LMFDB - Embedded newform 546.2.bd.a.361.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (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			361.6
Root			$-0.809195i$ of defining polynomial
Character	$\chi$	$=$	546.361
Dual form			546.2.bd.a.121.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.63424 + 0.246484i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.63424 + 0.246484i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.686034 q^{10} -4.38424i 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} +(-0.500000 + 0.866025i) q^{16} +(2.03400 + 3.52300i) q^{17} +(0.866025 + 0.500000i) q^{18} +7.17954i q^{19} +(-0.594123 - 0.343017i) q^{20} +(-2.63424 - 0.246484i) q^{21} +(2.19212 - 3.79686i) q^{22} +(0.862111 - 1.49322i) q^{23} -1.00000i q^{24} +(-2.26468 + 3.92254i) q^{25} +(1.97075 + 3.01929i) q^{26} -1.00000 q^{27} +(1.10366 + 2.40456i) q^{28} +(-0.181197 - 0.313842i) q^{29} +0.686034 q^{30} +(3.49717 + 2.01909i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.38424i q^{33} +4.06801i q^{34} +(-1.64961 + 0.757149i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.49583 - 3.17302i) q^{37} +(-3.58977 + 6.21767i) q^{38} +(-3.21637 - 1.62941i) q^{39} +(-0.343017 - 0.594123i) q^{40} +(5.74820 - 3.31872i) q^{41} +(-2.15808 - 1.53058i) q^{42} +(2.41586 - 4.18440i) q^{43} +(3.79686 - 2.19212i) q^{44} +(-0.594123 + 0.343017i) q^{45} +(1.49322 - 0.862111i) q^{46} +(9.38446 - 5.41812i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.87849 + 1.29860i) q^{49} +(-3.92254 + 2.26468i) q^{50} +(-2.03400 - 3.52300i) q^{51} +(0.197077 + 3.60016i) q^{52} +(-1.12532 + 1.94912i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.50387 + 2.60478i) q^{55} +(-0.246484 + 2.63424i) q^{56} -7.17954i q^{57} -0.362393i q^{58} +(-2.16065 + 1.24745i) q^{59} +(0.594123 + 0.343017i) q^{60} -8.04943 q^{61} +(2.01909 + 3.49717i) q^{62} +(2.63424 + 0.246484i) q^{63} -1.00000 q^{64} +(-2.46983 + 0.135202i) q^{65} +(-2.19212 + 3.79686i) q^{66} -3.84402i q^{67} +(-2.03400 + 3.52300i) q^{68} +(-0.862111 + 1.49322i) q^{69} +(-1.80718 - 0.169096i) q^{70} +(-13.3513 - 7.70839i) q^{71} +1.00000i q^{72} +(-10.0106 - 5.77964i) q^{73} +(-3.17302 - 5.49583i) q^{74} +(2.26468 - 3.92254i) 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} -0.686034i q^{80} +1.00000 q^{81} +6.63745 q^{82} +5.79090i q^{83} +(-1.10366 - 2.40456i) q^{84} +(-2.41690 - 1.39540i) q^{85} +(4.18440 - 2.41586i) q^{86} +(0.181197 + 0.313842i) q^{87} +4.38424 q^{88} +(-7.10156 - 4.10009i) q^{89} -0.686034 q^{90} +(8.07108 + 5.08504i) q^{91} +1.72422 q^{92} +(-3.49717 - 2.01909i) q^{93} +10.8362 q^{94} +(-2.46271 - 4.26553i) q^{95} +(0.866025 - 0.500000i) q^{96} +(2.62440 + 1.51520i) q^{97} +(5.30765 + 4.56386i) q^{98} -4.38424i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.594123	+	0.343017i	−0.265700	+	0.153402i	−0.626932	−	0.779074i	$-0.715690\pi$
$5$	−0.594123	+	0.343017i	−0.265700	+	0.153402i	0.361232	+	0.932476i	$0.382356\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	2.63424	+	0.246484i	0.995651	+	0.0931622i
$7$	2.63424	+	0.246484i	0.995651	+	0.0931622i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−0.686034			−0.216943
$11$		−	4.38424i		−	1.32190i	−0.750431	−	0.660949i	$-0.770154\pi$
$11$		−	4.38424i		−	1.32190i	0.750431	−	0.660949i	$-0.229846\pi$
$12$	−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
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.03400	+	3.52300i	0.493319	+	0.854453i	0.999970	−	0.00769791i	$-0.00245035\pi$
$17$	2.03400	+	3.52300i	0.493319	+	0.854453i	−0.506652	+	0.862151i	$0.669117\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$			7.17954i			1.64710i	0.567244	+	0.823550i	$0.308010\pi$
$19$			7.17954i			1.64710i	−0.567244	+	0.823550i	$0.691990\pi$
$20$	−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
$23$	0.862111	−	1.49322i	0.179762	−	0.311358i	−0.762037	−	0.647534i	$-0.775800\pi$
$23$	0.862111	−	1.49322i	0.179762	−	0.311358i	0.941799	+	0.336176i	$0.109134\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−2.26468	+	3.92254i	−0.452936	+	0.784508i
$26$	1.97075	+	3.01929i	0.386497	+	0.592132i
$27$	−1.00000			−0.192450
$28$	1.10366	+	2.40456i	0.208572	+	0.454420i
$29$	−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	$0.844046\pi$
$30$	0.686034			0.125252
$31$	3.49717	+	2.01909i	0.628111	+	0.362640i	0.780020	−	0.625755i	$-0.215209\pi$
$31$	3.49717	+	2.01909i	0.628111	+	0.362640i	−0.151909	+	0.988394i	$0.548542\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$			4.38424i			0.763198i
$34$			4.06801i			0.697658i
$35$	−1.64961	+	0.757149i	−0.278836	+	0.127982i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−5.49583	−	3.17302i	−0.903508	−	0.521641i	−0.0251714	−	0.999683i	$-0.508013\pi$
$37$	−5.49583	−	3.17302i	−0.903508	−	0.521641i	−0.878337	+	0.478042i	$0.841346\pi$
$38$	−3.58977	+	6.21767i	−0.582338	+	1.00864i
$39$	−3.21637	−	1.62941i	−0.515031	−	0.260914i
$40$	−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	$0.159899\pi$
$42$	−2.15808	−	1.53058i	−0.332999	−	0.236174i
$43$	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
$45$	−0.594123	+	0.343017i	−0.0885667	+	0.0511340i
$46$	1.49322	−	0.862111i	0.220163	−	0.127111i
$47$	9.38446	−	5.41812i	1.36886	−	0.790314i	0.378082	−	0.925772i	$-0.376584\pi$
$47$	9.38446	−	5.41812i	1.36886	−	0.790314i	0.990783	+	0.135458i	$0.0432505\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	6.87849	+	1.29860i	0.982642	+	0.185514i
$50$	−3.92254	+	2.26468i	−0.554731	+	0.320274i
$51$	−2.03400	−	3.52300i	−0.284818	−	0.493319i
$52$	0.197077	+	3.60016i	0.0273297	+	0.499253i
$53$	−1.12532	+	1.94912i	−0.154575	+	0.267732i	−0.932904	−	0.360125i	$-0.882734\pi$
$53$	−1.12532	+	1.94912i	−0.154575	+	0.267732i	0.778329	+	0.627856i	$0.216067\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$	1.50387	+	2.60478i	0.202782	+	0.351228i
$56$	−0.246484	+	2.63424i	−0.0329378	+	0.352016i
$57$		−	7.17954i		−	0.950954i
$58$		−	0.362393i		−	0.0475845i
$59$	−2.16065	+	1.24745i	−0.281293	+	0.162405i	−0.634009	−	0.773326i	$-0.718592\pi$
$59$	−2.16065	+	1.24745i	−0.281293	+	0.162405i	0.352716	+	0.935731i	$0.385258\pi$
$60$	0.594123	+	0.343017i	0.0767010	+	0.0442833i
$61$	−8.04943			−1.03062			−0.515312	−	0.857003i	$-0.672324\pi$
$61$	−8.04943			−1.03062			−0.515312	+	0.857003i	$0.672324\pi$
$62$	2.01909	+	3.49717i	0.256425	+	0.444141i
$63$	2.63424	+	0.246484i	0.331884	+	0.0310541i
$64$	−1.00000			−0.125000
$65$	−2.46983	+	0.135202i	−0.306345	+	0.0167697i
$66$	−2.19212	+	3.79686i	−0.269831	+	0.467361i
$67$		−	3.84402i		−	0.469622i	−0.972041	−	0.234811i	$-0.924553\pi$
$67$		−	3.84402i		−	0.469622i	0.972041	−	0.234811i	$-0.0754471\pi$
$68$	−2.03400	+	3.52300i	−0.246659	+	0.427226i
$69$	−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	$-0.700999\pi$
$72$			1.00000i			0.117851i
$73$	−10.0106	−	5.77964i	−1.17166	−	0.676455i	−0.217586	−	0.976041i	$-0.569818\pi$
$73$	−10.0106	−	5.77964i	−1.17166	−	0.676455i	−0.954069	+	0.299586i	$0.903152\pi$
$74$	−3.17302	−	5.49583i	−0.368856	−	0.638877i
$75$	2.26468	−	3.92254i	0.261503	−	0.452936i
$76$	−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	0.935543	−	0.353212i	$-0.114911\pi$
$79$	1.43883	+	2.49213i	0.161881	+	0.280386i	−0.773662	+	0.633598i	$0.781577\pi$
$80$		−	0.686034i		−	0.0767010i
$81$	1.00000			0.111111
$82$	6.63745			0.732984
$83$			5.79090i			0.635634i	0.948152	+	0.317817i	$0.102950\pi$
$83$			5.79090i			0.635634i	−0.948152	+	0.317817i	$0.897050\pi$
$84$	−1.10366	−	2.40456i	−0.120419	−	0.262360i
$85$	−2.41690	−	1.39540i	−0.262149	−	0.151352i
$86$	4.18440	−	2.41586i	0.451215	−	0.260509i
$87$	0.181197	+	0.313842i	0.0194263	+	0.0336474i
$88$	4.38424			0.467361
$89$	−7.10156	−	4.10009i	−0.752764	−	0.434608i	0.0739279	−	0.997264i	$-0.476447\pi$
$89$	−7.10156	−	4.10009i	−0.752764	−	0.434608i	−0.826692	+	0.562655i	$0.809780\pi$
$90$	−0.686034			−0.0723144
$91$	8.07108	+	5.08504i	0.846079	+	0.533057i
$92$	1.72422			0.179762
$93$	−3.49717	−	2.01909i	−0.362640	−	0.209370i
$94$	10.8362			1.11767
$95$	−2.46271	−	4.26553i	−0.252668	−	0.437634i
$96$	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	$0.617501\pi$
$98$	5.30765	+	4.56386i	0.536154	+	0.461020i
$99$		−	4.38424i		−	0.440632i
$100$	−4.52936			−0.452936
$101$	−13.9039			−1.38348			−0.691742	−	0.722144i	$-0.743157\pi$
$101$	−13.9039			−1.38348			−0.691742	+	0.722144i	$0.743157\pi$
$102$		−	4.06801i		−	0.402793i
$103$	−6.46334	−	11.1948i	−0.636852	−	1.10306i	−0.986119	−	0.166037i	$-0.946903\pi$
$103$	−6.46334	−	11.1948i	−0.636852	−	1.10306i	0.349267	−	0.937023i	$-0.386431\pi$
$104$	−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
$107$	9.03970	−	15.6572i	0.873900	−	1.51364i	0.0159710	−	0.999872i	$-0.494916\pi$
$107$	9.03970	−	15.6572i	0.873900	−	1.51364i	0.857929	−	0.513768i	$-0.171751\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	5.76738	+	3.32980i	0.552415	+	0.318937i	0.750095	−	0.661330i	$-0.230008\pi$
$109$	5.76738	+	3.32980i	0.552415	+	0.318937i	−0.197681	+	0.980266i	$0.563341\pi$
$110$			3.00774i			0.286777i
$111$	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	$0.167125\pi$
$114$	3.58977	−	6.21767i	0.336213	−	0.582338i
$115$			1.18288i			0.110304i
$116$	0.181197	−	0.313842i	0.0168237	−	0.0291395i
$117$	3.21637	+	1.62941i	0.297353	+	0.150639i
$118$	−2.49491			−0.229675
$119$	4.48970	+	9.78179i	0.411570	+	0.896695i
$120$	0.343017	+	0.594123i	0.0313130	+	0.0542358i
$121$	−8.22153			−0.747412
$122$	−6.97101	−	4.02471i	−0.631125	−	0.364380i
$123$	−5.74820	+	3.31872i	−0.518298	+	0.299239i
$124$			4.03819i			0.362640i
$125$		−	6.53747i		−	0.584729i
$126$	2.15808	+	1.53058i	0.192257	+	0.136355i
$127$	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	$0.686669\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−2.41586	+	4.18440i	−0.212705	+	0.368416i
$130$	−2.20654	−	1.11783i	−0.193526	−	0.0980401i
$131$	−2.28496	−	3.95767i	−0.199638	−	0.345783i	0.748773	−	0.662826i	$-0.230643\pi$
$131$	−2.28496	−	3.95767i	−0.199638	−	0.345783i	−0.948411	+	0.317043i	$0.897310\pi$
$132$	−3.79686	+	2.19212i	−0.330474	+	0.190799i
$133$	−1.76964	+	18.9127i	−0.153447	+	1.63994i
$134$	1.92201	−	3.32902i	0.166036	−	0.287583i
$135$	0.594123	−	0.343017i	0.0511340	−	0.0295222i
$136$	−3.52300	+	2.03400i	−0.302095	+	0.174414i
$137$	−2.00069	+	1.15510i	−0.170930	+	0.0986867i	−0.583024	−	0.812455i	$-0.698131\pi$
$137$	−2.00069	+	1.15510i	−0.170930	+	0.0986867i	0.412094	+	0.911141i	$0.364797\pi$
$138$	−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	$-0.0314969\pi$
$140$	−1.48052	−	1.05003i	−0.125127	−	0.0887440i
$141$	−9.38446	+	5.41812i	−0.790314	+	0.456288i
$142$	−7.70839	−	13.3513i	−0.646873	−	1.12042i
$143$	7.14371	−	14.1013i	0.597387	−	1.17921i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.215306	+	0.124307i	0.0178802	+	0.0103231i
$146$	−5.77964	−	10.0106i	−0.478326	−	0.828485i
$147$	−6.87849	−	1.29860i	−0.567328	−	0.107107i
$148$		−	6.34603i		−	0.521641i
$149$			0.122152i			0.0100071i	0.999987	+	0.00500353i	$0.00159268\pi$
$149$			0.122152i			0.0100071i	−0.999987	+	0.00500353i	$0.998407\pi$
$150$	3.92254	−	2.26468i	0.320274	−	0.184910i
$151$	19.1419	+	11.0516i	1.55775	+	0.899367i	0.997472	+	0.0710609i	$0.0226385\pi$
$151$	19.1419	+	11.0516i	1.55775	+	0.899367i	0.560276	+	0.828306i	$0.310695\pi$
$152$	−7.17954			−0.582338
$153$	2.03400	+	3.52300i	0.164440	+	0.284818i
$154$	6.71044	−	9.46154i	0.540743	−	0.762432i
$155$	−2.77034			−0.222519
$156$	−0.197077	−	3.60016i	−0.0157788	−	0.288244i
$157$	−6.93082	+	12.0045i	−0.553140	+	0.958066i	0.444906	+	0.895577i	$0.353237\pi$
$157$	−6.93082	+	12.0045i	−0.553140	+	0.958066i	−0.998046	+	0.0624887i	$0.980096\pi$
$158$			2.87766i			0.228935i
$159$	1.12532	−	1.94912i	0.0892439	−	0.154575i
$160$	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
$163$		−	18.2904i		−	1.43261i	−0.697787	−	0.716305i	$-0.745832\pi$
$163$		−	18.2904i		−	1.43261i	0.697787	−	0.716305i	$-0.254168\pi$
$164$	5.74820	+	3.31872i	0.448859	+	0.259149i
$165$	−1.50387	−	2.60478i	−0.117076	−	0.202782i
$166$	−2.89545	+	5.01506i	−0.224730	+	0.389244i
$167$	−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
$171$			7.17954i			0.549033i
$172$	4.83173			0.368416
$173$	−22.6350			−1.72091			−0.860454	−	0.509529i	$-0.829820\pi$
$173$	−22.6350			−1.72091			−0.860454	+	0.509529i	$0.829820\pi$
$174$			0.362393i			0.0274730i
$175$	−6.93256	+	9.77472i	−0.524052	+	0.738899i
$176$	3.79686	+	2.19212i	0.286199	+	0.165237i
$177$	2.16065	−	1.24745i	0.162405	−	0.0937644i
$178$	−4.10009	−	7.10156i	−0.307314	−	0.532284i
$179$	4.08694			0.305473			0.152736	−	0.988267i	$-0.451191\pi$
$179$	4.08694			0.305473			0.152736	+	0.988267i	$0.451191\pi$
$180$	−0.594123	−	0.343017i	−0.0442833	−	0.0255670i
$181$	3.18758			0.236931			0.118465	−	0.992958i	$-0.462203\pi$
$181$	3.18758			0.236931			0.118465	+	0.992958i	$0.462203\pi$
$182$	4.44724	+	8.43932i	0.329652	+	0.625564i
$183$	8.04943			0.595031
$184$	1.49322	+	0.862111i	0.110082	+	0.0635556i
$185$	4.35360			0.320083
$186$	−2.01909	−	3.49717i	−0.148047	−	0.256425i
$187$	15.4457	−	8.91756i	1.12950	−	0.652116i
$188$	9.38446	+	5.41812i	0.684432	+	0.395157i
$189$	−2.63424	−	0.246484i	−0.191613	−	0.0179291i
$190$		−	4.92541i		−	0.357327i
$191$	11.2486			0.813917			0.406959	−	0.913447i	$-0.366589\pi$
$191$	11.2486			0.813917			0.406959	+	0.913447i	$0.366589\pi$
$192$	1.00000			0.0721688
$193$			13.3419i			0.960373i	0.877166	+	0.480187i	$0.159431\pi$
$193$			13.3419i			0.960373i	−0.877166	+	0.480187i	$0.840569\pi$
$194$	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	$0.578937\pi$
$198$	2.19212	−	3.79686i	0.155787	−	0.269831i
$199$	2.16509	+	3.75005i	0.153479	+	0.265834i	0.932504	−	0.361159i	$-0.117619\pi$
$199$	2.16509	+	3.75005i	0.153479	+	0.265834i	−0.779025	+	0.626993i	$0.784286\pi$
$200$	−3.92254	−	2.26468i	−0.277365	−	0.160137i
$201$			3.84402i			0.271136i
$202$	−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
$205$	−2.27676	+	3.94346i	−0.159016	+	0.275423i
$206$		−	12.9267i		−	0.900645i
$207$	0.862111	−	1.49322i	0.0599208	−	0.103786i
$208$	−3.01929	+	1.97075i	−0.209350	+	0.136647i
$209$	31.4768			2.17730
$210$	1.80718	+	0.169096i	0.124707	+	0.0116688i
$211$	−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	$-0.594972\pi$
$212$	−2.25064			−0.154575
$213$	13.3513	+	7.70839i	0.914817	+	0.528170i
$214$	15.6572	−	9.03970i	1.07031	−	0.617941i
$215$			3.31473i			0.226063i
$216$		−	1.00000i		−	0.0680414i
$217$	8.71473	+	6.18078i	0.591595	+	0.419579i
$218$	3.32980	+	5.76738i	0.225522	+	0.390616i
$219$	10.0106	+	5.77964i	0.676455	+	0.390552i
$220$	−1.50387	+	2.60478i	−0.101391	+	0.175614i
$221$	0.801711	+	14.6455i	0.0539289	+	0.985162i
$222$	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	$0.100677\pi$
$224$	−2.40456	+	1.10366i	−0.160662	+	0.0737415i
$225$	−2.26468	+	3.92254i	−0.150979	+	0.261503i
$226$	−0.0265329	+	0.0153188i	−0.00176494	+	0.00101899i
$227$	−25.7193	+	14.8490i	−1.70705	+	0.985566i	−0.768879	+	0.639394i	$0.779185\pi$
$227$	−25.7193	+	14.8490i	−1.70705	+	0.985566i	−0.938171	+	0.346172i	$0.887481\pi$
$228$	6.21767	−	3.58977i	0.411775	−	0.237738i
$229$	12.7224	−	7.34527i	0.840719	−	0.485389i	−0.0167896	−	0.999859i	$-0.505345\pi$
$229$	12.7224	−	7.34527i	0.840719	−	0.485389i	0.857509	+	0.514470i	$0.172011\pi$
$230$	−0.591438	+	1.02440i	−0.0389982	+	0.0675469i
$231$	−1.08064	+	11.5492i	−0.0711012	+	0.759878i
$232$	0.313842	−	0.181197i	0.0206047	−	0.0118961i
$233$	−8.21697	−	14.2322i	−0.538312	−	0.932383i	−0.998995	−	0.0448186i	$-0.985729\pi$
$233$	−8.21697	−	14.2322i	−0.538312	−	0.932383i	0.460683	−	0.887564i	$-0.347604\pi$
$234$	1.97075	+	3.01929i	0.128832	+	0.197377i
$235$	−3.71702	+	6.43806i	−0.242472	+	0.419973i
$236$	−2.16065	−	1.24745i	−0.140647	−	0.0812023i
$237$	−1.43883	−	2.49213i	−0.0934621	−	0.161881i
$238$	−1.00270	+	10.7161i	−0.0649953	+	0.694624i
$239$		−	13.9983i		−	0.905473i	−0.891644	−	0.452737i	$-0.850448\pi$
$239$		−	13.9983i		−	0.905473i	0.891644	−	0.452737i	$-0.149552\pi$
$240$			0.686034i			0.0442833i
$241$	−9.94503	+	5.74177i	−0.640616	+	0.369860i	−0.784852	−	0.619684i	$-0.787261\pi$
$241$	−9.94503	+	5.74177i	−0.640616	+	0.369860i	0.144236	+	0.989543i	$0.453928\pi$
$242$	−7.12006	−	4.11077i	−0.457695	−	0.264250i
$243$	−1.00000			−0.0641500
$244$	−4.02471	−	6.97101i	−0.257656	−	0.446273i
$245$	−4.53211	+	1.58791i	−0.289546	+	0.101448i
$246$	−6.63745			−0.423188
$247$	−11.6984	+	23.0921i	−0.744351	+	1.46931i
$248$	−2.01909	+	3.49717i	−0.128213	+	0.222071i
$249$		−	5.79090i		−	0.366983i
$250$	3.26873	−	5.66161i	0.206733	−	0.358072i
$251$	−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
$254$			10.0214i			0.628800i
$255$	2.41690	+	1.39540i	0.151352	+	0.0873832i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.7110	+	20.2841i	−0.730512	+	1.26528i	0.226152	+	0.974092i	$0.427385\pi$
$257$	−11.7110	+	20.2841i	−0.730512	+	1.26528i	−0.956665	+	0.291192i	$0.905948\pi$
$258$	−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
$262$		−	4.56992i		−	0.282331i
$263$	2.29367			0.141434			0.0707169	−	0.997496i	$-0.477471\pi$
$263$	2.29367			0.141434			0.0707169	+	0.997496i	$0.477471\pi$
$264$	−4.38424			−0.269831
$265$		−	1.54402i		−	0.0948484i
$266$	−10.9889	+	15.4940i	−0.673772	+	0.950000i
$267$	7.10156	+	4.10009i	0.434608	+	0.250921i
$268$	3.32902	−	1.92201i	0.203352	−	0.117405i
$269$	−2.68261	−	4.64642i	−0.163562	−	0.283297i	0.772582	−	0.634915i	$-0.218965\pi$
$269$	−2.68261	−	4.64642i	−0.163562	−	0.283297i	−0.936144	+	0.351618i	$0.885632\pi$
$270$	0.686034			0.0417507
$271$	0.729207	+	0.421008i	0.0442961	+	0.0255744i	0.521985	−	0.852955i	$-0.325192\pi$
$271$	0.729207	+	0.421008i	0.0442961	+	0.0255744i	−0.477688	+	0.878529i	$0.658525\pi$
$272$	−4.06801			−0.246659
$273$	−8.07108	−	5.08504i	−0.488484	−	0.307761i
$274$	−2.31020			−0.139564
$275$	17.1973	+	9.92889i	1.03704	+	0.598734i
$276$	−1.72422			−0.103786
$277$	−7.19119	−	12.4555i	−0.432077	−	0.748379i	0.564975	−	0.825108i	$-0.308886\pi$
$277$	−7.19119	−	12.4555i	−0.432077	−	0.748379i	−0.997052	+	0.0767288i	$0.975552\pi$
$278$	11.9074	−	6.87474i	0.714159	−	0.412320i
$279$	3.49717	+	2.01909i	0.209370	+	0.120880i
$280$	−0.757149	−	1.64961i	−0.0452483	−	0.0985833i
$281$			2.03385i			0.121330i	0.998158	+	0.0606648i	$0.0193221\pi$
$281$			2.03385i			0.121330i	−0.998158	+	0.0606648i	$0.980678\pi$
$282$	−10.8362			−0.645289
$283$	−32.3521			−1.92313			−0.961566	−	0.274576i	$-0.911463\pi$
$283$	−32.3521			−1.92313			−0.961566	+	0.274576i	$0.911463\pi$
$284$		−	15.4168i		−	0.914817i
$285$	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
$289$	0.225650	−	0.390837i	0.0132735	−	0.0229904i
$290$	0.124307	+	0.215306i	0.00729956	+	0.0126432i
$291$	−2.62440	−	1.51520i	−0.153845	−	0.0888224i
$292$		−	11.5593i		−	0.676455i
$293$	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
$296$	3.17302	−	5.49583i	0.184428	−	0.319438i
$297$			4.38424i			0.254399i
$298$	−0.0610758	+	0.105786i	−0.00353803	+	0.00612804i
$299$	5.20593	−	3.39802i	0.301067	−	0.196512i
$300$	4.52936			0.261503
$301$	7.39537	−	10.4273i	0.426262	−	0.601017i
$302$	11.0516	+	19.1419i	0.635948	+	1.10149i
$303$	13.9039			0.798755
$304$	−6.21767	−	3.58977i	−0.356608	−	0.205888i
$305$	4.78235	−	2.76109i	0.273837	−	0.158100i
$306$			4.06801i			0.232553i
$307$		−	3.66321i		−	0.209070i	−0.994521	−	0.104535i	$-0.966665\pi$
$307$		−	3.66321i		−	0.209070i	0.994521	−	0.104535i	$-0.0333355\pi$
$308$	10.5422	−	4.83871i	0.600697	−	0.275711i
$309$	6.46334	+	11.1948i	0.367687	+	0.636852i
$310$	−2.39918	−	1.38517i	−0.136264	−	0.0786722i
$311$	0.833909	−	1.44437i	0.0472867	−	0.0819029i	−0.841413	−	0.540392i	$-0.818276\pi$
$311$	0.833909	−	1.44437i	0.0472867	−	0.0819029i	0.888700	+	0.458489i	$0.151609\pi$
$312$	1.62941	−	3.21637i	0.0922470	−	0.182091i
$313$	2.83514	+	4.91060i	0.160251	+	0.277564i	0.934959	−	0.354756i	$-0.115436\pi$
$313$	2.83514	+	4.91060i	0.160251	+	0.277564i	−0.774707	+	0.632320i	$0.782103\pi$
$314$	−12.0045	+	6.93082i	−0.677455	+	0.391129i
$315$	−1.64961	+	0.757149i	−0.0929452	+	0.0426605i
$316$	−1.43883	+	2.49213i	−0.0809406	+	0.140193i
$317$	27.3539	−	15.7928i	1.53635	−	0.887012i	0.537301	−	0.843391i	$-0.319444\pi$
$317$	27.3539	−	15.7928i	1.53635	−	0.887012i	0.999048	−	0.0436211i	$-0.0138894\pi$
$318$	1.94912	−	1.12532i	0.109301	−	0.0631049i
$319$	−1.37596	+	0.794409i	−0.0770388	+	0.0444783i
$320$	0.594123	−	0.343017i	0.0332125	−	0.0191752i
$321$	−9.03970	+	15.6572i	−0.504547	+	0.873900i
$322$	4.14600	−	1.90296i	0.231048	−	0.106048i
$323$	−25.2935	+	14.6032i	−1.40737	+	0.812545i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−13.6755	+	8.92625i	−0.758578	+	0.495139i
$326$	9.14518	−	15.8399i	0.506504	−	0.877291i
$327$	−5.76738	−	3.32980i	−0.318937	−	0.184138i
$328$	3.31872	+	5.74820i	0.183246	+	0.317391i
$329$	26.0565	−	11.9595i	1.43654	−	0.659351i
$330$		−	3.00774i		−	0.165570i
$331$			26.0238i			1.43040i	0.698921	+	0.715199i	$0.253664\pi$
$331$			26.0238i			1.43040i	−0.698921	+	0.715199i	$0.746336\pi$
$332$	−5.01506	+	2.89545i	−0.275237	+	0.158908i
$333$	−5.49583	−	3.17302i	−0.301169	−	0.173880i
$334$	−7.41737			−0.405861
$335$	1.31857	+	2.28382i	0.0720409	+	0.124779i
$336$	1.53058	−	2.15808i	0.0835002	−	0.117733i
$337$	−17.9060			−0.975404			−0.487702	−	0.873010i	$-0.662165\pi$
$337$	−17.9060			−0.975404			−0.487702	+	0.873010i	$0.662165\pi$
$338$	1.41902	+	12.9223i	0.0771844	+	0.702882i
$339$	0.0153188	−	0.0265329i	0.000832003	−	0.00144107i
$340$		−	2.79079i		−	0.151352i
$341$	8.85218	−	15.3324i	0.479373	−	0.830298i
$342$	−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
$345$		−	1.18288i		−	0.0636839i
$346$	−19.6025	−	11.3175i	−1.05384	−	0.608433i
$347$	14.9388	+	25.8747i	0.801956	+	1.38903i	0.918327	+	0.395822i	$0.129540\pi$
$347$	14.9388	+	25.8747i	0.801956	+	1.38903i	−0.116372	+	0.993206i	$0.537126\pi$
$348$	−0.181197	+	0.313842i	−0.00971315	+	0.0168237i
$349$	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
$353$		−	0.732055i		−	0.0389634i	−0.999810	−	0.0194817i	$-0.993798\pi$
$353$		−	0.732055i		−	0.0389634i	0.999810	−	0.0194817i	$-0.00620160\pi$
$354$	2.49491			0.132603
$355$	10.5764			0.561339
$356$		−	8.20017i		−	0.434608i
$357$	−4.48970	−	9.78179i	−0.237620	−	0.517707i
$358$	3.53940	+	2.04347i	0.187063	+	0.108001i
$359$	−21.3122	+	12.3046i	−1.12482	+	0.649412i	−0.942626	−	0.333851i	$-0.891652\pi$
$359$	−21.3122	+	12.3046i	−1.12482	+	0.649412i	−0.182189	+	0.983263i	$0.558318\pi$
$360$	−0.343017	−	0.594123i	−0.0180786	−	0.0313130i
$361$	−32.5458			−1.71294
$362$	2.76052	+	1.59379i	0.145090	+	0.0837677i
$363$	8.22153			0.431519
$364$	−0.368233	+	9.53228i	−0.0193007	+	0.499627i
$365$	7.93006			0.415078
$366$	6.97101	+	4.02471i	0.364380	+	0.210375i
$367$	13.7876			0.719706			0.359853	−	0.933009i	$-0.382827\pi$
$367$	13.7876			0.719706			0.359853	+	0.933009i	$0.382827\pi$
$368$	0.862111	+	1.49322i	0.0449406	+	0.0778394i
$369$	5.74820	−	3.31872i	0.299239	−	0.172766i
$370$	3.77033	+	2.17680i	0.196010	+	0.113166i
$371$	−3.44480	+	4.85707i	−0.178845	+	0.252167i
$372$		−	4.03819i		−	0.209370i
$373$	−13.7033			−0.709527			−0.354764	−	0.934956i	$-0.615439\pi$
$373$	−13.7033			−0.709527			−0.354764	+	0.934956i	$0.615439\pi$
$374$	17.8351			0.922232
$375$			6.53747i			0.337593i
$376$	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	$0.0682857\pi$
$380$	2.46271	−	4.26553i	0.126334	−	0.218817i
$381$	−5.01071	−	8.67881i	−0.256707	−	0.444629i
$382$	9.74154	+	5.62428i	0.498420	+	0.287763i
$383$			19.6812i			1.00566i	0.864385	+	0.502831i	$0.167708\pi$
$383$			19.6812i			1.00566i	−0.864385	+	0.502831i	$0.832292\pi$
$384$	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
$387$	2.41586	−	4.18440i	0.122805	−	0.212705i
$388$			3.03039i			0.153845i
$389$	12.0388	−	20.8518i	0.610390	−	1.05723i	−0.380785	−	0.924664i	$-0.624346\pi$
$389$	12.0388	−	20.8518i	0.610390	−	1.05723i	0.991175	−	0.132563i	$-0.0423206\pi$
$390$	2.20654	+	1.11783i	0.111733	+	0.0566035i
$391$	7.01415			0.354721
$392$	−1.29860	+	6.87849i	−0.0655891	+	0.347416i
$393$	2.28496	+	3.95767i	0.115261	+	0.199638i
$394$	−19.5734			−0.986093
$395$	−1.70969	−	0.987088i	−0.0860237	−	0.0496658i
$396$	3.79686	−	2.19212i	0.190799	−	0.110158i
$397$		−	26.7878i		−	1.34444i	−0.740351	−	0.672220i	$-0.765341\pi$
$397$		−	26.7878i		−	1.34444i	0.740351	−	0.672220i	$-0.234659\pi$
$398$			4.33018i			0.217052i
$399$	1.76964	−	18.9127i	0.0885929	−	0.946818i
$400$	−2.26468	−	3.92254i	−0.113234	−	0.196127i
$401$	24.9872	+	14.4264i	1.24780	+	0.720419i	0.970671	−	0.240413i	$-0.0772828\pi$
$401$	24.9872	+	14.4264i	1.24780	+	0.720419i	0.277132	+	0.960832i	$0.410616\pi$
$402$	−1.92201	+	3.32902i	−0.0958612	+	0.166036i
$403$	7.95827	+	12.1925i	0.396430	+	0.607350i
$404$	−6.95193	−	12.0411i	−0.345871	−	0.599067i
$405$	−0.594123	+	0.343017i	−0.0295222	+	0.0170447i
$406$	0.0893241	−	0.954632i	0.00443308	−	0.0473776i
$407$	−13.9113	+	24.0950i	−0.689555	+	1.19434i
$408$	3.52300	−	2.03400i	0.174414	−	0.100698i
$409$	26.4739	−	15.2847i	1.30905	−	0.755781i	0.327113	−	0.944985i	$-0.393924\pi$
$409$	26.4739	−	15.2847i	1.30905	−	0.755781i	0.981938	+	0.189204i	$0.0605907\pi$
$410$	−3.94346	+	2.27676i	−0.194754	+	0.112441i
$411$	2.00069	−	1.15510i	0.0986867	−	0.0569768i
$412$	6.46334	−	11.1948i	0.318426	−	0.551530i
$413$	−5.99917	+	2.75353i	−0.295200	+	0.135492i
$414$	1.49322	−	0.862111i	0.0733877	−	0.0423704i
$415$	−1.98638	−	3.44051i	−0.0975074	−	0.168888i
$416$	−3.60016	+	0.197077i	−0.176512	+	0.00966249i
$417$	−6.87474	+	11.9074i	−0.336658	+	0.583108i
$418$	27.2597	+	15.7384i	1.33332	+	0.769791i
$419$	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	$0.773322\pi$
$420$	1.48052	+	1.05003i	0.0722419	+	0.0512364i
$421$			8.38578i			0.408698i	0.978898	+	0.204349i	$0.0655077\pi$
$421$			8.38578i			0.408698i	−0.978898	+	0.204349i	$0.934492\pi$
$422$		−	28.3179i		−	1.37849i
$423$	9.38446	−	5.41812i	0.456288	−	0.263438i
$424$	−1.94912	−	1.12532i	−0.0946574	−	0.0546505i
$425$	−18.4255			−0.893766
$426$	7.70839	+	13.3513i	0.373473	+	0.646873i
$427$	−21.2042	−	1.98405i	−1.02614	−	0.0960151i
$428$	18.0794			0.873900
$429$	−7.14371	+	14.1013i	−0.344901	+	0.680818i
$430$	−1.65737	+	2.87064i	−0.0799253	+	0.138435i
$431$			3.25173i			0.156630i	0.996929	+	0.0783152i	$0.0249541\pi$
$431$			3.25173i			0.156630i	−0.996929	+	0.0783152i	$0.975046\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−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
$436$			6.65959i			0.318937i
$437$	10.7206	+	6.18956i	0.512837	+	0.296087i
$438$	5.77964	+	10.0106i	0.276162	+	0.478326i
$439$	11.5089	−	19.9340i	0.549290	−	0.951398i	−0.449034	−	0.893515i	$-0.648232\pi$
$439$	11.5089	−	19.9340i	0.549290	−	0.951398i	0.998323	−	0.0578829i	$-0.0184350\pi$
$440$	−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	−0.984740	−	0.174033i	$-0.944320\pi$
$443$	−13.5354	−	23.4440i	−0.643087	−	1.11386i	0.341653	−	0.939826i	$-0.389013\pi$
$444$			6.34603i			0.301169i
$445$	5.62560			0.266679
$446$	19.9373			0.944057
$447$		−	0.122152i		−	0.00577757i
$448$	−2.63424	−	0.246484i	−0.124456	−	0.0116453i
$449$	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
$451$	−14.5501	−	25.2015i	−0.685136	−	1.18669i
$452$	−0.0306376			−0.00144107
$453$	−19.1419	−	11.0516i	−0.899367	−	0.519249i
$454$	−29.6981			−1.39380
$455$	−6.53947	−	0.252621i	−0.306575	−	0.0118430i
$456$	7.17954			0.336213
$457$	−12.4651	−	7.19673i	−0.583093	−	0.336649i	0.179269	−	0.983800i	$-0.442627\pi$
$457$	−12.4651	−	7.19673i	−0.583093	−	0.336649i	−0.762362	+	0.647151i	$0.775960\pi$
$458$	14.6905			0.686444
$459$	−2.03400	−	3.52300i	−0.0949392	−	0.164440i
$460$	−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	$0.357867\pi$
$462$	−6.71044	+	9.46154i	−0.312198	+	0.440191i
$463$		−	36.1762i		−	1.68125i	−0.541616	−	0.840626i	$-0.682187\pi$
$463$		−	36.1762i		−	1.68125i	0.541616	−	0.840626i	$-0.317813\pi$
$464$	0.362393			0.0168237
$465$	2.77034			0.128471
$466$		−	16.4339i		−	0.761288i
$467$	−17.4517	−	30.2272i	−0.807566	−	1.39875i	−0.914545	−	0.404484i	$-0.867451\pi$
$467$	−17.4517	−	30.2272i	−0.807566	−	1.39875i	0.106979	−	0.994261i	$-0.465882\pi$
$468$	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
$471$	6.93082	−	12.0045i	0.319355	−	0.553140i
$472$	−1.24745	−	2.16065i	−0.0574187	−	0.0994521i
$473$	−18.3454	−	10.5917i	−0.843522	−	0.487008i
$474$		−	2.87766i		−	0.132175i
$475$	−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
$478$	6.99914	−	12.1229i	0.320133	−	0.554487i
$479$			4.05100i			0.185095i	0.995708	+	0.0925474i	$0.0295010\pi$
$479$			4.05100i			0.185095i	−0.995708	+	0.0925474i	$0.970499\pi$
$480$	−0.343017	+	0.594123i	−0.0156565	+	0.0271179i
$481$	−12.5065	−	19.1605i	−0.570246	−	0.873645i
$482$	−11.4835			−0.523061
$483$	−2.63907	+	3.72101i	−0.120082	+	0.169312i
$484$	−4.11077	−	7.12006i	−0.186853	−	0.323639i
$485$	−2.07895			−0.0944005
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	5.85402	−	3.37982i	0.265271	−	0.153154i	−0.361466	−	0.932385i	$-0.617724\pi$
$487$	5.85402	−	3.37982i	0.265271	−	0.153154i	0.626737	+	0.779231i	$0.284390\pi$
$488$		−	8.04943i		−	0.364380i
$489$			18.2904i			0.827118i
$490$	−4.71888	−	0.890883i	−0.213177	−	0.0402460i
$491$	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	$0.821987\pi$
$492$	−5.74820	−	3.31872i	−0.259149	−	0.149620i
$493$	0.737109	−	1.27671i	0.0331977	−	0.0575002i
$494$	−21.6771	+	14.1491i	−0.975301	+	0.636599i
$495$	1.50387	+	2.60478i	0.0675939	+	0.117076i
$496$	−3.49717	+	2.01909i	−0.157028	+	0.0906600i
$497$	−33.2706	−	23.5967i	−1.49239	−	1.05846i
$498$	2.89545	−	5.01506i	0.129748	−	0.224730i
$499$	−5.29521	+	3.05719i	−0.237046	+	0.136859i	−0.613818	−	0.789447i	$-0.710367\pi$
$499$	−5.29521	+	3.05719i	−0.237046	+	0.136859i	0.376772	+	0.926306i	$0.377034\pi$
$500$	5.66161	−	3.26873i	0.253195	−	0.146182i
$501$	6.42363	−	3.70869i	0.286987	−	0.165692i
$502$	−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	$0.235871\pi$
$504$	−0.246484	+	2.63424i	−0.0109793	+	0.117339i
$505$	8.26060	−	4.76926i	0.367592	−	0.212229i
$506$	−3.77970	−	6.54663i	−0.168028	−	0.291033i
$507$	−7.69007	−	10.4815i	−0.341528	−	0.465502i
$508$	−5.01071	+	8.67881i	−0.222314	+	0.385060i
$509$	19.0762	+	11.0136i	0.845537	+	0.488171i	0.859142	−	0.511736i	$-0.170998\pi$
$509$	19.0762	+	11.0136i	0.845537	+	0.488171i	−0.0136055	+	0.999907i	$0.504331\pi$
$510$	1.39540	+	2.41690i	0.0617892	+	0.107022i
$511$	−24.9459	−	17.6924i	−1.10354	−	0.782667i
$512$		−	1.00000i		−	0.0441942i
$513$		−	7.17954i		−	0.316985i
$514$	−20.2841	+	11.7110i	−0.894691	+	0.516550i
$515$	7.68005	+	4.43408i	0.338423	+	0.195389i
$516$	−4.83173			−0.212705
$517$	−23.7543	−	41.1437i	−1.04471	−	1.80950i
$518$	−7.00387	−	15.2594i	−0.307732	−	0.670462i
$519$	22.6350			0.993566
$520$	−0.135202	−	2.46983i	−0.00592898	−	0.108309i
$521$	0.146783	−	0.254235i	0.00643067	−	0.0111383i	−0.862792	−	0.505559i	$-0.831286\pi$
$521$	0.146783	−	0.254235i	0.00643067	−	0.0111383i	0.869223	+	0.494421i	$0.164620\pi$
$522$		−	0.362393i		−	0.0158615i
$523$	−4.42940	+	7.67195i	−0.193684	+	0.335471i	−0.946468	−	0.322797i	$-0.895377\pi$
$523$	−4.42940	+	7.67195i	−0.193684	+	0.335471i	0.752784	+	0.658267i	$0.228710\pi$
$524$	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
$527$			16.4274i			0.715588i
$528$	−3.79686	−	2.19212i	−0.165237	−	0.0953997i
$529$	10.0135	+	17.3439i	0.435371	+	0.754085i
$530$	0.772010	−	1.33716i	0.0335340	−	0.0580825i
$531$	−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
$535$			12.4031i			0.536232i
$536$	3.84402			0.166036
$537$	−4.08694			−0.176365
$538$		−	5.36522i		−	0.231311i
$539$	5.69336	−	30.1569i	0.245230	−	1.29895i
$540$	0.594123	+	0.343017i	0.0255670	+	0.0147611i
$541$	−14.0782	+	8.12802i	−0.605267	+	0.349451i	−0.771111	−	0.636701i	$-0.780299\pi$
$541$	−14.0782	+	8.12802i	−0.605267	+	0.349451i	0.165844	+	0.986152i	$0.446965\pi$
$542$	0.421008	+	0.729207i	0.0180838	+	0.0313221i
$543$	−3.18758			−0.136792
$544$	−3.52300	−	2.03400i	−0.151047	−	0.0872072i
$545$	−4.56871			−0.195702
$546$	−4.44724	−	8.43932i	−0.190324	−	0.361169i
$547$	−21.7683			−0.930746			−0.465373	−	0.885115i	$-0.654080\pi$
$547$	−21.7683			−0.930746			−0.465373	+	0.885115i	$0.654080\pi$
$548$	−2.00069	−	1.15510i	−0.0854652	−	0.0493433i
$549$	−8.04943			−0.343541
$550$	9.92889	+	17.1973i	0.423369	+	0.733297i
$551$	2.25324	−	1.30091i	0.0959912	−	0.0554206i
$552$	−1.49322	−	0.862111i	−0.0635556	−	0.0366939i
$553$	3.17596	+	6.91953i	0.135056	+	0.294248i
$554$		−	14.3824i		−	0.611049i
$555$	−4.35360			−0.184800
$556$	13.7495			0.583108
$557$		−	30.2279i		−	1.28080i	−0.768044	−	0.640398i	$-0.778770\pi$
$557$		−	30.2279i		−	1.28080i	0.768044	−	0.640398i	$-0.221230\pi$
$558$	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
$562$	−1.01693	+	1.76137i	−0.0428965	+	0.0742989i
$563$	−11.1939	−	19.3884i	−0.471767	−	0.817124i	0.527711	−	0.849424i	$-0.323050\pi$
$563$	−11.1939	−	19.3884i	−0.471767	−	0.817124i	−0.999478	+	0.0322995i	$0.989717\pi$
$564$	−9.38446	−	5.41812i	−0.395157	−	0.228144i
$565$		−	0.0210184i		−	0.000884253i
$566$	−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
$569$	−9.78975	+	16.9564i	−0.410408	+	0.710847i	−0.994934	−	0.100527i	$-0.967947\pi$
$569$	−9.78975	+	16.9564i	−0.410408	+	0.710847i	0.584526	+	0.811375i	$0.301280\pi$
$570$			4.92541i			0.206303i
$571$	6.67181	−	11.5559i	0.279206	−	0.483600i	−0.691981	−	0.721915i	$-0.743262\pi$
$571$	6.67181	−	11.5559i	0.279206	−	0.483600i	0.971188	+	0.238316i	$0.0765953\pi$
$572$	15.7840	−	0.864032i	0.659961	−	0.0361270i
$573$	−11.2486			−0.469915
$574$	17.4847	+	1.63602i	0.729796	+	0.0682864i
$575$	3.90481	+	6.76332i	0.162842	+	0.282050i
$576$	−1.00000			−0.0416667
$577$	19.9482	+	11.5171i	0.830456	+	0.479464i	0.854009	−	0.520259i	$-0.174165\pi$
$577$	19.9482	+	11.5171i	0.830456	+	0.479464i	−0.0235531	+	0.999723i	$0.507498\pi$
$578$	0.390837	−	0.225650i	0.0162567	−	0.00938580i
$579$		−	13.3419i		−	0.554472i
$580$			0.248614i			0.0103231i
$581$	−1.42736	+	15.2546i	−0.0592170	+	0.632869i
$582$	−1.51520	−	2.62440i	−0.0628069	−	0.108785i
$583$	8.54538	+	4.93368i	0.353914	+	0.204332i
$584$	5.77964	−	10.0106i	0.239163	−	0.414243i
$585$	−2.46983	+	0.135202i	−0.102115	+	0.00558990i
$586$	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	$0.663498\pi$
$588$	−2.31463	−	6.60625i	−0.0954536	−	0.272437i
$589$	−14.4962	+	25.1081i	−0.597304	+	1.03456i
$590$	1.48228	−	0.855796i	0.0610246	−	0.0352326i
$591$	16.9510	−	9.78669i	0.697273	−	0.402571i
$592$	5.49583	−	3.17302i	0.225877	−	0.130410i
$593$	2.91474	−	1.68283i	0.119694	−	0.0691054i	−0.438958	−	0.898508i	$-0.644652\pi$
$593$	2.91474	−	1.68283i	0.119694	−	0.0691054i	0.558652	+	0.829402i	$0.311319\pi$
$594$	−2.19212	+	3.79686i	−0.0899437	+	0.155787i
$595$	−6.02276	−	4.27154i	−0.246909	−	0.175116i
$596$	−0.105786	+	0.0610758i	−0.00433318	+	0.00250176i
$597$	−2.16509	−	3.75005i	−0.0886113	−	0.153479i
$598$	6.20747	−	0.339804i	0.253843	−	0.0138956i
$599$	−3.69415	+	6.39846i	−0.150939	+	0.261434i	−0.931573	−	0.363555i	$-0.881563\pi$
$599$	−3.69415	+	6.39846i	−0.150939	+	0.261434i	0.780634	+	0.624988i	$0.214896\pi$
$600$	3.92254	+	2.26468i	0.160137	+	0.0924551i
$601$	−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	$-0.361383\pi$
$602$	11.6182	−	5.33259i	0.473523	−	0.217340i
$603$		−	3.84402i		−	0.156541i
$604$			22.1032i			0.899367i
$605$	4.88460	−	2.82013i	0.198587	−	0.114654i
$606$	12.0411	+	6.95193i	0.489136	+	0.282403i
$607$	−27.0999			−1.09995			−0.549975	−	0.835181i	$-0.685363\pi$
$607$	−27.0999			−1.09995			−0.549975	+	0.835181i	$0.685363\pi$
$608$	−3.58977	−	6.21767i	−0.145584	−	0.252160i
$609$	0.399959	+	0.871398i	0.0162072	+	0.0353108i
$610$	5.52218			0.223587
$611$	39.0122	−	2.13557i	1.57827	−	0.0863961i
$612$	−2.03400	+	3.52300i	−0.0822198	+	0.142409i
$613$		−	28.7712i		−	1.16206i	−0.813882	−	0.581030i	$-0.802650\pi$
$613$		−	28.7712i		−	1.16206i	0.813882	−	0.581030i	$-0.197350\pi$
$614$	1.83161	−	3.17243i	0.0739176	−	0.128029i
$615$	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	$0.809791\pi$
$618$			12.9267i			0.519988i
$619$	−4.81229	−	2.77838i	−0.193422	−	0.111672i	0.400161	−	0.916445i	$-0.368954\pi$
$619$	−4.81229	−	2.77838i	−0.193422	−	0.111672i	−0.593584	+	0.804772i	$0.702287\pi$
$620$	−1.38517	−	2.39918i	−0.0556297	−	0.0963534i
$621$	−0.862111	+	1.49322i	−0.0345953	+	0.0599208i
$622$	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
$626$			5.67027i			0.226630i
$627$	−31.4768			−1.25706
$628$	−13.8616			−0.553140
$629$		−	25.8157i		−	1.02934i
$630$	−1.80718	−	0.169096i	−0.0719999	−	0.00673696i
$631$	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
$633$	14.1589	+	24.5240i	0.562767	+	0.974741i
$634$	31.5856			1.25442
$635$	−5.95396	−	3.43752i	−0.236276	−	0.136414i
$636$	2.25064			0.0892439
$637$	20.0078	+	15.3846i	0.792739	+	0.609561i
$638$	−1.58882			−0.0629019
$639$	−13.3513	−	7.70839i	−0.528170	−	0.304939i
$640$	0.686034			0.0271179
$641$	−15.5919	−	27.0060i	−0.615843	−	1.06667i	−0.990236	−	0.139401i	$-0.955482\pi$
$641$	−15.5919	−	27.0060i	−0.615843	−	1.06667i	0.374393	−	0.927270i	$-0.377851\pi$
$642$	−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	$0.455498\pi$
$644$	4.54202	+	0.424993i	0.178981	+	0.0167471i
$645$		−	3.31473i		−	0.130517i
$646$	−29.2064			−1.14911
$647$	4.29829			0.168983			0.0844917	−	0.996424i	$-0.473073\pi$
$647$	4.29829			0.168983			0.0844917	+	0.996424i	$0.473073\pi$
$648$			1.00000i			0.0392837i
$649$	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
$653$	−6.63003	+	11.4835i	−0.259453	+	0.449386i	−0.966096	−	0.258185i	$-0.916876\pi$
$653$	−6.63003	+	11.4835i	−0.259453	+	0.449386i	0.706642	+	0.707571i	$0.250209\pi$
$654$	−3.32980	−	5.76738i	−0.130205	−	0.225522i
$655$	2.71510	+	1.56756i	0.106088	+	0.0612497i
$656$			6.63745i			0.259149i
$657$	−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	$0.206599\pi$
$660$	1.50387	−	2.60478i	0.0585380	−	0.101391i
$661$			20.6200i			0.802026i	0.916072	+	0.401013i	$0.131342\pi$
$661$			20.6200i			0.802026i	−0.916072	+	0.401013i	$0.868658\pi$
$662$	−13.0119	+	22.5373i	−0.505722	+	0.875936i
$663$	−0.801711	−	14.6455i	−0.0311359	−	0.568784i
$664$	−5.79090			−0.224730
$665$	−5.43599	−	11.8435i	−0.210799	−	0.459270i
$666$	−3.17302	−	5.49583i	−0.122952	−	0.212959i
$667$	−0.624846			−0.0241941
$668$	−6.42363	−	3.70869i	−0.248538	−	0.143493i
$669$	−17.2662	+	9.96863i	−0.667549	+	0.385409i
$670$			2.63713i			0.101881i
$671$			35.2906i			1.36238i
$672$	2.40456	−	1.10366i	0.0927581	−	0.0425746i
$673$	−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	$0.883329\pi$
$674$	−15.5071	−	8.95302i	−0.597310	−	0.344857i
$675$	2.26468	−	3.92254i	0.0871675	−	0.150979i
$676$	−5.23226	+	11.9006i	−0.201241	+	0.457714i
$677$	16.0806	+	27.8524i	0.618027	+	1.07045i	0.989845	+	0.142149i	$0.0454012\pi$
$677$	16.0806	+	27.8524i	0.618027	+	1.07045i	−0.371818	+	0.928306i	$0.621266\pi$
$678$	0.0265329	−	0.0153188i	0.00101899	−	0.000588315i
$679$	6.53984	+	4.63827i	0.250976	+	0.178001i
$680$	1.39540	−	2.41690i	0.0535110	−	0.0926838i
$681$	25.7193	−	14.8490i	0.985566	−	0.569017i
$682$	15.3324	−	8.85218i	0.587109	−	0.338968i
$683$	−14.1359	+	8.16136i	−0.540895	+	0.312286i	−0.745442	−	0.666571i	$-0.767761\pi$
$683$	−14.1359	+	8.16136i	−0.540895	+	0.312286i	0.204547	+	0.978857i	$0.434428\pi$
$684$	−6.21767	+	3.58977i	−0.237738	+	0.137258i
$685$	0.792437	−	1.37254i	0.0302775	−	0.0524421i
$686$	12.8567	+	13.3306i	0.490872	+	0.508964i
$687$	−12.7224	+	7.34527i	−0.485389	+	0.280240i
$688$	2.41586	+	4.18440i	0.0921040	+	0.159529i
$689$	−6.79536	+	4.43547i	−0.258882	+	0.168978i
$690$	0.591438	−	1.02440i	0.0225156	−	0.0389982i
$691$	38.0450	+	21.9653i	1.44730	+	0.835598i	0.998320	−	0.0579445i	$-0.0184547\pi$
$691$	38.0450	+	21.9653i	1.44730	+	0.835598i	0.448978	+	0.893543i	$0.351788\pi$
$692$	−11.3175	−	19.6025i	−0.430227	−	0.745175i
$693$	1.08064	−	11.5492i	0.0410503	−	0.438716i
$694$			29.8776i			1.13414i
$695$			9.43262i			0.357800i
$696$	−0.313842	+	0.181197i	−0.0118961	+	0.00686824i
$697$	23.3837	+	13.5006i	0.885722	+	0.511372i
$698$	0.432834			0.0163830
$699$	8.21697	+	14.2322i	0.310794	+	0.538312i
$700$	−11.9314	−	1.11641i	−0.450966	−	0.0421965i
$701$	23.1586			0.874688			0.437344	−	0.899294i	$-0.355919\pi$
$701$	23.1586			0.874688			0.437344	+	0.899294i	$0.355919\pi$
$702$	−1.97075	−	3.01929i	−0.0743813	−	0.113956i
$703$	22.7808	−	39.4575i	0.859194	−	1.48817i
$704$			4.38424i			0.165237i
$705$	3.71702	−	6.43806i	0.139991	−	0.242472i
$706$	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
$709$			47.0037i			1.76526i	0.470068	+	0.882630i	$0.344229\pi$
$709$			47.0037i			1.76526i	−0.470068	+	0.882630i	$0.655771\pi$
$710$	9.15946	+	5.28822i	0.343749	+	0.198463i
$711$	1.43883	+	2.49213i	0.0539604	+	0.0934621i
$712$	4.10009	−	7.10156i	0.153657	−	0.266142i
$713$	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
$717$			13.9983i			0.522775i
$718$	−24.6092			−0.918408
$719$	−16.4056			−0.611826			−0.305913	−	0.952059i	$-0.598962\pi$
$719$	−16.4056			−0.611826			−0.305913	+	0.952059i	$0.598962\pi$
$720$		−	0.686034i		−	0.0255670i
$721$	−14.2667	−	31.0831i	−0.531319	−	1.15759i
$722$	−28.1855	−	16.2729i	−1.04896	−	0.605615i
$723$	9.94503	−	5.74177i	0.369860	−	0.213539i
$724$	1.59379	+	2.76052i	0.0592327	+	0.102594i
$725$	1.64141			0.0609604
$726$	7.12006	+	4.11077i	0.264250	+	0.152565i
$727$	13.0415			0.483681			0.241841	−	0.970316i	$-0.422249\pi$
$727$	13.0415			0.483681			0.241841	+	0.970316i	$0.422249\pi$
$728$	−5.08504	+	8.07108i	−0.188464	+	0.299134i
$729$	1.00000			0.0370370
$730$	6.86763	+	3.96503i	0.254183	+	0.146752i
$731$	19.6555			0.726986
$732$	4.02471	+	6.97101i	0.148758	+	0.257656i
$733$	28.0127	−	16.1732i	1.03467	−	0.597369i	0.116354	−	0.993208i	$-0.462879\pi$
$733$	28.0127	−	16.1732i	1.03467	−	0.597369i	0.918320	+	0.395838i	$0.129546\pi$
$734$	11.9404	+	6.89379i	0.440728	+	0.254454i
$735$	4.53211	−	1.58791i	0.167170	−	0.0585711i
$736$			1.72422i			0.0635556i
$737$	−16.8531			−0.620792
$738$	6.63745			0.244328
$739$			1.05052i			0.0386439i	0.999813	+	0.0193220i	$0.00615075\pi$
$739$			1.05052i			0.0386439i	−0.999813	+	0.0193220i	$0.993849\pi$
$740$	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	$0.0488358\pi$
$744$	2.01909	−	3.49717i	0.0740236	−	0.128213i
$745$	−0.0419001	−	0.0725731i	−0.00153510	−	0.00265887i
$746$	−11.8674	−	6.85163i	−0.434495	−	0.250856i
$747$			5.79090i			0.211878i
$748$	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
$751$	−17.8165	+	30.8592i	−0.650135	+	1.12607i	0.332955	+	0.942943i	$0.391954\pi$
$751$	−17.8165	+	30.8592i	−0.650135	+	1.12607i	−0.983090	+	0.183124i	$0.941379\pi$
$752$			10.8362i			0.395157i
$753$	6.11401	−	10.5898i	0.222807	−	0.385913i
$754$	0.590486	−	1.16559i	0.0215042	−	0.0424483i
$755$	−15.1636			−0.551858
$756$	−1.10366	−	2.40456i	−0.0401398	−	0.0874532i
$757$	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	$0.542059\pi$
$758$	28.8021			1.04614
$759$	6.54663	+	3.77970i	0.237628	+	0.137194i
$760$	4.26553	−	2.46271i	0.154727	−	0.0893318i
$761$		−	10.3000i		−	0.373373i	−0.982420	−	0.186686i	$-0.940225\pi$
$761$		−	10.3000i		−	0.373373i	0.982420	−	0.186686i	$-0.0597749\pi$
$762$		−	10.0214i		−	0.363038i
$763$	14.3719	+	10.1931i	0.520299	+	0.369014i
$764$	5.62428	+	9.74154i	0.203479	+	0.352436i
$765$	−2.41690	−	1.39540i	−0.0873832	−	0.0504507i
$766$	−9.84060	+	17.0444i	−0.355555	+	0.615840i
$767$	−8.98207	+	0.491689i	−0.324324	+	0.0177539i
$768$	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	$0.0909875\pi$
$770$	−0.741359	+	7.92312i	−0.0267167	+	0.285529i
$771$	11.7110	−	20.2841i	0.421761	−	0.730512i
$772$	−11.5544	+	6.67096i	−0.415854	+	0.240093i
$773$	−12.4917	+	7.21208i	−0.449295	+	0.259400i	−0.707532	−	0.706681i	$-0.750192\pi$
$773$	−12.4917	+	7.21208i	−0.449295	+	0.259400i	0.258238	+	0.966081i	$0.416858\pi$
$774$	4.18440	−	2.41586i	0.150405	−	0.0868365i
$775$	−15.8399	+	9.14519i	−0.568987	+	0.328505i
$776$	−1.51520	+	2.62440i	−0.0543924	+	0.0942104i
$777$	13.6953	+	9.71313i	0.491314	+	0.348457i
$778$	20.8518	−	12.0388i	0.747572	−	0.431611i
$779$	23.8269	+	41.2694i	0.853688	+	1.47863i
$780$	1.35201	+	2.07134i	0.0484096	+	0.0741658i
$781$	−33.7954	+	58.5353i	−1.20929	+	2.09456i
$782$	6.07443	+	3.50707i	0.217221	+	0.125413i
$783$	0.181197	+	0.313842i	0.00647544	+	0.0112158i
$784$	−4.56386	+	5.30765i	−0.162995	+	0.189559i
$785$		−	9.50956i		−	0.339411i
$786$			4.56992i			0.163004i
$787$	27.1056	−	15.6494i	0.966210	−	0.557841i	0.0681310	−	0.997676i	$-0.478296\pi$
$787$	27.1056	−	15.6494i	0.966210	−	0.557841i	0.898079	+	0.439835i	$0.144963\pi$
$788$	−16.9510	−	9.78669i	−0.603856	−	0.348636i
$789$	−2.29367			−0.0816568
$790$	−0.987088	−	1.70969i	−0.0351190	−	0.0608279i
$791$	−0.0468934	+	0.0661184i	−0.00166734	+	0.00235090i
$792$	4.38424			0.155787
$793$	−25.8899	−	13.1158i	−0.919378	−	0.465755i
$794$	13.3939	−	23.1989i	0.475331	−	0.823298i
$795$			1.54402i			0.0547607i
$796$	−2.16509	+	3.75005i	−0.0767396	+	0.132917i
$797$	−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
$800$		−	4.52936i		−	0.160137i
$801$	−7.10156	−	4.10009i	−0.250921	−	0.144869i
$802$	14.4264	+	24.9872i	0.509413	+	0.882330i
$803$	−25.3393	+	43.8890i	−0.894205	+	1.54881i
$804$	−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
$808$		−	13.9039i		−	0.489136i
$809$	−13.7801			−0.484483			−0.242241	−	0.970216i	$-0.577883\pi$
$809$	−13.7801			−0.484483			−0.242241	+	0.970216i	$0.577883\pi$
$810$	−0.686034			−0.0241048
$811$			11.0037i			0.386392i	0.981160	+	0.193196i	$0.0618854\pi$
$811$			11.0037i			0.386392i	−0.981160	+	0.193196i	$0.938115\pi$
$812$	0.554673	−	0.782074i	0.0194652	−	0.0274454i
$813$	−0.729207	−	0.421008i	−0.0255744	−	0.0147654i
$814$	−24.0950	+	13.9113i	−0.844529	+	0.487589i
$815$	6.27391	+	10.8667i	0.219765	+	0.380645i
$816$	4.06801			0.142409
$817$	30.0421	+	17.3448i	1.05104	+	0.606818i
$818$	30.5695			1.06884
$819$	8.07108	+	5.08504i	0.282026	+	0.177686i
$820$	−4.55352			−0.159016
$821$	−16.1323	−	9.31400i	−0.563022	−	0.325061i	0.191335	−	0.981525i	$-0.438718\pi$
$821$	−16.1323	−	9.31400i	−0.563022	−	0.325061i	−0.754358	+	0.656464i	$0.772051\pi$
$822$	2.31020			0.0805773
$823$	10.2186	+	17.6991i	0.356198	+	0.616953i	0.987322	−	0.158729i	$-0.0507395\pi$
$823$	10.2186	+	17.6991i	0.356198	+	0.616953i	−0.631124	+	0.775682i	$0.717406\pi$
$824$	11.1948	−	6.46334i	0.389991	−	0.225161i
$825$	−17.1973	−	9.92889i	−0.598734	−	0.345679i
$826$	−6.57220	−	0.614955i	−0.228676	−	0.0213970i
$827$		−	45.1555i		−	1.57021i	−0.619362	−	0.785105i	$-0.712609\pi$
$827$		−	45.1555i		−	1.57021i	0.619362	−	0.785105i	$-0.287391\pi$
$828$	1.72422			0.0599208
$829$	−4.11794			−0.143022			−0.0715110	−	0.997440i	$-0.522782\pi$
$829$	−4.11794			−0.143022			−0.0715110	+	0.997440i	$0.522782\pi$
$830$		−	3.97275i		−	0.137896i
$831$	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
$835$	2.54429	−	4.40683i	0.0880487	−	0.152505i
$836$	15.7384	+	27.2597i	0.544324	+	0.942797i
$837$	−3.49717	−	2.01909i	−0.120880	−	0.0697901i
$838$			7.67261i			0.265046i
$839$	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
$842$	−4.19289	+	7.26230i	−0.144496	+	0.250275i
$843$		−	2.03385i		−	0.0700497i
$844$	14.1589	−	24.5240i	0.487371	−	0.844151i
$845$	−8.16420	−	3.58951i	−0.280857	−	0.123483i
$846$	10.8362			0.372558
$847$	−21.6575	−	2.02648i	−0.744162	−	0.0696305i
$848$	−1.12532	−	1.94912i	−0.0386437	−	0.0669329i
$849$	32.3521			1.11032
$850$	−15.9569	−	9.21273i	−0.547318	−	0.315994i
$851$	−9.47602	+	5.47098i	−0.324834	+	0.187543i
$852$			15.4168i			0.528170i
$853$			6.15317i			0.210680i	0.994436	+	0.105340i	$0.0335932\pi$
$853$			6.15317i			0.210680i	−0.994436	+	0.105340i	$0.966407\pi$
$854$	−17.3713	−	12.3203i	−0.594434	−	0.421593i
$855$	−2.46271	−	4.26553i	−0.0842228	−	0.145878i
$856$	15.6572	+	9.03970i	0.535153	+	0.308970i
$857$	10.2376	−	17.7321i	0.349711	−	0.605718i	−0.636487	−	0.771288i	$-0.719613\pi$
$857$	10.2376	−	17.7321i	0.349711	−	0.605718i	0.986198	+	0.165570i	$0.0529463\pi$
$858$	−13.2373	+	8.64025i	−0.451914	+	0.294973i
$859$	−9.60299	−	16.6329i	−0.327650	−	0.567506i	0.654395	−	0.756153i	$-0.272923\pi$
$859$	−9.60299	−	16.6329i	−0.327650	−	0.567506i	−0.982045	+	0.188647i	$0.939590\pi$
$860$	−2.87064	+	1.65737i	−0.0978881	+	0.0565157i
$861$	−15.9602	+	7.32549i	−0.543921	+	0.249652i
$862$	−1.62587	+	2.81608i	−0.0553772	+	0.0959161i
$863$	−27.1455	+	15.6725i	−0.924043	+	0.533497i	−0.884923	−	0.465738i	$-0.845789\pi$
$863$	−27.1455	+	15.6725i	−0.924043	+	0.533497i	−0.0391205	+	0.999235i	$0.512456\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	13.4480	−	7.76420i	0.457245	−	0.263991i
$866$	−7.94520	+	4.58716i	−0.269989	+	0.155878i
$867$	−0.225650	+	0.390837i	−0.00766347	+	0.0132735i
$868$	−0.995348	+	10.6376i	−0.0337843	+	0.361063i
$869$	10.9261	−	6.30818i	0.370642	−	0.213990i
$870$	−0.124307	−	0.215306i	−0.00421440	−	0.00729956i
$871$	6.26347	−	12.3638i	0.212230	−	0.418931i
$872$	−3.32980	+	5.76738i	−0.112761	+	0.195308i
$873$	2.62440	+	1.51520i	0.0888224	+	0.0512817i
$874$	6.18956	+	10.7206i	0.209365	+	0.362631i
$875$	1.61138	−	17.2213i	0.0544746	−	0.582186i
$876$			11.5593i			0.390552i
$877$			10.5478i			0.356176i	0.984015	+	0.178088i	$0.0569911\pi$
$877$			10.5478i			0.356176i	−0.984015	+	0.178088i	$0.943009\pi$
$878$	19.9340	−	11.5089i	0.672740	−	0.388406i
$879$	−17.9647	−	10.3719i	−0.605933	−	0.349835i
$880$	−3.00774			−0.101391
$881$	−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	$0.976368\pi$
$882$	5.30765	+	4.56386i	0.178718	+	0.153673i
$883$	−47.8763			−1.61116			−0.805582	−	0.592484i	$-0.798147\pi$
$883$	−47.8763			−1.61116			−0.805582	+	0.592484i	$0.798147\pi$
$884$	−12.2825	+	8.01705i	−0.413106	+	0.269642i
$885$	−0.855796	+	1.48228i	−0.0287673	+	0.0498264i
$886$		−	27.0708i		−	0.909462i
$887$	−9.47930	+	16.4186i	−0.318284	+	0.551284i	−0.980130	−	0.198356i	$-0.936440\pi$
$887$	−9.47930	+	16.4186i	−0.318284	+	0.551284i	0.661846	+	0.749640i	$0.269773\pi$
$888$	−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
$891$		−	4.38424i		−	0.146877i
$892$	17.2662	+	9.96863i	0.578114	+	0.333774i
$893$	38.8996	+	67.3762i	1.30173	+	2.25466i
$894$	0.0610758	−	0.105786i	0.00204268	−	0.00353803i
$895$	−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
$899$		−	1.46341i		−	0.0488075i
$900$	−4.52936			−0.150979
$901$	−9.15564			−0.305019
$902$		−	29.1001i		−	0.968929i
$903$	−7.39537	+	10.4273i	−0.246102	+	0.346998i
$904$	−0.0265329	−	0.0153188i	−0.000882472	−	0.000509496i
$905$	−1.89382	+	1.09339i	−0.0629525	+	0.0363457i
$906$	−11.0516	−	19.1419i	−0.367165	−	0.635948i
$907$	−15.5256			−0.515518			−0.257759	−	0.966209i	$-0.582984\pi$
$907$	−15.5256			−0.515518			−0.257759	+	0.966209i	$0.582984\pi$
$908$	−25.7193	−	14.8490i	−0.853525	−	0.492783i
$909$	−13.9039			−0.461162
$910$	−5.53704	−	3.48851i	−0.183551	−	0.115643i
$911$	8.53305			0.282713			0.141356	−	0.989959i	$-0.454854\pi$
$911$	8.53305			0.282713			0.141356	+	0.989959i	$0.454854\pi$
$912$	6.21767	+	3.58977i	0.205888	+	0.118869i
$913$	25.3887			0.840242
$914$	−7.19673	−	12.4651i	−0.238047	−	0.412309i
$915$	−4.78235	+	2.76109i	−0.158100	+	0.0912789i
$916$	12.7224	+	7.34527i	0.420359	+	0.242695i
$917$	−5.04364	−	10.9887i	−0.166556	−	0.362878i
$918$		−	4.06801i		−	0.134264i
$919$	45.1360			1.48890			0.744449	−	0.667679i	$-0.232712\pi$
$919$	45.1360			1.48890			0.744449	+	0.667679i	$0.232712\pi$
$920$	−1.18288			−0.0389982
$921$			3.66321i			0.120707i
$922$	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
$926$	18.0881	−	31.3295i	0.594412	−	1.02955i
$927$	−6.46334	−	11.1948i	−0.212284	−	0.367687i
$928$	0.313842	+	0.181197i	0.0103024	+	0.00594807i
$929$			45.7180i			1.49996i	0.661461	+	0.749980i	$0.269937\pi$
$929$			45.7180i			1.49996i	−0.661461	+	0.749980i	$0.730063\pi$
$930$	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
$933$	−0.833909	+	1.44437i	−0.0273010	+	0.0472867i
$934$		−	34.9033i		−	1.14207i
$935$	−6.11775	+	10.5963i	−0.200072	+	0.346535i
$936$	−1.62941	+	3.21637i	−0.0532588	+	0.105130i
$937$	−6.09263			−0.199037			−0.0995187	−	0.995036i	$-0.531730\pi$
$937$	−6.09263			−0.199037			−0.0995187	+	0.995036i	$0.531730\pi$
$938$	5.88360	−	8.29571i	0.192106	−	0.270864i
$939$	−2.83514	−	4.91060i	−0.0925212	−	0.160251i
$940$	−7.43404			−0.242472
$941$	19.9997	+	11.5469i	0.651973	+	0.376417i	0.789212	−	0.614121i	$-0.210489\pi$
$941$	19.9997	+	11.5469i	0.651973	+	0.376417i	−0.137239	+	0.990538i	$0.543823\pi$
$942$	12.0045	−	6.93082i	0.391129	−	0.225818i
$943$		−	11.4444i		−	0.372682i
$944$		−	2.49491i		−	0.0812023i
$945$	1.64961	−	0.757149i	0.0536620	−	0.0246301i
$946$	−10.5917	−	18.3454i	−0.344367	−	0.596460i
$947$	43.2813	+	24.9885i	1.40645	+	0.812017i	0.995044	−	0.0994330i	$-0.0317029\pi$
$947$	43.2813	+	24.9885i	1.40645	+	0.812017i	0.411411	+	0.911450i	$0.365036\pi$
$948$	1.43883	−	2.49213i	0.0467311	−	0.0809406i
$949$	−22.7805	−	34.9008i	−0.739486	−	1.13293i
$950$	−16.2594	−	28.1620i	−0.527523	−	0.913697i
$951$	−27.3539	+	15.7928i	−0.887012	+	0.512116i
$952$	−9.78179	+	4.48970i	−0.317030	+	0.145512i
$953$	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
$955$	−6.68303	+	3.85845i	−0.216258	+	0.124856i
$956$	12.1229	−	6.99914i	0.392082	−	0.226368i
$957$	1.37596	−	0.794409i	0.0444783	−	0.0256796i
$958$	−2.02550	+	3.50827i	−0.0654409	+	0.113347i
$959$	−5.55502	+	2.54967i	−0.179381	+	0.0823332i
$960$	−0.594123	+	0.343017i	−0.0191752	+	0.0110708i
$961$	−7.34652	−	12.7246i	−0.236985	−	0.410469i
$962$	−1.25066	−	22.8467i	−0.0403228	−	0.736608i
$963$	9.03970	−	15.6572i	0.291300	−	0.504547i
$964$	−9.94503	−	5.74177i	−0.320308	−	0.184930i
$965$	−4.57651	−	7.92675i	−0.147323	−	0.255171i
$966$	−4.14600	+	1.90296i	−0.133395	+	0.0612266i
$967$			38.4609i			1.23682i	0.785856	+	0.618410i	$0.212223\pi$
$967$			38.4609i			1.23682i	−0.785856	+	0.618410i	$0.787777\pi$
$968$		−	8.22153i		−	0.264250i
$969$	25.2935	−	14.6032i	0.812545	−	0.469123i
$970$	−1.80043	−	1.03948i	−0.0578083	−	0.0333756i
$971$	−29.9403			−0.960830			−0.480415	−	0.877041i	$-0.659514\pi$
$971$	−29.9403			−0.960830			−0.480415	+	0.877041i	$0.659514\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	21.0447	−	29.6725i	0.674663	−	0.951257i
$974$	6.75964			0.216593
$975$	13.6755	−	8.92625i	0.437965	−	0.285869i
$976$	4.02471	−	6.97101i	0.128828	−	0.223137i
$977$		−	16.1221i		−	0.515790i	−0.966173	−	0.257895i	$-0.916971\pi$
$977$		−	16.1221i		−	0.515790i	0.966173	−	0.257895i	$-0.0830289\pi$
$978$	−9.14518	+	15.8399i	−0.292430	+	0.506504i
$979$	−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
$982$			1.57932i			0.0503982i
$983$	17.2163	+	9.93984i	0.549115	+	0.317032i	0.748765	−	0.662836i	$-0.230647\pi$
$983$	17.2163	+	9.93984i	0.549115	+	0.317032i	−0.199650	+	0.979867i	$0.563980\pi$
$984$	−3.31872	−	5.74820i	−0.105797	−	0.183246i
$985$	6.71401	−	11.6290i	0.213926	−	0.370531i
$986$	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
$990$			3.00774i			0.0955922i
$991$	−15.0444			−0.477903			−0.238951	−	0.971032i	$-0.576804\pi$
$991$	−15.0444			−0.477903			−0.238951	+	0.971032i	$0.576804\pi$
$992$	−4.03819			−0.128213
$993$		−	26.0238i		−	0.825840i
$994$	−17.0149	−	37.0706i	−0.539680	−	1.17581i
$995$	−2.57266	−	1.48533i	−0.0815589	−	0.0470880i
$996$	5.01506	−	2.89545i	0.158908	−	0.0917458i
$997$	12.4575	+	21.5770i	0.394532	+	0.683350i	0.993041	−	0.117766i	$-0.0375733\pi$
$997$	12.4575	+	21.5770i	0.394532	+	0.683350i	−0.598509	+	0.801116i	$0.704240\pi$
$998$	−6.11438			−0.193547
$999$	5.49583	+	3.17302i	0.173880	+	0.100390i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.6	✓	16	91.30	even	6	inner
546.2.bd.a.361.6	yes	16	1.1	even	1	trivial
546.2.bm.a.205.3	yes	16	7.2	even	3
546.2.bm.a.277.7	yes	16	13.4	even	6
1638.2.cr.a.361.3		16	3.2	odd	2
1638.2.cr.a.667.3		16	273.212	odd	6
1638.2.dt.a.1297.6		16	21.2	odd	6
1638.2.dt.a.1369.2		16	39.17	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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.63424 + 0.246484i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.594123 + 0.343017i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(2.63424 + 0.246484i) q^{7} +1.00000i q^{8} +1.00000 q^{9} -0.686034 q^{10} -4.38424i 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} +(-0.500000 + 0.866025i) q^{16} +(2.03400 + 3.52300i) q^{17} +(0.866025 + 0.500000i) q^{18} +7.17954i q^{19} +(-0.594123 - 0.343017i) q^{20} +(-2.63424 - 0.246484i) q^{21} +(2.19212 - 3.79686i) q^{22} +(0.862111 - 1.49322i) q^{23} -1.00000i q^{24} +(-2.26468 + 3.92254i) q^{25} +(1.97075 + 3.01929i) q^{26} -1.00000 q^{27} +(1.10366 + 2.40456i) q^{28} +(-0.181197 - 0.313842i) q^{29} +0.686034 q^{30} +(3.49717 + 2.01909i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.38424i q^{33} +4.06801i q^{34} +(-1.64961 + 0.757149i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-5.49583 - 3.17302i) q^{37} +(-3.58977 + 6.21767i) q^{38} +(-3.21637 - 1.62941i) q^{39} +(-0.343017 - 0.594123i) q^{40} +(5.74820 - 3.31872i) q^{41} +(-2.15808 - 1.53058i) q^{42} +(2.41586 - 4.18440i) q^{43} +(3.79686 - 2.19212i) q^{44} +(-0.594123 + 0.343017i) q^{45} +(1.49322 - 0.862111i) q^{46} +(9.38446 - 5.41812i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.87849 + 1.29860i) q^{49} +(-3.92254 + 2.26468i) q^{50} +(-2.03400 - 3.52300i) q^{51} +(0.197077 + 3.60016i) q^{52} +(-1.12532 + 1.94912i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.50387 + 2.60478i) q^{55} +(-0.246484 + 2.63424i) q^{56} -7.17954i q^{57} -0.362393i q^{58} +(-2.16065 + 1.24745i) q^{59} +(0.594123 + 0.343017i) q^{60} -8.04943 q^{61} +(2.01909 + 3.49717i) q^{62} +(2.63424 + 0.246484i) q^{63} -1.00000 q^{64} +(-2.46983 + 0.135202i) q^{65} +(-2.19212 + 3.79686i) q^{66} -3.84402i q^{67} +(-2.03400 + 3.52300i) q^{68} +(-0.862111 + 1.49322i) q^{69} +(-1.80718 - 0.169096i) q^{70} +(-13.3513 - 7.70839i) q^{71} +1.00000i q^{72} +(-10.0106 - 5.77964i) q^{73} +(-3.17302 - 5.49583i) q^{74} +(2.26468 - 3.92254i) 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} -0.686034i q^{80} +1.00000 q^{81} +6.63745 q^{82} +5.79090i q^{83} +(-1.10366 - 2.40456i) q^{84} +(-2.41690 - 1.39540i) q^{85} +(4.18440 - 2.41586i) q^{86} +(0.181197 + 0.313842i) q^{87} +4.38424 q^{88} +(-7.10156 - 4.10009i) q^{89} -0.686034 q^{90} +(8.07108 + 5.08504i) q^{91} +1.72422 q^{92} +(-3.49717 - 2.01909i) q^{93} +10.8362 q^{94} +(-2.46271 - 4.26553i) q^{95} +(0.866025 - 0.500000i) q^{96} +(2.62440 + 1.51520i) q^{97} +(5.30765 + 4.56386i) q^{98} -4.38424i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

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