LMFDB - Embedded newform 930.2.n.g.721.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 31 x^{14} + 20 x^{13} + 474 x^{12} + 463 x^{11} + 6637 x^{10} + 13567 x^{9} + \cdots + 22848400 $ x^16 - x^15 + 31x^14 + 20x^13 + 474x^12 + 463x^11 + 6637x^10 + 13567x^9 + 108596x^8 + 172826x^7 + 917001x^6 + 1583565x^5 + 3229491x^4 - 1732290x^3 + 4672960x^2 - 5544800x + 22848400
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.1
Root			$-2.68002 + 1.94715i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.g.841.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.68002 - 1.94715i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.68002 - 1.94715i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(1.45577 + 1.05768i) q^{11} +(0.309017 - 0.951057i) q^{12} +(1.77729 + 5.46994i) q^{13} +(-2.68002 + 1.94715i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.91309 - 4.29611i) q^{17} +(0.309017 + 0.951057i) q^{18} +(2.60999 - 8.03271i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.02368 - 3.15056i) q^{21} +(1.45577 - 1.05768i) q^{22} +(4.98313 - 3.62045i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +5.75143 q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.02368 + 3.15056i) q^{28} +(0.0186923 - 0.0575291i) q^{29} +1.00000 q^{30} +(1.86206 + 5.24717i) q^{31} +1.00000 q^{32} +(-0.556055 + 1.71136i) q^{33} +(-2.25860 - 6.95125i) q^{34} +(-2.68002 - 1.94715i) q^{35} +1.00000 q^{36} +0.714692 q^{37} +(-6.83303 - 4.96449i) q^{38} +(-4.65301 + 3.38061i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-1.31600 + 4.05022i) q^{41} +(-2.68002 - 1.94715i) q^{42} +(2.95731 - 9.10166i) q^{43} +(-0.556055 - 1.71136i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-1.90338 - 5.85802i) q^{46} +(-2.74322 - 8.44276i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(1.22801 + 3.77943i) q^{49} +(0.309017 - 0.951057i) q^{50} +(5.91309 + 4.29611i) q^{51} +(1.77729 - 5.46994i) q^{52} +(-3.60555 + 2.61959i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.45577 + 1.05768i) q^{55} +3.31269 q^{56} +8.44609 q^{57} +(-0.0489371 - 0.0355549i) q^{58} +(4.11365 + 12.6605i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.95628 q^{61} +(5.56576 - 0.149456i) q^{62} +3.31269 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.77729 + 5.46994i) q^{65} +(1.45577 + 1.05768i) q^{66} +1.78397 q^{67} -7.30898 q^{68} +(4.98313 + 3.62045i) q^{69} +(-2.68002 + 1.94715i) q^{70} +(-1.09019 + 0.792067i) q^{71} +(0.309017 - 0.951057i) q^{72} +(10.4149 + 7.56687i) q^{73} +(0.220852 - 0.679712i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-6.83303 + 4.96449i) q^{76} +(-1.84204 - 5.66922i) q^{77} +(1.77729 + 5.46994i) q^{78} +(7.24080 - 5.26075i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.44533 + 2.50318i) q^{82} +(-0.862940 + 2.65586i) q^{83} +(-2.68002 + 1.94715i) q^{84} +(5.91309 - 4.29611i) q^{85} +(-7.74233 - 5.62513i) q^{86} +0.0604896 q^{87} -1.79943 q^{88} +(-12.0325 - 8.74212i) q^{89} +(0.309017 + 0.951057i) q^{90} +(5.88762 - 18.1202i) q^{91} -6.15948 q^{92} +(-4.41494 + 3.39238i) q^{93} -8.87725 q^{94} +(2.60999 - 8.03271i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-2.44450 - 1.77603i) q^{97} +3.97393 q^{98} -1.79943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−2.68002	−	1.94715i	−1.01295	−	0.735954i	−0.0481274	−	0.998841i	$-0.515325\pi$
$7$	−2.68002	−	1.94715i	−1.01295	−	0.735954i	−0.964827	+	0.262887i	$0.915325\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	1.45577	+	1.05768i	0.438932	+	0.318903i	0.785210	−	0.619229i	$-0.212555\pi$
$11$	1.45577	+	1.05768i	0.438932	+	0.318903i	−0.346279	+	0.938132i	$0.612555\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	1.77729	+	5.46994i	0.492932	+	1.51709i	0.820155	+	0.572141i	$0.193887\pi$
$13$	1.77729	+	5.46994i	0.492932	+	1.51709i	−0.327224	+	0.944947i	$0.606113\pi$
$14$	−2.68002	+	1.94715i	−0.716267	+	0.520398i
$15$	0.309017	+	0.951057i	0.0797878	+	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	5.91309	−	4.29611i	1.43413	−	1.04196i	0.444906	−	0.895577i	$-0.353237\pi$
$17$	5.91309	−	4.29611i	1.43413	−	1.04196i	0.989228	−	0.146382i	$-0.0467630\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	2.60999	−	8.03271i	0.598772	−	1.84283i	0.0637960	−	0.997963i	$-0.479679\pi$
$19$	2.60999	−	8.03271i	0.598772	−	1.84283i	0.534976	−	0.844867i	$-0.320321\pi$
$20$	−0.809017	−	0.587785i	−0.180902	−	0.131433i
$21$	1.02368	−	3.15056i	0.223385	−	0.687508i
$22$	1.45577	−	1.05768i	0.310372	−	0.225498i
$23$	4.98313	−	3.62045i	1.03905	−	0.754917i	0.0689530	−	0.997620i	$-0.478034\pi$
$23$	4.98313	−	3.62045i	1.03905	−	0.754917i	0.970101	+	0.242703i	$0.0780341\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	5.75143			1.12795
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	1.02368	+	3.15056i	0.193457	+	0.595399i
$29$	0.0186923	−	0.0575291i	0.00347108	−	0.0106829i	−0.949306	−	0.314354i	$-0.898212\pi$
$29$	0.0186923	−	0.0575291i	0.00347108	−	0.0106829i	0.952777	+	0.303671i	$0.0982123\pi$
$30$	1.00000			0.182574
$31$	1.86206	+	5.24717i	0.334435	+	0.942419i
$31$	1.86206	+	5.24717i	0.334435	+	0.942419i
$32$	1.00000			0.176777
$33$	−0.556055	+	1.71136i	−0.0967968	+	0.297910i
$34$	−2.25860	−	6.95125i	−0.387346	−	1.19213i
$35$	−2.68002	−	1.94715i	−0.453007	−	0.329129i
$36$	1.00000			0.166667
$37$	0.714692			0.117495			0.0587473	−	0.998273i	$-0.481289\pi$
$37$	0.714692			0.117495			0.0587473	+	0.998273i	$0.481289\pi$
$38$	−6.83303	−	4.96449i	−1.10846	−	0.805346i
$39$	−4.65301	+	3.38061i	−0.745078	+	0.541330i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−1.31600	+	4.05022i	−0.205524	+	0.632539i	0.794167	+	0.607699i	$0.207907\pi$
$41$	−1.31600	+	4.05022i	−0.205524	+	0.632539i	−0.999691	+	0.0248394i	$0.992093\pi$
$42$	−2.68002	−	1.94715i	−0.413537	−	0.300452i
$43$	2.95731	−	9.10166i	0.450985	−	1.38799i	−0.424799	−	0.905288i	$-0.639655\pi$
$43$	2.95731	−	9.10166i	0.450985	−	1.38799i	0.875785	−	0.482702i	$-0.160345\pi$
$44$	−0.556055	−	1.71136i	−0.0838285	−	0.257998i
$45$	−0.809017	+	0.587785i	−0.120601	+	0.0876219i
$46$	−1.90338	−	5.85802i	−0.280639	−	0.863717i
$47$	−2.74322	−	8.44276i	−0.400140	−	1.23150i	−0.924886	−	0.380245i	$-0.875840\pi$
$47$	−2.74322	−	8.44276i	−0.400140	−	1.23150i	0.524746	−	0.851259i	$-0.324160\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	1.22801	+	3.77943i	0.175430	+	0.539919i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	5.91309	+	4.29611i	0.827998	+	0.601576i
$52$	1.77729	−	5.46994i	0.246466	−	0.758544i
$53$	−3.60555	+	2.61959i	−0.495261	+	0.359828i	−0.807204	−	0.590273i	$-0.799020\pi$
$53$	−3.60555	+	2.61959i	−0.495261	+	0.359828i	0.311943	+	0.950101i	$0.399020\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	1.45577	+	1.05768i	0.196296	+	0.142618i
$56$	3.31269			0.442677
$57$	8.44609			1.11871
$58$	−0.0489371	−	0.0355549i	−0.00642576	−	0.00466859i
$59$	4.11365	+	12.6605i	0.535552	+	1.64826i	0.742453	+	0.669898i	$0.233662\pi$
$59$	4.11365	+	12.6605i	0.535552	+	1.64826i	−0.206901	+	0.978362i	$0.566338\pi$
$60$	0.309017	−	0.951057i	0.0398939	−	0.122781i
$61$	−3.95628			−0.506550			−0.253275	−	0.967394i	$-0.581508\pi$
$61$	−3.95628			−0.506550			−0.253275	+	0.967394i	$0.581508\pi$
$62$	5.56576	−	0.149456i	0.706852	−	0.0189810i
$63$	3.31269			0.417360
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.77729	+	5.46994i	0.220446	+	0.678462i
$66$	1.45577	+	1.05768i	0.179193	+	0.130191i
$67$	1.78397			0.217946			0.108973	−	0.994045i	$-0.465244\pi$
$67$	1.78397			0.217946			0.108973	+	0.994045i	$0.465244\pi$
$68$	−7.30898			−0.886344
$69$	4.98313	+	3.62045i	0.599898	+	0.435851i
$70$	−2.68002	+	1.94715i	−0.320324	+	0.232729i
$71$	−1.09019	+	0.792067i	−0.129381	+	0.0940010i	−0.650594	−	0.759426i	$-0.725480\pi$
$71$	−1.09019	+	0.792067i	−0.129381	+	0.0940010i	0.521212	+	0.853427i	$0.325480\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	10.4149	+	7.56687i	1.21897	+	0.885635i	0.996014	−	0.0891927i	$-0.0284287\pi$
$73$	10.4149	+	7.56687i	1.21897	+	0.885635i	0.222958	+	0.974828i	$0.428429\pi$
$74$	0.220852	−	0.679712i	0.0256735	−	0.0790150i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	−6.83303	+	4.96449i	−0.783803	+	0.569466i
$77$	−1.84204	−	5.66922i	−0.209920	−	0.646067i
$78$	1.77729	+	5.46994i	0.201239	+	0.619349i
$79$	7.24080	−	5.26075i	0.814653	−	0.591880i	−0.100523	−	0.994935i	$-0.532052\pi$
$79$	7.24080	−	5.26075i	0.814653	−	0.591880i	0.915176	+	0.403055i	$0.132052\pi$
$80$	0.309017	+	0.951057i	0.0345492	+	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.44533	+	2.50318i	0.380473	+	0.276430i
$83$	−0.862940	+	2.65586i	−0.0947200	+	0.291518i	−0.987181	−	0.159607i	$-0.948977\pi$
$83$	−0.862940	+	2.65586i	−0.0947200	+	0.291518i	0.892461	+	0.451125i	$0.148977\pi$
$84$	−2.68002	+	1.94715i	−0.292415	+	0.212452i
$85$	5.91309	−	4.29611i	0.641364	−	0.465978i
$86$	−7.74233	−	5.62513i	−0.834877	−	0.606574i
$87$	0.0604896			0.00648517
$88$	−1.79943			−0.191820
$89$	−12.0325	−	8.74212i	−1.27544	−	0.926663i	−0.276036	−	0.961147i	$-0.589021\pi$
$89$	−12.0325	−	8.74212i	−1.27544	−	0.926663i	−0.999405	+	0.0344847i	$0.989021\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	5.88762	−	18.1202i	0.617190	−	1.89952i
$92$	−6.15948			−0.642170
$93$	−4.41494	+	3.39238i	−0.457808	+	0.351774i
$94$	−8.87725			−0.915618
$95$	2.60999	−	8.03271i	0.267779	−	0.824139i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	−2.44450	−	1.77603i	−0.248201	−	0.180329i	0.456728	−	0.889606i	$-0.349021\pi$
$97$	−2.44450	−	1.77603i	−0.248201	−	0.180329i	−0.704929	+	0.709278i	$0.749021\pi$
$98$	3.97393			0.401428
$99$	−1.79943			−0.180850
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−6.76293	+	4.91356i	−0.672937	+	0.488917i	−0.871007	−	0.491271i	$-0.836533\pi$
$101$	−6.76293	+	4.91356i	−0.672937	+	0.488917i	0.198070	+	0.980188i	$0.436533\pi$
$102$	5.91309	−	4.29611i	0.585483	−	0.425378i
$103$	2.21606	−	6.82032i	0.218355	−	0.672027i	−0.780544	−	0.625101i	$-0.785058\pi$
$103$	2.21606	−	6.82032i	0.218355	−	0.672027i	0.998898	−	0.0469254i	$-0.0149423\pi$
$104$	−4.65301	−	3.38061i	−0.456265	−	0.331496i
$105$	1.02368	−	3.15056i	0.0999008	−	0.307463i
$106$	1.37720	+	4.23858i	0.133765	+	0.411687i
$107$	−14.1075	+	10.2497i	−1.36383	+	0.990878i	−0.365635	+	0.930758i	$0.619148\pi$
$107$	−14.1075	+	10.2497i	−1.36383	+	0.990878i	−0.998191	+	0.0601193i	$0.980852\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	6.09252	+	18.7508i	0.583557	+	1.79600i	0.604988	+	0.796235i	$0.293178\pi$
$109$	6.09252	+	18.7508i	0.583557	+	1.79600i	−0.0214306	+	0.999770i	$0.506822\pi$
$110$	1.45577	−	1.05768i	0.138802	−	0.100846i
$111$	0.220852	+	0.679712i	0.0209623	+	0.0645155i
$112$	1.02368	−	3.15056i	0.0967285	−	0.297700i
$113$	−11.1025	−	8.06646i	−1.04444	−	0.758829i	−0.0732912	−	0.997311i	$-0.523350\pi$
$113$	−11.1025	−	8.06646i	−1.04444	−	0.758829i	−0.971147	+	0.238482i	$0.923350\pi$
$114$	2.60999	−	8.03271i	0.244448	−	0.752332i
$115$	4.98313	−	3.62045i	0.464679	−	0.337609i
$116$	−0.0489371	+	0.0355549i	−0.00454370	+	0.00330119i
$117$	−4.65301	−	3.38061i	−0.430171	−	0.312537i
$118$	13.3121			1.22547
$119$	−24.2124			−2.21955
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−2.39860	−	7.38214i	−0.218055	−	0.671104i
$122$	−1.22256	+	3.76265i	−0.110685	+	0.340654i
$123$	−4.25866			−0.383990
$124$	1.57777	−	5.33953i	0.141688	−	0.479504i
$125$	1.00000			0.0894427
$126$	1.02368	−	3.15056i	0.0911965	−	0.280674i
$127$	−0.818934	−	2.52042i	−0.0726687	−	0.223651i	0.908125	−	0.418699i	$-0.137514\pi$
$127$	−0.818934	−	2.52042i	−0.0726687	−	0.223651i	−0.980794	+	0.195048i	$0.937514\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	9.57005			0.842596
$130$	5.75143			0.504434
$131$	14.3273	+	10.4094i	1.25178	+	0.909472i	0.998324	−	0.0578748i	$-0.0184324\pi$
$131$	14.3273	+	10.4094i	1.25178	+	0.909472i	0.253457	+	0.967347i	$0.418432\pi$
$132$	1.45577	−	1.05768i	0.126709	−	0.0920593i
$133$	−22.6357	+	16.4458i	−1.96277	+	1.42603i
$134$	0.551276	−	1.69665i	0.0476230	−	0.146568i
$135$	−0.809017	−	0.587785i	−0.0696291	−	0.0505885i
$136$	−2.25860	+	6.95125i	−0.193673	+	0.596065i
$137$	1.45819	+	4.48784i	0.124581	+	0.383422i	0.993825	−	0.110963i	$-0.0353934\pi$
$137$	1.45819	+	4.48784i	0.124581	+	0.383422i	−0.869243	+	0.494385i	$0.835393\pi$
$138$	4.98313	−	3.62045i	0.424192	−	0.308193i
$139$	4.76853	+	14.6760i	0.404461	+	1.24480i	0.921344	+	0.388747i	$0.127092\pi$
$139$	4.76853	+	14.6760i	0.404461	+	1.24480i	−0.516883	+	0.856056i	$0.672908\pi$
$140$	1.02368	+	3.15056i	0.0865166	+	0.266271i
$141$	7.18184	−	5.21791i	0.604820	−	0.439428i
$142$	0.416414	+	1.28159i	0.0349447	+	0.107549i
$143$	−3.19812	+	9.84279i	−0.267440	+	0.823095i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	0.0186923	−	0.0575291i	0.00155231	−	0.00477753i
$146$	10.4149	−	7.56687i	0.861944	−	0.626239i
$147$	−3.21498	+	2.33582i	−0.265167	+	0.192655i
$148$	−0.578198	−	0.420085i	−0.0475276	−	0.0345308i
$149$	−9.97523			−0.817203			−0.408602	−	0.912713i	$-0.633983\pi$
$149$	−9.97523			−0.817203			−0.408602	+	0.912713i	$0.633983\pi$
$150$	1.00000			0.0816497
$151$	−2.35256	−	1.70923i	−0.191449	−	0.139095i	0.487932	−	0.872882i	$-0.337751\pi$
$151$	−2.35256	−	1.70923i	−0.191449	−	0.139095i	−0.679381	+	0.733786i	$0.737751\pi$
$152$	2.60999	+	8.03271i	0.211698	+	0.651539i
$153$	−2.25860	+	6.95125i	−0.182597	+	0.561975i
$154$	−5.96097			−0.480349
$155$	1.86206	+	5.24717i	0.149564	+	0.421463i
$156$	5.75143			0.460483
$157$	0.772121	−	2.37634i	0.0616219	−	0.189653i	−0.915506	−	0.402304i	$-0.868210\pi$
$157$	0.772121	−	2.37634i	0.0616219	−	0.189653i	0.977128	+	0.212651i	$0.0682096\pi$
$158$	−2.76574	−	8.51207i	−0.220030	−	0.677184i
$159$	−3.60555	−	2.61959i	−0.285939	−	0.207747i
$160$	1.00000			0.0790569
$161$	−20.4045			−1.60810
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	15.3362	−	11.1424i	1.20123	−	0.872743i	0.206822	−	0.978379i	$-0.433688\pi$
$163$	15.3362	−	11.1424i	1.20123	−	0.872743i	0.994405	+	0.105636i	$0.0336878\pi$
$164$	3.44533	−	2.50318i	0.269035	−	0.195465i
$165$	−0.556055	+	1.71136i	−0.0432889	+	0.133229i
$166$	2.25921	+	1.64141i	0.175348	+	0.127398i
$167$	3.09822	−	9.53534i	0.239747	−	0.737867i	−0.756709	−	0.653752i	$-0.773194\pi$
$167$	3.09822	−	9.53534i	0.239747	−	0.737867i	0.996456	−	0.0841145i	$-0.0268062\pi$
$168$	1.02368	+	3.15056i	0.0789785	+	0.243071i
$169$	−16.2442	+	11.8021i	−1.24956	+	0.907856i
$170$	−2.25860	−	6.95125i	−0.173227	−	0.533137i
$171$	2.60999	+	8.03271i	0.199591	+	0.614277i
$172$	−7.74233	+	5.62513i	−0.590347	+	0.428912i
$173$	4.35933	+	13.4166i	0.331434	+	1.02005i	0.968452	+	0.249199i	$0.0801674\pi$
$173$	4.35933	+	13.4166i	0.331434	+	1.02005i	−0.637019	+	0.770848i	$0.719833\pi$
$174$	0.0186923	−	0.0575291i	0.00141706	−	0.00436127i
$175$	−2.68002	−	1.94715i	−0.202591	−	0.147191i
$176$	−0.556055	+	1.71136i	−0.0419143	+	0.128999i
$177$	−10.7697	+	7.82464i	−0.809499	+	0.588136i
$178$	−12.0325	+	8.74212i	−0.901873	+	0.655249i
$179$	−8.78132	−	6.38000i	−0.656347	−	0.476864i	0.209080	−	0.977898i	$-0.432953\pi$
$179$	−8.78132	−	6.38000i	−0.656347	−	0.476864i	−0.865427	+	0.501035i	$0.832953\pi$
$180$	1.00000			0.0745356
$181$	3.47408			0.258227			0.129113	−	0.991630i	$-0.458787\pi$
$181$	3.47408			0.258227			0.129113	+	0.991630i	$0.458787\pi$
$182$	−15.4140	−	11.1989i	−1.14256	−	0.830119i
$183$	−1.22256	−	3.76265i	−0.0903741	−	0.278143i
$184$	−1.90338	+	5.85802i	−0.140319	+	0.431859i
$185$	0.714692			0.0525452
$186$	1.86206	+	5.24717i	0.136533	+	0.384741i
$187$	13.1520			0.961771
$188$	−2.74322	+	8.44276i	−0.200070	+	0.615752i
$189$	1.02368	+	3.15056i	0.0744616	+	0.229169i
$190$	−6.83303	−	4.96449i	−0.495720	−	0.360162i
$191$	−0.855443			−0.0618977			−0.0309488	−	0.999521i	$-0.509853\pi$
$191$	−0.855443			−0.0618977			−0.0309488	+	0.999521i	$0.509853\pi$
$192$	1.00000			0.0721688
$193$	−3.98900	−	2.89818i	−0.287134	−	0.208615i	0.434889	−	0.900484i	$-0.356788\pi$
$193$	−3.98900	−	2.89818i	−0.287134	−	0.208615i	−0.722023	+	0.691869i	$0.756788\pi$
$194$	−2.44450	+	1.77603i	−0.175505	+	0.127512i
$195$	−4.65301	+	3.38061i	−0.333209	+	0.242090i
$196$	1.22801	−	3.77943i	0.0877152	−	0.269960i
$197$	−3.62388	−	2.63290i	−0.258191	−	0.187587i	0.451158	−	0.892444i	$-0.351011\pi$
$197$	−3.62388	−	2.63290i	−0.258191	−	0.187587i	−0.709349	+	0.704857i	$0.751011\pi$
$198$	−0.556055	+	1.71136i	−0.0395171	+	0.121621i
$199$	6.67417	+	20.5410i	0.473120	+	1.45611i	0.848477	+	0.529232i	$0.177520\pi$
$199$	6.67417	+	20.5410i	0.473120	+	1.45611i	−0.375357	+	0.926880i	$0.622480\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	0.551276	+	1.69665i	0.0388840	+	0.119673i
$202$	2.58321	+	7.95030i	0.181754	+	0.559381i
$203$	−0.162114	+	0.117782i	−0.0113782	+	0.00826671i
$204$	−2.25860	−	6.95125i	−0.158134	−	0.486685i
$205$	−1.31600	+	4.05022i	−0.0919133	+	0.282880i
$206$	−5.80171	−	4.21519i	−0.404225	−	0.293686i
$207$	−1.90338	+	5.85802i	−0.132294	+	0.407160i
$208$	−4.65301	+	3.38061i	−0.322628	+	0.234403i
$209$	12.2956	−	8.93327i	0.850503	−	0.617927i
$210$	−2.68002	−	1.94715i	−0.184939	−	0.134366i
$211$	−17.2960			−1.19070			−0.595352	−	0.803465i	$-0.702987\pi$
$211$	−17.2960			−1.19070			−0.595352	+	0.803465i	$0.702987\pi$
$212$	4.45671			0.306088
$213$	−1.09019	−	0.792067i	−0.0746983	−	0.0542715i
$214$	5.38860	+	16.5844i	0.368357	+	1.13369i
$215$	2.95731	−	9.10166i	0.201687	−	0.620728i
$216$	1.00000			0.0680414
$217$	5.22668	−	17.6882i	0.354810	−	1.20076i
$218$	19.7158			1.33532
$219$	−3.97814	+	12.2435i	−0.268818	+	0.827336i
$220$	−0.556055	−	1.71136i	−0.0374893	−	0.115380i
$221$	34.0087	+	24.7088i	2.28767	+	1.66209i
$222$	0.714692			0.0479670
$223$	−11.5853			−0.775812			−0.387906	−	0.921699i	$-0.626801\pi$
$223$	−11.5853			−0.775812			−0.387906	+	0.921699i	$0.626801\pi$
$224$	−2.68002	−	1.94715i	−0.179067	−	0.130100i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−11.1025	+	8.06646i	−0.738529	+	0.536573i
$227$	2.35078	−	7.23497i	0.156027	−	0.480202i	−0.842236	−	0.539108i	$-0.818761\pi$
$227$	2.35078	−	7.23497i	0.156027	−	0.480202i	0.998264	+	0.0589064i	$0.0187613\pi$
$228$	−6.83303	−	4.96449i	−0.452529	−	0.328781i
$229$	0.989105	−	3.04415i	0.0653619	−	0.201163i	−0.913042	−	0.407866i	$-0.866273\pi$
$229$	0.989105	−	3.04415i	0.0653619	−	0.201163i	0.978404	+	0.206702i	$0.0662732\pi$
$230$	−1.90338	−	5.85802i	−0.125505	−	0.386266i
$231$	4.82253	−	3.50377i	0.317299	−	0.230531i
$232$	0.0186923	+	0.0575291i	0.00122721	+	0.00377697i
$233$	−5.42243	−	16.6885i	−0.355235	−	1.09330i	−0.955873	−	0.293780i	$-0.905087\pi$
$233$	−5.42243	−	16.6885i	−0.355235	−	1.09330i	0.600638	−	0.799521i	$-0.294913\pi$
$234$	−4.65301	+	3.38061i	−0.304177	+	0.220997i
$235$	−2.74322	−	8.44276i	−0.178948	−	0.550745i
$236$	4.11365	−	12.6605i	0.267776	−	0.824130i
$237$	7.24080	+	5.26075i	0.470340	+	0.341722i
$238$	−7.48204	+	23.0274i	−0.484989	+	1.49264i
$239$	−8.97083	+	6.51769i	−0.580275	+	0.421595i	−0.838823	−	0.544404i	$-0.816756\pi$
$239$	−8.97083	+	6.51769i	−0.580275	+	0.421595i	0.258548	+	0.965998i	$0.416756\pi$
$240$	−0.809017	+	0.587785i	−0.0522218	+	0.0379414i
$241$	2.28932	+	1.66329i	0.147468	+	0.107142i	0.659073	−	0.752079i	$-0.270949\pi$
$241$	2.28932	+	1.66329i	0.147468	+	0.107142i	−0.511605	+	0.859221i	$0.670949\pi$
$242$	−7.76204			−0.498963
$243$	1.00000			0.0641500
$244$	3.20070	+	2.32544i	0.204904	+	0.148871i
$245$	1.22801	+	3.77943i	0.0784548	+	0.241459i
$246$	−1.31600	+	4.05022i	−0.0839050	+	0.258233i
$247$	48.5771			3.09089
$248$	−4.59064	−	3.15056i	−0.291506	−	0.200061i
$249$	−2.79253			−0.176970
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−3.07652	−	9.46855i	−0.194188	−	0.597650i	−0.999985	−	0.00545783i	$-0.998263\pi$
$251$	−3.07652	−	9.46855i	−0.194188	−	0.597650i	0.805797	−	0.592192i	$-0.201737\pi$
$252$	−2.68002	−	1.94715i	−0.168826	−	0.122659i
$253$	11.0836			0.696819
$254$	−2.65013			−0.166284
$255$	5.91309	+	4.29611i	0.370292	+	0.269033i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	7.27643	−	5.28664i	0.453891	−	0.329771i	−0.337239	−	0.941419i	$-0.609493\pi$
$257$	7.27643	−	5.28664i	0.453891	−	0.329771i	0.791130	+	0.611648i	$0.209493\pi$
$258$	2.95731	−	9.10166i	0.184114	−	0.566644i
$259$	−1.91539	−	1.39161i	−0.119017	−	0.0864707i
$260$	1.77729	−	5.46994i	0.110223	−	0.339231i
$261$	0.0186923	+	0.0575291i	0.00115703	+	0.00356096i
$262$	14.3273	−	10.4094i	0.885143	−	0.643094i
$263$	1.16237	+	3.57740i	0.0716746	+	0.220592i	0.980477	−	0.196636i	$-0.0630017\pi$
$263$	1.16237	+	3.57740i	0.0716746	+	0.220592i	−0.908802	+	0.417228i	$0.863002\pi$
$264$	−0.556055	−	1.71136i	−0.0342228	−	0.105327i
$265$	−3.60555	+	2.61959i	−0.221487	+	0.160920i
$266$	8.64608	+	26.6099i	0.530125	+	1.63156i
$267$	4.59600	−	14.1450i	0.281271	−	0.865663i
$268$	−1.44326	−	1.04859i	−0.0881610	−	0.0640527i
$269$	−7.78942	+	23.9734i	−0.474930	+	1.46168i	0.371123	+	0.928584i	$0.378973\pi$
$269$	−7.78942	+	23.9734i	−0.474930	+	1.46168i	−0.846053	+	0.533099i	$0.821027\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	−2.24991	+	1.63466i	−0.136673	+	0.0992984i	−0.654021	−	0.756476i	$-0.726919\pi$
$271$	−2.24991	+	1.63466i	−0.136673	+	0.0992984i	0.517348	+	0.855775i	$0.326919\pi$
$272$	5.91309	+	4.29611i	0.358534	+	0.260490i
$273$	19.0527			1.15312
$274$	4.71880			0.285073
$275$	1.45577	+	1.05768i	0.0877864	+	0.0637805i
$276$	−1.90338	−	5.85802i	−0.114570	−	0.352611i
$277$	−3.48988	+	10.7407i	−0.209686	+	0.645348i	0.789802	+	0.613362i	$0.210183\pi$
$277$	−3.48988	+	10.7407i	−0.209686	+	0.645348i	−0.999488	+	0.0319864i	$0.989817\pi$
$278$	15.4313			0.925506
$279$	−4.59064	−	3.15056i	−0.274834	−	0.188619i
$280$	3.31269			0.197971
$281$	−4.27771	+	13.1654i	−0.255187	+	0.785384i	0.738606	+	0.674137i	$0.235484\pi$
$281$	−4.27771	+	13.1654i	−0.255187	+	0.785384i	−0.993793	+	0.111247i	$0.964516\pi$
$282$	−2.74322	−	8.44276i	−0.163356	−	0.502759i
$283$	−17.2130	−	12.5060i	−1.02321	−	0.743404i	−0.0562698	−	0.998416i	$-0.517921\pi$
$283$	−17.2130	−	12.5060i	−1.02321	−	0.743404i	−0.966938	+	0.255012i	$0.917921\pi$
$284$	1.34754			0.0799620
$285$	8.44609			0.500303
$286$	8.37278	+	6.08318i	0.495093	+	0.359706i
$287$	11.4133	−	8.29225i	0.673706	−	0.489476i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	11.2548	−	34.6386i	0.662045	−	2.03756i
$290$	−0.0489371	−	0.0355549i	−0.00287369	−	0.00208786i
$291$	0.933715	−	2.87368i	0.0547353	−	0.168458i
$292$	−3.97814	−	12.2435i	−0.232803	−	0.716494i
$293$	−11.7938	+	8.56872i	−0.689003	+	0.500590i	−0.876332	−	0.481707i	$-0.840017\pi$
$293$	−11.7938	+	8.56872i	−0.689003	+	0.500590i	0.187329	+	0.982297i	$0.440017\pi$
$294$	1.22801	+	3.77943i	0.0716191	+	0.220421i
$295$	4.11365	+	12.6605i	0.239506	+	0.737124i
$296$	−0.578198	+	0.420085i	−0.0336071	+	0.0244170i
$297$	−0.556055	−	1.71136i	−0.0322656	−	0.0993033i
$298$	−3.08252	+	9.48701i	−0.178565	+	0.549568i
$299$	28.6601	+	20.8228i	1.65746	+	1.20421i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	−25.6480	+	18.6343i	−1.47832	+	1.07407i
$302$	−2.35256	+	1.70923i	−0.135375	+	0.0983554i
$303$	−6.76293	−	4.91356i	−0.388520	−	0.282277i
$304$	8.44609			0.484417
$305$	−3.95628			−0.226536
$306$	5.91309	+	4.29611i	0.338029	+	0.245592i
$307$	−4.36125	−	13.4225i	−0.248910	−	0.766065i	−0.994969	−	0.100186i	$-0.968056\pi$
$307$	−4.36125	−	13.4225i	−0.248910	−	0.766065i	0.746059	−	0.665880i	$-0.231944\pi$
$308$	−1.84204	+	5.66922i	−0.104960	+	0.323034i
$309$	7.17131			0.407962
$310$	5.56576	−	0.149456i	0.316114	−	0.00848854i
$311$	−32.0973			−1.82007			−0.910035	−	0.414532i	$-0.863945\pi$
$311$	−32.0973			−1.82007			−0.910035	+	0.414532i	$0.863945\pi$
$312$	1.77729	−	5.46994i	0.100619	−	0.309674i
$313$	−3.23066	−	9.94296i	−0.182608	−	0.562009i	0.817291	−	0.576225i	$-0.195475\pi$
$313$	−3.23066	−	9.94296i	−0.182608	−	0.562009i	−0.999899	+	0.0142158i	$0.995475\pi$
$314$	−2.02144	−	1.46866i	−0.114076	−	0.0828813i
$315$	3.31269			0.186649
$316$	−8.95012			−0.503483
$317$	4.61894	+	3.35586i	0.259426	+	0.188484i	0.709894	−	0.704309i	$-0.248743\pi$
$317$	4.61894	+	3.35586i	0.259426	+	0.188484i	−0.450468	+	0.892792i	$0.648743\pi$
$318$	−3.60555	+	2.61959i	−0.202189	+	0.146899i
$319$	0.0880591	−	0.0639787i	0.00493036	−	0.00358212i
$320$	0.309017	−	0.951057i	0.0172746	−	0.0531657i
$321$	−14.1075	−	10.2497i	−0.787405	−	0.572083i
$322$	−6.30533	+	19.4058i	−0.351382	+	1.08144i
$323$	−19.0763	−	58.7109i	−1.06144	−	3.26676i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	1.77729	+	5.46994i	0.0985864	+	0.303418i
$326$	−5.85792	−	18.0288i	−0.324440	−	0.998525i
$327$	−15.9504	+	11.5887i	−0.882060	+	0.640854i
$328$	−1.31600	−	4.05022i	−0.0726638	−	0.223636i
$329$	−9.08744	+	27.9683i	−0.501007	+	1.54194i
$330$	1.45577	+	1.05768i	0.0801376	+	0.0582234i
$331$	−5.10863	+	15.7227i	−0.280795	+	0.864200i	0.706832	+	0.707381i	$0.250124\pi$
$331$	−5.10863	+	15.7227i	−0.280795	+	0.864200i	−0.987627	+	0.156818i	$0.949876\pi$
$332$	2.25921	−	1.64141i	0.123990	−	0.0900841i
$333$	−0.578198	+	0.420085i	−0.0316851	+	0.0230205i
$334$	−8.11125	−	5.89316i	−0.443828	−	0.322460i
$335$	1.78397			0.0974684
$336$	3.31269			0.180722
$337$	8.84474	+	6.42608i	0.481804	+	0.350051i	0.802024	−	0.597292i	$-0.203757\pi$
$337$	8.84474	+	6.42608i	0.481804	+	0.350051i	−0.320220	+	0.947343i	$0.603757\pi$
$338$	6.20475	+	19.0963i	0.337494	+	1.03870i
$339$	4.24079	−	13.0518i	0.230328	−	0.708877i
$340$	−7.30898			−0.396385
$341$	−2.83910	+	9.60814i	−0.153746	+	0.520310i
$342$	8.44609			0.456712
$343$	−3.09772	+	9.53380i	−0.167261	+	0.514777i
$344$	2.95731	+	9.10166i	0.159447	+	0.490728i
$345$	4.98313	+	3.62045i	0.268282	+	0.194919i
$346$	14.1071			0.758401
$347$	−22.1520			−1.18918			−0.594590	−	0.804029i	$-0.702686\pi$
$347$	−22.1520			−1.18918			−0.594590	+	0.804029i	$0.702686\pi$
$348$	−0.0489371	−	0.0355549i	−0.00262331	−	0.00190594i
$349$	−18.9384	+	13.7596i	−1.01375	+	0.736533i	−0.964993	−	0.262277i	$-0.915526\pi$
$349$	−18.9384	+	13.7596i	−1.01375	+	0.736533i	−0.0487584	+	0.998811i	$0.515526\pi$
$350$	−2.68002	+	1.94715i	−0.143253	+	0.104080i
$351$	1.77729	−	5.46994i	0.0948648	−	0.291964i
$352$	1.45577	+	1.05768i	0.0775929	+	0.0563745i
$353$	4.55063	−	14.0054i	0.242205	−	0.745432i	−0.753878	−	0.657014i	$-0.771819\pi$
$353$	4.55063	−	14.0054i	0.242205	−	0.745432i	0.996084	−	0.0884173i	$-0.0281809\pi$
$354$	4.11365	+	12.6605i	0.218638	+	0.672899i
$355$	−1.09019	+	0.792067i	−0.0578611	+	0.0420385i
$356$	4.59600	+	14.1450i	0.243588	+	0.749686i
$357$	−7.48204	−	23.0274i	−0.395992	−	1.21874i
$358$	−8.78132	+	6.38000i	−0.464107	+	0.337194i
$359$	4.18150	+	12.8693i	0.220691	+	0.679217i	0.998700	+	0.0509645i	$0.0162295\pi$
$359$	4.18150	+	12.8693i	0.220691	+	0.679217i	−0.778009	+	0.628253i	$0.783770\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	−42.3411	−	30.7626i	−2.22848	−	1.61908i
$362$	1.07355	−	3.30405i	0.0564246	−	0.173657i
$363$	6.27962	−	4.56241i	0.329595	−	0.239465i
$364$	−15.4140	+	11.1989i	−0.807912	+	0.586983i
$365$	10.4149	+	7.56687i	0.545141	+	0.396068i
$366$	−3.95628			−0.206798
$367$	27.4308			1.43188			0.715939	−	0.698163i	$-0.245999\pi$
$367$	27.4308			1.43188			0.715939	+	0.698163i	$0.245999\pi$
$368$	4.98313	+	3.62045i	0.259763	+	0.188729i
$369$	−1.31600	−	4.05022i	−0.0685081	−	0.210846i
$370$	0.220852	−	0.679712i	0.0114815	−	0.0353366i
$371$	14.7637			0.766493
$372$	5.56576	−	0.149456i	0.288571	−	0.00774895i
$373$	26.5776			1.37614			0.688068	−	0.725646i	$-0.258459\pi$
$373$	26.5776			1.37614			0.688068	+	0.725646i	$0.258459\pi$
$374$	4.06420	−	12.5083i	0.210155	−	0.646789i
$375$	0.309017	+	0.951057i	0.0159576	+	0.0491123i
$376$	7.18184	+	5.21791i	0.370375	+	0.269093i
$377$	0.347902			0.0179179
$378$	3.31269			0.170387
$379$	26.1439	+	18.9946i	1.34292	+	0.975689i	0.999331	+	0.0365685i	$0.0116427\pi$
$379$	26.1439	+	18.9946i	1.34292	+	0.975689i	0.343589	+	0.939120i	$0.388357\pi$
$380$	−6.83303	+	4.96449i	−0.350527	+	0.254673i
$381$	2.14400	−	1.55771i	0.109840	−	0.0798037i
$382$	−0.264346	+	0.813574i	−0.0135251	+	0.0416261i
$383$	−9.12187	−	6.62743i	−0.466106	−	0.338646i	0.329816	−	0.944045i	$-0.393013\pi$
$383$	−9.12187	−	6.62743i	−0.466106	−	0.338646i	−0.795922	+	0.605400i	$0.793013\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	−1.84204	−	5.66922i	−0.0938791	−	0.288930i
$386$	−3.98900	+	2.89818i	−0.203035	+	0.147513i
$387$	2.95731	+	9.10166i	0.150328	+	0.462663i
$388$	0.933715	+	2.87368i	0.0474022	+	0.145889i
$389$	−1.22591	+	0.890679i	−0.0621563	+	0.0451592i	−0.618430	−	0.785840i	$-0.712231\pi$
$389$	−1.22591	+	0.890679i	−0.0621563	+	0.0451592i	0.556273	+	0.830999i	$0.312231\pi$
$390$	1.77729	+	5.46994i	0.0899966	+	0.276981i
$391$	13.9118	−	42.8161i	0.703550	−	2.16530i
$392$	−3.21498	−	2.33582i	−0.162381	−	0.117977i
$393$	−5.47254	+	16.8427i	−0.276053	+	0.849604i
$394$	−3.62388	+	2.63290i	−0.182568	+	0.132644i
$395$	7.24080	−	5.26075i	0.364324	−	0.264697i
$396$	1.45577	+	1.05768i	0.0731553	+	0.0531504i
$397$	−5.90867			−0.296548			−0.148274	−	0.988946i	$-0.547372\pi$
$397$	−5.90867			−0.296548			−0.148274	+	0.988946i	$0.547372\pi$
$398$	21.5981			1.08261
$399$	−22.6357	−	16.4458i	−1.13320	−	0.823321i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	8.53531	−	26.2690i	0.426233	−	1.31181i	−0.475576	−	0.879675i	$-0.657760\pi$
$401$	8.53531	−	26.2690i	0.426233	−	1.31181i	0.901809	−	0.432135i	$-0.142240\pi$
$402$	1.78397			0.0889761
$403$	−25.3923	+	19.5111i	−1.26488	+	0.971915i
$404$	8.35944			0.415898
$405$	0.309017	−	0.951057i	0.0153552	−	0.0472584i
$406$	0.0619219	+	0.190576i	0.00307313	+	0.00945813i
$407$	1.04043	+	0.755916i	0.0515721	+	0.0374693i
$408$	−7.30898			−0.361848
$409$	12.0602			0.596341			0.298170	−	0.954513i	$-0.403624\pi$
$409$	12.0602			0.596341			0.298170	+	0.954513i	$0.403624\pi$
$410$	3.44533	+	2.50318i	0.170153	+	0.123623i
$411$	−3.81759	+	2.77364i	−0.188308	+	0.136814i
$412$	−5.80171	+	4.21519i	−0.285830	+	0.207668i
$413$	13.6273	−	41.9404i	0.670554	−	2.06375i
$414$	4.98313	+	3.62045i	0.244907	+	0.177936i
$415$	−0.862940	+	2.65586i	−0.0423601	+	0.130371i
$416$	1.77729	+	5.46994i	0.0871388	+	0.268186i
$417$	−12.4842	+	9.07028i	−0.611352	+	0.444173i
$418$	−4.69650	−	14.4543i	−0.229713	−	0.706984i
$419$	−8.56001	−	26.3450i	−0.418184	−	1.28704i	−0.909372	−	0.415984i	$-0.863437\pi$
$419$	−8.56001	−	26.3450i	−0.418184	−	1.28704i	0.491188	−	0.871053i	$-0.336563\pi$
$420$	−2.68002	+	1.94715i	−0.130772	+	0.0950113i
$421$	−1.73656	−	5.34458i	−0.0846347	−	0.260479i	0.899779	−	0.436345i	$-0.143727\pi$
$421$	−1.73656	−	5.34458i	−0.0846347	−	0.260479i	−0.984414	+	0.175866i	$0.943727\pi$
$422$	−5.34475	+	16.4495i	−0.260178	+	0.800747i
$423$	7.18184	+	5.21791i	0.349193	+	0.253704i
$424$	1.37720	−	4.23858i	0.0668827	−	0.205844i
$425$	5.91309	−	4.29611i	0.286827	−	0.208392i
$426$	−1.09019	+	0.792067i	−0.0528197	+	0.0383758i
$427$	10.6029	+	7.70348i	0.513112	+	0.372797i
$428$	17.4379			0.842891
$429$	−10.3493			−0.499670
$430$	−7.74233	−	5.62513i	−0.373368	−	0.271268i
$431$	−0.561055	−	1.72675i	−0.0270250	−	0.0831745i	0.936634	−	0.350309i	$-0.113923\pi$
$431$	−0.561055	−	1.72675i	−0.0270250	−	0.0831745i	−0.963659	+	0.267134i	$0.913923\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	27.2094			1.30760			0.653800	−	0.756668i	$-0.273174\pi$
$433$	27.2094			1.30760			0.653800	+	0.756668i	$0.273174\pi$
$434$	−15.2074	−	10.4368i	−0.729978	−	0.500984i
$435$	0.0604896			0.00290026
$436$	6.09252	−	18.7508i	0.291779	−	0.898002i
$437$	−16.0762	−	49.4773i	−0.769027	−	2.36682i
$438$	10.4149	+	7.56687i	0.497643	+	0.361559i
$439$	−10.0110			−0.477797			−0.238898	−	0.971045i	$-0.576786\pi$
$439$	−10.0110			−0.477797			−0.238898	+	0.971045i	$0.576786\pi$
$440$	−1.79943			−0.0857846
$441$	−3.21498	−	2.33582i	−0.153094	−	0.111229i
$442$	34.0087	−	24.7088i	1.61763	−	1.17528i
$443$	−16.8159	+	12.2175i	−0.798947	+	0.580469i	−0.910605	−	0.413278i	$-0.864384\pi$
$443$	−16.8159	+	12.2175i	−0.798947	+	0.580469i	0.111658	+	0.993747i	$0.464384\pi$
$444$	0.220852	−	0.679712i	0.0104812	−	0.0322577i
$445$	−12.0325	−	8.74212i	−0.570395	−	0.414416i
$446$	−3.58007	+	11.0183i	−0.169521	+	0.521732i
$447$	−3.08252	−	9.48701i	−0.145798	−	0.448720i
$448$	−2.68002	+	1.94715i	−0.126619	+	0.0919943i
$449$	10.3364	+	31.8121i	0.487804	+	1.50131i	0.827878	+	0.560909i	$0.189548\pi$
$449$	10.3364	+	31.8121i	0.487804	+	1.50131i	−0.340073	+	0.940399i	$0.610452\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	−6.19964	+	4.50430i	−0.291929	+	0.212099i
$452$	4.24079	+	13.0518i	0.199470	+	0.613905i
$453$	0.898597	−	2.76560i	0.0422198	−	0.129939i
$454$	−6.15443	−	4.47146i	−0.288842	−	0.209856i
$455$	5.88762	−	18.1202i	0.276016	−	0.849489i
$456$	−6.83303	+	4.96449i	−0.319986	+	0.232483i
$457$	−6.51619	+	4.73429i	−0.304814	+	0.221461i	−0.729668	−	0.683801i	$-0.760325\pi$
$457$	−6.51619	+	4.73429i	−0.304814	+	0.221461i	0.424854	+	0.905262i	$0.360325\pi$
$458$	−2.58951	−	1.88139i	−0.121000	−	0.0879115i
$459$	−7.30898			−0.341154
$460$	−6.15948			−0.287187
$461$	32.4169	+	23.5522i	1.50980	+	1.09694i	0.966264	+	0.257555i	$0.0829168\pi$
$461$	32.4169	+	23.5522i	1.50980	+	1.09694i	0.543541	+	0.839383i	$0.317083\pi$
$462$	−1.84204	−	5.66922i	−0.0856995	−	0.263756i
$463$	−5.43222	+	16.7187i	−0.252457	+	0.776982i	0.741863	+	0.670551i	$0.233942\pi$
$463$	−5.43222	+	16.7187i	−0.252457	+	0.776982i	−0.994320	+	0.106431i	$0.966058\pi$
$464$	0.0604896			0.00280816
$465$	−4.41494	+	3.39238i	−0.204738	+	0.157318i
$466$	−17.5474			−0.812866
$467$	6.20434	−	19.0950i	0.287103	−	0.883611i	−0.698658	−	0.715456i	$-0.746219\pi$
$467$	6.20434	−	19.0950i	0.287103	−	0.883611i	0.985761	−	0.168155i	$-0.0537809\pi$
$468$	1.77729	+	5.46994i	0.0821553	+	0.252848i
$469$	−4.78107	−	3.47365i	−0.220769	−	0.160398i
$470$	−8.87725			−0.409477
$471$	2.49864			0.115131
$472$	−10.7697	−	7.82464i	−0.495715	−	0.360158i
$473$	13.9318	−	10.1221i	0.640585	−	0.465412i
$474$	7.24080	−	5.26075i	0.332581	−	0.241634i
$475$	2.60999	−	8.03271i	0.119754	−	0.368566i
$476$	19.5882	+	14.2317i	0.897826	+	0.652308i
$477$	1.37720	−	4.23858i	0.0630576	−	0.194071i
$478$	3.42655	+	10.5458i	0.156727	+	0.482356i
$479$	20.9767	−	15.2405i	0.958451	−	0.696355i	0.00566055	−	0.999984i	$-0.498198\pi$
$479$	20.9767	−	15.2405i	0.958451	−	0.696355i	0.952790	+	0.303629i	$0.0981982\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	1.27022	+	3.90932i	0.0579168	+	0.178250i
$482$	2.28932	−	1.66329i	0.104276	−	0.0757607i
$483$	−6.30533	−	19.4058i	−0.286902	−	0.882995i
$484$	−2.39860	+	7.38214i	−0.109027	+	0.335552i
$485$	−2.44450	−	1.77603i	−0.110999	−	0.0806454i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−9.57334	+	6.95544i	−0.433810	+	0.315181i	−0.783170	−	0.621807i	$-0.786399\pi$
$487$	−9.57334	+	6.95544i	−0.433810	+	0.315181i	0.349361	+	0.936988i	$0.386399\pi$
$488$	3.20070	−	2.32544i	0.144889	−	0.105268i
$489$	15.3362	+	11.1424i	0.693529	+	0.503878i
$490$	3.97393			0.179524
$491$	−15.1303			−0.682823			−0.341412	−	0.939914i	$-0.610905\pi$
$491$	−15.1303			−0.682823			−0.341412	+	0.939914i	$0.610905\pi$
$492$	3.44533	+	2.50318i	0.155327	+	0.112852i
$493$	−0.136622	−	0.420479i	−0.00615314	−	0.0189374i
$494$	15.0112	−	46.1996i	0.675384	−	2.07862i
$495$	−1.79943			−0.0808785
$496$	−4.41494	+	3.39238i	−0.198237	+	0.152323i
$497$	4.46400			0.200238
$498$	−0.862940	+	2.65586i	−0.0386693	+	0.119012i
$499$	−13.2526	−	40.7874i	−0.593269	−	1.82589i	−0.563162	−	0.826347i	$-0.690415\pi$
$499$	−13.2526	−	40.7874i	−0.593269	−	1.82589i	−0.0301067	−	0.999547i	$-0.509585\pi$
$500$	−0.809017	−	0.587785i	−0.0361803	−	0.0262866i
$501$	10.0261			0.447931
$502$	−9.95583			−0.444350
$503$	−13.5288	−	9.82927i	−0.603221	−	0.438266i	0.243800	−	0.969826i	$-0.421606\pi$
$503$	−13.5288	−	9.82927i	−0.603221	−	0.438266i	−0.847021	+	0.531560i	$0.821606\pi$
$504$	−2.68002	+	1.94715i	−0.119378	+	0.0867330i
$505$	−6.76293	+	4.91356i	−0.300947	+	0.218650i
$506$	3.42501	−	10.5411i	0.152260	−	0.468609i
$507$	−16.2442	−	11.8021i	−0.721432	−	0.524151i
$508$	−0.818934	+	2.52042i	−0.0363343	+	0.111826i
$509$	5.53693	+	17.0409i	0.245420	+	0.755325i	0.995567	+	0.0940541i	$0.0299827\pi$
$509$	5.53693	+	17.0409i	0.245420	+	0.755325i	−0.750147	+	0.661271i	$0.770017\pi$
$510$	5.91309	−	4.29611i	0.261836	−	0.190235i
$511$	−13.1784	−	40.5588i	−0.582976	−	1.79422i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−6.83303	+	4.96449i	−0.301686	+	0.219188i
$514$	−2.77935	−	8.55396i	−0.122592	−	0.377299i
$515$	2.21606	−	6.82032i	0.0976512	−	0.300539i
$516$	−7.74233	−	5.62513i	−0.340837	−	0.247633i
$517$	4.93624	−	15.1922i	0.217096	−	0.668152i
$518$	−1.91539	+	1.39161i	−0.0841575	+	0.0611440i
$519$	−11.4129	+	8.29193i	−0.500969	+	0.363976i
$520$	−4.65301	−	3.38061i	−0.204048	−	0.148249i
$521$	−13.4544			−0.589449			−0.294724	−	0.955582i	$-0.595228\pi$
$521$	−13.4544			−0.589449			−0.294724	+	0.955582i	$0.595228\pi$
$522$	0.0604896			0.00264756
$523$	−27.5041	−	19.9829i	−1.20267	−	0.873790i	−0.208124	−	0.978102i	$-0.566736\pi$
$523$	−27.5041	−	19.9829i	−1.20267	−	0.873790i	−0.994545	+	0.104313i	$0.966736\pi$
$524$	−5.47254	−	16.8427i	−0.239069	−	0.735778i
$525$	1.02368	−	3.15056i	0.0446770	−	0.137502i
$526$	3.76150			0.164009
$527$	33.5529	+	23.0274i	1.46159	+	1.00309i
$528$	−1.79943			−0.0783103
$529$	4.61647	−	14.2080i	0.200716	−	0.617741i
$530$	1.37720	+	4.23858i	0.0598217	+	0.184112i
$531$	−10.7697	−	7.82464i	−0.467365	−	0.339560i
$532$	27.9793			1.21306
$533$	−24.4934			−1.06093
$534$	−12.0325	−	8.74212i	−0.520697	−	0.378308i
$535$	−14.1075	+	10.2497i	−0.609922	+	0.443134i
$536$	−1.44326	+	1.04859i	−0.0623393	+	0.0452921i
$537$	3.35417	−	10.3231i	0.144743	−	0.445473i
$538$	20.3930	+	14.8164i	0.879204	+	0.638779i
$539$	−2.20973	+	6.80084i	−0.0951797	+	0.292933i
$540$	0.309017	+	0.951057i	0.0132980	+	0.0409270i
$541$	25.6046	−	18.6028i	1.10083	−	0.799798i	0.119633	−	0.992818i	$-0.461828\pi$
$541$	25.6046	−	18.6028i	1.10083	−	0.799798i	0.981195	+	0.193020i	$0.0618283\pi$
$542$	0.859391	+	2.64493i	0.0369140	+	0.113610i
$543$	1.07355	+	3.30405i	0.0460705	+	0.141790i
$544$	5.91309	−	4.29611i	0.253522	−	0.184194i
$545$	6.09252	+	18.7508i	0.260975	+	0.803198i
$546$	5.88762	−	18.1202i	0.251967	−	0.775474i
$547$	22.8181	+	16.5784i	0.975634	+	0.708839i	0.956729	−	0.290982i	$-0.0939820\pi$
$547$	22.8181	+	16.5784i	0.975634	+	0.708839i	0.0189051	+	0.999821i	$0.493982\pi$
$548$	1.45819	−	4.48784i	0.0622907	−	0.191711i
$549$	3.20070	−	2.32544i	0.136602	−	0.0992475i
$550$	1.45577	−	1.05768i	0.0620743	−	0.0450996i
$551$	−0.413328	−	0.300300i	−0.0176083	−	0.0127932i
$552$	−6.15948			−0.262165
$553$	−29.6490			−1.26080
$554$	9.13662	+	6.63814i	0.388178	+	0.282028i
$555$	0.220852	+	0.679712i	0.00937464	+	0.0288522i
$556$	4.76853	−	14.6760i	0.202231	−	0.622402i
$557$	28.0841			1.18996			0.594980	−	0.803740i	$-0.297160\pi$
$557$	28.0841			1.18996			0.594980	+	0.803740i	$0.297160\pi$
$558$	−4.41494	+	3.39238i	−0.186900	+	0.143611i
$559$	55.0415			2.32801
$560$	1.02368	−	3.15056i	0.0432583	−	0.133135i
$561$	4.06420	+	12.5083i	0.171591	+	0.528101i
$562$	11.1992	+	8.13669i	0.472409	+	0.343225i
$563$	−3.44362			−0.145131			−0.0725657	−	0.997364i	$-0.523119\pi$
$563$	−3.44362			−0.145131			−0.0725657	+	0.997364i	$0.523119\pi$
$564$	−8.87725			−0.373799
$565$	−11.1025	−	8.06646i	−0.467087	−	0.339359i
$566$	−17.2130	+	12.5060i	−0.723517	+	0.525666i
$567$	−2.68002	+	1.94715i	−0.112550	+	0.0817727i
$568$	0.416414	−	1.28159i	0.0174723	−	0.0537744i
$569$	16.9274	+	12.2985i	0.709635	+	0.515580i	0.883056	−	0.469268i	$-0.155482\pi$
$569$	16.9274	+	12.2985i	0.709635	+	0.515580i	−0.173421	+	0.984848i	$0.555482\pi$
$570$	2.60999	−	8.03271i	0.109320	−	0.336453i
$571$	−12.3211	−	37.9204i	−0.515621	−	1.58692i	−0.782149	−	0.623091i	$-0.785877\pi$
$571$	−12.3211	−	37.9204i	−0.515621	−	1.58692i	0.266528	−	0.963827i	$-0.414123\pi$
$572$	8.37278	−	6.08318i	0.350083	−	0.254350i
$573$	−0.264346	−	0.813574i	−0.0110432	−	0.0339876i
$574$	−4.35950	−	13.4171i	−0.181962	−	0.560021i
$575$	4.98313	−	3.62045i	0.207811	−	0.150983i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−2.47733	+	7.62444i	−0.103133	+	0.317410i	−0.989288	−	0.145979i	$-0.953367\pi$
$577$	−2.47733	+	7.62444i	−0.103133	+	0.317410i	0.886155	+	0.463389i	$0.153367\pi$
$578$	−29.4653	−	21.4078i	−1.22560	−	0.890448i
$579$	1.52366	−	4.68935i	0.0633212	−	0.194883i
$580$	−0.0489371	+	0.0355549i	−0.00203200	+	0.00147634i
$581$	7.48406	−	5.43749i	0.310491	−	0.225585i
$582$	−2.44450	−	1.77603i	−0.101328	−	0.0736188i
$583$	−8.01955			−0.332136
$584$	−12.8735			−0.532711
$585$	−4.65301	−	3.38061i	−0.192378	−	0.139771i
$586$	4.50484	+	13.8645i	0.186093	+	0.572737i
$587$	−1.51511	+	4.66302i	−0.0625352	+	0.192464i	−0.977443	−	0.211199i	$-0.932263\pi$
$587$	−1.51511	+	4.66302i	−0.0625352	+	0.192464i	0.914908	+	0.403663i	$0.132263\pi$
$588$	3.97393			0.163882
$589$	47.0089	−	1.26232i	1.93697	−	0.0520130i
$590$	13.3121			0.548049
$591$	1.38420	−	4.26013i	0.0569384	−	0.175238i
$592$	0.220852	+	0.679712i	0.00907696	+	0.0279360i
$593$	28.1622	+	20.4611i	1.15648	+	0.840235i	0.989330	−	0.145695i	$-0.0465418\pi$
$593$	28.1622	+	20.4611i	1.15648	+	0.840235i	0.167155	+	0.985931i	$0.446542\pi$
$594$	−1.79943			−0.0738316
$595$	−24.2124			−0.992611
$596$	8.07013	+	5.86330i	0.330566	+	0.240170i
$597$	−17.4732	+	12.6950i	−0.715131	+	0.519573i
$598$	28.6601	−	20.8228i	1.17200	−	0.851507i
$599$	−8.12865	+	25.0174i	−0.332128	+	1.02218i	0.635992	+	0.771696i	$0.280591\pi$
$599$	−8.12865	+	25.0174i	−0.332128	+	1.02218i	−0.968120	+	0.250488i	$0.919409\pi$
$600$	−0.809017	−	0.587785i	−0.0330280	−	0.0239962i
$601$	−12.9405	+	39.8269i	−0.527855	+	1.62457i	0.230744	+	0.973014i	$0.425884\pi$
$601$	−12.9405	+	39.8269i	−0.527855	+	1.62457i	−0.758599	+	0.651557i	$0.774116\pi$
$602$	9.79665	+	30.1510i	0.399282	+	1.22886i
$603$	−1.44326	+	1.04859i	−0.0587740	+	0.0427018i
$604$	0.898597	+	2.76560i	0.0365634	+	0.112531i
$605$	−2.39860	−	7.38214i	−0.0975171	−	0.300127i
$606$	−6.76293	+	4.91356i	−0.274725	+	0.199600i
$607$	−6.92678	−	21.3184i	−0.281149	−	0.865289i	−0.987526	−	0.157453i	$-0.949672\pi$
$607$	−6.92678	−	21.3184i	−0.281149	−	0.865289i	0.706377	−	0.707836i	$-0.250328\pi$
$608$	2.60999	−	8.03271i	0.105849	−	0.325769i
$609$	−0.162114	−	0.117782i	−0.00656918	−	0.00477279i
$610$	−1.22256	+	3.76265i	−0.0494999	+	0.152345i
$611$	41.3059	−	30.0105i	1.67106	−	1.21409i
$612$	5.91309	−	4.29611i	0.239022	−	0.173660i
$613$	18.1027	+	13.1524i	0.731162	+	0.531221i	0.889931	−	0.456095i	$-0.150752\pi$
$613$	18.1027	+	13.1524i	0.731162	+	0.531221i	−0.158769	+	0.987316i	$0.550752\pi$
$614$	−14.1133			−0.569567
$615$	−4.25866			−0.171726
$616$	4.82253	+	3.50377i	0.194305	+	0.141171i
$617$	2.20291	+	6.77987i	0.0886859	+	0.272947i	0.985557	−	0.169345i	$-0.0541653\pi$
$617$	2.20291	+	6.77987i	0.0886859	+	0.272947i	−0.896871	+	0.442293i	$0.854165\pi$
$618$	2.21606	−	6.82032i	0.0891429	−	0.274354i
$619$	9.14169			0.367436			0.183718	−	0.982979i	$-0.441187\pi$
$619$	9.14169			0.367436			0.183718	+	0.982979i	$0.441187\pi$
$620$	1.57777	−	5.33953i	0.0633649	−	0.214441i
$621$	−6.15948			−0.247172
$622$	−9.91860	+	30.5263i	−0.397700	+	1.22399i
$623$	15.2251	+	46.8582i	0.609983	+	1.87733i
$624$	−4.65301	−	3.38061i	−0.186269	−	0.135333i
$625$	1.00000			0.0400000
$626$	−10.4546			−0.417852
$627$	12.2956	+	8.93327i	0.491038	+	0.356760i
$628$	−2.02144	+	1.46866i	−0.0806642	+	0.0586059i
$629$	4.22604	−	3.07039i	0.168503	−	0.122425i
$630$	1.02368	−	3.15056i	0.0407843	−	0.125521i
$631$	−19.1134	−	13.8867i	−0.760890	−	0.552819i	0.138293	−	0.990391i	$-0.455838\pi$
$631$	−19.1134	−	13.8867i	−0.760890	−	0.552819i	−0.899183	+	0.437572i	$0.855838\pi$
$632$	−2.76574	+	8.51207i	−0.110015	+	0.338592i
$633$	−5.34475	−	16.4495i	−0.212435	−	0.653807i
$634$	4.61894	−	3.35586i	0.183442	−	0.133278i
$635$	−0.818934	−	2.52042i	−0.0324984	−	0.100020i
$636$	1.37720	+	4.23858i	0.0546095	+	0.168071i
$637$	−18.4907	+	13.4343i	−0.732630	+	0.532287i
$638$	−0.0336356	−	0.103520i	−0.00133165	−	0.00409838i
$639$	0.416414	−	1.28159i	0.0164731	−	0.0506989i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	2.03081	−	6.25018i	0.0802121	−	0.246867i	−0.902906	−	0.429837i	$-0.858571\pi$
$641$	2.03081	−	6.25018i	0.0802121	−	0.246867i	0.983119	+	0.182970i	$0.0585710\pi$
$642$	−14.1075	+	10.2497i	−0.556780	+	0.404524i
$643$	21.4058	−	15.5522i	0.844161	−	0.613319i	−0.0793692	−	0.996845i	$-0.525291\pi$
$643$	21.4058	−	15.5522i	0.844161	−	0.613319i	0.923530	+	0.383527i	$0.125291\pi$
$644$	16.5076	+	11.9934i	0.650489	+	0.472608i
$645$	9.57005			0.376820
$646$	−61.7323			−2.42882
$647$	6.53503	+	4.74797i	0.256918	+	0.186662i	0.708787	−	0.705422i	$-0.249243\pi$
$647$	6.53503	+	4.74797i	0.256918	+	0.186662i	−0.451869	+	0.892084i	$0.649243\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	−7.40225	+	22.7818i	−0.290564	+	0.894263i
$650$	5.75143			0.225590
$651$	18.4376	−	0.495103i	0.722628	−	0.0194046i
$652$	−18.9566			−0.742399
$653$	−10.7770	+	33.1683i	−0.421738	+	1.29798i	0.484345	+	0.874877i	$0.339058\pi$
$653$	−10.7770	+	33.1683i	−0.421738	+	1.29798i	−0.906083	+	0.423099i	$0.860942\pi$
$654$	6.09252	+	18.7508i	0.238236	+	0.733216i
$655$	14.3273	+	10.4094i	0.559813	+	0.406728i
$656$	−4.25866			−0.166273
$657$	−12.8735			−0.502244
$658$	23.7912	+	17.2853i	0.927479	+	0.673853i
$659$	−3.79591	+	2.75789i	−0.147868	+	0.107432i	−0.659259	−	0.751916i	$-0.729130\pi$
$659$	−3.79591	+	2.75789i	−0.147868	+	0.107432i	0.511392	+	0.859348i	$0.329130\pi$
$660$	1.45577	−	1.05768i	0.0566659	−	0.0411702i
$661$	−0.389131	+	1.19762i	−0.0151354	+	0.0465821i	−0.958339	−	0.285633i	$-0.907796\pi$
$661$	−0.389131	+	1.19762i	−0.0151354	+	0.0465821i	0.943204	+	0.332215i	$0.107796\pi$
$662$	13.3746	+	9.71718i	0.519817	+	0.377669i
$663$	−12.9902	+	39.9797i	−0.504497	+	1.55268i
$664$	−0.862940	−	2.65586i	−0.0334886	−	0.103067i
$665$	−22.6357	+	16.4458i	−0.877776	+	0.637742i
$666$	0.220852	+	0.679712i	0.00855784	+	0.0263383i
$667$	−0.115135	−	0.354349i	−0.00445805	−	0.0137205i
$668$	−8.11125	+	5.89316i	−0.313833	+	0.228013i
$669$	−3.58007	−	11.0183i	−0.138413	−	0.425993i
$670$	0.551276	−	1.69665i	0.0212976	−	0.0655474i
$671$	−5.75944	−	4.18448i	−0.222341	−	0.161540i
$672$	1.02368	−	3.15056i	0.0394892	−	0.121535i
$673$	−9.24006	+	6.71329i	−0.356178	+	0.258778i	−0.751456	−	0.659783i	$-0.770648\pi$
$673$	−9.24006	+	6.71329i	−0.356178	+	0.258778i	0.395278	+	0.918561i	$0.370648\pi$
$674$	8.84474	−	6.42608i	0.340687	−	0.247523i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	20.0790			0.772269
$677$	−31.0751			−1.19431			−0.597156	−	0.802125i	$-0.703703\pi$
$677$	−31.0751			−1.19431			−0.597156	+	0.802125i	$0.703703\pi$
$678$	−11.1025	−	8.06646i	−0.426390	−	0.309791i
$679$	3.09311	+	9.51961i	0.118703	+	0.365329i
$680$	−2.25860	+	6.95125i	−0.0866133	+	0.266568i
$681$	7.60730			0.291512
$682$	8.26055	+	5.66922i	0.316313	+	0.217086i
$683$	43.6099			1.66869			0.834343	−	0.551245i	$-0.185847\pi$
$683$	43.6099			1.66869			0.834343	+	0.551245i	$0.185847\pi$
$684$	2.60999	−	8.03271i	0.0997953	−	0.307138i
$685$	1.45819	+	4.48784i	0.0557145	+	0.171472i
$686$	8.10994	+	5.89221i	0.309639	+	0.224966i
$687$	3.20081			0.122119
$688$	9.57005			0.364855
$689$	−20.7371	−	15.0664i	−0.790020	−	0.573983i
$690$	4.98313	−	3.62045i	0.189704	−	0.137828i
$691$	19.4010	−	14.0957i	0.738049	−	0.536224i	−0.154050	−	0.988063i	$-0.549232\pi$
$691$	19.4010	−	14.0957i	0.738049	−	0.536224i	0.892100	+	0.451839i	$0.149232\pi$
$692$	4.35933	−	13.4166i	0.165717	−	0.510024i
$693$	4.82253	+	3.50377i	0.183193	+	0.133097i
$694$	−6.84533	+	21.0678i	−0.259845	+	0.799722i
$695$	4.76853	+	14.6760i	0.180880	+	0.556693i
$696$	−0.0489371	+	0.0355549i	−0.00185496	+	0.00134771i
$697$	9.61860	+	29.6030i	0.364330	+	1.12129i
$698$	7.23384	+	22.2635i	0.273805	+	0.842684i
$699$	14.1961	−	10.3141i	0.536946	−	0.390114i
$700$	1.02368	+	3.15056i	0.0386914	+	0.119080i
$701$	−7.64425	+	23.5266i	−0.288719	+	0.888587i	0.696540	+	0.717518i	$0.254722\pi$
$701$	−7.64425	+	23.5266i	−0.288719	+	0.888587i	−0.985259	+	0.171068i	$0.945278\pi$
$702$	−4.65301	−	3.38061i	−0.175616	−	0.127593i
$703$	1.86534	−	5.74091i	0.0703525	−	0.216523i
$704$	1.45577	−	1.05768i	0.0548665	−	0.0398628i
$705$	7.18184	−	5.21791i	0.270484	−	0.196518i
$706$	−11.9137	−	8.65581i	−0.448378	−	0.325766i
$707$	27.6923			1.04147
$708$	13.3121			0.500298
$709$	−13.4840	−	9.79671i	−0.506403	−	0.367923i	0.305055	−	0.952335i	$-0.401325\pi$
$709$	−13.4840	−	9.79671i	−0.506403	−	0.367923i	−0.811457	+	0.584412i	$0.801325\pi$
$710$	0.416414	+	1.28159i	0.0156277	+	0.0480972i
$711$	−2.76574	+	8.51207i	−0.103723	+	0.319227i
$712$	14.8730			0.557388
$713$	28.2760	+	19.4058i	1.05894	+	0.726753i
$714$	−24.2124			−0.906126
$715$	−3.19812	+	9.84279i	−0.119603	+	0.368099i
$716$	3.35417	+	10.3231i	0.125351	+	0.385791i
$717$	−8.97083	−	6.51769i	−0.335022	−	0.243408i
$718$	13.5316			0.504995
$719$	−34.2388			−1.27689			−0.638445	−	0.769667i	$-0.720422\pi$
$719$	−34.2388			−1.27689			−0.638445	+	0.769667i	$0.720422\pi$
$720$	−0.809017	−	0.587785i	−0.0301503	−	0.0219055i
$721$	−19.2193	+	13.9636i	−0.715764	+	0.520033i
$722$	−42.3411	+	30.7626i	−1.57577	+	1.14487i
$723$	−0.874443	+	2.69126i	−0.0325209	+	0.100089i
$724$	−2.81059	−	2.04201i	−0.104455	−	0.0758909i
$725$	0.0186923	−	0.0575291i	0.000694215	−	0.00213658i
$726$	−2.39860	−	7.38214i	−0.0890205	−	0.273977i
$727$	−0.404369	+	0.293792i	−0.0149972	+	0.0108961i	−0.595259	−	0.803534i	$-0.702950\pi$
$727$	−0.404369	+	0.293792i	−0.0149972	+	0.0108961i	0.580261	+	0.814430i	$0.302950\pi$
$728$	5.88762	+	18.1202i	0.218210	+	0.671580i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	10.4149	−	7.56687i	0.385473	−	0.280062i
$731$	−21.6149	−	66.5238i	−0.799456	−	2.46047i
$732$	−1.22256	+	3.76265i	−0.0451870	+	0.139071i
$733$	−9.77455	−	7.10162i	−0.361031	−	0.262304i	0.392451	−	0.919773i	$-0.371627\pi$
$733$	−9.77455	−	7.10162i	−0.361031	−	0.262304i	−0.753482	+	0.657468i	$0.771627\pi$
$734$	8.47660	−	26.0883i	0.312877	−	0.962936i
$735$	−3.21498	+	2.33582i	−0.118586	+	0.0861580i
$736$	4.98313	−	3.62045i	0.183680	−	0.133452i
$737$	2.59705	+	1.88687i	0.0956635	+	0.0695036i
$738$	−4.25866			−0.156763
$739$	−13.5873			−0.499817			−0.249909	−	0.968269i	$-0.580401\pi$
$739$	−13.5873			−0.499817			−0.249909	+	0.968269i	$0.580401\pi$
$740$	−0.578198	−	0.420085i	−0.0212550	−	0.0154426i
$741$	15.0112	+	46.1996i	0.551449	+	1.69718i
$742$	4.56223	−	14.0411i	0.167485	−	0.515466i
$743$	−20.8197			−0.763800			−0.381900	−	0.924204i	$-0.624730\pi$
$743$	−20.8197			−0.763800			−0.381900	+	0.924204i	$0.624730\pi$
$744$	1.57777	−	5.33953i	0.0578439	−	0.195757i
$745$	−9.97523			−0.365464
$746$	8.21294	−	25.2768i	0.300697	−	0.925450i
$747$	−0.862940	−	2.65586i	−0.0315733	−	0.0971727i
$748$	−10.6402	−	7.73056i	−0.389044	−	0.282657i
$749$	57.7663			2.11073
$750$	1.00000			0.0365148
$751$	−26.6997	−	19.3984i	−0.974284	−	0.707859i	−0.0178603	−	0.999840i	$-0.505685\pi$
$751$	−26.6997	−	19.3984i	−0.974284	−	0.707859i	−0.956424	+	0.291982i	$0.905685\pi$
$752$	7.18184	−	5.21791i	0.261895	−	0.190278i
$753$	8.05443	−	5.85189i	0.293520	−	0.213255i
$754$	0.107508	−	0.330875i	0.00391520	−	0.0120497i
$755$	−2.35256	−	1.70923i	−0.0856184	−	0.0622054i
$756$	1.02368	−	3.15056i	0.0372308	−	0.114585i
$757$	16.4283	+	50.5611i	0.597097	+	1.83768i	0.543999	+	0.839086i	$0.316910\pi$
$757$	16.4283	+	50.5611i	0.597097	+	1.83768i	0.0530978	+	0.998589i	$0.483090\pi$
$758$	26.1439	−	18.9946i	0.949588	−	0.689916i
$759$	3.42501	+	10.5411i	0.124320	+	0.382618i
$760$	2.60999	+	8.03271i	0.0946741	+	0.291377i
$761$	−9.03469	+	6.56408i	−0.327507	+	0.237948i	−0.739372	−	0.673297i	$-0.764878\pi$
$761$	−9.03469	+	6.56408i	−0.327507	+	0.237948i	0.411865	+	0.911245i	$0.364878\pi$
$762$	−0.818934	−	2.52042i	−0.0296669	−	0.0913052i
$763$	20.1826	−	62.1158i	0.730661	−	2.24874i
$764$	0.692068	+	0.502817i	0.0250381	+	0.0181913i
$765$	−2.25860	+	6.95125i	−0.0816598	+	0.251323i
$766$	−9.12187	+	6.62743i	−0.329587	+	0.239459i
$767$	−61.9411	+	45.0029i	−2.23656	+	1.62496i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	12.5010			0.450796			0.225398	−	0.974267i	$-0.427632\pi$
$769$	12.5010			0.450796			0.225398	+	0.974267i	$0.427632\pi$
$770$	−5.96097			−0.214818
$771$	7.27643	+	5.28664i	0.262054	+	0.190394i
$772$	1.52366	+	4.68935i	0.0548378	+	0.168773i
$773$	5.69182	−	17.5176i	0.204721	−	0.630065i	−0.795004	−	0.606604i	$-0.792531\pi$
$773$	5.69182	−	17.5176i	0.204721	−	0.630065i	0.999725	−	0.0234612i	$-0.00746863\pi$
$774$	9.57005			0.343988
$775$	1.86206	+	5.24717i	0.0668870	+	0.188484i
$776$	3.02156			0.108468
$777$	0.731615	−	2.25168i	0.0262465	−	0.0807785i
$778$	0.468258	+	1.44115i	0.0167878	+	0.0516677i
$779$	29.0995	+	21.1421i	1.04260	+	0.757493i
$780$	5.75143			0.205934
$781$	−2.42482			−0.0867667
$782$	−36.4216	−	26.4618i	−1.30243	−	0.946272i
$783$	−0.0489371	+	0.0355549i	−0.00174887	+	0.00127063i
$784$	−3.21498	+	2.33582i	−0.114821	+	0.0834221i
$785$	0.772121	−	2.37634i	0.0275582	−	0.0848153i
$786$	14.3273	+	10.4094i	0.511037	+	0.371290i
$787$	−11.8196	+	36.3770i	−0.421324	+	1.29670i	0.485147	+	0.874433i	$0.338766\pi$
$787$	−11.8196	+	36.3770i	−0.421324	+	1.29670i	−0.906471	+	0.422269i	$0.861234\pi$
$788$	1.38420	+	4.26013i	0.0493101	+	0.151761i
$789$	−3.04312	+	2.21095i	−0.108338	+	0.0787120i
$790$	−2.76574	−	8.51207i	−0.0984006	−	0.302846i
$791$	14.0484	+	43.2366i	0.499505	+	1.53732i
$792$	1.45577	−	1.05768i	0.0517286	−	0.0375830i
$793$	−7.03146	−	21.6406i	−0.249694	−	0.768480i
$794$	−1.82588	+	5.61948i	−0.0647981	+	0.199428i
$795$	−3.60555	−	2.61959i	−0.127876	−	0.0929072i
$796$	6.67417	−	20.5410i	0.236560	−	0.728056i
$797$	18.6189	−	13.5274i	0.659516	−	0.479167i	−0.206983	−	0.978344i	$-0.566365\pi$
$797$	18.6189	−	13.5274i	0.659516	−	0.479167i	0.866500	+	0.499178i	$0.166365\pi$
$798$	−22.6357	+	16.4458i	−0.801296	+	0.582176i
$799$	−52.4919	−	38.1376i	−1.85703	−	1.34921i
$800$	1.00000			0.0353553
$801$	14.8730			0.525511
$802$	−22.3457	−	16.2351i	−0.789055	−	0.573282i
$803$	7.15840	+	22.0313i	0.252614	+	0.777467i
$804$	0.551276	−	1.69665i	0.0194420	−	0.0598363i
$805$	−20.4045			−0.719163
$806$	10.7095	+	30.1787i	0.377226	+	1.06300i
$807$	−25.2071			−0.887332
$808$	2.58321	−	7.95030i	0.0908770	−	0.279691i
$809$	−1.31819	−	4.05698i	−0.0463452	−	0.142636i	0.925206	−	0.379465i	$-0.123892\pi$
$809$	−1.31819	−	4.05698i	−0.0463452	−	0.142636i	−0.971551	+	0.236829i	$0.923892\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	24.4553			0.858742			0.429371	−	0.903128i	$-0.358735\pi$
$811$	24.4553			0.858742			0.429371	+	0.903128i	$0.358735\pi$
$812$	0.200384			0.00703208
$813$	−2.24991	−	1.63466i	−0.0789079	−	0.0573300i
$814$	1.04043	−	0.755916i	0.0364670	−	0.0264948i
$815$	15.3362	−	11.1424i	0.537205	−	0.390302i
$816$	−2.25860	+	6.95125i	−0.0790668	+	0.243342i
$817$	−65.3925	−	47.5104i	−2.28779	−	1.66218i
$818$	3.72682	−	11.4700i	0.130305	−	0.401038i
$819$	5.88762	+	18.1202i	0.205730	+	0.633172i
$820$	3.44533	−	2.50318i	0.120316	−	0.0874147i
$821$	−6.77993	−	20.8665i	−0.236621	−	0.728246i	−0.996902	−	0.0786511i	$-0.974939\pi$
$821$	−6.77993	−	20.8665i	−0.236621	−	0.728246i	0.760281	−	0.649594i	$-0.225061\pi$
$822$	1.45819	+	4.48784i	0.0508602	+	0.156531i
$823$	8.83447	−	6.41862i	0.307950	−	0.223739i	−0.423066	−	0.906099i	$-0.639046\pi$
$823$	8.83447	−	6.41862i	0.307950	−	0.223739i	0.731016	+	0.682360i	$0.239046\pi$
$824$	2.21606	+	6.82032i	0.0772000	+	0.237597i
$825$	−0.556055	+	1.71136i	−0.0193594	+	0.0595820i
$826$	−35.6767	−	25.9206i	−1.24135	−	0.901893i
$827$	−11.0690	+	34.0670i	−0.384908	+	1.18463i	0.551639	+	0.834083i	$0.314003\pi$
$827$	−11.0690	+	34.0670i	−0.384908	+	1.18463i	−0.936547	+	0.350542i	$0.885997\pi$
$828$	4.98313	−	3.62045i	0.173176	−	0.125819i
$829$	26.6929	−	19.3935i	0.927082	−	0.673564i	−0.0181947	−	0.999834i	$-0.505792\pi$
$829$	26.6929	−	19.3935i	0.927082	−	0.673564i	0.945277	+	0.326270i	$0.105792\pi$
$830$	2.25921	+	1.64141i	0.0784182	+	0.0569742i
$831$	−11.2935			−0.391767
$832$	5.75143			0.199395
$833$	23.4982	+	17.0724i	0.814165	+	0.591525i
$834$	4.76853	+	14.6760i	0.165121	+	0.508189i
$835$	3.09822	−	9.53534i	0.107218	−	0.329984i
$836$	−15.1982			−0.525640
$837$	1.57777	−	5.33953i	0.0545358	−	0.184561i
$838$	−27.7008			−0.956907
$839$	13.9121	−	42.8172i	0.480301	−	1.47821i	−0.358373	−	0.933579i	$-0.616668\pi$
$839$	13.9121	−	42.8172i	0.480301	−	1.47821i	0.838673	−	0.544635i	$-0.183332\pi$
$840$	1.02368	+	3.15056i	0.0353203	+	0.108705i
$841$	23.4585	+	17.0436i	0.808915	+	0.587711i
$842$	−5.61962			−0.193665
$843$	−13.8430			−0.476777
$844$	13.9927	+	10.1663i	0.481650	+	0.349939i
$845$	−16.2442	+	11.8021i	−0.558819	+	0.406006i
$846$	7.18184	−	5.21791i	0.246917	−	0.179396i
$847$	−7.94583	+	24.4548i	−0.273022	+	0.840275i
$848$	−3.60555	−	2.61959i	−0.123815	−	0.0899570i
$849$	6.57479	−	20.2351i	0.225646	−	0.694467i
$850$	−2.25860	−	6.95125i	−0.0774693	−	0.238426i
$851$	3.56140	−	2.58751i	0.122083	−	0.0886987i
$852$	0.416414	+	1.28159i	0.0142661	+	0.0439066i
$853$	−6.11450	−	18.8185i	−0.209356	−	0.644333i	−0.999506	−	0.0314190i	$-0.989997\pi$
$853$	−6.11450	−	18.8185i	−0.209356	−	0.644333i	0.790150	−	0.612914i	$-0.210003\pi$
$854$	10.6029	−	7.70348i	0.362825	−	0.263608i
$855$	2.60999	+	8.03271i	0.0892596	+	0.274713i
$856$	5.38860	−	16.5844i	0.184178	−	0.566843i
$857$	18.6931	+	13.5813i	0.638543	+	0.463929i	0.859349	−	0.511389i	$-0.170869\pi$
$857$	18.6931	+	13.5813i	0.638543	+	0.463929i	−0.220806	+	0.975318i	$0.570869\pi$
$858$	−3.19812	+	9.84279i	−0.109182	+	0.336027i
$859$	−27.5154	+	19.9911i	−0.938813	+	0.682088i	−0.948135	−	0.317869i	$-0.897033\pi$
$859$	−27.5154	+	19.9911i	−0.938813	+	0.682088i	0.00932136	+	0.999957i	$0.497033\pi$
$860$	−7.74233	+	5.62513i	−0.264011	+	0.191815i
$861$	11.4133	+	8.29225i	0.388965	+	0.282599i
$862$	−1.81561			−0.0618399
$863$	0.210617			0.00716948			0.00358474	−	0.999994i	$-0.498859\pi$
$863$	0.210617			0.00716948			0.00358474	+	0.999994i	$0.498859\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	4.35933	+	13.4166i	0.148222	+	0.456179i
$866$	8.40816	−	25.8777i	0.285721	−	0.879359i
$867$	36.4212			1.23693
$868$	−14.6254	+	11.2379i	−0.496417	+	0.381440i
$869$	16.1051			0.546329
$870$	0.0186923	−	0.0575291i	0.000633729	−	0.00195042i
$871$	3.17063	+	9.75818i	0.107433	+	0.330643i
$872$	−15.9504	−	11.5887i	−0.540149	−	0.392441i
$873$	3.02156			0.102264
$874$	−52.0236			−1.75972
$875$	−2.68002	−	1.94715i	−0.0906014	−	0.0658257i
$876$	10.4149	−	7.56687i	0.351887	−	0.255661i
$877$	26.0278	−	18.9103i	0.878897	−	0.638556i	−0.0540622	−	0.998538i	$-0.517217\pi$
$877$	26.0278	−	18.9103i	0.878897	−	0.638556i	0.932960	+	0.359981i	$0.117217\pi$
$878$	−3.09355	+	9.52098i	−0.104402	+	0.321317i
$879$	−11.7938	−	8.56872i	−0.397796	−	0.289016i
$880$	−0.556055	+	1.71136i	−0.0187446	+	0.0576900i
$881$	8.60863	+	26.4946i	0.290032	+	0.892627i	0.984845	+	0.173436i	$0.0554871\pi$
$881$	8.60863	+	26.4946i	0.290032	+	0.892627i	−0.694813	+	0.719190i	$0.744513\pi$
$882$	−3.21498	+	2.33582i	−0.108254	+	0.0786511i
$883$	3.45551	+	10.6350i	0.116287	+	0.357895i	0.992213	−	0.124550i	$-0.0397488\pi$
$883$	3.45551	+	10.6350i	0.116287	+	0.357895i	−0.875926	+	0.482445i	$0.839749\pi$
$884$	−12.9902	−	39.9797i	−0.436907	−	1.34466i
$885$	−10.7697	+	7.82464i	−0.362019	+	0.263022i
$886$	6.42310	+	19.7683i	0.215788	+	0.664128i
$887$	−0.324880	+	0.999877i	−0.0109084	+	0.0335726i	−0.956363	−	0.292183i	$-0.905619\pi$
$887$	−0.324880	+	0.999877i	−0.0109084	+	0.0335726i	0.945454	+	0.325755i	$0.105619\pi$
$888$	−0.578198	−	0.420085i	−0.0194031	−	0.0140971i
$889$	−2.71288	+	8.34938i	−0.0909870	+	0.280029i
$890$	−12.0325	+	8.74212i	−0.403330	+	0.293036i
$891$	1.45577	−	1.05768i	0.0487702	−	0.0354336i
$892$	9.37274	+	6.80969i	0.313822	+	0.228005i
$893$	−74.9780			−2.50904
$894$	−9.97523			−0.333622
$895$	−8.78132	−	6.38000i	−0.293527	−	0.213260i
$896$	1.02368	+	3.15056i	0.0341987	+	0.105253i
$897$	−10.9472	+	33.6920i	−0.365516	+	1.12494i
$898$	33.4493			1.11622
$899$	0.336671	−	0.00904055i	0.0112286	−	0.000301519i
$900$	1.00000			0.0333333
$901$	−10.0659	+	30.9797i	−0.335344	+	1.03208i
$902$	2.36805	+	7.28811i	0.0788474	+	0.242667i
$903$	−25.6480	−	18.6343i	−0.853511	−	0.620112i
$904$	13.7235			0.456436
$905$	3.47408			0.115482
$906$	−2.35256	−	1.70923i	−0.0781585	−	0.0567855i
$907$	−26.6350	+	19.3514i	−0.884399	+	0.642554i	−0.934412	−	0.356195i	$-0.884074\pi$
$907$	−26.6350	+	19.3514i	−0.884399	+	0.642554i	0.0500124	+	0.998749i	$0.484074\pi$
$908$	−6.15443	+	4.47146i	−0.204242	+	0.148391i
$909$	2.58321	−	7.95030i	0.0856797	−	0.263695i
$910$	−15.4140	−	11.1989i	−0.510969	−	0.371240i
$911$	−12.7253	+	39.1645i	−0.421609	+	1.29758i	0.484596	+	0.874738i	$0.338967\pi$
$911$	−12.7253	+	39.1645i	−0.421609	+	1.29758i	−0.906204	+	0.422840i	$0.861033\pi$
$912$	2.60999	+	8.03271i	0.0864253	+	0.265990i
$913$	−4.06529	+	2.95361i	−0.134542	+	0.0977501i
$914$	2.48896	+	7.66023i	0.0823275	+	0.253378i
$915$	−1.22256	−	3.76265i	−0.0404165	−	0.124389i
$916$	−2.58951	+	1.88139i	−0.0855598	+	0.0621628i
$917$	−18.1288	−	55.7948i	−0.598667	−	1.84251i
$918$	−2.25860	+	6.95125i	−0.0745449	+	0.229425i
$919$	27.0449	+	19.6493i	0.892128	+	0.648169i	0.936432	−	0.350849i	$-0.114107\pi$
$919$	27.0449	+	19.6493i	0.892128	+	0.648169i	−0.0443039	+	0.999018i	$0.514107\pi$
$920$	−1.90338	+	5.85802i	−0.0627527	+	0.193133i
$921$	11.4179	−	8.29559i	0.376233	−	0.273349i
$922$	32.4169	−	23.5522i	1.06759	−	0.775652i
$923$	−6.27013	−	4.55552i	−0.206384	−	0.149947i
$924$	−5.96097			−0.196101
$925$	0.714692			0.0234989
$926$	14.2217	+	10.3327i	0.467355	+	0.339553i
$927$	2.21606	+	6.82032i	0.0727849	+	0.224009i
$928$	0.0186923	−	0.0575291i	0.000613606	−	0.00188848i
$929$	−49.5859			−1.62686			−0.813430	−	0.581663i	$-0.802402\pi$
$929$	−49.5859			−1.62686			−0.813430	+	0.581663i	$0.802402\pi$
$930$	1.86206	+	5.24717i	0.0610592	+	0.172061i
$931$	33.5642			1.10002
$932$	−5.42243	+	16.6885i	−0.177618	+	0.546651i
$933$	−9.91860	−	30.5263i	−0.324720	−	0.999387i
$934$	−16.2432	−	11.8014i	−0.531493	−	0.386152i
$935$	13.1520			0.430117
$936$	5.75143			0.187991
$937$	−32.8908	−	23.8966i	−1.07450	−	0.780668i	−0.0977816	−	0.995208i	$-0.531175\pi$
$937$	−32.8908	−	23.8966i	−1.07450	−	0.780668i	−0.976715	+	0.214540i	$0.931175\pi$
$938$	−4.78107	+	3.47365i	−0.156108	+	0.113419i
$939$	8.45798	−	6.14509i	0.276016	−	0.200537i
$940$	−2.74322	+	8.44276i	−0.0894740	+	0.275373i
$941$	1.92521	+	1.39875i	0.0627600	+	0.0455978i	0.618723	−	0.785609i	$-0.287650\pi$
$941$	1.92521	+	1.39875i	0.0627600	+	0.0455978i	−0.555963	+	0.831207i	$0.687650\pi$
$942$	0.772121	−	2.37634i	0.0251571	−	0.0774254i
$943$	8.10587	+	24.9473i	0.263963	+	0.812395i
$944$	−10.7697	+	7.82464i	−0.350523	+	0.254670i
$945$	1.02368	+	3.15056i	0.0333003	+	0.102488i
$946$	−5.32148	−	16.3778i	−0.173016	−	0.532489i
$947$	−10.0493	+	7.30125i	−0.326559	+	0.237259i	−0.738969	−	0.673739i	$-0.764687\pi$
$947$	−10.0493	+	7.30125i	−0.326559	+	0.237259i	0.412410	+	0.910998i	$0.364687\pi$
$948$	−2.76574	−	8.51207i	−0.0898270	−	0.276459i
$949$	−22.8800	+	70.4174i	−0.742716	+	2.28585i
$950$	−6.83303	−	4.96449i	−0.221693	−	0.161069i
$951$	−1.76428	+	5.42989i	−0.0572107	+	0.176076i
$952$	19.5882	−	14.2317i	0.634859	−	0.461252i
$953$	7.02535	−	5.10422i	0.227573	−	0.165342i	−0.468156	−	0.883646i	$-0.655081\pi$
$953$	7.02535	−	5.10422i	0.227573	−	0.165342i	0.695729	+	0.718304i	$0.255081\pi$
$954$	−3.60555	−	2.61959i	−0.116734	−	0.0848123i
$955$	−0.855443			−0.0276815
$956$	11.0886			0.358630
$957$	0.0880591	+	0.0639787i	0.00284655	+	0.00206814i
$958$	−8.01240	−	24.6596i	−0.258869	−	0.796716i
$959$	4.83053	−	14.8668i	0.155986	−	0.480075i
$960$	1.00000			0.0322749
$961$	−24.0655	+	19.5410i	−0.776306	+	0.630356i
$962$	4.11050			0.132528
$963$	5.38860	−	16.5844i	0.173645	−	0.534425i
$964$	−0.874443	−	2.69126i	−0.0281639	−	0.0866796i
$965$	−3.98900	−	2.89818i	−0.128410	−	0.0932956i
$966$	−20.4045			−0.656503
$967$	−21.9712			−0.706546			−0.353273	−	0.935520i	$-0.614931\pi$
$967$	−21.9712			−0.706546			−0.353273	+	0.935520i	$0.614931\pi$
$968$	6.27962	+	4.56241i	0.201835	+	0.146641i
$969$	49.9425	−	36.2853i	1.60438	−	1.16565i
$970$	−2.44450	+	1.77603i	−0.0784880	+	0.0570249i
$971$	4.25167	−	13.0853i	0.136443	−	0.419927i	−0.859369	−	0.511356i	$-0.829143\pi$
$971$	4.25167	−	13.0853i	0.136443	−	0.419927i	0.995812	+	0.0914289i	$0.0291434\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	15.7967	−	48.6171i	0.506418	−	1.55859i
$974$	3.65669	+	11.2541i	0.117168	+	0.360606i
$975$	−4.65301	+	3.38061i	−0.149016	+	0.108266i
$976$	−1.22256	−	3.76265i	−0.0391331	−	0.120439i
$977$	−3.01737	−	9.28650i	−0.0965341	−	0.297101i	0.891116	−	0.453775i	$-0.149923\pi$
$977$	−3.01737	−	9.28650i	−0.0965341	−	0.297101i	−0.987650	+	0.156673i	$0.949923\pi$
$978$	15.3362	−	11.1424i	0.490399	−	0.356296i
$979$	−8.27020	−	25.4531i	−0.264317	−	0.813483i
$980$	1.22801	−	3.77943i	0.0392274	−	0.120730i
$981$	−15.9504	−	11.5887i	−0.509258	−	0.369997i
$982$	−4.67553	+	14.3898i	−0.149202	+	0.459198i
$983$	−2.13034	+	1.54778i	−0.0679473	+	0.0493666i	−0.621240	−	0.783620i	$-0.713371\pi$
$983$	−2.13034	+	1.54778i	−0.0679473	+	0.0493666i	0.553293	+	0.832987i	$0.313371\pi$
$984$	3.44533	−	2.50318i	0.109833	−	0.0797984i
$985$	−3.62388	−	2.63290i	−0.115466	−	0.0838913i
$986$	−0.442117			−0.0140799
$987$	−29.4076			−0.936054
$988$	−39.2997	−	28.5529i	−1.25029	−	0.908390i
$989$	−18.2155	−	56.0615i	−0.579219	−	1.78265i
$990$	−0.556055	+	1.71136i	−0.0176726	+	0.0543907i
$991$	28.4263			0.902992			0.451496	−	0.892273i	$-0.350891\pi$
$991$	28.4263			0.902992			0.451496	+	0.892273i	$0.350891\pi$
$992$	1.86206	+	5.24717i	0.0591203	+	0.166598i
$993$	−16.5319			−0.524623
$994$	1.37945	−	4.24552i	0.0437536	−	0.134660i
$995$	6.67417	+	20.5410i	0.211586	+	0.651193i
$996$	2.25921	+	1.64141i	0.0715857	+	0.0520101i
$997$	30.0413			0.951419			0.475710	−	0.879602i	$-0.342191\pi$
$997$	30.0413			0.951419			0.475710	+	0.879602i	$0.342191\pi$
$998$	−42.8864			−1.35754
$999$	−0.578198	−	0.420085i	−0.0182934	−	0.0132909i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.g.721.1	✓	16
31.4	even	5	inner	930.2.n.g.841.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.g.721.1	✓	16	1.1	even	1	trivial
930.2.n.g.841.1	yes	16	31.4	even	5	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.68002 - 1.94715i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-2.68002 - 1.94715i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(1.45577 + 1.05768i) q^{11} +(0.309017 - 0.951057i) q^{12} +(1.77729 + 5.46994i) q^{13} +(-2.68002 + 1.94715i) q^{14} +(0.309017 + 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(5.91309 - 4.29611i) q^{17} +(0.309017 + 0.951057i) q^{18} +(2.60999 - 8.03271i) q^{19} +(-0.809017 - 0.587785i) q^{20} +(1.02368 - 3.15056i) q^{21} +(1.45577 - 1.05768i) q^{22} +(4.98313 - 3.62045i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +5.75143 q^{26} +(-0.809017 - 0.587785i) q^{27} +(1.02368 + 3.15056i) q^{28} +(0.0186923 - 0.0575291i) q^{29} +1.00000 q^{30} +(1.86206 + 5.24717i) q^{31} +1.00000 q^{32} +(-0.556055 + 1.71136i) q^{33} +(-2.25860 - 6.95125i) q^{34} +(-2.68002 - 1.94715i) q^{35} +1.00000 q^{36} +0.714692 q^{37} +(-6.83303 - 4.96449i) q^{38} +(-4.65301 + 3.38061i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-1.31600 + 4.05022i) q^{41} +(-2.68002 - 1.94715i) q^{42} +(2.95731 - 9.10166i) q^{43} +(-0.556055 - 1.71136i) q^{44} +(-0.809017 + 0.587785i) q^{45} +(-1.90338 - 5.85802i) q^{46} +(-2.74322 - 8.44276i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(1.22801 + 3.77943i) q^{49} +(0.309017 - 0.951057i) q^{50} +(5.91309 + 4.29611i) q^{51} +(1.77729 - 5.46994i) q^{52} +(-3.60555 + 2.61959i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.45577 + 1.05768i) q^{55} +3.31269 q^{56} +8.44609 q^{57} +(-0.0489371 - 0.0355549i) q^{58} +(4.11365 + 12.6605i) q^{59} +(0.309017 - 0.951057i) q^{60} -3.95628 q^{61} +(5.56576 - 0.149456i) q^{62} +3.31269 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.77729 + 5.46994i) q^{65} +(1.45577 + 1.05768i) q^{66} +1.78397 q^{67} -7.30898 q^{68} +(4.98313 + 3.62045i) q^{69} +(-2.68002 + 1.94715i) q^{70} +(-1.09019 + 0.792067i) q^{71} +(0.309017 - 0.951057i) q^{72} +(10.4149 + 7.56687i) q^{73} +(0.220852 - 0.679712i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-6.83303 + 4.96449i) q^{76} +(-1.84204 - 5.66922i) q^{77} +(1.77729 + 5.46994i) q^{78} +(7.24080 - 5.26075i) q^{79} +(0.309017 + 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.44533 + 2.50318i) q^{82} +(-0.862940 + 2.65586i) q^{83} +(-2.68002 + 1.94715i) q^{84} +(5.91309 - 4.29611i) q^{85} +(-7.74233 - 5.62513i) q^{86} +0.0604896 q^{87} -1.79943 q^{88} +(-12.0325 - 8.74212i) q^{89} +(0.309017 + 0.951057i) q^{90} +(5.88762 - 18.1202i) q^{91} -6.15948 q^{92} +(-4.41494 + 3.39238i) q^{93} -8.87725 q^{94} +(2.60999 - 8.03271i) q^{95} +(0.309017 + 0.951057i) q^{96} +(-2.44450 - 1.77603i) q^{97} +3.97393 q^{98} -1.79943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9	\( 16 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 16 q^{5} + 16 q^{6} + q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{12} + 4 q^{13} + q^{14} - 4 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 12 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 16 q^{25} + 4 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 16 q^{30} + 17 q^{31} + 16 q^{32} + 5 q^{33} + 3 q^{34} + q^{35} + 16 q^{36} + 4 q^{37} + 3 q^{38} - 6 q^{39} - 4 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} + 5 q^{44} - 4 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 33 q^{49} - 4 q^{50} + 3 q^{51} + 4 q^{52} + 9 q^{53} - 4 q^{54} + 6 q^{56} + 18 q^{57} - 15 q^{58} - 7 q^{59} - 4 q^{60} + 30 q^{61} + 12 q^{62} + 6 q^{63} - 4 q^{64} + 4 q^{65} + 86 q^{67} - 12 q^{68} - 2 q^{69} + q^{70} - 3 q^{71} - 4 q^{72} + 8 q^{73} - q^{74} - 4 q^{75} + 3 q^{76} + 2 q^{77} + 4 q^{78} + 30 q^{79} - 4 q^{80} - 4 q^{81} - 7 q^{82} + 16 q^{83} + q^{84} + 3 q^{85} - 12 q^{86} - 10 q^{88} - 29 q^{89} - 4 q^{90} + 30 q^{91} + 8 q^{92} - 8 q^{93} + 24 q^{94} - 12 q^{95} - 4 q^{96} - 5 q^{97} + 62 q^{98} - 10 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 16 * q^5 + 16 * q^6 + q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^12 + 4 * q^13 + q^14 - 4 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 12 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 16 * q^25 + 4 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 16 * q^30 + 17 * q^31 + 16 * q^32 + 5 * q^33 + 3 * q^34 + q^35 + 16 * q^36 + 4 * q^37 + 3 * q^38 - 6 * q^39 - 4 * q^40 - 7 * q^41 + q^42 - 2 * q^43 + 5 * q^44 - 4 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 33 * q^49 - 4 * q^50 + 3 * q^51 + 4 * q^52 + 9 * q^53 - 4 * q^54 + 6 * q^56 + 18 * q^57 - 15 * q^58 - 7 * q^59 - 4 * q^60 + 30 * q^61 + 12 * q^62 + 6 * q^63 - 4 * q^64 + 4 * q^65 + 86 * q^67 - 12 * q^68 - 2 * q^69 + q^70 - 3 * q^71 - 4 * q^72 + 8 * q^73 - q^74 - 4 * q^75 + 3 * q^76 + 2 * q^77 + 4 * q^78 + 30 * q^79 - 4 * q^80 - 4 * q^81 - 7 * q^82 + 16 * q^83 + q^84 + 3 * q^85 - 12 * q^86 - 10 * q^88 - 29 * q^89 - 4 * q^90 + 30 * q^91 + 8 * q^92 - 8 * q^93 + 24 * q^94 - 12 * q^95 - 4 * q^96 - 5 * q^97 + 62 * q^98 - 10 * q^99

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