LMFDB - Embedded newform 1183.2.e.g.170.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.3
Root			$0.756174 + 1.30973i$ of defining polynomial
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.g.508.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +0.562784 q^{6} +(-0.751763 - 2.53670i) q^{7} -2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})$	\(q+(-0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +0.562784 q^{6} +(-0.751763 - 2.53670i) q^{7} -2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(1.46456 + 2.53670i) q^{10} +(-0.448993 - 0.777679i) q^{11} +(0.421723 - 0.730446i) q^{12} +(2.18972 + 0.525403i) q^{14} -2.27559 q^{15} +(-0.0891447 + 0.154403i) q^{16} +(-0.968404 - 1.67733i) q^{17} +(1.09063 + 1.88902i) q^{18} +(0.519020 - 0.898968i) q^{19} +4.38990 q^{20} +(-1.20406 + 1.26915i) q^{21} +0.764299 q^{22} +(-2.82506 + 4.89315i) q^{23} +(0.921723 + 1.59647i) q^{24} +(-3.42189 - 5.92688i) q^{25} -3.67824 q^{27} +(2.32280 - 2.44835i) q^{28} -1.83594 q^{29} +(0.968404 - 1.67733i) q^{30} +(-4.56692 - 7.91014i) q^{31} +(-2.86381 - 4.96026i) q^{32} +(-0.296885 + 0.514219i) q^{33} +1.64847 q^{34} +(-8.85399 - 2.12444i) q^{35} +3.26905 q^{36} +(-5.30001 + 9.17989i) q^{37} +(0.441751 + 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +5.33143 q^{41} +(-0.423080 - 1.42761i) q^{42} -3.91465 q^{43} +(0.572729 - 0.991996i) q^{44} +(-4.40988 - 7.63814i) q^{45} +(-2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +0.117889 q^{48} +(-5.86970 + 3.81400i) q^{49} +5.82491 q^{50} +(-0.640331 + 1.10909i) q^{51} +(4.69324 + 8.12893i) q^{53} +(1.56532 - 2.71122i) q^{54} -3.09040 q^{55} +(2.09587 + 7.07216i) q^{56} -0.686375 q^{57} +(0.781307 - 1.35326i) q^{58} +(-0.255259 - 0.442121i) q^{59} +(-1.45135 - 2.51382i) q^{60} +(-0.718095 + 1.24378i) q^{61} +7.77405 q^{62} +(-6.59335 - 1.58202i) q^{63} +4.51834 q^{64} +(-0.252686 - 0.437665i) q^{66} +(-4.22466 - 7.31732i) q^{67} +(1.23528 - 2.13957i) q^{68} +3.73600 q^{69} +(5.33385 - 5.62216i) q^{70} +3.44837 q^{71} +(-3.57244 + 6.18764i) q^{72} +(5.45026 + 9.44013i) q^{73} +(-4.51097 - 7.81324i) q^{74} +(-2.26263 + 3.91899i) q^{75} +1.32411 q^{76} +(-1.63520 + 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} +(0.306789 + 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(-2.26886 + 3.92977i) q^{82} -1.51669 q^{83} +(-2.16996 - 0.520663i) q^{84} -6.66549 q^{85} +(1.66593 - 2.88547i) q^{86} +(0.606982 + 1.05132i) q^{87} +(1.25176 + 2.16812i) q^{88} +(6.80391 - 11.7847i) q^{89} +7.50673 q^{90} -7.20722 q^{92} +(-3.01976 + 5.23037i) q^{93} +(3.06035 + 5.30067i) q^{94} +(-1.78619 - 3.09378i) q^{95} +(-1.89362 + 3.27984i) q^{96} -0.506241 q^{97} +(-0.313356 - 5.94963i) q^{98} -2.30134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.425563	+	0.737096i	−0.300918	+	0.521206i	−0.976344	−	0.216222i	$-0.930626\pi$
$2$	−0.425563	+	0.737096i	−0.300918	+	0.521206i	0.675426	+	0.737428i	$0.263960\pi$
$3$	−0.330612	−	0.572636i	−0.190879	−	0.330612i	0.754663	−	0.656113i	$-0.227800\pi$
$3$	−0.330612	−	0.572636i	−0.190879	−	0.330612i	−0.945542	+	0.325501i	$0.894467\pi$
$4$	0.637793	+	1.10469i	0.318896	+	0.552345i
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	−0.168276	−	0.985740i	$-0.553820\pi$
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	0.937814	−	0.347139i	$-0.112847\pi$
$6$	0.562784			0.229756
$7$	−0.751763	−	2.53670i	−0.284140	−	0.958783i
$7$	−0.751763	−	2.53670i	−0.284140	−	0.958783i
$8$	−2.78793			−0.985684
$9$	1.28139	−	2.21944i	0.427131	−	0.739812i
$10$	1.46456	+	2.53670i	0.463136	+	0.802175i
$11$	−0.448993	−	0.777679i	−0.135377	−	0.234479i	0.790365	−	0.612637i	$-0.209891\pi$
$11$	−0.448993	−	0.777679i	−0.135377	−	0.234479i	−0.925741	+	0.378158i	$0.876558\pi$
$12$	0.421723	−	0.730446i	0.121741	−	0.210862i
$13$		0			0
$13$		0			0
$14$	2.18972	+	0.525403i	0.585226	+	0.140420i
$15$	−2.27559			−0.587554
$16$	−0.0891447	+	0.154403i	−0.0222862	+	0.0386008i
$17$	−0.968404	−	1.67733i	−0.234873	−	0.406811i	0.724363	−	0.689419i	$-0.242134\pi$
$17$	−0.968404	−	1.67733i	−0.234873	−	0.406811i	−0.959236	+	0.282607i	$0.908801\pi$
$18$	1.09063	+	1.88902i	0.257063	+	0.445246i
$19$	0.519020	−	0.898968i	0.119071	−	0.206237i	−0.800329	−	0.599562i	$-0.795342\pi$
$19$	0.519020	−	0.898968i	0.119071	−	0.206237i	0.919400	+	0.393324i	$0.128675\pi$
$20$	4.38990			0.981612
$21$	−1.20406	+	1.26915i	−0.262748	+	0.276951i
$22$	0.764299			0.162949
$23$	−2.82506	+	4.89315i	−0.589067	+	1.02029i	0.405288	+	0.914189i	$0.367171\pi$
$23$	−2.82506	+	4.89315i	−0.589067	+	1.02029i	−0.994355	+	0.106104i	$0.966162\pi$
$24$	0.921723	+	1.59647i	0.188146	+	0.325878i
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$		0			0
$27$	−3.67824			−0.707878
$28$	2.32280	−	2.44835i	0.438967	−	0.462696i
$29$	−1.83594			−0.340925			−0.170463	−	0.985364i	$-0.554526\pi$
$29$	−1.83594			−0.340925			−0.170463	+	0.985364i	$0.554526\pi$
$30$	0.968404	−	1.67733i	0.176806	−	0.306236i
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	−0.905501	−	0.424345i	$-0.860505\pi$
$31$	−4.56692	−	7.91014i	−0.820244	−	1.42070i	0.0852573	−	0.996359i	$-0.472829\pi$
$32$	−2.86381	−	4.96026i	−0.506254	−	0.876858i
$33$	−0.296885	+	0.514219i	−0.0516810	+	0.0895141i
$34$	1.64847			0.282710
$35$	−8.85399	−	2.12444i	−1.49660	−	0.359096i
$36$	3.26905			0.544842
$37$	−5.30001	+	9.17989i	−0.871316	+	1.50916i	−0.0106808	+	0.999943i	$0.503400\pi$
$37$	−5.30001	+	9.17989i	−0.871316	+	1.50916i	−0.860636	+	0.509221i	$0.829933\pi$
$38$	0.441751	+	0.765135i	0.0716614	+	0.124121i
$39$		0			0
$40$	−4.79731	+	8.30918i	−0.758521	+	1.31380i
$41$	5.33143			0.832629			0.416314	−	0.909221i	$-0.363322\pi$
$41$	5.33143			0.832629			0.416314	+	0.909221i	$0.363322\pi$
$42$	−0.423080	−	1.42761i	−0.0652827	−	0.220286i
$43$	−3.91465			−0.596978			−0.298489	−	0.954413i	$-0.596483\pi$
$43$	−3.91465			−0.596978			−0.298489	+	0.954413i	$0.596483\pi$
$44$	0.572729	−	0.991996i	0.0863422	−	0.149549i
$45$	−4.40988	−	7.63814i	−0.657387	−	1.13863i
$46$	−2.40448	−	4.16469i	−0.354522	−	0.614050i
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	−0.475115	−	0.879924i	$-0.657593\pi$
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	0.999594	−	0.0285004i	$-0.00907317\pi$
$48$	0.117889			0.0170158
$49$	−5.86970	+	3.81400i	−0.838529	+	0.544857i
$50$	5.82491			0.823767
$51$	−0.640331	+	1.10909i	−0.0896643	+	0.155303i
$52$		0			0
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	0.984378	+	0.176065i	$0.0563370\pi$
$53$	4.69324	+	8.12893i	0.644666	+	1.11659i	−0.339712	+	0.940529i	$0.610330\pi$
$54$	1.56532	−	2.71122i	0.213013	−	0.368950i
$55$	−3.09040			−0.416710
$56$	2.09587	+	7.07216i	0.280072	+	0.945056i
$57$	−0.686375			−0.0909127
$58$	0.781307	−	1.35326i	0.102591	−	0.177692i
$59$	−0.255259	−	0.442121i	−0.0332318	−	0.0575592i	0.848931	−	0.528503i	$-0.177247\pi$
$59$	−0.255259	−	0.442121i	−0.0332318	−	0.0575592i	−0.882163	+	0.470944i	$0.843913\pi$
$60$	−1.45135	−	2.51382i	−0.187369	−	0.324532i
$61$	−0.718095	+	1.24378i	−0.0919426	+	0.159249i	−0.908328	−	0.418258i	$-0.862641\pi$
$61$	−0.718095	+	1.24378i	−0.0919426	+	0.159249i	0.816386	+	0.577507i	$0.195974\pi$
$62$	7.77405			0.987305
$63$	−6.59335	−	1.58202i	−0.830684	−	0.199315i
$64$	4.51834			0.564792
$65$		0			0
$66$	−0.252686	−	0.437665i	−0.0311035	−	0.0538729i
$67$	−4.22466	−	7.31732i	−0.516124	−	0.893953i	−0.999825	−	0.0187197i	$-0.994041\pi$
$67$	−4.22466	−	7.31732i	−0.516124	−	0.893953i	0.483701	−	0.875233i	$-0.339292\pi$
$68$	1.23528	−	2.13957i	0.149800	−	0.259461i
$69$	3.73600			0.449761
$70$	5.33385	−	5.62216i	0.637516	−	0.671977i
$71$	3.44837			0.409247			0.204623	−	0.978841i	$-0.434403\pi$
$71$	3.44837			0.409247			0.204623	+	0.978841i	$0.434403\pi$
$72$	−3.57244	+	6.18764i	−0.421016	+	0.729221i
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	0.985892	+	0.167384i	$0.0535320\pi$
$73$	5.45026	+	9.44013i	0.637905	+	1.10488i	−0.347987	+	0.937499i	$0.613135\pi$
$74$	−4.51097	−	7.81324i	−0.524390	−	0.908270i
$75$	−2.26263	+	3.91899i	−0.261266	+	0.452526i
$76$	1.32411			0.151886
$77$	−1.63520	+	1.72359i	−0.186349	+	0.196422i
$78$		0			0
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	0.306789	+	0.531375i	0.0343001	+	0.0594095i
$81$	−2.62811	−	4.55201i	−0.292012	−	0.505779i
$82$	−2.26886	+	3.92977i	−0.250553	+	0.433971i
$83$	−1.51669			−0.166479			−0.0832393	−	0.996530i	$-0.526527\pi$
$83$	−1.51669			−0.166479			−0.0832393	+	0.996530i	$0.526527\pi$
$84$	−2.16996	−	0.520663i	−0.236762	−	0.0568090i
$85$	−6.66549			−0.722973
$86$	1.66593	−	2.88547i	0.179642	−	0.311148i
$87$	0.606982	+	1.05132i	0.0650754	+	0.112714i
$88$	1.25176	+	2.16812i	0.133438	+	0.231122i
$89$	6.80391	−	11.7847i	0.721213	−	1.24918i	−0.239301	−	0.970945i	$-0.576918\pi$
$89$	6.80391	−	11.7847i	0.721213	−	1.24918i	0.960514	−	0.278232i	$-0.0897484\pi$
$90$	7.50673			0.791279
$91$		0			0
$92$	−7.20722			−0.751405
$93$	−3.01976	+	5.23037i	−0.313134	+	0.542364i
$94$	3.06035	+	5.30067i	0.315651	+	0.546723i
$95$	−1.78619	−	3.09378i	−0.183260	−	0.317415i
$96$	−1.89362	+	3.27984i	−0.193266	+	0.334747i
$97$	−0.506241			−0.0514010			−0.0257005	−	0.999670i	$-0.508182\pi$
$97$	−0.506241			−0.0514010			−0.0257005	+	0.999670i	$0.508182\pi$
$98$	−0.313356	−	5.94963i	−0.0316538	−	0.601004i
$99$	−2.30134			−0.231294
$100$	4.36491	−	7.56025i	0.436491	−	0.756025i
$101$	2.99327	+	5.18450i	0.297842	+	0.515877i	0.975642	−	0.219369i	$-0.0703999\pi$
$101$	2.99327	+	5.18450i	0.297842	+	0.515877i	−0.677800	+	0.735246i	$0.737067\pi$
$102$	−0.545002	−	0.943972i	−0.0539633	−	0.0934671i
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	−0.746073	−	0.665865i	$-0.768063\pi$
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	0.949692	+	0.313186i	$0.101396\pi$
$104$		0			0
$105$	1.71070	+	5.77248i	0.166947	+	0.563336i
$106$	−7.98908			−0.775968
$107$	7.06169	−	12.2312i	0.682679	−	1.18243i	−0.291481	−	0.956577i	$-0.594148\pi$
$107$	7.06169	−	12.2312i	0.682679	−	1.18243i	0.974160	−	0.225858i	$-0.0725186\pi$
$108$	−2.34596	−	4.06331i	−0.225740	−	0.390993i
$109$	−2.10119	−	3.63936i	−0.201257	−	0.348588i	0.747677	−	0.664063i	$-0.231169\pi$
$109$	−2.10119	−	3.63936i	−0.201257	−	0.348588i	−0.948934	+	0.315475i	$0.897836\pi$
$110$	1.31516	−	2.27792i	0.125396	−	0.217191i
$111$	7.00898			0.665263
$112$	0.458690	+	0.110059i	0.0433421	+	0.0103996i
$113$	13.7694			1.29532			0.647660	−	0.761929i	$-0.275748\pi$
$113$	13.7694			1.29532			0.647660	+	0.761929i	$0.275748\pi$
$114$	0.292096	−	0.505925i	0.0273573	−	0.0473842i
$115$	9.72240	+	16.8397i	0.906618	+	1.57031i
$116$	−1.17095	−	2.02814i	−0.108720	−	0.188308i
$117$		0			0
$118$	0.434514			0.0400003
$119$	−3.52686	+	3.71750i	−0.323307	+	0.340783i
$120$	6.34418			0.579142
$121$	5.09681	−	8.82793i	0.463346	−	0.802539i
$122$	−0.611189	−	1.05861i	−0.0553344	−	0.0958420i
$123$	−1.76263	−	3.05297i	−0.158931	−	0.275277i
$124$	5.82550	−	10.0901i	0.523145	−	0.906114i
$125$	−6.34531			−0.567542
$126$	3.97198	−	4.18669i	0.353852	−	0.372980i
$127$	1.94496			0.172588			0.0862938	−	0.996270i	$-0.472498\pi$
$127$	1.94496			0.172588			0.0862938	+	0.996270i	$0.472498\pi$
$128$	3.80478	−	6.59007i	0.336298	−	0.582485i
$129$	1.29423	+	2.24167i	0.113950	+	0.197368i
$130$		0			0
$131$	6.01770	−	10.4230i	0.525769	−	0.910659i	−0.473780	−	0.880643i	$-0.657111\pi$
$131$	6.01770	−	10.4230i	0.525769	−	0.910659i	0.999549	−	0.0300158i	$-0.00955576\pi$
$132$	−0.757404			−0.0659235
$133$	−2.67059	−	0.640786i	−0.231570	−	0.0555632i
$134$	7.19143			0.621245
$135$	−6.32930	+	10.9627i	−0.544739	+	0.943516i
$136$	2.69985	+	4.67627i	0.231510	+	0.400987i
$137$	4.35857	+	7.54927i	0.372378	+	0.644978i	0.989931	−	0.141552i	$-0.0452092\pi$
$137$	4.35857	+	7.54927i	0.372378	+	0.644978i	−0.617553	+	0.786529i	$0.711876\pi$
$138$	−1.58990	+	2.75379i	−0.135341	+	0.234418i
$139$	4.21250			0.357299			0.178650	−	0.983913i	$-0.442827\pi$
$139$	4.21250			0.357299			0.178650	+	0.983913i	$0.442827\pi$
$140$	−3.30017	−	11.1359i	−0.278915	−	0.941152i
$141$	−4.75505			−0.400447
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$		0			0
$144$	0.228459	+	0.395702i	0.0190382	+	0.0329751i
$145$	−3.15917	+	5.47184i	−0.262355	+	0.454412i
$146$	−9.27771			−0.767829
$147$	4.12462	+	2.10025i	0.340193	+	0.173226i
$148$	−13.5212			−1.11144
$149$	2.93242	−	5.07910i	0.240233	−	0.416096i	−0.720548	−	0.693406i	$-0.756109\pi$
$149$	2.93242	−	5.07910i	0.240233	−	0.416096i	0.960781	+	0.277310i	$0.0894428\pi$
$150$	−1.92578	−	3.33555i	−0.157240	−	0.272347i
$151$	−8.42840	−	14.5984i	−0.685893	−	1.18800i	−0.973155	−	0.230150i	$-0.926078\pi$
$151$	−8.42840	−	14.5984i	−0.685893	−	1.18800i	0.287262	−	0.957852i	$-0.407255\pi$
$152$	−1.44699	+	2.50626i	−0.117367	+	0.203285i
$153$	−4.96362			−0.401285
$154$	−0.574572	−	1.93880i	−0.0463003	−	0.156233i
$155$	−31.4339			−2.52483
$156$		0			0
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	0.902116	−	0.431493i	$-0.142013\pi$
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	−0.824742	+	0.565509i	$0.808680\pi$
$158$	5.14581	+	8.91280i	0.409379	+	0.709065i
$159$	3.10328	−	5.37504i	0.246106	−	0.426268i
$160$	−19.7115			−1.55833
$161$	14.5362	+	3.48785i	1.14562	+	0.274881i
$162$	4.47370			0.351487
$163$	−5.94797	+	10.3022i	−0.465881	+	0.806929i	−0.999241	−	0.0389590i	$-0.987596\pi$
$163$	−5.94797	+	10.3022i	−0.465881	+	0.806929i	0.533360	+	0.845888i	$0.320929\pi$
$164$	3.40035	+	5.88957i	0.265522	+	0.459898i
$165$	1.02172	+	1.76968i	0.0795410	+	0.137769i
$166$	0.645448	−	1.11795i	0.0500965	−	0.0867696i
$167$	−16.5760			−1.28269			−0.641346	−	0.767252i	$-0.721624\pi$
$167$	−16.5760			−1.28269			−0.641346	+	0.767252i	$0.721624\pi$
$168$	3.35685	−	3.53831i	0.258987	−	0.272986i
$169$		0			0
$170$	2.83658	−	4.91310i	0.217556	−	0.376818i
$171$	−1.33013	−	2.30386i	−0.101718	−	0.176181i
$172$	−2.49673	−	4.32447i	−0.190374	−	0.329738i
$173$	4.99328	−	8.64862i	0.379632	−	0.657542i	−0.611377	−	0.791340i	$-0.709384\pi$
$173$	4.99328	−	8.64862i	0.379632	−	0.657542i	0.991009	+	0.133798i	$0.0427172\pi$
$174$	−1.03324			−0.0783295
$175$	−12.4623	+	13.1359i	−0.942060	+	0.992982i
$176$	0.160101			0.0120681
$177$	−0.168783	+	0.292341i	−0.0126865	+	0.0219737i
$178$	5.79098	+	10.0303i	0.434052	+	0.751801i
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	0.642033	−	0.766677i	$-0.278091\pi$
$179$	−4.58829	−	7.94715i	−0.342945	−	0.593998i	−0.984978	+	0.172679i	$0.944758\pi$
$180$	5.62518	−	9.74310i	0.419276	−	0.726208i
$181$	6.00489			0.446340			0.223170	−	0.974780i	$-0.428360\pi$
$181$	6.00489			0.446340			0.223170	+	0.974780i	$0.428360\pi$
$182$		0			0
$183$	0.949642			0.0701995
$184$	7.87609	−	13.6418i	0.580633	−	1.00569i
$185$	18.2399	+	31.5924i	1.34102	+	2.32272i
$186$	−2.57019	−	4.45170i	−0.188456	−	0.326415i
$187$	−0.869614	+	1.50622i	−0.0635925	+	0.110145i
$188$	9.17311			0.669018
$189$	2.76517	+	9.33060i	0.201136	+	0.678701i
$190$	3.04055			0.220585
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	−0.888851	−	0.458197i	$-0.848496\pi$
$191$	−0.658061	+	1.13980i	−0.0476156	+	0.0824727i	0.841235	+	0.540669i	$0.181829\pi$
$192$	−1.49382	−	2.58736i	−0.107807	−	0.186727i
$193$	−8.21270	−	14.2248i	−0.591163	−	1.02392i	−0.994076	−	0.108686i	$-0.965336\pi$
$193$	−8.21270	−	14.2248i	−0.591163	−	1.02392i	0.402913	−	0.915238i	$-0.367998\pi$
$194$	0.215437	−	0.373148i	0.0154675	−	0.0267905i
$195$		0			0
$196$	−7.95694	−	4.05166i	−0.568353	−	0.289404i
$197$	25.5875			1.82303			0.911517	−	0.411262i	$-0.134912\pi$
$197$	25.5875			1.82303			0.911517	+	0.411262i	$0.134912\pi$
$198$	0.979367	−	1.69631i	0.0696006	−	0.120552i
$199$	12.6894	+	21.9787i	0.899528	+	1.55803i	0.828099	+	0.560582i	$0.189422\pi$
$199$	12.6894	+	21.9787i	0.899528	+	1.55803i	0.0714284	+	0.997446i	$0.477244\pi$
$200$	9.54000	+	16.5238i	0.674580	+	1.16841i
$201$	−2.79344	+	4.83838i	−0.197034	+	0.341273i
$202$	−5.09530			−0.358504
$203$	1.38019	+	4.65723i	0.0968704	+	0.326873i
$204$	−1.63359			−0.114375
$205$	9.17399	−	15.8898i	0.640740	−	1.10979i
$206$	1.75886	+	3.04643i	0.122546	+	0.212255i
$207$	7.24003	+	12.5401i	0.503217	+	0.871597i
$208$		0			0
$209$	−0.932145			−0.0644778
$210$	−4.98288	−	1.19560i	−0.343852	−	0.0825043i
$211$	−5.69648			−0.392162			−0.196081	−	0.980588i	$-0.562822\pi$
$211$	−5.69648			−0.392162			−0.196081	+	0.980588i	$0.562822\pi$
$212$	−5.98663	+	10.3691i	−0.411164	+	0.712156i
$213$	−1.14007	−	1.97466i	−0.0781165	−	0.135302i
$214$	6.01038	+	10.4103i	0.410861	+	0.711633i
$215$	−6.73608	+	11.6672i	−0.459397	+	0.795699i
$216$	10.2547			0.697744
$217$	−16.6324	+	17.5315i	−1.12908	+	1.19011i
$218$	3.57675			0.242248
$219$	3.60384	−	6.24203i	0.243525	−	0.421797i
$220$	−1.97104	−	3.41393i	−0.132887	−	0.230167i
$221$		0			0
$222$	−2.98276	+	5.16629i	−0.200190	+	0.346739i
$223$	−2.35812			−0.157912			−0.0789558	−	0.996878i	$-0.525159\pi$
$223$	−2.35812			−0.157912			−0.0789558	+	0.996878i	$0.525159\pi$
$224$	−10.4298	+	10.9936i	−0.696870	+	0.734538i
$225$	−17.5391			−1.16927
$226$	−5.85976	+	10.1494i	−0.389786	+	0.675129i
$227$	13.1463	+	22.7701i	0.872551	+	1.51130i	0.859349	+	0.511390i	$0.170869\pi$
$227$	13.1463	+	22.7701i	0.872551	+	1.51130i	0.0132022	+	0.999913i	$0.495797\pi$
$228$	−0.437765	−	0.758232i	−0.0289917	−	0.0502151i
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	−0.864891	−	0.501960i	$-0.832612\pi$
$229$	0.0342777	−	0.0593708i	0.00226514	−	0.00392333i	0.867156	+	0.498037i	$0.165946\pi$
$230$	−16.5500			−1.09127
$231$	1.52761	+	0.366536i	0.100509	+	0.0241163i
$232$	5.11847			0.336044
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	−0.999751	−	0.0223253i	$-0.992893\pi$
$233$	−7.33514	+	12.7048i	−0.480541	+	0.832322i	0.519210	+	0.854647i	$0.326226\pi$
$234$		0			0
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	0.325604	−	0.563963i	0.0211950	−	0.0367109i
$237$	−7.99536			−0.519355
$238$	−1.23926	−	4.18167i	−0.0803291	−	0.271057i
$239$	−3.35434			−0.216974			−0.108487	−	0.994098i	$-0.534601\pi$
$239$	−3.35434			−0.216974			−0.108487	+	0.994098i	$0.534601\pi$
$240$	0.202856	−	0.351357i	0.0130943	−	0.0226800i
$241$	−4.28989	−	7.43031i	−0.276336	−	0.478628i	0.694135	−	0.719845i	$-0.255787\pi$
$241$	−4.28989	−	7.43031i	−0.276336	−	0.478628i	−0.970471	+	0.241216i	$0.922454\pi$
$242$	4.33802	+	7.51368i	0.278859	+	0.482998i
$243$	−7.25513	+	12.5662i	−0.465417	+	0.806125i
$244$	−1.83198			−0.117281
$245$	1.26704	+	24.0570i	0.0809482	+	1.53695i
$246$	3.00044			0.191301
$247$		0			0
$248$	12.7323	+	22.0530i	0.808501	+	1.40036i
$249$	0.501436	+	0.868513i	0.0317772	+	0.0550398i
$250$	2.70033	−	4.67711i	0.170784	−	0.295806i
$251$	21.5151			1.35802			0.679010	−	0.734129i	$-0.262409\pi$
$251$	21.5151			1.35802			0.679010	+	0.734129i	$0.262409\pi$
$252$	−2.45755	−	8.29260i	−0.154811	−	0.522385i
$253$	5.07374			0.318983
$254$	−0.827704	+	1.43363i	−0.0519348	+	0.0899537i
$255$	2.20369	+	3.81690i	0.138000	+	0.239023i
$256$	7.75668	+	13.4350i	0.484793	+	0.839686i
$257$	−2.46896	+	4.27636i	−0.154010	+	0.266752i	−0.932698	−	0.360659i	$-0.882552\pi$
$257$	−2.46896	+	4.27636i	−0.154010	+	0.266752i	0.778688	+	0.627411i	$0.215885\pi$
$258$	−2.20310			−0.137159
$259$	27.2710	+	6.54344i	1.69454	+	0.406590i
$260$		0			0
$261$	−2.35256	+	4.07475i	−0.145620	+	0.252221i
$262$	5.12182	+	8.87125i	0.316427	+	0.548068i
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	0.970406	−	0.241480i	$-0.0776327\pi$
$263$	4.47719	+	7.75473i	0.276076	+	0.478177i	−0.694330	+	0.719656i	$0.744299\pi$
$264$	0.827695	−	1.43361i	0.0509411	−	0.0882326i
$265$	32.3034			1.98438
$266$	1.60883	−	1.69579i	0.0986434	−	0.103976i
$267$	−8.99780			−0.550657
$268$	5.38891	−	9.33387i	0.329180	−	0.570157i
$269$	2.41172	+	4.17723i	0.147045	+	0.254690i	0.930134	−	0.367220i	$-0.119690\pi$
$269$	2.41172	+	4.17723i	0.147045	+	0.254690i	−0.783089	+	0.621910i	$0.786357\pi$
$270$	−5.38702	−	9.33060i	−0.327844	−	0.567842i
$271$	−3.71072	+	6.42715i	−0.225410	+	0.390422i	−0.956442	−	0.291921i	$-0.905706\pi$
$271$	−3.71072	+	6.42715i	−0.225410	+	0.390422i	0.731032	+	0.682343i	$0.239039\pi$
$272$	0.345312			0.0209376
$273$		0			0
$274$	−7.41938			−0.448221
$275$	−3.07281	+	5.32226i	−0.185297	+	0.320944i
$276$	2.38279	+	4.12712i	0.143427	+	0.248423i
$277$	−1.90816	−	3.30503i	−0.114650	−	0.198580i	0.802990	−	0.595993i	$-0.203241\pi$
$277$	−1.90816	−	3.30503i	−0.114650	−	0.198580i	−0.917640	+	0.397413i	$0.869908\pi$
$278$	−1.79268	+	3.10502i	−0.107518	+	0.186226i
$279$	−23.4081			−1.40140
$280$	24.6843	+	5.92280i	1.47517	+	0.353955i
$281$	−8.54978			−0.510037			−0.255019	−	0.966936i	$-0.582082\pi$
$281$	−8.54978			−0.510037			−0.255019	+	0.966936i	$0.582082\pi$
$282$	2.02357	−	3.50493i	0.120502	−	0.208715i
$283$	−7.63217	−	13.2193i	−0.453686	−	0.785807i	0.544926	−	0.838484i	$-0.316558\pi$
$283$	−7.63217	−	13.2193i	−0.453686	−	0.785807i	−0.998612	+	0.0526775i	$0.983224\pi$
$284$	2.19935	+	3.80938i	0.130507	+	0.226045i
$285$	−1.18107	+	2.04568i	−0.0699607	+	0.121176i
$286$		0			0
$287$	−4.00797	−	13.5242i	−0.236583	−	0.798310i
$288$	−14.6786			−0.864947
$289$	6.62439	−	11.4738i	0.389670	−	0.674928i
$290$	−2.68885	−	4.65723i	−0.157895	−	0.273482i
$291$	0.167369	+	0.289892i	0.00981135	+	0.0169938i
$292$	−6.95227	+	12.0417i	−0.406851	+	0.704687i
$293$	5.93964			0.346997			0.173499	−	0.984834i	$-0.444493\pi$
$293$	5.93964			0.346997			0.173499	+	0.984834i	$0.444493\pi$
$294$	−3.30337	+	2.14646i	−0.192657	+	0.125184i
$295$	−1.75693			−0.102293
$296$	14.7761	−	25.5929i	0.858842	−	1.48756i
$297$	1.65151	+	2.86049i	0.0958301	+	0.165983i
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$		0			0
$300$	−5.77236			−0.333267
$301$	2.94289	+	9.93028i	0.169625	+	0.572372i
$302$	14.3472			0.825591
$303$	1.97922	−	3.42811i	0.113703	−	0.196940i
$304$	0.0925356	+	0.160276i	0.00530728	+	0.00919248i
$305$	2.47131	+	4.28043i	0.141507	+	0.245097i
$306$	2.11233	−	3.65867i	0.120754	−	0.209152i
$307$	−22.2133			−1.26778			−0.633891	−	0.773422i	$-0.718543\pi$
$307$	−22.2133			−1.26778			−0.633891	+	0.773422i	$0.718543\pi$
$308$	−2.94695	−	0.707096i	−0.167918	−	0.0402906i
$309$	−2.73285			−0.155466
$310$	13.3771	−	23.1698i	0.759769	−	1.31596i
$311$	−4.92130	−	8.52394i	−0.279061	−	0.483348i	0.692091	−	0.721811i	$-0.256690\pi$
$311$	−4.92130	−	8.52394i	−0.279061	−	0.483348i	−0.971152	+	0.238463i	$0.923357\pi$
$312$		0			0
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	−0.403072	−	0.915168i	$-0.632058\pi$
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	0.994095	−	0.108513i	$-0.0346090\pi$
$314$	−1.65033			−0.0931337
$315$	−16.0605	+	16.9286i	−0.904906	+	0.953820i
$316$	15.4241			0.867673
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	0.251847	+	0.967767i	$0.418962\pi$
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	−0.964034	+	0.265778i	$0.914371\pi$
$318$	2.64128	+	4.57483i	0.148116	+	0.256544i
$319$	0.824324	+	1.42777i	0.0461533	+	0.0799398i
$320$	7.77489	−	13.4665i	0.434629	−	0.752800i
$321$	−9.33870			−0.521236
$322$	−8.75697	+	9.23032i	−0.488007	+	0.514385i
$323$	−2.01048			−0.111866
$324$	3.35237	−	5.80648i	0.186243	−	0.322582i
$325$		0			0
$326$	−5.06247	−	8.76845i	−0.280384	−	0.485640i
$327$	−1.38935	+	2.40643i	−0.0768314	+	0.133076i
$328$	−14.8637			−0.820709
$329$	−18.5012	−	4.43922i	−1.02001	−	0.244742i
$330$	−1.73923			−0.0957413
$331$	0.891417	−	1.54398i	0.0489967	−	0.0848648i	−0.840487	−	0.541832i	$-0.817731\pi$
$331$	0.891417	−	1.54398i	0.0489967	−	0.0848648i	0.889484	+	0.456967i	$0.151064\pi$
$332$	−0.967335	−	1.67547i	−0.0530894	−	0.0919536i
$333$	13.5828	+	23.5261i	0.744332	+	1.28922i
$334$	7.05414	−	12.2181i	0.385985	−	0.668546i
$335$	−29.0781			−1.58871
$336$	−0.0886247	−	0.299049i	−0.00483487	−	0.0163145i
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$		0			0
$339$	−4.55234	−	7.88488i	−0.247249	−	0.428248i
$340$	−4.25120	−	7.36329i	−0.230554	−	0.399331i
$341$	−4.10103	+	7.10320i	−0.222083	+	0.384660i
$342$	2.26422			0.122435
$343$	14.0876	+	12.0225i	0.760659	+	0.649152i
$344$	10.9138			0.588431
$345$	6.42867	−	11.1348i	0.346108	−	0.599477i
$346$	4.24991	+	7.36106i	0.228477	+	0.395733i
$347$	−0.316694	−	0.548531i	−0.0170010	−	0.0294467i	0.857400	−	0.514651i	$-0.172079\pi$
$347$	−0.316694	−	0.548531i	−0.0170010	−	0.0294467i	−0.874401	+	0.485204i	$0.838745\pi$
$348$	−0.774258	+	1.34105i	−0.0415046	+	0.0718881i
$349$	−30.5989			−1.63792			−0.818960	−	0.573850i	$-0.805449\pi$
$349$	−30.5989			−1.63792			−0.818960	+	0.573850i	$0.805449\pi$
$350$	−4.37895	−	14.7761i	−0.234065	−	0.789813i
$351$		0			0
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	−0.550173	−	0.952928i	−0.0292828	−	0.0507192i	0.851013	−	0.525145i	$-0.175989\pi$
$353$	−0.550173	−	0.952928i	−0.0292828	−	0.0507192i	−0.880295	+	0.474426i	$0.842656\pi$
$354$	−0.143655	−	0.248819i	−0.00763520	−	0.0132246i
$355$	5.93375	−	10.2776i	0.314931	−	0.545476i
$356$	17.3579			0.919969
$357$	3.29480	+	0.790559i	0.174379	+	0.0418408i
$358$	7.81042			0.412793
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	−0.965685	−	0.259716i	$-0.916371\pi$
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	0.707763	+	0.706450i	$0.249705\pi$
$360$	12.2945	+	21.2946i	0.647975	+	1.12233i
$361$	8.96124	+	15.5213i	0.471644	+	0.816912i
$362$	−2.55546	+	4.42618i	−0.134312	+	0.232635i
$363$	−6.74026			−0.353772
$364$		0			0
$365$	37.5139			1.96357
$366$	−0.404132	+	0.699977i	−0.0211243	+	0.0365884i
$367$	5.57363	+	9.65381i	0.290941	+	0.503925i	0.974033	−	0.226408i	$-0.0726983\pi$
$367$	5.57363	+	9.65381i	0.290941	+	0.503925i	−0.683092	+	0.730333i	$0.739365\pi$
$368$	−0.503679	−	0.872397i	−0.0262561	−	0.0454769i
$369$	6.83165	−	11.8328i	0.355641	−	0.615989i
$370$	−31.0488			−1.61415
$371$	17.0925	−	18.0164i	0.887397	−	0.935364i
$372$	−7.70391			−0.399429
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	−0.126902	−	0.991915i	$-0.540504\pi$
$373$	15.3651	−	26.6131i	0.795573	−	1.37797i	0.922475	−	0.386057i	$-0.126163\pi$
$374$	−0.740150	−	1.28198i	−0.0382723	−	0.0662895i
$375$	2.09783	+	3.63355i	0.108332	+	0.187636i
$376$	−10.0244	+	17.3628i	−0.516970	+	0.895419i
$377$		0			0
$378$	−8.05430	−	1.93256i	−0.414269	−	0.0994002i
$379$	−22.6572			−1.16382			−0.581912	−	0.813252i	$-0.697695\pi$
$379$	−22.6572			−1.16382			−0.581912	+	0.813252i	$0.697695\pi$
$380$	2.27844	−	3.94638i	0.116882	−	0.202445i
$381$	−0.643028	−	1.11376i	−0.0329433	−	0.0570595i
$382$	−0.560093	−	0.970109i	−0.0286568	−	0.0496351i
$383$	−0.294631	+	0.510317i	−0.0150550	+	0.0260760i	−0.873455	−	0.486905i	$-0.838126\pi$
$383$	−0.294631	+	0.510317i	−0.0150550	+	0.0260760i	0.858400	+	0.512981i	$0.171459\pi$
$384$	−5.03161			−0.256769
$385$	2.32325	+	7.83942i	0.118404	+	0.399534i
$386$	13.9801			0.711567
$387$	−5.01619	+	8.68830i	−0.254988	+	0.441651i
$388$	−0.322877	−	0.559239i	−0.0163916	−	0.0283910i
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	0.784695	−	0.619883i	$-0.212820\pi$
$389$	−2.84973	−	4.93587i	−0.144487	−	0.250259i	−0.929181	+	0.369624i	$0.879486\pi$
$390$		0			0
$391$	10.9432			0.553422
$392$	16.3643	−	10.6332i	0.826524	−	0.537056i
$393$	−7.95809			−0.401433
$394$	−10.8891	+	18.8605i	−0.548584	+	0.950176i
$395$	−20.8068	−	36.0384i	−1.04690	−	1.81329i
$396$	−1.46778	−	2.54227i	−0.0737588	−	0.127754i
$397$	−12.7641	+	22.1082i	−0.640614	+	1.10958i	0.344682	+	0.938720i	$0.387987\pi$
$397$	−12.7641	+	22.1082i	−0.640614	+	1.10958i	−0.985296	+	0.170857i	$0.945346\pi$
$398$	−21.6005			−1.08274
$399$	0.515992	+	1.74113i	0.0258319	+	0.0871655i
$400$	1.22017			0.0610086
$401$	12.7506	−	22.0846i	0.636733	−	1.10285i	−0.349413	−	0.936969i	$-0.613619\pi$
$401$	12.7506	−	22.0846i	0.636733	−	1.10285i	0.986145	−	0.165884i	$-0.0530478\pi$
$402$	−2.37757	−	4.11807i	−0.118582	−	0.205391i
$403$		0			0
$404$	−3.81817	+	6.61327i	−0.189961	+	0.329022i
$405$	−18.0891			−0.898857
$406$	−4.02018	−	0.964608i	−0.199518	−	0.0478727i
$407$	9.51867			0.471823
$408$	1.78520	−	3.09206i	0.0883807	−	0.153080i
$409$	0.0734938	+	0.127295i	0.00363403	+	0.00629433i	0.867837	−	0.496850i	$-0.165510\pi$
$409$	0.0734938	+	0.127295i	0.00363403	+	0.00629433i	−0.864203	+	0.503144i	$0.832177\pi$
$410$	7.80822	+	13.5242i	0.385621	+	0.667914i
$411$	2.88199	−	4.99175i	0.142158	−	0.246225i
$412$	5.27202			0.259734
$413$	−0.929635	+	0.979885i	−0.0457443	+	0.0482170i
$414$	−12.3243			−0.605709
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$		0			0
$417$	−1.39270	−	2.41223i	−0.0682008	−	0.118127i
$418$	0.396686	−	0.687080i	0.0194026	−	0.0336062i
$419$	13.6959			0.669088			0.334544	−	0.942380i	$-0.391418\pi$
$419$	13.6959			0.669088			0.334544	+	0.942380i	$0.391418\pi$
$420$	−5.28572	+	5.57144i	−0.257917	+	0.271858i
$421$	−3.44169			−0.167738			−0.0838688	−	0.996477i	$-0.526728\pi$
$421$	−3.44169			−0.167738			−0.0838688	+	0.996477i	$0.526728\pi$
$422$	2.42421	−	4.19885i	0.118009	−	0.204397i
$423$	−9.21486	−	15.9606i	−0.448042	−	0.776032i
$424$	−13.0844	−	22.6629i	−0.635437	−	1.10061i
$425$	−6.62754	+	11.4792i	−0.321483	+	0.556825i
$426$	1.94069			0.0940267
$427$	3.69493	+	0.886566i	0.178810	+	0.0429039i
$428$	18.0156			0.870816
$429$		0			0
$430$	−5.73325	−	9.93028i	−0.276482	−	0.478881i
$431$	11.1455	+	19.3046i	0.536861	+	0.929870i	0.999071	+	0.0430997i	$0.0137233\pi$
$431$	11.1455	+	19.3046i	0.536861	+	0.929870i	−0.462210	+	0.886771i	$0.652943\pi$
$432$	0.327896	−	0.567932i	0.0157759	−	0.0273246i
$433$	−25.8963			−1.24449			−0.622247	−	0.782821i	$-0.713780\pi$
$433$	−25.8963			−1.24449			−0.622247	+	0.782821i	$0.713780\pi$
$434$	−5.84424	−	19.7204i	−0.280533	−	0.946611i
$435$	4.17783			0.200312
$436$	2.68024	−	4.64232i	0.128360	−	0.222327i
$437$	2.93253	+	5.07929i	0.140282	+	0.242975i
$438$	3.06732	+	5.31275i	0.146562	+	0.253853i
$439$	13.9919	−	24.2347i	0.667798	−	1.15666i	−0.310721	−	0.950501i	$-0.600570\pi$
$439$	13.9919	−	24.2347i	0.667798	−	1.15666i	0.978519	−	0.206159i	$-0.0660963\pi$
$440$	8.61583			0.410744
$441$	0.943533	+	17.9147i	0.0449301	+	0.853079i
$442$		0			0
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	0.137741	+	0.990468i	$0.456016\pi$
$443$	−16.6044	+	28.7597i	−0.788900	+	1.36642i	−0.926641	+	0.375947i	$0.877317\pi$
$444$	4.47028	+	7.74275i	0.212150	+	0.367454i
$445$	−23.4155	−	40.5568i	−1.11000	−	1.92258i
$446$	1.00353	−	1.73816i	0.0475185	−	0.0823044i
$447$	−3.87796			−0.183421
$448$	−3.39672	−	11.4617i	−0.160480	−	0.541513i
$449$	−19.6864			−0.929059			−0.464529	−	0.885558i	$-0.653777\pi$
$449$	−19.6864			−0.929059			−0.464529	+	0.885558i	$0.653777\pi$
$450$	7.46399	−	12.9280i	0.351856	−	0.609433i
$451$	−2.39377	−	4.14614i	−0.112718	−	0.195234i
$452$	8.78205	+	15.2110i	0.413073	+	0.715464i
$453$	−5.57305	+	9.65281i	−0.261845	+	0.453528i
$454$	−22.3783			−1.05027
$455$		0			0
$456$	1.91357			0.0896111
$457$	−0.373471	+	0.646871i	−0.0174702	+	0.0302593i	−0.874628	−	0.484794i	$-0.838895\pi$
$457$	−0.373471	+	0.646871i	−0.0174702	+	0.0302593i	0.857158	+	0.515053i	$0.172228\pi$
$458$	0.0291746	+	0.0505320i	0.00136324	+	0.00236120i
$459$	3.56203	+	6.16961i	0.166261	+	0.287973i
$460$	−12.4017	+	21.4805i	−0.578235	+	1.00153i
$461$	33.1710			1.54493			0.772464	−	0.635058i	$-0.219024\pi$
$461$	33.1710			1.54493			0.772464	+	0.635058i	$0.219024\pi$
$462$	−0.920266	+	0.970010i	−0.0428146	+	0.0451289i
$463$	30.7521			1.42917			0.714586	−	0.699548i	$-0.246615\pi$
$463$	30.7521			1.42917			0.714586	+	0.699548i	$0.246615\pi$
$464$	0.163664	−	0.283475i	0.00759792	−	0.0131600i
$465$	10.3924	+	18.0002i	0.481937	+	0.834740i
$466$	−6.24313	−	10.8134i	−0.289207	−	0.500922i
$467$	14.8033	−	25.6400i	0.685013	−	1.18648i	−0.288420	−	0.957504i	$-0.593130\pi$
$467$	14.8033	−	25.6400i	0.685013	−	1.18648i	0.973433	−	0.228973i	$-0.0735367\pi$
$468$		0			0
$469$	−15.3859	+	16.2176i	−0.710456	+	0.748859i
$470$	21.0642			0.971621
$471$	0.641056	−	1.11034i	0.0295383	−	0.0511618i
$472$	0.711644	+	1.23260i	0.0327561	+	0.0567352i
$473$	1.75765	+	3.04434i	0.0808168	+	0.139979i
$474$	3.40253	−	5.89335i	0.156283	−	0.270691i
$475$	−7.10411			−0.325959
$476$	−6.35609	−	1.52509i	−0.291331	−	0.0699024i
$477$	24.0555			1.10143
$478$	1.42748	−	2.47247i	0.0652915	−	0.113088i
$479$	7.04527	+	12.2028i	0.321907	+	0.557559i	0.980881	−	0.194606i	$-0.0623429\pi$
$479$	7.04527	+	12.2028i	0.321907	+	0.557559i	−0.658975	+	0.752165i	$0.729010\pi$
$480$	6.51684	+	11.2875i	0.297452	+	0.515201i
$481$		0			0
$482$	7.30247			0.332618
$483$	−2.80858	−	9.47710i	−0.127795	−	0.431223i
$484$	13.0028			0.591038
$485$	−0.871108	+	1.50880i	−0.0395550	+	0.0685112i
$486$	−6.17502	−	10.6955i	−0.280105	−	0.485156i
$487$	−8.39773	−	14.5453i	−0.380537	−	0.659110i	0.610602	−	0.791938i	$-0.290928\pi$
$487$	−8.39773	−	14.5453i	−0.380537	−	0.659110i	−0.991139	+	0.132828i	$0.957594\pi$
$488$	2.00200	−	3.46757i	0.0906263	−	0.156969i
$489$	7.86587			0.355707
$490$	−18.2715	−	9.30384i	−0.825424	−	0.420304i
$491$	21.6690			0.977908			0.488954	−	0.872310i	$-0.337379\pi$
$491$	21.6690			0.977908			0.488954	+	0.872310i	$0.337379\pi$
$492$	2.24839	−	3.89432i	0.101365	−	0.175570i
$493$	1.77793	+	3.07947i	0.0800740	+	0.138692i
$494$		0			0
$495$	−3.96001	+	6.85895i	−0.177989	+	0.308287i
$496$	1.62847			0.0731203
$497$	−2.59236	−	8.74749i	−0.116283	−	0.392379i
$498$	−0.853570			−0.0382494
$499$	−11.6524	+	20.1825i	−0.521633	+	0.903495i	0.478051	+	0.878332i	$0.341344\pi$
$499$	−11.6524	+	20.1825i	−0.521633	+	0.903495i	−0.999683	+	0.0251622i	$0.991990\pi$
$500$	−4.04699	−	7.00960i	−0.180987	−	0.313479i
$501$	5.48023	+	9.49203i	0.244838	+	0.424073i
$502$	−9.15601	+	15.8587i	−0.408653	+	0.707807i
$503$	−43.8829			−1.95664			−0.978322	−	0.207090i	$-0.933601\pi$
$503$	−43.8829			−1.95664			−0.978322	+	0.207090i	$0.933601\pi$
$504$	18.3818	+	4.41056i	0.818791	+	0.196462i
$505$	20.6026			0.916802
$506$	−2.15919	+	3.73983i	−0.0959879	+	0.166256i
$507$		0			0
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	9.96210	−	17.2549i	0.441563	−	0.764809i	−0.556243	−	0.831020i	$-0.687758\pi$
$509$	9.96210	−	17.2549i	0.441563	−	0.764809i	0.997806	+	0.0662109i	$0.0210910\pi$
$510$	−3.75123			−0.166107
$511$	19.8495	−	20.9224i	0.878089	−	0.925553i
$512$	2.01529			0.0890641
$513$	−1.90908	+	3.30662i	−0.0842879	+	0.145991i
$514$	−2.10139	−	3.63972i	−0.0926886	−	0.160541i
$515$	−7.11185	−	12.3181i	−0.313386	−	0.542800i
$516$	−1.65090	+	2.85944i	−0.0726767	+	0.125880i
$517$	−6.45768			−0.284009
$518$	−16.4287	+	17.3167i	−0.721834	+	0.760852i
$519$	−6.60335			−0.289855
$520$		0			0
$521$	8.26204	+	14.3103i	0.361967	+	0.626944i	0.988284	−	0.152623i	$-0.0487721\pi$
$521$	8.26204	+	14.3103i	0.361967	+	0.626944i	−0.626318	+	0.779568i	$0.715439\pi$
$522$	−2.00232	−	3.46812i	−0.0876392	−	0.151796i
$523$	5.99809	−	10.3890i	0.262278	−	0.454279i	−0.704569	−	0.709636i	$-0.748860\pi$
$523$	5.99809	−	10.3890i	0.262278	−	0.454279i	0.966847	+	0.255357i	$0.0821929\pi$
$524$	15.3522			0.670664
$525$	11.6423	+	2.79346i	0.508111	+	0.121917i
$526$	−7.62131			−0.332305
$527$	−8.84526	+	15.3204i	−0.385305	+	0.667369i
$528$	−0.0529314	−	0.0916798i	−0.00230354	−	0.00398985i
$529$	−4.46197	−	7.72837i	−0.193999	−	0.336016i
$530$	−13.7471	+	23.8107i	−0.597137	+	1.03427i
$531$	−1.30835			−0.0567774
$532$	−0.995416	−	3.35886i	−0.0431567	−	0.145625i
$533$		0			0
$534$	3.82913	−	6.63225i	0.165703	−	0.287005i
$535$	−24.3026	−	42.0934i	−1.05070	−	1.81986i
$536$	11.7781	+	20.4002i	0.508735	+	0.881155i
$537$	−3.03388	+	5.25484i	−0.130922	+	0.226763i
$538$	−4.10536			−0.176995
$539$	5.60152	+	2.85229i	0.241275	+	0.122857i
$540$	−16.1471			−0.694861
$541$	18.1158	−	31.3775i	0.778860	−	1.34903i	−0.153739	−	0.988112i	$-0.549131\pi$
$541$	18.1158	−	31.3775i	0.778860	−	1.34903i	0.932599	−	0.360914i	$-0.117535\pi$
$542$	−3.15829	−	5.47031i	−0.135660	−	0.234970i
$543$	−1.98529	−	3.43862i	−0.0851968	−	0.147565i
$544$	−5.54665	+	9.60707i	−0.237811	+	0.411900i
$545$	−14.4624			−0.619500
$546$		0			0
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	−5.55973	+	9.62974i	−0.237500	+	0.411362i
$549$	1.84032	+	3.18753i	0.0785430	+	0.136040i
$550$	−2.61535	−	4.52991i	−0.111519	−	0.193156i
$551$	−0.952888	+	1.65045i	−0.0405944	+	0.0703115i
$552$	−10.4157			−0.443322
$553$	−31.1089	−	7.46431i	−1.32288	−	0.317415i
$554$	3.24816			0.138001
$555$	12.0606	−	20.8896i	0.511945	−	0.886715i
$556$	2.68670	+	4.65350i	0.113941	+	0.197352i
$557$	5.41399	+	9.37731i	0.229398	+	0.397329i	0.957630	−	0.288002i	$-0.0929909\pi$
$557$	5.41399	+	9.37731i	0.229398	+	0.397329i	−0.728232	+	0.685331i	$0.759658\pi$
$558$	9.96160	−	17.2540i	0.421708	−	0.730420i
$559$		0			0
$560$	1.11731	−	1.17770i	0.0472148	−	0.0497670i
$561$	1.15002			0.0485538
$562$	3.63847	−	6.30201i	0.153480	−	0.265834i
$563$	6.92997	+	12.0031i	0.292064	+	0.505869i	0.974298	−	0.225265i	$-0.0723248\pi$
$563$	6.92997	+	12.0031i	0.292064	+	0.505869i	−0.682234	+	0.731134i	$0.738991\pi$
$564$	−3.03274	−	5.25285i	−0.127701	−	0.221185i
$565$	23.6936	−	41.0386i	0.996798	−	1.72651i
$566$	12.9919			0.546089
$567$	−9.57138	+	10.0888i	−0.401960	+	0.423688i
$568$	−9.61384			−0.403388
$569$	−13.7060	+	23.7395i	−0.574586	+	0.995212i	0.421500	+	0.906828i	$0.361504\pi$
$569$	−13.7060	+	23.7395i	−0.574586	+	0.995212i	−0.996086	+	0.0883842i	$0.971830\pi$
$570$	−1.00524	−	1.74113i	−0.0421049	−	0.0729279i
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$		0			0
$573$	0.870251			0.0363552
$574$	11.6743	+	2.80115i	0.487276	+	0.116918i
$575$	38.6682			1.61258
$576$	5.78976	−	10.0282i	0.241240	−	0.417840i
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	0.829325	−	0.558766i	$-0.188725\pi$
$577$	−1.66328	−	2.88089i	−0.0692434	−	0.119933i	−0.898568	+	0.438833i	$0.855392\pi$
$578$	5.63818	+	9.76562i	0.234518	+	0.406196i
$579$	−5.43043	+	9.40577i	−0.225681	+	0.390891i
$580$	−8.05959			−0.334656
$581$	1.14019	+	3.84739i	0.0473032	+	0.159617i
$582$	−0.284904			−0.0118097
$583$	4.21447	−	7.29967i	0.174545	−	0.302321i
$584$	−15.1950	−	26.3185i	−0.628772	−	1.08907i
$585$		0			0
$586$	−2.52769	+	4.37809i	−0.104418	+	0.180857i
$587$	15.0810			0.622461			0.311230	−	0.950335i	$-0.399259\pi$
$587$	15.0810			0.622461			0.311230	+	0.950335i	$0.399259\pi$
$588$	0.310529	+	5.89596i	0.0128060	+	0.243145i
$589$	−9.48129			−0.390670
$590$	0.747686	−	1.29503i	0.0307817	−	0.0533155i
$591$	−8.45953	−	14.6523i	−0.347978	−	0.602716i
$592$	−0.944935	−	1.63668i	−0.0388366	−	0.0672670i
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	−0.468609	−	0.883405i	$-0.655245\pi$
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	0.999356	−	0.0358751i	$-0.0114218\pi$
$594$	−2.81128			−0.115348
$595$	5.01087	+	16.9083i	0.205426	+	0.693175i
$596$	7.48110			0.306438
$597$	8.39052	−	14.5328i	0.343401	−	0.594788i
$598$		0			0
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	0.958477	+	0.285170i	$0.0920501\pi$
$599$	17.7734	+	30.7845i	0.726203	+	1.25782i	−0.232274	+	0.972650i	$0.574617\pi$
$600$	6.30807	−	10.9259i	0.257526	−	0.446048i
$601$	−27.2947			−1.11338			−0.556688	−	0.830722i	$-0.687928\pi$
$601$	−27.2947			−1.11338			−0.556688	+	0.830722i	$0.687928\pi$
$602$	−8.57196	−	2.05677i	−0.349367	−	0.0838276i
$603$	−21.6538			−0.881810
$604$	10.7511	−	18.6215i	0.437458	−	0.757699i
$605$	−17.5406	−	30.3811i	−0.713125	−	1.23517i
$606$	1.68456	+	2.91775i	0.0684308	+	0.118526i
$607$	19.4629	−	33.7108i	0.789976	−	1.36828i	−0.136006	−	0.990708i	$-0.543426\pi$
$607$	19.4629	−	33.7108i	0.789976	−	1.36828i	0.925981	−	0.377570i	$-0.123240\pi$
$608$	−5.94549			−0.241121
$609$	2.21059	−	2.33008i	0.0895776	−	0.0944196i
$610$	−4.20679			−0.170328
$611$		0			0
$612$	−3.16576	−	5.48326i	−0.127968	−	0.221648i
$613$	0.443322	+	0.767857i	0.0179056	+	0.0310135i	0.874839	−	0.484413i	$-0.160967\pi$
$613$	0.443322	+	0.767857i	0.0179056	+	0.0310135i	−0.856934	+	0.515427i	$0.827633\pi$
$614$	9.45317	−	16.3734i	0.381499	−	0.660775i
$615$	−12.1321			−0.489214
$616$	4.55884	−	4.80526i	0.183681	−	0.193609i
$617$	−34.7888			−1.40054			−0.700272	−	0.713876i	$-0.746938\pi$
$617$	−34.7888			−1.40054			−0.700272	+	0.713876i	$0.746938\pi$
$618$	1.16300	−	2.01437i	0.0467827	−	0.0810300i
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	0.885942	−	0.463797i	$-0.153513\pi$
$619$	1.02781	+	1.78021i	0.0413111	+	0.0715529i	−0.844631	+	0.535350i	$0.820180\pi$
$620$	−20.0483	−	34.7247i	−0.805161	−	1.39458i
$621$	10.3913	−	17.9982i	0.416987	−	0.722243i
$622$	8.37728			0.335898
$623$	−35.0092	−	8.40016i	−1.40262	−	0.336545i
$624$		0			0
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	8.89959	+	15.4145i	0.355699	+	0.616089i
$627$	0.308178	+	0.533780i	0.0123074	+	0.0213171i
$628$	−1.23668	+	2.14199i	−0.0493489	+	0.0854749i
$629$	20.5302			0.818593
$630$	−5.64328	−	19.0423i	−0.224834	−	0.758664i
$631$	45.2337			1.80073			0.900363	−	0.435139i	$-0.143301\pi$
$631$	45.2337			1.80073			0.900363	+	0.435139i	$0.143301\pi$
$632$	−16.8555	+	29.1946i	−0.670477	+	1.16130i
$633$	1.88332	+	3.26201i	0.0748554	+	0.129653i
$634$	−10.7924	−	18.6930i	−0.428621	−	0.742393i
$635$	3.34678	−	5.79679i	0.132813	−	0.230038i
$636$	7.91700			0.313929
$637$		0			0
$638$	−1.40321			−0.0555534
$639$	4.41872	−	7.65345i	0.174802	−	0.302766i
$640$	−13.0941	−	22.6796i	−0.517588	−	0.896489i
$641$	9.53097	+	16.5081i	0.376451	+	0.652032i	0.990543	−	0.137202i	$-0.0438111\pi$
$641$	9.53097	+	16.5081i	0.376451	+	0.652032i	−0.614092	+	0.789234i	$0.710478\pi$
$642$	3.97420	−	6.88352i	0.156849	−	0.271671i
$643$	10.5351			0.415464			0.207732	−	0.978186i	$-0.433392\pi$
$643$	10.5351			0.415464			0.207732	+	0.978186i	$0.433392\pi$
$644$	5.41813	+	18.2826i	0.213504	+	0.720434i
$645$	8.90811			0.350756
$646$	0.855587	−	1.48192i	0.0336626	−	0.0583053i
$647$	12.0804	+	20.9239i	0.474930	+	0.822603i	0.999588	−	0.0287105i	$-0.00914011\pi$
$647$	12.0804	+	20.9239i	0.474930	+	0.822603i	−0.524658	+	0.851313i	$0.675807\pi$
$648$	7.32699	+	12.6907i	0.287831	+	0.498538i
$649$	−0.229219	+	0.397019i	−0.00899762	+	0.0155843i
$650$		0			0
$651$	15.5380	+	3.72822i	0.608983	+	0.146120i
$652$	−15.1743			−0.594271
$653$	16.8445	−	29.1755i	0.659176	−	1.14173i	−0.321653	−	0.946858i	$-0.604238\pi$
$653$	16.8445	−	29.1755i	0.659176	−	1.14173i	0.980829	−	0.194869i	$-0.0624282\pi$
$654$	−1.18251	−	2.04817i	−0.0462400	−	0.0800900i
$655$	−20.7098	−	35.8704i	−0.809199	−	1.40157i
$656$	−0.475268	+	0.823189i	−0.0185561	+	0.0321401i
$657$	27.9357			1.08987
$658$	11.1456	−	11.7480i	0.434500	−	0.457986i
$659$	−4.20059			−0.163632			−0.0818159	−	0.996647i	$-0.526072\pi$
$659$	−4.20059			−0.163632			−0.0818159	+	0.996647i	$0.526072\pi$
$660$	−1.30329	+	2.25737i	−0.0507307	+	0.0878681i
$661$	8.83631	+	15.3049i	0.343693	+	0.595293i	0.985115	−	0.171894i	$-0.0549888\pi$
$661$	8.83631	+	15.3049i	0.343693	+	0.595293i	−0.641423	+	0.767188i	$0.721655\pi$
$662$	0.758708	+	1.31412i	0.0294880	+	0.0510748i
$663$		0			0
$664$	4.22844			0.164095
$665$	−6.50520	+	6.85683i	−0.252261	+	0.265897i
$666$	−23.1213			−0.895932
$667$	5.18664	−	8.98353i	0.200828	−	0.347844i
$668$	−10.5721	−	18.3114i	−0.409046	−	0.708488i
$669$	0.779623	+	1.35035i	0.0301420	+	0.0522074i
$670$	12.3746	−	21.4334i	0.478071	−	0.828044i
$671$	1.28968			0.0497875
$672$	9.74352	+	2.33787i	0.375865	+	0.0901855i
$673$	−20.6103			−0.794469			−0.397235	−	0.917717i	$-0.630030\pi$
$673$	−20.6103			−0.794469			−0.397235	+	0.917717i	$0.630030\pi$
$674$	−4.06901	+	7.04774i	−0.156733	+	0.271469i
$675$	12.5865	+	21.8005i	0.484456	+	0.839102i
$676$		0			0
$677$	10.6537	−	18.4527i	0.409455	−	0.709196i	−0.585374	−	0.810763i	$-0.699052\pi$
$677$	10.6537	−	18.4527i	0.409455	−	0.709196i	0.994829	+	0.101567i	$0.0323857\pi$
$678$	7.74922			0.297607
$679$	0.380573	+	1.28418i	0.0146051	+	0.0492824i
$680$	18.5829			0.712623
$681$	8.69264	−	15.0561i	0.333103	−	0.576951i
$682$	−3.49049	−	6.04571i	−0.133658	−	0.231502i
$683$	−3.34878	−	5.80026i	−0.128138	−	0.221941i	0.794817	−	0.606849i	$-0.207567\pi$
$683$	−3.34878	−	5.80026i	−0.128138	−	0.221941i	−0.922955	+	0.384908i	$0.874233\pi$
$684$	1.69670	−	2.93877i	0.0648750	−	0.112367i
$685$	29.9999			1.14624
$686$	−14.8569	+	5.26761i	−0.567238	+	0.201118i
$687$	−0.0453305			−0.00172946
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$		0			0
$690$	5.47161	+	9.47710i	0.208301	+	0.360787i
$691$	−12.4632	+	21.5868i	−0.474121	+	0.821202i	−0.999561	−	0.0296291i	$-0.990567\pi$
$691$	−12.4632	+	21.5868i	−0.474121	+	0.821202i	0.525440	+	0.850831i	$0.323901\pi$
$692$	12.7387			0.484253
$693$	1.73007	+	5.83782i	0.0657198	+	0.221761i
$694$	0.539093			0.0204637
$695$	7.24861	−	12.5550i	0.274955	−	0.476237i
$696$	−1.69223	−	2.93102i	−0.0641437	−	0.111100i
$697$	−5.16298	−	8.94254i	−0.195562	−	0.338723i
$698$	13.0217	−	22.5543i	0.492880	−	0.853694i
$699$	9.70033			0.366900
$700$	−22.4595	−	5.38896i	−0.848888	−	0.203683i
$701$	−4.94583			−0.186801			−0.0934007	−	0.995629i	$-0.529774\pi$
$701$	−4.94583			−0.186801			−0.0934007	+	0.995629i	$0.529774\pi$
$702$		0			0
$703$	5.50162	+	9.52908i	0.207497	+	0.359396i
$704$	−2.02870	−	3.51382i	−0.0764597	−	0.132432i
$705$	−8.18220	+	14.1720i	−0.308160	+	0.533748i
$706$	0.936533			0.0352469
$707$	10.9013	−	11.4905i	0.409985	−	0.432147i
$708$	−0.430594			−0.0161827
$709$	−2.32249	+	4.02267i	−0.0872228	+	0.151074i	−0.906336	−	0.422557i	$-0.861133\pi$
$709$	−2.32249	+	4.02267i	−0.0872228	+	0.151074i	0.819113	+	0.573632i	$0.194466\pi$
$710$	5.05037	+	8.74749i	0.189537	+	0.328288i
$711$	−15.4943	−	26.8369i	−0.581082	−	1.00646i
$712$	−18.9688	+	32.8550i	−0.710888	+	1.23129i
$713$	51.6074			1.93271
$714$	−1.98486	+	2.09215i	−0.0742816	+	0.0782968i
$715$		0			0
$716$	5.85275	−	10.1373i	0.218728	−	0.378847i
$717$	1.10898	+	1.92082i	0.0414157	+	0.0717342i
$718$	−4.15939	−	7.20427i	−0.155227	−	0.268861i
$719$	−15.8706	+	27.4887i	−0.591875	+	1.02516i	0.402105	+	0.915594i	$0.368279\pi$
$719$	−15.8706	+	27.4887i	−0.591875	+	1.02516i	−0.993980	+	0.109564i	$0.965055\pi$
$720$	1.57247			0.0586025
$721$	−10.6331	−	2.55133i	−0.395999	−	0.0950165i
$722$	−15.2543			−0.567705
$723$	−2.83658	+	4.91309i	−0.105493	+	0.182720i
$724$	3.82987	+	6.63354i	0.142336	+	0.246533i
$725$	6.28237	+	10.8814i	0.233322	+	0.404125i
$726$	2.86840	−	4.96822i	0.106456	−	0.184388i
$727$	47.8755			1.77560			0.887801	−	0.460227i	$-0.152232\pi$
$727$	47.8755			1.77560			0.887801	+	0.460227i	$0.152232\pi$
$728$		0			0
$729$	−6.17412			−0.228671
$730$	−15.9645	+	27.6514i	−0.590873	+	1.02342i
$731$	3.79096	+	6.56613i	0.140214	+	0.242857i
$732$	0.605675	+	1.04906i	0.0223864	+	0.0387743i
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	−0.927645	−	0.373463i	$-0.878170\pi$
$733$	−3.80104	+	6.58359i	−0.140395	+	0.243171i	0.787251	+	0.616633i	$0.211504\pi$
$734$	−9.48771			−0.350198
$735$	13.3570	−	8.67908i	0.492681	−	0.320133i
$736$	32.3618			1.19287
$737$	−3.79368	+	6.57086i	−0.139742	+	0.242041i
$738$	5.81459	+	10.0712i	0.214038	+	0.370725i
$739$	−16.7118	−	28.9457i	−0.614754	−	1.06479i	−0.990428	−	0.138033i	$-0.955922\pi$
$739$	−16.7118	−	28.9457i	−0.614754	−	1.06479i	0.375673	−	0.926752i	$-0.377411\pi$
$740$	−23.2665	+	40.2988i	−0.855294	+	1.48141i
$741$		0			0
$742$	6.00589	+	20.2659i	0.220483	+	0.743984i
$743$	2.93823			0.107793			0.0538966	−	0.998547i	$-0.482836\pi$
$743$	2.93823			0.107793			0.0538966	+	0.998547i	$0.482836\pi$
$744$	8.41888	−	14.5819i	0.308651	−	0.534599i
$745$	−10.0919	−	17.4796i	−0.369737	−	0.640403i
$746$	13.0776	+	22.6511i	0.478805	+	0.829314i
$747$	−1.94348	+	3.36620i	−0.0711081	+	0.123163i
$748$	−2.21853			−0.0811176
$749$	−36.3356	−	8.71842i	−1.32767	−	0.318564i
$750$	−3.57104			−0.130396
$751$	−0.598389	+	1.03644i	−0.0218355	+	0.0378202i	−0.876737	−	0.480971i	$-0.840284\pi$
$751$	−0.598389	+	1.03644i	−0.0218355	+	0.0378202i	0.854901	+	0.518791i	$0.173618\pi$
$752$	0.641065	+	1.11036i	0.0233773	+	0.0404906i
$753$	−7.11313	−	12.3203i	−0.259217	−	0.448977i
$754$		0			0
$755$	−58.0123			−2.11128
$756$	−8.54381	+	9.00564i	−0.310735	+	0.327532i
$757$	11.5464			0.419662			0.209831	−	0.977738i	$-0.432709\pi$
$757$	11.5464			0.419662			0.209831	+	0.977738i	$0.432709\pi$
$758$	9.64207	−	16.7006i	0.350216	−	0.606592i
$759$	−1.67744	−	2.90541i	−0.0608871	−	0.105460i
$760$	4.97979	+	8.62525i	0.180636	+	0.312871i
$761$	17.3249	−	30.0075i	0.628026	−	1.08777i	−0.359921	−	0.932983i	$-0.617197\pi$
$761$	17.3249	−	30.0075i	0.628026	−	1.08777i	0.987947	−	0.154790i	$-0.0494702\pi$
$762$	1.09459			0.0396530
$763$	−7.65238	+	8.06602i	−0.277035	+	0.292010i
$764$	−1.67883			−0.0607378
$765$	−8.54110	+	14.7936i	−0.308804	+	0.534864i
$766$	−0.250768	−	0.434344i	−0.00906063	−	0.0156935i
$767$		0			0
$768$	5.12890	−	8.88351i	0.185073	−	0.320556i
$769$	6.54874			0.236154			0.118077	−	0.993004i	$-0.462327\pi$
$769$	6.54874			0.236154			0.118077	+	0.993004i	$0.462327\pi$
$770$	−6.76710	−	1.62371i	−0.243869	−	0.0585143i
$771$	3.26507			0.117589
$772$	10.4760	−	18.1450i	0.377039	−	0.653051i
$773$	16.9637	+	29.3821i	0.610143	+	1.05680i	0.991216	+	0.132254i	$0.0422214\pi$
$773$	16.9637	+	29.3821i	0.610143	+	1.05680i	−0.381073	+	0.924545i	$0.624445\pi$
$774$	−4.26941	−	7.39484i	−0.153461	−	0.265802i
$775$	−31.2550	+	54.1352i	−1.12271	+	1.94459i
$776$	1.41137			0.0506651
$777$	−5.26909	−	17.7797i	−0.189028	−	0.637843i
$778$	4.85095			0.173915
$779$	2.76711	−	4.79278i	0.0991422	−	0.171719i
$780$		0			0
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	−4.65703	+	8.06620i	−0.166535	+	0.288447i
$783$	6.75302			0.241333
$784$	−0.0656403	−	1.24630i	−0.00234430	−	0.0445106i
$785$	6.67303			0.238171
$786$	3.38667	−	5.86588i	0.120798	−	0.209229i
$787$	6.48717	+	11.2361i	0.231243	+	0.400524i	0.958174	−	0.286186i	$-0.0923876\pi$
$787$	6.48717	+	11.2361i	0.231243	+	0.400524i	−0.726932	+	0.686710i	$0.759054\pi$
$788$	16.3195	+	28.2662i	0.581359	+	1.00694i
$789$	2.96042	−	5.12760i	0.105394	−	0.182548i
$790$	35.4184			1.26013
$791$	−10.3514	−	34.9290i	−0.368052	−	1.24193i
$792$	6.41600			0.227983
$793$		0			0
$794$	−10.8639	−	18.8168i	−0.385545	−	0.667784i
$795$	−10.6799	−	18.4981i	−0.378776	−	0.656059i
$796$	−16.1864	+	28.0357i	−0.573712	+	0.993699i
$797$	4.41913			0.156533			0.0782667	−	0.996932i	$-0.475061\pi$
$797$	4.41913			0.156533			0.0782667	+	0.996932i	$0.475061\pi$
$798$	−1.50297	−	0.360624i	−0.0532044	−	0.0127660i
$799$	−13.9282			−0.492743
$800$	−19.5993	+	33.9469i	−0.692938	+	1.20020i
$801$	−17.4369	−	30.2017i	−0.616104	−	1.06712i
$802$	10.8523	+	18.7968i	0.383209	+	0.663737i
$803$	4.89426	−	8.47711i	0.172715	−	0.299151i
$804$	−7.12655			−0.251334
$805$	35.4083	−	37.3223i	1.24798	−	1.31544i
$806$		0			0
$807$	1.59469	−	2.76208i	0.0561356	−	0.0972298i
$808$	−8.34504	−	14.4540i	−0.293578	−	0.508491i
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	0.747403	−	0.664371i	$-0.231300\pi$
$809$	−5.73580	−	9.93470i	−0.201660	−	0.349285i	−0.949063	+	0.315085i	$0.897967\pi$
$810$	7.69807	−	13.3334i	0.270482	−	0.468489i
$811$	−23.8664			−0.838063			−0.419032	−	0.907972i	$-0.637630\pi$
$811$	−23.8664			−0.838063			−0.419032	+	0.907972i	$0.637630\pi$
$812$	−4.26451	+	4.49503i	−0.149655	+	0.157745i
$813$	4.90723			0.172104
$814$	−4.05079	+	7.01618i	−0.141980	+	0.245917i
$815$	20.4698	+	35.4548i	0.717026	+	1.24193i
$816$	−0.114164	−	0.197738i	−0.00399655	−	0.00692223i
$817$	−2.03178	+	3.51914i	−0.0710829	+	0.123119i
$818$	−0.125105			−0.00437419
$819$		0			0
$820$	23.4044			0.817318
$821$	15.4847	−	26.8203i	0.540420	−	0.936035i	−0.458460	−	0.888715i	$-0.651599\pi$
$821$	15.4847	−	26.8203i	0.540420	−	0.936035i	0.998880	−	0.0473197i	$-0.0150679\pi$
$822$	2.45293	+	4.24861i	0.0855559	+	0.148187i
$823$	4.30678	+	7.45957i	0.150125	+	0.260024i	0.931273	−	0.364321i	$-0.118699\pi$
$823$	4.30678	+	7.45957i	0.150125	+	0.260024i	−0.781148	+	0.624346i	$0.785366\pi$
$824$	−5.76129	+	9.97885i	−0.200704	+	0.347630i
$825$	4.06362			0.141477
$826$	−0.326652	−	1.10223i	−0.0113657	−	0.0383516i
$827$	−22.9128			−0.796756			−0.398378	−	0.917221i	$-0.630427\pi$
$827$	−22.9128			−0.796756			−0.398378	+	0.917221i	$0.630427\pi$
$828$	−9.23528	+	15.9960i	−0.320948	+	0.555898i
$829$	21.2806	+	36.8590i	0.739104	+	1.28017i	0.952899	+	0.303287i	$0.0980842\pi$
$829$	21.2806	+	36.8590i	0.739104	+	1.28017i	−0.213795	+	0.976879i	$0.568582\pi$
$830$	−2.22129	−	3.84739i	−0.0771022	−	0.133545i
$831$	−1.26172	+	2.18536i	−0.0437685	+	0.0758093i
$832$		0			0
$833$	12.0816	+	6.15191i	0.418601	+	0.213151i
$834$	2.37073			0.0820915
$835$	−28.5230	+	49.4033i	−0.987080	+	1.70967i
$836$	−0.594515	−	1.02973i	−0.0205617	−	0.0356140i
$837$	16.7982	+	29.0954i	0.580632	+	1.00568i
$838$	−5.82846	+	10.0952i	−0.201341	+	0.348733i
$839$	−1.84105			−0.0635601			−0.0317800	−	0.999495i	$-0.510118\pi$
$839$	−1.84105			−0.0635601			−0.0317800	+	0.999495i	$0.510118\pi$
$840$	−4.76932	−	16.0933i	−0.164557	−	0.555271i
$841$	−25.6293			−0.883770
$842$	1.46465	−	2.53686i	0.0504753	−	0.0874258i
$843$	2.82666	+	4.89591i	0.0973553	+	0.168624i
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$		0			0
$846$	15.6860			0.539296
$847$	−26.2254	−	6.29257i	−0.901116	−	0.216215i
$848$	−1.67351			−0.0574686
$849$	−5.04657	+	8.74092i	−0.173198	+	0.299988i
$850$	−5.64087	−	9.77027i	−0.193480	−	0.335118i
$851$	−29.9457	−	51.8675i	−1.02653	−	1.77800i
$852$	1.45426	−	2.51885i	0.0498221	−	0.0862944i
$853$	27.0293			0.925466			0.462733	−	0.886498i	$-0.346869\pi$
$853$	27.0293			0.925466			0.462733	+	0.886498i	$0.346869\pi$
$854$	−2.22591	+	2.34623i	−0.0761690	+	0.0802862i
$855$	−9.15526			−0.313103
$856$	−19.6875	+	34.0998i	−0.672906	+	1.16551i
$857$	−8.39268	−	14.5365i	−0.286688	−	0.496559i	0.686329	−	0.727291i	$-0.259221\pi$
$857$	−8.39268	−	14.5365i	−0.286688	−	0.496559i	−0.973017	+	0.230732i	$0.925888\pi$
$858$		0			0
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.0296769	+	0.999560i	$0.509448\pi$
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.850806	+	0.525481i	$0.823886\pi$
$860$	−17.1849			−0.586000
$861$	−6.41938	+	6.76638i	−0.218772	+	0.230598i
$862$	−18.9725			−0.646205
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	−0.616358	−	0.787466i	$-0.711393\pi$
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	0.990145	+	0.140049i	$0.0447259\pi$
$864$	10.5338	+	18.2450i	0.358366	+	0.620709i
$865$	−17.1843	−	29.7640i	−0.584283	−	1.01201i
$866$	11.0205	−	19.0880i	0.374491	−	0.648638i
$867$	−8.76040			−0.297519
$868$	−29.9749	−	7.19221i	−1.01741	−	0.244120i
$869$	−10.8583			−0.368341
$870$	−1.77793	+	3.07947i	−0.0602775	+	0.104404i
$871$		0			0
$872$	5.85797	+	10.1463i	0.198376	+	0.343597i
$873$	−0.648693	+	1.12357i	−0.0219549	+	0.0380270i
$874$	−4.99190			−0.168853
$875$	4.77017	+	16.0962i	0.161261	+	0.544150i
$876$	9.19401			0.310637
$877$	−4.80873	+	8.32896i	−0.162379	+	0.281249i	−0.935721	−	0.352740i	$-0.885250\pi$
$877$	−4.80873	+	8.32896i	−0.162379	+	0.281249i	0.773342	+	0.633989i	$0.218583\pi$
$878$	11.9089	+	20.6268i	0.401905	+	0.696120i
$879$	−1.96371	−	3.40125i	−0.0662344	−	0.114721i
$880$	0.275493	−	0.477167i	0.00928686	−	0.0160853i
$881$	28.9726			0.976110			0.488055	−	0.872813i	$-0.337707\pi$
$881$	28.9726			0.976110			0.488055	+	0.872813i	$0.337707\pi$
$882$	−13.6064	−	6.92834i	−0.458150	−	0.233289i
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$		0			0
$885$	0.580863	+	1.00608i	0.0195255	+	0.0338191i
$886$	−14.1325	−	24.4781i	−0.474789	−	0.822359i
$887$	15.7072	−	27.2057i	0.527397	−	0.913478i	−0.472094	−	0.881548i	$-0.656502\pi$
$887$	15.7072	−	27.2057i	0.527397	−	0.913478i	0.999490	−	0.0319293i	$-0.0101651\pi$
$888$	−19.5406			−0.655739
$889$	−1.46215	−	4.93379i	−0.0490390	−	0.165474i
$890$	39.8591			1.33608
$891$	−2.36000	+	4.08765i	−0.0790631	+	0.136941i
$892$	−1.50399	−	2.60499i	−0.0503574	−	0.0872216i
$893$	−3.73242	−	6.46474i	−0.124901	−	0.216334i
$894$	1.65032	−	2.85843i	0.0551949	−	0.0956003i
$895$	−31.5810			−1.05564
$896$	−19.5773	−	4.69741i	−0.654033	−	0.156930i
$897$		0			0
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	8.38459	+	14.5225i	0.279642	+	0.484354i
$900$	−11.1863	−	19.3753i	−0.372877	−	0.645843i
$901$	9.08991	−	15.7442i	0.302829	−	0.524515i
$902$	4.07480			0.135676
$903$	4.71349	−	4.96827i	0.156855	−	0.165334i
$904$	−38.3883			−1.27678
$905$	10.3328	−	17.8970i	0.343475	−	0.594917i
$906$	−4.74337	−	8.21575i	−0.157588	−	0.272950i
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	0.773813	−	0.633414i	$-0.218347\pi$
$907$	−4.86821	−	8.43198i	−0.161646	−	0.279979i	−0.935459	+	0.353435i	$0.885014\pi$
$908$	−16.7692	+	29.0452i	−0.556507	+	0.963898i
$909$	15.3422			0.508869
$910$		0			0
$911$	−38.4372			−1.27348			−0.636740	−	0.771078i	$-0.719718\pi$
$911$	−38.4372			−1.27348			−0.636740	+	0.771078i	$0.719718\pi$
$912$	0.0611867	−	0.105979i	0.00202609	−	0.00350930i
$913$	0.680984	+	1.17950i	0.0225373	+	0.0390357i
$914$	−0.317871	−	0.550568i	−0.0105142	−	0.0182112i
$915$	1.63409	−	2.83032i	0.0540212	−	0.0935675i
$916$	0.0874483			0.00288937
$917$	−30.9638	−	7.42951i	−1.02252	−	0.245344i
$918$	−6.06346			−0.200124
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.0618056	+	0.998088i	$0.519686\pi$
$919$	−27.1402	+	47.0082i	−0.895273	+	1.55066i	−0.833467	+	0.552569i	$0.813647\pi$
$920$	−27.1054	−	46.9479i	−0.893639	−	1.54783i
$921$	7.34398	+	12.7202i	0.241993	+	0.419143i
$922$	−14.1164	+	24.4502i	−0.464897	+	0.805226i
$923$		0			0
$924$	0.569388	+	1.92131i	0.0187315	+	0.0632063i
$925$	72.5442			2.38524
$926$	−13.0869	+	22.6673i	−0.430064	+	0.744892i
$927$	−5.29602	−	9.17297i	−0.173944	−	0.301280i
$928$	5.25777	+	9.10673i	0.172595	+	0.298943i
$929$	−19.0960	+	33.0752i	−0.626519	+	1.08516i	0.361726	+	0.932284i	$0.382188\pi$
$929$	−19.0960	+	33.0752i	−0.626519	+	1.08516i	−0.988245	+	0.152878i	$0.951146\pi$
$930$	−17.6905			−0.580095
$931$	0.382172	+	7.25622i	0.0125252	+	0.237813i
$932$	−18.7132			−0.612971
$933$	−3.25408	+	5.63622i	−0.106534	+	0.184522i
$934$	12.5994	+	21.8228i	0.412266	+	0.714065i
$935$	2.99276	+	5.18361i	0.0978736	+	0.169522i
$936$		0			0
$937$	−19.0376			−0.621931			−0.310966	−	0.950421i	$-0.600652\pi$
$937$	−19.0376			−0.621931			−0.310966	+	0.950421i	$0.600652\pi$
$938$	−5.40625	−	18.2425i	−0.176520	−	0.595639i
$939$	−13.8278			−0.451255
$940$	15.7845	−	27.3396i	0.514835	−	0.891720i
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	0.946646	+	0.322275i	$0.104448\pi$
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	−0.194224	+	0.980957i	$0.562219\pi$
$942$	0.545619	+	0.945040i	0.0177772	+	0.0307911i
$943$	−15.0616	+	26.0875i	−0.490474	+	0.849526i
$944$	0.0910198			0.00296244
$945$	32.5671	+	7.81420i	1.05941	+	0.254196i
$946$	−2.99196			−0.0972770
$947$	−4.59687	+	7.96201i	−0.149378	+	0.258730i	−0.930998	−	0.365025i	$-0.881060\pi$
$947$	−4.59687	+	7.96201i	−0.149378	+	0.258730i	0.781620	+	0.623755i	$0.214394\pi$
$948$	−5.09938	−	8.83239i	−0.165620	−	0.286863i
$949$		0			0
$950$	3.02324	−	5.23641i	0.0980869	−	0.169892i
$951$	16.7688			0.543766
$952$	9.83266	−	10.3642i	0.318678	−	0.335904i
$953$	−44.6463			−1.44624			−0.723118	−	0.690725i	$-0.757292\pi$
$953$	−44.6463			−1.44624			−0.723118	+	0.690725i	$0.757292\pi$
$954$	−10.2371	+	17.7312i	−0.331440	+	0.574070i
$955$	2.26470	+	3.92258i	0.0732841	+	0.126932i
$956$	−2.13937	−	3.70550i	−0.0691923	−	0.119844i
$957$	0.545062	−	0.944075i	0.0176194	−	0.0305176i
$958$	−11.9928			−0.387470
$959$	15.8736	−	16.7317i	0.512586	−	0.540293i
$960$	−10.2819			−0.331846
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$		0			0
$963$	−18.0976	−	31.3459i	−0.583186	−	1.01011i
$964$	5.47212	−	9.47799i	0.176245	−	0.305266i
$965$	−56.5276			−1.81969
$966$	8.18077	+	1.96290i	0.263212	+	0.0631554i
$967$	−13.8268			−0.444639			−0.222320	−	0.974974i	$-0.571363\pi$
$967$	−13.8268			−0.444639			−0.222320	+	0.974974i	$0.571363\pi$
$968$	−14.2096	+	24.6117i	−0.456713	+	0.791050i
$969$	0.664689	+	1.15128i	0.0213529	+	0.0369843i
$970$	−0.741422	−	1.28418i	−0.0238056	−	0.0412326i
$971$	−3.63437	+	6.29491i	−0.116632	+	0.202013i	−0.918431	−	0.395581i	$-0.870543\pi$
$971$	−3.63437	+	6.29491i	−0.116632	+	0.202013i	0.801799	+	0.597594i	$0.203877\pi$
$972$	−18.5091			−0.593679
$973$	−3.16680	−	10.6858i	−0.101523	−	0.342572i
$974$	14.2950			0.458043
$975$		0			0
$976$	−0.128029	−	0.221752i	−0.00409810	−	0.00709811i
$977$	21.4050	+	37.0746i	0.684808	+	1.18612i	0.973497	+	0.228699i	$0.0734473\pi$
$977$	21.4050	+	37.0746i	0.684808	+	1.18612i	−0.288689	+	0.957423i	$0.593219\pi$
$978$	−3.34742	+	5.79790i	−0.107039	+	0.185397i
$979$	−12.2196			−0.390541
$980$	−25.7674	+	16.7431i	−0.823110	+	0.534838i
$981$	−10.7698			−0.343852
$982$	−9.22152	+	15.9721i	−0.294270	+	0.509691i
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	−0.953166	−	0.302448i	$-0.902196\pi$
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	0.214655	−	0.976690i	$-0.431137\pi$
$984$	4.91410	+	8.51147i	0.156656	+	0.271336i
$985$	44.0294	−	76.2612i	1.40289	−	2.42988i
$986$	−3.02648			−0.0963829
$987$	3.57467	+	12.0621i	0.113783	+	0.383942i
$988$		0			0
$989$	11.0591	−	19.1550i	0.351660	−	0.609092i
$990$	−3.37047	−	5.83782i	−0.107121	−	0.185538i
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.791711	+	0.610896i	$0.209190\pi$
$991$	29.1162	+	50.4307i	0.924907	+	1.60199i	0.133195	+	0.991090i	$0.457476\pi$
$992$	−26.1576	+	45.3062i	−0.830504	+	1.43847i
$993$	−1.17885			−0.0374097
$994$	7.55096	+	1.81179i	0.239502	+	0.0574664i
$995$	87.3406			2.76888
$996$	−0.639625	+	1.10786i	−0.0202673	+	0.0351040i
$997$	2.24739	+	3.89260i	0.0711757	+	0.123280i	0.899417	−	0.437092i	$-0.143992\pi$
$997$	2.24739	+	3.89260i	0.0711757	+	0.123280i	−0.828241	+	0.560372i	$0.810658\pi$
$998$	−9.91765	−	17.1779i	−0.313938	−	0.543756i
$999$	19.4947	−	33.7658i	0.616786	−	1.06830i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.g.170.3		12
7.2	even	3		8281.2.a.ce.1.4		6
7.4	even	3	inner	1183.2.e.g.508.3		12
7.5	odd	6		8281.2.a.cf.1.4		6
13.4	even	6		91.2.h.b.16.3	yes	12
13.10	even	6		91.2.g.b.9.4	✓	12
13.12	even	2		1183.2.e.h.170.4		12
39.17	odd	6		819.2.s.d.289.4		12
39.23	odd	6		819.2.n.d.100.3		12
91.4	even	6		91.2.g.b.81.4	yes	12
91.10	odd	6		637.2.h.l.165.3		12
91.12	odd	6		8281.2.a.ca.1.3		6
91.17	odd	6		637.2.g.l.263.4		12
91.23	even	6		637.2.f.k.295.4		12
91.25	even	6		1183.2.e.h.508.4		12
91.30	even	6		637.2.f.k.393.4		12
91.51	even	6		8281.2.a.bz.1.3		6
91.62	odd	6		637.2.g.l.373.4		12
91.69	odd	6		637.2.h.l.471.3		12
91.75	odd	6		637.2.f.j.295.4		12
91.82	odd	6		637.2.f.j.393.4		12
91.88	even	6		91.2.h.b.74.3	yes	12
273.95	odd	6		819.2.n.d.172.3		12
273.179	odd	6		819.2.s.d.802.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	13.10	even	6
91.2.g.b.81.4	yes	12	91.4	even	6
91.2.h.b.16.3	yes	12	13.4	even	6
91.2.h.b.74.3	yes	12	91.88	even	6
637.2.f.j.295.4		12	91.75	odd	6
637.2.f.j.393.4		12	91.82	odd	6
637.2.f.k.295.4		12	91.23	even	6
637.2.f.k.393.4		12	91.30	even	6
637.2.g.l.263.4		12	91.17	odd	6
637.2.g.l.373.4		12	91.62	odd	6
637.2.h.l.165.3		12	91.10	odd	6
637.2.h.l.471.3		12	91.69	odd	6
819.2.n.d.100.3		12	39.23	odd	6
819.2.n.d.172.3		12	273.95	odd	6
819.2.s.d.289.4		12	39.17	odd	6
819.2.s.d.802.4		12	273.179	odd	6
1183.2.e.g.170.3		12	1.1	even	1	trivial
1183.2.e.g.508.3		12	7.4	even	3	inner
1183.2.e.h.170.4		12	13.12	even	2
1183.2.e.h.508.4		12	91.25	even	6
8281.2.a.bz.1.3		6	91.51	even	6
8281.2.a.ca.1.3		6	91.12	odd	6
8281.2.a.ce.1.4		6	7.2	even	3
8281.2.a.cf.1.4		6	7.5	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +0.562784 q^{6} +(-0.751763 - 2.53670i) q^{7} -2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +O(q^{10})\)	\(q+(-0.425563 + 0.737096i) q^{2} +(-0.330612 - 0.572636i) q^{3} +(0.637793 + 1.10469i) q^{4} +(1.72074 - 2.98041i) q^{5} +0.562784 q^{6} +(-0.751763 - 2.53670i) q^{7} -2.78793 q^{8} +(1.28139 - 2.21944i) q^{9} +(1.46456 + 2.53670i) q^{10} +(-0.448993 - 0.777679i) q^{11} +(0.421723 - 0.730446i) q^{12} +(2.18972 + 0.525403i) q^{14} -2.27559 q^{15} +(-0.0891447 + 0.154403i) q^{16} +(-0.968404 - 1.67733i) q^{17} +(1.09063 + 1.88902i) q^{18} +(0.519020 - 0.898968i) q^{19} +4.38990 q^{20} +(-1.20406 + 1.26915i) q^{21} +0.764299 q^{22} +(-2.82506 + 4.89315i) q^{23} +(0.921723 + 1.59647i) q^{24} +(-3.42189 - 5.92688i) q^{25} -3.67824 q^{27} +(2.32280 - 2.44835i) q^{28} -1.83594 q^{29} +(0.968404 - 1.67733i) q^{30} +(-4.56692 - 7.91014i) q^{31} +(-2.86381 - 4.96026i) q^{32} +(-0.296885 + 0.514219i) q^{33} +1.64847 q^{34} +(-8.85399 - 2.12444i) q^{35} +3.26905 q^{36} +(-5.30001 + 9.17989i) q^{37} +(0.441751 + 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +5.33143 q^{41} +(-0.423080 - 1.42761i) q^{42} -3.91465 q^{43} +(0.572729 - 0.991996i) q^{44} +(-4.40988 - 7.63814i) q^{45} +(-2.40448 - 4.16469i) q^{46} +(3.59565 - 6.22784i) q^{47} +0.117889 q^{48} +(-5.86970 + 3.81400i) q^{49} +5.82491 q^{50} +(-0.640331 + 1.10909i) q^{51} +(4.69324 + 8.12893i) q^{53} +(1.56532 - 2.71122i) q^{54} -3.09040 q^{55} +(2.09587 + 7.07216i) q^{56} -0.686375 q^{57} +(0.781307 - 1.35326i) q^{58} +(-0.255259 - 0.442121i) q^{59} +(-1.45135 - 2.51382i) q^{60} +(-0.718095 + 1.24378i) q^{61} +7.77405 q^{62} +(-6.59335 - 1.58202i) q^{63} +4.51834 q^{64} +(-0.252686 - 0.437665i) q^{66} +(-4.22466 - 7.31732i) q^{67} +(1.23528 - 2.13957i) q^{68} +3.73600 q^{69} +(5.33385 - 5.62216i) q^{70} +3.44837 q^{71} +(-3.57244 + 6.18764i) q^{72} +(5.45026 + 9.44013i) q^{73} +(-4.51097 - 7.81324i) q^{74} +(-2.26263 + 3.91899i) q^{75} +1.32411 q^{76} +(-1.63520 + 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} +(0.306789 + 0.531375i) q^{80} +(-2.62811 - 4.55201i) q^{81} +(-2.26886 + 3.92977i) q^{82} -1.51669 q^{83} +(-2.16996 - 0.520663i) q^{84} -6.66549 q^{85} +(1.66593 - 2.88547i) q^{86} +(0.606982 + 1.05132i) q^{87} +(1.25176 + 2.16812i) q^{88} +(6.80391 - 11.7847i) q^{89} +7.50673 q^{90} -7.20722 q^{92} +(-3.01976 + 5.23037i) q^{93} +(3.06035 + 5.30067i) q^{94} +(-1.78619 - 3.09378i) q^{95} +(-1.89362 + 3.27984i) q^{96} -0.506241 q^{97} +(-0.313356 - 5.94963i) q^{98} -2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9	\( 12 q - 2 q^{2} + q^{3} - 4 q^{4} - q^{5} - 18 q^{6} + 6 q^{7} + 6 q^{8} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 5 q^{12} - 2 q^{14} - 4 q^{15} + 8 q^{16} + 5 q^{17} - 3 q^{18} + q^{19} - 2 q^{20} + 9 q^{21} + 10 q^{22} - q^{23} + 11 q^{24} + 7 q^{25} - 8 q^{27} - 8 q^{28} - 6 q^{29} - 5 q^{30} - 16 q^{31} - 8 q^{32} - 16 q^{33} - 32 q^{34} - 28 q^{35} + 42 q^{36} + 13 q^{37} - 17 q^{38} - 5 q^{40} - 16 q^{41} - 52 q^{42} + 22 q^{43} - 21 q^{44} + 7 q^{45} - 16 q^{46} + q^{47} - 42 q^{48} + 6 q^{49} + 12 q^{50} - 20 q^{51} - 2 q^{53} + 18 q^{54} - 18 q^{55} + 9 q^{56} - 42 q^{57} + 8 q^{58} - 13 q^{59} - 20 q^{60} - 5 q^{61} - 10 q^{62} - 8 q^{63} - 30 q^{64} + 18 q^{66} + 11 q^{67} + 29 q^{68} - 46 q^{69} + 39 q^{70} + 12 q^{71} - 25 q^{72} + 30 q^{73} - 3 q^{74} - 3 q^{75} - 18 q^{76} + 11 q^{77} + 7 q^{79} + 7 q^{80} - 6 q^{81} + q^{82} + 54 q^{83} - 41 q^{84} - 2 q^{85} + 7 q^{86} + 16 q^{87} - 4 q^{89} - 16 q^{90} + 54 q^{92} + 7 q^{93} + 45 q^{94} - 6 q^{95} - 19 q^{96} - 70 q^{97} + 82 q^{98} + 20 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 + q^3 - 4 * q^4 - q^5 - 18 * q^6 + 6 * q^7 + 6 * q^8 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 5 * q^12 - 2 * q^14 - 4 * q^15 + 8 * q^16 + 5 * q^17 - 3 * q^18 + q^19 - 2 * q^20 + 9 * q^21 + 10 * q^22 - q^23 + 11 * q^24 + 7 * q^25 - 8 * q^27 - 8 * q^28 - 6 * q^29 - 5 * q^30 - 16 * q^31 - 8 * q^32 - 16 * q^33 - 32 * q^34 - 28 * q^35 + 42 * q^36 + 13 * q^37 - 17 * q^38 - 5 * q^40 - 16 * q^41 - 52 * q^42 + 22 * q^43 - 21 * q^44 + 7 * q^45 - 16 * q^46 + q^47 - 42 * q^48 + 6 * q^49 + 12 * q^50 - 20 * q^51 - 2 * q^53 + 18 * q^54 - 18 * q^55 + 9 * q^56 - 42 * q^57 + 8 * q^58 - 13 * q^59 - 20 * q^60 - 5 * q^61 - 10 * q^62 - 8 * q^63 - 30 * q^64 + 18 * q^66 + 11 * q^67 + 29 * q^68 - 46 * q^69 + 39 * q^70 + 12 * q^71 - 25 * q^72 + 30 * q^73 - 3 * q^74 - 3 * q^75 - 18 * q^76 + 11 * q^77 + 7 * q^79 + 7 * q^80 - 6 * q^81 + q^82 + 54 * q^83 - 41 * q^84 - 2 * q^85 + 7 * q^86 + 16 * q^87 - 4 * q^89 - 16 * q^90 + 54 * q^92 + 7 * q^93 + 45 * q^94 - 6 * q^95 - 19 * q^96 - 70 * q^97 + 82 * q^98 + 20 * q^99

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