LMFDB - Embedded newform 440.2.bi.b.301.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [440,2,Mod(141,440)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(440, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 0, 6]))

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

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

chi := DirichletCharacter("440.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.bi (of order $10$, 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:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			301.1
Root			$0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	440.301
Dual form			440.2.bi.b.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39680 + 0.221232i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(2.26007 + 0.357960i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(-1.39680 + 0.221232i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(2.26007 + 0.357960i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(1.00000 + 1.00000i) q^{10} +(3.30220 + 0.309017i) q^{11} -3.23607 q^{12} +(-3.07768 + 4.23607i) q^{13} +(3.36176 + 6.59783i) q^{14} +(0.500000 + 1.53884i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.11803 - 1.53884i) q^{17} +(0.481305 + 0.245237i) q^{18} +(-2.93893 - 0.954915i) q^{19} +(-1.61803 - 1.17557i) q^{20} +8.47214i q^{21} +(-4.68088 + 0.298915i) q^{22} +1.23607 q^{23} +(4.52015 - 0.715921i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(3.36176 - 6.59783i) q^{26} +(3.21644 + 4.42705i) q^{27} +(-6.15537 - 8.47214i) q^{28} +(-3.80423 + 1.23607i) q^{29} +(-1.03884 - 2.03884i) q^{30} +(-1.61803 - 1.17557i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.92705 - 2.12663i) q^{33} +(-2.61803 + 2.61803i) q^{34} +(-3.07768 + 4.23607i) q^{35} +(-0.726543 - 0.236068i) q^{36} +(-7.60845 + 2.47214i) q^{37} +(4.31636 + 0.683644i) q^{38} +(6.85410 - 4.97980i) q^{39} +(2.52015 + 1.28408i) q^{40} +(-2.97214 + 9.14729i) q^{41} +(-1.87431 - 11.8339i) q^{42} -4.85410i q^{43} +(6.47214 - 1.45309i) q^{44} +0.381966i q^{45} +(-1.72654 + 0.273457i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(-6.15537 + 2.00000i) q^{48} +(-16.5172 + 12.0005i) q^{49} +(0.221232 - 1.39680i) q^{50} +(-4.02874 + 1.30902i) q^{51} +(-3.23607 + 9.95959i) q^{52} +(4.25325 - 5.85410i) q^{53} +(-5.47214 - 5.47214i) q^{54} +(-1.69098 - 2.85317i) q^{55} +(10.4721 + 10.4721i) q^{56} +(4.04508 + 2.93893i) q^{57} +(5.04029 - 2.56816i) q^{58} +(0.587785 - 0.190983i) q^{59} +(1.90211 + 2.61803i) q^{60} +(-2.62866 - 3.61803i) q^{61} +(2.52015 + 1.28408i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(4.70228 - 6.47214i) q^{64} +5.23607 q^{65} +(7.35259 + 1.88046i) q^{66} +2.32624i q^{67} +(3.07768 - 4.23607i) q^{68} +(-1.90211 - 0.618034i) q^{69} +(3.36176 - 6.59783i) q^{70} +(5.61803 - 4.08174i) q^{71} +(1.06706 + 0.169006i) q^{72} +(-0.354102 - 1.08981i) q^{73} +(10.0806 - 5.13632i) q^{74} +(0.951057 - 1.30902i) q^{75} -6.18034 q^{76} +(-3.80423 - 16.9443i) q^{77} +(-8.47214 + 8.47214i) q^{78} +(-12.7082 - 9.23305i) q^{79} +(-3.80423 - 1.23607i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(2.12781 - 13.4345i) q^{82} +(-1.40008 - 1.92705i) q^{83} +(5.23607 + 16.1150i) q^{84} +(-2.48990 - 0.809017i) q^{85} +(1.07388 + 6.78022i) q^{86} +6.47214 q^{87} +(-8.71883 + 3.46151i) q^{88} +14.5623 q^{89} +(-0.0845030 - 0.533531i) q^{90} +(26.0746 + 8.47214i) q^{91} +(2.35114 - 0.763932i) q^{92} +(1.90211 + 2.61803i) q^{93} +(1.53629 - 9.69977i) q^{94} +(0.954915 + 2.93893i) q^{95} +(8.15537 - 4.15537i) q^{96} +(11.3992 + 8.28199i) q^{97} +(20.4164 - 20.4164i) q^{98} +(-0.951057 - 0.836881i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9	$ 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9} + 8 q^{10} - 8 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 4 q^{20} - 22 q^{22} - 8 q^{23} + 12 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{30} - 4 q^{31} - 32 q^{32} - 26 q^{33} - 12 q^{34} + 20 q^{38} + 28 q^{39} - 4 q^{40} + 12 q^{41} - 28 q^{42} + 16 q^{44} - 8 q^{46} - 44 q^{47} - 74 q^{49} + 2 q^{50} - 8 q^{52} - 8 q^{54} - 18 q^{55} + 48 q^{56} + 10 q^{57} - 8 q^{58} - 4 q^{62} + 4 q^{63} + 24 q^{65} + 4 q^{66} - 4 q^{70} + 36 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 40 q^{76} - 32 q^{78} - 48 q^{79} - 28 q^{81} + 22 q^{82} + 24 q^{84} + 18 q^{86} + 16 q^{87} - 4 q^{88} + 36 q^{89} + 2 q^{90} + 36 q^{94} + 30 q^{95} + 16 q^{96} + 42 q^{97} + 56 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9 + 8 * q^10 - 8 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 4 * q^20 - 22 * q^22 - 8 * q^23 + 12 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^30 - 4 * q^31 - 32 * q^32 - 26 * q^33 - 12 * q^34 + 20 * q^38 + 28 * q^39 - 4 * q^40 + 12 * q^41 - 28 * q^42 + 16 * q^44 - 8 * q^46 - 44 * q^47 - 74 * q^49 + 2 * q^50 - 8 * q^52 - 8 * q^54 - 18 * q^55 + 48 * q^56 + 10 * q^57 - 8 * q^58 - 4 * q^62 + 4 * q^63 + 24 * q^65 + 4 * q^66 - 4 * q^70 + 36 * q^71 - 4 * q^72 + 24 * q^73 - 16 * q^74 + 40 * q^76 - 32 * q^78 - 48 * q^79 - 28 * q^81 + 22 * q^82 + 24 * q^84 + 18 * q^86 + 16 * q^87 - 4 * q^88 + 36 * q^89 + 2 * q^90 + 36 * q^94 + 30 * q^95 + 16 * q^96 + 42 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.39680	+	0.221232i	−0.987688	+	0.156434i
$2$	−1.39680	+	0.221232i	−0.987688	+	0.156434i
$3$	−1.53884	−	0.500000i	−0.888451	−	0.288675i	−0.170989	−	0.985273i	$-0.554696\pi$
$3$	−1.53884	−	0.500000i	−0.888451	−	0.288675i	−0.717462	+	0.696598i	$0.754696\pi$
$4$	1.90211	−	0.618034i	0.951057	−	0.309017i
$5$	−0.587785	−	0.809017i	−0.262866	−	0.361803i
$5$	−0.587785	−	0.809017i	−0.262866	−	0.361803i
$6$	2.26007	+	0.357960i	0.922671	+	0.146137i
$7$	−1.61803	−	4.97980i	−0.611559	−	1.88219i	−0.443083	−	0.896480i	$-0.646115\pi$
$7$	−1.61803	−	4.97980i	−0.611559	−	1.88219i	−0.168476	−	0.985706i	$-0.553885\pi$
$8$	−2.52015	+	1.28408i	−0.891007	+	0.453990i
$9$	−0.309017	−	0.224514i	−0.103006	−	0.0748380i
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	3.30220	+	0.309017i	0.995650	+	0.0931721i
$11$	3.30220	+	0.309017i	0.995650	+	0.0931721i
$12$	−3.23607			−0.934172
$13$	−3.07768	+	4.23607i	−0.853596	+	1.17487i	0.129463	+	0.991584i	$0.458675\pi$
$13$	−3.07768	+	4.23607i	−0.853596	+	1.17487i	−0.983059	+	0.183290i	$0.941325\pi$
$14$	3.36176	+	6.59783i	0.898469	+	1.76334i
$15$	0.500000	+	1.53884i	0.129099	+	0.397327i
$16$	3.23607	−	2.35114i	0.809017	−	0.587785i
$17$	2.11803	−	1.53884i	0.513699	−	0.373224i	−0.300526	−	0.953774i	$-0.597162\pi$
$17$	2.11803	−	1.53884i	0.513699	−	0.373224i	0.814225	+	0.580550i	$0.197162\pi$
$18$	0.481305	+	0.245237i	0.113445	+	0.0578030i
$19$	−2.93893	−	0.954915i	−0.674236	−	0.219073i	−0.0481659	−	0.998839i	$-0.515338\pi$
$19$	−2.93893	−	0.954915i	−0.674236	−	0.219073i	−0.626070	+	0.779767i	$0.715338\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$			8.47214i			1.84877i
$22$	−4.68088	+	0.298915i	−0.997967	+	0.0637290i
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	4.52015	−	0.715921i	0.922671	−	0.146137i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	3.36176	−	6.59783i	0.659296	−	1.29394i
$27$	3.21644	+	4.42705i	0.619004	+	0.851986i
$28$	−6.15537	−	8.47214i	−1.16326	−	1.60108i
$29$	−3.80423	+	1.23607i	−0.706427	+	0.229532i	−0.640129	−	0.768268i	$-0.721119\pi$
$29$	−3.80423	+	1.23607i	−0.706427	+	0.229532i	−0.0662984	+	0.997800i	$0.521119\pi$
$30$	−1.03884	−	2.03884i	−0.189666	−	0.372240i
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	0.432923	−	0.901431i	$-0.357482\pi$
$31$	−1.61803	−	1.17557i	−0.290607	−	0.211139i	−0.723531	+	0.690292i	$0.757482\pi$
$32$	−4.00000	+	4.00000i	−0.707107	+	0.707107i
$33$	−4.92705	−	2.12663i	−0.857689	−	0.370198i
$34$	−2.61803	+	2.61803i	−0.448989	+	0.448989i
$35$	−3.07768	+	4.23607i	−0.520223	+	0.716026i
$36$	−0.726543	−	0.236068i	−0.121090	−	0.0393447i
$37$	−7.60845	+	2.47214i	−1.25082	+	0.406417i	−0.858215	−	0.513290i	$-0.828427\pi$
$37$	−7.60845	+	2.47214i	−1.25082	+	0.406417i	−0.392607	+	0.919707i	$0.628427\pi$
$38$	4.31636	+	0.683644i	0.700205	+	0.110902i
$39$	6.85410	−	4.97980i	1.09753	−	0.797406i
$40$	2.52015	+	1.28408i	0.398470	+	0.203031i
$41$	−2.97214	+	9.14729i	−0.464170	+	1.42857i	0.395854	+	0.918313i	$0.370449\pi$
$41$	−2.97214	+	9.14729i	−0.464170	+	1.42857i	−0.860024	+	0.510254i	$0.829551\pi$
$42$	−1.87431	−	11.8339i	−0.289212	−	1.82601i
$43$		−	4.85410i		−	0.740244i	−0.928983	−	0.370122i	$-0.879316\pi$
$43$		−	4.85410i		−	0.740244i	0.928983	−	0.370122i	$-0.120684\pi$
$44$	6.47214	−	1.45309i	0.975711	−	0.219061i
$45$			0.381966i			0.0569401i
$46$	−1.72654	+	0.273457i	−0.254565	+	0.0403191i
$47$	−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	$0.930953\pi$
$48$	−6.15537	+	2.00000i	−0.888451	+	0.288675i
$49$	−16.5172	+	12.0005i	−2.35960	+	1.71435i
$50$	0.221232	−	1.39680i	0.0312869	−	0.197538i
$51$	−4.02874	+	1.30902i	−0.564136	+	0.183299i
$52$	−3.23607	+	9.95959i	−0.448762	+	1.38115i
$53$	4.25325	−	5.85410i	0.584229	−	0.804123i	−0.409922	−	0.912121i	$-0.634444\pi$
$53$	4.25325	−	5.85410i	0.584229	−	0.804123i	0.994151	+	0.107998i	$0.0344440\pi$
$54$	−5.47214	−	5.47214i	−0.744663	−	0.744663i
$55$	−1.69098	−	2.85317i	−0.228012	−	0.384721i
$56$	10.4721	+	10.4721i	1.39940	+	1.39940i
$57$	4.04508	+	2.93893i	0.535785	+	0.389270i
$58$	5.04029	−	2.56816i	0.661823	−	0.337216i
$59$	0.587785	−	0.190983i	0.0765231	−	0.0248639i	−0.270505	−	0.962718i	$-0.587191\pi$
$59$	0.587785	−	0.190983i	0.0765231	−	0.0248639i	0.347028	+	0.937855i	$0.387191\pi$
$60$	1.90211	+	2.61803i	0.245562	+	0.337987i
$61$	−2.62866	−	3.61803i	−0.336565	−	0.463242i	0.606869	−	0.794802i	$-0.292425\pi$
$61$	−2.62866	−	3.61803i	−0.336565	−	0.463242i	−0.943434	+	0.331560i	$0.892425\pi$
$62$	2.52015	+	1.28408i	0.320059	+	0.163078i
$63$	−0.618034	+	1.90211i	−0.0778650	+	0.239644i
$64$	4.70228	−	6.47214i	0.587785	−	0.809017i
$65$	5.23607			0.649454
$66$	7.35259	+	1.88046i	0.905042	+	0.231468i
$67$			2.32624i			0.284195i	0.989853	+	0.142098i	$0.0453847\pi$
$67$			2.32624i			0.284195i	−0.989853	+	0.142098i	$0.954615\pi$
$68$	3.07768	−	4.23607i	0.373224	−	0.513699i
$69$	−1.90211	−	0.618034i	−0.228988	−	0.0744025i
$70$	3.36176	−	6.59783i	0.401807	−	0.788592i
$71$	5.61803	−	4.08174i	0.666738	−	0.484413i	−0.202194	−	0.979346i	$-0.564807\pi$
$71$	5.61803	−	4.08174i	0.666738	−	0.484413i	0.868932	+	0.494932i	$0.164807\pi$
$72$	1.06706	+	0.169006i	0.125754	+	0.0199175i
$73$	−0.354102	−	1.08981i	−0.0414445	−	0.127553i	0.928193	−	0.372098i	$-0.121361\pi$
$73$	−0.354102	−	1.08981i	−0.0414445	−	0.127553i	−0.969638	+	0.244545i	$0.921361\pi$
$74$	10.0806	−	5.13632i	1.17184	−	0.597085i
$75$	0.951057	−	1.30902i	0.109819	−	0.151152i
$76$	−6.18034			−0.708934
$77$	−3.80423	−	16.9443i	−0.433532	−	1.93098i
$78$	−8.47214	+	8.47214i	−0.959280	+	0.959280i
$79$	−12.7082	−	9.23305i	−1.42978	−	1.03880i	−0.990057	−	0.140668i	$-0.955075\pi$
$79$	−12.7082	−	9.23305i	−1.42978	−	1.03880i	−0.439728	−	0.898131i	$-0.644925\pi$
$80$	−3.80423	−	1.23607i	−0.425325	−	0.138197i
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	2.12781	−	13.4345i	0.234978	−	1.48359i
$83$	−1.40008	−	1.92705i	−0.153679	−	0.211521i	0.725235	−	0.688502i	$-0.241731\pi$
$83$	−1.40008	−	1.92705i	−0.153679	−	0.211521i	−0.878914	+	0.476980i	$0.841731\pi$
$84$	5.23607	+	16.1150i	0.571302	+	1.75829i
$85$	−2.48990	−	0.809017i	−0.270067	−	0.0877502i
$86$	1.07388	+	6.78022i	0.115800	+	0.731130i
$87$	6.47214			0.693886
$88$	−8.71883	+	3.46151i	−0.929430	+	0.368999i
$89$	14.5623			1.54360			0.771801	−	0.635865i	$-0.219356\pi$
$89$	14.5623			1.54360			0.771801	+	0.635865i	$0.219356\pi$
$90$	−0.0845030	−	0.533531i	−0.00890740	−	0.0562391i
$91$	26.0746	+	8.47214i	2.73336	+	0.888121i
$92$	2.35114	−	0.763932i	0.245123	−	0.0796454i
$93$	1.90211	+	2.61803i	0.197240	+	0.271477i
$94$	1.53629	−	9.69977i	0.158457	−	1.00046i
$95$	0.954915	+	2.93893i	0.0979722	+	0.301527i
$96$	8.15537	−	4.15537i	0.832354	−	0.424105i
$97$	11.3992	+	8.28199i	1.15741	+	0.840909i	0.989449	−	0.144884i	$-0.0462809\pi$
$97$	11.3992	+	8.28199i	1.15741	+	0.840909i	0.167963	+	0.985793i	$0.446281\pi$
$98$	20.4164	−	20.4164i	2.06237	−	2.06237i
$99$	−0.951057	−	0.836881i	−0.0955848	−	0.0841097i
$100$			2.00000i			0.200000i
$101$	−4.80828	+	6.61803i	−0.478442	+	0.658519i	−0.978205	−	0.207643i	$-0.933421\pi$
$101$	−4.80828	+	6.61803i	−0.478442	+	0.658519i	0.499763	+	0.866162i	$0.333421\pi$
$102$	5.33776	−	2.71972i	0.528517	−	0.269293i
$103$	−0.527864	−	1.62460i	−0.0520120	−	0.160076i	0.921677	−	0.387959i	$-0.126820\pi$
$103$	−0.527864	−	1.62460i	−0.0520120	−	0.160076i	−0.973689	+	0.227883i	$0.926820\pi$
$104$	2.31677	−	14.6275i	0.227178	−	1.43434i
$105$	6.85410	−	4.97980i	0.668892	−	0.485978i
$106$	−4.64584	+	9.11798i	−0.451244	+	0.885616i
$107$	−8.42075	−	2.73607i	−0.814065	−	0.264506i	−0.127746	−	0.991807i	$-0.540774\pi$
$107$	−8.42075	−	2.73607i	−0.814065	−	0.264506i	−0.686318	+	0.727301i	$0.740774\pi$
$108$	8.85410	+	6.43288i	0.851986	+	0.619004i
$109$			7.52786i			0.721039i	0.932752	+	0.360519i	$0.117401\pi$
$109$			7.52786i			0.721039i	−0.932752	+	0.360519i	$0.882599\pi$
$110$	2.99318	+	3.61121i	0.285389	+	0.344316i
$111$	12.9443			1.22862
$112$	−16.9443	−	12.3107i	−1.60108	−	1.16326i
$113$	1.10081	−	3.38795i	0.103556	−	0.318712i	−0.885833	−	0.464004i	$-0.846412\pi$
$113$	1.10081	−	3.38795i	0.103556	−	0.318712i	0.989389	+	0.145292i	$0.0464122\pi$
$114$	−6.30037	−	3.21020i	−0.590083	−	0.300663i
$115$	−0.726543	−	1.00000i	−0.0677504	−	0.0932505i
$116$	−6.47214	+	4.70228i	−0.600923	+	0.436596i
$117$	1.90211	−	0.618034i	0.175850	−	0.0571373i
$118$	−0.778768	+	0.396802i	−0.0716914	+	0.0365286i
$119$	−11.0902	−	8.05748i	−1.01663	−	0.738628i
$120$	−3.23607	−	3.23607i	−0.295411	−	0.295411i
$121$	10.8090	+	2.04087i	0.982638	+	0.185534i
$122$	4.47214	+	4.47214i	0.404888	+	0.404888i
$123$	9.14729	−	12.5902i	0.824784	−	1.13522i
$124$	−3.80423	−	1.23607i	−0.341630	−	0.111002i
$125$	0.951057	−	0.309017i	0.0850651	−	0.0276393i
$126$	0.442463	−	2.79360i	0.0394178	−	0.248874i
$127$	−3.47214	+	2.52265i	−0.308102	+	0.223849i	−0.731082	−	0.682290i	$-0.760984\pi$
$127$	−3.47214	+	2.52265i	−0.308102	+	0.223849i	0.422980	+	0.906139i	$0.360984\pi$
$128$	−5.13632	+	10.0806i	−0.453990	+	0.891007i
$129$	−2.42705	+	7.46969i	−0.213690	+	0.657670i
$130$	−7.31375	+	1.15838i	−0.641458	+	0.101597i
$131$		−	0.326238i		−	0.0285035i	−0.999898	−	0.0142518i	$-0.995463\pi$
$131$		−	0.326238i		−	0.0285035i	0.999898	−	0.0142518i	$-0.00453663\pi$
$132$	−10.6861	−	1.00000i	−0.930109	−	0.0870388i
$133$			16.1803i			1.40301i
$134$	−0.514638	−	3.24929i	−0.0444579	−	0.280696i
$135$	1.69098	−	5.20431i	0.145537	−	0.447916i
$136$	−3.36176	+	6.59783i	−0.288269	+	0.565759i
$137$	−7.39919	+	5.37582i	−0.632155	+	0.459288i	−0.857146	−	0.515073i	$-0.827765\pi$
$137$	−7.39919	+	5.37582i	−0.632155	+	0.459288i	0.224991	+	0.974361i	$0.427765\pi$
$138$	2.79360	+	0.442463i	0.237807	+	0.0376650i
$139$	−9.95959	+	3.23607i	−0.844762	+	0.274480i	−0.699250	−	0.714877i	$-0.746483\pi$
$139$	−9.95959	+	3.23607i	−0.844762	+	0.274480i	−0.145511	+	0.989357i	$0.546483\pi$
$140$	−3.23607	+	9.95959i	−0.273498	+	0.841739i
$141$	6.60440	−	9.09017i	0.556190	−	0.765530i
$142$	−6.94427	+	6.94427i	−0.582750	+	0.582750i
$143$	−11.4721	+	13.0373i	−0.959348	+	1.09023i
$144$	−1.52786			−0.127322
$145$	3.23607	+	2.35114i	0.268741	+	0.195252i
$146$	0.735712	+	1.44392i	0.0608879	+	0.119499i
$147$	31.4176	−	10.2082i	2.59128	−	0.841958i
$148$	−12.9443	+	9.40456i	−1.06401	+	0.773050i
$149$	−6.60440	−	9.09017i	−0.541053	−	0.744696i	0.447711	−	0.894178i	$-0.352239\pi$
$149$	−6.60440	−	9.09017i	−0.541053	−	0.744696i	−0.988764	+	0.149482i	$0.952239\pi$
$150$	−1.03884	+	2.03884i	−0.0848211	+	0.166471i
$151$	6.76393	−	20.8172i	0.550441	−	1.69408i	−0.157248	−	0.987559i	$-0.550262\pi$
$151$	6.76393	−	20.8172i	0.550441	−	1.69408i	0.707689	−	0.706524i	$-0.249738\pi$
$152$	8.63271	−	1.36729i	0.700205	−	0.110902i
$153$	−1.00000			−0.0808452
$154$	9.06236	+	22.8262i	0.730266	+	1.83939i
$155$			2.00000i			0.160644i
$156$	9.95959	−	13.7082i	0.797406	−	1.09753i
$157$	−3.52671	−	1.14590i	−0.281462	−	0.0914526i	0.164884	−	0.986313i	$-0.447275\pi$
$157$	−3.52671	−	1.14590i	−0.281462	−	0.0914526i	−0.446346	+	0.894860i	$0.647275\pi$
$158$	19.7935	+	10.0853i	1.57469	+	0.802342i
$159$	−9.47214	+	6.88191i	−0.751189	+	0.545771i
$160$	5.58721	+	0.884927i	0.441708	+	0.0699596i
$161$	−2.00000	−	6.15537i	−0.157622	−	0.485111i
$162$	4.94897	+	9.71290i	0.388828	+	0.763118i
$163$	3.88998	−	5.35410i	0.304687	−	0.419366i	−0.629028	−	0.777383i	$-0.716547\pi$
$163$	3.88998	−	5.35410i	0.304687	−	0.419366i	0.933715	+	0.358017i	$0.116547\pi$
$164$			19.2361i			1.50208i
$165$	1.17557	+	5.23607i	0.0915180	+	0.407627i
$166$	2.38197	+	2.38197i	0.184876	+	0.184876i
$167$	11.7082	+	8.50651i	0.906008	+	0.658253i	0.940002	−	0.341169i	$-0.110823\pi$
$167$	11.7082	+	8.50651i	0.906008	+	0.658253i	−0.0339941	+	0.999422i	$0.510823\pi$
$168$	−10.8789	−	21.3510i	−0.839325	−	1.64727i
$169$	−4.45492	−	13.7108i	−0.342686	−	1.05468i
$170$	3.65688	+	0.579192i	0.280470	+	0.0444220i
$171$	0.693786	+	0.954915i	0.0530552	+	0.0730242i
$172$	−3.00000	−	9.23305i	−0.228748	−	0.704014i
$173$	−4.53077	−	1.47214i	−0.344468	−	0.111924i	0.131673	−	0.991293i	$-0.457965\pi$
$173$	−4.53077	−	1.47214i	−0.344468	−	0.111924i	−0.476141	+	0.879369i	$0.657965\pi$
$174$	−9.04029	+	1.43184i	−0.685343	+	0.108548i
$175$	5.23607			0.395810
$176$	11.4127	−	6.76393i	0.860263	−	0.509851i
$177$	−1.00000			−0.0751646
$178$	−20.3407	+	3.22164i	−1.52460	+	0.241472i
$179$	−13.1760	−	4.28115i	−0.984823	−	0.319988i	−0.228038	−	0.973652i	$-0.573231\pi$
$179$	−13.1760	−	4.28115i	−0.984823	−	0.319988i	−0.756785	+	0.653664i	$0.773231\pi$
$180$	0.236068	+	0.726543i	0.0175955	+	0.0541533i
$181$	−11.7557	−	16.1803i	−0.873795	−	1.20268i	−0.978101	−	0.208130i	$-0.933262\pi$
$181$	−11.7557	−	16.1803i	−0.873795	−	1.20268i	0.104306	−	0.994545i	$-0.466738\pi$
$182$	−38.2953	−	6.06538i	−2.83864	−	0.449596i
$183$	2.23607	+	6.88191i	0.165295	+	0.508725i
$184$	−3.11507	+	1.58721i	−0.229646	+	0.117011i
$185$	6.47214	+	4.70228i	0.475841	+	0.345719i
$186$	−3.23607	−	3.23607i	−0.237280	−	0.237280i
$187$	7.46969	−	4.42705i	0.546238	−	0.323738i
$188$			13.8885i			1.01293i
$189$	16.8415	−	23.1803i	1.22504	−	1.68612i
$190$	−1.98401	−	3.89384i	−0.143935	−	0.282489i
$191$	−3.14590	−	9.68208i	−0.227629	−	0.700571i	−0.998014	−	0.0629915i	$-0.979936\pi$
$191$	−3.14590	−	9.68208i	−0.227629	−	0.700571i	0.770385	−	0.637579i	$-0.220064\pi$
$192$	−10.4721	+	7.60845i	−0.755761	+	0.549093i
$193$	4.85410	−	3.52671i	0.349406	−	0.253858i	−0.399214	−	0.916858i	$-0.630717\pi$
$193$	4.85410	−	3.52671i	0.349406	−	0.253858i	0.748620	+	0.663000i	$0.230717\pi$
$194$	−17.7546	−	9.04645i	−1.27471	−	0.649497i
$195$	−8.05748	−	2.61803i	−0.577008	−	0.187481i
$196$	−24.0009	+	33.0344i	−1.71435	+	2.35960i
$197$		−	2.94427i		−	0.209771i	−0.994484	−	0.104885i	$-0.966552\pi$
$197$		−	2.94427i		−	0.209771i	0.994484	−	0.104885i	$-0.0334476\pi$
$198$	1.51358	+	0.958553i	0.107566	+	0.0681214i
$199$	−22.6525			−1.60579			−0.802896	−	0.596120i	$-0.796708\pi$
$199$	−22.6525			−1.60579			−0.802896	+	0.596120i	$0.796708\pi$
$200$	−0.442463	−	2.79360i	−0.0312869	−	0.197538i
$201$	1.16312	−	3.57971i	0.0820401	−	0.252493i
$202$	5.25210	−	10.3078i	0.369537	−	0.725256i
$203$	12.3107	+	16.9443i	0.864044	+	1.18925i
$204$	−6.85410	+	4.97980i	−0.479883	+	0.348655i
$205$	9.14729	−	2.97214i	0.638875	−	0.207583i
$206$	1.09673	+	2.15246i	0.0764131	+	0.149969i
$207$	−0.381966	−	0.277515i	−0.0265485	−	0.0192886i
$208$			20.9443i			1.45222i
$209$	−9.40983	−	4.06150i	−0.650892	−	0.280940i
$210$	−8.47214	+	8.47214i	−0.584633	+	0.584633i
$211$	−8.73102	+	12.0172i	−0.601068	+	0.827300i	−0.995806	−	0.0914944i	$-0.970836\pi$
$211$	−8.73102	+	12.0172i	−0.601068	+	0.827300i	0.394737	+	0.918794i	$0.370836\pi$
$212$	4.47214	−	13.7638i	0.307148	−	0.945303i
$213$	−10.6861	+	3.47214i	−0.732202	+	0.237907i
$214$	12.3674	+	1.95881i	0.845420	+	0.133901i
$215$	−3.92705	+	2.85317i	−0.267823	+	0.194585i
$216$	−13.7906	−	7.02666i	−0.938331	−	0.478103i
$217$	−3.23607	+	9.95959i	−0.219679	+	0.676101i
$218$	−1.66540	−	10.5149i	−0.112795	−	0.712161i
$219$			1.85410i			0.125289i
$220$	−4.97980	−	4.38197i	−0.335738	−	0.295432i
$221$			13.7082i			0.922114i
$222$	−18.0806	+	2.86368i	−1.21349	+	0.192198i
$223$	2.00000	−	6.15537i	0.133930	−	0.412194i	−0.861492	−	0.507771i	$-0.830470\pi$
$223$	2.00000	−	6.15537i	0.133930	−	0.412194i	0.995422	+	0.0955771i	$0.0304696\pi$
$224$	26.3913	+	13.4471i	1.76334	+	0.898469i
$225$	0.309017	−	0.224514i	0.0206011	−	0.0149676i
$226$	−0.788095	+	4.97584i	−0.0524233	+	0.330988i
$227$	−20.6785	+	6.71885i	−1.37248	+	0.445946i	−0.900190	−	0.435498i	$-0.856572\pi$
$227$	−20.6785	+	6.71885i	−1.37248	+	0.445946i	−0.472290	+	0.881443i	$0.656572\pi$
$228$	9.51057	+	3.09017i	0.629853	+	0.204652i
$229$	15.6659	−	21.5623i	1.03523	−	1.42488i	0.134290	−	0.990942i	$-0.457125\pi$
$229$	15.6659	−	21.5623i	1.03523	−	1.42488i	0.900944	−	0.433935i	$-0.142875\pi$
$230$	1.23607	+	1.23607i	0.0815039	+	0.0815039i
$231$	−2.61803	+	27.9767i	−0.172254	+	1.84073i
$232$	8.00000	−	8.00000i	0.525226	−	0.525226i
$233$	−5.54508	−	4.02874i	−0.363271	−	0.263932i	0.391144	−	0.920329i	$-0.372079\pi$
$233$	−5.54508	−	4.02874i	−0.363271	−	0.263932i	−0.754415	+	0.656398i	$0.772079\pi$
$234$	−2.52015	+	1.28408i	−0.164747	+	0.0839429i
$235$	6.60440	−	2.14590i	0.430823	−	0.139983i
$236$	1.00000	−	0.726543i	0.0650945	−	0.0472939i
$237$	14.9394	+	20.5623i	0.970418	+	1.33567i
$238$	17.2733	+	8.80121i	1.11966	+	0.570498i
$239$	1.43769	−	4.42477i	0.0929967	−	0.286214i	−0.893730	−	0.448606i	$-0.851921\pi$
$239$	1.43769	−	4.42477i	0.0929967	−	0.286214i	0.986726	+	0.162391i	$0.0519207\pi$
$240$	5.23607	+	3.80423i	0.337987	+	0.245562i
$241$	−24.9787			−1.60902			−0.804510	−	0.593939i	$-0.797572\pi$
$241$	−24.9787			−1.60902			−0.804510	+	0.593939i	$0.797572\pi$
$242$	−15.5496	−	0.459395i	−0.999564	−	0.0295310i
$243$		−	3.94427i		−	0.253025i
$244$	−7.23607	−	5.25731i	−0.463242	−	0.336565i
$245$	19.4172	+	6.30902i	1.24052	+	0.403068i
$246$	−9.99162	+	19.6096i	−0.637042	+	1.25027i
$247$	13.0902	−	9.51057i	0.832908	−	0.605143i
$248$	5.58721	+	0.884927i	0.354788	+	0.0561929i
$249$	1.19098	+	3.66547i	0.0754755	+	0.232290i
$250$	−1.26007	+	0.642040i	−0.0796940	+	0.0406061i
$251$	7.05342	−	9.70820i	0.445208	−	0.612776i	−0.526151	−	0.850391i	$-0.676365\pi$
$251$	7.05342	−	9.70820i	0.445208	−	0.612776i	0.971360	+	0.237614i	$0.0763655\pi$
$252$			4.00000i			0.251976i
$253$	4.08174	+	0.381966i	0.256617	+	0.0240140i
$254$	4.29180	−	4.29180i	0.269291	−	0.269291i
$255$	3.42705	+	2.48990i	0.214610	+	0.155923i
$256$	4.94427	−	15.2169i	0.309017	−	0.951057i
$257$	−2.40983	−	7.41669i	−0.150321	−	0.462641i	0.847336	−	0.531058i	$-0.178205\pi$
$257$	−2.40983	−	7.41669i	−0.150321	−	0.462641i	−0.997657	+	0.0684169i	$0.978205\pi$
$258$	1.73758	−	10.9706i	0.108177	−	0.683001i
$259$	24.6215	+	33.8885i	1.52990	+	2.10573i
$260$	9.95959	−	3.23607i	0.617668	−	0.200692i
$261$	1.45309	+	0.472136i	0.0899437	+	0.0292245i
$262$	0.0721742	+	0.455690i	0.00445894	+	0.0281526i
$263$	−29.2361			−1.80277			−0.901387	−	0.433015i	$-0.857450\pi$
$263$	−29.2361			−1.80277			−0.901387	+	0.433015i	$0.857450\pi$
$264$	15.1477	−	0.967310i	0.932273	−	0.0595338i
$265$	−7.23607			−0.444508
$266$	−3.57960	−	22.6007i	−0.219480	−	1.38574i
$267$	−22.4091	−	7.28115i	−1.37141	−	0.445599i
$268$	1.43769	+	4.42477i	0.0878211	+	0.270286i
$269$	12.8658	+	17.7082i	0.784439	+	1.07969i	0.994778	+	0.102060i	$0.0325433\pi$
$269$	12.8658	+	17.7082i	0.784439	+	1.07969i	−0.210339	+	0.977629i	$0.567457\pi$
$270$	−1.21061	+	7.64349i	−0.0736754	+	0.465168i
$271$	0.708204	+	2.17963i	0.0430203	+	0.132403i	0.970260	−	0.242066i	$-0.0778250\pi$
$271$	0.708204	+	2.17963i	0.0430203	+	0.132403i	−0.927239	+	0.374469i	$0.877825\pi$
$272$	3.23607	−	9.95959i	0.196215	−	0.603889i
$273$	−35.8885	−	26.0746i	−2.17207	−	1.57810i
$274$	9.14590	−	9.14590i	0.552524	−	0.552524i
$275$	−1.31433	+	3.04508i	−0.0792569	+	0.183626i
$276$	−4.00000			−0.240772
$277$	7.88597	−	10.8541i	0.473822	−	0.652160i	−0.503481	−	0.864006i	$-0.667948\pi$
$277$	7.88597	−	10.8541i	0.473822	−	0.652160i	0.977303	+	0.211846i	$0.0679477\pi$
$278$	13.1957	−	6.72353i	0.791423	−	0.403250i
$279$	0.236068	+	0.726543i	0.0141330	+	0.0434970i
$280$	2.31677	−	14.6275i	0.138453	−	0.874161i
$281$	−2.54508	+	1.84911i	−0.151827	+	0.110309i	−0.661105	−	0.750293i	$-0.729912\pi$
$281$	−2.54508	+	1.84911i	−0.151827	+	0.110309i	0.509278	+	0.860602i	$0.329912\pi$
$282$	−7.21400	+	14.1583i	−0.429587	+	0.843113i
$283$	−1.45309	−	0.472136i	−0.0863769	−	0.0280656i	0.265510	−	0.964108i	$-0.414460\pi$
$283$	−1.45309	−	0.472136i	−0.0863769	−	0.0280656i	−0.351887	+	0.936043i	$0.614460\pi$
$284$	8.16348	−	11.2361i	0.484413	−	0.666738i
$285$		−	5.00000i		−	0.296174i
$286$	13.1400	−	20.7485i	0.776987	−	1.22688i
$287$	50.3607			2.97270
$288$	2.13412	−	0.338012i	0.125754	−	0.0199175i
$289$	−3.13525	+	9.64932i	−0.184427	+	0.567607i
$290$	−5.04029	−	2.56816i	−0.295976	−	0.150807i
$291$	−13.4005	−	18.4443i	−0.785554	−	1.08122i
$292$	−1.34708	−	1.85410i	−0.0788321	−	0.108503i
$293$	0.620541	−	0.201626i	0.0362524	−	0.0117791i	−0.290835	−	0.956773i	$-0.593933\pi$
$293$	0.620541	−	0.201626i	0.0362524	−	0.0117791i	0.327087	+	0.944994i	$0.393933\pi$
$294$	−41.6258	+	21.2094i	−2.42767	+	1.23696i
$295$	−0.500000	−	0.363271i	−0.0291111	−	0.0211505i
$296$	16.0000	−	16.0000i	0.929981	−	0.929981i
$297$	9.25329	+	15.6129i	0.536930	+	0.905954i
$298$	11.2361	+	11.2361i	0.650888	+	0.650888i
$299$	−3.80423	+	5.23607i	−0.220004	+	0.302810i
$300$	1.00000	−	3.07768i	0.0577350	−	0.177690i
$301$	−24.1724	+	7.85410i	−1.39328	+	0.452703i
$302$	−4.84244	+	30.5740i	−0.278651	+	1.75933i
$303$	10.7082	−	7.77997i	0.615170	−	0.446947i
$304$	−11.7557	+	3.81966i	−0.674236	+	0.219073i
$305$	−1.38197	+	4.25325i	−0.0791311	+	0.243541i
$306$	1.39680	−	0.221232i	0.0798499	−	0.0126470i
$307$		−	14.5623i		−	0.831115i	−0.909567	−	0.415557i	$-0.863587\pi$
$307$		−	14.5623i		−	0.831115i	0.909567	−	0.415557i	$-0.136413\pi$
$308$	−17.7082	−	29.8788i	−1.00902	−	1.70250i
$309$			2.76393i			0.157235i
$310$	−0.442463	−	2.79360i	−0.0251302	−	0.158666i
$311$	−10.0902	+	31.0543i	−0.572161	+	1.76093i	0.0734877	+	0.997296i	$0.476587\pi$
$311$	−10.0902	+	31.0543i	−0.572161	+	1.76093i	−0.645649	+	0.763635i	$0.723413\pi$
$312$	−10.8789	+	21.3510i	−0.615896	+	1.20876i
$313$	11.1180	−	8.07772i	0.628428	−	0.456580i	−0.227427	−	0.973795i	$-0.573031\pi$
$313$	11.1180	−	8.07772i	0.628428	−	0.456580i	0.855855	+	0.517215i	$0.173031\pi$
$314$	5.17963	+	0.820372i	0.292303	+	0.0462963i
$315$	1.90211	−	0.618034i	0.107172	−	0.0348223i
$316$	−29.8788	−	9.70820i	−1.68081	−	0.546129i
$317$	−17.5680	+	24.1803i	−0.986720	+	1.35810i	−0.0535901	+	0.998563i	$0.517066\pi$
$317$	−17.5680	+	24.1803i	−0.986720	+	1.35810i	−0.933130	+	0.359540i	$0.882934\pi$
$318$	11.7082	−	11.7082i	0.656563	−	0.656563i
$319$	−12.9443	+	2.90617i	−0.724740	+	0.162714i
$320$	−8.00000			−0.447214
$321$	11.5902	+	8.42075i	0.646900	+	0.470001i
$322$	4.15537	+	8.15537i	0.231570	+	0.454481i
$323$	−7.69421	+	2.50000i	−0.428117	+	0.139104i
$324$	−9.06154	−	12.4721i	−0.503419	−	0.692896i
$325$	−3.07768	−	4.23607i	−0.170719	−	0.234975i
$326$	−4.24904	+	8.33921i	−0.235333	+	0.461866i
$327$	3.76393	−	11.5842i	0.208146	−	0.640607i
$328$	−4.25563	−	26.8690i	−0.234978	−	1.48359i
$329$	36.3607			2.00463
$330$	−2.80042	−	7.05368i	−0.154158	−	0.388292i
$331$		−	19.0344i		−	1.04623i	−0.852263	−	0.523114i	$-0.824770\pi$
$331$		−	19.0344i		−	1.04623i	0.852263	−	0.523114i	$-0.175230\pi$
$332$	−3.85410	−	2.80017i	−0.211521	−	0.153679i
$333$	2.90617	+	0.944272i	0.159257	+	0.0517458i
$334$	−18.2360	−	9.29168i	−0.997827	−	0.508418i
$335$	1.88197	−	1.36733i	0.102823	−	0.0747051i
$336$	19.9192	+	27.4164i	1.08668	+	1.49569i
$337$	−7.07953	−	21.7885i	−0.385646	−	1.18690i	−0.936010	−	0.351973i	$-0.885511\pi$
$337$	−7.07953	−	21.7885i	−0.385646	−	1.18690i	0.550364	−	0.834925i	$-0.314489\pi$
$338$	9.25590	+	18.1657i	0.503455	+	0.988086i
$339$	−3.38795	+	4.66312i	−0.184008	+	0.253266i
$340$	−5.23607			−0.283966
$341$	−4.97980	−	4.38197i	−0.269671	−	0.237297i
$342$	−1.18034	−	1.18034i	−0.0638255	−	0.0638255i
$343$	56.8328	+	41.2915i	3.06868	+	2.22953i
$344$	6.23305	+	12.2331i	0.336064	+	0.659562i
$345$	0.618034	+	1.90211i	0.0332738	+	0.102406i
$346$	6.65427	+	1.05393i	0.357736	+	0.0566598i
$347$	−9.70232	−	13.3541i	−0.520848	−	0.716886i	0.464853	−	0.885388i	$-0.346107\pi$
$347$	−9.70232	−	13.3541i	−0.520848	−	0.716886i	−0.985701	+	0.168502i	$0.946107\pi$
$348$	12.3107	−	4.00000i	0.659925	−	0.214423i
$349$	0.898056	+	0.291796i	0.0480718	+	0.0156195i	0.332954	−	0.942943i	$-0.391955\pi$
$349$	0.898056	+	0.291796i	0.0480718	+	0.0156195i	−0.284882	+	0.958562i	$0.591955\pi$
$350$	−7.31375	+	1.15838i	−0.390936	+	0.0619183i
$351$	−28.6525			−1.52936
$352$	−14.4449	+	11.9727i	−0.769914	+	0.638148i
$353$	4.14590			0.220664			0.110332	−	0.993895i	$-0.464809\pi$
$353$	4.14590			0.220664			0.110332	+	0.993895i	$0.464809\pi$
$354$	1.39680	−	0.221232i	0.0742392	−	0.0117583i
$355$	−6.60440	−	2.14590i	−0.350525	−	0.113892i
$356$	27.6992	−	9.00000i	1.46805	−	0.476999i
$357$	13.0373	+	17.9443i	0.690006	+	0.949712i
$358$	19.3514	+	3.06497i	1.02276	+	0.161989i
$359$	−0.944272	−	2.90617i	−0.0498368	−	0.153382i	0.923041	−	0.384702i	$-0.125696\pi$
$359$	−0.944272	−	2.90617i	−0.0498368	−	0.153382i	−0.972878	+	0.231320i	$0.925696\pi$
$360$	−0.490475	−	0.962611i	−0.0258503	−	0.0507340i
$361$	−7.64590	−	5.55507i	−0.402416	−	0.292372i
$362$	20.0000	+	20.0000i	1.05118	+	1.05118i
$363$	−15.6129	−	8.54508i	−0.819466	−	0.448501i
$364$	54.8328			2.87402
$365$	−0.673542	+	0.927051i	−0.0352548	+	0.0485241i
$366$	−4.64584	−	9.11798i	−0.242842	−	0.476604i
$367$	−1.76393	−	5.42882i	−0.0920765	−	0.283382i	0.894404	−	0.447259i	$-0.147600\pi$
$367$	−1.76393	−	5.42882i	−0.0920765	−	0.283382i	−0.986481	+	0.163877i	$0.947600\pi$
$368$	4.00000	−	2.90617i	0.208514	−	0.151495i
$369$	2.97214	−	2.15938i	0.154723	−	0.112413i
$370$	−10.0806	−	5.13632i	−0.524065	−	0.267024i
$371$	−36.0341	−	11.7082i	−1.87080	−	0.607860i
$372$	5.23607	+	3.80423i	0.271477	+	0.197240i
$373$		−	7.52786i		−	0.389778i	−0.980825	−	0.194889i	$-0.937565\pi$
$373$		−	7.52786i		−	0.389778i	0.980825	−	0.194889i	$-0.0624347\pi$
$374$	−9.45428	+	7.83625i	−0.488869	+	0.405203i
$375$	−1.61803			−0.0835549
$376$	−3.07259	−	19.3995i	−0.158457	−	1.00046i
$377$	6.47214	−	19.9192i	0.333332	−	1.02589i
$378$	−18.3960	+	36.1042i	−0.946189	+	1.85700i
$379$	−1.33457	−	1.83688i	−0.0685524	−	0.0943542i	0.773364	−	0.633962i	$-0.218572\pi$
$379$	−1.33457	−	1.83688i	−0.0685524	−	0.0943542i	−0.841916	+	0.539608i	$0.818572\pi$
$380$	3.63271	+	5.00000i	0.186354	+	0.256495i
$381$	6.60440	−	2.14590i	0.338353	−	0.109938i
$382$	6.53618	+	12.8280i	0.334420	+	0.656336i
$383$	−9.94427	−	7.22494i	−0.508129	−	0.369177i	0.303985	−	0.952677i	$-0.401683\pi$
$383$	−9.94427	−	7.22494i	−0.508129	−	0.369177i	−0.812113	+	0.583500i	$0.801683\pi$
$384$	12.9443	−	12.9443i	0.660560	−	0.660560i
$385$	−11.4721	+	13.0373i	−0.584674	+	0.664441i
$386$	−6.00000	+	6.00000i	−0.305392	+	0.305392i
$387$	−1.08981	+	1.50000i	−0.0553983	+	0.0762493i
$388$	26.8011	+	8.70820i	1.36062	+	0.442092i
$389$	12.5882	−	4.09017i	0.638250	−	0.207380i	0.0280236	−	0.999607i	$-0.491079\pi$
$389$	12.5882	−	4.09017i	0.638250	−	0.207380i	0.610226	+	0.792227i	$0.291079\pi$
$390$	11.8339	+	1.87431i	0.599233	+	0.0949091i
$391$	2.61803	−	1.90211i	0.132400	−	0.0961940i
$392$	26.2163	−	51.4523i	1.32412	−	2.59874i
$393$	−0.163119	+	0.502029i	−0.00822826	+	0.0253240i
$394$	0.651366	+	4.11257i	0.0328154	+	0.207188i
$395$			15.7082i			0.790366i
$396$	−2.32624	−	1.00406i	−0.116898	−	0.0504558i
$397$		−	4.58359i		−	0.230044i	−0.993363	−	0.115022i	$-0.963306\pi$
$397$		−	4.58359i		−	0.230044i	0.993363	−	0.115022i	$-0.0366938\pi$
$398$	31.6410	−	5.01145i	1.58602	−	0.251201i
$399$	8.09017	−	24.8990i	0.405015	−	1.24651i
$400$	1.23607	+	3.80423i	0.0618034	+	0.190211i
$401$	−16.5451	+	12.0207i	−0.826222	+	0.600286i	−0.918488	−	0.395449i	$-0.870589\pi$
$401$	−16.5451	+	12.0207i	−0.826222	+	0.600286i	0.0922659	+	0.995734i	$0.470589\pi$
$402$	−0.832701	+	5.25747i	−0.0415314	+	0.262219i
$403$	9.95959	−	3.23607i	0.496123	−	0.161200i
$404$	−5.05573	+	15.5599i	−0.251532	+	0.774136i
$405$	−4.53077	+	6.23607i	−0.225136	+	0.309873i
$406$	−20.9443	−	20.9443i	−1.03945	−	1.03945i
$407$	−25.8885	+	5.81234i	−1.28325	+	0.288107i
$408$	8.47214	−	8.47214i	0.419433	−	0.419433i
$409$	17.7984	+	12.9313i	0.880073	+	0.639410i	0.933271	−	0.359174i	$-0.116941\pi$
$409$	17.7984	+	12.9313i	0.880073	+	0.639410i	−0.0531978	+	0.998584i	$0.516941\pi$
$410$	−12.1194	+	6.17516i	−0.598536	+	0.304969i
$411$	14.0741	−	4.57295i	0.694224	−	0.225567i
$412$	−2.00811	−	2.76393i	−0.0989327	−	0.136169i
$413$	−1.90211	−	2.61803i	−0.0935969	−	0.128825i
$414$	0.594926	+	0.303130i	0.0292390	+	0.0148980i
$415$	−0.736068	+	2.26538i	−0.0361322	+	0.111203i
$416$	−4.63354	−	29.2550i	−0.227178	−	1.43434i
$417$	16.9443			0.829765
$418$	14.0422	+	3.59135i	0.686827	+	0.175659i
$419$		−	18.0902i		−	0.883763i	−0.897074	−	0.441881i	$-0.854311\pi$
$419$		−	18.0902i		−	0.883763i	0.897074	−	0.441881i	$-0.145689\pi$
$420$	9.95959	−	13.7082i	0.485978	−	0.668892i
$421$	30.8828	+	10.0344i	1.50514	+	0.489049i	0.941511	−	0.336981i	$-0.109406\pi$
$421$	30.8828	+	10.0344i	1.50514	+	0.489049i	0.563626	+	0.826030i	$0.309406\pi$
$422$	9.53692	−	18.7173i	0.464250	−	0.911142i
$423$	2.14590	−	1.55909i	0.104337	−	0.0758054i
$424$	−3.20170	+	20.2147i	−0.155488	+	0.981713i
$425$	0.809017	+	2.48990i	0.0392431	+	0.120778i
$426$	14.1583	−	7.21400i	0.685971	−	0.349519i
$427$	−13.7638	+	18.9443i	−0.666078	+	0.916778i
$428$	−17.7082			−0.855958
$429$	24.1724	−	14.3262i	1.16706	−	0.691677i
$430$	4.85410	−	4.85410i	0.234086	−	0.234086i
$431$	9.70820	+	7.05342i	0.467628	+	0.339751i	0.796516	−	0.604617i	$-0.206674\pi$
$431$	9.70820	+	7.05342i	0.467628	+	0.339751i	−0.328888	+	0.944369i	$0.606674\pi$
$432$	20.8172	+	6.76393i	1.00157	+	0.325430i
$433$	−3.10081	−	9.54332i	−0.149016	−	0.458623i	0.848490	−	0.529212i	$-0.177512\pi$
$433$	−3.10081	−	9.54332i	−0.149016	−	0.458623i	−0.997506	+	0.0705888i	$0.977512\pi$
$434$	2.31677	−	14.6275i	0.111208	−	0.702143i
$435$	−3.80423	−	5.23607i	−0.182399	−	0.251050i
$436$	4.65248	+	14.3188i	0.222813	+	0.685748i
$437$	−3.63271	−	1.18034i	−0.173776	−	0.0564633i
$438$	−0.410186	−	2.58981i	−0.0195995	−	0.123746i
$439$	−24.6525			−1.17660			−0.588299	−	0.808643i	$-0.700202\pi$
$439$	−24.6525			−1.17660			−0.588299	+	0.808643i	$0.700202\pi$
$440$	7.92522	+	5.01905i	0.377820	+	0.239274i
$441$	7.79837			0.371351
$442$	−3.03269	−	19.1477i	−0.144250	−	0.910761i
$443$	−22.7396	−	7.38854i	−1.08039	−	0.351040i	−0.285865	−	0.958270i	$-0.592281\pi$
$443$	−22.7396	−	7.38854i	−1.08039	−	0.351040i	−0.794526	+	0.607230i	$0.792281\pi$
$444$	24.6215	−	8.00000i	1.16848	−	0.379663i
$445$	−8.55951	−	11.7812i	−0.405760	−	0.558480i
$446$	−1.43184	+	9.04029i	−0.0677997	+	0.428070i
$447$	5.61803	+	17.2905i	0.265724	+	0.817814i
$448$	−39.8384	−	12.9443i	−1.88219	−	0.611559i
$449$	8.20820	+	5.96361i	0.387369	+	0.281440i	0.764377	−	0.644770i	$-0.223047\pi$
$449$	8.20820	+	5.96361i	0.387369	+	0.281440i	−0.377007	+	0.926210i	$0.623047\pi$
$450$	−0.381966	+	0.381966i	−0.0180061	+	0.0180061i
$451$	−12.6412	+	29.2877i	−0.595253	+	1.37911i
$452$		−	7.12461i		−	0.335114i
$453$	−20.8172	+	28.6525i	−0.978079	+	1.34621i
$454$	27.3973	−	13.9596i	1.28582	−	0.655158i
$455$	−8.47214	−	26.0746i	−0.397180	−	1.22239i
$456$	−13.9680	−	2.21232i	−0.654113	−	0.103601i
$457$	32.4894	−	23.6049i	1.51979	−	1.10419i	0.558196	−	0.829709i	$-0.311494\pi$
$457$	32.4894	−	23.6049i	1.51979	−	1.10419i	0.961592	−	0.274481i	$-0.0885061\pi$
$458$	−17.1119	+	33.5841i	−0.799589	+	1.56928i
$459$	13.6251	+	4.42705i	0.635963	+	0.206637i
$460$	−2.00000	−	1.45309i	−0.0932505	−	0.0677504i
$461$			9.59675i			0.446965i	0.974708	+	0.223483i	$0.0717426\pi$
$461$			9.59675i			0.446965i	−0.974708	+	0.223483i	$0.928257\pi$
$462$	−2.53245	−	39.6571i	−0.117820	−	1.84501i
$463$	3.88854			0.180716			0.0903580	−	0.995909i	$-0.471199\pi$
$463$	3.88854			0.180716			0.0903580	+	0.995909i	$0.471199\pi$
$464$	−9.40456	+	12.9443i	−0.436596	+	0.600923i
$465$	1.00000	−	3.07768i	0.0463739	−	0.142724i
$466$	8.63667	+	4.40060i	0.400086	+	0.203854i
$467$	15.5599	+	21.4164i	0.720028	+	0.991033i	0.999523	+	0.0308861i	$0.00983290\pi$
$467$	15.5599	+	21.4164i	0.720028	+	0.991033i	−0.279495	+	0.960147i	$0.590167\pi$
$468$	3.23607	−	2.35114i	0.149587	−	0.108682i
$469$	11.5842	−	3.76393i	0.534908	−	0.173802i
$470$	−8.75029	+	4.45850i	−0.403621	+	0.205655i
$471$	4.85410	+	3.52671i	0.223665	+	0.162502i
$472$	−1.23607	+	1.23607i	−0.0568946	+	0.0568946i
$473$	1.50000	−	16.0292i	0.0689701	−	0.737024i
$474$	−25.4164	−	25.4164i	−1.16741	−	1.16741i
$475$	1.81636	−	2.50000i	0.0833401	−	0.114708i
$476$	−26.0746	−	8.47214i	−1.19513	−	0.388320i
$477$	−2.62866	+	0.854102i	−0.120358	+	0.0391066i
$478$	−1.02928	+	6.49859i	−0.0470780	+	0.297239i
$479$	22.9443	−	16.6700i	1.04835	−	0.761671i	0.0764524	−	0.997073i	$-0.475641\pi$
$479$	22.9443	−	16.6700i	1.04835	−	0.761671i	0.971898	+	0.235402i	$0.0756407\pi$
$480$	−8.15537	−	4.15537i	−0.372240	−	0.189666i
$481$	12.9443	−	39.8384i	0.590208	−	1.81647i
$482$	34.8903	−	5.52608i	1.58921	−	0.251706i
$483$			10.4721i			0.476499i
$484$	21.8213	−	2.79837i	0.991877	−	0.127199i
$485$		−	14.0902i		−	0.639802i
$486$	0.872598	+	5.50937i	0.0395819	+	0.249910i
$487$	−2.14590	+	6.60440i	−0.0972399	+	0.299274i	−0.987831	−	0.155531i	$-0.950291\pi$
$487$	−2.14590	+	6.60440i	−0.0972399	+	0.299274i	0.890591	+	0.454805i	$0.150291\pi$
$488$	11.2704	+	5.74258i	0.510189	+	0.259954i
$489$	−8.66312	+	6.29412i	−0.391760	+	0.284630i
$490$	−28.5177	−	4.51676i	−1.28830	−	0.204046i
$491$	29.5155	−	9.59017i	1.33202	−	0.432798i	0.445411	−	0.895326i	$-0.353057\pi$
$491$	29.5155	−	9.59017i	1.33202	−	0.432798i	0.886605	+	0.462528i	$0.153057\pi$
$492$	9.61803	−	29.6013i	0.433614	−	1.33453i
$493$	−6.15537	+	8.47214i	−0.277224	+	0.381566i
$494$	−16.1803	+	16.1803i	−0.727988	+	0.727988i
$495$	−0.118034	+	1.26133i	−0.00530523	+	0.0566924i
$496$	−8.00000			−0.359211
$497$	−29.4164	−	21.3723i	−1.31951	−	0.958677i
$498$	−2.47449	−	4.85645i	−0.110884	−	0.217623i
$499$	−19.3844	+	6.29837i	−0.867765	+	0.281954i	−0.708868	−	0.705341i	$-0.750794\pi$
$499$	−19.3844	+	6.29837i	−0.867765	+	0.281954i	−0.158897	+	0.987295i	$0.550794\pi$
$500$	1.61803	−	1.17557i	0.0723607	−	0.0525731i
$501$	−13.7638	−	18.9443i	−0.614922	−	0.846368i
$502$	−7.70447	+	15.1209i	−0.343868	+	0.674878i
$503$	−11.5066	+	35.4136i	−0.513053	+	1.57901i	0.273744	+	0.961803i	$0.411738\pi$
$503$	−11.5066	+	35.4136i	−0.513053	+	1.57901i	−0.786797	+	0.617212i	$0.788262\pi$
$504$	−0.884927	−	5.58721i	−0.0394178	−	0.248874i
$505$	8.18034			0.364020
$506$	−5.78589	+	0.369480i	−0.257214	+	0.0164254i
$507$			23.3262i			1.03595i
$508$	−5.04531	+	6.94427i	−0.223849	+	0.308102i
$509$	−22.3763	−	7.27051i	−0.991813	−	0.322260i	−0.232224	−	0.972662i	$-0.574600\pi$
$509$	−22.3763	−	7.27051i	−0.991813	−	0.322260i	−0.759590	+	0.650403i	$0.774600\pi$
$510$	−5.33776	−	2.71972i	−0.236360	−	0.120431i
$511$	−4.85410	+	3.52671i	−0.214733	+	0.156013i
$512$	−3.53971	+	22.3488i	−0.156434	+	0.987688i
$513$	−5.22542	−	16.0822i	−0.230708	−	0.710047i
$514$	5.00686	+	9.82652i	0.220843	+	0.433429i
$515$	−1.00406	+	1.38197i	−0.0442440	+	0.0608967i
$516$			15.7082i			0.691515i
$517$	−9.12705	+	21.1459i	−0.401407	+	0.929996i
$518$	−41.8885	−	41.8885i	−1.84048	−	1.84048i
$519$	6.23607	+	4.53077i	0.273733	+	0.198879i
$520$	−13.1957	+	6.72353i	−0.578668	+	0.294846i
$521$	−9.80902	−	30.1891i	−0.429741	−	1.32261i	−0.898381	−	0.439217i	$-0.855256\pi$
$521$	−9.80902	−	30.1891i	−0.429741	−	1.32261i	0.468640	−	0.883389i	$-0.344744\pi$
$522$	−2.13412	−	0.338012i	−0.0934081	−	0.0147944i
$523$	22.1846	+	30.5344i	0.970064	+	1.33518i	0.942015	+	0.335571i	$0.108929\pi$
$523$	22.1846	+	30.5344i	0.970064	+	1.33518i	0.0280488	+	0.999607i	$0.491071\pi$
$524$	−0.201626	−	0.620541i	−0.00880808	−	0.0271085i
$525$	−8.05748	−	2.61803i	−0.351657	−	0.114260i
$526$	40.8370	−	6.46795i	1.78058	−	0.282016i
$527$	−5.23607			−0.228087
$528$	−20.9443	+	4.70228i	−0.911482	+	0.204641i
$529$	−21.4721			−0.933571
$530$	10.1074	−	1.60085i	0.439035	−	0.0695364i
$531$	−0.224514	−	0.0729490i	−0.00974308	−	0.00316572i
$532$	10.0000	+	30.7768i	0.433555	+	1.33435i
$533$	−29.6013	−	40.7426i	−1.28217	−	1.76476i
$534$	32.9119	+	5.21273i	1.42424	+	0.225577i
$535$	2.73607	+	8.42075i	0.118291	+	0.364061i
$536$	−2.98707	−	5.86246i	−0.129022	−	0.253220i
$537$	18.1353	+	13.1760i	0.782594	+	0.568588i
$538$	−21.8885	−	21.8885i	−0.943682	−	0.943682i
$539$	−58.2515	+	34.5238i	−2.50907	+	1.48705i
$540$		−	10.9443i		−	0.470966i
$541$	9.78808	−	13.4721i	0.420822	−	0.579212i	−0.544994	−	0.838440i	$-0.683468\pi$
$541$	9.78808	−	13.4721i	0.420822	−	0.579212i	0.965816	+	0.259228i	$0.0834680\pi$
$542$	−1.47142	−	2.88783i	−0.0632031	−	0.124043i
$543$	10.0000	+	30.7768i	0.429141	+	1.32076i
$544$	−2.31677	+	14.6275i	−0.0993306	+	0.627149i
$545$	6.09017	−	4.42477i	0.260874	−	0.189536i
$546$	55.8977	+	28.4813i	2.39220	+	1.21889i
$547$	9.20029	+	2.98936i	0.393376	+	0.127816i	0.499024	−	0.866588i	$-0.333692\pi$
$547$	9.20029	+	2.98936i	0.393376	+	0.127816i	−0.105648	+	0.994404i	$0.533692\pi$
$548$	−10.7516	+	14.7984i	−0.459288	+	0.632155i
$549$			1.70820i			0.0729044i
$550$	1.16219	−	4.54415i	0.0495558	−	0.193763i
$551$	12.3607			0.526583
$552$	5.58721	−	0.884927i	0.237807	−	0.0376650i
$553$	−25.4164	+	78.2237i	−1.08082	+	3.32641i
$554$	−8.61386	+	16.9057i	−0.365968	+	0.718253i
$555$	−7.60845	−	10.4721i	−0.322961	−	0.444517i
$556$	−16.9443	+	12.3107i	−0.718597	+	0.522091i
$557$	−2.17963	+	0.708204i	−0.0923538	+	0.0300076i	−0.354829	−	0.934931i	$-0.615461\pi$
$557$	−2.17963	+	0.708204i	−0.0923538	+	0.0300076i	0.262476	+	0.964939i	$0.415461\pi$
$558$	−0.490475	−	0.962611i	−0.0207634	−	0.0407506i
$559$	20.5623	+	14.9394i	0.869693	+	0.631869i
$560$			20.9443i			0.885057i
$561$	−13.7082	+	3.07768i	−0.578761	+	0.129940i
$562$	3.14590	−	3.14590i	0.132702	−	0.132702i
$563$	20.4212	−	28.1074i	0.860652	−	1.18459i	−0.120762	−	0.992681i	$-0.538534\pi$
$563$	20.4212	−	28.1074i	0.860652	−	1.18459i	0.981414	−	0.191904i	$-0.0614662\pi$
$564$	6.94427	−	21.3723i	0.292407	−	0.899935i
$565$	−3.38795	+	1.10081i	−0.142532	+	0.0463116i
$566$	2.13412	+	0.338012i	0.0897039	+	0.0142077i
$567$	−32.6525	+	23.7234i	−1.37128	+	0.996290i
$568$	−8.91699	+	17.5006i	−0.374149	+	0.734308i
$569$	0.663119	−	2.04087i	0.0277994	−	0.0855577i	−0.936194	−	0.351483i	$-0.885677\pi$
$569$	0.663119	−	2.04087i	0.0277994	−	0.0855577i	0.963994	+	0.265925i	$0.0856775\pi$
$570$	1.10616	+	6.98401i	0.0463319	+	0.292528i
$571$			28.3607i			1.18686i	0.804887	+	0.593429i	$0.202226\pi$
$571$			28.3607i			1.18686i	−0.804887	+	0.593429i	$0.797774\pi$
$572$	−13.7638	+	31.8885i	−0.575494	+	1.33333i
$573$			16.4721i			0.688133i
$574$	−70.3439	+	11.1414i	−2.93610	+	0.465032i
$575$	−0.381966	+	1.17557i	−0.0159291	+	0.0490247i
$576$	−2.90617	+	0.944272i	−0.121090	+	0.0393447i
$577$	−38.2984	+	27.8254i	−1.59438	+	1.15839i	−0.697058	+	0.717015i	$0.745508\pi$
$577$	−38.2984	+	27.8254i	−1.59438	+	1.15839i	−0.897325	+	0.441371i	$0.854492\pi$
$578$	2.24459	−	14.1718i	0.0933628	−	0.589470i
$579$	−9.23305	+	3.00000i	−0.383712	+	0.124676i
$580$	7.60845	+	2.47214i	0.315924	+	0.102650i
$581$	−7.33094	+	10.0902i	−0.304139	+	0.418611i
$582$	22.7984	+	22.7984i	0.945023	+	0.945023i
$583$	15.8541	−	18.0171i	0.656610	−	0.746191i
$584$	2.29180	+	2.29180i	0.0948352	+	0.0948352i
$585$	−1.61803	−	1.17557i	−0.0668975	−	0.0486039i
$586$	−0.822168	+	0.418915i	−0.0339634	+	0.0173052i
$587$	8.92278	−	2.89919i	0.368283	−	0.119662i	−0.119028	−	0.992891i	$-0.537978\pi$
$587$	8.92278	−	2.89919i	0.368283	−	0.119662i	0.487311	+	0.873229i	$0.337978\pi$
$588$	53.4508	−	38.8343i	2.20428	−	1.60150i
$589$	3.63271	+	5.00000i	0.149683	+	0.206021i
$590$	0.778768	+	0.396802i	0.0320614	+	0.0163361i
$591$	−1.47214	+	4.53077i	−0.0605556	+	0.186371i
$592$	−18.8091	+	25.8885i	−0.773050	+	1.06401i
$593$	7.56231			0.310547			0.155273	−	0.987872i	$-0.450374\pi$
$593$	7.56231			0.310547			0.155273	+	0.987872i	$0.450374\pi$
$594$	−16.3791	−	19.7611i	−0.672042	−	0.810806i
$595$			13.7082i			0.561982i
$596$	−18.1803	−	13.2088i	−0.744696	−	0.541053i
$597$	34.8586	+	11.3262i	1.42667	+	0.463552i
$598$	4.15537	−	8.15537i	0.169926	−	0.333498i
$599$	−27.0344	+	19.6417i	−1.10460	+	0.802537i	−0.981804	−	0.189895i	$-0.939185\pi$
$599$	−27.0344	+	19.6417i	−1.10460	+	0.802537i	−0.122793	+	0.992432i	$0.539185\pi$
$600$	−0.715921	+	4.52015i	−0.0292274	+	0.184534i
$601$	1.08359	+	3.33495i	0.0442006	+	0.136036i	0.970721	−	0.240208i	$-0.0772156\pi$
$601$	1.08359	+	3.33495i	0.0442006	+	0.136036i	−0.926521	+	0.376243i	$0.877216\pi$
$602$	32.0265	−	16.3183i	1.30530	−	0.665086i
$603$	0.522273	−	0.718847i	0.0212686	−	0.0292737i
$604$		−	43.7771i		−	1.78126i
$605$	−4.70228	−	9.94427i	−0.191175	−	0.404292i
$606$	−13.2361	+	13.2361i	−0.537679	+	0.537679i
$607$	−6.94427	−	5.04531i	−0.281859	−	0.204783i	0.437869	−	0.899039i	$-0.355733\pi$
$607$	−6.94427	−	5.04531i	−0.281859	−	0.204783i	−0.719728	+	0.694256i	$0.755733\pi$
$608$	15.5754	−	7.93604i	0.631664	−	0.321849i
$609$	−10.4721	−	32.2299i	−0.424352	−	1.30602i
$610$	0.989378	−	6.24669i	0.0400588	−	0.252921i
$611$	−21.3723	−	29.4164i	−0.864630	−	1.19006i
$612$	−1.90211	+	0.618034i	−0.0768884	+	0.0249825i
$613$	18.4661	+	6.00000i	0.745839	+	0.242338i	0.657190	−	0.753725i	$-0.271745\pi$
$613$	18.4661	+	6.00000i	0.745839	+	0.242338i	0.0886491	+	0.996063i	$0.471745\pi$
$614$	3.22164	+	20.3407i	0.130015	+	0.820882i
$615$	−15.5623			−0.627533
$616$	31.3450	+	37.8171i	1.26293	+	1.52370i
$617$	21.3820			0.860806			0.430403	−	0.902637i	$-0.358372\pi$
$617$	21.3820			0.860806			0.430403	+	0.902637i	$0.358372\pi$
$618$	−0.611469	−	3.86067i	−0.0245969	−	0.155299i
$619$	−25.4868	−	8.28115i	−1.02440	−	0.332848i	−0.251826	−	0.967773i	$-0.581031\pi$
$619$	−25.4868	−	8.28115i	−1.02440	−	0.332848i	−0.772574	+	0.634925i	$0.781031\pi$
$620$	1.23607	+	3.80423i	0.0496417	+	0.152781i
$621$	3.97574	+	5.47214i	0.159541	+	0.219589i
$622$	7.22376	−	45.6091i	0.289647	−	1.82876i
$623$	−23.5623	−	72.5173i	−0.944004	−	2.90535i
$624$	10.4721	−	32.2299i	0.419221	−	1.29023i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−13.7426	+	13.7426i	−0.549267	+	0.549267i
$627$	12.4495	+	10.9549i	0.497185	+	0.437497i
$628$	−7.41641			−0.295947
$629$	−12.3107	+	16.9443i	−0.490861	+	0.675612i
$630$	−2.52015	+	1.28408i	−0.100405	+	0.0511589i
$631$	4.65248	+	14.3188i	0.185212	+	0.570024i	0.999952	−	0.00980237i	$-0.00312024\pi$
$631$	4.65248	+	14.3188i	0.185212	+	0.570024i	−0.814740	+	0.579827i	$0.803120\pi$
$632$	43.8825	+	6.95031i	1.74555	+	0.276468i
$633$	19.4443	−	14.1271i	0.772840	−	0.561501i
$634$	19.1896	−	37.6618i	0.762117	−	1.49574i
$635$	4.08174	+	1.32624i	0.161979	+	0.0526301i
$636$	−13.7638	+	18.9443i	−0.545771	+	0.751189i
$637$		−	106.902i		−	4.23560i
$638$	17.4377	−	6.92303i	0.690363	−	0.274085i
$639$	−2.65248			−0.104930
$640$	11.1744	−	1.76985i	0.441708	−	0.0699596i
$641$	−2.44427	+	7.52270i	−0.0965429	+	0.297129i	−0.987653	−	0.156659i	$-0.949928\pi$
$641$	−2.44427	+	7.52270i	−0.0965429	+	0.297129i	0.891110	+	0.453788i	$0.149928\pi$
$642$	−18.0521	−	9.19801i	−0.712460	−	0.363017i
$643$	−2.74717	−	3.78115i	−0.108338	−	0.149114i	0.751405	−	0.659841i	$-0.229376\pi$
$643$	−2.74717	−	3.78115i	−0.108338	−	0.149114i	−0.859743	+	0.510727i	$0.829376\pi$
$644$	−7.60845	−	10.4721i	−0.299815	−	0.412660i
$645$	7.46969	−	2.42705i	0.294119	−	0.0955650i
$646$	10.1942	−	5.19421i	0.401086	−	0.204363i
$647$	10.4721	+	7.60845i	0.411702	+	0.299119i	0.774291	−	0.632830i	$-0.218107\pi$
$647$	10.4721	+	7.60845i	0.411702	+	0.299119i	−0.362588	+	0.931949i	$0.618107\pi$
$648$	15.4164	+	15.4164i	0.605614	+	0.605614i
$649$	2.00000	−	0.449028i	0.0785069	−	0.0176259i
$650$	5.23607	+	5.23607i	0.205375	+	0.205375i
$651$	9.95959	−	13.7082i	0.390347	−	0.537267i
$652$	4.09017	−	12.5882i	0.160183	−	0.492994i
$653$	−17.8456	+	5.79837i	−0.698351	+	0.226908i	−0.636612	−	0.771184i	$-0.719665\pi$
$653$	−17.8456	+	5.79837i	−0.698351	+	0.226908i	−0.0617389	+	0.998092i	$0.519665\pi$
$654$	−2.69468	+	17.0135i	−0.105370	+	0.665282i
$655$	−0.263932	+	0.191758i	−0.0103127	+	0.00749260i
$656$	11.8885	+	36.5892i	0.464170	+	1.42857i
$657$	−0.135255	+	0.416272i	−0.00527680	+	0.0162403i
$658$	−50.7887	+	8.04414i	−1.97995	+	0.313593i
$659$			9.85410i			0.383861i	0.981408	+	0.191931i	$0.0614749\pi$
$659$			9.85410i			0.383861i	−0.981408	+	0.191931i	$0.938525\pi$
$660$	5.47214	+	9.23305i	0.213003	+	0.359396i
$661$			18.2918i			0.711468i	0.934587	+	0.355734i	$0.115769\pi$
$661$			18.2918i			0.711468i	−0.934587	+	0.355734i	$0.884231\pi$
$662$	4.21102	+	26.5874i	0.163666	+	1.03335i
$663$	6.85410	−	21.0948i	0.266191	−	0.819252i
$664$	6.00290	+	3.05863i	0.232958	+	0.118698i
$665$	13.0902	−	9.51057i	0.507615	−	0.368804i
$666$	−4.26825	−	0.676024i	−0.165391	−	0.0261954i
$667$	−4.70228	+	1.52786i	−0.182073	+	0.0591591i
$668$	27.5276	+	8.94427i	1.06508	+	0.346064i
$669$	−6.15537	+	8.47214i	−0.237980	+	0.327552i
$670$	−2.32624	+	2.32624i	−0.0898704	+	0.0898704i
$671$	−7.56231	−	12.7598i	−0.291940	−	0.492585i
$672$	−33.8885	−	33.8885i	−1.30728	−	1.30728i
$673$	−12.0623	−	8.76378i	−0.464968	−	0.337819i	0.330509	−	0.943803i	$-0.392780\pi$
$673$	−12.0623	−	8.76378i	−0.464968	−	0.337819i	−0.795477	+	0.605984i	$0.792780\pi$
$674$	14.7090	+	28.8681i	0.566570	+	1.11196i
$675$	−5.20431	+	1.69098i	−0.200314	+	0.0650860i
$676$	−16.9475	−	23.3262i	−0.651827	−	0.897163i
$677$	9.29856	+	12.7984i	0.357373	+	0.491881i	0.949414	−	0.314026i	$-0.101678\pi$
$677$	9.29856	+	12.7984i	0.357373	+	0.491881i	−0.592042	+	0.805907i	$0.701678\pi$
$678$	3.70067	−	7.26298i	0.142123	−	0.278933i
$679$	22.7984	−	70.1662i	0.874921	−	2.69273i
$680$	7.31375	−	1.15838i	0.280470	−	0.0444220i
$681$	35.1803			1.34811
$682$	7.92522	+	5.01905i	0.303472	+	0.192189i
$683$		−	43.7771i		−	1.67508i	−0.546373	−	0.837542i	$-0.683992\pi$
$683$		−	43.7771i		−	1.67508i	0.546373	−	0.837542i	$-0.316008\pi$
$684$	1.90983	+	1.38757i	0.0730242	+	0.0530552i
$685$	8.69827	+	2.82624i	0.332344	+	0.107985i
$686$	−88.5192	−	45.1028i	−3.37968	−	1.72203i
$687$	−34.8885	+	25.3480i	−1.33108	+	0.967087i
$688$	−11.4127	−	15.7082i	−0.435104	−	0.598870i
$689$	11.7082	+	36.0341i	0.446047	+	1.37279i
$690$	−1.28408	−	2.52015i	−0.0488841	−	0.0959404i
$691$	4.33901	−	5.97214i	0.165064	−	0.227191i	−0.718470	−	0.695558i	$-0.755157\pi$
$691$	4.33901	−	5.97214i	0.165064	−	0.227191i	0.883534	+	0.468367i	$0.155157\pi$
$692$	−9.52786			−0.362195
$693$	−2.62866	+	6.09017i	−0.0998544	+	0.231346i
$694$	16.5066	+	16.5066i	0.626581	+	0.626581i
$695$	8.47214	+	6.15537i	0.321366	+	0.233486i
$696$	−16.3107	+	8.31073i	−0.618257	+	0.315018i
$697$	7.78115	+	23.9479i	0.294732	+	0.907092i
$698$	−1.31896	−	0.208903i	−0.0499234	−	0.00790709i
$699$	6.51864	+	8.97214i	0.246558	+	0.339357i
$700$	9.95959	−	3.23607i	0.376437	−	0.122312i
$701$	32.6789	+	10.6180i	1.23427	+	0.401038i	0.852258	−	0.523121i	$-0.175232\pi$
$701$	32.6789	+	10.6180i	1.23427	+	0.401038i	0.382009	+	0.924159i	$0.375232\pi$
$702$	40.0218	−	6.33884i	1.51053	−	0.239244i
$703$	24.7214			0.932384
$704$	17.5279	−	19.9192i	0.660606	−	0.750733i
$705$	−11.2361			−0.423175
$706$	−5.79100	+	0.917204i	−0.217947	+	0.0345194i
$707$	40.7364	+	13.2361i	1.53205	+	0.497794i
$708$	−1.90211	+	0.618034i	−0.0714858	+	0.0232271i
$709$	−5.32282	−	7.32624i	−0.199903	−	0.275143i	0.697283	−	0.716796i	$-0.254392\pi$
$709$	−5.32282	−	7.32624i	−0.199903	−	0.275143i	−0.897186	+	0.441653i	$0.854392\pi$
$710$	9.69977	+	1.53629i	0.364026	+	0.0576561i
$711$	1.85410	+	5.70634i	0.0695343	+	0.214004i
$712$	−36.6992	+	18.6992i	−1.37536	+	0.700780i
$713$	−2.00000	−	1.45309i	−0.0749006	−	0.0544185i
$714$	−22.1803	−	22.1803i	−0.830078	−	0.830078i
$715$	17.2905	+	1.61803i	0.646629	+	0.0605110i
$716$	−27.7082			−1.03550
$717$	−4.42477	+	6.09017i	−0.165246	+	0.227442i
$718$	1.96190	+	3.85044i	0.0732174	+	0.143697i
$719$	11.1459	+	34.3035i	0.415672	+	1.27931i	0.911649	+	0.410971i	$0.134810\pi$
$719$	11.1459	+	34.3035i	0.415672	+	1.27931i	−0.495977	+	0.868336i	$0.665190\pi$
$720$	0.898056	+	1.23607i	0.0334686	+	0.0460655i
$721$	−7.23607	+	5.25731i	−0.269485	+	0.195792i
$722$	11.9088	+	6.06782i	0.443198	+	0.225821i
$723$	38.4383	+	12.4894i	1.42954	+	0.464484i
$724$	−32.3607	−	23.5114i	−1.20268	−	0.873795i
$725$		−	4.00000i		−	0.148556i
$726$	23.6986	+	8.48172i	0.879538	+	0.314786i
$727$	−7.23607			−0.268371			−0.134185	−	0.990956i	$-0.542842\pi$
$727$	−7.23607			−0.268371			−0.134185	+	0.990956i	$0.542842\pi$
$728$	−76.5906	+	12.1308i	−2.83864	+	0.449596i
$729$	−9.11803	+	28.0624i	−0.337705	+	1.03935i
$730$	0.735712	−	1.44392i	0.0272299	−	0.0534417i
$731$	−7.46969	−	10.2812i	−0.276277	−	0.380262i
$732$	8.50651	+	11.7082i	0.314410	+	0.432748i
$733$	−42.3610	+	13.7639i	−1.56464	+	0.508382i	−0.958042	−	0.286626i	$-0.907466\pi$
$733$	−42.3610	+	13.7639i	−1.56464	+	0.508382i	−0.606598	+	0.795009i	$0.707466\pi$
$734$	3.66489	+	7.19276i	0.135274	+	0.265489i
$735$	−26.7254	−	19.4172i	−0.985782	−	0.716213i
$736$	−4.94427	+	4.94427i	−0.182248	+	0.182248i
$737$	−0.718847	+	7.68170i	−0.0264791	+	0.282959i
$738$	−3.67376	+	3.67376i	−0.135233	+	0.135233i
$739$	20.6255	−	28.3885i	0.758721	−	1.04429i	−0.238599	−	0.971118i	$-0.576688\pi$
$739$	20.6255	−	28.3885i	0.758721	−	1.04429i	0.997319	−	0.0731712i	$-0.0233120\pi$
$740$	15.2169	+	4.94427i	0.559385	+	0.181755i
$741$	−24.8990	+	8.09017i	−0.914687	+	0.297200i
$742$	52.9228	+	8.38215i	1.94286	+	0.307718i
$743$	−6.32624	+	4.59628i	−0.232087	+	0.168621i	−0.697751	−	0.716341i	$-0.745816\pi$
$743$	−6.32624	+	4.59628i	−0.232087	+	0.168621i	0.465664	+	0.884962i	$0.345816\pi$
$744$	−8.15537	−	4.15537i	−0.298990	−	0.152343i
$745$	−3.47214	+	10.6861i	−0.127209	+	0.391510i
$746$	1.66540	+	10.5149i	0.0609747	+	0.384979i
$747$			0.909830i			0.0332889i
$748$	11.4721	−	13.0373i	0.419463	−	0.476690i
$749$			46.3607i			1.69398i
$750$	2.26007	−	0.357960i	0.0825262	−	0.0130709i
$751$	8.09017	−	24.8990i	0.295214	−	0.908577i	−0.687935	−	0.725772i	$-0.741483\pi$
$751$	8.09017	−	24.8990i	0.295214	−	0.908577i	0.983149	−	0.182804i	$-0.0585175\pi$
$752$	8.58359	+	26.4176i	0.313011	+	0.963350i
$753$	−15.7082	+	11.4127i	−0.572439	+	0.415901i
$754$	−4.63354	+	29.2550i	−0.168743	+	1.06540i
$755$	−20.8172	+	6.76393i	−0.757617	+	0.246165i
$756$	17.7082	−	54.5002i	0.644041	−	1.98215i
$757$	−21.4783	+	29.5623i	−0.780641	+	1.07446i	0.214570	+	0.976709i	$0.431165\pi$
$757$	−21.4783	+	29.5623i	−0.780641	+	1.07446i	−0.995211	+	0.0977516i	$0.968835\pi$
$758$	2.27051	+	2.27051i	0.0824686	+	0.0824686i
$759$	−6.09017	−	2.62866i	−0.221059	−	0.0954142i
$760$	−6.18034	−	6.18034i	−0.224184	−	0.224184i
$761$	−1.73607	−	1.26133i	−0.0629324	−	0.0457231i	0.555874	−	0.831266i	$-0.312384\pi$
$761$	−1.73607	−	1.26133i	−0.0629324	−	0.0457231i	−0.618807	+	0.785543i	$0.712384\pi$
$762$	−8.75029	+	4.45850i	−0.316990	+	0.161514i
$763$	37.4872	−	12.1803i	1.35713	−	0.440958i
$764$	−11.9677	−	16.4721i	−0.432976	−	0.595941i
$765$	0.587785	+	0.809017i	0.0212514	+	0.0292501i
$766$	15.4886	+	7.89182i	0.559625	+	0.285143i
$767$	−1.00000	+	3.07768i	−0.0361079	+	0.111129i
$768$	−15.2169	+	20.9443i	−0.549093	+	0.755761i
$769$	48.8328			1.76096			0.880478	−	0.474087i	$-0.157222\pi$
$769$	48.8328			1.76096			0.880478	+	0.474087i	$0.157222\pi$
$770$	13.1400	−	20.7485i	0.473534	−	0.747724i
$771$			12.6180i			0.454427i
$772$	7.05342	−	9.70820i	0.253858	−	0.349406i
$773$	31.5034	+	10.2361i	1.13310	+	0.368166i	0.814752	−	0.579809i	$-0.196873\pi$
$773$	31.5034	+	10.2361i	1.13310	+	0.368166i	0.318345	+	0.947975i	$0.396873\pi$
$774$	1.19041	−	2.33630i	0.0427883	−	0.0839767i
$775$	1.61803	−	1.17557i	0.0581215	−	0.0422277i
$776$	−39.3624	−	6.23439i	−1.41303	−	0.223801i
$777$	−20.9443	−	64.4598i	−0.751372	−	2.31248i
$778$	−16.6784	+	8.49808i	−0.597950	+	0.304671i
$779$	17.4698	−	24.0451i	0.625920	−	0.861505i
$780$	−16.9443			−0.606702
$781$	19.8132	−	11.7426i	0.708972	−	0.420185i
$782$	−3.23607	+	3.23607i	−0.115722	+	0.115722i
$783$	−17.7082	−	12.8658i	−0.632840	−	0.459785i
$784$	−25.2361	+	77.6686i	−0.901288	+	2.77388i
$785$	1.14590	+	3.52671i	0.0408989	+	0.125874i
$786$	0.116780	−	0.737322i	0.00416541	−	0.0262994i
$787$	−10.6004	−	14.5902i	−0.377863	−	0.520083i	0.577154	−	0.816635i	$-0.304163\pi$
$787$	−10.6004	−	14.5902i	−0.377863	−	0.520083i	−0.955017	+	0.296552i	$0.904163\pi$
$788$	−1.81966	−	5.60034i	−0.0648227	−	0.199504i
$789$	44.9897	+	14.6180i	1.60168	+	0.520416i
$790$	−3.47515	−	21.9413i	−0.123640	−	0.780635i
$791$	−18.6525			−0.663206
$792$	3.47142	+	0.887832i	0.123352	+	0.0315477i
$793$	23.4164			0.831541
$794$	1.01404	+	6.40237i	0.0359868	+	0.227212i
$795$	11.1352	+	3.61803i	0.394924	+	0.128318i
$796$	−43.0876	+	14.0000i	−1.52720	+	0.496217i
$797$	0.106001	+	0.145898i	0.00375475	+	0.00516797i	0.810890	−	0.585198i	$-0.198983\pi$
$797$	0.106001	+	0.145898i	0.00375475	+	0.00516797i	−0.807135	+	0.590366i	$0.798983\pi$
$798$	−5.79192	+	36.5688i	−0.205032	+	1.29452i
$799$	5.61803	+	17.2905i	0.198752	+	0.611695i
$800$	−2.56816	−	5.04029i	−0.0907981	−	0.178201i
$801$	−4.50000	−	3.26944i	−0.159000	−	0.115520i
$802$	20.4508	−	20.4508i	0.722145	−	0.722145i
$803$	−0.832544	−	3.70820i	−0.0293798	−	0.130860i
$804$		−	7.52786i		−	0.265487i
$805$	−3.80423	+	5.23607i	−0.134081	+	0.184547i
$806$	−13.1957	+	6.72353i	−0.464797	+	0.236826i
$807$	−10.9443	−	33.6830i	−0.385257	−	1.18570i
$808$	3.61950	−	22.8526i	0.127334	−	0.803953i
$809$	−12.6803	+	9.21281i	−0.445817	+	0.323905i	−0.787942	−	0.615749i	$-0.788853\pi$
$809$	−12.6803	+	9.21281i	−0.445817	+	0.323905i	0.342125	+	0.939654i	$0.388853\pi$
$810$	4.94897	−	9.71290i	0.173889	−	0.341277i
$811$	29.3440	+	9.53444i	1.03041	+	0.334800i	0.774951	−	0.632021i	$-0.217774\pi$
$811$	29.3440	+	9.53444i	1.03041	+	0.334800i	0.255456	+	0.966821i	$0.417774\pi$
$812$	33.8885	+	24.6215i	1.18925	+	0.864044i
$813$		−	3.70820i		−	0.130052i
$814$	34.8753	−	13.8461i	1.22238	−	0.485304i
$815$	−6.61803			−0.231820
$816$	−9.95959	+	13.7082i	−0.348655	+	0.479883i
$817$	−4.63525	+	14.2658i	−0.162167	+	0.499099i
$818$	−27.7216	−	14.1249i	−0.969264	−	0.493864i
$819$	−6.15537	−	8.47214i	−0.215086	−	0.296040i
$820$	15.5623	−	11.3067i	0.543459	−	0.394846i
$821$	37.9363	−	12.3262i	1.32398	−	0.430189i	0.440123	−	0.897937i	$-0.354935\pi$
$821$	37.9363	−	12.3262i	1.32398	−	0.430189i	0.883861	+	0.467749i	$0.154935\pi$
$822$	−18.6470	+	9.50114i	−0.650390	+	0.331390i
$823$	26.6525	+	19.3642i	0.929047	+	0.674992i	0.945759	−	0.324868i	$-0.105320\pi$
$823$	26.6525	+	19.3642i	0.929047	+	0.674992i	−0.0167124	+	0.999860i	$0.505320\pi$
$824$	3.41641	+	3.41641i	0.119016	+	0.119016i
$825$	3.54508	−	4.02874i	0.123424	−	0.140263i
$826$	3.23607	+	3.23607i	0.112597	+	0.112597i
$827$	−11.2864	+	15.5344i	−0.392468	+	0.540185i	−0.958834	−	0.283968i	$-0.908349\pi$
$827$	−11.2864	+	15.5344i	−0.392468	+	0.540185i	0.566366	+	0.824154i	$0.308349\pi$
$828$	−0.898056	−	0.291796i	−0.0312096	−	0.0101406i
$829$	11.9677	−	3.88854i	0.415656	−	0.135055i	−0.0937208	−	0.995599i	$-0.529876\pi$
$829$	11.9677	−	3.88854i	0.415656	−	0.135055i	0.509376	+	0.860544i	$0.329876\pi$
$830$	0.526966	−	3.32714i	0.0182913	−	0.115487i
$831$	−17.5623	+	12.7598i	−0.609230	+	0.442631i
$832$	12.9443	+	39.8384i	0.448762	+	1.38115i
$833$	−16.5172	+	50.8348i	−0.572288	+	1.76132i
$834$	−23.6678	+	3.74861i	−0.819549	+	0.129804i
$835$		−	14.4721i		−	0.500829i
$836$	−20.4087	−	1.90983i	−0.705850	−	0.0660529i
$837$		−	10.9443i		−	0.378289i
$838$	4.00212	+	25.2684i	0.138251	+	0.872882i
$839$	2.74265	−	8.44100i	0.0946866	−	0.291416i	−0.892485	−	0.451077i	$-0.851040\pi$
$839$	2.74265	−	8.44100i	0.0946866	−	0.291416i	0.987172	+	0.159661i	$0.0510401\pi$
$840$	−10.8789	+	21.3510i	−0.375357	+	0.736680i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	−45.3572	−	7.18387i	−1.56311	−	0.247572i
$843$	4.84104	−	1.57295i	0.166734	−	0.0541752i
$844$	−9.18034	+	28.2542i	−0.316000	+	0.972549i
$845$	−8.47375	+	11.6631i	−0.291506	+	0.401223i
$846$	−2.65248	+	2.65248i	−0.0911940	+	0.0911940i
$847$	−7.32624	−	57.1289i	−0.251733	−	1.96297i
$848$		−	28.9443i		−	0.993950i
$849$	2.00000	+	1.45309i	0.0686398	+	0.0498698i
$850$	−1.68088	−	3.29892i	−0.0576538	−	0.113152i
$851$	−9.40456	+	3.05573i	−0.322384	+	0.104749i
$852$	−18.1803	+	13.2088i	−0.622848	+	0.452526i
$853$	−25.3480	−	34.8885i	−0.867899	−	1.19456i	−0.979628	−	0.200822i	$-0.935639\pi$
$853$	−25.3480	−	34.8885i	−0.867899	−	1.19456i	0.111728	−	0.993739i	$-0.464361\pi$
$854$	15.0343	−	29.5064i	0.514462	−	1.00969i
$855$	0.364745	−	1.12257i	0.0124740	−	0.0383911i
$856$	24.7349	−	3.91762i	0.845420	−	0.133901i
$857$	−23.7984			−0.812937			−0.406468	−	0.913665i	$-0.633240\pi$
$857$	−23.7984			−0.812937			−0.406468	+	0.913665i	$0.633240\pi$
$858$	−30.5947	+	25.3586i	−1.04449	+	0.865729i
$859$		−	33.6312i		−	1.14748i	−0.819037	−	0.573741i	$-0.805492\pi$
$859$		−	33.6312i		−	1.14748i	0.819037	−	0.573741i	$-0.194508\pi$
$860$	−5.70634	+	7.85410i	−0.194585	+	0.267823i
$861$	−77.4971	−	25.1803i	−2.64109	−	0.858144i
$862$	−15.1209	−	7.70447i	−0.515019	−	0.262415i
$863$	23.9443	−	17.3965i	0.815072	−	0.592185i	−0.100224	−	0.994965i	$-0.531956\pi$
$863$	23.9443	−	17.3965i	0.815072	−	0.592185i	0.915297	+	0.402780i	$0.131956\pi$
$864$	−30.5740	−	4.84244i	−1.04015	−	0.164743i
$865$	1.47214	+	4.53077i	0.0500541	+	0.154051i
$866$	6.44251	+	12.6441i	0.218925	+	0.429665i
$867$	9.64932	−	13.2812i	0.327708	−	0.451052i
$868$			20.9443i			0.710895i
$869$	−39.1118	−	34.4164i	−1.32678	−	1.16750i
$870$	6.47214	+	6.47214i	0.219426	+	0.219426i
$871$	−9.85410	−	7.15942i	−0.333894	−	0.242588i
$872$	−9.66637	−	18.9713i	−0.327345	−	0.642450i
$873$	−1.66312	−	5.11855i	−0.0562880	−	0.173237i
$874$	5.33531	+	0.845030i	0.180470	+	0.0285836i
$875$	−3.07768	−	4.23607i	−0.104045	−	0.143205i
$876$	1.14590	+	3.52671i	0.0387163	+	0.119157i
$877$	−13.9353	−	4.52786i	−0.470563	−	0.152895i	0.0641302	−	0.997942i	$-0.479573\pi$
$877$	−13.9353	−	4.52786i	−0.470563	−	0.152895i	−0.534693	+	0.845046i	$0.679573\pi$
$878$	34.4346	−	5.45391i	1.16211	−	0.184061i
$879$	−1.05573			−0.0356088
$880$	−12.1803	−	5.25731i	−0.410599	−	0.177224i
$881$	−26.5623			−0.894907			−0.447453	−	0.894307i	$-0.647669\pi$
$881$	−26.5623			−0.894907			−0.447453	+	0.894307i	$0.647669\pi$
$882$	−10.8928	+	1.72525i	−0.366779	+	0.0580921i
$883$	12.3965	+	4.02786i	0.417175	+	0.135548i	0.510081	−	0.860126i	$-0.329615\pi$
$883$	12.3965	+	4.02786i	0.417175	+	0.135548i	−0.0929056	+	0.995675i	$0.529615\pi$
$884$	8.47214	+	26.0746i	0.284949	+	0.876982i
$885$	0.587785	+	0.809017i	0.0197582	+	0.0271948i
$886$	33.3973	+	5.28961i	1.12200	+	0.177708i
$887$	−7.76393	−	23.8949i	−0.260687	−	0.802313i	−0.992656	−	0.120974i	$-0.961398\pi$
$887$	−7.76393	−	23.8949i	−0.260687	−	0.802313i	0.731968	−	0.681339i	$-0.238602\pi$
$888$	−32.6215	+	16.6215i	−1.09470	+	0.557780i
$889$	18.1803	+	13.2088i	0.609749	+	0.443009i
$890$	14.5623	+	14.5623i	0.488130	+	0.488130i
$891$	−5.60034	−	24.9443i	−0.187618	−	0.835665i
$892$		−	12.9443i		−	0.433406i
$893$	12.6133	−	17.3607i	0.422087	−	0.580953i
$894$	−11.6725	−	22.9086i	−0.390387	−	0.766177i
$895$	4.28115	+	13.1760i	0.143103	+	0.440426i
$896$	58.5100	+	9.26708i	1.95468	+	0.309591i
$897$	8.47214	−	6.15537i	0.282876	−	0.205522i
$898$	−12.7846	−	6.51407i	−0.426627	−	0.217377i
$899$	7.60845	+	2.47214i	0.253756	+	0.0824504i
$900$	0.449028	−	0.618034i	0.0149676	−	0.0206011i
$901$		−	18.9443i		−	0.631125i
$902$	11.1779	−	43.7058i	0.372185	−	1.45524i
$903$	41.1246			1.36854
$904$	1.57619	+	9.95167i	0.0524233	+	0.330988i
$905$	−6.18034	+	19.0211i	−0.205441	+	0.632284i
$906$	22.7387	−	44.6273i	0.755444	−	1.48264i
$907$	−24.7477	−	34.0623i	−0.821734	−	1.13102i	−0.989406	−	0.145177i	$-0.953625\pi$
$907$	−24.7477	−	34.0623i	−0.821734	−	1.13102i	0.167671	−	0.985843i	$-0.446375\pi$
$908$	−35.1803	+	25.5600i	−1.16750	+	0.848239i
$909$	2.97168	−	0.965558i	0.0985645	−	0.0320255i
$910$	17.6024	+	34.5467i	0.583514	+	1.14521i
$911$	44.0689	+	32.0179i	1.46007	+	1.06080i	0.983345	+	0.181747i	$0.0581751\pi$
$911$	44.0689	+	32.0179i	1.46007	+	1.06080i	0.476722	+	0.879054i	$0.341825\pi$
$912$	20.0000			0.662266
$913$	−4.02786	−	6.79615i	−0.133303	−	0.224920i
$914$	−40.1591	+	40.1591i	−1.32834	+	1.32834i
$915$	4.25325	−	5.85410i	0.140608	−	0.193531i
$916$	16.4721	−	50.6960i	0.544255	−	1.67504i
$917$	−1.62460	+	0.527864i	−0.0536490	+	0.0174316i
$918$	−20.0109	−	3.16942i	−0.660459	−	0.104606i
$919$	38.3607	−	27.8707i	1.26540	−	0.919368i	0.266393	−	0.963865i	$-0.414168\pi$
$919$	38.3607	−	27.8707i	1.26540	−	0.919368i	0.999010	+	0.0444962i	$0.0141683\pi$
$920$	3.11507	+	1.58721i	0.102701	+	0.0523287i
$921$	−7.28115	+	22.4091i	−0.239922	+	0.738404i
$922$	−2.12311	−	13.4048i	−0.0699207	−	0.441462i
$923$			36.3607i			1.19683i
$924$	12.3107	+	54.8328i	0.404993	+	1.80387i
$925$		−	8.00000i		−	0.263038i
$926$	−5.43153	+	0.860269i	−0.178491	+	0.0282702i
$927$	−0.201626	+	0.620541i	−0.00662227	+	0.0203813i
$928$	10.2726	−	20.1612i	0.337216	−	0.661823i
$929$	22.6803	−	16.4782i	0.744118	−	0.540633i	−0.149880	−	0.988704i	$-0.547889\pi$
$929$	22.6803	−	16.4782i	0.744118	−	0.540633i	0.893998	+	0.448071i	$0.147889\pi$
$930$	−0.715921	+	4.52015i	−0.0234760	+	0.148221i
$931$	60.0023	−	19.4959i	1.96650	−	0.638953i
$932$	−13.0373	−	4.23607i	−0.427050	−	0.138757i
$933$	31.0543	−	42.7426i	1.01667	−	1.39933i
$934$	−26.4721	−	26.4721i	−0.866195	−	0.866195i
$935$	−7.97214	−	3.44095i	−0.260717	−	0.112531i
$936$	−4.00000	+	4.00000i	−0.130744	+	0.130744i
$937$	25.0623	+	18.2088i	0.818750	+	0.594857i	0.916354	−	0.400369i	$-0.131118\pi$
$937$	25.0623	+	18.2088i	0.818750	+	0.594857i	−0.0976043	+	0.995225i	$0.531118\pi$
$938$	−15.3481	+	7.82026i	−0.501134	+	0.255341i
$939$	−21.1478	+	6.87132i	−0.690131	+	0.224237i
$940$	11.2361	−	8.16348i	0.366480	−	0.266263i
$941$	34.7931	+	47.8885i	1.13422	+	1.56112i	0.779791	+	0.626039i	$0.215325\pi$
$941$	34.7931	+	47.8885i	1.13422	+	1.56112i	0.354430	+	0.935083i	$0.384675\pi$
$942$	−7.56044	−	3.85224i	−0.246332	−	0.125513i
$943$	−3.67376	+	11.3067i	−0.119634	+	0.368196i
$944$	1.45309	−	2.00000i	0.0472939	−	0.0650945i
$945$	−28.6525			−0.932065
$946$	1.45097	+	22.7215i	0.0471749	+	0.738739i
$947$		−	54.6180i		−	1.77485i	−0.460954	−	0.887424i	$-0.652493\pi$
$947$		−	54.6180i		−	1.77485i	0.460954	−	0.887424i	$-0.347507\pi$
$948$	41.1246	+	29.8788i	1.33567	+	0.970418i
$949$	5.70634	+	1.85410i	0.185236	+	0.0601867i
$950$	−1.98401	+	3.89384i	−0.0643698	+	0.126333i
$951$	39.1246	−	28.4257i	1.26870	−	0.921766i
$952$	38.2953	+	6.06538i	1.24116	+	0.196580i
$953$	−14.4787	−	44.5609i	−0.469012	−	1.44347i	−0.853867	−	0.520492i	$-0.825749\pi$
$953$	−14.4787	−	44.5609i	−0.469012	−	1.44347i	0.384855	−	0.922977i	$-0.374251\pi$
$954$	3.48276	−	1.77455i	0.112758	−	0.0574533i
$955$	−5.98385	+	8.23607i	−0.193633	+	0.266513i
$956$		−	9.30495i		−	0.300944i
$957$	21.3723	+	2.00000i	0.690867	+	0.0646508i
$958$	−28.3607	+	28.3607i	−0.916292	+	0.916292i
$959$	38.7426	+	28.1482i	1.25107	+	0.908952i
$960$	12.3107	+	4.00000i	0.397327	+	0.129099i
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	−9.26708	+	58.5100i	−0.298783	+	1.88644i
$963$	1.98787	+	2.73607i	0.0640582	+	0.0881686i
$964$	−47.5123	+	15.4377i	−1.53027	+	0.497215i
$965$	−5.70634	−	1.85410i	−0.183694	−	0.0596857i
$966$	−2.31677	−	14.6275i	−0.0745408	−	0.470632i
$967$	30.7214			0.987932			0.493966	−	0.869481i	$-0.335547\pi$
$967$	30.7214			0.987932			0.493966	+	0.869481i	$0.335547\pi$
$968$	−29.8610	+	8.73634i	−0.959767	+	0.280797i
$969$	13.0902			0.420517
$970$	3.11719	+	19.6812i	0.100087	+	0.631925i
$971$	−25.7315	−	8.36068i	−0.825764	−	0.268307i	−0.134504	−	0.990913i	$-0.542944\pi$
$971$	−25.7315	−	8.36068i	−0.825764	−	0.268307i	−0.691260	+	0.722606i	$0.742944\pi$
$972$	−2.43769	−	7.50245i	−0.0781891	−	0.240641i
$973$	32.2299	+	44.3607i	1.03324	+	1.42214i
$974$	1.53629	−	9.69977i	0.0492260	−	0.310801i
$975$	2.61803	+	8.05748i	0.0838442	+	0.258046i
$976$	−17.0130	−	5.52786i	−0.544573	−	0.176943i
$977$	−18.5623	−	13.4863i	−0.593861	−	0.431465i	0.249834	−	0.968289i	$-0.419624\pi$
$977$	−18.5623	−	13.4863i	−0.593861	−	0.431465i	−0.843694	+	0.536824i	$0.819624\pi$
$978$	10.7082	−	10.7082i	0.342411	−	0.342411i
$979$	48.0876	+	4.50000i	1.53689	+	0.143821i
$980$	40.8328			1.30436
$981$	1.69011	−	2.32624i	0.0539611	−	0.0742711i
$982$	−39.1057	+	19.9253i	−1.24791	+	0.635843i
$983$	5.05573	+	15.5599i	0.161253	+	0.496285i	0.998741	−	0.0501711i	$-0.0159767\pi$
$983$	5.05573	+	15.5599i	0.161253	+	0.496285i	−0.837488	+	0.546456i	$0.815977\pi$
$984$	−6.88575	+	43.4749i	−0.219510	+	1.38593i
$985$	−2.38197	+	1.73060i	−0.0758957	+	0.0551415i
$986$	6.72353	−	13.1957i	0.214121	−	0.420235i
$987$	−55.9533	−	18.1803i	−1.78101	−	0.578687i
$988$	19.0211	−	26.1803i	0.605143	−	0.832908i
$989$		−	6.00000i		−	0.190789i
$990$	−0.114175	−	1.78794i	−0.00362873	−	0.0568244i
$991$	−26.0689			−0.828105			−0.414053	−	0.910253i	$-0.635887\pi$
$991$	−26.0689			−0.828105			−0.414053	+	0.910253i	$0.635887\pi$
$992$	11.1744	−	1.76985i	0.354788	−	0.0561929i
$993$	−9.51722	+	29.2910i	−0.302020	+	0.929522i
$994$	45.8171	+	23.3450i	1.45323	+	0.740458i
$995$	13.3148	+	18.3262i	0.422107	+	0.580981i
$996$	4.53077	+	6.23607i	0.143563	+	0.197597i
$997$	−6.49839	+	2.11146i	−0.205806	+	0.0668705i	−0.410106	−	0.912038i	$-0.634508\pi$
$997$	−6.49839	+	2.11146i	−0.205806	+	0.0668705i	0.204300	+	0.978908i	$0.434508\pi$
$998$	25.6828	−	13.0860i	0.812974	−	0.414231i
$999$	−35.4164	−	25.7315i	−1.12053	−	0.814109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.bi.b.301.1	✓	8
8.5	even	2	inner	440.2.bi.b.301.2	yes	8
11.3	even	5	inner	440.2.bi.b.421.2	yes	8
88.69	even	10	inner	440.2.bi.b.421.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.bi.b.301.1	✓	8	1.1	even	1	trivial
440.2.bi.b.301.2	yes	8	8.5	even	2	inner
440.2.bi.b.421.1	yes	8	88.69	even	10	inner
440.2.bi.b.421.2	yes	8	11.3	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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39680 + 0.221232i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(2.26007 + 0.357960i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(-1.39680 + 0.221232i) q^{2} +(-1.53884 - 0.500000i) q^{3} +(1.90211 - 0.618034i) q^{4} +(-0.587785 - 0.809017i) q^{5} +(2.26007 + 0.357960i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(-2.52015 + 1.28408i) q^{8} +(-0.309017 - 0.224514i) q^{9} +(1.00000 + 1.00000i) q^{10} +(3.30220 + 0.309017i) q^{11} -3.23607 q^{12} +(-3.07768 + 4.23607i) q^{13} +(3.36176 + 6.59783i) q^{14} +(0.500000 + 1.53884i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.11803 - 1.53884i) q^{17} +(0.481305 + 0.245237i) q^{18} +(-2.93893 - 0.954915i) q^{19} +(-1.61803 - 1.17557i) q^{20} +8.47214i q^{21} +(-4.68088 + 0.298915i) q^{22} +1.23607 q^{23} +(4.52015 - 0.715921i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(3.36176 - 6.59783i) q^{26} +(3.21644 + 4.42705i) q^{27} +(-6.15537 - 8.47214i) q^{28} +(-3.80423 + 1.23607i) q^{29} +(-1.03884 - 2.03884i) q^{30} +(-1.61803 - 1.17557i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.92705 - 2.12663i) q^{33} +(-2.61803 + 2.61803i) q^{34} +(-3.07768 + 4.23607i) q^{35} +(-0.726543 - 0.236068i) q^{36} +(-7.60845 + 2.47214i) q^{37} +(4.31636 + 0.683644i) q^{38} +(6.85410 - 4.97980i) q^{39} +(2.52015 + 1.28408i) q^{40} +(-2.97214 + 9.14729i) q^{41} +(-1.87431 - 11.8339i) q^{42} -4.85410i q^{43} +(6.47214 - 1.45309i) q^{44} +0.381966i q^{45} +(-1.72654 + 0.273457i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(-6.15537 + 2.00000i) q^{48} +(-16.5172 + 12.0005i) q^{49} +(0.221232 - 1.39680i) q^{50} +(-4.02874 + 1.30902i) q^{51} +(-3.23607 + 9.95959i) q^{52} +(4.25325 - 5.85410i) q^{53} +(-5.47214 - 5.47214i) q^{54} +(-1.69098 - 2.85317i) q^{55} +(10.4721 + 10.4721i) q^{56} +(4.04508 + 2.93893i) q^{57} +(5.04029 - 2.56816i) q^{58} +(0.587785 - 0.190983i) q^{59} +(1.90211 + 2.61803i) q^{60} +(-2.62866 - 3.61803i) q^{61} +(2.52015 + 1.28408i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(4.70228 - 6.47214i) q^{64} +5.23607 q^{65} +(7.35259 + 1.88046i) q^{66} +2.32624i q^{67} +(3.07768 - 4.23607i) q^{68} +(-1.90211 - 0.618034i) q^{69} +(3.36176 - 6.59783i) q^{70} +(5.61803 - 4.08174i) q^{71} +(1.06706 + 0.169006i) q^{72} +(-0.354102 - 1.08981i) q^{73} +(10.0806 - 5.13632i) q^{74} +(0.951057 - 1.30902i) q^{75} -6.18034 q^{76} +(-3.80423 - 16.9443i) q^{77} +(-8.47214 + 8.47214i) q^{78} +(-12.7082 - 9.23305i) q^{79} +(-3.80423 - 1.23607i) q^{80} +(-2.38197 - 7.33094i) q^{81} +(2.12781 - 13.4345i) q^{82} +(-1.40008 - 1.92705i) q^{83} +(5.23607 + 16.1150i) q^{84} +(-2.48990 - 0.809017i) q^{85} +(1.07388 + 6.78022i) q^{86} +6.47214 q^{87} +(-8.71883 + 3.46151i) q^{88} +14.5623 q^{89} +(-0.0845030 - 0.533531i) q^{90} +(26.0746 + 8.47214i) q^{91} +(2.35114 - 0.763932i) q^{92} +(1.90211 + 2.61803i) q^{93} +(1.53629 - 9.69977i) q^{94} +(0.954915 + 2.93893i) q^{95} +(8.15537 - 4.15537i) q^{96} +(11.3992 + 8.28199i) q^{97} +(20.4164 - 20.4164i) q^{98} +(-0.951057 - 0.836881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9	\( 8 q - 2 q^{2} + 6 q^{6} - 4 q^{7} + 4 q^{8} + 2 q^{9} + 8 q^{10} - 8 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 8 q^{17} - 8 q^{18} - 4 q^{20} - 22 q^{22} - 8 q^{23} + 12 q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{30} - 4 q^{31} - 32 q^{32} - 26 q^{33} - 12 q^{34} + 20 q^{38} + 28 q^{39} - 4 q^{40} + 12 q^{41} - 28 q^{42} + 16 q^{44} - 8 q^{46} - 44 q^{47} - 74 q^{49} + 2 q^{50} - 8 q^{52} - 8 q^{54} - 18 q^{55} + 48 q^{56} + 10 q^{57} - 8 q^{58} - 4 q^{62} + 4 q^{63} + 24 q^{65} + 4 q^{66} - 4 q^{70} + 36 q^{71} - 4 q^{72} + 24 q^{73} - 16 q^{74} + 40 q^{76} - 32 q^{78} - 48 q^{79} - 28 q^{81} + 22 q^{82} + 24 q^{84} + 18 q^{86} + 16 q^{87} - 4 q^{88} + 36 q^{89} + 2 q^{90} + 36 q^{94} + 30 q^{95} + 16 q^{96} + 42 q^{97} + 56 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^6 - 4 * q^7 + 4 * q^8 + 2 * q^9 + 8 * q^10 - 8 * q^12 - 4 * q^14 + 4 * q^15 + 8 * q^16 + 8 * q^17 - 8 * q^18 - 4 * q^20 - 22 * q^22 - 8 * q^23 + 12 * q^24 + 2 * q^25 - 4 * q^26 + 4 * q^30 - 4 * q^31 - 32 * q^32 - 26 * q^33 - 12 * q^34 + 20 * q^38 + 28 * q^39 - 4 * q^40 + 12 * q^41 - 28 * q^42 + 16 * q^44 - 8 * q^46 - 44 * q^47 - 74 * q^49 + 2 * q^50 - 8 * q^52 - 8 * q^54 - 18 * q^55 + 48 * q^56 + 10 * q^57 - 8 * q^58 - 4 * q^62 + 4 * q^63 + 24 * q^65 + 4 * q^66 - 4 * q^70 + 36 * q^71 - 4 * q^72 + 24 * q^73 - 16 * q^74 + 40 * q^76 - 32 * q^78 - 48 * q^79 - 28 * q^81 + 22 * q^82 + 24 * q^84 + 18 * q^86 + 16 * q^87 - 4 * q^88 + 36 * q^89 + 2 * q^90 + 36 * q^94 + 30 * q^95 + 16 * q^96 + 42 * q^97 + 56 * q^98

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