LMFDB - Embedded newform 950.2.h.a.381.1

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			381.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	950.381
Dual form			950.2.h.a.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-1.00000 - 0.726543i) q^{6} -0.763932 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-1.00000 - 0.726543i) q^{6} -0.763932 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} +(0.690983 - 2.12663i) q^{10} +(0.618034 + 1.90211i) q^{11} +(-0.381966 + 1.17557i) q^{12} +(-1.50000 + 4.61653i) q^{13} +(0.236068 + 0.726543i) q^{14} +2.76393 q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.500000 - 0.363271i) q^{17} +1.47214 q^{18} +(0.809017 + 0.587785i) q^{19} -2.23607 q^{20} +(-0.763932 + 0.555029i) q^{21} +(1.61803 - 1.17557i) q^{22} +(0.145898 + 0.449028i) q^{23} +1.23607 q^{24} +(1.54508 + 4.75528i) q^{25} +4.85410 q^{26} +(1.70820 + 5.25731i) q^{27} +(0.618034 - 0.449028i) q^{28} +(-4.73607 + 3.44095i) q^{29} +(-0.854102 - 2.62866i) q^{30} +(0.618034 + 0.449028i) q^{31} -1.00000 q^{32} +(2.00000 + 1.45309i) q^{33} +(-0.190983 + 0.587785i) q^{34} +(-1.38197 - 1.00406i) q^{35} +(-0.454915 - 1.40008i) q^{36} +(1.04508 - 3.21644i) q^{37} +(0.309017 - 0.951057i) q^{38} +(1.85410 + 5.70634i) q^{39} +(0.690983 + 2.12663i) q^{40} +(0.881966 - 2.71441i) q^{41} +(0.763932 + 0.555029i) q^{42} +3.23607 q^{43} +(-1.61803 - 1.17557i) q^{44} +(-2.66312 + 1.93487i) q^{45} +(0.381966 - 0.277515i) q^{46} +(5.61803 - 4.08174i) q^{47} +(-0.381966 - 1.17557i) q^{48} -6.41641 q^{49} +(4.04508 - 2.93893i) q^{50} -0.763932 q^{51} +(-1.50000 - 4.61653i) q^{52} +(3.92705 - 2.85317i) q^{53} +(4.47214 - 3.24920i) q^{54} +(-1.38197 + 4.25325i) q^{55} +(-0.618034 - 0.449028i) q^{56} +1.23607 q^{57} +(4.73607 + 3.44095i) q^{58} +(-0.854102 + 2.62866i) q^{59} +(-2.23607 + 1.62460i) q^{60} +(3.11803 + 9.59632i) q^{61} +(0.236068 - 0.726543i) q^{62} +(0.347524 - 1.06957i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-8.78115 + 6.37988i) q^{65} +(0.763932 - 2.35114i) q^{66} +(-1.61803 - 1.17557i) q^{67} +0.618034 q^{68} +(0.472136 + 0.343027i) q^{69} +(-0.527864 + 1.62460i) q^{70} +(9.23607 - 6.71040i) q^{71} +(-1.19098 + 0.865300i) q^{72} +(-3.73607 - 11.4984i) q^{73} -3.38197 q^{74} +(5.00000 + 3.63271i) q^{75} -1.00000 q^{76} +(-0.472136 - 1.45309i) q^{77} +(4.85410 - 3.52671i) q^{78} +(-7.23607 + 5.25731i) q^{79} +(1.80902 - 1.31433i) q^{80} +(1.95492 + 1.42033i) q^{81} -2.85410 q^{82} +(5.47214 + 3.97574i) q^{83} +(0.291796 - 0.898056i) q^{84} +(-0.427051 - 1.31433i) q^{85} +(-1.00000 - 3.07768i) q^{86} +(-2.23607 + 6.88191i) q^{87} +(-0.618034 + 1.90211i) q^{88} +(-2.33688 - 7.19218i) q^{89} +(2.66312 + 1.93487i) q^{90} +(1.14590 - 3.52671i) q^{91} +(-0.381966 - 0.277515i) q^{92} +0.944272 q^{93} +(-5.61803 - 4.08174i) q^{94} +(0.690983 + 2.12663i) q^{95} +(-1.00000 + 0.726543i) q^{96} +(5.35410 - 3.88998i) q^{97} +(1.98278 + 6.10237i) q^{98} -2.94427 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	−0.260418	−	0.965496i	$-0.583860\pi$
$3$	1.00000	−	0.726543i	0.577350	−	0.419470i	0.837768	+	0.546027i	$0.183860\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$5$	1.80902	+	1.31433i	0.809017	+	0.587785i
$6$	−1.00000	−	0.726543i	−0.408248	−	0.296610i
$7$	−0.763932			−0.288739			−0.144370	−	0.989524i	$-0.546115\pi$
$7$	−0.763932			−0.288739			−0.144370	+	0.989524i	$0.546115\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.454915	+	1.40008i	−0.151638	+	0.466695i
$10$	0.690983	−	2.12663i	0.218508	−	0.672499i
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	0.999969	−	0.00788181i	$-0.00250889\pi$
$11$	0.618034	+	1.90211i	0.186344	+	0.573509i	−0.813625	+	0.581390i	$0.802509\pi$
$12$	−0.381966	+	1.17557i	−0.110264	+	0.339358i
$13$	−1.50000	+	4.61653i	−0.416025	+	1.28039i	0.495306	+	0.868719i	$0.335056\pi$
$13$	−1.50000	+	4.61653i	−0.416025	+	1.28039i	−0.911331	+	0.411675i	$0.864944\pi$
$14$	0.236068	+	0.726543i	0.0630918	+	0.194177i
$15$	2.76393			0.713644
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.500000	−	0.363271i	−0.121268	−	0.0881062i	0.525498	−	0.850795i	$-0.323879\pi$
$17$	−0.500000	−	0.363271i	−0.121268	−	0.0881062i	−0.646766	+	0.762688i	$0.723879\pi$
$18$	1.47214			0.346986
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	−2.23607			−0.500000
$21$	−0.763932	+	0.555029i	−0.166704	+	0.121117i
$22$	1.61803	−	1.17557i	0.344966	−	0.250632i
$23$	0.145898	+	0.449028i	0.0304218	+	0.0936288i	0.965115	−	0.261828i	$-0.0843253\pi$
$23$	0.145898	+	0.449028i	0.0304218	+	0.0936288i	−0.934693	+	0.355457i	$0.884325\pi$
$24$	1.23607			0.252311
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	4.85410			0.951968
$27$	1.70820	+	5.25731i	0.328744	+	1.01177i
$28$	0.618034	−	0.449028i	0.116797	−	0.0848583i
$29$	−4.73607	+	3.44095i	−0.879466	+	0.638969i	−0.933110	−	0.359591i	$-0.882916\pi$
$29$	−4.73607	+	3.44095i	−0.879466	+	0.638969i	0.0536443	+	0.998560i	$0.482916\pi$
$30$	−0.854102	−	2.62866i	−0.155937	−	0.479925i
$31$	0.618034	+	0.449028i	0.111002	+	0.0806478i	0.641902	−	0.766787i	$-0.278146\pi$
$31$	0.618034	+	0.449028i	0.111002	+	0.0806478i	−0.530899	+	0.847435i	$0.678146\pi$
$32$	−1.00000			−0.176777
$33$	2.00000	+	1.45309i	0.348155	+	0.252950i
$34$	−0.190983	+	0.587785i	−0.0327533	+	0.100804i
$35$	−1.38197	−	1.00406i	−0.233595	−	0.169717i
$36$	−0.454915	−	1.40008i	−0.0758192	−	0.233347i
$37$	1.04508	−	3.21644i	0.171811	−	0.528780i	−0.827663	−	0.561226i	$-0.810330\pi$
$37$	1.04508	−	3.21644i	0.171811	−	0.528780i	0.999473	+	0.0324464i	$0.0103298\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	1.85410	+	5.70634i	0.296894	+	0.913746i
$40$	0.690983	+	2.12663i	0.109254	+	0.336249i
$41$	0.881966	−	2.71441i	0.137740	−	0.423920i	−0.858266	−	0.513205i	$-0.828458\pi$
$41$	0.881966	−	2.71441i	0.137740	−	0.423920i	0.996006	+	0.0892848i	$0.0284581\pi$
$42$	0.763932	+	0.555029i	0.117877	+	0.0856428i
$43$	3.23607			0.493496			0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607			0.493496			0.246748	+	0.969080i	$0.420638\pi$
$44$	−1.61803	−	1.17557i	−0.243928	−	0.177224i
$45$	−2.66312	+	1.93487i	−0.396994	+	0.288433i
$46$	0.381966	−	0.277515i	0.0563178	−	0.0409173i
$47$	5.61803	−	4.08174i	0.819474	−	0.595383i	−0.0970874	−	0.995276i	$-0.530953\pi$
$47$	5.61803	−	4.08174i	0.819474	−	0.595383i	0.916562	+	0.399893i	$0.130953\pi$
$48$	−0.381966	−	1.17557i	−0.0551320	−	0.169679i
$49$	−6.41641			−0.916630
$50$	4.04508	−	2.93893i	0.572061	−	0.415627i
$51$	−0.763932			−0.106972
$52$	−1.50000	−	4.61653i	−0.208013	−	0.640197i
$53$	3.92705	−	2.85317i	0.539422	−	0.391913i	−0.284448	−	0.958691i	$-0.591810\pi$
$53$	3.92705	−	2.85317i	0.539422	−	0.391913i	0.823870	+	0.566778i	$0.191810\pi$
$54$	4.47214	−	3.24920i	0.608581	−	0.442160i
$55$	−1.38197	+	4.25325i	−0.186344	+	0.573509i
$56$	−0.618034	−	0.449028i	−0.0825883	−	0.0600039i
$57$	1.23607			0.163721
$58$	4.73607	+	3.44095i	0.621876	+	0.451820i
$59$	−0.854102	+	2.62866i	−0.111195	+	0.342222i	−0.991134	−	0.132864i	$-0.957583\pi$
$59$	−0.854102	+	2.62866i	−0.111195	+	0.342222i	0.879940	+	0.475085i	$0.157583\pi$
$60$	−2.23607	+	1.62460i	−0.288675	+	0.209735i
$61$	3.11803	+	9.59632i	0.399223	+	1.22868i	0.925623	+	0.378446i	$0.123541\pi$
$61$	3.11803	+	9.59632i	0.399223	+	1.22868i	−0.526400	+	0.850237i	$0.676459\pi$
$62$	0.236068	−	0.726543i	0.0299807	−	0.0922710i
$63$	0.347524	−	1.06957i	0.0437839	−	0.134753i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−8.78115	+	6.37988i	−1.08917	+	0.791327i
$66$	0.763932	−	2.35114i	0.0940335	−	0.289405i
$67$	−1.61803	−	1.17557i	−0.197674	−	0.143619i	0.484545	−	0.874766i	$-0.338985\pi$
$67$	−1.61803	−	1.17557i	−0.197674	−	0.143619i	−0.682219	+	0.731147i	$0.738985\pi$
$68$	0.618034			0.0749476
$69$	0.472136	+	0.343027i	0.0568385	+	0.0412956i
$70$	−0.527864	+	1.62460i	−0.0630918	+	0.194177i
$71$	9.23607	−	6.71040i	1.09612	−	0.796378i	0.115697	−	0.993285i	$-0.463090\pi$
$71$	9.23607	−	6.71040i	1.09612	−	0.796378i	0.980422	+	0.196907i	$0.0630897\pi$
$72$	−1.19098	+	0.865300i	−0.140359	+	0.101977i
$73$	−3.73607	−	11.4984i	−0.437274	−	1.34579i	−0.890739	−	0.454516i	$-0.849812\pi$
$73$	−3.73607	−	11.4984i	−0.437274	−	1.34579i	0.453465	−	0.891274i	$-0.350188\pi$
$74$	−3.38197			−0.393146
$75$	5.00000	+	3.63271i	0.577350	+	0.419470i
$76$	−1.00000			−0.114708
$77$	−0.472136	−	1.45309i	−0.0538049	−	0.165594i
$78$	4.85410	−	3.52671i	0.549619	−	0.399321i
$79$	−7.23607	+	5.25731i	−0.814121	+	0.591494i	−0.915023	−	0.403403i	$-0.867827\pi$
$79$	−7.23607	+	5.25731i	−0.814121	+	0.591494i	0.100901	+	0.994896i	$0.467827\pi$
$80$	1.80902	−	1.31433i	0.202254	−	0.146946i
$81$	1.95492	+	1.42033i	0.217213	+	0.157814i
$82$	−2.85410			−0.315183
$83$	5.47214	+	3.97574i	0.600645	+	0.436394i	0.846108	−	0.533012i	$-0.178940\pi$
$83$	5.47214	+	3.97574i	0.600645	+	0.436394i	−0.245463	+	0.969406i	$0.578940\pi$
$84$	0.291796	−	0.898056i	0.0318376	−	0.0979859i
$85$	−0.427051	−	1.31433i	−0.0463202	−	0.142559i
$86$	−1.00000	−	3.07768i	−0.107833	−	0.331875i
$87$	−2.23607	+	6.88191i	−0.239732	+	0.737818i
$88$	−0.618034	+	1.90211i	−0.0658826	+	0.202766i
$89$	−2.33688	−	7.19218i	−0.247709	−	0.762370i	−0.995179	−	0.0980743i	$-0.968732\pi$
$89$	−2.33688	−	7.19218i	−0.247709	−	0.762370i	0.747470	−	0.664295i	$-0.231268\pi$
$90$	2.66312	+	1.93487i	0.280717	+	0.203953i
$91$	1.14590	−	3.52671i	0.120123	−	0.369700i
$92$	−0.381966	−	0.277515i	−0.0398227	−	0.0289329i
$93$	0.944272			0.0979164
$94$	−5.61803	−	4.08174i	−0.579456	−	0.420999i
$95$	0.690983	+	2.12663i	0.0708934	+	0.218187i
$96$	−1.00000	+	0.726543i	−0.102062	+	0.0741524i
$97$	5.35410	−	3.88998i	0.543627	−	0.394968i	−0.281803	−	0.959472i	$-0.590933\pi$
$97$	5.35410	−	3.88998i	0.543627	−	0.394968i	0.825430	+	0.564504i	$0.190933\pi$
$98$	1.98278	+	6.10237i	0.200291	+	0.616432i
$99$	−2.94427			−0.295910
$100$	−4.04508	−	2.93893i	−0.404508	−	0.293893i
$101$	5.09017			0.506491			0.253245	−	0.967402i	$-0.418502\pi$
$101$	5.09017			0.506491			0.253245	+	0.967402i	$0.418502\pi$
$102$	0.236068	+	0.726543i	0.0233742	+	0.0719384i
$103$	16.3262	−	11.8617i	1.60867	−	1.16877i	0.741198	−	0.671287i	$-0.234258\pi$
$103$	16.3262	−	11.8617i	1.60867	−	1.16877i	0.867475	−	0.497482i	$-0.165742\pi$
$104$	−3.92705	+	2.85317i	−0.385079	+	0.279776i
$105$	−2.11146			−0.206057
$106$	−3.92705	−	2.85317i	−0.381429	−	0.277124i
$107$	9.23607			0.892884			0.446442	−	0.894812i	$-0.352691\pi$
$107$	9.23607			0.892884			0.446442	+	0.894812i	$0.352691\pi$
$108$	−4.47214	−	3.24920i	−0.430331	−	0.312654i
$109$	4.20820	−	12.9515i	0.403073	−	1.24053i	−0.519421	−	0.854519i	$-0.673852\pi$
$109$	4.20820	−	12.9515i	0.403073	−	1.24053i	0.922494	−	0.386012i	$-0.126148\pi$
$110$	4.47214			0.426401
$111$	−1.29180	−	3.97574i	−0.122612	−	0.377360i
$112$	−0.236068	+	0.726543i	−0.0223063	+	0.0686518i
$113$	1.95492	−	6.01661i	0.183903	−	0.565995i	−0.816025	−	0.578017i	$-0.803827\pi$
$113$	1.95492	−	6.01661i	0.183903	−	0.565995i	0.999928	+	0.0120219i	$0.00382677\pi$
$114$	−0.381966	−	1.17557i	−0.0357744	−	0.110102i
$115$	−0.326238	+	1.00406i	−0.0304218	+	0.0936288i
$116$	1.80902	−	5.56758i	0.167963	−	0.516937i
$117$	−5.78115	−	4.20025i	−0.534468	−	0.388314i
$118$	2.76393			0.254441
$119$	0.381966	+	0.277515i	0.0350148	+	0.0254397i
$120$	2.23607	+	1.62460i	0.204124	+	0.148305i
$121$	5.66312	−	4.11450i	0.514829	−	0.374045i
$122$	8.16312	−	5.93085i	0.739054	−	0.536954i
$123$	−1.09017	−	3.35520i	−0.0982973	−	0.302528i
$124$	−0.763932			−0.0686031
$125$	−3.45492	+	10.6331i	−0.309017	+	0.951057i
$126$	−1.12461			−0.100188
$127$	2.52786	+	7.77997i	0.224312	+	0.690360i	0.998361	+	0.0572347i	$0.0182283\pi$
$127$	2.52786	+	7.77997i	0.224312	+	0.690360i	−0.774049	+	0.633126i	$0.781772\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	3.23607	−	2.35114i	0.284920	−	0.207006i
$130$	8.78115	+	6.37988i	0.770158	+	0.559553i
$131$	−17.7984	−	12.9313i	−1.55505	−	1.12981i	−0.939924	−	0.341383i	$-0.889105\pi$
$131$	−17.7984	−	12.9313i	−1.55505	−	1.12981i	−0.615127	−	0.788428i	$-0.710895\pi$
$132$	−2.47214			−0.215172
$133$	−0.618034	−	0.449028i	−0.0535903	−	0.0389357i
$134$	−0.618034	+	1.90211i	−0.0533900	+	0.164318i
$135$	−3.81966	+	11.7557i	−0.328744	+	1.01177i
$136$	−0.190983	−	0.587785i	−0.0163767	−	0.0504022i
$137$	−2.20820	+	6.79615i	−0.188660	+	0.580635i	−0.999992	−	0.00395029i	$-0.998743\pi$
$137$	−2.20820	+	6.79615i	−0.188660	+	0.580635i	0.811333	+	0.584585i	$0.198743\pi$
$138$	0.180340	−	0.555029i	0.0153516	−	0.0472472i
$139$	5.85410	+	18.0171i	0.496538	+	1.52819i	0.814545	+	0.580100i	$0.196986\pi$
$139$	5.85410	+	18.0171i	0.496538	+	1.52819i	−0.318007	+	0.948088i	$0.603014\pi$
$140$	1.70820			0.144370
$141$	2.65248	−	8.16348i	0.223379	−	0.687489i
$142$	−9.23607	−	6.71040i	−0.775074	−	0.563124i
$143$	−9.70820			−0.811841
$144$	1.19098	+	0.865300i	0.0992486	+	0.0721083i
$145$	−13.0902			−1.08708
$146$	−9.78115	+	7.10642i	−0.809494	+	0.588132i
$147$	−6.41641	+	4.66179i	−0.529216	+	0.384498i
$148$	1.04508	+	3.21644i	0.0859055	+	0.264390i
$149$	−10.8541			−0.889203			−0.444601	−	0.895729i	$-0.646655\pi$
$149$	−10.8541			−0.889203			−0.444601	+	0.895729i	$0.646655\pi$
$150$	1.90983	−	5.87785i	0.155937	−	0.479925i
$151$	5.41641			0.440781			0.220391	−	0.975412i	$-0.429267\pi$
$151$	5.41641			0.440781			0.220391	+	0.975412i	$0.429267\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	0.736068	−	0.534785i	0.0595076	−	0.0432348i
$154$	−1.23607	+	0.898056i	−0.0996052	+	0.0723674i
$155$	0.527864	+	1.62460i	0.0423991	+	0.130491i
$156$	−4.85410	−	3.52671i	−0.388639	−	0.282363i
$157$	−3.85410			−0.307591			−0.153795	−	0.988103i	$-0.549150\pi$
$157$	−3.85410			−0.307591			−0.153795	+	0.988103i	$0.549150\pi$
$158$	7.23607	+	5.25731i	0.575671	+	0.418249i
$159$	1.85410	−	5.70634i	0.147040	−	0.452542i
$160$	−1.80902	−	1.31433i	−0.143015	−	0.103907i
$161$	−0.111456	−	0.343027i	−0.00878398	−	0.0270343i
$162$	0.746711	−	2.29814i	0.0586672	−	0.180559i
$163$	4.09017	−	12.5882i	0.320367	−	0.985988i	−0.653122	−	0.757253i	$-0.726541\pi$
$163$	4.09017	−	12.5882i	0.320367	−	0.985988i	0.973489	−	0.228735i	$-0.0734589\pi$
$164$	0.881966	+	2.71441i	0.0688700	+	0.211960i
$165$	1.70820	+	5.25731i	0.132983	+	0.409281i
$166$	2.09017	−	6.43288i	0.162229	−	0.499288i
$167$	6.47214	+	4.70228i	0.500829	+	0.363874i	0.809334	−	0.587349i	$-0.199829\pi$
$167$	6.47214	+	4.70228i	0.500829	+	0.363874i	−0.308505	+	0.951223i	$0.599829\pi$
$168$	−0.944272			−0.0728522
$169$	−8.54508	−	6.20837i	−0.657314	−	0.477567i
$170$	−1.11803	+	0.812299i	−0.0857493	+	0.0623005i
$171$	−1.19098	+	0.865300i	−0.0910767	+	0.0661711i
$172$	−2.61803	+	1.90211i	−0.199623	+	0.145035i
$173$	6.10081	+	18.7764i	0.463836	+	1.42754i	0.860440	+	0.509551i	$0.170189\pi$
$173$	6.10081	+	18.7764i	0.463836	+	1.42754i	−0.396604	+	0.917990i	$0.629811\pi$
$174$	7.23607			0.548565
$175$	−1.18034	−	3.63271i	−0.0892253	−	0.274607i
$176$	2.00000			0.150756
$177$	1.05573	+	3.24920i	0.0793534	+	0.244225i
$178$	−6.11803	+	4.44501i	−0.458566	+	0.333168i
$179$	−8.09017	+	5.87785i	−0.604688	+	0.439331i	−0.847540	−	0.530732i	$-0.821917\pi$
$179$	−8.09017	+	5.87785i	−0.604688	+	0.439331i	0.242852	+	0.970063i	$0.421917\pi$
$180$	1.01722	−	3.13068i	0.0758192	−	0.233347i
$181$	−9.97214	−	7.24518i	−0.741223	−	0.538530i	0.151871	−	0.988400i	$-0.451470\pi$
$181$	−9.97214	−	7.24518i	−0.741223	−	0.538530i	−0.893094	+	0.449870i	$0.851470\pi$
$182$	−3.70820			−0.274870
$183$	10.0902	+	7.33094i	0.745887	+	0.541918i
$184$	−0.145898	+	0.449028i	−0.0107557	+	0.0331028i
$185$	6.11803	−	4.44501i	0.449807	−	0.326804i
$186$	−0.291796	−	0.898056i	−0.0213955	−	0.0658487i
$187$	0.381966	−	1.17557i	0.0279321	−	0.0859662i
$188$	−2.14590	+	6.60440i	−0.156506	+	0.481675i
$189$	−1.30495	−	4.01623i	−0.0949213	−	0.292138i
$190$	1.80902	−	1.31433i	0.131240	−	0.0953514i
$191$	−2.47214	+	7.60845i	−0.178877	+	0.550528i	−0.999789	−	0.0205267i	$-0.993466\pi$
$191$	−2.47214	+	7.60845i	−0.178877	+	0.550528i	0.820912	+	0.571055i	$0.193466\pi$
$192$	1.00000	+	0.726543i	0.0721688	+	0.0524337i
$193$	1.32624			0.0954647			0.0477323	−	0.998860i	$-0.484801\pi$
$193$	1.32624			0.0954647			0.0477323	+	0.998860i	$0.484801\pi$
$194$	−5.35410	−	3.88998i	−0.384402	−	0.279284i
$195$	−4.14590	+	12.7598i	−0.296894	+	0.913746i
$196$	5.19098	−	3.77147i	0.370785	−	0.269391i
$197$	−22.6353	+	16.4455i	−1.61270	+	1.17169i	−0.758638	+	0.651512i	$0.774135\pi$
$197$	−22.6353	+	16.4455i	−1.61270	+	1.17169i	−0.854057	+	0.520179i	$0.825865\pi$
$198$	0.909830	+	2.80017i	0.0646588	+	0.198999i
$199$	−6.18034			−0.438113			−0.219056	−	0.975712i	$-0.570298\pi$
$199$	−6.18034			−0.438113			−0.219056	+	0.975712i	$0.570298\pi$
$200$	−1.54508	+	4.75528i	−0.109254	+	0.336249i
$201$	−2.47214			−0.174371
$202$	−1.57295	−	4.84104i	−0.110672	−	0.340614i
$203$	3.61803	−	2.62866i	0.253936	−	0.184495i
$204$	0.618034	−	0.449028i	0.0432710	−	0.0314382i
$205$	5.16312	−	3.75123i	0.360608	−	0.261997i
$206$	−16.3262	−	11.8617i	−1.13750	−	0.826444i
$207$	−0.695048			−0.0483092
$208$	3.92705	+	2.85317i	0.272292	+	0.197832i
$209$	−0.618034	+	1.90211i	−0.0427503	+	0.131572i
$210$	0.652476	+	2.00811i	0.0450251	+	0.138573i
$211$	−3.85410	−	11.8617i	−0.265327	−	0.816594i	−0.991618	−	0.129206i	$-0.958757\pi$
$211$	−3.85410	−	11.8617i	−0.265327	−	0.816594i	0.726290	−	0.687388i	$-0.241243\pi$
$212$	−1.50000	+	4.61653i	−0.103020	+	0.317064i
$213$	4.36068	−	13.4208i	0.298789	−	0.919578i
$214$	−2.85410	−	8.78402i	−0.195102	−	0.600463i
$215$	5.85410	+	4.25325i	0.399246	+	0.290070i
$216$	−1.70820	+	5.25731i	−0.116229	+	0.357715i
$217$	−0.472136	−	0.343027i	−0.0320507	−	0.0232862i
$218$	−13.6180			−0.922330
$219$	−12.0902	−	8.78402i	−0.816978	−	0.593569i
$220$	−1.38197	−	4.25325i	−0.0931721	−	0.286754i
$221$	2.42705	−	1.76336i	0.163261	−	0.118616i
$222$	−3.38197	+	2.45714i	−0.226983	+	0.164913i
$223$	−6.03444	−	18.5721i	−0.404096	−	1.24368i	−0.921648	−	0.388028i	$-0.873156\pi$
$223$	−6.03444	−	18.5721i	−0.404096	−	1.24368i	0.517552	−	0.855652i	$-0.326844\pi$
$224$	0.763932			0.0510424
$225$	−7.36068			−0.490712
$226$	−6.32624			−0.420815
$227$	3.18034	+	9.78808i	0.211087	+	0.649658i	0.999408	+	0.0343945i	$0.0109503\pi$
$227$	3.18034	+	9.78808i	0.211087	+	0.649658i	−0.788322	+	0.615263i	$0.789050\pi$
$228$	−1.00000	+	0.726543i	−0.0662266	+	0.0481165i
$229$	−17.3992	+	12.6412i	−1.14977	+	0.835357i	−0.988450	−	0.151545i	$-0.951575\pi$
$229$	−17.3992	+	12.6412i	−1.14977	+	0.835357i	−0.161320	+	0.986902i	$0.551575\pi$
$230$	1.05573			0.0696126
$231$	−1.52786	−	1.11006i	−0.100526	−	0.0730365i
$232$	−5.85410			−0.384341
$233$	14.2533	+	10.3556i	0.933764	+	0.678419i	0.946912	−	0.321494i	$-0.104185\pi$
$233$	14.2533	+	10.3556i	0.933764	+	0.678419i	−0.0131475	+	0.999914i	$0.504185\pi$
$234$	−2.20820	+	6.79615i	−0.144355	+	0.444278i
$235$	15.5279			1.01293
$236$	−0.854102	−	2.62866i	−0.0555973	−	0.171111i
$237$	−3.41641	+	10.5146i	−0.221920	+	0.682998i
$238$	0.145898	−	0.449028i	0.00945716	−	0.0291062i
$239$	0.527864	+	1.62460i	0.0341447	+	0.105087i	0.966676	−	0.256002i	$-0.0824053\pi$
$239$	0.527864	+	1.62460i	0.0341447	+	0.105087i	−0.932532	+	0.361088i	$0.882405\pi$
$240$	0.854102	−	2.62866i	0.0551320	−	0.169679i
$241$	4.13525	−	12.7270i	0.266375	−	0.819819i	−0.724998	−	0.688751i	$-0.758159\pi$
$241$	4.13525	−	12.7270i	0.266375	−	0.819819i	0.991373	−	0.131068i	$-0.0418406\pi$
$242$	−5.66312	−	4.11450i	−0.364039	−	0.264490i
$243$	−13.5967			−0.872232
$244$	−8.16312	−	5.93085i	−0.522590	−	0.379684i
$245$	−11.6074	−	8.43326i	−0.741569	−	0.538781i
$246$	−2.85410	+	2.07363i	−0.181971	+	0.132210i
$247$	−3.92705	+	2.85317i	−0.249872	+	0.181543i
$248$	0.236068	+	0.726543i	0.0149903	+	0.0461355i
$249$	8.36068			0.529837
$250$	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	$0.581245\pi$
$252$	0.347524	+	1.06957i	0.0218920	+	0.0673765i
$253$	−0.763932	+	0.555029i	−0.0480280	+	0.0348944i
$254$	6.61803	−	4.80828i	0.415252	−	0.301699i
$255$	−1.38197	−	1.00406i	−0.0865421	−	0.0628765i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	6.27051			0.391144			0.195572	−	0.980689i	$-0.437344\pi$
$257$	6.27051			0.391144			0.195572	+	0.980689i	$0.437344\pi$
$258$	−3.23607	−	2.35114i	−0.201469	−	0.146376i
$259$	−0.798374	+	2.45714i	−0.0496085	+	0.152679i
$260$	3.35410	−	10.3229i	0.208013	−	0.640197i
$261$	−2.66312	−	8.19624i	−0.164843	−	0.507334i
$262$	−6.79837	+	20.9232i	−0.420005	+	1.29264i
$263$	−6.56231	+	20.1967i	−0.404649	+	1.24538i	0.516539	+	0.856264i	$0.327220\pi$
$263$	−6.56231	+	20.1967i	−0.404649	+	1.24538i	−0.921188	+	0.389118i	$0.872780\pi$
$264$	0.763932	+	2.35114i	0.0470168	+	0.144703i
$265$	10.8541			0.666762
$266$	−0.236068	+	0.726543i	−0.0144743	+	0.0445472i
$267$	−7.56231	−	5.49434i	−0.462806	−	0.336248i
$268$	2.00000			0.122169
$269$	−2.07295	−	1.50609i	−0.126390	−	0.0918277i	0.522794	−	0.852459i	$-0.324890\pi$
$269$	−2.07295	−	1.50609i	−0.126390	−	0.0918277i	−0.649184	+	0.760631i	$0.724890\pi$
$270$	12.3607			0.752247
$271$	2.85410	−	2.07363i	0.173374	−	0.125964i	−0.497714	−	0.867341i	$-0.665827\pi$
$271$	2.85410	−	2.07363i	0.173374	−	0.125964i	0.671088	+	0.741377i	$0.265827\pi$
$272$	−0.500000	+	0.363271i	−0.0303170	+	0.0220266i
$273$	−1.41641	−	4.35926i	−0.0857249	−	0.263834i
$274$	7.14590			0.431699
$275$	−8.09017	+	5.87785i	−0.487856	+	0.354448i
$276$	−0.583592			−0.0351281
$277$	−0.135255	−	0.416272i	−0.00812668	−	0.0250114i	0.946911	−	0.321496i	$-0.104186\pi$
$277$	−0.135255	−	0.416272i	−0.00812668	−	0.0250114i	−0.955038	+	0.296485i	$0.904186\pi$
$278$	15.3262	−	11.1352i	0.919207	−	0.667843i
$279$	−0.909830	+	0.661030i	−0.0544701	+	0.0395748i
$280$	−0.527864	−	1.62460i	−0.0315459	−	0.0970883i
$281$	4.92705	+	3.57971i	0.293923	+	0.213548i	0.724968	−	0.688783i	$-0.241855\pi$
$281$	4.92705	+	3.57971i	0.293923	+	0.213548i	−0.431044	+	0.902331i	$0.641855\pi$
$282$	−8.58359			−0.511145
$283$	−9.85410	−	7.15942i	−0.585766	−	0.425584i	0.255033	−	0.966932i	$-0.417914\pi$
$283$	−9.85410	−	7.15942i	−0.585766	−	0.425584i	−0.840798	+	0.541349i	$0.817914\pi$
$284$	−3.52786	+	10.8576i	−0.209340	+	0.644283i
$285$	2.23607	+	1.62460i	0.132453	+	0.0962329i
$286$	3.00000	+	9.23305i	0.177394	+	0.545962i
$287$	−0.673762	+	2.07363i	−0.0397709	+	0.122402i
$288$	0.454915	−	1.40008i	0.0268061	−	0.0825008i
$289$	−5.13525	−	15.8047i	−0.302074	−	0.929688i
$290$	4.04508	+	12.4495i	0.237536	+	0.731059i
$291$	2.52786	−	7.77997i	0.148186	−	0.456070i
$292$	9.78115	+	7.10642i	0.572399	+	0.415872i
$293$	10.7984			0.630848			0.315424	−	0.948951i	$-0.397853\pi$
$293$	10.7984			0.630848			0.315424	+	0.948951i	$0.397853\pi$
$294$	6.41641	+	4.66179i	0.374213	+	0.271881i
$295$	−5.00000	+	3.63271i	−0.291111	+	0.211505i
$296$	2.73607	−	1.98787i	0.159031	−	0.115543i
$297$	−8.94427	+	6.49839i	−0.518999	+	0.377075i
$298$	3.35410	+	10.3229i	0.194298	+	0.597987i
$299$	−2.29180			−0.132538
$300$	−6.18034			−0.356822
$301$	−2.47214			−0.142492
$302$	−1.67376	−	5.15131i	−0.0963142	−	0.296425i
$303$	5.09017	−	3.69822i	0.292423	−	0.212457i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	−6.97214	+	21.4580i	−0.399223	+	1.22868i
$306$	−0.736068	−	0.534785i	−0.0420782	−	0.0305716i
$307$	14.7639			0.842622			0.421311	−	0.906916i	$-0.361570\pi$
$307$	14.7639			0.842622			0.421311	+	0.906916i	$0.361570\pi$
$308$	1.23607	+	0.898056i	0.0704315	+	0.0511715i
$309$	7.70820	−	23.7234i	0.438504	−	1.34958i
$310$	1.38197	−	1.00406i	0.0784904	−	0.0570266i
$311$	8.70820	+	26.8011i	0.493797	+	1.51975i	0.818823	+	0.574046i	$0.194627\pi$
$311$	8.70820	+	26.8011i	0.493797	+	1.51975i	−0.325026	+	0.945705i	$0.605373\pi$
$312$	−1.85410	+	5.70634i	−0.104968	+	0.323058i
$313$	7.38197	−	22.7194i	0.417253	−	1.28417i	−0.492966	−	0.870048i	$-0.664087\pi$
$313$	7.38197	−	22.7194i	0.417253	−	1.28417i	0.910220	−	0.414126i	$-0.135913\pi$
$314$	1.19098	+	3.66547i	0.0672111	+	0.206854i
$315$	2.03444	−	1.47811i	0.114628	−	0.0832820i
$316$	2.76393	−	8.50651i	0.155483	−	0.478528i
$317$	5.61803	+	4.08174i	0.315540	+	0.229253i	0.734270	−	0.678857i	$-0.237525\pi$
$317$	5.61803	+	4.08174i	0.315540	+	0.229253i	−0.418730	+	0.908111i	$0.637525\pi$
$318$	−6.00000			−0.336463
$319$	−9.47214	−	6.88191i	−0.530338	−	0.385313i
$320$	−0.690983	+	2.12663i	−0.0386271	+	0.118882i
$321$	9.23607	−	6.71040i	0.515507	−	0.374538i
$322$	−0.291796	+	0.212002i	−0.0162612	+	0.0118144i
$323$	−0.190983	−	0.587785i	−0.0106266	−	0.0327052i
$324$	−2.41641			−0.134245
$325$	−24.2705			−1.34629
$326$	−13.2361			−0.733078
$327$	−5.20163	−	16.0090i	−0.287651	−	0.885297i
$328$	2.30902	−	1.67760i	0.127494	−	0.0926299i
$329$	−4.29180	+	3.11817i	−0.236614	+	0.171910i
$330$	4.47214	−	3.24920i	0.246183	−	0.178862i
$331$	−9.70820	−	7.05342i	−0.533611	−	0.387691i	0.288096	−	0.957602i	$-0.406978\pi$
$331$	−9.70820	−	7.05342i	−0.533611	−	0.387691i	−0.821707	+	0.569910i	$0.806978\pi$
$332$	−6.76393			−0.371219
$333$	4.02786	+	2.92641i	0.220726	+	0.160367i
$334$	2.47214	−	7.60845i	0.135269	−	0.416316i
$335$	−1.38197	−	4.25325i	−0.0755049	−	0.232380i
$336$	0.291796	+	0.898056i	0.0159188	+	0.0489930i
$337$	1.67376	−	5.15131i	0.0911756	−	0.280610i	−0.895063	−	0.445941i	$-0.852869\pi$
$337$	1.67376	−	5.15131i	0.0911756	−	0.280610i	0.986238	+	0.165331i	$0.0528692\pi$
$338$	−3.26393	+	10.0453i	−0.177534	+	0.546395i
$339$	−2.41641	−	7.43694i	−0.131241	−	0.403919i
$340$	1.11803	+	0.812299i	0.0606339	+	0.0440531i
$341$	−0.472136	+	1.45309i	−0.0255676	+	0.0786890i
$342$	1.19098	+	0.865300i	0.0644010	+	0.0467901i
$343$	10.2492			0.553406
$344$	2.61803	+	1.90211i	0.141155	+	0.102555i
$345$	0.403252	+	1.24108i	0.0217104	+	0.0668177i
$346$	15.9721	−	11.6044i	0.858667	−	0.623858i
$347$	17.3262	−	12.5882i	0.930121	−	0.675773i	−0.0159013	−	0.999874i	$-0.505062\pi$
$347$	17.3262	−	12.5882i	0.930121	−	0.675773i	0.946022	+	0.324101i	$0.105062\pi$
$348$	−2.23607	−	6.88191i	−0.119866	−	0.368909i
$349$	−10.3262			−0.552751			−0.276375	−	0.961050i	$-0.589133\pi$
$349$	−10.3262			−0.552751			−0.276375	+	0.961050i	$0.589133\pi$
$350$	−3.09017	+	2.24514i	−0.165177	+	0.120008i
$351$	−26.8328			−1.43223
$352$	−0.618034	−	1.90211i	−0.0329413	−	0.101383i
$353$	−16.5623	+	12.0332i	−0.881523	+	0.640464i	−0.933654	−	0.358177i	$-0.883399\pi$
$353$	−16.5623	+	12.0332i	−0.881523	+	0.640464i	0.0521313	+	0.998640i	$0.483399\pi$
$354$	2.76393	−	2.00811i	0.146901	−	0.106730i
$355$	25.5279			1.35488
$356$	6.11803	+	4.44501i	0.324255	+	0.235585i
$357$	0.583592			0.0308870
$358$	8.09017	+	5.87785i	0.427579	+	0.310654i
$359$	7.56231	−	23.2744i	0.399123	−	1.22838i	−0.526580	−	0.850125i	$-0.676526\pi$
$359$	7.56231	−	23.2744i	0.399123	−	1.22838i	0.925704	−	0.378250i	$-0.123474\pi$
$360$	−3.29180			−0.173493
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	−3.80902	+	11.7229i	−0.200197	+	0.616145i
$363$	2.67376	−	8.22899i	0.140336	−	0.431910i
$364$	1.14590	+	3.52671i	0.0600614	+	0.184850i
$365$	8.35410	−	25.7113i	0.437274	−	1.34579i
$366$	3.85410	−	11.8617i	0.201457	−	0.620021i
$367$	−5.23607	−	3.80423i	−0.273321	−	0.198579i	0.442678	−	0.896681i	$-0.354028\pi$
$367$	−5.23607	−	3.80423i	−0.273321	−	0.198579i	−0.715999	+	0.698102i	$0.754028\pi$
$368$	0.472136			0.0246118
$369$	3.39919	+	2.46965i	0.176955	+	0.128565i
$370$	−6.11803	−	4.44501i	−0.318061	−	0.231085i
$371$	−3.00000	+	2.17963i	−0.155752	+	0.113161i
$372$	−0.763932	+	0.555029i	−0.0396080	+	0.0287769i
$373$	−2.61803	−	8.05748i	−0.135557	−	0.417201i	0.860120	−	0.510093i	$-0.170389\pi$
$373$	−2.61803	−	8.05748i	−0.135557	−	0.417201i	−0.995676	+	0.0928920i	$0.970389\pi$
$374$	−1.23607			−0.0639156
$375$	4.27051	+	13.1433i	0.220528	+	0.678716i
$376$	6.94427			0.358123
$377$	−8.78115	−	27.0256i	−0.452252	−	1.39189i
$378$	−3.41641	+	2.48217i	−0.175721	+	0.127669i
$379$	12.2361	−	8.89002i	0.628525	−	0.456650i	−0.227364	−	0.973810i	$-0.573011\pi$
$379$	12.2361	−	8.89002i	0.628525	−	0.456650i	0.855889	+	0.517160i	$0.173011\pi$
$380$	−1.80902	−	1.31433i	−0.0928006	−	0.0674236i
$381$	8.18034	+	5.94336i	0.419092	+	0.304488i
$382$	8.00000			0.409316
$383$	17.7082	+	12.8658i	0.904847	+	0.657410i	0.939706	−	0.341982i	$-0.111098\pi$
$383$	17.7082	+	12.8658i	0.904847	+	0.657410i	−0.0348594	+	0.999392i	$0.511098\pi$
$384$	0.381966	−	1.17557i	0.0194921	−	0.0599906i
$385$	1.05573	−	3.24920i	0.0538049	−	0.165594i
$386$	−0.409830	−	1.26133i	−0.0208598	−	0.0641999i
$387$	−1.47214	+	4.53077i	−0.0748329	+	0.230312i
$388$	−2.04508	+	6.29412i	−0.103823	+	0.319536i
$389$	−0.590170	−	1.81636i	−0.0299228	−	0.0920929i	0.934980	−	0.354701i	$-0.115417\pi$
$389$	−0.590170	−	1.81636i	−0.0299228	−	0.0920929i	−0.964903	+	0.262608i	$0.915417\pi$
$390$	13.4164			0.679366
$391$	0.0901699	−	0.277515i	0.00456009	−	0.0140345i
$392$	−5.19098	−	3.77147i	−0.262184	−	0.190488i
$393$	−27.1935			−1.37173
$394$	22.6353	+	16.4455i	1.14035	+	0.828511i
$395$	−20.0000			−1.00631
$396$	2.38197	−	1.73060i	0.119698	−	0.0869659i
$397$	17.3262	−	12.5882i	0.869579	−	0.631786i	−0.0608950	−	0.998144i	$-0.519395\pi$
$397$	17.3262	−	12.5882i	0.869579	−	0.631786i	0.930474	+	0.366358i	$0.119395\pi$
$398$	1.90983	+	5.87785i	0.0957311	+	0.294630i
$399$	−0.944272			−0.0472727
$400$	5.00000			0.250000
$401$	−11.6180			−0.580177			−0.290088	−	0.957000i	$-0.593685\pi$
$401$	−11.6180			−0.580177			−0.290088	+	0.957000i	$0.593685\pi$
$402$	0.763932	+	2.35114i	0.0381015	+	0.117264i
$403$	−3.00000	+	2.17963i	−0.149441	+	0.108575i
$404$	−4.11803	+	2.99193i	−0.204880	+	0.148854i
$405$	1.66970	+	5.13880i	0.0829679	+	0.255349i
$406$	−3.61803	−	2.62866i	−0.179560	−	0.130458i
$407$	6.76393			0.335276
$408$	−0.618034	−	0.449028i	−0.0305972	−	0.0222302i
$409$	4.89919	−	15.0781i	0.242249	−	0.745566i	−0.753828	−	0.657072i	$-0.771795\pi$
$409$	4.89919	−	15.0781i	0.242249	−	0.745566i	0.996077	−	0.0884940i	$-0.0282054\pi$
$410$	−5.16312	−	3.75123i	−0.254988	−	0.185260i
$411$	2.72949	+	8.40051i	0.134636	+	0.414366i
$412$	−6.23607	+	19.1926i	−0.307229	+	0.945554i
$413$	0.652476	−	2.00811i	0.0321062	−	0.0988128i
$414$	0.214782	+	0.661030i	0.0105559	+	0.0324879i
$415$	4.67376	+	14.3844i	0.229426	+	0.706100i
$416$	1.50000	−	4.61653i	0.0735436	−	0.226344i
$417$	18.9443	+	13.7638i	0.927705	+	0.674017i
$418$	2.00000			0.0978232
$419$	2.23607	+	1.62460i	0.109239	+	0.0793668i	0.641064	−	0.767488i	$-0.278493\pi$
$419$	2.23607	+	1.62460i	0.109239	+	0.0793668i	−0.531825	+	0.846855i	$0.678493\pi$
$420$	1.70820	−	1.24108i	0.0833518	−	0.0605586i
$421$	27.9164	−	20.2825i	1.36056	−	0.988506i	0.362154	−	0.932118i	$-0.382042\pi$
$421$	27.9164	−	20.2825i	1.36056	−	0.988506i	0.998409	−	0.0563880i	$-0.0179584\pi$
$422$	−10.0902	+	7.33094i	−0.491182	+	0.356864i
$423$	3.15905	+	9.72257i	0.153598	+	0.472727i
$424$	4.85410			0.235736
$425$	0.954915	−	2.93893i	0.0463202	−	0.142559i
$426$	−14.1115			−0.683702
$427$	−2.38197	−	7.33094i	−0.115271	−	0.354769i
$428$	−7.47214	+	5.42882i	−0.361179	+	0.262412i
$429$	−9.70820	+	7.05342i	−0.468717	+	0.340542i
$430$	2.23607	−	6.88191i	0.107833	−	0.331875i
$431$	20.9443	+	15.2169i	1.00885	+	0.732972i	0.963968	−	0.266020i	$-0.0857087\pi$
$431$	20.9443	+	15.2169i	1.00885	+	0.732972i	0.0448825	+	0.998992i	$0.485709\pi$
$432$	5.52786			0.265959
$433$	−8.30902	−	6.03685i	−0.399306	−	0.290113i	0.369952	−	0.929051i	$-0.379374\pi$
$433$	−8.30902	−	6.03685i	−0.399306	−	0.290113i	−0.769258	+	0.638938i	$0.779374\pi$
$434$	−0.180340	+	0.555029i	−0.00865659	+	0.0266422i
$435$	−13.0902	+	9.51057i	−0.627626	+	0.455997i
$436$	4.20820	+	12.9515i	0.201536	+	0.620265i
$437$	−0.145898	+	0.449028i	−0.00697925	+	0.0214799i
$438$	−4.61803	+	14.2128i	−0.220658	+	0.679116i
$439$	7.76393	+	23.8949i	0.370552	+	1.14044i	0.946431	+	0.322907i	$0.104660\pi$
$439$	7.76393	+	23.8949i	0.370552	+	1.14044i	−0.575878	+	0.817535i	$0.695340\pi$
$440$	−3.61803	+	2.62866i	−0.172483	+	0.125316i
$441$	2.91892	−	8.98351i	0.138996	−	0.427786i
$442$	−2.42705	−	1.76336i	−0.115443	−	0.0838743i
$443$	2.18034			0.103591			0.0517955	−	0.998658i	$-0.483506\pi$
$443$	2.18034			0.103591			0.0517955	+	0.998658i	$0.483506\pi$
$444$	3.38197	+	2.45714i	0.160501	+	0.116611i
$445$	5.22542	−	16.0822i	0.247709	−	0.762370i
$446$	−15.7984	+	11.4782i	−0.748075	+	0.543508i
$447$	−10.8541	+	7.88597i	−0.513381	+	0.372993i
$448$	−0.236068	−	0.726543i	−0.0111532	−	0.0343259i
$449$	−24.1459			−1.13952			−0.569758	−	0.821813i	$-0.692963\pi$
$449$	−24.1459			−1.13952			−0.569758	+	0.821813i	$0.692963\pi$
$450$	2.27458	+	7.00042i	0.107225	+	0.330003i
$451$	5.70820			0.268789
$452$	1.95492	+	6.01661i	0.0919515	+	0.282998i
$453$	5.41641	−	3.93525i	0.254485	−	0.184894i
$454$	8.32624	−	6.04937i	0.390770	−	0.283911i
$455$	6.70820	−	4.87380i	0.314485	−	0.228487i
$456$	1.00000	+	0.726543i	0.0468293	+	0.0340235i
$457$	−10.3607			−0.484652			−0.242326	−	0.970195i	$-0.577910\pi$
$457$	−10.3607			−0.484652			−0.242326	+	0.970195i	$0.577910\pi$
$458$	17.3992	+	12.6412i	0.813011	+	0.590687i
$459$	1.05573	−	3.24920i	0.0492772	−	0.151660i
$460$	−0.326238	−	1.00406i	−0.0152109	−	0.0468144i
$461$	12.6287	+	38.8671i	0.588176	+	1.81022i	0.586123	+	0.810222i	$0.300654\pi$
$461$	12.6287	+	38.8671i	0.588176	+	1.81022i	0.00205316	+	0.999998i	$0.499346\pi$
$462$	−0.583592	+	1.79611i	−0.0271512	+	0.0835627i
$463$	2.18034	−	6.71040i	0.101329	−	0.311859i	−0.887522	−	0.460765i	$-0.847575\pi$
$463$	2.18034	−	6.71040i	0.101329	−	0.311859i	0.988851	+	0.148906i	$0.0475752\pi$
$464$	1.80902	+	5.56758i	0.0839815	+	0.258468i
$465$	1.70820	+	1.24108i	0.0792161	+	0.0575538i
$466$	5.44427	−	16.7557i	0.252201	−	0.776195i
$467$	8.70820	+	6.32688i	0.402968	+	0.292773i	0.770749	−	0.637139i	$-0.219882\pi$
$467$	8.70820	+	6.32688i	0.402968	+	0.292773i	−0.367781	+	0.929912i	$0.619882\pi$
$468$	7.14590			0.330319
$469$	1.23607	+	0.898056i	0.0570763	+	0.0414684i
$470$	−4.79837	−	14.7679i	−0.221332	−	0.681191i
$471$	−3.85410	+	2.80017i	−0.177588	+	0.129025i
$472$	−2.23607	+	1.62460i	−0.102923	+	0.0747782i
$473$	2.00000	+	6.15537i	0.0919601	+	0.283024i
$474$	11.0557			0.507806
$475$	−1.54508	+	4.75528i	−0.0708934	+	0.218187i
$476$	−0.472136			−0.0216403
$477$	2.20820	+	6.79615i	0.101107	+	0.311174i
$478$	1.38197	−	1.00406i	0.0632097	−	0.0459245i
$479$	0.854102	−	0.620541i	0.0390249	−	0.0283533i	−0.568102	−	0.822958i	$-0.692322\pi$
$479$	0.854102	−	0.620541i	0.0390249	−	0.0283533i	0.607127	+	0.794605i	$0.292322\pi$
$480$	−2.76393			−0.126156
$481$	13.2812	+	9.64932i	0.605568	+	0.439971i
$482$	−13.3820			−0.609532
$483$	−0.360680	−	0.262049i	−0.0164115	−	0.0119237i
$484$	−2.16312	+	6.65740i	−0.0983236	+	0.302609i
$485$	14.7984			0.671960
$486$	4.20163	+	12.9313i	0.190590	+	0.586575i
$487$	−0.236068	+	0.726543i	−0.0106973	+	0.0329228i	−0.956263	−	0.292509i	$-0.905510\pi$
$487$	−0.236068	+	0.726543i	−0.0106973	+	0.0329228i	0.945565	+	0.325432i	$0.105510\pi$
$488$	−3.11803	+	9.59632i	−0.141147	+	0.434405i
$489$	−5.05573	−	15.5599i	−0.228628	−	0.703644i
$490$	−4.43363	+	13.6453i	−0.200291	+	0.616432i
$491$	−2.67376	+	8.22899i	−0.120665	+	0.371369i	−0.993086	−	0.117385i	$-0.962549\pi$
$491$	−2.67376	+	8.22899i	−0.120665	+	0.371369i	0.872421	+	0.488755i	$0.162549\pi$
$492$	2.85410	+	2.07363i	0.128673	+	0.0934863i
$493$	3.61803			0.162948
$494$	3.92705	+	2.85317i	0.176686	+	0.128370i
$495$	−5.32624	−	3.86974i	−0.239397	−	0.173932i
$496$	0.618034	−	0.449028i	0.0277505	−	0.0201620i
$497$	−7.05573	+	5.12629i	−0.316493	+	0.229945i
$498$	−2.58359	−	7.95148i	−0.115774	−	0.356314i
$499$	12.7639			0.571392			0.285696	−	0.958320i	$-0.407775\pi$
$499$	12.7639			0.571392			0.285696	+	0.958320i	$0.407775\pi$
$500$	−3.45492	−	10.6331i	−0.154508	−	0.475528i
$501$	9.88854			0.441788
$502$	2.47214	+	7.60845i	0.110337	+	0.339582i
$503$	27.1803	−	19.7477i	1.21191	−	0.880505i	0.216508	−	0.976281i	$-0.430533\pi$
$503$	27.1803	−	19.7477i	1.21191	−	0.880505i	0.995403	+	0.0957755i	$0.0305331\pi$
$504$	0.909830	−	0.661030i	0.0405271	−	0.0294446i
$505$	9.20820	+	6.69015i	0.409760	+	0.297708i
$506$	0.763932	+	0.555029i	0.0339609	+	0.0246741i
$507$	−13.0557			−0.579825
$508$	−6.61803	−	4.80828i	−0.293628	−	0.213333i
$509$	11.8090	−	36.3444i	0.523425	−	1.61094i	−0.243983	−	0.969780i	$-0.578454\pi$
$509$	11.8090	−	36.3444i	0.523425	−	1.61094i	0.767409	−	0.641158i	$-0.221546\pi$
$510$	−0.527864	+	1.62460i	−0.0233742	+	0.0719384i
$511$	2.85410	+	8.78402i	0.126258	+	0.388582i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−1.70820	+	5.25731i	−0.0754190	+	0.232116i
$514$	−1.93769	−	5.96361i	−0.0854680	−	0.263044i
$515$	45.1246			1.98843
$516$	−1.23607	+	3.80423i	−0.0544149	+	0.167472i
$517$	11.2361	+	8.16348i	0.494162	+	0.359029i
$518$	2.58359			0.113517
$519$	19.7426	+	14.3439i	0.866606	+	0.629626i
$520$	−10.8541			−0.475984
$521$	21.1074	−	15.3354i	0.924732	−	0.671857i	−0.0199656	−	0.999801i	$-0.506356\pi$
$521$	21.1074	−	15.3354i	0.924732	−	0.671857i	0.944697	+	0.327944i	$0.106356\pi$
$522$	−6.97214	+	5.06555i	−0.305162	+	0.221713i
$523$	−1.23607	−	3.80423i	−0.0540495	−	0.166347i	0.920388	−	0.391007i	$-0.127873\pi$
$523$	−1.23607	−	3.80423i	−0.0540495	−	0.166347i	−0.974437	+	0.224659i	$0.927873\pi$
$524$	22.0000			0.961074
$525$	−3.81966	−	2.77515i	−0.166704	−	0.121117i
$526$	21.2361			0.925937
$527$	−0.145898	−	0.449028i	−0.00635542	−	0.0195600i
$528$	2.00000	−	1.45309i	0.0870388	−	0.0632374i
$529$	18.4271	−	13.3880i	0.801176	−	0.582089i
$530$	−3.35410	−	10.3229i	−0.145693	−	0.448397i
$531$	−3.29180	−	2.39163i	−0.142852	−	0.103788i
$532$	0.763932			0.0331207
$533$	11.2082	+	8.14324i	0.485481	+	0.352723i
$534$	−2.88854	+	8.89002i	−0.125000	+	0.384709i
$535$	16.7082	+	12.1392i	0.722359	+	0.524824i
$536$	−0.618034	−	1.90211i	−0.0266950	−	0.0821588i
$537$	−3.81966	+	11.7557i	−0.164831	+	0.507296i
$538$	−0.791796	+	2.43690i	−0.0341368	+	0.105062i
$539$	−3.96556	−	12.2047i	−0.170809	−	0.525695i
$540$	−3.81966	−	11.7557i	−0.164372	−	0.505885i
$541$	2.62868	−	8.09024i	0.113016	−	0.347826i	−0.878512	−	0.477720i	$-0.841463\pi$
$541$	2.62868	−	8.09024i	0.113016	−	0.347826i	0.991528	+	0.129893i	$0.0414635\pi$
$542$	−2.85410	−	2.07363i	−0.122594	−	0.0890699i
$543$	−15.2361			−0.653842
$544$	0.500000	+	0.363271i	0.0214373	+	0.0155751i
$545$	24.6353	−	17.8986i	1.05526	−	0.766690i
$546$	−3.70820	+	2.69417i	−0.158696	+	0.115300i
$547$	−13.8541	+	10.0656i	−0.592359	+	0.430374i	−0.843158	−	0.537665i	$-0.819306\pi$
$547$	−13.8541	+	10.0656i	−0.592359	+	0.430374i	0.250800	+	0.968039i	$0.419306\pi$
$548$	−2.20820	−	6.79615i	−0.0943298	−	0.290317i
$549$	−14.8541			−0.633958
$550$	8.09017	+	5.87785i	0.344966	+	0.250632i
$551$	−5.85410			−0.249393
$552$	0.180340	+	0.555029i	0.00767578	+	0.0236236i
$553$	5.52786	−	4.01623i	0.235069	−	0.170787i
$554$	−0.354102	+	0.257270i	−0.0150444	+	0.0109304i
$555$	2.88854	−	8.89002i	0.122612	−	0.377360i
$556$	−15.3262	−	11.1352i	−0.649977	−	0.472236i
$557$	5.09017			0.215677			0.107839	−	0.994168i	$-0.465607\pi$
$557$	5.09017			0.215677			0.107839	+	0.994168i	$0.465607\pi$
$558$	0.909830	+	0.661030i	0.0385162	+	0.0279836i
$559$	−4.85410	+	14.9394i	−0.205307	+	0.631869i
$560$	−1.38197	+	1.00406i	−0.0583987	+	0.0424292i
$561$	−0.472136	−	1.45309i	−0.0199336	−	0.0613493i
$562$	1.88197	−	5.79210i	0.0793859	−	0.244325i
$563$	3.23607	−	9.95959i	0.136384	−	0.419747i	−0.859419	−	0.511272i	$-0.829174\pi$
$563$	3.23607	−	9.95959i	0.136384	−	0.419747i	0.995803	+	0.0915256i	$0.0291743\pi$
$564$	2.65248	+	8.16348i	0.111689	+	0.343745i
$565$	11.4443	−	8.31475i	0.481464	−	0.349804i
$566$	−3.76393	+	11.5842i	−0.158210	+	0.486920i
$567$	−1.49342	−	1.08503i	−0.0627178	−	0.0455672i
$568$	11.4164			0.479022
$569$	−10.0623	−	7.31069i	−0.421834	−	0.306480i	0.356541	−	0.934280i	$-0.383956\pi$
$569$	−10.0623	−	7.31069i	−0.421834	−	0.306480i	−0.778375	+	0.627799i	$0.783956\pi$
$570$	0.854102	−	2.62866i	0.0357744	−	0.110102i
$571$	12.8541	−	9.33905i	0.537927	−	0.390827i	−0.285387	−	0.958412i	$-0.592122\pi$
$571$	12.8541	−	9.33905i	0.537927	−	0.390827i	0.823315	+	0.567585i	$0.192122\pi$
$572$	7.85410	−	5.70634i	0.328397	−	0.238594i
$573$	3.05573	+	9.40456i	0.127655	+	0.392881i
$574$	2.18034			0.0910056
$575$	−1.90983	+	1.38757i	−0.0796454	+	0.0578658i
$576$	−1.47214			−0.0613390
$577$	5.09017	+	15.6659i	0.211907	+	0.652181i	0.999359	+	0.0358056i	$0.0113997\pi$
$577$	5.09017	+	15.6659i	0.211907	+	0.652181i	−0.787452	+	0.616376i	$0.788600\pi$
$578$	−13.4443	+	9.76784i	−0.559208	+	0.406288i
$579$	1.32624	−	0.963568i	0.0551166	−	0.0400445i
$580$	10.5902	−	7.69421i	0.439733	−	0.319485i
$581$	−4.18034	−	3.03719i	−0.173430	−	0.126004i
$582$	−8.18034			−0.339086
$583$	7.85410	+	5.70634i	0.325284	+	0.236332i
$584$	3.73607	−	11.4984i	0.154600	−	0.475809i
$585$	−4.93769	−	15.1967i	−0.204149	−	0.628305i
$586$	−3.33688	−	10.2699i	−0.137845	−	0.424244i
$587$	−5.56231	+	17.1190i	−0.229581	+	0.706577i	0.768213	+	0.640194i	$0.221146\pi$
$587$	−5.56231	+	17.1190i	−0.229581	+	0.706577i	−0.997794	+	0.0663834i	$0.978854\pi$
$588$	2.45085	−	7.54294i	0.101071	−	0.311066i
$589$	0.236068	+	0.726543i	0.00972701	+	0.0299367i
$590$	5.00000	+	3.63271i	0.205847	+	0.149556i
$591$	−10.6869	+	32.8910i	−0.439601	+	1.35295i
$592$	−2.73607	−	1.98787i	−0.112452	−	0.0817009i
$593$	−40.1033			−1.64685			−0.823423	−	0.567428i	$-0.807939\pi$
$593$	−40.1033			−1.64685			−0.823423	+	0.567428i	$0.807939\pi$
$594$	8.94427	+	6.49839i	0.366988	+	0.266632i
$595$	0.326238	+	1.00406i	0.0133745	+	0.0411623i
$596$	8.78115	−	6.37988i	0.359690	−	0.261330i
$597$	−6.18034	+	4.49028i	−0.252944	+	0.183775i
$598$	0.708204	+	2.17963i	0.0289606	+	0.0891316i
$599$	8.29180			0.338794			0.169397	−	0.985548i	$-0.445818\pi$
$599$	8.29180			0.338794			0.169397	+	0.985548i	$0.445818\pi$
$600$	1.90983	+	5.87785i	0.0779685	+	0.239962i
$601$	−23.9787			−0.978112			−0.489056	−	0.872252i	$-0.662659\pi$
$601$	−23.9787			−0.978112			−0.489056	+	0.872252i	$0.662659\pi$
$602$	0.763932	+	2.35114i	0.0311355	+	0.0958254i
$603$	2.38197	−	1.73060i	0.0970012	−	0.0704755i
$604$	−4.38197	+	3.18368i	−0.178300	+	0.129542i
$605$	15.6525			0.636364
$606$	−5.09017	−	3.69822i	−0.206774	−	0.150230i
$607$	48.1803			1.95558			0.977790	−	0.209588i	$-0.0672122\pi$
$607$	48.1803			1.95558			0.977790	+	0.209588i	$0.0672122\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	1.70820	−	5.25731i	0.0692199	−	0.213037i
$610$	22.5623			0.913521
$611$	10.4164	+	32.0584i	0.421403	+	1.29694i
$612$	−0.281153	+	0.865300i	−0.0113649	+	0.0349777i
$613$	1.10081	−	3.38795i	0.0444614	−	0.136838i	−0.926362	−	0.376635i	$-0.877081\pi$
$613$	1.10081	−	3.38795i	0.0444614	−	0.136838i	0.970823	+	0.239797i	$0.0770810\pi$
$614$	−4.56231	−	14.0413i	−0.184120	−	0.566662i
$615$	2.43769	−	7.50245i	0.0982973	−	0.302528i
$616$	0.472136	−	1.45309i	0.0190229	−	0.0585465i
$617$	−31.0517	−	22.5604i	−1.25009	−	0.908246i	−0.251866	−	0.967762i	$-0.581044\pi$
$617$	−31.0517	−	22.5604i	−1.25009	−	0.908246i	−0.998227	+	0.0595166i	$0.981044\pi$
$618$	−24.9443			−1.00341
$619$	2.76393	+	2.00811i	0.111092	+	0.0807129i	0.641944	−	0.766751i	$-0.278128\pi$
$619$	2.76393	+	2.00811i	0.111092	+	0.0807129i	−0.530852	+	0.847464i	$0.678128\pi$
$620$	−1.38197	−	1.00406i	−0.0555011	−	0.0403239i
$621$	−2.11146	+	1.53406i	−0.0847298	+	0.0615598i
$622$	22.7984	−	16.5640i	0.914132	−	0.664155i
$623$	1.78522	+	5.49434i	0.0715233	+	0.220126i
$624$	6.00000			0.240192
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	−23.8885			−0.954778
$627$	0.763932	+	2.35114i	0.0305085	+	0.0938955i
$628$	3.11803	−	2.26538i	0.124423	−	0.0903987i
$629$	−1.69098	+	1.22857i	−0.0674239	+	0.0489863i
$630$	−2.03444	−	1.47811i	−0.0810541	−	0.0588893i
$631$	18.7082	+	13.5923i	0.744762	+	0.541101i	0.894199	−	0.447670i	$-0.147746\pi$
$631$	18.7082	+	13.5923i	0.744762	+	0.541101i	−0.149437	+	0.988771i	$0.547746\pi$
$632$	−8.94427			−0.355784
$633$	−12.4721	−	9.06154i	−0.495723	−	0.360164i
$634$	2.14590	−	6.60440i	0.0852245	−	0.262294i
$635$	−5.65248	+	17.3965i	−0.224312	+	0.690360i
$636$	1.85410	+	5.70634i	0.0735199	+	0.226271i
$637$	9.62461	−	29.6215i	0.381341	−	1.17365i
$638$	−3.61803	+	11.1352i	−0.143239	+	0.440845i
$639$	5.19350	+	15.9839i	0.205452	+	0.632315i
$640$	2.23607			0.0883883
$641$	4.43769	−	13.6578i	0.175278	−	0.539451i	−0.824368	−	0.566055i	$-0.808469\pi$
$641$	4.43769	−	13.6578i	0.175278	−	0.539451i	0.999646	+	0.0266033i	$0.00846910\pi$
$642$	−9.23607	−	6.71040i	−0.364519	−	0.264838i
$643$	−3.34752			−0.132013			−0.0660067	−	0.997819i	$-0.521026\pi$
$643$	−3.34752			−0.132013			−0.0660067	+	0.997819i	$0.521026\pi$
$644$	0.291796	+	0.212002i	0.0114984	+	0.00835406i
$645$	8.94427			0.352180
$646$	−0.500000	+	0.363271i	−0.0196722	+	0.0142927i
$647$	25.0902	−	18.2291i	0.986396	−	0.716659i	0.0272674	−	0.999628i	$-0.491319\pi$
$647$	25.0902	−	18.2291i	0.986396	−	0.716659i	0.959129	+	0.282969i	$0.0913194\pi$
$648$	0.746711	+	2.29814i	0.0293336	+	0.0902795i
$649$	−5.52786			−0.216988
$650$	7.50000	+	23.0826i	0.294174	+	0.905375i
$651$	−0.721360			−0.0282723
$652$	4.09017	+	12.5882i	0.160183	+	0.492994i
$653$	32.2426	−	23.4257i	1.26175	−	0.916717i	0.262910	−	0.964820i	$-0.415318\pi$
$653$	32.2426	−	23.4257i	1.26175	−	0.916717i	0.998842	+	0.0481037i	$0.0153178\pi$
$654$	−13.6180	+	9.89408i	−0.532507	+	0.386889i
$655$	−15.2016	−	46.7858i	−0.593977	−	1.82807i
$656$	−2.30902	−	1.67760i	−0.0901520	−	0.0654992i
$657$	17.7984			0.694381
$658$	4.29180	+	3.11817i	0.167312	+	0.121559i
$659$	−6.58359	+	20.2622i	−0.256460	+	0.789304i	0.737078	+	0.675808i	$0.236205\pi$
$659$	−6.58359	+	20.2622i	−0.256460	+	0.789304i	−0.993538	+	0.113496i	$0.963795\pi$
$660$	−4.47214	−	3.24920i	−0.174078	−	0.126475i
$661$	8.90983	+	27.4216i	0.346552	+	1.06658i	0.960748	+	0.277424i	$0.0894807\pi$
$661$	8.90983	+	27.4216i	0.346552	+	1.06658i	−0.614195	+	0.789154i	$0.710519\pi$
$662$	−3.70820	+	11.4127i	−0.144123	+	0.443566i
$663$	1.14590	−	3.52671i	0.0445030	−	0.136966i
$664$	2.09017	+	6.43288i	0.0811143	+	0.249644i
$665$	−0.527864	−	1.62460i	−0.0204697	−	0.0629992i
$666$	1.53851	−	4.73504i	0.0596159	−	0.183479i
$667$	−2.23607	−	1.62460i	−0.0865809	−	0.0629047i
$668$	−8.00000			−0.309529
$669$	−19.5279	−	14.1878i	−0.754991	−	0.548533i
$670$	−3.61803	+	2.62866i	−0.139777	+	0.101554i
$671$	−16.3262	+	11.8617i	−0.630267	+	0.457916i
$672$	0.763932	−	0.555029i	0.0294693	−	0.0214107i
$673$	−8.04508	−	24.7602i	−0.310115	−	0.954437i	−0.977719	−	0.209919i	$-0.932680\pi$
$673$	−8.04508	−	24.7602i	−0.310115	−	0.954437i	0.667603	−	0.744517i	$-0.267320\pi$
$674$	−5.41641			−0.208632
$675$	−22.3607	+	16.2460i	−0.860663	+	0.625308i
$676$	10.5623			0.406243
$677$	−7.67376	−	23.6174i	−0.294927	−	0.907691i	−0.983246	−	0.182283i	$-0.941651\pi$
$677$	−7.67376	−	23.6174i	−0.294927	−	0.907691i	0.688319	−	0.725408i	$-0.258349\pi$
$678$	−6.32624	+	4.59628i	−0.242958	+	0.176519i
$679$	−4.09017	+	2.97168i	−0.156966	+	0.114043i
$680$	0.427051	−	1.31433i	0.0163767	−	0.0504022i
$681$	10.2918	+	7.47743i	0.394382	+	0.286536i
$682$	1.52786			0.0585049
$683$	−21.5623	−	15.6659i	−0.825059	−	0.599440i	0.0930983	−	0.995657i	$-0.470323\pi$
$683$	−21.5623	−	15.6659i	−0.825059	−	0.599440i	−0.918157	+	0.396217i	$0.870323\pi$
$684$	0.454915	−	1.40008i	0.0173941	−	0.0535336i
$685$	−12.9271	+	9.39205i	−0.493917	+	0.358852i
$686$	−3.16718	−	9.74759i	−0.120924	−	0.372165i
$687$	−8.21478	+	25.2825i	−0.313413	+	0.964587i
$688$	1.00000	−	3.07768i	0.0381246	−	0.117336i
$689$	7.28115	+	22.4091i	0.277390	+	0.853718i
$690$	1.05573	−	0.767031i	0.0401909	−	0.0292004i
$691$	−2.47214	+	7.60845i	−0.0940445	+	0.289439i	−0.987003	−	0.160699i	$-0.948625\pi$
$691$	−2.47214	+	7.60845i	−0.0940445	+	0.289439i	0.892959	+	0.450138i	$0.148625\pi$
$692$	−15.9721	−	11.6044i	−0.607170	−	0.441134i
$693$	2.24922			0.0854409
$694$	−17.3262	−	12.5882i	−0.657695	−	0.477843i
$695$	−13.0902	+	40.2874i	−0.496538	+	1.52819i
$696$	−5.85410	+	4.25325i	−0.221899	+	0.161219i
$697$	−1.42705	+	1.03681i	−0.0540534	+	0.0392721i
$698$	3.19098	+	9.82084i	0.120780	+	0.371724i
$699$	21.7771			0.823685
$700$	3.09017	+	2.24514i	0.116797	+	0.0848583i
$701$	−38.8541			−1.46750			−0.733750	−	0.679420i	$-0.762231\pi$
$701$	−38.8541			−1.46750			−0.733750	+	0.679420i	$0.762231\pi$
$702$	8.29180	+	25.5195i	0.312954	+	0.963172i
$703$	2.73607	−	1.98787i	0.103193	−	0.0749739i
$704$	−1.61803	+	1.17557i	−0.0609820	+	0.0443060i
$705$	15.5279	−	11.2817i	0.584813	−	0.424892i
$706$	16.5623	+	12.0332i	0.623331	+	0.452876i
$707$	−3.88854			−0.146244
$708$	−2.76393	−	2.00811i	−0.103875	−	0.0754696i
$709$	−6.11803	+	18.8294i	−0.229768	+	0.707152i	0.768005	+	0.640444i	$0.221250\pi$
$709$	−6.11803	+	18.8294i	−0.229768	+	0.707152i	−0.997773	+	0.0667080i	$0.978750\pi$
$710$	−7.88854	−	24.2784i	−0.296052	−	0.911154i
$711$	−4.06888	−	12.5227i	−0.152595	−	0.469639i
$712$	2.33688	−	7.19218i	0.0875783	−	0.269538i
$713$	−0.111456	+	0.343027i	−0.00417407	+	0.0128465i
$714$	−0.180340	−	0.555029i	−0.00674905	−	0.0207714i
$715$	−17.5623	−	12.7598i	−0.656793	−	0.477188i
$716$	3.09017	−	9.51057i	0.115485	−	0.355427i
$717$	1.70820	+	1.24108i	0.0637940	+	0.0463491i
$718$	−24.4721			−0.913292
$719$	9.47214	+	6.88191i	0.353251	+	0.256652i	0.750232	−	0.661175i	$-0.229942\pi$
$719$	9.47214	+	6.88191i	0.353251	+	0.256652i	−0.396981	+	0.917827i	$0.629942\pi$
$720$	1.01722	+	3.13068i	0.0379096	+	0.116674i
$721$	−12.4721	+	9.06154i	−0.464487	+	0.337469i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	−5.11146	−	15.7314i	−0.190097	−	0.585059i
$724$	12.3262			0.458101
$725$	−23.6803	−	17.2048i	−0.879466	−	0.638969i
$726$	−8.65248			−0.321123
$727$	−10.0344	−	30.8828i	−0.372157	−	1.14538i	−0.945377	−	0.325979i	$-0.894306\pi$
$727$	−10.0344	−	30.8828i	−0.372157	−	1.14538i	0.573220	−	0.819402i	$-0.305694\pi$
$728$	3.00000	−	2.17963i	0.111187	−	0.0807824i
$729$	−19.4615	+	14.1396i	−0.720796	+	0.523689i
$730$	−27.0344			−1.00059
$731$	−1.61803	−	1.17557i	−0.0598451	−	0.0434800i
$732$	−12.4721			−0.460983
$733$	15.7984	+	11.4782i	0.583526	+	0.423957i	0.839994	−	0.542596i	$-0.182559\pi$
$733$	15.7984	+	11.4782i	0.583526	+	0.423957i	−0.256467	+	0.966553i	$0.582559\pi$
$734$	−2.00000	+	6.15537i	−0.0738213	+	0.227199i
$735$	−17.7345			−0.654147
$736$	−0.145898	−	0.449028i	−0.00537787	−	0.0165514i
$737$	1.23607	−	3.80423i	0.0455311	−	0.140130i
$738$	1.29837	−	3.99598i	0.0477938	−	0.147094i
$739$	−6.90983	−	21.2663i	−0.254182	−	0.782292i	−0.993990	−	0.109474i	$-0.965083\pi$
$739$	−6.90983	−	21.2663i	−0.254182	−	0.782292i	0.739807	−	0.672819i	$-0.234917\pi$
$740$	−2.33688	+	7.19218i	−0.0859055	+	0.264390i
$741$	−1.85410	+	5.70634i	−0.0681121	+	0.209628i
$742$	3.00000	+	2.17963i	0.110133	+	0.0800166i
$743$	−25.7082			−0.943143			−0.471571	−	0.881828i	$-0.656313\pi$
$743$	−25.7082			−0.943143			−0.471571	+	0.881828i	$0.656313\pi$
$744$	0.763932	+	0.555029i	0.0280071	+	0.0203484i
$745$	−19.6353	−	14.2658i	−0.719380	−	0.522660i
$746$	−6.85410	+	4.97980i	−0.250947	+	0.182323i
$747$	−8.05573	+	5.85283i	−0.294744	+	0.214144i
$748$	0.381966	+	1.17557i	0.0139661	+	0.0429831i
$749$	−7.05573			−0.257811
$750$	11.1803	−	8.12299i	0.408248	−	0.296610i
$751$	−14.1803			−0.517448			−0.258724	−	0.965951i	$-0.583302\pi$
$751$	−14.1803			−0.517448			−0.258724	+	0.965951i	$0.583302\pi$
$752$	−2.14590	−	6.60440i	−0.0782528	−	0.240838i
$753$	−8.00000	+	5.81234i	−0.291536	+	0.211813i
$754$	−22.9894	+	16.7027i	−0.837223	+	0.608278i
$755$	9.79837	+	7.11894i	0.356599	+	0.259085i
$756$	3.41641	+	2.48217i	0.124254	+	0.0902755i
$757$	1.14590			0.0416484			0.0208242	−	0.999783i	$-0.493371\pi$
$757$	1.14590			0.0416484			0.0208242	+	0.999783i	$0.493371\pi$
$758$	−12.2361	−	8.89002i	−0.444434	−	0.322900i
$759$	−0.360680	+	1.11006i	−0.0130918	+	0.0402926i
$760$	−0.690983	+	2.12663i	−0.0250646	+	0.0771409i
$761$	3.31966	+	10.2169i	0.120338	+	0.370361i	0.993023	−	0.117922i	$-0.0376233\pi$
$761$	3.31966	+	10.2169i	0.120338	+	0.370361i	−0.872685	+	0.488283i	$0.837623\pi$
$762$	3.12461	−	9.61657i	0.113193	−	0.348371i
$763$	−3.21478	+	9.89408i	−0.116383	+	0.358190i
$764$	−2.47214	−	7.60845i	−0.0894387	−	0.275264i
$765$	2.03444			0.0735554
$766$	6.76393	−	20.8172i	0.244391	−	0.752158i
$767$	−10.8541	−	7.88597i	−0.391919	−	0.284746i
$768$	−1.23607			−0.0446028
$769$	−38.7426	−	28.1482i	−1.39710	−	1.01505i	−0.995044	−	0.0994321i	$-0.968297\pi$
$769$	−38.7426	−	28.1482i	−1.39710	−	1.01505i	−0.402051	−	0.915617i	$-0.631703\pi$
$770$	−3.41641			−0.123119
$771$	6.27051	−	4.55579i	0.225827	−	0.164073i
$772$	−1.07295	+	0.779543i	−0.0386163	+	0.0280564i
$773$	1.26393	+	3.88998i	0.0454605	+	0.139913i	0.971210	−	0.238223i	$-0.0765650\pi$
$773$	1.26393	+	3.88998i	0.0454605	+	0.139913i	−0.925750	+	0.378136i	$0.876565\pi$
$774$	4.76393			0.171236
$775$	−1.18034	+	3.63271i	−0.0423991	+	0.130491i
$776$	6.61803			0.237574
$777$	0.986844	+	3.03719i	0.0354028	+	0.108959i
$778$	−1.54508	+	1.12257i	−0.0553940	+	0.0402461i
$779$	2.30902	−	1.67760i	0.0827291	−	0.0601062i
$780$	−4.14590	−	12.7598i	−0.148447	−	0.456873i
$781$	18.4721	+	13.4208i	0.660985	+	0.480234i
$782$	−0.291796			−0.0104346
$783$	−26.1803	−	19.0211i	−0.935609	−	0.679760i
$784$	−1.98278	+	6.10237i	−0.0708135	+	0.217942i
$785$	−6.97214	−	5.06555i	−0.248846	−	0.180797i
$786$	8.40325	+	25.8626i	0.299734	+	0.922487i
$787$	6.47214	−	19.9192i	0.230707	−	0.710042i	−0.766955	−	0.641701i	$-0.778229\pi$
$787$	6.47214	−	19.9192i	0.230707	−	0.710042i	0.997662	−	0.0683417i	$-0.0217708\pi$
$788$	8.64590	−	26.6093i	0.307997	−	0.947918i
$789$	8.11146	+	24.9645i	0.288775	+	0.888760i
$790$	6.18034	+	19.0211i	0.219887	+	0.676741i
$791$	−1.49342	+	4.59628i	−0.0531000	+	0.163425i
$792$	−2.38197	−	1.73060i	−0.0846395	−	0.0614942i
$793$	−48.9787			−1.73929
$794$	−17.3262	−	12.5882i	−0.614885	−	0.446740i
$795$	10.8541	−	7.88597i	0.384955	−	0.279686i
$796$	5.00000	−	3.63271i	0.177220	−	0.128758i
$797$	28.8713	−	20.9762i	1.02267	−	0.743017i	0.0558453	−	0.998439i	$-0.482215\pi$
$797$	28.8713	−	20.9762i	1.02267	−	0.743017i	0.966829	+	0.255423i	$0.0822146\pi$
$798$	0.291796	+	0.898056i	0.0103295	+	0.0317908i
$799$	−4.29180			−0.151833
$800$	−1.54508	−	4.75528i	−0.0546270	−	0.168125i
$801$	11.1327			0.393356
$802$	3.59017	+	11.0494i	0.126773	+	0.390168i
$803$	19.5623	−	14.2128i	0.690339	−	0.501560i
$804$	2.00000	−	1.45309i	0.0705346	−	0.0512464i
$805$	0.249224	−	0.767031i	0.00878398	−	0.0270343i
$806$	3.00000	+	2.17963i	0.105670	+	0.0767741i
$807$	−3.16718			−0.111490
$808$	4.11803	+	2.99193i	0.144872	+	0.105256i
$809$	−9.04508	+	27.8379i	−0.318008	+	0.978729i	0.656490	+	0.754335i	$0.272040\pi$
$809$	−9.04508	+	27.8379i	−0.318008	+	0.978729i	−0.974498	+	0.224394i	$0.927960\pi$
$810$	4.37132	−	3.17595i	0.153593	−	0.111592i
$811$	10.6180	+	32.6789i	0.372850	+	1.14751i	0.944918	+	0.327307i	$0.106141\pi$
$811$	10.6180	+	32.6789i	0.372850	+	1.14751i	−0.572068	+	0.820206i	$0.693859\pi$
$812$	−1.38197	+	4.25325i	−0.0484975	+	0.149260i
$813$	1.34752	−	4.14725i	0.0472597	−	0.145451i
$814$	−2.09017	−	6.43288i	−0.0732604	−	0.225472i
$815$	23.9443	−	17.3965i	0.838731	−	0.609374i
$816$	−0.236068	+	0.726543i	−0.00826403	+	0.0254341i
$817$	2.61803	+	1.90211i	0.0915934	+	0.0665465i
$818$	−15.8541			−0.554326
$819$	4.41641	+	3.20871i	0.154322	+	0.112121i
$820$	−1.97214	+	6.06961i	−0.0688700	+	0.211960i
$821$	−25.0344	+	18.1886i	−0.873708	+	0.634786i	−0.931579	−	0.363538i	$-0.881569\pi$
$821$	−25.0344	+	18.1886i	−0.873708	+	0.634786i	0.0578713	+	0.998324i	$0.481569\pi$
$822$	7.14590	−	5.19180i	0.249242	−	0.181085i
$823$	−10.3820	−	31.9524i	−0.361893	−	1.11379i	−0.951904	−	0.306396i	$-0.900877\pi$
$823$	−10.3820	−	31.9524i	−0.361893	−	1.11379i	0.590012	−	0.807395i	$-0.299123\pi$
$824$	20.1803			0.703015
$825$	−3.81966	+	11.7557i	−0.132983	+	0.409281i
$826$	−2.11146			−0.0734670
$827$	−11.6180	−	35.7566i	−0.403999	−	1.24338i	−0.921728	−	0.387836i	$-0.873223\pi$
$827$	−11.6180	−	35.7566i	−0.403999	−	1.24338i	0.517730	−	0.855544i	$-0.326777\pi$
$828$	0.562306	−	0.408539i	0.0195415	−	0.0141977i
$829$	−34.4336	+	25.0175i	−1.19593	+	0.868894i	−0.993878	−	0.110481i	$-0.964761\pi$
$829$	−34.4336	+	25.0175i	−1.19593	+	0.868894i	−0.202051	+	0.979375i	$0.564761\pi$
$830$	12.2361	−	8.89002i	0.424720	−	0.308577i
$831$	−0.437694	−	0.318003i	−0.0151834	−	0.0110314i
$832$	−4.85410			−0.168286
$833$	3.20820	+	2.33090i	0.111158	+	0.0807608i
$834$	7.23607	−	22.2703i	0.250565	−	0.771158i
$835$	5.52786	+	17.0130i	0.191300	+	0.588760i
$836$	−0.618034	−	1.90211i	−0.0213752	−	0.0657860i
$837$	−1.30495	+	4.01623i	−0.0451057	+	0.138821i
$838$	0.854102	−	2.62866i	0.0295045	−	0.0908054i
$839$	1.05573	+	3.24920i	0.0364478	+	0.112175i	0.967625	−	0.252392i	$-0.0812172\pi$
$839$	1.05573	+	3.24920i	0.0364478	+	0.112175i	−0.931177	+	0.364567i	$0.881217\pi$
$840$	−1.70820	−	1.24108i	−0.0589386	−	0.0428214i
$841$	1.62868	−	5.01255i	0.0561613	−	0.172847i
$842$	−27.9164	−	20.2825i	−0.962063	−	0.698980i
$843$	7.52786			0.259273
$844$	10.0902	+	7.33094i	0.347318	+	0.252341i
$845$	−7.29837	−	22.4621i	−0.251072	−	0.772719i
$846$	8.27051	−	6.00888i	0.284346	−	0.206589i
$847$	−4.32624	+	3.14320i	−0.148651	+	0.108001i
$848$	−1.50000	−	4.61653i	−0.0515102	−	0.158532i
$849$	−15.0557			−0.516711
$850$	−3.09017			−0.105992
$851$	1.59675			0.0547358
$852$	4.36068	+	13.4208i	0.149394	+	0.459789i
$853$	−32.0517	+	23.2869i	−1.09743	+	0.797328i	−0.980638	−	0.195829i	$-0.937260\pi$
$853$	−32.0517	+	23.2869i	−1.09743	+	0.797328i	−0.116790	+	0.993157i	$0.537260\pi$
$854$	−6.23607	+	4.53077i	−0.213394	+	0.155040i
$855$	−3.29180			−0.112577
$856$	7.47214	+	5.42882i	0.255392	+	0.185553i
$857$	28.8328			0.984910			0.492455	−	0.870338i	$-0.336100\pi$
$857$	28.8328			0.984910			0.492455	+	0.870338i	$0.336100\pi$
$858$	9.70820	+	7.05342i	0.331433	+	0.240800i
$859$	−4.47214	+	13.7638i	−0.152587	+	0.469615i	−0.997908	−	0.0646431i	$-0.979409\pi$
$859$	−4.47214	+	13.7638i	−0.152587	+	0.469615i	0.845321	+	0.534259i	$0.179409\pi$
$860$	−7.23607			−0.246748
$861$	0.832816	+	2.56314i	0.0283823	+	0.0873517i
$862$	8.00000	−	24.6215i	0.272481	−	0.838611i
$863$	−0.708204	+	2.17963i	−0.0241075	+	0.0741954i	−0.962386	−	0.271684i	$-0.912419\pi$
$863$	−0.708204	+	2.17963i	−0.0241075	+	0.0741954i	0.938279	+	0.345880i	$0.112419\pi$
$864$	−1.70820	−	5.25731i	−0.0581143	−	0.178857i
$865$	−13.6418	+	41.9852i	−0.463836	+	1.42754i
$866$	−3.17376	+	9.76784i	−0.107849	+	0.331925i
$867$	−16.6180	−	12.0737i	−0.564378	−	0.410045i
$868$	0.583592			0.0198084
$869$	−14.4721	−	10.5146i	−0.490934	−	0.356684i
$870$	13.0902	+	9.51057i	0.443798	+	0.322438i
$871$	7.85410	−	5.70634i	0.266126	−	0.193352i
$872$	11.0172	−	8.00448i	0.373090	−	0.271066i
$873$	3.01064	+	9.26581i	0.101895	+	0.313600i
$874$	0.472136			0.0159702
$875$	2.63932	−	8.12299i	0.0892253	−	0.274607i
$876$	14.9443			0.504920
$877$	13.4443	+	41.3772i	0.453981	+	1.39721i	0.872328	+	0.488922i	$0.162610\pi$
$877$	13.4443	+	41.3772i	0.453981	+	1.39721i	−0.418347	+	0.908287i	$0.637390\pi$
$878$	20.3262	−	14.7679i	0.685977	−	0.498392i
$879$	10.7984	−	7.84548i	0.364220	−	0.264621i
$880$	3.61803	+	2.62866i	0.121964	+	0.0886120i
$881$	−1.61803	−	1.17557i	−0.0545130	−	0.0396060i	0.560195	−	0.828361i	$-0.310726\pi$
$881$	−1.61803	−	1.17557i	−0.0545130	−	0.0396060i	−0.614708	+	0.788755i	$0.710726\pi$
$882$	−9.44582			−0.318057
$883$	−3.47214	−	2.52265i	−0.116847	−	0.0848941i	0.527827	−	0.849352i	$-0.323007\pi$
$883$	−3.47214	−	2.52265i	−0.116847	−	0.0848941i	−0.644674	+	0.764458i	$0.723007\pi$
$884$	−0.927051	+	2.85317i	−0.0311801	+	0.0959625i
$885$	−2.36068	+	7.26543i	−0.0793534	+	0.244225i
$886$	−0.673762	−	2.07363i	−0.0226355	−	0.0696648i
$887$	14.2361	−	43.8141i	0.478000	−	1.47113i	−0.363868	−	0.931451i	$-0.618544\pi$
$887$	14.2361	−	43.8141i	0.478000	−	1.47113i	0.841868	−	0.539683i	$-0.181456\pi$
$888$	1.29180	−	3.97574i	0.0433498	−	0.133417i
$889$	−1.93112	−	5.94336i	−0.0647676	−	0.199334i
$890$	−16.9098			−0.566819
$891$	−1.49342	+	4.59628i	−0.0500315	+	0.153981i
$892$	15.7984	+	11.4782i	0.528969	+	0.384318i
$893$	6.94427			0.232381
$894$	10.8541	+	7.88597i	0.363015	+	0.263746i
$895$	−22.3607			−0.747435
$896$	−0.618034	+	0.449028i	−0.0206471	+	0.0150010i
$897$	−2.29180	+	1.66509i	−0.0765208	+	0.0555956i
$898$	7.46149	+	22.9641i	0.248993	+	0.766322i
$899$	−4.47214			−0.149154
$900$	5.95492	−	4.32650i	0.198497	−	0.144217i
$901$	−3.00000			−0.0999445
$902$	−1.76393	−	5.42882i	−0.0587325	−	0.180760i
$903$	−2.47214	+	1.79611i	−0.0822675	+	0.0597709i
$904$	5.11803	−	3.71847i	0.170223	−	0.123674i
$905$	−8.51722	−	26.2133i	−0.283122	−	0.871360i
$906$	−5.41641	−	3.93525i	−0.179948	−	0.130740i
$907$	−17.3475			−0.576015			−0.288008	−	0.957628i	$-0.592993\pi$
$907$	−17.3475			−0.576015			−0.288008	+	0.957628i	$0.592993\pi$
$908$	−8.32624	−	6.04937i	−0.276316	−	0.200755i
$909$	−2.31559	+	7.12667i	−0.0768034	+	0.236377i
$910$	−6.70820	−	4.87380i	−0.222375	−	0.161565i
$911$	15.0902	+	46.4428i	0.499960	+	1.53872i	0.809082	+	0.587695i	$0.199965\pi$
$911$	15.0902	+	46.4428i	0.499960	+	1.53872i	−0.309123	+	0.951022i	$0.600035\pi$
$912$	0.381966	−	1.17557i	0.0126482	−	0.0389270i
$913$	−4.18034	+	12.8658i	−0.138349	+	0.425795i
$914$	3.20163	+	9.85359i	0.105900	+	0.325928i
$915$	8.61803	+	26.5236i	0.284903	+	0.876843i
$916$	6.64590	−	20.4540i	0.219587	−	0.675818i
$917$	13.5967	+	9.87862i	0.449004	+	0.326221i
$918$	−3.41641			−0.112758
$919$	−15.6525	−	11.3722i	−0.516328	−	0.375134i	0.298891	−	0.954287i	$-0.403383\pi$
$919$	−15.6525	−	11.3722i	−0.516328	−	0.375134i	−0.815219	+	0.579153i	$0.803383\pi$
$920$	−0.854102	+	0.620541i	−0.0281589	+	0.0204586i
$921$	14.7639	−	10.7266i	0.486488	−	0.353454i
$922$	33.0623	−	24.0212i	1.08885	−	0.791095i
$923$	17.1246	+	52.7041i	0.563663	+	1.73478i
$924$	1.88854			0.0621285
$925$	16.9098			0.555992
$926$	−7.05573			−0.231866
$927$	9.18034	+	28.2542i	0.301522	+	0.927989i
$928$	4.73607	−	3.44095i	0.155469	−	0.112955i
$929$	32.6246	−	23.7032i	1.07038	−	0.777676i	0.0943985	−	0.995534i	$-0.469907\pi$
$929$	32.6246	−	23.7032i	1.07038	−	0.777676i	0.975980	+	0.217859i	$0.0699072\pi$
$930$	0.652476	−	2.00811i	0.0213955	−	0.0658487i
$931$	−5.19098	−	3.77147i	−0.170128	−	0.123605i
$932$	−17.6180			−0.577098
$933$	28.1803	+	20.4742i	0.922583	+	0.670296i
$934$	3.32624	−	10.2371i	0.108838	−	0.334968i
$935$	2.23607	−	1.62460i	0.0731272	−	0.0531301i
$936$	−2.20820	−	6.79615i	−0.0721774	−	0.222139i
$937$	5.71885	−	17.6008i	0.186827	−	0.574993i	−0.813148	−	0.582056i	$-0.802248\pi$
$937$	5.71885	−	17.6008i	0.186827	−	0.574993i	0.999975	+	0.00706321i	$0.00224831\pi$
$938$	0.472136	−	1.45309i	0.0154158	−	0.0474449i
$939$	−9.12461	−	28.0827i	−0.297770	−	0.916443i
$940$	−12.5623	+	9.12705i	−0.409737	+	0.297692i
$941$	5.51722	−	16.9803i	0.179856	−	0.553541i	−0.819966	−	0.572413i	$-0.806008\pi$
$941$	5.51722	−	16.9803i	0.179856	−	0.553541i	0.999822	+	0.0188721i	$0.00600753\pi$
$942$	3.85410	+	2.80017i	0.125573	+	0.0912344i
$943$	1.34752			0.0438814
$944$	2.23607	+	1.62460i	0.0727778	+	0.0528762i
$945$	2.91796	−	8.98056i	0.0949213	−	0.292138i
$946$	5.23607	−	3.80423i	0.170239	−	0.123686i
$947$	24.8885	−	18.0826i	0.808769	−	0.587605i	−0.104704	−	0.994503i	$-0.533390\pi$
$947$	24.8885	−	18.0826i	0.808769	−	0.587605i	0.913473	+	0.406898i	$0.133390\pi$
$948$	−3.41641	−	10.5146i	−0.110960	−	0.341499i
$949$	58.6869			1.90506
$950$	5.00000			0.162221
$951$	8.58359			0.278342
$952$	0.145898	+	0.449028i	0.00472858	+	0.0145531i
$953$	−28.5344	+	20.7315i	−0.924321	+	0.671559i	−0.944596	−	0.328236i	$-0.893546\pi$
$953$	−28.5344	+	20.7315i	−0.924321	+	0.671559i	0.0202746	+	0.999794i	$0.493546\pi$
$954$	5.78115	−	4.20025i	0.187172	−	0.135988i
$955$	−14.4721	+	10.5146i	−0.468307	+	0.340245i
$956$	−1.38197	−	1.00406i	−0.0446960	−	0.0324735i
$957$	−14.4721			−0.467818
$958$	−0.854102	−	0.620541i	−0.0275948	−	0.0200488i
$959$	1.68692	−	5.19180i	0.0544734	−	0.167652i
$960$	0.854102	+	2.62866i	0.0275660	+	0.0848395i
$961$	−9.39919	−	28.9277i	−0.303200	−	0.933152i
$962$	5.07295	−	15.6129i	0.163558	−	0.503381i
$963$	−4.20163	+	12.9313i	−0.135396	+	0.416705i
$964$	4.13525	+	12.7270i	0.133188	+	0.409909i
$965$	2.39919	+	1.74311i	0.0772326	+	0.0561127i
$966$	−0.137767	+	0.424005i	−0.00443259	+	0.0136421i
$967$	19.0344	+	13.8293i	0.612106	+	0.444721i	0.850155	−	0.526532i	$-0.176508\pi$
$967$	19.0344	+	13.8293i	0.612106	+	0.444721i	−0.238049	+	0.971253i	$0.576508\pi$
$968$	7.00000			0.224989
$969$	−0.618034	−	0.449028i	−0.0198541	−	0.0144249i
$970$	−4.57295	−	14.0741i	−0.146829	−	0.451892i
$971$	1.67376	−	1.21606i	0.0537136	−	0.0390252i	−0.560604	−	0.828084i	$-0.689431\pi$
$971$	1.67376	−	1.21606i	0.0537136	−	0.0390252i	0.614318	+	0.789058i	$0.289431\pi$
$972$	11.0000	−	7.99197i	0.352825	−	0.256342i
$973$	−4.47214	−	13.7638i	−0.143370	−	0.441248i
$974$	0.763932			0.0244780
$975$	−24.2705	+	17.6336i	−0.777278	+	0.564726i
$976$	10.0902			0.322978
$977$	1.93769	+	5.96361i	0.0619923	+	0.190793i	0.977256	−	0.212062i	$-0.0680179\pi$
$977$	1.93769	+	5.96361i	0.0619923	+	0.190793i	−0.915264	+	0.402855i	$0.868018\pi$
$978$	−13.2361	+	9.61657i	−0.423243	+	0.307504i
$979$	12.2361	−	8.89002i	0.391066	−	0.284126i
$980$	14.3475			0.458315
$981$	16.2188	+	11.7837i	0.517828	+	0.376224i
$982$	8.65248			0.276112
$983$	−16.2361	−	11.7962i	−0.517850	−	0.376240i	0.297943	−	0.954584i	$-0.403699\pi$
$983$	−16.2361	−	11.7962i	−0.517850	−	0.376240i	−0.815793	+	0.578343i	$0.803699\pi$
$984$	1.09017	−	3.35520i	0.0347533	−	0.106960i
$985$	−62.5623			−1.99340
$986$	−1.11803	−	3.44095i	−0.0356055	−	0.109582i
$987$	−2.02631	+	6.23634i	−0.0644982	+	0.198505i
$988$	1.50000	−	4.61653i	0.0477214	−	0.146871i
$989$	0.472136	+	1.45309i	0.0150130	+	0.0462054i
$990$	−2.03444	+	6.26137i	−0.0646588	+	0.198999i
$991$	−18.2016	+	56.0188i	−0.578194	+	1.77950i	0.0468434	+	0.998902i	$0.485084\pi$
$991$	−18.2016	+	56.0188i	−0.578194	+	1.77950i	−0.625037	+	0.780595i	$0.714916\pi$
$992$	−0.618034	−	0.449028i	−0.0196226	−	0.0142567i
$993$	−14.8328			−0.470705
$994$	7.05573	+	5.12629i	0.223794	+	0.162596i
$995$	−11.1803	−	8.12299i	−0.354441	−	0.257516i
$996$	−6.76393	+	4.91428i	−0.214323	+	0.155715i
$997$	14.5623	−	10.5801i	0.461193	−	0.335076i	−0.332806	−	0.942995i	$-0.607995\pi$
$997$	14.5623	−	10.5801i	0.461193	−	0.335076i	0.793999	+	0.607919i	$0.207995\pi$
$998$	−3.94427	−	12.1392i	−0.124854	−	0.384260i
$999$	18.6950			0.591485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.a.381.1	✓	4
25.21	even	5	inner	950.2.h.a.571.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.a.381.1	✓	4	1.1	even	1	trivial
950.2.h.a.571.1	yes	4	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-1.00000 - 0.726543i) q^{6} -0.763932 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.00000 - 0.726543i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 + 1.31433i) q^{5} +(-1.00000 - 0.726543i) q^{6} -0.763932 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.454915 + 1.40008i) q^{9} +(0.690983 - 2.12663i) q^{10} +(0.618034 + 1.90211i) q^{11} +(-0.381966 + 1.17557i) q^{12} +(-1.50000 + 4.61653i) q^{13} +(0.236068 + 0.726543i) q^{14} +2.76393 q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.500000 - 0.363271i) q^{17} +1.47214 q^{18} +(0.809017 + 0.587785i) q^{19} -2.23607 q^{20} +(-0.763932 + 0.555029i) q^{21} +(1.61803 - 1.17557i) q^{22} +(0.145898 + 0.449028i) q^{23} +1.23607 q^{24} +(1.54508 + 4.75528i) q^{25} +4.85410 q^{26} +(1.70820 + 5.25731i) q^{27} +(0.618034 - 0.449028i) q^{28} +(-4.73607 + 3.44095i) q^{29} +(-0.854102 - 2.62866i) q^{30} +(0.618034 + 0.449028i) q^{31} -1.00000 q^{32} +(2.00000 + 1.45309i) q^{33} +(-0.190983 + 0.587785i) q^{34} +(-1.38197 - 1.00406i) q^{35} +(-0.454915 - 1.40008i) q^{36} +(1.04508 - 3.21644i) q^{37} +(0.309017 - 0.951057i) q^{38} +(1.85410 + 5.70634i) q^{39} +(0.690983 + 2.12663i) q^{40} +(0.881966 - 2.71441i) q^{41} +(0.763932 + 0.555029i) q^{42} +3.23607 q^{43} +(-1.61803 - 1.17557i) q^{44} +(-2.66312 + 1.93487i) q^{45} +(0.381966 - 0.277515i) q^{46} +(5.61803 - 4.08174i) q^{47} +(-0.381966 - 1.17557i) q^{48} -6.41641 q^{49} +(4.04508 - 2.93893i) q^{50} -0.763932 q^{51} +(-1.50000 - 4.61653i) q^{52} +(3.92705 - 2.85317i) q^{53} +(4.47214 - 3.24920i) q^{54} +(-1.38197 + 4.25325i) q^{55} +(-0.618034 - 0.449028i) q^{56} +1.23607 q^{57} +(4.73607 + 3.44095i) q^{58} +(-0.854102 + 2.62866i) q^{59} +(-2.23607 + 1.62460i) q^{60} +(3.11803 + 9.59632i) q^{61} +(0.236068 - 0.726543i) q^{62} +(0.347524 - 1.06957i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-8.78115 + 6.37988i) q^{65} +(0.763932 - 2.35114i) q^{66} +(-1.61803 - 1.17557i) q^{67} +0.618034 q^{68} +(0.472136 + 0.343027i) q^{69} +(-0.527864 + 1.62460i) q^{70} +(9.23607 - 6.71040i) q^{71} +(-1.19098 + 0.865300i) q^{72} +(-3.73607 - 11.4984i) q^{73} -3.38197 q^{74} +(5.00000 + 3.63271i) q^{75} -1.00000 q^{76} +(-0.472136 - 1.45309i) q^{77} +(4.85410 - 3.52671i) q^{78} +(-7.23607 + 5.25731i) q^{79} +(1.80902 - 1.31433i) q^{80} +(1.95492 + 1.42033i) q^{81} -2.85410 q^{82} +(5.47214 + 3.97574i) q^{83} +(0.291796 - 0.898056i) q^{84} +(-0.427051 - 1.31433i) q^{85} +(-1.00000 - 3.07768i) q^{86} +(-2.23607 + 6.88191i) q^{87} +(-0.618034 + 1.90211i) q^{88} +(-2.33688 - 7.19218i) q^{89} +(2.66312 + 1.93487i) q^{90} +(1.14590 - 3.52671i) q^{91} +(-0.381966 - 0.277515i) q^{92} +0.944272 q^{93} +(-5.61803 - 4.08174i) q^{94} +(0.690983 + 2.12663i) q^{95} +(-1.00000 + 0.726543i) q^{96} +(5.35410 - 3.88998i) q^{97} +(1.98278 + 6.10237i) q^{98} -2.94427 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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