LMFDB - Embedded newform 605.2.g.m.511.2

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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			511.2
Root			$0.418926 - 1.28932i$ of defining polynomial
Character	$\chi$	$=$	605.511
Dual form			605.2.g.m.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.418926 + 1.28932i) q^{2} +(-0.465584 - 0.338266i) q^{3} +(0.131180 - 0.0953077i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.241089 - 0.741996i) q^{6} +(2.95244 - 2.14507i) q^{7} +(2.37136 + 1.72290i) q^{8} +(-0.824707 - 2.53819i) q^{9} +O(q^{10})$	\(q+(0.418926 + 1.28932i) q^{2} +(-0.465584 - 0.338266i) q^{3} +(0.131180 - 0.0953077i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.241089 - 0.741996i) q^{6} +(2.95244 - 2.14507i) q^{7} +(2.37136 + 1.72290i) q^{8} +(-0.824707 - 2.53819i) q^{9} -1.35567 q^{10} -0.0933146 q^{12} +(-0.874813 - 2.69240i) q^{13} +(4.00254 + 2.90802i) q^{14} +(0.465584 - 0.338266i) q^{15} +(-1.12773 + 3.47080i) q^{16} +(1.14088 - 3.51126i) q^{17} +(2.92705 - 2.12663i) q^{18} +(0.0769572 + 0.0559127i) q^{19} +(0.0501062 + 0.154211i) q^{20} -2.10021 q^{21} +1.16215 q^{23} +(-0.521270 - 1.60431i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.10489 - 2.25583i) q^{26} +(-1.00812 + 3.10269i) q^{27} +(0.182858 - 0.562780i) q^{28} +(5.46401 - 3.96984i) q^{29} +(0.631180 + 0.458579i) q^{30} +(2.09463 + 6.44661i) q^{31} +0.914918 q^{32} +5.00509 q^{34} +(1.12773 + 3.47080i) q^{35} +(-0.350094 - 0.254358i) q^{36} +(-7.96056 + 5.78369i) q^{37} +(-0.0398501 + 0.122646i) q^{38} +(-0.503449 + 1.54946i) q^{39} +(-2.37136 + 1.72290i) q^{40} +(6.72958 + 4.88933i) q^{41} +(-0.879834 - 2.70785i) q^{42} -2.96862 q^{43} +2.66881 q^{45} +(0.486854 + 1.49838i) q^{46} +(1.79999 + 1.30777i) q^{47} +(1.69911 - 1.23447i) q^{48} +(1.95244 - 6.00899i) q^{49} +(0.418926 - 1.28932i) q^{50} +(-1.71891 + 1.24886i) q^{51} +(-0.371364 - 0.269812i) q^{52} +(0.925174 + 2.84739i) q^{53} -4.42270 q^{54} +10.6970 q^{56} +(-0.0169166 - 0.0520641i) q^{57} +(7.40742 + 5.38181i) q^{58} +(6.88361 - 5.00123i) q^{59} +(0.0288358 - 0.0887475i) q^{60} +(-2.62058 + 8.06531i) q^{61} +(-7.43427 + 5.40131i) q^{62} +(-7.87949 - 5.72478i) q^{63} +(2.63875 + 8.12122i) q^{64} +2.83095 q^{65} -13.4153 q^{67} +(-0.184990 - 0.569341i) q^{68} +(-0.541077 - 0.393115i) q^{69} +(-4.00254 + 2.90802i) q^{70} +(2.56580 - 7.89671i) q^{71} +(2.41735 - 7.43985i) q^{72} +(1.06793 - 0.775895i) q^{73} +(-10.7919 - 7.84080i) q^{74} +(0.177837 + 0.547326i) q^{75} +0.0154241 q^{76} -2.20866 q^{78} +(-4.28486 - 13.1874i) q^{79} +(-2.95244 - 2.14507i) q^{80} +(-4.95843 + 3.60251i) q^{81} +(-3.48472 + 10.7249i) q^{82} +(-3.28932 + 10.1235i) q^{83} +(-0.275506 + 0.200167i) q^{84} +(2.98685 + 2.17008i) q^{85} +(-1.24363 - 3.82751i) q^{86} -3.88682 q^{87} -12.1612 q^{89} +(1.11803 + 3.44095i) q^{90} +(-8.35822 - 6.07260i) q^{91} +(0.152450 - 0.110762i) q^{92} +(1.20545 - 3.70998i) q^{93} +(-0.932072 + 2.86862i) q^{94} +(-0.0769572 + 0.0559127i) q^{95} +(-0.425971 - 0.309486i) q^{96} +(-1.33845 - 4.11934i) q^{97} +8.56545 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9	$ 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21} + 10 q^{23} - 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} + 19 q^{28} + 21 q^{29} + 7 q^{30} + 15 q^{31} + 16 q^{32} + 4 q^{34} + q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} - 14 q^{39} + q^{40} + 3 q^{41} - 21 q^{42} - 38 q^{43} - 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} + 3 q^{50} + 6 q^{51} + 17 q^{52} - 2 q^{53} + 16 q^{54} + 22 q^{56} + 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} + 6 q^{61} - 5 q^{62} - 30 q^{63} + 29 q^{64} + 2 q^{65} - 38 q^{67} - 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} + 5 q^{72} - 2 q^{73} - 20 q^{74} - 5 q^{75} - 16 q^{78} - 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} - 38 q^{83} - 17 q^{84} + 13 q^{85} + 2 q^{86} + 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} - 18 q^{94} - 5 q^{95} - 17 q^{96} - 56 q^{97} + 16 q^{98}+O(q^{100}) $ 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.418926	+	1.28932i	0.296226	+	0.911689i	0.982807	+	0.184636i	$0.0591106\pi$
$2$	0.418926	+	1.28932i	0.296226	+	0.911689i	−0.686581	+	0.727053i	$0.740889\pi$
$3$	−0.465584	−	0.338266i	−0.268805	−	0.195298i	0.445215	−	0.895424i	$-0.353127\pi$
$3$	−0.465584	−	0.338266i	−0.268805	−	0.195298i	−0.714020	+	0.700126i	$0.753127\pi$
$4$	0.131180	−	0.0953077i	0.0655899	−	0.0476539i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.241089	−	0.741996i	0.0984243	−	0.302919i
$7$	2.95244	−	2.14507i	1.11592	−	0.810761i	0.132331	−	0.991206i	$-0.457754\pi$
$7$	2.95244	−	2.14507i	1.11592	−	0.810761i	0.983585	+	0.180445i	$0.0577537\pi$
$8$	2.37136	+	1.72290i	0.838404	+	0.609136i
$9$	−0.824707	−	2.53819i	−0.274902	−	0.846062i
$10$	−1.35567			−0.428702
$11$		0			0
$11$		0			0
$12$	−0.0933146			−0.0269376
$13$	−0.874813	−	2.69240i	−0.242630	−	0.746737i	−0.996017	−	0.0891604i	$-0.971582\pi$
$13$	−0.874813	−	2.69240i	−0.242630	−	0.746737i	0.753388	−	0.657577i	$-0.228418\pi$
$14$	4.00254	+	2.90802i	1.06972	+	0.777201i
$15$	0.465584	−	0.338266i	0.120213	−	0.0873400i
$16$	−1.12773	+	3.47080i	−0.281933	+	0.867700i
$17$	1.14088	−	3.51126i	0.276703	−	0.851605i	−0.712060	−	0.702118i	$-0.752238\pi$
$17$	1.14088	−	3.51126i	0.276703	−	0.851605i	0.988764	−	0.149487i	$-0.0477622\pi$
$18$	2.92705	−	2.12663i	0.689913	−	0.501251i
$19$	0.0769572	+	0.0559127i	0.0176552	+	0.0128272i	0.596578	−	0.802555i	$-0.296527\pi$
$19$	0.0769572	+	0.0559127i	0.0176552	+	0.0128272i	−0.578923	+	0.815382i	$0.696527\pi$
$20$	0.0501062	+	0.154211i	0.0112041	+	0.0344827i
$21$	−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	$0.461338\pi$
$24$	−0.521270	−	1.60431i	−0.106404	−	0.327477i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	3.10489	−	2.25583i	0.608919	−	0.442405i
$27$	−1.00812	+	3.10269i	−0.194014	+	0.597113i
$28$	0.182858	−	0.562780i	0.0345570	−	0.106355i
$29$	5.46401	−	3.96984i	1.01464	−	0.737180i	0.0494639	−	0.998776i	$-0.484249\pi$
$29$	5.46401	−	3.96984i	1.01464	−	0.737180i	0.965178	+	0.261596i	$0.0842487\pi$
$30$	0.631180	+	0.458579i	0.115237	+	0.0837247i
$31$	2.09463	+	6.44661i	0.376207	+	1.15785i	0.942661	+	0.333753i	$0.108315\pi$
$31$	2.09463	+	6.44661i	0.376207	+	1.15785i	−0.566454	+	0.824094i	$0.691685\pi$
$32$	0.914918			0.161736
$33$		0			0
$34$	5.00509			0.858366
$35$	1.12773	+	3.47080i	0.190621	+	0.586672i
$36$	−0.350094	−	0.254358i	−0.0583490	−	0.0423930i
$37$	−7.96056	+	5.78369i	−1.30871	+	0.950832i	−1.00000		0.000324402i	$-0.999897\pi$
$37$	−7.96056	+	5.78369i	−1.30871	+	0.950832i	−0.308708	+	0.951157i	$0.599897\pi$
$38$	−0.0398501	+	0.122646i	−0.00646454	+	0.0198958i
$39$	−0.503449	+	1.54946i	−0.0806163	+	0.248112i
$40$	−2.37136	+	1.72290i	−0.374946	+	0.272414i
$41$	6.72958	+	4.88933i	1.05098	+	0.763585i	0.972399	−	0.233323i	$-0.0749598\pi$
$41$	6.72958	+	4.88933i	1.05098	+	0.763585i	0.0785849	+	0.996907i	$0.474960\pi$
$42$	−0.879834	−	2.70785i	−0.135761	−	0.417831i
$43$	−2.96862			−0.452710			−0.226355	−	0.974045i	$-0.572681\pi$
$43$	−2.96862			−0.452710			−0.226355	+	0.974045i	$0.572681\pi$
$44$		0			0
$45$	2.66881			0.397842
$46$	0.486854	+	1.49838i	0.0717827	+	0.220925i
$47$	1.79999	+	1.30777i	0.262555	+	0.190757i	0.711273	−	0.702916i	$-0.248119\pi$
$47$	1.79999	+	1.30777i	0.262555	+	0.190757i	−0.448718	+	0.893674i	$0.648119\pi$
$48$	1.69911	−	1.23447i	0.245245	−	0.178181i
$49$	1.95244	−	6.00899i	0.278920	−	0.858427i
$50$	0.418926	−	1.28932i	0.0592451	−	0.182338i
$51$	−1.71891	+	1.24886i	−0.240696	+	0.174876i
$52$	−0.371364	−	0.269812i	−0.0514990	−	0.0374162i
$53$	0.925174	+	2.84739i	0.127082	+	0.391120i	0.994275	−	0.106854i	$-0.0340777\pi$
$53$	0.925174	+	2.84739i	0.127082	+	0.391120i	−0.867192	+	0.497973i	$0.834078\pi$
$54$	−4.42270			−0.601853
$55$		0			0
$56$	10.6970			1.42945
$57$	−0.0169166	−	0.0520641i	−0.00224066	−	0.00689605i
$58$	7.40742	+	5.38181i	0.972642	+	0.706666i
$59$	6.88361	−	5.00123i	0.896169	−	0.651105i	−0.0413101	−	0.999146i	$-0.513153\pi$
$59$	6.88361	−	5.00123i	0.896169	−	0.651105i	0.937479	+	0.348041i	$0.113153\pi$
$60$	0.0288358	−	0.0887475i	0.00372269	−	0.0114572i
$61$	−2.62058	+	8.06531i	−0.335531	+	1.03266i	0.630929	+	0.775840i	$0.282674\pi$
$61$	−2.62058	+	8.06531i	−0.335531	+	1.03266i	−0.966460	+	0.256817i	$0.917326\pi$
$62$	−7.43427	+	5.40131i	−0.944153	+	0.685968i
$63$	−7.87949	−	5.72478i	−0.992722	−	0.721255i
$64$	2.63875	+	8.12122i	0.329843	+	1.01515i
$65$	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	$0.805732\pi$
$68$	−0.184990	−	0.569341i	−0.0224333	−	0.0690427i
$69$	−0.541077	−	0.393115i	−0.0651380	−	0.0473255i
$70$	−4.00254	+	2.90802i	−0.478396	+	0.347575i
$71$	2.56580	−	7.89671i	0.304504	−	0.937167i	−0.675358	−	0.737490i	$-0.736011\pi$
$71$	2.56580	−	7.89671i	0.304504	−	0.937167i	0.979862	−	0.199677i	$-0.0639892\pi$
$72$	2.41735	−	7.43985i	0.284888	−	0.876795i
$73$	1.06793	−	0.775895i	0.124991	−	0.0908116i	−0.523533	−	0.852005i	$-0.675386\pi$
$73$	1.06793	−	0.775895i	0.124991	−	0.0908116i	0.648525	+	0.761194i	$0.275386\pi$
$74$	−10.7919	−	7.84080i	−1.25454	−	0.911474i
$75$	0.177837	+	0.547326i	0.0205349	+	0.0631998i
$76$	0.0154241			0.00176927
$77$		0			0
$78$	−2.20866			−0.250081
$79$	−4.28486	−	13.1874i	−0.482084	−	1.48370i	−0.836160	−	0.548486i	$-0.815205\pi$
$79$	−4.28486	−	13.1874i	−0.482084	−	1.48370i	0.354076	−	0.935217i	$-0.384795\pi$
$80$	−2.95244	−	2.14507i	−0.330093	−	0.239826i
$81$	−4.95843	+	3.60251i	−0.550937	+	0.400279i
$82$	−3.48472	+	10.7249i	−0.384823	+	1.18436i
$83$	−3.28932	+	10.1235i	−0.361050	+	1.11120i	0.591368	+	0.806402i	$0.298588\pi$
$83$	−3.28932	+	10.1235i	−0.361050	+	1.11120i	−0.952418	+	0.304795i	$0.901412\pi$
$84$	−0.275506	+	0.200167i	−0.0300601	+	0.0218400i
$85$	2.98685	+	2.17008i	0.323970	+	0.235378i
$86$	−1.24363	−	3.82751i	−0.134104	−	0.412731i
$87$	−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	$0.722951\pi$
$90$	1.11803	+	3.44095i	0.117851	+	0.362708i
$91$	−8.35822	−	6.07260i	−0.876179	−	0.636582i
$92$	0.152450	−	0.110762i	0.0158940	−	0.0115477i
$93$	1.20545	−	3.70998i	0.124999	−	0.384707i
$94$	−0.932072	+	2.86862i	−0.0961359	+	0.295876i
$95$	−0.0769572	+	0.0559127i	−0.00789564	+	0.00573652i
$96$	−0.425971	−	0.309486i	−0.0434755	−	0.0315868i
$97$	−1.33845	−	4.11934i	−0.135899	−	0.418255i	0.859829	−	0.510581i	$-0.170570\pi$
$97$	−1.33845	−	4.11934i	−0.135899	−	0.418255i	−0.995729	+	0.0923261i	$0.970570\pi$
$98$	8.56545			0.865241
$99$		0			0
$100$	−0.162147			−0.0162147
$101$	3.06103	+	9.42088i	0.304584	+	0.937413i	0.979832	+	0.199822i	$0.0640365\pi$
$101$	3.06103	+	9.42088i	0.304584	+	0.937413i	−0.675248	+	0.737590i	$0.735964\pi$
$102$	−2.33029	−	1.69305i	−0.230733	−	0.167637i
$103$	−3.28939	+	2.38988i	−0.324113	+	0.235482i	−0.737928	−	0.674879i	$-0.764196\pi$
$103$	−3.28939	+	2.38988i	−0.324113	+	0.235482i	0.413816	+	0.910361i	$0.364196\pi$
$104$	2.56422	−	7.89187i	0.251443	−	0.773861i
$105$	0.649001	−	1.99742i	0.0633360	−	0.194928i
$106$	−3.28363	+	2.38570i	−0.318934	+	0.231719i
$107$	−1.56834	−	1.13947i	−0.151617	−	0.110156i	0.509390	−	0.860536i	$-0.329871\pi$
$107$	−1.56834	−	1.13947i	−0.151617	−	0.110156i	−0.661008	+	0.750379i	$0.729871\pi$
$108$	0.163465	+	0.503092i	0.0157294	+	0.0484101i
$109$	6.12664			0.586825			0.293413	−	0.955986i	$-0.405209\pi$
$109$	6.12664			0.586825			0.293413	+	0.955986i	$0.405209\pi$
$110$		0			0
$111$	5.66273			0.537483
$112$	4.11556	+	12.6664i	0.388884	+	1.19686i
$113$	−4.68038	−	3.40050i	−0.440293	−	0.319892i	0.345458	−	0.938434i	$-0.387724\pi$
$113$	−4.68038	−	3.40050i	−0.440293	−	0.319892i	−0.785751	+	0.618542i	$0.787724\pi$
$114$	0.0600406	−	0.0436220i	0.00562331	−	0.00408558i
$115$	−0.359123	+	1.10527i	−0.0334884	+	0.103067i
$116$	0.338412	−	1.04153i	0.0314208	−	0.0967032i
$117$	−6.11235	+	4.44088i	−0.565087	+	0.410559i
$118$	9.33193	+	6.78004i	0.859073	+	0.624153i
$119$	−4.16353	−	12.8140i	−0.381670	−	1.17466i
$120$	1.68687			0.153989
$121$		0			0
$122$	−11.4966			−1.04085
$123$	−1.47929	−	4.55278i	−0.133383	−	0.410511i
$124$	0.889186	+	0.646031i	0.0798512	+	0.0580153i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	4.08017	−	12.5575i	0.363490	−	1.11871i
$127$	0.753330	−	2.31851i	0.0668472	−	0.205735i	−0.912053	−	0.410071i	$-0.865504\pi$
$127$	0.753330	−	2.31851i	0.0668472	−	0.205735i	0.978901	+	0.204337i	$0.0655038\pi$
$128$	−7.88507	+	5.72884i	−0.696948	+	0.506363i
$129$	1.38214	+	1.00418i	0.121691	+	0.0884135i
$130$	1.18596	+	3.65001i	0.104016	+	0.320127i
$131$	7.04156			0.615224			0.307612	−	0.951512i	$-0.400470\pi$
$131$	7.04156			0.615224			0.307612	+	0.951512i	$0.400470\pi$
$132$		0			0
$133$	0.347148			0.0301016
$134$	−5.62002	−	17.2966i	−0.485496	−	1.49420i
$135$	−2.63930	−	1.91757i	−0.227155	−	0.165038i
$136$	8.75497	−	6.36086i	0.750732	−	0.545439i
$137$	−2.95818	+	9.10433i	−0.252734	+	0.777835i	0.741534	+	0.670916i	$0.234099\pi$
$137$	−2.95818	+	9.10433i	−0.252734	+	0.777835i	−0.994268	+	0.106920i	$0.965901\pi$
$138$	0.280181	−	0.862309i	0.0238506	−	0.0734046i
$139$	−0.417050	+	0.303004i	−0.0353737	+	0.0257005i	−0.605332	−	0.795973i	$-0.706959\pi$
$139$	−0.417050	+	0.303004i	−0.0353737	+	0.0257005i	0.569958	+	0.821674i	$0.306959\pi$
$140$	0.478730	+	0.347817i	0.0404600	+	0.0293959i
$141$	−0.395671	−	1.21775i	−0.0333215	−	0.102553i
$142$	11.2563			0.944607
$143$		0			0
$144$	9.73958			0.811632
$145$	2.08707	+	6.42333i	0.173321	+	0.533429i
$146$	1.44776	+	1.05186i	0.119818	+	0.0870526i
$147$	−2.94166	+	2.13724i	−0.242624	+	0.176277i
$148$	−0.493035	+	1.51741i	−0.0405272	+	0.124730i
$149$	−2.52153	+	7.76046i	−0.206571	+	0.635761i	0.793074	+	0.609126i	$0.208479\pi$
$149$	−2.52153	+	7.76046i	−0.206571	+	0.635761i	−0.999645	+	0.0266359i	$0.991521\pi$
$150$	−0.631180	+	0.458579i	−0.0515356	+	0.0374428i
$151$	−1.56968	−	1.14044i	−0.127738	−	0.0928073i	0.522082	−	0.852896i	$-0.325156\pi$
$151$	−1.56968	−	1.14044i	−0.127738	−	0.0928073i	−0.649820	+	0.760088i	$0.725156\pi$
$152$	0.0861618	+	0.265179i	0.00698864	+	0.0215088i
$153$	−9.85312			−0.796577
$154$		0			0
$155$	−6.77837			−0.544452
$156$	0.0816328	+	0.251240i	0.00653586	+	0.0201153i
$157$	−17.2114	−	12.5048i	−1.37362	−	0.997994i	−0.997445	−	0.0714455i	$-0.977239\pi$
$157$	−17.2114	−	12.5048i	−1.37362	−	0.997994i	−0.376176	−	0.926548i	$-0.622761\pi$
$158$	15.2078	−	11.0491i	1.20987	−	0.879021i
$159$	0.532431	−	1.63866i	0.0422246	−	0.129954i
$160$	−0.282725	+	0.870139i	−0.0223514	+	0.0687905i
$161$	3.43117	−	2.49289i	0.270414	−	0.196467i
$162$	−6.72202	−	4.88383i	−0.528132	−	0.383710i
$163$	−4.93839	−	15.1988i	−0.386804	−	1.19046i	−0.935163	−	0.354218i	$-0.884747\pi$
$163$	−4.93839	−	15.1988i	−0.386804	−	1.19046i	0.548359	−	0.836243i	$-0.315253\pi$
$164$	1.34878			0.105322
$165$		0			0
$166$	−14.4304			−1.12002
$167$	5.47239	+	16.8423i	0.423466	+	1.30330i	0.904455	+	0.426569i	$0.140278\pi$
$167$	5.47239	+	16.8423i	0.423466	+	1.30330i	−0.480989	+	0.876727i	$0.659722\pi$
$168$	−4.98037	−	3.61845i	−0.384244	−	0.279169i
$169$	4.03351	−	2.93052i	0.310270	−	0.225424i
$170$	−1.54666	+	4.76012i	−0.118623	+	0.365085i
$171$	0.0784497	−	0.241443i	0.00599920	−	0.0184636i
$172$	−0.389423	+	0.282932i	−0.0296932	+	0.0215734i
$173$	−12.8516	−	9.33725i	−0.977091	−	0.709898i	−0.0200344	−	0.999799i	$-0.506378\pi$
$173$	−12.8516	−	9.33725i	−0.977091	−	0.709898i	−0.957057	+	0.289901i	$0.906378\pi$
$174$	−1.62829	−	5.01136i	−0.123440	−	0.379910i
$175$	−3.64941			−0.275870
$176$		0			0
$177$	−4.89664			−0.368054
$178$	−5.09463	−	15.6797i	−0.381859	−	1.17524i
$179$	13.6570	+	9.92242i	1.02078	+	0.741637i	0.966442	−	0.256886i	$-0.0826965\pi$
$179$	13.6570	+	9.92242i	1.02078	+	0.741637i	0.0543338	+	0.998523i	$0.482696\pi$
$180$	0.350094	−	0.254358i	0.0260945	−	0.0189587i
$181$	−7.44341	+	22.9085i	−0.553264	+	1.70277i	0.147220	+	0.989104i	$0.452968\pi$
$181$	−7.44341	+	22.9085i	−0.553264	+	1.70277i	−0.700484	+	0.713668i	$0.747032\pi$
$182$	4.32807	−	13.3204i	0.320818	−	0.987375i
$183$	3.94832	−	2.86862i	0.291868	−	0.212055i
$184$	2.75587	+	2.00226i	0.203166	+	0.147609i
$185$	−3.04066	−	9.35820i	−0.223554	−	0.688029i
$186$	5.28836			0.387761
$187$		0			0
$188$	0.360762			0.0263113
$189$	3.67906	+	11.3230i	0.267613	+	0.823627i
$190$	−0.104329	−	0.0757994i	−0.00756881	−	0.00549906i
$191$	−4.35477	+	3.16393i	−0.315100	+	0.228934i	−0.734082	−	0.679061i	$-0.762387\pi$
$191$	−4.35477	+	3.16393i	−0.315100	+	0.228934i	0.418982	+	0.907995i	$0.362387\pi$
$192$	1.51858	−	4.67371i	0.109594	−	0.337296i
$193$	5.65008	−	17.3892i	0.406702	−	1.25170i	−0.512764	−	0.858530i	$-0.671378\pi$
$193$	5.65008	−	17.3892i	0.406702	−	1.25170i	0.919466	−	0.393170i	$-0.128622\pi$
$194$	4.75044	−	3.45140i	0.341062	−	0.247796i
$195$	−1.31805	−	0.957617i	−0.0943873	−	0.0685764i
$196$	−0.316582	−	0.974340i	−0.0226130	−	0.0695957i
$197$	2.64566			0.188496			0.0942478	−	0.995549i	$-0.469955\pi$
$197$	2.64566			0.188496			0.0942478	+	0.995549i	$0.469955\pi$
$198$		0			0
$199$	6.52800			0.462757			0.231379	−	0.972864i	$-0.425676\pi$
$199$	6.52800			0.462757			0.231379	+	0.972864i	$0.425676\pi$
$200$	−0.905781	−	2.78771i	−0.0640484	−	0.197121i
$201$	6.24594	+	4.53794i	0.440555	+	0.320082i
$202$	−10.8642	+	7.89331i	−0.764403	+	0.555371i
$203$	7.61657	−	23.4414i	0.534578	−	1.64526i
$204$	−0.106460	+	0.327652i	−0.00745372	+	0.0229402i
$205$	−6.72958	+	4.88933i	−0.470014	+	0.341485i
$206$	−4.45934	−	3.23990i	−0.310697	−	0.225734i
$207$	−0.958431	−	2.94975i	−0.0666155	−	0.205022i
$208$	10.3313			0.716349
$209$		0			0
$210$	2.84720			0.196476
$211$	−8.48183	−	26.1044i	−0.583913	−	1.79710i	−0.603591	−	0.797294i	$-0.706264\pi$
$211$	−8.48183	−	26.1044i	−0.583913	−	1.79710i	0.0196771	−	0.999806i	$-0.493736\pi$
$212$	0.392743	+	0.285344i	0.0269737	+	0.0195975i
$213$	−3.86578	+	2.80866i	−0.264879	+	0.192446i
$214$	0.812120	−	2.49945i	0.0555154	−	0.170859i
$215$	0.917354	−	2.82333i	0.0625630	−	0.192549i
$216$	−7.73624	+	5.62071i	−0.526385	+	0.382441i
$217$	20.0127	+	14.5401i	1.35855	+	0.987046i
$218$	2.56661	+	7.89921i	0.173833	+	0.535002i
$219$	−0.759669			−0.0513337
$220$		0			0
$221$	−10.4518			−0.703061
$222$	2.37227	+	7.30109i	0.159216	+	0.490017i
$223$	4.11137	+	2.98709i	0.275318	+	0.200030i	0.716873	−	0.697204i	$-0.245573\pi$
$223$	4.11137	+	2.98709i	0.275318	+	0.200030i	−0.441555	+	0.897234i	$0.645573\pi$
$224$	2.70124	−	1.96257i	0.180484	−	0.131129i
$225$	−0.824707	+	2.53819i	−0.0549805	+	0.169212i
$226$	2.42360	−	7.45908i	0.161216	−	0.496171i
$227$	−3.02556	+	2.19820i	−0.200814	+	0.145900i	−0.683648	−	0.729812i	$-0.739607\pi$
$227$	−3.02556	+	2.19820i	−0.200814	+	0.145900i	0.482834	+	0.875712i	$0.339607\pi$
$228$	−0.00718123	−	0.00521747i	−0.000475589	−	0.000345535i
$229$	8.32001	+	25.6064i	0.549802	+	1.69212i	0.709291	+	0.704916i	$0.249015\pi$
$229$	8.32001	+	25.6064i	0.549802	+	1.69212i	−0.159490	+	0.987200i	$0.550985\pi$
$230$	−1.57549			−0.103885
$231$		0			0
$232$	19.7968			1.29972
$233$	5.66017	+	17.4202i	0.370810	+	1.14124i	0.946262	+	0.323401i	$0.104826\pi$
$233$	5.66017	+	17.4202i	0.370810	+	1.14124i	−0.575452	+	0.817836i	$0.695174\pi$
$234$	−8.28635	−	6.02039i	−0.541696	−	0.393565i
$235$	−1.79999	+	1.30777i	−0.117418	+	0.0853093i
$236$	0.426334	−	1.31212i	0.0277520	−	0.0854118i
$237$	−2.46591	+	7.58928i	−0.160178	+	0.492977i
$238$	14.7772	−	10.7363i	0.957864	−	0.695929i
$239$	8.86348	+	6.43970i	0.573331	+	0.416549i	0.836314	−	0.548251i	$-0.184706\pi$
$239$	8.86348	+	6.43970i	0.573331	+	0.416549i	−0.262983	+	0.964801i	$0.584706\pi$
$240$	0.649001	+	1.99742i	0.0418929	+	0.128933i
$241$	−9.99444			−0.643798			−0.321899	−	0.946774i	$-0.604321\pi$
$241$	−9.99444			−0.643798			−0.321899	+	0.946774i	$0.604321\pi$
$242$		0			0
$243$	13.3143			0.854110
$244$	0.424919	+	1.30777i	0.0272027	+	0.0837212i
$245$	5.11155	+	3.71376i	0.326565	+	0.237263i
$246$	5.25029	−	3.81456i	0.334747	−	0.243208i
$247$	0.0832160	−	0.256113i	0.00529491	−	0.0162961i
$248$	−6.13972	+	18.8961i	−0.389872	+	1.19990i
$249$	4.95589	−	3.60066i	0.314067	−	0.228183i
$250$	1.09676	+	0.796845i	0.0693654	+	0.0503969i
$251$	2.98431	+	9.18476i	0.188368	+	0.579737i	0.999990	−	0.00444573i	$-0.00141513\pi$
$251$	2.98431	+	9.18476i	0.188368	+	0.579737i	−0.811622	+	0.584183i	$0.801415\pi$
$252$	−1.57925			−0.0994832
$253$		0			0
$254$	3.30490			0.207368
$255$	−0.656567	−	2.02070i	−0.0411158	−	0.126541i
$256$	3.12706	+	2.27194i	0.195441	+	0.141997i
$257$	−8.43608	+	6.12917i	−0.526228	+	0.382327i	−0.818945	−	0.573872i	$-0.805441\pi$
$257$	−8.43608	+	6.12917i	−0.526228	+	0.382327i	0.292717	+	0.956199i	$0.405441\pi$
$258$	−0.715702	+	2.20271i	−0.0445577	+	0.137134i
$259$	−11.0966	+	34.1520i	−0.689512	+	2.12210i
$260$	0.371364	−	0.269812i	0.0230310	−	0.0167330i
$261$	−14.5824	−	10.5947i	−0.902628	−	0.655797i
$262$	2.94989	+	9.07884i	0.182245	+	0.560893i
$263$	−10.9619			−0.675937			−0.337968	−	0.941157i	$-0.609740\pi$
$263$	−10.9619			−0.675937			−0.337968	+	0.941157i	$0.609740\pi$
$264$		0			0
$265$	−2.99393			−0.183915
$266$	0.145429	+	0.447586i	0.00891685	+	0.0274433i
$267$	5.66204	+	4.11371i	0.346511	+	0.251755i
$268$	−1.75982	+	1.27858i	−0.107498	+	0.0781018i
$269$	−0.0276091	+	0.0849721i	−0.00168336	+	0.00518084i	−0.951895	−	0.306425i	$-0.900867\pi$
$269$	−0.0276091	+	0.0849721i	−0.00168336	+	0.00518084i	0.950211	+	0.311606i	$0.100867\pi$
$270$	1.36669	−	4.20623i	0.0831740	−	0.255983i
$271$	10.8405	−	7.87606i	0.658511	−	0.478436i	−0.207649	−	0.978203i	$-0.566581\pi$
$271$	10.8405	−	7.87606i	0.658511	−	0.478436i	0.866160	+	0.499767i	$0.166581\pi$
$272$	10.9003	+	7.91951i	0.660926	+	0.480191i
$273$	1.83729	+	5.65461i	0.111198	+	0.342232i
$274$	−12.9777			−0.784010
$275$		0			0
$276$	−0.108445			−0.00652764
$277$	−1.20723	−	3.71548i	−0.0725356	−	0.223241i	0.908216	−	0.418502i	$-0.137445\pi$
$277$	−1.20723	−	3.71548i	−0.0725356	−	0.223241i	−0.980751	+	0.195261i	$0.937445\pi$
$278$	−0.565384	−	0.410775i	−0.0339095	−	0.0246367i
$279$	14.6353	−	10.6331i	0.876190	−	0.636589i
$280$	−3.30557	+	10.1735i	−0.197545	+	0.607982i
$281$	−0.475093	+	1.46218i	−0.0283416	+	0.0872266i	−0.964227	−	0.265079i	$-0.914602\pi$
$281$	−0.475093	+	1.46218i	−0.0283416	+	0.0872266i	0.935885	+	0.352305i	$0.114602\pi$
$282$	1.40432	−	1.02030i	0.0836258	−	0.0607577i
$283$	4.37815	+	3.18091i	0.260254	+	0.189086i	0.710259	−	0.703940i	$-0.248578\pi$
$283$	4.37815	+	3.18091i	0.260254	+	0.189086i	−0.450005	+	0.893026i	$0.648578\pi$
$284$	−0.416037	−	1.28043i	−0.0246872	−	0.0759795i
$285$	0.0547434			0.00324272
$286$		0			0
$287$	30.3566			1.79190
$288$	−0.754539	−	2.32223i	−0.0444617	−	0.136839i
$289$	2.72596	+	1.98052i	0.160351	+	0.116501i
$290$	−7.40742	+	5.38181i	−0.434979	+	0.316030i
$291$	−0.770271	+	2.37065i	−0.0451541	+	0.138970i
$292$	0.0661418	−	0.203564i	0.00387066	−	0.0119127i
$293$	−9.23613	+	6.71044i	−0.539581	+	0.392028i	−0.823929	−	0.566693i	$-0.808223\pi$
$293$	−9.23613	+	6.71044i	−0.539581	+	0.392028i	0.284349	+	0.958721i	$0.408223\pi$
$294$	−3.98793	−	2.89740i	−0.232581	−	0.168980i
$295$	2.62930	+	8.09216i	0.153084	+	0.471144i
$296$	−28.8421			−1.67641
$297$		0			0
$298$	−11.0621			−0.640808
$299$	−1.01666	−	3.12896i	−0.0587951	−	0.180953i
$300$	0.0754931	+	0.0548489i	0.00435860	+	0.00316671i
$301$	−8.76467	+	6.36790i	−0.505187	+	0.367040i
$302$	0.812812	−	2.50158i	0.0467720	−	0.143950i
$303$	1.76160	−	5.42165i	0.101201	−	0.311466i
$304$	−0.280849	+	0.204048i	−0.0161078	+	0.0117030i
$305$	−6.86076	−	4.98464i	−0.392846	−	0.285419i
$306$	−4.12773	−	12.7038i	−0.235967	−	0.726231i
$307$	−4.25008			−0.242565			−0.121282	−	0.992618i	$-0.538701\pi$
$307$	−4.25008			−0.242565			−0.121282	+	0.992618i	$0.538701\pi$
$308$		0			0
$309$	2.33990			0.133112
$310$	−2.83964	−	8.73951i	−0.161281	−	0.496371i
$311$	13.4454	+	9.76868i	0.762420	+	0.553931i	0.899652	−	0.436608i	$-0.143820\pi$
$311$	13.4454	+	9.76868i	0.762420	+	0.553931i	−0.137231	+	0.990539i	$0.543820\pi$
$312$	−3.86341	+	2.80694i	−0.218723	+	0.158911i
$313$	−8.21273	+	25.2762i	−0.464211	+	1.42869i	0.395761	+	0.918354i	$0.370481\pi$
$313$	−8.21273	+	25.2762i	−0.464211	+	1.42869i	−0.859972	+	0.510341i	$0.829519\pi$
$314$	8.91244	−	27.4297i	0.502958	−	1.54795i
$315$	7.87949	−	5.72478i	0.443959	−	0.322555i
$316$	−1.81895	−	1.32155i	−0.102324	−	0.0743427i
$317$	1.79135	+	5.51322i	0.100612	+	0.309653i	0.988676	−	0.150068i	$-0.0479493\pi$
$317$	1.79135	+	5.51322i	0.100612	+	0.309653i	−0.888063	+	0.459721i	$0.847949\pi$
$318$	2.33581			0.130985
$319$		0			0
$320$	−8.53916			−0.477353
$321$	0.344751	+	1.06103i	0.0192421	+	0.0592211i
$322$	4.65155	+	3.37955i	0.259220	+	0.188335i
$323$	0.284122	−	0.206427i	0.0158090	−	0.0114859i
$324$	−0.307099	+	0.945154i	−0.0170611	+	0.0525085i
$325$	−0.874813	+	2.69240i	−0.0485259	+	0.149347i
$326$	17.5273	−	12.7344i	0.970749	−	0.705290i
$327$	−2.85246	−	2.07244i	−0.157742	−	0.114606i
$328$	7.53448	+	23.1888i	0.416022	+	1.28038i
$329$	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	$0.615572\pi$
$332$	0.533354	+	1.64149i	0.0292716	+	0.0900887i
$333$	21.2452	+	15.4355i	1.16423	+	0.845863i
$334$	−19.4226	+	14.1114i	−1.06276	+	0.772139i
$335$	4.14555	−	12.7587i	0.226496	−	0.697082i
$336$	2.36847	−	7.28942i	0.129211	−	0.397670i
$337$	−10.8290	+	7.86773i	−0.589893	+	0.428582i	−0.842277	−	0.539045i	$-0.818785\pi$
$337$	−10.8290	+	7.86773i	−0.589893	+	0.428582i	0.252384	+	0.967627i	$0.418785\pi$
$338$	5.46813	+	3.97283i	0.297427	+	0.216093i
$339$	1.02884	+	3.16643i	0.0558787	+	0.171977i
$340$	0.598640			0.0324658
$341$		0			0
$342$	0.344163			0.0186102
$343$	0.768863	+	2.36632i	0.0415147	+	0.127769i
$344$	−7.03968	−	5.11463i	−0.379554	−	0.275762i
$345$	0.541077	−	0.393115i	0.0291306	−	0.0211646i
$346$	6.65485	−	20.4815i	0.357767	−	1.10109i
$347$	−2.61088	+	8.03547i	−0.140159	+	0.431366i	−0.996357	−	0.0852825i	$-0.972821\pi$
$347$	−2.61088	+	8.03547i	−0.140159	+	0.431366i	0.856197	+	0.516649i	$0.172821\pi$
$348$	−0.509872	+	0.370444i	−0.0273320	+	0.0198579i
$349$	8.41283	+	6.11228i	0.450328	+	0.327183i	0.789725	−	0.613461i	$-0.210223\pi$
$349$	8.41283	+	6.11228i	0.450328	+	0.327183i	−0.339397	+	0.940643i	$0.610223\pi$
$350$	−1.52884	−	4.70527i	−0.0817197	−	0.251507i
$351$	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	$0.330204\pi$
$354$	−2.05133	−	6.31335i	−0.109027	−	0.335551i
$355$	6.71734	+	4.88043i	0.356519	+	0.259027i
$356$	−1.59530	+	1.15905i	−0.0845507	+	0.0614297i
$357$	−2.39608	+	7.37439i	−0.126814	+	0.390294i
$358$	−7.07191	+	21.7651i	−0.373762	+	1.15032i
$359$	3.57114	−	2.59458i	0.188478	−	0.136937i	−0.489545	−	0.871978i	$-0.662837\pi$
$359$	3.57114	−	2.59458i	0.188478	−	0.136937i	0.678023	+	0.735041i	$0.262837\pi$
$360$	6.32872	+	4.59808i	0.333553	+	0.242340i
$361$	−5.86853	−	18.0615i	−0.308870	−	0.950604i
$362$	−32.6546			−1.71629
$363$		0			0
$364$	−1.67520			−0.0878041
$365$	0.407912	+	1.25542i	0.0213511	+	0.0657119i
$366$	5.35264	+	3.88892i	0.279787	+	0.203277i
$367$	23.7541	−	17.2584i	1.23996	−	0.900880i	0.242360	−	0.970186i	$-0.422078\pi$
$367$	23.7541	−	17.2584i	1.23996	−	0.900880i	0.997595	+	0.0693059i	$0.0220785\pi$
$368$	−1.31059	+	4.03358i	−0.0683192	+	0.210265i
$369$	6.86009	−	21.1132i	0.357122	−	1.09911i
$370$	10.7919	−	7.84080i	0.561046	−	0.407624i
$371$	8.83938	+	6.42219i	0.458918	+	0.333423i
$372$	−0.195460	−	0.601563i	−0.0101341	−	0.0311896i
$373$	−4.96478			−0.257067			−0.128533	−	0.991705i	$-0.541027\pi$
$373$	−4.96478			−0.257067			−0.128533	+	0.991705i	$0.541027\pi$
$374$		0			0
$375$	−0.575493			−0.0297183
$376$	2.01528	+	6.20239i	0.103930	+	0.319864i
$377$	−15.4684	−	11.2384i	−0.796662	−	0.578809i
$378$	−13.0577	+	9.48700i	−0.671618	+	0.487959i
$379$	2.44839	−	7.53536i	0.125765	−	0.387066i	−0.868274	−	0.496084i	$-0.834771\pi$
$379$	2.44839	−	7.53536i	0.125765	−	0.387066i	0.994040	+	0.109018i	$0.0347708\pi$
$380$	−0.00476632	+	0.0146692i	−0.000244507	+	0.000752516i
$381$	−1.13501	+	0.824635i	−0.0581485	+	0.0422473i
$382$	−5.90365	−	4.28925i	−0.302057	−	0.219457i
$383$	−7.57571	−	23.3156i	−0.387101	−	1.19137i	−0.934945	−	0.354793i	$-0.884551\pi$
$383$	−7.57571	−	23.3156i	−0.387101	−	1.19137i	0.547844	−	0.836580i	$-0.315449\pi$
$384$	5.60903			0.286235
$385$		0			0
$386$	24.7872			1.26164
$387$	2.44824	+	7.53491i	0.124451	+	0.383021i
$388$	−0.568183	−	0.412809i	−0.0288451	−	0.0209572i
$389$	−4.41799	+	3.20986i	−0.224001	+	0.162746i	−0.694126	−	0.719854i	$-0.744209\pi$
$389$	−4.41799	+	3.20986i	−0.224001	+	0.162746i	0.470125	+	0.882600i	$0.344209\pi$
$390$	0.682513	−	2.10056i	0.0345604	−	0.106366i
$391$	1.32587	−	4.08060i	0.0670520	−	0.206365i
$392$	14.9828	−	10.8856i	0.756746	−	0.549808i
$393$	−3.27843	−	2.38192i	−0.165375	−	0.120152i
$394$	1.10834	+	3.41111i	0.0558372	+	0.171849i
$395$	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	$0.551624\pi$
$398$	2.73475	+	8.41670i	0.137081	+	0.421891i
$399$	−0.161626	−	0.117429i	−0.00809144	−	0.00587878i
$400$	2.95244	−	2.14507i	0.147622	−	0.107254i
$401$	−4.54336	+	13.9830i	−0.226884	+	0.698278i	0.771211	+	0.636580i	$0.219652\pi$
$401$	−4.54336	+	13.9830i	−0.226884	+	0.698278i	−0.998095	+	0.0616980i	$0.980348\pi$
$402$	−3.23428	+	9.95410i	−0.161311	+	0.496465i
$403$	15.5244	−	11.2792i	0.773327	−	0.561855i
$404$	1.29943	+	0.944090i	0.0646490	+	0.0469702i
$405$	−1.89395	−	5.82899i	−0.0941112	−	0.289645i
$406$	33.4143			1.65832
$407$		0			0
$408$	−6.22784			−0.308324
$409$	1.35837	+	4.18062i	0.0671668	+	0.206718i	0.979007	−	0.203828i	$-0.0653382\pi$
$409$	1.35837	+	4.18062i	0.0671668	+	0.206718i	−0.911840	+	0.410546i	$0.865338\pi$
$410$	−9.12312	−	6.62834i	−0.450559	−	0.327350i
$411$	4.45697	−	3.23818i	0.219846	−	0.159727i
$412$	−0.203727	+	0.627008i	−0.0100369	+	0.0308905i
$413$	9.59542	−	29.5317i	0.472160	−	1.45316i
$414$	3.40166	−	2.47145i	0.167183	−	0.121465i
$415$	−8.61155	−	6.25666i	−0.422724	−	0.307127i
$416$	−0.800383	−	2.46332i	−0.0392420	−	0.120774i
$417$	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	$0.356367\pi$
$420$	−0.105234	−	0.323876i	−0.00513488	−	0.0158035i
$421$	3.90637	+	2.83814i	0.190385	+	0.138323i	0.678895	−	0.734236i	$-0.262459\pi$
$421$	3.90637	+	2.83814i	0.190385	+	0.138323i	−0.488510	+	0.872558i	$0.662459\pi$
$422$	30.1037	−	21.8716i	1.46543	−	1.06469i
$423$	1.83490	−	5.64723i	0.0892157	−	0.274578i
$424$	−2.71184	+	8.34619i	−0.131699	+	0.405327i
$425$	−2.98685	+	2.17008i	−0.144884	+	0.105264i
$426$	−5.24074	−	3.80762i	−0.253915	−	0.184480i
$427$	9.56357	+	29.4337i	0.462814	+	1.42439i
$428$	−0.314335			−0.0151939
$429$		0			0
$430$	4.02448			0.194078
$431$	−7.68647	−	23.6565i	−0.370244	−	1.13949i	−0.946631	−	0.322318i	$-0.895538\pi$
$431$	−7.68647	−	23.6565i	−0.370244	−	1.13949i	0.576387	−	0.817177i	$-0.304462\pi$
$432$	−9.63191	−	6.99800i	−0.463416	−	0.336691i
$433$	17.1918	−	12.4906i	0.826186	−	0.600259i	−0.0922919	−	0.995732i	$-0.529419\pi$
$433$	17.1918	−	12.4906i	0.826186	−	0.600259i	0.918478	+	0.395473i	$0.129419\pi$
$434$	−10.3630	+	31.8941i	−0.497441	+	1.53097i
$435$	1.20109	−	3.69658i	0.0575880	−	0.177238i
$436$	0.803691	−	0.583916i	0.0384898	−	0.0279645i
$437$	0.0894356	+	0.0649788i	0.00427828	+	0.00310836i
$438$	−0.318245	−	0.979458i	−0.0152064	−	0.0468003i
$439$	−15.9119			−0.759434			−0.379717	−	0.925103i	$-0.623979\pi$
$439$	−15.9119			−0.759434			−0.379717	+	0.925103i	$0.623979\pi$
$440$		0			0
$441$	−16.8621			−0.802958
$442$	−4.37852	−	13.4757i	−0.208265	−	0.640973i
$443$	−21.2671	−	15.4515i	−1.01043	−	0.734122i	−0.0461323	−	0.998935i	$-0.514690\pi$
$443$	−21.2671	−	15.4515i	−1.01043	−	0.734122i	−0.964300	+	0.264814i	$0.914690\pi$
$444$	0.742837	−	0.539702i	0.0352535	−	0.0256131i
$445$	3.75801	−	11.5660i	0.178147	−	0.548279i
$446$	−2.12896	+	6.55226i	−0.100809	+	0.310258i
$447$	3.79908	−	2.76020i	0.179690	−	0.130553i
$448$	25.2113	+	18.3171i	1.19112	+	0.865402i
$449$	−2.53073	−	7.78879i	−0.119433	−	0.367576i	0.873413	−	0.486980i	$-0.161902\pi$
$449$	−2.53073	−	7.78879i	−0.119433	−	0.367576i	−0.992846	+	0.119404i	$0.961902\pi$
$450$	−3.61803			−0.170556
$451$		0			0
$452$	−0.938065			−0.0441229
$453$	0.345044	+	1.06194i	0.0162116	+	0.0498941i
$454$	−4.10168	−	2.98004i	−0.192501	−	0.139860i
$455$	8.35822	−	6.07260i	0.391839	−	0.284688i
$456$	0.0495855	−	0.152608i	0.00232205	−	0.00714655i
$457$	3.68237	−	11.3332i	0.172254	−	0.530143i	−0.827244	−	0.561843i	$-0.810092\pi$
$457$	3.68237	−	11.3332i	0.172254	−	0.530143i	0.999497	+	0.0317007i	$0.0100923\pi$
$458$	−29.5294	+	21.4544i	−1.37982	+	1.00250i
$459$	9.74419	+	7.07957i	0.454820	+	0.330446i
$460$	0.0582308	+	0.179216i	0.00271503	+	0.00835599i
$461$	6.96172			0.324240			0.162120	−	0.986771i	$-0.448167\pi$
$461$	6.96172			0.324240			0.162120	+	0.986771i	$0.448167\pi$
$462$		0			0
$463$	12.4762			0.579817			0.289909	−	0.957054i	$-0.406375\pi$
$463$	12.4762			0.579817			0.289909	+	0.957054i	$0.406375\pi$
$464$	7.61657	+	23.4414i	0.353590	+	1.08824i
$465$	3.15590	+	2.29290i	0.146351	+	0.106330i
$466$	−20.0891	+	14.5956i	−0.930609	+	0.676127i
$467$	−1.89927	+	5.84535i	−0.0878877	+	0.270491i	−0.985335	−	0.170631i	$-0.945419\pi$
$467$	−1.89927	+	5.84535i	−0.0878877	+	0.270491i	0.897447	+	0.441122i	$0.145419\pi$
$468$	−0.378566	+	1.16511i	−0.0174992	+	0.0538571i
$469$	−39.6078	+	28.7768i	−1.82892	+	1.32879i
$470$	−2.44020	−	1.77291i	−0.112558	−	0.0817781i
$471$	3.78339	+	11.6441i	0.174330	+	0.536531i
$472$	24.9401			1.14796
$473$		0			0
$474$	−10.8181			−0.496890
$475$	−0.0293950	−	0.0904686i	−0.00134874	−	0.00415098i
$476$	−1.76745	−	1.28413i	−0.0810108	−	0.0588578i
$477$	6.46422	−	4.69653i	0.295976	−	0.215039i
$478$	−4.58970	+	14.1256i	−0.209928	+	0.646092i
$479$	6.85838	−	21.1079i	0.313367	−	0.964445i	−0.663054	−	0.748571i	$-0.730740\pi$
$479$	6.85838	−	21.1079i	0.313367	−	0.964445i	0.976421	−	0.215874i	$-0.0692599\pi$
$480$	0.425971	−	0.309486i	0.0194428	−	0.0141260i
$481$	22.5360	+	16.3734i	1.02755	+	0.746561i
$482$	−4.18693	−	12.8861i	−0.190710	−	0.586944i
$483$	−2.44076			−0.111058
$484$		0			0
$485$	4.33133			0.196675
$486$	5.57769	+	17.1664i	0.253009	+	0.778682i
$487$	27.6932	+	20.1203i	1.25490	+	0.911736i	0.998495	−	0.0548341i	$-0.0174630\pi$
$487$	27.6932	+	20.1203i	1.25490	+	0.911736i	0.256402	+	0.966570i	$0.417463\pi$
$488$	−20.1100	+	14.6108i	−0.910339	+	0.661400i
$489$	−2.84201	+	8.74680i	−0.128520	+	0.395544i
$490$	−2.64687	+	8.14623i	−0.119573	+	0.368009i
$491$	13.7498	−	9.98984i	0.620522	−	0.450835i	−0.232582	−	0.972577i	$-0.574717\pi$
$491$	13.7498	−	9.98984i	0.620522	−	0.450835i	0.853104	+	0.521741i	$0.174717\pi$
$492$	−0.627968	−	0.456246i	−0.0283110	−	0.0205691i
$493$	−7.70536	−	23.7146i	−0.347032	−	1.06805i
$494$	0.365073			0.0164254
$495$		0			0
$496$	−24.7371			−1.11073
$497$	−9.36365	−	28.8184i	−0.420017	−	1.29268i
$498$	6.71857	+	4.88133i	0.301066	+	0.218737i
$499$	−4.23072	+	3.07380i	−0.189393	+	0.137602i	−0.678441	−	0.734655i	$-0.737344\pi$
$499$	−4.23072	+	3.07380i	−0.189393	+	0.137602i	0.489048	+	0.872257i	$0.337344\pi$
$500$	0.0501062	−	0.154211i	0.00224082	−	0.00689653i
$501$	3.14932	−	9.69262i	0.140701	−	0.433034i
$502$	−10.5919	+	7.69548i	−0.472740	+	0.343466i
$503$	−33.9340	−	24.6545i	−1.51304	−	1.09929i	−0.964804	−	0.262970i	$-0.915298\pi$
$503$	−33.9340	−	24.6545i	−1.51304	−	1.09929i	−0.548240	−	0.836321i	$-0.684702\pi$
$504$	−8.82193	−	27.1511i	−0.392960	−	1.20941i
$505$	−9.90570			−0.440798
$506$		0			0
$507$	−2.86923			−0.127427
$508$	−0.122150	−	0.375940i	−0.00541955	−	0.0166797i
$509$	−16.4779	−	11.9719i	−0.730370	−	0.530645i	0.159311	−	0.987228i	$-0.449073\pi$
$509$	−16.4779	−	11.9719i	−0.730370	−	0.530645i	−0.889680	+	0.456584i	$0.849073\pi$
$510$	2.33029	−	1.69305i	0.103187	−	0.0749696i
$511$	1.48864	−	4.58156i	0.0658536	−	0.202676i
$512$	−7.64292	+	23.5225i	−0.337772	+	1.03956i
$513$	−0.251062	+	0.182407i	−0.0110847	+	0.00805348i
$514$	−11.4366	−	8.30916i	−0.504446	−	0.366501i
$515$	−1.25643	−	3.86690i	−0.0553651	−	0.170396i
$516$	0.277016			0.0121949
$517$		0			0
$518$	−48.6816			−2.13895
$519$	2.82503	+	8.69454i	0.124005	+	0.381648i
$520$	6.71323	+	4.87744i	0.294394	+	0.213890i
$521$	−11.7128	+	8.50988i	−0.513149	+	0.372824i	−0.814017	−	0.580841i	$-0.802724\pi$
$521$	−11.7128	+	8.50988i	−0.513149	+	0.372824i	0.300868	+	0.953666i	$0.402724\pi$
$522$	7.55108	−	23.2398i	0.330502	−	1.01718i
$523$	3.44867	−	10.6139i	0.150800	−	0.464114i	−0.846911	−	0.531734i	$-0.821541\pi$
$523$	3.44867	−	10.6139i	0.150800	−	0.464114i	0.997711	+	0.0676203i	$0.0215406\pi$
$524$	0.923710	−	0.671115i	0.0403525	−	0.0293178i
$525$	1.69911	+	1.23447i	0.0741551	+	0.0538769i
$526$	−4.59221	−	14.1334i	−0.200230	−	0.616244i
$527$	25.0254			1.09013
$528$		0			0
$529$	−21.6494			−0.941279
$530$	−1.25424	−	3.86014i	−0.0544805	−	0.167674i
$531$	−18.3710	−	13.3473i	−0.797234	−	0.579225i
$532$	0.0455388	−	0.0330859i	0.00197436	−	0.00143446i
$533$	7.27689	−	22.3960i	0.315197	−	0.970077i
$534$	−2.93193	+	9.02354i	−0.126877	+	0.390487i
$535$	1.56834	−	1.13947i	0.0678053	−	0.0492634i
$536$	−31.8125	−	23.1132i	−1.37409	−	0.998337i
$537$	−3.00208	−	9.23944i	−0.129549	−	0.398711i
$538$	−0.121123			−0.00522197
$539$		0			0
$540$	−0.528983			−0.0227638
$541$	3.30055	+	10.1580i	0.141902	+	0.436728i	0.996600	−	0.0823974i	$-0.0262577\pi$
$541$	3.30055	+	10.1580i	0.141902	+	0.436728i	−0.854698	+	0.519126i	$0.826258\pi$
$542$	14.6961	+	10.6774i	0.631253	+	0.458632i
$543$	11.2147	−	8.14795i	0.481268	−	0.349662i
$544$	1.04381	−	3.21251i	0.0447529	−	0.137735i
$545$	−1.89324	+	5.82678i	−0.0810973	+	0.249592i
$546$	−6.52092	+	4.73773i	−0.279070	+	0.202756i
$547$	−1.41384	−	1.02721i	−0.0604514	−	0.0439205i	0.557149	−	0.830412i	$-0.311895\pi$
$547$	−1.41384	−	1.02721i	−0.0604514	−	0.0439205i	−0.617601	+	0.786492i	$0.711895\pi$
$548$	0.479660	+	1.47624i	0.0204901	+	0.0630619i
$549$	22.6325			0.965930
$550$		0			0
$551$	0.642459			0.0273697
$552$	−0.605793	−	1.86444i	−0.0257843	−	0.0793558i
$553$	−40.9388	−	29.7438i	−1.74089	−	1.26483i
$554$	4.28471	−	3.11302i	0.182040	−	0.132260i
$555$	−1.74988	+	5.38558i	−0.0742783	+	0.228605i
$556$	−0.0258299	+	0.0794961i	−0.00109543	+	0.00337139i
$557$	15.7632	−	11.4526i	0.667908	−	0.485263i	−0.201416	−	0.979506i	$-0.564554\pi$
$557$	15.7632	−	11.4526i	0.667908	−	0.485263i	0.869324	+	0.494242i	$0.164554\pi$
$558$	19.8406	+	14.4151i	0.839921	+	0.610238i
$559$	2.59699	+	7.99271i	0.109841	+	0.338055i
$560$	−13.3182			−0.562798
$561$		0			0
$562$	−2.08426			−0.0879191
$563$	−4.53920	−	13.9702i	−0.191304	−	0.588775i	−1.00000		0.000546971i	$-0.999826\pi$
$563$	−4.53920	−	13.9702i	−0.191304	−	0.588775i	0.808695	−	0.588228i	$-0.200174\pi$
$564$	−0.167965	−	0.122034i	−0.00707261	−	0.00513855i
$565$	4.68038	−	3.40050i	0.196905	−	0.143060i
$566$	−2.26710	+	6.97742i	−0.0952934	+	0.293283i
$567$	−6.91181	+	21.2724i	−0.290269	+	0.893356i
$568$	19.6897	−	14.3054i	0.826159	−	0.600240i
$569$	−16.1266	−	11.7166i	−0.676061	−	0.491187i	0.195987	−	0.980606i	$-0.437209\pi$
$569$	−16.1266	−	11.7166i	−0.676061	−	0.491187i	−0.872049	+	0.489419i	$0.837209\pi$
$570$	0.0229335	+	0.0705819i	0.000960577	+	0.00295635i
$571$	5.24422			0.219464			0.109732	−	0.993961i	$-0.465001\pi$
$571$	5.24422			0.219464			0.109732	+	0.993961i	$0.465001\pi$
$572$		0			0
$573$	3.09776			0.129411
$574$	12.7172	+	39.1395i	0.530805	+	1.63365i
$575$	−0.940197	−	0.683093i	−0.0392089	−	0.0284869i
$576$	18.4370	−	13.3953i	0.768208	−	0.558136i
$577$	11.6192	−	35.7601i	0.483712	−	1.48871i	−0.350125	−	0.936703i	$-0.613861\pi$
$577$	11.6192	−	35.7601i	0.483712	−	1.48871i	0.833838	−	0.552010i	$-0.186139\pi$
$578$	−1.41156	+	4.34433i	−0.0587132	+	0.180701i
$579$	−8.51275	+	6.18488i	−0.353778	+	0.257035i
$580$	0.885974	+	0.643698i	0.0367881	+	0.0267281i
$581$	12.0041	+	36.9448i	0.498013	+	1.53273i
$582$	−3.37922			−0.140073
$583$		0			0
$584$	3.86923			0.160110
$585$	−2.33471	−	7.18549i	−0.0965283	−	0.297084i
$586$	−12.5212	−	9.09718i	−0.517246	−	0.375801i
$587$	−20.6875	+	15.0303i	−0.853863	+	0.620368i	−0.926208	−	0.377012i	$-0.876952\pi$
$587$	−20.6875	+	15.0303i	−0.853863	+	0.620368i	0.0723456	+	0.997380i	$0.476952\pi$
$588$	−0.182191	+	0.560726i	−0.00751343	+	0.0231240i
$589$	−0.199250	+	0.613230i	−0.00820997	+	0.0252677i
$590$	−9.33193	+	6.78004i	−0.384189	+	0.279130i
$591$	−1.23178	−	0.894938i	−0.0506685	−	0.0368128i
$592$	−11.0966	−	34.1520i	−0.456069	−	1.40364i
$593$	40.2260			1.65188			0.825942	−	0.563754i	$-0.190644\pi$
$593$	40.2260			1.65188			0.825942	+	0.563754i	$0.190644\pi$
$594$		0			0
$595$	13.4735			0.552358
$596$	0.408858	+	1.25834i	0.0167475	+	0.0515435i
$597$	−3.03933	−	2.20820i	−0.124391	−	0.0903757i
$598$	3.60834	−	2.62161i	0.147556	−	0.107206i
$599$	1.52344	−	4.68868i	0.0622462	−	0.191574i	−0.915097	−	0.403233i	$-0.867886\pi$
$599$	1.52344	−	4.68868i	0.0622462	−	0.191574i	0.977344	+	0.211659i	$0.0678865\pi$
$600$	−0.521270	+	1.60431i	−0.0212808	+	0.0654955i
$601$	−37.2873	+	27.0908i	−1.52098	+	1.10506i	−0.559981	+	0.828506i	$0.689191\pi$
$601$	−37.2873	+	27.0908i	−1.52098	+	1.10506i	−0.960999	+	0.276551i	$0.910809\pi$
$602$	−11.8820	−	8.63280i	−0.484276	−	0.351847i
$603$	11.0637	+	34.0505i	0.450548	+	1.38664i
$604$	−0.314602			−0.0128010
$605$		0			0
$606$	7.72824			0.313938
$607$	−13.9479	−	42.9273i	−0.566129	−	1.74237i	−0.664572	−	0.747224i	$-0.731386\pi$
$607$	−13.9479	−	42.9273i	−0.566129	−	1.74237i	0.0984428	−	0.995143i	$-0.468614\pi$
$608$	0.0704095	+	0.0511555i	0.00285548	+	0.00207463i
$609$	−11.4756	+	8.33750i	−0.465014	+	0.337853i
$610$	3.55265	−	10.9339i	0.143843	−	0.442702i
$611$	1.94638	−	5.99034i	0.0787420	−	0.242343i
$612$	−1.29253	+	0.939078i	−0.0522474	+	0.0379600i
$613$	−3.83003	−	2.78268i	−0.154694	−	0.112391i	0.507746	−	0.861507i	$-0.330479\pi$
$613$	−3.83003	−	2.78268i	−0.154694	−	0.112391i	−0.662440	+	0.749115i	$0.730479\pi$
$614$	−1.78047	−	5.47973i	−0.0718540	−	0.221144i
$615$	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	$0.383035\pi$
$618$	0.980246	+	3.01689i	0.0394313	+	0.121357i
$619$	−0.288781	−	0.209811i	−0.0116071	−	0.00843303i	0.581967	−	0.813213i	$-0.302283\pi$
$619$	−0.288781	−	0.209811i	−0.0116071	−	0.00843303i	−0.593574	+	0.804780i	$0.702283\pi$
$620$	−0.889186	+	0.646031i	−0.0357106	+	0.0259452i
$621$	−1.17159	+	3.60578i	−0.0470143	+	0.144695i
$622$	−6.96233	+	21.4279i	−0.279164	+	0.859179i
$623$	−35.9051	+	26.0866i	−1.43851	+	1.04514i
$624$	−4.81010	−	3.49474i	−0.192558	−	0.139902i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−36.0297			−1.44004
$627$		0			0
$628$	−3.44960			−0.137654
$629$	11.2260	+	34.5501i	0.447610	+	1.37760i
$630$	10.6820	+	7.76094i	0.425582	+	0.309203i
$631$	25.8822	−	18.8046i	1.03036	−	0.748597i	0.0619761	−	0.998078i	$-0.480260\pi$
$631$	25.8822	−	18.8046i	1.03036	−	0.748597i	0.968380	+	0.249480i	$0.0802598\pi$
$632$	12.5596	−	38.6546i	0.499595	−	1.53760i
$633$	−4.88124	+	15.0229i	−0.194012	+	0.597107i
$634$	−6.35787	+	4.61926i	−0.252503	+	0.183454i
$635$	1.97224	+	1.43292i	0.0782661	+	0.0568637i
$636$	−0.0863323	−	0.265703i	−0.00342330	−	0.0105358i
$637$	−17.8866			−0.708693
$638$		0			0
$639$	−22.1594			−0.876610
$640$	−3.01183	−	9.26945i	−0.119053	−	0.366407i
$641$	−0.819410	−	0.595336i	−0.0323647	−	0.0235144i	0.571485	−	0.820612i	$-0.306367\pi$
$641$	−0.819410	−	0.595336i	−0.0323647	−	0.0235144i	−0.603850	+	0.797098i	$0.706367\pi$
$642$	−1.22359	+	0.888990i	−0.0482912	+	0.0350856i
$643$	−4.62674	+	14.2396i	−0.182461	+	0.561556i	−0.999895	−	0.0144651i	$-0.995395\pi$
$643$	−4.62674	+	14.2396i	−0.182461	+	0.561556i	0.817435	+	0.576021i	$0.195395\pi$
$644$	0.212508	−	0.654034i	0.00837400	−	0.0257725i
$645$	−1.38214	+	1.00418i	−0.0544218	+	0.0395397i
$646$	0.385178	+	0.279848i	0.0151546	+	0.0110105i
$647$	5.52749	+	17.0119i	0.217308	+	0.668806i	0.998982	+	0.0451179i	$0.0143664\pi$
$647$	5.52749	+	17.0119i	0.217308	+	0.668806i	−0.781674	+	0.623688i	$0.785634\pi$
$648$	−17.9650			−0.705732
$649$		0			0
$650$	−3.83785			−0.150533
$651$	−4.39917	−	13.5393i	−0.172417	−	0.530645i
$652$	−2.09638	−	1.52311i	−0.0821006	−	0.0596495i
$653$	−37.0240	+	26.8995i	−1.44886	+	1.05266i	−0.462767	+	0.886480i	$0.653144\pi$
$653$	−37.0240	+	26.8995i	−1.44886	+	1.05266i	−0.986095	+	0.166181i	$0.946856\pi$
$654$	1.47707	−	4.54594i	0.0577579	−	0.177760i
$655$	−2.17596	+	6.69692i	−0.0850218	+	0.261670i
$656$	−24.5590	+	17.8432i	−0.958869	+	0.696659i
$657$	−2.85009	−	2.07071i	−0.111193	−	0.0807863i
$658$	3.40152	+	10.4688i	0.132605	+	0.408116i
$659$	−9.54036			−0.371640			−0.185820	−	0.982584i	$-0.559494\pi$
$659$	−9.54036			−0.371640			−0.185820	+	0.982584i	$0.559494\pi$
$660$		0			0
$661$	15.7769			0.613651			0.306825	−	0.951766i	$-0.400733\pi$
$661$	15.7769			0.613651			0.306825	+	0.951766i	$0.400733\pi$
$662$	−5.41377	−	16.6619i	−0.210412	−	0.647582i
$663$	4.86617	+	3.53548i	0.188986	+	0.137307i
$664$	−25.2419	+	18.3393i	−0.979575	+	0.711703i
$665$	−0.107275	+	0.330157i	−0.00415993	+	0.0128030i
$666$	−11.0012	+	33.8583i	−0.426289	+	1.31198i
$667$	6.34999	−	4.61353i	0.245872	−	0.178637i
$668$	2.32307	+	1.68781i	0.0898822	+	0.0653032i
$669$	−0.903757	−	2.78148i	−0.0349413	−	0.107538i
$670$	18.1868			0.702616
$671$		0			0
$672$	−1.92152			−0.0741243
$673$	14.6175	+	44.9879i	0.563462	+	1.73416i	0.672478	+	0.740117i	$0.265230\pi$
$673$	14.6175	+	44.9879i	0.563462	+	1.73416i	−0.109016	+	0.994040i	$0.534770\pi$
$674$	−14.6806	−	10.6661i	−0.565475	−	0.410842i
$675$	2.63930	−	1.91757i	0.101587	−	0.0738072i
$676$	0.249814	−	0.768850i	0.00960825	−	0.0295711i
$677$	8.51129	−	26.1950i	0.327115	−	1.00676i	−0.643361	−	0.765563i	$-0.722461\pi$
$677$	8.51129	−	26.1950i	0.327115	−	1.00676i	0.970477	−	0.241195i	$-0.0775393\pi$
$678$	−3.65155	+	2.65300i	−0.140237	+	0.101888i
$679$	−12.7880	−	9.29100i	−0.490757	−	0.356556i
$680$	3.34410	+	10.2921i	0.128240	+	0.394683i
$681$	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	$0.673940\pi$
$684$	−0.0127204	−	0.0391494i	−0.000486377	−	0.00149691i
$685$	−7.74461	−	5.62678i	−0.295906	−	0.214988i
$686$	−2.72885	+	1.98262i	−0.104188	+	0.0756969i
$687$	4.78811	−	14.7363i	0.182678	−	0.562224i
$688$	3.34780	−	10.3035i	0.127634	−	0.392817i
$689$	6.85696	−	4.98188i	0.261229	−	0.189794i
$690$	0.733524	+	0.532936i	0.0279248	+	0.0202885i
$691$	−2.32591	−	7.15841i	−0.0884817	−	0.272319i	0.897018	−	0.441993i	$-0.145728\pi$
$691$	−2.32591	−	7.15841i	−0.0884817	−	0.272319i	−0.985500	+	0.169674i	$0.945728\pi$
$692$	−2.57579			−0.0979167
$693$		0			0
$694$	−11.4541			−0.434791
$695$	−0.159299	−	0.490271i	−0.00604255	−	0.0185971i
$696$	−9.21706	−	6.69658i	−0.349372	−	0.253833i
$697$	24.8453	−	18.0512i	0.941083	−	0.683737i
$698$	−4.35634	+	13.4074i	−0.164890	+	0.507479i
$699$	3.25739	−	10.0252i	0.123206	−	0.379189i
$700$	−0.478730	+	0.347817i	−0.0180943	+	0.0131463i
$701$	25.7435	+	18.7038i	0.972319	+	0.706431i	0.955979	−	0.293435i	$-0.0947985\pi$
$701$	25.7435	+	18.7038i	0.972319	+	0.706431i	0.0163401	+	0.999866i	$0.494799\pi$
$702$	3.86903	+	11.9077i	0.146027	+	0.449426i
$703$	−0.936004			−0.0353021
$704$		0			0
$705$	1.28042			0.0482234
$706$	8.00454	+	24.6355i	0.301255	+	0.927167i
$707$	29.2460	+	21.2484i	1.09991	+	0.799130i
$708$	−0.642341	+	0.466688i	−0.0241406	+	0.0175392i
$709$	−4.46162	+	13.7315i	−0.167560	+	0.515696i	−0.999216	−	0.0395951i	$-0.987393\pi$
$709$	−4.46162	+	13.7315i	−0.167560	+	0.515696i	0.831656	+	0.555291i	$0.187393\pi$
$710$	−3.47838	+	10.7054i	−0.130541	+	0.401765i
$711$	−29.9384	+	21.7515i	−1.12278	+	0.815746i
$712$	−28.8385	−	20.9524i	−1.08077	−	0.785226i
$713$	2.43427	+	7.49191i	0.0911642	+	0.280574i
$714$	−10.5117			−0.393392
$715$		0			0
$716$	2.73721			0.102294
$717$	−1.94836	−	5.99644i	−0.0727628	−	0.223941i
$718$	4.84130	+	3.51741i	0.180676	+	0.131269i
$719$	−4.37682	+	3.17994i	−0.163228	+	0.118592i	−0.666401	−	0.745594i	$-0.732166\pi$
$719$	−4.37682	+	3.17994i	−0.163228	+	0.118592i	0.503173	+	0.864186i	$0.332166\pi$
$720$	−3.00970	+	9.26289i	−0.112165	+	0.345208i
$721$	−4.58525	+	14.1119i	−0.170763	+	0.525556i
$722$	20.8286	−	15.1329i	0.775160	−	0.563186i
$723$	4.65325	+	3.38078i	0.173056	+	0.125733i
$724$	1.20693	+	3.71454i	0.0448551	+	0.138050i
$725$	−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	$0.600691\pi$
$728$	−9.35791	−	28.8007i	−0.346827	−	1.06742i
$729$	8.67639	+	6.30377i	0.321348	+	0.233473i
$730$	−1.44776	+	1.05186i	−0.0535841	+	0.0389311i
$731$	−3.38683	+	10.4236i	−0.125266	+	0.385530i
$732$	0.244538	−	0.752611i	0.00903839	−	0.0278173i
$733$	11.3950	−	8.27899i	0.420886	−	0.305791i	−0.357108	−	0.934063i	$-0.616237\pi$
$733$	11.3950	−	8.27899i	0.420886	−	0.305791i	0.777994	+	0.628272i	$0.216237\pi$
$734$	32.2029	+	23.3968i	1.18863	+	0.863590i
$735$	−1.12361	−	3.45813i	−0.0414451	−	0.127555i
$736$	1.06327			0.0391926
$737$		0			0
$738$	30.0956			1.10783
$739$	−11.2314	−	34.5668i	−0.413155	−	1.27156i	−0.913891	−	0.405960i	$-0.866937\pi$
$739$	−11.2314	−	34.5668i	−0.413155	−	1.27156i	0.500736	−	0.865600i	$-0.333063\pi$
$740$	−1.29078	−	0.937809i	−0.0474501	−	0.0344745i
$741$	−0.125378	+	0.0910927i	−0.00460589	+	0.00334637i
$742$	−4.57722	+	14.0872i	−0.168035	+	0.517159i
$743$	−0.604796	+	1.86137i	−0.0221878	+	0.0682870i	−0.961537	−	0.274674i	$-0.911430\pi$
$743$	−0.604796	+	1.86137i	−0.0221878	+	0.0682870i	0.939350	+	0.342961i	$0.111430\pi$
$744$	9.25047	−	6.72086i	0.339139	−	0.246399i
$745$	−6.60144	−	4.79623i	−0.241858	−	0.175720i
$746$	−2.07988	−	6.40121i	−0.0761498	−	0.234365i
$747$	28.4080			1.03939
$748$		0			0
$749$	−7.07466			−0.258503
$750$	−0.241089	−	0.741996i	−0.00880333	−	0.0270939i
$751$	−15.1372	−	10.9978i	−0.552363	−	0.401316i	0.276293	−	0.961074i	$-0.410894\pi$
$751$	−15.1372	−	10.9978i	−0.552363	−	0.401316i	−0.828656	+	0.559758i	$0.810894\pi$
$752$	−6.56890	+	4.77258i	−0.239543	+	0.174038i
$753$	1.71745	−	5.28577i	0.0625874	−	0.192624i
$754$	8.00985	−	24.6518i	0.291702	−	0.897766i
$755$	1.56968	−	1.14044i	0.0571263	−	0.0415047i
$756$	1.56179	+	1.13471i	0.0568017	+	0.0412688i
$757$	−4.49528	−	13.8351i	−0.163384	−	0.502844i	0.835530	−	0.549445i	$-0.185161\pi$
$757$	−4.49528	−	13.8351i	−0.163384	−	0.502844i	−0.998914	+	0.0466015i	$0.985161\pi$
$758$	10.7412			0.390138
$759$		0			0
$760$	−0.278825			−0.0101141
$761$	4.06066	+	12.4974i	0.147199	+	0.453031i	0.997287	−	0.0736088i	$-0.0234516\pi$
$761$	4.06066	+	12.4974i	0.147199	+	0.453031i	−0.850088	+	0.526640i	$0.823452\pi$
$762$	−1.53871	−	1.11794i	−0.0557415	−	0.0404986i
$763$	18.0885	−	13.1421i	0.654848	−	0.475775i
$764$	−0.269711	+	0.830086i	−0.00975782	+	0.0300315i
$765$	3.04478	−	9.37087i	0.110084	−	0.338805i
$766$	26.8877	−	19.5351i	0.971492	−	0.705831i
$767$	−19.4872	−	14.1583i	−0.703641	−	0.511225i
$768$	−0.687387	−	2.11556i	−0.0248040	−	0.0763387i
$769$	38.9767			1.40554			0.702768	−	0.711419i	$-0.251947\pi$
$769$	38.9767			1.40554			0.702768	+	0.711419i	$0.251947\pi$
$770$		0			0
$771$	6.00099			0.216121
$772$	−0.916145	−	2.81960i	−0.0329728	−	0.101480i
$773$	31.3526	+	22.7790i	1.12767	+	0.819303i	0.985355	−	0.170518i	$-0.0545442\pi$
$773$	31.3526	+	22.7790i	1.12767	+	0.819303i	0.142319	+	0.989821i	$0.454544\pi$
$774$	−8.68930	+	6.31315i	−0.312331	+	0.226921i
$775$	2.09463	−	6.44661i	0.0752414	−	0.231569i
$776$	3.92323	−	12.0745i	0.140836	−	0.433448i
$777$	16.7189	−	12.1470i	0.599786	−	0.435770i
$778$	−5.98936	−	4.35152i	−0.214729	−	0.156010i
$779$	0.244514	+	0.752538i	0.00876064	+	0.0269625i
$780$	−0.264169			−0.00945878
$781$		0			0
$782$	5.81665			0.208003
$783$	6.80876	+	20.9552i	0.243325	+	0.748878i
$784$	18.6542	+	13.5530i	0.666220	+	0.484037i
$785$	17.2114	−	12.5048i	0.614302	−	0.446316i
$786$	1.69764	−	5.22481i	0.0605529	−	0.186363i
$787$	−6.60808	+	20.3376i	−0.235553	+	0.724957i	0.761495	+	0.648171i	$0.224466\pi$
$787$	−6.60808	+	20.3376i	−0.235553	+	0.724957i	−0.997048	+	0.0767858i	$0.975534\pi$
$788$	0.347057	−	0.252152i	0.0123634	−	0.00898254i
$789$	5.10366	+	3.70803i	0.181695	+	0.132009i
$790$	5.80887	+	17.8779i	0.206670	+	0.636066i
$791$	−21.1128			−0.750686
$792$		0			0
$793$	24.0075			0.852533
$794$	−2.69560	−	8.29621i	−0.0956634	−	0.294422i
$795$	1.39392	+	1.01274i	0.0494374	+	0.0359184i
$796$	0.856342	−	0.622169i	0.0303522	−	0.0220522i
$797$	−0.687426	+	2.11568i	−0.0243499	+	0.0749412i	−0.962493	−	0.271306i	$-0.912544\pi$
$797$	−0.687426	+	2.11568i	−0.0243499	+	0.0749412i	0.938143	+	0.346248i	$0.112544\pi$
$798$	0.0836937	−	0.257583i	0.00296272	−	0.00911833i
$799$	6.64547	−	4.82822i	0.235100	−	0.170810i
$800$	−0.740184	−	0.537775i	−0.0261695	−	0.0190132i
$801$	10.0294	+	30.8673i	0.354371	+	1.09064i
$802$	−19.9319			−0.703821
$803$		0			0
$804$	1.25184			0.0441491
$805$	1.31059	+	4.03358i	0.0461922	+	0.142165i
$806$	21.0461	+	15.2909i	0.741317	+	0.538598i
$807$	0.0415975	−	0.0302224i	0.00146430	−	0.00106388i
$808$	−8.97239	+	27.6142i	−0.315648	+	0.971463i
$809$	6.54133	−	20.1321i	0.229981	−	0.707809i	−0.767767	−	0.640730i	$-0.778632\pi$
$809$	6.54133	−	20.1321i	0.229981	−	0.707809i	0.997748	−	0.0670791i	$-0.0213680\pi$
$810$	6.72202	−	4.88383i	0.236188	−	0.171600i
$811$	29.7049	+	21.5818i	1.04308	+	0.757841i	0.970884	−	0.239550i	$-0.0769998\pi$
$811$	29.7049	+	21.5818i	1.04308	+	0.757841i	0.0721943	+	0.997391i	$0.477000\pi$
$812$	−1.23501	−	3.80096i	−0.0433402	−	0.133387i
$813$	−7.71135			−0.270449
$814$		0			0
$815$	15.9810			0.559788
$816$	−2.39608	−	7.37439i	−0.0838797	−	0.258155i
$817$	−0.228457	−	0.165983i	−0.00799269	−	0.00580703i
$818$	−4.82111	+	3.50274i	−0.168566	+	0.122471i
$819$	−8.52032	+	26.2228i	−0.297724	+	0.916300i
$820$	−0.416795	+	1.28276i	−0.0145551	+	0.0447960i
$821$	32.0932	−	23.3170i	1.12006	−	0.813771i	0.135841	−	0.990731i	$-0.456626\pi$
$821$	32.0932	−	23.3170i	1.12006	−	0.813771i	0.984218	+	0.176960i	$0.0566263\pi$
$822$	6.04220	+	4.38991i	0.210746	+	0.153116i
$823$	−14.1926	−	43.6804i	−0.494724	−	1.52260i	−0.817386	−	0.576090i	$-0.804578\pi$
$823$	−14.1926	−	43.6804i	−0.494724	−	1.52260i	0.322662	−	0.946514i	$-0.395422\pi$
$824$	−11.9178			−0.415178
$825$		0			0
$826$	42.0956			1.46469
$827$	−12.2664	−	37.7521i	−0.426545	−	1.31277i	−0.901507	−	0.432764i	$-0.857538\pi$
$827$	−12.2664	−	37.7521i	−0.426545	−	1.31277i	0.474962	−	0.880006i	$-0.342462\pi$
$828$	−0.406861	−	0.295601i	−0.0141394	−	0.0102729i
$829$	−6.19370	+	4.49999i	−0.215116	+	0.156291i	−0.690125	−	0.723690i	$-0.742445\pi$
$829$	−6.19370	+	4.49999i	−0.215116	+	0.156291i	0.475009	+	0.879981i	$0.342445\pi$
$830$	4.45925	−	13.7241i	0.154783	−	0.476372i
$831$	−0.694754	+	2.13823i	−0.0241007	+	0.0741745i
$832$	19.5572	−	14.2091i	0.678022	−	0.492612i
$833$	−18.8716	−	13.7110i	−0.653862	−	0.475059i
$834$	0.124282	+	0.382501i	0.00430353	+	0.0132449i
$835$	−17.7090			−0.612846
$836$		0			0
$837$	−22.1135			−0.764354
$838$	7.47894	+	23.0178i	0.258356	+	0.795137i
$839$	−22.3197	−	16.2162i	−0.770561	−	0.559845i	0.131571	−	0.991307i	$-0.457998\pi$
$839$	−22.3197	−	16.2162i	−0.770561	−	0.559845i	−0.902131	+	0.431462i	$0.857998\pi$
$840$	4.98037	−	3.61845i	0.171839	−	0.124848i
$841$	5.13432	−	15.8018i	0.177046	−	0.544891i
$842$	−2.02280	+	6.22554i	−0.0697103	+	0.214546i
$843$	0.715803	−	0.520061i	0.0246536	−	0.0179119i
$844$	−3.60060	−	2.61599i	−0.123938	−	0.0900460i
$845$	1.54066	+	4.74168i	0.0530005	+	0.163119i
$846$	8.04979			0.276757
$847$		0			0
$848$	−10.9261			−0.375203
$849$	−0.962401	−	2.96196i	−0.0330295	−	0.101654i
$850$	−4.04920	−	2.94192i	−0.138886	−	0.100907i
$851$	−9.25135	+	6.72150i	−0.317132	+	0.230410i
$852$	−0.239426	+	0.736878i	−0.00820261	+	0.0252450i
$853$	13.0250	−	40.0867i	0.445966	−	1.37254i	−0.435455	−	0.900210i	$-0.643413\pi$
$853$	13.0250	−	40.0867i	0.445966	−	1.37254i	0.881421	−	0.472331i	$-0.156587\pi$
$854$	−33.9430	+	24.6611i	−1.16151	+	0.843884i
$855$	0.205384	+	0.149220i	0.00702398	+	0.00510322i
$856$	−1.75592	−	5.40418i	−0.0600162	−	0.184711i
$857$	−45.0850			−1.54008			−0.770038	−	0.637998i	$-0.779763\pi$
$857$	−45.0850			−1.54008			−0.770038	+	0.637998i	$0.779763\pi$
$858$		0			0
$859$	−11.8257			−0.403488			−0.201744	−	0.979438i	$-0.564661\pi$
$859$	−11.8257			−0.403488			−0.201744	+	0.979438i	$0.564661\pi$
$860$	−0.148746	−	0.457794i	−0.00507221	−	0.0156107i
$861$	−14.1336	−	10.2686i	−0.481670	−	0.349954i
$862$	27.2808	−	19.8207i	0.929189	−	0.675095i
$863$	8.61271	−	26.5072i	0.293180	−	0.902315i	−0.690647	−	0.723192i	$-0.742674\pi$
$863$	8.61271	−	26.5072i	0.293180	−	0.902315i	0.983827	−	0.179123i	$-0.0573260\pi$
$864$	−0.922352	+	2.83871i	−0.0313790	+	0.0965747i
$865$	12.8516	−	9.33725i	0.436968	−	0.317476i
$866$	23.3065	+	16.9332i	0.791987	+	0.575412i
$867$	−0.599217	−	1.84420i	−0.0203505	−	0.0626323i
$868$	4.01105			0.136144
$869$		0			0
$870$	5.26926			0.178645
$871$	11.7359	+	36.1193i	0.397655	+	1.22386i
$872$	14.5285	+	10.5556i	0.491997	+	0.357457i
$873$	−9.35181	+	6.79449i	−0.316511	+	0.229959i
$874$	−0.0463117	+	0.142533i	−0.00156652	+	0.00482124i
$875$	1.12773	−	3.47080i	0.0381243	−	0.117334i
$876$	−0.0996532	+	0.0724023i	−0.00336697	+	0.00244625i
$877$	9.26093	+	6.72846i	0.312720	+	0.227204i	0.733063	−	0.680161i	$-0.238090\pi$
$877$	9.26093	+	6.72846i	0.312720	+	0.227204i	−0.420343	+	0.907365i	$0.638090\pi$
$878$	−6.66592	−	20.5156i	−0.224964	−	0.692367i
$879$	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	$0.209145\pi$
$882$	−7.06399	−	21.7407i	−0.237857	−	0.732048i
$883$	37.9547	+	27.5757i	1.27728	+	0.927997i	0.999467	−	0.0326386i	$-0.0103910\pi$
$883$	37.9547	+	27.5757i	1.27728	+	0.927997i	0.277811	+	0.960636i	$0.410391\pi$
$884$	−1.37106	+	0.996133i	−0.0461137	+	0.0335036i
$885$	1.51315	−	4.65698i	0.0508638	−	0.156543i
$886$	11.0126	−	33.8932i	0.369975	−	1.13867i
$887$	22.5252	−	16.3655i	0.756322	−	0.549500i	−0.141458	−	0.989944i	$-0.545179\pi$
$887$	22.5252	−	16.3655i	0.756322	−	0.549500i	0.897780	+	0.440444i	$0.145179\pi$
$888$	13.4284	+	9.75631i	0.450628	+	0.327400i
$889$	−2.74921	−	8.46121i	−0.0922057	−	0.283780i
$890$	16.4866			0.552631
$891$		0			0
$892$	0.824022			0.0275903
$893$	0.0654012	+	0.201284i	0.00218857	+	0.00673572i
$894$	5.15032	+	3.74193i	0.172252	+	0.125149i
$895$	−13.6570	+	9.92242i	−0.456505	+	0.331670i
$896$	−10.9914	+	33.8281i	−0.367197	+	1.13012i
$897$	−0.585082	+	1.80070i	−0.0195353	+	0.0601235i
$898$	8.98207	−	6.52586i	0.299736	−	0.217771i
$899$	37.0371	+	26.9090i	1.23526	+	0.897466i
$900$	0.133724	+	0.411560i	0.00445746	+	0.0137187i
$901$	11.0534			0.368244
$902$		0			0
$903$	6.23473			0.207479
$904$	−5.24018	−	16.1276i	−0.174286	−	0.536397i
$905$	−19.4871	−	14.1582i	−0.647773	−	0.470635i
$906$	−1.22463	+	0.889747i	−0.0406856	+	0.0295598i
$907$	−8.84508	+	27.2224i	−0.293696	+	0.903904i	0.689960	+	0.723847i	$0.257628\pi$
$907$	−8.84508	+	27.2224i	−0.293696	+	0.903904i	−0.983656	+	0.180056i	$0.942372\pi$
$908$	−0.187387	+	0.576719i	−0.00621867	+	0.0191391i
$909$	21.3875	−	15.5389i	0.709379	−	0.515394i
$910$	11.3310	+	8.23247i	0.375620	+	0.272904i
$911$	1.58471	+	4.87724i	0.0525038	+	0.161590i	0.973870	−	0.227105i	$-0.0729260\pi$
$911$	1.58471	+	4.87724i	0.0525038	+	0.161590i	−0.921367	+	0.388695i	$0.872926\pi$
$912$	0.199781			0.00661542
$913$		0			0
$914$	16.1547			0.534351
$915$	1.50812	+	4.64153i	0.0498571	+	0.153444i
$916$	3.53190	+	2.56608i	0.116697	+	0.0847855i
$917$	20.7898	−	15.1046i	0.686538	−	0.498799i
$918$	−5.04575	+	15.5292i	−0.166535	+	0.512541i
$919$	10.9024	−	33.5542i	0.359638	−	1.10685i	−0.593634	−	0.804735i	$-0.702307\pi$
$919$	10.9024	−	33.5542i	0.359638	−	1.10685i	0.953271	−	0.302116i	$-0.0976929\pi$
$920$	−2.75587	+	2.00226i	−0.0908585	+	0.0660126i
$921$	1.97877	+	1.43766i	0.0652026	+	0.0473725i
$922$	2.91645	+	8.97591i	0.0960481	+	0.295606i
$923$	−23.5057			−0.773699
$924$		0			0
$925$	9.83980			0.323531
$926$	5.22660	+	16.0858i	0.171757	+	0.528613i
$927$	8.77874	+	6.37813i	0.288332	+	0.209485i
$928$	4.99912	−	3.63208i	0.164104	−	0.119229i
$929$	−18.2761	+	56.2480i	−0.599619	+	1.84544i	−0.0693793	+	0.997590i	$0.522102\pi$
$929$	−18.2761	+	56.2480i	−0.599619	+	1.84544i	−0.530240	+	0.847848i	$0.677898\pi$
$930$	−1.63419	+	5.02953i	−0.0535873	+	0.164925i
$931$	0.486233	−	0.353269i	0.0159356	−	0.0115779i
$932$	2.40278	+	1.74572i	0.0787058	+	0.0571831i
$933$	−2.95556	−	9.09627i	−0.0967606	−	0.297799i
$934$	−8.33220			−0.272638
$935$		0			0
$936$	−22.1458			−0.723857
$937$	4.46299	+	13.7357i	0.145800	+	0.448725i	0.997113	−	0.0759326i	$-0.0241934\pi$
$937$	4.46299	+	13.7357i	0.145800	+	0.448725i	−0.851313	+	0.524657i	$0.824193\pi$
$938$	−53.6953	−	39.0119i	−1.75321	−	1.27378i
$939$	12.3738	−	8.99009i	0.403804	−	0.293381i
$940$	−0.111482	+	0.343105i	−0.00363613	+	0.0111909i
$941$	−5.76598	+	17.7459i	−0.187966	+	0.578499i	−0.999987	−	0.00512923i	$-0.998367\pi$
$941$	−5.76598	+	17.7459i	−0.187966	+	0.578499i	0.812021	+	0.583628i	$0.198367\pi$
$942$	−13.4280	+	9.75603i	−0.437509	+	0.317869i
$943$	7.82077	+	5.68212i	0.254679	+	0.185035i
$944$	9.59542	+	29.5317i	0.312304	+	0.961173i
$945$	−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	$0.505128\pi$
$948$	0.399840	+	1.23058i	0.0129862	+	0.0399674i
$949$	−3.02326	−	2.19652i	−0.0981390	−	0.0713022i
$950$	0.104329	−	0.0757994i	0.00338488	−	0.00245926i
$951$	1.03091	−	3.17282i	0.0334296	−	0.102886i
$952$	12.2040	−	37.5601i	0.395534	−	1.21733i
$953$	6.68575	−	4.85748i	0.216573	−	0.157349i	−0.474210	−	0.880412i	$-0.657266\pi$
$953$	6.68575	−	4.85748i	0.216573	−	0.157349i	0.690783	+	0.723063i	$0.257266\pi$
$954$	8.76338	+	6.36697i	0.283725	+	0.206138i
$955$	−1.66337	−	5.11934i	−0.0538255	−	0.165658i
$956$	1.77646			0.0574549
$957$		0			0
$958$	30.0881			0.972101
$959$	10.7956	+	33.2255i	0.348608	+	1.07291i
$960$	3.97569	+	2.88851i	0.128315	+	0.0932263i
$961$	−12.0918	+	8.78523i	−0.390059	+	0.283394i
$962$	−11.6696	+	35.9154i	−0.376244	+	1.15796i
$963$	−1.59876	+	4.92047i	−0.0515192	+	0.158560i
$964$	−1.31107	+	0.952547i	−0.0422267	+	0.0306795i
$965$	14.7921	+	10.7471i	0.476175	+	0.345961i
$966$	−1.02250	−	3.14692i	−0.0328983	−	0.101251i
$967$	7.36029			0.236691			0.118345	−	0.992972i	$-0.462241\pi$
$967$	7.36029			0.236691			0.118345	+	0.992972i	$0.462241\pi$
$968$		0			0
$969$	−0.202110			−0.00649271
$970$	1.81451	+	5.58448i	0.0582603	+	0.179307i
$971$	4.02674	+	2.92560i	0.129224	+	0.0938870i	0.650520	−	0.759489i	$-0.274551\pi$
$971$	4.02674	+	2.92560i	0.129224	+	0.0938870i	−0.521296	+	0.853376i	$0.674551\pi$
$972$	1.74656	−	1.26895i	0.0560210	−	0.0407016i
$973$	−0.581347	+	1.78920i	−0.0186371	+	0.0573592i
$974$	−14.3401	+	44.1343i	−0.459487	+	1.41416i
$975$	1.31805	−	0.957617i	0.0422113	−	0.0306683i
$976$	−25.0378	−	18.1910i	−0.801439	−	0.582280i
$977$	3.19425	+	9.83089i	0.102193	+	0.314518i	0.989061	−	0.147504i	$-0.0471240\pi$
$977$	3.19425	+	9.83089i	0.102193	+	0.314518i	−0.886868	+	0.462022i	$0.847124\pi$
$978$	−12.4680			−0.398684
$979$		0			0
$980$	1.02448			0.0327259
$981$	−5.05268	−	15.5506i	−0.161320	−	0.496491i
$982$	18.6403	+	13.5430i	0.594836	+	0.432174i
$983$	23.5111	−	17.0818i	0.749888	−	0.544826i	−0.145904	−	0.989299i	$-0.546609\pi$
$983$	23.5111	−	17.0818i	0.749888	−	0.544826i	0.895792	+	0.444473i	$0.146609\pi$
$984$	4.33604	−	13.3450i	0.138228	−	0.425422i
$985$	−0.817554	+	2.51617i	−0.0260494	+	0.0801719i
$986$	27.3479	−	19.8694i	0.870933	−	0.632770i
$987$	−3.78036	−	2.74659i	−0.120330	−	0.0874249i
$988$	−0.0134932	−	0.0415279i	−0.000429277	−	0.00132118i
$989$	−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	$0.460954\pi$
$992$	1.91642	+	5.89812i	0.0608463	+	0.187266i
$993$	6.01672	+	4.37141i	0.190935	+	0.138722i
$994$	33.2335	−	24.1455i	1.05410	−	0.765850i
$995$	−2.01726	+	6.20849i	−0.0639515	+	0.196823i
$996$	0.306941	−	0.944669i	0.00972581	−	0.0299330i
$997$	2.31717	−	1.68352i	0.0733855	−	0.0533177i	−0.550488	−	0.834843i	$-0.685558\pi$
$997$	2.31717	−	1.68352i	0.0733855	−	0.0533177i	0.623873	+	0.781526i	$0.285558\pi$
$998$	−5.73548	−	4.16707i	−0.181554	−	0.131906i
$999$	−9.91974	−	30.5298i	−0.313847	−	0.965921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.m.511.2		8
11.2	odd	10		605.2.g.e.251.1		8
11.3	even	5		605.2.a.j.1.4		4
11.4	even	5		55.2.g.b.36.1	yes	8
11.5	even	5		55.2.g.b.26.1	✓	8
11.6	odd	10		605.2.g.k.81.2		8
11.7	odd	10		605.2.g.k.366.2		8
11.8	odd	10		605.2.a.k.1.1		4
11.9	even	5	inner	605.2.g.m.251.2		8
11.10	odd	2		605.2.g.e.511.1		8
33.5	odd	10		495.2.n.e.136.2		8
33.8	even	10		5445.2.a.bi.1.4		4
33.14	odd	10		5445.2.a.bp.1.1		4
33.26	odd	10		495.2.n.e.91.2		8
44.3	odd	10		9680.2.a.cn.1.2		4
44.15	odd	10		880.2.bo.h.641.1		8
44.19	even	10		9680.2.a.cm.1.2		4
44.27	odd	10		880.2.bo.h.81.1		8
55.4	even	10		275.2.h.a.201.2		8
55.14	even	10		3025.2.a.bd.1.1		4
55.19	odd	10		3025.2.a.w.1.4		4
55.27	odd	20		275.2.z.a.224.4		16
55.37	odd	20		275.2.z.a.124.1		16
55.38	odd	20		275.2.z.a.224.1		16
55.48	odd	20		275.2.z.a.124.4		16
55.49	even	10		275.2.h.a.26.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.b.26.1	✓	8	11.5	even	5
55.2.g.b.36.1	yes	8	11.4	even	5
275.2.h.a.26.2		8	55.49	even	10
275.2.h.a.201.2		8	55.4	even	10
275.2.z.a.124.1		16	55.37	odd	20
275.2.z.a.124.4		16	55.48	odd	20
275.2.z.a.224.1		16	55.38	odd	20
275.2.z.a.224.4		16	55.27	odd	20
495.2.n.e.91.2		8	33.26	odd	10
495.2.n.e.136.2		8	33.5	odd	10
605.2.a.j.1.4		4	11.3	even	5
605.2.a.k.1.1		4	11.8	odd	10
605.2.g.e.251.1		8	11.2	odd	10
605.2.g.e.511.1		8	11.10	odd	2
605.2.g.k.81.2		8	11.6	odd	10
605.2.g.k.366.2		8	11.7	odd	10
605.2.g.m.251.2		8	11.9	even	5	inner
605.2.g.m.511.2		8	1.1	even	1	trivial
880.2.bo.h.81.1		8	44.27	odd	10
880.2.bo.h.641.1		8	44.15	odd	10
3025.2.a.w.1.4		4	55.19	odd	10
3025.2.a.bd.1.1		4	55.14	even	10
5445.2.a.bi.1.4		4	33.8	even	10
5445.2.a.bp.1.1		4	33.14	odd	10
9680.2.a.cm.1.2		4	44.19	even	10
9680.2.a.cn.1.2		4	44.3	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)

\(f(q)\)	\(=\)	\(q+(0.418926 + 1.28932i) q^{2} +(-0.465584 - 0.338266i) q^{3} +(0.131180 - 0.0953077i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.241089 - 0.741996i) q^{6} +(2.95244 - 2.14507i) q^{7} +(2.37136 + 1.72290i) q^{8} +(-0.824707 - 2.53819i) q^{9} +O(q^{10})\)	\(q+(0.418926 + 1.28932i) q^{2} +(-0.465584 - 0.338266i) q^{3} +(0.131180 - 0.0953077i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.241089 - 0.741996i) q^{6} +(2.95244 - 2.14507i) q^{7} +(2.37136 + 1.72290i) q^{8} +(-0.824707 - 2.53819i) q^{9} -1.35567 q^{10} -0.0933146 q^{12} +(-0.874813 - 2.69240i) q^{13} +(4.00254 + 2.90802i) q^{14} +(0.465584 - 0.338266i) q^{15} +(-1.12773 + 3.47080i) q^{16} +(1.14088 - 3.51126i) q^{17} +(2.92705 - 2.12663i) q^{18} +(0.0769572 + 0.0559127i) q^{19} +(0.0501062 + 0.154211i) q^{20} -2.10021 q^{21} +1.16215 q^{23} +(-0.521270 - 1.60431i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(3.10489 - 2.25583i) q^{26} +(-1.00812 + 3.10269i) q^{27} +(0.182858 - 0.562780i) q^{28} +(5.46401 - 3.96984i) q^{29} +(0.631180 + 0.458579i) q^{30} +(2.09463 + 6.44661i) q^{31} +0.914918 q^{32} +5.00509 q^{34} +(1.12773 + 3.47080i) q^{35} +(-0.350094 - 0.254358i) q^{36} +(-7.96056 + 5.78369i) q^{37} +(-0.0398501 + 0.122646i) q^{38} +(-0.503449 + 1.54946i) q^{39} +(-2.37136 + 1.72290i) q^{40} +(6.72958 + 4.88933i) q^{41} +(-0.879834 - 2.70785i) q^{42} -2.96862 q^{43} +2.66881 q^{45} +(0.486854 + 1.49838i) q^{46} +(1.79999 + 1.30777i) q^{47} +(1.69911 - 1.23447i) q^{48} +(1.95244 - 6.00899i) q^{49} +(0.418926 - 1.28932i) q^{50} +(-1.71891 + 1.24886i) q^{51} +(-0.371364 - 0.269812i) q^{52} +(0.925174 + 2.84739i) q^{53} -4.42270 q^{54} +10.6970 q^{56} +(-0.0169166 - 0.0520641i) q^{57} +(7.40742 + 5.38181i) q^{58} +(6.88361 - 5.00123i) q^{59} +(0.0288358 - 0.0887475i) q^{60} +(-2.62058 + 8.06531i) q^{61} +(-7.43427 + 5.40131i) q^{62} +(-7.87949 - 5.72478i) q^{63} +(2.63875 + 8.12122i) q^{64} +2.83095 q^{65} -13.4153 q^{67} +(-0.184990 - 0.569341i) q^{68} +(-0.541077 - 0.393115i) q^{69} +(-4.00254 + 2.90802i) q^{70} +(2.56580 - 7.89671i) q^{71} +(2.41735 - 7.43985i) q^{72} +(1.06793 - 0.775895i) q^{73} +(-10.7919 - 7.84080i) q^{74} +(0.177837 + 0.547326i) q^{75} +0.0154241 q^{76} -2.20866 q^{78} +(-4.28486 - 13.1874i) q^{79} +(-2.95244 - 2.14507i) q^{80} +(-4.95843 + 3.60251i) q^{81} +(-3.48472 + 10.7249i) q^{82} +(-3.28932 + 10.1235i) q^{83} +(-0.275506 + 0.200167i) q^{84} +(2.98685 + 2.17008i) q^{85} +(-1.24363 - 3.82751i) q^{86} -3.88682 q^{87} -12.1612 q^{89} +(1.11803 + 3.44095i) q^{90} +(-8.35822 - 6.07260i) q^{91} +(0.152450 - 0.110762i) q^{92} +(1.20545 - 3.70998i) q^{93} +(-0.932072 + 2.86862i) q^{94} +(-0.0769572 + 0.0559127i) q^{95} +(-0.425971 - 0.309486i) q^{96} +(-1.33845 - 4.11934i) q^{97} +8.56545 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9	\( 8 q + 3 q^{2} + 5 q^{3} + 3 q^{4} + 2 q^{5} + 8 q^{6} + 4 q^{7} - q^{8} + 5 q^{9} + 2 q^{10} + 16 q^{12} + 3 q^{13} + 14 q^{14} - 5 q^{15} - q^{16} + 12 q^{17} + 10 q^{18} + 5 q^{19} + 2 q^{20} - 20 q^{21} + 10 q^{23} - 2 q^{24} - 2 q^{25} + 5 q^{26} + 5 q^{27} + 19 q^{28} + 21 q^{29} + 7 q^{30} + 15 q^{31} + 16 q^{32} + 4 q^{34} + q^{35} + 15 q^{36} - 31 q^{37} - 20 q^{38} - 14 q^{39} + q^{40} + 3 q^{41} - 21 q^{42} - 38 q^{43} - 7 q^{46} - 5 q^{47} + 5 q^{48} - 4 q^{49} + 3 q^{50} + 6 q^{51} + 17 q^{52} - 2 q^{53} + 16 q^{54} + 22 q^{56} + 40 q^{57} + 2 q^{58} + 18 q^{59} + 4 q^{60} + 6 q^{61} - 5 q^{62} - 30 q^{63} + 29 q^{64} + 2 q^{65} - 38 q^{67} - 14 q^{68} + 9 q^{69} - 14 q^{70} + 15 q^{71} + 5 q^{72} - 2 q^{73} - 20 q^{74} - 5 q^{75} - 16 q^{78} - 3 q^{79} - 4 q^{80} - 12 q^{81} - 22 q^{82} - 38 q^{83} - 17 q^{84} + 13 q^{85} + 2 q^{86} + 38 q^{87} - 16 q^{89} - 36 q^{91} + q^{92} + 40 q^{93} - 18 q^{94} - 5 q^{95} - 17 q^{96} - 56 q^{97} + 16 q^{98}+O(q^{100}) \) 8 * q + 3 * q^2 + 5 * q^3 + 3 * q^4 + 2 * q^5 + 8 * q^6 + 4 * q^7 - q^8 + 5 * q^9 + 2 * q^10 + 16 * q^12 + 3 * q^13 + 14 * q^14 - 5 * q^15 - q^16 + 12 * q^17 + 10 * q^18 + 5 * q^19 + 2 * q^20 - 20 * q^21 + 10 * q^23 - 2 * q^24 - 2 * q^25 + 5 * q^26 + 5 * q^27 + 19 * q^28 + 21 * q^29 + 7 * q^30 + 15 * q^31 + 16 * q^32 + 4 * q^34 + q^35 + 15 * q^36 - 31 * q^37 - 20 * q^38 - 14 * q^39 + q^40 + 3 * q^41 - 21 * q^42 - 38 * q^43 - 7 * q^46 - 5 * q^47 + 5 * q^48 - 4 * q^49 + 3 * q^50 + 6 * q^51 + 17 * q^52 - 2 * q^53 + 16 * q^54 + 22 * q^56 + 40 * q^57 + 2 * q^58 + 18 * q^59 + 4 * q^60 + 6 * q^61 - 5 * q^62 - 30 * q^63 + 29 * q^64 + 2 * q^65 - 38 * q^67 - 14 * q^68 + 9 * q^69 - 14 * q^70 + 15 * q^71 + 5 * q^72 - 2 * q^73 - 20 * q^74 - 5 * q^75 - 16 * q^78 - 3 * q^79 - 4 * q^80 - 12 * q^81 - 22 * q^82 - 38 * q^83 - 17 * q^84 + 13 * q^85 + 2 * q^86 + 38 * q^87 - 16 * q^89 - 36 * q^91 + q^92 + 40 * q^93 - 18 * q^94 - 5 * q^95 - 17 * q^96 - 56 * q^97 + 16 * q^98

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