LMFDB - Embedded newform 950.2.u.e.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.2
Character	$\chi$	$=$	950.499
Dual form			950.2.u.e.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 - 0.939693i) q^{2} +(1.31143 + 0.231240i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(-2.05411 + 1.18594i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.15270 - 0.419550i) q^{9} +O(q^{10})$	\(q+(-0.342020 - 0.939693i) q^{2} +(1.31143 + 0.231240i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(-2.05411 + 1.18594i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.15270 - 0.419550i) q^{9} +(-1.33676 + 2.31534i) q^{11} +(-1.15325 + 0.665830i) q^{12} +(-0.955868 + 0.168545i) q^{13} +(1.81697 + 1.52462i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-1.93170 - 5.30729i) q^{17} +1.22668i q^{18} +(-2.94212 - 3.21620i) q^{19} +(-2.96806 + 1.08028i) q^{21} +(2.63291 + 0.464253i) q^{22} +(-5.49663 - 6.55063i) q^{23} +(1.02011 + 0.855975i) q^{24} +(0.485307 + 0.840576i) q^{26} +(-4.87443 - 2.81425i) q^{27} +(0.811231 - 2.22884i) q^{28} +(0.0701275 + 0.0255243i) q^{29} +(0.00986693 + 0.0170900i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(-2.28847 + 2.72729i) q^{33} +(-4.32654 + 3.63040i) q^{34} +(1.15270 - 0.419550i) q^{36} -1.17396i q^{37} +(-2.01598 + 3.86469i) q^{38} -1.29253 q^{39} +(-1.90311 + 10.7931i) q^{41} +(2.03027 + 2.41958i) q^{42} +(3.69269 - 4.40077i) q^{43} +(-0.464253 - 2.63291i) q^{44} +(-4.27562 + 7.40559i) q^{46} +(1.79973 - 4.94471i) q^{47} +(0.455455 - 1.25135i) q^{48} +(-0.687089 + 1.19007i) q^{49} +(-1.30602 - 7.40682i) q^{51} +(0.623898 - 0.743533i) q^{52} +(-0.0572129 - 0.0681837i) q^{53} +(-0.977379 + 5.54299i) q^{54} -2.37188 q^{56} +(-3.11466 - 4.89815i) q^{57} -0.0746282i q^{58} +(10.0952 - 3.67436i) q^{59} +(-6.12774 + 5.14179i) q^{61} +(0.0126847 - 0.0151170i) q^{62} +(2.86534 - 0.505237i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.34552 + 1.21767i) q^{66} +(-1.74678 + 4.79924i) q^{67} +(4.89123 + 2.82395i) q^{68} +(-5.69367 - 9.86173i) q^{69} +(-7.95955 - 6.67886i) q^{71} +(-0.788496 - 0.939693i) q^{72} +(8.38420 + 1.47836i) q^{73} +(-1.10316 + 0.401517i) q^{74} +(4.32113 + 0.572595i) q^{76} -6.34129i q^{77} +(0.442070 + 1.21458i) q^{78} +(-2.75957 + 15.6503i) q^{79} +(-2.92262 - 2.45237i) q^{81} +(10.7931 - 1.90311i) q^{82} +(-5.08485 + 2.93574i) q^{83} +(1.57927 - 2.73538i) q^{84} +(-5.39835 - 1.96484i) q^{86} +(0.0860650 + 0.0496897i) q^{87} +(-2.31534 + 1.33676i) q^{88} +(0.149473 + 0.847706i) q^{89} +(1.76357 - 1.47981i) q^{91} +(8.42133 + 1.48491i) q^{92} +(0.00898788 + 0.0246940i) q^{93} -5.26205 q^{94} -1.33166 q^{96} +(-3.79863 - 10.4367i) q^{97} +(1.35330 + 0.238624i) q^{98} +(2.51229 - 2.10806i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 36 q^{9}+O(q^{10}) $ 24 * q - 36 * q^9	$ 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) $ 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * 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 $

$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$3$	1.31143	+	0.231240i	0.757154	+	0.133507i	0.538882	−	0.842381i	$-0.318847\pi$
$3$	1.31143	+	0.231240i	0.757154	+	0.133507i	0.218272	+	0.975888i	$0.429958\pi$
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$		0			0
$5$		0			0
$6$	−0.231240	−	1.31143i	−0.0944035	−	0.535389i
$7$	−2.05411	+	1.18594i	−0.776380	+	0.448243i	−0.835146	−	0.550028i	$-0.814617\pi$
$7$	−2.05411	+	1.18594i	−0.776380	+	0.448243i	0.0587655	+	0.998272i	$0.481284\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−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	$0.298716\pi$
$12$	−1.15325	+	0.665830i	−0.332915	+	0.192209i
$13$	−0.955868	+	0.168545i	−0.265110	+	0.0467460i	−0.304623	−	0.952473i	$-0.598530\pi$
$13$	−0.955868	+	0.168545i	−0.265110	+	0.0467460i	0.0395130	+	0.999219i	$0.487419\pi$
$14$	1.81697	+	1.52462i	0.485605	+	0.407471i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.93170	−	5.30729i	−0.468505	−	1.28721i	−0.918940	−	0.394398i	$-0.870953\pi$
$17$	−1.93170	−	5.30729i	−0.468505	−	1.28721i	0.450435	−	0.892809i	$-0.351269\pi$
$18$			1.22668i			0.289132i
$19$	−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
$22$	2.63291	+	0.464253i	0.561338	+	0.0989791i
$23$	−5.49663	−	6.55063i	−1.14613	−	1.36590i	−0.920054	−	0.391791i	$-0.871856\pi$
$23$	−5.49663	−	6.55063i	−1.14613	−	1.36590i	−0.226073	−	0.974110i	$-0.572589\pi$
$24$	1.02011	+	0.855975i	0.208229	+	0.174725i
$25$		0			0
$26$	0.485307	+	0.840576i	0.0951765	+	0.164850i
$27$	−4.87443	−	2.81425i	−0.938084	−	0.541603i
$28$	0.811231	−	2.22884i	0.153308	−	0.421211i
$29$	0.0701275	+	0.0255243i	0.0130224	+	0.00473975i	0.348523	−	0.937300i	$-0.386683\pi$
$29$	0.0701275	+	0.0255243i	0.0130224	+	0.00473975i	−0.335501	+	0.942040i	$0.608906\pi$
$30$		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	$0.832769\pi$
$32$	−0.984808	+	0.173648i	−0.174091	+	0.0306970i
$33$	−2.28847	+	2.72729i	−0.398372	+	0.474761i
$34$	−4.32654	+	3.63040i	−0.741996	+	0.622609i
$35$		0			0
$36$	1.15270	−	0.419550i	0.192117	−	0.0699250i
$37$		−	1.17396i		−	0.192997i	−0.995333	−	0.0964987i	$-0.969236\pi$
$37$		−	1.17396i		−	0.192997i	0.995333	−	0.0964987i	$-0.0307644\pi$
$38$	−2.01598	+	3.86469i	−0.327034	+	0.626936i
$39$	−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	$0.728621\pi$
$42$	2.03027	+	2.41958i	0.313278	+	0.373350i
$43$	3.69269	−	4.40077i	0.563130	−	0.671112i	−0.407076	−	0.913394i	$-0.633452\pi$
$43$	3.69269	−	4.40077i	0.563130	−	0.671112i	0.970206	+	0.242283i	$0.0778961\pi$
$44$	−0.464253	−	2.63291i	−0.0699888	−	0.396926i
$45$		0			0
$46$	−4.27562	+	7.40559i	−0.630406	+	1.09190i
$47$	1.79973	−	4.94471i	0.262517	−	0.721260i	−0.736479	−	0.676461i	$-0.763513\pi$
$47$	1.79973	−	4.94471i	0.262517	−	0.721260i	0.998996	−	0.0447996i	$-0.0142649\pi$
$48$	0.455455	−	1.25135i	0.0657392	−	0.180617i
$49$	−0.687089	+	1.19007i	−0.0981556	+	0.170010i
$50$		0			0
$51$	−1.30602	−	7.40682i	−0.182880	−	1.03716i
$52$	0.623898	−	0.743533i	0.0865191	−	0.103109i
$53$	−0.0572129	−	0.0681837i	−0.00785879	−	0.00936575i	0.762101	−	0.647458i	$-0.224168\pi$
$53$	−0.0572129	−	0.0681837i	−0.00785879	−	0.00936575i	−0.769960	+	0.638093i	$0.779724\pi$
$54$	−0.977379	+	5.54299i	−0.133004	+	0.754306i
$55$		0			0
$56$	−2.37188			−0.316956
$57$	−3.11466	−	4.89815i	−0.412547	−	0.648776i
$58$		−	0.0746282i		−	0.00979916i
$59$	10.0952	−	3.67436i	1.31429	−	0.478361i	0.412663	−	0.910884i	$-0.364599\pi$
$59$	10.0952	−	3.67436i	1.31429	−	0.478361i	0.901623	+	0.432523i	$0.142377\pi$
$60$		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	$0.448909\pi$
$62$	0.0126847	−	0.0151170i	0.00161096	−	0.00191986i
$63$	2.86534	−	0.505237i	0.360999	−	0.0636539i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	3.34552	+	1.21767i	0.411805	+	0.149885i
$67$	−1.74678	+	4.79924i	−0.213403	+	0.586321i	−0.999495	−	0.0317896i	$-0.989879\pi$
$67$	−1.74678	+	4.79924i	−0.213403	+	0.586321i	0.786091	+	0.618111i	$0.212102\pi$
$68$	4.89123	+	2.82395i	0.593148	+	0.342454i
$69$	−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	$0.933697\pi$
$72$	−0.788496	−	0.939693i	−0.0929251	−	0.110744i
$73$	8.38420	+	1.47836i	0.981296	+	0.173029i	0.641210	−	0.767365i	$-0.278433\pi$
$73$	8.38420	+	1.47836i	0.981296	+	0.173029i	0.340086	+	0.940394i	$0.389544\pi$
$74$	−1.10316	+	0.401517i	−0.128240	+	0.0466754i
$75$		0			0
$76$	4.32113	+	0.572595i	0.495667	+	0.0656811i
$77$		−	6.34129i		−	0.722657i
$78$	0.442070	+	1.21458i	0.0500546	+	0.137524i
$79$	−2.75957	+	15.6503i	−0.310476	+	1.76079i	0.286063	+	0.958211i	$0.407653\pi$
$79$	−2.75957	+	15.6503i	−0.310476	+	1.76079i	−0.596539	+	0.802584i	$0.703458\pi$
$80$		0			0
$81$	−2.92262	−	2.45237i	−0.324735	−	0.272485i
$82$	10.7931	−	1.90311i	1.19190	−	0.210164i
$83$	−5.08485	+	2.93574i	−0.558134	+	0.322239i	−0.752396	−	0.658711i	$-0.771102\pi$
$83$	−5.08485	+	2.93574i	−0.558134	+	0.322239i	0.194262	+	0.980950i	$0.437769\pi$
$84$	1.57927	−	2.73538i	0.172312	−	0.298454i
$85$		0			0
$86$	−5.39835	−	1.96484i	−0.582119	−	0.211874i
$87$	0.0860650	+	0.0496897i	0.00922714	+	0.00532729i
$88$	−2.31534	+	1.33676i	−0.246816	+	0.142499i
$89$	0.149473	+	0.847706i	0.0158442	+	0.0898567i	0.991704	−	0.128539i	$-0.0410288\pi$
$89$	0.149473	+	0.847706i	0.0158442	+	0.0898567i	−0.975860	+	0.218396i	$0.929918\pi$
$90$		0			0
$91$	1.76357	−	1.47981i	0.184873	−	0.155127i
$92$	8.42133	+	1.48491i	0.877984	+	0.154812i
$93$	0.00898788	+	0.0246940i	0.000932000	+	0.00256065i
$94$	−5.26205			−0.542739
$95$		0			0
$96$	−1.33166			−0.135912
$97$	−3.79863	−	10.4367i	−0.385692	−	1.05968i	−0.968920	−	0.247373i	$-0.920433\pi$
$97$	−3.79863	−	10.4367i	−0.385692	−	1.05968i	0.583228	−	0.812309i	$-0.301789\pi$
$98$	1.35330	+	0.238624i	0.136704	+	0.0241046i
$99$	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	$0.875604\pi$
$102$	−6.51345	+	3.76054i	−0.644928	+	0.372349i
$103$	−0.0151012	−	0.00871870i	−0.00148797	−	0.000859079i	0.499256	−	0.866455i	$-0.333607\pi$
$103$	−0.0151012	−	0.00871870i	−0.00148797	−	0.000859079i	−0.500744	+	0.865596i	$0.666940\pi$
$104$	−0.912078	−	0.331969i	−0.0894366	−	0.0325523i
$105$		0			0
$106$	−0.0445037	+	0.0770827i	−0.00432258	+	0.00748693i
$107$	−9.97826	+	5.76095i	−0.964635	+	0.556932i	−0.897597	−	0.440818i	$-0.854688\pi$
$107$	−9.97826	+	5.76095i	−0.964635	+	0.556932i	−0.0670387	+	0.997750i	$0.521355\pi$
$108$	5.54299	−	0.977379i	0.533375	−	0.0940484i
$109$	7.16924	+	6.01570i	0.686688	+	0.576200i	0.917952	−	0.396691i	$-0.129842\pi$
$109$	7.16924	+	6.01570i	0.686688	+	0.576200i	−0.231264	+	0.972891i	$0.574286\pi$
$110$		0			0
$111$	0.271466	−	1.53956i	0.0257664	−	0.146129i
$112$	0.811231	+	2.22884i	0.0766541	+	0.210606i
$113$			9.03320i			0.849772i	0.905247	+	0.424886i	$0.139686\pi$
$113$			9.03320i			0.849772i	−0.905247	+	0.424886i	$0.860314\pi$
$114$	−3.53748	+	4.60209i	−0.331315	+	0.431026i
$115$		0			0
$116$	−0.0701275	+	0.0255243i	−0.00651118	+	0.00236987i
$117$	1.17255	+	0.206751i	0.108402	+	0.0191142i
$118$	−6.90554	−	8.22970i	−0.635706	−	0.757605i
$119$	10.2620	+	8.61088i	0.940721	+	0.789358i
$120$		0			0
$121$	1.92613	+	3.33615i	0.175103	+	0.303287i
$122$	6.92751	+	3.99960i	0.627188	+	0.362107i
$123$	−4.99159	+	13.7143i	−0.450077	+	1.23658i
$124$	−0.0185438	−	0.00674938i	−0.00166528	−	0.000606112i
$125$		0			0
$126$	−1.45477	−	2.51974i	−0.129601	−	0.224476i
$127$	−9.23057	+	1.62760i	−0.819081	+	0.144426i	−0.567461	−	0.823400i	$-0.692074\pi$
$127$	−9.23057	+	1.62760i	−0.819081	+	0.144426i	−0.251620	+	0.967826i	$0.580963\pi$
$128$	0.642788	−	0.766044i	0.0568149	−	0.0677094i
$129$	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	$0.300900\pi$
$132$		−	3.56023i		−	0.309878i
$133$	9.85766	+	3.11725i	0.854767	+	0.270300i
$134$	5.10725			0.441199
$135$		0			0
$136$	0.980748	−	5.56210i	0.0840984	−	0.476946i
$137$	9.56600	+	11.4003i	0.817279	+	0.973995i	0.999958	−	0.00917780i	$-0.00292142\pi$
$137$	9.56600	+	11.4003i	0.817279	+	0.973995i	−0.182679	+	0.983173i	$0.558477\pi$
$138$	−7.31965	+	8.72322i	−0.623090	+	0.742569i
$139$	−1.87014	−	10.6061i	−0.158624	−	0.899599i	−0.955398	−	0.295322i	$-0.904573\pi$
$139$	−1.87014	−	10.6061i	−0.158624	−	0.899599i	0.796774	−	0.604277i	$-0.206538\pi$
$140$		0			0
$141$	3.50363	−	6.06847i	0.295059	−	0.511057i
$142$	−3.55375	+	9.76384i	−0.298224	+	0.819363i
$143$	0.887529	−	2.43846i	0.0742189	−	0.203915i
$144$	−0.613341	+	1.06234i	−0.0511117	+	0.0885281i
$145$		0			0
$146$	−1.47836	−	8.38420i	−0.122350	−	0.693881i
$147$	−1.17626	+	1.40181i	−0.0970164	+	0.115620i
$148$	0.754605	+	0.899304i	0.0620282	+	0.0739223i
$149$	2.81132	−	15.9438i	0.230313	−	1.30617i	−0.621951	−	0.783056i	$-0.713660\pi$
$149$	2.81132	−	15.9438i	0.230313	−	1.30617i	0.852264	−	0.523112i	$-0.175229\pi$
$150$		0			0
$151$	6.11979			0.498022			0.249011	−	0.968501i	$-0.419895\pi$
$151$	6.11979			0.498022			0.249011	+	0.968501i	$0.419895\pi$
$152$	−0.939849	−	4.25637i	−0.0762318	−	0.345237i
$153$			6.92818i			0.560110i
$154$	−5.95886	+	2.16885i	−0.480179	+	0.174771i
$155$		0			0
$156$	0.990133	−	0.830820i	0.0792741	−	0.0665189i
$157$	−13.5539	+	16.1529i	−1.08172	+	1.28914i	−0.126910	+	0.991914i	$0.540506\pi$
$157$	−13.5539	+	16.1529i	−1.08172	+	1.28914i	−0.954807	+	0.297226i	$0.903939\pi$
$158$	15.6503	−	2.75957i	1.24507	−	0.219539i
$159$	−0.0592638	−	0.102648i	−0.00469993	−	0.00814051i
$160$		0			0
$161$	19.0594	+	6.93704i	1.50209	+	0.546715i
$162$	−1.30488	+	3.58512i	−0.102521	+	0.281674i
$163$	−14.0402	−	8.10611i	−1.09971	−	0.634920i	−0.163567	−	0.986532i	$-0.552300\pi$
$163$	−14.0402	−	8.10611i	−1.09971	−	0.634920i	−0.936146	+	0.351612i	$0.885633\pi$
$164$	−5.47979	−	9.49128i	−0.427900	−	0.741144i
$165$		0			0
$166$	4.49781	+	3.77411i	0.349098	+	0.292928i
$167$	−0.300481	−	0.358099i	−0.0232519	−	0.0277106i	0.754293	−	0.656538i	$-0.227980\pi$
$167$	−0.300481	−	0.358099i	−0.0232519	−	0.0277106i	−0.777545	+	0.628827i	$0.783535\pi$
$168$	−3.11055	−	0.548475i	−0.239984	−	0.0423157i
$169$	−11.3307	+	4.12405i	−0.871595	+	0.317234i
$170$		0			0
$171$	2.04203	+	4.94169i	0.156158	+	0.377900i
$172$			5.74480i			0.438037i
$173$	−8.79654	−	24.1683i	−0.668788	−	1.83748i	−0.531721	−	0.846919i	$-0.678455\pi$
$173$	−8.79654	−	24.1683i	−0.668788	−	1.83748i	−0.137067	−	0.990562i	$-0.543768\pi$
$174$	0.0172570	−	0.0978695i	0.00130825	−	0.00741947i
$175$		0			0
$176$	2.04804	+	1.71851i	0.154377	+	0.129538i
$177$	14.0888	−	2.48424i	1.05898	−	0.186727i
$178$	0.745460	−	0.430392i	0.0558746	−	0.0322592i
$179$	7.08189	−	12.2662i	0.529325	−	0.916818i	−0.470090	−	0.882619i	$-0.655779\pi$
$179$	7.08189	−	12.2662i	0.529325	−	0.916818i	0.999415	−	0.0341995i	$-0.0108882\pi$
$180$		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	$0.704654\pi$
$182$	−1.99375	−	1.15109i	−0.147786	−	0.0853245i
$183$	−9.22509	+	5.32611i	−0.681938	+	0.393717i
$184$	−1.48491	−	8.42133i	−0.109469	−	0.620829i
$185$		0			0
$186$	0.0201307	−	0.0168917i	0.00147606	−	0.00123856i
$187$	14.8704	+	2.62205i	1.08743	+	0.191744i
$188$	1.79973	+	4.94471i	0.131259	+	0.360630i
$189$	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	$0.503041\pi$
$192$	0.455455	+	1.25135i	0.0328696	+	0.0903085i
$193$	−3.07060	−	0.541429i	−0.221027	−	0.0389729i	0.0620381	−	0.998074i	$-0.480240\pi$
$193$	−3.07060	−	0.541429i	−0.221027	−	0.0389729i	−0.283065	+	0.959101i	$0.591351\pi$
$194$	−8.50804	+	7.13909i	−0.610841	+	0.512557i
$195$		0			0
$196$	−0.238624	−	1.35330i	−0.0170445	−	0.0966644i
$197$	18.1672	−	10.4888i	1.29436	−	0.747298i	0.314934	−	0.949113i	$-0.398018\pi$
$197$	18.1672	−	10.4888i	1.29436	−	0.747298i	0.979424	+	0.201816i	$0.0646842\pi$
$198$	−2.84019	−	1.63978i	−0.201843	−	0.116534i
$199$	−20.6330	−	7.50979i	−1.46263	−	0.532355i	−0.516544	−	0.856260i	$-0.672782\pi$
$199$	−20.6330	−	7.50979i	−1.46263	−	0.532355i	−0.946090	+	0.323905i	$0.895004\pi$
$200$		0			0
$201$	−3.40056	+	5.88994i	−0.239857	+	0.415444i
$202$	3.73526	−	2.15655i	0.262812	−	0.151735i
$203$	−0.174320	+	0.0307373i	−0.0122349	+	0.00215734i
$204$	5.76149	+	4.83446i	0.403385	+	0.338480i
$205$		0			0
$206$	−0.00302797	+	0.0171725i	−0.000210969	+	0.00119646i
$207$	3.58767	+	9.85705i	0.249360	+	0.685112i
$208$			0.970613i			0.0672999i
$209$	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	$0.228677\pi$
$212$	0.0876552	+	0.0154560i	0.00602019	+	0.00106152i
$213$	−8.89397	−	10.5994i	−0.609405	−	0.726260i
$214$	8.82629	+	7.40614i	0.603353	+	0.506273i
$215$		0			0
$216$	−2.81425	−	4.87443i	−0.191486	−	0.331663i
$217$	−0.0405355	−	0.0234032i	−0.00275173	−	0.00158871i
$218$	3.20089	−	8.79437i	0.216792	−	0.595630i
$219$	10.6534	+	3.87753i	0.719892	+	0.262019i
$220$		0			0
$221$	2.74096	+	4.74749i	0.184377	+	0.319351i
$222$	−1.53956	+	0.271466i	−0.103329	+	0.0182196i
$223$	−10.1108	+	12.0495i	−0.677067	+	0.806897i	−0.989727	−	0.142968i	$-0.954335\pi$
$223$	−10.1108	+	12.0495i	−0.677067	+	0.806897i	0.312661	+	0.949865i	$0.398780\pi$
$224$	1.81697	−	1.52462i	0.121401	−	0.101868i
$225$		0			0
$226$	8.48843	−	3.08954i	0.564642	−	0.205513i
$227$			8.01180i			0.531762i	0.964006	+	0.265881i	$0.0856628\pi$
$227$			8.01180i			0.531762i	−0.964006	+	0.265881i	$0.914337\pi$
$228$	5.53444	+	1.75014i	0.366528	+	0.115906i
$229$	−19.8826			−1.31388			−0.656939	−	0.753944i	$-0.728149\pi$
$229$	−19.8826			−1.31388			−0.656939	+	0.753944i	$0.728149\pi$
$230$		0			0
$231$	1.46636	−	8.31615i	0.0964795	−	0.547162i
$232$	0.0479701	+	0.0571685i	0.00314939	+	0.00375330i
$233$	16.0364	−	19.1114i	1.05058	−	1.25203i	0.0837839	−	0.996484i	$-0.473299\pi$
$233$	16.0364	−	19.1114i	1.05058	−	1.25203i	0.966796	−	0.255549i	$-0.0822561\pi$
$234$	−0.206751	−	1.17255i	−0.0135158	−	0.0766517i
$235$		0			0
$236$	−5.37155	+	9.30380i	−0.349658	+	0.605626i
$237$	−7.23796	+	19.8861i	−0.470156	+	1.29174i
$238$	4.58175	−	12.5883i	0.296991	−	0.815976i
$239$	5.32201	−	9.21799i	0.344252	−	0.596262i	−0.640965	−	0.767570i	$-0.721466\pi$
$239$	5.32201	−	9.21799i	0.344252	−	0.596262i	0.985218	+	0.171307i	$0.0547991\pi$
$240$		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	$-0.237553\pi$
$242$	2.47618	−	2.95100i	0.159175	−	0.189698i
$243$	7.58808	+	9.04312i	0.486775	+	0.580116i
$244$	1.38905	−	7.87768i	0.0889246	−	0.504317i
$245$		0			0
$246$	14.5944			0.930507
$247$	3.35435	+	2.57838i	0.213432	+	0.164058i
$248$			0.0197339i			0.00125310i
$249$	−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	$0.0237359\pi$
$252$	−1.87022	+	2.22884i	−0.117813	+	0.140404i
$253$	22.5146	−	3.96994i	1.41548	−	0.249588i
$254$	4.68648	+	8.11723i	0.294056	+	0.509320i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	7.71712	−	21.2026i	0.481380	−	1.32258i	−0.426930	−	0.904285i	$-0.640405\pi$
$257$	7.71712	−	21.2026i	0.481380	−	1.32258i	0.908310	−	0.418297i	$-0.137373\pi$
$258$	−6.62520	−	3.82506i	−0.412467	−	0.238138i
$259$	1.39224	+	2.41144i	0.0865099	+	0.149839i
$260$		0			0
$261$	−0.0701275	−	0.0588440i	−0.00434079	−	0.00364235i
$262$	−4.01574	−	4.78578i	−0.248093	−	0.295666i
$263$	−8.31518	−	1.46619i	−0.512736	−	0.0904091i	−0.0887068	−	0.996058i	$-0.528273\pi$
$263$	−8.31518	−	1.46619i	−0.512736	−	0.0904091i	−0.424029	+	0.905649i	$0.639385\pi$
$264$	−3.34552	+	1.21767i	−0.205902	+	0.0749424i
$265$		0			0
$266$	−0.442261	−	10.3293i	−0.0271168	−	0.633332i
$267$			1.14627i			0.0701506i
$268$	−1.74678	−	4.79924i	−0.106702	−	0.293160i
$269$	−4.57571	+	25.9501i	−0.278986	+	1.58221i	0.447024	+	0.894522i	$0.352484\pi$
$269$	−4.57571	+	25.9501i	−0.278986	+	1.58221i	−0.726010	+	0.687684i	$0.758627\pi$
$270$		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	$0.728103\pi$
$272$	−5.56210	+	0.980748i	−0.337252	+	0.0594666i
$273$	2.65499	−	1.53286i	0.160687	−	0.0927729i
$274$	7.44103	−	12.8882i	0.449529	−	0.778607i
$275$		0			0
$276$	10.7006	+	3.89470i	0.644101	+	0.234434i
$277$	5.89679	+	3.40451i	0.354304	+	0.204557i	0.666579	−	0.745434i	$-0.267758\pi$
$277$	5.89679	+	3.40451i	0.354304	+	0.204557i	−0.312275	+	0.949992i	$0.601091\pi$
$278$	−9.32686	+	5.38487i	−0.559388	+	0.322963i
$279$	−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	$0.0170546\pi$
$282$	−6.90081	−	1.21680i	−0.410937	−	0.0724593i
$283$	−11.0599	−	30.3868i	−0.657443	−	1.80631i	−0.588208	−	0.808710i	$-0.700166\pi$
$283$	−11.0599	−	30.3868i	−0.657443	−	1.80631i	−0.0692348	−	0.997600i	$-0.522056\pi$
$284$	10.3905			0.616560
$285$		0			0
$286$	−2.59496			−0.153443
$287$	−8.89076	−	24.4272i	−0.524805	−	1.44189i
$288$	1.20805	+	0.213011i	0.0711848	+	0.0125518i
$289$	−11.4131	+	9.57676i	−0.671361	+	0.563339i
$290$		0			0
$291$	−2.56826	−	14.5653i	−0.150554	−	0.853834i
$292$	−7.37294	+	4.25677i	−0.431469	+	0.249109i
$293$	23.1715	+	13.3781i	1.35369	+	0.781556i	0.988765	−	0.149479i	$-0.0477597\pi$
$293$	23.1715	+	13.3781i	1.35369	+	0.781556i	0.364930	+	0.931035i	$0.381093\pi$
$294$	1.71958	+	0.625876i	0.100288	+	0.0365018i
$295$		0			0
$296$	0.586979	−	1.01668i	0.0341175	−	0.0590932i
$297$	13.0319	−	7.52397i	0.756188	−	0.436585i
$298$	−15.9438	+	2.81132i	−0.923600	+	0.162856i
$299$	6.35813	+	5.33511i	0.367700	+	0.308537i
$300$		0			0
$301$	−2.36613	+	13.4190i	−0.136381	+	0.773457i
$302$	−2.09309	−	5.75072i	−0.120444	−	0.330917i
$303$			5.74359i			0.329961i
$304$	−3.67823	+	2.33893i	−0.210961	+	0.134147i
$305$		0			0
$306$	6.51036	−	2.36958i	0.372172	−	0.135460i
$307$	11.5754	+	2.04105i	0.660640	+	0.116489i	0.493909	−	0.869514i	$-0.335568\pi$
$307$	11.5754	+	2.04105i	0.660640	+	0.116489i	0.166731	+	0.986002i	$0.446679\pi$
$308$	4.07610	+	4.85771i	0.232257	+	0.276794i
$309$	−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	$0.924031\pi$
$312$	−1.11936	−	0.646263i	−0.0633713	−	0.0365875i
$313$	−0.122823	+	0.337454i	−0.00694238	+	0.0190740i	−0.943115	−	0.332466i	$-0.892119\pi$
$313$	−0.122823	+	0.337454i	−0.00694238	+	0.0190740i	0.936173	+	0.351540i	$0.114342\pi$
$314$	19.8144	+	7.21187i	1.11819	+	0.406989i
$315$		0			0
$316$	−7.94586	−	13.7626i	−0.446990	−	0.774209i
$317$	−25.5519	+	4.50550i	−1.43514	+	0.253054i	−0.836501	−	0.547965i	$-0.815403\pi$
$317$	−25.5519	+	4.50550i	−1.43514	+	0.253054i	−0.598639	+	0.801019i	$0.704292\pi$
$318$	−0.0761881	+	0.0907975i	−0.00427242	+	0.00509167i
$319$	−0.152841	+	0.128249i	−0.00855748	+	0.00718058i
$320$		0			0
$321$	−14.4180	+	5.24770i	−0.804732	+	0.292898i
$322$		−	20.2825i		−	1.13030i
$323$	−11.3860	+	21.8274i	−0.633536	+	1.21451i
$324$	3.81521			0.211956
$325$		0			0
$326$	−2.81522	+	15.9659i	−0.155921	+	0.884271i
$327$	8.01087	+	9.54699i	0.443002	+	0.527950i
$328$	−7.04468	+	8.39553i	−0.388978	+	0.463565i
$329$	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	$0.0462047\pi$
$332$	2.00816	−	5.51738i	0.110212	−	0.302806i
$333$	−0.492534	+	1.35323i	−0.0269907	+	0.0741563i
$334$	−0.233733	+	0.404837i	−0.0127893	+	0.0221517i
$335$		0			0
$336$	0.548475	+	3.11055i	0.0299217	+	0.169695i
$337$	−10.5517	+	12.5750i	−0.574786	+	0.685004i	−0.972606	−	0.232460i	$-0.925323\pi$
$337$	−10.5517	+	12.5750i	−0.574786	+	0.685004i	0.397820	+	0.917464i	$0.369767\pi$
$338$	7.75068	+	9.23689i	0.421581	+	0.502421i
$339$	−2.08884	+	11.8464i	−0.113450	+	0.643408i
$340$		0			0
$341$	−0.0527590			−0.00285706
$342$	3.94525	−	3.60904i	0.213335	−	0.195155i
$343$		−	19.8626i		−	1.07248i
$344$	5.39835	−	1.96484i	0.291059	−	0.105937i
$345$		0			0
$346$	−19.7022	+	16.5321i	−1.05920	+	0.888770i
$347$	4.32095	−	5.14951i	0.231961	−	0.276440i	−0.637491	−	0.770458i	$-0.720028\pi$
$347$	4.32095	−	5.14951i	0.231961	−	0.276440i	0.869452	+	0.494018i	$0.164472\pi$
$348$	−0.0978695	+	0.0172570i	−0.00524636	+	0.000925075i
$349$	−9.98033	−	17.2864i	−0.534235	−	0.925322i	−0.999200	−	0.0399930i	$-0.987266\pi$
$349$	−9.98033	−	17.2864i	−0.534235	−	0.925322i	0.464965	−	0.885329i	$-0.346067\pi$
$350$		0			0
$351$	5.13363	+	1.86849i	0.274013	+	0.0997326i
$352$	0.914400	−	2.51229i	0.0487377	−	0.133906i
$353$	21.9749	+	12.6872i	1.16961	+	0.675273i	0.953588	−	0.301116i	$-0.0973591\pi$
$353$	21.9749	+	12.6872i	1.16961	+	0.675273i	0.216020	+	0.976389i	$0.430692\pi$
$354$	−7.15308	−	12.3895i	−0.380182	−	0.658495i
$355$		0			0
$356$	−0.659398	−	0.553301i	−0.0349480	−	0.0293249i
$357$	11.4668	+	13.6656i	0.606886	+	0.723258i
$358$	−13.9486	−	2.45951i	−0.737206	−	0.129989i
$359$	−13.6119	+	4.95433i	−0.718409	+	0.261480i	−0.675250	−	0.737589i	$-0.735964\pi$
$359$	−13.6119	+	4.95433i	−0.718409	+	0.261480i	−0.0431590	+	0.999068i	$0.513742\pi$
$360$		0			0
$361$	−1.68788	+	18.9249i	−0.0888358	+	0.996046i
$362$			7.79400i			0.409643i
$363$	1.75453	+	4.82053i	0.0920889	+	0.253012i
$364$	−0.399769	+	2.26720i	−0.0209536	+	0.118834i
$365$		0			0
$366$	8.16007	+	6.84711i	0.426534	+	0.357904i
$367$	2.09575	−	0.369537i	0.109397	−	0.0192897i	−0.118682	−	0.992932i	$-0.537867\pi$
$367$	2.09575	−	0.369537i	0.109397	−	0.0192897i	0.228079	+	0.973643i	$0.426756\pi$
$368$	−7.40559	+	4.27562i	−0.386043	+	0.222882i
$369$	6.72196	−	11.6428i	0.349931	−	0.606099i
$370$		0			0
$371$	0.198383	+	0.0722056i	0.0102995	+	0.00374873i
$372$	−0.0227581	−	0.0131394i	−0.00117995	−	0.000681246i
$373$	23.8796	−	13.7869i	1.23644	−	0.713859i	0.268075	−	0.963398i	$-0.413613\pi$
$373$	23.8796	−	13.7869i	1.23644	−	0.713859i	0.968365	+	0.249539i	$0.0802792\pi$
$374$	−2.62205	−	14.8704i	−0.135583	−	0.768931i
$375$		0			0
$376$	4.03097	−	3.38238i	0.207881	−	0.174433i
$377$	−0.0713346	−	0.0125782i	−0.00367392	−	0.000647811i
$378$	−4.56602	−	12.5450i	−0.234851	−	0.645247i
$379$	2.88506			0.148195			0.0740977	−	0.997251i	$-0.476392\pi$
$379$	2.88506			0.148195			0.0740977	+	0.997251i	$0.476392\pi$
$380$		0			0
$381$	−12.4816			−0.639452
$382$	0.0903130	+	0.248133i	0.00462081	+	0.0126956i
$383$	−12.2562	−	2.16110i	−0.626262	−	0.110427i	−0.148494	−	0.988913i	$-0.547443\pi$
$383$	−12.2562	−	2.16110i	−0.626262	−	0.110427i	−0.477767	+	0.878486i	$0.658554\pi$
$384$	1.02011	−	0.855975i	0.0520573	−	0.0436813i
$385$		0			0
$386$	0.541429	+	3.07060i	0.0275580	+	0.156289i
$387$	−6.10292	+	3.52352i	−0.310229	+	0.179111i
$388$	9.61847	+	5.55323i	0.488304	+	0.281922i
$389$	29.1597	+	10.6132i	1.47845	+	0.538113i	0.950381	−	0.311087i	$-0.100693\pi$
$389$	29.1597	+	10.6132i	1.47845	+	0.538113i	0.528072	+	0.849200i	$0.322915\pi$
$390$		0			0
$391$	−24.1483	+	41.8261i	−1.22123	+	2.11524i
$392$	−1.19007	+	0.687089i	−0.0601078	+	0.0347032i
$393$	8.19301	−	1.44465i	0.413282	−	0.0728729i
$394$	−16.0698	−	13.4842i	−0.809585	−	0.679323i
$395$		0			0
$396$	−0.569490	+	3.22974i	−0.0286180	+	0.162301i
$397$	2.69088	+	7.39313i	0.135051	+	0.371050i	0.988722	−	0.149763i	$-0.0478510\pi$
$397$	2.69088	+	7.39313i	0.135051	+	0.371050i	−0.853671	+	0.520813i	$0.825629\pi$
$398$			21.9572i			1.10061i
$399$	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	$0.649138\pi$
$402$	6.69779	+	1.18100i	0.334056	+	0.0589030i
$403$	−0.0123119	−	0.0146728i	−0.000613301	−	0.000730903i
$404$	−3.30403	−	2.77241i	−0.164382	−	0.137933i
$405$		0			0
$406$	0.0885046	+	0.153294i	0.00439241	+	0.00760787i
$407$	2.71811	+	1.56930i	0.134732	+	0.0777875i
$408$	2.57236	−	7.06751i	0.127351	−	0.349894i
$409$	13.3081	+	4.84375i	0.658043	+	0.239508i	0.649391	−	0.760455i	$-0.275024\pi$
$409$	13.3081	+	4.84375i	0.658043	+	0.239508i	0.00865164	+	0.999963i	$0.497246\pi$
$410$		0			0
$411$	9.90892	+	17.1628i	0.488771	+	0.846576i
$412$	0.0171725	−	0.00302797i	0.000846028	−	0.000149177i
$413$	−16.3791	+	19.5199i	−0.805964	+	0.960510i
$414$	8.03554	−	6.74262i	0.394925	−	0.331382i
$415$		0			0
$416$	0.912078	−	0.331969i	0.0447183	−	0.0162761i
$417$		−	14.3416i		−	0.702312i
$418$	−6.25320	−	9.83385i	−0.305854	−	0.480989i
$419$	−30.0769			−1.46935			−0.734677	−	0.678417i	$-0.762666\pi$
$419$	−30.0769			−1.46935			−0.734677	+	0.678417i	$0.762666\pi$
$420$		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	$0.947882\pi$
$422$	−9.00719	−	10.7343i	−0.438463	−	0.522540i
$423$	−4.14911	+	4.94471i	−0.201736	+	0.240420i
$424$	−0.0154560	−	0.0876552i	−0.000750609	−	0.00425691i
$425$		0			0
$426$	−6.91828	+	11.9828i	−0.335192	+	0.580569i
$427$	6.48920	−	17.8289i	0.314035	−	0.862803i
$428$	3.94072	−	10.8271i	0.190482	−	0.523345i
$429$	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	$-0.308041\pi$
$432$	−3.61793	+	4.31168i	−0.174068	+	0.207446i
$433$	−0.621064	−	0.740155i	−0.0298464	−	0.0355696i	0.750915	−	0.660399i	$-0.229613\pi$
$433$	−0.621064	−	0.740155i	−0.0298464	−	0.0355696i	−0.780761	+	0.624830i	$0.785168\pi$
$434$	−0.00812785	+	0.0460953i	−0.000390149	+	0.00221265i
$435$		0			0
$436$	−9.35877			−0.448204
$437$	−4.89640	+	36.9510i	−0.234226	+	1.76761i
$438$		−	11.3371i		−	0.541709i
$439$	−22.1502	+	8.06200i	−1.05717	+	0.384778i	−0.811364	−	0.584541i	$-0.801275\pi$
$439$	−22.1502	+	8.06200i	−1.05717	+	0.384778i	−0.245805	+	0.969319i	$0.579052\pi$
$440$		0			0
$441$	1.29130	−	1.08353i	0.0614907	−	0.0515968i
$442$	3.52372	−	4.19940i	0.167606	−	0.199745i
$443$	0.670532	−	0.118233i	0.0318579	−	0.00561741i	−0.157696	−	0.987488i	$-0.550407\pi$
$443$	0.670532	−	0.118233i	0.0318579	−	0.00561741i	0.189554	+	0.981870i	$0.439296\pi$
$444$	0.781656	+	1.35387i	0.0370958	+	0.0642518i
$445$		0			0
$446$	14.7809	+	5.37982i	0.699898	+	0.254742i
$447$	7.37370	−	20.2591i	0.348764	−	0.958222i
$448$	−2.05411	−	1.18594i	−0.0970476	−	0.0560304i
$449$	−14.8474	−	25.7165i	−0.700693	−	1.21364i	−0.968223	−	0.250087i	$-0.919541\pi$
$449$	−14.8474	−	25.7165i	−0.700693	−	1.21364i	0.267530	−	0.963549i	$-0.413792\pi$
$450$		0			0
$451$	−22.4457	−	18.8341i	−1.05692	−	0.886865i
$452$	−5.80643	−	6.91983i	−0.273111	−	0.325482i
$453$	8.02567	+	1.41514i	0.377079	+	0.0664892i
$454$	7.52863	−	2.74020i	0.353336	−	0.128604i
$455$		0			0
$456$	−0.248301	−	5.79926i	−0.0116278	−	0.271575i
$457$			2.71312i			0.126914i	0.997985	+	0.0634572i	$0.0202126\pi$
$457$			2.71312i			0.126914i	−0.997985	+	0.0634572i	$0.979787\pi$
$458$	6.80024	+	18.6835i	0.317754	+	0.873023i
$459$	−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	$0.481731\pi$
$462$	−8.31615	+	1.46636i	−0.386902	+	0.0682213i
$463$	−27.6008	+	15.9354i	−1.28272	+	0.740579i	−0.977345	−	0.211653i	$-0.932115\pi$
$463$	−27.6008	+	15.9354i	−1.28272	+	0.740579i	−0.305375	+	0.952232i	$0.598782\pi$
$464$	0.0373141	−	0.0646299i	0.00173226	−	0.00300037i
$465$		0			0
$466$	−23.4437	−	8.53279i	−1.08601	−	0.395274i
$467$	−33.0631	−	19.0890i	−1.52998	−	0.883333i	−0.999362	−	0.0357205i	$-0.988627\pi$
$467$	−33.0631	−	19.0890i	−1.52998	−	0.883333i	−0.530616	−	0.847612i	$-0.678039\pi$
$468$	−1.03112	+	0.595317i	−0.0476635	+	0.0275185i
$469$	−2.10354	−	11.9298i	−0.0971323	−	0.550865i
$470$		0			0
$471$	−21.5101	+	18.0492i	−0.991135	+	0.831661i
$472$	10.5799	+	1.86552i	0.486979	+	0.0858676i
$473$	5.25305	+	14.4326i	0.241535	+	0.663613i
$474$	21.1624			0.972020
$475$		0			0
$476$	−13.3962			−0.614012
$477$	0.0373431	+	0.102599i	0.00170982	+	0.00469769i
$478$	−10.4823	−	1.84832i	−0.479450	−	0.0845400i
$479$	−22.4094	+	18.8037i	−1.02391	+	0.859163i	−0.990114	−	0.140266i	$-0.955204\pi$
$479$	−22.4094	+	18.8037i	−1.02391	+	0.859163i	−0.0337965	+	0.999429i	$0.510760\pi$
$480$		0			0
$481$	0.197865	+	1.12215i	0.00902187	+	0.0511655i
$482$	−14.5498	+	8.40034i	−0.662726	+	0.382625i
$483$	23.3909	+	13.5047i	1.06432	+	0.614486i
$484$	−3.61994	−	1.31755i	−0.164543	−	0.0598886i
$485$		0			0
$486$	5.90247	−	10.2234i	0.267742	−	0.463742i
$487$	−12.6228	+	7.28777i	−0.571993	+	0.330240i	−0.757945	−	0.652318i	$-0.773797\pi$
$487$	−12.6228	+	7.28777i	−0.571993	+	0.330240i	0.185952	+	0.982559i	$0.440463\pi$
$488$	−7.87768	+	1.38905i	−0.356606	+	0.0628792i
$489$	−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	$0.103581\pi$
$492$	−4.99159	−	13.7143i	−0.225038	−	0.618288i
$493$		−	0.421493i		−	0.0189831i
$494$	1.27563	−	4.03392i	0.0573933	−	0.181494i
$495$		0			0
$496$	0.0185438	−	0.00674938i	0.000832640	−	0.000303056i
$497$	24.2705	+	4.27955i	1.08868	+	0.191964i
$498$	5.02583	+	5.98956i	0.225213	+	0.268398i
$499$	−3.72597	−	3.12646i	−0.166797	−	0.139960i	0.555568	−	0.831471i	$-0.312501\pi$
$499$	−3.72597	−	3.12646i	−0.166797	−	0.139960i	−0.722366	+	0.691511i	$0.756945\pi$
$500$		0			0
$501$	−0.311253	−	0.539105i	−0.0139057	−	0.0240854i
$502$	−19.6484	−	11.3440i	−0.876952	−	0.506309i
$503$	2.23778	−	6.14824i	0.0997775	−	0.274137i	−0.879753	−	0.475430i	$-0.842292\pi$
$503$	2.23778	−	6.14824i	0.0997775	−	0.274137i	0.979531	+	0.201294i	$0.0645146\pi$
$504$	2.73408	+	0.995122i	0.121785	+	0.0443263i
$505$		0			0
$506$	−11.4310	−	19.7990i	−0.508169	−	0.880175i
$507$	−15.8131	+	2.78828i	−0.702284	+	0.123832i
$508$	6.02483	−	7.18011i	0.267309	−	0.318566i
$509$	−6.45683	+	5.41792i	−0.286194	+	0.240145i	−0.774570	−	0.632488i	$-0.782034\pi$
$509$	−6.45683	+	5.41792i	−0.286194	+	0.240145i	0.488376	+	0.872633i	$0.337589\pi$
$510$		0			0
$511$	−18.9753	+	6.90645i	−0.839418	+	0.305523i
$512$			1.00000i			0.0441942i
$513$	5.28994	+	23.9570i	0.233557	+	1.05773i
$514$	−22.5633			−0.995226
$515$		0			0
$516$	−1.32843	+	7.53390i	−0.0584809	+	0.331661i
$517$	9.04289	+	10.7769i	0.397706	+	0.473967i
$518$	1.78983	−	2.13304i	0.0786408	−	0.0937205i
$519$	−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	$-0.0536102\pi$
$522$	−0.0313102	+	0.0860242i	−0.00137041	+	0.00376517i
$523$	−9.32362	+	25.6164i	−0.407693	+	1.12013i	0.550706	+	0.834699i	$0.314358\pi$
$523$	−9.32362	+	25.6164i	−0.407693	+	1.12013i	−0.958400	+	0.285429i	$0.907864\pi$
$524$	−3.12369	+	5.41040i	−0.136459	+	0.236354i
$525$		0			0
$526$	1.46619	+	8.31518i	0.0639289	+	0.362559i
$527$	0.0716419	−	0.0853794i	0.00312077	−	0.00371919i
$528$	2.28847	+	2.72729i	0.0995929	+	0.118690i
$529$	−8.70390	+	49.3623i	−0.378430	+	2.14619i
$530$		0			0
$531$	−13.1784			−0.571893
$532$	−9.55513	+	3.94843i	−0.414267	+	0.171186i
$533$		−	10.6375i		−	0.460762i
$534$	1.07714	−	0.392048i	0.0466125	−	0.0169656i
$535$		0			0
$536$	−3.91238	+	3.28288i	−0.168989	+	0.141799i
$537$	12.1238	−	14.4486i	0.523182	−	0.623504i
$538$	25.9501	−	4.57571i	1.11879	−	0.197273i
$539$	−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	$0.805514\pi$
$542$	−0.208014	+	0.571515i	−0.00893498	+	0.0245487i
$543$	−8.98844	−	5.18948i	−0.385731	−	0.222702i
$544$	2.82395	+	4.89123i	0.121076	+	0.209710i
$545$		0			0
$546$	−2.34848	−	1.97061i	−0.100506	−	0.0843342i
$547$	−2.90170	−	3.45811i	−0.124068	−	0.147858i	0.700435	−	0.713716i	$-0.252989\pi$
$547$	−2.90170	−	3.45811i	−0.124068	−	0.147858i	−0.824503	+	0.565858i	$0.808545\pi$
$548$	−14.6560	−	2.58424i	−0.626072	−	0.110393i
$549$	9.22071	−	3.35606i	0.393530	−	0.143233i
$550$		0			0
$551$	−0.124232	−	0.300640i	−0.00529247	−	0.0128077i
$552$		−	11.3873i		−	0.484678i
$553$	−12.8919	−	35.4201i	−0.548218	−	1.50622i
$554$	1.18238	−	6.70558i	0.0502343	−	0.284893i
$555$		0			0
$556$	8.25009	+	6.92265i	0.349882	+	0.293586i
$557$	−20.8264	+	3.67225i	−0.882442	+	0.155598i	−0.596466	−	0.802639i	$-0.703429\pi$
$557$	−20.8264	+	3.67225i	−0.882442	+	0.155598i	−0.285976	+	0.958237i	$0.592318\pi$
$558$	−0.0209640	+	0.0121036i	−0.000887478	+	0.000512386i
$559$	−2.78799	+	4.82894i	−0.117919	+	0.204242i
$560$		0			0
$561$	18.8952	+	6.87728i	0.797755	+	0.290359i
$562$	−21.2103	−	12.2458i	−0.894703	−	0.516557i
$563$	16.2119	−	9.35993i	0.683249	−	0.394474i	−0.117829	−	0.993034i	$-0.537594\pi$
$563$	16.2119	−	9.35993i	0.683249	−	0.394474i	0.801078	+	0.598560i	$0.204260\pi$
$564$	1.21680	+	6.90081i	0.0512365	+	0.290576i
$565$		0			0
$566$	−24.7716	+	20.7858i	−1.04123	+	0.873693i
$567$	8.91174	+	1.57138i	0.374258	+	0.0659918i
$568$	−3.55375	−	9.76384i	−0.149112	−	0.409681i
$569$	41.7205			1.74902			0.874508	−	0.485011i	$-0.161184\pi$
$569$	41.7205			1.74902			0.874508	+	0.485011i	$0.161184\pi$
$570$		0			0
$571$	−33.6363			−1.40763			−0.703817	−	0.710381i	$-0.748522\pi$
$571$	−33.6363			−1.40763			−0.703817	+	0.710381i	$0.748522\pi$
$572$	0.887529	+	2.43846i	0.0371094	+	0.101957i
$573$	−0.346293	−	0.0610607i	−0.0144666	−	0.00255085i
$574$	−19.9132	+	16.7092i	−0.831161	+	0.697427i
$575$		0			0
$576$	−0.213011	−	1.20805i	−0.00887546	−	0.0503352i
$577$	14.4179	−	8.32416i	0.600223	−	0.346539i	−0.168906	−	0.985632i	$-0.554023\pi$
$577$	14.4179	−	8.32416i	0.600223	−	0.346539i	0.769129	+	0.639093i	$0.220690\pi$
$578$	12.9027	+	7.44940i	0.536683	+	0.309854i
$579$	−3.90167	−	1.42009i	−0.162148	−	0.0590170i
$580$		0			0
$581$	6.96322	−	12.0607i	0.288883	−	0.500360i
$582$	−12.8085	+	7.39501i	−0.530931	+	0.306533i
$583$	0.234349	−	0.0413220i	0.00970572	−	0.00171138i
$584$	6.52175	+	5.47240i	0.269872	+	0.226449i
$585$		0			0
$586$	4.64616	−	26.3497i	0.191931	−	1.08850i
$587$	2.50704	+	6.88805i	0.103477	+	0.284300i	0.980617	−	0.195934i	$-0.0627739\pi$
$587$	2.50704	+	6.88805i	0.103477	+	0.284300i	−0.877140	+	0.480234i	$0.840552\pi$
$588$		−	1.82994i		−	0.0754654i
$589$	0.0259353	−	0.0820149i	0.00106864	−	0.00337937i
$590$		0			0
$591$	26.2504	−	9.55437i	1.07980	−	0.393014i
$592$	−1.15612	−	0.203856i	−0.0475163	−	0.00837841i
$593$	−13.7873	−	16.4311i	−0.566177	−	0.674744i	0.404665	−	0.914465i	$-0.367388\pi$
$593$	−13.7873	−	16.4311i	−0.566177	−	0.674744i	−0.970842	+	0.239722i	$0.922944\pi$
$594$	−11.5274	−	9.67263i	−0.472975	−	0.396873i
$595$		0			0
$596$	8.09488	+	14.0208i	0.331579	+	0.574312i
$597$	−25.3221	−	14.6197i	−1.03637	−	0.598346i
$598$	2.83875	−	7.79940i	0.116085	−	0.318941i
$599$	8.88650	+	3.23442i	0.363093	+	0.132155i	0.517123	−	0.855911i	$-0.327003\pi$
$599$	8.88650	+	3.23442i	0.363093	+	0.132155i	−0.154030	+	0.988066i	$0.549225\pi$
$600$		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	$0.884044\pi$
$602$	13.4190	−	2.36613i	0.546917	−	0.0964362i
$603$	4.02704	−	4.79924i	0.163994	−	0.195440i
$604$	−4.68803	+	3.93373i	−0.190753	+	0.160061i
$605$		0			0
$606$	5.39721	−	1.96442i	0.219247	−	0.0797993i
$607$			1.12754i			0.0457656i	0.999738	+	0.0228828i	$0.00728446\pi$
$607$			1.12754i			0.0457656i	−0.999738	+	0.0228828i	$0.992716\pi$
$608$	3.45591	+	2.65644i	0.140156	+	0.107733i
$609$	−0.235716			−0.00955170
$610$		0			0
$611$	−0.886894	+	5.02982i	−0.0358799	+	0.203485i
$612$	−4.45335	−	5.30729i	−0.180016	−	0.214535i
$613$	−26.3081	+	31.3528i	−1.06258	+	1.26633i	−0.100095	+	0.994978i	$0.531915\pi$
$613$	−26.3081	+	31.3528i	−1.06258	+	1.26633i	−0.962481	+	0.271351i	$0.912530\pi$
$614$	−2.04105	−	11.5754i	−0.0823699	−	0.467143i
$615$		0			0
$616$	3.17064	−	5.49172i	0.127749	−	0.221268i
$617$	8.46227	−	23.2499i	0.340678	−	0.936005i	−0.644520	−	0.764587i	$-0.722943\pi$
$617$	8.46227	−	23.2499i	0.340678	−	0.936005i	0.985198	−	0.171418i	$-0.0548348\pi$
$618$	−0.00794194	+	0.0218203i	−0.000319472	+	0.000877741i
$619$	17.1323	−	29.6741i	0.688607	−	1.19270i	−0.283682	−	0.958918i	$-0.591556\pi$
$619$	17.1323	−	29.6741i	0.688607	−	1.19270i	0.972289	−	0.233784i	$-0.0751107\pi$
$620$		0			0
$621$	8.35781	+	47.3995i	0.335387	+	1.90208i
$622$	−6.37278	+	7.59479i	−0.255525	+	0.304523i
$623$	−1.31236	−	1.56402i	−0.0525788	−	0.0626609i
$624$	−0.224445	+	1.27289i	−0.00898499	+	0.0509564i
$625$		0			0
$626$	0.359111			0.0143530
$627$	15.5045	−	0.663840i	0.619189	−	0.0265112i
$628$		−	21.0861i		−	0.841427i
$629$	−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	$0.310856\pi$
$632$	−10.2150	+	12.1738i	−0.406331	+	0.484246i
$633$	18.3767	−	3.24030i	0.730406	−	0.128790i
$634$	12.9731	+	22.4700i	0.515226	+	0.892398i
$635$		0			0
$636$	0.111380	+	0.0405388i	0.00441649	+	0.00160747i
$637$	0.456185	−	1.25336i	0.0180747	−	0.0496598i
$638$	0.172790	+	0.0997602i	0.00684081	+	0.00394954i
$639$	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	$0.439460\pi$
$642$	9.86246	+	11.7536i	0.389240	+	0.463878i
$643$	40.1349	+	7.07687i	1.58277	+	0.279085i	0.894736	−	0.446596i	$-0.147364\pi$
$643$	40.1349	+	7.07687i	1.58277	+	0.279085i	0.688031	+	0.725681i	$0.258475\pi$
$644$	−19.0594	+	6.93704i	−0.751044	+	0.273358i
$645$		0			0
$646$	24.4053	+	3.23396i	0.960214	+	0.127238i
$647$			18.7570i			0.737414i	0.929546	+	0.368707i	$0.120200\pi$
$647$			18.7570i			0.737414i	−0.929546	+	0.368707i	$0.879800\pi$
$648$	−1.30488	−	3.58512i	−0.0512604	−	0.140837i
$649$	−4.98752	+	28.2856i	−0.195777	+	1.11031i
$650$		0			0
$651$	−0.0477477	−	0.0400651i	−0.00187138	−	0.00157027i
$652$	15.9659	−	2.81522i	0.625274	−	0.110253i
$653$	−14.6095	+	8.43478i	−0.571713	+	0.330078i	−0.757833	−	0.652449i	$-0.773742\pi$
$653$	−14.6095	+	8.43478i	−0.571713	+	0.330078i	0.186120	+	0.982527i	$0.440409\pi$
$654$	6.23135	−	10.7930i	0.243665	−	0.422040i
$655$		0			0
$656$	10.2986	+	3.74840i	0.402094	+	0.146350i
$657$	−9.04425	−	5.22170i	−0.352850	−	0.203718i
$658$	10.8088	−	6.24048i	0.421372	−	0.243279i
$659$	−1.19202	−	6.76028i	−0.0464345	−	0.263343i	0.952748	−	0.303761i	$-0.0982423\pi$
$659$	−1.19202	−	6.76028i	−0.0464345	−	0.263343i	−0.999183	+	0.0404175i	$0.987131\pi$
$660$		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	$0.174470\pi$
$662$	−13.2397	−	2.33452i	−0.514577	−	0.0907337i
$663$	2.49677	+	6.85982i	0.0969665	+	0.266413i
$664$	−5.87148			−0.227857
$665$		0			0
$666$	1.44007			0.0558017
$667$	−0.218265	−	0.599678i	−0.00845125	−	0.0232196i
$668$	0.460364	+	0.0811745i	0.0178120	+	0.00314074i
$669$	−16.0459	+	13.4641i	−0.620370	+	0.520552i
$670$		0			0
$671$	−3.71365	−	21.0612i	−0.143364	−	0.813058i
$672$	2.73538	−	1.57927i	0.105519	−	0.0609217i
$673$	−4.26530	−	2.46257i	−0.164415	−	0.0949251i	0.415535	−	0.909577i	$-0.363594\pi$
$673$	−4.26530	−	2.46257i	−0.164415	−	0.0949251i	−0.579950	+	0.814652i	$0.696928\pi$
$674$	15.4255	+	5.61443i	0.594169	+	0.216260i
$675$		0			0
$676$	6.02895	−	10.4425i	0.231883	−	0.401633i
$677$	4.67017	−	2.69632i	0.179489	−	0.103628i	−0.407563	−	0.913177i	$-0.633621\pi$
$677$	4.67017	−	2.69632i	0.179489	−	0.103628i	0.587053	+	0.809549i	$0.300288\pi$
$678$	11.8464	−	2.08884i	0.454958	−	0.0802214i
$679$	20.1801	+	16.9331i	0.774439	+	0.649832i
$680$		0			0
$681$	−1.85265	+	10.5069i	−0.0709937	+	0.402625i
$682$	0.0180446	+	0.0495773i	0.000690965	+	0.00189841i
$683$		−	17.4871i		−	0.669126i	−0.942373	−	0.334563i	$-0.891411\pi$
$683$		−	17.4871i		−	0.669126i	0.942373	−	0.334563i	$-0.108589\pi$
$684$	−4.74075	−	2.47296i	−0.181267	−	0.0945560i
$685$		0			0
$686$	−18.6647	+	6.79339i	−0.712622	+	0.259373i
$687$	−26.0746	−	4.59765i	−0.994807	−	0.175411i
$688$	−3.69269	−	4.40077i	−0.140782	−	0.167778i
$689$	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	$0.742577\pi$
$692$	22.2736	+	12.8597i	0.846716	+	0.488852i
$693$	−2.66049	+	7.30962i	−0.101063	+	0.277670i
$694$	−6.31681	−	2.29913i	−0.239783	−	0.0872738i
$695$		0			0
$696$	0.0496897	+	0.0860650i	0.00188348	+	0.00326229i
$697$	60.9583	−	10.7486i	2.30896	−	0.407132i
$698$	−12.8305	+	15.2908i	−0.485640	+	0.578764i
$699$	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	$0.434324\pi$
$702$		−	5.46310i		−	0.206191i
$703$	−3.77568	+	3.45392i	−0.142403	+	0.130267i
$704$	−2.67353			−0.100762
$705$		0			0
$706$	4.40623	−	24.9890i	0.165831	−	0.940472i
$707$	−6.57583	−	7.83677i	−0.247310	−	0.294732i
$708$	−9.19583	+	10.9592i	−0.345600	+	0.411870i
$709$	−6.22196	−	35.2865i	−0.233671	−	1.32521i	−0.845395	−	0.534141i	$-0.820635\pi$
$709$	−6.22196	−	35.2865i	−0.233671	−	1.32521i	0.611725	−	0.791071i	$-0.290476\pi$
$710$		0			0
$711$	9.74704	−	16.8824i	0.365543	−	0.633138i
$712$	−0.294405	+	0.808872i	−0.0110333	+	0.0303138i
$713$	0.0577156	−	0.158572i	0.00216147	−	0.00593858i
$714$	8.91956	−	15.4491i	0.333806	−	0.578169i
$715$		0			0
$716$	2.45951	+	13.9486i	0.0919163	+	0.521284i
$717$	9.11101	−	10.8581i	0.340257	−	0.405503i
$718$	9.31110	+	11.0965i	0.347487	+	0.414119i
$719$	−1.50797	+	8.55210i	−0.0562376	+	0.318940i	−0.999929	−	0.0118866i	$-0.996216\pi$
$719$	−1.50797	+	8.55210i	−0.0562376	+	0.318940i	0.943692	+	0.330826i	$0.107327\pi$
$720$		0			0
$721$	0.0413594			0.00154031
$722$	18.3609	−	4.88660i	0.683320	−	0.181860i
$723$		−	22.3728i		−	0.832053i
$724$	7.32396	−	2.66570i	0.272193	−	0.0990701i
$725$		0			0
$726$	3.92973	−	3.29744i	0.145846	−	0.122379i
$727$	19.1997	−	22.8813i	0.712078	−	0.848622i	−0.281758	−	0.959486i	$-0.590917\pi$
$727$	19.1997	−	22.8813i	0.712078	−	0.848622i	0.993836	+	0.110864i	$0.0353618\pi$
$728$	2.26720	−	0.399769i	0.0840282	−	0.0148164i
$729$	13.5829	+	23.5263i	0.503070	+	0.871343i
$730$		0			0
$731$	−30.4893	−	11.0972i	−1.12769	−	0.410445i
$732$	3.64327	−	10.0098i	0.134659	−	0.369973i
$733$	−11.1709	−	6.44955i	−0.412608	−	0.238220i	0.279301	−	0.960203i	$-0.409897\pi$
$733$	−11.1709	−	6.44955i	−0.412608	−	0.238220i	−0.691910	+	0.721984i	$0.743230\pi$
$734$	−1.06404	−	1.84297i	−0.0392744	−	0.0680253i
$735$		0			0
$736$	6.55063	+	5.49663i	0.241460	+	0.202609i
$737$	−8.77685	−	10.4598i	−0.323300	−	0.385293i
$738$	−13.2397	−	2.33451i	−0.487359	−	0.0859346i
$739$	−27.5586	+	10.0305i	−1.01376	+	0.368978i	−0.794875	−	0.606773i	$-0.792464\pi$
$739$	−27.5586	+	10.0305i	−1.01376	+	0.368978i	−0.218883	+	0.975751i	$0.570241\pi$
$740$		0			0
$741$	3.80277	+	4.15702i	0.139698	+	0.152712i
$742$		−	0.211115i		−	0.00775028i
$743$	−16.3402	−	44.8942i	−0.599462	−	1.64701i	−0.752349	−	0.658765i	$-0.771079\pi$
$743$	−16.3402	−	44.8942i	−0.599462	−	1.64701i	0.152886	−	0.988244i	$-0.451143\pi$
$744$	−0.00456327	+	0.0258796i	−0.000167297	+	0.000948791i
$745$		0			0
$746$	−21.1228	−	17.7241i	−0.773359	−	0.648925i
$747$	7.09301	−	1.25069i	0.259520	−	0.0457603i
$748$	−13.0768	+	7.54991i	−0.478136	+	0.276052i
$749$	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	$0.336400\pi$
$752$	−4.55707	−	2.63103i	−0.166179	−	0.0959436i
$753$	26.1650	−	15.1064i	0.953506	−	0.550507i
$754$	0.0125782	+	0.0713346i	0.000458072	+	0.00259785i
$755$		0			0
$756$	−10.2268	+	8.58131i	−0.371945	+	0.312099i
$757$	−25.7489	−	4.54023i	−0.935861	−	0.165017i	−0.315136	−	0.949046i	$-0.602050\pi$
$757$	−25.7489	−	4.54023i	−0.935861	−	0.165017i	−0.620724	+	0.784029i	$0.713161\pi$
$758$	−0.986748	−	2.71107i	−0.0358403	−	0.0984704i
$759$	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	$0.469606\pi$
$762$	4.26896	+	11.7289i	0.154648	+	0.424892i
$763$	−21.8607	−	3.85463i	−0.791409	−	0.139547i
$764$	0.202280	−	0.169733i	0.00731822	−	0.00614072i
$765$		0			0
$766$	2.16110	+	12.2562i	0.0780835	+	0.442834i
$767$	−9.03040	+	5.21370i	−0.326069	+	0.188256i
$768$	−1.15325	−	0.665830i	−0.0416144	−	0.0240261i
$769$	42.2718	+	15.3857i	1.52436	+	0.554822i	0.962233	−	0.272227i	$-0.0877603\pi$
$769$	42.2718	+	15.3857i	1.52436	+	0.554822i	0.562129	+	0.827050i	$0.309982\pi$
$770$		0			0
$771$	15.0233	−	26.0212i	0.541053	−	0.937131i
$772$	2.70024	−	1.55898i	0.0971837	−	0.0561091i
$773$	−3.05491	+	0.538663i	−0.109877	+	0.0193744i	−0.228316	−	0.973587i	$-0.573322\pi$
$773$	−3.05491	+	0.538663i	−0.109877	+	0.0193744i	0.118439	+	0.992961i	$0.462211\pi$
$774$	5.39835	+	4.52975i	0.194040	+	0.162819i
$775$		0			0
$776$	1.92862	−	10.9377i	0.0692332	−	0.392641i
$777$	1.26821	+	3.48437i	0.0454967	+	0.125001i
$778$		−	31.0311i		−	1.11252i
$779$	40.3119	−	25.6337i	1.44432	−	0.918424i
$780$		0			0
$781$	26.1039	−	9.50103i	0.934070	−	0.339974i
$782$	47.5629	+	8.38661i	1.70084	+	0.299905i
$783$	−0.270000	−	0.321773i	−0.00964900	−	0.0114992i
$784$	1.05268	+	0.883305i	0.0375958	+	0.0315466i
$785$		0			0
$786$	−4.15970	−	7.20481i	−0.148372	−	0.256987i
$787$	23.9244	+	13.8128i	0.852813	+	0.492372i	0.861599	−	0.507589i	$-0.169463\pi$
$787$	23.9244	+	13.8128i	0.852813	+	0.492372i	−0.00878567	+	0.999961i	$0.502797\pi$
$788$	−7.17478	+	19.7125i	−0.255591	+	0.702230i
$789$	−10.5657	−	3.84561i	−0.376150	−	0.136907i
$790$		0			0
$791$	−10.7128	−	18.5552i	−0.380905	−	0.659746i
$792$	3.22974	−	0.569490i	0.114764	−	0.0202360i
$793$	4.99069	−	5.94767i	0.177225	−	0.211208i
$794$	6.02693	−	5.05720i	0.213888	−	0.179473i
$795$		0			0
$796$	20.6330	−	7.50979i	0.731317	−	0.266178i
$797$			25.2302i			0.893700i	0.894609	+	0.446850i	$0.147454\pi$
$797$			25.2302i			0.893700i	−0.894609	+	0.446850i	$0.852546\pi$
$798$	1.80856	−	13.6485i	0.0640224	−	0.483150i
$799$	−29.7196			−1.05140
$800$		0			0
$801$	0.183356	−	1.03987i	0.00647858	−	0.0367418i
$802$	18.7801	+	22.3812i	0.663147	+	0.790308i
$803$	−14.6306	+	17.4361i	−0.516302	+	0.615305i
$804$	−1.18100	−	6.69779i	−0.0416507	−	0.236213i
$805$		0			0
$806$	−0.00957698	+	0.0165878i	−0.000337335	+	0.000584281i
$807$	−12.0014	+	32.9736i	−0.422470	+	1.16073i
$808$	−1.47517	+	4.05300i	−0.0518963	+	0.142584i
$809$	−15.2498	+	26.4134i	−0.536154	+	0.928646i	0.462952	+	0.886383i	$0.346790\pi$
$809$	−15.2498	+	26.4134i	−0.536154	+	0.928646i	−0.999107	+	0.0422629i	$0.986543\pi$
$810$		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	$0.988186\pi$
$812$	0.113779	−	0.135597i	0.00399287	−	0.00475852i
$813$	−0.520598	−	0.620425i	−0.0182582	−	0.0217592i
$814$	0.545013	−	3.09092i	0.0191027	−	0.108337i
$815$		0			0
$816$	−7.52109			−0.263291
$817$	−25.0181	+	1.07118i	−0.875272	+	0.0374757i
$818$		−	14.1622i		−	0.495169i
$819$	−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	$-0.0184049\pi$
$822$	12.7387	−	15.1813i	0.444312	−	0.529510i
$823$	−14.9529	+	2.63661i	−0.521227	+	0.0919063i	−0.428071	−	0.903745i	$-0.640807\pi$
$823$	−14.9529	+	2.63661i	−0.521227	+	0.0919063i	−0.0931558	+	0.995652i	$0.529695\pi$
$824$	−0.00871870	−	0.0151012i	−0.000303730	−	0.000526076i
$825$		0			0
$826$	23.9447	+	8.71515i	0.833141	+	0.303239i
$827$	−0.215224	+	0.591323i	−0.00748408	+	0.0205623i	−0.943378	−	0.331719i	$-0.892372\pi$
$827$	−0.215224	+	0.591323i	−0.00748408	+	0.0205623i	0.935894	+	0.352281i	$0.114594\pi$
$828$	−9.08431	−	5.24483i	−0.315701	−	0.182270i
$829$	−20.5684	−	35.6256i	−0.714372	−	1.23733i	−0.963201	−	0.268781i	$-0.913379\pi$
$829$	−20.5684	−	35.6256i	−0.714372	−	1.23733i	0.248830	−	0.968547i	$-0.419954\pi$
$830$		0			0
$831$	6.94596	+	5.82836i	0.240953	+	0.202183i
$832$	−0.623898	−	0.743533i	−0.0216298	−	0.0257774i
$833$	7.64331	+	1.34772i	0.264825	+	0.0466958i
$834$	−13.4767	+	4.90512i	−0.466660	+	0.169851i
$835$		0			0
$836$	−7.10207	+	9.23946i	−0.245630	+	0.319553i
$837$		−	0.111072i		−	0.00383921i
$838$	10.2869	+	28.2631i	0.355355	+	0.976331i
$839$	5.04229	−	28.5962i	0.174079	−	0.987252i	−0.765122	−	0.643885i	$-0.777321\pi$
$839$	5.04229	−	28.5962i	0.174079	−	0.987252i	0.939201	−	0.343367i	$-0.111567\pi$
$840$		0			0
$841$	−22.2110	−	18.6373i	−0.765897	−	0.642664i
$842$	13.4112	−	2.36476i	0.462181	−	0.0814950i
$843$	28.2449	−	16.3072i	0.972807	−	0.561650i
$844$	−7.00635	+	12.1353i	−0.241168	+	0.417716i
$845$		0			0
$846$	6.06559	+	2.20769i	0.208539	+	0.0759020i
$847$	−7.91296	−	4.56855i	−0.271893	−	0.156977i
$848$	−0.0770827	+	0.0445037i	−0.00264703	+	0.00152826i
$849$	−7.47762	−	42.4077i	−0.256631	−	1.45543i
$850$		0			0
$851$	−7.69017	+	6.45282i	−0.263615	+	0.221200i
$852$	13.6263	+	2.40269i	0.466831	+	0.0823149i
$853$	3.30684	+	9.08547i	0.113224	+	0.311081i	0.983343	−	0.181762i	$-0.0581800\pi$
$853$	3.30684	+	9.08547i	0.113224	+	0.311081i	−0.870118	+	0.492843i	$0.835958\pi$
$854$	−18.9732			−0.649248
$855$		0			0
$856$	−11.5219			−0.393811
$857$	10.1083	+	27.7722i	0.345292	+	0.948681i	0.983832	+	0.179093i	$0.0573163\pi$
$857$	10.1083	+	27.7722i	0.345292	+	0.948681i	−0.638540	+	0.769588i	$0.720461\pi$
$858$	−3.40311	−	0.600059i	−0.116180	−	0.0204857i
$859$	−26.3636	+	22.1217i	−0.899513	+	0.754781i	−0.970095	−	0.242725i	$-0.921959\pi$
$859$	−26.3636	+	22.1217i	−0.899513	+	0.754781i	0.0705819	+	0.997506i	$0.477514\pi$
$860$		0			0
$861$	−6.01105	−	34.0904i	−0.204856	−	1.16180i
$862$	−25.6241	+	14.7941i	−0.872762	+	0.503889i
$863$	−17.3598	−	10.0227i	−0.590934	−	0.341176i	0.174533	−	0.984651i	$-0.444159\pi$
$863$	−17.3598	−	10.0227i	−0.590934	−	0.341176i	−0.765467	+	0.643475i	$0.777492\pi$
$864$	5.28906	+	1.92506i	0.179938	+	0.0654919i
$865$		0			0
$866$	−0.483102	+	0.836757i	−0.0164165	+	0.0284342i
$867$	−17.1821	+	9.92007i	−0.583533	+	0.336903i
$868$	0.0460953	−	0.00812785i	0.00156458	−	0.000275877i
$869$	−32.5469	−	27.3101i	−1.10408	−	0.926431i
$870$		0			0
$871$	0.860802	−	4.88185i	0.0291672	−	0.165415i
$872$	3.20089	+	8.79437i	0.108396	+	0.297815i
$873$			13.6241i			0.461105i
$874$	36.3973	−	8.03688i	1.23116	−	0.271852i
$875$		0			0
$876$	−10.6534	+	3.87753i	−0.359946	+	0.131010i
$877$	−12.1084	−	2.13503i	−0.408871	−	0.0720949i	−0.0345699	−	0.999402i	$-0.511006\pi$
$877$	−12.1084	−	2.13503i	−0.408871	−	0.0720949i	−0.374301	+	0.927307i	$0.622117\pi$
$878$	15.1516	+	18.0570i	0.511342	+	0.609393i
$879$	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	$0.659882\pi$
$882$	−1.45984	−	0.842839i	−0.0491554	−	0.0283799i
$883$	−13.1283	+	36.0696i	−0.441801	+	1.21384i	0.496505	+	0.868034i	$0.334616\pi$
$883$	−13.1283	+	36.0696i	−0.441801	+	1.21384i	−0.938306	+	0.345805i	$0.887606\pi$
$884$	−5.15133	−	1.87493i	−0.173258	−	0.0630607i
$885$		0			0
$886$	−0.340438	−	0.589656i	−0.0114372	−	0.0198099i
$887$	−16.3575	+	2.88427i	−0.549232	+	0.0968444i	−0.441376	−	0.897322i	$-0.645510\pi$
$887$	−16.3575	+	2.88427i	−0.549232	+	0.0968444i	−0.107856	+	0.994167i	$0.534398\pi$
$888$	1.00488	−	1.19757i	0.0337215	−	0.0401877i
$889$	17.0304	−	14.2902i	0.571180	−	0.479277i
$890$		0			0
$891$	9.58492	−	3.48862i	0.321107	−	0.116873i
$892$		−	15.7296i		−	0.526664i
$893$	−21.1982	+	8.75964i	−0.709370	+	0.293130i
$894$	−21.5593			−0.721050
$895$		0			0
$896$	−0.411873	+	2.33585i	−0.0137597	+	0.0780352i
$897$	7.10455	+	8.46687i	0.237214	+	0.282701i
$898$	−19.0875	+	22.7476i	−0.636957	+	0.759096i
$899$	0.000255732		0.00145033i	8.52914e−6		4.83712e-5i
$900$		0			0
$901$	−0.251353	+	0.435356i	−0.00837377	+	0.0145038i
$902$	−10.0214	+	27.5337i	−0.333677	+	0.916771i
$903$	−6.20602	+	17.0509i	−0.206523	+	0.567418i
$904$	−4.51660	+	7.82298i	−0.150220	+	0.260188i
$905$		0			0
$906$	−1.41514	−	8.02567i	−0.0470150	−	0.266635i
$907$	−10.2694	+	12.2386i	−0.340989	+	0.406375i	−0.909101	−	0.416576i	$-0.863230\pi$
$907$	−10.2694	+	12.2386i	−0.340989	+	0.406375i	0.568111	+	0.822952i	$0.307674\pi$
$908$	−5.14988	−	6.13739i	−0.170905	−	0.203677i
$909$	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	$0.125307\pi$
$912$	−5.36460	+	2.21679i	−0.177640	+	0.0734053i
$913$		−	15.6975i		−	0.519513i
$914$	2.54950	−	0.927941i	0.0843299	−	0.0306936i
$915$		0			0
$916$	15.2309	−	12.7803i	0.503244	−	0.422272i
$917$	−9.52487	+	11.3513i	−0.314539	+	0.374853i
$918$	31.3063	−	5.52014i	1.03326	−	0.182192i
$919$	20.2845	+	35.1339i	0.669126	+	1.15896i	0.978149	+	0.207905i	$0.0666645\pi$
$919$	20.2845	+	35.1339i	0.669126	+	1.15896i	−0.309023	+	0.951054i	$0.600002\pi$
$920$		0			0
$921$	14.7083	+	5.35338i	0.484654	+	0.176400i
$922$	10.0704	−	27.6683i	0.331652	−	0.911206i
$923$	8.73397	+	5.04256i	0.287482	+	0.165978i
$924$	4.22222	+	7.31310i	0.138901	+	0.240583i
$925$		0			0
$926$	24.4144	+	20.4861i	0.802306	+	0.673215i
$927$	0.0137493	+	0.0163858i	0.000451587	+	0.000538180i
$928$	−0.0734944	−	0.0129590i	−0.00241257	−	0.000425401i
$929$	22.3308	−	8.12775i	0.732650	−	0.266663i	0.0513639	−	0.998680i	$-0.483643\pi$
$929$	22.3308	−	8.12775i	0.732650	−	0.266663i	0.681286	+	0.732017i	$0.261421\pi$
$930$		0			0
$931$	5.84901	−	1.29152i	0.191694	−	0.0423279i
$932$			24.9482i			0.817206i
$933$	−4.51551	−	12.4063i	−0.147831	−	0.406163i
$934$	−6.62954	+	37.5980i	−0.216925	+	1.23024i
$935$		0			0
$936$	0.912078	+	0.765324i	0.0298122	+	0.0250154i
$937$	−29.2148	+	5.15136i	−0.954406	+	0.168288i	−0.629103	−	0.777322i	$-0.716577\pi$
$937$	−29.2148	+	5.15136i	−0.954406	+	0.168288i	−0.325303	+	0.945610i	$0.605466\pi$
$938$	−10.4908	+	6.05689i	−0.342538	+	0.197765i
$939$	−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	$0.921307\pi$
$942$	24.3176	+	14.0398i	0.792309	+	0.457440i
$943$	81.1622	−	46.8590i	2.64301	−	1.52594i
$944$	−1.86552	−	10.5799i	−0.0607175	−	0.344346i
$945$		0			0
$946$	11.7656	−	9.87250i	0.382532	−	0.320983i
$947$	−23.2192	−	4.09416i	−0.754521	−	0.133042i	−0.216859	−	0.976203i	$-0.569581\pi$
$947$	−23.2192	−	4.09416i	−0.754521	−	0.133042i	−0.537662	+	0.843160i	$0.680692\pi$
$948$	−7.23796	−	19.8861i	−0.235078	−	0.645871i
$949$	−8.26335			−0.268240
$950$		0			0
$951$	−34.5514			−1.12041
$952$	4.58175	+	12.5883i	0.148496	+	0.407988i
$953$	−28.9205	−	5.09946i	−0.936825	−	0.165188i	−0.315665	−	0.948871i	$-0.602227\pi$
$953$	−28.9205	−	5.09946i	−0.936825	−	0.165188i	−0.621161	+	0.783683i	$0.713339\pi$
$954$	0.0836396	−	0.0701820i	0.00270793	−	0.00227223i
$955$		0			0
$956$	1.84832	+	10.4823i	0.0597788	+	0.339022i
$957$	−0.230097	+	0.132847i	−0.00743798	+	0.00429432i
$958$	25.3342	+	14.6267i	0.818509	+	0.472567i
$959$	−33.1697	−	12.0728i	−1.07111	−	0.389851i
$960$		0			0
$961$	15.4998	−	26.8465i	0.499994	−	0.866015i
$962$	0.986800	−	0.569729i	0.0318157	−	0.0183688i
$963$	13.9190	−	2.45429i	0.448533	−	0.0790885i
$964$	12.8701	+	10.7993i	0.414517	+	0.347821i
$965$		0			0
$966$	4.69014	−	26.5991i	0.150903	−	0.855812i
$967$	8.41119	+	23.1096i	0.270486	+	0.743153i	0.998349	+	0.0574316i	$0.0182911\pi$
$967$	8.41119	+	23.1096i	0.270486	+	0.743153i	−0.727864	+	0.685722i	$0.759487\pi$
$968$			3.85226i			0.123816i
$969$	−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	$0.482045\pi$
$972$	−11.6256	−	2.04991i	−0.372891	−	0.0657508i
$973$	16.4197	+	19.5682i	0.526392	+	0.627329i
$974$	11.1655	+	9.36898i	0.357766	+	0.300201i
$975$		0			0
$976$	3.99960	+	6.92751i	0.128024	+	0.221744i
$977$	−3.40407	−	1.96534i	−0.108906	−	0.0628768i	0.444558	−	0.895750i	$-0.353361\pi$
$977$	−3.40407	−	1.96534i	−0.108906	−	0.0628768i	−0.553464	+	0.832873i	$0.686694\pi$
$978$	−7.38393	+	20.2872i	−0.236112	+	0.648713i
$979$	−2.16254	−	0.787100i	−0.0691151	−	0.0251558i
$980$		0			0
$981$	−5.74012	−	9.94218i	−0.183268	−	0.317429i
$982$	6.55990	−	1.15669i	0.209335	−	0.0369114i
$983$	1.17464	−	1.39988i	0.0374651	−	0.0446492i	−0.746987	−	0.664839i	$-0.768500\pi$
$983$	1.17464	−	1.39988i	0.0374651	−	0.0446492i	0.784452	+	0.620190i	$0.212945\pi$
$984$	−11.1800	+	9.38112i	−0.356405	+	0.299059i
$985$		0			0
$986$	−0.396073	+	0.144159i	−0.0126135	+	0.00459096i
$987$			16.6204i			0.529033i
$988$	−4.22693	+	0.180981i	−0.134477	+	0.00575776i
$989$	−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	$0.0908746\pi$
$992$	−0.0126847	−	0.0151170i	−0.000402739	−	0.000479966i
$993$	11.5077	−	13.7143i	0.365186	−	0.435211i
$994$	−4.27955	−	24.2705i	−0.135739	−	0.769814i
$995$		0			0
$996$	3.90940	−	6.77129i	0.123874	−	0.214556i
$997$	1.80015	−	4.94588i	0.0570115	−	0.156638i	−0.907917	−	0.419149i	$-0.862328\pi$
$997$	1.80015	−	4.94588i	0.0570115	−	0.156638i	0.964929	+	0.262511i	$0.0845507\pi$
$998$	−1.66356	+	4.57058i	−0.0526589	+	0.144679i
$999$	−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.u.e.499.2		24
5.2	odd	4		190.2.k.b.81.2	yes	12
5.3	odd	4		950.2.l.h.651.1		12
5.4	even	2	inner	950.2.u.e.499.3		24
19.4	even	9	inner	950.2.u.e.99.3		24
95.2	even	36		3610.2.a.be.1.3		6
95.4	even	18	inner	950.2.u.e.99.2		24
95.17	odd	36		3610.2.a.bc.1.4		6
95.23	odd	36		950.2.l.h.251.1		12
95.42	odd	36		190.2.k.b.61.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.k.b.61.2	✓	12	95.42	odd	36
190.2.k.b.81.2	yes	12	5.2	odd	4
950.2.l.h.251.1		12	95.23	odd	36
950.2.l.h.651.1		12	5.3	odd	4
950.2.u.e.99.2		24	95.4	even	18	inner
950.2.u.e.99.3		24	19.4	even	9	inner
950.2.u.e.499.2		24	1.1	even	1	trivial
950.2.u.e.499.3		24	5.4	even	2	inner
3610.2.a.bc.1.4		6	95.17	odd	36
3610.2.a.be.1.3		6	95.2	even	36

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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 - 0.939693i) q^{2} +(1.31143 + 0.231240i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(-2.05411 + 1.18594i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.15270 - 0.419550i) q^{9} +O(q^{10})\)	\(q+(-0.342020 - 0.939693i) q^{2} +(1.31143 + 0.231240i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.231240 - 1.31143i) q^{6} +(-2.05411 + 1.18594i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-1.15270 - 0.419550i) q^{9} +(-1.33676 + 2.31534i) q^{11} +(-1.15325 + 0.665830i) q^{12} +(-0.955868 + 0.168545i) q^{13} +(1.81697 + 1.52462i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-1.93170 - 5.30729i) q^{17} +1.22668i q^{18} +(-2.94212 - 3.21620i) q^{19} +(-2.96806 + 1.08028i) q^{21} +(2.63291 + 0.464253i) q^{22} +(-5.49663 - 6.55063i) q^{23} +(1.02011 + 0.855975i) q^{24} +(0.485307 + 0.840576i) q^{26} +(-4.87443 - 2.81425i) q^{27} +(0.811231 - 2.22884i) q^{28} +(0.0701275 + 0.0255243i) q^{29} +(0.00986693 + 0.0170900i) q^{31} +(-0.984808 + 0.173648i) q^{32} +(-2.28847 + 2.72729i) q^{33} +(-4.32654 + 3.63040i) q^{34} +(1.15270 - 0.419550i) q^{36} -1.17396i q^{37} +(-2.01598 + 3.86469i) q^{38} -1.29253 q^{39} +(-1.90311 + 10.7931i) q^{41} +(2.03027 + 2.41958i) q^{42} +(3.69269 - 4.40077i) q^{43} +(-0.464253 - 2.63291i) q^{44} +(-4.27562 + 7.40559i) q^{46} +(1.79973 - 4.94471i) q^{47} +(0.455455 - 1.25135i) q^{48} +(-0.687089 + 1.19007i) q^{49} +(-1.30602 - 7.40682i) q^{51} +(0.623898 - 0.743533i) q^{52} +(-0.0572129 - 0.0681837i) q^{53} +(-0.977379 + 5.54299i) q^{54} -2.37188 q^{56} +(-3.11466 - 4.89815i) q^{57} -0.0746282i q^{58} +(10.0952 - 3.67436i) q^{59} +(-6.12774 + 5.14179i) q^{61} +(0.0126847 - 0.0151170i) q^{62} +(2.86534 - 0.505237i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.34552 + 1.21767i) q^{66} +(-1.74678 + 4.79924i) q^{67} +(4.89123 + 2.82395i) q^{68} +(-5.69367 - 9.86173i) q^{69} +(-7.95955 - 6.67886i) q^{71} +(-0.788496 - 0.939693i) q^{72} +(8.38420 + 1.47836i) q^{73} +(-1.10316 + 0.401517i) q^{74} +(4.32113 + 0.572595i) q^{76} -6.34129i q^{77} +(0.442070 + 1.21458i) q^{78} +(-2.75957 + 15.6503i) q^{79} +(-2.92262 - 2.45237i) q^{81} +(10.7931 - 1.90311i) q^{82} +(-5.08485 + 2.93574i) q^{83} +(1.57927 - 2.73538i) q^{84} +(-5.39835 - 1.96484i) q^{86} +(0.0860650 + 0.0496897i) q^{87} +(-2.31534 + 1.33676i) q^{88} +(0.149473 + 0.847706i) q^{89} +(1.76357 - 1.47981i) q^{91} +(8.42133 + 1.48491i) q^{92} +(0.00898788 + 0.0246940i) q^{93} -5.26205 q^{94} -1.33166 q^{96} +(-3.79863 - 10.4367i) q^{97} +(1.35330 + 0.238624i) q^{98} +(2.51229 - 2.10806i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 36 q^{9}+O(q^{10}) \) 24 * q - 36 * q^9	\( 24 q - 36 q^{9} + 12 q^{11} + 24 q^{21} + 12 q^{29} + 12 q^{31} + 36 q^{36} + 72 q^{39} - 12 q^{41} - 12 q^{44} - 24 q^{46} + 36 q^{49} + 24 q^{56} + 48 q^{59} - 60 q^{61} + 12 q^{64} + 48 q^{66} - 12 q^{69} - 84 q^{71} - 12 q^{74} + 36 q^{76} - 120 q^{79} + 36 q^{81} + 48 q^{84} - 72 q^{86} + 24 q^{89} + 48 q^{91} - 120 q^{94} + 24 q^{99}+O(q^{100}) \) 24 * q - 36 * q^9 + 12 * q^11 + 24 * q^21 + 12 * q^29 + 12 * q^31 + 36 * q^36 + 72 * q^39 - 12 * q^41 - 12 * q^44 - 24 * q^46 + 36 * q^49 + 24 * q^56 + 48 * q^59 - 60 * q^61 + 12 * q^64 + 48 * q^66 - 12 * q^69 - 84 * q^71 - 12 * q^74 + 36 * q^76 - 120 * q^79 + 36 * q^81 + 48 * q^84 - 72 * q^86 + 24 * q^89 + 48 * q^91 - 120 * q^94 + 24 * q^99

Introduction

L-functions

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