LMFDB - Embedded newform 930.2.z.a.529.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.2
Root			$-0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	930.529
Dual form			930.2.z.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +2.23607 q^{5} -1.00000 q^{6} +(3.07768 - 1.00000i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +2.23607 q^{5} -1.00000 q^{6} +(3.07768 - 1.00000i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.31433 - 1.80902i) q^{10} +(-1.42705 - 4.39201i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(4.02874 + 5.54508i) q^{13} +(1.00000 - 3.07768i) q^{14} +(-1.31433 - 1.80902i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.61653 + 1.50000i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-3.61803 - 2.62866i) q^{19} +(-0.690983 - 2.12663i) q^{20} +(-2.61803 - 1.90211i) q^{21} +(-4.39201 - 1.42705i) q^{22} +(0.812299 + 0.263932i) q^{23} +(0.309017 + 0.951057i) q^{24} +5.00000 q^{25} +6.85410 q^{26} +(0.951057 - 0.309017i) q^{27} +(-1.90211 - 2.61803i) q^{28} +(0.118034 + 0.0857567i) q^{29} -2.23607 q^{30} +(-3.30902 + 4.47777i) q^{31} +1.00000i q^{32} +(-2.71441 + 3.73607i) q^{33} +(3.92705 - 2.85317i) q^{34} +(6.88191 - 2.23607i) q^{35} +1.00000 q^{36} -4.14590i q^{37} +(-4.25325 + 1.38197i) q^{38} +(2.11803 - 6.51864i) q^{39} +(-2.12663 - 0.690983i) q^{40} +(-4.61803 - 3.35520i) q^{41} +(-3.07768 + 1.00000i) q^{42} +(-2.35114 + 3.23607i) q^{43} +(-3.73607 + 2.71441i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(0.690983 - 0.502029i) q^{46} +(-4.75528 - 6.54508i) q^{47} +(0.951057 + 0.309017i) q^{48} +(2.80902 - 2.04087i) q^{49} +(2.93893 - 4.04508i) q^{50} +(-1.50000 - 4.61653i) q^{51} +(4.02874 - 5.54508i) q^{52} +(5.42882 + 1.76393i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-3.19098 - 9.82084i) q^{55} -3.23607 q^{56} +4.47214i q^{57} +(0.138757 - 0.0450850i) q^{58} +(-7.97214 + 5.79210i) q^{59} +(-1.31433 + 1.80902i) q^{60} +7.23607 q^{61} +(1.67760 + 5.30902i) q^{62} +3.23607i q^{63} +(0.809017 + 0.587785i) q^{64} +(9.00854 + 12.3992i) q^{65} +(1.42705 + 4.39201i) q^{66} -8.00000i q^{67} -4.85410i q^{68} +(-0.263932 - 0.812299i) q^{69} +(2.23607 - 6.88191i) q^{70} +(-1.23607 + 3.80423i) q^{71} +(0.587785 - 0.809017i) q^{72} +(-14.2128 + 4.61803i) q^{73} +(-3.35410 - 2.43690i) q^{74} +(-2.93893 - 4.04508i) q^{75} +(-1.38197 + 4.25325i) q^{76} +(-8.78402 - 12.0902i) q^{77} +(-4.02874 - 5.54508i) q^{78} +(1.57295 - 4.84104i) q^{79} +(-1.80902 + 1.31433i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.42882 + 1.76393i) q^{82} +(4.25325 - 5.85410i) q^{83} +(-1.00000 + 3.07768i) q^{84} +(10.3229 + 3.35410i) q^{85} +(1.23607 + 3.80423i) q^{86} -0.145898i q^{87} +4.61803i q^{88} +(-4.85410 - 14.9394i) q^{89} +(1.31433 + 1.80902i) q^{90} +(17.9443 + 13.0373i) q^{91} -0.854102i q^{92} +(5.56758 + 0.0450850i) q^{93} -8.09017 q^{94} +(-8.09017 - 5.87785i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-16.1150 + 5.23607i) q^{97} -3.47214i q^{98} +4.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9} + 2 q^{11} + 8 q^{14} - 2 q^{16} - 20 q^{19} - 10 q^{20} - 12 q^{21} - 2 q^{24} + 40 q^{25} + 28 q^{26} - 8 q^{29} - 22 q^{31} + 18 q^{34} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 12 q^{44} - 10 q^{45} + 10 q^{46} + 18 q^{49} - 12 q^{51} - 2 q^{54} - 30 q^{55} - 8 q^{56} - 28 q^{59} + 40 q^{61} + 2 q^{64} - 2 q^{66} - 20 q^{69} + 8 q^{71} - 20 q^{76} + 26 q^{79} - 10 q^{80} - 2 q^{81} - 8 q^{84} - 8 q^{86} - 12 q^{89} + 72 q^{91} - 20 q^{94} - 20 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 + 2 * q^11 + 8 * q^14 - 2 * q^16 - 20 * q^19 - 10 * q^20 - 12 * q^21 - 2 * q^24 + 40 * q^25 + 28 * q^26 - 8 * q^29 - 22 * q^31 + 18 * q^34 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 12 * q^44 - 10 * q^45 + 10 * q^46 + 18 * q^49 - 12 * q^51 - 2 * q^54 - 30 * q^55 - 8 * q^56 - 28 * q^59 + 40 * q^61 + 2 * q^64 - 2 * q^66 - 20 * q^69 + 8 * q^71 - 20 * q^76 + 26 * q^79 - 10 * q^80 - 2 * q^81 - 8 * q^84 - 8 * q^86 - 12 * q^89 + 72 * q^91 - 20 * q^94 - 20 * q^95 + 2 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	2.23607			1.00000
$5$	2.23607			1.00000
$6$	−1.00000			−0.408248
$7$	3.07768	−	1.00000i	1.16326	−	0.377964i	0.337134	−	0.941457i	$-0.390543\pi$
$7$	3.07768	−	1.00000i	1.16326	−	0.377964i	0.826121	+	0.563492i	$0.190543\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	1.31433	−	1.80902i	0.415627	−	0.572061i
$11$	−1.42705	−	4.39201i	−0.430272	−	1.32424i	−0.897855	−	0.440292i	$-0.854875\pi$
$11$	−1.42705	−	4.39201i	−0.430272	−	1.32424i	0.467583	−	0.883949i	$-0.345125\pi$
$12$	−0.587785	+	0.809017i	−0.169679	+	0.233543i
$13$	4.02874	+	5.54508i	1.11737	+	1.53793i	0.810085	+	0.586313i	$0.199421\pi$
$13$	4.02874	+	5.54508i	1.11737	+	1.53793i	0.307287	+	0.951617i	$0.400579\pi$
$14$	1.00000	−	3.07768i	0.267261	−	0.822546i
$15$	−1.31433	−	1.80902i	−0.339358	−	0.467086i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	4.61653	+	1.50000i	1.11967	+	0.363803i	0.809642	−	0.586924i	$-0.199661\pi$
$17$	4.61653	+	1.50000i	1.11967	+	0.363803i	0.310029	+	0.950727i	$0.399661\pi$
$18$	0.587785	+	0.809017i	0.138542	+	0.190687i
$19$	−3.61803	−	2.62866i	−0.830034	−	0.603055i	0.0895350	−	0.995984i	$-0.471462\pi$
$19$	−3.61803	−	2.62866i	−0.830034	−	0.603055i	−0.919569	+	0.392929i	$0.871462\pi$
$20$	−0.690983	−	2.12663i	−0.154508	−	0.475528i
$21$	−2.61803	−	1.90211i	−0.571302	−	0.415075i
$22$	−4.39201	−	1.42705i	−0.936380	−	0.304248i
$23$	0.812299	+	0.263932i	0.169376	+	0.0550336i	0.392477	−	0.919762i	$-0.371618\pi$
$23$	0.812299	+	0.263932i	0.169376	+	0.0550336i	−0.223101	+	0.974795i	$0.571618\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	5.00000			1.00000
$26$	6.85410			1.34420
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−1.90211	−	2.61803i	−0.359466	−	0.494762i
$29$	0.118034	+	0.0857567i	0.0219184	+	0.0159246i	0.598691	−	0.800980i	$-0.295688\pi$
$29$	0.118034	+	0.0857567i	0.0219184	+	0.0159246i	−0.576772	+	0.816905i	$0.695688\pi$
$30$	−2.23607			−0.408248
$31$	−3.30902	+	4.47777i	−0.594317	+	0.804231i
$31$	−3.30902	+	4.47777i	−0.594317	+	0.804231i
$32$			1.00000i			0.176777i
$33$	−2.71441	+	3.73607i	−0.472519	+	0.650366i
$34$	3.92705	−	2.85317i	0.673484	−	0.489315i
$35$	6.88191	−	2.23607i	1.16326	−	0.377964i
$36$	1.00000			0.166667
$37$		−	4.14590i		−	0.681581i	−0.940139	−	0.340791i	$-0.889305\pi$
$37$		−	4.14590i		−	0.681581i	0.940139	−	0.340791i	$-0.110695\pi$
$38$	−4.25325	+	1.38197i	−0.689969	+	0.224184i
$39$	2.11803	−	6.51864i	0.339157	−	1.04382i
$40$	−2.12663	−	0.690983i	−0.336249	−	0.109254i
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	0.165557	−	0.986200i	$-0.447058\pi$
$41$	−4.61803	−	3.35520i	−0.721216	−	0.523994i	−0.886772	+	0.462206i	$0.847058\pi$
$42$	−3.07768	+	1.00000i	−0.474897	+	0.154303i
$43$	−2.35114	+	3.23607i	−0.358546	+	0.493496i	−0.949743	−	0.313031i	$-0.898656\pi$
$43$	−2.35114	+	3.23607i	−0.358546	+	0.493496i	0.591197	+	0.806527i	$0.298656\pi$
$44$	−3.73607	+	2.71441i	−0.563233	+	0.409213i
$45$	−0.690983	+	2.12663i	−0.103006	+	0.317019i
$46$	0.690983	−	0.502029i	0.101880	−	0.0740201i
$47$	−4.75528	−	6.54508i	−0.693629	−	0.954699i	−0.999996	−	0.00278525i	$-0.999113\pi$
$47$	−4.75528	−	6.54508i	−0.693629	−	0.954699i	0.306367	−	0.951914i	$-0.400887\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	2.80902	−	2.04087i	0.401288	−	0.291553i
$50$	2.93893	−	4.04508i	0.415627	−	0.572061i
$51$	−1.50000	−	4.61653i	−0.210042	−	0.646443i
$52$	4.02874	−	5.54508i	0.558686	−	0.768965i
$53$	5.42882	+	1.76393i	0.745706	+	0.242295i	0.657133	−	0.753775i	$-0.271769\pi$
$53$	5.42882	+	1.76393i	0.745706	+	0.242295i	0.0885737	+	0.996070i	$0.471769\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	−3.19098	−	9.82084i	−0.430272	−	1.32424i
$56$	−3.23607			−0.432438
$57$			4.47214i			0.592349i
$58$	0.138757	−	0.0450850i	0.0182197	−	0.00591995i
$59$	−7.97214	+	5.79210i	−1.03788	+	0.754067i	−0.969871	−	0.243618i	$-0.921666\pi$
$59$	−7.97214	+	5.79210i	−1.03788	+	0.754067i	−0.0680124	+	0.997684i	$0.521666\pi$
$60$	−1.31433	+	1.80902i	−0.169679	+	0.233543i
$61$	7.23607			0.926484			0.463242	−	0.886232i	$-0.346686\pi$
$61$	7.23607			0.926484			0.463242	+	0.886232i	$0.346686\pi$
$62$	1.67760	+	5.30902i	0.213055	+	0.674246i
$63$			3.23607i			0.407706i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	9.00854	+	12.3992i	1.11737	+	1.53793i
$66$	1.42705	+	4.39201i	0.175658	+	0.540619i
$67$		−	8.00000i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$67$		−	8.00000i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$68$		−	4.85410i		−	0.588646i
$69$	−0.263932	−	0.812299i	−0.0317737	−	0.0977893i
$70$	2.23607	−	6.88191i	0.267261	−	0.822546i
$71$	−1.23607	+	3.80423i	−0.146694	+	0.451479i	−0.997225	−	0.0744468i	$-0.976281\pi$
$71$	−1.23607	+	3.80423i	−0.146694	+	0.451479i	0.850531	+	0.525925i	$0.176281\pi$
$72$	0.587785	−	0.809017i	0.0692712	−	0.0953436i
$73$	−14.2128	+	4.61803i	−1.66349	+	0.540500i	−0.981599	−	0.190955i	$-0.938841\pi$
$73$	−14.2128	+	4.61803i	−1.66349	+	0.540500i	−0.681889	+	0.731455i	$0.738841\pi$
$74$	−3.35410	−	2.43690i	−0.389906	−	0.283284i
$75$	−2.93893	−	4.04508i	−0.339358	−	0.467086i
$76$	−1.38197	+	4.25325i	−0.158522	+	0.487882i
$77$	−8.78402	−	12.0902i	−1.00103	−	1.37780i
$78$	−4.02874	−	5.54508i	−0.456165	−	0.627857i
$79$	1.57295	−	4.84104i	0.176971	−	0.544659i	−0.822747	−	0.568407i	$-0.807560\pi$
$79$	1.57295	−	4.84104i	0.176971	−	0.544659i	0.999718	+	0.0237477i	$0.00755984\pi$
$80$	−1.80902	+	1.31433i	−0.202254	+	0.146946i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−5.42882	+	1.76393i	−0.599513	+	0.194794i
$83$	4.25325	−	5.85410i	0.466855	−	0.642571i	−0.509057	−	0.860733i	$-0.670006\pi$
$83$	4.25325	−	5.85410i	0.466855	−	0.642571i	0.975913	+	0.218161i	$0.0700059\pi$
$84$	−1.00000	+	3.07768i	−0.109109	+	0.335803i
$85$	10.3229	+	3.35410i	1.11967	+	0.363803i
$86$	1.23607	+	3.80423i	0.133289	+	0.410220i
$87$		−	0.145898i		−	0.0156419i
$88$			4.61803i			0.492284i
$89$	−4.85410	−	14.9394i	−0.514534	−	1.58357i	−0.784129	−	0.620598i	$-0.786890\pi$
$89$	−4.85410	−	14.9394i	−0.514534	−	1.58357i	0.269595	−	0.962974i	$-0.413110\pi$
$90$	1.31433	+	1.80902i	0.138542	+	0.190687i
$91$	17.9443	+	13.0373i	1.88107	+	1.36668i
$92$		−	0.854102i		−	0.0890463i
$93$	5.56758	+	0.0450850i	0.577331	+	0.00467509i
$94$	−8.09017			−0.834437
$95$	−8.09017	−	5.87785i	−0.830034	−	0.603055i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−16.1150	+	5.23607i	−1.63623	+	0.531642i	−0.975691	−	0.219152i	$-0.929671\pi$
$97$	−16.1150	+	5.23607i	−1.63623	+	0.531642i	−0.660536	+	0.750795i	$0.729671\pi$
$98$		−	3.47214i		−	0.350739i
$99$	4.61803			0.464130
$100$	−1.54508	−	4.75528i	−0.154508	−	0.475528i
$101$	1.66312	−	5.11855i	0.165487	−	0.509315i	−0.833585	−	0.552391i	$-0.813716\pi$
$101$	1.66312	−	5.11855i	0.165487	−	0.509315i	0.999072	+	0.0430756i	$0.0137156\pi$
$102$	−4.61653	−	1.50000i	−0.457104	−	0.148522i
$103$	−8.33499	+	11.4721i	−0.821271	+	1.13038i	0.168214	+	0.985751i	$0.446200\pi$
$103$	−8.33499	+	11.4721i	−0.821271	+	1.13038i	−0.989485	+	0.144633i	$0.953800\pi$
$104$	−2.11803	−	6.51864i	−0.207690	−	0.639205i
$105$	−5.85410	−	4.25325i	−0.571302	−	0.415075i
$106$	4.61803	−	3.35520i	0.448543	−	0.325886i
$107$	2.17963	+	0.708204i	0.210713	+	0.0684647i	0.412471	−	0.910971i	$-0.364666\pi$
$107$	2.17963	+	0.708204i	0.210713	+	0.0684647i	−0.201759	+	0.979435i	$0.564666\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	2.85410	−	2.07363i	0.273373	−	0.198617i	−0.442649	−	0.896695i	$-0.645961\pi$
$109$	2.85410	−	2.07363i	0.273373	−	0.198617i	0.716022	+	0.698078i	$0.245961\pi$
$110$	−9.82084	−	3.19098i	−0.936380	−	0.304248i
$111$	−3.35410	+	2.43690i	−0.318357	+	0.231300i
$112$	−1.90211	+	2.61803i	−0.179733	+	0.247381i
$113$	0.449028	−	0.145898i	0.0422410	−	0.0137249i	−0.287820	−	0.957684i	$-0.592931\pi$
$113$	0.449028	−	0.145898i	0.0422410	−	0.0137249i	0.330061	+	0.943960i	$0.392931\pi$
$114$	3.61803	+	2.62866i	0.338860	+	0.246196i
$115$	1.81636	+	0.590170i	0.169376	+	0.0550336i
$116$	0.0450850	−	0.138757i	0.00418603	−	0.0128833i
$117$	−6.51864	+	2.11803i	−0.602648	+	0.195812i
$118$			9.85410i			0.907144i
$119$	15.7082			1.43997
$120$	0.690983	+	2.12663i	0.0630778	+	0.194134i
$121$	−8.35410	+	6.06961i	−0.759464	+	0.551783i
$122$	4.25325	−	5.85410i	0.385072	−	0.530005i
$123$			5.70820i			0.514691i
$124$	5.28115	+	1.76336i	0.474262	+	0.158354i
$125$	11.1803			1.00000
$126$	2.61803	+	1.90211i	0.233233	+	0.169454i
$127$	12.4822	+	17.1803i	1.10762	+	1.52451i	0.824876	+	0.565313i	$0.191245\pi$
$127$	12.4822	+	17.1803i	1.10762	+	1.52451i	0.282744	+	0.959195i	$0.408755\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	4.00000			0.352180
$130$	15.3262			1.34420
$131$	5.80902	+	17.8783i	0.507536	+	1.56204i	0.796465	+	0.604685i	$0.206701\pi$
$131$	5.80902	+	17.8783i	0.507536	+	1.56204i	−0.288929	+	0.957351i	$0.593299\pi$
$132$	4.39201	+	1.42705i	0.382276	+	0.124209i
$133$	−13.7638	−	4.47214i	−1.19347	−	0.387783i
$134$	−6.47214	−	4.70228i	−0.559107	−	0.406215i
$135$	2.12663	−	0.690983i	0.183031	−	0.0594703i
$136$	−3.92705	−	2.85317i	−0.336742	−	0.244657i
$137$	10.2371	+	14.0902i	0.874615	+	1.20380i	0.977883	+	0.209151i	$0.0670700\pi$
$137$	10.2371	+	14.0902i	0.874615	+	1.20380i	−0.103268	+	0.994654i	$0.532930\pi$
$138$	−0.812299	−	0.263932i	−0.0691475	−	0.0224674i
$139$	−12.0902	+	8.78402i	−1.02547	+	0.745051i	−0.967398	−	0.253261i	$-0.918497\pi$
$139$	−12.0902	+	8.78402i	−1.02547	+	0.745051i	−0.0580769	+	0.998312i	$0.518497\pi$
$140$	−4.25325	−	5.85410i	−0.359466	−	0.494762i
$141$	−2.50000	+	7.69421i	−0.210538	+	0.647969i
$142$	2.35114	+	3.23607i	0.197303	+	0.271565i
$143$	18.6049	−	25.6074i	1.55582	−	2.14140i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	0.263932	+	0.191758i	0.0219184	+	0.0159246i
$146$	−4.61803	+	14.2128i	−0.382191	+	1.17626i
$147$	−3.30220	−	1.07295i	−0.272361	−	0.0884953i
$148$	−3.94298	+	1.28115i	−0.324111	+	0.105310i
$149$	12.3820			1.01437			0.507185	−	0.861837i	$-0.330686\pi$
$149$	12.3820			1.01437			0.507185	+	0.861837i	$0.330686\pi$
$150$	−5.00000			−0.408248
$151$	5.52786	+	17.0130i	0.449851	+	1.38450i	0.877075	+	0.480354i	$0.159492\pi$
$151$	5.52786	+	17.0130i	0.449851	+	1.38450i	−0.427224	+	0.904146i	$0.640508\pi$
$152$	2.62866	+	3.61803i	0.213212	+	0.293461i
$153$	−2.85317	+	3.92705i	−0.230665	+	0.317483i
$154$	−14.9443			−1.20424
$155$	−7.39919	+	10.0126i	−0.594317	+	0.804231i
$156$	−6.85410			−0.548767
$157$	−3.47371	+	4.78115i	−0.277232	+	0.381578i	−0.924815	−	0.380418i	$-0.875780\pi$
$157$	−3.47371	+	4.78115i	−0.277232	+	0.381578i	0.647582	+	0.761995i	$0.275780\pi$
$158$	−2.99193	−	4.11803i	−0.238025	−	0.327613i
$159$	−1.76393	−	5.42882i	−0.139889	−	0.430534i
$160$			2.23607i			0.176777i
$161$	2.76393			0.217828
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	15.2497	+	4.95492i	1.19445	+	0.388099i	0.837715	−	0.546108i	$-0.183891\pi$
$163$	15.2497	+	4.95492i	1.19445	+	0.388099i	0.356731	+	0.934207i	$0.383891\pi$
$164$	−1.76393	+	5.42882i	−0.137740	+	0.423920i
$165$	−6.06961	+	8.35410i	−0.472519	+	0.650366i
$166$	−2.23607	−	6.88191i	−0.173553	−	0.534140i
$167$	1.71036	−	2.35410i	0.132351	−	0.182166i	−0.737698	−	0.675131i	$-0.764087\pi$
$167$	1.71036	−	2.35410i	0.132351	−	0.182166i	0.870049	+	0.492965i	$0.164087\pi$
$168$	1.90211	+	2.61803i	0.146751	+	0.201986i
$169$	−10.5000	+	32.3157i	−0.807692	+	2.48582i
$170$	8.78115	−	6.37988i	0.673484	−	0.489315i
$171$	3.61803	−	2.62866i	0.276678	−	0.201018i
$172$	3.80423	+	1.23607i	0.290070	+	0.0942493i
$173$	5.98385	+	8.23607i	0.454944	+	0.626177i	0.973451	−	0.228897i	$-0.0735119\pi$
$173$	5.98385	+	8.23607i	0.454944	+	0.626177i	−0.518507	+	0.855074i	$0.673512\pi$
$174$	−0.118034	−	0.0857567i	−0.00894813	−	0.00650120i
$175$	15.3884	−	5.00000i	1.16326	−	0.377964i
$176$	3.73607	+	2.71441i	0.281617	+	0.204607i
$177$	9.37181	+	3.04508i	0.704428	+	0.228883i
$178$	−14.9394	−	4.85410i	−1.11975	−	0.363830i
$179$	−5.40983	−	16.6497i	−0.404350	−	1.24446i	−0.921437	−	0.388528i	$-0.872984\pi$
$179$	−5.40983	−	16.6497i	−0.404350	−	1.24446i	0.517087	−	0.855933i	$-0.327016\pi$
$180$	2.23607			0.166667
$181$	−8.76393			−0.651418			−0.325709	−	0.945470i	$-0.605603\pi$
$181$	−8.76393			−0.651418			−0.325709	+	0.945470i	$0.605603\pi$
$182$	21.0948	−	6.85410i	1.56365	−	0.508060i
$183$	−4.25325	−	5.85410i	−0.314410	−	0.432748i
$184$	−0.690983	−	0.502029i	−0.0509399	−	0.0370100i
$185$		−	9.27051i		−	0.681581i
$186$	3.30902	−	4.47777i	0.242629	−	0.328326i
$187$		−	22.4164i		−	1.63925i
$188$	−4.75528	+	6.54508i	−0.346815	+	0.477349i
$189$	2.61803	−	1.90211i	0.190434	−	0.138358i
$190$	−9.51057	+	3.09017i	−0.689969	+	0.224184i
$191$	−2.76393			−0.199991			−0.0999956	−	0.994988i	$-0.531883\pi$
$191$	−2.76393			−0.199991			−0.0999956	+	0.994988i	$0.531883\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	4.08174	−	1.32624i	0.293810	−	0.0954647i	−0.158403	−	0.987375i	$-0.550635\pi$
$193$	4.08174	−	1.32624i	0.293810	−	0.0954647i	0.452213	+	0.891910i	$0.350635\pi$
$194$	−5.23607	+	16.1150i	−0.375928	+	1.15699i
$195$	4.73607	−	14.5761i	0.339157	−	1.04382i
$196$	−2.80902	−	2.04087i	−0.200644	−	0.145776i
$197$	10.4086	−	3.38197i	0.741584	−	0.240955i	0.0862278	−	0.996275i	$-0.472519\pi$
$197$	10.4086	−	3.38197i	0.741584	−	0.240955i	0.655356	+	0.755320i	$0.272519\pi$
$198$	2.71441	−	3.73607i	0.192905	−	0.265511i
$199$	17.2984	−	12.5680i	1.22625	−	0.890922i	0.229646	−	0.973274i	$-0.426243\pi$
$199$	17.2984	−	12.5680i	1.22625	−	0.890922i	0.996603	+	0.0823520i	$0.0262432\pi$
$200$	−4.75528	−	1.54508i	−0.336249	−	0.109254i
$201$	−6.47214	+	4.70228i	−0.456509	+	0.331673i
$202$	−3.16344	−	4.35410i	−0.222579	−	0.306354i
$203$	0.449028	+	0.145898i	0.0315156	+	0.0102400i
$204$	−3.92705	+	2.85317i	−0.274949	+	0.199762i
$205$	−10.3262	−	7.50245i	−0.721216	−	0.523994i
$206$	4.38197	+	13.4863i	0.305306	+	0.939635i
$207$	−0.502029	+	0.690983i	−0.0348934	+	0.0480266i
$208$	−6.51864	−	2.11803i	−0.451986	−	0.146859i
$209$	−6.38197	+	19.6417i	−0.441450	+	1.35864i
$210$	−6.88191	+	2.23607i	−0.474897	+	0.154303i
$211$	−18.6525			−1.28409			−0.642045	−	0.766667i	$-0.721914\pi$
$211$	−18.6525			−1.28409			−0.642045	+	0.766667i	$0.721914\pi$
$212$		−	5.70820i		−	0.392041i
$213$	3.80423	−	1.23607i	0.260661	−	0.0846940i
$214$	1.85410	−	1.34708i	0.126744	−	0.0920848i
$215$	−5.25731	+	7.23607i	−0.358546	+	0.493496i
$216$	−1.00000			−0.0680414
$217$	−5.70634	+	17.0902i	−0.387372	+	1.16016i
$218$		−	3.52786i		−	0.238937i
$219$	12.0902	+	8.78402i	0.816978	+	0.593569i
$220$	−8.35410	+	6.06961i	−0.563233	+	0.409213i
$221$	10.2812	+	31.6421i	0.691585	+	2.12848i
$222$			4.14590i			0.278254i
$223$			9.88854i			0.662186i	0.943598	+	0.331093i	$0.107417\pi$
$223$			9.88854i			0.662186i	−0.943598	+	0.331093i	$0.892583\pi$
$224$	1.00000	+	3.07768i	0.0668153	+	0.205636i
$225$	−1.54508	+	4.75528i	−0.103006	+	0.317019i
$226$	0.145898	−	0.449028i	0.00970499	−	0.0298689i
$227$	−4.53077	+	6.23607i	−0.300718	+	0.413902i	−0.932458	−	0.361277i	$-0.882341\pi$
$227$	−4.53077	+	6.23607i	−0.300718	+	0.413902i	0.631741	+	0.775180i	$0.282341\pi$
$228$	4.25325	−	1.38197i	0.281679	−	0.0915229i
$229$	19.0902	+	13.8698i	1.26151	+	0.916544i	0.998831	−	0.0483387i	$-0.0153927\pi$
$229$	19.0902	+	13.8698i	1.26151	+	0.916544i	0.262683	+	0.964882i	$0.415393\pi$
$230$	1.54508	−	1.12257i	0.101880	−	0.0740201i
$231$	−4.61803	+	14.2128i	−0.303844	+	0.935137i
$232$	−0.0857567	−	0.118034i	−0.00563020	−	0.00774931i
$233$	−6.10237	−	8.39919i	−0.399779	−	0.550249i	0.560909	−	0.827877i	$-0.310452\pi$
$233$	−6.10237	−	8.39919i	−0.399779	−	0.550249i	−0.960689	+	0.277628i	$0.910452\pi$
$234$	−2.11803	+	6.51864i	−0.138460	+	0.426137i
$235$	−10.6331	−	14.6353i	−0.693629	−	0.954699i
$236$	7.97214	+	5.79210i	0.518942	+	0.377033i
$237$	−4.84104	+	1.57295i	−0.314459	+	0.102174i
$238$	9.23305	−	12.7082i	0.598490	−	0.823751i
$239$	7.76393	−	23.8949i	0.502207	−	1.54563i	−0.303209	−	0.952924i	$-0.598058\pi$
$239$	7.76393	−	23.8949i	0.502207	−	1.54563i	0.805416	−	0.592710i	$-0.201942\pi$
$240$	2.12663	+	0.690983i	0.137273	+	0.0446028i
$241$	2.97214	+	9.14729i	0.191452	+	0.589229i	1.00000		0.000798186i	$0.000254071\pi$
$241$	2.97214	+	9.14729i	0.191452	+	0.589229i	−0.808548	+	0.588431i	$0.799746\pi$
$242$			10.3262i			0.663796i
$243$			1.00000i			0.0641500i
$244$	−2.23607	−	6.88191i	−0.143150	−	0.440569i
$245$	6.28115	−	4.56352i	0.401288	−	0.291553i
$246$	4.61803	+	3.35520i	0.294435	+	0.213920i
$247$		−	30.6525i		−	1.95037i
$248$	4.53077	−	3.23607i	0.287704	−	0.205491i
$249$	−7.23607			−0.458567
$250$	6.57164	−	9.04508i	0.415627	−	0.572061i
$251$	1.54508	−	1.12257i	0.0975249	−	0.0708560i	−0.537954	−	0.842974i	$-0.680803\pi$
$251$	1.54508	−	1.12257i	0.0975249	−	0.0708560i	0.635479	+	0.772118i	$0.280803\pi$
$252$	3.07768	−	1.00000i	0.193876	−	0.0629941i
$253$		−	3.94427i		−	0.247974i
$254$	21.2361			1.33247
$255$	−3.35410	−	10.3229i	−0.210042	−	0.646443i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−10.8249	−	3.51722i	−0.675238	−	0.219398i	−0.0487288	−	0.998812i	$-0.515517\pi$
$257$	−10.8249	−	3.51722i	−0.675238	−	0.219398i	−0.626509	+	0.779414i	$0.715517\pi$
$258$	2.35114	−	3.23607i	0.146376	−	0.201469i
$259$	−4.14590	−	12.7598i	−0.257614	−	0.792853i
$260$	9.00854	−	12.3992i	0.558686	−	0.768965i
$261$	−0.118034	+	0.0857567i	−0.00730612	+	0.00530821i
$262$	17.8783	+	5.80902i	1.10453	+	0.358882i
$263$	13.1230	+	18.0623i	0.809201	+	1.11377i	0.991446	+	0.130516i	$0.0416635\pi$
$263$	13.1230	+	18.0623i	0.809201	+	1.11377i	−0.182245	+	0.983253i	$0.558336\pi$
$264$	3.73607	−	2.71441i	0.229939	−	0.167061i
$265$	12.1392	+	3.94427i	0.745706	+	0.242295i
$266$	−11.7082	+	8.50651i	−0.717876	+	0.521567i
$267$	−9.23305	+	12.7082i	−0.565054	+	0.777729i
$268$	−7.60845	+	2.47214i	−0.464760	+	0.151010i
$269$	−15.3992	−	11.1882i	−0.938905	−	0.682154i	0.00925184	−	0.999957i	$-0.497055\pi$
$269$	−15.3992	−	11.1882i	−0.938905	−	0.682154i	−0.948157	+	0.317803i	$0.897055\pi$
$270$	0.690983	−	2.12663i	0.0420519	−	0.129422i
$271$	−2.79180	+	8.59226i	−0.169590	+	0.521943i	−0.999345	−	0.0361840i	$-0.988480\pi$
$271$	−2.79180	+	8.59226i	−0.169590	+	0.521943i	0.829756	+	0.558127i	$0.188480\pi$
$272$	−4.61653	+	1.50000i	−0.279918	+	0.0909509i
$273$		−	22.1803i		−	1.34242i
$274$	17.4164			1.05216
$275$	−7.13525	−	21.9601i	−0.430272	−	1.32424i
$276$	−0.690983	+	0.502029i	−0.0415923	+	0.0302186i
$277$	9.73508	−	13.3992i	0.584924	−	0.805079i	−0.409300	−	0.912400i	$-0.634227\pi$
$277$	9.73508	−	13.3992i	0.584924	−	0.805079i	0.994224	+	0.107321i	$0.0342271\pi$
$278$			14.9443i			0.896298i
$279$	−3.23607	−	4.53077i	−0.193738	−	0.271250i
$280$	−7.23607			−0.432438
$281$	−26.1803	−	19.0211i	−1.56179	−	1.13471i	−0.934525	−	0.355898i	$-0.884175\pi$
$281$	−26.1803	−	19.0211i	−1.56179	−	1.13471i	−0.627263	−	0.778807i	$-0.715825\pi$
$282$	4.75528	+	6.54508i	0.283173	+	0.389754i
$283$	−5.06555	+	1.64590i	−0.301116	+	0.0978385i	−0.455678	−	0.890145i	$-0.650603\pi$
$283$	−5.06555	+	1.64590i	−0.301116	+	0.0978385i	0.154562	+	0.987983i	$0.450603\pi$
$284$	4.00000			0.237356
$285$			10.0000i			0.592349i
$286$	−9.78115	−	30.1033i	−0.578372	−	1.78005i
$287$	−17.5680	−	5.70820i	−1.03701	−	0.336945i
$288$	−0.951057	−	0.309017i	−0.0560415	−	0.0182090i
$289$	5.30902	+	3.85723i	0.312295	+	0.226896i
$290$	0.310271	−	0.100813i	0.0182197	−	0.00591995i
$291$	13.7082	+	9.95959i	0.803589	+	0.583842i
$292$	8.78402	+	12.0902i	0.514046	+	0.707524i
$293$	−10.6861	−	3.47214i	−0.624291	−	0.202844i	−0.0202463	−	0.999795i	$-0.506445\pi$
$293$	−10.6861	−	3.47214i	−0.624291	−	0.202844i	−0.604044	+	0.796951i	$0.706445\pi$
$294$	−2.80902	+	2.04087i	−0.163825	+	0.119026i
$295$	−17.8262	+	12.9515i	−1.03788	+	0.754067i
$296$	−1.28115	+	3.94298i	−0.0744655	+	0.229181i
$297$	−2.71441	−	3.73607i	−0.157506	−	0.216789i
$298$	7.27794	−	10.0172i	0.421600	−	0.580282i
$299$	1.80902	+	5.56758i	0.104618	+	0.321982i
$300$	−2.93893	+	4.04508i	−0.169679	+	0.233543i
$301$	−4.00000	+	12.3107i	−0.230556	+	0.709579i
$302$	17.0130	+	5.52786i	0.978989	+	0.318093i
$303$	−5.11855	+	1.66312i	−0.294053	+	0.0955437i
$304$	4.47214			0.256495
$305$	16.1803			0.926484
$306$	1.50000	+	4.61653i	0.0857493	+	0.263909i
$307$	−4.89404	−	6.73607i	−0.279318	−	0.384448i	0.646190	−	0.763176i	$-0.276361\pi$
$307$	−4.89404	−	6.73607i	−0.279318	−	0.384448i	−0.925508	+	0.378729i	$0.876361\pi$
$308$	−8.78402	+	12.0902i	−0.500516	+	0.688901i
$309$	14.1803			0.806691
$310$	3.75123	+	11.8713i	0.213055	+	0.674246i
$311$	−13.4164			−0.760775			−0.380387	−	0.924827i	$-0.624209\pi$
$311$	−13.4164			−0.760775			−0.380387	+	0.924827i	$0.624209\pi$
$312$	−4.02874	+	5.54508i	−0.228082	+	0.313929i
$313$	−0.449028	−	0.618034i	−0.0253806	−	0.0349333i	0.796138	−	0.605115i	$-0.206873\pi$
$313$	−0.449028	−	0.618034i	−0.0253806	−	0.0349333i	−0.821519	+	0.570182i	$0.806873\pi$
$314$	1.82624	+	5.62058i	0.103061	+	0.317188i
$315$			7.23607i			0.407706i
$316$	−5.09017			−0.286344
$317$	4.08174	−	1.32624i	0.229253	−	0.0744889i	−0.192138	−	0.981368i	$-0.561542\pi$
$317$	4.08174	−	1.32624i	0.229253	−	0.0744889i	0.421391	+	0.906879i	$0.361542\pi$
$318$	−5.42882	−	1.76393i	−0.304433	−	0.0989164i
$319$	0.208204	−	0.640786i	0.0116572	−	0.0358771i
$320$	1.80902	+	1.31433i	0.101127	+	0.0734732i
$321$	−0.708204	−	2.17963i	−0.0395281	−	0.121655i
$322$	1.62460	−	2.23607i	0.0905353	−	0.124611i
$323$	−12.7598	−	17.5623i	−0.709972	−	0.977193i
$324$	−0.309017	+	0.951057i	−0.0171676	+	0.0528365i
$325$	20.1437	+	27.7254i	1.11737	+	1.53793i
$326$	12.9721	−	9.42481i	0.718460	−	0.521992i
$327$	−3.35520	−	1.09017i	−0.185543	−	0.0602865i
$328$	3.35520	+	4.61803i	0.185260	+	0.254988i
$329$	−21.1803	−	15.3884i	−1.16771	−	0.848391i
$330$	3.19098	+	9.82084i	0.175658	+	0.540619i
$331$	−7.09017	−	5.15131i	−0.389711	−	0.283142i	0.375626	−	0.926771i	$-0.377428\pi$
$331$	−7.09017	−	5.15131i	−0.389711	−	0.283142i	−0.765337	+	0.643630i	$0.777428\pi$
$332$	−6.88191	−	2.23607i	−0.377694	−	0.122720i
$333$	3.94298	+	1.28115i	0.216074	+	0.0702067i
$334$	−0.899187	−	2.76741i	−0.0492013	−	0.151426i
$335$		−	17.8885i		−	0.977356i
$336$	3.23607			0.176542
$337$	−17.5680	+	5.70820i	−0.956992	+	0.310946i	−0.745554	−	0.666446i	$-0.767815\pi$
$337$	−17.5680	+	5.70820i	−0.956992	+	0.310946i	−0.211439	+	0.977391i	$0.567815\pi$
$338$	19.9722	+	27.4894i	1.08634	+	1.49522i
$339$	−0.381966	−	0.277515i	−0.0207455	−	0.0150725i
$340$		−	10.8541i		−	0.588646i
$341$	24.3885	+	8.14324i	1.32071	+	0.440981i
$342$		−	4.47214i		−	0.241825i
$343$	−6.71040	+	9.23607i	−0.362327	+	0.498701i
$344$	3.23607	−	2.35114i	0.174477	−	0.126765i
$345$	−0.590170	−	1.81636i	−0.0317737	−	0.0977893i
$346$	10.1803			0.547298
$347$		−	8.00000i		−	0.429463i	−0.976673	−	0.214731i	$-0.931112\pi$
$347$		−	8.00000i		−	0.429463i	0.976673	−	0.214731i	$-0.0688876\pi$
$348$	−0.138757	+	0.0450850i	−0.00743817	+	0.00241681i
$349$	1.14590	−	3.52671i	0.0613385	−	0.188781i	−0.915692	−	0.401882i	$-0.868356\pi$
$349$	1.14590	−	3.52671i	0.0613385	−	0.188781i	0.977030	+	0.213101i	$0.0683563\pi$
$350$	5.00000	−	15.3884i	0.267261	−	0.822546i
$351$	5.54508	+	4.02874i	0.295975	+	0.215038i
$352$	4.39201	−	1.42705i	0.234095	−	0.0760621i
$353$	−3.78398	+	5.20820i	−0.201401	+	0.277205i	−0.897756	−	0.440493i	$-0.854804\pi$
$353$	−3.78398	+	5.20820i	−0.201401	+	0.277205i	0.696355	+	0.717697i	$0.254804\pi$
$354$	7.97214	−	5.79210i	0.423714	−	0.307846i
$355$	−2.76393	+	8.50651i	−0.146694	+	0.451479i
$356$	−12.7082	+	9.23305i	−0.673533	+	0.489351i
$357$	−9.23305	−	12.7082i	−0.488665	−	0.672589i
$358$	−16.6497	−	5.40983i	−0.879966	−	0.285918i
$359$	−6.32624	+	4.59628i	−0.333886	+	0.242582i	−0.742078	−	0.670314i	$-0.766160\pi$
$359$	−6.32624	+	4.59628i	−0.333886	+	0.242582i	0.408192	+	0.912896i	$0.366160\pi$
$360$	1.31433	−	1.80902i	0.0692712	−	0.0953436i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−5.15131	+	7.09017i	−0.270747	+	0.372651i
$363$	9.82084	+	3.19098i	0.515460	+	0.167483i
$364$	6.85410	−	21.0948i	0.359253	−	1.10567i
$365$	−31.7809	+	10.3262i	−1.66349	+	0.540500i
$366$	−7.23607			−0.378235
$367$		−	25.2361i		−	1.31731i	−0.752444	−	0.658656i	$-0.771125\pi$
$367$		−	25.2361i		−	1.31731i	0.752444	−	0.658656i	$-0.228875\pi$
$368$	−0.812299	+	0.263932i	−0.0423440	+	0.0137584i
$369$	4.61803	−	3.35520i	0.240405	−	0.174665i
$370$	−7.50000	−	5.44907i	−0.389906	−	0.283284i
$371$	18.4721			0.959026
$372$	−1.67760	−	5.30902i	−0.0869795	−	0.275260i
$373$			8.96556i			0.464219i	0.972690	+	0.232110i	$0.0745628\pi$
$373$			8.96556i			0.464219i	−0.972690	+	0.232110i	$0.925437\pi$
$374$	−18.1353	−	13.1760i	−0.937752	−	0.681316i
$375$	−6.57164	−	9.04508i	−0.339358	−	0.467086i
$376$	2.50000	+	7.69421i	0.128928	+	0.396799i
$377$			1.00000i			0.0515026i
$378$		−	3.23607i		−	0.166445i
$379$	−0.854102	−	2.62866i	−0.0438723	−	0.135025i	0.926721	−	0.375750i	$-0.122615\pi$
$379$	−0.854102	−	2.62866i	−0.0438723	−	0.135025i	−0.970593	+	0.240725i	$0.922615\pi$
$380$	−3.09017	+	9.51057i	−0.158522	+	0.487882i
$381$	6.56231	−	20.1967i	0.336197	−	1.03471i
$382$	−1.62460	+	2.23607i	−0.0831217	+	0.114407i
$383$	25.3808	−	8.24671i	1.29690	−	0.421387i	0.422396	−	0.906411i	$-0.361189\pi$
$383$	25.3808	−	8.24671i	1.29690	−	0.421387i	0.874501	+	0.485024i	$0.161189\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−19.6417	−	27.0344i	−1.00103	−	1.37780i
$386$	1.32624	−	4.08174i	0.0675037	−	0.207755i
$387$	−2.35114	−	3.23607i	−0.119515	−	0.164499i
$388$	9.95959	+	13.7082i	0.505622	+	0.695929i
$389$	−4.32624	+	13.3148i	−0.219349	+	0.675087i	0.779467	+	0.626443i	$0.215490\pi$
$389$	−4.32624	+	13.3148i	−0.219349	+	0.675087i	−0.998816	+	0.0486437i	$0.984510\pi$
$390$	−9.00854	−	12.3992i	−0.456165	−	0.627857i
$391$	3.35410	+	2.43690i	0.169624	+	0.123239i
$392$	−3.30220	+	1.07295i	−0.166786	+	0.0541921i
$393$	11.0494	−	15.2082i	0.557369	−	0.767152i
$394$	3.38197	−	10.4086i	0.170381	−	0.524379i
$395$	3.51722	−	10.8249i	0.176971	−	0.544659i
$396$	−1.42705	−	4.39201i	−0.0717120	−	0.220707i
$397$			4.38197i			0.219925i	0.993936	+	0.109962i	$0.0350730\pi$
$397$			4.38197i			0.219925i	−0.993936	+	0.109962i	$0.964927\pi$
$398$		−	21.3820i		−	1.07178i
$399$	4.47214	+	13.7638i	0.223887	+	0.689053i
$400$	−4.04508	+	2.93893i	−0.202254	+	0.146946i
$401$	12.3262	+	8.95554i	0.615543	+	0.447218i	0.851362	−	0.524579i	$-0.175777\pi$
$401$	12.3262	+	8.95554i	0.615543	+	0.447218i	−0.235819	+	0.971797i	$0.575777\pi$
$402$			8.00000i			0.399004i
$403$	−38.1608	−	0.309017i	−1.90092	−	0.0153932i
$404$	−5.38197			−0.267763
$405$	−1.80902	−	1.31433i	−0.0898908	−	0.0653095i
$406$	0.381966	−	0.277515i	0.0189567	−	0.0137728i
$407$	−18.2088	+	5.91641i	−0.902578	+	0.293265i
$408$			4.85410i			0.240314i
$409$	10.4377			0.516111			0.258055	−	0.966130i	$-0.416918\pi$
$409$	10.4377			0.516111			0.258055	+	0.966130i	$0.416918\pi$
$410$	−12.1392	+	3.94427i	−0.599513	+	0.194794i
$411$	5.38197	−	16.5640i	0.265473	−	0.817041i
$412$	13.4863	+	4.38197i	0.664423	+	0.215884i
$413$	−18.7436	+	25.7984i	−0.922313	+	1.26945i
$414$	0.263932	+	0.812299i	0.0129716	+	0.0399223i
$415$	9.51057	−	13.0902i	0.466855	−	0.642571i
$416$	−5.54508	+	4.02874i	−0.271870	+	0.197525i
$417$	14.2128	+	4.61803i	0.696006	+	0.226146i
$418$	12.1392	+	16.7082i	0.593749	+	0.817225i
$419$	−29.4336	+	21.3848i	−1.43793	+	1.04472i	−0.449456	+	0.893302i	$0.648382\pi$
$419$	−29.4336	+	21.3848i	−1.43793	+	1.04472i	−0.988471	+	0.151413i	$0.951618\pi$
$420$	−2.23607	+	6.88191i	−0.109109	+	0.335803i
$421$	13.8541	−	10.0656i	0.675208	−	0.490567i	−0.196557	−	0.980492i	$-0.562976\pi$
$421$	13.8541	−	10.0656i	0.675208	−	0.490567i	0.871764	+	0.489925i	$0.162976\pi$
$422$	−10.9637	+	15.0902i	−0.533702	+	0.734578i
$423$	7.69421	−	2.50000i	0.374105	−	0.121554i
$424$	−4.61803	−	3.35520i	−0.224272	−	0.162943i
$425$	23.0826	+	7.50000i	1.11967	+	0.363803i
$426$	1.23607	−	3.80423i	0.0598877	−	0.184315i
$427$	22.2703	−	7.23607i	1.07774	−	0.350178i
$428$		−	2.29180i		−	0.110778i
$429$	−31.6525			−1.52820
$430$	2.76393	+	8.50651i	0.133289	+	0.410220i
$431$	15.1803	−	11.0292i	0.731211	−	0.531256i	−0.158735	−	0.987321i	$-0.550742\pi$
$431$	15.1803	−	11.0292i	0.731211	−	0.531256i	0.889946	+	0.456065i	$0.150742\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$			15.2361i			0.732199i	0.930576	+	0.366099i	$0.119307\pi$
$433$			15.2361i			0.732199i	−0.930576	+	0.366099i	$0.880693\pi$
$434$	10.4721	+	14.6619i	0.502679	+	0.703793i
$435$		−	0.326238i		−	0.0156419i
$436$	−2.85410	−	2.07363i	−0.136687	−	0.0993087i
$437$	−2.24514	−	3.09017i	−0.107400	−	0.147823i
$438$	14.2128	−	4.61803i	0.679116	−	0.220658i
$439$	2.03444			0.0970986			0.0485493	−	0.998821i	$-0.484540\pi$
$439$	2.03444			0.0970986			0.0485493	+	0.998821i	$0.484540\pi$
$440$			10.3262i			0.492284i
$441$	1.07295	+	3.30220i	0.0510928	+	0.157248i
$442$	31.6421	+	10.2812i	1.50506	+	0.489025i
$443$	16.2210	+	5.27051i	0.770681	+	0.250409i	0.667857	−	0.744290i	$-0.267212\pi$
$443$	16.2210	+	5.27051i	0.770681	+	0.250409i	0.102825	+	0.994700i	$0.467212\pi$
$444$	3.35410	+	2.43690i	0.159179	+	0.115650i
$445$	−10.8541	−	33.4055i	−0.514534	−	1.58357i
$446$	8.00000	+	5.81234i	0.378811	+	0.275222i
$447$	−7.27794	−	10.0172i	−0.344235	−	0.473798i
$448$	3.07768	+	1.00000i	0.145407	+	0.0472456i
$449$	−6.47214	+	4.70228i	−0.305439	+	0.221914i	−0.729937	−	0.683514i	$-0.760451\pi$
$449$	−6.47214	+	4.70228i	−0.305439	+	0.221914i	0.424498	+	0.905429i	$0.360451\pi$
$450$	2.93893	+	4.04508i	0.138542	+	0.190687i
$451$	−8.14590	+	25.0705i	−0.383575	+	1.18052i
$452$	−0.277515	−	0.381966i	−0.0130532	−	0.0179662i
$453$	10.5146	−	14.4721i	0.494020	−	0.679960i
$454$	2.38197	+	7.33094i	0.111791	+	0.344058i
$455$	40.1246	+	29.1522i	1.88107	+	1.36668i
$456$	1.38197	−	4.25325i	0.0647165	−	0.199177i
$457$	−4.42477	−	1.43769i	−0.206982	−	0.0672525i	0.203691	−	0.979035i	$-0.434706\pi$
$457$	−4.42477	−	1.43769i	−0.206982	−	0.0672525i	−0.410673	+	0.911783i	$0.634706\pi$
$458$	22.4418	−	7.29180i	1.04864	−	0.340723i
$459$	4.85410			0.226570
$460$		−	1.90983i		−	0.0890463i
$461$	−9.56231	−	29.4298i	−0.445361	−	1.37068i	−0.882087	−	0.471086i	$-0.843862\pi$
$461$	−9.56231	−	29.4298i	−0.445361	−	1.37068i	0.436726	−	0.899594i	$-0.356138\pi$
$462$	8.78402	+	12.0902i	0.408670	+	0.562486i
$463$	−21.9273	+	30.1803i	−1.01905	+	1.40260i	−0.106179	+	0.994347i	$0.533862\pi$
$463$	−21.9273	+	30.1803i	−1.01905	+	1.40260i	−0.912869	+	0.408252i	$0.866138\pi$
$464$	−0.145898			−0.00677315
$465$	12.4495	+	0.100813i	0.577331	+	0.00467509i
$466$	−10.3820			−0.480935
$467$	−10.3026	+	14.1803i	−0.476748	+	0.656188i	−0.977876	−	0.209186i	$-0.932919\pi$
$467$	−10.3026	+	14.1803i	−0.476748	+	0.656188i	0.501128	+	0.865373i	$0.332919\pi$
$468$	4.02874	+	5.54508i	0.186229	+	0.256322i
$469$	−8.00000	−	24.6215i	−0.369406	−	1.13691i
$470$	−18.0902			−0.834437
$471$	5.90983			0.272311
$472$	9.37181	−	3.04508i	0.431372	−	0.140161i
$473$	17.5680	+	5.70820i	0.807780	+	0.262463i
$474$	−1.57295	+	4.84104i	−0.0722479	+	0.222356i
$475$	−18.0902	−	13.1433i	−0.830034	−	0.603055i
$476$	−4.85410	−	14.9394i	−0.222487	−	0.684746i
$477$	−3.35520	+	4.61803i	−0.153624	+	0.211445i
$478$	−14.7679	−	20.3262i	−0.675467	−	0.929700i
$479$	5.52786	−	17.0130i	0.252575	−	0.777345i	−0.741723	−	0.670706i	$-0.765991\pi$
$479$	5.52786	−	17.0130i	0.252575	−	0.777345i	0.994298	−	0.106639i	$-0.0340088\pi$
$480$	1.80902	−	1.31433i	0.0825700	−	0.0599906i
$481$	22.9894	−	16.7027i	1.04822	−	0.761580i
$482$	9.14729	+	2.97214i	0.416648	+	0.135377i
$483$	−1.62460	−	2.23607i	−0.0739218	−	0.101745i
$484$	8.35410	+	6.06961i	0.379732	+	0.275891i
$485$	−36.0341	+	11.7082i	−1.63623	+	0.531642i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	−25.6255	−	8.32624i	−1.16120	−	0.377298i	−0.335851	−	0.941915i	$-0.609024\pi$
$487$	−25.6255	−	8.32624i	−1.16120	−	0.377298i	−0.825353	+	0.564617i	$0.809024\pi$
$488$	−6.88191	−	2.23607i	−0.311529	−	0.101222i
$489$	−4.95492	−	15.2497i	−0.224069	−	0.689613i
$490$		−	7.76393i		−	0.350739i
$491$	19.0344			0.859012			0.429506	−	0.903064i	$-0.358688\pi$
$491$	19.0344			0.859012			0.429506	+	0.903064i	$0.358688\pi$
$492$	5.42882	−	1.76393i	0.244750	−	0.0795242i
$493$	0.416272	+	0.572949i	0.0187479	+	0.0258043i
$494$	−24.7984	−	18.0171i	−1.11573	−	0.810626i
$495$	10.3262			0.464130
$496$	0.0450850	−	5.56758i	0.00202437	−	0.249992i
$497$			12.9443i			0.580630i
$498$	−4.25325	+	5.85410i	−0.190593	+	0.262329i
$499$	21.1803	−	15.3884i	0.948162	−	0.688880i	−0.00220926	−	0.999998i	$-0.500703\pi$
$499$	21.1803	−	15.3884i	0.948162	−	0.688880i	0.950371	+	0.311117i	$0.100703\pi$
$500$	−3.45492	−	10.6331i	−0.154508	−	0.475528i
$501$	−2.90983			−0.130002
$502$		−	1.90983i		−	0.0852399i
$503$	−17.4823	+	5.68034i	−0.779497	+	0.253274i	−0.671625	−	0.740891i	$-0.734403\pi$
$503$	−17.4823	+	5.68034i	−0.779497	+	0.253274i	−0.107871	+	0.994165i	$0.534403\pi$
$504$	1.00000	−	3.07768i	0.0445435	−	0.137091i
$505$	3.71885	−	11.4454i	0.165487	−	0.509315i
$506$	−3.19098	−	2.31838i	−0.141856	−	0.103065i
$507$	32.3157	−	10.5000i	1.43519	−	0.466321i
$508$	12.4822	−	17.1803i	0.553810	−	0.762254i
$509$	−9.59017	+	6.96767i	−0.425077	+	0.308836i	−0.779677	−	0.626182i	$-0.784617\pi$
$509$	−9.59017	+	6.96767i	−0.425077	+	0.308836i	0.354600	+	0.935018i	$0.384617\pi$
$510$	−10.3229	−	3.35410i	−0.457104	−	0.148522i
$511$	−39.1246	+	28.4257i	−1.73077	+	1.25748i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−4.25325	−	1.38197i	−0.187786	−	0.0610153i
$514$	−9.20820	+	6.69015i	−0.406156	+	0.295090i
$515$	−18.6376	+	25.6525i	−0.821271	+	1.13038i
$516$	−1.23607	−	3.80423i	−0.0544149	−	0.167472i
$517$	−21.9601	+	30.2254i	−0.965802	+	1.32931i
$518$	−12.7598	−	4.14590i	−0.560632	−	0.182160i
$519$	3.14590	−	9.68208i	0.138090	−	0.424996i
$520$	−4.73607	−	14.5761i	−0.207690	−	0.639205i
$521$	−15.5279			−0.680288			−0.340144	−	0.940373i	$-0.610476\pi$
$521$	−15.5279			−0.680288			−0.340144	+	0.940373i	$0.610476\pi$
$522$			0.145898i			0.00638578i
$523$	11.9475	−	3.88197i	0.522426	−	0.169747i	−0.0359200	−	0.999355i	$-0.511436\pi$
$523$	11.9475	−	3.88197i	0.522426	−	0.169747i	0.558346	+	0.829608i	$0.311436\pi$
$524$	15.2082	−	11.0494i	0.664373	−	0.482696i
$525$	−13.0902	−	9.51057i	−0.571302	−	0.415075i
$526$	22.3262			0.973470
$527$	−21.9928	+	15.7082i	−0.958022	+	0.684260i
$528$		−	4.61803i		−	0.200974i
$529$	−18.0172	−	13.0903i	−0.783357	−	0.569142i
$530$	10.3262	−	7.50245i	0.448543	−	0.325886i
$531$	−3.04508	−	9.37181i	−0.132145	−	0.406702i
$532$			14.4721i			0.627447i
$533$		−	39.1246i		−	1.69468i
$534$	4.85410	+	14.9394i	0.210058	+	0.646491i
$535$	4.87380	+	1.58359i	0.210713	+	0.0684647i
$536$	−2.47214	+	7.60845i	−0.106780	+	0.328635i
$537$	−10.2901	+	14.1631i	−0.444051	+	0.611184i
$538$	−18.1028	+	5.88197i	−0.780468	+	0.253590i
$539$	−12.9721	−	9.42481i	−0.558749	−	0.405955i
$540$	−1.31433	−	1.80902i	−0.0565597	−	0.0778477i
$541$	13.8197	−	42.5325i	0.594154	−	1.82862i	0.0352587	−	0.999378i	$-0.488774\pi$
$541$	13.8197	−	42.5325i	0.594154	−	1.82862i	0.558895	−	0.829239i	$-0.311226\pi$
$542$	5.31031	+	7.30902i	0.228097	+	0.313949i
$543$	5.15131	+	7.09017i	0.221064	+	0.304268i
$544$	−1.50000	+	4.61653i	−0.0643120	+	0.197932i
$545$	6.38197	−	4.63677i	0.273373	−	0.198617i
$546$	−17.9443	−	13.0373i	−0.767944	−	0.557944i
$547$	34.0463	−	11.0623i	1.45571	−	0.472990i	0.528956	−	0.848649i	$-0.322584\pi$
$547$	34.0463	−	11.0623i	1.45571	−	0.472990i	0.926758	+	0.375659i	$0.122584\pi$
$548$	10.2371	−	14.0902i	0.437308	−	0.601902i
$549$	−2.23607	+	6.88191i	−0.0954331	+	0.293713i
$550$	−21.9601	−	7.13525i	−0.936380	−	0.304248i
$551$	−0.201626	−	0.620541i	−0.00858956	−	0.0264360i
$552$			0.854102i			0.0363530i
$553$		−	16.4721i		−	0.700466i
$554$	−5.11803	−	15.7517i	−0.217444	−	0.669225i
$555$	−7.50000	+	5.44907i	−0.318357	+	0.231300i
$556$	12.0902	+	8.78402i	0.512737	+	0.372526i
$557$			22.6525i			0.959816i	0.877319	+	0.479908i	$0.159330\pi$
$557$			22.6525i			0.959816i	−0.877319	+	0.479908i	$0.840670\pi$
$558$	−5.56758	−	0.0450850i	−0.235695	−	0.00190860i
$559$	−27.4164			−1.15959
$560$	−4.25325	+	5.85410i	−0.179733	+	0.247381i
$561$	−18.1353	+	13.1760i	−0.765671	+	0.556293i
$562$	−30.7768	+	10.0000i	−1.29824	+	0.421825i
$563$		−	10.0000i		−	0.421450i	−0.977545	−	0.210725i	$-0.932418\pi$
$563$		−	10.0000i		−	0.421450i	0.977545	−	0.210725i	$-0.0675824\pi$
$564$	8.09017			0.340658
$565$	1.00406	−	0.326238i	0.0422410	−	0.0137249i
$566$	−1.64590	+	5.06555i	−0.0691823	+	0.212921i
$567$	−3.07768	−	1.00000i	−0.129251	−	0.0419961i
$568$	2.35114	−	3.23607i	0.0986517	−	0.135782i
$569$	−1.61803	−	4.97980i	−0.0678315	−	0.208764i	0.911395	−	0.411532i	$-0.135006\pi$
$569$	−1.61803	−	4.97980i	−0.0678315	−	0.208764i	−0.979227	+	0.202768i	$0.935006\pi$
$570$	8.09017	+	5.87785i	0.338860	+	0.246196i
$571$	−22.6525	+	16.4580i	−0.947977	+	0.688745i	−0.950327	−	0.311252i	$-0.899252\pi$
$571$	−22.6525	+	16.4580i	−0.947977	+	0.688745i	0.00235083	+	0.999997i	$0.499252\pi$
$572$	−30.1033	−	9.78115i	−1.25868	−	0.408971i
$573$	1.62460	+	2.23607i	0.0678686	+	0.0934131i
$574$	−14.9443	+	10.8576i	−0.623762	+	0.453190i
$575$	4.06150	+	1.31966i	0.169376	+	0.0550336i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	3.69822	−	5.09017i	0.153959	−	0.211907i	−0.725069	−	0.688676i	$-0.758192\pi$
$577$	3.69822	−	5.09017i	0.153959	−	0.211907i	0.879028	+	0.476769i	$0.158192\pi$
$578$	6.24112	−	2.02786i	0.259597	−	0.0843480i
$579$	−3.47214	−	2.52265i	−0.144297	−	0.104838i
$580$	0.100813	−	0.310271i	0.00418603	−	0.0128833i
$581$	7.23607	−	22.2703i	0.300203	−	0.923929i
$582$	16.1150	−	5.23607i	0.667987	−	0.217042i
$583$		−	26.3607i		−	1.09175i
$584$	14.9443			0.618398
$585$	−14.5761	+	4.73607i	−0.602648	+	0.195812i
$586$	−9.09017	+	6.60440i	−0.375511	+	0.272825i
$587$	12.2047	−	16.7984i	0.503743	−	0.693343i	−0.479105	−	0.877757i	$-0.659039\pi$
$587$	12.2047	−	16.7984i	0.503743	−	0.693343i	0.982849	+	0.184414i	$0.0590388\pi$
$588$			3.47214i			0.143188i
$589$	23.7426	−	7.50245i	0.978299	−	0.309133i
$590$			22.0344i			0.907144i
$591$	−8.85410	−	6.43288i	−0.364209	−	0.264613i
$592$	2.43690	+	3.35410i	0.100156	+	0.137853i
$593$	20.7315	−	6.73607i	0.851340	−	0.276617i	0.149333	−	0.988787i	$-0.452287\pi$
$593$	20.7315	−	6.73607i	0.851340	−	0.276617i	0.702007	+	0.712170i	$0.252287\pi$
$594$	−4.61803			−0.189480
$595$	35.1246			1.43997
$596$	−3.82624	−	11.7759i	−0.156729	−	0.482362i
$597$	−20.3355	−	6.60739i	−0.832275	−	0.270423i
$598$	5.56758	+	1.80902i	0.227675	+	0.0739762i
$599$	13.7984	+	10.0251i	0.563786	+	0.409615i	0.832843	−	0.553510i	$-0.186712\pi$
$599$	13.7984	+	10.0251i	0.563786	+	0.409615i	−0.269056	+	0.963124i	$0.586712\pi$
$600$	1.54508	+	4.75528i	0.0630778	+	0.194134i
$601$	−18.9164	−	13.7436i	−0.771616	−	0.560612i	0.130835	−	0.991404i	$-0.458234\pi$
$601$	−18.9164	−	13.7436i	−0.771616	−	0.560612i	−0.902451	+	0.430792i	$0.858234\pi$
$602$	7.60845	+	10.4721i	0.310097	+	0.426812i
$603$	7.60845	+	2.47214i	0.309840	+	0.100673i
$604$	14.4721	−	10.5146i	0.588863	−	0.427834i
$605$	−18.6803	+	13.5721i	−0.759464	+	0.551783i
$606$	−1.66312	+	5.11855i	−0.0675596	+	0.207927i
$607$	17.1190	+	23.5623i	0.694839	+	0.956364i	0.999992	+	0.00406093i	$0.00129264\pi$
$607$	17.1190	+	23.5623i	0.694839	+	0.956364i	−0.305152	+	0.952304i	$0.598707\pi$
$608$	2.62866	−	3.61803i	0.106606	−	0.146731i
$609$	−0.145898	−	0.449028i	−0.00591209	−	0.0181955i
$610$	9.51057	−	13.0902i	0.385072	−	0.530005i
$611$	17.1353	−	52.7369i	0.693218	−	2.13351i
$612$	4.61653	+	1.50000i	0.186612	+	0.0606339i
$613$	25.5928	−	8.31559i	1.03368	−	0.335864i	0.257437	−	0.966295i	$-0.417122\pi$
$613$	25.5928	−	8.31559i	1.03368	−	0.335864i	0.776245	+	0.630431i	$0.217122\pi$
$614$	−8.32624			−0.336020
$615$			12.7639i			0.514691i
$616$	4.61803	+	14.2128i	0.186066	+	0.572652i
$617$	−6.20837	−	8.54508i	−0.249939	−	0.344012i	0.665551	−	0.746353i	$-0.268197\pi$
$617$	−6.20837	−	8.54508i	−0.249939	−	0.344012i	−0.915490	+	0.402341i	$0.868197\pi$
$618$	8.33499	−	11.4721i	0.335283	−	0.461477i
$619$	24.6525			0.990867			0.495433	−	0.868646i	$-0.335009\pi$
$619$	24.6525			0.990867			0.495433	+	0.868646i	$0.335009\pi$
$620$	11.8090	+	3.94298i	0.474262	+	0.158354i
$621$	0.854102			0.0342739
$622$	−7.88597	+	10.8541i	−0.316198	+	0.435210i
$623$	−29.8788	−	41.1246i	−1.19707	−	1.64762i
$624$	2.11803	+	6.51864i	0.0847892	+	0.260954i
$625$	25.0000			1.00000
$626$	−0.763932			−0.0305329
$627$	19.6417	−	6.38197i	0.784413	−	0.254871i
$628$	5.62058	+	1.82624i	0.224286	+	0.0728748i
$629$	6.21885	−	19.1396i	0.247962	−	0.763148i
$630$	5.85410	+	4.25325i	0.233233	+	0.169454i
$631$	9.79180	+	30.1360i	0.389805	+	1.19970i	0.932934	+	0.360048i	$0.117240\pi$
$631$	9.79180	+	30.1360i	0.389805	+	1.19970i	−0.543129	+	0.839649i	$0.682760\pi$
$632$	−2.99193	+	4.11803i	−0.119012	+	0.163807i
$633$	10.9637	+	15.0902i	0.435766	+	0.599780i
$634$	1.32624	−	4.08174i	0.0526716	−	0.162107i
$635$	27.9112	+	38.4164i	1.10762	+	1.52451i
$636$	−4.61803	+	3.35520i	−0.183117	+	0.133042i
$637$	22.6336	+	7.35410i	0.896776	+	0.291380i
$638$	−0.396027	−	0.545085i	−0.0156789	−	0.0215801i
$639$	−3.23607	−	2.35114i	−0.128017	−	0.0930097i
$640$	2.12663	−	0.690983i	0.0840623	−	0.0273135i
$641$	−31.8885	−	23.1684i	−1.25952	−	0.915096i	−0.260788	−	0.965396i	$-0.583982\pi$
$641$	−31.8885	−	23.1684i	−1.25952	−	0.915096i	−0.998734	+	0.0503001i	$0.983982\pi$
$642$	−2.17963	−	0.708204i	−0.0860230	−	0.0279506i
$643$	4.11450	+	1.33688i	0.162260	+	0.0527214i	0.389021	−	0.921229i	$-0.372814\pi$
$643$	4.11450	+	1.33688i	0.162260	+	0.0527214i	−0.226761	+	0.973951i	$0.572814\pi$
$644$	−0.854102	−	2.62866i	−0.0336563	−	0.103584i
$645$	8.94427			0.352180
$646$	−21.7082			−0.854098
$647$	1.71036	−	0.555728i	0.0672410	−	0.0218479i	−0.275203	−	0.961386i	$-0.588745\pi$
$647$	1.71036	−	0.555728i	0.0672410	−	0.0218479i	0.342444	+	0.939538i	$0.388745\pi$
$648$	0.587785	+	0.809017i	0.0230904	+	0.0317812i
$649$	36.8156	+	26.7481i	1.44514	+	1.04995i
$650$	34.2705			1.34420
$651$	17.1803	−	5.42882i	0.673351	−	0.212772i
$652$		−	16.0344i		−	0.627957i
$653$	2.11412	−	2.90983i	0.0827317	−	0.113870i	−0.765645	−	0.643263i	$-0.777580\pi$
$653$	2.11412	−	2.90983i	0.0827317	−	0.113870i	0.848377	+	0.529393i	$0.177580\pi$
$654$	−2.85410	+	2.07363i	−0.111604	+	0.0810852i
$655$	12.9894	+	39.9771i	0.507536	+	1.56204i
$656$	5.70820			0.222868
$657$		−	14.9443i		−	0.583032i
$658$	−24.8990	+	8.09017i	−0.970663	+	0.315388i
$659$	−2.82624	+	8.69827i	−0.110095	+	0.338836i	−0.990892	−	0.134656i	$-0.957007\pi$
$659$	−2.82624	+	8.69827i	−0.110095	+	0.338836i	0.880798	+	0.473493i	$0.157007\pi$
$660$	9.82084	+	3.19098i	0.382276	+	0.124209i
$661$	4.70820	+	3.42071i	0.183128	+	0.133050i	0.675572	−	0.737294i	$-0.263897\pi$
$661$	4.70820	+	3.42071i	0.183128	+	0.133050i	−0.492445	+	0.870344i	$0.663897\pi$
$662$	−8.33499	+	2.70820i	−0.323949	+	0.105257i
$663$	19.5559	−	26.9164i	0.759489	−	1.04535i
$664$	−5.85410	+	4.25325i	−0.227183	+	0.165058i
$665$	−30.7768	−	10.0000i	−1.19347	−	0.387783i
$666$	3.35410	−	2.43690i	0.129969	−	0.0944279i
$667$	0.0732450	+	0.100813i	0.00283606	+	0.00390350i
$668$	−2.76741	−	0.899187i	−0.107074	−	0.0347906i
$669$	8.00000	−	5.81234i	0.309298	−	0.224718i
$670$	−14.4721	−	10.5146i	−0.559107	−	0.406215i
$671$	−10.3262	−	31.7809i	−0.398640	−	1.22689i
$672$	1.90211	−	2.61803i	0.0733756	−	0.100993i
$673$	−7.71445	−	2.50658i	−0.297370	−	0.0966215i	0.156532	−	0.987673i	$-0.449969\pi$
$673$	−7.71445	−	2.50658i	−0.297370	−	0.0966215i	−0.453902	+	0.891051i	$0.649969\pi$
$674$	−5.70820	+	17.5680i	−0.219872	+	0.676696i
$675$	4.75528	−	1.54508i	0.183031	−	0.0594703i
$676$	33.9787			1.30687
$677$		−	3.05573i		−	0.117441i	−0.998274	−	0.0587206i	$-0.981298\pi$
$677$		−	3.05573i		−	0.117441i	0.998274	−	0.0587206i	$-0.0187021\pi$
$678$	−0.449028	+	0.145898i	−0.0172448	+	0.00560318i
$679$	−44.3607	+	32.2299i	−1.70241	+	1.23687i
$680$	−8.78115	−	6.37988i	−0.336742	−	0.244657i
$681$	7.70820			0.295379
$682$	20.9232	−	14.9443i	0.801192	−	0.572246i
$683$		−	35.4164i		−	1.35517i	−0.735444	−	0.677586i	$-0.763026\pi$
$683$		−	35.4164i		−	1.35517i	0.735444	−	0.677586i	$-0.236974\pi$
$684$	−3.61803	−	2.62866i	−0.138339	−	0.100509i
$685$	22.8909	+	31.5066i	0.874615	+	1.20380i
$686$	3.52786	+	10.8576i	0.134694	+	0.414547i
$687$		−	23.5967i		−	0.900272i
$688$		−	4.00000i		−	0.152499i
$689$	12.0902	+	37.2097i	0.460599	+	1.41758i
$690$	−1.81636	−	0.590170i	−0.0691475	−	0.0224674i
$691$	12.2361	−	37.6587i	0.465482	−	1.43261i	−0.392893	−	0.919584i	$-0.628526\pi$
$691$	12.2361	−	37.6587i	0.465482	−	1.43261i	0.858375	−	0.513022i	$-0.171474\pi$
$692$	5.98385	−	8.23607i	0.227472	−	0.313088i
$693$	14.2128	−	4.61803i	0.539901	−	0.175425i
$694$	−6.47214	−	4.70228i	−0.245679	−	0.178496i
$695$	−27.0344	+	19.6417i	−1.02547	+	0.745051i
$696$	−0.0450850	+	0.138757i	−0.00170894	+	0.00525958i
$697$	−16.2865	−	22.4164i	−0.616894	−	0.849082i
$698$	−2.17963	−	3.00000i	−0.0825001	−	0.113552i
$699$	−3.20820	+	9.87384i	−0.121345	+	0.373463i
$700$	−9.51057	−	13.0902i	−0.359466	−	0.494762i
$701$	18.8262	+	13.6781i	0.711057	+	0.516613i	0.883515	−	0.468404i	$-0.155171\pi$
$701$	18.8262	+	13.6781i	0.711057	+	0.516613i	−0.172457	+	0.985017i	$0.555171\pi$
$702$	6.51864	−	2.11803i	0.246030	−	0.0799400i
$703$	−10.8981	+	15.0000i	−0.411031	+	0.565736i
$704$	1.42705	−	4.39201i	0.0537840	−	0.165530i
$705$	−5.59017	+	17.2048i	−0.210538	+	0.647969i
$706$	1.98936	+	6.12261i	0.0748704	+	0.230428i
$707$		−	17.4164i		−	0.655011i
$708$		−	9.85410i		−	0.370340i
$709$	−2.27051	−	6.98791i	−0.0852708	−	0.262436i	0.899325	−	0.437280i	$-0.144058\pi$
$709$	−2.27051	−	6.98791i	−0.0852708	−	0.262436i	−0.984596	+	0.174843i	$0.944058\pi$
$710$	5.25731	+	7.23607i	0.197303	+	0.271565i
$711$	4.11803	+	2.99193i	0.154438	+	0.112206i
$712$			15.7082i			0.588690i
$713$	−3.86974	+	2.76393i	−0.144923	+	0.103510i
$714$	−15.7082			−0.587865
$715$	41.6017	−	57.2599i	1.55582	−	2.14140i
$716$	−14.1631	+	10.2901i	−0.529301	+	0.384559i
$717$	−23.8949	+	7.76393i	−0.892372	+	0.289949i
$718$			7.81966i			0.291827i
$719$	31.8885			1.18924			0.594621	−	0.804006i	$-0.297302\pi$
$719$	31.8885			1.18924			0.594621	+	0.804006i	$0.297302\pi$
$720$	−0.690983	−	2.12663i	−0.0257514	−	0.0792547i
$721$	−14.1803	+	43.6426i	−0.528103	+	1.62534i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	5.65334	−	7.78115i	0.210250	−	0.289384i
$724$	2.70820	+	8.33499i	0.100650	+	0.309768i
$725$	0.590170	+	0.428784i	0.0219184	+	0.0159246i
$726$	8.35410	−	6.06961i	0.310050	−	0.225264i
$727$	−7.95148	−	2.58359i	−0.294904	−	0.0958201i	0.157828	−	0.987467i	$-0.449551\pi$
$727$	−7.95148	−	2.58359i	−0.294904	−	0.0958201i	−0.452732	+	0.891646i	$0.649551\pi$
$728$	−13.0373	−	17.9443i	−0.483194	−	0.665059i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	−10.3262	+	31.7809i	−0.382191	+	1.17626i
$731$	−15.7082	+	11.4127i	−0.580989	+	0.422113i
$732$	−4.25325	+	5.85410i	−0.157205	+	0.216374i
$733$	48.8267	−	15.8647i	1.80345	−	0.585978i	0.803498	−	0.595308i	$-0.202970\pi$
$733$	48.8267	−	15.8647i	1.80345	−	0.585978i	0.999956	+	0.00933034i	$0.00296998\pi$
$734$	−20.4164	−	14.8334i	−0.753583	−	0.547510i
$735$	−7.38394	−	2.39919i	−0.272361	−	0.0884953i
$736$	−0.263932	+	0.812299i	−0.00972866	+	0.0299417i
$737$	−35.1361	+	11.4164i	−1.29425	+	0.420529i
$738$		−	5.70820i		−	0.210122i
$739$	9.52786			0.350488			0.175244	−	0.984525i	$-0.443929\pi$
$739$	9.52786			0.350488			0.175244	+	0.984525i	$0.443929\pi$
$740$	−8.81678	+	2.86475i	−0.324111	+	0.105310i
$741$	−24.7984	+	18.0171i	−0.910991	+	0.661874i
$742$	10.8576	−	14.9443i	0.398597	−	0.548621i
$743$			34.9787i			1.28324i	0.767021	+	0.641622i	$0.221738\pi$
$743$			34.9787i			1.28324i	−0.767021	+	0.641622i	$0.778262\pi$
$744$	−5.28115	−	1.76336i	−0.193616	−	0.0646478i
$745$	27.6869			1.01437
$746$	7.25329	+	5.26982i	0.265562	+	0.192942i
$747$	4.25325	+	5.85410i	0.155618	+	0.214190i
$748$	−21.3193	+	6.92705i	−0.779510	+	0.253278i
$749$	7.41641			0.270990
$750$	−11.1803			−0.408248
$751$	−13.1910	−	40.5977i	−0.481346	−	1.48143i	−0.837204	−	0.546890i	$-0.815812\pi$
$751$	−13.1910	−	40.5977i	−0.481346	−	1.48143i	0.355859	−	0.934540i	$-0.384188\pi$
$752$	7.69421	+	2.50000i	0.280579	+	0.0911656i
$753$	−1.81636	−	0.590170i	−0.0661917	−	0.0215070i
$754$	0.809017	+	0.587785i	0.0294627	+	0.0214059i
$755$	12.3607	+	38.0423i	0.449851	+	1.38450i
$756$	−2.61803	−	1.90211i	−0.0952170	−	0.0691792i
$757$	−25.1110	−	34.5623i	−0.912674	−	1.25619i	−0.966245	−	0.257624i	$-0.917060\pi$
$757$	−25.1110	−	34.5623i	−0.912674	−	1.25619i	0.0535709	−	0.998564i	$-0.482940\pi$
$758$	−2.62866	−	0.854102i	−0.0954771	−	0.0310224i
$759$	−3.19098	+	2.31838i	−0.115825	+	0.0841520i
$760$	5.87785	+	8.09017i	0.213212	+	0.293461i
$761$	−10.7426	+	33.0625i	−0.389421	+	1.19851i	0.543802	+	0.839214i	$0.316984\pi$
$761$	−10.7426	+	33.0625i	−0.389421	+	1.19851i	−0.933222	+	0.359300i	$0.883016\pi$
$762$	−12.4822	−	17.1803i	−0.452184	−	0.622378i
$763$	6.71040	−	9.23607i	0.242933	−	0.334368i
$764$	0.854102	+	2.62866i	0.0309003	+	0.0951014i
$765$	−6.37988	+	8.78115i	−0.230665	+	0.317483i
$766$	8.24671	−	25.3808i	0.297966	−	0.917044i
$767$	−64.2353	−	20.8713i	−2.31940	−	0.753620i
$768$	−0.951057	+	0.309017i	−0.0343183	+	0.0111507i
$769$	24.9098			0.898271			0.449136	−	0.893464i	$-0.351732\pi$
$769$	24.9098			0.898271			0.449136	+	0.893464i	$0.351732\pi$
$770$	−33.4164			−1.20424
$771$	3.51722	+	10.8249i	0.126670	+	0.389849i
$772$	−2.52265	−	3.47214i	−0.0907923	−	0.124965i
$773$	−23.3804	+	32.1803i	−0.840934	+	1.15745i	0.144854	+	0.989453i	$0.453729\pi$
$773$	−23.3804	+	32.1803i	−0.840934	+	1.15745i	−0.985788	+	0.167993i	$0.946271\pi$
$774$	−4.00000			−0.143777
$775$	−16.5451	+	22.3888i	−0.594317	+	0.804231i
$776$	16.9443			0.608264
$777$	−7.88597	+	10.8541i	−0.282907	+	0.389389i
$778$	8.22899	+	11.3262i	0.295024	+	0.406065i
$779$	7.88854	+	24.2784i	0.282636	+	0.869865i
$780$	−15.3262			−0.548767
$781$	18.4721			0.660985
$782$	3.94298	−	1.28115i	0.141001	−	0.0458139i
$783$	0.138757	+	0.0450850i	0.00495878	+	0.00161121i
$784$	−1.07295	+	3.30220i	−0.0383196	+	0.117936i
$785$	−7.76745	+	10.6910i	−0.277232	+	0.381578i
$786$	−5.80902	−	17.8783i	−0.207201	−	0.637698i
$787$	−12.8455	+	17.6803i	−0.457893	+	0.630236i	−0.974070	−	0.226246i	$-0.927355\pi$
$787$	−12.8455	+	17.6803i	−0.457893	+	0.630236i	0.516177	+	0.856482i	$0.327355\pi$
$788$	−6.43288	−	8.85410i	−0.229162	−	0.315414i
$789$	6.89919	−	21.2335i	0.245618	−	0.755933i
$790$	−6.69015	−	9.20820i	−0.238025	−	0.327613i
$791$	1.23607	−	0.898056i	0.0439495	−	0.0319312i
$792$	−4.39201	−	1.42705i	−0.156063	−	0.0507080i
$793$	29.1522	+	40.1246i	1.03523	+	1.42487i
$794$	3.54508	+	2.57565i	0.125810	+	0.0914066i
$795$	−3.94427	−	12.1392i	−0.139889	−	0.430534i
$796$	−17.2984	−	12.5680i	−0.613125	−	0.445461i
$797$	−1.34708	−	0.437694i	−0.0477162	−	0.0155039i	0.285062	−	0.958509i	$-0.407986\pi$
$797$	−1.34708	−	0.437694i	−0.0477162	−	0.0155039i	−0.332778	+	0.943005i	$0.607986\pi$
$798$	13.7638	+	4.47214i	0.487234	+	0.158312i
$799$	−12.1353	−	37.3485i	−0.429314	−	1.32129i
$800$			5.00000i			0.176777i
$801$	15.7082			0.555022
$802$	14.4904	−	4.70820i	0.511672	−	0.166252i
$803$	40.5649	+	55.8328i	1.43150	+	1.97030i
$804$	6.47214	+	4.70228i	0.228255	+	0.165837i
$805$	6.18034			0.217828
$806$	−22.6803	+	30.6911i	−0.798881	+	1.08105i
$807$			19.0344i			0.670044i
$808$	−3.16344	+	4.35410i	−0.111289	+	0.153177i
$809$	−16.0902	+	11.6902i	−0.565700	+	0.411005i	−0.833541	−	0.552458i	$-0.813690\pi$
$809$	−16.0902	+	11.6902i	−0.565700	+	0.411005i	0.267841	+	0.963463i	$0.413690\pi$
$810$	−2.12663	+	0.690983i	−0.0747221	+	0.0242787i
$811$	10.3607			0.363813			0.181906	−	0.983316i	$-0.441773\pi$
$811$	10.3607			0.363813			0.181906	+	0.983316i	$0.441773\pi$
$812$		−	0.472136i		−	0.0165687i
$813$	8.59226	−	2.79180i	0.301344	−	0.0979126i
$814$	−5.91641	+	18.2088i	−0.207370	+	0.638219i
$815$	34.0993	+	11.0795i	1.19445	+	0.388099i
$816$	3.92705	+	2.85317i	0.137474	+	0.0998809i
$817$	17.0130	−	5.52786i	0.595210	−	0.193395i
$818$	6.13512	−	8.44427i	0.214510	−	0.295247i
$819$	−17.9443	+	13.0373i	−0.627024	+	0.455559i
$820$	−3.94427	+	12.1392i	−0.137740	+	0.423920i
$821$	−39.1074	+	28.4132i	−1.36486	+	0.991627i	−0.366738	+	0.930324i	$0.619525\pi$
$821$	−39.1074	+	28.4132i	−1.36486	+	0.991627i	−0.998119	+	0.0613027i	$0.980475\pi$
$822$	−10.2371	−	14.0902i	−0.357060	−	0.491451i
$823$	−20.0907	−	6.52786i	−0.700318	−	0.227547i	−0.0628488	−	0.998023i	$-0.520019\pi$
$823$	−20.0907	−	6.52786i	−0.700318	−	0.227547i	−0.637469	+	0.770476i	$0.720019\pi$
$824$	11.4721	−	8.33499i	0.399651	−	0.290363i
$825$	−13.5721	+	18.6803i	−0.472519	+	0.650366i
$826$	9.85410	+	30.3278i	0.342868	+	1.05524i
$827$	24.7275	−	34.0344i	0.859858	−	1.18349i	−0.121745	−	0.992561i	$-0.538849\pi$
$827$	24.7275	−	34.0344i	0.859858	−	1.18349i	0.981603	−	0.190932i	$-0.0611510\pi$
$828$	0.812299	+	0.263932i	0.0282294	+	0.00917227i
$829$	−11.0000	+	33.8545i	−0.382046	+	1.17582i	0.556555	+	0.830811i	$0.312123\pi$
$829$	−11.0000	+	33.8545i	−0.382046	+	1.17582i	−0.938601	+	0.345005i	$0.887877\pi$
$830$	−5.00000	−	15.3884i	−0.173553	−	0.534140i
$831$	−16.5623			−0.574540
$832$			6.85410i			0.237623i
$833$	16.0292	−	5.20820i	0.555379	−	0.180454i
$834$	12.0902	−	8.78402i	0.418648	−	0.304166i
$835$	3.82447	−	5.26393i	0.132351	−	0.182166i
$836$	20.6525			0.714281
$837$	−1.76336	+	5.28115i	−0.0609505	+	0.182543i
$838$			36.3820i			1.25679i
$839$	−10.4721	−	7.60845i	−0.361538	−	0.262673i	0.392155	−	0.919899i	$-0.371730\pi$
$839$	−10.4721	−	7.60845i	−0.361538	−	0.262673i	−0.753693	+	0.657226i	$0.771730\pi$
$840$	4.25325	+	5.85410i	0.146751	+	0.201986i
$841$	−8.95492	−	27.5604i	−0.308790	−	0.950358i
$842$		−	17.1246i		−	0.590153i
$843$			32.3607i			1.11456i
$844$	5.76393	+	17.7396i	0.198403	+	0.610621i
$845$	−23.4787	+	72.2601i	−0.807692	+	2.48582i
$846$	2.50000	−	7.69421i	0.0859518	−	0.264532i
$847$	−19.6417	+	27.0344i	−0.674896	+	0.928914i
$848$	−5.42882	+	1.76393i	−0.186427	+	0.0605737i
$849$	4.30902	+	3.13068i	0.147885	+	0.107445i
$850$	19.6353	−	14.2658i	0.673484	−	0.489315i
$851$	1.09424	−	3.36771i	0.0375099	−	0.115444i
$852$	−2.35114	−	3.23607i	−0.0805488	−	0.110866i
$853$	−24.1522	−	33.2426i	−0.826955	−	1.13821i	−0.988482	−	0.151338i	$-0.951642\pi$
$853$	−24.1522	−	33.2426i	−0.826955	−	1.13821i	0.161527	−	0.986868i	$-0.448358\pi$
$854$	7.23607	−	22.2703i	0.247613	−	0.762075i
$855$	8.09017	−	5.87785i	0.276678	−	0.201018i
$856$	−1.85410	−	1.34708i	−0.0633719	−	0.0460424i
$857$	−15.6862	+	5.09675i	−0.535830	+	0.174102i	−0.564417	−	0.825490i	$-0.690899\pi$
$857$	−15.6862	+	5.09675i	−0.535830	+	0.174102i	0.0285876	+	0.999591i	$0.490899\pi$
$858$	−18.6049	+	25.6074i	−0.635159	+	0.874222i
$859$	−8.32624	+	25.6255i	−0.284088	+	0.874332i	0.702583	+	0.711602i	$0.252030\pi$
$859$	−8.32624	+	25.6255i	−0.284088	+	0.874332i	−0.986671	+	0.162730i	$0.947970\pi$
$860$	8.50651	+	2.76393i	0.290070	+	0.0942493i
$861$	5.70820	+	17.5680i	0.194535	+	0.598717i
$862$		−	18.7639i		−	0.639102i
$863$			46.8328i			1.59421i	0.603842	+	0.797104i	$0.293636\pi$
$863$			46.8328i			1.59421i	−0.603842	+	0.797104i	$0.706364\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	13.3803	+	18.4164i	0.454944	+	0.626177i
$866$	12.3262	+	8.95554i	0.418863	+	0.304322i
$867$		−	6.56231i		−	0.222868i
$868$	18.0171	+	0.145898i	0.611539	+	0.00495210i
$869$	−23.5066			−0.797406
$870$	−0.263932	−	0.191758i	−0.00894813	−	0.00650120i
$871$	44.3607	−	32.2299i	1.50310	−	1.09207i
$872$	−3.35520	+	1.09017i	−0.113621	+	0.0369178i
$873$		−	16.9443i		−	0.573477i
$874$	−3.81966			−0.129202
$875$	34.4095	−	11.1803i	1.16326	−	0.377964i
$876$	4.61803	−	14.2128i	0.156029	−	0.480208i
$877$	5.70634	+	1.85410i	0.192689	+	0.0626086i	0.403772	−	0.914860i	$-0.367699\pi$
$877$	5.70634	+	1.85410i	0.192689	+	0.0626086i	−0.211083	+	0.977468i	$0.567699\pi$
$878$	1.19581	−	1.64590i	0.0403568	−	0.0555464i
$879$	3.47214	+	10.6861i	0.117112	+	0.360434i
$880$	8.35410	+	6.06961i	0.281617	+	0.204607i
$881$	15.1803	−	11.0292i	0.511439	−	0.371582i	−0.301930	−	0.953330i	$-0.597631\pi$
$881$	15.1803	−	11.0292i	0.511439	−	0.371582i	0.813369	+	0.581748i	$0.197631\pi$
$882$	3.30220	+	1.07295i	0.111191	+	0.0361281i
$883$	23.2869	+	32.0517i	0.783666	+	1.07862i	0.994868	+	0.101182i	$0.0322624\pi$
$883$	23.2869	+	32.0517i	0.783666	+	1.07862i	−0.211202	+	0.977443i	$0.567738\pi$
$884$	26.9164	−	19.5559i	0.905297	−	0.657737i
$885$	20.9560	+	6.80902i	0.704428	+	0.228883i
$886$	13.7984	−	10.0251i	0.463565	−	0.336800i
$887$	−6.45313	+	8.88197i	−0.216675	+	0.298227i	−0.903494	−	0.428601i	$-0.859007\pi$
$887$	−6.45313	+	8.88197i	−0.216675	+	0.298227i	0.686819	+	0.726829i	$0.259007\pi$
$888$	3.94298	−	1.28115i	0.132318	−	0.0429927i
$889$	55.5967	+	40.3934i	1.86466	+	1.35475i
$890$	−33.4055	−	10.8541i	−1.11975	−	0.363830i
$891$	−1.42705	+	4.39201i	−0.0478080	+	0.147138i
$892$	9.40456	−	3.05573i	0.314888	−	0.102313i
$893$			36.1803i			1.21073i
$894$	−12.3820			−0.414115
$895$	−12.0967	−	37.2300i	−0.404350	−	1.24446i
$896$	2.61803	−	1.90211i	0.0874624	−	0.0635451i
$897$	3.44095	−	4.73607i	0.114890	−	0.158133i
$898$			8.00000i			0.266963i
$899$	−0.774575	+	0.244758i	−0.0258335	+	0.00816315i
$900$	5.00000			0.166667
$901$	22.4164	+	16.2865i	0.746799	+	0.542581i
$902$	15.4944	+	21.3262i	0.515908	+	0.710086i
$903$	12.3107	−	4.00000i	0.409676	−	0.133112i
$904$	−0.472136			−0.0157030
$905$	−19.5967			−0.651418
$906$	−5.52786	−	17.0130i	−0.183651	−	0.565220i
$907$	−2.71441	−	0.881966i	−0.0901306	−	0.0292852i	0.263605	−	0.964631i	$-0.415089\pi$
$907$	−2.71441	−	0.881966i	−0.0901306	−	0.0292852i	−0.353735	+	0.935346i	$0.615089\pi$
$908$	7.33094	+	2.38197i	0.243286	+	0.0790483i
$909$	4.35410	+	3.16344i	0.144416	+	0.104925i
$910$	47.1693	−	15.3262i	1.56365	−	0.508060i
$911$	−3.56231	−	2.58817i	−0.118024	−	0.0857498i	0.527207	−	0.849737i	$-0.323239\pi$
$911$	−3.56231	−	2.58817i	−0.118024	−	0.0857498i	−0.645232	+	0.763987i	$0.723239\pi$
$912$	−2.62866	−	3.61803i	−0.0870435	−	0.119805i
$913$	−31.7809	−	10.3262i	−1.05179	−	0.341749i
$914$	−3.76393	+	2.73466i	−0.124500	+	0.0904544i
$915$	−9.51057	−	13.0902i	−0.314410	−	0.432748i
$916$	7.29180	−	22.4418i	0.240928	−	0.741499i
$917$	35.7566	+	49.2148i	1.18079	+	1.62522i
$918$	2.85317	−	3.92705i	0.0941686	−	0.129612i
$919$	−2.68034	−	8.24924i	−0.0884163	−	0.272117i	0.897066	−	0.441897i	$-0.145694\pi$
$919$	−2.68034	−	8.24924i	−0.0884163	−	0.272117i	−0.985482	+	0.169780i	$0.945694\pi$
$920$	−1.54508	−	1.12257i	−0.0509399	−	0.0370100i
$921$	−2.57295	+	7.91872i	−0.0847816	+	0.260931i
$922$	−29.4298	−	9.56231i	−0.969217	−	0.314918i
$923$	−26.0746	+	8.47214i	−0.858254	+	0.278864i
$924$	14.9443			0.491630
$925$		−	20.7295i		−	0.681581i
$926$	11.5279	+	35.4791i	0.378829	+	1.16592i
$927$	−8.33499	−	11.4721i	−0.273757	−	0.376794i
$928$	−0.0857567	+	0.118034i	−0.00281510	+	0.00387466i
$929$	−26.5836			−0.872179			−0.436090	−	0.899903i	$-0.643637\pi$
$929$	−26.5836			−0.872179			−0.436090	+	0.899903i	$0.643637\pi$
$930$	7.39919	−	10.0126i	0.242629	−	0.328326i
$931$	−15.5279			−0.508905
$932$	−6.10237	+	8.39919i	−0.199890	+	0.275125i
$933$	7.88597	+	10.8541i	0.258175	+	0.355347i
$934$	5.41641	+	16.6700i	0.177230	+	0.545459i
$935$		−	50.1246i		−	1.63925i
$936$	6.85410			0.224033
$937$	54.5002	−	17.7082i	1.78045	−	0.578502i	0.781478	−	0.623933i	$-0.214466\pi$
$937$	54.5002	−	17.7082i	1.78045	−	0.578502i	0.998967	+	0.0454310i	$0.0144661\pi$
$938$	−24.6215	−	8.00000i	−0.803919	−	0.261209i
$939$	−0.236068	+	0.726543i	−0.00770379	+	0.0237098i
$940$	−10.6331	+	14.6353i	−0.346815	+	0.477349i
$941$	5.93363	+	18.2618i	0.193431	+	0.595319i	0.999991	+	0.00416721i	$0.00132647\pi$
$941$	5.93363	+	18.2618i	0.193431	+	0.595319i	−0.806561	+	0.591151i	$0.798674\pi$
$942$	3.47371	−	4.78115i	0.113180	−	0.155778i
$943$	−2.86568	−	3.94427i	−0.0933194	−	0.128443i
$944$	3.04508	−	9.37181i	0.0991091	−	0.305026i
$945$	5.85410	−	4.25325i	0.190434	−	0.138358i
$946$	14.9443	−	10.8576i	0.485880	−	0.353013i
$947$	10.3026	+	3.34752i	0.334790	+	0.108780i	0.471588	−	0.881819i	$-0.343681\pi$
$947$	10.3026	+	3.34752i	0.334790	+	0.108780i	−0.136798	+	0.990599i	$0.543681\pi$
$948$	2.99193	+	4.11803i	0.0971733	+	0.133748i
$949$	−82.8673	−	60.2066i	−2.68999	−	1.95439i
$950$	−21.2663	+	6.90983i	−0.689969	+	0.224184i
$951$	−3.47214	−	2.52265i	−0.112592	−	0.0818027i
$952$	−14.9394	−	4.85410i	−0.484188	−	0.157322i
$953$	8.75127	+	2.84346i	0.283481	+	0.0921087i	0.447307	−	0.894381i	$-0.352383\pi$
$953$	8.75127	+	2.84346i	0.283481	+	0.0921087i	−0.163825	+	0.986489i	$0.552383\pi$
$954$	1.76393	+	5.42882i	0.0571094	+	0.175765i
$955$	−6.18034			−0.199991
$956$	−25.1246			−0.812588
$957$	−0.640786	+	0.208204i	−0.0207137	+	0.00673028i
$958$	−10.5146	−	14.4721i	−0.339712	−	0.467573i
$959$	45.5967	+	33.1280i	1.47240	+	1.06976i
$960$		−	2.23607i		−	0.0721688i
$961$	−9.10081	−	29.6340i	−0.293575	−	0.955936i
$962$		−	28.4164i		−	0.916182i
$963$	−1.34708	+	1.85410i	−0.0434092	+	0.0597476i
$964$	7.78115	−	5.65334i	0.250614	−	0.182082i
$965$	9.12705	−	2.96556i	0.293810	−	0.0954647i
$966$	−2.76393			−0.0889281
$967$		−	4.40325i		−	0.141599i	−0.997491	−	0.0707995i	$-0.977445\pi$
$967$		−	4.40325i		−	0.141599i	0.997491	−	0.0707995i	$-0.0225551\pi$
$968$	9.82084	−	3.19098i	0.315654	−	0.102562i
$969$	−6.70820	+	20.6457i	−0.215499	+	0.663236i
$970$	−11.7082	+	36.0341i	−0.375928	+	1.15699i
$971$	−38.9164	−	28.2744i	−1.24889	−	0.907369i	−0.250730	−	0.968057i	$-0.580671\pi$
$971$	−38.9164	−	28.2744i	−1.24889	−	0.907369i	−0.998157	+	0.0606875i	$0.980671\pi$
$972$	0.951057	−	0.309017i	0.0305052	−	0.00991172i
$973$	−28.4257	+	39.1246i	−0.911286	+	1.25428i
$974$	−21.7984	+	15.8374i	−0.698465	+	0.507464i
$975$	10.5902	−	32.5932i	0.339157	−	1.04382i
$976$	−5.85410	+	4.25325i	−0.187385	+	0.136143i
$977$	−16.4782	−	22.6803i	−0.527185	−	0.725608i	0.459513	−	0.888171i	$-0.348024\pi$
$977$	−16.4782	−	22.6803i	−0.527185	−	0.725608i	−0.986698	+	0.162563i	$0.948024\pi$
$978$	−15.2497	−	4.95492i	−0.487630	−	0.158441i
$979$	−58.6869	+	42.6385i	−1.87564	+	1.36273i
$980$	−6.28115	−	4.56352i	−0.200644	−	0.145776i
$981$	1.09017	+	3.35520i	0.0348064	+	0.107123i
$982$	11.1882	−	15.3992i	0.357029	−	0.491408i
$983$	−57.8882	−	18.8090i	−1.84635	−	0.599914i	−0.997451	−	0.0713544i	$-0.977268\pi$
$983$	−57.8882	−	18.8090i	−1.84635	−	0.599914i	−0.848896	−	0.528560i	$-0.822732\pi$
$984$	1.76393	−	5.42882i	0.0562321	−	0.173065i
$985$	23.2744	−	7.56231i	0.741584	−	0.240955i
$986$	0.708204			0.0225538
$987$			26.1803i			0.833329i
$988$	−29.1522	+	9.47214i	−0.927456	+	0.301349i
$989$	−2.76393	+	2.00811i	−0.0878879	+	0.0638543i
$990$	6.06961	−	8.35410i	0.192905	−	0.265511i
$991$	7.41641			0.235590			0.117795	−	0.993038i	$-0.462417\pi$
$991$	7.41641			0.235590			0.117795	+	0.993038i	$0.462417\pi$
$992$	−4.47777	−	3.30902i	−0.142169	−	0.105061i
$993$			8.76393i			0.278115i
$994$	10.4721	+	7.60845i	0.332156	+	0.241325i
$995$	38.6803	−	28.1029i	1.22625	−	0.890922i
$996$	2.23607	+	6.88191i	0.0708525	+	0.218062i
$997$		−	42.8541i		−	1.35720i	−0.734507	−	0.678602i	$-0.762586\pi$
$997$		−	42.8541i		−	1.35720i	0.734507	−	0.678602i	$-0.237414\pi$
$998$		−	26.1803i		−	0.828724i
$999$	−1.28115	−	3.94298i	−0.0405339	−	0.124750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.a.529.2	yes	8
5.4	even	2	inner	930.2.z.a.529.1	yes	8
31.16	even	5	inner	930.2.z.a.109.1	✓	8
155.109	even	10	inner	930.2.z.a.109.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.a.109.1	✓	8	31.16	even	5	inner
930.2.z.a.109.2	yes	8	155.109	even	10	inner
930.2.z.a.529.1	yes	8	5.4	even	2	inner
930.2.z.a.529.2	yes	8	1.1	even	1	trivial

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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +2.23607 q^{5} -1.00000 q^{6} +(3.07768 - 1.00000i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +2.23607 q^{5} -1.00000 q^{6} +(3.07768 - 1.00000i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.309017 + 0.951057i) q^{9} +(1.31433 - 1.80902i) q^{10} +(-1.42705 - 4.39201i) q^{11} +(-0.587785 + 0.809017i) q^{12} +(4.02874 + 5.54508i) q^{13} +(1.00000 - 3.07768i) q^{14} +(-1.31433 - 1.80902i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(4.61653 + 1.50000i) q^{17} +(0.587785 + 0.809017i) q^{18} +(-3.61803 - 2.62866i) q^{19} +(-0.690983 - 2.12663i) q^{20} +(-2.61803 - 1.90211i) q^{21} +(-4.39201 - 1.42705i) q^{22} +(0.812299 + 0.263932i) q^{23} +(0.309017 + 0.951057i) q^{24} +5.00000 q^{25} +6.85410 q^{26} +(0.951057 - 0.309017i) q^{27} +(-1.90211 - 2.61803i) q^{28} +(0.118034 + 0.0857567i) q^{29} -2.23607 q^{30} +(-3.30902 + 4.47777i) q^{31} +1.00000i q^{32} +(-2.71441 + 3.73607i) q^{33} +(3.92705 - 2.85317i) q^{34} +(6.88191 - 2.23607i) q^{35} +1.00000 q^{36} -4.14590i q^{37} +(-4.25325 + 1.38197i) q^{38} +(2.11803 - 6.51864i) q^{39} +(-2.12663 - 0.690983i) q^{40} +(-4.61803 - 3.35520i) q^{41} +(-3.07768 + 1.00000i) q^{42} +(-2.35114 + 3.23607i) q^{43} +(-3.73607 + 2.71441i) q^{44} +(-0.690983 + 2.12663i) q^{45} +(0.690983 - 0.502029i) q^{46} +(-4.75528 - 6.54508i) q^{47} +(0.951057 + 0.309017i) q^{48} +(2.80902 - 2.04087i) q^{49} +(2.93893 - 4.04508i) q^{50} +(-1.50000 - 4.61653i) q^{51} +(4.02874 - 5.54508i) q^{52} +(5.42882 + 1.76393i) q^{53} +(0.309017 - 0.951057i) q^{54} +(-3.19098 - 9.82084i) q^{55} -3.23607 q^{56} +4.47214i q^{57} +(0.138757 - 0.0450850i) q^{58} +(-7.97214 + 5.79210i) q^{59} +(-1.31433 + 1.80902i) q^{60} +7.23607 q^{61} +(1.67760 + 5.30902i) q^{62} +3.23607i q^{63} +(0.809017 + 0.587785i) q^{64} +(9.00854 + 12.3992i) q^{65} +(1.42705 + 4.39201i) q^{66} -8.00000i q^{67} -4.85410i q^{68} +(-0.263932 - 0.812299i) q^{69} +(2.23607 - 6.88191i) q^{70} +(-1.23607 + 3.80423i) q^{71} +(0.587785 - 0.809017i) q^{72} +(-14.2128 + 4.61803i) q^{73} +(-3.35410 - 2.43690i) q^{74} +(-2.93893 - 4.04508i) q^{75} +(-1.38197 + 4.25325i) q^{76} +(-8.78402 - 12.0902i) q^{77} +(-4.02874 - 5.54508i) q^{78} +(1.57295 - 4.84104i) q^{79} +(-1.80902 + 1.31433i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-5.42882 + 1.76393i) q^{82} +(4.25325 - 5.85410i) q^{83} +(-1.00000 + 3.07768i) q^{84} +(10.3229 + 3.35410i) q^{85} +(1.23607 + 3.80423i) q^{86} -0.145898i q^{87} +4.61803i q^{88} +(-4.85410 - 14.9394i) q^{89} +(1.31433 + 1.80902i) q^{90} +(17.9443 + 13.0373i) q^{91} -0.854102i q^{92} +(5.56758 + 0.0450850i) q^{93} -8.09017 q^{94} +(-8.09017 - 5.87785i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-16.1150 + 5.23607i) q^{97} -3.47214i q^{98} +4.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} - 8 q^{6} + 2 q^{9} + 2 q^{11} + 8 q^{14} - 2 q^{16} - 20 q^{19} - 10 q^{20} - 12 q^{21} - 2 q^{24} + 40 q^{25} + 28 q^{26} - 8 q^{29} - 22 q^{31} + 18 q^{34} + 8 q^{36} + 8 q^{39} - 28 q^{41} - 12 q^{44} - 10 q^{45} + 10 q^{46} + 18 q^{49} - 12 q^{51} - 2 q^{54} - 30 q^{55} - 8 q^{56} - 28 q^{59} + 40 q^{61} + 2 q^{64} - 2 q^{66} - 20 q^{69} + 8 q^{71} - 20 q^{76} + 26 q^{79} - 10 q^{80} - 2 q^{81} - 8 q^{84} - 8 q^{86} - 12 q^{89} + 72 q^{91} - 20 q^{94} - 20 q^{95} + 2 q^{96} + 28 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 - 8 * q^6 + 2 * q^9 + 2 * q^11 + 8 * q^14 - 2 * q^16 - 20 * q^19 - 10 * q^20 - 12 * q^21 - 2 * q^24 + 40 * q^25 + 28 * q^26 - 8 * q^29 - 22 * q^31 + 18 * q^34 + 8 * q^36 + 8 * q^39 - 28 * q^41 - 12 * q^44 - 10 * q^45 + 10 * q^46 + 18 * q^49 - 12 * q^51 - 2 * q^54 - 30 * q^55 - 8 * q^56 - 28 * q^59 + 40 * q^61 + 2 * q^64 - 2 * q^66 - 20 * q^69 + 8 * q^71 - 20 * q^76 + 26 * q^79 - 10 * q^80 - 2 * q^81 - 8 * q^84 - 8 * q^86 - 12 * q^89 + 72 * q^91 - 20 * q^94 - 20 * q^95 + 2 * q^96 + 28 * q^99

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