LMFDB - Embedded newform 670.2.e.i.171.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [670,2,Mod(171,670)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(670, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("670.171");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 670 = 2 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	670.e (of order $3$, degree $2$, 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:	$5.34997693543$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 31x^{6} - 2x^{5} + 597x^{4} - 4x^{3} + 5860x^{2} + 5264x + 35344 $ x^8 - 2x^7 + 31x^6 - 2x^5 + 597x^4 - 4x^3 + 5860x^2 + 5264*x + 35344
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			171.2
Root			$-1.43979 + 2.49379i$ of defining polynomial
Character	$\chi$	$=$	670.171
Dual form			670.2.e.i.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.207107 - 0.358719i) q^{12} +(2.03617 + 3.52675i) q^{13} +1.41421 q^{14} -0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.732684 - 1.26905i) q^{17} +(1.41421 + 2.44949i) q^{18} +(2.43979 + 4.22584i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.292893 - 0.507306i) q^{21} -2.00000 q^{22} +(2.17247 + 3.76284i) q^{23} -0.414214 q^{24} +1.00000 q^{25} +(2.03617 - 3.52675i) q^{26} +2.41421 q^{27} +(-0.707107 - 1.22474i) q^{28} +(0.378042 - 0.654788i) q^{29} +(0.207107 + 0.358719i) q^{30} +(-5.09728 + 8.82875i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.414214 + 0.717439i) q^{33} +(-0.732684 + 1.26905i) q^{34} +(-0.707107 + 1.22474i) q^{35} +(1.41421 - 2.44949i) q^{36} +(0.525577 + 0.910327i) q^{37} +(2.43979 - 4.22584i) q^{38} +(-0.843410 - 1.46083i) q^{39} +1.00000 q^{40} +(-5.76822 + 9.99085i) q^{41} -0.585786 q^{42} +11.7804 q^{43} +(1.00000 + 1.73205i) q^{44} -2.82843 q^{45} +(2.17247 - 3.76284i) q^{46} +(4.15749 - 7.20099i) q^{47} +(0.207107 + 0.358719i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.303488 + 0.525656i) q^{51} -4.07234 q^{52} +5.95193 q^{53} +(-1.20711 - 2.09077i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-0.707107 + 1.22474i) q^{56} +(-1.01059 - 1.75040i) q^{57} -0.756084 q^{58} +2.87958 q^{59} +(0.207107 - 0.358719i) q^{60} +(-5.57171 - 9.65048i) q^{61} +10.1946 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(2.03617 + 3.52675i) q^{65} +0.828427 q^{66} +(3.51150 + 7.39388i) q^{67} +1.46537 q^{68} +(-0.899869 - 1.55862i) q^{69} +1.41421 q^{70} +(1.23268 - 2.13507i) q^{71} -2.82843 q^{72} +(1.09574 + 1.89788i) q^{73} +(0.525577 - 0.910327i) q^{74} -0.414214 q^{75} -4.87958 q^{76} +(1.41421 + 2.44949i) q^{77} +(-0.843410 + 1.46083i) q^{78} +(-1.05115 + 1.82065i) q^{79} +(-0.500000 - 0.866025i) q^{80} +7.48528 q^{81} +11.5364 q^{82} +(5.51150 + 9.54619i) q^{83} +(0.292893 + 0.507306i) q^{84} +(-0.732684 - 1.26905i) q^{85} +(-5.89018 - 10.2021i) q^{86} +(-0.156590 + 0.271222i) q^{87} +(1.00000 - 1.73205i) q^{88} -12.7592 q^{89} +(1.41421 + 2.44949i) q^{90} -5.75916 q^{91} -4.34495 q^{92} +(2.11136 - 3.65699i) q^{93} -8.31498 q^{94} +(2.43979 + 4.22584i) q^{95} +(0.207107 - 0.358719i) q^{96} +(-8.30439 - 14.3836i) q^{97} +(2.50000 - 4.33013i) q^{98} +(-2.82843 + 4.89898i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	$ 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/670\mathbb{Z}\right)^\times$.

$n$	$471$	$537$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.414214			−0.239146			−0.119573	−	0.992825i	$-0.538153\pi$
$3$	−0.414214			−0.239146			−0.119573	+	0.992825i	$0.538153\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.207107	+	0.358719i	0.0845510	+	0.146447i
$7$	−0.707107	+	1.22474i	−0.267261	+	0.462910i	−0.968154	−	0.250357i	$-0.919452\pi$
$7$	−0.707107	+	1.22474i	−0.267261	+	0.462910i	0.700892	+	0.713267i	$0.252785\pi$
$8$	1.00000			0.353553
$9$	−2.82843			−0.942809
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	0.207107	−	0.358719i	0.0597866	−	0.103553i
$13$	2.03617	+	3.52675i	0.564732	+	0.978145i	0.997075	+	0.0764356i	$0.0243540\pi$
$13$	2.03617	+	3.52675i	0.564732	+	0.978145i	−0.432342	+	0.901710i	$0.642313\pi$
$14$	1.41421			0.377964
$15$	−0.414214			−0.106949
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.732684	−	1.26905i	−0.177702	−	0.307789i	0.763391	−	0.645937i	$-0.223533\pi$
$17$	−0.732684	−	1.26905i	−0.177702	−	0.307789i	−0.941093	+	0.338148i	$0.890200\pi$
$18$	1.41421	+	2.44949i	0.333333	+	0.577350i
$19$	2.43979	+	4.22584i	0.559726	+	0.969475i	0.997519	+	0.0703986i	$0.0224271\pi$
$19$	2.43979	+	4.22584i	0.559726	+	0.969475i	−0.437793	+	0.899076i	$0.644240\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$	0.292893	−	0.507306i	0.0639145	−	0.110703i
$22$	−2.00000			−0.426401
$23$	2.17247	+	3.76284i	0.452992	+	0.784606i	0.998570	−	0.0534543i	$-0.0170232\pi$
$23$	2.17247	+	3.76284i	0.452992	+	0.784606i	−0.545578	+	0.838060i	$0.683690\pi$
$24$	−0.414214			−0.0845510
$25$	1.00000			0.200000
$26$	2.03617	−	3.52675i	0.399326	−	0.691653i
$27$	2.41421			0.464616
$28$	−0.707107	−	1.22474i	−0.133631	−	0.231455i
$29$	0.378042	−	0.654788i	0.0702006	−	0.121591i	−0.828789	−	0.559562i	$-0.810969\pi$
$29$	0.378042	−	0.654788i	0.0702006	−	0.121591i	0.898989	+	0.437971i	$0.144303\pi$
$30$	0.207107	+	0.358719i	0.0378124	+	0.0654929i
$31$	−5.09728	+	8.82875i	−0.915499	+	1.58569i	−0.109330	+	0.994005i	$0.534871\pi$
$31$	−5.09728	+	8.82875i	−0.915499	+	1.58569i	−0.806169	+	0.591685i	$0.798463\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.414214	+	0.717439i	−0.0721053	+	0.124890i
$34$	−0.732684	+	1.26905i	−0.125654	+	0.217640i
$35$	−0.707107	+	1.22474i	−0.119523	+	0.207020i
$36$	1.41421	−	2.44949i	0.235702	−	0.408248i
$37$	0.525577	+	0.910327i	0.0864044	+	0.149657i	0.905989	−	0.423302i	$-0.139129\pi$
$37$	0.525577	+	0.910327i	0.0864044	+	0.149657i	−0.819584	+	0.572958i	$0.805796\pi$
$38$	2.43979	−	4.22584i	0.395786	−	0.685522i
$39$	−0.843410	−	1.46083i	−0.135054	−	0.233920i
$40$	1.00000			0.158114
$41$	−5.76822	+	9.99085i	−0.900844	+	1.56031i	−0.0744439	+	0.997225i	$0.523718\pi$
$41$	−5.76822	+	9.99085i	−0.900844	+	1.56031i	−0.826400	+	0.563083i	$0.809615\pi$
$42$	−0.585786			−0.0903888
$43$	11.7804			1.79649			0.898243	−	0.439498i	$-0.144844\pi$
$43$	11.7804			1.79649			0.898243	+	0.439498i	$0.144844\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−2.82843			−0.421637
$46$	2.17247	−	3.76284i	0.320314	−	0.554800i
$47$	4.15749	−	7.20099i	0.606433	−	1.05037i	−0.385391	−	0.922753i	$-0.625933\pi$
$47$	4.15749	−	7.20099i	0.606433	−	1.05037i	0.991823	−	0.127619i	$-0.0407333\pi$
$48$	0.207107	+	0.358719i	0.0298933	+	0.0517767i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.303488	+	0.525656i	0.0424968	+	0.0736066i
$52$	−4.07234			−0.564732
$53$	5.95193			0.817560			0.408780	−	0.912633i	$-0.365954\pi$
$53$	5.95193			0.817560			0.408780	+	0.912633i	$0.365954\pi$
$54$	−1.20711	−	2.09077i	−0.164266	−	0.284518i
$55$	1.00000	−	1.73205i	0.134840	−	0.233550i
$56$	−0.707107	+	1.22474i	−0.0944911	+	0.163663i
$57$	−1.01059	−	1.75040i	−0.133857	−	0.231846i
$58$	−0.756084			−0.0992786
$59$	2.87958			0.374890			0.187445	−	0.982275i	$-0.439979\pi$
$59$	2.87958			0.374890			0.187445	+	0.982275i	$0.439979\pi$
$60$	0.207107	−	0.358719i	0.0267374	−	0.0463105i
$61$	−5.57171	−	9.65048i	−0.713384	−	1.23562i	−0.963580	−	0.267422i	$-0.913828\pi$
$61$	−5.57171	−	9.65048i	−0.713384	−	1.23562i	0.250196	−	0.968195i	$-0.419505\pi$
$62$	10.1946			1.29471
$63$	2.00000	−	3.46410i	0.251976	−	0.436436i
$64$	1.00000			0.125000
$65$	2.03617	+	3.52675i	0.252556	+	0.437440i
$66$	0.828427			0.101972
$67$	3.51150	+	7.39388i	0.428998	+	0.903306i
$67$	3.51150	+	7.39388i	0.428998	+	0.903306i
$68$	1.46537			0.177702
$69$	−0.899869	−	1.55862i	−0.108331	−	0.187636i
$70$	1.41421			0.169031
$71$	1.23268	−	2.13507i	0.146293	−	0.253386i	−0.783562	−	0.621314i	$-0.786599\pi$
$71$	1.23268	−	2.13507i	0.146293	−	0.253386i	0.929854	+	0.367927i	$0.119933\pi$
$72$	−2.82843			−0.333333
$73$	1.09574	+	1.89788i	0.128247	+	0.222130i	0.922997	−	0.384806i	$-0.125732\pi$
$73$	1.09574	+	1.89788i	0.128247	+	0.222130i	−0.794750	+	0.606936i	$0.792398\pi$
$74$	0.525577	−	0.910327i	0.0610971	−	0.105823i
$75$	−0.414214			−0.0478293
$76$	−4.87958			−0.559726
$77$	1.41421	+	2.44949i	0.161165	+	0.279145i
$78$	−0.843410	+	1.46083i	−0.0954974	+	0.165406i
$79$	−1.05115	+	1.82065i	−0.118264	+	0.204839i	−0.919080	−	0.394071i	$-0.871066\pi$
$79$	−1.05115	+	1.82065i	−0.118264	+	0.204839i	0.800816	+	0.598911i	$0.204400\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	7.48528			0.831698
$82$	11.5364			1.27399
$83$	5.51150	+	9.54619i	0.604965	+	1.04783i	0.992057	+	0.125789i	$0.0401464\pi$
$83$	5.51150	+	9.54619i	0.604965	+	1.04783i	−0.387092	+	0.922041i	$0.626520\pi$
$84$	0.292893	+	0.507306i	0.0319573	+	0.0553516i
$85$	−0.732684	−	1.26905i	−0.0794707	−	0.137647i
$86$	−5.89018	−	10.2021i	−0.635154	−	1.10012i
$87$	−0.156590	+	0.271222i	−0.0167882	+	0.0290780i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	−12.7592			−1.35247			−0.676234	−	0.736687i	$-0.736389\pi$
$89$	−12.7592			−1.35247			−0.676234	+	0.736687i	$0.736389\pi$
$90$	1.41421	+	2.44949i	0.149071	+	0.258199i
$91$	−5.75916			−0.603724
$92$	−4.34495			−0.452992
$93$	2.11136	−	3.65699i	0.218938	−	0.379212i
$94$	−8.31498			−0.857625
$95$	2.43979	+	4.22584i	0.250317	+	0.433562i
$96$	0.207107	−	0.358719i	0.0211377	−	0.0366117i
$97$	−8.30439	−	14.3836i	−0.843183	−	1.46044i	−0.887190	−	0.461405i	$-0.847346\pi$
$97$	−8.30439	−	14.3836i	−0.843183	−	1.46044i	0.0440068	−	0.999031i	$-0.485988\pi$
$98$	2.50000	−	4.33013i	0.252538	−	0.437409i
$99$	−2.82843	+	4.89898i	−0.284268	+	0.492366i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	8.41512	−	14.5754i	0.837335	−	1.45031i	−0.0547795	−	0.998498i	$-0.517446\pi$
$101$	8.41512	−	14.5754i	0.837335	−	1.45031i	0.892115	−	0.451809i	$-0.149221\pi$
$102$	0.303488	−	0.525656i	0.0300498	−	0.0520477i
$103$	−0.863697	+	1.49597i	−0.0851026	+	0.147402i	−0.905435	−	0.424485i	$-0.860455\pi$
$103$	−0.863697	+	1.49597i	−0.0851026	+	0.147402i	0.820332	+	0.571887i	$0.193788\pi$
$104$	2.03617	+	3.52675i	0.199663	+	0.345827i
$105$	0.292893	−	0.507306i	0.0285835	−	0.0495080i
$106$	−2.97596	−	5.15452i	−0.289051	−	0.500651i
$107$	−2.29072			−0.221452			−0.110726	−	0.993851i	$-0.535318\pi$
$107$	−2.29072			−0.221452			−0.110726	+	0.993851i	$0.535318\pi$
$108$	−1.20711	+	2.09077i	−0.116154	+	0.201184i
$109$	−20.4896			−1.96255			−0.981276	−	0.192609i	$-0.938305\pi$
$109$	−20.4896			−1.96255			−0.981276	+	0.192609i	$0.938305\pi$
$110$	−2.00000			−0.190693
$111$	−0.217701	−	0.377070i	−0.0206633	−	0.0357899i
$112$	1.41421			0.133631
$113$	1.18217	−	2.04757i	0.111209	−	0.192620i	−0.805049	−	0.593208i	$-0.797861\pi$
$113$	1.18217	−	2.04757i	0.111209	−	0.192620i	0.916258	+	0.400589i	$0.131194\pi$
$114$	−1.01059	+	1.75040i	−0.0946508	+	0.163940i
$115$	2.17247	+	3.76284i	0.202584	+	0.350886i
$116$	0.378042	+	0.654788i	0.0351003	+	0.0607955i
$117$	−5.75916	−	9.97516i	−0.532435	−	0.922204i
$118$	−1.43979	−	2.49379i	−0.132543	−	0.229572i
$119$	2.07234			0.189971
$120$	−0.414214			−0.0378124
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−5.57171	+	9.65048i	−0.504439	+	0.873713i
$123$	2.38927	−	4.13834i	0.215434	−	0.373142i
$124$	−5.09728	−	8.82875i	−0.457750	−	0.792845i
$125$	1.00000			0.0894427
$126$	−4.00000			−0.356348
$127$	−6.29380	+	10.9012i	−0.558484	+	0.967323i	0.439139	+	0.898419i	$0.355283\pi$
$127$	−6.29380	+	10.9012i	−0.558484	+	0.967323i	−0.997623	+	0.0689037i	$0.978050\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.87958			−0.429623
$130$	2.03617	−	3.52675i	0.178584	−	0.309317i
$131$	−19.9718			−1.74495			−0.872474	−	0.488661i	$-0.837486\pi$
$131$	−19.9718			−1.74495			−0.872474	+	0.488661i	$0.837486\pi$
$132$	−0.414214	−	0.717439i	−0.0360527	−	0.0624450i
$133$	−6.90077			−0.598373
$134$	4.64754	−	6.73798i	0.401486	−	0.582073i
$135$	2.41421			0.207782
$136$	−0.732684	−	1.26905i	−0.0628271	−	0.108820i
$137$	−3.95320			−0.337745			−0.168872	−	0.985638i	$-0.554013\pi$
$137$	−3.95320			−0.337745			−0.168872	+	0.985638i	$0.554013\pi$
$138$	−0.899869	+	1.55862i	−0.0766019	+	0.132678i
$139$	7.22018			0.612407			0.306204	−	0.951966i	$-0.400941\pi$
$139$	7.22018			0.612407			0.306204	+	0.951966i	$0.400941\pi$
$140$	−0.707107	−	1.22474i	−0.0597614	−	0.103510i
$141$	−1.72209	+	2.98275i	−0.145026	+	0.251193i
$142$	−2.46537			−0.206889
$143$	8.14469			0.681093
$144$	1.41421	+	2.44949i	0.117851	+	0.204124i
$145$	0.378042	−	0.654788i	0.0313947	−	0.0543771i
$146$	1.09574	−	1.89788i	0.0906843	−	0.157070i
$147$	−1.03553	−	1.79360i	−0.0854094	−	0.147933i
$148$	−1.05115			−0.0864044
$149$	10.2127			0.836655			0.418327	−	0.908296i	$-0.362616\pi$
$149$	10.2127			0.836655			0.418327	+	0.908296i	$0.362616\pi$
$150$	0.207107	+	0.358719i	0.0169102	+	0.0292893i
$151$	−3.13345	−	5.42730i	−0.254997	−	0.441668i	0.709898	−	0.704305i	$-0.248741\pi$
$151$	−3.13345	−	5.42730i	−0.254997	−	0.441668i	−0.964895	+	0.262637i	$0.915408\pi$
$152$	2.43979	+	4.22584i	0.197893	+	0.342761i
$153$	2.07234	+	3.58940i	0.167539	+	0.290186i
$154$	1.41421	−	2.44949i	0.113961	−	0.197386i
$155$	−5.09728	+	8.82875i	−0.409424	+	0.709143i
$156$	1.68682			0.135054
$157$	−6.15839	−	10.6667i	−0.491493	−	0.851291i	0.508459	−	0.861086i	$-0.330215\pi$
$157$	−6.15839	−	10.6667i	−0.491493	−	0.851291i	−0.999952	+	0.00979492i	$0.996882\pi$
$158$	2.10231			0.167251
$159$	−2.46537			−0.195516
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−6.14469			−0.484269
$162$	−3.74264	−	6.48244i	−0.294050	−	0.509309i
$163$	1.15595	−	2.00217i	0.0905412	−	0.156822i	−0.817198	−	0.576357i	$-0.804474\pi$
$163$	1.15595	−	2.00217i	0.0905412	−	0.156822i	0.907739	+	0.419535i	$0.137807\pi$
$164$	−5.76822	−	9.99085i	−0.450422	−	0.780154i
$165$	−0.414214	+	0.717439i	−0.0322465	+	0.0558525i
$166$	5.51150	−	9.54619i	0.427775	−	0.740928i
$167$	2.55052	−	4.41762i	0.197365	−	0.341846i	−0.750308	−	0.661088i	$-0.770095\pi$
$167$	2.55052	−	4.41762i	0.197365	−	0.341846i	0.947673	+	0.319242i	$0.103428\pi$
$168$	0.292893	−	0.507306i	0.0225972	−	0.0391395i
$169$	−1.79199	+	3.10382i	−0.137845	+	0.238755i
$170$	−0.732684	+	1.26905i	−0.0561943	+	0.0973314i
$171$	−6.90077	−	11.9525i	−0.527715	−	0.914029i
$172$	−5.89018	+	10.2021i	−0.449122	+	0.777902i
$173$	2.31783	+	4.01460i	0.176222	+	0.305225i	0.940583	−	0.339563i	$-0.110279\pi$
$173$	2.31783	+	4.01460i	0.176222	+	0.305225i	−0.764362	+	0.644788i	$0.776946\pi$
$174$	0.313180			0.0237421
$175$	−0.707107	+	1.22474i	−0.0534522	+	0.0925820i
$176$	−2.00000			−0.150756
$177$	−1.19276			−0.0896535
$178$	6.37958	+	11.0498i	0.478170	+	0.828215i
$179$	15.8333			1.18344			0.591719	−	0.806145i	$-0.298450\pi$
$179$	15.8333			1.18344			0.591719	+	0.806145i	$0.298450\pi$
$180$	1.41421	−	2.44949i	0.105409	−	0.182574i
$181$	−8.41639	+	14.5776i	−0.625585	+	1.08355i	0.362842	+	0.931851i	$0.381807\pi$
$181$	−8.41639	+	14.5776i	−0.625585	+	1.08355i	−0.988427	+	0.151695i	$0.951527\pi$
$182$	2.87958	+	4.98758i	0.213449	+	0.369704i
$183$	2.30788	+	3.99736i	0.170603	+	0.295493i
$184$	2.17247	+	3.76284i	0.160157	+	0.277400i
$185$	0.525577	+	0.910327i	0.0386412	+	0.0669285i
$186$	−4.22273			−0.309625
$187$	−2.93074			−0.214317
$188$	4.15749	+	7.20099i	0.303216	+	0.525186i
$189$	−1.70711	+	2.95680i	−0.124174	+	0.215075i
$190$	2.43979	−	4.22584i	0.177001	−	0.306575i
$191$	8.66809	+	15.0136i	0.627201	+	1.08634i	0.988111	+	0.153743i	$0.0491328\pi$
$191$	8.66809	+	15.0136i	0.627201	+	1.08634i	−0.360910	+	0.932601i	$0.617534\pi$
$192$	−0.414214			−0.0298933
$193$	−21.5863			−1.55382			−0.776908	−	0.629614i	$-0.783213\pi$
$193$	−21.5863			−1.55382			−0.776908	+	0.629614i	$0.783213\pi$
$194$	−8.30439	+	14.3836i	−0.596220	+	1.03268i
$195$	−0.843410	−	1.46083i	−0.0603978	−	0.104612i
$196$	−5.00000			−0.357143
$197$	−8.48528	+	14.6969i	−0.604551	+	1.04711i	0.387571	+	0.921840i	$0.373314\pi$
$197$	−8.48528	+	14.6969i	−0.604551	+	1.04711i	−0.992122	+	0.125274i	$0.960019\pi$
$198$	5.65685			0.402015
$199$	−9.71797	−	16.8320i	−0.688888	−	1.19319i	−0.972198	−	0.234161i	$-0.924766\pi$
$199$	−9.71797	−	16.8320i	−0.688888	−	1.19319i	0.283310	−	0.959029i	$-0.408568\pi$
$200$	1.00000			0.0707107
$201$	−1.45451	−	3.06264i	−0.102593	−	0.216022i
$202$	−16.8302			−1.18417
$203$	0.534632	+	0.926009i	0.0375238	+	0.0649931i
$204$	−0.606975			−0.0424968
$205$	−5.76822	+	9.99085i	−0.402870	+	0.697791i
$206$	1.72739			0.120353
$207$	−6.14469	−	10.6429i	−0.427085	−	0.739733i
$208$	2.03617	−	3.52675i	0.141183	−	0.244536i
$209$	9.75916			0.675055
$210$	−0.585786			−0.0404231
$211$	−7.81873	−	13.5424i	−0.538264	−	0.932300i	−0.998998	−	0.0447620i	$-0.985747\pi$
$211$	−7.81873	−	13.5424i	−0.538264	−	0.932300i	0.460734	−	0.887538i	$-0.347586\pi$
$212$	−2.97596	+	5.15452i	−0.204390	+	0.354014i
$213$	−0.510594	+	0.884376i	−0.0349854	+	0.0605964i
$214$	1.14536	+	1.98382i	0.0782950	+	0.135611i
$215$	11.7804			0.803413
$216$	2.41421			0.164266
$217$	−7.20865	−	12.4857i	−0.489355	−	0.847587i
$218$	10.2448	+	17.7445i	0.693867	+	1.20181i
$219$	−0.453872	−	0.786129i	−0.0306698	−	0.0531217i
$220$	1.00000	+	1.73205i	0.0674200	+	0.116775i
$221$	2.98374	−	5.16799i	0.200708	−	0.347637i
$222$	−0.217701	+	0.377070i	−0.0146112	+	0.0253073i
$223$	7.44598			0.498620			0.249310	−	0.968424i	$-0.419796\pi$
$223$	7.44598			0.498620			0.249310	+	0.968424i	$0.419796\pi$
$224$	−0.707107	−	1.22474i	−0.0472456	−	0.0818317i
$225$	−2.82843			−0.188562
$226$	−2.36433			−0.157273
$227$	11.2071	−	19.4113i	0.743842	−	1.28837i	−0.206892	−	0.978364i	$-0.566335\pi$
$227$	11.2071	−	19.4113i	0.743842	−	1.28837i	0.950734	−	0.310008i	$-0.100332\pi$
$228$	2.02119			0.133857
$229$	−10.9378	−	18.9449i	−0.722793	−	1.25191i	−0.959876	−	0.280425i	$-0.909525\pi$
$229$	−10.9378	−	18.9449i	−0.722793	−	1.25191i	0.237083	−	0.971489i	$-0.423809\pi$
$230$	2.17247	−	3.76284i	0.143249	−	0.248114i
$231$	−0.585786	−	1.01461i	−0.0385419	−	0.0667566i
$232$	0.378042	−	0.654788i	0.0248197	−	0.0429889i
$233$	4.85310	−	8.40582i	0.317937	−	0.550684i	−0.662120	−	0.749398i	$-0.730343\pi$
$233$	4.85310	−	8.40582i	0.317937	−	0.550684i	0.980058	+	0.198714i	$0.0636765\pi$
$234$	−5.75916	+	9.97516i	−0.376488	+	0.652097i
$235$	4.15749	−	7.20099i	0.271205	−	0.469741i
$236$	−1.43979	+	2.49379i	−0.0937224	+	0.162332i
$237$	0.435403	−	0.754139i	0.0282824	−	0.0489866i
$238$	−1.03617	−	1.79470i	−0.0671650	−	0.116333i
$239$	4.60698	−	7.97952i	0.298000	−	0.516152i	−0.677678	−	0.735359i	$-0.737014\pi$
$239$	4.60698	−	7.97952i	0.298000	−	0.516152i	0.975678	+	0.219207i	$0.0703470\pi$
$240$	0.207107	+	0.358719i	0.0133687	+	0.0231552i
$241$	−4.84654			−0.312193			−0.156096	−	0.987742i	$-0.549891\pi$
$241$	−4.84654			−0.312193			−0.156096	+	0.987742i	$0.549891\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	−10.3431			−0.663513
$244$	11.1434			0.713384
$245$	2.50000	+	4.33013i	0.159719	+	0.276642i
$246$	−4.77855			−0.304669
$247$	−9.93567	+	17.2091i	−0.632191	+	1.09499i
$248$	−5.09728	+	8.82875i	−0.323678	+	0.560626i
$249$	−2.28294	−	3.95416i	−0.144675	−	0.250585i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	14.1337	+	24.4803i	0.892112	+	1.54518i	0.837338	+	0.546685i	$0.184111\pi$
$251$	14.1337	+	24.4803i	0.892112	+	1.54518i	0.0547743	+	0.998499i	$0.482556\pi$
$252$	2.00000	+	3.46410i	0.125988	+	0.218218i
$253$	8.68990			0.546329
$254$	12.5876			0.789816
$255$	0.303488	+	0.525656i	0.0190051	+	0.0329179i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.4385	−	25.0082i	0.900648	−	1.55997i	0.0739927	−	0.997259i	$-0.476426\pi$
$257$	14.4385	−	25.0082i	0.900648	−	1.55997i	0.826655	−	0.562709i	$-0.190241\pi$
$258$	2.43979	+	4.22584i	0.151895	+	0.263089i
$259$	−1.48656			−0.0923702
$260$	−4.07234			−0.252556
$261$	−1.06926	+	1.85202i	−0.0661858	+	0.114637i
$262$	9.98592	+	17.2961i	0.616932	+	1.06856i
$263$	9.62689			0.593619			0.296810	−	0.954937i	$-0.404077\pi$
$263$	9.62689			0.593619			0.296810	+	0.954937i	$0.404077\pi$
$264$	−0.414214	+	0.717439i	−0.0254931	+	0.0441553i
$265$	5.95193			0.365624
$266$	3.45039	+	5.97624i	0.211557	+	0.366427i
$267$	5.28502			0.323438
$268$	−8.15903	−	0.655892i	−0.498392	−	0.0400650i
$269$	3.83151			0.233611			0.116806	−	0.993155i	$-0.462735\pi$
$269$	3.83151			0.233611			0.116806	+	0.993155i	$0.462735\pi$
$270$	−1.20711	−	2.09077i	−0.0734622	−	0.127240i
$271$	18.6101			1.13048			0.565240	−	0.824926i	$-0.308783\pi$
$271$	18.6101			1.13048			0.565240	+	0.824926i	$0.308783\pi$
$272$	−0.732684	+	1.26905i	−0.0444255	+	0.0769472i
$273$	2.38552			0.144378
$274$	1.97660	+	3.42357i	0.119411	+	0.206826i
$275$	1.00000	−	1.73205i	0.0603023	−	0.104447i
$276$	1.79974			0.108331
$277$	8.26255			0.496449			0.248224	−	0.968703i	$-0.420153\pi$
$277$	8.26255			0.496449			0.248224	+	0.968703i	$0.420153\pi$
$278$	−3.61009	−	6.25286i	−0.216519	−	0.375021i
$279$	14.4173	−	24.9715i	0.863141	−	1.49500i
$280$	−0.707107	+	1.22474i	−0.0422577	+	0.0731925i
$281$	−3.15685	−	5.46783i	−0.188322	−	0.326184i	0.756369	−	0.654145i	$-0.226972\pi$
$281$	−3.15685	−	5.46783i	−0.188322	−	0.326184i	−0.944691	+	0.327962i	$0.893638\pi$
$282$	3.44418			0.205098
$283$	6.70493			0.398567			0.199283	−	0.979942i	$-0.436139\pi$
$283$	6.70493			0.398567			0.199283	+	0.979942i	$0.436139\pi$
$284$	1.23268	+	2.13507i	0.0731463	+	0.126693i
$285$	−1.01059	−	1.75040i	−0.0598625	−	0.103685i
$286$	−4.07234	−	7.05351i	−0.240803	−	0.417083i
$287$	−8.15749	−	14.1292i	−0.481522	−	0.834020i
$288$	1.41421	−	2.44949i	0.0833333	−	0.144338i
$289$	7.42635	−	12.8628i	0.436844	−	0.756636i
$290$	−0.756084			−0.0443988
$291$	3.43979	+	5.95789i	0.201644	+	0.349258i
$292$	−2.19149			−0.128247
$293$	3.56895			0.208500			0.104250	−	0.994551i	$-0.466756\pi$
$293$	3.56895			0.208500			0.104250	+	0.994551i	$0.466756\pi$
$294$	−1.03553	+	1.79360i	−0.0603936	+	0.104605i
$295$	2.87958			0.167656
$296$	0.525577	+	0.910327i	0.0305486	+	0.0529117i
$297$	2.41421	−	4.18154i	0.140087	−	0.242638i
$298$	−5.10634	−	8.84444i	−0.295802	−	0.512344i
$299$	−8.84706	+	15.3236i	−0.511639	+	0.886185i
$300$	0.207107	−	0.358719i	0.0119573	−	0.0207107i
$301$	−8.32997	+	14.4279i	−0.480131	+	0.831612i
$302$	−3.13345	+	5.42730i	−0.180310	+	0.312306i
$303$	−3.48566	+	6.03733i	−0.200246	+	0.346836i
$304$	2.43979	−	4.22584i	0.139932	−	0.242369i
$305$	−5.57171	−	9.65048i	−0.319035	−	0.552585i
$306$	2.07234	−	3.58940i	0.118468	−	0.205193i
$307$	16.2813	+	28.2000i	0.929220	+	1.60946i	0.784629	+	0.619965i	$0.212853\pi$
$307$	16.2813	+	28.2000i	0.929220	+	1.60946i	0.144591	+	0.989492i	$0.453813\pi$
$308$	−2.82843			−0.161165
$309$	0.357755	−	0.619650i	0.0203520	−	0.0352506i
$310$	10.1946			0.579012
$311$	−27.6829			−1.56975			−0.784877	−	0.619651i	$-0.787274\pi$
$311$	−27.6829			−1.56975			−0.784877	+	0.619651i	$0.787274\pi$
$312$	−0.843410	−	1.46083i	−0.0477487	−	0.0827032i
$313$	4.25947			0.240760			0.120380	−	0.992728i	$-0.461589\pi$
$313$	4.25947			0.240760			0.120380	+	0.992728i	$0.461589\pi$
$314$	−6.15839	+	10.6667i	−0.347538	+	0.601954i
$315$	2.00000	−	3.46410i	0.112687	−	0.195180i
$316$	−1.05115	−	1.82065i	−0.0591321	−	0.102420i
$317$	−0.695874	−	1.20529i	−0.0390842	−	0.0676958i	0.845822	−	0.533466i	$-0.179111\pi$
$317$	−0.695874	−	1.20529i	−0.0390842	−	0.0676958i	−0.884906	+	0.465770i	$0.845777\pi$
$318$	1.23268	+	2.13507i	0.0691255	+	0.119729i
$319$	−0.756084	−	1.30958i	−0.0423326	−	0.0733221i
$320$	1.00000			0.0559017
$321$	0.948845			0.0529594
$322$	3.07234	+	5.32146i	0.171215	+	0.296553i
$323$	3.57519	−	6.19241i	0.198929	−	0.344555i
$324$	−3.74264	+	6.48244i	−0.207924	+	0.360136i
$325$	2.03617	+	3.52675i	0.112946	+	0.195629i
$326$	−2.31190			−0.128045
$327$	8.48709			0.469337
$328$	−5.76822	+	9.99085i	−0.318497	+	0.551652i
$329$	5.87958	+	10.1837i	0.324152	+	0.561447i
$330$	0.828427			0.0456034
$331$	9.68371	−	16.7727i	0.532265	−	0.921909i	−0.467026	−	0.884244i	$-0.654674\pi$
$331$	9.68371	−	16.7727i	0.532265	−	0.921909i	0.999290	−	0.0376657i	$-0.0119922\pi$
$332$	−11.0230			−0.604965
$333$	−1.48656	−	2.57479i	−0.0814628	−	0.141098i
$334$	−5.10103			−0.279116
$335$	3.51150	+	7.39388i	0.191854	+	0.403971i
$336$	−0.585786			−0.0319573
$337$	10.2298	+	17.7186i	0.557255	+	0.965193i	0.997724	+	0.0674259i	$0.0214786\pi$
$337$	10.2298	+	17.7186i	0.557255	+	0.965193i	−0.440470	+	0.897768i	$0.645188\pi$
$338$	3.58398			0.194943
$339$	−0.489670	+	0.848133i	−0.0265952	+	0.0460643i
$340$	1.46537			0.0794707
$341$	10.1946	+	17.6575i	0.552067	+	0.956208i
$342$	−6.90077	+	11.9525i	−0.373151	+	0.646316i
$343$	−16.9706			−0.916324
$344$	11.7804			0.635154
$345$	−0.899869	−	1.55862i	−0.0484473	−	0.0839132i
$346$	2.31783	−	4.01460i	0.124607	−	0.215826i
$347$	12.0137	−	20.8083i	0.644928	−	1.11705i	−0.339390	−	0.940646i	$-0.610221\pi$
$347$	12.0137	−	20.8083i	0.644928	−	1.11705i	0.984318	−	0.176402i	$-0.0564459\pi$
$348$	−0.156590	−	0.271222i	−0.00839411	−	0.0145390i
$349$	−16.0361			−0.858394			−0.429197	−	0.903211i	$-0.641203\pi$
$349$	−16.0361			−0.858394			−0.429197	+	0.903211i	$0.641203\pi$
$350$	1.41421			0.0755929
$351$	4.91575	+	8.51433i	0.262384	+	0.454462i
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	15.5224	+	26.8855i	0.826172	+	1.43097i	0.901021	+	0.433776i	$0.142819\pi$
$353$	15.5224	+	26.8855i	0.826172	+	1.43097i	−0.0748490	+	0.997195i	$0.523847\pi$
$354$	0.596381	+	1.03296i	0.0316973	+	0.0549013i
$355$	1.23268	−	2.13507i	0.0654241	−	0.113318i
$356$	6.37958	−	11.0498i	0.338117	−	0.585636i
$357$	−0.858393			−0.0454310
$358$	−7.91666	−	13.7120i	−0.418408	−	0.724704i
$359$	15.1279			0.798418			0.399209	−	0.916860i	$-0.369285\pi$
$359$	15.1279			0.798418			0.399209	+	0.916860i	$0.369285\pi$
$360$	−2.82843			−0.149071
$361$	−2.40516	+	4.16586i	−0.126587	+	0.219256i
$362$	16.8328			0.884711
$363$	−1.44975	−	2.51104i	−0.0760920	−	0.131795i
$364$	2.87958	−	4.98758i	0.150931	−	0.261420i
$365$	1.09574	+	1.89788i	0.0573538	+	0.0993397i
$366$	2.30788	−	3.99736i	0.120635	−	0.208945i
$367$	−0.363961	+	0.630399i	−0.0189986	+	0.0329066i	−0.875368	−	0.483456i	$-0.839381\pi$
$367$	−0.363961	+	0.630399i	−0.0189986	+	0.0329066i	0.856370	+	0.516363i	$0.172714\pi$
$368$	2.17247	−	3.76284i	0.113248	−	0.196151i
$369$	16.3150	−	28.2584i	0.849324	−	1.47107i
$370$	0.525577	−	0.910327i	0.0273235	−	0.0473256i
$371$	−4.20865	+	7.28959i	−0.218502	+	0.378457i
$372$	2.11136	+	3.65699i	0.109469	+	0.189606i
$373$	5.93979	−	10.2880i	0.307551	−	0.532693i	−0.670275	−	0.742113i	$-0.733824\pi$
$373$	5.93979	−	10.2880i	0.307551	−	0.532693i	0.977826	+	0.209419i	$0.0671573\pi$
$374$	1.46537	+	2.53809i	0.0757724	+	0.131242i
$375$	−0.414214			−0.0213899
$376$	4.15749	−	7.20099i	0.214406	−	0.371363i
$377$	3.07903			0.158578
$378$	3.41421			0.175608
$379$	11.5576	+	20.0184i	0.593675	+	1.02828i	0.993732	+	0.111786i	$0.0356570\pi$
$379$	11.5576	+	20.0184i	0.593675	+	1.02828i	−0.400057	+	0.916490i	$0.631010\pi$
$380$	−4.87958			−0.250317
$381$	2.60698	−	4.51541i	0.133559	−	0.231332i
$382$	8.66809	−	15.0136i	0.443498	−	0.768161i
$383$	−4.10103	−	7.10320i	−0.209553	−	0.362956i	0.742021	−	0.670377i	$-0.233868\pi$
$383$	−4.10103	−	7.10320i	−0.209553	−	0.362956i	−0.951574	+	0.307420i	$0.900534\pi$
$384$	0.207107	+	0.358719i	0.0105689	+	0.0183058i
$385$	1.41421	+	2.44949i	0.0720750	+	0.124838i
$386$	10.7932	+	18.6943i	0.549357	+	0.951515i
$387$	−33.3199			−1.69374
$388$	16.6088			0.843183
$389$	−5.44948	−	9.43878i	−0.276300	−	0.478565i	0.694162	−	0.719818i	$-0.255775\pi$
$389$	−5.44948	−	9.43878i	−0.276300	−	0.478565i	−0.970462	+	0.241253i	$0.922442\pi$
$390$	−0.843410	+	1.46083i	−0.0427077	+	0.0739719i
$391$	3.18348	−	5.51394i	0.160995	−	0.278852i
$392$	2.50000	+	4.33013i	0.126269	+	0.218704i
$393$	8.27261			0.417298
$394$	16.9706			0.854965
$395$	−1.05115	+	1.82065i	−0.0528893	+	0.0916070i
$396$	−2.82843	−	4.89898i	−0.142134	−	0.246183i
$397$	7.56640			0.379747			0.189873	−	0.981809i	$-0.439192\pi$
$397$	7.56640			0.379747			0.189873	+	0.981809i	$0.439192\pi$
$398$	−9.71797	+	16.8320i	−0.487118	+	0.843712i
$399$	2.85839			0.143099
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	2.19846			0.109786			0.0548929	−	0.998492i	$-0.482518\pi$
$401$	2.19846			0.109786			0.0548929	+	0.998492i	$0.482518\pi$
$402$	−1.92507	+	2.79096i	−0.0960139	+	0.139201i
$403$	−41.5158			−2.06805
$404$	8.41512	+	14.5754i	0.418668	+	0.725154i
$405$	7.48528			0.371947
$406$	0.534632	−	0.926009i	0.0265333	−	0.0459571i
$407$	2.10231			0.104208
$408$	0.303488	+	0.525656i	0.0150249	+	0.0260239i
$409$	1.23359	−	2.13663i	0.0609969	−	0.105650i	−0.833914	−	0.551894i	$-0.813905\pi$
$409$	1.23359	−	2.13663i	0.0609969	−	0.105650i	0.894911	+	0.446244i	$0.147239\pi$
$410$	11.5364			0.569744
$411$	1.63747			0.0807704
$412$	−0.863697	−	1.49597i	−0.0425513	−	0.0737010i
$413$	−2.03617	+	3.52675i	−0.100193	+	0.173540i
$414$	−6.14469	+	10.6429i	−0.301995	+	0.523071i
$415$	5.51150	+	9.54619i	0.270549	+	0.468604i
$416$	−4.07234			−0.199663
$417$	−2.99069			−0.146455
$418$	−4.87958	−	8.45168i	−0.238668	−	0.413385i
$419$	7.17026	+	12.4193i	0.350290	+	0.606721i	0.986300	−	0.164960i	$-0.0527496\pi$
$419$	7.17026	+	12.4193i	0.350290	+	0.606721i	−0.636010	+	0.771681i	$0.719416\pi$
$420$	0.292893	+	0.507306i	0.0142917	+	0.0247540i
$421$	10.2426	+	17.7408i	0.499196	+	0.864632i	1.00000		0.000928405i	$-0.000295520\pi$
$421$	10.2426	+	17.7408i	0.499196	+	0.864632i	−0.500804	+	0.865561i	$0.666962\pi$
$422$	−7.81873	+	13.5424i	−0.380610	+	0.659236i
$423$	−11.7592	+	20.3675i	−0.571750	+	0.990300i
$424$	5.95193			0.289051
$425$	−0.732684	−	1.26905i	−0.0355404	−	0.0615578i
$426$	1.02119			0.0494768
$427$	15.7592			0.762639
$428$	1.14536	−	1.98382i	0.0553630	−	0.0958914i
$429$	−3.37364			−0.162881
$430$	−5.89018	−	10.2021i	−0.284050	−	0.491988i
$431$	5.23268	−	9.06327i	0.252050	−	0.436563i	−0.712040	−	0.702138i	$-0.752229\pi$
$431$	5.23268	−	9.06327i	0.252050	−	0.436563i	0.964090	+	0.265576i	$0.0855621\pi$
$432$	−1.20711	−	2.09077i	−0.0580770	−	0.100592i
$433$	−0.612266	+	1.06048i	−0.0294236	+	0.0509632i	−0.880362	−	0.474302i	$-0.842701\pi$
$433$	−0.612266	+	1.06048i	−0.0294236	+	0.0509632i	0.850939	+	0.525265i	$0.176034\pi$
$434$	−7.20865	+	12.4857i	−0.346026	+	0.599335i
$435$	−0.156590	+	0.271222i	−0.00750792	+	0.0130041i
$436$	10.2448	−	17.7445i	0.490638	−	0.849810i
$437$	−10.6008	+	18.3611i	−0.507104	+	0.878329i
$438$	−0.453872	+	0.786129i	−0.0216868	+	0.0375627i
$439$	0.595743	+	1.03186i	0.0284333	+	0.0492479i	0.879892	−	0.475174i	$-0.157615\pi$
$439$	0.595743	+	1.03186i	0.0284333	+	0.0492479i	−0.851459	+	0.524422i	$0.824282\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−7.07107	−	12.2474i	−0.336718	−	0.583212i
$442$	−5.96748			−0.283844
$443$	−4.74174	+	8.21293i	−0.225287	+	0.390208i	−0.956405	−	0.292042i	$-0.905665\pi$
$443$	−4.74174	+	8.21293i	−0.225287	+	0.390208i	0.731119	+	0.682250i	$0.238999\pi$
$444$	0.435403			0.0206633
$445$	−12.7592			−0.604842
$446$	−3.72299	−	6.44841i	−0.176289	−	0.305341i
$447$	−4.23023			−0.200083
$448$	−0.707107	+	1.22474i	−0.0334077	+	0.0578638i
$449$	13.2835	−	23.0076i	0.626885	−	1.08580i	−0.361288	−	0.932454i	$-0.617663\pi$
$449$	13.2835	−	23.0076i	0.626885	−	1.08580i	0.988173	−	0.153343i	$-0.0490039\pi$
$450$	1.41421	+	2.44949i	0.0666667	+	0.115470i
$451$	11.5364	+	19.9817i	0.543230	+	0.940901i
$452$	1.18217	+	2.04757i	0.0556045	+	0.0963098i
$453$	1.29792	+	2.24806i	0.0609816	+	0.105623i
$454$	−22.4142			−1.05195
$455$	−5.75916			−0.269994
$456$	−1.01059	−	1.75040i	−0.0473254	−	0.0819700i
$457$	16.4619	−	28.5128i	0.770054	−	1.33377i	−0.167478	−	0.985876i	$-0.553562\pi$
$457$	16.4619	−	28.5128i	0.770054	−	1.33377i	0.937533	−	0.347897i	$-0.113104\pi$
$458$	−10.9378	+	18.9449i	−0.511092	+	0.885237i
$459$	−1.76886	−	3.06375i	−0.0825631	−	0.143004i
$460$	−4.34495			−0.202584
$461$	−26.3424			−1.22689			−0.613444	−	0.789738i	$-0.710216\pi$
$461$	−26.3424			−1.22689			−0.613444	+	0.789738i	$0.710216\pi$
$462$	−0.585786	+	1.01461i	−0.0272533	+	0.0472040i
$463$	9.10013	+	15.7619i	0.422919	+	0.732517i	0.996224	−	0.0868252i	$-0.0276722\pi$
$463$	9.10013	+	15.7619i	0.422919	+	0.732517i	−0.573305	+	0.819342i	$0.694339\pi$
$464$	−0.756084			−0.0351003
$465$	2.11136	−	3.65699i	0.0979121	−	0.169589i
$466$	−9.70620			−0.449631
$467$	1.75106	+	3.03292i	0.0810293	+	0.140347i	0.903692	−	0.428182i	$-0.140846\pi$
$467$	1.75106	+	3.03292i	0.0810293	+	0.140347i	−0.822663	+	0.568529i	$0.807513\pi$
$468$	11.5183			0.532435
$469$	−11.5386	−	0.927572i	−0.532804	−	0.0428313i
$470$	−8.31498			−0.383542
$471$	2.55089	+	4.41827i	0.117539	+	0.203583i
$472$	2.87958			0.132543
$473$	11.7804	−	20.4042i	0.541661	−	0.938185i
$474$	−0.870805			−0.0399974
$475$	2.43979	+	4.22584i	0.111945	+	0.193895i
$476$	−1.03617	+	1.79470i	−0.0474929	+	0.0822600i
$477$	−16.8346			−0.770803
$478$	−9.21395			−0.421436
$479$	10.9669	+	18.9952i	0.501091	+	0.867915i	0.999999	+	0.00126003i	$0.000401082\pi$
$479$	10.9669	+	18.9952i	0.501091	+	0.867915i	−0.498908	+	0.866655i	$0.666266\pi$
$480$	0.207107	−	0.358719i	0.00945309	−	0.0163732i
$481$	−2.14033	+	3.70716i	−0.0975907	+	0.169032i
$482$	2.42327	+	4.19722i	0.110377	+	0.191178i
$483$	2.54521			0.115811
$484$	−7.00000			−0.318182
$485$	−8.30439	−	14.3836i	−0.377083	−	0.653127i
$486$	5.17157	+	8.95743i	0.234587	+	0.406317i
$487$	−5.12132	−	8.87039i	−0.232069	−	0.401956i	0.726348	−	0.687327i	$-0.241216\pi$
$487$	−5.12132	−	8.87039i	−0.232069	−	0.401956i	−0.958417	+	0.285372i	$0.907883\pi$
$488$	−5.57171	−	9.65048i	−0.252219	−	0.436857i
$489$	−0.478811	+	0.829325i	−0.0216526	+	0.0375034i
$490$	2.50000	−	4.33013i	0.112938	−	0.195615i
$491$	1.91708			0.0865164			0.0432582	−	0.999064i	$-0.486226\pi$
$491$	1.91708			0.0865164			0.0432582	+	0.999064i	$0.486226\pi$
$492$	2.38927	+	4.13834i	0.107717	+	0.186571i
$493$	−1.10794			−0.0498991
$494$	19.8713			0.894054
$495$	−2.82843	+	4.89898i	−0.127128	+	0.220193i
$496$	10.1946			0.457750
$497$	1.74328	+	3.01945i	0.0781967	+	0.135441i
$498$	−2.28294	+	3.95416i	−0.102301	+	0.177190i
$499$	7.66432	+	13.2750i	0.343102	+	0.594270i	0.985007	−	0.172514i	$-0.0551889\pi$
$499$	7.66432	+	13.2750i	0.343102	+	0.594270i	−0.641905	+	0.766784i	$0.721856\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−1.05646	+	1.82984i	−0.0471991	+	0.0817512i
$502$	14.1337	−	24.4803i	0.630819	−	1.09261i
$503$	10.8122	−	18.7272i	0.482091	−	0.835006i	−0.517698	−	0.855563i	$-0.673211\pi$
$503$	10.8122	−	18.7272i	0.482091	−	0.835006i	0.999789	+	0.0205578i	$0.00654421\pi$
$504$	2.00000	−	3.46410i	0.0890871	−	0.154303i
$505$	8.41512	−	14.5754i	0.374468	−	0.648597i
$506$	−4.34495	−	7.52567i	−0.193157	−	0.334557i
$507$	0.742267	−	1.28564i	0.0329652	−	0.0570975i
$508$	−6.29380	−	10.9012i	−0.279242	−	0.483661i
$509$	−28.3935			−1.25852			−0.629260	−	0.777195i	$-0.716642\pi$
$509$	−28.3935			−1.25852			−0.629260	+	0.777195i	$0.716642\pi$
$510$	0.303488	−	0.525656i	0.0134387	−	0.0232764i
$511$	−3.09923			−0.137102
$512$	1.00000			0.0441942
$513$	5.89018	+	10.2021i	0.260058	+	0.450433i
$514$	−28.8770			−1.27371
$515$	−0.863697	+	1.49597i	−0.0380590	+	0.0659202i
$516$	2.43979	−	4.22584i	0.107406	−	0.186032i
$517$	−8.31498	−	14.4020i	−0.365693	−	0.633398i
$518$	0.743279	+	1.28740i	0.0326578	+	0.0565649i
$519$	−0.960078	−	1.66290i	−0.0421427	−	0.0729934i
$520$	2.03617	+	3.52675i	0.0892920	+	0.154658i
$521$	0.436678			0.0191312			0.00956561	−	0.999954i	$-0.496955\pi$
$521$	0.436678			0.0191312			0.00956561	+	0.999954i	$0.496955\pi$
$522$	2.13853			0.0936008
$523$	−14.4029	−	24.9466i	−0.629797	−	1.09084i	−0.987592	−	0.157040i	$-0.949805\pi$
$523$	−14.4029	−	24.9466i	−0.629797	−	1.09084i	0.357795	−	0.933800i	$-0.383529\pi$
$524$	9.98592	−	17.2961i	0.436237	−	0.755584i
$525$	0.292893	−	0.507306i	0.0127829	−	0.0221406i
$526$	−4.81344	−	8.33713i	−0.209876	−	0.363516i
$527$	14.9388			0.650744
$528$	0.828427			0.0360527
$529$	2.06070	−	3.56925i	0.0895959	−	0.155185i
$530$	−2.97596	−	5.15452i	−0.129268	−	0.223898i
$531$	−8.14469			−0.353449
$532$	3.45039	−	5.97624i	0.149593	−	0.259103i
$533$	−46.9803			−2.03494
$534$	−2.64251	−	4.57696i	−0.114353	−	0.198064i
$535$	−2.29072			−0.0990363
$536$	3.51150	+	7.39388i	0.151674	+	0.319367i
$537$	−6.55837			−0.283015
$538$	−1.91575	−	3.31818i	−0.0825940	−	0.143057i
$539$	10.0000			0.430730
$540$	−1.20711	+	2.09077i	−0.0519456	+	0.0899724i
$541$	4.03252			0.173371			0.0866857	−	0.996236i	$-0.472372\pi$
$541$	4.03252			0.173371			0.0866857	+	0.996236i	$0.472372\pi$
$542$	−9.30503	−	16.1168i	−0.399685	−	0.692275i
$543$	3.48618	−	6.03825i	0.149606	−	0.259126i
$544$	1.46537			0.0628271
$545$	−20.4896			−0.877680
$546$	−1.19276	−	2.06592i	−0.0510455	−	0.0884134i
$547$	5.73114	−	9.92663i	0.245046	−	0.424432i	−0.717099	−	0.696972i	$-0.754530\pi$
$547$	5.73114	−	9.92663i	0.245046	−	0.424432i	0.962145	+	0.272540i	$0.0878636\pi$
$548$	1.97660	−	3.42357i	0.0844362	−	0.146248i
$549$	15.7592	+	27.2957i	0.672585	+	1.16495i
$550$	−2.00000			−0.0852803
$551$	3.68937			0.157173
$552$	−0.899869	−	1.55862i	−0.0383010	−	0.0663392i
$553$	−1.48656	−	2.57479i	−0.0632148	−	0.109491i
$554$	−4.13128	−	7.15558i	−0.175521	−	0.304012i
$555$	−0.217701	−	0.377070i	−0.00924090	−	0.0160057i
$556$	−3.61009	+	6.25286i	−0.153102	+	0.265180i
$557$	−5.13255	+	8.88984i	−0.217473	+	0.376675i	−0.954035	−	0.299696i	$-0.903115\pi$
$557$	−5.13255	+	8.88984i	−0.217473	+	0.376675i	0.736562	+	0.676370i	$0.236448\pi$
$558$	−28.8346			−1.22067
$559$	23.9868	+	41.5464i	1.01453	+	1.75723i
$560$	1.41421			0.0597614
$561$	1.21395			0.0512530
$562$	−3.15685	+	5.46783i	−0.133164	+	0.230647i
$563$	−37.4297			−1.57747			−0.788737	−	0.614731i	$-0.789265\pi$
$563$	−37.4297			−1.57747			−0.788737	+	0.614731i	$0.789265\pi$
$564$	−1.72209	−	2.98275i	−0.0725131	−	0.125596i
$565$	1.18217	−	2.04757i	0.0497342	−	0.0861421i
$566$	−3.35246	−	5.80664i	−0.140915	−	0.244071i
$567$	−5.29289	+	9.16756i	−0.222281	+	0.385001i
$568$	1.23268	−	2.13507i	0.0517223	−	0.0895856i
$569$	8.05890	−	13.9584i	0.337847	−	0.585168i	−0.646181	−	0.763184i	$-0.723635\pi$
$569$	8.05890	−	13.9584i	0.337847	−	0.585168i	0.984027	+	0.178017i	$0.0569681\pi$
$570$	−1.01059	+	1.75040i	−0.0423291	+	0.0733162i
$571$	−13.3917	+	23.1951i	−0.560426	+	0.970686i	0.437033	+	0.899445i	$0.356029\pi$
$571$	−13.3917	+	23.1951i	−0.560426	+	0.970686i	−0.997459	+	0.0712408i	$0.977304\pi$
$572$	−4.07234	+	7.05351i	−0.170273	+	0.294922i
$573$	−3.59044	−	6.21882i	−0.149993	−	0.259795i
$574$	−8.15749	+	14.1292i	−0.340487	+	0.589741i
$575$	2.17247	+	3.76284i	0.0905985	+	0.156921i
$576$	−2.82843			−0.117851
$577$	−11.1999	+	19.3987i	−0.466256	+	0.807579i	−0.999257	−	0.0385352i	$-0.987731\pi$
$577$	−11.1999	+	19.3987i	−0.466256	+	0.807579i	0.533001	+	0.846115i	$0.321064\pi$
$578$	−14.8527			−0.617791
$579$	8.94134			0.371590
$580$	0.378042	+	0.654788i	0.0156973	+	0.0271886i
$581$	−15.5889			−0.646735
$582$	3.43979	−	5.95789i	0.142584	−	0.246963i
$583$	5.95193	−	10.3090i	0.246504	−	0.426957i
$584$	1.09574	+	1.89788i	0.0453422	+	0.0785349i
$585$	−5.75916	−	9.97516i	−0.238112	−	0.412422i
$586$	−1.78448	−	3.09080i	−0.0737160	−	0.127680i
$587$	−18.0810	−	31.3172i	−0.746282	−	1.29260i	−0.949593	−	0.313485i	$-0.898504\pi$
$587$	−18.0810	−	31.3172i	−0.746282	−	1.29260i	0.203311	−	0.979114i	$-0.434830\pi$
$588$	2.07107			0.0854094
$589$	−49.7452			−2.04972
$590$	−1.43979	−	2.49379i	−0.0592753	−	0.102668i
$591$	3.51472	−	6.08767i	0.144576	−	0.250413i
$592$	0.525577	−	0.910327i	0.0216011	−	0.0374142i
$593$	−5.59638	−	9.69322i	−0.229816	−	0.398053i	0.727938	−	0.685643i	$-0.240479\pi$
$593$	−5.59638	−	9.69322i	−0.229816	−	0.398053i	−0.957753	+	0.287591i	$0.907146\pi$
$594$	−4.82843			−0.198113
$595$	2.07234			0.0849578
$596$	−5.10634	+	8.84444i	−0.209164	+	0.362282i
$597$	4.02531	+	6.97205i	0.164745	+	0.285347i
$598$	17.6941			0.723567
$599$	0.149108	−	0.258263i	0.00609239	−	0.0105523i	−0.862963	−	0.505267i	$-0.831394\pi$
$599$	0.149108	−	0.258263i	0.00609239	−	0.0105523i	0.869056	+	0.494715i	$0.164727\pi$
$600$	−0.414214			−0.0169102
$601$	15.3424	+	26.5738i	0.625828	+	1.08397i	0.988380	+	0.152003i	$0.0485722\pi$
$601$	15.3424	+	26.5738i	0.625828	+	1.08397i	−0.362552	+	0.931964i	$0.618094\pi$
$602$	16.6599			0.679008
$603$	−9.93201	−	20.9130i	−0.404463	−	0.851645i
$604$	6.26691			0.254997
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$	6.97131			0.283190
$607$	−3.81652	+	6.61041i	−0.154908	+	0.268308i	−0.933026	−	0.359810i	$-0.882841\pi$
$607$	−3.81652	+	6.61041i	−0.154908	+	0.268308i	0.778118	+	0.628119i	$0.216175\pi$
$608$	−4.87958			−0.197893
$609$	−0.221452	−	0.383566i	−0.00897368	−	0.0155429i
$610$	−5.57171	+	9.65048i	−0.225592	+	0.390736i
$611$	33.8615			1.36989
$612$	−4.14469			−0.167539
$613$	2.40516	+	4.16586i	0.0971435	+	0.168257i	0.910501	−	0.413506i	$-0.135696\pi$
$613$	2.40516	+	4.16586i	0.0971435	+	0.168257i	−0.813358	+	0.581764i	$0.802363\pi$
$614$	16.2813	−	28.2000i	0.657058	−	1.13806i
$615$	2.38927	−	4.13834i	0.0963448	−	0.166874i
$616$	1.41421	+	2.44949i	0.0569803	+	0.0986928i
$617$	32.8064			1.32074			0.660368	−	0.750942i	$-0.270400\pi$
$617$	32.8064			1.32074			0.660368	+	0.750942i	$0.270400\pi$
$618$	−0.715510			−0.0287820
$619$	−19.2828	−	33.3988i	−0.775042	−	1.34241i	−0.934771	−	0.355252i	$-0.884395\pi$
$619$	−19.2828	−	33.3988i	−0.775042	−	1.34241i	0.159728	−	0.987161i	$-0.448938\pi$
$620$	−5.09728	−	8.82875i	−0.204712	−	0.354571i
$621$	5.24482	+	9.08429i	0.210467	+	0.364540i
$622$	13.8415	+	23.9741i	0.554992	+	0.961275i
$623$	9.02209	−	15.6267i	0.361462	−	0.626071i
$624$	−0.843410	+	1.46083i	−0.0337634	+	0.0584800i
$625$	1.00000			0.0400000
$626$	−2.12974	−	3.68881i	−0.0851214	−	0.147435i
$627$	−4.04238			−0.161437
$628$	12.3168			0.491493
$629$	0.770164	−	1.33396i	0.0307085	−	0.0531886i
$630$	−4.00000			−0.159364
$631$	−0.564597	−	0.977912i	−0.0224763	−	0.0389300i	0.854568	−	0.519339i	$-0.173822\pi$
$631$	−0.564597	−	0.977912i	−0.0224763	−	0.0389300i	−0.877045	+	0.480409i	$0.840488\pi$
$632$	−1.05115	+	1.82065i	−0.0418127	+	0.0724217i
$633$	3.23863	+	5.60946i	0.128724	+	0.222956i
$634$	−0.695874	+	1.20529i	−0.0276367	+	0.0478682i
$635$	−6.29380	+	10.9012i	−0.249762	+	0.432600i
$636$	1.23268	−	2.13507i	0.0488791	−	0.0846611i
$637$	−10.1809	+	17.6338i	−0.403380	+	0.698675i
$638$	−0.756084	+	1.30958i	−0.0299336	+	0.0518466i
$639$	−3.48656	+	6.03889i	−0.137926	+	0.238895i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−14.1178	+	24.4528i	−0.557621	+	0.965828i	0.440074	+	0.897962i	$0.354952\pi$
$641$	−14.1178	+	24.4528i	−0.557621	+	0.965828i	−0.997694	+	0.0678660i	$0.978381\pi$
$642$	−0.474423	−	0.821724i	−0.0187240	−	0.0324309i
$643$	−16.1372			−0.636387			−0.318194	−	0.948026i	$-0.603076\pi$
$643$	−16.1372			−0.636387			−0.318194	+	0.948026i	$0.603076\pi$
$644$	3.07234	−	5.32146i	0.121067	−	0.209695i
$645$	−4.87958			−0.192133
$646$	−7.15038			−0.281328
$647$	−17.3692	−	30.0844i	−0.682854	−	1.18274i	−0.974106	−	0.226092i	$-0.927405\pi$
$647$	−17.3692	−	30.0844i	−0.682854	−	1.18274i	0.291251	−	0.956647i	$-0.405928\pi$
$648$	7.48528			0.294050
$649$	2.87958	−	4.98758i	0.113033	−	0.195780i
$650$	2.03617	−	3.52675i	0.0798652	−	0.138331i
$651$	2.98592	+	5.17176i	0.117027	+	0.202697i
$652$	1.15595	+	2.00217i	0.0452706	+	0.0784109i
$653$	15.6315	+	27.0746i	0.611709	+	1.05951i	0.990952	+	0.134215i	$0.0428512\pi$
$653$	15.6315	+	27.0746i	0.611709	+	1.05951i	−0.379243	+	0.925297i	$0.623815\pi$
$654$	−4.24354	−	7.35003i	−0.165936	−	0.287409i
$655$	−19.9718			−0.780364
$656$	11.5364			0.450422
$657$	−3.09923	−	5.36802i	−0.120912	−	0.209427i
$658$	5.87958	−	10.1837i	0.229210	−	0.397003i
$659$	−3.02866	+	5.24579i	−0.117980	+	0.204347i	−0.918967	−	0.394335i	$-0.870975\pi$
$659$	−3.02866	+	5.24579i	−0.117980	+	0.204347i	0.800987	+	0.598681i	$0.204308\pi$
$660$	−0.414214	−	0.717439i	−0.0161232	−	0.0279263i
$661$	34.5858			1.34523			0.672616	−	0.739992i	$-0.265171\pi$
$661$	34.5858			1.34523			0.672616	+	0.739992i	$0.265171\pi$
$662$	−19.3674			−0.752736
$663$	−1.23591	+	2.14065i	−0.0479986	+	0.0831360i
$664$	5.51150	+	9.54619i	0.213888	+	0.370464i
$665$	−6.90077			−0.267600
$666$	−1.48656	+	2.57479i	−0.0576029	+	0.0997712i
$667$	3.28515			0.127201
$668$	2.55052	+	4.41762i	0.0986825	+	0.170923i
$669$	−3.08423			−0.119243
$670$	4.64754	−	6.73798i	0.179550	−	0.260311i
$671$	−22.2868			−0.860373
$672$	0.292893	+	0.507306i	0.0112986	+	0.0195698i
$673$	1.29762			0.0500197			0.0250098	−	0.999687i	$-0.492038\pi$
$673$	1.29762			0.0500197			0.0250098	+	0.999687i	$0.492038\pi$
$674$	10.2298	−	17.7186i	0.394039	−	0.682495i
$675$	2.41421			0.0929231
$676$	−1.79199	−	3.10382i	−0.0689227	−	0.119378i
$677$	−17.7488	+	30.7419i	−0.682143	+	1.18151i	0.292182	+	0.956363i	$0.405619\pi$
$677$	−17.7488	+	30.7419i	−0.682143	+	1.18151i	−0.974326	+	0.225144i	$0.927715\pi$
$678$	0.979339			0.0376113
$679$	23.4884			0.901401
$680$	−0.732684	−	1.26905i	−0.0280972	−	0.0486657i
$681$	−4.64214	+	8.04041i	−0.177887	+	0.308109i
$682$	10.1946	−	17.6575i	0.390370	−	0.676141i
$683$	−9.45410	−	16.3750i	−0.361751	−	0.626571i	0.626498	−	0.779423i	$-0.284488\pi$
$683$	−9.45410	−	16.3750i	−0.361751	−	0.626571i	−0.988249	+	0.152852i	$0.951154\pi$
$684$	13.8015			0.527715
$685$	−3.95320			−0.151044
$686$	8.48528	+	14.6969i	0.323970	+	0.561132i
$687$	4.53060	+	7.84724i	0.172853	+	0.299391i
$688$	−5.89018	−	10.2021i	−0.224561	−	0.388951i
$689$	12.1191	+	20.9910i	0.461703	+	0.799692i
$690$	−0.899869	+	1.55862i	−0.0342574	+	0.0593356i
$691$	19.1222	−	33.1207i	0.727444	−	1.25997i	−0.230517	−	0.973068i	$-0.574042\pi$
$691$	19.1222	−	33.1207i	0.727444	−	1.25997i	0.957960	−	0.286901i	$-0.0926251\pi$
$692$	−4.63567			−0.176222
$693$	−4.00000	−	6.92820i	−0.151947	−	0.263181i
$694$	−24.0273			−0.912066
$695$	7.22018			0.273877
$696$	−0.156590	+	0.271222i	−0.00593553	+	0.0102806i
$697$	16.9051			0.640327
$698$	8.01806	+	13.8877i	0.303488	+	0.525657i
$699$	−2.01022	+	3.48180i	−0.0760335	+	0.131694i
$700$	−0.707107	−	1.22474i	−0.0267261	−	0.0462910i
$701$	21.3873	−	37.0439i	0.807788	−	1.39913i	−0.106604	−	0.994302i	$-0.533998\pi$
$701$	21.3873	−	37.0439i	0.807788	−	1.39913i	0.914393	−	0.404829i	$-0.132669\pi$
$702$	4.91575	−	8.51433i	0.185533	−	0.321353i
$703$	−2.56460	+	4.44201i	−0.0967256	+	0.167534i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−1.72209	+	2.98275i	−0.0648576	+	0.112337i
$706$	15.5224	−	26.8855i	0.584192	−	1.01185i
$707$	11.9008	+	20.6127i	0.447575	+	0.775222i
$708$	0.596381	−	1.03296i	0.0224134	−	0.0388211i
$709$	−19.5083	−	33.7893i	−0.732649	−	1.26898i	−0.955747	−	0.294189i	$-0.904951\pi$
$709$	−19.5083	−	33.7893i	−0.732649	−	1.26898i	0.223099	−	0.974796i	$-0.428383\pi$
$710$	−2.46537			−0.0925236
$711$	2.97311	−	5.14958i	0.111500	−	0.193125i
$712$	−12.7592			−0.478170
$713$	−44.2949			−1.65886
$714$	0.429196	+	0.743390i	0.0160623	+	0.0278207i
$715$	8.14469			0.304594
$716$	−7.91666	+	13.7120i	−0.295859	+	0.512443i
$717$	−1.90827	+	3.30522i	−0.0712657	+	0.123436i
$718$	−7.56393	−	13.1011i	−0.282283	−	0.488929i
$719$	1.28696	+	2.22909i	0.0479957	+	0.0831310i	0.889025	−	0.457858i	$-0.151383\pi$
$719$	1.28696	+	2.22909i	0.0479957	+	0.0831310i	−0.841030	+	0.540989i	$0.818050\pi$
$720$	1.41421	+	2.44949i	0.0527046	+	0.0912871i
$721$	−1.22145	−	2.11562i	−0.0454892	−	0.0787897i
$722$	4.81032			0.179022
$723$	2.00750			0.0746598
$724$	−8.41639	−	14.5776i	−0.312793	−	0.541773i
$725$	0.378042	−	0.654788i	0.0140401	−	0.0243182i
$726$	−1.44975	+	2.51104i	−0.0538052	+	0.0931933i
$727$	14.3362	+	24.8310i	0.531699	+	0.920930i	0.999315	+	0.0369984i	$0.0117797\pi$
$727$	14.3362	+	24.8310i	0.531699	+	0.920930i	−0.467616	+	0.883932i	$0.654887\pi$
$728$	−5.75916			−0.213449
$729$	−18.1716			−0.673021
$730$	1.09574	−	1.89788i	0.0405553	−	0.0702438i
$731$	−8.63128	−	14.9498i	−0.319239	−	0.552939i
$732$	−4.61575			−0.170603
$733$	−10.3783	+	17.9757i	−0.383330	+	0.663948i	−0.991536	−	0.129832i	$-0.958556\pi$
$733$	−10.3783	+	17.9757i	−0.383330	+	0.663948i	0.608206	+	0.793779i	$0.291890\pi$
$734$	0.727922			0.0268681
$735$	−1.03553	−	1.79360i	−0.0381962	−	0.0661578i
$736$	−4.34495			−0.160157
$737$	16.3181	+	1.31178i	0.601084	+	0.0483202i
$738$	−32.6300			−1.20113
$739$	−6.19895	−	10.7369i	−0.228032	−	0.394963i	0.729193	−	0.684308i	$-0.239896\pi$
$739$	−6.19895	−	10.7369i	−0.228032	−	0.394963i	−0.957225	+	0.289345i	$0.906562\pi$
$740$	−1.05115			−0.0386412
$741$	4.11549	−	7.12823i	0.151186	−	0.261862i
$742$	8.41729			0.309009
$743$	5.15531	+	8.92927i	0.189130	+	0.327583i	0.944960	−	0.327185i	$-0.106100\pi$
$743$	5.15531	+	8.92927i	0.189130	+	0.327583i	−0.755830	+	0.654768i	$0.772767\pi$
$744$	2.11136	−	3.65699i	0.0774064	−	0.134072i
$745$	10.2127			0.374163
$746$	−11.8796			−0.434942
$747$	−15.5889	−	27.0007i	−0.570367	−	0.987904i
$748$	1.46537	−	2.53809i	0.0535792	−	0.0928018i
$749$	1.61978	−	2.80554i	0.0591855	−	0.102512i
$750$	0.207107	+	0.358719i	0.00756247	+	0.0130986i
$751$	23.1677			0.845401			0.422700	−	0.906270i	$-0.361082\pi$
$751$	23.1677			0.845401			0.422700	+	0.906270i	$0.361082\pi$
$752$	−8.31498			−0.303216
$753$	−5.85438	−	10.1401i	−0.213345	−	0.369525i
$754$	−1.53952	−	2.66652i	−0.0560659	−	0.0971089i
$755$	−3.13345	−	5.42730i	−0.114038	−	0.197520i
$756$	−1.70711	−	2.95680i	−0.0620869	−	0.107538i
$757$	3.03902	−	5.26374i	0.110455	−	0.191314i	−0.805499	−	0.592597i	$-0.798103\pi$
$757$	3.03902	−	5.26374i	0.110455	−	0.191314i	0.915954	+	0.401284i	$0.131436\pi$
$758$	11.5576	−	20.0184i	0.419792	−	0.727101i
$759$	−3.59947			−0.130653
$760$	2.43979	+	4.22584i	0.0885005	+	0.153287i
$761$	18.7055			0.678072			0.339036	−	0.940773i	$-0.389899\pi$
$761$	18.7055			0.678072			0.339036	+	0.940773i	$0.389899\pi$
$762$	−5.21395			−0.188882
$763$	14.4884	−	25.0946i	0.524514	−	0.908485i
$764$	−17.3362			−0.627201
$765$	2.07234	+	3.58940i	0.0749257	+	0.129775i
$766$	−4.10103	+	7.10320i	−0.148176	+	0.256649i
$767$	5.86332	+	10.1556i	0.211712	+	0.366697i
$768$	0.207107	−	0.358719i	0.00747332	−	0.0129442i
$769$	−2.88269	+	4.99297i	−0.103953	+	0.180051i	−0.913310	−	0.407266i	$-0.866482\pi$
$769$	−2.88269	+	4.99297i	−0.103953	+	0.180051i	0.809357	+	0.587317i	$0.199816\pi$
$770$	1.41421	−	2.44949i	0.0509647	−	0.0882735i
$771$	−5.98062	+	10.3587i	−0.215387	+	0.373061i
$772$	10.7932	−	18.6943i	0.388454	−	0.672822i
$773$	15.0832	−	26.1249i	0.542505	−	0.939646i	−0.456254	−	0.889849i	$-0.650809\pi$
$773$	15.0832	−	26.1249i	0.542505	−	0.939646i	0.998759	−	0.0497969i	$-0.0158574\pi$
$774$	16.6599	+	28.8559i	0.598829	+	1.03720i
$775$	−5.09728	+	8.82875i	−0.183100	+	0.317138i
$776$	−8.30439	−	14.3836i	−0.298110	−	0.516342i
$777$	0.615752			0.0220900
$778$	−5.44948	+	9.43878i	−0.195373	+	0.338397i
$779$	−56.2930			−2.01691
$780$	1.68682			0.0603978
$781$	−2.46537	−	4.27014i	−0.0882178	−	0.152798i
$782$	−6.36695			−0.227682
$783$	0.912674	−	1.58080i	0.0326163	−	0.0564931i
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$	−6.15839	−	10.6667i	−0.219803	−	0.380709i
$786$	−4.13630	−	7.16429i	−0.147537	−	0.255542i
$787$	23.1696	+	40.1310i	0.825908	+	1.43051i	0.901223	+	0.433355i	$0.142670\pi$
$787$	23.1696	+	40.1310i	0.825908	+	1.43051i	−0.0753154	+	0.997160i	$0.523996\pi$
$788$	−8.48528	−	14.6969i	−0.302276	−	0.523557i
$789$	−3.98759			−0.141962
$790$	2.10231			0.0747968
$791$	1.67184	+	2.89571i	0.0594437	+	0.102959i
$792$	−2.82843	+	4.89898i	−0.100504	+	0.174078i
$793$	22.6899	−	39.3001i	0.805742	−	1.39559i
$794$	−3.78320	−	6.55270i	−0.134261	−	0.232546i
$795$	−2.46537			−0.0874376
$796$	19.4359			0.688888
$797$	1.73077	−	2.99778i	0.0613070	−	0.106187i	−0.833743	−	0.552153i	$-0.813806\pi$
$797$	1.73077	−	2.99778i	0.0613070	−	0.106187i	0.895050	+	0.445966i	$0.147140\pi$
$798$	−1.42920	−	2.47544i	−0.0505930	−	0.0876297i
$799$	−12.1845			−0.431057
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	36.0884			1.27512
$802$	−1.09923	−	1.90392i	−0.0388151	−	0.0672298i
$803$	4.38297			0.154672
$804$	3.37958	+	0.271680i	0.119189	+	0.00958140i
$805$	−6.14469			−0.216572
$806$	20.7579	+	35.9537i	0.731165	+	1.26642i
$807$	−1.58706			−0.0558672
$808$	8.41512	−	14.5754i	0.296043	−	0.512761i
$809$	−3.22895			−0.113524			−0.0567620	−	0.998388i	$-0.518078\pi$
$809$	−3.22895			−0.113524			−0.0567620	+	0.998388i	$0.518078\pi$
$810$	−3.74264	−	6.48244i	−0.131503	−	0.227770i
$811$	−9.83373	+	17.0325i	−0.345309	+	0.598093i	−0.985410	−	0.170198i	$-0.945559\pi$
$811$	−9.83373	+	17.0325i	−0.345309	+	0.598093i	0.640101	+	0.768291i	$0.278893\pi$
$812$	−1.06926			−0.0375238
$813$	−7.70854			−0.270350
$814$	−1.05115	−	1.82065i	−0.0368430	−	0.0638139i
$815$	1.15595	−	2.00217i	0.0404912	−	0.0701329i
$816$	0.303488	−	0.525656i	0.0106242	−	0.0184016i
$817$	28.7416	+	49.7819i	1.00554	+	1.74165i
$818$	−2.46717			−0.0862627
$819$	16.2894			0.569197
$820$	−5.76822	−	9.99085i	−0.201435	−	0.348895i
$821$	12.6440	+	21.9001i	0.441280	+	0.764320i	0.997785	−	0.0665246i	$-0.0211911\pi$
$821$	12.6440	+	21.9001i	0.441280	+	0.764320i	−0.556504	+	0.830845i	$0.687858\pi$
$822$	−0.818735	−	1.41809i	−0.0285567	−	0.0494616i
$823$	−7.36614	−	12.7585i	−0.256767	−	0.444734i	0.708607	−	0.705604i	$-0.249324\pi$
$823$	−7.36614	−	12.7585i	−0.256767	−	0.444734i	−0.965374	+	0.260869i	$0.915991\pi$
$824$	−0.863697	+	1.49597i	−0.0300883	+	0.0521145i
$825$	−0.414214	+	0.717439i	−0.0144211	+	0.0249780i
$826$	4.07234			0.141695
$827$	−1.75481	−	3.03942i	−0.0610206	−	0.105691i	0.833901	−	0.551914i	$-0.186102\pi$
$827$	−1.75481	−	3.03942i	−0.0610206	−	0.105691i	−0.894922	+	0.446223i	$0.852769\pi$
$828$	12.2894			0.427085
$829$	−20.3175			−0.705657			−0.352829	−	0.935688i	$-0.614780\pi$
$829$	−20.3175			−0.705657			−0.352829	+	0.935688i	$0.614780\pi$
$830$	5.51150	−	9.54619i	0.191307	−	0.331353i
$831$	−3.42246			−0.118724
$832$	2.03617	+	3.52675i	0.0705916	+	0.122268i
$833$	3.66342	−	6.34523i	0.126930	−	0.219849i
$834$	1.49535	+	2.59002i	0.0517796	+	0.0896850i
$835$	2.55052	−	4.41762i	0.0882643	−	0.152878i
$836$	−4.87958	+	8.45168i	−0.168764	+	0.292308i
$837$	−12.3059	+	21.3145i	−0.425355	+	0.736737i
$838$	7.17026	−	12.4193i	0.247693	−	0.429016i
$839$	−4.59081	+	7.95152i	−0.158492	+	0.274517i	−0.934325	−	0.356422i	$-0.883997\pi$
$839$	−4.59081	+	7.95152i	−0.158492	+	0.274517i	0.775833	+	0.630939i	$0.217330\pi$
$840$	0.292893	−	0.507306i	0.0101058	−	0.0175037i
$841$	14.2142	+	24.6197i	0.490144	+	0.848954i
$842$	10.2426	−	17.7408i	0.352985	−	0.611387i
$843$	1.30761	+	2.26485i	0.0450365	+	0.0780056i
$844$	15.6375			0.538264
$845$	−1.79199	+	3.10382i	−0.0616464	+	0.106775i
$846$	23.5183			0.808577
$847$	−9.89949			−0.340151
$848$	−2.97596	−	5.15452i	−0.102195	−	0.177007i
$849$	−2.77727			−0.0953157
$850$	−0.732684	+	1.26905i	−0.0251309	+	0.0435279i
$851$	−2.28361	+	3.95532i	−0.0782810	+	0.135587i
$852$	−0.510594	−	0.884376i	−0.0174927	−	0.0302982i
$853$	−7.03077	−	12.1777i	−0.240729	−	0.416955i	0.720193	−	0.693774i	$-0.244053\pi$
$853$	−7.03077	−	12.1777i	−0.240729	−	0.416955i	−0.960922	+	0.276819i	$0.910720\pi$
$854$	−7.87958	−	13.6478i	−0.269634	−	0.467019i
$855$	−6.90077	−	11.9525i	−0.236001	−	0.408766i
$856$	−2.29072			−0.0782950
$857$	43.6349			1.49054			0.745269	−	0.666764i	$-0.232321\pi$
$857$	43.6349			1.49054			0.745269	+	0.666764i	$0.232321\pi$
$858$	1.68682	+	2.92166i	0.0575871	+	0.0997438i
$859$	13.0455	−	22.5955i	0.445106	−	0.770947i	−0.552953	−	0.833212i	$-0.686499\pi$
$859$	13.0455	−	22.5955i	0.445106	−	0.770947i	0.998060	+	0.0622654i	$0.0198325\pi$
$860$	−5.89018	+	10.2021i	−0.200853	+	0.347888i
$861$	3.37894	+	5.85250i	0.115154	+	0.199453i
$862$	−10.4654			−0.356452
$863$	−57.6711			−1.96315			−0.981573	−	0.191087i	$-0.938799\pi$
$863$	−57.6711			−1.96315			−0.981573	+	0.191087i	$0.938799\pi$
$864$	−1.20711	+	2.09077i	−0.0410666	+	0.0711294i
$865$	2.31783	+	4.01460i	0.0788087	+	0.136501i
$866$	1.22453			0.0416113
$867$	−3.07609	+	5.32795i	−0.104470	+	0.180947i
$868$	14.4173			0.489355
$869$	2.10231	+	3.64131i	0.0713160	+	0.123523i
$870$	0.313180			0.0106178
$871$	−18.9264	+	27.4394i	−0.641295	+	0.929748i
$872$	−20.4896			−0.693867
$873$	23.4884	+	40.6830i	0.794961	+	1.37691i
$874$	21.2015			0.717153
$875$	−0.707107	+	1.22474i	−0.0239046	+	0.0414039i
$876$	0.907743			0.0306698
$877$	26.4041	+	45.7333i	0.891604	+	1.54430i	0.837953	+	0.545743i	$0.183753\pi$
$877$	26.4041	+	45.7333i	0.891604	+	1.54430i	0.0536510	+	0.998560i	$0.482914\pi$
$878$	0.595743	−	1.03186i	0.0201054	−	0.0348235i
$879$	−1.47831			−0.0498621
$880$	−2.00000			−0.0674200
$881$	−3.76822	−	6.52675i	−0.126954	−	0.219892i	0.795541	−	0.605900i	$-0.207187\pi$
$881$	−3.76822	−	6.52675i	−0.126954	−	0.219892i	−0.922495	+	0.386008i	$0.873854\pi$
$882$	−7.07107	+	12.2474i	−0.238095	+	0.412393i
$883$	−18.1465	+	31.4306i	−0.610678	+	1.05773i	0.380448	+	0.924802i	$0.375770\pi$
$883$	−18.1465	+	31.4306i	−0.610678	+	1.05773i	−0.991126	+	0.132923i	$0.957564\pi$
$884$	2.98374	+	5.16799i	0.100354	+	0.173818i
$885$	−1.19276			−0.0400942
$886$	9.48348			0.318604
$887$	−24.6278	−	42.6566i	−0.826920	−	1.43227i	−0.900443	−	0.434974i	$-0.856757\pi$
$887$	−24.6278	−	42.6566i	−0.826920	−	1.43227i	0.0735225	−	0.997294i	$-0.476576\pi$
$888$	−0.217701	−	0.377070i	−0.00730558	−	0.0126536i
$889$	−8.90077	−	15.4166i	−0.298522	−	0.517056i
$890$	6.37958	+	11.0498i	0.213844	+	0.370389i
$891$	7.48528	−	12.9649i	0.250766	−	0.434340i
$892$	−3.72299	+	6.44841i	−0.124655	+	0.215909i
$893$	40.5736			1.35775
$894$	2.11511	+	3.66349i	0.0707400	+	0.122525i
$895$	15.8333			0.529249
$896$	1.41421			0.0472456
$897$	3.66457	−	6.34723i	0.122357	−	0.211928i
$898$	−26.5669			−0.886550
$899$	3.85397	+	6.67527i	0.128537	+	0.222633i
$900$	1.41421	−	2.44949i	0.0471405	−	0.0816497i
$901$	−4.36088	−	7.55327i	−0.145282	−	0.251636i
$902$	11.5364	−	19.9817i	0.384121	−	0.665318i
$903$	3.45039	−	5.97624i	0.114822	−	0.198877i
$904$	1.18217	−	2.04757i	0.0393183	−	0.0681013i
$905$	−8.41639	+	14.5776i	−0.279770	+	0.484576i
$906$	1.29792	−	2.24806i	0.0431205	−	0.0746869i
$907$	−2.19651	+	3.80447i	−0.0729340	+	0.126325i	−0.900186	−	0.435506i	$-0.856570\pi$
$907$	−2.19651	+	3.80447i	−0.0729340	+	0.126325i	0.827252	+	0.561831i	$0.189903\pi$
$908$	11.2071	+	19.4113i	0.371921	+	0.644186i
$909$	−23.8015	+	41.2255i	−0.789447	+	1.36736i
$910$	2.87958	+	4.98758i	0.0954572	+	0.165337i
$911$	−35.0230			−1.16036			−0.580182	−	0.814487i	$-0.697018\pi$
$911$	−35.0230			−1.16036			−0.580182	+	0.814487i	$0.697018\pi$
$912$	−1.01059	+	1.75040i	−0.0334641	+	0.0579616i
$913$	22.0460			0.729616
$914$	−32.9238			−1.08902
$915$	2.30788	+	3.99736i	0.0762960	+	0.132149i
$916$	21.8757			0.722793
$917$	14.1222	−	24.4604i	0.466357	−	0.807754i
$918$	−1.76886	+	3.06375i	−0.0583809	+	0.101119i
$919$	22.8133	+	39.5138i	0.752541	+	1.30344i	0.946587	+	0.322448i	$0.104506\pi$
$919$	22.8133	+	39.5138i	0.752541	+	1.30344i	−0.194046	+	0.980992i	$0.562161\pi$
$920$	2.17247	+	3.76284i	0.0716244	+	0.124057i
$921$	−6.74392	−	11.6808i	−0.222220	−	0.384896i
$922$	13.1712	+	22.8132i	0.433770	+	0.751312i
$923$	10.0398			0.330465
$924$	1.17157			0.0385419
$925$	0.525577	+	0.910327i	0.0172809	+	0.0299314i
$926$	9.10013	−	15.7619i	0.299049	−	0.517968i
$927$	2.44290	−	4.23123i	0.0802355	−	0.138972i
$928$	0.378042	+	0.654788i	0.0124098	+	0.0214945i
$929$	40.9819			1.34457			0.672286	−	0.740291i	$-0.265312\pi$
$929$	40.9819			1.34457			0.672286	+	0.740291i	$0.265312\pi$
$930$	−4.22273			−0.138469
$931$	−12.1990	+	21.1292i	−0.399805	+	0.692482i
$932$	4.85310	+	8.40582i	0.158969	+	0.275342i
$933$	11.4666			0.375401
$934$	1.75106	−	3.03292i	0.0572963	−	0.0992402i
$935$	−2.93074			−0.0958453
$936$	−5.75916	−	9.97516i	−0.188244	−	0.326048i
$937$	59.7196			1.95095			0.975477	−	0.220100i	$-0.0706384\pi$
$937$	59.7196			1.95095			0.975477	+	0.220100i	$0.0706384\pi$
$938$	4.96601	+	10.4565i	0.162146	+	0.341417i
$939$	−1.76433			−0.0575768
$940$	4.15749	+	7.20099i	0.135602	+	0.234870i
$941$	15.8914			0.518046			0.259023	−	0.965871i	$-0.416599\pi$
$941$	15.8914			0.518046			0.259023	+	0.965871i	$0.416599\pi$
$942$	2.55089	−	4.41827i	0.0831125	−	0.143955i
$943$	−50.1252			−1.63230
$944$	−1.43979	−	2.49379i	−0.0468612	−	0.0811660i
$945$	−1.70711	+	2.95680i	−0.0555322	+	0.0961846i
$946$	−23.5607			−0.766025
$947$	19.8316			0.644440			0.322220	−	0.946665i	$-0.395571\pi$
$947$	19.8316			0.644440			0.322220	+	0.946665i	$0.395571\pi$
$948$	0.435403	+	0.754139i	0.0141412	+	0.0244933i
$949$	−4.46224	+	7.72883i	−0.144851	+	0.250888i
$950$	2.43979	−	4.22584i	0.0791573	−	0.137104i
$951$	0.288241	+	0.499247i	0.00934684	+	0.0161892i
$952$	2.07234			0.0671650
$953$	34.3080			1.11135			0.555673	−	0.831401i	$-0.312461\pi$
$953$	34.3080			1.11135			0.555673	+	0.831401i	$0.312461\pi$
$954$	8.41729	+	14.5792i	0.272520	+	0.472018i
$955$	8.66809	+	15.0136i	0.280493	+	0.485828i
$956$	4.60698	+	7.97952i	0.149000	+	0.258076i
$957$	0.313180	+	0.542444i	0.0101237	+	0.0175347i
$958$	10.9669	−	18.9952i	0.354325	−	0.613708i
$959$	2.79534	−	4.84166i	0.0902661	−	0.156345i
$960$	−0.414214			−0.0133687
$961$	−36.4646	−	63.1585i	−1.17628	−	2.03737i
$962$	4.28066			0.138014
$963$	6.47912			0.208787
$964$	2.42327	−	4.19722i	0.0780482	−	0.135183i
$965$	−21.5863			−0.694888
$966$	−1.27261	−	2.20422i	−0.0409454	−	0.0709196i
$967$	15.7957	−	27.3590i	0.507956	−	0.879805i	−0.492002	−	0.870594i	$-0.663735\pi$
$967$	15.7957	−	27.3590i	0.507956	−	0.879805i	0.999958	−	0.00921101i	$-0.00293200\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	−1.48089	+	2.56498i	−0.0475731	+	0.0823991i
$970$	−8.30439	+	14.3836i	−0.266638	+	0.461830i
$971$	11.4116	−	19.7655i	0.366217	−	0.634306i	−0.622754	−	0.782418i	$-0.713986\pi$
$971$	11.4116	−	19.7655i	0.366217	−	0.634306i	0.988971	+	0.148112i	$0.0473196\pi$
$972$	5.17157	−	8.95743i	0.165878	−	0.287310i
$973$	−5.10544	+	8.84287i	−0.163673	+	0.283490i
$974$	−5.12132	+	8.87039i	−0.164098	+	0.284226i
$975$	−0.843410	−	1.46083i	−0.0270107	−	0.0467840i
$976$	−5.57171	+	9.65048i	−0.178346	+	0.308904i
$977$	−21.6048	−	37.4205i	−0.691197	−	1.19719i	−0.971446	−	0.237261i	$-0.923750\pi$
$977$	−21.6048	−	37.4205i	−0.691197	−	1.19719i	0.280249	−	0.959927i	$-0.409583\pi$
$978$	0.957622			0.0306214
$979$	−12.7592	+	22.0995i	−0.407785	+	0.706304i
$980$	−5.00000			−0.159719
$981$	57.9534			1.85031
$982$	−0.958538	−	1.66024i	−0.0305882	−	0.0529803i
$983$	−35.7336			−1.13972			−0.569862	−	0.821741i	$-0.693003\pi$
$983$	−35.7336			−1.13972			−0.569862	+	0.821741i	$0.693003\pi$
$984$	2.38927	−	4.13834i	0.0761673	−	0.131926i
$985$	−8.48528	+	14.6969i	−0.270364	+	0.468283i
$986$	0.553970	+	0.959505i	0.0176420	+	0.0305569i
$987$	−2.43540	−	4.21824i	−0.0775197	−	0.134268i
$988$	−9.93567	−	17.2091i	−0.316096	−	0.547494i
$989$	25.5925	+	44.3275i	0.813795	+	1.40953i
$990$	5.65685			0.179787
$991$	33.4385			1.06221			0.531104	−	0.847307i	$-0.321777\pi$
$991$	33.4385			1.06221			0.531104	+	0.847307i	$0.321777\pi$
$992$	−5.09728	−	8.82875i	−0.161839	−	0.280313i
$993$	−4.01112	+	6.94747i	−0.127289	+	0.220471i
$994$	1.74328	−	3.01945i	0.0552934	−	0.0957710i
$995$	−9.71797	−	16.8320i	−0.308080	−	0.533611i
$996$	4.56587			0.144675
$997$	−57.0109			−1.80555			−0.902776	−	0.430111i	$-0.858474\pi$
$997$	−57.0109			−1.80555			−0.902776	+	0.430111i	$0.858474\pi$
$998$	7.66432	−	13.2750i	0.242610	−	0.420213i
$999$	1.26886	+	2.19772i	0.0401448	+	0.0695329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	670.2.e.i.171.2	✓	8
67.29	even	3	inner	670.2.e.i.431.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
670.2.e.i.171.2	✓	8	1.1	even	1	trivial
670.2.e.i.431.2	yes	8	67.29	even	3	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:	\( N \)	\(=\)	\( 670 = 2 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	670.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -0.414214 q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(0.207107 + 0.358719i) q^{6} +(-0.707107 + 1.22474i) q^{7} +1.00000 q^{8} -2.82843 q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(0.207107 - 0.358719i) q^{12} +(2.03617 + 3.52675i) q^{13} +1.41421 q^{14} -0.414214 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.732684 - 1.26905i) q^{17} +(1.41421 + 2.44949i) q^{18} +(2.43979 + 4.22584i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.292893 - 0.507306i) q^{21} -2.00000 q^{22} +(2.17247 + 3.76284i) q^{23} -0.414214 q^{24} +1.00000 q^{25} +(2.03617 - 3.52675i) q^{26} +2.41421 q^{27} +(-0.707107 - 1.22474i) q^{28} +(0.378042 - 0.654788i) q^{29} +(0.207107 + 0.358719i) q^{30} +(-5.09728 + 8.82875i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.414214 + 0.717439i) q^{33} +(-0.732684 + 1.26905i) q^{34} +(-0.707107 + 1.22474i) q^{35} +(1.41421 - 2.44949i) q^{36} +(0.525577 + 0.910327i) q^{37} +(2.43979 - 4.22584i) q^{38} +(-0.843410 - 1.46083i) q^{39} +1.00000 q^{40} +(-5.76822 + 9.99085i) q^{41} -0.585786 q^{42} +11.7804 q^{43} +(1.00000 + 1.73205i) q^{44} -2.82843 q^{45} +(2.17247 - 3.76284i) q^{46} +(4.15749 - 7.20099i) q^{47} +(0.207107 + 0.358719i) q^{48} +(2.50000 + 4.33013i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.303488 + 0.525656i) q^{51} -4.07234 q^{52} +5.95193 q^{53} +(-1.20711 - 2.09077i) q^{54} +(1.00000 - 1.73205i) q^{55} +(-0.707107 + 1.22474i) q^{56} +(-1.01059 - 1.75040i) q^{57} -0.756084 q^{58} +2.87958 q^{59} +(0.207107 - 0.358719i) q^{60} +(-5.57171 - 9.65048i) q^{61} +10.1946 q^{62} +(2.00000 - 3.46410i) q^{63} +1.00000 q^{64} +(2.03617 + 3.52675i) q^{65} +0.828427 q^{66} +(3.51150 + 7.39388i) q^{67} +1.46537 q^{68} +(-0.899869 - 1.55862i) q^{69} +1.41421 q^{70} +(1.23268 - 2.13507i) q^{71} -2.82843 q^{72} +(1.09574 + 1.89788i) q^{73} +(0.525577 - 0.910327i) q^{74} -0.414214 q^{75} -4.87958 q^{76} +(1.41421 + 2.44949i) q^{77} +(-0.843410 + 1.46083i) q^{78} +(-1.05115 + 1.82065i) q^{79} +(-0.500000 - 0.866025i) q^{80} +7.48528 q^{81} +11.5364 q^{82} +(5.51150 + 9.54619i) q^{83} +(0.292893 + 0.507306i) q^{84} +(-0.732684 - 1.26905i) q^{85} +(-5.89018 - 10.2021i) q^{86} +(-0.156590 + 0.271222i) q^{87} +(1.00000 - 1.73205i) q^{88} -12.7592 q^{89} +(1.41421 + 2.44949i) q^{90} -5.75916 q^{91} -4.34495 q^{92} +(2.11136 - 3.65699i) q^{93} -8.31498 q^{94} +(2.43979 + 4.22584i) q^{95} +(0.207107 - 0.358719i) q^{96} +(-8.30439 - 14.3836i) q^{97} +(2.50000 - 4.33013i) q^{98} +(-2.82843 + 4.89898i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8	\( 8 q - 4 q^{2} + 8 q^{3} - 4 q^{4} + 8 q^{5} - 4 q^{6} + 8 q^{8} - 4 q^{10} + 8 q^{11} - 4 q^{12} + 8 q^{15} - 4 q^{16} + 2 q^{17} + 6 q^{19} - 4 q^{20} + 8 q^{21} - 16 q^{22} - 4 q^{23} + 8 q^{24} + 8 q^{25} + 8 q^{27} + 8 q^{29} - 4 q^{30} + 6 q^{31} - 4 q^{32} + 8 q^{33} + 2 q^{34} + 2 q^{37} + 6 q^{38} + 4 q^{39} + 8 q^{40} - 10 q^{41} - 16 q^{42} + 12 q^{43} + 8 q^{44} - 4 q^{46} - 4 q^{48} + 20 q^{49} - 4 q^{50} - 6 q^{51} - 12 q^{53} - 4 q^{54} + 8 q^{55} + 6 q^{57} - 16 q^{58} - 4 q^{59} - 4 q^{60} - 12 q^{62} + 16 q^{63} + 8 q^{64} - 16 q^{66} - 30 q^{67} - 4 q^{68} + 4 q^{69} + 2 q^{71} - 6 q^{73} + 2 q^{74} + 8 q^{75} - 12 q^{76} + 4 q^{78} - 4 q^{79} - 4 q^{80} - 8 q^{81} + 20 q^{82} - 14 q^{83} + 8 q^{84} + 2 q^{85} - 6 q^{86} - 12 q^{87} + 8 q^{88} - 48 q^{89} + 8 q^{91} + 8 q^{92} + 26 q^{93} + 6 q^{95} - 4 q^{96} - 14 q^{97} + 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 8 * q^3 - 4 * q^4 + 8 * q^5 - 4 * q^6 + 8 * q^8 - 4 * q^10 + 8 * q^11 - 4 * q^12 + 8 * q^15 - 4 * q^16 + 2 * q^17 + 6 * q^19 - 4 * q^20 + 8 * q^21 - 16 * q^22 - 4 * q^23 + 8 * q^24 + 8 * q^25 + 8 * q^27 + 8 * q^29 - 4 * q^30 + 6 * q^31 - 4 * q^32 + 8 * q^33 + 2 * q^34 + 2 * q^37 + 6 * q^38 + 4 * q^39 + 8 * q^40 - 10 * q^41 - 16 * q^42 + 12 * q^43 + 8 * q^44 - 4 * q^46 - 4 * q^48 + 20 * q^49 - 4 * q^50 - 6 * q^51 - 12 * q^53 - 4 * q^54 + 8 * q^55 + 6 * q^57 - 16 * q^58 - 4 * q^59 - 4 * q^60 - 12 * q^62 + 16 * q^63 + 8 * q^64 - 16 * q^66 - 30 * q^67 - 4 * q^68 + 4 * q^69 + 2 * q^71 - 6 * q^73 + 2 * q^74 + 8 * q^75 - 12 * q^76 + 4 * q^78 - 4 * q^79 - 4 * q^80 - 8 * q^81 + 20 * q^82 - 14 * q^83 + 8 * q^84 + 2 * q^85 - 6 * q^86 - 12 * q^87 + 8 * q^88 - 48 * q^89 + 8 * q^91 + 8 * q^92 + 26 * q^93 + 6 * q^95 - 4 * q^96 - 14 * q^97 + 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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