LMFDB - Embedded newform 546.2.cg.b.409.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			409.2
Character	$\chi$	$=$	546.409
Dual form			546.2.cg.b.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.445159 + 1.66136i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.60723 - 0.449857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.445159 + 1.66136i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.60723 - 0.449857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.859981 - 1.48953i) q^{10} +(1.45759 - 5.43980i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.62078 - 3.22072i) q^{13} +(2.16168 - 1.52549i) q^{14} +(0.445159 + 1.66136i) q^{15} -1.00000 q^{16} +7.65864 q^{17} +(0.258819 + 0.965926i) q^{18} +(-0.350714 + 0.0939735i) q^{19} +(1.66136 + 0.445159i) q^{20} +(-2.48285 + 0.914026i) q^{21} +(2.81585 + 4.87719i) q^{22} +6.34721i q^{23} +(0.965926 + 0.258819i) q^{24} +(1.76819 + 1.02087i) q^{25} +(1.13133 + 3.42346i) q^{26} -1.00000i q^{27} +(-0.449857 + 2.60723i) q^{28} +(3.90529 - 6.76416i) q^{29} +(-1.48953 - 0.859981i) q^{30} +(0.143335 - 0.0384066i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.45759 - 5.43980i) q^{33} +(-5.41548 + 5.41548i) q^{34} +(1.90800 - 4.13127i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-4.94934 - 4.94934i) q^{37} +(0.181543 - 0.314441i) q^{38} +(-0.206724 - 3.59962i) q^{39} +(-1.48953 + 0.859981i) q^{40} +(8.72661 - 2.33829i) q^{41} +(1.10933 - 2.40196i) q^{42} +(-6.41578 + 3.70415i) q^{43} +(-5.43980 - 1.45759i) q^{44} +(1.21620 + 1.21620i) q^{45} +(-4.48816 - 4.48816i) q^{46} +(0.730514 + 0.195741i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(6.59526 + 2.34576i) q^{49} +(-1.97216 + 0.528439i) q^{50} +(6.63258 - 3.82932i) q^{51} +(-3.22072 - 1.62078i) q^{52} +(0.431525 - 0.747424i) q^{53} +(0.707107 + 0.707107i) q^{54} +(8.38858 + 4.84315i) q^{55} +(-1.52549 - 2.16168i) q^{56} +(-0.256740 + 0.256740i) q^{57} +(2.02153 + 7.54443i) q^{58} +(-0.917790 + 0.917790i) q^{59} +(1.66136 - 0.445159i) q^{60} +(-6.74691 - 3.89533i) q^{61} +(-0.0741959 + 0.128511i) q^{62} +(-1.69320 + 2.03300i) q^{63} +1.00000i q^{64} +(4.62926 + 4.12643i) q^{65} +(4.87719 + 2.81585i) q^{66} +(3.22438 + 0.863971i) q^{67} -7.65864i q^{68} +(3.17361 + 5.49685i) q^{69} +(1.57209 + 4.27041i) q^{70} +(-14.4500 - 3.87187i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.26342 - 8.44718i) q^{73} +6.99942 q^{74} +2.04173 q^{75} +(0.0939735 + 0.350714i) q^{76} +(-6.24739 + 13.5271i) q^{77} +(2.69149 + 2.39914i) q^{78} +(6.10060 + 10.5665i) q^{79} +(0.445159 - 1.66136i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.51723 + 7.82407i) q^{82} +(-1.17131 - 1.17131i) q^{83} +(0.914026 + 2.48285i) q^{84} +(-3.40931 + 12.7237i) q^{85} +(1.91741 - 7.15588i) q^{86} -7.81057i q^{87} +(4.87719 - 2.81585i) q^{88} +(2.96033 - 2.96033i) q^{89} -1.71996 q^{90} +(-5.67461 + 7.66804i) q^{91} +6.34721 q^{92} +(0.104929 - 0.104929i) q^{93} +(-0.654961 + 0.378142i) q^{94} -0.624494i q^{95} +(0.258819 - 0.965926i) q^{96} +(-0.740288 + 2.76279i) q^{97} +(-6.32225 + 3.00485i) q^{98} +(-3.98221 - 3.98221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		−	1.00000i		−	0.500000i
$5$	−0.445159	+	1.66136i	−0.199081	+	0.742981i	0.792091	+	0.610403i	$0.208992\pi$
$5$	−0.445159	+	1.66136i	−0.199081	+	0.742981i	−0.991173	+	0.132578i	$0.957674\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−2.60723	−	0.449857i	−0.985439	−	0.170030i
$7$	−2.60723	−	0.449857i	−0.985439	−	0.170030i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.859981	−	1.48953i	−0.271950	−	0.471031i
$11$	1.45759	−	5.43980i	0.439480	−	1.64016i	−0.290634	−	0.956834i	$-0.593866\pi$
$11$	1.45759	−	5.43980i	0.439480	−	1.64016i	0.730114	−	0.683326i	$-0.239467\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.62078	−	3.22072i	0.449524	−	0.893268i
$13$	1.62078	−	3.22072i	0.449524	−	0.893268i
$14$	2.16168	−	1.52549i	0.577734	−	0.407705i
$15$	0.445159	+	1.66136i	0.114940	+	0.428960i
$16$	−1.00000			−0.250000
$17$	7.65864			1.85749			0.928747	−	0.370714i	$-0.120887\pi$
$17$	7.65864			1.85749			0.928747	+	0.370714i	$0.120887\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−0.350714	+	0.0939735i	−0.0804593	+	0.0215590i	−0.298824	−	0.954308i	$-0.596594\pi$
$19$	−0.350714	+	0.0939735i	−0.0804593	+	0.0215590i	0.218365	+	0.975867i	$0.429928\pi$
$20$	1.66136	+	0.445159i	0.371490	+	0.0995406i
$21$	−2.48285	+	0.914026i	−0.541803	+	0.199457i
$22$	2.81585	+	4.87719i	0.600340	+	1.03982i
$23$			6.34721i			1.32349i	0.749731	+	0.661743i	$0.230183\pi$
$23$			6.34721i			1.32349i	−0.749731	+	0.661743i	$0.769817\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	1.76819	+	1.02087i	0.353638	+	0.204173i
$26$	1.13133	+	3.42346i	0.221872	+	0.671396i
$27$		−	1.00000i		−	0.192450i
$28$	−0.449857	+	2.60723i	−0.0850149	+	0.492719i
$29$	3.90529	−	6.76416i	0.725194	−	1.25607i	−0.233701	−	0.972309i	$-0.575084\pi$
$29$	3.90529	−	6.76416i	0.725194	−	1.25607i	0.958894	−	0.283763i	$-0.0915831\pi$
$30$	−1.48953	−	0.859981i	−0.271950	−	0.157010i
$31$	0.143335	−	0.0384066i	0.0257438	−	0.00689803i	−0.245924	−	0.969289i	$-0.579091\pi$
$31$	0.143335	−	0.0384066i	0.0257438	−	0.00689803i	0.271668	+	0.962391i	$0.412425\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.45759	−	5.43980i	−0.253734	−	0.946947i
$34$	−5.41548	+	5.41548i	−0.928747	+	0.928747i
$35$	1.90800	−	4.13127i	0.322511	−	0.698313i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−4.94934	−	4.94934i	−0.813667	−	0.813667i	0.171515	−	0.985182i	$-0.445134\pi$
$37$	−4.94934	−	4.94934i	−0.813667	−	0.813667i	−0.985182	+	0.171515i	$0.945134\pi$
$38$	0.181543	−	0.314441i	0.0294501	−	0.0510091i
$39$	−0.206724	−	3.59962i	−0.0331024	−	0.576401i
$40$	−1.48953	+	0.859981i	−0.235516	+	0.135975i
$41$	8.72661	−	2.33829i	1.36287	−	0.365179i	0.497999	−	0.867178i	$-0.334068\pi$
$41$	8.72661	−	2.33829i	1.36287	−	0.365179i	0.864869	+	0.501998i	$0.167402\pi$
$42$	1.10933	−	2.40196i	0.171173	−	0.370630i
$43$	−6.41578	+	3.70415i	−0.978398	+	0.564878i	−0.901786	−	0.432183i	$-0.857744\pi$
$43$	−6.41578	+	3.70415i	−0.978398	+	0.564878i	−0.0766118	+	0.997061i	$0.524410\pi$
$44$	−5.43980	−	1.45759i	−0.820080	−	0.219740i
$45$	1.21620	+	1.21620i	0.181300	+	0.181300i
$46$	−4.48816	−	4.48816i	−0.661743	−	0.661743i
$47$	0.730514	+	0.195741i	0.106556	+	0.0285517i	0.311703	−	0.950179i	$-0.399101\pi$
$47$	0.730514	+	0.195741i	0.106556	+	0.0285517i	−0.205147	+	0.978731i	$0.565767\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	6.59526	+	2.34576i	0.942180	+	0.335108i
$50$	−1.97216	+	0.528439i	−0.278906	+	0.0747325i
$51$	6.63258	−	3.82932i	0.928747	−	0.536212i
$52$	−3.22072	−	1.62078i	−0.446634	−	0.224762i
$53$	0.431525	−	0.747424i	0.0592745	−	0.102667i	−0.834865	−	0.550454i	$-0.814455\pi$
$53$	0.431525	−	0.747424i	0.0592745	−	0.102667i	0.894140	+	0.447788i	$0.147788\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	8.38858	+	4.84315i	1.13112	+	0.653050i
$56$	−1.52549	−	2.16168i	−0.203852	−	0.288867i
$57$	−0.256740	+	0.256740i	−0.0340061	+	0.0340061i
$58$	2.02153	+	7.54443i	0.265439	+	0.990633i
$59$	−0.917790	+	0.917790i	−0.119486	+	0.119486i	−0.764321	−	0.644835i	$-0.776926\pi$
$59$	−0.917790	+	0.917790i	−0.119486	+	0.119486i	0.644835	+	0.764321i	$0.276926\pi$
$60$	1.66136	−	0.445159i	0.214480	−	0.0574698i
$61$	−6.74691	−	3.89533i	−0.863853	−	0.498746i	0.00144778	−	0.999999i	$-0.499539\pi$
$61$	−6.74691	−	3.89533i	−0.863853	−	0.498746i	−0.865301	+	0.501253i	$0.832872\pi$
$62$	−0.0741959	+	0.128511i	−0.00942289	+	0.0163209i
$63$	−1.69320	+	2.03300i	−0.213323	+	0.256133i
$64$			1.00000i			0.125000i
$65$	4.62926	+	4.12643i	0.574190	+	0.511821i
$66$	4.87719	+	2.81585i	0.600340	+	0.346607i
$67$	3.22438	+	0.863971i	0.393921	+	0.105551i	0.450342	−	0.892856i	$-0.351302\pi$
$67$	3.22438	+	0.863971i	0.393921	+	0.105551i	−0.0564206	+	0.998407i	$0.517969\pi$
$68$		−	7.65864i		−	0.928747i
$69$	3.17361	+	5.49685i	0.382057	+	0.661743i
$70$	1.57209	+	4.27041i	0.187901	+	0.510412i
$71$	−14.4500	−	3.87187i	−1.71490	−	0.459507i	−0.738285	−	0.674489i	$-0.764364\pi$
$71$	−14.4500	−	3.87187i	−1.71490	−	0.459507i	−0.976618	+	0.214982i	$0.931031\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	−2.26342	−	8.44718i	−0.264913	−	0.988668i	−0.962304	−	0.271977i	$-0.912323\pi$
$73$	−2.26342	−	8.44718i	−0.264913	−	0.988668i	0.697391	−	0.716691i	$-0.254344\pi$
$74$	6.99942			0.813667
$75$	2.04173			0.235759
$76$	0.0939735	+	0.350714i	0.0107795	+	0.0402296i
$77$	−6.24739	+	13.5271i	−0.711956	+	1.54155i
$78$	2.69149	+	2.39914i	0.304751	+	0.271649i
$79$	6.10060	+	10.5665i	0.686371	+	1.18883i	0.973004	+	0.230789i	$0.0741307\pi$
$79$	6.10060	+	10.5665i	0.686371	+	1.18883i	−0.286633	+	0.958041i	$0.592536\pi$
$80$	0.445159	−	1.66136i	0.0497703	−	0.185745i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.51723	+	7.82407i	−0.498844	+	0.864023i
$83$	−1.17131	−	1.17131i	−0.128568	−	0.128568i	0.639895	−	0.768463i	$-0.278978\pi$
$83$	−1.17131	−	1.17131i	−0.128568	−	0.128568i	−0.768463	+	0.639895i	$0.778978\pi$
$84$	0.914026	+	2.48285i	0.0997284	+	0.270901i
$85$	−3.40931	+	12.7237i	−0.369792	+	1.38008i
$86$	1.91741	−	7.15588i	0.206760	−	0.771638i
$87$		−	7.81057i		−	0.837381i
$88$	4.87719	−	2.81585i	0.519910	−	0.300170i
$89$	2.96033	−	2.96033i	0.313795	−	0.313795i	−0.532583	−	0.846378i	$-0.678779\pi$
$89$	2.96033	−	2.96033i	0.313795	−	0.313795i	0.846378	+	0.532583i	$0.178779\pi$
$90$	−1.71996			−0.181300
$91$	−5.67461	+	7.66804i	−0.594861	+	0.803829i
$92$	6.34721			0.661743
$93$	0.104929	−	0.104929i	0.0108806	−	0.0108806i
$94$	−0.654961	+	0.378142i	−0.0675541	+	0.0390024i
$95$		−	0.624494i		−	0.0640717i
$96$	0.258819	−	0.965926i	0.0264156	−	0.0985844i
$97$	−0.740288	+	2.76279i	−0.0751648	+	0.280519i	−0.993271	−	0.115816i	$-0.963052\pi$
$97$	−0.740288	+	2.76279i	−0.0751648	+	0.280519i	0.918106	+	0.396335i	$0.129718\pi$
$98$	−6.32225	+	3.00485i	−0.638644	+	0.303536i
$99$	−3.98221	−	3.98221i	−0.400227	−	0.400227i
$100$	1.02087	−	1.76819i	0.102087	−	0.176819i
$101$	−3.52192	−	6.10015i	−0.350445	−	0.606988i	0.635883	−	0.771786i	$-0.280636\pi$
$101$	−3.52192	−	6.10015i	−0.350445	−	0.606988i	−0.986327	+	0.164798i	$0.947303\pi$
$102$	−1.98220	+	7.39768i	−0.196267	+	0.732480i
$103$	−3.37530	−	5.84620i	−0.332579	−	0.576043i	0.650438	−	0.759559i	$-0.274585\pi$
$103$	−3.37530	−	5.84620i	−0.332579	−	0.576043i	−0.983017	+	0.183516i	$0.941252\pi$
$104$	3.42346	−	1.13133i	0.335698	−	0.110936i
$105$	−0.413258	−	4.53179i	−0.0403299	−	0.442257i
$106$	0.223374	+	0.833643i	0.0216960	+	0.0809705i
$107$	17.1799			1.66084			0.830422	−	0.557135i	$-0.188099\pi$
$107$	17.1799			1.66084			0.830422	+	0.557135i	$0.188099\pi$
$108$	−1.00000			−0.0962250
$109$	−1.43625	−	5.36017i	−0.137568	−	0.513411i	−0.999974	−	0.00719395i	$-0.997710\pi$
$109$	−1.43625	−	5.36017i	−0.137568	−	0.513411i	0.862406	−	0.506217i	$-0.168957\pi$
$110$	−9.35624	+	2.50700i	−0.892083	+	0.239033i
$111$	−6.76092	−	1.81158i	−0.641719	−	0.171948i
$112$	2.60723	+	0.449857i	0.246360	+	0.0425075i
$113$	6.03531	+	10.4535i	0.567754	+	0.983379i	0.996788	+	0.0800906i	$0.0255209\pi$
$113$	6.03531	+	10.4535i	0.567754	+	0.983379i	−0.429033	+	0.903289i	$0.641146\pi$
$114$		−	0.363086i		−	0.0340061i
$115$	−10.5450	−	2.82552i	−0.983324	−	0.263481i
$116$	−6.76416	−	3.90529i	−0.628036	−	0.362597i
$117$	−1.97884	−	3.01400i	−0.182944	−	0.278644i
$118$		−	1.29795i		−	0.119486i
$119$	−19.9678	−	3.44529i	−1.83045	−	0.315829i
$120$	−0.859981	+	1.48953i	−0.0785052	+	0.135975i
$121$	−17.9405	−	10.3580i	−1.63096	−	0.941634i
$122$	7.52520	−	2.01637i	0.681299	−	0.182554i
$123$	6.38832	−	6.38832i	0.576016	−	0.576016i
$124$	−0.0384066	−	0.143335i	−0.00344902	−	0.0128719i
$125$	−8.56413	+	8.56413i	−0.765999	+	0.765999i
$126$	−0.240272	−	2.63482i	−0.0214051	−	0.234728i
$127$	3.08064	+	1.77861i	0.273363	+	0.157826i	0.630415	−	0.776258i	$-0.282885\pi$
$127$	3.08064	+	1.77861i	0.273363	+	0.157826i	−0.357052	+	0.934084i	$0.616218\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−3.70415	+	6.41578i	−0.326133	+	0.564878i
$130$	−6.19121	+	0.355558i	−0.543005	+	0.0311845i
$131$	−15.3929	+	8.88709i	−1.34488	+	0.776469i	−0.987520	−	0.157497i	$-0.949658\pi$
$131$	−15.3929	+	8.88709i	−1.34488	+	0.776469i	−0.357364	+	0.933965i	$0.616324\pi$
$132$	−5.43980	+	1.45759i	−0.473473	+	0.126867i
$133$	0.956665	−	0.0872392i	0.0829534	−	0.00756460i
$134$	−2.89090	+	1.66906i	−0.249736	+	0.144185i
$135$	1.66136	+	0.445159i	0.142987	+	0.0383132i
$136$	5.41548	+	5.41548i	0.464374	+	0.464374i
$137$	5.45803	+	5.45803i	0.466311	+	0.466311i	0.900717	−	0.434406i	$-0.143042\pi$
$137$	5.45803	+	5.45803i	0.466311	+	0.466311i	−0.434406	+	0.900717i	$0.643042\pi$
$138$	−6.13094	−	1.64278i	−0.521900	−	0.139843i
$139$	5.78099	−	3.33766i	0.490337	−	0.283096i	−0.234377	−	0.972146i	$-0.575305\pi$
$139$	5.78099	−	3.33766i	0.490337	−	0.283096i	0.724714	+	0.689049i	$0.241972\pi$
$140$	−4.13127	−	1.90800i	−0.349156	−	0.161256i
$141$	0.730514	−	0.195741i	0.0615204	−	0.0164843i
$142$	12.9555	−	7.47989i	1.08720	−	0.627698i
$143$	−15.1577	−	13.5112i	−1.26755	−	1.12986i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	9.49919	+	9.49919i	0.788865	+	0.788865i
$146$	7.57354	+	4.37258i	0.626790	+	0.361878i
$147$	6.88454	−	1.26614i	0.567827	−	0.104430i
$148$	−4.94934	+	4.94934i	−0.406833	+	0.406833i
$149$	5.25723	+	19.6203i	0.430689	+	1.60735i	0.751176	+	0.660102i	$0.229487\pi$
$149$	5.25723	+	19.6203i	0.430689	+	1.60735i	−0.320487	+	0.947253i	$0.603847\pi$
$150$	−1.44372	+	1.44372i	−0.117879	+	0.117879i
$151$	−14.2709	+	3.82389i	−1.16135	+	0.311184i	−0.787506	−	0.616307i	$-0.788628\pi$
$151$	−14.2709	+	3.82389i	−1.16135	+	0.311184i	−0.373847	+	0.927490i	$0.621962\pi$
$152$	−0.314441	−	0.181543i	−0.0255046	−	0.0147251i
$153$	3.82932	−	6.63258i	0.309582	−	0.536212i
$154$	−5.14751	−	13.9827i	−0.414798	−	1.12675i
$155$			0.255228i			0.0205004i
$156$	−3.59962	+	0.206724i	−0.288200	+	0.0165512i
$157$	−8.08225	−	4.66629i	−0.645033	−	0.372410i	0.141517	−	0.989936i	$-0.454802\pi$
$157$	−8.08225	−	4.66629i	−0.645033	−	0.372410i	−0.786551	+	0.617526i	$0.788135\pi$
$158$	−11.7855	−	3.15790i	−0.937600	−	0.251229i
$159$		−	0.863050i		−	0.0684443i
$160$	0.859981	+	1.48953i	0.0679875	+	0.117758i
$161$	2.85534	−	16.5486i	0.225032	−	1.30421i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−8.29744	+	2.22329i	−0.649906	+	0.174142i	−0.568686	−	0.822555i	$-0.692548\pi$
$163$	−8.29744	+	2.22329i	−0.649906	+	0.174142i	−0.0812194	+	0.996696i	$0.525881\pi$
$164$	−2.33829	−	8.72661i	−0.182590	−	0.681434i
$165$	9.68629			0.754077
$166$	1.65648			0.128568
$167$	4.01471	+	14.9831i	0.310668	+	1.15943i	0.927956	+	0.372691i	$0.121565\pi$
$167$	4.01471	+	14.9831i	0.310668	+	1.15943i	−0.617288	+	0.786738i	$0.711768\pi$
$168$	−2.40196	−	1.10933i	−0.185315	−	0.0855865i
$169$	−7.74613	−	10.4402i	−0.595856	−	0.803091i
$170$	−6.58629	−	11.4078i	−0.505145	−	0.874937i
$171$	−0.0939735	+	0.350714i	−0.00718633	+	0.0268198i
$172$	3.70415	+	6.41578i	0.282439	+	0.489199i
$173$	2.27602	−	3.94219i	0.173043	−	0.299719i	−0.766439	−	0.642317i	$-0.777973\pi$
$173$	2.27602	−	3.94219i	0.173043	−	0.299719i	0.939482	+	0.342598i	$0.111307\pi$
$174$	5.52291	+	5.52291i	0.418691	+	0.418691i
$175$	−4.15083	−	3.45706i	−0.313773	−	0.261329i
$176$	−1.45759	+	5.43980i	−0.109870	+	0.410040i
$177$	−0.335934	+	1.25372i	−0.0252504	+	0.0942357i
$178$			4.18654i			0.313795i
$179$	−1.45144	+	0.837989i	−0.108486	+	0.0626342i	−0.553261	−	0.833008i	$-0.686617\pi$
$179$	−1.45144	+	0.837989i	−0.108486	+	0.0626342i	0.444775	+	0.895642i	$0.353283\pi$
$180$	1.21620	−	1.21620i	0.0906500	−	0.0906500i
$181$	−1.85011			−0.137518			−0.0687588	−	0.997633i	$-0.521904\pi$
$181$	−1.85011			−0.137518			−0.0687588	+	0.997633i	$0.521904\pi$
$182$	−1.40957	−	9.43468i	−0.104484	−	0.699345i
$183$	−7.79066			−0.575902
$184$	−4.48816	+	4.48816i	−0.330871	+	0.330871i
$185$	10.4259	−	6.01937i	0.766524	−	0.442553i
$186$			0.148392i			0.0108806i
$187$	11.1632	−	41.6615i	0.816331	−	3.04659i
$188$	0.195741	−	0.730514i	0.0142759	−	0.0532782i
$189$	−0.449857	+	2.60723i	−0.0327223	+	0.189648i
$190$	0.441584	+	0.441584i	0.0320358	+	0.0320358i
$191$	2.25766	−	3.91038i	0.163359	−	0.282946i	−0.772713	−	0.634756i	$-0.781101\pi$
$191$	2.25766	−	3.91038i	0.163359	−	0.282946i	0.936071	+	0.351811i	$0.114434\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−6.11471	+	22.8204i	−0.440147	+	1.64265i	0.288295	+	0.957542i	$0.406912\pi$
$193$	−6.11471	+	22.8204i	−0.440147	+	1.64265i	−0.728442	+	0.685108i	$0.759755\pi$
$194$	−1.43013	−	2.47705i	−0.102677	−	0.177842i
$195$	6.07227	+	1.25896i	0.434845	+	0.0901560i
$196$	2.34576	−	6.59526i	0.167554	−	0.471090i
$197$	4.81988	+	17.9880i	0.343402	+	1.28159i	0.894468	+	0.447132i	$0.147555\pi$
$197$	4.81988	+	17.9880i	0.343402	+	1.28159i	−0.551066	+	0.834462i	$0.685779\pi$
$198$	5.63169			0.400227
$199$	13.0391			0.924318			0.462159	−	0.886797i	$-0.347075\pi$
$199$	13.0391			0.924318			0.462159	+	0.886797i	$0.347075\pi$
$200$	0.528439	+	1.97216i	0.0373663	+	0.139453i
$201$	3.22438	−	0.863971i	0.227430	−	0.0609398i
$202$	6.80384	+	1.82308i	0.478716	+	0.128272i
$203$	−13.2249	+	15.8789i	−0.928204	+	1.11448i
$204$	−3.82932	−	6.63258i	−0.268106	−	0.464374i
$205$			15.5389i			1.08528i
$206$	6.52059	+	1.74719i	0.454311	+	0.121732i
$207$	5.49685	+	3.17361i	0.382057	+	0.220581i
$208$	−1.62078	+	3.22072i	−0.112381	+	0.223317i
$209$			2.04479i			0.141441i
$210$	3.49668	+	2.91224i	0.241294	+	0.200964i
$211$	−8.05119	+	13.9451i	−0.554267	+	0.960018i	0.443694	+	0.896179i	$0.353668\pi$
$211$	−8.05119	+	13.9451i	−0.554267	+	0.960018i	−0.997960	+	0.0638394i	$0.979665\pi$
$212$	−0.747424	−	0.431525i	−0.0513333	−	0.0296373i
$213$	−14.4500	+	3.87187i	−0.990100	+	0.265296i
$214$	−12.1480	+	12.1480i	−0.830422	+	0.830422i
$215$	−3.29787	−	12.3078i	−0.224913	−	0.839387i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−0.390986	+	0.0356544i	−0.0265418	+	0.00242038i
$218$	4.80580	+	2.77463i	0.325490	+	0.187922i
$219$	−6.18377	−	6.18377i	−0.417860	−	0.417860i
$220$	4.84315	−	8.38858i	0.326525	−	0.565558i
$221$	12.4130	−	24.6664i	0.834988	−	1.65924i
$222$	6.06168	−	3.49971i	0.406833	−	0.234885i
$223$	13.2808	−	3.55858i	0.889348	−	0.238300i	0.214912	−	0.976633i	$-0.431054\pi$
$223$	13.2808	−	3.55858i	0.889348	−	0.238300i	0.674436	+	0.738333i	$0.264387\pi$
$224$	−2.16168	+	1.52549i	−0.144434	+	0.101926i
$225$	1.76819	−	1.02087i	0.117879	−	0.0680577i
$226$	−11.6593	−	3.12411i	−0.775567	−	0.207812i
$227$	19.8321	+	19.8321i	1.31630	+	1.31630i	0.916680	+	0.399621i	$0.130858\pi$
$227$	19.8321	+	19.8321i	1.31630	+	1.31630i	0.399621	+	0.916680i	$0.369142\pi$
$228$	0.256740	+	0.256740i	0.0170030	+	0.0170030i
$229$	14.1090	+	3.78049i	0.932347	+	0.249822i	0.692855	−	0.721077i	$-0.256352\pi$
$229$	14.1090	+	3.78049i	0.932347	+	0.249822i	0.239492	+	0.970898i	$0.423019\pi$
$230$	9.45437	−	5.45848i	0.623403	−	0.359922i
$231$	1.35314	+	14.8385i	0.0890298	+	0.976301i
$232$	7.54443	−	2.02153i	0.495316	−	0.132720i
$233$	−0.538452	+	0.310875i	−0.0352751	+	0.0203661i	−0.517534	−	0.855663i	$-0.673150\pi$
$233$	−0.538452	+	0.310875i	−0.0352751	+	0.0203661i	0.482259	+	0.876029i	$0.339817\pi$
$234$	3.53047	+	0.731970i	0.230794	+	0.0478504i
$235$	−0.650390	+	1.12651i	−0.0424268	+	0.0734853i
$236$	0.917790	+	0.917790i	0.0597430	+	0.0597430i
$237$	10.5665	+	6.10060i	0.686371	+	0.396276i
$238$	16.5556	−	11.6832i	1.07314	−	0.757309i
$239$	−11.6685	+	11.6685i	−0.754774	+	0.754774i	−0.975366	−	0.220592i	$-0.929201\pi$
$239$	−11.6685	+	11.6685i	−0.754774	+	0.754774i	0.220592	+	0.975366i	$0.429201\pi$
$240$	−0.445159	−	1.66136i	−0.0287349	−	0.107240i
$241$	−6.53898	+	6.53898i	−0.421213	+	0.421213i	−0.885621	−	0.464408i	$-0.846267\pi$
$241$	−6.53898	+	6.53898i	−0.421213	+	0.421213i	0.464408	+	0.885621i	$0.346267\pi$
$242$	20.0101	−	5.36168i	1.28630	−	0.344662i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−3.89533	+	6.74691i	−0.249373	+	0.431926i
$245$	−6.83307	+	9.91284i	−0.436549	+	0.633308i
$246$			9.03445i			0.576016i
$247$	−0.265768	+	1.28186i	−0.0169104	+	0.0815630i
$248$	0.128511	+	0.0741959i	0.00816046	+	0.00471144i
$249$	−1.60004	−	0.428729i	−0.101398	−	0.0271696i
$250$		−	12.1115i		−	0.765999i
$251$	−12.1225	−	20.9967i	−0.765163	−	1.32530i	−0.940160	−	0.340732i	$-0.889325\pi$
$251$	−12.1225	−	20.9967i	−0.765163	−	1.32530i	0.174998	−	0.984569i	$-0.444008\pi$
$252$	2.03300	+	1.69320i	0.128067	+	0.106662i
$253$	34.5275	+	9.25163i	2.17073	+	0.581645i
$254$	−3.43601	+	0.920675i	−0.215594	+	0.0577683i
$255$	3.40931	+	12.7237i	0.213500	+	0.796791i
$256$	1.00000			0.0625000
$257$	−10.1272			−0.631715			−0.315858	−	0.948807i	$-0.602292\pi$
$257$	−10.1272			−0.631715			−0.315858	+	0.948807i	$0.602292\pi$
$258$	−1.91741	−	7.15588i	−0.119373	−	0.445505i
$259$	10.6776	+	15.1305i	0.663471	+	0.940166i
$260$	4.12643	−	4.62926i	0.255910	−	0.287095i
$261$	−3.90529	−	6.76416i	−0.241731	−	0.418691i
$262$	4.60030	−	17.1685i	0.284207	−	1.06068i
$263$	2.67718	+	4.63702i	0.165082	+	0.285931i	0.936685	−	0.350174i	$-0.113878\pi$
$263$	2.67718	+	4.63702i	0.165082	+	0.285931i	−0.771602	+	0.636105i	$0.780544\pi$
$264$	2.81585	−	4.87719i	0.173303	−	0.300170i
$265$	1.04964	+	1.04964i	0.0644788	+	0.0644788i
$266$	−0.614777	+	0.738152i	−0.0376944	+	0.0452590i
$267$	1.08356	−	4.04389i	0.0663126	−	0.247482i
$268$	0.863971	−	3.22438i	0.0527754	−	0.196961i
$269$			16.2584i			0.991291i	0.868525	+	0.495645i	$0.165068\pi$
$269$			16.2584i			0.991291i	−0.868525	+	0.495645i	$0.834932\pi$
$270$	−1.48953	+	0.859981i	−0.0906500	+	0.0523368i
$271$	13.4057	−	13.4057i	0.814340	−	0.814340i	−0.170941	−	0.985281i	$-0.554681\pi$
$271$	13.4057	−	13.4057i	0.814340	−	0.814340i	0.985281	+	0.170941i	$0.0546809\pi$
$272$	−7.65864			−0.464374
$273$	−1.08034	+	9.47802i	−0.0653849	+	0.573636i
$274$	−7.71881			−0.466311
$275$	8.13059	−	8.13059i	0.490293	−	0.490293i
$276$	5.49685	−	3.17361i	0.330871	−	0.191029i
$277$		−	4.57205i		−	0.274708i	−0.990522	−	0.137354i	$-0.956140\pi$
$277$		−	4.57205i		−	0.274708i	0.990522	−	0.137354i	$-0.0438597\pi$
$278$	−1.72770	+	6.44786i	−0.103620	+	0.386717i
$279$	0.0384066	−	0.143335i	0.00229934	−	0.00858127i
$280$	4.27041	−	1.57209i	0.255206	−	0.0939503i
$281$	−0.329312	−	0.329312i	−0.0196451	−	0.0196451i	0.697216	−	0.716861i	$-0.254422\pi$
$281$	−0.329312	−	0.329312i	−0.0196451	−	0.0196451i	−0.716861	+	0.697216i	$0.754422\pi$
$282$	−0.378142	+	0.654961i	−0.0225180	+	0.0390024i
$283$	−10.4820	−	18.1554i	−0.623092	−	1.07923i	−0.988906	−	0.148540i	$-0.952543\pi$
$283$	−10.4820	−	18.1554i	−0.623092	−	1.07923i	0.365814	−	0.930688i	$-0.380791\pi$
$284$	−3.87187	+	14.4500i	−0.229753	+	0.857451i
$285$	−0.312247	−	0.540827i	−0.0184959	−	0.0320358i
$286$	20.2719	−	1.16421i	1.19871	−	0.0688410i
$287$	−23.8041	+	2.17072i	−1.40511	+	0.128134i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	41.6548			2.45028
$290$	−13.4339			−0.788865
$291$	0.740288	+	2.76279i	0.0433964	+	0.161958i
$292$	−8.44718	+	2.26342i	−0.494334	+	0.132456i
$293$	13.5614	+	3.63378i	0.792268	+	0.212288i	0.632186	−	0.774816i	$-0.282158\pi$
$293$	13.5614	+	3.63378i	0.792268	+	0.212288i	0.160081	+	0.987104i	$0.448824\pi$
$294$	−3.97280	+	5.76340i	−0.231699	+	0.336129i
$295$	−1.11621	−	1.93334i	−0.0649884	−	0.112563i
$296$		−	6.99942i		−	0.406833i
$297$	−5.43980	−	1.45759i	−0.315649	−	0.0845779i
$298$	−17.5910	−	10.1562i	−1.01902	−	0.588333i
$299$	20.4426	+	10.2874i	1.18223	+	0.594938i
$300$		−	2.04173i		−	0.117879i
$301$	18.3937	−	6.77139i	1.06020	−	0.390296i
$302$	7.38719	−	12.7950i	0.425085	−	0.736269i
$303$	−6.10015	−	3.52192i	−0.350445	−	0.202329i
$304$	0.350714	−	0.0939735i	0.0201148	−	0.00538975i
$305$	9.47497	−	9.47497i	0.542535	−	0.542535i
$306$	1.98220	+	7.39768i	0.113315	+	0.422897i
$307$	8.18103	−	8.18103i	0.466916	−	0.466916i	−0.433998	−	0.900914i	$-0.642898\pi$
$307$	8.18103	−	8.18103i	0.466916	−	0.466916i	0.900914	+	0.433998i	$0.142898\pi$
$308$	13.5271	+	6.24739i	0.770776	+	0.355978i
$309$	−5.84620	−	3.37530i	−0.332579	−	0.192014i
$310$	−0.180474	−	0.180474i	−0.0102502	−	0.0102502i
$311$	−0.769431	+	1.33269i	−0.0436304	+	0.0755701i	−0.887016	−	0.461739i	$-0.847226\pi$
$311$	−0.769431	+	1.33269i	−0.0436304	+	0.0755701i	0.843386	+	0.537309i	$0.180559\pi$
$312$	2.39914	−	2.69149i	0.135825	−	0.152376i
$313$	13.7899	−	7.96159i	0.779450	−	0.450016i	−0.0567851	−	0.998386i	$-0.518085\pi$
$313$	13.7899	−	7.96159i	0.779450	−	0.450016i	0.836235	+	0.548371i	$0.184752\pi$
$314$	9.01457	−	2.41545i	0.508722	−	0.136312i
$315$	−2.62379	−	3.71801i	−0.147834	−	0.209486i
$316$	10.5665	−	6.10060i	0.594415	−	0.343186i
$317$	2.53244	+	0.678566i	0.142236	+	0.0381121i	0.329235	−	0.944248i	$-0.393209\pi$
$317$	2.53244	+	0.678566i	0.142236	+	0.0381121i	−0.186998	+	0.982360i	$0.559876\pi$
$318$	0.610269	+	0.610269i	0.0342222	+	0.0342222i
$319$	−31.1033	−	31.1033i	−1.74145	−	1.74145i
$320$	−1.66136	−	0.445159i	−0.0928726	−	0.0248851i
$321$	14.8782	−	8.58995i	0.830422	−	0.479444i
$322$	9.68262	+	13.7207i	0.539591	+	0.764623i
$323$	−2.68599	+	0.719710i	−0.149453	+	0.0400457i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	6.15378	−	4.04025i	0.341350	−	0.224113i
$326$	4.29507	−	7.43928i	0.237882	−	0.412024i
$327$	−3.92392	−	3.92392i	−0.216993	−	0.216993i
$328$	7.82407	+	4.51723i	0.432012	+	0.249422i
$329$	−1.81656	−	0.838967i	−0.100150	−	0.0462538i
$330$	−6.84924	+	6.84924i	−0.377039	+	0.377039i
$331$	1.92648	+	7.18972i	0.105889	+	0.395183i	0.998444	−	0.0557547i	$-0.0177565\pi$
$331$	1.92648	+	7.18972i	0.105889	+	0.395183i	−0.892556	+	0.450937i	$0.851090\pi$
$332$	−1.17131	+	1.17131i	−0.0642840	+	0.0642840i
$333$	−6.76092	+	1.81158i	−0.370496	+	0.0992742i
$334$	−13.4335	−	7.75583i	−0.735048	−	0.424380i
$335$	−2.87073	+	4.97224i	−0.156845	+	0.271663i
$336$	2.48285	−	0.914026i	0.135451	−	0.0498642i
$337$			18.7350i			1.02056i	0.860008	+	0.510280i	$0.170458\pi$
$337$			18.7350i			1.02056i	−0.860008	+	0.510280i	$0.829542\pi$
$338$	12.8597	+	1.90498i	0.699474	+	0.103617i
$339$	10.4535	+	6.03531i	0.567754	+	0.327793i
$340$	12.7237	+	3.40931i	0.690041	+	0.184896i
$341$		−	0.835697i		−	0.0452555i
$342$	−0.181543	−	0.314441i	−0.00981671	−	0.0170030i
$343$	−16.1401	−	9.08284i	−0.871482	−	0.490427i
$344$	−7.15588	−	1.91741i	−0.385819	−	0.103380i
$345$	−10.5450	+	2.82552i	−0.567723	+	0.152121i
$346$	1.17816	+	4.39694i	0.0633381	+	0.236381i
$347$	−14.7616			−0.792444			−0.396222	−	0.918155i	$-0.629679\pi$
$347$	−14.7616			−0.792444			−0.396222	+	0.918155i	$0.629679\pi$
$348$	−7.81057			−0.418691
$349$	−5.94235	−	22.1772i	−0.318087	−	1.18712i	−0.921081	−	0.389371i	$-0.872692\pi$
$349$	−5.94235	−	22.1772i	−0.318087	−	1.18712i	0.602994	−	0.797746i	$-0.293974\pi$
$350$	5.37959	−	0.490570i	0.287551	−	0.0262221i
$351$	−3.22072	−	1.62078i	−0.171910	−	0.0865109i
$352$	−2.81585	−	4.87719i	−0.150085	−	0.259955i
$353$	−4.74497	+	17.7085i	−0.252549	+	0.942528i	0.716888	+	0.697189i	$0.245566\pi$
$353$	−4.74497	+	17.7085i	−0.252549	+	0.942528i	−0.969437	+	0.245339i	$0.921101\pi$
$354$	−0.648975	−	1.12406i	−0.0344927	−	0.0597430i
$355$	12.8651	−	22.2830i	0.682810	−	1.18266i
$356$	−2.96033	−	2.96033i	−0.156897	−	0.156897i
$357$	−19.0153	+	7.00020i	−1.00640	+	0.370490i
$358$	0.433775	−	1.61887i	0.0229257	−	0.0855600i
$359$	2.88428	−	10.7643i	0.152226	−	0.568116i	−0.847101	−	0.531433i	$-0.821654\pi$
$359$	2.88428	−	10.7643i	0.152226	−	0.568116i	0.999327	−	0.0366838i	$-0.0116794\pi$
$360$			1.71996i			0.0906500i
$361$	−16.3403	+	9.43408i	−0.860016	+	0.496531i
$362$	1.30822	−	1.30822i	0.0687588	−	0.0687588i
$363$	−20.7159			−1.08730
$364$	7.66804	+	5.67461i	0.401914	+	0.297430i
$365$	15.0414			0.787300
$366$	5.50883	−	5.50883i	0.287951	−	0.287951i
$367$	14.7544	−	8.51847i	0.770175	−	0.444661i	−0.0627622	−	0.998029i	$-0.519991\pi$
$367$	14.7544	−	8.51847i	0.770175	−	0.444661i	0.832937	+	0.553368i	$0.186658\pi$
$368$		−	6.34721i		−	0.330871i
$369$	2.33829	−	8.72661i	0.121726	−	0.454289i
$370$	−3.11586	+	11.6285i	−0.161986	+	0.604539i
$371$	−1.46132	+	1.75458i	−0.0758678	+	0.0910931i
$372$	−0.104929	−	0.104929i	−0.00544031	−	0.00544031i
$373$	−14.2863	+	24.7446i	−0.739717	+	1.28123i	0.212906	+	0.977073i	$0.431707\pi$
$373$	−14.2863	+	24.7446i	−0.739717	+	1.28123i	−0.952623	+	0.304155i	$0.901626\pi$
$374$	21.5656	+	37.3526i	1.11513	+	1.93146i
$375$	−3.13469	+	11.6988i	−0.161875	+	0.604124i
$376$	0.378142	+	0.654961i	0.0195012	+	0.0337771i
$377$	−15.4559	−	23.5411i	−0.796017	−	1.21243i
$378$	−1.52549	−	2.16168i	−0.0784628	−	0.111185i
$379$	−5.26352	−	19.6437i	−0.270369	−	1.00903i	−0.958882	−	0.283806i	$-0.908403\pi$
$379$	−5.26352	−	19.6437i	−0.270369	−	1.00903i	0.688513	−	0.725224i	$-0.258264\pi$
$380$	−0.624494			−0.0320358
$381$	3.55722			0.182242
$382$	1.16865	+	4.36147i	0.0597934	+	0.223152i
$383$	8.21939	−	2.20238i	0.419991	−	0.112536i	−0.0426329	−	0.999091i	$-0.513575\pi$
$383$	8.21939	−	2.20238i	0.419991	−	0.112536i	0.462624	+	0.886554i	$0.346908\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−19.6922	−	16.4008i	−1.00361	−	0.835864i
$386$	−11.8127	−	20.4602i	−0.601251	−	1.04140i
$387$			7.40831i			0.376585i
$388$	2.76279	+	0.740288i	0.140259	+	0.0375824i
$389$	−16.6395	−	9.60684i	−0.843658	−	0.487086i	0.0148482	−	0.999890i	$-0.495273\pi$
$389$	−16.6395	−	9.60684i	−0.843658	−	0.487086i	−0.858506	+	0.512804i	$0.828607\pi$
$390$	−5.18397	+	3.40353i	−0.262500	+	0.172344i
$391$			48.6111i			2.45837i
$392$	3.00485	+	6.32225i	0.151768	+	0.319322i
$393$	−8.88709	+	15.3929i	−0.448294	+	0.776469i
$394$	−16.1276	−	9.31129i	−0.812498	−	0.469096i
$395$	−20.2705	+	5.43147i	−1.01992	+	0.273287i
$396$	−3.98221	+	3.98221i	−0.200113	+	0.200113i
$397$	7.98259	+	29.7914i	0.400635	+	1.49519i	0.811967	+	0.583703i	$0.198397\pi$
$397$	7.98259	+	29.7914i	0.400635	+	1.49519i	−0.411333	+	0.911485i	$0.634937\pi$
$398$	−9.22004	+	9.22004i	−0.462159	+	0.462159i
$399$	0.784877	−	0.553884i	0.0392930	−	0.0277289i
$400$	−1.76819	−	1.02087i	−0.0884095	−	0.0510433i
$401$	20.2498	+	20.2498i	1.01122	+	1.01122i	0.999936	+	0.0112885i	$0.00359332\pi$
$401$	20.2498	+	20.2498i	1.01122	+	1.01122i	0.0112885	+	0.999936i	$0.496407\pi$
$402$	−1.66906	+	2.89090i	−0.0832453	+	0.144185i
$403$	0.108618	−	0.523893i	0.00541067	−	0.0260970i
$404$	−6.10015	+	3.52192i	−0.303494	+	0.175222i
$405$	1.66136	−	0.445159i	0.0825534	−	0.0221201i
$406$	−1.87666	−	20.5794i	−0.0931371	−	1.02134i
$407$	−34.1375	+	19.7093i	−1.69213	+	0.976953i
$408$	7.39768	+	1.98220i	0.366240	+	0.0981337i
$409$	3.86485	+	3.86485i	0.191105	+	0.191105i	0.796173	−	0.605069i	$-0.206854\pi$
$409$	3.86485	+	3.86485i	0.191105	+	0.191105i	−0.605069	+	0.796173i	$0.706854\pi$
$410$	−10.9877	−	10.9877i	−0.542642	−	0.542642i
$411$	7.45580	+	1.99778i	0.367768	+	0.0985430i
$412$	−5.84620	+	3.37530i	−0.288022	+	0.166289i
$413$	2.80576	−	1.98001i	0.138062	−	0.0974300i
$414$	−6.13094	+	1.64278i	−0.301319	+	0.0807382i
$415$	2.46738	−	1.42454i	0.121119	−	0.0699281i
$416$	−1.13133	−	3.42346i	−0.0554680	−	0.167849i
$417$	3.33766	−	5.78099i	0.163446	−	0.283096i
$418$	−1.44588	−	1.44588i	−0.0707204	−	0.0707204i
$419$	−12.2654	−	7.08143i	−0.599204	−	0.345950i	0.169525	−	0.985526i	$-0.445777\pi$
$419$	−12.2654	−	7.08143i	−0.599204	−	0.345950i	−0.768728	+	0.639576i	$0.779110\pi$
$420$	−4.53179	+	0.413258i	−0.221129	+	0.0201649i
$421$	13.1845	−	13.1845i	0.642573	−	0.642573i	−0.308614	−	0.951187i	$-0.599865\pi$
$421$	13.1845	−	13.1845i	0.642573	−	0.642573i	0.951187	+	0.308614i	$0.0998653\pi$
$422$	−4.16760	−	15.5537i	−0.202876	−	0.757142i
$423$	0.534774	−	0.534774i	0.0260016	−	0.0260016i
$424$	0.833643	−	0.223374i	0.0404853	−	0.0108480i
$425$	13.5419	+	7.81844i	0.656881	+	0.379250i
$426$	7.47989	−	12.9555i	0.362402	−	0.627698i
$427$	15.8384	+	13.1911i	0.766473	+	0.638364i
$428$		−	17.1799i		−	0.830422i
$429$	−19.8825	−	4.12223i	−0.959937	−	0.199023i
$430$	11.0349	+	6.37100i	0.532150	+	0.307237i
$431$	13.8724	+	3.71709i	0.668208	+	0.179046i	0.576947	−	0.816781i	$-0.304244\pi$
$431$	13.8724	+	3.71709i	0.668208	+	0.179046i	0.0912603	+	0.995827i	$0.470910\pi$
$432$			1.00000i			0.0481125i
$433$	−11.0126	−	19.0743i	−0.529230	−	0.916653i	−0.999419	−	0.0340875i	$-0.989148\pi$
$433$	−11.0126	−	19.0743i	−0.529230	−	0.916653i	0.470189	−	0.882566i	$-0.344186\pi$
$434$	0.251257	−	0.301680i	0.0120607	−	0.0144811i
$435$	12.9761	+	3.47695i	0.622158	+	0.166707i
$436$	−5.36017	+	1.43625i	−0.256706	+	0.0687841i
$437$	−0.596470	−	2.22606i	−0.0285330	−	0.106487i
$438$	8.74517			0.417860
$439$	−13.2204			−0.630974			−0.315487	−	0.948930i	$-0.602168\pi$
$439$	−13.2204			−0.630974			−0.315487	+	0.948930i	$0.602168\pi$
$440$	2.50700	+	9.35624i	0.119516	+	0.446041i
$441$	5.32911	−	4.53878i	0.253767	−	0.216133i
$442$	8.66446	+	26.2191i	0.412126	+	1.24711i
$443$	−17.8431	−	30.9052i	−0.847752	−	1.46835i	−0.883210	−	0.468978i	$-0.844622\pi$
$443$	−17.8431	−	30.9052i	−0.847752	−	1.46835i	0.0354579	−	0.999371i	$-0.488711\pi$
$444$	−1.81158	+	6.76092i	−0.0859740	+	0.320859i
$445$	3.60035	+	6.23598i	0.170673	+	0.295614i
$446$	−6.87464	+	11.9072i	−0.325524	+	0.563824i
$447$	14.3630	+	14.3630i	0.679348	+	0.679348i
$448$	0.449857	−	2.60723i	0.0212537	−	0.123180i
$449$	−1.32333	+	4.93874i	−0.0624519	+	0.233074i	−0.990096	−	0.140392i	$-0.955164\pi$
$449$	−1.32333	+	4.93874i	−0.0624519	+	0.233074i	0.927644	+	0.373465i	$0.121831\pi$
$450$	−0.528439	+	1.97216i	−0.0249108	+	0.0929685i
$451$		−	50.8792i		−	2.39581i
$452$	10.4535	−	6.03531i	0.491690	−	0.283877i
$453$	−10.4471	+	10.4471i	−0.490846	+	0.490846i
$454$	−28.0468			−1.31630
$455$	−10.2132	−	12.8410i	−0.478804	−	0.601997i
$456$	−0.363086			−0.0170030
$457$	14.6095	−	14.6095i	0.683403	−	0.683403i	−0.277362	−	0.960765i	$-0.589460\pi$
$457$	14.6095	−	14.6095i	0.683403	−	0.683403i	0.960765	+	0.277362i	$0.0894603\pi$
$458$	−12.6498	+	7.30334i	−0.591085	+	0.341263i
$459$		−	7.65864i		−	0.357475i
$460$	−2.82552	+	10.5450i	−0.131741	+	0.491662i
$461$	1.92392	−	7.18018i	0.0896060	−	0.334414i	−0.906541	−	0.422119i	$-0.861287\pi$
$461$	1.92392	−	7.18018i	0.0896060	−	0.334414i	0.996147	+	0.0877047i	$0.0279532\pi$
$462$	−11.4492	−	9.53558i	−0.532665	−	0.443635i
$463$	2.57262	+	2.57262i	0.119560	+	0.119560i	0.764355	−	0.644795i	$-0.223057\pi$
$463$	2.57262	+	2.57262i	0.119560	+	0.119560i	−0.644795	+	0.764355i	$0.723057\pi$
$464$	−3.90529	+	6.76416i	−0.181298	+	0.314018i
$465$	0.127614	+	0.221034i	0.00591796	+	0.0102502i
$466$	0.160921	−	0.600565i	0.00745452	−	0.0278206i
$467$	4.99519	+	8.65193i	0.231150	+	0.400363i	0.958147	−	0.286277i	$-0.0924179\pi$
$467$	4.99519	+	8.65193i	0.231150	+	0.400363i	−0.726997	+	0.686641i	$0.759085\pi$
$468$	−3.01400	+	1.97884i	−0.139322	+	0.0914718i
$469$	−8.01804	−	3.70308i	−0.370238	−	0.170992i
$470$	−0.336667	−	1.25646i	−0.0155293	−	0.0579560i
$471$	−9.33257			−0.430022
$472$	−1.29795			−0.0597430
$473$	10.7983	+	40.2997i	0.496505	+	1.85298i
$474$	−11.7855	+	3.15790i	−0.541324	+	0.145047i
$475$	−0.716063	−	0.191869i	−0.0328552	−	0.00880353i
$476$	−3.44529	+	19.9678i	−0.157915	+	0.915224i
$477$	−0.431525	−	0.747424i	−0.0197582	−	0.0342222i
$478$		−	16.5018i		−	0.754774i
$479$	24.0620	+	6.44740i	1.09942	+	0.294589i	0.762529	−	0.646954i	$-0.223957\pi$
$479$	24.0620	+	6.44740i	1.09942	+	0.294589i	0.336893	+	0.941543i	$0.390624\pi$
$480$	1.48953	+	0.859981i	0.0679875	+	0.0392526i
$481$	−23.9623	+	7.91866i	−1.09259	+	0.361060i
$482$		−	9.24751i		−	0.421213i
$483$	−5.80152	−	15.7592i	−0.263978	−	0.717068i
$484$	−10.3580	+	17.9405i	−0.470817	+	0.815479i
$485$	−4.26043	−	2.45976i	−0.193456	−	0.111692i
$486$	0.965926	−	0.258819i	0.0438153	−	0.0117403i
$487$	−22.3607	+	22.3607i	−1.01326	+	1.01326i	−0.0133493	+	0.999911i	$0.504249\pi$
$487$	−22.3607	+	22.3607i	−1.01326	+	1.01326i	−0.999911	+	0.0133493i	$0.995751\pi$
$488$	−2.01637	−	7.52520i	−0.0912768	−	0.340650i
$489$	−6.07415	+	6.07415i	−0.274682	+	0.274682i
$490$	−2.17772	−	11.8411i	−0.0983794	−	0.534928i
$491$	−6.01809	−	3.47455i	−0.271593	−	0.156804i	0.358019	−	0.933714i	$-0.383452\pi$
$491$	−6.01809	−	3.47455i	−0.271593	−	0.156804i	−0.629611	+	0.776910i	$0.716786\pi$
$492$	−6.38832	−	6.38832i	−0.288008	−	0.288008i
$493$	29.9092	−	51.8043i	1.34704	−	2.33315i
$494$	−0.718488	−	1.09434i	−0.0323263	−	0.0492367i
$495$	8.38858	−	4.84315i	0.377039	−	0.217683i
$496$	−0.143335	+	0.0384066i	−0.00643595	+	0.00172451i
$497$	35.9327	+	16.5953i	1.61180	+	0.744401i
$498$	1.43456	−	0.828241i	0.0642840	−	0.0371144i
$499$	−26.8168	−	7.18554i	−1.20049	−	0.321669i	−0.397463	−	0.917618i	$-0.630109\pi$
$499$	−26.8168	−	7.18554i	−1.20049	−	0.321669i	−0.803022	+	0.595949i	$0.796776\pi$
$500$	8.56413	+	8.56413i	0.383000	+	0.383000i
$501$	10.9684	+	10.9684i	0.490032	+	0.490032i
$502$	23.4188	+	6.27505i	1.04523	+	0.280069i
$503$	25.2684	−	14.5887i	1.12666	−	0.650478i	0.183568	−	0.983007i	$-0.441235\pi$
$503$	25.2684	−	14.5887i	1.12666	−	0.650478i	0.943093	+	0.332529i	$0.107902\pi$
$504$	−2.63482	+	0.240272i	−0.117364	+	0.0107026i
$505$	11.7023	−	3.13563i	0.520747	−	0.139534i
$506$	−30.9565	+	17.8728i	−1.37619	+	0.794542i
$507$	−11.9284	−	5.16840i	−0.529761	−	0.229537i
$508$	1.77861	−	3.08064i	0.0789130	−	0.136681i
$509$	−20.5516	−	20.5516i	−0.910934	−	0.910934i	0.0854118	−	0.996346i	$-0.472779\pi$
$509$	−20.5516	−	20.5516i	−0.910934	−	0.910934i	−0.996346	+	0.0854118i	$0.972779\pi$
$510$	−11.4078	−	6.58629i	−0.505145	−	0.291646i
$511$	2.10122	+	23.0419i	0.0929523	+	1.01931i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.0939735	+	0.350714i	0.00414903	+	0.0154844i
$514$	7.16099	−	7.16099i	0.315858	−	0.315858i
$515$	11.2152	−	3.00509i	0.494199	−	0.132420i
$516$	6.41578	+	3.70415i	0.282439	+	0.163066i
$517$	2.12958	−	3.68854i	0.0936588	−	0.162222i
$518$	−18.2491	−	3.14874i	−0.801819	−	0.138348i
$519$		−	4.55205i		−	0.199813i
$520$	0.355558	+	6.19121i	0.0155922	+	0.271503i
$521$	−19.8371	−	11.4529i	−0.869077	−	0.501762i	−0.00203587	−	0.999998i	$-0.500648\pi$
$521$	−19.8371	−	11.4529i	−0.869077	−	0.501762i	−0.867042	+	0.498236i	$0.833981\pi$
$522$	7.54443	+	2.02153i	0.330211	+	0.0884798i
$523$			35.4842i			1.55161i	0.630970	+	0.775807i	$0.282657\pi$
$523$			35.4842i			1.55161i	−0.630970	+	0.775807i	$0.717343\pi$
$524$	8.88709	+	15.3929i	0.388234	+	0.672442i
$525$	−5.32325	−	0.918486i	−0.232326	−	0.0400860i
$526$	−5.17192	−	1.38581i	−0.225507	−	0.0604243i
$527$	1.09776	−	0.294143i	0.0478190	−	0.0128131i
$528$	1.45759	+	5.43980i	0.0634334	+	0.236737i
$529$	−17.2871			−0.751614
$530$	−1.48441			−0.0644788
$531$	0.335934	+	1.25372i	0.0145783	+	0.0544070i
$532$	−0.0872392	−	0.956665i	−0.00378230	−	0.0414767i
$533$	6.61295	−	31.8959i	0.286439	−	1.38156i
$534$	2.09327	+	3.62565i	0.0905847	+	0.156897i
$535$	−7.64779	+	28.5419i	−0.330643	+	1.23398i
$536$	1.66906	+	2.89090i	0.0720926	+	0.124868i
$537$	−0.837989	+	1.45144i	−0.0361619	+	0.0626342i
$538$	−11.4964	−	11.4964i	−0.495645	−	0.495645i
$539$	22.3736	−	32.4577i	0.963699	−	1.39805i
$540$	0.445159	−	1.66136i	0.0191566	−	0.0714934i
$541$	−4.64871	+	17.3492i	−0.199864	+	0.745901i	0.791090	+	0.611699i	$0.209514\pi$
$541$	−4.64871	+	17.3492i	−0.199864	+	0.745901i	−0.990954	+	0.134202i	$0.957153\pi$
$542$			18.9586i			0.814340i
$543$	−1.60224	+	0.925054i	−0.0687588	+	0.0396979i
$544$	5.41548	−	5.41548i	0.232187	−	0.232187i
$545$	9.54451			0.408842
$546$	−5.93806	−	7.46589i	−0.254126	−	0.319510i
$547$	13.7457			0.587723			0.293862	−	0.955848i	$-0.405060\pi$
$547$	13.7457			0.587723			0.293862	+	0.955848i	$0.405060\pi$
$548$	5.45803	−	5.45803i	0.233155	−	0.233155i
$549$	−6.74691	+	3.89533i	−0.287951	+	0.166249i
$550$			11.4984i			0.490293i
$551$	−0.733987	+	2.73928i	−0.0312689	+	0.116697i
$552$	−1.64278	+	6.13094i	−0.0699214	+	0.260950i
$553$	−11.1522	−	30.2938i	−0.474240	−	1.28822i
$554$	3.23292	+	3.23292i	0.137354	+	0.137354i
$555$	6.01937	−	10.4259i	0.255508	−	0.442553i
$556$	−3.33766	−	5.78099i	−0.141548	−	0.245169i
$557$	−1.16249	+	4.33848i	−0.0492564	+	0.183827i	−0.986171	−	0.165731i	$-0.947002\pi$
$557$	−1.16249	+	4.33848i	−0.0492564	+	0.183827i	0.936915	+	0.349558i	$0.113668\pi$
$558$	0.0741959	+	0.128511i	0.00314096	+	0.00544031i
$559$	1.53148	+	26.6671i	0.0647746	+	1.12790i
$560$	−1.90800	+	4.13127i	−0.0806278	+	0.174578i
$561$	−11.1632	−	41.6615i	−0.471309	−	1.75895i
$562$	0.465718			0.0196451
$563$	6.05367			0.255132			0.127566	−	0.991830i	$-0.459284\pi$
$563$	6.05367			0.255132			0.127566	+	0.991830i	$0.459284\pi$
$564$	−0.195741	−	0.730514i	−0.00824217	−	0.0307602i
$565$	−20.0536	+	5.37334i	−0.843661	+	0.226058i
$566$	20.2497	+	5.42590i	0.851160	+	0.228068i
$567$	0.914026	+	2.48285i	0.0383855	+	0.104270i
$568$	−7.47989	−	12.9555i	−0.313849	−	0.543602i
$569$			23.0535i			0.966453i	0.875495	+	0.483226i	$0.160535\pi$
$569$			23.0535i			0.966453i	−0.875495	+	0.483226i	$0.839465\pi$
$570$	0.603215	+	0.161631i	0.0252659	+	0.00676997i
$571$	23.8718	+	13.7824i	0.999005	+	0.576776i	0.907954	−	0.419070i	$-0.137644\pi$
$571$	23.8718	+	13.7824i	0.999005	+	0.576776i	0.0910513	+	0.995846i	$0.470977\pi$
$572$	−13.5112	+	15.1577i	−0.564932	+	0.633773i
$573$		−	4.51532i		−	0.188630i
$574$	15.2971	−	18.3670i	0.638490	−	0.766624i
$575$	−6.47965	+	11.2231i	−0.270220	+	0.468035i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−43.9428	+	11.7744i	−1.82936	+	0.490176i	−0.997863	−	0.0653474i	$-0.979184\pi$
$577$	−43.9428	+	11.7744i	−1.82936	+	0.490176i	−0.831501	+	0.555524i	$0.812518\pi$
$578$	−29.4544	+	29.4544i	−1.22514	+	1.22514i
$579$	6.11471	+	22.8204i	0.254119	+	0.948384i
$580$	9.49919	−	9.49919i	0.394433	−	0.394433i
$581$	2.52695	+	3.58079i	0.104836	+	0.148556i
$582$	−2.47705	−	1.43013i	−0.102677	−	0.0592806i
$583$	−3.43685	−	3.43685i	−0.142340	−	0.142340i
$584$	4.37258	−	7.57354i	0.180939	−	0.313395i
$585$	5.88822	−	1.94585i	0.243448	−	0.0804508i
$586$	−12.1589	+	7.01992i	−0.502278	+	0.289990i
$587$	42.4335	−	11.3700i	1.75142	−	0.469291i	0.766489	−	0.642257i	$-0.222002\pi$
$587$	42.4335	−	11.3700i	1.75142	−	0.469291i	0.984928	+	0.172966i	$0.0553352\pi$
$588$	−1.26614	−	6.88454i	−0.0522149	−	0.283914i
$589$	−0.0466605	+	0.0269395i	−0.00192261	+	0.00111002i
$590$	2.15636	+	0.577794i	0.0887759	+	0.0237874i
$591$	13.1682	+	13.1682i	0.541665	+	0.541665i
$592$	4.94934	+	4.94934i	0.203417	+	0.203417i
$593$	−13.0143	−	3.48718i	−0.534434	−	0.143201i	−0.0184992	−	0.999829i	$-0.505889\pi$
$593$	−13.0143	−	3.48718i	−0.534434	−	0.143201i	−0.515935	+	0.856628i	$0.672555\pi$
$594$	4.87719	−	2.81585i	0.200113	−	0.115536i
$595$	14.6127	−	31.6400i	0.599063	−	1.29711i
$596$	19.6203	−	5.25723i	0.803677	−	0.215345i
$597$	11.2922	−	6.51955i	0.462159	−	0.266828i
$598$	−21.7294	+	7.18080i	−0.888583	+	0.293645i
$599$	−7.08320	+	12.2685i	−0.289412	+	0.501276i	−0.973669	−	0.227965i	$-0.926793\pi$
$599$	−7.08320	+	12.2685i	−0.289412	+	0.501276i	0.684258	+	0.729240i	$0.260126\pi$
$600$	1.44372	+	1.44372i	0.0589397	+	0.0589397i
$601$	−32.7519	−	18.9093i	−1.33598	−	0.771327i	−0.349769	−	0.936836i	$-0.613740\pi$
$601$	−32.7519	−	18.9093i	−1.33598	−	0.771327i	−0.986208	+	0.165509i	$0.947073\pi$
$602$	−8.21824	+	17.7944i	−0.334951	+	0.725247i
$603$	2.36041	−	2.36041i	0.0961234	−	0.0961234i
$604$	3.82389	+	14.2709i	0.155592	+	0.580677i
$605$	25.1947	−	25.1947i	1.02431	−	1.02431i
$606$	6.80384	−	1.82308i	0.276387	−	0.0740576i
$607$	35.5716	+	20.5373i	1.44381	+	0.833583i	0.998101	−	0.0615956i	$-0.0196189\pi$
$607$	35.5716	+	20.5373i	1.44381	+	0.833583i	0.445707	+	0.895179i	$0.352952\pi$
$608$	−0.181543	+	0.314441i	−0.00736254	+	0.0127523i
$609$	−3.51364	+	20.3639i	−0.142380	+	0.825188i
$610$			13.3996i			0.542535i
$611$	1.81443	−	2.03553i	0.0734040	−	0.0823488i
$612$	−6.63258	−	3.82932i	−0.268106	−	0.154791i
$613$	−22.9357	−	6.14560i	−0.926363	−	0.248218i	−0.236060	−	0.971738i	$-0.575856\pi$
$613$	−22.9357	−	6.14560i	−0.926363	−	0.248218i	−0.690303	+	0.723520i	$0.742523\pi$
$614$			11.5697i			0.466916i
$615$	7.76946	+	13.4571i	0.313295	+	0.542642i
$616$	−13.9827	+	5.14751i	−0.563377	+	0.207399i
$617$	−22.7619	−	6.09903i	−0.916358	−	0.245538i	−0.230330	−	0.973113i	$-0.573981\pi$
$617$	−22.7619	−	6.09903i	−0.916358	−	0.245538i	−0.686028	+	0.727575i	$0.740647\pi$
$618$	6.52059	−	1.74719i	0.262296	−	0.0702821i
$619$	3.00915	+	11.2303i	0.120948	+	0.451384i	0.999663	−	0.0259629i	$-0.00826519\pi$
$619$	3.00915	+	11.2303i	0.120948	+	0.451384i	−0.878715	+	0.477347i	$0.841599\pi$
$620$	0.255228			0.0102502
$621$	6.34721			0.254705
$622$	−0.398287	−	1.48643i	−0.0159698	−	0.0596002i
$623$	−9.04998	+	6.38653i	−0.362580	+	0.255871i
$624$	0.206724	+	3.59962i	0.00827559	+	0.144100i
$625$	−5.31134	−	9.19952i	−0.212454	−	0.367981i
$626$	−4.12122	+	15.3806i	−0.164717	+	0.614733i
$627$	1.02239	+	1.77084i	0.0408305	+	0.0707204i
$628$	−4.66629	+	8.08225i	−0.186205	+	0.322517i
$629$	−37.9052	−	37.9052i	−1.51138	−	1.51138i
$630$	4.48433	+	0.773736i	0.178660	+	0.0308264i
$631$	−2.59285	+	9.67665i	−0.103220	+	0.385222i	−0.998137	−	0.0610104i	$-0.980568\pi$
$631$	−2.59285	+	9.67665i	−0.103220	+	0.385222i	0.894917	+	0.446232i	$0.147234\pi$
$632$	−3.15790	+	11.7855i	−0.125615	+	0.468800i
$633$			16.1024i			0.640012i
$634$	−2.27053	+	1.31089i	−0.0901742	+	0.0520621i
$635$	−4.32628	+	4.32628i	−0.171683	+	0.171683i
$636$	−0.863050			−0.0342222
$637$	18.2445	−	17.4396i	0.722874	−	0.690980i
$638$	43.9867			1.74145
$639$	−10.5782	+	10.5782i	−0.418465	+	0.418465i
$640$	1.48953	−	0.859981i	0.0588789	−	0.0339937i
$641$		−	28.0633i		−	1.10843i	−0.832373	−	0.554216i	$-0.813018\pi$
$641$		−	28.0633i		−	1.10843i	0.832373	−	0.554216i	$-0.186982\pi$
$642$	−4.44649	+	16.5945i	−0.175489	+	0.654933i
$643$	−3.74858	+	13.9899i	−0.147830	+	0.551708i	0.851783	+	0.523894i	$0.175521\pi$
$643$	−3.74858	+	13.9899i	−0.147830	+	0.551708i	−0.999613	+	0.0278139i	$0.991145\pi$
$644$	−16.5486	−	2.85534i	−0.652107	−	0.112516i
$645$	−9.00996	−	9.00996i	−0.354767	−	0.354767i
$646$	1.39037	−	2.40820i	0.0547035	−	0.0947492i
$647$	1.67763	+	2.90575i	0.0659545	+	0.114237i	0.897117	−	0.441793i	$-0.145657\pi$
$647$	1.67763	+	2.90575i	0.0659545	+	0.114237i	−0.831162	+	0.556030i	$0.812324\pi$
$648$	0.258819	−	0.965926i	0.0101674	−	0.0379452i
$649$	3.65483	+	6.33035i	0.143465	+	0.248488i
$650$	−1.49449	+	7.20827i	−0.0586185	+	0.282732i
$651$	−0.320776	+	0.226370i	−0.0125722	+	0.00887215i
$652$	2.22329	+	8.29744i	0.0870708	+	0.324953i
$653$	38.8317			1.51960			0.759801	−	0.650156i	$-0.225296\pi$
$653$	38.8317			1.51960			0.759801	+	0.650156i	$0.225296\pi$
$654$	5.54926			0.216993
$655$	−7.91234	−	29.5292i	−0.309161	−	1.15380i
$656$	−8.72661	+	2.33829i	−0.340717	+	0.0912948i
$657$	−8.44718	−	2.26342i	−0.329556	−	0.0883043i
$658$	1.87774	−	0.691263i	0.0732020	−	0.0269483i
$659$	−18.4258	−	31.9145i	−0.717769	−	1.24321i	−0.961882	−	0.273465i	$-0.911830\pi$
$659$	−18.4258	−	31.9145i	−0.717769	−	1.24321i	0.244113	−	0.969747i	$-0.421503\pi$
$660$		−	9.68629i		−	0.377039i
$661$	−20.1870	−	5.40908i	−0.785182	−	0.210389i	−0.156114	−	0.987739i	$-0.549897\pi$
$661$	−20.1870	−	5.40908i	−0.785182	−	0.210389i	−0.629068	+	0.777350i	$0.716563\pi$
$662$	−6.44612	−	3.72167i	−0.250536	−	0.144647i
$663$	−1.58323	−	27.5682i	−0.0614875	−	1.07066i
$664$		−	1.65648i		−	0.0642840i
$665$	−0.280933	+	1.62820i	−0.0108941	+	0.0631387i
$666$	3.49971	−	6.06168i	0.135611	−	0.234885i
$667$	42.9335	+	24.7877i	1.66239	+	0.959783i
$668$	14.9831	−	4.01471i	0.579714	−	0.155334i
$669$	9.72221	−	9.72221i	0.375883	−	0.375883i
$670$	−1.48600	−	5.54582i	−0.0574091	−	0.214254i
$671$	−31.0240	+	31.0240i	−1.19767	+	1.19767i
$672$	−1.10933	+	2.40196i	−0.0427933	+	0.0926575i
$673$	24.0567	+	13.8891i	0.927316	+	0.535386i	0.885962	−	0.463758i	$-0.153499\pi$
$673$	24.0567	+	13.8891i	0.927316	+	0.535386i	0.0413542	+	0.999145i	$0.486833\pi$
$674$	−13.2477	−	13.2477i	−0.510280	−	0.510280i
$675$	1.02087	−	1.76819i	0.0392931	−	0.0680577i
$676$	−10.4402	+	7.74613i	−0.401545	+	0.297928i
$677$	11.4753	−	6.62524i	0.441030	−	0.254629i	−0.263004	−	0.964795i	$-0.584713\pi$
$677$	11.4753	−	6.62524i	0.441030	−	0.254629i	0.704034	+	0.710166i	$0.251380\pi$
$678$	−11.6593	+	3.12411i	−0.447774	+	0.119981i
$679$	3.17296	−	6.87020i	0.121767	−	0.263654i
$680$	−11.4078	+	6.58629i	−0.437469	+	0.252573i
$681$	27.0911	+	7.25905i	1.03813	+	0.278167i
$682$	0.590927	+	0.590927i	0.0226278	+	0.0226278i
$683$	−7.13736	−	7.13736i	−0.273104	−	0.273104i	0.557245	−	0.830348i	$-0.311859\pi$
$683$	−7.13736	−	7.13736i	−0.273104	−	0.273104i	−0.830348	+	0.557245i	$0.811859\pi$
$684$	0.350714	+	0.0939735i	0.0134099	+	0.00359317i
$685$	−11.4974	+	6.63803i	−0.439294	+	0.253626i
$686$	17.8353	−	4.99022i	0.680955	−	0.190528i
$687$	14.1090	−	3.78049i	0.538291	−	0.144235i
$688$	6.41578	−	3.70415i	0.244599	−	0.141220i
$689$	−1.70784	−	2.60123i	−0.0650634	−	0.0990991i
$690$	5.45848	−	9.45437i	0.207801	−	0.359922i
$691$	−4.54270	−	4.54270i	−0.172812	−	0.172812i	0.615401	−	0.788214i	$-0.288994\pi$
$691$	−4.54270	−	4.54270i	−0.172812	−	0.172812i	−0.788214	+	0.615401i	$0.788994\pi$
$692$	−3.94219	−	2.27602i	−0.149859	−	0.0865214i
$693$	8.59109	+	12.1739i	0.326349	+	0.462450i
$694$	10.4380	−	10.4380i	0.396222	−	0.396222i
$695$	2.97158	+	11.0901i	0.112718	+	0.420671i
$696$	5.52291	−	5.52291i	0.209345	−	0.209345i
$697$	66.8340	−	17.9081i	2.53152	−	0.678318i
$698$	19.8835	+	11.4797i	0.752602	+	0.434515i
$699$	−0.310875	+	0.538452i	−0.0117584	+	0.0203661i
$700$	−3.45706	+	4.15083i	−0.130665	+	0.156887i
$701$			6.99459i			0.264182i	0.991238	+	0.132091i	$0.0421691\pi$
$701$			6.99459i			0.264182i	−0.991238	+	0.132091i	$0.957831\pi$
$702$	3.42346	−	1.13133i	0.129210	−	0.0426993i
$703$	2.20091	+	1.27070i	0.0830089	+	0.0479252i
$704$	5.43980	+	1.45759i	0.205020	+	0.0549349i
$705$			1.30078i			0.0489902i
$706$	−9.16659	−	15.8770i	−0.344989	−	0.597539i
$707$	6.43826	+	17.4888i	0.242136	+	0.657735i
$708$	1.25372	+	0.335934i	0.0471178	+	0.0126252i
$709$	−14.6119	+	3.91524i	−0.548761	+	0.147040i	−0.522538	−	0.852616i	$-0.675015\pi$
$709$	−14.6119	+	3.91524i	−0.548761	+	0.147040i	−0.0262231	+	0.999656i	$0.508348\pi$
$710$	6.65948	+	24.8535i	0.249926	+	0.932735i
$711$	12.2012			0.457581
$712$	4.18654			0.156897
$713$	0.243775	+	0.909781i	0.00912945	+	0.0340716i
$714$	8.49595	−	18.3957i	0.317953	−	0.688443i
$715$	29.1945	−	19.1676i	1.09181	−	0.716828i
$716$	0.837989	+	1.45144i	0.0313171	+	0.0542428i
$717$	−4.27097	+	15.9395i	−0.159502	+	0.595271i
$718$	5.57200	+	9.65098i	0.207945	+	0.360171i
$719$	2.79553	−	4.84201i	0.104256	−	0.180576i	−0.809178	−	0.587563i	$-0.800087\pi$
$719$	2.79553	−	4.84201i	0.104256	−	0.180576i	0.913434	+	0.406987i	$0.133421\pi$
$720$	−1.21620	−	1.21620i	−0.0453250	−	0.0453250i
$721$	6.17023	+	16.7608i	0.229791	+	0.624203i
$722$	4.88344	−	18.2253i	0.181743	−	0.678274i
$723$	−2.39343	+	8.93241i	−0.0890127	+	0.332200i
$724$			1.85011i			0.0687588i
$725$	13.8106	−	7.97354i	0.512912	−	0.296130i
$726$	14.6484	−	14.6484i	0.543652	−	0.543652i
$727$	21.2421			0.787826			0.393913	−	0.919148i	$-0.371121\pi$
$727$	21.2421			0.787826			0.393913	+	0.919148i	$0.371121\pi$
$728$	−9.43468	+	1.40957i	−0.349672	+	0.0522421i
$729$	−1.00000			−0.0370370
$730$	−10.6358	+	10.6358i	−0.393650	+	0.393650i
$731$	−49.1362	+	28.3688i	−1.81737	+	1.04926i
$732$			7.79066i			0.287951i
$733$	−5.47343	+	20.4271i	−0.202166	+	0.754492i	0.788129	+	0.615510i	$0.211050\pi$
$733$	−5.47343	+	20.4271i	−0.202166	+	0.754492i	−0.990295	+	0.138983i	$0.955617\pi$
$734$	−4.40949	+	16.4564i	−0.162757	+	0.607418i
$735$	−0.961197	+	12.0013i	−0.0354543	+	0.442675i
$736$	4.48816	+	4.48816i	0.165436	+	0.165436i
$737$	9.39965	−	16.2807i	0.346241	−	0.599706i
$738$	4.51723	+	7.82407i	0.166281	+	0.288008i
$739$	7.47879	−	27.9112i	0.275112	−	1.02673i	−0.680655	−	0.732604i	$-0.738305\pi$
$739$	7.47879	−	27.9112i	0.275112	−	1.02673i	0.955767	−	0.294126i	$-0.0950286\pi$
$740$	−6.01937	−	10.4259i	−0.221277	−	0.383262i
$741$	0.410770	+	1.24301i	0.0150900	+	0.0456631i
$742$	−0.207367	−	2.27398i	−0.00761267	−	0.0834805i
$743$	−4.32089	−	16.1258i	−0.158518	−	0.591597i	−0.998778	−	0.0494140i	$-0.984265\pi$
$743$	−4.32089	−	16.1258i	−0.158518	−	0.591597i	0.840260	−	0.542183i	$-0.182402\pi$
$744$	0.148392			0.00544031
$745$	−34.9365			−1.27998
$746$	−7.39514	−	27.5990i	−0.270755	−	1.01047i
$747$	−1.60004	+	0.428729i	−0.0585424	+	0.0156864i
$748$	−41.6615	−	11.1632i	−1.52329	−	0.408165i
$749$	−44.7919	−	7.72849i	−1.63666	−	0.282393i
$750$	−6.05575	−	10.4889i	−0.221125	−	0.383000i
$751$		−	1.93172i		−	0.0704895i	−0.999379	−	0.0352448i	$-0.988779\pi$
$751$		−	1.93172i		−	0.0704895i	0.999379	−	0.0352448i	$-0.0112211\pi$
$752$	−0.730514	−	0.195741i	−0.0266391	−	0.00713793i
$753$	−20.9967	−	12.1225i	−0.765163	−	0.441767i
$754$	27.5750	+	5.71710i	1.00422	+	0.208205i
$755$		−	25.4114i		−	0.924814i
$756$	2.60723	+	0.449857i	0.0948239	+	0.0163611i
$757$	−4.58127	+	7.93499i	−0.166509	+	0.288402i	−0.937190	−	0.348819i	$-0.886583\pi$
$757$	−4.58127	+	7.93499i	−0.166509	+	0.288402i	0.770681	+	0.637221i	$0.219916\pi$
$758$	17.6121	+	10.1683i	0.639700	+	0.369331i
$759$	34.5275	−	9.25163i	1.25327	−	0.335813i
$760$	0.441584	−	0.441584i	0.0160179	−	0.0160179i
$761$	0.378608	+	1.41298i	0.0137245	+	0.0512206i	0.972449	−	0.233118i	$-0.0748928\pi$
$761$	0.378608	+	1.41298i	0.0137245	+	0.0512206i	−0.958724	+	0.284338i	$0.908226\pi$
$762$	−2.51533	+	2.51533i	−0.0911209	+	0.0911209i
$763$	1.33333	+	14.6213i	0.0482698	+	0.529326i
$764$	−3.91038	−	2.25766i	−0.141473	−	0.0816793i
$765$	9.31442	+	9.31442i	0.336764	+	0.336764i
$766$	−4.25467	+	7.36930i	−0.153727	+	0.266264i
$767$	1.46841	+	4.44349i	0.0530213	+	0.160445i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	6.35786	−	1.70358i	0.229270	−	0.0614328i	−0.142355	−	0.989816i	$-0.545467\pi$
$769$	6.35786	−	1.70358i	0.229270	−	0.0614328i	0.371625	+	0.928383i	$0.378801\pi$
$770$	25.5216	−	2.32734i	0.919736	−	0.0838716i
$771$	−8.77038	+	5.06358i	−0.315858	+	0.182360i
$772$	22.8204	+	6.11471i	0.821325	+	0.220073i
$773$	−15.3491	−	15.3491i	−0.552070	−	0.552070i	0.374968	−	0.927038i	$-0.377654\pi$
$773$	−15.3491	−	15.3491i	−0.552070	−	0.552070i	−0.927038	+	0.374968i	$0.877654\pi$
$774$	−5.23847	−	5.23847i	−0.188293	−	0.188293i
$775$	0.292652	+	0.0784160i	0.0105124	+	0.00281679i
$776$	−2.47705	+	1.43013i	−0.0889209	+	0.0513385i
$777$	16.8123	+	7.76466i	0.603138	+	0.278555i
$778$	18.5590	−	4.97286i	0.665372	−	0.178286i
$779$	−2.84081	+	1.64014i	−0.101782	+	0.0587641i
$780$	1.25896	−	6.07227i	0.0450780	−	0.217422i
$781$	−42.1244	+	72.9616i	−1.50733	+	2.61077i
$782$	−34.3732	−	34.3732i	−1.22918	−	1.22918i
$783$	−6.76416	−	3.90529i	−0.241731	−	0.139564i
$784$	−6.59526	−	2.34576i	−0.235545	−	0.0837770i
$785$	11.3502	−	11.3502i	0.405108	−	0.405108i
$786$	−4.60030	−	17.1685i	−0.164087	−	0.612382i
$787$	−0.630760	+	0.630760i	−0.0224842	+	0.0224842i	−0.718259	−	0.695775i	$-0.755061\pi$
$787$	−0.630760	+	0.630760i	−0.0224842	+	0.0224842i	0.695775	+	0.718259i	$0.255061\pi$
$788$	17.9880	−	4.81988i	0.640797	−	0.171701i
$789$	4.63702	+	2.67718i	0.165082	+	0.0953103i
$790$	10.4928	−	18.1741i	0.373317	−	0.646604i
$791$	−11.0329	−	29.9696i	−0.392283	−	1.06560i
$792$		−	5.63169i		−	0.200113i
$793$	−23.4810	+	15.4165i	−0.833836	+	0.547454i
$794$	−26.7103	−	15.4212i	−0.947912	−	0.547277i
$795$	1.43383	+	0.384195i	0.0508528	+	0.0136260i
$796$		−	13.0391i		−	0.462159i
$797$	−19.6735	−	34.0755i	−0.696872	−	1.20702i	−0.969546	−	0.244911i	$-0.921241\pi$
$797$	−19.6735	−	34.0755i	−0.696872	−	1.20702i	0.272673	−	0.962107i	$-0.412092\pi$
$798$	−0.163337	+	0.946647i	−0.00578205	+	0.0335109i
$799$	5.59475	+	1.49911i	0.197928	+	0.0530347i
$800$	1.97216	−	0.528439i	0.0697264	−	0.0186831i
$801$	−1.08356	−	4.04389i	−0.0382856	−	0.142884i
$802$	−28.6375			−1.01122
$803$	−49.2501			−1.73800
$804$	−0.863971	−	3.22438i	−0.0304699	−	0.113715i
$805$	26.2221	+	12.1105i	0.924207	+	0.426839i
$806$	0.293643	+	0.447253i	0.0103431	+	0.0157538i
$807$	8.12919	+	14.0802i	0.286161	+	0.495645i
$808$	1.82308	−	6.80384i	0.0641358	−	0.239358i
$809$	3.62112	+	6.27197i	0.127312	+	0.220511i	0.922634	−	0.385676i	$-0.126032\pi$
$809$	3.62112	+	6.27197i	0.127312	+	0.220511i	−0.795322	+	0.606187i	$0.792698\pi$
$810$	−0.859981	+	1.48953i	−0.0302167	+	0.0523368i
$811$	−30.3347	−	30.3347i	−1.06520	−	1.06520i	−0.997721	−	0.0674741i	$-0.978506\pi$
$811$	−30.3347	−	30.3347i	−1.06520	−	1.06520i	−0.0674741	−	0.997721i	$-0.521494\pi$
$812$	15.8789	+	13.2249i	0.557239	+	0.464102i
$813$	4.90684	−	18.3126i	0.172090	−	0.642249i
$814$	10.2023	−	38.0754i	0.357590	−	1.33454i
$815$		−	14.7747i		−	0.517536i
$816$	−6.63258	+	3.82932i	−0.232187	+	0.134053i
$817$	1.90201	−	1.90201i	0.0665430	−	0.0665430i
$818$	−5.46573			−0.191105
$819$	3.80341	+	8.74837i	0.132902	+	0.305693i
$820$	15.5389			0.542642
$821$	−3.57191	+	3.57191i	−0.124661	+	0.124661i	−0.766685	−	0.642024i	$-0.778095\pi$
$821$	−3.57191	+	3.57191i	−0.124661	+	0.124661i	0.642024	+	0.766685i	$0.278095\pi$
$822$	−6.68469	+	3.85941i	−0.233155	+	0.134612i
$823$		−	0.170697i		−	0.00595012i	−0.999996	−	0.00297506i	$-0.999053\pi$
$823$		−	0.170697i		−	0.00595012i	0.999996	−	0.00297506i	$-0.000946993\pi$
$824$	1.74719	−	6.52059i	0.0608661	−	0.227155i
$825$	2.97600	−	11.1066i	0.103611	−	0.386682i
$826$	−0.583892	+	3.38405i	−0.0203162	+	0.117746i
$827$	−6.15597	−	6.15597i	−0.214064	−	0.214064i	0.591927	−	0.805991i	$-0.298367\pi$
$827$	−6.15597	−	6.15597i	−0.214064	−	0.214064i	−0.805991	+	0.591927i	$0.798367\pi$
$828$	3.17361	−	5.49685i	0.110290	−	0.191029i
$829$	−4.39368	−	7.61008i	−0.152599	−	0.264309i	0.779583	−	0.626299i	$-0.215431\pi$
$829$	−4.39368	−	7.61008i	−0.152599	−	0.264309i	−0.932182	+	0.361990i	$0.882098\pi$
$830$	−0.737398	+	2.75201i	−0.0255955	+	0.0955236i
$831$	−2.28602	−	3.95951i	−0.0793013	−	0.137354i
$832$	3.22072	+	1.62078i	0.111659	+	0.0561905i
$833$	50.5107	+	17.9653i	1.75009	+	0.622461i
$834$	1.72770	+	6.44786i	0.0598253	+	0.223271i
$835$	−26.6795			−0.923281
$836$	2.04479			0.0707204
$837$	−0.0384066	−	0.143335i	−0.00132753	−	0.00495440i
$838$	13.6803	−	3.66562i	0.472577	−	0.126627i
$839$	−25.4509	−	6.81955i	−0.878663	−	0.235437i	−0.208833	−	0.977951i	$-0.566966\pi$
$839$	−25.4509	−	6.81955i	−0.878663	−	0.235437i	−0.669830	+	0.742515i	$0.733633\pi$
$840$	2.91224	−	3.49668i	0.100482	−	0.120647i
$841$	−16.0025	−	27.7172i	−0.551811	−	0.955765i
$842$			18.6457i			0.642573i
$843$	−0.449849	−	0.120537i	−0.0154936	−	0.00415150i
$844$	13.9451	+	8.05119i	0.480009	+	0.277133i
$845$	20.7931	−	8.22154i	0.715305	−	0.282830i
$846$			0.756284i			0.0260016i
$847$	42.1154	+	35.0762i	1.44710	+	1.20523i
$848$	−0.431525	+	0.747424i	−0.0148186	+	0.0256666i
$849$	−18.1554	−	10.4820i	−0.623092	−	0.359743i
$850$	−15.1041	+	4.04712i	−0.518065	+	0.138815i
$851$	31.4145	−	31.4145i	1.07688	−	1.07688i
$852$	3.87187	+	14.4500i	0.132648	+	0.495050i
$853$	−31.4788	+	31.4788i	−1.07781	+	1.07781i	−0.0811070	+	0.996705i	$0.525846\pi$
$853$	−31.4788	+	31.4788i	−1.07781	+	1.07781i	−0.996705	+	0.0811070i	$0.974154\pi$
$854$	−20.5270	+	1.87187i	−0.702418	+	0.0640542i
$855$	−0.540827	−	0.312247i	−0.0184959	−	0.0106786i
$856$	12.1480	+	12.1480i	0.415211	+	0.415211i
$857$	−12.9532	+	22.4355i	−0.442471	+	0.766383i	−0.997872	−	0.0651999i	$-0.979232\pi$
$857$	−12.9532	+	22.4355i	−0.442471	+	0.766383i	0.555401	+	0.831583i	$0.312565\pi$
$858$	16.9739	−	11.1442i	0.579480	−	0.380457i
$859$	20.7081	−	11.9558i	0.706552	−	0.407928i	−0.103231	−	0.994657i	$-0.532918\pi$
$859$	20.7081	−	11.9558i	0.706552	−	0.407928i	0.809783	+	0.586730i	$0.199585\pi$
$860$	−12.3078	+	3.29787i	−0.419694	+	0.112457i
$861$	−19.5296	+	13.7820i	−0.665568	+	0.469688i
$862$	−12.4376	+	7.18086i	−0.423627	+	0.244581i
$863$	38.2491	+	10.2488i	1.30201	+	0.348874i	0.842211	−	0.539148i	$-0.181254\pi$
$863$	38.2491	+	10.2488i	1.30201	+	0.348874i	0.459803	+	0.888021i	$0.347920\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$	5.53618	+	5.53618i	0.188236	+	0.188236i
$866$	21.2746	+	5.70052i	0.722942	+	0.193712i
$867$	36.0741	−	20.8274i	1.22514	−	0.707336i
$868$	0.0356544	+	0.390986i	0.00121019	+	0.0132709i
$869$	66.3720	−	17.7843i	2.25152	−	0.603292i
$870$	−11.6341	+	6.71695i	−0.394433	+	0.227726i
$871$	8.00863	−	8.98454i	0.271362	−	0.304430i
$872$	2.77463	−	4.80580i	0.0939608	−	0.162745i
$873$	2.02250	+	2.02250i	0.0684514	+	0.0684514i
$874$	1.99583	+	1.15229i	0.0675099	+	0.0389768i
$875$	26.1813	−	18.4760i	0.885088	−	0.624603i
$876$	−6.18377	+	6.18377i	−0.208930	+	0.208930i
$877$	2.51270	+	9.37752i	0.0848478	+	0.316656i	0.995285	−	0.0969903i	$-0.0309216\pi$
$877$	2.51270	+	9.37752i	0.0848478	+	0.316656i	−0.910438	+	0.413647i	$0.864255\pi$
$878$	9.34821	−	9.34821i	0.315487	−	0.315487i
$879$	13.5614	−	3.63378i	0.457416	−	0.122564i
$880$	−8.38858	−	4.84315i	−0.282779	−	0.163262i
$881$	−10.0018	+	17.3236i	−0.336969	+	0.583648i	−0.983861	−	0.178934i	$-0.942735\pi$
$881$	−10.0018	+	17.3236i	−0.336969	+	0.583648i	0.646892	+	0.762582i	$0.276068\pi$
$882$	−0.558848	+	6.97766i	−0.0188174	+	0.234950i
$883$			39.4548i			1.32776i	0.747839	+	0.663880i	$0.231092\pi$
$883$			39.4548i			1.32776i	−0.747839	+	0.663880i	$0.768908\pi$
$884$	−24.6664	−	12.4130i	−0.829620	−	0.417494i
$885$	−1.93334	−	1.11621i	−0.0649884	−	0.0375211i
$886$	34.4702	+	9.23627i	1.15805	+	0.310299i
$887$			2.94100i			0.0987492i	0.998780	+	0.0493746i	$0.0157228\pi$
$887$			2.94100i			0.0987492i	−0.998780	+	0.0493746i	$0.984277\pi$
$888$	−3.49971	−	6.06168i	−0.117443	−	0.203417i
$889$	−7.23181	−	6.02308i	−0.242547	−	0.202008i
$890$	−6.95533	−	1.86368i	−0.233143	−	0.0624706i
$891$	−5.43980	+	1.45759i	−0.182240	+	0.0488311i
$892$	−3.55858	−	13.2808i	−0.119150	−	0.444674i
$893$	−0.274596			−0.00918900
$894$	−20.3124			−0.679348
$895$	−0.746077	−	2.78440i	−0.0249386	−	0.0930721i
$896$	1.52549	+	2.16168i	0.0509631	+	0.0722168i
$897$	22.8476	−	1.31212i	0.762858	−	0.0438105i
$898$	−2.55648	−	4.42796i	−0.0853109	−	0.147763i
$899$	0.299978	−	1.11953i	0.0100048	−	0.0373385i
$900$	−1.02087	−	1.76819i	−0.0340288	−	0.0589397i
$901$	3.30490	−	5.72425i	0.110102	−	0.190702i
$902$	35.9771	+	35.9771i	1.19790	+	1.19790i
$903$	12.5438	−	15.0611i	0.417430	−	0.501201i
$904$	−3.12411	+	11.6593i	−0.103906	+	0.387783i
$905$	0.823593	−	3.07369i	0.0273771	−	0.102173i
$906$		−	14.7744i		−	0.490846i
$907$	−20.5243	+	11.8497i	−0.681498	+	0.393463i	−0.800419	−	0.599441i	$-0.795390\pi$
$907$	−20.5243	+	11.8497i	−0.681498	+	0.393463i	0.118922	+	0.992904i	$0.462056\pi$
$908$	19.8321	−	19.8321i	0.658151	−	0.658151i
$909$	−7.04385			−0.233630
$910$	16.3018	+	1.85814i	0.540401	+	0.0615966i
$911$	28.7034			0.950985			0.475493	−	0.879720i	$-0.342270\pi$
$911$	28.7034			0.950985			0.475493	+	0.879720i	$0.342270\pi$
$912$	0.256740	−	0.256740i	0.00850152	−	0.00850152i
$913$	−8.07898	+	4.66440i	−0.267375	+	0.154369i
$914$			20.6609i			0.683403i
$915$	3.46808	−	12.9431i	0.114651	−	0.427884i
$916$	3.78049	−	14.1090i	0.124911	−	0.466174i
$917$	44.1307	−	16.2461i	1.45732	−	0.536492i
$918$	5.41548	+	5.41548i	0.178737	+	0.178737i
$919$	−2.54004	+	4.39948i	−0.0837882	+	0.145125i	−0.904874	−	0.425679i	$-0.860035\pi$
$919$	−2.54004	+	4.39948i	−0.0837882	+	0.145125i	0.821086	+	0.570805i	$0.193369\pi$
$920$	−5.45848	−	9.45437i	−0.179961	−	0.311701i
$921$	2.99446	−	11.1755i	0.0986709	−	0.368245i
$922$	3.71673	+	6.43757i	0.122404	+	0.212010i
$923$	−35.8906	+	40.2641i	−1.18135	+	1.32531i
$924$	14.8385	−	1.35314i	0.488150	−	0.0445149i
$925$	−3.69877	−	13.8040i	−0.121615	−	0.453872i
$926$	−3.63823			−0.119560
$927$	−6.75061			−0.221719
$928$	−2.02153	−	7.54443i	−0.0663598	−	0.247658i
$929$	22.5380	−	6.03903i	0.739446	−	0.198134i	0.130614	−	0.991433i	$-0.458305\pi$
$929$	22.5380	−	6.03903i	0.739446	−	0.198134i	0.608832	+	0.793299i	$0.291638\pi$
$930$	−0.246532	−	0.0660579i	−0.00808409	−	0.00216613i
$931$	−2.53349	−	0.202910i	−0.0830317	−	0.00665010i
$932$	0.310875	+	0.538452i	0.0101831	+	0.0176376i
$933$			1.53886i			0.0503801i
$934$	−9.64997	−	2.58570i	−0.315757	−	0.0846068i
$935$	64.2451	+	37.0919i	2.10104	+	1.21304i
$936$	0.731970	−	3.53047i	0.0239252	−	0.115397i
$937$			24.6163i			0.804180i	0.915600	+	0.402090i	$0.131716\pi$
$937$			24.6163i			0.804180i	−0.915600	+	0.402090i	$0.868284\pi$
$938$	8.28808	−	3.05114i	0.270615	−	0.0996231i
$939$	7.96159	−	13.7899i	0.259817	−	0.450016i
$940$	1.12651	+	0.650390i	0.0367427	+	0.0212134i
$941$	3.93169	−	1.05349i	0.128169	−	0.0343429i	−0.194164	−	0.980969i	$-0.562199\pi$
$941$	3.93169	−	1.05349i	0.128169	−	0.0343429i	0.322334	+	0.946626i	$0.395533\pi$
$942$	6.59913	−	6.59913i	0.215011	−	0.215011i
$943$	14.8416	+	55.3897i	0.483310	+	1.80374i
$944$	0.917790	−	0.917790i	0.0298715	−	0.0298715i
$945$	−4.13127	−	1.90800i	−0.134390	−	0.0620673i
$946$	−36.1317	−	20.8607i	−1.17474	−	0.678238i
$947$	−13.4333	−	13.4333i	−0.436524	−	0.436524i	0.454317	−	0.890840i	$-0.349884\pi$
$947$	−13.4333	−	13.4333i	−0.436524	−	0.436524i	−0.890840	+	0.454317i	$0.849884\pi$
$948$	6.10060	−	10.5665i	0.198138	−	0.343186i
$949$	−30.8745	−	6.40120i	−1.00223	−	0.207792i
$950$	0.642005	−	0.370662i	0.0208294	−	0.0120258i
$951$	2.53244	−	0.678566i	0.0821201	−	0.0220040i
$952$	−11.6832	−	16.5556i	−0.378654	−	0.536569i
$953$	−15.4454	+	8.91740i	−0.500325	+	0.288863i	−0.728848	−	0.684676i	$-0.759944\pi$
$953$	−15.4454	+	8.91740i	−0.500325	+	0.288863i	0.228523	+	0.973539i	$0.426611\pi$
$954$	0.833643	+	0.223374i	0.0269902	+	0.00723200i
$955$	5.49152	+	5.49152i	0.177701	+	0.177701i
$956$	11.6685	+	11.6685i	0.377387	+	0.377387i
$957$	−42.4879	−	11.3846i	−1.37344	−	0.368012i
$958$	−21.5734	+	12.4554i	−0.697006	+	0.402416i
$959$	−11.7750	−	16.6856i	−0.380234	−	0.538807i
$960$	−1.66136	+	0.445159i	−0.0536200	+	0.0143674i
$961$	−26.8277	+	15.4890i	−0.865410	+	0.499645i
$962$	11.3445	−	22.5432i	0.365763	−	0.726822i
$963$	8.58995	−	14.8782i	0.276807	−	0.479444i
$964$	6.53898	+	6.53898i	0.210606	+	0.210606i
$965$	−35.1908	−	20.3174i	−1.13283	−	0.654041i
$966$	15.2457	+	7.04114i	0.490523	+	0.226545i
$967$	19.2108	−	19.2108i	0.617778	−	0.617778i	−0.327183	−	0.944961i	$-0.606099\pi$
$967$	19.2108	−	19.2108i	0.617778	−	0.617778i	0.944961	+	0.327183i	$0.106099\pi$
$968$	−5.36168	−	20.0101i	−0.172331	−	0.643148i
$969$	−1.96628	+	1.96628i	−0.0631661	+	0.0631661i
$970$	4.75190	−	1.27327i	0.152574	−	0.0408821i
$971$	49.6274	+	28.6524i	1.59262	+	0.919500i	0.992855	+	0.119323i	$0.0380724\pi$
$971$	49.6274	+	28.6524i	1.59262	+	0.919500i	0.599765	+	0.800177i	$0.295261\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−16.5738	+	6.10141i	−0.531332	+	0.195602i
$974$		−	31.6228i		−	1.01326i
$975$	3.30920	−	6.57585i	0.105979	−	0.210596i
$976$	6.74691	+	3.89533i	0.215963	+	0.124686i
$977$	−36.4826	−	9.77549i	−1.16718	−	0.312746i	−0.377352	−	0.926070i	$-0.623165\pi$
$977$	−36.4826	−	9.77549i	−1.16718	−	0.312746i	−0.789831	+	0.613324i	$0.789832\pi$
$978$		−	8.59014i		−	0.274682i
$979$	−11.7887	−	20.4185i	−0.376767	−	0.652580i
$980$	9.91284	+	6.83307i	0.316654	+	0.218275i
$981$	−5.36017	−	1.43625i	−0.171137	−	0.0458560i
$982$	6.71231	−	1.79856i	0.214198	−	0.0573943i
$983$	0.643779	+	2.40262i	0.0205334	+	0.0766316i	0.975432	−	0.220300i	$-0.0707035\pi$
$983$	0.643779	+	2.40262i	0.0205334	+	0.0766316i	−0.954899	+	0.296931i	$0.904037\pi$
$984$	9.03445			0.288008
$985$	−32.0301			−1.02056
$986$	15.4821	+	57.7801i	0.493052	+	1.84009i
$987$	−1.99267	+	0.181714i	−0.0634274	+	0.00578401i
$988$	1.28186	+	0.265768i	0.0407815	+	0.00845520i
$989$	−23.5111	−	40.7223i	−0.747608	−	1.29490i
$990$	−2.50700	+	9.35624i	−0.0796776	+	0.297361i
$991$	−8.84061	−	15.3124i	−0.280831	−	0.486414i	0.690758	−	0.723086i	$-0.257277\pi$
$991$	−8.84061	−	15.3124i	−0.280831	−	0.486414i	−0.971590	+	0.236672i	$0.923943\pi$
$992$	0.0741959	−	0.128511i	0.00235572	−	0.00408023i
$993$	5.26324	+	5.26324i	0.167024	+	0.167024i
$994$	−37.1429	+	13.6736i	−1.17810	+	0.433701i
$995$	−5.80448	+	21.6626i	−0.184014	+	0.686751i
$996$	−0.428729	+	1.60004i	−0.0135848	+	0.0506992i
$997$			18.7730i			0.594548i	0.954792	+	0.297274i	$0.0960774\pi$
$997$			18.7730i			0.594548i	−0.954792	+	0.297274i	$0.903923\pi$
$998$	24.0433	−	13.8814i	0.761077	−	0.439408i
$999$	−4.94934	+	4.94934i	−0.156590	+	0.156590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.409.2	yes	40
7.5	odd	6		546.2.by.b.19.7	✓	40
13.11	odd	12		546.2.by.b.115.7	yes	40
91.89	even	12	inner	546.2.cg.b.271.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.7	✓	40	7.5	odd	6
546.2.by.b.115.7	yes	40	13.11	odd	12
546.2.cg.b.271.2	yes	40	91.89	even	12	inner
546.2.cg.b.409.2	yes	40	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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.445159 + 1.66136i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.60723 - 0.449857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} -1.00000i q^{4} +(-0.445159 + 1.66136i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.60723 - 0.449857i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.859981 - 1.48953i) q^{10} +(1.45759 - 5.43980i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.62078 - 3.22072i) q^{13} +(2.16168 - 1.52549i) q^{14} +(0.445159 + 1.66136i) q^{15} -1.00000 q^{16} +7.65864 q^{17} +(0.258819 + 0.965926i) q^{18} +(-0.350714 + 0.0939735i) q^{19} +(1.66136 + 0.445159i) q^{20} +(-2.48285 + 0.914026i) q^{21} +(2.81585 + 4.87719i) q^{22} +6.34721i q^{23} +(0.965926 + 0.258819i) q^{24} +(1.76819 + 1.02087i) q^{25} +(1.13133 + 3.42346i) q^{26} -1.00000i q^{27} +(-0.449857 + 2.60723i) q^{28} +(3.90529 - 6.76416i) q^{29} +(-1.48953 - 0.859981i) q^{30} +(0.143335 - 0.0384066i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.45759 - 5.43980i) q^{33} +(-5.41548 + 5.41548i) q^{34} +(1.90800 - 4.13127i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-4.94934 - 4.94934i) q^{37} +(0.181543 - 0.314441i) q^{38} +(-0.206724 - 3.59962i) q^{39} +(-1.48953 + 0.859981i) q^{40} +(8.72661 - 2.33829i) q^{41} +(1.10933 - 2.40196i) q^{42} +(-6.41578 + 3.70415i) q^{43} +(-5.43980 - 1.45759i) q^{44} +(1.21620 + 1.21620i) q^{45} +(-4.48816 - 4.48816i) q^{46} +(0.730514 + 0.195741i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(6.59526 + 2.34576i) q^{49} +(-1.97216 + 0.528439i) q^{50} +(6.63258 - 3.82932i) q^{51} +(-3.22072 - 1.62078i) q^{52} +(0.431525 - 0.747424i) q^{53} +(0.707107 + 0.707107i) q^{54} +(8.38858 + 4.84315i) q^{55} +(-1.52549 - 2.16168i) q^{56} +(-0.256740 + 0.256740i) q^{57} +(2.02153 + 7.54443i) q^{58} +(-0.917790 + 0.917790i) q^{59} +(1.66136 - 0.445159i) q^{60} +(-6.74691 - 3.89533i) q^{61} +(-0.0741959 + 0.128511i) q^{62} +(-1.69320 + 2.03300i) q^{63} +1.00000i q^{64} +(4.62926 + 4.12643i) q^{65} +(4.87719 + 2.81585i) q^{66} +(3.22438 + 0.863971i) q^{67} -7.65864i q^{68} +(3.17361 + 5.49685i) q^{69} +(1.57209 + 4.27041i) q^{70} +(-14.4500 - 3.87187i) q^{71} +(0.965926 - 0.258819i) q^{72} +(-2.26342 - 8.44718i) q^{73} +6.99942 q^{74} +2.04173 q^{75} +(0.0939735 + 0.350714i) q^{76} +(-6.24739 + 13.5271i) q^{77} +(2.69149 + 2.39914i) q^{78} +(6.10060 + 10.5665i) q^{79} +(0.445159 - 1.66136i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.51723 + 7.82407i) q^{82} +(-1.17131 - 1.17131i) q^{83} +(0.914026 + 2.48285i) q^{84} +(-3.40931 + 12.7237i) q^{85} +(1.91741 - 7.15588i) q^{86} -7.81057i q^{87} +(4.87719 - 2.81585i) q^{88} +(2.96033 - 2.96033i) q^{89} -1.71996 q^{90} +(-5.67461 + 7.66804i) q^{91} +6.34721 q^{92} +(0.104929 - 0.104929i) q^{93} +(-0.654961 + 0.378142i) q^{94} -0.624494i q^{95} +(0.258819 - 0.965926i) q^{96} +(-0.740288 + 2.76279i) q^{97} +(-6.32225 + 3.00485i) q^{98} +(-3.98221 - 3.98221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more