LMFDB - Embedded newform 50.2.d.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,2,Mod(11,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("50.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	50.d (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:	$0.399252010106$
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			31.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	50.31
Dual form			50.2.d.a.21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.224514i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.309017 - 0.224514i) q^{6} -3.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.224514i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.309017 - 0.224514i) q^{6} -3.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +(-1.80902 - 1.31433i) q^{10} +(1.30902 + 4.02874i) q^{11} +(-0.118034 + 0.363271i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.927051 + 2.85317i) q^{14} +(0.263932 - 0.812299i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.927051 - 0.673542i) q^{17} +2.85410 q^{18} +(-4.73607 - 3.44095i) q^{19} +(-0.690983 + 2.12663i) q^{20} +(-0.927051 + 0.673542i) q^{21} +(3.42705 - 2.48990i) q^{22} +(-0.545085 - 1.67760i) q^{23} +0.381966 q^{24} +(1.54508 - 4.75528i) q^{25} -1.00000 q^{26} +(0.690983 + 2.12663i) q^{27} +(2.42705 - 1.76336i) q^{28} +(7.66312 - 5.56758i) q^{29} -0.854102 q^{30} +(0.190983 + 0.138757i) q^{31} -1.00000 q^{32} +(1.30902 + 0.951057i) q^{33} +(-0.354102 + 1.08981i) q^{34} +(-5.42705 + 3.94298i) q^{35} +(-0.881966 - 2.71441i) q^{36} +(-2.57295 + 7.91872i) q^{37} +(-1.80902 + 5.56758i) q^{38} +(-0.118034 - 0.363271i) q^{39} +2.23607 q^{40} +(0.454915 - 1.40008i) q^{41} +(0.927051 + 0.673542i) q^{42} -6.23607 q^{43} +(-3.42705 - 2.48990i) q^{44} +(1.97214 + 6.06961i) q^{45} +(-1.42705 + 1.03681i) q^{46} +(9.66312 - 7.02067i) q^{47} +(-0.118034 - 0.363271i) q^{48} +2.00000 q^{49} -5.00000 q^{50} -0.437694 q^{51} +(0.309017 + 0.951057i) q^{52} +(-8.47214 + 6.15537i) q^{53} +(1.80902 - 1.31433i) q^{54} +(7.66312 + 5.56758i) q^{55} +(-2.42705 - 1.76336i) q^{56} -2.23607 q^{57} +(-7.66312 - 5.56758i) q^{58} +(-1.38197 + 4.25325i) q^{59} +(0.263932 + 0.812299i) q^{60} +(-2.73607 - 8.42075i) q^{61} +(0.0729490 - 0.224514i) q^{62} +(2.64590 - 8.14324i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.690983 - 2.12663i) q^{65} +(0.500000 - 1.53884i) q^{66} +(8.28115 + 6.01661i) q^{67} +1.14590 q^{68} +(-0.545085 - 0.396027i) q^{69} +(5.42705 + 3.94298i) q^{70} +(2.42705 - 1.76336i) q^{71} +(-2.30902 + 1.67760i) q^{72} +(2.38197 + 7.33094i) q^{73} +8.32624 q^{74} +(-0.590170 - 1.81636i) q^{75} +5.85410 q^{76} +(-3.92705 - 12.0862i) q^{77} +(-0.309017 + 0.224514i) q^{78} +(5.85410 - 4.25325i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-6.23607 - 4.53077i) q^{81} -1.47214 q^{82} +(3.66312 + 2.66141i) q^{83} +(0.354102 - 1.08981i) q^{84} -2.56231 q^{85} +(1.92705 + 5.93085i) q^{86} +(1.11803 - 3.44095i) q^{87} +(-1.30902 + 4.02874i) q^{88} +(1.38197 + 4.25325i) q^{89} +(5.16312 - 3.75123i) q^{90} +(-0.927051 + 2.85317i) q^{91} +(1.42705 + 1.03681i) q^{92} +0.0901699 q^{93} +(-9.66312 - 7.02067i) q^{94} -13.0902 q^{95} +(-0.309017 + 0.224514i) q^{96} +(-7.73607 + 5.62058i) q^{97} +(-0.618034 - 1.90211i) q^{98} -12.0902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9} - 5 q^{10} + 3 q^{11} + 4 q^{12} - q^{13} - 3 q^{14} + 10 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} - 5 q^{25} - 4 q^{26} + 5 q^{27} + 3 q^{28} + 15 q^{29} + 10 q^{30} + 3 q^{31} - 4 q^{32} + 3 q^{33} + 12 q^{34} - 15 q^{35} - 8 q^{36} - 17 q^{37} - 5 q^{38} + 4 q^{39} + 13 q^{41} - 3 q^{42} - 16 q^{43} - 7 q^{44} - 10 q^{45} + q^{46} + 23 q^{47} + 4 q^{48} + 8 q^{49} - 20 q^{50} - 42 q^{51} - q^{52} - 16 q^{53} + 5 q^{54} + 15 q^{55} - 3 q^{56} - 15 q^{58} - 10 q^{59} + 10 q^{60} - 2 q^{61} + 7 q^{62} + 24 q^{63} - q^{64} - 5 q^{65} + 2 q^{66} + 13 q^{67} + 18 q^{68} + 9 q^{69} + 15 q^{70} + 3 q^{71} - 7 q^{72} + 14 q^{73} + 2 q^{74} + 20 q^{75} + 10 q^{76} - 9 q^{77} + q^{78} + 10 q^{79} - 5 q^{80} - 16 q^{81} + 12 q^{82} - q^{83} - 12 q^{84} + 30 q^{85} + q^{86} - 3 q^{88} + 10 q^{89} + 5 q^{90} + 3 q^{91} - q^{92} - 22 q^{93} - 23 q^{94} - 30 q^{95} + q^{96} - 22 q^{97} + 2 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9 - 5 * q^10 + 3 * q^11 + 4 * q^12 - q^13 - 3 * q^14 + 10 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 - 5 * q^25 - 4 * q^26 + 5 * q^27 + 3 * q^28 + 15 * q^29 + 10 * q^30 + 3 * q^31 - 4 * q^32 + 3 * q^33 + 12 * q^34 - 15 * q^35 - 8 * q^36 - 17 * q^37 - 5 * q^38 + 4 * q^39 + 13 * q^41 - 3 * q^42 - 16 * q^43 - 7 * q^44 - 10 * q^45 + q^46 + 23 * q^47 + 4 * q^48 + 8 * q^49 - 20 * q^50 - 42 * q^51 - q^52 - 16 * q^53 + 5 * q^54 + 15 * q^55 - 3 * q^56 - 15 * q^58 - 10 * q^59 + 10 * q^60 - 2 * q^61 + 7 * q^62 + 24 * q^63 - q^64 - 5 * q^65 + 2 * q^66 + 13 * q^67 + 18 * q^68 + 9 * q^69 + 15 * q^70 + 3 * q^71 - 7 * q^72 + 14 * q^73 + 2 * q^74 + 20 * q^75 + 10 * q^76 - 9 * q^77 + q^78 + 10 * q^79 - 5 * q^80 - 16 * q^81 + 12 * q^82 - q^83 - 12 * q^84 + 30 * q^85 + q^86 - 3 * q^88 + 10 * q^89 + 5 * q^90 + 3 * q^91 - q^92 - 22 * q^93 - 23 * q^94 - 30 * q^95 + q^96 - 22 * q^97 + 2 * q^98 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	0.309017	−	0.224514i	0.178411	−	0.129623i	−0.494996	−	0.868895i	$-0.664830\pi$
$3$	0.309017	−	0.224514i	0.178411	−	0.129623i	0.673407	+	0.739272i	$0.264830\pi$
$4$	−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
$6$	−0.309017	−	0.224514i	−0.126156	−	0.0916575i
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.881966	+	2.71441i	−0.293989	+	0.904804i
$10$	−1.80902	−	1.31433i	−0.572061	−	0.415627i
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	0.929208	+	0.369558i	$0.120491\pi$
$11$	1.30902	+	4.02874i	0.394683	+	1.21471i	−0.534524	+	0.845153i	$0.679509\pi$
$12$	−0.118034	+	0.363271i	−0.0340735	+	0.104867i
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i	−0.899014	−	0.437919i	$-0.855716\pi$
$13$	0.309017	−	0.951057i	0.0857059	−	0.263776i	0.984720	+	0.174143i	$0.0557156\pi$
$14$	0.927051	+	2.85317i	0.247765	+	0.762542i
$15$	0.263932	−	0.812299i	0.0681470	−	0.209735i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.927051	−	0.673542i	−0.224843	−	0.163358i	0.469661	−	0.882847i	$-0.344376\pi$
$17$	−0.927051	−	0.673542i	−0.224843	−	0.163358i	−0.694504	+	0.719489i	$0.744376\pi$
$18$	2.85410			0.672718
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.107719	−	0.994181i	$-0.534355\pi$
$19$	−4.73607	−	3.44095i	−1.08653	−	0.789409i	−0.978810	+	0.204772i	$0.934355\pi$
$20$	−0.690983	+	2.12663i	−0.154508	+	0.475528i
$21$	−0.927051	+	0.673542i	−0.202299	+	0.146979i
$22$	3.42705	−	2.48990i	0.730650	−	0.530848i
$23$	−0.545085	−	1.67760i	−0.113658	−	0.349804i	0.878007	−	0.478648i	$-0.158873\pi$
$23$	−0.545085	−	1.67760i	−0.113658	−	0.349804i	−0.991665	+	0.128845i	$0.958873\pi$
$24$	0.381966			0.0779685
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	−1.00000			−0.196116
$27$	0.690983	+	2.12663i	0.132980	+	0.409270i
$28$	2.42705	−	1.76336i	0.458670	−	0.333243i
$29$	7.66312	−	5.56758i	1.42301	−	1.03387i	0.431739	−	0.901998i	$-0.357900\pi$
$29$	7.66312	−	5.56758i	1.42301	−	1.03387i	0.991266	−	0.131875i	$-0.0420999\pi$
$30$	−0.854102			−0.155937
$31$	0.190983	+	0.138757i	0.0343016	+	0.0249215i	0.604804	−	0.796374i	$-0.293251\pi$
$31$	0.190983	+	0.138757i	0.0343016	+	0.0249215i	−0.570502	+	0.821296i	$0.693251\pi$
$32$	−1.00000			−0.176777
$33$	1.30902	+	0.951057i	0.227871	+	0.165558i
$34$	−0.354102	+	1.08981i	−0.0607280	+	0.186902i
$35$	−5.42705	+	3.94298i	−0.917339	+	0.666486i
$36$	−0.881966	−	2.71441i	−0.146994	−	0.452402i
$37$	−2.57295	+	7.91872i	−0.422990	+	1.30183i	0.481915	+	0.876218i	$0.339941\pi$
$37$	−2.57295	+	7.91872i	−0.422990	+	1.30183i	−0.904906	+	0.425612i	$0.860059\pi$
$38$	−1.80902	+	5.56758i	−0.293461	+	0.903181i
$39$	−0.118034	−	0.363271i	−0.0189006	−	0.0581700i
$40$	2.23607			0.353553
$41$	0.454915	−	1.40008i	0.0710458	−	0.218656i	−0.909229	−	0.416297i	$-0.863328\pi$
$41$	0.454915	−	1.40008i	0.0710458	−	0.218656i	0.980275	+	0.197640i	$0.0633278\pi$
$42$	0.927051	+	0.673542i	0.143047	+	0.103930i
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$	−3.42705	−	2.48990i	−0.516647	−	0.375366i
$45$	1.97214	+	6.06961i	0.293989	+	0.904804i
$46$	−1.42705	+	1.03681i	−0.210407	+	0.152870i
$47$	9.66312	−	7.02067i	1.40951	−	1.02407i	0.416117	−	0.909311i	$-0.363391\pi$
$47$	9.66312	−	7.02067i	1.40951	−	1.02407i	0.993393	−	0.114759i	$-0.0366095\pi$
$48$	−0.118034	−	0.363271i	−0.0170367	−	0.0524337i
$49$	2.00000			0.285714
$50$	−5.00000			−0.707107
$51$	−0.437694			−0.0612894
$52$	0.309017	+	0.951057i	0.0428529	+	0.131888i
$53$	−8.47214	+	6.15537i	−1.16374	+	0.845505i	−0.990246	−	0.139331i	$-0.955505\pi$
$53$	−8.47214	+	6.15537i	−1.16374	+	0.845505i	−0.173491	+	0.984835i	$0.555505\pi$
$54$	1.80902	−	1.31433i	0.246176	−	0.178857i
$55$	7.66312	+	5.56758i	1.03329	+	0.750733i
$56$	−2.42705	−	1.76336i	−0.324328	−	0.235638i
$57$	−2.23607			−0.296174
$58$	−7.66312	−	5.56758i	−1.00622	−	0.731059i
$59$	−1.38197	+	4.25325i	−0.179917	+	0.553727i	−0.999824	−	0.0187700i	$-0.994025\pi$
$59$	−1.38197	+	4.25325i	−0.179917	+	0.553727i	0.819907	+	0.572496i	$0.194025\pi$
$60$	0.263932	+	0.812299i	0.0340735	+	0.104867i
$61$	−2.73607	−	8.42075i	−0.350318	−	1.07817i	−0.958675	−	0.284504i	$-0.908171\pi$
$61$	−2.73607	−	8.42075i	−0.350318	−	1.07817i	0.608357	−	0.793663i	$-0.291829\pi$
$62$	0.0729490	−	0.224514i	0.00926453	−	0.0285133i
$63$	2.64590	−	8.14324i	0.333352	−	1.02595i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.690983	−	2.12663i	−0.0857059	−	0.263776i
$66$	0.500000	−	1.53884i	0.0615457	−	0.189418i
$67$	8.28115	+	6.01661i	1.01170	+	0.735046i	0.964566	−	0.263843i	$-0.0849899\pi$
$67$	8.28115	+	6.01661i	1.01170	+	0.735046i	0.0471381	+	0.998888i	$0.484990\pi$
$68$	1.14590			0.138961
$69$	−0.545085	−	0.396027i	−0.0656205	−	0.0476761i
$70$	5.42705	+	3.94298i	0.648657	+	0.471277i
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	−0.434378	−	0.900731i	$-0.643032\pi$
$71$	2.42705	−	1.76336i	0.288038	−	0.209272i	0.722416	+	0.691459i	$0.243032\pi$
$72$	−2.30902	+	1.67760i	−0.272120	+	0.197707i
$73$	2.38197	+	7.33094i	0.278788	+	0.858021i	0.988192	+	0.153219i	$0.0489641\pi$
$73$	2.38197	+	7.33094i	0.278788	+	0.858021i	−0.709404	+	0.704802i	$0.751036\pi$
$74$	8.32624			0.967905
$75$	−0.590170	−	1.81636i	−0.0681470	−	0.209735i
$76$	5.85410			0.671512
$77$	−3.92705	−	12.0862i	−0.447529	−	1.37735i
$78$	−0.309017	+	0.224514i	−0.0349893	+	0.0254212i
$79$	5.85410	−	4.25325i	0.658638	−	0.478528i	−0.207565	−	0.978221i	$-0.566554\pi$
$79$	5.85410	−	4.25325i	0.658638	−	0.478528i	0.866203	+	0.499693i	$0.166554\pi$
$80$	−0.690983	−	2.12663i	−0.0772542	−	0.237764i
$81$	−6.23607	−	4.53077i	−0.692896	−	0.503419i
$82$	−1.47214			−0.162570
$83$	3.66312	+	2.66141i	0.402080	+	0.292128i	0.770387	−	0.637576i	$-0.220063\pi$
$83$	3.66312	+	2.66141i	0.402080	+	0.292128i	−0.368308	+	0.929704i	$0.620063\pi$
$84$	0.354102	−	1.08981i	0.0386357	−	0.118908i
$85$	−2.56231			−0.277921
$86$	1.92705	+	5.93085i	0.207799	+	0.639540i
$87$	1.11803	−	3.44095i	0.119866	−	0.368909i
$88$	−1.30902	+	4.02874i	−0.139542	+	0.429465i
$89$	1.38197	+	4.25325i	0.146488	+	0.450844i	0.997199	−	0.0747893i	$-0.0238284\pi$
$89$	1.38197	+	4.25325i	0.146488	+	0.450844i	−0.850711	+	0.525633i	$0.823828\pi$
$90$	5.16312	−	3.75123i	0.544241	−	0.395414i
$91$	−0.927051	+	2.85317i	−0.0971813	+	0.299093i
$92$	1.42705	+	1.03681i	0.148780	+	0.108095i
$93$	0.0901699			0.00935019
$94$	−9.66312	−	7.02067i	−0.996675	−	0.724126i
$95$	−13.0902			−1.34302
$96$	−0.309017	+	0.224514i	−0.0315389	+	0.0229144i
$97$	−7.73607	+	5.62058i	−0.785479	+	0.570684i	−0.906618	−	0.421952i	$-0.861345\pi$
$97$	−7.73607	+	5.62058i	−0.785479	+	0.570684i	0.121140	+	0.992635i	$0.461345\pi$
$98$	−0.618034	−	1.90211i	−0.0624309	−	0.192142i
$99$	−12.0902			−1.21511
$100$	1.54508	+	4.75528i	0.154508	+	0.475528i
$101$	0.618034			0.0614967			0.0307483	−	0.999527i	$-0.490211\pi$
$101$	0.618034			0.0614967			0.0307483	+	0.999527i	$0.490211\pi$
$102$	0.135255	+	0.416272i	0.0133922	+	0.0412171i
$103$	10.6353	−	7.72696i	1.04792	−	0.761360i	0.0761065	−	0.997100i	$-0.475751\pi$
$103$	10.6353	−	7.72696i	1.04792	−	0.761360i	0.971816	+	0.235739i	$0.0757511\pi$
$104$	0.809017	−	0.587785i	0.0793306	−	0.0576371i
$105$	−0.791796	+	2.43690i	−0.0772714	+	0.237817i
$106$	8.47214	+	6.15537i	0.822887	+	0.597862i
$107$	−1.09017			−0.105391			−0.0526954	−	0.998611i	$-0.516781\pi$
$107$	−1.09017			−0.105391			−0.0526954	+	0.998611i	$0.516781\pi$
$108$	−1.80902	−	1.31433i	−0.174073	−	0.126471i
$109$	−4.63525	+	14.2658i	−0.443977	+	1.36642i	0.439625	+	0.898181i	$0.355111\pi$
$109$	−4.63525	+	14.2658i	−0.443977	+	1.36642i	−0.883602	+	0.468239i	$0.844889\pi$
$110$	2.92705	−	9.00854i	0.279083	−	0.858930i
$111$	0.982779	+	3.02468i	0.0932813	+	0.287090i
$112$	−0.927051	+	2.85317i	−0.0875981	+	0.269599i
$113$	1.16312	−	3.57971i	0.109417	−	0.336751i	−0.881325	−	0.472511i	$-0.843348\pi$
$113$	1.16312	−	3.57971i	0.109417	−	0.336751i	0.990742	+	0.135760i	$0.0433477\pi$
$114$	0.690983	+	2.12663i	0.0647165	+	0.199177i
$115$	−3.19098	−	2.31838i	−0.297561	−	0.216191i
$116$	−2.92705	+	9.00854i	−0.271770	+	0.836422i
$117$	2.30902	+	1.67760i	0.213469	+	0.155094i
$118$	4.47214			0.411693
$119$	2.78115	+	2.02063i	0.254948	+	0.185230i
$120$	0.690983	−	0.502029i	0.0630778	−	0.0458287i
$121$	−5.61803	+	4.08174i	−0.510730	+	0.371067i
$122$	−7.16312	+	5.20431i	−0.648518	+	0.471176i
$123$	−0.173762	−	0.534785i	−0.0156676	−	0.0482199i
$124$	−0.236068			−0.0211995
$125$	−3.45492	−	10.6331i	−0.309017	−	0.951057i
$126$	−8.56231			−0.762791
$127$	−1.09017	−	3.35520i	−0.0967369	−	0.297726i	0.890966	−	0.454071i	$-0.150029\pi$
$127$	−1.09017	−	3.35520i	−0.0967369	−	0.297726i	−0.987702	+	0.156345i	$0.950029\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−1.92705	+	1.40008i	−0.169667	+	0.123271i
$130$	−1.80902	+	1.31433i	−0.158661	+	0.115274i
$131$	13.2812	+	9.64932i	1.16038	+	0.843065i	0.989826	−	0.142283i	$-0.0454444\pi$
$131$	13.2812	+	9.64932i	1.16038	+	0.843065i	0.170554	+	0.985348i	$0.445444\pi$
$132$	−1.61803			−0.140832
$133$	14.2082	+	10.3229i	1.23201	+	0.895106i
$134$	3.16312	−	9.73508i	0.273252	−	0.840983i
$135$	4.04508	+	2.93893i	0.348145	+	0.252942i
$136$	−0.354102	−	1.08981i	−0.0303640	−	0.0934508i
$137$	1.57295	−	4.84104i	0.134386	−	0.413598i	−0.861108	−	0.508422i	$-0.830229\pi$
$137$	1.57295	−	4.84104i	0.134386	−	0.413598i	0.995494	+	0.0948243i	$0.0302289\pi$
$138$	−0.208204	+	0.640786i	−0.0177235	+	0.0545473i
$139$	−1.64590	−	5.06555i	−0.139603	−	0.429655i	0.856674	−	0.515858i	$-0.172527\pi$
$139$	−1.64590	−	5.06555i	−0.139603	−	0.429655i	−0.996278	+	0.0862030i	$0.972527\pi$
$140$	2.07295	−	6.37988i	0.175196	−	0.539198i
$141$	1.40983	−	4.33901i	0.118729	−	0.365411i
$142$	−2.42705	−	1.76336i	−0.203674	−	0.147978i
$143$	4.23607			0.354238
$144$	2.30902	+	1.67760i	0.192418	+	0.139800i
$145$	6.54508	−	20.1437i	0.543540	−	1.67284i
$146$	6.23607	−	4.53077i	0.516101	−	0.374969i
$147$	0.618034	−	0.449028i	0.0509746	−	0.0370352i
$148$	−2.57295	−	7.91872i	−0.211495	−	0.650915i
$149$	2.23607			0.183186			0.0915929	−	0.995797i	$-0.470804\pi$
$149$	2.23607			0.183186			0.0915929	+	0.995797i	$0.470804\pi$
$150$	−1.54508	+	1.12257i	−0.126156	+	0.0916575i
$151$	−9.70820			−0.790042			−0.395021	−	0.918672i	$-0.629263\pi$
$151$	−9.70820			−0.790042			−0.395021	+	0.918672i	$0.629263\pi$
$152$	−1.80902	−	5.56758i	−0.146731	−	0.451591i
$153$	2.64590	−	1.92236i	0.213908	−	0.155413i
$154$	−10.2812	+	7.46969i	−0.828479	+	0.601925i
$155$	0.527864			0.0423991
$156$	0.309017	+	0.224514i	0.0247412	+	0.0179755i
$157$	4.56231			0.364112			0.182056	−	0.983288i	$-0.441725\pi$
$157$	4.56231			0.364112			0.182056	+	0.983288i	$0.441725\pi$
$158$	−5.85410	−	4.25325i	−0.465727	−	0.338371i
$159$	−1.23607	+	3.80423i	−0.0980266	+	0.301695i
$160$	−1.80902	+	1.31433i	−0.143015	+	0.103907i
$161$	1.63525	+	5.03280i	0.128876	+	0.396640i
$162$	−2.38197	+	7.33094i	−0.187145	+	0.575973i
$163$	0.572949	−	1.76336i	0.0448768	−	0.138117i	−0.926108	−	0.377260i	$-0.876866\pi$
$163$	0.572949	−	1.76336i	0.0448768	−	0.138117i	0.970984	+	0.239143i	$0.0768664\pi$
$164$	0.454915	+	1.40008i	0.0355229	+	0.109328i
$165$	3.61803			0.281664
$166$	1.39919	−	4.30625i	0.108598	−	0.334230i
$167$	−10.8262	−	7.86572i	−0.837759	−	0.608668i	0.0839844	−	0.996467i	$-0.473235\pi$
$167$	−10.8262	−	7.86572i	−0.837759	−	0.608668i	−0.921744	+	0.387799i	$0.873235\pi$
$168$	−1.14590			−0.0884080
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$	0.791796	+	2.43690i	0.0607280	+	0.186902i
$171$	13.5172	−	9.82084i	1.03369	−	0.751018i
$172$	5.04508	−	3.66547i	0.384684	−	0.279489i
$173$	−0.381966	−	1.17557i	−0.0290403	−	0.0893770i	0.935486	−	0.353364i	$-0.114962\pi$
$173$	−0.381966	−	1.17557i	−0.0290403	−	0.0893770i	−0.964526	+	0.263987i	$0.914962\pi$
$174$	−3.61803			−0.274282
$175$	−4.63525	+	14.2658i	−0.350392	+	1.07840i
$176$	4.23607			0.319306
$177$	0.527864	+	1.62460i	0.0396767	+	0.122112i
$178$	3.61803	−	2.62866i	0.271183	−	0.197026i
$179$	−9.04508	+	6.57164i	−0.676061	+	0.491187i	−0.872049	−	0.489419i	$-0.837209\pi$
$179$	−9.04508	+	6.57164i	−0.676061	+	0.491187i	0.195987	+	0.980606i	$0.437209\pi$
$180$	−5.16312	−	3.75123i	−0.384836	−	0.279600i
$181$	−4.38197	−	3.18368i	−0.325709	−	0.236641i	0.412899	−	0.910777i	$-0.364516\pi$
$181$	−4.38197	−	3.18368i	−0.325709	−	0.236641i	−0.738608	+	0.674136i	$0.764516\pi$
$182$	3.00000			0.222375
$183$	−2.73607	−	1.98787i	−0.202256	−	0.146948i
$184$	0.545085	−	1.67760i	0.0401842	−	0.123674i
$185$	5.75329	+	17.7068i	0.422990	+	1.30183i
$186$	−0.0278640	−	0.0857567i	−0.00204309	−	0.00628799i
$187$	1.50000	−	4.61653i	0.109691	−	0.337594i
$188$	−3.69098	+	11.3597i	−0.269193	+	0.828490i
$189$	−2.07295	−	6.37988i	−0.150785	−	0.464068i
$190$	4.04508	+	12.4495i	0.293461	+	0.903181i
$191$	−4.21885	+	12.9843i	−0.305265	+	0.939509i	0.674313	+	0.738446i	$0.264440\pi$
$191$	−4.21885	+	12.9843i	−0.305265	+	0.939509i	−0.979578	+	0.201064i	$0.935560\pi$
$192$	0.309017	+	0.224514i	0.0223014	+	0.0162029i
$193$	−14.6525			−1.05471			−0.527354	−	0.849646i	$-0.676816\pi$
$193$	−14.6525			−1.05471			−0.527354	+	0.849646i	$0.676816\pi$
$194$	7.73607	+	5.62058i	0.555417	+	0.403534i
$195$	−0.690983	−	0.502029i	−0.0494823	−	0.0359510i
$196$	−1.61803	+	1.17557i	−0.115574	+	0.0839693i
$197$	−9.70820	+	7.05342i	−0.691681	+	0.502536i	−0.877212	−	0.480103i	$-0.840599\pi$
$197$	−9.70820	+	7.05342i	−0.691681	+	0.502536i	0.185531	+	0.982638i	$0.440599\pi$
$198$	3.73607	+	11.4984i	0.265511	+	0.817158i
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$	4.04508	−	2.93893i	0.286031	−	0.207813i
$201$	3.90983			0.275778
$202$	−0.190983	−	0.587785i	−0.0134375	−	0.0413564i
$203$	−22.9894	+	16.7027i	−1.61354	+	1.17230i
$204$	0.354102	−	0.257270i	0.0247921	−	0.0180125i
$205$	−1.01722	−	3.13068i	−0.0710458	−	0.218656i
$206$	−10.6353	−	7.72696i	−0.740993	−	0.538363i
$207$	5.03444			0.349918
$208$	−0.809017	−	0.587785i	−0.0560952	−	0.0407556i
$209$	7.66312	−	23.5847i	0.530069	−	1.63138i
$210$	2.56231			0.176816
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	−0.847604	−	0.530629i	$-0.821956\pi$
$211$	−6.88197	−	21.1805i	−0.473774	−	1.45813i	0.373830	−	0.927497i	$-0.378044\pi$
$212$	3.23607	−	9.95959i	0.222254	−	0.684028i
$213$	0.354102	−	1.08981i	0.0242627	−	0.0746728i
$214$	0.336881	+	1.03681i	0.0230287	+	0.0708751i
$215$	−11.2812	+	8.19624i	−0.769368	+	0.558979i
$216$	−0.690983	+	2.12663i	−0.0470154	+	0.144699i
$217$	−0.572949	−	0.416272i	−0.0388943	−	0.0282584i
$218$	15.0000			1.01593
$219$	2.38197	+	1.73060i	0.160958	+	0.116943i
$220$	−9.47214			−0.638611
$221$	−0.927051	+	0.673542i	−0.0623602	+	0.0453073i
$222$	2.57295	−	1.86936i	0.172685	−	0.125463i
$223$	−2.78115	−	8.55951i	−0.186240	−	0.573187i	0.813728	−	0.581246i	$-0.197435\pi$
$223$	−2.78115	−	8.55951i	−0.186240	−	0.573187i	−0.999968	+	0.00805911i	$0.997435\pi$
$224$	3.00000			0.200446
$225$	11.5451	+	8.38800i	0.769672	+	0.559200i
$226$	−3.76393			−0.250373
$227$	9.07295	+	27.9237i	0.602193	+	1.85336i	0.515044	+	0.857163i	$0.327775\pi$
$227$	9.07295	+	27.9237i	0.602193	+	1.85336i	0.0871483	+	0.996195i	$0.472225\pi$
$228$	1.80902	−	1.31433i	0.119805	−	0.0870435i
$229$	2.07295	−	1.50609i	0.136984	−	0.0995249i	−0.517183	−	0.855875i	$-0.673019\pi$
$229$	2.07295	−	1.50609i	0.136984	−	0.0995249i	0.654167	+	0.756350i	$0.273019\pi$
$230$	−1.21885	+	3.75123i	−0.0803684	+	0.247348i
$231$	−3.92705	−	2.85317i	−0.258381	−	0.187725i
$232$	9.47214			0.621876
$233$	−11.5623	−	8.40051i	−0.757472	−	0.550336i	0.140662	−	0.990058i	$-0.455077\pi$
$233$	−11.5623	−	8.40051i	−0.757472	−	0.550336i	−0.898134	+	0.439722i	$0.855077\pi$
$234$	0.881966	−	2.71441i	0.0576559	−	0.177447i
$235$	8.25329	−	25.4010i	0.538385	−	1.65698i
$236$	−1.38197	−	4.25325i	−0.0899583	−	0.276863i
$237$	0.854102	−	2.62866i	0.0554799	−	0.170750i
$238$	1.06231	−	3.26944i	0.0688591	−	0.211926i
$239$	−2.13525	−	6.57164i	−0.138118	−	0.425084i	0.857944	−	0.513743i	$-0.171742\pi$
$239$	−2.13525	−	6.57164i	−0.138118	−	0.425084i	−0.996062	+	0.0886595i	$0.971742\pi$
$240$	−0.690983	−	0.502029i	−0.0446028	−	0.0324058i
$241$	4.82624	−	14.8536i	0.310885	−	0.956807i	−0.666530	−	0.745478i	$-0.732221\pi$
$241$	4.82624	−	14.8536i	0.310885	−	0.956807i	0.977415	−	0.211328i	$-0.0677789\pi$
$242$	5.61803	+	4.08174i	0.361141	+	0.262384i
$243$	−9.65248			−0.619207
$244$	7.16312	+	5.20431i	0.458572	+	0.333172i
$245$	3.61803	−	2.62866i	0.231148	−	0.167939i
$246$	−0.454915	+	0.330515i	−0.0290043	+	0.0210729i
$247$	−4.73607	+	3.44095i	−0.301349	+	0.218943i
$248$	0.0729490	+	0.224514i	0.00463227	+	0.0142567i
$249$	1.72949			0.109602
$250$	−9.04508	+	6.57164i	−0.572061	+	0.415627i
$251$	0.819660			0.0517365			0.0258682	−	0.999665i	$-0.491765\pi$
$251$	0.819660			0.0517365			0.0258682	+	0.999665i	$0.491765\pi$
$252$	2.64590	+	8.14324i	0.166676	+	0.512976i
$253$	6.04508	−	4.39201i	0.380051	−	0.276123i
$254$	−2.85410	+	2.07363i	−0.179082	+	0.130111i
$255$	−0.791796	+	0.575274i	−0.0495842	+	0.0360250i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	25.7426			1.60578			0.802891	−	0.596126i	$-0.203294\pi$
$257$	25.7426			1.60578			0.802891	+	0.596126i	$0.203294\pi$
$258$	1.92705	+	1.40008i	0.119973	+	0.0871655i
$259$	7.71885	−	23.7562i	0.479626	−	1.47614i
$260$	1.80902	+	1.31433i	0.112190	+	0.0815111i
$261$	8.35410	+	25.7113i	0.517106	+	1.59149i
$262$	5.07295	−	15.6129i	0.313408	−	0.964570i
$263$	1.42705	−	4.39201i	0.0879957	−	0.270823i	−0.897369	−	0.441280i	$-0.854524\pi$
$263$	1.42705	−	4.39201i	0.0879957	−	0.270823i	0.985365	+	0.170457i	$0.0545245\pi$
$264$	0.500000	+	1.53884i	0.0307729	+	0.0947092i
$265$	−7.23607	+	22.2703i	−0.444508	+	1.36806i
$266$	5.42705	−	16.7027i	0.332754	−	1.02411i
$267$	1.38197	+	1.00406i	0.0845749	+	0.0614473i
$268$	−10.2361			−0.625267
$269$	−1.54508	−	1.12257i	−0.0942055	−	0.0684443i	0.539685	−	0.841867i	$-0.318543\pi$
$269$	−1.54508	−	1.12257i	−0.0942055	−	0.0684443i	−0.633891	+	0.773422i	$0.718543\pi$
$270$	1.54508	−	4.75528i	0.0940309	−	0.289397i
$271$	−23.0623	+	16.7557i	−1.40094	+	1.01784i	−0.406372	+	0.913708i	$0.633206\pi$
$271$	−23.0623	+	16.7557i	−1.40094	+	1.01784i	−0.994564	+	0.104131i	$0.966794\pi$
$272$	−0.927051	+	0.673542i	−0.0562107	+	0.0408395i
$273$	0.354102	+	1.08981i	0.0214312	+	0.0659585i
$274$	−5.09017			−0.307508
$275$	21.1803			1.27722
$276$	0.673762			0.0405557
$277$	0.0901699	+	0.277515i	0.00541779	+	0.0166742i	0.953729	−	0.300668i	$-0.0972096\pi$
$277$	0.0901699	+	0.277515i	0.00541779	+	0.0166742i	−0.948311	+	0.317342i	$0.897210\pi$
$278$	−4.30902	+	3.13068i	−0.258438	+	0.187766i
$279$	−0.545085	+	0.396027i	−0.0326334	+	0.0237095i
$280$	−6.70820			−0.400892
$281$	−2.57295	−	1.86936i	−0.153489	−	0.111516i	0.508390	−	0.861127i	$-0.330241\pi$
$281$	−2.57295	−	1.86936i	−0.153489	−	0.111516i	−0.661879	+	0.749610i	$0.730241\pi$
$282$	−4.56231			−0.271681
$283$	9.94427	+	7.22494i	0.591126	+	0.429478i	0.842718	−	0.538355i	$-0.180954\pi$
$283$	9.94427	+	7.22494i	0.591126	+	0.429478i	−0.251592	+	0.967833i	$0.580954\pi$
$284$	−0.927051	+	2.85317i	−0.0550104	+	0.169304i
$285$	−4.04508	+	2.93893i	−0.239610	+	0.174087i
$286$	−1.30902	−	4.02874i	−0.0774038	−	0.238224i
$287$	−1.36475	+	4.20025i	−0.0805584	+	0.247933i
$288$	0.881966	−	2.71441i	0.0519703	−	0.159948i
$289$	−4.84752	−	14.9191i	−0.285148	−	0.877597i
$290$	−21.1803			−1.24375
$291$	−1.12868	+	3.47371i	−0.0661642	+	0.203633i
$292$	−6.23607	−	4.53077i	−0.364938	−	0.265143i
$293$	8.56231			0.500215			0.250108	−	0.968218i	$-0.419534\pi$
$293$	8.56231			0.500215			0.250108	+	0.968218i	$0.419534\pi$
$294$	−0.618034	−	0.449028i	−0.0360445	−	0.0261878i
$295$	3.09017	+	9.51057i	0.179917	+	0.553727i
$296$	−6.73607	+	4.89404i	−0.391526	+	0.284460i
$297$	−7.66312	+	5.56758i	−0.444659	+	0.323064i
$298$	−0.690983	−	2.12663i	−0.0400276	−	0.123192i
$299$	−1.76393			−0.102011
$300$	1.54508	+	1.12257i	0.0892055	+	0.0648116i
$301$	18.7082			1.07832
$302$	3.00000	+	9.23305i	0.172631	+	0.531302i
$303$	0.190983	−	0.138757i	0.0109717	−	0.00797140i
$304$	−4.73607	+	3.44095i	−0.271632	+	0.197352i
$305$	−16.0172	−	11.6372i	−0.917143	−	0.666344i
$306$	−2.64590	−	1.92236i	−0.151256	−	0.109894i
$307$	−23.1246			−1.31979			−0.659896	−	0.751357i	$-0.729400\pi$
$307$	−23.1246			−1.31979			−0.659896	+	0.751357i	$0.729400\pi$
$308$	10.2812	+	7.46969i	0.585823	+	0.425625i
$309$	1.55166	−	4.77553i	0.0882710	−	0.271670i
$310$	−0.163119	−	0.502029i	−0.00926453	−	0.0285133i
$311$	−3.06231	−	9.42481i	−0.173647	−	0.534432i	0.825922	−	0.563785i	$-0.190655\pi$
$311$	−3.06231	−	9.42481i	−0.173647	−	0.534432i	−0.999569	+	0.0293530i	$0.990655\pi$
$312$	0.118034	−	0.363271i	0.00668236	−	0.0205662i
$313$	−5.11803	+	15.7517i	−0.289288	+	0.890338i	0.695792	+	0.718243i	$0.255054\pi$
$313$	−5.11803	+	15.7517i	−0.289288	+	0.890338i	−0.985080	+	0.172095i	$0.944946\pi$
$314$	−1.40983	−	4.33901i	−0.0795613	−	0.244865i
$315$	−5.91641	−	18.2088i	−0.333352	−	1.02595i
$316$	−2.23607	+	6.88191i	−0.125789	+	0.387138i
$317$	−6.78115	−	4.92680i	−0.380867	−	0.276716i	0.380835	−	0.924643i	$-0.375636\pi$
$317$	−6.78115	−	4.92680i	−0.380867	−	0.276716i	−0.761703	+	0.647926i	$0.775636\pi$
$318$	4.00000			0.224309
$319$	32.4615	+	23.5847i	1.81749	+	1.32049i
$320$	1.80902	+	1.31433i	0.101127	+	0.0734732i
$321$	−0.336881	+	0.244758i	−0.0188029	+	0.0136611i
$322$	4.28115	−	3.11044i	0.238579	−	0.173338i
$323$	2.07295	+	6.37988i	0.115342	+	0.354986i
$324$	7.70820			0.428234
$325$	−4.04508	−	2.93893i	−0.224381	−	0.163022i
$326$	−1.85410			−0.102689
$327$	1.77051	+	5.44907i	0.0979094	+	0.301334i
$328$	1.19098	−	0.865300i	0.0657610	−	0.0477782i
$329$	−28.9894	+	21.0620i	−1.59823	+	1.16119i
$330$	−1.11803	−	3.44095i	−0.0615457	−	0.189418i
$331$	12.5902	+	9.14729i	0.692018	+	0.502781i	0.877323	−	0.479900i	$-0.159327\pi$
$331$	12.5902	+	9.14729i	0.692018	+	0.502781i	−0.185305	+	0.982681i	$0.559327\pi$
$332$	−4.52786			−0.248499
$333$	−19.2254	−	13.9681i	−1.05355	−	0.765447i
$334$	−4.13525	+	12.7270i	−0.226271	+	0.696391i
$335$	22.8885			1.25053
$336$	0.354102	+	1.08981i	0.0193178	+	0.0594542i
$337$	−1.41641	+	4.35926i	−0.0771567	+	0.237464i	−0.982194	−	0.187868i	$-0.939842\pi$
$337$	−1.41641	+	4.35926i	−0.0771567	+	0.237464i	0.905038	+	0.425331i	$0.139842\pi$
$338$	3.70820	−	11.4127i	0.201700	−	0.620768i
$339$	−0.444272	−	1.36733i	−0.0241295	−	0.0742631i
$340$	2.07295	−	1.50609i	0.112421	−	0.0816790i
$341$	−0.309017	+	0.951057i	−0.0167342	+	0.0515026i
$342$	−13.5172	−	9.82084i	−0.730928	−	0.531050i
$343$	15.0000			0.809924
$344$	−5.04508	−	3.66547i	−0.272013	−	0.197629i
$345$	−1.50658			−0.0811114
$346$	−1.00000	+	0.726543i	−0.0537603	+	0.0390592i
$347$	17.0623	−	12.3965i	0.915953	−	0.665478i	−0.0265607	−	0.999647i	$-0.508456\pi$
$347$	17.0623	−	12.3965i	0.915953	−	0.665478i	0.942513	+	0.334169i	$0.108456\pi$
$348$	1.11803	+	3.44095i	0.0599329	+	0.184455i
$349$	−17.7639			−0.950881			−0.475441	−	0.879748i	$-0.657711\pi$
$349$	−17.7639			−0.950881			−0.475441	+	0.879748i	$0.657711\pi$
$350$	15.0000			0.801784
$351$	2.23607			0.119352
$352$	−1.30902	−	4.02874i	−0.0697708	−	0.214733i
$353$	17.1803	−	12.4822i	0.914417	−	0.664363i	−0.0277109	−	0.999616i	$-0.508822\pi$
$353$	17.1803	−	12.4822i	0.914417	−	0.664363i	0.942128	+	0.335253i	$0.108822\pi$
$354$	1.38197	−	1.00406i	0.0734507	−	0.0533650i
$355$	2.07295	−	6.37988i	0.110021	−	0.338609i
$356$	−3.61803	−	2.62866i	−0.191755	−	0.139318i
$357$	1.31308			0.0694957
$358$	9.04508	+	6.57164i	0.478048	+	0.347322i
$359$	−2.50000	+	7.69421i	−0.131945	+	0.406085i	−0.995102	−	0.0988502i	$-0.968484\pi$
$359$	−2.50000	+	7.69421i	−0.131945	+	0.406085i	0.863157	+	0.504935i	$0.168484\pi$
$360$	−1.97214	+	6.06961i	−0.103941	+	0.319897i
$361$	4.71885	+	14.5231i	0.248360	+	0.764375i
$362$	−1.67376	+	5.15131i	−0.0879710	+	0.270747i
$363$	−0.819660	+	2.52265i	−0.0430210	+	0.132405i
$364$	−0.927051	−	2.85317i	−0.0485907	−	0.149547i
$365$	13.9443	+	10.1311i	0.729877	+	0.530286i
$366$	−1.04508	+	3.21644i	−0.0546275	+	0.168126i
$367$	−28.7533	−	20.8905i	−1.50091	−	1.09047i	−0.970018	−	0.243035i	$-0.921857\pi$
$367$	−28.7533	−	20.8905i	−1.50091	−	1.09047i	−0.530892	−	0.847440i	$-0.678143\pi$
$368$	−1.76393			−0.0919513
$369$	3.39919	+	2.46965i	0.176955	+	0.128565i
$370$	15.0623	−	10.9434i	0.783052	−	0.568921i
$371$	25.4164	−	18.4661i	1.31955	−	0.958712i
$372$	−0.0729490	+	0.0530006i	−0.00378223	+	0.00274795i
$373$	−3.63525	−	11.1882i	−0.188226	−	0.579301i	0.811763	−	0.583987i	$-0.198508\pi$
$373$	−3.63525	−	11.1882i	−0.188226	−	0.579301i	−0.999989	+	0.00468631i	$0.998508\pi$
$374$	−4.85410			−0.251000
$375$	−3.45492	−	2.51014i	−0.178411	−	0.129623i
$376$	11.9443			0.615979
$377$	−2.92705	−	9.00854i	−0.150751	−	0.463963i
$378$	−5.42705	+	3.94298i	−0.279137	+	0.202805i
$379$	−7.66312	+	5.56758i	−0.393628	+	0.285987i	−0.766941	−	0.641718i	$-0.778222\pi$
$379$	−7.66312	+	5.56758i	−0.393628	+	0.285987i	0.373313	+	0.927706i	$0.378222\pi$
$380$	10.5902	−	7.69421i	0.543264	−	0.394705i
$381$	−1.09017	−	0.792055i	−0.0558511	−	0.0405782i
$382$	13.6525			0.698521
$383$	−9.16312	−	6.65740i	−0.468214	−	0.340177i	0.328531	−	0.944493i	$-0.393446\pi$
$383$	−9.16312	−	6.65740i	−0.468214	−	0.340177i	−0.796745	+	0.604316i	$0.793446\pi$
$384$	0.118034	−	0.363271i	0.00602340	−	0.0185381i
$385$	−22.9894	−	16.7027i	−1.17165	−	0.851251i
$386$	4.52786	+	13.9353i	0.230462	+	0.709290i
$387$	5.50000	−	16.9273i	0.279581	−	0.860461i
$388$	2.95492	−	9.09429i	0.150013	−	0.461693i
$389$	5.62868	+	17.3233i	0.285385	+	0.878326i	0.986283	+	0.165064i	$0.0527830\pi$
$389$	5.62868	+	17.3233i	0.285385	+	0.878326i	−0.700898	+	0.713262i	$0.747217\pi$
$390$	−0.263932	+	0.812299i	−0.0133647	+	0.0411324i
$391$	−0.624612	+	1.92236i	−0.0315880	+	0.0972178i
$392$	1.61803	+	1.17557i	0.0817231	+	0.0593753i
$393$	6.27051			0.316305
$394$	9.70820	+	7.05342i	0.489092	+	0.355346i
$395$	5.00000	−	15.3884i	0.251577	−	0.774275i
$396$	9.78115	−	7.10642i	0.491521	−	0.357111i
$397$	8.28115	−	6.01661i	0.415619	−	0.301965i	−0.360254	−	0.932854i	$-0.617310\pi$
$397$	8.28115	−	6.01661i	0.415619	−	0.301965i	0.775873	+	0.630889i	$0.217310\pi$
$398$	−0.791796	−	2.43690i	−0.0396892	−	0.122151i
$399$	6.70820			0.335830
$400$	−4.04508	−	2.93893i	−0.202254	−	0.146946i
$401$	−14.1803			−0.708132			−0.354066	−	0.935220i	$-0.615201\pi$
$401$	−14.1803			−0.708132			−0.354066	+	0.935220i	$0.615201\pi$
$402$	−1.20820	−	3.71847i	−0.0602597	−	0.185460i
$403$	0.190983	−	0.138757i	0.00951354	−	0.00691199i
$404$	−0.500000	+	0.363271i	−0.0248759	+	0.0180734i
$405$	−17.2361			−0.856467
$406$	22.9894	+	16.7027i	1.14094	+	0.828943i
$407$	−35.2705			−1.74829
$408$	−0.354102	−	0.257270i	−0.0175307	−	0.0127368i
$409$	−2.07295	+	6.37988i	−0.102501	+	0.315465i	−0.989136	−	0.147005i	$-0.953037\pi$
$409$	−2.07295	+	6.37988i	−0.102501	+	0.315465i	0.886635	+	0.462470i	$0.153037\pi$
$410$	−2.66312	+	1.93487i	−0.131522	+	0.0955564i
$411$	−0.600813	−	1.84911i	−0.0296359	−	0.0912100i
$412$	−4.06231	+	12.5025i	−0.200135	+	0.615954i
$413$	4.14590	−	12.7598i	0.204006	−	0.627867i
$414$	−1.55573	−	4.78804i	−0.0764599	−	0.235319i
$415$	10.1246			0.496998
$416$	−0.309017	+	0.951057i	−0.0151508	+	0.0466294i
$417$	−1.64590	−	1.19581i	−0.0806000	−	0.0585593i
$418$	−24.7984			−1.21293
$419$	−18.4164	−	13.3803i	−0.899700	−	0.653671i	0.0386886	−	0.999251i	$-0.487682\pi$
$419$	−18.4164	−	13.3803i	−0.899700	−	0.653671i	−0.938389	+	0.345581i	$0.887682\pi$
$420$	−0.791796	−	2.43690i	−0.0386357	−	0.118908i
$421$	−17.2082	+	12.5025i	−0.838677	+	0.609334i	−0.922001	−	0.387188i	$-0.873446\pi$
$421$	−17.2082	+	12.5025i	−0.838677	+	0.609334i	0.0833241	+	0.996522i	$0.473446\pi$
$422$	−18.0172	+	13.0903i	−0.877065	+	0.637225i
$423$	10.5344	+	32.4217i	0.512202	+	1.57640i
$424$	−10.4721			−0.508572
$425$	−4.63525	+	3.36771i	−0.224843	+	0.163358i
$426$	−1.14590			−0.0555189
$427$	8.20820	+	25.2623i	0.397223	+	1.22253i
$428$	0.881966	−	0.640786i	0.0426314	−	0.0309736i
$429$	1.30902	−	0.951057i	0.0631999	−	0.0459174i
$430$	11.2812	+	8.19624i	0.544026	+	0.395258i
$431$	−21.0902	−	15.3229i	−1.01588	−	0.738078i	−0.0504440	−	0.998727i	$-0.516064\pi$
$431$	−21.0902	−	15.3229i	−1.01588	−	0.738078i	−0.965434	+	0.260649i	$0.916064\pi$
$432$	2.23607			0.107583
$433$	17.2812	+	12.5555i	0.830479	+	0.603378i	0.919695	−	0.392634i	$-0.128436\pi$
$433$	17.2812	+	12.5555i	0.830479	+	0.603378i	−0.0892157	+	0.996012i	$0.528436\pi$
$434$	−0.218847	+	0.673542i	−0.0105050	+	0.0323310i
$435$	−2.50000	−	7.69421i	−0.119866	−	0.368909i
$436$	−4.63525	−	14.2658i	−0.221988	−	0.683210i
$437$	−3.19098	+	9.82084i	−0.152645	+	0.469794i
$438$	0.909830	−	2.80017i	0.0434734	−	0.133797i
$439$	7.92705	+	24.3970i	0.378338	+	1.16440i	0.941199	+	0.337852i	$0.109700\pi$
$439$	7.92705	+	24.3970i	0.378338	+	1.16440i	−0.562862	+	0.826551i	$0.690300\pi$
$440$	2.92705	+	9.00854i	0.139542	+	0.429465i
$441$	−1.76393	+	5.42882i	−0.0839968	+	0.258515i
$442$	0.927051	+	0.673542i	0.0440953	+	0.0320371i
$443$	19.4164			0.922501			0.461251	−	0.887270i	$-0.347401\pi$
$443$	19.4164			0.922501			0.461251	+	0.887270i	$0.347401\pi$
$444$	−2.57295	−	1.86936i	−0.122107	−	0.0887158i
$445$	8.09017	+	5.87785i	0.383511	+	0.278637i
$446$	−7.28115	+	5.29007i	−0.344773	+	0.250492i
$447$	0.690983	−	0.502029i	0.0326824	−	0.0237451i
$448$	−0.927051	−	2.85317i	−0.0437990	−	0.134800i
$449$	−3.94427			−0.186142			−0.0930709	−	0.995659i	$-0.529668\pi$
$449$	−3.94427			−0.186142			−0.0930709	+	0.995659i	$0.529668\pi$
$450$	4.40983	−	13.5721i	0.207881	−	0.639793i
$451$	6.23607			0.293645
$452$	1.16312	+	3.57971i	0.0547085	+	0.168375i
$453$	−3.00000	+	2.17963i	−0.140952	+	0.102408i
$454$	23.7533	−	17.2578i	1.11480	−	0.809947i
$455$	2.07295	+	6.37988i	0.0971813	+	0.299093i
$456$	−1.80902	−	1.31433i	−0.0847150	−	0.0615490i
$457$	40.2148			1.88117			0.940584	−	0.339561i	$-0.110278\pi$
$457$	40.2148			1.88117			0.940584	+	0.339561i	$0.110278\pi$
$458$	−2.07295	−	1.50609i	−0.0968625	−	0.0703748i
$459$	0.791796	−	2.43690i	0.0369579	−	0.113745i
$460$	3.94427			0.183903
$461$	1.79837	+	5.53483i	0.0837586	+	0.257783i	0.984161	−	0.177275i	$-0.0567281\pi$
$461$	1.79837	+	5.53483i	0.0837586	+	0.257783i	−0.900403	+	0.435057i	$0.856728\pi$
$462$	−1.50000	+	4.61653i	−0.0697863	+	0.214780i
$463$	−10.8090	+	33.2667i	−0.502338	+	1.54604i	0.302863	+	0.953034i	$0.402057\pi$
$463$	−10.8090	+	33.2667i	−0.502338	+	1.54604i	−0.805201	+	0.593002i	$0.797943\pi$
$464$	−2.92705	−	9.00854i	−0.135885	−	0.418211i
$465$	0.163119	−	0.118513i	0.00756446	−	0.00549590i
$466$	−4.41641	+	13.5923i	−0.204586	+	0.629651i
$467$	15.5172	+	11.2739i	0.718051	+	0.521695i	0.885761	−	0.464142i	$-0.153637\pi$
$467$	15.5172	+	11.2739i	0.718051	+	0.521695i	−0.167710	+	0.985836i	$0.553637\pi$
$468$	−2.85410			−0.131931
$469$	−24.8435	−	18.0498i	−1.14716	−	0.833464i
$470$	−26.7082			−1.23196
$471$	1.40983	−	1.02430i	0.0649615	−	0.0471973i
$472$	−3.61803	+	2.62866i	−0.166534	+	0.120994i
$473$	−8.16312	−	25.1235i	−0.375341	−	1.15518i
$474$	−2.76393			−0.126952
$475$	−23.6803	+	17.2048i	−1.08653	+	0.789409i
$476$	−3.43769			−0.157566
$477$	−9.23607	−	28.4257i	−0.422891	−	1.30152i
$478$	−5.59017	+	4.06150i	−0.255688	+	0.185769i
$479$	12.2984	−	8.93529i	0.561927	−	0.408264i	−0.270237	−	0.962794i	$-0.587102\pi$
$479$	12.2984	−	8.93529i	0.561927	−	0.408264i	0.832164	+	0.554530i	$0.187102\pi$
$480$	−0.263932	+	0.812299i	−0.0120468	+	0.0370762i
$481$	6.73607	+	4.89404i	0.307138	+	0.223149i
$482$	−15.6180			−0.711382
$483$	1.63525	+	1.18808i	0.0744067	+	0.0540596i
$484$	2.14590	−	6.60440i	0.0975408	−	0.300200i
$485$	−6.60739	+	20.3355i	−0.300026	+	0.923386i
$486$	2.98278	+	9.18005i	0.135302	+	0.416416i
$487$	6.83688	−	21.0418i	0.309809	−	0.953493i	−0.668030	−	0.744134i	$-0.732862\pi$
$487$	6.83688	−	21.0418i	0.309809	−	0.953493i	0.977839	−	0.209359i	$-0.0671377\pi$
$488$	2.73607	−	8.42075i	0.123856	−	0.381190i
$489$	−0.218847	−	0.673542i	−0.00989661	−	0.0304586i
$490$	−3.61803	−	2.62866i	−0.163446	−	0.118751i
$491$	5.94427	−	18.2946i	0.268261	−	0.825623i	−0.722663	−	0.691201i	$-0.757082\pi$
$491$	5.94427	−	18.2946i	0.268261	−	0.825623i	0.990924	−	0.134423i	$-0.0429179\pi$
$492$	0.454915	+	0.330515i	0.0205092	+	0.0149008i
$493$	−10.8541			−0.488844
$494$	4.73607	+	3.44095i	0.213086	+	0.154816i
$495$	−21.8713	+	15.8904i	−0.983043	+	0.714222i
$496$	0.190983	−	0.138757i	0.00857539	−	0.00623039i
$497$	−7.28115	+	5.29007i	−0.326604	+	0.237292i
$498$	−0.534442	−	1.64484i	−0.0239489	−	0.0737072i
$499$	34.1459			1.52858			0.764290	−	0.644873i	$-0.223090\pi$
$499$	34.1459			1.52858			0.764290	+	0.644873i	$0.223090\pi$
$500$	9.04508	+	6.57164i	0.404508	+	0.293893i
$501$	−5.11146			−0.228363
$502$	−0.253289	−	0.779543i	−0.0113048	−	0.0347927i
$503$	24.6803	−	17.9313i	1.10044	−	0.799518i	0.119310	−	0.992857i	$-0.461932\pi$
$503$	24.6803	−	17.9313i	1.10044	−	0.799518i	0.981132	+	0.193339i	$0.0619318\pi$
$504$	6.92705	−	5.03280i	0.308555	−	0.224179i
$505$	1.11803	−	0.812299i	0.0497519	−	0.0361468i
$506$	−6.04508	−	4.39201i	−0.268737	−	0.195249i
$507$	4.58359			0.203564
$508$	2.85410	+	2.07363i	0.126630	+	0.0920023i
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	−0.963284	−	0.268486i	$-0.913477\pi$
$509$	−0.590170	+	1.81636i	−0.0261588	+	0.0805086i	0.937125	+	0.348994i	$0.113477\pi$
$510$	0.791796	+	0.575274i	0.0350613	+	0.0254735i
$511$	−7.14590	−	21.9928i	−0.316116	−	0.972905i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.04508	−	12.4495i	0.178595	−	0.549658i
$514$	−7.95492	−	24.4827i	−0.350876	−	1.07989i
$515$	9.08359	−	27.9564i	0.400271	−	1.23191i
$516$	0.736068	−	2.26538i	0.0324036	−	0.0997280i
$517$	40.9336	+	29.7400i	1.80026	+	1.30796i
$518$	−24.9787			−1.09750
$519$	−0.381966	−	0.277515i	−0.0167664	−	0.0121815i
$520$	0.690983	−	2.12663i	0.0303016	−	0.0932588i
$521$	18.9721	−	13.7841i	0.831184	−	0.603891i	−0.0887098	−	0.996058i	$-0.528274\pi$
$521$	18.9721	−	13.7841i	0.831184	−	0.603891i	0.919894	+	0.392167i	$0.128274\pi$
$522$	21.8713	−	15.8904i	0.957282	−	0.695506i
$523$	−1.43769	−	4.42477i	−0.0628660	−	0.193482i	0.914691	−	0.404155i	$-0.132434\pi$
$523$	−1.43769	−	4.42477i	−0.0628660	−	0.193482i	−0.977557	+	0.210673i	$0.932434\pi$
$524$	−16.4164			−0.717154
$525$	1.77051	+	5.44907i	0.0772714	+	0.237817i
$526$	−4.61803			−0.201356
$527$	−0.0835921	−	0.257270i	−0.00364133	−	0.0112069i
$528$	1.30902	−	0.951057i	0.0569677	−	0.0413894i
$529$	16.0902	−	11.6902i	0.699573	−	0.508269i
$530$	23.4164			1.01714
$531$	−10.3262	−	7.50245i	−0.448121	−	0.325579i
$532$	−17.5623			−0.761423
$533$	−1.19098	−	0.865300i	−0.0515872	−	0.0374803i
$534$	0.527864	−	1.62460i	0.0228429	−	0.0703033i
$535$	−1.97214	+	1.43284i	−0.0852629	+	0.0619471i
$536$	3.16312	+	9.73508i	0.136626	+	0.420491i
$537$	−1.31966	+	4.06150i	−0.0569475	+	0.175266i
$538$	−0.590170	+	1.81636i	−0.0254440	+	0.0783087i
$539$	2.61803	+	8.05748i	0.112767	+	0.347060i
$540$	−5.00000			−0.215166
$541$	4.72542	−	14.5434i	0.203162	−	0.625268i	−0.796622	−	0.604478i	$-0.793382\pi$
$541$	4.72542	−	14.5434i	0.203162	−	0.625268i	0.999784	−	0.0207902i	$-0.00661819\pi$
$542$	23.0623	+	16.7557i	0.990611	+	0.719721i
$543$	−2.06888			−0.0887843
$544$	0.927051	+	0.673542i	0.0397470	+	0.0288779i
$545$	10.3647	+	31.8994i	0.443977	+	1.36642i
$546$	0.927051	−	0.673542i	0.0396741	−	0.0288249i
$547$	−6.78115	+	4.92680i	−0.289941	+	0.210655i	−0.723242	−	0.690595i	$-0.757349\pi$
$547$	−6.78115	+	4.92680i	−0.289941	+	0.210655i	0.433301	+	0.901249i	$0.357349\pi$
$548$	1.57295	+	4.84104i	0.0671931	+	0.206799i
$549$	25.2705			1.07852
$550$	−6.54508	−	20.1437i	−0.279083	−	0.858930i
$551$	−55.4508			−2.36229
$552$	−0.208204	−	0.640786i	−0.00886175	−	0.0272737i
$553$	−17.5623	+	12.7598i	−0.746825	+	0.542600i
$554$	0.236068	−	0.171513i	0.0100296	−	0.00728691i
$555$	5.75329	+	4.18001i	0.244214	+	0.177432i
$556$	4.30902	+	3.13068i	0.182743	+	0.132771i
$557$	24.8885			1.05456			0.527281	−	0.849691i	$-0.323212\pi$
$557$	24.8885			1.05456			0.527281	+	0.849691i	$0.323212\pi$
$558$	0.545085	+	0.396027i	0.0230753	+	0.0167652i
$559$	−1.92705	+	5.93085i	−0.0815056	+	0.250848i
$560$	2.07295	+	6.37988i	0.0875981	+	0.269599i
$561$	−0.572949	−	1.76336i	−0.0241899	−	0.0744489i
$562$	−0.982779	+	3.02468i	−0.0414560	+	0.127589i
$563$	−8.69756	+	26.7683i	−0.366558	+	1.12815i	0.582441	+	0.812873i	$0.302098\pi$
$563$	−8.69756	+	26.7683i	−0.366558	+	1.12815i	−0.948999	+	0.315278i	$0.897902\pi$
$564$	1.40983	+	4.33901i	0.0593646	+	0.182705i
$565$	−2.60081	−	8.00448i	−0.109417	−	0.336751i
$566$	3.79837	−	11.6902i	0.159658	−	0.491375i
$567$	18.7082	+	13.5923i	0.785671	+	0.570823i
$568$	3.00000			0.125877
$569$	−14.3713	−	10.4414i	−0.602477	−	0.437725i	0.244280	−	0.969705i	$-0.421448\pi$
$569$	−14.3713	−	10.4414i	−0.602477	−	0.437725i	−0.846757	+	0.531979i	$0.821448\pi$
$570$	4.04508	+	2.93893i	0.169430	+	0.123098i
$571$	−14.0172	+	10.1841i	−0.586602	+	0.426192i	−0.841098	−	0.540882i	$-0.818090\pi$
$571$	−14.0172	+	10.1841i	−0.586602	+	0.426192i	0.254496	+	0.967074i	$0.418090\pi$
$572$	−3.42705	+	2.48990i	−0.143292	+	0.104108i
$573$	1.61146	+	4.95955i	0.0673195	+	0.207188i
$574$	4.41641			0.184337
$575$	−8.81966			−0.367805
$576$	−2.85410			−0.118921
$577$	−13.2877	−	40.8954i	−0.553175	−	1.70250i	−0.700714	−	0.713443i	$-0.747135\pi$
$577$	−13.2877	−	40.8954i	−0.553175	−	1.70250i	0.147538	−	0.989056i	$-0.452865\pi$
$578$	−12.6910	+	9.22054i	−0.527875	+	0.383524i
$579$	−4.52786	+	3.28969i	−0.188172	+	0.136715i
$580$	6.54508	+	20.1437i	0.271770	+	0.836422i
$581$	−10.9894	−	7.98424i	−0.455915	−	0.331242i
$582$	3.65248			0.151400
$583$	−35.8885	−	26.0746i	−1.48635	−	1.07990i
$584$	−2.38197	+	7.33094i	−0.0985665	+	0.303356i
$585$	6.38197			0.263862
$586$	−2.64590	−	8.14324i	−0.109301	−	0.336394i
$587$	−10.5623	+	32.5074i	−0.435953	+	1.34173i	0.456154	+	0.889901i	$0.349227\pi$
$587$	−10.5623	+	32.5074i	−0.435953	+	1.34173i	−0.892107	+	0.451824i	$0.850773\pi$
$588$	−0.236068	+	0.726543i	−0.00973528	+	0.0299621i
$589$	−0.427051	−	1.31433i	−0.0175963	−	0.0541559i
$590$	8.09017	−	5.87785i	0.333067	−	0.241987i
$591$	−1.41641	+	4.35926i	−0.0582632	+	0.179316i
$592$	6.73607	+	4.89404i	0.276851	+	0.201144i
$593$	29.0132			1.19143			0.595714	−	0.803197i	$-0.296869\pi$
$593$	29.0132			1.19143			0.595714	+	0.803197i	$0.296869\pi$
$594$	7.66312	+	5.56758i	0.314422	+	0.228441i
$595$	7.68692			0.315133
$596$	−1.80902	+	1.31433i	−0.0741002	+	0.0538370i
$597$	0.791796	−	0.575274i	0.0324061	−	0.0235444i
$598$	0.545085	+	1.67760i	0.0222902	+	0.0686021i
$599$	8.94427			0.365453			0.182727	−	0.983164i	$-0.441508\pi$
$599$	8.94427			0.365453			0.182727	+	0.983164i	$0.441508\pi$
$600$	0.590170	−	1.81636i	0.0240936	−	0.0741524i
$601$	38.8328			1.58402			0.792012	−	0.610506i	$-0.209034\pi$
$601$	38.8328			1.58402			0.792012	+	0.610506i	$0.209034\pi$
$602$	−5.78115	−	17.7926i	−0.235622	−	0.725171i
$603$	−23.6353	+	17.1720i	−0.962502	+	0.699299i
$604$	7.85410	−	5.70634i	0.319579	−	0.232188i
$605$	−4.79837	+	14.7679i	−0.195082	+	0.600400i
$606$	−0.190983	−	0.138757i	−0.00775815	−	0.00563663i
$607$	−33.8541			−1.37410			−0.687048	−	0.726612i	$-0.741094\pi$
$607$	−33.8541			−1.37410			−0.687048	+	0.726612i	$0.741094\pi$
$608$	4.73607	+	3.44095i	0.192073	+	0.139549i
$609$	−3.35410	+	10.3229i	−0.135915	+	0.418304i
$610$	−6.11803	+	18.8294i	−0.247712	+	0.762379i
$611$	−3.69098	−	11.3597i	−0.149321	−	0.459563i
$612$	−1.01064	+	3.11044i	−0.0408528	+	0.125732i
$613$	−6.62461	+	20.3885i	−0.267566	+	0.823482i	0.723526	+	0.690297i	$0.242520\pi$
$613$	−6.62461	+	20.3885i	−0.267566	+	0.823482i	−0.991091	+	0.133185i	$0.957480\pi$
$614$	7.14590	+	21.9928i	0.288385	+	0.887558i
$615$	−1.01722	−	0.739054i	−0.0410183	−	0.0298015i
$616$	3.92705	−	12.0862i	0.158225	−	0.486968i
$617$	−11.6180	−	8.44100i	−0.467724	−	0.339822i	0.328829	−	0.944389i	$-0.393346\pi$
$617$	−11.6180	−	8.44100i	−0.467724	−	0.339822i	−0.796554	+	0.604568i	$0.793346\pi$
$618$	−5.02129			−0.201986
$619$	−37.9894	−	27.6009i	−1.52692	−	1.10937i	−0.957920	−	0.287037i	$-0.907330\pi$
$619$	−37.9894	−	27.6009i	−1.52692	−	1.10937i	−0.569002	−	0.822336i	$-0.692670\pi$
$620$	−0.427051	+	0.310271i	−0.0171508	+	0.0124608i
$621$	3.19098	−	2.31838i	0.128050	−	0.0930336i
$622$	−8.01722	+	5.82485i	−0.321461	+	0.233555i
$623$	−4.14590	−	12.7598i	−0.166102	−	0.511209i
$624$	−0.381966			−0.0152909
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	16.5623			0.661963
$627$	−2.92705	−	9.00854i	−0.116895	−	0.359766i
$628$	−3.69098	+	2.68166i	−0.147286	+	0.107010i
$629$	7.71885	−	5.60807i	0.307771	−	0.223608i
$630$	−15.4894	+	11.2537i	−0.617111	+	0.448357i
$631$	36.2705	+	26.3521i	1.44391	+	1.04906i	0.987208	+	0.159438i	$0.0509681\pi$
$631$	36.2705	+	26.3521i	1.44391	+	1.04906i	0.456698	+	0.889622i	$0.349032\pi$
$632$	7.23607			0.287835
$633$	−6.88197	−	5.00004i	−0.273534	−	0.198734i
$634$	−2.59017	+	7.97172i	−0.102869	+	0.316598i
$635$	−6.38197	−	4.63677i	−0.253261	−	0.184005i
$636$	−1.23607	−	3.80423i	−0.0490133	−	0.150847i
$637$	0.618034	−	1.90211i	0.0244874	−	0.0753645i
$638$	12.3992	−	38.1608i	0.490889	−	1.51080i
$639$	2.64590	+	8.14324i	0.104670	+	0.322141i
$640$	0.690983	−	2.12663i	0.0273135	−	0.0840623i
$641$	−9.38197	+	28.8747i	−0.370565	+	1.14048i	0.575857	+	0.817551i	$0.304669\pi$
$641$	−9.38197	+	28.8747i	−0.370565	+	1.14048i	−0.946422	+	0.322932i	$0.895331\pi$
$642$	0.336881	+	0.244758i	0.0132956	+	0.00965984i
$643$	−31.7639			−1.25265			−0.626324	−	0.779563i	$-0.715441\pi$
$643$	−31.7639			−1.25265			−0.626324	+	0.779563i	$0.715441\pi$
$644$	−4.28115	−	3.11044i	−0.168701	−	0.122568i
$645$	−1.64590	+	5.06555i	−0.0648072	+	0.199456i
$646$	5.42705	−	3.94298i	0.213524	−	0.155135i
$647$	19.1353	−	13.9026i	0.752284	−	0.546567i	−0.144250	−	0.989541i	$-0.546077\pi$
$647$	19.1353	−	13.9026i	0.752284	−	0.546567i	0.896534	+	0.442975i	$0.146077\pi$
$648$	−2.38197	−	7.33094i	−0.0935725	−	0.287986i
$649$	−18.9443			−0.743628
$650$	−1.54508	+	4.75528i	−0.0606032	+	0.186518i
$651$	−0.270510			−0.0106021
$652$	0.572949	+	1.76336i	0.0224384	+	0.0690583i
$653$	6.95492	−	5.05304i	0.272167	−	0.197741i	−0.443327	−	0.896360i	$-0.646202\pi$
$653$	6.95492	−	5.05304i	0.272167	−	0.197741i	0.715494	+	0.698619i	$0.246202\pi$
$654$	4.63525	−	3.36771i	0.181253	−	0.131688i
$655$	36.7082			1.43431
$656$	−1.19098	−	0.865300i	−0.0465001	−	0.0337843i
$657$	−22.0000			−0.858302
$658$	28.9894	+	21.0620i	1.13012	+	0.821082i
$659$	−7.92705	+	24.3970i	−0.308794	+	0.950370i	0.669440	+	0.742866i	$0.266534\pi$
$659$	−7.92705	+	24.3970i	−0.308794	+	0.950370i	−0.978234	+	0.207504i	$0.933466\pi$
$660$	−2.92705	+	2.12663i	−0.113935	+	0.0827788i
$661$	−8.42705	−	25.9358i	−0.327774	−	1.00879i	−0.970173	−	0.242415i	$-0.922061\pi$
$661$	−8.42705	−	25.9358i	−0.327774	−	1.00879i	0.642398	−	0.766371i	$-0.277939\pi$
$662$	4.80902	−	14.8006i	0.186908	−	0.575243i
$663$	−0.135255	+	0.416272i	−0.00525287	+	0.0161667i
$664$	1.39919	+	4.30625i	0.0542990	+	0.167115i
$665$	39.2705			1.52285
$666$	−7.34346	+	22.6008i	−0.284553	+	0.875765i
$667$	−13.5172	−	9.82084i	−0.523389	−	0.380264i
$668$	13.3820			0.517764
$669$	−2.78115	−	2.02063i	−0.107526	−	0.0781219i
$670$	−7.07295	−	21.7683i	−0.273252	−	0.840983i
$671$	30.3435	−	22.0458i	1.17140	−	0.851069i
$672$	0.927051	−	0.673542i	0.0357618	−	0.0259824i
$673$	1.00000	+	3.07768i	0.0385472	+	0.118636i	0.968478	−	0.249097i	$-0.0801339\pi$
$673$	1.00000	+	3.07768i	0.0385472	+	0.118636i	−0.929931	+	0.367733i	$0.880134\pi$
$674$	4.58359			0.176553
$675$	11.1803			0.430331
$676$	−12.0000			−0.461538
$677$	2.59017	+	7.97172i	0.0995483	+	0.306378i	0.988412	−	0.151793i	$-0.0485047\pi$
$677$	2.59017	+	7.97172i	0.0995483	+	0.306378i	−0.888864	+	0.458171i	$0.848505\pi$
$678$	−1.16312	+	0.845055i	−0.0446693	+	0.0324542i
$679$	23.2082	−	16.8617i	0.890649	−	0.647094i
$680$	−2.07295	−	1.50609i	−0.0794940	−	0.0577557i
$681$	9.07295	+	6.59188i	0.347676	+	0.252602i
$682$	1.00000			0.0382920
$683$	9.19098	+	6.67764i	0.351683	+	0.255513i	0.749575	−	0.661920i	$-0.230258\pi$
$683$	9.19098	+	6.67764i	0.351683	+	0.255513i	−0.397892	+	0.917432i	$0.630258\pi$
$684$	−5.16312	+	15.8904i	−0.197417	+	0.607586i
$685$	−3.51722	−	10.8249i	−0.134386	−	0.413598i
$686$	−4.63525	−	14.2658i	−0.176975	−	0.544673i
$687$	0.302439	−	0.930812i	0.0115388	−	0.0355127i
$688$	−1.92705	+	5.93085i	−0.0734681	+	0.226112i
$689$	3.23607	+	9.95959i	0.123284	+	0.379430i
$690$	0.465558	+	1.43284i	0.0177235	+	0.0545473i
$691$	−9.97214	+	30.6911i	−0.379358	+	1.16754i	0.561133	+	0.827725i	$0.310366\pi$
$691$	−9.97214	+	30.6911i	−0.379358	+	1.16754i	−0.940491	+	0.339818i	$0.889634\pi$
$692$	1.00000	+	0.726543i	0.0380143	+	0.0276190i
$693$	36.2705			1.37780
$694$	−17.0623	−	12.3965i	−0.647676	−	0.470564i
$695$	−9.63525	−	7.00042i	−0.365486	−	0.265541i
$696$	2.92705	−	2.12663i	0.110950	−	0.0806096i
$697$	−1.36475	+	0.991545i	−0.0516934	+	0.0375575i
$698$	5.48936	+	16.8945i	0.207775	+	0.639466i
$699$	−5.45898			−0.206478
$700$	−4.63525	−	14.2658i	−0.175196	−	0.539198i
$701$	18.1803			0.686662			0.343331	−	0.939214i	$-0.388445\pi$
$701$	18.1803			0.686662			0.343331	+	0.939214i	$0.388445\pi$
$702$	−0.690983	−	2.12663i	−0.0260795	−	0.0802644i
$703$	39.4336	−	28.6502i	1.48727	−	1.08056i
$704$	−3.42705	+	2.48990i	−0.129162	+	0.0938416i
$705$	−3.15248	−	9.70232i	−0.118729	−	0.365411i
$706$	−17.1803	−	12.4822i	−0.646591	−	0.469776i
$707$	−1.85410			−0.0697307
$708$	−1.38197	−	1.00406i	−0.0519375	−	0.0377348i
$709$	3.78115	−	11.6372i	0.142004	−	0.437044i	−0.854609	−	0.519271i	$-0.826203\pi$
$709$	3.78115	−	11.6372i	0.142004	−	0.437044i	0.996614	+	0.0822274i	$0.0262034\pi$
$710$	−6.70820			−0.251754
$711$	6.38197	+	19.6417i	0.239342	+	0.736620i
$712$	−1.38197	+	4.25325i	−0.0517914	+	0.159397i
$713$	0.128677	−	0.396027i	0.00481900	−	0.0148313i
$714$	−0.405765	−	1.24882i	−0.0151854	−	0.0467357i
$715$	7.66312	−	5.56758i	0.286584	−	0.208216i
$716$	3.45492	−	10.6331i	0.129116	−	0.397379i
$717$	−2.13525	−	1.55135i	−0.0797426	−	0.0579364i
$718$	8.09017			0.301922
$719$	−9.30902	−	6.76340i	−0.347168	−	0.252232i	0.400512	−	0.916291i	$-0.368832\pi$
$719$	−9.30902	−	6.76340i	−0.347168	−	0.252232i	−0.747680	+	0.664059i	$0.768832\pi$
$720$	6.38197			0.237842
$721$	−31.9058	+	23.1809i	−1.18823	+	0.863302i
$722$	12.3541	−	8.97578i	0.459772	−	0.334044i
$723$	−1.84346	−	5.67358i	−0.0685590	−	0.211003i
$724$	5.41641			0.201299
$725$	−14.6353	−	45.0427i	−0.543540	−	1.67284i
$726$	2.65248			0.0984426
$727$	0.819660	+	2.52265i	0.0303995	+	0.0935601i	0.965105	−	0.261863i	$-0.0843368\pi$
$727$	0.819660	+	2.52265i	0.0303995	+	0.0935601i	−0.934706	+	0.355423i	$0.884337\pi$
$728$	−2.42705	+	1.76336i	−0.0899525	+	0.0653543i
$729$	15.7254	−	11.4252i	0.582423	−	0.423155i
$730$	5.32624	−	16.3925i	0.197133	−	0.606713i
$731$	5.78115	+	4.20025i	0.213824	+	0.155352i
$732$	3.38197			0.125001
$733$	−25.7082	−	18.6781i	−0.949554	−	0.689891i	0.00114721	−	0.999999i	$-0.499635\pi$
$733$	−25.7082	−	18.6781i	−0.949554	−	0.689891i	−0.950701	+	0.310108i	$0.899635\pi$
$734$	−10.9828	+	33.8015i	−0.405382	+	1.24764i
$735$	0.527864	−	1.62460i	0.0194706	−	0.0599242i
$736$	0.545085	+	1.67760i	0.0200921	+	0.0618371i
$737$	−13.3992	+	41.2385i	−0.493565	+	1.51904i
$738$	1.29837	−	3.99598i	0.0477938	−	0.147094i
$739$	9.27051	+	28.5317i	0.341021	+	1.04956i	0.963679	+	0.267062i	$0.0860527\pi$
$739$	9.27051	+	28.5317i	0.341021	+	1.04956i	−0.622658	+	0.782494i	$0.713947\pi$
$740$	−15.0623	−	10.9434i	−0.553701	−	0.402288i
$741$	−0.690983	+	2.12663i	−0.0253839	+	0.0781236i
$742$	−25.4164	−	18.4661i	−0.933066	−	0.677912i
$743$	15.2705			0.560221			0.280110	−	0.959968i	$-0.409629\pi$
$743$	15.2705			0.560221			0.280110	+	0.959968i	$0.409629\pi$
$744$	0.0729490	+	0.0530006i	0.00267444	+	0.00194309i
$745$	4.04508	−	2.93893i	0.148200	−	0.107674i
$746$	−9.51722	+	6.91467i	−0.348450	+	0.253164i
$747$	−10.4549	+	7.59594i	−0.382525	+	0.277921i
$748$	1.50000	+	4.61653i	0.0548454	+	0.168797i
$749$	3.27051			0.119502
$750$	−1.31966	+	4.06150i	−0.0481872	+	0.148305i
$751$	7.85410			0.286600			0.143300	−	0.989679i	$-0.454229\pi$
$751$	7.85410			0.286600			0.143300	+	0.989679i	$0.454229\pi$
$752$	−3.69098	−	11.3597i	−0.134596	−	0.414245i
$753$	0.253289	−	0.184025i	0.00923036	−	0.00670625i
$754$	−7.66312	+	5.56758i	−0.279074	+	0.202759i
$755$	−17.5623	+	12.7598i	−0.639158	+	0.464375i
$756$	5.42705	+	3.94298i	0.197380	+	0.143405i
$757$	−16.4164			−0.596664			−0.298332	−	0.954462i	$-0.596430\pi$
$757$	−16.4164			−0.596664			−0.298332	+	0.954462i	$0.596430\pi$
$758$	7.66312	+	5.56758i	0.278337	+	0.202224i
$759$	0.881966	−	2.71441i	0.0320133	−	0.0985269i
$760$	−10.5902	−	7.69421i	−0.384146	−	0.279098i
$761$	8.31966	+	25.6053i	0.301587	+	0.928191i	0.980929	+	0.194368i	$0.0622656\pi$
$761$	8.31966	+	25.6053i	0.301587	+	0.928191i	−0.679341	+	0.733823i	$0.737734\pi$
$762$	−0.416408	+	1.28157i	−0.0150849	+	0.0464264i
$763$	13.9058	−	42.7975i	0.503422	−	1.54938i
$764$	−4.21885	−	12.9843i	−0.152633	−	0.469755i
$765$	2.25987	−	6.95515i	0.0817057	−	0.251464i
$766$	−3.50000	+	10.7719i	−0.126460	+	0.389204i
$767$	3.61803	+	2.62866i	0.130640	+	0.0949153i
$768$	−0.381966			−0.0137830
$769$	−2.76393	−	2.00811i	−0.0996699	−	0.0724144i	0.536834	−	0.843688i	$-0.319620\pi$
$769$	−2.76393	−	2.00811i	−0.0996699	−	0.0724144i	−0.636504	+	0.771273i	$0.719620\pi$
$770$	−8.78115	+	27.0256i	−0.316451	+	0.973935i
$771$	7.95492	−	5.77958i	0.286489	−	0.208147i
$772$	11.8541	−	8.61251i	0.426638	−	0.309971i
$773$	9.51722	+	29.2910i	0.342311	+	1.05352i	0.963008	+	0.269473i	$0.0868496\pi$
$773$	9.51722	+	29.2910i	0.342311	+	1.05352i	−0.620697	+	0.784050i	$0.713150\pi$
$774$	−17.7984			−0.639749
$775$	0.954915	−	0.693786i	0.0343016	−	0.0249215i
$776$	−9.56231			−0.343267
$777$	−2.94834	−	9.07405i	−0.105771	−	0.325530i
$778$	14.7361	−	10.7064i	0.528314	−	0.383842i
$779$	−6.97214	+	5.06555i	−0.249803	+	0.181492i
$780$	0.854102			0.0305818
$781$	10.2812	+	7.46969i	0.367889	+	0.267287i
$782$	2.02129			0.0722810
$783$	17.1353	+	12.4495i	0.612364	+	0.444909i
$784$	0.618034	−	1.90211i	0.0220726	−	0.0679326i
$785$	8.25329	−	5.99637i	0.294573	−	0.214019i
$786$	−1.93769	−	5.96361i	−0.0691153	−	0.212715i
$787$	−3.52786	+	10.8576i	−0.125755	+	0.387033i	−0.994038	−	0.109036i	$-0.965224\pi$
$787$	−3.52786	+	10.8576i	−0.125755	+	0.387033i	0.868283	+	0.496069i	$0.165224\pi$
$788$	3.70820	−	11.4127i	0.132099	−	0.406560i
$789$	−0.545085	−	1.67760i	−0.0194055	−	0.0597241i
$790$	−16.1803			−0.575671
$791$	−3.48936	+	10.7391i	−0.124067	+	0.381840i
$792$	−9.78115	−	7.10642i	−0.347558	−	0.252516i
$793$	−8.85410			−0.314418
$794$	−8.28115	−	6.01661i	−0.293887	−	0.213521i
$795$	2.76393	+	8.50651i	0.0980266	+	0.301695i
$796$	−2.07295	+	1.50609i	−0.0734737	+	0.0533818i
$797$	−4.54508	+	3.30220i	−0.160995	+	0.116970i	−0.665366	−	0.746517i	$-0.731724\pi$
$797$	−4.54508	+	3.30220i	−0.160995	+	0.116970i	0.504371	+	0.863487i	$0.331724\pi$
$798$	−2.07295	−	6.37988i	−0.0733816	−	0.225845i
$799$	−13.6869			−0.484208
$800$	−1.54508	+	4.75528i	−0.0546270	+	0.168125i
$801$	−12.7639			−0.450991
$802$	4.38197	+	13.4863i	0.154733	+	0.476218i
$803$	−26.4164	+	19.1926i	−0.932215	+	0.677294i
$804$	−3.16312	+	2.29814i	−0.111555	+	0.0810492i
$805$	9.57295	+	6.95515i	0.337402	+	0.245137i
$806$	−0.190983	−	0.138757i	−0.00672709	−	0.00488752i
$807$	−0.729490			−0.0256793
$808$	0.500000	+	0.363271i	0.0175899	+	0.0127798i
$809$	−0.690983	+	2.12663i	−0.0242937	+	0.0747682i	−0.962468	−	0.271394i	$-0.912515\pi$
$809$	−0.690983	+	2.12663i	−0.0242937	+	0.0747682i	0.938175	+	0.346162i	$0.112515\pi$
$810$	5.32624	+	16.3925i	0.187145	+	0.575973i
$811$	12.6525	+	38.9403i	0.444289	+	1.36738i	0.883262	+	0.468880i	$0.155342\pi$
$811$	12.6525	+	38.9403i	0.444289	+	1.36738i	−0.438974	+	0.898500i	$0.644658\pi$
$812$	8.78115	−	27.0256i	0.308158	−	0.948413i
$813$	−3.36475	+	10.3556i	−0.118007	+	0.363187i
$814$	10.8992	+	33.5442i	0.382016	+	1.17573i
$815$	−1.28115	−	3.94298i	−0.0448768	−	0.138117i
$816$	−0.135255	+	0.416272i	−0.00473487	+	0.0145724i
$817$	29.5344	+	21.4580i	1.03328	+	0.750721i
$818$	6.70820			0.234547
$819$	−6.92705	−	5.03280i	−0.242051	−	0.175860i
$820$	2.66312	+	1.93487i	0.0930001	+	0.0675686i
$821$	−31.6803	+	23.0171i	−1.10565	+	0.803303i	−0.981973	−	0.189020i	$-0.939469\pi$
$821$	−31.6803	+	23.0171i	−1.10565	+	0.803303i	−0.123678	+	0.992322i	$0.539469\pi$
$822$	−1.57295	+	1.14281i	−0.0548629	+	0.0398602i
$823$	−6.43769	−	19.8132i	−0.224404	−	0.690644i	−0.998352	−	0.0573946i	$-0.981721\pi$
$823$	−6.43769	−	19.8132i	−0.224404	−	0.690644i	0.773948	−	0.633250i	$-0.218279\pi$
$824$	13.1459			0.457959
$825$	6.54508	−	4.75528i	0.227871	−	0.165558i
$826$	−13.4164			−0.466817
$827$	−1.55573	−	4.78804i	−0.0540980	−	0.166496i	0.920357	−	0.391079i	$-0.127898\pi$
$827$	−1.55573	−	4.78804i	−0.0540980	−	0.166496i	−0.974455	+	0.224583i	$0.927898\pi$
$828$	−4.07295	+	2.95917i	−0.141545	+	0.102838i
$829$	−43.2148	+	31.3974i	−1.50091	+	1.09048i	−0.530895	+	0.847438i	$0.678144\pi$
$829$	−43.2148	+	31.3974i	−1.50091	+	1.09048i	−0.970017	+	0.243038i	$0.921856\pi$
$830$	−3.12868	−	9.62908i	−0.108598	−	0.334230i
$831$	0.0901699	+	0.0655123i	0.00312796	+	0.00227260i
$832$	1.00000			0.0346688
$833$	−1.85410	−	1.34708i	−0.0642408	−	0.0466737i
$834$	−0.628677	+	1.93487i	−0.0217693	+	0.0669990i
$835$	−29.9230			−1.03553
$836$	7.66312	+	23.5847i	0.265035	+	0.815692i
$837$	−0.163119	+	0.502029i	−0.00563822	+	0.0173526i
$838$	−7.03444	+	21.6498i	−0.243001	+	0.747879i
$839$	−17.0729	−	52.5451i	−0.589424	−	1.81406i	−0.580729	−	0.814097i	$-0.697232\pi$
$839$	−17.0729	−	52.5451i	−0.589424	−	1.81406i	−0.00869515	−	0.999962i	$-0.502768\pi$
$840$	−2.07295	+	1.50609i	−0.0715235	+	0.0519649i
$841$	18.7639	−	57.7494i	0.647032	−	1.99136i
$842$	17.2082	+	12.5025i	0.593034	+	0.430864i
$843$	−1.21478			−0.0418393
$844$	18.0172	+	13.0903i	0.620178	+	0.450586i
$845$	26.8328			0.923077
$846$	27.5795	−	20.0377i	0.948204	−	0.688910i
$847$	16.8541	−	12.2452i	0.579114	−	0.420751i
$848$	3.23607	+	9.95959i	0.111127	+	0.342014i
$849$	4.69505			0.161134
$850$	4.63525	+	3.36771i	0.158988	+	0.115511i
$851$	14.6869			0.503461
$852$	0.354102	+	1.08981i	0.0121313	+	0.0373364i
$853$	14.6803	−	10.6659i	0.502645	−	0.365193i	−0.307381	−	0.951586i	$-0.599453\pi$
$853$	14.6803	−	10.6659i	0.502645	−	0.365193i	0.810026	+	0.586393i	$0.199453\pi$
$854$	21.4894	−	15.6129i	0.735351	−	0.534264i
$855$	11.5451	−	35.5321i	0.394834	−	1.21517i
$856$	−0.881966	−	0.640786i	−0.0301450	−	0.0219016i
$857$	−56.3394			−1.92452			−0.962259	−	0.272137i	$-0.912270\pi$
$857$	−56.3394			−1.92452			−0.962259	+	0.272137i	$0.912270\pi$
$858$	−1.30902	−	0.951057i	−0.0446891	−	0.0324685i
$859$	10.6287	−	32.7117i	0.362646	−	1.11611i	−0.588796	−	0.808281i	$-0.700398\pi$
$859$	10.6287	−	32.7117i	0.362646	−	1.11611i	0.951442	−	0.307828i	$-0.0996020\pi$
$860$	4.30902	−	13.2618i	0.146936	−	0.452223i
$861$	0.521286	+	1.60435i	0.0177654	+	0.0546762i
$862$	−8.05573	+	24.7930i	−0.274379	+	0.844452i
$863$	−3.47214	+	10.6861i	−0.118193	+	0.363760i	−0.992600	−	0.121433i	$-0.961251\pi$
$863$	−3.47214	+	10.6861i	−0.118193	+	0.363760i	0.874407	+	0.485194i	$0.161251\pi$
$864$	−0.690983	−	2.12663i	−0.0235077	−	0.0723493i
$865$	−2.23607	−	1.62460i	−0.0760286	−	0.0552380i
$866$	6.60081	−	20.3152i	0.224305	−	0.690339i
$867$	−4.84752	−	3.52193i	−0.164631	−	0.119611i
$868$	0.708204			0.0240380
$869$	24.7984	+	18.0171i	0.841227	+	0.611187i
$870$	−6.54508	+	4.75528i	−0.221899	+	0.161219i
$871$	8.28115	−	6.01661i	0.280596	−	0.203865i
$872$	−12.1353	+	8.81678i	−0.410952	+	0.298574i
$873$	−8.43363	−	25.9560i	−0.285435	−	0.878479i
$874$	10.3262			0.349290
$875$	10.3647	+	31.8994i	0.350392	+	1.07840i
$876$	−2.94427			−0.0994777
$877$	1.37132	+	4.22050i	0.0463063	+	0.142516i	0.971536	−	0.236890i	$-0.0761282\pi$
$877$	1.37132	+	4.22050i	0.0463063	+	0.142516i	−0.925230	+	0.379406i	$0.876128\pi$
$878$	20.7533	−	15.0781i	0.700390	−	0.508863i
$879$	2.64590	−	1.92236i	0.0892439	−	0.0648395i
$880$	7.66312	−	5.56758i	0.258324	−	0.187683i
$881$	−30.8885	−	22.4418i	−1.04066	−	0.756085i	−0.0702469	−	0.997530i	$-0.522379\pi$
$881$	−30.8885	−	22.4418i	−1.04066	−	0.756085i	−0.970415	+	0.241445i	$0.922379\pi$
$882$	5.70820			0.192205
$883$	33.7254	+	24.5030i	1.13495	+	0.824590i	0.986408	−	0.164316i	$-0.0525416\pi$
$883$	33.7254	+	24.5030i	1.13495	+	0.824590i	0.148543	+	0.988906i	$0.452542\pi$
$884$	0.354102	−	1.08981i	0.0119097	−	0.0366544i
$885$	3.09017	+	2.24514i	0.103875	+	0.0754696i
$886$	−6.00000	−	18.4661i	−0.201574	−	0.620381i
$887$	10.2533	−	31.5564i	0.344272	−	1.05956i	−0.617701	−	0.786413i	$-0.711936\pi$
$887$	10.2533	−	31.5564i	0.344272	−	1.05956i	0.961973	−	0.273146i	$-0.0880643\pi$
$888$	−0.982779	+	3.02468i	−0.0329799	+	0.101502i
$889$	3.27051	+	10.0656i	0.109689	+	0.337589i
$890$	3.09017	−	9.51057i	0.103583	−	0.318795i
$891$	10.0902	−	31.0543i	0.338033	−	1.04036i
$892$	7.28115	+	5.29007i	0.243791	+	0.177125i
$893$	−69.9230			−2.33988
$894$	−0.690983	−	0.502029i	−0.0231099	−	0.0167903i
$895$	−7.72542	+	23.7764i	−0.258232	+	0.794758i
$896$	−2.42705	+	1.76336i	−0.0810821	+	0.0589096i
$897$	−0.545085	+	0.396027i	−0.0181999	+	0.0132230i
$898$	1.21885	+	3.75123i	0.0406735	+	0.125180i
$899$	2.23607			0.0745770
$900$	−14.2705			−0.475684
$901$	12.0000			0.399778
$902$	−1.92705	−	5.93085i	−0.0641638	−	0.197476i
$903$	5.78115	−	4.20025i	0.192385	−	0.139776i
$904$	3.04508	−	2.21238i	0.101278	−	0.0735828i
$905$	−12.1115			−0.402598
$906$	3.00000	+	2.17963i	0.0996683	+	0.0724133i
$907$	25.6180			0.850633			0.425316	−	0.905045i	$-0.360163\pi$
$907$	25.6180			0.850633			0.425316	+	0.905045i	$0.360163\pi$
$908$	−23.7533	−	17.2578i	−0.788281	−	0.572719i
$909$	−0.545085	+	1.67760i	−0.0180793	+	0.0556424i
$910$	5.42705	−	3.94298i	0.179905	−	0.130709i
$911$	−5.07295	−	15.6129i	−0.168074	−	0.517280i	0.831175	−	0.556010i	$-0.187669\pi$
$911$	−5.07295	−	15.6129i	−0.168074	−	0.517280i	−0.999250	+	0.0387308i	$0.987669\pi$
$912$	−0.690983	+	2.12663i	−0.0228807	+	0.0704197i
$913$	−5.92705	+	18.2416i	−0.196157	+	0.603708i
$914$	−12.4271	−	38.2465i	−0.411050	−	1.26508i
$915$	−7.56231			−0.250002
$916$	−0.791796	+	2.43690i	−0.0261617	+	0.0805174i
$917$	−39.8435	−	28.9480i	−1.31575	−	0.955946i
$918$	−2.56231			−0.0845687
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	0.660649	−	0.750695i	$-0.270281\pi$
$919$	4.57295	+	3.32244i	0.150848	+	0.109597i	−0.509801	+	0.860292i	$0.670281\pi$
$920$	−1.21885	−	3.75123i	−0.0401842	−	0.123674i
$921$	−7.14590	+	5.19180i	−0.235465	+	0.171076i
$922$	4.70820	−	3.42071i	0.155056	−	0.112655i
$923$	−0.927051	−	2.85317i	−0.0305143	−	0.0939132i
$924$	4.85410			0.159688
$925$	33.6803	+	24.4702i	1.10740	+	0.804575i
$926$	34.9787			1.14947
$927$	11.5942	+	35.6834i	0.380805	+	1.17200i
$928$	−7.66312	+	5.56758i	−0.251554	+	0.182765i
$929$	42.7877	−	31.0871i	1.40382	−	1.01993i	0.409635	−	0.912250i	$-0.365656\pi$
$929$	42.7877	−	31.0871i	1.40382	−	1.01993i	0.994185	−	0.107685i	$-0.0343439\pi$
$930$	−0.163119	−	0.118513i	−0.00534888	−	0.00388619i
$931$	−9.47214	−	6.88191i	−0.310437	−	0.225545i
$932$	14.2918			0.468143
$933$	−3.06231	−	2.22490i	−0.100255	−	0.0728398i
$934$	5.92705	−	18.2416i	0.193939	−	0.596883i
$935$	−3.35410	−	10.3229i	−0.109691	−	0.337594i
$936$	0.881966	+	2.71441i	0.0288280	+	0.0887233i
$937$	12.9549	−	39.8711i	0.423219	−	1.30253i	−0.481471	−	0.876462i	$-0.659897\pi$
$937$	12.9549	−	39.8711i	0.423219	−	1.30253i	0.904690	−	0.426071i	$-0.140103\pi$
$938$	−9.48936	+	29.2052i	−0.309838	+	0.953585i
$939$	1.95492	+	6.01661i	0.0637962	+	0.196345i
$940$	8.25329	+	25.4010i	0.269193	+	0.828490i
$941$	−2.89919	+	8.92278i	−0.0945108	+	0.290874i	−0.987126	−	0.159945i	$-0.948868\pi$
$941$	−2.89919	+	8.92278i	−0.0945108	+	0.290874i	0.892615	+	0.450820i	$0.148868\pi$
$942$	−1.40983	−	1.02430i	−0.0459347	−	0.0333735i
$943$	−2.59675			−0.0845617
$944$	3.61803	+	2.62866i	0.117757	+	0.0855555i
$945$	−12.1353	−	8.81678i	−0.394760	−	0.286810i
$946$	−21.3713	+	15.5272i	−0.694842	+	0.504832i
$947$	31.8607	−	23.1481i	1.03533	−	0.752213i	0.0659639	−	0.997822i	$-0.478988\pi$
$947$	31.8607	−	23.1481i	1.03533	−	0.752213i	0.969369	+	0.245609i	$0.0789878\pi$
$948$	0.854102	+	2.62866i	0.0277399	+	0.0853748i
$949$	7.70820			0.250219
$950$	23.6803	+	17.2048i	0.768292	+	0.558197i
$951$	−3.20163			−0.103820
$952$	1.06231	+	3.26944i	0.0344295	+	0.105963i
$953$	−36.0967	+	26.2258i	−1.16929	+	0.849538i	−0.990924	−	0.134427i	$-0.957081\pi$
$953$	−36.0967	+	26.2258i	−1.16929	+	0.849538i	−0.178365	+	0.983964i	$0.557081\pi$
$954$	−24.1803	+	17.5680i	−0.782867	+	0.568786i
$955$	9.43363	+	29.0337i	0.305265	+	0.939509i
$956$	5.59017	+	4.06150i	0.180799	+	0.131358i
$957$	15.3262			0.495427
$958$	−12.2984	−	8.93529i	−0.397342	−	0.288686i
$959$	−4.71885	+	14.5231i	−0.152380	+	0.468976i
$960$	0.854102			0.0275660
$961$	−9.56231	−	29.4298i	−0.308461	−	0.949347i
$962$	2.57295	−	7.91872i	0.0829552	−	0.255310i
$963$	0.961493	−	2.95917i	0.0309837	−	0.0953579i
$964$	4.82624	+	14.8536i	0.155443	+	0.478403i
$965$	−26.5066	+	19.2582i	−0.853277	+	0.619942i
$966$	0.624612	−	1.92236i	0.0200966	−	0.0618508i
$967$	10.6180	+	7.71445i	0.341453	+	0.248080i	0.745275	−	0.666758i	$-0.232318\pi$
$967$	10.6180	+	7.71445i	0.341453	+	0.248080i	−0.403822	+	0.914838i	$0.632318\pi$
$968$	−6.94427			−0.223197
$969$	2.07295	+	1.50609i	0.0665927	+	0.0483824i
$970$	21.3820			0.686534
$971$	−4.90983	+	3.56720i	−0.157564	+	0.114477i	−0.663774	−	0.747934i	$-0.731046\pi$
$971$	−4.90983	+	3.56720i	−0.157564	+	0.114477i	0.506210	+	0.862410i	$0.331046\pi$
$972$	7.80902	−	5.67358i	0.250474	−	0.181980i
$973$	4.93769	+	15.1967i	0.158295	+	0.487183i
$974$	−22.1246			−0.708918
$975$	−1.90983			−0.0611635
$976$	−8.85410			−0.283413
$977$	15.4549	+	47.5653i	0.494447	+	1.52175i	0.817817	+	0.575478i	$0.195184\pi$
$977$	15.4549	+	47.5653i	0.494447	+	1.52175i	−0.323371	+	0.946272i	$0.604816\pi$
$978$	−0.572949	+	0.416272i	−0.0183209	+	0.0133109i
$979$	−15.3262	+	11.1352i	−0.489829	+	0.355881i
$980$	−1.38197	+	4.25325i	−0.0441453	+	0.135865i
$981$	−34.6353	−	25.1640i	−1.10582	−	0.803424i
$982$	−19.2361			−0.613848
$983$	−31.1353	−	22.6211i	−0.993060	−	0.721501i	−0.0324712	−	0.999473i	$-0.510338\pi$
$983$	−31.1353	−	22.6211i	−0.993060	−	0.721501i	−0.960589	+	0.277972i	$0.910338\pi$
$984$	0.173762	−	0.534785i	0.00553933	−	0.0170483i
$985$	−8.29180	+	25.5195i	−0.264199	+	0.813120i
$986$	3.35410	+	10.3229i	0.106816	+	0.328747i
$987$	−4.22949	+	13.0170i	−0.134626	+	0.414337i
$988$	1.80902	−	5.56758i	0.0575525	−	0.177128i
$989$	3.39919	+	10.4616i	0.108088	+	0.332660i
$990$	21.8713	+	15.8904i	0.695116	+	0.505032i
$991$	−1.06637	+	3.28195i	−0.0338744	+	0.104255i	−0.966564	−	0.256425i	$-0.917455\pi$
$991$	−1.06637	+	3.28195i	−0.0338744	+	0.104255i	0.932690	+	0.360680i	$0.117455\pi$
$992$	−0.190983	−	0.138757i	−0.00606372	−	0.00440555i
$993$	5.94427			0.188636
$994$	7.28115	+	5.29007i	0.230944	+	0.167791i
$995$	4.63525	−	3.36771i	0.146947	−	0.106764i
$996$	−1.39919	+	1.01657i	−0.0443349	+	0.0322112i
$997$	−22.0451	+	16.0167i	−0.698175	+	0.507254i	−0.879337	−	0.476199i	$-0.842014\pi$
$997$	−22.0451	+	16.0167i	−0.698175	+	0.507254i	0.181162	+	0.983453i	$0.442014\pi$
$998$	−10.5517	−	32.4747i	−0.334007	−	1.02797i
$999$	−18.6180			−0.589049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.2.d.a.31.1	yes	4
3.2	odd	2		450.2.h.a.181.1		4
4.3	odd	2		400.2.u.c.81.1		4
5.2	odd	4		250.2.e.b.99.2		8
5.3	odd	4		250.2.e.b.99.1		8
5.4	even	2		250.2.d.a.151.1		4
25.2	odd	20		1250.2.b.b.1249.1		4
25.3	odd	20		250.2.e.b.149.2		8
25.4	even	10		250.2.d.a.101.1		4
25.11	even	5		1250.2.a.a.1.2		2
25.14	even	10		1250.2.a.d.1.1		2
25.21	even	5	inner	50.2.d.a.21.1	✓	4
25.22	odd	20		250.2.e.b.149.1		8
25.23	odd	20		1250.2.b.b.1249.4		4
75.71	odd	10		450.2.h.a.271.1		4
100.11	odd	10		10000.2.a.n.1.1		2
100.39	odd	10		10000.2.a.a.1.2		2
100.71	odd	10		400.2.u.c.321.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.21.1	✓	4	25.21	even	5	inner
50.2.d.a.31.1	yes	4	1.1	even	1	trivial
250.2.d.a.101.1		4	25.4	even	10
250.2.d.a.151.1		4	5.4	even	2
250.2.e.b.99.1		8	5.3	odd	4
250.2.e.b.99.2		8	5.2	odd	4
250.2.e.b.149.1		8	25.22	odd	20
250.2.e.b.149.2		8	25.3	odd	20
400.2.u.c.81.1		4	4.3	odd	2
400.2.u.c.321.1		4	100.71	odd	10
450.2.h.a.181.1		4	3.2	odd	2
450.2.h.a.271.1		4	75.71	odd	10
1250.2.a.a.1.2		2	25.11	even	5
1250.2.a.d.1.1		2	25.14	even	10
1250.2.b.b.1249.1		4	25.2	odd	20
1250.2.b.b.1249.4		4	25.23	odd	20
10000.2.a.a.1.2		2	100.39	odd	10
10000.2.a.n.1.1		2	100.11	odd	10

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	50.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.224514i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.309017 - 0.224514i) q^{6} -3.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.309017 - 0.224514i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.80902 - 1.31433i) q^{5} +(-0.309017 - 0.224514i) q^{6} -3.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +(-1.80902 - 1.31433i) q^{10} +(1.30902 + 4.02874i) q^{11} +(-0.118034 + 0.363271i) q^{12} +(0.309017 - 0.951057i) q^{13} +(0.927051 + 2.85317i) q^{14} +(0.263932 - 0.812299i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.927051 - 0.673542i) q^{17} +2.85410 q^{18} +(-4.73607 - 3.44095i) q^{19} +(-0.690983 + 2.12663i) q^{20} +(-0.927051 + 0.673542i) q^{21} +(3.42705 - 2.48990i) q^{22} +(-0.545085 - 1.67760i) q^{23} +0.381966 q^{24} +(1.54508 - 4.75528i) q^{25} -1.00000 q^{26} +(0.690983 + 2.12663i) q^{27} +(2.42705 - 1.76336i) q^{28} +(7.66312 - 5.56758i) q^{29} -0.854102 q^{30} +(0.190983 + 0.138757i) q^{31} -1.00000 q^{32} +(1.30902 + 0.951057i) q^{33} +(-0.354102 + 1.08981i) q^{34} +(-5.42705 + 3.94298i) q^{35} +(-0.881966 - 2.71441i) q^{36} +(-2.57295 + 7.91872i) q^{37} +(-1.80902 + 5.56758i) q^{38} +(-0.118034 - 0.363271i) q^{39} +2.23607 q^{40} +(0.454915 - 1.40008i) q^{41} +(0.927051 + 0.673542i) q^{42} -6.23607 q^{43} +(-3.42705 - 2.48990i) q^{44} +(1.97214 + 6.06961i) q^{45} +(-1.42705 + 1.03681i) q^{46} +(9.66312 - 7.02067i) q^{47} +(-0.118034 - 0.363271i) q^{48} +2.00000 q^{49} -5.00000 q^{50} -0.437694 q^{51} +(0.309017 + 0.951057i) q^{52} +(-8.47214 + 6.15537i) q^{53} +(1.80902 - 1.31433i) q^{54} +(7.66312 + 5.56758i) q^{55} +(-2.42705 - 1.76336i) q^{56} -2.23607 q^{57} +(-7.66312 - 5.56758i) q^{58} +(-1.38197 + 4.25325i) q^{59} +(0.263932 + 0.812299i) q^{60} +(-2.73607 - 8.42075i) q^{61} +(0.0729490 - 0.224514i) q^{62} +(2.64590 - 8.14324i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.690983 - 2.12663i) q^{65} +(0.500000 - 1.53884i) q^{66} +(8.28115 + 6.01661i) q^{67} +1.14590 q^{68} +(-0.545085 - 0.396027i) q^{69} +(5.42705 + 3.94298i) q^{70} +(2.42705 - 1.76336i) q^{71} +(-2.30902 + 1.67760i) q^{72} +(2.38197 + 7.33094i) q^{73} +8.32624 q^{74} +(-0.590170 - 1.81636i) q^{75} +5.85410 q^{76} +(-3.92705 - 12.0862i) q^{77} +(-0.309017 + 0.224514i) q^{78} +(5.85410 - 4.25325i) q^{79} +(-0.690983 - 2.12663i) q^{80} +(-6.23607 - 4.53077i) q^{81} -1.47214 q^{82} +(3.66312 + 2.66141i) q^{83} +(0.354102 - 1.08981i) q^{84} -2.56231 q^{85} +(1.92705 + 5.93085i) q^{86} +(1.11803 - 3.44095i) q^{87} +(-1.30902 + 4.02874i) q^{88} +(1.38197 + 4.25325i) q^{89} +(5.16312 - 3.75123i) q^{90} +(-0.927051 + 2.85317i) q^{91} +(1.42705 + 1.03681i) q^{92} +0.0901699 q^{93} +(-9.66312 - 7.02067i) q^{94} -13.0902 q^{95} +(-0.309017 + 0.224514i) q^{96} +(-7.73607 + 5.62058i) q^{97} +(-0.618034 - 1.90211i) q^{98} -12.0902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9	\( 4 q + q^{2} - q^{3} - q^{4} + 5 q^{5} + q^{6} - 12 q^{7} + q^{8} - 8 q^{9} - 5 q^{10} + 3 q^{11} + 4 q^{12} - q^{13} - 3 q^{14} + 10 q^{15} - q^{16} + 3 q^{17} - 2 q^{18} - 10 q^{19} - 5 q^{20} + 3 q^{21} + 7 q^{22} + 9 q^{23} + 6 q^{24} - 5 q^{25} - 4 q^{26} + 5 q^{27} + 3 q^{28} + 15 q^{29} + 10 q^{30} + 3 q^{31} - 4 q^{32} + 3 q^{33} + 12 q^{34} - 15 q^{35} - 8 q^{36} - 17 q^{37} - 5 q^{38} + 4 q^{39} + 13 q^{41} - 3 q^{42} - 16 q^{43} - 7 q^{44} - 10 q^{45} + q^{46} + 23 q^{47} + 4 q^{48} + 8 q^{49} - 20 q^{50} - 42 q^{51} - q^{52} - 16 q^{53} + 5 q^{54} + 15 q^{55} - 3 q^{56} - 15 q^{58} - 10 q^{59} + 10 q^{60} - 2 q^{61} + 7 q^{62} + 24 q^{63} - q^{64} - 5 q^{65} + 2 q^{66} + 13 q^{67} + 18 q^{68} + 9 q^{69} + 15 q^{70} + 3 q^{71} - 7 q^{72} + 14 q^{73} + 2 q^{74} + 20 q^{75} + 10 q^{76} - 9 q^{77} + q^{78} + 10 q^{79} - 5 q^{80} - 16 q^{81} + 12 q^{82} - q^{83} - 12 q^{84} + 30 q^{85} + q^{86} - 3 q^{88} + 10 q^{89} + 5 q^{90} + 3 q^{91} - q^{92} - 22 q^{93} - 23 q^{94} - 30 q^{95} + q^{96} - 22 q^{97} + 2 q^{98} - 26 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 - q^4 + 5 * q^5 + q^6 - 12 * q^7 + q^8 - 8 * q^9 - 5 * q^10 + 3 * q^11 + 4 * q^12 - q^13 - 3 * q^14 + 10 * q^15 - q^16 + 3 * q^17 - 2 * q^18 - 10 * q^19 - 5 * q^20 + 3 * q^21 + 7 * q^22 + 9 * q^23 + 6 * q^24 - 5 * q^25 - 4 * q^26 + 5 * q^27 + 3 * q^28 + 15 * q^29 + 10 * q^30 + 3 * q^31 - 4 * q^32 + 3 * q^33 + 12 * q^34 - 15 * q^35 - 8 * q^36 - 17 * q^37 - 5 * q^38 + 4 * q^39 + 13 * q^41 - 3 * q^42 - 16 * q^43 - 7 * q^44 - 10 * q^45 + q^46 + 23 * q^47 + 4 * q^48 + 8 * q^49 - 20 * q^50 - 42 * q^51 - q^52 - 16 * q^53 + 5 * q^54 + 15 * q^55 - 3 * q^56 - 15 * q^58 - 10 * q^59 + 10 * q^60 - 2 * q^61 + 7 * q^62 + 24 * q^63 - q^64 - 5 * q^65 + 2 * q^66 + 13 * q^67 + 18 * q^68 + 9 * q^69 + 15 * q^70 + 3 * q^71 - 7 * q^72 + 14 * q^73 + 2 * q^74 + 20 * q^75 + 10 * q^76 - 9 * q^77 + q^78 + 10 * q^79 - 5 * q^80 - 16 * q^81 + 12 * q^82 - q^83 - 12 * q^84 + 30 * q^85 + q^86 - 3 * q^88 + 10 * q^89 + 5 * q^90 + 3 * q^91 - q^92 - 22 * q^93 - 23 * q^94 - 30 * q^95 + q^96 - 22 * q^97 + 2 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more