LMFDB - Embedded newform 275.2.k.a.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [275,2,Mod(36,275)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("275.36"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(275, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.k (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,-6,-2,-5,3,-2,-5,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$2.19588605559$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	275.191
Dual form			275.2.k.a.36.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 1.53884i) q^{2} -2.61803 q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.30902 + 4.02874i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-1.80902 - 1.31433i) q^{8} +3.85410 q^{9} +(-1.11803 + 3.44095i) q^{10} +(-0.809017 + 3.21644i) q^{11} +(1.30902 - 0.951057i) q^{12} +1.85410 q^{13} +(-2.11803 + 1.53884i) q^{14} +(4.73607 + 3.44095i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(1.30902 + 4.02874i) q^{17} +(-1.92705 - 5.93085i) q^{18} +(-0.690983 - 0.502029i) q^{19} +1.38197 q^{20} +(1.30902 + 4.02874i) q^{21} +(5.35410 - 0.363271i) q^{22} +(-3.30902 - 2.40414i) q^{23} +(4.73607 + 3.44095i) q^{24} +(1.54508 + 4.75528i) q^{25} +(-0.927051 - 2.85317i) q^{26} -2.23607 q^{27} +(0.809017 + 0.587785i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(2.92705 - 9.00854i) q^{30} +(1.73607 - 1.26133i) q^{31} +3.38197 q^{32} +(2.11803 - 8.42075i) q^{33} +(5.54508 - 4.02874i) q^{34} +(-1.11803 + 3.44095i) q^{35} +(-1.92705 + 1.40008i) q^{36} +(2.42705 + 1.76336i) q^{37} +(-0.427051 + 1.31433i) q^{38} -4.85410 q^{39} +(1.54508 + 4.75528i) q^{40} +(-2.30902 - 7.10642i) q^{41} +(5.54508 - 4.02874i) q^{42} -12.0902 q^{43} +(-0.763932 - 1.90211i) q^{44} +(-6.97214 - 5.06555i) q^{45} +(-2.04508 + 6.29412i) q^{46} -8.32624 q^{47} +(3.92705 - 12.0862i) q^{48} +(3.54508 - 2.57565i) q^{49} +(6.54508 - 4.75528i) q^{50} +(-3.42705 - 10.5474i) q^{51} +(-0.927051 + 0.673542i) q^{52} +(-3.47214 + 10.6861i) q^{53} +(1.11803 + 3.44095i) q^{54} +(5.69098 - 4.75528i) q^{55} +(-1.11803 + 3.44095i) q^{56} +(1.80902 + 1.31433i) q^{57} +(5.85410 + 4.25325i) q^{58} +(-8.78115 - 6.37988i) q^{59} -3.61803 q^{60} -2.47214 q^{61} +(-2.80902 - 2.04087i) q^{62} +(-1.92705 - 5.93085i) q^{63} +(1.30902 + 4.02874i) q^{64} +(-3.35410 - 2.43690i) q^{65} +(-14.0172 + 0.951057i) q^{66} +(-3.00000 + 9.23305i) q^{67} +(-2.11803 - 1.53884i) q^{68} +(8.66312 + 6.29412i) q^{69} +5.85410 q^{70} +(2.42705 + 1.76336i) q^{71} +(-6.97214 - 5.06555i) q^{72} +(3.39919 - 10.4616i) q^{73} +(1.50000 - 4.61653i) q^{74} +(-4.04508 - 12.4495i) q^{75} +0.527864 q^{76} +(5.35410 - 0.363271i) q^{77} +(2.42705 + 7.46969i) q^{78} +(-2.33688 + 7.19218i) q^{79} +(8.78115 - 6.37988i) q^{80} -5.70820 q^{81} +(-9.78115 + 7.10642i) q^{82} +(1.85410 + 5.70634i) q^{83} +(-2.11803 - 1.53884i) q^{84} +(2.92705 - 9.00854i) q^{85} +(6.04508 + 18.6049i) q^{86} +(9.47214 - 6.88191i) q^{87} +(5.69098 - 4.75528i) q^{88} +(-1.54508 - 1.12257i) q^{89} +(-4.30902 + 13.2618i) q^{90} +(-0.927051 - 2.85317i) q^{91} +2.52786 q^{92} +(-4.54508 + 3.30220i) q^{93} +(4.16312 + 12.8128i) q^{94} +(0.590170 + 1.81636i) q^{95} -8.85410 q^{96} +(4.33688 - 13.3475i) q^{97} +(-5.73607 - 4.16750i) q^{98} +(-3.11803 + 12.3965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} - q^{11} + 3 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} - 6 q^{16} + 3 q^{17} - q^{18} - 5 q^{19} + 10 q^{20} + 3 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 - q^11 + 3 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 - 6 * q^16 + 3 * q^17 - q^18 - 5 * q^19 + 10 * q^20 + 3 * q^21 + 8 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 3 * q^26 + q^28 - 10 * q^29 + 5 * q^30 - 2 * q^31 + 18 * q^32 + 4 * q^33 + 11 * q^34 - q^36 + 3 * q^37 + 5 * q^38 - 6 * q^39 - 5 * q^40 - 7 * q^41 + 11 * q^42 - 26 * q^43 - 12 * q^44 - 10 * q^45 + 3 * q^46 - 2 * q^47 + 9 * q^48 + 3 * q^49 + 15 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 + 25 * q^55 + 5 * q^57 + 10 * q^58 - 15 * q^59 - 10 * q^60 + 8 * q^61 - 9 * q^62 - q^63 + 3 * q^64 - 27 * q^66 - 12 * q^67 - 4 * q^68 + 19 * q^69 + 10 * q^70 + 3 * q^71 - 10 * q^72 - 11 * q^73 + 6 * q^74 - 5 * q^75 + 20 * q^76 + 8 * q^77 + 3 * q^78 - 25 * q^79 + 15 * q^80 + 4 * q^81 - 19 * q^82 - 6 * q^83 - 4 * q^84 + 5 * q^85 + 13 * q^86 + 20 * q^87 + 25 * q^88 + 5 * q^89 - 15 * q^90 + 3 * q^91 + 28 * q^92 - 7 * q^93 + q^94 - 20 * q^95 - 22 * q^96 + 33 * q^97 - 14 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	−0.956844	−	0.290604i	$-0.906144\pi$
$2$	−0.500000	−	1.53884i	−0.353553	−	1.08813i	0.603290	−	0.797522i	$-0.293856\pi$
$3$	−2.61803			−1.51152			−0.755761	−	0.654847i	$-0.772733\pi$
$3$	−2.61803			−1.51152			−0.755761	+	0.654847i	$0.772733\pi$
$4$	−0.500000	+	0.363271i	−0.250000	+	0.181636i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$5$	−1.80902	−	1.31433i	−0.809017	−	0.587785i
$6$	1.30902	+	4.02874i	0.534404	+	1.64473i
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	0.811012	−	0.585030i	$-0.198917\pi$
$7$	−0.500000	−	1.53884i	−0.188982	−	0.581628i	−0.999994	+	0.00340203i	$0.998917\pi$
$8$	−1.80902	−	1.31433i	−0.639584	−	0.464685i
$9$	3.85410			1.28470
$10$	−1.11803	+	3.44095i	−0.353553	+	1.08813i
$11$	−0.809017	+	3.21644i	−0.243928	+	0.969793i
$11$	−0.809017	+	3.21644i	−0.243928	+	0.969793i
$12$	1.30902	−	0.951057i	0.377881	−	0.274546i
$13$	1.85410			0.514235			0.257118	−	0.966380i	$-0.417227\pi$
$13$	1.85410			0.514235			0.257118	+	0.966380i	$0.417227\pi$
$14$	−2.11803	+	1.53884i	−0.566068	+	0.411273i
$15$	4.73607	+	3.44095i	1.22285	+	0.888451i
$16$	−1.50000	+	4.61653i	−0.375000	+	1.15413i
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	0.974720	+	0.223429i	$0.0717251\pi$
$17$	1.30902	+	4.02874i	0.317483	+	0.977113i	−0.657237	+	0.753684i	$0.728275\pi$
$18$	−1.92705	−	5.93085i	−0.454210	−	1.39792i
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	0.505696	−	0.862712i	$-0.331236\pi$
$19$	−0.690983	−	0.502029i	−0.158522	−	0.115173i	−0.664219	+	0.747538i	$0.731236\pi$
$20$	1.38197			0.309017
$21$	1.30902	+	4.02874i	0.285651	+	0.879143i
$22$	5.35410	−	0.363271i	1.14150	−	0.0774497i
$23$	−3.30902	−	2.40414i	−0.689978	−	0.501298i	0.186675	−	0.982422i	$-0.440229\pi$
$23$	−3.30902	−	2.40414i	−0.689978	−	0.501298i	−0.876653	+	0.481124i	$0.840229\pi$
$24$	4.73607	+	3.44095i	0.966746	+	0.702382i
$25$	1.54508	+	4.75528i	0.309017	+	0.951057i
$26$	−0.927051	−	2.85317i	−0.181810	−	0.559553i
$27$	−2.23607			−0.430331
$28$	0.809017	+	0.587785i	0.152890	+	0.111081i
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	−0.870645	−	0.491912i	$-0.836298\pi$
$29$	−3.61803	+	2.62866i	−0.671852	+	0.488129i	0.198793	+	0.980042i	$0.436298\pi$
$30$	2.92705	−	9.00854i	0.534404	−	1.64473i
$31$	1.73607	−	1.26133i	0.311807	−	0.226541i	−0.420864	−	0.907124i	$-0.638273\pi$
$31$	1.73607	−	1.26133i	0.311807	−	0.226541i	0.732671	+	0.680582i	$0.238273\pi$
$32$	3.38197			0.597853
$33$	2.11803	−	8.42075i	0.368702	−	1.46586i
$34$	5.54508	−	4.02874i	0.950974	−	0.690923i
$35$	−1.11803	+	3.44095i	−0.188982	+	0.581628i
$36$	−1.92705	+	1.40008i	−0.321175	+	0.233347i
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	0.769135	−	0.639086i	$-0.220687\pi$
$37$	2.42705	+	1.76336i	0.399005	+	0.289894i	−0.370131	+	0.928980i	$0.620687\pi$
$38$	−0.427051	+	1.31433i	−0.0692768	+	0.213212i
$39$	−4.85410			−0.777278
$40$	1.54508	+	4.75528i	0.244299	+	0.751876i
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	−0.952686	−	0.303956i	$-0.901692\pi$
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	0.592078	−	0.805881i	$-0.298308\pi$
$42$	5.54508	−	4.02874i	0.855625	−	0.621648i
$43$	−12.0902			−1.84373			−0.921867	−	0.387507i	$-0.873336\pi$
$43$	−12.0902			−1.84373			−0.921867	+	0.387507i	$0.873336\pi$
$44$	−0.763932	−	1.90211i	−0.115167	−	0.286754i
$45$	−6.97214	−	5.06555i	−1.03934	−	0.755128i
$46$	−2.04508	+	6.29412i	−0.301531	+	0.928018i
$47$	−8.32624			−1.21451			−0.607253	−	0.794508i	$-0.707729\pi$
$47$	−8.32624			−1.21451			−0.607253	+	0.794508i	$0.707729\pi$
$48$	3.92705	−	12.0862i	0.566821	−	1.74450i
$49$	3.54508	−	2.57565i	0.506441	−	0.367951i
$50$	6.54508	−	4.75528i	0.925615	−	0.672499i
$51$	−3.42705	−	10.5474i	−0.479883	−	1.47693i
$52$	−0.927051	+	0.673542i	−0.128559	+	0.0934035i
$53$	−3.47214	+	10.6861i	−0.476935	+	1.46785i	0.366396	+	0.930459i	$0.380591\pi$
$53$	−3.47214	+	10.6861i	−0.476935	+	1.46785i	−0.843331	+	0.537395i	$0.819409\pi$
$54$	1.11803	+	3.44095i	0.152145	+	0.468255i
$55$	5.69098	−	4.75528i	0.767372	−	0.641202i
$56$	−1.11803	+	3.44095i	−0.149404	+	0.459817i
$57$	1.80902	+	1.31433i	0.239610	+	0.174087i
$58$	5.85410	+	4.25325i	0.768681	+	0.558480i
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.155646	−	0.987813i	$-0.549746\pi$
$59$	−8.78115	−	6.37988i	−1.14321	−	0.830590i	−0.987563	+	0.157223i	$0.949746\pi$
$60$	−3.61803			−0.467086
$61$	−2.47214			−0.316525			−0.158262	−	0.987397i	$-0.550589\pi$
$61$	−2.47214			−0.316525			−0.158262	+	0.987397i	$0.550589\pi$
$62$	−2.80902	−	2.04087i	−0.356746	−	0.259191i
$63$	−1.92705	−	5.93085i	−0.242786	−	0.747217i
$64$	1.30902	+	4.02874i	0.163627	+	0.503593i
$65$	−3.35410	−	2.43690i	−0.416025	−	0.302260i
$66$	−14.0172	+	0.951057i	−1.72540	+	0.117067i
$67$	−3.00000	+	9.23305i	−0.366508	+	1.12800i	0.582523	+	0.812814i	$0.302066\pi$
$67$	−3.00000	+	9.23305i	−0.366508	+	1.12800i	−0.949031	+	0.315182i	$0.897934\pi$
$68$	−2.11803	−	1.53884i	−0.256849	−	0.186612i
$69$	8.66312	+	6.29412i	1.04292	+	0.757724i
$70$	5.85410			0.699699
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	0.722416	−	0.691459i	$-0.243032\pi$
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	−0.434378	+	0.900731i	$0.643032\pi$
$72$	−6.97214	−	5.06555i	−0.821674	−	0.596981i
$73$	3.39919	−	10.4616i	0.397845	−	1.22444i	−0.528879	−	0.848697i	$-0.677388\pi$
$73$	3.39919	−	10.4616i	0.397845	−	1.22444i	0.926724	−	0.375743i	$-0.122612\pi$
$74$	1.50000	−	4.61653i	0.174371	−	0.536660i
$75$	−4.04508	−	12.4495i	−0.467086	−	1.43754i
$76$	0.527864			0.0605502
$77$	5.35410	−	0.363271i	0.610157	−	0.0413986i
$78$	2.42705	+	7.46969i	0.274809	+	0.845776i
$79$	−2.33688	+	7.19218i	−0.262920	+	0.809184i	0.729246	+	0.684252i	$0.239871\pi$
$79$	−2.33688	+	7.19218i	−0.262920	+	0.809184i	−0.992165	+	0.124932i	$0.960129\pi$
$80$	8.78115	−	6.37988i	0.981763	−	0.713292i
$81$	−5.70820			−0.634245
$82$	−9.78115	+	7.10642i	−1.08015	+	0.784773i
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	0.999771	+	0.0213936i	$0.00681031\pi$
$83$	1.85410	+	5.70634i	0.203514	+	0.626352i	−0.796257	+	0.604959i	$0.793190\pi$
$84$	−2.11803	−	1.53884i	−0.231096	−	0.167901i
$85$	2.92705	−	9.00854i	0.317483	−	0.977113i
$86$	6.04508	+	18.6049i	0.651858	+	2.00621i
$87$	9.47214	−	6.88191i	1.01552	−	0.737818i
$88$	5.69098	−	4.75528i	0.606661	−	0.506915i
$89$	−1.54508	−	1.12257i	−0.163779	−	0.118992i	0.502877	−	0.864358i	$-0.332275\pi$
$89$	−1.54508	−	1.12257i	−0.163779	−	0.118992i	−0.666656	+	0.745366i	$0.732275\pi$
$90$	−4.30902	+	13.2618i	−0.454210	+	1.39792i
$91$	−0.927051	−	2.85317i	−0.0971813	−	0.299093i
$92$	2.52786			0.263548
$93$	−4.54508	+	3.30220i	−0.471303	+	0.342422i
$94$	4.16312	+	12.8128i	0.429393	+	1.32154i
$95$	0.590170	+	1.81636i	0.0605502	+	0.186354i
$96$	−8.85410			−0.903668
$97$	4.33688	−	13.3475i	0.440344	−	1.35524i	−0.447167	−	0.894451i	$-0.647567\pi$
$97$	4.33688	−	13.3475i	0.440344	−	1.35524i	0.887510	−	0.460788i	$-0.152433\pi$
$98$	−5.73607	−	4.16750i	−0.579430	−	0.420981i
$99$	−3.11803	+	12.3965i	−0.313374	+	1.24589i
$100$	−2.50000	−	1.81636i	−0.250000	−	0.181636i
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	0.701952	−	0.712225i	$-0.252312\pi$
$101$	2.42705	+	1.76336i	0.241501	+	0.175460i	−0.460451	+	0.887685i	$0.652312\pi$
$102$	−14.5172	+	10.5474i	−1.43742	+	1.04435i
$103$	−16.1353	+	11.7229i	−1.58985	+	1.15510i	−0.685705	+	0.727880i	$0.740506\pi$
$103$	−16.1353	+	11.7229i	−1.58985	+	1.15510i	−0.904149	+	0.427216i	$0.859494\pi$
$104$	−3.35410	−	2.43690i	−0.328897	−	0.238957i
$105$	2.92705	−	9.00854i	0.285651	−	0.879143i
$106$	18.1803			1.76583
$107$	2.59017	−	7.97172i	0.250401	−	0.770656i	−0.744300	−	0.667846i	$-0.767217\pi$
$107$	2.59017	−	7.97172i	0.250401	−	0.770656i	0.994701	−	0.102810i	$-0.0327834\pi$
$108$	1.11803	−	0.812299i	0.107583	−	0.0781635i
$109$	1.38197	−	1.00406i	0.132368	−	0.0961712i	−0.519631	−	0.854391i	$-0.673931\pi$
$109$	1.38197	−	1.00406i	0.132368	−	0.0961712i	0.651999	+	0.758220i	$0.273931\pi$
$110$	−10.1631	−	6.37988i	−0.969015	−	0.608298i
$111$	−6.35410	−	4.61653i	−0.603105	−	0.438181i
$112$	7.85410			0.742143
$113$	2.54508	+	7.83297i	0.239421	+	0.736863i	0.996504	+	0.0835443i	$0.0266240\pi$
$113$	2.54508	+	7.83297i	0.239421	+	0.736863i	−0.757083	+	0.653319i	$0.773376\pi$
$114$	1.11803	−	3.44095i	0.104713	−	0.322275i
$115$	2.82624	+	8.69827i	0.263548	+	0.811117i
$116$	0.854102	−	2.62866i	0.0793014	−	0.244065i
$117$	7.14590			0.660639
$118$	−5.42705	+	16.7027i	−0.499601	+	1.53761i
$119$	5.54508	−	4.02874i	0.508317	−	0.369314i
$120$	−4.04508	−	12.4495i	−0.369264	−	1.13648i
$121$	−9.69098	−	5.20431i	−0.880998	−	0.473119i
$122$	1.23607	+	3.80423i	0.111908	+	0.344418i
$123$	6.04508	+	18.6049i	0.545067	+	1.67754i
$124$	−0.409830	+	1.26133i	−0.0368038	+	0.113271i
$125$	3.45492	−	10.6331i	0.309017	−	0.951057i
$126$	−8.16312	+	5.93085i	−0.727228	+	0.528362i
$127$	22.1246			1.96324			0.981621	−	0.190841i	$-0.0611216\pi$
$127$	22.1246			1.96324			0.981621	+	0.190841i	$0.0611216\pi$
$128$	11.0172	−	8.00448i	0.973794	−	0.707503i
$129$	31.6525			2.78685
$130$	−2.07295	+	6.37988i	−0.181810	+	0.559553i
$131$	4.92705	−	15.1639i	0.430478	−	1.32488i	−0.467171	−	0.884167i	$-0.654727\pi$
$131$	4.92705	−	15.1639i	0.430478	−	1.32488i	0.897650	−	0.440710i	$-0.145273\pi$
$132$	2.00000	+	4.97980i	0.174078	+	0.433436i
$133$	−0.427051	+	1.31433i	−0.0370300	+	0.113967i
$134$	15.7082			1.35698
$135$	4.04508	+	2.93893i	0.348145	+	0.252942i
$136$	2.92705	−	9.00854i	0.250993	−	0.772476i
$137$	2.06231	−	6.34712i	0.176195	−	0.542271i	−0.823491	−	0.567329i	$-0.807977\pi$
$137$	2.06231	−	6.34712i	0.176195	−	0.542271i	0.999686	+	0.0250574i	$0.00797685\pi$
$138$	5.35410	−	16.4782i	0.455771	−	1.40272i
$139$	−1.21885	+	3.75123i	−0.103381	+	0.318175i	−0.989347	−	0.145576i	$-0.953497\pi$
$139$	−1.21885	+	3.75123i	−0.103381	+	0.318175i	0.885966	+	0.463750i	$0.153497\pi$
$140$	−0.690983	−	2.12663i	−0.0583987	−	0.179733i
$141$	21.7984			1.83575
$142$	1.50000	−	4.61653i	0.125877	−	0.387410i
$143$	−1.50000	+	5.96361i	−0.125436	+	0.498702i
$144$	−5.78115	+	17.7926i	−0.481763	+	1.48271i
$145$	10.0000			0.830455
$146$	−17.7984			−1.47300
$147$	−9.28115	+	6.74315i	−0.765497	+	0.556166i
$148$	−1.85410			−0.152406
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.960828	−	0.277146i	$-0.910612\pi$
$149$	−12.1353	+	8.81678i	−0.994159	+	0.722299i	−0.0333309	+	0.999444i	$0.510612\pi$
$150$	−17.1353	+	12.4495i	−1.39909	+	1.01650i
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	0.590170	+	1.81636i	0.0478691	+	0.147326i
$153$	5.04508	+	15.5272i	0.407871	+	1.25530i
$154$	−3.23607	−	8.05748i	−0.260770	−	0.649290i
$155$	−4.79837			−0.385415
$156$	2.42705	−	1.76336i	0.194320	−	0.141181i
$157$	−4.80902	+	14.8006i	−0.383801	+	1.18122i	0.553545	+	0.832819i	$0.313275\pi$
$157$	−4.80902	+	14.8006i	−0.383801	+	1.18122i	−0.937346	+	0.348400i	$0.886725\pi$
$158$	12.2361			0.973449
$159$	9.09017	−	27.9767i	0.720897	−	2.21869i
$160$	−6.11803	−	4.44501i	−0.483673	−	0.351409i
$161$	−2.04508	+	6.29412i	−0.161175	+	0.496046i
$162$	2.85410	+	8.78402i	0.224239	+	0.690138i
$163$	−21.5623			−1.68889			−0.844445	−	0.535642i	$-0.820070\pi$
$163$	−21.5623			−1.68889			−0.844445	+	0.535642i	$0.820070\pi$
$164$	3.73607	+	2.71441i	0.291738	+	0.211960i
$165$	−14.8992	+	12.4495i	−1.15990	+	0.969192i
$166$	7.85410	−	5.70634i	0.609597	−	0.442898i
$167$	−4.28115	+	3.11044i	−0.331286	+	0.240693i	−0.740976	−	0.671532i	$-0.765637\pi$
$167$	−4.28115	+	3.11044i	−0.331286	+	0.240693i	0.409690	+	0.912225i	$0.365637\pi$
$168$	2.92705	−	9.00854i	0.225827	−	0.695024i
$169$	−9.56231			−0.735562
$170$	−15.3262			−1.17547
$171$	−2.66312	−	1.93487i	−0.203654	−	0.147963i
$172$	6.04508	−	4.39201i	0.460933	−	0.334888i
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	−0.756817	−	0.653627i	$-0.773247\pi$
$173$	−4.85410	+	3.52671i	−0.369051	+	0.268131i	0.387767	+	0.921758i	$0.373247\pi$
$174$	−15.3262	−	11.1352i	−1.16188	−	0.844155i
$175$	6.54508	−	4.75528i	0.494762	−	0.359466i
$176$	−13.6353	−	8.55951i	−1.02780	−	0.645197i
$177$	22.9894	+	16.7027i	1.72799	+	1.25546i
$178$	−0.954915	+	2.93893i	−0.0715739	+	0.220282i
$179$	−11.1803			−0.835658			−0.417829	−	0.908526i	$-0.637209\pi$
$179$	−11.1803			−0.835658			−0.417829	+	0.908526i	$0.637209\pi$
$180$	5.32624			0.396994
$181$	3.70820	+	11.4127i	0.275629	+	0.848298i	0.989052	+	0.147565i	$0.0471435\pi$
$181$	3.70820	+	11.4127i	0.275629	+	0.848298i	−0.713424	+	0.700733i	$0.752856\pi$
$182$	−3.92705	+	2.85317i	−0.291092	+	0.211491i
$183$	6.47214			0.478434
$184$	2.82624	+	8.69827i	0.208353	+	0.641245i
$185$	−2.07295	−	6.37988i	−0.152406	−	0.469058i
$186$	7.35410	+	5.34307i	0.539229	+	0.391773i
$187$	−14.0172	+	0.951057i	−1.02504	+	0.0695481i
$188$	4.16312	−	3.02468i	0.303627	−	0.220598i
$189$	1.11803	+	3.44095i	0.0813250	+	0.250293i
$190$	2.50000	−	1.81636i	0.181369	−	0.131772i
$191$	2.42705	+	1.76336i	0.175615	+	0.127592i	0.672121	−	0.740442i	$-0.265384\pi$
$191$	2.42705	+	1.76336i	0.175615	+	0.127592i	−0.496505	+	0.868034i	$0.665384\pi$
$192$	−3.42705	−	10.5474i	−0.247326	−	0.761191i
$193$	−3.57295	+	2.59590i	−0.257186	+	0.186857i	−0.708906	−	0.705303i	$-0.750811\pi$
$193$	−3.57295	+	2.59590i	−0.257186	+	0.186857i	0.451719	+	0.892160i	$0.350811\pi$
$194$	−22.7082			−1.63035
$195$	8.78115	+	6.37988i	0.628831	+	0.456873i
$196$	−0.836881	+	2.57565i	−0.0597772	+	0.183975i
$197$	−0.437694	−	1.34708i	−0.0311844	−	0.0959758i	0.934253	−	0.356611i	$-0.116068\pi$
$197$	−0.437694	−	1.34708i	−0.0311844	−	0.0959758i	−0.965437	+	0.260635i	$0.916068\pi$
$198$	20.6353	−	1.40008i	1.46648	−	0.0994997i
$199$	−17.5623			−1.24496			−0.622479	−	0.782636i	$-0.713875\pi$
$199$	−17.5623			−1.24496			−0.622479	+	0.782636i	$0.713875\pi$
$200$	3.45492	−	10.6331i	0.244299	−	0.751876i
$201$	7.85410	−	24.1724i	0.553986	−	1.70499i
$202$	1.50000	−	4.61653i	0.105540	−	0.324818i
$203$	5.85410	+	4.25325i	0.410877	+	0.298520i
$204$	5.54508	+	4.02874i	0.388234	+	0.282068i
$205$	−5.16312	+	15.8904i	−0.360608	+	1.10984i
$206$	26.1074	+	18.9681i	1.81899	+	1.32157i
$207$	−12.7533	−	9.26581i	−0.886415	−	0.644018i
$208$	−2.78115	+	8.55951i	−0.192838	+	0.593495i
$209$	2.17376	−	1.81636i	0.150362	−	0.125640i
$210$	−15.3262			−1.05761
$211$	−6.41641	−	19.7477i	−0.441724	−	1.35949i	−0.886037	−	0.463614i	$-0.846552\pi$
$211$	−6.41641	−	19.7477i	−0.441724	−	1.35949i	0.444313	−	0.895871i	$-0.353448\pi$
$212$	−2.14590	−	6.60440i	−0.147381	−	0.453592i
$213$	−6.35410	−	4.61653i	−0.435376	−	0.316319i
$214$	−13.5623			−0.927100
$215$	21.8713	+	15.8904i	1.49161	+	1.08372i
$216$	4.04508	+	2.93893i	0.275233	+	0.199969i
$217$	−2.80902	−	2.04087i	−0.190688	−	0.138543i
$218$	−2.23607	−	1.62460i	−0.151446	−	0.110032i
$219$	−8.89919	+	27.3889i	−0.601351	+	1.85077i
$220$	−1.11803	+	4.44501i	−0.0753778	+	0.299683i
$221$	2.42705	+	7.46969i	0.163261	+	0.502466i
$222$	−3.92705	+	12.0862i	−0.263566	+	0.811174i
$223$	−9.42705	+	6.84915i	−0.631282	+	0.458653i	−0.856844	−	0.515576i	$-0.827578\pi$
$223$	−9.42705	+	6.84915i	−0.631282	+	0.458653i	0.225562	+	0.974229i	$0.427578\pi$
$224$	−1.69098	−	5.20431i	−0.112984	−	0.347728i
$225$	5.95492	+	18.3273i	0.396994	+	1.22182i
$226$	10.7812	−	7.83297i	0.717152	−	0.521041i
$227$	9.23607	−	28.4257i	0.613019	−	1.88668i	0.185603	−	0.982625i	$-0.440576\pi$
$227$	9.23607	−	28.4257i	0.613019	−	1.88668i	0.427417	−	0.904055i	$-0.359424\pi$
$228$	−1.38197			−0.0915229
$229$	0.263932	−	0.812299i	0.0174411	−	0.0536782i	−0.941957	−	0.335733i	$-0.891016\pi$
$229$	0.263932	−	0.812299i	0.0174411	−	0.0536782i	0.959398	+	0.282055i	$0.0910160\pi$
$230$	11.9721	−	8.69827i	0.789419	−	0.573547i
$231$	−14.0172	+	0.951057i	−0.922265	+	0.0625749i
$232$	10.0000			0.656532
$233$	23.2984	−	16.9273i	1.52633	−	1.10894i	0.568090	−	0.822966i	$-0.307682\pi$
$233$	23.2984	−	16.9273i	1.52633	−	1.10894i	0.958237	−	0.285975i	$-0.0923176\pi$
$234$	−3.57295	−	10.9964i	−0.233571	−	0.718858i
$235$	15.0623	+	10.9434i	0.982556	+	0.713869i
$236$	6.70820			0.436667
$237$	6.11803	−	18.8294i	0.397409	−	1.22310i
$238$	−8.97214	−	6.51864i	−0.581577	−	0.422541i
$239$	−6.28115	+	4.56352i	−0.406294	+	0.295190i	−0.772100	−	0.635501i	$-0.780793\pi$
$239$	−6.28115	+	4.56352i	−0.406294	+	0.295190i	0.365806	+	0.930691i	$0.380793\pi$
$240$	−22.9894	+	16.7027i	−1.48396	+	1.07816i
$241$	−4.11803	+	2.99193i	−0.265266	+	0.192727i	−0.712465	−	0.701707i	$-0.752421\pi$
$241$	−4.11803	+	2.99193i	−0.265266	+	0.192727i	0.447199	+	0.894434i	$0.352421\pi$
$242$	−3.16312	+	17.5150i	−0.203333	+	1.12591i
$243$	21.6525			1.38901
$244$	1.23607	−	0.898056i	0.0791311	−	0.0574921i
$245$	−9.79837			−0.625995
$246$	25.6074	−	18.6049i	1.63267	−	1.18620i
$247$	−1.28115	−	0.930812i	−0.0815178	−	0.0592262i
$248$	−4.79837			−0.304697
$249$	−4.85410	−	14.9394i	−0.307616	−	0.946745i
$250$	−18.0902			−1.14412
$251$	−0.0729490	−	0.0530006i	−0.00460450	−	0.00334537i	0.585481	−	0.810686i	$-0.300906\pi$
$251$	−0.0729490	−	0.0530006i	−0.00460450	−	0.00334537i	−0.590085	+	0.807341i	$0.700906\pi$
$252$	3.11803	+	2.26538i	0.196418	+	0.142706i
$253$	10.4098	−	8.69827i	0.654460	−	0.546855i
$254$	−11.0623	−	34.0463i	−0.694111	−	2.13625i
$255$	−7.66312	+	23.5847i	−0.479883	+	1.47693i
$256$	−10.9721	−	7.97172i	−0.685758	−	0.498233i
$257$	4.39919	+	13.5393i	0.274414	+	0.844559i	0.989374	+	0.145393i	$0.0464448\pi$
$257$	4.39919	+	13.5393i	0.274414	+	0.844559i	−0.714960	+	0.699165i	$0.753555\pi$
$258$	−15.8262	−	48.7082i	−0.985299	−	3.03244i
$259$	1.50000	−	4.61653i	0.0932055	−	0.286857i
$260$	2.56231			0.158907
$261$	−13.9443	+	10.1311i	−0.863129	+	0.627100i
$262$	−25.7984			−1.59383
$263$	6.00000	−	4.35926i	0.369976	−	0.268803i	−0.387225	−	0.921985i	$-0.626566\pi$
$263$	6.00000	−	4.35926i	0.369976	−	0.268803i	0.757201	+	0.653182i	$0.226566\pi$
$264$	−14.8992	+	12.4495i	−0.916982	+	0.766213i
$265$	20.3262	−	14.7679i	1.24863	−	0.907183i
$266$	2.23607			0.137102
$267$	4.04508	+	2.93893i	0.247555	+	0.179859i
$268$	−1.85410	−	5.70634i	−0.113257	−	0.348570i
$269$	−5.06231	−	15.5802i	−0.308654	−	0.949940i	−0.978288	−	0.207249i	$-0.933549\pi$
$269$	−5.06231	−	15.5802i	−0.308654	−	0.949940i	0.669634	−	0.742691i	$-0.266451\pi$
$270$	2.50000	−	7.69421i	0.152145	−	0.468255i
$271$	17.9164	−	13.0170i	1.08834	−	0.790728i	0.109225	−	0.994017i	$-0.465163\pi$
$271$	17.9164	−	13.0170i	1.08834	−	0.790728i	0.979119	+	0.203289i	$0.0651630\pi$
$272$	−20.5623			−1.24677
$273$	2.42705	+	7.46969i	0.146892	+	0.452086i
$274$	−10.7984			−0.652354
$275$	−16.5451	+	1.12257i	−0.997706	+	0.0676935i
$276$	−6.61803			−0.398359
$277$	−8.85410	−	27.2501i	−0.531991	−	1.63730i	−0.750061	−	0.661368i	$-0.769976\pi$
$277$	−8.85410	−	27.2501i	−0.531991	−	1.63730i	0.218070	−	0.975933i	$-0.430024\pi$
$278$	6.38197			0.382765
$279$	6.69098	−	4.86128i	0.400579	−	0.291037i
$280$	6.54508	−	4.75528i	0.391144	−	0.284182i
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	0.814969	−	0.579505i	$-0.196754\pi$
$281$	−3.10081	−	9.54332i	−0.184979	−	0.569307i	−0.999948	+	0.0101977i	$0.996754\pi$
$282$	−10.8992	−	33.5442i	−0.649037	−	1.99753i
$283$	−23.1074	−	16.7885i	−1.37359	−	0.997973i	−0.997447	−	0.0714120i	$-0.977249\pi$
$283$	−23.1074	−	16.7885i	−1.37359	−	0.997973i	−0.376145	−	0.926561i	$-0.622751\pi$
$284$	−1.85410			−0.110021
$285$	−1.54508	−	4.75528i	−0.0915229	−	0.281679i
$286$	9.92705	−	0.673542i	0.586999	−	0.0398274i
$287$	−9.78115	+	7.10642i	−0.577363	+	0.419479i
$288$	13.0344			0.768062
$289$	−0.763932	+	0.555029i	−0.0449372	+	0.0326488i
$290$	−5.00000	−	15.3884i	−0.293610	−	0.903639i
$291$	−11.3541	+	34.9443i	−0.665589	+	2.04847i
$292$	2.10081	+	6.46564i	0.122941	+	0.378373i
$293$	5.67376	+	17.4620i	0.331465	+	1.02014i	0.968437	+	0.249257i	$0.0801864\pi$
$293$	5.67376	+	17.4620i	0.331465	+	1.02014i	−0.636973	+	0.770886i	$0.719814\pi$
$294$	15.0172	+	10.9106i	0.875822	+	0.636322i
$295$	7.50000	+	23.0826i	0.436667	+	1.34392i
$296$	−2.07295	−	6.37988i	−0.120488	−	0.370823i
$297$	1.80902	−	7.19218i	0.104970	−	0.417333i
$298$	19.6353	+	14.2658i	1.13744	+	0.826398i
$299$	−6.13525	−	4.45752i	−0.354811	−	0.257785i
$300$	6.54508	+	4.75528i	0.377881	+	0.274546i
$301$	6.04508	+	18.6049i	0.348433	+	1.07237i
$302$	−3.23607			−0.186215
$303$	−6.35410	−	4.61653i	−0.365034	−	0.265212i
$304$	3.35410	−	2.43690i	0.192371	−	0.139766i
$305$	4.47214	+	3.24920i	0.256074	+	0.186048i
$306$	21.3713	−	15.5272i	1.22172	−	0.887630i
$307$	0.416408			0.0237657			0.0118828	−	0.999929i	$-0.496217\pi$
$307$	0.416408			0.0237657			0.0118828	+	0.999929i	$0.496217\pi$
$308$	−2.54508	+	2.12663i	−0.145020	+	0.121176i
$309$	42.2426	−	30.6911i	2.40310	−	1.74595i
$310$	2.39919	+	7.38394i	0.136265	+	0.419380i
$311$	15.0902	−	10.9637i	0.855685	−	0.621692i	−0.0710226	−	0.997475i	$-0.522626\pi$
$311$	15.0902	−	10.9637i	0.855685	−	0.621692i	0.926708	+	0.375783i	$0.122626\pi$
$312$	8.78115	+	6.37988i	0.497135	+	0.361190i
$313$	1.10081	−	3.38795i	0.0622216	−	0.191498i	−0.915114	−	0.403196i	$-0.867899\pi$
$313$	1.10081	−	3.38795i	0.0622216	−	0.191498i	0.977335	+	0.211698i	$0.0678992\pi$
$314$	25.1803			1.42101
$315$	−4.30902	+	13.2618i	−0.242786	+	0.747217i
$316$	−1.44427	−	4.44501i	−0.0812466	−	0.250051i
$317$	−20.1353	+	14.6291i	−1.13091	+	0.821653i	−0.985827	−	0.167766i	$-0.946345\pi$
$317$	−20.1353	+	14.6291i	−1.13091	+	0.821653i	−0.145082	+	0.989420i	$0.546345\pi$
$318$	−47.5967			−2.66909
$319$	−5.52786	−	13.7638i	−0.309501	−	0.770626i
$320$	2.92705	−	9.00854i	0.163627	−	0.503593i
$321$	−6.78115	+	20.8702i	−0.378487	+	1.16486i
$322$	10.7082			0.596745
$323$	1.11803	−	3.44095i	0.0622091	−	0.191460i
$324$	2.85410	−	2.07363i	0.158561	−	0.115201i
$325$	2.86475	+	8.81678i	0.158907	+	0.489067i
$326$	10.7812	+	33.1810i	0.597113	+	1.83772i
$327$	−3.61803	+	2.62866i	−0.200078	+	0.145365i
$328$	−5.16312	+	15.8904i	−0.285086	+	0.877403i
$329$	4.16312	+	12.8128i	0.229520	+	0.706390i
$330$	26.6074	+	16.7027i	1.46469	+	0.919456i
$331$	−2.24671	+	6.91467i	−0.123490	+	0.380064i	−0.993623	−	0.112753i	$-0.964033\pi$
$331$	−2.24671	+	6.91467i	−0.123490	+	0.380064i	0.870133	+	0.492818i	$0.164033\pi$
$332$	−3.00000	−	2.17963i	−0.164646	−	0.119623i
$333$	9.35410	+	6.79615i	0.512602	+	0.372427i
$334$	6.92705	+	5.03280i	0.379031	+	0.275382i
$335$	17.5623	−	12.7598i	0.959531	−	0.697140i
$336$	−20.5623			−1.12177
$337$	10.5172	+	7.64121i	0.572910	+	0.416243i	0.836161	−	0.548484i	$-0.184795\pi$
$337$	10.5172	+	7.64121i	0.572910	+	0.416243i	−0.263251	+	0.964727i	$0.584795\pi$
$338$	4.78115	+	14.7149i	0.260060	+	0.800384i
$339$	−6.66312	−	20.5070i	−0.361891	−	1.11379i
$340$	1.80902	+	5.56758i	0.0981077	+	0.301945i
$341$	2.65248	+	6.60440i	0.143640	+	0.357648i
$342$	−1.64590	+	5.06555i	−0.0890000	+	0.273914i
$343$	−14.8992	−	10.8249i	−0.804480	−	0.584489i
$344$	21.8713	+	15.8904i	1.17922	+	0.856755i
$345$	−7.39919	−	22.7724i	−0.398359	−	1.22602i
$346$	7.85410	+	5.70634i	0.422239	+	0.306775i
$347$	11.2082	+	8.14324i	0.601688	+	0.437152i	0.846478	−	0.532424i	$-0.178719\pi$
$347$	11.2082	+	8.14324i	0.601688	+	0.437152i	−0.244790	+	0.969576i	$0.578719\pi$
$348$	−2.23607	+	6.88191i	−0.119866	+	0.368909i
$349$	4.14590	−	12.7598i	0.221925	−	0.683014i	−0.776664	−	0.629915i	$-0.783090\pi$
$349$	4.14590	−	12.7598i	0.221925	−	0.683014i	0.998589	−	0.0530998i	$-0.0169101\pi$
$350$	−10.5902	−	7.69421i	−0.566068	−	0.411273i
$351$	−4.14590			−0.221292
$352$	−2.73607	+	10.8779i	−0.145833	+	0.579794i
$353$	−1.70163	−	5.23707i	−0.0905684	−	0.278741i	0.895505	−	0.445051i	$-0.146815\pi$
$353$	−1.70163	−	5.23707i	−0.0905684	−	0.278741i	−0.986073	+	0.166310i	$0.946815\pi$
$354$	14.2082	−	43.7284i	0.755158	−	2.32414i
$355$	−2.07295	−	6.37988i	−0.110021	−	0.338609i
$356$	1.18034			0.0625579
$357$	−14.5172	+	10.5474i	−0.768333	+	0.558226i
$358$	5.59017	+	17.2048i	0.295450	+	0.909301i
$359$	21.1803	+	15.3884i	1.11786	+	0.812170i	0.983883	−	0.178815i	$-0.0572265\pi$
$359$	21.1803	+	15.3884i	1.11786	+	0.812170i	0.133973	+	0.990985i	$0.457226\pi$
$360$	5.95492	+	18.3273i	0.313852	+	0.965936i
$361$	−5.64590	−	17.3763i	−0.297153	−	0.914541i
$362$	15.7082	−	11.4127i	0.825605	−	0.599837i
$363$	25.3713	+	13.6251i	1.33165	+	0.715130i
$364$	1.50000	+	1.08981i	0.0786214	+	0.0571218i
$365$	−19.8992	+	14.4576i	−1.04157	+	0.756746i
$366$	−3.23607	−	9.95959i	−0.169152	−	0.520596i
$367$	−0.562306			−0.0293521			−0.0146761	−	0.999892i	$-0.504672\pi$
$367$	−0.562306			−0.0293521			−0.0146761	+	0.999892i	$0.504672\pi$
$368$	16.0623	−	11.6699i	0.837306	−	0.608338i
$369$	−8.89919	−	27.3889i	−0.463273	−	1.42581i
$370$	−8.78115	+	6.37988i	−0.456510	+	0.331674i
$371$	18.1803			0.943876
$372$	1.07295	−	3.30220i	0.0556298	−	0.171211i
$373$	−12.2533	−	8.90254i	−0.634451	−	0.460956i	0.223488	−	0.974707i	$-0.428256\pi$
$373$	−12.2533	−	8.90254i	−0.634451	−	0.460956i	−0.857939	+	0.513751i	$0.828256\pi$
$374$	8.47214	+	21.0948i	0.438084	+	1.09078i
$375$	−9.04508	+	27.8379i	−0.467086	+	1.43754i
$376$	15.0623	+	10.9434i	0.776779	+	0.564363i
$377$	−6.70820	+	4.87380i	−0.345490	+	0.251013i
$378$	4.73607	−	3.44095i	0.243597	−	0.176984i
$379$	25.3885	+	18.4459i	1.30412	+	0.947500i	0.999987	−	0.00512891i	$-0.00163259\pi$
$379$	25.3885	+	18.4459i	1.30412	+	0.947500i	0.304135	+	0.952629i	$0.401633\pi$
$380$	−0.954915	−	0.693786i	−0.0489861	−	0.0355905i
$381$	−57.9230			−2.96748
$382$	1.50000	−	4.61653i	0.0767467	−	0.236202i
$383$	20.2082	−	14.6821i	1.03259	−	0.750221i	0.0637654	−	0.997965i	$-0.479689\pi$
$383$	20.2082	−	14.6821i	1.03259	−	0.750221i	0.968826	+	0.247744i	$0.0796891\pi$
$384$	−28.8435	+	20.9560i	−1.47191	+	1.06941i
$385$	−10.1631	−	6.37988i	−0.517961	−	0.325149i
$386$	5.78115	+	4.20025i	0.294253	+	0.213787i
$387$	−46.5967			−2.36865
$388$	2.68034	+	8.24924i	0.136074	+	0.418792i
$389$	4.47214	−	13.7638i	0.226746	−	0.697853i	−0.771363	−	0.636395i	$-0.780425\pi$
$389$	4.47214	−	13.7638i	0.226746	−	0.697853i	0.998110	−	0.0614584i	$-0.0195751\pi$
$390$	5.42705	−	16.7027i	0.274809	−	0.845776i
$391$	5.35410	−	16.4782i	0.270769	−	0.833340i
$392$	−9.79837			−0.494893
$393$	−12.8992	+	39.6996i	−0.650678	+	2.00258i
$394$	−1.85410	+	1.34708i	−0.0934083	+	0.0678651i
$395$	13.6803	−	9.93935i	0.688333	−	0.500103i
$396$	−2.94427	−	7.33094i	−0.147955	−	0.368393i
$397$	−4.21885	−	12.9843i	−0.211738	−	0.651662i	−0.999369	−	0.0355153i	$-0.988693\pi$
$397$	−4.21885	−	12.9843i	−0.211738	−	0.651662i	0.787631	−	0.616147i	$-0.211307\pi$
$398$	8.78115	+	27.0256i	0.440159	+	1.35467i
$399$	1.11803	−	3.44095i	0.0559717	−	0.172263i
$400$	−24.2705			−1.21353
$401$	−22.1074	+	16.0620i	−1.10399	+	0.802096i	−0.981707	−	0.190399i	$-0.939022\pi$
$401$	−22.1074	+	16.0620i	−1.10399	+	0.802096i	−0.122284	+	0.992495i	$0.539022\pi$
$402$	−41.1246			−2.05111
$403$	3.21885	−	2.33863i	0.160342	−	0.116495i
$404$	−1.85410			−0.0922450
$405$	10.3262	+	7.50245i	0.513115	+	0.372800i
$406$	3.61803	−	11.1352i	0.179560	−	0.552629i
$407$	−7.63525	+	6.37988i	−0.378466	+	0.316239i
$408$	−7.66312	+	23.5847i	−0.379381	+	1.16761i
$409$	−25.8541			−1.27840			−0.639202	−	0.769039i	$-0.720735\pi$
$409$	−25.8541			−1.27840			−0.639202	+	0.769039i	$0.720735\pi$
$410$	27.0344			1.33514
$411$	−5.39919	+	16.6170i	−0.266322	+	0.819656i
$412$	3.80902	−	11.7229i	0.187657	−	0.577548i
$413$	−5.42705	+	16.7027i	−0.267048	+	0.821888i
$414$	−7.88197	+	24.2582i	−0.387377	+	1.19223i
$415$	4.14590	−	12.7598i	0.203514	−	0.626352i
$416$	6.27051			0.307437
$417$	3.19098	−	9.82084i	0.156263	−	0.480928i
$418$	−3.88197	−	2.43690i	−0.189873	−	0.119193i
$419$	−8.57953	+	26.4051i	−0.419137	+	1.28997i	0.489360	+	0.872082i	$0.337230\pi$
$419$	−8.57953	+	26.4051i	−0.419137	+	1.28997i	−0.908498	+	0.417890i	$0.862770\pi$
$420$	1.80902	+	5.56758i	0.0882710	+	0.271670i
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	−27.1803	+	19.7477i	−1.32312	+	0.961302i
$423$	−32.0902			−1.56028
$424$	20.3262	−	14.7679i	0.987129	−	0.717191i
$425$	−17.1353	+	12.4495i	−0.831182	+	0.603889i
$426$	−3.92705	+	12.0862i	−0.190266	+	0.585579i
$427$	1.23607	+	3.80423i	0.0598175	+	0.184099i
$428$	1.60081	+	4.92680i	0.0773782	+	0.238146i
$429$	3.92705	−	15.6129i	0.189600	−	0.753799i
$430$	13.5172	−	41.6017i	0.651858	−	2.00621i
$431$	−19.0172	+	13.8168i	−0.916027	+	0.665533i	−0.942532	−	0.334116i	$-0.891562\pi$
$431$	−19.0172	+	13.8168i	−0.916027	+	0.665533i	0.0265047	+	0.999649i	$0.491562\pi$
$432$	3.35410	−	10.3229i	0.161374	−	0.496659i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$	−1.73607	+	5.34307i	−0.0833339	+	0.256475i
$435$	−26.1803			−1.25525
$436$	−0.326238	+	1.00406i	−0.0156240	+	0.0480856i
$437$	1.07953	+	3.32244i	0.0516408	+	0.158934i
$438$	46.5967			2.22648
$439$	15.3262	+	11.1352i	0.731481	+	0.531452i	0.890032	−	0.455899i	$-0.150682\pi$
$439$	15.3262	+	11.1352i	0.731481	+	0.531452i	−0.158550	+	0.987351i	$0.550682\pi$
$440$	−16.5451	+	1.12257i	−0.788756	+	0.0535164i
$441$	13.6631	−	9.92684i	0.650625	−	0.472707i
$442$	10.2812	−	7.46969i	0.489025	−	0.355297i
$443$	10.4721	−	32.2299i	0.497546	−	1.53129i	−0.315405	−	0.948957i	$-0.602140\pi$
$443$	10.4721	−	32.2299i	0.497546	−	1.53129i	0.812951	−	0.582332i	$-0.197860\pi$
$444$	4.85410			0.230365
$445$	1.31966	+	4.06150i	0.0625579	+	0.192533i
$446$	15.2533	+	11.0822i	0.722264	+	0.524756i
$447$	31.7705	−	23.0826i	1.50269	−	1.09177i
$448$	5.54508	−	4.02874i	0.261981	−	0.190340i
$449$	2.23607	+	1.62460i	0.105527	+	0.0766695i	0.639297	−	0.768960i	$-0.279225\pi$
$449$	2.23607	+	1.62460i	0.105527	+	0.0766695i	−0.533771	+	0.845629i	$0.679225\pi$
$450$	25.2254	−	18.3273i	1.18914	−	0.863959i
$451$	24.7254	−	1.67760i	1.16427	−	0.0789951i
$452$	−4.11803	−	2.99193i	−0.193696	−	0.140728i
$453$	−1.61803	+	4.97980i	−0.0760219	+	0.233971i
$454$	−48.3607			−2.26968
$455$	−2.07295	+	6.37988i	−0.0971813	+	0.299093i
$456$	−1.54508	−	4.75528i	−0.0723552	−	0.222687i
$457$	−24.0172	+	17.4495i	−1.12348	+	0.816255i	−0.984733	−	0.174073i	$-0.944307\pi$
$457$	−24.0172	+	17.4495i	−1.12348	+	0.816255i	−0.138746	+	0.990328i	$0.544307\pi$
$458$	−1.38197			−0.0645750
$459$	−2.92705	−	9.00854i	−0.136623	−	0.420482i
$460$	−4.57295	−	3.32244i	−0.213215	−	0.154910i
$461$	7.85410	+	5.70634i	0.365802	+	0.265771i	0.755468	−	0.655186i	$-0.227410\pi$
$461$	7.85410	+	5.70634i	0.365802	+	0.265771i	−0.389666	+	0.920956i	$0.627410\pi$
$462$	8.47214	+	21.0948i	0.394159	+	0.981417i
$463$	26.9164	−	19.5559i	1.25091	−	0.908840i	0.252637	−	0.967561i	$-0.418702\pi$
$463$	26.9164	−	19.5559i	1.25091	−	0.908840i	0.998274	+	0.0587207i	$0.0187021\pi$
$464$	−6.70820	−	20.6457i	−0.311421	−	0.958454i
$465$	12.5623			0.582563
$466$	−37.6976	−	27.3889i	−1.74631	−	1.26877i
$467$	7.36475	+	22.6664i	0.340800	+	1.04887i	0.963794	+	0.266647i	$0.0859159\pi$
$467$	7.36475	+	22.6664i	0.340800	+	1.04887i	−0.622994	+	0.782226i	$0.714084\pi$
$468$	−3.57295	+	2.59590i	−0.165160	+	0.119995i
$469$	15.7082			0.725337
$470$	9.30902	−	28.6502i	0.429393	−	1.32154i
$471$	12.5902	−	38.7486i	0.580124	−	1.78544i
$472$	7.50000	+	23.0826i	0.345215	+	1.06246i
$473$	9.78115	−	38.8873i	0.449738	−	1.78804i
$474$	−32.0344			−1.47139
$475$	1.31966	−	4.06150i	0.0605502	−	0.186354i
$476$	−1.30902	+	4.02874i	−0.0599987	+	0.184657i
$477$	−13.3820	+	41.1855i	−0.612718	+	1.88575i
$478$	10.1631	+	7.38394i	0.464850	+	0.337733i
$479$	−10.3262	−	7.50245i	−0.471818	−	0.342796i	0.326331	−	0.945255i	$-0.394187\pi$
$479$	−10.3262	−	7.50245i	−0.471818	−	0.342796i	−0.798149	+	0.602460i	$0.794187\pi$
$480$	16.0172	+	11.6372i	0.731083	+	0.531163i
$481$	4.50000	+	3.26944i	0.205182	+	0.149074i
$482$	6.66312	+	4.84104i	0.303497	+	0.220503i
$483$	5.35410	−	16.4782i	0.243620	−	0.749785i
$484$	6.73607	−	0.918300i	0.306185	−	0.0417409i
$485$	−25.3885	+	18.4459i	−1.15283	+	0.837583i
$486$	−10.8262	−	33.3197i	−0.491088	−	1.51141i
$487$	3.97214	+	12.2250i	0.179995	+	0.553967i	0.999826	−	0.0186380i	$-0.00593302\pi$
$487$	3.97214	+	12.2250i	0.179995	+	0.553967i	−0.819832	+	0.572605i	$0.805933\pi$
$488$	4.47214	+	3.24920i	0.202444	+	0.147084i
$489$	56.4508			2.55280
$490$	4.89919	+	15.0781i	0.221323	+	0.681161i
$491$	1.40983	+	1.02430i	0.0636247	+	0.0462261i	0.619143	−	0.785278i	$-0.287480\pi$
$491$	1.40983	+	1.02430i	0.0636247	+	0.0462261i	−0.555518	+	0.831504i	$0.687480\pi$
$492$	−9.78115	−	7.10642i	−0.440968	−	0.320382i
$493$	−15.3262	−	11.1352i	−0.690259	−	0.501503i
$494$	−0.791796	+	2.43690i	−0.0356246	+	0.109641i
$495$	21.9336	−	18.3273i	0.985843	−	0.823753i
$496$	3.21885	+	9.90659i	0.144530	+	0.444819i
$497$	1.50000	−	4.61653i	0.0672842	−	0.207079i
$498$	−20.5623	+	14.9394i	−0.921419	+	0.669450i
$499$	5.48936	+	16.8945i	0.245737	+	0.756302i	0.995514	+	0.0946112i	$0.0301608\pi$
$499$	5.48936	+	16.8945i	0.245737	+	0.756302i	−0.749777	+	0.661691i	$0.769839\pi$
$500$	2.13525	+	6.57164i	0.0954915	+	0.293893i
$501$	11.2082	−	8.14324i	0.500746	−	0.363813i
$502$	−0.0450850	+	0.138757i	−0.00201224	+	0.00619304i
$503$	11.1246			0.496022			0.248011	−	0.968757i	$-0.420223\pi$
$503$	11.1246			0.496022			0.248011	+	0.968757i	$0.420223\pi$
$504$	−4.30902	+	13.2618i	−0.191939	+	0.590727i
$505$	−2.07295	−	6.37988i	−0.0922450	−	0.283901i
$506$	−18.5902	−	11.6699i	−0.826434	−	0.518792i
$507$	25.0344			1.11182
$508$	−11.0623	+	8.03724i	−0.490810	+	0.356595i
$509$	5.52786	+	17.0130i	0.245018	+	0.754089i	0.995633	+	0.0933491i	$0.0297573\pi$
$509$	5.52786	+	17.0130i	0.245018	+	0.754089i	−0.750615	+	0.660740i	$0.770243\pi$
$510$	40.1246			1.77675
$511$	−17.7984			−0.787354
$512$	1.63525	−	5.03280i	0.0722687	−	0.222420i
$513$	1.54508	+	1.12257i	0.0682172	+	0.0495627i
$514$	18.6353	−	13.5393i	0.821966	−	0.597193i
$515$	44.5967			1.96517
$516$	−15.8262	+	11.4984i	−0.696711	+	0.506190i
$517$	6.73607	−	26.7809i	0.296252	−	1.17782i
$518$	−7.85410			−0.345089
$519$	12.7082	−	9.23305i	0.557828	−	0.405286i
$520$	2.86475	+	8.81678i	0.125627	+	0.386641i
$521$	−31.4164	+	22.8254i	−1.37638	+	0.999997i	−0.379170	+	0.925327i	$0.623790\pi$
$521$	−31.4164	+	22.8254i	−1.37638	+	0.999997i	−0.997208	+	0.0746698i	$0.976210\pi$
$522$	22.5623	+	16.3925i	0.987525	+	0.717479i
$523$	−4.65248			−0.203439			−0.101719	−	0.994813i	$-0.532434\pi$
$523$	−4.65248			−0.203439			−0.101719	+	0.994813i	$0.532434\pi$
$524$	3.04508	+	9.37181i	0.133025	+	0.409409i
$525$	−17.1353	+	12.4495i	−0.747844	+	0.543340i
$526$	−9.70820	−	7.05342i	−0.423298	−	0.307544i
$527$	7.35410	+	5.34307i	0.320350	+	0.232748i
$528$	35.6976	+	22.4091i	1.55354	+	0.975230i
$529$	−1.93769	−	5.96361i	−0.0842476	−	0.259287i
$530$	−32.8885	−	23.8949i	−1.42859	−	1.03793i
$531$	−33.8435	−	24.5887i	−1.46868	−	1.06706i
$532$	−0.263932	−	0.812299i	−0.0114429	−	0.0352176i
$533$	−4.28115	−	13.1760i	−0.185437	−	0.570717i
$534$	2.50000	−	7.69421i	0.108186	−	0.332961i
$535$	−15.1631	+	11.0167i	−0.655559	+	0.476291i
$536$	17.5623	−	12.7598i	0.758576	−	0.551138i
$537$	29.2705			1.26312
$538$	−21.4443	+	15.5802i	−0.924528	+	0.671709i
$539$	5.41641	+	13.4863i	0.233301	+	0.580896i
$540$	−3.09017			−0.132980
$541$	29.5623			1.27098			0.635491	−	0.772108i	$-0.280798\pi$
$541$	29.5623			1.27098			0.635491	+	0.772108i	$0.280798\pi$
$542$	−28.9894	−	21.0620i	−1.24520	−	0.904690i
$543$	−9.70820	−	29.8788i	−0.416619	−	1.28222i
$544$	4.42705	+	13.6251i	0.189808	+	0.584170i
$545$	−3.81966			−0.163616
$546$	10.2812	−	7.46969i	0.439993	−	0.319673i
$547$	−27.0689			−1.15738			−0.578691	−	0.815547i	$-0.696436\pi$
$547$	−27.0689			−1.15738			−0.578691	+	0.815547i	$0.696436\pi$
$548$	1.27458	+	3.92274i	0.0544472	+	0.167571i
$549$	−9.52786			−0.406639
$550$	10.0000	+	24.8990i	0.426401	+	1.06170i
$551$	3.81966			0.162723
$552$	−7.39919	−	22.7724i	−0.314930	−	0.969256i
$553$	12.2361			0.520331
$554$	−37.5066	+	27.2501i	−1.59350	+	1.15775i
$555$	5.42705	+	16.7027i	0.230365	+	0.708992i
$556$	−0.753289	−	2.31838i	−0.0319466	−	0.0983214i
$557$	3.15654	+	9.71483i	0.133747	+	0.411631i	0.995393	−	0.0958789i	$-0.0305662\pi$
$557$	3.15654	+	9.71483i	0.133747	+	0.411631i	−0.861646	+	0.507510i	$0.830566\pi$
$558$	−10.8262	−	7.86572i	−0.458311	−	0.332983i
$559$	−22.4164			−0.948113
$560$	−14.2082	−	10.3229i	−0.600406	−	0.436221i
$561$	36.6976	−	2.48990i	1.54937	−	0.105124i
$562$	−13.1353	+	9.54332i	−0.554077	+	0.402561i
$563$	24.9443			1.05128			0.525638	−	0.850708i	$-0.323827\pi$
$563$	24.9443			1.05128			0.525638	+	0.850708i	$0.323827\pi$
$564$	−10.8992	+	7.91872i	−0.458939	+	0.333438i
$565$	5.69098	−	17.5150i	0.239421	−	0.736863i
$566$	−14.2812	+	43.9529i	−0.600282	+	1.84748i
$567$	2.85410	+	8.78402i	0.119861	+	0.368894i
$568$	−2.07295	−	6.37988i	−0.0869790	−	0.267694i
$569$	−29.6976	−	21.5765i	−1.24499	−	0.904536i	−0.247066	−	0.968999i	$-0.579467\pi$
$569$	−29.6976	−	21.5765i	−1.24499	−	0.904536i	−0.997920	+	0.0644629i	$0.979467\pi$
$570$	−6.54508	+	4.75528i	−0.274143	+	0.199177i
$571$	−7.10739	−	21.8743i	−0.297435	−	0.915411i	−0.982393	−	0.186828i	$-0.940179\pi$
$571$	−7.10739	−	21.8743i	−0.297435	−	0.915411i	0.684958	−	0.728583i	$-0.259821\pi$
$572$	−1.41641	−	3.52671i	−0.0592230	−	0.147459i
$573$	−6.35410	−	4.61653i	−0.265446	−	0.192858i
$574$	15.8262	+	11.4984i	0.660574	+	0.479935i
$575$	6.31966	−	19.4499i	0.263548	−	0.811117i
$576$	5.04508	+	15.5272i	0.210212	+	0.646966i
$577$	7.12461			0.296601			0.148301	−	0.988942i	$-0.452620\pi$
$577$	7.12461			0.296601			0.148301	+	0.988942i	$0.452620\pi$
$578$	1.23607	+	0.898056i	0.0514136	+	0.0373542i
$579$	9.35410	−	6.79615i	0.388743	−	0.282438i
$580$	−5.00000	+	3.63271i	−0.207614	+	0.150840i
$581$	7.85410	−	5.70634i	0.325843	−	0.236739i
$582$	59.4508			2.46432
$583$	−31.5623	−	19.8132i	−1.30718	−	0.820578i
$584$	−19.8992	+	14.4576i	−0.823434	+	0.598260i
$585$	−12.9271	−	9.39205i	−0.534468	−	0.388314i
$586$	24.0344	−	17.4620i	0.992854	−	0.721350i
$587$	2.42705	+	1.76336i	0.100175	+	0.0727815i	0.636745	−	0.771074i	$-0.280280\pi$
$587$	2.42705	+	1.76336i	0.100175	+	0.0727815i	−0.536570	+	0.843856i	$0.680280\pi$
$588$	2.19098	−	6.74315i	0.0903546	−	0.278083i
$589$	−1.83282			−0.0755199
$590$	31.7705	−	23.0826i	1.30797	−	0.950297i
$591$	1.14590	+	3.52671i	0.0471359	+	0.145070i
$592$	−11.7812	+	8.55951i	−0.484202	+	0.351794i
$593$	−4.20163			−0.172540			−0.0862701	−	0.996272i	$-0.527495\pi$
$593$	−4.20163			−0.172540			−0.0862701	+	0.996272i	$0.527495\pi$
$594$	−11.9721	+	0.812299i	−0.491223	+	0.0333290i
$595$	−15.3262			−0.628314
$596$	2.86475	−	8.81678i	0.117345	−	0.361149i
$597$	45.9787			1.88178
$598$	−3.79180	+	11.6699i	−0.155058	+	0.477220i
$599$	−6.28115	+	4.56352i	−0.256641	+	0.186461i	−0.708665	−	0.705545i	$-0.750702\pi$
$599$	−6.28115	+	4.56352i	−0.256641	+	0.186461i	0.452024	+	0.892006i	$0.350702\pi$
$600$	−9.04508	+	27.8379i	−0.369264	+	1.13648i
$601$	−1.25329	−	3.85723i	−0.0511227	−	0.157340i	0.922236	−	0.386628i	$-0.126360\pi$
$601$	−1.25329	−	3.85723i	−0.0511227	−	0.157340i	−0.973359	+	0.229288i	$0.926360\pi$
$602$	25.6074	−	18.6049i	1.04368	−	0.758277i
$603$	−11.5623	+	35.5851i	−0.470853	+	1.44914i
$604$	0.381966	+	1.17557i	0.0155420	+	0.0478333i
$605$	10.6910	+	22.1518i	0.434650	+	0.900599i
$606$	−3.92705	+	12.0862i	−0.159526	+	0.490969i
$607$	−7.14590	−	5.19180i	−0.290043	−	0.210729i	0.433243	−	0.901277i	$-0.357369\pi$
$607$	−7.14590	−	5.19180i	−0.290043	−	0.210729i	−0.723286	+	0.690549i	$0.757369\pi$
$608$	−2.33688	−	1.69784i	−0.0947730	−	0.0688566i
$609$	−15.3262	−	11.1352i	−0.621051	−	0.451220i
$610$	2.76393	−	8.50651i	0.111908	−	0.344418i
$611$	−15.4377			−0.624542
$612$	−8.16312	−	5.93085i	−0.329975	−	0.239741i
$613$	−4.48936	−	13.8168i	−0.181323	−	0.558056i	0.818542	−	0.574446i	$-0.194783\pi$
$613$	−4.48936	−	13.8168i	−0.181323	−	0.558056i	−0.999866	+	0.0163902i	$0.994783\pi$
$614$	−0.208204	−	0.640786i	−0.00840243	−	0.0258600i
$615$	13.5172	−	41.6017i	0.545067	−	1.67754i
$616$	−10.1631	−	6.37988i	−0.409484	−	0.257053i
$617$	10.0517	−	30.9358i	0.404665	−	1.24543i	−0.516510	−	0.856281i	$-0.672769\pi$
$617$	10.0517	−	30.9358i	0.404665	−	1.24543i	0.921175	−	0.389149i	$-0.127231\pi$
$618$	−68.3500	−	49.6592i	−2.74944	−	1.99759i
$619$	11.7082	+	8.50651i	0.470592	+	0.341905i	0.797672	−	0.603091i	$-0.206065\pi$
$619$	11.7082	+	8.50651i	0.470592	+	0.341905i	−0.327080	+	0.944997i	$0.606065\pi$
$620$	2.39919	−	1.74311i	0.0963537	−	0.0700050i
$621$	7.39919	+	5.37582i	0.296919	+	0.215724i
$622$	−24.4164	−	17.7396i	−0.979009	−	0.711292i
$623$	−0.954915	+	2.93893i	−0.0382579	+	0.117746i
$624$	7.28115	−	22.4091i	0.291479	−	0.897081i
$625$	−20.2254	+	14.6946i	−0.809017	+	0.587785i
$626$	−5.76393			−0.230373
$627$	−5.69098	+	4.75528i	−0.227276	+	0.189908i
$628$	−2.97214	−	9.14729i	−0.118601	−	0.365017i
$629$	−3.92705	+	12.0862i	−0.156582	+	0.481909i
$630$	22.5623			0.898904
$631$	16.1459			0.642758			0.321379	−	0.946951i	$-0.395854\pi$
$631$	16.1459			0.642758			0.321379	+	0.946951i	$0.395854\pi$
$632$	13.6803	−	9.93935i	0.544175	−	0.395366i
$633$	16.7984	+	51.7001i	0.667675	+	2.05489i
$634$	32.5795	+	23.6704i	1.29390	+	0.940072i
$635$	−40.0238	−	29.0790i	−1.58830	−	1.15396i
$636$	5.61803	+	17.2905i	0.222770	+	0.685614i
$637$	6.57295	−	4.77553i	0.260430	−	0.189213i
$638$	−18.4164	+	15.3884i	−0.729113	+	0.609233i
$639$	9.35410	+	6.79615i	0.370043	+	0.268852i
$640$	−30.4508			−1.20368
$641$	3.21885	+	9.90659i	0.127137	+	0.391287i	0.994284	−	0.106764i	$-0.0340491\pi$
$641$	3.21885	+	9.90659i	0.127137	+	0.391287i	−0.867148	+	0.498051i	$0.834049\pi$
$642$	35.5066			1.40133
$643$	−1.66312	+	1.20833i	−0.0655870	+	0.0476518i	−0.620096	−	0.784526i	$-0.712906\pi$
$643$	−1.66312	+	1.20833i	−0.0655870	+	0.0476518i	0.554509	+	0.832178i	$0.312906\pi$
$644$	−1.26393	−	3.88998i	−0.0498059	−	0.153287i
$645$	−57.2599	−	41.6017i	−2.25461	−	1.63807i
$646$	−5.85410			−0.230327
$647$	−0.0729490	+	0.224514i	−0.00286792	+	0.00882656i	−0.952480	−	0.304600i	$-0.901477\pi$
$647$	−0.0729490	+	0.224514i	−0.00286792	+	0.00882656i	0.949612	+	0.313427i	$0.101477\pi$
$648$	10.3262	+	7.50245i	0.405653	+	0.294724i
$649$	27.6246	−	23.0826i	1.08436	−	0.906072i
$650$	12.1353	−	8.81678i	0.475984	−	0.345823i
$651$	7.35410	+	5.34307i	0.288230	+	0.209411i
$652$	10.7812	−	7.83297i	0.422223	−	0.306763i
$653$	−12.1910	+	8.85727i	−0.477070	+	0.346612i	−0.800190	−	0.599746i	$-0.795268\pi$
$653$	−12.1910	+	8.85727i	−0.477070	+	0.346612i	0.323120	+	0.946358i	$0.395268\pi$
$654$	5.85410	+	4.25325i	0.228914	+	0.166315i
$655$	−28.8435	+	20.9560i	−1.12701	+	0.818819i
$656$	36.2705			1.41613
$657$	13.1008	−	40.3202i	0.511111	−	1.57304i
$658$	17.6353	−	12.8128i	0.687494	−	0.499493i
$659$	−5.00000	+	3.63271i	−0.194772	+	0.141510i	−0.680897	−	0.732379i	$-0.738410\pi$
$659$	−5.00000	+	3.63271i	−0.194772	+	0.141510i	0.486125	+	0.873889i	$0.338410\pi$
$660$	2.92705	−	11.6372i	0.113935	−	0.452977i
$661$	−19.3435	−	14.0538i	−0.752373	−	0.546631i	0.144188	−	0.989550i	$-0.453943\pi$
$661$	−19.3435	−	14.0538i	−0.752373	−	0.546631i	−0.896562	+	0.442919i	$0.853943\pi$
$662$	11.7639			0.457218
$663$	−6.35410	−	19.5559i	−0.246773	−	0.759489i
$664$	4.14590	−	12.7598i	0.160892	−	0.495175i
$665$	2.50000	−	1.81636i	0.0969458	−	0.0704353i
$666$	5.78115	−	17.7926i	0.224015	−	0.689448i
$667$	18.2918			0.708261
$668$	1.01064	−	3.11044i	0.0391030	−	0.120347i
$669$	24.6803	−	17.9313i	0.954197	−	0.693265i
$670$	−28.4164	−	20.6457i	−1.09782	−	0.797614i
$671$	2.00000	−	7.95148i	0.0772091	−	0.306963i
$672$	4.42705	+	13.6251i	0.170777	+	0.525598i
$673$	7.93363	+	24.4172i	0.305819	+	0.941214i	0.979370	+	0.202073i	$0.0647680\pi$
$673$	7.93363	+	24.4172i	0.305819	+	0.941214i	−0.673551	+	0.739140i	$0.735232\pi$
$674$	6.50000	−	20.0049i	0.250371	−	0.770562i
$675$	−3.45492	−	10.6331i	−0.132980	−	0.409270i
$676$	4.78115	−	3.47371i	0.183890	−	0.133604i
$677$	7.85410			0.301858			0.150929	−	0.988545i	$-0.451774\pi$
$677$	7.85410			0.301858			0.150929	+	0.988545i	$0.451774\pi$
$678$	−28.2254	+	20.5070i	−1.08399	+	0.787565i
$679$	−22.7082			−0.871461
$680$	−17.1353	+	12.4495i	−0.657107	+	0.477416i
$681$	−24.1803	+	74.4194i	−0.926593	+	2.85176i
$682$	8.83688	−	7.38394i	0.338382	−	0.282746i
$683$	−7.61803	+	23.4459i	−0.291496	+	0.897132i	0.692880	+	0.721053i	$0.256342\pi$
$683$	−7.61803	+	23.4459i	−0.291496	+	0.897132i	−0.984376	+	0.176079i	$0.943658\pi$
$684$	2.03444			0.0777888
$685$	−12.0729	+	8.77151i	−0.461284	+	0.335142i
$686$	−9.20820	+	28.3399i	−0.351571	+	1.08202i
$687$	−0.690983	+	2.12663i	−0.0263626	+	0.0811359i
$688$	18.1353	−	55.8146i	0.691400	−	2.12791i
$689$	−6.43769	+	19.8132i	−0.245257	+	0.754822i
$690$	−31.3435	+	22.7724i	−1.19323	+	0.866929i
$691$	3.70820			0.141067			0.0705334	−	0.997509i	$-0.477530\pi$
$691$	3.70820			0.141067			0.0705334	+	0.997509i	$0.477530\pi$
$692$	1.14590	−	3.52671i	0.0435605	−	0.134065i
$693$	20.6353	−	1.40008i	0.783869	−	0.0531848i
$694$	6.92705	−	21.3193i	0.262947	−	0.809268i
$695$	7.13525	−	5.18407i	0.270656	−	0.196643i
$696$	−26.1803			−0.992363
$697$	25.6074	−	18.6049i	0.969949	−	0.704709i
$698$	−21.7082			−0.821668
$699$	−60.9959	+	44.3161i	−2.30708	+	1.67619i
$700$	−1.54508	+	4.75528i	−0.0583987	+	0.179733i
$701$	−11.6803	+	35.9484i	−0.441160	+	1.35775i	0.445480	+	0.895292i	$0.353033\pi$
$701$	−11.6803	+	35.9484i	−0.441160	+	1.35775i	−0.886640	+	0.462460i	$0.846967\pi$
$702$	2.07295	+	6.37988i	0.0782384	+	0.240793i
$703$	−0.791796	−	2.43690i	−0.0298632	−	0.0919093i
$704$	−14.0172	+	0.951057i	−0.528294	+	0.0358443i
$705$	−39.4336	−	28.6502i	−1.48516	−	1.07903i
$706$	−7.20820	+	5.23707i	−0.271284	+	0.197100i
$707$	1.50000	−	4.61653i	0.0564133	−	0.173622i
$708$	−17.5623			−0.660032
$709$	−6.70820	+	20.6457i	−0.251932	+	0.775367i	0.742487	+	0.669861i	$0.233646\pi$
$709$	−6.70820	+	20.6457i	−0.251932	+	0.775367i	−0.994419	+	0.105506i	$0.966354\pi$
$710$	−8.78115	+	6.37988i	−0.329551	+	0.239433i
$711$	−9.00658	+	27.7194i	−0.337773	+	1.03956i
$712$	1.31966	+	4.06150i	0.0494564	+	0.152211i
$713$	−8.77709			−0.328705
$714$	23.4894	+	17.0660i	0.879067	+	0.638680i
$715$	10.5517	−	8.81678i	0.394610	−	0.329729i
$716$	5.59017	−	4.06150i	0.208914	−	0.151785i
$717$	16.4443	−	11.9475i	0.614123	−	0.446186i
$718$	13.0902	−	40.2874i	0.488521	−	1.50351i
$719$	−14.6738			−0.547239			−0.273619	−	0.961838i	$-0.588221\pi$
$719$	−14.6738			−0.547239			−0.273619	+	0.961838i	$0.588221\pi$
$720$	33.8435	−	24.5887i	1.26127	−	0.916367i
$721$	26.1074	+	18.9681i	0.972290	+	0.706410i
$722$	−23.9164	+	17.3763i	−0.890077	+	0.646678i
$723$	10.7812	−	7.83297i	0.400955	−	0.291311i
$724$	−6.00000	−	4.35926i	−0.222988	−	0.162010i
$725$	−18.0902	−	13.1433i	−0.671852	−	0.488129i
$726$	8.28115	−	45.8550i	0.307342	−	1.70184i
$727$	−7.04508	−	5.11855i	−0.261288	−	0.189837i	0.449427	−	0.893317i	$-0.351628\pi$
$727$	−7.04508	−	5.11855i	−0.261288	−	0.189837i	−0.710715	+	0.703480i	$0.751628\pi$
$728$	−2.07295	+	6.37988i	−0.0768286	+	0.236454i
$729$	−39.5623			−1.46527
$730$	32.1976	+	23.3929i	1.19169	+	0.865810i
$731$	−15.8262	−	48.7082i	−0.585355	−	1.80154i
$732$	−3.23607	+	2.35114i	−0.119609	+	0.0869007i
$733$	−9.00000			−0.332423			−0.166211	−	0.986090i	$-0.553153\pi$
$733$	−9.00000			−0.332423			−0.166211	+	0.986090i	$0.553153\pi$
$734$	0.281153	+	0.865300i	0.0103775	+	0.0319388i
$735$	25.6525			0.946206
$736$	−11.1910	−	8.13073i	−0.412505	−	0.299703i
$737$	−27.2705	−	17.1190i	−1.00452	−	0.630587i
$738$	−37.6976	+	27.3889i	−1.38767	+	1.00820i
$739$	−1.84752	−	5.68609i	−0.0679623	−	0.209166i	0.911308	−	0.411726i	$-0.135074\pi$
$739$	−1.84752	−	5.68609i	−0.0679623	−	0.209166i	−0.979270	+	0.202560i	$0.935074\pi$
$740$	3.35410	+	2.43690i	0.123299	+	0.0895821i
$741$	3.35410	+	2.43690i	0.123216	+	0.0895217i
$742$	−9.09017	−	27.9767i	−0.333711	−	1.02706i
$743$	−4.32624	+	3.14320i	−0.158714	+	0.115313i	−0.664308	−	0.747459i	$-0.731274\pi$
$743$	−4.32624	+	3.14320i	−0.158714	+	0.115313i	0.505594	+	0.862772i	$0.331274\pi$
$744$	12.5623			0.460556
$745$	33.5410			1.22885
$746$	−7.57295	+	23.3071i	−0.277265	+	0.853335i
$747$	7.14590	+	21.9928i	0.261455	+	0.804675i
$748$	6.66312	−	5.56758i	0.243628	−	0.203571i
$749$	−13.5623			−0.495556
$750$	47.3607			1.72937
$751$	−13.9164	+	42.8303i	−0.507817	+	1.56290i	0.288166	+	0.957581i	$0.406955\pi$
$751$	−13.9164	+	42.8303i	−0.507817	+	1.56290i	−0.795983	+	0.605319i	$0.793045\pi$
$752$	12.4894	−	38.4383i	0.455440	−	1.40170i
$753$	0.190983	+	0.138757i	0.00695981	+	0.00505660i
$754$	10.8541	+	7.88597i	0.395283	+	0.287190i
$755$	−3.61803	+	2.62866i	−0.131674	+	0.0956666i
$756$	−1.80902	−	1.31433i	−0.0657933	−	0.0478016i
$757$	14.6631	+	10.6534i	0.532940	+	0.387204i	0.821456	−	0.570271i	$-0.193162\pi$
$757$	14.6631	+	10.6534i	0.532940	+	0.387204i	−0.288516	+	0.957475i	$0.593162\pi$
$758$	15.6910	−	48.2919i	0.569922	−	1.75404i
$759$	−27.2533	+	22.7724i	−0.989232	+	0.826584i
$760$	1.31966	−	4.06150i	0.0478691	−	0.147326i
$761$	−6.41641	−	19.7477i	−0.232595	−	0.715853i	−0.997431	−	0.0716285i	$-0.977180\pi$
$761$	−6.41641	−	19.7477i	−0.232595	−	0.715853i	0.764837	−	0.644224i	$-0.222820\pi$
$762$	28.9615	+	89.1343i	1.04916	+	3.22900i
$763$	−2.23607	−	1.62460i	−0.0809511	−	0.0588144i
$764$	−1.85410			−0.0670791
$765$	11.2812	−	34.7198i	0.407871	−	1.25530i
$766$	−32.6976	−	23.7562i	−1.18141	−	0.858345i
$767$	−16.2812	−	11.8290i	−0.587878	−	0.427119i
$768$	28.7254	+	20.8702i	1.03654	+	0.753090i
$769$	−7.96556	+	24.5155i	−0.287245	+	0.884050i	0.698471	+	0.715638i	$0.253864\pi$
$769$	−7.96556	+	24.5155i	−0.287245	+	0.884050i	−0.985717	+	0.168412i	$0.946136\pi$
$770$	−4.73607	+	18.8294i	−0.170676	+	0.678563i
$771$	−11.5172	−	35.4464i	−0.414783	−	1.27657i
$772$	0.843459	−	2.59590i	0.0303567	−	0.0934285i
$773$	40.6976	−	29.5685i	1.46379	−	1.06351i	0.481434	−	0.876482i	$-0.340116\pi$
$773$	40.6976	−	29.5685i	1.46379	−	1.06351i	0.982356	−	0.187023i	$-0.0598839\pi$
$774$	23.2984	+	71.7050i	0.837443	+	2.57738i
$775$	8.68034	+	6.30664i	0.311807	+	0.226541i
$776$	−25.3885	+	18.4459i	−0.911396	+	0.662168i
$777$	−3.92705	+	12.0862i	−0.140882	+	0.433591i
$778$	−23.4164			−0.839519
$779$	−1.97214	+	6.06961i	−0.0706591	+	0.217466i
$780$	−6.70820			−0.240192
$781$	−7.63525	+	6.37988i	−0.273211	+	0.228290i
$782$	−28.0344			−1.00251
$783$	8.09017	−	5.87785i	0.289119	−	0.210057i
$784$	6.57295	+	20.2295i	0.234748	+	0.722481i
$785$	28.1525	−	20.4540i	1.00480	−	0.730034i
$786$	67.5410			2.40911
$787$	13.7082	−	42.1895i	0.488645	−	1.50389i	−0.337987	−	0.941151i	$-0.609746\pi$
$787$	13.7082	−	42.1895i	0.488645	−	1.50389i	0.826632	−	0.562743i	$-0.190254\pi$
$788$	0.708204	+	0.514540i	0.0252287	+	0.0183297i
$789$	−15.7082	+	11.4127i	−0.559227	+	0.406302i
$790$	−22.1353	−	16.0822i	−0.787537	−	0.572179i
$791$	10.7812	−	7.83297i	0.383334	−	0.278508i
$792$	21.9336	−	18.3273i	0.779378	−	0.651234i
$793$	−4.58359			−0.162768
$794$	−17.8713	+	12.9843i	−0.634230	+	0.460795i
$795$	−53.2148	+	38.6628i	−1.88733	+	1.37123i
$796$	8.78115	−	6.37988i	0.311240	−	0.226129i
$797$	−17.4721	−	12.6942i	−0.618895	−	0.449653i	0.233640	−	0.972323i	$-0.424936\pi$
$797$	−17.4721	−	12.6942i	−0.618895	−	0.449653i	−0.852535	+	0.522670i	$0.824936\pi$
$798$	−5.85410			−0.207233
$799$	−10.8992	−	33.5442i	−0.385586	−	1.18671i
$800$	5.22542	+	16.0822i	0.184747	+	0.568592i
$801$	−5.95492	−	4.32650i	−0.210407	−	0.152869i
$802$	35.7705	+	25.9888i	1.26310	+	0.917696i
$803$	30.8992	+	19.3969i	1.09041	+	0.684502i
$804$	4.85410	+	14.9394i	0.171191	+	0.526872i
$805$	11.9721	−	8.69827i	0.421962	−	0.306574i
$806$	−5.20820	−	3.78398i	−0.183451	−	0.133285i
$807$	13.2533	+	40.7894i	0.466538	+	1.43586i
$808$	−2.07295	−	6.37988i	−0.0729261	−	0.224443i
$809$	−5.85410	+	18.0171i	−0.205819	+	0.633447i	0.793859	+	0.608101i	$0.208069\pi$
$809$	−5.85410	+	18.0171i	−0.205819	+	0.633447i	−0.999679	+	0.0253453i	$0.991931\pi$
$810$	6.38197	−	19.6417i	0.224239	−	0.690138i
$811$	12.0623	−	8.76378i	0.423565	−	0.307738i	−0.355506	−	0.934674i	$-0.615691\pi$
$811$	12.0623	−	8.76378i	0.423565	−	0.307738i	0.779071	+	0.626936i	$0.215691\pi$
$812$	−4.47214			−0.156941
$813$	−46.9058	+	34.0790i	−1.64506	+	1.19520i
$814$	13.6353	+	8.55951i	0.477915	+	0.300011i
$815$	39.0066	+	28.3399i	1.36634	+	0.992705i
$816$	53.8328			1.88453
$817$	8.35410	+	6.06961i	0.292273	+	0.212349i
$818$	12.9271	+	39.7854i	0.451984	+	1.39106i
$819$	−3.57295	−	10.9964i	−0.124849	−	0.384246i
$820$	−3.19098	−	9.82084i	−0.111434	−	0.342958i
$821$	−9.87132	+	7.17194i	−0.344512	+	0.250302i	−0.746563	−	0.665315i	$-0.768297\pi$
$821$	−9.87132	+	7.17194i	−0.344512	+	0.250302i	0.402051	+	0.915617i	$0.368297\pi$
$822$	28.2705			0.986047
$823$	1.32624	+	4.08174i	0.0462297	+	0.142281i	0.971507	−	0.237011i	$-0.0761677\pi$
$823$	1.32624	+	4.08174i	0.0462297	+	0.142281i	−0.925277	+	0.379292i	$0.876168\pi$
$824$	44.5967			1.55360
$825$	43.3156	−	2.93893i	1.50806	−	0.102320i
$826$	28.4164			0.988733
$827$	5.88197	+	18.1028i	0.204536	+	0.629497i	0.999732	+	0.0231448i	$0.00736787\pi$
$827$	5.88197	+	18.1028i	0.204536	+	0.629497i	−0.795196	+	0.606352i	$0.792632\pi$
$828$	9.74265			0.338580
$829$	9.47214	−	6.88191i	0.328981	−	0.239019i	−0.411017	−	0.911628i	$-0.634826\pi$
$829$	9.47214	−	6.88191i	0.328981	−	0.239019i	0.739998	+	0.672609i	$0.234826\pi$
$830$	−21.7082			−0.753503
$831$	23.1803	+	71.3418i	0.804117	+	2.47482i
$832$	2.42705	+	7.46969i	0.0841429	+	0.258965i
$833$	15.0172	+	10.9106i	0.520316	+	0.378032i
$834$	−16.7082			−0.578558
$835$	11.8328			0.409491
$836$	−0.427051	+	1.69784i	−0.0147699	+	0.0587211i
$837$	−3.88197	+	2.82041i	−0.134180	+	0.0974877i
$838$	44.9230			1.55184
$839$	−0.527864	+	0.383516i	−0.0182239	+	0.0132404i	−0.596860	−	0.802345i	$-0.703585\pi$
$839$	−0.527864	+	0.383516i	−0.0182239	+	0.0132404i	0.578636	+	0.815586i	$0.303585\pi$
$840$	−17.1353	+	12.4495i	−0.591222	+	0.429548i
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$	−1.00000	−	3.07768i	−0.0344623	−	0.106064i
$843$	8.11803	+	24.9847i	0.279600	+	0.860520i
$844$	10.3820	+	7.54294i	0.357362	+	0.259639i
$845$	17.2984	+	12.5680i	0.595082	+	0.432352i
$846$	16.0451	+	49.3817i	0.551641	+	1.69778i
$847$	−3.16312	+	17.5150i	−0.108686	+	0.601824i
$848$	−44.1246	−	32.0584i	−1.51525	−	1.10089i
$849$	60.4959	+	43.9529i	2.07622	+	1.50846i
$850$	27.7254	+	20.1437i	0.950974	+	0.690923i
$851$	−3.79180	−	11.6699i	−0.129981	−	0.400041i
$852$	4.85410			0.166299
$853$	−14.0623	−	10.2169i	−0.481484	−	0.349819i	0.320416	−	0.947277i	$-0.396177\pi$
$853$	−14.0623	−	10.2169i	−0.481484	−	0.349819i	−0.801900	+	0.597458i	$0.796177\pi$
$854$	5.23607	−	3.80423i	0.179175	−	0.130178i
$855$	2.27458	+	7.00042i	0.0777888	+	0.239409i
$856$	−15.1631	+	11.0167i	−0.518265	+	0.376541i
$857$	−1.09017			−0.0372395			−0.0186197	−	0.999827i	$-0.505927\pi$
$857$	−1.09017			−0.0372395			−0.0186197	+	0.999827i	$0.505927\pi$
$858$	−25.9894	+	1.76336i	−0.887262	+	0.0602000i
$859$	−4.73607	+	3.44095i	−0.161593	+	0.117404i	−0.665643	−	0.746270i	$-0.731843\pi$
$859$	−4.73607	+	3.44095i	−0.161593	+	0.117404i	0.504050	+	0.863674i	$0.331843\pi$
$860$	−16.7082			−0.569745
$861$	25.6074	−	18.6049i	0.872698	−	0.634052i
$862$	30.7705	+	22.3561i	1.04805	+	0.761451i
$863$	−4.06231	+	12.5025i	−0.138283	+	0.425590i	−0.996086	−	0.0883878i	$-0.971829\pi$
$863$	−4.06231	+	12.5025i	−0.138283	+	0.425590i	0.857804	+	0.513978i	$0.171829\pi$
$864$	−7.56231			−0.257275
$865$	13.4164			0.456172
$866$	7.00000	+	21.5438i	0.237870	+	0.732088i
$867$	2.00000	−	1.45309i	0.0679236	−	0.0493494i
$868$	2.14590			0.0728365
$869$	−21.2426	−	13.3350i	−0.720607	−	0.452360i
$870$	13.0902	+	40.2874i	0.443798	+	1.36587i
$871$	−5.56231	+	17.1190i	−0.188472	+	0.580056i
$872$	−3.81966			−0.129350
$873$	16.7148	−	51.4428i	0.565710	−	1.74108i
$874$	4.57295	−	3.32244i	0.154682	−	0.112383i
$875$	−18.0902			−0.611559
$876$	−5.50000	−	16.9273i	−0.185828	−	0.571919i
$877$	−30.4615	+	22.1316i	−1.02861	+	0.747330i	−0.968030	−	0.250833i	$-0.919295\pi$
$877$	−30.4615	+	22.1316i	−1.02861	+	0.747330i	−0.0605812	+	0.998163i	$0.519295\pi$
$878$	9.47214	−	29.1522i	0.319669	−	0.983840i
$879$	−14.8541	−	45.7162i	−0.501016	−	1.54197i
$880$	13.4164	+	33.4055i	0.452267	+	1.12610i
$881$	12.0238	−	37.0054i	0.405092	−	1.24675i	−0.515726	−	0.856753i	$-0.672478\pi$
$881$	12.0238	−	37.0054i	0.405092	−	1.24675i	0.920818	−	0.389992i	$-0.127522\pi$
$882$	−22.1074	−	16.0620i	−0.744395	−	0.540834i
$883$	36.9787	+	26.8666i	1.24443	+	0.904133i	0.997885	−	0.0649974i	$-0.0207039\pi$
$883$	36.9787	+	26.8666i	1.24443	+	0.904133i	0.246547	+	0.969131i	$0.420704\pi$
$884$	−3.92705	−	2.85317i	−0.132081	−	0.0959625i
$885$	−19.6353	−	60.4311i	−0.660032	−	2.03137i
$886$	−54.8328			−1.84214
$887$	11.7361	+	8.52675i	0.394059	+	0.286300i	0.767117	−	0.641508i	$-0.221691\pi$
$887$	11.7361	+	8.52675i	0.394059	+	0.286300i	−0.373058	+	0.927808i	$0.621691\pi$
$888$	5.42705	+	16.7027i	0.182120	+	0.560507i
$889$	−11.0623	−	34.0463i	−0.371018	−	1.14188i
$890$	5.59017	−	4.06150i	0.187383	−	0.136142i
$891$	4.61803	−	18.3601i	0.154710	−	0.615086i
$892$	2.22542	−	6.84915i	0.0745127	−	0.229327i
$893$	5.75329	+	4.18001i	0.192526	+	0.139879i
$894$	−51.4058	−	37.3485i	−1.71927	−	1.24912i
$895$	20.2254	+	14.6946i	0.676061	+	0.491187i
$896$	−17.8262	−	12.9515i	−0.595533	−	0.432680i
$897$	16.0623	+	11.6699i	0.536305	+	0.389648i
$898$	1.38197	−	4.25325i	0.0461168	−	0.141933i
$899$	−2.96556	+	9.12705i	−0.0989069	+	0.304404i
$900$	−9.63525	−	7.00042i	−0.321175	−	0.233347i
$901$	−47.5967			−1.58568
$902$	−14.9443	−	37.2097i	−0.497590	−	1.23895i
$903$	−15.8262	−	48.7082i	−0.526664	−	1.62091i
$904$	5.69098	−	17.5150i	0.189279	−	0.582542i
$905$	8.29180	−	25.5195i	0.275629	−	0.848298i
$906$	8.47214			0.281468
$907$	17.2254	−	12.5150i	0.571961	−	0.415554i	−0.263856	−	0.964562i	$-0.584994\pi$
$907$	17.2254	−	12.5150i	0.571961	−	0.415554i	0.835817	+	0.549008i	$0.184994\pi$
$908$	5.70820	+	17.5680i	0.189433	+	0.583016i
$909$	9.35410	+	6.79615i	0.310256	+	0.225414i
$910$	10.8541			0.359810
$911$	6.69756	+	20.6130i	0.221900	+	0.682938i	0.998591	+	0.0530569i	$0.0168965\pi$
$911$	6.69756	+	20.6130i	0.221900	+	0.682938i	−0.776691	+	0.629881i	$0.783104\pi$
$912$	−8.78115	+	6.37988i	−0.290773	+	0.211259i
$913$	−19.8541	+	1.34708i	−0.657075	+	0.0445820i
$914$	38.8607	+	28.2339i	1.28540	+	0.933896i
$915$	−11.7082	−	8.50651i	−0.387061	−	0.281216i
$916$	0.163119	+	0.502029i	0.00538960	+	0.0165875i
$917$	−25.7984			−0.851937
$918$	−12.3992	+	9.00854i	−0.409234	+	0.297326i
$919$	−11.8713	−	36.5362i	−0.391599	−	1.20522i	−0.931579	−	0.363539i	$-0.881568\pi$
$919$	−11.8713	−	36.5362i	−0.391599	−	1.20522i	0.539980	−	0.841678i	$-0.318432\pi$
$920$	6.31966	−	19.4499i	0.208353	−	0.641245i
$921$	−1.09017			−0.0359223
$922$	4.85410	−	14.9394i	0.159861	−	0.492003i
$923$	4.50000	+	3.26944i	0.148119	+	0.107615i
$924$	6.66312	−	5.56758i	0.219201	−	0.183160i
$925$	−4.63525	+	14.2658i	−0.152406	+	0.469058i
$926$	−43.5517	−	31.6421i	−1.43120	−	1.03983i
$927$	−62.1869	+	45.1814i	−2.04249	+	1.48395i
$928$	−12.2361	+	8.89002i	−0.401669	+	0.291829i
$929$	5.95492	+	4.32650i	0.195374	+	0.141948i	0.681172	−	0.732124i	$-0.261471\pi$
$929$	5.95492	+	4.32650i	0.195374	+	0.141948i	−0.485797	+	0.874071i	$0.661471\pi$
$930$	−6.28115	−	19.3314i	−0.205967	−	0.633902i
$931$	−3.74265			−0.122660
$932$	−5.50000	+	16.9273i	−0.180158	+	0.554471i
$933$	−39.5066	+	28.7032i	−1.29339	+	0.939701i
$934$	31.1976	−	22.6664i	1.02082	−	0.741666i
$935$	26.6074	+	16.7027i	0.870155	+	0.546238i
$936$	−12.9271	−	9.39205i	−0.422534	−	0.306989i
$937$	−15.6869			−0.512469			−0.256235	−	0.966615i	$-0.582482\pi$
$937$	−15.6869			−0.512469			−0.256235	+	0.966615i	$0.582482\pi$
$938$	−7.85410	−	24.1724i	−0.256446	−	0.789258i
$939$	−2.88197	+	8.86978i	−0.0940494	+	0.289454i
$940$	−11.5066			−0.375303
$941$	8.83282	−	27.1846i	0.287942	−	0.886193i	−0.697560	−	0.716526i	$-0.745731\pi$
$941$	8.83282	−	27.1846i	0.287942	−	0.886193i	0.985502	−	0.169667i	$-0.0542691\pi$
$942$	−65.9230			−2.14789
$943$	−9.44427	+	29.0665i	−0.307548	+	0.946535i
$944$	42.6246	−	30.9686i	1.38731	−	1.00794i
$945$	2.50000	−	7.69421i	0.0813250	−	0.250293i
$946$	−64.7320	+	4.39201i	−2.10462	+	0.142797i
$947$	−12.1074	−	37.2627i	−0.393437	−	1.21088i	−0.930172	−	0.367124i	$-0.880342\pi$
$947$	−12.1074	−	37.2627i	−0.393437	−	1.21088i	0.536735	−	0.843751i	$-0.319658\pi$
$948$	3.78115	+	11.6372i	0.122806	+	0.377958i
$949$	6.30244	−	19.3969i	0.204586	−	0.629650i
$950$	−6.90983			−0.224184
$951$	52.7148	−	38.2995i	1.70939	−	1.24195i
$952$	−15.3262			−0.496726
$953$	1.00000	−	0.726543i	0.0323932	−	0.0235350i	−0.571471	−	0.820622i	$-0.693627\pi$
$953$	1.00000	−	0.726543i	0.0323932	−	0.0235350i	0.603864	+	0.797087i	$0.293627\pi$
$954$	70.0689			2.26856
$955$	−2.07295	−	6.37988i	−0.0670791	−	0.206448i
$956$	1.48278	−	4.56352i	0.0479565	−	0.147595i
$957$	14.4721	+	36.0341i	0.467818	+	1.16482i
$958$	−6.38197	+	19.6417i	−0.206192	+	0.634594i
$959$	−10.7984			−0.348698
$960$	−7.66312	+	23.5847i	−0.247326	+	0.761191i
$961$	−8.15654	+	25.1033i	−0.263114	+	0.809782i
$962$	2.78115	−	8.55951i	0.0896680	−	0.275970i
$963$	9.98278	−	30.7238i	0.321691	−	0.990062i
$964$	0.972136	−	2.99193i	0.0313104	−	0.0963635i
$965$	9.87539			0.317900
$966$	−28.0344			−0.901993
$967$	−2.96149	+	9.11454i	−0.0952352	+	0.293104i	−0.987315	−	0.158774i	$-0.949246\pi$
$967$	−2.96149	+	9.11454i	−0.0952352	+	0.293104i	0.892080	+	0.451878i	$0.149246\pi$
$968$	10.6910	+	22.1518i	0.343621	+	0.711986i
$969$	−2.92705	+	9.00854i	−0.0940304	+	0.289396i
$970$	41.0795	+	29.8460i	1.31898	+	0.958298i
$971$	8.38197			0.268990			0.134495	−	0.990914i	$-0.457059\pi$
$971$	8.38197			0.268990			0.134495	+	0.990914i	$0.457059\pi$
$972$	−10.8262	+	7.86572i	−0.347252	+	0.252293i
$973$	6.38197			0.204596
$974$	16.8262	−	12.2250i	0.539147	−	0.391714i
$975$	−7.50000	−	23.0826i	−0.240192	−	0.739236i
$976$	3.70820	−	11.4127i	0.118697	−	0.365311i
$977$	−3.16312	−	9.73508i	−0.101197	−	0.311453i	0.887622	−	0.460573i	$-0.152356\pi$
$977$	−3.16312	−	9.73508i	−0.101197	−	0.311453i	−0.988819	+	0.149120i	$0.952356\pi$
$978$	−28.2254	−	86.8689i	−0.902550	−	2.77776i
$979$	4.86068	−	4.06150i	0.155348	−	0.129806i
$980$	4.89919	−	3.55947i	0.156499	−	0.113703i
$981$	5.32624	−	3.86974i	0.170054	−	0.123551i
$982$	0.871323	−	2.68166i	0.0278050	−	0.0855751i
$983$	7.58359			0.241879			0.120940	−	0.992660i	$-0.461409\pi$
$983$	7.58359			0.241879			0.120940	+	0.992660i	$0.461409\pi$
$984$	13.5172	−	41.6017i	0.430913	−	1.32621i
$985$	−0.978714	+	3.01217i	−0.0311844	+	0.0959758i
$986$	−9.47214	+	29.1522i	−0.301654	+	0.928396i
$987$	−10.8992	−	33.5442i	−0.346925	−	1.06773i
$988$	0.978714			0.0311370
$989$	40.0066	+	29.0665i	1.27214	+	0.924260i
$990$	−39.1697	−	24.5887i	−1.24489	−	0.781481i
$991$	−38.0238	+	27.6259i	−1.20787	+	0.877566i	−0.995035	−	0.0995233i	$-0.968268\pi$
$991$	−38.0238	+	27.6259i	−1.20787	+	0.877566i	−0.212831	+	0.977089i	$0.568268\pi$
$992$	5.87132	−	4.26577i	0.186415	−	0.135438i
$993$	5.88197	−	18.1028i	0.186659	−	0.574476i
$994$	−7.85410			−0.249117
$995$	31.7705	+	23.0826i	1.00719	+	0.731768i
$996$	7.85410	+	5.70634i	0.248867	+	0.180812i
$997$	−21.4164	+	15.5599i	−0.678264	+	0.492788i	−0.872781	−	0.488111i	$-0.837686\pi$
$997$	−21.4164	+	15.5599i	−0.678264	+	0.492788i	0.194517	+	0.980899i	$0.437686\pi$
$998$	23.2533	−	16.8945i	0.736070	−	0.534786i
$999$	−5.42705	−	3.94298i	−0.171704	−	0.124750i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.k.a.191.1	yes	4
11.3	even	5		275.2.l.c.91.1	yes	4
25.11	even	5		275.2.l.c.136.1	yes	4
275.36	even	5	inner	275.2.k.a.36.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.k.a.36.1	✓	4	275.36	even	5	inner
275.2.k.a.191.1	yes	4	1.1	even	1	trivial
275.2.l.c.91.1	yes	4	11.3	even	5
275.2.l.c.136.1	yes	4	25.11	even	5

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 1.53884i) q^{2} -2.61803 q^{3} +(-0.500000 + 0.363271i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.30902 + 4.02874i) q^{6} +(-0.500000 - 1.53884i) q^{7} +(-1.80902 - 1.31433i) q^{8} +3.85410 q^{9} +(-1.11803 + 3.44095i) q^{10} +(-0.809017 + 3.21644i) q^{11} +(1.30902 - 0.951057i) q^{12} +1.85410 q^{13} +(-2.11803 + 1.53884i) q^{14} +(4.73607 + 3.44095i) q^{15} +(-1.50000 + 4.61653i) q^{16} +(1.30902 + 4.02874i) q^{17} +(-1.92705 - 5.93085i) q^{18} +(-0.690983 - 0.502029i) q^{19} +1.38197 q^{20} +(1.30902 + 4.02874i) q^{21} +(5.35410 - 0.363271i) q^{22} +(-3.30902 - 2.40414i) q^{23} +(4.73607 + 3.44095i) q^{24} +(1.54508 + 4.75528i) q^{25} +(-0.927051 - 2.85317i) q^{26} -2.23607 q^{27} +(0.809017 + 0.587785i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(2.92705 - 9.00854i) q^{30} +(1.73607 - 1.26133i) q^{31} +3.38197 q^{32} +(2.11803 - 8.42075i) q^{33} +(5.54508 - 4.02874i) q^{34} +(-1.11803 + 3.44095i) q^{35} +(-1.92705 + 1.40008i) q^{36} +(2.42705 + 1.76336i) q^{37} +(-0.427051 + 1.31433i) q^{38} -4.85410 q^{39} +(1.54508 + 4.75528i) q^{40} +(-2.30902 - 7.10642i) q^{41} +(5.54508 - 4.02874i) q^{42} -12.0902 q^{43} +(-0.763932 - 1.90211i) q^{44} +(-6.97214 - 5.06555i) q^{45} +(-2.04508 + 6.29412i) q^{46} -8.32624 q^{47} +(3.92705 - 12.0862i) q^{48} +(3.54508 - 2.57565i) q^{49} +(6.54508 - 4.75528i) q^{50} +(-3.42705 - 10.5474i) q^{51} +(-0.927051 + 0.673542i) q^{52} +(-3.47214 + 10.6861i) q^{53} +(1.11803 + 3.44095i) q^{54} +(5.69098 - 4.75528i) q^{55} +(-1.11803 + 3.44095i) q^{56} +(1.80902 + 1.31433i) q^{57} +(5.85410 + 4.25325i) q^{58} +(-8.78115 - 6.37988i) q^{59} -3.61803 q^{60} -2.47214 q^{61} +(-2.80902 - 2.04087i) q^{62} +(-1.92705 - 5.93085i) q^{63} +(1.30902 + 4.02874i) q^{64} +(-3.35410 - 2.43690i) q^{65} +(-14.0172 + 0.951057i) q^{66} +(-3.00000 + 9.23305i) q^{67} +(-2.11803 - 1.53884i) q^{68} +(8.66312 + 6.29412i) q^{69} +5.85410 q^{70} +(2.42705 + 1.76336i) q^{71} +(-6.97214 - 5.06555i) q^{72} +(3.39919 - 10.4616i) q^{73} +(1.50000 - 4.61653i) q^{74} +(-4.04508 - 12.4495i) q^{75} +0.527864 q^{76} +(5.35410 - 0.363271i) q^{77} +(2.42705 + 7.46969i) q^{78} +(-2.33688 + 7.19218i) q^{79} +(8.78115 - 6.37988i) q^{80} -5.70820 q^{81} +(-9.78115 + 7.10642i) q^{82} +(1.85410 + 5.70634i) q^{83} +(-2.11803 - 1.53884i) q^{84} +(2.92705 - 9.00854i) q^{85} +(6.04508 + 18.6049i) q^{86} +(9.47214 - 6.88191i) q^{87} +(5.69098 - 4.75528i) q^{88} +(-1.54508 - 1.12257i) q^{89} +(-4.30902 + 13.2618i) q^{90} +(-0.927051 - 2.85317i) q^{91} +2.52786 q^{92} +(-4.54508 + 3.30220i) q^{93} +(4.16312 + 12.8128i) q^{94} +(0.590170 + 1.81636i) q^{95} -8.85410 q^{96} +(4.33688 - 13.3475i) q^{97} +(-5.73607 - 4.16750i) q^{98} +(-3.11803 + 12.3965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} - q^{11} + 3 q^{12} - 6 q^{13} - 4 q^{14} + 10 q^{15} - 6 q^{16} + 3 q^{17} - q^{18} - 5 q^{19} + 10 q^{20} + 3 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 - q^11 + 3 * q^12 - 6 * q^13 - 4 * q^14 + 10 * q^15 - 6 * q^16 + 3 * q^17 - q^18 - 5 * q^19 + 10 * q^20 + 3 * q^21 + 8 * q^22 - 11 * q^23 + 10 * q^24 - 5 * q^25 + 3 * q^26 + q^28 - 10 * q^29 + 5 * q^30 - 2 * q^31 + 18 * q^32 + 4 * q^33 + 11 * q^34 - q^36 + 3 * q^37 + 5 * q^38 - 6 * q^39 - 5 * q^40 - 7 * q^41 + 11 * q^42 - 26 * q^43 - 12 * q^44 - 10 * q^45 + 3 * q^46 - 2 * q^47 + 9 * q^48 + 3 * q^49 + 15 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 + 25 * q^55 + 5 * q^57 + 10 * q^58 - 15 * q^59 - 10 * q^60 + 8 * q^61 - 9 * q^62 - q^63 + 3 * q^64 - 27 * q^66 - 12 * q^67 - 4 * q^68 + 19 * q^69 + 10 * q^70 + 3 * q^71 - 10 * q^72 - 11 * q^73 + 6 * q^74 - 5 * q^75 + 20 * q^76 + 8 * q^77 + 3 * q^78 - 25 * q^79 + 15 * q^80 + 4 * q^81 - 19 * q^82 - 6 * q^83 - 4 * q^84 + 5 * q^85 + 13 * q^86 + 20 * q^87 + 25 * q^88 + 5 * q^89 - 15 * q^90 + 3 * q^91 + 28 * q^92 - 7 * q^93 + q^94 - 20 * q^95 - 22 * q^96 + 33 * q^97 - 14 * q^98 - 8 * q^99

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