LMFDB - Embedded newform 62.2.g.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [62,2,Mod(7,62)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(62, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("62.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	62.g (of order $15$, degree $8$, 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:	$0.495072492532$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			59.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	62.59
Dual form			62.2.g.a.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.169131 + 1.60917i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.22256 + 2.11754i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.171962i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.373619 + 0.0794152i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.169131 + 1.60917i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.22256 + 2.11754i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.171962i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.373619 + 0.0794152i) q^{9} +(-0.255585 - 2.43173i) q^{10} +(-1.39547 - 1.54983i) q^{11} +(1.47815 + 0.658114i) q^{12} +(4.27222 - 1.90211i) q^{13} +(-0.553432 + 0.614648i) q^{14} +(-3.20071 - 2.32545i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.03286 - 4.47894i) q^{17} +(-0.348943 + 0.155360i) q^{18} +(-5.75036 - 2.56023i) q^{19} +(1.63611 + 1.81708i) q^{20} +(0.139886 + 1.33093i) q^{21} +(2.03993 + 0.433600i) q^{22} +(1.57811 + 4.85692i) q^{23} +(-1.58268 + 0.336408i) q^{24} +(-0.489318 - 0.847523i) q^{25} +(-2.33826 + 4.04999i) q^{26} +(-1.69098 + 5.20431i) q^{27} +(0.0864545 - 0.822560i) q^{28} +(-5.37345 + 3.90404i) q^{29} +3.95630 q^{30} +(2.33777 - 5.05320i) q^{31} +1.00000 q^{32} +(2.72995 - 1.98343i) q^{33} +(-0.629994 + 5.99399i) q^{34} +(-0.624938 + 1.92336i) q^{35} +(0.190983 - 0.330792i) q^{36} +(1.98272 + 3.43416i) q^{37} +(6.15701 - 1.30871i) q^{38} +(2.33826 + 7.19643i) q^{39} +(-2.39169 - 0.508370i) q^{40} +(-1.10171 - 10.4820i) q^{41} +(-0.895472 - 0.994522i) q^{42} +(-3.70498 - 1.64956i) q^{43} +(-1.90520 + 0.848249i) q^{44} +(-0.624938 + 0.694064i) q^{45} +(-4.13154 - 3.00174i) q^{46} +(-3.74346 - 2.71978i) q^{47} +(1.08268 - 1.20243i) q^{48} +(-5.76988 + 2.56892i) q^{49} +(0.894028 + 0.398047i) q^{50} +(6.52530 + 7.24708i) q^{51} +(-0.488830 - 4.65090i) q^{52} +(-1.59901 - 0.339879i) q^{53} +(-1.69098 - 5.20431i) q^{54} +(4.98787 - 1.06021i) q^{55} +(0.413545 + 0.716282i) q^{56} +(5.09240 - 8.82030i) q^{57} +(2.05248 - 6.31687i) q^{58} +(1.15543 - 10.9931i) q^{59} +(-3.20071 + 2.32545i) q^{60} +10.5530 q^{61} +(1.07890 + 5.46223i) q^{62} +0.315921 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.19525 + 11.3720i) q^{65} +(-1.04275 + 3.20925i) q^{66} +(0.0971366 - 0.168246i) q^{67} +(-3.01351 - 5.21954i) q^{68} +(-8.08251 + 1.71799i) q^{69} +(-0.624938 - 1.92336i) q^{70} +(5.12319 + 1.08897i) q^{71} +(0.0399263 + 0.379874i) q^{72} +(-0.985705 - 1.09474i) q^{73} +(-3.62260 - 1.61289i) q^{74} +(1.44657 - 0.644054i) q^{75} +(-4.21188 + 4.67777i) q^{76} +(-1.39547 - 1.01387i) q^{77} +(-6.12165 - 4.44764i) q^{78} +(-8.33915 + 9.26157i) q^{79} +(2.23373 - 0.994522i) q^{80} +(-7.04179 - 3.13521i) q^{81} +(7.05248 + 7.83257i) q^{82} +(0.0835291 + 0.794726i) q^{83} +(1.30902 + 0.278240i) q^{84} +(4.55392 + 14.0155i) q^{85} +(3.96698 - 0.843207i) q^{86} +(-5.37345 - 9.30710i) q^{87} +(1.04275 - 1.80610i) q^{88} +(-0.991653 + 3.05199i) q^{89} +(0.0976248 - 0.928838i) q^{90} +(3.12920 - 2.27350i) q^{91} +5.10686 q^{92} +(7.73607 + 4.61653i) q^{93} +4.62717 q^{94} +(12.4516 - 9.04659i) q^{95} +(-0.169131 + 1.60917i) q^{96} +(-3.98223 + 12.2560i) q^{97} +(3.15796 - 5.46975i) q^{98} +(-0.398295 - 0.689867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.169131	+	1.60917i	−0.0976476	+	0.929055i	0.830544	+	0.556953i	$0.188030\pi$
$3$	−0.169131	+	1.60917i	−0.0976476	+	0.929055i	−0.928192	+	0.372102i	$0.878637\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.22256	+	2.11754i	−0.546747	+	0.946993i	0.451748	+	0.892145i	$0.350801\pi$
$5$	−1.22256	+	2.11754i	−0.546747	+	0.946993i	−0.998495	+	0.0548473i	$0.982533\pi$
$6$	−0.809017	−	1.40126i	−0.330280	−	0.572061i
$7$	0.809017	−	0.171962i	0.305780	−	0.0649955i	−0.0524664	−	0.998623i	$-0.516708\pi$
$7$	0.809017	−	0.171962i	0.305780	−	0.0649955i	0.358246	+	0.933627i	$0.383375\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.373619	+	0.0794152i	0.124540	+	0.0264717i
$10$	−0.255585	−	2.43173i	−0.0808231	−	0.768981i
$11$	−1.39547	−	1.54983i	−0.420750	−	0.467291i	0.495085	−	0.868845i	$-0.335137\pi$
$11$	−1.39547	−	1.54983i	−0.420750	−	0.467291i	−0.915835	+	0.401554i	$0.868470\pi$
$12$	1.47815	+	0.658114i	0.426704	+	0.189981i
$13$	4.27222	−	1.90211i	1.18490	−	0.527551i	0.282842	−	0.959167i	$-0.408723\pi$
$13$	4.27222	−	1.90211i	1.18490	−	0.527551i	0.902058	+	0.431615i	$0.142056\pi$
$14$	−0.553432	+	0.614648i	−0.147911	+	0.164272i
$15$	−3.20071	−	2.32545i	−0.826420	−	0.600429i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	4.03286	−	4.47894i	0.978112	−	1.08630i	−0.0181430	−	0.999835i	$-0.505775\pi$
$17$	4.03286	−	4.47894i	0.978112	−	1.08630i	0.996255	−	0.0864676i	$-0.0275579\pi$
$18$	−0.348943	+	0.155360i	−0.0822467	+	0.0366186i
$19$	−5.75036	−	2.56023i	−1.31922	−	0.587356i	−0.378209	−	0.925720i	$-0.623460\pi$
$19$	−5.75036	−	2.56023i	−1.31922	−	0.587356i	−0.941015	+	0.338364i	$0.890126\pi$
$20$	1.63611	+	1.81708i	0.365845	+	0.406312i
$21$	0.139886	+	1.33093i	0.0305257	+	0.290433i
$22$	2.03993	+	0.433600i	0.434914	+	0.0924438i
$23$	1.57811	+	4.85692i	0.329058	+	1.01274i	0.969575	+	0.244793i	$0.0787200\pi$
$23$	1.57811	+	4.85692i	0.329058	+	1.01274i	−0.640517	+	0.767944i	$0.721280\pi$
$24$	−1.58268	+	0.336408i	−0.323062	+	0.0686690i
$25$	−0.489318	−	0.847523i	−0.0978636	−	0.169505i
$26$	−2.33826	+	4.04999i	−0.458571	+	0.794268i
$27$	−1.69098	+	5.20431i	−0.325430	+	1.00157i
$28$	0.0864545	−	0.822560i	0.0163384	−	0.155449i
$29$	−5.37345	+	3.90404i	−0.997825	+	0.724963i	−0.961621	−	0.274382i	$-0.911527\pi$
$29$	−5.37345	+	3.90404i	−0.997825	+	0.724963i	−0.0362045	+	0.999344i	$0.511527\pi$
$30$	3.95630			0.722317
$31$	2.33777	−	5.05320i	0.419876	−	0.907581i
$31$	2.33777	−	5.05320i	0.419876	−	0.907581i
$32$	1.00000			0.176777
$33$	2.72995	−	1.98343i	0.475224	−	0.345270i
$34$	−0.629994	+	5.99399i	−0.108043	+	1.02796i
$35$	−0.624938	+	1.92336i	−0.105634	+	0.325107i
$36$	0.190983	−	0.330792i	0.0318305	−	0.0551320i
$37$	1.98272	+	3.43416i	0.325957	+	0.564573i	0.981705	−	0.190406i	$-0.0609804\pi$
$37$	1.98272	+	3.43416i	0.325957	+	0.564573i	−0.655749	+	0.754979i	$0.727647\pi$
$38$	6.15701	−	1.30871i	0.998798	−	0.212301i
$39$	2.33826	+	7.19643i	0.374421	+	1.15235i
$40$	−2.39169	−	0.508370i	−0.378160	−	0.0803804i
$41$	−1.10171	−	10.4820i	−0.172057	−	1.63702i	−0.650934	−	0.759135i	$-0.725622\pi$
$41$	−1.10171	−	10.4820i	−0.172057	−	1.63702i	0.478876	−	0.877882i	$-0.341044\pi$
$42$	−0.895472	−	0.994522i	−0.138174	−	0.153458i
$43$	−3.70498	−	1.64956i	−0.565004	−	0.251556i	0.104299	−	0.994546i	$-0.466740\pi$
$43$	−3.70498	−	1.64956i	−0.565004	−	0.251556i	−0.669302	+	0.742990i	$0.733407\pi$
$44$	−1.90520	+	0.848249i	−0.287219	+	0.127878i
$45$	−0.624938	+	0.694064i	−0.0931602	+	0.103465i
$46$	−4.13154	−	3.00174i	−0.609162	−	0.442582i
$47$	−3.74346	−	2.71978i	−0.546040	−	0.396721i	0.280283	−	0.959917i	$-0.409572\pi$
$47$	−3.74346	−	2.71978i	−0.546040	−	0.396721i	−0.826323	+	0.563196i	$0.809572\pi$
$48$	1.08268	−	1.20243i	0.156271	−	0.173556i
$49$	−5.76988	+	2.56892i	−0.824269	+	0.366988i
$50$	0.894028	+	0.398047i	0.126435	+	0.0562924i
$51$	6.52530	+	7.24708i	0.913725	+	1.01479i
$52$	−0.488830	−	4.65090i	−0.0677885	−	0.644964i
$53$	−1.59901	−	0.339879i	−0.219640	−	0.0466860i	0.0967770	−	0.995306i	$-0.469147\pi$
$53$	−1.59901	−	0.339879i	−0.219640	−	0.0466860i	−0.316417	+	0.948620i	$0.602480\pi$
$54$	−1.69098	−	5.20431i	−0.230114	−	0.708217i
$55$	4.98787	−	1.06021i	0.672565	−	0.142958i
$56$	0.413545	+	0.716282i	0.0552623	+	0.0957172i
$57$	5.09240	−	8.82030i	0.674505	−	1.16828i
$58$	2.05248	−	6.31687i	0.269503	−	0.829446i
$59$	1.15543	−	10.9931i	0.150424	−	1.43118i	−0.615441	−	0.788183i	$-0.711022\pi$
$59$	1.15543	−	10.9931i	0.150424	−	1.43118i	0.765865	−	0.643002i	$-0.222311\pi$
$60$	−3.20071	+	2.32545i	−0.413210	+	0.300215i
$61$	10.5530			1.35117			0.675584	−	0.737283i	$-0.263891\pi$
$61$	10.5530			1.35117			0.675584	+	0.737283i	$0.263891\pi$
$62$	1.07890	+	5.46223i	0.137020	+	0.693704i
$63$	0.315921			0.0398023
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−1.19525	+	11.3720i	−0.148252	+	1.41053i
$66$	−1.04275	+	3.20925i	−0.128354	+	0.395032i
$67$	0.0971366	−	0.168246i	0.0118671	−	0.0205545i	−0.860031	−	0.510242i	$-0.829556\pi$
$67$	0.0971366	−	0.168246i	0.0118671	−	0.0205545i	0.871898	+	0.489688i	$0.162889\pi$
$68$	−3.01351	−	5.21954i	−0.365441	−	0.632963i
$69$	−8.08251	+	1.71799i	−0.973020	+	0.206822i
$70$	−0.624938	−	1.92336i	−0.0746943	−	0.229886i
$71$	5.12319	+	1.08897i	0.608011	+	0.129237i	0.501621	−	0.865088i	$-0.332737\pi$
$71$	5.12319	+	1.08897i	0.608011	+	0.129237i	0.106390	+	0.994324i	$0.466071\pi$
$72$	0.0399263	+	0.379874i	0.00470536	+	0.0447685i
$73$	−0.985705	−	1.09474i	−0.115368	−	0.128129i	0.682694	−	0.730704i	$-0.260808\pi$
$73$	−0.985705	−	1.09474i	−0.115368	−	0.128129i	−0.798062	+	0.602575i	$0.794141\pi$
$74$	−3.62260	−	1.61289i	−0.421119	−	0.187494i
$75$	1.44657	−	0.644054i	0.167035	−	0.0743689i
$76$	−4.21188	+	4.67777i	−0.483136	+	0.536577i
$77$	−1.39547	−	1.01387i	−0.159029	−	0.115541i
$78$	−6.12165	−	4.44764i	−0.693140	−	0.503596i
$79$	−8.33915	+	9.26157i	−0.938228	+	1.04201i	0.0608097	+	0.998149i	$0.480632\pi$
$79$	−8.33915	+	9.26157i	−0.938228	+	1.04201i	−0.999038	+	0.0438584i	$0.986035\pi$
$80$	2.23373	−	0.994522i	0.249739	−	0.111191i
$81$	−7.04179	−	3.13521i	−0.782422	−	0.348357i
$82$	7.05248	+	7.83257i	0.778816	+	0.864963i
$83$	0.0835291	+	0.794726i	0.00916851	+	0.0872325i	0.998149	−	0.0608116i	$-0.0193689\pi$
$83$	0.0835291	+	0.794726i	0.00916851	+	0.0872325i	−0.988981	+	0.148044i	$0.952702\pi$
$84$	1.30902	+	0.278240i	0.142825	+	0.0303585i
$85$	4.55392	+	14.0155i	0.493942	+	1.52020i
$86$	3.96698	−	0.843207i	0.427770	−	0.0909254i
$87$	−5.37345	−	9.30710i	−0.576095	−	0.997825i
$88$	1.04275	−	1.80610i	0.111157	−	0.192530i
$89$	−0.991653	+	3.05199i	−0.105115	+	0.323511i	−0.989757	−	0.142759i	$-0.954403\pi$
$89$	−0.991653	+	3.05199i	−0.105115	+	0.323511i	0.884642	+	0.466270i	$0.154403\pi$
$90$	0.0976248	−	0.928838i	0.0102906	−	0.0979082i
$91$	3.12920	−	2.27350i	0.328030	−	0.238328i
$92$	5.10686			0.532427
$93$	7.73607	+	4.61653i	0.802193	+	0.478711i
$94$	4.62717			0.477256
$95$	12.4516	−	9.04659i	1.27750	−	0.928160i
$96$	−0.169131	+	1.60917i	−0.0172618	+	0.164235i
$97$	−3.98223	+	12.2560i	−0.404334	+	1.24441i	0.517116	+	0.855915i	$0.327006\pi$
$97$	−3.98223	+	12.2560i	−0.404334	+	1.24441i	−0.921450	+	0.388497i	$0.872994\pi$
$98$	3.15796	−	5.46975i	0.319002	−	0.552528i
$99$	−0.398295	−	0.689867i	−0.0400301	−	0.0693343i
$100$	−0.957250	+	0.203470i	−0.0957250	+	0.0203470i
$101$	1.31359	+	4.04280i	0.130707	+	0.402274i	0.994898	−	0.100890i	$-0.0321691\pi$
$101$	1.31359	+	4.04280i	0.130707	+	0.402274i	−0.864191	+	0.503164i	$0.832169\pi$
$102$	−9.53881	−	2.02754i	−0.944483	−	0.200756i
$103$	0.489153	+	4.65398i	0.0481977	+	0.458570i	0.991829	+	0.127572i	$0.0407185\pi$
$103$	0.489153	+	4.65398i	0.0481977	+	0.458570i	−0.943632	+	0.330998i	$0.892615\pi$
$104$	3.12920	+	3.47533i	0.306844	+	0.340784i
$105$	−2.98932	−	1.33093i	−0.291728	−	0.129885i
$106$	1.49340	−	0.664904i	0.145052	−	0.0645812i
$107$	3.68682	−	4.09463i	0.356418	−	0.395842i	−0.538095	−	0.842884i	$-0.680856\pi$
$107$	3.68682	−	4.09463i	0.356418	−	0.395842i	0.894513	+	0.447042i	$0.147522\pi$
$108$	4.42705	+	3.21644i	0.425993	+	0.309502i
$109$	−5.85239	−	4.25201i	−0.560557	−	0.407269i	0.271105	−	0.962550i	$-0.412611\pi$
$109$	−5.85239	−	4.25201i	−0.560557	−	0.407269i	−0.831663	+	0.555281i	$0.812611\pi$
$110$	−3.41210	+	3.78952i	−0.325331	+	0.361317i
$111$	−5.86149	+	2.60971i	−0.556348	+	0.247702i
$112$	−0.755585	−	0.336408i	−0.0713961	−	0.0317876i
$113$	−11.3788	−	12.6374i	−1.07043	−	1.18883i	−0.981235	−	0.192813i	$-0.938239\pi$
$113$	−11.3788	−	12.6374i	−1.07043	−	1.18883i	−0.0891899	−	0.996015i	$-0.528428\pi$
$114$	1.06460	+	10.1290i	0.0997091	+	0.948669i
$115$	−12.2141	−	2.59618i	−1.13897	−	0.242095i
$116$	2.05248	+	6.31687i	0.190568	+	0.586507i
$117$	1.74724	−	0.371387i	0.161532	−	0.0343347i
$118$	5.52685	+	9.57278i	0.508787	+	0.881246i
$119$	2.49244	−	4.31704i	0.228482	−	0.395742i
$120$	1.22256	−	3.76266i	0.111604	−	0.343482i
$121$	0.695187	−	6.61426i	0.0631988	−	0.601296i
$122$	−8.53753	+	6.20288i	−0.772951	+	0.561582i
$123$	17.0537			1.53768
$124$	−4.08347	−	3.78488i	−0.366706	−	0.339892i
$125$	−9.83274			−0.879467
$126$	−0.255585	+	0.185693i	−0.0227693	+	0.0165429i
$127$	0.102028	−	0.970733i	0.00905353	−	0.0861386i	−0.989062	−	0.147500i	$-0.952877\pi$
$127$	0.102028	−	0.970733i	0.00905353	−	0.0861386i	0.998116	+	0.0613611i	$0.0195441\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	3.28105	−	5.68295i	0.288880	−	0.500356i
$130$	−5.71734	−	9.90272i	−0.501444	−	0.868526i
$131$	6.19673	−	1.31716i	0.541411	−	0.115080i	0.0709146	−	0.997482i	$-0.477408\pi$
$131$	6.19673	−	1.31716i	0.541411	−	0.115080i	0.470496	+	0.882402i	$0.344075\pi$
$132$	−1.04275	−	3.20925i	−0.0907597	−	0.279330i
$133$	−5.09240	−	1.08242i	−0.441567	−	0.0938580i
$134$	0.0203071	+	0.193209i	0.00175427	+	0.0166907i
$135$	−8.95300	−	9.94332i	−0.770552	−	0.855785i
$136$	5.50595	+	2.45141i	0.472131	+	0.210206i
$137$	−2.18294	+	0.971907i	−0.186501	+	0.0830356i	−0.497863	−	0.867256i	$-0.665882\pi$
$137$	−2.18294	+	0.971907i	−0.186501	+	0.0830356i	0.311362	+	0.950291i	$0.399215\pi$
$138$	5.52908	−	6.14066i	0.470666	−	0.522728i
$139$	17.6460	+	12.8206i	1.49671	+	1.08743i	0.971667	+	0.236352i	$0.0759519\pi$
$139$	17.6460	+	12.8206i	1.49671	+	1.08743i	0.525046	+	0.851074i	$0.324048\pi$
$140$	1.63611	+	1.18870i	0.138276	+	0.100464i
$141$	5.00973	−	5.56387i	0.421895	−	0.468562i
$142$	−4.78483	+	2.13034i	−0.401534	+	0.178774i
$143$	−8.90970	−	3.96686i	−0.745067	−	0.331725i
$144$	−0.255585	−	0.283856i	−0.0212988	−	0.0236547i
$145$	−1.69758	−	16.1514i	−0.140977	−	1.34130i
$146$	1.44092	+	0.306277i	0.119251	+	0.0253477i
$147$	−3.15796	−	9.71920i	−0.260464	−	0.801626i
$148$	3.87878	−	0.824460i	0.318834	−	0.0677702i
$149$	0.218194	+	0.377923i	0.0178751	+	0.0309606i	0.874825	−	0.484440i	$-0.160977\pi$
$149$	0.218194	+	0.377923i	0.0178751	+	0.0309606i	−0.856949	+	0.515400i	$0.827643\pi$
$150$	−0.791733	+	1.37132i	−0.0646447	+	0.111968i
$151$	−2.97437	+	9.15417i	−0.242051	+	0.744956i	0.754057	+	0.656809i	$0.228094\pi$
$151$	−2.97437	+	9.15417i	−0.242051	+	0.744956i	−0.996108	+	0.0881463i	$0.971906\pi$
$152$	0.657960	−	6.26007i	0.0533676	−	0.507759i
$153$	1.86245	−	1.35315i	0.150570	−	0.109396i
$154$	1.72490			0.138996
$155$	7.84228	+	11.1282i	0.629907	+	0.893837i
$156$	7.56677			0.605827
$157$	−11.7585	+	8.54308i	−0.938434	+	0.681812i	−0.948043	−	0.318142i	$-0.896941\pi$
$157$	−11.7585	+	8.54308i	−0.938434	+	0.681812i	0.00960915	+	0.999954i	$0.496941\pi$
$158$	1.30270	−	12.3944i	0.103638	−	0.986045i
$159$	0.817364	−	2.51559i	0.0648212	−	0.199499i
$160$	−1.22256	+	2.11754i	−0.0966520	+	0.167406i
$161$	2.11192	+	3.65795i	0.166443	+	0.288287i
$162$	7.53976	−	1.60263i	0.592380	−	0.125914i
$163$	3.56586	+	10.9746i	0.279300	+	0.859596i	0.988050	+	0.154136i	$0.0492594\pi$
$163$	3.56586	+	10.9746i	0.279300	+	0.859596i	−0.708750	+	0.705460i	$0.750741\pi$
$164$	−10.3094	−	2.19134i	−0.805032	−	0.171115i
$165$	0.862449	+	8.20565i	0.0671416	+	0.638809i
$166$	−0.534705	−	0.593850i	−0.0415011	−	0.0460917i
$167$	14.3378	+	6.38360i	1.10949	+	0.493978i	0.877904	−	0.478836i	$-0.158941\pi$
$167$	14.3378	+	6.38360i	1.10949	+	0.493978i	0.231588	+	0.972814i	$0.425608\pi$
$168$	−1.22256	+	0.544320i	−0.0943227	+	0.0419952i
$169$	5.93510	−	6.59159i	0.456546	−	0.507046i
$170$	−11.9223	−	8.66207i	−0.914400	−	0.664350i
$171$	−1.94512	−	1.41322i	−0.148747	−	0.108071i
$172$	−2.71373	+	3.01390i	−0.206920	+	0.229808i
$173$	−18.2294	+	8.11626i	−1.38596	+	0.617068i	−0.958010	−	0.286735i	$-0.907430\pi$
$173$	−18.2294	+	8.11626i	−1.38596	+	0.617068i	−0.427948	+	0.903804i	$0.640763\pi$
$174$	9.81779	+	4.37116i	0.744285	+	0.331377i
$175$	−0.541608	−	0.601517i	−0.0409417	−	0.0454704i
$176$	0.217994	+	2.07407i	0.0164319	+	0.156339i
$177$	17.4944	+	3.71855i	1.31496	+	0.279504i
$178$	−0.991653	−	3.05199i	−0.0743275	−	0.228757i
$179$	2.14728	−	0.456418i	0.160495	−	0.0341143i	−0.126963	−	0.991907i	$-0.540523\pi$
$179$	2.14728	−	0.456418i	0.160495	−	0.0341143i	0.287458	+	0.957793i	$0.407190\pi$
$180$	0.466977	+	0.808828i	0.0348064	+	0.0602865i
$181$	3.27504	−	5.67253i	0.243432	−	0.421636i	−0.718258	−	0.695777i	$-0.755060\pi$
$181$	3.27504	−	5.67253i	0.243432	−	0.421636i	0.961690	+	0.274141i	$0.0883935\pi$
$182$	−1.19525	+	3.67860i	−0.0885978	+	0.272676i
$183$	−1.78483	+	16.9815i	−0.131938	+	1.25531i
$184$	−4.13154	+	3.00174i	−0.304581	+	0.221291i
$185$	−9.69598			−0.712862
$186$	−8.97214	+	0.812299i	−0.657869	+	0.0595607i
$187$	−12.5693			−0.919160
$188$	−3.74346	+	2.71978i	−0.273020	+	0.198361i
$189$	−0.473091	+	4.50116i	−0.0344123	+	0.327411i
$190$	−4.75607	+	14.6377i	−0.345042	+	1.06193i
$191$	−9.97197	+	17.2720i	−0.721546	+	1.24976i	0.238833	+	0.971061i	$0.423235\pi$
$191$	−9.97197	+	17.2720i	−0.721546	+	1.24976i	−0.960380	+	0.278695i	$0.910098\pi$
$192$	−0.809017	−	1.40126i	−0.0583858	−	0.101127i
$193$	11.6768	−	2.48199i	0.840516	−	0.178657i	0.232514	−	0.972593i	$-0.425305\pi$
$193$	11.6768	−	2.48199i	0.840516	−	0.178657i	0.608002	+	0.793936i	$0.291971\pi$
$194$	−3.98223	−	12.2560i	−0.285907	−	0.879932i
$195$	−18.0974	−	3.84672i	−1.29598	−	0.275469i
$196$	0.660193	+	6.28132i	0.0471567	+	0.448666i
$197$	8.54742	+	9.49287i	0.608978	+	0.676339i	0.966234	−	0.257668i	$-0.0829540\pi$
$197$	8.54742	+	9.49287i	0.608978	+	0.676339i	−0.357255	+	0.934007i	$0.616287\pi$
$198$	0.727721	+	0.324002i	0.0517169	+	0.0230258i
$199$	16.1517	−	7.19121i	1.14497	−	0.509771i	0.255516	−	0.966805i	$-0.417755\pi$
$199$	16.1517	−	7.19121i	1.14497	−	0.509771i	0.889449	+	0.457034i	$0.151088\pi$
$200$	0.654835	−	0.727268i	0.0463038	−	0.0514256i
$201$	0.254307	+	0.184765i	0.0179374	+	0.0130323i
$202$	−3.43901	−	2.49859i	−0.241968	−	0.175800i
$203$	−3.67587	+	4.08247i	−0.257995	+	0.286533i
$204$	8.90881	−	3.96646i	0.623742	−	0.277708i
$205$	23.5430	+	10.4820i	1.64432	+	0.732096i
$206$	−3.13127	−	3.47763i	−0.218166	−	0.242298i
$207$	0.203898	+	1.93996i	0.0141719	+	0.134837i
$208$	−4.57433	−	0.972304i	−0.317173	−	0.0674171i
$209$	4.05656	+	12.4848i	0.280598	+	0.863592i
$210$	3.20071	−	0.680332i	0.220870	−	0.0469474i
$211$	−11.9646	−	20.7233i	−0.823676	−	1.42665i	−0.902927	−	0.429793i	$-0.858586\pi$
$211$	−11.9646	−	20.7233i	−0.823676	−	1.42665i	0.0792517	−	0.996855i	$-0.474747\pi$
$212$	−0.817364	+	1.41572i	−0.0561368	+	0.0972318i
$213$	−2.61882	+	8.05991i	−0.179439	+	0.552256i
$214$	−0.575938	+	5.47968i	−0.0393703	+	0.374583i
$215$	8.02258	−	5.82875i	0.547135	−	0.397517i
$216$	−5.47214			−0.372332
$217$	1.02234	−	4.49013i	0.0694010	−	0.304810i
$218$	7.23395			0.489945
$219$	1.92833	−	1.40101i	0.130304	−	0.0946717i
$220$	0.533023	−	5.07137i	0.0359364	−	0.341912i
$221$	8.70978	−	26.8060i	0.585883	−	1.80316i
$222$	3.20810	−	5.55660i	0.215314	−	0.372934i
$223$	−8.12010	−	14.0644i	−0.543762	−	0.941824i	−0.998684	−	0.0512923i	$-0.983666\pi$
$223$	−8.12010	−	14.0644i	−0.543762	−	0.941824i	0.454921	−	0.890532i	$-0.349667\pi$
$224$	0.809017	−	0.171962i	0.0540547	−	0.0114897i
$225$	−0.115512	−	0.355510i	−0.00770082	−	0.0237007i
$226$	16.6337	+	3.53560i	1.10646	+	0.235185i
$227$	−0.185438	−	1.76433i	−0.0123080	−	0.117102i	0.986643	−	0.162898i	$-0.0520843\pi$
$227$	−0.185438	−	1.76433i	−0.0123080	−	0.117102i	−0.998951	+	0.0457959i	$0.985418\pi$
$228$	−6.81497	−	7.56879i	−0.451332	−	0.501255i
$229$	−3.85285	−	1.71540i	−0.254603	−	0.113357i	0.275467	−	0.961311i	$-0.411168\pi$
$229$	−3.85285	−	1.71540i	−0.254603	−	0.113357i	−0.530070	+	0.847954i	$0.677834\pi$
$230$	11.4074	−	5.07889i	0.752180	−	0.334892i
$231$	1.86751	−	2.07407i	0.122873	−	0.136464i
$232$	−5.37345	−	3.90404i	−0.352785	−	0.256313i
$233$	14.5633	+	10.5809i	0.954075	+	0.693176i	0.951767	−	0.306822i	$-0.0992655\pi$
$233$	14.5633	+	10.5809i	0.954075	+	0.693176i	0.00230755	+	0.999997i	$0.499265\pi$
$234$	−1.19525	+	1.32746i	−0.0781359	+	0.0867787i
$235$	10.3359	−	4.60182i	0.674237	−	0.300190i
$236$	−10.0980	−	4.49594i	−0.657327	−	0.292661i
$237$	−13.4930	−	14.9855i	−0.876467	−	0.973415i
$238$	0.521062	+	4.95758i	0.0337755	+	0.321352i
$239$	−3.14870	−	0.669277i	−0.203672	−	0.0432919i	0.104946	−	0.994478i	$-0.466533\pi$
$239$	−3.14870	−	0.669277i	−0.203672	−	0.0432919i	−0.308618	+	0.951186i	$0.599866\pi$
$240$	1.22256	+	3.76266i	0.0789161	+	0.242879i
$241$	−14.5397	+	3.09050i	−0.936582	+	0.199077i	−0.650827	−	0.759226i	$-0.725578\pi$
$241$	−14.5397	+	3.09050i	−0.936582	+	0.199077i	−0.285755	+	0.958303i	$0.592244\pi$
$242$	3.32535	+	5.75967i	0.213761	+	0.370245i
$243$	−1.97214	+	3.41584i	−0.126513	+	0.219126i
$244$	3.26105	−	10.0365i	0.208767	−	0.642519i
$245$	1.61426	−	15.3586i	0.103131	−	0.981226i
$246$	−13.7967	+	10.0239i	−0.879647	+	0.639101i
$247$	−29.4366			−1.87301
$248$	5.52829	+	0.661830i	0.351047	+	0.0420262i
$249$	−1.29298			−0.0819391
$250$	7.95485	−	5.77954i	0.503109	−	0.365530i
$251$	0.586391	−	5.57914i	0.0370127	−	0.352152i	−0.960305	−	0.278953i	$-0.910013\pi$
$251$	0.586391	−	5.57914i	0.0370127	−	0.352152i	0.997317	−	0.0731990i	$-0.0233208\pi$
$252$	0.0976248	−	0.300458i	0.00614979	−	0.0189271i
$253$	5.32518	−	9.22348i	0.334791	−	0.579875i
$254$	0.488040	+	0.845310i	0.0306223	+	0.0530394i
$255$	−23.3236	+	4.95758i	−1.46058	+	0.310456i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	17.1983	+	3.65561i	1.07280	+	0.228030i	0.710261	−	0.703939i	$-0.248577\pi$
$257$	17.1983	+	3.65561i	1.07280	+	0.228030i	0.362538	+	0.931969i	$0.381910\pi$
$258$	0.685926	+	6.52615i	0.0427039	+	0.406301i
$259$	2.19460	+	2.43735i	0.136366	+	0.151449i
$260$	10.4461	+	4.65090i	0.647840	+	0.288437i
$261$	−2.31767	+	1.03189i	−0.143460	+	0.0638725i
$262$	−4.23906	+	4.70795i	−0.261890	+	0.290858i
$263$	6.24452	+	4.53691i	0.385053	+	0.279758i	0.763425	−	0.645896i	$-0.223516\pi$
$263$	6.24452	+	4.53691i	0.385053	+	0.279758i	−0.378372	+	0.925654i	$0.623516\pi$
$264$	2.72995	+	1.98343i	0.168017	+	0.122072i
$265$	2.67459	−	2.97043i	0.164299	−	0.182472i
$266$	4.75607	−	2.11754i	0.291614	−	0.129835i
$267$	−4.74346	−	2.11192i	−0.290295	−	0.129248i
$268$	−0.129994	−	0.144373i	−0.00794066	−	0.00881900i
$269$	−0.442688	−	4.21189i	−0.0269911	−	0.256804i	−0.999694	−	0.0247482i	$-0.992122\pi$
$269$	−0.442688	−	4.21189i	−0.0269911	−	0.256804i	0.972703	−	0.232055i	$-0.0745451\pi$
$270$	13.0877	+	2.78187i	0.796490	+	0.169299i
$271$	−5.97683	−	18.3948i	−0.363066	−	1.11740i	−0.951183	−	0.308627i	$-0.900130\pi$
$271$	−5.97683	−	18.3948i	−0.363066	−	1.11740i	0.588117	−	0.808776i	$-0.299870\pi$
$272$	−5.89531	+	1.25309i	−0.357455	+	0.0759795i
$273$	3.12920	+	5.41994i	0.189388	+	0.328030i
$274$	1.19476	−	2.06939i	0.0721782	−	0.125016i
$275$	−0.630687	+	1.94105i	−0.0380318	+	0.117050i
$276$	−0.863727	+	8.21781i	−0.0519903	+	0.494654i
$277$	7.07183	−	5.13798i	0.424905	−	0.308712i	−0.354703	−	0.934979i	$-0.615418\pi$
$277$	7.07183	−	5.13798i	0.424905	−	0.308712i	0.779608	+	0.626267i	$0.215418\pi$
$278$	−21.8116			−1.30818
$279$	1.27474	−	1.70232i	0.0763165	−	0.101915i
$280$	−2.02234			−0.120858
$281$	−19.9446	+	14.4906i	−1.18979	+	0.864437i	−0.993243	−	0.116057i	$-0.962975\pi$
$281$	−19.9446	+	14.4906i	−1.18979	+	0.864437i	−0.196552	+	0.980493i	$0.562975\pi$
$282$	−0.782596	+	7.44591i	−0.0466029	+	0.443397i
$283$	−6.82585	+	21.0078i	−0.405755	+	1.24878i	0.514509	+	0.857485i	$0.327974\pi$
$283$	−6.82585	+	21.0078i	−0.405755	+	1.24878i	−0.920264	+	0.391299i	$0.872026\pi$
$284$	2.61882	−	4.53594i	0.155399	−	0.269158i
$285$	12.4516	+	21.5667i	0.737567	+	1.27750i
$286$	9.53976	−	2.02774i	0.564098	−	0.119903i
$287$	−2.69381	−	8.29068i	−0.159010	−	0.489384i
$288$	0.373619	+	0.0794152i	0.0220157	+	0.00467959i
$289$	−2.02000	−	19.2190i	−0.118823	−	1.13053i
$290$	10.8670	+	12.0690i	0.638130	+	0.708715i
$291$	−19.0485	−	8.48095i	−1.11664	−	0.497162i
$292$	−1.34576	+	0.599169i	−0.0787544	+	0.0350637i
$293$	8.96330	−	9.95475i	0.523642	−	0.581563i	−0.422073	−	0.906562i	$-0.638697\pi$
$293$	8.96330	−	9.95475i	0.523642	−	0.581563i	0.945714	+	0.324999i	$0.105364\pi$
$294$	8.26765	+	6.00680i	0.482179	+	0.350324i
$295$	21.8658	+	15.8865i	1.27308	+	0.924945i
$296$	−2.65339	+	2.94689i	−0.154225	+	0.171285i
$297$	10.4255	−	4.64173i	0.604949	−	0.269341i
$298$	−0.398660	−	0.177495i	−0.0230937	−	0.0102820i
$299$	15.9804	+	17.7481i	0.924172	+	1.02640i
$300$	−0.165517	−	1.57479i	−0.00955614	−	0.0909206i
$301$	−3.28105	−	0.697409i	−0.189117	−	0.0401980i
$302$	−2.97437	−	9.15417i	−0.171156	−	0.526763i
$303$	−6.72772	+	1.43002i	−0.386497	+	0.0821526i
$304$	3.14728	+	5.45125i	0.180509	+	0.312650i
$305$	−12.9017	+	22.3463i	−0.738747	+	1.27955i
$306$	−0.711392	+	2.18944i	−0.0406676	+	0.125162i
$307$	0.152377	−	1.44977i	0.00869659	−	0.0827425i	−0.989313	−	0.145809i	$-0.953421\pi$
$307$	0.152377	−	1.44977i	0.00869659	−	0.0827425i	0.998009	+	0.0630667i	$0.0200881\pi$
$308$	−1.39547	+	1.01387i	−0.0795144	+	0.0577706i
$309$	−7.57177			−0.430743
$310$	−12.8855	−	4.39331i	−0.731848	−	0.249523i
$311$	16.7688			0.950874			0.475437	−	0.879750i	$-0.342290\pi$
$311$	16.7688			0.950874			0.475437	+	0.879750i	$0.342290\pi$
$312$	−6.12165	+	4.44764i	−0.346570	+	0.251798i
$313$	0.160524	−	1.52728i	0.00907334	−	0.0863271i	−0.989048	−	0.147593i	$-0.952847\pi$
$313$	0.160524	−	1.52728i	0.00907334	−	0.0863271i	0.998121	+	0.0612664i	$0.0195139\pi$
$314$	4.49136	−	13.8230i	0.253462	−	0.780077i
$315$	−0.386233	+	0.668975i	−0.0217617	+	0.0376925i
$316$	6.23133	+	10.7930i	0.350540	+	0.607153i
$317$	6.71287	−	1.42686i	0.377032	−	0.0801407i	−0.0154977	−	0.999880i	$-0.504933\pi$
$317$	6.71287	−	1.42686i	0.377032	−	0.0801407i	0.392530	+	0.919739i	$0.371600\pi$
$318$	0.817364	+	2.51559i	0.0458355	+	0.141067i
$319$	13.5491	+	2.87995i	0.758604	+	0.161246i
$320$	−0.255585	−	2.43173i	−0.0142876	−	0.135938i
$321$	5.96540	+	6.62525i	0.332956	+	0.369785i
$322$	−3.85867	−	1.71799i	−0.215035	−	0.0957399i
$323$	−34.6575	+	15.4305i	−1.92840	+	0.858577i
$324$	−5.15780	+	5.72831i	−0.286544	+	0.318240i
$325$	−3.70256	−	2.69007i	−0.205381	−	0.149218i
$326$	−9.33554	−	6.78267i	−0.517048	−	0.375657i
$327$	7.83203	−	8.69835i	0.433112	−	0.481020i
$328$	9.62855	−	4.28691i	0.531648	−	0.236705i
$329$	−3.49622	−	1.55662i	−0.192753	−	0.0858191i
$330$	−5.52090	−	6.13158i	−0.303915	−	0.337532i
$331$	−0.939444	−	8.93821i	−0.0516365	−	0.491288i	−0.989526	−	0.144354i	$-0.953889\pi$
$331$	−0.939444	−	8.93821i	−0.0516365	−	0.491288i	0.937890	−	0.346934i	$-0.112777\pi$
$332$	0.781641	+	0.166143i	0.0428981	+	0.00911828i
$333$	0.468056	+	1.44053i	0.0256493	+	0.0789404i
$334$	−15.3517	+	3.26311i	−0.840008	+	0.178549i
$335$	0.237511	+	0.411382i	0.0129766	+	0.0224762i
$336$	0.669131	−	1.15897i	0.0365041	−	0.0632269i
$337$	2.94249	−	9.05605i	0.160288	−	0.493314i	−0.838371	−	0.545101i	$-0.816491\pi$
$337$	2.94249	−	9.05605i	0.160288	−	0.493314i	0.998658	+	0.0517863i	$0.0164915\pi$
$338$	−0.927153	+	8.82127i	−0.0504305	+	0.479814i
$339$	22.2602	−	16.1730i	1.20901	−	0.878398i
$340$	14.7368			0.799215
$341$	−11.0939	+	3.42845i	−0.600768	+	0.185661i
$342$	2.40431			0.130010
$343$	−8.91009	+	6.47356i	−0.481100	+	0.349539i
$344$	0.423926	−	4.03338i	0.0228565	−	0.217466i
$345$	6.24346	−	19.2154i	0.336137	−	1.03452i
$346$	9.97729	−	17.2812i	0.536383	−	0.929042i
$347$	10.3893	+	17.9948i	0.557727	+	0.966011i	0.997686	+	0.0679930i	$0.0216596\pi$
$347$	10.3893	+	17.9948i	0.557727	+	0.966011i	−0.439959	+	0.898018i	$0.645007\pi$
$348$	−10.5121	+	2.23441i	−0.563506	+	0.119777i
$349$	−9.34476	−	28.7602i	−0.500214	−	1.53950i	−0.808671	−	0.588261i	$-0.799813\pi$
$349$	−9.34476	−	28.7602i	−0.500214	−	1.53950i	0.308458	−	0.951238i	$-0.400187\pi$
$350$	0.791733	+	0.168288i	0.0423199	+	0.00899537i
$351$	2.67494	+	25.4504i	0.142778	+	1.35844i
$352$	−1.39547	−	1.54983i	−0.0743789	−	0.0826061i
$353$	−8.41044	−	3.74457i	−0.447643	−	0.199303i	0.170519	−	0.985354i	$-0.445456\pi$
$353$	−8.41044	−	3.74457i	−0.447643	−	0.199303i	−0.618162	+	0.786051i	$0.712122\pi$
$354$	−16.3390	+	7.27459i	−0.868407	+	0.386640i
$355$	−8.56936	+	9.51724i	−0.454814	+	0.505122i
$356$	2.59618	+	1.88624i	0.137597	+	0.0999703i
$357$	6.52530	+	4.74091i	0.345356	+	0.250915i
$358$	−1.46891	+	1.63139i	−0.0776342	+	0.0862216i
$359$	14.7629	−	6.57284i	0.779153	−	0.346901i	0.0216779	−	0.999765i	$-0.493099\pi$
$359$	14.7629	−	6.57284i	0.779153	−	0.346901i	0.757476	+	0.652864i	$0.226432\pi$
$360$	−0.853210	−	0.379874i	−0.0449681	−	0.0200211i
$361$	13.7984	+	15.3247i	0.726234	+	0.806564i
$362$	0.684670	+	6.51420i	0.0359854	+	0.342379i
$363$	10.5259	+	2.23735i	0.552466	+	0.117430i
$364$	−1.19525	−	3.67860i	−0.0626481	−	0.192811i
$365$	3.52323	−	0.748886i	0.184414	−	0.0391985i
$366$	−8.53753	−	14.7874i	−0.446264	−	0.772951i
$367$	−0.888891	+	1.53960i	−0.0463997	+	0.0803667i	−0.888293	−	0.459278i	$-0.848108\pi$
$367$	−0.888891	+	1.53960i	−0.0463997	+	0.0803667i	0.841893	+	0.539645i	$0.181441\pi$
$368$	1.57811	−	4.85692i	0.0822645	−	0.253184i
$369$	0.420814	−	4.00378i	0.0219067	−	0.208428i
$370$	7.84421	−	5.69915i	0.407801	−	0.296285i
$371$	−1.35207			−0.0701959
$372$	6.78115	−	5.93085i	0.351586	−	0.307500i
$373$	−19.1685			−0.992508			−0.496254	−	0.868177i	$-0.665292\pi$
$373$	−19.1685			−0.992508			−0.496254	+	0.868177i	$0.665292\pi$
$374$	10.1688	−	7.38807i	0.525816	−	0.382028i
$375$	1.66302	−	15.8225i	0.0858778	−	0.817073i
$376$	1.42987	−	4.40070i	0.0737401	−	0.226949i
$377$	−15.5306	+	26.8998i	−0.799868	+	1.38541i
$378$	−2.26298	−	3.91959i	−0.116395	−	0.201602i
$379$	−24.9806	+	5.30979i	−1.28317	+	0.272746i	−0.798523	−	0.601965i	$-0.794385\pi$
$379$	−24.9806	+	5.30979i	−1.28317	+	0.272746i	−0.484646	+	0.874711i	$0.661051\pi$
$380$	−4.75607	−	14.6377i	−0.243981	−	0.750898i
$381$	1.54482	+	0.328361i	0.0791434	+	0.0168225i
$382$	−2.08471	−	19.8347i	−0.106663	−	1.01483i
$383$	−1.89614	−	2.10588i	−0.0968884	−	0.107605i	0.692750	−	0.721177i	$-0.256399\pi$
$383$	−1.89614	−	2.10588i	−0.0968884	−	0.107605i	−0.789639	+	0.613572i	$0.789732\pi$
$384$	1.47815	+	0.658114i	0.0754314	+	0.0335842i
$385$	3.85296	−	1.71545i	0.196365	−	0.0874274i
$386$	−7.98787	+	8.87143i	−0.406572	+	0.451544i
$387$	−1.25325	−	0.910539i	−0.0637063	−	0.0462853i
$388$	10.4256	+	7.57465i	0.529280	+	0.384544i
$389$	10.9834	−	12.1983i	0.556883	−	0.618481i	−0.397306	−	0.917686i	$-0.630055\pi$
$389$	10.9834	−	12.1983i	0.556883	−	0.618481i	0.954189	+	0.299205i	$0.0967215\pi$
$390$	16.9021	−	7.52532i	0.855873	−	0.381059i
$391$	28.1181	+	12.5190i	1.42199	+	0.633113i
$392$	−4.22618	−	4.69364i	−0.213454	−	0.237065i
$393$	1.07147	+	10.1944i	0.0540486	+	0.514238i
$394$	−12.4948	−	2.65585i	−0.629478	−	0.133800i
$395$	−9.41661	−	28.9813i	−0.473801	−	1.45821i
$396$	−0.779183	+	0.165620i	−0.0391554	+	0.00832274i
$397$	7.54967	+	13.0764i	0.378907	+	0.656287i	0.990904	−	0.134574i	$-0.0429666\pi$
$397$	7.54967	+	13.0764i	0.378907	+	0.656287i	−0.611996	+	0.790861i	$0.709633\pi$
$398$	−8.84013	+	15.3116i	−0.443116	+	0.767499i
$399$	2.60309	−	8.01147i	0.130317	−	0.401075i
$400$	−0.102295	+	0.973275i	−0.00511476	+	0.0486637i
$401$	−11.3356	+	8.23579i	−0.566073	+	0.411276i	−0.833676	−	0.552253i	$-0.813768\pi$
$401$	−11.3356	+	8.23579i	−0.566073	+	0.411276i	0.267604	+	0.963529i	$0.413768\pi$
$402$	−0.314341			−0.0156779
$403$	0.375716	−	26.0351i	0.0187157	−	1.29690i
$404$	4.25085			0.211488
$405$	15.2480	−	11.0783i	0.757677	−	0.550485i
$406$	0.574227	−	5.46341i	0.0284984	−	0.271144i
$407$	2.55554	−	7.86515i	0.126673	−	0.389861i
$408$	−4.87595	+	8.44540i	−0.241396	+	0.418110i
$409$	13.9065	+	24.0868i	0.687633	+	1.19102i	0.972602	+	0.232478i	$0.0746835\pi$
$409$	13.9065	+	24.0868i	0.687633	+	1.19102i	−0.284969	+	0.958537i	$0.591983\pi$
$410$	−25.2079	+	5.35810i	−1.24493	+	0.264618i
$411$	−1.19476	−	3.67710i	−0.0589332	−	0.181378i
$412$	4.57735	+	0.972946i	0.225510	+	0.0479336i
$413$	−0.955642	−	9.09233i	−0.0470241	−	0.447404i
$414$	−1.30524	−	1.44961i	−0.0641490	−	0.0712447i
$415$	−1.78498	−	0.794726i	−0.0876214	−	0.0390116i
$416$	4.27222	−	1.90211i	0.209463	−	0.0932588i
$417$	−23.6149	+	26.2271i	−1.15643	+	1.28434i
$418$	−10.6202	−	7.71603i	−0.519451	−	0.377403i
$419$	−21.2657	−	15.4505i	−1.03890	−	0.754804i	−0.0688289	−	0.997628i	$-0.521926\pi$
$419$	−21.2657	−	15.4505i	−1.03890	−	0.754804i	−0.970070	+	0.242824i	$0.921926\pi$
$420$	−2.18954	+	2.43173i	−0.106839	+	0.118656i
$421$	11.1903	−	4.98223i	0.545380	−	0.242819i	−0.115504	−	0.993307i	$-0.536848\pi$
$421$	11.1903	−	4.98223i	0.545380	−	0.242819i	0.660884	+	0.750488i	$0.270182\pi$
$422$	21.8604	+	9.73287i	1.06415	+	0.473788i
$423$	−1.18264	−	1.31345i	−0.0575017	−	0.0638621i
$424$	−0.170876	−	1.62577i	−0.00829845	−	0.0789545i
$425$	−5.76936	−	1.22631i	−0.279855	−	0.0594850i
$426$	−2.61882	−	8.05991i	−0.126882	−	0.390504i
$427$	8.53753	−	1.81471i	0.413160	−	0.0878199i
$428$	−2.75493	−	4.77168i	−0.133165	−	0.230648i
$429$	7.89025	−	13.6663i	0.380945	−	0.659816i
$430$	−3.06435	+	9.43111i	−0.147776	+	0.454808i
$431$	−4.03209	+	38.3628i	−0.194219	+	1.84787i	0.270883	+	0.962612i	$0.412684\pi$
$431$	−4.03209	+	38.3628i	−0.194219	+	1.84787i	−0.465102	+	0.885257i	$0.653982\pi$
$432$	4.42705	−	3.21644i	0.212997	−	0.154751i
$433$	−34.3573			−1.65110			−0.825552	−	0.564326i	$-0.809136\pi$
$433$	−34.3573			−1.65110			−0.825552	+	0.564326i	$0.809136\pi$
$434$	1.81214	+	4.23351i	0.0869856	+	0.203215i
$435$	26.2775			1.25991
$436$	−5.85239	+	4.25201i	−0.280279	+	0.203634i
$437$	3.36011	−	31.9693i	0.160736	−	1.52930i
$438$	−0.736556	+	2.26689i	−0.0351940	+	0.108316i
$439$	5.60715	−	9.71187i	0.267615	−	0.463522i	−0.700631	−	0.713524i	$-0.747098\pi$
$439$	5.60715	−	9.71187i	0.267615	−	0.463522i	0.968245	+	0.250002i	$0.0804312\pi$
$440$	2.54965	+	4.41613i	0.121550	+	0.210531i
$441$	−2.35975	+	0.501580i	−0.112369	+	0.0238848i
$442$	8.70978	+	26.8060i	0.414282	+	1.27503i
$443$	19.0315	+	4.04527i	0.904215	+	0.192197i	0.636478	−	0.771295i	$-0.280391\pi$
$443$	19.0315	+	4.04527i	0.904215	+	0.192197i	0.267737	+	0.963492i	$0.413724\pi$
$444$	0.670676	+	6.38106i	0.0318289	+	0.302831i
$445$	−5.25036	−	5.83112i	−0.248891	−	0.276422i
$446$	14.8362	+	6.60549i	0.702513	+	0.312779i
$447$	−0.645045	+	0.287193i	−0.0305096	+	0.0135837i
$448$	−0.553432	+	0.614648i	−0.0261472	+	0.0290394i
$449$	6.43083	+	4.67227i	0.303490	+	0.220498i	0.729098	−	0.684409i	$-0.239940\pi$
$449$	6.43083	+	4.67227i	0.303490	+	0.220498i	−0.425608	+	0.904907i	$0.639940\pi$
$450$	0.302415	+	0.219717i	0.0142560	+	0.0103576i
$451$	−14.7079	+	16.3348i	−0.692570	+	0.769177i
$452$	−15.5351	+	6.91669i	−0.730711	+	0.325334i
$453$	−14.2276	−	6.33452i	−0.668469	−	0.297622i
$454$	1.18707	+	1.31837i	0.0557119	+	0.0618743i
$455$	0.988580	+	9.40571i	0.0463454	+	0.440947i
$456$	9.96224	+	2.11754i	0.466525	+	0.0991629i
$457$	4.58771	+	14.1195i	0.214604	+	0.660483i	0.999181	+	0.0404525i	$0.0128800\pi$
$457$	4.58771	+	14.1195i	0.214604	+	0.660483i	−0.784577	+	0.620031i	$0.787120\pi$
$458$	4.12530	−	0.876860i	0.192763	−	0.0409730i
$459$	16.4903	+	28.5621i	0.769702	+	1.33316i
$460$	−6.24346	+	10.8140i	−0.291103	+	0.504205i
$461$	1.31891	−	4.05919i	0.0614277	−	0.189055i	−0.915633	−	0.402014i	$-0.868310\pi$
$461$	1.31891	−	4.05919i	0.0614277	−	0.189055i	0.977061	+	0.212959i	$0.0683102\pi$
$462$	−0.291733	+	2.77565i	−0.0135726	+	0.129135i
$463$	27.9284	−	20.2912i	1.29794	−	0.943011i	0.298011	−	0.954563i	$-0.403677\pi$
$463$	27.9284	−	20.2912i	1.29794	−	0.943011i	0.999933	+	0.0115511i	$0.00367690\pi$
$464$	6.64195			0.308345
$465$	−19.2335	+	10.7374i	−0.891932	+	0.497937i
$466$	−18.0012			−0.833892
$467$	19.2172	−	13.9621i	0.889265	−	0.646089i	−0.0464214	−	0.998922i	$-0.514782\pi$
$467$	19.2172	−	13.9621i	0.889265	−	0.646089i	0.935686	+	0.352833i	$0.114782\pi$
$468$	0.186716	−	1.77649i	0.00863097	−	0.0821182i
$469$	0.0496534	−	0.152817i	0.00229278	−	0.00705645i
$470$	−5.65701	+	9.79822i	−0.260938	+	0.451958i
$471$	−11.7585	−	20.3664i	−0.541805	−	0.938434i
$472$	10.8121	−	2.29819i	0.497669	−	0.105783i
$473$	2.61365	+	8.04399i	0.120176	+	0.369863i
$474$	19.7244	+	4.19254i	0.905970	+	0.192570i
$475$	0.643904	+	6.12633i	0.0295443	+	0.281095i
$476$	−3.33554	−	3.70449i	−0.152884	−	0.169795i
$477$	−0.570427	−	0.253971i	−0.0261181	−	0.0116285i
$478$	2.94074	−	1.30930i	0.134506	−	0.0598861i
$479$	−0.585313	+	0.650056i	−0.0267436	+	0.0297018i	−0.756368	−	0.654146i	$-0.773028\pi$
$479$	−0.585313	+	0.650056i	−0.0267436	+	0.0297018i	0.729625	+	0.683848i	$0.239695\pi$
$480$	−3.20071	−	2.32545i	−0.146092	−	0.106142i
$481$	15.0028	+	10.9001i	0.684067	+	0.497004i
$482$	9.94628	−	11.0465i	0.453041	−	0.503153i
$483$	−6.24346	+	2.77977i	−0.284087	+	0.126484i
$484$	−6.07571	−	2.70508i	−0.276169	−	0.122958i
$485$	−21.0841	−	23.4163i	−0.957381	−	1.06328i
$486$	−0.412289	−	3.92266i	−0.0187018	−	0.177936i
$487$	−29.0069	−	6.16560i	−1.31443	−	0.279390i	−0.503225	−	0.864156i	$-0.667853\pi$
$487$	−29.0069	−	6.16560i	−1.31443	−	0.279390i	−0.811202	+	0.584766i	$0.801187\pi$
$488$	3.26105	+	10.0365i	0.147621	+	0.454329i
$489$	−18.2631	+	3.88194i	−0.825885	+	0.175547i
$490$	7.72161	+	13.3742i	0.348827	+	0.604186i
$491$	0.0640119	−	0.110872i	0.00288882	−	0.00500358i	−0.864577	−	0.502500i	$-0.832414\pi$
$491$	0.0640119	−	0.110872i	0.00288882	−	0.00500358i	0.867466	+	0.497496i	$0.165747\pi$
$492$	5.26988	−	16.2190i	0.237585	−	0.731210i
$493$	−4.18439	+	39.8118i	−0.188456	+	1.79304i
$494$	23.8147	−	17.3024i	1.07148	−	0.778473i
$495$	1.94776			0.0875454
$496$	−4.86149	+	2.71402i	−0.218288	+	0.121863i
$497$	4.33201			0.194317
$498$	1.04604	−	0.759993i	0.0468742	−	0.0340561i
$499$	−2.00884	+	19.1128i	−0.0899280	+	0.855608i	0.852843	+	0.522167i	$0.174876\pi$
$499$	−2.00884	+	19.1128i	−0.0899280	+	0.855608i	−0.942771	+	0.333441i	$0.891790\pi$
$500$	−3.03848	+	9.35149i	−0.135885	+	0.418211i
$501$	−12.6973	+	21.9923i	−0.567272	+	0.982543i
$502$	2.80494	+	4.85829i	0.125190	+	0.216836i
$503$	−6.96665	+	1.48081i	−0.310628	+	0.0660260i	−0.360588	−	0.932725i	$-0.617424\pi$
$503$	−6.96665	+	1.48081i	−0.310628	+	0.0660260i	0.0499601	+	0.998751i	$0.484091\pi$
$504$	0.0976248	+	0.300458i	0.00434856	+	0.0133835i
$505$	−10.1667	−	2.16101i	−0.452414	−	0.0961635i
$506$	1.11327	+	10.5920i	0.0494907	+	0.470873i
$507$	9.60319	+	10.6654i	0.426493	+	0.473668i
$508$	−0.891693	−	0.397007i	−0.0395625	−	0.0176144i
$509$	−33.7080	+	15.0077i	−1.49408	+	0.665207i	−0.981154	−	0.193227i	$-0.938105\pi$
$509$	−33.7080	+	15.0077i	−1.49408	+	0.665207i	−0.512925	+	0.858434i	$0.671438\pi$
$510$	15.9552	−	17.7200i	0.706507	−	0.784656i
$511$	−0.985705	−	0.716156i	−0.0436050	−	0.0316809i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	23.0480	−	25.5974i	1.01759	−	1.13015i
$514$	−16.0624	+	7.15144i	−0.708482	+	0.315437i
$515$	−10.4530	−	4.65398i	−0.460614	−	0.205079i
$516$	−4.39090	−	4.87659i	−0.193299	−	0.214680i
$517$	1.00870	+	9.59710i	0.0443624	+	0.422080i
$518$	−3.20810	−	0.681903i	−0.140956	−	0.0299611i
$519$	−9.97729	−	30.7070i	−0.437955	−	1.34789i
$520$	−11.1848	+	2.37740i	−0.490486	+	0.104256i
$521$	0.407432	+	0.705692i	0.0178499	+	0.0309169i	0.874812	−	0.484462i	$-0.160985\pi$
$521$	0.407432	+	0.705692i	0.0178499	+	0.0309169i	−0.856962	+	0.515379i	$0.827651\pi$
$522$	1.26850	−	2.19711i	0.0555208	−	0.0961648i
$523$	8.33412	−	25.6498i	0.364426	−	1.12159i	−0.585914	−	0.810373i	$-0.699265\pi$
$523$	8.33412	−	25.6498i	0.364426	−	1.12159i	0.950340	−	0.311214i	$-0.100735\pi$
$524$	0.662206	−	6.30047i	0.0289286	−	0.275237i
$525$	1.05955	−	0.769805i	0.0462424	−	0.0335970i
$526$	−7.71865			−0.336549
$527$	−13.2051	−	30.8496i	−0.575222	−	1.34383i
$528$	−3.37441			−0.146852
$529$	−2.49182	+	1.81041i	−0.108340	+	0.0787136i
$530$	−0.417812	+	3.97522i	−0.0181486	+	0.172672i
$531$	1.30471	−	4.01549i	0.0566196	−	0.174257i
$532$	−2.60309	+	4.50868i	−0.112858	+	0.195476i
$533$	−24.6447	−	42.6859i	−1.06748	−	1.84893i
$534$	5.07890	−	1.07955i	0.219785	−	0.0467168i
$535$	4.16317	+	12.8129i	0.179990	+	0.553951i
$536$	0.190028	+	0.0403917i	0.00820796	+	0.00174466i
$537$	0.371284	+	3.53253i	0.0160221	+	0.152440i
$538$	2.83383	+	3.14729i	0.122175	+	0.135689i
$539$	12.0331	+	5.35747i	0.518302	+	0.230763i
$540$	−12.2233	+	5.44216i	−0.526007	+	0.234193i
$541$	7.46070	−	8.28595i	0.320760	−	0.356241i	−0.561103	−	0.827746i	$-0.689623\pi$
$541$	7.46070	−	8.28595i	0.320760	−	0.356241i	0.881863	+	0.471506i	$0.156289\pi$
$542$	15.6475	+	11.3686i	0.672119	+	0.488323i
$543$	8.57416	+	6.22949i	0.367953	+	0.267333i
$544$	4.03286	−	4.47894i	0.172907	−	0.192033i
$545$	16.1587	−	7.19433i	0.692163	−	0.308171i
$546$	−5.71734	−	2.54552i	−0.244680	−	0.108938i
$547$	−1.56292	−	1.73580i	−0.0668256	−	0.0742174i	0.708805	−	0.705405i	$-0.249235\pi$
$547$	−1.56292	−	1.73580i	−0.0668256	−	0.0742174i	−0.775631	+	0.631187i	$0.782568\pi$
$548$	0.249773	+	2.37643i	0.0106698	+	0.101516i
$549$	3.94279	+	0.838066i	0.168274	+	0.0357678i
$550$	−0.630687	−	1.94105i	−0.0268926	−	0.0827668i
$551$	40.8945	−	8.69240i	1.74217	−	0.370309i
$552$	−4.13154	−	7.15604i	−0.175850	−	0.304581i
$553$	−5.15388	+	8.92678i	−0.219165	+	0.379605i
$554$	−2.70120	+	8.31343i	−0.114763	+	0.353204i
$555$	1.63989	−	15.6025i	0.0696093	−	0.662288i
$556$	17.6460	−	12.8206i	0.748357	−	0.543713i
$557$	28.7268			1.21719			0.608596	−	0.793480i	$-0.291733\pi$
$557$	28.7268			1.21719			0.608596	+	0.793480i	$0.291733\pi$
$558$	−0.0306875	+	2.12648i	−0.00129910	+	0.0900209i
$559$	−18.9661			−0.802181
$560$	1.63611	−	1.18870i	0.0691382	−	0.0502318i
$561$	2.12586	−	20.2262i	0.0897538	−	0.853950i
$562$	7.61816	−	23.4463i	0.321353	−	0.989022i
$563$	15.5510	−	26.9352i	0.655398	−	1.13518i	−0.326396	−	0.945233i	$-0.605834\pi$
$563$	15.5510	−	26.9352i	0.655398	−	1.13518i	0.981794	−	0.189949i	$-0.0608324\pi$
$564$	−3.74346	−	6.48386i	−0.157628	−	0.273020i
$565$	40.6715	−	8.64499i	1.71106	−	0.363698i
$566$	−6.82585	−	21.0078i	−0.286912	−	0.883024i
$567$	−6.23607	−	1.32552i	−0.261890	−	0.0556665i
$568$	0.547483	+	5.20896i	0.0229719	+	0.218563i
$569$	−2.17837	−	2.41932i	−0.0913220	−	0.101423i	0.695752	−	0.718283i	$-0.255071\pi$
$569$	−2.17837	−	2.41932i	−0.0913220	−	0.101423i	−0.787074	+	0.616859i	$0.788405\pi$
$570$	−22.7501	−	10.1290i	−0.952898	−	0.424258i
$571$	29.6242	−	13.1895i	1.23973	−	0.551965i	0.321089	−	0.947049i	$-0.395951\pi$
$571$	29.6242	−	13.1895i	1.23973	−	0.551965i	0.918645	+	0.395084i	$0.129284\pi$
$572$	−6.52595	+	7.24781i	−0.272864	+	0.303046i
$573$	−26.1070	−	18.9678i	−1.09063	−	0.792392i
$574$	7.05248	+	5.12392i	0.294365	+	0.213868i
$575$	3.34415	−	3.71406i	0.139461	−	0.154887i
$576$	−0.348943	+	0.155360i	−0.0145393	+	0.00647332i
$577$	28.1629	+	12.5389i	1.17244	+	0.522003i	0.898169	−	0.439650i	$-0.144898\pi$
$577$	28.1629	+	12.5389i	1.17244	+	0.522003i	0.274268	+	0.961653i	$0.411564\pi$
$578$	12.9309	+	14.3612i	0.537853	+	0.597346i
$579$	2.01903	+	19.2098i	0.0839080	+	0.798331i
$580$	−15.8855	−	3.37657i	−0.659610	−	0.140204i
$581$	0.204239	+	0.628583i	0.00847326	+	0.0260780i
$582$	20.3956	−	4.33521i	0.845423	−	0.179700i
$583$	1.70461	+	2.95247i	0.0705978	+	0.122279i
$584$	0.736556	−	1.27575i	0.0304789	−	0.0527910i
$585$	−1.34968	+	4.15389i	−0.0558024	+	0.171742i
$586$	−1.40021	+	13.3221i	−0.0578419	+	0.550329i
$587$	−19.5529	+	14.2060i	−0.807036	+	0.586346i	−0.912970	−	0.408027i	$-0.866217\pi$
$587$	−19.5529	+	14.2060i	−0.807036	+	0.586346i	0.105934	+	0.994373i	$0.466217\pi$
$588$	−10.2194			−0.421440
$589$	−26.3804	+	23.0725i	−1.08698	+	0.950686i
$590$	−27.0277			−1.11271
$591$	−16.7213	+	12.1487i	−0.687821	+	0.499732i
$592$	0.414501	−	3.94371i	0.0170359	−	0.162085i
$593$	6.83706	−	21.0423i	0.280764	−	0.864104i	−0.706872	−	0.707341i	$-0.749894\pi$
$593$	6.83706	−	21.0423i	0.280764	−	0.864104i	0.987636	−	0.156762i	$-0.0501056\pi$
$594$	−5.70607	+	9.88320i	−0.234123	+	0.405513i
$595$	6.09433	+	10.5557i	0.249843	+	0.432741i
$596$	0.426851	−	0.0907300i	0.0174845	−	0.00371645i
$597$	8.84013	+	27.2071i	0.361802	+	1.11351i
$598$	−23.3605	−	4.96542i	−0.955281	−	0.203051i
$599$	2.74224	+	26.0907i	0.112045	+	1.06604i	0.895644	+	0.444771i	$0.146715\pi$
$599$	2.74224	+	26.0907i	0.112045	+	1.06604i	−0.783599	+	0.621267i	$0.786618\pi$
$600$	1.05955	+	1.17674i	0.0432558	+	0.0480404i
$601$	4.79541	+	2.13505i	0.195609	+	0.0870907i	0.502203	−	0.864750i	$-0.332523\pi$
$601$	4.79541	+	2.13505i	0.195609	+	0.0870907i	−0.306595	+	0.951840i	$0.599190\pi$
$602$	3.06435	−	1.36434i	0.124894	−	0.0556063i
$603$	0.0496534	−	0.0551457i	0.00202204	−	0.00224570i
$604$	7.78700	+	5.65759i	0.316849	+	0.230204i
$605$	13.1561	+	9.55843i	0.534870	+	0.388605i
$606$	4.60230	−	5.11137i	0.186955	−	0.207635i
$607$	−35.2905	+	15.7123i	−1.43240	+	0.637744i	−0.968696	−	0.248248i	$-0.920145\pi$
$607$	−35.2905	+	15.7123i	−1.43240	+	0.637744i	−0.463700	+	0.885992i	$0.653479\pi$
$608$	−5.75036	−	2.56023i	−0.233208	−	0.103831i
$609$	−5.94768	−	6.60557i	−0.241012	−	0.267671i
$610$	−2.69718	−	25.6620i	−0.109206	−	1.03902i
$611$	−21.1662	−	4.49902i	−0.856293	−	0.182011i
$612$	−0.711392	−	2.18944i	−0.0287563	−	0.0885029i
$613$	−33.2212	+	7.06138i	−1.34179	+	0.285206i	−0.822195	−	0.569206i	$-0.807251\pi$
$613$	−33.2212	+	7.06138i	−1.34179	+	0.285206i	−0.519596	+	0.854412i	$0.673917\pi$
$614$	0.728876	+	1.26245i	0.0294150	+	0.0509483i
$615$	−20.8492	+	36.1119i	−0.840721	+	1.45617i
$616$	0.533023	−	1.64048i	0.0214761	−	0.0660966i
$617$	−1.43314	+	13.6354i	−0.0576959	+	0.548940i	0.927050	+	0.374939i	$0.122336\pi$
$617$	−1.43314	+	13.6354i	−0.0576959	+	0.548940i	−0.984745	+	0.174001i	$0.944330\pi$
$618$	6.12569	−	4.45058i	0.246412	−	0.179028i
$619$	23.6453			0.950385			0.475192	−	0.879882i	$-0.342379\pi$
$619$	23.6453			0.950385			0.475192	+	0.879882i	$0.342379\pi$
$620$	13.0069	−	4.01965i	0.522371	−	0.161433i
$621$	−27.9455			−1.12141
$622$	−13.5663	+	9.85648i	−0.543958	+	0.395209i
$623$	−0.277438	+	2.63964i	−0.0111153	+	0.105755i
$624$	2.33826	−	7.19643i	0.0936054	−	0.288088i
$625$	14.4677	−	25.0588i	0.578709	−	1.00235i
$626$	0.767847	+	1.32995i	0.0306893	+	0.0531555i
$627$	−20.7763	+	4.41613i	−0.829724	+	0.176363i
$628$	4.49136	+	13.8230i	0.179225	+	0.551598i
$629$	23.3774	+	4.96903i	0.932119	+	0.198128i
$630$	−0.0807446	−	0.768234i	−0.00321694	−	0.0306072i
$631$	5.20071	+	5.77597i	0.207037	+	0.229938i	0.837716	−	0.546106i	$-0.183890\pi$
$631$	5.20071	+	5.77597i	0.207037	+	0.229938i	−0.630679	+	0.776044i	$0.717224\pi$
$632$	−11.3852	−	5.06902i	−0.452880	−	0.201635i
$633$	35.3708	−	15.7481i	1.40586	−	0.625931i
$634$	−4.59214	+	5.10008i	−0.182377	+	0.202550i
$635$	1.93083	+	1.40283i	0.0766226	+	0.0556696i
$636$	−2.13989	−	1.55472i	−0.0848520	−	0.0616486i
$637$	−19.7638	+	21.9499i	−0.783070	+	0.869688i
$638$	−12.6542	+	5.63403i	−0.500986	+	0.223053i
$639$	1.82764	+	0.813719i	0.0723004	+	0.0321902i
$640$	1.63611	+	1.81708i	0.0646728	+	0.0718265i
$641$	2.07826	+	19.7733i	0.0820863	+	0.780999i	0.955693	+	0.294366i	$0.0951085\pi$
$641$	2.07826	+	19.7733i	0.0820863	+	0.780999i	−0.873606	+	0.486633i	$0.838225\pi$
$642$	−8.72033	−	1.85356i	−0.344164	−	0.0731543i
$643$	13.9998	+	43.0868i	0.552097	+	1.69918i	0.703490	+	0.710705i	$0.251624\pi$
$643$	13.9998	+	43.0868i	0.552097	+	1.69918i	−0.151394	+	0.988474i	$0.548376\pi$
$644$	4.13154	−	0.878186i	0.162805	−	0.0346054i
$645$	8.02258	+	13.8955i	0.315889	+	0.547135i
$646$	18.9687	−	32.8547i	0.746313	−	1.29265i
$647$	3.60016	−	11.0802i	0.141537	−	0.435606i	−0.855013	−	0.518607i	$-0.826451\pi$
$647$	3.60016	−	11.0802i	0.141537	−	0.435606i	0.996549	+	0.0830016i	$0.0264507\pi$
$648$	0.805727	−	7.66598i	0.0316519	−	0.301148i
$649$	−18.6498	+	13.5499i	−0.732070	+	0.531880i
$650$	4.57661			0.179510
$651$	7.05248	+	2.40454i	0.276408	+	0.0942413i
$652$	11.5394			0.451916
$653$	8.18018	−	5.94325i	0.320115	−	0.232577i	−0.416109	−	0.909315i	$-0.636607\pi$
$653$	8.18018	−	5.94325i	0.320115	−	0.232577i	0.736225	+	0.676737i	$0.236607\pi$
$654$	−1.22348	+	11.6407i	−0.0478420	+	0.455186i
$655$	−4.78676	+	14.7321i	−0.187034	+	0.575632i
$656$	−5.26988	+	9.12770i	−0.205754	+	0.356377i
$657$	−0.281339	−	0.487294i	−0.0109761	−	0.0190112i
$658$	3.74346	−	0.795697i	0.145935	−	0.0310195i
$659$	−9.96984	−	30.6840i	−0.388370	−	1.19528i	−0.934006	−	0.357257i	$-0.883712\pi$
$659$	−9.96984	−	30.6840i	−0.388370	−	1.19528i	0.545636	−	0.838022i	$-0.316288\pi$
$660$	8.07055	+	1.71545i	0.314146	+	0.0667737i
$661$	2.61378	+	24.8685i	0.101664	+	0.967271i	0.919838	+	0.392299i	$0.128320\pi$
$661$	2.61378	+	24.8685i	0.101664	+	0.967271i	−0.818173	+	0.574972i	$0.805013\pi$
$662$	6.01377	+	6.67897i	0.233732	+	0.259586i
$663$	41.6623	+	18.5492i	1.61803	+	0.720393i
$664$	−0.730017	+	0.325025i	−0.0283302	+	0.0126134i
$665$	8.51786	−	9.46004i	0.330308	−	0.366845i
$666$	−1.22539	−	0.890295i	−0.0474827	−	0.0344982i
$667$	−27.4415	−	19.9374i	−1.06254	−	0.771980i
$668$	10.5018	−	11.6634i	0.406326	−	0.451271i
$669$	24.0054	−	10.6879i	0.928103	−	0.413218i
$670$	−0.433955	−	0.193209i	−0.0167651	−	0.00746432i
$671$	−14.7264	−	16.3553i	−0.568505	−	0.631389i
$672$	0.139886	+	1.33093i	0.00539623	+	0.0513417i
$673$	23.0462	+	4.89862i	0.888365	+	0.188828i	0.629421	−	0.777065i	$-0.283292\pi$
$673$	23.0462	+	4.89862i	0.888365	+	0.188828i	0.258944	+	0.965892i	$0.416626\pi$
$674$	2.94249	+	9.05605i	0.113340	+	0.348826i
$675$	5.23820	−	1.11341i	0.201619	−	0.0428553i
$676$	−4.43493	−	7.68153i	−0.170574	−	0.295443i
$677$	16.1449	−	27.9638i	0.620499	−	1.07474i	−0.368894	−	0.929471i	$-0.620263\pi$
$677$	16.1449	−	27.9638i	0.620499	−	1.07474i	0.989393	−	0.145264i	$-0.0464032\pi$
$678$	−8.50266	+	26.1685i	−0.326543	+	1.00499i
$679$	−1.11412	+	10.6001i	−0.0427560	+	0.406796i
$680$	−11.9223	+	8.66207i	−0.457200	+	0.332175i
$681$	2.87047			0.109996
$682$	6.95995	−	9.29450i	0.266510	−	0.355905i
$683$	25.3278			0.969140			0.484570	−	0.874753i	$-0.338976\pi$
$683$	25.3278			0.969140			0.484570	+	0.874753i	$0.338976\pi$
$684$	−1.94512	+	1.41322i	−0.0743737	+	0.0540357i
$685$	0.610727	−	5.81068i	0.0233347	−	0.222014i
$686$	3.40335	−	10.4744i	0.129941	−	0.399916i
$687$	3.41200	−	5.90976i	0.130176	−	0.225471i
$688$	2.02780	+	3.51225i	0.0773092	+	0.133903i
$689$	−7.47778	+	1.58945i	−0.284881	+	0.0605533i
$690$	6.24346	+	19.2154i	0.237684	+	0.731518i
$691$	−8.52776	−	1.81263i	−0.324411	−	0.0689557i	0.0428274	−	0.999082i	$-0.486363\pi$
$691$	−8.52776	−	1.81263i	−0.324411	−	0.0689557i	−0.367239	+	0.930127i	$0.619697\pi$
$692$	2.08582	+	19.8453i	0.0792911	+	0.754404i
$693$	−0.440858	−	0.489623i	−0.0167468	−	0.0185992i
$694$	−18.9822	−	8.45141i	−0.720554	−	0.320811i
$695$	−48.7214	+	21.6922i	−1.84811	+	0.822831i
$696$	7.19109	−	7.98651i	0.272577	−	0.302728i
$697$	−51.3914	−	37.3380i	−1.94659	−	1.41428i
$698$	24.4649	+	17.7748i	0.926010	+	0.672786i
$699$	−19.4895	+	21.6453i	−0.737161	+	0.818701i
$700$	−0.739443	+	0.329221i	−0.0279483	+	0.0124434i
$701$	−6.82346	−	3.03800i	−0.257719	−	0.114744i	0.273811	−	0.961784i	$-0.411716\pi$
$701$	−6.82346	−	3.03800i	−0.257719	−	0.114744i	−0.531529	+	0.847040i	$0.678382\pi$
$702$	−17.1234	−	19.0175i	−0.646282	−	0.717769i
$703$	−2.60910	−	24.8239i	−0.0984040	−	0.936251i
$704$	2.03993	+	0.433600i	0.0768826	+	0.0163419i
$705$	5.65701	+	17.4105i	0.213055	+	0.655716i
$706$	9.00519	−	1.91411i	0.338915	−	0.0720386i
$707$	1.75792	+	3.04481i	0.0661134	+	0.114512i
$708$	8.94262	−	15.4891i	0.336084	−	0.582115i
$709$	15.9096	−	48.9647i	0.597497	−	1.83891i	0.0556156	−	0.998452i	$-0.482288\pi$
$709$	15.9096	−	48.9647i	0.597497	−	1.83891i	0.541882	−	0.840455i	$-0.317712\pi$
$710$	1.33866	−	12.7365i	0.0502392	−	0.477994i
$711$	−3.85118	+	2.79804i	−0.144430	+	0.104935i
$712$	−3.20906			−0.120264
$713$	28.2322	+	3.37988i	1.05730	+	0.126577i
$714$	−8.06572			−0.301852
$715$	19.2926	−	14.0169i	0.721504	−	0.524203i
$716$	0.229466	−	2.18322i	0.00857555	−	0.0815909i
$717$	1.60952	−	4.95360i	0.0601087	−	0.184996i
$718$	−8.07998	+	13.9949i	−0.301542	+	0.522286i
$719$	0.311539	+	0.539601i	0.0116184	+	0.0201237i	0.871776	−	0.489904i	$-0.162968\pi$
$719$	0.311539	+	0.539601i	0.0116184	+	0.0201237i	−0.860158	+	0.510028i	$0.829635\pi$
$720$	0.913545	−	0.194180i	0.0340458	−	0.00723666i
$721$	1.19604	+	3.68103i	0.0445428	+	0.137089i
$722$	−20.1708	−	4.28744i	−0.750680	−	0.159562i
$723$	−2.51404	−	23.9195i	−0.0934982	−	0.889575i
$724$	−4.38286	−	4.86766i	−0.162888	−	0.180905i
$725$	5.93810	+	2.64381i	0.220535	+	0.0981886i
$726$	−9.83070	+	4.37691i	−0.364852	+	0.162442i
$727$	−10.2432	+	11.3762i	−0.379898	+	0.421919i	−0.902522	−	0.430644i	$-0.858286\pi$
$727$	−10.2432	+	11.3762i	−0.379898	+	0.421919i	0.522624	+	0.852563i	$0.324953\pi$
$728$	3.12920	+	2.27350i	0.115976	+	0.0842615i
$729$	−23.8713	−	17.3435i	−0.884123	−	0.642353i
$730$	−2.41017	+	2.67677i	−0.0892044	+	0.0990715i
$731$	−22.3299	+	9.94193i	−0.825903	+	0.367715i
$732$	15.5988	+	6.94505i	0.576550	+	0.256696i
$733$	5.26711	+	5.84972i	0.194545	+	0.216064i	0.832523	−	0.553990i	$-0.186896\pi$
$733$	5.26711	+	5.84972i	0.194545	+	0.216064i	−0.637978	+	0.770055i	$0.720229\pi$
$734$	−0.185829	−	1.76804i	−0.00685907	−	0.0652597i
$735$	24.4416	+	5.19522i	0.901542	+	0.191629i
$736$	1.57811	+	4.85692i	0.0581698	+	0.179028i
$737$	−0.396303	+	0.0842368i	−0.0145980	+	0.00310290i
$738$	2.01292	+	3.48647i	0.0740964	+	0.128339i
$739$	13.8728	−	24.0284i	0.510319	−	0.883899i	−0.489609	−	0.871942i	$-0.662861\pi$
$739$	13.8728	−	24.0284i	0.510319	−	0.883899i	0.999929	−	0.0119571i	$-0.00380615\pi$
$740$	−2.99622	+	9.22142i	−0.110143	+	0.338986i
$741$	4.97864	−	47.3686i	0.182895	−	1.74013i
$742$	1.09385	−	0.794726i	0.0401564	−	0.0291753i
$743$	−13.1002			−0.480598			−0.240299	−	0.970699i	$-0.577246\pi$
$743$	−13.1002			−0.480598			−0.240299	+	0.970699i	$0.577246\pi$
$744$	−2.00000	+	8.78402i	−0.0733236	+	0.322038i
$745$	−1.06702			−0.0390927
$746$	15.5077	−	11.2670i	0.567775	−	0.412513i
$747$	−0.0319053	+	0.303558i	−0.00116735	+	0.0111066i
$748$	−3.88414	+	11.9541i	−0.142018	+	0.437087i
$749$	2.27858	−	3.94661i	0.0832575	−	0.144206i
$750$	7.95485	+	13.7782i	0.290470	+	0.503109i
$751$	30.9745	−	6.58383i	1.13027	−	0.240247i	0.395439	−	0.918492i	$-0.370593\pi$
$751$	30.9745	−	6.58383i	1.13027	−	0.240247i	0.734836	+	0.678245i	$0.237259\pi$
$752$	1.42987	+	4.40070i	0.0521422	+	0.160477i
$753$	8.87861	+	1.88721i	0.323555	+	0.0687737i
$754$	−3.24678	−	30.8911i	−0.118241	−	1.12499i
$755$	−15.7480	−	17.4899i	−0.573127	−	0.636522i
$756$	4.13466	+	1.84087i	0.150376	+	0.0669518i
$757$	−2.54984	+	1.13526i	−0.0926755	+	0.0412618i	−0.452551	−	0.891739i	$-0.649486\pi$
$757$	−2.54984	+	1.13526i	−0.0926755	+	0.0412618i	0.359875	+	0.933000i	$0.382819\pi$
$758$	17.0887	−	18.9790i	0.620691	−	0.689347i
$759$	13.9415	+	10.1291i	0.506045	+	0.367663i
$760$	12.4516	+	9.04659i	0.451666	+	0.328154i
$761$	−27.4310	+	30.4652i	−0.994372	+	1.10436i	0.000167484		1.00000i	$0.499947\pi$
$761$	−27.4310	+	30.4652i	−0.994372	+	1.10436i	−0.994539	+	0.104362i	$0.966720\pi$
$762$	−1.44279	+	0.642371i	−0.0522668	+	0.0232707i
$763$	−5.46587	−	2.43356i	−0.197878	−	0.0881008i
$764$	13.3451	+	14.8212i	0.482809	+	0.536214i
$765$	0.588386	+	5.59812i	0.0212731	+	0.202400i
$766$	2.77182	+	0.589168i	0.100150	+	0.0212875i
$767$	−15.9740	−	49.1628i	−0.576786	−	1.77517i
$768$	−1.58268	+	0.336408i	−0.0571099	+	0.0121391i
$769$	−21.2508	−	36.8074i	−0.766323	−	1.32731i	−0.939544	−	0.342427i	$-0.888751\pi$
$769$	−21.2508	−	36.8074i	−0.766323	−	1.32731i	0.173221	−	0.984883i	$-0.444582\pi$
$770$	−2.10880	+	3.65254i	−0.0759957	+	0.131628i
$771$	−8.79124	+	27.0567i	−0.316609	+	0.974422i
$772$	1.24783	−	11.8723i	0.0449103	−	0.427293i
$773$	−22.3969	+	16.2723i	−0.805560	+	0.585274i	−0.912540	−	0.408987i	$-0.865882\pi$
$773$	−22.3969	+	16.2723i	−0.805560	+	0.585274i	0.106980	+	0.994261i	$0.465882\pi$
$774$	1.54910			0.0556813
$775$	−5.42662	+	0.491303i	−0.194930	+	0.0176481i
$776$	−12.8868			−0.462608
$777$	−4.29328	+	3.11925i	−0.154021	+	0.111902i
$778$	−1.71578	+	16.3246i	−0.0615138	+	0.585264i
$779$	−20.5012	+	63.0961i	−0.734530	+	2.26065i
$780$	−9.25085	+	16.0229i	−0.331234	+	0.573713i
$781$	−5.46156	−	9.45969i	−0.195430	−	0.338494i
$782$	−30.1065	+	6.39934i	−1.07661	+	0.228840i
$783$	−11.2314	−	34.5668i	−0.401379	−	1.23532i
$784$	6.17790	+	1.31315i	0.220639	+	0.0468983i
$785$	−3.71477	−	35.3436i	−0.132586	−	1.26147i
$786$	−6.85894	−	7.61762i	−0.244650	−	0.271712i
$787$	10.7667	+	4.79365i	0.383792	+	0.170875i	0.589558	−	0.807726i	$-0.299302\pi$
$787$	10.7667	+	4.79365i	0.383792	+	0.170875i	−0.205766	+	0.978601i	$0.565969\pi$
$788$	11.6696	−	5.19562i	0.415711	−	0.185086i
$789$	−8.35679	+	9.28116i	−0.297510	+	0.330418i
$790$	24.6530	+	17.9115i	0.877114	+	0.637261i
$791$	−11.3788	−	8.26717i	−0.404583	−	0.293947i
$792$	0.533023	−	0.591982i	0.0189401	−	0.0210352i
$793$	45.0845	−	20.0729i	1.60100	−	0.712811i
$794$	−13.7939	−	6.14146i	−0.489529	−	0.217952i
$795$	4.32758	+	4.80626i	0.153483	+	0.170461i
$796$	−1.84809	−	17.5834i	−0.0655038	−	0.623227i
$797$	40.6090	+	8.63171i	1.43844	+	0.305751i	0.860135	−	0.510066i	$-0.170379\pi$
$797$	40.6090	+	8.63171i	1.43844	+	0.305751i	0.578310	+	0.815817i	$0.303713\pi$
$798$	2.60309	+	8.01147i	0.0921482	+	0.283603i
$799$	−27.2786	+	5.79824i	−0.965047	+	0.205127i
$800$	−0.489318	−	0.847523i	−0.0173000	−	0.0299645i
$801$	−0.612875	+	1.06153i	−0.0216549	+	0.0375074i
$802$	4.32981	−	13.3258i	0.152891	−	0.470550i
$803$	−0.321130	+	3.05535i	−0.0113324	+	0.107821i
$804$	0.254307	−	0.184765i	0.00896872	−	0.00651615i
$805$	−10.3278			−0.364008
$806$	14.9991	+	21.2836i	0.528320	+	0.749685i
$807$	6.85252			0.241220
$808$	−3.43901	+	2.49859i	−0.120984	+	0.0879000i
$809$	−3.22793	+	30.7117i	−0.113488	+	1.07977i	0.778480	+	0.627669i	$0.215991\pi$
$809$	−3.22793	+	30.7117i	−0.113488	+	1.07977i	−0.891968	+	0.452098i	$0.850676\pi$
$810$	−5.82420	+	17.9251i	−0.204642	+	0.629822i
$811$	14.7364	−	25.5242i	0.517465	−	0.896276i	−0.482329	−	0.875990i	$-0.660209\pi$
$811$	14.7364	−	25.5242i	0.517465	−	0.896276i	0.999794	−	0.0202858i	$-0.00645762\pi$
$812$	2.74675	+	4.75751i	0.0963920	+	0.166956i
$813$	30.6112	−	6.50661i	1.07358	−	0.228197i
$814$	2.55554	+	7.86515i	0.0895717	+	0.275673i
$815$	−27.5986	−	5.86627i	−0.966737	−	0.205486i
$816$	−1.01935	−	9.69849i	−0.0356845	−	0.339515i
$817$	17.0817	+	18.9712i	0.597613	+	0.663717i
$818$	−25.4085	−	11.3126i	−0.888386	−	0.395535i
$819$	1.34968	−	0.600917i	0.0471617	−	0.0209977i
$820$	17.2442	−	19.1516i	0.602193	−	0.668803i
$821$	17.4512	+	12.6791i	0.609052	+	0.442502i	0.849081	−	0.528263i	$-0.177157\pi$
$821$	17.4512	+	12.6791i	0.609052	+	0.442502i	−0.240028	+	0.970766i	$0.577157\pi$
$822$	3.12793	+	2.27257i	0.109099	+	0.0792650i
$823$	31.5977	−	35.0928i	1.10143	−	1.22326i	0.128606	−	0.991696i	$-0.458950\pi$
$823$	31.5977	−	35.0928i	1.10143	−	1.22326i	0.972820	−	0.231562i	$-0.0743835\pi$
$824$	−4.27504	+	1.90337i	−0.148928	+	0.0663070i
$825$	−3.01682	−	1.34317i	−0.105032	−	0.0467633i
$826$	6.11747	+	6.79413i	0.212854	+	0.236398i
$827$	−1.24362	−	11.8323i	−0.0432450	−	0.411449i	−0.994634	−	0.103457i	$-0.967010\pi$
$827$	−1.24362	−	11.8323i	−0.0432450	−	0.411449i	0.951389	−	0.307992i	$-0.0996570\pi$
$828$	1.90802	+	0.405563i	0.0663083	+	0.0140943i
$829$	13.5292	+	41.6385i	0.469887	+	1.44616i	0.852731	+	0.522350i	$0.174945\pi$
$829$	13.5292	+	41.6385i	0.469887	+	1.44616i	−0.382844	+	0.923813i	$0.625055\pi$
$830$	1.91121	−	0.406240i	0.0663391	−	0.0141008i
$831$	7.07183	+	12.2488i	0.245319	+	0.424905i
$832$	−2.33826	+	4.04999i	−0.0810646	+	0.140408i
$833$	−11.7631	+	36.2030i	−0.407567	+	1.25436i
$834$	3.68902	−	35.0987i	0.127740	−	1.21537i
$835$	−31.0464	+	22.5565i	−1.07440	+	0.780600i
$836$	13.1273			0.454017
$837$	22.3453	+	20.7114i	0.772366	+	0.715890i
$838$	26.2859			0.908031
$839$	−5.63256	+	4.09230i	−0.194458	+	0.141282i	−0.680754	−	0.732512i	$-0.738348\pi$
$839$	−5.63256	+	4.09230i	−0.194458	+	0.141282i	0.486296	+	0.873794i	$0.338348\pi$
$840$	0.342040	−	3.25429i	0.0118015	−	0.112284i
$841$	4.67096	−	14.3758i	0.161068	−	0.495716i
$842$	−6.12464	+	10.6082i	−0.211069	+	0.365582i
$843$	−19.9446	−	34.5451i	−0.686928	−	1.18979i
$844$	−23.4062	+	4.97515i	−0.805676	+	0.171252i
$845$	6.70194	+	20.6264i	0.230554	+	0.709571i
$846$	1.72880	+	0.367468i	0.0594374	+	0.0126338i
$847$	−0.574983	−	5.47059i	−0.0197566	−	0.187972i
$848$	1.09385	+	1.21484i	0.0375628	+	0.0417178i
$849$	−32.6507	−	14.5370i	−1.12057	−	0.498909i
$850$	5.38832	−	2.39903i	0.184818	−	0.0822862i
$851$	−13.5505	+	15.0494i	−0.464506	+	0.515886i
$852$	6.85617	+	4.98130i	0.234889	+	0.170656i
$853$	−10.6194	−	7.71548i	−0.363603	−	0.264173i	0.390950	−	0.920412i	$-0.372146\pi$
$853$	−10.6194	−	7.71548i	−0.363603	−	0.264173i	−0.754553	+	0.656239i	$0.772146\pi$
$854$	−5.84035	+	6.48636i	−0.199853	+	0.221959i
$855$	5.37058	−	2.39114i	0.183670	−	0.0817751i
$856$	5.03351	+	2.24106i	0.172042	+	0.0765980i
$857$	23.4304	+	26.0221i	0.800368	+	0.888899i	0.995775	−	0.0918230i	$-0.0292694\pi$
$857$	23.4304	+	26.0221i	0.800368	+	0.888899i	−0.195407	+	0.980722i	$0.562603\pi$
$858$	1.64951	+	15.6941i	0.0563134	+	0.535786i
$859$	−32.3587	−	6.87806i	−1.10407	−	0.234676i	−0.380396	−	0.924824i	$-0.624212\pi$
$859$	−32.3587	−	6.87806i	−1.10407	−	0.234676i	−0.723669	+	0.690147i	$0.757546\pi$
$860$	−3.06435	−	9.43111i	−0.104494	−	0.321598i
$861$	13.7967	−	2.93258i	0.470191	−	0.0999422i
$862$	−19.2870	−	33.4061i	−0.656919	−	1.13782i
$863$	−23.6328	+	40.9332i	−0.804470	+	1.39338i	0.112179	+	0.993688i	$0.464217\pi$
$863$	−23.6328	+	40.9332i	−0.804470	+	1.39338i	−0.916649	+	0.399694i	$0.869116\pi$
$864$	−1.69098	+	5.20431i	−0.0575284	+	0.177054i
$865$	5.10010	−	48.5242i	0.173408	−	1.64987i
$866$	27.7956	−	20.1947i	0.944533	−	0.686244i
$867$	31.2683			1.06193
$868$	−3.95445	−	2.35983i	−0.134223	−	0.0800979i
$869$	25.9909			0.881681
$870$	−21.2590	+	15.4455i	−0.720747	+	0.523653i
$871$	0.0949666	−	0.903546i	0.00321782	−	0.0306155i
$872$	2.23541	−	6.87990i	0.0757007	−	0.232983i
$873$	−2.46115	+	4.26284i	−0.0832974	+	0.144275i
$874$	16.0727	+	27.8388i	0.543668	+	0.941660i
$875$	−7.95485	+	1.69086i	−0.268923	+	0.0571614i
$876$	−0.736556	−	2.26689i	−0.0248859	−	0.0765910i
$877$	−51.0174	−	10.8441i	−1.72273	−	0.366179i	−0.762850	−	0.646575i	$-0.776201\pi$
$877$	−51.0174	−	10.8441i	−1.72273	−	0.366179i	−0.959884	+	0.280396i	$0.909534\pi$
$878$	1.17221	+	11.1529i	0.0395603	+	0.376391i
$879$	14.5029	+	16.1071i	0.489172	+	0.543280i
$880$	−4.65845	−	2.07407i	−0.157036	−	0.0699171i
$881$	37.5195	−	16.7048i	1.26407	−	0.562798i	0.338351	−	0.941020i	$-0.390131\pi$
$881$	37.5195	−	16.7048i	1.26407	−	0.562798i	0.925715	+	0.378222i	$0.123464\pi$
$882$	1.61426	−	1.79281i	0.0543548	−	0.0603671i
$883$	34.8746	+	25.3379i	1.17363	+	0.852689i	0.991438	−	0.130575i	$-0.0416825\pi$
$883$	34.8746	+	25.3379i	1.17363	+	0.852689i	0.182187	+	0.983264i	$0.441682\pi$
$884$	−22.8025	−	16.5670i	−0.766931	−	0.557208i
$885$	−29.2622	+	32.4990i	−0.983638	+	1.09244i
$886$	−17.7746	+	7.91375i	−0.597148	+	0.265868i
$887$	−15.5844	−	6.93864i	−0.523274	−	0.232977i	0.128062	−	0.991766i	$-0.459124\pi$
$887$	−15.5844	−	6.93864i	−0.523274	−	0.232977i	−0.651336	+	0.758789i	$0.725791\pi$
$888$	−4.29328	−	4.76817i	−0.144073	−	0.160009i
$889$	−0.0843865	−	0.802884i	−0.00283023	−	0.0269279i
$890$	7.67508	+	1.63139i	0.257269	+	0.0546843i
$891$	4.96759	+	15.2887i	0.166420	+	0.512190i
$892$	−15.8853	+	3.37653i	−0.531880	+	0.113055i
$893$	14.5630	+	25.2238i	0.487332	+	0.844084i
$894$	0.353045	−	0.611492i	0.0118076	−	0.0204513i
$895$	−1.65870	+	5.10495i	−0.0554442	+	0.170640i
$896$	0.0864545	−	0.822560i	0.00288824	−	0.0274798i
$897$	−31.2624	+	22.7135i	−1.04382	+	0.758381i
$898$	−7.94894			−0.265260
$899$	7.16599	+	36.2799i	0.238999	+	1.21000i
$900$	−0.373806			−0.0124602
$901$	−7.97086	+	5.79117i	−0.265548	+	0.192932i
$902$	2.29761	−	21.8603i	0.0765019	−	0.727867i
$903$	1.67718	−	5.16182i	0.0558129	−	0.171774i
$904$	8.50266	−	14.7270i	0.282794	−	0.489814i
$905$	8.00788	+	13.8701i	0.266191	+	0.461056i
$906$	15.2337	−	3.23802i	0.506105	−	0.107576i
$907$	−3.93702	−	12.1169i	−0.130726	−	0.402335i	0.864174	−	0.503192i	$-0.167841\pi$
$907$	−3.93702	−	12.1169i	−0.130726	−	0.402335i	−0.994901	+	0.100858i	$0.967841\pi$
$908$	−1.73528	−	0.368845i	−0.0575872	−	0.0122405i
$909$	0.169721	+	1.61479i	0.00562929	+	0.0535591i
$910$	−6.32832	−	7.02831i	−0.209782	−	0.232986i
$911$	−6.55040	−	2.91643i	−0.217025	−	0.0966256i	0.295345	−	0.955391i	$-0.404565\pi$
$911$	−6.55040	−	2.91643i	−0.217025	−	0.0966256i	−0.512369	+	0.858765i	$0.671232\pi$
$912$	−9.30428	+	4.14253i	−0.308096	+	0.137173i
$913$	1.11513	−	1.23847i	0.0369053	−	0.0409875i
$914$	−12.0108	−	8.72635i	−0.397281	−	0.288642i
$915$	−33.7770	−	24.5404i	−1.11663	−	0.811281i
$916$	−2.82203	+	3.13419i	−0.0932426	+	0.103556i
$917$	4.78676	−	2.13120i	0.158073	−	0.0703785i
$918$	−30.1293	−	13.4144i	−0.994415	−	0.442742i
$919$	22.0046	+	24.4386i	0.725864	+	0.806154i	0.987266	−	0.159076i	$-0.0508516\pi$
$919$	22.0046	+	24.4386i	0.725864	+	0.806154i	−0.261402	+	0.965230i	$0.584185\pi$
$920$	−1.30524	−	12.4185i	−0.0430324	−	0.409426i
$921$	2.30715	+	0.490400i	0.0760231	+	0.0161592i
$922$	1.31891	+	4.05919i	0.0434360	+	0.133682i
$923$	23.9587	−	5.09258i	0.788611	−	0.167624i
$924$	−1.39547	−	2.41703i	−0.0459076	−	0.0795144i
$925$	1.94036	−	3.36080i	0.0637985	−	0.110502i
$926$	−10.6677	+	32.8318i	−0.350563	+	1.07892i
$927$	−0.186840	+	1.77766i	−0.00613662	+	0.0583861i
$928$	−5.37345	+	3.90404i	−0.176392	+	0.128156i
$929$	13.1887			0.432709			0.216354	−	0.976315i	$-0.430583\pi$
$929$	13.1887			0.432709			0.216354	+	0.976315i	$0.430583\pi$
$930$	9.24892	−	19.9919i	0.303284	−	0.655562i
$931$	39.7559			1.30295
$932$	14.5633	−	10.5809i	0.477037	−	0.346588i
$933$	−2.83613	+	26.9839i	−0.0928506	+	0.883414i
$934$	−7.34031	+	22.5911i	−0.240182	+	0.739205i
$935$	15.3668	−	26.6161i	0.502548	−	0.870438i
$936$	0.893136	+	1.54696i	0.0291931	+	0.0505639i
$937$	35.2923	−	7.50161i	1.15295	−	0.245067i	0.408508	−	0.912755i	$-0.366049\pi$
$937$	35.2923	−	7.50161i	1.15295	−	0.245067i	0.744442	+	0.667688i	$0.232716\pi$
$938$	0.0496534	+	0.152817i	0.00162124	+	0.00498966i
$939$	2.43051	+	0.516620i	0.0793166	+	0.0168593i
$940$	−1.18264	−	11.2520i	−0.0385733	−	0.367001i
$941$	−4.17375	−	4.63542i	−0.136061	−	0.151111i	0.671264	−	0.741219i	$-0.265752\pi$
$941$	−4.17375	−	4.63542i	−0.136061	−	0.151111i	−0.807324	+	0.590108i	$0.799085\pi$
$942$	21.4839	+	9.56526i	0.699984	+	0.311653i
$943$	49.1717	−	21.8927i	1.60125	−	0.712923i
$944$	−7.39636	+	8.21449i	−0.240731	+	0.267359i
$945$	−8.95300	−	6.50474i	−0.291241	−	0.211599i
$946$	−6.84263	−	4.97146i	−0.222473	−	0.161636i
$947$	2.30840	−	2.56374i	0.0750130	−	0.0833104i	−0.704470	−	0.709734i	$-0.748815\pi$
$947$	2.30840	−	2.56374i	0.0750130	−	0.0833104i	0.779483	+	0.626423i	$0.215482\pi$
$948$	−18.4217	+	8.20185i	−0.598308	+	0.266384i
$949$	−6.29345	−	2.80203i	−0.204294	−	0.0909576i
$950$	−4.12190	−	4.57783i	−0.133732	−	0.148524i
$951$	1.16072	+	11.0435i	0.0376388	+	0.358109i
$952$	4.87595	+	1.03642i	0.158031	+	0.0335904i
$953$	−12.4740	−	38.3912i	−0.404074	−	1.24361i	−0.921666	−	0.387984i	$-0.873172\pi$
$953$	−12.4740	−	38.3912i	−0.404074	−	1.24361i	0.517592	−	0.855627i	$-0.326828\pi$
$954$	0.610766	−	0.129822i	0.0197743	−	0.00420315i
$955$	−24.3827	−	42.2321i	−0.789006	−	1.36660i
$956$	−1.60952	+	2.78777i	−0.0520557	+	0.0901630i
$957$	−6.92590	+	21.3157i	−0.223882	+	0.689039i
$958$	0.0914349	−	0.869945i	0.00295413	−	0.0281066i
$959$	−1.59890	+	1.16167i	−0.0516313	+	0.0375123i
$960$	3.95630			0.127689
$961$	−20.0696	−	23.6265i	−0.647408	−	0.762144i
$962$	−18.5444			−0.597896
$963$	1.70264	−	1.23704i	0.0548669	−	0.0398631i
$964$	−1.55376	+	14.7831i	−0.0500433	+	0.476130i
$965$	−9.01994	+	27.7605i	−0.290362	+	0.893643i
$966$	3.41716	−	5.91869i	0.109945	−	0.190431i
$967$	12.6277	+	21.8718i	0.406079	+	0.703349i	0.994446	−	0.105244i	$-0.0335625\pi$
$967$	12.6277	+	21.8718i	0.406079	+	0.703349i	−0.588368	+	0.808594i	$0.700229\pi$
$968$	6.50536	−	1.38276i	0.209090	−	0.0444435i
$969$	−18.9687	−	58.3796i	−0.609362	−	1.87542i
$970$	30.8212	+	6.55124i	0.989608	+	0.210348i
$971$	−2.69763	−	25.6662i	−0.0865711	−	0.823669i	−0.948529	−	0.316690i	$-0.897429\pi$
$971$	−2.69763	−	25.6662i	−0.0865711	−	0.823669i	0.861958	−	0.506979i	$-0.169238\pi$
$972$	2.63923	+	2.93117i	0.0846534	+	0.0940172i
$973$	16.4806	+	7.33762i	0.528342	+	0.235233i
$974$	27.0911	−	12.0617i	0.868055	−	0.386483i
$975$	4.95499	−	5.50307i	0.158687	−	0.176239i
$976$	−8.53753	−	6.20288i	−0.273280	−	0.198549i
$977$	−24.0467	−	17.4709i	−0.769321	−	0.558945i	0.132434	−	0.991192i	$-0.457721\pi$
$977$	−24.0467	−	17.4709i	−0.769321	−	0.558945i	−0.901755	+	0.432247i	$0.857721\pi$
$978$	12.4934	−	13.8753i	0.399495	−	0.443684i
$979$	6.11389	−	2.72208i	0.195401	−	0.0869980i
$980$	−14.1081	−	6.28132i	−0.450666	−	0.200649i
$981$	−1.84889	−	2.05340i	−0.0590306	−	0.0655601i
$982$	0.0133821	+	0.127322i	0.000427041	+	0.00406302i
$983$	31.0599	+	6.60199i	0.990657	+	0.210571i	0.674611	−	0.738173i	$-0.264311\pi$
$983$	31.0599	+	6.60199i	0.990657	+	0.210571i	0.316046	+	0.948744i	$0.397645\pi$
$984$	5.26988	+	16.2190i	0.167998	+	0.517044i
$985$	−30.5513	+	6.49388i	−0.973445	+	0.206912i
$986$	−20.0156	−	34.6680i	−0.637425	−	1.10405i
$987$	3.09618	−	5.36274i	0.0985525	−	0.170698i
$988$	−9.09642	+	27.9959i	−0.289396	+	0.890668i
$989$	2.16493	−	20.5979i	0.0688408	−	0.654977i
$990$	−1.57577	+	1.14487i	−0.0500813	+	0.0363862i
$991$	20.6284			0.655284			0.327642	−	0.944802i	$-0.393746\pi$
$991$	20.6284			0.655284			0.327642	+	0.944802i	$0.393746\pi$
$992$	2.33777	−	5.05320i	0.0742244	−	0.160439i
$993$	14.5420			0.461476
$994$	−3.50467	+	2.54629i	−0.111161	+	0.0807635i
$995$	−4.51881	+	42.9936i	−0.143256	+	1.36299i
$996$	−0.399552	+	1.22969i	−0.0126603	+	0.0389643i
$997$	−5.80623	+	10.0567i	−0.183885	+	0.318499i	−0.943200	−	0.332225i	$-0.892201\pi$
$997$	−5.80623	+	10.0567i	−0.183885	+	0.318499i	0.759315	+	0.650723i	$0.225534\pi$
$998$	−9.60906	−	16.6434i	−0.304169	−	0.526837i
$999$	−21.2252	+	4.51156i	−0.671536	+	0.142739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.2.g.a.59.1	yes	8
3.2	odd	2		558.2.ba.f.307.1		8
4.3	odd	2		496.2.bg.a.369.1		8
31.10	even	15	inner	62.2.g.a.41.1	✓	8
31.14	even	15		1922.2.a.q.1.4		4
31.17	odd	30		1922.2.a.o.1.2		4
93.41	odd	30		558.2.ba.f.289.1		8
124.103	odd	30		496.2.bg.a.289.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.2.g.a.41.1	✓	8	31.10	even	15	inner
62.2.g.a.59.1	yes	8	1.1	even	1	trivial
496.2.bg.a.289.1		8	124.103	odd	30
496.2.bg.a.369.1		8	4.3	odd	2
558.2.ba.f.289.1		8	93.41	odd	30
558.2.ba.f.307.1		8	3.2	odd	2
1922.2.a.o.1.2		4	31.17	odd	30
1922.2.a.q.1.4		4	31.14	even	15

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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	62.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.169131 + 1.60917i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.22256 + 2.11754i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.171962i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.373619 + 0.0794152i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.169131 + 1.60917i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-1.22256 + 2.11754i) q^{5} +(-0.809017 - 1.40126i) q^{6} +(0.809017 - 0.171962i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.373619 + 0.0794152i) q^{9} +(-0.255585 - 2.43173i) q^{10} +(-1.39547 - 1.54983i) q^{11} +(1.47815 + 0.658114i) q^{12} +(4.27222 - 1.90211i) q^{13} +(-0.553432 + 0.614648i) q^{14} +(-3.20071 - 2.32545i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(4.03286 - 4.47894i) q^{17} +(-0.348943 + 0.155360i) q^{18} +(-5.75036 - 2.56023i) q^{19} +(1.63611 + 1.81708i) q^{20} +(0.139886 + 1.33093i) q^{21} +(2.03993 + 0.433600i) q^{22} +(1.57811 + 4.85692i) q^{23} +(-1.58268 + 0.336408i) q^{24} +(-0.489318 - 0.847523i) q^{25} +(-2.33826 + 4.04999i) q^{26} +(-1.69098 + 5.20431i) q^{27} +(0.0864545 - 0.822560i) q^{28} +(-5.37345 + 3.90404i) q^{29} +3.95630 q^{30} +(2.33777 - 5.05320i) q^{31} +1.00000 q^{32} +(2.72995 - 1.98343i) q^{33} +(-0.629994 + 5.99399i) q^{34} +(-0.624938 + 1.92336i) q^{35} +(0.190983 - 0.330792i) q^{36} +(1.98272 + 3.43416i) q^{37} +(6.15701 - 1.30871i) q^{38} +(2.33826 + 7.19643i) q^{39} +(-2.39169 - 0.508370i) q^{40} +(-1.10171 - 10.4820i) q^{41} +(-0.895472 - 0.994522i) q^{42} +(-3.70498 - 1.64956i) q^{43} +(-1.90520 + 0.848249i) q^{44} +(-0.624938 + 0.694064i) q^{45} +(-4.13154 - 3.00174i) q^{46} +(-3.74346 - 2.71978i) q^{47} +(1.08268 - 1.20243i) q^{48} +(-5.76988 + 2.56892i) q^{49} +(0.894028 + 0.398047i) q^{50} +(6.52530 + 7.24708i) q^{51} +(-0.488830 - 4.65090i) q^{52} +(-1.59901 - 0.339879i) q^{53} +(-1.69098 - 5.20431i) q^{54} +(4.98787 - 1.06021i) q^{55} +(0.413545 + 0.716282i) q^{56} +(5.09240 - 8.82030i) q^{57} +(2.05248 - 6.31687i) q^{58} +(1.15543 - 10.9931i) q^{59} +(-3.20071 + 2.32545i) q^{60} +10.5530 q^{61} +(1.07890 + 5.46223i) q^{62} +0.315921 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-1.19525 + 11.3720i) q^{65} +(-1.04275 + 3.20925i) q^{66} +(0.0971366 - 0.168246i) q^{67} +(-3.01351 - 5.21954i) q^{68} +(-8.08251 + 1.71799i) q^{69} +(-0.624938 - 1.92336i) q^{70} +(5.12319 + 1.08897i) q^{71} +(0.0399263 + 0.379874i) q^{72} +(-0.985705 - 1.09474i) q^{73} +(-3.62260 - 1.61289i) q^{74} +(1.44657 - 0.644054i) q^{75} +(-4.21188 + 4.67777i) q^{76} +(-1.39547 - 1.01387i) q^{77} +(-6.12165 - 4.44764i) q^{78} +(-8.33915 + 9.26157i) q^{79} +(2.23373 - 0.994522i) q^{80} +(-7.04179 - 3.13521i) q^{81} +(7.05248 + 7.83257i) q^{82} +(0.0835291 + 0.794726i) q^{83} +(1.30902 + 0.278240i) q^{84} +(4.55392 + 14.0155i) q^{85} +(3.96698 - 0.843207i) q^{86} +(-5.37345 - 9.30710i) q^{87} +(1.04275 - 1.80610i) q^{88} +(-0.991653 + 3.05199i) q^{89} +(0.0976248 - 0.928838i) q^{90} +(3.12920 - 2.27350i) q^{91} +5.10686 q^{92} +(7.73607 + 4.61653i) q^{93} +4.62717 q^{94} +(12.4516 - 9.04659i) q^{95} +(-0.169131 + 1.60917i) q^{96} +(-3.98223 + 12.2560i) q^{97} +(3.15796 - 5.46975i) q^{98} +(-0.398295 - 0.689867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} + 3 q^{3} - 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} - 4 q^{9} - 4 q^{10} - 13 q^{11} + 3 q^{12} + 2 q^{14} - 6 q^{15} - 2 q^{16} - 2 q^{17} + q^{18} - 3 q^{19} - 4 q^{20} + q^{21} + 17 q^{22} + 3 q^{23} - 2 q^{24} + q^{25} - 10 q^{26} - 18 q^{27} + 7 q^{28} + 11 q^{29} + 14 q^{30} + 11 q^{31} + 8 q^{32} - 2 q^{33} + 18 q^{34} + 16 q^{35} + 6 q^{36} + 6 q^{37} + 12 q^{38} + 10 q^{39} - 4 q^{40} - 19 q^{41} - 9 q^{42} - 26 q^{43} + 7 q^{44} + 16 q^{45} - 17 q^{46} + q^{47} - 2 q^{48} - 23 q^{49} - 19 q^{50} - 16 q^{51} + 17 q^{53} - 18 q^{54} + 7 q^{55} - 3 q^{56} + 6 q^{57} - 19 q^{58} + 8 q^{59} - 6 q^{60} + 48 q^{61} - 19 q^{62} - 14 q^{63} - 2 q^{64} - 30 q^{65} + 3 q^{66} + 12 q^{67} - 17 q^{68} - 7 q^{69} + 16 q^{70} + 9 q^{71} + q^{72} - 33 q^{73} - 19 q^{74} + 18 q^{75} - 18 q^{76} - 13 q^{77} - 10 q^{78} - 19 q^{79} + 11 q^{80} - 16 q^{81} + 21 q^{82} + 40 q^{83} + 6 q^{84} + 29 q^{85} + 19 q^{86} + 11 q^{87} - 3 q^{88} + 8 q^{89} + 11 q^{90} + 20 q^{91} + 28 q^{92} + 44 q^{93} + 26 q^{94} + 36 q^{95} + 3 q^{96} - 23 q^{97} + 17 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 3 * q^3 - 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 - 4 * q^9 - 4 * q^10 - 13 * q^11 + 3 * q^12 + 2 * q^14 - 6 * q^15 - 2 * q^16 - 2 * q^17 + q^18 - 3 * q^19 - 4 * q^20 + q^21 + 17 * q^22 + 3 * q^23 - 2 * q^24 + q^25 - 10 * q^26 - 18 * q^27 + 7 * q^28 + 11 * q^29 + 14 * q^30 + 11 * q^31 + 8 * q^32 - 2 * q^33 + 18 * q^34 + 16 * q^35 + 6 * q^36 + 6 * q^37 + 12 * q^38 + 10 * q^39 - 4 * q^40 - 19 * q^41 - 9 * q^42 - 26 * q^43 + 7 * q^44 + 16 * q^45 - 17 * q^46 + q^47 - 2 * q^48 - 23 * q^49 - 19 * q^50 - 16 * q^51 + 17 * q^53 - 18 * q^54 + 7 * q^55 - 3 * q^56 + 6 * q^57 - 19 * q^58 + 8 * q^59 - 6 * q^60 + 48 * q^61 - 19 * q^62 - 14 * q^63 - 2 * q^64 - 30 * q^65 + 3 * q^66 + 12 * q^67 - 17 * q^68 - 7 * q^69 + 16 * q^70 + 9 * q^71 + q^72 - 33 * q^73 - 19 * q^74 + 18 * q^75 - 18 * q^76 - 13 * q^77 - 10 * q^78 - 19 * q^79 + 11 * q^80 - 16 * q^81 + 21 * q^82 + 40 * q^83 + 6 * q^84 + 29 * q^85 + 19 * q^86 + 11 * q^87 - 3 * q^88 + 8 * q^89 + 11 * q^90 + 20 * q^91 + 28 * q^92 + 44 * q^93 + 26 * q^94 + 36 * q^95 + 3 * q^96 - 23 * q^97 + 17 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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