LMFDB - Embedded newform 363.2.e.k.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.k.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.118034 + 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.500000 + 1.53884i) q^{5} +(0.118034 + 0.363271i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.618034 q^{10} +1.85410 q^{12} +(-1.30902 + 4.02874i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(1.30902 + 0.951057i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-2.42705 - 7.46969i) q^{17} +(0.309017 + 0.224514i) q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.927051 + 2.85317i) q^{20} +1.00000 q^{21} -4.23607 q^{23} +(-0.454915 + 1.40008i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-1.30902 - 0.951057i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.572949 + 1.76336i) q^{28} +(4.85410 + 3.52671i) q^{29} +(-0.500000 + 0.363271i) q^{30} +(1.57295 - 4.84104i) q^{31} -4.14590 q^{32} +3.00000 q^{34} +(-0.500000 + 1.53884i) q^{35} +(1.50000 - 1.08981i) q^{36} +(1.42705 + 1.03681i) q^{37} +(0.100813 + 0.310271i) q^{38} +(1.30902 + 4.02874i) q^{39} +(-1.92705 - 1.40008i) q^{40} +(3.42705 - 2.48990i) q^{41} +(-0.118034 + 0.363271i) q^{42} +6.70820 q^{43} +1.61803 q^{45} +(0.500000 - 1.53884i) q^{46} +(-0.881966 + 0.640786i) q^{47} +(2.54508 + 1.84911i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(0.281153 + 0.865300i) q^{50} +(-6.35410 - 4.61653i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(-0.809017 + 2.48990i) q^{53} +0.381966 q^{54} -1.47214 q^{56} +(0.263932 - 0.812299i) q^{57} +(-1.85410 + 1.34708i) q^{58} +(-7.78115 - 5.65334i) q^{59} +(0.927051 + 2.85317i) q^{60} +(2.64590 + 8.14324i) q^{61} +(1.57295 + 1.14281i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-1.45492 + 4.47777i) q^{64} -6.85410 q^{65} -4.85410 q^{67} +(4.50000 - 13.8496i) q^{68} +(-3.42705 + 2.48990i) q^{69} +(-0.500000 - 0.363271i) q^{70} +(-1.64590 - 5.06555i) q^{71} +(0.454915 + 1.40008i) q^{72} +(-6.23607 - 4.53077i) q^{73} +(-0.545085 + 0.396027i) q^{74} +(0.736068 - 2.26538i) q^{75} +1.58359 q^{76} -1.61803 q^{78} +(3.39919 - 10.4616i) q^{79} +(-4.11803 + 2.99193i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.500000 + 1.53884i) q^{82} +(-2.30902 - 7.10642i) q^{83} +(1.50000 + 1.08981i) q^{84} +(10.2812 - 7.46969i) q^{85} +(-0.791796 + 2.43690i) q^{86} +6.00000 q^{87} -3.76393 q^{89} +(-0.190983 + 0.587785i) q^{90} +(-3.42705 + 2.48990i) q^{91} +(-6.35410 - 4.61653i) q^{92} +(-1.57295 - 4.84104i) q^{93} +(-0.128677 - 0.396027i) q^{94} +(1.11803 + 0.812299i) q^{95} +(-3.35410 + 2.43690i) q^{96} +(0.354102 - 1.08981i) q^{97} +2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} - 4 q^{6} + q^{7} - 7 q^{8} - q^{9} + 2 q^{10} - 6 q^{12} - 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + 3 q^{20} + 4 q^{21} - 8 q^{23}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 - 4 * q^6 + q^7 - 7 * q^8 - q^9 + 2 * q^10 - 6 * q^12 - 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 - 3 * q^17 - q^18 + 5 * q^19 + 3 * q^20 + 4 * q^21 - 8 * q^23 - 13 * q^24 + q^25 - 3 * q^26 + q^27 + 9 * q^28 + 6 * q^29 - 2 * q^30 + 13 * q^31 - 30 * q^32 + 12 * q^34 - 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 + 3 * q^39 - q^40 + 7 * q^41 + 4 * q^42 + 2 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 - 19 * q^50 - 12 * q^51 - 12 * q^52 - q^53 + 6 * q^54 + 12 * q^56 + 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 + 24 * q^61 + 13 * q^62 + q^63 - 17 * q^64 - 14 * q^65 - 6 * q^67 + 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 + 13 * q^72 - 16 * q^73 + 9 * q^74 - 6 * q^75 + 60 * q^76 - 2 * q^78 - 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 - 7 * q^83 + 6 * q^84 + 21 * q^85 - 30 * q^86 + 24 * q^87 - 24 * q^89 - 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 - 43 * q^94 - 12 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	−0.984076	−	0.177750i	$-0.943118\pi$
$2$	−0.118034	+	0.363271i	−0.0834626	+	0.256872i	0.900613	+	0.434622i	$0.143118\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	1.50000	+	1.08981i	0.750000	+	0.544907i
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	0.998430	+	0.0560130i	$0.0178388\pi$
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	−0.774823	+	0.632178i	$0.782161\pi$
$6$	0.118034	+	0.363271i	0.0481872	+	0.148305i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	0.730084	−	0.683358i	$-0.239481\pi$
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i	−0.424304	+	0.905520i	$0.639481\pi$
$8$	−1.19098	+	0.865300i	−0.421076	+	0.305930i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.618034			−0.195440
$11$		0			0
$11$		0			0
$12$	1.85410			0.535233
$13$	−1.30902	+	4.02874i	−0.363056	+	1.11737i	0.588133	+	0.808764i	$0.299863\pi$
$13$	−1.30902	+	4.02874i	−0.363056	+	1.11737i	−0.951189	+	0.308608i	$0.900137\pi$
$14$	−0.309017	+	0.224514i	−0.0825883	+	0.0600039i
$15$	1.30902	+	0.951057i	0.337987	+	0.245562i
$16$	0.972136	+	2.99193i	0.243034	+	0.747982i
$17$	−2.42705	−	7.46969i	−0.588646	−	1.81167i	−0.584106	−	0.811677i	$-0.698555\pi$
$17$	−2.42705	−	7.46969i	−0.588646	−	1.81167i	−0.00454037	−	0.999990i	$-0.501445\pi$
$18$	0.309017	+	0.224514i	0.0728360	+	0.0529185i
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	−0.505696	−	0.862712i	$-0.668764\pi$
$19$	0.690983	−	0.502029i	0.158522	−	0.115173i	0.664219	+	0.747538i	$0.268764\pi$
$20$	−0.927051	+	2.85317i	−0.207295	+	0.637988i
$21$	1.00000			0.218218
$22$		0			0
$23$	−4.23607			−0.883281			−0.441641	−	0.897192i	$-0.645603\pi$
$23$	−4.23607			−0.883281			−0.441641	+	0.897192i	$0.645603\pi$
$24$	−0.454915	+	1.40008i	−0.0928591	+	0.285791i
$25$	1.92705	−	1.40008i	0.385410	−	0.280017i
$26$	−1.30902	−	0.951057i	−0.256719	−	0.186518i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.572949	+	1.76336i	0.108277	+	0.333243i
$29$	4.85410	+	3.52671i	0.901384	+	0.654894i	0.938821	−	0.344405i	$-0.111919\pi$
$29$	4.85410	+	3.52671i	0.901384	+	0.654894i	−0.0374370	+	0.999299i	$0.511919\pi$
$30$	−0.500000	+	0.363271i	−0.0912871	+	0.0663240i
$31$	1.57295	−	4.84104i	0.282510	−	0.869476i	−0.704624	−	0.709581i	$-0.748884\pi$
$31$	1.57295	−	4.84104i	0.282510	−	0.869476i	0.987134	−	0.159895i	$-0.0511157\pi$
$32$	−4.14590			−0.732898
$33$		0			0
$34$	3.00000			0.514496
$35$	−0.500000	+	1.53884i	−0.0845154	+	0.260112i
$36$	1.50000	−	1.08981i	0.250000	−	0.181636i
$37$	1.42705	+	1.03681i	0.234606	+	0.170451i	0.698877	−	0.715242i	$-0.253684\pi$
$37$	1.42705	+	1.03681i	0.234606	+	0.170451i	−0.464271	+	0.885693i	$0.653684\pi$
$38$	0.100813	+	0.310271i	0.0163540	+	0.0503326i
$39$	1.30902	+	4.02874i	0.209610	+	0.645115i
$40$	−1.92705	−	1.40008i	−0.304694	−	0.221373i
$41$	3.42705	−	2.48990i	0.535215	−	0.388857i	−0.287090	−	0.957904i	$-0.592688\pi$
$41$	3.42705	−	2.48990i	0.535215	−	0.388857i	0.822305	+	0.569047i	$0.192688\pi$
$42$	−0.118034	+	0.363271i	−0.0182130	+	0.0560540i
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$		0			0
$45$	1.61803			0.241202
$46$	0.500000	−	1.53884i	0.0737210	−	0.226890i
$47$	−0.881966	+	0.640786i	−0.128648	+	0.0934682i	−0.650248	−	0.759722i	$-0.725335\pi$
$47$	−0.881966	+	0.640786i	−0.128648	+	0.0934682i	0.521600	+	0.853190i	$0.325335\pi$
$48$	2.54508	+	1.84911i	0.367351	+	0.266896i
$49$	−1.85410	−	5.70634i	−0.264872	−	0.815191i
$50$	0.281153	+	0.865300i	0.0397610	+	0.122372i
$51$	−6.35410	−	4.61653i	−0.889752	−	0.646443i
$52$	−6.35410	+	4.61653i	−0.881155	+	0.640197i
$53$	−0.809017	+	2.48990i	−0.111127	+	0.342014i	−0.991120	−	0.132974i	$-0.957547\pi$
$53$	−0.809017	+	2.48990i	−0.111127	+	0.342014i	0.879993	+	0.474988i	$0.157547\pi$
$54$	0.381966			0.0519790
$55$		0			0
$56$	−1.47214			−0.196722
$57$	0.263932	−	0.812299i	0.0349587	−	0.107592i
$58$	−1.85410	+	1.34708i	−0.243456	+	0.176881i
$59$	−7.78115	−	5.65334i	−1.01302	−	0.736002i	−0.0481795	−	0.998839i	$-0.515342\pi$
$59$	−7.78115	−	5.65334i	−1.01302	−	0.736002i	−0.964840	+	0.262837i	$0.915342\pi$
$60$	0.927051	+	2.85317i	0.119682	+	0.368343i
$61$	2.64590	+	8.14324i	0.338773	+	1.04263i	0.964834	+	0.262861i	$0.0846660\pi$
$61$	2.64590	+	8.14324i	0.338773	+	1.04263i	−0.626061	+	0.779774i	$0.715334\pi$
$62$	1.57295	+	1.14281i	0.199765	+	0.145138i
$63$	0.809017	−	0.587785i	0.101927	−	0.0740540i
$64$	−1.45492	+	4.47777i	−0.181864	+	0.559721i
$65$	−6.85410			−0.850147
$66$		0			0
$67$	−4.85410			−0.593023			−0.296511	−	0.955029i	$-0.595823\pi$
$67$	−4.85410			−0.593023			−0.296511	+	0.955029i	$0.595823\pi$
$68$	4.50000	−	13.8496i	0.545705	−	1.67951i
$69$	−3.42705	+	2.48990i	−0.412568	+	0.299749i
$70$	−0.500000	−	0.363271i	−0.0597614	−	0.0434192i
$71$	−1.64590	−	5.06555i	−0.195332	−	0.601171i	−0.999973	−	0.00740814i	$-0.997642\pi$
$71$	−1.64590	−	5.06555i	−0.195332	−	0.601171i	0.804640	−	0.593762i	$-0.202358\pi$
$72$	0.454915	+	1.40008i	0.0536123	+	0.165002i
$73$	−6.23607	−	4.53077i	−0.729877	−	0.530286i	0.159648	−	0.987174i	$-0.448964\pi$
$73$	−6.23607	−	4.53077i	−0.729877	−	0.530286i	−0.889524	+	0.456888i	$0.848964\pi$
$74$	−0.545085	+	0.396027i	−0.0633648	+	0.0460373i
$75$	0.736068	−	2.26538i	0.0849938	−	0.261584i
$76$	1.58359			0.181650
$77$		0			0
$78$	−1.61803			−0.183206
$79$	3.39919	−	10.4616i	0.382438	−	1.17702i	−0.555883	−	0.831260i	$-0.687620\pi$
$79$	3.39919	−	10.4616i	0.382438	−	1.17702i	0.938322	−	0.345764i	$-0.112380\pi$
$80$	−4.11803	+	2.99193i	−0.460410	+	0.334508i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	0.500000	+	1.53884i	0.0552158	+	0.169937i
$83$	−2.30902	−	7.10642i	−0.253448	−	0.780031i	−0.994132	−	0.108178i	$-0.965498\pi$
$83$	−2.30902	−	7.10642i	−0.253448	−	0.780031i	0.740684	−	0.671854i	$-0.234502\pi$
$84$	1.50000	+	1.08981i	0.163663	+	0.118908i
$85$	10.2812	−	7.46969i	1.11515	−	0.810202i
$86$	−0.791796	+	2.43690i	−0.0853816	+	0.262777i
$87$	6.00000			0.643268
$88$		0			0
$89$	−3.76393			−0.398976			−0.199488	−	0.979900i	$-0.563928\pi$
$89$	−3.76393			−0.398976			−0.199488	+	0.979900i	$0.563928\pi$
$90$	−0.190983	+	0.587785i	−0.0201314	+	0.0619580i
$91$	−3.42705	+	2.48990i	−0.359253	+	0.261012i
$92$	−6.35410	−	4.61653i	−0.662461	−	0.481306i
$93$	−1.57295	−	4.84104i	−0.163107	−	0.501992i
$94$	−0.128677	−	0.396027i	−0.0132720	−	0.0408471i
$95$	1.11803	+	0.812299i	0.114708	+	0.0833401i
$96$	−3.35410	+	2.43690i	−0.342327	+	0.248715i
$97$	0.354102	−	1.08981i	0.0359536	−	0.110654i	−0.931469	−	0.363821i	$-0.881472\pi$
$97$	0.354102	−	1.08981i	0.0359536	−	0.110654i	0.967423	+	0.253167i	$0.0814721\pi$
$98$	2.29180			0.231506
$99$		0			0
$100$	4.41641			0.441641
$101$	−1.78115	+	5.48183i	−0.177231	+	0.545462i	−0.999728	−	0.0233075i	$-0.992580\pi$
$101$	−1.78115	+	5.48183i	−0.177231	+	0.545462i	0.822497	+	0.568769i	$0.192580\pi$
$102$	2.42705	−	1.76336i	0.240314	−	0.174598i
$103$	−5.61803	−	4.08174i	−0.553561	−	0.402186i	0.275535	−	0.961291i	$-0.411145\pi$
$103$	−5.61803	−	4.08174i	−0.553561	−	0.402186i	−0.829097	+	0.559105i	$0.811145\pi$
$104$	−1.92705	−	5.93085i	−0.188963	−	0.581568i
$105$	0.500000	+	1.53884i	0.0487950	+	0.150176i
$106$	−0.809017	−	0.587785i	−0.0785787	−	0.0570908i
$107$	2.04508	−	1.48584i	0.197706	−	0.143642i	−0.484528	−	0.874776i	$-0.661009\pi$
$107$	2.04508	−	1.48584i	0.197706	−	0.143642i	0.682234	+	0.731134i	$0.261009\pi$
$108$	0.572949	−	1.76336i	0.0551320	−	0.169679i
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$		0			0
$111$	1.76393			0.167425
$112$	−0.972136	+	2.99193i	−0.0918582	+	0.282711i
$113$	−3.66312	+	2.66141i	−0.344597	+	0.250365i	−0.746599	−	0.665274i	$-0.768315\pi$
$113$	−3.66312	+	2.66141i	−0.344597	+	0.250365i	0.402002	+	0.915639i	$0.368315\pi$
$114$	0.263932	+	0.191758i	0.0247195	+	0.0179598i
$115$	−2.11803	−	6.51864i	−0.197508	−	0.607866i
$116$	3.43769	+	10.5801i	0.319182	+	0.982341i
$117$	3.42705	+	2.48990i	0.316831	+	0.230191i
$118$	2.97214	−	2.15938i	0.273607	−	0.198787i
$119$	2.42705	−	7.46969i	0.222487	−	0.684746i
$120$	−2.38197			−0.217443
$121$		0			0
$122$	−3.27051			−0.296098
$123$	1.30902	−	4.02874i	0.118030	−	0.363259i
$124$	7.63525	−	5.54734i	0.685666	−	0.498166i
$125$	9.66312	+	7.02067i	0.864296	+	0.627948i
$126$	0.118034	+	0.363271i	0.0105153	+	0.0323628i
$127$	−1.76393	−	5.42882i	−0.156524	−	0.481730i	0.841788	−	0.539808i	$-0.181503\pi$
$127$	−1.76393	−	5.42882i	−0.156524	−	0.481730i	−0.998312	+	0.0580773i	$0.981503\pi$
$128$	−8.16312	−	5.93085i	−0.721525	−	0.524218i
$129$	5.42705	−	3.94298i	0.477825	−	0.347160i
$130$	0.809017	−	2.48990i	0.0709555	−	0.218379i
$131$	12.7984			1.11820			0.559100	−	0.829101i	$-0.311147\pi$
$131$	12.7984			1.11820			0.559100	+	0.829101i	$0.311147\pi$
$132$		0			0
$133$	0.854102			0.0740600
$134$	0.572949	−	1.76336i	0.0494953	−	0.152331i
$135$	1.30902	−	0.951057i	0.112662	−	0.0818539i
$136$	9.35410	+	6.79615i	0.802108	+	0.582765i
$137$	4.39919	+	13.5393i	0.375848	+	1.15674i	0.942905	+	0.333062i	$0.108082\pi$
$137$	4.39919	+	13.5393i	0.375848	+	1.15674i	−0.567057	+	0.823679i	$0.691918\pi$
$138$	−0.500000	−	1.53884i	−0.0425628	−	0.130995i
$139$	4.50000	+	3.26944i	0.381685	+	0.277310i	0.762040	−	0.647530i	$-0.224198\pi$
$139$	4.50000	+	3.26944i	0.381685	+	0.277310i	−0.380355	+	0.924841i	$0.624198\pi$
$140$	−2.42705	+	1.76336i	−0.205123	+	0.149031i
$141$	−0.336881	+	1.03681i	−0.0283705	+	0.0873154i
$142$	2.03444			0.170727
$143$		0			0
$144$	3.14590			0.262158
$145$	−3.00000	+	9.23305i	−0.249136	+	0.766763i
$146$	2.38197	−	1.73060i	0.197133	−	0.143225i
$147$	−4.85410	−	3.52671i	−0.400360	−	0.290878i
$148$	1.01064	+	3.11044i	0.0830744	+	0.255677i
$149$	0.0729490	+	0.224514i	0.00597622	+	0.0183929i	0.954000	−	0.299806i	$-0.0969220\pi$
$149$	0.0729490	+	0.224514i	0.00597622	+	0.0183929i	−0.948024	+	0.318199i	$0.896922\pi$
$150$	0.736068	+	0.534785i	0.0600997	+	0.0436650i
$151$	−15.3262	+	11.1352i	−1.24723	+	0.906167i	−0.998058	−	0.0622921i	$-0.980159\pi$
$151$	−15.3262	+	11.1352i	−1.24723	+	0.906167i	−0.249174	+	0.968459i	$0.580159\pi$
$152$	−0.388544	+	1.19581i	−0.0315151	+	0.0969934i
$153$	−7.85410			−0.634967
$154$		0			0
$155$	8.23607			0.661537
$156$	−2.42705	+	7.46969i	−0.194320	+	0.598054i
$157$	−1.85410	+	1.34708i	−0.147973	+	0.107509i	−0.659309	−	0.751872i	$-0.729151\pi$
$157$	−1.85410	+	1.34708i	−0.147973	+	0.107509i	0.511335	+	0.859381i	$0.329151\pi$
$158$	3.39919	+	2.46965i	0.270425	+	0.196475i
$159$	0.809017	+	2.48990i	0.0641592	+	0.197462i
$160$	−2.07295	−	6.37988i	−0.163881	−	0.504374i
$161$	−3.42705	−	2.48990i	−0.270089	−	0.196231i
$162$	0.309017	−	0.224514i	0.0242787	−	0.0176395i
$163$	−3.66312	+	11.2739i	−0.286918	+	0.883042i	0.698900	+	0.715220i	$0.253673\pi$
$163$	−3.66312	+	11.2739i	−0.286918	+	0.883042i	−0.985817	+	0.167822i	$0.946327\pi$
$164$	7.85410			0.613302
$165$		0			0
$166$	2.85410			0.221521
$167$	−5.26393	+	16.2007i	−0.407335	+	1.25365i	0.511594	+	0.859227i	$0.329055\pi$
$167$	−5.26393	+	16.2007i	−0.407335	+	1.25365i	−0.918929	+	0.394422i	$0.870945\pi$
$168$	−1.19098	+	0.865300i	−0.0918863	+	0.0667593i
$169$	−4.00000	−	2.90617i	−0.307692	−	0.223552i
$170$	1.50000	+	4.61653i	0.115045	+	0.354071i
$171$	−0.263932	−	0.812299i	−0.0201834	−	0.0621181i
$172$	10.0623	+	7.31069i	0.767244	+	0.557435i
$173$	−8.92705	+	6.48588i	−0.678711	+	0.493112i	−0.872930	−	0.487846i	$-0.837783\pi$
$173$	−8.92705	+	6.48588i	−0.678711	+	0.493112i	0.194219	+	0.980958i	$0.437783\pi$
$174$	−0.708204	+	2.17963i	−0.0536888	+	0.165237i
$175$	2.38197			0.180060
$176$		0			0
$177$	−9.61803			−0.722936
$178$	0.444272	−	1.36733i	0.0332996	−	0.102486i
$179$	14.1353	−	10.2699i	1.05652	−	0.767606i	0.0830774	−	0.996543i	$-0.473525\pi$
$179$	14.1353	−	10.2699i	1.05652	−	0.767606i	0.973441	+	0.228937i	$0.0735251\pi$
$180$	2.42705	+	1.76336i	0.180902	+	0.131433i
$181$	3.54508	+	10.9106i	0.263504	+	0.810982i	0.992034	+	0.125968i	$0.0402038\pi$
$181$	3.54508	+	10.9106i	0.263504	+	0.810982i	−0.728530	+	0.685014i	$0.759796\pi$
$182$	−0.500000	−	1.53884i	−0.0370625	−	0.114067i
$183$	6.92705	+	5.03280i	0.512062	+	0.372035i
$184$	5.04508	−	3.66547i	0.371929	−	0.270222i
$185$	−0.881966	+	2.71441i	−0.0648434	+	0.199568i
$186$	1.94427			0.142561
$187$		0			0
$188$	−2.02129			−0.147417
$189$	0.309017	−	0.951057i	0.0224777	−	0.0691792i
$190$	−0.427051	+	0.310271i	−0.0309815	+	0.0225094i
$191$	18.7533	+	13.6251i	1.35694	+	0.985875i	0.998633	+	0.0522712i	$0.0166460\pi$
$191$	18.7533	+	13.6251i	1.35694	+	0.985875i	0.358307	+	0.933604i	$0.383354\pi$
$192$	1.45492	+	4.47777i	0.104999	+	0.323155i
$193$	−3.04508	−	9.37181i	−0.219190	−	0.674597i	−0.998830	−	0.0483689i	$-0.984598\pi$
$193$	−3.04508	−	9.37181i	−0.219190	−	0.674597i	0.779640	−	0.626229i	$-0.215402\pi$
$194$	0.354102	+	0.257270i	0.0254230	+	0.0184709i
$195$	−5.54508	+	4.02874i	−0.397092	+	0.288504i
$196$	3.43769	−	10.5801i	0.245550	−	0.755724i
$197$	−16.0344			−1.14241			−0.571203	−	0.820809i	$-0.693523\pi$
$197$	−16.0344			−1.14241			−0.571203	+	0.820809i	$0.693523\pi$
$198$		0			0
$199$	−6.70820			−0.475532			−0.237766	−	0.971322i	$-0.576415\pi$
$199$	−6.70820			−0.475532			−0.237766	+	0.971322i	$0.576415\pi$
$200$	−1.08359	+	3.33495i	−0.0766215	+	0.235817i
$201$	−3.92705	+	2.85317i	−0.276993	+	0.201247i
$202$	−1.78115	−	1.29408i	−0.125321	−	0.0910514i
$203$	1.85410	+	5.70634i	0.130132	+	0.400506i
$204$	−4.50000	−	13.8496i	−0.315063	−	0.969664i
$205$	5.54508	+	4.02874i	0.387286	+	0.281379i
$206$	2.14590	−	1.55909i	0.149512	−	0.108627i
$207$	−1.30902	+	4.02874i	−0.0909830	+	0.280017i
$208$	−13.3262			−0.924008
$209$		0			0
$210$	−0.618034			−0.0426484
$211$	0.427051	−	1.31433i	0.0293994	−	0.0904821i	−0.935280	−	0.353908i	$-0.884853\pi$
$211$	0.427051	−	1.31433i	0.0293994	−	0.0904821i	0.964680	+	0.263426i	$0.0848525\pi$
$212$	−3.92705	+	2.85317i	−0.269711	+	0.195956i
$213$	−4.30902	−	3.13068i	−0.295249	−	0.214511i
$214$	0.298374	+	0.918300i	0.0203964	+	0.0627737i
$215$	3.35410	+	10.3229i	0.228748	+	0.704014i
$216$	1.19098	+	0.865300i	0.0810361	+	0.0588762i
$217$	4.11803	−	2.99193i	0.279550	−	0.203105i
$218$	1.41641	−	4.35926i	0.0959312	−	0.295246i
$219$	−7.70820			−0.520872
$220$		0			0
$221$	33.2705			2.23802
$222$	−0.208204	+	0.640786i	−0.0139737	+	0.0430067i
$223$	12.2812	−	8.92278i	0.822407	−	0.597514i	−0.0949941	−	0.995478i	$-0.530283\pi$
$223$	12.2812	−	8.92278i	0.822407	−	0.597514i	0.917401	+	0.397964i	$0.130283\pi$
$224$	−3.35410	−	2.43690i	−0.224105	−	0.162822i
$225$	−0.736068	−	2.26538i	−0.0490712	−	0.151026i
$226$	−0.534442	−	1.64484i	−0.0355505	−	0.109413i
$227$	7.42705	+	5.39607i	0.492951	+	0.358150i	0.806318	−	0.591482i	$-0.201457\pi$
$227$	7.42705	+	5.39607i	0.492951	+	0.358150i	−0.313367	+	0.949632i	$0.601457\pi$
$228$	1.28115	−	0.930812i	0.0848464	−	0.0616445i
$229$	−2.61803	+	8.05748i	−0.173005	+	0.532453i	−0.999537	−	0.0304362i	$-0.990310\pi$
$229$	−2.61803	+	8.05748i	−0.173005	+	0.532453i	0.826532	+	0.562890i	$0.190310\pi$
$230$	2.61803			0.172628
$231$		0			0
$232$	−8.83282			−0.579903
$233$	−3.35410	+	10.3229i	−0.219735	+	0.676273i	0.779049	+	0.626963i	$0.215702\pi$
$233$	−3.35410	+	10.3229i	−0.219735	+	0.676273i	−0.998784	+	0.0493103i	$0.984298\pi$
$234$	−1.30902	+	0.951057i	−0.0855731	+	0.0621725i
$235$	−1.42705	−	1.03681i	−0.0930905	−	0.0676342i
$236$	−5.51064	−	16.9600i	−0.358712	−	1.10400i
$237$	−3.39919	−	10.4616i	−0.220801	−	0.679555i
$238$	2.42705	+	1.76336i	0.157322	+	0.114301i
$239$	−2.11803	+	1.53884i	−0.137004	+	0.0995394i	−0.654176	−	0.756342i	$-0.726985\pi$
$239$	−2.11803	+	1.53884i	−0.137004	+	0.0995394i	0.517172	+	0.855881i	$0.326985\pi$
$240$	−1.57295	+	4.84104i	−0.101533	+	0.312488i
$241$	21.7082			1.39835			0.699174	−	0.714951i	$-0.253551\pi$
$241$	21.7082			1.39835			0.699174	+	0.714951i	$0.253551\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	−4.90576	+	15.0984i	−0.314059	+	0.966575i
$245$	7.85410	−	5.70634i	0.501780	−	0.364565i
$246$	1.30902	+	0.951057i	0.0834599	+	0.0606371i
$247$	1.11803	+	3.44095i	0.0711388	+	0.218943i
$248$	2.31559	+	7.12667i	0.147040	+	0.452544i
$249$	−6.04508	−	4.39201i	−0.383092	−	0.278332i
$250$	−3.69098	+	2.68166i	−0.233438	+	0.169603i
$251$	7.71885	−	23.7562i	0.487209	−	1.49948i	−0.341546	−	0.939865i	$-0.610951\pi$
$251$	7.71885	−	23.7562i	0.487209	−	1.49948i	0.828755	−	0.559611i	$-0.189049\pi$
$252$	1.85410			0.116797
$253$		0			0
$254$	2.18034			0.136807
$255$	3.92705	−	12.0862i	0.245921	−	0.756868i
$256$	−4.50000	+	3.26944i	−0.281250	+	0.204340i
$257$	10.3090	+	7.48994i	0.643059	+	0.467210i	0.860900	−	0.508775i	$-0.169901\pi$
$257$	10.3090	+	7.48994i	0.643059	+	0.467210i	−0.217841	+	0.975984i	$0.569901\pi$
$258$	0.791796	+	2.43690i	0.0492951	+	0.151715i
$259$	0.545085	+	1.67760i	0.0338699	+	0.104241i
$260$	−10.2812	−	7.46969i	−0.637610	−	0.463251i
$261$	4.85410	−	3.52671i	0.300461	−	0.218298i
$262$	−1.51064	+	4.64928i	−0.0933278	+	0.287234i
$263$	18.2705			1.12661			0.563304	−	0.826250i	$-0.309530\pi$
$263$	18.2705			1.12661			0.563304	+	0.826250i	$0.309530\pi$
$264$		0			0
$265$	−4.23607			−0.260220
$266$	−0.100813	+	0.310271i	−0.00618125	+	0.0190239i
$267$	−3.04508	+	2.21238i	−0.186356	+	0.135396i
$268$	−7.28115	−	5.29007i	−0.444767	−	0.323142i
$269$	0.437694	+	1.34708i	0.0266867	+	0.0821332i	0.963513	−	0.267662i	$-0.0862511\pi$
$269$	0.437694	+	1.34708i	0.0266867	+	0.0821332i	−0.936826	+	0.349795i	$0.886251\pi$
$270$	0.190983	+	0.587785i	0.0116229	+	0.0357715i
$271$	−13.2533	−	9.62908i	−0.805080	−	0.584925i	0.107320	−	0.994225i	$-0.465773\pi$
$271$	−13.2533	−	9.62908i	−0.805080	−	0.584925i	−0.912400	+	0.409300i	$0.865773\pi$
$272$	19.9894	−	14.5231i	1.21203	−	0.880593i
$273$	−1.30902	+	4.02874i	−0.0792253	+	0.243830i
$274$	−5.43769			−0.328503
$275$		0			0
$276$	−7.85410			−0.472761
$277$	6.86475	−	21.1275i	0.412463	−	1.26943i	−0.502038	−	0.864845i	$-0.667416\pi$
$277$	6.86475	−	21.1275i	0.412463	−	1.26943i	0.914501	−	0.404584i	$-0.132584\pi$
$278$	−1.71885	+	1.24882i	−0.103090	+	0.0748990i
$279$	−4.11803	−	2.99193i	−0.246540	−	0.179122i
$280$	−0.736068	−	2.26538i	−0.0439885	−	0.135383i
$281$	9.03444	+	27.8052i	0.538950	+	1.65872i	0.734957	+	0.678114i	$0.237202\pi$
$281$	9.03444	+	27.8052i	0.538950	+	1.65872i	−0.196007	+	0.980602i	$0.562798\pi$
$282$	−0.336881	−	0.244758i	−0.0200610	−	0.0145752i
$283$	−6.23607	+	4.53077i	−0.370696	+	0.269326i	−0.757499	−	0.652836i	$-0.773579\pi$
$283$	−6.23607	+	4.53077i	−0.370696	+	0.269326i	0.386804	+	0.922162i	$0.373579\pi$
$284$	3.05166	−	9.39205i	0.181083	−	0.557316i
$285$	1.38197			0.0818606
$286$		0			0
$287$	4.23607			0.250047
$288$	−1.28115	+	3.94298i	−0.0754927	+	0.232343i
$289$	−36.1525	+	26.2663i	−2.12662	+	1.54508i
$290$	−3.00000	−	2.17963i	−0.176166	−	0.127992i
$291$	−0.354102	−	1.08981i	−0.0207578	−	0.0638860i
$292$	−4.41641	−	13.5923i	−0.258451	−	0.795430i
$293$	−7.80902	−	5.67358i	−0.456208	−	0.331454i	0.335834	−	0.941921i	$-0.390982\pi$
$293$	−7.80902	−	5.67358i	−0.456208	−	0.331454i	−0.792042	+	0.610467i	$0.790982\pi$
$294$	1.85410	−	1.34708i	0.108133	−	0.0785635i
$295$	4.80902	−	14.8006i	0.279992	−	0.861726i
$296$	−2.59675			−0.150933
$297$		0			0
$298$	−0.0901699			−0.00522340
$299$	5.54508	−	17.0660i	0.320681	−	0.986953i
$300$	3.57295	−	2.59590i	0.206284	−	0.149874i
$301$	5.42705	+	3.94298i	0.312810	+	0.227270i
$302$	−2.23607	−	6.88191i	−0.128671	−	0.396009i
$303$	1.78115	+	5.48183i	0.102325	+	0.314923i
$304$	2.17376	+	1.57933i	0.124674	+	0.0905808i
$305$	−11.2082	+	8.14324i	−0.641780	+	0.466280i
$306$	0.927051	−	2.85317i	0.0529960	−	0.163105i
$307$	−18.9787			−1.08317			−0.541586	−	0.840645i	$-0.682176\pi$
$307$	−18.9787			−1.08317			−0.541586	+	0.840645i	$0.682176\pi$
$308$		0			0
$309$	−6.94427			−0.395046
$310$	−0.972136	+	2.99193i	−0.0552136	+	0.169930i
$311$	15.8992	−	11.5514i	0.901560	−	0.655022i	−0.0373061	−	0.999304i	$-0.511878\pi$
$311$	15.8992	−	11.5514i	0.901560	−	0.655022i	0.938866	+	0.344282i	$0.111878\pi$
$312$	−5.04508	−	3.66547i	−0.285622	−	0.207516i
$313$	−3.54508	−	10.9106i	−0.200380	−	0.616706i	−0.999872	−	0.0160289i	$-0.994898\pi$
$313$	−3.54508	−	10.9106i	−0.200380	−	0.616706i	0.799491	−	0.600677i	$-0.205102\pi$
$314$	−0.270510	−	0.832544i	−0.0152658	−	0.0469832i
$315$	1.30902	+	0.951057i	0.0737548	+	0.0535860i
$316$	16.5000	−	11.9880i	0.928198	−	0.674375i
$317$	−9.01722	+	27.7522i	−0.506458	+	1.55872i	0.291849	+	0.956464i	$0.405730\pi$
$317$	−9.01722	+	27.7522i	−0.506458	+	1.55872i	−0.798306	+	0.602252i	$0.794270\pi$
$318$	−1.00000			−0.0560772
$319$		0			0
$320$	−7.61803			−0.425861
$321$	0.781153	−	2.40414i	0.0435997	−	0.134186i
$322$	1.30902	−	0.951057i	0.0729487	−	0.0530003i
$323$	−5.42705	−	3.94298i	−0.301969	−	0.219393i
$324$	−0.572949	−	1.76336i	−0.0318305	−	0.0979642i
$325$	3.11803	+	9.59632i	0.172957	+	0.532308i
$326$	−3.66312	−	2.66141i	−0.202881	−	0.147402i
$327$	−9.70820	+	7.05342i	−0.536865	+	0.390055i
$328$	−1.92705	+	5.93085i	−0.106404	+	0.327477i
$329$	−1.09017			−0.0601030
$330$		0			0
$331$	3.29180			0.180933			0.0904667	−	0.995899i	$-0.471164\pi$
$331$	3.29180			0.180933			0.0904667	+	0.995899i	$0.471164\pi$
$332$	4.28115	−	13.1760i	0.234959	−	0.723129i
$333$	1.42705	−	1.03681i	0.0782019	−	0.0568170i
$334$	−5.26393	−	3.82447i	−0.288030	−	0.209266i
$335$	−2.42705	−	7.46969i	−0.132604	−	0.408113i
$336$	0.972136	+	2.99193i	0.0530344	+	0.163223i
$337$	−3.38197	−	2.45714i	−0.184227	−	0.133849i	0.491849	−	0.870680i	$-0.336321\pi$
$337$	−3.38197	−	2.45714i	−0.184227	−	0.133849i	−0.676077	+	0.736831i	$0.736321\pi$
$338$	1.52786	−	1.11006i	0.0831048	−	0.0603792i
$339$	−1.39919	+	4.30625i	−0.0759934	+	0.233884i
$340$	23.5623			1.27785
$341$		0			0
$342$	0.326238			0.0176409
$343$	4.01722	−	12.3637i	0.216910	−	0.667579i
$344$	−7.98936	+	5.80461i	−0.430757	+	0.312963i
$345$	−5.54508	−	4.02874i	−0.298537	−	0.216900i
$346$	−1.30244	−	4.00850i	−0.0700196	−	0.215498i
$347$	−3.23607	−	9.95959i	−0.173721	−	0.534659i	0.825852	−	0.563888i	$-0.190695\pi$
$347$	−3.23607	−	9.95959i	−0.173721	−	0.534659i	−0.999573	+	0.0292287i	$0.990695\pi$
$348$	9.00000	+	6.53888i	0.482451	+	0.350521i
$349$	0.572949	−	0.416272i	0.0306693	−	0.0222825i	−0.572345	−	0.820013i	$-0.693966\pi$
$349$	0.572949	−	0.416272i	0.0306693	−	0.0222825i	0.603014	+	0.797730i	$0.293966\pi$
$350$	−0.281153	+	0.865300i	−0.0150283	+	0.0462522i
$351$	4.23607			0.226105
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	1.13525	−	3.49396i	0.0603381	−	0.185702i
$355$	6.97214	−	5.06555i	0.370043	−	0.268852i
$356$	−5.64590	−	4.10199i	−0.299232	−	0.217405i
$357$	−2.42705	−	7.46969i	−0.128453	−	0.395338i
$358$	2.06231	+	6.34712i	0.108996	+	0.335456i
$359$	−3.00000	−	2.17963i	−0.158334	−	0.115036i	0.505797	−	0.862652i	$-0.331198\pi$
$359$	−3.00000	−	2.17963i	−0.158334	−	0.115036i	−0.664131	+	0.747616i	$0.731198\pi$
$360$	−1.92705	+	1.40008i	−0.101565	+	0.0737909i
$361$	−5.64590	+	17.3763i	−0.297153	+	0.914541i
$362$	−4.38197			−0.230311
$363$		0			0
$364$	−7.85410			−0.411667
$365$	3.85410	−	11.8617i	0.201733	−	0.620870i
$366$	−2.64590	+	1.92236i	−0.138303	+	0.100483i
$367$	−23.3435	−	16.9600i	−1.21852	−	0.885306i	−0.222542	−	0.974923i	$-0.571436\pi$
$367$	−23.3435	−	16.9600i	−1.21852	−	0.885306i	−0.995976	+	0.0896174i	$0.971436\pi$
$368$	−4.11803	−	12.6740i	−0.214667	−	0.660678i
$369$	−1.30902	−	4.02874i	−0.0681447	−	0.209728i
$370$	−0.881966	−	0.640786i	−0.0458512	−	0.0333129i
$371$	−2.11803	+	1.53884i	−0.109963	+	0.0798927i
$372$	2.91641	−	8.97578i	0.151209	−	0.465373i
$373$	−34.8885			−1.80646			−0.903230	−	0.429156i	$-0.858811\pi$
$373$	−34.8885			−1.80646			−0.903230	+	0.429156i	$0.858811\pi$
$374$		0			0
$375$	11.9443			0.616800
$376$	0.495935	−	1.52633i	0.0255759	−	0.0787145i
$377$	−20.5623	+	14.9394i	−1.05901	+	0.769418i
$378$	0.309017	+	0.224514i	0.0158941	+	0.0115478i
$379$	3.36475	+	10.3556i	0.172835	+	0.531932i	0.999528	−	0.0307213i	$-0.00978043\pi$
$379$	3.36475	+	10.3556i	0.172835	+	0.531932i	−0.826693	+	0.562654i	$0.809780\pi$
$380$	0.791796	+	2.43690i	0.0406183	+	0.125010i
$381$	−4.61803	−	3.35520i	−0.236589	−	0.171892i
$382$	−7.16312	+	5.20431i	−0.366497	+	0.266276i
$383$	0.218847	−	0.673542i	0.0111826	−	0.0344164i	−0.945310	−	0.326175i	$-0.894240\pi$
$383$	0.218847	−	0.673542i	0.0111826	−	0.0344164i	0.956492	+	0.291758i	$0.0942403\pi$
$384$	−10.0902			−0.514912
$385$		0			0
$386$	3.76393			0.191579
$387$	2.07295	−	6.37988i	0.105374	−	0.324308i
$388$	1.71885	−	1.24882i	0.0872612	−	0.0633990i
$389$	−4.64590	−	3.37544i	−0.235556	−	0.171142i	0.463745	−	0.885969i	$-0.346505\pi$
$389$	−4.64590	−	3.37544i	−0.235556	−	0.171142i	−0.699301	+	0.714827i	$0.746505\pi$
$390$	−0.809017	−	2.48990i	−0.0409662	−	0.126081i
$391$	10.2812	+	31.6421i	0.519940	+	1.60021i
$392$	7.14590	+	5.19180i	0.360922	+	0.262225i
$393$	10.3541	−	7.52270i	0.522295	−	0.379470i
$394$	1.89261	−	5.82485i	0.0953483	−	0.293452i
$395$	17.7984			0.895533
$396$		0			0
$397$	−5.29180			−0.265588			−0.132794	−	0.991144i	$-0.542395\pi$
$397$	−5.29180			−0.265588			−0.132794	+	0.991144i	$0.542395\pi$
$398$	0.791796	−	2.43690i	0.0396892	−	0.122151i
$399$	0.690983	−	0.502029i	0.0345924	−	0.0251329i
$400$	6.06231	+	4.40452i	0.303115	+	0.220226i
$401$	8.86475	+	27.2829i	0.442684	+	1.36244i	0.885004	+	0.465584i	$0.154156\pi$
$401$	8.86475	+	27.2829i	0.442684	+	1.36244i	−0.442319	+	0.896858i	$0.645844\pi$
$402$	−0.572949	−	1.76336i	−0.0285761	−	0.0879482i
$403$	17.4443	+	12.6740i	0.868961	+	0.631337i
$404$	−8.64590	+	6.28161i	−0.430150	+	0.312522i
$405$	0.500000	−	1.53884i	0.0248452	−	0.0764657i
$406$	−2.29180			−0.113740
$407$		0			0
$408$	11.5623			0.572419
$409$	0.763932	−	2.35114i	0.0377740	−	0.116256i	−0.930391	−	0.366567i	$-0.880533\pi$
$409$	0.763932	−	2.35114i	0.0377740	−	0.116256i	0.968165	+	0.250311i	$0.0805329\pi$
$410$	−2.11803	+	1.53884i	−0.104602	+	0.0759980i
$411$	11.5172	+	8.36775i	0.568103	+	0.412751i
$412$	−3.97871	−	12.2452i	−0.196017	−	0.603279i
$413$	−2.97214	−	9.14729i	−0.146249	−	0.450109i
$414$	−1.30902	−	0.951057i	−0.0643347	−	0.0467419i
$415$	9.78115	−	7.10642i	0.480138	−	0.348841i
$416$	5.42705	−	16.7027i	0.266083	−	0.818919i
$417$	5.56231			0.272387
$418$		0			0
$419$	−24.4508			−1.19450			−0.597251	−	0.802054i	$-0.703740\pi$
$419$	−24.4508			−1.19450			−0.597251	+	0.802054i	$0.703740\pi$
$420$	−0.927051	+	2.85317i	−0.0452355	+	0.139220i
$421$	22.2533	−	16.1680i	1.08456	−	0.787978i	0.106087	−	0.994357i	$-0.466168\pi$
$421$	22.2533	−	16.1680i	1.08456	−	0.787978i	0.978472	+	0.206379i	$0.0661679\pi$
$422$	0.427051	+	0.310271i	0.0207885	+	0.0151037i
$423$	0.336881	+	1.03681i	0.0163797	+	0.0504116i
$424$	−1.19098	−	3.66547i	−0.0578392	−	0.178011i
$425$	−15.1353	−	10.9964i	−0.734168	−	0.533404i
$426$	1.64590	−	1.19581i	0.0797440	−	0.0579374i
$427$	−2.64590	+	8.14324i	−0.128044	+	0.394079i
$428$	4.68692			0.226551
$429$		0			0
$430$	−4.14590			−0.199933
$431$	−5.28115	+	16.2537i	−0.254384	+	0.782914i	0.739566	+	0.673084i	$0.235031\pi$
$431$	−5.28115	+	16.2537i	−0.254384	+	0.782914i	−0.993950	+	0.109830i	$0.964969\pi$
$432$	2.54508	−	1.84911i	0.122450	−	0.0889655i
$433$	22.0902	+	16.0494i	1.06159	+	0.771287i	0.974381	−	0.224903i	$-0.0722066\pi$
$433$	22.0902	+	16.0494i	1.06159	+	0.771287i	0.0872047	+	0.996190i	$0.472207\pi$
$434$	0.600813	+	1.84911i	0.0288399	+	0.0887602i
$435$	3.00000	+	9.23305i	0.143839	+	0.442691i
$436$	−18.0000	−	13.0778i	−0.862044	−	0.626311i
$437$	−2.92705	+	2.12663i	−0.140020	+	0.101730i
$438$	0.909830	−	2.80017i	0.0434734	−	0.133797i
$439$	36.7082			1.75199			0.875993	−	0.482323i	$-0.160207\pi$
$439$	36.7082			1.75199			0.875993	+	0.482323i	$0.160207\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−3.92705	+	12.0862i	−0.186791	+	0.574883i
$443$	−14.2361	+	10.3431i	−0.676376	+	0.491416i	−0.872153	−	0.489232i	$-0.837277\pi$
$443$	−14.2361	+	10.3431i	−0.676376	+	0.491416i	0.195777	+	0.980648i	$0.437277\pi$
$444$	2.64590	+	1.92236i	0.125569	+	0.0912310i
$445$	−1.88197	−	5.79210i	−0.0892137	−	0.274572i
$446$	1.79180	+	5.51458i	0.0848440	+	0.261123i
$447$	0.190983	+	0.138757i	0.00903319	+	0.00656299i
$448$	−3.80902	+	2.76741i	−0.179959	+	0.130748i
$449$	−8.32624	+	25.6255i	−0.392939	+	1.20934i	0.537615	+	0.843190i	$0.319325\pi$
$449$	−8.32624	+	25.6255i	−0.392939	+	1.20934i	−0.930555	+	0.366153i	$0.880675\pi$
$450$	0.909830			0.0428898
$451$		0			0
$452$	−8.39512			−0.394873
$453$	−5.85410	+	18.0171i	−0.275050	+	0.846516i
$454$	−2.83688	+	2.06111i	−0.133141	+	0.0967329i
$455$	−5.54508	−	4.02874i	−0.259958	−	0.188870i
$456$	0.388544	+	1.19581i	0.0181952	+	0.0559992i
$457$	−7.10081	−	21.8541i	−0.332162	−	1.02229i	−0.968103	−	0.250552i	$-0.919388\pi$
$457$	−7.10081	−	21.8541i	−0.332162	−	1.02229i	0.635941	−	0.771738i	$-0.280612\pi$
$458$	−2.61803	−	1.90211i	−0.122333	−	0.0888799i
$459$	−6.35410	+	4.61653i	−0.296584	+	0.215481i
$460$	3.92705	−	12.0862i	0.183100	−	0.563523i
$461$	−24.2705			−1.13039			−0.565195	−	0.824957i	$-0.691199\pi$
$461$	−24.2705			−1.13039			−0.565195	+	0.824957i	$0.691199\pi$
$462$		0			0
$463$	35.2705			1.63916			0.819580	−	0.572965i	$-0.194207\pi$
$463$	35.2705			1.63916			0.819580	+	0.572965i	$0.194207\pi$
$464$	−5.83282	+	17.9516i	−0.270782	+	0.833380i
$465$	6.66312	−	4.84104i	0.308995	−	0.224498i
$466$	−3.35410	−	2.43690i	−0.155376	−	0.112887i
$467$	−4.60081	−	14.1598i	−0.212900	−	0.655240i	−0.999296	−	0.0375166i	$-0.988055\pi$
$467$	−4.60081	−	14.1598i	−0.212900	−	0.655240i	0.786396	−	0.617723i	$-0.211945\pi$
$468$	2.42705	+	7.46969i	0.112190	+	0.345287i
$469$	−3.92705	−	2.85317i	−0.181334	−	0.131747i
$470$	0.545085	−	0.396027i	0.0251429	−	0.0182674i
$471$	−0.708204	+	2.17963i	−0.0326323	+	0.100432i
$472$	14.1591			0.651723
$473$		0			0
$474$	4.20163			0.192987
$475$	0.628677	−	1.93487i	0.0288457	−	0.0887779i
$476$	11.7812	−	8.55951i	0.539988	−	0.392324i
$477$	2.11803	+	1.53884i	0.0969781	+	0.0704587i
$478$	−0.309017	−	0.951057i	−0.0141341	−	0.0435003i
$479$	−9.46149	−	29.1195i	−0.432307	−	1.33050i	−0.895822	−	0.444414i	$-0.853412\pi$
$479$	−9.46149	−	29.1195i	−0.432307	−	1.33050i	0.463515	−	0.886089i	$-0.346588\pi$
$480$	−5.42705	−	3.94298i	−0.247710	−	0.179972i
$481$	−6.04508	+	4.39201i	−0.275632	+	0.200258i
$482$	−2.56231	+	7.88597i	−0.116710	+	0.359196i
$483$	−4.23607			−0.192748
$484$		0			0
$485$	1.85410			0.0841904
$486$	0.118034	−	0.363271i	0.00535413	−	0.0164783i
$487$	−0.572949	+	0.416272i	−0.0259628	+	0.0188631i	−0.600691	−	0.799481i	$-0.705108\pi$
$487$	−0.572949	+	0.416272i	−0.0259628	+	0.0188631i	0.574728	+	0.818344i	$0.305108\pi$
$488$	−10.1976	−	7.40896i	−0.461622	−	0.335388i
$489$	3.66312	+	11.2739i	0.165652	+	0.509824i
$490$	1.14590	+	3.52671i	0.0517664	+	0.159321i
$491$	23.5344	+	17.0988i	1.06209	+	0.771657i	0.974475	−	0.224497i	$-0.0720740\pi$
$491$	23.5344	+	17.0988i	1.06209	+	0.771657i	0.0876198	+	0.996154i	$0.472074\pi$
$492$	6.35410	−	4.61653i	0.286465	−	0.208129i
$493$	14.5623	−	44.8182i	0.655853	−	2.01851i
$494$	−1.38197			−0.0621776
$495$		0			0
$496$	16.0132			0.719012
$497$	1.64590	−	5.06555i	0.0738286	−	0.227221i
$498$	2.30902	−	1.67760i	0.103470	−	0.0751750i
$499$	20.1074	+	14.6089i	0.900130	+	0.653983i	0.938500	−	0.345281i	$-0.112216\pi$
$499$	20.1074	+	14.6089i	0.900130	+	0.653983i	−0.0383691	+	0.999264i	$0.512216\pi$
$500$	6.84346	+	21.0620i	0.306049	+	0.941921i
$501$	5.26393	+	16.2007i	0.235175	+	0.723795i
$502$	7.71885	+	5.60807i	0.344509	+	0.250300i
$503$	18.3262	−	13.3148i	0.817127	−	0.593677i	−0.0987614	−	0.995111i	$-0.531488\pi$
$503$	18.3262	−	13.3148i	0.817127	−	0.593677i	0.915888	+	0.401434i	$0.131488\pi$
$504$	−0.454915	+	1.40008i	−0.0202635	+	0.0623647i
$505$	−9.32624			−0.415012
$506$		0			0
$507$	−4.94427			−0.219583
$508$	3.27051	−	10.0656i	0.145105	−	0.446589i
$509$	3.02786	−	2.19987i	0.134208	−	0.0975076i	−0.518656	−	0.854983i	$-0.673567\pi$
$509$	3.02786	−	2.19987i	0.134208	−	0.0975076i	0.652864	+	0.757475i	$0.273567\pi$
$510$	3.92705	+	2.85317i	0.173893	+	0.126340i
$511$	−2.38197	−	7.33094i	−0.105372	−	0.324302i
$512$	−6.89261	−	21.2133i	−0.304613	−	0.937503i
$513$	−0.690983	−	0.502029i	−0.0305076	−	0.0221651i
$514$	−3.93769	+	2.86090i	−0.173684	+	0.126189i
$515$	3.47214	−	10.6861i	0.153001	−	0.470887i
$516$	12.4377			0.547539
$517$		0			0
$518$	−0.673762			−0.0296034
$519$	−3.40983	+	10.4944i	−0.149675	+	0.460652i
$520$	8.16312	−	5.93085i	0.357976	−	0.260085i
$521$	7.23607	+	5.25731i	0.317018	+	0.230327i	0.734902	−	0.678173i	$-0.237228\pi$
$521$	7.23607	+	5.25731i	0.317018	+	0.230327i	−0.417884	+	0.908500i	$0.637228\pi$
$522$	0.708204	+	2.17963i	0.0309972	+	0.0953997i
$523$	−4.71885	−	14.5231i	−0.206341	−	0.635052i	−0.999656	−	0.0262401i	$-0.991647\pi$
$523$	−4.71885	−	14.5231i	−0.206341	−	0.635052i	0.793315	−	0.608812i	$-0.208353\pi$
$524$	19.1976	+	13.9478i	0.838649	+	0.609314i
$525$	1.92705	−	1.40008i	0.0841034	−	0.0611047i
$526$	−2.15654	+	6.63715i	−0.0940297	+	0.289394i
$527$	−39.9787			−1.74150
$528$		0			0
$529$	−5.05573			−0.219814
$530$	0.500000	−	1.53884i	0.0217186	−	0.0668430i
$531$	−7.78115	+	5.65334i	−0.337673	+	0.245334i
$532$	1.28115	+	0.930812i	0.0555450	+	0.0403558i
$533$	5.54508	+	17.0660i	0.240184	+	0.739211i
$534$	−0.444272	−	1.36733i	−0.0192255	−	0.0591701i
$535$	3.30902	+	2.40414i	0.143061	+	0.103940i
$536$	5.78115	−	4.20025i	0.249708	−	0.181423i
$537$	5.39919	−	16.6170i	0.232992	−	0.717076i
$538$	−0.541020			−0.0233250
$539$		0			0
$540$	3.00000			0.129099
$541$	−14.0623	+	43.2793i	−0.604586	+	1.86072i	−0.104972	+	0.994475i	$0.533475\pi$
$541$	−14.0623	+	43.2793i	−0.604586	+	1.86072i	−0.499613	+	0.866248i	$0.666525\pi$
$542$	5.06231	−	3.67798i	0.217445	−	0.157983i
$543$	9.28115	+	6.74315i	0.398292	+	0.289376i
$544$	10.0623	+	30.9686i	0.431418	+	1.32777i
$545$	−6.00000	−	18.4661i	−0.257012	−	0.791001i
$546$	−1.30902	−	0.951057i	−0.0560208	−	0.0407015i
$547$	−9.50000	+	6.90215i	−0.406191	+	0.295115i	−0.772058	−	0.635552i	$-0.780772\pi$
$547$	−9.50000	+	6.90215i	−0.406191	+	0.295115i	0.365867	+	0.930667i	$0.380772\pi$
$548$	−8.15654	+	25.1033i	−0.348430	+	1.07236i
$549$	8.56231			0.365430
$550$		0			0
$551$	5.12461			0.218316
$552$	1.92705	−	5.93085i	0.0820207	−	0.252434i
$553$	8.89919	−	6.46564i	0.378432	−	0.274947i
$554$	6.86475	+	4.98753i	0.291655	+	0.211900i
$555$	0.881966	+	2.71441i	0.0374374	+	0.115220i
$556$	3.18692	+	9.80832i	0.135155	+	0.415966i
$557$	32.8713	+	23.8824i	1.39280	+	1.01193i	0.995551	+	0.0942205i	$0.0300359\pi$
$557$	32.8713	+	23.8824i	1.39280	+	1.01193i	0.397251	+	0.917710i	$0.369964\pi$
$558$	1.57295	−	1.14281i	0.0665882	−	0.0483792i
$559$	−8.78115	+	27.0256i	−0.371403	+	1.14306i
$560$	−5.09017			−0.215099
$561$		0			0
$562$	−11.1672			−0.471059
$563$	−2.65654	+	8.17599i	−0.111960	+	0.344577i	−0.991301	−	0.131616i	$-0.957984\pi$
$563$	−2.65654	+	8.17599i	−0.111960	+	0.344577i	0.879341	+	0.476193i	$0.157984\pi$
$564$	−1.63525	+	1.18808i	−0.0688567	+	0.0500273i
$565$	−5.92705	−	4.30625i	−0.249353	−	0.181165i
$566$	−0.909830	−	2.80017i	−0.0382430	−	0.117700i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	6.34346	+	4.60879i	0.266166	+	0.193381i
$569$	−9.56231	+	6.94742i	−0.400873	+	0.291251i	−0.769896	−	0.638169i	$-0.779692\pi$
$569$	−9.56231	+	6.94742i	−0.400873	+	0.291251i	0.369024	+	0.929420i	$0.379692\pi$
$570$	−0.163119	+	0.502029i	−0.00683230	+	0.0210277i
$571$	2.09017			0.0874709			0.0437354	−	0.999043i	$-0.486074\pi$
$571$	2.09017			0.0874709			0.0437354	+	0.999043i	$0.486074\pi$
$572$		0			0
$573$	23.1803			0.968373
$574$	−0.500000	+	1.53884i	−0.0208696	+	0.0642300i
$575$	−8.16312	+	5.93085i	−0.340426	+	0.247334i
$576$	3.80902	+	2.76741i	0.158709	+	0.115309i
$577$	5.65248	+	17.3965i	0.235316	+	0.724227i	0.997079	+	0.0763722i	$0.0243337\pi$
$577$	5.65248	+	17.3965i	0.235316	+	0.724227i	−0.761764	+	0.647855i	$0.775666\pi$
$578$	−5.27458	−	16.2335i	−0.219393	−	0.675223i
$579$	−7.97214	−	5.79210i	−0.331311	−	0.240711i
$580$	−14.5623	+	10.5801i	−0.604667	+	0.439316i
$581$	2.30902	−	7.10642i	0.0957942	−	0.294824i
$582$	0.437694			0.0181430
$583$		0			0
$584$	11.3475			0.469564
$585$	−2.11803	+	6.51864i	−0.0875699	+	0.269513i
$586$	2.98278	−	2.16712i	0.123217	−	0.0895227i
$587$	−30.8435	−	22.4091i	−1.27305	−	0.924922i	−0.273726	−	0.961808i	$-0.588256\pi$
$587$	−30.8435	−	22.4091i	−1.27305	−	0.924922i	−0.999319	+	0.0368857i	$0.988256\pi$
$588$	−3.43769	−	10.5801i	−0.141768	−	0.436317i
$589$	−1.34346	−	4.13474i	−0.0553563	−	0.170369i
$590$	4.80902	+	3.49396i	0.197984	+	0.143844i
$591$	−12.9721	+	9.42481i	−0.533602	+	0.387685i
$592$	−1.71478	+	5.27756i	−0.0704771	+	0.216906i
$593$	15.0344			0.617391			0.308695	−	0.951161i	$-0.400108\pi$
$593$	15.0344			0.617391			0.308695	+	0.951161i	$0.400108\pi$
$594$		0			0
$595$	12.7082			0.520986
$596$	−0.135255	+	0.416272i	−0.00554026	+	0.0170512i
$597$	−5.42705	+	3.94298i	−0.222114	+	0.161376i
$598$	5.54508	+	4.02874i	0.226755	+	0.164747i
$599$	−5.76393	−	17.7396i	−0.235508	−	0.724819i	−0.997054	−	0.0767076i	$-0.975559\pi$
$599$	−5.76393	−	17.7396i	−0.235508	−	0.724819i	0.761546	−	0.648111i	$-0.224441\pi$
$600$	1.08359	+	3.33495i	0.0442375	+	0.136149i
$601$	−23.3713	−	16.9803i	−0.953336	−	0.692639i	−0.00174258	−	0.999998i	$-0.500555\pi$
$601$	−23.3713	−	16.9803i	−0.953336	−	0.692639i	−0.951594	+	0.307359i	$0.900555\pi$
$602$	−2.07295	+	1.50609i	−0.0844871	+	0.0613835i
$603$	−1.50000	+	4.61653i	−0.0610847	+	0.187999i
$604$	−35.1246			−1.42920
$605$		0			0
$606$	−2.20163			−0.0894349
$607$	1.10081	−	3.38795i	0.0446806	−	0.137513i	−0.926228	−	0.376965i	$-0.876968\pi$
$607$	1.10081	−	3.38795i	0.0446806	−	0.137513i	0.970908	+	0.239452i	$0.0769678\pi$
$608$	−2.86475	+	2.08136i	−0.116181	+	0.0844103i
$609$	4.85410	+	3.52671i	0.196698	+	0.142910i
$610$	−1.63525	−	5.03280i	−0.0662095	−	0.203772i
$611$	−1.42705	−	4.39201i	−0.0577323	−	0.177682i
$612$	−11.7812	−	8.55951i	−0.476225	−	0.345998i
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	−0.0344546	−	0.999406i	$-0.510969\pi$
$613$	22.4164	−	16.2865i	0.905390	−	0.657804i	0.939845	+	0.341602i	$0.110969\pi$
$614$	2.24013	−	6.89442i	0.0904044	−	0.278236i
$615$	6.85410			0.276384
$616$		0			0
$617$	−11.1803			−0.450104			−0.225052	−	0.974347i	$-0.572255\pi$
$617$	−11.1803			−0.450104			−0.225052	+	0.974347i	$0.572255\pi$
$618$	0.819660	−	2.52265i	0.0329716	−	0.101476i
$619$	13.0451	−	9.47781i	0.524326	−	0.380945i	−0.293905	−	0.955835i	$-0.594955\pi$
$619$	13.0451	−	9.47781i	0.524326	−	0.380945i	0.818231	+	0.574889i	$0.194955\pi$
$620$	12.3541	+	8.97578i	0.496153	+	0.360476i
$621$	1.30902	+	4.02874i	0.0525290	+	0.161668i
$622$	2.31966	+	7.13918i	0.0930099	+	0.286255i
$623$	−3.04508	−	2.21238i	−0.121999	−	0.0886373i
$624$	−10.7812	+	7.83297i	−0.431592	+	0.313570i
$625$	−2.29180	+	7.05342i	−0.0916718	+	0.282137i
$626$	4.38197			0.175139
$627$		0			0
$628$	−4.24922			−0.169562
$629$	4.28115	−	13.1760i	0.170701	−	0.525363i
$630$	−0.500000	+	0.363271i	−0.0199205	+	0.0144731i
$631$	26.0623	+	18.9354i	1.03752	+	0.753805i	0.969801	−	0.243899i	$-0.0784265\pi$
$631$	26.0623	+	18.9354i	1.03752	+	0.753805i	0.0677233	+	0.997704i	$0.478426\pi$
$632$	5.00407	+	15.4009i	0.199051	+	0.612616i
$633$	−0.427051	−	1.31433i	−0.0169738	−	0.0522398i
$634$	−9.01722	−	6.55139i	−0.358120	−	0.260189i
$635$	7.47214	−	5.42882i	0.296523	−	0.215436i
$636$	−1.50000	+	4.61653i	−0.0594789	+	0.183057i
$637$	25.4164			1.00703
$638$		0			0
$639$	−5.32624			−0.210703
$640$	5.04508	−	15.5272i	0.199424	−	0.613765i
$641$	11.2533	−	8.17599i	0.444478	−	0.322932i	−0.342934	−	0.939360i	$-0.611421\pi$
$641$	11.2533	−	8.17599i	0.444478	−	0.322932i	0.787412	+	0.616427i	$0.211421\pi$
$642$	0.781153	+	0.567541i	0.0308296	+	0.0223991i
$643$	4.37132	+	13.4535i	0.172388	+	0.530556i	0.999505	−	0.0314745i	$-0.0100203\pi$
$643$	4.37132	+	13.4535i	0.172388	+	0.530556i	−0.827116	+	0.562031i	$0.810020\pi$
$644$	−2.42705	−	7.46969i	−0.0956392	−	0.294347i
$645$	8.78115	+	6.37988i	0.345758	+	0.251208i
$646$	2.07295	−	1.50609i	0.0815591	−	0.0592561i
$647$	4.93363	−	15.1841i	0.193961	−	0.596950i	−0.806026	−	0.591880i	$-0.798386\pi$
$647$	4.93363	−	15.1841i	0.193961	−	0.596950i	0.999987	−	0.00507058i	$-0.00161402\pi$
$648$	1.47214			0.0578310
$649$		0			0
$650$	−3.85410			−0.151170
$651$	1.57295	−	4.84104i	0.0616487	−	0.189735i
$652$	−17.7812	+	12.9188i	−0.696364	+	0.505938i
$653$	2.73607	+	1.98787i	0.107071	+	0.0777914i	0.640032	−	0.768348i	$-0.278921\pi$
$653$	2.73607	+	1.98787i	0.107071	+	0.0777914i	−0.532962	+	0.846139i	$0.678921\pi$
$654$	−1.41641	−	4.35926i	−0.0553859	−	0.170460i
$655$	6.39919	+	19.6947i	0.250037	+	0.769535i
$656$	10.7812	+	7.83297i	0.420933	+	0.305826i
$657$	−6.23607	+	4.53077i	−0.243292	+	0.176762i
$658$	0.128677	−	0.396027i	0.00501636	−	0.0154388i
$659$	−0.875388			−0.0341003			−0.0170501	−	0.999855i	$-0.505427\pi$
$659$	−0.875388			−0.0341003			−0.0170501	+	0.999855i	$0.505427\pi$
$660$		0			0
$661$	16.4377			0.639352			0.319676	−	0.947527i	$-0.396426\pi$
$661$	16.4377			0.639352			0.319676	+	0.947527i	$0.396426\pi$
$662$	−0.388544	+	1.19581i	−0.0151012	+	0.0464767i
$663$	26.9164	−	19.5559i	1.04535	−	0.759489i
$664$	8.89919	+	6.46564i	0.345355	+	0.250915i
$665$	0.427051	+	1.31433i	0.0165603	+	0.0509674i
$666$	0.208204	+	0.640786i	0.00806774	+	0.0248299i
$667$	−20.5623	−	14.9394i	−0.796176	−	0.578455i
$668$	−25.5517	+	18.5644i	−0.988624	+	0.718277i
$669$	4.69098	−	14.4374i	0.181364	−	0.558181i
$670$	3.00000			0.115900
$671$		0			0
$672$	−4.14590			−0.159931
$673$	−5.51064	+	16.9600i	−0.212420	+	0.653761i	0.786907	+	0.617072i	$0.211681\pi$
$673$	−5.51064	+	16.9600i	−0.212420	+	0.653761i	−0.999327	+	0.0366890i	$0.988319\pi$
$674$	1.29180	−	0.938545i	0.0497581	−	0.0361514i
$675$	−1.92705	−	1.40008i	−0.0741722	−	0.0538893i
$676$	−2.83282	−	8.71851i	−0.108954	−	0.335327i
$677$	6.94427	+	21.3723i	0.266890	+	0.821403i	0.991252	+	0.131983i	$0.0421345\pi$
$677$	6.94427	+	21.3723i	0.266890	+	0.821403i	−0.724362	+	0.689420i	$0.757866\pi$
$678$	−1.39919	−	1.01657i	−0.0537355	−	0.0390411i
$679$	0.927051	−	0.673542i	0.0355770	−	0.0258482i
$680$	−5.78115	+	17.7926i	−0.221697	+	0.682314i
$681$	9.18034			0.351791
$682$		0			0
$683$	−49.0689			−1.87757			−0.938784	−	0.344505i	$-0.888047\pi$
$683$	−49.0689			−1.87757			−0.938784	+	0.344505i	$0.888047\pi$
$684$	0.489357	−	1.50609i	0.0187110	−	0.0575866i
$685$	−18.6353	+	13.5393i	−0.712016	+	0.517310i
$686$	4.01722	+	2.91868i	0.153378	+	0.111436i
$687$	2.61803	+	8.05748i	0.0998842	+	0.307412i
$688$	6.52129	+	20.0705i	0.248622	+	0.765179i
$689$	−8.97214	−	6.51864i	−0.341811	−	0.248340i
$690$	2.11803	−	1.53884i	0.0806322	−	0.0585827i
$691$	10.0902	−	31.0543i	0.383848	−	1.18136i	−0.553464	−	0.832873i	$-0.686694\pi$
$691$	10.0902	−	31.0543i	0.383848	−	1.18136i	0.937312	−	0.348490i	$-0.113306\pi$
$692$	−20.4590			−0.777734
$693$		0			0
$694$	4.00000			0.151838
$695$	−2.78115	+	8.55951i	−0.105495	+	0.324681i
$696$	−7.14590	+	5.19180i	−0.270865	+	0.196795i
$697$	−26.9164	−	19.5559i	−1.01953	−	0.740733i
$698$	0.0835921	+	0.257270i	0.00316401	+	0.00973782i
$699$	3.35410	+	10.3229i	0.126864	+	0.390447i
$700$	3.57295	+	2.59590i	0.135045	+	0.0981158i
$701$	8.25329	−	5.99637i	0.311722	−	0.226480i	−0.420913	−	0.907101i	$-0.638290\pi$
$701$	8.25329	−	5.99637i	0.311722	−	0.226480i	0.732635	+	0.680622i	$0.238290\pi$
$702$	−0.500000	+	1.53884i	−0.0188713	+	0.0580798i
$703$	1.50658			0.0568217
$704$		0			0
$705$	−1.76393			−0.0664335
$706$	1.41641	−	4.35926i	0.0533072	−	0.164063i
$707$	−4.66312	+	3.38795i	−0.175375	+	0.127417i
$708$	−14.4271	−	10.4819i	−0.542202	−	0.393933i
$709$	−12.4271	−	38.2465i	−0.466708	−	1.43638i	−0.856822	−	0.515612i	$-0.827565\pi$
$709$	−12.4271	−	38.2465i	−0.466708	−	1.43638i	0.390114	−	0.920766i	$-0.372435\pi$
$710$	1.01722	+	3.13068i	0.0381756	+	0.117492i
$711$	−8.89919	−	6.46564i	−0.333746	−	0.242480i
$712$	4.48278	−	3.25693i	0.167999	−	0.122059i
$713$	−6.66312	+	20.5070i	−0.249536	+	0.767992i
$714$	3.00000			0.112272
$715$		0			0
$716$	32.3951			1.21066
$717$	−0.809017	+	2.48990i	−0.0302133	+	0.0929870i
$718$	1.14590	−	0.832544i	0.0427645	−	0.0310703i
$719$	−37.6074	−	27.3234i	−1.40252	−	1.01899i	−0.994358	−	0.106080i	$-0.966170\pi$
$719$	−37.6074	−	27.3234i	−1.40252	−	1.01899i	−0.408161	−	0.912910i	$-0.633830\pi$
$720$	1.57295	+	4.84104i	0.0586203	+	0.180415i
$721$	−2.14590	−	6.60440i	−0.0799174	−	0.245961i
$722$	−5.64590	−	4.10199i	−0.210119	−	0.152660i
$723$	17.5623	−	12.7598i	0.653149	−	0.474541i
$724$	−6.57295	+	20.2295i	−0.244282	+	0.751822i
$725$	14.2918			0.530784
$726$		0			0
$727$	−15.8541			−0.587996			−0.293998	−	0.955806i	$-0.594986\pi$
$727$	−15.8541			−0.587996			−0.293998	+	0.955806i	$0.594986\pi$
$728$	1.92705	−	5.93085i	0.0714213	−	0.219812i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	3.85410	+	2.80017i	0.142647	+	0.103639i
$731$	−16.2812	−	50.1082i	−0.602180	−	1.85332i
$732$	4.90576	+	15.0984i	0.181322	+	0.558053i
$733$	40.1246	+	29.1522i	1.48204	+	1.07676i	0.976893	+	0.213727i	$0.0685602\pi$
$733$	40.1246	+	29.1522i	1.48204	+	1.07676i	0.505143	+	0.863036i	$0.331440\pi$
$734$	8.91641	−	6.47815i	0.329111	−	0.239113i
$735$	3.00000	−	9.23305i	0.110657	−	0.340566i
$736$	17.5623			0.647355
$737$		0			0
$738$	1.61803			0.0595607
$739$	0.927051	−	2.85317i	0.0341021	−	0.104956i	−0.932557	−	0.361024i	$-0.882427\pi$
$739$	0.927051	−	2.85317i	0.0341021	−	0.104956i	0.966659	+	0.256068i	$0.0824272\pi$
$740$	−4.28115	+	3.11044i	−0.157378	+	0.114342i
$741$	2.92705	+	2.12663i	0.107528	+	0.0781236i
$742$	−0.309017	−	0.951057i	−0.0113444	−	0.0349144i
$743$	−2.19756	−	6.76340i	−0.0806207	−	0.248125i	0.902620	−	0.430439i	$-0.141641\pi$
$743$	−2.19756	−	6.76340i	−0.0806207	−	0.248125i	−0.983240	+	0.182314i	$0.941641\pi$
$744$	6.06231	+	4.40452i	0.222255	+	0.161478i
$745$	−0.309017	+	0.224514i	−0.0113215	+	0.00822556i
$746$	4.11803	−	12.6740i	0.150772	−	0.464028i
$747$	−7.47214			−0.273391
$748$		0			0
$749$	2.52786			0.0923661
$750$	−1.40983	+	4.33901i	−0.0514797	+	0.158438i
$751$	−18.4894	+	13.4333i	−0.674686	+	0.490188i	−0.871591	−	0.490234i	$-0.836911\pi$
$751$	−18.4894	+	13.4333i	−0.674686	+	0.490188i	0.196904	+	0.980423i	$0.436911\pi$
$752$	−2.77458	−	2.01585i	−0.101178	−	0.0735104i
$753$	−7.71885	−	23.7562i	−0.281290	−	0.865723i
$754$	−3.00000	−	9.23305i	−0.109254	−	0.336248i
$755$	−24.7984	−	18.0171i	−0.902505	−	0.655708i
$756$	1.50000	−	1.08981i	0.0545545	−	0.0396361i
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	−0.919044	−	0.394156i	$-0.871037\pi$
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	0.975201	+	0.221322i	$0.0710371\pi$
$758$	−4.15905			−0.151064
$759$		0			0
$760$	−2.03444			−0.0737970
$761$	13.1976	−	40.6179i	0.478411	−	1.47240i	−0.362890	−	0.931832i	$-0.618210\pi$
$761$	13.1976	−	40.6179i	0.478411	−	1.47240i	0.841301	−	0.540566i	$-0.181790\pi$
$762$	1.76393	−	1.28157i	0.0639005	−	0.0464264i
$763$	−9.70820	−	7.05342i	−0.351461	−	0.255351i
$764$	13.2812	+	40.8752i	0.480495	+	1.47881i
$765$	−3.92705	−	12.0862i	−0.141983	−	0.436978i
$766$	0.218847	+	0.159002i	0.00790727	+	0.00574496i
$767$	32.9615	−	23.9479i	1.19017	−	0.864710i
$768$	−1.71885	+	5.29007i	−0.0620236	+	0.190889i
$769$	3.50658			0.126450			0.0632252	−	0.997999i	$-0.479861\pi$
$769$	3.50658			0.126450			0.0632252	+	0.997999i	$0.479861\pi$
$770$		0			0
$771$	12.7426			0.458915
$772$	5.64590	−	17.3763i	0.203200	−	0.625386i
$773$	−3.89919	+	2.83293i	−0.140244	+	0.101893i	−0.655695	−	0.755026i	$-0.727624\pi$
$773$	−3.89919	+	2.83293i	−0.140244	+	0.101893i	0.515451	+	0.856919i	$0.327624\pi$
$774$	2.07295	+	1.50609i	0.0745106	+	0.0541351i
$775$	−3.74671	−	11.5312i	−0.134586	−	0.414213i
$776$	0.521286	+	1.60435i	0.0187131	+	0.0575930i
$777$	1.42705	+	1.03681i	0.0511952	+	0.0371955i
$778$	1.77458	−	1.28930i	0.0636216	−	0.0462238i
$779$	1.11803	−	3.44095i	0.0400577	−	0.123285i
$780$	−12.7082			−0.455027
$781$		0			0
$782$	−12.7082			−0.454444
$783$	1.85410	−	5.70634i	0.0662602	−	0.203928i
$784$	15.2705	−	11.0947i	0.545375	−	0.396238i
$785$	−3.00000	−	2.17963i	−0.107075	−	0.0777942i
$786$	1.51064	+	4.64928i	0.0538829	+	0.165834i
$787$	1.14590	+	3.52671i	0.0408469	+	0.125714i	0.969401	−	0.245485i	$-0.0789470\pi$
$787$	1.14590	+	3.52671i	0.0408469	+	0.125714i	−0.928554	+	0.371198i	$0.878947\pi$
$788$	−24.0517	−	17.4746i	−0.856805	−	0.622505i
$789$	14.7812	−	10.7391i	0.526223	−	0.382323i
$790$	−2.10081	+	6.46564i	−0.0747436	+	0.230037i
$791$	−4.52786			−0.160992
$792$		0			0
$793$	−36.2705			−1.28800
$794$	0.624612	−	1.92236i	0.0221666	−	0.0682219i
$795$	−3.42705	+	2.48990i	−0.121545	+	0.0883076i
$796$	−10.0623	−	7.31069i	−0.356649	−	0.259121i
$797$	−15.0000	−	46.1653i	−0.531327	−	1.63526i	−0.751454	−	0.659786i	$-0.770647\pi$
$797$	−15.0000	−	46.1653i	−0.531327	−	1.63526i	0.220126	−	0.975471i	$-0.429353\pi$
$798$	0.100813	+	0.310271i	0.00356874	+	0.0109835i
$799$	6.92705	+	5.03280i	0.245061	+	0.178048i
$800$	−7.98936	+	5.80461i	−0.282466	+	0.205224i
$801$	−1.16312	+	3.57971i	−0.0410968	+	0.126483i
$802$	−10.9574			−0.386920
$803$		0			0
$804$	−9.00000			−0.317406
$805$	2.11803	−	6.51864i	0.0746509	−	0.229752i
$806$	−6.66312	+	4.84104i	−0.234698	+	0.170518i
$807$	1.14590	+	0.832544i	0.0403375	+	0.0293069i
$808$	−2.62210	−	8.06999i	−0.0922451	−	0.283901i
$809$	4.91641	+	15.1311i	0.172852	+	0.531983i	0.999529	−	0.0306937i	$-0.00977165\pi$
$809$	4.91641	+	15.1311i	0.172852	+	0.531983i	−0.826677	+	0.562677i	$0.809772\pi$
$810$	0.500000	+	0.363271i	0.0175682	+	0.0127641i
$811$	−13.2984	+	9.66183i	−0.466969	+	0.339273i	−0.796259	−	0.604956i	$-0.793191\pi$
$811$	−13.2984	+	9.66183i	−0.466969	+	0.339273i	0.329290	+	0.944229i	$0.393191\pi$
$812$	−3.43769	+	10.5801i	−0.120639	+	0.371290i
$813$	−16.3820			−0.574541
$814$		0			0
$815$	−19.1803			−0.671858
$816$	7.63525	−	23.4989i	0.267287	−	0.822626i
$817$	4.63525	−	3.36771i	0.162167	−	0.117821i
$818$	0.763932	+	0.555029i	0.0267103	+	0.0194061i
$819$	1.30902	+	4.02874i	0.0457408	+	0.140776i
$820$	3.92705	+	12.0862i	0.137139	+	0.422069i
$821$	6.95492	+	5.05304i	0.242728	+	0.176352i	0.702498	−	0.711686i	$-0.252068\pi$
$821$	6.95492	+	5.05304i	0.242728	+	0.176352i	−0.459770	+	0.888038i	$0.652068\pi$
$822$	−4.39919	+	3.19620i	−0.153439	+	0.111480i
$823$	7.98278	−	24.5685i	0.278262	−	0.856403i	−0.710076	−	0.704125i	$-0.751339\pi$
$823$	7.98278	−	24.5685i	0.278262	−	0.856403i	0.988338	−	0.152277i	$-0.0486607\pi$
$824$	10.2229			0.356132
$825$		0			0
$826$	3.67376			0.127827
$827$	6.38197	−	19.6417i	0.221923	−	0.683008i	−0.776667	−	0.629912i	$-0.783091\pi$
$827$	6.38197	−	19.6417i	0.221923	−	0.683008i	0.998589	−	0.0530961i	$-0.0169090\pi$
$828$	−6.35410	+	4.61653i	−0.220820	+	0.160435i
$829$	−34.2984	−	24.9192i	−1.19123	−	0.865481i	−0.197838	−	0.980235i	$-0.563392\pi$
$829$	−34.2984	−	24.9192i	−1.19123	−	0.865481i	−0.993394	+	0.114754i	$0.963392\pi$
$830$	1.42705	+	4.39201i	0.0495337	+	0.152449i
$831$	−6.86475	−	21.1275i	−0.238135	−	0.732905i
$832$	−16.1353	−	11.7229i	−0.559389	−	0.406420i
$833$	−38.1246	+	27.6992i	−1.32094	+	0.959719i
$834$	−0.656541	+	2.02063i	−0.0227342	+	0.0699686i
$835$	−27.5623			−0.953833
$836$		0			0
$837$	−5.09017			−0.175942
$838$	2.88603	−	8.88229i	0.0996963	−	0.306834i
$839$	−28.9894	+	21.0620i	−1.00082	+	0.727141i	−0.962265	−	0.272115i	$-0.912277\pi$
$839$	−28.9894	+	21.0620i	−1.00082	+	0.727141i	−0.0385591	+	0.999256i	$0.512277\pi$
$840$	−1.92705	−	1.40008i	−0.0664896	−	0.0483075i
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	3.24671	+	9.99235i	0.111889	+	0.344359i
$843$	23.6525	+	17.1845i	0.814635	+	0.591867i
$844$	2.07295	−	1.50609i	0.0713538	−	0.0518416i
$845$	2.47214	−	7.60845i	0.0850441	−	0.261739i
$846$	−0.416408			−0.0143164
$847$		0			0
$848$	−8.23607			−0.282828
$849$	−2.38197	+	7.33094i	−0.0817489	+	0.251597i
$850$	5.78115	−	4.20025i	0.198292	−	0.144068i
$851$	−6.04508	−	4.39201i	−0.207223	−	0.150556i
$852$	−3.05166	−	9.39205i	−0.104548	−	0.321766i
$853$	−0.669697	−	2.06111i	−0.0229300	−	0.0705712i	0.938937	−	0.344090i	$-0.111812\pi$
$853$	−0.669697	−	2.06111i	−0.0229300	−	0.0705712i	−0.961867	+	0.273519i	$0.911812\pi$
$854$	−2.64590	−	1.92236i	−0.0905408	−	0.0657817i
$855$	1.11803	−	0.812299i	0.0382360	−	0.0277800i
$856$	−1.14996	+	3.53922i	−0.0393049	+	0.120968i
$857$	32.2361			1.10116			0.550582	−	0.834781i	$-0.314406\pi$
$857$	32.2361			1.10116			0.550582	+	0.834781i	$0.314406\pi$
$858$		0			0
$859$	−7.58359			−0.258749			−0.129374	−	0.991596i	$-0.541297\pi$
$859$	−7.58359			−0.258749			−0.129374	+	0.991596i	$0.541297\pi$
$860$	−6.21885	+	19.1396i	−0.212061	+	0.652656i
$861$	3.42705	−	2.48990i	0.116794	−	0.0848555i
$862$	−5.28115	−	3.83698i	−0.179877	−	0.130688i
$863$	11.0902	+	34.1320i	0.377514	+	1.16187i	0.941767	+	0.336266i	$0.109164\pi$
$863$	11.0902	+	34.1320i	0.377514	+	1.16187i	−0.564253	+	0.825602i	$0.690836\pi$
$864$	1.28115	+	3.94298i	0.0435857	+	0.134143i
$865$	−14.4443	−	10.4944i	−0.491120	−	0.356820i
$866$	−8.43769	+	6.13034i	−0.286725	+	0.208318i
$867$	−13.8090	+	42.4998i	−0.468979	+	1.44337i
$868$	9.43769			0.320336
$869$		0			0
$870$	−3.70820			−0.125720
$871$	6.35410	−	19.5559i	0.215301	−	0.662627i
$872$	14.2918	−	10.3836i	0.483981	−	0.351633i
$873$	−0.927051	−	0.673542i	−0.0313759	−	0.0227959i
$874$	−0.427051	−	1.31433i	−0.0144452	−	0.0444578i
$875$	3.69098	+	11.3597i	0.124778	+	0.384027i
$876$	−11.5623	−	8.40051i	−0.390654	−	0.283827i
$877$	32.4058	−	23.5442i	1.09426	−	0.795030i	0.114151	−	0.993463i	$-0.463585\pi$
$877$	32.4058	−	23.5442i	1.09426	−	0.795030i	0.980114	+	0.198433i	$0.0635854\pi$
$878$	−4.33282	+	13.3350i	−0.146225	+	0.450036i
$879$	−9.65248			−0.325570
$880$		0			0
$881$	30.7984			1.03762			0.518812	−	0.854888i	$-0.326375\pi$
$881$	30.7984			1.03762			0.518812	+	0.854888i	$0.326375\pi$
$882$	0.708204	−	2.17963i	0.0238465	−	0.0733919i
$883$	−15.3262	+	11.1352i	−0.515769	+	0.374728i	−0.815008	−	0.579450i	$-0.803267\pi$
$883$	−15.3262	+	11.1352i	−0.515769	+	0.374728i	0.299239	+	0.954178i	$0.403267\pi$
$884$	49.9058	+	36.2587i	1.67851	+	1.21951i
$885$	−4.80902	−	14.8006i	−0.161653	−	0.497518i
$886$	−2.07701	−	6.39239i	−0.0697787	−	0.214757i
$887$	−24.6631	−	17.9188i	−0.828106	−	0.601655i	0.0909165	−	0.995859i	$-0.471020\pi$
$887$	−24.6631	−	17.9188i	−0.828106	−	0.601655i	−0.919023	+	0.394204i	$0.871020\pi$
$888$	−2.10081	+	1.52633i	−0.0704987	+	0.0512203i
$889$	1.76393	−	5.42882i	0.0591604	−	0.182077i
$890$	2.32624			0.0779757
$891$		0			0
$892$	28.1459			0.942394
$893$	−0.287731	+	0.885544i	−0.00962854	+	0.0296336i
$894$	−0.0729490	+	0.0530006i	−0.00243978	+	0.00177260i
$895$	22.8713	+	16.6170i	0.764504	+	0.555445i
$896$	−3.11803	−	9.59632i	−0.104166	−	0.320591i
$897$	−5.54508	−	17.0660i	−0.185145	−	0.569818i
$898$	−8.32624	−	6.04937i	−0.277850	−	0.201870i
$899$	24.7082	−	17.9516i	0.824065	−	0.598718i
$900$	1.36475	−	4.20025i	0.0454915	−	0.140008i
$901$	20.5623			0.685030
$902$		0			0
$903$	6.70820			0.223235
$904$	2.05979	−	6.33939i	0.0685077	−	0.210845i
$905$	−15.0172	+	10.9106i	−0.499189	+	0.362682i
$906$	−5.85410	−	4.25325i	−0.194490	−	0.141305i
$907$	9.70163	+	29.8585i	0.322137	+	0.991436i	0.972716	+	0.231998i	$0.0745262\pi$
$907$	9.70163	+	29.8585i	0.322137	+	0.991436i	−0.650579	+	0.759439i	$0.725474\pi$
$908$	5.25987	+	16.1882i	0.174555	+	0.537224i
$909$	4.66312	+	3.38795i	0.154666	+	0.112371i
$910$	2.11803	−	1.53884i	0.0702121	−	0.0510121i
$911$	−3.27458	+	10.0781i	−0.108492	+	0.333903i	−0.990534	−	0.137267i	$-0.956168\pi$
$911$	−3.27458	+	10.0781i	−0.108492	+	0.333903i	0.882043	+	0.471170i	$0.156168\pi$
$912$	2.68692			0.0889727
$913$		0			0
$914$	8.77709			0.290320
$915$	−4.28115	+	13.1760i	−0.141531	+	0.435586i
$916$	−12.7082	+	9.23305i	−0.419891	+	0.305069i
$917$	10.3541	+	7.52270i	0.341923	+	0.248421i
$918$	−0.927051	−	2.85317i	−0.0305972	−	0.0941686i
$919$	−1.74671	−	5.37582i	−0.0576187	−	0.177332i	0.918105	−	0.396337i	$-0.129719\pi$
$919$	−1.74671	−	5.37582i	−0.0576187	−	0.177332i	−0.975724	+	0.219005i	$0.929719\pi$
$920$	8.16312	+	5.93085i	0.269130	+	0.195534i
$921$	−15.3541	+	11.1554i	−0.505935	+	0.367583i
$922$	2.86475	−	8.81678i	0.0943454	−	0.290365i
$923$	22.5623			0.742647
$924$		0			0
$925$	4.20163			0.138149
$926$	−4.16312	+	12.8128i	−0.136809	+	0.421054i
$927$	−5.61803	+	4.08174i	−0.184520	+	0.134062i
$928$	−20.1246	−	14.6214i	−0.660623	−	0.479971i
$929$	0.218847	+	0.673542i	0.00718014	+	0.0220982i	0.954582	−	0.297947i	$-0.0963019\pi$
$929$	0.218847	+	0.673542i	0.00718014	+	0.0220982i	−0.947402	+	0.320045i	$0.896302\pi$
$930$	0.972136	+	2.99193i	0.0318776	+	0.0981091i
$931$	−4.14590	−	3.01217i	−0.135876	−	0.0987199i
$932$	−16.2812	+	11.8290i	−0.533307	+	0.387470i
$933$	6.07295	−	18.6906i	0.198819	−	0.611903i
$934$	5.68692			0.186082
$935$		0			0
$936$	−6.23607			−0.203832
$937$	3.19756	−	9.84108i	0.104460	−	0.321494i	−0.885144	−	0.465318i	$-0.845940\pi$
$937$	3.19756	−	9.84108i	0.104460	−	0.321494i	0.989603	+	0.143824i	$0.0459399\pi$
$938$	1.50000	−	1.08981i	0.0489767	−	0.0355837i
$939$	−9.28115	−	6.74315i	−0.302879	−	0.220054i
$940$	−1.01064	−	3.11044i	−0.0329635	−	0.101451i
$941$	12.8090	+	39.4221i	0.417562	+	1.28512i	0.909939	+	0.414742i	$0.136128\pi$
$941$	12.8090	+	39.4221i	0.417562	+	1.28512i	−0.492377	+	0.870382i	$0.663872\pi$
$942$	−0.708204	−	0.514540i	−0.0230745	−	0.0167646i
$943$	−14.5172	+	10.5474i	−0.472746	+	0.343470i
$944$	9.35004	−	28.7765i	0.304318	−	0.936594i
$945$	1.61803			0.0526346
$946$		0			0
$947$	41.3951			1.34516			0.672580	−	0.740024i	$-0.265186\pi$
$947$	41.3951			1.34516			0.672580	+	0.740024i	$0.265186\pi$
$948$	6.30244	−	19.3969i	0.204694	−	0.629982i
$949$	26.4164	−	19.1926i	0.857513	−	0.623020i
$950$	0.628677	+	0.456761i	0.0203970	+	0.0148193i
$951$	9.01722	+	27.7522i	0.292403	+	0.899925i
$952$	3.57295	+	10.9964i	0.115800	+	0.356396i
$953$	−34.5066	−	25.0705i	−1.11778	−	0.812113i	−0.133907	−	0.990994i	$-0.542752\pi$
$953$	−34.5066	−	25.0705i	−1.11778	−	0.812113i	−0.983871	+	0.178881i	$0.942752\pi$
$954$	−0.809017	+	0.587785i	−0.0261929	+	0.0190303i
$955$	−11.5902	+	35.6709i	−0.375049	+	1.15428i
$956$	−4.85410			−0.156993
$957$		0			0
$958$	11.6950			0.377850
$959$	−4.39919	+	13.5393i	−0.142057	+	0.437207i
$960$	−6.16312	+	4.47777i	−0.198914	+	0.144519i
$961$	4.11803	+	2.99193i	0.132840	+	0.0965138i
$962$	−0.881966	−	2.71441i	−0.0284357	−	0.0875162i
$963$	−0.781153	−	2.40414i	−0.0251723	−	0.0774724i
$964$	32.5623	+	23.6579i	1.04876	+	0.761970i
$965$	12.8992	−	9.37181i	0.415240	−	0.301689i
$966$	0.500000	−	1.53884i	0.0160872	−	0.0495114i
$967$	−20.9230			−0.672838			−0.336419	−	0.941712i	$-0.609216\pi$
$967$	−20.9230			−0.672838			−0.336419	+	0.941712i	$0.609216\pi$
$968$		0			0
$969$	−6.70820			−0.215499
$970$	−0.218847	+	0.673542i	−0.00702676	+	0.0216261i
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.110957	−	0.993825i	$-0.464608\pi$
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.979472	+	0.201582i	$0.0646083\pi$
$972$	−1.50000	−	1.08981i	−0.0481125	−	0.0349558i
$973$	1.71885	+	5.29007i	0.0551037	+	0.169592i
$974$	−0.0835921	−	0.257270i	−0.00267846	−	0.00824347i
$975$	8.16312	+	5.93085i	0.261429	+	0.189939i
$976$	−21.7918	+	15.8327i	−0.697538	+	0.506791i
$977$	15.0172	−	46.2183i	0.480443	−	1.47865i	−0.358030	−	0.933710i	$-0.616551\pi$
$977$	15.0172	−	46.2183i	0.480443	−	1.47865i	0.838473	−	0.544943i	$-0.183449\pi$
$978$	−4.52786			−0.144785
$979$		0			0
$980$	18.0000			0.574989
$981$	−3.70820	+	11.4127i	−0.118394	+	0.364379i
$982$	−8.98936	+	6.53115i	−0.286862	+	0.208417i
$983$	35.5066	+	25.7970i	1.13248	+	0.822798i	0.986054	−	0.166423i	$-0.0532218\pi$
$983$	35.5066	+	25.7970i	1.13248	+	0.822798i	0.146430	+	0.989221i	$0.453222\pi$
$984$	1.92705	+	5.93085i	0.0614321	+	0.189069i
$985$	−8.01722	−	24.6745i	−0.255450	−	0.786194i
$986$	14.5623	+	10.5801i	0.463758	+	0.336940i
$987$	−0.881966	+	0.640786i	−0.0280733	+	0.0203964i
$988$	−2.07295	+	6.37988i	−0.0659493	+	0.202971i
$989$	−28.4164			−0.903589
$990$		0			0
$991$	−38.7426			−1.23070			−0.615350	−	0.788254i	$-0.710985\pi$
$991$	−38.7426			−1.23070			−0.615350	+	0.788254i	$0.710985\pi$
$992$	−6.52129	+	20.0705i	−0.207051	+	0.637238i
$993$	2.66312	−	1.93487i	0.0845115	−	0.0614012i
$994$	1.64590	+	1.19581i	0.0522047	+	0.0379289i
$995$	−3.35410	−	10.3229i	−0.106332	−	0.327257i
$996$	−4.28115	−	13.1760i	−0.135654	−	0.417499i
$997$	37.0517	+	26.9196i	1.17344	+	0.852553i	0.991416	−	0.130742i	$-0.0417359\pi$
$997$	37.0517	+	26.9196i	1.17344	+	0.852553i	0.182022	+	0.983295i	$0.441736\pi$
$998$	−7.68034	+	5.58009i	−0.243117	+	0.176635i
$999$	0.545085	−	1.67760i	0.0172457	−	0.0530769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.k.130.1		4
11.2	odd	10		363.2.e.f.124.1		4
11.3	even	5		33.2.e.b.4.1	✓	4
11.4	even	5		363.2.a.d.1.2		2
11.5	even	5	inner	363.2.e.k.148.1		4
11.6	odd	10		363.2.e.b.148.1		4
11.7	odd	10		363.2.a.i.1.1		2
11.8	odd	10		363.2.e.f.202.1		4
11.9	even	5		33.2.e.b.25.1	yes	4
11.10	odd	2		363.2.e.b.130.1		4
33.14	odd	10		99.2.f.a.37.1		4
33.20	odd	10		99.2.f.a.91.1		4
33.26	odd	10		1089.2.a.t.1.1		2
33.29	even	10		1089.2.a.l.1.2		2
44.3	odd	10		528.2.y.b.433.1		4
44.7	even	10		5808.2.a.ci.1.2		2
44.15	odd	10		5808.2.a.cj.1.2		2
44.31	odd	10		528.2.y.b.289.1		4
55.3	odd	20		825.2.bx.d.499.2		8
55.4	even	10		9075.2.a.cb.1.1		2
55.9	even	10		825.2.n.c.751.1		4
55.14	even	10		825.2.n.c.301.1		4
55.29	odd	10		9075.2.a.u.1.2		2
55.42	odd	20		825.2.bx.d.124.2		8
55.47	odd	20		825.2.bx.d.499.1		8
55.53	odd	20		825.2.bx.d.124.1		8
99.14	odd	30		891.2.n.b.136.1		8
99.20	odd	30		891.2.n.b.190.1		8
99.25	even	15		891.2.n.c.433.1		8
99.31	even	15		891.2.n.c.784.1		8
99.47	odd	30		891.2.n.b.433.1		8
99.58	even	15		891.2.n.c.136.1		8
99.86	odd	30		891.2.n.b.784.1		8
99.97	even	15		891.2.n.c.190.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.4.1	✓	4	11.3	even	5
33.2.e.b.25.1	yes	4	11.9	even	5
99.2.f.a.37.1		4	33.14	odd	10
99.2.f.a.91.1		4	33.20	odd	10
363.2.a.d.1.2		2	11.4	even	5
363.2.a.i.1.1		2	11.7	odd	10
363.2.e.b.130.1		4	11.10	odd	2
363.2.e.b.148.1		4	11.6	odd	10
363.2.e.f.124.1		4	11.2	odd	10
363.2.e.f.202.1		4	11.8	odd	10
363.2.e.k.130.1		4	1.1	even	1	trivial
363.2.e.k.148.1		4	11.5	even	5	inner
528.2.y.b.289.1		4	44.31	odd	10
528.2.y.b.433.1		4	44.3	odd	10
825.2.n.c.301.1		4	55.14	even	10
825.2.n.c.751.1		4	55.9	even	10
825.2.bx.d.124.1		8	55.53	odd	20
825.2.bx.d.124.2		8	55.42	odd	20
825.2.bx.d.499.1		8	55.47	odd	20
825.2.bx.d.499.2		8	55.3	odd	20
891.2.n.b.136.1		8	99.14	odd	30
891.2.n.b.190.1		8	99.20	odd	30
891.2.n.b.433.1		8	99.47	odd	30
891.2.n.b.784.1		8	99.86	odd	30
891.2.n.c.136.1		8	99.58	even	15
891.2.n.c.190.1		8	99.97	even	15
891.2.n.c.433.1		8	99.25	even	15
891.2.n.c.784.1		8	99.31	even	15
1089.2.a.l.1.2		2	33.29	even	10
1089.2.a.t.1.1		2	33.26	odd	10
5808.2.a.ci.1.2		2	44.7	even	10
5808.2.a.cj.1.2		2	44.15	odd	10
9075.2.a.u.1.2		2	55.29	odd	10
9075.2.a.cb.1.1		2	55.4	even	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.118034 + 0.363271i) q^{2} +(0.809017 - 0.587785i) q^{3} +(1.50000 + 1.08981i) q^{4} +(0.500000 + 1.53884i) q^{5} +(0.118034 + 0.363271i) q^{6} +(0.809017 + 0.587785i) q^{7} +(-1.19098 + 0.865300i) q^{8} +(0.309017 - 0.951057i) q^{9} -0.618034 q^{10} +1.85410 q^{12} +(-1.30902 + 4.02874i) q^{13} +(-0.309017 + 0.224514i) q^{14} +(1.30902 + 0.951057i) q^{15} +(0.972136 + 2.99193i) q^{16} +(-2.42705 - 7.46969i) q^{17} +(0.309017 + 0.224514i) q^{18} +(0.690983 - 0.502029i) q^{19} +(-0.927051 + 2.85317i) q^{20} +1.00000 q^{21} -4.23607 q^{23} +(-0.454915 + 1.40008i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-1.30902 - 0.951057i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.572949 + 1.76336i) q^{28} +(4.85410 + 3.52671i) q^{29} +(-0.500000 + 0.363271i) q^{30} +(1.57295 - 4.84104i) q^{31} -4.14590 q^{32} +3.00000 q^{34} +(-0.500000 + 1.53884i) q^{35} +(1.50000 - 1.08981i) q^{36} +(1.42705 + 1.03681i) q^{37} +(0.100813 + 0.310271i) q^{38} +(1.30902 + 4.02874i) q^{39} +(-1.92705 - 1.40008i) q^{40} +(3.42705 - 2.48990i) q^{41} +(-0.118034 + 0.363271i) q^{42} +6.70820 q^{43} +1.61803 q^{45} +(0.500000 - 1.53884i) q^{46} +(-0.881966 + 0.640786i) q^{47} +(2.54508 + 1.84911i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(0.281153 + 0.865300i) q^{50} +(-6.35410 - 4.61653i) q^{51} +(-6.35410 + 4.61653i) q^{52} +(-0.809017 + 2.48990i) q^{53} +0.381966 q^{54} -1.47214 q^{56} +(0.263932 - 0.812299i) q^{57} +(-1.85410 + 1.34708i) q^{58} +(-7.78115 - 5.65334i) q^{59} +(0.927051 + 2.85317i) q^{60} +(2.64590 + 8.14324i) q^{61} +(1.57295 + 1.14281i) q^{62} +(0.809017 - 0.587785i) q^{63} +(-1.45492 + 4.47777i) q^{64} -6.85410 q^{65} -4.85410 q^{67} +(4.50000 - 13.8496i) q^{68} +(-3.42705 + 2.48990i) q^{69} +(-0.500000 - 0.363271i) q^{70} +(-1.64590 - 5.06555i) q^{71} +(0.454915 + 1.40008i) q^{72} +(-6.23607 - 4.53077i) q^{73} +(-0.545085 + 0.396027i) q^{74} +(0.736068 - 2.26538i) q^{75} +1.58359 q^{76} -1.61803 q^{78} +(3.39919 - 10.4616i) q^{79} +(-4.11803 + 2.99193i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(0.500000 + 1.53884i) q^{82} +(-2.30902 - 7.10642i) q^{83} +(1.50000 + 1.08981i) q^{84} +(10.2812 - 7.46969i) q^{85} +(-0.791796 + 2.43690i) q^{86} +6.00000 q^{87} -3.76393 q^{89} +(-0.190983 + 0.587785i) q^{90} +(-3.42705 + 2.48990i) q^{91} +(-6.35410 - 4.61653i) q^{92} +(-1.57295 - 4.84104i) q^{93} +(-0.128677 - 0.396027i) q^{94} +(1.11803 + 0.812299i) q^{95} +(-3.35410 + 2.43690i) q^{96} +(0.354102 - 1.08981i) q^{97} +2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + q^{3} + 6 q^{4} + 2 q^{5} - 4 q^{6} + q^{7} - 7 q^{8} - q^{9} + 2 q^{10} - 6 q^{12} - 3 q^{13} + q^{14} + 3 q^{15} - 14 q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + 3 q^{20} + 4 q^{21} - 8 q^{23}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + q^3 + 6 * q^4 + 2 * q^5 - 4 * q^6 + q^7 - 7 * q^8 - q^9 + 2 * q^10 - 6 * q^12 - 3 * q^13 + q^14 + 3 * q^15 - 14 * q^16 - 3 * q^17 - q^18 + 5 * q^19 + 3 * q^20 + 4 * q^21 - 8 * q^23 - 13 * q^24 + q^25 - 3 * q^26 + q^27 + 9 * q^28 + 6 * q^29 - 2 * q^30 + 13 * q^31 - 30 * q^32 + 12 * q^34 - 2 * q^35 + 6 * q^36 - q^37 + 25 * q^38 + 3 * q^39 - q^40 + 7 * q^41 + 4 * q^42 + 2 * q^45 + 2 * q^46 - 8 * q^47 - q^48 + 6 * q^49 - 19 * q^50 - 12 * q^51 - 12 * q^52 - q^53 + 6 * q^54 + 12 * q^56 + 10 * q^57 + 6 * q^58 - 11 * q^59 - 3 * q^60 + 24 * q^61 + 13 * q^62 + q^63 - 17 * q^64 - 14 * q^65 - 6 * q^67 + 18 * q^68 - 7 * q^69 - 2 * q^70 - 20 * q^71 + 13 * q^72 - 16 * q^73 + 9 * q^74 - 6 * q^75 + 60 * q^76 - 2 * q^78 - 11 * q^79 - 12 * q^80 - q^81 + 2 * q^82 - 7 * q^83 + 6 * q^84 + 21 * q^85 - 30 * q^86 + 24 * q^87 - 24 * q^89 - 3 * q^90 - 7 * q^91 - 12 * q^92 - 13 * q^93 - 43 * q^94 - 12 * q^97 + 36 * q^98

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