LMFDB - Embedded newform 950.2.h.a.761.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			761.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	950.761
Dual form			950.2.h.a.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-1.00000 - 3.07768i) q^{6} -5.23607 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-1.00000 - 3.07768i) q^{6} -5.23607 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +(1.80902 + 1.31433i) q^{10} +(-1.61803 + 1.17557i) q^{11} +(-2.61803 - 1.90211i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(-4.23607 + 3.07768i) q^{14} +7.23607 q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.500000 - 1.53884i) q^{17} -7.47214 q^{18} +(-0.309017 - 0.951057i) q^{19} +2.23607 q^{20} +(-5.23607 + 16.1150i) q^{21} +(-0.618034 + 1.90211i) q^{22} +(6.85410 - 4.97980i) q^{23} -3.23607 q^{24} +(-4.04508 + 2.93893i) q^{25} -1.85410 q^{26} +(-11.7082 + 8.50651i) q^{27} +(-1.61803 + 4.97980i) q^{28} +(-0.263932 + 0.812299i) q^{29} +(5.85410 - 4.25325i) q^{30} +(-1.61803 - 4.97980i) q^{31} -1.00000 q^{32} +(2.00000 + 6.15537i) q^{33} +(-1.30902 - 0.951057i) q^{34} +(-3.61803 - 11.1352i) q^{35} +(-6.04508 + 4.39201i) q^{36} +(-4.54508 - 3.30220i) q^{37} +(-0.809017 - 0.587785i) q^{38} +(-4.85410 + 3.52671i) q^{39} +(1.80902 - 1.31433i) q^{40} +(3.11803 + 2.26538i) q^{41} +(5.23607 + 16.1150i) q^{42} -1.23607 q^{43} +(0.618034 + 1.90211i) q^{44} +(5.16312 - 15.8904i) q^{45} +(2.61803 - 8.05748i) q^{46} +(3.38197 - 10.4086i) q^{47} +(-2.61803 + 1.90211i) q^{48} +20.4164 q^{49} +(-1.54508 + 4.75528i) q^{50} -5.23607 q^{51} +(-1.50000 + 1.08981i) q^{52} +(0.572949 - 1.76336i) q^{53} +(-4.47214 + 13.7638i) q^{54} +(-3.61803 - 2.62866i) q^{55} +(1.61803 + 4.97980i) q^{56} -3.23607 q^{57} +(0.263932 + 0.812299i) q^{58} +(5.85410 + 4.25325i) q^{59} +(2.23607 - 6.88191i) q^{60} +(0.881966 - 0.640786i) q^{61} +(-4.23607 - 3.07768i) q^{62} +(31.6525 + 22.9969i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.28115 - 3.94298i) q^{65} +(5.23607 + 3.80423i) q^{66} +(0.618034 + 1.90211i) q^{67} -1.61803 q^{68} +(-8.47214 - 26.0746i) q^{69} +(-9.47214 - 6.88191i) q^{70} +(4.76393 - 14.6619i) q^{71} +(-2.30902 + 7.10642i) q^{72} +(0.736068 - 0.534785i) q^{73} -5.61803 q^{74} +(5.00000 + 15.3884i) q^{75} -1.00000 q^{76} +(8.47214 - 6.15537i) q^{77} +(-1.85410 + 5.70634i) q^{78} +(-2.76393 + 8.50651i) q^{79} +(0.690983 - 2.12663i) q^{80} +(7.54508 + 23.2214i) q^{81} +3.85410 q^{82} +(-3.47214 - 10.6861i) q^{83} +(13.7082 + 9.95959i) q^{84} +(2.92705 - 2.12663i) q^{85} +(-1.00000 + 0.726543i) q^{86} +(2.23607 + 1.62460i) q^{87} +(1.61803 + 1.17557i) q^{88} +(-10.1631 + 7.38394i) q^{89} +(-5.16312 - 15.8904i) q^{90} +(7.85410 + 5.70634i) q^{91} +(-2.61803 - 8.05748i) q^{92} -16.9443 q^{93} +(-3.38197 - 10.4086i) q^{94} +(1.80902 - 1.31433i) q^{95} +(-1.00000 + 3.07768i) q^{96} +(-1.35410 + 4.16750i) q^{97} +(16.5172 - 12.0005i) q^{98} +14.9443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 4 q^{3} - q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 13 q^{9}+O(q^{10}) $ 4 * q + q^2 + 4 * q^3 - q^4 + 5 * q^5 - 4 * q^6 - 12 * q^7 + q^8 - 13 * q^9	\( 4 q + q^{2} + 4 q^{3} - q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 13 q^{9} + 5 q^{10} - 2 q^{11} - 6 q^{12} - 6 q^{13} - 8 q^{14} + 20 q^{15} - q^{16} - 2 q^{17} - 12 q^{18} + q^{19} - 12 q^{21} + 2 q^{22} + 14 q^{23} - 4 q^{24} - 5 q^{25} + 6 q^{26} - 20 q^{27} - 2 q^{28} - 10 q^{29} + 10 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 3 q^{34} - 10 q^{35} - 13 q^{36} - 7 q^{37} - q^{38} - 6 q^{39} + 5 q^{40} + 8 q^{41} + 12 q^{42} + 4 q^{43} - 2 q^{44} + 5 q^{45} + 6 q^{46} + 18 q^{47} - 6 q^{48} + 28 q^{49} + 5 q^{50} - 12 q^{51} - 6 q^{52} + 9 q^{53} - 10 q^{55} + 2 q^{56} - 4 q^{57} + 10 q^{58} + 10 q^{59} + 8 q^{61} - 8 q^{62} + 64 q^{63} - q^{64} - 15 q^{65} + 12 q^{66} - 2 q^{67} - 2 q^{68} - 16 q^{69} - 20 q^{70} + 28 q^{71} - 7 q^{72} - 6 q^{73} - 18 q^{74} + 20 q^{75} - 4 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} + 5 q^{80} + 19 q^{81} + 2 q^{82} + 4 q^{83} + 28 q^{84} + 5 q^{85} - 4 q^{86} + 2 q^{88} - 25 q^{89} - 5 q^{90} + 18 q^{91} - 6 q^{92} - 32 q^{93} - 18 q^{94} + 5 q^{95} - 4 q^{96} + 8 q^{97} + 37 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 - q^4 + 5 * q^5 - 4 * q^6 - 12 * q^7 + q^8 - 13 * q^9 + 5 * q^10 - 2 * q^11 - 6 * q^12 - 6 * q^13 - 8 * q^14 + 20 * q^15 - q^16 - 2 * q^17 - 12 * q^18 + q^19 - 12 * q^21 + 2 * q^22 + 14 * q^23 - 4 * q^24 - 5 * q^25 + 6 * q^26 - 20 * q^27 - 2 * q^28 - 10 * q^29 + 10 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 3 * q^34 - 10 * q^35 - 13 * q^36 - 7 * q^37 - q^38 - 6 * q^39 + 5 * q^40 + 8 * q^41 + 12 * q^42 + 4 * q^43 - 2 * q^44 + 5 * q^45 + 6 * q^46 + 18 * q^47 - 6 * q^48 + 28 * q^49 + 5 * q^50 - 12 * q^51 - 6 * q^52 + 9 * q^53 - 10 * q^55 + 2 * q^56 - 4 * q^57 + 10 * q^58 + 10 * q^59 + 8 * q^61 - 8 * q^62 + 64 * q^63 - q^64 - 15 * q^65 + 12 * q^66 - 2 * q^67 - 2 * q^68 - 16 * q^69 - 20 * q^70 + 28 * q^71 - 7 * q^72 - 6 * q^73 - 18 * q^74 + 20 * q^75 - 4 * q^76 + 16 * q^77 + 6 * q^78 - 20 * q^79 + 5 * q^80 + 19 * q^81 + 2 * q^82 + 4 * q^83 + 28 * q^84 + 5 * q^85 - 4 * q^86 + 2 * q^88 - 25 * q^89 - 5 * q^90 + 18 * q^91 - 6 * q^92 - 32 * q^93 - 18 * q^94 + 5 * q^95 - 4 * q^96 + 8 * q^97 + 37 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	−0.0506828	−	0.998715i	$-0.516140\pi$
$3$	1.00000	−	3.07768i	0.577350	−	1.77690i	0.628033	−	0.778187i	$-0.283860\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$5$	0.690983	+	2.12663i	0.309017	+	0.951057i
$6$	−1.00000	−	3.07768i	−0.408248	−	1.25646i
$7$	−5.23607			−1.97905			−0.989524	−	0.144370i	$-0.953885\pi$
$7$	−5.23607			−1.97905			−0.989524	+	0.144370i	$0.953885\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−6.04508	−	4.39201i	−2.01503	−	1.46400i
$10$	1.80902	+	1.31433i	0.572061	+	0.415627i
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	−0.804359	−	0.594144i	$-0.797491\pi$
$11$	−1.61803	+	1.17557i	−0.487856	+	0.354448i	0.316503	+	0.948591i	$0.397491\pi$
$12$	−2.61803	−	1.90211i	−0.755761	−	0.549093i
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	0.360011	−	0.932948i	$-0.382773\pi$
$13$	−1.50000	−	1.08981i	−0.416025	−	0.302260i	−0.776037	+	0.630688i	$0.782773\pi$
$14$	−4.23607	+	3.07768i	−1.13214	+	0.822546i
$15$	7.23607			1.86834
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.500000	−	1.53884i	−0.121268	−	0.373224i	0.871935	−	0.489622i	$-0.162865\pi$
$17$	−0.500000	−	1.53884i	−0.121268	−	0.373224i	−0.993203	+	0.116398i	$0.962865\pi$
$18$	−7.47214			−1.76120
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	2.23607			0.500000
$21$	−5.23607	+	16.1150i	−1.14260	+	3.51657i
$22$	−0.618034	+	1.90211i	−0.131765	+	0.405532i
$23$	6.85410	−	4.97980i	1.42918	−	1.03836i	0.439010	−	0.898482i	$-0.355329\pi$
$23$	6.85410	−	4.97980i	1.42918	−	1.03836i	0.990169	−	0.139877i	$-0.0446708\pi$
$24$	−3.23607			−0.660560
$25$	−4.04508	+	2.93893i	−0.809017	+	0.587785i
$26$	−1.85410			−0.363619
$27$	−11.7082	+	8.50651i	−2.25324	+	1.63708i
$28$	−1.61803	+	4.97980i	−0.305780	+	0.941093i
$29$	−0.263932	+	0.812299i	−0.0490109	+	0.150840i	−0.972567	−	0.232624i	$-0.925269\pi$
$29$	−0.263932	+	0.812299i	−0.0490109	+	0.150840i	0.923556	+	0.383464i	$0.125269\pi$
$30$	5.85410	−	4.25325i	1.06881	−	0.776534i
$31$	−1.61803	−	4.97980i	−0.290607	−	0.894398i	−0.984662	−	0.174475i	$-0.944177\pi$
$31$	−1.61803	−	4.97980i	−0.290607	−	0.894398i	0.694054	−	0.719923i	$-0.255823\pi$
$32$	−1.00000			−0.176777
$33$	2.00000	+	6.15537i	0.348155	+	1.07151i
$34$	−1.30902	−	0.951057i	−0.224495	−	0.163105i
$35$	−3.61803	−	11.1352i	−0.611559	−	1.88219i
$36$	−6.04508	+	4.39201i	−1.00751	+	0.732002i
$37$	−4.54508	−	3.30220i	−0.747207	−	0.542878i	0.147753	−	0.989024i	$-0.452796\pi$
$37$	−4.54508	−	3.30220i	−0.747207	−	0.542878i	−0.894960	+	0.446146i	$0.852796\pi$
$38$	−0.809017	−	0.587785i	−0.131240	−	0.0953514i
$39$	−4.85410	+	3.52671i	−0.777278	+	0.564726i
$40$	1.80902	−	1.31433i	0.286031	−	0.207813i
$41$	3.11803	+	2.26538i	0.486955	+	0.353794i	0.804012	−	0.594613i	$-0.202695\pi$
$41$	3.11803	+	2.26538i	0.486955	+	0.353794i	−0.317057	+	0.948406i	$0.602695\pi$
$42$	5.23607	+	16.1150i	0.807943	+	2.48659i
$43$	−1.23607			−0.188499			−0.0942493	−	0.995549i	$-0.530045\pi$
$43$	−1.23607			−0.188499			−0.0942493	+	0.995549i	$0.530045\pi$
$44$	0.618034	+	1.90211i	0.0931721	+	0.286754i
$45$	5.16312	−	15.8904i	0.769672	−	2.36881i
$46$	2.61803	−	8.05748i	0.386008	−	1.18801i
$47$	3.38197	−	10.4086i	0.493310	−	1.51825i	−0.326263	−	0.945279i	$-0.605789\pi$
$47$	3.38197	−	10.4086i	0.493310	−	1.51825i	0.819573	−	0.572974i	$-0.194211\pi$
$48$	−2.61803	+	1.90211i	−0.377881	+	0.274546i
$49$	20.4164			2.91663
$50$	−1.54508	+	4.75528i	−0.218508	+	0.672499i
$51$	−5.23607			−0.733196
$52$	−1.50000	+	1.08981i	−0.208013	+	0.151130i
$53$	0.572949	−	1.76336i	0.0787006	−	0.242216i	−0.903964	−	0.427609i	$-0.859356\pi$
$53$	0.572949	−	1.76336i	0.0787006	−	0.242216i	0.982664	+	0.185394i	$0.0593560\pi$
$54$	−4.47214	+	13.7638i	−0.608581	+	1.87302i
$55$	−3.61803	−	2.62866i	−0.487856	−	0.354448i
$56$	1.61803	+	4.97980i	0.216219	+	0.665453i
$57$	−3.23607			−0.428628
$58$	0.263932	+	0.812299i	0.0346560	+	0.106660i
$59$	5.85410	+	4.25325i	0.762139	+	0.553727i	0.899566	−	0.436785i	$-0.143883\pi$
$59$	5.85410	+	4.25325i	0.762139	+	0.553727i	−0.137427	+	0.990512i	$0.543883\pi$
$60$	2.23607	−	6.88191i	0.288675	−	0.888451i
$61$	0.881966	−	0.640786i	0.112924	−	0.0820442i	−0.529890	−	0.848066i	$-0.677767\pi$
$61$	0.881966	−	0.640786i	0.112924	−	0.0820442i	0.642814	+	0.766022i	$0.277767\pi$
$62$	−4.23607	−	3.07768i	−0.537981	−	0.390866i
$63$	31.6525	+	22.9969i	3.98784	+	2.89733i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	1.28115	−	3.94298i	0.158907	−	0.489067i
$66$	5.23607	+	3.80423i	0.644515	+	0.468268i
$67$	0.618034	+	1.90211i	0.0755049	+	0.232380i	0.981685	−	0.190512i	$-0.0610149\pi$
$67$	0.618034	+	1.90211i	0.0755049	+	0.232380i	−0.906180	+	0.422892i	$0.861015\pi$
$68$	−1.61803			−0.196215
$69$	−8.47214	−	26.0746i	−1.01993	−	3.13901i
$70$	−9.47214	−	6.88191i	−1.13214	−	0.822546i
$71$	4.76393	−	14.6619i	0.565375	−	1.74004i	−0.101461	−	0.994840i	$-0.532352\pi$
$71$	4.76393	−	14.6619i	0.565375	−	1.74004i	0.666836	−	0.745205i	$-0.267648\pi$
$72$	−2.30902	+	7.10642i	−0.272120	+	0.837500i
$73$	0.736068	−	0.534785i	0.0861502	−	0.0625918i	−0.543876	−	0.839165i	$-0.683044\pi$
$73$	0.736068	−	0.534785i	0.0861502	−	0.0625918i	0.630027	+	0.776574i	$0.283044\pi$
$74$	−5.61803			−0.653083
$75$	5.00000	+	15.3884i	0.577350	+	1.77690i
$76$	−1.00000			−0.114708
$77$	8.47214	−	6.15537i	0.965489	−	0.701469i
$78$	−1.85410	+	5.70634i	−0.209936	+	0.646116i
$79$	−2.76393	+	8.50651i	−0.310967	+	0.957057i	0.666416	+	0.745580i	$0.267827\pi$
$79$	−2.76393	+	8.50651i	−0.310967	+	0.957057i	−0.977383	+	0.211477i	$0.932173\pi$
$80$	0.690983	−	2.12663i	0.0772542	−	0.237764i
$81$	7.54508	+	23.2214i	0.838343	+	2.58015i
$82$	3.85410			0.425614
$83$	−3.47214	−	10.6861i	−0.381116	−	1.17296i	−0.939259	−	0.343210i	$-0.888486\pi$
$83$	−3.47214	−	10.6861i	−0.381116	−	1.17296i	0.558142	−	0.829745i	$-0.311514\pi$
$84$	13.7082	+	9.95959i	1.49569	+	1.08668i
$85$	2.92705	−	2.12663i	0.317483	−	0.230665i
$86$	−1.00000	+	0.726543i	−0.107833	+	0.0783451i
$87$	2.23607	+	1.62460i	0.239732	+	0.174175i
$88$	1.61803	+	1.17557i	0.172483	+	0.125316i
$89$	−10.1631	+	7.38394i	−1.07729	+	0.782696i	−0.977208	−	0.212283i	$-0.931910\pi$
$89$	−10.1631	+	7.38394i	−1.07729	+	0.782696i	−0.100080	+	0.994979i	$0.531910\pi$
$90$	−5.16312	−	15.8904i	−0.544241	−	1.67500i
$91$	7.85410	+	5.70634i	0.823334	+	0.598187i
$92$	−2.61803	−	8.05748i	−0.272949	−	0.840050i
$93$	−16.9443			−1.75704
$94$	−3.38197	−	10.4086i	−0.348823	−	1.07357i
$95$	1.80902	−	1.31433i	0.185601	−	0.134847i
$96$	−1.00000	+	3.07768i	−0.102062	+	0.314115i
$97$	−1.35410	+	4.16750i	−0.137488	+	0.423145i	−0.995969	−	0.0897009i	$-0.971409\pi$
$97$	−1.35410	+	4.16750i	−0.137488	+	0.423145i	0.858481	+	0.512846i	$0.171409\pi$
$98$	16.5172	−	12.0005i	1.66849	−	1.21223i
$99$	14.9443			1.50196
$100$	1.54508	+	4.75528i	0.154508	+	0.475528i
$101$	−6.09017			−0.605995			−0.302997	−	0.952991i	$-0.597987\pi$
$101$	−6.09017			−0.605995			−0.302997	+	0.952991i	$0.597987\pi$
$102$	−4.23607	+	3.07768i	−0.419433	+	0.304736i
$103$	0.673762	−	2.07363i	0.0663878	−	0.204320i	−0.912360	−	0.409389i	$-0.865742\pi$
$103$	0.673762	−	2.07363i	0.0663878	−	0.204320i	0.978748	+	0.205069i	$0.0657418\pi$
$104$	−0.572949	+	1.76336i	−0.0561823	+	0.172911i
$105$	−37.8885			−3.69754
$106$	−0.572949	−	1.76336i	−0.0556497	−	0.171272i
$107$	4.76393			0.460547			0.230273	−	0.973126i	$-0.426038\pi$
$107$	4.76393			0.460547			0.230273	+	0.973126i	$0.426038\pi$
$108$	4.47214	+	13.7638i	0.430331	+	1.32442i
$109$	−9.20820	−	6.69015i	−0.881986	−	0.640800i	0.0517902	−	0.998658i	$-0.483507\pi$
$109$	−9.20820	−	6.69015i	−0.881986	−	0.640800i	−0.933776	+	0.357858i	$0.883507\pi$
$110$	−4.47214			−0.426401
$111$	−14.7082	+	10.6861i	−1.39604	+	1.01428i
$112$	4.23607	+	3.07768i	0.400271	+	0.290814i
$113$	7.54508	+	5.48183i	0.709782	+	0.515687i	0.883103	−	0.469179i	$-0.155450\pi$
$113$	7.54508	+	5.48183i	0.709782	+	0.515687i	−0.173321	+	0.984865i	$0.555450\pi$
$114$	−2.61803	+	1.90211i	−0.245201	+	0.178149i
$115$	15.3262	+	11.1352i	1.42918	+	1.03836i
$116$	0.690983	+	0.502029i	0.0641562	+	0.0466122i
$117$	4.28115	+	13.1760i	0.395793	+	1.21812i
$118$	7.23607			0.666134
$119$	2.61803	+	8.05748i	0.239995	+	0.738628i
$120$	−2.23607	−	6.88191i	−0.204124	−	0.628230i
$121$	−2.16312	+	6.65740i	−0.196647	+	0.605218i
$122$	0.336881	−	1.03681i	0.0304998	−	0.0938687i
$123$	10.0902	−	7.33094i	0.909800	−	0.661008i
$124$	−5.23607			−0.470213
$125$	−9.04508	−	6.57164i	−0.809017	−	0.587785i
$126$	39.1246			3.48550
$127$	11.4721	−	8.33499i	1.01799	−	0.739611i	0.0521181	−	0.998641i	$-0.483403\pi$
$127$	11.4721	−	8.33499i	1.01799	−	0.739611i	0.965869	+	0.259030i	$0.0834028\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	−1.23607	+	3.80423i	−0.108830	+	0.334943i
$130$	−1.28115	−	3.94298i	−0.112365	−	0.345823i
$131$	6.79837	+	20.9232i	0.593977	+	1.82807i	0.559755	+	0.828658i	$0.310895\pi$
$131$	6.79837	+	20.9232i	0.593977	+	1.82807i	0.0342214	+	0.999414i	$0.489105\pi$
$132$	6.47214			0.563327
$133$	1.61803	+	4.97980i	0.140301	+	0.431803i
$134$	1.61803	+	1.17557i	0.139777	+	0.101554i
$135$	−26.1803	−	19.0211i	−2.25324	−	1.63708i
$136$	−1.30902	+	0.951057i	−0.112247	+	0.0815524i
$137$	11.2082	+	8.14324i	0.957581	+	0.695724i	0.952588	−	0.304264i	$-0.0984105\pi$
$137$	11.2082	+	8.14324i	0.957581	+	0.695724i	0.00499369	+	0.999988i	$0.498410\pi$
$138$	−22.1803	−	16.1150i	−1.88812	−	1.37180i
$139$	−0.854102	+	0.620541i	−0.0724440	+	0.0526336i	−0.623418	−	0.781889i	$-0.714256\pi$
$139$	−0.854102	+	0.620541i	−0.0724440	+	0.0526336i	0.550974	+	0.834523i	$0.314256\pi$
$140$	−11.7082			−0.989524
$141$	−28.6525	−	20.8172i	−2.41297	−	1.75313i
$142$	−4.76393	−	14.6619i	−0.399780	−	1.23040i
$143$	3.70820			0.310096
$144$	2.30902	+	7.10642i	0.192418	+	0.592202i
$145$	−1.90983			−0.158603
$146$	0.281153	−	0.865300i	0.0232684	−	0.0716127i
$147$	20.4164	−	62.8352i	1.68392	−	5.18256i
$148$	−4.54508	+	3.30220i	−0.373604	+	0.271439i
$149$	−4.14590			−0.339645			−0.169823	−	0.985475i	$-0.554319\pi$
$149$	−4.14590			−0.339645			−0.169823	+	0.985475i	$0.554319\pi$
$150$	13.0902	+	9.51057i	1.06881	+	0.776534i
$151$	−21.4164			−1.74284			−0.871421	−	0.490535i	$-0.836801\pi$
$151$	−21.4164			−1.74284			−0.871421	+	0.490535i	$0.836801\pi$
$152$	−0.809017	+	0.587785i	−0.0656199	+	0.0476757i
$153$	−3.73607	+	11.4984i	−0.302043	+	0.929593i
$154$	3.23607	−	9.95959i	0.260770	−	0.802567i
$155$	9.47214	−	6.88191i	0.760820	−	0.552768i
$156$	1.85410	+	5.70634i	0.148447	+	0.456873i
$157$	2.85410			0.227782			0.113891	−	0.993493i	$-0.463669\pi$
$157$	2.85410			0.227782			0.113891	+	0.993493i	$0.463669\pi$
$158$	2.76393	+	8.50651i	0.219887	+	0.676741i
$159$	−4.85410	−	3.52671i	−0.384955	−	0.279686i
$160$	−0.690983	−	2.12663i	−0.0546270	−	0.168125i
$161$	−35.8885	+	26.0746i	−2.82841	+	2.05496i
$162$	19.7533	+	14.3516i	1.55196	+	1.12757i
$163$	−7.09017	−	5.15131i	−0.555345	−	0.403482i	0.274407	−	0.961614i	$-0.411518\pi$
$163$	−7.09017	−	5.15131i	−0.555345	−	0.403482i	−0.829752	+	0.558132i	$0.811518\pi$
$164$	3.11803	−	2.26538i	0.243478	−	0.176897i
$165$	−11.7082	+	8.50651i	−0.911482	+	0.662231i
$166$	−9.09017	−	6.60440i	−0.705534	−	0.512600i
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	−1.00000		0.000538710i	$-0.999829\pi$
$167$	−2.47214	−	7.60845i	−0.191300	−	0.588760i	0.808700	−	0.588221i	$-0.200171\pi$
$168$	16.9443			1.30728
$169$	−2.95492	−	9.09429i	−0.227301	−	0.699561i
$170$	1.11803	−	3.44095i	0.0857493	−	0.263909i
$171$	−2.30902	+	7.10642i	−0.176575	+	0.543442i
$172$	−0.381966	+	1.17557i	−0.0291246	+	0.0896364i
$173$	18.3992	−	13.3678i	1.39886	−	1.01633i	0.404038	−	0.914742i	$-0.367606\pi$
$173$	18.3992	−	13.3678i	1.39886	−	1.01633i	0.994826	−	0.101592i	$-0.0323937\pi$
$174$	2.76393			0.209533
$175$	21.1803	−	15.3884i	1.60108	−	1.16326i
$176$	2.00000			0.150756
$177$	18.9443	−	13.7638i	1.42394	−	1.03455i
$178$	−3.88197	+	11.9475i	−0.290966	+	0.895500i
$179$	3.09017	−	9.51057i	0.230970	−	0.710853i	−0.766660	−	0.642053i	$-0.778083\pi$
$179$	3.09017	−	9.51057i	0.230970	−	0.710853i	0.997630	−	0.0688001i	$-0.0219171\pi$
$180$	−13.5172	−	9.82084i	−1.00751	−	0.732002i
$181$	−1.02786	−	3.16344i	−0.0764005	−	0.235137i	0.905561	−	0.424215i	$-0.139450\pi$
$181$	−1.02786	−	3.16344i	−0.0764005	−	0.235137i	−0.981962	+	0.189078i	$0.939450\pi$
$182$	9.70820			0.719620
$183$	−1.09017	−	3.35520i	−0.0805877	−	0.248023i
$184$	−6.85410	−	4.97980i	−0.505291	−	0.367115i
$185$	3.88197	−	11.9475i	0.285408	−	0.878395i
$186$	−13.7082	+	9.95959i	−1.00513	+	0.730273i
$187$	2.61803	+	1.90211i	0.191450	+	0.139096i
$188$	−8.85410	−	6.43288i	−0.645752	−	0.469166i
$189$	61.3050	−	44.5407i	4.45928	−	3.23986i
$190$	0.690983	−	2.12663i	0.0501292	−	0.154282i
$191$	6.47214	+	4.70228i	0.468307	+	0.340245i	0.796781	−	0.604268i	$-0.206534\pi$
$191$	6.47214	+	4.70228i	0.468307	+	0.340245i	−0.328474	+	0.944513i	$0.606534\pi$
$192$	1.00000	+	3.07768i	0.0721688	+	0.222113i
$193$	−14.3262			−1.03123			−0.515613	−	0.856822i	$-0.672436\pi$
$193$	−14.3262			−1.03123			−0.515613	+	0.856822i	$0.672436\pi$
$194$	1.35410	+	4.16750i	0.0972189	+	0.299209i
$195$	−10.8541	−	7.88597i	−0.777278	−	0.564726i
$196$	6.30902	−	19.4172i	0.450644	−	1.38694i
$197$	−5.86475	+	18.0498i	−0.417846	+	1.28600i	0.491835	+	0.870689i	$0.336326\pi$
$197$	−5.86475	+	18.0498i	−0.417846	+	1.28600i	−0.909681	+	0.415309i	$0.863674\pi$
$198$	12.0902	−	8.78402i	0.859211	−	0.624253i
$199$	16.1803			1.14699			0.573497	−	0.819208i	$-0.305586\pi$
$199$	16.1803			1.14699			0.573497	+	0.819208i	$0.305586\pi$
$200$	4.04508	+	2.93893i	0.286031	+	0.207813i
$201$	6.47214			0.456509
$202$	−4.92705	+	3.57971i	−0.346666	+	0.251868i
$203$	1.38197	−	4.25325i	0.0969950	−	0.298520i
$204$	−1.61803	+	4.97980i	−0.113285	+	0.348655i
$205$	−2.66312	+	8.19624i	−0.186000	+	0.572450i
$206$	−0.673762	−	2.07363i	−0.0469432	−	0.144476i
$207$	−63.3050			−4.40000
$208$	0.572949	+	1.76336i	0.0397269	+	0.122267i
$209$	1.61803	+	1.17557i	0.111922	+	0.0813159i
$210$	−30.6525	+	22.2703i	−2.11522	+	1.53680i
$211$	2.85410	−	2.07363i	0.196484	−	0.142754i	−0.485193	−	0.874407i	$-0.661251\pi$
$211$	2.85410	−	2.07363i	0.196484	−	0.142754i	0.681678	+	0.731653i	$0.261251\pi$
$212$	−1.50000	−	1.08981i	−0.103020	−	0.0748487i
$213$	−40.3607	−	29.3238i	−2.76547	−	2.00923i
$214$	3.85410	−	2.80017i	0.263461	−	0.191416i
$215$	−0.854102	−	2.62866i	−0.0582493	−	0.179273i
$216$	11.7082	+	8.50651i	0.796642	+	0.578795i
$217$	8.47214	+	26.0746i	0.575126	+	1.77006i
$218$	−11.3820			−0.770884
$219$	−0.909830	−	2.80017i	−0.0614806	−	0.189218i
$220$	−3.61803	+	2.62866i	−0.243928	+	0.177224i
$221$	−0.927051	+	2.85317i	−0.0623602	+	0.191925i
$222$	−5.61803	+	17.2905i	−0.377058	+	1.16046i
$223$	23.0344	−	16.7355i	1.54250	−	1.12069i	0.593757	−	0.804644i	$-0.297644\pi$
$223$	23.0344	−	16.7355i	1.54250	−	1.12069i	0.948743	−	0.316048i	$-0.102356\pi$
$224$	5.23607			0.349850
$225$	37.3607			2.49071
$226$	9.32624			0.620372
$227$	−19.1803	+	13.9353i	−1.27304	+	0.924921i	−0.999319	−	0.0368876i	$-0.988256\pi$
$227$	−19.1803	+	13.9353i	−1.27304	+	0.924921i	−0.273724	+	0.961808i	$0.588256\pi$
$228$	−1.00000	+	3.07768i	−0.0662266	+	0.203825i
$229$	−5.10081	+	15.6987i	−0.337071	+	1.03740i	0.628622	+	0.777711i	$0.283619\pi$
$229$	−5.10081	+	15.6987i	−0.337071	+	1.03740i	−0.965693	+	0.259687i	$0.916381\pi$
$230$	18.9443			1.24915
$231$	−10.4721	−	32.2299i	−0.689016	−	2.12057i
$232$	0.854102			0.0560745
$233$	−4.75329	−	14.6291i	−0.311398	−	0.958385i	−0.977212	−	0.212267i	$-0.931915\pi$
$233$	−4.75329	−	14.6291i	−0.311398	−	0.958385i	0.665813	−	0.746118i	$-0.268085\pi$
$234$	11.2082	+	8.14324i	0.732703	+	0.532340i
$235$	24.4721			1.59639
$236$	5.85410	−	4.25325i	0.381070	−	0.276863i
$237$	23.4164	+	17.0130i	1.52106	+	1.10511i
$238$	6.85410	+	4.97980i	0.444285	+	0.322792i
$239$	9.47214	−	6.88191i	0.612702	−	0.445154i	−0.237663	−	0.971348i	$-0.576381\pi$
$239$	9.47214	−	6.88191i	0.612702	−	0.445154i	0.850365	+	0.526194i	$0.176381\pi$
$240$	−5.85410	−	4.25325i	−0.377881	−	0.274546i
$241$	−12.6353	−	9.18005i	−0.813908	−	0.591339i	0.101053	−	0.994881i	$-0.467779\pi$
$241$	−12.6353	−	9.18005i	−0.813908	−	0.591339i	−0.914961	+	0.403542i	$0.867779\pi$
$242$	2.16312	+	6.65740i	0.139051	+	0.427954i
$243$	35.5967			2.28353
$244$	−0.336881	−	1.03681i	−0.0215666	−	0.0663752i
$245$	14.1074	+	43.4181i	0.901288	+	2.77388i
$246$	3.85410	−	11.8617i	0.245729	−	0.756275i
$247$	−0.572949	+	1.76336i	−0.0364559	+	0.112200i
$248$	−4.23607	+	3.07768i	−0.268991	+	0.195433i
$249$	−36.3607			−2.30426
$250$	−11.1803			−0.707107
$251$	−8.00000			−0.504956			−0.252478	−	0.967603i	$-0.581245\pi$
$251$	−8.00000			−0.504956			−0.252478	+	0.967603i	$0.581245\pi$
$252$	31.6525	−	22.9969i	1.99392	−	1.44867i
$253$	−5.23607	+	16.1150i	−0.329189	+	1.01314i
$254$	4.38197	−	13.4863i	0.274949	−	0.846206i
$255$	−3.61803	−	11.1352i	−0.226570	−	0.697311i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−27.2705			−1.70109			−0.850544	−	0.525904i	$-0.823727\pi$
$257$	−27.2705			−1.70109			−0.850544	+	0.525904i	$0.823727\pi$
$258$	1.23607	+	3.80423i	0.0769542	+	0.236841i
$259$	23.7984	+	17.2905i	1.47876	+	1.07438i
$260$	−3.35410	−	2.43690i	−0.208013	−	0.151130i
$261$	5.16312	−	3.75123i	0.319589	−	0.232195i
$262$	17.7984	+	12.9313i	1.09959	+	0.798897i
$263$	13.5623	+	9.85359i	0.836288	+	0.607599i	0.921331	−	0.388779i	$-0.127103\pi$
$263$	13.5623	+	9.85359i	0.836288	+	0.607599i	−0.0850436	+	0.996377i	$0.527103\pi$
$264$	5.23607	−	3.80423i	0.322258	−	0.234134i
$265$	4.14590			0.254680
$266$	4.23607	+	3.07768i	0.259730	+	0.188705i
$267$	12.5623	+	38.6628i	0.768801	+	2.36613i
$268$	2.00000			0.122169
$269$	−5.42705	−	16.7027i	−0.330893	−	1.01838i	−0.968710	−	0.248196i	$-0.920162\pi$
$269$	−5.42705	−	16.7027i	−0.330893	−	1.01838i	0.637817	−	0.770188i	$-0.279838\pi$
$270$	−32.3607			−1.96941
$271$	−3.85410	+	11.8617i	−0.234120	+	0.720547i	0.763117	+	0.646260i	$0.223668\pi$
$271$	−3.85410	+	11.8617i	−0.234120	+	0.720547i	−0.997237	+	0.0742869i	$0.976332\pi$
$272$	−0.500000	+	1.53884i	−0.0303170	+	0.0933060i
$273$	25.4164	−	18.4661i	1.53827	−	1.11762i
$274$	13.8541			0.836957
$275$	3.09017	−	9.51057i	0.186344	−	0.573509i
$276$	−27.4164			−1.65027
$277$	16.6353	−	12.0862i	0.999516	−	0.726191i	0.0375313	−	0.999295i	$-0.488051\pi$
$277$	16.6353	−	12.0862i	0.999516	−	0.726191i	0.961984	+	0.273105i	$0.0880506\pi$
$278$	−0.326238	+	1.00406i	−0.0195665	+	0.0602193i
$279$	−12.0902	+	37.2097i	−0.723820	+	2.22769i
$280$	−9.47214	+	6.88191i	−0.566068	+	0.411273i
$281$	1.57295	+	4.84104i	0.0938343	+	0.288792i	0.986948	−	0.161038i	$-0.0514843\pi$
$281$	1.57295	+	4.84104i	0.0938343	+	0.288792i	−0.893114	+	0.449831i	$0.851484\pi$
$282$	−35.4164			−2.10902
$283$	−3.14590	−	9.68208i	−0.187004	−	0.575540i	0.812973	−	0.582302i	$-0.197848\pi$
$283$	−3.14590	−	9.68208i	−0.187004	−	0.575540i	−0.999977	+	0.00676167i	$0.997848\pi$
$284$	−12.4721	−	9.06154i	−0.740085	−	0.537703i
$285$	−2.23607	−	6.88191i	−0.132453	−	0.407649i
$286$	3.00000	−	2.17963i	0.177394	−	0.128884i
$287$	−16.3262	−	11.8617i	−0.963707	−	0.700174i
$288$	6.04508	+	4.39201i	0.356210	+	0.258802i
$289$	11.6353	−	8.45351i	0.684427	−	0.497265i
$290$	−1.54508	+	1.12257i	−0.0907305	+	0.0659196i
$291$	11.4721	+	8.33499i	0.672509	+	0.488606i
$292$	−0.281153	−	0.865300i	−0.0164532	−	0.0506378i
$293$	−13.7984			−0.806110			−0.403055	−	0.915176i	$-0.632052\pi$
$293$	−13.7984			−0.806110			−0.403055	+	0.915176i	$0.632052\pi$
$294$	−20.4164	−	62.8352i	−1.19071	−	3.66463i
$295$	−5.00000	+	15.3884i	−0.291111	+	0.895948i
$296$	−1.73607	+	5.34307i	−0.100907	+	0.310560i
$297$	8.94427	−	27.5276i	0.518999	−	1.59732i
$298$	−3.35410	+	2.43690i	−0.194298	+	0.141166i
$299$	−15.7082			−0.908429
$300$	16.1803			0.934172
$301$	6.47214			0.373048
$302$	−17.3262	+	12.5882i	−0.997013	+	0.724372i
$303$	−6.09017	+	18.7436i	−0.349871	+	1.07679i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	1.97214	+	1.43284i	0.112924	+	0.0820442i
$306$	3.73607	+	11.4984i	0.213577	+	0.657322i
$307$	19.2361			1.09786			0.548930	−	0.835868i	$-0.315035\pi$
$307$	19.2361			1.09786			0.548930	+	0.835868i	$0.315035\pi$
$308$	−3.23607	−	9.95959i	−0.184392	−	0.567500i
$309$	−5.70820	−	4.14725i	−0.324728	−	0.235929i
$310$	3.61803	−	11.1352i	0.205491	−	0.632435i
$311$	−4.70820	+	3.42071i	−0.266978	+	0.193971i	−0.713218	−	0.700943i	$-0.752763\pi$
$311$	−4.70820	+	3.42071i	−0.266978	+	0.193971i	0.446240	+	0.894913i	$0.352763\pi$
$312$	4.85410	+	3.52671i	0.274809	+	0.199661i
$313$	9.61803	+	6.98791i	0.543643	+	0.394980i	0.825436	−	0.564495i	$-0.190929\pi$
$313$	9.61803	+	6.98791i	0.543643	+	0.394980i	−0.281793	+	0.959475i	$0.590929\pi$
$314$	2.30902	−	1.67760i	0.130305	−	0.0946724i
$315$	−27.0344	+	83.2035i	−1.52322	+	4.68798i
$316$	7.23607	+	5.25731i	0.407061	+	0.295747i
$317$	3.38197	+	10.4086i	0.189950	+	0.584606i	0.999998	−	0.00175672i	$-0.000559182\pi$
$317$	3.38197	+	10.4086i	0.189950	+	0.584606i	−0.810048	+	0.586363i	$0.800559\pi$
$318$	−6.00000			−0.336463
$319$	−0.527864	−	1.62460i	−0.0295547	−	0.0909601i
$320$	−1.80902	−	1.31433i	−0.101127	−	0.0734732i
$321$	4.76393	−	14.6619i	0.265897	−	0.818346i
$322$	−13.7082	+	42.1895i	−0.763928	+	2.35113i
$323$	−1.30902	+	0.951057i	−0.0728357	+	0.0529182i
$324$	24.4164			1.35647
$325$	9.27051			0.514235
$326$	−8.76393			−0.485389
$327$	−29.7984	+	21.6498i	−1.64785	+	1.19724i
$328$	1.19098	−	3.66547i	0.0657610	−	0.202392i
$329$	−17.7082	+	54.5002i	−0.976285	+	3.00470i
$330$	−4.47214	+	13.7638i	−0.246183	+	0.757673i
$331$	3.70820	+	11.4127i	0.203821	+	0.627298i	0.999760	+	0.0219199i	$0.00697788\pi$
$331$	3.70820	+	11.4127i	0.203821	+	0.627298i	−0.795938	+	0.605378i	$0.793022\pi$
$332$	−11.2361			−0.616659
$333$	12.9721	+	39.9241i	0.710869	+	2.18783i
$334$	−6.47214	−	4.70228i	−0.354140	−	0.257297i
$335$	−3.61803	+	2.62866i	−0.197674	+	0.143619i
$336$	13.7082	−	9.95959i	0.747844	−	0.543340i
$337$	17.3262	+	12.5882i	0.943820	+	0.685726i	0.949337	−	0.314259i	$-0.101756\pi$
$337$	17.3262	+	12.5882i	0.943820	+	0.685726i	−0.00551691	+	0.999985i	$0.501756\pi$
$338$	−7.73607	−	5.62058i	−0.420787	−	0.305719i
$339$	24.4164	−	17.7396i	1.32612	−	0.963481i
$340$	−1.11803	−	3.44095i	−0.0606339	−	0.186612i
$341$	8.47214	+	6.15537i	0.458792	+	0.333332i
$342$	2.30902	+	7.10642i	0.124857	+	0.384271i
$343$	−70.2492			−3.79310
$344$	0.381966	+	1.17557i	0.0205942	+	0.0633825i
$345$	49.5967	−	36.0341i	2.67020	−	1.94001i
$346$	7.02786	−	21.6295i	0.377820	−	1.16281i
$347$	1.67376	−	5.15131i	0.0898523	−	0.276537i	−0.896026	−	0.444002i	$-0.853558\pi$
$347$	1.67376	−	5.15131i	0.0898523	−	0.276537i	0.985878	+	0.167465i	$0.0535582\pi$
$348$	2.23607	−	1.62460i	0.119866	−	0.0870876i
$349$	5.32624			0.285107			0.142553	−	0.989787i	$-0.454469\pi$
$349$	5.32624			0.285107			0.142553	+	0.989787i	$0.454469\pi$
$350$	8.09017	−	24.8990i	0.432438	−	1.33091i
$351$	26.8328			1.43223
$352$	1.61803	−	1.17557i	0.0862415	−	0.0626581i
$353$	3.56231	−	10.9637i	0.189602	−	0.583536i	−0.810395	−	0.585884i	$-0.800747\pi$
$353$	3.56231	−	10.9637i	0.189602	−	0.583536i	0.999997	+	0.00234791i	$0.000747364\pi$
$354$	7.23607	−	22.2703i	0.384593	−	1.18365i
$355$	34.4721			1.82959
$356$	3.88197	+	11.9475i	0.205744	+	0.633214i
$357$	27.4164			1.45103
$358$	−3.09017	−	9.51057i	−0.163321	−	0.502649i
$359$	−12.5623	−	9.12705i	−0.663013	−	0.481707i	0.204666	−	0.978832i	$-0.434389\pi$
$359$	−12.5623	−	9.12705i	−0.663013	−	0.481707i	−0.867679	+	0.497125i	$0.834389\pi$
$360$	−16.7082			−0.880600
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−2.69098	−	1.95511i	−0.141435	−	0.102758i
$363$	18.3262	+	13.3148i	0.961878	+	0.698845i
$364$	7.85410	−	5.70634i	0.411667	−	0.299093i
$365$	1.64590	+	1.19581i	0.0861502	+	0.0625918i
$366$	−2.85410	−	2.07363i	−0.149186	−	0.108390i
$367$	−0.763932	−	2.35114i	−0.0398769	−	0.122729i	0.929136	−	0.369737i	$-0.120552\pi$
$367$	−0.763932	−	2.35114i	−0.0398769	−	0.122729i	−0.969013	+	0.247009i	$0.920552\pi$
$368$	−8.47214			−0.441641
$369$	−8.89919	−	27.3889i	−0.463273	−	1.42581i
$370$	−3.88197	−	11.9475i	−0.201814	−	0.621119i
$371$	−3.00000	+	9.23305i	−0.155752	+	0.479356i
$372$	−5.23607	+	16.1150i	−0.271477	+	0.835522i
$373$	−0.381966	+	0.277515i	−0.0197775	+	0.0143692i	−0.597630	−	0.801772i	$-0.703891\pi$
$373$	−0.381966	+	0.277515i	−0.0197775	+	0.0143692i	0.577853	+	0.816141i	$0.303891\pi$
$374$	3.23607			0.167333
$375$	−29.2705	+	21.2663i	−1.51152	+	1.09819i
$376$	−10.9443			−0.564408
$377$	1.28115	−	0.930812i	0.0659827	−	0.0479393i
$378$	23.4164	−	72.0683i	1.20441	−	3.70679i
$379$	7.76393	−	23.8949i	0.398806	−	1.22740i	−0.527151	−	0.849772i	$-0.676740\pi$
$379$	7.76393	−	23.8949i	0.398806	−	1.22740i	0.925957	−	0.377628i	$-0.123260\pi$
$380$	−0.690983	−	2.12663i	−0.0354467	−	0.109094i
$381$	−14.1803	−	43.6426i	−0.726481	−	2.23588i
$382$	8.00000			0.409316
$383$	4.29180	+	13.2088i	0.219301	+	0.674938i	0.998820	+	0.0485600i	$0.0154632\pi$
$383$	4.29180	+	13.2088i	0.219301	+	0.674938i	−0.779520	+	0.626378i	$0.784537\pi$
$384$	2.61803	+	1.90211i	0.133601	+	0.0970668i
$385$	18.9443	+	13.7638i	0.965489	+	0.701469i
$386$	−11.5902	+	8.42075i	−0.589924	+	0.428605i
$387$	7.47214	+	5.42882i	0.379830	+	0.275963i
$388$	3.54508	+	2.57565i	0.179974	+	0.130759i
$389$	10.5902	−	7.69421i	0.536943	−	0.390112i	−0.286005	−	0.958228i	$-0.592328\pi$
$389$	10.5902	−	7.69421i	0.536943	−	0.390112i	0.822948	+	0.568116i	$0.192328\pi$
$390$	−13.4164			−0.679366
$391$	−11.0902	−	8.05748i	−0.560854	−	0.407484i
$392$	−6.30902	−	19.4172i	−0.318653	−	0.980715i
$393$	71.1935			3.59124
$394$	5.86475	+	18.0498i	0.295462	+	0.909337i
$395$	−20.0000			−1.00631
$396$	4.61803	−	14.2128i	0.232065	−	0.714222i
$397$	1.67376	−	5.15131i	0.0840037	−	0.258537i	−0.900229	−	0.435418i	$-0.856601\pi$
$397$	1.67376	−	5.15131i	0.0840037	−	0.258537i	0.984232	+	0.176881i	$0.0566007\pi$
$398$	13.0902	−	9.51057i	0.656151	−	0.476722i
$399$	16.9443			0.848275
$400$	5.00000			0.250000
$401$	−9.38197			−0.468513			−0.234257	−	0.972175i	$-0.575266\pi$
$401$	−9.38197			−0.468513			−0.234257	+	0.972175i	$0.575266\pi$
$402$	5.23607	−	3.80423i	0.261151	−	0.189738i
$403$	−3.00000	+	9.23305i	−0.149441	+	0.459931i
$404$	−1.88197	+	5.79210i	−0.0936313	+	0.288168i
$405$	−44.1697	+	32.0912i	−2.19481	+	1.59462i
$406$	−1.38197	−	4.25325i	−0.0685858	−	0.211085i
$407$	11.2361			0.556951
$408$	1.61803	+	4.97980i	0.0801046	+	0.246537i
$409$	−7.39919	−	5.37582i	−0.365866	−	0.265817i	0.389628	−	0.920972i	$-0.372603\pi$
$409$	−7.39919	−	5.37582i	−0.365866	−	0.265817i	−0.755495	+	0.655155i	$0.772603\pi$
$410$	2.66312	+	8.19624i	0.131522	+	0.404783i
$411$	36.2705	−	26.3521i	1.78909	−	1.29985i
$412$	−1.76393	−	1.28157i	−0.0869027	−	0.0631385i
$413$	−30.6525	−	22.2703i	−1.50831	−	1.09585i
$414$	−51.2148	+	37.2097i	−2.51707	+	1.82876i
$415$	20.3262	−	14.7679i	0.997776	−	0.724927i
$416$	1.50000	+	1.08981i	0.0735436	+	0.0534325i
$417$	1.05573	+	3.24920i	0.0516992	+	0.159114i
$418$	2.00000			0.0978232
$419$	−2.23607	−	6.88191i	−0.109239	−	0.336203i	0.881463	−	0.472253i	$-0.156559\pi$
$419$	−2.23607	−	6.88191i	−0.109239	−	0.336203i	−0.990702	+	0.136050i	$0.956559\pi$
$420$	−11.7082	+	36.0341i	−0.571302	+	1.75829i
$421$	1.08359	−	3.33495i	0.0528110	−	0.162536i	−0.921172	−	0.389155i	$-0.872767\pi$
$421$	1.08359	−	3.33495i	0.0528110	−	0.162536i	0.973984	+	0.226619i	$0.0727672\pi$
$422$	1.09017	−	3.35520i	0.0530686	−	0.163328i
$423$	−66.1591	+	48.0674i	−3.21676	+	2.33712i
$424$	−1.85410			−0.0900432
$425$	6.54508	+	4.75528i	0.317483	+	0.230665i
$426$	−49.8885			−2.41711
$427$	−4.61803	+	3.35520i	−0.223482	+	0.162369i
$428$	1.47214	−	4.53077i	0.0711584	−	0.219003i
$429$	3.70820	−	11.4127i	0.179034	−	0.551009i
$430$	−2.23607	−	1.62460i	−0.107833	−	0.0783451i
$431$	3.05573	+	9.40456i	0.147189	+	0.453002i	0.997286	−	0.0736246i	$-0.0234567\pi$
$431$	3.05573	+	9.40456i	0.147189	+	0.453002i	−0.850097	+	0.526626i	$0.823457\pi$
$432$	14.4721			0.696291
$433$	−7.19098	−	22.1316i	−0.345577	−	1.06358i	−0.961274	−	0.275593i	$-0.911126\pi$
$433$	−7.19098	−	22.1316i	−0.345577	−	1.06358i	0.615698	−	0.787982i	$-0.288874\pi$
$434$	22.1803	+	16.1150i	1.06469	+	0.773543i
$435$	−1.90983	+	5.87785i	−0.0915693	+	0.281821i
$436$	−9.20820	+	6.69015i	−0.440993	+	0.320400i
$437$	−6.85410	−	4.97980i	−0.327876	−	0.238216i
$438$	−2.38197	−	1.73060i	−0.113815	−	0.0826912i
$439$	12.2361	−	8.89002i	0.583996	−	0.424298i	−0.256167	−	0.966633i	$-0.582460\pi$
$439$	12.2361	−	8.89002i	0.583996	−	0.424298i	0.840162	+	0.542335i	$0.182460\pi$
$440$	−1.38197	+	4.25325i	−0.0658826	+	0.202766i
$441$	−123.419	−	89.6691i	−5.87709	−	4.26996i
$442$	0.927051	+	2.85317i	0.0440953	+	0.135711i
$443$	−20.1803			−0.958797			−0.479398	−	0.877597i	$-0.659145\pi$
$443$	−20.1803			−0.958797			−0.479398	+	0.877597i	$0.659145\pi$
$444$	5.61803	+	17.2905i	0.266620	+	0.820572i
$445$	−22.7254	−	16.5110i	−1.07729	−	0.782696i
$446$	8.79837	−	27.0786i	0.416615	−	1.28221i
$447$	−4.14590	+	12.7598i	−0.196094	+	0.603516i
$448$	4.23607	−	3.07768i	0.200135	−	0.145407i
$449$	−30.8541			−1.45610			−0.728048	−	0.685527i	$-0.759572\pi$
$449$	−30.8541			−1.45610			−0.728048	+	0.685527i	$0.759572\pi$
$450$	30.2254	−	21.9601i	1.42484	−	1.03521i
$451$	−7.70820			−0.362965
$452$	7.54508	−	5.48183i	0.354891	−	0.257843i
$453$	−21.4164	+	65.9129i	−1.00623	+	3.09686i
$454$	−7.32624	+	22.5478i	−0.343837	+	1.05822i
$455$	−6.70820	+	20.6457i	−0.314485	+	0.967887i
$456$	1.00000	+	3.07768i	0.0468293	+	0.144126i
$457$	34.3607			1.60732			0.803662	−	0.595085i	$-0.202882\pi$
$457$	34.3607			1.60732			0.803662	+	0.595085i	$0.202882\pi$
$458$	5.10081	+	15.6987i	0.238345	+	0.733552i
$459$	18.9443	+	13.7638i	0.884243	+	0.642440i
$460$	15.3262	−	11.1352i	0.714590	−	0.519180i
$461$	33.8713	−	24.6090i	1.57754	−	1.14615i	0.658103	−	0.752928i	$-0.271359\pi$
$461$	33.8713	−	24.6090i	1.57754	−	1.14615i	0.919442	−	0.393225i	$-0.128641\pi$
$462$	−27.4164	−	19.9192i	−1.27553	−	0.926724i
$463$	−20.1803	−	14.6619i	−0.937860	−	0.681395i	0.0100446	−	0.999950i	$-0.496803\pi$
$463$	−20.1803	−	14.6619i	−0.937860	−	0.681395i	−0.947905	+	0.318554i	$0.896803\pi$
$464$	0.690983	−	0.502029i	0.0320781	−	0.0233061i
$465$	−11.7082	−	36.0341i	−0.542955	−	1.67104i
$466$	−12.4443	−	9.04129i	−0.576470	−	0.418830i
$467$	−4.70820	−	14.4904i	−0.217870	−	0.670534i	−0.998937	−	0.0460876i	$-0.985325\pi$
$467$	−4.70820	−	14.4904i	−0.217870	−	0.670534i	0.781068	−	0.624446i	$-0.214675\pi$
$468$	13.8541			0.640406
$469$	−3.23607	−	9.95959i	−0.149428	−	0.459891i
$470$	19.7984	−	14.3844i	0.913231	−	0.663501i
$471$	2.85410	−	8.78402i	0.131510	−	0.404746i
$472$	2.23607	−	6.88191i	0.102923	−	0.316766i
$473$	2.00000	−	1.45309i	0.0919601	−	0.0668129i
$474$	28.9443			1.32945
$475$	4.04508	+	2.93893i	0.185601	+	0.134847i
$476$	8.47214			0.388320
$477$	−11.2082	+	8.14324i	−0.513188	+	0.372853i
$478$	3.61803	−	11.1352i	0.165485	−	0.509311i
$479$	−5.85410	+	18.0171i	−0.267481	+	0.823221i	0.723631	+	0.690187i	$0.242472\pi$
$479$	−5.85410	+	18.0171i	−0.267481	+	0.823221i	−0.991112	+	0.133034i	$0.957528\pi$
$480$	−7.23607			−0.330280
$481$	3.21885	+	9.90659i	0.146767	+	0.451702i
$482$	−15.6180			−0.711382
$483$	44.3607	+	136.528i	2.01848	+	6.21225i
$484$	5.66312	+	4.11450i	0.257414	+	0.187023i
$485$	−9.79837			−0.444921
$486$	28.7984	−	20.9232i	1.30632	−	0.949098i
$487$	4.23607	+	3.07768i	0.191955	+	0.139463i	0.679612	−	0.733572i	$-0.262148\pi$
$487$	4.23607	+	3.07768i	0.191955	+	0.139463i	−0.487657	+	0.873035i	$0.662148\pi$
$488$	−0.881966	−	0.640786i	−0.0399247	−	0.0290070i
$489$	−22.9443	+	16.6700i	−1.03758	+	0.753843i
$490$	36.9336	+	26.8339i	1.66849	+	1.21223i
$491$	−18.3262	−	13.3148i	−0.827052	−	0.600888i	0.0916721	−	0.995789i	$-0.470779\pi$
$491$	−18.3262	−	13.3148i	−0.827052	−	0.600888i	−0.918724	+	0.394901i	$0.870779\pi$
$492$	−3.85410	−	11.8617i	−0.173756	−	0.534767i
$493$	1.38197			0.0622406
$494$	0.572949	+	1.76336i	0.0257782	+	0.0793371i
$495$	10.3262	+	31.7809i	0.464130	+	1.42844i
$496$	−1.61803	+	4.97980i	−0.0726519	+	0.223599i
$497$	−24.9443	+	76.7706i	−1.11890	+	3.44363i
$498$	−29.4164	+	21.3723i	−1.31818	+	0.957714i
$499$	17.2361			0.771592			0.385796	−	0.922584i	$-0.373927\pi$
$499$	17.2361			0.771592			0.385796	+	0.922584i	$0.373927\pi$
$500$	−9.04508	+	6.57164i	−0.404508	+	0.293893i
$501$	−25.8885			−1.15661
$502$	−6.47214	+	4.70228i	−0.288866	+	0.209873i
$503$	4.81966	−	14.8334i	0.214898	−	0.661388i	−0.784263	−	0.620429i	$-0.786959\pi$
$503$	4.81966	−	14.8334i	0.214898	−	0.661388i	0.999161	−	0.0409593i	$-0.0130414\pi$
$504$	12.0902	−	37.2097i	0.538539	−	1.65745i
$505$	−4.20820	−	12.9515i	−0.187263	−	0.576335i
$506$	5.23607	+	16.1150i	0.232772	+	0.716397i
$507$	−30.9443			−1.37428
$508$	−4.38197	−	13.4863i	−0.194418	−	0.598358i
$509$	10.6910	+	7.76745i	0.473869	+	0.344286i	0.798947	−	0.601401i	$-0.205391\pi$
$509$	10.6910	+	7.76745i	0.473869	+	0.344286i	−0.325078	+	0.945687i	$0.605391\pi$
$510$	−9.47214	−	6.88191i	−0.419433	−	0.304736i
$511$	−3.85410	+	2.80017i	−0.170495	+	0.123872i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	11.7082	+	8.50651i	0.516930	+	0.375572i
$514$	−22.0623	+	16.0292i	−0.973127	+	0.707018i
$515$	4.87539			0.214835
$516$	3.23607	+	2.35114i	0.142460	+	0.103503i
$517$	6.76393	+	20.8172i	0.297477	+	0.915541i
$518$	29.4164			1.29248
$519$	−22.7426	−	69.9947i	−0.998291	−	3.07242i
$520$	−4.14590			−0.181810
$521$	−4.60739	+	14.1801i	−0.201853	+	0.621241i	0.797974	+	0.602691i	$0.205905\pi$
$521$	−4.60739	+	14.1801i	−0.201853	+	0.621241i	−0.999828	+	0.0185498i	$0.994095\pi$
$522$	1.97214	−	6.06961i	0.0863180	−	0.265660i
$523$	3.23607	−	2.35114i	0.141503	−	0.102808i	−0.514782	−	0.857321i	$-0.672127\pi$
$523$	3.23607	−	2.35114i	0.141503	−	0.102808i	0.656285	+	0.754513i	$0.272127\pi$
$524$	22.0000			0.961074
$525$	−26.1803	−	80.5748i	−1.14260	−	3.51657i
$526$	16.7639			0.730942
$527$	−6.85410	+	4.97980i	−0.298569	+	0.216923i
$528$	2.00000	−	6.15537i	0.0870388	−	0.267878i
$529$	15.0729	−	46.3898i	0.655346	−	2.01695i
$530$	3.35410	−	2.43690i	0.145693	−	0.105852i
$531$	−16.7082	−	51.4226i	−0.725074	−	2.23155i
$532$	5.23607			0.227012
$533$	−2.20820	−	6.79615i	−0.0956479	−	0.294374i
$534$	32.8885	+	23.8949i	1.42323	+	1.03403i
$535$	3.29180	+	10.1311i	0.142317	+	0.438006i
$536$	1.61803	−	1.17557i	0.0698884	−	0.0507769i
$537$	−26.1803	−	19.0211i	−1.12977	−	0.820822i
$538$	−14.2082	−	10.3229i	−0.612559	−	0.445050i
$539$	−33.0344	+	24.0009i	−1.42289	+	1.03379i
$540$	−26.1803	+	19.0211i	−1.12662	+	0.818539i
$541$	23.8713	+	17.3435i	1.02631	+	0.745657i	0.967566	−	0.252617i	$-0.0812911\pi$
$541$	23.8713	+	17.3435i	1.02631	+	0.745657i	0.0587419	+	0.998273i	$0.481291\pi$
$542$	3.85410	+	11.8617i	0.165548	+	0.509504i
$543$	−10.7639			−0.461925
$544$	0.500000	+	1.53884i	0.0214373	+	0.0659773i
$545$	7.86475	−	24.2052i	0.336889	−	1.03684i
$546$	9.70820	−	29.8788i	0.415473	−	1.27869i
$547$	−7.14590	+	21.9928i	−0.305537	+	0.940345i	0.673940	+	0.738786i	$0.264601\pi$
$547$	−7.14590	+	21.9928i	−0.305537	+	0.940345i	−0.979476	+	0.201559i	$0.935399\pi$
$548$	11.2082	−	8.14324i	0.478791	−	0.347862i
$549$	−8.14590			−0.347658
$550$	−3.09017	−	9.51057i	−0.131765	−	0.405532i
$551$	0.854102			0.0363860
$552$	−22.1803	+	16.1150i	−0.944058	+	0.685898i
$553$	14.4721	−	44.5407i	0.615418	−	1.89406i
$554$	6.35410	−	19.5559i	0.269960	−	0.830851i
$555$	−32.8885	−	23.8949i	−1.39604	−	1.01428i
$556$	0.326238	+	1.00406i	0.0138356	+	0.0425815i
$557$	−6.09017			−0.258049			−0.129024	−	0.991641i	$-0.541185\pi$
$557$	−6.09017			−0.258049			−0.129024	+	0.991641i	$0.541185\pi$
$558$	12.0902	+	37.2097i	0.511818	+	1.57521i
$559$	1.85410	+	1.34708i	0.0784202	+	0.0569756i
$560$	−3.61803	+	11.1352i	−0.152890	+	0.470547i
$561$	8.47214	−	6.15537i	0.357694	−	0.259880i
$562$	4.11803	+	2.99193i	0.173709	+	0.126207i
$563$	−1.23607	−	0.898056i	−0.0520941	−	0.0378485i	0.561434	−	0.827522i	$-0.310250\pi$
$563$	−1.23607	−	0.898056i	−0.0520941	−	0.0378485i	−0.613528	+	0.789673i	$0.710250\pi$
$564$	−28.6525	+	20.8172i	−1.20649	+	0.876564i
$565$	−6.44427	+	19.8334i	−0.271113	+	0.834399i
$566$	−8.23607	−	5.98385i	−0.346188	−	0.251520i
$567$	−39.5066	−	121.589i	−1.65912	−	5.10625i
$568$	−15.4164			−0.646858
$569$	10.0623	+	30.9686i	0.421834	+	1.29827i	0.905994	+	0.423291i	$0.139125\pi$
$569$	10.0623	+	30.9686i	0.421834	+	1.29827i	−0.484160	+	0.874980i	$0.660875\pi$
$570$	−5.85410	−	4.25325i	−0.245201	−	0.178149i
$571$	6.14590	−	18.9151i	0.257198	−	0.791574i	−0.736191	−	0.676774i	$-0.763377\pi$
$571$	6.14590	−	18.9151i	0.257198	−	0.791574i	0.993389	−	0.114800i	$-0.0366226\pi$
$572$	1.14590	−	3.52671i	0.0479124	−	0.147459i
$573$	20.9443	−	15.2169i	0.874960	−	0.635695i
$574$	−20.1803			−0.842311
$575$	−13.0902	+	40.2874i	−0.545898	+	1.68010i
$576$	7.47214			0.311339
$577$	−6.09017	+	4.42477i	−0.253537	+	0.184205i	−0.707293	−	0.706921i	$-0.750084\pi$
$577$	−6.09017	+	4.42477i	−0.253537	+	0.184205i	0.453756	+	0.891126i	$0.350084\pi$
$578$	4.44427	−	13.6781i	0.184857	−	0.568932i
$579$	−14.3262	+	44.0916i	−0.595378	+	1.83239i
$580$	−0.590170	+	1.81636i	−0.0245055	+	0.0754201i
$581$	18.1803	+	55.9533i	0.754248	+	2.32134i
$582$	14.1803			0.587794
$583$	1.14590	+	3.52671i	0.0474582	+	0.146061i
$584$	−0.736068	−	0.534785i	−0.0304587	−	0.0221295i
$585$	−25.0623	+	18.2088i	−1.03620	+	0.752843i
$586$	−11.1631	+	8.11048i	−0.461144	+	0.335041i
$587$	14.5623	+	10.5801i	0.601051	+	0.436689i	0.846252	−	0.532783i	$-0.178854\pi$
$587$	14.5623	+	10.5801i	0.601051	+	0.436689i	−0.245201	+	0.969472i	$0.578854\pi$
$588$	−53.4508	−	38.8343i	−2.20428	−	1.60150i
$589$	−4.23607	+	3.07768i	−0.174544	+	0.126814i
$590$	5.00000	+	15.3884i	0.205847	+	0.633531i
$591$	49.6869	+	36.0997i	2.04385	+	1.48494i
$592$	1.73607	+	5.34307i	0.0713520	+	0.219599i
$593$	47.1033			1.93430			0.967151	−	0.254203i	$-0.0818132\pi$
$593$	47.1033			1.93430			0.967151	+	0.254203i	$0.0818132\pi$
$594$	−8.94427	−	27.5276i	−0.366988	−	1.12947i
$595$	−15.3262	+	11.1352i	−0.628314	+	0.456497i
$596$	−1.28115	+	3.94298i	−0.0524781	+	0.161511i
$597$	16.1803	−	49.7980i	0.662217	−	2.03810i
$598$	−12.7082	+	9.23305i	−0.519677	+	0.377568i
$599$	21.7082			0.886973			0.443487	−	0.896281i	$-0.353741\pi$
$599$	21.7082			0.886973			0.443487	+	0.896281i	$0.353741\pi$
$600$	13.0902	−	9.51057i	0.534404	−	0.388267i
$601$	22.9787			0.937321			0.468661	−	0.883378i	$-0.344737\pi$
$601$	22.9787			0.937321			0.468661	+	0.883378i	$0.344737\pi$
$602$	5.23607	−	3.80423i	0.213406	−	0.155049i
$603$	4.61803	−	14.2128i	0.188061	−	0.578792i
$604$	−6.61803	+	20.3682i	−0.269284	+	0.828771i
$605$	−15.6525			−0.636364
$606$	6.09017	+	18.7436i	0.247396	+	0.761407i
$607$	25.8197			1.04799			0.523994	−	0.851722i	$-0.324441\pi$
$607$	25.8197			1.04799			0.523994	+	0.851722i	$0.324441\pi$
$608$	0.309017	+	0.951057i	0.0125323	+	0.0385704i
$609$	−11.7082	−	8.50651i	−0.474440	−	0.344701i
$610$	2.43769			0.0986993
$611$	−16.4164	+	11.9272i	−0.664137	+	0.482524i
$612$	9.78115	+	7.10642i	0.395380	+	0.287260i
$613$	13.3992	+	9.73508i	0.541188	+	0.393196i	0.824526	−	0.565824i	$-0.191442\pi$
$613$	13.3992	+	9.73508i	0.541188	+	0.393196i	−0.283338	+	0.959020i	$0.591442\pi$
$614$	15.5623	−	11.3067i	0.628044	−	0.456300i
$615$	22.5623	+	16.3925i	0.909800	+	0.661008i
$616$	−8.47214	−	6.15537i	−0.341352	−	0.248007i
$617$	12.5517	+	38.6300i	0.505311	+	1.55519i	0.800247	+	0.599670i	$0.204702\pi$
$617$	12.5517	+	38.6300i	0.505311	+	1.55519i	−0.294936	+	0.955517i	$0.595298\pi$
$618$	−7.05573			−0.283823
$619$	7.23607	+	22.2703i	0.290842	+	0.895120i	0.984586	+	0.174899i	$0.0559598\pi$
$619$	7.23607	+	22.2703i	0.290842	+	0.895120i	−0.693744	+	0.720221i	$0.744040\pi$
$620$	−3.61803	−	11.1352i	−0.145304	−	0.447199i
$621$	−37.8885	+	116.609i	−1.52041	+	4.67936i
$622$	−1.79837	+	5.53483i	−0.0721082	+	0.221926i
$623$	53.2148	−	38.6628i	2.13201	−	1.54899i
$624$	6.00000			0.240192
$625$	7.72542	−	23.7764i	0.309017	−	0.951057i
$626$	11.8885			0.475162
$627$	5.23607	−	3.80423i	0.209108	−	0.151926i
$628$	0.881966	−	2.71441i	0.0351943	−	0.108317i
$629$	−2.80902	+	8.64527i	−0.112003	+	0.344709i
$630$	27.0344	+	83.2035i	1.07708	+	3.31491i
$631$	5.29180	+	16.2865i	0.210663	+	0.648354i	0.999433	+	0.0336659i	$0.0107182\pi$
$631$	5.29180	+	16.2865i	0.210663	+	0.648354i	−0.788770	+	0.614688i	$0.789282\pi$
$632$	8.94427			0.355784
$633$	−3.52786	−	10.8576i	−0.140220	−	0.431553i
$634$	8.85410	+	6.43288i	0.351641	+	0.255482i
$635$	25.6525	+	18.6376i	1.01799	+	0.739611i
$636$	−4.85410	+	3.52671i	−0.192478	+	0.139843i
$637$	−30.6246	−	22.2501i	−1.21339	−	0.881580i
$638$	−1.38197	−	1.00406i	−0.0547126	−	0.0397510i
$639$	−93.1935	+	67.7090i	−3.68668	+	2.67853i
$640$	−2.23607			−0.0883883
$641$	24.5623	+	17.8456i	0.970153	+	0.704857i	0.955486	−	0.295035i	$-0.0953314\pi$
$641$	24.5623	+	17.8456i	0.970153	+	0.704857i	0.0146664	+	0.999892i	$0.495331\pi$
$642$	−4.76393	−	14.6619i	−0.188017	−	0.578658i
$643$	−34.6525			−1.36656			−0.683280	−	0.730156i	$-0.739447\pi$
$643$	−34.6525			−1.36656			−0.683280	+	0.730156i	$0.739447\pi$
$644$	13.7082	+	42.1895i	0.540179	+	1.66250i
$645$	−8.94427			−0.352180
$646$	−0.500000	+	1.53884i	−0.0196722	+	0.0605449i
$647$	13.9098	−	42.8101i	0.546852	−	1.68304i	−0.169694	−	0.985497i	$-0.554278\pi$
$647$	13.9098	−	42.8101i	0.546852	−	1.68304i	0.716546	−	0.697540i	$-0.245722\pi$
$648$	19.7533	−	14.3516i	0.775982	−	0.563784i
$649$	−14.4721			−0.568081
$650$	7.50000	−	5.44907i	0.294174	−	0.213730i
$651$	88.7214			3.47726
$652$	−7.09017	+	5.15131i	−0.277672	+	0.201741i
$653$	−10.2426	+	31.5236i	−0.400826	+	1.23361i	0.523505	+	0.852023i	$0.324624\pi$
$653$	−10.2426	+	31.5236i	−0.400826	+	1.23361i	−0.924331	+	0.381592i	$0.875376\pi$
$654$	−11.3820	+	35.0301i	−0.445070	+	1.36978i
$655$	−39.7984	+	28.9152i	−1.55505	+	1.12981i
$656$	−1.19098	−	3.66547i	−0.0465001	−	0.143113i
$657$	−6.79837			−0.265230
$658$	17.7082	+	54.5002i	0.690338	+	2.12464i
$659$	−33.4164	−	24.2784i	−1.30172	−	0.945754i	−0.301748	−	0.953388i	$-0.597570\pi$
$659$	−33.4164	−	24.2784i	−1.30172	−	0.945754i	−0.999971	+	0.00763405i	$0.997570\pi$
$660$	4.47214	+	13.7638i	0.174078	+	0.535756i
$661$	20.0902	−	14.5964i	0.781417	−	0.567733i	−0.123987	−	0.992284i	$-0.539568\pi$
$661$	20.0902	−	14.5964i	0.781417	−	0.567733i	0.905404	+	0.424551i	$0.139568\pi$
$662$	9.70820	+	7.05342i	0.377320	+	0.274139i
$663$	7.85410	+	5.70634i	0.305028	+	0.221616i
$664$	−9.09017	+	6.60440i	−0.352767	+	0.256300i
$665$	−9.47214	+	6.88191i	−0.367314	+	0.266869i
$666$	33.9615	+	24.6745i	1.31598	+	0.956116i
$667$	2.23607	+	6.88191i	0.0865809	+	0.266469i
$668$	−8.00000			−0.309529
$669$	−28.4721	−	87.6282i	−1.10080	−	3.38790i
$670$	−1.38197	+	4.25325i	−0.0533900	+	0.164318i
$671$	−0.673762	+	2.07363i	−0.0260103	+	0.0800515i
$672$	5.23607	−	16.1150i	0.201986	−	0.621648i
$673$	−2.45492	+	1.78360i	−0.0946300	+	0.0687527i	−0.634094	−	0.773256i	$-0.718627\pi$
$673$	−2.45492	+	1.78360i	−0.0946300	+	0.0687527i	0.539464	+	0.842009i	$0.318627\pi$
$674$	21.4164			0.824929
$675$	22.3607	−	68.8191i	0.860663	−	2.64885i
$676$	−9.56231			−0.367781
$677$	−23.3262	+	16.9475i	−0.896500	+	0.651345i	−0.937565	−	0.347811i	$-0.886925\pi$
$677$	−23.3262	+	16.9475i	−0.896500	+	0.651345i	0.0410645	+	0.999156i	$0.486925\pi$
$678$	9.32624	−	28.7032i	0.358172	−	1.10234i
$679$	7.09017	−	21.8213i	0.272096	−	0.837425i
$680$	−2.92705	−	2.12663i	−0.112247	−	0.0815524i
$681$	23.7082	+	72.9663i	0.908500	+	2.79608i
$682$	10.4721			0.400999
$683$	−1.43769	−	4.42477i	−0.0550118	−	0.169309i	0.919776	−	0.392445i	$-0.128371\pi$
$683$	−1.43769	−	4.42477i	−0.0550118	−	0.169309i	−0.974787	+	0.223136i	$0.928371\pi$
$684$	6.04508	+	4.39201i	0.231140	+	0.167933i
$685$	−9.57295	+	29.4625i	−0.365764	+	1.12570i
$686$	−56.8328	+	41.2915i	−2.16989	+	1.57652i
$687$	43.2148	+	31.3974i	1.64875	+	1.19788i
$688$	1.00000	+	0.726543i	0.0381246	+	0.0276992i
$689$	−2.78115	+	2.02063i	−0.105953	+	0.0769797i
$690$	18.9443	−	58.3045i	0.721196	−	2.21961i
$691$	6.47214	+	4.70228i	0.246212	+	0.178883i	0.704046	−	0.710154i	$-0.251375\pi$
$691$	6.47214	+	4.70228i	0.246212	+	0.178883i	−0.457835	+	0.889037i	$0.651375\pi$
$692$	−7.02786	−	21.6295i	−0.267159	−	0.822232i
$693$	−78.2492			−2.97244
$694$	−1.67376	−	5.15131i	−0.0635351	−	0.195541i
$695$	−1.90983	−	1.38757i	−0.0724440	−	0.0526336i
$696$	0.854102	−	2.62866i	0.0323747	−	0.0996389i
$697$	1.92705	−	5.93085i	0.0729923	−	0.224647i
$698$	4.30902	−	3.13068i	0.163099	−	0.118498i
$699$	−49.7771			−1.88274
$700$	−8.09017	−	24.8990i	−0.305780	−	0.941093i
$701$	−32.1459			−1.21413			−0.607067	−	0.794651i	$-0.707654\pi$
$701$	−32.1459			−1.21413			−0.607067	+	0.794651i	$0.707654\pi$
$702$	21.7082	−	15.7719i	0.819323	−	0.595273i
$703$	−1.73607	+	5.34307i	−0.0654770	+	0.201518i
$704$	0.618034	−	1.90211i	0.0232930	−	0.0716886i
$705$	24.4721	−	75.3175i	0.921674	−	2.83662i
$706$	−3.56231	−	10.9637i	−0.134069	−	0.412622i
$707$	31.8885			1.19929
$708$	−7.23607	−	22.2703i	−0.271948	−	0.836970i
$709$	−3.88197	−	2.82041i	−0.145790	−	0.105923i	0.512499	−	0.858688i	$-0.328720\pi$
$709$	−3.88197	−	2.82041i	−0.145790	−	0.105923i	−0.658290	+	0.752765i	$0.728720\pi$
$710$	27.8885	−	20.2622i	1.04664	−	0.760427i
$711$	54.0689	−	39.2833i	2.02774	−	1.47324i
$712$	10.1631	+	7.38394i	0.380879	+	0.276725i
$713$	−35.8885	−	26.0746i	−1.34404	−	0.976500i
$714$	22.1803	−	16.1150i	0.830078	−	0.603087i
$715$	2.56231	+	7.88597i	0.0958248	+	0.294918i
$716$	−8.09017	−	5.87785i	−0.302344	−	0.219666i
$717$	−11.7082	−	36.0341i	−0.437251	−	1.34572i
$718$	−15.5279			−0.579495
$719$	0.527864	+	1.62460i	0.0196860	+	0.0605873i	0.960417	−	0.278567i	$-0.0898593\pi$
$719$	0.527864	+	1.62460i	0.0196860	+	0.0605873i	−0.940731	+	0.339154i	$0.889859\pi$
$720$	−13.5172	+	9.82084i	−0.503757	+	0.366001i
$721$	−3.52786	+	10.8576i	−0.131385	+	0.404360i
$722$	−0.309017	+	0.951057i	−0.0115004	+	0.0353947i
$723$	−40.8885	+	29.7073i	−1.52066	+	1.10483i
$724$	−3.32624			−0.123619
$725$	−1.31966	−	4.06150i	−0.0490109	−	0.150840i
$726$	22.6525			0.840712
$727$	19.0344	−	13.8293i	0.705948	−	0.512902i	−0.175916	−	0.984405i	$-0.556289\pi$
$727$	19.0344	−	13.8293i	0.705948	−	0.512902i	0.881864	+	0.471504i	$0.156289\pi$
$728$	3.00000	−	9.23305i	0.111187	−	0.342200i
$729$	12.9615	−	39.8914i	0.480055	−	1.47746i
$730$	2.03444			0.0752981
$731$	0.618034	+	1.90211i	0.0228588	+	0.0703522i
$732$	−3.52786			−0.130394
$733$	−8.79837	−	27.0786i	−0.324975	−	1.00017i	−0.971452	−	0.237237i	$-0.923758\pi$
$733$	−8.79837	−	27.0786i	−0.324975	−	1.00017i	0.646476	−	0.762934i	$-0.276242\pi$
$734$	−2.00000	−	1.45309i	−0.0738213	−	0.0536343i
$735$	147.735			5.44927
$736$	−6.85410	+	4.97980i	−0.252646	+	0.183558i
$737$	−3.23607	−	2.35114i	−0.119202	−	0.0866054i
$738$	−23.2984	−	16.9273i	−0.857625	−	0.623101i
$739$	−18.0902	+	13.1433i	−0.665458	+	0.483483i	−0.868502	−	0.495686i	$-0.834917\pi$
$739$	−18.0902	+	13.1433i	−0.665458	+	0.483483i	0.203044	+	0.979170i	$0.434917\pi$
$740$	−10.1631	−	7.38394i	−0.373604	−	0.271439i
$741$	4.85410	+	3.52671i	0.178320	+	0.129557i
$742$	3.00000	+	9.23305i	0.110133	+	0.338956i
$743$	−12.2918			−0.450942			−0.225471	−	0.974250i	$-0.572392\pi$
$743$	−12.2918			−0.450942			−0.225471	+	0.974250i	$0.572392\pi$
$744$	5.23607	+	16.1150i	0.191964	+	0.590803i
$745$	−2.86475	−	8.81678i	−0.104956	−	0.323022i
$746$	−0.145898	+	0.449028i	−0.00534171	+	0.0164401i
$747$	−25.9443	+	79.8483i	−0.949251	+	2.92150i
$748$	2.61803	−	1.90211i	0.0957248	−	0.0695481i
$749$	−24.9443			−0.911444
$750$	−11.1803	+	34.4095i	−0.408248	+	1.25646i
$751$	8.18034			0.298505			0.149252	−	0.988799i	$-0.452313\pi$
$751$	8.18034			0.298505			0.149252	+	0.988799i	$0.452313\pi$
$752$	−8.85410	+	6.43288i	−0.322876	+	0.234583i
$753$	−8.00000	+	24.6215i	−0.291536	+	0.897256i
$754$	0.489357	−	1.50609i	0.0178213	−	0.0548484i
$755$	−14.7984	−	45.5447i	−0.538568	−	1.65754i
$756$	−23.4164	−	72.0683i	−0.851647	−	2.62110i
$757$	7.85410			0.285462			0.142731	−	0.989762i	$-0.454412\pi$
$757$	7.85410			0.285462			0.142731	+	0.989762i	$0.454412\pi$
$758$	−7.76393	−	23.8949i	−0.281999	−	0.867903i
$759$	44.3607	+	32.2299i	1.61019	+	1.16987i
$760$	−1.80902	−	1.31433i	−0.0656199	−	0.0476757i
$761$	25.6803	−	18.6579i	0.930912	−	0.676347i	−0.0153043	−	0.999883i	$-0.504872\pi$
$761$	25.6803	−	18.6579i	0.930912	−	0.676347i	0.946216	+	0.323536i	$0.104872\pi$
$762$	−37.1246	−	26.9726i	−1.34488	−	0.977115i
$763$	48.2148	+	35.0301i	1.74549	+	1.26817i
$764$	6.47214	−	4.70228i	0.234154	−	0.170123i
$765$	−27.0344			−0.977432
$766$	11.2361	+	8.16348i	0.405976	+	0.294959i
$767$	−4.14590	−	12.7598i	−0.149700	−	0.460728i
$768$	3.23607			0.116772
$769$	3.74265	+	11.5187i	0.134963	+	0.415374i	0.995584	−	0.0938717i	$-0.0299244\pi$
$769$	3.74265	+	11.5187i	0.134963	+	0.415374i	−0.860621	+	0.509246i	$0.829924\pi$
$770$	23.4164			0.843869
$771$	−27.2705	+	83.9300i	−0.982123	+	3.02267i
$772$	−4.42705	+	13.6251i	−0.159333	+	0.490377i
$773$	5.73607	−	4.16750i	0.206312	−	0.149894i	−0.479831	−	0.877361i	$-0.659302\pi$
$773$	5.73607	−	4.16750i	0.206312	−	0.149894i	0.686144	+	0.727466i	$0.259302\pi$
$774$	9.23607			0.331984
$775$	21.1803	+	15.3884i	0.760820	+	0.552768i
$776$	4.38197			0.157303
$777$	77.0132	−	55.9533i	2.76283	−	2.00731i
$778$	4.04508	−	12.4495i	0.145023	−	0.446336i
$779$	1.19098	−	3.66547i	0.0426714	−	0.131329i
$780$	−10.8541	+	7.88597i	−0.388639	+	0.282363i
$781$	9.52786	+	29.3238i	0.340934	+	1.04929i
$782$	−13.7082			−0.490204
$783$	−3.81966	−	11.7557i	−0.136504	−	0.420115i
$784$	−16.5172	−	12.0005i	−0.589901	−	0.428588i
$785$	1.97214	+	6.06961i	0.0703886	+	0.216634i
$786$	57.5967	−	41.8465i	2.05441	−	1.49261i
$787$	−2.47214	−	1.79611i	−0.0881221	−	0.0640245i	0.542852	−	0.839829i	$-0.317345\pi$
$787$	−2.47214	−	1.79611i	−0.0881221	−	0.0640245i	−0.630974	+	0.775804i	$0.717345\pi$
$788$	15.3541	+	11.1554i	0.546967	+	0.397395i
$789$	43.8885	−	31.8869i	1.56247	−	1.13520i
$790$	−16.1803	+	11.7557i	−0.575671	+	0.418249i
$791$	−39.5066	−	28.7032i	−1.40469	−	1.02057i
$792$	−4.61803	−	14.2128i	−0.164095	−	0.505032i
$793$	−2.02129			−0.0717780
$794$	−1.67376	−	5.15131i	−0.0593996	−	0.182813i
$795$	4.14590	−	12.7598i	0.147040	−	0.452542i
$796$	5.00000	−	15.3884i	0.177220	−	0.545428i
$797$	7.62868	−	23.4787i	0.270222	−	0.831657i	−0.720223	−	0.693743i	$-0.755960\pi$
$797$	7.62868	−	23.4787i	0.270222	−	0.831657i	0.990444	−	0.137914i	$-0.0440396\pi$
$798$	13.7082	−	9.95959i	0.485265	−	0.352566i
$799$	−17.7082			−0.626471
$800$	4.04508	−	2.93893i	0.143015	−	0.103907i
$801$	93.8673			3.31664
$802$	−7.59017	+	5.51458i	−0.268018	+	0.194727i
$803$	−0.562306	+	1.73060i	−0.0198433	+	0.0610715i
$804$	2.00000	−	6.15537i	0.0705346	−	0.217083i
$805$	−80.2492	−	58.3045i	−2.82841	−	2.05496i
$806$	3.00000	+	9.23305i	0.105670	+	0.325220i
$807$	−56.8328			−2.00061
$808$	1.88197	+	5.79210i	0.0662073	+	0.203765i
$809$	−3.45492	−	2.51014i	−0.121468	−	0.0882519i	0.525392	−	0.850860i	$-0.323919\pi$
$809$	−3.45492	−	2.51014i	−0.121468	−	0.0882519i	−0.646861	+	0.762608i	$0.723919\pi$
$810$	−16.8713	+	51.9246i	−0.592798	+	1.82444i
$811$	8.38197	−	6.08985i	0.294331	−	0.213844i	−0.430813	−	0.902441i	$-0.641773\pi$
$811$	8.38197	−	6.08985i	0.294331	−	0.213844i	0.725144	+	0.688597i	$0.241773\pi$
$812$	−3.61803	−	2.62866i	−0.126968	−	0.0922477i
$813$	32.6525	+	23.7234i	1.14517	+	0.832016i
$814$	9.09017	−	6.60440i	0.318610	−	0.231484i
$815$	6.05573	−	18.6376i	0.212123	−	0.652847i
$816$	4.23607	+	3.07768i	0.148292	+	0.107740i
$817$	0.381966	+	1.17557i	0.0133633	+	0.0411280i
$818$	−9.14590			−0.319779
$819$	−22.4164	−	68.9906i	−0.783293	−	2.41073i
$820$	6.97214	+	5.06555i	0.243478	+	0.176897i
$821$	4.03444	−	12.4167i	0.140803	−	0.433347i	−0.855644	−	0.517564i	$-0.826839\pi$
$821$	4.03444	−	12.4167i	0.140803	−	0.433347i	0.996447	+	0.0842170i	$0.0268389\pi$
$822$	13.8541	−	42.6385i	0.483217	−	1.48719i
$823$	−12.6180	+	9.16754i	−0.439837	+	0.319560i	−0.785570	−	0.618773i	$-0.787630\pi$
$823$	−12.6180	+	9.16754i	−0.439837	+	0.319560i	0.345733	+	0.938333i	$0.387630\pi$
$824$	−2.18034			−0.0759557
$825$	−26.1803	−	19.0211i	−0.911482	−	0.662231i
$826$	−37.8885			−1.31831
$827$	−9.38197	+	6.81640i	−0.326243	+	0.237029i	−0.738835	−	0.673887i	$-0.764624\pi$
$827$	−9.38197	+	6.81640i	−0.326243	+	0.237029i	0.412592	+	0.910916i	$0.364624\pi$
$828$	−19.5623	+	60.2066i	−0.679837	+	2.09232i
$829$	6.93363	−	21.3395i	0.240815	−	0.741152i	−0.755482	−	0.655170i	$-0.772597\pi$
$829$	6.93363	−	21.3395i	0.240815	−	0.741152i	0.996297	−	0.0859823i	$-0.0274029\pi$
$830$	7.76393	−	23.8949i	0.269490	−	0.829405i
$831$	−20.5623	−	63.2843i	−0.713298	−	2.19531i
$832$	1.85410			0.0642794
$833$	−10.2082	−	31.4176i	−0.353693	−	1.08856i
$834$	2.76393	+	2.00811i	0.0957071	+	0.0695353i
$835$	14.4721	−	10.5146i	0.500829	−	0.363874i
$836$	1.61803	−	1.17557i	0.0559609	−	0.0406580i
$837$	61.3050	+	44.5407i	2.11901	+	1.53955i
$838$	−5.85410	−	4.25325i	−0.202227	−	0.146926i
$839$	18.9443	−	13.7638i	0.654029	−	0.475180i	−0.210612	−	0.977570i	$-0.567546\pi$
$839$	18.9443	−	13.7638i	0.654029	−	0.475180i	0.864641	+	0.502390i	$0.167546\pi$
$840$	11.7082	+	36.0341i	0.403971	+	1.24330i
$841$	22.8713	+	16.6170i	0.788666	+	0.573000i
$842$	−1.08359	−	3.33495i	−0.0373431	−	0.114930i
$843$	16.4721			0.567330
$844$	−1.09017	−	3.35520i	−0.0375252	−	0.115491i
$845$	17.2984	−	12.5680i	0.595082	−	0.432352i
$846$	−25.2705	+	77.7746i	−0.868818	+	2.67395i
$847$	11.3262	−	34.8586i	0.389174	−	1.19775i
$848$	−1.50000	+	1.08981i	−0.0515102	+	0.0374244i
$849$	−32.9443			−1.13064
$850$	8.09017			0.277491
$851$	−47.5967			−1.63160
$852$	−40.3607	+	29.3238i	−1.38273	+	1.00462i
$853$	11.5517	−	35.5524i	0.395521	−	1.21729i	−0.533033	−	0.846094i	$-0.678948\pi$
$853$	11.5517	−	35.5524i	0.395521	−	1.21729i	0.928555	−	0.371195i	$-0.121052\pi$
$854$	−1.76393	+	5.42882i	−0.0603605	+	0.185771i
$855$	−16.7082			−0.571409
$856$	−1.47214	−	4.53077i	−0.0503166	−	0.154858i
$857$	−24.8328			−0.848273			−0.424136	−	0.905598i	$-0.639422\pi$
$857$	−24.8328			−0.848273			−0.424136	+	0.905598i	$0.639422\pi$
$858$	−3.70820	−	11.4127i	−0.126596	−	0.389622i
$859$	4.47214	+	3.24920i	0.152587	+	0.110861i	0.661459	−	0.749981i	$-0.269937\pi$
$859$	4.47214	+	3.24920i	0.152587	+	0.110861i	−0.508872	+	0.860842i	$0.669937\pi$
$860$	−2.76393			−0.0942493
$861$	−52.8328	+	38.3853i	−1.80054	+	1.30817i
$862$	8.00000	+	5.81234i	0.272481	+	0.197969i
$863$	12.7082	+	9.23305i	0.432592	+	0.314297i	0.782685	−	0.622419i	$-0.213850\pi$
$863$	12.7082	+	9.23305i	0.432592	+	0.314297i	−0.350092	+	0.936715i	$0.613850\pi$
$864$	11.7082	−	8.50651i	0.398321	−	0.289397i
$865$	41.1418	+	29.8913i	1.39886	+	1.01633i
$866$	−18.8262	−	13.6781i	−0.639742	−	0.464799i
$867$	−14.3820	−	44.2631i	−0.488437	−	1.50326i
$868$	27.4164			0.930574
$869$	−5.52786	−	17.0130i	−0.187520	−	0.577127i
$870$	1.90983	+	5.87785i	0.0647493	+	0.199278i
$871$	1.14590	−	3.52671i	0.0388273	−	0.119498i
$872$	−3.51722	+	10.8249i	−0.119108	+	0.366577i
$873$	26.4894	−	19.2456i	0.896529	−	0.651366i
$874$	−8.47214			−0.286574
$875$	47.3607	+	34.4095i	1.60108	+	1.16326i
$876$	−2.94427			−0.0994777
$877$	−4.44427	+	3.22895i	−0.150072	+	0.109034i	−0.660288	−	0.751013i	$-0.729566\pi$
$877$	−4.44427	+	3.22895i	−0.150072	+	0.109034i	0.510215	+	0.860047i	$0.329566\pi$
$878$	4.67376	−	14.3844i	0.157732	−	0.485449i
$879$	−13.7984	+	42.4670i	−0.465408	+	1.43238i
$880$	1.38197	+	4.25325i	0.0465861	+	0.143377i
$881$	0.618034	+	1.90211i	0.0208221	+	0.0640838i	0.960928	−	0.276800i	$-0.0892738\pi$
$881$	0.618034	+	1.90211i	0.0208221	+	0.0640838i	−0.940106	+	0.340883i	$0.889274\pi$
$882$	−152.554			−5.13677
$883$	5.47214	+	16.8415i	0.184152	+	0.566762i	0.999933	−	0.0115997i	$-0.00369237\pi$
$883$	5.47214	+	16.8415i	0.184152	+	0.566762i	−0.815781	+	0.578361i	$0.803692\pi$
$884$	2.42705	+	1.76336i	0.0816306	+	0.0593081i
$885$	42.3607	+	30.7768i	1.42394	+	1.03455i
$886$	−16.3262	+	11.8617i	−0.548491	+	0.398502i
$887$	9.76393	+	7.09391i	0.327841	+	0.238190i	0.739514	−	0.673141i	$-0.235055\pi$
$887$	9.76393	+	7.09391i	0.327841	+	0.238190i	−0.411673	+	0.911332i	$0.635055\pi$
$888$	14.7082	+	10.6861i	0.493575	+	0.358603i
$889$	−60.0689	+	43.6426i	−2.01465	+	1.46373i
$890$	−28.0902			−0.941585
$891$	−39.5066	−	28.7032i	−1.32352	−	0.961594i
$892$	−8.79837	−	27.0786i	−0.294591	−	0.906659i
$893$	−10.9443			−0.366236
$894$	4.14590	+	12.7598i	0.138660	+	0.426750i
$895$	22.3607			0.747435
$896$	1.61803	−	4.97980i	0.0540547	−	0.166363i
$897$	−15.7082	+	48.3449i	−0.524482	+	1.61419i
$898$	−24.9615	+	18.1356i	−0.832976	+	0.605192i
$899$	4.47214			0.149154
$900$	11.5451	−	35.5321i	0.384836	−	1.18440i
$901$	−3.00000			−0.0999445
$902$	−6.23607	+	4.53077i	−0.207638	+	0.150858i
$903$	6.47214	−	19.9192i	0.215379	−	0.662869i
$904$	2.88197	−	8.86978i	0.0958528	−	0.295004i
$905$	6.01722	−	4.37177i	0.200019	−	0.145322i
$906$	21.4164	+	65.9129i	0.711512	+	2.18981i
$907$	−48.6525			−1.61548			−0.807739	−	0.589540i	$-0.799309\pi$
$907$	−48.6525			−1.61548			−0.807739	+	0.589540i	$0.799309\pi$
$908$	7.32624	+	22.5478i	0.243130	+	0.748276i
$909$	36.8156	+	26.7481i	1.22110	+	0.887178i
$910$	6.70820	+	20.6457i	0.222375	+	0.684399i
$911$	3.90983	−	2.84066i	0.129538	−	0.0941152i	−0.521129	−	0.853478i	$-0.674489\pi$
$911$	3.90983	−	2.84066i	0.129538	−	0.0941152i	0.650668	+	0.759363i	$0.274489\pi$
$912$	2.61803	+	1.90211i	0.0866918	+	0.0629853i
$913$	18.1803	+	13.2088i	0.601681	+	0.437147i
$914$	27.7984	−	20.1967i	0.919488	−	0.668047i
$915$	6.38197	−	4.63677i	0.210981	−	0.153287i
$916$	13.3541	+	9.70232i	0.441232	+	0.320574i
$917$	−35.5967	−	109.556i	−1.17551	−	3.61784i
$918$	23.4164			0.772857
$919$	15.6525	+	48.1734i	0.516328	+	1.58909i	0.780853	+	0.624714i	$0.214785\pi$
$919$	15.6525	+	48.1734i	0.516328	+	1.58909i	−0.264526	+	0.964379i	$0.585215\pi$
$920$	5.85410	−	18.0171i	0.193004	−	0.594005i
$921$	19.2361	−	59.2025i	0.633850	−	1.95079i
$922$	12.9377	−	39.8181i	0.426080	−	1.31134i
$923$	−23.1246	+	16.8010i	−0.761156	+	0.553012i
$924$	−33.8885			−1.11485
$925$	28.0902			0.923599
$926$	−24.9443			−0.819720
$927$	−13.1803	+	9.57608i	−0.432899	+	0.314520i
$928$	0.263932	−	0.812299i	0.00866399	−	0.0266650i
$929$	−7.62461	+	23.4661i	−0.250155	+	0.769899i	0.744590	+	0.667522i	$0.232645\pi$
$929$	−7.62461	+	23.4661i	−0.250155	+	0.769899i	−0.994746	+	0.102377i	$0.967355\pi$
$930$	−30.6525	−	22.2703i	−1.00513	−	0.730273i
$931$	−6.30902	−	19.4172i	−0.206770	−	0.636372i
$932$	−15.3820			−0.503853
$933$	5.81966	+	17.9111i	0.190527	+	0.586382i
$934$	−12.3262	−	8.95554i	−0.403327	−	0.293034i
$935$	−2.23607	+	6.88191i	−0.0731272	+	0.225063i
$936$	11.2082	−	8.14324i	0.366352	−	0.266170i
$937$	15.7812	+	11.4657i	0.515548	+	0.374567i	0.814924	−	0.579568i	$-0.196779\pi$
$937$	15.7812	+	11.4657i	0.515548	+	0.374567i	−0.299376	+	0.954135i	$0.596779\pi$
$938$	−8.47214	−	6.15537i	−0.276625	−	0.200980i
$939$	31.1246	−	22.6134i	1.01571	−	0.737959i
$940$	7.56231	−	23.2744i	0.246655	−	0.759127i
$941$	−9.01722	−	6.55139i	−0.293953	−	0.213569i	0.431027	−	0.902339i	$-0.358151\pi$
$941$	−9.01722	−	6.55139i	−0.293953	−	0.213569i	−0.724980	+	0.688769i	$0.758151\pi$
$942$	−2.85410	−	8.78402i	−0.0929917	−	0.286199i
$943$	32.6525			1.06331
$944$	−2.23607	−	6.88191i	−0.0727778	−	0.223987i
$945$	137.082	+	99.5959i	4.45928	+	3.23986i
$946$	0.763932	−	2.35114i	0.0248376	−	0.0764422i
$947$	−10.8885	+	33.5115i	−0.353830	+	1.08898i	0.602855	+	0.797851i	$0.294030\pi$
$947$	−10.8885	+	33.5115i	−0.353830	+	1.08898i	−0.956685	+	0.291126i	$0.905970\pi$
$948$	23.4164	−	17.0130i	0.760530	−	0.552557i
$949$	−1.68692			−0.0547597
$950$	5.00000			0.162221
$951$	35.4164			1.14846
$952$	6.85410	−	4.97980i	0.222143	−	0.161396i
$953$	0.534442	−	1.64484i	0.0173123	−	0.0532817i	−0.942027	−	0.335537i	$-0.891082\pi$
$953$	0.534442	−	1.64484i	0.0173123	−	0.0532817i	0.959339	+	0.282255i	$0.0910824\pi$
$954$	−4.28115	+	13.1760i	−0.138607	+	0.426590i
$955$	−5.52786	+	17.0130i	−0.178877	+	0.550528i
$956$	−3.61803	−	11.1352i	−0.117016	−	0.360137i
$957$	−5.52786			−0.178690
$958$	5.85410	+	18.0171i	0.189137	+	0.582105i
$959$	−58.6869	−	42.6385i	−1.89510	−	1.37687i
$960$	−5.85410	+	4.25325i	−0.188940	+	0.137273i
$961$	2.89919	−	2.10638i	0.0935222	−	0.0679478i
$962$	8.42705	+	6.12261i	0.271699	+	0.197401i
$963$	−28.7984	−	20.9232i	−0.928015	−	0.674242i
$964$	−12.6353	+	9.18005i	−0.406954	+	0.295670i
$965$	−9.89919	−	30.4666i	−0.318666	−	0.980753i
$966$	116.138	+	84.3790i	3.73667	+	2.71485i
$967$	−10.0344	−	30.8828i	−0.322686	−	0.993125i	−0.972474	−	0.233010i	$-0.925143\pi$
$967$	−10.0344	−	30.8828i	−0.322686	−	0.993125i	0.649788	−	0.760115i	$-0.274857\pi$
$968$	7.00000			0.224989
$969$	1.61803	+	4.97980i	0.0519787	+	0.159974i
$970$	−7.92705	+	5.75934i	−0.254522	+	0.184921i
$971$	17.3262	−	53.3247i	0.556025	−	1.71127i	−0.137194	−	0.990544i	$-0.543809\pi$
$971$	17.3262	−	53.3247i	0.556025	−	1.71127i	0.693220	−	0.720726i	$-0.256191\pi$
$972$	11.0000	−	33.8545i	0.352825	−	1.08588i
$973$	4.47214	−	3.24920i	0.143370	−	0.104164i
$974$	5.23607			0.167774
$975$	9.27051	−	28.5317i	0.296894	−	0.913746i
$976$	−1.09017			−0.0348955
$977$	22.0623	−	16.0292i	0.705836	−	0.512820i	−0.175992	−	0.984392i	$-0.556313\pi$
$977$	22.0623	−	16.0292i	0.705836	−	0.512820i	0.881828	+	0.471572i	$0.156313\pi$
$978$	−8.76393	+	26.9726i	−0.280240	+	0.862489i
$979$	7.76393	−	23.8949i	0.248136	−	0.763685i
$980$	45.6525			1.45831
$981$	26.2812	+	80.8851i	0.839093	+	2.58246i
$982$	−22.6525			−0.722870
$983$	−11.7639	−	36.2057i	−0.375211	−	1.15478i	−0.943336	−	0.331839i	$-0.892331\pi$
$983$	−11.7639	−	36.2057i	−0.375211	−	1.15478i	0.568125	−	0.822942i	$-0.307669\pi$
$984$	−10.0902	−	7.33094i	−0.321663	−	0.233702i
$985$	−42.4377			−1.35218
$986$	1.11803	−	0.812299i	0.0356055	−	0.0258689i
$987$	150.026	+	109.000i	4.77539	+	3.46952i
$988$	1.50000	+	1.08981i	0.0477214	+	0.0346716i
$989$	−8.47214	+	6.15537i	−0.269398	+	0.195729i
$990$	27.0344	+	19.6417i	0.859211	+	0.624253i
$991$	−42.7984	−	31.0948i	−1.35954	−	0.987760i	−0.998474	−	0.0552178i	$-0.982415\pi$
$991$	−42.7984	−	31.0948i	−1.35954	−	0.987760i	−0.361061	−	0.932542i	$-0.617585\pi$
$992$	1.61803	+	4.97980i	0.0513726	+	0.158109i
$993$	38.8328			1.23232
$994$	24.9443	+	76.7706i	0.791184	+	2.43501i
$995$	11.1803	+	34.4095i	0.354441	+	1.09086i
$996$	−11.2361	+	34.5811i	−0.356028	+	1.09574i
$997$	−5.56231	+	17.1190i	−0.176160	+	0.542165i	−0.999685	−	0.0251159i	$-0.992005\pi$
$997$	−5.56231	+	17.1190i	−0.176160	+	0.542165i	0.823525	+	0.567281i	$0.192005\pi$
$998$	13.9443	−	10.1311i	0.441398	−	0.320695i
$999$	81.3050			2.57237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.a.761.1	yes	4
25.16	even	5	inner	950.2.h.a.191.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.a.191.1	✓	4	25.16	even	5	inner
950.2.h.a.761.1	yes	4	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-1.00000 - 3.07768i) q^{6} -5.23607 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(1.00000 - 3.07768i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-1.00000 - 3.07768i) q^{6} -5.23607 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-6.04508 - 4.39201i) q^{9} +(1.80902 + 1.31433i) q^{10} +(-1.61803 + 1.17557i) q^{11} +(-2.61803 - 1.90211i) q^{12} +(-1.50000 - 1.08981i) q^{13} +(-4.23607 + 3.07768i) q^{14} +7.23607 q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.500000 - 1.53884i) q^{17} -7.47214 q^{18} +(-0.309017 - 0.951057i) q^{19} +2.23607 q^{20} +(-5.23607 + 16.1150i) q^{21} +(-0.618034 + 1.90211i) q^{22} +(6.85410 - 4.97980i) q^{23} -3.23607 q^{24} +(-4.04508 + 2.93893i) q^{25} -1.85410 q^{26} +(-11.7082 + 8.50651i) q^{27} +(-1.61803 + 4.97980i) q^{28} +(-0.263932 + 0.812299i) q^{29} +(5.85410 - 4.25325i) q^{30} +(-1.61803 - 4.97980i) q^{31} -1.00000 q^{32} +(2.00000 + 6.15537i) q^{33} +(-1.30902 - 0.951057i) q^{34} +(-3.61803 - 11.1352i) q^{35} +(-6.04508 + 4.39201i) q^{36} +(-4.54508 - 3.30220i) q^{37} +(-0.809017 - 0.587785i) q^{38} +(-4.85410 + 3.52671i) q^{39} +(1.80902 - 1.31433i) q^{40} +(3.11803 + 2.26538i) q^{41} +(5.23607 + 16.1150i) q^{42} -1.23607 q^{43} +(0.618034 + 1.90211i) q^{44} +(5.16312 - 15.8904i) q^{45} +(2.61803 - 8.05748i) q^{46} +(3.38197 - 10.4086i) q^{47} +(-2.61803 + 1.90211i) q^{48} +20.4164 q^{49} +(-1.54508 + 4.75528i) q^{50} -5.23607 q^{51} +(-1.50000 + 1.08981i) q^{52} +(0.572949 - 1.76336i) q^{53} +(-4.47214 + 13.7638i) q^{54} +(-3.61803 - 2.62866i) q^{55} +(1.61803 + 4.97980i) q^{56} -3.23607 q^{57} +(0.263932 + 0.812299i) q^{58} +(5.85410 + 4.25325i) q^{59} +(2.23607 - 6.88191i) q^{60} +(0.881966 - 0.640786i) q^{61} +(-4.23607 - 3.07768i) q^{62} +(31.6525 + 22.9969i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(1.28115 - 3.94298i) q^{65} +(5.23607 + 3.80423i) q^{66} +(0.618034 + 1.90211i) q^{67} -1.61803 q^{68} +(-8.47214 - 26.0746i) q^{69} +(-9.47214 - 6.88191i) q^{70} +(4.76393 - 14.6619i) q^{71} +(-2.30902 + 7.10642i) q^{72} +(0.736068 - 0.534785i) q^{73} -5.61803 q^{74} +(5.00000 + 15.3884i) q^{75} -1.00000 q^{76} +(8.47214 - 6.15537i) q^{77} +(-1.85410 + 5.70634i) q^{78} +(-2.76393 + 8.50651i) q^{79} +(0.690983 - 2.12663i) q^{80} +(7.54508 + 23.2214i) q^{81} +3.85410 q^{82} +(-3.47214 - 10.6861i) q^{83} +(13.7082 + 9.95959i) q^{84} +(2.92705 - 2.12663i) q^{85} +(-1.00000 + 0.726543i) q^{86} +(2.23607 + 1.62460i) q^{87} +(1.61803 + 1.17557i) q^{88} +(-10.1631 + 7.38394i) q^{89} +(-5.16312 - 15.8904i) q^{90} +(7.85410 + 5.70634i) q^{91} +(-2.61803 - 8.05748i) q^{92} -16.9443 q^{93} +(-3.38197 - 10.4086i) q^{94} +(1.80902 - 1.31433i) q^{95} +(-1.00000 + 3.07768i) q^{96} +(-1.35410 + 4.16750i) q^{97} +(16.5172 - 12.0005i) q^{98} +14.9443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 4 q^{3} - q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 13 q^{9}+O(q^{10}) \) 4 * q + q^2 + 4 * q^3 - q^4 + 5 * q^5 - 4 * q^6 - 12 * q^7 + q^8 - 13 * q^9	\( 4 q + q^{2} + 4 q^{3} - q^{4} + 5 q^{5} - 4 q^{6} - 12 q^{7} + q^{8} - 13 q^{9} + 5 q^{10} - 2 q^{11} - 6 q^{12} - 6 q^{13} - 8 q^{14} + 20 q^{15} - q^{16} - 2 q^{17} - 12 q^{18} + q^{19} - 12 q^{21} + 2 q^{22} + 14 q^{23} - 4 q^{24} - 5 q^{25} + 6 q^{26} - 20 q^{27} - 2 q^{28} - 10 q^{29} + 10 q^{30} - 2 q^{31} - 4 q^{32} + 8 q^{33} - 3 q^{34} - 10 q^{35} - 13 q^{36} - 7 q^{37} - q^{38} - 6 q^{39} + 5 q^{40} + 8 q^{41} + 12 q^{42} + 4 q^{43} - 2 q^{44} + 5 q^{45} + 6 q^{46} + 18 q^{47} - 6 q^{48} + 28 q^{49} + 5 q^{50} - 12 q^{51} - 6 q^{52} + 9 q^{53} - 10 q^{55} + 2 q^{56} - 4 q^{57} + 10 q^{58} + 10 q^{59} + 8 q^{61} - 8 q^{62} + 64 q^{63} - q^{64} - 15 q^{65} + 12 q^{66} - 2 q^{67} - 2 q^{68} - 16 q^{69} - 20 q^{70} + 28 q^{71} - 7 q^{72} - 6 q^{73} - 18 q^{74} + 20 q^{75} - 4 q^{76} + 16 q^{77} + 6 q^{78} - 20 q^{79} + 5 q^{80} + 19 q^{81} + 2 q^{82} + 4 q^{83} + 28 q^{84} + 5 q^{85} - 4 q^{86} + 2 q^{88} - 25 q^{89} - 5 q^{90} + 18 q^{91} - 6 q^{92} - 32 q^{93} - 18 q^{94} + 5 q^{95} - 4 q^{96} + 8 q^{97} + 37 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 - q^4 + 5 * q^5 - 4 * q^6 - 12 * q^7 + q^8 - 13 * q^9 + 5 * q^10 - 2 * q^11 - 6 * q^12 - 6 * q^13 - 8 * q^14 + 20 * q^15 - q^16 - 2 * q^17 - 12 * q^18 + q^19 - 12 * q^21 + 2 * q^22 + 14 * q^23 - 4 * q^24 - 5 * q^25 + 6 * q^26 - 20 * q^27 - 2 * q^28 - 10 * q^29 + 10 * q^30 - 2 * q^31 - 4 * q^32 + 8 * q^33 - 3 * q^34 - 10 * q^35 - 13 * q^36 - 7 * q^37 - q^38 - 6 * q^39 + 5 * q^40 + 8 * q^41 + 12 * q^42 + 4 * q^43 - 2 * q^44 + 5 * q^45 + 6 * q^46 + 18 * q^47 - 6 * q^48 + 28 * q^49 + 5 * q^50 - 12 * q^51 - 6 * q^52 + 9 * q^53 - 10 * q^55 + 2 * q^56 - 4 * q^57 + 10 * q^58 + 10 * q^59 + 8 * q^61 - 8 * q^62 + 64 * q^63 - q^64 - 15 * q^65 + 12 * q^66 - 2 * q^67 - 2 * q^68 - 16 * q^69 - 20 * q^70 + 28 * q^71 - 7 * q^72 - 6 * q^73 - 18 * q^74 + 20 * q^75 - 4 * q^76 + 16 * q^77 + 6 * q^78 - 20 * q^79 + 5 * q^80 + 19 * q^81 + 2 * q^82 + 4 * q^83 + 28 * q^84 + 5 * q^85 - 4 * q^86 + 2 * q^88 - 25 * q^89 - 5 * q^90 + 18 * q^91 - 6 * q^92 - 32 * q^93 - 18 * q^94 + 5 * q^95 - 4 * q^96 + 8 * q^97 + 37 * q^98 + 24 * q^99

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