LMFDB - Embedded newform 277.2.e.c.117.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [277,2,Mod(117,277)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(277, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("277.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	277.e (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:	$2.21185613599$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.13
Character	$\chi$	$=$	277.117
Dual form			277.2.e.c.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.56173i q^{2} +(-1.64359 - 2.84678i) q^{3} -0.438996 q^{4} +(-2.62385 - 1.51488i) q^{5} +(4.44590 - 2.56684i) q^{6} +(-0.443045 + 0.767376i) q^{7} +2.43786i q^{8} +(-3.90277 + 6.75979i) q^{9} +O(q^{10})$	\(q+1.56173i q^{2} +(-1.64359 - 2.84678i) q^{3} -0.438996 q^{4} +(-2.62385 - 1.51488i) q^{5} +(4.44590 - 2.56684i) q^{6} +(-0.443045 + 0.767376i) q^{7} +2.43786i q^{8} +(-3.90277 + 6.75979i) q^{9} +(2.36583 - 4.09775i) q^{10} +(2.84494 + 1.64253i) q^{11} +(0.721528 + 1.24972i) q^{12} -6.41601 q^{13} +(-1.19843 - 0.691916i) q^{14} +9.95937i q^{15} -4.68527 q^{16} +(1.81283 + 1.04664i) q^{17} +(-10.5570 - 6.09506i) q^{18} -4.91680 q^{19} +(1.15186 + 0.665027i) q^{20} +2.91273 q^{21} +(-2.56518 + 4.44303i) q^{22} +(1.12008 - 1.94004i) q^{23} +(6.94006 - 4.00685i) q^{24} +(2.08974 + 3.61953i) q^{25} -10.0201i q^{26} +15.7966 q^{27} +(0.194495 - 0.336875i) q^{28} +(-0.870130 - 1.50711i) q^{29} -15.5538 q^{30} +(-8.33548 + 4.81249i) q^{31} -2.44140i q^{32} -10.7986i q^{33} +(-1.63456 + 2.83114i) q^{34} +(2.32497 - 1.34232i) q^{35} +(1.71330 - 2.96752i) q^{36} -8.51897i q^{37} -7.67870i q^{38} +(10.5453 + 18.2650i) q^{39} +(3.69308 - 6.39660i) q^{40} +3.53323 q^{41} +4.54890i q^{42} +(-0.455948 - 0.263242i) q^{43} +(-1.24892 - 0.721062i) q^{44} +(20.4806 - 11.8245i) q^{45} +(3.02982 + 1.74927i) q^{46} +(-3.41044 - 5.90705i) q^{47} +(7.70066 + 13.3379i) q^{48} +(3.10742 + 5.38221i) q^{49} +(-5.65272 + 3.26360i) q^{50} -6.88095i q^{51} +2.81660 q^{52} +(-8.62411 - 4.97913i) q^{53} +24.6701i q^{54} +(-4.97647 - 8.61950i) q^{55} +(-1.87076 - 1.08008i) q^{56} +(8.08119 + 13.9970i) q^{57} +(2.35369 - 1.35891i) q^{58} -2.37970 q^{59} -4.37212i q^{60} +0.0797142i q^{61} +(-7.51580 - 13.0177i) q^{62} +(-3.45820 - 5.98978i) q^{63} -5.55775 q^{64} +(16.8347 + 9.71949i) q^{65} +16.8644 q^{66} +(-4.32281 + 7.48733i) q^{67} +(-0.795823 - 0.459468i) q^{68} -7.36384 q^{69} +(2.09634 + 3.63097i) q^{70} +(-2.17790 + 3.77224i) q^{71} +(-16.4795 - 9.51442i) q^{72} -9.47645i q^{73} +13.3043 q^{74} +(6.86933 - 11.8980i) q^{75} +2.15845 q^{76} +(-2.52087 + 1.45543i) q^{77} +(-28.5249 + 16.4689i) q^{78} +(1.49464 + 2.58879i) q^{79} +(12.2935 + 7.09764i) q^{80} +(-14.2549 - 24.6902i) q^{81} +5.51795i q^{82} +(-1.23578 - 2.14043i) q^{83} -1.27868 q^{84} +(-3.17106 - 5.49244i) q^{85} +(0.411112 - 0.712067i) q^{86} +(-2.86027 + 4.95413i) q^{87} +(-4.00426 + 6.93558i) q^{88} +(5.22689 + 9.05324i) q^{89} +(18.4666 + 31.9851i) q^{90} +(2.84258 - 4.92349i) q^{91} +(-0.491712 + 0.851671i) q^{92} +(27.4002 + 15.8195i) q^{93} +(9.22520 - 5.32617i) q^{94} +(12.9010 + 7.44837i) q^{95} +(-6.95011 + 4.01265i) q^{96} +(-3.37839 + 1.95052i) q^{97} +(-8.40556 + 4.85295i) q^{98} +(-22.2063 + 12.8208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 3 q^{3} - 26 q^{4} - 12 q^{5} + 12 q^{6} - 39 q^{9}+O(q^{10}) $ 32 * q + 3 * q^3 - 26 * q^4 - 12 * q^5 + 12 * q^6 - 39 * q^9	$ 32 q + 3 q^{3} - 26 q^{4} - 12 q^{5} + 12 q^{6} - 39 q^{9} - 10 q^{10} - 3 q^{11} - 16 q^{12} + 10 q^{13} - 36 q^{14} + 50 q^{16} - 6 q^{17} - 39 q^{18} - 18 q^{19} - 33 q^{20} + 10 q^{21} + 31 q^{22} - 14 q^{23} + 27 q^{24} + 16 q^{25} + 60 q^{27} - 2 q^{28} + 6 q^{29} + 54 q^{30} + 12 q^{31} - 17 q^{34} - 3 q^{35} + 49 q^{36} + 16 q^{39} + 17 q^{40} - 24 q^{41} - 36 q^{43} + 24 q^{44} - 18 q^{45} - 63 q^{46} + 26 q^{47} + 49 q^{48} - 16 q^{49} - 45 q^{50} - 22 q^{52} - 33 q^{53} - 43 q^{55} + 72 q^{56} + 11 q^{57} - 27 q^{58} - 42 q^{59} + 19 q^{62} + 33 q^{63} - 80 q^{64} + 42 q^{65} + 8 q^{66} + 3 q^{67} - 12 q^{68} - 18 q^{69} + 35 q^{70} - 10 q^{71} + 72 q^{72} + 50 q^{74} + 49 q^{75} - 54 q^{76} + 87 q^{77} - 135 q^{78} - 32 q^{79} + 198 q^{80} - 32 q^{81} + 22 q^{83} - 176 q^{84} - 34 q^{85} + 6 q^{86} - 70 q^{87} - 103 q^{88} + 36 q^{89} - 31 q^{90} + 65 q^{91} + 29 q^{92} + 66 q^{93} + 39 q^{94} - 15 q^{95} - 12 q^{96} - 51 q^{97} + 15 q^{98} + 48 q^{99}+O(q^{100}) $ 32 * q + 3 * q^3 - 26 * q^4 - 12 * q^5 + 12 * q^6 - 39 * q^9 - 10 * q^10 - 3 * q^11 - 16 * q^12 + 10 * q^13 - 36 * q^14 + 50 * q^16 - 6 * q^17 - 39 * q^18 - 18 * q^19 - 33 * q^20 + 10 * q^21 + 31 * q^22 - 14 * q^23 + 27 * q^24 + 16 * q^25 + 60 * q^27 - 2 * q^28 + 6 * q^29 + 54 * q^30 + 12 * q^31 - 17 * q^34 - 3 * q^35 + 49 * q^36 + 16 * q^39 + 17 * q^40 - 24 * q^41 - 36 * q^43 + 24 * q^44 - 18 * q^45 - 63 * q^46 + 26 * q^47 + 49 * q^48 - 16 * q^49 - 45 * q^50 - 22 * q^52 - 33 * q^53 - 43 * q^55 + 72 * q^56 + 11 * q^57 - 27 * q^58 - 42 * q^59 + 19 * q^62 + 33 * q^63 - 80 * q^64 + 42 * q^65 + 8 * q^66 + 3 * q^67 - 12 * q^68 - 18 * q^69 + 35 * q^70 - 10 * q^71 + 72 * q^72 + 50 * q^74 + 49 * q^75 - 54 * q^76 + 87 * q^77 - 135 * q^78 - 32 * q^79 + 198 * q^80 - 32 * q^81 + 22 * q^83 - 176 * q^84 - 34 * q^85 + 6 * q^86 - 70 * q^87 - 103 * q^88 + 36 * q^89 - 31 * q^90 + 65 * q^91 + 29 * q^92 + 66 * q^93 + 39 * q^94 - 15 * q^95 - 12 * q^96 - 51 * q^97 + 15 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/277\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.56173i			1.10431i	0.833742	+	0.552154i	$0.186194\pi$
$2$			1.56173i			1.10431i	−0.833742	+	0.552154i	$0.813806\pi$
$3$	−1.64359	−	2.84678i	−0.948926	−	1.64359i	−0.747692	−	0.664046i	$-0.768838\pi$
$3$	−1.64359	−	2.84678i	−0.948926	−	1.64359i	−0.201234	−	0.979543i	$-0.564495\pi$
$4$	−0.438996			−0.219498
$5$	−2.62385	−	1.51488i	−1.17342	−	0.677476i	−0.218939	−	0.975739i	$-0.570260\pi$
$5$	−2.62385	−	1.51488i	−1.17342	−	0.677476i	−0.954484	+	0.298263i	$0.903593\pi$
$6$	4.44590	−	2.56684i	1.81503	−	1.04791i
$7$	−0.443045	+	0.767376i	−0.167455	+	0.290041i	−0.937524	−	0.347919i	$-0.886888\pi$
$7$	−0.443045	+	0.767376i	−0.167455	+	0.290041i	0.770069	+	0.637960i	$0.220222\pi$
$8$			2.43786i			0.861915i
$9$	−3.90277	+	6.75979i	−1.30092	+	2.25326i
$10$	2.36583	−	4.09775i	0.748143	−	1.29582i
$11$	2.84494	+	1.64253i	0.857782	+	0.495241i	0.863269	−	0.504744i	$-0.168413\pi$
$11$	2.84494	+	1.64253i	0.857782	+	0.495241i	−0.00548692	+	0.999985i	$0.501747\pi$
$12$	0.721528	+	1.24972i	0.208287	+	0.360764i
$13$	−6.41601			−1.77948			−0.889740	−	0.456468i	$-0.849114\pi$
$13$	−6.41601			−1.77948			−0.889740	+	0.456468i	$0.849114\pi$
$14$	−1.19843	−	0.691916i	−0.320295	−	0.184922i
$15$			9.95937i			2.57150i
$16$	−4.68527			−1.17132
$17$	1.81283	+	1.04664i	0.439675	+	0.253846i	0.703460	−	0.710735i	$-0.251638\pi$
$17$	1.81283	+	1.04664i	0.439675	+	0.253846i	−0.263785	+	0.964582i	$0.584971\pi$
$18$	−10.5570	−	6.09506i	−2.48830	−	1.43662i
$19$	−4.91680			−1.12799			−0.563995	−	0.825778i	$-0.690736\pi$
$19$	−4.91680			−1.12799			−0.563995	+	0.825778i	$0.690736\pi$
$20$	1.15186	+	0.665027i	0.257564	+	0.148704i
$21$	2.91273			0.635611
$22$	−2.56518	+	4.44303i	−0.546899	+	0.947256i
$23$	1.12008	−	1.94004i	0.233554	−	0.404527i	−0.725298	−	0.688435i	$-0.758298\pi$
$23$	1.12008	−	1.94004i	0.233554	−	0.404527i	0.958851	+	0.283908i	$0.0916312\pi$
$24$	6.94006	−	4.00685i	1.41663	−	0.817894i
$25$	2.08974	+	3.61953i	0.417947	+	0.723906i
$26$		−	10.0201i		−	1.96509i
$27$	15.7966			3.04007
$28$	0.194495	−	0.336875i	0.0367560	−	0.0636633i
$29$	−0.870130	−	1.50711i	−0.161579	−	0.279863i	0.773856	−	0.633361i	$-0.218325\pi$
$29$	−0.870130	−	1.50711i	−0.161579	−	0.279863i	−0.935435	+	0.353498i	$0.884992\pi$
$30$	−15.5538			−2.83973
$31$	−8.33548	+	4.81249i	−1.49710	+	0.864349i	−0.999994	−	0.00334409i	$-0.998936\pi$
$31$	−8.33548	+	4.81249i	−1.49710	+	0.864349i	−0.497101	+	0.867693i	$0.665602\pi$
$32$		−	2.44140i		−	0.431582i
$33$		−	10.7986i		−	1.87979i
$34$	−1.63456	+	2.83114i	−0.280325	+	0.485537i
$35$	2.32497	−	1.34232i	0.392991	−	0.226894i
$36$	1.71330	−	2.96752i	0.285550	−	0.494586i
$37$		−	8.51897i		−	1.40051i	−0.713893	−	0.700255i	$-0.753070\pi$
$37$		−	8.51897i		−	1.40051i	0.713893	−	0.700255i	$-0.246930\pi$
$38$		−	7.67870i		−	1.24565i
$39$	10.5453	+	18.2650i	1.68860	+	2.92473i
$40$	3.69308	−	6.39660i	0.583927	−	1.01139i
$41$	3.53323			0.551798			0.275899	−	0.961187i	$-0.411025\pi$
$41$	3.53323			0.551798			0.275899	+	0.961187i	$0.411025\pi$
$42$			4.54890i			0.701910i
$43$	−0.455948	−	0.263242i	−0.0695314	−	0.0401440i	0.464831	−	0.885399i	$-0.346115\pi$
$43$	−0.455948	−	0.263242i	−0.0695314	−	0.0401440i	−0.534363	+	0.845255i	$0.679448\pi$
$44$	−1.24892	−	0.721062i	−0.188281	−	0.108704i
$45$	20.4806	−	11.8245i	3.05306	−	1.76269i
$46$	3.02982	+	1.74927i	0.446723	+	0.257916i
$47$	−3.41044	−	5.90705i	−0.497463	−	0.861631i	0.502533	−	0.864558i	$-0.332402\pi$
$47$	−3.41044	−	5.90705i	−0.497463	−	0.861631i	−0.999996	+	0.00292690i	$0.999068\pi$
$48$	7.70066	+	13.3379i	1.11150	+	1.92517i
$49$	3.10742	+	5.38221i	0.443918	+	0.768888i
$50$	−5.65272	+	3.26360i	−0.799416	+	0.461543i
$51$		−	6.88095i		−	0.963526i
$52$	2.81660			0.390592
$53$	−8.62411	−	4.97913i	−1.18461	−	0.683936i	−0.227536	−	0.973770i	$-0.573067\pi$
$53$	−8.62411	−	4.97913i	−1.18461	−	0.683936i	−0.957077	+	0.289833i	$0.906400\pi$
$54$			24.6701i			3.35717i
$55$	−4.97647	−	8.61950i	−0.671027	−	1.16225i
$56$	−1.87076	−	1.08008i	−0.249991	−	0.144332i
$57$	8.08119	+	13.9970i	1.07038	+	1.85395i
$58$	2.35369	−	1.35891i	0.309055	−	0.178433i
$59$	−2.37970			−0.309810			−0.154905	−	0.987929i	$-0.549507\pi$
$59$	−2.37970			−0.309810			−0.154905	+	0.987929i	$0.549507\pi$
$60$		−	4.37212i		−	0.564438i
$61$			0.0797142i			0.0102064i	0.999987	+	0.00510318i	$0.00162440\pi$
$61$			0.0797142i			0.0102064i	−0.999987	+	0.00510318i	$0.998376\pi$
$62$	−7.51580	−	13.0177i	−0.954508	−	1.65326i
$63$	−3.45820	−	5.98978i	−0.435693	−	0.754642i
$64$	−5.55775			−0.694719
$65$	16.8347	+	9.71949i	2.08808	+	1.20555i
$66$	16.8644			2.07587
$67$	−4.32281	+	7.48733i	−0.528116	+	0.914723i	0.471347	+	0.881948i	$0.343768\pi$
$67$	−4.32281	+	7.48733i	−0.528116	+	0.914723i	−0.999463	+	0.0327754i	$0.989565\pi$
$68$	−0.795823	−	0.459468i	−0.0965077	−	0.0557187i
$69$	−7.36384			−0.886502
$70$	2.09634	+	3.63097i	0.250561	+	0.433984i
$71$	−2.17790	+	3.77224i	−0.258470	+	0.447683i	−0.965832	−	0.259168i	$-0.916552\pi$
$71$	−2.17790	+	3.77224i	−0.258470	+	0.447683i	0.707363	+	0.706851i	$0.249885\pi$
$72$	−16.4795	−	9.51442i	−1.94212	−	1.12129i
$73$		−	9.47645i		−	1.10913i	−0.832139	−	0.554567i	$-0.812884\pi$
$73$		−	9.47645i		−	1.10913i	0.832139	−	0.554567i	$-0.187116\pi$
$74$	13.3043			1.54660
$75$	6.86933	−	11.8980i	0.793202	−	1.37387i
$76$	2.15845			0.247591
$77$	−2.52087	+	1.45543i	−0.287280	+	0.165861i
$78$	−28.5249	+	16.4689i	−3.22981	+	1.86473i
$79$	1.49464	+	2.58879i	0.168160	+	0.291262i	0.937773	−	0.347249i	$-0.112884\pi$
$79$	1.49464	+	2.58879i	0.168160	+	0.291262i	−0.769613	+	0.638511i	$0.779551\pi$
$80$	12.2935	+	7.09764i	1.37445	+	0.793540i
$81$	−14.2549	−	24.6902i	−1.58388	−	2.74336i
$82$			5.51795i			0.609355i
$83$	−1.23578	−	2.14043i	−0.135644	−	0.234942i	0.790199	−	0.612850i	$-0.209977\pi$
$83$	−1.23578	−	2.14043i	−0.135644	−	0.234942i	−0.925843	+	0.377908i	$0.876644\pi$
$84$	−1.27868			−0.139515
$85$	−3.17106	−	5.49244i	−0.343950	−	0.595738i
$86$	0.411112	−	0.712067i	0.0443314	−	0.0767842i
$87$	−2.86027	+	4.95413i	−0.306653	+	0.531139i
$88$	−4.00426	+	6.93558i	−0.426856	+	0.739336i
$89$	5.22689	+	9.05324i	0.554049	+	0.959642i	0.997977	+	0.0635791i	$0.0202515\pi$
$89$	5.22689	+	9.05324i	0.554049	+	0.959642i	−0.443927	+	0.896063i	$0.646415\pi$
$90$	18.4666	+	31.9851i	1.94655	+	3.37153i
$91$	2.84258	−	4.92349i	0.297983	−	0.516122i
$92$	−0.491712	+	0.851671i	−0.0512645	+	0.0887928i
$93$	27.4002	+	15.8195i	2.84127	+	1.64041i
$94$	9.22520	−	5.32617i	0.951507	−	0.549353i
$95$	12.9010	+	7.44837i	1.32361	+	0.764186i
$96$	−6.95011	+	4.01265i	−0.709343	+	0.409539i
$97$	−3.37839	+	1.95052i	−0.343024	+	0.198045i	−0.661608	−	0.749850i	$-0.730126\pi$
$97$	−3.37839	+	1.95052i	−0.343024	+	0.198045i	0.318585	+	0.947894i	$0.396793\pi$
$98$	−8.40556	+	4.85295i	−0.849089	+	0.490222i
$99$	−22.2063	+	12.8208i	−2.23182	+	1.28854i
$100$	−0.917385	−	1.58896i	−0.0917385	−	0.158896i
$101$	16.0127	+	9.24491i	1.59332	+	0.919903i	0.992732	+	0.120343i	$0.0383995\pi$
$101$	16.0127	+	9.24491i	1.59332	+	0.919903i	0.600587	+	0.799560i	$0.294934\pi$
$102$	10.7462			1.06403
$103$	−0.993420	−	0.573551i	−0.0978845	−	0.0565137i	0.450259	−	0.892898i	$-0.351332\pi$
$103$	−0.993420	−	0.573551i	−0.0978845	−	0.0565137i	−0.548143	+	0.836385i	$0.684665\pi$
$104$		−	15.6414i		−	1.53376i
$105$	−7.64259	−	4.41245i	−0.745840	−	0.430611i
$106$	7.77605	−	13.4685i	0.755277	−	1.30818i
$107$	−0.280489	+	0.161941i	−0.0271159	+	0.0156554i	−0.513497	−	0.858092i	$-0.671650\pi$
$107$	−0.280489	+	0.161941i	−0.0271159	+	0.0156554i	0.486381	+	0.873747i	$0.338317\pi$
$108$	−6.93466			−0.667288
$109$		−	17.2418i		−	1.65147i	−0.564060	−	0.825734i	$-0.690761\pi$
$109$		−	17.2418i		−	1.65147i	0.564060	−	0.825734i	$-0.309239\pi$
$110$	13.4613	−	7.77190i	1.28349	−	0.741021i
$111$	−24.2516	+	14.0017i	−2.30186	+	1.32898i
$112$	2.07579	−	3.59537i	0.196143	−	0.339730i
$113$	−0.0612996			−0.00576658			−0.00288329	−	0.999996i	$-0.500918\pi$
$113$	−0.0612996			−0.00576658			−0.00288329	+	0.999996i	$0.500918\pi$
$114$	−21.8596	+	12.6206i	−2.04734	+	1.18203i
$115$	−5.87788	+	3.39359i	−0.548115	+	0.316454i
$116$	0.381983	+	0.661614i	0.0354662	+	0.0614293i
$117$	25.0402	−	43.3709i	2.31497	−	4.00964i
$118$		−	3.71644i		−	0.342126i
$119$	−1.60633	+	0.927413i	−0.147252	+	0.0850158i
$120$	−24.2796			−2.21641
$121$	−0.104207	−	0.180492i	−0.00947337	−	0.0164084i
$122$	−0.124492			−0.0112710
$123$	−5.80718	−	10.0583i	−0.523616	−	0.906929i
$124$	3.65924	−	2.11266i	0.328609	−	0.189723i
$125$			2.48600i			0.222355i
$126$	9.35441	−	5.40077i	0.833357	−	0.481139i
$127$	−4.39941	−	2.54000i	−0.390384	−	0.225388i	0.291942	−	0.956436i	$-0.405698\pi$
$127$	−4.39941	−	2.54000i	−0.390384	−	0.225388i	−0.682327	+	0.731047i	$0.739032\pi$
$128$		−	13.5625i		−	1.19877i
$129$			1.73064i			0.152375i
$130$	−15.1792	+	26.2912i	−1.33130	+	2.30589i
$131$	0.908495			0.0793755			0.0396878	−	0.999212i	$-0.487364\pi$
$131$	0.908495			0.0793755			0.0396878	+	0.999212i	$0.487364\pi$
$132$			4.74052i			0.412609i
$133$	2.17836	−	3.77303i	0.188888	−	0.327163i
$134$	−11.6932	−	6.75106i	−1.01014	−	0.583203i
$135$	−41.4481	−	23.9301i	−3.56728	−	2.05957i
$136$	−2.55156	+	4.41943i	−0.218794	+	0.378963i
$137$	−0.708711	+	0.409174i	−0.0605492	+	0.0349581i	−0.529969	−	0.848017i	$-0.677796\pi$
$137$	−0.708711	+	0.409174i	−0.0605492	+	0.0349581i	0.469420	+	0.882975i	$0.344463\pi$
$138$		−	11.5003i		−	0.978971i
$139$			8.18993i			0.694661i	0.937743	+	0.347330i	$0.112912\pi$
$139$			8.18993i			0.694661i	−0.937743	+	0.347330i	$0.887088\pi$
$140$	−1.02065	+	0.589273i	−0.0862607	+	0.0498027i
$141$	−11.2107	+	19.4175i	−0.944112	+	1.63525i
$142$	−5.89121	−	3.40129i	−0.494380	−	0.285430i
$143$	−18.2532	−	10.5385i	−1.52641	−	0.881271i
$144$	18.2855	−	31.6715i	1.52379	−	2.63929i
$145$			5.27258i			0.437864i
$146$	14.7996			1.22483
$147$	10.2146	−	17.6923i	0.842490	−	1.45924i
$148$			3.73979i			0.307409i
$149$		−	15.6208i		−	1.27971i	−0.768497	−	0.639853i	$-0.778995\pi$
$149$		−	15.6208i		−	1.27971i	0.768497	−	0.639853i	$-0.221005\pi$
$150$	18.5815	+	10.7280i	1.51717	+	0.875940i
$151$	2.01099	−	1.16105i	0.163652	−	0.0944845i	−0.415937	−	0.909393i	$-0.636546\pi$
$151$	2.01099	−	1.16105i	0.163652	−	0.0944845i	0.579589	+	0.814909i	$0.303213\pi$
$152$		−	11.9865i		−	0.972232i
$153$	−14.1501	+	8.16955i	−1.14397	+	0.660469i
$154$	−2.27298	−	3.93692i	−0.183162	−	0.317246i
$155$	29.1614			2.34230
$156$	−4.62933	−	8.01823i	−0.370643	−	0.641972i
$157$	14.6889			1.17230			0.586149	−	0.810203i	$-0.300643\pi$
$157$	14.6889			1.17230			0.586149	+	0.810203i	$0.300643\pi$
$158$	−4.04299	+	2.33422i	−0.321643	+	0.185700i
$159$			32.7346i			2.59602i
$160$	−3.69843	+	6.40586i	−0.292386	+	0.506428i
$161$	0.992495	+	1.71905i	0.0782196	+	0.135480i
$162$	38.5594	−	22.2623i	3.02951	−	1.74909i
$163$	−13.9902	+	8.07723i	−1.09579	+	0.632658i	−0.935113	−	0.354349i	$-0.884703\pi$
$163$	−13.9902	+	8.07723i	−1.09579	+	0.632658i	−0.160682	+	0.987006i	$0.551369\pi$
$164$	−1.55107			−0.121118
$165$	−16.3585	+	28.3338i	−1.27351	+	2.20579i
$166$	3.34276	−	1.92995i	0.259449	−	0.149793i
$167$	1.88116	−	1.08609i	0.145568	−	0.0840440i	−0.425447	−	0.904983i	$-0.639883\pi$
$167$	1.88116	−	1.08609i	0.145568	−	0.0840440i	0.571015	+	0.820939i	$0.306550\pi$
$168$			7.10085i			0.547843i
$169$	28.1651			2.16655
$170$	8.57769	−	4.95233i	0.657879	−	0.379827i
$171$	19.1891	−	33.2365i	1.46743	−	2.54166i
$172$	0.200159	+	0.115562i	0.0152620	+	0.00881152i
$173$			9.76077i			0.742098i	0.928613	+	0.371049i	$0.121002\pi$
$173$			9.76077i			0.742098i	−0.928613	+	0.371049i	$0.878998\pi$
$174$	−7.73701	−	4.46697i	−0.586541	−	0.338640i
$175$	−3.70339			−0.279950
$176$	−13.3293	−	7.69569i	−1.00474	−	0.580085i
$177$	3.91125	+	6.77448i	0.293987	+	0.509201i
$178$	−14.1387	+	8.16299i	−1.05974	+	0.611842i
$179$	−12.4627	+	7.19536i	−0.931509	+	0.537807i	−0.887288	−	0.461215i	$-0.847414\pi$
$179$	−12.4627	+	7.19536i	−0.931509	+	0.537807i	−0.0442203	+	0.999022i	$0.514080\pi$
$180$	−8.99088	+	5.19089i	−0.670141	+	0.386906i
$181$	−11.2936	+	6.52038i	−0.839449	+	0.484656i	−0.857077	−	0.515189i	$-0.827722\pi$
$181$	−11.2936	+	6.52038i	−0.839449	+	0.484656i	0.0176282	+	0.999845i	$0.494388\pi$
$182$	7.68915	+	4.43933i	0.569958	+	0.329065i
$183$	0.226929	−	0.131017i	0.0167751	−	0.00968508i
$184$	4.72956	+	2.73062i	0.348668	+	0.201304i
$185$	−12.9052	+	22.3525i	−0.948812	+	1.64339i
$186$	−24.7058	+	42.7916i	−1.81151	+	3.13764i
$187$	3.43826	+	5.95523i	0.251430	+	0.435490i
$188$	1.49717	+	2.59317i	0.109192	+	0.189126i
$189$	−6.99862	+	12.1220i	−0.509075	+	0.881744i
$190$	−11.6323	+	20.1478i	−0.843898	+	1.46167i
$191$	−7.99574	+	13.8490i	−0.578552	+	1.00208i	0.417094	+	0.908863i	$0.363049\pi$
$191$	−7.99574	+	13.8490i	−0.578552	+	1.00208i	−0.995646	+	0.0932176i	$0.970285\pi$
$192$	9.13466	+	15.8217i	0.659237	+	1.14183i
$193$	−14.3574			−1.03347			−0.516735	−	0.856145i	$-0.672853\pi$
$193$	−14.3574			−1.03347			−0.516735	+	0.856145i	$0.672853\pi$
$194$	−3.04618	−	5.27613i	−0.218703	−	0.378804i
$195$		−	63.8994i		−	4.57593i
$196$	−1.36414	−	2.36277i	−0.0974389	−	0.168769i
$197$	13.3391	+	7.70131i	0.950369	+	0.548696i	0.893195	−	0.449669i	$-0.148458\pi$
$197$	13.3391	+	7.70131i	0.950369	+	0.548696i	0.0571733	+	0.998364i	$0.481791\pi$
$198$	−20.0226	−	34.6802i	−1.42295	−	2.46461i
$199$	17.4186	−	10.0566i	1.23477	−	0.712896i	0.266751	−	0.963766i	$-0.414050\pi$
$199$	17.4186	−	10.0566i	1.23477	−	0.712896i	0.968021	+	0.250870i	$0.0807166\pi$
$200$	−8.82393	+	5.09450i	−0.623946	+	0.360235i
$201$	28.4197			2.00457
$202$	−14.4380	+	25.0074i	−1.01586	+	1.75952i
$203$	1.54203			0.108229
$204$			3.02071i			0.211492i
$205$	−9.27068	−	5.35243i	−0.647492	−	0.373830i
$206$	0.895731	−	1.55145i	0.0624085	−	0.108095i
$207$	8.74286	+	15.1431i	0.607671	+	1.05252i
$208$	30.0607			2.08434
$209$	−13.9880	−	8.07597i	−0.967570	−	0.558627i
$210$	6.89105	−	11.9356i	0.475527	−	0.823638i
$211$	21.1882			1.45865			0.729327	−	0.684165i	$-0.239833\pi$
$211$	21.1882			1.45865			0.729327	+	0.684165i	$0.239833\pi$
$212$	3.78595	+	2.18582i	0.260020	+	0.150123i
$213$	14.3183			0.981075
$214$	−0.252907	−	0.438048i	−0.0172884	−	0.0299444i
$215$	0.797561	+	1.38142i	0.0543932	+	0.0942118i
$216$			38.5101i			2.62028i
$217$		−	8.52859i		−	0.578959i
$218$	26.9270			1.82373
$219$	−26.9774	+	15.5754i	−1.82296	+	1.05249i
$220$	2.18465	+	3.78392i	0.147289	+	0.255112i
$221$	−11.6311	−	6.71522i	−0.782393	−	0.451715i
$222$	−21.8668	−	37.8745i	−1.46761	−	2.54197i
$223$			21.6031i			1.44665i	0.690508	+	0.723325i	$0.257387\pi$
$223$			21.6031i			1.44665i	−0.690508	+	0.723325i	$0.742613\pi$
$224$	1.87347	+	1.08165i	0.125176	+	0.0722706i
$225$	−32.6230			−2.17487
$226$		−	0.0957334i		−	0.00636809i
$227$	−17.1311	+	9.89065i	−1.13703	+	0.656465i	−0.945694	−	0.325059i	$-0.894616\pi$
$227$	−17.1311	+	9.89065i	−1.13703	+	0.656465i	−0.191338	+	0.981524i	$0.561283\pi$
$228$	−3.54761	−	6.14464i	−0.234946	−	0.406938i
$229$	−10.5772	−	18.3202i	−0.698958	−	1.21063i	−0.968828	−	0.247735i	$-0.920314\pi$
$229$	−10.5772	−	18.3202i	−0.698958	−	1.21063i	0.269870	−	0.962897i	$-0.413019\pi$
$230$	−5.29987	−	9.17965i	−0.349463	−	0.605288i
$231$	8.28656	+	4.78425i	0.545215	+	0.314780i
$232$	3.67413	−	2.12126i	0.241218	−	0.139267i
$233$	−5.25142	−	3.03191i	−0.344032	−	0.198627i	0.318022	−	0.948083i	$-0.396981\pi$
$233$	−5.25142	−	3.03191i	−0.344032	−	0.198627i	−0.662053	+	0.749457i	$0.730315\pi$
$234$	67.7335	+	39.1060i	4.42788	+	2.55644i
$235$			20.6656i			1.34808i
$236$	1.04468			0.0680027
$237$	4.91314	−	8.50981i	0.319143	−	0.552771i
$238$	−1.44837	−	2.50865i	−0.0938837	−	0.162611i
$239$			20.0414i			1.29637i	0.761483	+	0.648185i	$0.224472\pi$
$239$			20.0414i			1.29637i	−0.761483	+	0.648185i	$0.775528\pi$
$240$		−	46.6624i		−	3.01204i
$241$	−2.87846	+	4.98563i	−0.185418	+	0.321153i	−0.943717	−	0.330754i	$-0.892697\pi$
$241$	−2.87846	+	4.98563i	−0.185418	+	0.321153i	0.758300	+	0.651906i	$0.226030\pi$
$242$	0.281880	−	0.162743i	0.0181199	−	0.0104615i
$243$	−23.1634	+	40.1202i	−1.48593	+	2.57371i
$244$		−	0.0349942i		−	0.00224027i
$245$		−	18.8295i		−	1.20297i
$246$	15.7084	−	9.06923i	1.00153	−	0.578233i
$247$	31.5462			2.00724
$248$	−11.7322	−	20.3208i	−0.744995	−	1.29037i
$249$	−4.06221	+	7.03596i	−0.257432	+	0.445886i
$250$	−3.88246			−0.245548
$251$			9.82009i			0.619838i	0.950763	+	0.309919i	$0.100302\pi$
$251$			9.82009i			0.619838i	−0.950763	+	0.309919i	$0.899698\pi$
$252$	1.51814	+	2.62949i	0.0956335	+	0.165642i
$253$	6.37315	−	3.67954i	0.400677	−	0.231331i
$254$	3.96679	−	6.87068i	0.248898	−	0.431105i
$255$	−10.4238	+	18.0546i	−0.652766	+	1.13062i
$256$	10.0654			0.629089
$257$	−6.96822	−	4.02311i	−0.434666	−	0.250954i	0.266667	−	0.963789i	$-0.414078\pi$
$257$	−6.96822	−	4.02311i	−0.434666	−	0.250954i	−0.701332	+	0.712834i	$0.747411\pi$
$258$	−2.70280			−0.168269
$259$	6.53726	+	3.77429i	0.406205	+	0.234523i
$260$	−7.39034	−	4.26681i	−0.458329	−	0.264617i
$261$	13.5837			0.840807
$262$			1.41882i			0.0876551i
$263$	3.28842	+	1.89857i	0.202773	+	0.117071i	0.597948	−	0.801535i	$-0.295983\pi$
$263$	3.28842	+	1.89857i	0.202773	+	0.117071i	−0.395175	+	0.918606i	$0.629316\pi$
$264$	26.3254			1.62022
$265$	15.0856	+	26.1290i	0.926701	+	1.60509i
$266$	5.89245	+	3.40201i	0.361289	+	0.208591i
$267$	17.1817	−	29.7596i	1.05150	−	1.82126i
$268$	1.89770	−	3.28691i	0.115920	−	0.200780i
$269$		−	16.7522i		−	1.02140i	−0.859759	−	0.510700i	$-0.829386\pi$
$269$		−	16.7522i		−	1.02140i	0.859759	−	0.510700i	$-0.170614\pi$
$270$	37.3723	−	64.7307i	2.27440	−	3.93938i
$271$	−7.90452	+	4.56368i	−0.480165	+	0.277224i	−0.720485	−	0.693470i	$-0.756081\pi$
$271$	−7.90452	+	4.56368i	−0.480165	+	0.277224i	0.240320	+	0.970694i	$0.422748\pi$
$272$	−8.49359	−	4.90377i	−0.514999	−	0.297335i
$273$	−18.6881			−1.13106
$274$	−0.639019	−	1.10681i	−0.0386046	−	0.0668651i
$275$			13.7298i			0.827938i
$276$	3.23269			0.194585
$277$	−1.96619	+	16.5268i	−0.118137	+	0.992997i
$277$	−1.96619	+	16.5268i	−0.118137	+	0.992997i
$278$	−12.7904			−0.767120
$279$		−	75.1281i		−	4.49780i
$280$	3.27240	+	5.66796i	0.195563	+	0.338725i
$281$	−7.50429			−0.447668			−0.223834	−	0.974627i	$-0.571857\pi$
$281$	−7.50429			−0.447668			−0.223834	+	0.974627i	$0.571857\pi$
$282$	−30.3249	−	17.5081i	−1.80582	−	1.04259i
$283$	1.95489	−	1.12866i	0.116206	−	0.0670917i	−0.440770	−	0.897620i	$-0.645295\pi$
$283$	1.95489	−	1.12866i	0.116206	−	0.0670917i	0.556977	+	0.830528i	$0.311961\pi$
$284$	0.956090	−	1.65600i	0.0567335	−	0.0982653i
$285$		−	48.9682i		−	2.90063i
$286$	16.4582	−	28.5065i	0.973195	−	1.68562i
$287$	−1.56538	+	2.71132i	−0.0924014	+	0.160044i
$288$	16.5033	+	9.52820i	0.972468	+	0.561455i
$289$	−6.30911	−	10.9277i	−0.371124	−	0.642806i
$290$	−8.23433			−0.483537
$291$	11.1054	+	6.41169i	0.651009	+	0.375860i
$292$			4.16012i			0.243453i
$293$	8.36484			0.488679			0.244339	−	0.969690i	$-0.421429\pi$
$293$	8.36484			0.488679			0.244339	+	0.969690i	$0.421429\pi$
$294$	27.6306	+	15.9525i	1.61145	+	0.930369i
$295$	6.24398	+	3.60496i	0.363538	+	0.209889i
$296$	20.7681			1.20712
$297$	44.9405	+	25.9464i	2.60771	+	1.50556i
$298$	24.3954			1.41319
$299$	−7.18647	+	12.4473i	−0.415604	+	0.719848i
$300$	−3.01561	+	5.22319i	−0.174106	+	0.301561i
$301$	0.404011	−	0.233256i	0.0232868	−	0.0134446i
$302$	1.81324	+	3.14062i	0.104340	+	0.180722i
$303$		−	60.7793i		−	3.49168i
$304$	23.0365			1.32124
$305$	0.120758	−	0.209158i	0.00691456	−	0.0119764i
$306$	−12.7586	−	22.0986i	−0.729362	−	1.26329i
$307$	−5.24160			−0.299154			−0.149577	−	0.988750i	$-0.547791\pi$
$307$	−5.24160			−0.299154			−0.149577	+	0.988750i	$0.547791\pi$
$308$	1.10665	−	0.638926i	0.0630573	−	0.0364062i
$309$			3.77073i			0.214509i
$310$			45.5422i			2.58662i
$311$	10.9905	−	19.0361i	0.623213	−	1.07944i	−0.365671	−	0.930744i	$-0.619160\pi$
$311$	10.9905	−	19.0361i	0.623213	−	1.07944i	0.988884	−	0.148692i	$-0.0475063\pi$
$312$	−44.5275	+	25.7080i	−2.52087	+	1.45543i
$313$	−0.780198	+	1.35134i	−0.0440994	+	0.0763824i	−0.887233	−	0.461322i	$-0.847375\pi$
$313$	−0.780198	+	1.35134i	−0.0440994	+	0.0763824i	0.843133	+	0.537705i	$0.180708\pi$
$314$			22.9400i			1.29458i
$315$			20.9551i			1.18068i
$316$	−0.656139	−	1.13647i	−0.0369107	−	0.0639313i
$317$	−1.25508	+	2.17387i	−0.0704925	+	0.122097i	−0.899117	−	0.437708i	$-0.855790\pi$
$317$	−1.25508	+	2.17387i	−0.0704925	+	0.122097i	0.828625	+	0.559804i	$0.189124\pi$
$318$	−51.1225			−2.86681
$319$		−	5.71685i		−	0.320082i
$320$	14.5827	+	8.41934i	0.815199	+	0.470655i
$321$	0.922018	+	0.532328i	0.0514620	+	0.0297116i
$322$	−2.68469	+	1.55001i	−0.149612	+	0.0863786i
$323$	−8.91330	−	5.14609i	−0.495949	−	0.286336i
$324$	6.25783	+	10.8389i	0.347657	+	0.602160i
$325$	−13.4078	−	23.2229i	−0.743729	−	1.28818i
$326$	−12.6144	−	21.8489i	−0.698649	−	1.21010i
$327$	−49.0837	+	28.3385i	−2.71433	+	1.56712i
$328$			8.61354i			0.475603i
$329$	6.04390			0.333211
$330$	−44.2497	−	25.5476i	−2.43587	−	1.40635i
$331$			17.8090i			0.978873i	0.872039	+	0.489437i	$0.162798\pi$
$331$			17.8090i			0.978873i	−0.872039	+	0.489437i	$0.837202\pi$
$332$	0.542500	+	0.939638i	0.0297736	+	0.0515693i
$333$	57.5865	+	33.2476i	3.15572	+	1.82196i
$334$	1.69617	+	2.93786i	0.0928105	+	0.160753i
$335$	22.6849	−	13.0971i	1.23941	−	0.715571i
$336$	−13.6470			−0.744502
$337$		−	20.0263i		−	1.09090i	−0.838142	−	0.545452i	$-0.816358\pi$
$337$		−	20.0263i		−	1.09090i	0.838142	−	0.545452i	$-0.183642\pi$
$338$			43.9863i			2.39254i
$339$	0.100751	+	0.174506i	0.00547206	+	0.00947789i
$340$	1.39208	+	2.41115i	0.0754962	+	0.130763i
$341$	−31.6186			−1.71224
$342$	51.9064	+	29.9682i	2.80678	+	1.62049i
$343$	−11.7095			−0.632256
$344$	0.641748	−	1.11154i	0.0346007	−	0.0599302i
$345$	19.3216	+	11.1553i	1.04024	+	0.600583i
$346$	−15.2437			−0.819505
$347$	5.54712	+	9.60790i	0.297785	+	0.515779i	0.975629	−	0.219427i	$-0.0704187\pi$
$347$	5.54712	+	9.60790i	0.297785	+	0.515779i	−0.677844	+	0.735206i	$0.737085\pi$
$348$	1.25565	−	2.17484i	0.0673097	−	0.116584i
$349$	−24.2982	−	14.0286i	−1.30065	−	0.750933i	−0.320138	−	0.947371i	$-0.603729\pi$
$349$	−24.2982	−	14.0286i	−1.30065	−	0.750933i	−0.980516	+	0.196438i	$0.937062\pi$
$350$		−	5.78369i		−	0.309151i
$351$	−101.351			−5.40974
$352$	4.01006	−	6.94563i	0.213737	−	0.370203i
$353$	−3.49953			−0.186261			−0.0931306	−	0.995654i	$-0.529687\pi$
$353$	−3.49953			−0.186261			−0.0931306	+	0.995654i	$0.529687\pi$
$354$	−10.5799	+	6.10830i	−0.562315	+	0.324653i
$355$	11.4290	−	6.59854i	0.606588	−	0.350214i
$356$	−2.29458	−	3.97433i	−0.121613	−	0.210639i
$357$	5.28028	+	3.04857i	0.279462	+	0.161347i
$358$	−11.2372	−	19.4634i	−0.593905	−	1.02867i
$359$		−	27.8616i		−	1.47048i	−0.677808	−	0.735239i	$-0.737070\pi$
$359$		−	27.8616i		−	1.47048i	0.677808	−	0.735239i	$-0.262930\pi$
$360$	28.8265	+	49.9289i	1.51929	+	2.63148i
$361$	5.17489			0.272362
$362$	−10.1831	−	17.6376i	−0.535210	−	0.927010i
$363$	−0.342547	+	0.593309i	−0.0179791	+	0.0311407i
$364$	−1.24788	+	2.16139i	−0.0654066	+	0.113288i
$365$	−14.3557	+	24.8648i	−0.751412	+	1.30148i
$366$	0.204613	+	0.354401i	0.0106953	+	0.0185248i
$367$	−7.69950	−	13.3359i	−0.401911	−	0.696129i	0.592046	−	0.805904i	$-0.298320\pi$
$367$	−7.69950	−	13.3359i	−0.401911	−	0.696129i	−0.993956	+	0.109775i	$0.964987\pi$
$368$	−5.24790	+	9.08964i	−0.273566	+	0.473830i
$369$	−13.7894	+	23.8839i	−0.717846	+	1.24335i
$370$	−34.9086	−	20.1545i	−1.81481	−	1.04778i
$371$	7.64173	−	4.41196i	0.396739	−	0.229057i
$372$	−12.0286	−	6.94469i	−0.623652	−	0.360066i
$373$	12.5148	−	7.22540i	0.647990	−	0.374117i	−0.139696	−	0.990194i	$-0.544612\pi$
$373$	12.5148	−	7.22540i	0.647990	−	0.374117i	0.787686	+	0.616077i	$0.211279\pi$
$374$	−9.30046	+	5.36962i	−0.480915	+	0.277657i
$375$	7.07710	−	4.08597i	0.365460	−	0.210998i
$376$	14.4006	−	8.31418i	0.742653	−	0.428771i
$377$	5.58276	+	9.66962i	0.287527	+	0.498011i
$378$	−18.9312	−	10.9299i	−0.973717	−	0.562176i
$379$	−6.47919			−0.332814			−0.166407	−	0.986057i	$-0.553216\pi$
$379$	−6.47919			−0.332814			−0.166407	+	0.986057i	$0.553216\pi$
$380$	−5.66346	−	3.26980i	−0.290529	−	0.167737i
$381$			16.6989i			0.855508i
$382$	−21.6284	−	12.4872i	−1.10661	−	0.638900i
$383$	4.12838	−	7.15056i	0.210950	−	0.365377i	−0.741062	−	0.671437i	$-0.765677\pi$
$383$	4.12838	−	7.15056i	0.210950	−	0.365377i	0.952012	+	0.306060i	$0.0990108\pi$
$384$	−38.6094	+	22.2912i	−1.97028	+	1.13754i
$385$	8.81920			0.449468
$386$		−	22.4224i		−	1.14127i
$387$	3.55892	−	2.05474i	0.180910	−	0.104448i
$388$	1.48310	−	0.856268i	0.0752929	−	0.0434704i
$389$	2.40963	−	4.17359i	0.122173	−	0.211610i	−0.798451	−	0.602059i	$-0.794347\pi$
$389$	2.40963	−	4.17359i	0.122173	−	0.211610i	0.920624	+	0.390450i	$0.127680\pi$
$390$	99.7935			5.05324
$391$	4.06104	−	2.34464i	0.205376	−	0.118574i
$392$	−13.1211	+	7.57548i	−0.662716	+	0.382619i
$393$	−1.49319	−	2.58628i	−0.0753215	−	0.130461i
$394$	−12.0274	+	20.8320i	−0.605929	+	1.04950i
$395$		−	9.05680i		−	0.455697i
$396$	9.74846	−	5.62828i	0.489879	−	0.282832i
$397$	−25.7348			−1.29159			−0.645796	−	0.763510i	$-0.723474\pi$
$397$	−25.7348			−1.29159			−0.645796	+	0.763510i	$0.723474\pi$
$398$	15.7057	+	27.2031i	0.787257	+	1.36357i
$399$	−14.3213			−0.716963
$400$	−9.79099	−	16.9585i	−0.489549	−	0.847924i
$401$	−1.99356	+	1.15098i	−0.0995536	+	0.0574773i	−0.548950	−	0.835855i	$-0.684972\pi$
$401$	−1.99356	+	1.15098i	−0.0995536	+	0.0574773i	0.449397	+	0.893332i	$0.351639\pi$
$402$			44.3839i			2.21367i
$403$	53.4805	−	30.8770i	2.66405	−	1.53809i
$404$	−7.02948	−	4.05847i	−0.349730	−	0.201917i
$405$			86.3779i			4.29215i
$406$			2.40823i			0.119518i
$407$	13.9926	−	24.2360i	0.693590	−	1.20133i
$408$	16.7748			0.830478
$409$		−	0.816890i		−	0.0403926i	−0.999796	−	0.0201963i	$-0.993571\pi$
$409$		−	0.816890i		−	0.0403926i	0.999796	−	0.0201963i	$-0.00642912\pi$
$410$	8.35904	−	14.4783i	0.412823	−	0.715031i
$411$	2.32966	+	1.34503i	0.114914	+	0.0663454i
$412$	0.436107	+	0.251786i	0.0214854	+	0.0124046i
$413$	1.05431	−	1.82612i	0.0518793	−	0.0898577i
$414$	−23.6494	+	13.6540i	−1.16230	+	0.671056i
$415$			7.48822i			0.367582i
$416$			15.6640i			0.767991i
$417$	23.3149	−	13.4609i	1.14174	−	0.659182i
$418$	12.6125	−	21.8454i	0.616896	−	1.06850i
$419$	−5.43942	−	3.14045i	−0.265733	−	0.153421i	0.361214	−	0.932483i	$-0.382362\pi$
$419$	−5.43942	−	3.14045i	−0.265733	−	0.153421i	−0.626947	+	0.779062i	$0.715696\pi$
$420$	3.35506	+	1.93705i	0.163710	+	0.0945181i
$421$	17.3014	−	29.9669i	0.843219	−	1.46050i	−0.0439403	−	0.999034i	$-0.513991\pi$
$421$	17.3014	−	29.9669i	0.843219	−	1.46050i	0.887159	−	0.461464i	$-0.152676\pi$
$422$			33.0902i			1.61080i
$423$	53.2405			2.58864
$424$	12.1385	−	21.0244i	0.589495	−	1.02104i
$425$			8.74877i			0.424378i
$426$			22.3613i			1.08341i
$427$	−0.0611708	−	0.0353170i	−0.00296026	−	0.00170911i
$428$	0.123134	−	0.0710912i	0.00595189	−	0.00343632i
$429$			69.2836i			3.34504i
$430$	−2.15740	+	1.24557i	−0.104039	+	0.0600669i
$431$	−2.82995	−	4.90161i	−0.136314	−	0.236102i	0.789785	−	0.613384i	$-0.210192\pi$
$431$	−2.82995	−	4.90161i	−0.136314	−	0.236102i	−0.926099	+	0.377282i	$0.876859\pi$
$432$	−74.0116			−3.56089
$433$	17.0149	+	29.4706i	0.817682	+	1.41627i	0.907386	+	0.420299i	$0.138075\pi$
$433$	17.0149	+	29.4706i	0.817682	+	1.41627i	−0.0897037	+	0.995968i	$0.528592\pi$
$434$	13.3193			0.639349
$435$	15.0099	−	8.66595i	0.719668	−	0.415500i
$436$			7.56908i			0.362493i
$437$	−5.50723	+	9.53880i	−0.263446	+	0.456303i
$438$	−24.3245	−	42.1313i	−1.16227	−	2.01311i
$439$	−27.2013	+	15.7047i	−1.29825	+	0.749543i	−0.980101	−	0.198500i	$-0.936393\pi$
$439$	−27.2013	+	15.7047i	−1.29825	+	0.749543i	−0.318145	+	0.948042i	$0.603060\pi$
$440$	21.0132	−	12.1320i	1.00176	−	0.578369i
$441$	−48.5102			−2.31001
$442$	10.4873	−	18.1646i	0.498832	−	0.864003i
$443$	26.9373	−	15.5523i	1.27983	−	0.738911i	0.303014	−	0.952986i	$-0.402007\pi$
$443$	26.9373	−	15.5523i	1.27983	−	0.738911i	0.976817	+	0.214075i	$0.0686737\pi$
$444$	10.6464	−	6.14668i	0.505254	−	0.291708i
$445$		−	31.6725i		−	1.50142i
$446$	−33.7382			−1.59755
$447$	−44.4690	+	25.6742i	−2.10331	+	1.21435i
$448$	2.46233	−	4.26489i	0.116334	−	0.201497i
$449$	21.1043	+	12.1846i	0.995976	+	0.575027i	0.907055	−	0.421012i	$-0.138325\pi$
$449$	21.1043	+	12.1846i	0.995976	+	0.575027i	0.0889204	+	0.996039i	$0.471658\pi$
$450$		−	50.9483i		−	2.40173i
$451$	10.0518	+	5.80343i	0.473322	+	0.273273i
$452$	0.0269103			0.00126575
$453$	−6.61048	−	3.81656i	−0.310587	−	0.179318i
$454$	−15.4465	−	26.7541i	−0.724940	−	1.25563i
$455$	−14.9170	+	8.61234i	−0.699320	+	0.403753i
$456$	−34.1229	+	19.7009i	−1.59795	+	0.922577i
$457$	−29.3319	+	16.9348i	−1.37209	+	0.792175i	−0.991191	−	0.132442i	$-0.957718\pi$
$457$	−29.3319	+	16.9348i	−1.37209	+	0.792175i	−0.380897	+	0.924617i	$0.624385\pi$
$458$	28.6111	−	16.5187i	1.33691	−	0.771866i
$459$	28.6366	+	16.5333i	1.33664	+	0.771710i
$460$	2.58036	−	1.48977i	0.120310	−	0.0694610i
$461$	16.2640	+	9.39000i	0.757488	+	0.437336i	0.828393	−	0.560147i	$-0.189255\pi$
$461$	16.2640	+	9.39000i	0.757488	+	0.437336i	−0.0709053	+	0.997483i	$0.522589\pi$
$462$	−7.47169	+	12.9413i	−0.347615	+	0.602086i
$463$	4.72141	−	8.17772i	0.219422	−	0.380051i	−0.735209	−	0.677840i	$-0.762916\pi$
$463$	4.72141	−	8.17772i	0.219422	−	0.380051i	0.954632	+	0.297790i	$0.0962494\pi$
$464$	4.07680	+	7.06122i	0.189261	+	0.327809i
$465$	−47.9294	−	83.0161i	−2.22267	−	3.84978i
$466$	4.73501	−	8.20129i	0.219345	−	0.379917i
$467$	12.6471	−	21.9054i	0.585239	−	1.01366i	−0.409607	−	0.912262i	$-0.634334\pi$
$467$	12.6471	−	21.9054i	0.585239	−	1.01366i	0.994846	−	0.101401i	$-0.0323326\pi$
$468$	−10.9925	+	19.0396i	−0.508130	+	0.880107i
$469$	−3.83040	−	6.63445i	−0.176871	−	0.306350i
$470$	−32.2741			−1.48869
$471$	−24.1424	−	41.8159i	−1.11243	−	1.92678i
$472$		−	5.80138i		−	0.267030i
$473$	−0.864764	−	1.49781i	−0.0397619	−	0.0688696i
$474$	13.2900	+	7.67299i	0.610430	+	0.352432i
$475$	−10.2748	−	17.7965i	−0.471441	−	0.816559i
$476$	0.705170	−	0.407130i	0.0323214	−	0.0186608i
$477$	67.3158	−	38.8648i	3.08218	−	1.77950i
$478$	−31.2992			−1.43159
$479$	−7.74963	+	13.4228i	−0.354090	+	0.613301i	−0.986962	−	0.160955i	$-0.948543\pi$
$479$	−7.74963	+	13.4228i	−0.354090	+	0.613301i	0.632872	+	0.774256i	$0.281876\pi$
$480$	24.3148			1.10981
$481$			54.6578i			2.49218i
$482$	−7.78620	−	4.49537i	−0.354652	−	0.204758i
$483$	3.26251	−	5.65083i	0.148449	−	0.257122i
$484$	0.0457465	+	0.0792352i	0.00207938	+	0.00360160i
$485$	11.8192			0.536682
$486$	−62.6568	−	36.1749i	−2.84217	−	1.64093i
$487$	−17.6568	+	30.5825i	−0.800106	+	1.38582i	0.119440	+	0.992841i	$0.461890\pi$
$487$	−17.6568	+	30.5825i	−0.800106	+	1.38582i	−0.919546	+	0.392983i	$0.871443\pi$
$488$	−0.194332			−0.00879701
$489$	45.9882	+	26.5513i	2.07966	+	1.20069i
$490$	29.4066			1.32845
$491$	4.97358	+	8.61450i	0.224455	+	0.388767i	0.956156	−	0.292859i	$-0.0946066\pi$
$491$	4.97358	+	8.61450i	0.224455	+	0.388767i	−0.731701	+	0.681626i	$0.761273\pi$
$492$	2.54932	+	4.41556i	0.114932	+	0.199069i
$493$		−	3.64284i		−	0.164065i
$494$			49.2666i			2.21661i
$495$	77.6881			3.49182
$496$	39.0540	−	22.5478i	1.75358	−	1.01243i
$497$	−1.92982	−	3.34254i	−0.0865642	−	0.149934i
$498$	−10.9883	−	6.34408i	−0.492396	−	0.284285i
$499$	8.44480	+	14.6268i	0.378041	+	0.654786i	0.990777	−	0.135501i	$-0.0432645\pi$
$499$	8.44480	+	14.6268i	0.378041	+	0.654786i	−0.612736	+	0.790288i	$0.709931\pi$
$500$		−	1.09134i		−	0.0488064i
$501$	−6.18370	−	3.57016i	−0.276268	−	0.159503i
$502$	−15.3363			−0.684493
$503$		−	31.7108i		−	1.41391i	−0.707256	−	0.706957i	$-0.750067\pi$
$503$		−	31.7108i		−	1.41391i	0.707256	−	0.706957i	$-0.249933\pi$
$504$	14.6023	−	8.43063i	0.650437	−	0.375530i
$505$	−28.0099	−	48.5146i	−1.24642	−	2.15887i
$506$	5.74644	+	9.95313i	0.255461	+	0.442471i
$507$	−46.2919	−	80.1799i	−2.05589	−	3.56091i
$508$	1.93132	+	1.11505i	0.0856885	+	0.0494723i
$509$	−21.9154	+	12.6528i	−0.971382	+	0.560827i	−0.899657	−	0.436597i	$-0.856184\pi$
$509$	−21.9154	+	12.6528i	−0.971382	+	0.560827i	−0.0717244	+	0.997424i	$0.522850\pi$
$510$	−28.1964	−	16.2792i	−1.24856	−	0.720855i
$511$	7.27200	+	4.19849i	0.321695	+	0.185730i
$512$		−	11.4055i		−	0.504058i
$513$	−77.6689			−3.42917
$514$	6.28300	−	10.8825i	0.277131	−	0.480005i
$515$	1.73772	+	3.00983i	0.0765733	+	0.132629i
$516$		−	0.759745i		−	0.0334459i
$517$		−	22.4069i		−	0.985456i
$518$	−5.89441	+	10.2094i	−0.258986	+	0.448576i
$519$	27.7868	−	16.0427i	1.21970	−	0.704196i
$520$	−23.6948	+	41.0406i	−1.03909	+	1.79975i
$521$		−	3.59139i		−	0.157342i	−0.996901	−	0.0786709i	$-0.974932\pi$
$521$		−	3.59139i		−	0.157342i	0.996901	−	0.0786709i	$-0.0250676\pi$
$522$			21.2140i			0.928511i
$523$	3.34735	−	1.93259i	0.146369	−	0.0845063i	−0.425027	−	0.905181i	$-0.639735\pi$
$523$	3.34735	−	1.93259i	0.146369	−	0.0845063i	0.571396	+	0.820674i	$0.306402\pi$
$524$	−0.398825			−0.0174228
$525$	6.08685	+	10.5427i	0.265652	+	0.460122i
$526$	−2.96505	+	5.13562i	−0.129282	+	0.223924i
$527$	−20.1477			−0.877647
$528$			50.5942i			2.20183i
$529$	8.99082	+	15.5726i	0.390905	+	0.677068i
$530$	−40.8064	+	23.5596i	−1.77252	+	1.02336i
$531$	9.28741	−	16.0863i	0.403039	−	0.698084i
$532$	−0.956291	+	1.65634i	−0.0414605	+	0.0718116i
$533$	−22.6692			−0.981913
$534$	46.4764	+	26.8332i	2.01123	+	1.16119i
$535$	0.981284			0.0424246
$536$	−18.2531	−	10.5384i	−0.788414	−	0.455191i
$537$	40.9672	+	23.6524i	1.76787	+	1.02068i
$538$	26.1624			1.12794
$539$			20.4161i			0.879384i
$540$	18.1955	+	10.5052i	0.783011	+	0.452071i
$541$	12.6853			0.545384			0.272692	−	0.962101i	$-0.412086\pi$
$541$	12.6853			0.545384			0.272692	+	0.962101i	$0.412086\pi$
$542$	−7.12722	−	12.3447i	−0.306140	−	0.530251i
$543$	37.1242	+	21.4336i	1.59315	+	0.919805i
$544$	2.55525	−	4.42583i	0.109556	−	0.189756i
$545$	−26.1193	+	45.2400i	−1.11883	+	1.93787i
$546$		−	29.1858i		−	1.24904i
$547$	−15.0060	+	25.9911i	−0.641610	+	1.11130i	0.343463	+	0.939166i	$0.388400\pi$
$547$	−15.0060	+	25.9911i	−0.641610	+	1.11130i	−0.985073	+	0.172135i	$0.944933\pi$
$548$	0.311121	−	0.179626i	0.0132904	−	0.00767323i
$549$	−0.538851	−	0.311106i	−0.0229976	−	0.0132777i
$550$	−21.4422			−0.914299
$551$	4.27825	+	7.41015i	0.182260	+	0.315683i
$552$		−	17.9520i		−	0.764089i
$553$	−2.64877			−0.112637
$554$	−25.8103	−	3.07066i	−1.09658	−	0.130460i
$555$	84.8436			3.60141
$556$		−	3.59534i		−	0.152476i
$557$	−3.45318	−	5.98109i	−0.146316	−	0.253427i	0.783547	−	0.621332i	$-0.213408\pi$
$557$	−3.45318	−	5.98109i	−0.146316	−	0.253427i	−0.929863	+	0.367905i	$0.880075\pi$
$558$	117.330			4.96696
$559$	2.92537	+	1.68896i	0.123730	+	0.0714354i
$560$	−10.8931	+	6.28914i	−0.460318	+	0.265765i
$561$	11.3022	−	19.5759i	0.477177	−	0.826496i
$562$		−	11.7197i		−	0.494364i
$563$	−11.7095	+	20.2815i	−0.493498	+	0.854763i	−0.999972	−	0.00749185i	$-0.997615\pi$
$563$	−11.7095	+	20.2815i	−0.493498	+	0.854763i	0.506474	+	0.862255i	$0.330949\pi$
$564$	4.92145	−	8.52420i	0.207230	−	0.358934i
$565$	0.160841	+	0.0928617i	0.00676664	+	0.00390672i
$566$	1.76266	+	3.05301i	0.0740900	+	0.128328i
$567$	25.2622			1.06091
$568$	−9.19621	−	5.30944i	−0.385864	−	0.222779i
$569$		−	41.7153i		−	1.74880i	−0.485208	−	0.874399i	$-0.661256\pi$
$569$		−	41.7153i		−	1.74880i	0.485208	−	0.874399i	$-0.338744\pi$
$570$	76.4750			3.20319
$571$	−19.7093	−	11.3792i	−0.824809	−	0.476204i	0.0272631	−	0.999628i	$-0.491321\pi$
$571$	−19.7093	−	11.3792i	−0.824809	−	0.476204i	−0.852072	+	0.523425i	$0.824654\pi$
$572$	8.01305	+	4.62634i	0.335043	+	0.193437i
$573$	52.5669			2.19601
$574$	−4.23434	−	2.44470i	−0.176738	−	0.102040i
$575$	9.36273			0.390453
$576$	21.6906	−	37.5692i	0.903776	−	1.56539i
$577$	16.0021	−	27.7165i	0.666177	−	1.15385i	−0.312788	−	0.949823i	$-0.601263\pi$
$577$	16.0021	−	27.7165i	0.666177	−	1.15385i	0.978965	−	0.204029i	$-0.0654037\pi$
$578$	17.0661	−	9.85311i	0.709856	−	0.409835i
$579$	23.5977	+	40.8724i	0.980687	+	1.69860i
$580$		−	2.31464i		−	0.0961101i
$581$	2.19002			0.0908572
$582$	−10.0133	+	17.3436i	−0.415065	+	0.718914i
$583$	−16.3567	−	28.3307i	−0.677426	−	1.17334i
$584$	23.1023			0.955981
$585$	−131.404	+	75.8659i	−5.43287	+	3.13667i
$586$			13.0636i			0.539652i
$587$			38.1994i			1.57666i	0.615254	+	0.788329i	$0.289053\pi$
$587$			38.1994i			1.57666i	−0.615254	+	0.788329i	$0.710947\pi$
$588$	−4.48419	+	7.76684i	−0.184925	+	0.320299i
$589$	40.9838	−	23.6620i	1.68871	−	0.974977i
$590$	−5.62997	+	9.75140i	−0.231782	+	0.401459i
$591$		−	50.6311i		−	2.08269i
$592$			39.9137i			1.64044i
$593$	−9.09388	−	15.7511i	−0.373441	−	0.646819i	0.616651	−	0.787236i	$-0.288489\pi$
$593$	−9.09388	−	15.7511i	−0.373441	−	0.646819i	−0.990092	+	0.140418i	$0.955155\pi$
$594$	−40.5213	+	70.1849i	−1.66261	+	2.87972i
$595$	5.61969			0.230385
$596$			6.85746i			0.280893i
$597$	−57.2580	−	33.0579i	−2.34341	−	1.35297i
$598$	−19.4394	−	11.2233i	−0.794934	−	0.458955i
$599$	−6.57839	+	3.79804i	−0.268786	+	0.155184i	−0.628336	−	0.777942i	$-0.716264\pi$
$599$	−6.57839	+	3.79804i	−0.268786	+	0.155184i	0.359550	+	0.933126i	$0.382930\pi$
$600$	29.0058	+	16.7465i	1.18416	+	0.683673i
$601$	3.52918	+	6.11272i	0.143958	+	0.249343i	0.928984	−	0.370120i	$-0.120684\pi$
$601$	3.52918	+	6.11272i	0.143958	+	0.249343i	−0.785026	+	0.619463i	$0.787350\pi$
$602$	0.364282	+	0.630955i	0.0148470	+	0.0257158i
$603$	−33.7419	−	58.4426i	−1.37408	−	2.37997i
$604$	−0.882815	+	0.509694i	−0.0359212	+	0.0207391i
$605$			0.631446i			0.0256719i
$606$	94.9208			3.85589
$607$	−9.86168	−	5.69364i	−0.400273	−	0.231098i	0.286329	−	0.958131i	$-0.407565\pi$
$607$	−9.86168	−	5.69364i	−0.400273	−	0.231098i	−0.686602	+	0.727034i	$0.740898\pi$
$608$			12.0038i			0.486820i
$609$	−2.53446	−	4.38981i	−0.102701	−	0.177884i
$610$	0.326648	+	0.188591i	0.0132256	+	0.00763581i
$611$	21.8814	+	37.8996i	0.885225	+	1.53326i
$612$	6.21182	−	3.58640i	0.251098	−	0.144972i
$613$	−27.1506			−1.09660			−0.548301	−	0.836281i	$-0.684725\pi$
$613$	−27.1506			−1.09660			−0.548301	+	0.836281i	$0.684725\pi$
$614$		−	8.18595i		−	0.330358i
$615$			35.1888i			1.41895i
$616$	−3.54813	−	6.14555i	−0.142958	−	0.247611i
$617$	−5.19092	−	8.99093i	−0.208978	−	0.361961i	0.742415	−	0.669941i	$-0.233681\pi$
$617$	−5.19092	−	8.99093i	−0.208978	−	0.361961i	−0.951393	+	0.307979i	$0.900347\pi$
$618$	−5.88885			−0.236884
$619$	−42.3195	−	24.4332i	−1.70097	−	0.982053i	−0.944785	−	0.327691i	$-0.893729\pi$
$619$	−42.3195	−	24.4332i	−1.70097	−	0.982053i	−0.756181	−	0.654362i	$-0.772937\pi$
$620$	−12.8017			−0.514130
$621$	17.6936	−	30.6462i	0.710019	−	1.22979i
$622$	29.7292	+	17.1641i	1.19203	+	0.688219i
$623$	−9.26299			−0.371114
$624$	−49.4075	−	85.5763i	−1.97788	−	3.42579i
$625$	14.2147	−	24.6206i	0.568587	−	0.984822i
$626$	−2.11043	−	1.21846i	−0.0843498	−	0.0486994i
$627$			53.0943i			2.12038i
$628$	−6.44834			−0.257317
$629$	8.91626	−	15.4434i	0.355515	−	0.615769i
$630$	−32.7261			−1.30384
$631$	−5.29858	+	3.05914i	−0.210933	+	0.121782i	−0.601745	−	0.798688i	$-0.705528\pi$
$631$	−5.29858	+	3.05914i	−0.210933	+	0.121782i	0.390812	+	0.920471i	$0.372194\pi$
$632$	−6.31112	+	3.64373i	−0.251043	+	0.144940i
$633$	−34.8246	−	60.3180i	−1.38416	−	2.39743i
$634$	−3.39499	−	1.96010i	−0.134832	−	0.0778455i
$635$	7.69560	+	13.3292i	0.305390	+	0.528952i
$636$		−	14.3703i		−	0.569821i
$637$	−19.9372	−	34.5323i	−0.789942	−	1.36822i
$638$	8.92816			0.353469
$639$	−16.9997	−	29.4444i	−0.672498	−	1.16480i
$640$	−20.5456	+	35.5860i	−0.812135	+	1.40666i
$641$	−19.5221	+	33.8133i	−0.771078	+	1.33555i	0.165895	+	0.986143i	$0.446949\pi$
$641$	−19.5221	+	33.8133i	−0.771078	+	1.33555i	−0.936973	+	0.349402i	$0.886385\pi$
$642$	−0.831351	+	1.43994i	−0.0328108	+	0.0568300i
$643$	14.7606	+	25.5662i	0.582103	+	1.00823i	0.995230	+	0.0975584i	$0.0311033\pi$
$643$	14.7606	+	25.5662i	0.582103	+	1.00823i	−0.413127	+	0.910673i	$0.635563\pi$
$644$	−0.435701	−	0.754656i	−0.0171690	−	0.0297376i
$645$	2.62172	−	4.54096i	0.103230	−	0.178800i
$646$	8.03680	−	13.9201i	0.316204	−	0.547681i
$647$	30.4367	+	17.5726i	1.19659	+	0.690851i	0.959793	−	0.280708i	$-0.0905694\pi$
$647$	30.4367	+	17.5726i	1.19659	+	0.690851i	0.236796	+	0.971559i	$0.423903\pi$
$648$	60.1914	−	34.7515i	2.36454	−	1.36517i
$649$	−6.77010	−	3.90872i	−0.265750	−	0.153431i
$650$	36.2679	−	20.9393i	1.42254	−	0.821306i
$651$	−24.2790	+	14.0175i	−0.951570	+	0.549389i
$652$	6.14162	−	3.54587i	0.240525	−	0.138867i
$653$	−13.7935	+	7.96368i	−0.539781	+	0.311643i	−0.744990	−	0.667075i	$-0.767546\pi$
$653$	−13.7935	+	7.96368i	−0.539781	+	0.311643i	0.205209	+	0.978718i	$0.434213\pi$
$654$	−44.2570	−	76.6554i	−1.73059	−	2.99746i
$655$	−2.38376	−	1.37626i	−0.0931411	−	0.0537750i
$656$	−16.5542			−0.646331
$657$	64.0589	+	36.9844i	2.49917	+	1.44290i
$658$			9.43893i			0.367968i
$659$	−7.79942	−	4.50300i	−0.303822	−	0.175412i	0.340336	−	0.940304i	$-0.389459\pi$
$659$	−7.79942	−	4.50300i	−0.303822	−	0.175412i	−0.644159	+	0.764892i	$0.722792\pi$
$660$	7.18133	−	12.4384i	0.279533	−	0.484165i
$661$	−32.9800	+	19.0410i	−1.28277	+	0.740609i	−0.977354	−	0.211609i	$-0.932130\pi$
$661$	−32.9800	+	19.0410i	−1.28277	+	0.740609i	−0.305419	+	0.952218i	$0.598796\pi$
$662$	−27.8129			−1.08098
$663$			44.1482i			1.71458i
$664$	5.21807	−	3.01265i	0.202500	−	0.116914i
$665$	−11.4314	+	6.59992i	−0.443291	+	0.255934i
$666$	−51.9237	+	89.9345i	−2.01200	+	3.48489i
$667$	−3.89848			−0.150950
$668$	−0.825821	+	0.476788i	−0.0319520	+	0.0184475i
$669$	61.4992	−	35.5066i	2.37770	−	1.37276i
$670$	20.4541	+	35.4276i	0.790212	+	1.36869i
$671$	−0.130933	+	0.226782i	−0.00505460	+	0.00875483i
$672$		−	7.11113i		−	0.274318i
$673$	29.4361	−	16.9949i	1.13468	−	0.655107i	0.189571	−	0.981867i	$-0.439290\pi$
$673$	29.4361	−	16.9949i	1.13468	−	0.655107i	0.945107	+	0.326760i	$0.105957\pi$
$674$	31.2757			1.20470
$675$	33.0108	+	57.1764i	1.27059	+	2.20072i
$676$	−12.3644			−0.475552
$677$	15.8204	+	27.4017i	0.608028	+	1.05313i	0.991565	+	0.129609i	$0.0413723\pi$
$677$	15.8204	+	27.4017i	0.608028	+	1.05313i	−0.383538	+	0.923525i	$0.625294\pi$
$678$	−0.272532	+	0.157346i	−0.0104665	+	0.00604285i
$679$		−	3.45666i		−	0.132655i
$680$	13.3898	−	7.73062i	0.513476	−	0.296456i
$681$	56.3130	+	32.5123i	2.15792	+	1.24587i
$682$		−	49.3796i		−	1.89084i
$683$		−	30.8377i		−	1.17997i	−0.807413	−	0.589987i	$-0.799133\pi$
$683$		−	30.8377i		−	1.17997i	0.807413	−	0.589987i	$-0.200867\pi$
$684$	−8.42394	+	14.5907i	−0.322097	+	0.557889i
$685$	2.47940			0.0947331
$686$		−	18.2871i		−	0.698205i
$687$	−34.7690	+	60.2217i	−1.32652	+	2.29760i
$688$	2.13624	+	1.23336i	0.0814435	+	0.0470214i
$689$	55.3323	+	31.9461i	2.10799	+	1.21705i
$690$	−17.4216	+	30.1751i	−0.663230	+	1.14875i
$691$	−14.1831	+	8.18862i	−0.539551	+	0.311510i	−0.744897	−	0.667180i	$-0.767501\pi$
$691$	−14.1831	+	8.18862i	−0.539551	+	0.311510i	0.205346	+	0.978689i	$0.434168\pi$
$692$		−	4.28493i		−	0.162889i
$693$		−	22.7208i		−	0.863091i
$694$	−15.0049	+	8.66310i	−0.569579	+	0.328847i
$695$	12.4068	−	21.4892i	0.470616	−	0.815131i
$696$	−12.0775	−	6.97295i	−0.457797	−	0.264309i
$697$	6.40513	+	3.69800i	0.242612	+	0.140072i
$698$	21.9088	−	37.9472i	0.829262	−	1.43632i
$699$			19.9328i			0.753929i
$700$	1.62577			0.0614484
$701$	−15.8501	+	27.4532i	−0.598651	+	1.03689i	0.394370	+	0.918952i	$0.370963\pi$
$701$	−15.8501	+	27.4532i	−0.598651	+	1.03689i	−0.993020	+	0.117942i	$0.962370\pi$
$702$		−	158.283i		−	5.97402i
$703$			41.8861i			1.57976i
$704$	−15.8115	−	9.12876i	−0.595917	−	0.344053i
$705$	58.8305	−	33.9658i	2.21568	−	1.27923i
$706$		−	5.46532i		−	0.205690i
$707$	−14.1886	+	8.19182i	−0.533619	+	0.308085i
$708$	−1.71702	−	2.97396i	−0.0645295	−	0.111768i
$709$	16.1989			0.608362			0.304181	−	0.952614i	$-0.401617\pi$
$709$	16.1989			0.608362			0.304181	+	0.952614i	$0.401617\pi$
$710$	10.3051	+	17.8490i	0.386744	+	0.669861i
$711$	−23.3329			−0.875052
$712$	−22.0706	+	12.7425i	−0.827130	+	0.477544i
$713$			21.5616i			0.807488i
$714$	−4.76104	+	8.24636i	−0.178177	+	0.308612i
$715$	31.9291	+	55.3028i	1.19408	+	2.06821i
$716$	5.47109	−	3.15873i	0.204464	−	0.118047i
$717$	57.0534	−	32.9398i	2.13070	−	1.23016i
$718$	43.5122			1.62386
$719$	9.67665	−	16.7605i	0.360878	−	0.625060i	−0.627227	−	0.778836i	$-0.715810\pi$
$719$	9.67665	−	16.7605i	0.360878	−	0.625060i	0.988106	+	0.153777i	$0.0491436\pi$
$720$	−95.9571	+	55.4009i	−3.57611	+	2.06467i
$721$	0.880259	−	0.508218i	0.0327825	−	0.0189270i
$722$			8.08177i			0.300772i
$723$	18.9240			0.703791
$724$	4.95785	−	2.86242i	0.184257	−	0.106381i
$725$	3.63668	−	6.29892i	0.135063	−	0.233936i
$726$	−0.926588	−	0.534966i	−0.0343889	−	0.0198544i
$727$			5.27438i			0.195616i	0.995205	+	0.0978079i	$0.0311831\pi$
$727$			5.27438i			0.195616i	−0.995205	+	0.0978079i	$0.968817\pi$
$728$	12.0028	+	6.92982i	0.444853	+	0.256836i
$729$	66.7550			2.47241
$730$	−38.8321	−	22.4197i	−1.43724	−	0.829791i
$731$	−0.551036	−	0.954423i	−0.0203808	−	0.0353006i
$732$	−0.0996207	+	0.0575160i	−0.00368209	+	0.00212585i
$733$	−8.52481	+	4.92180i	−0.314871	+	0.181791i	−0.649104	−	0.760700i	$-0.724856\pi$
$733$	−8.52481	+	4.92180i	−0.314871	+	0.181791i	0.334233	+	0.942490i	$0.391523\pi$
$734$	20.8271	−	12.0245i	0.768742	−	0.443833i
$735$	−53.6035	+	30.9480i	−1.97719	+	1.14153i
$736$	−4.73641	−	2.73457i	−0.174587	−	0.100798i
$737$	−24.5963	+	14.2007i	−0.906016	+	0.523089i
$738$	−37.3002	−	21.5353i	−1.37304	−	0.792724i
$739$	10.2448	−	17.7444i	0.376859	−	0.652739i	−0.613744	−	0.789505i	$-0.710337\pi$
$739$	10.2448	−	17.7444i	0.376859	−	0.652739i	0.990603	+	0.136766i	$0.0436707\pi$
$740$	5.66534	−	9.81266i	0.208262	−	0.360721i
$741$	−51.8490	−	89.8050i	−1.90472	−	3.29907i
$742$	6.89028	+	11.9343i	0.252950	+	0.438122i
$743$	9.09357	−	15.7505i	0.333611	−	0.577831i	−0.649606	−	0.760271i	$-0.725066\pi$
$743$	9.09357	−	15.7505i	0.333611	−	0.577831i	0.983217	+	0.182440i	$0.0583996\pi$
$744$	−38.5658	+	66.7980i	−1.41389	+	2.44893i
$745$	−23.6637	+	40.9867i	−0.866970	+	1.50164i
$746$	11.2841	+	19.5447i	0.413141	+	0.715581i
$747$	19.2918			0.705849
$748$	−1.50938	−	2.61432i	−0.0551884	−	0.0955890i
$749$		−	0.286988i		−	0.0104863i
$750$	6.38117	+	11.0525i	0.233007	+	0.403581i
$751$	16.1588	+	9.32926i	0.589641	+	0.340430i	0.764956	−	0.644083i	$-0.222761\pi$
$751$	16.1588	+	9.32926i	0.589641	+	0.340430i	−0.175314	+	0.984513i	$0.556094\pi$
$752$	15.9788	+	27.6761i	0.582688	+	1.00924i
$753$	27.9556	−	16.1402i	1.01876	−	0.588181i
$754$	−15.1013	+	8.71875i	−0.549958	+	0.317518i
$755$	−7.03539			−0.256044
$756$	3.07236	−	5.32149i	0.111741	−	0.193541i
$757$	17.7131			0.643794			0.321897	−	0.946775i	$-0.395680\pi$
$757$	17.7131			0.643794			0.321897	+	0.946775i	$0.395680\pi$
$758$		−	10.1187i		−	0.367529i
$759$	−20.9497	−	12.0953i	−0.760425	−	0.439032i
$760$	−18.1581	+	31.4508i	−0.658664	+	1.14084i
$761$	−25.3075	−	43.8338i	−0.917394	−	1.58897i	−0.803357	−	0.595497i	$-0.796955\pi$
$761$	−25.3075	−	43.8338i	−0.917394	−	1.58897i	−0.114037	−	0.993476i	$-0.536378\pi$
$762$	−26.0791			−0.944745
$763$	13.2310	+	7.63890i	0.478993	+	0.276547i
$764$	3.51010	−	6.07966i	0.126991	−	0.219955i
$765$	49.5036			1.78981
$766$	11.1672	+	6.44741i	0.403489	+	0.232954i
$767$	15.2682			0.551301
$768$	−16.5434	−	28.6540i	−0.596959	−	1.03396i
$769$	−16.8056	−	29.1081i	−0.606025	−	1.04967i	−0.991889	−	0.127110i	$-0.959430\pi$
$769$	−16.8056	−	29.1081i	−0.606025	−	1.04967i	0.385864	−	0.922556i	$-0.373903\pi$
$770$			13.7732i			0.496351i
$771$			26.4493i			0.952549i
$772$	6.30285			0.226844
$773$	−15.5016	+	8.94986i	−0.557554	+	0.321904i	−0.752163	−	0.658977i	$-0.770989\pi$
$773$	−15.5016	+	8.94986i	−0.557554	+	0.321904i	0.194609	+	0.980881i	$0.437656\pi$
$774$	3.20895	+	5.55807i	0.115343	+	0.199781i
$775$	−34.8379	−	20.1137i	−1.25141	−	0.722504i
$776$	−4.75509	−	8.23606i	−0.170698	−	0.295657i
$777$		−	24.8135i		−	0.890179i
$778$	6.51802	+	3.76318i	0.233682	+	0.134917i
$779$	−17.3722			−0.622423
$780$			28.0515i			1.00441i
$781$	−12.3920	+	7.15453i	−0.443421	+	0.256009i
$782$	3.66169	+	6.34224i	0.130942	+	0.226798i
$783$	−13.7451	−	23.8073i	−0.491211	−	0.850802i
$784$	−14.5591	−	25.2171i	−0.519969	−	0.900612i
$785$	−38.5414	−	22.2519i	−1.37560	−	0.794204i
$786$	4.03907	−	2.33196i	0.144069	−	0.0831782i
$787$	9.86577	+	5.69601i	0.351677	+	0.203041i	0.665424	−	0.746466i	$-0.268251\pi$
$787$	9.86577	+	5.69601i	0.351677	+	0.203041i	−0.313747	+	0.949507i	$0.601584\pi$
$788$	−5.85579	−	3.38084i	−0.208604	−	0.120437i
$789$		−	12.4819i		−	0.444366i
$790$	14.1443			0.503230
$791$	0.0271585	−	0.0470399i	0.000965644	−	0.00167255i
$792$	−31.2554	−	54.1359i	−1.11061	−	1.92364i
$793$		−	0.511447i		−	0.0181620i
$794$		−	40.1907i		−	1.42632i
$795$	49.5890	−	85.8907i	1.75874	−	3.04623i
$796$	−7.64669	+	4.41482i	−0.271030	+	0.156479i
$797$	2.97942	−	5.16050i	0.105536	−	0.182794i	−0.808421	−	0.588605i	$-0.799677\pi$
$797$	2.97942	−	5.16050i	0.105536	−	0.182794i	0.913957	+	0.405811i	$0.133011\pi$
$798$		−	22.3660i		−	0.791748i
$799$		−	14.2779i		−	0.505117i
$800$	8.83670	−	5.10187i	0.312425	−	0.180378i
$801$	−81.5974			−2.88310
$802$	−1.79752	−	3.11340i	−0.0634727	−	0.109938i
$803$	15.5653	−	26.9600i	0.549289	−	0.951396i
$804$	−12.4761			−0.439999
$805$		−	6.01406i		−	0.211968i
$806$	48.2214	+	83.5219i	1.69853	+	2.94193i
$807$	−47.6898	+	27.5337i	−1.67876	+	0.969233i
$808$	−22.5378	+	39.0367i	−0.792879	+	1.37331i
$809$	2.38157	−	4.12501i	0.0837317	−	0.145028i	−0.821118	−	0.570758i	$-0.806649\pi$
$809$	2.38157	−	4.12501i	0.0837317	−	0.145028i	0.904850	+	0.425730i	$0.139983\pi$
$810$	−134.899			−4.73986
$811$	−21.0449	−	12.1503i	−0.738985	−	0.426653i	0.0827154	−	0.996573i	$-0.473641\pi$
$811$	−21.0449	−	12.1503i	−0.738985	−	0.426653i	−0.821700	+	0.569920i	$0.806974\pi$
$812$	−0.676942			−0.0237560
$813$	25.9836	+	15.0016i	0.911283	+	0.526130i
$814$	37.8500	+	21.8527i	1.32664	+	0.765937i
$815$	48.9442			1.71444
$816$			32.2392i			1.12860i
$817$	2.24180	+	1.29431i	0.0784308	+	0.0452820i
$818$	1.27576			0.0446059
$819$	22.1878	+	38.4305i	0.775306	+	1.34287i
$820$	4.06979	+	2.34969i	0.142123	+	0.0820548i
$821$	−23.9320	+	41.4515i	−0.835233	+	1.44667i	0.0586077	+	0.998281i	$0.481334\pi$
$821$	−23.9320	+	41.4515i	−0.835233	+	1.44667i	−0.893841	+	0.448385i	$0.851999\pi$
$822$	−2.10057	+	3.63829i	−0.0732658	+	0.126900i
$823$			49.8666i			1.73824i	0.494600	+	0.869121i	$0.335315\pi$
$823$			49.8666i			1.73824i	−0.494600	+	0.869121i	$0.664685\pi$
$824$	1.39824	−	2.42182i	0.0487100	−	0.0843682i
$825$	39.0857	−	22.5661i	1.36079	−	0.785652i
$826$	2.85191	+	1.64655i	0.0992306	+	0.0572908i
$827$	−14.4402			−0.502135			−0.251068	−	0.967970i	$-0.580782\pi$
$827$	−14.4402			−0.502135			−0.251068	+	0.967970i	$0.580782\pi$
$828$	−3.83808	−	6.64774i	−0.133382	−	0.231025i
$829$		−	30.1925i		−	1.04863i	−0.851525	−	0.524314i	$-0.824322\pi$
$829$		−	30.1925i		−	1.04863i	0.851525	−	0.524314i	$-0.175678\pi$
$830$	−11.6946			−0.405924
$831$	50.2797	−	21.5659i	1.74418	−	0.748113i
$832$	35.6586			1.23624
$833$			13.0094i			0.450748i
$834$	21.0222	+	36.4116i	0.727940	+	1.26083i
$835$	−6.58118			−0.227751
$836$	6.14067	+	3.54532i	0.212379	+	0.122617i
$837$	−131.673	+	76.0212i	−4.55127	+	2.62768i
$838$	4.90453	−	8.49489i	0.169424	−	0.293451i
$839$			20.9647i			0.723782i	0.932220	+	0.361891i	$0.117869\pi$
$839$			20.9647i			0.723782i	−0.932220	+	0.361891i	$0.882131\pi$
$840$	10.7570	−	18.6316i	0.371150	−	0.642851i
$841$	12.9857	−	22.4920i	0.447784	−	0.775585i
$842$	46.8002	+	27.0201i	1.61284	+	0.931174i
$843$	12.3340	+	21.3631i	0.424804	+	0.735783i
$844$	−9.30151			−0.320171
$845$	−73.9011	−	42.6668i	−2.54228	−	1.46778i
$846$			83.1473i			2.85866i
$847$	0.184674			0.00634546
$848$	40.4063	+	23.3286i	1.38756	+	0.801107i
$849$	−6.42608	−	3.71010i	−0.220542	−	0.127330i
$850$	−13.6632			−0.468644
$851$	−16.5272	−	9.54197i	−0.566544	−	0.327095i
$852$	−6.28568			−0.215344
$853$	−13.1247	+	22.7326i	−0.449380	+	0.778349i	−0.998346	−	0.0574956i	$-0.981688\pi$
$853$	−13.1247	+	22.7326i	−0.449380	+	0.778349i	0.548966	+	0.835845i	$0.315022\pi$
$854$	0.0551555	−	0.0955321i	0.00188738	−	0.00326904i
$855$	−100.699	+	58.1385i	−3.44383	+	1.98829i
$856$	−0.394789	−	0.683795i	−0.0134936	−	0.0233716i
$857$		−	48.1864i		−	1.64602i	−0.568029	−	0.823009i	$-0.692294\pi$
$857$		−	48.1864i		−	1.64602i	0.568029	−	0.823009i	$-0.307706\pi$
$858$	−108.202			−3.69396
$859$	−10.5802	+	18.3254i	−0.360991	+	0.625255i	−0.988124	−	0.153657i	$-0.950895\pi$
$859$	−10.5802	+	18.3254i	−0.360991	+	0.625255i	0.627133	+	0.778912i	$0.284228\pi$
$860$	−0.350126	−	0.606435i	−0.0119392	−	0.0206793i
$861$	10.2914			0.350729
$862$	7.65498	−	4.41961i	0.260730	−	0.150532i
$863$			12.0026i			0.408573i	0.978911	+	0.204286i	$0.0654874\pi$
$863$			12.0026i			0.408573i	−0.978911	+	0.204286i	$0.934513\pi$
$864$		−	38.5659i		−	1.31204i
$865$	14.7864	−	25.6108i	0.502753	−	0.870794i
$866$	−46.0251	+	26.5726i	−1.56400	+	0.902974i
$867$	−20.7392	+	35.9213i	−0.704339	+	1.21995i
$868$			3.74401i			0.127080i
$869$			9.81994i			0.333119i
$870$	13.5339	+	23.4413i	0.458841	+	0.794735i
$871$	27.7352	−	48.0388i	0.939771	−	1.62773i
$872$	42.0332			1.42343
$873$		−	30.4496i		−	1.03056i
$874$	−14.8970	−	8.60080i	−0.503899	−	0.290926i
$875$	−1.90770	−	1.10141i	−0.0644920	−	0.0372345i
$876$	11.8429	−	6.83753i	0.400136	−	0.231019i
$877$	−2.46621	−	1.42387i	−0.0832781	−	0.0480806i	0.457783	−	0.889064i	$-0.348644\pi$
$877$	−2.46621	−	1.42387i	−0.0832781	−	0.0480806i	−0.541061	+	0.840984i	$0.681977\pi$
$878$	−24.5264	−	42.4810i	−0.827726	−	1.43366i
$879$	−13.7484	−	23.8128i	−0.463720	−	0.803187i
$880$	23.3161	+	40.3847i	0.785987	+	1.36137i
$881$	10.3759	−	5.99054i	0.349574	−	0.201826i	−0.314924	−	0.949117i	$-0.601979\pi$
$881$	10.3759	−	5.99054i	0.349574	−	0.201826i	0.664497	+	0.747291i	$0.268646\pi$
$882$		−	75.7598i		−	2.55096i
$883$	7.45594			0.250912			0.125456	−	0.992099i	$-0.459961\pi$
$883$	7.45594			0.250912			0.125456	+	0.992099i	$0.459961\pi$
$884$	5.10600	+	2.94795i	0.171733	+	0.0991503i
$885$		−	23.7003i		−	0.796677i
$886$	24.2884	+	42.0688i	0.815986	+	1.41333i
$887$	8.06679	+	4.65736i	0.270856	+	0.156379i	0.629277	−	0.777181i	$-0.283351\pi$
$887$	8.06679	+	4.65736i	0.270856	+	0.156379i	−0.358420	+	0.933560i	$0.616685\pi$
$888$	−34.1342	−	59.1222i	−1.14547	−	1.98401i
$889$	3.89827	−	2.25067i	0.130744	−	0.0754849i
$890$	49.4639			1.65803
$891$		−	93.6562i		−	3.13760i
$892$		−	9.48366i		−	0.317537i
$893$	16.7684	+	29.0437i	0.561134	+	0.971912i
$894$	−40.0961	−	69.4485i	−1.34101	−	2.32270i
$895$	43.6005			1.45740
$896$	10.4075	+	6.00879i	0.347691	+	0.200740i
$897$	47.2464			1.57751
$898$	−19.0290	+	32.9593i	−0.635007	+	1.09986i
$899$	14.5059	+	8.37498i	0.483798	+	0.279321i
$900$	14.3214			0.477379
$901$	−10.4227	−	18.0526i	−0.347230	−	0.601419i
$902$	−9.06338	+	15.6982i	−0.301777	+	0.522694i
$903$	−1.32806	−	0.766753i	−0.0441949	−	0.0255160i
$904$		−	0.149440i		−	0.00497031i
$905$	39.5104			1.31337
$906$	5.96043	−	10.3238i	0.198022	−	0.342984i
$907$	−3.32129			−0.110281			−0.0551407	−	0.998479i	$-0.517561\pi$
$907$	−3.32129			−0.110281			−0.0551407	+	0.998479i	$0.517561\pi$
$908$	7.52048	−	4.34195i	0.249576	−	0.144093i
$909$	−124.987	+	72.1615i	−4.14557	+	2.39345i
$910$	−13.4501	−	23.2963i	−0.445868	−	0.772266i
$911$	−16.9493	−	9.78568i	−0.561555	−	0.324214i	0.192214	−	0.981353i	$-0.438433\pi$
$911$	−16.9493	−	9.78568i	−0.561555	−	0.324214i	−0.753770	+	0.657139i	$0.771767\pi$
$912$	−37.8626	−	65.5799i	−1.25376	−	2.17157i
$913$		−	8.11918i		−	0.268706i
$914$	−26.4475	−	45.8084i	−0.874806	−	1.51521i
$915$	−0.793903			−0.0262456
$916$	4.64333	+	8.04248i	0.153420	+	0.265731i
$917$	−0.402504	+	0.697157i	−0.0132918	+	0.0230222i
$918$	−25.8206	+	44.7226i	−0.852206	+	1.47606i
$919$	4.40358	−	7.62723i	0.145261	−	0.251599i	−0.784209	−	0.620496i	$-0.786931\pi$
$919$	4.40358	−	7.62723i	0.145261	−	0.251599i	0.929470	+	0.368897i	$0.120265\pi$
$920$	−8.27312	−	14.3295i	−0.272757	−	0.472429i
$921$	8.61503	+	14.9217i	0.283875	+	0.491686i
$922$	−14.6646	+	25.3999i	−0.482954	+	0.836500i
$923$	13.9734	−	24.2027i	0.459941	−	0.796642i
$924$	−3.63776	−	2.10026i	−0.119674	−	0.0690936i
$925$	30.8347	−	17.8024i	1.01384	−	0.585340i
$926$	12.7714	+	7.37356i	0.419694	+	0.242310i
$927$	7.75417	−	4.47687i	0.254680	−	0.147040i
$928$	−3.67945	+	2.12433i	−0.120784	+	0.0697346i
$929$	12.2853	−	7.09291i	0.403067	−	0.232711i	−0.284740	−	0.958605i	$-0.591907\pi$
$929$	12.2853	−	7.09291i	0.403067	−	0.232711i	0.687806	+	0.725894i	$0.258574\pi$
$930$	129.649	−	74.8527i	4.25135	−	2.45452i
$931$	−15.2786	−	26.4632i	−0.500735	−	0.867298i
$932$	2.30535	+	1.33099i	0.0755142	+	0.0435981i
$933$	−72.2553			−2.36553
$934$	34.2104	+	19.7514i	1.11940	+	0.646284i
$935$		−	20.8342i		−	0.681352i
$936$	105.732	+	61.0446i	3.45597	+	1.99530i
$937$	−16.5827	+	28.7220i	−0.541732	+	0.938307i	0.457073	+	0.889429i	$0.348898\pi$
$937$	−16.5827	+	28.7220i	−0.541732	+	0.938307i	−0.998805	+	0.0488778i	$0.984436\pi$
$938$	10.3612	−	5.98204i	0.338305	−	0.195321i
$939$	5.12930			0.167388
$940$		−	9.07212i		−	0.295900i
$941$	−3.99241	+	2.30502i	−0.130149	+	0.0751414i	−0.563661	−	0.826006i	$-0.690607\pi$
$941$	−3.99241	+	2.30502i	−0.130149	+	0.0751414i	0.433512	+	0.901148i	$0.357274\pi$
$942$	65.3052	−	37.7039i	2.12776	−	1.22846i
$943$	3.95752	−	6.85462i	0.128874	−	0.223217i
$944$	11.1495			0.362887
$945$	36.7267	−	21.2042i	1.19472	−	0.689772i
$946$	2.33918	−	1.35053i	0.0760533	−	0.0439094i
$947$	22.7544	+	39.4118i	0.739418	+	1.28071i	0.952758	+	0.303732i	$0.0982327\pi$
$947$	22.7544	+	39.4118i	0.739418	+	1.28071i	−0.213339	+	0.976978i	$0.568434\pi$
$948$	−2.15685	+	3.73577i	−0.0700511	+	0.121332i
$949$			60.8010i			1.97368i
$950$	27.7933	−	16.0465i	0.901733	−	0.520616i
$951$	8.25136			0.267569
$952$	−2.26091	−	3.91601i	−0.0732764	−	0.126919i
$953$	−30.0512			−0.973455			−0.486728	−	0.873554i	$-0.661810\pi$
$953$	−30.0512			−0.973455			−0.486728	+	0.873554i	$0.661810\pi$
$954$	60.6963	+	105.129i	1.96511	+	3.40368i
$955$	41.9593	−	24.2252i	1.35777	−	0.783910i
$956$		−	8.79809i		−	0.284550i
$957$	−16.2746	+	9.39615i	−0.526083	+	0.303734i
$958$	−20.9627	−	12.1028i	−0.677274	−	0.391024i
$959$		−	0.725130i		−	0.0234157i
$960$		−	55.3517i		−	1.78647i
$961$	30.8201	−	53.3820i	0.994197	−	1.72200i
$962$	−85.3606			−2.75214
$963$		−	2.52807i		−	0.0814658i
$964$	1.26363	−	2.18867i	0.0406988	−	0.0704923i
$965$	37.6718	+	21.7498i	1.21270	+	0.700151i
$966$	8.82506	+	5.09515i	0.283942	+	0.163934i
$967$	−10.8467	+	18.7871i	−0.348807	+	0.604152i	−0.986038	−	0.166521i	$-0.946747\pi$
$967$	−10.8467	+	18.7871i	−0.348807	+	0.604152i	0.637230	+	0.770673i	$0.280080\pi$
$968$	0.440015	−	0.254043i	0.0141426	−	0.00816525i
$969$			33.8323i			1.08685i
$970$			18.4584i			0.592663i
$971$	−18.8562	+	10.8867i	−0.605125	+	0.349369i	−0.771055	−	0.636768i	$-0.780271\pi$
$971$	−18.8562	+	10.8867i	−0.605125	+	0.349369i	0.165930	+	0.986138i	$0.446937\pi$
$972$	10.1686	−	17.6126i	0.326159	−	0.564923i
$973$	−6.28476	−	3.62851i	−0.201480	−	0.116325i
$974$	−47.7615	−	27.5751i	−1.53038	−	0.883564i
$975$	−44.0737	+	76.3379i	−1.41149	+	2.44477i
$976$		−	0.373483i		−	0.0119549i
$977$	−43.9657			−1.40659			−0.703293	−	0.710900i	$-0.748288\pi$
$977$	−43.9657			−1.40659			−0.703293	+	0.710900i	$0.748288\pi$
$978$	−41.4659	+	71.8211i	−1.32593	+	2.29658i
$979$			34.3413i			1.09755i
$980$			8.26607i			0.264050i
$981$	116.551	+	67.2908i	3.72119	+	2.14843i
$982$	−13.4535	+	7.76739i	−0.429319	+	0.247867i
$983$			10.6409i			0.339393i	0.985496	+	0.169697i	$0.0542788\pi$
$983$			10.6409i			0.339393i	−0.985496	+	0.169697i	$0.945721\pi$
$984$	24.5208	−	14.1571i	0.781696	−	0.451312i
$985$	−23.3332	−	40.4142i	−0.743456	−	1.28770i
$986$	5.68912			0.181178
$987$	−9.93369	−	17.2057i	−0.316193	−	0.547662i
$988$	−13.8486			−0.440584
$989$	−1.02140	+	0.589706i	−0.0324787	+	0.0187516i
$990$			121.328i			3.85605i
$991$	21.5148	−	37.2647i	0.683440	−	1.18375i	−0.290484	−	0.956880i	$-0.593816\pi$
$991$	21.5148	−	37.2647i	0.683440	−	1.18375i	0.973924	−	0.226873i	$-0.0728503\pi$
$992$	11.7492	+	20.3502i	0.373037	+	0.646119i
$993$	50.6984	−	29.2707i	1.60886	−	0.928879i
$994$	5.22014	−	3.01385i	0.165573	−	0.0955936i
$995$	−60.9385			−1.93188
$996$	1.78329	−	3.08876i	0.0565058	−	0.0978710i
$997$	−22.6629	+	13.0844i	−0.717742	+	0.414389i	−0.813921	−	0.580975i	$-0.802671\pi$
$997$	−22.6629	+	13.0844i	−0.717742	+	0.414389i	0.0961789	+	0.995364i	$0.469338\pi$
$998$	−22.8431	+	13.1885i	−0.723086	+	0.417474i
$999$		−	134.571i		−	4.25765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	277.2.e.c.117.13	✓	32
277.161	even	6	inner	277.2.e.c.161.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
277.2.e.c.117.13	✓	32	1.1	even	1	trivial
277.2.e.c.161.4	yes	32	277.161	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	277.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.56173i q^{2} +(-1.64359 - 2.84678i) q^{3} -0.438996 q^{4} +(-2.62385 - 1.51488i) q^{5} +(4.44590 - 2.56684i) q^{6} +(-0.443045 + 0.767376i) q^{7} +2.43786i q^{8} +(-3.90277 + 6.75979i) q^{9} +O(q^{10})\)	\(q+1.56173i q^{2} +(-1.64359 - 2.84678i) q^{3} -0.438996 q^{4} +(-2.62385 - 1.51488i) q^{5} +(4.44590 - 2.56684i) q^{6} +(-0.443045 + 0.767376i) q^{7} +2.43786i q^{8} +(-3.90277 + 6.75979i) q^{9} +(2.36583 - 4.09775i) q^{10} +(2.84494 + 1.64253i) q^{11} +(0.721528 + 1.24972i) q^{12} -6.41601 q^{13} +(-1.19843 - 0.691916i) q^{14} +9.95937i q^{15} -4.68527 q^{16} +(1.81283 + 1.04664i) q^{17} +(-10.5570 - 6.09506i) q^{18} -4.91680 q^{19} +(1.15186 + 0.665027i) q^{20} +2.91273 q^{21} +(-2.56518 + 4.44303i) q^{22} +(1.12008 - 1.94004i) q^{23} +(6.94006 - 4.00685i) q^{24} +(2.08974 + 3.61953i) q^{25} -10.0201i q^{26} +15.7966 q^{27} +(0.194495 - 0.336875i) q^{28} +(-0.870130 - 1.50711i) q^{29} -15.5538 q^{30} +(-8.33548 + 4.81249i) q^{31} -2.44140i q^{32} -10.7986i q^{33} +(-1.63456 + 2.83114i) q^{34} +(2.32497 - 1.34232i) q^{35} +(1.71330 - 2.96752i) q^{36} -8.51897i q^{37} -7.67870i q^{38} +(10.5453 + 18.2650i) q^{39} +(3.69308 - 6.39660i) q^{40} +3.53323 q^{41} +4.54890i q^{42} +(-0.455948 - 0.263242i) q^{43} +(-1.24892 - 0.721062i) q^{44} +(20.4806 - 11.8245i) q^{45} +(3.02982 + 1.74927i) q^{46} +(-3.41044 - 5.90705i) q^{47} +(7.70066 + 13.3379i) q^{48} +(3.10742 + 5.38221i) q^{49} +(-5.65272 + 3.26360i) q^{50} -6.88095i q^{51} +2.81660 q^{52} +(-8.62411 - 4.97913i) q^{53} +24.6701i q^{54} +(-4.97647 - 8.61950i) q^{55} +(-1.87076 - 1.08008i) q^{56} +(8.08119 + 13.9970i) q^{57} +(2.35369 - 1.35891i) q^{58} -2.37970 q^{59} -4.37212i q^{60} +0.0797142i q^{61} +(-7.51580 - 13.0177i) q^{62} +(-3.45820 - 5.98978i) q^{63} -5.55775 q^{64} +(16.8347 + 9.71949i) q^{65} +16.8644 q^{66} +(-4.32281 + 7.48733i) q^{67} +(-0.795823 - 0.459468i) q^{68} -7.36384 q^{69} +(2.09634 + 3.63097i) q^{70} +(-2.17790 + 3.77224i) q^{71} +(-16.4795 - 9.51442i) q^{72} -9.47645i q^{73} +13.3043 q^{74} +(6.86933 - 11.8980i) q^{75} +2.15845 q^{76} +(-2.52087 + 1.45543i) q^{77} +(-28.5249 + 16.4689i) q^{78} +(1.49464 + 2.58879i) q^{79} +(12.2935 + 7.09764i) q^{80} +(-14.2549 - 24.6902i) q^{81} +5.51795i q^{82} +(-1.23578 - 2.14043i) q^{83} -1.27868 q^{84} +(-3.17106 - 5.49244i) q^{85} +(0.411112 - 0.712067i) q^{86} +(-2.86027 + 4.95413i) q^{87} +(-4.00426 + 6.93558i) q^{88} +(5.22689 + 9.05324i) q^{89} +(18.4666 + 31.9851i) q^{90} +(2.84258 - 4.92349i) q^{91} +(-0.491712 + 0.851671i) q^{92} +(27.4002 + 15.8195i) q^{93} +(9.22520 - 5.32617i) q^{94} +(12.9010 + 7.44837i) q^{95} +(-6.95011 + 4.01265i) q^{96} +(-3.37839 + 1.95052i) q^{97} +(-8.40556 + 4.85295i) q^{98} +(-22.2063 + 12.8208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 3 q^{3} - 26 q^{4} - 12 q^{5} + 12 q^{6} - 39 q^{9}+O(q^{10}) \) 32 * q + 3 * q^3 - 26 * q^4 - 12 * q^5 + 12 * q^6 - 39 * q^9	\( 32 q + 3 q^{3} - 26 q^{4} - 12 q^{5} + 12 q^{6} - 39 q^{9} - 10 q^{10} - 3 q^{11} - 16 q^{12} + 10 q^{13} - 36 q^{14} + 50 q^{16} - 6 q^{17} - 39 q^{18} - 18 q^{19} - 33 q^{20} + 10 q^{21} + 31 q^{22} - 14 q^{23} + 27 q^{24} + 16 q^{25} + 60 q^{27} - 2 q^{28} + 6 q^{29} + 54 q^{30} + 12 q^{31} - 17 q^{34} - 3 q^{35} + 49 q^{36} + 16 q^{39} + 17 q^{40} - 24 q^{41} - 36 q^{43} + 24 q^{44} - 18 q^{45} - 63 q^{46} + 26 q^{47} + 49 q^{48} - 16 q^{49} - 45 q^{50} - 22 q^{52} - 33 q^{53} - 43 q^{55} + 72 q^{56} + 11 q^{57} - 27 q^{58} - 42 q^{59} + 19 q^{62} + 33 q^{63} - 80 q^{64} + 42 q^{65} + 8 q^{66} + 3 q^{67} - 12 q^{68} - 18 q^{69} + 35 q^{70} - 10 q^{71} + 72 q^{72} + 50 q^{74} + 49 q^{75} - 54 q^{76} + 87 q^{77} - 135 q^{78} - 32 q^{79} + 198 q^{80} - 32 q^{81} + 22 q^{83} - 176 q^{84} - 34 q^{85} + 6 q^{86} - 70 q^{87} - 103 q^{88} + 36 q^{89} - 31 q^{90} + 65 q^{91} + 29 q^{92} + 66 q^{93} + 39 q^{94} - 15 q^{95} - 12 q^{96} - 51 q^{97} + 15 q^{98} + 48 q^{99}+O(q^{100}) \) 32 * q + 3 * q^3 - 26 * q^4 - 12 * q^5 + 12 * q^6 - 39 * q^9 - 10 * q^10 - 3 * q^11 - 16 * q^12 + 10 * q^13 - 36 * q^14 + 50 * q^16 - 6 * q^17 - 39 * q^18 - 18 * q^19 - 33 * q^20 + 10 * q^21 + 31 * q^22 - 14 * q^23 + 27 * q^24 + 16 * q^25 + 60 * q^27 - 2 * q^28 + 6 * q^29 + 54 * q^30 + 12 * q^31 - 17 * q^34 - 3 * q^35 + 49 * q^36 + 16 * q^39 + 17 * q^40 - 24 * q^41 - 36 * q^43 + 24 * q^44 - 18 * q^45 - 63 * q^46 + 26 * q^47 + 49 * q^48 - 16 * q^49 - 45 * q^50 - 22 * q^52 - 33 * q^53 - 43 * q^55 + 72 * q^56 + 11 * q^57 - 27 * q^58 - 42 * q^59 + 19 * q^62 + 33 * q^63 - 80 * q^64 + 42 * q^65 + 8 * q^66 + 3 * q^67 - 12 * q^68 - 18 * q^69 + 35 * q^70 - 10 * q^71 + 72 * q^72 + 50 * q^74 + 49 * q^75 - 54 * q^76 + 87 * q^77 - 135 * q^78 - 32 * q^79 + 198 * q^80 - 32 * q^81 + 22 * q^83 - 176 * q^84 - 34 * q^85 + 6 * q^86 - 70 * q^87 - 103 * q^88 + 36 * q^89 - 31 * q^90 + 65 * q^91 + 29 * q^92 + 66 * q^93 + 39 * q^94 - 15 * q^95 - 12 * q^96 - 51 * q^97 + 15 * q^98 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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