LMFDB - Embedded newform 770.2.w.b.139.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(139,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 7]))

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

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

chi := DirichletCharacter("770.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.5
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.704096 + 2.16698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.29948 - 1.81971i) q^{5} +(-1.84335 + 1.33927i) q^{6} +(-0.555990 - 2.58667i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.77302 - 1.28817i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.704096 + 2.16698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.29948 - 1.81971i) q^{5} +(-1.84335 + 1.33927i) q^{6} +(-0.555990 - 2.58667i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.77302 - 1.28817i) q^{9} +(2.12090 - 0.708357i) q^{10} +(3.16583 + 0.988709i) q^{11} -2.27850 q^{12} +(-3.75841 + 5.17301i) q^{13} +(1.07060 - 2.41946i) q^{14} +(3.02832 + 4.09721i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.68401 + 3.69422i) q^{17} +(-0.677232 - 2.08431i) q^{18} +(-2.04968 + 6.30827i) q^{19} +(2.13221 + 0.673563i) q^{20} +(5.99675 + 0.616444i) q^{21} +(1.98006 + 2.66071i) q^{22} +7.23991i q^{23} +(-1.84335 - 1.33927i) q^{24} +(-1.62268 - 4.72937i) q^{25} +(-6.08123 + 1.97591i) q^{26} +(-1.49022 + 1.08271i) q^{27} +(2.28826 - 1.32810i) q^{28} +(6.55107 - 2.12857i) q^{29} +(0.0416797 + 5.09471i) q^{30} +(1.57964 - 2.17419i) q^{31} -1.00000 q^{32} +(-4.37156 + 6.16415i) q^{33} +4.56630i q^{34} +(-5.42949 - 2.34960i) q^{35} +(0.677232 - 2.08431i) q^{36} +(4.55444 - 1.47983i) q^{37} +(-5.36614 + 3.89873i) q^{38} +(-8.56354 - 11.7867i) q^{39} +(1.32908 + 1.79820i) q^{40} +(2.61032 - 8.03374i) q^{41} +(4.48913 + 4.02351i) q^{42} -3.77888 q^{43} +(0.0379755 + 3.31641i) q^{44} +(-4.64811 + 1.55241i) q^{45} +(-4.25551 + 5.85721i) q^{46} +(0.990513 - 3.04849i) q^{47} +(-0.704096 - 2.16698i) q^{48} +(-6.38175 + 2.87633i) q^{49} +(1.46708 - 4.77992i) q^{50} +(-9.89510 + 3.21511i) q^{51} +(-6.08123 - 1.97591i) q^{52} +(3.73200 - 5.13665i) q^{53} -1.84201 q^{54} +(5.91311 - 4.47607i) q^{55} +(2.63188 + 0.270548i) q^{56} +(-12.2268 - 8.88326i) q^{57} +(6.55107 + 2.12857i) q^{58} +(10.0280 - 3.25829i) q^{59} +(-2.96088 + 4.14621i) q^{60} +(0.595869 - 0.432924i) q^{61} +(2.55592 - 0.830467i) q^{62} +(-2.34630 + 5.30242i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.52937 + 13.5615i) q^{65} +(-7.15986 + 2.41736i) q^{66} -0.302004i q^{67} +(-2.68401 + 3.69422i) q^{68} +(-15.6888 - 5.09759i) q^{69} +(-3.01149 - 5.09224i) q^{70} +(-5.81086 + 4.22183i) q^{71} +(1.77302 - 1.28817i) q^{72} +(2.50805 - 0.814915i) q^{73} +(4.55444 + 1.47983i) q^{74} +(11.3910 - 0.186391i) q^{75} -6.63291 q^{76} +(0.797301 - 8.73867i) q^{77} -14.5692i q^{78} +(3.61392 - 4.97414i) q^{79} +(0.0182926 + 2.23599i) q^{80} +(-3.32865 - 10.2445i) q^{81} +(6.83391 - 4.96512i) q^{82} +(1.41972 + 1.95408i) q^{83} +(1.26682 + 5.89374i) q^{84} +(10.2102 - 0.0835295i) q^{85} +(-3.05718 - 2.22117i) q^{86} +15.6948i q^{87} +(-1.91861 + 2.70535i) q^{88} -1.93594i q^{89} +(-4.67288 - 1.47616i) q^{90} +(15.4705 + 6.84564i) q^{91} +(-6.88557 + 2.23726i) q^{92} +(3.59922 + 4.95390i) q^{93} +(2.59320 - 1.88407i) q^{94} +(8.81569 + 11.9273i) q^{95} +(0.704096 - 2.16698i) q^{96} +(-10.4319 - 7.57921i) q^{97} +(-6.85361 - 1.42410i) q^{98} +(-4.33943 - 5.83113i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−0.704096	+	2.16698i	−0.406510	+	1.25111i	0.513118	+	0.858318i	$0.328490\pi$
$3$	−0.704096	+	2.16698i	−0.406510	+	1.25111i	−0.919628	+	0.392791i	$0.871510\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.29948	−	1.81971i	0.581147	−	0.813798i
$5$	1.29948	−	1.81971i	0.581147	−	0.813798i
$6$	−1.84335	+	1.33927i	−0.752543	+	0.546755i
$7$	−0.555990	−	2.58667i	−0.210144	−	0.977670i
$7$	−0.555990	−	2.58667i	−0.210144	−	0.977670i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−1.77302	−	1.28817i	−0.591005	−	0.429391i
$10$	2.12090	−	0.708357i	0.670688	−	0.224002i
$11$	3.16583	+	0.988709i	0.954532	+	0.298107i
$11$	3.16583	+	0.988709i	0.954532	+	0.298107i
$12$	−2.27850			−0.657747
$13$	−3.75841	+	5.17301i	−1.04240	+	1.43473i	−0.147175	+	0.989110i	$0.547018\pi$
$13$	−3.75841	+	5.17301i	−1.04240	+	1.43473i	−0.895220	+	0.445624i	$0.852982\pi$
$14$	1.07060	−	2.41946i	0.286131	−	0.646629i
$15$	3.02832	+	4.09721i	0.781908	+	1.05790i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	2.68401	+	3.69422i	0.650967	+	0.895979i	0.999141	−	0.0414510i	$-0.0131980\pi$
$17$	2.68401	+	3.69422i	0.650967	+	0.895979i	−0.348174	+	0.937430i	$0.613198\pi$
$18$	−0.677232	−	2.08431i	−0.159625	−	0.491276i
$19$	−2.04968	+	6.30827i	−0.470229	+	1.44722i	0.382056	+	0.924139i	$0.375216\pi$
$19$	−2.04968	+	6.30827i	−0.470229	+	1.44722i	−0.852285	+	0.523078i	$0.824784\pi$
$20$	2.13221	+	0.673563i	0.476776	+	0.150613i
$21$	5.99675	+	0.616444i	1.30860	+	0.134519i
$22$	1.98006	+	2.66071i	0.422150	+	0.567265i
$23$			7.23991i			1.50963i	0.655940	+	0.754813i	$0.272272\pi$
$23$			7.23991i			1.50963i	−0.655940	+	0.754813i	$0.727728\pi$
$24$	−1.84335	−	1.33927i	−0.376272	−	0.273377i
$25$	−1.62268	−	4.72937i	−0.324536	−	0.945873i
$26$	−6.08123	+	1.97591i	−1.19263	+	0.387508i
$27$	−1.49022	+	1.08271i	−0.286793	+	0.208367i
$28$	2.28826	−	1.32810i	0.432441	−	0.250988i
$29$	6.55107	−	2.12857i	1.21650	−	0.395266i	0.370696	−	0.928754i	$-0.379119\pi$
$29$	6.55107	−	2.12857i	1.21650	−	0.395266i	0.845808	+	0.533488i	$0.179119\pi$
$30$	0.0416797	+	5.09471i	0.00760964	+	0.930163i
$31$	1.57964	−	2.17419i	0.283712	−	0.390496i	−0.643247	−	0.765659i	$-0.722413\pi$
$31$	1.57964	−	2.17419i	0.283712	−	0.390496i	0.926959	+	0.375162i	$0.122413\pi$
$32$	−1.00000			−0.176777
$33$	−4.37156	+	6.16415i	−0.760991	+	1.07304i
$34$			4.56630i			0.783114i
$35$	−5.42949	−	2.34960i	−0.917751	−	0.397155i
$36$	0.677232	−	2.08431i	0.112872	−	0.347384i
$37$	4.55444	−	1.47983i	0.748746	−	0.243282i	0.0903045	−	0.995914i	$-0.471216\pi$
$37$	4.55444	−	1.47983i	0.748746	−	0.243282i	0.658442	+	0.752632i	$0.271216\pi$
$38$	−5.36614	+	3.89873i	−0.870502	+	0.632457i
$39$	−8.56354	−	11.7867i	−1.37126	−	1.88738i
$40$	1.32908	+	1.79820i	0.210146	+	0.284321i
$41$	2.61032	−	8.03374i	0.407663	−	1.25466i	−0.510987	−	0.859588i	$-0.670720\pi$
$41$	2.61032	−	8.03374i	0.407663	−	1.25466i	0.918651	−	0.395071i	$-0.129280\pi$
$42$	4.48913	+	4.02351i	0.692688	+	0.620842i
$43$	−3.77888			−0.576274			−0.288137	−	0.957589i	$-0.593036\pi$
$43$	−3.77888			−0.576274			−0.288137	+	0.957589i	$0.593036\pi$
$44$	0.0379755	+	3.31641i	0.00572502	+	0.499967i
$45$	−4.64811	+	1.55241i	−0.692899	+	0.231420i
$46$	−4.25551	+	5.85721i	−0.627441	+	0.863599i
$47$	0.990513	−	3.04849i	0.144481	−	0.444667i	−0.852463	−	0.522788i	$-0.824892\pi$
$47$	0.990513	−	3.04849i	0.144481	−	0.444667i	0.996944	+	0.0781206i	$0.0248919\pi$
$48$	−0.704096	−	2.16698i	−0.101627	−	0.312777i
$49$	−6.38175	+	2.87633i	−0.911679	+	0.410904i
$50$	1.46708	−	4.77992i	0.207476	−	0.675983i
$51$	−9.89510	+	3.21511i	−1.38559	+	0.450206i
$52$	−6.08123	−	1.97591i	−0.843316	−	0.274010i
$53$	3.73200	−	5.13665i	0.512629	−	0.705573i	−0.471731	−	0.881743i	$-0.656371\pi$
$53$	3.73200	−	5.13665i	0.512629	−	0.705573i	0.984360	+	0.176169i	$0.0563706\pi$
$54$	−1.84201			−0.250666
$55$	5.91311	−	4.47607i	0.797323	−	0.603553i
$56$	2.63188	+	0.270548i	0.351700	+	0.0361535i
$57$	−12.2268	−	8.88326i	−1.61947	−	1.17662i
$58$	6.55107	+	2.12857i	0.860198	+	0.279495i
$59$	10.0280	−	3.25829i	1.30553	−	0.424193i	0.428030	−	0.903764i	$-0.359208\pi$
$59$	10.0280	−	3.25829i	1.30553	−	0.424193i	0.877503	+	0.479571i	$0.159208\pi$
$60$	−2.96088	+	4.14621i	−0.382248	+	0.535273i
$61$	0.595869	−	0.432924i	0.0762933	−	0.0554303i	−0.548985	−	0.835832i	$-0.684986\pi$
$61$	0.595869	−	0.432924i	0.0762933	−	0.0554303i	0.625278	+	0.780402i	$0.284986\pi$
$62$	2.55592	−	0.830467i	0.324602	−	0.105469i
$63$	−2.34630	+	5.30242i	−0.295606	+	0.668043i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	4.52937	+	13.5615i	0.561799	+	1.68209i
$66$	−7.15986	+	2.41736i	−0.881318	+	0.297556i
$67$		−	0.302004i		−	0.0368956i	−0.999830	−	0.0184478i	$-0.994128\pi$
$67$		−	0.302004i		−	0.0368956i	0.999830	−	0.0184478i	$-0.00587245\pi$
$68$	−2.68401	+	3.69422i	−0.325483	+	0.447990i
$69$	−15.6888	−	5.09759i	−1.88871	−	0.613678i
$70$	−3.01149	−	5.09224i	−0.359942	−	0.608639i
$71$	−5.81086	+	4.22183i	−0.689622	+	0.501040i	−0.876536	−	0.481337i	$-0.840151\pi$
$71$	−5.81086	+	4.22183i	−0.689622	+	0.501040i	0.186914	+	0.982376i	$0.440151\pi$
$72$	1.77302	−	1.28817i	0.208952	−	0.151813i
$73$	2.50805	−	0.814915i	0.293545	−	0.0953785i	−0.158542	−	0.987352i	$-0.550679\pi$
$73$	2.50805	−	0.814915i	0.293545	−	0.0953785i	0.452087	+	0.891974i	$0.350679\pi$
$74$	4.55444	+	1.47983i	0.529443	+	0.172027i
$75$	11.3910	−	0.186391i	1.31532	−	0.0215226i
$76$	−6.63291			−0.760847
$77$	0.797301	−	8.73867i	0.0908608	−	0.995864i
$78$		−	14.5692i		−	1.64963i
$79$	3.61392	−	4.97414i	0.406598	−	0.559634i	−0.555786	−	0.831325i	$-0.687583\pi$
$79$	3.61392	−	4.97414i	0.406598	−	0.559634i	0.962385	+	0.271691i	$0.0875828\pi$
$80$	0.0182926	+	2.23599i	0.00204517	+	0.249992i
$81$	−3.32865	−	10.2445i	−0.369850	−	1.13828i
$82$	6.83391	−	4.96512i	0.754679	−	0.548306i
$83$	1.41972	+	1.95408i	0.155835	+	0.214489i	0.879795	−	0.475354i	$-0.157680\pi$
$83$	1.41972	+	1.95408i	0.155835	+	0.214489i	−0.723960	+	0.689842i	$0.757680\pi$
$84$	1.26682	+	5.89374i	0.138222	+	0.643059i
$85$	10.2102	−	0.0835295i	1.10745	−	0.00906005i
$86$	−3.05718	−	2.22117i	−0.329664	−	0.239515i
$87$			15.6948i			1.68266i
$88$	−1.91861	+	2.70535i	−0.204525	+	0.288391i
$89$		−	1.93594i		−	0.205209i	−0.994722	−	0.102605i	$-0.967282\pi$
$89$		−	1.93594i		−	0.205209i	0.994722	−	0.102605i	$-0.0327176\pi$
$90$	−4.67288	−	1.47616i	−0.492565	−	0.155601i
$91$	15.4705	+	6.84564i	1.62175	+	0.717618i
$92$	−6.88557	+	2.23726i	−0.717870	+	0.233250i
$93$	3.59922	+	4.95390i	0.373222	+	0.513695i
$94$	2.59320	−	1.88407i	0.267468	−	0.194327i
$95$	8.81569	+	11.9273i	0.904470	+	1.22372i
$96$	0.704096	−	2.16698i	0.0718615	−	0.221167i
$97$	−10.4319	−	7.57921i	−1.05920	−	0.769553i	−0.0852584	−	0.996359i	$-0.527172\pi$
$97$	−10.4319	−	7.57921i	−1.05920	−	0.769553i	−0.973940	+	0.226806i	$0.927172\pi$
$98$	−6.85361	−	1.42410i	−0.692319	−	0.143856i
$99$	−4.33943	−	5.83113i	−0.436129	−	0.586050i
$100$	3.99646	−	3.00471i	0.399646	−	0.300471i
$101$	−6.91398	−	5.02330i	−0.687967	−	0.499837i	0.188024	−	0.982164i	$-0.439792\pi$
$101$	−6.91398	−	5.02330i	−0.687967	−	0.499837i	−0.875991	+	0.482327i	$0.839792\pi$
$102$	−9.89510	−	3.21511i	−0.979761	−	0.318344i
$103$	−2.29520	−	7.06390i	−0.226153	−	0.696027i	−0.998173	−	0.0604285i	$-0.980753\pi$
$103$	−2.29520	−	7.06390i	−0.226153	−	0.696027i	0.772020	−	0.635599i	$-0.219247\pi$
$104$	−3.75841	−	5.17301i	−0.368542	−	0.507255i
$105$	8.91443	−	10.1113i	0.869959	−	0.986759i
$106$	6.03850	−	1.96203i	0.586511	−	0.190569i
$107$	−6.19437	+	19.0643i	−0.598832	+	1.84302i	−0.0641880	+	0.997938i	$0.520446\pi$
$107$	−6.19437	+	19.0643i	−0.598832	+	1.84302i	−0.534644	+	0.845077i	$0.679554\pi$
$108$	−1.49022	−	1.08271i	−0.143396	−	0.104184i
$109$			2.86586i			0.274500i	0.990536	+	0.137250i	$0.0438263\pi$
$109$			2.86586i			0.274500i	−0.990536	+	0.137250i	$0.956174\pi$
$110$	7.41477	−	0.145579i	0.706971	−	0.0138804i
$111$			10.9113i			1.03566i
$112$	1.97021	+	1.76586i	0.186168	+	0.166858i
$113$	1.76625	+	0.573891i	0.166155	+	0.0539871i	0.390913	−	0.920427i	$-0.372159\pi$
$113$	1.76625	+	0.573891i	0.166155	+	0.0539871i	−0.224758	+	0.974415i	$0.572159\pi$
$114$	−4.67020	−	14.3734i	−0.437405	−	1.34619i
$115$	13.1745	+	9.40816i	1.22853	+	0.877315i
$116$	4.04879	+	5.57268i	0.375920	+	0.517410i
$117$	13.3274	−	4.33035i	1.23212	−	0.400341i
$118$	10.0280	+	3.25829i	0.923151	+	0.299950i
$119$	8.06345	−	8.99659i	0.739175	−	0.824716i
$120$	−4.83248	+	1.61399i	−0.441143	+	0.147337i
$121$	9.04491	+	6.26016i	0.822264	+	0.569106i
$122$	0.736535			0.0666827
$123$	15.5711	+	11.3130i	1.40400	+	1.02006i
$124$	2.55592	+	0.830467i	0.229528	+	0.0745782i
$125$	−10.7147	−	3.19294i	−0.958353	−	0.285585i
$126$	−5.01488	+	2.91063i	−0.446761	+	0.259300i
$127$	−3.41122	+	2.47839i	−0.302697	+	0.219922i	−0.728756	−	0.684773i	$-0.759901\pi$
$127$	−3.41122	+	2.47839i	−0.302697	+	0.219922i	0.426060	+	0.904695i	$0.359901\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.66070	−	8.18878i	0.234261	−	0.720982i
$130$	−4.30689	+	13.6337i	−0.377739	+	1.19576i
$131$	−2.03914			−0.178161			−0.0890803	−	0.996024i	$-0.528393\pi$
$131$	−2.03914			−0.178161			−0.0890803	+	0.996024i	$0.528393\pi$
$132$	−7.21334	−	2.25278i	−0.627841	−	0.196079i
$133$	17.4570	+	1.79452i	1.51372	+	0.155605i
$134$	0.177513	−	0.244326i	0.0153348	−	0.0211066i
$135$	0.0336952	+	4.11873i	0.00290002	+	0.354483i
$136$	−4.34281	+	1.41107i	−0.372393	+	0.120998i
$137$	−10.3181	−	14.2016i	−0.881533	−	1.21333i	−0.975994	−	0.217798i	$-0.930113\pi$
$137$	−10.3181	−	14.2016i	−0.881533	−	1.21333i	0.0944607	−	0.995529i	$-0.469887\pi$
$138$	−9.69620	−	13.3457i	−0.825395	−	1.13606i
$139$	−2.58643	−	7.96021i	−0.219378	−	0.675176i	−0.998814	−	0.0486938i	$-0.984494\pi$
$139$	−2.58643	−	7.96021i	−0.219378	−	0.675176i	0.779436	−	0.626482i	$-0.215506\pi$
$140$	0.556800	−	5.88982i	0.0470582	−	0.497781i
$141$	5.90860	+	4.29285i	0.497594	+	0.361523i
$142$	−7.18261			−0.602752
$143$	−17.0131	+	12.6609i	−1.42270	+	1.05875i
$144$	2.19157			0.182631
$145$	4.63964	−	14.6871i	0.385301	−	1.21970i
$146$	2.50805	+	0.814915i	0.207568	+	0.0674428i
$147$	−1.73959	−	15.8544i	−0.143479	−	1.30765i
$148$	2.81480	+	3.87424i	0.231375	+	0.318461i
$149$	−4.63134	−	6.37450i	−0.379415	−	0.522219i	0.576015	−	0.817439i	$-0.304607\pi$
$149$	−4.63134	−	6.37450i	−0.379415	−	0.522219i	−0.955429	+	0.295220i	$0.904607\pi$
$150$	9.32506	+	6.54466i	0.761388	+	0.534369i
$151$	17.5140	+	5.69065i	1.42527	+	0.463099i	0.917273	−	0.398260i	$-0.130386\pi$
$151$	17.5140	+	5.69065i	1.42527	+	0.463099i	0.507998	+	0.861358i	$0.330386\pi$
$152$	−5.36614	−	3.89873i	−0.435251	−	0.316229i
$153$		−	10.0074i		−	0.809048i
$154$	5.78149	−	6.60109i	0.465886	−	0.531931i
$155$	−1.90367	−	5.69982i	−0.152907	−	0.457821i
$156$	8.56354	−	11.7867i	0.685632	−	0.943692i
$157$	3.16069	−	9.72760i	0.252251	−	0.776347i	−0.742108	−	0.670280i	$-0.766174\pi$
$157$	3.16069	−	9.72760i	0.252251	−	0.776347i	0.994359	−	0.106067i	$-0.0338259\pi$
$158$	5.84745	−	1.89995i	0.465198	−	0.151152i
$159$	8.50336	+	11.7039i	0.674360	+	0.928177i
$160$	−1.29948	+	1.81971i	−0.102733	+	0.143861i
$161$	18.7273	−	4.02532i	1.47592	−	0.317240i
$162$	3.32865	−	10.2445i	0.261523	−	0.804886i
$163$	3.76914	−	5.18778i	0.295222	−	0.406339i	−0.635479	−	0.772118i	$-0.719198\pi$
$163$	3.76914	−	5.18778i	0.295222	−	0.406339i	0.930702	+	0.365779i	$0.119198\pi$
$164$	8.44717			0.659613
$165$	5.53617	+	15.9652i	0.430991	+	1.24289i
$166$			2.41538i			0.187470i
$167$	4.79103	−	6.59429i	0.370741	−	0.510281i	−0.582361	−	0.812930i	$-0.697871\pi$
$167$	4.79103	−	6.59429i	0.370741	−	0.510281i	0.953102	+	0.302649i	$0.0978710\pi$
$168$	−2.43937	+	5.51275i	−0.188201	+	0.425318i
$169$	−8.61714	−	26.5208i	−0.662857	−	2.04006i
$170$	8.30934	+	5.93384i	0.637297	+	0.455105i
$171$	11.7603	−	8.54433i	0.899330	−	0.653401i
$172$	−1.16774	−	3.59393i	−0.0890393	−	0.274035i
$173$	−1.07120	−	0.348055i	−0.0814420	−	0.0264621i	0.268013	−	0.963415i	$-0.413633\pi$
$173$	−1.07120	−	0.348055i	−0.0814420	−	0.0264621i	−0.349455	+	0.936953i	$0.613633\pi$
$174$	−9.22517	+	12.6974i	−0.699358	+	0.962584i
$175$	−11.3311	+	6.82682i	−0.856553	+	0.516059i
$176$	−3.14236	+	1.06094i	−0.236864	+	0.0799716i
$177$			24.0246i			1.80580i
$178$	1.13792	−	1.56621i	0.0852904	−	0.117392i
$179$	3.37804	−	10.3965i	0.252487	−	0.777074i	−0.741828	−	0.670590i	$-0.766041\pi$
$179$	3.37804	−	10.3965i	0.252487	−	0.777074i	0.994314	−	0.106484i	$-0.0339592\pi$
$180$	−2.91278	−	3.94089i	−0.217106	−	0.293736i
$181$	−0.689460	−	0.948960i	−0.0512471	−	0.0705356i	0.782624	−	0.622494i	$-0.213881\pi$
$181$	−0.689460	−	0.948960i	−0.0512471	−	0.0705356i	−0.833871	+	0.551959i	$0.813881\pi$
$182$	8.49214	+	14.6316i	0.629480	+	1.08456i
$183$	0.518591	+	1.59606i	0.0383354	+	0.117984i
$184$	−6.88557	−	2.23726i	−0.507611	−	0.164933i
$185$	3.22557	−	10.2108i	0.237149	−	0.750711i
$186$			6.12336i			0.448986i
$187$	4.84459	+	14.3489i	0.354271	+	1.04930i
$188$	3.20537			0.233776
$189$	3.62916	+	3.25273i	0.263982	+	0.236602i
$190$	0.121333	+	14.8311i	0.00880243	+	1.07596i
$191$	3.01844	+	9.28979i	0.218406	+	0.672186i	0.998894	+	0.0470149i	$0.0149708\pi$
$191$	3.01844	+	9.28979i	0.218406	+	0.672186i	−0.780488	+	0.625171i	$0.785029\pi$
$192$	1.84335	−	1.33927i	0.133032	−	0.0966535i
$193$	−11.0353	+	8.01764i	−0.794341	+	0.577122i	−0.909248	−	0.416254i	$-0.863343\pi$
$193$	−11.0353	+	8.01764i	−0.794341	+	0.577122i	0.114908	+	0.993376i	$0.463343\pi$
$194$	−3.98463	−	12.2634i	−0.286080	−	0.880463i
$195$	−32.5766	+	0.266508i	−2.33286	+	0.0190850i
$196$	−4.70762	−	5.18057i	−0.336259	−	0.370041i
$197$	23.3142			1.66107			0.830536	−	0.556966i	$-0.188035\pi$
$197$	23.3142			1.66107			0.830536	+	0.556966i	$0.188035\pi$
$198$	−0.0832258	−	7.26814i	−0.00591460	−	0.516524i
$199$			7.86393i			0.557459i	0.960370	+	0.278730i	$0.0899133\pi$
$199$			7.86393i			0.557459i	−0.960370	+	0.278730i	$0.910087\pi$
$200$	4.99933	−	0.0818042i	0.353506	−	0.00578443i
$201$	0.654437	+	0.212639i	0.0461604	+	0.0149984i
$202$	−2.64091	−	8.12787i	−0.185813	−	0.571875i
$203$	−9.14825	−	15.7620i	−0.642081	−	1.10628i
$204$	−6.11551	−	8.41728i	−0.428171	−	0.589327i
$205$	−11.2270	−	15.1897i	−0.784127	−	1.06090i
$206$	2.29520	−	7.06390i	0.159914	−	0.492166i
$207$	9.32625	−	12.8365i	0.648219	−	0.892197i
$208$		−	6.39419i		−	0.443357i
$209$	−12.7260	+	17.9444i	−0.880275	+	1.24124i
$210$	13.1552	−	2.94042i	0.907794	−	0.202908i
$211$	−3.78410	+	5.20837i	−0.260508	+	0.358559i	−0.919157	−	0.393892i	$-0.871128\pi$
$211$	−3.78410	+	5.20837i	−0.260508	+	0.358559i	0.658648	+	0.752451i	$0.271128\pi$
$212$	6.03850	+	1.96203i	0.414726	+	0.134753i
$213$	−5.05725	−	15.5646i	−0.346517	−	1.06647i
$214$	−16.2171	+	11.7824i	−1.10858	+	0.805427i
$215$	−4.91060	+	6.87647i	−0.334900	+	0.468971i
$216$	−0.569213	−	1.75186i	−0.0387300	−	0.119199i
$217$	−6.50219	−	2.87719i	−0.441397	−	0.195316i
$218$	−1.68451	+	2.31853i	−0.114090	+	0.157031i
$219$			6.00868i			0.406029i
$220$	6.08424	+	4.24052i	0.410200	+	0.285896i
$221$	−29.1978			−1.96406
$222$	−6.41353	+	8.82747i	−0.430448	+	0.592461i
$223$	8.71755	−	26.8299i	0.583771	−	1.79666i	−0.0203816	−	0.999792i	$-0.506488\pi$
$223$	8.71755	−	26.8299i	0.583771	−	1.79666i	0.604152	−	0.796869i	$-0.293512\pi$
$224$	0.555990	+	2.58667i	0.0371486	+	0.172829i
$225$	−3.21520	+	10.4755i	−0.214347	+	0.698369i
$226$	1.09161	+	1.50247i	0.0726125	+	0.0999426i
$227$	−2.26160	+	0.734839i	−0.150108	+	0.0487730i	−0.383107	−	0.923704i	$-0.625146\pi$
$227$	−2.26160	+	0.734839i	−0.150108	+	0.0487730i	0.232999	+	0.972477i	$0.425146\pi$
$228$	4.67020	−	14.3734i	0.309292	−	0.951902i
$229$	−1.67810	+	2.30970i	−0.110892	+	0.152629i	−0.860855	−	0.508850i	$-0.830071\pi$
$229$	−1.67810	+	2.30970i	−0.110892	+	0.152629i	0.749964	+	0.661479i	$0.230071\pi$
$230$	5.12844	+	15.3552i	0.338160	+	1.01249i
$231$	18.3752	+	7.88060i	1.20900	+	0.518505i
$232$			6.88821i			0.452233i
$233$	−19.7751	−	14.3674i	−1.29551	−	0.941241i	−0.295606	−	0.955310i	$-0.595522\pi$
$233$	−19.7751	−	14.3674i	−1.29551	−	0.941241i	−0.999901	+	0.0140687i	$0.995522\pi$
$234$	13.3274	+	4.33035i	0.871242	+	0.283084i
$235$	−4.26020	−	5.76391i	−0.277905	−	0.375996i
$236$	6.19764	+	8.53032i	0.403432	+	0.555276i
$237$	8.23433	+	11.3336i	0.534877	+	0.736195i
$238$	11.8115	−	2.53882i	0.765628	−	0.164567i
$239$	−15.1024	−	4.90708i	−0.976895	−	0.317413i	−0.223299	−	0.974750i	$-0.571683\pi$
$239$	−15.1024	−	4.90708i	−0.976895	−	0.317413i	−0.753596	+	0.657337i	$0.771683\pi$
$240$	−4.85824	−	1.53471i	−0.313598	−	0.0990653i
$241$	−7.78306			−0.501351			−0.250676	−	0.968071i	$-0.580653\pi$
$241$	−7.78306			−0.501351			−0.250676	+	0.968071i	$0.580653\pi$
$242$	3.63785	+	10.3810i	0.233850	+	0.667319i
$243$	19.0174			1.21997
$244$	0.595869	+	0.432924i	0.0381466	+	0.0277151i
$245$	−3.05891	+	15.3507i	−0.195427	+	0.980718i
$246$	5.94762	+	18.3049i	0.379206	+	1.16708i
$247$	−24.9292	−	34.3121i	−1.58621	−	2.18323i
$248$	1.57964	+	2.17419i	0.100307	+	0.138061i
$249$	−5.23409	+	1.70066i	−0.331697	+	0.107775i
$250$	−6.79163	−	8.88109i	−0.429540	−	0.561690i
$251$	−1.55802	+	2.14443i	−0.0983414	+	0.135355i	−0.855352	−	0.518047i	$-0.826659\pi$
$251$	−1.55802	+	2.14443i	−0.0983414	+	0.135355i	0.757011	+	0.653403i	$0.226659\pi$
$252$	−5.76795	−	0.592925i	−0.363347	−	0.0373507i
$253$	−7.15817	+	22.9203i	−0.450030	+	1.44099i
$254$	−4.21650			−0.264567
$255$	−7.00797	+	22.1842i	−0.438856	+	1.38923i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−3.54922	−	10.9234i	−0.221394	−	0.681382i	−0.998638	−	0.0521818i	$-0.983382\pi$
$257$	−3.54922	−	10.9234i	−0.221394	−	0.681382i	0.777243	−	0.629200i	$-0.216618\pi$
$258$	6.96579	−	5.06094i	0.433671	−	0.315081i
$259$	−6.36006	−	10.9581i	−0.395195	−	0.680902i
$260$	−11.4981	+	8.49841i	−0.713079	+	0.527049i
$261$	−14.3571	−	4.66491i	−0.888684	−	0.288751i
$262$	−1.64970	−	1.19858i	−0.101919	−	0.0740483i
$263$	4.03855			0.249028			0.124514	−	0.992218i	$-0.460263\pi$
$263$	4.03855			0.249028			0.124514	+	0.992218i	$0.460263\pi$
$264$	−4.51157	−	6.06243i	−0.277668	−	0.373117i
$265$	−4.49754	−	13.4661i	−0.276282	−	0.827219i
$266$	13.0682	+	11.7128i	0.801266	+	0.718157i
$267$	4.19515	+	1.36309i	0.256739	+	0.0834195i
$268$	0.287222	−	0.0933242i	0.0175449	−	0.00570069i
$269$	16.1617	+	22.2447i	0.985396	+	1.35628i	0.933871	+	0.357609i	$0.116408\pi$
$269$	16.1617	+	22.2447i	0.985396	+	1.35628i	0.0515240	+	0.998672i	$0.483592\pi$
$270$	−2.39367	+	3.35192i	−0.145674	+	0.203992i
$271$	8.99633	+	27.6879i	0.546488	+	1.68192i	0.717425	+	0.696635i	$0.245320\pi$
$271$	8.99633	+	27.6879i	0.546488	+	1.68192i	−0.170937	+	0.985282i	$0.554680\pi$
$272$	−4.34281	−	1.41107i	−0.263322	−	0.0855584i
$273$	−25.7271	+	28.7044i	−1.55708	+	1.73727i
$274$		−	17.5542i		−	1.06049i
$275$	−0.461148	−	16.5767i	−0.0278083	−	0.999613i
$276$		−	16.4962i		−	0.992952i
$277$	14.5290	+	10.5560i	0.872966	+	0.634247i	0.931381	−	0.364046i	$-0.118605\pi$
$277$	14.5290	+	10.5560i	0.872966	+	0.634247i	−0.0584153	+	0.998292i	$0.518605\pi$
$278$	2.58643	−	7.96021i	0.155124	−	0.477421i
$279$	−5.60147	+	1.82003i	−0.335351	+	0.108962i
$280$	3.91241	−	4.43769i	0.233811	−	0.265202i
$281$	10.2088	+	14.0512i	0.609005	+	0.838223i	0.996495	−	0.0836507i	$-0.0266580\pi$
$281$	10.2088	+	14.0512i	0.609005	+	0.838223i	−0.387490	+	0.921874i	$0.626658\pi$
$282$	2.25689	+	6.94598i	0.134396	+	0.413627i
$283$	14.7161	+	4.78154i	0.874779	+	0.284233i	0.711788	−	0.702395i	$-0.247886\pi$
$283$	14.7161	+	4.78154i	0.874779	+	0.284233i	0.162991	+	0.986628i	$0.447886\pi$
$284$	−5.81086	−	4.22183i	−0.344811	−	0.250520i
$285$	−32.0534	+	10.7055i	−1.89868	+	0.634137i
$286$	−21.2057	+	0.242822i	−1.25392	+	0.0143584i
$287$	−22.2320	−	2.28537i	−1.31231	−	0.134901i
$288$	1.77302	+	1.28817i	0.104476	+	0.0759063i
$289$	−1.19006	+	3.66263i	−0.0700036	+	0.215449i
$290$	12.3864	−	9.15500i	0.727355	−	0.537600i
$291$	23.7691	−	17.2692i	1.39337	−	1.01234i
$292$	1.55006	+	2.13347i	0.0907104	+	0.124852i
$293$	15.2809	−	4.96506i	0.892719	−	0.290062i	0.173491	−	0.984836i	$-0.444495\pi$
$293$	15.2809	−	4.96506i	0.892719	−	0.290062i	0.719229	+	0.694774i	$0.244495\pi$
$294$	7.91160	−	13.8490i	0.461414	−	0.807687i
$295$	7.10208	−	22.4821i	0.413499	−	1.30896i
$296$			4.78883i			0.278345i
$297$	−5.78826	+	1.95427i	−0.335869	+	0.113398i
$298$		−	7.87931i		−	0.456436i
$299$	−37.4521	−	27.2106i	−2.16591	−	1.57363i
$300$	3.69728	+	10.7759i	0.213462	+	0.622145i
$301$	2.10102	+	9.77474i	0.121101	+	0.563406i
$302$	10.8243	+	14.8983i	0.622866	+	0.857302i
$303$	15.7535	−	11.4456i	0.905016	−	0.657532i
$304$	−2.04968	−	6.30827i	−0.117557	−	0.361804i
$305$	−0.0134731	−	1.64689i	−0.000771469	−	0.0943005i
$306$	5.88218	−	8.09613i	0.336262	−	0.462825i
$307$			5.40785i			0.308643i	0.988021	+	0.154321i	$0.0493191\pi$
$307$			5.40785i			0.308643i	−0.988021	+	0.154321i	$0.950681\pi$
$308$	8.55735	−	1.94212i	0.487600	−	0.110662i
$309$	16.9234			0.962739
$310$	1.81017	−	5.73020i	0.102810	−	0.325454i
$311$	−21.9630	−	7.13622i	−1.24541	−	0.404658i	−0.389135	−	0.921181i	$-0.627226\pi$
$311$	−21.9630	−	7.13622i	−1.24541	−	0.404658i	−0.856273	+	0.516523i	$0.827226\pi$
$312$	13.8561	−	4.50212i	0.784447	−	0.254882i
$313$	5.02633	−	3.65185i	0.284105	−	0.206415i	−0.436601	−	0.899655i	$-0.643818\pi$
$313$	5.02633	−	3.65185i	0.284105	−	0.206415i	0.720706	+	0.693241i	$0.243818\pi$
$314$	8.27479	−	6.01199i	0.466974	−	0.339276i
$315$	6.59988	+	11.1600i	0.371861	+	0.628795i
$316$	5.84745	+	1.89995i	0.328945	+	0.106881i
$317$	13.7319	−	18.9004i	0.771263	−	1.06155i	−0.224930	−	0.974375i	$-0.572215\pi$
$317$	13.7319	−	18.9004i	0.771263	−	1.06155i	0.996193	−	0.0871776i	$-0.0277848\pi$
$318$			14.4668i			0.811257i
$319$	22.8441	−	0.261583i	1.27902	−	0.0146458i
$320$	−2.12090	+	0.708357i	−0.118562	+	0.0395984i
$321$	−36.9506	−	26.8462i	−2.06238	−	1.49841i
$322$	17.5167	+	7.75107i	0.976168	+	0.431950i
$323$	−28.8055	+	9.35947i	−1.60278	+	0.520775i
$324$	8.71451	−	6.33147i	0.484140	−	0.351748i
$325$	30.5637	+	9.38077i	1.69537	+	0.520352i
$326$	6.09860	−	1.98156i	0.337770	−	0.109748i
$327$	−6.21028	−	2.01784i	−0.343429	−	0.111587i
$328$	6.83391	+	4.96512i	0.377339	+	0.274153i
$329$	−8.43615	−	0.867206i	−0.465100	−	0.0478106i
$330$	−4.90524	+	16.1702i	−0.270025	+	0.890139i
$331$	2.51487			0.138230			0.0691149	−	0.997609i	$-0.477982\pi$
$331$	2.51487			0.138230			0.0691149	+	0.997609i	$0.477982\pi$
$332$	−1.41972	+	1.95408i	−0.0779175	+	0.107244i
$333$	−9.98138	−	3.24315i	−0.546976	−	0.177723i
$334$	7.75205	−	2.51879i	0.424173	−	0.137822i
$335$	−0.549559	−	0.392449i	−0.0300256	−	0.0214418i
$336$	−5.21381	+	3.02609i	−0.284437	+	0.165087i
$337$	1.41170	+	4.34476i	0.0769001	+	0.236674i	0.982116	−	0.188279i	$-0.0602908\pi$
$337$	1.41170	+	4.34476i	0.0769001	+	0.236674i	−0.905216	+	0.424953i	$0.860291\pi$
$338$	8.61714	−	26.5208i	0.468711	−	1.44254i
$339$	−2.48722	+	3.42337i	−0.135088	+	0.185932i
$340$	3.23457	+	9.68469i	0.175419	+	0.525226i
$341$	7.15052	−	5.32131i	0.387222	−	0.288165i
$342$	14.5365			0.786043
$343$	10.9883	+	14.9083i	0.593313	+	0.804972i
$344$	1.16774	−	3.59393i	0.0629603	−	0.193772i
$345$	−29.6635	+	21.9248i	−1.59703	+	1.18039i
$346$	−0.662039	−	0.911219i	−0.0355914	−	0.0489874i
$347$	−18.8292	+	13.6802i	−1.01080	+	0.734392i	−0.964378	−	0.264530i	$-0.914783\pi$
$347$	−18.8292	+	13.6802i	−1.01080	+	0.734392i	−0.0464263	+	0.998922i	$0.514783\pi$
$348$	−14.9266	+	4.84996i	−0.800151	+	0.259985i
$349$	0.491894	−	1.51389i	0.0263305	−	0.0810369i	−0.937028	−	0.349255i	$-0.886435\pi$
$349$	0.491894	−	1.51389i	0.0263305	−	0.0810369i	0.963358	+	0.268218i	$0.0864347\pi$
$350$	−13.1798	−	1.13726i	−0.704489	−	0.0607891i
$351$		−	11.7782i		−	0.628672i
$352$	−3.16583	−	0.988709i	−0.168739	−	0.0526984i
$353$	18.7369			0.997264			0.498632	−	0.866814i	$-0.333836\pi$
$353$	18.7369			0.997264			0.498632	+	0.866814i	$0.333836\pi$
$354$	−14.1213	+	19.4363i	−0.750540	+	1.03303i
$355$	0.131389	+	16.0603i	0.00697338	+	0.852391i
$356$	1.84119	−	0.598238i	0.0975827	−	0.0317065i
$357$	13.8180	+	23.8078i	0.731327	+	1.26004i
$358$	8.84383	−	6.42542i	0.467411	−	0.339594i
$359$	20.0708	−	6.52140i	1.05930	−	0.344186i	0.272986	−	0.962018i	$-0.411989\pi$
$359$	20.0708	−	6.52140i	1.05930	−	0.344186i	0.786310	+	0.617832i	$0.211989\pi$
$360$	−0.0400895	−	4.90033i	−0.00211290	−	0.258270i
$361$	−20.2218	−	14.6920i	−1.06430	−	0.773263i
$362$		−	1.17298i		−	0.0616504i
$363$	−19.9342	+	15.1924i	−1.04627	+	0.797395i
$364$	−1.72994	+	16.8288i	−0.0906732	+	0.882066i
$365$	1.77626	−	5.62289i	0.0929739	−	0.294315i
$366$	−0.518591	+	1.59606i	−0.0271072	+	0.0834274i
$367$	−0.145119	−	0.446629i	−0.00757513	−	0.0233139i	0.947198	−	0.320651i	$-0.103902\pi$
$367$	−0.145119	−	0.446629i	−0.00757513	−	0.0233139i	−0.954773	+	0.297337i	$0.903902\pi$
$368$	−4.25551	−	5.85721i	−0.221834	−	0.305328i
$369$	−14.9770	+	10.8814i	−0.779670	+	0.566463i
$370$	8.61129	−	6.36475i	0.447680	−	0.330887i
$371$	−15.3618	−	6.79753i	−0.797544	−	0.352910i
$372$	−3.59922	+	4.95390i	−0.186611	+	0.256848i
$373$	33.7017			1.74501			0.872504	−	0.488607i	$-0.162495\pi$
$373$	33.7017			1.74501			0.872504	+	0.488607i	$0.162495\pi$
$374$	−4.51475	+	14.4561i	−0.233452	+	0.747508i
$375$	14.4632	−	20.9705i	0.746878	−	1.08291i
$376$	2.59320	+	1.88407i	0.133734	+	0.0971634i
$377$	−13.6105	+	41.8888i	−0.700976	+	2.15738i
$378$	1.02414	+	4.76468i	0.0526761	+	0.245069i
$379$	4.32563	−	3.14276i	0.222193	−	0.161433i	−0.471120	−	0.882069i	$-0.656150\pi$
$379$	4.32563	−	3.14276i	0.222193	−	0.161433i	0.693313	+	0.720636i	$0.256150\pi$
$380$	−8.61937	+	12.0700i	−0.442164	+	0.619176i
$381$	−2.96882	−	9.13708i	−0.152097	−	0.468107i
$382$	−3.01844	+	9.28979i	−0.154437	+	0.475307i
$383$	19.8509	+	14.4225i	1.01433	+	0.736957i	0.965114	−	0.261831i	$-0.0843264\pi$
$383$	19.8509	+	14.4225i	1.01433	+	0.736957i	0.0492202	+	0.998788i	$0.484326\pi$
$384$	2.27850			0.116274
$385$	−14.8657	−	12.8066i	−0.757629	−	0.652686i
$386$	−13.6404			−0.694279
$387$	6.70002	+	4.86785i	0.340581	+	0.247447i
$388$	3.98463	−	12.2634i	0.202289	−	0.622581i
$389$	9.12749	+	28.0915i	0.462782	+	1.42430i	0.861751	+	0.507332i	$0.169368\pi$
$389$	9.12749	+	28.0915i	0.462782	+	1.42430i	−0.398969	+	0.916965i	$0.630632\pi$
$390$	−26.5116	−	18.9324i	−1.34247	−	0.958680i
$391$	−26.7458	+	19.4320i	−1.35259	+	0.982717i
$392$	−0.763480	−	6.95824i	−0.0385616	−	0.351444i
$393$	1.43575	−	4.41878i	0.0724240	−	0.222898i
$394$	18.8616	+	13.7038i	0.950235	+	0.690386i
$395$	−4.35524	−	13.0401i	−0.219136	−	0.656119i
$396$	4.20477	−	5.92896i	0.211298	−	0.297942i
$397$	19.2410			0.965679			0.482839	−	0.875709i	$-0.339606\pi$
$397$	19.2410			0.965679			0.482839	+	0.875709i	$0.339606\pi$
$398$	−4.62230	+	6.36205i	−0.231695	+	0.318901i
$399$	−16.1801	+	36.5656i	−0.810019	+	1.83057i
$400$	4.09263	+	2.87235i	0.204631	+	0.143618i
$401$	12.1072	−	8.79639i	0.604604	−	0.439271i	−0.242906	−	0.970050i	$-0.578101\pi$
$401$	12.1072	−	8.79639i	0.604604	−	0.439271i	0.847510	+	0.530779i	$0.178101\pi$
$402$	0.404464	+	0.556697i	0.0201728	+	0.0277655i
$403$	5.31017	+	16.3430i	0.264518	+	0.814103i
$404$	2.64091	−	8.12787i	0.131390	−	0.404377i
$405$	−22.9676	−	7.25544i	−1.14127	−	0.360526i
$406$	1.86359	−	18.1289i	0.0924885	−	0.899725i
$407$	15.8817	−	0.181858i	0.787227	−	0.00901436i
$408$		−	10.4043i		−	0.515091i
$409$	12.3190	+	8.95030i	0.609137	+	0.442564i	0.849110	−	0.528216i	$-0.177139\pi$
$409$	12.3190	+	8.95030i	0.609137	+	0.442564i	−0.239974	+	0.970779i	$0.577139\pi$
$410$	−0.154521	−	18.8878i	−0.00763123	−	0.932803i
$411$	38.0396	−	12.3598i	1.87635	−	0.609665i
$412$	6.00892	−	4.36573i	0.296038	−	0.215084i
$413$	−14.0036	−	24.1276i	−0.689072	−	1.18724i
$414$	15.0902	−	4.90310i	0.741643	−	0.240974i
$415$	5.40077	−	0.0441836i	0.265114	−	0.00216889i
$416$	3.75841	−	5.17301i	0.184271	−	0.253628i
$417$	19.0707			0.933898
$418$	−20.8430	+	7.03714i	−1.01946	+	0.344198i
$419$			0.446137i			0.0217952i	0.999941	+	0.0108976i	$0.00346889\pi$
$419$			0.446137i			0.0217952i	−0.999941	+	0.0108976i	$0.996531\pi$
$420$	12.3711	+	5.35357i	0.603648	+	0.261228i
$421$	−0.753877	+	2.32020i	−0.0367417	+	0.113079i	−0.967745	−	0.251931i	$-0.918934\pi$
$421$	−0.753877	+	2.32020i	−0.0367417	+	0.113079i	0.931004	+	0.365010i	$0.118934\pi$
$422$	−6.12281	+	1.98942i	−0.298054	+	0.0968435i
$423$	−5.68317	+	4.12907i	−0.276325	+	0.200762i
$424$	3.73200	+	5.13665i	0.181242	+	0.249458i
$425$	13.1160	−	18.6882i	0.636221	−	0.906510i
$426$	5.05725	−	15.5646i	0.245024	−	0.754108i
$427$	−1.45113	−	1.30062i	−0.0702252	−	0.0629413i
$428$	−20.0454			−0.968930
$429$	−15.4571	−	45.7815i	−0.746274	−	2.21035i
$430$	−8.01465	+	2.67680i	−0.386501	+	0.129087i
$431$	−15.4223	+	21.2270i	−0.742865	+	1.02247i	0.255583	+	0.966787i	$0.417732\pi$
$431$	−15.4223	+	21.2270i	−0.742865	+	1.02247i	−0.998449	+	0.0556793i	$0.982268\pi$
$432$	0.569213	−	1.75186i	0.0273863	−	0.0842863i
$433$	−6.08490	−	18.7274i	−0.292421	−	0.899981i	−0.984075	−	0.177752i	$-0.943118\pi$
$433$	−6.08490	−	18.7274i	−0.292421	−	0.899981i	0.691654	−	0.722229i	$-0.256882\pi$
$434$	−3.56921	−	6.14959i	−0.171328	−	0.295190i
$435$	28.5599	+	20.3951i	1.36934	+	0.977872i
$436$	−2.72560	+	0.885600i	−0.130532	+	0.0424126i
$437$	−45.6714	−	14.8395i	−2.18476	−	0.709871i
$438$	−3.53181	+	4.86112i	−0.168757	+	0.232273i
$439$	13.4365			0.641288			0.320644	−	0.947200i	$-0.396101\pi$
$439$	13.4365			0.641288			0.320644	+	0.947200i	$0.396101\pi$
$440$	2.42974	+	7.00688i	0.115833	+	0.334040i
$441$	15.0202	+	3.12102i	0.715245	+	0.148620i
$442$	−23.6215	−	17.1620i	−1.12356	−	0.816315i
$443$	−7.96079	−	2.58662i	−0.378229	−	0.122894i	0.113732	−	0.993511i	$-0.463720\pi$
$443$	−7.96079	−	2.58662i	−0.378229	−	0.122894i	−0.491961	+	0.870618i	$0.663720\pi$
$444$	−10.3773	+	3.37179i	−0.492485	+	0.160018i
$445$	−3.52284	−	2.51572i	−0.166999	−	0.119257i
$446$	22.8229	−	16.5818i	1.08069	−	0.785170i
$447$	17.0743	−	5.54779i	0.807589	−	0.262402i
$448$	−1.07060	+	2.41946i	−0.0505812	+	0.114309i
$449$	5.16501	+	3.75260i	0.243752	+	0.177096i	0.702953	−	0.711236i	$-0.251864\pi$
$449$	5.16501	+	3.75260i	0.243752	+	0.177096i	−0.459201	+	0.888332i	$0.651864\pi$
$450$	−8.75852	+	6.58504i	−0.412880	+	0.310422i
$451$	16.2068	−	22.8526i	0.763151	−	1.07609i
$452$			1.85715i			0.0873530i
$453$	−24.6631	+	33.9458i	−1.15877	+	1.59491i
$454$	−2.26160	−	0.734839i	−0.106142	−	0.0344877i
$455$	32.5608	−	19.2560i	1.52647	−	0.902736i
$456$	12.2268	−	8.88326i	0.572570	−	0.415997i
$457$	4.36139	−	3.16873i	0.204017	−	0.148227i	−0.481085	−	0.876674i	$-0.659757\pi$
$457$	4.36139	−	3.16873i	0.204017	−	0.148227i	0.685103	+	0.728447i	$0.259757\pi$
$458$	−2.71521	+	0.882227i	−0.126874	+	0.0412238i
$459$	−7.99951	−	2.59920i	−0.373385	−	0.121320i
$460$	−4.87654	+	15.4370i	−0.227370	+	0.719754i
$461$	−29.0701			−1.35393			−0.676964	−	0.736016i	$-0.736705\pi$
$461$	−29.0701			−1.35393			−0.676964	+	0.736016i	$0.736705\pi$
$462$	10.2337	+	17.1762i	0.476116	+	0.799109i
$463$			19.7018i			0.915620i	0.889050	+	0.457810i	$0.151366\pi$
$463$			19.7018i			0.915620i	−0.889050	+	0.457810i	$0.848634\pi$
$464$	−4.04879	+	5.57268i	−0.187960	+	0.258705i
$465$	13.6918	−	0.112012i	0.634941	−	0.00519444i
$466$	−7.55340	−	23.2470i	−0.349905	−	1.07690i
$467$	−14.1709	+	10.2957i	−0.655750	+	0.476430i	−0.865225	−	0.501384i	$-0.832824\pi$
$467$	−14.1709	+	10.2957i	−0.655750	+	0.476430i	0.209475	+	0.977814i	$0.432824\pi$
$468$	8.23681	+	11.3370i	0.380747	+	0.524053i
$469$	−0.781184	+	0.167911i	−0.0360717	+	0.00775341i
$470$	−0.0586345	−	7.16718i	−0.00270461	−	0.330597i
$471$	18.8541	+	13.6983i	0.868752	+	0.631186i
$472$			10.5441i			0.485329i
$473$	−11.9633	−	3.73622i	−0.550073	−	0.171792i
$474$			14.0091i			0.643458i
$475$	33.1601	−	0.542600i	1.52149	−	0.0248962i
$476$	11.0480	+	4.88870i	0.506385	+	0.224073i
$477$	−13.2338	+	4.29992i	−0.605933	+	0.196880i
$478$	−9.33382	−	12.8469i	−0.426919	−	0.587603i
$479$	8.86604	−	6.44155i	0.405100	−	0.294322i	−0.366515	−	0.930412i	$-0.619449\pi$
$479$	8.86604	−	6.44155i	0.405100	−	0.294322i	0.771615	+	0.636090i	$0.219449\pi$
$480$	−3.02832	−	4.09721i	−0.138223	−	0.187011i
$481$	−9.46230	+	29.1220i	−0.431444	+	1.32785i
$482$	−6.29663	−	4.57477i	−0.286804	−	0.208375i
$483$	−4.46300	+	43.4159i	−0.203074	+	1.97549i
$484$	−3.15874	+	10.5367i	−0.143579	+	0.478942i
$485$	−27.3480	+	9.13393i	−1.24181	+	0.414750i
$486$	15.3854	+	11.1781i	0.697895	+	0.507050i
$487$	−14.9022	−	4.84200i	−0.675281	−	0.219412i	−0.0487530	−	0.998811i	$-0.515525\pi$
$487$	−14.9022	−	4.84200i	−0.675281	−	0.219412i	−0.626528	+	0.779399i	$0.715525\pi$
$488$	0.227602	+	0.700486i	0.0103031	+	0.0317095i
$489$	8.58800	+	11.8204i	0.388363	+	0.534536i
$490$	−11.4976	+	10.6210i	−0.519409	+	0.479807i
$491$	−33.3372	+	10.8319i	−1.50449	+	0.488838i	−0.941323	−	0.337507i	$-0.890416\pi$
$491$	−33.3372	+	10.8319i	−1.50449	+	0.488838i	−0.563164	+	0.826345i	$0.690416\pi$
$492$	−5.94762	+	18.3049i	−0.268139	+	0.825248i
$493$	25.4465	+	18.4880i	1.14605	+	0.832657i
$494$		−	42.4121i		−	1.90821i
$495$	−16.2500	+	0.319045i	−0.730382	+	0.0143400i
$496$			2.68745i			0.120670i
$497$	14.1513	+	12.6835i	0.634772	+	0.568932i
$498$	−5.23409	−	1.70066i	−0.234545	−	0.0762083i
$499$	3.73319	+	11.4896i	0.167121	+	0.514345i	0.999186	−	0.0403326i	$-0.0128417\pi$
$499$	3.73319	+	11.4896i	0.167121	+	0.514345i	−0.832066	+	0.554677i	$0.812842\pi$
$500$	−0.274364	−	11.1770i	−0.0122699	−	0.499849i
$501$	10.9164	+	15.0251i	0.487707	+	0.671272i
$502$	−2.52093	+	0.819100i	−0.112515	+	0.0365582i
$503$	−27.7344	−	9.01145i	−1.23662	−	0.401801i	−0.383509	−	0.923537i	$-0.625284\pi$
$503$	−27.7344	−	9.01145i	−1.23662	−	0.401801i	−0.853107	+	0.521737i	$0.825284\pi$
$504$	−4.31786	−	3.87000i	−0.192333	−	0.172384i
$505$	−18.1256	+	6.05373i	−0.806576	+	0.269387i
$506$	−19.2633	+	14.3355i	−0.856358	+	0.637288i
$507$	63.5375			2.82180
$508$	−3.41122	−	2.47839i	−0.151348	−	0.109961i
$509$	−24.1800	−	7.85656i	−1.07176	−	0.348236i	−0.280587	−	0.959829i	$-0.590529\pi$
$509$	−24.1800	−	7.85656i	−1.07176	−	0.348236i	−0.791173	+	0.611593i	$0.790529\pi$
$510$	−18.7091	+	13.8282i	−0.828453	+	0.612324i
$511$	−3.50237	−	6.03442i	−0.154936	−	0.266947i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−3.77554	−	11.6199i	−0.166694	−	0.513032i
$514$	3.54922	−	10.9234i	0.156550	−	0.481810i
$515$	−15.8368	−	5.00284i	−0.697854	−	0.220451i
$516$	8.61019			0.379043
$517$	6.14986	−	8.67165i	0.270471	−	0.381379i
$518$	1.29561	−	12.6036i	0.0569257	−	0.553772i
$519$	1.50846	−	2.07621i	0.0662139	−	0.0911356i
$520$	−14.2974	+	0.116966i	−0.626981	+	0.00512931i
$521$	−38.4820	+	12.5036i	−1.68593	+	0.547791i	−0.986047	−	0.166469i	$-0.946763\pi$
$521$	−38.4820	+	12.5036i	−1.68593	+	0.547791i	−0.699880	+	0.714260i	$0.746763\pi$
$522$	−8.87319	−	12.2129i	−0.388369	−	0.534544i
$523$	−17.0514	−	23.4692i	−0.745606	−	1.02624i	−0.998276	−	0.0586859i	$-0.981309\pi$
$523$	−17.0514	−	23.4692i	−0.745606	−	1.02624i	0.252671	−	0.967552i	$-0.418691\pi$
$524$	−0.630129	−	1.93934i	−0.0275273	−	0.0847204i
$525$	−6.81540	−	29.3611i	−0.297449	−	1.28142i
$526$	3.26726	+	2.37380i	0.142459	+	0.103503i
$527$	12.2717			0.534564
$528$	−0.0865271	−	7.55644i	−0.00376561	−	0.328852i
$529$	−29.4164			−1.27897
$530$	4.27662	−	13.5379i	0.185764	−	0.588050i
$531$	−21.9770	−	7.14077i	−0.953722	−	0.309883i
$532$	3.68783	+	17.1572i	0.159888	+	0.743858i
$533$	31.7479	+	43.6973i	1.37516	+	1.89274i
$534$	2.59274	+	3.56861i	0.112199	+	0.154429i
$535$	26.6420	+	36.0457i	1.15183	+	1.55839i
$536$	0.287222	+	0.0933242i	0.0124061	+	0.00403099i
$537$	20.1507	+	14.6403i	0.869566	+	0.631776i
$538$			27.4959i			1.18543i
$539$	−23.0474	+	2.79625i	−0.992720	+	0.120443i
$540$	−3.90673	+	1.30480i	−0.168119	+	0.0561497i
$541$	6.00712	−	8.26809i	0.258266	−	0.355473i	−0.660119	−	0.751161i	$-0.729494\pi$
$541$	6.00712	−	8.26809i	0.258266	−	0.355473i	0.918385	+	0.395689i	$0.129494\pi$
$542$	−8.99633	+	27.6879i	−0.386425	+	1.18930i
$543$	2.54183	−	0.825889i	0.109080	−	0.0354423i
$544$	−2.68401	−	3.69422i	−0.115076	−	0.158388i
$545$	5.21503	+	3.72414i	0.223388	+	0.159525i
$546$	−37.6857	+	8.10031i	−1.61280	+	0.346661i
$547$	8.17875	−	25.1716i	0.349698	−	1.07626i	−0.609322	−	0.792923i	$-0.708558\pi$
$547$	8.17875	−	25.1716i	0.349698	−	1.07626i	0.959020	−	0.283337i	$-0.0914415\pi$
$548$	10.3181	−	14.2016i	0.440767	−	0.606663i
$549$	−1.61417			−0.0688910
$550$	9.37047	−	13.6819i	0.399558	−	0.583398i
$551$			45.6889i			1.94641i
$552$	9.69620	−	13.3457i	0.412698	−	0.568029i
$553$	−14.8758	−	6.58247i	−0.632582	−	0.279915i
$554$	5.54960	+	17.0799i	0.235780	+	0.725656i
$555$	19.8555	+	14.1791i	0.842818	+	0.601871i
$556$	6.77136	−	4.91968i	0.287169	−	0.208641i
$557$	−8.67129	−	26.6875i	−0.367415	−	1.13079i	−0.948455	−	0.316911i	$-0.897354\pi$
$557$	−8.67129	−	26.6875i	−0.367415	−	1.13079i	0.581041	−	0.813874i	$-0.302646\pi$
$558$	−5.60147	−	1.82003i	−0.237129	−	0.0770479i
$559$	14.2026	−	19.5482i	0.600706	−	0.826801i
$560$	5.77361	−	1.29051i	0.243980	−	0.0545338i
$561$	−34.5050	+	0.395109i	−1.45680	+	0.0166815i
$562$			17.3682i			0.732634i
$563$	−1.96487	+	2.70441i	−0.0828094	+	0.113977i	−0.848412	−	0.529336i	$-0.822441\pi$
$563$	−1.96487	+	2.70441i	−0.0828094	+	0.113977i	0.765603	+	0.643314i	$0.222441\pi$
$564$	−2.25689	+	6.94598i	−0.0950320	+	0.292479i
$565$	3.33954	−	2.46831i	0.140495	−	0.103842i
$566$	9.09503	+	12.5182i	0.382292	+	0.526180i
$567$	−24.6485	+	14.3060i	−1.03514	+	0.600795i
$568$	−2.21955	−	6.83107i	−0.0931302	−	0.286625i
$569$	−11.8716	−	3.85732i	−0.497684	−	0.161707i	0.0494099	−	0.998779i	$-0.484266\pi$
$569$	−11.8716	−	3.85732i	−0.497684	−	0.161707i	−0.547094	+	0.837071i	$0.684266\pi$
$570$	−32.2243	−	10.1796i	−1.34973	−	0.426377i
$571$		−	11.9780i		−	0.501263i	−0.968083	−	0.250631i	$-0.919362\pi$
$571$		−	11.9780i		−	0.501263i	0.968083	−	0.250631i	$-0.0806382\pi$
$572$	−17.2985	−	12.2680i	−0.723288	−	0.512950i
$573$	−22.2561			−0.929762
$574$	−16.6427	−	14.9165i	−0.694654	−	0.622603i
$575$	34.2402	−	11.7481i	1.42792	−	0.489928i
$576$	0.677232	+	2.08431i	0.0282180	+	0.0868461i
$577$	16.6321	−	12.0840i	0.692405	−	0.503062i	−0.185045	−	0.982730i	$-0.559243\pi$
$577$	16.6321	−	12.0840i	0.692405	−	0.503062i	0.877450	+	0.479668i	$0.159243\pi$
$578$	−3.11562	+	2.26363i	−0.129593	+	0.0941547i
$579$	−9.60416	−	29.5586i	−0.399135	−	1.22841i
$580$	15.4020	−	0.126003i	0.639533	−	0.00523200i
$581$	4.26522	−	4.75881i	0.176951	−	0.197429i
$582$	29.3802			1.21785
$583$	16.8935	−	12.5719i	0.699657	−	0.520674i
$584$			2.63712i			0.109125i
$585$	9.43884	−	29.8793i	0.390248	−	1.23536i
$586$	15.2809	+	4.96506i	0.631248	+	0.205105i
$587$	−6.67513	−	20.5439i	−0.275512	−	0.847939i	−0.989083	−	0.147357i	$-0.952923\pi$
$587$	−6.67513	−	20.5439i	−0.275512	−	0.847939i	0.713571	−	0.700583i	$-0.247077\pi$
$588$	14.5408	−	6.55372i	0.599654	−	0.270271i
$589$	10.4776	+	14.4212i	0.431723	+	0.594216i
$590$	18.9604	−	14.0139i	0.780586	−	0.576944i
$591$	−16.4155	+	50.5216i	−0.675242	+	2.07818i
$592$	−2.81480	+	3.87424i	−0.115688	+	0.159230i
$593$			40.0620i			1.64515i	0.568658	+	0.822574i	$0.307463\pi$
$593$			40.0620i			1.64515i	−0.568658	+	0.822574i	$0.692537\pi$
$594$	−5.83149	−	1.82121i	−0.239269	−	0.0747253i
$595$	−5.89284	−	26.3641i	−0.241583	−	1.08082i
$596$	4.63134	−	6.37450i	0.189707	−	0.261110i
$597$	−17.0410	−	5.53696i	−0.697442	−	0.226613i
$598$	−14.3054	−	44.0276i	−0.584993	−	1.80042i
$599$	−3.18118	+	2.31126i	−0.129979	+	0.0944356i	−0.650875	−	0.759185i	$-0.725598\pi$
$599$	−3.18118	+	2.31126i	−0.129979	+	0.0944356i	0.520896	+	0.853620i	$0.325598\pi$
$600$	−3.34274	+	10.8911i	−0.136467	+	0.444626i
$601$	3.87998	+	11.9414i	0.158268	+	0.487098i	0.998477	−	0.0551636i	$-0.0175680\pi$
$601$	3.87998	+	11.9414i	0.158268	+	0.487098i	−0.840209	+	0.542262i	$0.817568\pi$
$602$	−4.04568	+	9.14288i	−0.164890	+	0.372636i
$603$	−0.389033	+	0.535457i	−0.0158426	+	0.0218055i
$604$			18.4153i			0.749309i
$605$	23.1454	−	8.32411i	0.940994	−	0.338423i
$606$	19.4724			0.791013
$607$	−18.6551	+	25.6766i	−0.757188	+	1.04218i	0.240255	+	0.970710i	$0.422769\pi$
$607$	−18.6551	+	25.6766i	−0.757188	+	1.04218i	−0.997443	+	0.0714695i	$0.977231\pi$
$608$	2.04968	−	6.30827i	0.0831256	−	0.255834i
$609$	40.5973	−	8.72614i	1.64508	−	0.353601i
$610$	0.957116	−	1.34028i	0.0387525	−	0.0542663i
$611$	12.0471	+	16.5814i	0.487373	+	0.670811i
$612$	9.51757	−	3.09245i	0.384725	−	0.125005i
$613$	−7.71017	+	23.7295i	−0.311411	+	0.958424i	0.665796	+	0.746134i	$0.268092\pi$
$613$	−7.71017	+	23.7295i	−0.311411	+	0.958424i	−0.977207	+	0.212290i	$0.931908\pi$
$614$	−3.17866	+	4.37505i	−0.128280	+	0.176562i
$615$	40.8208	−	13.6337i	1.64605	−	0.549763i
$616$	8.06459	+	3.45867i	0.324931	+	0.139354i
$617$			26.9376i			1.08447i	0.840228	+	0.542234i	$0.182421\pi$
$617$			26.9376i			1.08447i	−0.840228	+	0.542234i	$0.817579\pi$
$618$	13.6913	+	9.94733i	0.550746	+	0.400140i
$619$	4.09557	+	1.33073i	0.164615	+	0.0534866i	0.390165	−	0.920745i	$-0.372418\pi$
$619$	4.09557	+	1.33073i	0.164615	+	0.0534866i	−0.225550	+	0.974232i	$0.572418\pi$
$620$	4.83258	−	3.57184i	0.194081	−	0.143449i
$621$	−7.83871	−	10.7891i	−0.314556	−	0.432950i
$622$	−13.5739	−	18.6829i	−0.544263	−	0.749114i
$623$	−5.00764	+	1.07636i	−0.200627	+	0.0431235i
$624$	13.8561	+	4.50212i	0.554688	+	0.180229i
$625$	−19.7338	+	15.3485i	−0.789353	+	0.613939i
$626$	6.21289			0.248317
$627$	−29.9248	−	40.2115i	−1.19508	−	1.60589i
$628$	10.2282			0.408150
$629$	17.6910	+	12.8532i	0.705385	+	0.512492i
$630$	−1.22026	+	12.9079i	−0.0486165	+	0.514265i
$631$	−8.72876	−	26.8644i	−0.347486	−	1.06945i	−0.960239	−	0.279179i	$-0.909938\pi$
$631$	−8.72876	−	26.8644i	−0.347486	−	1.06945i	0.612753	−	0.790275i	$-0.290062\pi$
$632$	3.61392	+	4.97414i	0.143754	+	0.197861i
$633$	−8.62209	−	11.8673i	−0.342697	−	0.471682i
$634$	22.2188	−	7.21931i	0.882420	−	0.286716i
$635$	0.0771306	+	9.42806i	0.00306084	+	0.374141i
$636$	−8.50336	+	11.7039i	−0.337180	+	0.464089i
$637$	9.10597	−	43.8233i	0.360792	−	1.73634i
$638$	18.6350	+	13.2158i	0.737768	+	0.523219i
$639$	15.7412			0.622712
$640$	−2.13221	−	0.673563i	−0.0842829	−	0.0266249i
$641$	−0.152861	+	0.470457i	−0.00603764	+	0.0185819i	−0.954030	−	0.299711i	$-0.903110\pi$
$641$	−0.152861	+	0.470457i	−0.00603764	+	0.0185819i	0.947992	+	0.318293i	$0.103110\pi$
$642$	−14.1139	−	43.4380i	−0.557030	−	1.71436i
$643$	15.1592	−	11.0138i	0.597819	−	0.434341i	−0.247285	−	0.968943i	$-0.579538\pi$
$643$	15.1592	−	11.0138i	0.597819	−	0.434341i	0.845104	+	0.534602i	$0.179538\pi$
$644$	9.61536	+	16.5668i	0.378898	+	0.652824i
$645$	−11.4437	−	15.4829i	−0.450594	−	0.609638i
$646$	−28.8055	−	9.35947i	−1.13334	−	0.368243i
$647$	−13.4449	−	9.76830i	−0.528574	−	0.384031i	0.291250	−	0.956647i	$-0.405929\pi$
$647$	−13.4449	−	9.76830i	−0.528574	−	0.384031i	−0.819824	+	0.572615i	$0.805929\pi$
$648$	10.7717			0.423154
$649$	34.9684	−	0.400415i	1.37263	−	0.0157177i
$650$	19.2127	+	25.5541i	0.753584	+	1.00232i
$651$	10.8130	−	12.0643i	0.423794	−	0.472838i
$652$	6.09860	+	1.98156i	0.238840	+	0.0776038i
$653$	30.6013	−	9.94296i	1.19752	−	0.389098i	0.358673	−	0.933463i	$-0.383229\pi$
$653$	30.6013	−	9.94296i	1.19752	−	0.389098i	0.838848	+	0.544365i	$0.183229\pi$
$654$	−3.83816	−	5.28278i	−0.150084	−	0.206573i
$655$	−2.64983	+	3.71064i	−0.103538	+	0.144987i
$656$	2.61032	+	8.03374i	0.101916	+	0.313665i
$657$	−5.49656	−	1.78594i	−0.214441	−	0.0696762i
$658$	−6.31526	−	5.66023i	−0.246194	−	0.220659i
$659$		−	41.7916i		−	1.62797i	−0.580886	−	0.813985i	$-0.697294\pi$
$659$		−	41.7916i		−	1.62797i	0.580886	−	0.813985i	$-0.302706\pi$
$660$	−13.4730	+	10.1987i	−0.524437	+	0.396985i
$661$		−	47.6106i		−	1.85184i	−0.377722	−	0.925919i	$-0.623292\pi$
$661$		−	47.6106i		−	1.85184i	0.377722	−	0.925919i	$-0.376708\pi$
$662$	2.03457	+	1.47820i	0.0790759	+	0.0574520i
$663$	20.5580	−	63.2712i	0.798408	−	2.45725i
$664$	−2.29716	+	0.746394i	−0.0891472	+	0.0289657i
$665$	25.9507	−	29.4348i	1.00632	−	1.14143i
$666$	−6.16883	−	8.49067i	−0.239037	−	0.329007i
$667$	15.4107	+	47.4292i	0.596704	+	1.83647i
$668$	7.75205	+	2.51879i	0.299936	+	0.0974551i
$669$	52.0019	+	37.7816i	2.01051	+	1.46072i
$670$	−0.213926	−	0.640520i	−0.00826470	−	0.0247455i
$671$	2.31446	−	0.781422i	0.0893485	−	0.0301665i
$672$	−5.99675	−	0.616444i	−0.231330	−	0.0237798i
$673$	−34.1266	−	24.7944i	−1.31548	−	0.955755i	−0.999977	−	0.00683185i	$-0.997825\pi$
$673$	−34.1266	−	24.7944i	−1.31548	−	0.955755i	−0.315507	−	0.948923i	$-0.602175\pi$
$674$	−1.41170	+	4.34476i	−0.0543765	+	0.167354i
$675$	7.53867	+	5.29091i	0.290163	+	0.203647i
$676$	22.5600	−	16.3908i	0.867691	−	0.630414i
$677$	12.3620	+	17.0148i	0.475108	+	0.653931i	0.977556	−	0.210677i	$-0.0675669\pi$
$677$	12.3620	+	17.0148i	0.475108	+	0.653931i	−0.502447	+	0.864608i	$0.667567\pi$
$678$	−4.02441	+	1.30761i	−0.154557	+	0.0502185i
$679$	−13.8049	+	31.1979i	−0.529784	+	1.19726i
$680$	−3.07569	+	9.73631i	−0.117947	+	0.373370i
$681$		−	5.41825i		−	0.207628i
$682$	8.91268	−	0.102057i	0.341284	−	0.00390797i
$683$		−	40.1634i		−	1.53681i	−0.639963	−	0.768406i	$-0.721050\pi$
$683$		−	40.1634i		−	1.53681i	0.639963	−	0.768406i	$-0.278950\pi$
$684$	11.7603	+	8.54433i	0.449665	+	0.326701i
$685$	−39.2510	+	0.321111i	−1.49970	+	0.0122690i
$686$	0.126852	+	18.5198i	0.00484325	+	0.707090i
$687$	−3.82354	−	5.26265i	−0.145877	−	0.200783i
$688$	3.05718	−	2.22117i	0.116554	−	0.0846814i
$689$	12.5456	+	38.6113i	0.477948	+	1.47097i
$690$	−36.8853	+	0.301757i	−1.40420	+	0.0114877i
$691$	17.2066	−	23.6829i	0.654570	−	0.900939i	−0.344716	−	0.938707i	$-0.612025\pi$
$691$	17.2066	−	23.6829i	0.654570	−	0.900939i	0.999287	+	0.0377683i	$0.0120249\pi$
$692$		−	1.12633i		−	0.0428166i
$693$	−12.6705	+	14.4667i	−0.481314	+	0.549546i
$694$	−23.2742			−0.883475
$695$	−17.8463	−	5.63762i	−0.676948	−	0.213847i
$696$	−14.9266	−	4.84996i	−0.565793	−	0.183837i
$697$	36.6845	−	11.9195i	1.38952	−	0.451484i
$698$	1.28780	−	0.935638i	0.0487438	−	0.0354144i
$699$	45.0575	−	32.7362i	1.70423	−	1.23820i
$700$	−9.99420	−	8.66694i	−0.377745	−	0.327580i
$701$	20.1704	+	6.55375i	0.761824	+	0.247532i	0.664061	−	0.747678i	$-0.268831\pi$
$701$	20.1704	+	6.55375i	0.761824	+	0.247532i	0.0977627	+	0.995210i	$0.468831\pi$
$702$	6.92303	−	9.52874i	0.261293	−	0.359639i
$703$			31.7639i			1.19800i
$704$	−1.98006	−	2.66071i	−0.0746262	−	0.100279i
$705$	15.4899	−	5.17344i	0.583383	−	0.194843i
$706$	15.1585	+	11.0133i	0.570496	+	0.414490i
$707$	−9.14953	+	20.6771i	−0.344103	+	0.777643i
$708$	−22.8488	+	7.42402i	−0.858710	+	0.279012i
$709$	−26.1540	+	19.0020i	−0.982235	+	0.713636i	−0.958207	−	0.286076i	$-0.907649\pi$
$709$	−26.1540	+	19.0020i	−0.982235	+	0.713636i	−0.0240280	+	0.999711i	$0.507649\pi$
$710$	−9.33370	+	13.0703i	−0.350287	+	0.490518i
$711$	−12.8151	+	4.16388i	−0.480603	+	0.156158i
$712$	1.84119	+	0.598238i	0.0690014	+	0.0224199i
$713$	15.7410	+	11.4365i	0.589504	+	0.428300i
$714$	−2.81487	+	27.3830i	−0.105344	+	1.02478i
$715$	0.930857	+	47.4114i	0.0348121	+	1.77309i
$716$	10.9316			0.408532
$717$	21.2671	−	29.2717i	0.794235	−	1.09317i
$718$	20.0708	+	6.52140i	0.749036	+	0.243376i
$719$	7.13958	−	2.31979i	0.266261	−	0.0865135i	−0.172844	−	0.984949i	$-0.555296\pi$
$719$	7.13958	−	2.31979i	0.266261	−	0.0865135i	0.439105	+	0.898436i	$0.355296\pi$
$720$	2.84791	−	3.98802i	0.106135	−	0.148625i
$721$	−16.9959	+	9.86440i	−0.632960	+	0.367369i
$722$	−7.72404	−	23.7721i	−0.287459	−	0.884707i
$723$	5.48002	−	16.8658i	0.203804	−	0.627245i
$724$	0.689460	−	0.948960i	0.0256236	−	0.0352678i
$725$	−20.6971	−	27.5284i	−0.768671	−	1.02238i
$726$	−25.0569	+	0.573919i	−0.929950	+	0.0213001i
$727$	−14.6519			−0.543410			−0.271705	−	0.962381i	$-0.587587\pi$
$727$	−14.6519			−0.543410			−0.271705	+	0.962381i	$0.587587\pi$
$728$	−11.2912	+	12.5979i	−0.418481	+	0.466910i
$729$	−3.40411	+	10.4768i	−0.126078	+	0.388028i
$730$	4.74208	−	3.50495i	0.175512	−	0.129724i
$731$	−10.1425	−	13.9600i	−0.375136	−	0.516330i
$732$	−1.35769	+	0.986419i	−0.0501816	+	0.0364591i
$733$	−23.1829	+	7.53258i	−0.856280	+	0.278222i	−0.704074	−	0.710127i	$-0.748638\pi$
$733$	−23.1829	+	7.53258i	−0.856280	+	0.278222i	−0.152206	+	0.988349i	$0.548638\pi$
$734$	0.145119	−	0.446629i	0.00535643	−	0.0164854i
$735$	−31.1109	−	17.4369i	−1.14754	−	0.643172i
$736$		−	7.23991i		−	0.266867i
$737$	0.298594	−	0.956091i	0.0109988	−	0.0352181i
$738$	−18.5126			−0.681457
$739$	−26.4959	+	36.4684i	−0.974666	+	1.34151i	−0.0350116	+	0.999387i	$0.511147\pi$
$739$	−26.4959	+	36.4684i	−0.974666	+	1.34151i	−0.939654	+	0.342126i	$0.888853\pi$
$740$	10.7078	−	0.0876000i	0.393626	−	0.00322024i
$741$	91.9063	−	29.8622i	3.37626	−	1.09701i
$742$	−8.43246	−	14.5287i	−0.309565	−	0.533367i
$743$	−24.0246	+	17.4549i	−0.881376	+	0.640357i	−0.933615	−	0.358278i	$-0.883364\pi$
$743$	−24.0246	+	17.4549i	−0.881376	+	0.640357i	0.0522395	+	0.998635i	$0.483364\pi$
$744$	−5.82366	+	1.89222i	−0.213506	+	0.0693722i
$745$	−17.6181	+	0.144133i	−0.645477	+	0.00528063i
$746$	27.2653	+	19.8094i	0.998252	+	0.725272i
$747$		−	5.29347i		−	0.193678i
$748$	−12.1496	+	9.04154i	−0.444233	+	0.330592i
$749$	52.7571	+	5.42324i	1.92770	+	0.198161i
$750$	24.0271	−	8.46420i	0.877347	−	0.309069i
$751$	14.8696	−	45.7639i	0.542600	−	1.66995i	−0.184030	−	0.982921i	$-0.558914\pi$
$751$	14.8696	−	45.7639i	0.542600	−	1.66995i	0.726630	−	0.687029i	$-0.241086\pi$
$752$	0.990513	+	3.04849i	0.0361203	+	0.111167i
$753$	−3.54995	−	4.88609i	−0.129368	−	0.178059i
$754$	−35.6327	+	25.8887i	−1.29767	+	0.942811i
$755$	33.1145	−	24.4755i	1.20516	−	0.890755i
$756$	−1.97206	+	4.45668i	−0.0717232	+	0.162088i
$757$	26.6175	−	36.6358i	0.967428	−	1.33155i	0.0240924	−	0.999710i	$-0.492330\pi$
$757$	26.6175	−	36.6358i	0.967428	−	1.33155i	0.943336	−	0.331840i	$-0.107670\pi$
$758$	5.34678			0.194204
$759$	−44.6279	−	31.6497i	−1.61989	−	1.14881i
$760$	−14.0678	+	4.69847i	−0.510291	+	0.170431i
$761$	−1.92920	−	1.40165i	−0.0699336	−	0.0508097i	0.552269	−	0.833666i	$-0.313762\pi$
$761$	−1.92920	−	1.40165i	−0.0699336	−	0.0508097i	−0.622203	+	0.782856i	$0.713762\pi$
$762$	2.96882	−	9.13708i	0.107549	−	0.331001i
$763$	7.41305	−	1.59339i	0.268370	−	0.0576846i
$764$	−7.90237	+	5.74141i	−0.285898	+	0.207717i
$765$	−18.2105	−	13.0044i	−0.658402	−	0.470176i
$766$	7.58237	+	23.3361i	0.273962	+	0.843169i
$767$	−20.8341	+	64.1209i	−0.752277	+	2.31527i
$768$	1.84335	+	1.33927i	0.0665160	+	0.0483267i
$769$	−2.99554			−0.108022			−0.0540110	−	0.998540i	$-0.517201\pi$
$769$	−2.99554			−0.108022			−0.0540110	+	0.998540i	$0.517201\pi$
$770$	−4.49910	−	19.0986i	−0.162136	−	0.688267i
$771$	26.1698			0.942482
$772$	−11.0353	−	8.01764i	−0.397170	−	0.288561i
$773$	13.4895	−	41.5166i	0.485185	−	1.49325i	−0.346527	−	0.938040i	$-0.612639\pi$
$773$	13.4895	−	41.5166i	0.485185	−	1.49325i	0.831712	−	0.555207i	$-0.187361\pi$
$774$	2.55918	+	7.87635i	0.0919879	+	0.283110i
$775$	−12.8458	−	3.94270i	−0.461435	−	0.141626i
$776$	10.4319	−	7.57921i	0.374483	−	0.272078i
$777$	28.2241	−	6.06660i	1.01253	−	0.217638i
$778$	−9.12749	+	28.0915i	−0.327236	+	1.00713i
$779$	45.3287	+	32.9332i	1.62407	+	1.17995i
$780$	−10.3202	−	30.8998i	−0.369522	−	1.10639i
$781$	−22.5703	+	7.62034i	−0.807630	+	0.272677i
$782$	−33.0596			−1.18221
$783$	−7.45791	+	10.2649i	−0.266524	+	0.366839i
$784$	3.47228	−	6.07810i	0.124010	−	0.217075i
$785$	−13.5941	−	18.3924i	−0.485195	−	0.656453i
$786$	3.75884	−	2.73096i	0.134073	−	0.0974101i
$787$	−9.42575	−	12.9734i	−0.335992	−	0.462453i	0.607274	−	0.794493i	$-0.292263\pi$
$787$	−9.42575	−	12.9734i	−0.335992	−	0.462453i	−0.943265	+	0.332040i	$0.892263\pi$
$788$	7.20450	+	22.1732i	0.256650	+	0.789886i
$789$	−2.84353	+	8.75148i	−0.101232	+	0.311561i
$790$	4.14131	−	13.1096i	0.147341	−	0.466419i
$791$	0.502448	−	4.88780i	0.0178650	−	0.173790i
$792$	6.88669	−	2.32513i	0.244708	−	0.0826199i
$793$			4.70954i			0.167241i
$794$	15.5663	+	11.3096i	0.552427	+	0.401362i
$795$	32.3476	−	0.264635i	1.14725	−	0.00938563i
$796$	−7.47904	+	2.43009i	−0.265088	+	0.0861322i
$797$	8.61791	−	6.26128i	0.305262	−	0.221786i	−0.424599	−	0.905382i	$-0.639585\pi$
$797$	8.61791	−	6.26128i	0.305262	−	0.221786i	0.729861	+	0.683596i	$0.239585\pi$
$798$	−34.5827	+	20.0718i	−1.22421	+	0.710533i
$799$	13.9203	−	4.52298i	0.492465	−	0.160012i
$800$	1.62268	+	4.72937i	0.0573704	+	0.167208i
$801$	−2.49382	+	3.43245i	−0.0881148	+	0.121280i
$802$	14.9653			0.528444
$803$	8.74576	−	0.100146i	0.308631	−	0.00353407i
$804$			0.688116i			0.0242680i
$805$	17.0109	−	39.3090i	0.599556	−	1.38546i
$806$	−5.31017	+	16.3430i	−0.187043	+	0.575658i
$807$	−59.5832	+	19.3597i	−2.09743	+	0.681495i
$808$	6.91398	−	5.02330i	0.243233	−	0.176719i
$809$	8.56738	+	11.7920i	0.301213	+	0.414584i	0.932616	−	0.360871i	$-0.117521\pi$
$809$	8.56738	+	11.7920i	0.301213	+	0.414584i	−0.631403	+	0.775455i	$0.717521\pi$
$810$	−14.3165	−	19.3698i	−0.503031	−	0.680585i
$811$	17.4483	−	53.7002i	0.612691	−	1.88567i	0.181561	−	0.983380i	$-0.441885\pi$
$811$	17.4483	−	53.7002i	0.612691	−	1.88567i	0.431130	−	0.902290i	$-0.358115\pi$
$812$	12.1636	−	13.5712i	0.426859	−	0.476257i
$813$	−66.3334			−2.32641
$814$	12.9555	+	9.18790i	0.454089	+	0.322036i
$815$	−4.54231	−	13.6002i	−0.159110	−	0.476394i
$816$	6.11551	−	8.41728i	0.214086	−	0.294664i
$817$	7.74551	−	23.8382i	0.270981	−	0.833994i
$818$	4.70545	+	14.4819i	0.164522	+	0.506347i
$819$	−18.6111	−	32.0661i	−0.650325	−	1.12048i
$820$	10.9770	−	15.3714i	0.383332	−	0.536792i
$821$	−37.2590	+	12.1062i	−1.30035	+	0.422509i	−0.875702	−	0.482851i	$-0.839601\pi$
$821$	−37.2590	+	12.1062i	−1.30035	+	0.422509i	−0.424645	+	0.905360i	$0.639601\pi$
$822$	38.0396	+	12.3598i	1.32678	+	0.431098i
$823$	−22.1075	+	30.4283i	−0.770618	+	1.06067i	0.225638	+	0.974211i	$0.427553\pi$
$823$	−22.1075	+	30.4283i	−0.770618	+	1.06067i	−0.996256	+	0.0864538i	$0.972447\pi$
$824$	7.42743			0.258747
$825$	36.2462	+	10.6723i	1.26193	+	0.371561i
$826$	2.85267	−	27.7507i	0.0992572	−	0.965571i
$827$	−35.2387	−	25.6024i	−1.22537	−	0.890283i	−0.228835	−	0.973465i	$-0.573492\pi$
$827$	−35.2387	−	25.6024i	−1.22537	−	0.890283i	−0.996534	+	0.0831824i	$0.973492\pi$
$828$	15.0902	+	4.90310i	0.524421	+	0.170395i
$829$	6.92935	−	2.25148i	0.240666	−	0.0781972i	−0.186200	−	0.982512i	$-0.559617\pi$
$829$	6.92935	−	2.25148i	0.240666	−	0.0781972i	0.426867	+	0.904315i	$0.359617\pi$
$830$	4.39529	+	3.13875i	0.152563	+	0.108948i
$831$	−33.1045	+	24.0518i	−1.14838	+	0.834348i
$832$	6.08123	−	1.97591i	0.210829	−	0.0685025i
$833$	−27.7544	−	15.8555i	−0.961634	−	0.549360i
$834$	15.4285	+	11.2095i	0.534247	+	0.388153i
$835$	−5.77381	−	17.2875i	−0.199811	−	0.598257i
$836$	−20.9986	−	6.55802i	−0.726253	−	0.226814i
$837$			4.95031i			0.171108i
$838$	−0.262233	+	0.360933i	−0.00905868	+	0.0124682i
$839$	0.342197	+	0.111187i	0.0118140	+	0.00383859i	0.314918	−	0.949119i	$-0.398023\pi$
$839$	0.342197	+	0.111187i	0.0118140	+	0.00383859i	−0.303104	+	0.952957i	$0.598023\pi$
$840$	6.86168	+	11.6027i	0.236750	+	0.400331i
$841$	14.9243	−	10.8431i	0.514630	−	0.373900i
$842$	−1.97368	+	1.43396i	−0.0680174	+	0.0494175i
$843$	−37.6366	+	12.2289i	−1.29627	+	0.421185i
$844$	−6.12281	−	1.98942i	−0.210756	−	0.0684787i
$845$	−59.4580	−	18.7827i	−2.04542	−	0.646146i
$846$	−7.02479			−0.241517
$847$	11.1641	−	26.8768i	0.383604	−	0.923498i
$848$			6.34925i			0.218034i
$849$	−20.7230	+	28.5228i	−0.711213	+	0.978900i
$850$	21.5957	−	7.40964i	0.740727	−	0.254149i
$851$	10.7138	+	32.9738i	0.367265	+	1.13033i
$852$	13.2400	−	9.61946i	0.453596	−	0.329557i
$853$	12.4264	+	17.1034i	0.425470	+	0.585609i	0.966906	−	0.255133i	$-0.0821191\pi$
$853$	12.4264	+	17.1034i	0.425470	+	0.585609i	−0.541436	+	0.840742i	$0.682119\pi$
$854$	−0.409506	−	1.90517i	−0.0140130	−	0.0651937i
$855$	−0.265910	−	32.5035i	−0.00909393	−	1.11160i
$856$	−16.2171	−	11.7824i	−0.554288	−	0.402714i
$857$		−	36.4654i		−	1.24563i	−0.782368	−	0.622817i	$-0.785988\pi$
$857$		−	36.4654i		−	1.24563i	0.782368	−	0.622817i	$-0.214012\pi$
$858$	14.4047	−	46.1235i	0.491767	−	1.57463i
$859$			6.44307i			0.219835i	0.993941	+	0.109917i	$0.0350586\pi$
$859$			6.44307i			0.219835i	−0.993941	+	0.109917i	$0.964941\pi$
$860$	−8.05737	−	2.54532i	−0.274754	−	0.0867945i
$861$	20.6058	−	46.5672i	0.702243	−	1.58701i
$862$	−24.9538	+	8.10797i	−0.849929	+	0.276159i
$863$	19.3153	+	26.5852i	0.657500	+	0.904971i	0.999395	−	0.0347668i	$-0.0110689\pi$
$863$	19.3153	+	26.5852i	0.657500	+	0.904971i	−0.341895	+	0.939738i	$0.611069\pi$
$864$	1.49022	−	1.08271i	0.0506983	−	0.0368344i
$865$	−2.02537	+	1.49698i	−0.0688646	+	0.0508990i
$866$	6.08490	−	18.7274i	0.206773	−	0.636382i
$867$	−7.09895	−	5.15769i	−0.241093	−	0.175164i
$868$	0.727084	−	7.07305i	0.0246788	−	0.240075i
$869$	16.3590	−	12.1741i	0.554942	−	0.412979i
$870$	11.1175	+	33.2871i	0.376919	+	1.12854i
$871$	1.56227	+	1.13505i	0.0529354	+	0.0384598i
$872$	−2.72560	−	0.885600i	−0.0923004	−	0.0299902i
$873$	8.73259	+	26.8761i	0.295553	+	0.909620i
$874$	−28.2264	−	38.8504i	−0.954774	−	1.31413i
$875$	−2.30181	+	29.4907i	−0.0778155	+	0.996968i
$876$	−5.71459	+	1.85678i	−0.193078	+	0.0627349i
$877$	−1.29478	+	3.98493i	−0.0437217	+	0.134562i	−0.970535	−	0.240962i	$-0.922537\pi$
$877$	−1.29478	+	3.98493i	−0.0437217	+	0.134562i	0.926813	+	0.375524i	$0.122537\pi$
$878$	10.8703	+	7.89776i	0.366856	+	0.266536i
$879$			36.6093i			1.23480i
$880$	−2.15284	+	7.09685i	−0.0725721	+	0.239235i
$881$			2.11541i			0.0712699i	0.999365	+	0.0356349i	$0.0113454\pi$
$881$			2.11541i			0.0712699i	−0.999365	+	0.0356349i	$0.988655\pi$
$882$	10.3171	+	11.3536i	0.347394	+	0.382295i
$883$	8.28690	+	2.69258i	0.278876	+	0.0906124i	0.445116	−	0.895473i	$-0.353162\pi$
$883$	8.28690	+	2.69258i	0.278876	+	0.0906124i	−0.166239	+	0.986085i	$0.553162\pi$
$884$	−9.02262	−	27.7688i	−0.303463	−	0.933964i
$885$	43.7178	+	31.2197i	1.46956	+	1.04944i
$886$	−4.92004	−	6.77186i	−0.165292	−	0.227505i
$887$	38.8192	−	12.6131i	1.30342	−	0.423507i	0.426651	−	0.904416i	$-0.359693\pi$
$887$	38.8192	−	12.6131i	1.30342	−	0.423507i	0.876770	+	0.480909i	$0.159693\pi$
$888$	−10.3773	−	3.37179i	−0.348240	−	0.113150i
$889$	8.30740	+	7.44574i	0.278621	+	0.249722i
$890$	−1.37134	−	4.10594i	−0.0459673	−	0.137631i
$891$	−0.409062	−	35.7235i	−0.0137041	−	1.19678i
$892$	28.2106			0.944561
$893$	17.2004	+	12.4969i	0.575591	+	0.418191i
$894$	17.0743	+	5.54779i	0.571052	+	0.185546i
$895$	−14.5290	−	19.6572i	−0.485650	−	0.657068i
$896$	−2.28826	+	1.32810i	−0.0764455	+	0.0443688i
$897$	85.3347	−	61.9993i	2.84924	−	2.07010i
$898$	1.97286	+	6.07184i	0.0658352	+	0.202620i
$899$	5.72043	−	17.6057i	0.190787	−	0.587182i
$900$	−10.9564	+	0.179280i	−0.365213	+	0.00597599i
$901$	28.9926			0.965884
$902$	26.5440	−	8.96197i	0.883819	−	0.298401i
$903$	−22.6610	−	2.32947i	−0.754111	−	0.0775199i
$904$	−1.09161	+	1.50247i	−0.0363063	+	0.0499713i
$905$	−2.62277	+	0.0214568i	−0.0871839	+	0.000713249i
$906$	−39.9057	+	12.9662i	−1.32578	+	0.430772i
$907$	20.0572	+	27.6064i	0.665989	+	0.916655i	0.999661	−	0.0260343i	$-0.00828792\pi$
$907$	20.0572	+	27.6064i	0.665989	+	0.916655i	−0.333672	+	0.942689i	$0.608288\pi$
$908$	−1.39775	−	1.92383i	−0.0463859	−	0.0638447i
$909$	5.78773	+	17.8128i	0.191967	+	0.590813i
$910$	37.6606	+	3.56028i	1.24844	+	0.118022i
$911$	−24.3053	−	17.6589i	−0.805271	−	0.585064i	0.107184	−	0.994239i	$-0.465816\pi$
$911$	−24.3053	−	17.6589i	−0.805271	−	0.585064i	−0.912456	+	0.409175i	$0.865816\pi$
$912$	15.1131			0.500445
$913$	2.56258	+	7.58998i	0.0848090	+	0.251192i
$914$	5.39097			0.178318
$915$	3.57826	+	1.13037i	0.118294	+	0.0373689i
$916$	−2.71521	−	0.882227i	−0.0897132	−	0.0291496i
$917$	1.13374	+	5.27459i	0.0374394	+	0.174182i
$918$	−4.94397	−	6.80479i	−0.163175	−	0.224592i
$919$	−20.8496	−	28.6970i	−0.687764	−	0.946626i	0.312230	−	0.950006i	$-0.398924\pi$
$919$	−20.8496	−	28.6970i	−0.687764	−	0.946626i	−0.999994	+	0.00338051i	$0.998924\pi$
$920$	−13.0188	+	9.62244i	−0.429219	+	0.317243i
$921$	−11.7187	−	3.80765i	−0.386145	−	0.125466i
$922$	−23.5182	−	17.0869i	−0.774530	−	0.562729i
$923$		−	45.9270i		−	1.51171i
$924$	−1.81665	+	19.9111i	−0.0597634	+	0.655026i
$925$	−14.3891	−	19.1384i	−0.473109	−	0.629265i
$926$	−11.5804	+	15.9391i	−0.380556	+	0.523791i
$927$	−5.03009	+	15.4810i	−0.165210	+	0.508464i
$928$	−6.55107	+	2.12857i	−0.215050	+	0.0698738i
$929$	13.6486	+	18.7857i	0.447797	+	0.616340i	0.971923	−	0.235301i	$-0.0756076\pi$
$929$	13.6486	+	18.7857i	0.447797	+	0.616340i	−0.524125	+	0.851641i	$0.675608\pi$
$930$	11.1427	+	7.95721i	0.365384	+	0.260927i
$931$	−5.06410	−	46.1534i	−0.165969	−	1.51262i
$932$	7.55340	−	23.2470i	0.247420	−	0.761480i
$933$	30.9281	−	42.5689i	1.01254	−	1.39364i
$934$	−17.5162			−0.573146
$935$	32.4064	+	9.83050i	1.05980	+	0.321492i
$936$			14.0133i			0.458039i
$937$	−27.2821	+	37.5506i	−0.891268	+	1.22673i	0.0819027	+	0.996640i	$0.473900\pi$
$937$	−27.2821	+	37.5506i	−0.891268	+	1.22673i	−0.973171	+	0.230085i	$0.926100\pi$
$938$	−0.730687	−	0.323326i	−0.0238578	−	0.0105570i
$939$	4.37447	+	13.4632i	0.142755	+	0.439356i
$940$	4.16533	−	5.83284i	0.135858	−	0.190246i
$941$	−3.65435	+	2.65504i	−0.119129	+	0.0865519i	−0.645754	−	0.763545i	$-0.723457\pi$
$941$	−3.65435	+	2.65504i	−0.119129	+	0.0865519i	0.526626	+	0.850097i	$0.323457\pi$
$942$	7.20164	+	22.1644i	0.234642	+	0.722154i
$943$	58.1636	+	18.8985i	1.89407	+	0.615419i
$944$	−6.19764	+	8.53032i	−0.201716	+	0.277638i
$945$	10.6351	−	2.37713i	0.345959	−	0.0773280i
$946$	−7.48241	−	10.0545i	−0.243274	−	0.326900i
$947$		−	21.1352i		−	0.686803i	−0.939189	−	0.343401i	$-0.888421\pi$
$947$		−	21.1352i		−	0.686803i	0.939189	−	0.343401i	$-0.111579\pi$
$948$	−8.23433	+	11.3336i	−0.267439	+	0.368098i
$949$	−5.21072	+	16.0369i	−0.169147	+	0.520581i
$950$	27.1460	+	19.0521i	0.880733	+	0.618130i
$951$	31.2883	+	43.0646i	1.01459	+	1.39647i
$952$	6.06452	+	10.4489i	0.196552	+	0.338651i
$953$	−8.46285	−	26.0460i	−0.274139	−	0.843712i	−0.989446	−	0.144902i	$-0.953713\pi$
$953$	−8.46285	−	26.0460i	−0.274139	−	0.843712i	0.715308	−	0.698810i	$-0.246287\pi$
$954$	−13.2338	−	4.29992i	−0.428459	−	0.139215i
$955$	20.8271	+	6.57927i	0.673950	+	0.212900i
$956$		−	15.8796i		−	0.513584i
$957$	−15.5176	+	49.6870i	−0.501612	+	1.60615i
$958$	10.9590			0.354070
$959$	−30.9982	+	34.5855i	−1.00098	+	1.11682i
$960$	−0.0416797	−	5.09471i	−0.00134521	−	0.164431i
$961$	7.34769	+	22.6139i	0.237022	+	0.729479i
$962$	−24.7726	+	17.9984i	−0.798702	+	0.580291i
$963$	35.5408	−	25.8219i	1.14529	−	0.832099i
$964$	−2.40510	−	7.40213i	−0.0774630	−	0.238407i
$965$	0.249519	+	30.4999i	0.00803229	+	0.981826i
$966$	−29.1299	+	32.5009i	−0.937239	+	1.04570i
$967$	−54.6835			−1.75850			−0.879252	−	0.476357i	$-0.841957\pi$
$967$	−54.6835			−1.75850			−0.879252	+	0.476357i	$0.841957\pi$
$968$	−8.74880	+	6.66772i	−0.281197	+	0.214309i
$969$		−	69.0110i		−	2.21695i
$970$	−27.4938	−	8.68527i	−0.882774	−	0.278867i
$971$	−13.7839	−	4.47865i	−0.442345	−	0.143727i	0.0793721	−	0.996845i	$-0.474708\pi$
$971$	−13.7839	−	4.47865i	−0.442345	−	0.143727i	−0.521717	+	0.853118i	$0.674708\pi$
$972$	5.87669	+	18.0866i	0.188495	+	0.580128i
$973$	−19.1524	+	11.1160i	−0.613998	+	0.356364i
$974$	−9.21004	−	12.6765i	−0.295109	−	0.406182i
$975$	−41.8478	+	59.6262i	−1.34020	+	1.90957i
$976$	−0.227602	+	0.700486i	−0.00728536	+	0.0224220i
$977$	−33.6470	+	46.3112i	−1.07646	+	1.48163i	−0.213108	+	0.977029i	$0.568359\pi$
$977$	−33.6470	+	46.3112i	−1.07646	+	1.48163i	−0.863355	+	0.504597i	$0.831641\pi$
$978$			14.6108i			0.467201i
$979$	1.91408	−	6.12884i	0.0611743	−	0.195879i
$980$	−15.5446	+	1.83442i	−0.496554	+	0.0585984i
$981$	3.69172	−	5.08122i	0.117868	−	0.162231i
$982$	−33.3372	−	10.8319i	−1.06383	−	0.345660i
$983$	−2.81726	−	8.67063i	−0.0898566	−	0.276550i	0.896023	−	0.444009i	$-0.146444\pi$
$983$	−2.81726	−	8.67063i	−0.0898566	−	0.276550i	−0.985879	+	0.167458i	$0.946444\pi$
$984$	−15.5711	+	11.3130i	−0.496387	+	0.360647i
$985$	30.2965	−	42.4251i	0.965327	−	1.35178i
$986$	9.71971	+	29.9142i	0.309539	+	0.952662i
$987$	7.81908	−	17.6704i	0.248884	−	0.562455i
$988$	24.9292	−	34.3121i	0.793103	−	1.09161i
$989$		−	27.3588i		−	0.869959i
$990$	−13.3340	−	9.29338i	−0.423784	−	0.295363i
$991$	−16.7642			−0.532532			−0.266266	−	0.963900i	$-0.585790\pi$
$991$	−16.7642			−0.532532			−0.266266	+	0.963900i	$0.585790\pi$
$992$	−1.57964	+	2.17419i	−0.0501537	+	0.0690307i
$993$	−1.77071	+	5.44968i	−0.0561918	+	0.172940i
$994$	3.99346	+	18.5791i	0.126665	+	0.589292i
$995$	14.3101	+	10.2191i	0.453660	+	0.323966i
$996$	−3.23485	−	4.45238i	−0.102500	−	0.141079i
$997$	−45.4896	+	14.7805i	−1.44067	+	0.468102i	−0.922107	−	0.386936i	$-0.873533\pi$
$997$	−45.4896	+	14.7805i	−1.44067	+	0.468102i	−0.518565	+	0.855038i	$0.673533\pi$
$998$	−3.73319	+	11.4896i	−0.118172	+	0.363697i
$999$	−5.18490	+	7.13640i	−0.164043	+	0.225786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.w.b.139.5	yes	96
5.4	even	2		770.2.w.a.139.20	yes	96
7.6	odd	2	inner	770.2.w.b.139.20	yes	96
11.8	odd	10		770.2.w.a.349.5	yes	96
35.34	odd	2		770.2.w.a.139.5	✓	96
55.19	odd	10	inner	770.2.w.b.349.20	yes	96
77.41	even	10		770.2.w.a.349.20	yes	96
385.349	even	10	inner	770.2.w.b.349.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.w.a.139.5	✓	96	35.34	odd	2
770.2.w.a.139.20	yes	96	5.4	even	2
770.2.w.a.349.5	yes	96	11.8	odd	10
770.2.w.a.349.20	yes	96	77.41	even	10
770.2.w.b.139.5	yes	96	1.1	even	1	trivial
770.2.w.b.139.20	yes	96	7.6	odd	2	inner
770.2.w.b.349.5	yes	96	385.349	even	10	inner
770.2.w.b.349.20	yes	96	55.19	odd	10	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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.704096 + 2.16698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.29948 - 1.81971i) q^{5} +(-1.84335 + 1.33927i) q^{6} +(-0.555990 - 2.58667i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.77302 - 1.28817i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.704096 + 2.16698i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.29948 - 1.81971i) q^{5} +(-1.84335 + 1.33927i) q^{6} +(-0.555990 - 2.58667i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.77302 - 1.28817i) q^{9} +(2.12090 - 0.708357i) q^{10} +(3.16583 + 0.988709i) q^{11} -2.27850 q^{12} +(-3.75841 + 5.17301i) q^{13} +(1.07060 - 2.41946i) q^{14} +(3.02832 + 4.09721i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(2.68401 + 3.69422i) q^{17} +(-0.677232 - 2.08431i) q^{18} +(-2.04968 + 6.30827i) q^{19} +(2.13221 + 0.673563i) q^{20} +(5.99675 + 0.616444i) q^{21} +(1.98006 + 2.66071i) q^{22} +7.23991i q^{23} +(-1.84335 - 1.33927i) q^{24} +(-1.62268 - 4.72937i) q^{25} +(-6.08123 + 1.97591i) q^{26} +(-1.49022 + 1.08271i) q^{27} +(2.28826 - 1.32810i) q^{28} +(6.55107 - 2.12857i) q^{29} +(0.0416797 + 5.09471i) q^{30} +(1.57964 - 2.17419i) q^{31} -1.00000 q^{32} +(-4.37156 + 6.16415i) q^{33} +4.56630i q^{34} +(-5.42949 - 2.34960i) q^{35} +(0.677232 - 2.08431i) q^{36} +(4.55444 - 1.47983i) q^{37} +(-5.36614 + 3.89873i) q^{38} +(-8.56354 - 11.7867i) q^{39} +(1.32908 + 1.79820i) q^{40} +(2.61032 - 8.03374i) q^{41} +(4.48913 + 4.02351i) q^{42} -3.77888 q^{43} +(0.0379755 + 3.31641i) q^{44} +(-4.64811 + 1.55241i) q^{45} +(-4.25551 + 5.85721i) q^{46} +(0.990513 - 3.04849i) q^{47} +(-0.704096 - 2.16698i) q^{48} +(-6.38175 + 2.87633i) q^{49} +(1.46708 - 4.77992i) q^{50} +(-9.89510 + 3.21511i) q^{51} +(-6.08123 - 1.97591i) q^{52} +(3.73200 - 5.13665i) q^{53} -1.84201 q^{54} +(5.91311 - 4.47607i) q^{55} +(2.63188 + 0.270548i) q^{56} +(-12.2268 - 8.88326i) q^{57} +(6.55107 + 2.12857i) q^{58} +(10.0280 - 3.25829i) q^{59} +(-2.96088 + 4.14621i) q^{60} +(0.595869 - 0.432924i) q^{61} +(2.55592 - 0.830467i) q^{62} +(-2.34630 + 5.30242i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(4.52937 + 13.5615i) q^{65} +(-7.15986 + 2.41736i) q^{66} -0.302004i q^{67} +(-2.68401 + 3.69422i) q^{68} +(-15.6888 - 5.09759i) q^{69} +(-3.01149 - 5.09224i) q^{70} +(-5.81086 + 4.22183i) q^{71} +(1.77302 - 1.28817i) q^{72} +(2.50805 - 0.814915i) q^{73} +(4.55444 + 1.47983i) q^{74} +(11.3910 - 0.186391i) q^{75} -6.63291 q^{76} +(0.797301 - 8.73867i) q^{77} -14.5692i q^{78} +(3.61392 - 4.97414i) q^{79} +(0.0182926 + 2.23599i) q^{80} +(-3.32865 - 10.2445i) q^{81} +(6.83391 - 4.96512i) q^{82} +(1.41972 + 1.95408i) q^{83} +(1.26682 + 5.89374i) q^{84} +(10.2102 - 0.0835295i) q^{85} +(-3.05718 - 2.22117i) q^{86} +15.6948i q^{87} +(-1.91861 + 2.70535i) q^{88} -1.93594i q^{89} +(-4.67288 - 1.47616i) q^{90} +(15.4705 + 6.84564i) q^{91} +(-6.88557 + 2.23726i) q^{92} +(3.59922 + 4.95390i) q^{93} +(2.59320 - 1.88407i) q^{94} +(8.81569 + 11.9273i) q^{95} +(0.704096 - 2.16698i) q^{96} +(-10.4319 - 7.57921i) q^{97} +(-6.85361 - 1.42410i) q^{98} +(-4.33943 - 5.83113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more