LMFDB - Embedded newform 418.2.f.d.229.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, 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("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			229.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	418.229
Dual form			418.2.f.d.115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(1.61803 - 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(3.92705 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(1.61803 - 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(3.92705 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} -2.00000 q^{12} +(0.763932 - 2.35114i) q^{13} +(3.92705 - 2.85317i) q^{14} +(2.61803 + 1.90211i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.04508 + 3.21644i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.500000 - 1.53884i) q^{20} +9.70820 q^{21} +(-3.30902 - 0.224514i) q^{22} -7.85410 q^{23} +(-0.618034 + 1.90211i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-2.00000 - 1.45309i) q^{26} +(1.23607 + 3.80423i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-8.47214 - 6.15537i) q^{29} +(2.61803 - 1.90211i) q^{30} +(0.618034 - 1.90211i) q^{31} +1.00000 q^{32} +(-5.09017 - 4.25325i) q^{33} +3.38197 q^{34} +(-2.42705 + 7.46969i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.23607 - 2.35114i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.52786 - 4.70228i) q^{39} +(-1.30902 - 0.951057i) q^{40} +(3.85410 - 2.80017i) q^{41} +(3.00000 - 9.23305i) q^{42} -9.09017 q^{43} +(-1.23607 + 3.07768i) q^{44} +1.61803 q^{45} +(-2.42705 + 7.46969i) q^{46} +(-1.11803 + 0.812299i) q^{47} +(1.61803 + 1.17557i) q^{48} +(5.11803 + 15.7517i) q^{49} +(-0.736068 - 2.26538i) q^{50} +(5.47214 + 3.97574i) q^{51} +(-2.00000 + 1.45309i) q^{52} +(-1.47214 + 4.53077i) q^{53} +4.00000 q^{54} +(4.54508 - 2.85317i) q^{55} -4.85410 q^{56} +(-0.618034 + 1.90211i) q^{57} +(-8.47214 + 6.15537i) q^{58} +(2.85410 + 2.07363i) q^{59} +(-1.00000 - 3.07768i) q^{60} +(-2.95492 - 9.09429i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(3.92705 - 2.85317i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-5.61803 + 3.52671i) q^{66} +2.76393 q^{67} +(1.04508 - 3.21644i) q^{68} +(-12.7082 + 9.23305i) q^{69} +(6.35410 + 4.61653i) q^{70} +(1.52786 + 4.70228i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.3262 + 8.22899i) q^{73} +(-3.23607 + 2.35114i) q^{74} +(1.47214 - 4.53077i) q^{75} +1.00000 q^{76} +(6.00000 - 14.9394i) q^{77} -4.94427 q^{78} +(1.14590 - 3.52671i) q^{79} +(-1.30902 + 0.951057i) q^{80} +(8.89919 + 6.46564i) q^{81} +(-1.47214 - 4.53077i) q^{82} +(-4.26393 - 13.1230i) q^{83} +(-7.85410 - 5.70634i) q^{84} +(-4.42705 + 3.21644i) q^{85} +(-2.80902 + 8.64527i) q^{86} -20.9443 q^{87} +(2.54508 + 2.12663i) q^{88} +11.2361 q^{89} +(0.500000 - 1.53884i) q^{90} +(9.70820 - 7.05342i) q^{91} +(6.35410 + 4.61653i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(0.427051 + 1.31433i) q^{94} +(-1.30902 - 0.951057i) q^{95} +(1.61803 - 1.17557i) q^{96} +(-2.85410 + 8.78402i) q^{97} +16.5623 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9	\( 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9} + 2 q^{10} - q^{11} - 8 q^{12} + 12 q^{13} + 9 q^{14} + 6 q^{15} - q^{16} - 7 q^{17} - q^{18} - q^{19} + 2 q^{20} + 12 q^{21} - 11 q^{22} - 18 q^{23} + 2 q^{24} + q^{25} - 8 q^{26} - 4 q^{27} - 6 q^{28} - 16 q^{29} + 6 q^{30} - 2 q^{31} + 4 q^{32} + 2 q^{33} + 18 q^{34} - 3 q^{35} - q^{36} - 4 q^{37} - q^{38} - 24 q^{39} - 3 q^{40} + 2 q^{41} + 12 q^{42} - 14 q^{43} + 4 q^{44} + 2 q^{45} - 3 q^{46} + 2 q^{48} + 16 q^{49} + 6 q^{50} + 4 q^{51} - 8 q^{52} + 12 q^{53} + 16 q^{54} + 7 q^{55} - 6 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{59} - 4 q^{60} - 23 q^{61} - 2 q^{62} + 9 q^{63} - q^{64} + 16 q^{65} - 18 q^{66} + 20 q^{67} - 7 q^{68} - 24 q^{69} + 12 q^{70} + 24 q^{71} - q^{72} + 14 q^{73} - 4 q^{74} - 12 q^{75} + 4 q^{76} + 24 q^{77} + 16 q^{78} + 18 q^{79} - 3 q^{80} + 11 q^{81} + 12 q^{82} - 26 q^{83} - 18 q^{84} - 11 q^{85} - 9 q^{86} - 48 q^{87} - q^{88} + 36 q^{89} + 2 q^{90} + 12 q^{91} + 12 q^{92} + 4 q^{93} - 5 q^{94} - 3 q^{95} + 2 q^{96} + 2 q^{97} + 26 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9 + 2 * q^10 - q^11 - 8 * q^12 + 12 * q^13 + 9 * q^14 + 6 * q^15 - q^16 - 7 * q^17 - q^18 - q^19 + 2 * q^20 + 12 * q^21 - 11 * q^22 - 18 * q^23 + 2 * q^24 + q^25 - 8 * q^26 - 4 * q^27 - 6 * q^28 - 16 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^33 + 18 * q^34 - 3 * q^35 - q^36 - 4 * q^37 - q^38 - 24 * q^39 - 3 * q^40 + 2 * q^41 + 12 * q^42 - 14 * q^43 + 4 * q^44 + 2 * q^45 - 3 * q^46 + 2 * q^48 + 16 * q^49 + 6 * q^50 + 4 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 7 * q^55 - 6 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^59 - 4 * q^60 - 23 * q^61 - 2 * q^62 + 9 * q^63 - q^64 + 16 * q^65 - 18 * q^66 + 20 * q^67 - 7 * q^68 - 24 * q^69 + 12 * q^70 + 24 * q^71 - q^72 + 14 * q^73 - 4 * q^74 - 12 * q^75 + 4 * q^76 + 24 * q^77 + 16 * q^78 + 18 * q^79 - 3 * q^80 + 11 * q^81 + 12 * q^82 - 26 * q^83 - 18 * q^84 - 11 * q^85 - 9 * q^86 - 48 * q^87 - q^88 + 36 * q^89 + 2 * q^90 + 12 * q^91 + 12 * q^92 + 4 * q^93 - 5 * q^94 - 3 * q^95 + 2 * q^96 + 2 * q^97 + 26 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	1.61803	−	1.17557i	0.934172	−	0.678716i	−0.0128385	−	0.999918i	$-0.504087\pi$
$3$	1.61803	−	1.17557i	0.934172	−	0.678716i	0.947011	+	0.321202i	$0.104087\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	0.998430	+	0.0560130i	$0.0178388\pi$
$5$	0.500000	+	1.53884i	0.223607	+	0.688191i	−0.774823	+	0.632178i	$0.782161\pi$
$6$	−0.618034	−	1.90211i	−0.252311	−	0.776534i
$7$	3.92705	+	2.85317i	1.48429	+	1.07840i	0.976144	+	0.217123i	$0.0696673\pi$
$7$	3.92705	+	2.85317i	1.48429	+	1.07840i	0.508142	+	0.861274i	$0.330333\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	1.61803			0.511667
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$11$	−0.809017	−	3.21644i	−0.243928	−	0.969793i
$12$	−2.00000			−0.577350
$13$	0.763932	−	2.35114i	0.211877	−	0.652089i	−0.787484	−	0.616335i	$-0.788617\pi$
$13$	0.763932	−	2.35114i	0.211877	−	0.652089i	0.999361	−	0.0357541i	$-0.0113833\pi$
$14$	3.92705	−	2.85317i	1.04955	−	0.762542i
$15$	2.61803	+	1.90211i	0.675973	+	0.491123i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.04508	+	3.21644i	0.253470	+	0.780101i	0.994127	+	0.108218i	$0.0345144\pi$
$17$	1.04508	+	3.21644i	0.253470	+	0.780101i	−0.740657	+	0.671883i	$0.765486\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$19$	−0.809017	+	0.587785i	−0.185601	+	0.134847i
$20$	0.500000	−	1.53884i	0.111803	−	0.344095i
$21$	9.70820			2.11850
$22$	−3.30902	−	0.224514i	−0.705485	−	0.0478665i
$23$	−7.85410			−1.63769			−0.818847	−	0.574012i	$-0.805386\pi$
$23$	−7.85410			−1.63769			−0.818847	+	0.574012i	$0.805386\pi$
$24$	−0.618034	+	1.90211i	−0.126156	+	0.388267i
$25$	1.92705	−	1.40008i	0.385410	−	0.280017i
$26$	−2.00000	−	1.45309i	−0.392232	−	0.284973i
$27$	1.23607	+	3.80423i	0.237881	+	0.732124i
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	−8.47214	−	6.15537i	−1.57324	−	1.14302i	−0.923972	−	0.382460i	$-0.875077\pi$
$29$	−8.47214	−	6.15537i	−1.57324	−	1.14302i	−0.649264	−	0.760563i	$-0.724923\pi$
$30$	2.61803	−	1.90211i	0.477985	−	0.347277i
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	−0.880090	−	0.474807i	$-0.842518\pi$
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	0.991092	+	0.133177i	$0.0425179\pi$
$32$	1.00000			0.176777
$33$	−5.09017	−	4.25325i	−0.886085	−	0.740396i
$34$	3.38197			0.580002
$35$	−2.42705	+	7.46969i	−0.410246	+	1.26261i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−3.23607	−	2.35114i	−0.532006	−	0.386525i	0.289101	−	0.957298i	$-0.406644\pi$
$37$	−3.23607	−	2.35114i	−0.532006	−	0.386525i	−0.821108	+	0.570773i	$0.806644\pi$
$38$	0.309017	+	0.951057i	0.0501292	+	0.154282i
$39$	−1.52786	−	4.70228i	−0.244654	−	0.752968i
$40$	−1.30902	−	0.951057i	−0.206974	−	0.150375i
$41$	3.85410	−	2.80017i	0.601910	−	0.437313i	−0.244647	−	0.969612i	$-0.578672\pi$
$41$	3.85410	−	2.80017i	0.601910	−	0.437313i	0.846556	+	0.532299i	$0.178672\pi$
$42$	3.00000	−	9.23305i	0.462910	−	1.42469i
$43$	−9.09017			−1.38624			−0.693119	−	0.720823i	$-0.743764\pi$
$43$	−9.09017			−1.38624			−0.693119	+	0.720823i	$0.743764\pi$
$44$	−1.23607	+	3.07768i	−0.186344	+	0.463978i
$45$	1.61803			0.241202
$46$	−2.42705	+	7.46969i	−0.357849	+	1.10135i
$47$	−1.11803	+	0.812299i	−0.163082	+	0.118486i	−0.666333	−	0.745654i	$-0.732137\pi$
$47$	−1.11803	+	0.812299i	−0.163082	+	0.118486i	0.503251	+	0.864140i	$0.332137\pi$
$48$	1.61803	+	1.17557i	0.233543	+	0.169679i
$49$	5.11803	+	15.7517i	0.731148	+	2.25024i
$50$	−0.736068	−	2.26538i	−0.104096	−	0.320374i
$51$	5.47214	+	3.97574i	0.766252	+	0.556715i
$52$	−2.00000	+	1.45309i	−0.277350	+	0.201507i
$53$	−1.47214	+	4.53077i	−0.202213	+	0.622349i	0.797603	+	0.603183i	$0.206101\pi$
$53$	−1.47214	+	4.53077i	−0.202213	+	0.622349i	−0.999816	+	0.0191660i	$0.993899\pi$
$54$	4.00000			0.544331
$55$	4.54508	−	2.85317i	0.612859	−	0.384721i
$56$	−4.85410			−0.648657
$57$	−0.618034	+	1.90211i	−0.0818606	+	0.251941i
$58$	−8.47214	+	6.15537i	−1.11245	+	0.808239i
$59$	2.85410	+	2.07363i	0.371572	+	0.269963i	0.757863	−	0.652414i	$-0.226244\pi$
$59$	2.85410	+	2.07363i	0.371572	+	0.269963i	−0.386290	+	0.922377i	$0.626244\pi$
$60$	−1.00000	−	3.07768i	−0.129099	−	0.397327i
$61$	−2.95492	−	9.09429i	−0.378338	−	1.16440i	−0.941199	−	0.337853i	$-0.890299\pi$
$61$	−2.95492	−	9.09429i	−0.378338	−	1.16440i	0.562861	−	0.826552i	$-0.309701\pi$
$62$	−1.61803	−	1.17557i	−0.205491	−	0.149298i
$63$	3.92705	−	2.85317i	0.494762	−	0.359466i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.00000			0.496139
$66$	−5.61803	+	3.52671i	−0.691532	+	0.434108i
$67$	2.76393			0.337668			0.168834	−	0.985644i	$-0.446000\pi$
$67$	2.76393			0.337668			0.168834	+	0.985644i	$0.446000\pi$
$68$	1.04508	−	3.21644i	0.126735	−	0.390051i
$69$	−12.7082	+	9.23305i	−1.52989	+	1.11153i
$70$	6.35410	+	4.61653i	0.759460	+	0.551780i
$71$	1.52786	+	4.70228i	0.181324	+	0.558058i	0.999866	−	0.0163891i	$-0.00521704\pi$
$71$	1.52786	+	4.70228i	0.181324	+	0.558058i	−0.818542	+	0.574447i	$0.805217\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	11.3262	+	8.22899i	1.32564	+	0.963131i	0.999844	+	0.0176895i	$0.00563103\pi$
$73$	11.3262	+	8.22899i	1.32564	+	0.963131i	0.325792	+	0.945441i	$0.394369\pi$
$74$	−3.23607	+	2.35114i	−0.376185	+	0.273315i
$75$	1.47214	−	4.53077i	0.169988	−	0.523168i
$76$	1.00000			0.114708
$77$	6.00000	−	14.9394i	0.683763	−	1.70250i
$78$	−4.94427			−0.559829
$79$	1.14590	−	3.52671i	0.128924	−	0.396786i	−0.865672	−	0.500612i	$-0.833108\pi$
$79$	1.14590	−	3.52671i	0.128924	−	0.396786i	0.994596	+	0.103826i	$0.0331084\pi$
$80$	−1.30902	+	0.951057i	−0.146353	+	0.106331i
$81$	8.89919	+	6.46564i	0.988799	+	0.718404i
$82$	−1.47214	−	4.53077i	−0.162570	−	0.500340i
$83$	−4.26393	−	13.1230i	−0.468027	−	1.44044i	−0.855135	−	0.518405i	$-0.826526\pi$
$83$	−4.26393	−	13.1230i	−0.468027	−	1.44044i	0.387108	−	0.922035i	$-0.373474\pi$
$84$	−7.85410	−	5.70634i	−0.856953	−	0.622613i
$85$	−4.42705	+	3.21644i	−0.480181	+	0.348872i
$86$	−2.80902	+	8.64527i	−0.302904	+	0.932243i
$87$	−20.9443			−2.24546
$88$	2.54508	+	2.12663i	0.271307	+	0.226699i
$89$	11.2361			1.19102			0.595510	−	0.803348i	$-0.296950\pi$
$89$	11.2361			1.19102			0.595510	+	0.803348i	$0.296950\pi$
$90$	0.500000	−	1.53884i	0.0527046	−	0.162208i
$91$	9.70820	−	7.05342i	1.01770	−	0.739400i
$92$	6.35410	+	4.61653i	0.662461	+	0.481306i
$93$	−1.23607	−	3.80423i	−0.128174	−	0.394480i
$94$	0.427051	+	1.31433i	0.0440469	+	0.135563i
$95$	−1.30902	−	0.951057i	−0.134302	−	0.0975763i
$96$	1.61803	−	1.17557i	0.165140	−	0.119981i
$97$	−2.85410	+	8.78402i	−0.289790	+	0.891882i	0.695132	+	0.718882i	$0.255346\pi$
$97$	−2.85410	+	8.78402i	−0.289790	+	0.891882i	−0.984922	+	0.173000i	$0.944654\pi$
$98$	16.5623			1.67305
$99$	−3.30902	−	0.224514i	−0.332569	−	0.0225645i
$100$	−2.38197			−0.238197
$101$	−4.50000	+	13.8496i	−0.447767	+	1.37808i	0.431654	+	0.902039i	$0.357930\pi$
$101$	−4.50000	+	13.8496i	−0.447767	+	1.37808i	−0.879421	+	0.476045i	$0.842070\pi$
$102$	5.47214	−	3.97574i	0.541822	−	0.393657i
$103$	3.85410	+	2.80017i	0.379756	+	0.275909i	0.761245	−	0.648465i	$-0.224589\pi$
$103$	3.85410	+	2.80017i	0.379756	+	0.275909i	−0.381489	+	0.924373i	$0.624589\pi$
$104$	0.763932	+	2.35114i	0.0749097	+	0.230548i
$105$	4.85410	+	14.9394i	0.473712	+	1.45794i
$106$	3.85410	+	2.80017i	0.374343	+	0.271976i
$107$	−4.85410	+	3.52671i	−0.469264	+	0.340940i	−0.797154	−	0.603776i	$-0.793662\pi$
$107$	−4.85410	+	3.52671i	−0.469264	+	0.340940i	0.327891	+	0.944716i	$0.393662\pi$
$108$	1.23607	−	3.80423i	0.118941	−	0.366062i
$109$	3.23607			0.309959			0.154980	−	0.987918i	$-0.450469\pi$
$109$	3.23607			0.309959			0.154980	+	0.987918i	$0.450469\pi$
$110$	−1.30902	−	5.20431i	−0.124810	−	0.496212i
$111$	−8.00000			−0.759326
$112$	−1.50000	+	4.61653i	−0.141737	+	0.436221i
$113$	−4.47214	+	3.24920i	−0.420703	+	0.305659i	−0.777921	−	0.628362i	$-0.783725\pi$
$113$	−4.47214	+	3.24920i	−0.420703	+	0.305659i	0.357218	+	0.934021i	$0.383725\pi$
$114$	1.61803	+	1.17557i	0.151543	+	0.110102i
$115$	−3.92705	−	12.0862i	−0.366199	−	1.12705i
$116$	3.23607	+	9.95959i	0.300461	+	0.924725i
$117$	−2.00000	−	1.45309i	−0.184900	−	0.134338i
$118$	2.85410	−	2.07363i	0.262741	−	0.190893i
$119$	−5.07295	+	15.6129i	−0.465036	+	1.43124i
$120$	−3.23607			−0.295411
$121$	−9.69098	+	5.20431i	−0.880998	+	0.473119i
$122$	−9.56231			−0.865730
$123$	2.94427	−	9.06154i	0.265476	−	0.817051i
$124$	−1.61803	+	1.17557i	−0.145304	+	0.105569i
$125$	9.66312	+	7.02067i	0.864296	+	0.627948i
$126$	−1.50000	−	4.61653i	−0.133631	−	0.411273i
$127$	−6.00000	−	18.4661i	−0.532414	−	1.63860i	−0.749172	−	0.662376i	$-0.769548\pi$
$127$	−6.00000	−	18.4661i	−0.532414	−	1.63860i	0.216758	−	0.976225i	$-0.430452\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−14.7082	+	10.6861i	−1.29499	+	0.940862i
$130$	1.23607	−	3.80423i	0.108410	−	0.333653i
$131$	−12.0902			−1.05632			−0.528162	−	0.849144i	$-0.677118\pi$
$131$	−12.0902			−1.05632			−0.528162	+	0.849144i	$0.677118\pi$
$132$	1.61803	+	6.43288i	0.140832	+	0.559910i
$133$	−4.85410			−0.420904
$134$	0.854102	−	2.62866i	0.0737832	−	0.227081i
$135$	−5.23607	+	3.80423i	−0.450649	+	0.327416i
$136$	−2.73607	−	1.98787i	−0.234616	−	0.170458i
$137$	−1.20820	−	3.71847i	−0.103224	−	0.317690i	0.886086	−	0.463522i	$-0.153414\pi$
$137$	−1.20820	−	3.71847i	−0.103224	−	0.317690i	−0.989309	+	0.145831i	$0.953414\pi$
$138$	4.85410	+	14.9394i	0.413209	+	1.27173i
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	0.882717	−	0.469905i	$-0.155712\pi$
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	−0.174131	+	0.984722i	$0.555712\pi$
$140$	6.35410	−	4.61653i	0.537020	−	0.390168i
$141$	−0.854102	+	2.62866i	−0.0719284	+	0.221373i
$142$	4.94427			0.414914
$143$	−8.18034	−	0.555029i	−0.684074	−	0.0464139i
$144$	1.00000			0.0833333
$145$	5.23607	−	16.1150i	0.434832	−	1.33827i
$146$	11.3262	−	8.22899i	0.937366	−	0.681036i
$147$	26.7984	+	19.4702i	2.21029	+	1.60587i
$148$	1.23607	+	3.80423i	0.101604	+	0.312705i
$149$	−3.56231	−	10.9637i	−0.291835	−	0.898177i	−0.984266	−	0.176693i	$-0.943460\pi$
$149$	−3.56231	−	10.9637i	−0.291835	−	0.898177i	0.692431	−	0.721484i	$-0.256540\pi$
$150$	−3.85410	−	2.80017i	−0.314686	−	0.228633i
$151$	11.0902	−	8.05748i	0.902505	−	0.655708i	−0.0366030	−	0.999330i	$-0.511654\pi$
$151$	11.0902	−	8.05748i	0.902505	−	0.655708i	0.939108	+	0.343621i	$0.111654\pi$
$152$	0.309017	−	0.951057i	0.0250646	−	0.0771409i
$153$	3.38197			0.273416
$154$	−12.3541	−	10.3229i	−0.995522	−	0.831840i
$155$	3.23607			0.259927
$156$	−1.52786	+	4.70228i	−0.122327	+	0.376484i
$157$	−18.8713	+	13.7108i	−1.50610	+	1.09424i	−0.538223	+	0.842803i	$0.680904\pi$
$157$	−18.8713	+	13.7108i	−1.50610	+	1.09424i	−0.967873	+	0.251440i	$0.919096\pi$
$158$	−3.00000	−	2.17963i	−0.238667	−	0.173402i
$159$	2.94427	+	9.06154i	0.233496	+	0.718627i
$160$	0.500000	+	1.53884i	0.0395285	+	0.121656i
$161$	−30.8435	−	22.4091i	−2.43081	−	1.76608i
$162$	8.89919	−	6.46564i	0.699186	−	0.507988i
$163$	−0.208204	+	0.640786i	−0.0163078	+	0.0501902i	−0.958879	−	0.283814i	$-0.908400\pi$
$163$	−0.208204	+	0.640786i	−0.0163078	+	0.0501902i	0.942571	+	0.334005i	$0.108400\pi$
$164$	−4.76393			−0.372001
$165$	4.00000	−	9.95959i	0.311400	−	0.775353i
$166$	−13.7984			−1.07096
$167$	0.437694	−	1.34708i	0.0338698	−	0.104240i	−0.932692	−	0.360673i	$-0.882547\pi$
$167$	0.437694	−	1.34708i	0.0338698	−	0.104240i	0.966562	+	0.256432i	$0.0825471\pi$
$168$	−7.85410	+	5.70634i	−0.605957	+	0.440254i
$169$	5.57295	+	4.04898i	0.428688	+	0.311460i
$170$	1.69098	+	5.20431i	0.129692	+	0.399152i
$171$	0.309017	+	0.951057i	0.0236311	+	0.0727291i
$172$	7.35410	+	5.34307i	0.560745	+	0.407405i
$173$	16.9443	−	12.3107i	1.28825	−	0.935968i	0.288481	−	0.957486i	$-0.406850\pi$
$173$	16.9443	−	12.3107i	1.28825	−	0.935968i	0.999768	+	0.0215179i	$0.00684990\pi$
$174$	−6.47214	+	19.9192i	−0.490651	+	1.51007i
$175$	11.5623			0.874028
$176$	2.80902	−	1.76336i	0.211738	−	0.132918i
$177$	7.05573			0.530341
$178$	3.47214	−	10.6861i	0.260248	−	0.800960i
$179$	−1.76393	+	1.28157i	−0.131842	+	0.0957892i	−0.651752	−	0.758432i	$-0.725966\pi$
$179$	−1.76393	+	1.28157i	−0.131842	+	0.0957892i	0.519909	+	0.854221i	$0.325966\pi$
$180$	−1.30902	−	0.951057i	−0.0975684	−	0.0708876i
$181$	−0.0901699	−	0.277515i	−0.00670228	−	0.0206275i	0.947649	−	0.319313i	$-0.103452\pi$
$181$	−0.0901699	−	0.277515i	−0.00670228	−	0.0206275i	−0.954352	+	0.298685i	$0.903452\pi$
$182$	−3.70820	−	11.4127i	−0.274870	−	0.845964i
$183$	−15.4721	−	11.2412i	−1.14373	−	0.830971i
$184$	6.35410	−	4.61653i	0.468431	−	0.340335i
$185$	2.00000	−	6.15537i	0.147043	−	0.452552i
$186$	−4.00000			−0.293294
$187$	9.50000	−	5.96361i	0.694709	−	0.436102i
$188$	1.38197			0.100790
$189$	−6.00000	+	18.4661i	−0.436436	+	1.34321i
$190$	−1.30902	+	0.951057i	−0.0949661	+	0.0689969i
$191$	−4.07295	−	2.95917i	−0.294708	−	0.214118i	0.430599	−	0.902543i	$-0.358302\pi$
$191$	−4.07295	−	2.95917i	−0.294708	−	0.214118i	−0.725307	+	0.688425i	$0.758302\pi$
$192$	−0.618034	−	1.90211i	−0.0446028	−	0.137273i
$193$	5.90983	+	18.1886i	0.425399	+	1.30924i	0.902612	+	0.430455i	$0.141647\pi$
$193$	5.90983	+	18.1886i	0.425399	+	1.30924i	−0.477213	+	0.878788i	$0.658353\pi$
$194$	7.47214	+	5.42882i	0.536468	+	0.389767i
$195$	6.47214	−	4.70228i	0.463479	−	0.336737i
$196$	5.11803	−	15.7517i	0.365574	−	1.12512i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−1.23607	+	3.07768i	−0.0878435	+	0.218721i
$199$	14.5623			1.03229			0.516147	−	0.856500i	$-0.327366\pi$
$199$	14.5623			1.03229			0.516147	+	0.856500i	$0.327366\pi$
$200$	−0.736068	+	2.26538i	−0.0520479	+	0.160187i
$201$	4.47214	−	3.24920i	0.315440	−	0.229181i
$202$	11.7812	+	8.55951i	0.828919	+	0.602245i
$203$	−15.7082	−	48.3449i	−1.10250	−	3.39315i
$204$	−2.09017	−	6.43288i	−0.146341	−	0.450392i
$205$	6.23607	+	4.53077i	0.435546	+	0.316443i
$206$	3.85410	−	2.80017i	0.268528	−	0.195097i
$207$	−2.42705	+	7.46969i	−0.168692	+	0.519180i
$208$	2.47214			0.171412
$209$	2.54508	+	2.12663i	0.176047	+	0.147102i
$210$	15.7082			1.08397
$211$	4.76393	−	14.6619i	0.327963	−	1.00937i	−0.642123	−	0.766602i	$-0.721946\pi$
$211$	4.76393	−	14.6619i	0.327963	−	1.00937i	0.970086	−	0.242763i	$-0.0780539\pi$
$212$	3.85410	−	2.80017i	0.264701	−	0.192316i
$213$	8.00000	+	5.81234i	0.548151	+	0.398255i
$214$	1.85410	+	5.70634i	0.126744	+	0.390077i
$215$	−4.54508	−	13.9883i	−0.309972	−	0.953996i
$216$	−3.23607	−	2.35114i	−0.220187	−	0.159975i
$217$	7.85410	−	5.70634i	0.533171	−	0.387372i
$218$	1.00000	−	3.07768i	0.0677285	−	0.208447i
$219$	28.0000			1.89206
$220$	−5.35410	−	0.363271i	−0.360973	−	0.0244917i
$221$	8.36068			0.562400
$222$	−2.47214	+	7.60845i	−0.165919	+	0.510646i
$223$	7.85410	−	5.70634i	0.525950	−	0.382125i	−0.292891	−	0.956146i	$-0.594617\pi$
$223$	7.85410	−	5.70634i	0.525950	−	0.382125i	0.818840	+	0.574021i	$0.194617\pi$
$224$	3.92705	+	2.85317i	0.262387	+	0.190635i
$225$	−0.736068	−	2.26538i	−0.0490712	−	0.151026i
$226$	1.70820	+	5.25731i	0.113628	+	0.349711i
$227$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$227$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$228$	1.61803	−	1.17557i	0.107157	−	0.0778541i
$229$	−2.86475	+	8.81678i	−0.189308	+	0.582629i	−0.999996	−	0.00284891i	$-0.999093\pi$
$229$	−2.86475	+	8.81678i	−0.189308	+	0.582629i	0.810688	+	0.585478i	$0.199093\pi$
$230$	−12.7082			−0.837954
$231$	−7.85410	−	31.2259i	−0.516762	−	2.05451i
$232$	10.4721			0.687529
$233$	1.79180	−	5.51458i	0.117384	−	0.361272i	−0.875052	−	0.484028i	$-0.839173\pi$
$233$	1.79180	−	5.51458i	0.117384	−	0.361272i	0.992437	+	0.122756i	$0.0391732\pi$
$234$	−2.00000	+	1.45309i	−0.130744	+	0.0949911i
$235$	−1.80902	−	1.31433i	−0.118007	−	0.0857373i
$236$	−1.09017	−	3.35520i	−0.0709640	−	0.218405i
$237$	−2.29180	−	7.05342i	−0.148868	−	0.458169i
$238$	13.2812	+	9.64932i	0.860889	+	0.625473i
$239$	−14.8262	+	10.7719i	−0.959030	+	0.696776i	−0.952925	−	0.303206i	$-0.901943\pi$
$239$	−14.8262	+	10.7719i	−0.959030	+	0.696776i	−0.00610444	+	0.999981i	$0.501943\pi$
$240$	−1.00000	+	3.07768i	−0.0645497	+	0.198664i
$241$	10.0000			0.644157			0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000			0.644157			0.322078	+	0.946713i	$0.395619\pi$
$242$	1.95492	+	10.8249i	0.125667	+	0.695850i
$243$	10.0000			0.641500
$244$	−2.95492	+	9.09429i	−0.189169	+	0.582202i
$245$	−21.6803	+	15.7517i	−1.38511	+	1.00634i
$246$	−7.70820	−	5.60034i	−0.491457	−	0.357065i
$247$	0.763932	+	2.35114i	0.0486078	+	0.149600i
$248$	0.618034	+	1.90211i	0.0392452	+	0.120784i
$249$	−22.3262	−	16.2210i	−1.41487	−	1.02796i
$250$	9.66312	−	7.02067i	0.611149	−	0.444026i
$251$	1.28115	−	3.94298i	0.0808657	−	0.248879i	−0.902448	−	0.430800i	$-0.858231\pi$
$251$	1.28115	−	3.94298i	0.0808657	−	0.248879i	0.983313	+	0.181921i	$0.0582315\pi$
$252$	−4.85410			−0.305780
$253$	6.35410	+	25.2623i	0.399479	+	1.58822i
$254$	−19.4164			−1.21829
$255$	−3.38197	+	10.4086i	−0.211787	+	0.651813i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−5.61803	−	4.08174i	−0.350443	−	0.254612i	0.398612	−	0.917120i	$-0.369492\pi$
$257$	−5.61803	−	4.08174i	−0.350443	−	0.254612i	−0.749055	+	0.662508i	$0.769492\pi$
$258$	5.61803	+	17.2905i	0.349764	+	1.07646i
$259$	−6.00000	−	18.4661i	−0.372822	−	1.14743i
$260$	−3.23607	−	2.35114i	−0.200692	−	0.145812i
$261$	−8.47214	+	6.15537i	−0.524412	+	0.381008i
$262$	−3.73607	+	11.4984i	−0.230815	+	0.710376i
$263$	−2.47214			−0.152438			−0.0762192	−	0.997091i	$-0.524285\pi$
$263$	−2.47214			−0.152438			−0.0762192	+	0.997091i	$0.524285\pi$
$264$	6.61803	+	0.449028i	0.407312	+	0.0276358i
$265$	−7.70820			−0.473511
$266$	−1.50000	+	4.61653i	−0.0919709	+	0.283057i
$267$	18.1803	−	13.2088i	1.11262	−	0.808365i
$268$	−2.23607	−	1.62460i	−0.136590	−	0.0992381i
$269$	−3.90983	−	12.0332i	−0.238387	−	0.733678i	−0.996654	−	0.0817349i	$-0.973954\pi$
$269$	−3.90983	−	12.0332i	−0.238387	−	0.733678i	0.758268	−	0.651943i	$-0.226046\pi$
$270$	2.00000	+	6.15537i	0.121716	+	0.374604i
$271$	−16.3541	−	11.8820i	−0.993441	−	0.721777i	−0.0327690	−	0.999463i	$-0.510433\pi$
$271$	−16.3541	−	11.8820i	−0.993441	−	0.721777i	−0.960672	+	0.277686i	$0.910433\pi$
$272$	−2.73607	+	1.98787i	−0.165898	+	0.120532i
$273$	7.41641	−	22.8254i	0.448861	−	1.38145i
$274$	−3.90983			−0.236201
$275$	−6.06231	−	5.06555i	−0.365571	−	0.305464i
$276$	15.7082			0.945523
$277$	−3.85410	+	11.8617i	−0.231571	+	0.712701i	0.765987	+	0.642856i	$0.222251\pi$
$277$	−3.85410	+	11.8617i	−0.231571	+	0.712701i	−0.997558	+	0.0698451i	$0.977749\pi$
$278$	8.35410	−	6.06961i	0.501046	−	0.364031i
$279$	−1.61803	−	1.17557i	−0.0968692	−	0.0703796i
$280$	−2.42705	−	7.46969i	−0.145044	−	0.446400i
$281$	−8.23607	−	25.3480i	−0.491323	−	1.51214i	−0.822610	−	0.568606i	$-0.807483\pi$
$281$	−8.23607	−	25.3480i	−0.491323	−	1.51214i	0.331288	−	0.943530i	$-0.392517\pi$
$282$	2.23607	+	1.62460i	0.133156	+	0.0967434i
$283$	−8.54508	+	6.20837i	−0.507953	+	0.369049i	−0.812046	−	0.583593i	$-0.801646\pi$
$283$	−8.54508	+	6.20837i	−0.507953	+	0.369049i	0.304094	+	0.952642i	$0.401646\pi$
$284$	1.52786	−	4.70228i	0.0906621	−	0.279029i
$285$	−3.23607			−0.191688
$286$	−3.05573	+	7.60845i	−0.180689	+	0.449897i
$287$	23.1246			1.36500
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	4.50000	−	3.26944i	0.264706	−	0.192320i
$290$	−13.7082	−	9.95959i	−0.804973	−	0.584847i
$291$	5.70820	+	17.5680i	0.334621	+	1.02986i
$292$	−4.32624	−	13.3148i	−0.253174	−	0.779189i
$293$	24.7984	+	18.0171i	1.44874	+	1.05257i	0.986124	+	0.166008i	$0.0530877\pi$
$293$	24.7984	+	18.0171i	1.44874	+	1.05257i	0.462612	+	0.886561i	$0.346912\pi$
$294$	26.7984	−	19.4702i	1.56291	−	1.13552i
$295$	−1.76393	+	5.42882i	−0.102700	+	0.316078i
$296$	4.00000			0.232495
$297$	11.2361	−	7.05342i	0.651983	−	0.409281i
$298$	−11.5279			−0.667791
$299$	−6.00000	+	18.4661i	−0.346989	+	1.06792i
$300$	−3.85410	+	2.80017i	−0.222517	+	0.161668i
$301$	−35.6976	−	25.9358i	−2.05757	−	1.49491i
$302$	−4.23607	−	13.0373i	−0.243758	−	0.750211i
$303$	9.00000	+	27.6992i	0.517036	+	1.59127i
$304$	−0.809017	−	0.587785i	−0.0464003	−	0.0337118i
$305$	12.5172	−	9.09429i	0.716734	−	0.520738i
$306$	1.04508	−	3.21644i	0.0597435	−	0.183872i
$307$	−0.583592			−0.0333074			−0.0166537	−	0.999861i	$-0.505301\pi$
$307$	−0.583592			−0.0333074			−0.0166537	+	0.999861i	$0.505301\pi$
$308$	−13.6353	+	8.55951i	−0.776941	+	0.487723i
$309$	9.52786			0.542021
$310$	1.00000	−	3.07768i	0.0567962	−	0.174801i
$311$	23.2984	−	16.9273i	1.32113	−	0.959857i	0.321212	−	0.947007i	$-0.395910\pi$
$311$	23.2984	−	16.9273i	1.32113	−	0.959857i	0.999917	−	0.0128496i	$-0.00409025\pi$
$312$	4.00000	+	2.90617i	0.226455	+	0.164529i
$313$	3.42705	+	10.5474i	0.193708	+	0.596173i	0.999989	+	0.00464017i	$0.00147702\pi$
$313$	3.42705	+	10.5474i	0.193708	+	0.596173i	−0.806281	+	0.591533i	$0.798523\pi$
$314$	7.20820	+	22.1846i	0.406782	+	1.25195i
$315$	6.35410	+	4.61653i	0.358013	+	0.260112i
$316$	−3.00000	+	2.17963i	−0.168763	+	0.122614i
$317$	−6.23607	+	19.1926i	−0.350252	+	1.07797i	0.608459	+	0.793585i	$0.291788\pi$
$317$	−6.23607	+	19.1926i	−0.350252	+	1.07797i	−0.958711	+	0.284381i	$0.908212\pi$
$318$	9.52786			0.534296
$319$	−12.9443	+	32.2299i	−0.724740	+	1.80453i
$320$	1.61803			0.0904508
$321$	−3.70820	+	11.4127i	−0.206972	+	0.636994i
$322$	−30.8435	+	22.4091i	−1.71884	+	1.24881i
$323$	−2.73607	−	1.98787i	−0.152239	−	0.110608i
$324$	−3.39919	−	10.4616i	−0.188844	−	0.581201i
$325$	−1.81966	−	5.60034i	−0.100937	−	0.310651i
$326$	0.545085	+	0.396027i	0.0301895	+	0.0219339i
$327$	5.23607	−	3.80423i	0.289555	−	0.210374i
$328$	−1.47214	+	4.53077i	−0.0812851	+	0.250170i
$329$	−6.70820			−0.369835
$330$	−8.23607	−	6.88191i	−0.453381	−	0.378837i
$331$	3.70820			0.203821			0.101911	−	0.994794i	$-0.467504\pi$
$331$	3.70820			0.203821			0.101911	+	0.994794i	$0.467504\pi$
$332$	−4.26393	+	13.1230i	−0.234014	+	0.720220i
$333$	−3.23607	+	2.35114i	−0.177335	+	0.128842i
$334$	−1.14590	−	0.832544i	−0.0627008	−	0.0455548i
$335$	1.38197	+	4.25325i	0.0755049	+	0.232380i
$336$	3.00000	+	9.23305i	0.163663	+	0.503704i
$337$	28.2705	+	20.5397i	1.53999	+	1.11887i	0.950340	+	0.311213i	$0.100735\pi$
$337$	28.2705	+	20.5397i	1.53999	+	1.11887i	0.589653	+	0.807657i	$0.299265\pi$
$338$	5.57295	−	4.04898i	0.303128	−	0.220236i
$339$	−3.41641	+	10.5146i	−0.185554	+	0.571076i
$340$	5.47214			0.296768
$341$	−6.61803	−	0.449028i	−0.358387	−	0.0243162i
$342$	1.00000			0.0540738
$343$	−14.3435	+	44.1446i	−0.774474	+	2.38359i
$344$	7.35410	−	5.34307i	0.396507	−	0.288079i
$345$	−20.5623	−	14.9394i	−1.10704	−	0.804310i
$346$	−6.47214	−	19.9192i	−0.347944	−	1.07086i
$347$	−3.57295	−	10.9964i	−0.191806	−	0.590318i	−0.999999	−	0.00140040i	$-0.999554\pi$
$347$	−3.57295	−	10.9964i	−0.191806	−	0.590318i	0.808193	−	0.588918i	$-0.200446\pi$
$348$	16.9443	+	12.3107i	0.908308	+	0.659925i
$349$	21.0172	−	15.2699i	1.12503	−	0.817379i	0.140063	−	0.990143i	$-0.455270\pi$
$349$	21.0172	−	15.2699i	1.12503	−	0.817379i	0.984963	+	0.172763i	$0.0552696\pi$
$350$	3.57295	−	10.9964i	0.190982	−	0.587783i
$351$	9.88854			0.527811
$352$	−0.809017	−	3.21644i	−0.0431208	−	0.171437i
$353$	17.6180			0.937713			0.468857	−	0.883274i	$-0.344666\pi$
$353$	17.6180			0.937713			0.468857	+	0.883274i	$0.344666\pi$
$354$	2.18034	−	6.71040i	0.115884	−	0.356654i
$355$	−6.47214	+	4.70228i	−0.343505	+	0.249571i
$356$	−9.09017	−	6.60440i	−0.481778	−	0.350032i
$357$	10.1459	+	31.2259i	0.536978	+	1.65265i
$358$	0.673762	+	2.07363i	0.0356094	+	0.109595i
$359$	−4.11803	−	2.99193i	−0.217342	−	0.157908i	0.473788	−	0.880639i	$-0.342886\pi$
$359$	−4.11803	−	2.99193i	−0.217342	−	0.157908i	−0.691129	+	0.722731i	$0.742886\pi$
$360$	−1.30902	+	0.951057i	−0.0689913	+	0.0501251i
$361$	0.309017	−	0.951057i	0.0162641	−	0.0500556i
$362$	−0.291796			−0.0153365
$363$	−9.56231	+	19.8132i	−0.501891	+	1.03992i
$364$	−12.0000			−0.628971
$365$	−7.00000	+	21.5438i	−0.366397	+	1.12765i
$366$	−15.4721	+	11.2412i	−0.808742	+	0.587585i
$367$	1.16312	+	0.845055i	0.0607143	+	0.0441115i	0.617728	−	0.786391i	$-0.288053\pi$
$367$	1.16312	+	0.845055i	0.0607143	+	0.0441115i	−0.557014	+	0.830503i	$0.688053\pi$
$368$	−2.42705	−	7.46969i	−0.126519	−	0.389385i
$369$	−1.47214	−	4.53077i	−0.0766363	−	0.235862i
$370$	−5.23607	−	3.80423i	−0.272210	−	0.197772i
$371$	−18.7082	+	13.5923i	−0.971282	+	0.705677i
$372$	−1.23607	+	3.80423i	−0.0640871	+	0.197240i
$373$	14.3607			0.743568			0.371784	−	0.928319i	$-0.378746\pi$
$373$	14.3607			0.743568			0.371784	+	0.928319i	$0.378746\pi$
$374$	−2.73607	−	10.8779i	−0.141479	−	0.562482i
$375$	23.8885			1.23360
$376$	0.427051	−	1.31433i	0.0220235	−	0.0677813i
$377$	−20.9443	+	15.2169i	−1.07868	+	0.783710i
$378$	15.7082	+	11.4127i	0.807943	+	0.587005i
$379$	−1.00000	−	3.07768i	−0.0513665	−	0.158090i	0.922083	−	0.386993i	$-0.126486\pi$
$379$	−1.00000	−	3.07768i	−0.0513665	−	0.158090i	−0.973449	+	0.228903i	$0.926486\pi$
$380$	0.500000	+	1.53884i	0.0256495	+	0.0789409i
$381$	−31.4164	−	22.8254i	−1.60951	−	1.16938i
$382$	−4.07295	+	2.95917i	−0.208390	+	0.151404i
$383$	−0.909830	+	2.80017i	−0.0464901	+	0.143082i	−0.971607	−	0.236601i	$-0.923967\pi$
$383$	−0.909830	+	2.80017i	−0.0464901	+	0.143082i	0.925117	+	0.379682i	$0.123967\pi$
$384$	−2.00000			−0.102062
$385$	25.9894	+	1.76336i	1.32454	+	0.0898689i
$386$	19.1246			0.973417
$387$	−2.80902	+	8.64527i	−0.142790	+	0.439464i
$388$	7.47214	−	5.42882i	0.379340	−	0.275607i
$389$	12.9721	+	9.42481i	0.657713	+	0.477857i	0.865890	−	0.500235i	$-0.166753\pi$
$389$	12.9721	+	9.42481i	0.657713	+	0.477857i	−0.208177	+	0.978091i	$0.566753\pi$
$390$	−2.47214	−	7.60845i	−0.125181	−	0.385269i
$391$	−8.20820	−	25.2623i	−0.415107	−	1.27757i
$392$	−13.3992	−	9.73508i	−0.676761	−	0.491696i
$393$	−19.5623	+	14.2128i	−0.986788	+	0.716943i
$394$	−5.56231	+	17.1190i	−0.280225	+	0.862444i
$395$	6.00000			0.301893
$396$	2.54508	+	2.12663i	0.127895	+	0.106867i
$397$	14.1459			0.709962			0.354981	−	0.934873i	$-0.384487\pi$
$397$	14.1459			0.709962			0.354981	+	0.934873i	$0.384487\pi$
$398$	4.50000	−	13.8496i	0.225565	−	0.694217i
$399$	−7.85410	+	5.70634i	−0.393197	+	0.285674i
$400$	1.92705	+	1.40008i	0.0963525	+	0.0700042i
$401$	1.09017	+	3.35520i	0.0544405	+	0.167551i	0.974580	−	0.224040i	$-0.0719248\pi$
$401$	1.09017	+	3.35520i	0.0544405	+	0.167551i	−0.920139	+	0.391591i	$0.871925\pi$
$402$	−1.70820	−	5.25731i	−0.0851975	−	0.262211i
$403$	−4.00000	−	2.90617i	−0.199254	−	0.144767i
$404$	11.7812	−	8.55951i	0.586134	−	0.425851i
$405$	−5.50000	+	16.9273i	−0.273297	+	0.841122i
$406$	−50.8328			−2.52279
$407$	−4.94427	+	12.3107i	−0.245078	+	0.610220i
$408$	−6.76393			−0.334865
$409$	−1.56231	+	4.80828i	−0.0772511	+	0.237754i	−0.982223	−	0.187716i	$-0.939891\pi$
$409$	−1.56231	+	4.80828i	−0.0772511	+	0.237754i	0.904972	+	0.425471i	$0.139891\pi$
$410$	6.23607	−	4.53077i	0.307977	−	0.223759i
$411$	−6.32624	−	4.59628i	−0.312050	−	0.226718i
$412$	−1.47214	−	4.53077i	−0.0725269	−	0.223215i
$413$	5.29180	+	16.2865i	0.260392	+	0.801405i
$414$	6.35410	+	4.61653i	0.312287	+	0.226890i
$415$	18.0623	−	13.1230i	0.886644	−	0.644184i
$416$	0.763932	−	2.35114i	0.0374548	−	0.115274i
$417$	20.6525			1.01136
$418$	2.80902	−	1.76336i	0.137394	−	0.0862485i
$419$	−6.32624			−0.309057			−0.154528	−	0.987988i	$-0.549386\pi$
$419$	−6.32624			−0.309057			−0.154528	+	0.987988i	$0.549386\pi$
$420$	4.85410	−	14.9394i	0.236856	−	0.728968i
$421$	−22.6525	+	16.4580i	−1.10401	+	0.802113i	−0.981711	−	0.190380i	$-0.939028\pi$
$421$	−22.6525	+	16.4580i	−1.10401	+	0.802113i	−0.122304	+	0.992493i	$0.539028\pi$
$422$	−12.4721	−	9.06154i	−0.607134	−	0.441109i
$423$	0.427051	+	1.31433i	0.0207639	+	0.0639048i
$424$	−1.47214	−	4.53077i	−0.0714932	−	0.220034i
$425$	6.51722	+	4.73504i	0.316132	+	0.229683i
$426$	8.00000	−	5.81234i	0.387601	−	0.281609i
$427$	14.3435	−	44.1446i	0.694129	−	2.13631i
$428$	6.00000			0.290021
$429$	−13.8885	+	8.71851i	−0.670545	+	0.420934i
$430$	−14.7082			−0.709293
$431$	0.0344419	−	0.106001i	0.00165901	−	0.00510589i	−0.950224	−	0.311569i	$-0.899146\pi$
$431$	0.0344419	−	0.106001i	0.00165901	−	0.00510589i	0.951883	+	0.306463i	$0.0991456\pi$
$432$	−3.23607	+	2.35114i	−0.155695	+	0.113119i
$433$	−11.7082	−	8.50651i	−0.562660	−	0.408797i	0.269771	−	0.962924i	$-0.413052\pi$
$433$	−11.7082	−	8.50651i	−0.562660	−	0.408797i	−0.832432	+	0.554128i	$0.813052\pi$
$434$	−3.00000	−	9.23305i	−0.144005	−	0.443201i
$435$	−10.4721	−	32.2299i	−0.502100	−	1.54531i
$436$	−2.61803	−	1.90211i	−0.125381	−	0.0910947i
$437$	6.35410	−	4.61653i	0.303958	−	0.220838i
$438$	8.65248	−	26.6296i	0.413431	−	1.27241i
$439$	−17.1246			−0.817313			−0.408657	−	0.912688i	$-0.634003\pi$
$439$	−17.1246			−0.817313			−0.408657	+	0.912688i	$0.634003\pi$
$440$	−2.00000	+	4.97980i	−0.0953463	+	0.237402i
$441$	16.5623			0.788681
$442$	2.58359	−	7.95148i	0.122889	−	0.378213i
$443$	30.1074	−	21.8743i	1.43045	−	1.03928i	0.440512	−	0.897747i	$-0.354797\pi$
$443$	30.1074	−	21.8743i	1.43045	−	1.03928i	0.989934	−	0.141532i	$-0.0452030\pi$
$444$	6.47214	+	4.70228i	0.307154	+	0.223160i
$445$	5.61803	+	17.2905i	0.266320	+	0.819650i
$446$	−3.00000	−	9.23305i	−0.142054	−	0.437198i
$447$	−18.6525	−	13.5518i	−0.882232	−	0.640979i
$448$	3.92705	−	2.85317i	0.185536	−	0.134800i
$449$	4.38197	−	13.4863i	0.206798	−	0.636458i	−0.792837	−	0.609434i	$-0.791397\pi$
$449$	4.38197	−	13.4863i	0.206798	−	0.636458i	0.999635	−	0.0270243i	$-0.00860316\pi$
$450$	−2.38197			−0.112287
$451$	−12.1246	−	10.1311i	−0.570926	−	0.477055i
$452$	5.52786			0.260009
$453$	8.47214	−	26.0746i	0.398056	−	1.22509i
$454$		0			0
$455$	15.7082	+	11.4127i	0.736412	+	0.535035i
$456$	−0.618034	−	1.90211i	−0.0289421	−	0.0890746i
$457$	−7.91641	−	24.3642i	−0.370314	−	1.13971i	−0.946586	−	0.322451i	$-0.895493\pi$
$457$	−7.91641	−	24.3642i	−0.370314	−	1.13971i	0.576272	−	0.817258i	$-0.304507\pi$
$458$	7.50000	+	5.44907i	0.350452	+	0.254618i
$459$	−10.9443	+	7.95148i	−0.510835	+	0.371143i
$460$	−3.92705	+	12.0862i	−0.183100	+	0.563523i
$461$	29.7984			1.38785			0.693924	−	0.720048i	$-0.255880\pi$
$461$	29.7984			1.38785			0.693924	+	0.720048i	$0.255880\pi$
$462$	−32.1246	−	2.17963i	−1.49457	−	0.101405i
$463$	−21.7984			−1.01306			−0.506528	−	0.862223i	$-0.669071\pi$
$463$	−21.7984			−1.01306			−0.506528	+	0.862223i	$0.669071\pi$
$464$	3.23607	−	9.95959i	0.150231	−	0.462363i
$465$	5.23607	−	3.80423i	0.242817	−	0.176417i
$466$	−4.69098	−	3.40820i	−0.217306	−	0.157882i
$467$	6.15248	+	18.9354i	0.284703	+	0.876225i	0.986488	+	0.163836i	$0.0523867\pi$
$467$	6.15248	+	18.9354i	0.284703	+	0.876225i	−0.701785	+	0.712389i	$0.747613\pi$
$468$	0.763932	+	2.35114i	0.0353128	+	0.108682i
$469$	10.8541	+	7.88597i	0.501196	+	0.364140i
$470$	−1.80902	+	1.31433i	−0.0834437	+	0.0606254i
$471$	−14.4164	+	44.3691i	−0.664273	+	2.04442i
$472$	−3.52786			−0.162383
$473$	7.35410	+	29.2380i	0.338142	+	1.34436i
$474$	−7.41641			−0.340647
$475$	−0.736068	+	2.26538i	−0.0337731	+	0.103943i
$476$	13.2812	−	9.64932i	0.608741	−	0.442276i
$477$	3.85410	+	2.80017i	0.176467	+	0.128211i
$478$	5.66312	+	17.4293i	0.259025	+	0.797197i
$479$	0.336881	+	1.03681i	0.0153925	+	0.0473732i	0.958458	−	0.285235i	$-0.0920715\pi$
$479$	0.336881	+	1.03681i	0.0153925	+	0.0473732i	−0.943065	+	0.332608i	$0.892071\pi$
$480$	2.61803	+	1.90211i	0.119496	+	0.0868192i
$481$	−8.00000	+	5.81234i	−0.364769	+	0.265020i
$482$	3.09017	−	9.51057i	0.140753	−	0.433194i
$483$	−76.2492			−3.46946
$484$	10.8992	+	1.48584i	0.495418	+	0.0675382i
$485$	−14.9443			−0.678584
$486$	3.09017	−	9.51057i	0.140173	−	0.431408i
$487$	−8.09017	+	5.87785i	−0.366601	+	0.266351i	−0.755800	−	0.654803i	$-0.772752\pi$
$487$	−8.09017	+	5.87785i	−0.366601	+	0.266351i	0.389199	+	0.921154i	$0.372752\pi$
$488$	7.73607	+	5.62058i	0.350195	+	0.254432i
$489$	0.416408	+	1.28157i	0.0188306	+	0.0579547i
$490$	8.28115	+	25.4868i	0.374104	+	1.15137i
$491$	13.6353	+	9.90659i	0.615350	+	0.447078i	0.851294	−	0.524688i	$-0.175818\pi$
$491$	13.6353	+	9.90659i	0.615350	+	0.447078i	−0.235944	+	0.971767i	$0.575818\pi$
$492$	−7.70820	+	5.60034i	−0.347513	+	0.252483i
$493$	10.9443	−	33.6830i	0.492905	−	1.51701i
$494$	2.47214			0.111227
$495$	−1.30902	−	5.20431i	−0.0588359	−	0.233916i
$496$	2.00000			0.0898027
$497$	−7.41641	+	22.8254i	−0.332671	+	1.02386i
$498$	−22.3262	+	16.2210i	−1.00046	+	0.726879i
$499$	2.07295	+	1.50609i	0.0927979	+	0.0674217i	0.633217	−	0.773975i	$-0.281734\pi$
$499$	2.07295	+	1.50609i	0.0927979	+	0.0674217i	−0.540419	+	0.841396i	$0.681734\pi$
$500$	−3.69098	−	11.3597i	−0.165066	−	0.508020i
$501$	−0.875388	−	2.69417i	−0.0391095	−	0.120367i
$502$	−3.35410	−	2.43690i	−0.149701	−	0.108764i
$503$	−26.9443	+	19.5762i	−1.20139	+	0.872858i	−0.994420	−	0.105490i	$-0.966359\pi$
$503$	−26.9443	+	19.5762i	−1.20139	+	0.872858i	−0.206965	+	0.978348i	$0.566359\pi$
$504$	−1.50000	+	4.61653i	−0.0668153	+	0.205636i
$505$	−23.5623			−1.04851
$506$	25.9894	+	1.76336i	1.15537	+	0.0783907i
$507$	13.7771			0.611862
$508$	−6.00000	+	18.4661i	−0.266207	+	0.819301i
$509$	−27.2705	+	19.8132i	−1.20874	+	0.878204i	−0.995116	−	0.0987111i	$-0.968528\pi$
$509$	−27.2705	+	19.8132i	−1.20874	+	0.878204i	−0.213628	+	0.976915i	$0.568528\pi$
$510$	8.85410	+	6.43288i	0.392066	+	0.284853i
$511$	21.0000	+	64.6314i	0.928985	+	2.85912i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−3.23607	−	2.35114i	−0.142876	−	0.103805i
$514$	−5.61803	+	4.08174i	−0.247801	+	0.180038i
$515$	−2.38197	+	7.33094i	−0.104962	+	0.323040i
$516$	18.1803			0.800345
$517$	3.51722	+	2.93893i	0.154687	+	0.129254i
$518$	−19.4164			−0.853108
$519$	12.9443	−	39.8384i	0.568190	−	1.74871i
$520$	−3.23607	+	2.35114i	−0.141911	+	0.103104i
$521$	16.3262	+	11.8617i	0.715265	+	0.519671i	0.884868	−	0.465842i	$-0.154248\pi$
$521$	16.3262	+	11.8617i	0.715265	+	0.519671i	−0.169603	+	0.985513i	$0.554248\pi$
$522$	3.23607	+	9.95959i	0.141639	+	0.435920i
$523$	3.43769	+	10.5801i	0.150320	+	0.462637i	0.997657	−	0.0684189i	$-0.0217954\pi$
$523$	3.43769	+	10.5801i	0.150320	+	0.462637i	−0.847337	+	0.531056i	$0.821795\pi$
$524$	9.78115	+	7.10642i	0.427292	+	0.310446i
$525$	18.7082	−	13.5923i	0.816493	−	0.593217i
$526$	−0.763932	+	2.35114i	−0.0333090	+	0.102515i
$527$	6.76393			0.294642
$528$	2.47214	−	6.15537i	0.107586	−	0.267878i
$529$	38.6869			1.68204
$530$	−2.38197	+	7.33094i	−0.103466	+	0.318436i
$531$	2.85410	−	2.07363i	0.123857	−	0.0899877i
$532$	3.92705	+	2.85317i	0.170259	+	0.123701i
$533$	−3.63932	−	11.2007i	−0.157636	−	0.485155i
$534$	−6.94427	−	21.3723i	−0.300508	−	0.924869i
$535$	−7.85410	−	5.70634i	−0.339562	−	0.246707i
$536$	−2.23607	+	1.62460i	−0.0965834	+	0.0701720i
$537$	−1.34752	+	4.14725i	−0.0581500	+	0.178967i
$538$	−12.6525			−0.545487
$539$	46.5238	−	29.2052i	2.00392	−	1.25796i
$540$	6.47214			0.278516
$541$	10.4615	−	32.1972i	0.449775	−	1.38426i	−0.427387	−	0.904069i	$-0.640566\pi$
$541$	10.4615	−	32.1972i	0.449775	−	1.38426i	0.877162	−	0.480195i	$-0.159434\pi$
$542$	−16.3541	+	11.8820i	−0.702469	+	0.510373i
$543$	−0.472136	−	0.343027i	−0.0202613	−	0.0147207i
$544$	1.04508	+	3.21644i	0.0448076	+	0.137904i
$545$	1.61803	+	4.97980i	0.0693090	+	0.213311i
$546$	−19.4164	−	14.1068i	−0.830946	−	0.603717i
$547$	−15.9443	+	11.5842i	−0.681728	+	0.495304i	−0.873930	−	0.486051i	$-0.838437\pi$
$547$	−15.9443	+	11.5842i	−0.681728	+	0.495304i	0.192203	+	0.981355i	$0.438437\pi$
$548$	−1.20820	+	3.71847i	−0.0516119	+	0.158845i
$549$	−9.56231			−0.408109
$550$	−6.69098	+	4.20025i	−0.285304	+	0.179099i
$551$	10.4721			0.446128
$552$	4.85410	−	14.9394i	0.206604	−	0.635863i
$553$	14.5623	−	10.5801i	0.619252	−	0.449913i
$554$	10.0902	+	7.33094i	0.428690	+	0.311462i
$555$	−4.00000	−	12.3107i	−0.169791	−	0.522562i
$556$	−3.19098	−	9.82084i	−0.135328	−	0.416496i
$557$	16.5451	+	12.0207i	0.701038	+	0.509334i	0.880270	−	0.474473i	$-0.157361\pi$
$557$	16.5451	+	12.0207i	0.701038	+	0.509334i	−0.179232	+	0.983807i	$0.557361\pi$
$558$	−1.61803	+	1.17557i	−0.0684968	+	0.0497659i
$559$	−6.94427	+	21.3723i	−0.293711	+	0.903951i
$560$	−7.85410			−0.331896
$561$	8.36068	−	20.8172i	0.352988	−	0.878905i
$562$	−26.6525			−1.12427
$563$	1.14590	−	3.52671i	0.0482938	−	0.148633i	−0.924002	−	0.382389i	$-0.875102\pi$
$563$	1.14590	−	3.52671i	0.0482938	−	0.148633i	0.972295	+	0.233756i	$0.0751015\pi$
$564$	2.23607	−	1.62460i	0.0941554	−	0.0684079i
$565$	−7.23607	−	5.25731i	−0.304424	−	0.221177i
$566$	3.26393	+	10.0453i	0.137193	+	0.422238i
$567$	16.5000	+	50.7818i	0.692935	+	2.13263i
$568$	−4.00000	−	2.90617i	−0.167836	−	0.121940i
$569$	−11.8541	+	8.61251i	−0.496950	+	0.361055i	−0.807851	−	0.589387i	$-0.799369\pi$
$569$	−11.8541	+	8.61251i	−0.496950	+	0.361055i	0.310901	+	0.950442i	$0.399369\pi$
$570$	−1.00000	+	3.07768i	−0.0418854	+	0.128910i
$571$	12.8541			0.537927			0.268964	−	0.963150i	$-0.413319\pi$
$571$	12.8541			0.537927			0.268964	+	0.963150i	$0.413319\pi$
$572$	6.29180	+	5.25731i	0.263073	+	0.219819i
$573$	−10.0689			−0.420634
$574$	7.14590	−	21.9928i	0.298264	−	0.917962i
$575$	−15.1353	+	10.9964i	−0.631184	+	0.458582i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	1.09017	+	3.35520i	0.0453844	+	0.139679i	0.971181	−	0.238343i	$-0.0766043\pi$
$577$	1.09017	+	3.35520i	0.0453844	+	0.139679i	−0.925797	+	0.378022i	$0.876604\pi$
$578$	−1.71885	−	5.29007i	−0.0714946	−	0.220038i
$579$	30.9443	+	22.4823i	1.28600	+	0.934334i
$580$	−13.7082	+	9.95959i	−0.569202	+	0.413550i
$581$	20.6976	−	63.7005i	0.858680	−	2.64274i
$582$	18.4721			0.765695
$583$	15.7639	+	1.06957i	0.652875	+	0.0442970i
$584$	−14.0000			−0.579324
$585$	1.23607	−	3.80423i	0.0511051	−	0.157285i
$586$	24.7984	−	18.0171i	1.02441	−	0.744278i
$587$	−8.94427	−	6.49839i	−0.369170	−	0.268217i	0.387697	−	0.921787i	$-0.373271\pi$
$587$	−8.94427	−	6.49839i	−0.369170	−	0.268217i	−0.756867	+	0.653569i	$0.773271\pi$
$588$	−10.2361	−	31.5034i	−0.422128	−	1.29918i
$589$	0.618034	+	1.90211i	0.0254656	+	0.0783752i
$590$	4.61803	+	3.35520i	0.190121	+	0.138131i
$591$	−29.1246	+	21.1603i	−1.19803	+	0.870417i
$592$	1.23607	−	3.80423i	0.0508021	−	0.156353i
$593$	11.4508			0.470230			0.235115	−	0.971968i	$-0.424453\pi$
$593$	11.4508			0.470230			0.235115	+	0.971968i	$0.424453\pi$
$594$	−3.23607	−	12.8658i	−0.132777	−	0.527889i
$595$	−26.5623			−1.08895
$596$	−3.56231	+	10.9637i	−0.145918	+	0.449089i
$597$	23.5623	−	17.1190i	0.964341	−	0.700635i
$598$	15.7082	+	11.4127i	0.642356	+	0.466699i
$599$	−10.3820	−	31.9524i	−0.424196	−	1.30554i	−0.903762	−	0.428035i	$-0.859206\pi$
$599$	−10.3820	−	31.9524i	−0.424196	−	1.30554i	0.479567	−	0.877505i	$-0.340794\pi$
$600$	1.47214	+	4.53077i	0.0600997	+	0.184968i
$601$	−14.7984	−	10.7516i	−0.603638	−	0.438569i	0.243530	−	0.969893i	$-0.421695\pi$
$601$	−14.7984	−	10.7516i	−0.603638	−	0.438569i	−0.847168	+	0.531324i	$0.821695\pi$
$602$	−35.6976	+	25.9358i	−1.45492	+	1.05706i
$603$	0.854102	−	2.62866i	0.0347817	−	0.107047i
$604$	−13.7082			−0.557779
$605$	−12.8541	−	12.3107i	−0.522594	−	0.500503i
$606$	29.1246			1.18311
$607$	2.18034	−	6.71040i	0.0884973	−	0.272367i	−0.897007	−	0.442016i	$-0.854263\pi$
$607$	2.18034	−	6.71040i	0.0884973	−	0.272367i	0.985505	+	0.169649i	$0.0542635\pi$
$608$	−0.809017	+	0.587785i	−0.0328100	+	0.0238378i
$609$	−82.2492	−	59.7576i	−3.33291	−	2.42150i
$610$	−4.78115	−	14.7149i	−0.193583	−	0.595788i
$611$	1.05573	+	3.24920i	0.0427102	+	0.131448i
$612$	−2.73607	−	1.98787i	−0.110599	−	0.0803549i
$613$	33.3885	−	24.2582i	1.34855	−	0.979779i	0.349468	−	0.936948i	$-0.386362\pi$
$613$	33.3885	−	24.2582i	1.34855	−	0.979779i	0.999082	−	0.0428311i	$-0.0136377\pi$
$614$	−0.180340	+	0.555029i	−0.00727793	+	0.0223992i
$615$	15.4164			0.621650
$616$	3.92705	+	15.6129i	0.158225	+	0.629063i
$617$	−46.7214			−1.88093			−0.940466	−	0.339889i	$-0.889610\pi$
$617$	−46.7214			−1.88093			−0.940466	+	0.339889i	$0.889610\pi$
$618$	2.94427	−	9.06154i	0.118436	−	0.364508i
$619$	6.11803	−	4.44501i	0.245905	−	0.178660i	−0.458005	−	0.888949i	$-0.651436\pi$
$619$	6.11803	−	4.44501i	0.245905	−	0.178660i	0.703910	+	0.710289i	$0.251436\pi$
$620$	−2.61803	−	1.90211i	−0.105143	−	0.0763907i
$621$	−9.70820	−	29.8788i	−0.389577	−	1.19899i
$622$	−8.89919	−	27.3889i	−0.356825	−	1.09819i
$623$	44.1246	+	32.0584i	1.76782	+	1.28439i
$624$	4.00000	−	2.90617i	0.160128	−	0.116340i
$625$	−2.29180	+	7.05342i	−0.0916718	+	0.282137i
$626$	11.0902			0.443252
$627$	6.61803	+	0.449028i	0.264299	+	0.0179325i
$628$	23.3262			0.930818
$629$	4.18034	−	12.8658i	0.166681	−	0.512992i
$630$	6.35410	−	4.61653i	0.253153	−	0.183927i
$631$	−16.4721	−	11.9677i	−0.655745	−	0.476427i	0.209478	−	0.977813i	$-0.432824\pi$
$631$	−16.4721	−	11.9677i	−0.655745	−	0.476427i	−0.865223	+	0.501386i	$0.832824\pi$
$632$	1.14590	+	3.52671i	0.0455814	+	0.140285i
$633$	−9.52786	−	29.3238i	−0.378699	−	1.16551i
$634$	16.3262	+	11.8617i	0.648398	+	0.471089i
$635$	25.4164	−	18.4661i	1.00862	−	0.732805i
$636$	2.94427	−	9.06154i	0.116748	−	0.359313i
$637$	40.9443			1.62227
$638$	26.6525	+	22.2703i	1.05518	+	0.881691i
$639$	4.94427			0.195592
$640$	0.500000	−	1.53884i	0.0197642	−	0.0608281i
$641$	33.4164	−	24.2784i	1.31987	−	0.958941i	0.319935	−	0.947440i	$-0.396339\pi$
$641$	33.4164	−	24.2784i	1.31987	−	0.958941i	0.999934	−	0.0115013i	$-0.00366104\pi$
$642$	9.70820	+	7.05342i	0.383152	+	0.278376i
$643$	−13.5729	−	41.7732i	−0.535265	−	1.64738i	−0.743076	−	0.669207i	$-0.766634\pi$
$643$	−13.5729	−	41.7732i	−0.535265	−	1.64738i	0.207811	−	0.978169i	$-0.433366\pi$
$644$	11.7812	+	36.2587i	0.464242	+	1.42879i
$645$	−23.7984	−	17.2905i	−0.937060	−	0.680814i
$646$	−2.73607	+	1.98787i	−0.107649	+	0.0782117i
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	−0.997111	−	0.0759575i	$-0.975799\pi$
$647$	−3.70820	+	11.4127i	−0.145785	+	0.448679i	0.851327	+	0.524636i	$0.175799\pi$
$648$	−11.0000			−0.432121
$649$	4.36068	−	10.8576i	0.171172	−	0.426200i
$650$	−5.88854			−0.230968
$651$	6.00000	−	18.4661i	0.235159	−	0.723744i
$652$	0.545085	−	0.396027i	0.0213472	−	0.0155096i
$653$	−0.500000	−	0.363271i	−0.0195665	−	0.0142159i	0.577959	−	0.816066i	$-0.303849\pi$
$653$	−0.500000	−	0.363271i	−0.0195665	−	0.0142159i	−0.597526	+	0.801850i	$0.703849\pi$
$654$	−2.00000	−	6.15537i	−0.0782062	−	0.240694i
$655$	−6.04508	−	18.6049i	−0.236201	−	0.726952i
$656$	3.85410	+	2.80017i	0.150477	+	0.109328i
$657$	11.3262	−	8.22899i	0.441879	−	0.321044i
$658$	−2.07295	+	6.37988i	−0.0808120	+	0.248714i
$659$	33.7082			1.31309			0.656543	−	0.754289i	$-0.272018\pi$
$659$	33.7082			1.31309			0.656543	+	0.754289i	$0.272018\pi$
$660$	−9.09017	+	5.70634i	−0.353834	+	0.222119i
$661$	−29.5967			−1.15118			−0.575590	−	0.817738i	$-0.695228\pi$
$661$	−29.5967			−1.15118			−0.575590	+	0.817738i	$0.695228\pi$
$662$	1.14590	−	3.52671i	0.0445366	−	0.137070i
$663$	13.5279	−	9.82857i	0.525379	−	0.381710i
$664$	11.1631	+	8.11048i	0.433213	+	0.314748i
$665$	−2.42705	−	7.46969i	−0.0941170	−	0.289662i
$666$	1.23607	+	3.80423i	0.0478967	+	0.147411i
$667$	66.5410	+	48.3449i	2.57648	+	1.87192i
$668$	−1.14590	+	0.832544i	−0.0443361	+	0.0322121i
$669$	6.00000	−	18.4661i	0.231973	−	0.713941i
$670$	4.47214			0.172774
$671$	−26.8607	+	16.8617i	−1.03695	+	0.650941i
$672$	9.70820			0.374502
$673$	9.58359	−	29.4953i	0.369420	−	1.13696i	−0.577746	−	0.816217i	$-0.696068\pi$
$673$	9.58359	−	29.4953i	0.369420	−	1.13696i	0.947166	−	0.320742i	$-0.103932\pi$
$674$	28.2705	−	20.5397i	1.08894	−	0.791161i
$675$	7.70820	+	5.60034i	0.296689	+	0.215557i
$676$	−2.12868	−	6.55139i	−0.0818722	−	0.251977i
$677$	6.27051	+	19.2986i	0.240995	+	0.741707i	0.996269	+	0.0862981i	$0.0275038\pi$
$677$	6.27051	+	19.2986i	0.240995	+	0.741707i	−0.755274	+	0.655409i	$0.772496\pi$
$678$	8.94427	+	6.49839i	0.343503	+	0.249569i
$679$	−36.2705	+	26.3521i	−1.39193	+	1.01130i
$680$	1.69098	−	5.20431i	0.0648462	−	0.199576i
$681$		0			0
$682$	−2.47214	+	6.15537i	−0.0946630	+	0.235701i
$683$	38.0689			1.45667			0.728333	−	0.685224i	$-0.240296\pi$
$683$	38.0689			1.45667			0.728333	+	0.685224i	$0.240296\pi$
$684$	0.309017	−	0.951057i	0.0118156	−	0.0363646i
$685$	5.11803	−	3.71847i	0.195550	−	0.142075i
$686$	37.5517	+	27.2829i	1.43373	+	1.04167i
$687$	5.72949	+	17.6336i	0.218594	+	0.672762i
$688$	−2.80902	−	8.64527i	−0.107093	−	0.329598i
$689$	9.52786	+	6.92240i	0.362983	+	0.263722i
$690$	−20.5623	+	14.9394i	−0.782794	+	0.568733i
$691$	−1.44427	+	4.44501i	−0.0549427	+	0.169096i	−0.974762	−	0.223245i	$-0.928335\pi$
$691$	−1.44427	+	4.44501i	−0.0549427	+	0.169096i	0.919820	+	0.392342i	$0.128335\pi$
$692$	−20.9443			−0.796182
$693$	−12.3541	−	10.3229i	−0.469294	−	0.392133i
$694$	−11.5623			−0.438899
$695$	−5.16312	+	15.8904i	−0.195848	+	0.602759i
$696$	16.9443	−	12.3107i	0.642271	−	0.466637i
$697$	13.0344	+	9.47008i	0.493715	+	0.358705i
$698$	−8.02786	−	24.7072i	−0.303859	−	0.935182i
$699$	−3.58359	−	11.0292i	−0.135544	−	0.417161i
$700$	−9.35410	−	6.79615i	−0.353552	−	0.256870i
$701$	22.4443	−	16.3067i	0.847708	−	0.615896i	−0.0768048	−	0.997046i	$-0.524472\pi$
$701$	22.4443	−	16.3067i	0.847708	−	0.615896i	0.924513	+	0.381150i	$0.124472\pi$
$702$	3.05573	−	9.40456i	0.115331	−	0.354952i
$703$	4.00000			0.150863
$704$	−3.30902	−	0.224514i	−0.124713	−	0.00846169i
$705$	−4.47214			−0.168430
$706$	5.44427	−	16.7557i	0.204898	−	0.630611i
$707$	−57.1869	+	41.5487i	−2.15074	+	1.56260i
$708$	−5.70820	−	4.14725i	−0.214527	−	0.155863i
$709$	9.20820	+	28.3399i	0.345821	+	1.06433i	0.961143	+	0.276052i	$0.0890263\pi$
$709$	9.20820	+	28.3399i	0.345821	+	1.06433i	−0.615321	+	0.788276i	$0.710974\pi$
$710$	2.47214	+	7.60845i	0.0927776	+	0.285540i
$711$	−3.00000	−	2.17963i	−0.112509	−	0.0817424i
$712$	−9.09017	+	6.60440i	−0.340669	+	0.247510i
$713$	−4.85410	+	14.9394i	−0.181788	+	0.559485i
$714$	32.8328			1.22874
$715$	−3.23607	−	12.8658i	−0.121022	−	0.481152i
$716$	2.18034			0.0814831
$717$	−11.3262	+	34.8586i	−0.422986	+	1.30182i
$718$	−4.11803	+	2.99193i	−0.153684	+	0.111658i
$719$	3.78115	+	2.74717i	0.141013	+	0.102452i	0.656055	−	0.754713i	$-0.272224\pi$
$719$	3.78115	+	2.74717i	0.141013	+	0.102452i	−0.515042	+	0.857165i	$0.672224\pi$
$720$	0.500000	+	1.53884i	0.0186339	+	0.0573492i
$721$	7.14590	+	21.9928i	0.266127	+	0.819055i
$722$	−0.809017	−	0.587785i	−0.0301085	−	0.0218751i
$723$	16.1803	−	11.7557i	0.601753	−	0.437199i
$724$	−0.0901699	+	0.277515i	−0.00335114	+	0.0103137i
$725$	−24.9443			−0.926407
$726$	15.8885	+	15.2169i	0.589679	+	0.564752i
$727$	12.1459			0.450466			0.225233	−	0.974305i	$-0.427686\pi$
$727$	12.1459			0.450466			0.225233	+	0.974305i	$0.427686\pi$
$728$	−3.70820	+	11.4127i	−0.137435	+	0.422982i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$	18.3262	+	13.3148i	0.678284	+	0.492803i
$731$	−9.50000	−	29.2380i	−0.351370	−	1.08141i
$732$	5.90983	+	18.1886i	0.218434	+	0.672270i
$733$	−23.1976	−	16.8540i	−0.856821	−	0.622517i	0.0701969	−	0.997533i	$-0.477637\pi$
$733$	−23.1976	−	16.8540i	−0.856821	−	0.622517i	−0.927018	+	0.375016i	$0.877637\pi$
$734$	1.16312	−	0.845055i	0.0429315	−	0.0311916i
$735$	−16.5623	+	50.9735i	−0.610910	+	1.88019i
$736$	−7.85410			−0.289506
$737$	−2.23607	−	8.89002i	−0.0823666	−	0.327468i
$738$	−4.76393			−0.175363
$739$	3.84752	−	11.8415i	0.141533	−	0.435595i	−0.855015	−	0.518602i	$-0.826452\pi$
$739$	3.84752	−	11.8415i	0.141533	−	0.435595i	0.996549	+	0.0830073i	$0.0264525\pi$
$740$	−5.23607	+	3.80423i	−0.192482	+	0.139846i
$741$	4.00000	+	2.90617i	0.146944	+	0.106761i
$742$	7.14590	+	21.9928i	0.262334	+	0.807382i
$743$	−0.819660	−	2.52265i	−0.0300704	−	0.0925472i	0.934895	−	0.354925i	$-0.115493\pi$
$743$	−0.819660	−	2.52265i	−0.0300704	−	0.0925472i	−0.964965	+	0.262377i	$0.915493\pi$
$744$	3.23607	+	2.35114i	0.118640	+	0.0861970i
$745$	15.0902	−	10.9637i	0.552861	−	0.401677i
$746$	4.43769	−	13.6578i	0.162476	−	0.500048i
$747$	−13.7984			−0.504856
$748$	−11.1910	−	0.759299i	−0.409183	−	0.0277627i
$749$	−29.1246			−1.06419
$750$	7.38197	−	22.7194i	0.269551	−	0.829594i
$751$	8.56231	−	6.22088i	0.312443	−	0.227003i	−0.420501	−	0.907292i	$-0.638146\pi$
$751$	8.56231	−	6.22088i	0.312443	−	0.227003i	0.732944	+	0.680289i	$0.238146\pi$
$752$	−1.11803	−	0.812299i	−0.0407705	−	0.0296215i
$753$	−2.56231	−	7.88597i	−0.0933756	−	0.287381i
$754$	8.00000	+	24.6215i	0.291343	+	0.896661i
$755$	17.9443	+	13.0373i	0.653059	+	0.474475i
$756$	15.7082	−	11.4127i	0.571302	−	0.415075i
$757$	−7.85410	+	24.1724i	−0.285462	+	0.878562i	0.700798	+	0.713360i	$0.252828\pi$
$757$	−7.85410	+	24.1724i	−0.285462	+	0.878562i	−0.986260	+	0.165202i	$0.947172\pi$
$758$	−3.23607			−0.117539
$759$	39.9787	+	33.4055i	1.45114	+	1.21254i
$760$	1.61803			0.0586923
$761$	−3.49342	+	10.7516i	−0.126636	+	0.389747i	−0.994196	−	0.107587i	$-0.965688\pi$
$761$	−3.49342	+	10.7516i	−0.126636	+	0.389747i	0.867559	+	0.497334i	$0.165688\pi$
$762$	−31.4164	+	22.8254i	−1.13810	+	0.826875i
$763$	12.7082	+	9.23305i	0.460068	+	0.334259i
$764$	1.55573	+	4.78804i	0.0562843	+	0.173225i
$765$	1.69098	+	5.20431i	0.0611376	+	0.188162i
$766$	2.38197	+	1.73060i	0.0860639	+	0.0625291i
$767$	7.05573	−	5.12629i	0.254768	−	0.185099i
$768$	−0.618034	+	1.90211i	−0.0223014	+	0.0686366i
$769$	−3.50658			−0.126450			−0.0632252	−	0.997999i	$-0.520139\pi$
$769$	−3.50658			−0.126450			−0.0632252	+	0.997999i	$0.520139\pi$
$770$	9.70820	−	24.1724i	0.349859	−	0.871114i
$771$	−13.8885			−0.500184
$772$	5.90983	−	18.1886i	0.212699	−	0.654622i
$773$	−12.6180	+	9.16754i	−0.453839	+	0.329733i	−0.791110	−	0.611674i	$-0.790496\pi$
$773$	−12.6180	+	9.16754i	−0.453839	+	0.329733i	0.337271	+	0.941408i	$0.390496\pi$
$774$	7.35410	+	5.34307i	0.264338	+	0.192053i
$775$	−1.47214	−	4.53077i	−0.0528807	−	0.162750i
$776$	−2.85410	−	8.78402i	−0.102456	−	0.315328i
$777$	−31.4164	−	22.8254i	−1.12706	−	0.818855i
$778$	12.9721	−	9.42481i	0.465074	−	0.337896i
$779$	−1.47214	+	4.53077i	−0.0527447	+	0.162332i
$780$	−8.00000			−0.286446
$781$	13.8885	−	8.71851i	0.496971	−	0.311973i
$782$	−26.5623			−0.949866
$783$	12.9443	−	39.8384i	0.462591	−	1.42371i
$784$	−13.3992	+	9.73508i	−0.478542	+	0.347681i
$785$	−30.5344	−	22.1846i	−1.08982	−	0.791801i
$786$	7.47214	+	22.9969i	0.266522	+	0.820271i
$787$	−7.74265	−	23.8294i	−0.275996	−	0.849427i	−0.988954	−	0.148221i	$-0.952645\pi$
$787$	−7.74265	−	23.8294i	−0.275996	−	0.849427i	0.712959	−	0.701206i	$-0.247355\pi$
$788$	14.5623	+	10.5801i	0.518761	+	0.376902i
$789$	−4.00000	+	2.90617i	−0.142404	+	0.103462i
$790$	1.85410	−	5.70634i	0.0659660	−	0.203022i
$791$	−26.8328			−0.954065
$792$	2.80902	−	1.76336i	0.0998141	−	0.0626581i
$793$	−23.6393			−0.839457
$794$	4.37132	−	13.4535i	0.155132	−	0.477449i
$795$	−12.4721	+	9.06154i	−0.442341	+	0.321380i
$796$	−11.7812	−	8.55951i	−0.417572	−	0.303384i
$797$	5.49342	+	16.9070i	0.194587	+	0.598877i	0.999981	+	0.00613760i	$0.00195367\pi$
$797$	5.49342	+	16.9070i	0.194587	+	0.598877i	−0.805394	+	0.592740i	$0.798046\pi$
$798$	3.00000	+	9.23305i	0.106199	+	0.326846i
$799$	−3.78115	−	2.74717i	−0.133768	−	0.0971878i
$800$	1.92705	−	1.40008i	0.0681315	−	0.0495005i
$801$	3.47214	−	10.6861i	0.122682	−	0.377576i
$802$	3.52786			0.124573
$803$	17.3050	−	43.0876i	0.610678	−	1.52053i
$804$	−5.52786			−0.194953
$805$	19.0623	−	58.6677i	0.671858	−	2.06777i
$806$	−4.00000	+	2.90617i	−0.140894	+	0.102365i
$807$	−20.4721	−	14.8739i	−0.720653	−	0.523585i
$808$	−4.50000	−	13.8496i	−0.158309	−	0.487226i
$809$	−4.50000	−	13.8496i	−0.158212	−	0.486925i	0.840261	−	0.542183i	$-0.182402\pi$
$809$	−4.50000	−	13.8496i	−0.158212	−	0.486925i	−0.998472	+	0.0552577i	$0.982402\pi$
$810$	14.3992	+	10.4616i	0.505936	+	0.367584i
$811$	−32.5623	+	23.6579i	−1.14342	+	0.830741i	−0.987592	−	0.157043i	$-0.949804\pi$
$811$	−32.5623	+	23.6579i	−1.14342	+	0.830741i	−0.155826	+	0.987785i	$0.549804\pi$
$812$	−15.7082	+	48.3449i	−0.551250	+	1.69657i
$813$	−40.4296			−1.41793
$814$	10.1803	+	8.50651i	0.356821	+	0.298153i
$815$	−1.09017			−0.0381870
$816$	−2.09017	+	6.43288i	−0.0731706	+	0.225196i
$817$	7.35410	−	5.34307i	0.257287	−	0.186930i
$818$	4.09017	+	2.97168i	0.143009	+	0.103902i
$819$	−3.70820	−	11.4127i	−0.129575	−	0.398791i
$820$	−2.38197	−	7.33094i	−0.0831819	−	0.256007i
$821$	−12.2082	−	8.86978i	−0.426069	−	0.309557i	0.354006	−	0.935243i	$-0.384819\pi$
$821$	−12.2082	−	8.86978i	−0.426069	−	0.309557i	−0.780075	+	0.625686i	$0.784819\pi$
$822$	−6.32624	+	4.59628i	−0.220653	+	0.160314i
$823$	2.20820	−	6.79615i	0.0769732	−	0.236899i	−0.905165	−	0.425060i	$-0.860253\pi$
$823$	2.20820	−	6.79615i	0.0769732	−	0.236899i	0.982138	+	0.188161i	$0.0602528\pi$
$824$	−4.76393			−0.165959
$825$	−15.7639	−	1.06957i	−0.548830	−	0.0372376i
$826$	17.1246			0.595841
$827$	−16.1459	+	49.6920i	−0.561448	+	1.72796i	0.116829	+	0.993152i	$0.462727\pi$
$827$	−16.1459	+	49.6920i	−0.561448	+	1.72796i	−0.678276	+	0.734807i	$0.737273\pi$
$828$	6.35410	−	4.61653i	0.220820	−	0.160435i
$829$	−28.1803	−	20.4742i	−0.978744	−	0.711099i	−0.0213162	−	0.999773i	$-0.506786\pi$
$829$	−28.1803	−	20.4742i	−0.978744	−	0.711099i	−0.957427	+	0.288674i	$0.906786\pi$
$830$	−6.89919	−	21.2335i	−0.239474	−	0.737026i
$831$	7.70820	+	23.7234i	0.267395	+	0.822956i
$832$	−2.00000	−	1.45309i	−0.0693375	−	0.0503767i
$833$	−45.3156	+	32.9237i	−1.57009	+	1.14074i
$834$	6.38197	−	19.6417i	0.220989	−	0.680135i
$835$	2.29180			0.0793109
$836$	−0.809017	−	3.21644i	−0.0279804	−	0.111243i
$837$	8.00000			0.276520
$838$	−1.95492	+	6.01661i	−0.0675314	+	0.207840i
$839$	1.47214	−	1.06957i	0.0508238	−	0.0369256i	−0.562083	−	0.827081i	$-0.690000\pi$
$839$	1.47214	−	1.06957i	0.0508238	−	0.0369256i	0.612907	+	0.790155i	$0.290000\pi$
$840$	−12.7082	−	9.23305i	−0.438475	−	0.318571i
$841$	24.9271	+	76.7176i	0.859553	+	2.64543i
$842$	8.65248	+	26.6296i	0.298184	+	0.917716i
$843$	−43.1246	−	31.3319i	−1.48529	−	1.07913i
$844$	−12.4721	+	9.06154i	−0.429309	+	0.311911i
$845$	−3.44427	+	10.6004i	−0.118487	+	0.364664i
$846$	1.38197			0.0475130
$847$	−52.9058	−	7.21242i	−1.81786	−	0.247822i
$848$	−4.76393			−0.163594
$849$	−6.52786	+	20.0907i	−0.224036	+	0.689511i
$850$	6.51722	−	4.73504i	0.223539	−	0.162410i
$851$	25.4164	+	18.4661i	0.871263	+	0.633010i
$852$	−3.05573	−	9.40456i	−0.104688	−	0.322195i
$853$	9.04508	+	27.8379i	0.309698	+	0.953152i	0.977882	+	0.209156i	$0.0670717\pi$
$853$	9.04508	+	27.8379i	0.309698	+	0.953152i	−0.668184	+	0.743996i	$0.732928\pi$
$854$	−37.5517	−	27.2829i	−1.28499	−	0.933601i
$855$	−1.30902	+	0.951057i	−0.0447674	+	0.0325254i
$856$	1.85410	−	5.70634i	0.0633719	−	0.195039i
$857$	57.0132			1.94753			0.973766	−	0.227551i	$-0.0730719\pi$
$857$	57.0132			1.94753			0.973766	+	0.227551i	$0.0730719\pi$
$858$	4.00000	+	15.9030i	0.136558	+	0.542918i
$859$	−26.6869			−0.910546			−0.455273	−	0.890352i	$-0.650458\pi$
$859$	−26.6869			−0.910546			−0.455273	+	0.890352i	$0.650458\pi$
$860$	−4.54508	+	13.9883i	−0.154986	+	0.476998i
$861$	37.4164	−	27.1846i	1.27515	−	0.926449i
$862$	−0.0901699	−	0.0655123i	−0.00307120	−	0.00223136i
$863$	7.97871	+	24.5560i	0.271599	+	0.835894i	0.990099	+	0.140368i	$0.0448287\pi$
$863$	7.97871	+	24.5560i	0.271599	+	0.835894i	−0.718501	+	0.695526i	$0.755171\pi$
$864$	1.23607	+	3.80423i	0.0420519	+	0.129422i
$865$	27.4164	+	19.9192i	0.932186	+	0.677273i
$866$	−11.7082	+	8.50651i	−0.397861	+	0.289063i
$867$	3.43769	−	10.5801i	0.116750	−	0.359320i
$868$	−9.70820			−0.329518
$869$	−12.2705	−	0.832544i	−0.416249	−	0.0282421i
$870$	−33.8885			−1.14893
$871$	2.11146	−	6.49839i	0.0715440	−	0.220190i
$872$	−2.61803	+	1.90211i	−0.0886578	+	0.0644137i
$873$	7.47214	+	5.42882i	0.252893	+	0.183738i
$874$	−2.42705	−	7.46969i	−0.0820962	−	0.252666i
$875$	17.9164	+	55.1410i	0.605685	+	1.86411i
$876$	−22.6525	−	16.4580i	−0.765356	−	0.556064i
$877$	33.5066	−	24.3440i	1.13144	−	0.822037i	0.145533	−	0.989353i	$-0.453510\pi$
$877$	33.5066	−	24.3440i	1.13144	−	0.822037i	0.985903	+	0.167316i	$0.0535101\pi$
$878$	−5.29180	+	16.2865i	−0.178589	+	0.549642i
$879$	61.3050			2.06776
$880$	4.11803	+	3.44095i	0.138819	+	0.115995i
$881$	−1.41641			−0.0477200			−0.0238600	−	0.999715i	$-0.507596\pi$
$881$	−1.41641			−0.0477200			−0.0238600	+	0.999715i	$0.507596\pi$
$882$	5.11803	−	15.7517i	0.172333	−	0.530387i
$883$	−39.9615	+	29.0337i	−1.34481	+	0.977063i	−0.345559	+	0.938397i	$0.612311\pi$
$883$	−39.9615	+	29.0337i	−1.34481	+	0.977063i	−0.999252	+	0.0386656i	$0.987689\pi$
$884$	−6.76393	−	4.91428i	−0.227496	−	0.165285i
$885$	3.52786	+	10.8576i	0.118588	+	0.364976i
$886$	−11.5000	−	35.3934i	−0.386350	−	1.18906i
$887$	−38.7426	−	28.1482i	−1.30085	−	0.945123i	−0.300887	−	0.953660i	$-0.597283\pi$
$887$	−38.7426	−	28.1482i	−1.30085	−	0.945123i	−0.999964	+	0.00853637i	$0.997283\pi$
$888$	6.47214	−	4.70228i	0.217191	−	0.157798i
$889$	29.1246	−	89.6363i	0.976808	−	3.00631i
$890$	18.1803			0.609406
$891$	13.5967	−	33.8545i	0.455508	−	1.13417i
$892$	−9.70820			−0.325055
$893$	0.427051	−	1.31433i	0.0142907	−	0.0439823i
$894$	−18.6525	+	13.5518i	−0.623832	+	0.453241i
$895$	−2.85410	−	2.07363i	−0.0954021	−	0.0693137i
$896$	−1.50000	−	4.61653i	−0.0501115	−	0.154227i
$897$	12.0000	+	36.9322i	0.400668	+	1.23313i
$898$	−11.4721	−	8.33499i	−0.382830	−	0.278142i
$899$	−16.9443	+	12.3107i	−0.565123	+	0.410586i
$900$	−0.736068	+	2.26538i	−0.0245356	+	0.0755128i
$901$	−16.1115			−0.536750
$902$	−13.3820	+	8.40051i	−0.445571	+	0.279706i
$903$	−88.2492			−2.93675
$904$	1.70820	−	5.25731i	0.0568140	−	0.174856i
$905$	0.381966	−	0.277515i	0.0126970	−	0.00922490i
$906$	−22.1803	−	16.1150i	−0.736892	−	0.535384i
$907$	7.05573	+	21.7153i	0.234282	+	0.721045i	0.997216	+	0.0745686i	$0.0237580\pi$
$907$	7.05573	+	21.7153i	0.234282	+	0.721045i	−0.762934	+	0.646476i	$0.776242\pi$
$908$		0			0
$909$	11.7812	+	8.55951i	0.390756	+	0.283901i
$910$	15.7082	−	11.4127i	0.520722	−	0.378327i
$911$	−4.14590	+	12.7598i	−0.137360	+	0.422750i	−0.995950	−	0.0899133i	$-0.971341\pi$
$911$	−4.14590	+	12.7598i	−0.137360	+	0.422750i	0.858590	+	0.512663i	$0.171341\pi$
$912$	−2.00000			−0.0662266
$913$	−38.7599	+	24.3314i	−1.28276	+	0.805253i
$914$	−25.6180			−0.847369
$915$	9.56231	−	29.4298i	0.316120	−	0.972918i
$916$	7.50000	−	5.44907i	0.247807	−	0.180042i
$917$	−47.4787	−	34.4953i	−1.56789	−	1.13914i
$918$	4.18034	+	12.8658i	0.137972	+	0.424633i
$919$	9.79180	+	30.1360i	0.323002	+	0.994097i	0.972335	+	0.233592i	$0.0750481\pi$
$919$	9.79180	+	30.1360i	0.323002	+	0.994097i	−0.649333	+	0.760504i	$0.724952\pi$
$920$	10.2812	+	7.46969i	0.338960	+	0.246269i
$921$	−0.944272	+	0.686054i	−0.0311148	+	0.0226062i
$922$	9.20820	−	28.3399i	0.303256	−	0.933326i
$923$	12.2229			0.402322
$924$	−12.0000	+	29.8788i	−0.394771	+	0.982940i
$925$	−9.52786			−0.313274
$926$	−6.73607	+	20.7315i	−0.221361	+	0.681279i
$927$	3.85410	−	2.80017i	0.126585	−	0.0919696i
$928$	−8.47214	−	6.15537i	−0.278111	−	0.202060i
$929$	4.55166	+	14.0086i	0.149335	+	0.459607i	0.997543	−	0.0700571i	$-0.0223182\pi$
$929$	4.55166	+	14.0086i	0.149335	+	0.459607i	−0.848208	+	0.529664i	$0.822318\pi$
$930$	−2.00000	−	6.15537i	−0.0655826	−	0.201842i
$931$	−13.3992	−	9.73508i	−0.439141	−	0.319054i
$932$	−4.69098	+	3.40820i	−0.153658	+	0.111639i
$933$	17.7984	−	54.7778i	0.582693	−	1.79334i
$934$	19.9098			0.651470
$935$	13.9271	+	11.6372i	0.455463	+	0.380577i
$936$	2.47214			0.0808043
$937$	−13.5385	+	41.6672i	−0.442284	+	1.36121i	0.443152	+	0.896447i	$0.353860\pi$
$937$	−13.5385	+	41.6672i	−0.442284	+	1.36121i	−0.885435	+	0.464763i	$0.846140\pi$
$938$	10.8541	−	7.88597i	0.354399	−	0.257486i
$939$	17.9443	+	13.0373i	0.585589	+	0.425455i
$940$	0.690983	+	2.12663i	0.0225374	+	0.0693629i
$941$	−2.76393	−	8.50651i	−0.0901016	−	0.277304i	0.895845	−	0.444368i	$-0.146572\pi$
$941$	−2.76393	−	8.50651i	−0.0901016	−	0.277304i	−0.985946	+	0.167063i	$0.946572\pi$
$942$	37.7426	+	27.4216i	1.22972	+	0.893445i
$943$	−30.2705	+	21.9928i	−0.985743	+	0.716185i
$944$	−1.09017	+	3.35520i	−0.0354820	+	0.109202i
$945$	−31.4164			−1.02198
$946$	30.0795	+	2.04087i	0.977970	+	0.0663544i
$947$	26.9230			0.874879			0.437440	−	0.899248i	$-0.355885\pi$
$947$	26.9230			0.874879			0.437440	+	0.899248i	$0.355885\pi$
$948$	−2.29180	+	7.05342i	−0.0744341	+	0.229085i
$949$	28.0000	−	20.3432i	0.908918	−	0.660368i
$950$	1.92705	+	1.40008i	0.0625218	+	0.0454247i
$951$	12.4721	+	38.3853i	0.404437	+	1.24473i
$952$	−5.07295	−	15.6129i	−0.164415	−	0.506018i
$953$	17.6180	+	12.8003i	0.570704	+	0.414641i	0.835361	−	0.549702i	$-0.185259\pi$
$953$	17.6180	+	12.8003i	0.570704	+	0.414641i	−0.264657	+	0.964343i	$0.585259\pi$
$954$	3.85410	−	2.80017i	0.124781	−	0.0906588i
$955$	2.51722	−	7.74721i	0.0814554	−	0.250694i
$956$	18.3262			0.592713
$957$	16.9443	+	67.3660i	0.547731	+	2.17763i
$958$	1.09017			0.0352218
$959$	5.86475	−	18.0498i	0.189382	−	0.582859i
$960$	2.61803	−	1.90211i	0.0844967	−	0.0613904i
$961$	21.8435	+	15.8702i	0.704628	+	0.511942i
$962$	3.05573	+	9.40456i	0.0985206	+	0.303215i
$963$	1.85410	+	5.70634i	0.0597476	+	0.183884i
$964$	−8.09017	−	5.87785i	−0.260567	−	0.189313i
$965$	−25.0344	+	18.1886i	−0.805887	+	0.585511i
$966$	−23.5623	+	72.5173i	−0.758105	+	2.33321i
$967$	−24.7295			−0.795247			−0.397623	−	0.917549i	$-0.630165\pi$
$967$	−24.7295			−0.795247			−0.397623	+	0.917549i	$0.630165\pi$
$968$	4.78115	−	9.90659i	0.153672	−	0.318410i
$969$	−6.76393			−0.217289
$970$	−4.61803	+	14.2128i	−0.148276	+	0.456347i
$971$	−8.38197	+	6.08985i	−0.268990	+	0.195433i	−0.714101	−	0.700043i	$-0.753164\pi$
$971$	−8.38197	+	6.08985i	−0.268990	+	0.195433i	0.445111	+	0.895475i	$0.353164\pi$
$972$	−8.09017	−	5.87785i	−0.259492	−	0.188532i
$973$	15.4894	+	47.6713i	0.496566	+	1.52827i
$974$	3.09017	+	9.51057i	0.0990154	+	0.304738i
$975$	−9.52786	−	6.92240i	−0.305136	−	0.221694i
$976$	7.73607	−	5.62058i	0.247626	−	0.179910i
$977$	−13.8541	+	42.6385i	−0.443232	+	1.36413i	0.441179	+	0.897419i	$0.354560\pi$
$977$	−13.8541	+	42.6385i	−0.443232	+	1.36413i	−0.884411	+	0.466709i	$0.845440\pi$
$978$	1.34752			0.0430891
$979$	−9.09017	−	36.1401i	−0.290523	−	1.15504i
$980$	26.7984			0.856043
$981$	1.00000	−	3.07768i	0.0319275	−	0.0982629i
$982$	13.6353	−	9.90659i	0.435118	−	0.316132i
$983$	−47.0344	−	34.1725i	−1.50017	−	1.08993i	−0.970315	−	0.241843i	$-0.922248\pi$
$983$	−47.0344	−	34.1725i	−1.50017	−	1.08993i	−0.529850	−	0.848091i	$-0.677752\pi$
$984$	2.94427	+	9.06154i	0.0938600	+	0.288871i
$985$	−9.00000	−	27.6992i	−0.286764	−	0.882568i
$986$	−28.6525	−	20.8172i	−0.912481	−	0.662956i
$987$	−10.8541	+	7.88597i	−0.345490	+	0.251013i
$988$	0.763932	−	2.35114i	0.0243039	−	0.0747998i
$989$	71.3951			2.27023
$990$	−5.35410	−	0.363271i	−0.170165	−	0.0115455i
$991$	18.3607			0.583246			0.291623	−	0.956533i	$-0.405805\pi$
$991$	18.3607			0.583246			0.291623	+	0.956533i	$0.405805\pi$
$992$	0.618034	−	1.90211i	0.0196226	−	0.0603921i
$993$	6.00000	−	4.35926i	0.190404	−	0.138337i
$994$	19.4164	+	14.1068i	0.615851	+	0.447442i
$995$	7.28115	+	22.4091i	0.230828	+	0.710416i
$996$	8.52786	+	26.2461i	0.270216	+	0.831638i
$997$	−9.92705	−	7.21242i	−0.314393	−	0.228420i	0.419386	−	0.907808i	$-0.362245\pi$
$997$	−9.92705	−	7.21242i	−0.314393	−	0.228420i	−0.733779	+	0.679388i	$0.762245\pi$
$998$	2.07295	−	1.50609i	0.0656181	−	0.0476743i
$999$	4.94427	−	15.2169i	0.156430	−	0.481442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.d.229.1	yes	4
11.4	even	5		4598.2.a.bb.1.2		2
11.5	even	5	inner	418.2.f.d.115.1	✓	4
11.7	odd	10		4598.2.a.t.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.d.115.1	✓	4	11.5	even	5	inner
418.2.f.d.229.1	yes	4	1.1	even	1	trivial
4598.2.a.t.1.2		2	11.7	odd	10
4598.2.a.bb.1.2		2	11.4	even	5

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.61803 - 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(3.92705 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(1.61803 - 1.17557i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 + 1.53884i) q^{5} +(-0.618034 - 1.90211i) q^{6} +(3.92705 + 2.85317i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +1.61803 q^{10} +(-0.809017 - 3.21644i) q^{11} -2.00000 q^{12} +(0.763932 - 2.35114i) q^{13} +(3.92705 - 2.85317i) q^{14} +(2.61803 + 1.90211i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.04508 + 3.21644i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-0.809017 + 0.587785i) q^{19} +(0.500000 - 1.53884i) q^{20} +9.70820 q^{21} +(-3.30902 - 0.224514i) q^{22} -7.85410 q^{23} +(-0.618034 + 1.90211i) q^{24} +(1.92705 - 1.40008i) q^{25} +(-2.00000 - 1.45309i) q^{26} +(1.23607 + 3.80423i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(-8.47214 - 6.15537i) q^{29} +(2.61803 - 1.90211i) q^{30} +(0.618034 - 1.90211i) q^{31} +1.00000 q^{32} +(-5.09017 - 4.25325i) q^{33} +3.38197 q^{34} +(-2.42705 + 7.46969i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-3.23607 - 2.35114i) q^{37} +(0.309017 + 0.951057i) q^{38} +(-1.52786 - 4.70228i) q^{39} +(-1.30902 - 0.951057i) q^{40} +(3.85410 - 2.80017i) q^{41} +(3.00000 - 9.23305i) q^{42} -9.09017 q^{43} +(-1.23607 + 3.07768i) q^{44} +1.61803 q^{45} +(-2.42705 + 7.46969i) q^{46} +(-1.11803 + 0.812299i) q^{47} +(1.61803 + 1.17557i) q^{48} +(5.11803 + 15.7517i) q^{49} +(-0.736068 - 2.26538i) q^{50} +(5.47214 + 3.97574i) q^{51} +(-2.00000 + 1.45309i) q^{52} +(-1.47214 + 4.53077i) q^{53} +4.00000 q^{54} +(4.54508 - 2.85317i) q^{55} -4.85410 q^{56} +(-0.618034 + 1.90211i) q^{57} +(-8.47214 + 6.15537i) q^{58} +(2.85410 + 2.07363i) q^{59} +(-1.00000 - 3.07768i) q^{60} +(-2.95492 - 9.09429i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(3.92705 - 2.85317i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +(-5.61803 + 3.52671i) q^{66} +2.76393 q^{67} +(1.04508 - 3.21644i) q^{68} +(-12.7082 + 9.23305i) q^{69} +(6.35410 + 4.61653i) q^{70} +(1.52786 + 4.70228i) q^{71} +(0.309017 + 0.951057i) q^{72} +(11.3262 + 8.22899i) q^{73} +(-3.23607 + 2.35114i) q^{74} +(1.47214 - 4.53077i) q^{75} +1.00000 q^{76} +(6.00000 - 14.9394i) q^{77} -4.94427 q^{78} +(1.14590 - 3.52671i) q^{79} +(-1.30902 + 0.951057i) q^{80} +(8.89919 + 6.46564i) q^{81} +(-1.47214 - 4.53077i) q^{82} +(-4.26393 - 13.1230i) q^{83} +(-7.85410 - 5.70634i) q^{84} +(-4.42705 + 3.21644i) q^{85} +(-2.80902 + 8.64527i) q^{86} -20.9443 q^{87} +(2.54508 + 2.12663i) q^{88} +11.2361 q^{89} +(0.500000 - 1.53884i) q^{90} +(9.70820 - 7.05342i) q^{91} +(6.35410 + 4.61653i) q^{92} +(-1.23607 - 3.80423i) q^{93} +(0.427051 + 1.31433i) q^{94} +(-1.30902 - 0.951057i) q^{95} +(1.61803 - 1.17557i) q^{96} +(-2.85410 + 8.78402i) q^{97} +16.5623 q^{98} +(-3.30902 - 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9	\( 4 q - q^{2} + 2 q^{3} - q^{4} + 2 q^{5} + 2 q^{6} + 9 q^{7} - q^{8} - q^{9} + 2 q^{10} - q^{11} - 8 q^{12} + 12 q^{13} + 9 q^{14} + 6 q^{15} - q^{16} - 7 q^{17} - q^{18} - q^{19} + 2 q^{20} + 12 q^{21} - 11 q^{22} - 18 q^{23} + 2 q^{24} + q^{25} - 8 q^{26} - 4 q^{27} - 6 q^{28} - 16 q^{29} + 6 q^{30} - 2 q^{31} + 4 q^{32} + 2 q^{33} + 18 q^{34} - 3 q^{35} - q^{36} - 4 q^{37} - q^{38} - 24 q^{39} - 3 q^{40} + 2 q^{41} + 12 q^{42} - 14 q^{43} + 4 q^{44} + 2 q^{45} - 3 q^{46} + 2 q^{48} + 16 q^{49} + 6 q^{50} + 4 q^{51} - 8 q^{52} + 12 q^{53} + 16 q^{54} + 7 q^{55} - 6 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{59} - 4 q^{60} - 23 q^{61} - 2 q^{62} + 9 q^{63} - q^{64} + 16 q^{65} - 18 q^{66} + 20 q^{67} - 7 q^{68} - 24 q^{69} + 12 q^{70} + 24 q^{71} - q^{72} + 14 q^{73} - 4 q^{74} - 12 q^{75} + 4 q^{76} + 24 q^{77} + 16 q^{78} + 18 q^{79} - 3 q^{80} + 11 q^{81} + 12 q^{82} - 26 q^{83} - 18 q^{84} - 11 q^{85} - 9 q^{86} - 48 q^{87} - q^{88} + 36 q^{89} + 2 q^{90} + 12 q^{91} + 12 q^{92} + 4 q^{93} - 5 q^{94} - 3 q^{95} + 2 q^{96} + 2 q^{97} + 26 q^{98} - 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + 2 * q^3 - q^4 + 2 * q^5 + 2 * q^6 + 9 * q^7 - q^8 - q^9 + 2 * q^10 - q^11 - 8 * q^12 + 12 * q^13 + 9 * q^14 + 6 * q^15 - q^16 - 7 * q^17 - q^18 - q^19 + 2 * q^20 + 12 * q^21 - 11 * q^22 - 18 * q^23 + 2 * q^24 + q^25 - 8 * q^26 - 4 * q^27 - 6 * q^28 - 16 * q^29 + 6 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^33 + 18 * q^34 - 3 * q^35 - q^36 - 4 * q^37 - q^38 - 24 * q^39 - 3 * q^40 + 2 * q^41 + 12 * q^42 - 14 * q^43 + 4 * q^44 + 2 * q^45 - 3 * q^46 + 2 * q^48 + 16 * q^49 + 6 * q^50 + 4 * q^51 - 8 * q^52 + 12 * q^53 + 16 * q^54 + 7 * q^55 - 6 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^59 - 4 * q^60 - 23 * q^61 - 2 * q^62 + 9 * q^63 - q^64 + 16 * q^65 - 18 * q^66 + 20 * q^67 - 7 * q^68 - 24 * q^69 + 12 * q^70 + 24 * q^71 - q^72 + 14 * q^73 - 4 * q^74 - 12 * q^75 + 4 * q^76 + 24 * q^77 + 16 * q^78 + 18 * q^79 - 3 * q^80 + 11 * q^81 + 12 * q^82 - 26 * q^83 - 18 * q^84 - 11 * q^85 - 9 * q^86 - 48 * q^87 - q^88 + 36 * q^89 + 2 * q^90 + 12 * q^91 + 12 * q^92 + 4 * q^93 - 5 * q^94 - 3 * q^95 + 2 * q^96 + 2 * q^97 + 26 * q^98 - 11 * q^99

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