LMFDB - Embedded newform 121.2.c.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(3,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("121.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.c (of order $5$, degree $4$, not 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:	$0.966189864457$
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			3.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	121.3
Dual form			121.2.c.b.81.1

$q$-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} +(0.618034 + 1.90211i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} -2.00000 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.04508 + 2.93893i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.85410 + 5.70634i) q^{19} +(0.809017 - 0.587785i) q^{20} -4.00000 q^{21} +2.00000 q^{23} +(4.85410 - 3.52671i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.309017 - 0.951057i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(2.78115 - 8.55951i) q^{29} +(0.618034 + 1.90211i) q^{30} +(1.61803 - 1.17557i) q^{31} +5.00000 q^{32} -5.00000 q^{34} +(1.61803 - 1.17557i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(-0.927051 + 2.85317i) q^{37} +(-4.85410 - 3.52671i) q^{38} +(-1.61803 - 1.17557i) q^{39} +(-0.927051 + 2.85317i) q^{40} +(-1.54508 - 4.75528i) q^{41} +(3.23607 - 2.35114i) q^{42} +1.00000 q^{45} +(-1.61803 + 1.17557i) q^{46} +(0.618034 + 1.90211i) q^{47} +(-0.618034 + 1.90211i) q^{48} +(2.42705 + 1.76336i) q^{49} +(3.23607 + 2.35114i) q^{50} +(-3.09017 + 9.51057i) q^{51} +(-0.309017 - 0.951057i) q^{52} +(-7.28115 + 5.29007i) q^{53} -4.00000 q^{54} +6.00000 q^{56} +(-9.70820 + 7.05342i) q^{57} +(2.78115 + 8.55951i) q^{58} +(2.47214 - 7.60845i) q^{59} +(1.61803 + 1.17557i) q^{60} +(-4.85410 - 3.52671i) q^{61} +(-0.618034 + 1.90211i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-5.66312 + 4.11450i) q^{64} +1.00000 q^{65} +2.00000 q^{67} +(-4.04508 + 2.93893i) q^{68} +(1.23607 + 3.80423i) q^{69} +(-0.618034 + 1.90211i) q^{70} +(-9.70820 - 7.05342i) q^{71} +(2.42705 + 1.76336i) q^{72} +(-0.618034 + 1.90211i) q^{73} +(-0.927051 - 2.85317i) q^{74} +(6.47214 - 4.70228i) q^{75} -6.00000 q^{76} +2.00000 q^{78} +(8.09017 - 5.87785i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(4.04508 + 2.93893i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(1.23607 - 3.80423i) q^{84} +(-1.54508 - 4.75528i) q^{85} +18.0000 q^{87} -9.00000 q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.618034 - 1.90211i) q^{91} +(-0.618034 + 1.90211i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-1.61803 - 1.17557i) q^{94} +(1.85410 - 5.70634i) q^{95} +(3.09017 + 9.51057i) q^{96} +(10.5172 - 7.64121i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 3 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} - q^{13} + 2 q^{14} - 2 q^{15} + q^{16} + 5 q^{17} - q^{18} - 6 q^{19} + q^{20} - 16 q^{21} + 8 q^{23}+ \cdots - 12 q^{98}+O(q^{100}) $ 4 * q - q^2 - 2 * q^3 + q^4 - q^5 - 2 * q^6 + 2 * q^7 + 3 * q^8 - q^9 + 4 * q^10 - 8 * q^12 - q^13 + 2 * q^14 - 2 * q^15 + q^16 + 5 * q^17 - q^18 - 6 * q^19 + q^20 - 16 * q^21 + 8 * q^23 + 6 * q^24 + 4 * q^25 - q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - 2 * q^30 + 2 * q^31 + 20 * q^32 - 20 * q^34 + 2 * q^35 + q^36 + 3 * q^37 - 6 * q^38 - 2 * q^39 + 3 * q^40 + 5 * q^41 + 4 * q^42 + 4 * q^45 - 2 * q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 + 4 * q^50 + 10 * q^51 + q^52 - 9 * q^53 - 16 * q^54 + 24 * q^56 - 12 * q^57 - 9 * q^58 - 8 * q^59 + 2 * q^60 - 6 * q^61 + 2 * q^62 + 2 * q^63 - 7 * q^64 + 4 * q^65 + 8 * q^67 - 5 * q^68 - 4 * q^69 + 2 * q^70 - 12 * q^71 + 3 * q^72 + 2 * q^73 + 3 * q^74 + 8 * q^75 - 24 * q^76 + 8 * q^78 + 10 * q^79 + q^80 + 11 * q^81 + 5 * q^82 - 6 * q^83 - 4 * q^84 + 5 * q^85 + 72 * q^87 - 36 * q^89 - q^90 + 2 * q^91 + 2 * q^92 + 4 * q^93 - 2 * q^94 - 6 * q^95 - 10 * q^96 + 13 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i	−0.835853	−	0.548953i	$-0.815027\pi$
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i	0.263792	+	0.964580i	$0.415027\pi$
$3$	0.618034	+	1.90211i	0.356822	+	1.09819i	0.954945	+	0.296781i	$0.0959133\pi$
$3$	0.618034	+	1.90211i	0.356822	+	1.09819i	−0.598123	+	0.801404i	$0.704087\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	0.392000	−	0.919965i	$-0.371783\pi$
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i	−0.753804	+	0.657099i	$0.771783\pi$
$6$	−1.61803	−	1.17557i	−0.660560	−	0.479925i
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	0.763710	+	0.645560i	$0.223376\pi$
$7$	−0.618034	+	1.90211i	−0.233595	+	0.718931i	−0.997305	+	0.0733714i	$0.976624\pi$
$8$	−0.927051	−	2.85317i	−0.327762	−	1.00875i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.00000			0.316228
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.577350
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	−0.694297	−	0.719689i	$-0.744284\pi$
$13$	−0.809017	+	0.587785i	−0.224381	+	0.163022i	0.469916	+	0.882711i	$0.344284\pi$
$14$	−0.618034	−	1.90211i	−0.165177	−	0.508361i
$15$	0.618034	−	1.90211i	0.159576	−	0.491123i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.957949	−	0.286938i	$-0.0926374\pi$
$17$	4.04508	+	2.93893i	0.981077	+	0.712794i	0.0231281	+	0.999733i	$0.492637\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	0.902649	+	0.430377i	$0.141620\pi$
$19$	1.85410	+	5.70634i	0.425360	+	1.30912i	−0.477289	+	0.878746i	$0.658380\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−4.00000			−0.872872
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	4.85410	−	3.52671i	0.990839	−	0.719887i
$25$	−1.23607	−	3.80423i	−0.247214	−	0.760845i
$26$	0.309017	−	0.951057i	0.0606032	−	0.186518i
$27$	3.23607	+	2.35114i	0.622782	+	0.452477i
$28$	−1.61803	−	1.17557i	−0.305780	−	0.222162i
$29$	2.78115	−	8.55951i	0.516447	−	1.58946i	−0.264186	−	0.964472i	$-0.585103\pi$
$29$	2.78115	−	8.55951i	0.516447	−	1.58946i	0.780633	−	0.624989i	$-0.214897\pi$
$30$	0.618034	+	1.90211i	0.112837	+	0.347277i
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	−0.432923	−	0.901431i	$-0.642518\pi$
$31$	1.61803	−	1.17557i	0.290607	−	0.211139i	0.723531	+	0.690292i	$0.242518\pi$
$32$	5.00000			0.883883
$33$		0			0
$34$	−5.00000			−0.857493
$35$	1.61803	−	1.17557i	0.273498	−	0.198708i
$36$	−0.309017	−	0.951057i	−0.0515028	−	0.158509i
$37$	−0.927051	+	2.85317i	−0.152406	+	0.469058i	−0.997889	−	0.0649448i	$-0.979313\pi$
$37$	−0.927051	+	2.85317i	−0.152406	+	0.469058i	0.845483	+	0.534003i	$0.179313\pi$
$38$	−4.85410	−	3.52671i	−0.787439	−	0.572108i
$39$	−1.61803	−	1.17557i	−0.259093	−	0.188242i
$40$	−0.927051	+	2.85317i	−0.146580	+	0.451126i
$41$	−1.54508	−	4.75528i	−0.241302	−	0.742650i	−0.996223	−	0.0868346i	$-0.972325\pi$
$41$	−1.54508	−	4.75528i	−0.241302	−	0.742650i	0.754921	−	0.655816i	$-0.227675\pi$
$42$	3.23607	−	2.35114i	0.499336	−	0.362789i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$	−1.61803	+	1.17557i	−0.238566	+	0.173328i
$47$	0.618034	+	1.90211i	0.0901495	+	0.277452i	0.985959	−	0.166986i	$-0.0534035\pi$
$47$	0.618034	+	1.90211i	0.0901495	+	0.277452i	−0.895810	+	0.444438i	$0.853403\pi$
$48$	−0.618034	+	1.90211i	−0.0892055	+	0.274546i
$49$	2.42705	+	1.76336i	0.346722	+	0.251908i
$50$	3.23607	+	2.35114i	0.457649	+	0.332502i
$51$	−3.09017	+	9.51057i	−0.432710	+	1.33175i
$52$	−0.309017	−	0.951057i	−0.0428529	−	0.131888i
$53$	−7.28115	+	5.29007i	−1.00014	+	0.726647i	−0.962119	−	0.272630i	$-0.912106\pi$
$53$	−7.28115	+	5.29007i	−1.00014	+	0.726647i	−0.0380244	+	0.999277i	$0.512106\pi$
$54$	−4.00000			−0.544331
$55$		0			0
$56$	6.00000			0.801784
$57$	−9.70820	+	7.05342i	−1.28588	+	0.934249i
$58$	2.78115	+	8.55951i	0.365183	+	1.12392i
$59$	2.47214	−	7.60845i	0.321845	−	0.990536i	−0.651000	−	0.759078i	$-0.725650\pi$
$59$	2.47214	−	7.60845i	0.321845	−	0.990536i	0.972845	−	0.231458i	$-0.0743497\pi$
$60$	1.61803	+	1.17557i	0.208887	+	0.151765i
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	0.231942	−	0.972730i	$-0.425492\pi$
$61$	−4.85410	−	3.52671i	−0.621504	−	0.451549i	−0.853447	+	0.521180i	$0.825492\pi$
$62$	−0.618034	+	1.90211i	−0.0784904	+	0.241569i
$63$	−0.618034	−	1.90211i	−0.0778650	−	0.239644i
$64$	−5.66312	+	4.11450i	−0.707890	+	0.514312i
$65$	1.00000			0.124035
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−4.04508	+	2.93893i	−0.490539	+	0.356397i
$69$	1.23607	+	3.80423i	0.148805	+	0.457975i
$70$	−0.618034	+	1.90211i	−0.0738692	+	0.227346i
$71$	−9.70820	−	7.05342i	−1.15215	−	0.837087i	−0.163386	−	0.986562i	$-0.552242\pi$
$71$	−9.70820	−	7.05342i	−1.15215	−	0.837087i	−0.988766	+	0.149475i	$0.952242\pi$
$72$	2.42705	+	1.76336i	0.286031	+	0.207813i
$73$	−0.618034	+	1.90211i	−0.0723354	+	0.222625i	−0.980688	−	0.195580i	$-0.937341\pi$
$73$	−0.618034	+	1.90211i	−0.0723354	+	0.222625i	0.908352	+	0.418206i	$0.137341\pi$
$74$	−0.927051	−	2.85317i	−0.107767	−	0.331674i
$75$	6.47214	−	4.70228i	0.747338	−	0.542973i
$76$	−6.00000			−0.688247
$77$		0			0
$78$	2.00000			0.226455
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	−0.0308541	−	0.999524i	$-0.509823\pi$
$79$	8.09017	−	5.87785i	0.910215	−	0.661310i	0.941069	+	0.338214i	$0.109823\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	−3.39919	+	10.4616i	−0.377687	+	1.16240i
$82$	4.04508	+	2.93893i	0.446705	+	0.324550i
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	0.288600	−	0.957450i	$-0.406810\pi$
$83$	−4.85410	−	3.52671i	−0.532807	−	0.387107i	−0.821407	+	0.570343i	$0.806810\pi$
$84$	1.23607	−	3.80423i	0.134866	−	0.415075i
$85$	−1.54508	−	4.75528i	−0.167588	−	0.515783i
$86$		0			0
$87$	18.0000			1.92980
$88$		0			0
$89$	−9.00000			−0.953998			−0.476999	−	0.878904i	$-0.658275\pi$
$89$	−9.00000			−0.953998			−0.476999	+	0.878904i	$0.658275\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	−0.618034	−	1.90211i	−0.0647876	−	0.199396i
$92$	−0.618034	+	1.90211i	−0.0644345	+	0.198309i
$93$	3.23607	+	2.35114i	0.335565	+	0.243802i
$94$	−1.61803	−	1.17557i	−0.166887	−	0.121251i
$95$	1.85410	−	5.70634i	0.190227	−	0.585458i
$96$	3.09017	+	9.51057i	0.315389	+	0.970668i
$97$	10.5172	−	7.64121i	1.06786	−	0.775847i	0.0923353	−	0.995728i	$-0.470567\pi$
$97$	10.5172	−	7.64121i	1.06786	−	0.775847i	0.975527	+	0.219881i	$0.0705669\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	4.00000			0.400000
$101$	8.09017	−	5.87785i	0.805002	−	0.584868i	−0.107375	−	0.994219i	$-0.534245\pi$
$101$	8.09017	−	5.87785i	0.805002	−	0.584868i	0.912377	+	0.409350i	$0.134245\pi$
$102$	−3.09017	−	9.51057i	−0.305972	−	0.941686i
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	−0.752279	−	0.658845i	$-0.771045\pi$
$103$	2.47214	−	7.60845i	0.243587	−	0.749683i	0.995866	−	0.0908382i	$-0.0289546\pi$
$104$	2.42705	+	1.76336i	0.237992	+	0.172911i
$105$	3.23607	+	2.35114i	0.315808	+	0.229448i
$106$	2.78115	−	8.55951i	0.270129	−	0.831373i
$107$	1.85410	+	5.70634i	0.179243	+	0.551653i	0.999802	−	0.0199092i	$-0.00633772\pi$
$107$	1.85410	+	5.70634i	0.179243	+	0.551653i	−0.820559	+	0.571562i	$0.806338\pi$
$108$	−3.23607	+	2.35114i	−0.311391	+	0.226239i
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	−1.61803	+	1.17557i	−0.152890	+	0.111081i
$113$	−2.78115	−	8.55951i	−0.261629	−	0.805211i	−0.992451	−	0.122643i	$-0.960863\pi$
$113$	−2.78115	−	8.55951i	−0.261629	−	0.805211i	0.730822	−	0.682568i	$-0.239137\pi$
$114$	3.70820	−	11.4127i	0.347305	−	1.06890i
$115$	−1.61803	−	1.17557i	−0.150882	−	0.109623i
$116$	7.28115	+	5.29007i	0.676038	+	0.491170i
$117$	0.309017	−	0.951057i	0.0285686	−	0.0879252i
$118$	2.47214	+	7.60845i	0.227579	+	0.700415i
$119$	−8.09017	+	5.87785i	−0.741625	+	0.538822i
$120$	−6.00000			−0.547723
$121$		0			0
$122$	6.00000			0.543214
$123$	8.09017	−	5.87785i	0.729466	−	0.529988i
$124$	0.618034	+	1.90211i	0.0555011	+	0.170815i
$125$	−2.78115	+	8.55951i	−0.248754	+	0.765586i
$126$	1.61803	+	1.17557i	0.144146	+	0.104728i
$127$	12.9443	+	9.40456i	1.14862	+	0.834520i	0.988297	−	0.152545i	$-0.0487468\pi$
$127$	12.9443	+	9.40456i	1.14862	+	0.834520i	0.160322	+	0.987065i	$0.448747\pi$
$128$	−0.927051	+	2.85317i	−0.0819405	+	0.252187i
$129$		0			0
$130$	−0.809017	+	0.587785i	−0.0709555	+	0.0515522i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−12.0000			−1.04053
$134$	−1.61803	+	1.17557i	−0.139777	+	0.101554i
$135$	−1.23607	−	3.80423i	−0.106384	−	0.327416i
$136$	4.63525	−	14.2658i	0.397470	−	1.22329i
$137$	8.09017	+	5.87785i	0.691190	+	0.502179i	0.877051	−	0.480397i	$-0.159507\pi$
$137$	8.09017	+	5.87785i	0.691190	+	0.502179i	−0.185861	+	0.982576i	$0.559507\pi$
$138$	−3.23607	−	2.35114i	−0.275472	−	0.200142i
$139$	−0.618034	+	1.90211i	−0.0524210	+	0.161335i	−0.973840	−	0.227236i	$-0.927031\pi$
$139$	−0.618034	+	1.90211i	−0.0524210	+	0.161335i	0.921419	+	0.388571i	$0.127031\pi$
$140$	0.618034	+	1.90211i	0.0522334	+	0.160758i
$141$	−3.23607	+	2.35114i	−0.272526	+	0.198002i
$142$	12.0000			1.00702
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−7.28115	+	5.29007i	−0.604667	+	0.439316i
$146$	−0.618034	−	1.90211i	−0.0511489	−	0.157420i
$147$	−1.85410	+	5.70634i	−0.152924	+	0.470651i
$148$	−2.42705	−	1.76336i	−0.199502	−	0.144947i
$149$	−13.7533	−	9.99235i	−1.12671	−	0.818605i	−0.141500	−	0.989938i	$-0.545193\pi$
$149$	−13.7533	−	9.99235i	−1.12671	−	0.818605i	−0.985213	+	0.171333i	$0.945193\pi$
$150$	−2.47214	+	7.60845i	−0.201849	+	0.621228i
$151$	−4.94427	−	15.2169i	−0.402359	−	1.23833i	−0.923080	−	0.384607i	$-0.874337\pi$
$151$	−4.94427	−	15.2169i	−0.402359	−	1.23833i	0.520721	−	0.853727i	$-0.325663\pi$
$152$	14.5623	−	10.5801i	1.18116	−	0.858162i
$153$	−5.00000			−0.404226
$154$		0			0
$155$	−2.00000			−0.160644
$156$	1.61803	−	1.17557i	0.129546	−	0.0941210i
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	0.972685	−	0.232129i	$-0.0745691\pi$
$157$	0.618034	+	1.90211i	0.0493245	+	0.151805i	−0.923361	+	0.383934i	$0.874569\pi$
$158$	−3.09017	+	9.51057i	−0.245841	+	0.756620i
$159$	−14.5623	−	10.5801i	−1.15487	−	0.839059i
$160$	−4.04508	−	2.93893i	−0.319792	−	0.232343i
$161$	−1.23607	+	3.80423i	−0.0974158	+	0.299815i
$162$	−3.39919	−	10.4616i	−0.267065	−	0.821943i
$163$	1.61803	−	1.17557i	0.126734	−	0.0920778i	−0.522612	−	0.852570i	$-0.675042\pi$
$163$	1.61803	−	1.17557i	0.126734	−	0.0920778i	0.649347	+	0.760493i	$0.275042\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	6.00000			0.465690
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	−0.896212	−	0.443626i	$-0.853692\pi$
$167$	−9.70820	+	7.05342i	−0.751243	+	0.545810i	0.144969	+	0.989436i	$0.453692\pi$
$168$	3.70820	+	11.4127i	0.286094	+	0.880507i
$169$	−3.70820	+	11.4127i	−0.285246	+	0.877898i
$170$	4.04508	+	2.93893i	0.310244	+	0.225405i
$171$	−4.85410	−	3.52671i	−0.371202	−	0.269694i
$172$		0			0
$173$	1.85410	+	5.70634i	0.140965	+	0.433845i	0.996470	−	0.0839492i	$-0.0267533\pi$
$173$	1.85410	+	5.70634i	0.140965	+	0.433845i	−0.855505	+	0.517794i	$0.826753\pi$
$174$	−14.5623	+	10.5801i	−1.10397	+	0.802078i
$175$	8.00000			0.604743
$176$		0			0
$177$	16.0000			1.20263
$178$	7.28115	−	5.29007i	0.545745	−	0.396507i
$179$	7.41641	+	22.8254i	0.554328	+	1.70605i	0.697710	+	0.716380i	$0.254202\pi$
$179$	7.41641	+	22.8254i	0.554328	+	1.70605i	−0.143382	+	0.989667i	$0.545798\pi$
$180$	−0.309017	+	0.951057i	−0.0230328	+	0.0708876i
$181$	−0.809017	−	0.587785i	−0.0601338	−	0.0436897i	0.557312	−	0.830303i	$-0.311833\pi$
$181$	−0.809017	−	0.587785i	−0.0601338	−	0.0436897i	−0.617446	+	0.786613i	$0.711833\pi$
$182$	1.61803	+	1.17557i	0.119937	+	0.0871391i
$183$	3.70820	−	11.4127i	0.274118	−	0.843649i
$184$	−1.85410	−	5.70634i	−0.136686	−	0.420677i
$185$	2.42705	−	1.76336i	0.178440	−	0.129644i
$186$	−4.00000			−0.293294
$187$		0			0
$188$	−2.00000			−0.145865
$189$	−6.47214	+	4.70228i	−0.470779	+	0.342041i
$190$	1.85410	+	5.70634i	0.134511	+	0.413981i
$191$	2.47214	−	7.60845i	0.178877	−	0.550528i	−0.820912	−	0.571055i	$-0.806534\pi$
$191$	2.47214	−	7.60845i	0.178877	−	0.550528i	0.999789	+	0.0205267i	$0.00653431\pi$
$192$	−11.3262	−	8.22899i	−0.817401	−	0.593876i
$193$	4.04508	+	2.93893i	0.291172	+	0.211549i	0.723775	−	0.690036i	$-0.242405\pi$
$193$	4.04508	+	2.93893i	0.291172	+	0.211549i	−0.432604	+	0.901584i	$0.642405\pi$
$194$	−4.01722	+	12.3637i	−0.288420	+	0.887664i
$195$	0.618034	+	1.90211i	0.0442583	+	0.136213i
$196$	−2.42705	+	1.76336i	−0.173361	+	0.125954i
$197$	−11.0000			−0.783718			−0.391859	−	0.920025i	$-0.628168\pi$
$197$	−11.0000			−0.783718			−0.391859	+	0.920025i	$0.628168\pi$
$198$		0			0
$199$	24.0000			1.70131			0.850657	−	0.525720i	$-0.176204\pi$
$199$	24.0000			1.70131			0.850657	+	0.525720i	$0.176204\pi$
$200$	−9.70820	+	7.05342i	−0.686474	+	0.498752i
$201$	1.23607	+	3.80423i	0.0871855	+	0.268329i
$202$	−3.09017	+	9.51057i	−0.217424	+	0.669161i
$203$	14.5623	+	10.5801i	1.02207	+	0.742580i
$204$	−8.09017	−	5.87785i	−0.566425	−	0.411532i
$205$	−1.54508	+	4.75528i	−0.107913	+	0.332123i
$206$	2.47214	+	7.60845i	0.172242	+	0.530106i
$207$	−1.61803	+	1.17557i	−0.112461	+	0.0817078i
$208$	−1.00000			−0.0693375
$209$		0			0
$210$	−4.00000			−0.276026
$211$	−9.70820	+	7.05342i	−0.668340	+	0.485578i	−0.869469	−	0.493987i	$-0.835539\pi$
$211$	−9.70820	+	7.05342i	−0.668340	+	0.485578i	0.201129	+	0.979565i	$0.435539\pi$
$212$	−2.78115	−	8.55951i	−0.191010	−	0.587869i
$213$	7.41641	−	22.8254i	0.508164	−	1.56397i
$214$	−4.85410	−	3.52671i	−0.331820	−	0.241081i
$215$		0			0
$216$	3.70820	−	11.4127i	0.252311	−	0.776534i
$217$	1.23607	+	3.80423i	0.0839098	+	0.258248i
$218$	8.89919	−	6.46564i	0.602729	−	0.437908i
$219$	−4.00000			−0.270295
$220$		0			0
$221$	−5.00000			−0.336336
$222$	4.85410	−	3.52671i	0.325786	−	0.236697i
$223$	−6.18034	−	19.0211i	−0.413866	−	1.27375i	−0.913261	−	0.407375i	$-0.866444\pi$
$223$	−6.18034	−	19.0211i	−0.413866	−	1.27375i	0.499395	−	0.866374i	$-0.333556\pi$
$224$	−3.09017	+	9.51057i	−0.206471	+	0.635451i
$225$	3.23607	+	2.35114i	0.215738	+	0.156743i
$226$	7.28115	+	5.29007i	0.484335	+	0.351890i
$227$	−7.41641	+	22.8254i	−0.492244	+	1.51497i	0.328963	+	0.944343i	$0.393301\pi$
$227$	−7.41641	+	22.8254i	−0.492244	+	1.51497i	−0.821208	+	0.570629i	$0.806699\pi$
$228$	−3.70820	−	11.4127i	−0.245582	−	0.755823i
$229$	−7.28115	+	5.29007i	−0.481152	+	0.349577i	−0.801772	−	0.597631i	$-0.796109\pi$
$229$	−7.28115	+	5.29007i	−0.481152	+	0.349577i	0.320619	+	0.947208i	$0.396109\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$	−27.0000			−1.77264
$233$	16.9894	−	12.3435i	1.11301	−	0.808649i	0.129875	−	0.991530i	$-0.458542\pi$
$233$	16.9894	−	12.3435i	1.11301	−	0.808649i	0.983135	+	0.182881i	$0.0585425\pi$
$234$	0.309017	+	0.951057i	0.0202011	+	0.0621725i
$235$	0.618034	−	1.90211i	0.0403161	−	0.124080i
$236$	6.47214	+	4.70228i	0.421300	+	0.306092i
$237$	16.1803	+	11.7557i	1.05103	+	0.763615i
$238$	3.09017	−	9.51057i	0.200306	−	0.616478i
$239$	1.85410	+	5.70634i	0.119932	+	0.369112i	0.992944	−	0.118587i	$-0.0378363\pi$
$239$	1.85410	+	5.70634i	0.119932	+	0.369112i	−0.873012	+	0.487699i	$0.837836\pi$
$240$	1.61803	−	1.17557i	0.104444	−	0.0758827i
$241$	22.0000			1.41714			0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000			1.41714			0.708572	+	0.705638i	$0.249340\pi$
$242$		0			0
$243$	−10.0000			−0.641500
$244$	4.85410	−	3.52671i	0.310752	−	0.225775i
$245$	−0.927051	−	2.85317i	−0.0592271	−	0.182282i
$246$	−3.09017	+	9.51057i	−0.197022	+	0.606371i
$247$	−4.85410	−	3.52671i	−0.308859	−	0.224399i
$248$	−4.85410	−	3.52671i	−0.308236	−	0.223946i
$249$	3.70820	−	11.4127i	0.234998	−	0.723249i
$250$	−2.78115	−	8.55951i	−0.175896	−	0.541351i
$251$	1.61803	−	1.17557i	0.102129	−	0.0742014i	−0.535548	−	0.844504i	$-0.679895\pi$
$251$	1.61803	−	1.17557i	0.102129	−	0.0742014i	0.637678	+	0.770303i	$0.279895\pi$
$252$	2.00000			0.125988
$253$		0			0
$254$	−16.0000			−1.00393
$255$	8.09017	−	5.87785i	0.506626	−	0.368085i
$256$	−5.25329	−	16.1680i	−0.328331	−	1.01050i
$257$	5.87132	−	18.0701i	0.366243	−	1.12718i	−0.582956	−	0.812504i	$-0.698104\pi$
$257$	5.87132	−	18.0701i	0.366243	−	1.12718i	0.949199	−	0.314676i	$-0.101896\pi$
$258$		0			0
$259$	−4.85410	−	3.52671i	−0.301619	−	0.219139i
$260$	−0.309017	+	0.951057i	−0.0191644	+	0.0589820i
$261$	2.78115	+	8.55951i	0.172149	+	0.529820i
$262$		0			0
$263$	−22.0000			−1.35658			−0.678289	−	0.734795i	$-0.737278\pi$
$263$	−22.0000			−1.35658			−0.678289	+	0.734795i	$0.737278\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	9.70820	−	7.05342i	0.595248	−	0.432473i
$267$	−5.56231	−	17.1190i	−0.340408	−	1.04767i
$268$	−0.618034	+	1.90211i	−0.0377524	+	0.116190i
$269$	−0.809017	−	0.587785i	−0.0493266	−	0.0358379i	0.562849	−	0.826560i	$-0.309705\pi$
$269$	−0.809017	−	0.587785i	−0.0493266	−	0.0358379i	−0.612175	+	0.790722i	$0.709705\pi$
$270$	3.23607	+	2.35114i	0.196941	+	0.143086i
$271$	6.18034	−	19.0211i	0.375429	−	1.15545i	−0.567760	−	0.823194i	$-0.692190\pi$
$271$	6.18034	−	19.0211i	0.375429	−	1.15545i	0.943189	−	0.332257i	$-0.107810\pi$
$272$	1.54508	+	4.75528i	0.0936845	+	0.288331i
$273$	3.23607	−	2.35114i	0.195856	−	0.142298i
$274$	−10.0000			−0.604122
$275$		0			0
$276$	−4.00000			−0.240772
$277$	−0.809017	+	0.587785i	−0.0486091	+	0.0353166i	−0.611825	−	0.790994i	$-0.709564\pi$
$277$	−0.809017	+	0.587785i	−0.0486091	+	0.0353166i	0.563215	+	0.826310i	$0.309564\pi$
$278$	−0.618034	−	1.90211i	−0.0370672	−	0.114081i
$279$	−0.618034	+	1.90211i	−0.0370007	+	0.113877i
$280$	−4.85410	−	3.52671i	−0.290088	−	0.210761i
$281$	−4.85410	−	3.52671i	−0.289571	−	0.210386i	0.433510	−	0.901149i	$-0.357275\pi$
$281$	−4.85410	−	3.52671i	−0.289571	−	0.210386i	−0.723081	+	0.690763i	$0.757275\pi$
$282$	1.23607	−	3.80423i	0.0736068	−	0.226538i
$283$	8.65248	+	26.6296i	0.514336	+	1.58296i	0.784486	+	0.620146i	$0.212927\pi$
$283$	8.65248	+	26.6296i	0.514336	+	1.58296i	−0.270150	+	0.962818i	$0.587073\pi$
$284$	9.70820	−	7.05342i	0.576076	−	0.418544i
$285$	12.0000			0.710819
$286$		0			0
$287$	10.0000			0.590281
$288$	−4.04508	+	2.93893i	−0.238359	+	0.173178i
$289$	2.47214	+	7.60845i	0.145420	+	0.447556i
$290$	2.78115	−	8.55951i	0.163315	−	0.502632i
$291$	21.0344	+	15.2824i	1.23306	+	0.895871i
$292$	−1.61803	−	1.17557i	−0.0946883	−	0.0687951i
$293$	2.78115	−	8.55951i	0.162477	−	0.500052i	−0.836365	−	0.548173i	$-0.815323\pi$
$293$	2.78115	−	8.55951i	0.162477	−	0.500052i	0.998841	+	0.0481214i	$0.0153234\pi$
$294$	−1.85410	−	5.70634i	−0.108133	−	0.332800i
$295$	−6.47214	+	4.70228i	−0.376822	+	0.273777i
$296$	9.00000			0.523114
$297$		0			0
$298$	17.0000			0.984784
$299$	−1.61803	+	1.17557i	−0.0935733	+	0.0679850i
$300$	2.47214	+	7.60845i	0.142729	+	0.439274i
$301$		0			0
$302$	12.9443	+	9.40456i	0.744859	+	0.541172i
$303$	16.1803	+	11.7557i	0.929536	+	0.675348i
$304$	−1.85410	+	5.70634i	−0.106340	+	0.327281i
$305$	1.85410	+	5.70634i	0.106166	+	0.326744i
$306$	4.04508	−	2.93893i	0.231242	−	0.168007i
$307$	−22.0000			−1.25561			−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000			−1.25561			−0.627803	+	0.778372i	$0.716046\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$	1.61803	−	1.17557i	0.0918982	−	0.0667679i
$311$	7.41641	+	22.8254i	0.420546	+	1.29431i	0.907195	+	0.420710i	$0.138219\pi$
$311$	7.41641	+	22.8254i	0.420546	+	1.29431i	−0.486649	+	0.873597i	$0.661781\pi$
$312$	−1.85410	+	5.70634i	−0.104968	+	0.323058i
$313$	−18.6074	−	13.5191i	−1.05175	−	0.764142i	−0.0792071	−	0.996858i	$-0.525239\pi$
$313$	−18.6074	−	13.5191i	−1.05175	−	0.764142i	−0.972545	+	0.232716i	$0.925239\pi$
$314$	−1.61803	−	1.17557i	−0.0913109	−	0.0663413i
$315$	−0.618034	+	1.90211i	−0.0348223	+	0.107172i
$316$	3.09017	+	9.51057i	0.173836	+	0.535011i
$317$	1.61803	−	1.17557i	0.0908778	−	0.0660266i	−0.541418	−	0.840753i	$-0.682113\pi$
$317$	1.61803	−	1.17557i	0.0908778	−	0.0660266i	0.632296	+	0.774727i	$0.282113\pi$
$318$	18.0000			1.00939
$319$		0			0
$320$	7.00000			0.391312
$321$	−9.70820	+	7.05342i	−0.541859	+	0.393684i
$322$	−1.23607	−	3.80423i	−0.0688834	−	0.212001i
$323$	−9.27051	+	28.5317i	−0.515825	+	1.58755i
$324$	−8.89919	−	6.46564i	−0.494399	−	0.359202i
$325$	3.23607	+	2.35114i	0.179505	+	0.130418i
$326$	−0.618034	+	1.90211i	−0.0342297	+	0.105348i
$327$	−6.79837	−	20.9232i	−0.375951	−	1.15706i
$328$	−12.1353	+	8.81678i	−0.670057	+	0.486825i
$329$	−4.00000			−0.220527
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	4.85410	−	3.52671i	0.266403	−	0.193553i
$333$	−0.927051	−	2.85317i	−0.0508021	−	0.156353i
$334$	3.70820	−	11.4127i	0.202904	−	0.624474i
$335$	−1.61803	−	1.17557i	−0.0884026	−	0.0642283i
$336$	−3.23607	−	2.35114i	−0.176542	−	0.128265i
$337$	−4.01722	+	12.3637i	−0.218832	+	0.673496i	0.780027	+	0.625745i	$0.215205\pi$
$337$	−4.01722	+	12.3637i	−0.218832	+	0.673496i	−0.998859	+	0.0477501i	$0.984795\pi$
$338$	−3.70820	−	11.4127i	−0.201700	−	0.620768i
$339$	14.5623	−	10.5801i	0.790916	−	0.574634i
$340$	5.00000			0.271163
$341$		0			0
$342$	6.00000			0.324443
$343$	−16.1803	+	11.7557i	−0.873656	+	0.634748i
$344$		0			0
$345$	1.23607	−	3.80423i	0.0665477	−	0.204813i
$346$	−4.85410	−	3.52671i	−0.260958	−	0.189597i
$347$	−22.6525	−	16.4580i	−1.21605	−	0.883511i	−0.220283	−	0.975436i	$-0.570698\pi$
$347$	−22.6525	−	16.4580i	−1.21605	−	0.883511i	−0.995766	+	0.0919250i	$0.970698\pi$
$348$	−5.56231	+	17.1190i	−0.298171	+	0.917676i
$349$	−8.34346	−	25.6785i	−0.446615	−	1.37454i	−0.880703	−	0.473669i	$-0.842929\pi$
$349$	−8.34346	−	25.6785i	−0.446615	−	1.37454i	0.434088	−	0.900871i	$-0.357071\pi$
$350$	−6.47214	+	4.70228i	−0.345950	+	0.251348i
$351$	−4.00000			−0.213504
$352$		0			0
$353$	−9.00000			−0.479022			−0.239511	−	0.970894i	$-0.576987\pi$
$353$	−9.00000			−0.479022			−0.239511	+	0.970894i	$0.576987\pi$
$354$	−12.9443	+	9.40456i	−0.687980	+	0.499847i
$355$	3.70820	+	11.4127i	0.196811	+	0.605722i
$356$	2.78115	−	8.55951i	0.147401	−	0.453653i
$357$	−16.1803	−	11.7557i	−0.856354	−	0.622178i
$358$	−19.4164	−	14.1068i	−1.02619	−	0.745570i
$359$	−0.618034	+	1.90211i	−0.0326186	+	0.100390i	−0.966040	−	0.258391i	$-0.916808\pi$
$359$	−0.618034	+	1.90211i	−0.0326186	+	0.100390i	0.933422	+	0.358781i	$0.116808\pi$
$360$	−0.927051	−	2.85317i	−0.0488599	−	0.150375i
$361$	−13.7533	+	9.99235i	−0.723857	+	0.525913i
$362$	1.00000			0.0525588
$363$		0			0
$364$	2.00000			0.104828
$365$	1.61803	−	1.17557i	0.0846918	−	0.0615322i
$366$	3.70820	+	11.4127i	0.193831	+	0.596550i
$367$	−4.32624	+	13.3148i	−0.225828	+	0.695026i	0.772379	+	0.635162i	$0.219067\pi$
$367$	−4.32624	+	13.3148i	−0.225828	+	0.695026i	−0.998207	+	0.0598642i	$0.980933\pi$
$368$	1.61803	+	1.17557i	0.0843459	+	0.0612808i
$369$	4.04508	+	2.93893i	0.210579	+	0.152994i
$370$	−0.927051	+	2.85317i	−0.0481951	+	0.148329i
$371$	−5.56231	−	17.1190i	−0.288781	−	0.888775i
$372$	−3.23607	+	2.35114i	−0.167782	+	0.121901i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$		0			0
$375$	−18.0000			−0.929516
$376$	4.85410	−	3.52671i	0.250331	−	0.181876i
$377$	2.78115	+	8.55951i	0.143237	+	0.440837i
$378$	2.47214	−	7.60845i	0.127153	−	0.391337i
$379$	25.8885	+	18.8091i	1.32981	+	0.966160i	0.999754	+	0.0221971i	$0.00706614\pi$
$379$	25.8885	+	18.8091i	1.32981	+	0.966160i	0.330052	+	0.943963i	$0.392934\pi$
$380$	4.85410	+	3.52671i	0.249010	+	0.180916i
$381$	−9.88854	+	30.4338i	−0.506605	+	1.55917i
$382$	2.47214	+	7.60845i	0.126485	+	0.389282i
$383$	−16.1803	+	11.7557i	−0.826777	+	0.600688i	−0.918646	−	0.395083i	$-0.870716\pi$
$383$	−16.1803	+	11.7557i	−0.826777	+	0.600688i	0.0918688	+	0.995771i	$0.470716\pi$
$384$	−6.00000			−0.306186
$385$		0			0
$386$	−5.00000			−0.254493
$387$		0			0
$388$	4.01722	+	12.3637i	0.203943	+	0.627674i
$389$	−0.927051	+	2.85317i	−0.0470034	+	0.144661i	−0.971804	−	0.235791i	$-0.924232\pi$
$389$	−0.927051	+	2.85317i	−0.0470034	+	0.144661i	0.924800	+	0.380453i	$0.124232\pi$
$390$	−1.61803	−	1.17557i	−0.0819323	−	0.0595273i
$391$	8.09017	+	5.87785i	0.409137	+	0.297256i
$392$	2.78115	−	8.55951i	0.140469	−	0.432320i
$393$		0			0
$394$	8.89919	−	6.46564i	0.448335	−	0.325734i
$395$	−10.0000			−0.503155
$396$		0			0
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	−19.4164	+	14.1068i	−0.973257	+	0.707112i
$399$	−7.41641	−	22.8254i	−0.371285	−	1.14270i
$400$	1.23607	−	3.80423i	0.0618034	−	0.190211i
$401$	−18.6074	−	13.5191i	−0.929209	−	0.675110i	0.0165902	−	0.999862i	$-0.494719\pi$
$401$	−18.6074	−	13.5191i	−0.929209	−	0.675110i	−0.945799	+	0.324753i	$0.894719\pi$
$402$	−3.23607	−	2.35114i	−0.161400	−	0.117264i
$403$	−0.618034	+	1.90211i	−0.0307865	+	0.0947510i
$404$	3.09017	+	9.51057i	0.153742	+	0.473168i
$405$	8.89919	−	6.46564i	0.442204	−	0.321280i
$406$	−18.0000			−0.893325
$407$		0			0
$408$	30.0000			1.48522
$409$	16.9894	−	12.3435i	0.840070	−	0.610346i	−0.0823205	−	0.996606i	$-0.526233\pi$
$409$	16.9894	−	12.3435i	0.840070	−	0.610346i	0.922390	+	0.386260i	$0.126233\pi$
$410$	−1.54508	−	4.75528i	−0.0763063	−	0.234847i
$411$	−6.18034	+	19.0211i	−0.304854	+	0.938243i
$412$	6.47214	+	4.70228i	0.318859	+	0.231665i
$413$	12.9443	+	9.40456i	0.636946	+	0.462768i
$414$	0.618034	−	1.90211i	0.0303747	−	0.0934838i
$415$	1.85410	+	5.70634i	0.0910143	+	0.280113i
$416$	−4.04508	+	2.93893i	−0.198327	+	0.144093i
$417$	−4.00000			−0.195881
$418$		0			0
$419$	2.00000			0.0977064			0.0488532	−	0.998806i	$-0.484443\pi$
$419$	2.00000			0.0977064			0.0488532	+	0.998806i	$0.484443\pi$
$420$	−3.23607	+	2.35114i	−0.157904	+	0.114724i
$421$	4.01722	+	12.3637i	0.195787	+	0.602572i	0.999967	+	0.00818455i	$0.00260525\pi$
$421$	4.01722	+	12.3637i	0.195787	+	0.602572i	−0.804179	+	0.594387i	$0.797395\pi$
$422$	3.70820	−	11.4127i	0.180513	−	0.555560i
$423$	−1.61803	−	1.17557i	−0.0786715	−	0.0571582i
$424$	21.8435	+	15.8702i	1.06081	+	0.770725i
$425$	6.18034	−	19.0211i	0.299791	−	0.922660i
$426$	7.41641	+	22.8254i	0.359326	+	1.10589i
$427$	9.70820	−	7.05342i	0.469813	−	0.341339i
$428$	−6.00000			−0.290021
$429$		0			0
$430$		0			0
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	−0.796516	−	0.604617i	$-0.793326\pi$
$431$	−9.70820	+	7.05342i	−0.467628	+	0.339751i	0.328888	+	0.944369i	$0.393326\pi$
$432$	1.23607	+	3.80423i	0.0594703	+	0.183031i
$433$	5.87132	−	18.0701i	0.282158	−	0.868392i	−0.705078	−	0.709129i	$-0.749088\pi$
$433$	5.87132	−	18.0701i	0.282158	−	0.868392i	0.987236	−	0.159263i	$-0.0509118\pi$
$434$	−3.23607	−	2.35114i	−0.155336	−	0.112858i
$435$	−14.5623	−	10.5801i	−0.698209	−	0.507279i
$436$	3.39919	−	10.4616i	0.162792	−	0.501021i
$437$	3.70820	+	11.4127i	0.177387	+	0.545942i
$438$	3.23607	−	2.35114i	0.154625	−	0.112342i
$439$	22.0000			1.05000			0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000			1.05000			0.525001	+	0.851101i	$0.324065\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	4.04508	−	2.93893i	0.192405	−	0.139790i
$443$	−6.18034	−	19.0211i	−0.293637	−	0.903721i	−0.983676	−	0.179949i	$-0.942407\pi$
$443$	−6.18034	−	19.0211i	−0.293637	−	0.903721i	0.690039	−	0.723772i	$-0.257593\pi$
$444$	1.85410	−	5.70634i	0.0879918	−	0.270811i
$445$	7.28115	+	5.29007i	0.345160	+	0.250773i
$446$	16.1803	+	11.7557i	0.766161	+	0.556649i
$447$	10.5066	−	32.3359i	0.496944	−	1.52944i
$448$	−4.32624	−	13.3148i	−0.204396	−	0.629065i
$449$	10.5172	−	7.64121i	0.496338	−	0.360611i	−0.311278	−	0.950319i	$-0.600757\pi$
$449$	10.5172	−	7.64121i	0.496338	−	0.360611i	0.807617	+	0.589708i	$0.200757\pi$
$450$	−4.00000			−0.188562
$451$		0			0
$452$	9.00000			0.423324
$453$	25.8885	−	18.8091i	1.21635	−	0.883730i
$454$	−7.41641	−	22.8254i	−0.348069	−	1.07125i
$455$	−0.618034	+	1.90211i	−0.0289739	+	0.0891724i
$456$	29.1246	+	21.1603i	1.36388	+	0.990920i
$457$	−31.5517	−	22.9236i	−1.47592	−	1.07232i	−0.978842	−	0.204619i	$-0.934405\pi$
$457$	−31.5517	−	22.9236i	−1.47592	−	1.07232i	−0.497083	−	0.867703i	$-0.665595\pi$
$458$	2.78115	−	8.55951i	0.129955	−	0.399960i
$459$	6.18034	+	19.0211i	0.288474	+	0.887830i
$460$	1.61803	−	1.17557i	0.0754412	−	0.0548113i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$	7.28115	−	5.29007i	0.338019	−	0.245585i
$465$	−1.23607	−	3.80423i	−0.0573213	−	0.176417i
$466$	−6.48936	+	19.9722i	−0.300614	+	0.925194i
$467$	−9.70820	−	7.05342i	−0.449242	−	0.326393i	0.340054	−	0.940406i	$-0.389555\pi$
$467$	−9.70820	−	7.05342i	−0.449242	−	0.326393i	−0.789296	+	0.614012i	$0.789555\pi$
$468$	0.809017	+	0.587785i	0.0373968	+	0.0271704i
$469$	−1.23607	+	3.80423i	−0.0570763	+	0.175663i
$470$	0.618034	+	1.90211i	0.0285078	+	0.0877379i
$471$	−3.23607	+	2.35114i	−0.149110	+	0.108335i
$472$	−24.0000			−1.10469
$473$		0			0
$474$	−20.0000			−0.918630
$475$	19.4164	−	14.1068i	0.890886	−	0.647266i
$476$	−3.09017	−	9.51057i	−0.141638	−	0.435916i
$477$	2.78115	−	8.55951i	0.127340	−	0.391913i
$478$	−4.85410	−	3.52671i	−0.222021	−	0.161308i
$479$	12.9443	+	9.40456i	0.591439	+	0.429705i	0.842830	−	0.538180i	$-0.180888\pi$
$479$	12.9443	+	9.40456i	0.591439	+	0.429705i	−0.251391	+	0.967886i	$0.580888\pi$
$480$	3.09017	−	9.51057i	0.141046	−	0.434096i
$481$	−0.927051	−	2.85317i	−0.0422699	−	0.130093i
$482$	−17.7984	+	12.9313i	−0.810694	+	0.589003i
$483$	−8.00000			−0.364013
$484$		0			0
$485$	−13.0000			−0.590300
$486$	8.09017	−	5.87785i	0.366978	−	0.266625i
$487$	0.618034	+	1.90211i	0.0280058	+	0.0861930i	0.964082	−	0.265603i	$-0.0855711\pi$
$487$	0.618034	+	1.90211i	0.0280058	+	0.0861930i	−0.936077	+	0.351796i	$0.885571\pi$
$488$	−5.56231	+	17.1190i	−0.251794	+	0.774942i
$489$	3.23607	+	2.35114i	0.146340	+	0.106322i
$490$	2.42705	+	1.76336i	0.109643	+	0.0796603i
$491$	−0.618034	+	1.90211i	−0.0278915	+	0.0858412i	−0.964033	−	0.265782i	$-0.914370\pi$
$491$	−0.618034	+	1.90211i	−0.0278915	+	0.0858412i	0.936142	+	0.351623i	$0.114370\pi$
$492$	3.09017	+	9.51057i	0.139316	+	0.428769i
$493$	36.4058	−	26.4503i	1.63963	−	1.19126i
$494$	6.00000			0.269953
$495$		0			0
$496$	2.00000			0.0898027
$497$	19.4164	−	14.1068i	0.870945	−	0.632779i
$498$	3.70820	+	11.4127i	0.166169	+	0.511414i
$499$	2.47214	−	7.60845i	0.110668	−	0.340601i	−0.880351	−	0.474323i	$-0.842693\pi$
$499$	2.47214	−	7.60845i	0.110668	−	0.340601i	0.991019	+	0.133722i	$0.0426929\pi$
$500$	−7.28115	−	5.29007i	−0.325623	−	0.236579i
$501$	−19.4164	−	14.1068i	−0.867461	−	0.630247i
$502$	−0.618034	+	1.90211i	−0.0275842	+	0.0848955i
$503$	−11.7426	−	36.1401i	−0.523579	−	1.61141i	−0.767109	−	0.641516i	$-0.778306\pi$
$503$	−11.7426	−	36.1401i	−0.523579	−	1.61141i	0.243531	−	0.969893i	$-0.421694\pi$
$504$	−4.85410	+	3.52671i	−0.216219	+	0.157092i
$505$	−10.0000			−0.444994
$506$		0			0
$507$	−24.0000			−1.06588
$508$	−12.9443	+	9.40456i	−0.574309	+	0.417260i
$509$	−12.9787	−	39.9444i	−0.575271	−	1.77050i	−0.635253	−	0.772304i	$-0.719104\pi$
$509$	−12.9787	−	39.9444i	−0.575271	−	1.77050i	0.0599820	−	0.998199i	$-0.480896\pi$
$510$	−3.09017	+	9.51057i	−0.136835	+	0.421135i
$511$	−3.23607	−	2.35114i	−0.143155	−	0.104008i
$512$	8.89919	+	6.46564i	0.393292	+	0.285744i
$513$	−7.41641	+	22.8254i	−0.327442	+	1.00776i
$514$	5.87132	+	18.0701i	0.258973	+	0.797037i
$515$	−6.47214	+	4.70228i	−0.285196	+	0.207207i
$516$		0			0
$517$		0			0
$518$	6.00000			0.263625
$519$	−9.70820	+	7.05342i	−0.426143	+	0.309611i
$520$	−0.927051	−	2.85317i	−0.0406539	−	0.125120i
$521$	9.27051	−	28.5317i	0.406148	−	1.25000i	−0.513784	−	0.857920i	$-0.671757\pi$
$521$	9.27051	−	28.5317i	0.406148	−	1.25000i	0.919933	−	0.392077i	$-0.128243\pi$
$522$	−7.28115	−	5.29007i	−0.318687	−	0.231540i
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	0.833655	−	0.552286i	$-0.186244\pi$
$523$	12.9443	+	9.40456i	0.566013	+	0.411233i	−0.267641	+	0.963519i	$0.586244\pi$
$524$		0			0
$525$	4.94427	+	15.2169i	0.215786	+	0.664120i
$526$	17.7984	−	12.9313i	0.776046	−	0.563830i
$527$	10.0000			0.435607
$528$		0			0
$529$	−19.0000			−0.826087
$530$	−7.28115	+	5.29007i	−0.316273	+	0.229786i
$531$	2.47214	+	7.60845i	0.107282	+	0.330179i
$532$	3.70820	−	11.4127i	0.160771	−	0.494802i
$533$	4.04508	+	2.93893i	0.175212	+	0.127299i
$534$	14.5623	+	10.5801i	0.630173	+	0.457847i
$535$	1.85410	−	5.70634i	0.0801598	−	0.246707i
$536$	−1.85410	−	5.70634i	−0.0800850	−	0.246476i
$537$	−38.8328	+	28.2137i	−1.67576	+	1.21751i
$538$	1.00000			0.0431131
$539$		0			0
$540$	4.00000			0.172133
$541$	−27.5066	+	19.9847i	−1.18260	+	0.859209i	−0.992463	−	0.122548i	$-0.960893\pi$
$541$	−27.5066	+	19.9847i	−1.18260	+	0.859209i	−0.190138	+	0.981757i	$0.560893\pi$
$542$	6.18034	+	19.0211i	0.265468	+	0.817028i
$543$	0.618034	−	1.90211i	0.0265224	−	0.0816275i
$544$	20.2254	+	14.6946i	0.867158	+	0.630027i
$545$	8.89919	+	6.46564i	0.381199	+	0.276957i
$546$	−1.23607	+	3.80423i	−0.0528988	+	0.162806i
$547$	−4.94427	−	15.2169i	−0.211402	−	0.650628i	−0.999390	−	0.0349369i	$-0.988877\pi$
$547$	−4.94427	−	15.2169i	−0.211402	−	0.650628i	0.787988	−	0.615691i	$-0.211123\pi$
$548$	−8.09017	+	5.87785i	−0.345595	+	0.251089i
$549$	6.00000			0.256074
$550$		0			0
$551$	54.0000			2.30048
$552$	9.70820	−	7.05342i	0.413209	−	0.300214i
$553$	6.18034	+	19.0211i	0.262815	+	0.808861i
$554$	0.309017	−	0.951057i	0.0131289	−	0.0404065i
$555$	4.85410	+	3.52671i	0.206045	+	0.149701i
$556$	−1.61803	−	1.17557i	−0.0686199	−	0.0498553i
$557$	−0.618034	+	1.90211i	−0.0261869	+	0.0805951i	−0.963296	−	0.268442i	$-0.913491\pi$
$557$	−0.618034	+	1.90211i	−0.0261869	+	0.0805951i	0.937109	+	0.349037i	$0.113491\pi$
$558$	−0.618034	−	1.90211i	−0.0261635	−	0.0805229i
$559$		0			0
$560$	2.00000			0.0845154
$561$		0			0
$562$	6.00000			0.253095
$563$	−27.5066	+	19.9847i	−1.15926	+	0.842255i	−0.989685	−	0.143262i	$-0.954241\pi$
$563$	−27.5066	+	19.9847i	−1.15926	+	0.842255i	−0.169579	+	0.985517i	$0.554241\pi$
$564$	−1.23607	−	3.80423i	−0.0520479	−	0.160187i
$565$	−2.78115	+	8.55951i	−0.117004	+	0.360101i
$566$	−22.6525	−	16.4580i	−0.952155	−	0.691781i
$567$	−17.7984	−	12.9313i	−0.747461	−	0.543063i
$568$	−11.1246	+	34.2380i	−0.466778	+	1.43660i
$569$	1.85410	+	5.70634i	0.0777280	+	0.239222i	0.982369	−	0.186952i	$-0.0598610\pi$
$569$	1.85410	+	5.70634i	0.0777280	+	0.239222i	−0.904641	+	0.426174i	$0.859861\pi$
$570$	−9.70820	+	7.05342i	−0.406632	+	0.295435i
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$		0			0
$573$	16.0000			0.668410
$574$	−8.09017	+	5.87785i	−0.337677	+	0.245337i
$575$	−2.47214	−	7.60845i	−0.103095	−	0.317294i
$576$	2.16312	−	6.65740i	0.0901300	−	0.277391i
$577$	16.9894	+	12.3435i	0.707276	+	0.513866i	0.882294	−	0.470699i	$-0.155998\pi$
$577$	16.9894	+	12.3435i	0.707276	+	0.513866i	−0.175018	+	0.984565i	$0.555998\pi$
$578$	−6.47214	−	4.70228i	−0.269205	−	0.195589i
$579$	−3.09017	+	9.51057i	−0.128423	+	0.395246i
$580$	−2.78115	−	8.55951i	−0.115481	−	0.355414i
$581$	9.70820	−	7.05342i	0.402764	−	0.292625i
$582$	−26.0000			−1.07773
$583$		0			0
$584$	6.00000			0.248282
$585$	−0.809017	+	0.587785i	−0.0334487	+	0.0243019i
$586$	2.78115	+	8.55951i	0.114888	+	0.353590i
$587$	−4.32624	+	13.3148i	−0.178563	+	0.549560i	−0.999778	−	0.0210582i	$-0.993296\pi$
$587$	−4.32624	+	13.3148i	−0.178563	+	0.549560i	0.821215	+	0.570618i	$0.193296\pi$
$588$	−4.85410	−	3.52671i	−0.200180	−	0.145439i
$589$	9.70820	+	7.05342i	0.400020	+	0.290631i
$590$	2.47214	−	7.60845i	0.101776	−	0.313235i
$591$	−6.79837	−	20.9232i	−0.279648	−	0.860667i
$592$	−2.42705	+	1.76336i	−0.0997512	+	0.0724735i
$593$	11.0000			0.451716			0.225858	−	0.974160i	$-0.427481\pi$
$593$	11.0000			0.451716			0.225858	+	0.974160i	$0.427481\pi$
$594$		0			0
$595$	10.0000			0.409960
$596$	13.7533	−	9.99235i	0.563357	−	0.409303i
$597$	14.8328	+	45.6507i	0.607067	+	1.86836i
$598$	0.618034	−	1.90211i	0.0252733	−	0.0777832i
$599$	−27.5066	−	19.9847i	−1.12389	−	0.816553i	−0.139094	−	0.990279i	$-0.544419\pi$
$599$	−27.5066	−	19.9847i	−1.12389	−	0.816553i	−0.984794	+	0.173726i	$0.944419\pi$
$600$	−19.4164	−	14.1068i	−0.792672	−	0.575910i
$601$	−4.01722	+	12.3637i	−0.163866	+	0.504327i	−0.998951	−	0.0457936i	$-0.985418\pi$
$601$	−4.01722	+	12.3637i	−0.163866	+	0.504327i	0.835085	+	0.550121i	$0.185418\pi$
$602$		0			0
$603$	−1.61803	+	1.17557i	−0.0658914	+	0.0478729i
$604$	16.0000			0.651031
$605$		0			0
$606$	−20.0000			−0.812444
$607$	8.09017	−	5.87785i	0.328370	−	0.238575i	−0.411369	−	0.911469i	$-0.634949\pi$
$607$	8.09017	−	5.87785i	0.328370	−	0.238575i	0.739739	+	0.672894i	$0.234949\pi$
$608$	9.27051	+	28.5317i	0.375969	+	1.15711i
$609$	−11.1246	+	34.2380i	−0.450792	+	1.38740i
$610$	−4.85410	−	3.52671i	−0.196537	−	0.142792i
$611$	−1.61803	−	1.17557i	−0.0654586	−	0.0475585i
$612$	1.54508	−	4.75528i	0.0624564	−	0.192221i
$613$	5.25329	+	16.1680i	0.212178	+	0.653018i	0.999342	+	0.0362735i	$0.0115487\pi$
$613$	5.25329	+	16.1680i	0.212178	+	0.653018i	−0.787164	+	0.616744i	$0.788451\pi$
$614$	17.7984	−	12.9313i	0.718284	−	0.521864i
$615$	−10.0000			−0.403239
$616$		0			0
$617$	−9.00000			−0.362326			−0.181163	−	0.983453i	$-0.557986\pi$
$617$	−9.00000			−0.362326			−0.181163	+	0.983453i	$0.557986\pi$
$618$	−12.9443	+	9.40456i	−0.520695	+	0.378307i
$619$	0.618034	+	1.90211i	0.0248409	+	0.0764524i	0.962708	−	0.270541i	$-0.0872026\pi$
$619$	0.618034	+	1.90211i	0.0248409	+	0.0764524i	−0.937868	+	0.346993i	$0.887203\pi$
$620$	0.618034	−	1.90211i	0.0248208	−	0.0763907i
$621$	6.47214	+	4.70228i	0.259718	+	0.188696i
$622$	−19.4164	−	14.1068i	−0.778527	−	0.565633i
$623$	5.56231	−	17.1190i	0.222849	−	0.685859i
$624$	−0.618034	−	1.90211i	−0.0247412	−	0.0761455i
$625$	−8.89919	+	6.46564i	−0.355967	+	0.258626i
$626$	23.0000			0.919265
$627$		0			0
$628$	−2.00000			−0.0798087
$629$	−12.1353	+	8.81678i	−0.483864	+	0.351548i
$630$	−0.618034	−	1.90211i	−0.0246231	−	0.0757820i
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	−0.999496	−	0.0317495i	$-0.989892\pi$
$631$	−4.32624	+	13.3148i	−0.172225	+	0.530053i	0.827271	+	0.561803i	$0.189892\pi$
$632$	−24.2705	−	17.6336i	−0.965429	−	0.701425i
$633$	−19.4164	−	14.1068i	−0.771733	−	0.560697i
$634$	−0.618034	+	1.90211i	−0.0245453	+	0.0755426i
$635$	−4.94427	−	15.2169i	−0.196207	−	0.603864i
$636$	14.5623	−	10.5801i	0.577433	−	0.419530i
$637$	−3.00000			−0.118864
$638$		0			0
$639$	12.0000			0.474713
$640$	2.42705	−	1.76336i	0.0959376	−	0.0697028i
$641$	−2.78115	−	8.55951i	−0.109849	−	0.338080i	0.880989	−	0.473137i	$-0.156878\pi$
$641$	−2.78115	−	8.55951i	−0.109849	−	0.338080i	−0.990838	+	0.135057i	$0.956878\pi$
$642$	3.70820	−	11.4127i	0.146351	−	0.450422i
$643$	8.09017	+	5.87785i	0.319045	+	0.231800i	0.735768	−	0.677234i	$-0.236821\pi$
$643$	8.09017	+	5.87785i	0.319045	+	0.231800i	−0.416723	+	0.909034i	$0.636821\pi$
$644$	−3.23607	−	2.35114i	−0.127519	−	0.0926479i
$645$		0			0
$646$	−9.27051	−	28.5317i	−0.364743	−	1.12256i
$647$	−16.1803	+	11.7557i	−0.636115	+	0.462164i	−0.858513	−	0.512791i	$-0.828611\pi$
$647$	−16.1803	+	11.7557i	−0.636115	+	0.462164i	0.222398	+	0.974956i	$0.428611\pi$
$648$	33.0000			1.29636
$649$		0			0
$650$	−4.00000			−0.156893
$651$	−6.47214	+	4.70228i	−0.253663	+	0.184297i
$652$	0.618034	+	1.90211i	0.0242041	+	0.0744925i
$653$	−4.32624	+	13.3148i	−0.169299	+	0.521048i	−0.999327	−	0.0366729i	$-0.988324\pi$
$653$	−4.32624	+	13.3148i	−0.169299	+	0.521048i	0.830029	+	0.557721i	$0.188324\pi$
$654$	17.7984	+	12.9313i	0.695971	+	0.505653i
$655$		0			0
$656$	1.54508	−	4.75528i	0.0603254	−	0.185663i
$657$	−0.618034	−	1.90211i	−0.0241118	−	0.0742085i
$658$	3.23607	−	2.35114i	0.126155	−	0.0916570i
$659$	22.0000			0.856998			0.428499	−	0.903542i	$-0.359042\pi$
$659$	22.0000			0.856998			0.428499	+	0.903542i	$0.359042\pi$
$660$		0			0
$661$	13.0000			0.505641			0.252821	−	0.967513i	$-0.418642\pi$
$661$	13.0000			0.505641			0.252821	+	0.967513i	$0.418642\pi$
$662$	16.1803	−	11.7557i	0.628867	−	0.456898i
$663$	−3.09017	−	9.51057i	−0.120012	−	0.369360i
$664$	−5.56231	+	17.1190i	−0.215859	+	0.664347i
$665$	9.70820	+	7.05342i	0.376468	+	0.273520i
$666$	2.42705	+	1.76336i	0.0940463	+	0.0683286i
$667$	5.56231	−	17.1190i	0.215373	−	0.662851i
$668$	−3.70820	−	11.4127i	−0.143475	−	0.441570i
$669$	32.3607	−	23.5114i	1.25114	−	0.909004i
$670$	2.00000			0.0772667
$671$		0			0
$672$	−20.0000			−0.771517
$673$	8.09017	−	5.87785i	0.311853	−	0.226575i	−0.420838	−	0.907136i	$-0.638264\pi$
$673$	8.09017	−	5.87785i	0.311853	−	0.226575i	0.732691	+	0.680561i	$0.238264\pi$
$674$	−4.01722	−	12.3637i	−0.154738	−	0.476233i
$675$	4.94427	−	15.2169i	0.190305	−	0.585699i
$676$	−9.70820	−	7.05342i	−0.373392	−	0.271286i
$677$	21.8435	+	15.8702i	0.839512	+	0.609941i	0.922234	−	0.386631i	$-0.126361\pi$
$677$	21.8435	+	15.8702i	0.839512	+	0.609941i	−0.0827221	+	0.996573i	$0.526361\pi$
$678$	−5.56231	+	17.1190i	−0.213619	+	0.657452i
$679$	8.03444	+	24.7275i	0.308334	+	0.948953i
$680$	−12.1353	+	8.81678i	−0.465366	+	0.338108i
$681$	−48.0000			−1.83936
$682$		0			0
$683$	2.00000			0.0765279			0.0382639	−	0.999268i	$-0.487817\pi$
$683$	2.00000			0.0765279			0.0382639	+	0.999268i	$0.487817\pi$
$684$	4.85410	−	3.52671i	0.185601	−	0.134847i
$685$	−3.09017	−	9.51057i	−0.118069	−	0.363380i
$686$	6.18034	−	19.0211i	0.235966	−	0.726230i
$687$	−14.5623	−	10.5801i	−0.555587	−	0.403657i
$688$		0			0
$689$	2.78115	−	8.55951i	0.105953	−	0.326091i
$690$	1.23607	+	3.80423i	0.0470563	+	0.144824i
$691$	−16.1803	+	11.7557i	−0.615529	+	0.447208i	−0.851357	−	0.524587i	$-0.824220\pi$
$691$	−16.1803	+	11.7557i	−0.615529	+	0.447208i	0.235828	+	0.971795i	$0.424220\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	28.0000			1.06287
$695$	1.61803	−	1.17557i	0.0613755	−	0.0445919i
$696$	−16.6869	−	51.3571i	−0.632516	−	1.94668i
$697$	7.72542	−	23.7764i	0.292621	−	0.900596i
$698$	21.8435	+	15.8702i	0.826787	+	0.600696i
$699$	33.9787	+	24.6870i	1.28519	+	0.933747i
$700$	−2.47214	+	7.60845i	−0.0934380	+	0.287572i
$701$	5.25329	+	16.1680i	0.198414	+	0.610655i	0.999920	+	0.0126684i	$0.00403259\pi$
$701$	5.25329	+	16.1680i	0.198414	+	0.610655i	−0.801506	+	0.597987i	$0.795967\pi$
$702$	3.23607	−	2.35114i	0.122138	−	0.0887381i
$703$	−18.0000			−0.678883
$704$		0			0
$705$	4.00000			0.150649
$706$	7.28115	−	5.29007i	0.274030	−	0.199094i
$707$	6.18034	+	19.0211i	0.232436	+	0.715363i
$708$	−4.94427	+	15.2169i	−0.185817	+	0.571886i
$709$	8.09017	+	5.87785i	0.303833	+	0.220747i	0.729246	−	0.684252i	$-0.239871\pi$
$709$	8.09017	+	5.87785i	0.303833	+	0.220747i	−0.425413	+	0.904999i	$0.639871\pi$
$710$	−9.70820	−	7.05342i	−0.364342	−	0.264710i
$711$	−3.09017	+	9.51057i	−0.115890	+	0.356674i
$712$	8.34346	+	25.6785i	0.312684	+	0.962343i
$713$	3.23607	−	2.35114i	0.121192	−	0.0880509i
$714$	20.0000			0.748481
$715$		0			0
$716$	−24.0000			−0.896922
$717$	−9.70820	+	7.05342i	−0.362560	+	0.263415i
$718$	−0.618034	−	1.90211i	−0.0230648	−	0.0709862i
$719$	9.27051	−	28.5317i	0.345732	−	1.06405i	−0.615459	−	0.788169i	$-0.711029\pi$
$719$	9.27051	−	28.5317i	0.345732	−	1.06405i	0.961191	−	0.275884i	$-0.0889706\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	12.9443	+	9.40456i	0.482070	+	0.350244i
$722$	5.25329	−	16.1680i	0.195507	−	0.601709i
$723$	13.5967	+	41.8465i	0.505668	+	1.55629i
$724$	0.809017	−	0.587785i	0.0300669	−	0.0218449i
$725$	−36.0000			−1.33701
$726$		0			0
$727$	−42.0000			−1.55769			−0.778847	−	0.627214i	$-0.784195\pi$
$727$	−42.0000			−1.55769			−0.778847	+	0.627214i	$0.784195\pi$
$728$	−4.85410	+	3.52671i	−0.179905	+	0.130709i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	−0.618034	+	1.90211i	−0.0228745	+	0.0704004i
$731$		0			0
$732$	9.70820	+	7.05342i	0.358826	+	0.260702i
$733$	2.78115	−	8.55951i	0.102724	−	0.316153i	−0.886465	−	0.462795i	$-0.846847\pi$
$733$	2.78115	−	8.55951i	0.102724	−	0.316153i	0.989190	+	0.146642i	$0.0468466\pi$
$734$	−4.32624	−	13.3148i	−0.159684	−	0.491458i
$735$	4.85410	−	3.52671i	0.179046	−	0.130085i
$736$	10.0000			0.368605
$737$		0			0
$738$	−5.00000			−0.184053
$739$	8.09017	−	5.87785i	0.297602	−	0.216220i	−0.428957	−	0.903325i	$-0.641119\pi$
$739$	8.09017	−	5.87785i	0.297602	−	0.216220i	0.726558	+	0.687105i	$0.241119\pi$
$740$	0.927051	+	2.85317i	0.0340791	+	0.104885i
$741$	3.70820	−	11.4127i	0.136224	−	0.419255i
$742$	14.5623	+	10.5801i	0.534599	+	0.388409i
$743$	30.7426	+	22.3358i	1.12784	+	0.819422i	0.985379	−	0.170378i	$-0.0544989\pi$
$743$	30.7426	+	22.3358i	1.12784	+	0.819422i	0.142460	+	0.989801i	$0.454499\pi$
$744$	3.70820	−	11.4127i	0.135949	−	0.418409i
$745$	5.25329	+	16.1680i	0.192466	+	0.592348i
$746$	−17.7984	+	12.9313i	−0.651645	+	0.473448i
$747$	6.00000			0.219529
$748$		0			0
$749$	−12.0000			−0.438470
$750$	14.5623	−	10.5801i	0.531740	−	0.386332i
$751$	−6.18034	−	19.0211i	−0.225524	−	0.694091i	−0.998238	−	0.0593368i	$-0.981101\pi$
$751$	−6.18034	−	19.0211i	−0.225524	−	0.694091i	0.772714	−	0.634754i	$-0.218899\pi$
$752$	−0.618034	+	1.90211i	−0.0225374	+	0.0693629i
$753$	3.23607	+	2.35114i	0.117929	+	0.0856803i
$754$	−7.28115	−	5.29007i	−0.265164	−	0.192653i
$755$	−4.94427	+	15.2169i	−0.179940	+	0.553800i
$756$	−2.47214	−	7.60845i	−0.0899107	−	0.276717i
$757$	−42.8779	+	31.1526i	−1.55842	+	1.13226i	−0.621137	+	0.783702i	$0.713329\pi$
$757$	−42.8779	+	31.1526i	−1.55842	+	1.13226i	−0.937287	+	0.348559i	$0.886671\pi$
$758$	−32.0000			−1.16229
$759$		0			0
$760$	−18.0000			−0.652929
$761$	16.9894	−	12.3435i	0.615864	−	0.447451i	−0.235611	−	0.971848i	$-0.575709\pi$
$761$	16.9894	−	12.3435i	0.615864	−	0.447451i	0.851474	+	0.524396i	$0.175709\pi$
$762$	−9.88854	−	30.4338i	−0.358224	−	1.10250i
$763$	6.79837	−	20.9232i	0.246118	−	0.757472i
$764$	6.47214	+	4.70228i	0.234154	+	0.170123i
$765$	4.04508	+	2.93893i	0.146250	+	0.106257i
$766$	6.18034	−	19.0211i	0.223305	−	0.687261i
$767$	2.47214	+	7.60845i	0.0892637	+	0.274725i
$768$	27.5066	−	19.9847i	0.992558	−	0.721136i
$769$	11.0000			0.396670			0.198335	−	0.980134i	$-0.436447\pi$
$769$	11.0000			0.396670			0.198335	+	0.980134i	$0.436447\pi$
$770$		0			0
$771$	38.0000			1.36854
$772$	−4.04508	+	2.93893i	−0.145586	+	0.105774i
$773$	−12.9787	−	39.9444i	−0.466812	−	1.43670i	−0.856689	−	0.515833i	$-0.827483\pi$
$773$	−12.9787	−	39.9444i	−0.466812	−	1.43670i	0.389878	−	0.920867i	$-0.372517\pi$
$774$		0			0
$775$	−6.47214	−	4.70228i	−0.232486	−	0.168911i
$776$	−31.5517	−	22.9236i	−1.13264	−	0.822910i
$777$	3.70820	−	11.4127i	0.133031	−	0.409428i
$778$	−0.927051	−	2.85317i	−0.0332364	−	0.102291i
$779$	24.2705	−	17.6336i	0.869581	−	0.631788i
$780$	−2.00000			−0.0716115
$781$		0			0
$782$	−10.0000			−0.357599
$783$	29.1246	−	21.1603i	1.04083	−	0.756206i
$784$	0.927051	+	2.85317i	0.0331090	+	0.101899i
$785$	0.618034	−	1.90211i	0.0220586	−	0.0678893i
$786$		0			0
$787$	−22.6525	−	16.4580i	−0.807474	−	0.586664i	0.105623	−	0.994406i	$-0.466316\pi$
$787$	−22.6525	−	16.4580i	−0.807474	−	0.586664i	−0.913097	+	0.407742i	$0.866316\pi$
$788$	3.39919	−	10.4616i	0.121091	−	0.372680i
$789$	−13.5967	−	41.8465i	−0.484057	−	1.48977i
$790$	8.09017	−	5.87785i	0.287835	−	0.209125i
$791$	18.0000			0.640006
$792$		0			0
$793$	6.00000			0.213066
$794$	−10.5172	+	7.64121i	−0.373242	+	0.271176i
$795$	5.56231	+	17.1190i	0.197275	+	0.607149i
$796$	−7.41641	+	22.8254i	−0.262868	+	0.809023i
$797$	8.09017	+	5.87785i	0.286569	+	0.208204i	0.721777	−	0.692125i	$-0.243325\pi$
$797$	8.09017	+	5.87785i	0.286569	+	0.208204i	−0.435209	+	0.900330i	$0.643325\pi$
$798$	19.4164	+	14.1068i	0.687333	+	0.499377i
$799$	−3.09017	+	9.51057i	−0.109322	+	0.336460i
$800$	−6.18034	−	19.0211i	−0.218508	−	0.672499i
$801$	7.28115	−	5.29007i	0.257267	−	0.186915i
$802$	23.0000			0.812158
$803$		0			0
$804$	−4.00000			−0.141069
$805$	3.23607	−	2.35114i	0.114056	−	0.0828668i
$806$	−0.618034	−	1.90211i	−0.0217693	−	0.0669991i
$807$	0.618034	−	1.90211i	0.0217558	−	0.0669575i
$808$	−24.2705	−	17.6336i	−0.853834	−	0.620346i
$809$	−4.85410	−	3.52671i	−0.170661	−	0.123993i	0.499176	−	0.866501i	$-0.333636\pi$
$809$	−4.85410	−	3.52671i	−0.170661	−	0.123993i	−0.669837	+	0.742508i	$0.733636\pi$
$810$	−3.39919	+	10.4616i	−0.119435	+	0.367584i
$811$	8.65248	+	26.6296i	0.303830	+	0.935091i	0.980111	+	0.198448i	$0.0635901\pi$
$811$	8.65248	+	26.6296i	0.303830	+	0.935091i	−0.676282	+	0.736643i	$0.736410\pi$
$812$	−14.5623	+	10.5801i	−0.511037	+	0.371290i
$813$	40.0000			1.40286
$814$		0			0
$815$	−2.00000			−0.0700569
$816$	−8.09017	+	5.87785i	−0.283213	+	0.205766i
$817$		0			0
$818$	−6.48936	+	19.9722i	−0.226895	+	0.698311i
$819$	1.61803	+	1.17557i	0.0565387	+	0.0410778i
$820$	−4.04508	−	2.93893i	−0.141260	−	0.102632i
$821$	−0.618034	+	1.90211i	−0.0215695	+	0.0663842i	−0.961262	−	0.275637i	$-0.911111\pi$
$821$	−0.618034	+	1.90211i	−0.0215695	+	0.0663842i	0.939692	+	0.342021i	$0.111111\pi$
$822$	−6.18034	−	19.0211i	−0.215564	−	0.663438i
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	−0.195486	−	0.980707i	$-0.562628\pi$
$823$	19.4164	−	14.1068i	0.676813	−	0.491734i	0.872299	+	0.488973i	$0.162628\pi$
$824$	−24.0000			−0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	8.09017	−	5.87785i	0.281323	−	0.204393i	−0.438171	−	0.898891i	$-0.644374\pi$
$827$	8.09017	−	5.87785i	0.281323	−	0.204393i	0.719494	+	0.694498i	$0.244374\pi$
$828$	−0.618034	−	1.90211i	−0.0214782	−	0.0661030i
$829$	−14.5238	+	44.6997i	−0.504432	+	1.55248i	0.297290	+	0.954787i	$0.403917\pi$
$829$	−14.5238	+	44.6997i	−0.504432	+	1.55248i	−0.801723	+	0.597696i	$0.796083\pi$
$830$	−4.85410	−	3.52671i	−0.168488	−	0.122414i
$831$	−1.61803	−	1.17557i	−0.0561290	−	0.0407801i
$832$	2.16312	−	6.65740i	0.0749927	−	0.230804i
$833$	4.63525	+	14.2658i	0.160602	+	0.494282i
$834$	3.23607	−	2.35114i	0.112056	−	0.0814134i
$835$	12.0000			0.415277
$836$		0			0
$837$	8.00000			0.276520
$838$	−1.61803	+	1.17557i	−0.0558941	+	0.0406094i
$839$	14.2148	+	43.7486i	0.490749	+	1.51037i	0.823479	+	0.567347i	$0.192030\pi$
$839$	14.2148	+	43.7486i	0.490749	+	1.51037i	−0.332730	+	0.943022i	$0.607970\pi$
$840$	3.70820	−	11.4127i	0.127945	−	0.393775i
$841$	−42.0689	−	30.5648i	−1.45065	−	1.05396i
$842$	−10.5172	−	7.64121i	−0.362447	−	0.263333i
$843$	3.70820	−	11.4127i	0.127717	−	0.393074i
$844$	−3.70820	−	11.4127i	−0.127642	−	0.392841i
$845$	9.70820	−	7.05342i	0.333972	−	0.242645i
$846$	2.00000			0.0687614
$847$		0			0
$848$	−9.00000			−0.309061
$849$	−45.3050	+	32.9160i	−1.55486	+	1.12967i
$850$	6.18034	+	19.0211i	0.211984	+	0.652419i
$851$	−1.85410	+	5.70634i	−0.0635578	+	0.195611i
$852$	19.4164	+	14.1068i	0.665195	+	0.483293i
$853$	−13.7533	−	9.99235i	−0.470904	−	0.342132i	0.326890	−	0.945062i	$-0.393999\pi$
$853$	−13.7533	−	9.99235i	−0.470904	−	0.342132i	−0.797793	+	0.602931i	$0.793999\pi$
$854$	−3.70820	+	11.4127i	−0.126892	+	0.390534i
$855$	1.85410	+	5.70634i	0.0634089	+	0.195153i
$856$	14.5623	−	10.5801i	0.497729	−	0.361622i
$857$	−22.0000			−0.751506			−0.375753	−	0.926720i	$-0.622616\pi$
$857$	−22.0000			−0.751506			−0.375753	+	0.926720i	$0.622616\pi$
$858$		0			0
$859$	24.0000			0.818869			0.409435	−	0.912339i	$-0.365726\pi$
$859$	24.0000			0.818869			0.409435	+	0.912339i	$0.365726\pi$
$860$		0			0
$861$	6.18034	+	19.0211i	0.210625	+	0.648238i
$862$	3.70820	−	11.4127i	0.126302	−	0.388717i
$863$	43.6869	+	31.7404i	1.48712	+	1.08046i	0.975174	+	0.221438i	$0.0710750\pi$
$863$	43.6869	+	31.7404i	1.48712	+	1.08046i	0.511946	+	0.859018i	$0.328925\pi$
$864$	16.1803	+	11.7557i	0.550466	+	0.399937i
$865$	1.85410	−	5.70634i	0.0630414	−	0.194021i
$866$	5.87132	+	18.0701i	0.199516	+	0.614046i
$867$	−12.9443	+	9.40456i	−0.439611	+	0.319396i
$868$	−4.00000			−0.135769
$869$		0			0
$870$	18.0000			0.610257
$871$	−1.61803	+	1.17557i	−0.0548250	+	0.0398327i
$872$	10.1976	+	31.3849i	0.345333	+	1.06283i
$873$	−4.01722	+	12.3637i	−0.135962	+	0.418449i
$874$	−9.70820	−	7.05342i	−0.328385	−	0.238586i
$875$	−14.5623	−	10.5801i	−0.492296	−	0.357674i
$876$	1.23607	−	3.80423i	0.0417629	−	0.128533i
$877$	−8.34346	−	25.6785i	−0.281739	−	0.867102i	−0.987357	−	0.158510i	$-0.949331\pi$
$877$	−8.34346	−	25.6785i	−0.281739	−	0.867102i	0.705619	−	0.708592i	$-0.250669\pi$
$878$	−17.7984	+	12.9313i	−0.600666	+	0.436409i
$879$	18.0000			0.607125
$880$		0			0
$881$	35.0000			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$881$	35.0000			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$882$	2.42705	−	1.76336i	0.0817231	−	0.0593753i
$883$	−6.18034	−	19.0211i	−0.207985	−	0.640112i	−0.999578	−	0.0290628i	$-0.990748\pi$
$883$	−6.18034	−	19.0211i	−0.207985	−	0.640112i	0.791593	−	0.611049i	$-0.209252\pi$
$884$	1.54508	−	4.75528i	0.0519668	−	0.159937i
$885$	−12.9443	−	9.40456i	−0.435117	−	0.316131i
$886$	16.1803	+	11.7557i	0.543589	+	0.394941i
$887$	−14.2148	+	43.7486i	−0.477286	+	1.46893i	0.365565	+	0.930786i	$0.380876\pi$
$887$	−14.2148	+	43.7486i	−0.477286	+	1.46893i	−0.842850	+	0.538148i	$0.819124\pi$
$888$	5.56231	+	17.1190i	0.186659	+	0.574477i
$889$	−25.8885	+	18.8091i	−0.868274	+	0.630838i
$890$	−9.00000			−0.301681
$891$		0			0
$892$	20.0000			0.669650
$893$	−9.70820	+	7.05342i	−0.324873	+	0.236034i
$894$	10.5066	+	32.3359i	0.351393	+	1.08147i
$895$	7.41641	−	22.8254i	0.247903	−	0.762968i
$896$	−4.85410	−	3.52671i	−0.162164	−	0.117819i
$897$	−3.23607	−	2.35114i	−0.108049	−	0.0785023i
$898$	−4.01722	+	12.3637i	−0.134056	+	0.412583i
$899$	−5.56231	−	17.1190i	−0.185513	−	0.570951i
$900$	−3.23607	+	2.35114i	−0.107869	+	0.0783714i
$901$	−45.0000			−1.49917
$902$		0			0
$903$		0			0
$904$	−21.8435	+	15.8702i	−0.726503	+	0.527835i
$905$	0.309017	+	0.951057i	0.0102721	+	0.0316142i
$906$	−9.88854	+	30.4338i	−0.328525	+	1.01110i
$907$	−9.70820	−	7.05342i	−0.322356	−	0.234205i	0.414824	−	0.909902i	$-0.363843\pi$
$907$	−9.70820	−	7.05342i	−0.322356	−	0.234205i	−0.737180	+	0.675696i	$0.763843\pi$
$908$	−19.4164	−	14.1068i	−0.644356	−	0.468152i
$909$	−3.09017	+	9.51057i	−0.102494	+	0.315446i
$910$	−0.618034	−	1.90211i	−0.0204876	−	0.0630544i
$911$	19.4164	−	14.1068i	0.643294	−	0.467381i	−0.217686	−	0.976019i	$-0.569851\pi$
$911$	19.4164	−	14.1068i	0.643294	−	0.467381i	0.860980	+	0.508638i	$0.169851\pi$
$912$	−12.0000			−0.397360
$913$		0			0
$914$	39.0000			1.29001
$915$	−9.70820	+	7.05342i	−0.320943	+	0.233179i
$916$	−2.78115	−	8.55951i	−0.0918919	−	0.282814i
$917$		0			0
$918$	−16.1803	−	11.7557i	−0.534031	−	0.387996i
$919$	−22.6525	−	16.4580i	−0.747236	−	0.542899i	0.147733	−	0.989027i	$-0.452802\pi$
$919$	−22.6525	−	16.4580i	−0.747236	−	0.542899i	−0.894969	+	0.446128i	$0.852802\pi$
$920$	−1.85410	+	5.70634i	−0.0611279	+	0.188132i
$921$	−13.5967	−	41.8465i	−0.448028	−	1.37889i
$922$	−26.6976	+	19.3969i	−0.879237	+	0.638803i
$923$	12.0000			0.394985
$924$		0			0
$925$	12.0000			0.394558
$926$	16.1803	−	11.7557i	0.531719	−	0.386316i
$927$	2.47214	+	7.60845i	0.0811956	+	0.249894i
$928$	13.9058	−	42.7975i	0.456479	−	1.40490i
$929$	16.9894	+	12.3435i	0.557403	+	0.404977i	0.830507	−	0.557008i	$-0.188051\pi$
$929$	16.9894	+	12.3435i	0.557403	+	0.404977i	−0.273105	+	0.961984i	$0.588051\pi$
$930$	3.23607	+	2.35114i	0.106115	+	0.0770970i
$931$	−5.56231	+	17.1190i	−0.182297	+	0.561053i
$932$	6.48936	+	19.9722i	0.212566	+	0.654211i
$933$	−38.8328	+	28.2137i	−1.27133	+	0.923675i
$934$	12.0000			0.392652
$935$		0			0
$936$	−3.00000			−0.0980581
$937$	−18.6074	+	13.5191i	−0.607877	+	0.441648i	−0.848666	−	0.528929i	$-0.822594\pi$
$937$	−18.6074	+	13.5191i	−0.607877	+	0.441648i	0.240789	+	0.970577i	$0.422594\pi$
$938$	−1.23607	−	3.80423i	−0.0403591	−	0.124212i
$939$	14.2148	−	43.7486i	0.463882	−	1.42768i
$940$	1.61803	+	1.17557i	0.0527744	+	0.0383429i
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	0.883843	−	0.467784i	$-0.154947\pi$
$941$	21.8435	+	15.8702i	0.712076	+	0.517354i	−0.171766	+	0.985138i	$0.554947\pi$
$942$	1.23607	−	3.80423i	0.0402733	−	0.123948i
$943$	−3.09017	−	9.51057i	−0.100630	−	0.309707i
$944$	6.47214	−	4.70228i	0.210650	−	0.153046i
$945$	8.00000			0.260240
$946$		0			0
$947$	−42.0000			−1.36482			−0.682408	−	0.730971i	$-0.739067\pi$
$947$	−42.0000			−1.36482			−0.682408	+	0.730971i	$0.739067\pi$
$948$	−16.1803	+	11.7557i	−0.525513	+	0.381808i
$949$	−0.618034	−	1.90211i	−0.0200622	−	0.0617452i
$950$	−7.41641	+	22.8254i	−0.240620	+	0.740552i
$951$	3.23607	+	2.35114i	0.104937	+	0.0762410i
$952$	24.2705	+	17.6336i	0.786612	+	0.571507i
$953$	9.57953	−	29.4828i	0.310311	−	0.955040i	−0.667330	−	0.744762i	$-0.732563\pi$
$953$	9.57953	−	29.4828i	0.310311	−	0.955040i	0.977642	−	0.210278i	$-0.0674370\pi$
$954$	2.78115	+	8.55951i	0.0900432	+	0.277124i
$955$	−6.47214	+	4.70228i	−0.209433	+	0.152162i
$956$	−6.00000			−0.194054
$957$		0			0
$958$	−16.0000			−0.516937
$959$	−16.1803	+	11.7557i	−0.522490	+	0.379612i
$960$	4.32624	+	13.3148i	0.139629	+	0.429733i
$961$	−8.34346	+	25.6785i	−0.269144	+	0.828340i
$962$	2.42705	+	1.76336i	0.0782513	+	0.0568529i
$963$	−4.85410	−	3.52671i	−0.156421	−	0.113647i
$964$	−6.79837	+	20.9232i	−0.218961	+	0.673892i
$965$	−1.54508	−	4.75528i	−0.0497380	−	0.153078i
$966$	6.47214	−	4.70228i	0.208238	−	0.151293i
$967$	22.0000			0.707472			0.353736	−	0.935345i	$-0.384911\pi$
$967$	22.0000			0.707472			0.353736	+	0.935345i	$0.384911\pi$
$968$		0			0
$969$	−60.0000			−1.92748
$970$	10.5172	−	7.64121i	0.337688	−	0.245344i
$971$	0.618034	+	1.90211i	0.0198337	+	0.0610417i	0.960483	−	0.278337i	$-0.0897832\pi$
$971$	0.618034	+	1.90211i	0.0198337	+	0.0610417i	−0.940650	+	0.339379i	$0.889783\pi$
$972$	3.09017	−	9.51057i	0.0991172	−	0.305052i
$973$	−3.23607	−	2.35114i	−0.103744	−	0.0753741i
$974$	−1.61803	−	1.17557i	−0.0518452	−	0.0376677i
$975$	−2.47214	+	7.60845i	−0.0791717	+	0.243665i
$976$	−1.85410	−	5.70634i	−0.0593484	−	0.182655i
$977$	46.1140	−	33.5038i	1.47532	−	1.07188i	0.496288	−	0.868158i	$-0.334696\pi$
$977$	46.1140	−	33.5038i	1.47532	−	1.07188i	0.979029	−	0.203722i	$-0.0653039\pi$
$978$	−4.00000			−0.127906
$979$		0			0
$980$	3.00000			0.0958315
$981$	8.89919	−	6.46564i	0.284129	−	0.206432i
$982$	−0.618034	−	1.90211i	−0.0197223	−	0.0606989i
$983$	−11.1246	+	34.2380i	−0.354820	+	1.09202i	0.601294	+	0.799028i	$0.294652\pi$
$983$	−11.1246	+	34.2380i	−0.354820	+	1.09202i	−0.956114	+	0.292996i	$0.905348\pi$
$984$	−24.2705	−	17.6336i	−0.773716	−	0.562137i
$985$	8.89919	+	6.46564i	0.283552	+	0.206012i
$986$	−13.9058	+	42.7975i	−0.442850	+	1.36295i
$987$	−2.47214	−	7.60845i	−0.0786890	−	0.242180i
$988$	4.85410	−	3.52671i	0.154430	−	0.112200i
$989$		0			0
$990$		0			0
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	8.09017	−	5.87785i	0.256863	−	0.186622i
$993$	−12.3607	−	38.0423i	−0.392254	−	1.20723i
$994$	−7.41641	+	22.8254i	−0.235234	+	0.723976i
$995$	−19.4164	−	14.1068i	−0.615542	−	0.447217i
$996$	9.70820	+	7.05342i	0.307616	+	0.223496i
$997$	16.3779	−	50.4060i	0.518693	−	1.59637i	−0.257767	−	0.966207i	$-0.582987\pi$
$997$	16.3779	−	50.4060i	0.518693	−	1.59637i	0.776460	−	0.630167i	$-0.217013\pi$
$998$	2.47214	+	7.60845i	0.0782541	+	0.240841i
$999$	−9.70820	+	7.05342i	−0.307154	+	0.223160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.c.b.3.1		4
11.2	odd	10		121.2.a.a.1.1	✓	1
11.3	even	5	inner	121.2.c.b.27.1		4
11.4	even	5	inner	121.2.c.b.81.1		4
11.5	even	5	inner	121.2.c.b.9.1		4
11.6	odd	10		121.2.c.d.9.1		4
11.7	odd	10		121.2.c.d.81.1		4
11.8	odd	10		121.2.c.d.27.1		4
11.9	even	5		121.2.a.c.1.1	yes	1
11.10	odd	2		121.2.c.d.3.1		4
33.2	even	10		1089.2.a.i.1.1		1
33.20	odd	10		1089.2.a.c.1.1		1
44.31	odd	10		1936.2.a.b.1.1		1
44.35	even	10		1936.2.a.a.1.1		1
55.9	even	10		3025.2.a.b.1.1		1
55.24	odd	10		3025.2.a.e.1.1		1
77.13	even	10		5929.2.a.a.1.1		1
77.20	odd	10		5929.2.a.g.1.1		1
88.13	odd	10		7744.2.a.f.1.1		1
88.35	even	10		7744.2.a.be.1.1		1
88.53	even	10		7744.2.a.c.1.1		1
88.75	odd	10		7744.2.a.bf.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.a.a.1.1	✓	1	11.2	odd	10
121.2.a.c.1.1	yes	1	11.9	even	5
121.2.c.b.3.1		4	1.1	even	1	trivial
121.2.c.b.9.1		4	11.5	even	5	inner
121.2.c.b.27.1		4	11.3	even	5	inner
121.2.c.b.81.1		4	11.4	even	5	inner
121.2.c.d.3.1		4	11.10	odd	2
121.2.c.d.9.1		4	11.6	odd	10
121.2.c.d.27.1		4	11.8	odd	10
121.2.c.d.81.1		4	11.7	odd	10
1089.2.a.c.1.1		1	33.20	odd	10
1089.2.a.i.1.1		1	33.2	even	10
1936.2.a.a.1.1		1	44.35	even	10
1936.2.a.b.1.1		1	44.31	odd	10
3025.2.a.b.1.1		1	55.9	even	10
3025.2.a.e.1.1		1	55.24	odd	10
5929.2.a.a.1.1		1	77.13	even	10
5929.2.a.g.1.1		1	77.20	odd	10
7744.2.a.c.1.1		1	88.53	even	10
7744.2.a.f.1.1		1	88.13	odd	10
7744.2.a.be.1.1		1	88.35	even	10
7744.2.a.bf.1.1		1	88.75	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.618034 + 1.90211i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-1.61803 - 1.17557i) q^{6} +(-0.618034 + 1.90211i) q^{7} +(-0.927051 - 2.85317i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.00000 q^{10} -2.00000 q^{12} +(-0.809017 + 0.587785i) q^{13} +(-0.618034 - 1.90211i) q^{14} +(0.618034 - 1.90211i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.04508 + 2.93893i) q^{17} +(0.309017 - 0.951057i) q^{18} +(1.85410 + 5.70634i) q^{19} +(0.809017 - 0.587785i) q^{20} -4.00000 q^{21} +2.00000 q^{23} +(4.85410 - 3.52671i) q^{24} +(-1.23607 - 3.80423i) q^{25} +(0.309017 - 0.951057i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-1.61803 - 1.17557i) q^{28} +(2.78115 - 8.55951i) q^{29} +(0.618034 + 1.90211i) q^{30} +(1.61803 - 1.17557i) q^{31} +5.00000 q^{32} -5.00000 q^{34} +(1.61803 - 1.17557i) q^{35} +(-0.309017 - 0.951057i) q^{36} +(-0.927051 + 2.85317i) q^{37} +(-4.85410 - 3.52671i) q^{38} +(-1.61803 - 1.17557i) q^{39} +(-0.927051 + 2.85317i) q^{40} +(-1.54508 - 4.75528i) q^{41} +(3.23607 - 2.35114i) q^{42} +1.00000 q^{45} +(-1.61803 + 1.17557i) q^{46} +(0.618034 + 1.90211i) q^{47} +(-0.618034 + 1.90211i) q^{48} +(2.42705 + 1.76336i) q^{49} +(3.23607 + 2.35114i) q^{50} +(-3.09017 + 9.51057i) q^{51} +(-0.309017 - 0.951057i) q^{52} +(-7.28115 + 5.29007i) q^{53} -4.00000 q^{54} +6.00000 q^{56} +(-9.70820 + 7.05342i) q^{57} +(2.78115 + 8.55951i) q^{58} +(2.47214 - 7.60845i) q^{59} +(1.61803 + 1.17557i) q^{60} +(-4.85410 - 3.52671i) q^{61} +(-0.618034 + 1.90211i) q^{62} +(-0.618034 - 1.90211i) q^{63} +(-5.66312 + 4.11450i) q^{64} +1.00000 q^{65} +2.00000 q^{67} +(-4.04508 + 2.93893i) q^{68} +(1.23607 + 3.80423i) q^{69} +(-0.618034 + 1.90211i) q^{70} +(-9.70820 - 7.05342i) q^{71} +(2.42705 + 1.76336i) q^{72} +(-0.618034 + 1.90211i) q^{73} +(-0.927051 - 2.85317i) q^{74} +(6.47214 - 4.70228i) q^{75} -6.00000 q^{76} +2.00000 q^{78} +(8.09017 - 5.87785i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(-3.39919 + 10.4616i) q^{81} +(4.04508 + 2.93893i) q^{82} +(-4.85410 - 3.52671i) q^{83} +(1.23607 - 3.80423i) q^{84} +(-1.54508 - 4.75528i) q^{85} +18.0000 q^{87} -9.00000 q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.618034 - 1.90211i) q^{91} +(-0.618034 + 1.90211i) q^{92} +(3.23607 + 2.35114i) q^{93} +(-1.61803 - 1.17557i) q^{94} +(1.85410 - 5.70634i) q^{95} +(3.09017 + 9.51057i) q^{96} +(10.5172 - 7.64121i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} + q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 3 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} - q^{13} + 2 q^{14} - 2 q^{15} + q^{16} + 5 q^{17} - q^{18} - 6 q^{19} + q^{20} - 16 q^{21} + 8 q^{23}+ \cdots - 12 q^{98}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 + q^4 - q^5 - 2 * q^6 + 2 * q^7 + 3 * q^8 - q^9 + 4 * q^10 - 8 * q^12 - q^13 + 2 * q^14 - 2 * q^15 + q^16 + 5 * q^17 - q^18 - 6 * q^19 + q^20 - 16 * q^21 + 8 * q^23 + 6 * q^24 + 4 * q^25 - q^26 + 4 * q^27 - 2 * q^28 - 9 * q^29 - 2 * q^30 + 2 * q^31 + 20 * q^32 - 20 * q^34 + 2 * q^35 + q^36 + 3 * q^37 - 6 * q^38 - 2 * q^39 + 3 * q^40 + 5 * q^41 + 4 * q^42 + 4 * q^45 - 2 * q^46 - 2 * q^47 + 2 * q^48 + 3 * q^49 + 4 * q^50 + 10 * q^51 + q^52 - 9 * q^53 - 16 * q^54 + 24 * q^56 - 12 * q^57 - 9 * q^58 - 8 * q^59 + 2 * q^60 - 6 * q^61 + 2 * q^62 + 2 * q^63 - 7 * q^64 + 4 * q^65 + 8 * q^67 - 5 * q^68 - 4 * q^69 + 2 * q^70 - 12 * q^71 + 3 * q^72 + 2 * q^73 + 3 * q^74 + 8 * q^75 - 24 * q^76 + 8 * q^78 + 10 * q^79 + q^80 + 11 * q^81 + 5 * q^82 - 6 * q^83 - 4 * q^84 + 5 * q^85 + 72 * q^87 - 36 * q^89 - q^90 + 2 * q^91 + 2 * q^92 + 4 * q^93 - 2 * q^94 - 6 * q^95 - 10 * q^96 + 13 * q^97 - 12 * q^98

Introduction

L-functions

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