LMFDB - Embedded newform 605.2.g.k.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:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$0.418926 + 1.28932i$ of defining polynomial
Character	$\chi$	$=$	605.366
Dual form			605.2.g.k.81.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09676 - 0.796845i) q^{2} +(0.177837 + 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.631180 + 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +O(q^{10})$	\(q+(1.09676 - 0.796845i) q^{2} +(0.177837 + 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.631180 + 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +1.35567 q^{10} -0.0933146 q^{12} +(-2.29029 + 1.66399i) q^{13} +(-1.52884 - 4.70527i) q^{14} +(-0.177837 + 0.547326i) q^{15} +(2.95244 + 2.14507i) q^{16} +(2.98685 + 2.17008i) q^{17} +(1.11803 - 3.44095i) q^{18} +(0.0293950 + 0.0904686i) q^{19} +(-0.131180 + 0.0953077i) q^{20} +2.10021 q^{21} +1.16215 q^{23} +(-1.36470 + 0.991515i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.18596 + 3.65001i) q^{26} +(2.63930 + 1.91757i) q^{27} +(0.478730 + 0.347817i) q^{28} +(2.08707 - 6.42333i) q^{29} +(0.241089 + 0.741996i) q^{30} +(-5.48382 + 3.98423i) q^{31} -0.914918 q^{32} +5.00509 q^{34} +(2.95244 - 2.14507i) q^{35} +(0.133724 + 0.411560i) q^{36} +(3.04066 - 9.35820i) q^{37} +(0.104329 + 0.0757994i) q^{38} +(-1.31805 - 0.957617i) q^{39} +(-0.905781 + 2.78771i) q^{40} +(2.57047 + 7.91110i) q^{41} +(2.30344 - 1.67354i) q^{42} +2.96862 q^{43} +2.66881 q^{45} +(1.27460 - 0.926052i) q^{46} +(-0.687534 - 2.11601i) q^{47} +(-0.649001 + 1.99742i) q^{48} +(-5.11155 - 3.71376i) q^{49} +(1.09676 + 0.796845i) q^{50} +(-0.656567 + 2.02070i) q^{51} +(-0.141849 - 0.436565i) q^{52} +(-2.42214 + 1.75979i) q^{53} +4.42270 q^{54} +10.6970 q^{56} +(-0.0442883 + 0.0321774i) q^{57} +(-2.82938 - 8.70794i) q^{58} +(-2.62930 + 8.09216i) q^{59} +(-0.0754931 - 0.0548489i) q^{60} +(-6.86076 - 4.98464i) q^{61} +(-2.83964 + 8.73951i) q^{62} +(-3.00970 - 9.26289i) q^{63} +(-6.90832 + 5.01919i) q^{64} -2.83095 q^{65} -13.4153 q^{67} +(-0.484310 + 0.351872i) q^{68} +(0.206673 + 0.636074i) q^{69} +(1.52884 - 4.70527i) q^{70} +(-6.71734 - 4.88043i) q^{71} +(6.32872 + 4.59808i) q^{72} +(0.407912 - 1.25542i) q^{73} +(-4.12215 - 12.6867i) q^{74} +(-0.465584 + 0.338266i) q^{75} -0.0154241 q^{76} -2.20866 q^{78} +(-11.2179 + 8.15028i) q^{79} +(1.12773 + 3.47080i) q^{80} +(1.89395 - 5.82899i) q^{81} +(9.12312 + 6.62834i) q^{82} +(-8.61155 - 6.25666i) q^{83} +(-0.105234 + 0.323876i) q^{84} +(1.14088 + 3.51126i) q^{85} +(3.25587 - 2.36553i) q^{86} +3.88682 q^{87} -12.1612 q^{89} +(2.92705 - 2.12663i) q^{90} +(3.19256 + 9.82567i) q^{91} +(-0.0582308 + 0.179216i) q^{92} +(-3.15590 - 2.29290i) q^{93} +(-2.44020 - 1.77291i) q^{94} +(-0.0293950 + 0.0904686i) q^{95} +(-0.162706 - 0.500759i) q^{96} +(3.50412 - 2.54589i) q^{97} -8.56545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	$ 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23} - 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} + 6 q^{28} + 9 q^{29} + 8 q^{30} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} - 15 q^{36} + 24 q^{37} - 21 q^{39} + 4 q^{40} - 8 q^{41} + 9 q^{42} + 38 q^{43} - 3 q^{46} + 5 q^{48} + q^{49} + 2 q^{50} - q^{51} + 28 q^{52} + 13 q^{53} - 16 q^{54} + 22 q^{56} + 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} - 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} + 30 q^{72} - 13 q^{73} - 20 q^{74} + 5 q^{75} - 16 q^{78} - 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} - 27 q^{83} - 28 q^{84} + 12 q^{85} - 3 q^{86} - 38 q^{87} - 16 q^{89} + 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} - 17 q^{94} + 15 q^{95} + 17 q^{96} + 24 q^{97} - 16 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * 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 $

$2$	1.09676	−	0.796845i	0.775529	−	0.563455i	−0.128105	−	0.991761i	$-0.540889\pi$
$2$	1.09676	−	0.796845i	0.775529	−	0.563455i	0.903634	+	0.428306i	$0.140889\pi$
$3$	0.177837	+	0.547326i	0.102674	+	0.315999i	0.989178	−	0.146723i	$-0.0468727\pi$
$3$	0.177837	+	0.547326i	0.102674	+	0.315999i	−0.886503	+	0.462722i	$0.846873\pi$
$4$	−0.0501062	+	0.154211i	−0.0250531	+	0.0771056i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.631180	+	0.458579i	0.257678	+	0.187214i
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	−0.475558	−	0.879685i	$-0.657754\pi$
$7$	1.12773	−	3.47080i	0.426242	−	1.31184i	0.901800	−	0.432154i	$-0.142246\pi$
$8$	0.905781	+	2.78771i	0.320242	+	0.985603i
$9$	2.15911	−	1.56869i	0.719704	−	0.522895i
$10$	1.35567			0.428702
$11$		0			0
$11$		0			0
$12$	−0.0933146			−0.0269376
$13$	−2.29029	+	1.66399i	−0.635212	+	0.461509i	−0.858202	−	0.513312i	$-0.828418\pi$
$13$	−2.29029	+	1.66399i	−0.635212	+	0.461509i	0.222990	+	0.974821i	$0.428418\pi$
$14$	−1.52884	−	4.70527i	−0.408599	−	1.25754i
$15$	−0.177837	+	0.547326i	−0.0459174	+	0.141319i
$16$	2.95244	+	2.14507i	0.738109	+	0.536268i
$17$	2.98685	+	2.17008i	0.724419	+	0.526321i	0.887793	−	0.460243i	$-0.152238\pi$
$17$	2.98685	+	2.17008i	0.724419	+	0.526321i	−0.163374	+	0.986564i	$0.552238\pi$
$18$	1.11803	−	3.44095i	0.263523	−	0.811041i
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	0.954372	−	0.298621i	$-0.0965267\pi$
$19$	0.0293950	+	0.0904686i	0.00674368	+	0.0207549i	−0.947628	+	0.319376i	$0.896527\pi$
$20$	−0.131180	+	0.0953077i	−0.0293327	+	0.0213115i
$21$	2.10021			0.458304
$22$		0			0
$23$	1.16215			0.242324			0.121162	−	0.992633i	$-0.461338\pi$
$23$	1.16215			0.242324			0.121162	+	0.992633i	$0.461338\pi$
$24$	−1.36470	+	0.991515i	−0.278569	+	0.202392i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.18596	+	3.65001i	−0.232586	+	0.715827i
$27$	2.63930	+	1.91757i	0.507934	+	0.369036i
$28$	0.478730	+	0.347817i	0.0904714	+	0.0657313i
$29$	2.08707	−	6.42333i	0.387559	−	1.19278i	−0.547049	−	0.837101i	$-0.684249\pi$
$29$	2.08707	−	6.42333i	0.387559	−	1.19278i	0.934607	−	0.355682i	$-0.115751\pi$
$30$	0.241089	+	0.741996i	0.0440167	+	0.135469i
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.958803	−	0.284071i	$-0.908315\pi$
$31$	−5.48382	+	3.98423i	−0.984923	+	0.715588i	−0.0261194	+	0.999659i	$0.508315\pi$
$32$	−0.914918			−0.161736
$33$		0			0
$34$	5.00509			0.858366
$35$	2.95244	−	2.14507i	0.499053	−	0.362583i
$36$	0.133724	+	0.411560i	0.0222873	+	0.0685933i
$37$	3.04066	−	9.35820i	0.499882	−	1.53848i	−0.309326	−	0.950956i	$-0.600103\pi$
$37$	3.04066	−	9.35820i	0.499882	−	1.53848i	0.809208	−	0.587523i	$-0.199897\pi$
$38$	0.104329	+	0.0757994i	0.0169244	+	0.0122963i
$39$	−1.31805	−	0.957617i	−0.211056	−	0.153341i
$40$	−0.905781	+	2.78771i	−0.143216	+	0.440775i
$41$	2.57047	+	7.91110i	0.401440	+	1.23551i	0.923831	+	0.382800i	$0.125040\pi$
$41$	2.57047	+	7.91110i	0.401440	+	1.23551i	−0.522391	+	0.852706i	$0.674960\pi$
$42$	2.30344	−	1.67354i	0.355428	−	0.258234i
$43$	2.96862			0.452710			0.226355	−	0.974045i	$-0.427319\pi$
$43$	2.96862			0.452710			0.226355	+	0.974045i	$0.427319\pi$
$44$		0			0
$45$	2.66881			0.397842
$46$	1.27460	−	0.926052i	0.187930	−	0.136539i
$47$	−0.687534	−	2.11601i	−0.100287	−	0.308652i	0.888308	−	0.459248i	$-0.151881\pi$
$47$	−0.687534	−	2.11601i	−0.100287	−	0.308652i	−0.988595	+	0.150595i	$0.951881\pi$
$48$	−0.649001	+	1.99742i	−0.0936753	+	0.288303i
$49$	−5.11155	−	3.71376i	−0.730221	−	0.530537i
$50$	1.09676	+	0.796845i	0.155106	+	0.112691i
$51$	−0.656567	+	2.02070i	−0.0919377	+	0.282955i
$52$	−0.141849	−	0.436565i	−0.0196708	−	0.0605407i
$53$	−2.42214	+	1.75979i	−0.332706	+	0.241725i	−0.741578	−	0.670867i	$-0.765922\pi$
$53$	−2.42214	+	1.75979i	−0.332706	+	0.241725i	0.408872	+	0.912592i	$0.365922\pi$
$54$	4.42270			0.601853
$55$		0			0
$56$	10.6970			1.42945
$57$	−0.0442883	+	0.0321774i	−0.00586613	+	0.00426200i
$58$	−2.82938	−	8.70794i	−0.371516	−	1.14341i
$59$	−2.62930	+	8.09216i	−0.342306	+	1.05351i	0.620704	+	0.784045i	$0.286847\pi$
$59$	−2.62930	+	8.09216i	−0.342306	+	1.05351i	−0.963010	+	0.269465i	$0.913153\pi$
$60$	−0.0754931	−	0.0548489i	−0.00974612	−	0.00708097i
$61$	−6.86076	−	4.98464i	−0.878431	−	0.638217i	0.0544052	−	0.998519i	$-0.482674\pi$
$61$	−6.86076	−	4.98464i	−0.878431	−	0.638217i	−0.932836	+	0.360302i	$0.882674\pi$
$62$	−2.83964	+	8.73951i	−0.360634	+	1.10992i
$63$	−3.00970	−	9.26289i	−0.379186	−	1.16702i
$64$	−6.90832	+	5.01919i	−0.863541	+	0.627399i
$65$	−2.83095			−0.351137
$66$		0			0
$67$	−13.4153			−1.63894			−0.819469	−	0.573123i	$-0.805732\pi$
$67$	−13.4153			−1.63894			−0.819469	+	0.573123i	$0.805732\pi$
$68$	−0.484310	+	0.351872i	−0.0587312	+	0.0426707i
$69$	0.206673	+	0.636074i	0.0248805	+	0.0765743i
$70$	1.52884	−	4.70527i	0.182731	−	0.562388i
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	0.112890	−	0.993607i	$-0.463989\pi$
$71$	−6.71734	−	4.88043i	−0.797202	−	0.579201i	−0.910092	+	0.414406i	$0.863989\pi$
$72$	6.32872	+	4.59808i	0.745846	+	0.541889i
$73$	0.407912	−	1.25542i	0.0477425	−	0.146936i	−0.924343	−	0.381562i	$-0.875386\pi$
$73$	0.407912	−	1.25542i	0.0477425	−	0.146936i	0.972086	+	0.234625i	$0.0753864\pi$
$74$	−4.12215	−	12.6867i	−0.479190	−	1.47480i
$75$	−0.465584	+	0.338266i	−0.0537610	+	0.0390596i
$76$	−0.0154241			−0.00176927
$77$		0			0
$78$	−2.20866			−0.250081
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.998859	−	0.0477484i	$-0.984795\pi$
$79$	−11.2179	+	8.15028i	−1.26211	+	0.916978i	−0.263253	+	0.964727i	$0.584795\pi$
$80$	1.12773	+	3.47080i	0.126084	+	0.388047i
$81$	1.89395	−	5.82899i	0.210439	−	0.647665i
$82$	9.12312	+	6.62834i	1.00748	+	0.731977i
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	0.00443607	−	0.999990i	$-0.498588\pi$
$83$	−8.61155	−	6.25666i	−0.945240	−	0.686757i	−0.949676	+	0.313233i	$0.898588\pi$
$84$	−0.105234	+	0.323876i	−0.0114819	+	0.0353378i
$85$	1.14088	+	3.51126i	0.123745	+	0.380849i
$86$	3.25587	−	2.36553i	0.351090	−	0.255082i
$87$	3.88682			0.416710
$88$		0			0
$89$	−12.1612			−1.28908			−0.644540	−	0.764570i	$-0.722951\pi$
$89$	−12.1612			−1.28908			−0.644540	+	0.764570i	$0.722951\pi$
$90$	2.92705	−	2.12663i	0.308538	−	0.224166i
$91$	3.19256	+	9.82567i	0.334671	+	1.03001i
$92$	−0.0582308	+	0.179216i	−0.00607098	+	0.0186846i
$93$	−3.15590	−	2.29290i	−0.327252	−	0.237762i
$94$	−2.44020	−	1.77291i	−0.251687	−	0.182861i
$95$	−0.0293950	+	0.0904686i	−0.00301587	+	0.00928188i
$96$	−0.162706	−	0.500759i	−0.0166062	−	0.0511085i
$97$	3.50412	−	2.54589i	0.355789	−	0.258496i	−0.395504	−	0.918464i	$-0.629430\pi$
$97$	3.50412	−	2.54589i	0.355789	−	0.258496i	0.751294	+	0.659968i	$0.229430\pi$
$98$	−8.56545			−0.865241
$99$		0			0
$100$	−0.162147			−0.0162147
$101$	8.01388	−	5.82242i	0.797411	−	0.579353i	−0.112743	−	0.993624i	$-0.535964\pi$
$101$	8.01388	−	5.82242i	0.797411	−	0.579353i	0.910153	+	0.414271i	$0.135964\pi$
$102$	0.890091	+	2.73942i	0.0881321	+	0.271243i
$103$	1.25643	−	3.86690i	0.123800	−	0.381017i	−0.869880	−	0.493263i	$-0.835804\pi$
$103$	1.25643	−	3.86690i	0.123800	−	0.381017i	0.993681	+	0.112245i	$0.0358042\pi$
$104$	−6.71323	−	4.87744i	−0.658286	−	0.478273i
$105$	1.69911	+	1.23447i	0.165816	+	0.120472i
$106$	−1.25424	+	3.86014i	−0.121822	+	0.374930i
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	0.917916	−	0.396776i	$-0.129871\pi$
$107$	−0.599053	−	1.84369i	−0.0579126	−	0.178237i	−0.975828	+	0.218539i	$0.929871\pi$
$108$	−0.427956	+	0.310928i	−0.0411801	+	0.0299191i
$109$	−6.12664			−0.586825			−0.293413	−	0.955986i	$-0.594791\pi$
$109$	−6.12664			−0.586825			−0.293413	+	0.955986i	$0.594791\pi$
$110$		0			0
$111$	5.66273			0.537483
$112$	10.7747	−	7.82825i	1.01811	−	0.739700i
$113$	1.78775	+	5.50212i	0.168177	+	0.517596i	0.999256	−	0.0385582i	$-0.0122765\pi$
$113$	1.78775	+	5.50212i	0.168177	+	0.517596i	−0.831079	+	0.556154i	$0.812276\pi$
$114$	−0.0229335	+	0.0705819i	−0.00214791	+	0.00661060i
$115$	0.940197	+	0.683093i	0.0876738	+	0.0636987i
$116$	0.885974	+	0.643698i	0.0822606	+	0.0597659i
$117$	−2.33471	+	7.18549i	−0.215844	+	0.664299i
$118$	3.56448	+	10.9703i	0.328137	+	1.00990i
$119$	10.9003	−	7.91951i	0.999226	−	0.725980i
$120$	−1.68687			−0.153989
$121$		0			0
$122$	−11.4966			−1.04085
$123$	−3.87283	+	2.81377i	−0.349201	+	0.253710i
$124$	−0.339639	−	1.04530i	−0.0305005	−	0.0938708i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−10.6820	−	7.76094i	−0.951630	−	0.691400i
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	0.671841	−	0.740695i	$-0.265504\pi$
$127$	1.97224	+	1.43292i	0.175008	+	0.127151i	−0.496833	+	0.867846i	$0.665504\pi$
$128$	−3.01183	+	9.26945i	−0.266211	+	0.819312i
$129$	0.527931	+	1.62480i	0.0464817	+	0.143056i
$130$	−3.10489	+	2.25583i	−0.272317	+	0.197850i
$131$	−7.04156			−0.615224			−0.307612	−	0.951512i	$-0.599530\pi$
$131$	−7.04156			−0.615224			−0.307612	+	0.951512i	$0.599530\pi$
$132$		0			0
$133$	0.347148			0.0301016
$134$	−14.7134	+	10.6899i	−1.27104	+	0.923468i
$135$	1.00812	+	3.10269i	0.0867655	+	0.267037i
$136$	−3.34410	+	10.2921i	−0.286754	+	0.882539i
$137$	7.74461	+	5.62678i	0.661666	+	0.480729i	0.867225	−	0.497916i	$-0.165901\pi$
$137$	7.74461	+	5.62678i	0.661666	+	0.480729i	−0.205559	+	0.978645i	$0.565901\pi$
$138$	0.733524	+	0.532936i	0.0624417	+	0.0453666i
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	−0.957585	−	0.288151i	$-0.906959\pi$
$139$	−0.159299	+	0.490271i	−0.0135116	+	0.0415843i	0.944073	+	0.329735i	$0.106959\pi$
$140$	0.182858	+	0.562780i	0.0154544	+	0.0475636i
$141$	1.03588	−	0.752611i	0.0872369	−	0.0633813i
$142$	−11.2563			−0.944607
$143$		0			0
$144$	9.73958			0.811632
$145$	5.46401	−	3.96984i	0.453761	−	0.329677i
$146$	−0.552996	−	1.70195i	−0.0457663	−	0.140854i
$147$	1.12361	−	3.45813i	0.0926742	−	0.285222i
$148$	1.29078	+	0.937809i	0.106102	+	0.0770874i
$149$	−6.60144	−	4.79623i	−0.540811	−	0.392922i	0.283575	−	0.958950i	$-0.408479\pi$
$149$	−6.60144	−	4.79623i	−0.540811	−	0.392922i	−0.824386	+	0.566028i	$0.808479\pi$
$150$	−0.241089	+	0.741996i	−0.0196849	+	0.0605838i
$151$	−0.599563	−	1.84526i	−0.0487917	−	0.150165i	0.923692	−	0.383135i	$-0.125156\pi$
$151$	−0.599563	−	1.84526i	−0.0487917	−	0.150165i	−0.972484	+	0.232970i	$0.925156\pi$
$152$	−0.225574	+	0.163889i	−0.0182965	+	0.0132932i
$153$	9.85312			0.796577
$154$		0			0
$155$	−6.77837			−0.544452
$156$	0.213718	−	0.155275i	0.0171111	−	0.0124319i
$157$	6.57418	+	20.2332i	0.524676	+	1.61479i	0.764955	+	0.644084i	$0.222761\pi$
$157$	6.57418	+	20.2332i	0.524676	+	1.61479i	−0.240279	+	0.970704i	$0.577239\pi$
$158$	−5.80887	+	17.8779i	−0.462129	+	1.42229i
$159$	−1.39392	−	1.01274i	−0.110545	−	0.0803159i
$160$	−0.740184	−	0.537775i	−0.0585167	−	0.0425149i
$161$	1.31059	−	4.03358i	0.103289	−	0.317891i
$162$	−2.56758	−	7.90221i	−0.201728	−	0.620856i
$163$	12.9289	−	9.39337i	1.01267	−	0.735746i	0.0479001	−	0.998852i	$-0.484747\pi$
$163$	12.9289	−	9.39337i	1.01267	−	0.735746i	0.964767	+	0.263107i	$0.0847471\pi$
$164$	−1.34878			−0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.126199	−	0.992005i	$-0.459722\pi$
$167$	14.3269	−	10.4091i	1.10865	−	0.805481i	0.982450	+	0.186524i	$0.0597223\pi$
$168$	1.90233	+	5.85477i	0.146768	+	0.451706i
$169$	−1.54066	+	4.74168i	−0.118513	+	0.364744i
$170$	4.04920	+	2.94192i	0.310560	+	0.225635i
$171$	0.205384	+	0.149220i	0.0157061	+	0.0114112i
$172$	−0.148746	+	0.457794i	−0.0113418	+	0.0349065i
$173$	−4.90888	−	15.1080i	−0.373216	−	1.14864i	−0.944675	−	0.328009i	$-0.893622\pi$
$173$	−4.90888	−	15.1080i	−0.373216	−	1.14864i	0.571459	−	0.820631i	$-0.306378\pi$
$174$	4.26292	−	3.09719i	0.323171	−	0.234798i
$175$	3.64941			0.275870
$176$		0			0
$177$	−4.89664			−0.368054
$178$	−13.3379	+	9.69057i	−0.999719	+	0.726339i
$179$	−5.21653	−	16.0548i	−0.389902	−	1.19999i	−0.932862	−	0.360235i	$-0.882696\pi$
$179$	−5.21653	−	16.0548i	−0.389902	−	1.19999i	0.542960	−	0.839759i	$-0.317304\pi$
$180$	−0.133724	+	0.411560i	−0.00996719	+	0.0306759i
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.986187	+	0.165636i	$0.0529676\pi$
$181$	19.4871	+	14.1582i	1.44846	+	1.05237i	0.462277	+	0.886735i	$0.347032\pi$
$182$	11.3310	+	8.23247i	0.839911	+	0.610231i
$183$	1.50812	−	4.64153i	0.111484	−	0.343112i
$184$	1.05265	+	3.23972i	0.0776024	+	0.238836i
$185$	7.96056	−	5.78369i	0.585272	−	0.425225i
$186$	−5.28836			−0.387761
$187$		0			0
$188$	0.360762			0.0263113
$189$	9.63191	−	6.99800i	0.700619	−	0.509029i
$190$	0.0398501	+	0.122646i	0.00289103	+	0.00889767i
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	−0.872669	−	0.488312i	$-0.837613\pi$
$191$	1.66337	−	5.11934i	0.120358	−	0.370422i	0.993027	+	0.117890i	$0.0376129\pi$
$192$	−3.97569	−	2.88851i	−0.286921	−	0.208460i
$193$	14.7921	+	10.7471i	1.06476	+	0.773593i	0.974963	−	0.222367i	$-0.0713785\pi$
$193$	14.7921	+	10.7471i	1.06476	+	0.773593i	0.0897961	+	0.995960i	$0.471378\pi$
$194$	1.81451	−	5.58448i	0.130274	−	0.400942i
$195$	−0.503449	−	1.54946i	−0.0360527	−	0.110959i
$196$	0.828823	−	0.602175i	0.0592017	−	0.0430125i
$197$	−2.64566			−0.188496			−0.0942478	−	0.995549i	$-0.530045\pi$
$197$	−2.64566			−0.188496			−0.0942478	+	0.995549i	$0.530045\pi$
$198$		0			0
$199$	6.52800			0.462757			0.231379	−	0.972864i	$-0.425676\pi$
$199$	6.52800			0.462757			0.231379	+	0.972864i	$0.425676\pi$
$200$	−2.37136	+	1.72290i	−0.167681	+	0.121827i
$201$	−2.38574	−	7.34254i	−0.168277	−	0.517903i
$202$	4.14976	−	12.7716i	0.291976	−	0.898610i
$203$	−19.9404	−	14.4876i	−1.39954	−	1.01683i
$204$	−0.278717	−	0.202500i	−0.0195141	−	0.0141778i
$205$	−2.57047	+	7.91110i	−0.179530	+	0.552535i
$206$	−1.70331	−	5.24226i	−0.118676	−	0.365246i
$207$	2.50920	−	1.82304i	0.174402	−	0.126710i
$208$	−10.3313			−0.716349
$209$		0			0
$210$	2.84720			0.196476
$211$	−22.2057	+	16.1334i	−1.52871	+	1.11067i	−0.571752	+	0.820426i	$0.693736\pi$
$211$	−22.2057	+	16.1334i	−1.52871	+	1.11067i	−0.956953	+	0.290243i	$0.906264\pi$
$212$	−0.150014	−	0.461697i	−0.0103030	−	0.0317095i
$213$	1.47660	−	4.54450i	0.101175	−	0.311384i
$214$	−2.12616	−	1.54474i	−0.145341	−	0.105597i
$215$	2.40166	+	1.74491i	0.163792	+	0.119002i
$216$	−2.95498	+	9.09450i	−0.201061	+	0.618802i
$217$	7.64418	+	23.5264i	0.518921	+	1.59707i
$218$	−6.71947	+	4.88198i	−0.455100	+	0.330650i
$219$	0.759669			0.0513337
$220$		0			0
$221$	−10.4518			−0.703061
$222$	6.21068	−	4.51232i	0.416834	−	0.302847i
$223$	−1.57040	−	4.83321i	−0.105162	−	0.323656i	0.884606	−	0.466338i	$-0.154427\pi$
$223$	−1.57040	−	4.83321i	−0.105162	−	0.323656i	−0.989768	+	0.142683i	$0.954427\pi$
$224$	−1.03178	+	3.17550i	−0.0689388	+	0.212172i
$225$	2.15911	+	1.56869i	0.143941	+	0.104579i
$226$	6.34507	+	4.60997i	0.422068	+	0.306650i
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	−0.982055	−	0.188593i	$-0.939607\pi$
$227$	−1.15566	+	3.55676i	−0.0767040	+	0.236071i	0.905351	+	0.424663i	$0.139607\pi$
$228$	−0.00274299	−	0.00844204i	−0.000181659	−	0.000559088i
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.451232	+	0.892407i	$0.649015\pi$
$229$	−21.7821	+	15.8256i	−1.43940	+	1.04578i	−0.988168	+	0.153378i	$0.950985\pi$
$230$	1.57549			0.103885
$231$		0			0
$232$	19.7968			1.29972
$233$	14.8185	−	10.7663i	0.970794	−	0.705323i	0.0151615	−	0.999885i	$-0.495174\pi$
$233$	14.8185	−	10.7663i	0.970794	−	0.705323i	0.955632	+	0.294562i	$0.0951737\pi$
$234$	3.16510	+	9.74119i	0.206909	+	0.636801i
$235$	0.687534	−	2.11601i	0.0448498	−	0.138033i
$236$	−1.11616	−	0.810936i	−0.0726557	−	0.0527874i
$237$	−6.45582	−	4.69043i	−0.419351	−	0.304676i
$238$	5.64439	−	17.3717i	0.365872	−	1.12604i
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	0.998846	+	0.0480283i	$0.0152938\pi$
$239$	3.38555	+	10.4196i	0.218993	+	0.673991i	−0.779853	+	0.625963i	$0.784706\pi$
$240$	−1.69911	+	1.23447i	−0.109677	+	0.0796849i
$241$	9.99444			0.643798			0.321899	−	0.946774i	$-0.395679\pi$
$241$	9.99444			0.643798			0.321899	+	0.946774i	$0.395679\pi$
$242$		0			0
$243$	13.3143			0.854110
$244$	1.11245	−	0.808245i	0.0712175	−	0.0517426i
$245$	−1.95244	−	6.00899i	−0.124737	−	0.383900i
$246$	−2.00543	+	6.17209i	−0.127862	+	0.393518i
$247$	−0.217862	−	0.158286i	−0.0138622	−	0.0100715i
$248$	−16.0740	−	11.6784i	−1.02070	−	0.741581i
$249$	1.89298	−	5.82599i	0.119963	−	0.369207i
$250$	0.418926	+	1.28932i	0.0264952	+	0.0815439i
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	−0.806396	−	0.591376i	$-0.798585\pi$
$251$	−7.81303	+	5.67650i	−0.493154	+	0.358297i	0.313242	+	0.949673i	$0.398585\pi$
$252$	1.57925			0.0994832
$253$		0			0
$254$	3.30490			0.207368
$255$	−1.71891	+	1.24886i	−0.107643	+	0.0782069i
$256$	−1.19443	−	3.67608i	−0.0746520	−	0.229755i
$257$	3.22230	−	9.91721i	0.201001	−	0.618618i	−0.798853	−	0.601527i	$-0.794559\pi$
$257$	3.22230	−	9.91721i	0.201001	−	0.618618i	0.999854	−	0.0170916i	$-0.00544069\pi$
$258$	1.87373	+	1.36135i	0.116654	+	0.0847538i
$259$	−29.0514	−	21.1071i	−1.80517	−	1.31153i
$260$	0.141849	−	0.436565i	0.00879707	−	0.0270746i
$261$	−5.56998	−	17.1426i	−0.344773	−	1.06110i
$262$	−7.72292	+	5.61103i	−0.477124	+	0.346651i
$263$	10.9619			0.675937			0.337968	−	0.941157i	$-0.390260\pi$
$263$	10.9619			0.675937			0.337968	+	0.941157i	$0.390260\pi$
$264$		0			0
$265$	−2.99393			−0.183915
$266$	0.380739	−	0.276623i	0.0233446	−	0.0169609i
$267$	−2.16271	−	6.65613i	−0.132355	−	0.407348i
$268$	0.672190	−	2.06879i	0.0410605	−	0.126371i
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	0.589987	−	0.807413i	$-0.299133\pi$
$269$	0.0722816	+	0.0525156i	0.00440708	+	0.00320193i	−0.585580	+	0.810615i	$0.699133\pi$
$270$	3.57804	+	2.59960i	0.217752	+	0.158206i
$271$	4.14069	−	12.7437i	0.251529	−	0.774126i	−0.742965	−	0.669330i	$-0.766581\pi$
$271$	4.14069	−	12.7437i	0.251529	−	0.774126i	0.994494	−	0.104796i	$-0.0334190\pi$
$272$	4.16353	+	12.8140i	0.252451	+	0.776965i
$273$	−4.81010	+	3.49474i	−0.291120	+	0.211511i
$274$	12.9777			0.784010
$275$		0			0
$276$	−0.108445			−0.00652764
$277$	−3.16057	+	2.29629i	−0.189901	+	0.137971i	−0.678673	−	0.734440i	$-0.737445\pi$
$277$	−3.16057	+	2.29629i	−0.189901	+	0.137971i	0.488773	+	0.872411i	$0.337445\pi$
$278$	0.215957	+	0.664648i	0.0129523	+	0.0398630i
$279$	−5.59017	+	17.2048i	−0.334675	+	1.03002i
$280$	8.65409	+	6.28756i	0.517181	+	0.375754i
$281$	−1.24381	−	0.903680i	−0.0741994	−	0.0539090i	0.550067	−	0.835120i	$-0.314602\pi$
$281$	−1.24381	−	0.903680i	−0.0741994	−	0.0539090i	−0.624267	+	0.781211i	$0.714602\pi$
$282$	0.536401	−	1.65087i	0.0319422	−	0.0983081i
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	0.988377	−	0.152020i	$-0.0485778\pi$
$283$	1.67231	+	5.14683i	0.0994083	+	0.305947i	−0.888969	+	0.457967i	$0.848578\pi$
$284$	1.08920	−	0.791349i	0.0646320	−	0.0469579i
$285$	−0.0547434			−0.00324272
$286$		0			0
$287$	30.3566			1.79190
$288$	−1.97541	+	1.43522i	−0.116402	+	0.0845711i
$289$	−1.04122	−	3.20456i	−0.0612484	−	0.188503i
$290$	2.82938	−	8.70794i	0.166147	−	0.511348i
$291$	2.01659	+	1.46514i	0.118215	+	0.0858881i
$292$	0.173162	+	0.125809i	0.0101335	+	0.00736243i
$293$	−3.52789	+	10.8577i	−0.206102	+	0.634315i	0.793565	+	0.608486i	$0.208223\pi$
$293$	−3.52789	+	10.8577i	−0.206102	+	0.634315i	−0.999666	+	0.0258295i	$0.991777\pi$
$294$	−1.52326	−	4.68810i	−0.0888381	−	0.273415i
$295$	−6.88361	+	5.00123i	−0.400779	+	0.291183i
$296$	28.8421			1.67641
$297$		0			0
$298$	−11.0621			−0.640808
$299$	−2.66165	+	1.93381i	−0.153927	+	0.111835i
$300$	−0.0288358	−	0.0887475i	−0.00166484	−	0.00512384i
$301$	3.34780	−	10.3035i	0.192964	−	0.593883i
$302$	−2.12797	−	1.54606i	−0.122451	−	0.0889657i
$303$	4.61193	+	3.35077i	0.264949	+	0.192496i
$304$	−0.107275	+	0.330157i	−0.00615262	+	0.0189358i
$305$	−2.62058	−	8.06531i	−0.150054	−	0.461818i
$306$	10.8065	−	7.85141i	0.617769	−	0.448835i
$307$	4.25008			0.242565			0.121282	−	0.992618i	$-0.461299\pi$
$307$	4.25008			0.242565			0.121282	+	0.992618i	$0.461299\pi$
$308$		0			0
$309$	2.33990			0.133112
$310$	−7.43427	+	5.40131i	−0.422238	+	0.306774i
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	−0.984465	−	0.175579i	$-0.943820\pi$
$311$	−5.13570	−	15.8061i	−0.291219	−	0.896279i	0.693247	−	0.720700i	$-0.256180\pi$
$312$	1.47569	−	4.54172i	0.0835447	−	0.257124i
$313$	21.5012	+	15.6215i	1.21532	+	0.882982i	0.995703	−	0.0926041i	$-0.0295191\pi$
$313$	21.5012	+	15.6215i	1.21532	+	0.882982i	0.219617	+	0.975586i	$0.429519\pi$
$314$	23.3331	+	16.9525i	1.31676	+	0.956683i
$315$	3.00970	−	9.26289i	0.169577	−	0.521905i
$316$	−0.694778	−	2.13831i	−0.0390843	−	0.120289i
$317$	−4.68982	+	3.40736i	−0.263407	+	0.191376i	−0.711648	−	0.702537i	$-0.752051\pi$
$317$	−4.68982	+	3.40736i	−0.263407	+	0.191376i	0.448241	+	0.893913i	$0.352051\pi$
$318$	−2.33581			−0.130985
$319$		0			0
$320$	−8.53916			−0.477353
$321$	0.902569	−	0.655755i	0.0503765	−	0.0366007i
$322$	−1.77673	−	5.46822i	−0.0990134	−	0.304732i
$323$	−0.108525	+	0.334006i	−0.00603850	+	0.0185846i
$324$	0.803996	+	0.584137i	0.0446664	+	0.0324521i
$325$	−2.29029	−	1.66399i	−0.127042	−	0.0923018i
$326$	6.69484	−	20.6046i	0.370793	−	1.14118i
$327$	−1.08954	−	3.35327i	−0.0602519	−	0.185436i
$328$	−19.7255	+	14.3314i	−1.08916	+	0.791321i
$329$	−8.11961			−0.447648
$330$		0			0
$331$	−12.9230			−0.710311			−0.355155	−	0.934807i	$-0.615572\pi$
$331$	−12.9230			−0.710311			−0.355155	+	0.934807i	$0.615572\pi$
$332$	1.39634	−	1.01450i	0.0766340	−	0.0556779i
$333$	−8.11495	−	24.9752i	−0.444696	−	1.36863i
$334$	7.41878	−	22.8327i	0.405938	−	1.24935i
$335$	−10.8532	−	7.88531i	−0.592974	−	0.430820i
$336$	6.20075	+	4.50511i	0.338278	+	0.245774i
$337$	−4.13631	+	12.7303i	−0.225319	+	0.693461i	0.772940	+	0.634479i	$0.218785\pi$
$337$	−4.13631	+	12.7303i	−0.225319	+	0.693461i	−0.998259	+	0.0589818i	$0.981215\pi$
$338$	2.08864	+	6.42817i	0.113607	+	0.349646i
$339$	−2.69353	+	1.95696i	−0.146292	+	0.106288i
$340$	−0.598640			−0.0324658
$341$		0			0
$342$	0.344163			0.0186102
$343$	2.01291	−	1.46246i	0.108687	−	0.0789656i
$344$	2.68892	+	8.27564i	0.144977	+	0.446193i
$345$	−0.206673	+	0.636074i	−0.0111269	+	0.0342451i
$346$	−17.4226	−	12.6583i	−0.936646	−	0.680513i
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	0.389000	−	0.921238i	$-0.372821\pi$
$347$	−6.83538	−	4.96619i	−0.366942	−	0.266599i	−0.755942	+	0.654639i	$0.772821\pi$
$348$	−0.194754	+	0.599391i	−0.0104399	+	0.0321307i
$349$	3.21341	+	9.88987i	0.172010	+	0.529393i	0.999484	−	0.0321111i	$-0.0102230\pi$
$349$	3.21341	+	9.88987i	0.172010	+	0.529393i	−0.827474	+	0.561504i	$0.810223\pi$
$350$	4.00254	−	2.90802i	0.213945	−	0.155440i
$351$	−9.23559			−0.492959
$352$		0			0
$353$	19.1073			1.01698			0.508489	−	0.861069i	$-0.330204\pi$
$353$	19.1073			1.01698			0.508489	+	0.861069i	$0.330204\pi$
$354$	−5.37046	+	3.90187i	−0.285437	+	0.207382i
$355$	−2.56580	−	7.89671i	−0.136178	−	0.419114i
$356$	0.609350	−	1.87539i	0.0322955	−	0.0993953i
$357$	6.27303	+	4.55762i	0.332004	+	0.241215i
$358$	−18.5145	−	13.4516i	−0.978522	−	0.710938i
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	−0.908586	−	0.417698i	$-0.862837\pi$
$359$	1.36405	−	4.19813i	0.0719920	−	0.221569i	0.980578	+	0.196129i	$0.0628371\pi$
$360$	2.41735	+	7.43985i	0.127406	+	0.392115i
$361$	15.3640	−	11.1626i	0.808632	−	0.587505i
$362$	32.6546			1.71629
$363$		0			0
$364$	−1.67520			−0.0878041
$365$	1.06793	−	0.775895i	0.0558979	−	0.0406122i
$366$	−2.04453	−	6.29240i	−0.106869	−	0.328909i
$367$	−9.07327	+	27.9247i	−0.473621	+	1.45766i	0.374188	+	0.927353i	$0.377922\pi$
$367$	−9.07327	+	27.9247i	−0.473621	+	1.45766i	−0.847809	+	0.530302i	$0.822078\pi$
$368$	3.43117	+	2.49289i	0.178862	+	0.129951i
$369$	17.9600	+	13.0487i	0.934958	+	0.679287i
$370$	4.12215	−	12.6867i	0.214300	−	0.659549i
$371$	3.37634	+	10.3913i	0.175291	+	0.539490i
$372$	0.511720	−	0.371787i	0.0265315	−	0.0192762i
$373$	4.96478			0.257067			0.128533	−	0.991705i	$-0.458973\pi$
$373$	4.96478			0.257067			0.128533	+	0.991705i	$0.458973\pi$
$374$		0			0
$375$	−0.575493			−0.0297183
$376$	5.27606	−	3.83329i	0.272092	−	0.197687i
$377$	5.90839	+	18.1842i	0.304298	+	0.936532i
$378$	4.98761	−	15.3503i	0.256535	−	0.789534i
$379$	−6.40996	−	4.65711i	−0.329258	−	0.239220i	0.410858	−	0.911699i	$-0.365229\pi$
$379$	−6.40996	−	4.65711i	−0.329258	−	0.239220i	−0.740116	+	0.672480i	$0.765229\pi$
$380$	−0.0124784	−	0.00906608i	−0.000640128	−	0.000465080i
$381$	−0.433536	+	1.33429i	−0.0222107	+	0.0683576i
$382$	−2.25499	−	6.94016i	−0.115375	−	0.355089i
$383$	19.8335	−	14.4099i	1.01344	−	0.736309i	0.0485140	−	0.998823i	$-0.484551\pi$
$383$	19.8335	−	14.4099i	1.01344	−	0.736309i	0.964928	+	0.262514i	$0.0845514\pi$
$384$	−5.60903			−0.286235
$385$		0			0
$386$	24.7872			1.26164
$387$	6.40958	−	4.65683i	0.325817	−	0.236720i
$388$	0.217026	+	0.667939i	0.0110179	+	0.0339095i
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	−0.899118	−	0.437706i	$-0.855791\pi$
$389$	1.68752	−	5.19366i	0.0855608	−	0.263329i	0.984679	+	0.174377i	$0.0557911\pi$
$390$	−1.78684	−	1.29822i	−0.0904802	−	0.0657377i
$391$	3.47116	+	2.52195i	0.175544	+	0.127540i
$392$	5.72292	−	17.6133i	0.289051	−	0.889608i
$393$	−1.25225	−	3.85403i	−0.0631677	−	0.194410i
$394$	−2.90166	+	2.10818i	−0.146184	+	0.106209i
$395$	−13.8661			−0.697679
$396$		0			0
$397$	−6.43455			−0.322941			−0.161470	−	0.986878i	$-0.551624\pi$
$397$	−6.43455			−0.322941			−0.161470	+	0.986878i	$0.551624\pi$
$398$	7.15967	−	5.20180i	0.358882	−	0.260743i
$399$	0.0617358	+	0.190003i	0.00309066	+	0.00951206i
$400$	−1.12773	+	3.47080i	−0.0563865	+	0.173540i
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	0.843741	−	0.536751i	$-0.180348\pi$
$401$	11.8947	+	8.64197i	0.593991	+	0.431560i	−0.249750	+	0.968310i	$0.580348\pi$
$402$	−8.46746	−	6.15197i	−0.422319	−	0.306832i
$403$	5.92981	−	18.2501i	0.295385	−	0.909101i
$404$	0.496337	+	1.52757i	0.0246937	+	0.0759994i
$405$	4.95843	−	3.60251i	0.246386	−	0.179010i
$406$	−33.4143			−1.65832
$407$		0			0
$408$	−6.22784			−0.308324
$409$	3.55625	−	2.58376i	0.175845	−	0.127759i	−0.496381	−	0.868105i	$-0.665338\pi$
$409$	3.55625	−	2.58376i	0.175845	−	0.127759i	0.672226	+	0.740346i	$0.265338\pi$
$410$	3.48472	+	10.7249i	0.172098	+	0.529664i
$411$	−1.70241	+	5.23948i	−0.0839737	+	0.258444i
$412$	0.533365	+	0.387512i	0.0262770	+	0.0190914i
$413$	25.1211	+	18.2516i	1.23613	+	0.898101i
$414$	1.29932	−	3.99890i	0.0638581	−	0.196535i
$415$	−3.28932	−	10.1235i	−0.161466	−	0.496942i
$416$	2.09543	−	1.52242i	0.102737	−	0.0746427i
$417$	−0.296668			−0.0145279
$418$		0			0
$419$	17.8526			0.872159			0.436079	−	0.899908i	$-0.356367\pi$
$419$	17.8526			0.872159			0.436079	+	0.899908i	$0.356367\pi$
$420$	−0.275506	+	0.200167i	−0.0134433	+	0.00976713i
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	0.908090	−	0.418776i	$-0.137541\pi$
$421$	−1.49210	−	4.59221i	−0.0727205	−	0.223811i	−0.980810	+	0.194965i	$0.937541\pi$
$422$	−11.4986	+	35.3891i	−0.559743	+	1.72271i
$423$	−4.80382	−	3.49018i	−0.233570	−	0.169698i
$424$	−7.09969	−	5.15823i	−0.344792	−	0.250506i
$425$	−1.14088	+	3.51126i	−0.0553407	+	0.170321i
$426$	−2.00179	−	6.16086i	−0.0969868	−	0.298495i
$427$	−25.0378	+	18.1910i	−1.21166	+	0.880324i
$428$	0.314335			0.0151939
$429$		0			0
$430$	4.02448			0.194078
$431$	−20.1234	+	14.6205i	−0.969312	+	0.704247i	−0.955295	−	0.295655i	$-0.904462\pi$
$431$	−20.1234	+	14.6205i	−0.969312	+	0.704247i	−0.0140175	+	0.999902i	$0.504462\pi$
$432$	3.67906	+	11.3230i	0.177009	+	0.544778i
$433$	−6.56669	+	20.2102i	−0.315575	+	0.971240i	0.659942	+	0.751316i	$0.270581\pi$
$433$	−6.56669	+	20.2102i	−0.315575	+	0.971240i	−0.975517	+	0.219923i	$0.929419\pi$
$434$	27.1307	+	19.7116i	1.30232	+	0.946188i
$435$	3.14450	+	2.28461i	0.150767	+	0.109539i
$436$	0.306983	−	0.944796i	0.0147018	−	0.0452475i
$437$	0.0341614	+	0.105138i	0.00163416	+	0.00502943i
$438$	0.833177	−	0.605339i	0.0398107	−	0.0289242i
$439$	15.9119			0.759434			0.379717	−	0.925103i	$-0.376021\pi$
$439$	15.9119			0.759434			0.379717	+	0.925103i	$0.376021\pi$
$440$		0			0
$441$	−16.8621			−0.802958
$442$	−11.4631	+	8.32843i	−0.545244	+	0.396143i
$443$	8.12332	+	25.0010i	0.385951	+	1.18783i	0.935788	+	0.352562i	$0.114690\pi$
$443$	8.12332	+	25.0010i	0.385951	+	1.18783i	−0.549838	+	0.835272i	$0.685310\pi$
$444$	−0.283738	+	0.873257i	−0.0134656	+	0.0414429i
$445$	−9.83859	−	7.14815i	−0.466394	−	0.338855i
$446$	−5.57368	−	4.04952i	−0.263922	−	0.191750i
$447$	1.45112	−	4.46609i	0.0686356	−	0.211239i
$448$	9.62987	+	29.6377i	0.454969	+	1.40025i
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	−0.420366	−	0.907354i	$-0.638098\pi$
$449$	6.62554	−	4.81373i	0.312678	−	0.227174i	0.733045	+	0.680180i	$0.238098\pi$
$450$	3.61803			0.170556
$451$		0			0
$452$	−0.938065			−0.0441229
$453$	0.903337	−	0.656313i	0.0424425	−	0.0308363i
$454$	1.56670	+	4.82181i	0.0735289	+	0.226299i
$455$	−3.19256	+	9.82567i	−0.149669	+	0.460635i
$456$	−0.129817	−	0.0943172i	−0.00607922	−	0.00441681i
$457$	9.64056	+	7.00428i	0.450966	+	0.327646i	0.789977	−	0.613136i	$-0.210092\pi$
$457$	9.64056	+	7.00428i	0.450966	+	0.327646i	−0.339011	+	0.940782i	$0.610092\pi$
$458$	−11.2792	+	34.7139i	−0.527043	+	1.62207i
$459$	3.72195	+	11.4550i	0.173726	+	0.534673i
$460$	−0.152450	+	0.110762i	−0.00710803	+	0.00516429i
$461$	−6.96172			−0.324240			−0.162120	−	0.986771i	$-0.551833\pi$
$461$	−6.96172			−0.324240			−0.162120	+	0.986771i	$0.551833\pi$
$462$		0			0
$463$	12.4762			0.579817			0.289909	−	0.957054i	$-0.406375\pi$
$463$	12.4762			0.579817			0.289909	+	0.957054i	$0.406375\pi$
$464$	19.9404	−	14.4876i	0.925712	−	0.672569i
$465$	−1.20545	−	3.70998i	−0.0559012	−	0.172046i
$466$	7.67335	−	23.6161i	0.355461	−	1.09400i
$467$	4.97235	+	3.61263i	0.230093	+	0.167172i	0.696858	−	0.717209i	$-0.254581\pi$
$467$	4.97235	+	3.61263i	0.230093	+	0.167172i	−0.466765	+	0.884381i	$0.654581\pi$
$468$	−0.991100	−	0.720076i	−0.0458136	−	0.0332855i
$469$	−15.1288	+	46.5618i	−0.698585	+	2.15002i
$470$	−0.932072	−	2.86862i	−0.0429933	−	0.132320i
$471$	−9.90505	+	7.19644i	−0.456401	+	0.331594i
$472$	−24.9401			−1.14796
$473$		0			0
$474$	−10.8181			−0.496890
$475$	−0.0769572	+	0.0559127i	−0.00353104	+	0.00256545i
$476$	0.675105	+	2.07776i	0.0309434	+	0.0952340i
$477$	−2.46911	+	7.59915i	−0.113053	+	0.347941i
$478$	12.0160	+	8.73013i	0.549599	+	0.399307i
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	0.916829	−	0.399281i	$-0.130740\pi$
$479$	17.9555	+	13.0454i	0.820406	+	0.596060i	−0.0964228	+	0.995340i	$0.530740\pi$
$480$	0.162706	−	0.500759i	0.00742650	−	0.0228564i
$481$	8.60798	+	26.4926i	0.392490	+	1.20796i
$482$	10.9615	−	7.96402i	0.499284	−	0.362751i
$483$	2.44076			0.111058
$484$		0			0
$485$	4.33133			0.196675
$486$	14.6026	−	10.6094i	0.662387	−	0.481252i
$487$	−10.5778	−	32.5553i	−0.479328	−	1.47522i	−0.840030	−	0.542539i	$-0.817463\pi$
$487$	−10.5778	−	32.5553i	−0.479328	−	1.47522i	0.360702	−	0.932681i	$-0.382537\pi$
$488$	7.68135	−	23.6408i	0.347719	−	1.07017i
$489$	7.44047	+	5.40582i	0.336470	+	0.244460i
$490$	−6.92960	−	5.03465i	−0.313047	−	0.227442i
$491$	5.25197	−	16.1639i	0.237018	−	0.729467i	−0.759829	−	0.650123i	$-0.774717\pi$
$491$	5.25197	−	16.1639i	0.237018	−	0.729467i	0.996847	−	0.0793441i	$-0.0252826\pi$
$492$	−0.239863	−	0.738221i	−0.0108138	−	0.0332816i
$493$	20.1729	−	14.6565i	0.908541	−	0.660094i
$494$	−0.365073			−0.0164254
$495$		0			0
$496$	−24.7371			−1.11073
$497$	−24.5144	+	17.8107i	−1.09962	+	0.798920i
$498$	−2.56626	−	7.89815i	−0.114997	−	0.353925i
$499$	1.61599	−	4.97352i	0.0723418	−	0.222645i	−0.908348	−	0.418215i	$-0.862656\pi$
$499$	1.61599	−	4.97352i	0.0723418	−	0.222645i	0.980690	+	0.195570i	$0.0626558\pi$
$500$	−0.131180	−	0.0953077i	−0.00586654	−	0.00426229i
$501$	8.24504	+	5.99037i	0.368361	+	0.267630i
$502$	−4.04575	+	12.4515i	−0.180571	+	0.555740i
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	−0.625973	−	0.779845i	$-0.715298\pi$
$503$	−12.9617	−	39.8919i	−0.577931	−	1.77869i	0.0480416	−	0.998845i	$-0.484702\pi$
$504$	23.0961	−	16.7803i	1.02878	−	0.747454i
$505$	9.90570			0.440798
$506$		0			0
$507$	−2.86923			−0.127427
$508$	−0.319794	+	0.232344i	−0.0141886	+	0.0103086i
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	0.988140	+	0.153557i	$0.0490728\pi$
$509$	6.29399	+	19.3709i	0.278976	+	0.858601i	−0.709163	+	0.705044i	$0.750927\pi$
$510$	−0.890091	+	2.73942i	−0.0394139	+	0.121303i
$511$	−3.89731	−	2.83156i	−0.172407	−	0.125261i
$512$	−20.0094	−	14.5377i	−0.884300	−	0.642481i
$513$	−0.0958972	+	0.295141i	−0.00423396	+	0.0130308i
$514$	−4.36838	−	13.4445i	−0.192681	−	0.593012i
$515$	3.28939	−	2.38988i	0.144948	−	0.105311i
$516$	−0.277016			−0.0121949
$517$		0			0
$518$	−48.6816			−2.13895
$519$	7.39602	−	5.37352i	0.324649	−	0.235872i
$520$	−2.56422	−	7.89187i	−0.112449	−	0.346081i
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	−0.803958	−	0.594686i	$-0.797276\pi$
$521$	4.47391	−	13.7693i	0.196005	−	0.603243i	0.999963	−	0.00855656i	$-0.00272367\pi$
$522$	−19.7690	−	14.3630i	−0.865265	−	0.628652i
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	0.767419	−	0.641146i	$-0.221541\pi$
$523$	9.02873	+	6.55975i	0.394799	+	0.286838i	−0.372620	+	0.927984i	$0.621541\pi$
$524$	0.352826	−	1.08589i	0.0154133	−	0.0474372i
$525$	0.649001	+	1.99742i	0.0283247	+	0.0871746i
$526$	12.0226	−	8.73490i	0.524209	−	0.380860i
$527$	−25.0254			−1.09013
$528$		0			0
$529$	−21.6494			−0.941279
$530$	−3.28363	+	2.38570i	−0.142632	+	0.103628i
$531$	7.01710	+	21.5964i	0.304516	+	0.937205i
$532$	−0.0173943	+	0.0535341i	−0.000754138	+	0.00232100i
$533$	−19.0511	−	13.8415i	−0.825197	−	0.599540i
$534$	−7.67588	−	5.57685i	−0.332168	−	0.241334i
$535$	0.599053	−	1.84369i	0.0258993	−	0.0797099i
$536$	−12.1513	−	37.3979i	−0.524857	−	1.61534i
$537$	7.85954	−	5.71029i	0.339164	−	0.246417i
$538$	0.121123			0.00522197
$539$		0			0
$540$	−0.528983			−0.0227638
$541$	8.64094	−	6.27801i	0.371503	−	0.269913i	−0.386331	−	0.922360i	$-0.626258\pi$
$541$	8.64094	−	6.27801i	0.371503	−	0.269913i	0.757834	+	0.652447i	$0.226258\pi$
$542$	−5.61343	−	17.2763i	−0.241117	−	0.742083i
$543$	−4.28363	+	13.1837i	−0.183828	+	0.565765i
$544$	−2.73273	−	1.98544i	−0.117165	−	0.0851251i
$545$	−4.95655	−	3.60115i	−0.212315	−	0.154256i
$546$	−2.49077	+	7.66581i	−0.106595	+	0.328066i
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	0.938847	−	0.344334i	$-0.111895\pi$
$547$	−0.540038	−	1.66207i	−0.0230904	−	0.0710648i	−0.961938	+	0.273269i	$0.911895\pi$
$548$	−1.25577	+	0.912367i	−0.0536437	+	0.0389744i
$549$	−22.6325			−0.965930
$550$		0			0
$551$	0.642459			0.0273697
$552$	−1.58599	+	1.15229i	−0.0675041	+	0.0490446i
$553$	15.6372	+	48.1264i	0.664962	+	2.04654i
$554$	−1.63661	+	5.03698i	−0.0695331	+	0.214001i
$555$	4.58125	+	3.32847i	0.194463	+	0.141286i
$556$	−0.0676235	−	0.0491313i	−0.00286787	−	0.00208363i
$557$	6.02100	−	18.5307i	0.255118	−	0.785173i	−0.738688	−	0.674047i	$-0.764554\pi$
$557$	6.02100	−	18.5307i	0.255118	−	0.785173i	0.993806	−	0.111126i	$-0.0354456\pi$
$558$	7.57845	+	23.3241i	0.320821	+	0.987387i
$559$	−6.79900	+	4.93976i	−0.287567	+	0.208930i
$560$	13.3182			0.562798
$561$		0			0
$562$	−2.08426			−0.0879191
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	−0.809338	−	0.587343i	$-0.800174\pi$
$563$	−11.8838	+	8.63407i	−0.500842	+	0.363883i	0.308497	+	0.951225i	$0.400174\pi$
$564$	0.0641570	+	0.197455i	0.00270150	+	0.00831435i
$565$	−1.78775	+	5.50212i	−0.0752111	+	0.231476i
$566$	5.93535	+	4.31228i	0.249481	+	0.181259i
$567$	−18.0954	−	13.1471i	−0.759934	−	0.552124i
$568$	7.52078	−	23.1466i	0.315565	−	0.971209i
$569$	−6.15980	−	18.9579i	−0.258232	−	0.794758i	−0.993176	−	0.116629i	$-0.962791\pi$
$569$	−6.15980	−	18.9579i	−0.258232	−	0.794758i	0.734943	−	0.678129i	$-0.237209\pi$
$570$	−0.0600406	+	0.0436220i	−0.00251482	+	0.00182713i
$571$	−5.24422			−0.219464			−0.109732	−	0.993961i	$-0.534999\pi$
$571$	−5.24422			−0.219464			−0.109732	+	0.993961i	$0.534999\pi$
$572$		0			0
$573$	3.09776			0.129411
$574$	33.2940	−	24.1895i	1.38967	−	1.00965i
$575$	0.359123	+	1.10527i	0.0149765	+	0.0460928i
$576$	−7.04230	+	21.6740i	−0.293429	+	0.903083i
$577$	−30.4194	−	22.1010i	−1.26637	−	0.920075i	−0.267323	−	0.963607i	$-0.586139\pi$
$577$	−30.4194	−	22.1010i	−1.26637	−	0.920075i	−0.999052	+	0.0435320i	$0.986139\pi$
$578$	−3.69551	−	2.68495i	−0.153713	−	0.111679i
$579$	−3.25158	+	10.0073i	−0.135131	+	0.415891i
$580$	0.338412	+	1.04153i	0.0140518	+	0.0432470i
$581$	−31.4271	+	22.8331i	−1.30382	+	0.947278i
$582$	3.37922			0.140073
$583$		0			0
$584$	3.86923			0.160110
$585$	−6.11235	+	4.44088i	−0.252714	+	0.183608i
$586$	4.78267	+	14.7195i	0.197570	+	0.608059i
$587$	7.90191	−	24.3196i	0.326147	−	1.00378i	−0.644774	−	0.764373i	$-0.723048\pi$
$587$	7.90191	−	24.3196i	0.326147	−	1.00378i	0.970920	−	0.239403i	$-0.0769516\pi$
$588$	0.476982	+	0.346548i	0.0196704	+	0.0142914i
$589$	−0.521644	−	0.378997i	−0.0214940	−	0.0156163i
$590$	−3.56448	+	10.9703i	−0.146747	+	0.451642i
$591$	−0.470497	−	1.44804i	−0.0193536	−	0.0595644i
$592$	29.0514	−	21.1071i	1.19400	−	0.867495i
$593$	−40.2260			−1.65188			−0.825942	−	0.563754i	$-0.809356\pi$
$593$	−40.2260			−1.65188			−0.825942	+	0.563754i	$0.809356\pi$
$594$		0			0
$595$	13.4735			0.552358
$596$	1.07040	−	0.777695i	0.0438455	−	0.0318556i
$597$	1.16092	+	3.57295i	0.0475133	+	0.146231i
$598$	−1.37826	+	4.24185i	−0.0563613	+	0.173462i
$599$	−3.98843	−	2.89776i	−0.162963	−	0.118399i	0.503315	−	0.864103i	$-0.332114\pi$
$599$	−3.98843	−	2.89776i	−0.162963	−	0.118399i	−0.666278	+	0.745704i	$0.732114\pi$
$600$	−1.36470	−	0.991515i	−0.0557138	−	0.0404784i
$601$	−14.2425	+	43.8338i	−0.580963	+	1.78802i	0.0339497	+	0.999424i	$0.489191\pi$
$601$	−14.2425	+	43.8338i	−0.580963	+	1.78802i	−0.614912	+	0.788596i	$0.710809\pi$
$602$	−4.53853	−	13.9682i	−0.184977	−	0.569300i
$603$	−28.9651	+	21.0444i	−1.17955	+	0.856993i
$604$	0.314602			0.0128010
$605$		0			0
$606$	7.72824			0.313938
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.505288	+	0.862951i	$0.668614\pi$
$607$	−36.5162	+	26.5306i	−1.48215	+	1.07684i	−0.976857	+	0.213891i	$0.931386\pi$
$608$	−0.0268941	−	0.0827714i	−0.00109070	−	0.00335682i
$609$	4.38328	−	13.4904i	0.177620	−	0.546657i
$610$	−9.30096	−	6.75754i	−0.376585	−	0.273605i
$611$	5.09568	+	3.70223i	0.206149	+	0.149776i
$612$	−0.493703	+	1.51946i	−0.0199567	+	0.0614206i
$613$	−1.46294	−	4.50247i	−0.0590877	−	0.181853i	0.917156	−	0.398528i	$-0.130479\pi$
$613$	−1.46294	−	4.50247i	−0.0590877	−	0.181853i	−0.976244	+	0.216675i	$0.930479\pi$
$614$	4.66133	−	3.38666i	0.188116	−	0.136674i
$615$	−4.78708			−0.193034
$616$		0			0
$617$	17.8468			0.718486			0.359243	−	0.933244i	$-0.383035\pi$
$617$	17.8468			0.718486			0.359243	+	0.933244i	$0.383035\pi$
$618$	2.56632	−	1.86454i	0.103232	−	0.0750027i
$619$	0.110304	+	0.339482i	0.00443351	+	0.0136449i	0.953249	−	0.302187i	$-0.0977166\pi$
$619$	0.110304	+	0.339482i	0.00443351	+	0.0136449i	−0.948815	+	0.315832i	$0.897717\pi$
$620$	0.339639	−	1.04530i	0.0136402	−	0.0419803i
$621$	3.06726	+	2.22850i	0.123085	+	0.0894264i
$622$	−18.2276	−	13.2431i	−0.730861	−	0.531002i
$623$	−13.7145	+	42.2089i	−0.549461	+	1.69107i
$624$	−1.83729	−	5.65461i	−0.0735506	−	0.226365i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	36.0297			1.44004
$627$		0			0
$628$	−3.44960			−0.137654
$629$	29.3900	−	21.3531i	1.17186	−	0.851404i
$630$	−4.08017	−	12.5575i	−0.162558	−	0.500302i
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	0.536516	+	0.843890i	$0.319740\pi$
$631$	−9.88614	+	30.4264i	−0.393561	+	1.21126i	−0.930077	+	0.367366i	$0.880260\pi$
$632$	−32.8815	−	23.8898i	−1.30796	−	0.950287i
$633$	−12.7792	−	9.28466i	−0.507929	−	0.369032i
$634$	−2.42849	+	7.47413i	−0.0964477	+	0.296836i
$635$	0.753330	+	2.31851i	0.0298950	+	0.0920073i
$636$	0.226021	−	0.164214i	0.00896231	−	0.00651150i
$637$	17.8866			0.708693
$638$		0			0
$639$	−22.1594			−0.876610
$640$	−7.88507	+	5.72884i	−0.311685	+	0.226452i
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	0.957047	−	0.289932i	$-0.0936326\pi$
$641$	0.312987	+	0.963274i	0.0123622	+	0.0380470i	−0.944685	+	0.327979i	$0.893633\pi$
$642$	0.467370	−	1.43842i	0.0184456	−	0.0567697i
$643$	12.1130	+	8.80057i	0.477688	+	0.347061i	0.800430	−	0.599426i	$-0.204605\pi$
$643$	12.1130	+	8.80057i	0.477688	+	0.347061i	−0.322742	+	0.946487i	$0.604605\pi$
$644$	0.556354	+	0.404215i	0.0219234	+	0.0159283i
$645$	−0.527931	+	1.62480i	−0.0207873	+	0.0639766i
$646$	0.147125	+	0.452803i	0.00578855	+	0.0178153i
$647$	−14.4712	+	10.5139i	−0.568920	+	0.413345i	−0.834713	−	0.550686i	$-0.814366\pi$
$647$	−14.4712	+	10.5139i	−0.568920	+	0.413345i	0.265793	+	0.964030i	$0.414366\pi$
$648$	17.9650			0.705732
$649$		0			0
$650$	−3.83785			−0.150533
$651$	−11.5172	+	8.36772i	−0.451394	+	0.327957i
$652$	0.800746	+	2.46444i	0.0313596	+	0.0965150i
$653$	14.1419	−	43.5244i	0.553416	−	1.70324i	−0.146673	−	0.989185i	$-0.546856\pi$
$653$	14.1419	−	43.5244i	0.553416	−	1.70324i	0.700089	−	0.714055i	$-0.253144\pi$
$654$	−3.86701	−	2.80955i	−0.151212	−	0.109862i
$655$	−5.69674	−	4.13892i	−0.222590	−	0.161721i
$656$	−9.38072	+	28.8709i	−0.366255	+	1.12722i
$657$	−1.08864	−	3.35049i	−0.0424719	−	0.130715i
$658$	−8.90529	+	6.47007i	−0.347164	+	0.252230i
$659$	9.54036			0.371640			0.185820	−	0.982584i	$-0.440506\pi$
$659$	9.54036			0.371640			0.185820	+	0.982584i	$0.440506\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$	−14.1734	+	10.2976i	−0.550866	+	0.400228i
$663$	−1.85871	−	5.72052i	−0.0721863	−	0.222167i
$664$	9.64154	−	29.6736i	0.374164	−	1.15156i
$665$	0.280849	+	0.204048i	0.0108908	+	0.00791266i
$666$	−28.8016	−	20.9256i	−1.11604	−	0.810850i
$667$	2.42548	−	7.46486i	0.0939149	−	0.289040i
$668$	0.887333	+	2.73093i	0.0343319	+	0.105663i
$669$	2.36607	−	1.71905i	0.0914774	−	0.0664622i
$670$	−18.1868			−0.702616
$671$		0			0
$672$	−1.92152			−0.0741243
$673$	38.2690	−	27.8041i	1.47516	−	1.07177i	0.496086	−	0.868273i	$-0.334770\pi$
$673$	38.2690	−	27.8041i	1.47516	−	1.07177i	0.979076	−	0.203494i	$-0.0652299\pi$
$674$	5.60749	+	17.2581i	0.215992	+	0.664756i
$675$	−1.00812	+	3.10269i	−0.0388027	+	0.119423i
$676$	−0.654023	−	0.475175i	−0.0251547	−	0.0182760i
$677$	22.2828	+	16.1894i	0.856399	+	0.622210i	0.926903	−	0.375301i	$-0.122461\pi$
$677$	22.2828	+	16.1894i	0.856399	+	0.622210i	−0.0705039	+	0.997512i	$0.522461\pi$
$678$	−1.39477	+	4.29265i	−0.0535657	+	0.164858i
$679$	−4.88457	−	15.0332i	−0.187453	−	0.576920i
$680$	−8.75497	+	6.36086i	−0.335738	+	0.243928i
$681$	−2.15223			−0.0824736
$682$		0			0
$683$	−27.1617			−1.03931			−0.519656	−	0.854375i	$-0.673940\pi$
$683$	−27.1617			−1.03931			−0.519656	+	0.854375i	$0.673940\pi$
$684$	−0.0333024	+	0.0241956i	−0.00127335	+	0.000925143i
$685$	2.95818	+	9.10433i	0.113026	+	0.347859i
$686$	1.04233	−	3.20795i	0.0397962	−	0.122480i
$687$	−12.5354	−	9.10752i	−0.478256	−	0.347474i
$688$	8.76467	+	6.36790i	0.334150	+	0.242774i
$689$	2.61913	−	8.06084i	0.0997808	−	0.307094i
$690$	0.280181	+	0.862309i	0.0106663	+	0.0328275i
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	−0.465906	−	0.884834i	$-0.654272\pi$
$691$	6.08931	−	4.42414i	0.231648	−	0.168302i	0.697554	+	0.716532i	$0.254272\pi$
$692$	2.57579			0.0979167
$693$		0			0
$694$	−11.4541			−0.434791
$695$	−0.417050	+	0.303004i	−0.0158196	+	0.0114936i
$696$	3.52060	+	10.8353i	0.133448	+	0.410711i
$697$	−9.49007	+	29.2074i	−0.359462	+	1.10631i
$698$	11.4051	+	8.28625i	0.431688	+	0.313639i
$699$	8.52796	+	6.19593i	0.322557	+	0.234351i
$700$	−0.182858	+	0.562780i	−0.00691140	+	0.0212711i
$701$	9.83315	+	30.2633i	0.371393	+	1.14303i	0.945880	+	0.324516i	$0.105201\pi$
$701$	9.83315	+	30.2633i	0.371393	+	1.14303i	−0.574487	+	0.818513i	$0.694799\pi$
$702$	−10.1293	+	7.35934i	−0.382304	+	0.277760i
$703$	0.936004			0.0353021
$704$		0			0
$705$	1.28042			0.0482234
$706$	20.9562	−	15.2255i	0.788696	−	0.573021i
$707$	−11.1710	−	34.3807i	−0.420127	−	1.29302i
$708$	0.245352	−	0.755117i	0.00922091	−	0.0283790i
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	0.785109	−	0.619357i	$-0.212607\pi$
$709$	11.6807	+	8.48651i	0.438677	+	0.318718i	−0.346432	+	0.938075i	$0.612607\pi$
$710$	−9.10653	−	6.61628i	−0.341762	−	0.248305i
$711$	−11.4355	+	35.1947i	−0.428863	+	1.31991i
$712$	−11.0153	−	33.9017i	−0.412817	−	1.27052i
$713$	−6.37300	+	4.63026i	−0.238671	+	0.173405i
$714$	10.5117			0.393392
$715$		0			0
$716$	2.73721			0.102294
$717$	−5.10087	+	3.70600i	−0.190496	+	0.138403i
$718$	−1.84921	−	5.69129i	−0.0690120	−	0.212397i
$719$	1.67179	−	5.14526i	0.0623474	−	0.191886i	−0.915031	−	0.403383i	$-0.867834\pi$
$719$	1.67179	−	5.14526i	0.0623474	−	0.191886i	0.977378	+	0.211498i	$0.0678341\pi$
$720$	7.87949	+	5.72478i	0.293651	+	0.213350i
$721$	−12.0043	−	8.72166i	−0.447065	−	0.324811i
$722$	7.95581	−	24.4855i	0.296085	−	0.911255i
$723$	1.77738	+	5.47022i	0.0661016	+	0.203440i
$724$	−3.15978	+	2.29571i	−0.117432	+	0.0853195i
$725$	6.75389			0.250833
$726$		0			0
$727$	−16.7753			−0.622161			−0.311080	−	0.950384i	$-0.600691\pi$
$727$	−16.7753			−0.622161			−0.311080	+	0.950384i	$0.600691\pi$
$728$	−24.4993	+	17.7998i	−0.908006	+	0.659705i
$729$	−3.31409	−	10.1997i	−0.122744	−	0.377767i
$730$	0.552996	−	1.70195i	0.0204673	−	0.0629919i
$731$	8.86684	+	6.44213i	0.327952	+	0.238271i
$732$	0.640209	+	0.465139i	0.0236628	+	0.0171920i
$733$	4.35252	−	13.3957i	0.160764	−	0.494781i	−0.837935	−	0.545770i	$-0.816237\pi$
$733$	4.35252	−	13.3957i	0.160764	−	0.494781i	0.998699	+	0.0509889i	$0.0162373\pi$
$734$	12.3004	+	37.8567i	0.454016	+	1.39732i
$735$	2.94166	−	2.13724i	0.108505	−	0.0788334i
$736$	−1.06327			−0.0391926
$737$		0			0
$738$	30.0956			1.10783
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.977971	−	0.208743i	$-0.933063\pi$
$739$	−29.4043	+	21.3635i	−1.08165	+	0.785868i	−0.103683	+	0.994610i	$0.533063\pi$
$740$	0.493035	+	1.51741i	0.0181243	+	0.0557810i
$741$	0.0478902	−	0.147391i	0.00175929	−	0.00541454i
$742$	11.9833	+	8.70640i	0.439922	+	0.319622i
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	0.558362	−	0.829597i	$-0.311430\pi$
$743$	−1.58338	−	1.15039i	−0.0580884	−	0.0422037i	−0.616451	+	0.787394i	$0.711430\pi$
$744$	3.53336	−	10.8746i	0.129539	−	0.398681i
$745$	−2.52153	−	7.76046i	−0.0923815	−	0.284321i
$746$	5.44519	−	3.95617i	0.199363	−	0.144846i
$747$	−28.4080			−1.03939
$748$		0			0
$749$	−7.07466			−0.258503
$750$	−0.631180	+	0.458579i	−0.0230474	+	0.0167449i
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	0.999414	+	0.0342181i	$0.0108941\pi$
$751$	5.78189	+	17.7948i	0.210984	+	0.649342i	−0.788430	+	0.615124i	$0.789106\pi$
$752$	2.50910	−	7.72220i	0.0914973	−	0.281600i
$753$	−4.49634	−	3.26678i	−0.163856	−	0.119048i
$754$	20.9701	+	15.2356i	0.763685	+	0.554850i
$755$	0.599563	−	1.84526i	0.0218203	−	0.0671560i
$756$	0.596550	+	1.83599i	0.0216963	+	0.0667744i
$757$	11.7688	−	8.55054i	0.427744	−	0.310775i	−0.353002	−	0.935623i	$-0.614839\pi$
$757$	11.7688	−	8.55054i	0.427744	−	0.310775i	0.780746	+	0.624848i	$0.214839\pi$
$758$	−10.7412			−0.390138
$759$		0			0
$760$	−0.278825			−0.0101141
$761$	10.6309	−	7.72383i	0.385371	−	0.279989i	−0.378185	−	0.925730i	$-0.623452\pi$
$761$	10.6309	−	7.72383i	0.385371	−	0.279989i	0.763556	+	0.645741i	$0.223452\pi$
$762$	0.587734	+	1.80886i	0.0212914	+	0.0655281i
$763$	−6.90920	+	21.2643i	−0.250130	+	0.769820i
$764$	0.706114	+	0.513022i	0.0255463	+	0.0185605i
$765$	7.97134	+	5.79152i	0.288204	+	0.209393i
$766$	10.2702	−	31.6084i	0.371077	−	1.14206i
$767$	−7.44344	−	22.9085i	−0.268767	−	0.827180i
$768$	1.79960	−	1.30749i	0.0649376	−	0.0471799i
$769$	−38.9767			−1.40554			−0.702768	−	0.711419i	$-0.748053\pi$
$769$	−38.9767			−1.40554			−0.702768	+	0.711419i	$0.748053\pi$
$770$		0			0
$771$	6.00099			0.216121
$772$	−2.39850	+	1.74261i	−0.0863239	+	0.0627179i
$773$	−11.9756	−	36.8571i	−0.430733	−	1.32566i	−0.897397	−	0.441225i	$-0.854544\pi$
$773$	−11.9756	−	36.8571i	−0.430733	−	1.32566i	0.466664	−	0.884435i	$-0.345456\pi$
$774$	3.31902	−	10.2149i	0.119300	−	0.367167i
$775$	−5.48382	−	3.98423i	−0.196985	−	0.143118i
$776$	10.2712	+	7.46243i	0.368713	+	0.267886i
$777$	6.38604	−	19.6542i	0.229098	−	0.705091i
$778$	−2.28773	−	7.04091i	−0.0820192	−	0.252429i
$779$	−0.640147	+	0.465094i	−0.0229356	+	0.0166637i
$780$	0.264169			0.00945878
$781$		0			0
$782$	5.81665			0.208003
$783$	17.8256	−	12.9510i	0.637034	−	0.462832i
$784$	−7.12525	−	21.9293i	−0.254473	−	0.783188i
$785$	−6.57418	+	20.2332i	−0.234642	+	0.722155i
$786$	−4.44449	−	3.22911i	−0.158530	−	0.115179i
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	0.235077	−	0.971977i	$-0.424466\pi$
$787$	−17.3002	−	12.5693i	−0.616685	−	0.448048i	−0.851762	+	0.523929i	$0.824466\pi$
$788$	0.132564	−	0.407990i	0.00472240	−	0.0145341i
$789$	1.94943	+	5.99971i	0.0694014	+	0.213595i
$790$	−15.2078	+	11.0491i	−0.541070	+	0.393110i
$791$	21.1128			0.750686
$792$		0			0
$793$	24.0075			0.852533
$794$	−7.05718	+	5.12734i	−0.250450	+	0.181963i
$795$	−0.532431	−	1.63866i	−0.0188834	−	0.0581171i
$796$	−0.327093	+	1.00669i	−0.0115935	+	0.0356812i
$797$	1.79970	+	1.30756i	0.0637488	+	0.0463162i	0.619203	−	0.785231i	$-0.287456\pi$
$797$	1.79970	+	1.30756i	0.0637488	+	0.0463162i	−0.555454	+	0.831547i	$0.687456\pi$
$798$	0.219113	+	0.159195i	0.00775651	+	0.00563543i
$799$	2.53834	−	7.81222i	0.0898002	−	0.276377i
$800$	−0.282725	−	0.870139i	−0.00999585	−	0.0307641i
$801$	−26.2573	+	19.0770i	−0.927756	+	0.674054i
$802$	19.9319			0.703821
$803$		0			0
$804$	1.25184			0.0441491
$805$	3.43117	−	2.49289i	0.120933	−	0.0878628i
$806$	−8.03889	−	24.7412i	−0.283158	−	0.871470i
$807$	−0.0158888	+	0.0489008i	−0.000559314	+	0.00172139i
$808$	23.4900	+	17.0665i	0.826376	+	0.600397i
$809$	17.1254	+	12.4424i	0.602098	+	0.437450i	0.846623	−	0.532193i	$-0.178632\pi$
$809$	17.1254	+	12.4424i	0.602098	+	0.437450i	−0.244525	+	0.969643i	$0.578632\pi$
$810$	2.56758	−	7.90221i	0.0902156	−	0.277655i
$811$	11.3462	+	34.9201i	0.398420	+	1.22621i	0.926266	+	0.376871i	$0.123000\pi$
$811$	11.3462	+	34.9201i	0.398420	+	1.22621i	−0.527845	+	0.849341i	$0.677000\pi$
$812$	3.23329	−	2.34912i	0.113466	−	0.0824380i
$813$	7.71135			0.270449
$814$		0			0
$815$	15.9810			0.559788
$816$	−6.27303	+	4.55762i	−0.219600	+	0.159549i
$817$	0.0872627	+	0.268567i	0.00305294	+	0.00939597i
$818$	1.84150	−	5.66756i	0.0643866	−	0.198161i
$819$	22.3065	+	16.2066i	0.779451	+	0.566305i
$820$	−1.09118	−	0.792791i	−0.0381058	−	0.0276855i
$821$	12.2585	−	37.7278i	0.427825	−	1.31671i	−0.472439	−	0.881363i	$-0.656626\pi$
$821$	12.2585	−	37.7278i	0.427825	−	1.31671i	0.900264	−	0.435345i	$-0.143374\pi$
$822$	2.30791	+	7.10303i	0.0804977	+	0.247747i
$823$	37.1568	−	26.9960i	1.29520	−	0.941021i	0.295308	−	0.955402i	$-0.404578\pi$
$823$	37.1568	−	26.9960i	1.29520	−	0.941021i	0.999897	+	0.0143810i	$0.00457777\pi$
$824$	11.9178			0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.983707	−	0.179779i	$-0.942462\pi$
$827$	−32.1139	+	23.3321i	−1.11671	+	0.811337i	−0.133002	+	0.991116i	$0.542462\pi$
$828$	0.155407	+	0.478293i	0.00540076	+	0.0166218i
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	−0.901530	−	0.432716i	$-0.857555\pi$
$829$	2.36578	−	7.28113i	0.0821671	−	0.252884i	0.983697	+	0.179832i	$0.0575553\pi$
$830$	−11.6745	−	8.48199i	−0.405226	−	0.294414i
$831$	−1.81889	−	1.32150i	−0.0630966	−	0.0458423i
$832$	7.47017	−	22.9908i	0.258982	−	0.797063i
$833$	−7.20831	−	22.1849i	−0.249753	−	0.768661i
$834$	−0.325374	+	0.236398i	−0.0112668	+	0.00818580i
$835$	17.7090			0.612846
$836$		0			0
$837$	−22.1135			−0.764354
$838$	19.5801	−	14.2258i	0.676384	−	0.491422i
$839$	8.52536	+	26.2383i	0.294328	+	0.905848i	0.983446	+	0.181200i	$0.0579980\pi$
$839$	8.52536	+	26.2383i	0.294328	+	0.905848i	−0.689118	+	0.724649i	$0.742002\pi$
$840$	−1.90233	+	5.85477i	−0.0656367	+	0.202009i
$841$	−13.4418	−	9.76607i	−0.463512	−	0.336761i
$842$	−5.29576	−	3.84760i	−0.182504	−	0.132597i
$843$	0.273412	−	0.841477i	0.00941683	−	0.0289820i
$844$	−1.37531	−	4.23276i	−0.0473400	−	0.145697i
$845$	−4.03351	+	2.93052i	−0.138757	+	0.100813i
$846$	−8.04979			−0.276757
$847$		0			0
$848$	−10.9261			−0.375203
$849$	−2.51960	+	1.83059i	−0.0864724	+	0.0628258i
$850$	1.54666	+	4.76012i	0.0530499	+	0.163271i
$851$	3.53370	−	10.8756i	0.121134	−	0.372811i
$852$	0.626826	+	0.455416i	0.0214747	+	0.0156023i
$853$	34.0998	+	24.7749i	1.16755	+	0.848277i	0.990714	−	0.135962i	$-0.0434126\pi$
$853$	34.0998	+	24.7749i	1.16755	+	0.848277i	0.176840	+	0.984240i	$0.443413\pi$
$854$	−12.9651	+	39.9024i	−0.443656	+	1.36543i
$855$	0.0784497	+	0.241443i	0.00268292	+	0.00825719i
$856$	4.59707	−	3.33997i	0.157125	−	0.114158i
$857$	45.0850			1.54008			0.770038	−	0.637998i	$-0.220237\pi$
$857$	45.0850			1.54008			0.770038	+	0.637998i	$0.220237\pi$
$858$		0			0
$859$	−11.8257			−0.403488			−0.201744	−	0.979438i	$-0.564661\pi$
$859$	−11.8257			−0.403488			−0.201744	+	0.979438i	$0.564661\pi$
$860$	−0.389423	+	0.282932i	−0.0132792	+	0.00964792i
$861$	5.39854	+	16.6150i	0.183982	+	0.566237i
$862$	−10.4204	+	32.0705i	−0.354919	+	1.09233i
$863$	−22.5484	−	16.3823i	−0.767555	−	0.557662i	0.133663	−	0.991027i	$-0.457326\pi$
$863$	−22.5484	−	16.3823i	−0.767555	−	0.557662i	−0.901218	+	0.433365i	$0.857326\pi$
$864$	−2.41475	−	1.75442i	−0.0821514	−	0.0596865i
$865$	4.90888	−	15.1080i	0.166907	−	0.513687i
$866$	8.90229	+	27.3984i	0.302512	+	0.931037i
$867$	1.56877	−	1.13978i	0.0532782	−	0.0387089i
$868$	−4.01105			−0.136144
$869$		0			0
$870$	5.26926			0.178645
$871$	30.7249	−	22.3230i	1.04107	−	0.756384i
$872$	−5.54939	−	17.0793i	−0.187926	−	0.578377i
$873$	3.57207	−	10.9937i	0.120896	−	0.372081i
$874$	0.121246	+	0.0880900i	0.00410119	+	0.00297969i
$875$	2.95244	+	2.14507i	0.0998106	+	0.0725167i
$876$	−0.0380642	+	0.117149i	−0.00128607	+	0.00395811i
$877$	3.53736	+	10.8869i	0.119448	+	0.367624i	0.992849	−	0.119379i	$-0.0380902\pi$
$877$	3.53736	+	10.8869i	0.119448	+	0.367624i	−0.873401	+	0.487003i	$0.838090\pi$
$878$	17.4516	−	12.6793i	0.588963	−	0.427907i
$879$	−6.57011			−0.221604
$880$		0			0
$881$	47.0037			1.58360			0.791798	−	0.610783i	$-0.209145\pi$
$881$	47.0037			1.58360			0.791798	+	0.610783i	$0.209145\pi$
$882$	−18.4938	+	13.4365i	−0.622717	+	0.452431i
$883$	−14.4974	−	44.6185i	−0.487877	−	1.50153i	−0.827770	−	0.561067i	$-0.810391\pi$
$883$	−14.4974	−	44.6185i	−0.487877	−	1.50153i	0.339894	−	0.940464i	$-0.389609\pi$
$884$	0.523698	−	1.61178i	0.0176139	−	0.0542099i
$885$	−3.96147	−	2.87817i	−0.133163	−	0.0967488i
$886$	28.8313	+	20.9472i	0.968607	+	0.703734i
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	−0.696316	−	0.717735i	$-0.745179\pi$
$887$	8.60386	−	26.4800i	0.288889	−	0.889110i	0.985206	−	0.171375i	$-0.0548210\pi$
$888$	5.12920	+	15.7860i	0.172125	+	0.529745i
$889$	7.19754	−	5.22932i	0.241398	−	0.175386i
$890$	−16.4866			−0.552631
$891$		0			0
$892$	0.824022			0.0275903
$893$	0.171223	−	0.124401i	0.00572975	−	0.00416290i
$894$	−1.96725	−	6.05456i	−0.0657946	−	0.202495i
$895$	5.21653	−	16.0548i	0.174369	−	0.536653i
$896$	28.7759	+	20.9069i	0.961335	+	0.698451i
$897$	−1.53176	−	1.11289i	−0.0511441	−	0.0371584i
$898$	3.43085	−	10.5591i	0.114489	−	0.352360i
$899$	14.1469	+	43.5397i	0.471826	+	1.45213i
$900$	−0.350094	+	0.254358i	−0.0116698	+	0.00847860i
$901$	−11.0534			−0.368244
$902$		0			0
$903$	6.23473			0.207479
$904$	−13.7190	+	9.96742i	−0.456287	+	0.331512i
$905$	7.44341	+	22.9085i	0.247427	+	0.761503i
$906$	0.467767	−	1.43964i	0.0155405	−	0.0478288i
$907$	23.1567	+	16.8243i	0.768907	+	0.558643i	0.901629	−	0.432510i	$-0.142372\pi$
$907$	23.1567	+	16.8243i	0.768907	+	0.558643i	−0.132723	+	0.991153i	$0.542372\pi$
$908$	−0.490586	−	0.356432i	−0.0162807	−	0.0118286i
$909$	8.16930	−	25.1425i	0.270959	−	0.833925i
$910$	4.32807	+	13.3204i	0.143474	+	0.441567i
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	−0.654389	−	0.756158i	$-0.727074\pi$
$911$	−4.14883	+	3.01430i	−0.137457	+	0.0998682i	0.516932	+	0.856026i	$0.327074\pi$
$912$	−0.199781			−0.00661542
$913$		0			0
$914$	16.1547			0.534351
$915$	3.94832	−	2.86862i	0.130527	−	0.0948338i
$916$	−1.34907	−	4.15200i	−0.0445744	−	0.137186i
$917$	−7.94098	+	24.4398i	−0.262234	+	0.807074i
$918$	13.2100	+	9.59759i	0.435993	+	0.316768i
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	0.948792	−	0.315902i	$-0.102307\pi$
$919$	28.5429	+	20.7376i	0.941544	+	0.684072i	−0.00724799	+	0.999974i	$0.502307\pi$
$920$	−1.05265	+	3.23972i	−0.0347049	+	0.106811i
$921$	0.755822	+	2.32618i	0.0249052	+	0.0766503i
$922$	−7.63536	+	5.54742i	−0.251457	+	0.182694i
$923$	23.5057			0.773699
$924$		0			0
$925$	9.83980			0.323531
$926$	13.6834	−	9.94159i	0.449665	−	0.326701i
$927$	−3.35318	−	10.3200i	−0.110133	−	0.338954i
$928$	−1.90950	+	5.87682i	−0.0626823	+	0.192916i
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.927325	+	0.374256i	$0.122102\pi$
$929$	47.8474	+	34.7632i	1.56982	+	1.14054i	0.642498	+	0.766287i	$0.277898\pi$
$930$	−4.27837	−	3.10842i	−0.140293	−	0.101929i
$931$	0.185724	−	0.571601i	0.00608687	−	0.0187335i
$932$	0.917781	+	2.82464i	0.0300629	+	0.0925242i
$933$	7.73775	−	5.62181i	0.253323	−	0.184050i
$934$	8.33220			0.272638
$935$		0			0
$936$	−22.1458			−0.723857
$937$	11.6843	−	8.48911i	0.381708	−	0.277327i	−0.380341	−	0.924846i	$-0.624193\pi$
$937$	11.6843	−	8.48911i	0.381708	−	0.277327i	0.762049	+	0.647519i	$0.224193\pi$
$938$	20.5098	+	63.1226i	0.669668	+	2.06103i
$939$	−4.72637	+	14.5463i	−0.154239	+	0.474700i
$940$	0.291863	+	0.212051i	0.00951952	+	0.00691634i
$941$	−15.0955	−	10.9675i	−0.492100	−	0.357532i	0.313891	−	0.949459i	$-0.398367\pi$
$941$	−15.0955	−	10.9675i	−0.492100	−	0.357532i	−0.805991	+	0.591927i	$0.798367\pi$
$942$	−5.12905	+	15.7856i	−0.167113	+	0.514322i
$943$	2.98727	+	9.19386i	0.0972788	+	0.299393i
$944$	−25.1211	+	18.2516i	−0.817623	+	0.594038i
$945$	11.9057			0.387292
$946$		0			0
$947$	−0.991391			−0.0322159			−0.0161079	−	0.999870i	$-0.505128\pi$
$947$	−0.991391			−0.0322159			−0.0161079	+	0.999870i	$0.505128\pi$
$948$	1.04679	−	0.760540i	0.0339983	−	0.0247012i
$949$	1.15478	+	3.55405i	0.0374858	+	0.115369i
$950$	−0.0398501	+	0.122646i	−0.00129291	+	0.00397916i
$951$	−2.69896	−	1.96091i	−0.0875198	−	0.0635869i
$952$	31.9505	+	23.2134i	1.03552	+	0.752351i
$953$	2.55373	−	7.85957i	0.0827234	−	0.254597i	−0.901137	−	0.433535i	$-0.857266\pi$
$953$	2.55373	−	7.85957i	0.0827234	−	0.254597i	0.983860	+	0.178938i	$0.0572662\pi$
$954$	3.34731	+	10.3020i	0.108373	+	0.333539i
$955$	4.35477	−	3.16393i	0.140917	−	0.102382i
$956$	−1.77646			−0.0574549
$957$		0			0
$958$	30.0881			0.972101
$959$	28.2633	−	20.5345i	0.912669	−	0.663093i
$960$	−1.51858	−	4.67371i	−0.0490119	−	0.150843i
$961$	4.61867	−	14.2148i	0.148989	−	0.458542i
$962$	30.5515	+	22.1969i	0.985019	+	0.715658i
$963$	−4.18560	−	3.04102i	−0.134879	−	0.0979954i
$964$	−0.500784	+	1.54125i	−0.0161292	+	0.0496404i
$965$	5.65008	+	17.3892i	0.181883	+	0.559777i
$966$	2.67693	−	1.94491i	0.0861289	−	0.0625763i
$967$	−7.36029			−0.236691			−0.118345	−	0.992972i	$-0.537759\pi$
$967$	−7.36029			−0.236691			−0.118345	+	0.992972i	$0.537759\pi$
$968$		0			0
$969$	−0.202110			−0.00649271
$970$	4.75044	−	3.45140i	0.152527	−	0.110818i
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	0.923339	−	0.383986i	$-0.125449\pi$
$971$	−1.53808	−	4.73372i	−0.0493593	−	0.151912i	−0.972698	+	0.232074i	$0.925449\pi$
$972$	−0.667127	+	2.05321i	−0.0213981	+	0.0658566i
$973$	1.52199	+	1.10579i	0.0487927	+	0.0354500i
$974$	−37.5429	−	27.2765i	−1.20295	−	0.873996i
$975$	0.503449	−	1.54946i	0.0161233	−	0.0496223i
$976$	−9.56357	−	29.4337i	−0.306123	−	0.942148i
$977$	−8.36266	+	6.07583i	−0.267545	+	0.194383i	−0.713467	−	0.700689i	$-0.752876\pi$
$977$	−8.36266	+	6.07583i	−0.267545	+	0.194383i	0.445922	+	0.895072i	$0.352876\pi$
$978$	12.4680			0.398684
$979$		0			0
$980$	1.02448			0.0327259
$981$	−13.2281	+	9.61077i	−0.422340	+	0.306848i
$982$	−7.11996	−	21.9130i	−0.227207	−	0.699272i
$983$	−8.98045	+	27.6390i	−0.286432	+	0.881547i	0.699534	+	0.714599i	$0.253391\pi$
$983$	−8.98045	+	27.6390i	−0.286432	+	0.881547i	−0.985966	+	0.166947i	$0.946609\pi$
$984$	−11.3519	−	8.24764i	−0.361886	−	0.262925i
$985$	−2.14038	−	1.55508i	−0.0681983	−	0.0495490i
$986$	10.4460	−	32.1493i	0.332667	−	1.02384i
$987$	−1.44397	−	4.44408i	−0.0459620	−	0.141456i
$988$	0.0353258	−	0.0256657i	0.00112386	−	0.000816534i
$989$	3.44997			0.109703
$990$		0			0
$991$	7.70381			0.244719			0.122360	−	0.992486i	$-0.460954\pi$
$991$	7.70381			0.244719			0.122360	+	0.992486i	$0.460954\pi$
$992$	5.01724	−	3.64524i	0.159298	−	0.115737i
$993$	−2.29818	−	7.07308i	−0.0729307	−	0.224458i
$994$	−12.6941	+	39.0683i	−0.402631	+	1.23917i
$995$	5.28126	+	3.83706i	0.167427	+	0.121643i
$996$	0.803583	+	0.583837i	0.0254625	+	0.0184996i
$997$	0.885080	−	2.72400i	0.0280308	−	0.0862698i	−0.936062	−	0.351834i	$-0.885558\pi$
$997$	0.885080	−	2.72400i	0.0280308	−	0.0862698i	0.964093	+	0.265564i	$0.0855582\pi$
$998$	−2.19076	−	6.74247i	−0.0693473	−	0.213429i
$999$	25.9702	−	18.8685i	0.821661	−	0.596972i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.k.366.2		8
11.2	odd	10		605.2.a.j.1.4		4
11.3	even	5		605.2.g.e.511.1		8
11.4	even	5	inner	605.2.g.k.81.2		8
11.5	even	5		605.2.g.e.251.1		8
11.6	odd	10		605.2.g.m.251.2		8
11.7	odd	10		55.2.g.b.26.1	✓	8
11.8	odd	10		605.2.g.m.511.2		8
11.9	even	5		605.2.a.k.1.1		4
11.10	odd	2		55.2.g.b.36.1	yes	8
33.2	even	10		5445.2.a.bp.1.1		4
33.20	odd	10		5445.2.a.bi.1.4		4
33.29	even	10		495.2.n.e.136.2		8
33.32	even	2		495.2.n.e.91.2		8
44.7	even	10		880.2.bo.h.81.1		8
44.31	odd	10		9680.2.a.cm.1.2		4
44.35	even	10		9680.2.a.cn.1.2		4
44.43	even	2		880.2.bo.h.641.1		8
55.7	even	20		275.2.z.a.224.4		16
55.9	even	10		3025.2.a.w.1.4		4
55.18	even	20		275.2.z.a.224.1		16
55.24	odd	10		3025.2.a.bd.1.1		4
55.29	odd	10		275.2.h.a.26.2		8
55.32	even	4		275.2.z.a.124.1		16
55.43	even	4		275.2.z.a.124.4		16
55.54	odd	2		275.2.h.a.201.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	11.7	odd	10
55.2.g.b.36.1	yes	8	11.10	odd	2
275.2.h.a.26.2		8	55.29	odd	10
275.2.h.a.201.2		8	55.54	odd	2
275.2.z.a.124.1		16	55.32	even	4
275.2.z.a.124.4		16	55.43	even	4
275.2.z.a.224.1		16	55.18	even	20
275.2.z.a.224.4		16	55.7	even	20
495.2.n.e.91.2		8	33.32	even	2
495.2.n.e.136.2		8	33.29	even	10
605.2.a.j.1.4		4	11.2	odd	10
605.2.a.k.1.1		4	11.9	even	5
605.2.g.e.251.1		8	11.5	even	5
605.2.g.e.511.1		8	11.3	even	5
605.2.g.k.81.2		8	11.4	even	5	inner
605.2.g.k.366.2		8	1.1	even	1	trivial
605.2.g.m.251.2		8	11.6	odd	10
605.2.g.m.511.2		8	11.8	odd	10
880.2.bo.h.81.1		8	44.7	even	10
880.2.bo.h.641.1		8	44.43	even	2
3025.2.a.w.1.4		4	55.9	even	10
3025.2.a.bd.1.1		4	55.24	odd	10
5445.2.a.bi.1.4		4	33.20	odd	10
5445.2.a.bp.1.1		4	33.2	even	10
9680.2.a.cm.1.2		4	44.31	odd	10
9680.2.a.cn.1.2		4	44.35	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.09676 - 0.796845i) q^{2} +(0.177837 + 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.631180 + 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +O(q^{10})\)	\(q+(1.09676 - 0.796845i) q^{2} +(0.177837 + 0.547326i) q^{3} +(-0.0501062 + 0.154211i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.631180 + 0.458579i) q^{6} +(1.12773 - 3.47080i) q^{7} +(0.905781 + 2.78771i) q^{8} +(2.15911 - 1.56869i) q^{9} +1.35567 q^{10} -0.0933146 q^{12} +(-2.29029 + 1.66399i) q^{13} +(-1.52884 - 4.70527i) q^{14} +(-0.177837 + 0.547326i) q^{15} +(2.95244 + 2.14507i) q^{16} +(2.98685 + 2.17008i) q^{17} +(1.11803 - 3.44095i) q^{18} +(0.0293950 + 0.0904686i) q^{19} +(-0.131180 + 0.0953077i) q^{20} +2.10021 q^{21} +1.16215 q^{23} +(-1.36470 + 0.991515i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.18596 + 3.65001i) q^{26} +(2.63930 + 1.91757i) q^{27} +(0.478730 + 0.347817i) q^{28} +(2.08707 - 6.42333i) q^{29} +(0.241089 + 0.741996i) q^{30} +(-5.48382 + 3.98423i) q^{31} -0.914918 q^{32} +5.00509 q^{34} +(2.95244 - 2.14507i) q^{35} +(0.133724 + 0.411560i) q^{36} +(3.04066 - 9.35820i) q^{37} +(0.104329 + 0.0757994i) q^{38} +(-1.31805 - 0.957617i) q^{39} +(-0.905781 + 2.78771i) q^{40} +(2.57047 + 7.91110i) q^{41} +(2.30344 - 1.67354i) q^{42} +2.96862 q^{43} +2.66881 q^{45} +(1.27460 - 0.926052i) q^{46} +(-0.687534 - 2.11601i) q^{47} +(-0.649001 + 1.99742i) q^{48} +(-5.11155 - 3.71376i) q^{49} +(1.09676 + 0.796845i) q^{50} +(-0.656567 + 2.02070i) q^{51} +(-0.141849 - 0.436565i) q^{52} +(-2.42214 + 1.75979i) q^{53} +4.42270 q^{54} +10.6970 q^{56} +(-0.0442883 + 0.0321774i) q^{57} +(-2.82938 - 8.70794i) q^{58} +(-2.62930 + 8.09216i) q^{59} +(-0.0754931 - 0.0548489i) q^{60} +(-6.86076 - 4.98464i) q^{61} +(-2.83964 + 8.73951i) q^{62} +(-3.00970 - 9.26289i) q^{63} +(-6.90832 + 5.01919i) q^{64} -2.83095 q^{65} -13.4153 q^{67} +(-0.484310 + 0.351872i) q^{68} +(0.206673 + 0.636074i) q^{69} +(1.52884 - 4.70527i) q^{70} +(-6.71734 - 4.88043i) q^{71} +(6.32872 + 4.59808i) q^{72} +(0.407912 - 1.25542i) q^{73} +(-4.12215 - 12.6867i) q^{74} +(-0.465584 + 0.338266i) q^{75} -0.0154241 q^{76} -2.20866 q^{78} +(-11.2179 + 8.15028i) q^{79} +(1.12773 + 3.47080i) q^{80} +(1.89395 - 5.82899i) q^{81} +(9.12312 + 6.62834i) q^{82} +(-8.61155 - 6.25666i) q^{83} +(-0.105234 + 0.323876i) q^{84} +(1.14088 + 3.51126i) q^{85} +(3.25587 - 2.36553i) q^{86} +3.88682 q^{87} -12.1612 q^{89} +(2.92705 - 2.12663i) q^{90} +(3.19256 + 9.82567i) q^{91} +(-0.0582308 + 0.179216i) q^{92} +(-3.15590 - 2.29290i) q^{93} +(-2.44020 - 1.77291i) q^{94} +(-0.0293950 + 0.0904686i) q^{95} +(-0.162706 - 0.500759i) q^{96} +(3.50412 - 2.54589i) q^{97} -8.56545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9	\( 8 q + 2 q^{2} - 5 q^{3} - 2 q^{4} + 2 q^{5} + 7 q^{6} + q^{7} - 4 q^{8} - 5 q^{9} - 2 q^{10} + 16 q^{12} + 2 q^{13} - 16 q^{14} + 5 q^{15} + 4 q^{16} + 13 q^{17} - 15 q^{19} - 3 q^{20} + 20 q^{21} + 10 q^{23} - 13 q^{24} - 2 q^{25} + 10 q^{26} + 10 q^{27} + 6 q^{28} + 9 q^{29} + 8 q^{30} - 10 q^{31} - 16 q^{32} + 4 q^{34} + 4 q^{35} - 15 q^{36} + 24 q^{37} - 21 q^{39} + 4 q^{40} - 8 q^{41} + 9 q^{42} + 38 q^{43} - 3 q^{46} + 5 q^{48} + q^{49} + 2 q^{50} - q^{51} + 28 q^{52} + 13 q^{53} - 16 q^{54} + 22 q^{56} + 45 q^{57} + 12 q^{58} - 27 q^{59} + 4 q^{60} - 6 q^{61} + 30 q^{62} - 25 q^{63} - 26 q^{64} - 2 q^{65} - 38 q^{67} - 11 q^{68} - q^{69} + 16 q^{70} - 20 q^{71} + 30 q^{72} - 13 q^{73} - 20 q^{74} + 5 q^{75} - 16 q^{78} - 37 q^{79} + q^{80} + 8 q^{81} + 28 q^{82} - 27 q^{83} - 28 q^{84} + 12 q^{85} - 3 q^{86} - 38 q^{87} - 16 q^{89} + 10 q^{90} + 44 q^{91} + 11 q^{92} - 35 q^{93} - 17 q^{94} + 15 q^{95} + 17 q^{96} + 24 q^{97} - 16 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 5 * q^3 - 2 * q^4 + 2 * q^5 + 7 * q^6 + q^7 - 4 * q^8 - 5 * q^9 - 2 * q^10 + 16 * q^12 + 2 * q^13 - 16 * q^14 + 5 * q^15 + 4 * q^16 + 13 * q^17 - 15 * q^19 - 3 * q^20 + 20 * q^21 + 10 * q^23 - 13 * q^24 - 2 * q^25 + 10 * q^26 + 10 * q^27 + 6 * q^28 + 9 * q^29 + 8 * q^30 - 10 * q^31 - 16 * q^32 + 4 * q^34 + 4 * q^35 - 15 * q^36 + 24 * q^37 - 21 * q^39 + 4 * q^40 - 8 * q^41 + 9 * q^42 + 38 * q^43 - 3 * q^46 + 5 * q^48 + q^49 + 2 * q^50 - q^51 + 28 * q^52 + 13 * q^53 - 16 * q^54 + 22 * q^56 + 45 * q^57 + 12 * q^58 - 27 * q^59 + 4 * q^60 - 6 * q^61 + 30 * q^62 - 25 * q^63 - 26 * q^64 - 2 * q^65 - 38 * q^67 - 11 * q^68 - q^69 + 16 * q^70 - 20 * q^71 + 30 * q^72 - 13 * q^73 - 20 * q^74 + 5 * q^75 - 16 * q^78 - 37 * q^79 + q^80 + 8 * q^81 + 28 * q^82 - 27 * q^83 - 28 * q^84 + 12 * q^85 - 3 * q^86 - 38 * q^87 - 16 * q^89 + 10 * q^90 + 44 * q^91 + 11 * q^92 - 35 * q^93 - 17 * q^94 + 15 * q^95 + 17 * q^96 + 24 * q^97 - 16 * q^98

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