LMFDB - Embedded newform 605.2.g.g.366.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			366.2
Root			$-0.628998 - 0.456994i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.g.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82676 - 1.32722i) q^{2} +(0.240256 + 0.739431i) q^{3} +(0.957503 - 2.94689i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.42027 + 1.03189i) q^{6} +(-0.0383089 + 0.117903i) q^{7} +(-0.766520 - 2.35911i) q^{8} +(1.93801 - 1.40805i) q^{9} +O(q^{10})$	\(q+(1.82676 - 1.32722i) q^{2} +(0.240256 + 0.739431i) q^{3} +(0.957503 - 2.94689i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.42027 + 1.03189i) q^{6} +(-0.0383089 + 0.117903i) q^{7} +(-0.766520 - 2.35911i) q^{8} +(1.93801 - 1.40805i) q^{9} -2.25800 q^{10} +2.40907 q^{12} +(4.44479 - 3.22933i) q^{13} +(0.0865012 + 0.266223i) q^{14} +(0.240256 - 0.739431i) q^{15} +(0.482260 + 0.350382i) q^{16} +(0.420275 + 0.305348i) q^{17} +(1.67149 - 5.14433i) q^{18} +(-0.976324 - 3.00482i) q^{19} +(-2.50678 + 1.82128i) q^{20} -0.0963848 q^{21} -7.92856 q^{23} +(1.56024 - 1.13358i) q^{24} +(0.309017 + 0.951057i) q^{25} +(3.83353 - 11.7984i) q^{26} +(3.39377 + 2.46572i) q^{27} +(0.310765 + 0.225784i) q^{28} +(1.25974 - 3.87709i) q^{29} +(-0.542497 - 1.66963i) q^{30} +(-5.70279 + 4.14332i) q^{31} +6.30703 q^{32} +1.17300 q^{34} +(0.100294 - 0.0728678i) q^{35} +(-2.29372 - 7.05933i) q^{36} +(-2.71550 + 8.35745i) q^{37} +(-5.77155 - 4.19328i) q^{38} +(3.45576 + 2.51075i) q^{39} +(-0.766520 + 2.35911i) q^{40} +(2.33353 + 7.18188i) q^{41} +(-0.176072 + 0.127923i) q^{42} -3.42310 q^{43} -2.39552 q^{45} +(-14.4836 + 10.5229i) q^{46} +(0.141042 + 0.434084i) q^{47} +(-0.143218 + 0.440780i) q^{48} +(5.65069 + 4.10546i) q^{49} +(1.82676 + 1.32722i) q^{50} +(-0.124810 + 0.384126i) q^{51} +(-5.26058 - 16.1904i) q^{52} +(-0.0287041 + 0.0208547i) q^{53} +9.47214 q^{54} +0.307509 q^{56} +(1.98729 - 1.44385i) q^{57} +(-2.84450 - 8.75446i) q^{58} +(-1.69182 + 5.20690i) q^{59} +(-1.94898 - 1.41602i) q^{60} +(6.22053 + 4.51948i) q^{61} +(-4.91853 + 15.1377i) q^{62} +(0.0917696 + 0.282438i) q^{63} +(10.5569 - 7.67003i) q^{64} -5.49406 q^{65} -2.53792 q^{67} +(1.30224 - 0.946133i) q^{68} +(-1.90488 - 5.86263i) q^{69} +(0.0865012 - 0.266223i) q^{70} +(-9.92925 - 7.21402i) q^{71} +(-4.80727 - 3.49269i) q^{72} +(-2.63319 + 8.10411i) q^{73} +(6.13159 + 18.8711i) q^{74} +(-0.628998 + 0.456994i) q^{75} -9.78970 q^{76} +9.64514 q^{78} +(5.07554 - 3.68759i) q^{79} +(-0.184207 - 0.566931i) q^{80} +(1.21291 - 3.73296i) q^{81} +(13.7947 + 10.0224i) q^{82} +(0.506776 + 0.368194i) q^{83} +(-0.0922887 + 0.284036i) q^{84} +(-0.160531 - 0.494063i) q^{85} +(-6.25318 + 4.54320i) q^{86} +3.16951 q^{87} -10.1852 q^{89} +(-4.37603 + 3.17937i) q^{90} +(0.210471 + 0.647764i) q^{91} +(-7.59162 + 23.3646i) q^{92} +(-4.43383 - 3.22136i) q^{93} +(0.833774 + 0.605772i) q^{94} +(-0.976324 + 3.00482i) q^{95} +(1.51530 + 4.66362i) q^{96} +(1.48446 - 1.07852i) q^{97} +15.7713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9	$ 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9} - 6 q^{10} - 28 q^{12} + 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} + 4 q^{17} + 16 q^{18} + 11 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} + 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} + 11 q^{28} + 11 q^{29} - 13 q^{30} - 9 q^{31} - 12 q^{32} - 20 q^{34} + 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} + 6 q^{39} + 7 q^{40} - 11 q^{41} - 31 q^{42} - 42 q^{43} - 29 q^{46} - q^{47} + 21 q^{48} - q^{50} + 22 q^{51} + q^{52} + 8 q^{53} + 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} + 2 q^{61} - 27 q^{62} + 4 q^{63} + 21 q^{64} - 14 q^{65} - 2 q^{67} + 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} - 21 q^{72} - 32 q^{73} + 12 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} + 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} - 10 q^{83} - 51 q^{84} - q^{85} + 34 q^{86} - 30 q^{87} - 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} + 22 q^{94} + 11 q^{95} - 3 q^{96} - 18 q^{97} + 84 q^{98}+O(q^{100}) $ 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9 - 6 * q^10 - 28 * q^12 + 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 + 4 * q^17 + 16 * q^18 + 11 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 + 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 + 11 * q^28 + 11 * q^29 - 13 * q^30 - 9 * q^31 - 12 * q^32 - 20 * q^34 + 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 + 6 * q^39 + 7 * q^40 - 11 * q^41 - 31 * q^42 - 42 * q^43 - 29 * q^46 - q^47 + 21 * q^48 - q^50 + 22 * q^51 + q^52 + 8 * q^53 + 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 + 2 * q^61 - 27 * q^62 + 4 * q^63 + 21 * q^64 - 14 * q^65 - 2 * q^67 + 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 - 21 * q^72 - 32 * q^73 + 12 * q^74 + q^75 - 16 * q^76 + 12 * q^78 + 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 - 10 * q^83 - 51 * q^84 - q^85 + 34 * q^86 - 30 * q^87 - 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 + 22 * q^94 + 11 * q^95 - 3 * q^96 - 18 * q^97 + 84 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.82676	−	1.32722i	1.29171	−	0.938484i	0.291874	−	0.956457i	$-0.405721\pi$
$2$	1.82676	−	1.32722i	1.29171	−	0.938484i	0.999838	+	0.0179729i	$0.00572125\pi$
$3$	0.240256	+	0.739431i	0.138712	+	0.426911i	0.996149	−	0.0876778i	$-0.0279446\pi$
$3$	0.240256	+	0.739431i	0.138712	+	0.426911i	−0.857437	+	0.514589i	$0.827945\pi$
$4$	0.957503	−	2.94689i	0.478752	−	1.47345i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	1.42027	+	1.03189i	0.579825	+	0.421267i
$7$	−0.0383089	+	0.117903i	−0.0144794	+	0.0445630i	−0.958035	−	0.286651i	$-0.907458\pi$
$7$	−0.0383089	+	0.117903i	−0.0144794	+	0.0445630i	0.943556	+	0.331214i	$0.107458\pi$
$8$	−0.766520	−	2.35911i	−0.271006	−	0.834070i
$9$	1.93801	−	1.40805i	0.646005	−	0.469350i
$10$	−2.25800			−0.714041
$11$		0			0
$11$		0			0
$12$	2.40907			0.695439
$13$	4.44479	−	3.22933i	1.23276	−	0.895655i	0.235669	−	0.971833i	$-0.424272\pi$
$13$	4.44479	−	3.22933i	1.23276	−	0.895655i	0.997094	+	0.0761784i	$0.0242719\pi$
$14$	0.0865012	+	0.266223i	0.0231184	+	0.0711512i
$15$	0.240256	−	0.739431i	0.0620338	−	0.190920i
$16$	0.482260	+	0.350382i	0.120565	+	0.0875956i
$17$	0.420275	+	0.305348i	0.101932	+	0.0740577i	0.637584	−	0.770381i	$-0.279934\pi$
$17$	0.420275	+	0.305348i	0.101932	+	0.0740577i	−0.535652	+	0.844439i	$0.679934\pi$
$18$	1.67149	−	5.14433i	0.393975	−	1.21253i
$19$	−0.976324	−	3.00482i	−0.223984	−	0.689352i	−0.998393	−	0.0566668i	$-0.981953\pi$
$19$	−0.976324	−	3.00482i	−0.223984	−	0.689352i	0.774409	−	0.632685i	$-0.218047\pi$
$20$	−2.50678	+	1.82128i	−0.560532	+	0.407250i
$21$	−0.0963848			−0.0210329
$22$		0			0
$23$	−7.92856			−1.65322			−0.826609	−	0.562776i	$-0.809733\pi$
$23$	−7.92856			−1.65322			−0.826609	+	0.562776i	$0.809733\pi$
$24$	1.56024	−	1.13358i	0.318482	−	0.231391i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	3.83353	−	11.7984i	0.751818	−	2.31386i
$27$	3.39377	+	2.46572i	0.653131	+	0.474528i
$28$	0.310765	+	0.225784i	0.0587291	+	0.0426692i
$29$	1.25974	−	3.87709i	0.233929	−	0.719958i	−0.763333	−	0.646005i	$-0.776438\pi$
$29$	1.25974	−	3.87709i	0.233929	−	0.719958i	0.997262	−	0.0739532i	$-0.0235615\pi$
$30$	−0.542497	−	1.66963i	−0.0990459	−	0.304832i
$31$	−5.70279	+	4.14332i	−1.02425	+	0.744162i	−0.967150	−	0.254207i	$-0.918186\pi$
$31$	−5.70279	+	4.14332i	−1.02425	+	0.744162i	−0.0571009	+	0.998368i	$0.518186\pi$
$32$	6.30703			1.11494
$33$		0			0
$34$	1.17300			0.201168
$35$	0.100294	−	0.0728678i	0.0169528	−	0.0123169i
$36$	−2.29372	−	7.05933i	−0.382286	−	1.17656i
$37$	−2.71550	+	8.35745i	−0.446425	+	1.37396i	0.434488	+	0.900678i	$0.356929\pi$
$37$	−2.71550	+	8.35745i	−0.446425	+	1.37396i	−0.880913	+	0.473278i	$0.843071\pi$
$38$	−5.77155	−	4.19328i	−0.936269	−	0.680239i
$39$	3.45576	+	2.51075i	0.553364	+	0.402042i
$40$	−0.766520	+	2.35911i	−0.121197	+	0.373008i
$41$	2.33353	+	7.18188i	0.364437	+	1.12162i	0.950333	+	0.311235i	$0.100743\pi$
$41$	2.33353	+	7.18188i	0.364437	+	1.12162i	−0.585896	+	0.810386i	$0.699257\pi$
$42$	−0.176072	+	0.127923i	−0.0271684	+	0.0197390i
$43$	−3.42310			−0.522018			−0.261009	−	0.965336i	$-0.584055\pi$
$43$	−3.42310			−0.522018			−0.261009	+	0.965336i	$0.584055\pi$
$44$		0			0
$45$	−2.39552			−0.357103
$46$	−14.4836	+	10.5229i	−2.13548	+	1.55152i
$47$	0.141042	+	0.434084i	0.0205731	+	0.0633176i	0.960816	−	0.277187i	$-0.0894021\pi$
$47$	0.141042	+	0.434084i	0.0205731	+	0.0633176i	−0.940243	+	0.340505i	$0.889402\pi$
$48$	−0.143218	+	0.440780i	−0.0206717	+	0.0636210i
$49$	5.65069	+	4.10546i	0.807241	+	0.586495i
$50$	1.82676	+	1.32722i	0.258342	+	0.187697i
$51$	−0.124810	+	0.384126i	−0.0174769	+	0.0537884i
$52$	−5.26058	−	16.1904i	−0.729512	−	2.24521i
$53$	−0.0287041	+	0.0208547i	−0.00394281	+	0.00286462i	−0.589755	−	0.807582i	$-0.700776\pi$
$53$	−0.0287041	+	0.0208547i	−0.00394281	+	0.00286462i	0.585812	+	0.810447i	$0.300776\pi$
$54$	9.47214			1.28899
$55$		0			0
$56$	0.307509			0.0410926
$57$	1.98729	−	1.44385i	0.263223	−	0.191242i
$58$	−2.84450	−	8.75446i	−0.373501	−	1.14952i
$59$	−1.69182	+	5.20690i	−0.220257	+	0.677880i	0.778482	+	0.627667i	$0.215990\pi$
$59$	−1.69182	+	5.20690i	−0.220257	+	0.677880i	−0.998739	+	0.0502131i	$0.984010\pi$
$60$	−1.94898	−	1.41602i	−0.251612	−	0.182807i
$61$	6.22053	+	4.51948i	0.796457	+	0.578660i	0.909873	−	0.414888i	$-0.136179\pi$
$61$	6.22053	+	4.51948i	0.796457	+	0.578660i	−0.113416	+	0.993548i	$0.536179\pi$
$62$	−4.91853	+	15.1377i	−0.624654	+	1.92249i
$63$	0.0917696	+	0.282438i	0.0115619	+	0.0355838i
$64$	10.5569	−	7.67003i	1.31961	−	0.958754i
$65$	−5.49406			−0.681455
$66$		0			0
$67$	−2.53792			−0.310056			−0.155028	−	0.987910i	$-0.549547\pi$
$67$	−2.53792			−0.310056			−0.155028	+	0.987910i	$0.549547\pi$
$68$	1.30224	−	0.946133i	0.157920	−	0.114736i
$69$	−1.90488	−	5.86263i	−0.229321	−	0.705777i
$70$	0.0865012	−	0.266223i	0.0103389	−	0.0318198i
$71$	−9.92925	−	7.21402i	−1.17839	−	0.856147i	−0.186397	−	0.982475i	$-0.559681\pi$
$71$	−9.92925	−	7.21402i	−1.17839	−	0.856147i	−0.991989	+	0.126328i	$0.959681\pi$
$72$	−4.80727	−	3.49269i	−0.566542	−	0.411617i
$73$	−2.63319	+	8.10411i	−0.308191	+	0.948515i	0.670276	+	0.742112i	$0.266176\pi$
$73$	−2.63319	+	8.10411i	−0.308191	+	0.948515i	−0.978467	+	0.206403i	$0.933824\pi$
$74$	6.13159	+	18.8711i	0.712782	+	2.19372i
$75$	−0.628998	+	0.456994i	−0.0726304	+	0.0527691i
$76$	−9.78970			−1.12296
$77$		0			0
$78$	9.64514			1.09210
$79$	5.07554	−	3.68759i	0.571043	−	0.414887i	−0.264441	−	0.964402i	$-0.585188\pi$
$79$	5.07554	−	3.68759i	0.571043	−	0.414887i	0.835484	+	0.549515i	$0.185188\pi$
$80$	−0.184207	−	0.566931i	−0.0205950	−	0.0633848i
$81$	1.21291	−	3.73296i	0.134768	−	0.414773i
$82$	13.7947	+	10.0224i	1.52337	+	1.10679i
$83$	0.506776	+	0.368194i	0.0556259	+	0.0404146i	0.615251	−	0.788331i	$-0.289055\pi$
$83$	0.506776	+	0.368194i	0.0556259	+	0.0404146i	−0.559625	+	0.828746i	$0.689055\pi$
$84$	−0.0922887	+	0.284036i	−0.0100695	+	0.0309908i
$85$	−0.160531	−	0.494063i	−0.0174120	−	0.0535886i
$86$	−6.25318	+	4.54320i	−0.674298	+	0.489906i
$87$	3.16951			0.339807
$88$		0			0
$89$	−10.1852			−1.07963			−0.539816	−	0.841783i	$-0.681506\pi$
$89$	−10.1852			−1.07963			−0.539816	+	0.841783i	$0.681506\pi$
$90$	−4.37603	+	3.17937i	−0.461274	+	0.335135i
$91$	0.210471	+	0.647764i	0.0220634	+	0.0679041i
$92$	−7.59162	+	23.3646i	−0.791481	+	2.43593i
$93$	−4.43383	−	3.22136i	−0.459766	−	0.334040i
$94$	0.833774	+	0.605772i	0.0859972	+	0.0624806i
$95$	−0.976324	+	3.00482i	−0.100169	+	0.308288i
$96$	1.51530	+	4.66362i	0.154655	+	0.475978i
$97$	1.48446	−	1.07852i	0.150724	−	0.109507i	−0.509867	−	0.860253i	$-0.670306\pi$
$97$	1.48446	−	1.07852i	0.150724	−	0.109507i	0.660591	+	0.750746i	$0.270306\pi$
$98$	15.7713			1.59314
$99$		0			0
$100$	3.09855			0.309855
$101$	0.993224	−	0.721619i	0.0988295	−	0.0718038i	−0.537273	−	0.843408i	$-0.680546\pi$
$101$	0.993224	−	0.721619i	0.0988295	−	0.0718038i	0.636103	+	0.771605i	$0.280546\pi$
$102$	0.281821	+	0.867355i	0.0279044	+	0.0858809i
$103$	−0.728624	+	2.24247i	−0.0717935	+	0.220958i	−0.980515	−	0.196446i	$-0.937060\pi$
$103$	−0.728624	+	2.24247i	−0.0717935	+	0.220958i	0.908721	+	0.417404i	$0.137060\pi$
$104$	−11.0254	−	8.01039i	−1.08113	−	0.785483i
$105$	0.0779769	+	0.0566535i	0.00760977	+	0.00552882i
$106$	−0.0247566	+	0.0761931i	−0.00240458	+	0.00740053i
$107$	−1.78668	−	5.49882i	−0.172725	−	0.531591i	0.826798	−	0.562499i	$-0.190160\pi$
$107$	−1.78668	−	5.49882i	−0.172725	−	0.531591i	−0.999522	+	0.0309080i	$0.990160\pi$
$108$	10.5158	−	7.64014i	1.01188	−	0.735173i
$109$	−4.21902			−0.404109			−0.202054	−	0.979374i	$-0.564762\pi$
$109$	−4.21902			−0.404109			−0.202054	+	0.979374i	$0.564762\pi$
$110$		0			0
$111$	−6.83217			−0.648481
$112$	−0.0597858	+	0.0434369i	−0.00564923	+	0.00410440i
$113$	4.67192	+	14.3787i	0.439497	+	1.35263i	0.888407	+	0.459057i	$0.151813\pi$
$113$	4.67192	+	14.3787i	0.439497	+	1.35263i	−0.448909	+	0.893577i	$0.648187\pi$
$114$	1.71399	−	5.27512i	0.160530	−	0.494061i
$115$	6.41434	+	4.66029i	0.598140	+	0.434574i
$116$	−10.2192	−	7.42466i	−0.948826	−	0.689362i
$117$	4.06701	−	12.5170i	0.375995	−	1.15720i
$118$	3.82013	+	11.7571i	0.351671	+	1.08233i
$119$	−0.0521015	+	0.0378540i	−0.00477614	+	0.00347007i
$120$	−1.92856			−0.176053
$121$		0			0
$122$	17.3617			1.57186
$123$	−4.74986	+	3.45098i	−0.428281	+	0.311164i
$124$	6.74947	+	20.7727i	0.606120	+	1.86545i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	0.542497	+	0.394147i	0.0483294	+	0.0351134i
$127$	−8.66448	−	6.29511i	−0.768848	−	0.558601i	0.132763	−	0.991148i	$-0.457615\pi$
$127$	−8.66448	−	6.29511i	−0.768848	−	0.558601i	−0.901611	+	0.432547i	$0.857615\pi$
$128$	5.20712	−	16.0259i	0.460249	−	1.41650i
$129$	−0.822421	−	2.53115i	−0.0724101	−	0.222855i
$130$	−10.0363	+	7.29181i	−0.880244	+	0.639534i
$131$	−6.56014			−0.573163			−0.286581	−	0.958056i	$-0.592519\pi$
$131$	−6.56014			−0.573163			−0.286581	+	0.958056i	$0.592519\pi$
$132$		0			0
$133$	0.391677			0.0339627
$134$	−4.63616	+	3.36837i	−0.400503	+	0.290983i
$135$	−1.29630	−	3.98962i	−0.111568	−	0.343371i
$136$	0.398198	−	1.22553i	0.0341452	−	0.105088i
$137$	−6.77574	−	4.92286i	−0.578890	−	0.420588i	0.259434	−	0.965761i	$-0.416464\pi$
$137$	−6.77574	−	4.92286i	−0.578890	−	0.420588i	−0.838324	+	0.545173i	$0.816464\pi$
$138$	−11.2607	−	8.18140i	−0.958577	−	0.696447i
$139$	4.94656	−	15.2240i	0.419562	−	1.29128i	−0.488544	−	0.872539i	$-0.662472\pi$
$139$	4.94656	−	15.2240i	0.419562	−	1.29128i	0.908106	−	0.418740i	$-0.137528\pi$
$140$	−0.118702	−	0.365326i	−0.0100321	−	0.0308757i
$141$	−0.287089	+	0.208582i	−0.0241773	+	0.0175658i
$142$	−27.7129			−2.32561
$143$		0			0
$144$	1.42798			0.118999
$145$	−3.29805	+	2.39618i	−0.273888	+	0.198992i
$146$	5.94572	+	18.2991i	0.492072	+	1.51444i
$147$	−1.67810	+	5.16466i	−0.138407	+	0.425974i
$148$	22.0284	+	16.0046i	1.81072	+	1.31557i
$149$	−11.2352	−	8.16282i	−0.920420	−	0.668724i	0.0232084	−	0.999731i	$-0.492612\pi$
$149$	−11.2352	−	8.16282i	−0.920420	−	0.668724i	−0.943629	+	0.331006i	$0.892612\pi$
$150$	−0.542497	+	1.66963i	−0.0442947	+	0.136325i
$151$	−2.54927	−	7.84586i	−0.207457	−	0.638487i	−0.999604	−	0.0281558i	$-0.991037\pi$
$151$	−2.54927	−	7.84586i	−0.207457	−	0.638487i	0.792147	−	0.610331i	$-0.208963\pi$
$152$	−6.34031	+	4.60650i	−0.514267	+	0.373637i
$153$	1.24444			0.100607
$154$		0			0
$155$	7.04903			0.566192
$156$	10.7078	−	7.77968i	0.857311	−	0.622873i
$157$	3.17827	+	9.78171i	0.253654	+	0.780666i	0.994092	+	0.108541i	$0.0346180\pi$
$157$	3.17827	+	9.78171i	0.253654	+	0.780666i	−0.740438	+	0.672124i	$0.765382\pi$
$158$	4.37754	−	13.4727i	0.348258	−	1.07183i
$159$	−0.0223170	−	0.0162142i	−0.00176985	−	0.00128587i
$160$	−5.10249	−	3.70718i	−0.403388	−	0.293078i
$161$	0.303734	−	0.934797i	0.0239376	−	0.0736723i
$162$	−2.73875	−	8.42900i	−0.215176	−	0.662245i
$163$	1.68962	−	1.22758i	0.132342	−	0.0961518i	−0.519645	−	0.854382i	$-0.673936\pi$
$163$	1.68962	−	1.22758i	0.132342	−	0.0961518i	0.651987	+	0.758230i	$0.273936\pi$
$164$	23.3986			1.82712
$165$		0			0
$166$	1.41443			0.109781
$167$	13.4524	−	9.77375i	1.04098	−	0.756315i	0.0705022	−	0.997512i	$-0.477540\pi$
$167$	13.4524	−	9.77375i	1.04098	−	0.756315i	0.970476	+	0.241196i	$0.0775398\pi$
$168$	0.0738809	+	0.227382i	0.00570003	+	0.0175429i
$169$	5.31038	−	16.3437i	0.408490	−	1.25720i
$170$	−0.948979	−	0.689474i	−0.0727834	−	0.0528802i
$171$	−6.12306	−	4.44866i	−0.468242	−	0.340198i
$172$	−3.27763	+	10.0875i	−0.249917	+	0.769166i
$173$	5.97157	+	18.3786i	0.454010	+	1.39730i	0.872293	+	0.488983i	$0.162632\pi$
$173$	5.97157	+	18.3786i	0.454010	+	1.39730i	−0.418283	+	0.908317i	$0.637368\pi$
$174$	5.78992	−	4.20662i	0.438933	−	0.318903i
$175$	−0.123970			−0.00937126
$176$		0			0
$177$	−4.25661			−0.319947
$178$	−18.6059	+	13.5180i	−1.39457	+	1.01322i
$179$	−0.896450	−	2.75899i	−0.0670038	−	0.206217i	0.911949	−	0.410304i	$-0.134577\pi$
$179$	−0.896450	−	2.75899i	−0.0670038	−	0.206217i	−0.978953	+	0.204087i	$0.934577\pi$
$180$	−2.29372	+	7.05933i	−0.170964	+	0.526172i
$181$	−8.10396	−	5.88787i	−0.602363	−	0.437642i	0.244354	−	0.969686i	$-0.421424\pi$
$181$	−8.10396	−	5.88787i	−0.602363	−	0.437642i	−0.846717	+	0.532044i	$0.821424\pi$
$182$	1.24420	+	0.903967i	0.0922265	+	0.0670065i
$183$	−1.84733	+	5.68548i	−0.136558	+	0.420283i
$184$	6.07740	+	18.7043i	0.448032	+	1.37890i
$185$	7.10927	−	5.16519i	0.522684	−	0.379752i
$186$	−12.3750			−0.907377
$187$		0			0
$188$	1.41425			0.103145
$189$	−0.420726	+	0.305675i	−0.0306033	+	0.0222346i
$190$	2.20454	+	6.78486i	0.159934	+	0.492226i
$191$	−4.19165	+	12.9006i	−0.303297	+	0.933453i	0.677010	+	0.735974i	$0.263275\pi$
$191$	−4.19165	+	12.9006i	−0.303297	+	0.933453i	−0.980307	+	0.197479i	$0.936725\pi$
$192$	8.20781	+	5.96333i	0.592348	+	0.430366i
$193$	11.0775	+	8.04824i	0.797373	+	0.579325i	0.910142	−	0.414296i	$-0.135972\pi$
$193$	11.0775	+	8.04824i	0.797373	+	0.579325i	−0.112769	+	0.993621i	$0.535972\pi$
$194$	1.28031	−	3.94040i	0.0919211	−	0.282904i
$195$	−1.31998	−	4.06248i	−0.0945258	−	0.290921i
$196$	17.5089	−	12.7210i	1.25064	−	0.908640i
$197$	−2.59965			−0.185217			−0.0926087	−	0.995703i	$-0.529521\pi$
$197$	−2.59965			−0.185217			−0.0926087	+	0.995703i	$0.529521\pi$
$198$		0			0
$199$	17.6907			1.25406			0.627029	−	0.778996i	$-0.284271\pi$
$199$	17.6907			1.25406			0.627029	+	0.778996i	$0.284271\pi$
$200$	2.00678	−	1.45801i	0.141900	−	0.103097i
$201$	−0.609750	−	1.87662i	−0.0430085	−	0.132366i
$202$	0.856633	−	2.63645i	0.0602725	−	0.185500i
$203$	0.408860	+	0.297054i	0.0286963	+	0.0208491i
$204$	1.01247	+	0.735604i	0.0708872	+	0.0515026i
$205$	2.33353	−	7.18188i	0.162981	−	0.501604i
$206$	1.64523	+	5.06350i	0.114629	+	0.352791i
$207$	−15.3657	+	11.1638i	−1.06799	+	0.775938i
$208$	3.27504			0.227083
$209$		0			0
$210$	0.217636			0.0150183
$211$	14.8600	−	10.7964i	1.02300	−	0.743255i	0.0561063	−	0.998425i	$-0.482131\pi$
$211$	14.8600	−	10.7964i	1.02300	−	0.743255i	0.966896	+	0.255170i	$0.0821314\pi$
$212$	0.0339724	+	0.104556i	0.00233323	+	0.00718096i
$213$	2.94871	−	9.07521i	0.202043	−	0.621823i
$214$	−10.5620	−	7.67371i	−0.722000	−	0.524564i
$215$	2.76935	+	2.01205i	0.188868	+	0.137221i
$216$	3.21550	−	9.89629i	0.218787	−	0.673357i
$217$	−0.270040	−	0.831099i	−0.0183315	−	0.0564187i
$218$	−7.70712	+	5.59955i	−0.521992	+	0.379250i
$219$	−6.62507			−0.447681
$220$		0			0
$221$	2.85410			0.191988
$222$	−12.4807	+	9.06778i	−0.837651	+	0.608589i
$223$	0.596106	+	1.83463i	0.0399182	+	0.122856i	0.969030	−	0.246944i	$-0.0794264\pi$
$223$	0.596106	+	1.83463i	0.0399182	+	0.122856i	−0.929112	+	0.369800i	$0.879426\pi$
$224$	−0.241615	+	0.743615i	−0.0161436	+	0.0496848i
$225$	1.93801	+	1.40805i	0.129201	+	0.0938700i
$226$	27.6181	+	20.0657i	1.83713	+	1.33475i
$227$	−9.08098	+	27.9484i	−0.602726	+	1.85500i	−0.0909982	+	0.995851i	$0.529006\pi$
$227$	−9.08098	+	27.9484i	−0.602726	+	1.85500i	−0.511728	+	0.859148i	$0.670994\pi$
$228$	−2.35203	−	7.23881i	−0.155767	−	0.479402i
$229$	15.8825	−	11.5393i	1.04955	−	0.762540i	0.0774207	−	0.996999i	$-0.475332\pi$
$229$	15.8825	−	11.5393i	1.04955	−	0.762540i	0.972126	+	0.234458i	$0.0753315\pi$
$230$	17.9027			1.18047
$231$		0			0
$232$	−10.1121			−0.663892
$233$	4.10029	−	2.97904i	0.268619	−	0.195163i	−0.445319	−	0.895372i	$-0.646910\pi$
$233$	4.10029	−	2.97904i	0.268619	−	0.195163i	0.713938	+	0.700209i	$0.246910\pi$
$234$	−9.18330	−	28.2633i	−0.600331	−	1.84763i
$235$	0.141042	−	0.434084i	0.00920059	−	0.0283165i
$236$	13.7242	+	9.97124i	0.893372	+	0.649072i
$237$	3.94615	+	2.86705i	0.256330	+	0.186235i
$238$	−0.0449364	+	0.138300i	−0.00291279	+	0.00896466i
$239$	−6.95383	−	21.4017i	−0.449806	−	1.38436i	−0.877126	−	0.480260i	$-0.840542\pi$
$239$	−6.95383	−	21.4017i	−0.449806	−	1.38436i	0.427320	−	0.904101i	$-0.359458\pi$
$240$	0.374949	−	0.272417i	0.0242029	−	0.0175844i
$241$	27.6924			1.78382			0.891911	−	0.452212i	$-0.149365\pi$
$241$	27.6924			1.78382			0.891911	+	0.452212i	$0.149365\pi$
$242$		0			0
$243$	15.6365			1.00308
$244$	19.2746	−	14.0038i	1.23393	−	0.896502i
$245$	−2.15837	−	6.64278i	−0.137893	−	0.424392i
$246$	−4.09665	+	12.6082i	−0.261193	+	0.803869i
$247$	−14.0431	−	10.2029i	−0.893541	−	0.649195i
$248$	14.1458	+	10.2775i	0.898261	+	0.652625i
$249$	−0.150499	+	0.463187i	−0.00953746	+	0.0293533i
$250$	−0.697759	−	2.14748i	−0.0441302	−	0.135819i
$251$	3.53485	−	2.56822i	0.223118	−	0.162105i	−0.470611	−	0.882341i	$-0.655967\pi$
$251$	3.53485	−	2.56822i	0.223118	−	0.162105i	0.693729	+	0.720236i	$0.255967\pi$
$252$	0.920183			0.0579661
$253$		0			0
$254$	−24.1829			−1.51737
$255$	0.326757	−	0.237403i	0.0204623	−	0.0148667i
$256$	−3.69292	−	11.3656i	−0.230807	−	0.710352i
$257$	5.58175	−	17.1789i	0.348180	−	1.07159i	−0.611679	−	0.791106i	$-0.709506\pi$
$257$	5.58175	−	17.1789i	0.348180	−	1.07159i	0.959859	−	0.280482i	$-0.0904944\pi$
$258$	−4.86175	−	3.53227i	−0.302679	−	0.219909i
$259$	−0.881337	−	0.640329i	−0.0547636	−	0.0397881i
$260$	−5.26058	+	16.1904i	−0.326248	+	1.00409i
$261$	−3.01774	−	9.28765i	−0.186793	−	0.574891i
$262$	−11.9838	+	8.70673i	−0.740361	+	0.537904i
$263$	−13.4340			−0.828377			−0.414188	−	0.910191i	$-0.635935\pi$
$263$	−13.4340			−0.828377			−0.414188	+	0.910191i	$0.635935\pi$
$264$		0			0
$265$	0.0354802			0.00217953
$266$	0.715499	−	0.519841i	0.0438701	−	0.0318735i
$267$	−2.44706	−	7.53127i	−0.149758	−	0.460906i
$268$	−2.43007	+	7.47898i	−0.148440	+	0.456851i
$269$	3.44479	+	2.50279i	0.210033	+	0.152598i	0.687828	−	0.725873i	$-0.258564\pi$
$269$	3.44479	+	2.50279i	0.210033	+	0.152598i	−0.477796	+	0.878471i	$0.658564\pi$
$270$	−7.66312	−	5.56758i	−0.466363	−	0.338832i
$271$	−3.90933	+	12.0317i	−0.237475	+	0.730873i	0.759308	+	0.650731i	$0.225537\pi$
$271$	−3.90933	+	12.0317i	−0.237475	+	0.730873i	−0.996783	+	0.0801423i	$0.974463\pi$
$272$	0.0956933	+	0.294514i	0.00580226	+	0.0178575i
$273$	−0.428410	+	0.311258i	−0.0259286	+	0.0188382i
$274$	−18.9113			−1.14248
$275$		0			0
$276$	−19.1005			−1.14971
$277$	−25.8701	+	18.7957i	−1.55438	+	1.12932i	−0.613948	+	0.789346i	$0.710420\pi$
$277$	−25.8701	+	18.7957i	−1.55438	+	1.12932i	−0.940433	+	0.339978i	$0.889580\pi$
$278$	−11.1693	−	34.3756i	−0.669891	−	2.06171i
$279$	−5.21809	+	16.0596i	−0.312399	+	0.961464i
$280$	−0.248780	−	0.180749i	−0.0148675	−	0.0108018i
$281$	−23.3667	−	16.9769i	−1.39394	−	1.01276i	−0.995420	−	0.0956009i	$-0.969523\pi$
$281$	−23.3667	−	16.9769i	−1.39394	−	1.01276i	−0.398523	−	0.917158i	$-0.630477\pi$
$282$	−0.247608	+	0.762059i	−0.0147448	+	0.0453799i
$283$	1.49944	+	4.61480i	0.0891324	+	0.274321i	0.985680	−	0.168626i	$-0.0539330\pi$
$283$	1.49944	+	4.61480i	0.0891324	+	0.274321i	−0.896548	+	0.442947i	$0.853933\pi$
$284$	−30.7662	+	22.3530i	−1.82564	+	1.32641i
$285$	−2.45642			−0.145506
$286$		0			0
$287$	−0.936157			−0.0552596
$288$	12.2231	−	8.88061i	0.720254	−	0.523295i
$289$	−5.16990	−	15.9113i	−0.304111	−	0.935959i
$290$	−2.84450	+	8.75446i	−0.167035	+	0.514080i
$291$	1.15414	+	0.838534i	0.0676571	+	0.0491558i
$292$	21.3607	+	15.5194i	1.25004	+	0.908206i
$293$	−1.23842	+	3.81145i	−0.0723490	+	0.222667i	−0.980692	−	0.195559i	$-0.937348\pi$
$293$	−1.23842	+	3.81145i	−0.0723490	+	0.222667i	0.908343	+	0.418226i	$0.137348\pi$
$294$	3.78914	+	11.6618i	0.220987	+	0.680128i
$295$	4.42925	−	3.21804i	0.257881	−	0.187361i
$296$	21.7976			1.26696
$297$		0			0
$298$	−31.3577			−1.81651
$299$	−35.2408	+	25.6039i	−2.03803	+	1.48071i
$300$	0.744444	+	2.29116i	0.0429805	+	0.132280i
$301$	0.131135	−	0.403593i	0.00755851	−	0.0232627i
$302$	−15.0701	−	10.9490i	−0.867184	−	0.630046i
$303$	0.772216	+	0.561048i	0.0443626	+	0.0322313i
$304$	0.581993	−	1.79119i	0.0333796	−	0.102732i
$305$	−2.37603	−	7.31267i	−0.136051	−	0.418722i
$306$	2.27330	−	1.65165i	0.129956	−	0.0944183i
$307$	−3.68515			−0.210323			−0.105161	−	0.994455i	$-0.533536\pi$
$307$	−3.68515			−0.210323			−0.105161	+	0.994455i	$0.533536\pi$
$308$		0			0
$309$	−1.83321			−0.104288
$310$	12.8769	−	9.35559i	0.731357	−	0.531362i
$311$	−3.08014	−	9.47969i	−0.174659	−	0.537544i	0.824959	−	0.565192i	$-0.191198\pi$
$311$	−3.08014	−	9.47969i	−0.174659	−	0.537544i	−0.999618	+	0.0276485i	$0.991198\pi$
$312$	3.27423	−	10.0770i	0.185367	−	0.570500i
$313$	−15.2590	−	11.0863i	−0.862492	−	0.626637i	0.0660696	−	0.997815i	$-0.478954\pi$
$313$	−15.2590	−	11.0863i	−0.862492	−	0.626637i	−0.928562	+	0.371178i	$0.878954\pi$
$314$	18.7884	+	13.6506i	1.06029	+	0.770346i
$315$	0.0917696	−	0.282438i	0.00517063	−	0.0159136i
$316$	−6.00710	−	18.4879i	−0.337926	−	1.04003i
$317$	−3.15069	+	2.28911i	−0.176960	+	0.128569i	−0.672739	−	0.739879i	$-0.734882\pi$
$317$	−3.15069	+	2.28911i	−0.176960	+	0.128569i	0.495779	+	0.868449i	$0.334882\pi$
$318$	−0.0622875			−0.00349291
$319$		0			0
$320$	−13.0490			−0.729463
$321$	3.63674	−	2.64225i	0.202983	−	0.147476i
$322$	−0.685830	−	2.11077i	−0.0382198	−	0.117629i
$323$	0.507189	−	1.56097i	0.0282207	−	0.0868545i
$324$	−9.83925	−	7.14864i	−0.546625	−	0.397146i
$325$	4.44479	+	3.22933i	0.246553	+	0.179131i
$326$	1.45726	−	4.48499i	0.0807103	−	0.248401i
$327$	−1.01364	−	3.11968i	−0.0560546	−	0.172518i
$328$	15.1541	−	11.0101i	0.836746	−	0.607932i
$329$	−0.0565828			−0.00311951
$330$		0			0
$331$	7.97626			0.438415			0.219207	−	0.975678i	$-0.429653\pi$
$331$	7.97626			0.438415			0.219207	+	0.975678i	$0.429653\pi$
$332$	1.57027	−	1.14087i	0.0861797	−	0.0626132i
$333$	6.50503	+	20.0204i	0.356473	+	1.09711i
$334$	11.6024	−	35.7085i	0.634855	−	1.95388i
$335$	2.05322	+	1.49175i	0.112179	+	0.0815031i
$336$	−0.0464825	−	0.0337715i	−0.00253583	−	0.00184239i
$337$	4.24351	−	13.0602i	0.231159	−	0.711434i	−0.766449	−	0.642305i	$-0.777978\pi$
$337$	4.24351	−	13.0602i	0.231159	−	0.711434i	0.997608	−	0.0691285i	$-0.0220218\pi$
$338$	−11.9908	−	36.9039i	−0.652214	−	2.00731i
$339$	−9.50960	+	6.90913i	−0.516491	+	0.375253i
$340$	−1.60966			−0.0872960
$341$		0			0
$342$	−17.0897			−0.924105
$343$	−1.40257	+	1.01903i	−0.0757318	+	0.0550224i
$344$	2.62388	+	8.07547i	0.141470	+	0.435400i
$345$	−1.90488	+	5.86263i	−0.102555	+	0.315633i
$346$	35.3010	+	25.6477i	1.89779	+	1.37883i
$347$	0.131827	+	0.0957777i	0.00707682	+	0.00514161i	0.591318	−	0.806438i	$-0.298608\pi$
$347$	0.131827	+	0.0957777i	0.00707682	+	0.00514161i	−0.584241	+	0.811580i	$0.698608\pi$
$348$	3.03481	−	9.34019i	0.162683	−	0.500687i
$349$	0.847154	+	2.60727i	0.0453471	+	0.139564i	0.971167	−	0.238402i	$-0.0766236\pi$
$349$	0.847154	+	2.60727i	0.0453471	+	0.139564i	−0.925819	+	0.377966i	$0.876624\pi$
$350$	−0.226463	+	0.164535i	−0.0121050	+	0.00879477i
$351$	23.0472			1.23017
$352$		0			0
$353$	−5.13584			−0.273353			−0.136677	−	0.990616i	$-0.543642\pi$
$353$	−5.13584			−0.273353			−0.136677	+	0.990616i	$0.543642\pi$
$354$	−7.77580	+	5.64945i	−0.413279	+	0.300265i
$355$	3.79264	+	11.6725i	0.201292	+	0.619514i
$356$	−9.75238	+	30.0147i	−0.516875	+	1.59078i
$357$	−0.0405081	−	0.0294309i	−0.00214392	−	0.00155765i
$358$	−5.29937	−	3.85022i	−0.280081	−	0.203490i
$359$	4.68965	−	14.4333i	0.247510	−	0.761758i	−0.747703	−	0.664033i	$-0.768843\pi$
$359$	4.68965	−	14.4333i	0.247510	−	0.761758i	0.995213	−	0.0977249i	$-0.0311565\pi$
$360$	1.83621	+	5.65128i	0.0967769	+	0.297849i
$361$	7.29561	−	5.30057i	0.383980	−	0.278978i
$362$	−22.6185			−1.18880
$363$		0			0
$364$	2.11042			0.110616
$365$	6.89377	−	5.00862i	0.360836	−	0.262163i
$366$	4.17125	+	12.8378i	0.218035	+	0.671043i
$367$	6.23112	−	19.1774i	0.325262	−	1.00105i	−0.646060	−	0.763286i	$-0.723585\pi$
$367$	6.23112	−	19.1774i	0.325262	−	1.00105i	0.971322	−	0.237767i	$-0.0764154\pi$
$368$	−3.82363	−	2.77803i	−0.199320	−	0.144815i
$369$	14.6349	+	10.6329i	0.761861	+	0.553524i
$370$	6.13159	−	18.8711i	0.318766	−	0.981061i
$371$	−0.00135921	−	0.00418321i	−7.05664e−5	−	0.000217181i
$372$	−13.7384	+	9.98154i	−0.712304	+	0.517519i
$373$	−11.2539			−0.582707			−0.291354	−	0.956615i	$-0.594106\pi$
$373$	−11.2539			−0.582707			−0.291354	+	0.956615i	$0.594106\pi$
$374$		0			0
$375$	0.777484			0.0401491
$376$	0.915938	−	0.665468i	0.0472359	−	0.0343189i
$377$	−6.92111	−	21.3010i	−0.356456	−	1.09706i
$378$	−0.362867	+	1.11679i	−0.0186638	+	0.0574414i
$379$	16.9507	+	12.3154i	0.870697	+	0.632598i	0.930774	−	0.365595i	$-0.119135\pi$
$379$	16.9507	+	12.3154i	0.870697	+	0.632598i	−0.0600770	+	0.998194i	$0.519135\pi$
$380$	7.92003	+	5.75424i	0.406289	+	0.295186i
$381$	2.57311	−	7.91923i	0.131825	−	0.405714i
$382$	9.46473	+	29.1294i	0.484258	+	1.49039i
$383$	−13.6164	+	9.89292i	−0.695767	+	0.505505i	−0.878551	−	0.477649i	$-0.841489\pi$
$383$	−13.6164	+	9.89292i	−0.695767	+	0.505505i	0.182784	+	0.983153i	$0.441489\pi$
$384$	13.1011			0.668562
$385$		0			0
$386$	30.9176			1.57366
$387$	−6.63403	+	4.81990i	−0.337226	+	0.245009i
$388$	−1.75692	−	5.40723i	−0.0891939	−	0.274511i
$389$	4.87103	−	14.9915i	0.246971	−	0.760098i	−0.748335	−	0.663321i	$-0.769147\pi$
$389$	4.87103	−	14.9915i	0.246971	−	0.760098i	0.995306	−	0.0967773i	$-0.0308535\pi$
$390$	−7.80308	−	5.66927i	−0.395124	−	0.287075i
$391$	−3.33217	−	2.42097i	−0.168515	−	0.122434i
$392$	5.35386	−	16.4775i	0.270411	−	0.832239i
$393$	−1.57611	−	4.85078i	−0.0795044	−	0.244689i
$394$	−4.74893	+	3.45030i	−0.239248	+	0.173824i
$395$	−6.27371			−0.315665
$396$		0			0
$397$	6.85466			0.344025			0.172013	−	0.985095i	$-0.444973\pi$
$397$	6.85466			0.344025			0.172013	+	0.985095i	$0.444973\pi$
$398$	32.3166	−	23.4794i	1.61988	−	1.17691i
$399$	0.0941028	+	0.289618i	0.00471103	+	0.0144991i
$400$	−0.184207	+	0.566931i	−0.00921034	+	0.0283465i
$401$	0.114149	+	0.0829338i	0.00570031	+	0.00414152i	0.590632	−	0.806941i	$-0.298879\pi$
$401$	0.114149	+	0.0829338i	0.00570031	+	0.00414152i	−0.584931	+	0.811083i	$0.698879\pi$
$402$	−3.60454	−	2.61885i	−0.179778	−	0.130617i
$403$	−11.9676	+	36.8324i	−0.596147	+	1.83475i
$404$	−1.17552	−	3.61788i	−0.0584843	−	0.179996i
$405$	−3.17544	+	2.30709i	−0.157789	+	0.114640i
$406$	1.14114			0.0566340
$407$		0			0
$408$	1.00186			0.0495996
$409$	23.2581	−	16.8980i	1.15004	−	0.835554i	0.161555	−	0.986864i	$-0.448349\pi$
$409$	23.2581	−	16.8980i	1.15004	−	0.835554i	0.988486	+	0.151310i	$0.0483492\pi$
$410$	−5.26911	−	16.2166i	−0.260223	−	0.800883i
$411$	2.01221	−	6.19294i	0.0992549	−	0.305475i
$412$	5.91067	+	4.29435i	0.291198	+	0.211568i
$413$	−0.549094	−	0.398940i	−0.0270192	−	0.0196306i
$414$	−13.2525	+	40.7871i	−0.651327	+	2.00458i
$415$	−0.193571	−	0.595751i	−0.00950204	−	0.0292443i
$416$	28.0334	−	20.3675i	1.37445	−	0.998598i
$417$	12.4455			0.609459
$418$		0			0
$419$	−11.0837			−0.541472			−0.270736	−	0.962654i	$-0.587267\pi$
$419$	−11.0837			−0.541472			−0.270736	+	0.962654i	$0.587267\pi$
$420$	0.241615	−	0.175544i	0.0117896	−	0.00856565i
$421$	−1.05169	−	3.23677i	−0.0512562	−	0.157750i	0.922152	−	0.386828i	$-0.126429\pi$
$421$	−1.05169	−	3.23677i	−0.0512562	−	0.157750i	−0.973408	+	0.229077i	$0.926429\pi$
$422$	12.8164	−	39.4448i	0.623892	−	1.92014i
$423$	0.884554	+	0.642666i	0.0430085	+	0.0312475i
$424$	0.0712008	+	0.0517304i	0.00345782	+	0.00251225i
$425$	−0.160531	+	0.494063i	−0.00778688	+	0.0239656i
$426$	−6.65819	−	20.4918i	−0.322590	−	0.992830i
$427$	−0.771159	+	0.560280i	−0.0373190	+	0.0271138i
$428$	−17.9152			−0.865963
$429$		0			0
$430$	7.72935			0.372743
$431$	−11.0615	+	8.03663i	−0.532812	+	0.387111i	−0.821409	−	0.570340i	$-0.806811\pi$
$431$	−11.0615	+	8.03663i	−0.532812	+	0.387111i	0.288597	+	0.957451i	$0.406811\pi$
$432$	0.772735	+	2.37823i	0.0371782	+	0.114423i
$433$	−4.77264	+	14.6887i	−0.229359	+	0.705893i	0.768461	+	0.639896i	$0.221023\pi$
$433$	−4.77264	+	14.6887i	−0.229359	+	0.705893i	−0.997820	+	0.0659968i	$0.978977\pi$
$434$	−1.59635	−	1.15981i	−0.0766271	−	0.0556728i
$435$	−2.56418	−	1.86299i	−0.122943	−	0.0893235i
$436$	−4.03972	+	12.4330i	−0.193468	+	0.595432i
$437$	7.74084	+	23.8239i	0.370295	+	1.13965i
$438$	−12.1024	+	8.79291i	−0.578275	+	0.420141i
$439$	−9.87042			−0.471089			−0.235545	−	0.971864i	$-0.575687\pi$
$439$	−9.87042			−0.471089			−0.235545	+	0.971864i	$0.575687\pi$
$440$		0			0
$441$	16.7318			0.796753
$442$	5.21375	−	3.78801i	0.247993	−	0.180177i
$443$	9.67223	+	29.7681i	0.459541	+	1.41432i	0.865720	+	0.500529i	$0.166861\pi$
$443$	9.67223	+	29.7681i	0.459541	+	1.41432i	−0.406178	+	0.913794i	$0.633139\pi$
$444$	−6.54183	+	20.1337i	−0.310461	+	0.955502i
$445$	8.24002	+	5.98672i	0.390614	+	0.283798i
$446$	3.52389	+	2.56025i	0.166861	+	0.121232i
$447$	3.33653	−	10.2688i	0.157813	−	0.485697i
$448$	0.499894	+	1.53851i	0.0236177	+	0.0726880i
$449$	10.2965	−	7.48086i	0.485923	−	0.353043i	−0.317692	−	0.948194i	$-0.602908\pi$
$449$	10.2965	−	7.48086i	0.485923	−	0.353043i	0.803614	+	0.595151i	$0.202908\pi$
$450$	5.40907			0.254986
$451$		0			0
$452$	46.8459			2.20344
$453$	5.18899	−	3.77003i	0.243800	−	0.177131i
$454$	20.5048	+	63.1073i	0.962338	+	2.96177i
$455$	0.210471	−	0.647764i	0.00986705	−	0.0303676i
$456$	−4.92949	−	3.58148i	−0.230845	−	0.167718i
$457$	−3.48813	−	2.53427i	−0.163168	−	0.118548i	0.503205	−	0.864167i	$-0.332154\pi$
$457$	−3.48813	−	2.53427i	−0.163168	−	0.118548i	−0.666373	+	0.745619i	$0.732154\pi$
$458$	13.6983	−	42.1591i	0.640081	−	1.96997i
$459$	0.673415	+	2.07256i	0.0314323	+	0.0967388i
$460$	19.8751	−	14.4401i	0.926682	−	0.673274i
$461$	17.7315			0.825837			0.412918	−	0.910768i	$-0.364509\pi$
$461$	17.7315			0.825837			0.412918	+	0.910768i	$0.364509\pi$
$462$		0			0
$463$	3.43092			0.159448			0.0797242	−	0.996817i	$-0.474596\pi$
$463$	3.43092			0.159448			0.0797242	+	0.996817i	$0.474596\pi$
$464$	1.96599	−	1.42837i	0.0912688	−	0.0663106i
$465$	1.69357	+	5.21228i	0.0785375	+	0.241714i
$466$	3.53641	−	10.8840i	0.163821	−	0.504190i
$467$	12.6515	+	9.19187i	0.585443	+	0.425349i	0.840682	−	0.541529i	$-0.182154\pi$
$467$	12.6515	+	9.19187i	0.585443	+	0.425349i	−0.255239	+	0.966878i	$0.582154\pi$
$468$	−32.9920	−	23.9701i	−1.52506	−	1.10802i
$469$	0.0972248	−	0.299227i	0.00448942	−	0.0138170i
$470$	−0.318473	−	0.980160i	−0.0146901	−	0.0452114i
$471$	−6.46931	+	4.70023i	−0.298090	+	0.216575i
$472$	13.5804			0.625090
$473$		0			0
$474$	11.0138			0.505883
$475$	2.55605	−	1.85708i	0.117280	−	0.0852086i
$476$	0.0616642	+	0.189783i	0.00282637	+	0.00869868i
$477$	−0.0262644	+	0.0808336i	−0.00120257	+	0.00370112i
$478$	−41.1077	−	29.8665i	−1.88022	−	1.36606i
$479$	−31.1531	−	22.6341i	−1.42342	−	1.03418i	−0.991195	−	0.132414i	$-0.957727\pi$
$479$	−31.1531	−	22.6341i	−1.42342	−	1.03418i	−0.432229	−	0.901764i	$-0.642273\pi$
$480$	1.51530	−	4.66362i	0.0691637	−	0.212864i
$481$	14.9191	+	45.9163i	0.680254	+	2.09361i
$482$	50.5872	−	36.7538i	2.30418	−	1.67409i
$483$	0.764192			0.0347720
$484$		0			0
$485$	−1.83489			−0.0833182
$486$	28.5640	−	20.7530i	1.29569	−	0.941374i
$487$	−2.78750	−	8.57905i	−0.126314	−	0.388754i	0.867824	−	0.496871i	$-0.165518\pi$
$487$	−2.78750	−	8.57905i	−0.126314	−	0.388754i	−0.994138	+	0.108117i	$0.965518\pi$
$488$	5.89377	−	18.1392i	0.266798	−	0.821121i
$489$	1.31366	+	0.954427i	0.0594056	+	0.0431607i
$490$	−12.7592	−	9.27012i	−0.576403	−	0.418781i
$491$	1.46186	−	4.49915i	0.0659730	−	0.203044i	−0.912636	−	0.408773i	$-0.865957\pi$
$491$	1.46186	−	4.49915i	0.0659730	−	0.203044i	0.978609	+	0.205729i	$0.0659567\pi$
$492$	5.62165	+	17.3016i	0.253443	+	0.780018i
$493$	1.71330	−	1.24479i	0.0771632	−	0.0560623i
$494$	−39.1948			−1.76346
$495$		0			0
$496$	−4.20197			−0.188674
$497$	1.23093	−	0.894323i	0.0552147	−	0.0401159i
$498$	0.339825	+	1.04587i	0.0152279	+	0.0468668i
$499$	0.353862	−	1.08907i	0.0158410	−	0.0487536i	−0.942824	−	0.333292i	$-0.891840\pi$
$499$	0.353862	−	1.08907i	0.0158410	−	0.0487536i	0.958665	+	0.284539i	$0.0918404\pi$
$500$	−2.50678	−	1.82128i	−0.112106	−	0.0814501i
$501$	10.4590	+	7.59893i	0.467275	+	0.339495i
$502$	3.04873	−	9.38303i	0.136071	−	0.418785i
$503$	−5.14255	−	15.8271i	−0.229295	−	0.705697i	−0.997827	−	0.0658862i	$-0.979013\pi$
$503$	−5.14255	−	15.8271i	−0.229295	−	0.705697i	0.768532	−	0.639811i	$-0.220987\pi$
$504$	0.595957	−	0.432988i	0.0265461	−	0.0192868i
$505$	−1.22769			−0.0546316
$506$		0			0
$507$	13.3609			0.593377
$508$	−26.8473	+	19.5057i	−1.19116	+	0.865425i
$509$	−9.14004	−	28.1302i	−0.405125	−	1.24685i	−0.920791	−	0.390057i	$-0.872455\pi$
$509$	−9.14004	−	28.1302i	−0.405125	−	1.24685i	0.515665	−	0.856790i	$-0.327545\pi$
$510$	0.281821	−	0.867355i	0.0124792	−	0.0384071i
$511$	−0.854621	−	0.620919i	−0.0378062	−	0.0274678i
$512$	5.43413	+	3.94813i	0.240157	+	0.174484i
$513$	4.09561	−	12.6050i	0.180826	−	0.556524i
$514$	−12.6036	−	38.7898i	−0.555920	−	1.71095i
$515$	1.90756	−	1.38593i	0.0840573	−	0.0610712i
$516$	−8.24650			−0.363032
$517$		0			0
$518$	−2.45984			−0.108079
$519$	−12.1550	+	8.83114i	−0.533546	+	0.387644i
$520$	4.21131	+	12.9611i	0.184678	+	0.568381i
$521$	−2.04435	+	6.29187i	−0.0895647	+	0.275652i	−0.985799	−	0.167929i	$-0.946292\pi$
$521$	−2.04435	+	6.29187i	−0.0895647	+	0.275652i	0.896234	+	0.443581i	$0.146292\pi$
$522$	−17.8394	−	12.9611i	−0.780809	−	0.567291i
$523$	29.3457	+	21.3209i	1.28320	+	0.932298i	0.999645	−	0.0266578i	$-0.00848644\pi$
$523$	29.3457	+	21.3209i	1.28320	+	0.932298i	0.283554	+	0.958956i	$0.408486\pi$
$524$	−6.28136	+	19.3320i	−0.274402	+	0.844524i
$525$	−0.0297845	−	0.0916674i	−0.00129990	−	0.00400069i
$526$	−24.5407	+	17.8298i	−1.07002	+	0.777418i
$527$	−3.66189			−0.159514
$528$		0			0
$529$	39.8620			1.73313
$530$	0.0648137	−	0.0470899i	0.00281533	−	0.00204545i
$531$	4.05279	+	12.4732i	0.175876	+	0.541291i
$532$	0.375032	−	1.15423i	0.0162597	−	0.0500422i
$533$	33.5647	+	24.3862i	1.45385	+	1.05628i
$534$	−14.4658	−	10.5100i	−0.625997	−	0.454813i
$535$	−1.78668	+	5.49882i	−0.0772448	+	0.237735i
$536$	1.94537	+	5.98722i	0.0840271	+	0.258609i
$537$	1.82471	−	1.32573i	0.0787419	−	0.0572093i
$538$	9.61454			0.414512
$539$		0			0
$540$	−12.9982			−0.559353
$541$	−7.20348	+	5.23363i	−0.309702	+	0.225011i	−0.731769	−	0.681553i	$-0.761305\pi$
$541$	−7.20348	+	5.23363i	−0.309702	+	0.225011i	0.422067	+	0.906565i	$0.361305\pi$
$542$	8.82726	+	27.1675i	0.379163	+	1.16694i
$543$	2.40665	−	7.40692i	0.103279	−	0.317861i
$544$	2.65069	+	1.92584i	0.113647	+	0.0825695i
$545$	3.41326	+	2.47988i	0.146208	+	0.106226i
$546$	−0.369494	+	1.13719i	−0.0158129	+	0.0486671i
$547$	−5.27213	−	16.2260i	−0.225420	−	0.693772i	−0.998249	−	0.0591570i	$-0.981159\pi$
$547$	−5.27213	−	16.2260i	−0.225420	−	0.693772i	0.772829	−	0.634615i	$-0.218841\pi$
$548$	−20.9949	+	15.2537i	−0.896859	+	0.651606i
$549$	18.4191			0.786109
$550$		0			0
$551$	−12.8799			−0.548701
$552$	−12.3704	+	8.98764i	−0.526520	+	0.382539i
$553$	0.240339	+	0.739686i	0.0102202	+	0.0314547i
$554$	−22.3124	+	68.6704i	−0.947961	+	2.91752i
$555$	5.52734	+	4.01585i	0.234623	+	0.170463i
$556$	−40.1270	−	29.1540i	−1.70176	−	1.23640i
$557$	8.99070	−	27.6705i	0.380948	−	1.17244i	−0.558429	−	0.829552i	$-0.688596\pi$
$557$	8.99070	−	27.6705i	0.380948	−	1.17244i	0.939377	−	0.342886i	$-0.111404\pi$
$558$	11.7824	+	36.2626i	0.498790	+	1.53512i
$559$	−15.2150	+	11.0543i	−0.643525	+	0.467548i
$560$	0.0738993			0.00312282
$561$		0			0
$562$	−65.2174			−2.75103
$563$	−8.94717	+	6.50050i	−0.377078	+	0.273963i	−0.760140	−	0.649759i	$-0.774870\pi$
$563$	−8.94717	+	6.50050i	−0.377078	+	0.273963i	0.383062	+	0.923723i	$0.374870\pi$
$564$	0.339781	+	1.04574i	0.0143074	+	0.0440335i
$565$	4.67192	−	14.3787i	0.196549	−	0.604916i
$566$	8.86395	+	6.44003i	0.372579	+	0.270695i
$567$	0.393660	+	0.286011i	0.0165322	+	0.0120113i
$568$	−9.40768	+	28.9539i	−0.394737	+	1.21488i
$569$	0.964015	+	2.96693i	0.0404136	+	0.124380i	0.969228	−	0.246165i	$-0.0791707\pi$
$569$	0.964015	+	2.96693i	0.0404136	+	0.124380i	−0.928814	+	0.370546i	$0.879171\pi$
$570$	−4.48729	+	3.26021i	−0.187952	+	0.136555i
$571$	−9.68683			−0.405381			−0.202691	−	0.979243i	$-0.564969\pi$
$571$	−9.68683			−0.405381			−0.202691	+	0.979243i	$0.564969\pi$
$572$		0			0
$573$	−10.5462			−0.440572
$574$	−1.71013	+	1.24248i	−0.0713795	+	0.0518602i
$575$	−2.45006	−	7.54051i	−0.102175	−	0.314461i
$576$	9.65962	−	29.7293i	0.402484	−	1.23872i
$577$	−2.44766	−	1.77833i	−0.101897	−	0.0740328i	0.535670	−	0.844428i	$-0.320059\pi$
$577$	−2.44766	−	1.77833i	−0.101897	−	0.0740328i	−0.637567	+	0.770395i	$0.720059\pi$
$578$	−30.5619	−	22.2045i	−1.27121	−	0.923586i
$579$	−3.28970	+	10.1247i	−0.136715	+	0.420766i
$580$	3.90337	+	12.0134i	0.162079	+	0.498827i
$581$	−0.0628251	+	0.0456451i	−0.00260642	+	0.00189368i
$582$	3.22126			0.133525
$583$		0			0
$584$	21.1369			0.874649
$585$	−10.6476	+	7.73592i	−0.440223	+	0.319841i
$586$	2.79634	+	8.60624i	0.115516	+	0.355521i
$587$	−13.6061	+	41.8753i	−0.561584	+	1.72838i	0.116307	+	0.993213i	$0.462894\pi$
$587$	−13.6061	+	41.8753i	−0.561584	+	1.72838i	−0.677890	+	0.735163i	$0.737106\pi$
$588$	13.6129	+	9.89035i	0.561387	+	0.407871i
$589$	18.0177	+	13.0906i	0.742405	+	0.539389i
$590$	3.82013	−	11.7571i	0.157272	−	0.484034i
$591$	−0.624581	−	1.92226i	−0.0256918	−	0.0790713i
$592$	−4.23788	+	3.07900i	−0.174176	+	0.126546i
$593$	6.60880			0.271391			0.135696	−	0.990751i	$-0.456673\pi$
$593$	6.60880			0.271391			0.135696	+	0.990751i	$0.456673\pi$
$594$		0			0
$595$	0.0644010			0.00264018
$596$	−34.8127	+	25.2929i	−1.42598	+	1.03604i
$597$	4.25029	+	13.0810i	0.173953	+	0.535371i
$598$	−30.3944	+	93.5443i	−1.24292	+	3.82531i
$599$	22.8211	+	16.5805i	0.932447	+	0.677462i	0.946591	−	0.322438i	$-0.104502\pi$
$599$	22.8211	+	16.5805i	0.932447	+	0.677462i	−0.0141440	+	0.999900i	$0.504502\pi$
$600$	1.56024	+	1.13358i	0.0636964	+	0.0462781i
$601$	−1.29088	+	3.97292i	−0.0526560	+	0.162059i	−0.973926	−	0.226864i	$-0.927153\pi$
$601$	−1.29088	+	3.97292i	−0.0526560	+	0.162059i	0.921270	+	0.388923i	$0.127153\pi$
$602$	−0.296103	−	0.911310i	−0.0120682	−	0.0371422i
$603$	−4.91853	+	3.57352i	−0.200298	+	0.145525i
$604$	−25.5618			−1.04010
$605$		0			0
$606$	2.15528			0.0875524
$607$	11.0657	−	8.03970i	0.449143	−	0.326321i	−0.340115	−	0.940384i	$-0.610466\pi$
$607$	11.0657	−	8.03970i	0.449143	−	0.326321i	0.789257	+	0.614063i	$0.210466\pi$
$608$	−6.15770	−	18.9515i	−0.249728	−	0.768583i
$609$	−0.121420	+	0.373693i	−0.00492019	+	0.0151428i
$610$	−14.0459	−	10.2050i	−0.568703	−	0.413187i
$611$	2.02870	+	1.47394i	0.0820726	+	0.0596292i
$612$	1.19156	−	3.66724i	0.0481659	−	0.148239i
$613$	10.0157	+	30.8253i	0.404532	+	1.24502i	0.921286	+	0.388887i	$0.127140\pi$
$613$	10.0157	+	30.8253i	0.404532	+	1.24502i	−0.516754	+	0.856134i	$0.672860\pi$
$614$	−6.73188	+	4.89100i	−0.271677	+	0.197385i
$615$	5.87115			0.236748
$616$		0			0
$617$	−37.0480			−1.49150			−0.745749	−	0.666227i	$-0.767908\pi$
$617$	−37.0480			−1.49150			−0.745749	+	0.666227i	$0.767908\pi$
$618$	−3.34883	+	2.43307i	−0.134710	+	0.0978724i
$619$	6.13285	+	18.8750i	0.246500	+	0.758650i	0.995386	+	0.0959506i	$0.0305891\pi$
$619$	6.13285	+	18.8750i	0.246500	+	0.758650i	−0.748886	+	0.662699i	$0.769411\pi$
$620$	6.74947	−	20.7727i	0.271065	−	0.834253i
$621$	−26.9077	−	19.5496i	−1.07977	−	0.784498i
$622$	−18.2083	−	13.2291i	−0.730085	−	0.530438i
$623$	0.390184	−	1.20086i	0.0156324	−	0.0481116i
$624$	0.786849	+	2.42167i	0.0314992	+	0.0969444i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	−42.5886			−1.70218
$627$		0			0
$628$	31.8689			1.27171
$629$	−3.69318	+	2.68325i	−0.147257	+	0.106988i
$630$	−0.207215	−	0.637743i	−0.00825566	−	0.0254083i
$631$	−14.4820	+	44.5711i	−0.576520	+	1.77435i	0.0544238	+	0.998518i	$0.482668\pi$
$631$	−14.4820	+	44.5711i	−0.576520	+	1.77435i	−0.630944	+	0.775828i	$0.717332\pi$
$632$	−12.5899	−	9.14712i	−0.500801	−	0.363853i
$633$	11.5534	+	8.39403i	0.459206	+	0.333633i
$634$	−2.71740	+	8.36328i	−0.107922	+	0.332148i
$635$	3.30954	+	10.1857i	0.131335	+	0.404207i
$636$	−0.0691502	+	0.0502405i	−0.00274198	+	0.00199217i
$637$	38.3740			1.52043
$638$		0			0
$639$	−29.4007			−1.16308
$640$	−13.6324	+	9.90454i	−0.538869	+	0.391511i
$641$	−4.60033	−	14.1584i	−0.181702	−	0.559222i	0.818174	−	0.574971i	$-0.194987\pi$
$641$	−4.60033	−	14.1584i	−0.181702	−	0.559222i	−0.999876	+	0.0157492i	$0.994987\pi$
$642$	3.13661	−	9.65350i	0.123792	−	0.380993i
$643$	26.7499	+	19.4350i	1.05491	+	0.766440i	0.973141	−	0.230211i	$-0.0739415\pi$
$643$	26.7499	+	19.4350i	1.05491	+	0.766440i	0.0817738	+	0.996651i	$0.473941\pi$
$644$	−2.46392	−	1.79014i	−0.0970921	−	0.0705415i
$645$	−0.822421	+	2.53115i	−0.0323828	+	0.0996640i
$646$	−1.14523	−	3.52466i	−0.0450585	−	0.138676i
$647$	35.4920	−	25.7865i	1.39534	−	1.01377i	0.400080	−	0.916480i	$-0.368982\pi$
$647$	35.4920	−	25.7865i	1.39534	−	1.01377i	0.995256	−	0.0972911i	$-0.0310178\pi$
$648$	−9.73616			−0.382473
$649$		0			0
$650$	12.4056			0.486587
$651$	0.549662	−	0.399353i	0.0215429	−	0.0156519i
$652$	−1.99974	−	6.15455i	−0.0783157	−	0.241031i
$653$	10.5463	−	32.4581i	0.412708	−	1.27018i	−0.501578	−	0.865112i	$-0.667247\pi$
$653$	10.5463	−	32.4581i	0.412708	−	1.27018i	0.914285	−	0.405071i	$-0.132753\pi$
$654$	−5.99217	−	4.35356i	−0.234312	−	0.170238i
$655$	5.30727	+	3.85596i	0.207372	+	0.150665i
$656$	−1.39103	+	4.28116i	−0.0543107	+	0.167151i
$657$	6.30784	+	19.4135i	0.246092	+	0.757395i
$658$	−0.103363	+	0.0750976i	−0.00402951	+	0.00292761i
$659$	−10.4408			−0.406716			−0.203358	−	0.979104i	$-0.565185\pi$
$659$	−10.4408			−0.406716			−0.203358	+	0.979104i	$0.565185\pi$
$660$		0			0
$661$	−45.6827			−1.77685			−0.888426	−	0.459020i	$-0.848201\pi$
$661$	−45.6827			−1.77685			−0.888426	+	0.459020i	$0.848201\pi$
$662$	14.5707	−	10.5862i	0.566306	−	0.411445i
$663$	0.685715	+	2.11041i	0.0266310	+	0.0819616i
$664$	0.480156	−	1.47777i	0.0186337	−	0.0573485i
$665$	−0.316874	−	0.230222i	−0.0122878	−	0.00892763i
$666$	38.4545	+	27.9389i	1.49008	+	1.08261i
$667$	−9.98796	+	30.7398i	−0.386735	+	1.19025i
$668$	−15.9215	−	49.0012i	−0.616019	−	1.89591i
$669$	−1.21336	+	0.881559i	−0.0469113	+	0.0340830i
$670$	5.73061			0.221393
$671$		0			0
$672$	−0.607902			−0.0234503
$673$	−23.5545	+	17.1134i	−0.907960	+	0.659671i	−0.940498	−	0.339799i	$-0.889641\pi$
$673$	−23.5545	+	17.1134i	−0.907960	+	0.659671i	0.0325383	+	0.999470i	$0.489641\pi$
$674$	−9.58183	−	29.4898i	−0.369078	−	1.13591i
$675$	−1.29630	+	3.98962i	−0.0498948	+	0.153560i
$676$	−43.0783	−	31.2982i	−1.65686	−	1.20378i
$677$	−26.0787	−	18.9473i	−1.00229	−	0.728205i	−0.0397102	−	0.999211i	$-0.512643\pi$
$677$	−26.0787	−	18.9473i	−1.00229	−	0.728205i	−0.962577	+	0.271007i	$0.912643\pi$
$678$	−8.20182	+	25.2426i	−0.314989	+	0.969437i
$679$	0.0702926	+	0.216338i	0.00269758	+	0.00830231i
$680$	−1.04250	+	0.757418i	−0.0399779	+	0.0290457i
$681$	−22.8477			−0.875524
$682$		0			0
$683$	−11.0364			−0.422295			−0.211148	−	0.977454i	$-0.567720\pi$
$683$	−11.0364			−0.422295			−0.211148	+	0.977454i	$0.567720\pi$
$684$	−18.9726	+	13.7844i	−0.725435	+	0.527059i
$685$	2.58810	+	7.96536i	0.0988863	+	0.304341i
$686$	−1.20969	+	3.72304i	−0.0461861	+	0.142146i
$687$	12.3484	+	8.97165i	0.471121	+	0.342290i
$688$	−1.65083	−	1.19939i	−0.0629371	−	0.0457265i
$689$	−0.0602368	+	0.185390i	−0.00229484	+	0.00706279i
$690$	4.30122	+	13.2378i	0.163745	+	0.503954i
$691$	−29.2549	+	21.2549i	−1.11291	+	0.808576i	−0.983119	−	0.182966i	$-0.941430\pi$
$691$	−29.2549	+	21.2549i	−1.11291	+	0.808576i	−0.129790	+	0.991542i	$0.541430\pi$
$692$	59.8776			2.27620
$693$		0			0
$694$	0.367933			0.0139665
$695$	−12.9503	+	9.40892i	−0.491232	+	0.356901i
$696$	−2.42949	−	7.47720i	−0.0920896	−	0.283423i
$697$	−1.21224	+	3.73090i	−0.0459170	+	0.141318i
$698$	5.00796	+	3.63849i	0.189554	+	0.137719i
$699$	3.18791	+	2.31616i	0.120578	+	0.0876050i
$700$	−0.118702	+	0.365326i	−0.00448650	+	0.0138080i
$701$	−4.37168	−	13.4547i	−0.165116	−	0.508176i	0.833929	−	0.551872i	$-0.186086\pi$
$701$	−4.37168	−	13.4547i	−0.165116	−	0.508176i	−0.999045	+	0.0436968i	$0.986086\pi$
$702$	42.1017	−	30.5887i	1.58902	−	1.15449i
$703$	27.7638			1.04713
$704$		0			0
$705$	0.354862			0.0133649
$706$	−9.38194	+	6.81638i	−0.353094	+	0.256538i
$707$	0.0470315	+	0.144748i	0.00176880	+	0.00544381i
$708$	−4.07572	+	12.5438i	−0.153175	+	0.471424i
$709$	−13.8850	−	10.0880i	−0.521462	−	0.378865i	0.295692	−	0.955283i	$-0.404450\pi$
$709$	−13.8850	−	10.0880i	−0.521462	−	0.378865i	−0.817154	+	0.576419i	$0.804450\pi$
$710$	22.4202	+	16.2892i	0.841415	+	0.611324i
$711$	4.64415	−	14.2932i	0.174169	−	0.536038i
$712$	7.80718	+	24.0280i	0.292586	+	0.900488i
$713$	45.2149	−	32.8505i	1.69331	−	1.23026i
$714$	−0.113060			−0.00423115
$715$		0			0
$716$	−8.98880			−0.335927
$717$	14.1544	−	10.2838i	0.528605	−	0.384054i
$718$	−10.5892	−	32.5902i	−0.395186	−	1.21626i
$719$	−5.67192	+	17.4564i	−0.211527	+	0.651013i	0.787855	+	0.615861i	$0.211192\pi$
$719$	−5.67192	+	17.4564i	−0.211527	+	0.651013i	−0.999382	+	0.0351523i	$0.988808\pi$
$720$	−1.15526	−	0.839347i	−0.0430541	−	0.0312806i
$721$	−0.236481	−	0.171813i	−0.00880700	−	0.00639866i
$722$	6.29230	−	19.3657i	0.234175	−	0.720717i
$723$	6.65325	+	20.4766i	0.247437	+	0.761533i
$724$	−25.1105	+	18.2438i	−0.933224	+	0.678027i
$725$	4.07662			0.151402
$726$		0			0
$727$	47.2976			1.75417			0.877085	−	0.480336i	$-0.159485\pi$
$727$	47.2976			1.75417			0.877085	+	0.480336i	$0.159485\pi$
$728$	1.36681	−	0.993049i	0.0506575	−	0.0368048i
$729$	0.118019	+	0.363226i	0.00437109	+	0.0134528i
$730$	5.94572	−	18.2991i	0.220061	−	0.677278i
$731$	−1.43864	−	1.04524i	−0.0532102	−	0.0386595i
$732$	14.9857	+	10.8877i	0.553887	+	0.402422i
$733$	−8.88330	+	27.3400i	−0.328112	+	1.00983i	0.641904	+	0.766785i	$0.278145\pi$
$733$	−8.88330	+	27.3400i	−0.328112	+	1.00983i	−0.970016	+	0.243041i	$0.921855\pi$
$734$	−14.0698	−	43.3025i	−0.519327	−	1.59833i
$735$	4.39332	−	3.19193i	0.162050	−	0.117736i
$736$	−50.0056			−1.84323
$737$		0			0
$738$	40.8464			1.50358
$739$	27.8468	−	20.2319i	1.02436	−	0.744241i	0.0571881	−	0.998363i	$-0.481787\pi$
$739$	27.8468	−	20.2319i	1.02436	−	0.744241i	0.967172	+	0.254122i	$0.0817865\pi$
$740$	−8.41410	−	25.8959i	−0.309308	−	0.951953i
$741$	4.17041	−	12.8352i	0.153204	−	0.471513i
$742$	−0.00803496	−	0.00583774i	−0.000294973	−	0.000214310i
$743$	9.85626	+	7.16099i	0.361591	+	0.262711i	0.753715	−	0.657201i	$-0.228260\pi$
$743$	9.85626	+	7.16099i	0.361591	+	0.262711i	−0.392124	+	0.919912i	$0.628260\pi$
$744$	−4.20092	+	12.9291i	−0.154013	+	0.474004i
$745$	4.29145	+	13.2077i	0.157227	+	0.483894i
$746$	−20.5582	+	14.9364i	−0.752690	+	0.546861i
$747$	1.50058			0.0549032
$748$		0			0
$749$	0.716771			0.0261902
$750$	1.42027	−	1.03189i	0.0518611	−	0.0376793i
$751$	−15.9412	−	49.0619i	−0.581702	−	1.79029i	−0.612130	−	0.790757i	$-0.709687\pi$
$751$	−15.9412	−	49.0619i	−0.581702	−	1.79029i	0.0304278	−	0.999537i	$-0.490313\pi$
$752$	−0.0840762	+	0.258760i	−0.00306594	+	0.00943601i
$753$	2.74829	+	1.99675i	0.100153	+	0.0727656i
$754$	−40.9142	−	29.7259i	−1.49001	−	1.08255i
$755$	−2.54927	+	7.84586i	−0.0927775	+	0.285540i
$756$	0.497946	+	1.53252i	0.0181101	+	0.0557372i
$757$	−8.96530	+	6.51367i	−0.325849	+	0.236743i	−0.738667	−	0.674070i	$-0.764545\pi$
$757$	−8.96530	+	6.51367i	−0.325849	+	0.236743i	0.412818	+	0.910814i	$0.364545\pi$
$758$	47.3099			1.71837
$759$		0			0
$760$	7.83705			0.284280
$761$	1.04945	−	0.762471i	0.0380426	−	0.0276396i	−0.568601	−	0.822613i	$-0.692515\pi$
$761$	1.04945	−	0.762471i	0.0380426	−	0.0276396i	0.606644	+	0.794974i	$0.292515\pi$
$762$	−5.81008	−	17.8816i	−0.210477	−	0.647781i
$763$	0.161626	−	0.497433i	0.00585125	−	0.0180083i
$764$	34.0031	+	24.7047i	1.23019	+	0.893784i
$765$	−1.00678	−	0.731466i	−0.0364001	−	0.0264462i
$766$	−11.7439	+	36.1439i	−0.424323	+	1.30593i
$767$	9.29498	+	28.6070i	0.335622	+	1.03294i
$768$	7.51686	−	5.46132i	0.271241	−	0.197068i
$769$	24.2693			0.875173			0.437587	−	0.899176i	$-0.355833\pi$
$769$	24.2693			0.875173			0.437587	+	0.899176i	$0.355833\pi$
$770$		0			0
$771$	14.0436			0.505769
$772$	34.3240	−	24.9379i	1.23535	−	0.897533i
$773$	−8.21247	−	25.2754i	−0.295382	−	0.909093i	−0.983093	−	0.183108i	$-0.941384\pi$
$773$	−8.21247	−	25.2754i	−0.295382	−	0.909093i	0.687711	−	0.725985i	$-0.258616\pi$
$774$	−5.72170	+	17.6096i	−0.205662	+	0.632963i
$775$	−5.70279	−	4.14332i	−0.204850	−	0.148832i
$776$	−3.68222	−	2.67529i	−0.132184	−	0.0960372i
$777$	0.261733	−	0.805531i	0.00938961	−	0.0288983i
$778$	−10.9988	−	33.8507i	−0.394325	−	1.21361i
$779$	19.3019	−	14.0237i	0.691563	−	0.502450i
$780$	−13.2356			−0.473910
$781$		0			0
$782$	−9.30022			−0.332575
$783$	13.8351	−	10.0518i	0.494426	−	0.359222i
$784$	1.28662	+	3.95980i	0.0459506	+	0.141421i
$785$	3.17827	−	9.78171i	0.113437	−	0.349124i
$786$	−9.31721	−	6.76935i	−0.332334	−	0.241455i
$787$	43.9164	+	31.9071i	1.56545	+	1.13737i	0.931356	+	0.364110i	$0.118627\pi$
$787$	43.9164	+	31.9071i	1.56545	+	1.13737i	0.634094	+	0.773256i	$0.281373\pi$
$788$	−2.48917	+	7.66089i	−0.0886731	+	0.272908i
$789$	−3.22760	−	9.93353i	−0.114906	−	0.353643i
$790$	−11.4605	+	8.32657i	−0.407748	+	0.296246i
$791$	−1.87426			−0.0666410
$792$		0			0
$793$	42.2438			1.50012
$794$	12.5218	−	9.09762i	0.444382	−	0.322862i
$795$	0.00852432	+	0.0262352i	0.000302327	+	0.000930466i
$796$	16.9389	−	52.1325i	0.600383	−	1.84779i
$797$	−6.14793	−	4.46673i	−0.217771	−	0.158220i	0.473552	−	0.880766i	$-0.342972\pi$
$797$	−6.14793	−	4.46673i	−0.217771	−	0.158220i	−0.691323	+	0.722546i	$0.742972\pi$
$798$	0.556289	+	0.404168i	0.0196924	+	0.0143074i
$799$	−0.0732699	+	0.225502i	−0.00259210	+	0.00797767i
$800$	1.94898	+	5.99834i	0.0689068	+	0.212073i
$801$	−19.7391	+	14.3413i	−0.697447	+	0.506725i
$802$	0.318593			0.0112499
$803$		0			0
$804$	−6.11403			−0.215625
$805$	−0.795186	+	0.577736i	−0.0280266	+	0.0203625i
$806$	27.0227	+	83.1673i	0.951834	+	2.92944i
$807$	−1.02301	+	3.14850i	−0.0360116	+	0.110832i
$808$	−2.46370	−	1.78999i	−0.0866728	−	0.0629715i
$809$	42.5268	+	30.8975i	1.49516	+	1.08630i	0.972259	+	0.233907i	$0.0751512\pi$
$809$	42.5268	+	30.8975i	1.49516	+	1.08630i	0.522904	+	0.852392i	$0.324849\pi$
$810$	−2.73875	+	8.42900i	−0.0962298	+	0.296165i
$811$	−8.19480	−	25.2210i	−0.287758	−	0.885629i	−0.985558	−	0.169336i	$-0.945838\pi$
$811$	−8.19480	−	25.2210i	−0.287758	−	0.885629i	0.697800	−	0.716293i	$-0.254162\pi$
$812$	1.26687	−	0.920436i	0.0444585	−	0.0323010i
$813$	−9.83585			−0.344958
$814$		0			0
$815$	−2.08849			−0.0731566
$816$	−0.194782	+	0.141517i	−0.00681873	+	0.00495410i
$817$	3.34206	+	10.2858i	0.116924	+	0.359854i
$818$	20.0596	−	61.7372i	0.701368	−	2.15859i
$819$	1.31998	+	0.959022i	0.0461239	+	0.0335110i
$820$	−18.9298	−	13.7533i	−0.661059	−	0.480287i
$821$	9.39437	−	28.9129i	0.327866	−	1.00907i	−0.642265	−	0.766483i	$-0.722005\pi$
$821$	9.39437	−	28.9129i	0.327866	−	1.00907i	0.970130	−	0.242584i	$-0.0779950\pi$
$822$	−4.54356	−	13.9836i	−0.158475	−	0.487735i
$823$	−19.9095	+	14.4651i	−0.694002	+	0.504222i	−0.877973	−	0.478709i	$-0.841105\pi$
$823$	−19.9095	+	14.4651i	−0.694002	+	0.504222i	0.183971	+	0.982932i	$0.441105\pi$
$824$	5.84874			0.203751
$825$		0			0
$826$	−1.53254			−0.0533240
$827$	12.9524	−	9.41049i	0.450400	−	0.327235i	−0.339354	−	0.940659i	$-0.610208\pi$
$827$	12.9524	−	9.41049i	0.450400	−	0.327235i	0.789754	+	0.613424i	$0.210208\pi$
$828$	18.1859	+	55.9703i	0.632003	+	1.94510i
$829$	−5.14396	+	15.8315i	−0.178657	+	0.549850i	−0.999782	−	0.0208989i	$-0.993347\pi$
$829$	−5.14396	+	15.8315i	−0.178657	+	0.549850i	0.821124	+	0.570749i	$0.193347\pi$
$830$	−1.14430	−	0.831381i	−0.0397192	−	0.0288577i
$831$	−20.1136	−	14.6134i	−0.697732	−	0.506932i
$832$	22.1541	−	68.1834i	0.768056	−	2.36383i
$833$	1.12125	+	3.45085i	0.0388489	+	0.119565i
$834$	22.7349	−	16.5179i	0.787246	−	0.571968i
$835$	−16.6281			−0.575439
$836$		0			0
$837$	−29.5702			−1.02210
$838$	−20.2472	+	14.7104i	−0.699426	+	0.508163i
$839$	0.632681	+	1.94719i	0.0218426	+	0.0672246i	0.961384	−	0.275212i	$-0.0887479\pi$
$839$	0.632681	+	1.94719i	0.0218426	+	0.0672246i	−0.939541	+	0.342436i	$0.888748\pi$
$840$	0.0738809	−	0.227382i	0.00254913	−	0.00784542i
$841$	10.0166	+	7.27748i	0.345400	+	0.250948i
$842$	−6.21707	−	4.51697i	−0.214254	−	0.155665i
$843$	6.93928	−	21.3569i	0.239002	−	0.735571i
$844$	−17.5874	−	54.1283i	−0.605382	−	1.86317i
$845$	−13.9027	+	10.1009i	−0.478269	+	0.347483i
$846$	2.46882			0.0848799
$847$		0			0
$848$	−0.0211500			−0.000726293
$849$	−3.05208	+	2.21746i	−0.104747	+	0.0761032i
$850$	0.362478	+	1.11559i	0.0124329	+	0.0382645i
$851$	21.5300	−	66.2625i	0.738039	−	2.27145i
$852$	−23.9203	−	17.3791i	−0.819495	−	0.595398i
$853$	−28.4820	−	20.6934i	−0.975206	−	0.708528i	−0.0185736	−	0.999827i	$-0.505912\pi$
$853$	−28.4820	−	20.6934i	−0.975206	−	0.708528i	−0.956632	+	0.291299i	$0.905912\pi$
$854$	−0.665108	+	2.04699i	−0.0227595	+	0.0700466i
$855$	2.33880	+	7.19809i	0.0799853	+	0.246170i
$856$	−11.6028	+	8.42992i	−0.396575	+	0.288129i
$857$	−21.9827			−0.750915			−0.375458	−	0.926840i	$-0.622514\pi$
$857$	−21.9827			−0.750915			−0.375458	+	0.926840i	$0.622514\pi$
$858$		0			0
$859$	−13.4218			−0.457945			−0.228972	−	0.973433i	$-0.573537\pi$
$859$	−13.4218			−0.457945			−0.228972	+	0.973433i	$0.573537\pi$
$860$	8.58095	−	6.23443i	0.292608	−	0.212592i
$861$	−0.224917	−	0.692224i	−0.00766515	−	0.0235909i
$862$	−9.54027	+	29.3619i	−0.324943	+	1.00007i
$863$	13.0103	+	9.45256i	0.442877	+	0.321769i	0.786777	−	0.617237i	$-0.211748\pi$
$863$	13.0103	+	9.45256i	0.442877	+	0.321769i	−0.343900	+	0.939006i	$0.611748\pi$
$864$	21.4046	+	15.5514i	0.728199	+	0.529068i
$865$	5.97157	−	18.3786i	0.203040	−	0.624892i
$866$	10.7766	+	33.1670i	0.366204	+	1.12706i
$867$	10.5232	−	7.64557i	0.357387	−	0.259657i
$868$	−2.70772			−0.0919061
$869$		0			0
$870$	−7.15673			−0.242636
$871$	−11.2805	+	8.19578i	−0.382226	+	0.277703i
$872$	3.23396	+	9.95312i	0.109516	+	0.337055i
$873$	1.35829	−	4.18039i	0.0459711	−	0.141485i
$874$	45.7601	+	33.2466i	1.54786	+	1.12458i
$875$	0.100294	+	0.0728678i	0.00339055	+	0.00246338i
$876$	−6.34353	+	19.5234i	−0.214328	+	0.659634i
$877$	−10.6117	−	32.6595i	−0.358332	−	1.10283i	−0.954052	−	0.299641i	$-0.903133\pi$
$877$	−10.6117	−	32.6595i	−0.358332	−	1.10283i	0.595719	−	0.803193i	$-0.296867\pi$
$878$	−18.0309	+	13.1002i	−0.608512	+	0.442110i
$879$	−3.11584			−0.105095
$880$		0			0
$881$	6.08507			0.205011			0.102506	−	0.994732i	$-0.467314\pi$
$881$	6.08507			0.205011			0.102506	+	0.994732i	$0.467314\pi$
$882$	30.5650	−	22.2067i	1.02918	−	0.747740i
$883$	1.43919	+	4.42936i	0.0484325	+	0.149060i	0.972348	−	0.233537i	$-0.0750299\pi$
$883$	1.43919	+	4.42936i	0.0484325	+	0.149060i	−0.923915	+	0.382597i	$0.875030\pi$
$884$	2.73281	−	8.41073i	0.0919144	−	0.282883i
$885$	3.44367	+	2.50197i	0.115758	+	0.0841029i
$886$	57.1775	+	41.5419i	1.92091	+	1.39563i
$887$	6.84340	−	21.0618i	0.229779	−	0.707187i	−0.767992	−	0.640459i	$-0.778744\pi$
$887$	6.84340	−	21.0618i	0.229779	−	0.707187i	0.997771	−	0.0667278i	$-0.0212559\pi$
$888$	5.23700	+	16.1178i	0.175742	+	0.540879i
$889$	1.07414	−	0.780405i	0.0360254	−	0.0261740i
$890$	22.9982			0.770901
$891$		0			0
$892$	5.97722			0.200132
$893$	1.16664	−	0.847613i	0.0390401	−	0.0283643i
$894$	−7.53388	−	23.1869i	−0.251971	−	0.775486i
$895$	−0.896450	+	2.75899i	−0.0299650	+	0.0922229i
$896$	1.69001	+	1.22787i	0.0564594	+	0.0410201i
$897$	−27.3992	−	19.9067i	−0.914831	−	0.664664i
$898$	8.88051	−	27.3314i	0.296347	−	0.912061i
$899$	8.87998	+	27.3298i	0.296164	+	0.911499i
$900$	6.00503	−	4.36291i	0.200168	−	0.145430i
$901$	−0.0184315			−0.000614044
$902$		0			0
$903$	0.329935			0.0109796
$904$	30.3398	−	22.0431i	1.00909	−	0.733143i
$905$	3.09544	+	9.52678i	0.102896	+	0.316681i
$906$	4.47539	−	13.7738i	0.148685	−	0.457605i
$907$	−29.8210	−	21.6662i	−0.990189	−	0.719414i	−0.0302264	−	0.999543i	$-0.509623\pi$
$907$	−29.8210	−	21.6662i	−0.990189	−	0.719414i	−0.959962	+	0.280129i	$0.909623\pi$
$908$	73.6658	+	53.5213i	2.44468	+	1.77617i
$909$	0.908806	−	2.79702i	0.0301432	−	0.0927712i
$910$	−0.475243	−	1.46265i	−0.0157542	−	0.0484863i
$911$	−13.4773	+	9.79184i	−0.446523	+	0.324418i	−0.788222	−	0.615392i	$-0.788998\pi$
$911$	−13.4773	+	9.79184i	−0.446523	+	0.324418i	0.341698	+	0.939810i	$0.388998\pi$
$912$	1.46429			0.0484874
$913$		0			0
$914$	−9.73549			−0.322021
$915$	4.83636	−	3.51382i	0.159885	−	0.116163i
$916$	−18.7976	−	57.8530i	−0.621090	−	1.91152i
$917$	0.251312	−	0.773458i	0.00829904	−	0.0255418i
$918$	3.98090	+	2.89229i	0.131389	+	0.0954599i
$919$	−40.6911	−	29.5638i	−1.34228	−	0.975220i	−0.999357	−	0.0358550i	$-0.988585\pi$
$919$	−40.6911	−	29.5638i	−1.34228	−	0.975220i	−0.342918	−	0.939365i	$-0.611415\pi$
$920$	6.07740	−	18.7043i	0.200366	−	0.616663i
$921$	−0.885380	−	2.72492i	−0.0291743	−	0.0897891i
$922$	32.3911	−	23.5335i	1.06674	−	0.775035i
$923$	−67.4299			−2.21948
$924$		0			0
$925$	−8.78754			−0.288933
$926$	6.26746	−	4.55358i	0.205962	−	0.149640i
$927$	1.74543	+	5.37189i	0.0573275	+	0.176436i
$928$	7.94524	−	24.4529i	0.260815	−	0.802707i
$929$	−31.3521	−	22.7786i	−1.02863	−	0.747343i	−0.0605954	−	0.998162i	$-0.519300\pi$
$929$	−31.3521	−	22.7786i	−1.02863	−	0.747343i	−0.968034	+	0.250819i	$0.919300\pi$
$930$	10.0116	+	7.27383i	0.328292	+	0.238518i
$931$	6.81926	−	20.9875i	0.223492	−	0.687839i
$932$	−4.85286	−	14.9356i	−0.158961	−	0.489231i
$933$	6.26956	−	4.55510i	0.205256	−	0.149127i
$934$	35.3109			1.15541
$935$		0			0
$936$	−32.6463			−1.06708
$937$	12.6795	−	9.21216i	0.414220	−	0.300948i	−0.361088	−	0.932532i	$-0.617595\pi$
$937$	12.6795	−	9.21216i	0.414220	−	0.300948i	0.775308	+	0.631583i	$0.217595\pi$
$938$	−0.219533	−	0.675654i	−0.00716801	−	0.0220609i
$939$	4.53152	−	13.9466i	0.147881	−	0.455129i
$940$	−1.14415	−	0.831274i	−0.0373181	−	0.0271132i
$941$	−22.9104	−	16.6454i	−0.746858	−	0.542624i	0.147994	−	0.988988i	$-0.452719\pi$
$941$	−22.9104	−	16.6454i	−0.746858	−	0.542624i	−0.894851	+	0.446364i	$0.852719\pi$
$942$	−5.57963	+	17.1723i	−0.181794	+	0.559505i
$943$	−18.5016	−	56.9419i	−0.602494	−	1.85428i
$944$	−2.64030	+	1.91829i	−0.0859345	+	0.0624351i
$945$	0.520046			0.0169171
$946$		0			0
$947$	10.1955			0.331309			0.165654	−	0.986184i	$-0.447026\pi$
$947$	10.1955			0.331309			0.165654	+	0.986184i	$0.447026\pi$
$948$	12.2273	−	8.88367i	0.397125	−	0.288528i
$949$	14.4669	+	44.5245i	0.469615	+	1.44533i
$950$	2.20454	−	6.78486i	0.0715246	−	0.220130i
$951$	−2.44961	−	1.77974i	−0.0794340	−	0.0577122i
$952$	0.129238	+	0.0938972i	0.00418864	+	0.00304323i
$953$	−1.43463	+	4.41533i	−0.0464722	+	0.143027i	−0.971600	−	0.236629i	$-0.923957\pi$
$953$	−1.43463	+	4.41533i	−0.0464722	+	0.143027i	0.925128	+	0.379655i	$0.123957\pi$
$954$	0.0593050	+	0.182522i	0.00192007	+	0.00590936i
$955$	10.9739	−	7.97299i	0.355107	−	0.258000i
$956$	−69.7268			−2.25513
$957$		0			0
$958$	−86.9496			−2.80921
$959$	0.839988	−	0.610287i	0.0271246	−	0.0197072i
$960$	−3.13511	−	9.64887i	−0.101185	−	0.311416i
$961$	5.77517	−	17.7742i	0.186296	−	0.573360i
$962$	88.1946	+	64.0771i	2.84351	+	2.06593i
$963$	−11.2052	−	8.14107i	−0.361083	−	0.262342i
$964$	26.5155	−	81.6064i	0.854007	−	2.62836i
$965$	−4.23121	−	13.0223i	−0.136208	−	0.419204i
$966$	1.39599	−	1.01425i	0.0449154	−	0.0326329i
$967$	38.0543			1.22374			0.611872	−	0.790957i	$-0.290417\pi$
$967$	38.0543			1.22374			0.611872	+	0.790957i	$0.290417\pi$
$968$		0			0
$969$	1.27608			0.0409937
$970$	−3.35190	+	2.43530i	−0.107623	+	0.0781928i
$971$	9.79084	+	30.1331i	0.314203	+	0.967017i	0.976081	+	0.217406i	$0.0697595\pi$
$971$	9.79084	+	30.1331i	0.314203	+	0.967017i	−0.661878	+	0.749611i	$0.730240\pi$
$972$	14.9720	−	46.0790i	0.480226	−	1.47798i
$973$	1.60545	+	1.16642i	0.0514682	+	0.0373939i
$974$	−16.4783	−	11.9722i	−0.528000	−	0.383615i
$975$	−1.31998	+	4.06248i	−0.0422732	+	0.130104i
$976$	1.41637	+	4.35913i	0.0453368	+	0.139532i
$977$	−32.7797	+	23.8159i	−1.04872	+	0.761937i	−0.971968	−	0.235113i	$-0.924454\pi$
$977$	−32.7797	+	23.8159i	−1.04872	+	0.761937i	−0.0767484	+	0.997050i	$0.524454\pi$
$978$	3.66646			0.117241
$979$		0			0
$980$	−21.6422			−0.691335
$981$	−8.17652	+	5.94059i	−0.261056	+	0.189668i
$982$	−3.30088	−	10.1591i	−0.105335	−	0.324189i
$983$	−5.82123	+	17.9159i	−0.185669	+	0.571429i	−0.999959	−	0.00902830i	$-0.997126\pi$
$983$	−5.82123	+	17.9159i	−0.185669	+	0.571429i	0.814291	+	0.580457i	$0.197126\pi$
$984$	11.7821	+	8.56019i	0.375599	+	0.272889i
$985$	2.10316	+	1.52804i	0.0670123	+	0.0486873i
$986$	1.47768	−	4.54784i	0.0470590	−	0.144833i
$987$	−0.0135943	−	0.0418391i	−0.000432713	−	0.00133175i
$988$	−43.5132	+	31.6142i	−1.38434	+	1.00578i
$989$	27.1403			0.863011
$990$		0			0
$991$	4.63565			0.147256			0.0736281	−	0.997286i	$-0.476542\pi$
$991$	4.63565			0.147256			0.0736281	+	0.997286i	$0.476542\pi$
$992$	−35.9676	+	26.1320i	−1.14197	+	0.829692i
$993$	1.91634	+	5.89789i	0.0608133	+	0.187164i
$994$	1.06165	−	3.26742i	0.0336735	−	0.103636i
$995$	−14.3121	−	10.3983i	−0.453723	−	0.329649i
$996$	1.22086	+	0.887006i	0.0386844	+	0.0281059i
$997$	−6.24028	+	19.2056i	−0.197632	+	0.608248i	0.802304	+	0.596915i	$0.203607\pi$
$997$	−6.24028	+	19.2056i	−0.197632	+	0.608248i	−0.999936	+	0.0113322i	$0.996393\pi$
$998$	−0.799018	−	2.45912i	−0.0252925	−	0.0778422i
$999$	−29.8229	+	21.6676i	−0.943554	+	0.685532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.g.366.2		8
11.2	odd	10		605.2.a.l.1.3		4
11.3	even	5		605.2.g.n.511.1		8
11.4	even	5	inner	605.2.g.g.81.2		8
11.5	even	5		605.2.g.n.251.1		8
11.6	odd	10		55.2.g.a.31.2	yes	8
11.7	odd	10		605.2.g.j.81.1		8
11.8	odd	10		55.2.g.a.16.2	✓	8
11.9	even	5		605.2.a.i.1.2		4
11.10	odd	2		605.2.g.j.366.1		8
33.2	even	10		5445.2.a.bg.1.2		4
33.8	even	10		495.2.n.f.181.1		8
33.17	even	10		495.2.n.f.361.1		8
33.20	odd	10		5445.2.a.bu.1.3		4
44.19	even	10		880.2.bo.e.401.2		8
44.31	odd	10		9680.2.a.cv.1.2		4
44.35	even	10		9680.2.a.cs.1.2		4
44.39	even	10		880.2.bo.e.801.2		8
55.8	even	20		275.2.z.b.49.4		16
55.9	even	10		3025.2.a.be.1.3		4
55.17	even	20		275.2.z.b.174.4		16
55.19	odd	10		275.2.h.b.126.1		8
55.24	odd	10		3025.2.a.v.1.2		4
55.28	even	20		275.2.z.b.174.1		16
55.39	odd	10		275.2.h.b.251.1		8
55.52	even	20		275.2.z.b.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.16.2	✓	8	11.8	odd	10
55.2.g.a.31.2	yes	8	11.6	odd	10
275.2.h.b.126.1		8	55.19	odd	10
275.2.h.b.251.1		8	55.39	odd	10
275.2.z.b.49.1		16	55.52	even	20
275.2.z.b.49.4		16	55.8	even	20
275.2.z.b.174.1		16	55.28	even	20
275.2.z.b.174.4		16	55.17	even	20
495.2.n.f.181.1		8	33.8	even	10
495.2.n.f.361.1		8	33.17	even	10
605.2.a.i.1.2		4	11.9	even	5
605.2.a.l.1.3		4	11.2	odd	10
605.2.g.g.81.2		8	11.4	even	5	inner
605.2.g.g.366.2		8	1.1	even	1	trivial
605.2.g.j.81.1		8	11.7	odd	10
605.2.g.j.366.1		8	11.10	odd	2
605.2.g.n.251.1		8	11.5	even	5
605.2.g.n.511.1		8	11.3	even	5
880.2.bo.e.401.2		8	44.19	even	10
880.2.bo.e.801.2		8	44.39	even	10
3025.2.a.v.1.2		4	55.24	odd	10
3025.2.a.be.1.3		4	55.9	even	10
5445.2.a.bg.1.2		4	33.2	even	10
5445.2.a.bu.1.3		4	33.20	odd	10
9680.2.a.cs.1.2		4	44.35	even	10
9680.2.a.cv.1.2		4	44.31	odd	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.82676 - 1.32722i) q^{2} +(0.240256 + 0.739431i) q^{3} +(0.957503 - 2.94689i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.42027 + 1.03189i) q^{6} +(-0.0383089 + 0.117903i) q^{7} +(-0.766520 - 2.35911i) q^{8} +(1.93801 - 1.40805i) q^{9} +O(q^{10})\)	\(q+(1.82676 - 1.32722i) q^{2} +(0.240256 + 0.739431i) q^{3} +(0.957503 - 2.94689i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(1.42027 + 1.03189i) q^{6} +(-0.0383089 + 0.117903i) q^{7} +(-0.766520 - 2.35911i) q^{8} +(1.93801 - 1.40805i) q^{9} -2.25800 q^{10} +2.40907 q^{12} +(4.44479 - 3.22933i) q^{13} +(0.0865012 + 0.266223i) q^{14} +(0.240256 - 0.739431i) q^{15} +(0.482260 + 0.350382i) q^{16} +(0.420275 + 0.305348i) q^{17} +(1.67149 - 5.14433i) q^{18} +(-0.976324 - 3.00482i) q^{19} +(-2.50678 + 1.82128i) q^{20} -0.0963848 q^{21} -7.92856 q^{23} +(1.56024 - 1.13358i) q^{24} +(0.309017 + 0.951057i) q^{25} +(3.83353 - 11.7984i) q^{26} +(3.39377 + 2.46572i) q^{27} +(0.310765 + 0.225784i) q^{28} +(1.25974 - 3.87709i) q^{29} +(-0.542497 - 1.66963i) q^{30} +(-5.70279 + 4.14332i) q^{31} +6.30703 q^{32} +1.17300 q^{34} +(0.100294 - 0.0728678i) q^{35} +(-2.29372 - 7.05933i) q^{36} +(-2.71550 + 8.35745i) q^{37} +(-5.77155 - 4.19328i) q^{38} +(3.45576 + 2.51075i) q^{39} +(-0.766520 + 2.35911i) q^{40} +(2.33353 + 7.18188i) q^{41} +(-0.176072 + 0.127923i) q^{42} -3.42310 q^{43} -2.39552 q^{45} +(-14.4836 + 10.5229i) q^{46} +(0.141042 + 0.434084i) q^{47} +(-0.143218 + 0.440780i) q^{48} +(5.65069 + 4.10546i) q^{49} +(1.82676 + 1.32722i) q^{50} +(-0.124810 + 0.384126i) q^{51} +(-5.26058 - 16.1904i) q^{52} +(-0.0287041 + 0.0208547i) q^{53} +9.47214 q^{54} +0.307509 q^{56} +(1.98729 - 1.44385i) q^{57} +(-2.84450 - 8.75446i) q^{58} +(-1.69182 + 5.20690i) q^{59} +(-1.94898 - 1.41602i) q^{60} +(6.22053 + 4.51948i) q^{61} +(-4.91853 + 15.1377i) q^{62} +(0.0917696 + 0.282438i) q^{63} +(10.5569 - 7.67003i) q^{64} -5.49406 q^{65} -2.53792 q^{67} +(1.30224 - 0.946133i) q^{68} +(-1.90488 - 5.86263i) q^{69} +(0.0865012 - 0.266223i) q^{70} +(-9.92925 - 7.21402i) q^{71} +(-4.80727 - 3.49269i) q^{72} +(-2.63319 + 8.10411i) q^{73} +(6.13159 + 18.8711i) q^{74} +(-0.628998 + 0.456994i) q^{75} -9.78970 q^{76} +9.64514 q^{78} +(5.07554 - 3.68759i) q^{79} +(-0.184207 - 0.566931i) q^{80} +(1.21291 - 3.73296i) q^{81} +(13.7947 + 10.0224i) q^{82} +(0.506776 + 0.368194i) q^{83} +(-0.0922887 + 0.284036i) q^{84} +(-0.160531 - 0.494063i) q^{85} +(-6.25318 + 4.54320i) q^{86} +3.16951 q^{87} -10.1852 q^{89} +(-4.37603 + 3.17937i) q^{90} +(0.210471 + 0.647764i) q^{91} +(-7.59162 + 23.3646i) q^{92} +(-4.43383 - 3.22136i) q^{93} +(0.833774 + 0.605772i) q^{94} +(-0.976324 + 3.00482i) q^{95} +(1.51530 + 4.66362i) q^{96} +(1.48446 - 1.07852i) q^{97} +15.7713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9	\( 8 q - q^{2} + q^{3} - q^{4} - 2 q^{5} + 12 q^{6} + 8 q^{7} + 7 q^{8} + 5 q^{9} - 6 q^{10} - 28 q^{12} + 11 q^{13} - 14 q^{14} + q^{15} + 15 q^{16} + 4 q^{17} + 16 q^{18} + 11 q^{19} - 6 q^{20} + 12 q^{21} - 18 q^{23} + 10 q^{24} - 2 q^{25} + q^{26} - 5 q^{27} + 11 q^{28} + 11 q^{29} - 13 q^{30} - 9 q^{31} - 12 q^{32} - 20 q^{34} + 3 q^{35} - 29 q^{36} - q^{37} - 6 q^{38} + 6 q^{39} + 7 q^{40} - 11 q^{41} - 31 q^{42} - 42 q^{43} - 29 q^{46} - q^{47} + 21 q^{48} - q^{50} + 22 q^{51} + q^{52} + 8 q^{53} + 40 q^{54} + 30 q^{56} + 4 q^{58} + 26 q^{59} - 8 q^{60} + 2 q^{61} - 27 q^{62} + 4 q^{63} + 21 q^{64} - 14 q^{65} - 2 q^{67} + 20 q^{68} + 49 q^{69} - 14 q^{70} - 25 q^{71} - 21 q^{72} - 32 q^{73} + 12 q^{74} + q^{75} - 16 q^{76} + 12 q^{78} + 23 q^{79} - 20 q^{80} + 20 q^{81} + 42 q^{82} - 10 q^{83} - 51 q^{84} - q^{85} + 34 q^{86} - 30 q^{87} - 14 q^{90} + 8 q^{91} - 99 q^{92} - 8 q^{93} + 22 q^{94} + 11 q^{95} - 3 q^{96} - 18 q^{97} + 84 q^{98}+O(q^{100}) \) 8 * q - q^2 + q^3 - q^4 - 2 * q^5 + 12 * q^6 + 8 * q^7 + 7 * q^8 + 5 * q^9 - 6 * q^10 - 28 * q^12 + 11 * q^13 - 14 * q^14 + q^15 + 15 * q^16 + 4 * q^17 + 16 * q^18 + 11 * q^19 - 6 * q^20 + 12 * q^21 - 18 * q^23 + 10 * q^24 - 2 * q^25 + q^26 - 5 * q^27 + 11 * q^28 + 11 * q^29 - 13 * q^30 - 9 * q^31 - 12 * q^32 - 20 * q^34 + 3 * q^35 - 29 * q^36 - q^37 - 6 * q^38 + 6 * q^39 + 7 * q^40 - 11 * q^41 - 31 * q^42 - 42 * q^43 - 29 * q^46 - q^47 + 21 * q^48 - q^50 + 22 * q^51 + q^52 + 8 * q^53 + 40 * q^54 + 30 * q^56 + 4 * q^58 + 26 * q^59 - 8 * q^60 + 2 * q^61 - 27 * q^62 + 4 * q^63 + 21 * q^64 - 14 * q^65 - 2 * q^67 + 20 * q^68 + 49 * q^69 - 14 * q^70 - 25 * q^71 - 21 * q^72 - 32 * q^73 + 12 * q^74 + q^75 - 16 * q^76 + 12 * q^78 + 23 * q^79 - 20 * q^80 + 20 * q^81 + 42 * q^82 - 10 * q^83 - 51 * q^84 - q^85 + 34 * q^86 - 30 * q^87 - 14 * q^90 + 8 * q^91 - 99 * q^92 - 8 * q^93 + 22 * q^94 + 11 * q^95 - 3 * q^96 - 18 * q^97 + 84 * q^98

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