658i
$973$	−3.24164	−	0.868595i	−0.103922	−	0.0278459i
$974$	−5.16286			−0.165429
$975$	11.0678	+	11.2829i	0.354452	+	0.361341i
$976$	2.84211			0.0909737
$977$	−38.6789	−	10.3640i	−1.23745	−	0.331573i	−0.419973	−	0.907537i	$-0.637960\pi$
$977$	−38.6789	−	10.3640i	−1.23745	−	0.331573i	−0.817476	+	0.575963i	$0.804627\pi$
$978$	7.31511	−	33.2056i	0.233912	−	1.06180i
$979$	54.9296	+	31.7136i	1.75556	+	1.01357i
$980$	−1.11112	+	1.11112i	−0.0354934	+	0.0354934i
$981$	−20.2333	−	55.1331i	−0.645999	−	1.76026i
$982$	2.69076	+	10.0420i	0.0858655	+	0.320454i
$983$	−34.2403	−	34.2403i	−1.09209	−	1.09209i	−0.995305	−	0.0967901i	$-0.969142\pi$
$983$	−34.2403	−	34.2403i	−1.09209	−	1.09209i	−0.0967901	−	0.995305i	$-0.530858\pi$
$984$	0.528647	+	1.66890i	0.0168527	+	0.0532026i
$985$	−1.23210	+	0.711353i	−0.0392579	+	0.0226656i
$986$	11.2984	−	42.1663i	0.359816	−	1.34285i
$987$	−7.80413	+	8.53952i	−0.248408	+	0.271816i
$988$	−14.3017	+	12.8197i	−0.454996	+	0.407848i
$989$		−	2.16055i		−	0.0687013i
$990$	3.22197	−	18.5617i	0.102401	−	0.589930i
$991$	6.78475	+	11.7515i	0.215525	+	0.373299i	0.953435	−	0.301599i	$-0.0975205\pi$
$991$	6.78475	+	11.7515i	0.215525	+	0.373299i	−0.737910	+	0.674899i	$0.764187\pi$
$992$	2.49566	−	4.32262i	0.0792374	−	0.137243i
$993$	−41.1389	+	1.85107i	−1.30551	+	0.0587419i
$994$	11.9980	−	3.21485i	0.380553	−	0.101969i
$995$	11.2760	−	3.02139i	0.357473	−	0.0957847i
$996$	−5.00928	+	0.225395i	−0.158725	+	0.00714191i
$997$	30.4208	−	52.6904i	0.963437	−	1.66872i	0.249682	−	0.968328i	$-0.419674\pi$
$997$	30.4208	−	52.6904i	0.963437	−	1.66872i	0.713756	−	0.700395i	$-0.246993\pi$
$998$	−7.48226	−	12.9597i	−0.236847	−	0.410231i
$999$	−30.5187	−	39.4454i	−0.965570	−	1.24800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.323.8	yes	56
3.2	odd	2		546.2.bu.a.323.5	yes	56
13.6	odd	12		546.2.bu.a.71.5	✓	56
39.32	even	12	inner	546.2.bu.b.71.8	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.5	✓	56	13.6	odd	12
546.2.bu.a.323.5	yes	56	3.2	odd	2
546.2.bu.b.71.8	yes	56	39.32	even	12	inner
546.2.bu.b.323.8	yes	56	1.1	even	1	trivial

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.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.69149 - 0.372632i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.11112 - 1.11112i) q^{5} +(-1.53741 - 0.797725i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.72229 + 1.26061i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.69149 - 0.372632i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.11112 - 1.11112i) q^{5} +(-1.53741 - 0.797725i) q^{6} +(0.258819 + 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.72229 + 1.26061i) q^{9} +(1.36084 - 0.785680i) q^{10} +(1.03434 - 3.86021i) q^{11} +(-1.27856 - 1.16845i) q^{12} +(-1.97046 + 3.01949i) q^{13} +1.00000i q^{14} +(-2.29349 + 1.46541i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.65413 - 4.59709i) q^{17} +(2.30326 + 1.92223i) q^{18} +(5.14536 - 1.37869i) q^{19} +(1.51782 - 0.406698i) q^{20} +(-0.0778557 - 1.73030i) q^{21} +(1.99819 - 3.46097i) q^{22} +(1.44928 + 2.51022i) q^{23} +(-0.932575 - 1.45956i) q^{24} +2.53083i q^{25} +(-2.68482 + 2.40661i) q^{26} +(-4.13499 - 3.14672i) q^{27} +(-0.258819 + 0.965926i) q^{28} +(7.12197 - 4.11187i) q^{29} +(-2.59462 + 0.821880i) q^{30} +(-3.52940 - 3.52940i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-3.18801 + 6.14408i) q^{33} +(3.75351 - 3.75351i) q^{34} +(1.36084 + 0.785680i) q^{35} +(1.72727 + 2.45286i) q^{36} +(9.27105 + 2.48417i) q^{37} +5.32686 q^{38} +(4.45817 - 4.37318i) q^{39} +1.57136 q^{40} +(-0.976286 - 0.261595i) q^{41} +(0.372632 - 1.69149i) q^{42} +(-0.645525 - 0.372694i) q^{43} +(2.82587 - 2.82587i) q^{44} +(4.42548 - 1.62410i) q^{45} +(0.750200 + 2.79979i) q^{46} +(-4.72278 - 4.72278i) q^{47} +(-0.523037 - 1.65119i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.655026 + 2.44459i) q^{50} +(-6.20247 + 6.78693i) q^{51} +(-3.21621 + 1.62972i) q^{52} +7.57938i q^{53} +(-3.17966 - 4.10971i) q^{54} +(-3.13988 - 5.43843i) q^{55} +(-0.500000 + 0.866025i) q^{56} +(-9.21707 + 0.414727i) q^{57} +(7.94353 - 2.12846i) q^{58} +(-9.73021 + 2.60720i) q^{59} +(-2.71892 + 0.122339i) q^{60} +(1.42106 - 2.46134i) q^{61} +(-2.49566 - 4.32262i) q^{62} +(-0.513072 + 2.95580i) q^{63} +1.00000i q^{64} +(1.16560 + 5.54442i) q^{65} +(-4.66959 + 5.10961i) q^{66} +(-4.21963 + 15.7479i) q^{67} +(4.59709 - 2.65413i) q^{68} +(-1.51605 - 4.78606i) q^{69} +(1.11112 + 1.11112i) q^{70} +(-3.21485 - 11.9980i) q^{71} +(1.03357 + 2.81633i) q^{72} +(-3.67841 + 3.67841i) q^{73} +(8.31219 + 4.79905i) q^{74} +(0.943067 - 4.28088i) q^{75} +(5.14536 + 1.37869i) q^{76} +3.99638 q^{77} +(5.43812 - 3.07031i) q^{78} -11.4102 q^{79} +(1.51782 + 0.406698i) q^{80} +(5.82174 + 6.86348i) q^{81} +(-0.875314 - 0.505363i) q^{82} +(2.04710 - 2.04710i) q^{83} +(0.797725 - 1.53741i) q^{84} +(-2.15886 - 8.05698i) q^{85} +(-0.527069 - 0.527069i) q^{86} +(-13.5790 + 4.30133i) q^{87} +(3.46097 - 1.99819i) q^{88} +(-4.10776 + 15.3304i) q^{89} +(4.69503 - 0.423368i) q^{90} +(-3.42659 - 1.12182i) q^{91} +2.89855i q^{92} +(4.65479 + 7.28512i) q^{93} +(-3.33951 - 5.78420i) q^{94} +(4.18521 - 7.24900i) q^{95} +(-0.0778557 - 1.73030i) q^{96} +(-7.62598 + 2.04337i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(7.68198 - 9.20471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

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