LMFDB - Embedded newform 950.2.l.h.651.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(101,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("950.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.l (of order $9$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 105x^{8} + 394x^{6} + 1077x^{4} + 1443x^{2} + 1369 $ x^12 + 12x^10 + 105x^8 + 394x^6 + 1077x^4 + 1443*x^2 + 1369
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			651.1
Root			$-0.665830 + 1.15325i$ of defining polynomial
Character	$\chi$	$=$	950.651
Dual form			950.2.l.h.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.231240 + 1.31143i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(1.18594 + 2.05411i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.15270 + 0.419550i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.231240 + 1.31143i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(1.18594 + 2.05411i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.15270 + 0.419550i) q^{9} +(-1.33676 + 2.31534i) q^{11} +(0.665830 + 1.15325i) q^{12} +(-0.168545 - 0.955868i) q^{13} +(-1.81697 - 1.52462i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-5.30729 + 1.93170i) q^{17} -1.22668 q^{18} +(2.94212 + 3.21620i) q^{19} +(-2.96806 + 1.08028i) q^{21} +(0.464253 - 2.63291i) q^{22} +(6.55063 - 5.49663i) q^{23} +(-1.02011 - 0.855975i) q^{24} +(0.485307 + 0.840576i) q^{26} +(-2.81425 + 4.87443i) q^{27} +(2.22884 + 0.811231i) q^{28} +(-0.0701275 - 0.0255243i) q^{29} +(0.00986693 + 0.0170900i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.72729 - 2.28847i) q^{33} +(4.32654 - 3.63040i) q^{34} +(1.15270 - 0.419550i) q^{36} -1.17396 q^{37} +(-3.86469 - 2.01598i) q^{38} +1.29253 q^{39} +(-1.90311 + 10.7931i) q^{41} +(2.41958 - 2.03027i) q^{42} +(4.40077 + 3.69269i) q^{43} +(0.464253 + 2.63291i) q^{44} +(-4.27562 + 7.40559i) q^{46} +(-4.94471 - 1.79973i) q^{47} +(1.25135 + 0.455455i) q^{48} +(0.687089 - 1.19007i) q^{49} +(-1.30602 - 7.40682i) q^{51} +(-0.743533 - 0.623898i) q^{52} +(0.0681837 - 0.0572129i) q^{53} +(0.977379 - 5.54299i) q^{54} -2.37188 q^{56} +(-4.89815 + 3.11466i) q^{57} +0.0746282 q^{58} +(-10.0952 + 3.67436i) q^{59} +(-6.12774 + 5.14179i) q^{61} +(-0.0151170 - 0.0126847i) q^{62} +(0.505237 + 2.86534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.34552 + 1.21767i) q^{66} +(4.79924 + 1.74678i) q^{67} +(-2.82395 + 4.89123i) q^{68} +(5.69367 + 9.86173i) q^{69} +(-7.95955 - 6.67886i) q^{71} +(-0.939693 + 0.788496i) q^{72} +(-1.47836 + 8.38420i) q^{73} +(1.10316 - 0.401517i) q^{74} +(4.32113 + 0.572595i) q^{76} -6.34129 q^{77} +(-1.21458 + 0.442070i) q^{78} +(2.75957 - 15.6503i) q^{79} +(-2.92262 - 2.45237i) q^{81} +(-1.90311 - 10.7931i) q^{82} +(-2.93574 - 5.08485i) q^{83} +(-1.57927 + 2.73538i) q^{84} +(-5.39835 - 1.96484i) q^{86} +(0.0496897 - 0.0860650i) q^{87} +(-1.33676 - 2.31534i) q^{88} +(-0.149473 - 0.847706i) q^{89} +(1.76357 - 1.47981i) q^{91} +(1.48491 - 8.42133i) q^{92} +(-0.0246940 + 0.00898788i) q^{93} +5.26205 q^{94} -1.33166 q^{96} +(-10.4367 + 3.79863i) q^{97} +(-0.238624 + 1.35330i) q^{98} +(-2.51229 + 2.10806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	$ 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.231240	+	1.31143i	−0.133507	+	0.757154i	0.842381	+	0.538882i	$0.181153\pi$
$3$	−0.231240	+	1.31143i	−0.133507	+	0.757154i	−0.975888	+	0.218272i	$0.929958\pi$
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.231240	−	1.31143i	−0.0944035	−	0.535389i
$7$	1.18594	+	2.05411i	0.448243	+	0.776380i	0.998272	−	0.0587655i	$-0.0187164\pi$
$7$	1.18594	+	2.05411i	0.448243	+	0.776380i	−0.550028	+	0.835146i	$0.685383\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	1.15270	+	0.419550i	0.384235	+	0.139850i
$10$		0			0
$11$	−1.33676	+	2.31534i	−0.403049	+	0.698102i	−0.994092	−	0.108538i	$-0.965383\pi$
$11$	−1.33676	+	2.31534i	−0.403049	+	0.698102i	0.591043	+	0.806640i	$0.298716\pi$
$12$	0.665830	+	1.15325i	0.192209	+	0.332915i
$13$	−0.168545	−	0.955868i	−0.0467460	−	0.265110i	0.952473	−	0.304623i	$-0.0985305\pi$
$13$	−0.168545	−	0.955868i	−0.0467460	−	0.265110i	−0.999219	+	0.0395130i	$0.987419\pi$
$14$	−1.81697	−	1.52462i	−0.485605	−	0.407471i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−5.30729	+	1.93170i	−1.28721	+	0.468505i	−0.892809	−	0.450435i	$-0.851269\pi$
$17$	−5.30729	+	1.93170i	−1.28721	+	0.468505i	−0.394398	+	0.918940i	$0.629047\pi$
$18$	−1.22668			−0.289132
$19$	2.94212	+	3.21620i	0.674968	+	0.737847i
$19$	2.94212	+	3.21620i	0.674968	+	0.737847i
$20$		0			0
$21$	−2.96806	+	1.08028i	−0.647683	+	0.235737i
$22$	0.464253	−	2.63291i	0.0989791	−	0.561338i
$23$	6.55063	−	5.49663i	1.36590	−	1.14613i	0.391791	−	0.920054i	$-0.371856\pi$
$23$	6.55063	−	5.49663i	1.36590	−	1.14613i	0.974110	−	0.226073i	$-0.0725888\pi$
$24$	−1.02011	−	0.855975i	−0.208229	−	0.174725i
$25$		0			0
$26$	0.485307	+	0.840576i	0.0951765	+	0.164850i
$27$	−2.81425	+	4.87443i	−0.541603	+	0.938084i
$28$	2.22884	+	0.811231i	0.421211	+	0.153308i
$29$	−0.0701275	−	0.0255243i	−0.0130224	−	0.00473975i	0.335501	−	0.942040i	$-0.391094\pi$
$29$	−0.0701275	−	0.0255243i	−0.0130224	−	0.00473975i	−0.348523	+	0.937300i	$0.613317\pi$
$30$		0			0
$31$	0.00986693	+	0.0170900i	0.00177215	+	0.00306946i	0.866910	−	0.498464i	$-0.166103\pi$
$31$	0.00986693	+	0.0170900i	0.00177215	+	0.00306946i	−0.865138	+	0.501534i	$0.832769\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−2.72729	−	2.28847i	−0.474761	−	0.398372i
$34$	4.32654	−	3.63040i	0.741996	−	0.622609i
$35$		0			0
$36$	1.15270	−	0.419550i	0.192117	−	0.0699250i
$37$	−1.17396			−0.192997			−0.0964987	−	0.995333i	$-0.530764\pi$
$37$	−1.17396			−0.192997			−0.0964987	+	0.995333i	$0.530764\pi$
$38$	−3.86469	−	2.01598i	−0.626936	−	0.327034i
$39$	1.29253			0.206970
$40$		0			0
$41$	−1.90311	+	10.7931i	−0.297216	+	1.68560i	0.360840	+	0.932628i	$0.382490\pi$
$41$	−1.90311	+	10.7931i	−0.297216	+	1.68560i	−0.658056	+	0.752969i	$0.728621\pi$
$42$	2.41958	−	2.03027i	0.373350	−	0.313278i
$43$	4.40077	+	3.69269i	0.671112	+	0.563130i	0.913394	−	0.407076i	$-0.133452\pi$
$43$	4.40077	+	3.69269i	0.671112	+	0.563130i	−0.242283	+	0.970206i	$0.577896\pi$
$44$	0.464253	+	2.63291i	0.0699888	+	0.396926i
$45$		0			0
$46$	−4.27562	+	7.40559i	−0.630406	+	1.09190i
$47$	−4.94471	−	1.79973i	−0.721260	−	0.262517i	−0.0447996	−	0.998996i	$-0.514265\pi$
$47$	−4.94471	−	1.79973i	−0.721260	−	0.262517i	−0.676461	+	0.736479i	$0.736487\pi$
$48$	1.25135	+	0.455455i	0.180617	+	0.0657392i
$49$	0.687089	−	1.19007i	0.0981556	−	0.170010i
$50$		0			0
$51$	−1.30602	−	7.40682i	−0.182880	−	1.03716i
$52$	−0.743533	−	0.623898i	−0.103109	−	0.0865191i
$53$	0.0681837	−	0.0572129i	0.00936575	−	0.00785879i	−0.638093	−	0.769960i	$-0.720276\pi$
$53$	0.0681837	−	0.0572129i	0.00936575	−	0.00785879i	0.647458	+	0.762101i	$0.275832\pi$
$54$	0.977379	−	5.54299i	0.133004	−	0.754306i
$55$		0			0
$56$	−2.37188			−0.316956
$57$	−4.89815	+	3.11466i	−0.648776	+	0.412547i
$58$	0.0746282			0.00979916
$59$	−10.0952	+	3.67436i	−1.31429	+	0.478361i	−0.901623	−	0.432523i	$-0.857623\pi$
$59$	−10.0952	+	3.67436i	−1.31429	+	0.478361i	−0.412663	+	0.910884i	$0.635401\pi$
$60$		0			0
$61$	−6.12774	+	5.14179i	−0.784577	+	0.658339i	−0.944397	−	0.328808i	$-0.893353\pi$
$61$	−6.12774	+	5.14179i	−0.784577	+	0.658339i	0.159820	+	0.987146i	$0.448909\pi$
$62$	−0.0151170	−	0.0126847i	−0.00191986	−	0.00161096i
$63$	0.505237	+	2.86534i	0.0636539	+	0.360999i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	3.34552	+	1.21767i	0.411805	+	0.149885i
$67$	4.79924	+	1.74678i	0.586321	+	0.213403i	0.618111	−	0.786091i	$-0.287898\pi$
$67$	4.79924	+	1.74678i	0.586321	+	0.213403i	−0.0317896	+	0.999495i	$0.510121\pi$
$68$	−2.82395	+	4.89123i	−0.342454	+	0.593148i
$69$	5.69367	+	9.86173i	0.685438	+	1.18721i
$70$		0			0
$71$	−7.95955	−	6.67886i	−0.944625	−	0.792635i	0.0337592	−	0.999430i	$-0.489252\pi$
$71$	−7.95955	−	6.67886i	−0.944625	−	0.792635i	−0.978384	+	0.206795i	$0.933697\pi$
$72$	−0.939693	+	0.788496i	−0.110744	+	0.0929251i
$73$	−1.47836	+	8.38420i	−0.173029	+	0.981296i	0.767365	+	0.641210i	$0.221567\pi$
$73$	−1.47836	+	8.38420i	−0.173029	+	0.981296i	−0.940394	+	0.340086i	$0.889544\pi$
$74$	1.10316	−	0.401517i	0.128240	−	0.0466754i
$75$		0			0
$76$	4.32113	+	0.572595i	0.495667	+	0.0656811i
$77$	−6.34129			−0.722657
$78$	−1.21458	+	0.442070i	−0.137524	+	0.0500546i
$79$	2.75957	−	15.6503i	0.310476	−	1.76079i	−0.286063	−	0.958211i	$-0.592347\pi$
$79$	2.75957	−	15.6503i	0.310476	−	1.76079i	0.596539	−	0.802584i	$-0.296542\pi$
$80$		0			0
$81$	−2.92262	−	2.45237i	−0.324735	−	0.272485i
$82$	−1.90311	−	10.7931i	−0.210164	−	1.19190i
$83$	−2.93574	−	5.08485i	−0.322239	−	0.558134i	0.658711	−	0.752396i	$-0.271102\pi$
$83$	−2.93574	−	5.08485i	−0.322239	−	0.558134i	−0.980950	+	0.194262i	$0.937769\pi$
$84$	−1.57927	+	2.73538i	−0.172312	+	0.298454i
$85$		0			0
$86$	−5.39835	−	1.96484i	−0.582119	−	0.211874i
$87$	0.0496897	−	0.0860650i	0.00532729	−	0.00922714i
$88$	−1.33676	−	2.31534i	−0.142499	−	0.246816i
$89$	−0.149473	−	0.847706i	−0.0158442	−	0.0898567i	0.975860	−	0.218396i	$-0.0700824\pi$
$89$	−0.149473	−	0.847706i	−0.0158442	−	0.0898567i	−0.991704	+	0.128539i	$0.958971\pi$
$90$		0			0
$91$	1.76357	−	1.47981i	0.184873	−	0.155127i
$92$	1.48491	−	8.42133i	0.154812	−	0.877984i
$93$	−0.0246940	+	0.00898788i	−0.00256065	+	0.000932000i
$94$	5.26205			0.542739
$95$		0			0
$96$	−1.33166			−0.135912
$97$	−10.4367	+	3.79863i	−1.05968	+	0.385692i	−0.812309	−	0.583228i	$-0.801789\pi$
$97$	−10.4367	+	3.79863i	−1.05968	+	0.385692i	−0.247373	+	0.968920i	$0.579567\pi$
$98$	−0.238624	+	1.35330i	−0.0241046	+	0.136704i
$99$	−2.51229	+	2.10806i	−0.252495	+	0.211868i
$100$		0			0
$101$	0.748963	+	4.24758i	0.0745246	+	0.422650i	0.999129	+	0.0417220i	$0.0132844\pi$
$101$	0.748963	+	4.24758i	0.0745246	+	0.422650i	−0.924605	+	0.380928i	$0.875604\pi$
$102$	3.76054	+	6.51345i	0.372349	+	0.644928i
$103$	0.00871870	−	0.0151012i	0.000859079	−	0.00148797i	−0.865596	−	0.500744i	$-0.833060\pi$
$103$	0.00871870	−	0.0151012i	0.000859079	−	0.00148797i	0.866455	+	0.499256i	$0.166393\pi$
$104$	0.912078	+	0.331969i	0.0894366	+	0.0325523i
$105$		0			0
$106$	−0.0445037	+	0.0770827i	−0.00432258	+	0.00748693i
$107$	5.76095	+	9.97826i	0.556932	+	0.964635i	0.997750	+	0.0670387i	$0.0213551\pi$
$107$	5.76095	+	9.97826i	0.556932	+	0.964635i	−0.440818	+	0.897597i	$0.645312\pi$
$108$	0.977379	+	5.54299i	0.0940484	+	0.533375i
$109$	−7.16924	−	6.01570i	−0.686688	−	0.576200i	0.231264	−	0.972891i	$-0.425714\pi$
$109$	−7.16924	−	6.01570i	−0.686688	−	0.576200i	−0.917952	+	0.396691i	$0.870158\pi$
$110$		0			0
$111$	0.271466	−	1.53956i	0.0257664	−	0.146129i
$112$	2.22884	−	0.811231i	0.210606	−	0.0766541i
$113$	−9.03320			−0.849772			−0.424886	−	0.905247i	$-0.639686\pi$
$113$	−9.03320			−0.849772			−0.424886	+	0.905247i	$0.639686\pi$
$114$	3.53748	−	4.60209i	0.331315	−	0.431026i
$115$		0			0
$116$	−0.0701275	+	0.0255243i	−0.00651118	+	0.00236987i
$117$	0.206751	−	1.17255i	0.0191142	−	0.108402i
$118$	8.22970	−	6.90554i	0.757605	−	0.635706i
$119$	−10.2620	−	8.61088i	−0.940721	−	0.789358i
$120$		0			0
$121$	1.92613	+	3.33615i	0.175103	+	0.303287i
$122$	3.99960	−	6.92751i	0.362107	−	0.627188i
$123$	−13.7143	−	4.99159i	−1.23658	−	0.450077i
$124$	0.0185438	+	0.00674938i	0.00166528	+	0.000606112i
$125$		0			0
$126$	−1.45477	−	2.51974i	−0.129601	−	0.224476i
$127$	1.62760	+	9.23057i	0.144426	+	0.819081i	0.967826	+	0.251620i	$0.0809632\pi$
$127$	1.62760	+	9.23057i	0.144426	+	0.819081i	−0.823400	+	0.567461i	$0.807926\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−5.86033	+	4.91740i	−0.515974	+	0.432953i
$130$		0			0
$131$	5.87062	−	2.13673i	0.512919	−	0.186687i	−0.0725767	−	0.997363i	$-0.523122\pi$
$131$	5.87062	−	2.13673i	0.512919	−	0.186687i	0.585496	+	0.810676i	$0.300900\pi$
$132$	−3.56023			−0.309878
$133$	−3.11725	+	9.85766i	−0.270300	+	0.854767i
$134$	−5.10725			−0.441199
$135$		0			0
$136$	0.980748	−	5.56210i	0.0840984	−	0.476946i
$137$	11.4003	−	9.56600i	0.973995	−	0.817279i	−0.00917780	−	0.999958i	$-0.502921\pi$
$137$	11.4003	−	9.56600i	0.973995	−	0.817279i	0.983173	+	0.182679i	$0.0584770\pi$
$138$	−8.72322	−	7.31965i	−0.742569	−	0.623090i
$139$	1.87014	+	10.6061i	0.158624	+	0.899599i	0.955398	+	0.295322i	$0.0954269\pi$
$139$	1.87014	+	10.6061i	0.158624	+	0.899599i	−0.796774	+	0.604277i	$0.793462\pi$
$140$		0			0
$141$	3.50363	−	6.06847i	0.295059	−	0.511057i
$142$	9.76384	+	3.55375i	0.819363	+	0.298224i
$143$	2.43846	+	0.887529i	0.203915	+	0.0742189i
$144$	0.613341	−	1.06234i	0.0511117	−	0.0885281i
$145$		0			0
$146$	−1.47836	−	8.38420i	−0.122350	−	0.693881i
$147$	1.40181	+	1.17626i	0.115620	+	0.0970164i
$148$	−0.899304	+	0.754605i	−0.0739223	+	0.0620282i
$149$	−2.81132	+	15.9438i	−0.230313	+	1.30617i	0.621951	+	0.783056i	$0.286340\pi$
$149$	−2.81132	+	15.9438i	−0.230313	+	1.30617i	−0.852264	+	0.523112i	$0.824771\pi$
$150$		0			0
$151$	6.11979			0.498022			0.249011	−	0.968501i	$-0.419895\pi$
$151$	6.11979			0.498022			0.249011	+	0.968501i	$0.419895\pi$
$152$	−4.25637	+	0.939849i	−0.345237	+	0.0762318i
$153$	−6.92818			−0.560110
$154$	5.95886	−	2.16885i	0.480179	−	0.174771i
$155$		0			0
$156$	0.990133	−	0.830820i	0.0792741	−	0.0665189i
$157$	16.1529	+	13.5539i	1.28914	+	1.08172i	0.991914	+	0.126910i	$0.0405059\pi$
$157$	16.1529	+	13.5539i	1.28914	+	1.08172i	0.297226	+	0.954807i	$0.403939\pi$
$158$	2.75957	+	15.6503i	0.219539	+	1.24507i
$159$	0.0592638	+	0.102648i	0.00469993	+	0.00814051i
$160$		0			0
$161$	19.0594	+	6.93704i	1.50209	+	0.546715i
$162$	3.58512	+	1.30488i	0.281674	+	0.102521i
$163$	8.10611	−	14.0402i	0.634920	−	1.09971i	−0.351612	−	0.936146i	$-0.614367\pi$
$163$	8.10611	−	14.0402i	0.634920	−	1.09971i	0.986532	−	0.163567i	$-0.0523001\pi$
$164$	5.47979	+	9.49128i	0.427900	+	0.741144i
$165$		0			0
$166$	4.49781	+	3.77411i	0.349098	+	0.292928i
$167$	−0.358099	+	0.300481i	−0.0277106	+	0.0232519i	−0.656538	−	0.754293i	$-0.727980\pi$
$167$	−0.358099	+	0.300481i	−0.0277106	+	0.0232519i	0.628827	+	0.777545i	$0.283535\pi$
$168$	0.548475	−	3.11055i	0.0423157	−	0.239984i
$169$	11.3307	−	4.12405i	0.871595	−	0.317234i
$170$		0			0
$171$	2.04203	+	4.94169i	0.156158	+	0.377900i
$172$	5.74480			0.438037
$173$	24.1683	−	8.79654i	1.83748	−	0.668788i	0.846919	−	0.531721i	$-0.178455\pi$
$173$	24.1683	−	8.79654i	1.83748	−	0.668788i	0.990562	−	0.137067i	$-0.0437676\pi$
$174$	−0.0172570	+	0.0978695i	−0.00130825	+	0.00741947i
$175$		0			0
$176$	2.04804	+	1.71851i	0.154377	+	0.129538i
$177$	−2.48424	−	14.0888i	−0.186727	−	1.05898i
$178$	0.430392	+	0.745460i	0.0322592	+	0.0558746i
$179$	−7.08189	+	12.2662i	−0.529325	+	0.916818i	0.470090	+	0.882619i	$0.344221\pi$
$179$	−7.08189	+	12.2662i	−0.529325	+	0.916818i	−0.999415	+	0.0341995i	$0.989112\pi$
$180$		0			0
$181$	−7.32396	−	2.66570i	−0.544386	−	0.198140i	0.0551645	−	0.998477i	$-0.482432\pi$
$181$	−7.32396	−	2.66570i	−0.544386	−	0.198140i	−0.599550	+	0.800337i	$0.704654\pi$
$182$	−1.15109	+	1.99375i	−0.0853245	+	0.147786i
$183$	−5.32611	−	9.22509i	−0.393717	−	0.681938i
$184$	1.48491	+	8.42133i	0.109469	+	0.620829i
$185$		0			0
$186$	0.0201307	−	0.0168917i	0.00147606	−	0.00123856i
$187$	2.62205	−	14.8704i	0.191744	−	1.08743i
$188$	−4.94471	+	1.79973i	−0.360630	+	0.131259i
$189$	−13.3501			−0.971080
$190$		0			0
$191$	−0.264057			−0.0191065			−0.00955326	−	0.999954i	$-0.503041\pi$
$191$	−0.264057			−0.0191065			−0.00955326	+	0.999954i	$0.503041\pi$
$192$	1.25135	−	0.455455i	0.0903085	−	0.0328696i
$193$	0.541429	−	3.07060i	0.0389729	−	0.221027i	−0.959101	−	0.283065i	$-0.908649\pi$
$193$	0.541429	−	3.07060i	0.0389729	−	0.221027i	0.998074	+	0.0620381i	$0.0197600\pi$
$194$	8.50804	−	7.13909i	0.610841	−	0.512557i
$195$		0			0
$196$	−0.238624	−	1.35330i	−0.0170445	−	0.0966644i
$197$	−10.4888	−	18.1672i	−0.747298	−	1.29436i	−0.949113	−	0.314934i	$-0.898018\pi$
$197$	−10.4888	−	18.1672i	−0.747298	−	1.29436i	0.201816	−	0.979424i	$-0.435316\pi$
$198$	1.63978	−	2.84019i	0.116534	−	0.201843i
$199$	20.6330	+	7.50979i	1.46263	+	0.532355i	0.946090	−	0.323905i	$-0.104996\pi$
$199$	20.6330	+	7.50979i	1.46263	+	0.532355i	0.516544	+	0.856260i	$0.327218\pi$
$200$		0			0
$201$	−3.40056	+	5.88994i	−0.239857	+	0.415444i
$202$	−2.15655	−	3.73526i	−0.151735	−	0.262812i
$203$	−0.0307373	−	0.174320i	−0.00215734	−	0.0122349i
$204$	−5.76149	−	4.83446i	−0.403385	−	0.338480i
$205$		0			0
$206$	−0.00302797	+	0.0171725i	−0.000210969	+	0.00119646i
$207$	9.85705	−	3.58767i	0.685112	−	0.249360i
$208$	−0.970613			−0.0672999
$209$	−11.3795	+	2.51271i	−0.787137	+	0.173808i
$210$		0			0
$211$	13.1676	−	4.79262i	0.906497	−	0.329938i	0.153644	−	0.988126i	$-0.450899\pi$
$211$	13.1676	−	4.79262i	0.906497	−	0.329938i	0.752853	+	0.658189i	$0.228677\pi$
$212$	0.0154560	−	0.0876552i	0.00106152	−	0.00602019i
$213$	10.5994	−	8.89397i	0.726260	−	0.609405i
$214$	−8.82629	−	7.40614i	−0.603353	−	0.506273i
$215$		0			0
$216$	−2.81425	−	4.87443i	−0.191486	−	0.331663i
$217$	−0.0234032	+	0.0405355i	−0.00158871	+	0.00275173i
$218$	8.79437	+	3.20089i	0.595630	+	0.216792i
$219$	−10.6534	−	3.87753i	−0.719892	−	0.262019i
$220$		0			0
$221$	2.74096	+	4.74749i	0.184377	+	0.319351i
$222$	0.271466	+	1.53956i	0.0182196	+	0.103329i
$223$	−12.0495	−	10.1108i	−0.806897	−	0.677067i	0.142968	−	0.989727i	$-0.454335\pi$
$223$	−12.0495	−	10.1108i	−0.806897	−	0.677067i	−0.949865	+	0.312661i	$0.898780\pi$
$224$	−1.81697	+	1.52462i	−0.121401	+	0.101868i
$225$		0			0
$226$	8.48843	−	3.08954i	0.564642	−	0.205513i
$227$	8.01180			0.531762			0.265881	−	0.964006i	$-0.414337\pi$
$227$	8.01180			0.531762			0.265881	+	0.964006i	$0.414337\pi$
$228$	−1.75014	+	5.53444i	−0.115906	+	0.366528i
$229$	19.8826			1.31388			0.656939	−	0.753944i	$-0.271851\pi$
$229$	19.8826			1.31388			0.656939	+	0.753944i	$0.271851\pi$
$230$		0			0
$231$	1.46636	−	8.31615i	0.0964795	−	0.547162i
$232$	0.0571685	−	0.0479701i	0.00375330	−	0.00314939i
$233$	19.1114	+	16.0364i	1.25203	+	1.05058i	0.996484	+	0.0837839i	$0.0267005\pi$
$233$	19.1114	+	16.0364i	1.25203	+	1.05058i	0.255549	+	0.966796i	$0.417744\pi$
$234$	0.206751	+	1.17255i	0.0135158	+	0.0766517i
$235$		0			0
$236$	−5.37155	+	9.30380i	−0.349658	+	0.605626i
$237$	19.8861	+	7.23796i	1.29174	+	0.470156i
$238$	12.5883	+	4.58175i	0.815976	+	0.296991i
$239$	−5.32201	+	9.21799i	−0.344252	+	0.596262i	−0.985218	−	0.171307i	$-0.945201\pi$
$239$	−5.32201	+	9.21799i	−0.344252	+	0.596262i	0.640965	+	0.767570i	$0.278534\pi$
$240$		0			0
$241$	−2.91741	−	16.5454i	−0.187927	−	1.06579i	−0.922137	−	0.386863i	$-0.873559\pi$
$241$	−2.91741	−	16.5454i	−0.187927	−	1.06579i	0.734210	−	0.678922i	$-0.237553\pi$
$242$	−2.95100	−	2.47618i	−0.189698	−	0.159175i
$243$	−9.04312	+	7.58808i	−0.580116	+	0.486775i
$244$	−1.38905	+	7.87768i	−0.0889246	+	0.504317i
$245$		0			0
$246$	14.5944			0.930507
$247$	2.57838	−	3.35435i	0.164058	−	0.213432i
$248$	−0.0197339			−0.00125310
$249$	7.34728	−	2.67419i	0.465615	−	0.169470i
$250$		0			0
$251$	17.3801	−	14.5836i	1.09702	−	0.920508i	0.0997980	−	0.995008i	$-0.468180\pi$
$251$	17.3801	−	14.5836i	1.09702	−	0.920508i	0.997221	+	0.0744994i	$0.0237359\pi$
$252$	2.22884	+	1.87022i	0.140404	+	0.117813i
$253$	3.96994	+	22.5146i	0.249588	+	1.41548i
$254$	−4.68648	−	8.11723i	−0.294056	−	0.509320i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−21.2026	−	7.71712i	−1.32258	−	0.481380i	−0.418297	−	0.908310i	$-0.637373\pi$
$257$	−21.2026	−	7.71712i	−1.32258	−	0.481380i	−0.904285	+	0.426930i	$0.859595\pi$
$258$	3.82506	−	6.62520i	0.238138	−	0.412467i
$259$	−1.39224	−	2.41144i	−0.0865099	−	0.149839i
$260$		0			0
$261$	−0.0701275	−	0.0588440i	−0.00434079	−	0.00364235i
$262$	−4.78578	+	4.01574i	−0.295666	+	0.248093i
$263$	1.46619	−	8.31518i	0.0904091	−	0.512736i	−0.905649	−	0.424029i	$-0.860615\pi$
$263$	1.46619	−	8.31518i	0.0904091	−	0.512736i	0.996058	−	0.0887068i	$-0.0282734\pi$
$264$	3.34552	−	1.21767i	0.205902	−	0.0749424i
$265$		0			0
$266$	−0.442261	−	10.3293i	−0.0271168	−	0.633332i
$267$	1.14627			0.0701506
$268$	4.79924	−	1.74678i	0.293160	−	0.106702i
$269$	4.57571	−	25.9501i	0.278986	−	1.58221i	−0.447024	−	0.894522i	$-0.647516\pi$
$269$	4.57571	−	25.9501i	0.278986	−	1.58221i	0.726010	−	0.687684i	$-0.241373\pi$
$270$		0			0
$271$	−0.465903	−	0.390939i	−0.0283016	−	0.0237479i	0.628527	−	0.777788i	$-0.283658\pi$
$271$	−0.465903	−	0.390939i	−0.0283016	−	0.0237479i	−0.656829	+	0.754040i	$0.728103\pi$
$272$	0.980748	+	5.56210i	0.0594666	+	0.337252i
$273$	1.53286	+	2.65499i	0.0927729	+	0.160687i
$274$	−7.44103	+	12.8882i	−0.449529	+	0.778607i
$275$		0			0
$276$	10.7006	+	3.89470i	0.644101	+	0.234434i
$277$	3.40451	−	5.89679i	0.204557	−	0.354304i	−0.745434	−	0.666579i	$-0.767758\pi$
$277$	3.40451	−	5.89679i	0.204557	−	0.354304i	0.949992	+	0.312275i	$0.101091\pi$
$278$	−5.38487	−	9.32686i	−0.322963	−	0.559388i
$279$	0.00420353	+	0.0238394i	0.000251659	+	0.00142723i
$280$		0			0
$281$	18.7616	−	15.7429i	1.11922	−	0.939141i	0.120659	−	0.992694i	$-0.461499\pi$
$281$	18.7616	−	15.7429i	1.11922	−	0.939141i	0.998565	+	0.0535531i	$0.0170546\pi$
$282$	−1.21680	+	6.90081i	−0.0724593	+	0.410937i
$283$	30.3868	−	11.0599i	1.80631	−	0.657443i	0.808710	−	0.588208i	$-0.200166\pi$
$283$	30.3868	−	11.0599i	1.80631	−	0.657443i	0.997600	−	0.0692348i	$-0.0220558\pi$
$284$	−10.3905			−0.616560
$285$		0			0
$286$	−2.59496			−0.153443
$287$	−24.4272	+	8.89076i	−1.44189	+	0.524805i
$288$	−0.213011	+	1.20805i	−0.0125518	+	0.0711848i
$289$	11.4131	−	9.57676i	0.671361	−	0.563339i
$290$		0			0
$291$	−2.56826	−	14.5653i	−0.150554	−	0.853834i
$292$	4.25677	+	7.37294i	0.249109	+	0.431469i
$293$	−13.3781	+	23.1715i	−0.781556	+	1.35369i	0.149479	+	0.988765i	$0.452240\pi$
$293$	−13.3781	+	23.1715i	−0.781556	+	1.35369i	−0.931035	+	0.364930i	$0.881093\pi$
$294$	−1.71958	−	0.625876i	−0.100288	−	0.0365018i
$295$		0			0
$296$	0.586979	−	1.01668i	0.0341175	−	0.0590932i
$297$	−7.52397	−	13.0319i	−0.436585	−	0.756188i
$298$	−2.81132	−	15.9438i	−0.162856	−	0.923600i
$299$	−6.35813	−	5.33511i	−0.367700	−	0.308537i
$300$		0			0
$301$	−2.36613	+	13.4190i	−0.136381	+	0.773457i
$302$	−5.75072	+	2.09309i	−0.330917	+	0.120444i
$303$	−5.74359			−0.329961
$304$	3.67823	−	2.33893i	0.210961	−	0.134147i
$305$		0			0
$306$	6.51036	−	2.36958i	0.372172	−	0.135460i
$307$	2.04105	−	11.5754i	0.116489	−	0.660640i	−0.869514	−	0.493909i	$-0.835568\pi$
$307$	2.04105	−	11.5754i	0.116489	−	0.660640i	0.986002	−	0.166731i	$-0.0533212\pi$
$308$	−4.85771	+	4.07610i	−0.276794	+	0.232257i
$309$	0.0177881	+	0.0149260i	0.00101193	+	0.000849109i
$310$		0			0
$311$	−4.95715	−	8.58603i	−0.281094	−	0.486869i	0.690560	−	0.723275i	$-0.257364\pi$
$311$	−4.95715	−	8.58603i	−0.281094	−	0.486869i	−0.971654	+	0.236406i	$0.924031\pi$
$312$	−0.646263	+	1.11936i	−0.0365875	+	0.0633713i
$313$	−0.337454	−	0.122823i	−0.0190740	−	0.00694238i	0.332466	−	0.943115i	$-0.392119\pi$
$313$	−0.337454	−	0.122823i	−0.0190740	−	0.00694238i	−0.351540	+	0.936173i	$0.614342\pi$
$314$	−19.8144	−	7.21187i	−1.11819	−	0.406989i
$315$		0			0
$316$	−7.94586	−	13.7626i	−0.446990	−	0.774209i
$317$	4.50550	+	25.5519i	0.253054	+	1.43514i	0.801019	+	0.598639i	$0.204292\pi$
$317$	4.50550	+	25.5519i	0.253054	+	1.43514i	−0.547965	+	0.836501i	$0.684597\pi$
$318$	−0.0907975	−	0.0761881i	−0.00509167	−	0.00427242i
$319$	0.152841	−	0.128249i	0.00855748	−	0.00718058i
$320$		0			0
$321$	−14.4180	+	5.24770i	−0.804732	+	0.292898i
$322$	−20.2825			−1.13030
$323$	−21.8274	−	11.3860i	−1.21451	−	0.633536i
$324$	−3.81521			−0.211956
$325$		0			0
$326$	−2.81522	+	15.9659i	−0.155921	+	0.884271i
$327$	9.54699	−	8.01087i	0.527950	−	0.443002i
$328$	−8.39553	−	7.04468i	−0.463565	−	0.388978i
$329$	−2.16730	−	12.2913i	−0.119487	−	0.677644i
$330$		0			0
$331$	6.72198	−	11.6428i	0.369474	−	0.639947i	−0.620010	−	0.784594i	$-0.712871\pi$
$331$	6.72198	−	11.6428i	0.369474	−	0.639947i	0.989483	+	0.144647i	$0.0462047\pi$
$332$	−5.51738	−	2.00816i	−0.302806	−	0.110212i
$333$	−1.35323	−	0.492534i	−0.0741563	−	0.0269907i
$334$	0.233733	−	0.404837i	0.0127893	−	0.0221517i
$335$		0			0
$336$	0.548475	+	3.11055i	0.0299217	+	0.169695i
$337$	12.5750	+	10.5517i	0.685004	+	0.574786i	0.917464	−	0.397820i	$-0.130233\pi$
$337$	12.5750	+	10.5517i	0.685004	+	0.574786i	−0.232460	+	0.972606i	$0.574677\pi$
$338$	−9.23689	+	7.75068i	−0.502421	+	0.421581i
$339$	2.08884	−	11.8464i	0.113450	−	0.643408i
$340$		0			0
$341$	−0.0527590			−0.00285706
$342$	−3.60904	−	3.94525i	−0.195155	−	0.213335i
$343$	19.8626			1.07248
$344$	−5.39835	+	1.96484i	−0.291059	+	0.105937i
$345$		0			0
$346$	−19.7022	+	16.5321i	−1.05920	+	0.888770i
$347$	−5.14951	−	4.32095i	−0.276440	−	0.231961i	0.494018	−	0.869452i	$-0.335528\pi$
$347$	−5.14951	−	4.32095i	−0.276440	−	0.231961i	−0.770458	+	0.637491i	$0.779972\pi$
$348$	−0.0172570	−	0.0978695i	−0.000925075	−	0.00524636i
$349$	9.98033	+	17.2864i	0.534235	+	0.925322i	0.999200	+	0.0399930i	$0.0127336\pi$
$349$	9.98033	+	17.2864i	0.534235	+	0.925322i	−0.464965	+	0.885329i	$0.653933\pi$
$350$		0			0
$351$	5.13363	+	1.86849i	0.274013	+	0.0997326i
$352$	−2.51229	−	0.914400i	−0.133906	−	0.0487377i
$353$	−12.6872	+	21.9749i	−0.675273	+	1.16961i	0.301116	+	0.953588i	$0.402641\pi$
$353$	−12.6872	+	21.9749i	−0.675273	+	1.16961i	−0.976389	+	0.216020i	$0.930692\pi$
$354$	7.15308	+	12.3895i	0.380182	+	0.658495i
$355$		0			0
$356$	−0.659398	−	0.553301i	−0.0349480	−	0.0293249i
$357$	13.6656	−	11.4668i	0.723258	−	0.606886i
$358$	2.45951	−	13.9486i	0.129989	−	0.737206i
$359$	13.6119	−	4.95433i	0.718409	−	0.261480i	0.0431590	−	0.999068i	$-0.486258\pi$
$359$	13.6119	−	4.95433i	0.718409	−	0.261480i	0.675250	+	0.737589i	$0.264036\pi$
$360$		0			0
$361$	−1.68788	+	18.9249i	−0.0888358	+	0.996046i
$362$	7.79400			0.409643
$363$	−4.82053	+	1.75453i	−0.253012	+	0.0920889i
$364$	0.399769	−	2.26720i	0.0209536	−	0.118834i
$365$		0			0
$366$	8.16007	+	6.84711i	0.426534	+	0.357904i
$367$	−0.369537	−	2.09575i	−0.0192897	−	0.109397i	0.973643	−	0.228079i	$-0.0732444\pi$
$367$	−0.369537	−	2.09575i	−0.0192897	−	0.109397i	−0.992932	+	0.118682i	$0.962133\pi$
$368$	−4.27562	−	7.40559i	−0.222882	−	0.386043i
$369$	−6.72196	+	11.6428i	−0.349931	+	0.606099i
$370$		0			0
$371$	0.198383	+	0.0722056i	0.0102995	+	0.00374873i
$372$	−0.0131394	+	0.0227581i	−0.000681246	+	0.00117995i
$373$	13.7869	+	23.8796i	0.713859	+	1.23644i	0.963398	+	0.268075i	$0.0863875\pi$
$373$	13.7869	+	23.8796i	0.713859	+	1.23644i	−0.249539	+	0.968365i	$0.580279\pi$
$374$	2.62205	+	14.8704i	0.135583	+	0.768931i
$375$		0			0
$376$	4.03097	−	3.38238i	0.207881	−	0.174433i
$377$	−0.0125782	+	0.0713346i	−0.000647811	+	0.00367392i
$378$	12.5450	−	4.56602i	0.645247	−	0.234851i
$379$	−2.88506			−0.148195			−0.0740977	−	0.997251i	$-0.523608\pi$
$379$	−2.88506			−0.148195			−0.0740977	+	0.997251i	$0.523608\pi$
$380$		0			0
$381$	−12.4816			−0.639452
$382$	0.248133	−	0.0903130i	0.0126956	−	0.00462081i
$383$	2.16110	−	12.2562i	0.110427	−	0.626262i	−0.878486	−	0.477767i	$-0.841446\pi$
$383$	2.16110	−	12.2562i	0.110427	−	0.626262i	0.988913	−	0.148494i	$-0.0474427\pi$
$384$	−1.02011	+	0.855975i	−0.0520573	+	0.0436813i
$385$		0			0
$386$	0.541429	+	3.07060i	0.0275580	+	0.156289i
$387$	3.52352	+	6.10292i	0.179111	+	0.310229i
$388$	−5.55323	+	9.61847i	−0.281922	+	0.488304i
$389$	−29.1597	−	10.6132i	−1.47845	−	0.538113i	−0.528072	−	0.849200i	$-0.677085\pi$
$389$	−29.1597	−	10.6132i	−1.47845	−	0.538113i	−0.950381	+	0.311087i	$0.899307\pi$
$390$		0			0
$391$	−24.1483	+	41.8261i	−1.22123	+	2.11524i
$392$	0.687089	+	1.19007i	0.0347032	+	0.0601078i
$393$	1.44465	+	8.19301i	0.0728729	+	0.413282i
$394$	16.0698	+	13.4842i	0.809585	+	0.679323i
$395$		0			0
$396$	−0.569490	+	3.22974i	−0.0286180	+	0.162301i
$397$	7.39313	−	2.69088i	0.371050	−	0.135051i	−0.149763	−	0.988722i	$-0.547851\pi$
$397$	7.39313	−	2.69088i	0.371050	−	0.135051i	0.520813	+	0.853671i	$0.325629\pi$
$398$	−21.9572			−1.10061
$399$	−12.2068	−	6.36754i	−0.611104	−	0.318776i
$400$		0			0
$401$	−27.4546	+	9.99266i	−1.37102	+	0.499010i	−0.919443	−	0.393224i	$-0.871360\pi$
$401$	−27.4546	+	9.99266i	−1.37102	+	0.499010i	−0.451575	+	0.892233i	$0.649138\pi$
$402$	1.18100	−	6.69779i	0.0589030	−	0.334056i
$403$	0.0146728	−	0.0123119i	0.000730903	−	0.000613301i
$404$	3.30403	+	2.77241i	0.164382	+	0.137933i
$405$		0			0
$406$	0.0885046	+	0.153294i	0.00439241	+	0.00760787i
$407$	1.56930	−	2.71811i	0.0777875	−	0.134732i
$408$	7.06751	+	2.57236i	0.349894	+	0.127351i
$409$	−13.3081	−	4.84375i	−0.658043	−	0.239508i	−0.00865164	−	0.999963i	$-0.502754\pi$
$409$	−13.3081	−	4.84375i	−0.658043	−	0.239508i	−0.649391	+	0.760455i	$0.724976\pi$
$410$		0			0
$411$	9.90892	+	17.1628i	0.488771	+	0.846576i
$412$	−0.00302797	−	0.0171725i	−0.000149177	−	0.000846028i
$413$	−19.5199	−	16.3791i	−0.960510	−	0.805964i
$414$	−8.03554	+	6.74262i	−0.394925	+	0.331382i
$415$		0			0
$416$	0.912078	−	0.331969i	0.0447183	−	0.0162761i
$417$	−14.3416			−0.702312
$418$	9.83385	−	6.25320i	0.480989	−	0.305854i
$419$	30.0769			1.46935			0.734677	−	0.678417i	$-0.237334\pi$
$419$	30.0769			1.46935			0.734677	+	0.678417i	$0.237334\pi$
$420$		0			0
$421$	−2.36476	+	13.4112i	−0.115251	+	0.653623i	0.871374	+	0.490619i	$0.163229\pi$
$421$	−2.36476	+	13.4112i	−0.115251	+	0.653623i	−0.986625	+	0.163004i	$0.947882\pi$
$422$	−10.7343	+	9.00719i	−0.522540	+	0.438463i
$423$	−4.94471	−	4.14911i	−0.240420	−	0.201736i
$424$	0.0154560	+	0.0876552i	0.000750609	+	0.00425691i
$425$		0			0
$426$	−6.91828	+	11.9828i	−0.335192	+	0.580569i
$427$	−17.8289	−	6.48920i	−0.862803	−	0.314035i
$428$	10.8271	+	3.94072i	0.523345	+	0.190482i
$429$	−1.72780	+	2.99264i	−0.0834191	+	0.144486i
$430$		0			0
$431$	−5.13794	−	29.1387i	−0.247486	−	1.40356i	−0.814648	−	0.579956i	$-0.803070\pi$
$431$	−5.13794	−	29.1387i	−0.247486	−	1.40356i	0.567162	−	0.823606i	$-0.308041\pi$
$432$	4.31168	+	3.61793i	0.207446	+	0.174068i
$433$	0.740155	−	0.621064i	0.0355696	−	0.0298464i	−0.624830	−	0.780761i	$-0.714832\pi$
$433$	0.740155	−	0.621064i	0.0355696	−	0.0298464i	0.660399	+	0.750915i	$0.270387\pi$
$434$	0.00812785	−	0.0460953i	0.000390149	−	0.00221265i
$435$		0			0
$436$	−9.35877			−0.448204
$437$	36.9510	+	4.89640i	1.76761	+	0.234226i
$438$	11.3371			0.541709
$439$	22.1502	−	8.06200i	1.05717	−	0.384778i	0.245805	−	0.969319i	$-0.420948\pi$
$439$	22.1502	−	8.06200i	1.05717	−	0.384778i	0.811364	+	0.584541i	$0.198725\pi$
$440$		0			0
$441$	1.29130	−	1.08353i	0.0614907	−	0.0515968i
$442$	−4.19940	−	3.52372i	−0.199745	−	0.167606i
$443$	0.118233	+	0.670532i	0.00561741	+	0.0318579i	0.987488	−	0.157696i	$-0.0504068\pi$
$443$	0.118233	+	0.670532i	0.00561741	+	0.0318579i	−0.981870	+	0.189554i	$0.939296\pi$
$444$	−0.781656	−	1.35387i	−0.0370958	−	0.0642518i
$445$		0			0
$446$	14.7809	+	5.37982i	0.699898	+	0.254742i
$447$	−20.2591	−	7.37370i	−0.958222	−	0.348764i
$448$	1.18594	−	2.05411i	0.0560304	−	0.0970476i
$449$	14.8474	+	25.7165i	0.700693	+	1.21364i	0.968223	+	0.250087i	$0.0804591\pi$
$449$	14.8474	+	25.7165i	0.700693	+	1.21364i	−0.267530	+	0.963549i	$0.586208\pi$
$450$		0			0
$451$	−22.4457	−	18.8341i	−1.05692	−	0.886865i
$452$	−6.91983	+	5.80643i	−0.325482	+	0.273111i
$453$	−1.41514	+	8.02567i	−0.0664892	+	0.377079i
$454$	−7.52863	+	2.74020i	−0.353336	+	0.128604i
$455$		0			0
$456$	−0.248301	−	5.79926i	−0.0116278	−	0.271575i
$457$	2.71312			0.126914			0.0634572	−	0.997985i	$-0.479787\pi$
$457$	2.71312			0.126914			0.0634572	+	0.997985i	$0.479787\pi$
$458$	−18.6835	+	6.80024i	−0.873023	+	0.317754i
$459$	5.52014	−	31.3063i	0.257658	−	1.46125i
$460$		0			0
$461$	22.5554	+	18.9262i	1.05051	+	0.881482i	0.993147	−	0.116872i	$-0.0372867\pi$
$461$	22.5554	+	18.9262i	1.05051	+	0.881482i	0.0573618	+	0.998353i	$0.481731\pi$
$462$	1.46636	+	8.31615i	0.0682213	+	0.386902i
$463$	−15.9354	−	27.6008i	−0.740579	−	1.28272i	−0.952232	−	0.305375i	$-0.901218\pi$
$463$	−15.9354	−	27.6008i	−0.740579	−	1.28272i	0.211653	−	0.977345i	$-0.432115\pi$
$464$	−0.0373141	+	0.0646299i	−0.00173226	+	0.00300037i
$465$		0			0
$466$	−23.4437	−	8.53279i	−1.08601	−	0.395274i
$467$	−19.0890	+	33.0631i	−0.883333	+	1.52998i	−0.0357205	+	0.999362i	$0.511373\pi$
$467$	−19.0890	+	33.0631i	−0.883333	+	1.52998i	−0.847612	+	0.530616i	$0.821961\pi$
$468$	−0.595317	−	1.03112i	−0.0275185	−	0.0476635i
$469$	2.10354	+	11.9298i	0.0971323	+	0.550865i
$470$		0			0
$471$	−21.5101	+	18.0492i	−0.991135	+	0.831661i
$472$	1.86552	−	10.5799i	0.0858676	−	0.486979i
$473$	−14.4326	+	5.25305i	−0.663613	+	0.241535i
$474$	−21.1624			−0.972020
$475$		0			0
$476$	−13.3962			−0.614012
$477$	0.102599	−	0.0373431i	0.00469769	−	0.00170982i
$478$	1.84832	−	10.4823i	0.0845400	−	0.479450i
$479$	22.4094	−	18.8037i	1.02391	−	0.859163i	0.0337965	−	0.999429i	$-0.489240\pi$
$479$	22.4094	−	18.8037i	1.02391	−	0.859163i	0.990114	+	0.140266i	$0.0447957\pi$
$480$		0			0
$481$	0.197865	+	1.12215i	0.00902187	+	0.0511655i
$482$	8.40034	+	14.5498i	0.382625	+	0.662726i
$483$	−13.5047	+	23.3909i	−0.614486	+	1.06432i
$484$	3.61994	+	1.31755i	0.164543	+	0.0598886i
$485$		0			0
$486$	5.90247	−	10.2234i	0.267742	−	0.463742i
$487$	7.28777	+	12.6228i	0.330240	+	0.571993i	0.982559	−	0.185952i	$-0.0595368\pi$
$487$	7.28777	+	12.6228i	0.330240	+	0.571993i	−0.652318	+	0.757945i	$0.726203\pi$
$488$	−1.38905	−	7.87768i	−0.0628792	−	0.356606i
$489$	16.5383	+	13.8773i	0.747886	+	0.627551i
$490$		0			0
$491$	−1.15669	+	6.55990i	−0.0522006	+	0.296044i	−0.999720	−	0.0236533i	$-0.992470\pi$
$491$	−1.15669	+	6.55990i	−0.0522006	+	0.296044i	0.947520	+	0.319698i	$0.103581\pi$
$492$	−13.7143	+	4.99159i	−0.618288	+	0.225038i
$493$	0.421493			0.0189831
$494$	−1.27563	+	4.03392i	−0.0573933	+	0.181494i
$495$		0			0
$496$	0.0185438	−	0.00674938i	0.000832640	−	0.000303056i
$497$	4.27955	−	24.2705i	0.191964	−	1.08868i
$498$	−5.98956	+	5.02583i	−0.268398	+	0.225213i
$499$	3.72597	+	3.12646i	0.166797	+	0.139960i	0.722366	−	0.691511i	$-0.243055\pi$
$499$	3.72597	+	3.12646i	0.166797	+	0.139960i	−0.555568	+	0.831471i	$0.687499\pi$
$500$		0			0
$501$	−0.311253	−	0.539105i	−0.0139057	−	0.0240854i
$502$	−11.3440	+	19.6484i	−0.506309	+	0.876952i
$503$	6.14824	+	2.23778i	0.274137	+	0.0997775i	0.475430	−	0.879753i	$-0.342292\pi$
$503$	6.14824	+	2.23778i	0.274137	+	0.0997775i	−0.201294	+	0.979531i	$0.564515\pi$
$504$	−2.73408	−	0.995122i	−0.121785	−	0.0443263i
$505$		0			0
$506$	−11.4310	−	19.7990i	−0.508169	−	0.880175i
$507$	2.78828	+	15.8131i	0.123832	+	0.702284i
$508$	7.18011	+	6.02483i	0.318566	+	0.267309i
$509$	6.45683	−	5.41792i	0.286194	−	0.240145i	−0.488376	−	0.872633i	$-0.662411\pi$
$509$	6.45683	−	5.41792i	0.286194	−	0.240145i	0.774570	+	0.632488i	$0.217966\pi$
$510$		0			0
$511$	−18.9753	+	6.90645i	−0.839418	+	0.305523i
$512$	1.00000			0.0441942
$513$	−23.9570	+	5.28994i	−1.05773	+	0.233557i
$514$	22.5633			0.995226
$515$		0			0
$516$	−1.32843	+	7.53390i	−0.0584809	+	0.331661i
$517$	10.7769	−	9.04289i	0.473967	−	0.397706i
$518$	2.13304	+	1.78983i	0.0937205	+	0.0786408i
$519$	5.94735	+	33.7291i	0.261060	+	1.48054i
$520$		0			0
$521$	14.5648	−	25.2269i	0.638094	−	1.10521i	−0.347757	−	0.937585i	$-0.613056\pi$
$521$	14.5648	−	25.2269i	0.638094	−	1.10521i	0.985851	−	0.167626i	$-0.0536102\pi$
$522$	0.0860242	+	0.0313102i	0.00376517	+	0.00137041i
$523$	−25.6164	−	9.32362i	−1.12013	−	0.407693i	−0.285429	−	0.958400i	$-0.592136\pi$
$523$	−25.6164	−	9.32362i	−1.12013	−	0.407693i	−0.834699	+	0.550706i	$0.814358\pi$
$524$	3.12369	−	5.41040i	0.136459	−	0.236354i
$525$		0			0
$526$	1.46619	+	8.31518i	0.0639289	+	0.362559i
$527$	−0.0853794	−	0.0716419i	−0.00371919	−	0.00312077i
$528$	−2.72729	+	2.28847i	−0.118690	+	0.0995929i
$529$	8.70390	−	49.3623i	0.378430	−	2.14619i
$530$		0			0
$531$	−13.1784			−0.571893
$532$	3.94843	+	9.55513i	0.171186	+	0.414267i
$533$	10.6375			0.460762
$534$	−1.07714	+	0.392048i	−0.0466125	+	0.0169656i
$535$		0			0
$536$	−3.91238	+	3.28288i	−0.168989	+	0.141799i
$537$	−14.4486	−	12.1238i	−0.623504	−	0.523182i
$538$	4.57571	+	25.9501i	0.197273	+	1.11879i
$539$	1.83695	+	3.18169i	0.0791230	+	0.137045i
$540$		0			0
$541$	−25.0683	−	9.12412i	−1.07777	−	0.392277i	−0.258694	−	0.965959i	$-0.583292\pi$
$541$	−25.0683	−	9.12412i	−1.07777	−	0.392277i	−0.819077	+	0.573683i	$0.805514\pi$
$542$	0.571515	+	0.208014i	0.0245487	+	0.00893498i
$543$	5.18948	−	8.98844i	0.222702	−	0.385731i
$544$	−2.82395	−	4.89123i	−0.121076	−	0.209710i
$545$		0			0
$546$	−2.34848	−	1.97061i	−0.100506	−	0.0843342i
$547$	−3.45811	+	2.90170i	−0.147858	+	0.124068i	−0.713716	−	0.700435i	$-0.752989\pi$
$547$	−3.45811	+	2.90170i	−0.147858	+	0.124068i	0.565858	+	0.824503i	$0.308545\pi$
$548$	2.58424	−	14.6560i	0.110393	−	0.626072i
$549$	−9.22071	+	3.35606i	−0.393530	+	0.143233i
$550$		0			0
$551$	−0.124232	−	0.300640i	−0.00529247	−	0.0128077i
$552$	−11.3873			−0.484678
$553$	35.4201	−	12.8919i	1.50622	−	0.548218i
$554$	−1.18238	+	6.70558i	−0.0502343	+	0.284893i
$555$		0			0
$556$	8.25009	+	6.92265i	0.349882	+	0.293586i
$557$	3.67225	+	20.8264i	0.155598	+	0.882442i	0.958237	+	0.285976i	$0.0923177\pi$
$557$	3.67225	+	20.8264i	0.155598	+	0.882442i	−0.802639	+	0.596466i	$0.796571\pi$
$558$	−0.0121036	−	0.0209640i	−0.000512386	−	0.000887478i
$559$	2.78799	−	4.82894i	0.117919	−	0.204242i
$560$		0			0
$561$	18.8952	+	6.87728i	0.797755	+	0.290359i
$562$	−12.2458	+	21.2103i	−0.516557	+	0.894703i
$563$	9.35993	+	16.2119i	0.394474	+	0.683249i	0.993034	−	0.117829i	$-0.0375935\pi$
$563$	9.35993	+	16.2119i	0.394474	+	0.683249i	−0.598560	+	0.801078i	$0.704260\pi$
$564$	−1.21680	−	6.90081i	−0.0512365	−	0.290576i
$565$		0			0
$566$	−24.7716	+	20.7858i	−1.04123	+	0.873693i
$567$	1.57138	−	8.91174i	0.0659918	−	0.374258i
$568$	9.76384	−	3.55375i	0.409681	−	0.149112i
$569$	−41.7205			−1.74902			−0.874508	−	0.485011i	$-0.838816\pi$
$569$	−41.7205			−1.74902			−0.874508	+	0.485011i	$0.838816\pi$
$570$		0			0
$571$	−33.6363			−1.40763			−0.703817	−	0.710381i	$-0.748522\pi$
$571$	−33.6363			−1.40763			−0.703817	+	0.710381i	$0.748522\pi$
$572$	2.43846	−	0.887529i	0.101957	−	0.0371094i
$573$	0.0610607	−	0.346293i	0.00255085	−	0.0144666i
$574$	19.9132	−	16.7092i	0.831161	−	0.697427i
$575$		0			0
$576$	−0.213011	−	1.20805i	−0.00887546	−	0.0503352i
$577$	−8.32416	−	14.4179i	−0.346539	−	0.600223i	0.639093	−	0.769129i	$-0.279310\pi$
$577$	−8.32416	−	14.4179i	−0.346539	−	0.600223i	−0.985632	+	0.168906i	$0.945977\pi$
$578$	−7.44940	+	12.9027i	−0.309854	+	0.536683i
$579$	3.90167	+	1.42009i	0.162148	+	0.0590170i
$580$		0			0
$581$	6.96322	−	12.0607i	0.288883	−	0.500360i
$582$	7.39501	+	12.8085i	0.306533	+	0.530931i
$583$	0.0413220	+	0.234349i	0.00171138	+	0.00970572i
$584$	−6.52175	−	5.47240i	−0.269872	−	0.226449i
$585$		0			0
$586$	4.64616	−	26.3497i	0.191931	−	1.08850i
$587$	6.88805	−	2.50704i	0.284300	−	0.103477i	−0.195934	−	0.980617i	$-0.562774\pi$
$587$	6.88805	−	2.50704i	0.284300	−	0.103477i	0.480234	+	0.877140i	$0.340552\pi$
$588$	1.82994			0.0754654
$589$	−0.0259353	+	0.0820149i	−0.00106864	+	0.00337937i
$590$		0			0
$591$	26.2504	−	9.55437i	1.07980	−	0.393014i
$592$	−0.203856	+	1.15612i	−0.00837841	+	0.0475163i
$593$	16.4311	−	13.7873i	0.674744	−	0.566177i	−0.239722	−	0.970842i	$-0.577056\pi$
$593$	16.4311	−	13.7873i	0.674744	−	0.566177i	0.914465	+	0.404665i	$0.132612\pi$
$594$	11.5274	+	9.67263i	0.472975	+	0.396873i
$595$		0			0
$596$	8.09488	+	14.0208i	0.331579	+	0.574312i
$597$	−14.6197	+	25.3221i	−0.598346	+	1.03637i
$598$	7.79940	+	2.83875i	0.318941	+	0.116085i
$599$	−8.88650	−	3.23442i	−0.363093	−	0.132155i	0.154030	−	0.988066i	$-0.450775\pi$
$599$	−8.88650	−	3.23442i	−0.363093	−	0.132155i	−0.517123	+	0.855911i	$0.672997\pi$
$600$		0			0
$601$	−3.88906	−	6.73606i	−0.158638	−	0.274769i	0.775740	−	0.631053i	$-0.217377\pi$
$601$	−3.88906	−	6.73606i	−0.158638	−	0.274769i	−0.934378	+	0.356284i	$0.884044\pi$
$602$	−2.36613	−	13.4190i	−0.0964362	−	0.546917i
$603$	4.79924	+	4.02704i	0.195440	+	0.163994i
$604$	4.68803	−	3.93373i	0.190753	−	0.160061i
$605$		0			0
$606$	5.39721	−	1.96442i	0.219247	−	0.0797993i
$607$	1.12754			0.0457656			0.0228828	−	0.999738i	$-0.492716\pi$
$607$	1.12754			0.0457656			0.0228828	+	0.999738i	$0.492716\pi$
$608$	−2.65644	+	3.45591i	−0.107733	+	0.140156i
$609$	0.235716			0.00955170
$610$		0			0
$611$	−0.886894	+	5.02982i	−0.0358799	+	0.203485i
$612$	−5.30729	+	4.45335i	−0.214535	+	0.180016i
$613$	−31.3528	−	26.3081i	−1.26633	−	1.06258i	−0.994978	−	0.100095i	$-0.968085\pi$
$613$	−31.3528	−	26.3081i	−1.26633	−	1.06258i	−0.271351	−	0.962481i	$-0.587470\pi$
$614$	2.04105	+	11.5754i	0.0823699	+	0.467143i
$615$		0			0
$616$	3.17064	−	5.49172i	0.127749	−	0.221268i
$617$	−23.2499	−	8.46227i	−0.936005	−	0.340678i	−0.171418	−	0.985198i	$-0.554835\pi$
$617$	−23.2499	−	8.46227i	−0.936005	−	0.340678i	−0.764587	+	0.644520i	$0.777057\pi$
$618$	−0.0218203	−	0.00794194i	−0.000877741	−	0.000319472i
$619$	−17.1323	+	29.6741i	−0.688607	+	1.19270i	0.283682	+	0.958918i	$0.408444\pi$
$619$	−17.1323	+	29.6741i	−0.688607	+	1.19270i	−0.972289	+	0.233784i	$0.924889\pi$
$620$		0			0
$621$	8.35781	+	47.3995i	0.335387	+	1.90208i
$622$	7.59479	+	6.37278i	0.304523	+	0.255525i
$623$	1.56402	−	1.31236i	0.0626609	−	0.0525788i
$624$	0.224445	−	1.27289i	0.00898499	−	0.0509564i
$625$		0			0
$626$	0.359111			0.0143530
$627$	−0.663840	−	15.5045i	−0.0265112	−	0.619189i
$628$	21.0861			0.841427
$629$	6.23054	−	2.26773i	0.248428	−	0.0904203i
$630$		0			0
$631$	−3.99216	+	3.34982i	−0.158925	+	0.133354i	−0.718783	−	0.695235i	$-0.755300\pi$
$631$	−3.99216	+	3.34982i	−0.158925	+	0.133354i	0.559857	+	0.828589i	$0.310856\pi$
$632$	12.1738	+	10.2150i	0.484246	+	0.406331i
$633$	3.24030	+	18.3767i	0.128790	+	0.730406i
$634$	−12.9731	−	22.4700i	−0.515226	−	0.892398i
$635$		0			0
$636$	0.111380	+	0.0405388i	0.00441649	+	0.00160747i
$637$	−1.25336	−	0.456185i	−0.0496598	−	0.0180747i
$638$	−0.0997602	+	0.172790i	−0.00394954	+	0.00684081i
$639$	−6.37289	−	11.0382i	−0.252108	−	0.436663i
$640$		0			0
$641$	30.1012	+	25.2579i	1.18893	+	0.997627i	0.999877	+	0.0156594i	$0.00498475\pi$
$641$	30.1012	+	25.2579i	1.18893	+	0.997627i	0.189048	+	0.981968i	$0.439460\pi$
$642$	11.7536	−	9.86246i	0.463878	−	0.389240i
$643$	−7.07687	+	40.1349i	−0.279085	+	1.58277i	0.446596	+	0.894736i	$0.352636\pi$
$643$	−7.07687	+	40.1349i	−0.279085	+	1.58277i	−0.725681	+	0.688031i	$0.758475\pi$
$644$	19.0594	−	6.93704i	0.751044	−	0.273358i
$645$		0			0
$646$	24.4053	+	3.23396i	0.960214	+	0.127238i
$647$	18.7570			0.737414			0.368707	−	0.929546i	$-0.379800\pi$
$647$	18.7570			0.737414			0.368707	+	0.929546i	$0.379800\pi$
$648$	3.58512	−	1.30488i	0.140837	−	0.0512604i
$649$	4.98752	−	28.2856i	0.195777	−	1.11031i
$650$		0			0
$651$	−0.0477477	−	0.0400651i	−0.00187138	−	0.00157027i
$652$	−2.81522	−	15.9659i	−0.110253	−	0.625274i
$653$	−8.43478	−	14.6095i	−0.330078	−	0.571713i	0.652449	−	0.757833i	$-0.273742\pi$
$653$	−8.43478	−	14.6095i	−0.330078	−	0.571713i	−0.982527	+	0.186120i	$0.940409\pi$
$654$	−6.23135	+	10.7930i	−0.243665	+	0.422040i
$655$		0			0
$656$	10.2986	+	3.74840i	0.402094	+	0.146350i
$657$	−5.22170	+	9.04425i	−0.203718	+	0.352850i
$658$	6.24048	+	10.8088i	0.243279	+	0.421372i
$659$	1.19202	+	6.76028i	0.0464345	+	0.263343i	0.999183	−	0.0404175i	$-0.0128688\pi$
$659$	1.19202	+	6.76028i	0.0464345	+	0.263343i	−0.952748	+	0.303761i	$0.901758\pi$
$660$		0			0
$661$	12.5608	−	10.5398i	0.488558	−	0.409949i	−0.364951	−	0.931027i	$-0.618914\pi$
$661$	12.5608	−	10.5398i	0.488558	−	0.409949i	0.853509	+	0.521078i	$0.174470\pi$
$662$	−2.33452	+	13.2397i	−0.0907337	+	0.514577i
$663$	−6.85982	+	2.49677i	−0.266413	+	0.0969665i
$664$	5.87148			0.227857
$665$		0			0
$666$	1.44007			0.0558017
$667$	−0.599678	+	0.218265i	−0.0232196	+	0.00845125i
$668$	−0.0811745	+	0.460364i	−0.00314074	+	0.0178120i
$669$	16.0459	−	13.4641i	0.620370	−	0.520552i
$670$		0			0
$671$	−3.71365	−	21.0612i	−0.143364	−	0.813058i
$672$	−1.57927	−	2.73538i	−0.0609217	−	0.105519i
$673$	2.46257	−	4.26530i	0.0949251	−	0.164415i	−0.814652	−	0.579950i	$-0.803072\pi$
$673$	2.46257	−	4.26530i	0.0949251	−	0.164415i	0.909577	+	0.415535i	$0.136406\pi$
$674$	−15.4255	−	5.61443i	−0.594169	−	0.216260i
$675$		0			0
$676$	6.02895	−	10.4425i	0.231883	−	0.401633i
$677$	−2.69632	−	4.67017i	−0.103628	−	0.179489i	0.809549	−	0.587053i	$-0.199712\pi$
$677$	−2.69632	−	4.67017i	−0.103628	−	0.179489i	−0.913177	+	0.407563i	$0.866379\pi$
$678$	2.08884	+	11.8464i	0.0802214	+	0.454958i
$679$	−20.1801	−	16.9331i	−0.774439	−	0.649832i
$680$		0			0
$681$	−1.85265	+	10.5069i	−0.0709937	+	0.402625i
$682$	0.0495773	−	0.0180446i	0.00189841	−	0.000690965i
$683$	17.4871			0.669126			0.334563	−	0.942373i	$-0.391411\pi$
$683$	17.4871			0.669126			0.334563	+	0.942373i	$0.391411\pi$
$684$	4.74075	+	2.47296i	0.181267	+	0.0945560i
$685$		0			0
$686$	−18.6647	+	6.79339i	−0.712622	+	0.259373i
$687$	−4.59765	+	26.0746i	−0.175411	+	0.994807i
$688$	4.40077	−	3.69269i	0.167778	−	0.140782i
$689$	−0.0661800	−	0.0555316i	−0.00252126	−	0.00211558i
$690$		0			0
$691$	7.39377	+	12.8064i	0.281272	+	0.487178i	0.971698	−	0.236225i	$-0.0759102\pi$
$691$	7.39377	+	12.8064i	0.281272	+	0.487178i	−0.690426	+	0.723403i	$0.742577\pi$
$692$	12.8597	−	22.2736i	0.488852	−	0.846716i
$693$	−7.30962	−	2.66049i	−0.277670	−	0.101063i
$694$	6.31681	+	2.29913i	0.239783	+	0.0872738i
$695$		0			0
$696$	0.0496897	+	0.0860650i	0.00188348	+	0.00326229i
$697$	−10.7486	−	60.9583i	−0.407132	−	2.30896i
$698$	−15.2908	−	12.8305i	−0.578764	−	0.485640i
$699$	−25.4500	+	21.3550i	−0.962606	+	0.807722i
$700$		0			0
$701$	−7.07843	+	2.57634i	−0.267349	+	0.0973069i	−0.472216	−	0.881483i	$-0.656546\pi$
$701$	−7.07843	+	2.57634i	−0.267349	+	0.0973069i	0.204868	+	0.978790i	$0.434324\pi$
$702$	−5.46310			−0.206191
$703$	−3.45392	−	3.77568i	−0.130267	−	0.142403i
$704$	2.67353			0.100762
$705$		0			0
$706$	4.40623	−	24.9890i	0.165831	−	0.940472i
$707$	−7.83677	+	6.57583i	−0.294732	+	0.247310i
$708$	−10.9592	−	9.19583i	−0.411870	−	0.345600i
$709$	6.22196	+	35.2865i	0.233671	+	1.32521i	0.845395	+	0.534141i	$0.179365\pi$
$709$	6.22196	+	35.2865i	0.233671	+	1.32521i	−0.611725	+	0.791071i	$0.709524\pi$
$710$		0			0
$711$	9.74704	−	16.8824i	0.365543	−	0.633138i
$712$	0.808872	+	0.294405i	0.0303138	+	0.0110333i
$713$	0.158572	+	0.0577156i	0.00593858	+	0.00216147i
$714$	−8.91956	+	15.4491i	−0.333806	+	0.578169i
$715$		0			0
$716$	2.45951	+	13.9486i	0.0919163	+	0.521284i
$717$	−10.8581	−	9.11101i	−0.405503	−	0.340257i
$718$	−11.0965	+	9.31110i	−0.414119	+	0.347487i
$719$	1.50797	−	8.55210i	0.0562376	−	0.318940i	−0.943692	−	0.330826i	$-0.892673\pi$
$719$	1.50797	−	8.55210i	0.0562376	−	0.318940i	0.999929	+	0.0118866i	$0.00378372\pi$
$720$		0			0
$721$	0.0413594			0.00154031
$722$	−4.88660	−	18.3609i	−0.181860	−	0.683320i
$723$	22.3728			0.832053
$724$	−7.32396	+	2.66570i	−0.272193	+	0.0990701i
$725$		0			0
$726$	3.92973	−	3.29744i	0.145846	−	0.122379i
$727$	−22.8813	−	19.1997i	−0.848622	−	0.712078i	0.110864	−	0.993836i	$-0.464638\pi$
$727$	−22.8813	−	19.1997i	−0.848622	−	0.712078i	−0.959486	+	0.281758i	$0.909083\pi$
$728$	0.399769	+	2.26720i	0.0148164	+	0.0840282i
$729$	−13.5829	−	23.5263i	−0.503070	−	0.871343i
$730$		0			0
$731$	−30.4893	−	11.0972i	−1.12769	−	0.410445i
$732$	−10.0098	−	3.64327i	−0.369973	−	0.134659i
$733$	6.44955	−	11.1709i	0.238220	−	0.412608i	−0.721984	−	0.691910i	$-0.756770\pi$
$733$	6.44955	−	11.1709i	0.238220	−	0.412608i	0.960203	+	0.279301i	$0.0901029\pi$
$734$	1.06404	+	1.84297i	0.0392744	+	0.0680253i
$735$		0			0
$736$	6.55063	+	5.49663i	0.241460	+	0.202609i
$737$	−10.4598	+	8.77685i	−0.385293	+	0.323300i
$738$	2.33451	−	13.2397i	0.0859346	−	0.487359i
$739$	27.5586	−	10.0305i	1.01376	−	0.368978i	0.218883	−	0.975751i	$-0.429759\pi$
$739$	27.5586	−	10.0305i	1.01376	−	0.368978i	0.794875	+	0.606773i	$0.207536\pi$
$740$		0			0
$741$	3.80277	+	4.15702i	0.139698	+	0.152712i
$742$	−0.211115			−0.00775028
$743$	44.8942	−	16.3402i	1.64701	−	0.599462i	0.658765	−	0.752349i	$-0.271079\pi$
$743$	44.8942	−	16.3402i	1.64701	−	0.599462i	0.988244	+	0.152886i	$0.0488569\pi$
$744$	0.00456327	−	0.0258796i	0.000167297	−	0.000948791i
$745$		0			0
$746$	−21.1228	−	17.7241i	−0.773359	−	0.648925i
$747$	−1.25069	−	7.09301i	−0.0457603	−	0.259520i
$748$	−7.54991	−	13.0768i	−0.276052	−	0.478136i
$749$	−13.6643	+	23.6673i	−0.499283	+	0.864783i
$750$		0			0
$751$	39.1332	+	14.2433i	1.42799	+	0.519745i	0.936354	−	0.351056i	$-0.114177\pi$
$751$	39.1332	+	14.2433i	1.42799	+	0.519745i	0.491635	+	0.870802i	$0.336400\pi$
$752$	−2.63103	+	4.55707i	−0.0959436	+	0.166179i
$753$	15.1064	+	26.1650i	0.550507	+	0.953506i
$754$	−0.0125782	−	0.0713346i	−0.000458072	−	0.00259785i
$755$		0			0
$756$	−10.2268	+	8.58131i	−0.371945	+	0.312099i
$757$	−4.54023	+	25.7489i	−0.165017	+	0.935861i	0.784029	+	0.620724i	$0.213161\pi$
$757$	−4.54023	+	25.7489i	−0.165017	+	0.935861i	−0.949046	+	0.315136i	$0.897950\pi$
$758$	2.71107	−	0.986748i	0.0984704	−	0.0358403i
$759$	−30.4444			−1.10506
$760$		0			0
$761$	5.26023			0.190683			0.0953415	−	0.995445i	$-0.469606\pi$
$761$	5.26023			0.190683			0.0953415	+	0.995445i	$0.469606\pi$
$762$	11.7289	−	4.26896i	0.424892	−	0.154648i
$763$	3.85463	−	21.8607i	0.139547	−	0.791409i
$764$	−0.202280	+	0.169733i	−0.00731822	+	0.00614072i
$765$		0			0
$766$	2.16110	+	12.2562i	0.0780835	+	0.442834i
$767$	5.21370	+	9.03040i	0.188256	+	0.326069i
$768$	0.665830	−	1.15325i	0.0240261	−	0.0416144i
$769$	−42.2718	−	15.3857i	−1.52436	−	0.554822i	−0.562129	−	0.827050i	$-0.690018\pi$
$769$	−42.2718	−	15.3857i	−1.52436	−	0.554822i	−0.962233	+	0.272227i	$0.912240\pi$
$770$		0			0
$771$	15.0233	−	26.0212i	0.541053	−	0.937131i
$772$	−1.55898	−	2.70024i	−0.0561091	−	0.0971837i
$773$	−0.538663	−	3.05491i	−0.0193744	−	0.109877i	0.973587	−	0.228316i	$-0.0733221\pi$
$773$	−0.538663	−	3.05491i	−0.0193744	−	0.109877i	−0.992961	+	0.118439i	$0.962211\pi$
$774$	−5.39835	−	4.52975i	−0.194040	−	0.162819i
$775$		0			0
$776$	1.92862	−	10.9377i	0.0692332	−	0.392641i
$777$	3.48437	−	1.26821i	0.125001	−	0.0454967i
$778$	31.0311			1.11252
$779$	−40.3119	+	25.6337i	−1.44432	+	0.918424i
$780$		0			0
$781$	26.1039	−	9.50103i	0.934070	−	0.339974i
$782$	8.38661	−	47.5629i	0.299905	−	1.70084i
$783$	0.321773	−	0.270000i	0.0114992	−	0.00964900i
$784$	−1.05268	−	0.883305i	−0.0375958	−	0.0315466i
$785$		0			0
$786$	−4.15970	−	7.20481i	−0.148372	−	0.256987i
$787$	13.8128	−	23.9244i	0.492372	−	0.852813i	−0.507589	−	0.861599i	$-0.669463\pi$
$787$	13.8128	−	23.9244i	0.492372	−	0.852813i	0.999961	+	0.00878567i	$0.00279660\pi$
$788$	−19.7125	−	7.17478i	−0.702230	−	0.255591i
$789$	10.5657	+	3.84561i	0.376150	+	0.136907i
$790$		0			0
$791$	−10.7128	−	18.5552i	−0.380905	−	0.659746i
$792$	−0.569490	−	3.22974i	−0.0202360	−	0.114764i
$793$	5.94767	+	4.99069i	0.211208	+	0.177225i
$794$	−6.02693	+	5.05720i	−0.213888	+	0.179473i
$795$		0			0
$796$	20.6330	−	7.50979i	0.731317	−	0.266178i
$797$	25.2302			0.893700			0.446850	−	0.894609i	$-0.352546\pi$
$797$	25.2302			0.893700			0.446850	+	0.894609i	$0.352546\pi$
$798$	13.6485	+	1.80856i	0.483150	+	0.0640224i
$799$	29.7196			1.05140
$800$		0			0
$801$	0.183356	−	1.03987i	0.00647858	−	0.0367418i
$802$	22.3812	−	18.7801i	0.790308	−	0.663147i
$803$	−17.4361	−	14.6306i	−0.615305	−	0.516302i
$804$	1.18100	+	6.69779i	0.0416507	+	0.236213i
$805$		0			0
$806$	−0.00957698	+	0.0165878i	−0.000337335	+	0.000584281i
$807$	32.9736	+	12.0014i	1.16073	+	0.422470i
$808$	−4.05300	−	1.47517i	−0.142584	−	0.0518963i
$809$	15.2498	−	26.4134i	0.536154	−	0.928646i	−0.462952	−	0.886383i	$-0.653210\pi$
$809$	15.2498	−	26.4134i	0.536154	−	0.928646i	0.999107	−	0.0422629i	$-0.0134567\pi$
$810$		0			0
$811$	−1.35482	−	7.68358i	−0.0475742	−	0.269807i	0.951737	−	0.306915i	$-0.0992966\pi$
$811$	−1.35482	−	7.68358i	−0.0475742	−	0.269807i	−0.999311	+	0.0371078i	$0.988186\pi$
$812$	−0.135597	−	0.113779i	−0.00475852	−	0.00399287i
$813$	0.620425	−	0.520598i	0.0217592	−	0.0182582i
$814$	−0.545013	+	3.09092i	−0.0191027	+	0.108337i
$815$		0			0
$816$	−7.52109			−0.263291
$817$	1.07118	+	25.0181i	0.0374757	+	0.875272i
$818$	14.1622			0.495169
$819$	2.65373	−	0.965879i	0.0927289	−	0.0337505i
$820$		0			0
$821$	35.2031	−	29.5389i	1.22860	−	1.03092i	0.230269	−	0.973127i	$-0.426040\pi$
$821$	35.2031	−	29.5389i	1.22860	−	1.03092i	0.998329	−	0.0577885i	$-0.0184049\pi$
$822$	−15.1813	−	12.7387i	−0.529510	−	0.444312i
$823$	−2.63661	−	14.9529i	−0.0919063	−	0.521227i	−0.995652	−	0.0931558i	$-0.970305\pi$
$823$	−2.63661	−	14.9529i	−0.0919063	−	0.521227i	0.903745	−	0.428071i	$-0.140807\pi$
$824$	0.00871870	+	0.0151012i	0.000303730	+	0.000526076i
$825$		0			0
$826$	23.9447	+	8.71515i	0.833141	+	0.303239i
$827$	0.591323	+	0.215224i	0.0205623	+	0.00748408i	0.352281	−	0.935894i	$-0.385406\pi$
$827$	0.591323	+	0.215224i	0.0205623	+	0.00748408i	−0.331719	+	0.943378i	$0.607628\pi$
$828$	5.24483	−	9.08431i	0.182270	−	0.315701i
$829$	20.5684	+	35.6256i	0.714372	+	1.23733i	0.963201	+	0.268781i	$0.0866207\pi$
$829$	20.5684	+	35.6256i	0.714372	+	1.23733i	−0.248830	+	0.968547i	$0.580046\pi$
$830$		0			0
$831$	6.94596	+	5.82836i	0.240953	+	0.202183i
$832$	−0.743533	+	0.623898i	−0.0257774	+	0.0216298i
$833$	−1.34772	+	7.64331i	−0.0466958	+	0.264825i
$834$	13.4767	−	4.90512i	0.466660	−	0.169851i
$835$		0			0
$836$	−7.10207	+	9.23946i	−0.245630	+	0.319553i
$837$	−0.111072			−0.00383921
$838$	−28.2631	+	10.2869i	−0.976331	+	0.355355i
$839$	−5.04229	+	28.5962i	−0.174079	+	0.987252i	0.765122	+	0.643885i	$0.222679\pi$
$839$	−5.04229	+	28.5962i	−0.174079	+	0.987252i	−0.939201	+	0.343367i	$0.888433\pi$
$840$		0			0
$841$	−22.2110	−	18.6373i	−0.765897	−	0.642664i
$842$	−2.36476	−	13.4112i	−0.0814950	−	0.462181i
$843$	16.3072	+	28.2449i	0.561650	+	0.972807i
$844$	7.00635	−	12.1353i	0.241168	−	0.417716i
$845$		0			0
$846$	6.06559	+	2.20769i	0.208539	+	0.0759020i
$847$	−4.56855	+	7.91296i	−0.156977	+	0.271893i
$848$	−0.0445037	−	0.0770827i	−0.00152826	−	0.00264703i
$849$	7.47762	+	42.4077i	0.256631	+	1.45543i
$850$		0			0
$851$	−7.69017	+	6.45282i	−0.263615	+	0.221200i
$852$	2.40269	−	13.6263i	0.0823149	−	0.466831i
$853$	−9.08547	+	3.30684i	−0.311081	+	0.113224i	−0.492843	−	0.870118i	$-0.664042\pi$
$853$	−9.08547	+	3.30684i	−0.311081	+	0.113224i	0.181762	+	0.983343i	$0.441820\pi$
$854$	18.9732			0.649248
$855$		0			0
$856$	−11.5219			−0.393811
$857$	27.7722	−	10.1083i	0.948681	−	0.345292i	0.179093	−	0.983832i	$-0.442684\pi$
$857$	27.7722	−	10.1083i	0.948681	−	0.345292i	0.769588	+	0.638540i	$0.220461\pi$
$858$	0.600059	−	3.40311i	0.0204857	−	0.116180i
$859$	26.3636	−	22.1217i	0.899513	−	0.754781i	−0.0705819	−	0.997506i	$-0.522486\pi$
$859$	26.3636	−	22.1217i	0.899513	−	0.754781i	0.970095	+	0.242725i	$0.0780412\pi$
$860$		0			0
$861$	−6.01105	−	34.0904i	−0.204856	−	1.16180i
$862$	14.7941	+	25.6241i	0.503889	+	0.872762i
$863$	10.0227	−	17.3598i	0.341176	−	0.590934i	−0.643475	−	0.765467i	$-0.722508\pi$
$863$	10.0227	−	17.3598i	0.341176	−	0.590934i	0.984651	+	0.174533i	$0.0558415\pi$
$864$	−5.28906	−	1.92506i	−0.179938	−	0.0654919i
$865$		0			0
$866$	−0.483102	+	0.836757i	−0.0164165	+	0.0284342i
$867$	9.92007	+	17.1821i	0.336903	+	0.583533i
$868$	0.00812785	+	0.0460953i	0.000275877	+	0.00156458i
$869$	32.5469	+	27.3101i	1.10408	+	0.926431i
$870$		0			0
$871$	0.860802	−	4.88185i	0.0291672	−	0.165415i
$872$	8.79437	−	3.20089i	0.297815	−	0.108396i
$873$	−13.6241			−0.461105
$874$	−36.3973	+	8.03688i	−1.23116	+	0.271852i
$875$		0			0
$876$	−10.6534	+	3.87753i	−0.359946	+	0.131010i
$877$	−2.13503	+	12.1084i	−0.0720949	+	0.408871i	0.927307	+	0.374301i	$0.122117\pi$
$877$	−2.13503	+	12.1084i	−0.0720949	+	0.408871i	−0.999402	+	0.0345699i	$0.988994\pi$
$878$	−18.0570	+	15.1516i	−0.609393	+	0.511342i
$879$	−27.2942	−	22.9026i	−0.920612	−	0.772485i
$880$		0			0
$881$	15.3853	+	26.6481i	0.518344	+	0.897799i	0.999773	+	0.0213134i	$0.00678479\pi$
$881$	15.3853	+	26.6481i	0.518344	+	0.897799i	−0.481428	+	0.876485i	$0.659882\pi$
$882$	−0.842839	+	1.45984i	−0.0283799	+	0.0491554i
$883$	−36.0696	−	13.1283i	−1.21384	−	0.441801i	−0.345805	−	0.938306i	$-0.612394\pi$
$883$	−36.0696	−	13.1283i	−1.21384	−	0.441801i	−0.868034	+	0.496505i	$0.834616\pi$
$884$	5.15133	+	1.87493i	0.173258	+	0.0630607i
$885$		0			0
$886$	−0.340438	−	0.589656i	−0.0114372	−	0.0198099i
$887$	2.88427	+	16.3575i	0.0968444	+	0.549232i	0.994167	+	0.107856i	$0.0343985\pi$
$887$	2.88427	+	16.3575i	0.0968444	+	0.549232i	−0.897322	+	0.441376i	$0.854490\pi$
$888$	1.19757	+	1.00488i	0.0401877	+	0.0337215i
$889$	−17.0304	+	14.2902i	−0.571180	+	0.479277i
$890$		0			0
$891$	9.58492	−	3.48862i	0.321107	−	0.116873i
$892$	−15.7296			−0.526664
$893$	−8.75964	−	21.1982i	−0.293130	−	0.709370i
$894$	21.5593			0.721050
$895$		0			0
$896$	−0.411873	+	2.33585i	−0.0137597	+	0.0780352i
$897$	8.46687	−	7.10455i	0.282701	−	0.237214i
$898$	−22.7476	−	19.0875i	−0.759096	−	0.636957i
$899$	−0.000255732	−	0.00145033i	−8.52914e−6	−	4.83712e-5i
$900$		0			0
$901$	−0.251353	+	0.435356i	−0.00837377	+	0.0145038i
$902$	27.5337	+	10.0214i	0.916771	+	0.333677i
$903$	−17.0509	−	6.20602i	−0.567418	−	0.206523i
$904$	4.51660	−	7.82298i	0.150220	−	0.260188i
$905$		0			0
$906$	−1.41514	−	8.02567i	−0.0470150	−	0.266635i
$907$	12.2386	+	10.2694i	0.406375	+	0.340989i	0.822952	−	0.568111i	$-0.192326\pi$
$907$	12.2386	+	10.2694i	0.406375	+	0.340989i	−0.416576	+	0.909101i	$0.636770\pi$
$908$	6.13739	−	5.14988i	0.203677	−	0.170905i
$909$	−0.918740	+	5.21043i	−0.0304727	+	0.172819i
$910$		0			0
$911$	55.7482			1.84702			0.923510	−	0.383573i	$-0.125307\pi$
$911$	55.7482			1.84702			0.923510	+	0.383573i	$0.125307\pi$
$912$	2.21679	+	5.36460i	0.0734053	+	0.177640i
$913$	15.6975			0.519513
$914$	−2.54950	+	0.927941i	−0.0843299	+	0.0306936i
$915$		0			0
$916$	15.2309	−	12.7803i	0.503244	−	0.422272i
$917$	11.3513	+	9.52487i	0.374853	+	0.314539i
$918$	5.52014	+	31.3063i	0.182192	+	1.03326i
$919$	−20.2845	−	35.1339i	−0.669126	−	1.15896i	−0.978149	−	0.207905i	$-0.933336\pi$
$919$	−20.2845	−	35.1339i	−0.669126	−	1.15896i	0.309023	−	0.951054i	$-0.399998\pi$
$920$		0			0
$921$	14.7083	+	5.35338i	0.484654	+	0.176400i
$922$	−27.6683	−	10.0704i	−0.911206	−	0.331652i
$923$	−5.04256	+	8.73397i	−0.165978	+	0.287482i
$924$	−4.22222	−	7.31310i	−0.138901	−	0.240583i
$925$		0			0
$926$	24.4144	+	20.4861i	0.802306	+	0.673215i
$927$	0.0163858	−	0.0137493i	0.000538180	−	0.000451587i
$928$	0.0129590	−	0.0734944i	0.000425401	−	0.00241257i
$929$	−22.3308	+	8.12775i	−0.732650	+	0.266663i	−0.681286	−	0.732017i	$-0.738579\pi$
$929$	−22.3308	+	8.12775i	−0.732650	+	0.266663i	−0.0513639	+	0.998680i	$0.516357\pi$
$930$		0			0
$931$	5.84901	−	1.29152i	0.191694	−	0.0423279i
$932$	24.9482			0.817206
$933$	12.4063	−	4.51551i	0.406163	−	0.147831i
$934$	6.62954	−	37.5980i	0.216925	−	1.23024i
$935$		0			0
$936$	0.912078	+	0.765324i	0.0298122	+	0.0250154i
$937$	5.15136	+	29.2148i	0.168288	+	0.954406i	0.945610	+	0.325303i	$0.105466\pi$
$937$	5.15136	+	29.2148i	0.168288	+	0.954406i	−0.777322	+	0.629103i	$0.783423\pi$
$938$	−6.05689	−	10.4908i	−0.197765	−	0.342538i
$939$	0.239107	−	0.414145i	0.00780296	−	0.0135151i
$940$		0			0
$941$	−47.7023	−	17.3622i	−1.55505	−	0.565993i	−0.585456	−	0.810704i	$-0.699084\pi$
$941$	−47.7023	−	17.3622i	−1.55505	−	0.565993i	−0.969596	+	0.244712i	$0.921307\pi$
$942$	14.0398	−	24.3176i	0.457440	−	0.792309i
$943$	46.8590	+	81.1622i	1.52594	+	2.64301i
$944$	1.86552	+	10.5799i	0.0607175	+	0.344346i
$945$		0			0
$946$	11.7656	−	9.87250i	0.382532	−	0.320983i
$947$	−4.09416	+	23.2192i	−0.133042	+	0.754521i	0.843160	+	0.537662i	$0.180692\pi$
$947$	−4.09416	+	23.2192i	−0.133042	+	0.754521i	−0.976203	+	0.216859i	$0.930419\pi$
$948$	19.8861	−	7.23796i	0.645871	−	0.235078i
$949$	8.26335			0.268240
$950$		0			0
$951$	−34.5514			−1.12041
$952$	12.5883	−	4.58175i	0.407988	−	0.148496i
$953$	5.09946	−	28.9205i	0.165188	−	0.936825i	−0.783683	−	0.621161i	$-0.786661\pi$
$953$	5.09946	−	28.9205i	0.165188	−	0.936825i	0.948871	−	0.315665i	$-0.102227\pi$
$954$	−0.0836396	+	0.0701820i	−0.00270793	+	0.00227223i
$955$		0			0
$956$	1.84832	+	10.4823i	0.0597788	+	0.339022i
$957$	0.132847	+	0.230097i	0.00429432	+	0.00743798i
$958$	−14.6267	+	25.3342i	−0.472567	+	0.818509i
$959$	33.1697	+	12.0728i	1.07111	+	0.389851i
$960$		0			0
$961$	15.4998	−	26.8465i	0.499994	−	0.866015i
$962$	−0.569729	−	0.986800i	−0.0183688	−	0.0318157i
$963$	2.45429	+	13.9190i	0.0790885	+	0.448533i
$964$	−12.8701	−	10.7993i	−0.414517	−	0.347821i
$965$		0			0
$966$	4.69014	−	26.5991i	0.150903	−	0.855812i
$967$	23.1096	−	8.41119i	0.743153	−	0.270486i	0.0574316	−	0.998349i	$-0.481709\pi$
$967$	23.1096	−	8.41119i	0.743153	−	0.270486i	0.685722	+	0.727864i	$0.259487\pi$
$968$	−3.85226			−0.123816
$969$	19.9793	−	25.9922i	0.641829	−	0.834989i
$970$		0			0
$971$	−16.8954	+	6.14944i	−0.542200	+	0.197345i	−0.598578	−	0.801065i	$-0.704267\pi$
$971$	−16.8954	+	6.14944i	−0.542200	+	0.197345i	0.0563774	+	0.998410i	$0.482045\pi$
$972$	−2.04991	+	11.6256i	−0.0657508	+	0.372891i
$973$	−19.5682	+	16.4197i	−0.627329	+	0.526392i
$974$	−11.1655	−	9.36898i	−0.357766	−	0.300201i
$975$		0			0
$976$	3.99960	+	6.92751i	0.128024	+	0.221744i
$977$	−1.96534	+	3.40407i	−0.0628768	+	0.108906i	−0.895750	−	0.444558i	$-0.853361\pi$
$977$	−1.96534	+	3.40407i	−0.0628768	+	0.108906i	0.832873	+	0.553464i	$0.186694\pi$
$978$	−20.2872	−	7.38393i	−0.648713	−	0.236112i
$979$	2.16254	+	0.787100i	0.0691151	+	0.0251558i
$980$		0			0
$981$	−5.74012	−	9.94218i	−0.183268	−	0.317429i
$982$	−1.15669	−	6.55990i	−0.0369114	−	0.209335i
$983$	1.39988	+	1.17464i	0.0446492	+	0.0374651i	0.664839	−	0.746987i	$-0.268500\pi$
$983$	1.39988	+	1.17464i	0.0446492	+	0.0374651i	−0.620190	+	0.784452i	$0.712945\pi$
$984$	11.1800	−	9.38112i	0.356405	−	0.299059i
$985$		0			0
$986$	−0.396073	+	0.144159i	−0.0126135	+	0.00459096i
$987$	16.6204			0.529033
$988$	−0.180981	−	4.22693i	−0.00575776	−	0.134477i
$989$	49.1252			1.56209
$990$		0			0
$991$	−1.21061	+	6.86571i	−0.0384563	+	0.218096i	−0.997980	−	0.0635322i	$-0.979763\pi$
$991$	−1.21061	+	6.86571i	−0.0384563	+	0.218096i	0.959524	+	0.281628i	$0.0908746\pi$
$992$	−0.0151170	+	0.0126847i	−0.000479966	+	0.000402739i
$993$	13.7143	+	11.5077i	0.435211	+	0.365186i
$994$	4.27955	+	24.2705i	0.135739	+	0.769814i
$995$		0			0
$996$	3.90940	−	6.77129i	0.123874	−	0.214556i
$997$	−4.94588	−	1.80015i	−0.156638	−	0.0570115i	0.262511	−	0.964929i	$-0.415449\pi$
$997$	−4.94588	−	1.80015i	−0.156638	−	0.0570115i	−0.419149	+	0.907917i	$0.637672\pi$
$998$	−4.57058	−	1.66356i	−0.144679	−	0.0526589i
$999$	3.30381	−	5.72237i	0.104528	−	0.181048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.l.h.651.1		12
5.2	odd	4		950.2.u.e.499.2		24
5.3	odd	4		950.2.u.e.499.3		24
5.4	even	2		190.2.k.b.81.2	yes	12
19.4	even	9	inner	950.2.l.h.251.1		12
95.4	even	18		190.2.k.b.61.2	✓	12
95.23	odd	36		950.2.u.e.99.2		24
95.42	odd	36		950.2.u.e.99.3		24
95.59	odd	18		3610.2.a.be.1.3		6
95.74	even	18		3610.2.a.bc.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.61.2	✓	12	95.4	even	18
190.2.k.b.81.2	yes	12	5.4	even	2
950.2.l.h.251.1		12	19.4	even	9	inner
950.2.l.h.651.1		12	1.1	even	1	trivial
950.2.u.e.99.2		24	95.23	odd	36
950.2.u.e.99.3		24	95.42	odd	36
950.2.u.e.499.2		24	5.2	odd	4
950.2.u.e.499.3		24	5.3	odd	4
3610.2.a.bc.1.4		6	95.74	even	18
3610.2.a.be.1.3		6	95.59	odd	18

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.231240 + 1.31143i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(1.18594 + 2.05411i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.15270 + 0.419550i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.231240 + 1.31143i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(1.18594 + 2.05411i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.15270 + 0.419550i) q^{9} +(-1.33676 + 2.31534i) q^{11} +(0.665830 + 1.15325i) q^{12} +(-0.168545 - 0.955868i) q^{13} +(-1.81697 - 1.52462i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-5.30729 + 1.93170i) q^{17} -1.22668 q^{18} +(2.94212 + 3.21620i) q^{19} +(-2.96806 + 1.08028i) q^{21} +(0.464253 - 2.63291i) q^{22} +(6.55063 - 5.49663i) q^{23} +(-1.02011 - 0.855975i) q^{24} +(0.485307 + 0.840576i) q^{26} +(-2.81425 + 4.87443i) q^{27} +(2.22884 + 0.811231i) q^{28} +(-0.0701275 - 0.0255243i) q^{29} +(0.00986693 + 0.0170900i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-2.72729 - 2.28847i) q^{33} +(4.32654 - 3.63040i) q^{34} +(1.15270 - 0.419550i) q^{36} -1.17396 q^{37} +(-3.86469 - 2.01598i) q^{38} +1.29253 q^{39} +(-1.90311 + 10.7931i) q^{41} +(2.41958 - 2.03027i) q^{42} +(4.40077 + 3.69269i) q^{43} +(0.464253 + 2.63291i) q^{44} +(-4.27562 + 7.40559i) q^{46} +(-4.94471 - 1.79973i) q^{47} +(1.25135 + 0.455455i) q^{48} +(0.687089 - 1.19007i) q^{49} +(-1.30602 - 7.40682i) q^{51} +(-0.743533 - 0.623898i) q^{52} +(0.0681837 - 0.0572129i) q^{53} +(0.977379 - 5.54299i) q^{54} -2.37188 q^{56} +(-4.89815 + 3.11466i) q^{57} +0.0746282 q^{58} +(-10.0952 + 3.67436i) q^{59} +(-6.12774 + 5.14179i) q^{61} +(-0.0151170 - 0.0126847i) q^{62} +(0.505237 + 2.86534i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(3.34552 + 1.21767i) q^{66} +(4.79924 + 1.74678i) q^{67} +(-2.82395 + 4.89123i) q^{68} +(5.69367 + 9.86173i) q^{69} +(-7.95955 - 6.67886i) q^{71} +(-0.939693 + 0.788496i) q^{72} +(-1.47836 + 8.38420i) q^{73} +(1.10316 - 0.401517i) q^{74} +(4.32113 + 0.572595i) q^{76} -6.34129 q^{77} +(-1.21458 + 0.442070i) q^{78} +(2.75957 - 15.6503i) q^{79} +(-2.92262 - 2.45237i) q^{81} +(-1.90311 - 10.7931i) q^{82} +(-2.93574 - 5.08485i) q^{83} +(-1.57927 + 2.73538i) q^{84} +(-5.39835 - 1.96484i) q^{86} +(0.0496897 - 0.0860650i) q^{87} +(-1.33676 - 2.31534i) q^{88} +(-0.149473 - 0.847706i) q^{89} +(1.76357 - 1.47981i) q^{91} +(1.48491 - 8.42133i) q^{92} +(-0.0246940 + 0.00898788i) q^{93} +5.26205 q^{94} -1.33166 q^{96} +(-10.4367 + 3.79863i) q^{97} +(-0.238624 + 1.35330i) q^{98} +(-2.51229 + 2.10806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9}+O(q^{10}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9	\( 12 q - 6 q^{7} - 6 q^{8} + 18 q^{9} + 6 q^{11} - 6 q^{13} + 18 q^{17} + 12 q^{18} + 12 q^{21} + 6 q^{22} + 30 q^{23} - 6 q^{29} + 6 q^{31} + 24 q^{33} + 18 q^{36} - 36 q^{37} - 18 q^{38} - 36 q^{39} - 6 q^{41} + 30 q^{42} + 6 q^{44} - 12 q^{46} + 6 q^{47} - 18 q^{49} + 12 q^{52} + 12 q^{53} + 12 q^{56} + 18 q^{57} + 36 q^{58} - 24 q^{59} - 30 q^{61} + 6 q^{62} - 18 q^{63} - 6 q^{64} + 24 q^{66} - 12 q^{67} - 12 q^{68} + 6 q^{69} - 42 q^{71} - 6 q^{73} + 6 q^{74} + 18 q^{76} + 24 q^{77} - 48 q^{78} + 60 q^{79} + 18 q^{81} - 6 q^{82} - 24 q^{83} - 24 q^{84} - 36 q^{86} - 54 q^{87} + 6 q^{88} - 12 q^{89} + 24 q^{91} - 24 q^{92} - 6 q^{93} + 60 q^{94} - 30 q^{97} - 36 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^7 - 6 * q^8 + 18 * q^9 + 6 * q^11 - 6 * q^13 + 18 * q^17 + 12 * q^18 + 12 * q^21 + 6 * q^22 + 30 * q^23 - 6 * q^29 + 6 * q^31 + 24 * q^33 + 18 * q^36 - 36 * q^37 - 18 * q^38 - 36 * q^39 - 6 * q^41 + 30 * q^42 + 6 * q^44 - 12 * q^46 + 6 * q^47 - 18 * q^49 + 12 * q^52 + 12 * q^53 + 12 * q^56 + 18 * q^57 + 36 * q^58 - 24 * q^59 - 30 * q^61 + 6 * q^62 - 18 * q^63 - 6 * q^64 + 24 * q^66 - 12 * q^67 - 12 * q^68 + 6 * q^69 - 42 * q^71 - 6 * q^73 + 6 * q^74 + 18 * q^76 + 24 * q^77 - 48 * q^78 + 60 * q^79 + 18 * q^81 - 6 * q^82 - 24 * q^83 - 24 * q^84 - 36 * q^86 - 54 * q^87 + 6 * q^88 - 12 * q^89 + 24 * q^91 - 24 * q^92 - 6 * q^93 + 60 * q^94 - 30 * q^97 - 36 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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