LMFDB - Embedded newform 122.2.f.a.75.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [122,2,Mod(75,122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(122, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("122.75");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 122 = 2 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	122.f (of order $6$, degree $2$, 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:	$0.974174904660$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.110502144.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 11x^{6} - 14x^{5} + 7x^{4} + 18x^{3} - 18x^{2} - 36x + 36 $ x^8 - 4x^7 + 11x^6 - 14x^5 + 7x^4 + 18x^3 - 18x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			75.3
Root			$1.43748 - 1.63270i$ of defining polynomial
Character	$\chi$	$=$	122.75
Dual form			122.2.f.a.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -0.142909 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.437480 + 0.757738i) q^{5} +(-0.123763 + 0.0714546i) q^{6} +(2.59586 - 1.49872i) q^{7} -1.00000i q^{8} -2.97958 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -0.142909 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.437480 + 0.757738i) q^{5} +(-0.123763 + 0.0714546i) q^{6} +(2.59586 - 1.49872i) q^{7} -1.00000i q^{8} -2.97958 q^{9} +(0.757738 + 0.437480i) q^{10} +1.62743i q^{11} +(-0.0714546 + 0.123763i) q^{12} +(0.571455 + 0.989788i) q^{13} +(1.49872 - 2.59586i) q^{14} +(-0.0625200 - 0.108288i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.64036 - 3.25646i) q^{17} +(-2.58039 + 1.48979i) q^{18} +(-3.19394 + 5.53207i) q^{19} +0.874960 q^{20} +(-0.370973 + 0.214181i) q^{21} +(0.813717 + 1.40940i) q^{22} +6.85454i q^{23} +0.142909i q^{24} +(2.11722 - 3.66714i) q^{25} +(0.989788 + 0.571455i) q^{26} +0.854537 q^{27} -2.99745i q^{28} +(-0.172085 - 0.0993531i) q^{29} +(-0.108288 - 0.0625200i) q^{30} +(-1.32792 - 0.766672i) q^{31} +(-0.866025 - 0.500000i) q^{32} -0.232575i q^{33} -6.51292 q^{34} +(2.27128 + 1.31132i) q^{35} +(-1.48979 + 2.58039i) q^{36} -5.49505i q^{37} +6.38788i q^{38} +(-0.0816662 - 0.141450i) q^{39} +(0.757738 - 0.437480i) q^{40} -0.178283 q^{41} +(-0.214181 + 0.370973i) q^{42} +(5.54975 - 3.20415i) q^{43} +(1.40940 + 0.813717i) q^{44} +(-1.30351 - 2.25774i) q^{45} +(3.42727 + 5.93620i) q^{46} +(0.0612431 - 0.106076i) q^{47} +(0.0714546 + 0.123763i) q^{48} +(0.992342 - 1.71879i) q^{49} -4.23444i q^{50} +(0.806059 + 0.465378i) q^{51} +1.14291 q^{52} +2.78087i q^{53} +(0.740051 - 0.427269i) q^{54} +(-1.23317 + 0.711970i) q^{55} +(-1.49872 - 2.59586i) q^{56} +(0.456444 - 0.790584i) q^{57} -0.198706 q^{58} +(7.06523 - 4.07911i) q^{59} -0.125040 q^{60} +(3.46410 - 7.00000i) q^{61} -1.53334 q^{62} +(-7.73458 + 4.46556i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.116288 - 0.201416i) q^{66} +(8.05691 - 4.65166i) q^{67} +(-5.64036 + 3.25646i) q^{68} -0.979577i q^{69} +2.62265 q^{70} +(-10.1075 - 5.83557i) q^{71} +2.97958i q^{72} +(0.543556 - 0.941467i) q^{73} +(-2.74753 - 4.75885i) q^{74} +(-0.302571 + 0.524068i) q^{75} +(3.19394 + 5.53207i) q^{76} +(2.43907 + 4.22460i) q^{77} +(-0.141450 - 0.0816662i) q^{78} +(10.6354 - 6.14036i) q^{79} +(0.437480 - 0.757738i) q^{80} +8.81661 q^{81} +(-0.154398 + 0.0891415i) q^{82} +(5.66060 + 9.80444i) q^{83} +0.428363i q^{84} -5.69855i q^{85} +(3.20415 - 5.54975i) q^{86} +(0.0245925 + 0.0141985i) q^{87} +1.62743 q^{88} -0.607011i q^{89} +(-2.25774 - 1.30351i) q^{90} +(2.96684 + 1.71290i) q^{91} +(5.93620 + 3.42727i) q^{92} +(0.189771 + 0.109565i) q^{93} -0.122486i q^{94} -5.58914 q^{95} +(0.123763 + 0.0714546i) q^{96} +(-9.01292 + 15.6108i) q^{97} -1.98468i q^{98} -4.84906i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	$ 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/122\mathbb{Z}\right)^\times$.

$n$	$63$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.142909			−0.0825087			−0.0412544	−	0.999149i	$-0.513135\pi$
$3$	−0.142909			−0.0825087			−0.0412544	+	0.999149i	$0.513135\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.437480	+	0.757738i	0.195647	+	0.338871i	0.947112	−	0.320902i	$-0.103986\pi$
$5$	0.437480	+	0.757738i	0.195647	+	0.338871i	−0.751465	+	0.659772i	$0.770653\pi$
$6$	−0.123763	+	0.0714546i	−0.0505261	+	0.0291712i
$7$	2.59586	−	1.49872i	0.981145	−	0.566464i	0.0785291	−	0.996912i	$-0.474978\pi$
$7$	2.59586	−	1.49872i	0.981145	−	0.566464i	0.902616	+	0.430448i	$0.141644\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.97958			−0.993192
$10$	0.757738	+	0.437480i	0.239618	+	0.138343i
$11$			1.62743i			0.490690i	0.969436	+	0.245345i	$0.0789012\pi$
$11$			1.62743i			0.490690i	−0.969436	+	0.245345i	$0.921099\pi$
$12$	−0.0714546	+	0.123763i	−0.0206272	+	0.0357273i
$13$	0.571455	+	0.989788i	0.158493	+	0.274518i	0.934325	−	0.356421i	$-0.116003\pi$
$13$	0.571455	+	0.989788i	0.158493	+	0.274518i	−0.775832	+	0.630939i	$0.782670\pi$
$14$	1.49872	−	2.59586i	0.400551	−	0.693774i
$15$	−0.0625200	−	0.108288i	−0.0161426	−	0.0279598i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−5.64036	−	3.25646i	−1.36799	−	0.789808i	−0.377316	−	0.926084i	$-0.623153\pi$
$17$	−5.64036	−	3.25646i	−1.36799	−	0.789808i	−0.990671	+	0.136277i	$0.956486\pi$
$18$	−2.58039	+	1.48979i	−0.608204	+	0.351147i
$19$	−3.19394	+	5.53207i	−0.732740	+	1.26914i	0.222967	+	0.974826i	$0.428426\pi$
$19$	−3.19394	+	5.53207i	−0.732740	+	1.26914i	−0.955708	+	0.294318i	$0.904908\pi$
$20$	0.874960			0.195647
$21$	−0.370973	+	0.214181i	−0.0809530	+	0.0467382i
$22$	0.813717	+	1.40940i	0.173485	+	0.300485i
$23$			6.85454i			1.42927i	0.699498	+	0.714635i	$0.253407\pi$
$23$			6.85454i			1.42927i	−0.699498	+	0.714635i	$0.746593\pi$
$24$			0.142909i			0.0291712i
$25$	2.11722	−	3.66714i	0.423444	−	0.733427i
$26$	0.989788	+	0.571455i	0.194113	+	0.112071i
$27$	0.854537			0.164456
$28$		−	2.99745i		−	0.566464i
$29$	−0.172085	−	0.0993531i	−0.0319553	−	0.0184494i	0.483937	−	0.875103i	$-0.339206\pi$
$29$	−0.172085	−	0.0993531i	−0.0319553	−	0.0184494i	−0.515893	+	0.856653i	$0.672540\pi$
$30$	−0.108288	−	0.0625200i	−0.0197705	−	0.0114145i
$31$	−1.32792	−	0.766672i	−0.238501	−	0.137698i	0.375987	−	0.926625i	$-0.377304\pi$
$31$	−1.32792	−	0.766672i	−0.238501	−	0.137698i	−0.614487	+	0.788927i	$0.710637\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		−	0.232575i		−	0.0404862i
$34$	−6.51292			−1.11696
$35$	2.27128	+	1.31132i	0.383916	+	0.221654i
$36$	−1.48979	+	2.58039i	−0.248298	+	0.430065i
$37$		−	5.49505i		−	0.903381i	−0.892175	−	0.451691i	$-0.850821\pi$
$37$		−	5.49505i		−	0.903381i	0.892175	−	0.451691i	$-0.149179\pi$
$38$			6.38788i			1.03625i
$39$	−0.0816662	−	0.141450i	−0.0130771	−	0.0226501i
$40$	0.757738	−	0.437480i	0.119809	−	0.0691717i
$41$	−0.178283			−0.0278431			−0.0139216	−	0.999903i	$-0.504432\pi$
$41$	−0.178283			−0.0278431			−0.0139216	+	0.999903i	$0.504432\pi$
$42$	−0.214181	+	0.370973i	−0.0330489	+	0.0572424i
$43$	5.54975	−	3.20415i	0.846330	−	0.488629i	−0.0130811	−	0.999914i	$-0.504164\pi$
$43$	5.54975	−	3.20415i	0.846330	−	0.488629i	0.859411	+	0.511286i	$0.170831\pi$
$44$	1.40940	+	0.813717i	0.212475	+	0.122672i
$45$	−1.30351	−	2.25774i	−0.194315	−	0.336564i
$46$	3.42727	+	5.93620i	0.505323	+	0.875245i
$47$	0.0612431	−	0.106076i	0.00893323	−	0.0154728i	−0.861524	−	0.507716i	$-0.830490\pi$
$47$	0.0612431	−	0.106076i	0.00893323	−	0.0154728i	0.870457	+	0.492244i	$0.163823\pi$
$48$	0.0714546	+	0.123763i	0.0103136	+	0.0178637i
$49$	0.992342	−	1.71879i	0.141763	−	0.245541i
$50$		−	4.23444i		−	0.598841i
$51$	0.806059	+	0.465378i	0.112871	+	0.0651660i
$52$	1.14291			0.158493
$53$			2.78087i			0.381982i	0.981592	+	0.190991i	$0.0611701\pi$
$53$			2.78087i			0.381982i	−0.981592	+	0.190991i	$0.938830\pi$
$54$	0.740051	−	0.427269i	0.100708	−	0.0581439i
$55$	−1.23317	+	0.711970i	−0.166280	+	0.0960020i
$56$	−1.49872	−	2.59586i	−0.200275	−	0.346887i
$57$	0.456444	−	0.790584i	0.0604575	−	0.104715i
$58$	−0.198706			−0.0260914
$59$	7.06523	−	4.07911i	0.919815	−	0.531055i	0.0362387	−	0.999343i	$-0.488462\pi$
$59$	7.06523	−	4.07911i	0.919815	−	0.531055i	0.883576	+	0.468288i	$0.155129\pi$
$60$	−0.125040			−0.0161426
$61$	3.46410	−	7.00000i	0.443533	−	0.896258i
$61$	3.46410	−	7.00000i	0.443533	−	0.896258i
$62$	−1.53334			−0.194735
$63$	−7.73458	+	4.46556i	−0.974465	+	0.562608i
$64$	−1.00000			−0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−0.116288	−	0.201416i	−0.0143140	−	0.0247926i
$67$	8.05691	−	4.65166i	0.984309	−	0.568291i	0.0807405	−	0.996735i	$-0.474271\pi$
$67$	8.05691	−	4.65166i	0.984309	−	0.568291i	0.903568	+	0.428444i	$0.140938\pi$
$68$	−5.64036	+	3.25646i	−0.683994	+	0.394904i
$69$		−	0.979577i		−	0.117927i
$70$	2.62265			0.313466
$71$	−10.1075	−	5.83557i	−1.19954	−	0.692555i	−0.239088	−	0.970998i	$-0.576848\pi$
$71$	−10.1075	−	5.83557i	−1.19954	−	0.692555i	−0.960453	+	0.278443i	$0.910182\pi$
$72$			2.97958i			0.351147i
$73$	0.543556	−	0.941467i	0.0636184	−	0.110190i	−0.832462	−	0.554082i	$-0.813069\pi$
$73$	0.543556	−	0.941467i	0.0636184	−	0.110190i	0.896080	+	0.443892i	$0.146403\pi$
$74$	−2.74753	−	4.75885i	−0.319393	−	0.553206i
$75$	−0.302571	+	0.524068i	−0.0349379	+	0.0605141i
$76$	3.19394	+	5.53207i	0.366370	+	0.634572i
$77$	2.43907	+	4.22460i	0.277958	+	0.481438i
$78$	−0.141450	−	0.0816662i	−0.0160161	−	0.00924687i
$79$	10.6354	−	6.14036i	1.19658	−	0.690844i	0.236786	−	0.971562i	$-0.423906\pi$
$79$	10.6354	−	6.14036i	1.19658	−	0.690844i	0.959790	+	0.280718i	$0.0905725\pi$
$80$	0.437480	−	0.757738i	0.0489118	−	0.0847176i
$81$	8.81661			0.979623
$82$	−0.154398	+	0.0891415i	−0.0170504	+	0.00984404i
$83$	5.66060	+	9.80444i	0.621331	+	1.07618i	0.989238	+	0.146315i	$0.0467412\pi$
$83$	5.66060	+	9.80444i	0.621331	+	1.07618i	−0.367907	+	0.929863i	$0.619926\pi$
$84$			0.428363i			0.0467382i
$85$		−	5.69855i		−	0.618094i
$86$	3.20415	−	5.54975i	0.345513	−	0.598445i
$87$	0.0245925	+	0.0141985i	0.00263659	+	0.00152224i
$88$	1.62743			0.173485
$89$		−	0.607011i		−	0.0643430i	−0.999482	−	0.0321715i	$-0.989758\pi$
$89$		−	0.607011i		−	0.0643430i	0.999482	−	0.0321715i	$-0.0102423\pi$
$90$	−2.25774	−	1.30351i	−0.237986	−	0.137402i
$91$	2.96684	+	1.71290i	0.311009	+	0.179561i
$92$	5.93620	+	3.42727i	0.618892	+	0.357317i
$93$	0.189771	+	0.109565i	0.0196784	+	0.0113613i
$94$		−	0.122486i		−	0.0126335i
$95$	−5.58914			−0.573434
$96$	0.123763	+	0.0714546i	0.0126315	+	0.00729281i
$97$	−9.01292	+	15.6108i	−0.915124	+	1.58504i	−0.108403	+	0.994107i	$0.534574\pi$
$97$	−9.01292	+	15.6108i	−0.915124	+	1.58504i	−0.806720	+	0.590933i	$0.798760\pi$
$98$		−	1.98468i		−	0.200483i
$99$		−	4.84906i		−	0.487349i
$100$	−2.11722	−	3.66714i	−0.211722	−	0.366714i
$101$	−14.8724	+	8.58659i	−1.47986	+	0.854397i	−0.999740	−	0.0228055i	$-0.992740\pi$
$101$	−14.8724	+	8.58659i	−1.47986	+	0.854397i	−0.480120	+	0.877203i	$0.659407\pi$
$102$	0.930757			0.0921587
$103$	−3.83159	+	6.63650i	−0.377537	+	0.653914i	−0.990703	−	0.136040i	$-0.956562\pi$
$103$	−3.83159	+	6.63650i	−0.377537	+	0.653914i	0.613166	+	0.789954i	$0.289896\pi$
$104$	0.989788	−	0.571455i	0.0970567	−	0.0560357i
$105$	−0.324587	−	0.187400i	−0.0316764	−	0.0182884i
$106$	1.39044	+	2.40830i	0.135051	+	0.233915i
$107$	4.94863	+	8.57127i	0.478402	+	0.828616i	0.999693	−	0.0247625i	$-0.00788294\pi$
$107$	4.94863	+	8.57127i	0.478402	+	0.828616i	−0.521292	+	0.853379i	$0.674550\pi$
$108$	0.427269	−	0.740051i	0.0411139	−	0.0712114i
$109$	−6.53954	−	11.3268i	−0.626375	−	1.08491i	−0.988273	−	0.152695i	$-0.951205\pi$
$109$	−6.53954	−	11.3268i	−0.626375	−	1.08491i	0.361899	−	0.932217i	$-0.382129\pi$
$110$	−0.711970	+	1.23317i	−0.0678837	+	0.117578i
$111$			0.785294i			0.0745368i
$112$	−2.59586	−	1.49872i	−0.245286	−	0.141616i
$113$	−9.74992			−0.917195			−0.458598	−	0.888644i	$-0.651648\pi$
$113$	−9.74992			−0.917195			−0.458598	+	0.888644i	$0.651648\pi$
$114$		−	0.912888i		−	0.0854998i
$115$	−5.19394	+	2.99872i	−0.484337	+	0.279632i
$116$	−0.172085	+	0.0993531i	−0.0159776	+	0.00922470i
$117$	−1.70269	−	2.94915i	−0.157414	−	0.272649i
$118$	4.07911	−	7.06523i	0.375513	−	0.650407i
$119$	−19.5221			−1.78959
$120$	−0.108288	+	0.0625200i	−0.00988527	+	0.00570727i
$121$	8.35146			0.759224
$122$	−0.500000	−	7.79423i	−0.0452679	−	0.705656i
$123$	0.0254783			0.00229730
$124$	−1.32792	+	0.766672i	−0.119250	+	0.0688492i
$125$	8.07977			0.722677
$126$	−4.46556	+	7.73458i	−0.397824	+	0.689051i
$127$	3.77959	+	6.54645i	0.335385	+	0.580903i	0.983559	−	0.180589i	$-0.0578004\pi$
$127$	3.77959	+	6.54645i	0.335385	+	0.580903i	−0.648174	+	0.761492i	$0.724467\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−0.793111	+	0.457903i	−0.0698296	+	0.0403161i
$130$			1.00000i			0.0877058i
$131$	−2.96613			−0.259152			−0.129576	−	0.991569i	$-0.541362\pi$
$131$	−2.96613			−0.259152			−0.129576	+	0.991569i	$0.541362\pi$
$132$	−0.201416	−	0.116288i	−0.0175310	−	0.0101215i
$133$			19.1473i			1.66028i
$134$	4.65166	−	8.05691i	0.401842	−	0.696011i
$135$	0.373843	+	0.647515i	0.0321753	+	0.0557292i
$136$	−3.25646	+	5.64036i	−0.279239	+	0.483657i
$137$	−10.8520	−	18.7962i	−0.927148	−	1.60587i	−0.788070	−	0.615585i	$-0.788920\pi$
$137$	−10.8520	−	18.7962i	−0.927148	−	1.60587i	−0.139077	−	0.990282i	$-0.544414\pi$
$138$	−0.489788	−	0.848339i	−0.0416936	−	0.0722154i
$139$	3.19506	+	1.84467i	0.271001	+	0.156463i	0.629343	−	0.777128i	$-0.283324\pi$
$139$	3.19506	+	1.84467i	0.271001	+	0.156463i	−0.358341	+	0.933591i	$0.616658\pi$
$140$	2.27128	−	1.31132i	0.191958	−	0.110827i
$141$	−0.00875221	+	0.0151593i	−0.000737069	+	0.00127664i
$142$	−11.6711			−0.979421
$143$	−1.61082	+	0.930005i	−0.134703	+	0.0777709i
$144$	1.48979	+	2.58039i	0.124149	+	0.215032i
$145$		−	0.173860i		−	0.0144383i
$146$		−	1.08711i		−	0.0899701i
$147$	−0.141815	+	0.245631i	−0.0116967	+	0.0202593i
$148$	−4.75885	−	2.74753i	−0.391175	−	0.225845i
$149$	−1.24018			−0.101600			−0.0507999	−	0.998709i	$-0.516177\pi$
$149$	−1.24018			−0.101600			−0.0507999	+	0.998709i	$0.516177\pi$
$150$			0.605141i			0.0494096i
$151$	−10.8520	−	6.26540i	−0.883122	−	0.509871i	−0.0114354	−	0.999935i	$-0.503640\pi$
$151$	−10.8520	−	6.26540i	−0.883122	−	0.509871i	−0.871686	+	0.490064i	$0.836973\pi$
$152$	5.53207	+	3.19394i	0.448710	+	0.259063i
$153$	16.8059	+	9.70288i	1.35867	+	0.784431i
$154$	4.22460	+	2.43907i	0.340428	+	0.196546i
$155$		−	1.34162i		−	0.107761i
$156$	−0.163332			−0.0130771
$157$	2.12071	+	1.22439i	0.169251	+	0.0977172i	0.582233	−	0.813022i	$-0.302179\pi$
$157$	2.12071	+	1.22439i	0.169251	+	0.0977172i	−0.412982	+	0.910739i	$0.635513\pi$
$158$	6.14036	−	10.6354i	0.488500	−	0.846108i
$159$		−	0.397412i		−	0.0315168i
$160$		−	0.874960i		−	0.0691717i
$161$	10.2731	+	17.7935i	0.809630	+	1.40232i
$162$	7.63541	−	4.40830i	0.599894	−	0.346349i
$163$	−6.24497			−0.489144			−0.244572	−	0.969631i	$-0.578647\pi$
$163$	−6.24497			−0.489144			−0.244572	+	0.969631i	$0.578647\pi$
$164$	−0.0891415	+	0.154398i	−0.00696078	+	0.0120564i
$165$	0.176231	−	0.101747i	0.0137196	−	0.00792100i
$166$	9.80444	+	5.66060i	0.760972	+	0.439347i
$167$	1.19871	+	2.07622i	0.0927587	+	0.160663i	0.908671	−	0.417513i	$-0.137098\pi$
$167$	1.19871	+	2.07622i	0.0927587	+	0.160663i	−0.815912	+	0.578176i	$0.803765\pi$
$168$	0.214181	+	0.370973i	0.0165245	+	0.0286212i
$169$	5.84688	−	10.1271i	0.449760	−	0.779007i
$170$	−2.84927	−	4.93509i	−0.218529	−	0.378504i
$171$	9.51659	−	16.4832i	0.727752	−	1.26050i
$172$		−	6.40830i		−	0.488629i
$173$	12.0536	+	6.95915i	0.916419	+	0.529095i	0.882491	−	0.470330i	$-0.155865\pi$
$173$	12.0536	+	6.95915i	0.916419	+	0.529095i	0.0339280	+	0.999424i	$0.489198\pi$
$174$	0.0283969			0.00215277
$175$		−	12.6925i		−	0.959464i
$176$	1.40940	−	0.813717i	0.106237	−	0.0613362i
$177$	−1.00969	+	0.582943i	−0.0758927	+	0.0438167i
$178$	−0.303505	−	0.525687i	−0.0227487	−	0.0394019i
$179$	9.71530	−	16.8274i	0.726156	−	1.25774i	−0.232341	−	0.972634i	$-0.574639\pi$
$179$	9.71530	−	16.8274i	0.726156	−	1.25774i	0.958497	−	0.285104i	$-0.0920281\pi$
$180$	−2.60701			−0.194315
$181$	−14.4796	+	8.35980i	−1.07626	+	0.621379i	−0.929885	−	0.367850i	$-0.880094\pi$
$181$	−14.4796	+	8.35980i	−1.07626	+	0.621379i	−0.146375	+	0.989229i	$0.546761\pi$
$182$	3.42581			0.253938
$183$	−0.495052	+	1.00036i	−0.0365953	+	0.0739491i
$184$	6.85454			0.505323
$185$	4.16381	−	2.40398i	0.306129	−	0.176744i
$186$	0.219129			0.0160673
$187$	5.29967	−	9.17931i	0.387551	−	0.671257i
$188$	−0.0612431	−	0.106076i	−0.00446661	−	0.00773640i
$189$	2.21826	−	1.28071i	0.161355	−	0.0931583i
$190$	−4.84034	+	2.79457i	−0.351155	+	0.202739i
$191$			18.9522i			1.37133i	0.727917	+	0.685666i	$0.240489\pi$
$191$			18.9522i			1.37133i	−0.727917	+	0.685666i	$0.759511\pi$
$192$	0.142909			0.0103136
$193$	21.9010	+	12.6445i	1.57647	+	0.910173i	0.995347	+	0.0963538i	$0.0307180\pi$
$193$	21.9010	+	12.6445i	1.57647	+	0.910173i	0.581118	+	0.813819i	$0.302615\pi$
$194$			18.0258i			1.29418i
$195$	0.0714546	−	0.123763i	0.00511697	−	0.00886286i
$196$	−0.992342	−	1.71879i	−0.0708816	−	0.122771i
$197$	9.04882	−	15.6730i	0.644702	−	1.11666i	−0.339669	−	0.940545i	$-0.610315\pi$
$197$	9.04882	−	15.6730i	0.644702	−	1.11666i	0.984370	−	0.176111i	$-0.0563518\pi$
$198$	−2.42453	−	4.19941i	−0.172304	−	0.298439i
$199$	−10.4871	−	18.1641i	−0.743407	−	1.28762i	−0.950935	−	0.309390i	$-0.899875\pi$
$199$	−10.4871	−	18.1641i	−0.743407	−	1.28762i	0.207528	−	0.978229i	$-0.433458\pi$
$200$	−3.66714	−	2.11722i	−0.259306	−	0.149710i
$201$	−1.15141	+	0.664766i	−0.0812140	+	0.0468889i
$202$	−8.58659	+	14.8724i	−0.604150	+	1.04642i
$203$	−0.595611			−0.0418037
$204$	0.806059	−	0.465378i	0.0564354	−	0.0325830i
$205$	−0.0779953	−	0.135092i	−0.00544743	−	0.00943522i
$206$			7.66317i			0.533919i
$207$		−	20.4236i		−	1.41954i
$208$	0.571455	−	0.989788i	0.0396233	−	0.0686295i
$209$	−9.00308	−	5.19793i	−0.622756	−	0.359548i
$210$	−0.374800			−0.0258637
$211$		−	2.82427i		−	0.194431i	−0.995263	−	0.0972154i	$-0.969006\pi$
$211$		−	2.82427i		−	0.194431i	0.995263	−	0.0972154i	$-0.0309936\pi$
$212$	2.40830	+	1.39044i	0.165403	+	0.0954955i
$213$	1.44446	+	0.833958i	0.0989726	+	0.0571418i
$214$	8.57127	+	4.94863i	0.585920	+	0.338281i
$215$	4.85581	+	2.80351i	0.331164	+	0.191197i
$216$		−	0.854537i		−	0.0581439i
$217$	−4.59612			−0.312005
$218$	−11.3268	−	6.53954i	−0.767149	−	0.442914i
$219$	−0.0776792	+	0.134544i	−0.00524908	+	0.00909167i
$220$			1.42394i			0.0960020i
$221$		−	7.44368i		−	0.500716i
$222$	0.392647	+	0.680085i	0.0263527	+	0.0456443i
$223$	−5.97541	+	3.44990i	−0.400143	+	0.231023i	−0.686546	−	0.727087i	$-0.740874\pi$
$223$	−5.97541	+	3.44990i	−0.400143	+	0.231023i	0.286403	+	0.958109i	$0.407540\pi$
$224$	−2.99745			−0.200275
$225$	−6.30843	+	10.9265i	−0.420562	+	0.728434i
$226$	−8.44368	+	4.87496i	−0.561665	+	0.324278i
$227$	22.0907	+	12.7541i	1.46621	+	0.846519i	0.999286	−	0.0377771i	$-0.0120277\pi$
$227$	22.0907	+	12.7541i	1.46621	+	0.846519i	0.466927	+	0.884296i	$0.345361\pi$
$228$	−0.456444	−	0.790584i	−0.0302287	−	0.0523577i
$229$	10.8075	+	18.7191i	0.714179	+	1.23699i	0.963275	+	0.268516i	$0.0865332\pi$
$229$	10.8075	+	18.7191i	0.714179	+	1.23699i	−0.249096	+	0.968479i	$0.580133\pi$
$230$	−2.99872	+	5.19394i	−0.197730	+	0.342478i
$231$	−0.348566	−	0.603734i	−0.0229340	−	0.0397228i
$232$	−0.0993531	+	0.172085i	−0.00652285	+	0.0112979i
$233$		−	2.10275i		−	0.137756i	−0.997625	−	0.0688778i	$-0.978058\pi$
$233$		−	2.10275i		−	0.137756i	0.997625	−	0.0688778i	$-0.0219419\pi$
$234$	−2.94915	−	1.70269i	−0.192792	−	0.111309i
$235$	0.107171			0.00699104
$236$		−	8.15822i		−	0.531055i
$237$	−1.51990	+	0.877514i	−0.0987280	+	0.0570006i
$238$	−16.9067	+	9.76107i	−1.09590	+	0.632716i
$239$	−5.32119	−	9.21658i	−0.344199	−	0.596171i	0.641009	−	0.767534i	$-0.278516\pi$
$239$	−5.32119	−	9.21658i	−0.344199	−	0.596171i	−0.985208	+	0.171363i	$0.945183\pi$
$240$	−0.0625200	+	0.108288i	−0.00403565	+	0.00698994i
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	7.23258	−	4.17573i	0.464928	−	0.268426i
$243$	−3.82359			−0.245283
$244$	−4.33013	−	6.50000i	−0.277208	−	0.416120i
$245$	1.73652			0.110942
$246$	0.0220649	−	0.0127392i	0.00140680	−	0.000812219i
$247$	−7.30077			−0.464537
$248$	−0.766672	+	1.32792i	−0.0486837	+	0.0843227i
$249$	−0.808952	−	1.40115i	−0.0512652	−	0.0887940i
$250$	6.99729	−	4.03989i	0.442547	−	0.255505i
$251$	−3.97017	+	2.29218i	−0.250595	+	0.144681i	−0.620037	−	0.784573i	$-0.712882\pi$
$251$	−3.97017	+	2.29218i	−0.250595	+	0.144681i	0.369442	+	0.929254i	$0.379549\pi$
$252$			8.93112i			0.562608i
$253$	−11.1553			−0.701328
$254$	6.54645	+	3.77959i	0.410761	+	0.237153i
$255$			0.814375i			0.0509982i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.52058	−	9.56192i	−0.344364	−	0.596456i	0.640874	−	0.767646i	$-0.278572\pi$
$257$	−5.52058	−	9.56192i	−0.344364	−	0.596456i	−0.985238	+	0.171190i	$0.945239\pi$
$258$	−0.457903	+	0.793111i	−0.0285078	+	0.0493770i
$259$	−8.23556	−	14.2644i	−0.511733	−	0.886347i
$260$	0.500000	+	0.866025i	0.0310087	+	0.0537086i
$261$	0.512739	+	0.296030i	0.0317378	+	0.0183238i
$262$	−2.56874	+	1.48307i	−0.158698	+	0.0916241i
$263$	−7.79585	+	13.5028i	−0.480713	+	0.832619i	−0.999755	−	0.0221298i	$-0.992955\pi$
$263$	−7.79585	+	13.5028i	−0.480713	+	0.832619i	0.519043	+	0.854748i	$0.326289\pi$
$264$	−0.232575			−0.0143140
$265$	−2.10717	+	1.21658i	−0.129442	+	0.0747336i
$266$	9.57367	+	16.5821i	0.586999	+	1.01671i
$267$			0.0867475i			0.00530886i
$268$		−	9.30332i		−	0.568291i
$269$	9.26982	−	16.0558i	0.565191	−	0.978939i	−0.431841	−	0.901950i	$-0.642136\pi$
$269$	9.26982	−	16.0558i	0.565191	−	0.978939i	0.997032	−	0.0769895i	$-0.0245308\pi$
$270$	0.647515	+	0.373843i	0.0394065	+	0.0227514i
$271$	−25.2472			−1.53366			−0.766829	−	0.641851i	$-0.778167\pi$
$271$	−25.2472			−1.53366			−0.766829	+	0.641851i	$0.778167\pi$
$272$			6.51292i			0.394904i
$273$	−0.423989	−	0.244790i	−0.0256610	−	0.0148154i
$274$	−18.7962	−	10.8520i	−1.13552	−	0.655592i
$275$	5.96802	+	3.44564i	0.359885	+	0.207780i
$276$	−0.848339	−	0.489788i	−0.0510640	−	0.0294818i
$277$			28.1283i			1.69006i	0.534716	+	0.845032i	$0.320419\pi$
$277$			28.1283i			1.69006i	−0.534716	+	0.845032i	$0.679581\pi$
$278$	3.68934			0.221272
$279$	3.95663	+	2.28436i	0.236877	+	0.136761i
$280$	1.31132	−	2.27128i	0.0783665	−	0.135735i
$281$		−	10.0179i		−	0.597616i	−0.954313	−	0.298808i	$-0.903411\pi$
$281$		−	10.0179i		−	0.597616i	0.954313	−	0.298808i	$-0.0965890\pi$
$282$			0.0175044i			0.00104237i
$283$	−0.492841	−	0.853625i	−0.0292963	−	0.0507427i	0.851006	−	0.525157i	$-0.175993\pi$
$283$	−0.492841	−	0.853625i	−0.0292963	−	0.0507427i	−0.880302	+	0.474414i	$0.842660\pi$
$284$	−10.1075	+	5.83557i	−0.599770	+	0.346278i
$285$	0.798740			0.0473133
$286$	−0.930005	+	1.61082i	−0.0549923	+	0.0952495i
$287$	−0.462799	+	0.267197i	−0.0273181	+	0.0157721i
$288$	2.58039	+	1.48979i	0.152051	+	0.0877866i
$289$	12.7091	+	22.0128i	0.747593	+	1.29487i
$290$	−0.0869300	−	0.150567i	−0.00510470	−	0.00884161i
$291$	1.28803	−	2.23093i	0.0755057	−	0.130780i
$292$	−0.543556	−	0.941467i	−0.0318092	−	0.0550952i
$293$	6.08005	−	10.5310i	0.355200	−	0.615225i	−0.631952	−	0.775007i	$-0.717746\pi$
$293$	6.08005	−	10.5310i	0.355200	−	0.615225i	0.987152	+	0.159783i	$0.0510794\pi$
$294$			0.283630i			0.0165416i
$295$	6.18179	+	3.56906i	0.359918	+	0.207799i
$296$	−5.49505			−0.319393
$297$			1.39070i			0.0806967i
$298$	−1.07403	+	0.620092i	−0.0622170	+	0.0359210i
$299$	−6.78454	+	3.91706i	−0.392360	+	0.226529i
$300$	0.302571	+	0.524068i	0.0174689	+	0.0302571i
$301$	9.60427	−	16.6351i	0.553581	−	0.958831i
$302$	−12.5308			−0.721066
$303$	2.12540	−	1.22710i	0.122101	−	0.0704952i
$304$	6.38788			0.366370
$305$	6.81964	−	0.437480i	0.390491	−	0.0250500i
$306$	19.4058			1.10935
$307$	−26.0995	+	15.0686i	−1.48958	+	0.860008i	−0.999929	−	0.0119118i	$-0.996208\pi$
$307$	−26.0995	+	15.0686i	−1.48958	+	0.860008i	−0.489649	+	0.871920i	$0.662875\pi$
$308$	4.87815			0.277958
$309$	0.547569	−	0.948418i	0.0311501	−	0.0539536i
$310$	−0.670808	−	1.16187i	−0.0380993	−	0.0659900i
$311$	23.7183	−	13.6938i	1.34494	−	0.776503i	0.357415	−	0.933946i	$-0.383658\pi$
$311$	23.7183	−	13.6938i	1.34494	−	0.776503i	0.987528	+	0.157443i	$0.0503250\pi$
$312$	−0.141450	+	0.0816662i	−0.00800803	+	0.00462344i
$313$			3.46921i			0.196091i	0.995182	+	0.0980456i	$0.0312591\pi$
$313$			3.46921i			0.196091i	−0.995182	+	0.0980456i	$0.968741\pi$
$314$	2.44879			0.138193
$315$	−6.76745	−	3.90719i	−0.381302	−	0.220145i
$316$		−	12.2807i		−	0.690844i
$317$	−12.2005	+	21.1319i	−0.685247	+	1.18688i	0.288112	+	0.957597i	$0.406973\pi$
$317$	−12.2005	+	21.1319i	−0.685247	+	1.18688i	−0.973359	+	0.229286i	$0.926361\pi$
$318$	−0.198706	−	0.344169i	−0.0111429	−	0.0193000i
$319$	0.161691	−	0.280056i	0.00905293	−	0.0156801i
$320$	−0.437480	−	0.757738i	−0.0244559	−	0.0423588i
$321$	−0.707205	−	1.22491i	−0.0394723	−	0.0683681i
$322$	17.7935	+	10.2731i	0.991590	+	0.572495i
$323$	36.0299	−	20.8019i	2.00476	−	1.15745i
$324$	4.40830	−	7.63541i	0.244906	−	0.424189i
$325$	4.83959			0.268452
$326$	−5.40830	+	3.12249i	−0.299538	+	0.172939i
$327$	0.934561	+	1.61871i	0.0516814	+	0.0895147i
$328$			0.178283i			0.00984404i
$329$		−	0.367146i		−	0.0202414i
$330$	0.101747	−	0.176231i	0.00560099	−	0.00970121i
$331$	4.53592	+	2.61882i	0.249317	+	0.143943i	0.619451	−	0.785035i	$-0.287355\pi$
$331$	4.53592	+	2.61882i	0.249317	+	0.143943i	−0.370135	+	0.928978i	$0.620688\pi$
$332$	11.3212			0.621331
$333$			16.3729i			0.897231i
$334$	2.07622	+	1.19871i	0.113606	+	0.0655903i
$335$	7.04948	+	4.07002i	0.385154	+	0.222369i
$336$	0.370973	+	0.214181i	0.0202382	+	0.0116846i
$337$	−19.5106	−	11.2644i	−1.06281	−	0.613613i	−0.136601	−	0.990626i	$-0.543618\pi$
$337$	−19.5106	−	11.2644i	−1.06281	−	0.613613i	−0.926208	+	0.377013i	$0.876951\pi$
$338$		−	11.6938i		−	0.636057i
$339$	1.39335			0.0756766
$340$	−4.93509	−	2.84927i	−0.267643	−	0.154524i
$341$	1.24771	−	2.16109i	0.0675672	−	0.117030i
$342$		−	19.0332i		−	1.02920i
$343$			15.0331i			0.811713i
$344$	−3.20415	−	5.54975i	−0.172756	−	0.299223i
$345$	0.742262	−	0.428545i	0.0399621	−	0.0230721i
$346$	13.9183			0.748253
$347$	−6.58182	+	11.4001i	−0.353331	+	0.611987i	−0.986831	−	0.161756i	$-0.948284\pi$
$347$	−6.58182	+	11.4001i	−0.353331	+	0.611987i	0.633500	+	0.773743i	$0.281618\pi$
$348$	0.0245925	−	0.0141985i	0.00131830	−	0.000761118i
$349$	11.2760	+	6.51021i	0.603591	+	0.348484i	0.770453	−	0.637497i	$-0.220030\pi$
$349$	11.2760	+	6.51021i	0.603591	+	0.348484i	−0.166862	+	0.985980i	$0.553363\pi$
$350$	−6.34626	−	10.9920i	−0.339222	−	0.587550i
$351$	0.488329	+	0.845811i	0.0260651	+	0.0451460i
$352$	0.813717	−	1.40940i	0.0433713	−	0.0751212i
$353$	−8.84146	−	15.3139i	−0.470583	−	0.815074i	0.528851	−	0.848715i	$-0.322623\pi$
$353$	−8.84146	−	15.3139i	−0.470583	−	0.815074i	−0.999434	+	0.0336408i	$0.989290\pi$
$354$	−0.582943	+	1.00969i	−0.0309831	+	0.0536643i
$355$		−	10.2118i		−	0.541985i
$356$	−0.525687	−	0.303505i	−0.0278613	−	0.0160858i
$357$	2.78989			0.147657
$358$		−	19.4306i		−	1.02694i
$359$	−3.77985	+	2.18230i	−0.199493	+	0.115177i	−0.596419	−	0.802673i	$-0.703410\pi$
$359$	−3.77985	+	2.18230i	−0.199493	+	0.115177i	0.396926	+	0.917851i	$0.370077\pi$
$360$	−2.25774	+	1.30351i	−0.118993	+	0.0687008i
$361$	−10.9025	−	18.8837i	−0.573817	−	0.993880i
$362$	−8.35980	+	14.4796i	−0.439381	+	0.761031i
$363$	−1.19350			−0.0626426
$364$	2.96684	−	1.71290i	0.155505	−	0.0897806i
$365$	0.951180			0.0497870
$366$	0.0714546	+	1.11387i	0.00373499	+	0.0582228i
$367$	−9.92920			−0.518300			−0.259150	−	0.965837i	$-0.583442\pi$
$367$	−9.92920			−0.518300			−0.259150	+	0.965837i	$0.583442\pi$
$368$	5.93620	−	3.42727i	0.309446	−	0.178659i
$369$	0.531208			0.0276536
$370$	2.40398	−	4.16381i	0.124977	−	0.216466i
$371$	4.16776	+	7.21876i	0.216379	+	0.374780i
$372$	0.189771	−	0.109565i	0.00983919	−	0.00568066i
$373$	−21.8372	+	12.6077i	−1.13069	+	0.652802i	−0.944107	−	0.329639i	$-0.893073\pi$
$373$	−21.8372	+	12.6077i	−1.13069	+	0.652802i	−0.186578	+	0.982440i	$0.559740\pi$
$374$		−	10.5993i		−	0.548079i
$375$	−1.15467			−0.0596271
$376$	−0.106076	−	0.0612431i	−0.00547046	−	0.00315837i
$377$		−	0.227103i		−	0.0116964i
$378$	1.28071	−	2.21826i	0.0658728	−	0.114095i
$379$	12.5078	+	21.6642i	0.642483	+	1.11281i	0.984877	+	0.173257i	$0.0554291\pi$
$379$	12.5078	+	21.6642i	0.642483	+	1.11281i	−0.342393	+	0.939557i	$0.611238\pi$
$380$	−2.79457	+	4.84034i	−0.143358	+	0.248304i
$381$	−0.540139	−	0.935548i	−0.0276722	−	0.0479296i
$382$	9.47609	+	16.4131i	0.484839	+	0.839766i
$383$	−11.7423	−	6.77941i	−0.600003	−	0.346412i	0.169040	−	0.985609i	$-0.445933\pi$
$383$	−11.7423	−	6.77941i	−0.600003	−	0.346412i	−0.769043	+	0.639197i	$0.779267\pi$
$384$	0.123763	−	0.0714546i	0.00631576	−	0.00364640i
$385$	−2.13409	+	3.69635i	−0.108763	+	0.188384i
$386$	25.2890			1.28718
$387$	−16.5359	+	9.54702i	−0.840568	+	0.485302i
$388$	9.01292	+	15.6108i	0.457562	+	0.792520i
$389$		−	18.2447i		−	0.925041i	−0.886609	−	0.462520i	$-0.846945\pi$
$389$		−	18.2447i		−	0.925041i	0.886609	−	0.462520i	$-0.153055\pi$
$390$		−	0.142909i		−	0.00723649i
$391$	22.3215	−	38.6620i	1.12885	−	1.95522i
$392$	−1.71879	−	0.992342i	−0.0868119	−	0.0501208i
$393$	0.423888			0.0213823
$394$		−	18.0976i		−	0.911746i
$395$	9.30556	+	5.37257i	0.468213	+	0.270323i
$396$	−4.19941	−	2.42453i	−0.211028	−	0.121837i
$397$	3.79473	+	2.19089i	0.190452	+	0.109958i	0.592194	−	0.805795i	$-0.298262\pi$
$397$	3.79473	+	2.19089i	0.190452	+	0.109958i	−0.401742	+	0.915753i	$0.631595\pi$
$398$	−18.1641	−	10.4871i	−0.910484	−	0.525668i
$399$		−	2.73633i		−	0.136988i
$400$	−4.23444			−0.211722
$401$	29.0645	+	16.7804i	1.45141	+	0.837972i	0.998562	−	0.0536162i	$-0.0170747\pi$
$401$	29.0645	+	16.7804i	1.45141	+	0.837972i	0.452848	+	0.891588i	$0.350408\pi$
$402$	−0.664766	+	1.15141i	−0.0331555	+	0.0574270i
$403$		−	1.75247i		−	0.0872969i
$404$			17.1732i			0.854397i
$405$	3.85709	+	6.68068i	0.191660	+	0.331966i
$406$	−0.515814	+	0.297805i	−0.0255994	+	0.0147798i
$407$	8.94283			0.443280
$408$	0.465378	−	0.806059i	0.0230397	−	0.0399059i
$409$	3.74976	−	2.16493i	0.185414	−	0.107049i	−0.404420	−	0.914573i	$-0.632527\pi$
$409$	3.74976	−	2.16493i	0.185414	−	0.107049i	0.589834	+	0.807525i	$0.299193\pi$
$410$	−0.135092	−	0.0779953i	−0.00667171	−	0.00385191i
$411$	1.55085	+	2.68615i	0.0764977	+	0.132498i
$412$	3.83159	+	6.63650i	0.188769	+	0.326957i
$413$	12.2269	−	21.1776i	0.601647	−	1.04208i
$414$	−10.2118	−	17.6874i	−0.501883	−	0.869287i
$415$	−4.95280	+	8.57849i	−0.243123	+	0.421102i
$416$		−	1.14291i		−	0.0560357i
$417$	−0.456603	−	0.263620i	−0.0223600	−	0.0129095i
$418$	−10.3959			−0.508478
$419$			40.0095i			1.95459i	0.211876	+	0.977297i	$0.432043\pi$
$419$			40.0095i			1.95459i	−0.211876	+	0.977297i	$0.567957\pi$
$420$	−0.324587	+	0.187400i	−0.0158382	+	0.00914419i
$421$	−0.561653	+	0.324271i	−0.0273733	+	0.0158040i	−0.513624	−	0.858015i	$-0.671697\pi$
$421$	−0.561653	+	0.324271i	−0.0273733	+	0.0158040i	0.486251	+	0.873819i	$0.338364\pi$
$422$	−1.41214	−	2.44589i	−0.0687417	−	0.119064i
$423$	−0.182479	+	0.316062i	−0.00887241	+	0.0153675i
$424$	2.78087			0.135051
$425$	−23.8838	+	13.7893i	−1.15853	+	0.668879i
$426$	1.66792			0.0808108
$427$	−1.49872	−	23.3628i	−0.0725283	−	1.13060i
$428$	9.89725			0.478402
$429$	0.230200	−	0.132906i	0.0111142	−	0.00641678i
$430$	5.60701			0.270394
$431$	−10.3359	+	17.9023i	−0.497862	+	0.862323i	−0.999997	−	0.00246668i	$-0.999215\pi$
$431$	−10.3359	+	17.9023i	−0.497862	+	0.862323i	0.502135	+	0.864789i	$0.332548\pi$
$432$	−0.427269	−	0.740051i	−0.0205570	−	0.0356057i
$433$	18.9556	−	10.9440i	0.910948	−	0.525936i	0.0302119	−	0.999544i	$-0.490382\pi$
$433$	18.9556	−	10.9440i	0.910948	−	0.525936i	0.880736	+	0.473607i	$0.157048\pi$
$434$	−3.98036	+	2.29806i	−0.191063	+	0.110310i
$435$			0.0248462i			0.00119128i
$436$	−13.0791			−0.626375
$437$	−37.9198	−	21.8930i	−1.81395	−	1.04728i
$438$			0.155358i			0.00742331i
$439$	−11.5506	+	20.0061i	−0.551278	+	0.954841i	0.446905	+	0.894582i	$0.352526\pi$
$439$	−11.5506	+	20.0061i	−0.551278	+	0.954841i	−0.998183	+	0.0602599i	$0.980807\pi$
$440$	0.711970	+	1.23317i	0.0339418	+	0.0587890i
$441$	−2.95676	+	5.12126i	−0.140798	+	0.243869i
$442$	−3.72184	−	6.44641i	−0.177030	−	0.306625i
$443$	−10.0474	−	17.4025i	−0.477365	−	0.826820i	0.522299	−	0.852762i	$-0.325075\pi$
$443$	−10.0474	−	17.4025i	−0.477365	−	0.826820i	−0.999663	+	0.0259429i	$0.991741\pi$
$444$	0.680085	+	0.392647i	0.0322754	+	0.0186342i
$445$	0.459955	−	0.265555i	0.0218040	−	0.0125885i
$446$	−3.44990	+	5.97541i	−0.163358	+	0.282944i
$447$	0.177234			0.00838287
$448$	−2.59586	+	1.49872i	−0.122643	+	0.0708080i
$449$	−1.74190	−	3.01705i	−0.0822052	−	0.142384i	0.821992	−	0.569500i	$-0.192863\pi$
$449$	−1.74190	−	3.01705i	−0.0822052	−	0.142384i	−0.904197	+	0.427116i	$0.859530\pi$
$450$			12.6169i			0.594764i
$451$		−	0.290144i		−	0.0136623i
$452$	−4.87496	+	8.44368i	−0.229299	+	0.397157i
$453$	1.55085	+	0.895383i	0.0728652	+	0.0420688i
$454$	25.5082			1.19716
$455$			2.99745i			0.140522i
$456$	−0.790584	−	0.456444i	−0.0370225	−	0.0213749i
$457$	31.8213	+	18.3721i	1.48854	+	0.859409i	0.999914	−	0.0130847i	$-0.00416511\pi$
$457$	31.8213	+	18.3721i	1.48854	+	0.859409i	0.488626	+	0.872494i	$0.337498\pi$
$458$	18.7191	+	10.8075i	0.874687	+	0.505001i
$459$	−4.81989	−	2.78277i	−0.224973	−	0.129888i
$460$			5.99745i			0.279632i
$461$	−37.1280			−1.72922			−0.864611	−	0.502443i	$-0.832435\pi$
$461$	−37.1280			−1.72922			−0.864611	+	0.502443i	$0.832435\pi$
$462$	−0.603734	−	0.348566i	−0.0280883	−	0.0162168i
$463$	−0.956626	+	1.65693i	−0.0444582	+	0.0770038i	−0.887398	−	0.461004i	$-0.847489\pi$
$463$	−0.956626	+	1.65693i	−0.0444582	+	0.0770038i	0.842940	+	0.538008i	$0.180823\pi$
$464$			0.198706i			0.00922470i
$465$			0.191729i			0.00889123i
$466$	−1.05137	−	1.82103i	−0.0487039	−	0.0843577i
$467$	24.2868	−	14.0220i	1.12386	−	0.648861i	0.181477	−	0.983395i	$-0.441912\pi$
$467$	24.2868	−	14.0220i	1.12386	−	0.648861i	0.942384	+	0.334534i	$0.108579\pi$
$468$	−3.40539			−0.157414
$469$	13.9431	−	24.1502i	0.643833	−	1.11515i
$470$	0.0928124	−	0.0535853i	0.00428112	−	0.00247170i
$471$	−0.303069	−	0.174977i	−0.0139647	−	0.00806252i
$472$	−4.07911	−	7.06523i	−0.187756	−	0.325204i
$473$	5.21455	+	9.03186i	0.239765	+	0.415285i
$474$	−0.877514	+	1.51990i	−0.0403055	+	0.0698112i
$475$	13.5246	+	23.4252i	0.620550	+	1.07482i
$476$	−9.76107	+	16.9067i	−0.447398	+	0.774916i
$477$		−	8.28582i		−	0.379382i
$478$	−9.21658	−	5.32119i	−0.421556	−	0.243386i
$479$	−26.0740			−1.19135			−0.595675	−	0.803225i	$-0.703115\pi$
$479$	−26.0740			−1.19135			−0.595675	+	0.803225i	$0.703115\pi$
$480$			0.125040i			0.00570727i
$481$	5.43894	−	3.14017i	0.247994	−	0.143180i
$482$	−15.5885	+	9.00000i	−0.710035	+	0.409939i
$483$	−1.46811	−	2.54285i	−0.0668015	−	0.115704i
$484$	4.17573	−	7.23258i	0.189806	−	0.328753i
$485$	−15.7719			−0.716165
$486$	−3.31132	+	1.91179i	−0.150205	+	0.0867207i
$487$	35.6913			1.61732			0.808662	−	0.588273i	$-0.200192\pi$
$487$	35.6913			1.61732			0.808662	+	0.588273i	$0.200192\pi$
$488$	−7.00000	−	3.46410i	−0.316875	−	0.156813i
$489$	0.892465			0.0403586
$490$	1.50387	−	0.868260i	0.0679379	−	0.0392240i
$491$	−15.1024			−0.681563			−0.340782	−	0.940143i	$-0.610692\pi$
$491$	−15.1024			−0.681563			−0.340782	+	0.940143i	$0.610692\pi$
$492$	0.0127392	−	0.0220649i	0.000574325	−	0.000994761i
$493$	0.647079	+	1.12077i	0.0291430	+	0.0504771i
$494$	−6.32265	+	3.65038i	−0.284470	+	0.164239i
$495$	3.67432	−	2.12137i	0.165148	−	0.0953484i
$496$			1.53334i			0.0688492i
$497$	−34.9836			−1.56923
$498$	−1.40115	−	0.808952i	−0.0627868	−	0.0362500i
$499$			9.55085i			0.427555i	0.976882	+	0.213777i	$0.0685767\pi$
$499$			9.55085i			0.427555i	−0.976882	+	0.213777i	$0.931423\pi$
$500$	4.03989	−	6.99729i	0.180669	−	0.312928i
$501$	−0.171306	−	0.296711i	−0.00765340	−	0.0132561i
$502$	−2.29218	+	3.97017i	−0.102305	+	0.177197i
$503$	4.60990	+	7.98459i	0.205545	+	0.356015i	0.950306	−	0.311316i	$-0.100770\pi$
$503$	4.60990	+	7.98459i	0.205545	+	0.356015i	−0.744761	+	0.667331i	$0.767436\pi$
$504$	4.46556	+	7.73458i	0.198912	+	0.344526i
$505$	−13.0128	−	7.51292i	−0.579060	−	0.334321i
$506$	−9.66078	+	5.57765i	−0.429474	+	0.247957i
$507$	−0.835573	+	1.44726i	−0.0371091	+	0.0642749i
$508$	7.55919			0.335385
$509$	6.98533	−	4.03298i	0.309619	−	0.178759i	−0.337137	−	0.941456i	$-0.609459\pi$
$509$	6.98533	−	4.03298i	0.309619	−	0.178759i	0.646756	+	0.762697i	$0.276125\pi$
$510$	0.407188	+	0.705270i	0.0180306	+	0.0312299i
$511$		−	3.25856i		−	0.144150i
$512$			1.00000i			0.0441942i
$513$	−2.72934	+	4.72736i	−0.120503	+	0.208718i
$514$	−9.56192	−	5.52058i	−0.421758	−	0.243502i
$515$	−6.70497			−0.295456
$516$			0.915806i			0.0403161i
$517$	0.172632	+	0.0996691i	0.00759235	+	0.00438344i
$518$	−14.2644	−	8.23556i	−0.626742	−	0.361850i
$519$	−1.72257	−	0.994528i	−0.0756125	−	0.0436549i
$520$	0.866025	+	0.500000i	0.0379777	+	0.0219265i
$521$		−	22.4360i		−	0.982938i	−0.870895	−	0.491469i	$-0.836460\pi$
$521$		−	22.4360i		−	0.982938i	0.870895	−	0.491469i	$-0.163540\pi$
$522$	0.592060			0.0259138
$523$	24.5708	+	14.1860i	1.07441	+	0.620309i	0.929382	−	0.369119i	$-0.120341\pi$
$523$	24.5708	+	14.1860i	1.07441	+	0.620309i	0.145024	+	0.989428i	$0.453674\pi$
$524$	−1.48307	+	2.56874i	−0.0647880	+	0.112216i
$525$			1.81388i			0.0791642i
$526$			15.5917i			0.679830i
$527$	4.99328	+	8.64861i	0.217511	+	0.376739i
$528$	−0.201416	+	0.116288i	−0.00876552	+	0.00506077i
$529$	−23.9847			−1.04281
$530$	−1.21658	+	2.10717i	−0.0528447	+	0.0915296i
$531$	−21.0514	+	12.1540i	−0.913553	+	0.527440i
$532$	16.5821	+	9.57367i	0.718924	+	0.415071i
$533$	−0.101881	−	0.176463i	−0.00441294	−	0.00764344i
$534$	0.0433737	+	0.0751255i	0.00187697	+	0.00325100i
$535$	−4.32985	+	7.49952i	−0.187196	+	0.324233i
$536$	−4.65166	−	8.05691i	−0.200921	−	0.348006i
$537$	−1.38841	+	2.40479i	−0.0599142	+	0.103774i
$538$		−	18.5396i		−	0.799301i
$539$	2.79721	+	1.61497i	0.120484	+	0.0695617i
$540$	0.747686			0.0321753
$541$		−	32.9847i		−	1.41812i	−0.705147	−	0.709061i	$-0.749119\pi$
$541$		−	32.9847i		−	1.41812i	0.705147	−	0.709061i	$-0.250881\pi$
$542$	−21.8647	+	12.6236i	−0.939170	+	0.542230i
$543$	2.06927	−	1.19469i	0.0888008	−	0.0512692i
$544$	3.25646	+	5.64036i	0.139620	+	0.241828i
$545$	5.72184	−	9.91052i	0.245097	−	0.424520i
$546$	−0.489580			−0.0209521
$547$	−1.93153	+	1.11517i	−0.0825863	+	0.0476812i	−0.540724	−	0.841200i	$-0.681850\pi$
$547$	−1.93153	+	1.11517i	−0.0825863	+	0.0476812i	0.458138	+	0.888881i	$0.348517\pi$
$548$	−21.7040			−0.927148
$549$	−10.3216	+	20.8570i	−0.440513	+	0.890157i
$550$	6.89128			0.293845
$551$	1.09926	−	0.634656i	0.0468299	−	0.0270372i
$552$	−0.979577			−0.0416936
$553$	18.4054	−	31.8791i	0.782677	−	1.35564i
$554$	14.0641	+	24.3598i	0.597528	+	1.03495i
$555$	−0.595047	+	0.343550i	−0.0252583	+	0.0145829i
$556$	3.19506	−	1.84467i	0.135501	−	0.0782313i
$557$		−	23.8571i		−	1.01086i	−0.862868	−	0.505430i	$-0.831334\pi$
$557$		−	23.8571i		−	1.01086i	0.862868	−	0.505430i	$-0.168666\pi$
$558$	4.56872			0.193409
$559$	6.34287	+	3.66206i	0.268275	+	0.154888i
$560$		−	2.62265i		−	0.110827i
$561$	−0.757373	+	1.31181i	−0.0319763	+	0.0553846i
$562$	−5.00893	−	8.67573i	−0.211289	−	0.365964i
$563$	19.9388	−	34.5349i	0.840318	−	1.45547i	−0.0493075	−	0.998784i	$-0.515701\pi$
$563$	19.9388	−	34.5349i	0.840318	−	1.45547i	0.889626	−	0.456690i	$-0.150965\pi$
$564$	0.00875221	+	0.0151593i	0.000368534	+	0.000638320i
$565$	−4.26540	−	7.38788i	−0.179447	−	0.310811i
$566$	−0.853625	−	0.492841i	−0.0358805	−	0.0207156i
$567$	22.8867	−	13.2137i	0.961152	−	0.554921i
$568$	−5.83557	+	10.1075i	−0.244855	+	0.424102i
$569$	31.4130			1.31690			0.658452	−	0.752623i	$-0.271212\pi$
$569$	31.4130			1.31690			0.658452	+	0.752623i	$0.271212\pi$
$570$	0.691729	−	0.399370i	0.0289734	−	0.0167278i
$571$	−4.31786	−	7.47876i	−0.180697	−	0.312976i	0.761421	−	0.648258i	$-0.224502\pi$
$571$	−4.31786	−	7.47876i	−0.180697	−	0.312976i	−0.942118	+	0.335281i	$0.891169\pi$
$572$			1.86001i			0.0777709i
$573$		−	2.70844i		−	0.113147i
$574$	−0.267197	+	0.462799i	−0.0111526	+	0.0193168i
$575$	25.1365	+	14.5126i	1.04827	+	0.605216i
$576$	2.97958			0.124149
$577$			5.50422i			0.229144i	0.993415	+	0.114572i	$0.0365496\pi$
$577$			5.50422i			0.229144i	−0.993415	+	0.114572i	$0.963450\pi$
$578$	22.0128	+	12.7091i	0.915610	+	0.528628i
$579$	−3.12985	−	1.80702i	−0.130072	−	0.0750972i
$580$	−0.150567	−	0.0869300i	−0.00625196	−	0.00360957i
$581$	29.3883	+	16.9673i	1.21923	+	0.703924i
$582$		−	2.57606i		−	0.106781i
$583$	−4.52568			−0.187435
$584$	−0.941467	−	0.543556i	−0.0389582	−	0.0224925i
$585$	1.48979	−	2.58039i	0.0615952	−	0.106686i
$586$		−	12.1601i		−	0.502329i
$587$			8.15567i			0.336621i	0.985734	+	0.168310i	$0.0538311\pi$
$587$			8.15567i			0.336621i	−0.985734	+	0.168310i	$0.946169\pi$
$588$	0.141815	+	0.245631i	0.00584835	+	0.0101296i
$589$	8.48257	−	4.89741i	0.349518	−	0.201794i
$590$	7.13812			0.293872
$591$	−1.29316	+	2.23982i	−0.0531935	+	0.0921339i
$592$	−4.75885	+	2.74753i	−0.195588	+	0.112923i
$593$	−17.2227	−	9.94352i	−0.707251	−	0.408331i	0.102792	−	0.994703i	$-0.467223\pi$
$593$	−17.2227	−	9.94352i	−0.707251	−	0.408331i	−0.810042	+	0.586372i	$0.800556\pi$
$594$	0.695351	+	1.20438i	0.0285306	+	0.0494165i
$595$	−8.54054	−	14.7927i	−0.350128	−	0.606440i
$596$	−0.620092	+	1.07403i	−0.0254000	+	0.0439940i
$597$	1.49870	+	2.59582i	0.0613376	+	0.106240i
$598$	−3.91706	+	6.78454i	−0.160180	+	0.277441i
$599$			5.50495i			0.224926i	0.993656	+	0.112463i	$0.0358740\pi$
$599$			5.50495i			0.224926i	−0.993656	+	0.112463i	$0.964126\pi$
$600$	0.524068	+	0.302571i	0.0213950	+	0.0123524i
$601$	12.3355			0.503176			0.251588	−	0.967834i	$-0.419047\pi$
$601$	12.3355			0.503176			0.251588	+	0.967834i	$0.419047\pi$
$602$		−	19.2085i		−	0.782882i
$603$	−24.0062	+	13.8600i	−0.977608	+	0.564422i
$604$	−10.8520	+	6.26540i	−0.441561	+	0.254935i
$605$	3.65360	+	6.32821i	0.148540	+	0.257279i
$606$	1.22710	−	2.12540i	0.0498477	−	0.0863387i
$607$	24.3018			0.986378			0.493189	−	0.869922i	$-0.335831\pi$
$607$	24.3018			0.986378			0.493189	+	0.869922i	$0.335831\pi$
$608$	5.53207	−	3.19394i	0.224355	−	0.129531i
$609$	0.0851183			0.00344917
$610$	5.68724	−	3.78869i	0.230270	−	0.153400i
$611$	0.139991			0.00566341
$612$	16.8059	−	9.70288i	0.679337	−	0.392215i
$613$	−21.6157			−0.873050			−0.436525	−	0.899692i	$-0.643791\pi$
$613$	−21.6157			−0.873050			−0.436525	+	0.899692i	$0.643791\pi$
$614$	−15.0686	+	26.0995i	−0.608118	+	1.05329i
$615$	0.0111462	+	0.0193059i	0.000449460	+	0.000778488i
$616$	4.22460	−	2.43907i	0.170214	−	0.0982730i
$617$	25.5343	−	14.7423i	1.02797	−	0.593501i	0.111570	−	0.993757i	$-0.464412\pi$
$617$	25.5343	−	14.7423i	1.02797	−	0.593501i	0.916404	+	0.400256i	$0.131079\pi$
$618$		−	1.09514i		−	0.0440529i
$619$	−30.0204			−1.20662			−0.603311	−	0.797506i	$-0.706152\pi$
$619$	−30.0204			−1.20662			−0.603311	+	0.797506i	$0.706152\pi$
$620$	−1.16187	−	0.670808i	−0.0466619	−	0.0269403i
$621$			5.85746i			0.235052i
$622$	13.6938	−	23.7183i	0.549071	−	0.951018i
$623$	−0.909741	−	1.57572i	−0.0364480	−	0.0631298i
$624$	−0.0816662	+	0.141450i	−0.00326926	+	0.00566253i
$625$	−7.05137	−	12.2133i	−0.282055	−	0.488534i
$626$	1.73460	+	3.00442i	0.0693287	+	0.120081i
$627$	1.28662	+	0.742832i	0.0513828	+	0.0296659i
$628$	2.12071	−	1.22439i	0.0846256	−	0.0488586i
$629$	−17.8944	+	30.9940i	−0.713497	+	1.23581i
$630$	−7.81438			−0.311332
$631$	34.2545	−	19.7769i	1.36365	−	0.787304i	0.373543	−	0.927613i	$-0.378143\pi$
$631$	34.2545	−	19.7769i	1.36365	−	0.787304i	0.990108	+	0.140309i	$0.0448094\pi$
$632$	−6.14036	−	10.6354i	−0.244250	−	0.423054i
$633$			0.403614i			0.0160422i
$634$			24.4010i			0.969086i
$635$	−3.30699	+	5.72788i	−0.131234	+	0.227304i
$636$	−0.344169	−	0.198706i	−0.0136472	−	0.00787921i
$637$	2.26831			0.0898739
$638$		−	0.323381i		−	0.0128028i
$639$	30.1161	+	17.3875i	1.19137	+	0.687840i
$640$	−0.757738	−	0.437480i	−0.0299522	−	0.0172929i
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	0.278093	−	0.960554i	$-0.410298\pi$
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	−0.692818	+	0.721113i	$0.743631\pi$
$642$	−1.22491	−	0.707205i	−0.0483435	−	0.0279111i
$643$		−	18.8032i		−	0.741524i	−0.928728	−	0.370762i	$-0.879096\pi$
$643$		−	18.8032i		−	0.741524i	0.928728	−	0.370762i	$-0.120904\pi$
$644$	20.5461			0.809630
$645$	−0.693941	−	0.400647i	−0.0273239	−	0.0157755i
$646$	20.8019	−	36.0299i	0.818439	−	1.41758i
$647$		−	37.9445i		−	1.49175i	−0.666084	−	0.745876i	$-0.732031\pi$
$647$		−	37.9445i		−	1.49175i	0.666084	−	0.745876i	$-0.267969\pi$
$648$		−	8.81661i		−	0.346349i
$649$	6.63849	+	11.4982i	0.260583	+	0.451344i
$650$	4.19120	−	2.41979i	0.164393	−	0.0949121i
$651$	0.656828			0.0257431
$652$	−3.12249	+	5.40830i	−0.122286	+	0.211806i
$653$	9.48648	−	5.47702i	0.371235	−	0.214332i	−0.302763	−	0.953066i	$-0.597909\pi$
$653$	9.48648	−	5.47702i	0.371235	−	0.214332i	0.673998	+	0.738733i	$0.264576\pi$
$654$	1.61871	+	0.934561i	0.0632965	+	0.0365442i
$655$	−1.29762	−	2.24755i	−0.0507023	−	0.0878190i
$656$	0.0891415	+	0.154398i	0.00348039	+	0.00602822i
$657$	−1.61957	+	2.80517i	−0.0631853	+	0.109440i
$658$	−0.183573	−	0.317958i	−0.00715642	−	0.0123953i
$659$	7.41482	−	12.8428i	0.288840	−	0.500286i	−0.684693	−	0.728832i	$-0.740064\pi$
$659$	7.41482	−	12.8428i	0.288840	−	0.500286i	0.973533	+	0.228546i	$0.0733970\pi$
$660$		−	0.203494i		−	0.00792100i
$661$	33.4258	+	19.2984i	1.30011	+	0.750622i	0.980424	−	0.196900i	$-0.0630875\pi$
$661$	33.4258	+	19.2984i	1.30011	+	0.750622i	0.319691	+	0.947522i	$0.396421\pi$
$662$	5.23763			0.203566
$663$			1.06377i			0.0413134i
$664$	9.80444	−	5.66060i	0.380486	−	0.219674i
$665$	−14.5087	+	8.37658i	−0.562622	+	0.324830i
$666$	8.18647	+	14.1794i	0.317219	+	0.549440i
$667$	0.681019	−	1.17956i	0.0263692	−	0.0456727i
$668$	2.39741			0.0927587
$669$	0.853941	−	0.493023i	0.0330153	−	0.0190614i
$670$	8.14004			0.314477
$671$	11.3920	+	5.63760i	0.439785	+	0.217637i
$672$	0.428363			0.0165245
$673$	−18.4967	+	10.6791i	−0.712996	+	0.411648i	−0.812169	−	0.583422i	$-0.801713\pi$
$673$	−18.4967	+	10.6791i	−0.712996	+	0.411648i	0.0991734	+	0.995070i	$0.468380\pi$
$674$	−22.5289			−0.867780
$675$	1.80924	−	3.13370i	0.0696379	−	0.120616i
$676$	−5.84688	−	10.1271i	−0.224880	−	0.389504i
$677$	−9.22715	+	5.32730i	−0.354628	+	0.204745i	−0.666722	−	0.745307i	$-0.732303\pi$
$677$	−9.22715	+	5.32730i	−0.354628	+	0.204745i	0.312094	+	0.950051i	$0.398970\pi$
$678$	1.20668	−	0.696677i	0.0463423	−	0.0267557i
$679$			54.0315i			2.07354i
$680$	−5.69855			−0.218529
$681$	−3.15697	−	1.82268i	−0.120975	−	0.0698452i
$682$		−	2.49542i		−	0.0955545i
$683$	−9.99156	+	17.3059i	−0.382317	+	0.662192i	−0.991393	−	0.130920i	$-0.958207\pi$
$683$	−9.99156	+	17.3059i	−0.382317	+	0.662192i	0.609076	+	0.793112i	$0.291540\pi$
$684$	−9.51659	−	16.4832i	−0.363876	−	0.630252i
$685$	9.49505	−	16.4459i	0.362787	−	0.628366i
$686$	7.51657	+	13.0191i	0.286984	+	0.497071i
$687$	−1.54449	−	2.67514i	−0.0589260	−	0.102063i
$688$	−5.54975	−	3.20415i	−0.211582	−	0.122157i
$689$	−2.75247	+	1.58914i	−0.104861	+	0.0605415i
$690$	0.428545	−	0.742262i	0.0163144	−	0.0282574i
$691$	−12.7875			−0.486461			−0.243230	−	0.969969i	$-0.578207\pi$
$691$	−12.7875			−0.486461			−0.243230	+	0.969969i	$0.578207\pi$
$692$	12.0536	−	6.95915i	0.458209	−	0.264547i
$693$	−7.26741	−	12.5875i	−0.276066	−	0.478160i
$694$			13.1636i			0.499685i
$695$			3.22802i			0.122446i
$696$	0.0141985	−	0.0245925i	0.000538192	−	0.000932175i
$697$	1.00558	+	0.580572i	0.0380891	+	0.0219907i
$698$	13.0204			0.492830
$699$			0.300502i			0.0113660i
$700$	−10.9920	−	6.34626i	−0.415460	−	0.239866i
$701$	−18.0321	−	10.4109i	−0.681064	−	0.393213i	0.119192	−	0.992871i	$-0.461970\pi$
$701$	−18.0321	−	10.4109i	−0.681064	−	0.393213i	−0.800256	+	0.599659i	$0.795303\pi$
$702$	0.845811	+	0.488329i	0.0319231	+	0.0184308i
$703$	30.3990	+	17.5509i	1.14652	+	0.661944i
$704$		−	1.62743i		−	0.0613362i
$705$	−0.0153157			−0.000576821
$706$	−15.3139	−	8.84146i	−0.576344	−	0.332753i
$707$	−25.7378	+	44.5792i	−0.967971	+	1.67657i
$708$			1.16589i			0.0438167i
$709$			19.1229i			0.718174i	0.933304	+	0.359087i	$0.116912\pi$
$709$			19.1229i			0.718174i	−0.933304	+	0.359087i	$0.883088\pi$
$710$	−5.10589	−	8.84367i	−0.191621	−	0.331897i
$711$	−31.6890	+	18.2957i	−1.18843	+	0.686141i
$712$	−0.607011			−0.0227487
$713$	5.25518	−	9.10225i	0.196808	−	0.340882i
$714$	2.41612	−	1.39495i	0.0904210	−	0.0522046i
$715$	−1.40940	−	0.813717i	−0.0527085	−	0.0304313i
$716$	−9.71530	−	16.8274i	−0.363078	−	0.628869i
$717$	0.760448	+	1.31713i	0.0283994	+	0.0491893i
$718$	−2.18230	+	3.77985i	−0.0814426	+	0.141063i
$719$	−5.00670	−	8.67185i	−0.186718	−	0.323406i	0.757436	−	0.652910i	$-0.226452\pi$
$719$	−5.00670	−	8.67185i	−0.186718	−	0.323406i	−0.944154	+	0.329504i	$0.893118\pi$
$720$	−1.30351	+	2.25774i	−0.0485788	+	0.0841409i
$721$			22.9699i			0.855446i
$722$	−18.8837	−	10.9025i	−0.702779	−	0.405750i
$723$	2.57237			0.0956674
$724$			16.7196i			0.621379i
$725$	−0.728683	+	0.420705i	−0.0270626	+	0.0156246i
$726$	−1.03360	+	0.596750i	−0.0383606	+	0.0221475i
$727$	−18.7362	−	32.4521i	−0.694888	−	1.20358i	−0.970218	−	0.242232i	$-0.922121\pi$
$727$	−18.7362	−	32.4521i	−0.694888	−	1.20358i	0.275331	−	0.961350i	$-0.411213\pi$
$728$	1.71290	−	2.96684i	0.0634845	−	0.109958i
$729$	−25.9034			−0.959385
$730$	0.823746	−	0.475590i	0.0304882	−	0.0176024i
$731$	−41.7368			−1.54369
$732$	0.618815	+	0.928910i	0.0228721	+	0.0343335i
$733$	−23.7806			−0.878355			−0.439177	−	0.898400i	$-0.644730\pi$
$733$	−23.7806			−0.878355			−0.439177	+	0.898400i	$0.644730\pi$
$734$	−8.59894	+	4.96460i	−0.317393	+	0.183247i
$735$	−0.248165			−0.00915370
$736$	3.42727	−	5.93620i	0.126331	−	0.218811i
$737$	7.57027	+	13.1121i	0.278855	+	0.482990i
$738$	0.460040	−	0.265604i	0.0169343	−	0.00977702i
$739$	−34.3493	+	19.8316i	−1.26356	+	0.729517i	−0.973761	−	0.227571i	$-0.926922\pi$
$739$	−34.3493	+	19.8316i	−1.26356	+	0.729517i	−0.289798	+	0.957088i	$0.593588\pi$
$740$		−	4.80795i		−	0.176744i
$741$	1.04335			0.0383283
$742$	7.21876	+	4.16776i	0.265009	+	0.153003i
$743$		−	7.15946i		−	0.262655i	−0.991339	−	0.131328i	$-0.958076\pi$
$743$		−	7.15946i		−	0.262655i	0.991339	−	0.131328i	$-0.0419240\pi$
$744$	0.109565	−	0.189771i	0.00401683	−	0.00695736i
$745$	−0.542556	−	0.939734i	−0.0198777	−	0.0344292i
$746$	−12.6077	+	21.8372i	−0.461600	+	0.799515i
$747$	−16.8662	−	29.2131i	−0.617101	−	1.06885i
$748$	−5.29967	−	9.17931i	−0.193775	−	0.335629i
$749$	25.6919	+	14.8332i	0.938763	+	0.541995i
$750$	−0.999977	+	0.577337i	−0.0365140	+	0.0210814i
$751$	18.4373	−	31.9344i	0.672787	−	1.16530i	−0.304323	−	0.952569i	$-0.598430\pi$
$751$	18.4373	−	31.9344i	0.672787	−	1.16530i	0.977110	−	0.212733i	$-0.0682365\pi$
$752$	−0.122486			−0.00446661
$753$	0.567374	−	0.327573i	0.0206762	−	0.0119374i
$754$	−0.113552	−	0.196677i	−0.00413530	−	0.00716255i
$755$		−	10.9639i		−	0.399019i
$756$		−	2.56143i		−	0.0931583i
$757$	−20.7404	+	35.9234i	−0.753822	+	1.30566i	0.192135	+	0.981368i	$0.438459\pi$
$757$	−20.7404	+	35.9234i	−0.753822	+	1.30566i	−0.945958	+	0.324290i	$0.894875\pi$
$758$	21.6642	+	12.5078i	0.786878	+	0.454304i
$759$	1.59420			0.0578657
$760$			5.58914i			0.202739i
$761$	−18.9578	−	10.9453i	−0.687220	−	0.396767i	0.115350	−	0.993325i	$-0.463201\pi$
$761$	−18.9578	−	10.9453i	−0.687220	−	0.396767i	−0.802570	+	0.596558i	$0.796534\pi$
$762$	−0.935548	−	0.540139i	−0.0338913	−	0.0195672i
$763$	−33.9515	−	19.6019i	−1.22913	−	0.709637i
$764$	16.4131	+	9.47609i	0.593804	+	0.342833i
$765$			16.9793i			0.613886i
$766$	−13.5588			−0.489900
$767$	8.07492	+	4.66206i	0.291568	+	0.168337i
$768$	0.0714546	−	0.123763i	0.00257840	−	0.00446591i
$769$			46.0816i			1.66174i	0.556463	+	0.830872i	$0.312158\pi$
$769$			46.0816i			1.66174i	−0.556463	+	0.830872i	$0.687842\pi$
$770$			4.26818i			0.153815i
$771$	0.788942	+	1.36649i	0.0284131	+	0.0492129i
$772$	21.9010	−	12.6445i	0.788233	−	0.455086i
$773$	3.20126			0.115141			0.0575707	−	0.998341i	$-0.481665\pi$
$773$	3.20126			0.115141			0.0575707	+	0.998341i	$0.481665\pi$
$774$	−9.54702	+	16.5359i	−0.343160	+	0.594371i
$775$	−5.62298	+	3.24643i	−0.201984	+	0.116615i
$776$	15.6108	+	9.01292i	0.560396	+	0.323545i
$777$	1.17694	+	2.03852i	0.0422224	+	0.0731314i
$778$	−9.12233	−	15.8003i	−0.327051	−	0.566469i
$779$	0.569426	−	0.986274i	0.0204018	−	0.0353369i
$780$	−0.0714546	−	0.123763i	−0.00255849	−	0.00443143i
$781$	9.49701	−	16.4493i	0.339830	−	0.588602i
$782$		−	44.6431i		−	1.59643i
$783$	−0.147053	−	0.0849009i	−0.00525523	−	0.00303411i
$784$	−1.98468			−0.0708816
$785$			2.14259i			0.0764723i
$786$	0.367097	−	0.211944i	0.0130939	−	0.00755978i
$787$	5.77462	−	3.33398i	0.205843	−	0.118844i	−0.393535	−	0.919310i	$-0.628748\pi$
$787$	5.77462	−	3.33398i	0.205843	−	0.118844i	0.599378	+	0.800466i	$0.295415\pi$
$788$	−9.04882	−	15.6730i	−0.322351	−	0.558328i
$789$	1.11410	−	1.92968i	0.0396630	−	0.0686983i
$790$	10.7451			0.382295
$791$	−25.3095	+	14.6124i	−0.899901	+	0.519558i
$792$	−4.84906			−0.172304
$793$	8.90810	−	0.571455i	0.316336	−	0.0202929i
$794$	4.38178			0.155503
$795$	0.301134	−	0.173860i	0.0106801	−	0.00616618i
$796$	−20.9741			−0.743407
$797$	18.7184	−	32.4212i	0.663039	−	1.14842i	−0.316774	−	0.948501i	$-0.602600\pi$
$797$	18.7184	−	32.4212i	0.663039	−	1.14842i	0.979813	−	0.199916i	$-0.0640669\pi$
$798$	−1.36817	−	2.36973i	−0.0484325	−	0.0838876i
$799$	−0.690866	+	0.398872i	−0.0244411	+	0.0141111i
$800$	−3.66714	+	2.11722i	−0.129653	+	0.0748551i
$801$			1.80864i			0.0639050i
$802$	33.5607			1.18507
$803$	1.53218	+	0.884602i	0.0540693	+	0.0312169i
$804$			1.32953i			0.0468889i
$805$	−8.98851	+	15.5686i	−0.316803	+	0.548720i
$806$	−0.876237	−	1.51769i	−0.0308641	−	0.0534582i
$807$	−1.32474	+	2.29452i	−0.0466332	+	0.0807710i
$808$	8.58659	+	14.8724i	0.302075	+	0.523209i
$809$	8.47463	+	14.6785i	0.297952	+	0.516068i	0.975667	−	0.219256i	$-0.0703631\pi$
$809$	8.47463	+	14.6785i	0.297952	+	0.516068i	−0.677715	+	0.735324i	$0.737030\pi$
$810$	6.68068	+	3.85709i	0.234735	+	0.135524i
$811$	−3.27461	+	1.89060i	−0.114987	+	0.0663878i	−0.556390	−	0.830921i	$-0.687814\pi$
$811$	−3.27461	+	1.89060i	−0.114987	+	0.0663878i	0.441403	+	0.897309i	$0.354481\pi$
$812$	−0.297805	+	0.515814i	−0.0104509	+	0.0181015i
$813$	3.60806			0.126540
$814$	7.74472	−	4.47142i	0.271452	−	0.156723i
$815$	−2.73205	−	4.73205i	−0.0956996	−	0.165757i
$816$		−	0.930757i		−	0.0325830i
$817$			40.9355i			1.43215i
$818$	2.16493	−	3.74976i	0.0756948	−	0.131107i
$819$	−8.83992	−	5.10373i	−0.308892	−	0.178339i
$820$	−0.155991			−0.00544743
$821$			28.9533i			1.01048i	0.862980	+	0.505239i	$0.168596\pi$
$821$			28.9533i			1.01048i	−0.862980	+	0.505239i	$0.831404\pi$
$822$	2.68615	+	1.55085i	0.0936902	+	0.0540921i
$823$	−0.424305	−	0.244972i	−0.0147903	−	0.00853920i	0.492587	−	0.870263i	$-0.336051\pi$
$823$	−0.424305	−	0.244972i	−0.0147903	−	0.00853920i	−0.507377	+	0.861724i	$0.669385\pi$
$824$	6.63650	+	3.83159i	0.231194	+	0.133480i
$825$	−0.852886	−	0.492414i	−0.0296937	−	0.0171437i
$826$		−	24.4538i		−	0.850858i
$827$	53.3409			1.85485			0.927423	−	0.374015i	$-0.122019\pi$
$827$	53.3409			1.85485			0.927423	+	0.374015i	$0.122019\pi$
$828$	−17.6874	−	10.2118i	−0.614679	−	0.354885i
$829$	15.7094	−	27.2095i	0.545611	−	0.945027i	−0.452957	−	0.891532i	$-0.649631\pi$
$829$	15.7094	−	27.2095i	0.545611	−	0.945027i	0.998568	−	0.0534941i	$-0.0170358\pi$
$830$			9.90559i			0.343828i
$831$		−	4.01979i		−	0.139445i
$832$	−0.571455	−	0.989788i	−0.0198116	−	0.0343147i
$833$	−11.1943	+	6.46305i	−0.387860	+	0.223931i
$834$	−0.527240			−0.0182568
$835$	−1.04882	+	1.81661i	−0.0362959	+	0.0628664i
$836$	−9.00308	+	5.19793i	−0.311378	+	0.179774i
$837$	−1.13475	−	0.655150i	−0.0392228	−	0.0226453i
$838$	20.0048	+	34.6493i	0.691053	+	1.19694i
$839$	−14.0140	−	24.2730i	−0.483818	−	0.837998i	0.516009	−	0.856583i	$-0.327417\pi$
$839$	−14.0140	−	24.2730i	−0.483818	−	0.837998i	−0.999827	+	0.0185852i	$0.994084\pi$
$840$	−0.187400	+	0.324587i	−0.00646592	+	0.0111993i
$841$	−14.4803	−	25.0805i	−0.499319	−	0.864846i
$842$	−0.324271	+	0.561653i	−0.0111751	+	0.0193558i
$843$			1.43165i			0.0493085i
$844$	−2.44589	−	1.41214i	−0.0841910	−	0.0486077i
$845$	10.2316			0.351977
$846$			0.364957i			0.0125475i
$847$	21.6793	−	12.5165i	0.744908	−	0.430073i
$848$	2.40830	−	1.39044i	0.0827015	−	0.0477477i
$849$	0.0704315	+	0.121991i	0.00241720	+	0.00418672i
$850$	−13.7893	+	23.8838i	−0.472969	+	0.819207i
$851$	37.6660			1.29118
$852$	1.44446	−	0.833958i	0.0494863	−	0.0285709i
$853$	24.9974			0.855894			0.427947	−	0.903804i	$-0.359237\pi$
$853$	24.9974			0.855894			0.427947	+	0.903804i	$0.359237\pi$
$854$	−12.9793	−	19.4834i	−0.444143	−	0.666708i
$855$	16.6533			0.569530
$856$	8.57127	−	4.94863i	0.292960	−	0.169141i
$857$	20.2143			0.690509			0.345254	−	0.938509i	$-0.387793\pi$
$857$	20.2143			0.690509			0.345254	+	0.938509i	$0.387793\pi$
$858$	0.132906	−	0.230200i	0.00453735	−	0.00785891i
$859$	−27.7609	−	48.0833i	−0.947189	−	1.64058i	−0.751308	−	0.659952i	$-0.770577\pi$
$859$	−27.7609	−	48.0833i	−0.947189	−	1.64058i	−0.195881	−	0.980628i	$-0.562757\pi$
$860$	4.85581	−	2.80351i	0.165582	−	0.0955987i
$861$	0.0661382	−	0.0381849i	0.00225398	−	0.00130134i
$862$			20.6718i			0.704084i
$863$	−0.324111			−0.0110329			−0.00551643	−	0.999985i	$-0.501756\pi$
$863$	−0.324111			−0.0110329			−0.00551643	+	0.999985i	$0.501756\pi$
$864$	−0.740051	−	0.427269i	−0.0251770	−	0.0145360i
$865$			12.1780i			0.414063i
$866$	10.9440	−	18.9556i	0.371893	−	0.644138i
$867$	−1.81624	−	3.14583i	−0.0616829	−	0.106838i
$868$	−2.29806	+	3.98036i	−0.0780012	+	0.135102i
$869$	9.99302	+	17.3084i	0.338990	+	0.587148i
$870$	0.0124231	+	0.0215174i	0.000421182	+	0.000729509i
$871$	9.20832	+	5.31643i	0.312012	+	0.180140i
$872$	−11.3268	+	6.53954i	−0.383575	+	0.221457i
$873$	26.8547	−	46.5137i	0.908894	−	1.57425i
$874$	−43.7860			−1.48108
$875$	20.9740	−	12.1093i	0.709050	−	0.409370i
$876$	0.0776792	+	0.134544i	0.00262454	+	0.00454583i
$877$		−	28.2351i		−	0.953431i	−0.879058	−	0.476715i	$-0.841827\pi$
$877$		−	28.2351i		−	0.953431i	0.879058	−	0.476715i	$-0.158173\pi$
$878$			23.1011i			0.779625i
$879$	−0.868895	+	1.50497i	−0.0293071	+	0.0507614i
$880$	1.23317	+	0.711970i	0.0415701	+	0.0240005i
$881$	27.2705			0.918767			0.459383	−	0.888238i	$-0.348070\pi$
$881$	27.2705			0.918767			0.459383	+	0.888238i	$0.348070\pi$
$882$			5.91352i			0.199119i
$883$	−6.70117	−	3.86892i	−0.225512	−	0.130200i	0.382988	−	0.923753i	$-0.374895\pi$
$883$	−6.70117	−	3.86892i	−0.225512	−	0.130200i	−0.608500	+	0.793554i	$0.708228\pi$
$884$	−6.44641	−	3.72184i	−0.216816	−	0.125179i
$885$	−0.883436	−	0.510052i	−0.0296964	−	0.0171452i
$886$	−17.4025	−	10.0474i	−0.584650	−	0.337548i
$887$			19.2700i			0.647023i	0.946224	+	0.323512i	$0.104863\pi$
$887$			19.2700i			0.647023i	−0.946224	+	0.323512i	$0.895137\pi$
$888$	0.785294			0.0263527
$889$	19.6226	+	11.3291i	0.658122	+	0.379967i
$890$	0.265555	−	0.459955i	0.00890143	−	0.0154177i
$891$			14.3484i			0.480691i
$892$			6.89981i			0.231023i
$893$	0.391214	+	0.677602i	0.0130915	+	0.0226751i
$894$	0.153489	−	0.0886169i	0.00513344	−	0.00296379i
$895$	17.0010			0.568281
$896$	−1.49872	+	2.59586i	−0.0500688	+	0.0867218i
$897$	0.969574	−	0.559784i	0.0323731	−	0.0186906i
$898$	−3.01705	−	1.74190i	−0.100680	−	0.0581279i
$899$	0.152342	+	0.263865i	0.00508091	+	0.00880039i
$900$	6.30843	+	10.9265i	0.210281	+	0.364217i
$901$	9.05580	−	15.6851i	0.301692	−	0.522546i
$902$	−0.145072	−	0.251272i	−0.00483037	−	0.00836644i
$903$	−1.37254	+	2.37731i	−0.0456753	+	0.0791119i
$904$			9.74992i			0.324278i
$905$	−12.6691	−	7.31449i	−0.421134	−	0.243142i
$906$	1.79077			0.0594942
$907$			4.77627i			0.158593i	0.996851	+	0.0792967i	$0.0252675\pi$
$907$			4.77627i			0.158593i	−0.996851	+	0.0792967i	$0.974733\pi$
$908$	22.0907	−	12.7541i	0.733107	−	0.423259i
$909$	44.3135	−	25.5844i	1.46979	−	0.848581i
$910$	1.49872	+	2.59586i	0.0496822	+	0.0860521i
$911$	−11.7604	+	20.3697i	−0.389641	+	0.674878i	−0.992401	−	0.123044i	$-0.960734\pi$
$911$	−11.7604	+	20.3697i	−0.389641	+	0.674878i	0.602760	+	0.797922i	$0.294068\pi$
$912$	−0.912888			−0.0302287
$913$	−15.9561	+	9.21225i	−0.528069	+	0.304881i
$914$	36.7441			1.21539
$915$	−0.974590	+	0.0625200i	−0.0322189	+	0.00206685i
$916$	21.6150			0.714179
$917$	−7.69967	+	4.44541i	−0.254266	+	0.146800i
$918$	−5.56553			−0.183690
$919$	−0.922503	+	1.59782i	−0.0304306	+	0.0527073i	−0.880840	−	0.473415i	$-0.843021\pi$
$919$	−0.922503	+	1.59782i	−0.0304306	+	0.0527073i	0.850409	+	0.526122i	$0.176355\pi$
$920$	2.99872	+	5.19394i	0.0988650	+	0.171239i
$921$	3.72986	−	2.15344i	0.122903	−	0.0709582i
$922$	−32.1537	+	18.5640i	−1.05893	+	0.611372i
$923$		−	13.3391i		−	0.439061i
$924$	−0.697132			−0.0229340
$925$	−20.1511	−	11.6342i	−0.662564	−	0.382532i
$926$			1.91325i			0.0628734i
$927$	11.4165	−	19.7740i	0.374967	−	0.649462i
$928$	0.0993531	+	0.172085i	0.00326142	+	0.00564895i
$929$	−6.85454	+	11.8724i	−0.224890	+	0.389521i	−0.956286	−	0.292432i	$-0.905536\pi$
$929$	−6.85454	+	11.8724i	−0.224890	+	0.389521i	0.731396	+	0.681953i	$0.238869\pi$
$930$	0.0958646	+	0.166042i	0.00314353	+	0.00544475i
$931$	6.33896	+	10.9794i	0.207751	+	0.359836i
$932$	−1.82103	−	1.05137i	−0.0596499	−	0.0344389i
$933$	−3.38957	+	1.95697i	−0.110969	+	0.0640683i
$934$	14.0220	−	24.2868i	0.458814	−	0.794690i
$935$	9.27401			0.303292
$936$	−2.94915	+	1.70269i	−0.0963960	+	0.0556543i
$937$	−22.4586	−	38.8995i	−0.733691	−	1.27079i	−0.955295	−	0.295654i	$-0.904462\pi$
$937$	−22.4586	−	38.8995i	−0.733691	−	1.27079i	0.221604	−	0.975137i	$-0.428871\pi$
$938$		−	27.8862i		−	0.910517i
$939$		−	0.495782i		−	0.0161792i
$940$	0.0535853	−	0.0928124i	0.00174776	−	0.00302721i
$941$	−7.97246	−	4.60290i	−0.259895	−	0.150050i	0.364392	−	0.931246i	$-0.381277\pi$
$941$	−7.97246	−	4.60290i	−0.259895	−	0.150050i	−0.624287	+	0.781195i	$0.714610\pi$
$942$	−0.349954			−0.0114021
$943$		−	1.22205i		−	0.0397954i
$944$	−7.06523	−	4.07911i	−0.229954	−	0.132764i
$945$	1.94089	+	1.12057i	0.0631372	+	0.0364523i
$946$	9.03186	+	5.21455i	0.293651	+	0.169540i
$947$	−17.2184	−	9.94103i	−0.559522	−	0.323040i	0.193432	−	0.981114i	$-0.438038\pi$
$947$	−17.2184	−	9.94103i	−0.559522	−	0.323040i	−0.752954	+	0.658074i	$0.771372\pi$
$948$			1.75503i			0.0570006i
$949$	1.24247			0.0403323
$950$	23.4252	+	13.5246i	0.760015	+	0.438795i
$951$	1.74356	−	3.01994i	0.0565389	−	0.0979282i
$952$			19.5221i			0.632716i
$953$		−	20.3838i		−	0.660297i	−0.943929	−	0.330148i	$-0.892901\pi$
$953$		−	20.3838i		−	0.660297i	0.943929	−	0.330148i	$-0.107099\pi$
$954$	−4.14291	−	7.17573i	−0.134132	−	0.232323i
$955$	−14.3608	+	8.29120i	−0.464704	+	0.268297i
$956$	−10.6424			−0.344199
$957$	−0.0231071	+	0.0400226i	−0.000746946	+	0.00129375i
$958$	−22.5807	+	13.0370i	−0.729550	+	0.421206i
$959$	−56.3406	−	32.5282i	−1.81933	−	1.05039i
$960$	0.0625200	+	0.108288i	0.00201782	+	0.00349497i
$961$	−14.3244	−	24.8106i	−0.462078	−	0.800343i
$962$	3.14017	−	5.43894i	0.101243	−	0.175358i
$963$	−14.7448	−	25.5388i	−0.475145	−	0.822975i
$964$	−9.00000	+	15.5885i	−0.289870	+	0.502070i
$965$			22.1269i			0.712290i
$966$	−2.54285	−	1.46811i	−0.0818148	−	0.0472358i
$967$	30.8483			0.992016			0.496008	−	0.868318i	$-0.334799\pi$
$967$	30.8483			0.992016			0.496008	+	0.868318i	$0.334799\pi$
$968$		−	8.35146i		−	0.268426i
$969$	−5.14901	+	2.97278i	−0.165410	+	0.0954995i
$970$	−13.6589	+	7.88595i	−0.438560	+	0.253202i
$971$	4.90593	+	8.49733i	0.157439	+	0.272692i	0.933944	−	0.357418i	$-0.116343\pi$
$971$	4.90593	+	8.49733i	0.157439	+	0.272692i	−0.776506	+	0.630110i	$0.783010\pi$
$972$	−1.91179	+	3.31132i	−0.0613208	+	0.106211i
$973$	11.0586			0.354522
$974$	30.9095	−	17.8456i	0.990405	−	0.571811i
$975$	−0.691622			−0.0221496
$976$	−7.79423	+	0.500000i	−0.249487	+	0.0160046i
$977$	11.0983			0.355065			0.177533	−	0.984115i	$-0.443188\pi$
$977$	11.0983			0.355065			0.177533	+	0.984115i	$0.443188\pi$
$978$	0.772897	−	0.446232i	0.0247145	−	0.0142689i
$979$	0.987870			0.0315725
$980$	0.868260	−	1.50387i	0.0277355	−	0.0480394i
$981$	19.4851	+	33.7491i	0.622110	+	1.07753i
$982$	−13.0791	+	7.55121i	−0.417370	+	0.240969i
$983$	33.1072	−	19.1145i	1.05596	−	0.609657i	0.131645	−	0.991297i	$-0.457974\pi$
$983$	33.1072	−	19.1145i	1.05596	−	0.609657i	0.924311	+	0.381640i	$0.124641\pi$
$984$		−	0.0254783i		−	0.000812219i
$985$	15.8347			0.504536
$986$	1.12077	+	0.647079i	0.0356927	+	0.0206072i
$987$			0.0524685i			0.00167009i
$988$	−3.65038	+	6.32265i	−0.116134	+	0.201150i
$989$	21.9630	+	38.0410i	0.698382	+	1.20963i
$990$	2.12137	−	3.67432i	0.0674215	−	0.116778i
$991$	−0.746155	−	1.29238i	−0.0237024	−	0.0410538i	0.853931	−	0.520386i	$-0.174212\pi$
$991$	−0.746155	−	1.29238i	−0.0237024	−	0.0410538i	−0.877633	+	0.479333i	$0.840879\pi$
$992$	0.766672	+	1.32792i	0.0243419	+	0.0421614i
$993$	−0.648225	−	0.374253i	−0.0205708	−	0.0118766i
$994$	−30.2967	+	17.4918i	−0.960954	+	0.554807i
$995$	9.17575	−	15.8929i	0.290891	−	0.503838i
$996$	−1.61790			−0.0512652
$997$	−47.6779	+	27.5269i	−1.50998	+	0.871785i	−0.510043	+	0.860149i	$0.670371\pi$
$997$	−47.6779	+	27.5269i	−1.50998	+	0.871785i	−0.999932	+	0.0116360i	$0.996296\pi$
$998$	4.77542	+	8.27128i	0.151163	+	0.261823i
$999$		−	4.69573i		−	0.148566i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	122.2.f.a.75.3	✓	8
3.2	odd	2		1098.2.o.a.685.1		8
4.3	odd	2		976.2.ba.b.929.3		8
61.29	odd	12		7442.2.a.l.1.3		4
61.32	odd	12		7442.2.a.m.1.3		4
61.48	even	6	inner	122.2.f.a.109.3	yes	8
183.170	odd	6		1098.2.o.a.109.1		8
244.231	odd	6		976.2.ba.b.353.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
122.2.f.a.75.3	✓	8	1.1	even	1	trivial
122.2.f.a.109.3	yes	8	61.48	even	6	inner
976.2.ba.b.353.3		8	244.231	odd	6
976.2.ba.b.929.3		8	4.3	odd	2
1098.2.o.a.109.1		8	183.170	odd	6
1098.2.o.a.685.1		8	3.2	odd	2
7442.2.a.l.1.3		4	61.29	odd	12
7442.2.a.m.1.3		4	61.32	odd	12

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:	\( N \)	\(=\)	\( 122 = 2 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	122.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -0.142909 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.437480 + 0.757738i) q^{5} +(-0.123763 + 0.0714546i) q^{6} +(2.59586 - 1.49872i) q^{7} -1.00000i q^{8} -2.97958 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -0.142909 q^{3} +(0.500000 - 0.866025i) q^{4} +(0.437480 + 0.757738i) q^{5} +(-0.123763 + 0.0714546i) q^{6} +(2.59586 - 1.49872i) q^{7} -1.00000i q^{8} -2.97958 q^{9} +(0.757738 + 0.437480i) q^{10} +1.62743i q^{11} +(-0.0714546 + 0.123763i) q^{12} +(0.571455 + 0.989788i) q^{13} +(1.49872 - 2.59586i) q^{14} +(-0.0625200 - 0.108288i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-5.64036 - 3.25646i) q^{17} +(-2.58039 + 1.48979i) q^{18} +(-3.19394 + 5.53207i) q^{19} +0.874960 q^{20} +(-0.370973 + 0.214181i) q^{21} +(0.813717 + 1.40940i) q^{22} +6.85454i q^{23} +0.142909i q^{24} +(2.11722 - 3.66714i) q^{25} +(0.989788 + 0.571455i) q^{26} +0.854537 q^{27} -2.99745i q^{28} +(-0.172085 - 0.0993531i) q^{29} +(-0.108288 - 0.0625200i) q^{30} +(-1.32792 - 0.766672i) q^{31} +(-0.866025 - 0.500000i) q^{32} -0.232575i q^{33} -6.51292 q^{34} +(2.27128 + 1.31132i) q^{35} +(-1.48979 + 2.58039i) q^{36} -5.49505i q^{37} +6.38788i q^{38} +(-0.0816662 - 0.141450i) q^{39} +(0.757738 - 0.437480i) q^{40} -0.178283 q^{41} +(-0.214181 + 0.370973i) q^{42} +(5.54975 - 3.20415i) q^{43} +(1.40940 + 0.813717i) q^{44} +(-1.30351 - 2.25774i) q^{45} +(3.42727 + 5.93620i) q^{46} +(0.0612431 - 0.106076i) q^{47} +(0.0714546 + 0.123763i) q^{48} +(0.992342 - 1.71879i) q^{49} -4.23444i q^{50} +(0.806059 + 0.465378i) q^{51} +1.14291 q^{52} +2.78087i q^{53} +(0.740051 - 0.427269i) q^{54} +(-1.23317 + 0.711970i) q^{55} +(-1.49872 - 2.59586i) q^{56} +(0.456444 - 0.790584i) q^{57} -0.198706 q^{58} +(7.06523 - 4.07911i) q^{59} -0.125040 q^{60} +(3.46410 - 7.00000i) q^{61} -1.53334 q^{62} +(-7.73458 + 4.46556i) q^{63} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-0.116288 - 0.201416i) q^{66} +(8.05691 - 4.65166i) q^{67} +(-5.64036 + 3.25646i) q^{68} -0.979577i q^{69} +2.62265 q^{70} +(-10.1075 - 5.83557i) q^{71} +2.97958i q^{72} +(0.543556 - 0.941467i) q^{73} +(-2.74753 - 4.75885i) q^{74} +(-0.302571 + 0.524068i) q^{75} +(3.19394 + 5.53207i) q^{76} +(2.43907 + 4.22460i) q^{77} +(-0.141450 - 0.0816662i) q^{78} +(10.6354 - 6.14036i) q^{79} +(0.437480 - 0.757738i) q^{80} +8.81661 q^{81} +(-0.154398 + 0.0891415i) q^{82} +(5.66060 + 9.80444i) q^{83} +0.428363i q^{84} -5.69855i q^{85} +(3.20415 - 5.54975i) q^{86} +(0.0245925 + 0.0141985i) q^{87} +1.62743 q^{88} -0.607011i q^{89} +(-2.25774 - 1.30351i) q^{90} +(2.96684 + 1.71290i) q^{91} +(5.93620 + 3.42727i) q^{92} +(0.189771 + 0.109565i) q^{93} -0.122486i q^{94} -5.58914 q^{95} +(0.123763 + 0.0714546i) q^{96} +(-9.01292 + 15.6108i) q^{97} -1.98468i q^{98} -4.84906i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9	\( 8 q + 4 q^{4} - 4 q^{5} + 6 q^{6} + 12 q^{7} + 4 q^{9} + 6 q^{10} + 4 q^{13} - 10 q^{14} - 8 q^{15} - 4 q^{16} - 12 q^{18} + 4 q^{19} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 2 q^{25} - 6 q^{26} - 36 q^{27} - 24 q^{29} + 6 q^{30} + 12 q^{31} - 8 q^{34} - 18 q^{35} + 2 q^{36} - 14 q^{39} + 6 q^{40} + 24 q^{41} - 4 q^{42} - 6 q^{43} + 6 q^{44} + 4 q^{45} + 6 q^{46} - 14 q^{47} + 38 q^{49} + 36 q^{51} + 8 q^{52} + 18 q^{54} + 42 q^{55} + 10 q^{56} + 6 q^{57} - 4 q^{58} + 6 q^{59} - 16 q^{60} + 4 q^{62} + 6 q^{63} - 8 q^{64} - 4 q^{65} - 20 q^{66} + 30 q^{67} + 52 q^{70} - 6 q^{71} + 2 q^{73} - 8 q^{74} - 22 q^{75} - 4 q^{76} - 8 q^{77} + 18 q^{78} + 12 q^{79} - 4 q^{80} + 8 q^{81} - 36 q^{82} + 32 q^{83} + 10 q^{86} - 12 q^{87} + 12 q^{88} - 18 q^{90} + 36 q^{91} + 18 q^{92} + 12 q^{93} - 32 q^{95} - 6 q^{96} - 28 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^5 + 6 * q^6 + 12 * q^7 + 4 * q^9 + 6 * q^10 + 4 * q^13 - 10 * q^14 - 8 * q^15 - 4 * q^16 - 12 * q^18 + 4 * q^19 - 8 * q^20 - 24 * q^21 + 6 * q^22 + 2 * q^25 - 6 * q^26 - 36 * q^27 - 24 * q^29 + 6 * q^30 + 12 * q^31 - 8 * q^34 - 18 * q^35 + 2 * q^36 - 14 * q^39 + 6 * q^40 + 24 * q^41 - 4 * q^42 - 6 * q^43 + 6 * q^44 + 4 * q^45 + 6 * q^46 - 14 * q^47 + 38 * q^49 + 36 * q^51 + 8 * q^52 + 18 * q^54 + 42 * q^55 + 10 * q^56 + 6 * q^57 - 4 * q^58 + 6 * q^59 - 16 * q^60 + 4 * q^62 + 6 * q^63 - 8 * q^64 - 4 * q^65 - 20 * q^66 + 30 * q^67 + 52 * q^70 - 6 * q^71 + 2 * q^73 - 8 * q^74 - 22 * q^75 - 4 * q^76 - 8 * q^77 + 18 * q^78 + 12 * q^79 - 4 * q^80 + 8 * q^81 - 36 * q^82 + 32 * q^83 + 10 * q^86 - 12 * q^87 + 12 * q^88 - 18 * q^90 + 36 * q^91 + 18 * q^92 + 12 * q^93 - 32 * q^95 - 6 * q^96 - 28 * q^97

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