LMFDB - Embedded newform 440.2.bi.b.301.2

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			301.2
Root			$-0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	440.301
Dual form			440.2.bi.b.421.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.221232 - 1.39680i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.587785 + 0.809017i) q^{5} +(0.357960 - 2.26007i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(-0.221232 - 1.39680i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.587785 + 0.809017i) q^{5} +(0.357960 - 2.26007i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(1.28408 + 2.52015i) 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} +(-6.59783 + 3.36176i) q^{14} +(0.500000 + 1.53884i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.11803 - 1.53884i) q^{17} +(-0.245237 + 0.481305i) q^{18} +(2.93893 + 0.954915i) q^{19} +(-1.61803 - 1.17557i) q^{20} -8.47214i q^{21} +(0.298915 + 4.68088i) q^{22} +1.23607 q^{23} +(0.715921 + 4.52015i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-6.59783 - 3.36176i) q^{26} +(-3.21644 - 4.42705i) q^{27} +(6.15537 + 8.47214i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.03884 - 1.03884i) 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} +(0.683644 - 4.31636i) q^{38} +(6.85410 - 4.97980i) q^{39} +(-1.28408 + 2.52015i) q^{40} +(-2.97214 + 9.14729i) q^{41} +(-11.8339 + 1.87431i) q^{42} +4.85410i q^{43} +(6.47214 - 1.45309i) q^{44} -0.381966i q^{45} +(-0.273457 - 1.72654i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(6.15537 - 2.00000i) q^{48} +(-16.5172 + 12.0005i) q^{49} +(1.39680 + 0.221232i) 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} +(-2.56816 - 5.04029i) q^{58} +(-0.587785 + 0.190983i) q^{59} +(-1.90211 - 2.61803i) q^{60} +(2.62866 + 3.61803i) q^{61} +(-1.28408 + 2.52015i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(-4.70228 + 6.47214i) q^{64} +5.23607 q^{65} +(-1.88046 + 7.35259i) q^{66} -2.32624i q^{67} +(-3.07768 + 4.23607i) q^{68} +(1.90211 + 0.618034i) q^{69} +(-6.59783 - 3.36176i) q^{70} +(5.61803 - 4.08174i) q^{71} +(0.169006 - 1.06706i) q^{72} +(-0.354102 - 1.08981i) q^{73} +(-5.13632 - 10.0806i) 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} +(13.4345 + 2.12781i) q^{82} +(1.40008 + 1.92705i) q^{83} +(5.23607 + 16.1150i) q^{84} +(2.48990 + 0.809017i) q^{85} +(6.78022 - 1.07388i) q^{86} +6.47214 q^{87} +(-3.46151 - 8.71883i) q^{88} +14.5623 q^{89} +(-0.533531 + 0.0845030i) q^{90} +(-26.0746 - 8.47214i) q^{91} +(-2.35114 + 0.763932i) q^{92} +(-1.90211 - 2.61803i) q^{93} +(9.69977 + 1.53629i) q^{94} +(0.954915 + 2.93893i) q^{95} +(-4.15537 - 8.15537i) 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 $

$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$2$	−0.221232	−	1.39680i	−0.156434	−	0.987688i
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.717462	−	0.696598i	$-0.245304\pi$
$3$	1.53884	+	0.500000i	0.888451	+	0.288675i	0.170989	+	0.985273i	$0.445304\pi$
$4$	−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
$6$	0.357960	−	2.26007i	0.146137	−	0.922671i
$7$	−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	$-0.553885\pi$
$8$	1.28408	+	2.52015i	0.453990	+	0.891007i
$9$	−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	$-0.541325\pi$
$13$	3.07768	−	4.23607i	0.853596	−	1.17487i	0.983059	−	0.183290i	$-0.0586746\pi$
$14$	−6.59783	+	3.36176i	−1.76334	+	0.898469i
$15$	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	$0.197162\pi$
$18$	−0.245237	+	0.481305i	−0.0578030	+	0.113445i
$19$	2.93893	+	0.954915i	0.674236	+	0.219073i	0.626070	−	0.779767i	$-0.284662\pi$
$19$	2.93893	+	0.954915i	0.674236	+	0.219073i	0.0481659	+	0.998839i	$0.484662\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$		−	8.47214i		−	1.84877i
$22$	0.298915	+	4.68088i	0.0637290	+	0.997967i
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	0.715921	+	4.52015i	0.146137	+	0.922671i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−6.59783	−	3.36176i	−1.29394	−	0.659296i
$27$	−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	0.0662984	−	0.997800i	$-0.478881\pi$
$29$	3.80423	−	1.23607i	0.706427	−	0.229532i	0.640129	+	0.768268i	$0.278881\pi$
$30$	2.03884	−	1.03884i	0.372240	−	0.189666i
$31$	−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	0.392607	−	0.919707i	$-0.371573\pi$
$37$	7.60845	−	2.47214i	1.25082	−	0.406417i	0.858215	+	0.513290i	$0.171573\pi$
$38$	0.683644	−	4.31636i	0.110902	−	0.700205i
$39$	6.85410	−	4.97980i	1.09753	−	0.797406i
$40$	−1.28408	+	2.52015i	−0.203031	+	0.398470i
$41$	−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	$0.829551\pi$
$42$	−11.8339	+	1.87431i	−1.82601	+	0.289212i
$43$			4.85410i			0.740244i	0.928983	+	0.370122i	$0.120684\pi$
$43$			4.85410i			0.740244i	−0.928983	+	0.370122i	$0.879316\pi$
$44$	6.47214	−	1.45309i	0.975711	−	0.219061i
$45$		−	0.381966i		−	0.0569401i
$46$	−0.273457	−	1.72654i	−0.0403191	−	0.254565i
$47$	−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
$50$	1.39680	+	0.221232i	0.197538	+	0.0312869i
$51$	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	−0.994151	−	0.107998i	$-0.965556\pi$
$53$	−4.25325	+	5.85410i	−0.584229	+	0.804123i	0.409922	+	0.912121i	$0.365556\pi$
$54$	−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
$58$	−2.56816	−	5.04029i	−0.337216	−	0.661823i
$59$	−0.587785	+	0.190983i	−0.0765231	+	0.0248639i	−0.347028	−	0.937855i	$-0.612809\pi$
$59$	−0.587785	+	0.190983i	−0.0765231	+	0.0248639i	0.270505	+	0.962718i	$0.412809\pi$
$60$	−1.90211	−	2.61803i	−0.245562	−	0.337987i
$61$	2.62866	+	3.61803i	0.336565	+	0.463242i	0.943434	−	0.331560i	$-0.107575\pi$
$61$	2.62866	+	3.61803i	0.336565	+	0.463242i	−0.606869	+	0.794802i	$0.707575\pi$
$62$	−1.28408	+	2.52015i	−0.163078	+	0.320059i
$63$	−0.618034	+	1.90211i	−0.0778650	+	0.239644i
$64$	−4.70228	+	6.47214i	−0.587785	+	0.809017i
$65$	5.23607			0.649454
$66$	−1.88046	+	7.35259i	−0.231468	+	0.905042i
$67$		−	2.32624i		−	0.284195i	−0.989853	−	0.142098i	$-0.954615\pi$
$67$		−	2.32624i		−	0.284195i	0.989853	−	0.142098i	$-0.0453847\pi$
$68$	−3.07768	+	4.23607i	−0.373224	+	0.513699i
$69$	1.90211	+	0.618034i	0.228988	+	0.0744025i
$70$	−6.59783	−	3.36176i	−0.788592	−	0.401807i
$71$	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	$0.164807\pi$
$72$	0.169006	−	1.06706i	0.0199175	−	0.125754i
$73$	−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	$0.921361\pi$
$74$	−5.13632	−	10.0806i	−0.597085	−	1.17184i
$75$	−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
$82$	13.4345	+	2.12781i	1.48359	+	0.234978i
$83$	1.40008	+	1.92705i	0.153679	+	0.211521i	0.878914	−	0.476980i	$-0.158269\pi$
$83$	1.40008	+	1.92705i	0.153679	+	0.211521i	−0.725235	+	0.688502i	$0.758269\pi$
$84$	5.23607	+	16.1150i	0.571302	+	1.75829i
$85$	2.48990	+	0.809017i	0.270067	+	0.0877502i
$86$	6.78022	−	1.07388i	0.731130	−	0.115800i
$87$	6.47214			0.693886
$88$	−3.46151	−	8.71883i	−0.368999	−	0.929430i
$89$	14.5623			1.54360			0.771801	−	0.635865i	$-0.219356\pi$
$89$	14.5623			1.54360			0.771801	+	0.635865i	$0.219356\pi$
$90$	−0.533531	+	0.0845030i	−0.0562391	+	0.00890740i
$91$	−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
$94$	9.69977	+	1.53629i	1.00046	+	0.158457i
$95$	0.954915	+	2.93893i	0.0979722	+	0.301527i
$96$	−4.15537	−	8.15537i	−0.424105	−	0.832354i
$97$	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	−0.499763	−	0.866162i	$-0.666579\pi$
$101$	4.80828	−	6.61803i	0.478442	−	0.658519i	0.978205	+	0.207643i	$0.0665794\pi$
$102$	−2.71972	−	5.33776i	−0.269293	−	0.528517i
$103$	−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	$0.926820\pi$
$104$	14.6275	+	2.31677i	1.43434	+	0.227178i
$105$	6.85410	−	4.97980i	0.668892	−	0.485978i
$106$	9.11798	+	4.64584i	0.885616	+	0.451244i
$107$	8.42075	+	2.73607i	0.814065	+	0.264506i	0.686318	−	0.727301i	$-0.259226\pi$
$107$	8.42075	+	2.73607i	0.814065	+	0.264506i	0.127746	+	0.991807i	$0.459226\pi$
$108$	8.85410	+	6.43288i	0.851986	+	0.619004i
$109$		−	7.52786i		−	0.721039i	−0.932752	−	0.360519i	$-0.882599\pi$
$109$		−	7.52786i		−	0.721039i	0.932752	−	0.360519i	$-0.117401\pi$
$110$	−3.61121	+	2.99318i	−0.344316	+	0.285389i
$111$	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	$0.0464122\pi$
$114$	3.21020	−	6.30037i	0.300663	−	0.590083i
$115$	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
$118$	0.396802	+	0.778768i	0.0365286	+	0.0716914i
$119$	−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
$126$	2.79360	+	0.442463i	0.248874	+	0.0394178i
$127$	−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	$0.360984\pi$
$128$	10.0806	+	5.13632i	0.891007	+	0.453990i
$129$	−2.42705	+	7.46969i	−0.213690	+	0.657670i
$130$	−1.15838	−	7.31375i	−0.101597	−	0.641458i
$131$			0.326238i			0.0285035i	0.999898	+	0.0142518i	$0.00453663\pi$
$131$			0.326238i			0.0285035i	−0.999898	+	0.0142518i	$0.995463\pi$
$132$	10.6861	+	1.00000i	0.930109	+	0.0870388i
$133$		−	16.1803i		−	1.40301i
$134$	−3.24929	+	0.514638i	−0.280696	+	0.0444579i
$135$	1.69098	−	5.20431i	0.145537	−	0.447916i
$136$	6.59783	+	3.36176i	0.565759	+	0.288269i
$137$	−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	$0.427765\pi$
$138$	0.442463	−	2.79360i	0.0376650	−	0.237807i
$139$	9.95959	−	3.23607i	0.844762	−	0.274480i	0.145511	−	0.989357i	$-0.453517\pi$
$139$	9.95959	−	3.23607i	0.844762	−	0.274480i	0.699250	+	0.714877i	$0.253517\pi$
$140$	−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
$146$	−1.44392	+	0.735712i	−0.119499	+	0.0608879i
$147$	−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	0.988764	−	0.149482i	$-0.0477607\pi$
$149$	6.60440	+	9.09017i	0.541053	+	0.744696i	−0.447711	+	0.894178i	$0.647761\pi$
$150$	2.03884	+	1.03884i	0.166471	+	0.0848211i
$151$	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	$-0.249738\pi$
$152$	1.36729	+	8.63271i	0.110902	+	0.700205i
$153$	−1.00000			−0.0808452
$154$	22.8262	−	9.06236i	1.83939	−	0.730266i
$155$		−	2.00000i		−	0.160644i
$156$	−9.95959	+	13.7082i	−0.797406	+	1.09753i
$157$	3.52671	+	1.14590i	0.281462	+	0.0914526i	0.446346	−	0.894860i	$-0.352725\pi$
$157$	3.52671	+	1.14590i	0.281462	+	0.0914526i	−0.164884	+	0.986313i	$0.552725\pi$
$158$	−10.0853	+	19.7935i	−0.802342	+	1.57469i
$159$	−9.47214	+	6.88191i	−0.751189	+	0.545771i
$160$	0.884927	−	5.58721i	0.0699596	−	0.441708i
$161$	−2.00000	−	6.15537i	−0.157622	−	0.485111i
$162$	−9.71290	+	4.94897i	−0.763118	+	0.388828i
$163$	−3.88998	+	5.35410i	−0.304687	+	0.419366i	−0.933715	−	0.358017i	$-0.883453\pi$
$163$	−3.88998	+	5.35410i	−0.304687	+	0.419366i	0.629028	+	0.777383i	$0.283453\pi$
$164$		−	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	$0.510823\pi$
$168$	21.3510	−	10.8789i	1.64727	−	0.839325i
$169$	−4.45492	−	13.7108i	−0.342686	−	1.05468i
$170$	0.579192	−	3.65688i	0.0444220	−	0.280470i
$171$	−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	0.476141	−	0.879369i	$-0.342035\pi$
$173$	4.53077	+	1.47214i	0.344468	+	0.111924i	−0.131673	+	0.991293i	$0.542035\pi$
$174$	−1.43184	−	9.04029i	−0.108548	−	0.685343i
$175$	5.23607			0.395810
$176$	−11.4127	+	6.76393i	−0.860263	+	0.509851i
$177$	−1.00000			−0.0751646
$178$	−3.22164	−	20.3407i	−0.241472	−	1.52460i
$179$	13.1760	+	4.28115i	0.984823	+	0.319988i	0.756785	−	0.653664i	$-0.226769\pi$
$179$	13.1760	+	4.28115i	0.984823	+	0.319988i	0.228038	+	0.973652i	$0.426769\pi$
$180$	0.236068	+	0.726543i	0.0175955	+	0.0541533i
$181$	11.7557	+	16.1803i	0.873795	+	1.20268i	0.978101	+	0.208130i	$0.0667377\pi$
$181$	11.7557	+	16.1803i	0.873795	+	1.20268i	−0.104306	+	0.994545i	$0.533262\pi$
$182$	−6.06538	+	38.2953i	−0.449596	+	2.83864i
$183$	2.23607	+	6.88191i	0.165295	+	0.508725i
$184$	1.58721	+	3.11507i	0.117011	+	0.229646i
$185$	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
$190$	3.89384	−	1.98401i	0.282489	−	0.143935i
$191$	−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	$0.230717\pi$
$194$	9.04645	−	17.7546i	0.649497	−	1.27471i
$195$	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	$0.0334476\pi$
$197$			2.94427i			0.209771i	−0.994484	+	0.104885i	$0.966552\pi$
$198$	0.958553	−	1.51358i	0.0681214	−	0.107566i
$199$	−22.6525			−1.60579			−0.802896	−	0.596120i	$-0.796708\pi$
$199$	−22.6525			−1.60579			−0.802896	+	0.596120i	$0.796708\pi$
$200$	−2.79360	+	0.442463i	−0.197538	+	0.0312869i
$201$	1.16312	−	3.57971i	0.0820401	−	0.252493i
$202$	−10.3078	−	5.25210i	−0.725256	−	0.369537i
$203$	−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
$206$	−2.15246	+	1.09673i	−0.149969	+	0.0764131i
$207$	−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	−0.394737	−	0.918794i	$-0.629164\pi$
$211$	8.73102	−	12.0172i	0.601068	−	0.827300i	0.995806	+	0.0914944i	$0.0291644\pi$
$212$	4.47214	−	13.7638i	0.307148	−	0.945303i
$213$	10.6861	−	3.47214i	0.732202	−	0.237907i
$214$	1.95881	−	12.3674i	0.133901	−	0.845420i
$215$	−3.92705	+	2.85317i	−0.267823	+	0.194585i
$216$	7.02666	−	13.7906i	0.478103	−	0.938331i
$217$	−3.23607	+	9.95959i	−0.219679	+	0.676101i
$218$	−10.5149	+	1.66540i	−0.712161	+	0.112795i
$219$		−	1.85410i		−	0.125289i
$220$	4.97980	+	4.38197i	0.335738	+	0.295432i
$221$		−	13.7082i		−	0.922114i
$222$	−2.86368	−	18.0806i	−0.192198	−	1.21349i
$223$	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	$0.0304696\pi$
$224$	−13.4471	+	26.3913i	−0.898469	+	1.76334i
$225$	0.309017	−	0.224514i	0.0206011	−	0.0149676i
$226$	−4.97584	−	0.788095i	−0.330988	−	0.0524233i
$227$	20.6785	−	6.71885i	1.37248	−	0.445946i	0.472290	−	0.881443i	$-0.343428\pi$
$227$	20.6785	−	6.71885i	1.37248	−	0.445946i	0.900190	+	0.435498i	$0.143428\pi$
$228$	−9.51057	−	3.09017i	−0.629853	−	0.204652i
$229$	−15.6659	+	21.5623i	−1.03523	+	1.42488i	−0.134290	+	0.990942i	$0.542875\pi$
$229$	−15.6659	+	21.5623i	−1.03523	+	1.42488i	−0.900944	+	0.433935i	$0.857125\pi$
$230$	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	$0.772079\pi$
$234$	1.28408	+	2.52015i	0.0839429	+	0.164747i
$235$	−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
$238$	−8.80121	+	17.2733i	−0.570498	+	1.11966i
$239$	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	$0.797572\pi$
$242$	0.459395	−	15.5496i	0.0295310	−	0.999564i
$243$			3.94427i			0.253025i
$244$	−7.23607	−	5.25731i	−0.463242	−	0.336565i
$245$	−19.4172	−	6.30902i	−1.24052	−	0.403068i
$246$	19.6096	+	9.99162i	1.25027	+	0.637042i
$247$	13.0902	−	9.51057i	0.832908	−	0.605143i
$248$	0.884927	−	5.58721i	0.0561929	−	0.354788i
$249$	1.19098	+	3.66547i	0.0754755	+	0.232290i
$250$	0.642040	+	1.26007i	0.0406061	+	0.0796940i
$251$	−7.05342	+	9.70820i	−0.445208	+	0.612776i	−0.971360	−	0.237614i	$-0.923635\pi$
$251$	−7.05342	+	9.70820i	−0.445208	+	0.612776i	0.526151	+	0.850391i	$0.323635\pi$
$252$		−	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	$0.978205\pi$
$258$	10.9706	+	1.73758i	0.683001	+	0.108177i
$259$	−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
$262$	0.455690	−	0.0721742i	0.0281526	−	0.00445894i
$263$	−29.2361			−1.80277			−0.901387	−	0.433015i	$-0.857450\pi$
$263$	−29.2361			−1.80277			−0.901387	+	0.433015i	$0.857450\pi$
$264$	−0.967310	−	15.1477i	−0.0595338	−	0.932273i
$265$	−7.23607			−0.444508
$266$	−22.6007	+	3.57960i	−1.38574	+	0.219480i
$267$	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	$-0.967457\pi$
$269$	−12.8658	−	17.7082i	−0.784439	−	1.07969i	0.210339	−	0.977629i	$-0.432543\pi$
$270$	−7.64349	−	1.21061i	−0.465168	−	0.0736754i
$271$	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	−0.977303	−	0.211846i	$-0.932052\pi$
$277$	−7.88597	+	10.8541i	−0.473822	+	0.652160i	0.503481	+	0.864006i	$0.332052\pi$
$278$	−6.72353	−	13.1957i	−0.403250	−	0.791423i
$279$	0.236068	+	0.726543i	0.0141330	+	0.0434970i
$280$	14.6275	+	2.31677i	0.874161	+	0.138453i
$281$	−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	$0.329912\pi$
$282$	14.1583	+	7.21400i	0.843113	+	0.429587i
$283$	1.45309	+	0.472136i	0.0863769	+	0.0280656i	0.351887	−	0.936043i	$-0.385540\pi$
$283$	1.45309	+	0.472136i	0.0863769	+	0.0280656i	−0.265510	+	0.964108i	$0.585540\pi$
$284$	−8.16348	+	11.2361i	−0.484413	+	0.666738i
$285$			5.00000i			0.296174i
$286$	20.7485	+	13.1400i	1.22688	+	0.776987i
$287$	50.3607			2.97270
$288$	0.338012	+	2.13412i	0.0199175	+	0.125754i
$289$	−3.13525	+	9.64932i	−0.184427	+	0.567607i
$290$	2.56816	−	5.04029i	0.150807	−	0.295976i
$291$	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	−0.327087	−	0.944994i	$-0.606067\pi$
$293$	−0.620541	+	0.201626i	−0.0362524	+	0.0117791i	0.290835	+	0.956773i	$0.406067\pi$
$294$	21.2094	+	41.6258i	1.23696	+	2.42767i
$295$	−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
$302$	−30.5740	−	4.84244i	−1.75933	−	0.278651i
$303$	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
$306$	0.221232	+	1.39680i	0.0126470	+	0.0798499i
$307$			14.5623i			0.831115i	0.909567	+	0.415557i	$0.136413\pi$
$307$			14.5623i			0.831115i	−0.909567	+	0.415557i	$0.863587\pi$
$308$	−17.7082	−	29.8788i	−1.00902	−	1.70250i
$309$		−	2.76393i		−	0.157235i
$310$	−2.79360	+	0.442463i	−0.158666	+	0.0251302i
$311$	−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	$0.723413\pi$
$312$	21.3510	+	10.8789i	1.20876	+	0.615896i
$313$	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	$0.173031\pi$
$314$	0.820372	−	5.17963i	0.0462963	−	0.292303i
$315$	−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	$-0.482934\pi$
$317$	17.5680	−	24.1803i	0.986720	−	1.35810i	0.933130	−	0.359540i	$-0.117066\pi$
$318$	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
$322$	−8.15537	+	4.15537i	−0.454481	+	0.231570i
$323$	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
$326$	8.33921	+	4.24904i	0.461866	+	0.235333i
$327$	3.76393	−	11.5842i	0.208146	−	0.640607i
$328$	−26.8690	+	4.25563i	−1.48359	+	0.234978i
$329$	36.3607			2.00463
$330$	−7.05368	+	2.80042i	−0.388292	+	0.154158i
$331$			19.0344i			1.04623i	0.852263	+	0.523114i	$0.175230\pi$
$331$			19.0344i			1.04623i	−0.852263	+	0.523114i	$0.824770\pi$
$332$	−3.85410	−	2.80017i	−0.211521	−	0.153679i
$333$	−2.90617	−	0.944272i	−0.159257	−	0.0517458i
$334$	9.29168	−	18.2360i	0.508418	−	0.997827i
$335$	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	$-0.314489\pi$
$338$	−18.1657	+	9.25590i	−0.988086	+	0.503455i
$339$	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
$344$	−12.2331	+	6.23305i	−0.659562	+	0.336064i
$345$	0.618034	+	1.90211i	0.0332738	+	0.102406i
$346$	1.05393	−	6.65427i	0.0566598	−	0.357736i
$347$	9.70232	+	13.3541i	0.520848	+	0.716886i	0.985701	−	0.168502i	$-0.0538929\pi$
$347$	9.70232	+	13.3541i	0.520848	+	0.716886i	−0.464853	+	0.885388i	$0.653893\pi$
$348$	−12.3107	+	4.00000i	−0.659925	+	0.214423i
$349$	−0.898056	−	0.291796i	−0.0480718	−	0.0156195i	0.284882	−	0.958562i	$-0.408045\pi$
$349$	−0.898056	−	0.291796i	−0.0480718	−	0.0156195i	−0.332954	+	0.942943i	$0.608045\pi$
$350$	−1.15838	−	7.31375i	−0.0619183	−	0.390936i
$351$	−28.6525			−1.52936
$352$	11.9727	+	14.4449i	0.638148	+	0.769914i
$353$	4.14590			0.220664			0.110332	−	0.993895i	$-0.464809\pi$
$353$	4.14590			0.220664			0.110332	+	0.993895i	$0.464809\pi$
$354$	0.221232	+	1.39680i	0.0117583	+	0.0742392i
$355$	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
$358$	3.06497	−	19.3514i	0.161989	−	1.02276i
$359$	−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	$0.925696\pi$
$360$	0.962611	−	0.490475i	0.0507340	−	0.0258503i
$361$	−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
$366$	9.11798	−	4.64584i	0.476604	−	0.242842i
$367$	−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
$370$	5.13632	−	10.0806i	0.267024	−	0.524065i
$371$	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	$0.0624347\pi$
$373$			7.52786i			0.389778i	−0.980825	+	0.194889i	$0.937565\pi$
$374$	7.83625	+	9.45428i	0.405203	+	0.488869i
$375$	−1.61803			−0.0835549
$376$	−19.3995	+	3.07259i	−1.00046	+	0.158457i
$377$	6.47214	−	19.9192i	0.333332	−	1.02589i
$378$	36.1042	+	18.3960i	1.85700	+	0.946189i
$379$	1.33457	+	1.83688i	0.0685524	+	0.0943542i	0.841916	−	0.539608i	$-0.181428\pi$
$379$	1.33457	+	1.83688i	0.0685524	+	0.0943542i	−0.773364	+	0.633962i	$0.781428\pi$
$380$	−3.63271	−	5.00000i	−0.186354	−	0.256495i
$381$	−6.60440	+	2.14590i	−0.338353	+	0.109938i
$382$	−12.8280	+	6.53618i	−0.656336	+	0.334420i
$383$	−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	−0.610226	−	0.792227i	$-0.708921\pi$
$389$	−12.5882	+	4.09017i	−0.638250	+	0.207380i	−0.0280236	+	0.999607i	$0.508921\pi$
$390$	1.87431	−	11.8339i	0.0949091	−	0.599233i
$391$	2.61803	−	1.90211i	0.132400	−	0.0961940i
$392$	−51.4523	−	26.2163i	−2.59874	−	1.32412i
$393$	−0.163119	+	0.502029i	−0.00822826	+	0.0253240i
$394$	4.11257	−	0.651366i	0.207188	−	0.0328154i
$395$		−	15.7082i		−	0.790366i
$396$	−2.32624	−	1.00406i	−0.116898	−	0.0504558i
$397$			4.58359i			0.230044i	0.993363	+	0.115022i	$0.0366938\pi$
$397$			4.58359i			0.230044i	−0.993363	+	0.115022i	$0.963306\pi$
$398$	5.01145	+	31.6410i	0.251201	+	1.58602i
$399$	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	$0.470589\pi$
$402$	−5.25747	−	0.832701i	−0.262219	−	0.0415314i
$403$	−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	$0.516941\pi$
$410$	6.17516	+	12.1194i	0.304969	+	0.598536i
$411$	−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
$414$	−0.303130	+	0.594926i	−0.0148980	+	0.0292390i
$415$	−0.736068	+	2.26538i	−0.0361322	+	0.111203i
$416$	−29.2550	+	4.63354i	−1.43434	+	0.227178i
$417$	16.9443			0.829765
$418$	−3.59135	+	14.0422i	−0.175659	+	0.686827i
$419$			18.0902i			0.883763i	0.897074	+	0.441881i	$0.145689\pi$
$419$			18.0902i			0.883763i	−0.897074	+	0.441881i	$0.854311\pi$
$420$	−9.95959	+	13.7082i	−0.485978	+	0.668892i
$421$	−30.8828	−	10.0344i	−1.50514	−	0.489049i	−0.563626	−	0.826030i	$-0.690594\pi$
$421$	−30.8828	−	10.0344i	−1.50514	−	0.489049i	−0.941511	+	0.336981i	$0.890594\pi$
$422$	−18.7173	−	9.53692i	−0.911142	−	0.464250i
$423$	2.14590	−	1.55909i	0.104337	−	0.0758054i
$424$	−20.2147	−	3.20170i	−0.981713	−	0.155488i
$425$	0.809017	+	2.48990i	0.0392431	+	0.120778i
$426$	−7.21400	−	14.1583i	−0.349519	−	0.685971i
$427$	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	$0.977512\pi$
$434$	14.6275	+	2.31677i	0.702143	+	0.111208i
$435$	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
$438$	−2.58981	+	0.410186i	−0.123746	+	0.0195995i
$439$	−24.6525			−1.17660			−0.588299	−	0.808643i	$-0.700202\pi$
$439$	−24.6525			−1.17660			−0.588299	+	0.808643i	$0.700202\pi$
$440$	5.01905	−	7.92522i	0.239274	−	0.377820i
$441$	7.79837			0.371351
$442$	−19.1477	+	3.03269i	−0.910761	+	0.144250i
$443$	22.7396	+	7.38854i	1.08039	+	0.351040i	0.794526	−	0.607230i	$-0.207719\pi$
$443$	22.7396	+	7.38854i	1.08039	+	0.351040i	0.285865	+	0.958270i	$0.407719\pi$
$444$	−24.6215	+	8.00000i	−1.16848	+	0.379663i
$445$	8.55951	+	11.7812i	0.405760	+	0.558480i
$446$	−9.04029	−	1.43184i	−0.428070	−	0.0677997i
$447$	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
$454$	−13.9596	−	27.3973i	−0.655158	−	1.28582i
$455$	−8.47214	−	26.0746i	−0.397180	−	1.22239i
$456$	−2.21232	+	13.9680i	−0.103601	+	0.654113i
$457$	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	$-0.0885061\pi$
$458$	33.5841	+	17.1119i	1.56928	+	0.799589i
$459$	−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	$-0.928257\pi$
$461$		−	9.59675i		−	0.446965i	0.974708	−	0.223483i	$-0.0717426\pi$
$462$	39.6571	−	2.53245i	1.84501	−	0.117820i
$463$	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
$466$	−4.40060	+	8.63667i	−0.203854	+	0.400086i
$467$	−15.5599	−	21.4164i	−0.720028	−	0.991033i	−0.999523	−	0.0308861i	$-0.990167\pi$
$467$	−15.5599	−	21.4164i	−0.720028	−	0.991033i	0.279495	−	0.960147i	$-0.409833\pi$
$468$	3.23607	−	2.35114i	0.149587	−	0.108682i
$469$	−11.5842	+	3.76393i	−0.534908	+	0.173802i
$470$	4.45850	+	8.75029i	0.205655	+	0.403621i
$471$	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
$478$	−6.49859	−	1.02928i	−0.297239	−	0.0470780i
$479$	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	$0.0756407\pi$
$480$	4.15537	−	8.15537i	0.189666	−	0.372240i
$481$	12.9443	−	39.8384i	0.590208	−	1.81647i
$482$	5.52608	+	34.8903i	0.251706	+	1.58921i
$483$		−	10.4721i		−	0.476499i
$484$	−21.8213	+	2.79837i	−0.991877	+	0.127199i
$485$			14.0902i			0.639802i
$486$	5.50937	−	0.872598i	0.249910	−	0.0395819i
$487$	−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	$0.150291\pi$
$488$	−5.74258	+	11.2704i	−0.259954	+	0.510189i
$489$	−8.66312	+	6.29412i	−0.391760	+	0.284630i
$490$	−4.51676	+	28.5177i	−0.204046	+	1.28830i
$491$	−29.5155	+	9.59017i	−1.33202	+	0.432798i	−0.886605	−	0.462528i	$-0.846943\pi$
$491$	−29.5155	+	9.59017i	−1.33202	+	0.432798i	−0.445411	+	0.895326i	$0.646943\pi$
$492$	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
$498$	4.85645	−	2.47449i	0.217623	−	0.110884i
$499$	19.3844	−	6.29837i	0.867765	−	0.281954i	0.158897	−	0.987295i	$-0.449206\pi$
$499$	19.3844	−	6.29837i	0.867765	−	0.281954i	0.708868	+	0.705341i	$0.249206\pi$
$500$	1.61803	−	1.17557i	0.0723607	−	0.0525731i
$501$	13.7638	+	18.9443i	0.614922	+	0.846368i
$502$	15.1209	+	7.70447i	0.674878	+	0.343868i
$503$	−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	$0.788262\pi$
$504$	−5.58721	+	0.884927i	−0.248874	+	0.0394178i
$505$	8.18034			0.364020
$506$	0.369480	+	5.78589i	0.0164254	+	0.257214i
$507$		−	23.3262i		−	1.03595i
$508$	5.04531	−	6.94427i	0.223849	−	0.308102i
$509$	22.3763	+	7.27051i	0.991813	+	0.322260i	0.759590	−	0.650403i	$-0.225400\pi$
$509$	22.3763	+	7.27051i	0.991813	+	0.322260i	0.232224	+	0.972662i	$0.425400\pi$
$510$	2.71972	−	5.33776i	0.120431	−	0.236360i
$511$	−4.85410	+	3.52671i	−0.214733	+	0.156013i
$512$	−22.3488	−	3.53971i	−0.987688	−	0.156434i
$513$	−5.22542	−	16.0822i	−0.230708	−	0.710047i
$514$	−9.82652	+	5.00686i	−0.433429	+	0.220843i
$515$	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
$520$	6.72353	+	13.1957i	0.294846	+	0.578668i
$521$	−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	$-0.344744\pi$
$522$	−0.338012	+	2.13412i	−0.0147944	+	0.0934081i
$523$	−22.1846	−	30.5344i	−0.970064	−	1.33518i	−0.942015	−	0.335571i	$-0.891071\pi$
$523$	−22.1846	−	30.5344i	−0.970064	−	1.33518i	−0.0280488	−	0.999607i	$-0.508929\pi$
$524$	−0.201626	−	0.620541i	−0.00880808	−	0.0271085i
$525$	8.05748	+	2.61803i	0.351657	+	0.114260i
$526$	6.46795	+	40.8370i	0.282016	+	1.78058i
$527$	−5.23607			−0.228087
$528$	−20.9443	+	4.70228i	−0.911482	+	0.204641i
$529$	−21.4721			−0.933571
$530$	1.60085	+	10.1074i	0.0695364	+	0.439035i
$531$	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
$534$	5.21273	−	32.9119i	0.225577	−	1.42424i
$535$	2.73607	+	8.42075i	0.118291	+	0.364061i
$536$	5.86246	−	2.98707i	0.253220	−	0.129022i
$537$	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	−0.965816	−	0.259228i	$-0.916532\pi$
$541$	−9.78808	+	13.4721i	−0.420822	+	0.579212i	0.544994	+	0.838440i	$0.316532\pi$
$542$	2.88783	−	1.47142i	0.124043	−	0.0632031i
$543$	10.0000	+	30.7768i	0.429141	+	1.32076i
$544$	−14.6275	−	2.31677i	−0.627149	−	0.0993306i
$545$	6.09017	−	4.42477i	0.260874	−	0.189536i
$546$	−28.4813	+	55.8977i	−1.21889	+	2.39220i
$547$	−9.20029	−	2.98936i	−0.393376	−	0.127816i	0.105648	−	0.994404i	$-0.466308\pi$
$547$	−9.20029	−	2.98936i	−0.393376	−	0.127816i	−0.499024	+	0.866588i	$0.666308\pi$
$548$	10.7516	−	14.7984i	0.459288	−	0.632155i
$549$		−	1.70820i		−	0.0729044i
$550$	−4.54415	−	1.16219i	−0.193763	−	0.0495558i
$551$	12.3607			0.526583
$552$	0.884927	+	5.58721i	0.0376650	+	0.237807i
$553$	−25.4164	+	78.2237i	−1.08082	+	3.32641i
$554$	16.9057	+	8.61386i	0.718253	+	0.365968i
$555$	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	−0.262476	−	0.964939i	$-0.584539\pi$
$557$	2.17963	−	0.708204i	0.0923538	−	0.0300076i	0.354829	+	0.934931i	$0.384539\pi$
$558$	0.962611	−	0.490475i	0.0407506	−	0.0207634i
$559$	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	$0.461466\pi$
$563$	−20.4212	+	28.1074i	−0.860652	+	1.18459i	−0.981414	+	0.191904i	$0.938534\pi$
$564$	6.94427	−	21.3723i	0.292407	−	0.899935i
$565$	3.38795	−	1.10081i	0.142532	−	0.0463116i
$566$	0.338012	−	2.13412i	0.0142077	−	0.0897039i
$567$	−32.6525	+	23.7234i	−1.37128	+	0.996290i
$568$	17.5006	+	8.91699i	0.734308	+	0.374149i
$569$	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	$0.0856775\pi$
$570$	6.98401	−	1.10616i	0.292528	−	0.0463319i
$571$		−	28.3607i		−	1.18686i	−0.804887	−	0.593429i	$-0.797774\pi$
$571$		−	28.3607i		−	1.18686i	0.804887	−	0.593429i	$-0.202226\pi$
$572$	13.7638	−	31.8885i	0.575494	−	1.33333i
$573$		−	16.4721i		−	0.688133i
$574$	−11.1414	−	70.3439i	−0.465032	−	2.93610i
$575$	−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	$0.854492\pi$
$578$	14.1718	+	2.24459i	0.589470	+	0.0933628i
$579$	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
$586$	0.418915	+	0.822168i	0.0173052	+	0.0339634i
$587$	−8.92278	+	2.89919i	−0.368283	+	0.119662i	−0.487311	−	0.873229i	$-0.662022\pi$
$587$	−8.92278	+	2.89919i	−0.368283	+	0.119662i	0.119028	+	0.992891i	$0.462022\pi$
$588$	53.4508	−	38.8343i	2.20428	−	1.60150i
$589$	−3.63271	−	5.00000i	−0.149683	−	0.206021i
$590$	−0.396802	+	0.778768i	−0.0163361	+	0.0320614i
$591$	−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	$0.450374\pi$
$594$	19.7611	−	16.3791i	0.810806	−	0.672042i
$595$		−	13.7082i		−	0.561982i
$596$	−18.1803	−	13.2088i	−0.744696	−	0.541053i
$597$	−34.8586	−	11.3262i	−1.42667	−	0.463552i
$598$	−8.15537	−	4.15537i	−0.333498	−	0.169926i
$599$	−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	$0.539185\pi$
$600$	−4.52015	−	0.715921i	−0.184534	−	0.0292274i
$601$	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	$0.877216\pi$
$602$	−16.3183	−	32.0265i	−0.665086	−	1.30530i
$603$	−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	$0.755733\pi$
$608$	−7.93604	−	15.5754i	−0.321849	−	0.631664i
$609$	−10.4721	−	32.2299i	−0.424352	−	1.30602i
$610$	6.24669	+	0.989378i	0.252921	+	0.0400588i
$611$	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	−0.0886491	−	0.996063i	$-0.528255\pi$
$613$	−18.4661	−	6.00000i	−0.745839	−	0.242338i	−0.657190	+	0.753725i	$0.728255\pi$
$614$	20.3407	−	3.22164i	0.820882	−	0.130015i
$615$	−15.5623			−0.627533
$616$	−37.8171	+	31.3450i	−1.52370	+	1.26293i
$617$	21.3820			0.860806			0.430403	−	0.902637i	$-0.358372\pi$
$617$	21.3820			0.860806			0.430403	+	0.902637i	$0.358372\pi$
$618$	−3.86067	+	0.611469i	−0.155299	+	0.0245969i
$619$	25.4868	+	8.28115i	1.02440	+	0.332848i	0.772574	−	0.634925i	$-0.218969\pi$
$619$	25.4868	+	8.28115i	1.02440	+	0.332848i	0.251826	+	0.967773i	$0.418969\pi$
$620$	1.23607	+	3.80423i	0.0496417	+	0.152781i
$621$	−3.97574	−	5.47214i	−0.159541	−	0.219589i
$622$	45.6091	+	7.22376i	1.82876	+	0.289647i
$623$	−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
$630$	1.28408	+	2.52015i	0.0511589	+	0.100405i
$631$	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	$0.803120\pi$
$632$	6.95031	−	43.8825i	0.276468	−	1.74555i
$633$	19.4443	−	14.1271i	0.772840	−	0.561501i
$634$	−37.6618	−	19.1896i	−1.49574	−	0.762117i
$635$	−4.08174	−	1.32624i	−0.161979	−	0.0526301i
$636$	13.7638	−	18.9443i	0.545771	−	0.751189i
$637$			106.902i			4.23560i
$638$	6.92303	+	17.4377i	0.274085	+	0.690363i
$639$	−2.65248			−0.104930
$640$	1.76985	+	11.1744i	0.0699596	+	0.441708i
$641$	−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	$0.149928\pi$
$642$	9.19801	−	18.0521i	0.363017	−	0.712460i
$643$	2.74717	+	3.78115i	0.108338	+	0.149114i	0.859743	−	0.510727i	$-0.170624\pi$
$643$	2.74717	+	3.78115i	0.108338	+	0.149114i	−0.751405	+	0.659841i	$0.770624\pi$
$644$	7.60845	+	10.4721i	0.299815	+	0.412660i
$645$	−7.46969	+	2.42705i	−0.294119	+	0.0955650i
$646$	−5.19421	−	10.1942i	−0.204363	−	0.401086i
$647$	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	0.0617389	−	0.998092i	$-0.480335\pi$
$653$	17.8456	−	5.79837i	0.698351	−	0.226908i	0.636612	+	0.771184i	$0.280335\pi$
$654$	−17.0135	−	2.69468i	−0.665282	−	0.105370i
$655$	−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
$658$	−8.04414	−	50.7887i	−0.313593	−	1.97995i
$659$		−	9.85410i		−	0.383861i	−0.981408	−	0.191931i	$-0.938525\pi$
$659$		−	9.85410i		−	0.383861i	0.981408	−	0.191931i	$-0.0614749\pi$
$660$	5.47214	+	9.23305i	0.213003	+	0.359396i
$661$		−	18.2918i		−	0.711468i	−0.934587	−	0.355734i	$-0.884231\pi$
$661$		−	18.2918i		−	0.711468i	0.934587	−	0.355734i	$-0.115769\pi$
$662$	26.5874	−	4.21102i	1.03335	−	0.163666i
$663$	6.85410	−	21.0948i	0.266191	−	0.819252i
$664$	−3.05863	+	6.00290i	−0.118698	+	0.232958i
$665$	13.0902	−	9.51057i	0.507615	−	0.368804i
$666$	−0.676024	+	4.26825i	−0.0261954	+	0.165391i
$667$	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	$0.792780\pi$
$674$	−28.8681	+	14.7090i	−1.11196	+	0.566570i
$675$	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	0.592042	−	0.805907i	$-0.298322\pi$
$677$	−9.29856	−	12.7984i	−0.357373	−	0.491881i	−0.949414	+	0.314026i	$0.898322\pi$
$678$	−7.26298	−	3.70067i	−0.278933	−	0.142123i
$679$	22.7984	−	70.1662i	0.874921	−	2.69273i
$680$	1.15838	+	7.31375i	0.0444220	+	0.280470i
$681$	35.1803			1.34811
$682$	5.01905	−	7.92522i	0.192189	−	0.303472i
$683$			43.7771i			1.67508i	0.546373	+	0.837542i	$0.316008\pi$
$683$			43.7771i			1.67508i	−0.546373	+	0.837542i	$0.683992\pi$
$684$	1.90983	+	1.38757i	0.0730242	+	0.0530552i
$685$	−8.69827	−	2.82624i	−0.332344	−	0.107985i
$686$	45.1028	−	88.5192i	1.72203	−	3.37968i
$687$	−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
$690$	2.52015	−	1.28408i	0.0959404	−	0.0488841i
$691$	−4.33901	+	5.97214i	−0.165064	+	0.227191i	−0.883534	−	0.468367i	$-0.844843\pi$
$691$	−4.33901	+	5.97214i	−0.165064	+	0.227191i	0.718470	+	0.695558i	$0.244843\pi$
$692$	−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
$696$	8.31073	+	16.3107i	0.315018	+	0.618257i
$697$	7.78115	+	23.9479i	0.294732	+	0.907092i
$698$	−0.208903	+	1.31896i	−0.00790709	+	0.0499234i
$699$	−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	−0.382009	−	0.924159i	$-0.624768\pi$
$701$	−32.6789	−	10.6180i	−1.23427	−	0.401038i	−0.852258	+	0.523121i	$0.824768\pi$
$702$	6.33884	+	40.0218i	0.239244	+	1.51053i
$703$	24.7214			0.932384
$704$	17.5279	−	19.9192i	0.660606	−	0.750733i
$705$	−11.2361			−0.423175
$706$	−0.917204	−	5.79100i	−0.0345194	−	0.217947i
$707$	−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	0.897186	−	0.441653i	$-0.145608\pi$
$709$	5.32282	+	7.32624i	0.199903	+	0.275143i	−0.697283	+	0.716796i	$0.745608\pi$
$710$	1.53629	−	9.69977i	0.0576561	−	0.364026i
$711$	1.85410	+	5.70634i	0.0695343	+	0.214004i
$712$	18.6992	+	36.6992i	0.700780	+	1.37536i
$713$	−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
$718$	−3.85044	+	1.96190i	−0.143697	+	0.0732174i
$719$	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
$722$	−6.06782	+	11.9088i	−0.225821	+	0.443198i
$723$	−38.4383	−	12.4894i	−1.42954	−	0.464484i
$724$	−32.3607	−	23.5114i	−1.20268	−	0.873795i
$725$			4.00000i			0.148556i
$726$	8.48172	−	23.6986i	0.314786	−	0.879538i
$727$	−7.23607			−0.268371			−0.134185	−	0.990956i	$-0.542842\pi$
$727$	−7.23607			−0.268371			−0.134185	+	0.990956i	$0.542842\pi$
$728$	−12.1308	−	76.5906i	−0.449596	−	2.83864i
$729$	−9.11803	+	28.0624i	−0.337705	+	1.03935i
$730$	−1.44392	−	0.735712i	−0.0534417	−	0.0272299i
$731$	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	0.606598	−	0.795009i	$-0.292534\pi$
$733$	42.3610	−	13.7639i	1.56464	−	0.508382i	0.958042	+	0.286626i	$0.0925339\pi$
$734$	−7.19276	+	3.66489i	−0.265489	+	0.135274i
$735$	−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	$0.423312\pi$
$739$	−20.6255	+	28.3885i	−0.758721	+	1.04429i	−0.997319	+	0.0731712i	$0.976688\pi$
$740$	−15.2169	−	4.94427i	−0.559385	−	0.181755i
$741$	24.8990	−	8.09017i	0.914687	−	0.297200i
$742$	8.38215	−	52.9228i	0.307718	−	1.94286i
$743$	−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	$0.345816\pi$
$744$	4.15537	−	8.15537i	0.152343	−	0.298990i
$745$	−3.47214	+	10.6861i	−0.127209	+	0.391510i
$746$	10.5149	−	1.66540i	0.384979	−	0.0609747i
$747$		−	0.909830i		−	0.0332889i
$748$	11.4721	−	13.0373i	0.419463	−	0.476690i
$749$		−	46.3607i		−	1.69398i
$750$	0.357960	+	2.26007i	0.0130709	+	0.0825262i
$751$	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
$754$	−29.2550	−	4.63354i	−1.06540	−	0.168743i
$755$	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	$-0.568835\pi$
$757$	21.4783	−	29.5623i	0.780641	−	1.07446i	0.995211	−	0.0977516i	$-0.0311651\pi$
$758$	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	$0.712384\pi$
$762$	4.45850	+	8.75029i	0.161514	+	0.316990i
$763$	−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
$766$	−7.89182	+	15.4886i	−0.285143	+	0.559625i
$767$	−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	$0.157222\pi$
$770$	20.7485	+	13.1400i	0.747724	+	0.473534i
$771$		−	12.6180i		−	0.454427i
$772$	−7.05342	+	9.70820i	−0.253858	+	0.349406i
$773$	−31.5034	−	10.2361i	−1.13310	−	0.368166i	−0.318345	−	0.947975i	$-0.603127\pi$
$773$	−31.5034	−	10.2361i	−1.13310	−	0.368166i	−0.814752	+	0.579809i	$0.803127\pi$
$774$	−2.33630	−	1.19041i	−0.0839767	−	0.0427883i
$775$	1.61803	−	1.17557i	0.0581215	−	0.0422277i
$776$	−6.23439	+	39.3624i	−0.223801	+	1.41303i
$777$	−20.9443	−	64.4598i	−0.751372	−	2.31248i
$778$	8.49808	+	16.6784i	0.304671	+	0.597950i
$779$	−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
$786$	0.737322	+	0.116780i	0.0262994	+	0.00416541i
$787$	10.6004	+	14.5902i	0.377863	+	0.520083i	0.955017	−	0.296552i	$-0.0958368\pi$
$787$	10.6004	+	14.5902i	0.377863	+	0.520083i	−0.577154	+	0.816635i	$0.695837\pi$
$788$	−1.81966	−	5.60034i	−0.0648227	−	0.199504i
$789$	−44.9897	−	14.6180i	−1.60168	−	0.520416i
$790$	−21.9413	+	3.47515i	−0.780635	+	0.123640i
$791$	−18.6525			−0.663206
$792$	−0.887832	+	3.47142i	−0.0315477	+	0.123352i
$793$	23.4164			0.831541
$794$	6.40237	−	1.01404i	0.227212	−	0.0359868i
$795$	−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	0.807135	−	0.590366i	$-0.201017\pi$
$797$	−0.106001	−	0.145898i	−0.00375475	−	0.00516797i	−0.810890	+	0.585198i	$0.801017\pi$
$798$	−36.5688	−	5.79192i	−1.29452	−	0.205032i
$799$	5.61803	+	17.2905i	0.198752	+	0.611695i
$800$	5.04029	−	2.56816i	0.178201	−	0.0907981i
$801$	−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
$806$	6.72353	+	13.1957i	0.236826	+	0.464797i
$807$	−10.9443	−	33.6830i	−0.385257	−	1.18570i
$808$	22.8526	+	3.61950i	0.803953	+	0.127334i
$809$	−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	$0.388853\pi$
$810$	−9.71290	−	4.94897i	−0.341277	−	0.173889i
$811$	−29.3440	−	9.53444i	−1.03041	−	0.334800i	−0.255456	−	0.966821i	$-0.582226\pi$
$811$	−29.3440	−	9.53444i	−1.03041	−	0.334800i	−0.774951	+	0.632021i	$0.782226\pi$
$812$	33.8885	+	24.6215i	1.18925	+	0.864044i
$813$			3.70820i			0.130052i
$814$	13.8461	+	34.8753i	0.485304	+	1.22238i
$815$	−6.61803			−0.231820
$816$	9.95959	−	13.7082i	0.348655	−	0.479883i
$817$	−4.63525	+	14.2658i	−0.162167	+	0.499099i
$818$	14.1249	−	27.7216i	0.493864	−	0.969264i
$819$	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	−0.883861	−	0.467749i	$-0.845065\pi$
$821$	−37.9363	+	12.3262i	−1.32398	+	0.430189i	−0.440123	+	0.897937i	$0.645065\pi$
$822$	9.50114	+	18.6470i	0.331390	+	0.650390i
$823$	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	−0.566366	−	0.824154i	$-0.691651\pi$
$827$	11.2864	−	15.5344i	0.392468	−	0.540185i	0.958834	+	0.283968i	$0.0916511\pi$
$828$	0.898056	+	0.291796i	0.0312096	+	0.0101406i
$829$	−11.9677	+	3.88854i	−0.415656	+	0.135055i	−0.509376	−	0.860544i	$-0.670124\pi$
$829$	−11.9677	+	3.88854i	−0.415656	+	0.135055i	0.0937208	+	0.995599i	$0.470124\pi$
$830$	3.32714	+	0.526966i	0.115487	+	0.0182913i
$831$	−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
$834$	−3.74861	−	23.6678i	−0.129804	−	0.819549i
$835$			14.4721i			0.500829i
$836$	20.4087	+	1.90983i	0.705850	+	0.0660529i
$837$			10.9443i			0.378289i
$838$	25.2684	−	4.00212i	0.872882	−	0.138251i
$839$	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	$0.0510401\pi$
$840$	21.3510	+	10.8789i	0.736680	+	0.375357i
$841$	−10.5172	+	7.64121i	−0.362663	+	0.263490i
$842$	−7.18387	+	45.3572i	−0.247572	+	1.56311i
$843$	−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
$850$	3.29892	−	1.68088i	0.113152	−	0.0576538i
$851$	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	$0.0643614\pi$
$853$	25.3480	+	34.8885i	0.867899	+	1.19456i	−0.111728	+	0.993739i	$0.535639\pi$
$854$	−29.5064	−	15.0343i	−1.00969	−	0.514462i
$855$	0.364745	−	1.12257i	0.0124740	−	0.0383911i
$856$	3.91762	+	24.7349i	0.133901	+	0.845420i
$857$	−23.7984			−0.812937			−0.406468	−	0.913665i	$-0.633240\pi$
$857$	−23.7984			−0.812937			−0.406468	+	0.913665i	$0.633240\pi$
$858$	25.3586	+	30.5947i	0.865729	+	1.04449i
$859$			33.6312i			1.14748i	0.819037	+	0.573741i	$0.194508\pi$
$859$			33.6312i			1.14748i	−0.819037	+	0.573741i	$0.805492\pi$
$860$	5.70634	−	7.85410i	0.194585	−	0.267823i
$861$	77.4971	+	25.1803i	2.64109	+	0.858144i
$862$	7.70447	−	15.1209i	0.262415	−	0.515019i
$863$	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	$0.131956\pi$
$864$	−4.84244	+	30.5740i	−0.164743	+	1.04015i
$865$	1.47214	+	4.53077i	0.0500541	+	0.154051i
$866$	−12.6441	+	6.44251i	−0.429665	+	0.218925i
$867$	−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
$872$	18.9713	−	9.66637i	0.642450	−	0.327345i
$873$	−1.66312	−	5.11855i	−0.0562880	−	0.173237i
$874$	0.845030	−	5.33531i	0.0285836	−	0.180470i
$875$	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	0.534693	−	0.845046i	$-0.320427\pi$
$877$	13.9353	+	4.52786i	0.470563	+	0.152895i	−0.0641302	+	0.997942i	$0.520427\pi$
$878$	5.45391	+	34.4346i	0.184061	+	1.16211i
$879$	−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	$0.647669\pi$
$882$	−1.72525	−	10.8928i	−0.0580921	−	0.366779i
$883$	−12.3965	−	4.02786i	−0.417175	−	0.135548i	0.0929056	−	0.995675i	$-0.470385\pi$
$883$	−12.3965	−	4.02786i	−0.417175	−	0.135548i	−0.510081	+	0.860126i	$0.670385\pi$
$884$	8.47214	+	26.0746i	0.284949	+	0.876982i
$885$	−0.587785	−	0.809017i	−0.0197582	−	0.0271948i
$886$	5.28961	−	33.3973i	0.177708	−	1.12200i
$887$	−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	$-0.238602\pi$
$888$	16.6215	+	32.6215i	0.557780	+	1.09470i
$889$	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
$894$	22.9086	−	11.6725i	0.766177	−	0.390387i
$895$	4.28115	+	13.1760i	0.143103	+	0.440426i
$896$	9.26708	−	58.5100i	0.309591	−	1.95468i
$897$	8.47214	−	6.15537i	0.282876	−	0.205522i
$898$	6.51407	−	12.7846i	0.217377	−	0.426627i
$899$	−7.60845	−	2.47214i	−0.253756	−	0.0824504i
$900$	−0.449028	+	0.618034i	−0.0149676	+	0.0206011i
$901$			18.9443i			0.631125i
$902$	−43.7058	−	11.1779i	−1.45524	−	0.372185i
$903$	41.1246			1.36854
$904$	9.95167	−	1.57619i	0.330988	−	0.0524233i
$905$	−6.18034	+	19.0211i	−0.205441	+	0.632284i
$906$	−44.6273	−	22.7387i	−1.48264	−	0.755444i
$907$	24.7477	+	34.0623i	0.821734	+	1.13102i	0.989406	+	0.145177i	$0.0463753\pi$
$907$	24.7477	+	34.0623i	0.821734	+	1.13102i	−0.167671	+	0.985843i	$0.553625\pi$
$908$	−35.1803	+	25.5600i	−1.16750	+	0.848239i
$909$	−2.97168	+	0.965558i	−0.0985645	+	0.0320255i
$910$	−34.5467	+	17.6024i	−1.14521	+	0.583514i
$911$	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
$918$	−3.16942	+	20.0109i	−0.104606	+	0.660459i
$919$	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	$0.0141683\pi$
$920$	−1.58721	+	3.11507i	−0.0523287	+	0.102701i
$921$	−7.28115	+	22.4091i	−0.239922	+	0.738404i
$922$	−13.4048	+	2.12311i	−0.441462	+	0.0699207i
$923$		−	36.3607i		−	1.19683i
$924$	−12.3107	−	54.8328i	−0.404993	−	1.80387i
$925$			8.00000i			0.263038i
$926$	−0.860269	−	5.43153i	−0.0282702	−	0.178491i
$927$	−0.201626	+	0.620541i	−0.00662227	+	0.0203813i
$928$	−20.1612	−	10.2726i	−0.661823	−	0.337216i
$929$	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	$0.147889\pi$
$930$	−4.52015	−	0.715921i	−0.148221	−	0.0234760i
$931$	−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	$0.531118\pi$
$938$	7.82026	+	15.3481i	0.255341	+	0.501134i
$939$	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	$-0.784675\pi$
$941$	−34.7931	−	47.8885i	−1.13422	−	1.56112i	−0.354430	−	0.935083i	$-0.615325\pi$
$942$	3.85224	−	7.56044i	0.125513	−	0.246332i
$943$	−3.67376	+	11.3067i	−0.119634	+	0.368196i
$944$	−1.45309	+	2.00000i	−0.0472939	+	0.0650945i
$945$	−28.6525			−0.932065
$946$	−22.7215	+	1.45097i	−0.738739	+	0.0471749i
$947$			54.6180i			1.77485i	0.460954	+	0.887424i	$0.347507\pi$
$947$			54.6180i			1.77485i	−0.460954	+	0.887424i	$0.652493\pi$
$948$	41.1246	+	29.8788i	1.33567	+	0.970418i
$949$	−5.70634	−	1.85410i	−0.185236	−	0.0601867i
$950$	3.89384	+	1.98401i	0.126333	+	0.0643698i
$951$	39.1246	−	28.4257i	1.26870	−	0.921766i
$952$	6.06538	−	38.2953i	0.196580	−	1.24116i
$953$	−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	$-0.374251\pi$
$954$	−1.77455	−	3.48276i	−0.0574533	−	0.112758i
$955$	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
$962$	−58.5100	−	9.26708i	−1.88644	−	0.298783i
$963$	−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
$966$	−14.6275	+	2.31677i	−0.470632	+	0.0745408i
$967$	30.7214			0.987932			0.493966	−	0.869481i	$-0.335547\pi$
$967$	30.7214			0.987932			0.493966	+	0.869481i	$0.335547\pi$
$968$	8.73634	+	29.8610i	0.280797	+	0.959767i
$969$	13.0902			0.420517
$970$	19.6812	−	3.11719i	0.631925	−	0.100087i
$971$	25.7315	+	8.36068i	0.825764	+	0.268307i	0.691260	−	0.722606i	$-0.257056\pi$
$971$	25.7315	+	8.36068i	0.825764	+	0.268307i	0.134504	+	0.990913i	$0.457056\pi$
$972$	−2.43769	−	7.50245i	−0.0781891	−	0.240641i
$973$	−32.2299	−	44.3607i	−1.03324	−	1.42214i
$974$	9.69977	+	1.53629i	0.310801	+	0.0492260i
$975$	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
$982$	19.9253	+	39.1057i	0.635843	+	1.24791i
$983$	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	$0.815977\pi$
$984$	−43.4749	−	6.88575i	−1.38593	−	0.219510i
$985$	−2.38197	+	1.73060i	−0.0758957	+	0.0551415i
$986$	−13.1957	−	6.72353i	−0.420235	−	0.214121i
$987$	55.9533	+	18.1803i	1.78101	+	0.578687i
$988$	−19.0211	+	26.1803i	−0.605143	+	0.832908i
$989$			6.00000i			0.190789i
$990$	1.78794	−	0.114175i	0.0568244	−	0.00362873i
$991$	−26.0689			−0.828105			−0.414053	−	0.910253i	$-0.635887\pi$
$991$	−26.0689			−0.828105			−0.414053	+	0.910253i	$0.635887\pi$
$992$	1.76985	+	11.1744i	0.0561929	+	0.354788i
$993$	−9.51722	+	29.2910i	−0.302020	+	0.929522i
$994$	−23.3450	+	45.8171i	−0.740458	+	1.45323i
$995$	−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	−0.204300	−	0.978908i	$-0.565492\pi$
$997$	6.49839	−	2.11146i	0.205806	−	0.0668705i	0.410106	+	0.912038i	$0.365492\pi$
$998$	−13.0860	−	25.6828i	−0.414231	−	0.812974i
$999$	−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.301.2	yes	8
8.5	even	2	inner	440.2.bi.b.301.1	✓	8
11.3	even	5	inner	440.2.bi.b.421.1	yes	8
88.69	even	10	inner	440.2.bi.b.421.2	yes	8

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

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.587785 + 0.809017i) q^{5} +(0.357960 - 2.26007i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(-0.221232 - 1.39680i) q^{2} +(1.53884 + 0.500000i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(0.587785 + 0.809017i) q^{5} +(0.357960 - 2.26007i) q^{6} +(-1.61803 - 4.97980i) q^{7} +(1.28408 + 2.52015i) 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} +(-6.59783 + 3.36176i) q^{14} +(0.500000 + 1.53884i) q^{15} +(3.23607 - 2.35114i) q^{16} +(2.11803 - 1.53884i) q^{17} +(-0.245237 + 0.481305i) q^{18} +(2.93893 + 0.954915i) q^{19} +(-1.61803 - 1.17557i) q^{20} -8.47214i q^{21} +(0.298915 + 4.68088i) q^{22} +1.23607 q^{23} +(0.715921 + 4.52015i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-6.59783 - 3.36176i) q^{26} +(-3.21644 - 4.42705i) q^{27} +(6.15537 + 8.47214i) q^{28} +(3.80423 - 1.23607i) q^{29} +(2.03884 - 1.03884i) 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} +(0.683644 - 4.31636i) q^{38} +(6.85410 - 4.97980i) q^{39} +(-1.28408 + 2.52015i) q^{40} +(-2.97214 + 9.14729i) q^{41} +(-11.8339 + 1.87431i) q^{42} +4.85410i q^{43} +(6.47214 - 1.45309i) q^{44} -0.381966i q^{45} +(-0.273457 - 1.72654i) q^{46} +(-2.14590 + 6.60440i) q^{47} +(6.15537 - 2.00000i) q^{48} +(-16.5172 + 12.0005i) q^{49} +(1.39680 + 0.221232i) 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} +(-2.56816 - 5.04029i) q^{58} +(-0.587785 + 0.190983i) q^{59} +(-1.90211 - 2.61803i) q^{60} +(2.62866 + 3.61803i) q^{61} +(-1.28408 + 2.52015i) q^{62} +(-0.618034 + 1.90211i) q^{63} +(-4.70228 + 6.47214i) q^{64} +5.23607 q^{65} +(-1.88046 + 7.35259i) q^{66} -2.32624i q^{67} +(-3.07768 + 4.23607i) q^{68} +(1.90211 + 0.618034i) q^{69} +(-6.59783 - 3.36176i) q^{70} +(5.61803 - 4.08174i) q^{71} +(0.169006 - 1.06706i) q^{72} +(-0.354102 - 1.08981i) q^{73} +(-5.13632 - 10.0806i) 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} +(13.4345 + 2.12781i) q^{82} +(1.40008 + 1.92705i) q^{83} +(5.23607 + 16.1150i) q^{84} +(2.48990 + 0.809017i) q^{85} +(6.78022 - 1.07388i) q^{86} +6.47214 q^{87} +(-3.46151 - 8.71883i) q^{88} +14.5623 q^{89} +(-0.533531 + 0.0845030i) q^{90} +(-26.0746 - 8.47214i) q^{91} +(-2.35114 + 0.763932i) q^{92} +(-1.90211 - 2.61803i) q^{93} +(9.69977 + 1.53629i) q^{94} +(0.954915 + 2.93893i) q^{95} +(-4.15537 - 8.15537i) 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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