LMFDB - Embedded newform 775.2.j.a.311.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [775,2,Mod(156,775)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("775.156");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.j (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:	$6.18840615665$
Analytic rank:	$1$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			311.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	775.311
Dual form			775.2.j.a.466.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61803 + 1.17557i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-0.763932 - 2.35114i) q^{6} +4.23607 q^{7} +(1.19098 + 0.865300i) q^{9} +O(q^{10})$	\(q+(-1.61803 + 1.17557i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-0.763932 - 2.35114i) q^{6} +4.23607 q^{7} +(1.19098 + 0.865300i) q^{9} +4.47214 q^{10} +(-2.30902 + 1.67760i) q^{11} +(2.00000 + 1.45309i) q^{12} +(-3.73607 - 2.71441i) q^{13} +(-6.85410 + 4.97980i) q^{14} +(2.23607 - 1.62460i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-0.0729490 - 0.224514i) q^{17} -2.94427 q^{18} +(-1.38197 - 4.25325i) q^{19} +(-3.61803 + 2.62866i) q^{20} +(-1.61803 + 4.97980i) q^{21} +(1.76393 - 5.42882i) q^{22} +(-6.66312 + 4.84104i) q^{23} +(1.54508 + 4.75528i) q^{25} +9.23607 q^{26} +(-4.47214 + 3.24920i) q^{27} +(2.61803 - 8.05748i) q^{28} +(-0.690983 + 2.12663i) q^{29} +(-1.70820 + 5.25731i) q^{30} +(0.309017 + 0.951057i) q^{31} -8.00000 q^{32} +(-1.09017 - 3.35520i) q^{33} +(0.381966 + 0.277515i) q^{34} +(-7.66312 - 5.56758i) q^{35} +(2.38197 - 1.73060i) q^{36} +(-8.16312 - 5.93085i) q^{37} +(7.23607 + 5.25731i) q^{38} +(4.61803 - 3.35520i) q^{39} +(-8.16312 - 5.93085i) q^{41} +(-3.23607 - 9.95959i) q^{42} -3.47214 q^{43} +(1.76393 + 5.42882i) q^{44} +(-1.01722 - 3.13068i) q^{45} +(5.09017 - 15.6659i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(-4.00000 + 2.90617i) q^{48} +10.9443 q^{49} +(-8.09017 - 5.87785i) q^{50} +0.291796 q^{51} +(-7.47214 + 5.42882i) q^{52} +(2.64590 - 8.14324i) q^{53} +(3.41641 - 10.5146i) q^{54} +6.38197 q^{55} +5.52786 q^{57} +(-1.38197 - 4.25325i) q^{58} +(9.89919 + 7.19218i) q^{59} +(-1.70820 - 5.25731i) q^{60} +(1.04508 - 0.759299i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(5.04508 + 3.66547i) q^{63} +(6.47214 - 4.70228i) q^{64} +(3.19098 + 9.82084i) q^{65} +(5.70820 + 4.14725i) q^{66} +(-3.26393 - 10.0453i) q^{67} -0.472136 q^{68} +(-3.14590 - 9.68208i) q^{69} +18.9443 q^{70} +(1.73607 - 5.34307i) q^{71} +(-9.59017 + 6.96767i) q^{73} +20.1803 q^{74} -6.18034 q^{75} -8.94427 q^{76} +(-9.78115 + 7.10642i) q^{77} +(-3.52786 + 10.8576i) q^{78} +(-0.954915 + 2.93893i) q^{79} +(-2.76393 - 8.50651i) q^{80} +(-0.746711 - 2.29814i) q^{81} +20.1803 q^{82} +(0.736068 + 2.26538i) q^{83} +(8.47214 + 6.15537i) q^{84} +(-0.163119 + 0.502029i) q^{85} +(5.61803 - 4.08174i) q^{86} +(-2.23607 - 1.62460i) q^{87} +(13.5172 - 9.82084i) q^{89} +(5.32624 + 3.86974i) q^{90} +(-15.8262 - 11.4984i) q^{91} +(5.09017 + 15.6659i) q^{92} -1.23607 q^{93} +(-4.29180 - 13.2088i) q^{94} +(-3.09017 + 9.51057i) q^{95} +(3.05573 - 9.40456i) q^{96} +(2.59017 - 7.97172i) q^{97} +(-17.7082 + 12.8658i) q^{98} -4.20163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9} - 7 q^{11} + 8 q^{12} - 6 q^{13} - 14 q^{14} + 4 q^{16} - 7 q^{17} + 24 q^{18} - 10 q^{19} - 10 q^{20} - 2 q^{21} + 16 q^{22} - 11 q^{23} - 5 q^{25} + 28 q^{26} + 6 q^{28} - 5 q^{29} + 20 q^{30} - q^{31} - 32 q^{32} + 18 q^{33} + 6 q^{34} - 15 q^{35} + 14 q^{36} - 17 q^{37} + 20 q^{38} + 14 q^{39} - 17 q^{41} - 4 q^{42} + 4 q^{43} + 16 q^{44} + 25 q^{45} - 2 q^{46} - 22 q^{47} - 16 q^{48} + 8 q^{49} - 10 q^{50} + 28 q^{51} - 12 q^{52} + 24 q^{53} - 40 q^{54} + 30 q^{55} + 40 q^{57} - 10 q^{58} + 15 q^{59} + 20 q^{60} - 7 q^{61} - 2 q^{62} + 9 q^{63} + 8 q^{64} + 15 q^{65} - 4 q^{66} - 22 q^{67} + 16 q^{68} - 26 q^{69} + 40 q^{70} - 2 q^{71} - 16 q^{73} + 36 q^{74} + 20 q^{75} - 19 q^{77} - 32 q^{78} - 15 q^{79} - 20 q^{80} - 41 q^{81} + 36 q^{82} - 6 q^{83} + 16 q^{84} + 15 q^{85} + 18 q^{86} + 25 q^{89} - 10 q^{90} - 32 q^{91} - 2 q^{92} + 4 q^{93} - 44 q^{94} + 10 q^{95} + 48 q^{96} - 12 q^{97} - 44 q^{98} - 66 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9 - 7 * q^11 + 8 * q^12 - 6 * q^13 - 14 * q^14 + 4 * q^16 - 7 * q^17 + 24 * q^18 - 10 * q^19 - 10 * q^20 - 2 * q^21 + 16 * q^22 - 11 * q^23 - 5 * q^25 + 28 * q^26 + 6 * q^28 - 5 * q^29 + 20 * q^30 - q^31 - 32 * q^32 + 18 * q^33 + 6 * q^34 - 15 * q^35 + 14 * q^36 - 17 * q^37 + 20 * q^38 + 14 * q^39 - 17 * q^41 - 4 * q^42 + 4 * q^43 + 16 * q^44 + 25 * q^45 - 2 * q^46 - 22 * q^47 - 16 * q^48 + 8 * q^49 - 10 * q^50 + 28 * q^51 - 12 * q^52 + 24 * q^53 - 40 * q^54 + 30 * q^55 + 40 * q^57 - 10 * q^58 + 15 * q^59 + 20 * q^60 - 7 * q^61 - 2 * q^62 + 9 * q^63 + 8 * q^64 + 15 * q^65 - 4 * q^66 - 22 * q^67 + 16 * q^68 - 26 * q^69 + 40 * q^70 - 2 * q^71 - 16 * q^73 + 36 * q^74 + 20 * q^75 - 19 * q^77 - 32 * q^78 - 15 * q^79 - 20 * q^80 - 41 * q^81 + 36 * q^82 - 6 * q^83 + 16 * q^84 + 15 * q^85 + 18 * q^86 + 25 * q^89 - 10 * q^90 - 32 * q^91 - 2 * q^92 + 4 * q^93 - 44 * q^94 + 10 * q^95 + 48 * q^96 - 12 * q^97 - 44 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.61803	+	1.17557i	−1.14412	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$2$	−1.61803	+	1.17557i	−1.14412	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	0.778187	+	0.628033i	$0.216140\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	−0.998715	+	0.0506828i	$0.983860\pi$
$4$	0.618034	−	1.90211i	0.309017	−	0.951057i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$	−0.763932	−	2.35114i	−0.311874	−	0.959849i
$7$	4.23607			1.60108			0.800542	−	0.599277i	$-0.204545\pi$
$7$	4.23607			1.60108			0.800542	+	0.599277i	$0.204545\pi$
$8$		0			0
$9$	1.19098	+	0.865300i	0.396994	+	0.288433i
$10$	4.47214			1.41421
$11$	−2.30902	+	1.67760i	−0.696195	+	0.505815i	−0.878691	−	0.477391i	$-0.841582\pi$
$11$	−2.30902	+	1.67760i	−0.696195	+	0.505815i	0.182496	+	0.983207i	$0.441582\pi$
$12$	2.00000	+	1.45309i	0.577350	+	0.419470i
$13$	−3.73607	−	2.71441i	−1.03620	−	0.752843i	−0.0666589	−	0.997776i	$-0.521234\pi$
$13$	−3.73607	−	2.71441i	−1.03620	−	0.752843i	−0.969540	+	0.244933i	$0.921234\pi$
$14$	−6.85410	+	4.97980i	−1.83184	+	1.33091i
$15$	2.23607	−	1.62460i	0.577350	−	0.419470i
$16$	3.23607	+	2.35114i	0.809017	+	0.587785i
$17$	−0.0729490	−	0.224514i	−0.0176927	−	0.0544526i	0.941820	−	0.336117i	$-0.109114\pi$
$17$	−0.0729490	−	0.224514i	−0.0176927	−	0.0544526i	−0.959513	+	0.281664i	$0.909114\pi$
$18$	−2.94427			−0.693972
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	−0.974905	−	0.222623i	$-0.928538\pi$
$19$	−1.38197	−	4.25325i	−0.317045	−	0.975763i	0.657860	−	0.753140i	$-0.271462\pi$
$20$	−3.61803	+	2.62866i	−0.809017	+	0.587785i
$21$	−1.61803	+	4.97980i	−0.353084	+	1.08668i
$22$	1.76393	−	5.42882i	0.376072	−	1.15743i
$23$	−6.66312	+	4.84104i	−1.38936	+	1.00943i	−0.393421	+	0.919359i	$0.628708\pi$
$23$	−6.66312	+	4.84104i	−1.38936	+	1.00943i	−0.995936	+	0.0900679i	$0.971292\pi$
$24$		0			0
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	9.23607			1.81134
$27$	−4.47214	+	3.24920i	−0.860663	+	0.625308i
$28$	2.61803	−	8.05748i	0.494762	−	1.52272i
$29$	−0.690983	+	2.12663i	−0.128312	+	0.394905i	−0.994490	−	0.104831i	$-0.966570\pi$
$29$	−0.690983	+	2.12663i	−0.128312	+	0.394905i	0.866178	+	0.499736i	$0.166570\pi$
$30$	−1.70820	+	5.25731i	−0.311874	+	0.959849i
$31$	0.309017	+	0.951057i	0.0555011	+	0.170815i
$31$	0.309017	+	0.951057i	0.0555011	+	0.170815i
$32$	−8.00000			−1.41421
$33$	−1.09017	−	3.35520i	−0.189774	−	0.584065i
$34$	0.381966	+	0.277515i	0.0655066	+	0.0475934i
$35$	−7.66312	−	5.56758i	−1.29530	−	0.941093i
$36$	2.38197	−	1.73060i	0.396994	−	0.288433i
$37$	−8.16312	−	5.93085i	−1.34201	−	0.975026i	−0.999368	−	0.0355598i	$-0.988679\pi$
$37$	−8.16312	−	5.93085i	−1.34201	−	0.975026i	−0.342641	−	0.939466i	$-0.611321\pi$
$38$	7.23607	+	5.25731i	1.17385	+	0.852848i
$39$	4.61803	−	3.35520i	0.739477	−	0.537262i
$40$		0			0
$41$	−8.16312	−	5.93085i	−1.27486	−	0.926244i	−0.275480	−	0.961307i	$-0.588837\pi$
$41$	−8.16312	−	5.93085i	−1.27486	−	0.926244i	−0.999385	+	0.0350632i	$0.988837\pi$
$42$	−3.23607	−	9.95959i	−0.499336	−	1.53680i
$43$	−3.47214			−0.529496			−0.264748	−	0.964318i	$-0.585289\pi$
$43$	−3.47214			−0.529496			−0.264748	+	0.964318i	$0.585289\pi$
$44$	1.76393	+	5.42882i	0.265923	+	0.818426i
$45$	−1.01722	−	3.13068i	−0.151638	−	0.466695i
$46$	5.09017	−	15.6659i	0.750505	−	2.30982i
$47$	−2.14590	+	6.60440i	−0.313011	+	0.963350i	0.663554	+	0.748129i	$0.269047\pi$
$47$	−2.14590	+	6.60440i	−0.313011	+	0.963350i	−0.976565	+	0.215222i	$0.930953\pi$
$48$	−4.00000	+	2.90617i	−0.577350	+	0.419470i
$49$	10.9443			1.56347
$50$	−8.09017	−	5.87785i	−1.14412	−	0.831254i
$51$	0.291796			0.0408596
$52$	−7.47214	+	5.42882i	−1.03620	+	0.752843i
$53$	2.64590	−	8.14324i	0.363442	−	1.11856i	−0.587509	−	0.809218i	$-0.699891\pi$
$53$	2.64590	−	8.14324i	0.363442	−	1.11856i	0.950951	−	0.309342i	$-0.100109\pi$
$54$	3.41641	−	10.5146i	0.464914	−	1.43086i
$55$	6.38197			0.860544
$56$		0			0
$57$	5.52786			0.732183
$58$	−1.38197	−	4.25325i	−0.181461	−	0.558480i
$59$	9.89919	+	7.19218i	1.28876	+	0.936342i	0.999780	−	0.0209916i	$-0.00668232\pi$
$59$	9.89919	+	7.19218i	1.28876	+	0.936342i	0.288985	+	0.957334i	$0.406682\pi$
$60$	−1.70820	−	5.25731i	−0.220528	−	0.678716i
$61$	1.04508	−	0.759299i	0.133809	−	0.0972182i	−0.518867	−	0.854855i	$-0.673646\pi$
$61$	1.04508	−	0.759299i	0.133809	−	0.0972182i	0.652677	+	0.757637i	$0.273646\pi$
$62$	−1.61803	−	1.17557i	−0.205491	−	0.149298i
$63$	5.04508	+	3.66547i	0.635621	+	0.461806i
$64$	6.47214	−	4.70228i	0.809017	−	0.587785i
$65$	3.19098	+	9.82084i	0.395793	+	1.21812i
$66$	5.70820	+	4.14725i	0.702631	+	0.510492i
$67$	−3.26393	−	10.0453i	−0.398753	−	1.22723i	−0.926000	−	0.377523i	$-0.876776\pi$
$67$	−3.26393	−	10.0453i	−0.398753	−	1.22723i	0.527247	−	0.849712i	$-0.323224\pi$
$68$	−0.472136			−0.0572549
$69$	−3.14590	−	9.68208i	−0.378722	−	1.16559i
$70$	18.9443			2.26427
$71$	1.73607	−	5.34307i	0.206033	−	0.634105i	−0.793636	−	0.608393i	$-0.791815\pi$
$71$	1.73607	−	5.34307i	0.206033	−	0.634105i	0.999669	−	0.0257126i	$-0.00818548\pi$
$72$		0			0
$73$	−9.59017	+	6.96767i	−1.12244	+	0.815504i	−0.984578	−	0.174947i	$-0.944025\pi$
$73$	−9.59017	+	6.96767i	−1.12244	+	0.815504i	−0.137867	+	0.990451i	$0.544025\pi$
$74$	20.1803			2.34592
$75$	−6.18034			−0.713644
$76$	−8.94427			−1.02598
$77$	−9.78115	+	7.10642i	−1.11467	+	0.809852i
$78$	−3.52786	+	10.8576i	−0.399452	+	1.22939i
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	−0.990295	−	0.138985i	$-0.955616\pi$
$79$	−0.954915	+	2.93893i	−0.107436	+	0.330655i	0.882858	+	0.469640i	$0.155616\pi$
$80$	−2.76393	−	8.50651i	−0.309017	−	0.951057i
$81$	−0.746711	−	2.29814i	−0.0829679	−	0.255349i
$82$	20.1803			2.22855
$83$	0.736068	+	2.26538i	0.0807940	+	0.248658i	0.983292	−	0.182036i	$-0.0582687\pi$
$83$	0.736068	+	2.26538i	0.0807940	+	0.248658i	−0.902498	+	0.430694i	$0.858269\pi$
$84$	8.47214	+	6.15537i	0.924386	+	0.671606i
$85$	−0.163119	+	0.502029i	−0.0176927	+	0.0544526i
$86$	5.61803	−	4.08174i	0.605808	−	0.440145i
$87$	−2.23607	−	1.62460i	−0.239732	−	0.174175i
$88$		0			0
$89$	13.5172	−	9.82084i	1.43282	−	1.04101i	0.443340	−	0.896353i	$-0.353793\pi$
$89$	13.5172	−	9.82084i	1.43282	−	1.04101i	0.989482	−	0.144653i	$-0.0462066\pi$
$90$	5.32624	+	3.86974i	0.561435	+	0.407906i
$91$	−15.8262	−	11.4984i	−1.65904	−	1.20536i
$92$	5.09017	+	15.6659i	0.530687	+	1.63329i
$93$	−1.23607			−0.128174
$94$	−4.29180	−	13.2088i	−0.442665	−	1.36238i
$95$	−3.09017	+	9.51057i	−0.317045	+	0.975763i
$96$	3.05573	−	9.40456i	0.311874	−	0.959849i
$97$	2.59017	−	7.97172i	0.262992	−	0.809406i	−0.729157	−	0.684346i	$-0.760088\pi$
$97$	2.59017	−	7.97172i	0.262992	−	0.809406i	0.992149	−	0.125060i	$-0.0399123\pi$
$98$	−17.7082	+	12.8658i	−1.78880	+	1.29964i
$99$	−4.20163			−0.422279
$100$	10.0000			1.00000
$101$	−11.9443			−1.18850			−0.594250	−	0.804281i	$-0.702551\pi$
$101$	−11.9443			−1.18850			−0.594250	+	0.804281i	$0.702551\pi$
$102$	−0.472136	+	0.343027i	−0.0467484	+	0.0339647i
$103$	−1.33688	+	4.11450i	−0.131727	+	0.405413i	−0.995067	−	0.0992097i	$-0.968369\pi$
$103$	−1.33688	+	4.11450i	−0.131727	+	0.405413i	0.863340	+	0.504623i	$0.168369\pi$
$104$		0			0
$105$	9.47214	−	6.88191i	0.924386	−	0.671606i
$106$	5.29180	+	16.2865i	0.513985	+	1.58188i
$107$	4.23607			0.409516			0.204758	−	0.978813i	$-0.434359\pi$
$107$	4.23607			0.409516			0.204758	+	0.978813i	$0.434359\pi$
$108$	3.41641	+	10.5146i	0.328744	+	1.01177i
$109$	5.00000	+	3.63271i	0.478913	+	0.347951i	0.800905	−	0.598792i	$-0.204352\pi$
$109$	5.00000	+	3.63271i	0.478913	+	0.347951i	−0.321992	+	0.946743i	$0.604352\pi$
$110$	−10.3262	+	7.50245i	−0.984568	+	0.715331i
$111$	10.0902	−	7.33094i	0.957717	−	0.695822i
$112$	13.7082	+	9.95959i	1.29530	+	0.941093i
$113$	−12.0902	−	8.78402i	−1.13735	−	0.826331i	−0.150600	−	0.988595i	$-0.548121\pi$
$113$	−12.0902	−	8.78402i	−1.13735	−	0.826331i	−0.986747	+	0.162263i	$0.948121\pi$
$114$	−8.94427	+	6.49839i	−0.837708	+	0.608630i
$115$	18.4164			1.71734
$116$	3.61803	+	2.62866i	0.335926	+	0.244065i
$117$	−2.10081	−	6.46564i	−0.194220	−	0.597748i
$118$	−24.4721			−2.25284
$119$	−0.309017	−	0.951057i	−0.0283275	−	0.0871832i
$120$		0			0
$121$	−0.881966	+	2.71441i	−0.0801787	+	0.246765i
$122$	−0.798374	+	2.45714i	−0.0722814	+	0.222459i
$123$	10.0902	−	7.33094i	0.909800	−	0.661008i
$124$	2.00000			0.179605
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	−12.4721			−1.11111
$127$	−13.7533	+	9.99235i	−1.22041	+	0.886678i	−0.996134	−	0.0878487i	$-0.972001\pi$
$127$	−13.7533	+	9.99235i	−1.22041	+	0.886678i	−0.224273	+	0.974526i	$0.572001\pi$
$128$		0			0
$129$	1.32624	−	4.08174i	0.116769	−	0.359377i
$130$	−16.7082	−	12.1392i	−1.46541	−	1.06468i
$131$	−2.63525	−	8.11048i	−0.230243	−	0.708616i	−0.997717	−	0.0675354i	$-0.978486\pi$
$131$	−2.63525	−	8.11048i	−0.230243	−	0.708616i	0.767474	−	0.641081i	$-0.221514\pi$
$132$	−7.05573			−0.614122
$133$	−5.85410	−	18.0171i	−0.507615	−	1.56228i
$134$	17.0902	+	12.4167i	1.47637	+	1.07264i
$135$	12.3607			1.06384
$136$		0			0
$137$	−13.7533	−	9.99235i	−1.17502	−	0.853704i	−0.183421	−	0.983034i	$-0.558717\pi$
$137$	−13.7533	−	9.99235i	−1.17502	−	0.853704i	−0.991602	+	0.129330i	$0.958717\pi$
$138$	16.4721	+	11.9677i	1.40220	+	1.01876i
$139$	−9.04508	+	6.57164i	−0.767194	+	0.557399i	−0.901108	−	0.433594i	$-0.857245\pi$
$139$	−9.04508	+	6.57164i	−0.767194	+	0.557399i	0.133914	+	0.990993i	$0.457245\pi$
$140$	−15.3262	+	11.1352i	−1.29530	+	0.941093i
$141$	−6.94427	−	5.04531i	−0.584813	−	0.424892i
$142$	3.47214	+	10.6861i	0.291375	+	0.896761i
$143$	13.1803			1.10220
$144$	1.81966	+	5.60034i	0.151638	+	0.466695i
$145$	4.04508	−	2.93893i	0.335926	−	0.244065i
$146$	7.32624	−	22.5478i	0.606324	−	1.86607i
$147$	−4.18034	+	12.8658i	−0.344789	+	1.06115i
$148$	−16.3262	+	11.8617i	−1.34201	+	0.975026i
$149$	−22.0344			−1.80513			−0.902566	−	0.430552i	$-0.858319\pi$
$149$	−22.0344			−1.80513			−0.902566	+	0.430552i	$0.858319\pi$
$150$	10.0000	−	7.26543i	0.816497	−	0.593219i
$151$	−13.0000			−1.05792			−0.528962	−	0.848645i	$-0.677419\pi$
$151$	−13.0000			−1.05792			−0.528962	+	0.848645i	$0.677419\pi$
$152$		0			0
$153$	0.107391	−	0.330515i	0.00868204	−	0.0267206i
$154$	7.47214	−	22.9969i	0.602122	−	1.85314i
$155$	0.690983	−	2.12663i	0.0555011	−	0.170815i
$156$	−3.52786	−	10.8576i	−0.282455	−	0.869308i
$157$	12.6525			1.00978			0.504889	−	0.863184i	$-0.331534\pi$
$157$	12.6525			1.00978			0.504889	+	0.863184i	$0.331534\pi$
$158$	−1.90983	−	5.87785i	−0.151938	−	0.467617i
$159$	8.56231	+	6.22088i	0.679035	+	0.493348i
$160$	14.4721	+	10.5146i	1.14412	+	0.831254i
$161$	−28.2254	+	20.5070i	−2.22448	+	1.61618i
$162$	3.90983	+	2.84066i	0.307185	+	0.223183i
$163$	0.572949	+	0.416272i	0.0448768	+	0.0326049i	0.609998	−	0.792403i	$-0.291170\pi$
$163$	0.572949	+	0.416272i	0.0448768	+	0.0326049i	−0.565121	+	0.825008i	$0.691170\pi$
$164$	−16.3262	+	11.8617i	−1.27486	+	0.926244i
$165$	−2.43769	+	7.50245i	−0.189774	+	0.584065i
$166$	−3.85410	−	2.80017i	−0.299136	−	0.217335i
$167$	3.11803	+	9.59632i	0.241281	+	0.742586i	0.996226	+	0.0867978i	$0.0276634\pi$
$167$	3.11803	+	9.59632i	0.241281	+	0.742586i	−0.754945	+	0.655788i	$0.772337\pi$
$168$		0			0
$169$	2.57295	+	7.91872i	0.197919	+	0.609133i
$170$	−0.326238	−	1.00406i	−0.0250213	−	0.0770077i
$171$	2.03444	−	6.26137i	0.155578	−	0.478819i
$172$	−2.14590	+	6.60440i	−0.163623	+	0.503580i
$173$	−5.70820	+	4.14725i	−0.433987	+	0.315310i	−0.783241	−	0.621718i	$-0.786435\pi$
$173$	−5.70820	+	4.14725i	−0.433987	+	0.315310i	0.349254	+	0.937028i	$0.386435\pi$
$174$	5.52786			0.419066
$175$	6.54508	+	20.1437i	0.494762	+	1.52272i
$176$	−11.4164			−0.860544
$177$	−12.2361	+	8.89002i	−0.919719	+	0.668215i
$178$	−10.3262	+	31.7809i	−0.773984	+	2.38208i
$179$	−2.60081	+	8.00448i	−0.194394	+	0.598283i	0.805589	+	0.592474i	$0.201849\pi$
$179$	−2.60081	+	8.00448i	−0.194394	+	0.598283i	−0.999983	+	0.00580843i	$0.998151\pi$
$180$	−6.58359			−0.490712
$181$	5.19098	+	15.9762i	0.385843	+	1.18750i	0.935867	+	0.352353i	$0.114618\pi$
$181$	5.19098	+	15.9762i	0.385843	+	1.18750i	−0.550024	+	0.835149i	$0.685382\pi$
$182$	39.1246			2.90011
$183$	0.493422	+	1.51860i	0.0364748	+	0.112258i
$184$		0			0
$185$	6.97214	+	21.4580i	0.512602	+	1.57763i
$186$	2.00000	−	1.45309i	0.146647	−	0.106545i
$187$	0.545085	+	0.396027i	0.0398606	+	0.0289604i
$188$	11.2361	+	8.16348i	0.819474	+	0.595383i
$189$	−18.9443	+	13.7638i	−1.37799	+	1.00117i
$190$	−6.18034	−	19.0211i	−0.448369	−	1.37994i
$191$	−13.7533	−	9.99235i	−0.995153	−	0.723021i	−0.0341095	−	0.999418i	$-0.510860\pi$
$191$	−13.7533	−	9.99235i	−0.995153	−	0.723021i	−0.961044	+	0.276397i	$0.910860\pi$
$192$	3.05573	+	9.40456i	0.220528	+	0.678716i
$193$	6.32624			0.455373			0.227686	−	0.973735i	$-0.426884\pi$
$193$	6.32624			0.455373			0.227686	+	0.973735i	$0.426884\pi$
$194$	5.18034	+	15.9434i	0.371927	+	1.14467i
$195$	−12.7639			−0.914044
$196$	6.76393	−	20.8172i	0.483138	−	1.48695i
$197$	1.14590	−	3.52671i	0.0816419	−	0.251268i	−0.901901	−	0.431943i	$-0.857828\pi$
$197$	1.14590	−	3.52671i	0.0816419	−	0.251268i	0.983543	+	0.180675i	$0.0578282\pi$
$198$	6.79837	−	4.93931i	0.483139	−	0.351021i
$199$	15.6525			1.10957			0.554787	−	0.831992i	$-0.312800\pi$
$199$	15.6525			1.10957			0.554787	+	0.831992i	$0.312800\pi$
$200$		0			0
$201$	13.0557			0.920880
$202$	19.3262	−	14.0413i	1.35979	−	0.987945i
$203$	−2.92705	+	9.00854i	−0.205439	+	0.632275i
$204$	0.180340	−	0.555029i	0.0126263	−	0.0388598i
$205$	6.97214	+	21.4580i	0.486955	+	1.49869i
$206$	−2.67376	−	8.22899i	−0.186290	−	0.573341i
$207$	−12.1246			−0.842719
$208$	−5.70820	−	17.5680i	−0.395793	−	1.21812i
$209$	10.3262	+	7.50245i	0.714281	+	0.518955i
$210$	−7.23607	+	22.2703i	−0.499336	+	1.53680i
$211$	3.80902	−	2.76741i	0.262224	−	0.190517i	−0.448903	−	0.893580i	$-0.648185\pi$
$211$	3.80902	−	2.76741i	0.262224	−	0.190517i	0.711127	+	0.703064i	$0.248185\pi$
$212$	−13.8541	−	10.0656i	−0.951504	−	0.691308i
$213$	5.61803	+	4.08174i	0.384941	+	0.279676i
$214$	−6.85410	+	4.97980i	−0.468537	+	0.340412i
$215$	6.28115	+	4.56352i	0.428371	+	0.311230i
$216$		0			0
$217$	1.30902	+	4.02874i	0.0888619	+	0.273489i
$218$	−12.3607			−0.837171
$219$	−4.52786	−	13.9353i	−0.305965	−	0.941663i
$220$	3.94427	−	12.1392i	0.265923	−	0.818426i
$221$	−0.336881	+	1.03681i	−0.0226611	+	0.0697436i
$222$	−7.70820	+	23.7234i	−0.517341	+	1.59221i
$223$	9.51722	−	6.91467i	0.637320	−	0.463040i	−0.221608	−	0.975136i	$-0.571131\pi$
$223$	9.51722	−	6.91467i	0.637320	−	0.463040i	0.858929	+	0.512096i	$0.171131\pi$
$224$	−33.8885			−2.26427
$225$	−2.27458	+	7.00042i	−0.151638	+	0.466695i
$226$	29.8885			1.98816
$227$	19.9894	−	14.5231i	1.32674	−	0.963933i	0.326918	−	0.945053i	$-0.393990\pi$
$227$	19.9894	−	14.5231i	1.32674	−	0.963933i	0.999822	−	0.0188806i	$-0.00601025\pi$
$228$	3.41641	−	10.5146i	0.226257	−	0.696348i
$229$	−0.0623059	+	0.191758i	−0.00411729	+	0.0126717i	−0.953094	−	0.302674i	$-0.902121\pi$
$229$	−0.0623059	+	0.191758i	−0.00411729	+	0.0126717i	0.948977	+	0.315346i	$0.102121\pi$
$230$	−29.7984	+	21.6498i	−1.96485	+	1.42754i
$231$	−4.61803	−	14.2128i	−0.303844	−	0.935137i
$232$		0			0
$233$	3.76393	+	11.5842i	0.246583	+	0.758906i	0.995372	+	0.0960967i	$0.0306358\pi$
$233$	3.76393	+	11.5842i	0.246583	+	0.758906i	−0.748789	+	0.662809i	$0.769364\pi$
$234$	11.0000	+	7.99197i	0.719092	+	0.522451i
$235$	12.5623	−	9.12705i	0.819474	−	0.595383i
$236$	19.7984	−	14.3844i	1.28876	−	0.936342i
$237$	−3.09017	−	2.24514i	−0.200728	−	0.145838i
$238$	1.61803	+	1.17557i	0.104882	+	0.0762009i
$239$	−1.38197	+	1.00406i	−0.0893920	+	0.0649471i	−0.631584	−	0.775308i	$-0.717595\pi$
$239$	−1.38197	+	1.00406i	−0.0893920	+	0.0649471i	0.542192	+	0.840255i	$0.317595\pi$
$240$	11.0557			0.713644
$241$	−7.30902	−	5.31031i	−0.470815	−	0.342067i	0.326944	−	0.945044i	$-0.393981\pi$
$241$	−7.30902	−	5.31031i	−0.470815	−	0.342067i	−0.797759	+	0.602977i	$0.793981\pi$
$242$	−1.76393	−	5.42882i	−0.113390	−	0.348978i
$243$	−13.5967			−0.872232
$244$	−0.798374	−	2.45714i	−0.0511107	−	0.157302i
$245$	−19.7984	−	14.3844i	−1.26487	−	0.918983i
$246$	−7.70820	+	23.7234i	−0.491457	+	1.51255i
$247$	−6.38197	+	19.6417i	−0.406075	+	1.24977i
$248$		0			0
$249$	−2.94427			−0.186586
$250$	6.90983	+	21.2663i	0.437016	+	1.34500i
$251$	15.0902			0.952483			0.476242	−	0.879315i	$-0.341999\pi$
$251$	15.0902			0.952483			0.476242	+	0.879315i	$0.341999\pi$
$252$	10.0902	−	7.33094i	0.635621	−	0.461806i
$253$	7.26393	−	22.3561i	0.456679	−	1.40551i
$254$	10.5066	−	32.3359i	0.659241	−	2.02894i
$255$	−0.527864	−	0.383516i	−0.0330561	−	0.0240167i
$256$	4.94427	+	15.2169i	0.309017	+	0.951057i
$257$	−3.20163			−0.199712			−0.0998560	−	0.995002i	$-0.531838\pi$
$257$	−3.20163			−0.199712			−0.0998560	+	0.995002i	$0.531838\pi$
$258$	2.65248	+	8.16348i	0.165136	+	0.508236i
$259$	−34.5795	−	25.1235i	−2.14867	−	1.56110i
$260$	20.6525			1.28081
$261$	−2.66312	+	1.93487i	−0.164843	+	0.119765i
$262$	13.7984	+	10.0251i	0.852466	+	0.619353i
$263$	−0.809017	−	0.587785i	−0.0498861	−	0.0362444i	0.562563	−	0.826755i	$-0.309815\pi$
$263$	−0.809017	−	0.587785i	−0.0498861	−	0.0362444i	−0.612449	+	0.790510i	$0.709815\pi$
$264$		0			0
$265$	−15.4894	+	11.2537i	−0.951504	+	0.691308i
$266$	30.6525	+	22.2703i	1.87942	+	1.36548i
$267$	6.38197	+	19.6417i	0.390570	+	1.20205i
$268$	−21.1246			−1.29039
$269$	4.83688	+	14.8864i	0.294910	+	0.907639i	0.983252	+	0.182253i	$0.0583389\pi$
$269$	4.83688	+	14.8864i	0.294910	+	0.907639i	−0.688342	+	0.725386i	$0.741661\pi$
$270$	−20.0000	+	14.5309i	−1.21716	+	0.884319i
$271$	−3.42705	+	10.5474i	−0.208179	+	0.640708i	0.791389	+	0.611312i	$0.209358\pi$
$271$	−3.42705	+	10.5474i	−0.208179	+	0.640708i	−0.999568	+	0.0293952i	$0.990642\pi$
$272$	0.291796	−	0.898056i	0.0176927	−	0.0544526i
$273$	19.5623	−	14.2128i	1.18396	−	0.860201i
$274$	34.0000			2.05402
$275$	−11.5451	−	8.38800i	−0.696195	−	0.505815i
$276$	−20.3607			−1.22557
$277$	−14.0172	+	10.1841i	−0.842213	+	0.611904i	−0.922988	−	0.384829i	$-0.874261\pi$
$277$	−14.0172	+	10.1841i	−0.842213	+	0.611904i	0.0807748	+	0.996732i	$0.474261\pi$
$278$	6.90983	−	21.2663i	0.414424	−	1.27547i
$279$	−0.454915	+	1.40008i	−0.0272351	+	0.0838209i
$280$		0			0
$281$	6.10739	+	18.7966i	0.364336	+	1.12131i	0.950396	+	0.311044i	$0.100679\pi$
$281$	6.10739	+	18.7966i	0.364336	+	1.12131i	−0.586059	+	0.810268i	$0.699321\pi$
$282$	17.1672			1.02229
$283$	−4.69098	−	14.4374i	−0.278850	−	0.858212i	−0.988175	−	0.153330i	$-0.951000\pi$
$283$	−4.69098	−	14.4374i	−0.278850	−	0.858212i	0.709325	−	0.704882i	$-0.249000\pi$
$284$	−9.09017	−	6.60440i	−0.539402	−	0.391899i
$285$	−10.0000	−	7.26543i	−0.592349	−	0.430367i
$286$	−21.3262	+	15.4944i	−1.26105	+	0.916204i
$287$	−34.5795	−	25.1235i	−2.04116	−	1.48299i
$288$	−9.52786	−	6.92240i	−0.561435	−	0.407906i
$289$	13.7082	−	9.95959i	0.806365	−	0.585858i
$290$	−3.09017	+	9.51057i	−0.181461	+	0.558480i
$291$	8.38197	+	6.08985i	0.491360	+	0.356994i
$292$	7.32624	+	22.5478i	0.428736	+	1.31951i
$293$	6.32624			0.369583			0.184791	−	0.982778i	$-0.440839\pi$
$293$	6.32624			0.369583			0.184791	+	0.982778i	$0.440839\pi$
$294$	−8.36068	−	25.7315i	−0.487605	−	1.50069i
$295$	−8.45492	−	26.0216i	−0.492264	−	1.51503i
$296$		0			0
$297$	4.87539	−	15.0049i	0.282899	−	0.870673i
$298$	35.6525	−	25.9030i	2.06529	−	1.50052i
$299$	38.0344			2.19959
$300$	−3.81966	+	11.7557i	−0.220528	+	0.678716i
$301$	−14.7082			−0.847767
$302$	21.0344	−	15.2824i	1.21040	−	0.879404i
$303$	4.56231	−	14.0413i	0.262098	−	0.806654i
$304$	5.52786	−	17.0130i	0.317045	−	0.975763i
$305$	−2.88854			−0.165398
$306$	0.214782	+	0.661030i	0.0122783	+	0.0377886i
$307$	−4.90983			−0.280219			−0.140109	−	0.990136i	$-0.544745\pi$
$307$	−4.90983			−0.280219			−0.140109	+	0.990136i	$0.544745\pi$
$308$	7.47214	+	22.9969i	0.425764	+	1.31037i
$309$	−4.32624	−	3.14320i	−0.246111	−	0.178810i
$310$	1.38197	+	4.25325i	0.0784904	+	0.241569i
$311$	23.7082	−	17.2250i	1.34437	−	0.976741i	0.345098	−	0.938567i	$-0.387846\pi$
$311$	23.7082	−	17.2250i	1.34437	−	0.976741i	0.999271	−	0.0381745i	$-0.0121543\pi$
$312$		0			0
$313$	21.7533	+	15.8047i	1.22957	+	0.893334i	0.996858	−	0.0792121i	$-0.0252404\pi$
$313$	21.7533	+	15.8047i	1.22957	+	0.893334i	0.232711	+	0.972546i	$0.425240\pi$
$314$	−20.4721	+	14.8739i	−1.15531	+	0.839381i
$315$	−4.30902	−	13.2618i	−0.242786	−	0.747217i
$316$	5.00000	+	3.63271i	0.281272	+	0.204356i
$317$	5.12868	+	15.7844i	0.288055	+	0.886543i	0.985466	+	0.169871i	$0.0543352\pi$
$317$	5.12868	+	15.7844i	0.288055	+	0.886543i	−0.697411	+	0.716671i	$0.745665\pi$
$318$	−21.1672			−1.18700
$319$	−1.97214	−	6.06961i	−0.110418	−	0.339833i
$320$	−17.8885			−1.00000
$321$	−1.61803	+	4.97980i	−0.0903099	+	0.277945i
$322$	21.5623	−	66.3620i	1.20162	−	3.69821i
$323$	−0.854102	+	0.620541i	−0.0475235	+	0.0345278i
$324$	−4.83282			−0.268490
$325$	7.13525	−	21.9601i	0.395793	−	1.21812i
$326$	−1.41641			−0.0784476
$327$	−6.18034	+	4.49028i	−0.341774	+	0.248313i
$328$		0			0
$329$	−9.09017	+	27.9767i	−0.501157	+	1.54240i
$330$	−4.87539	−	15.0049i	−0.268381	−	0.825993i
$331$	−6.25329	−	19.2456i	−0.343712	−	1.05784i	−0.962270	−	0.272097i	$-0.912283\pi$
$331$	−6.25329	−	19.2456i	−0.343712	−	1.05784i	0.618558	−	0.785739i	$-0.287717\pi$
$332$	4.76393			0.261455
$333$	−4.59017	−	14.1271i	−0.251540	−	0.774160i
$334$	−16.3262	−	11.8617i	−0.893332	−	0.649044i
$335$	−7.29837	+	22.4621i	−0.398753	+	1.22723i
$336$	−16.9443	+	12.3107i	−0.924386	+	0.671606i
$337$	13.1803	+	9.57608i	0.717979	+	0.521642i	0.885738	−	0.464186i	$-0.153653\pi$
$337$	13.1803	+	9.57608i	0.717979	+	0.521642i	−0.167759	+	0.985828i	$0.553653\pi$
$338$	−13.4721	−	9.78808i	−0.732788	−	0.532401i
$339$	14.9443	−	10.8576i	0.811661	−	0.589707i
$340$	0.854102	+	0.620541i	0.0463202	+	0.0336536i
$341$	−2.30902	−	1.67760i	−0.125040	−	0.0908471i
$342$	4.06888	+	12.5227i	0.220020	+	0.677152i
$343$	16.7082			0.902158
$344$		0			0
$345$	−7.03444	+	21.6498i	−0.378722	+	1.16559i
$346$	4.36068	−	13.4208i	0.234432	−	0.721506i
$347$	7.22542	−	22.2376i	0.387881	−	1.19378i	−0.546487	−	0.837467i	$-0.684035\pi$
$347$	7.22542	−	22.2376i	0.387881	−	1.19378i	0.934369	−	0.356308i	$-0.115965\pi$
$348$	−4.47214	+	3.24920i	−0.239732	+	0.174175i
$349$	−21.7082			−1.16201			−0.581007	−	0.813899i	$-0.697341\pi$
$349$	−21.7082			−1.16201			−0.581007	+	0.813899i	$0.697341\pi$
$350$	−34.2705	−	24.8990i	−1.83184	−	1.33091i
$351$	25.5279			1.36258
$352$	18.4721	−	13.4208i	0.984568	−	0.715331i
$353$	6.22542	−	19.1599i	0.331346	−	1.01978i	−0.637148	−	0.770741i	$-0.719886\pi$
$353$	6.22542	−	19.1599i	0.331346	−	1.01978i	0.968494	−	0.249037i	$-0.0801139\pi$
$354$	9.34752	−	28.7687i	0.496815	−	1.52904i
$355$	−10.1631	+	7.38394i	−0.539402	+	0.391899i
$356$	−10.3262	−	31.7809i	−0.547290	−	1.68438i
$357$	1.23607			0.0654197
$358$	−5.20163	−	16.0090i	−0.274914	−	0.846100i
$359$	19.7984	+	14.3844i	1.04492	+	0.759178i	0.971240	−	0.238105i	$-0.0765261\pi$
$359$	19.7984	+	14.3844i	1.04492	+	0.759178i	0.0736787	+	0.997282i	$0.476526\pi$
$360$		0			0
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−27.1803	−	19.7477i	−1.42857	−	1.03791i
$363$	−2.85410	−	2.07363i	−0.149802	−	0.108837i
$364$	−31.6525	+	22.9969i	−1.65904	+	1.20536i
$365$	26.5066			1.38742
$366$	−2.58359	−	1.87709i	−0.135047	−	0.0981170i
$367$	2.69098	+	8.28199i	0.140468	+	0.432317i	0.996400	−	0.0847714i	$-0.0270160\pi$
$367$	2.69098	+	8.28199i	0.140468	+	0.432317i	−0.855932	+	0.517088i	$0.827016\pi$
$368$	−32.9443			−1.71734
$369$	−4.59017	−	14.1271i	−0.238955	−	0.735427i
$370$	−36.5066	−	26.5236i	−1.89789	−	1.37890i
$371$	11.2082	−	34.4953i	0.581901	−	1.79091i
$372$	−0.763932	+	2.35114i	−0.0396080	+	0.121901i
$373$	−15.8713	+	11.5312i	−0.821786	+	0.597062i	−0.917224	−	0.398373i	$-0.869575\pi$
$373$	−15.8713	+	11.5312i	−0.821786	+	0.597062i	0.0954376	+	0.995435i	$0.469575\pi$
$374$	−1.34752			−0.0696788
$375$	11.1803	+	8.12299i	0.577350	+	0.419470i
$376$		0			0
$377$	8.35410	−	6.06961i	0.430258	−	0.312601i
$378$	14.4721	−	44.5407i	0.744366	−	2.29092i
$379$	−4.08359	+	12.5680i	−0.209760	+	0.645575i	0.789724	+	0.613462i	$0.210224\pi$
$379$	−4.08359	+	12.5680i	−0.209760	+	0.645575i	−0.999484	+	0.0321130i	$0.989776\pi$
$380$	16.1803	+	11.7557i	0.830034	+	0.603055i
$381$	−6.49342	−	19.9847i	−0.332668	−	1.02385i
$382$	34.0000			1.73959
$383$	0.572949	+	1.76336i	0.0292763	+	0.0901033i	0.964627	−	0.263618i	$-0.0849160\pi$
$383$	0.572949	+	1.76336i	0.0292763	+	0.0901033i	−0.935351	+	0.353722i	$0.884916\pi$
$384$		0			0
$385$	27.0344			1.37780
$386$	−10.2361	+	7.43694i	−0.521002	+	0.378530i
$387$	−4.13525	−	3.00444i	−0.210207	−	0.152724i
$388$	−13.5623	−	9.85359i	−0.688522	−	0.500240i
$389$	−3.45492	+	2.51014i	−0.175171	+	0.127269i	−0.671916	−	0.740627i	$-0.734528\pi$
$389$	−3.45492	+	2.51014i	−0.175171	+	0.127269i	0.496745	+	0.867897i	$0.334528\pi$
$390$	20.6525	−	15.0049i	1.04578	−	0.759803i
$391$	1.57295	+	1.14281i	0.0795475	+	0.0577946i
$392$		0			0
$393$	10.5410			0.531724
$394$	2.29180	+	7.05342i	0.115459	+	0.355346i
$395$	5.59017	−	4.06150i	0.281272	−	0.204356i
$396$	−2.59675	+	7.99197i	−0.130491	+	0.401611i
$397$	−12.2467	+	37.6915i	−0.614645	+	1.89168i	−0.207858	+	0.978159i	$0.566649\pi$
$397$	−12.2467	+	37.6915i	−0.614645	+	1.89168i	−0.406786	+	0.913523i	$0.633351\pi$
$398$	−25.3262	+	18.4006i	−1.26949	+	0.922338i
$399$	23.4164			1.17229
$400$	−6.18034	+	19.0211i	−0.309017	+	0.951057i
$401$	−9.38197			−0.468513			−0.234257	−	0.972175i	$-0.575266\pi$
$401$	−9.38197			−0.468513			−0.234257	+	0.972175i	$0.575266\pi$
$402$	−21.1246	+	15.3479i	−1.05360	+	0.765485i
$403$	1.42705	−	4.39201i	0.0710865	−	0.218782i
$404$	−7.38197	+	22.7194i	−0.367267	+	1.13033i
$405$	−1.66970	+	5.13880i	−0.0829679	+	0.255349i
$406$	−5.85410	−	18.0171i	−0.290534	−	0.894172i
$407$	28.7984			1.42748
$408$		0			0
$409$	−2.23607	−	1.62460i	−0.110566	−	0.0803312i	0.531128	−	0.847292i	$-0.321768\pi$
$409$	−2.23607	−	1.62460i	−0.110566	−	0.0803312i	−0.641695	+	0.766960i	$0.721768\pi$
$410$	−36.5066	−	26.5236i	−1.80293	−	1.30991i
$411$	17.0000	−	12.3512i	0.838548	−	0.609241i
$412$	7.00000	+	5.08580i	0.344865	+	0.250559i
$413$	41.9336	+	30.4666i	2.06342	+	1.49916i
$414$	19.6180	−	14.2533i	0.964174	−	0.700513i
$415$	1.64590	−	5.06555i	0.0807940	−	0.248658i
$416$	29.8885	+	21.7153i	1.46541	+	1.06468i
$417$	−4.27051	−	13.1433i	−0.209128	−	0.643629i
$418$	−25.5279			−1.24861
$419$	2.33688	+	7.19218i	0.114164	+	0.351361i	0.991772	−	0.128019i	$-0.0408617\pi$
$419$	2.33688	+	7.19218i	0.114164	+	0.351361i	−0.877608	+	0.479380i	$0.840862\pi$
$420$	−7.23607	−	22.2703i	−0.353084	−	1.08668i
$421$	−4.70820	+	14.4904i	−0.229464	+	0.706217i	0.768344	+	0.640037i	$0.221081\pi$
$421$	−4.70820	+	14.4904i	−0.229464	+	0.706217i	−0.997808	+	0.0661798i	$0.978919\pi$
$422$	−2.90983	+	8.95554i	−0.141648	+	0.435949i
$423$	−8.27051	+	6.00888i	−0.402126	+	0.292162i
$424$		0			0
$425$	0.954915	−	0.693786i	0.0463202	−	0.0336536i
$426$	−13.8885			−0.672902
$427$	4.42705	−	3.21644i	0.214240	−	0.155654i
$428$	2.61803	−	8.05748i	0.126547	−	0.389473i
$429$	−5.03444	+	15.4944i	−0.243065	+	0.748078i
$430$	−15.5279			−0.748820
$431$	1.14590	+	3.52671i	0.0551960	+	0.169876i	0.974854	−	0.222844i	$-0.0715342\pi$
$431$	1.14590	+	3.52671i	0.0551960	+	0.169876i	−0.919658	+	0.392720i	$0.871534\pi$
$432$	−22.1115			−1.06384
$433$	−0.381966	−	1.17557i	−0.0183561	−	0.0564943i	0.941459	−	0.337128i	$-0.109455\pi$
$433$	−0.381966	−	1.17557i	−0.0183561	−	0.0564943i	−0.959815	+	0.280634i	$0.909455\pi$
$434$	−6.85410	−	4.97980i	−0.329007	−	0.239038i
$435$	1.90983	+	5.87785i	0.0915693	+	0.281821i
$436$	10.0000	−	7.26543i	0.478913	−	0.347951i
$437$	29.7984	+	21.6498i	1.42545	+	1.03565i
$438$	23.7082	+	17.2250i	1.13282	+	0.823043i
$439$	−17.6631	+	12.8330i	−0.843015	+	0.612486i	−0.923211	−	0.384293i	$-0.874445\pi$
$439$	−17.6631	+	12.8330i	−0.843015	+	0.612486i	0.0801965	+	0.996779i	$0.474445\pi$
$440$		0			0
$441$	13.0344	+	9.47008i	0.620688	+	0.450956i
$442$	−0.673762	−	2.07363i	−0.0320476	−	0.0986324i
$443$	−14.1246			−0.671081			−0.335540	−	0.942026i	$-0.608919\pi$
$443$	−14.1246			−0.671081			−0.335540	+	0.942026i	$0.608919\pi$
$444$	−7.70820	−	23.7234i	−0.365815	−	1.12586i
$445$	−37.3607			−1.77107
$446$	−7.27051	+	22.3763i	−0.344269	+	1.05955i
$447$	8.41641	−	25.9030i	0.398082	−	1.22517i
$448$	27.4164	−	19.9192i	1.29530	−	0.941093i
$449$	8.41641			0.397195			0.198597	−	0.980081i	$-0.436361\pi$
$449$	8.41641			0.397195			0.198597	+	0.980081i	$0.436361\pi$
$450$	−4.54915	−	14.0008i	−0.214449	−	0.660006i
$451$	28.7984			1.35606
$452$	−24.1803	+	17.5680i	−1.13735	+	0.826331i
$453$	4.96556	−	15.2824i	0.233302	−	0.718031i
$454$	−15.2705	+	46.9978i	−0.716681	+	2.20572i
$455$	13.5172	+	41.6017i	0.633697	+	1.95032i
$456$		0			0
$457$	−0.763932			−0.0357352			−0.0178676	−	0.999840i	$-0.505688\pi$
$457$	−0.763932			−0.0357352			−0.0178676	+	0.999840i	$0.505688\pi$
$458$	−0.124612	−	0.383516i	−0.00582273	−	0.0179205i
$459$	1.05573	+	0.767031i	0.0492772	+	0.0358020i
$460$	11.3820	−	35.0301i	0.530687	−	1.63329i
$461$	−28.4894	+	20.6987i	−1.32688	+	0.964036i	−0.327063	+	0.945003i	$0.606059\pi$
$461$	−28.4894	+	20.6987i	−1.32688	+	0.964036i	−0.999819	+	0.0190333i	$0.993941\pi$
$462$	24.1803	+	17.5680i	1.12497	+	0.817339i
$463$	−17.5172	−	12.7270i	−0.814094	−	0.591474i	0.100920	−	0.994894i	$-0.467821\pi$
$463$	−17.5172	−	12.7270i	−0.814094	−	0.591474i	−0.915015	+	0.403420i	$0.867821\pi$
$464$	−7.23607	+	5.25731i	−0.335926	+	0.244065i
$465$	2.23607	+	1.62460i	0.103695	+	0.0753390i
$466$	−19.7082	−	14.3188i	−0.912965	−	0.663308i
$467$	7.06231	+	21.7355i	0.326805	+	1.00580i	0.970619	+	0.240620i	$0.0773507\pi$
$467$	7.06231	+	21.7355i	0.326805	+	1.00580i	−0.643815	+	0.765181i	$0.722649\pi$
$468$	−13.5967			−0.628510
$469$	−13.8262	−	42.5528i	−0.638436	−	1.96491i
$470$	−9.59675	+	29.5358i	−0.442665	+	1.36238i
$471$	−4.83282	+	14.8739i	−0.222684	+	0.685352i
$472$		0			0
$473$	8.01722	−	5.82485i	0.368632	−	0.267827i
$474$	7.63932			0.350886
$475$	18.0902	−	13.1433i	0.830034	−	0.603055i
$476$	−2.00000			−0.0916698
$477$	10.1976	−	7.40896i	0.466914	−	0.339233i
$478$	1.05573	−	3.24920i	0.0482879	−	0.148615i
$479$	7.01064	−	21.5765i	0.320324	−	0.985857i	−0.653183	−	0.757200i	$-0.726567\pi$
$479$	7.01064	−	21.5765i	0.320324	−	0.985857i	0.973507	−	0.228657i	$-0.0734334\pi$
$480$	−17.8885	+	12.9968i	−0.816497	+	0.593219i
$481$	14.3992	+	44.3161i	0.656546	+	2.02064i
$482$	18.0689			0.823015
$483$	−13.3262	−	41.0139i	−0.606365	−	1.86620i
$484$	4.61803	+	3.35520i	0.209911	+	0.152509i
$485$	−15.1631	+	11.0167i	−0.688522	+	0.500240i
$486$	22.0000	−	15.9839i	0.997940	−	0.725046i
$487$	−2.04508	−	1.48584i	−0.0926716	−	0.0673299i	0.540485	−	0.841354i	$-0.318241\pi$
$487$	−2.04508	−	1.48584i	−0.0926716	−	0.0673299i	−0.633156	+	0.774024i	$0.718241\pi$
$488$		0			0
$489$	−0.708204	+	0.514540i	−0.0320261	+	0.0232683i
$490$	48.9443			2.21108
$491$	−14.2812	−	10.3759i	−0.644499	−	0.468256i	0.216894	−	0.976195i	$-0.430408\pi$
$491$	−14.2812	−	10.3759i	−0.644499	−	0.468256i	−0.861393	+	0.507939i	$0.830408\pi$
$492$	−7.70820	−	23.7234i	−0.347513	−	1.06953i
$493$	0.527864			0.0237738
$494$	−12.7639	−	39.2833i	−0.574276	−	1.76744i
$495$	7.60081	+	5.52231i	0.341631	+	0.248210i
$496$	−1.23607	+	3.80423i	−0.0555011	+	0.170815i
$497$	7.35410	−	22.6336i	0.329877	−	1.01526i
$498$	4.76393	−	3.46120i	0.213477	−	0.155100i
$499$	20.1246			0.900901			0.450451	−	0.892801i	$-0.351263\pi$
$499$	20.1246			0.900901			0.450451	+	0.892801i	$0.351263\pi$
$500$	−18.0902	−	13.1433i	−0.809017	−	0.587785i
$501$	−12.4721			−0.557214
$502$	−24.4164	+	17.7396i	−1.08976	+	0.791755i
$503$	−10.7082	+	32.9565i	−0.477455	+	1.46946i	0.365162	+	0.930944i	$0.381013\pi$
$503$	−10.7082	+	32.9565i	−0.477455	+	1.46946i	−0.842618	+	0.538512i	$0.818987\pi$
$504$		0			0
$505$	21.6074	+	15.6987i	0.961516	+	0.698582i
$506$	14.5279	+	44.7122i	0.645842	+	1.98770i
$507$	−10.2918			−0.457075
$508$	10.5066	+	32.3359i	0.466154	+	1.43467i
$509$	−11.4443	−	8.31475i	−0.507258	−	0.368545i	0.304524	−	0.952505i	$-0.401503\pi$
$509$	−11.4443	−	8.31475i	−0.507258	−	0.368545i	−0.811783	+	0.583960i	$0.801503\pi$
$510$	1.30495			0.0577842
$511$	−40.6246	+	29.5155i	−1.79713	+	1.30569i
$512$	−25.8885	−	18.8091i	−1.14412	−	0.831254i
$513$	20.0000	+	14.5309i	0.883022	+	0.641553i
$514$	5.18034	−	3.76374i	0.228495	−	0.166011i
$515$	7.82624	−	5.68609i	0.344865	−	0.250559i
$516$	−6.94427	−	5.04531i	−0.305705	−	0.222107i
$517$	−6.12461	−	18.8496i	−0.269360	−	0.829005i
$518$	85.4853			3.75601
$519$	−2.69505	−	8.29451i	−0.118299	−	0.364088i
$520$		0			0
$521$	10.1287	−	31.1729i	0.443745	−	1.36571i	−0.440108	−	0.897945i	$-0.645060\pi$
$521$	10.1287	−	31.1729i	0.443745	−	1.36571i	0.883854	−	0.467763i	$-0.154940\pi$
$522$	2.03444	−	6.26137i	0.0890451	−	0.274053i
$523$	−8.20820	+	5.96361i	−0.358920	+	0.260770i	−0.752601	−	0.658476i	$-0.771201\pi$
$523$	−8.20820	+	5.96361i	−0.358920	+	0.260770i	0.393682	+	0.919247i	$0.371201\pi$
$524$	−17.0557			−0.745083
$525$	−26.1803			−1.14260
$526$	2.00000			0.0872041
$527$	0.190983	−	0.138757i	0.00831935	−	0.00604436i
$528$	4.36068	−	13.4208i	0.189774	−	0.584065i
$529$	13.8541	−	42.6385i	0.602352	−	1.85385i
$530$	11.8328	−	36.4177i	0.513985	−	1.58188i
$531$	5.56637	+	17.1315i	0.241560	+	0.743445i
$532$	−37.8885			−1.64268
$533$	14.3992	+	44.3161i	0.623698	+	1.91955i
$534$	−33.4164	−	24.2784i	−1.44607	−	1.05063i
$535$	−7.66312	−	5.56758i	−0.331306	−	0.240708i
$536$		0			0
$537$	−8.41641	−	6.11488i	−0.363195	−	0.263876i
$538$	−25.3262	−	18.4006i	−1.09189	−	0.793306i
$539$	−25.2705	+	18.3601i	−1.08848	+	0.790825i
$540$	7.63932	−	23.5114i	0.328744	−	1.01177i
$541$	−1.61803	−	1.17557i	−0.0695647	−	0.0505417i	0.552459	−	0.833540i	$-0.313689\pi$
$541$	−1.61803	−	1.17557i	−0.0695647	−	0.0505417i	−0.622024	+	0.782998i	$0.713689\pi$
$542$	−6.85410	−	21.0948i	−0.294409	−	0.906097i
$543$	−20.7639			−0.891066
$544$	0.583592	+	1.79611i	0.0250213	+	0.0770077i
$545$	−4.27051	−	13.1433i	−0.182929	−	0.562996i
$546$	−14.9443	+	45.9937i	−0.639556	+	1.96835i
$547$	−0.600813	+	1.84911i	−0.0256889	+	0.0790623i	−0.963079	−	0.269219i	$-0.913235\pi$
$547$	−0.600813	+	1.84911i	−0.0256889	+	0.0790623i	0.937390	+	0.348281i	$0.113235\pi$
$548$	−27.5066	+	19.9847i	−1.17502	+	0.853704i
$549$	1.90170			0.0811626
$550$	28.5410			1.21699
$551$	10.0000			0.426014
$552$		0			0
$553$	−4.04508	+	12.4495i	−0.172015	+	0.529406i
$554$	10.7082	−	32.9565i	0.454948	−	1.40019i
$555$	−27.8885			−1.18380
$556$	6.90983	+	21.2663i	0.293042	+	0.901891i
$557$	21.7984			0.923627			0.461813	−	0.886977i	$-0.347199\pi$
$557$	21.7984			0.923627			0.461813	+	0.886977i	$0.347199\pi$
$558$	−0.909830	−	2.80017i	−0.0385162	−	0.118541i
$559$	12.9721	+	9.42481i	0.548663	+	0.398627i
$560$	−11.7082	−	36.0341i	−0.494762	−	1.52272i
$561$	−0.673762	+	0.489517i	−0.0284463	+	0.0206674i
$562$	−31.9787	−	23.2339i	−1.34894	−	0.980063i
$563$	−6.66312	−	4.84104i	−0.280817	−	0.204025i	0.438457	−	0.898752i	$-0.355525\pi$
$563$	−6.66312	−	4.84104i	−0.280817	−	0.204025i	−0.719274	+	0.694727i	$0.755525\pi$
$564$	−13.8885	+	10.0906i	−0.584813	+	0.424892i
$565$	10.3262	+	31.7809i	0.434428	+	1.33703i
$566$	24.5623	+	17.8456i	1.03243	+	0.750105i
$567$	−3.16312	−	9.73508i	−0.132839	−	0.408835i
$568$		0			0
$569$	−1.84752	−	5.68609i	−0.0774522	−	0.238373i	0.904833	−	0.425768i	$-0.139996\pi$
$569$	−1.84752	−	5.68609i	−0.0774522	−	0.238373i	−0.982285	+	0.187394i	$0.939996\pi$
$570$	24.7214			1.03546
$571$	2.69098	−	8.28199i	0.112614	−	0.346591i	−0.878828	−	0.477139i	$-0.841674\pi$
$571$	2.69098	−	8.28199i	0.112614	−	0.346591i	0.991442	+	0.130548i	$0.0416738\pi$
$572$	8.14590	−	25.0705i	0.340597	−	1.04825i
$573$	17.0000	−	12.3512i	0.710185	−	0.515980i
$574$	85.4853			3.56809
$575$	−33.3156	−	24.2052i	−1.38936	−	1.00943i
$576$	11.7771			0.490712
$577$	−14.4443	+	10.4944i	−0.601323	+	0.436887i	−0.846348	−	0.532630i	$-0.821204\pi$
$577$	−14.4443	+	10.4944i	−0.601323	+	0.436887i	0.245025	+	0.969517i	$0.421204\pi$
$578$	−10.4721	+	32.2299i	−0.435583	+	1.34059i
$579$	−2.41641	+	7.43694i	−0.100422	+	0.309069i
$580$	−3.09017	−	9.51057i	−0.128312	−	0.394905i
$581$	3.11803	+	9.59632i	0.129358	+	0.398123i
$582$	−20.7214			−0.858928
$583$	7.55166	+	23.2416i	0.312758	+	0.962570i
$584$		0			0
$585$	−4.69756	+	14.4576i	−0.194220	+	0.597748i
$586$	−10.2361	+	7.43694i	−0.422848	+	0.307217i
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.993437	−	0.114377i	$-0.0364873\pi$
$587$	28.8713	+	20.9762i	1.19165	+	0.865782i	0.198210	+	0.980160i	$0.436487\pi$
$588$	21.8885	+	15.9030i	0.902668	+	0.655827i
$589$	3.61803	−	2.62866i	0.149078	−	0.108312i
$590$	44.2705	+	32.1644i	1.82259	+	1.32419i
$591$	3.70820	+	2.69417i	0.152535	+	0.110823i
$592$	−12.4721	−	38.3853i	−0.512602	−	1.57763i
$593$	−30.3820			−1.24764			−0.623819	−	0.781569i	$-0.714420\pi$
$593$	−30.3820			−1.24764			−0.623819	+	0.781569i	$0.714420\pi$
$594$	9.75078	+	30.0098i	0.400079	+	1.23132i
$595$	−0.690983	+	2.12663i	−0.0283275	+	0.0871832i
$596$	−13.6180	+	41.9120i	−0.557816	+	1.71678i
$597$	−5.97871	+	18.4006i	−0.244692	+	0.753086i
$598$	−61.5410	+	44.7122i	−2.51660	+	1.82842i
$599$	3.29180			0.134499			0.0672496	−	0.997736i	$-0.478578\pi$
$599$	3.29180			0.134499			0.0672496	+	0.997736i	$0.478578\pi$
$600$		0			0
$601$	33.1803			1.35345			0.676727	−	0.736234i	$-0.263398\pi$
$601$	33.1803			1.35345			0.676727	+	0.736234i	$0.263398\pi$
$602$	23.7984	−	17.2905i	0.969949	−	0.704709i
$603$	4.80495	−	14.7881i	0.195673	−	0.602219i
$604$	−8.03444	+	24.7275i	−0.326917	+	1.00615i
$605$	5.16312	−	3.75123i	0.209911	−	0.152509i
$606$	9.12461	+	28.0827i	0.370662	+	1.14078i
$607$	24.2361			0.983712			0.491856	−	0.870677i	$-0.336319\pi$
$607$	24.2361			0.983712			0.491856	+	0.870677i	$0.336319\pi$
$608$	11.0557	+	34.0260i	0.448369	+	1.37994i
$609$	−9.47214	−	6.88191i	−0.383830	−	0.278869i
$610$	4.67376	−	3.39569i	0.189235	−	0.137487i
$611$	25.9443	−	18.8496i	1.04959	−	0.762574i
$612$	−0.562306	−	0.408539i	−0.0227299	−	0.0165142i
$613$	15.4721	+	11.2412i	0.624914	+	0.454026i	0.854634	−	0.519230i	$-0.173781\pi$
$613$	15.4721	+	11.2412i	0.624914	+	0.454026i	−0.229721	+	0.973257i	$0.573781\pi$
$614$	7.94427	−	5.77185i	0.320605	−	0.232933i
$615$	−27.8885			−1.12457
$616$		0			0
$617$	9.13525	+	28.1154i	0.367772	+	1.13188i	0.948227	+	0.317593i	$0.102874\pi$
$617$	9.13525	+	28.1154i	0.367772	+	1.13188i	−0.580456	+	0.814292i	$0.697126\pi$
$618$	10.6950			0.430218
$619$	−14.8607	−	45.7365i	−0.597301	−	1.83830i	−0.542921	−	0.839784i	$-0.682682\pi$
$619$	−14.8607	−	45.7365i	−0.597301	−	1.83830i	−0.0543799	−	0.998520i	$-0.517318\pi$
$620$	−3.61803	−	2.62866i	−0.145304	−	0.105569i
$621$	14.0689	−	43.2996i	0.564565	−	1.73755i
$622$	−18.1115	+	55.7413i	−0.726203	+	2.23502i
$623$	57.2599	−	41.6017i	2.29407	−	1.66674i
$624$	22.8328			0.914044
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	−53.7771			−2.14936
$627$	−12.7639	+	9.27354i	−0.509742	+	0.370349i
$628$	7.81966	−	24.0664i	0.312038	−	0.960355i
$629$	−0.736068	+	2.26538i	−0.0293490	+	0.0903268i
$630$	22.5623	+	16.3925i	0.898904	+	0.653092i
$631$	−9.05573	−	27.8707i	−0.360503	−	1.10951i	−0.952750	−	0.303757i	$-0.901759\pi$
$631$	−9.05573	−	27.8707i	−0.360503	−	1.10951i	0.592247	−	0.805757i	$-0.298241\pi$
$632$		0			0
$633$	1.79837	+	5.53483i	0.0714789	+	0.219990i
$634$	−26.8541	−	19.5106i	−1.06651	−	0.774867i
$635$	38.0132			1.50851
$636$	17.1246	−	12.4418i	0.679035	−	0.493348i
$637$	−40.8885	−	29.7073i	−1.62006	−	1.17704i
$638$	10.3262	+	7.50245i	0.408820	+	0.297025i
$639$	6.69098	−	4.86128i	0.264691	−	0.192309i
$640$		0			0
$641$	−11.2533	−	8.17599i	−0.444478	−	0.322932i	0.342934	−	0.939360i	$-0.388579\pi$
$641$	−11.2533	−	8.17599i	−0.444478	−	0.322932i	−0.787412	+	0.616427i	$0.788579\pi$
$642$	−3.23607	−	9.95959i	−0.127717	−	0.393074i
$643$	40.7984			1.60893			0.804465	−	0.594000i	$-0.202452\pi$
$643$	40.7984			1.60893			0.804465	+	0.594000i	$0.202452\pi$
$644$	21.5623	+	66.3620i	0.849674	+	2.61503i
$645$	−7.76393	+	5.64083i	−0.305705	+	0.222107i
$646$	0.652476	−	2.00811i	0.0256713	−	0.0790082i
$647$	3.01722	−	9.28605i	0.118619	−	0.365072i	−0.874065	−	0.485808i	$-0.838525\pi$
$647$	3.01722	−	9.28605i	0.118619	−	0.365072i	0.992685	+	0.120736i	$0.0385254\pi$
$648$		0			0
$649$	−34.9230			−1.37085
$650$	14.2705	+	43.9201i	0.559735	+	1.72269i
$651$	−5.23607			−0.205218
$652$	1.14590	−	0.832544i	0.0448768	−	0.0326049i
$653$	2.64590	−	8.14324i	0.103542	−	0.318669i	−0.885843	−	0.463984i	$-0.846419\pi$
$653$	2.64590	−	8.14324i	0.103542	−	0.318669i	0.989385	+	0.145315i	$0.0464195\pi$
$654$	4.72136	−	14.5309i	0.184620	−	0.568201i
$655$	−5.89261	+	18.1356i	−0.230243	+	0.708616i
$656$	−12.4721	−	38.3853i	−0.486955	−	1.49869i
$657$	−17.4508			−0.680822
$658$	−18.1803	−	55.9533i	−0.708743	−	2.18129i
$659$	6.44427	+	4.68204i	0.251033	+	0.182386i	0.706185	−	0.708028i	$-0.250415\pi$
$659$	6.44427	+	4.68204i	0.251033	+	0.182386i	−0.455151	+	0.890414i	$0.650415\pi$
$660$	12.7639	+	9.27354i	0.496835	+	0.360972i
$661$	−35.4615	+	25.7643i	−1.37929	+	1.00211i	−0.382346	+	0.924019i	$0.624884\pi$
$661$	−35.4615	+	25.7643i	−1.37929	+	1.00211i	−0.996946	+	0.0780954i	$0.975116\pi$
$662$	32.7426	+	23.7889i	1.27258	+	0.924583i
$663$	−1.09017	−	0.792055i	−0.0423387	−	0.0307609i
$664$		0			0
$665$	−13.0902	+	40.2874i	−0.507615	+	1.56228i
$666$	24.0344	+	17.4620i	0.931316	+	0.676640i
$667$	−5.69098	−	17.5150i	−0.220356	−	0.678185i
$668$	20.1803			0.780801
$669$	4.49342	+	13.8293i	0.173726	+	0.534673i
$670$	−14.5967	−	44.9242i	−0.563922	−	1.73557i
$671$	−1.13932	+	3.50647i	−0.0439830	+	0.135366i
$672$	12.9443	−	39.8384i	0.499336	−	1.53680i
$673$	−22.1525	+	16.0947i	−0.853915	+	0.620406i	−0.926223	−	0.376977i	$-0.876964\pi$
$673$	−22.1525	+	16.0947i	−0.853915	+	0.620406i	0.0723076	+	0.997382i	$0.476964\pi$
$674$	−32.5836			−1.25507
$675$	−22.3607	−	16.2460i	−0.860663	−	0.625308i
$676$	16.6525			0.640480
$677$	5.78115	−	4.20025i	0.222188	−	0.161429i	−0.471123	−	0.882067i	$-0.656151\pi$
$677$	5.78115	−	4.20025i	0.222188	−	0.161429i	0.693311	+	0.720639i	$0.256151\pi$
$678$	−11.4164	+	35.1361i	−0.438445	+	1.34939i
$679$	10.9721	−	33.7688i	0.421072	−	1.29593i
$680$		0			0
$681$	9.43769	+	29.0462i	0.361653	+	1.11305i
$682$	5.70820			0.218578
$683$	5.63525	+	17.3435i	0.215627	+	0.663632i	0.999108	+	0.0422166i	$0.0134420\pi$
$683$	5.63525	+	17.3435i	0.215627	+	0.663632i	−0.783481	+	0.621415i	$0.786558\pi$
$684$	−10.6525	−	7.73948i	−0.407308	−	0.295926i
$685$	11.7467	+	36.1527i	0.448819	+	1.38132i
$686$	−27.0344	+	19.6417i	−1.03218	+	0.749923i
$687$	−0.201626	−	0.146490i	−0.00769252	−	0.00558894i
$688$	−11.2361	−	8.16348i	−0.428371	−	0.311230i
$689$	−31.9894	+	23.2416i	−1.21870	+	0.885436i
$690$	−14.0689	−	43.2996i	−0.535593	−	1.64839i
$691$	−7.73607	−	5.62058i	−0.294294	−	0.213817i	0.430834	−	0.902431i	$-0.358219\pi$
$691$	−7.73607	−	5.62058i	−0.294294	−	0.213817i	−0.725128	+	0.688614i	$0.758219\pi$
$692$	4.36068	+	13.4208i	0.165768	+	0.510182i
$693$	−17.7984			−0.676104
$694$	14.4508	+	44.4751i	0.548547	+	1.68825i
$695$	25.0000			0.948304
$696$		0			0
$697$	−0.736068	+	2.26538i	−0.0278806	+	0.0858075i
$698$	35.1246	−	25.5195i	1.32949	−	0.965928i
$699$	−15.0557			−0.569460
$700$	42.3607			1.60108
$701$	−34.3820			−1.29859			−0.649294	−	0.760537i	$-0.724936\pi$
$701$	−34.3820			−1.29859			−0.649294	+	0.760537i	$0.724936\pi$
$702$	−41.3050	+	30.0098i	−1.55895	+	1.13265i
$703$	−13.9443	+	42.9161i	−0.525918	+	1.61861i
$704$	−7.05573	+	21.7153i	−0.265923	+	0.818426i
$705$	5.93112	+	18.2541i	0.223379	+	0.687489i
$706$	12.4508	+	38.3198i	0.468594	+	1.44218i
$707$	−50.5967			−1.90289
$708$	9.34752	+	28.7687i	0.351301	+	1.08119i
$709$	11.7082	+	8.50651i	0.439711	+	0.319469i	0.785520	−	0.618836i	$-0.212396\pi$
$709$	11.7082	+	8.50651i	0.439711	+	0.319469i	−0.345809	+	0.938305i	$0.612396\pi$
$710$	7.76393	−	23.8949i	0.291375	−	0.896761i
$711$	−3.68034	+	2.67392i	−0.138024	+	0.100280i
$712$		0			0
$713$	−6.66312	−	4.84104i	−0.249536	−	0.181298i
$714$	−2.00000	+	1.45309i	−0.0748481	+	0.0543803i
$715$	−23.8435	−	17.3233i	−0.891695	−	0.647854i
$716$	13.6180	+	9.89408i	0.508930	+	0.369759i
$717$	−0.652476	−	2.00811i	−0.0243672	−	0.0749944i
$718$	−48.9443			−1.82658
$719$	3.35410	+	10.3229i	0.125087	+	0.384978i	0.993917	−	0.110133i	$-0.0351276\pi$
$719$	3.35410	+	10.3229i	0.125087	+	0.384978i	−0.868830	+	0.495111i	$0.835128\pi$
$720$	4.06888	−	12.5227i	0.151638	−	0.466695i
$721$	−5.66312	+	17.4293i	−0.210906	+	0.649101i
$722$	0.618034	−	1.90211i	0.0230008	−	0.0707893i
$723$	9.03444	−	6.56391i	0.335995	−	0.244114i
$724$	33.5967			1.24861
$725$	−11.1803			−0.415227
$726$	7.05573			0.261863
$727$	−14.8090	+	10.7594i	−0.549236	+	0.399043i	−0.827504	−	0.561460i	$-0.810240\pi$
$727$	−14.8090	+	10.7594i	−0.549236	+	0.399043i	0.278268	+	0.960504i	$0.410240\pi$
$728$		0			0
$729$	7.43363	−	22.8784i	0.275320	−	0.847347i
$730$	−42.8885	+	31.1604i	−1.58738	+	1.15330i
$731$	0.253289	+	0.779543i	0.00936823	+	0.0288324i
$732$	3.19350			0.118035
$733$	−14.3885	−	44.2834i	−0.531453	−	1.63564i	−0.751191	−	0.660085i	$-0.770520\pi$
$733$	−14.3885	−	44.2834i	−0.531453	−	1.63564i	0.219738	−	0.975559i	$-0.429480\pi$
$734$	−14.0902	−	10.2371i	−0.520078	−	0.377859i
$735$	24.4721	−	17.7800i	0.902668	−	0.655827i
$736$	53.3050	−	38.7283i	1.96485	−	1.42754i
$737$	24.3885	+	17.7193i	0.898364	+	0.652699i
$738$	24.0344	+	17.4620i	0.884720	+	0.642787i
$739$	6.44427	−	4.68204i	0.237056	−	0.172232i	−0.462914	−	0.886403i	$-0.653196\pi$
$739$	6.44427	−	4.68204i	0.237056	−	0.172232i	0.699971	+	0.714171i	$0.253196\pi$
$740$	45.1246			1.65881
$741$	−20.6525	−	15.0049i	−0.758688	−	0.551219i
$742$	22.4164	+	68.9906i	0.822932	+	2.53272i
$743$	15.4721			0.567618			0.283809	−	0.958881i	$-0.408402\pi$
$743$	15.4721			0.567618			0.283809	+	0.958881i	$0.408402\pi$
$744$		0			0
$745$	39.8607	+	28.9605i	1.46038	+	1.06103i
$746$	12.1246	−	37.3157i	0.443914	−	1.36623i
$747$	−1.08359	+	3.33495i	−0.0396466	+	0.122020i
$748$	1.09017	−	0.792055i	0.0398606	−	0.0289604i
$749$	17.9443			0.655669
$750$	−27.6393			−1.00925
$751$	−11.0902			−0.404686			−0.202343	−	0.979315i	$-0.564856\pi$
$751$	−11.0902			−0.404686			−0.202343	+	0.979315i	$0.564856\pi$
$752$	−22.4721	+	16.3270i	−0.819474	+	0.595383i
$753$	−5.76393	+	17.7396i	−0.210049	+	0.646465i
$754$	−6.38197	+	19.6417i	−0.232417	+	0.715307i
$755$	23.5172	+	17.0863i	0.855879	+	0.621833i
$756$	14.4721	+	44.5407i	0.526346	+	1.61993i
$757$	−20.7639			−0.754678			−0.377339	−	0.926075i	$-0.623161\pi$
$757$	−20.7639			−0.754678			−0.377339	+	0.926075i	$0.623161\pi$
$758$	−8.16718	−	25.1360i	−0.296645	−	0.912981i
$759$	23.5066	+	17.0785i	0.853235	+	0.619911i
$760$		0			0
$761$	−10.2984	+	7.48221i	−0.373316	+	0.271230i	−0.758585	−	0.651575i	$-0.774109\pi$
$761$	−10.2984	+	7.48221i	−0.373316	+	0.271230i	0.385269	+	0.922804i	$0.374109\pi$
$762$	34.0000	+	24.7024i	1.23169	+	0.894875i
$763$	21.1803	+	15.3884i	0.766780	+	0.557098i
$764$	−27.5066	+	19.9847i	−0.995153	+	0.723021i
$765$	−0.628677	+	0.456761i	−0.0227299	+	0.0165142i
$766$	−3.00000	−	2.17963i	−0.108394	−	0.0787531i
$767$	−17.4615	−	53.7409i	−0.630498	−	1.94047i
$768$	−19.7771			−0.713644
$769$	11.2188	+	34.5281i	0.404562	+	1.24511i	0.921260	+	0.388946i	$0.127161\pi$
$769$	11.2188	+	34.5281i	0.404562	+	1.24511i	−0.516698	+	0.856167i	$0.672839\pi$
$770$	−43.7426	+	31.7809i	−1.57638	+	1.14530i
$771$	1.22291	−	3.76374i	0.0440421	−	0.135548i
$772$	3.90983	−	12.0332i	0.140718	−	0.433085i
$773$	15.4721	−	11.2412i	0.556494	−	0.404317i	−0.273680	−	0.961821i	$-0.588241\pi$
$773$	15.4721	−	11.2412i	0.556494	−	0.404317i	0.830174	+	0.557504i	$0.188241\pi$
$774$	10.2229			0.367455
$775$	−4.04508	+	2.93893i	−0.145304	+	0.105569i
$776$		0			0
$777$	42.7426	−	31.0543i	1.53338	−	1.11407i
$778$	2.63932	−	8.12299i	0.0946242	−	0.291223i
$779$	−13.9443	+	42.9161i	−0.499605	+	1.53763i
$780$	−7.88854	+	24.2784i	−0.282455	+	0.869308i
$781$	4.95492	+	15.2497i	0.177301	+	0.545676i
$782$	−3.88854			−0.139054
$783$	−3.81966	−	11.7557i	−0.136504	−	0.420115i
$784$	35.4164	+	25.7315i	1.26487	+	0.918983i
$785$	−22.8885	−	16.6295i	−0.816927	−	0.593532i
$786$	−17.0557	+	12.3917i	−0.608358	+	0.441998i
$787$	−4.54508	−	3.30220i	−0.162015	−	0.117711i	0.503824	−	0.863806i	$-0.331926\pi$
$787$	−4.54508	−	3.30220i	−0.162015	−	0.117711i	−0.665839	+	0.746096i	$0.731926\pi$
$788$	−6.00000	−	4.35926i	−0.213741	−	0.155292i
$789$	1.00000	−	0.726543i	0.0356009	−	0.0258656i
$790$	−4.27051	+	13.1433i	−0.151938	+	0.467617i
$791$	−51.2148	−	37.2097i	−1.82099	−	1.32303i
$792$		0			0
$793$	−5.96556			−0.211843
$794$	−24.4934	−	75.3830i	−0.869239	−	2.67524i
$795$	−7.31308	−	22.5074i	−0.259368	−	0.798254i
$796$	9.67376	−	29.7728i	0.342877	−	1.05527i
$797$	5.09017	−	15.6659i	0.180303	−	0.554916i	−0.819533	−	0.573032i	$-0.805767\pi$
$797$	5.09017	−	15.6659i	0.180303	−	0.554916i	0.999836	+	0.0181165i	$0.00576697\pi$
$798$	−37.8885	+	27.5276i	−1.34124	+	0.974468i
$799$	1.63932			0.0579950
$800$	−12.3607	−	38.0423i	−0.437016	−	1.34500i
$801$	24.5967			0.869083
$802$	15.1803	−	11.0292i	0.536036	−	0.389453i
$803$	10.4549	−	32.1769i	0.368946	−	1.13550i
$804$	8.06888	−	24.8335i	0.284568	−	0.875809i
$805$	78.0132			2.74960
$806$	2.85410	+	8.78402i	0.100531	+	0.309404i
$807$	−19.3475			−0.681065
$808$		0			0
$809$	−41.6074	−	30.2295i	−1.46284	−	1.06281i	−0.982612	−	0.185669i	$-0.940555\pi$
$809$	−41.6074	−	30.2295i	−1.46284	−	1.06281i	−0.480226	−	0.877145i	$-0.659445\pi$
$810$	−3.33939	−	10.2776i	−0.117334	−	0.361118i
$811$	−6.71885	+	4.88153i	−0.235931	+	0.171414i	−0.699468	−	0.714664i	$-0.746580\pi$
$811$	−6.71885	+	4.88153i	−0.235931	+	0.171414i	0.463538	+	0.886077i	$0.346580\pi$
$812$	15.3262	+	11.1352i	0.537846	+	0.390768i
$813$	−11.0902	−	8.05748i	−0.388949	−	0.282588i
$814$	−46.5967	+	33.8545i	−1.63322	+	1.18660i
$815$	−0.489357	−	1.50609i	−0.0171414	−	0.0527559i
$816$	0.944272	+	0.686054i	0.0330561	+	0.0240167i
$817$	4.79837	+	14.7679i	0.167874	+	0.516663i
$818$	5.52786			0.193277
$819$	−8.89919	−	27.3889i	−0.310963	−	0.957045i
$820$	45.1246			1.57582
$821$	−12.8992	+	39.6996i	−0.450185	+	1.38553i	0.426512	+	0.904482i	$0.359742\pi$
$821$	−12.8992	+	39.6996i	−0.450185	+	1.38553i	−0.876696	+	0.481044i	$0.840258\pi$
$822$	−12.9868	+	39.9694i	−0.452968	+	1.39409i
$823$	24.4164	−	17.7396i	0.851102	−	0.618362i	−0.0743473	−	0.997232i	$-0.523687\pi$
$823$	24.4164	−	17.7396i	0.851102	−	0.618362i	0.925450	+	0.378870i	$0.123687\pi$
$824$		0			0
$825$	14.2705	−	10.3681i	0.496835	−	0.360972i
$826$	−103.666			−3.60699
$827$	−12.0451	+	8.75127i	−0.418849	+	0.304311i	−0.777174	−	0.629285i	$-0.783348\pi$
$827$	−12.0451	+	8.75127i	−0.418849	+	0.304311i	0.358326	+	0.933597i	$0.383348\pi$
$828$	−7.49342	+	23.0624i	−0.260414	+	0.801473i
$829$	−0.753289	+	2.31838i	−0.0261628	+	0.0805208i	−0.963285	−	0.268480i	$-0.913479\pi$
$829$	−0.753289	+	2.31838i	−0.0261628	+	0.0805208i	0.937123	+	0.349000i	$0.113479\pi$
$830$	3.29180	+	10.1311i	0.114260	+	0.351656i
$831$	−6.61803	−	20.3682i	−0.229577	−	0.706566i
$832$	−36.9443			−1.28081
$833$	−0.798374	−	2.45714i	−0.0276620	−	0.0851349i
$834$	22.3607	+	16.2460i	0.774287	+	0.562552i
$835$	6.97214	−	21.4580i	0.241281	−	0.742586i
$836$	20.6525	−	15.0049i	0.714281	−	0.518955i
$837$	−4.47214	−	3.24920i	−0.154580	−	0.112309i
$838$	−12.2361	−	8.89002i	−0.422688	−	0.307101i
$839$	−7.29837	+	5.30258i	−0.251968	+	0.183065i	−0.706598	−	0.707615i	$-0.749771\pi$
$839$	−7.29837	+	5.30258i	−0.251968	+	0.183065i	0.454631	+	0.890680i	$0.349771\pi$
$840$		0			0
$841$	19.4164	+	14.1068i	0.669531	+	0.486443i
$842$	−9.41641	−	28.9807i	−0.324511	−	0.998742i
$843$	−24.4296			−0.841399
$844$	−2.90983	−	8.95554i	−0.100160	−	0.308262i
$845$	5.75329	−	17.7068i	0.197919	−	0.609133i
$846$	6.31811	−	19.4451i	0.217221	−	0.668538i
$847$	−3.73607	+	11.4984i	−0.128373	+	0.395091i
$848$	27.7082	−	20.1312i	0.951504	−	0.691308i
$849$	18.7639			0.643976
$850$	−0.729490	+	2.24514i	−0.0250213	+	0.0770077i
$851$	83.1033			2.84875
$852$	11.2361	−	8.16348i	0.384941	−	0.279676i
$853$	16.9164	−	52.0633i	0.579207	−	1.78262i	−0.0421786	−	0.999110i	$-0.513430\pi$
$853$	16.9164	−	52.0633i	0.579207	−	1.78262i	0.621385	−	0.783505i	$-0.286570\pi$
$854$	−3.38197	+	10.4086i	−0.115728	+	0.356176i
$855$	−11.9098	+	8.65300i	−0.407308	+	0.295926i
$856$		0			0
$857$	−5.03444			−0.171973			−0.0859866	−	0.996296i	$-0.527404\pi$
$857$	−5.03444			−0.171973			−0.0859866	+	0.996296i	$0.527404\pi$
$858$	−10.0689	−	30.9888i	−0.343746	−	1.05794i
$859$	−30.6525	−	22.2703i	−1.04585	−	0.759854i	−0.0744303	−	0.997226i	$-0.523714\pi$
$859$	−30.6525	−	22.2703i	−1.04585	−	0.759854i	−0.971419	+	0.237372i	$0.923714\pi$
$860$	12.5623	−	9.12705i	0.428371	−	0.311230i
$861$	42.7426	−	31.0543i	1.45667	−	1.05833i
$862$	−6.00000	−	4.35926i	−0.204361	−	0.148477i
$863$	−34.3885	−	24.9847i	−1.17060	−	0.850490i	−0.179519	−	0.983754i	$-0.557454\pi$
$863$	−34.3885	−	24.9847i	−1.17060	−	0.850490i	−0.991081	+	0.133264i	$0.957454\pi$
$864$	35.7771	−	25.9936i	1.21716	−	0.884319i
$865$	15.7771			0.536437
$866$	2.00000	+	1.45309i	0.0679628	+	0.0493778i
$867$	6.47214	+	19.9192i	0.219805	+	0.676491i
$868$	8.47214			0.287563
$869$	−2.72542	−	8.38800i	−0.0924537	−	0.284543i
$870$	−10.0000	−	7.26543i	−0.339032	−	0.246321i
$871$	−15.0729	+	46.3898i	−0.510727	+	1.57186i
$872$		0			0
$873$	9.98278	−	7.25291i	0.337866	−	0.245474i
$874$	−73.6656			−2.49178
$875$	14.6353	−	45.0427i	0.494762	−	1.52272i
$876$	−29.3050			−0.990123
$877$	15.5172	−	11.2739i	0.523979	−	0.380693i	−0.294122	−	0.955768i	$-0.595027\pi$
$877$	15.5172	−	11.2739i	0.523979	−	0.380693i	0.818101	+	0.575075i	$0.195027\pi$
$878$	13.4934	−	41.5285i	0.455381	−	1.40152i
$879$	−2.41641	+	7.43694i	−0.0815034	+	0.250842i
$880$	20.6525	+	15.0049i	0.696195	+	0.505815i
$881$	−5.70163	−	17.5478i	−0.192093	−	0.591200i	−0.999998	−	0.00188844i	$-0.999399\pi$
$881$	−5.70163	−	17.5478i	−0.192093	−	0.591200i	0.807906	−	0.589312i	$-0.200601\pi$
$882$	−32.2229			−1.08500
$883$	5.04508	+	15.5272i	0.169781	+	0.522531i	0.999357	−	0.0358626i	$-0.0114179\pi$
$883$	5.04508	+	15.5272i	0.169781	+	0.522531i	−0.829576	+	0.558394i	$0.811418\pi$
$884$	1.76393	+	1.28157i	0.0593275	+	0.0431039i
$885$	33.8197			1.13684
$886$	22.8541	−	16.6045i	0.767799	−	0.557838i
$887$	37.0238	+	26.8994i	1.24314	+	0.903192i	0.997803	−	0.0662463i	$-0.0211023\pi$
$887$	37.0238	+	26.8994i	1.24314	+	0.903192i	0.245334	+	0.969439i	$0.421102\pi$
$888$		0			0
$889$	−58.2599	+	42.3283i	−1.95397	+	1.41964i
$890$	60.4508	−	43.9201i	2.02632	−	1.47221i
$891$	5.57953	+	4.05376i	0.186921	+	0.135806i
$892$	−7.27051	−	22.3763i	−0.243435	−	0.749215i
$893$	31.0557			1.03924
$894$	16.8328	+	51.8061i	0.562974	+	1.73265i
$895$	15.2254	−	11.0619i	0.508930	−	0.369759i
$896$		0			0
$897$	−14.5279	+	44.7122i	−0.485071	+	1.49290i
$898$	−13.6180	+	9.89408i	−0.454440	+	0.330170i
$899$	−2.23607			−0.0745770
$900$	11.9098	+	8.65300i	0.396994	+	0.288433i
$901$	−2.02129			−0.0673388
$902$	−46.5967	+	33.8545i	−1.55150	+	1.12723i
$903$	5.61803	−	17.2905i	0.186956	−	0.575393i
$904$		0			0
$905$	11.6074	−	35.7239i	0.385843	−	1.18750i
$906$	9.93112	+	30.5648i	0.329939	+	1.01545i
$907$	33.9098			1.12596			0.562979	−	0.826471i	$-0.309655\pi$
$907$	33.9098			1.12596			0.562979	+	0.826471i	$0.309655\pi$
$908$	−15.2705	−	46.9978i	−0.506770	−	1.55968i
$909$	−14.2254	−	10.3354i	−0.471828	−	0.342803i
$910$	−70.7771	−	51.4226i	−2.34624	−	1.70464i
$911$	8.70820	−	6.32688i	0.288516	−	0.209619i	−0.434108	−	0.900861i	$-0.642936\pi$
$911$	8.70820	−	6.32688i	0.288516	−	0.209619i	0.722623	+	0.691242i	$0.242936\pi$
$912$	17.8885	+	12.9968i	0.592349	+	0.430367i
$913$	−5.50000	−	3.99598i	−0.182023	−	0.132248i
$914$	1.23607	−	0.898056i	0.0408855	−	0.0297051i
$915$	1.10333	−	3.39569i	0.0364748	−	0.112258i
$916$	0.326238	+	0.237026i	0.0107792	+	0.00783155i
$917$	−11.1631	−	34.3565i	−0.368639	−	1.13455i
$918$	−2.60990			−0.0861396
$919$	12.5385	+	38.5896i	0.413607	+	1.27295i	0.913491	+	0.406859i	$0.133376\pi$
$919$	12.5385	+	38.5896i	0.413607	+	1.27295i	−0.499884	+	0.866093i	$0.666624\pi$
$920$		0			0
$921$	1.87539	−	5.77185i	0.0617961	−	0.190189i
$922$	21.7639	−	66.9825i	0.716757	−	2.20595i
$923$	−20.9894	+	15.2497i	−0.690873	+	0.501949i
$924$	−29.8885			−0.983261
$925$	15.5902	−	47.9816i	0.512602	−	1.57763i
$926$	43.3050			1.42309
$927$	−5.15248	+	3.74349i	−0.169230	+	0.122952i
$928$	5.52786	−	17.0130i	0.181461	−	0.558480i
$929$	−5.38854	+	16.5842i	−0.176792	+	0.544111i	−0.999711	−	0.0240486i	$-0.992344\pi$
$929$	−5.38854	+	16.5842i	−0.176792	+	0.544111i	0.822918	+	0.568160i	$0.192344\pi$
$930$	−5.52786			−0.181266
$931$	−15.1246	−	46.5488i	−0.495689	−	1.52557i
$932$	24.3607			0.797961
$933$	11.1935	+	34.4500i	0.366459	+	1.12784i
$934$	−36.9787	−	26.8666i	−1.20998	−	0.879102i
$935$	−0.465558	−	1.43284i	−0.0152254	−	0.0468589i
$936$		0			0
$937$	−0.927051	−	0.673542i	−0.0302854	−	0.0220037i	0.572540	−	0.819877i	$-0.305958\pi$
$937$	−0.927051	−	0.673542i	−0.0302854	−	0.0220037i	−0.602825	+	0.797873i	$0.705958\pi$
$938$	72.3951	+	52.5981i	2.36378	+	1.71739i
$939$	−26.8885	+	19.5357i	−0.877474	+	0.637523i
$940$	−9.59675	−	29.5358i	−0.313011	−	0.963350i
$941$	31.0066	+	22.5276i	1.01079	+	0.734379i	0.964374	−	0.264544i	$-0.0852213\pi$
$941$	31.0066	+	22.5276i	1.01079	+	0.734379i	0.0464119	+	0.998922i	$0.485221\pi$
$942$	−9.66563	−	29.7478i	−0.314923	−	0.969234i
$943$	83.1033			2.70622
$944$	15.1246	+	46.5488i	0.492264	+	1.51503i
$945$	52.3607			1.70329
$946$	−6.12461	+	18.8496i	−0.199128	+	0.612854i
$947$	−6.74265	+	20.7517i	−0.219107	+	0.674341i	0.779730	+	0.626116i	$0.215356\pi$
$947$	−6.74265	+	20.7517i	−0.219107	+	0.674341i	−0.998837	+	0.0482247i	$0.984644\pi$
$948$	−6.18034	+	4.49028i	−0.200728	+	0.145838i
$949$	54.7426			1.77702
$950$	−13.8197	+	42.5325i	−0.448369	+	1.37994i
$951$	−20.5147			−0.665235
$952$		0			0
$953$	2.24265	−	6.90215i	0.0726464	−	0.223583i	−0.908140	−	0.418666i	$-0.862498\pi$
$953$	2.24265	−	6.90215i	0.0726464	−	0.223583i	0.980787	+	0.195083i	$0.0624978\pi$
$954$	−7.79024	+	23.9759i	−0.252218	+	0.776249i
$955$	11.7467	+	36.1527i	0.380115	+	1.16987i
$956$	1.05573	+	3.24920i	0.0341447	+	0.105087i
$957$	7.88854			0.255000
$958$	14.0213	+	43.1531i	0.453007	+	1.39421i
$959$	−58.2599	−	42.3283i	−1.88131	−	1.36685i
$960$	6.83282	−	21.0292i	0.220528	−	0.678716i
$961$	−0.809017	+	0.587785i	−0.0260973	+	0.0189608i
$962$	−75.3951	−	54.7778i	−2.43084	−	1.76611i
$963$	5.04508	+	3.66547i	0.162576	+	0.118118i
$964$	−14.6180	+	10.6206i	−0.470815	+	0.342067i
$965$	−11.4443	−	8.31475i	−0.368404	−	0.267661i
$966$	69.7771	+	50.6960i	2.24504	+	1.63112i
$967$	1.18441	+	3.64522i	0.0380879	+	0.117223i	0.968293	−	0.249818i	$-0.0803709\pi$
$967$	1.18441	+	3.64522i	0.0380879	+	0.117223i	−0.930205	+	0.367041i	$0.880371\pi$
$968$		0			0
$969$	−0.403252	−	1.24108i	−0.0129543	−	0.0398693i
$970$	11.5836	−	35.6506i	0.371927	−	1.14467i
$971$	0.881966	−	2.71441i	0.0283036	−	0.0871096i	−0.935907	−	0.352248i	$-0.885418\pi$
$971$	0.881966	−	2.71441i	0.0283036	−	0.0871096i	0.964210	+	0.265138i	$0.0854175\pi$
$972$	−8.40325	+	25.8626i	−0.269534	+	0.829542i
$973$	−38.3156	+	27.8379i	−1.22834	+	0.892442i
$974$	5.05573			0.161996
$975$	23.0902	+	16.7760i	0.739477	+	0.537262i
$976$	5.16718			0.165398
$977$	35.8435	−	26.0418i	1.14673	−	0.833151i	0.158691	−	0.987328i	$-0.449273\pi$
$977$	35.8435	−	26.0418i	1.14673	−	0.833151i	0.988043	+	0.154177i	$0.0492727\pi$
$978$	0.541020	−	1.66509i	0.0172999	−	0.0532436i
$979$	−14.7361	+	45.3530i	−0.470967	+	1.44949i
$980$	−39.5967	+	28.7687i	−1.26487	+	0.918983i
$981$	2.81153	+	8.65300i	0.0897652	+	0.276269i
$982$	35.3050			1.12663
$983$	7.70820	+	23.7234i	0.245854	+	0.756659i	0.995495	+	0.0948151i	$0.0302260\pi$
$983$	7.70820	+	23.7234i	0.245854	+	0.756659i	−0.749641	+	0.661844i	$0.769774\pi$
$984$		0			0
$985$	−6.70820	+	4.87380i	−0.213741	+	0.155292i
$986$	−0.854102	+	0.620541i	−0.0272001	+	0.0197621i
$987$	−29.4164	−	21.3723i	−0.936335	−	0.680287i
$988$	33.4164	+	24.2784i	1.06312	+	0.772400i
$989$	23.1353	−	16.8087i	0.735658	−	0.534487i
$990$	−18.7902			−0.597193
$991$	−19.0795	−	13.8621i	−0.606081	−	0.440344i	0.241951	−	0.970288i	$-0.422213\pi$
$991$	−19.0795	−	13.8621i	−0.606081	−	0.440344i	−0.848032	+	0.529945i	$0.822213\pi$
$992$	−2.47214	−	7.60845i	−0.0784904	−	0.241569i
$993$	25.0132			0.793769
$994$	14.7082	+	45.2672i	0.466516	+	1.43579i
$995$	−28.3156	−	20.5725i	−0.897665	−	0.652192i
$996$	−1.81966	+	5.60034i	−0.0576581	+	0.177453i
$997$	−11.9828	+	36.8792i	−0.379498	+	1.16798i	0.560895	+	0.827887i	$0.310457\pi$
$997$	−11.9828	+	36.8792i	−0.379498	+	1.16798i	−0.940393	+	0.340089i	$0.889543\pi$
$998$	−32.5623	+	23.6579i	−1.03074	+	0.748878i
$999$	55.7771			1.76471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.j.a.311.1	✓	4
25.16	even	5	inner	775.2.j.a.466.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
775.2.j.a.311.1	✓	4	1.1	even	1	trivial
775.2.j.a.466.1	yes	4	25.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-0.763932 - 2.35114i) q^{6} +4.23607 q^{7} +(1.19098 + 0.865300i) q^{9} +O(q^{10})\)	\(q+(-1.61803 + 1.17557i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.618034 - 1.90211i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(-0.763932 - 2.35114i) q^{6} +4.23607 q^{7} +(1.19098 + 0.865300i) q^{9} +4.47214 q^{10} +(-2.30902 + 1.67760i) q^{11} +(2.00000 + 1.45309i) q^{12} +(-3.73607 - 2.71441i) q^{13} +(-6.85410 + 4.97980i) q^{14} +(2.23607 - 1.62460i) q^{15} +(3.23607 + 2.35114i) q^{16} +(-0.0729490 - 0.224514i) q^{17} -2.94427 q^{18} +(-1.38197 - 4.25325i) q^{19} +(-3.61803 + 2.62866i) q^{20} +(-1.61803 + 4.97980i) q^{21} +(1.76393 - 5.42882i) q^{22} +(-6.66312 + 4.84104i) q^{23} +(1.54508 + 4.75528i) q^{25} +9.23607 q^{26} +(-4.47214 + 3.24920i) q^{27} +(2.61803 - 8.05748i) q^{28} +(-0.690983 + 2.12663i) q^{29} +(-1.70820 + 5.25731i) q^{30} +(0.309017 + 0.951057i) q^{31} -8.00000 q^{32} +(-1.09017 - 3.35520i) q^{33} +(0.381966 + 0.277515i) q^{34} +(-7.66312 - 5.56758i) q^{35} +(2.38197 - 1.73060i) q^{36} +(-8.16312 - 5.93085i) q^{37} +(7.23607 + 5.25731i) q^{38} +(4.61803 - 3.35520i) q^{39} +(-8.16312 - 5.93085i) q^{41} +(-3.23607 - 9.95959i) q^{42} -3.47214 q^{43} +(1.76393 + 5.42882i) q^{44} +(-1.01722 - 3.13068i) q^{45} +(5.09017 - 15.6659i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(-4.00000 + 2.90617i) q^{48} +10.9443 q^{49} +(-8.09017 - 5.87785i) q^{50} +0.291796 q^{51} +(-7.47214 + 5.42882i) q^{52} +(2.64590 - 8.14324i) q^{53} +(3.41641 - 10.5146i) q^{54} +6.38197 q^{55} +5.52786 q^{57} +(-1.38197 - 4.25325i) q^{58} +(9.89919 + 7.19218i) q^{59} +(-1.70820 - 5.25731i) q^{60} +(1.04508 - 0.759299i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(5.04508 + 3.66547i) q^{63} +(6.47214 - 4.70228i) q^{64} +(3.19098 + 9.82084i) q^{65} +(5.70820 + 4.14725i) q^{66} +(-3.26393 - 10.0453i) q^{67} -0.472136 q^{68} +(-3.14590 - 9.68208i) q^{69} +18.9443 q^{70} +(1.73607 - 5.34307i) q^{71} +(-9.59017 + 6.96767i) q^{73} +20.1803 q^{74} -6.18034 q^{75} -8.94427 q^{76} +(-9.78115 + 7.10642i) q^{77} +(-3.52786 + 10.8576i) q^{78} +(-0.954915 + 2.93893i) q^{79} +(-2.76393 - 8.50651i) q^{80} +(-0.746711 - 2.29814i) q^{81} +20.1803 q^{82} +(0.736068 + 2.26538i) q^{83} +(8.47214 + 6.15537i) q^{84} +(-0.163119 + 0.502029i) q^{85} +(5.61803 - 4.08174i) q^{86} +(-2.23607 - 1.62460i) q^{87} +(13.5172 - 9.82084i) q^{89} +(5.32624 + 3.86974i) q^{90} +(-15.8262 - 11.4984i) q^{91} +(5.09017 + 15.6659i) q^{92} -1.23607 q^{93} +(-4.29180 - 13.2088i) q^{94} +(-3.09017 + 9.51057i) q^{95} +(3.05573 - 9.40456i) q^{96} +(2.59017 - 7.97172i) q^{97} +(-17.7082 + 12.8658i) q^{98} -4.20163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} - 12 q^{6} + 8 q^{7} + 7 q^{9} - 7 q^{11} + 8 q^{12} - 6 q^{13} - 14 q^{14} + 4 q^{16} - 7 q^{17} + 24 q^{18} - 10 q^{19} - 10 q^{20} - 2 q^{21} + 16 q^{22} - 11 q^{23} - 5 q^{25} + 28 q^{26} + 6 q^{28} - 5 q^{29} + 20 q^{30} - q^{31} - 32 q^{32} + 18 q^{33} + 6 q^{34} - 15 q^{35} + 14 q^{36} - 17 q^{37} + 20 q^{38} + 14 q^{39} - 17 q^{41} - 4 q^{42} + 4 q^{43} + 16 q^{44} + 25 q^{45} - 2 q^{46} - 22 q^{47} - 16 q^{48} + 8 q^{49} - 10 q^{50} + 28 q^{51} - 12 q^{52} + 24 q^{53} - 40 q^{54} + 30 q^{55} + 40 q^{57} - 10 q^{58} + 15 q^{59} + 20 q^{60} - 7 q^{61} - 2 q^{62} + 9 q^{63} + 8 q^{64} + 15 q^{65} - 4 q^{66} - 22 q^{67} + 16 q^{68} - 26 q^{69} + 40 q^{70} - 2 q^{71} - 16 q^{73} + 36 q^{74} + 20 q^{75} - 19 q^{77} - 32 q^{78} - 15 q^{79} - 20 q^{80} - 41 q^{81} + 36 q^{82} - 6 q^{83} + 16 q^{84} + 15 q^{85} + 18 q^{86} + 25 q^{89} - 10 q^{90} - 32 q^{91} - 2 q^{92} + 4 q^{93} - 44 q^{94} + 10 q^{95} + 48 q^{96} - 12 q^{97} - 44 q^{98} - 66 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 - 12 * q^6 + 8 * q^7 + 7 * q^9 - 7 * q^11 + 8 * q^12 - 6 * q^13 - 14 * q^14 + 4 * q^16 - 7 * q^17 + 24 * q^18 - 10 * q^19 - 10 * q^20 - 2 * q^21 + 16 * q^22 - 11 * q^23 - 5 * q^25 + 28 * q^26 + 6 * q^28 - 5 * q^29 + 20 * q^30 - q^31 - 32 * q^32 + 18 * q^33 + 6 * q^34 - 15 * q^35 + 14 * q^36 - 17 * q^37 + 20 * q^38 + 14 * q^39 - 17 * q^41 - 4 * q^42 + 4 * q^43 + 16 * q^44 + 25 * q^45 - 2 * q^46 - 22 * q^47 - 16 * q^48 + 8 * q^49 - 10 * q^50 + 28 * q^51 - 12 * q^52 + 24 * q^53 - 40 * q^54 + 30 * q^55 + 40 * q^57 - 10 * q^58 + 15 * q^59 + 20 * q^60 - 7 * q^61 - 2 * q^62 + 9 * q^63 + 8 * q^64 + 15 * q^65 - 4 * q^66 - 22 * q^67 + 16 * q^68 - 26 * q^69 + 40 * q^70 - 2 * q^71 - 16 * q^73 + 36 * q^74 + 20 * q^75 - 19 * q^77 - 32 * q^78 - 15 * q^79 - 20 * q^80 - 41 * q^81 + 36 * q^82 - 6 * q^83 + 16 * q^84 + 15 * q^85 + 18 * q^86 + 25 * q^89 - 10 * q^90 - 32 * q^91 - 2 * q^92 + 4 * q^93 - 44 * q^94 + 10 * q^95 + 48 * q^96 - 12 * q^97 - 44 * q^98 - 66 * q^99

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