LMFDB - Embedded newform 66.2.e.a.31.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [66,2,Mod(25,66)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(66, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("66.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 66 = 2 \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	66.e (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.527012653340$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			31.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	66.31
Dual form			66.2.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.881966 + 2.71441i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-3.73607 - 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.881966 + 2.71441i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-3.73607 - 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.85410 q^{10} +(1.23607 + 3.07768i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.07768i) q^{13} +(-3.73607 + 2.71441i) q^{14} +(2.30902 + 1.67760i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.763932 - 2.35114i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(2.61803 - 1.90211i) q^{19} +(0.881966 - 2.71441i) q^{20} -4.61803 q^{21} +(3.30902 - 0.224514i) q^{22} -3.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-2.54508 + 1.84911i) q^{25} +(2.61803 + 1.90211i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.42705 + 4.39201i) q^{28} +(0.309017 + 0.224514i) q^{29} +(2.30902 - 1.67760i) q^{30} +(2.66312 - 8.19624i) q^{31} +1.00000 q^{32} +(2.80902 + 1.76336i) q^{33} -2.47214 q^{34} +(4.07295 - 12.5352i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.23607 - 0.898056i) q^{37} +(-1.00000 - 3.07768i) q^{38} +(1.00000 + 3.07768i) q^{39} +(-2.30902 - 1.67760i) q^{40} +(2.61803 - 1.90211i) q^{41} +(-1.42705 + 4.39201i) q^{42} -3.23607 q^{43} +(0.809017 - 3.21644i) q^{44} +2.85410 q^{45} +(-1.00000 + 3.07768i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.42705 + 13.6251i) q^{49} +(0.972136 + 2.99193i) q^{50} +(-2.00000 - 1.45309i) q^{51} +(2.61803 - 1.90211i) q^{52} +(-1.19098 + 3.66547i) q^{53} -1.00000 q^{54} +(-7.26393 + 6.06961i) q^{55} +4.61803 q^{56} +(1.00000 - 3.07768i) q^{57} +(0.309017 - 0.224514i) q^{58} +(3.11803 + 2.26538i) q^{59} +(-0.881966 - 2.71441i) q^{60} +(-2.09017 - 6.43288i) q^{61} +(-6.97214 - 5.06555i) q^{62} +(-3.73607 + 2.71441i) q^{63} +(0.309017 - 0.951057i) q^{64} -9.23607 q^{65} +(2.54508 - 2.12663i) q^{66} +4.00000 q^{67} +(-0.763932 + 2.35114i) q^{68} +(-2.61803 + 1.90211i) q^{69} +(-10.6631 - 7.74721i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(9.16312 + 6.65740i) q^{73} +(-1.23607 + 0.898056i) q^{74} +(-0.972136 + 2.99193i) q^{75} -3.23607 q^{76} +(3.73607 - 14.8536i) q^{77} +3.23607 q^{78} +(-2.88197 + 8.86978i) q^{79} +(-2.30902 + 1.67760i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.00000 - 3.07768i) q^{82} +(-0.208204 - 0.640786i) q^{83} +(3.73607 + 2.71441i) q^{84} +(5.70820 - 4.14725i) q^{85} +(-1.00000 + 3.07768i) q^{86} +0.381966 q^{87} +(-2.80902 - 1.76336i) q^{88} -11.7082 q^{89} +(0.881966 - 2.71441i) q^{90} +(12.0902 - 8.78402i) q^{91} +(2.61803 + 1.90211i) q^{92} +(-2.66312 - 8.19624i) q^{93} +(0.763932 + 2.35114i) q^{94} +(7.47214 + 5.42882i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.50000 - 10.7719i) q^{97} +14.3262 q^{98} +(3.30902 - 0.224514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{14} + 7 q^{15} - q^{16} - 12 q^{17} - q^{18} + 6 q^{19} + 8 q^{20} - 14 q^{21} + 11 q^{22} - 4 q^{23} + q^{24} + q^{25} + 6 q^{26} + q^{27} - q^{28} - q^{29} + 7 q^{30} - 5 q^{31} + 4 q^{32} + 9 q^{33} + 8 q^{34} + 23 q^{35} - q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 7 q^{40} + 6 q^{41} + q^{42} - 4 q^{43} + q^{44} - 2 q^{45} - 4 q^{46} - 8 q^{47} + q^{48} + 11 q^{49} - 14 q^{50} - 8 q^{51} + 6 q^{52} - 7 q^{53} - 4 q^{54} - 38 q^{55} + 14 q^{56} + 4 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + 14 q^{61} - 10 q^{62} - 6 q^{63} - q^{64} - 28 q^{65} - q^{66} + 16 q^{67} - 12 q^{68} - 6 q^{69} - 27 q^{70} + 2 q^{71} - q^{72} + 21 q^{73} + 4 q^{74} + 14 q^{75} - 4 q^{76} + 6 q^{77} + 4 q^{78} - 16 q^{79} - 7 q^{80} - q^{81} - 4 q^{82} + 26 q^{83} + 6 q^{84} - 4 q^{85} - 4 q^{86} + 6 q^{87} - 9 q^{88} - 20 q^{89} + 8 q^{90} + 26 q^{91} + 6 q^{92} + 5 q^{93} + 12 q^{94} + 12 q^{95} + q^{96} + 14 q^{97} + 26 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^14 + 7 * q^15 - q^16 - 12 * q^17 - q^18 + 6 * q^19 + 8 * q^20 - 14 * q^21 + 11 * q^22 - 4 * q^23 + q^24 + q^25 + 6 * q^26 + q^27 - q^28 - q^29 + 7 * q^30 - 5 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 + 23 * q^35 - q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 7 * q^40 + 6 * q^41 + q^42 - 4 * q^43 + q^44 - 2 * q^45 - 4 * q^46 - 8 * q^47 + q^48 + 11 * q^49 - 14 * q^50 - 8 * q^51 + 6 * q^52 - 7 * q^53 - 4 * q^54 - 38 * q^55 + 14 * q^56 + 4 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + 14 * q^61 - 10 * q^62 - 6 * q^63 - q^64 - 28 * q^65 - q^66 + 16 * q^67 - 12 * q^68 - 6 * q^69 - 27 * q^70 + 2 * q^71 - q^72 + 21 * q^73 + 4 * q^74 + 14 * q^75 - 4 * q^76 + 6 * q^77 + 4 * q^78 - 16 * q^79 - 7 * q^80 - q^81 - 4 * q^82 + 26 * q^83 + 6 * q^84 - 4 * q^85 - 4 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^89 + 8 * q^90 + 26 * q^91 + 6 * q^92 + 5 * q^93 + 12 * q^94 + 12 * q^95 + q^96 + 14 * q^97 + 26 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/66\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.881966	+	2.71441i	0.394427	+	1.21392i	0.929407	+	0.369057i	$0.120319\pi$
$5$	0.881966	+	2.71441i	0.394427	+	1.21392i	−0.534980	+	0.844865i	$0.679681\pi$
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$	−3.73607	−	2.71441i	−1.41210	−	1.02595i	−0.993013	−	0.118006i	$-0.962350\pi$
$7$	−3.73607	−	2.71441i	−1.41210	−	1.02595i	−0.419088	−	0.907946i	$-0.637650\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	2.85410			0.902546
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$12$	−1.00000			−0.288675
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	0.711238	+	0.702951i	$0.248135\pi$
$13$	−1.00000	+	3.07768i	−0.277350	+	0.853596i	−0.988588	+	0.150644i	$0.951865\pi$
$14$	−3.73607	+	2.71441i	−0.998506	+	0.725457i
$15$	2.30902	+	1.67760i	0.596186	+	0.433154i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.763932	−	2.35114i	−0.185281	−	0.570235i	0.814672	−	0.579922i	$-0.196917\pi$
$17$	−0.763932	−	2.35114i	−0.185281	−	0.570235i	−0.999953	+	0.00968605i	$0.996917\pi$
$18$	−0.809017	−	0.587785i	−0.190687	−	0.138542i
$19$	2.61803	−	1.90211i	0.600618	−	0.436375i	−0.245480	−	0.969402i	$-0.578946\pi$
$19$	2.61803	−	1.90211i	0.600618	−	0.436375i	0.846098	+	0.533027i	$0.178946\pi$
$20$	0.881966	−	2.71441i	0.197214	−	0.606961i
$21$	−4.61803			−1.00774
$22$	3.30902	−	0.224514i	0.705485	−	0.0478665i
$23$	−3.23607			−0.674767			−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607			−0.674767			−0.337383	+	0.941367i	$0.609542\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	−2.54508	+	1.84911i	−0.509017	+	0.369822i
$26$	2.61803	+	1.90211i	0.513439	+	0.373035i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.42705	+	4.39201i	0.269687	+	0.830012i
$29$	0.309017	+	0.224514i	0.0573830	+	0.0416912i	0.616107	−	0.787662i	$-0.288709\pi$
$29$	0.309017	+	0.224514i	0.0573830	+	0.0416912i	−0.558724	+	0.829354i	$0.688709\pi$
$30$	2.30902	−	1.67760i	0.421567	−	0.306286i
$31$	2.66312	−	8.19624i	0.478310	−	1.47209i	−0.363130	−	0.931738i	$-0.618292\pi$
$31$	2.66312	−	8.19624i	0.478310	−	1.47209i	0.841441	−	0.540349i	$-0.181708\pi$
$32$	1.00000			0.176777
$33$	2.80902	+	1.76336i	0.488987	+	0.306961i
$34$	−2.47214			−0.423968
$35$	4.07295	−	12.5352i	0.688454	−	2.11884i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−1.23607	−	0.898056i	−0.203208	−	0.147639i	0.481527	−	0.876431i	$-0.340082\pi$
$37$	−1.23607	−	0.898056i	−0.203208	−	0.147639i	−0.684735	+	0.728792i	$0.740082\pi$
$38$	−1.00000	−	3.07768i	−0.162221	−	0.499266i
$39$	1.00000	+	3.07768i	0.160128	+	0.492824i
$40$	−2.30902	−	1.67760i	−0.365088	−	0.265252i
$41$	2.61803	−	1.90211i	0.408868	−	0.297060i	−0.364275	−	0.931291i	$-0.618683\pi$
$41$	2.61803	−	1.90211i	0.408868	−	0.297060i	0.773143	+	0.634231i	$0.218683\pi$
$42$	−1.42705	+	4.39201i	−0.220199	+	0.677702i
$43$	−3.23607			−0.493496			−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607			−0.493496			−0.246748	+	0.969080i	$0.579362\pi$
$44$	0.809017	−	3.21644i	0.121964	−	0.484897i
$45$	2.85410			0.425464
$46$	−1.00000	+	3.07768i	−0.147442	+	0.453780i
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	−0.724018	−	0.689782i	$-0.757707\pi$
$47$	−2.00000	+	1.45309i	−0.291730	+	0.211954i	0.432288	+	0.901736i	$0.357707\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	4.42705	+	13.6251i	0.632436	+	1.94644i
$50$	0.972136	+	2.99193i	0.137481	+	0.423122i
$51$	−2.00000	−	1.45309i	−0.280056	−	0.203473i
$52$	2.61803	−	1.90211i	0.363056	−	0.263776i
$53$	−1.19098	+	3.66547i	−0.163594	+	0.503491i	−0.998930	−	0.0462491i	$-0.985273\pi$
$53$	−1.19098	+	3.66547i	−0.163594	+	0.503491i	0.835336	+	0.549740i	$0.185273\pi$
$54$	−1.00000			−0.136083
$55$	−7.26393	+	6.06961i	−0.979468	+	0.818426i
$56$	4.61803			0.617111
$57$	1.00000	−	3.07768i	0.132453	−	0.407649i
$58$	0.309017	−	0.224514i	0.0405759	−	0.0294801i
$59$	3.11803	+	2.26538i	0.405933	+	0.294928i	0.771953	−	0.635679i	$-0.219280\pi$
$59$	3.11803	+	2.26538i	0.405933	+	0.294928i	−0.366020	+	0.930607i	$0.619280\pi$
$60$	−0.881966	−	2.71441i	−0.113861	−	0.350429i
$61$	−2.09017	−	6.43288i	−0.267619	−	0.823646i	−0.991078	−	0.133279i	$-0.957449\pi$
$61$	−2.09017	−	6.43288i	−0.267619	−	0.823646i	0.723460	−	0.690367i	$-0.242551\pi$
$62$	−6.97214	−	5.06555i	−0.885462	−	0.643326i
$63$	−3.73607	+	2.71441i	−0.470700	+	0.341984i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−9.23607			−1.14559
$66$	2.54508	−	2.12663i	0.313278	−	0.261770i
$67$	4.00000			0.488678			0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000			0.488678			0.244339	+	0.969690i	$0.421429\pi$
$68$	−0.763932	+	2.35114i	−0.0926404	+	0.285118i
$69$	−2.61803	+	1.90211i	−0.315174	+	0.228988i
$70$	−10.6631	−	7.74721i	−1.27449	−	0.925969i
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	0.868297	+	0.496045i	$0.165215\pi$
$71$	3.85410	+	11.8617i	0.457398	+	1.40773i	−0.410899	+	0.911681i	$0.634785\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	9.16312	+	6.65740i	1.07246	+	0.779189i	0.976353	−	0.216182i	$-0.0693603\pi$
$73$	9.16312	+	6.65740i	1.07246	+	0.779189i	0.0961088	+	0.995371i	$0.469360\pi$
$74$	−1.23607	+	0.898056i	−0.143690	+	0.104397i
$75$	−0.972136	+	2.99193i	−0.112253	+	0.345478i
$76$	−3.23607			−0.371202
$77$	3.73607	−	14.8536i	0.425764	−	1.69273i
$78$	3.23607			0.366413
$79$	−2.88197	+	8.86978i	−0.324247	+	0.997928i	0.647533	+	0.762037i	$0.275801\pi$
$79$	−2.88197	+	8.86978i	−0.324247	+	0.997928i	−0.971780	+	0.235891i	$0.924199\pi$
$80$	−2.30902	+	1.67760i	−0.258156	+	0.187561i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.00000	−	3.07768i	−0.110432	−	0.339873i
$83$	−0.208204	−	0.640786i	−0.0228534	−	0.0703354i	0.938979	−	0.343973i	$-0.111773\pi$
$83$	−0.208204	−	0.640786i	−0.0228534	−	0.0703354i	−0.961833	+	0.273638i	$0.911773\pi$
$84$	3.73607	+	2.71441i	0.407638	+	0.296167i
$85$	5.70820	−	4.14725i	0.619142	−	0.449833i
$86$	−1.00000	+	3.07768i	−0.107833	+	0.331875i
$87$	0.381966			0.0409511
$88$	−2.80902	−	1.76336i	−0.299442	−	0.187974i
$89$	−11.7082			−1.24107			−0.620534	−	0.784180i	$-0.713084\pi$
$89$	−11.7082			−1.24107			−0.620534	+	0.784180i	$0.713084\pi$
$90$	0.881966	−	2.71441i	0.0929674	−	0.286124i
$91$	12.0902	−	8.78402i	1.26739	−	0.920816i
$92$	2.61803	+	1.90211i	0.272949	+	0.198309i
$93$	−2.66312	−	8.19624i	−0.276153	−	0.849910i
$94$	0.763932	+	2.35114i	0.0787936	+	0.242502i
$95$	7.47214	+	5.42882i	0.766625	+	0.556986i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	3.50000	−	10.7719i	0.355371	−	1.09372i	−0.600423	−	0.799683i	$-0.705001\pi$
$97$	3.50000	−	10.7719i	0.355371	−	1.09372i	0.955794	−	0.294037i	$-0.0949990\pi$
$98$	14.3262			1.44717
$99$	3.30902	−	0.224514i	0.332569	−	0.0225645i
$100$	3.14590			0.314590
$101$	−3.82624	+	11.7759i	−0.380725	+	1.17175i	0.558809	+	0.829296i	$0.311258\pi$
$101$	−3.82624	+	11.7759i	−0.380725	+	1.17175i	−0.939534	+	0.342455i	$0.888742\pi$
$102$	−2.00000	+	1.45309i	−0.198030	+	0.143877i
$103$	−9.73607	−	7.07367i	−0.959323	−	0.696989i	−0.00632980	−	0.999980i	$-0.502015\pi$
$103$	−9.73607	−	7.07367i	−0.959323	−	0.696989i	−0.952993	+	0.302991i	$0.902015\pi$
$104$	−1.00000	−	3.07768i	−0.0980581	−	0.301792i
$105$	−4.07295	−	12.5352i	−0.397479	−	1.22331i
$106$	3.11803	+	2.26538i	0.302850	+	0.220034i
$107$	−4.35410	+	3.16344i	−0.420927	+	0.305821i	−0.778011	−	0.628251i	$-0.783771\pi$
$107$	−4.35410	+	3.16344i	−0.420927	+	0.305821i	0.357084	+	0.934072i	$0.383771\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	17.4164			1.66819			0.834095	−	0.551621i	$-0.185991\pi$
$109$	17.4164			1.66819			0.834095	+	0.551621i	$0.185991\pi$
$110$	3.52786	+	8.78402i	0.336369	+	0.837524i
$111$	−1.52786			−0.145018
$112$	1.42705	−	4.39201i	0.134844	−	0.415006i
$113$	10.0902	−	7.33094i	0.949203	−	0.689637i	−0.00141497	−	0.999999i	$-0.500450\pi$
$113$	10.0902	−	7.33094i	0.949203	−	0.689637i	0.950618	+	0.310362i	$0.100450\pi$
$114$	−2.61803	−	1.90211i	−0.245201	−	0.178149i
$115$	−2.85410	−	8.78402i	−0.266146	−	0.819114i
$116$	−0.118034	−	0.363271i	−0.0109592	−	0.0337289i
$117$	2.61803	+	1.90211i	0.242037	+	0.175850i
$118$	3.11803	−	2.26538i	0.287038	−	0.208546i
$119$	−3.52786	+	10.8576i	−0.323399	+	0.995319i
$120$	−2.85410			−0.260543
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$	−6.76393			−0.612378
$123$	1.00000	−	3.07768i	0.0901670	−	0.277505i
$124$	−6.97214	+	5.06555i	−0.626116	+	0.454900i
$125$	4.28115	+	3.11044i	0.382918	+	0.278206i
$126$	1.42705	+	4.39201i	0.127132	+	0.391271i
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	0.969579	+	0.244778i	$0.0787150\pi$
$127$	3.70820	+	11.4127i	0.329050	+	1.01271i	−0.640529	+	0.767934i	$0.721285\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	−2.61803	+	1.90211i	−0.230505	+	0.167472i
$130$	−2.85410	+	8.78402i	−0.250321	+	0.770410i
$131$	−15.2705			−1.33419			−0.667095	−	0.744972i	$-0.732463\pi$
$131$	−15.2705			−1.33419			−0.667095	+	0.744972i	$0.732463\pi$
$132$	−1.23607	−	3.07768i	−0.107586	−	0.267878i
$133$	−14.9443			−1.29583
$134$	1.23607	−	3.80423i	0.106780	−	0.328635i
$135$	2.30902	−	1.67760i	0.198729	−	0.144385i
$136$	2.00000	+	1.45309i	0.171499	+	0.124601i
$137$	−7.14590	−	21.9928i	−0.610515	−	1.87897i	−0.453156	−	0.891431i	$-0.649702\pi$
$137$	−7.14590	−	21.9928i	−0.610515	−	1.87897i	−0.157360	−	0.987541i	$-0.550298\pi$
$138$	1.00000	+	3.07768i	0.0851257	+	0.261990i
$139$	−10.7082	−	7.77997i	−0.908258	−	0.659888i	0.0323157	−	0.999478i	$-0.489712\pi$
$139$	−10.7082	−	7.77997i	−0.908258	−	0.659888i	−0.940574	+	0.339590i	$0.889712\pi$
$140$	−10.6631	+	7.74721i	−0.901198	+	0.654759i
$141$	−0.763932	+	2.35114i	−0.0643347	+	0.198002i
$142$	12.4721			1.04664
$143$	−10.7082	+	0.726543i	−0.895465	+	0.0607565i
$144$	1.00000			0.0833333
$145$	−0.336881	+	1.03681i	−0.0279764	+	0.0861027i
$146$	9.16312	−	6.65740i	0.758345	−	0.550970i
$147$	11.5902	+	8.42075i	0.955941	+	0.694532i
$148$	0.472136	+	1.45309i	0.0388093	+	0.119443i
$149$	0.427051	+	1.31433i	0.0349854	+	0.107674i	0.967024	−	0.254685i	$-0.0819716\pi$
$149$	0.427051	+	1.31433i	0.0349854	+	0.107674i	−0.932039	+	0.362358i	$0.881972\pi$
$150$	2.54508	+	1.84911i	0.207805	+	0.150979i
$151$	−7.54508	+	5.48183i	−0.614010	+	0.446105i	−0.850824	−	0.525450i	$-0.823897\pi$
$151$	−7.54508	+	5.48183i	−0.614010	+	0.446105i	0.236814	+	0.971555i	$0.423897\pi$
$152$	−1.00000	+	3.07768i	−0.0811107	+	0.249633i
$153$	−2.47214			−0.199860
$154$	−12.9721	−	8.14324i	−1.04532	−	0.656201i
$155$	24.5967			1.97566
$156$	1.00000	−	3.07768i	0.0800641	−	0.246412i
$157$	−3.61803	+	2.62866i	−0.288751	+	0.209790i	−0.722725	−	0.691136i	$-0.757111\pi$
$157$	−3.61803	+	2.62866i	−0.288751	+	0.209790i	0.433975	+	0.900925i	$0.357111\pi$
$158$	7.54508	+	5.48183i	0.600255	+	0.436111i
$159$	1.19098	+	3.66547i	0.0944511	+	0.290691i
$160$	0.881966	+	2.71441i	0.0697255	+	0.214593i
$161$	12.0902	+	8.78402i	0.952839	+	0.692278i
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	0.646830	+	0.762634i	$0.276094\pi$
$163$	−4.14590	+	12.7598i	−0.324732	+	0.999422i	−0.971562	+	0.236787i	$0.923906\pi$
$164$	−3.23607			−0.252694
$165$	−2.30902	+	9.18005i	−0.179757	+	0.714666i
$166$	−0.673762			−0.0522941
$167$	2.23607	−	6.88191i	0.173032	−	0.532538i	−0.826506	−	0.562928i	$-0.809675\pi$
$167$	2.23607	−	6.88191i	0.173032	−	0.532538i	0.999538	+	0.0303898i	$0.00967485\pi$
$168$	3.73607	−	2.71441i	0.288244	−	0.209421i
$169$	2.04508	+	1.48584i	0.157314	+	0.114295i
$170$	−2.18034	−	6.71040i	−0.167224	−	0.514664i
$171$	−1.00000	−	3.07768i	−0.0764719	−	0.235356i
$172$	2.61803	+	1.90211i	0.199623	+	0.145035i
$173$	3.35410	−	2.43690i	0.255008	−	0.185274i	−0.452936	−	0.891543i	$-0.649623\pi$
$173$	3.35410	−	2.43690i	0.255008	−	0.185274i	0.707943	+	0.706269i	$0.249623\pi$
$174$	0.118034	−	0.363271i	0.00894813	−	0.0275395i
$175$	14.5279			1.09820
$176$	−2.54508	+	2.12663i	−0.191843	+	0.160301i
$177$	3.85410			0.289692
$178$	−3.61803	+	11.1352i	−0.271183	+	0.834616i
$179$	5.16312	−	3.75123i	0.385910	−	0.280380i	−0.377868	−	0.925860i	$-0.623343\pi$
$179$	5.16312	−	3.75123i	0.385910	−	0.280380i	0.763777	+	0.645480i	$0.223343\pi$
$180$	−2.30902	−	1.67760i	−0.172104	−	0.125041i
$181$	−5.09017	−	15.6659i	−0.378349	−	1.16444i	−0.941191	−	0.337875i	$-0.890292\pi$
$181$	−5.09017	−	15.6659i	−0.378349	−	1.16444i	0.562842	−	0.826565i	$-0.309708\pi$
$182$	−4.61803	−	14.2128i	−0.342311	−	1.05353i
$183$	−5.47214	−	3.97574i	−0.404512	−	0.293895i
$184$	2.61803	−	1.90211i	0.193004	−	0.140226i
$185$	1.34752	−	4.14725i	0.0990719	−	0.304912i
$186$	−8.61803			−0.631905
$187$	6.29180	−	5.25731i	0.460102	−	0.384453i
$188$	2.47214			0.180299
$189$	−1.42705	+	4.39201i	−0.103803	+	0.319472i
$190$	7.47214	−	5.42882i	0.542086	−	0.393848i
$191$	−18.1803	−	13.2088i	−1.31548	−	0.955755i	−0.999977	−	0.00683111i	$-0.997826\pi$
$191$	−18.1803	−	13.2088i	−1.31548	−	0.955755i	−0.315507	−	0.948923i	$-0.602174\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	0.100813	+	0.310271i	0.00725668	+	0.0223338i	0.954619	−	0.297829i	$-0.0962625\pi$
$193$	0.100813	+	0.310271i	0.00725668	+	0.0223338i	−0.947363	+	0.320163i	$0.896262\pi$
$194$	−9.16312	−	6.65740i	−0.657874	−	0.477973i
$195$	−7.47214	+	5.42882i	−0.535091	+	0.388766i
$196$	4.42705	−	13.6251i	0.316218	−	0.973219i
$197$	6.09017			0.433907			0.216953	−	0.976182i	$-0.430388\pi$
$197$	6.09017			0.433907			0.216953	+	0.976182i	$0.430388\pi$
$198$	0.809017	−	3.21644i	0.0574943	−	0.228582i
$199$	13.1459			0.931888			0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459			0.931888			0.465944	+	0.884814i	$0.345715\pi$
$200$	0.972136	−	2.99193i	0.0687404	−	0.211561i
$201$	3.23607	−	2.35114i	0.228255	−	0.165837i
$202$	10.0172	+	7.27794i	0.704809	+	0.512074i
$203$	−0.545085	−	1.67760i	−0.0382575	−	0.117744i
$204$	0.763932	+	2.35114i	0.0534859	+	0.164613i
$205$	7.47214	+	5.42882i	0.521877	+	0.379166i
$206$	−9.73607	+	7.07367i	−0.678344	+	0.492846i
$207$	−1.00000	+	3.07768i	−0.0695048	+	0.213914i
$208$	−3.23607			−0.224381
$209$	9.09017	+	5.70634i	0.628780	+	0.394716i
$210$	−13.1803			−0.909530
$211$	−1.43769	+	4.42477i	−0.0989749	+	0.304614i	−0.988269	−	0.152722i	$-0.951196\pi$
$211$	−1.43769	+	4.42477i	−0.0989749	+	0.304614i	0.889294	+	0.457335i	$0.151196\pi$
$212$	3.11803	−	2.26538i	0.214147	−	0.155587i
$213$	10.0902	+	7.33094i	0.691367	+	0.502308i
$214$	1.66312	+	5.11855i	0.113688	+	0.349897i
$215$	−2.85410	−	8.78402i	−0.194648	−	0.599065i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	−32.1976	+	23.3929i	−2.18571	+	1.58801i
$218$	5.38197	−	16.5640i	0.364513	−	1.12185i
$219$	11.3262			0.765356
$220$	9.44427	−	0.640786i	0.636733	−	0.0432018i
$221$	8.00000			0.538138
$222$	−0.472136	+	1.45309i	−0.0316877	+	0.0975247i
$223$	1.54508	−	1.12257i	0.103467	−	0.0751728i	−0.534849	−	0.844948i	$-0.679632\pi$
$223$	1.54508	−	1.12257i	0.103467	−	0.0751728i	0.638316	+	0.769775i	$0.279632\pi$
$224$	−3.73607	−	2.71441i	−0.249627	−	0.181364i
$225$	0.972136	+	2.99193i	0.0648091	+	0.199462i
$226$	−3.85410	−	11.8617i	−0.256371	−	0.789029i
$227$	5.78115	+	4.20025i	0.383709	+	0.278781i	0.762873	−	0.646549i	$-0.223788\pi$
$227$	5.78115	+	4.20025i	0.383709	+	0.278781i	−0.379164	+	0.925330i	$0.623788\pi$
$228$	−2.61803	+	1.90211i	−0.173384	+	0.125971i
$229$	7.09017	−	21.8213i	0.468532	−	1.44199i	−0.385954	−	0.922518i	$-0.626128\pi$
$229$	7.09017	−	21.8213i	0.468532	−	1.44199i	0.854486	−	0.519474i	$-0.173872\pi$
$230$	−9.23607			−0.609008
$231$	−5.70820	−	14.2128i	−0.375572	−	0.935137i
$232$	−0.381966			−0.0250773
$233$	−2.76393	+	8.50651i	−0.181071	+	0.557280i	−0.999859	−	0.0168170i	$-0.994647\pi$
$233$	−2.76393	+	8.50651i	−0.181071	+	0.557280i	0.818787	+	0.574097i	$0.194647\pi$
$234$	2.61803	−	1.90211i	0.171146	−	0.124345i
$235$	−5.70820	−	4.14725i	−0.372362	−	0.270537i
$236$	−1.19098	−	3.66547i	−0.0775264	−	0.238602i
$237$	2.88197	+	8.86978i	0.187204	+	0.576154i
$238$	9.23607	+	6.71040i	0.598685	+	0.434970i
$239$	13.3262	−	9.68208i	0.862003	−	0.626282i	−0.0664264	−	0.997791i	$-0.521160\pi$
$239$	13.3262	−	9.68208i	0.862003	−	0.626282i	0.928429	+	0.371510i	$0.121160\pi$
$240$	−0.881966	+	2.71441i	−0.0569307	+	0.175215i
$241$	−2.43769			−0.157026			−0.0785128	−	0.996913i	$-0.525017\pi$
$241$	−2.43769			−0.157026			−0.0785128	+	0.996913i	$0.525017\pi$
$242$	4.78115	+	9.90659i	0.307344	+	0.636820i
$243$	−1.00000			−0.0641500
$244$	−2.09017	+	6.43288i	−0.133809	+	0.411823i
$245$	−33.0795	+	24.0337i	−2.11337	+	1.53546i
$246$	−2.61803	−	1.90211i	−0.166920	−	0.121274i
$247$	3.23607	+	9.95959i	0.205906	+	0.633714i
$248$	2.66312	+	8.19624i	0.169108	+	0.520462i
$249$	−0.545085	−	0.396027i	−0.0345434	−	0.0250972i
$250$	4.28115	−	3.11044i	0.270764	−	0.196721i
$251$	−5.97214	+	18.3803i	−0.376958	+	1.16016i	0.565190	+	0.824961i	$0.308803\pi$
$251$	−5.97214	+	18.3803i	−0.376958	+	1.16016i	−0.942148	+	0.335197i	$0.891197\pi$
$252$	4.61803			0.290909
$253$	−4.00000	−	9.95959i	−0.251478	−	0.626154i
$254$	12.0000			0.752947
$255$	2.18034	−	6.71040i	0.136538	−	0.420221i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	1.47214	+	1.06957i	0.0918293	+	0.0667179i	0.632753	−	0.774354i	$-0.281925\pi$
$257$	1.47214	+	1.06957i	0.0918293	+	0.0667179i	−0.540923	+	0.841072i	$0.681925\pi$
$258$	1.00000	+	3.07768i	0.0622573	+	0.191608i
$259$	2.18034	+	6.71040i	0.135480	+	0.416964i
$260$	7.47214	+	5.42882i	0.463402	+	0.336681i
$261$	0.309017	−	0.224514i	0.0191277	−	0.0138971i
$262$	−4.71885	+	14.5231i	−0.291531	+	0.897241i
$263$	7.70820			0.475308			0.237654	−	0.971350i	$-0.423622\pi$
$263$	7.70820			0.475308			0.237654	+	0.971350i	$0.423622\pi$
$264$	−3.30902	+	0.224514i	−0.203656	+	0.0138179i
$265$	−11.0000			−0.675725
$266$	−4.61803	+	14.2128i	−0.283150	+	0.871446i
$267$	−9.47214	+	6.88191i	−0.579685	+	0.421166i
$268$	−3.23607	−	2.35114i	−0.197674	−	0.143619i
$269$	−0.909830	−	2.80017i	−0.0554733	−	0.170729i	0.919481	−	0.393134i	$-0.128609\pi$
$269$	−0.909830	−	2.80017i	−0.0554733	−	0.170729i	−0.974954	+	0.222405i	$0.928609\pi$
$270$	−0.881966	−	2.71441i	−0.0536747	−	0.165194i
$271$	−18.9443	−	13.7638i	−1.15078	−	0.836092i	−0.162198	−	0.986758i	$-0.551858\pi$
$271$	−18.9443	−	13.7638i	−1.15078	−	0.836092i	−0.988585	+	0.150666i	$0.951858\pi$
$272$	2.00000	−	1.45309i	0.121268	−	0.0881062i
$273$	4.61803	−	14.2128i	0.279496	−	0.860201i
$274$	−23.1246			−1.39701
$275$	−8.83688	−	5.54734i	−0.532884	−	0.334517i
$276$	3.23607			0.194788
$277$	3.43769	−	10.5801i	0.206551	−	0.635699i	−0.793095	−	0.609098i	$-0.791532\pi$
$277$	3.43769	−	10.5801i	0.206551	−	0.635699i	0.999646	−	0.0266009i	$-0.00846832\pi$
$278$	−10.7082	+	7.77997i	−0.642235	+	0.466611i
$279$	−6.97214	−	5.06555i	−0.417411	−	0.303267i
$280$	4.07295	+	12.5352i	0.243405	+	0.749124i
$281$	7.14590	+	21.9928i	0.426289	+	1.31198i	0.901755	+	0.432247i	$0.142279\pi$
$281$	7.14590	+	21.9928i	0.426289	+	1.31198i	−0.475467	+	0.879734i	$0.657721\pi$
$282$	2.00000	+	1.45309i	0.119098	+	0.0865300i
$283$	19.3262	−	14.0413i	1.14883	−	0.834671i	0.160501	−	0.987036i	$-0.448689\pi$
$283$	19.3262	−	14.0413i	1.14883	−	0.834671i	0.988324	+	0.152365i	$0.0486889\pi$
$284$	3.85410	−	11.8617i	0.228699	−	0.703863i
$285$	9.23607			0.547097
$286$	−2.61803	+	10.4086i	−0.154808	+	0.615475i
$287$	−14.9443			−0.882132
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	8.80902	−	6.40013i	0.518177	−	0.376478i
$290$	0.881966	+	0.640786i	0.0517908	+	0.0376282i
$291$	−3.50000	−	10.7719i	−0.205174	−	0.631460i
$292$	−3.50000	−	10.7719i	−0.204822	−	0.630377i
$293$	−18.5902	−	13.5065i	−1.08605	−	0.789061i	−0.107322	−	0.994224i	$-0.534227\pi$
$293$	−18.5902	−	13.5065i	−1.08605	−	0.789061i	−0.978728	+	0.205163i	$0.934227\pi$
$294$	11.5902	−	8.42075i	0.675952	−	0.491108i
$295$	−3.39919	+	10.4616i	−0.197908	+	0.609099i
$296$	1.52786			0.0888053
$297$	2.54508	−	2.12663i	0.147681	−	0.123399i
$298$	1.38197			0.0800551
$299$	3.23607	−	9.95959i	0.187147	−	0.575978i
$300$	2.54508	−	1.84911i	0.146941	−	0.106759i
$301$	12.0902	+	8.78402i	0.696866	+	0.506303i
$302$	2.88197	+	8.86978i	0.165839	+	0.510398i
$303$	3.82624	+	11.7759i	0.219812	+	0.676511i
$304$	2.61803	+	1.90211i	0.150155	+	0.109094i
$305$	15.6180	−	11.3472i	0.894286	−	0.649737i
$306$	−0.763932	+	2.35114i	−0.0436711	+	0.134406i
$307$	−16.6525			−0.950407			−0.475203	−	0.879876i	$-0.657626\pi$
$307$	−16.6525			−0.950407			−0.475203	+	0.879876i	$0.657626\pi$
$308$	−11.7533	+	9.82084i	−0.669706	+	0.559594i
$309$	−12.0344			−0.684615
$310$	7.60081	−	23.3929i	0.431697	−	1.32863i
$311$	19.3262	−	14.0413i	1.09589	−	0.796211i	0.115506	−	0.993307i	$-0.463151\pi$
$311$	19.3262	−	14.0413i	1.09589	−	0.796211i	0.980384	+	0.197096i	$0.0631510\pi$
$312$	−2.61803	−	1.90211i	−0.148217	−	0.107686i
$313$	4.68034	+	14.4046i	0.264548	+	0.814196i	0.991797	+	0.127822i	$0.0407987\pi$
$313$	4.68034	+	14.4046i	0.264548	+	0.814196i	−0.727249	+	0.686374i	$0.759201\pi$
$314$	1.38197	+	4.25325i	0.0779889	+	0.240025i
$315$	−10.6631	−	7.74721i	−0.600799	−	0.436506i
$316$	7.54508	−	5.48183i	0.424444	−	0.308377i
$317$	−6.14590	+	18.9151i	−0.345188	+	1.06238i	0.616295	+	0.787515i	$0.288633\pi$
$317$	−6.14590	+	18.9151i	−0.345188	+	1.06238i	−0.961483	+	0.274864i	$0.911367\pi$
$318$	3.85410			0.216127
$319$	−0.309017	+	1.22857i	−0.0173016	+	0.0687868i
$320$	2.85410			0.159549
$321$	−1.66312	+	5.11855i	−0.0928262	+	0.285690i
$322$	12.0902	−	8.78402i	0.673759	−	0.489514i
$323$	−6.47214	−	4.70228i	−0.360119	−	0.261642i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	−3.14590	−	9.68208i	−0.174503	−	0.537065i
$326$	10.8541	+	7.88597i	0.601153	+	0.436763i
$327$	14.0902	−	10.2371i	0.779188	−	0.566113i
$328$	−1.00000	+	3.07768i	−0.0552158	+	0.169937i
$329$	11.4164			0.629407
$330$	8.01722	+	5.03280i	0.441333	+	0.277046i
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$	−0.208204	+	0.640786i	−0.0114267	+	0.0351677i
$333$	−1.23607	+	0.898056i	−0.0677361	+	0.0492132i
$334$	−5.85410	−	4.25325i	−0.320322	−	0.232728i
$335$	3.52786	+	10.8576i	0.192748	+	0.593217i
$336$	−1.42705	−	4.39201i	−0.0778520	−	0.239604i
$337$	−5.61803	−	4.08174i	−0.306034	−	0.222347i	0.424159	−	0.905588i	$-0.360570\pi$
$337$	−5.61803	−	4.08174i	−0.306034	−	0.222347i	−0.730193	+	0.683241i	$0.760570\pi$
$338$	2.04508	−	1.48584i	0.111238	−	0.0808191i
$339$	3.85410	−	11.8617i	0.209326	−	0.644239i
$340$	−7.05573			−0.382651
$341$	28.5172	−	1.93487i	1.54429	−	0.104779i
$342$	−3.23607			−0.174987
$343$	10.4549	−	32.1769i	0.564512	−	1.73739i
$344$	2.61803	−	1.90211i	0.141155	−	0.102555i
$345$	−7.47214	−	5.42882i	−0.402286	−	0.292278i
$346$	−1.28115	−	3.94298i	−0.0688752	−	0.211976i
$347$	3.66312	+	11.2739i	0.196647	+	0.605216i	0.999953	+	0.00965049i	$0.00307189\pi$
$347$	3.66312	+	11.2739i	0.196647	+	0.605216i	−0.803307	+	0.595565i	$0.796928\pi$
$348$	−0.309017	−	0.224514i	−0.0165650	−	0.0120352i
$349$	10.7082	−	7.77997i	0.573197	−	0.416452i	−0.263068	−	0.964777i	$-0.584734\pi$
$349$	10.7082	−	7.77997i	0.573197	−	0.416452i	0.836265	+	0.548325i	$0.184734\pi$
$350$	4.48936	−	13.8168i	0.239966	−	0.738540i
$351$	3.23607			0.172729
$352$	1.23607	+	3.07768i	0.0658826	+	0.164041i
$353$	−21.5967			−1.14948			−0.574739	−	0.818336i	$-0.694897\pi$
$353$	−21.5967			−1.14948			−0.574739	+	0.818336i	$0.694897\pi$
$354$	1.19098	−	3.66547i	0.0633000	−	0.194817i
$355$	−28.7984	+	20.9232i	−1.52846	+	1.11049i
$356$	9.47214	+	6.88191i	0.502022	+	0.364740i
$357$	3.52786	+	10.8576i	0.186714	+	0.574648i
$358$	−1.97214	−	6.06961i	−0.104231	−	0.320789i
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	0.280940	−	0.959725i	$-0.409354\pi$
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	−0.825938	+	0.563761i	$0.809354\pi$
$360$	−2.30902	+	1.67760i	−0.121696	+	0.0884172i
$361$	−2.63525	+	8.11048i	−0.138698	+	0.426867i
$362$	−16.4721			−0.865756
$363$	−1.95492	+	10.8249i	−0.102606	+	0.568160i
$364$	−14.9443			−0.783293
$365$	−9.98936	+	30.7441i	−0.522867	+	1.60922i
$366$	−5.47214	+	3.97574i	−0.286033	+	0.207815i
$367$	30.3435	+	22.0458i	1.58392	+	1.15078i	0.912027	+	0.410130i	$0.134517\pi$
$367$	30.3435	+	22.0458i	1.58392	+	1.15078i	0.671888	+	0.740652i	$0.265483\pi$
$368$	−1.00000	−	3.07768i	−0.0521286	−	0.160435i
$369$	−1.00000	−	3.07768i	−0.0520579	−	0.160218i
$370$	−3.52786	−	2.56314i	−0.183405	−	0.133251i
$371$	14.3992	−	10.4616i	0.747569	−	0.543140i
$372$	−2.66312	+	8.19624i	−0.138076	+	0.424955i
$373$	−9.52786			−0.493334			−0.246667	−	0.969100i	$-0.579335\pi$
$373$	−9.52786			−0.493334			−0.246667	+	0.969100i	$0.579335\pi$
$374$	−3.05573	−	7.60845i	−0.158008	−	0.393424i
$375$	5.29180			0.273267
$376$	0.763932	−	2.35114i	0.0393968	−	0.121251i
$377$	−1.00000	+	0.726543i	−0.0515026	+	0.0374188i
$378$	3.73607	+	2.71441i	0.192163	+	0.139614i
$379$	1.14590	+	3.52671i	0.0588608	+	0.181155i	0.976164	−	0.217035i	$-0.0696385\pi$
$379$	1.14590	+	3.52671i	0.0588608	+	0.181155i	−0.917303	+	0.398190i	$0.869639\pi$
$380$	−2.85410	−	8.78402i	−0.146412	−	0.450611i
$381$	9.70820	+	7.05342i	0.497366	+	0.361358i
$382$	−18.1803	+	13.2088i	−0.930187	+	0.675820i
$383$	4.09017	−	12.5882i	0.208998	−	0.643229i	−0.790528	−	0.612426i	$-0.790194\pi$
$383$	4.09017	−	12.5882i	0.208998	−	0.643229i	0.999525	−	0.0308030i	$-0.00980645\pi$
$384$	−1.00000			−0.0510310
$385$	43.6140	−	2.95917i	2.22277	−	0.150813i
$386$	0.326238			0.0166051
$387$	−1.00000	+	3.07768i	−0.0508329	+	0.156447i
$388$	−9.16312	+	6.65740i	−0.465187	+	0.337978i
$389$	−31.5066	−	22.8909i	−1.59745	−	1.16061i	−0.892189	−	0.451662i	$-0.850831\pi$
$389$	−31.5066	−	22.8909i	−1.59745	−	1.16061i	−0.705258	−	0.708951i	$-0.749169\pi$
$390$	2.85410	+	8.78402i	0.144523	+	0.444796i
$391$	2.47214	+	7.60845i	0.125021	+	0.384776i
$392$	−11.5902	−	8.42075i	−0.585392	−	0.425312i
$393$	−12.3541	+	8.97578i	−0.623182	+	0.452768i
$394$	1.88197	−	5.79210i	0.0948121	−	0.291802i
$395$	−26.6180			−1.33930
$396$	−2.80902	−	1.76336i	−0.141158	−	0.0886120i
$397$	9.88854			0.496292			0.248146	−	0.968723i	$-0.420179\pi$
$397$	9.88854			0.496292			0.248146	+	0.968723i	$0.420179\pi$
$398$	4.06231	−	12.5025i	0.203625	−	0.626693i
$399$	−12.0902	+	8.78402i	−0.605266	+	0.439751i
$400$	−2.54508	−	1.84911i	−0.127254	−	0.0924556i
$401$	3.18034	+	9.78808i	0.158819	+	0.488793i	0.998528	−	0.0542430i	$-0.0172746\pi$
$401$	3.18034	+	9.78808i	0.158819	+	0.488793i	−0.839709	+	0.543036i	$0.817275\pi$
$402$	−1.23607	−	3.80423i	−0.0616495	−	0.189738i
$403$	22.5623	+	16.3925i	1.12391	+	0.816567i
$404$	10.0172	−	7.27794i	0.498375	−	0.362091i
$405$	0.881966	−	2.71441i	0.0438252	−	0.134880i
$406$	−1.76393			−0.0875425
$407$	1.23607	−	4.91428i	0.0612696	−	0.243592i
$408$	2.47214			0.122389
$409$	−3.73607	+	11.4984i	−0.184737	+	0.568561i	−0.999944	−	0.0106086i	$-0.996623\pi$
$409$	−3.73607	+	11.4984i	−0.184737	+	0.568561i	0.815207	+	0.579170i	$0.196623\pi$
$410$	7.47214	−	5.42882i	0.369022	−	0.268111i
$411$	−18.7082	−	13.5923i	−0.922808	−	0.670459i
$412$	3.71885	+	11.4454i	0.183214	+	0.563876i
$413$	−5.50000	−	16.9273i	−0.270637	−	0.832936i
$414$	2.61803	+	1.90211i	0.128669	+	0.0934838i
$415$	1.55573	−	1.13030i	0.0763677	−	0.0554844i
$416$	−1.00000	+	3.07768i	−0.0490290	+	0.150896i
$417$	−13.2361			−0.648173
$418$	8.23607	−	6.88191i	0.402839	−	0.336605i
$419$	−17.9787			−0.878318			−0.439159	−	0.898409i	$-0.644723\pi$
$419$	−17.9787			−0.878318			−0.439159	+	0.898409i	$0.644723\pi$
$420$	−4.07295	+	12.5352i	−0.198740	+	0.611657i
$421$	−28.4164	+	20.6457i	−1.38493	+	1.00621i	−0.388531	+	0.921436i	$0.627017\pi$
$421$	−28.4164	+	20.6457i	−1.38493	+	1.00621i	−0.996400	+	0.0847756i	$0.972983\pi$
$422$	3.76393	+	2.73466i	0.183225	+	0.133121i
$423$	0.763932	+	2.35114i	0.0371436	+	0.114316i
$424$	−1.19098	−	3.66547i	−0.0578392	−	0.178011i
$425$	6.29180	+	4.57126i	0.305197	+	0.221739i
$426$	10.0902	−	7.33094i	0.488870	−	0.355185i
$427$	−9.65248	+	29.7073i	−0.467116	+	1.43764i
$428$	5.38197			0.260147
$429$	−8.23607	+	6.88191i	−0.397641	+	0.332262i
$430$	−9.23607			−0.445403
$431$	−2.23607	+	6.88191i	−0.107708	+	0.331490i	−0.990356	−	0.138543i	$-0.955758\pi$
$431$	−2.23607	+	6.88191i	−0.107708	+	0.331490i	0.882649	+	0.470033i	$0.155758\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−9.97214	−	7.24518i	−0.479230	−	0.348181i	0.321797	−	0.946809i	$-0.395713\pi$
$433$	−9.97214	−	7.24518i	−0.479230	−	0.348181i	−0.801028	+	0.598627i	$0.795713\pi$
$434$	12.2984	+	37.8505i	0.590341	+	1.81688i
$435$	0.336881	+	1.03681i	0.0161522	+	0.0497114i
$436$	−14.0902	−	10.2371i	−0.674797	−	0.490269i
$437$	−8.47214	+	6.15537i	−0.405277	+	0.294451i
$438$	3.50000	−	10.7719i	0.167236	−	0.514701i
$439$	16.0344			0.765282			0.382641	−	0.923897i	$-0.375015\pi$
$439$	16.0344			0.765282			0.382641	+	0.923897i	$0.375015\pi$
$440$	2.30902	−	9.18005i	0.110078	−	0.437642i
$441$	14.3262			0.682202
$442$	2.47214	−	7.60845i	0.117588	−	0.361897i
$443$	1.35410	−	0.983813i	0.0643353	−	0.0467424i	−0.555153	−	0.831748i	$-0.687340\pi$
$443$	1.35410	−	0.983813i	0.0643353	−	0.0467424i	0.619488	+	0.785006i	$0.287340\pi$
$444$	1.23607	+	0.898056i	0.0586612	+	0.0426198i
$445$	−10.3262	−	31.7809i	−0.489511	−	1.50656i
$446$	−0.590170	−	1.81636i	−0.0279454	−	0.0860070i
$447$	1.11803	+	0.812299i	0.0528812	+	0.0384204i
$448$	−3.73607	+	2.71441i	−0.176513	+	0.128244i
$449$	11.0902	−	34.1320i	0.523377	−	1.61079i	−0.244125	−	0.969744i	$-0.578501\pi$
$449$	11.0902	−	34.1320i	0.523377	−	1.61079i	0.767502	−	0.641046i	$-0.221499\pi$
$450$	3.14590			0.148299
$451$	9.09017	+	5.70634i	0.428039	+	0.268701i
$452$	−12.4721			−0.586640
$453$	−2.88197	+	8.86978i	−0.135407	+	0.416739i
$454$	5.78115	−	4.20025i	0.271323	−	0.197128i
$455$	34.5066	+	25.0705i	1.61769	+	1.17532i
$456$	1.00000	+	3.07768i	0.0468293	+	0.144126i
$457$	−6.79180	−	20.9030i	−0.317707	−	0.977801i	−0.974626	−	0.223840i	$-0.928141\pi$
$457$	−6.79180	−	20.9030i	−0.317707	−	0.977801i	0.656919	−	0.753961i	$-0.271859\pi$
$458$	−18.5623	−	13.4863i	−0.867360	−	0.630174i
$459$	−2.00000	+	1.45309i	−0.0933520	+	0.0678242i
$460$	−2.85410	+	8.78402i	−0.133073	+	0.409557i
$461$	40.8328			1.90177			0.950887	−	0.309538i	$-0.100175\pi$
$461$	40.8328			1.90177			0.950887	+	0.309538i	$0.100175\pi$
$462$	−15.2812	+	1.03681i	−0.710944	+	0.0482369i
$463$	19.0902			0.887195			0.443598	−	0.896226i	$-0.353702\pi$
$463$	19.0902			0.887195			0.443598	+	0.896226i	$0.353702\pi$
$464$	−0.118034	+	0.363271i	−0.00547959	+	0.0168644i
$465$	19.8992	−	14.4576i	0.922803	−	0.670455i
$466$	7.23607	+	5.25731i	0.335204	+	0.243540i
$467$	6.04508	+	18.6049i	0.279733	+	0.860930i	0.987928	+	0.154913i	$0.0495098\pi$
$467$	6.04508	+	18.6049i	0.279733	+	0.860930i	−0.708195	+	0.706017i	$0.750490\pi$
$468$	−1.00000	−	3.07768i	−0.0462250	−	0.142266i
$469$	−14.9443	−	10.8576i	−0.690062	−	0.501360i
$470$	−5.70820	+	4.14725i	−0.263300	+	0.191299i
$471$	−1.38197	+	4.25325i	−0.0636776	+	0.195980i
$472$	−3.85410			−0.177399
$473$	−4.00000	−	9.95959i	−0.183920	−	0.457943i
$474$	9.32624			0.428368
$475$	−3.14590	+	9.68208i	−0.144344	+	0.444244i
$476$	9.23607	−	6.71040i	0.423334	−	0.307571i
$477$	3.11803	+	2.26538i	0.142765	+	0.103725i
$478$	−5.09017	−	15.6659i	−0.232819	−	0.716543i
$479$	−2.23607	−	6.88191i	−0.102169	−	0.314442i	0.886887	−	0.461987i	$-0.152863\pi$
$479$	−2.23607	−	6.88191i	−0.102169	−	0.314442i	−0.989055	+	0.147544i	$0.952863\pi$
$480$	2.30902	+	1.67760i	0.105392	+	0.0765716i
$481$	4.00000	−	2.90617i	0.182384	−	0.132510i
$482$	−0.753289	+	2.31838i	−0.0343114	+	0.105600i
$483$	14.9443			0.679988
$484$	10.8992	−	1.48584i	0.495418	−	0.0675382i
$485$	32.3262			1.46786
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−20.2082	+	14.6821i	−0.915721	+	0.665310i	−0.942455	−	0.334332i	$-0.891489\pi$
$487$	−20.2082	+	14.6821i	−0.915721	+	0.665310i	0.0267342	+	0.999643i	$0.491489\pi$
$488$	5.47214	+	3.97574i	0.247712	+	0.179973i
$489$	4.14590	+	12.7598i	0.187484	+	0.577016i
$490$	12.6353	+	38.8873i	0.570803	+	1.75675i
$491$	−34.1803	−	24.8335i	−1.54254	−	1.12072i	−0.948719	−	0.316119i	$-0.897620\pi$
$491$	−34.1803	−	24.8335i	−1.54254	−	1.12072i	−0.593818	−	0.804600i	$-0.702380\pi$
$492$	−2.61803	+	1.90211i	−0.118030	+	0.0857539i
$493$	0.291796	−	0.898056i	0.0131418	−	0.0404464i
$494$	10.4721			0.471164
$495$	3.52786	+	8.78402i	0.158566	+	0.394812i
$496$	8.61803			0.386961
$497$	17.7984	−	54.7778i	0.798366	−	2.45712i
$498$	−0.545085	+	0.396027i	−0.0244258	+	0.0177464i
$499$	6.00000	+	4.35926i	0.268597	+	0.195147i	0.713928	−	0.700219i	$-0.246914\pi$
$499$	6.00000	+	4.35926i	0.268597	+	0.195147i	−0.445332	+	0.895366i	$0.646914\pi$
$500$	−1.63525	−	5.03280i	−0.0731308	−	0.225074i
$501$	−2.23607	−	6.88191i	−0.0999001	−	0.307461i
$502$	15.6353	+	11.3597i	0.697836	+	0.507007i
$503$	−3.52786	+	2.56314i	−0.157300	+	0.114285i	−0.663651	−	0.748042i	$-0.730994\pi$
$503$	−3.52786	+	2.56314i	−0.157300	+	0.114285i	0.506351	+	0.862327i	$0.330994\pi$
$504$	1.42705	−	4.39201i	0.0635659	−	0.195636i
$505$	−35.3394			−1.57258
$506$	−10.7082	+	0.726543i	−0.476038	+	0.0322988i
$507$	2.52786			0.112266
$508$	3.70820	−	11.4127i	0.164525	−	0.506356i
$509$	−2.59017	+	1.88187i	−0.114807	+	0.0834124i	−0.643707	−	0.765272i	$-0.722605\pi$
$509$	−2.59017	+	1.88187i	−0.114807	+	0.0834124i	0.528900	+	0.848684i	$0.322605\pi$
$510$	−5.70820	−	4.14725i	−0.252764	−	0.183643i
$511$	−16.1631	−	49.7450i	−0.715014	−	2.20059i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−2.61803	−	1.90211i	−0.115589	−	0.0839803i
$514$	1.47214	−	1.06957i	0.0649331	−	0.0471767i
$515$	10.6140	−	32.6664i	0.467707	−	1.43946i
$516$	3.23607			0.142460
$517$	−6.94427	−	4.35926i	−0.305409	−	0.191720i
$518$	7.05573			0.310011
$519$	1.28115	−	3.94298i	0.0562364	−	0.173078i
$520$	7.47214	−	5.42882i	0.327675	−	0.238070i
$521$	−25.4164	−	18.4661i	−1.11351	−	0.809015i	−0.130300	−	0.991475i	$-0.541594\pi$
$521$	−25.4164	−	18.4661i	−1.11351	−	0.809015i	−0.983213	+	0.182460i	$0.941594\pi$
$522$	−0.118034	−	0.363271i	−0.00516621	−	0.0159000i
$523$	6.05573	+	18.6376i	0.264799	+	0.814966i	0.991740	+	0.128266i	$0.0409412\pi$
$523$	6.05573	+	18.6376i	0.264799	+	0.814966i	−0.726941	+	0.686700i	$0.759059\pi$
$524$	12.3541	+	8.97578i	0.539691	+	0.392109i
$525$	11.7533	−	8.53926i	0.512956	−	0.372684i
$526$	2.38197	−	7.33094i	0.103859	−	0.319644i
$527$	−21.3050			−0.928058
$528$	−0.809017	+	3.21644i	−0.0352079	+	0.139978i
$529$	−12.5279			−0.544690
$530$	−3.39919	+	10.4616i	−0.147651	+	0.454424i
$531$	3.11803	−	2.26538i	0.135311	−	0.0983093i
$532$	12.0902	+	8.78402i	0.524175	+	0.380836i
$533$	3.23607	+	9.95959i	0.140170	+	0.431398i
$534$	3.61803	+	11.1352i	0.156568	+	0.481866i
$535$	−12.4271	−	9.02878i	−0.537268	−	0.390348i
$536$	−3.23607	+	2.35114i	−0.139777	+	0.101554i
$537$	1.97214	−	6.06961i	0.0851039	−	0.261923i
$538$	−2.94427			−0.126937
$539$	−36.4615	+	30.4666i	−1.57051	+	1.31229i
$540$	−2.85410			−0.122821
$541$	2.32624	−	7.15942i	0.100013	−	0.307808i	−0.888515	−	0.458848i	$-0.848262\pi$
$541$	2.32624	−	7.15942i	0.100013	−	0.307808i	0.988528	+	0.151040i	$0.0482623\pi$
$542$	−18.9443	+	13.7638i	−0.813726	+	0.591207i
$543$	−13.3262	−	9.68208i	−0.571884	−	0.415498i
$544$	−0.763932	−	2.35114i	−0.0327533	−	0.100804i
$545$	15.3607	+	47.2753i	0.657979	+	2.02505i
$546$	−12.0902	−	8.78402i	−0.517412	−	0.375921i
$547$	−14.7082	+	10.6861i	−0.628877	+	0.456906i	−0.856011	−	0.516957i	$-0.827065\pi$
$547$	−14.7082	+	10.6861i	−0.628877	+	0.456906i	0.227134	+	0.973864i	$0.427065\pi$
$548$	−7.14590	+	21.9928i	−0.305258	+	0.939486i
$549$	−6.76393			−0.288678
$550$	−8.00658	+	6.69015i	−0.341402	+	0.285269i
$551$	1.23607			0.0526583
$552$	1.00000	−	3.07768i	0.0425628	−	0.130995i
$553$	34.8435	−	25.3153i	1.48169	−	1.07651i
$554$	−9.00000	−	6.53888i	−0.382373	−	0.277811i
$555$	−1.34752	−	4.14725i	−0.0571992	−	0.176041i
$556$	4.09017	+	12.5882i	0.173462	+	0.533861i
$557$	34.0066	+	24.7072i	1.44090	+	1.04688i	0.987852	+	0.155395i	$0.0496650\pi$
$557$	34.0066	+	24.7072i	1.44090	+	1.04688i	0.453053	+	0.891484i	$0.350335\pi$
$558$	−6.97214	+	5.06555i	−0.295154	+	0.214442i
$559$	3.23607	−	9.95959i	0.136871	−	0.421246i
$560$	13.1803			0.556971
$561$	2.00000	−	7.95148i	0.0844401	−	0.335712i
$562$	23.1246			0.975453
$563$	−14.4721	+	44.5407i	−0.609928	+	1.87716i	−0.151433	+	0.988467i	$0.548389\pi$
$563$	−14.4721	+	44.5407i	−0.609928	+	1.87716i	−0.458494	+	0.888697i	$0.651611\pi$
$564$	2.00000	−	1.45309i	0.0842152	−	0.0611859i
$565$	28.7984	+	20.9232i	1.21156	+	0.880247i
$566$	−7.38197	−	22.7194i	−0.310287	−	0.954966i
$567$	1.42705	+	4.39201i	0.0599305	+	0.184447i
$568$	−10.0902	−	7.33094i	−0.423374	−	0.307599i
$569$	−29.7984	+	21.6498i	−1.24921	+	0.907606i	−0.998176	−	0.0603713i	$-0.980772\pi$
$569$	−29.7984	+	21.6498i	−1.24921	+	0.907606i	−0.251037	+	0.967978i	$0.580772\pi$
$570$	2.85410	−	8.78402i	0.119545	−	0.367922i
$571$	9.59675			0.401611			0.200806	−	0.979631i	$-0.435644\pi$
$571$	9.59675			0.401611			0.200806	+	0.979631i	$0.435644\pi$
$572$	9.09017	+	5.70634i	0.380079	+	0.238594i
$573$	−22.4721			−0.938787
$574$	−4.61803	+	14.2128i	−0.192753	+	0.593233i
$575$	8.23607	−	5.98385i	0.343468	−	0.249544i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	2.19098	+	6.74315i	0.0912118	+	0.280721i	0.986248	−	0.165273i	$-0.0528504\pi$
$577$	2.19098	+	6.74315i	0.0912118	+	0.280721i	−0.895036	+	0.445994i	$0.852850\pi$
$578$	−3.36475	−	10.3556i	−0.139955	−	0.430737i
$579$	0.263932	+	0.191758i	0.0109686	+	0.00796918i
$580$	0.881966	−	0.640786i	0.0366216	−	0.0266072i
$581$	−0.961493	+	2.95917i	−0.0398894	+	0.122767i
$582$	−11.3262			−0.469488
$583$	−12.7533	+	0.865300i	−0.528187	+	0.0358371i
$584$	−11.3262			−0.468683
$585$	−2.85410	+	8.78402i	−0.118003	+	0.363175i
$586$	−18.5902	+	13.5065i	−0.767953	+	0.557950i
$587$	19.4894	+	14.1598i	0.804412	+	0.584439i	0.912205	−	0.409734i	$-0.134378\pi$
$587$	19.4894	+	14.1598i	0.804412	+	0.584439i	−0.107793	+	0.994173i	$0.534378\pi$
$588$	−4.42705	−	13.6251i	−0.182569	−	0.561888i
$589$	−8.61803	−	26.5236i	−0.355100	−	1.09289i
$590$	8.89919	+	6.46564i	0.366374	+	0.266186i
$591$	4.92705	−	3.57971i	0.202672	−	0.147250i
$592$	0.472136	−	1.45309i	0.0194047	−	0.0597214i
$593$	24.4721			1.00495			0.502475	−	0.864592i	$-0.332423\pi$
$593$	24.4721			1.00495			0.502475	+	0.864592i	$0.332423\pi$
$594$	−1.23607	−	3.07768i	−0.0507165	−	0.126279i
$595$	−32.5836			−1.33580
$596$	0.427051	−	1.31433i	0.0174927	−	0.0538370i
$597$	10.6353	−	7.72696i	0.435272	−	0.316244i
$598$	−8.47214	−	6.15537i	−0.346451	−	0.251712i
$599$	2.58359	+	7.95148i	0.105563	+	0.324889i	0.989862	−	0.142032i	$-0.0453635\pi$
$599$	2.58359	+	7.95148i	0.105563	+	0.324889i	−0.884299	+	0.466920i	$0.845363\pi$
$600$	−0.972136	−	2.99193i	−0.0396873	−	0.122145i
$601$	19.2082	+	13.9556i	0.783519	+	0.569260i	0.906033	−	0.423207i	$-0.139096\pi$
$601$	19.2082	+	13.9556i	0.783519	+	0.569260i	−0.122514	+	0.992467i	$0.539096\pi$
$602$	12.0902	−	8.78402i	0.492759	−	0.358010i
$603$	1.23607	−	3.80423i	0.0503366	−	0.154920i
$604$	9.32624			0.379479
$605$	−27.6591	−	14.8536i	−1.12450	−	0.603886i
$606$	12.3820			0.502983
$607$	7.34752	−	22.6134i	0.298227	−	0.917848i	−0.683892	−	0.729584i	$-0.739714\pi$
$607$	7.34752	−	22.6134i	0.298227	−	0.917848i	0.982118	−	0.188264i	$-0.0602861\pi$
$608$	2.61803	−	1.90211i	0.106175	−	0.0771409i
$609$	−1.42705	−	1.03681i	−0.0578270	−	0.0420138i
$610$	−5.96556	−	18.3601i	−0.241538	−	0.743379i
$611$	−2.47214	−	7.60845i	−0.100012	−	0.307805i
$612$	2.00000	+	1.45309i	0.0808452	+	0.0587375i
$613$	11.5623	−	8.40051i	0.466997	−	0.339293i	−0.329273	−	0.944235i	$-0.606804\pi$
$613$	11.5623	−	8.40051i	0.466997	−	0.339293i	0.796270	+	0.604942i	$0.206804\pi$
$614$	−5.14590	+	15.8374i	−0.207672	+	0.639147i
$615$	9.23607			0.372434
$616$	5.70820	+	14.2128i	0.229990	+	0.572652i
$617$	−30.2918			−1.21950			−0.609751	−	0.792593i	$-0.708731\pi$
$617$	−30.2918			−1.21950			−0.609751	+	0.792593i	$0.708731\pi$
$618$	−3.71885	+	11.4454i	−0.149594	+	0.460403i
$619$	20.4721	−	14.8739i	0.822845	−	0.597832i	−0.0946813	−	0.995508i	$-0.530183\pi$
$619$	20.4721	−	14.8739i	0.822845	−	0.597832i	0.917526	+	0.397676i	$0.130183\pi$
$620$	−19.8992	−	14.4576i	−0.799171	−	0.580631i
$621$	1.00000	+	3.07768i	0.0401286	+	0.123503i
$622$	−7.38197	−	22.7194i	−0.295990	−	0.910963i
$623$	43.7426	+	31.7809i	1.75251	+	1.27327i
$624$	−2.61803	+	1.90211i	−0.104805	+	0.0761455i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	15.1459			0.605352
$627$	10.7082	−	0.726543i	0.427644	−	0.0290153i
$628$	4.47214			0.178458
$629$	−1.16718	+	3.59222i	−0.0465387	+	0.143231i
$630$	−10.6631	+	7.74721i	−0.424829	+	0.308656i
$631$	13.8713	+	10.0781i	0.552209	+	0.401203i	0.828599	−	0.559842i	$-0.189138\pi$
$631$	13.8713	+	10.0781i	0.552209	+	0.401203i	−0.276390	+	0.961045i	$0.589138\pi$
$632$	−2.88197	−	8.86978i	−0.114638	−	0.352821i
$633$	1.43769	+	4.42477i	0.0571432	+	0.175869i
$634$	16.0902	+	11.6902i	0.639022	+	0.464277i
$635$	−27.7082	+	20.1312i	−1.09957	+	0.798882i
$636$	1.19098	−	3.66547i	0.0472255	−	0.145345i
$637$	−46.3607			−1.83688
$638$	1.07295	+	0.673542i	0.0424785	+	0.0266658i
$639$	12.4721			0.493390
$640$	0.881966	−	2.71441i	0.0348628	−	0.107297i
$641$	−38.1246	+	27.6992i	−1.50583	+	1.09405i	−0.537847	+	0.843043i	$0.680762\pi$
$641$	−38.1246	+	27.6992i	−1.50583	+	1.09405i	−0.967985	+	0.251008i	$0.919238\pi$
$642$	4.35410	+	3.16344i	0.171843	+	0.124851i
$643$	3.38197	+	10.4086i	0.133372	+	0.410476i	0.995333	−	0.0964978i	$-0.0307641\pi$
$643$	3.38197	+	10.4086i	0.133372	+	0.410476i	−0.861961	+	0.506974i	$0.830764\pi$
$644$	−4.61803	−	14.2128i	−0.181976	−	0.560065i
$645$	−7.47214	−	5.42882i	−0.294215	−	0.213760i
$646$	−6.47214	+	4.70228i	−0.254643	+	0.185009i
$647$	−0.888544	+	2.73466i	−0.0349323	+	0.107510i	−0.967002	−	0.254768i	$-0.918001\pi$
$647$	−0.888544	+	2.73466i	−0.0349323	+	0.107510i	0.932070	+	0.362278i	$0.118001\pi$
$648$	1.00000			0.0392837
$649$	−3.11803	+	12.3965i	−0.122394	+	0.486605i
$650$	−10.1803			−0.399306
$651$	−12.2984	+	37.8505i	−0.482011	+	1.48348i
$652$	10.8541	−	7.88597i	0.425079	−	0.308838i
$653$	17.1074	+	12.4292i	0.669464	+	0.486394i	0.869846	−	0.493324i	$-0.164218\pi$
$653$	17.1074	+	12.4292i	0.669464	+	0.486394i	−0.200382	+	0.979718i	$0.564218\pi$
$654$	−5.38197	−	16.5640i	−0.210452	−	0.647703i
$655$	−13.4681	−	41.4505i	−0.526241	−	1.61960i
$656$	2.61803	+	1.90211i	0.102217	+	0.0742650i
$657$	9.16312	−	6.65740i	0.357487	−	0.259730i
$658$	3.52786	−	10.8576i	0.137530	−	0.423275i
$659$	43.1459			1.68073			0.840363	−	0.542024i	$-0.182342\pi$
$659$	43.1459			1.68073			0.840363	+	0.542024i	$0.182342\pi$
$660$	7.26393	−	6.06961i	0.282748	−	0.236259i
$661$	5.81966			0.226359			0.113179	−	0.993575i	$-0.463897\pi$
$661$	5.81966			0.226359			0.113179	+	0.993575i	$0.463897\pi$
$662$	2.76393	−	8.50651i	0.107423	−	0.330615i
$663$	6.47214	−	4.70228i	0.251357	−	0.182622i
$664$	0.545085	+	0.396027i	0.0211534	+	0.0153688i
$665$	−13.1803	−	40.5649i	−0.511112	−	1.57304i
$666$	0.472136	+	1.45309i	0.0182949	+	0.0563059i
$667$	−1.00000	−	0.726543i	−0.0387202	−	0.0281318i
$668$	−5.85410	+	4.25325i	−0.226502	+	0.164563i
$669$	0.590170	−	1.81636i	0.0228173	−	0.0702244i
$670$	11.4164			0.441054
$671$	17.2148	−	14.3844i	0.664569	−	0.555302i
$672$	−4.61803			−0.178145
$673$	−2.15248	+	6.62464i	−0.0829718	+	0.255361i	−0.983933	−	0.178539i	$-0.942863\pi$
$673$	−2.15248	+	6.62464i	−0.0829718	+	0.255361i	0.900961	+	0.433900i	$0.142863\pi$
$674$	−5.61803	+	4.08174i	−0.216399	+	0.157223i
$675$	2.54508	+	1.84911i	0.0979604	+	0.0711724i
$676$	−0.781153	−	2.40414i	−0.0300443	−	0.0924670i
$677$	−12.5172	−	38.5240i	−0.481076	−	1.48060i	−0.837585	−	0.546307i	$-0.816033\pi$
$677$	−12.5172	−	38.5240i	−0.481076	−	1.48060i	0.356509	−	0.934292i	$-0.383967\pi$
$678$	−10.0902	−	7.33094i	−0.387511	−	0.281543i
$679$	−42.3156	+	30.7441i	−1.62392	+	1.17985i
$680$	−2.18034	+	6.71040i	−0.0836122	+	0.257332i
$681$	7.14590			0.273831
$682$	6.97214	−	27.7194i	0.266977	−	1.06143i
$683$	45.7426			1.75029			0.875147	−	0.483857i	$-0.160765\pi$
$683$	45.7426			1.75029			0.875147	+	0.483857i	$0.160765\pi$
$684$	−1.00000	+	3.07768i	−0.0382360	+	0.117678i
$685$	53.3951	−	38.7938i	2.04012	−	1.48224i
$686$	−27.3713	−	19.8864i	−1.04504	−	0.759267i
$687$	−7.09017	−	21.8213i	−0.270507	−	0.832534i
$688$	−1.00000	−	3.07768i	−0.0381246	−	0.117336i
$689$	−10.0902	−	7.33094i	−0.384405	−	0.279286i
$690$	−7.47214	+	5.42882i	−0.284459	+	0.206672i
$691$	−0.0901699	+	0.277515i	−0.00343023	+	0.0105572i	−0.952757	−	0.303734i	$-0.901767\pi$
$691$	−0.0901699	+	0.277515i	−0.00343023	+	0.0105572i	0.949327	+	0.314291i	$0.101767\pi$
$692$	−4.14590			−0.157603
$693$	−12.9721	−	8.14324i	−0.492771	−	0.309336i
$694$	11.8541			0.449976
$695$	11.6738	−	35.9281i	0.442811	−	1.36283i
$696$	−0.309017	+	0.224514i	−0.0117133	+	0.00851018i
$697$	−6.47214	−	4.70228i	−0.245150	−	0.178112i
$698$	−4.09017	−	12.5882i	−0.154815	−	0.476472i
$699$	2.76393	+	8.50651i	0.104542	+	0.321746i
$700$	−11.7533	−	8.53926i	−0.444233	−	0.322754i
$701$	−0.854102	+	0.620541i	−0.0322590	+	0.0234375i	−0.603798	−	0.797137i	$-0.706347\pi$
$701$	−0.854102	+	0.620541i	−0.0322590	+	0.0234375i	0.571539	+	0.820575i	$0.306347\pi$
$702$	1.00000	−	3.07768i	0.0377426	−	0.116160i
$703$	−4.94427			−0.186477
$704$	3.30902	−	0.224514i	0.124713	−	0.00846169i
$705$	−7.05573			−0.265734
$706$	−6.67376	+	20.5397i	−0.251170	+	0.773023i
$707$	46.2599	−	33.6098i	1.73978	−	1.26403i
$708$	−3.11803	−	2.26538i	−0.117183	−	0.0851384i
$709$	10.8197	+	33.2995i	0.406341	+	1.25059i	0.919770	+	0.392457i	$0.128375\pi$
$709$	10.8197	+	33.2995i	0.406341	+	1.25059i	−0.513430	+	0.858132i	$0.671625\pi$
$710$	11.0000	+	33.8545i	0.412823	+	1.27054i
$711$	7.54508	+	5.48183i	0.282963	+	0.205585i
$712$	9.47214	−	6.88191i	0.354983	−	0.257910i
$713$	−8.61803	+	26.5236i	−0.322748	+	0.993316i
$714$	11.4164			0.427248
$715$	−11.4164	−	28.4257i	−0.426949	−	1.06306i
$716$	−6.38197			−0.238505
$717$	5.09017	−	15.6659i	0.190096	−	0.585055i
$718$	−10.3262	+	7.50245i	−0.385372	+	0.279989i
$719$	−8.85410	−	6.43288i	−0.330202	−	0.239906i	0.410314	−	0.911944i	$-0.365419\pi$
$719$	−8.85410	−	6.43288i	−0.330202	−	0.239906i	−0.740516	+	0.672038i	$0.765419\pi$
$720$	0.881966	+	2.71441i	0.0328689	+	0.101160i
$721$	17.1738	+	52.8554i	0.639584	+	1.96844i
$722$	6.89919	+	5.01255i	0.256761	+	0.186548i
$723$	−1.97214	+	1.43284i	−0.0733445	+	0.0532879i
$724$	−5.09017	+	15.6659i	−0.189175	+	0.582220i
$725$	−1.20163			−0.0446273
$726$	9.69098	+	5.20431i	0.359666	+	0.193150i
$727$	3.41641			0.126708			0.0633538	−	0.997991i	$-0.479820\pi$
$727$	3.41641			0.126708			0.0633538	+	0.997991i	$0.479820\pi$
$728$	−4.61803	+	14.2128i	−0.171156	+	0.526763i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	26.1525	+	19.0009i	0.967947	+	0.703254i
$731$	2.47214	+	7.60845i	0.0914353	+	0.281409i
$732$	2.09017	+	6.43288i	0.0772549	+	0.237766i
$733$	35.3607	+	25.6910i	1.30608	+	0.948920i	0.999995	−	0.00308526i	$-0.000982070\pi$
$733$	35.3607	+	25.6910i	1.30608	+	0.948920i	0.306081	+	0.952005i	$0.400982\pi$
$734$	30.3435	−	22.0458i	1.12000	−	0.813726i
$735$	−12.6353	+	38.8873i	−0.466058	+	1.43438i
$736$	−3.23607			−0.119283
$737$	4.94427	+	12.3107i	0.182125	+	0.453472i
$738$	−3.23607			−0.119121
$739$	4.65248	−	14.3188i	0.171144	−	0.526727i	−0.828292	−	0.560296i	$-0.810687\pi$
$739$	4.65248	−	14.3188i	0.171144	−	0.526727i	0.999436	+	0.0335689i	$0.0106873\pi$
$740$	−3.52786	+	2.56314i	−0.129687	+	0.0942230i
$741$	8.47214	+	6.15537i	0.311232	+	0.226123i
$742$	−5.50000	−	16.9273i	−0.201911	−	0.621419i
$743$	−11.6738	−	35.9281i	−0.428269	−	1.31808i	−0.899829	−	0.436242i	$-0.856309\pi$
$743$	−11.6738	−	35.9281i	−0.428269	−	1.31808i	0.471561	−	0.881834i	$-0.343691\pi$
$744$	6.97214	+	5.06555i	0.255611	+	0.185712i
$745$	−3.19098	+	2.31838i	−0.116909	+	0.0849390i
$746$	−2.94427	+	9.06154i	−0.107797	+	0.331766i
$747$	−0.673762			−0.0246517
$748$	−8.18034	+	0.555029i	−0.299103	+	0.0202939i
$749$	24.8541			0.908149
$750$	1.63525	−	5.03280i	0.0597111	−	0.183772i
$751$	8.18034	−	5.94336i	0.298505	−	0.216876i	−0.428444	−	0.903569i	$-0.640938\pi$
$751$	8.18034	−	5.94336i	0.298505	−	0.216876i	0.726948	+	0.686692i	$0.240938\pi$
$752$	−2.00000	−	1.45309i	−0.0729325	−	0.0529886i
$753$	5.97214	+	18.3803i	0.217637	+	0.669817i
$754$	0.381966	+	1.17557i	0.0139104	+	0.0428118i
$755$	−21.5344	−	15.6457i	−0.783719	−	0.569405i
$756$	3.73607	−	2.71441i	0.135879	−	0.0987222i
$757$	−9.43769	+	29.0462i	−0.343019	+	1.05570i	0.619617	+	0.784904i	$0.287288\pi$
$757$	−9.43769	+	29.0462i	−0.343019	+	1.05570i	−0.962636	+	0.270799i	$0.912712\pi$
$758$	3.70820			0.134688
$759$	−9.09017	−	5.70634i	−0.329952	−	0.207127i
$760$	−9.23607			−0.335027
$761$	3.18034	−	9.78808i	0.115287	−	0.354818i	−0.876720	−	0.481002i	$-0.840273\pi$
$761$	3.18034	−	9.78808i	0.115287	−	0.354818i	0.992007	+	0.126184i	$0.0402730\pi$
$762$	9.70820	−	7.05342i	0.351691	−	0.255519i
$763$	−65.0689	−	47.2753i	−2.35565	−	1.71148i
$764$	6.94427	+	21.3723i	0.251235	+	0.773222i
$765$	−2.18034	−	6.71040i	−0.0788304	−	0.242615i
$766$	−10.7082	−	7.77997i	−0.386903	−	0.281102i
$767$	−10.0902	+	7.33094i	−0.364335	+	0.264705i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	−4.27051			−0.153999			−0.0769993	−	0.997031i	$-0.524534\pi$
$769$	−4.27051			−0.153999			−0.0769993	+	0.997031i	$0.524534\pi$
$770$	10.6631	−	42.3938i	0.384272	−	1.52777i
$771$	1.81966			0.0655335
$772$	0.100813	−	0.310271i	0.00362834	−	0.0111669i
$773$	−7.69098	+	5.58783i	−0.276625	+	0.200980i	−0.717444	−	0.696616i	$-0.754688\pi$
$773$	−7.69098	+	5.58783i	−0.276625	+	0.200980i	0.440819	+	0.897596i	$0.354688\pi$
$774$	2.61803	+	1.90211i	0.0941033	+	0.0683700i
$775$	8.37790	+	25.7845i	0.300943	+	0.926208i
$776$	3.50000	+	10.7719i	0.125643	+	0.386688i
$777$	5.70820	+	4.14725i	0.204781	+	0.148782i
$778$	−31.5066	+	22.8909i	−1.12957	+	0.820677i
$779$	3.23607	−	9.95959i	0.115944	−	0.356839i
$780$	9.23607			0.330704
$781$	−31.7426	+	26.5236i	−1.13584	+	0.949088i
$782$	8.00000			0.286079
$783$	0.118034	−	0.363271i	0.00421819	−	0.0129823i
$784$	−11.5902	+	8.42075i	−0.413935	+	0.300741i
$785$	−10.3262	−	7.50245i	−0.368559	−	0.267774i
$786$	4.71885	+	14.5231i	0.168316	+	0.518022i
$787$	−11.5836	−	35.6506i	−0.412910	−	1.27081i	−0.914107	−	0.405474i	$-0.867106\pi$
$787$	−11.5836	−	35.6506i	−0.412910	−	1.27081i	0.501196	−	0.865334i	$-0.332894\pi$
$788$	−4.92705	−	3.57971i	−0.175519	−	0.127522i
$789$	6.23607	−	4.53077i	0.222010	−	0.161300i
$790$	−8.22542	+	25.3153i	−0.292647	+	0.900676i
$791$	−57.5967			−2.04790
$792$	−2.54508	+	2.12663i	−0.0904357	+	0.0755664i
$793$	21.8885			0.777285
$794$	3.05573	−	9.40456i	0.108444	−	0.333755i
$795$	−8.89919	+	6.46564i	−0.315622	+	0.229313i
$796$	−10.6353	−	7.72696i	−0.376957	−	0.273875i
$797$	−6.98936	−	21.5110i	−0.247576	−	0.761960i	−0.995202	−	0.0978402i	$-0.968807\pi$
$797$	−6.98936	−	21.5110i	−0.247576	−	0.761960i	0.747626	−	0.664120i	$-0.231193\pi$
$798$	4.61803	+	14.2128i	0.163477	+	0.503129i
$799$	4.94427	+	3.59222i	0.174916	+	0.127084i
$800$	−2.54508	+	1.84911i	−0.0899823	+	0.0653760i
$801$	−3.61803	+	11.1352i	−0.127837	+	0.393442i
$802$	10.2918			0.363416
$803$	−9.16312	+	36.4302i	−0.323359	+	1.28559i
$804$	−4.00000			−0.141069
$805$	−13.1803	+	40.5649i	−0.464546	+	1.42973i
$806$	22.5623	−	16.3925i	0.794723	−	0.577400i
$807$	−2.38197	−	1.73060i	−0.0838492	−	0.0609200i
$808$	−3.82624	−	11.7759i	−0.134607	−	0.414276i
$809$	9.34752	+	28.7687i	0.328641	+	1.01145i	0.969770	+	0.244021i	$0.0784665\pi$
$809$	9.34752	+	28.7687i	0.328641	+	1.01145i	−0.641129	+	0.767434i	$0.721533\pi$
$810$	−2.30902	−	1.67760i	−0.0811306	−	0.0589448i
$811$	32.9787	−	23.9604i	1.15804	−	0.841365i	0.168510	−	0.985700i	$-0.446104\pi$
$811$	32.9787	−	23.9604i	1.15804	−	0.841365i	0.989529	+	0.144335i	$0.0461043\pi$
$812$	−0.545085	+	1.67760i	−0.0191287	+	0.0588722i
$813$	−23.4164			−0.821249
$814$	−4.29180	−	2.69417i	−0.150427	−	0.0944305i
$815$	−38.2918			−1.34130
$816$	0.763932	−	2.35114i	0.0267430	−	0.0823064i
$817$	−8.47214	+	6.15537i	−0.296403	+	0.215349i
$818$	9.78115	+	7.10642i	0.341990	+	0.248470i
$819$	−4.61803	−	14.2128i	−0.161367	−	0.496637i
$820$	−2.85410	−	8.78402i	−0.0996696	−	0.306751i
$821$	−17.0623	−	12.3965i	−0.595479	−	0.432641i	0.248793	−	0.968557i	$-0.419966\pi$
$821$	−17.0623	−	12.3965i	−0.595479	−	0.432641i	−0.844271	+	0.535916i	$0.819966\pi$
$822$	−18.7082	+	13.5923i	−0.652524	+	0.474086i
$823$	−0.993422	+	3.05744i	−0.0346285	+	0.106576i	−0.966877	−	0.255244i	$-0.917844\pi$
$823$	−0.993422	+	3.05744i	−0.0346285	+	0.106576i	0.932248	+	0.361819i	$0.117844\pi$
$824$	12.0344			0.419240
$825$	−10.4098	+	0.706298i	−0.362424	+	0.0245901i
$826$	−17.7984			−0.619285
$827$	3.30244	−	10.1639i	0.114837	−	0.353432i	−0.877076	−	0.480352i	$-0.840509\pi$
$827$	3.30244	−	10.1639i	0.114837	−	0.353432i	0.991913	+	0.126920i	$0.0405090\pi$
$828$	2.61803	−	1.90211i	0.0909830	−	0.0661030i
$829$	−5.90983	−	4.29374i	−0.205257	−	0.149128i	0.480408	−	0.877045i	$-0.340489\pi$
$829$	−5.90983	−	4.29374i	−0.205257	−	0.149128i	−0.685665	+	0.727917i	$0.740489\pi$
$830$	−0.594235	−	1.82887i	−0.0206262	−	0.0634809i
$831$	−3.43769	−	10.5801i	−0.119252	−	0.367021i
$832$	2.61803	+	1.90211i	0.0907640	+	0.0659439i
$833$	28.6525	−	20.8172i	0.992749	−	0.721275i
$834$	−4.09017	+	12.5882i	−0.141631	+	0.435895i
$835$	20.6525			0.714708
$836$	−4.00000	−	9.95959i	−0.138343	−	0.344460i
$837$	−8.61803			−0.297883
$838$	−5.55573	+	17.0988i	−0.191919	+	0.590667i
$839$	2.52786	−	1.83660i	0.0872716	−	0.0634065i	−0.543294	−	0.839543i	$-0.682823\pi$
$839$	2.52786	−	1.83660i	0.0872716	−	0.0634065i	0.630565	+	0.776136i	$0.282823\pi$
$840$	10.6631	+	7.74721i	0.367913	+	0.267304i
$841$	−8.91641	−	27.4419i	−0.307462	−	0.946272i
$842$	10.8541	+	33.4055i	0.374057	+	1.15123i
$843$	18.7082	+	13.5923i	0.644345	+	0.468144i
$844$	3.76393	−	2.73466i	0.129560	−	0.0941308i
$845$	−2.22949	+	6.86167i	−0.0766968	+	0.236048i
$846$	2.47214			0.0849938
$847$	50.3328	−	6.86167i	1.72946	−	0.235770i
$848$	−3.85410			−0.132350
$849$	7.38197	−	22.7194i	0.253348	−	0.779726i
$850$	6.29180	−	4.57126i	0.215807	−	0.156793i
$851$	4.00000	+	2.90617i	0.137118	+	0.0996222i
$852$	−3.85410	−	11.8617i	−0.132039	−	0.406375i
$853$	4.65248	+	14.3188i	0.159298	+	0.490268i	0.998571	−	0.0534419i	$-0.0170192\pi$
$853$	4.65248	+	14.3188i	0.159298	+	0.490268i	−0.839273	+	0.543710i	$0.817019\pi$
$854$	25.2705	+	18.3601i	0.864739	+	0.628270i
$855$	7.47214	−	5.42882i	0.255542	−	0.185662i
$856$	1.66312	−	5.11855i	0.0568442	−	0.174949i
$857$	8.76393			0.299370			0.149685	−	0.988734i	$-0.452174\pi$
$857$	8.76393			0.299370			0.149685	+	0.988734i	$0.452174\pi$
$858$	4.00000	+	9.95959i	0.136558	+	0.340015i
$859$	4.40325			0.150237			0.0751185	−	0.997175i	$-0.476066\pi$
$859$	4.40325			0.150237			0.0751185	+	0.997175i	$0.476066\pi$
$860$	−2.85410	+	8.78402i	−0.0973241	+	0.299533i
$861$	−12.0902	+	8.78402i	−0.412032	+	0.299359i
$862$	5.85410	+	4.25325i	0.199392	+	0.144866i
$863$	0.854102	+	2.62866i	0.0290740	+	0.0894805i	0.964541	−	0.263935i	$-0.0850203\pi$
$863$	0.854102	+	2.62866i	0.0290740	+	0.0894805i	−0.935467	+	0.353415i	$0.885020\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	9.57295	+	6.95515i	0.325490	+	0.236482i
$866$	−9.97214	+	7.24518i	−0.338867	+	0.246201i
$867$	3.36475	−	10.3556i	0.114273	−	0.351695i
$868$	39.7984			1.35084
$869$	−30.8607	+	2.09387i	−1.04688	+	0.0710297i
$870$	1.09017			0.0369602
$871$	−4.00000	+	12.3107i	−0.135535	+	0.417133i
$872$	−14.0902	+	10.2371i	−0.477153	+	0.346672i
$873$	−9.16312	−	6.65740i	−0.310125	−	0.225319i
$874$	3.23607	+	9.95959i	0.109462	+	0.336888i
$875$	−7.55166	−	23.2416i	−0.255293	−	0.785710i
$876$	−9.16312	−	6.65740i	−0.309593	−	0.224933i
$877$	24.5623	−	17.8456i	0.829410	−	0.602602i	−0.0899822	−	0.995943i	$-0.528681\pi$
$877$	24.5623	−	17.8456i	0.829410	−	0.602602i	0.919392	+	0.393342i	$0.128681\pi$
$878$	4.95492	−	15.2497i	0.167220	−	0.514651i
$879$	−22.9787			−0.775053
$880$	−8.01722	−	5.03280i	−0.270260	−	0.169656i
$881$	−12.2918			−0.414121			−0.207061	−	0.978328i	$-0.566390\pi$
$881$	−12.2918			−0.414121			−0.207061	+	0.978328i	$0.566390\pi$
$882$	4.42705	−	13.6251i	0.149067	−	0.458780i
$883$	−22.5066	+	16.3520i	−0.757407	+	0.550288i	−0.898114	−	0.439763i	$-0.855062\pi$
$883$	−22.5066	+	16.3520i	−0.757407	+	0.550288i	0.140707	+	0.990051i	$0.455062\pi$
$884$	−6.47214	−	4.70228i	−0.217681	−	0.158155i
$885$	3.39919	+	10.4616i	0.114262	+	0.351664i
$886$	−0.517221	−	1.59184i	−0.0173764	−	0.0534790i
$887$	23.0902	+	16.7760i	0.775292	+	0.563283i	0.903562	−	0.428457i	$-0.140943\pi$
$887$	23.0902	+	16.7760i	0.775292	+	0.563283i	−0.128270	+	0.991739i	$0.540943\pi$
$888$	1.23607	−	0.898056i	0.0414797	−	0.0301368i
$889$	17.1246	−	52.7041i	0.574341	−	1.76764i
$890$	−33.4164			−1.12012
$891$	0.809017	−	3.21644i	0.0271031	−	0.107755i
$892$	−1.90983			−0.0639458
$893$	−2.47214	+	7.60845i	−0.0827269	+	0.254607i
$894$	1.11803	−	0.812299i	0.0373927	−	0.0271674i
$895$	14.7361	+	10.7064i	0.492572	+	0.357875i
$896$	1.42705	+	4.39201i	0.0476744	+	0.146727i
$897$	−3.23607	−	9.95959i	−0.108049	−	0.332541i
$898$	−29.0344	−	21.0948i	−0.968892	−	0.703941i
$899$	2.66312	−	1.93487i	0.0888200	−	0.0645315i
$900$	0.972136	−	2.99193i	0.0324045	−	0.0997309i
$901$	9.52786			0.317419
$902$	8.23607	−	6.88191i	0.274231	−	0.229143i
$903$	14.9443			0.497314
$904$	−3.85410	+	11.8617i	−0.128186	+	0.394514i
$905$	38.0344	−	27.6336i	1.26431	−	0.918573i
$906$	7.54508	+	5.48183i	0.250669	+	0.182121i
$907$	−2.52786	−	7.77997i	−0.0839363	−	0.258330i	0.900276	−	0.435319i	$-0.143364\pi$
$907$	−2.52786	−	7.77997i	−0.0839363	−	0.258330i	−0.984213	+	0.176989i	$0.943364\pi$
$908$	−2.20820	−	6.79615i	−0.0732818	−	0.225538i
$909$	10.0172	+	7.27794i	0.332250	+	0.241394i
$910$	34.5066	−	25.0705i	1.14388	−	0.831079i
$911$	13.5066	−	41.5690i	0.447493	−	1.37724i	−0.432234	−	0.901762i	$-0.642274\pi$
$911$	13.5066	−	41.5690i	0.447493	−	1.37724i	0.879727	−	0.475480i	$-0.157726\pi$
$912$	3.23607			0.107157
$913$	1.71478	−	1.43284i	0.0567510	−	0.0474201i
$914$	−21.9787			−0.726991
$915$	5.96556	−	18.3601i	0.197215	−	0.606966i
$916$	−18.5623	+	13.4863i	−0.613316	+	0.445600i
$917$	57.0517	+	41.4505i	1.88401	+	1.36881i
$918$	0.763932	+	2.35114i	0.0252135	+	0.0775992i
$919$	15.5344	+	47.8101i	0.512434	+	1.57711i	0.787903	+	0.615800i	$0.211167\pi$
$919$	15.5344	+	47.8101i	0.512434	+	1.57711i	−0.275469	+	0.961310i	$0.588833\pi$
$920$	7.47214	+	5.42882i	0.246349	+	0.178983i
$921$	−13.4721	+	9.78808i	−0.443922	+	0.322528i
$922$	12.6180	−	38.8343i	0.415553	−	1.27894i
$923$	−40.3607			−1.32849
$924$	−3.73607	+	14.8536i	−0.122908	+	0.488649i
$925$	4.80650			0.158037
$926$	5.89919	−	18.1558i	0.193859	−	0.596638i
$927$	−9.73607	+	7.07367i	−0.319774	+	0.232330i
$928$	0.309017	+	0.224514i	0.0101440	+	0.00737003i
$929$	−7.14590	−	21.9928i	−0.234449	−	0.721561i	−0.997194	−	0.0748610i	$-0.976149\pi$
$929$	−7.14590	−	21.9928i	−0.234449	−	0.721561i	0.762745	−	0.646700i	$-0.223851\pi$
$930$	−7.60081	−	23.3929i	−0.249240	−	0.767083i
$931$	37.5066	+	27.2501i	1.22923	+	0.893087i
$932$	7.23607	−	5.25731i	0.237025	−	0.172209i
$933$	7.38197	−	22.7194i	0.241675	−	0.743798i
$934$	19.5623			0.640098
$935$	19.8197	+	12.4418i	0.648172	+	0.406889i
$936$	−3.23607			−0.105774
$937$	8.48278	−	26.1073i	0.277120	−	0.852889i	−0.711530	−	0.702655i	$-0.751998\pi$
$937$	8.48278	−	26.1073i	0.277120	−	0.852889i	0.988651	−	0.150233i	$-0.0480024\pi$
$938$	−14.9443	+	10.8576i	−0.487948	+	0.354515i
$939$	12.2533	+	8.90254i	0.399871	+	0.290523i
$940$	2.18034	+	6.71040i	0.0711148	+	0.218869i
$941$	−2.72949	−	8.40051i	−0.0889788	−	0.273849i	0.896659	−	0.442722i	$-0.145987\pi$
$941$	−2.72949	−	8.40051i	−0.0889788	−	0.273849i	−0.985638	+	0.168873i	$0.945987\pi$
$942$	3.61803	+	2.62866i	0.117882	+	0.0856462i
$943$	−8.47214	+	6.15537i	−0.275891	+	0.200446i
$944$	−1.19098	+	3.66547i	−0.0387632	+	0.119301i
$945$	−13.1803			−0.428756
$946$	−10.7082	+	0.726543i	−0.348154	+	0.0236219i
$947$	2.32624			0.0755926			0.0377963	−	0.999285i	$-0.487966\pi$
$947$	2.32624			0.0755926			0.0377963	+	0.999285i	$0.487966\pi$
$948$	2.88197	−	8.86978i	0.0936019	−	0.288077i
$949$	−29.6525	+	21.5438i	−0.962560	+	0.699341i
$950$	8.23607	+	5.98385i	0.267213	+	0.194142i
$951$	6.14590	+	18.9151i	0.199294	+	0.613365i
$952$	−3.52786	−	10.8576i	−0.114339	−	0.351898i
$953$	−39.4164	−	28.6377i	−1.27682	−	0.927666i	−0.277371	−	0.960763i	$-0.589463\pi$
$953$	−39.4164	−	28.6377i	−1.27682	−	0.927666i	−0.999452	+	0.0330970i	$0.989463\pi$
$954$	3.11803	−	2.26538i	0.100950	−	0.0733445i
$955$	19.8197	−	60.9986i	0.641349	−	1.97387i
$956$	−16.4721			−0.532747
$957$	0.472136	+	1.17557i	0.0152620	+	0.0380008i
$958$	−7.23607			−0.233787
$959$	−33.0000	+	101.564i	−1.06563	+	3.27966i
$960$	2.30902	−	1.67760i	0.0745232	−	0.0541443i
$961$	−35.0066	−	25.4338i	−1.12924	−	0.820444i
$962$	−1.52786	−	4.70228i	−0.0492603	−	0.151608i
$963$	1.66312	+	5.11855i	0.0535933	+	0.164943i
$964$	1.97214	+	1.43284i	0.0635182	+	0.0461487i
$965$	−0.753289	+	0.547296i	−0.0242492	+	0.0176181i
$966$	4.61803	−	14.2128i	0.148583	−	0.457291i
$967$	13.6869			0.440142			0.220071	−	0.975484i	$-0.429371\pi$
$967$	13.6869			0.440142			0.220071	+	0.975484i	$0.429371\pi$
$968$	1.95492	−	10.8249i	0.0628333	−	0.347925i
$969$	−8.00000			−0.256997
$970$	9.98936	−	30.7441i	0.320739	−	0.987133i
$971$	7.52786	−	5.46931i	0.241581	−	0.175519i	−0.460407	−	0.887708i	$-0.652296\pi$
$971$	7.52786	−	5.46931i	0.241581	−	0.175519i	0.701987	+	0.712190i	$0.252296\pi$
$972$	0.809017	+	0.587785i	0.0259492	+	0.0188532i
$973$	18.8885	+	58.1330i	0.605539	+	1.86366i
$974$	7.71885	+	23.7562i	0.247328	+	0.761197i
$975$	−8.23607	−	5.98385i	−0.263765	−	0.191637i
$976$	5.47214	−	3.97574i	0.175159	−	0.127260i
$977$	−11.3607	+	34.9646i	−0.363460	+	1.11862i	0.587479	+	0.809239i	$0.300120\pi$
$977$	−11.3607	+	34.9646i	−0.363460	+	1.11862i	−0.950940	+	0.309377i	$0.899880\pi$
$978$	13.4164			0.429009
$979$	−14.4721	−	36.0341i	−0.462531	−	1.15166i
$980$	40.8885			1.30614
$981$	5.38197	−	16.5640i	0.171833	−	0.528847i
$982$	−34.1803	+	24.8335i	−1.09074	+	0.792468i
$983$	7.38197	+	5.36331i	0.235448	+	0.171063i	0.699253	−	0.714874i	$-0.253516\pi$
$983$	7.38197	+	5.36331i	0.235448	+	0.171063i	−0.463805	+	0.885937i	$0.653516\pi$
$984$	1.00000	+	3.07768i	0.0318788	+	0.0981130i
$985$	5.37132	+	16.5312i	0.171145	+	0.526729i
$986$	−0.763932	−	0.555029i	−0.0243286	−	0.0176757i
$987$	9.23607	−	6.71040i	0.293987	−	0.213594i
$988$	3.23607	−	9.95959i	0.102953	−	0.316857i
$989$	10.4721			0.332995
$990$	9.44427	−	0.640786i	0.300159	−	0.0203655i
$991$	−45.6869			−1.45129			−0.725646	−	0.688068i	$-0.758459\pi$
$991$	−45.6869			−1.45129			−0.725646	+	0.688068i	$0.758459\pi$
$992$	2.66312	−	8.19624i	0.0845541	−	0.260231i
$993$	7.23607	−	5.25731i	0.229630	−	0.166836i
$994$	−46.5967	−	33.8545i	−1.47796	−	1.07380i
$995$	11.5942	+	35.6834i	0.367562	+	1.13124i
$996$	0.208204	+	0.640786i	0.00659719	+	0.0203041i
$997$	−46.8885	−	34.0665i	−1.48498	−	1.07890i	−0.975911	−	0.218169i	$-0.929992\pi$
$997$	−46.8885	−	34.0665i	−1.48498	−	1.07890i	−0.509064	−	0.860729i	$-0.670008\pi$
$998$	6.00000	−	4.35926i	0.189927	−	0.137990i
$999$	−0.472136	+	1.45309i	−0.0149377	+	0.0459736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	66.2.e.a.31.1	✓	4
3.2	odd	2		198.2.f.c.163.1		4
4.3	odd	2		528.2.y.d.97.1		4
11.2	odd	10		726.2.e.n.487.1		4
11.3	even	5		726.2.e.f.565.1		4
11.4	even	5		726.2.a.l.1.2		2
11.5	even	5	inner	66.2.e.a.49.1	yes	4
11.6	odd	10		726.2.e.r.511.1		4
11.7	odd	10		726.2.a.j.1.2		2
11.8	odd	10		726.2.e.n.565.1		4
11.9	even	5		726.2.e.f.487.1		4
11.10	odd	2		726.2.e.r.493.1		4
33.5	odd	10		198.2.f.c.181.1		4
33.26	odd	10		2178.2.a.t.1.1		2
33.29	even	10		2178.2.a.bb.1.1		2
44.7	even	10		5808.2.a.cg.1.2		2
44.15	odd	10		5808.2.a.cb.1.2		2
44.27	odd	10		528.2.y.d.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.31.1	✓	4	1.1	even	1	trivial
66.2.e.a.49.1	yes	4	11.5	even	5	inner
198.2.f.c.163.1		4	3.2	odd	2
198.2.f.c.181.1		4	33.5	odd	10
528.2.y.d.49.1		4	44.27	odd	10
528.2.y.d.97.1		4	4.3	odd	2
726.2.a.j.1.2		2	11.7	odd	10
726.2.a.l.1.2		2	11.4	even	5
726.2.e.f.487.1		4	11.9	even	5
726.2.e.f.565.1		4	11.3	even	5
726.2.e.n.487.1		4	11.2	odd	10
726.2.e.n.565.1		4	11.8	odd	10
726.2.e.r.493.1		4	11.10	odd	2
726.2.e.r.511.1		4	11.6	odd	10
2178.2.a.t.1.1		2	33.26	odd	10
2178.2.a.bb.1.1		2	33.29	even	10
5808.2.a.cb.1.2		2	44.15	odd	10
5808.2.a.cg.1.2		2	44.7	even	10

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:	\( N \)	\(=\)	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	66.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.881966 + 2.71441i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-3.73607 - 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.881966 + 2.71441i) q^{5} +(-0.309017 - 0.951057i) q^{6} +(-3.73607 - 2.71441i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.85410 q^{10} +(1.23607 + 3.07768i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.07768i) q^{13} +(-3.73607 + 2.71441i) q^{14} +(2.30902 + 1.67760i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.763932 - 2.35114i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(2.61803 - 1.90211i) q^{19} +(0.881966 - 2.71441i) q^{20} -4.61803 q^{21} +(3.30902 - 0.224514i) q^{22} -3.23607 q^{23} +(-0.309017 + 0.951057i) q^{24} +(-2.54508 + 1.84911i) q^{25} +(2.61803 + 1.90211i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.42705 + 4.39201i) q^{28} +(0.309017 + 0.224514i) q^{29} +(2.30902 - 1.67760i) q^{30} +(2.66312 - 8.19624i) q^{31} +1.00000 q^{32} +(2.80902 + 1.76336i) q^{33} -2.47214 q^{34} +(4.07295 - 12.5352i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.23607 - 0.898056i) q^{37} +(-1.00000 - 3.07768i) q^{38} +(1.00000 + 3.07768i) q^{39} +(-2.30902 - 1.67760i) q^{40} +(2.61803 - 1.90211i) q^{41} +(-1.42705 + 4.39201i) q^{42} -3.23607 q^{43} +(0.809017 - 3.21644i) q^{44} +2.85410 q^{45} +(-1.00000 + 3.07768i) q^{46} +(-2.00000 + 1.45309i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.42705 + 13.6251i) q^{49} +(0.972136 + 2.99193i) q^{50} +(-2.00000 - 1.45309i) q^{51} +(2.61803 - 1.90211i) q^{52} +(-1.19098 + 3.66547i) q^{53} -1.00000 q^{54} +(-7.26393 + 6.06961i) q^{55} +4.61803 q^{56} +(1.00000 - 3.07768i) q^{57} +(0.309017 - 0.224514i) q^{58} +(3.11803 + 2.26538i) q^{59} +(-0.881966 - 2.71441i) q^{60} +(-2.09017 - 6.43288i) q^{61} +(-6.97214 - 5.06555i) q^{62} +(-3.73607 + 2.71441i) q^{63} +(0.309017 - 0.951057i) q^{64} -9.23607 q^{65} +(2.54508 - 2.12663i) q^{66} +4.00000 q^{67} +(-0.763932 + 2.35114i) q^{68} +(-2.61803 + 1.90211i) q^{69} +(-10.6631 - 7.74721i) q^{70} +(3.85410 + 11.8617i) q^{71} +(0.309017 + 0.951057i) q^{72} +(9.16312 + 6.65740i) q^{73} +(-1.23607 + 0.898056i) q^{74} +(-0.972136 + 2.99193i) q^{75} -3.23607 q^{76} +(3.73607 - 14.8536i) q^{77} +3.23607 q^{78} +(-2.88197 + 8.86978i) q^{79} +(-2.30902 + 1.67760i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.00000 - 3.07768i) q^{82} +(-0.208204 - 0.640786i) q^{83} +(3.73607 + 2.71441i) q^{84} +(5.70820 - 4.14725i) q^{85} +(-1.00000 + 3.07768i) q^{86} +0.381966 q^{87} +(-2.80902 - 1.76336i) q^{88} -11.7082 q^{89} +(0.881966 - 2.71441i) q^{90} +(12.0902 - 8.78402i) q^{91} +(2.61803 + 1.90211i) q^{92} +(-2.66312 - 8.19624i) q^{93} +(0.763932 + 2.35114i) q^{94} +(7.47214 + 5.42882i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.50000 - 10.7719i) q^{97} +14.3262 q^{98} +(3.30902 - 0.224514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9	\( 4 q - q^{2} + q^{3} - q^{4} + 8 q^{5} + q^{6} - 6 q^{7} - q^{8} - q^{9} - 2 q^{10} - 4 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{14} + 7 q^{15} - q^{16} - 12 q^{17} - q^{18} + 6 q^{19} + 8 q^{20} - 14 q^{21} + 11 q^{22} - 4 q^{23} + q^{24} + q^{25} + 6 q^{26} + q^{27} - q^{28} - q^{29} + 7 q^{30} - 5 q^{31} + 4 q^{32} + 9 q^{33} + 8 q^{34} + 23 q^{35} - q^{36} + 4 q^{37} - 4 q^{38} + 4 q^{39} - 7 q^{40} + 6 q^{41} + q^{42} - 4 q^{43} + q^{44} - 2 q^{45} - 4 q^{46} - 8 q^{47} + q^{48} + 11 q^{49} - 14 q^{50} - 8 q^{51} + 6 q^{52} - 7 q^{53} - 4 q^{54} - 38 q^{55} + 14 q^{56} + 4 q^{57} - q^{58} + 8 q^{59} - 8 q^{60} + 14 q^{61} - 10 q^{62} - 6 q^{63} - q^{64} - 28 q^{65} - q^{66} + 16 q^{67} - 12 q^{68} - 6 q^{69} - 27 q^{70} + 2 q^{71} - q^{72} + 21 q^{73} + 4 q^{74} + 14 q^{75} - 4 q^{76} + 6 q^{77} + 4 q^{78} - 16 q^{79} - 7 q^{80} - q^{81} - 4 q^{82} + 26 q^{83} + 6 q^{84} - 4 q^{85} - 4 q^{86} + 6 q^{87} - 9 q^{88} - 20 q^{89} + 8 q^{90} + 26 q^{91} + 6 q^{92} + 5 q^{93} + 12 q^{94} + 12 q^{95} + q^{96} + 14 q^{97} + 26 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 8 * q^5 + q^6 - 6 * q^7 - q^8 - q^9 - 2 * q^10 - 4 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^14 + 7 * q^15 - q^16 - 12 * q^17 - q^18 + 6 * q^19 + 8 * q^20 - 14 * q^21 + 11 * q^22 - 4 * q^23 + q^24 + q^25 + 6 * q^26 + q^27 - q^28 - q^29 + 7 * q^30 - 5 * q^31 + 4 * q^32 + 9 * q^33 + 8 * q^34 + 23 * q^35 - q^36 + 4 * q^37 - 4 * q^38 + 4 * q^39 - 7 * q^40 + 6 * q^41 + q^42 - 4 * q^43 + q^44 - 2 * q^45 - 4 * q^46 - 8 * q^47 + q^48 + 11 * q^49 - 14 * q^50 - 8 * q^51 + 6 * q^52 - 7 * q^53 - 4 * q^54 - 38 * q^55 + 14 * q^56 + 4 * q^57 - q^58 + 8 * q^59 - 8 * q^60 + 14 * q^61 - 10 * q^62 - 6 * q^63 - q^64 - 28 * q^65 - q^66 + 16 * q^67 - 12 * q^68 - 6 * q^69 - 27 * q^70 + 2 * q^71 - q^72 + 21 * q^73 + 4 * q^74 + 14 * q^75 - 4 * q^76 + 6 * q^77 + 4 * q^78 - 16 * q^79 - 7 * q^80 - q^81 - 4 * q^82 + 26 * q^83 + 6 * q^84 - 4 * q^85 - 4 * q^86 + 6 * q^87 - 9 * q^88 - 20 * q^89 + 8 * q^90 + 26 * q^91 + 6 * q^92 + 5 * q^93 + 12 * q^94 + 12 * q^95 + q^96 + 14 * q^97 + 26 * q^98 + 11 * q^99

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