LMFDB - Embedded newform 546.2.bm.a.205.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(205,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("546.205");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			205.3
Root			$0.809195i$ of defining polynomial
Character	$\chi$	$=$	546.205
Dual form			546.2.bm.a.277.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.53058 + 2.15808i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.53058 + 2.15808i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.343017 - 0.594123i) q^{10} +(3.79686 + 2.19212i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.21637 + 1.62941i) q^{13} +(2.15808 - 1.53058i) q^{14} +(0.594123 - 0.343017i) q^{15} +1.00000 q^{16} -4.06801 q^{17} +(-0.866025 + 0.500000i) q^{18} +(6.21767 - 3.58977i) q^{19} +(-0.594123 - 0.343017i) q^{20} +(2.63424 - 0.246484i) q^{21} +(2.19212 - 3.79686i) q^{22} -1.72422 q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.26468 - 3.92254i) q^{25} +(1.62941 - 3.21637i) q^{26} -1.00000 q^{27} +(-1.53058 - 2.15808i) q^{28} +(-0.181197 - 0.313842i) q^{29} +(-0.343017 - 0.594123i) q^{30} +(-3.49717 + 2.01909i) q^{31} -1.00000i q^{32} +(3.79686 - 2.19212i) q^{33} +4.06801i q^{34} +(0.169096 + 1.80718i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.34603i q^{37} +(-3.58977 - 6.21767i) q^{38} +(3.01929 - 1.97075i) q^{39} +(-0.343017 + 0.594123i) q^{40} +(5.74820 - 3.31872i) q^{41} +(-0.246484 - 2.63424i) q^{42} +(2.41586 - 4.18440i) q^{43} +(-3.79686 - 2.19212i) q^{44} -0.686034i q^{45} +1.72422i q^{46} +(-9.38446 - 5.41812i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.31463 + 6.60625i) q^{49} +(-3.92254 + 2.26468i) q^{50} +(-2.03400 + 3.52300i) q^{51} +(-3.21637 - 1.62941i) q^{52} +(-1.12532 - 1.94912i) q^{53} +1.00000i q^{54} +(1.50387 + 2.60478i) q^{55} +(-2.15808 + 1.53058i) q^{56} -7.17954i q^{57} +(-0.313842 + 0.181197i) q^{58} -2.49491i q^{59} +(-0.594123 + 0.343017i) q^{60} +(4.02471 + 6.97101i) q^{61} +(2.01909 + 3.49717i) q^{62} +(1.10366 - 2.40456i) q^{63} -1.00000 q^{64} +(1.35201 + 2.07134i) q^{65} +(-2.19212 - 3.79686i) q^{66} +(3.32902 + 1.92201i) q^{67} +4.06801 q^{68} +(-0.862111 + 1.49322i) q^{69} +(1.80718 - 0.169096i) q^{70} +(-13.3513 - 7.70839i) q^{71} +(0.866025 - 0.500000i) q^{72} +(10.0106 - 5.77964i) q^{73} +6.34603 q^{74} -4.52936 q^{75} +(-6.21767 + 3.58977i) q^{76} +(1.08064 + 11.5492i) q^{77} +(-1.97075 - 3.01929i) q^{78} +(1.43883 - 2.49213i) q^{79} +(0.594123 + 0.343017i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.31872 - 5.74820i) q^{82} +5.79090i q^{83} +(-2.63424 + 0.246484i) q^{84} +(-2.41690 - 1.39540i) q^{85} +(-4.18440 - 2.41586i) q^{86} -0.362393 q^{87} +(-2.19212 + 3.79686i) q^{88} +8.20017i q^{89} -0.686034 q^{90} +(1.40653 + 9.43513i) q^{91} +1.72422 q^{92} +4.03819i q^{93} +(-5.41812 + 9.38446i) q^{94} +4.92541 q^{95} +(-0.866025 - 0.500000i) q^{96} +(2.62440 + 1.51520i) q^{97} +(6.60625 + 2.31463i) q^{98} -4.38424i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	$ 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) $ 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.00000			−0.500000
$5$	0.594123	+	0.343017i	0.265700	+	0.153402i	0.626932	−	0.779074i	$-0.284310\pi$
$5$	0.594123	+	0.343017i	0.265700	+	0.153402i	−0.361232	+	0.932476i	$0.617644\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	1.53058	+	2.15808i	0.578506	+	0.815678i
$7$	1.53058	+	2.15808i	0.578506	+	0.815678i
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.343017	−	0.594123i	0.108472	−	0.187878i
$11$	3.79686	+	2.19212i	1.14480	+	0.660949i	0.947614	−	0.319418i	$-0.103487\pi$
$11$	3.79686	+	2.19212i	1.14480	+	0.660949i	0.197183	+	0.980367i	$0.436821\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	3.21637	+	1.62941i	0.892060	+	0.451916i
$13$	3.21637	+	1.62941i	0.892060	+	0.451916i
$14$	2.15808	−	1.53058i	0.576771	−	0.409066i
$15$	0.594123	−	0.343017i	0.153402	−	0.0885667i
$16$	1.00000			0.250000
$17$	−4.06801			−0.986637			−0.493319	−	0.869849i	$-0.664216\pi$
$17$	−4.06801			−0.986637			−0.493319	+	0.869849i	$0.664216\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	6.21767	−	3.58977i	1.42643	−	0.823550i	0.429593	−	0.903022i	$-0.358657\pi$
$19$	6.21767	−	3.58977i	1.42643	−	0.823550i	0.996837	+	0.0794724i	$0.0253235\pi$
$20$	−0.594123	−	0.343017i	−0.132850	−	0.0767010i
$21$	2.63424	−	0.246484i	0.574839	−	0.0537872i
$22$	2.19212	−	3.79686i	0.467361	−	0.809493i
$23$	−1.72422			−0.359525			−0.179762	−	0.983710i	$-0.557533\pi$
$23$	−1.72422			−0.359525			−0.179762	+	0.983710i	$0.557533\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$	−2.26468	−	3.92254i	−0.452936	−	0.784508i
$26$	1.62941	−	3.21637i	0.319553	−	0.630782i
$27$	−1.00000			−0.192450
$28$	−1.53058	−	2.15808i	−0.289253	−	0.407839i
$29$	−0.181197	−	0.313842i	−0.0336474	−	0.0582789i	0.848711	−	0.528856i	$-0.177379\pi$
$29$	−0.181197	−	0.313842i	−0.0336474	−	0.0582789i	−0.882359	+	0.470577i	$0.844046\pi$
$30$	−0.343017	−	0.594123i	−0.0626261	−	0.108472i
$31$	−3.49717	+	2.01909i	−0.628111	+	0.362640i	−0.780020	−	0.625755i	$-0.784791\pi$
$31$	−3.49717	+	2.01909i	−0.628111	+	0.362640i	0.151909	+	0.988394i	$0.451458\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.79686	−	2.19212i	0.660949	−	0.381599i
$34$			4.06801i			0.697658i
$35$	0.169096	+	1.80718i	0.0285825	+	0.305470i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			6.34603i			1.04328i	0.853165	+	0.521641i	$0.174680\pi$
$37$			6.34603i			1.04328i	−0.853165	+	0.521641i	$0.825320\pi$
$38$	−3.58977	−	6.21767i	−0.582338	−	1.00864i
$39$	3.01929	−	1.97075i	0.483474	−	0.315573i
$40$	−0.343017	+	0.594123i	−0.0542358	+	0.0939391i
$41$	5.74820	−	3.31872i	0.897718	−	0.518298i	0.0212588	−	0.999774i	$-0.493233\pi$
$41$	5.74820	−	3.31872i	0.897718	−	0.518298i	0.876459	+	0.481476i	$0.159899\pi$
$42$	−0.246484	−	2.63424i	−0.0380333	−	0.406473i
$43$	2.41586	−	4.18440i	0.368416	−	0.638115i	−0.620902	−	0.783888i	$-0.713234\pi$
$43$	2.41586	−	4.18440i	0.368416	−	0.638115i	0.989318	+	0.145773i	$0.0465669\pi$
$44$	−3.79686	−	2.19212i	−0.572398	−	0.330474i
$45$		−	0.686034i		−	0.102268i
$46$			1.72422i			0.254223i
$47$	−9.38446	−	5.41812i	−1.36886	−	0.790314i	−0.378082	−	0.925772i	$-0.623416\pi$
$47$	−9.38446	−	5.41812i	−1.36886	−	0.790314i	−0.990783	+	0.135458i	$0.956749\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.31463	+	6.60625i	−0.330661	+	0.943750i
$50$	−3.92254	+	2.26468i	−0.554731	+	0.320274i
$51$	−2.03400	+	3.52300i	−0.284818	+	0.493319i
$52$	−3.21637	−	1.62941i	−0.446030	−	0.225958i
$53$	−1.12532	−	1.94912i	−0.154575	−	0.267732i	0.778329	−	0.627856i	$-0.216067\pi$
$53$	−1.12532	−	1.94912i	−0.154575	−	0.267732i	−0.932904	+	0.360125i	$0.882734\pi$
$54$			1.00000i			0.136083i
$55$	1.50387	+	2.60478i	0.202782	+	0.351228i
$56$	−2.15808	+	1.53058i	−0.288386	+	0.204533i
$57$		−	7.17954i		−	0.950954i
$58$	−0.313842	+	0.181197i	−0.0412094	+	0.0237923i
$59$		−	2.49491i		−	0.324809i	−0.986724	−	0.162405i	$-0.948075\pi$
$59$		−	2.49491i		−	0.324809i	0.986724	−	0.162405i	$-0.0519250\pi$
$60$	−0.594123	+	0.343017i	−0.0767010	+	0.0442833i
$61$	4.02471	+	6.97101i	0.515312	+	0.892546i	0.999842	+	0.0177716i	$0.00565717\pi$
$61$	4.02471	+	6.97101i	0.515312	+	0.892546i	−0.484530	+	0.874774i	$0.661009\pi$
$62$	2.01909	+	3.49717i	0.256425	+	0.444141i
$63$	1.10366	−	2.40456i	0.139048	−	0.302947i
$64$	−1.00000			−0.125000
$65$	1.35201	+	2.07134i	0.167696	+	0.256918i
$66$	−2.19212	−	3.79686i	−0.269831	−	0.467361i
$67$	3.32902	+	1.92201i	0.406704	+	0.234811i	0.689373	−	0.724407i	$-0.257886\pi$
$67$	3.32902	+	1.92201i	0.406704	+	0.234811i	−0.282668	+	0.959218i	$0.591220\pi$
$68$	4.06801			0.493319
$69$	−0.862111	+	1.49322i	−0.103786	+	0.179762i
$70$	1.80718	−	0.169096i	0.216000	−	0.0202109i
$71$	−13.3513	−	7.70839i	−1.58451	−	0.914817i	−0.994189	−	0.107649i	$-0.965668\pi$
$71$	−13.3513	−	7.70839i	−1.58451	−	0.914817i	−0.590321	−	0.807169i	$-0.700999\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	10.0106	−	5.77964i	1.17166	−	0.676455i	0.217586	−	0.976041i	$-0.430182\pi$
$73$	10.0106	−	5.77964i	1.17166	−	0.676455i	0.954069	+	0.299586i	$0.0968485\pi$
$74$	6.34603			0.737711
$75$	−4.52936			−0.523005
$76$	−6.21767	+	3.58977i	−0.713215	+	0.411775i
$77$	1.08064	+	11.5492i	0.123151	+	1.31615i
$78$	−1.97075	−	3.01929i	−0.223144	−	0.341868i
$79$	1.43883	−	2.49213i	0.161881	−	0.280386i	−0.773662	−	0.633598i	$-0.781577\pi$
$79$	1.43883	−	2.49213i	0.161881	−	0.280386i	0.935543	+	0.353212i	$0.114911\pi$
$80$	0.594123	+	0.343017i	0.0664250	+	0.0383505i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.31872	−	5.74820i	−0.366492	−	0.634782i
$83$			5.79090i			0.635634i	0.948152	+	0.317817i	$0.102950\pi$
$83$			5.79090i			0.635634i	−0.948152	+	0.317817i	$0.897050\pi$
$84$	−2.63424	+	0.246484i	−0.287420	+	0.0268936i
$85$	−2.41690	−	1.39540i	−0.262149	−	0.151352i
$86$	−4.18440	−	2.41586i	−0.451215	−	0.260509i
$87$	−0.362393			−0.0388526
$88$	−2.19212	+	3.79686i	−0.233681	+	0.404747i
$89$			8.20017i			0.869217i	0.900620	+	0.434608i	$0.143113\pi$
$89$			8.20017i			0.869217i	−0.900620	+	0.434608i	$0.856887\pi$
$90$	−0.686034			−0.0723144
$91$	1.40653	+	9.43513i	0.147445	+	0.989070i
$92$	1.72422			0.179762
$93$			4.03819i			0.418740i
$94$	−5.41812	+	9.38446i	−0.558837	+	0.967934i
$95$	4.92541			0.505337
$96$	−0.866025	−	0.500000i	−0.0883883	−	0.0510310i
$97$	2.62440	+	1.51520i	0.266467	+	0.153845i	0.627281	−	0.778793i	$-0.284168\pi$
$97$	2.62440	+	1.51520i	0.266467	+	0.153845i	−0.360814	+	0.932638i	$0.617501\pi$
$98$	6.60625	+	2.31463i	0.667332	+	0.233813i
$99$		−	4.38424i		−	0.440632i
$100$	2.26468	+	3.92254i	0.226468	+	0.392254i
$101$	6.95193	−	12.0411i	0.691742	−	1.19813i	−0.279524	−	0.960139i	$-0.590177\pi$
$101$	6.95193	−	12.0411i	0.691742	−	1.19813i	0.971267	−	0.237994i	$-0.0764900\pi$
$102$	3.52300	+	2.03400i	0.348829	+	0.201396i
$103$	−6.46334	+	11.1948i	−0.636852	+	1.10306i	0.349267	+	0.937023i	$0.386431\pi$
$103$	−6.46334	+	11.1948i	−0.636852	+	1.10306i	−0.986119	+	0.166037i	$0.946903\pi$
$104$	−1.62941	+	3.21637i	−0.159776	+	0.315391i
$105$	1.64961	+	0.757149i	0.160986	+	0.0738902i
$106$	−1.94912	+	1.12532i	−0.189315	+	0.109301i
$107$	−18.0794			−1.74780			−0.873900	−	0.486105i	$-0.838417\pi$
$107$	−18.0794			−1.74780			−0.873900	+	0.486105i	$0.838417\pi$
$108$	1.00000			0.0962250
$109$	−5.76738	+	3.32980i	−0.552415	+	0.318937i	−0.750095	−	0.661330i	$-0.769992\pi$
$109$	−5.76738	+	3.32980i	−0.552415	+	0.318937i	0.197681	+	0.980266i	$0.436659\pi$
$110$	2.60478	−	1.50387i	0.248356	−	0.143388i
$111$	5.49583	+	3.17302i	0.521641	+	0.301169i
$112$	1.53058	+	2.15808i	0.144627	+	0.203919i
$113$	−0.0153188	+	0.0265329i	−0.00144107	+	0.00249601i	−0.866745	−	0.498751i	$-0.833792\pi$
$113$	−0.0153188	+	0.0265329i	−0.00144107	+	0.00249601i	0.865304	+	0.501247i	$0.167125\pi$
$114$	−7.17954			−0.672426
$115$	−1.02440	−	0.591438i	−0.0955258	−	0.0551518i
$116$	0.181197	+	0.313842i	0.0168237	+	0.0291395i
$117$	−0.197077	−	3.60016i	−0.0182198	−	0.332835i
$118$	−2.49491			−0.229675
$119$	−6.22643	−	8.77909i	−0.570776	−	0.804778i
$120$	0.343017	+	0.594123i	0.0313130	+	0.0542358i
$121$	4.11077	+	7.12006i	0.373706	+	0.647278i
$122$	6.97101	−	4.02471i	0.631125	−	0.364380i
$123$		−	6.63745i		−	0.598479i
$124$	3.49717	−	2.01909i	0.314055	−	0.181320i
$125$		−	6.53747i		−	0.584729i
$126$	−2.40456	−	1.10366i	−0.214216	−	0.0983219i
$127$	5.01071	+	8.67881i	0.444629	+	0.770120i	0.998026	−	0.0627977i	$-0.0200023\pi$
$127$	5.01071	+	8.67881i	0.444629	+	0.770120i	−0.553398	+	0.832917i	$0.686669\pi$
$128$			1.00000i			0.0883883i
$129$	−2.41586	−	4.18440i	−0.212705	−	0.368416i
$130$	2.07134	−	1.35201i	0.181668	−	0.118579i
$131$	−2.28496	+	3.95767i	−0.199638	+	0.345783i	−0.948411	−	0.317043i	$-0.897310\pi$
$131$	−2.28496	+	3.95767i	−0.199638	+	0.345783i	0.748773	+	0.662826i	$0.230643\pi$
$132$	−3.79686	+	2.19212i	−0.330474	+	0.190799i
$133$	17.2637	+	7.92378i	1.49695	+	0.687079i
$134$	1.92201	−	3.32902i	0.166036	−	0.287583i
$135$	−0.594123	−	0.343017i	−0.0511340	−	0.0295222i
$136$		−	4.06801i		−	0.348829i
$137$		−	2.31020i		−	0.197373i	−0.995119	−	0.0986867i	$-0.968536\pi$
$137$		−	2.31020i		−	0.197373i	0.995119	−	0.0986867i	$-0.0314642\pi$
$138$	1.49322	+	0.862111i	0.127111	+	0.0733877i
$139$	6.87474	−	11.9074i	0.583108	−	1.00997i	−0.412000	−	0.911184i	$-0.635170\pi$
$139$	6.87474	−	11.9074i	0.583108	−	1.00997i	0.995108	−	0.0987892i	$-0.0314969\pi$
$140$	−0.169096	−	1.80718i	−0.0142913	−	0.152735i
$141$	−9.38446	+	5.41812i	−0.790314	+	0.456288i
$142$	−7.70839	+	13.3513i	−0.646873	+	1.12042i
$143$	8.64025	+	13.2373i	0.722534	+	1.10696i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		−	0.248614i		−	0.0206463i
$146$	−5.77964	−	10.0106i	−0.478326	−	0.828485i
$147$	4.56386	+	5.30765i	0.376421	+	0.437768i
$148$		−	6.34603i		−	0.521641i
$149$	0.105786	−	0.0610758i	0.00866636	−	0.00500353i	−0.495661	−	0.868516i	$-0.665074\pi$
$149$	0.105786	−	0.0610758i	0.00866636	−	0.00500353i	0.504327	+	0.863513i	$0.331741\pi$
$150$			4.52936i			0.369820i
$151$	−19.1419	+	11.0516i	−1.55775	+	0.899367i	−0.560276	+	0.828306i	$0.689305\pi$
$151$	−19.1419	+	11.0516i	−1.55775	+	0.899367i	−0.997472	+	0.0710609i	$0.977362\pi$
$152$	3.58977	+	6.21767i	0.291169	+	0.504319i
$153$	2.03400	+	3.52300i	0.164440	+	0.284818i
$154$	11.5492	−	1.08064i	0.930657	−	0.0870808i
$155$	−2.77034			−0.222519
$156$	−3.01929	+	1.97075i	−0.241737	+	0.157787i
$157$	−6.93082	−	12.0045i	−0.553140	−	0.958066i	−0.998046	−	0.0624887i	$-0.980096\pi$
$157$	−6.93082	−	12.0045i	−0.553140	−	0.958066i	0.444906	−	0.895577i	$-0.353237\pi$
$158$	−2.49213	−	1.43883i	−0.198263	−	0.114467i
$159$	−2.25064			−0.178488
$160$	0.343017	−	0.594123i	0.0271179	−	0.0469696i
$161$	−2.63907	−	3.72101i	−0.207987	−	0.293257i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−15.8399	+	9.14518i	−1.24068	+	0.716305i	−0.969232	−	0.246148i	$-0.920835\pi$
$163$	−15.8399	+	9.14518i	−1.24068	+	0.716305i	−0.271445	+	0.962454i	$0.587502\pi$
$164$	−5.74820	+	3.31872i	−0.448859	+	0.259149i
$165$	3.00774			0.234152
$166$	5.79090			0.449461
$167$	−6.42363	+	3.70869i	−0.497076	+	0.286987i	−0.727505	−	0.686102i	$-0.759320\pi$
$167$	−6.42363	+	3.70869i	−0.497076	+	0.286987i	0.230429	+	0.973089i	$0.425987\pi$
$168$	0.246484	+	2.63424i	0.0190167	+	0.203236i
$169$	7.69007	+	10.4815i	0.591544	+	0.806273i
$170$	−1.39540	+	2.41690i	−0.107022	+	0.185368i
$171$	−6.21767	−	3.58977i	−0.475477	−	0.274517i
$172$	−2.41586	+	4.18440i	−0.184208	+	0.319058i
$173$	11.3175	+	19.6025i	0.860454	+	1.49035i	0.871492	+	0.490411i	$0.163153\pi$
$173$	11.3175	+	19.6025i	0.860454	+	1.49035i	−0.0110378	+	0.999939i	$0.503514\pi$
$174$			0.362393i			0.0274730i
$175$	4.99887	−	10.8911i	0.377879	−	0.823292i
$176$	3.79686	+	2.19212i	0.286199	+	0.165237i
$177$	−2.16065	−	1.24745i	−0.162405	−	0.0937644i
$178$	8.20017			0.614629
$179$	−2.04347	+	3.53940i	−0.152736	+	0.264547i	−0.932232	−	0.361860i	$-0.882142\pi$
$179$	−2.04347	+	3.53940i	−0.152736	+	0.264547i	0.779496	+	0.626407i	$0.215475\pi$
$180$			0.686034i			0.0511340i
$181$	3.18758			0.236931			0.118465	−	0.992958i	$-0.462203\pi$
$181$	3.18758			0.236931			0.118465	+	0.992958i	$0.462203\pi$
$182$	9.43513	−	1.40653i	0.699378	−	0.104259i
$183$	8.04943			0.595031
$184$		−	1.72422i		−	0.127111i
$185$	−2.17680	+	3.77033i	−0.160041	+	0.277200i
$186$	4.03819			0.296094
$187$	−15.4457	−	8.91756i	−1.12950	−	0.652116i
$188$	9.38446	+	5.41812i	0.684432	+	0.395157i
$189$	−1.53058	−	2.15808i	−0.111334	−	0.156977i
$190$		−	4.92541i		−	0.357327i
$191$	−5.62428	−	9.74154i	−0.406959	−	0.704873i	0.587589	−	0.809160i	$-0.300077\pi$
$191$	−5.62428	−	9.74154i	−0.406959	−	0.704873i	−0.994547	+	0.104287i	$0.966744\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−11.5544	−	6.67096i	−0.831707	−	0.480187i	0.0227295	−	0.999742i	$-0.492764\pi$
$193$	−11.5544	−	6.67096i	−0.831707	−	0.480187i	−0.854437	+	0.519555i	$0.826098\pi$
$194$	1.51520	−	2.62440i	0.108785	−	0.188421i
$195$	2.46983	−	0.135202i	0.176869	−	0.00968199i
$196$	2.31463	−	6.60625i	0.165330	−	0.471875i
$197$	−16.9510	+	9.78669i	−1.20771	+	0.697273i	−0.962259	−	0.272136i	$-0.912270\pi$
$197$	−16.9510	+	9.78669i	−1.20771	+	0.697273i	−0.245453	+	0.969409i	$0.578937\pi$
$198$	−4.38424			−0.311574
$199$	−4.33018			−0.306958			−0.153479	−	0.988152i	$-0.549048\pi$
$199$	−4.33018			−0.306958			−0.153479	+	0.988152i	$0.549048\pi$
$200$	3.92254	−	2.26468i	0.277365	−	0.160137i
$201$	3.32902	−	1.92201i	0.234811	−	0.135568i
$202$	−12.0411	−	6.95193i	−0.847208	−	0.489136i
$203$	0.399959	−	0.871398i	0.0280716	−	0.0611601i
$204$	2.03400	−	3.52300i	0.142409	−	0.246659i
$205$	4.55352			0.318032
$206$	11.1948	+	6.46334i	0.779982	+	0.450323i
$207$	0.862111	+	1.49322i	0.0599208	+	0.103786i
$208$	3.21637	+	1.62941i	0.223015	+	0.112979i
$209$	31.4768			2.17730
$210$	0.757149	−	1.64961i	0.0522483	−	0.113834i
$211$	−14.1589	−	24.5240i	−0.974741	−	1.68830i	−0.680786	−	0.732483i	$-0.738361\pi$
$211$	−14.1589	−	24.5240i	−0.974741	−	1.68830i	−0.293956	−	0.955819i	$-0.594972\pi$
$212$	1.12532	+	1.94912i	0.0772875	+	0.133866i
$213$	−13.3513	+	7.70839i	−0.914817	+	0.528170i
$214$			18.0794i			1.23588i
$215$	2.87064	−	1.65737i	0.195776	−	0.113031i
$216$		−	1.00000i		−	0.0680414i
$217$	−9.71008	−	4.45679i	−0.659163	−	0.302547i
$218$	3.32980	+	5.76738i	0.225522	+	0.390616i
$219$		−	11.5593i		−	0.781103i
$220$	−1.50387	−	2.60478i	−0.101391	−	0.175614i
$221$	−13.0842	−	6.62844i	−0.880140	−	0.445877i
$222$	3.17302	−	5.49583i	0.212959	−	0.368856i
$223$	17.2662	−	9.96863i	1.15623	−	0.667549i	0.205831	−	0.978588i	$-0.434010\pi$
$223$	17.2662	−	9.96863i	1.15623	−	0.667549i	0.950397	+	0.311039i	$0.100677\pi$
$224$	2.15808	−	1.53058i	0.144193	−	0.102266i
$225$	−2.26468	+	3.92254i	−0.150979	+	0.261503i
$226$	0.0265329	+	0.0153188i	0.00176494	+	0.00101899i
$227$		−	29.6981i		−	1.97113i	−0.169292	−	0.985566i	$-0.554148\pi$
$227$		−	29.6981i		−	1.97113i	0.169292	−	0.985566i	$-0.445852\pi$
$228$			7.17954i			0.475477i
$229$	−12.7224	−	7.34527i	−0.840719	−	0.485389i	0.0167896	−	0.999859i	$-0.494655\pi$
$229$	−12.7224	−	7.34527i	−0.840719	−	0.485389i	−0.857509	+	0.514470i	$0.827989\pi$
$230$	−0.591438	+	1.02440i	−0.0389982	+	0.0675469i
$231$	10.5422	+	4.83871i	0.693625	+	0.318364i
$232$	0.313842	−	0.181197i	0.0206047	−	0.0118961i
$233$	−8.21697	+	14.2322i	−0.538312	+	0.932383i	0.460683	+	0.887564i	$0.347604\pi$
$233$	−8.21697	+	14.2322i	−0.538312	+	0.932383i	−0.998995	+	0.0448186i	$0.985729\pi$
$234$	−3.60016	+	0.197077i	−0.235350	+	0.0128833i
$235$	−3.71702	−	6.43806i	−0.242472	−	0.419973i
$236$			2.49491i			0.162405i
$237$	−1.43883	−	2.49213i	−0.0934621	−	0.161881i
$238$	−8.77909	+	6.22643i	−0.569064	+	0.403599i
$239$		−	13.9983i		−	0.905473i	−0.891644	−	0.452737i	$-0.850448\pi$
$239$		−	13.9983i		−	0.905473i	0.891644	−	0.452737i	$-0.149552\pi$
$240$	0.594123	−	0.343017i	0.0383505	−	0.0221417i
$241$		−	11.4835i		−	0.739719i	−0.929088	−	0.369860i	$-0.879406\pi$
$241$		−	11.4835i		−	0.739719i	0.929088	−	0.369860i	$-0.120594\pi$
$242$	7.12006	−	4.11077i	0.457695	−	0.264250i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−4.02471	−	6.97101i	−0.257656	−	0.446273i
$245$	−3.64123	+	3.13097i	−0.232630	+	0.200030i
$246$	−6.63745			−0.423188
$247$	25.8475	−	1.41492i	1.64464	−	0.0900294i
$248$	−2.01909	−	3.49717i	−0.128213	−	0.222071i
$249$	5.01506	+	2.89545i	0.317817	+	0.183492i
$250$	−6.53747			−0.413466
$251$	−6.11401	+	10.5898i	−0.385913	+	0.668420i	−0.991895	−	0.127058i	$-0.959447\pi$
$251$	−6.11401	+	10.5898i	−0.385913	+	0.668420i	0.605983	+	0.795478i	$0.292780\pi$
$252$	−1.10366	+	2.40456i	−0.0695241	+	0.151473i
$253$	−6.54663	−	3.77970i	−0.411583	−	0.237628i
$254$	8.67881	−	5.01071i	0.544557	−	0.314400i
$255$	−2.41690	+	1.39540i	−0.151352	+	0.0873832i
$256$	1.00000			0.0625000
$257$	23.4220			1.46102			0.730512	−	0.682900i	$-0.239281\pi$
$257$	23.4220			1.46102			0.730512	+	0.682900i	$0.239281\pi$
$258$	−4.18440	+	2.41586i	−0.260509	+	0.150405i
$259$	−13.6953	+	9.71313i	−0.850982	+	0.603545i
$260$	−1.35201	−	2.07134i	−0.0838478	−	0.128459i
$261$	−0.181197	+	0.313842i	−0.0112158	+	0.0194263i
$262$	3.95767	+	2.28496i	0.244505	+	0.141165i
$263$	−1.14684	+	1.98638i	−0.0707169	+	0.122485i	−0.899216	−	0.437506i	$-0.855862\pi$
$263$	−1.14684	+	1.98638i	−0.0707169	+	0.122485i	0.828499	+	0.559991i	$0.189195\pi$
$264$	2.19212	+	3.79686i	0.134916	+	0.233681i
$265$		−	1.54402i		−	0.0948484i
$266$	7.92378	−	17.2637i	0.485838	−	1.05850i
$267$	7.10156	+	4.10009i	0.434608	+	0.250921i
$268$	−3.32902	−	1.92201i	−0.203352	−	0.117405i
$269$	5.36522			0.327123			0.163562	−	0.986533i	$-0.447702\pi$
$269$	5.36522			0.327123			0.163562	+	0.986533i	$0.447702\pi$
$270$	−0.343017	+	0.594123i	−0.0208754	+	0.0361572i
$271$		−	0.842015i		−	0.0511488i	−0.999673	−	0.0255744i	$-0.991859\pi$
$271$		−	0.842015i		−	0.0511488i	0.999673	−	0.0255744i	$-0.00814147\pi$
$272$	−4.06801			−0.246659
$273$	8.87433	+	3.49947i	0.537099	+	0.211798i
$274$	−2.31020			−0.139564
$275$		−	19.8578i		−	1.19747i
$276$	0.862111	−	1.49322i	0.0518930	−	0.0898812i
$277$	14.3824			0.864154			0.432077	−	0.901837i	$-0.357781\pi$
$277$	14.3824			0.864154			0.432077	+	0.901837i	$0.357781\pi$
$278$	−11.9074	−	6.87474i	−0.714159	−	0.412320i
$279$	3.49717	+	2.01909i	0.209370	+	0.120880i
$280$	−1.80718	+	0.169096i	−0.108000	+	0.0101054i
$281$			2.03385i			0.121330i	0.998158	+	0.0606648i	$0.0193221\pi$
$281$			2.03385i			0.121330i	−0.998158	+	0.0606648i	$0.980678\pi$
$282$	5.41812	+	9.38446i	0.322645	+	0.558837i
$283$	16.1760	−	28.0177i	0.961566	−	1.66548i	0.242993	−	0.970028i	$-0.421871\pi$
$283$	16.1760	−	28.0177i	0.961566	−	1.66548i	0.718572	−	0.695452i	$-0.244796\pi$
$284$	13.3513	+	7.70839i	0.792255	+	0.457409i
$285$	2.46271	−	4.26553i	0.145878	−	0.252668i
$286$	13.2373	−	8.64025i	0.782738	−	0.510909i
$287$	15.9602	+	7.32549i	0.942099	+	0.432410i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−0.451300			−0.0265471
$290$	−0.248614			−0.0145991
$291$	2.62440	−	1.51520i	0.153845	−	0.0888224i
$292$	−10.0106	+	5.77964i	−0.585828	+	0.338228i
$293$	17.9647	+	10.3719i	1.04951	+	0.605933i	0.922511	−	0.385971i	$-0.126133\pi$
$293$	17.9647	+	10.3719i	1.04951	+	0.605933i	0.126995	+	0.991903i	$0.459467\pi$
$294$	5.30765	−	4.56386i	0.309548	−	0.266170i
$295$	0.855796	−	1.48228i	0.0498264	−	0.0863018i
$296$	−6.34603			−0.368856
$297$	−3.79686	−	2.19212i	−0.220316	−	0.127200i
$298$	−0.0610758	−	0.105786i	−0.00353803	−	0.00612804i
$299$	−5.54573	−	2.80946i	−0.320718	−	0.162475i
$300$	4.52936			0.261503
$301$	12.7280	−	1.19094i	0.733627	−	0.0686449i
$302$	11.0516	+	19.1419i	0.635948	+	1.10149i
$303$	−6.95193	−	12.0411i	−0.399378	−	0.691742i
$304$	6.21767	−	3.58977i	0.356608	−	0.205888i
$305$			5.52218i			0.316199i
$306$	3.52300	−	2.03400i	0.201396	−	0.116276i
$307$		−	3.66321i		−	0.209070i	−0.994521	−	0.104535i	$-0.966665\pi$
$307$		−	3.66321i		−	0.209070i	0.994521	−	0.104535i	$-0.0333355\pi$
$308$	−1.08064	−	11.5492i	−0.0615754	−	0.658074i
$309$	6.46334	+	11.1948i	0.367687	+	0.636852i
$310$			2.77034i			0.157344i
$311$	0.833909	+	1.44437i	0.0472867	+	0.0819029i	0.888700	−	0.458489i	$-0.151609\pi$
$311$	0.833909	+	1.44437i	0.0472867	+	0.0819029i	−0.841413	+	0.540392i	$0.818276\pi$
$312$	1.97075	+	3.01929i	0.111572	+	0.170934i
$313$	2.83514	−	4.91060i	0.160251	−	0.277564i	−0.774707	−	0.632320i	$-0.782103\pi$
$313$	2.83514	−	4.91060i	0.160251	−	0.277564i	0.934959	+	0.354756i	$0.115436\pi$
$314$	−12.0045	+	6.93082i	−0.677455	+	0.391129i
$315$	1.48052	−	1.05003i	0.0834177	−	0.0591627i
$316$	−1.43883	+	2.49213i	−0.0809406	+	0.140193i
$317$	−27.3539	−	15.7928i	−1.53635	−	0.887012i	−0.999048	−	0.0436211i	$-0.986111\pi$
$317$	−27.3539	−	15.7928i	−1.53635	−	0.887012i	−0.537301	−	0.843391i	$-0.680556\pi$
$318$			2.25064i			0.126210i
$319$		−	1.58882i		−	0.0889567i
$320$	−0.594123	−	0.343017i	−0.0332125	−	0.0191752i
$321$	−9.03970	+	15.6572i	−0.504547	+	0.873900i
$322$	−3.72101	+	2.63907i	−0.207364	+	0.147069i
$323$	−25.2935	+	14.6032i	−1.40737	+	0.812545i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−0.892632	−	16.3064i	−0.0495143	−	0.904517i
$326$	9.14518	+	15.8399i	0.506504	+	0.877291i
$327$			6.65959i			0.368276i
$328$	3.31872	+	5.74820i	0.183246	+	0.317391i
$329$	−2.67096	−	28.5453i	−0.147255	−	1.57375i
$330$		−	3.00774i		−	0.165570i
$331$	22.5373	−	13.0119i	1.23876	−	0.715199i	0.269920	−	0.962883i	$-0.413003\pi$
$331$	22.5373	−	13.0119i	1.23876	−	0.715199i	0.968841	+	0.247684i	$0.0796695\pi$
$332$		−	5.79090i		−	0.317817i
$333$	5.49583	−	3.17302i	0.301169	−	0.173880i
$334$	3.70869	+	6.42363i	0.202930	+	0.351486i
$335$	1.31857	+	2.28382i	0.0720409	+	0.124779i
$336$	2.63424	−	0.246484i	0.143710	−	0.0134468i
$337$	−17.9060			−0.975404			−0.487702	−	0.873010i	$-0.662165\pi$
$337$	−17.9060			−0.975404			−0.487702	+	0.873010i	$0.662165\pi$
$338$	10.4815	−	7.69007i	0.570121	−	0.418284i
$339$	0.0153188	+	0.0265329i	0.000832003	+	0.00144107i
$340$	2.41690	+	1.39540i	0.131075	+	0.0756760i
$341$	−17.7044			−0.958745
$342$	−3.58977	+	6.21767i	−0.194113	+	0.336213i
$343$	−17.7995	+	5.11626i	−0.961085	+	0.276252i
$344$	4.18440	+	2.41586i	0.225608	+	0.130255i
$345$	−1.02440	+	0.591438i	−0.0551518	+	0.0318419i
$346$	19.6025	−	11.3175i	1.05384	−	0.608433i
$347$	−29.8776			−1.60391			−0.801956	−	0.597384i	$-0.796207\pi$
$347$	−29.8776			−1.60391			−0.801956	+	0.597384i	$0.796207\pi$
$348$	0.362393			0.0194263
$349$	0.374845	−	0.216417i	0.0200650	−	0.0115845i	−0.489934	−	0.871760i	$-0.662979\pi$
$349$	0.374845	−	0.216417i	0.0200650	−	0.0115845i	0.509999	+	0.860175i	$0.329646\pi$
$350$	−10.8911	−	4.99887i	−0.582156	−	0.267201i
$351$	−3.21637	−	1.62941i	−0.171677	−	0.0869713i
$352$	2.19212	−	3.79686i	0.116840	−	0.202373i
$353$	0.633978	+	0.366028i	0.0337433	+	0.0194817i	0.516777	−	0.856120i	$-0.327132\pi$
$353$	0.633978	+	0.366028i	0.0337433	+	0.0194817i	−0.483033	+	0.875602i	$0.660465\pi$
$354$	−1.24745	+	2.16065i	−0.0663014	+	0.114837i
$355$	−5.28822	−	9.15946i	−0.280670	−	0.486134i
$356$		−	8.20017i		−	0.434608i
$357$	−10.7161	+	1.00270i	−0.567158	+	0.0530685i
$358$	3.53940	+	2.04347i	0.187063	+	0.108001i
$359$	21.3122	+	12.3046i	1.12482	+	0.649412i	0.942626	−	0.333851i	$-0.108348\pi$
$359$	21.3122	+	12.3046i	1.12482	+	0.649412i	0.182189	+	0.983263i	$0.441682\pi$
$360$	0.686034			0.0361572
$361$	16.2729	−	28.1855i	0.856469	−	1.48345i
$362$		−	3.18758i		−	0.167535i
$363$	8.22153			0.431519
$364$	−1.40653	−	9.43513i	−0.0737223	−	0.494535i
$365$	7.93006			0.415078
$366$		−	8.04943i		−	0.420750i
$367$	−6.89379	+	11.9404i	−0.359853	+	0.623283i	−0.987936	−	0.154863i	$-0.950506\pi$
$367$	−6.89379	+	11.9404i	−0.359853	+	0.623283i	0.628083	+	0.778146i	$0.283840\pi$
$368$	−1.72422			−0.0898812
$369$	−5.74820	−	3.31872i	−0.299239	−	0.172766i
$370$	3.77033	+	2.17680i	0.196010	+	0.113166i
$371$	2.48395	−	5.41182i	0.128960	−	0.280968i
$372$		−	4.03819i		−	0.209370i
$373$	6.85163	+	11.8674i	0.354764	+	0.614469i	0.987077	−	0.160244i	$-0.0512280\pi$
$373$	6.85163	+	11.8674i	0.354764	+	0.614469i	−0.632314	+	0.774712i	$0.717895\pi$
$374$	−8.91756	+	15.4457i	−0.461116	+	0.798676i
$375$	−5.66161	−	3.26873i	−0.292364	−	0.168797i
$376$	5.41812	−	9.38446i	0.279418	−	0.483967i
$377$	−0.0714193	−	1.30467i	−0.00367828	−	0.0671941i
$378$	−2.15808	+	1.53058i	−0.111000	+	0.0787247i
$379$	24.9433	−	14.4010i	1.28125	−	0.739732i	0.304176	−	0.952616i	$-0.401619\pi$
$379$	24.9433	−	14.4010i	1.28125	−	0.739732i	0.977077	+	0.212884i	$0.0682857\pi$
$380$	−4.92541			−0.252668
$381$	10.0214			0.513413
$382$	−9.74154	+	5.62428i	−0.498420	+	0.287763i
$383$	17.0444	−	9.84060i	0.870929	−	0.502831i	0.00327202	−	0.999995i	$-0.498958\pi$
$383$	17.0444	−	9.84060i	0.870929	−	0.502831i	0.867657	+	0.497164i	$0.165625\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	−3.31952	+	7.23230i	−0.169179	+	0.368592i
$386$	−6.67096	+	11.5544i	−0.339543	+	0.588106i
$387$	−4.83173			−0.245611
$388$	−2.62440	−	1.51520i	−0.133234	−	0.0769225i
$389$	12.0388	+	20.8518i	0.610390	+	1.05723i	0.991175	+	0.132563i	$0.0423206\pi$
$389$	12.0388	+	20.8518i	0.610390	+	1.05723i	−0.380785	+	0.924664i	$0.624346\pi$
$390$	−0.135202	−	2.46983i	−0.00684620	−	0.125065i
$391$	7.01415			0.354721
$392$	−6.60625	−	2.31463i	−0.333666	−	0.116906i
$393$	2.28496	+	3.95767i	0.115261	+	0.199638i
$394$	9.78669	+	16.9510i	0.493046	+	0.853981i
$395$	1.70969	−	0.987088i	0.0860237	−	0.0496658i
$396$			4.38424i			0.220316i
$397$	−23.1989	+	13.3939i	−1.16432	+	0.672220i	−0.952335	−	0.305053i	$-0.901326\pi$
$397$	−23.1989	+	13.3939i	−1.16432	+	0.672220i	−0.211984	+	0.977273i	$0.567993\pi$
$398$			4.33018i			0.217052i
$399$	15.4940	−	10.9889i	0.775672	−	0.550133i
$400$	−2.26468	−	3.92254i	−0.113234	−	0.196127i
$401$		−	28.8528i		−	1.44084i	−0.693539	−	0.720419i	$-0.743950\pi$
$401$		−	28.8528i		−	1.44084i	0.693539	−	0.720419i	$-0.256050\pi$
$402$	−1.92201	−	3.32902i	−0.0958612	−	0.166036i
$403$	−14.5381	+	0.795834i	−0.724196	+	0.0396433i
$404$	−6.95193	+	12.0411i	−0.345871	+	0.599067i
$405$	−0.594123	+	0.343017i	−0.0295222	+	0.0170447i
$406$	−0.871398	−	0.399959i	−0.0432467	−	0.0198496i
$407$	−13.9113	+	24.0950i	−0.689555	+	1.19434i
$408$	−3.52300	−	2.03400i	−0.174414	−	0.100698i
$409$			30.5695i			1.51156i	0.654824	+	0.755781i	$0.272743\pi$
$409$			30.5695i			1.51156i	−0.654824	+	0.755781i	$0.727257\pi$
$410$		−	4.55352i		−	0.224882i
$411$	−2.00069	−	1.15510i	−0.0986867	−	0.0569768i
$412$	6.46334	−	11.1948i	0.318426	−	0.551530i
$413$	5.38421	−	3.81866i	0.264940	−	0.187904i
$414$	1.49322	−	0.862111i	0.0733877	−	0.0423704i
$415$	−1.98638	+	3.44051i	−0.0975074	+	0.168888i
$416$	1.62941	−	3.21637i	0.0798882	−	0.157695i
$417$	−6.87474	−	11.9074i	−0.336658	−	0.583108i
$418$		−	31.4768i		−	1.53958i
$419$	3.83631	+	6.64468i	0.187416	+	0.324614i	0.944388	−	0.328834i	$-0.106656\pi$
$419$	3.83631	+	6.64468i	0.187416	+	0.324614i	−0.756972	+	0.653447i	$0.773322\pi$
$420$	−1.64961	−	0.757149i	−0.0804929	−	0.0369451i
$421$			8.38578i			0.408698i	0.978898	+	0.204349i	$0.0655077\pi$
$421$			8.38578i			0.408698i	−0.978898	+	0.204349i	$0.934492\pi$
$422$	−24.5240	+	14.1589i	−1.19381	+	0.689246i
$423$			10.8362i			0.526876i
$424$	1.94912	−	1.12532i	0.0946574	−	0.0546505i
$425$	9.21273	+	15.9569i	0.446883	+	0.774024i
$426$	7.70839	+	13.3513i	0.373473	+	0.646873i
$427$	−8.88384	+	19.3554i	−0.429919	+	0.936672i
$428$	18.0794			0.873900
$429$	15.7840	−	0.864032i	0.762057	−	0.0417159i
$430$	−1.65737	−	2.87064i	−0.0799253	−	0.138435i
$431$	−2.81608	−	1.62587i	−0.135646	−	0.0783152i	0.430641	−	0.902523i	$-0.358287\pi$
$431$	−2.81608	−	1.62587i	−0.135646	−	0.0783152i	−0.566287	+	0.824208i	$0.691621\pi$
$432$	−1.00000			−0.0481125
$433$	−4.58716	+	7.94520i	−0.220445	+	0.381822i	−0.954943	−	0.296789i	$-0.904084\pi$
$433$	−4.58716	+	7.94520i	−0.220445	+	0.381822i	0.734498	+	0.678611i	$0.237418\pi$
$434$	−4.45679	+	9.71008i	−0.213933	+	0.466099i
$435$	−0.215306	−	0.124307i	−0.0103231	−	0.00596007i
$436$	5.76738	−	3.32980i	0.276207	−	0.159468i
$437$	−10.7206	+	6.18956i	−0.512837	+	0.296087i
$438$	−11.5593			−0.552324
$439$	−23.0178			−1.09858			−0.549290	−	0.835632i	$-0.685102\pi$
$439$	−23.0178			−1.09858			−0.549290	+	0.835632i	$0.685102\pi$
$440$	−2.60478	+	1.50387i	−0.124178	+	0.0716941i
$441$	6.87849	−	1.29860i	0.327547	−	0.0618380i
$442$	−6.62844	+	13.0842i	−0.315283	+	0.622353i
$443$	−13.5354	+	23.4440i	−0.643087	+	1.11386i	0.341653	+	0.939826i	$0.389013\pi$
$443$	−13.5354	+	23.4440i	−0.643087	+	1.11386i	−0.984740	+	0.174033i	$0.944320\pi$
$444$	−5.49583	−	3.17302i	−0.260820	−	0.150585i
$445$	−2.81280	+	4.87191i	−0.133340	+	0.230951i
$446$	−9.96863	−	17.2662i	−0.472028	−	0.817577i
$447$		−	0.122152i		−	0.00577757i
$448$	−1.53058	−	2.15808i	−0.0723133	−	0.101960i
$449$	17.0920	+	9.86807i	0.806621	+	0.465703i	0.845781	−	0.533530i	$-0.179135\pi$
$449$	17.0920	+	9.86807i	0.806621	+	0.465703i	−0.0391598	+	0.999233i	$0.512468\pi$
$450$	3.92254	+	2.26468i	0.184910	+	0.106758i
$451$	29.1001			1.37027
$452$	0.0153188	−	0.0265329i	0.000720536	−	0.00124800i
$453$			22.1032i			1.03850i
$454$	−29.6981			−1.39380
$455$	−2.40076	+	6.08809i	−0.112549	+	0.285414i
$456$	7.17954			0.336213
$457$			14.3935i			0.673298i	0.941630	+	0.336649i	$0.109294\pi$
$457$			14.3935i			0.673298i	−0.941630	+	0.336649i	$0.890706\pi$
$458$	−7.34527	+	12.7224i	−0.343222	+	0.594478i
$459$	4.06801			0.189878
$460$	1.02440	+	0.591438i	0.0477629	+	0.0275759i
$461$	30.6790	+	17.7125i	1.42886	+	0.824955i	0.997031	−	0.0769978i	$-0.0245334\pi$
$461$	30.6790	+	17.7125i	1.42886	+	0.824955i	0.431834	+	0.901953i	$0.357867\pi$
$462$	4.83871	−	10.5422i	0.225117	−	0.490467i
$463$		−	36.1762i		−	1.68125i	−0.541616	−	0.840626i	$-0.682187\pi$
$463$		−	36.1762i		−	1.68125i	0.541616	−	0.840626i	$-0.317813\pi$
$464$	−0.181197	−	0.313842i	−0.00841184	−	0.0145697i
$465$	−1.38517	+	2.39918i	−0.0642356	+	0.111259i
$466$	14.2322	+	8.21697i	0.659294	+	0.380644i
$467$	−17.4517	+	30.2272i	−0.807566	+	1.39875i	0.106979	+	0.994261i	$0.465882\pi$
$467$	−17.4517	+	30.2272i	−0.807566	+	1.39875i	−0.914545	+	0.404484i	$0.867451\pi$
$468$	0.197077	+	3.60016i	0.00910989	+	0.166418i
$469$	0.947489	+	10.1261i	0.0437510	+	0.467579i
$470$	−6.43806	+	3.71702i	−0.296966	+	0.171453i
$471$	−13.8616			−0.638711
$472$	2.49491			0.114837
$473$	18.3454	−	10.5917i	0.843522	−	0.487008i
$474$	−2.49213	+	1.43883i	−0.114467	+	0.0660877i
$475$	−28.1620	−	16.2594i	−1.29216	−	0.746030i
$476$	6.22643	+	8.77909i	0.285388	+	0.402389i
$477$	−1.12532	+	1.94912i	−0.0515250	+	0.0892439i
$478$	−13.9983			−0.640266
$479$	−3.50827	−	2.02550i	−0.160297	−	0.0925474i	0.417706	−	0.908582i	$-0.362834\pi$
$479$	−3.50827	−	2.02550i	−0.160297	−	0.0925474i	−0.578003	+	0.816035i	$0.696168\pi$
$480$	−0.343017	−	0.594123i	−0.0156565	−	0.0271179i
$481$	−10.3403	+	20.4112i	−0.471476	+	0.930670i
$482$	−11.4835			−0.523061
$483$	−4.54202	+	0.424993i	−0.206669	+	0.0193378i
$484$	−4.11077	−	7.12006i	−0.186853	−	0.323639i
$485$	1.03948	+	1.80043i	0.0472002	+	0.0817532i
$486$	0.866025	−	0.500000i	0.0392837	−	0.0226805i
$487$			6.75964i			0.306309i	0.988202	+	0.153154i	$0.0489432\pi$
$487$			6.75964i			0.306309i	−0.988202	+	0.153154i	$0.951057\pi$
$488$	−6.97101	+	4.02471i	−0.315563	+	0.182190i
$489$			18.2904i			0.827118i
$490$	3.13097	+	3.64123i	0.141443	+	0.164494i
$491$	0.789661	+	1.36773i	0.0356369	+	0.0617249i	0.883294	−	0.468820i	$-0.155321\pi$
$491$	0.789661	+	1.36773i	0.0356369	+	0.0617249i	−0.847657	+	0.530545i	$0.821987\pi$
$492$			6.63745i			0.299239i
$493$	0.737109	+	1.27671i	0.0331977	+	0.0575002i
$494$	−1.41492	−	25.8475i	−0.0636604	−	1.16293i
$495$	1.50387	−	2.60478i	0.0675939	−	0.117076i
$496$	−3.49717	+	2.01909i	−0.157028	+	0.0906600i
$497$	−3.79999	−	40.6116i	−0.170453	−	1.82168i
$498$	2.89545	−	5.01506i	0.129748	−	0.224730i
$499$	5.29521	+	3.05719i	0.237046	+	0.136859i	0.613818	−	0.789447i	$-0.289633\pi$
$499$	5.29521	+	3.05719i	0.237046	+	0.136859i	−0.376772	+	0.926306i	$0.622966\pi$
$500$			6.53747i			0.292364i
$501$			7.41737i			0.331384i
$502$	10.5898	+	6.11401i	0.472644	+	0.272881i
$503$	−4.83770	+	8.37914i	−0.215702	+	0.373608i	−0.953490	−	0.301426i	$-0.902537\pi$
$503$	−4.83770	+	8.37914i	−0.215702	+	0.373608i	0.737787	+	0.675033i	$0.235871\pi$
$504$	2.40456	+	1.10366i	0.107108	+	0.0491610i
$505$	8.26060	−	4.76926i	0.367592	−	0.212229i
$506$	−3.77970	+	6.54663i	−0.168028	+	0.291033i
$507$	12.9223	−	1.41902i	0.573900	−	0.0630208i
$508$	−5.01071	−	8.67881i	−0.222314	−	0.385060i
$509$		−	22.0273i		−	0.976342i	−0.872748	−	0.488171i	$-0.837664\pi$
$509$		−	22.0273i		−	0.976342i	0.872748	−	0.488171i	$-0.162336\pi$
$510$	1.39540	+	2.41690i	0.0617892	+	0.107022i
$511$	27.7950	+	12.7575i	1.22958	+	0.564360i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.21767	+	3.58977i	−0.274517	+	0.158492i
$514$		−	23.4220i		−	1.03310i
$515$	−7.68005	+	4.43408i	−0.338423	+	0.195389i
$516$	2.41586	+	4.18440i	0.106353	+	0.184208i
$517$	−23.7543	−	41.1437i	−1.04471	−	1.80950i
$518$	9.71313	+	13.6953i	0.426771	+	0.601735i
$519$	22.6350			0.993566
$520$	−2.07134	+	1.35201i	−0.0908342	+	0.0592894i
$521$	0.146783	+	0.254235i	0.00643067	+	0.0111383i	0.869223	−	0.494421i	$-0.164620\pi$
$521$	0.146783	+	0.254235i	0.00643067	+	0.0111383i	−0.862792	+	0.505559i	$0.831286\pi$
$522$	0.313842	+	0.181197i	0.0137365	+	0.00793076i
$523$	8.85880			0.387368			0.193684	−	0.981064i	$-0.437956\pi$
$523$	8.85880			0.387368			0.193684	+	0.981064i	$0.437956\pi$
$524$	2.28496	−	3.95767i	0.0998189	−	0.172891i
$525$	−6.93256	−	9.77472i	−0.302562	−	0.426604i
$526$	1.98638	+	1.14684i	0.0866101	+	0.0500044i
$527$	14.2265	−	8.21369i	0.619717	−	0.357794i
$528$	3.79686	−	2.19212i	0.165237	−	0.0953997i
$529$	−20.0271			−0.870742
$530$	−1.54402			−0.0670679
$531$	−2.16065	+	1.24745i	−0.0937644	+	0.0541349i
$532$	−17.2637	−	7.92378i	−0.748475	−	0.343539i
$533$	23.8959	−	1.30809i	1.03505	−	0.0566596i
$534$	4.10009	−	7.10156i	0.177428	−	0.307314i
$535$	−10.7414	−	6.20154i	−0.464391	−	0.268116i
$536$	−1.92201	+	3.32902i	−0.0830182	+	0.143792i
$537$	2.04347	+	3.53940i	0.0881823	+	0.152736i
$538$		−	5.36522i		−	0.231311i
$539$	−23.2700	+	20.0091i	−1.00231	+	0.861851i
$540$	0.594123	+	0.343017i	0.0255670	+	0.0147611i
$541$	14.0782	+	8.12802i	0.605267	+	0.349451i	0.771111	−	0.636701i	$-0.219701\pi$
$541$	14.0782	+	8.12802i	0.605267	+	0.349451i	−0.165844	+	0.986152i	$0.553035\pi$
$542$	−0.842015			−0.0361677
$543$	1.59379	−	2.76052i	0.0683961	−	0.118465i
$544$			4.06801i			0.174414i
$545$	−4.56871			−0.195702
$546$	3.49947	−	8.87433i	0.149764	−	0.379786i
$547$	−21.7683			−0.930746			−0.465373	−	0.885115i	$-0.654080\pi$
$547$	−21.7683			−0.930746			−0.465373	+	0.885115i	$0.654080\pi$
$548$			2.31020i			0.0986867i
$549$	4.02471	−	6.97101i	0.171771	−	0.297515i
$550$	−19.8578			−0.846738
$551$	−2.25324	−	1.30091i	−0.0959912	−	0.0554206i
$552$	−1.49322	−	0.862111i	−0.0635556	−	0.0366939i
$553$	7.58047	−	0.709298i	0.322354	−	0.0301624i
$554$		−	14.3824i		−	0.611049i
$555$	2.17680	+	3.77033i	0.0923999	+	0.160041i
$556$	−6.87474	+	11.9074i	−0.291554	+	0.504986i
$557$	26.1781	+	15.1139i	1.10920	+	0.640398i	0.938622	−	0.344946i	$-0.112103\pi$
$557$	26.1781	+	15.1139i	1.10920	+	0.640398i	0.170579	+	0.985344i	$0.445436\pi$
$558$	2.01909	−	3.49717i	0.0854750	−	0.148047i
$559$	14.5884	−	9.52215i	0.617024	−	0.402744i
$560$	0.169096	+	1.80718i	0.00714563	+	0.0763674i
$561$	−15.4457	+	8.91756i	−0.652116	+	0.376500i
$562$	2.03385			0.0857930
$563$	22.3878			0.943534			0.471767	−	0.881723i	$-0.343616\pi$
$563$	22.3878			0.943534			0.471767	+	0.881723i	$0.343616\pi$
$564$	9.38446	−	5.41812i	0.395157	−	0.228144i
$565$	−0.0182025	+	0.0105092i	−0.000765785	+	0.000442126i
$566$	−28.0177	−	16.1760i	−1.17767	−	0.679930i
$567$	−2.63424	+	0.246484i	−0.110628	+	0.0103514i
$568$	7.70839	−	13.3513i	0.323437	−	0.560209i
$569$	19.5795			0.820816			0.410408	−	0.911902i	$-0.365386\pi$
$569$	19.5795			0.820816			0.410408	+	0.911902i	$0.365386\pi$
$570$	−4.26553	−	2.46271i	−0.178664	−	0.103151i
$571$	6.67181	+	11.5559i	0.279206	+	0.483600i	0.971188	−	0.238316i	$-0.0765953\pi$
$571$	6.67181	+	11.5559i	0.279206	+	0.483600i	−0.691981	+	0.721915i	$0.743262\pi$
$572$	−8.64025	−	13.2373i	−0.361267	−	0.553479i
$573$	−11.2486			−0.469915
$574$	7.32549	−	15.9602i	0.305760	−	0.666165i
$575$	3.90481	+	6.76332i	0.162842	+	0.282050i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−19.9482	+	11.5171i	−0.830456	+	0.479464i	−0.854009	−	0.520259i	$-0.825835\pi$
$577$	−19.9482	+	11.5171i	−0.830456	+	0.479464i	0.0235531	+	0.999723i	$0.492502\pi$
$578$			0.451300i			0.0187716i
$579$	−11.5544	+	6.67096i	−0.480187	+	0.277236i
$580$			0.248614i			0.0103231i
$581$	−12.4972	+	8.86345i	−0.518472	+	0.367718i
$582$	−1.51520	−	2.62440i	−0.0628069	−	0.108785i
$583$		−	9.86736i		−	0.408664i
$584$	5.77964	+	10.0106i	0.239163	+	0.414243i
$585$	1.11783	−	2.20654i	0.0462166	−	0.0912292i
$586$	10.3719	−	17.9647i	0.428459	−	0.742113i
$587$	−36.1315	+	20.8605i	−1.49130	+	0.861005i	−0.999950	−	0.00995469i	$-0.996831\pi$
$587$	−36.1315	+	20.8605i	−1.49130	+	0.861005i	−0.491354	+	0.870960i	$0.663498\pi$
$588$	−4.56386	−	5.30765i	−0.188211	−	0.218884i
$589$	−14.4962	+	25.1081i	−0.597304	+	1.03456i
$590$	−1.48228	−	0.855796i	−0.0610246	−	0.0352326i
$591$			19.5734i			0.805141i
$592$			6.34603i			0.260820i
$593$	−2.91474	−	1.68283i	−0.119694	−	0.0691054i	0.438958	−	0.898508i	$-0.355348\pi$
$593$	−2.91474	−	1.68283i	−0.119694	−	0.0691054i	−0.558652	+	0.829402i	$0.688681\pi$
$594$	−2.19212	+	3.79686i	−0.0899437	+	0.155787i
$595$	−0.687886	−	7.35164i	−0.0282006	−	0.301388i
$596$	−0.105786	+	0.0610758i	−0.00433318	+	0.00250176i
$597$	−2.16509	+	3.75005i	−0.0886113	+	0.153479i
$598$	−2.80946	+	5.54573i	−0.114887	+	0.226782i
$599$	−3.69415	−	6.39846i	−0.150939	−	0.261434i	0.780634	−	0.624988i	$-0.214896\pi$
$599$	−3.69415	−	6.39846i	−0.150939	−	0.261434i	−0.931573	+	0.363555i	$0.881563\pi$
$600$		−	4.52936i		−	0.184910i
$601$	−14.0785	−	24.3848i	−0.574276	−	0.994675i	−0.996120	−	0.0880066i	$-0.971950\pi$
$601$	−14.0785	−	24.3848i	−0.574276	−	0.994675i	0.421844	−	0.906668i	$-0.361383\pi$
$602$	−1.19094	−	12.7280i	−0.0485392	−	0.518753i
$603$		−	3.84402i		−	0.156541i
$604$	19.1419	−	11.0516i	0.778874	−	0.449683i
$605$			5.64025i			0.229309i
$606$	−12.0411	+	6.95193i	−0.489136	+	0.282403i
$607$	13.5499	+	23.4692i	0.549975	+	0.952585i	0.998276	+	0.0587022i	$0.0186962\pi$
$607$	13.5499	+	23.4692i	0.549975	+	0.952585i	−0.448300	+	0.893883i	$0.647970\pi$
$608$	−3.58977	−	6.21767i	−0.145584	−	0.252160i
$609$	−0.554673	−	0.782074i	−0.0224765	−	0.0316912i
$610$	5.52218			0.223587
$611$	−21.3556	−	32.7178i	−0.863954	−	1.32362i
$612$	−2.03400	−	3.52300i	−0.0822198	−	0.142409i
$613$	24.9166	+	14.3856i	1.00637	+	0.581030i	0.910128	−	0.414328i	$-0.135983\pi$
$613$	24.9166	+	14.3856i	1.00637	+	0.581030i	0.0962452	+	0.995358i	$0.469317\pi$
$614$	−3.66321			−0.147835
$615$	2.27676	−	3.94346i	0.0918078	−	0.159016i
$616$	−11.5492	+	1.08064i	−0.465329	+	0.0435404i
$617$	−18.6996	−	10.7962i	−0.752817	−	0.434639i	0.0738940	−	0.997266i	$-0.476457\pi$
$617$	−18.6996	−	10.7962i	−0.752817	−	0.434639i	−0.826711	+	0.562627i	$0.809791\pi$
$618$	11.1948	−	6.46334i	0.450323	−	0.259994i
$619$	4.81229	−	2.77838i	0.193422	−	0.111672i	−0.400161	−	0.916445i	$-0.631046\pi$
$619$	4.81229	−	2.77838i	0.193422	−	0.111672i	0.593584	+	0.804772i	$0.297713\pi$
$620$	2.77034			0.111259
$621$	1.72422			0.0691906
$622$	1.44437	−	0.833909i	0.0579141	−	0.0334367i
$623$	−17.6966	+	12.5511i	−0.709001	+	0.502847i
$624$	3.01929	−	1.97075i	0.120868	−	0.0788933i
$625$	−9.08093	+	15.7286i	−0.363237	+	0.629145i
$626$	−4.91060	−	2.83514i	−0.196267	−	0.113315i
$627$	15.7384	−	27.2597i	0.628531	−	1.08865i
$628$	6.93082	+	12.0045i	0.276570	+	0.479033i
$629$		−	25.8157i		−	1.02934i
$630$	−1.05003	−	1.48052i	−0.0418343	−	0.0589852i
$631$	17.2787	+	9.97585i	0.687854	+	0.397132i	0.802807	−	0.596238i	$-0.203339\pi$
$631$	17.2787	+	9.97585i	0.687854	+	0.397132i	−0.114954	+	0.993371i	$0.536672\pi$
$632$	2.49213	+	1.43883i	0.0991316	+	0.0572336i
$633$	−28.3179			−1.12553
$634$	−15.7928	+	27.3539i	−0.627212	+	1.08636i
$635$			6.87504i			0.272828i
$636$	2.25064			0.0892439
$637$	−18.2090	+	17.4767i	−0.721465	+	0.692451i
$638$	−1.58882			−0.0629019
$639$			15.4168i			0.609878i
$640$	−0.343017	+	0.594123i	−0.0135589	+	0.0234848i
$641$	31.1838			1.23169			0.615843	−	0.787869i	$-0.288816\pi$
$641$	31.1838			1.23169			0.615843	+	0.787869i	$0.288816\pi$
$642$	15.6572	+	9.03970i	0.617941	+	0.356768i
$643$	27.0463	+	15.6152i	1.06660	+	0.615804i	0.927252	−	0.374439i	$-0.122165\pi$
$643$	27.0463	+	15.6152i	1.06660	+	0.615804i	0.139352	+	0.990243i	$0.455498\pi$
$644$	2.63907	+	3.72101i	0.103994	+	0.146628i
$645$		−	3.31473i		−	0.130517i
$646$	14.6032	+	25.2935i	0.574556	+	0.995160i
$647$	−2.14915	+	3.72243i	−0.0844917	+	0.146344i	−0.905174	−	0.425040i	$-0.860260\pi$
$647$	−2.14915	+	3.72243i	−0.0844917	+	0.146344i	0.820683	+	0.571384i	$0.193593\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	5.46913	−	9.47281i	0.214682	−	0.371840i
$650$	−16.3064	+	0.892632i	−0.639590	+	0.0350119i
$651$	−8.71473	+	6.18078i	−0.341557	+	0.242244i
$652$	15.8399	−	9.14518i	0.620339	−	0.358153i
$653$	13.2601			0.518906			0.259453	−	0.965756i	$-0.416458\pi$
$653$	13.2601			0.518906			0.259453	+	0.965756i	$0.416458\pi$
$654$	6.65959			0.260411
$655$	−2.71510	+	1.56756i	−0.106088	+	0.0612497i
$656$	5.74820	−	3.31872i	0.224429	−	0.129574i
$657$	−10.0106	−	5.77964i	−0.390552	−	0.225485i
$658$	−28.5453	+	2.67096i	−1.11281	+	0.104125i
$659$	−3.21198	+	5.56331i	−0.125121	+	0.216716i	−0.921780	−	0.387713i	$-0.873265\pi$
$659$	−3.21198	+	5.56331i	−0.125121	+	0.216716i	0.796659	+	0.604429i	$0.206599\pi$
$660$	−3.00774			−0.117076
$661$	−17.8575	−	10.3100i	−0.694575	−	0.401013i	0.110749	−	0.993848i	$-0.464675\pi$
$661$	−17.8575	−	10.3100i	−0.694575	−	0.401013i	−0.805324	+	0.592835i	$0.798008\pi$
$662$	−13.0119	−	22.5373i	−0.505722	−	0.875936i
$663$	−12.2825	+	8.01705i	−0.477013	+	0.311356i
$664$	−5.79090			−0.224730
$665$	7.53876	+	10.6294i	0.292340	+	0.412192i
$666$	−3.17302	−	5.49583i	−0.122952	−	0.212959i
$667$	0.312423	+	0.541132i	0.0120971	+	0.0209527i
$668$	6.42363	−	3.70869i	0.248538	−	0.143493i
$669$		−	19.9373i		−	0.770819i
$670$	2.28382	−	1.31857i	0.0882317	−	0.0509406i
$671$			35.2906i			1.36238i
$672$	−0.246484	−	2.63424i	−0.00950833	−	0.101618i
$673$	−4.05791	−	7.02850i	−0.156421	−	0.270929i	0.777155	−	0.629310i	$-0.216662\pi$
$673$	−4.05791	−	7.02850i	−0.156421	−	0.270929i	−0.933575	+	0.358381i	$0.883329\pi$
$674$			17.9060i			0.689715i
$675$	2.26468	+	3.92254i	0.0871675	+	0.150979i
$676$	−7.69007	−	10.4815i	−0.295772	−	0.403137i
$677$	16.0806	−	27.8524i	0.618027	−	1.07045i	−0.371818	−	0.928306i	$-0.621266\pi$
$677$	16.0806	−	27.8524i	0.618027	−	1.07045i	0.989845	−	0.142149i	$-0.0454012\pi$
$678$	0.0265329	−	0.0153188i	0.00101899	−	0.000588315i
$679$	0.746944	+	7.98280i	0.0286651	+	0.306352i
$680$	1.39540	−	2.41690i	0.0535110	−	0.0926838i
$681$	−25.7193	−	14.8490i	−0.985566	−	0.569017i
$682$			17.7044i			0.677935i
$683$		−	16.3227i		−	0.624572i	−0.949988	−	0.312286i	$-0.898905\pi$
$683$		−	16.3227i		−	0.624572i	0.949988	−	0.312286i	$-0.101095\pi$
$684$	6.21767	+	3.58977i	0.237738	+	0.137258i
$685$	0.792437	−	1.37254i	0.0302775	−	0.0524421i
$686$	5.11626	+	17.7995i	0.195340	+	0.679590i
$687$	−12.7224	+	7.34527i	−0.485389	+	0.280240i
$688$	2.41586	−	4.18440i	0.0921040	−	0.159529i
$689$	−0.443550	−	8.10268i	−0.0168979	−	0.308688i
$690$	0.591438	+	1.02440i	0.0225156	+	0.0389982i
$691$		−	43.9305i		−	1.67120i	−0.549341	−	0.835598i	$-0.685121\pi$
$691$		−	43.9305i		−	1.67120i	0.549341	−	0.835598i	$-0.314879\pi$
$692$	−11.3175	−	19.6025i	−0.430227	−	0.745175i
$693$	9.46154	−	6.71044i	0.359414	−	0.254909i
$694$			29.8776i			1.13414i
$695$	8.16889	−	4.71631i	0.309864	−	0.178900i
$696$		−	0.362393i		−	0.0137365i
$697$	−23.3837	+	13.5006i	−0.885722	+	0.511372i
$698$	−0.216417	−	0.374845i	−0.00819151	−	0.0141881i
$699$	8.21697	+	14.2322i	0.310794	+	0.538312i
$700$	−4.99887	+	10.8911i	−0.188940	+	0.411646i
$701$	23.1586			0.874688			0.437344	−	0.899294i	$-0.355919\pi$
$701$	23.1586			0.874688			0.437344	+	0.899294i	$0.355919\pi$
$702$	−1.62941	+	3.21637i	−0.0614980	+	0.121394i
$703$	22.7808	+	39.4575i	0.859194	+	1.48817i
$704$	−3.79686	−	2.19212i	−0.143100	−	0.0826186i
$705$	−7.43404			−0.279982
$706$	0.366028	−	0.633978i	0.0137756	−	0.0238601i
$707$	36.6261	−	3.42708i	1.37747	−	0.128888i
$708$	2.16065	+	1.24745i	0.0812023	+	0.0468822i
$709$	40.7064	−	23.5018i	1.52876	−	0.882630i	0.529346	−	0.848406i	$-0.322437\pi$
$709$	40.7064	−	23.5018i	1.52876	−	0.882630i	0.999414	−	0.0342240i	$-0.0108960\pi$
$710$	−9.15946	+	5.28822i	−0.343749	+	0.198463i
$711$	−2.87766			−0.107921
$712$	−8.20017			−0.307314
$713$	6.02990	−	3.48136i	0.225821	−	0.130378i
$714$	1.00270	+	10.7161i	0.0375251	+	0.401041i
$715$	0.592756	+	10.8283i	0.0221678	+	0.404957i
$716$	2.04347	−	3.53940i	0.0763681	−	0.132273i
$717$	−12.1229	−	6.99914i	−0.452737	−	0.261388i
$718$	12.3046	−	21.3122i	0.459204	−	0.795365i
$719$	8.20281	+	14.2077i	0.305913	+	0.529857i	0.977464	−	0.211101i	$-0.0677049\pi$
$719$	8.20281	+	14.2077i	0.305913	+	0.529857i	−0.671551	+	0.740958i	$0.734372\pi$
$720$		−	0.686034i		−	0.0255670i
$721$	−34.0521	+	3.18622i	−1.26817	+	0.118661i
$722$	−28.1855	−	16.2729i	−1.04896	−	0.605615i
$723$	−9.94503	−	5.74177i	−0.369860	−	0.213539i
$724$	−3.18758			−0.118465
$725$	−0.820704	+	1.42150i	−0.0304802	+	0.0527932i
$726$		−	8.22153i		−	0.305130i
$727$	13.0415			0.483681			0.241841	−	0.970316i	$-0.422249\pi$
$727$	13.0415			0.483681			0.241841	+	0.970316i	$0.422249\pi$
$728$	−9.43513	+	1.40653i	−0.349689	+	0.0521295i
$729$	1.00000			0.0370370
$730$		−	7.93006i		−	0.293505i
$731$	−9.82776	+	17.0222i	−0.363493	+	0.629588i
$732$	−8.04943			−0.297515
$733$	−28.0127	−	16.1732i	−1.03467	−	0.597369i	−0.116354	−	0.993208i	$-0.537121\pi$
$733$	−28.0127	−	16.1732i	−1.03467	−	0.597369i	−0.918320	+	0.395838i	$0.870454\pi$
$734$	11.9404	+	6.89379i	0.440728	+	0.254454i
$735$	0.890883	+	4.71888i	0.0328607	+	0.174059i
$736$			1.72422i			0.0635556i
$737$	8.42655	+	14.5952i	0.310396	+	0.537621i
$738$	−3.31872	+	5.74820i	−0.122164	+	0.211594i
$739$	−0.909775	−	0.525259i	−0.0334666	−	0.0193220i	0.483173	−	0.875525i	$-0.339484\pi$
$739$	−0.909775	−	0.525259i	−0.0334666	−	0.0193220i	−0.516640	+	0.856203i	$0.672817\pi$
$740$	2.17680	−	3.77033i	0.0800207	−	0.138600i
$741$	11.6984	−	23.0921i	0.429751	−	0.848308i
$742$	−5.41182	−	2.48395i	−0.198674	−	0.0911886i
$743$	36.7993	−	21.2461i	1.35003	−	0.779443i	0.361780	−	0.932263i	$-0.382169\pi$
$743$	36.7993	−	21.2461i	1.35003	−	0.779443i	0.988254	+	0.152821i	$0.0488358\pi$
$744$	−4.03819			−0.148047
$745$	0.0838002			0.00307020
$746$	11.8674	−	6.85163i	0.434495	−	0.250856i
$747$	5.01506	−	2.89545i	0.183492	−	0.105939i
$748$	15.4457	+	8.91756i	0.564749	+	0.326058i
$749$	−27.6720	−	39.0168i	−1.01111	−	1.42564i
$750$	−3.26873	+	5.66161i	−0.119357	+	0.206733i
$751$	35.6331			1.30027			0.650135	−	0.759819i	$-0.274712\pi$
$751$	35.6331			1.30027			0.650135	+	0.759819i	$0.274712\pi$
$752$	−9.38446	−	5.41812i	−0.342216	−	0.197579i
$753$	6.11401	+	10.5898i	0.222807	+	0.385913i
$754$	−1.30467	+	0.0714193i	−0.0475134	+	0.00260094i
$755$	−15.1636			−0.551858
$756$	1.53058	+	2.15808i	0.0556668	+	0.0784886i
$757$	21.8074	+	37.7715i	0.792602	+	1.37283i	0.924351	+	0.381544i	$0.124608\pi$
$757$	21.8074	+	37.7715i	0.792602	+	1.37283i	−0.131748	+	0.991283i	$0.542059\pi$
$758$	−14.4010	−	24.9433i	−0.523069	−	0.905983i
$759$	−6.54663	+	3.77970i	−0.237628	+	0.137194i
$760$			4.92541i			0.178664i
$761$	−8.92002	+	5.14998i	−0.323350	+	0.186686i	−0.652885	−	0.757457i	$-0.726442\pi$
$761$	−8.92002	+	5.14998i	−0.323350	+	0.186686i	0.329535	+	0.944144i	$0.393108\pi$
$762$		−	10.0214i		−	0.363038i
$763$	−16.0134	−	7.34994i	−0.579725	−	0.266086i
$764$	5.62428	+	9.74154i	0.203479	+	0.352436i
$765$			2.79079i			0.100901i
$766$	−9.84060	−	17.0444i	−0.355555	−	0.615840i
$767$	4.06522	−	8.02454i	0.146787	−	0.289749i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	33.1368	−	19.1315i	1.19494	−	0.689901i	0.235520	−	0.971870i	$-0.424321\pi$
$769$	33.1368	−	19.1315i	1.19494	−	0.689901i	0.959424	+	0.281969i	$0.0909875\pi$
$770$	7.23230	+	3.31952i	0.260634	+	0.119627i
$771$	11.7110	−	20.2841i	0.421761	−	0.730512i
$772$	11.5544	+	6.67096i	0.415854	+	0.240093i
$773$		−	14.4242i		−	0.518801i	−0.965770	−	0.259400i	$-0.916475\pi$
$773$		−	14.4242i		−	0.518801i	0.965770	−	0.259400i	$-0.0835249\pi$
$774$			4.83173i			0.173673i
$775$	15.8399	+	9.14519i	0.568987	+	0.328505i
$776$	−1.51520	+	2.62440i	−0.0543924	+	0.0942104i
$777$	1.56420	+	16.7170i	0.0561152	+	0.599719i
$778$	20.8518	−	12.0388i	0.747572	−	0.431611i
$779$	23.8269	−	41.2694i	0.853688	−	1.47863i
$780$	−2.46983	+	0.135202i	−0.0884343	+	0.00484099i
$781$	−33.7954	−	58.5353i	−1.20929	−	2.09456i
$782$		−	7.01415i		−	0.250825i
$783$	0.181197	+	0.313842i	0.00647544	+	0.0112158i
$784$	−2.31463	+	6.60625i	−0.0826652	+	0.235937i
$785$		−	9.50956i		−	0.339411i
$786$	3.95767	−	2.28496i	0.141165	−	0.0815018i
$787$			31.2988i			1.11568i	0.829948	+	0.557841i	$0.188370\pi$
$787$			31.2988i			1.11568i	−0.829948	+	0.557841i	$0.811630\pi$
$788$	16.9510	−	9.78669i	0.603856	−	0.348636i
$789$	1.14684	+	1.98638i	0.0408284	+	0.0707169i
$790$	−0.987088	−	1.70969i	−0.0351190	−	0.0608279i
$791$	−0.0807069	+	0.00755168i	−0.00286961	+	0.000268507i
$792$	4.38424			0.155787
$793$	1.58636	+	28.9792i	0.0563332	+	1.02908i
$794$	13.3939	+	23.1989i	0.475331	+	0.823298i
$795$	−1.33716	−	0.772010i	−0.0474242	−	0.0273804i
$796$	4.33018			0.153479
$797$	−4.39044	+	7.60447i	−0.155517	+	0.269364i	−0.933247	−	0.359235i	$-0.883038\pi$
$797$	−4.39044	+	7.60447i	−0.155517	+	0.269364i	0.777730	+	0.628599i	$0.216371\pi$
$798$	−10.9889	−	15.4940i	−0.389003	−	0.548483i
$799$	38.1761	+	22.0410i	1.35057	+	0.779754i
$800$	−3.92254	+	2.26468i	−0.138683	+	0.0800685i
$801$	7.10156	−	4.10009i	0.250921	−	0.144869i
$802$	−28.8528			−1.01883
$803$	50.6786			1.78841
$804$	−3.32902	+	1.92201i	−0.117405	+	0.0677841i
$805$	−0.291560	−	3.11598i	−0.0102761	−	0.109824i
$806$	0.795834	+	14.5381i	0.0280320	+	0.512084i
$807$	2.68261	−	4.64642i	0.0944324	−	0.163562i
$808$	12.0411	+	6.95193i	0.423604	+	0.244568i
$809$	6.89006	−	11.9339i	0.242241	−	0.419575i	−0.719111	−	0.694895i	$-0.755451\pi$
$809$	6.89006	−	11.9339i	0.242241	−	0.419575i	0.961352	+	0.275321i	$0.0887840\pi$
$810$	0.343017	+	0.594123i	0.0120524	+	0.0208754i
$811$			11.0037i			0.386392i	0.981160	+	0.193196i	$0.0618854\pi$
$811$			11.0037i			0.386392i	−0.981160	+	0.193196i	$0.938115\pi$
$812$	−0.399959	+	0.871398i	−0.0140358	+	0.0305801i
$813$	−0.729207	−	0.421008i	−0.0255744	−	0.0147654i
$814$	24.0950	+	13.9113i	0.844529	+	0.487589i
$815$	−12.5478			−0.439531
$816$	−2.03400	+	3.52300i	−0.0712044	+	0.123330i
$817$		−	34.6896i		−	1.21364i
$818$	30.5695			1.06884
$819$	7.46780	−	5.93566i	0.260946	−	0.207409i
$820$	−4.55352			−0.159016
$821$			18.6280i			0.650122i	0.945693	+	0.325061i	$0.105385\pi$
$821$			18.6280i			0.650122i	−0.945693	+	0.325061i	$0.894615\pi$
$822$	−1.15510	+	2.00069i	−0.0402887	+	0.0697820i
$823$	−20.4372			−0.712396			−0.356198	−	0.934410i	$-0.615927\pi$
$823$	−20.4372			−0.712396			−0.356198	+	0.934410i	$0.615927\pi$
$824$	−11.1948	−	6.46334i	−0.389991	−	0.225161i
$825$	−17.1973	−	9.92889i	−0.598734	−	0.345679i
$826$	−3.81866	−	5.38421i	−0.132868	−	0.187341i
$827$		−	45.1555i		−	1.57021i	−0.619362	−	0.785105i	$-0.712609\pi$
$827$		−	45.1555i		−	1.57021i	0.619362	−	0.785105i	$-0.287391\pi$
$828$	−0.862111	−	1.49322i	−0.0299604	−	0.0518930i
$829$	2.05897	−	3.56624i	0.0715110	−	0.123861i	−0.828053	−	0.560650i	$-0.810551\pi$
$829$	2.05897	−	3.56624i	0.0715110	−	0.123861i	0.899564	+	0.436790i	$0.143885\pi$
$830$	3.44051	+	1.98638i	0.119422	+	0.0689482i
$831$	7.19119	−	12.4555i	0.249460	−	0.432077i
$832$	−3.21637	−	1.62941i	−0.111508	−	0.0564895i
$833$	9.41592	−	26.8743i	0.326242	−	0.931138i
$834$	−11.9074	+	6.87474i	−0.412320	+	0.238053i
$835$	−5.08857			−0.176097
$836$	−31.4768			−1.08865
$837$	3.49717	−	2.01909i	0.120880	−	0.0697901i
$838$	6.64468	−	3.83631i	0.229536	−	0.132523i
$839$	15.9503	+	9.20889i	0.550664	+	0.317926i	0.749390	−	0.662129i	$-0.230347\pi$
$839$	15.9503	+	9.20889i	0.550664	+	0.317926i	−0.198726	+	0.980055i	$0.563680\pi$
$840$	−0.757149	+	1.64961i	−0.0261241	+	0.0569171i
$841$	14.4343	−	25.0010i	0.497736	−	0.862104i
$842$	8.38578			0.288993
$843$	1.76137	+	1.01693i	0.0606648	+	0.0350248i
$844$	14.1589	+	24.5240i	0.487371	+	0.844151i
$845$	0.973495	+	8.86516i	0.0334892	+	0.304971i
$846$	10.8362			0.372558
$847$	−9.07379	+	19.7692i	−0.311779	+	0.679278i
$848$	−1.12532	−	1.94912i	−0.0386437	−	0.0669329i
$849$	−16.1760	−	28.0177i	−0.555160	−	0.961566i
$850$	15.9569	−	9.21273i	0.547318	−	0.315994i
$851$		−	10.9420i		−	0.375086i
$852$	13.3513	−	7.70839i	0.457409	−	0.264085i
$853$			6.15317i			0.210680i	0.994436	+	0.105340i	$0.0335932\pi$
$853$			6.15317i			0.210680i	−0.994436	+	0.105340i	$0.966407\pi$
$854$	19.3554	+	8.88384i	0.662327	+	0.303999i
$855$	−2.46271	−	4.26553i	−0.0842228	−	0.145878i
$856$		−	18.0794i		−	0.617941i
$857$	10.2376	+	17.7321i	0.349711	+	0.605718i	0.986198	−	0.165570i	$-0.0529463\pi$
$857$	10.2376	+	17.7321i	0.349711	+	0.605718i	−0.636487	+	0.771288i	$0.719613\pi$
$858$	−0.864032	−	15.7840i	−0.0294976	−	0.538855i
$859$	−9.60299	+	16.6329i	−0.327650	+	0.567506i	−0.982045	−	0.188647i	$-0.939590\pi$
$859$	−9.60299	+	16.6329i	−0.327650	+	0.567506i	0.654395	+	0.756153i	$0.272923\pi$
$860$	−2.87064	+	1.65737i	−0.0978881	+	0.0565157i
$861$	14.3242	−	10.1592i	0.488166	−	0.346224i
$862$	−1.62587	+	2.81608i	−0.0553772	+	0.0959161i
$863$	27.1455	+	15.6725i	0.924043	+	0.533497i	0.884923	−	0.465738i	$-0.154211\pi$
$863$	27.1455	+	15.6725i	0.924043	+	0.533497i	0.0391205	+	0.999235i	$0.487544\pi$
$864$			1.00000i			0.0340207i
$865$			15.5284i			0.527981i
$866$	7.94520	+	4.58716i	0.269989	+	0.155878i
$867$	−0.225650	+	0.390837i	−0.00766347	+	0.0132735i
$868$	9.71008	+	4.45679i	0.329582	+	0.151273i
$869$	10.9261	−	6.30818i	0.370642	−	0.213990i
$870$	−0.124307	+	0.215306i	−0.00421440	+	0.00729956i
$871$	7.57562	+	11.6062i	0.256690	+	0.393262i
$872$	−3.32980	−	5.76738i	−0.112761	−	0.195308i
$873$		−	3.03039i		−	0.102563i
$874$	6.18956	+	10.7206i	0.209365	+	0.362631i
$875$	14.1084	−	10.0061i	0.476950	−	0.338269i
$876$			11.5593i			0.390552i
$877$	9.13470	−	5.27392i	0.308457	−	0.178088i	−0.337779	−	0.941226i	$-0.609676\pi$
$877$	9.13470	−	5.27392i	0.308457	−	0.178088i	0.646236	+	0.763138i	$0.276342\pi$
$878$			23.0178i			0.776813i
$879$	17.9647	−	10.3719i	0.605933	−	0.349835i
$880$	1.50387	+	2.60478i	0.0506954	+	0.0878070i
$881$	−12.8933	−	22.3319i	−0.434387	−	0.752380i	0.562858	−	0.826553i	$-0.309702\pi$
$881$	−12.8933	−	22.3319i	−0.434387	−	0.752380i	−0.997245	+	0.0741730i	$0.976368\pi$
$882$	−1.29860	−	6.87849i	−0.0437261	−	0.231611i
$883$	−47.8763			−1.61116			−0.805582	−	0.592484i	$-0.798147\pi$
$883$	−47.8763			−1.61116			−0.805582	+	0.592484i	$0.798147\pi$
$884$	13.0842	+	6.62844i	0.440070	+	0.222939i
$885$	−0.855796	−	1.48228i	−0.0287673	−	0.0498264i
$886$	23.4440	+	13.5354i	0.787617	+	0.454731i
$887$	18.9586			0.636568			0.318284	−	0.947995i	$-0.396894\pi$
$887$	18.9586			0.636568			0.318284	+	0.947995i	$0.396894\pi$
$888$	−3.17302	+	5.49583i	−0.106479	+	0.184428i
$889$	−11.0603	+	24.0972i	−0.370949	+	0.808193i
$890$	4.87191	+	2.81280i	0.163307	+	0.0942853i
$891$	−3.79686	+	2.19212i	−0.127200	+	0.0734387i
$892$	−17.2662	+	9.96863i	−0.578114	+	0.333774i
$893$	−77.7993			−2.60345
$894$	−0.122152			−0.00408536
$895$	−2.42815	+	1.40189i	−0.0811641	+	0.0468601i
$896$	−2.15808	+	1.53058i	−0.0720964	+	0.0511332i
$897$	−5.20593	+	3.39802i	−0.173821	+	0.113456i
$898$	9.86807	−	17.0920i	0.329302	−	0.570368i
$899$	1.26735	+	0.731706i	0.0422685	+	0.0244037i
$900$	2.26468	−	3.92254i	0.0754893	−	0.130751i
$901$	4.57782	+	7.92902i	0.152509	+	0.264154i
$902$		−	29.1001i		−	0.968929i
$903$	5.33259	−	11.6182i	0.177458	−	0.386630i
$904$	−0.0265329	−	0.0153188i	−0.000882472	−	0.000509496i
$905$	1.89382	+	1.09339i	0.0629525	+	0.0363457i
$906$	22.1032			0.734330
$907$	7.76279	−	13.4455i	0.257759	−	0.446452i	−0.707882	−	0.706331i	$-0.750349\pi$
$907$	7.76279	−	13.4455i	0.257759	−	0.446452i	0.965641	+	0.259879i	$0.0836825\pi$
$908$			29.6981i			0.985566i
$909$	−13.9039			−0.461162
$910$	6.08809	+	2.40076i	0.201818	+	0.0795844i
$911$	8.53305			0.282713			0.141356	−	0.989959i	$-0.454854\pi$
$911$	8.53305			0.282713			0.141356	+	0.989959i	$0.454854\pi$
$912$		−	7.17954i		−	0.237738i
$913$	−12.6943	+	21.9872i	−0.420121	+	0.727671i
$914$	14.3935			0.476093
$915$	4.78235	+	2.76109i	0.158100	+	0.0912789i
$916$	12.7224	+	7.34527i	0.420359	+	0.242695i
$917$	−12.0383	+	1.12641i	−0.397539	+	0.0371974i
$918$		−	4.06801i		−	0.134264i
$919$	−22.5680	−	39.0889i	−0.744449	−	1.28942i	−0.950452	−	0.310872i	$-0.899379\pi$
$919$	−22.5680	−	39.0889i	−0.744449	−	1.28942i	0.206003	−	0.978551i	$-0.433954\pi$
$920$	0.591438	−	1.02440i	0.0194991	−	0.0337735i
$921$	−3.17243	−	1.83161i	−0.104535	−	0.0603534i
$922$	17.7125	−	30.6790i	0.583332	−	1.01036i
$923$	−30.3827	−	46.5478i	−1.00006	−	1.53214i
$924$	−10.5422	−	4.83871i	−0.346812	−	0.159182i
$925$	24.8926	−	14.3717i	0.818462	−	0.472539i
$926$	−36.1762			−1.18882
$927$	12.9267			0.424568
$928$	−0.313842	+	0.181197i	−0.0103024	+	0.00594807i
$929$	39.5930	−	22.8590i	1.29900	−	0.749980i	0.318771	−	0.947832i	$-0.396730\pi$
$929$	39.5930	−	22.8590i	1.29900	−	0.749980i	0.980232	+	0.197852i	$0.0633966\pi$
$930$	2.39918	+	1.38517i	0.0786722	+	0.0454214i
$931$	9.32334	+	49.3844i	0.305560	+	1.61851i
$932$	8.21697	−	14.2322i	0.269156	−	0.466192i
$933$	1.66782			0.0546019
$934$	30.2272	+	17.4517i	0.989063	+	0.571036i
$935$	−6.11775	−	10.5963i	−0.200072	−	0.346535i
$936$	3.60016	−	0.197077i	0.117675	−	0.00644166i
$937$	−6.09263			−0.199037			−0.0995187	−	0.995036i	$-0.531730\pi$
$937$	−6.09263			−0.199037			−0.0995187	+	0.995036i	$0.531730\pi$
$938$	10.1261	−	0.947489i	0.330629	−	0.0309366i
$939$	−2.83514	−	4.91060i	−0.0925212	−	0.160251i
$940$	3.71702	+	6.43806i	0.121236	+	0.209987i
$941$	−19.9997	+	11.5469i	−0.651973	+	0.376417i	−0.789212	−	0.614121i	$-0.789511\pi$
$941$	−19.9997	+	11.5469i	−0.651973	+	0.376417i	0.137239	+	0.990538i	$0.456177\pi$
$942$			13.8616i			0.451637i
$943$	−9.91117	+	5.72222i	−0.322752	+	0.186341i
$944$		−	2.49491i		−	0.0812023i
$945$	−0.169096	−	1.80718i	−0.00550071	−	0.0587877i
$946$	−10.5917	−	18.3454i	−0.344367	−	0.596460i
$947$		−	49.9770i		−	1.62403i	−0.583634	−	0.812017i	$-0.698370\pi$
$947$		−	49.9770i		−	1.62403i	0.583634	−	0.812017i	$-0.301630\pi$
$948$	1.43883	+	2.49213i	0.0467311	+	0.0809406i
$949$	41.6153	−	2.27807i	1.35089	−	0.0739492i
$950$	−16.2594	+	28.1620i	−0.527523	+	0.913697i
$951$	−27.3539	+	15.7928i	−0.887012	+	0.512116i
$952$	8.77909	−	6.22643i	0.284532	−	0.201800i
$953$	2.81809	−	4.88108i	0.0912870	−	0.158114i	−0.816766	−	0.576969i	$-0.804235\pi$
$953$	2.81809	−	4.88108i	0.0912870	−	0.158114i	0.908053	+	0.418855i	$0.137569\pi$
$954$	1.94912	+	1.12532i	0.0631049	+	0.0364337i
$955$		−	7.71690i		−	0.249713i
$956$			13.9983i			0.452737i
$957$	−1.37596	−	0.794409i	−0.0444783	−	0.0256796i
$958$	−2.02550	+	3.50827i	−0.0654409	+	0.113347i
$959$	4.98559	−	3.53595i	0.160993	−	0.114182i
$960$	−0.594123	+	0.343017i	−0.0191752	+	0.0110708i
$961$	−7.34652	+	12.7246i	−0.236985	+	0.410469i
$962$	20.4112	+	10.3403i	0.658083	+	0.333384i
$963$	9.03970	+	15.6572i	0.291300	+	0.504547i
$964$			11.4835i			0.369860i
$965$	−4.57651	−	7.92675i	−0.147323	−	0.255171i
$966$	0.424993	+	4.54202i	0.0136739	+	0.146137i
$967$			38.4609i			1.23682i	0.785856	+	0.618410i	$0.212223\pi$
$967$			38.4609i			1.23682i	−0.785856	+	0.618410i	$0.787777\pi$
$968$	−7.12006	+	4.11077i	−0.228847	+	0.132125i
$969$			29.2064i			0.938246i
$970$	1.80043	−	1.03948i	0.0578083	−	0.0333756i
$971$	14.9702	+	25.9291i	0.480415	+	0.832103i	0.999748	−	0.0224690i	$-0.00715271\pi$
$971$	14.9702	+	25.9291i	0.480415	+	0.832103i	−0.519333	+	0.854572i	$0.673819\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	36.2195	−	3.38903i	1.16114	−	0.108647i
$974$	6.75964			0.216593
$975$	−14.5681	−	7.38017i	−0.466552	−	0.236354i
$976$	4.02471	+	6.97101i	0.128828	+	0.223137i
$977$	13.9621	+	8.06103i	0.446688	+	0.257895i	0.706430	−	0.707783i	$-0.250304\pi$
$977$	13.9621	+	8.06103i	0.446688	+	0.257895i	−0.259743	+	0.965678i	$0.583638\pi$
$978$	18.2904			0.584861
$979$	−17.9758	+	31.1349i	−0.574507	+	0.995076i
$980$	3.64123	−	3.13097i	0.116315	−	0.100015i
$981$	5.76738	+	3.32980i	0.184138	+	0.106312i
$982$	1.36773	−	0.789661i	0.0436461	−	0.0251991i
$983$	−17.2163	+	9.93984i	−0.549115	+	0.317032i	−0.748765	−	0.662836i	$-0.769353\pi$
$983$	−17.2163	+	9.93984i	−0.549115	+	0.317032i	0.199650	+	0.979867i	$0.436020\pi$
$984$	6.63745			0.211594
$985$	−13.4280			−0.427852
$986$	1.27671	−	0.737109i	0.0406588	−	0.0234743i
$987$	−26.0565	−	11.9595i	−0.829386	−	0.380676i
$988$	−25.8475	+	1.41492i	−0.822319	+	0.0450147i
$989$	−4.16548	+	7.21483i	−0.132455	+	0.229418i
$990$	−2.60478	−	1.50387i	−0.0827852	−	0.0477961i
$991$	7.52222	−	13.0289i	0.238951	−	0.413876i	−0.721462	−	0.692454i	$-0.756530\pi$
$991$	7.52222	−	13.0289i	0.238951	−	0.413876i	0.960414	+	0.278578i	$0.0898630\pi$
$992$	2.01909	+	3.49717i	0.0641063	+	0.111035i
$993$		−	26.0238i		−	0.825840i
$994$	−40.6116	+	3.79999i	−1.28812	+	0.120528i
$995$	−2.57266	−	1.48533i	−0.0815589	−	0.0470880i
$996$	−5.01506	−	2.89545i	−0.158908	−	0.0917458i
$997$	−24.9150			−0.789065			−0.394532	−	0.918882i	$-0.629093\pi$
$997$	−24.9150			−0.789065			−0.394532	+	0.918882i	$0.629093\pi$
$998$	3.05719	−	5.29521i	0.0967737	−	0.167617i
$999$		−	6.34603i		−	0.200780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bm.a.205.3	yes	16
3.2	odd	2		1638.2.dt.a.1297.6		16
7.4	even	3		546.2.bd.a.361.6	yes	16
13.4	even	6		546.2.bd.a.121.6	✓	16
21.11	odd	6		1638.2.cr.a.361.3		16
39.17	odd	6		1638.2.cr.a.667.3		16
91.4	even	6	inner	546.2.bm.a.277.7	yes	16
273.95	odd	6		1638.2.dt.a.1369.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.6	✓	16	13.4	even	6
546.2.bd.a.361.6	yes	16	7.4	even	3
546.2.bm.a.205.3	yes	16	1.1	even	1	trivial
546.2.bm.a.277.7	yes	16	91.4	even	6	inner
1638.2.cr.a.361.3		16	21.11	odd	6
1638.2.cr.a.667.3		16	39.17	odd	6
1638.2.dt.a.1297.6		16	3.2	odd	2
1638.2.dt.a.1369.2		16	273.95	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.53058 + 2.15808i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(1.53058 + 2.15808i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.343017 - 0.594123i) q^{10} +(3.79686 + 2.19212i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(3.21637 + 1.62941i) q^{13} +(2.15808 - 1.53058i) q^{14} +(0.594123 - 0.343017i) q^{15} +1.00000 q^{16} -4.06801 q^{17} +(-0.866025 + 0.500000i) q^{18} +(6.21767 - 3.58977i) q^{19} +(-0.594123 - 0.343017i) q^{20} +(2.63424 - 0.246484i) q^{21} +(2.19212 - 3.79686i) q^{22} -1.72422 q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.26468 - 3.92254i) q^{25} +(1.62941 - 3.21637i) q^{26} -1.00000 q^{27} +(-1.53058 - 2.15808i) q^{28} +(-0.181197 - 0.313842i) q^{29} +(-0.343017 - 0.594123i) q^{30} +(-3.49717 + 2.01909i) q^{31} -1.00000i q^{32} +(3.79686 - 2.19212i) q^{33} +4.06801i q^{34} +(0.169096 + 1.80718i) q^{35} +(0.500000 + 0.866025i) q^{36} +6.34603i q^{37} +(-3.58977 - 6.21767i) q^{38} +(3.01929 - 1.97075i) q^{39} +(-0.343017 + 0.594123i) q^{40} +(5.74820 - 3.31872i) q^{41} +(-0.246484 - 2.63424i) q^{42} +(2.41586 - 4.18440i) q^{43} +(-3.79686 - 2.19212i) q^{44} -0.686034i q^{45} +1.72422i q^{46} +(-9.38446 - 5.41812i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.31463 + 6.60625i) q^{49} +(-3.92254 + 2.26468i) q^{50} +(-2.03400 + 3.52300i) q^{51} +(-3.21637 - 1.62941i) q^{52} +(-1.12532 - 1.94912i) q^{53} +1.00000i q^{54} +(1.50387 + 2.60478i) q^{55} +(-2.15808 + 1.53058i) q^{56} -7.17954i q^{57} +(-0.313842 + 0.181197i) q^{58} -2.49491i q^{59} +(-0.594123 + 0.343017i) q^{60} +(4.02471 + 6.97101i) q^{61} +(2.01909 + 3.49717i) q^{62} +(1.10366 - 2.40456i) q^{63} -1.00000 q^{64} +(1.35201 + 2.07134i) q^{65} +(-2.19212 - 3.79686i) q^{66} +(3.32902 + 1.92201i) q^{67} +4.06801 q^{68} +(-0.862111 + 1.49322i) q^{69} +(1.80718 - 0.169096i) q^{70} +(-13.3513 - 7.70839i) q^{71} +(0.866025 - 0.500000i) q^{72} +(10.0106 - 5.77964i) q^{73} +6.34603 q^{74} -4.52936 q^{75} +(-6.21767 + 3.58977i) q^{76} +(1.08064 + 11.5492i) q^{77} +(-1.97075 - 3.01929i) q^{78} +(1.43883 - 2.49213i) q^{79} +(0.594123 + 0.343017i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.31872 - 5.74820i) q^{82} +5.79090i q^{83} +(-2.63424 + 0.246484i) q^{84} +(-2.41690 - 1.39540i) q^{85} +(-4.18440 - 2.41586i) q^{86} -0.362393 q^{87} +(-2.19212 + 3.79686i) q^{88} +8.20017i q^{89} -0.686034 q^{90} +(1.40653 + 9.43513i) q^{91} +1.72422 q^{92} +4.03819i q^{93} +(-5.41812 + 9.38446i) q^{94} +4.92541 q^{95} +(-0.866025 - 0.500000i) q^{96} +(2.62440 + 1.51520i) q^{97} +(6.60625 + 2.31463i) q^{98} -4.38424i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9	\( 16 q + 8 q^{3} - 16 q^{4} - 2 q^{7} - 8 q^{9} + 4 q^{10} + 6 q^{11} - 8 q^{12} - 10 q^{13} + 4 q^{14} + 16 q^{16} + 18 q^{19} + 8 q^{21} + 6 q^{22} + 32 q^{23} - 4 q^{26} - 16 q^{27} + 2 q^{28} - 4 q^{29} - 4 q^{30} - 12 q^{31} + 6 q^{33} - 2 q^{35} + 8 q^{36} - 2 q^{38} - 14 q^{39} - 4 q^{40} - 18 q^{41} + 2 q^{42} - 32 q^{43} - 6 q^{44} - 66 q^{47} + 8 q^{48} + 22 q^{49} + 36 q^{50} + 10 q^{52} + 2 q^{53} + 16 q^{55} - 4 q^{56} + 24 q^{58} + 4 q^{61} + 4 q^{62} + 10 q^{63} - 16 q^{64} + 38 q^{65} - 6 q^{66} + 36 q^{67} + 16 q^{69} + 6 q^{70} - 30 q^{71} + 18 q^{73} - 12 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} - 8 q^{81} + 6 q^{82} - 8 q^{84} + 72 q^{85} - 8 q^{87} - 6 q^{88} - 8 q^{90} - 2 q^{91} - 32 q^{92} - 24 q^{94} + 80 q^{95} - 6 q^{97} - 60 q^{98}+O(q^{100}) \) 16 * q + 8 * q^3 - 16 * q^4 - 2 * q^7 - 8 * q^9 + 4 * q^10 + 6 * q^11 - 8 * q^12 - 10 * q^13 + 4 * q^14 + 16 * q^16 + 18 * q^19 + 8 * q^21 + 6 * q^22 + 32 * q^23 - 4 * q^26 - 16 * q^27 + 2 * q^28 - 4 * q^29 - 4 * q^30 - 12 * q^31 + 6 * q^33 - 2 * q^35 + 8 * q^36 - 2 * q^38 - 14 * q^39 - 4 * q^40 - 18 * q^41 + 2 * q^42 - 32 * q^43 - 6 * q^44 - 66 * q^47 + 8 * q^48 + 22 * q^49 + 36 * q^50 + 10 * q^52 + 2 * q^53 + 16 * q^55 - 4 * q^56 + 24 * q^58 + 4 * q^61 + 4 * q^62 + 10 * q^63 - 16 * q^64 + 38 * q^65 - 6 * q^66 + 36 * q^67 + 16 * q^69 + 6 * q^70 - 30 * q^71 + 18 * q^73 - 12 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 - 8 * q^81 + 6 * q^82 - 8 * q^84 + 72 * q^85 - 8 * q^87 - 6 * q^88 - 8 * q^90 - 2 * q^91 - 32 * q^92 - 24 * q^94 + 80 * q^95 - 6 * q^97 - 60 * q^98

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