LMFDB - Embedded newform 925.2.bc.e.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.4
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29514 - 1.54348i) q^{2} +(0.697445 - 0.831183i) q^{3} +(-0.357666 + 2.02842i) q^{4} -2.18620 q^{6} +(-0.550712 - 1.51307i) q^{7} +(0.104199 - 0.0601595i) q^{8} +(0.316509 + 1.79501i) q^{9} +O(q^{10})$	\(q+(-1.29514 - 1.54348i) q^{2} +(0.697445 - 0.831183i) q^{3} +(-0.357666 + 2.02842i) q^{4} -2.18620 q^{6} +(-0.550712 - 1.51307i) q^{7} +(0.104199 - 0.0601595i) q^{8} +(0.316509 + 1.79501i) q^{9} +(1.39480 + 2.41587i) q^{11} +(1.43654 + 1.71200i) q^{12} +(4.52572 + 0.798007i) q^{13} +(-1.62215 + 2.80965i) q^{14} +(3.64319 + 1.32601i) q^{16} +(-2.48663 + 0.438460i) q^{17} +(2.36065 - 2.81331i) q^{18} +(2.66793 + 2.23866i) q^{19} +(-1.64173 - 0.597541i) q^{21} +(1.92240 - 5.28174i) q^{22} +(4.10436 + 2.36966i) q^{23} +(0.0226698 - 0.128567i) q^{24} +(-4.62971 - 8.01890i) q^{26} +(4.53173 + 2.61640i) q^{27} +(3.26612 - 0.575905i) q^{28} +(1.25908 + 2.18079i) q^{29} -6.81513 q^{31} +(-2.75405 - 7.56670i) q^{32} +(2.98083 + 0.525601i) q^{33} +(3.89728 + 3.27020i) q^{34} -3.75425 q^{36} +(4.29802 - 4.30431i) q^{37} -7.01727i q^{38} +(3.81973 - 3.20514i) q^{39} +(-0.0425588 + 0.241363i) q^{41} +(1.20397 + 3.30788i) q^{42} -0.304979i q^{43} +(-5.39929 + 1.96518i) q^{44} +(-1.65819 - 9.40404i) q^{46} +(-0.512655 - 0.295982i) q^{47} +(3.64309 - 2.10334i) q^{48} +(3.37622 - 2.83298i) q^{49} +(-1.36985 + 2.37264i) q^{51} +(-3.23739 + 8.89466i) q^{52} +(-3.06883 + 8.43153i) q^{53} +(-1.83084 - 10.3832i) q^{54} +(-0.148409 - 0.124530i) q^{56} +(3.72147 - 0.656196i) q^{57} +(1.73533 - 4.76779i) q^{58} +(4.35895 + 1.58653i) q^{59} +(0.0335326 - 0.190173i) q^{61} +(8.82652 + 10.5190i) q^{62} +(2.54167 - 1.46744i) q^{63} +(-4.23519 + 7.33556i) q^{64} +(-3.04933 - 5.28159i) q^{66} +(-1.74899 - 4.80530i) q^{67} -5.20076i q^{68} +(4.83219 - 1.75877i) q^{69} +(7.16448 + 6.01171i) q^{71} +(0.140967 + 0.167998i) q^{72} +3.08153i q^{73} +(-12.2101 - 1.05925i) q^{74} +(-5.49517 + 4.61100i) q^{76} +(2.88725 - 3.44089i) q^{77} +(-9.89414 - 1.74460i) q^{78} +(7.37091 - 2.68279i) q^{79} +(0.196992 - 0.0716991i) q^{81} +(0.427659 - 0.246909i) q^{82} +(1.51956 - 0.267940i) q^{83} +(1.79926 - 3.11640i) q^{84} +(-0.470730 + 0.394989i) q^{86} +(2.69077 + 0.474456i) q^{87} +(0.290676 + 0.167822i) q^{88} +(-8.78368 - 3.19700i) q^{89} +(-1.28493 - 7.28720i) q^{91} +(-6.27466 + 7.47784i) q^{92} +(-4.75318 + 5.66462i) q^{93} +(0.207116 + 1.17461i) q^{94} +(-8.21011 - 2.98824i) q^{96} +(-8.30821 - 4.79674i) q^{97} +(-8.74531 - 1.54203i) q^{98} +(-3.89506 + 3.26834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.29514	−	1.54348i	−0.915799	−	1.09141i	−0.995516	−	0.0945895i	$-0.969846\pi$
$2$	−1.29514	−	1.54348i	−0.915799	−	1.09141i	0.0797171	−	0.996818i	$-0.474598\pi$
$3$	0.697445	−	0.831183i	0.402670	−	0.479884i	−0.526162	−	0.850384i	$-0.676369\pi$
$3$	0.697445	−	0.831183i	0.402670	−	0.479884i	0.928832	+	0.370501i	$0.120814\pi$
$4$	−0.357666	+	2.02842i	−0.178833	+	1.01421i
$5$		0			0
$5$		0			0
$6$	−2.18620			−0.892514
$7$	−0.550712	−	1.51307i	−0.208150	−	0.571887i	0.791056	−	0.611744i	$-0.209532\pi$
$7$	−0.550712	−	1.51307i	−0.208150	−	0.571887i	−0.999205	+	0.0398576i	$0.987310\pi$
$8$	0.104199	−	0.0601595i	0.0368400	−	0.0212696i
$9$	0.316509	+	1.79501i	0.105503	+	0.598338i
$10$		0			0
$11$	1.39480	+	2.41587i	0.420550	+	0.728413i	0.995993	−	0.0894282i	$-0.0285040\pi$
$11$	1.39480	+	2.41587i	0.420550	+	0.728413i	−0.575444	+	0.817841i	$0.695171\pi$
$12$	1.43654	+	1.71200i	0.414693	+	0.494212i
$13$	4.52572	+	0.798007i	1.25521	+	0.221327i	0.761422	−	0.648256i	$-0.224501\pi$
$13$	4.52572	+	0.798007i	1.25521	+	0.221327i	0.493786	+	0.869583i	$0.335612\pi$
$14$	−1.62215	+	2.80965i	−0.433538	+	0.750909i
$15$		0			0
$16$	3.64319	+	1.32601i	0.910798	+	0.331503i
$17$	−2.48663	+	0.438460i	−0.603096	+	0.106342i	−0.466855	−	0.884334i	$-0.654613\pi$
$17$	−2.48663	+	0.438460i	−0.603096	+	0.106342i	−0.136241	+	0.990676i	$0.543502\pi$
$18$	2.36065	−	2.81331i	0.556411	−	0.663104i
$19$	2.66793	+	2.23866i	0.612065	+	0.513583i	0.895298	−	0.445468i	$-0.146963\pi$
$19$	2.66793	+	2.23866i	0.612065	+	0.513583i	−0.283233	+	0.959051i	$0.591407\pi$
$20$		0			0
$21$	−1.64173	−	0.597541i	−0.358255	−	0.130394i
$22$	1.92240	−	5.28174i	0.409856	−	1.12607i
$23$	4.10436	+	2.36966i	0.855819	+	0.494107i	0.862610	−	0.505870i	$-0.168828\pi$
$23$	4.10436	+	2.36966i	0.855819	+	0.494107i	−0.00679100	+	0.999977i	$0.502162\pi$
$24$	0.0226698	−	0.128567i	0.00462745	−	0.0262436i
$25$		0			0
$26$	−4.62971	−	8.01890i	−0.907961	−	1.57264i
$27$	4.53173	+	2.61640i	0.872132	+	0.503526i
$28$	3.26612	−	0.575905i	0.617238	−	0.108836i
$29$	1.25908	+	2.18079i	0.233805	+	0.404962i	0.958925	−	0.283660i	$-0.0915489\pi$
$29$	1.25908	+	2.18079i	0.233805	+	0.404962i	−0.725120	+	0.688623i	$0.758216\pi$
$30$		0			0
$31$	−6.81513			−1.22403			−0.612017	−	0.790845i	$-0.709642\pi$
$31$	−6.81513			−1.22403			−0.612017	+	0.790845i	$0.709642\pi$
$32$	−2.75405	−	7.56670i	−0.486852	−	1.33762i
$33$	2.98083	+	0.525601i	0.518896	+	0.0914954i
$34$	3.89728	+	3.27020i	0.668377	+	0.560835i
$35$		0			0
$36$	−3.75425			−0.625709
$37$	4.29802	−	4.30431i	0.706589	−	0.707624i
$37$	4.29802	−	4.30431i	0.706589	−	0.707624i
$38$		−	7.01727i		−	1.13835i
$39$	3.81973	−	3.20514i	0.611647	−	0.513232i
$40$		0			0
$41$	−0.0425588	+	0.241363i	−0.00664657	+	0.0376946i	−0.987951	−	0.154769i	$-0.950537\pi$
$41$	−0.0425588	+	0.241363i	−0.00664657	+	0.0376946i	0.981304	+	0.192464i	$0.0616478\pi$
$42$	1.20397	+	3.30788i	0.185776	+	0.510417i
$43$		−	0.304979i		−	0.0465089i	−0.999730	−	0.0232544i	$-0.992597\pi$
$43$		−	0.304979i		−	0.0465089i	0.999730	−	0.0232544i	$-0.00740279\pi$
$44$	−5.39929	+	1.96518i	−0.813973	+	0.296262i
$45$		0			0
$46$	−1.65819	−	9.40404i	−0.244486	−	1.38655i
$47$	−0.512655	−	0.295982i	−0.0747784	−	0.0431733i	0.462145	−	0.886805i	$-0.347080\pi$
$47$	−0.512655	−	0.295982i	−0.0747784	−	0.0431733i	−0.536923	+	0.843631i	$0.680413\pi$
$48$	3.64309	−	2.10334i	0.525834	−	0.303591i
$49$	3.37622	−	2.83298i	0.482317	−	0.404712i
$50$		0			0
$51$	−1.36985	+	2.37264i	−0.191817	+	0.332237i
$52$	−3.23739	+	8.89466i	−0.448945	+	1.23347i
$53$	−3.06883	+	8.43153i	−0.421536	+	1.15816i	0.529292	+	0.848440i	$0.322457\pi$
$53$	−3.06883	+	8.43153i	−0.421536	+	1.15816i	−0.950828	+	0.309720i	$0.899765\pi$
$54$	−1.83084	−	10.3832i	−0.249146	−	1.41298i
$55$		0			0
$56$	−0.148409	−	0.124530i	−0.0198320	−	0.0166411i
$57$	3.72147	−	0.656196i	0.492921	−	0.0869152i
$58$	1.73533	−	4.76779i	0.227860	−	0.626041i
$59$	4.35895	+	1.58653i	0.567486	+	0.206548i	0.609799	−	0.792556i	$-0.291250\pi$
$59$	4.35895	+	1.58653i	0.567486	+	0.206548i	−0.0423124	+	0.999104i	$0.513472\pi$
$60$		0			0
$61$	0.0335326	−	0.190173i	0.00429341	−	0.0243491i	−0.982586	−	0.185809i	$-0.940509\pi$
$61$	0.0335326	−	0.190173i	0.00429341	−	0.0243491i	0.986879	+	0.161460i	$0.0516204\pi$
$62$	8.82652	+	10.5190i	1.12097	+	1.33592i
$63$	2.54167	−	1.46744i	0.320221	−	0.184880i
$64$	−4.23519	+	7.33556i	−0.529399	+	0.916945i
$65$		0			0
$66$	−3.04933	−	5.28159i	−0.375346	−	0.650119i
$67$	−1.74899	−	4.80530i	−0.213673	−	0.587061i	0.785835	−	0.618436i	$-0.212234\pi$
$67$	−1.74899	−	4.80530i	−0.213673	−	0.587061i	−0.999508	+	0.0313751i	$0.990011\pi$
$68$		−	5.20076i		−	0.630684i
$69$	4.83219	−	1.75877i	0.581727	−	0.211731i
$70$		0			0
$71$	7.16448	+	6.01171i	0.850267	+	0.713459i	0.959849	−	0.280519i	$-0.0905065\pi$
$71$	7.16448	+	6.01171i	0.850267	+	0.713459i	−0.109581	+	0.993978i	$0.534951\pi$
$72$	0.140967	+	0.167998i	0.0166132	+	0.0197988i
$73$			3.08153i			0.360666i	0.983606	+	0.180333i	$0.0577176\pi$
$73$			3.08153i			0.360666i	−0.983606	+	0.180333i	$0.942282\pi$
$74$	−12.2101	−	1.05925i	−1.41940	−	0.123135i
$75$		0			0
$76$	−5.49517	+	4.61100i	−0.630340	+	0.528918i
$77$	2.88725	−	3.44089i	0.329032	−	0.392126i
$78$	−9.89414	−	1.74460i	−1.12029	−	0.197538i
$79$	7.37091	−	2.68279i	0.829292	−	0.301838i	0.107724	−	0.994181i	$-0.465644\pi$
$79$	7.37091	−	2.68279i	0.829292	−	0.301838i	0.721568	+	0.692343i	$0.243422\pi$
$80$		0			0
$81$	0.196992	−	0.0716991i	0.0218880	−	0.00796657i
$82$	0.427659	−	0.246909i	0.0472271	−	0.0272666i
$83$	1.51956	−	0.267940i	0.166794	−	0.0294102i	−0.0896276	−	0.995975i	$-0.528568\pi$
$83$	1.51956	−	0.267940i	0.166794	−	0.0294102i	0.256421	+	0.966565i	$0.417457\pi$
$84$	1.79926	−	3.11640i	0.196315	−	0.340027i
$85$		0			0
$86$	−0.470730	+	0.394989i	−0.0507601	+	0.0425928i
$87$	2.69077	+	0.474456i	0.288481	+	0.0508670i
$88$	0.290676	+	0.167822i	0.0309861	+	0.0178898i
$89$	−8.78368	−	3.19700i	−0.931068	−	0.338881i	−0.168435	−	0.985713i	$-0.553871\pi$
$89$	−8.78368	−	3.19700i	−0.931068	−	0.338881i	−0.762633	+	0.646832i	$0.776094\pi$
$90$		0			0
$91$	−1.28493	−	7.28720i	−0.134697	−	0.763906i
$92$	−6.27466	+	7.47784i	−0.654178	+	0.779619i
$93$	−4.75318	+	5.66462i	−0.492882	+	0.587394i
$94$	0.207116	+	1.17461i	0.0213623	+	0.121152i
$95$		0			0
$96$	−8.21011	−	2.98824i	−0.837941	−	0.304986i
$97$	−8.30821	−	4.79674i	−0.843570	−	0.487036i	0.0149058	−	0.999889i	$-0.495255\pi$
$97$	−8.30821	−	4.79674i	−0.843570	−	0.487036i	−0.858476	+	0.512853i	$0.828588\pi$
$98$	−8.74531	−	1.54203i	−0.883410	−	0.155769i
$99$	−3.89506	+	3.26834i	−0.391468	+	0.328481i
$100$		0			0
$101$	7.98745	−	13.8347i	0.794781	−	1.37660i	−0.128197	−	0.991749i	$-0.540919\pi$
$101$	7.98745	−	13.8347i	0.794781	−	1.37660i	0.922978	−	0.384853i	$-0.125748\pi$
$102$	5.43627	−	0.958562i	0.538271	−	0.0949118i
$103$	−13.5697	+	7.83449i	−1.33707	+	0.771955i	−0.986371	−	0.164534i	$-0.947388\pi$
$103$	−13.5697	+	7.83449i	−1.33707	+	0.771955i	−0.350695	+	0.936490i	$0.614054\pi$
$104$	0.519585	−	0.189113i	0.0509495	−	0.0185441i
$105$		0			0
$106$	16.9885	−	6.18329i	1.65007	−	0.600575i
$107$	1.56508	+	0.275966i	0.151302	+	0.0266787i	0.248786	−	0.968558i	$-0.419968\pi$
$107$	1.56508	+	0.275966i	0.151302	+	0.0266787i	−0.0974839	+	0.995237i	$0.531079\pi$
$108$	−6.92800	+	8.25647i	−0.666647	+	0.794480i
$109$	10.5182	−	8.82581i	1.00746	−	0.845359i	0.0194596	−	0.999811i	$-0.493805\pi$
$109$	10.5182	−	8.82581i	1.00746	−	0.845359i	0.988000	+	0.154451i	$0.0493610\pi$
$110$		0			0
$111$	−0.580036	−	6.57446i	−0.0550546	−	0.624020i
$112$		−	6.24265i		−	0.589875i
$113$	−10.7366	−	12.7953i	−1.01001	−	1.20368i	−0.978936	−	0.204167i	$-0.934551\pi$
$113$	−10.7366	−	12.7953i	−1.01001	−	1.20368i	−0.0310748	−	0.999517i	$-0.509893\pi$
$114$	−5.83263	−	4.89416i	−0.546276	−	0.458380i
$115$		0			0
$116$	−4.87390	+	1.77395i	−0.452530	+	0.164707i
$117$			8.37631i			0.774390i
$118$	−3.19665	−	8.78272i	−0.294275	−	0.808515i
$119$	2.03284	+	3.52098i	0.186350	+	0.322767i
$120$		0			0
$121$	1.60904	−	2.78694i	0.146276	−	0.253358i
$122$	−0.336957	+	0.194542i	−0.0305067	+	0.0176130i
$123$	0.170935	+	0.203712i	0.0154126	+	0.0183681i
$124$	2.43754	−	13.8240i	0.218898	−	1.24143i
$125$		0			0
$126$	−5.55678	−	2.02250i	−0.495037	−	0.180179i
$127$	4.64399	−	12.7592i	0.412087	−	1.13220i	−0.543992	−	0.839091i	$-0.683088\pi$
$127$	4.64399	−	12.7592i	0.412087	−	1.13220i	0.956079	−	0.293110i	$-0.0946901\pi$
$128$	0.947507	−	0.167071i	0.0837486	−	0.0147671i
$129$	−0.253494	−	0.212706i	−0.0223189	−	0.0187277i
$130$		0			0
$131$	3.75429	+	21.2917i	0.328014	+	1.86026i	0.487586	+	0.873075i	$0.337877\pi$
$131$	3.75429	+	21.2917i	0.328014	+	1.86026i	−0.159572	+	0.987186i	$0.551011\pi$
$132$	−2.13228	+	5.85840i	−0.185592	+	0.509909i
$133$	1.91798	−	5.26962i	0.166310	−	0.456934i
$134$	−5.15173	+	8.92305i	−0.445041	+	0.770834i
$135$		0			0
$136$	−0.232728	+	0.195282i	−0.0199562	+	0.0167453i
$137$	−11.3236	+	6.53770i	−0.967443	+	0.558553i	−0.898456	−	0.439064i	$-0.855310\pi$
$137$	−11.3236	+	6.53770i	−0.967443	+	0.558553i	−0.0689870	+	0.997618i	$0.521977\pi$
$138$	−8.97297	−	5.18055i	−0.763830	−	0.440998i
$139$	−0.305282	−	1.73134i	−0.0258937	−	0.146850i	0.969120	−	0.246590i	$-0.0793101\pi$
$139$	−0.305282	−	1.73134i	−0.0258937	−	0.146850i	−0.995014	+	0.0997397i	$0.968199\pi$
$140$		0			0
$141$	−0.603564	+	0.219679i	−0.0508292	+	0.0185003i
$142$		−	18.8442i		−	1.58137i
$143$	4.38461	+	12.0466i	0.366660	+	1.00739i
$144$	−1.22711	+	6.95927i	−0.102259	+	0.579939i
$145$		0			0
$146$	4.75629	−	3.99100i	0.393634	−	0.330298i
$147$		−	4.78210i		−	0.394421i
$148$	7.19371	+	10.2577i	0.591319	+	0.843178i
$149$	−7.97746			−0.653539			−0.326769	−	0.945104i	$-0.605960\pi$
$149$	−7.97746			−0.653539			−0.326769	+	0.945104i	$0.605960\pi$
$150$		0			0
$151$	6.20598	+	5.20744i	0.505036	+	0.423775i	0.859378	−	0.511340i	$-0.170851\pi$
$151$	6.20598	+	5.20744i	0.505036	+	0.423775i	−0.354342	+	0.935116i	$0.615295\pi$
$152$	0.412673	+	0.0727654i	0.0334722	+	0.00590205i
$153$	−1.57408	−	4.32475i	−0.127257	−	0.349636i
$154$	−9.05033			−0.729296
$155$		0			0
$156$	5.13519	+	8.89440i	0.411144	+	0.712122i
$157$	21.0813	−	3.71720i	1.68247	−	0.296665i	0.750952	−	0.660357i	$-0.229595\pi$
$157$	21.0813	−	3.71720i	1.68247	−	0.296665i	0.931519	+	0.363692i	$0.118484\pi$
$158$	−13.6872	−	7.90229i	−1.08889	−	0.628673i
$159$	4.86781	+	8.43129i	0.386042	+	0.668644i
$160$		0			0
$161$	1.32513	−	7.51519i	0.104435	−	0.592280i
$162$	−0.365797	−	0.211193i	−0.0287398	−	0.0165929i
$163$	−1.32665	+	3.64494i	−0.103911	+	0.285494i	−0.980743	−	0.195304i	$-0.937431\pi$
$163$	−1.32665	+	3.64494i	−0.103911	+	0.285494i	0.876831	+	0.480798i	$0.159653\pi$
$164$	−0.474365	−	0.172655i	−0.0370417	−	0.0134821i
$165$		0			0
$166$	−2.38160	−	1.99840i	−0.184848	−	0.155106i
$167$	−10.0189	+	11.9400i	−0.775285	+	0.923948i	−0.998710	−	0.0507725i	$-0.983832\pi$
$167$	−10.0189	+	11.9400i	−0.775285	+	0.923948i	0.223425	+	0.974721i	$0.428276\pi$
$168$	−0.207015	+	0.0365023i	−0.0159716	+	0.00281622i
$169$	7.62932	+	2.77685i	0.586871	+	0.213604i
$170$		0			0
$171$	−3.17400	+	5.49753i	−0.242722	+	0.420406i
$172$	0.618627	+	0.109081i	0.0471699	+	0.00831732i
$173$	9.57868	+	11.4154i	0.728254	+	0.867899i	0.995405	−	0.0957558i	$-0.0305268\pi$
$173$	9.57868	+	11.4154i	0.728254	+	0.867899i	−0.267151	+	0.963655i	$0.586082\pi$
$174$	−2.75260	−	4.76765i	−0.208674	−	0.361435i
$175$		0			0
$176$	1.87806	+	10.6510i	0.141564	+	0.802851i
$177$	4.35882	−	2.51657i	0.327629	−	0.189157i
$178$	6.44155	+	17.6980i	0.482814	+	1.32652i
$179$	4.53294			0.338808			0.169404	−	0.985547i	$-0.445816\pi$
$179$	4.53294			0.338808			0.169404	+	0.985547i	$0.445816\pi$
$180$		0			0
$181$	−2.07090	+	11.7447i	−0.153929	+	0.872974i	0.805830	+	0.592148i	$0.201720\pi$
$181$	−2.07090	+	11.7447i	−0.153929	+	0.872974i	−0.959758	+	0.280827i	$0.909391\pi$
$182$	−9.58351	+	11.4212i	−0.710377	+	0.846594i
$183$	−0.134681	−	0.160507i	−0.00995592	−	0.0118650i
$184$	0.570229			0.0420379
$185$		0			0
$186$	14.8993			1.09247
$187$	−4.52762	−	5.39581i	−0.331093	−	0.394581i
$188$	0.783735	−	0.934019i	0.0571598	−	0.0681204i
$189$	1.46311	−	8.29770i	0.106426	−	0.603569i
$190$		0			0
$191$	−0.597365			−0.0432238			−0.0216119	−	0.999766i	$-0.506880\pi$
$191$	−0.597365			−0.0432238			−0.0216119	+	0.999766i	$0.506880\pi$
$192$	3.14338	+	8.63637i	0.226854	+	0.623277i
$193$	10.4639	−	6.04135i	0.753210	−	0.434866i	−0.0736423	−	0.997285i	$-0.523462\pi$
$193$	10.4639	−	6.04135i	0.753210	−	0.434866i	0.826853	+	0.562418i	$0.190129\pi$
$194$	3.35656	+	19.0360i	0.240987	+	1.36671i
$195$		0			0
$196$	4.53893	+	7.86166i	0.324209	+	0.561547i
$197$	0.541405	+	0.645221i	0.0385735	+	0.0459701i	0.784986	−	0.619513i	$-0.212670\pi$
$197$	0.541405	+	0.645221i	0.0385735	+	0.0459701i	−0.746413	+	0.665483i	$0.768226\pi$
$198$	10.0893	+	1.77901i	0.717012	+	0.126429i
$199$	9.58626	−	16.6039i	0.679552	−	1.17702i	−0.295564	−	0.955323i	$-0.595508\pi$
$199$	9.58626	−	16.6039i	0.679552	−	1.17702i	0.975116	−	0.221696i	$-0.0711591\pi$
$200$		0			0
$201$	−5.21391	−	1.89771i	−0.367761	−	0.133854i
$202$	−31.6984	+	5.58929i	−2.23029	+	0.393261i
$203$	2.60630	−	3.10606i	0.182926	−	0.218003i
$204$	−4.32278	−	3.62724i	−0.302655	−	0.253958i
$205$		0			0
$206$	29.6671	+	10.7979i	2.06700	+	0.752327i
$207$	−2.95449	+	8.11741i	−0.205352	+	0.564199i
$208$	15.4299	+	8.90845i	1.06987	+	0.617690i
$209$	−1.68707	+	9.56787i	−0.116697	+	0.661823i
$210$		0			0
$211$	12.9399	+	22.4125i	0.890817	+	1.54294i	0.838897	+	0.544290i	$0.183201\pi$
$211$	12.9399	+	22.4125i	0.890817	+	1.54294i	0.0519199	+	0.998651i	$0.483466\pi$
$212$	−16.0051	−	9.24055i	−1.09923	−	0.634643i
$213$	9.99367	−	1.76215i	0.684755	−	0.120741i
$214$	−1.60105	−	2.77309i	−0.109445	−	0.189565i
$215$		0			0
$216$	0.629605			0.0428392
$217$	3.75318	+	10.3118i	0.254782	+	0.700009i
$218$	−27.2450	−	4.80402i	−1.84526	−	0.325370i
$219$	2.56132	+	2.14920i	0.173078	+	0.145230i
$220$		0			0
$221$	−11.6037			−0.780548
$222$	−9.39634	+	9.41009i	−0.630641	+	0.631564i
$223$			19.4013i			1.29921i	0.760273	+	0.649603i	$0.225065\pi$
$223$			19.4013i			1.29921i	−0.760273	+	0.649603i	$0.774935\pi$
$224$	−9.93225	+	8.33414i	−0.663626	+	0.556848i
$225$		0			0
$226$	−5.84408	+	33.1434i	−0.388742	+	2.20467i
$227$	0.615312	+	1.69056i	0.0408397	+	0.112206i	0.958436	−	0.285307i	$-0.0920956\pi$
$227$	0.615312	+	1.69056i	0.0408397	+	0.112206i	−0.917597	+	0.397513i	$0.869873\pi$
$228$			7.78342i			0.515469i
$229$	15.6280	−	5.68813i	1.03273	−	0.375882i	0.230609	−	0.973047i	$-0.425928\pi$
$229$	15.6280	−	5.68813i	1.03273	−	0.375882i	0.802119	+	0.597164i	$0.203706\pi$
$230$		0			0
$231$	−0.846310	−	4.79966i	−0.0556831	−	0.315795i
$232$	0.262391	+	0.151491i	0.0172268	+	0.00994589i
$233$	22.5861	−	13.0401i	1.47967	−	0.854285i	0.479931	−	0.877306i	$-0.340662\pi$
$233$	22.5861	−	13.0401i	1.47967	−	0.854285i	0.999735	+	0.0230209i	$0.00732841\pi$
$234$	12.9287	−	10.8485i	0.845174	−	0.709186i
$235$		0			0
$236$	−4.77719	+	8.27434i	−0.310969	+	0.538614i
$237$	2.91092	−	7.99768i	0.189084	−	0.519505i
$238$	2.80177	−	7.69779i	0.181612	−	0.498974i
$239$	−3.81605	−	21.6419i	−0.246839	−	1.39990i	−0.816182	−	0.577796i	$-0.803913\pi$
$239$	−3.81605	−	21.6419i	−0.246839	−	1.39990i	0.569342	−	0.822101i	$-0.307198\pi$
$240$		0			0
$241$	−8.02027	−	6.72980i	−0.516631	−	0.433505i	0.346824	−	0.937930i	$-0.387260\pi$
$241$	−8.02027	−	6.72980i	−0.516631	−	0.433505i	−0.863455	+	0.504425i	$0.831704\pi$
$242$	−6.38551	+	1.12594i	−0.410476	+	0.0723780i
$243$	−5.29136	+	14.5379i	−0.339441	+	0.932607i
$244$	0.373757	+	0.136037i	0.0239274	+	0.00870884i
$245$		0			0
$246$	0.0930423	−	0.527669i	0.00593216	−	0.0336429i
$247$	10.2878	+	12.2606i	0.654599	+	0.780121i
$248$	−0.710133	+	0.409995i	−0.0450935	+	0.0260347i
$249$	0.837105	−	1.44991i	0.0530494	−	0.0918842i
$250$		0			0
$251$	7.33490	+	12.7044i	0.462975	+	0.801895i	0.999108	−	0.0422380i	$-0.0134488\pi$
$251$	7.33490	+	12.7044i	0.462975	+	0.801895i	−0.536133	+	0.844134i	$0.680115\pi$
$252$	2.06751	+	5.68045i	0.130241	+	0.357834i
$253$			13.2208i			0.831186i
$254$	−25.7083	+	9.35705i	−1.61308	+	0.587113i
$255$		0			0
$256$	11.4924	+	9.64323i	0.718272	+	0.602702i
$257$	10.4516	+	12.4557i	0.651953	+	0.776967i	0.986207	−	0.165516i	$-0.0529289\pi$
$257$	10.4516	+	12.4557i	0.651953	+	0.776967i	−0.334254	+	0.942483i	$0.608484\pi$
$258$			0.666747i			0.0415098i
$259$	−8.87969	−	4.13276i	−0.551757	−	0.256797i
$260$		0			0
$261$	−3.51604	+	2.95031i	−0.217637	+	0.182619i
$262$	28.0010	−	33.3703i	1.72991	−	2.06162i
$263$	−14.9616	−	2.63813i	−0.922569	−	0.162674i	−0.307864	−	0.951431i	$-0.599614\pi$
$263$	−14.9616	−	2.63813i	−0.922569	−	0.162674i	−0.614706	+	0.788757i	$0.710725\pi$
$264$	0.342221	−	0.124558i	0.0210622	−	0.00766603i
$265$		0			0
$266$	−10.6176	+	3.86450i	−0.651008	+	0.236947i
$267$	−8.78343	+	5.07112i	−0.537537	+	0.310347i
$268$	10.3727	−	1.82899i	0.633616	−	0.111724i
$269$	−7.10971	+	12.3144i	−0.433487	+	0.750821i	−0.997171	−	0.0751693i	$-0.976050\pi$
$269$	−7.10971	+	12.3144i	−0.433487	+	0.750821i	0.563684	+	0.825991i	$0.309384\pi$
$270$		0			0
$271$	7.97092	−	6.68840i	0.484199	−	0.406291i	−0.367743	−	0.929927i	$-0.619869\pi$
$271$	7.97092	−	6.68840i	0.484199	−	0.406291i	0.851942	+	0.523636i	$0.175425\pi$
$272$	−9.64066	−	1.69991i	−0.584551	−	0.103072i
$273$	−6.95317	−	4.01441i	−0.420825	−	0.242963i
$274$	24.7565	+	9.01061i	1.49559	+	0.544351i
$275$		0			0
$276$	1.83923	+	10.4308i	0.110708	+	0.627859i
$277$	−17.9614	+	21.4055i	−1.07919	+	1.28613i	−0.123318	+	0.992367i	$0.539353\pi$
$277$	−17.9614	+	21.4055i	−1.07919	+	1.28613i	−0.955877	+	0.293767i	$0.905091\pi$
$278$	−2.27691	+	2.71352i	−0.136560	+	0.162746i
$279$	−2.15705	−	12.2333i	−0.129139	−	0.732386i
$280$		0			0
$281$	−25.9010	−	9.42720i	−1.54513	−	0.562380i	−0.577858	−	0.816138i	$-0.696111\pi$
$281$	−25.9010	−	9.42720i	−1.54513	−	0.562380i	−0.967268	+	0.253758i	$0.918333\pi$
$282$	1.12077	+	0.647076i	0.0667408	+	0.0385328i
$283$	11.7915	+	2.07916i	0.700931	+	0.123593i	0.512746	−	0.858541i	$-0.328628\pi$
$283$	11.7915	+	2.07916i	0.700931	+	0.123593i	0.188185	+	0.982134i	$0.439740\pi$
$284$	−14.7568	+	12.3824i	−0.875654	+	0.734761i
$285$		0			0
$286$	12.9151	−	22.3696i	0.763685	−	1.32274i
$287$	0.388637	−	0.0685272i	0.0229405	−	0.00404503i
$288$	12.7106	−	7.33849i	0.748982	−	0.432425i
$289$	−9.98370	+	3.63377i	−0.587277	+	0.213751i
$290$		0			0
$291$	−9.78149	+	3.56017i	−0.573401	+	0.208701i
$292$	−6.25066	−	1.10216i	−0.365792	−	0.0644990i
$293$	17.4943	−	20.8490i	1.02203	−	1.21801i	0.0463243	−	0.998926i	$-0.485249\pi$
$293$	17.4943	−	20.8490i	1.02203	−	1.21801i	0.975706	−	0.219082i	$-0.0703063\pi$
$294$	−7.38109	+	6.19347i	−0.430474	+	0.361211i
$295$		0			0
$296$	0.188905	−	0.707073i	0.0109799	−	0.0410978i
$297$			14.5974i			0.847030i
$298$	10.3319	+	12.3131i	0.598510	+	0.713277i
$299$	16.6842	+	13.9997i	0.964872	+	0.809624i
$300$		0			0
$301$	−0.461455	+	0.167956i	−0.0265978	+	0.00968081i
$302$		−	16.3232i		−	0.939293i
$303$	−5.92833	−	16.2880i	−0.340574	−	0.935719i
$304$	6.75129	+	11.6936i	0.387213	+	0.670672i
$305$		0			0
$306$	−4.63653	+	8.03071i	−0.265053	+	0.459085i
$307$	−16.4838	+	9.51695i	−0.940783	+	0.543161i	−0.890206	−	0.455559i	$-0.849439\pi$
$307$	−16.4838	+	9.51695i	−0.940783	+	0.543161i	−0.0505773	+	0.998720i	$0.516106\pi$
$308$	5.94691	+	7.08725i	0.338857	+	0.403834i
$309$	−2.95225	+	16.7431i	−0.167948	+	0.952480i
$310$		0			0
$311$	−26.4730	−	9.63537i	−1.50114	−	0.546372i	−0.544787	−	0.838574i	$-0.683390\pi$
$311$	−26.4730	−	9.63537i	−1.50114	−	0.546372i	−0.956356	+	0.292203i	$0.905612\pi$
$312$	0.205194	−	0.563766i	0.0116168	−	0.0319170i
$313$	−30.5149	+	5.38060i	−1.72480	+	0.304129i	−0.946247	−	0.323445i	$-0.895159\pi$
$313$	−30.5149	+	5.38060i	−1.72480	+	0.304129i	−0.778556	+	0.627575i	$0.784048\pi$
$314$	−33.0406	−	27.7243i	−1.86459	−	1.56458i
$315$		0			0
$316$	2.80552	+	15.9109i	0.157823	+	0.895057i
$317$	2.15869	−	5.93096i	0.121244	−	0.333116i	−0.864192	−	0.503163i	$-0.832170\pi$
$317$	2.15869	−	5.93096i	0.121244	−	0.333116i	0.985436	+	0.170047i	$0.0543919\pi$
$318$	6.70908	−	18.4330i	0.376226	−	1.03367i
$319$	−3.51234	+	6.08355i	−0.196653	+	0.340614i
$320$		0			0
$321$	1.32094	−	1.10840i	0.0737276	−	0.0618648i
$322$	−13.3158	+	7.68787i	−0.742060	+	0.428428i
$323$	−7.61571	−	4.39693i	−0.423749	−	0.244652i
$324$	0.0749790	+	0.425227i	0.00416550	+	0.0236237i
$325$		0			0
$326$	7.34410	−	2.67303i	0.406752	−	0.148046i
$327$		−	14.8981i		−	0.823865i
$328$	0.0100857	+	0.0277102i	0.000556889	+	0.00153004i
$329$	−0.165515	+	0.938684i	−0.00912515	+	0.0517513i
$330$		0			0
$331$	25.9591	−	21.7823i	1.42684	−	1.19726i	0.479291	−	0.877656i	$-0.340894\pi$
$331$	25.9591	−	21.7823i	1.42684	−	1.19726i	0.947551	−	0.319606i	$-0.103550\pi$
$332$			3.17815i			0.174424i
$333$	9.08665	+	6.35264i	0.497945	+	0.348123i
$334$	31.4051			1.71841
$335$		0			0
$336$	−5.18879	−	4.35391i	−0.283072	−	0.237525i
$337$	11.3239	+	1.99671i	0.616851	+	0.108768i	0.473338	−	0.880881i	$-0.343049\pi$
$337$	11.3239	+	1.99671i	0.616851	+	0.108768i	0.143513	+	0.989648i	$0.454160\pi$
$338$	−5.59499	−	15.3721i	−0.304328	−	0.836133i
$339$	−18.1234			−0.984330
$340$		0			0
$341$	−9.50578	−	16.4645i	−0.514767	−	0.891603i
$342$	12.5961	−	2.22103i	0.681119	−	0.120100i
$343$	−15.9070	−	9.18390i	−0.858897	−	0.495884i
$344$	−0.0183474	−	0.0317786i	−0.000989226	−	0.00171339i
$345$		0			0
$346$	5.21382	−	29.5691i	0.280297	−	1.58964i
$347$	−13.8168	−	7.97714i	−0.741726	−	0.428235i	0.0809708	−	0.996716i	$-0.474198\pi$
$347$	−13.8168	−	7.97714i	−0.741726	−	0.428235i	−0.822696	+	0.568481i	$0.807531\pi$
$348$	−1.92480	+	5.28833i	−0.103180	+	0.283484i
$349$	−8.27111	−	3.01044i	−0.442742	−	0.161145i	0.111023	−	0.993818i	$-0.464587\pi$
$349$	−8.27111	−	3.01044i	−0.442742	−	0.161145i	−0.553765	+	0.832673i	$0.686810\pi$
$350$		0			0
$351$	18.4214	+	15.4574i	0.983264	+	0.825056i
$352$	14.4388	−	17.2075i	0.769591	−	0.917163i
$353$	−18.3819	+	3.24123i	−0.978371	+	0.172513i	−0.639895	−	0.768462i	$-0.721022\pi$
$353$	−18.3819	+	3.24123i	−0.978371	+	0.172513i	−0.338475	+	0.940975i	$0.609911\pi$
$354$	−9.52954	−	3.46847i	−0.506489	−	0.184347i
$355$		0			0
$356$	9.62649	−	16.6736i	0.510203	−	0.883697i
$357$	4.34437	+	0.766029i	0.229928	+	0.0405426i
$358$	−5.87077	−	6.99652i	−0.310280	−	0.369777i
$359$	7.77409	+	13.4651i	0.410301	+	0.710662i	0.994923	−	0.100644i	$-0.0320903\pi$
$359$	7.77409	+	13.4651i	0.410301	+	0.710662i	−0.584622	+	0.811306i	$0.698757\pi$
$360$		0			0
$361$	−1.19306	−	6.76619i	−0.0627927	−	0.356115i
$362$	20.8098	−	12.0145i	1.09374	−	0.631470i
$363$	−1.19424	−	3.28114i	−0.0626812	−	0.172215i
$364$	15.2411			0.798851
$365$		0			0
$366$	−0.0733090	+	0.415756i	−0.00383192	+	0.0217319i
$367$	−2.36442	+	2.81781i	−0.123422	+	0.147088i	−0.824217	−	0.566274i	$-0.808384\pi$
$367$	−2.36442	+	2.81781i	−0.123422	+	0.147088i	0.700795	+	0.713363i	$0.252829\pi$
$368$	11.8108	+	14.0755i	0.615680	+	0.733739i
$369$	−0.446720			−0.0232553
$370$		0			0
$371$	14.4475			0.750078
$372$	−9.79021	−	11.6675i	−0.507599	−	0.604932i
$373$	−0.199618	+	0.237896i	−0.0103358	+	0.0123178i	−0.771188	−	0.636608i	$-0.780337\pi$
$373$	−0.199618	+	0.237896i	−0.0103358	+	0.0123178i	0.760852	+	0.648926i	$0.224781\pi$
$374$	−2.46445	+	13.9766i	−0.127434	+	0.722714i
$375$		0			0
$376$	−0.0712245			−0.00367312
$377$	3.95796	+	10.8744i	0.203845	+	0.560060i
$378$	−14.7023	+	8.48837i	−0.756204	+	0.436595i
$379$	−4.88252	−	27.6902i	−0.250798	−	1.42235i	−0.806632	−	0.591054i	$-0.798712\pi$
$379$	−4.88252	−	27.6902i	−0.250798	−	1.42235i	0.555833	−	0.831294i	$-0.312399\pi$
$380$		0			0
$381$	−7.36634	−	12.7589i	−0.377389	−	0.653657i
$382$	0.773669	+	0.922023i	0.0395844	+	0.0471748i
$383$	19.3123	+	3.40529i	0.986814	+	0.174002i	0.643689	−	0.765287i	$-0.277403\pi$
$383$	19.3123	+	3.40529i	0.986814	+	0.174002i	0.343126	+	0.939289i	$0.388514\pi$
$384$	0.521968	−	0.904074i	0.0266365	−	0.0461359i
$385$		0			0
$386$	−22.8769	−	8.32653i	−1.16441	−	0.423809i
$387$	0.547442	−	0.0965288i	0.0278280	−	0.00490683i
$388$	12.7014	−	15.1369i	0.644815	−	0.768461i
$389$	−15.3384	−	12.8705i	−0.777690	−	0.652559i	0.164976	−	0.986298i	$-0.447245\pi$
$389$	−15.3384	−	12.8705i	−0.777690	−	0.652559i	−0.942666	+	0.333738i	$0.891690\pi$
$390$		0			0
$391$	−11.2450	−	4.09285i	−0.568685	−	0.206985i
$392$	0.181369	−	0.498306i	0.00916050	−	0.0251683i
$393$	20.3157	+	11.7293i	1.02479	+	0.591663i
$394$	0.294695	−	1.67130i	0.0148465	−	0.0841987i
$395$		0			0
$396$	−5.23645	−	9.06980i	−0.263142	−	0.455775i
$397$	3.16465	+	1.82711i	0.158829	+	0.0917002i	0.577308	−	0.816526i	$-0.304103\pi$
$397$	3.16465	+	1.82711i	0.158829	+	0.0917002i	−0.418479	+	0.908227i	$0.637437\pi$
$398$	−38.0433	+	6.70806i	−1.90694	+	0.336245i
$399$	−3.04233	−	5.26947i	−0.152307	−	0.263803i
$400$		0			0
$401$	−17.3420			−0.866018			−0.433009	−	0.901390i	$-0.642548\pi$
$401$	−17.3420			−0.866018			−0.433009	+	0.901390i	$0.642548\pi$
$402$	3.82364	+	10.5054i	0.190706	+	0.523960i
$403$	−30.8434	−	5.43852i	−1.53642	−	0.270912i
$404$	25.2057	+	21.1501i	1.25403	+	1.05226i
$405$		0			0
$406$	−8.16966			−0.405453
$407$	16.3936	+	4.37979i	0.812598	+	0.217098i
$408$			0.329637i			0.0163195i
$409$	20.2181	−	16.9650i	0.999723	−	0.838867i	0.0127768	−	0.999918i	$-0.495933\pi$
$409$	20.2181	−	16.9650i	0.999723	−	0.838867i	0.986946	+	0.161051i	$0.0514885\pi$
$410$		0			0
$411$	−2.46359	+	13.9717i	−0.121520	+	0.689173i
$412$	−11.0382	−	30.3273i	−0.543815	−	1.49412i
$413$		−	7.46911i		−	0.367531i
$414$	16.3555	−	5.95293i	0.803831	−	0.292571i
$415$		0			0
$416$	−6.42580	−	36.4425i	−0.315051	−	1.78674i
$417$	−1.65198	−	0.953770i	−0.0808977	−	0.0467063i
$418$	16.9528	−	9.78772i	0.829190	−	0.478733i
$419$	−1.74574	+	1.46485i	−0.0852851	+	0.0715627i	−0.684433	−	0.729075i	$-0.739950\pi$
$419$	−1.74574	+	1.46485i	−0.0852851	+	0.0715627i	0.599148	+	0.800638i	$0.295506\pi$
$420$		0			0
$421$	−13.0789	+	22.6532i	−0.637424	+	1.10405i	0.348572	+	0.937282i	$0.386667\pi$
$421$	−13.0789	+	22.6532i	−0.637424	+	1.10405i	−0.985996	+	0.166769i	$0.946666\pi$
$422$	17.8344	−	48.9997i	0.868167	−	2.38527i
$423$	0.369031	−	1.01390i	0.0179429	−	0.0492977i
$424$	0.187467	+	1.06318i	0.00910421	+	0.0516325i
$425$		0			0
$426$	−15.6630	−	13.1428i	−0.758875	−	0.636772i
$427$	−0.306211	+	0.0539933i	−0.0148186	+	0.00261292i
$428$	−1.11955	+	3.07595i	−0.0541156	+	0.148682i
$429$	13.0710	+	4.75745i	0.631073	+	0.229692i
$430$		0			0
$431$	−3.44174	+	19.5191i	−0.165783	+	0.940201i	0.782471	+	0.622687i	$0.213959\pi$
$431$	−3.44174	+	19.5191i	−0.165783	+	0.940201i	−0.948254	+	0.317514i	$0.897152\pi$
$432$	13.0406	+	15.5412i	0.627415	+	0.747725i
$433$	16.6598	−	9.61853i	0.800618	−	0.462237i	−0.0430690	−	0.999072i	$-0.513714\pi$
$433$	16.6598	−	9.61853i	0.800618	−	0.462237i	0.843687	+	0.536835i	$0.180380\pi$
$434$	11.0552	−	19.1481i	0.530665	−	0.919139i
$435$		0			0
$436$	14.1405	+	24.4920i	0.677206	+	1.17296i
$437$	5.64530	+	15.5103i	0.270051	+	0.741960i
$438$		−	6.73686i		−	0.321900i
$439$	−11.7083	+	4.26146i	−0.558805	+	0.203388i	−0.605954	−	0.795500i	$-0.707208\pi$
$439$	−11.7083	+	4.26146i	−0.558805	+	0.203388i	0.0471495	+	0.998888i	$0.484986\pi$
$440$		0			0
$441$	6.15384	+	5.16369i	0.293040	+	0.245890i
$442$	15.0283	+	17.9101i	0.714825	+	0.851895i
$443$		−	15.8882i		−	0.754872i	−0.926036	−	0.377436i	$-0.876806\pi$
$443$		−	15.8882i		−	0.754872i	0.926036	−	0.377436i	$-0.123194\pi$
$444$	13.5432	+	1.17490i	0.642734	+	0.0557583i
$445$		0			0
$446$	29.9456	−	25.1273i	1.41796	−	1.18981i
$447$	−5.56384	+	6.63073i	−0.263161	+	0.313623i
$448$	13.4316	+	2.36835i	0.634583	+	0.111894i
$449$	13.1686	−	4.79298i	0.621464	−	0.226195i	−0.0120476	−	0.999927i	$-0.503835\pi$
$449$	13.1686	−	4.79298i	0.621464	−	0.226195i	0.633512	+	0.773733i	$0.281613\pi$
$450$		0			0
$451$	−0.642464	+	0.233838i	−0.0302525	+	0.0110110i
$452$	29.7945	−	17.2018i	1.40141	−	0.809107i
$453$	8.65667	−	1.52640i	0.406726	−	0.0717167i
$454$	1.81243	−	3.13922i	0.0850616	−	0.147331i
$455$		0			0
$456$	0.348298	−	0.292257i	0.0163106	−	0.0136862i
$457$	6.85458	+	1.20865i	0.320644	+	0.0565381i	0.331653	−	0.943401i	$-0.392394\pi$
$457$	6.85458	+	1.20865i	0.320644	+	0.0565381i	−0.0110099	+	0.999939i	$0.503505\pi$
$458$	−29.0199	−	16.7547i	−1.35601	−	0.782894i
$459$	−12.4159	−	4.51902i	−0.579525	−	0.210930i
$460$		0			0
$461$	−3.86251	−	21.9054i	−0.179895	−	1.02024i	−0.932341	−	0.361581i	$-0.882237\pi$
$461$	−3.86251	−	21.9054i	−0.179895	−	1.02024i	0.752446	−	0.658654i	$-0.228874\pi$
$462$	−6.31211	+	7.52248i	−0.293666	+	0.349977i
$463$	−21.8973	+	26.0961i	−1.01765	+	1.21279i	−0.0407352	+	0.999170i	$0.512970\pi$
$463$	−21.8973	+	26.0961i	−1.01765	+	1.21279i	−0.976917	+	0.213620i	$0.931474\pi$
$464$	1.69531	+	9.61459i	0.0787029	+	0.446346i
$465$		0			0
$466$	−49.3793	−	17.9726i	−2.28745	−	0.832564i
$467$	1.06863	+	0.616975i	0.0494504	+	0.0285502i	0.524521	−	0.851397i	$-0.324244\pi$
$467$	1.06863	+	0.616975i	0.0494504	+	0.0285502i	−0.475071	+	0.879947i	$0.657578\pi$
$468$	−16.9907	−	2.99592i	−0.785395	−	0.138486i
$469$	−6.30757	+	5.29268i	−0.291257	+	0.244393i
$470$		0			0
$471$	11.6134	−	20.1150i	0.535116	−	0.926849i
$472$	0.549644	−	0.0969171i	0.0252994	−	0.00446097i
$473$	0.736791	−	0.425387i	0.0338777	−	0.0195593i
$474$	−16.1143	+	5.86513i	−0.740155	+	0.269394i
$475$		0			0
$476$	−7.86911	+	2.86412i	−0.360680	+	0.131277i
$477$	−16.1060	−	2.83993i	−0.737444	−	0.130031i
$478$	−28.4616	+	33.9192i	−1.30180	+	1.55143i
$479$	6.06933	−	5.09277i	0.277315	−	0.232695i	−0.493513	−	0.869738i	$-0.664287\pi$
$479$	6.06933	−	5.09277i	0.277315	−	0.232695i	0.770828	+	0.637044i	$0.219843\pi$
$480$		0			0
$481$	22.8865	−	16.0502i	1.04353	−	0.731828i
$482$			21.0952i			0.960858i
$483$	−5.32229	−	6.34286i	−0.242173	−	0.288610i
$484$	5.07759	+	4.26060i	0.230800	+	0.193664i
$485$		0			0
$486$	29.2920	−	10.6614i	1.32871	−	0.483612i
$487$			11.9901i			0.543325i	0.962393	+	0.271663i	$0.0875735\pi$
$487$			11.9901i			0.543325i	−0.962393	+	0.271663i	$0.912427\pi$
$488$	−0.00794662	−	0.0218332i	−0.000359727	−	0.000988341i
$489$	2.10435	+	3.64484i	0.0951620	+	0.164825i
$490$		0			0
$491$	−6.73154	+	11.6594i	−0.303790	+	0.526180i	−0.976991	−	0.213280i	$-0.931585\pi$
$491$	−6.73154	+	11.6594i	−0.303790	+	0.526180i	0.673201	+	0.739459i	$0.264919\pi$
$492$	−0.474351	+	0.273867i	−0.0213854	+	0.0123469i
$493$	−4.08705	−	4.87076i	−0.184072	−	0.219368i
$494$	5.59983	−	31.7582i	0.251948	−	1.42887i
$495$		0			0
$496$	−24.8288	−	9.03696i	−1.11485	−	0.405771i
$497$	5.15057	−	14.1511i	0.231035	−	0.634763i
$498$	−3.32207	+	0.585771i	−0.148866	+	0.0262490i
$499$	−24.8121	−	20.8198i	−1.11074	−	0.932022i	−0.112641	−	0.993636i	$-0.535931\pi$
$499$	−24.8121	−	20.8198i	−1.11074	−	0.932022i	−0.998100	+	0.0616133i	$0.980375\pi$
$500$		0			0
$501$	2.93674	+	16.6551i	0.131204	+	0.744093i
$502$	10.1094	−	27.7752i	0.451203	−	1.23967i
$503$	9.07894	−	24.9442i	0.404810	−	1.11221i	−0.555072	−	0.831802i	$-0.687309\pi$
$503$	9.07894	−	24.9442i	0.404810	−	1.11221i	0.959882	−	0.280404i	$-0.0904685\pi$
$504$	0.176561	−	0.305812i	0.00786464	−	0.0136219i
$505$		0			0
$506$	20.4061	−	17.1228i	0.907163	−	0.761200i
$507$	7.62910	−	4.40466i	0.338820	−	0.195618i
$508$	24.2202	+	13.9835i	1.07460	+	0.620418i
$509$	3.90495	+	22.1460i	0.173084	+	0.981606i	0.940333	+	0.340257i	$0.110514\pi$
$509$	3.90495	+	22.1460i	0.173084	+	0.981606i	−0.767249	+	0.641350i	$0.778375\pi$
$510$		0			0
$511$	4.66258	−	1.69704i	0.206260	−	0.0750726i
$512$		−	32.1518i		−	1.42092i
$513$	6.23312	+	17.1254i	0.275199	+	0.756103i
$514$	5.68896	−	32.2637i	0.250929	−	1.42309i
$515$		0			0
$516$	0.522125	−	0.438115i	0.0229853	−	0.0192869i
$517$		−	1.65135i		−	0.0726261i
$518$	5.12155	+	19.0581i	0.225028	+	0.837366i
$519$	16.1689			0.709737
$520$		0			0
$521$	−16.4086	−	13.7685i	−0.718875	−	0.603208i	0.208199	−	0.978086i	$-0.433240\pi$
$521$	−16.4086	−	13.7685i	−0.718875	−	0.603208i	−0.927074	+	0.374879i	$0.877684\pi$
$522$	9.10749	+	1.60590i	0.398624	+	0.0702882i
$523$	−0.394250	−	1.08319i	−0.0172393	−	0.0473647i	0.930774	−	0.365594i	$-0.119134\pi$
$523$	−0.394250	−	1.08319i	−0.0172393	−	0.0473647i	−0.948014	+	0.318229i	$0.896912\pi$
$524$	−44.5313			−1.94536
$525$		0			0
$526$	15.3053	+	26.5096i	0.667345	+	1.15588i
$527$	16.9467	−	2.98816i	0.738210	−	0.130166i
$528$	10.1628	+	5.86749i	0.442279	+	0.255350i
$529$	−0.269467	−	0.466731i	−0.0117160	−	0.0202926i
$530$		0			0
$531$	−1.46819	+	8.32652i	−0.0637140	+	0.361340i
$532$	10.0030	+	5.77525i	0.433686	+	0.250389i
$533$	−0.385219	+	1.05838i	−0.0166857	+	0.0458435i
$534$	19.2029	+	6.98929i	0.830991	+	0.302456i
$535$		0			0
$536$	−0.471328	−	0.395491i	−0.0203583	−	0.0170826i
$537$	3.16148	−	3.76770i	0.136428	−	0.162588i
$538$	28.2151	−	4.97508i	1.21644	−	0.214491i
$539$	11.5533	+	4.20505i	0.497635	+	0.181124i
$540$		0			0
$541$	20.6528	−	35.7717i	0.887932	−	1.53794i	0.0456167	−	0.998959i	$-0.485475\pi$
$541$	20.6528	−	35.7717i	0.887932	−	1.53794i	0.842316	−	0.538985i	$-0.181192\pi$
$542$	−20.6468	−	3.64060i	−0.886858	−	0.156377i
$543$	8.31763	+	9.91257i	0.356944	+	0.425389i
$544$	10.1660	+	17.6080i	0.435863	+	0.754937i
$545$		0			0
$546$	2.80912	+	15.9313i	0.120219	+	0.681797i
$547$	−4.76811	+	2.75287i	−0.203870	+	0.117704i	−0.598459	−	0.801153i	$-0.704220\pi$
$547$	−4.76811	+	2.75287i	−0.203870	+	0.117704i	0.394590	+	0.918857i	$0.370887\pi$
$548$	−9.21115	−	25.3074i	−0.393481	−	1.08108i
$549$	0.351976			0.0150220
$550$		0			0
$551$	−1.52291	+	8.63684i	−0.0648781	+	0.367942i
$552$	0.397704	−	0.473965i	0.0169274	−	0.0201733i
$553$	−8.11850	−	9.67525i	−0.345234	−	0.411434i
$554$	56.3015			2.39202
$555$		0			0
$556$	3.62108			0.153568
$557$	−21.3022	−	25.3870i	−0.902603	−	1.07568i	−0.996785	−	0.0801258i	$-0.974468\pi$
$557$	−21.3022	−	25.3870i	−0.902603	−	1.07568i	0.0941814	−	0.995555i	$-0.469977\pi$
$558$	−16.0881	+	19.1731i	−0.681065	+	0.811662i
$559$	0.243375	−	1.38025i	0.0102937	−	0.0583784i
$560$		0			0
$561$	−7.64268			−0.322674
$562$	18.9946	+	52.1873i	0.801240	+	2.20139i
$563$	27.7300	−	16.0099i	1.16868	−	0.674738i	0.215312	−	0.976545i	$-0.430923\pi$
$563$	27.7300	−	16.0099i	1.16868	−	0.674738i	0.953369	+	0.301807i	$0.0975899\pi$
$564$	−0.229728	−	1.30285i	−0.00967331	−	0.0548601i
$565$		0			0
$566$	−12.0624	−	20.8927i	−0.507022	−	0.878187i
$567$	−0.216972	−	0.258577i	−0.00911195	−	0.0108592i
$568$	1.10820	+	0.195405i	0.0464989	+	0.00819901i
$569$	−10.5257	+	18.2310i	−0.441259	+	0.764283i	−0.997783	−	0.0665484i	$-0.978801\pi$
$569$	−10.5257	+	18.2310i	−0.441259	+	0.764283i	0.556524	+	0.830831i	$0.312135\pi$
$570$		0			0
$571$	−38.6513	−	14.0679i	−1.61751	−	0.588725i	−0.634603	−	0.772838i	$-0.718836\pi$
$571$	−38.6513	−	14.0679i	−1.61751	−	0.588725i	−0.982905	+	0.184113i	$0.941059\pi$
$572$	−26.0039	+	4.58519i	−1.08728	+	0.191716i
$573$	−0.416630	+	0.496520i	−0.0174050	+	0.0207424i
$574$	−0.609108	−	0.511102i	−0.0254237	−	0.0213330i
$575$		0			0
$576$	−14.5079	−	5.28045i	−0.604496	−	0.220019i
$577$	5.68058	−	15.6073i	0.236486	−	0.649739i	−0.763507	−	0.645800i	$-0.776524\pi$
$577$	5.68058	−	15.6073i	0.236486	−	0.649739i	0.999992	−	0.00393877i	$-0.00125375\pi$
$578$	18.5389	+	10.7034i	0.771117	+	0.445205i
$579$	2.27655	−	12.9110i	0.0946102	−	0.536561i
$580$		0			0
$581$	−1.24225	−	2.15165i	−0.0515374	−	0.0892653i
$582$	18.1634	+	10.4867i	0.752898	+	0.434686i
$583$	−24.6499	+	4.34644i	−1.02090	+	0.180011i
$584$	0.185384	+	0.321094i	0.00767123	+	0.0132870i
$585$		0			0
$586$	−54.8376			−2.26532
$587$	−9.51570	−	26.1442i	−0.392755	−	1.07908i	−0.965738	−	0.259518i	$-0.916436\pi$
$587$	−9.51570	−	26.1442i	−0.392755	−	1.07908i	0.572983	−	0.819567i	$-0.305786\pi$
$588$	9.70013	+	1.71039i	0.400027	+	0.0705355i
$589$	−18.1823	−	15.2568i	−0.749188	−	0.628644i
$590$		0			0
$591$	0.913897			0.0375927
$592$	21.3661	−	9.98219i	0.878140	−	0.410265i
$593$			4.43146i			0.181978i	0.995852	+	0.0909892i	$0.0290029\pi$
$593$			4.43146i			0.181978i	−0.995852	+	0.0909892i	$0.970997\pi$
$594$	22.5309	−	18.9057i	0.924454	−	0.775709i
$595$		0			0
$596$	2.85326	−	16.1817i	0.116874	−	0.662827i
$597$	−7.11498	−	19.5482i	−0.291197	−	0.800056i
$598$		−	43.8833i		−	1.79452i
$599$	−30.6972	+	11.1729i	−1.25425	+	0.456510i	−0.881836	−	0.471556i	$-0.843693\pi$
$599$	−30.6972	+	11.1729i	−1.25425	+	0.456510i	−0.372416	+	0.928066i	$0.621470\pi$
$600$		0			0
$601$	−5.71426	−	32.4072i	−0.233090	−	1.32192i	−0.846600	−	0.532230i	$-0.821354\pi$
$601$	−5.71426	−	32.4072i	−0.233090	−	1.32192i	0.613510	−	0.789687i	$-0.289757\pi$
$602$	0.856883	+	0.494722i	0.0349240	+	0.0201634i
$603$	8.07201	−	4.66038i	0.328718	−	0.189785i
$604$	−12.7826	+	10.7258i	−0.520115	+	0.436428i
$605$		0			0
$606$	−17.4622	+	30.2454i	−0.709353	+	1.22864i
$607$	−5.17055	+	14.2060i	−0.209866	+	0.576603i	−0.999307	−	0.0372241i	$-0.988148\pi$
$607$	−5.17055	+	14.2060i	−0.209866	+	0.576603i	0.789441	+	0.613827i	$0.210371\pi$
$608$	9.59163	−	26.3528i	0.388992	−	1.06875i
$609$	−0.763958	−	4.33262i	−0.0309571	−	0.175567i
$610$		0			0
$611$	−2.08394	−	1.74863i	−0.0843071	−	0.0707421i
$612$	9.33543	−	1.64609i	0.377362	−	0.0665392i
$613$	11.8189	−	32.4722i	0.477362	−	1.31154i	−0.434363	−	0.900738i	$-0.643026\pi$
$613$	11.8189	−	32.4722i	0.477362	−	1.31154i	0.911725	−	0.410802i	$-0.134751\pi$
$614$	36.0381	+	13.1168i	1.45438	+	0.529350i
$615$		0			0
$616$	0.0938472	−	0.532234i	0.00378121	−	0.0214443i
$617$	−1.78300	−	2.12489i	−0.0717808	−	0.0855450i	0.728959	−	0.684557i	$-0.240004\pi$
$617$	−1.78300	−	2.12489i	−0.0717808	−	0.0855450i	−0.800740	+	0.599012i	$0.795560\pi$
$618$	29.6662	−	17.1278i	1.19335	−	0.688981i
$619$	−23.5767	+	40.8360i	−0.947627	+	1.64134i	−0.197224	+	0.980358i	$0.563193\pi$
$619$	−23.5767	+	40.8360i	−0.947627	+	1.64134i	−0.750403	+	0.660981i	$0.770141\pi$
$620$		0			0
$621$	12.3999	+	21.4773i	0.497591	+	0.861853i
$622$	19.4141	+	53.3397i	0.778433	+	2.13873i
$623$			15.0509i			0.603003i
$624$	18.1661	−	6.61191i	0.727225	−	0.264688i
$625$		0			0
$626$	47.8258	+	40.1306i	1.91150	+	1.60394i
$627$	6.77601	+	8.07533i	0.270608	+	0.322498i
$628$			44.0913i			1.75944i
$629$	−8.80030	+	12.5877i	−0.350891	+	0.501905i
$630$		0			0
$631$	−26.4127	+	22.1629i	−1.05147	+	0.882291i	−0.993248	−	0.116012i	$-0.962989\pi$
$631$	−26.4127	+	22.1629i	−1.05147	+	0.882291i	−0.0582257	+	0.998303i	$0.518544\pi$
$632$	0.606649	−	0.722976i	0.0241312	−	0.0287584i
$633$	27.6538	+	4.87610i	1.09914	+	0.193808i
$634$	−11.9501	+	4.34949i	−0.474600	+	0.172740i
$635$		0			0
$636$	−18.8433	+	6.85839i	−0.747184	+	0.271953i
$637$	17.5405	−	10.1270i	0.694982	−	0.401248i
$638$	13.9388	−	2.45779i	0.551843	−	0.0973048i
$639$	−8.52348	+	14.7631i	−0.337184	+	0.584019i
$640$		0			0
$641$	21.8760	−	18.3561i	0.864049	−	0.725023i	−0.0987874	−	0.995109i	$-0.531496\pi$
$641$	21.8760	−	18.3561i	0.864049	−	0.725023i	0.962836	+	0.270085i	$0.0870519\pi$
$642$	−3.42159	−	0.603318i	−0.135039	−	0.0238111i
$643$	−17.4392	−	10.0686i	−0.687737	−	0.397065i	0.115027	−	0.993362i	$-0.463305\pi$
$643$	−17.4392	−	10.0686i	−0.687737	−	0.397065i	−0.802764	+	0.596298i	$0.796638\pi$
$644$	14.7700	+	5.37585i	0.582021	+	0.211838i
$645$		0			0
$646$	3.07679	+	17.4493i	0.121055	+	0.686535i
$647$	−28.2660	+	33.6861i	−1.11125	+	1.32434i	−0.170456	+	0.985365i	$0.554524\pi$
$647$	−28.2660	+	33.6861i	−1.11125	+	1.32434i	−0.940796	+	0.338974i	$0.889920\pi$
$648$	0.0162130	−	0.0193219i	0.000636908	−	0.000759037i
$649$	2.24703	+	12.7436i	0.0882037	+	0.500228i
$650$		0			0
$651$	11.1886	+	4.07232i	0.438516	+	0.159607i
$652$	−6.91899	−	3.99468i	−0.270969	−	0.156444i
$653$	41.1075	+	7.24836i	1.60866	+	0.283650i	0.904527	−	0.426417i	$-0.140225\pi$
$653$	41.1075	+	7.24836i	1.60866	+	0.283650i	0.704134	+	0.710068i	$0.251336\pi$
$654$	−22.9949	+	19.2950i	−0.899172	+	0.754495i
$655$		0			0
$656$	−0.475101	+	0.822899i	−0.0185496	+	0.0321288i
$657$	−5.53140	+	0.975334i	−0.215800	+	0.0380514i
$658$	1.66321	−	0.960253i	0.0648385	−	0.0374345i
$659$	−26.9793	+	9.81968i	−1.05097	+	0.382520i	−0.809027	−	0.587771i	$-0.800006\pi$
$659$	−26.9793	+	9.81968i	−1.05097	+	0.382520i	−0.241939	+	0.970292i	$0.577783\pi$
$660$		0			0
$661$	−11.5283	+	4.19596i	−0.448399	+	0.163204i	−0.556342	−	0.830953i	$-0.687796\pi$
$661$	−11.5283	+	4.19596i	−0.448399	+	0.163204i	0.107943	+	0.994157i	$0.465573\pi$
$662$	−67.2411	−	11.8564i	−2.61340	−	0.460813i
$663$	−8.09293	+	9.64478i	−0.314303	+	0.374572i
$664$	0.142218	−	0.119335i	0.00551914	−	0.00463111i
$665$		0			0
$666$	−1.96325	−	22.2526i	−0.0760745	−	0.862272i
$667$			11.9343i			0.462099i
$668$	−20.6361	−	24.5931i	−0.798433	−	0.951535i
$669$	16.1260	+	13.5313i	0.623468	+	0.523152i
$670$		0			0
$671$	0.506204	−	0.184243i	0.0195418	−	0.00711263i
$672$			14.0681i			0.542690i
$673$	−10.5202	−	28.9039i	−0.405523	−	1.11416i	−0.959519	−	0.281645i	$-0.909120\pi$
$673$	−10.5202	−	28.9039i	−0.405523	−	1.11416i	0.553996	−	0.832519i	$-0.313102\pi$
$674$	−11.5841	−	20.0642i	−0.446202	−	0.772845i
$675$		0			0
$676$	−8.36137	+	14.4823i	−0.321591	+	0.557012i
$677$	28.3379	−	16.3609i	1.08911	−	0.628801i	0.155774	−	0.987793i	$-0.450213\pi$
$677$	28.3379	−	16.3609i	1.08911	−	0.628801i	0.933341	+	0.358992i	$0.116879\pi$
$678$	23.4723	+	27.9732i	0.901449	+	1.07430i
$679$	−2.68238	+	15.2125i	−0.102940	+	0.583803i
$680$		0			0
$681$	1.83431	+	0.667633i	0.0702908	+	0.0255838i
$682$	−13.1014	+	35.9958i	−0.501678	+	1.37835i
$683$	−22.8436	+	4.02794i	−0.874085	+	0.154125i	−0.592655	−	0.805457i	$-0.701920\pi$
$683$	−22.8436	+	4.02794i	−0.874085	+	0.154125i	−0.281431	+	0.959582i	$0.590809\pi$
$684$	−10.0161	−	8.40449i	−0.382974	−	0.321354i
$685$		0			0
$686$	6.42651	+	36.4466i	0.245365	+	1.39154i
$687$	6.17181	−	16.9569i	0.235469	−	0.646946i
$688$	0.404406	−	1.11110i	0.0154179	−	0.0423602i
$689$	−20.6171	+	35.7098i	−0.785447	+	1.36043i
$690$		0			0
$691$	−12.9760	+	10.8882i	−0.493632	+	0.414206i	−0.855326	−	0.518091i	$-0.826643\pi$
$691$	−12.9760	+	10.8882i	−0.493632	+	0.414206i	0.361694	+	0.932297i	$0.382199\pi$
$692$	−26.5813	+	15.3467i	−1.01047	+	0.583395i
$693$	7.09028	+	4.09358i	0.269338	+	0.155502i
$694$	5.58207	+	31.6575i	0.211893	+	1.20170i
$695$		0			0
$696$	0.308920	−	0.112438i	0.0117096	−	0.00426194i
$697$		−	0.618841i		−	0.0234403i
$698$	6.06565	+	16.6652i	0.229588	+	0.630789i
$699$	4.91387	−	27.8680i	0.185860	−	1.05406i
$700$		0			0
$701$	19.9161	−	16.7116i	0.752221	−	0.631189i	−0.183868	−	0.982951i	$-0.558862\pi$
$701$	19.9161	−	16.7116i	0.752221	−	0.631189i	0.936089	+	0.351762i	$0.114417\pi$
$702$		−	48.4526i		−	1.82873i
$703$	21.1027	−	1.86180i	0.795902	−	0.0702190i
$704$	−23.6291			−0.890553
$705$		0			0
$706$	28.8099	+	24.1743i	1.08427	+	0.909813i
$707$	−25.3316	−	4.46665i	−0.952693	−	0.167986i
$708$	3.54566	+	9.74162i	0.133254	+	0.366113i
$709$	−9.02241			−0.338844			−0.169422	−	0.985544i	$-0.554190\pi$
$709$	−9.02241			−0.338844			−0.169422	+	0.985544i	$0.554190\pi$
$710$		0			0
$711$	7.14861	+	12.3818i	0.268094	+	0.464352i
$712$	−1.10758	+	0.195297i	−0.0415085	+	0.00731906i
$713$	−27.9718	−	16.1495i	−1.04755	−	0.604804i
$714$	−4.44419	−	7.69757i	−0.166320	−	0.288074i
$715$		0			0
$716$	−1.62128	+	9.19473i	−0.0605900	+	0.343623i
$717$	−20.6498	−	11.9222i	−0.771182	−	0.445242i
$718$	10.7147	−	29.4383i	0.399868	−	1.09863i
$719$	16.2013	+	5.89680i	0.604207	+	0.219913i	0.625967	−	0.779850i	$-0.284705\pi$
$719$	16.2013	+	5.89680i	0.604207	+	0.219913i	−0.0217595	+	0.999763i	$0.506927\pi$
$720$		0			0
$721$	19.3272	+	16.2174i	0.719781	+	0.603968i
$722$	−8.89831	+	10.6046i	−0.331161	+	0.394662i
$723$	−11.1874	+	1.97264i	−0.416064	+	0.0733633i
$724$	−23.0825	−	8.40133i	−0.857853	−	0.312233i
$725$		0			0
$726$	−3.51768	+	6.09281i	−0.130554	+	0.226125i
$727$	−50.8310	−	8.96288i	−1.88522	−	0.332415i	−0.892322	−	0.451400i	$-0.850925\pi$
$727$	−50.8310	−	8.96288i	−1.88522	−	0.332415i	−0.992896	+	0.118986i	$0.962036\pi$
$728$	−0.572284	−	0.682021i	−0.0212102	−	0.0252774i
$729$	8.70767	+	15.0821i	0.322506	+	0.558597i
$730$		0			0
$731$	0.133721	+	0.758370i	0.00494585	+	0.0280493i
$732$	0.373747	−	0.215783i	0.0138141	−	0.00797556i
$733$	11.6676	+	32.0566i	0.430954	+	1.18404i	0.945228	+	0.326411i	$0.105839\pi$
$733$	11.6676	+	32.0566i	0.430954	+	1.18404i	−0.514274	+	0.857626i	$0.671939\pi$
$734$	7.41148			0.273563
$735$		0			0
$736$	6.62683	−	37.5826i	0.244268	−	1.38531i
$737$	9.16951	−	10.9278i	0.337763	−	0.402530i
$738$	0.578564	+	0.689505i	0.0212972	+	0.0253810i
$739$	−11.7210			−0.431165			−0.215582	−	0.976486i	$-0.569165\pi$
$739$	−11.7210			−0.431165			−0.215582	+	0.976486i	$0.569165\pi$
$740$		0			0
$741$	17.3660			0.637955
$742$	−18.7115	−	22.2995i	−0.686921	−	0.818641i
$743$	10.3925	−	12.3852i	0.381262	−	0.454371i	−0.540950	−	0.841055i	$-0.681935\pi$
$743$	10.3925	−	12.3852i	0.381262	−	0.454371i	0.922212	+	0.386684i	$0.126380\pi$
$744$	−0.154498	+	0.876200i	−0.00566416	+	0.0321230i
$745$		0			0
$746$	0.625721			0.0229093
$747$	0.961911	+	2.64283i	0.0351945	+	0.0966961i
$748$	12.5644	−	7.25404i	0.459399	−	0.265234i
$749$	−0.444354	−	2.52006i	−0.0162363	−	0.0920809i
$750$		0			0
$751$	20.8256	+	36.0710i	0.759937	+	1.31625i	0.942882	+	0.333126i	$0.108104\pi$
$751$	20.8256	+	36.0710i	0.759937	+	1.31625i	−0.182945	+	0.983123i	$0.558563\pi$
$752$	−1.47523	−	1.75810i	−0.0537959	−	0.0641115i
$753$	15.6754	+	2.76399i	0.571243	+	0.100726i
$754$	11.6584	−	20.1929i	0.424572	−	0.735381i
$755$		0			0
$756$	16.3080	+	5.93561i	0.593115	+	0.215876i
$757$	−15.8986	+	2.80335i	−0.577845	+	0.101890i	−0.454929	−	0.890527i	$-0.650336\pi$
$757$	−15.8986	+	2.80335i	−0.577845	+	0.101890i	−0.122915	+	0.992417i	$0.539224\pi$
$758$	−36.4158	+	43.3986i	−1.32268	+	1.57631i
$759$	10.9889	+	9.22081i	0.398873	+	0.334694i
$760$		0			0
$761$	13.9124	+	5.06368i	0.504322	+	0.183558i	0.581637	−	0.813448i	$-0.302412\pi$
$761$	13.9124	+	5.06368i	0.504322	+	0.183558i	−0.0773147	+	0.997007i	$0.524635\pi$
$762$	−10.1527	+	27.8943i	−0.367793	+	1.01050i
$763$	−19.1466	−	11.0543i	−0.693152	−	0.400192i
$764$	0.213657	−	1.21171i	0.00772985	−	0.0438381i
$765$		0			0
$766$	−19.7561	−	34.2186i	−0.713817	−	1.23637i
$767$	18.4613	+	10.6586i	0.666599	+	0.384861i
$768$	16.0306	−	2.82662i	0.578454	−	0.101997i
$769$	−17.0710	−	29.5679i	−0.615597	−	1.06625i	−0.990279	−	0.139092i	$-0.955582\pi$
$769$	−17.0710	−	29.5679i	−0.615597	−	1.06625i	0.374682	−	0.927153i	$-0.377752\pi$
$770$		0			0
$771$	17.6424			0.635376
$772$	8.51184	+	23.3861i	0.306348	+	0.841683i
$773$	5.63721	+	0.993992i	0.202756	+	0.0357514i	0.274104	−	0.961700i	$-0.411619\pi$
$773$	5.63721	+	0.993992i	0.202756	+	0.0357514i	−0.0713475	+	0.997452i	$0.522730\pi$
$774$	−0.858002	−	0.719949i	−0.0308402	−	0.0258780i
$775$		0			0
$776$	−1.15428			−0.0414362
$777$	−9.62818	+	4.49827i	−0.345409	+	0.161375i
$778$			40.3436i			1.44639i
$779$	−0.653874	+	0.548665i	−0.0234275	+	0.0196580i
$780$		0			0
$781$	−4.53048	+	25.6936i	−0.162113	+	0.919391i
$782$	8.24658	+	22.6573i	0.294897	+	0.810223i
$783$			13.1770i			0.470908i
$784$	16.0568	−	5.84419i	0.573456	−	0.208721i
$785$		0			0
$786$	−8.20765	−	46.5479i	−0.292757	−	1.66031i
$787$	4.67462	+	2.69889i	0.166632	+	0.0962051i	0.580997	−	0.813906i	$-0.302663\pi$
$787$	4.67462	+	2.69889i	0.166632	+	0.0962051i	−0.414365	+	0.910111i	$0.635996\pi$
$788$	−1.50242	+	0.867424i	−0.0535216	+	0.0309007i
$789$	−12.6276	+	10.5958i	−0.449556	+	0.377222i
$790$		0			0
$791$	−13.4475	+	23.2917i	−0.478137	+	0.828158i
$792$	−0.209241	+	0.574884i	−0.00743504	+	0.0204276i
$793$	0.303518	−	0.833909i	0.0107782	−	0.0296130i
$794$	−1.27854	−	7.25095i	−0.0453736	−	0.257327i
$795$		0			0
$796$	30.2510	+	25.3836i	1.07222	+	0.899699i
$797$	17.0388	−	3.00441i	0.603547	−	0.106422i	0.136479	−	0.990643i	$-0.456421\pi$
$797$	17.0388	−	3.00441i	0.603547	−	0.106422i	0.467068	+	0.884221i	$0.345310\pi$
$798$	−4.19310	+	11.5205i	−0.148434	+	0.407820i
$799$	1.40456	+	0.511218i	0.0496897	+	0.0180856i
$800$		0			0
$801$	2.95854	−	16.7787i	0.104535	−	0.592846i
$802$	22.4602	+	26.7671i	0.793099	+	0.945178i
$803$	−7.44459	+	4.29814i	−0.262714	+	0.151678i
$804$	5.71419	−	9.89727i	0.201524	−	0.349050i
$805$		0			0
$806$	31.5521	+	54.6499i	1.11138	+	1.92496i
$807$	5.27687	+	14.4981i	0.185755	+	0.510357i
$808$		−	1.92209i		−	0.0676187i
$809$	−27.1468	+	9.88062i	−0.954430	+	0.347384i	−0.771848	−	0.635807i	$-0.780668\pi$
$809$	−27.1468	+	9.88062i	−0.954430	+	0.347384i	−0.182581	+	0.983191i	$0.558445\pi$
$810$		0			0
$811$	24.6882	+	20.7159i	0.866920	+	0.727432i	0.963447	−	0.267898i	$-0.0863290\pi$
$811$	24.6882	+	20.7159i	0.866920	+	0.727432i	−0.0965272	+	0.995330i	$0.530773\pi$
$812$	5.36823	+	6.39761i	0.188388	+	0.224512i
$813$		−	11.2901i		−	0.395961i
$814$	−14.4717	−	30.9756i	−0.507234	−	1.08569i
$815$		0			0
$816$	−8.13677	+	6.82756i	−0.284844	+	0.239013i
$817$	0.682744	−	0.813663i	0.0238862	−	0.0284665i
$818$	−52.3705	−	9.23433i	−1.83109	−	0.322871i
$819$	12.6739	−	4.61293i	0.442863	−	0.161189i
$820$		0			0
$821$	−46.7876	+	17.0293i	−1.63290	+	0.594326i	−0.985777	−	0.168061i	$-0.946249\pi$
$821$	−46.7876	+	17.0293i	−1.63290	+	0.594326i	−0.647121	+	0.762387i	$0.724027\pi$
$822$	24.7557	−	14.2927i	0.863456	−	0.498516i
$823$	7.03136	−	1.23982i	0.245098	−	0.0432174i	−0.0497495	−	0.998762i	$-0.515842\pi$
$823$	7.03136	−	1.23982i	0.245098	−	0.0432174i	0.294847	+	0.955544i	$0.404731\pi$
$824$	−0.942639	+	1.63270i	−0.0328384	+	0.0568777i
$825$		0			0
$826$	−11.5284	+	9.67351i	−0.401126	+	0.336584i
$827$	−39.4807	−	6.96151i	−1.37288	−	0.242075i	−0.561925	−	0.827188i	$-0.689939\pi$
$827$	−39.4807	−	6.96151i	−1.37288	−	0.242075i	−0.810952	+	0.585113i	$0.801050\pi$
$828$	−15.4088	−	8.89629i	−0.535493	−	0.309167i
$829$	15.7906	+	5.74730i	0.548430	+	0.199612i	0.601349	−	0.798987i	$-0.294630\pi$
$829$	15.7906	+	5.74730i	0.548430	+	0.199612i	−0.0529189	+	0.998599i	$0.516852\pi$
$830$		0			0
$831$	5.26484	+	29.8584i	0.182635	+	1.03578i
$832$	−25.0211	+	29.8190i	−0.867451	+	1.03379i
$833$	−7.15324	+	8.52490i	−0.247845	+	0.295370i
$834$	0.667408	+	3.78506i	0.0231105	+	0.131066i
$835$		0			0
$836$	−18.8043	−	6.84420i	−0.650360	−	0.236712i
$837$	−30.8843	−	17.8311i	−1.06752	−	0.616332i
$838$	4.52195	+	0.797341i	0.156208	+	0.0275437i
$839$	22.8801	−	19.1987i	0.789910	−	0.662813i	−0.155813	−	0.987787i	$-0.549800\pi$
$839$	22.8801	−	19.1987i	0.789910	−	0.662813i	0.945723	+	0.324973i	$0.105355\pi$
$840$		0			0
$841$	11.3294	−	19.6232i	0.390670	−	0.676661i
$842$	51.9038	−	9.15204i	1.78872	−	0.315400i
$843$	−25.9003	+	14.9535i	−0.892053	+	0.515027i
$844$	−50.0902	+	18.2313i	−1.72418	+	0.627549i
$845$		0			0
$846$	−2.04289	+	0.743550i	−0.0702359	+	0.0255638i
$847$	−5.10295	−	0.899787i	−0.175339	−	0.0309170i
$848$	−22.3606	+	26.6484i	−0.767867	+	0.915109i
$849$	9.95207	−	8.35078i	0.341554	−	0.286598i
$850$		0			0
$851$	27.8403	−	7.48163i	0.954355	−	0.256467i
$852$			20.9017i			0.716079i
$853$	7.42808	+	8.85244i	0.254333	+	0.303102i	0.878070	−	0.478532i	$-0.158831\pi$
$853$	7.42808	+	8.85244i	0.254333	+	0.303102i	−0.623737	+	0.781634i	$0.714387\pi$
$854$	0.479923	+	0.402703i	0.0164226	+	0.0137802i
$855$		0			0
$856$	0.179683	−	0.0653991i	0.00614143	−	0.00223530i
$857$		−	1.03275i		−	0.0352781i	−0.999844	−	0.0176390i	$-0.994385\pi$
$857$		−	1.03275i		−	0.0352781i	0.999844	−	0.0176390i	$-0.00561497\pi$
$858$	−9.58566	−	26.3364i	−0.327249	−	0.899109i
$859$	9.45725	+	16.3804i	0.322677	+	0.558893i	0.981040	−	0.193808i	$-0.0620838\pi$
$859$	9.45725	+	16.3804i	0.322677	+	0.558893i	−0.658362	+	0.752701i	$0.728751\pi$
$860$		0			0
$861$	0.214094	−	0.370822i	0.00729632	−	0.0126376i
$862$	34.5849	−	19.9676i	1.17797	−	0.680099i
$863$	6.02460	+	7.17984i	0.205080	+	0.244404i	0.858774	−	0.512354i	$-0.171226\pi$
$863$	6.02460	+	7.17984i	0.205080	+	0.244404i	−0.653695	+	0.756758i	$0.726782\pi$
$864$	7.31685	−	41.4959i	0.248924	−	1.41172i
$865$		0			0
$866$	−36.4227	−	13.2568i	−1.23769	−	0.450484i
$867$	−3.94276	+	10.8326i	−0.133903	+	0.367896i
$868$	−22.2590	+	3.92487i	−0.755521	+	0.133219i
$869$	16.7623	+	14.0652i	0.568621	+	0.477130i
$870$		0			0
$871$	−4.08076	−	23.1432i	−0.138271	−	0.784176i
$872$	0.565032	−	1.55241i	0.0191344	−	0.0525714i
$873$	5.98060	−	16.4316i	0.202413	−	0.556124i
$874$	16.6285	−	28.8014i	0.562468	−	0.974223i
$875$		0			0
$876$	−5.27559	+	4.42674i	−0.178246	+	0.149566i
$877$	16.7511	−	9.67123i	0.565643	−	0.326574i	−0.189764	−	0.981830i	$-0.560772\pi$
$877$	16.7511	−	9.67123i	0.565643	−	0.326574i	0.755407	+	0.655256i	$0.227439\pi$
$878$	21.7413	+	12.5523i	0.733732	+	0.423620i
$879$	−5.12794	−	29.0820i	−0.172961	−	0.980912i
$880$		0			0
$881$	18.3625	−	6.68341i	0.618649	−	0.225170i	−0.0136343	−	0.999907i	$-0.504340\pi$
$881$	18.3625	−	6.68341i	0.618649	−	0.225170i	0.632283	+	0.774737i	$0.282118\pi$
$882$		−	16.1860i		−	0.545012i
$883$	−6.66525	−	18.3126i	−0.224304	−	0.616269i	0.775584	−	0.631244i	$-0.217455\pi$
$883$	−6.66525	−	18.3126i	−0.224304	−	0.616269i	−0.999888	+	0.0149750i	$0.995233\pi$
$884$	4.15024	−	23.5372i	0.139588	−	0.791641i
$885$		0			0
$886$	−24.5232	+	20.5774i	−0.823873	+	0.691311i
$887$		−	39.6323i		−	1.33072i	−0.746521	−	0.665362i	$-0.768277\pi$
$887$		−	39.6323i		−	1.33072i	0.746521	−	0.665362i	$-0.231723\pi$
$888$	−0.455956	−	0.650160i	−0.0153009	−	0.0218179i
$889$	−21.8631			−0.733266
$890$		0			0
$891$	0.447981	+	0.375901i	0.0150079	+	0.0125932i
$892$	−39.3540	−	6.93918i	−1.31767	−	0.232341i
$893$	−0.705126	−	1.93732i	−0.0235961	−	0.0648299i
$894$	17.4403			0.583292
$895$		0			0
$896$	−0.774594	−	1.34164i	−0.0258774	−	0.0448209i
$897$	23.2726	−	4.10359i	0.777051	−	0.137015i
$898$	−24.4530	−	14.1179i	−0.816007	−	0.471122i
$899$	−8.58080	−	14.8624i	−0.286186	−	0.495688i
$900$		0			0
$901$	3.93414	−	22.3116i	0.131065	−	0.743308i
$902$	1.19300	+	0.688781i	0.0397227	+	0.0229339i
$903$	−0.182237	+	0.500693i	−0.00606448	+	0.0166620i
$904$	−1.88850	−	0.687360i	−0.0628107	−	0.0228612i
$905$		0			0
$906$	−13.5675	−	11.3845i	−0.450751	−	0.378225i
$907$	2.20926	−	2.63289i	0.0733572	−	0.0874237i	−0.728118	−	0.685452i	$-0.759605\pi$
$907$	2.20926	−	2.63289i	0.0733572	−	0.0874237i	0.801475	+	0.598028i	$0.204049\pi$
$908$	−3.64924	+	0.643459i	−0.121104	+	0.0213539i
$909$	27.3615	+	9.95878i	0.907525	+	0.330312i
$910$		0			0
$911$	1.44333	−	2.49993i	0.0478197	−	0.0828262i	−0.841125	−	0.540841i	$-0.818106\pi$
$911$	1.44333	−	2.49993i	0.0478197	−	0.0828262i	0.888945	+	0.458015i	$0.151439\pi$
$912$	14.4281	+	2.54407i	0.477764	+	0.0842426i
$913$	2.76680	+	3.29735i	0.0915678	+	0.109126i
$914$	−7.01208	−	12.1453i	−0.231939	−	0.401730i
$915$		0			0
$916$	5.94833	+	33.7347i	0.196538	+	1.11463i
$917$	30.1482	−	17.4061i	0.995582	−	0.574800i
$918$	9.10526	+	25.0165i	0.300518	+	0.825667i
$919$	36.2600			1.19611			0.598053	−	0.801456i	$-0.295941\pi$
$919$	36.2600			1.19611			0.598053	+	0.801456i	$0.295941\pi$
$920$		0			0
$921$	−3.58625	+	20.3387i	−0.118171	+	0.670181i
$922$	−28.8081	+	34.3322i	−0.948744	+	1.13067i
$923$	27.6270	+	32.9246i	0.909355	+	1.08373i
$924$	10.0384			0.330241
$925$		0			0
$926$	68.6389			2.25561
$927$	−18.3580	−	21.8782i	−0.602955	−	0.718574i
$928$	13.0338	−	15.5331i	0.427856	−	0.509898i
$929$	7.00848	−	39.7471i	0.229941	−	1.30406i	−0.623070	−	0.782166i	$-0.714115\pi$
$929$	7.00848	−	39.7471i	0.229941	−	1.30406i	0.853011	−	0.521893i	$-0.174774\pi$
$930$		0			0
$931$	15.3496			0.503062
$932$	18.3726	+	50.4782i	0.601814	+	1.65347i
$933$	−26.4722	+	15.2837i	−0.866661	+	0.500367i
$934$	−0.431733	−	2.44848i	−0.0141267	−	0.0801167i
$935$		0			0
$936$	0.503915	+	0.872806i	0.0164710	+	0.0285285i
$937$	24.1048	+	28.7270i	0.787470	+	0.938470i	0.999245	−	0.0388482i	$-0.0123689\pi$
$937$	24.1048	+	28.7270i	0.787470	+	0.938470i	−0.211775	+	0.977318i	$0.567924\pi$
$938$	16.3383	+	2.88089i	0.533465	+	0.0940643i
$939$	−16.8102	+	29.1161i	−0.548580	+	0.950169i
$940$		0			0
$941$	2.95590	+	1.07586i	0.0963594	+	0.0350720i	0.389750	−	0.920921i	$-0.372561\pi$
$941$	2.95590	+	1.07586i	0.0963594	+	0.0350720i	−0.293391	+	0.955993i	$0.594784\pi$
$942$	−46.0880	+	8.12656i	−1.50163	+	0.264778i
$943$	−0.746625	+	0.889792i	−0.0243134	+	0.0289756i
$944$	13.7767	+	11.5600i	0.448394	+	0.376247i
$945$		0			0
$946$	−1.61082	−	0.586291i	−0.0523723	−	0.0190620i
$947$	19.7171	−	54.1723i	0.640719	−	1.76036i	−0.00873519	−	0.999962i	$-0.502781\pi$
$947$	19.7171	−	54.1723i	0.640719	−	1.76036i	0.649455	−	0.760400i	$-0.274997\pi$
$948$	15.1815	+	8.76507i	0.493074	+	0.284676i
$949$	−2.45908	+	13.9462i	−0.0798253	+	0.452712i
$950$		0			0
$951$	−3.42414	−	5.93079i	−0.111035	−	0.192319i
$952$	0.423641	+	0.244589i	0.0137303	+	0.00792718i
$953$	−52.0281	+	9.17395i	−1.68535	+	0.297173i	−0.932542	−	0.361062i	$-0.882414\pi$
$953$	−52.0281	+	9.17395i	−1.68535	+	0.297173i	−0.752812	+	0.658235i	$0.771303\pi$
$954$	16.4761	+	28.5375i	0.533434	+	0.923934i
$955$		0			0
$956$	45.2638			1.46393
$957$	2.60688	+	7.16234i	0.0842685	+	0.231526i
$958$	−15.7212	−	2.77207i	−0.507929	−	0.0895616i
$959$	16.1281	+	13.5330i	0.520802	+	0.437005i
$960$		0			0
$961$	15.4460			0.498260
$962$	−54.4144	−	14.5376i	−1.75439	−	0.468712i
$963$			2.89669i			0.0933445i
$964$	16.5195	−	13.8615i	0.532056	−	0.446448i
$965$		0			0
$966$	−2.89700	+	16.4297i	−0.0932096	+	0.528618i
$967$	14.7145	+	40.4278i	0.473187	+	1.30007i	0.915177	+	0.403052i	$0.132050\pi$
$967$	14.7145	+	40.4278i	0.473187	+	1.30007i	−0.441990	+	0.897020i	$0.645727\pi$
$968$		−	0.387196i		−	0.0124450i
$969$	−8.96620	+	3.26343i	−0.288036	+	0.104836i
$970$		0			0
$971$	−9.00419	−	51.0653i	−0.288958	−	1.63876i	−0.690794	−	0.723051i	$-0.742739\pi$
$971$	−9.00419	−	51.0653i	−0.288958	−	1.63876i	0.401836	−	0.915712i	$-0.368372\pi$
$972$	−27.5965	−	15.9328i	−0.885158	−	0.511046i
$973$	−2.45152	+	1.41538i	−0.0785920	+	0.0453751i
$974$	18.5066	−	15.5289i	0.592989	−	0.497577i
$975$		0			0
$976$	0.374337	−	0.648371i	0.0119822	−	0.0207538i
$977$	4.87712	−	13.3998i	0.156033	−	0.428697i	−0.836903	−	0.547352i	$-0.815636\pi$
$977$	4.87712	−	13.3998i	0.156033	−	0.428697i	0.992936	+	0.118655i	$0.0378583\pi$
$978$	2.90033	−	7.96859i	0.0927423	−	0.254807i
$979$	−4.52798	−	25.6794i	−0.144715	−	0.820719i
$980$		0			0
$981$	19.1716	+	16.0868i	0.612101	+	0.513613i
$982$	26.7143	−	4.71045i	0.852487	−	0.150316i
$983$	−2.42218	+	6.65488i	−0.0772554	+	0.212258i	−0.972308	−	0.233703i	$-0.924916\pi$
$983$	−2.42218	+	6.65488i	−0.0772554	+	0.212258i	0.895053	+	0.445961i	$0.147138\pi$
$984$	0.0300665	+	0.0109433i	0.000958484	+	0.000348860i
$985$		0			0
$986$	−2.22464	+	12.6166i	−0.0708471	+	0.401794i
$987$	0.664780	+	0.792254i	0.0211602	+	0.0252177i
$988$	−28.5492	+	16.4829i	−0.908272	+	0.524391i
$989$	0.722696	−	1.25175i	0.0229804	−	0.0398032i
$990$		0			0
$991$	1.61062	+	2.78967i	0.0511630	+	0.0886169i	0.890473	−	0.455037i	$-0.150374\pi$
$991$	1.61062	+	2.78967i	0.0511630	+	0.0886169i	−0.839310	+	0.543654i	$0.817041\pi$
$992$	18.7692	+	51.5680i	0.595924	+	1.63729i
$993$		−	36.7687i		−	1.16682i
$994$	−28.5126	+	10.3778i	−0.904366	+	0.329162i
$995$		0			0
$996$	2.64162	+	2.21659i	0.0837031	+	0.0702352i
$997$	24.0184	+	28.6240i	0.760671	+	0.906532i	0.997890	−	0.0649237i	$-0.0206804\pi$
$997$	24.0184	+	28.6240i	0.760671	+	0.906532i	−0.237219	+	0.971456i	$0.576236\pi$
$998$			65.2615i			2.06582i
$999$	30.7392	−	8.26065i	0.972546	−	0.261355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.4		156
5.2	odd	4		925.2.p.f.826.12	yes	78
5.3	odd	4		925.2.p.e.826.2	yes	78
5.4	even	2	inner	925.2.bc.e.49.23		156
37.34	even	9	inner	925.2.bc.e.774.23		156
185.34	even	18	inner	925.2.bc.e.774.4		156
185.108	odd	36		925.2.p.e.626.2	✓	78
185.182	odd	36		925.2.p.f.626.12	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.2	✓	78	185.108	odd	36
925.2.p.e.826.2	yes	78	5.3	odd	4
925.2.p.f.626.12	yes	78	185.182	odd	36
925.2.p.f.826.12	yes	78	5.2	odd	4
925.2.bc.e.49.4		156	1.1	even	1	trivial
925.2.bc.e.49.23		156	5.4	even	2	inner
925.2.bc.e.774.4		156	185.34	even	18	inner
925.2.bc.e.774.23		156	37.34	even	9	inner

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.29514 - 1.54348i) q^{2} +(0.697445 - 0.831183i) q^{3} +(-0.357666 + 2.02842i) q^{4} -2.18620 q^{6} +(-0.550712 - 1.51307i) q^{7} +(0.104199 - 0.0601595i) q^{8} +(0.316509 + 1.79501i) q^{9} +O(q^{10})\)	\(q+(-1.29514 - 1.54348i) q^{2} +(0.697445 - 0.831183i) q^{3} +(-0.357666 + 2.02842i) q^{4} -2.18620 q^{6} +(-0.550712 - 1.51307i) q^{7} +(0.104199 - 0.0601595i) q^{8} +(0.316509 + 1.79501i) q^{9} +(1.39480 + 2.41587i) q^{11} +(1.43654 + 1.71200i) q^{12} +(4.52572 + 0.798007i) q^{13} +(-1.62215 + 2.80965i) q^{14} +(3.64319 + 1.32601i) q^{16} +(-2.48663 + 0.438460i) q^{17} +(2.36065 - 2.81331i) q^{18} +(2.66793 + 2.23866i) q^{19} +(-1.64173 - 0.597541i) q^{21} +(1.92240 - 5.28174i) q^{22} +(4.10436 + 2.36966i) q^{23} +(0.0226698 - 0.128567i) q^{24} +(-4.62971 - 8.01890i) q^{26} +(4.53173 + 2.61640i) q^{27} +(3.26612 - 0.575905i) q^{28} +(1.25908 + 2.18079i) q^{29} -6.81513 q^{31} +(-2.75405 - 7.56670i) q^{32} +(2.98083 + 0.525601i) q^{33} +(3.89728 + 3.27020i) q^{34} -3.75425 q^{36} +(4.29802 - 4.30431i) q^{37} -7.01727i q^{38} +(3.81973 - 3.20514i) q^{39} +(-0.0425588 + 0.241363i) q^{41} +(1.20397 + 3.30788i) q^{42} -0.304979i q^{43} +(-5.39929 + 1.96518i) q^{44} +(-1.65819 - 9.40404i) q^{46} +(-0.512655 - 0.295982i) q^{47} +(3.64309 - 2.10334i) q^{48} +(3.37622 - 2.83298i) q^{49} +(-1.36985 + 2.37264i) q^{51} +(-3.23739 + 8.89466i) q^{52} +(-3.06883 + 8.43153i) q^{53} +(-1.83084 - 10.3832i) q^{54} +(-0.148409 - 0.124530i) q^{56} +(3.72147 - 0.656196i) q^{57} +(1.73533 - 4.76779i) q^{58} +(4.35895 + 1.58653i) q^{59} +(0.0335326 - 0.190173i) q^{61} +(8.82652 + 10.5190i) q^{62} +(2.54167 - 1.46744i) q^{63} +(-4.23519 + 7.33556i) q^{64} +(-3.04933 - 5.28159i) q^{66} +(-1.74899 - 4.80530i) q^{67} -5.20076i q^{68} +(4.83219 - 1.75877i) q^{69} +(7.16448 + 6.01171i) q^{71} +(0.140967 + 0.167998i) q^{72} +3.08153i q^{73} +(-12.2101 - 1.05925i) q^{74} +(-5.49517 + 4.61100i) q^{76} +(2.88725 - 3.44089i) q^{77} +(-9.89414 - 1.74460i) q^{78} +(7.37091 - 2.68279i) q^{79} +(0.196992 - 0.0716991i) q^{81} +(0.427659 - 0.246909i) q^{82} +(1.51956 - 0.267940i) q^{83} +(1.79926 - 3.11640i) q^{84} +(-0.470730 + 0.394989i) q^{86} +(2.69077 + 0.474456i) q^{87} +(0.290676 + 0.167822i) q^{88} +(-8.78368 - 3.19700i) q^{89} +(-1.28493 - 7.28720i) q^{91} +(-6.27466 + 7.47784i) q^{92} +(-4.75318 + 5.66462i) q^{93} +(0.207116 + 1.17461i) q^{94} +(-8.21011 - 2.98824i) q^{96} +(-8.30821 - 4.79674i) q^{97} +(-8.74531 - 1.54203i) q^{98} +(-3.89506 + 3.26834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more