LMFDB - Embedded newform 527.2.h.c.35.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [527,2,Mod(35,527)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(527, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("527.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 527 = 17 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	527.h (of order $5$, degree $4$, 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:	$4.20811618652$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			35.1
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834890 - 2.56953i) q^{2} +(-0.676586 + 2.08232i) q^{3} +(-4.28739 + 3.11497i) q^{4} -3.73062 q^{5} +5.91544 q^{6} +(-2.19901 + 1.59768i) q^{7} +(7.21196 + 5.23979i) q^{8} +(-1.45123 - 1.05438i) q^{9} +O(q^{10})$	\(q+(-0.834890 - 2.56953i) q^{2} +(-0.676586 + 2.08232i) q^{3} +(-4.28739 + 3.11497i) q^{4} -3.73062 q^{5} +5.91544 q^{6} +(-2.19901 + 1.59768i) q^{7} +(7.21196 + 5.23979i) q^{8} +(-1.45123 - 1.05438i) q^{9} +(3.11466 + 9.58594i) q^{10} +(-3.72715 + 2.70793i) q^{11} +(-3.58557 - 11.0353i) q^{12} +(1.63410 - 5.02926i) q^{13} +(5.94120 + 4.31653i) q^{14} +(2.52409 - 7.76835i) q^{15} +(4.16733 - 12.8257i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.49764 + 4.60926i) q^{18} +(-1.13252 - 3.48555i) q^{19} +(15.9946 - 11.6208i) q^{20} +(-1.83905 - 5.66001i) q^{21} +(10.0699 + 7.31618i) q^{22} +(4.02195 + 2.92212i) q^{23} +(-15.7904 + 11.4724i) q^{24} +8.91756 q^{25} -14.2871 q^{26} +(-2.13654 + 1.55229i) q^{27} +(4.45131 - 13.6997i) q^{28} +(1.43386 + 4.41297i) q^{29} -22.0683 q^{30} +(3.86152 - 4.01106i) q^{31} -18.6063 q^{32} +(-3.11704 - 9.59325i) q^{33} +(-0.834890 + 2.56953i) q^{34} +(8.20369 - 5.96033i) q^{35} +9.50634 q^{36} -0.0760375 q^{37} +(-8.01068 + 5.82010i) q^{38} +(9.36690 + 6.80545i) q^{39} +(-26.9051 - 19.5477i) q^{40} +(-2.92076 - 8.98916i) q^{41} +(-13.0081 + 9.45096i) q^{42} +(0.801685 + 2.46733i) q^{43} +(7.54461 - 23.2199i) q^{44} +(5.41399 + 3.93349i) q^{45} +(4.15058 - 12.7742i) q^{46} +(-2.45107 + 7.54362i) q^{47} +(23.8876 + 17.3554i) q^{48} +(0.119966 - 0.369216i) q^{49} +(-7.44518 - 22.9139i) q^{50} +(1.77133 - 1.28694i) q^{51} +(8.65995 + 26.6526i) q^{52} +(-4.93522 - 3.58565i) q^{53} +(5.77243 + 4.19391i) q^{54} +(13.9046 - 10.1023i) q^{55} -24.2307 q^{56} +8.02427 q^{57} +(10.1421 - 7.36869i) q^{58} +(-0.794154 + 2.44416i) q^{59} +(13.3764 + 41.1684i) q^{60} +5.45626 q^{61} +(-13.5305 - 6.57349i) q^{62} +4.87582 q^{63} +(7.19956 + 22.1580i) q^{64} +(-6.09623 + 18.7623i) q^{65} +(-22.0477 + 16.0186i) q^{66} -2.61859 q^{67} +5.29951 q^{68} +(-8.80598 + 6.39792i) q^{69} +(-22.1644 - 16.1034i) q^{70} +(-0.504720 - 0.366701i) q^{71} +(-4.94147 - 15.2083i) q^{72} +(4.42412 - 3.21431i) q^{73} +(0.0634830 + 0.195380i) q^{74} +(-6.03350 + 18.5692i) q^{75} +(15.7130 + 11.4161i) q^{76} +(3.86964 - 11.9095i) q^{77} +(9.66646 - 29.7503i) q^{78} +(3.16963 + 2.30287i) q^{79} +(-15.5467 + 47.8479i) q^{80} +(-3.44976 - 10.6173i) q^{81} +(-20.6594 + 15.0099i) q^{82} +(1.13943 + 3.50681i) q^{83} +(25.5155 + 18.5381i) q^{84} +(3.01814 + 2.19281i) q^{85} +(5.67056 - 4.11990i) q^{86} -10.1593 q^{87} -41.0690 q^{88} +(7.45329 - 5.41513i) q^{89} +(5.58713 - 17.1954i) q^{90} +(4.44170 + 13.6702i) q^{91} -26.3460 q^{92} +(5.73965 + 10.7548i) q^{93} +21.4299 q^{94} +(4.22502 + 13.0033i) q^{95} +(12.5888 - 38.7442i) q^{96} +(11.1718 - 8.11678i) q^{97} -1.04887 q^{98} +8.26412 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) $ 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/527\mathbb{Z}\right)^\times$.

$n$	$156$	$375$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.834890	−	2.56953i	−0.590356	−	1.81693i	−0.576604	−	0.817024i	$-0.695622\pi$
$2$	−0.834890	−	2.56953i	−0.590356	−	1.81693i	−0.0137524	−	0.999905i	$-0.504378\pi$
$3$	−0.676586	+	2.08232i	−0.390627	+	1.20223i	0.541688	+	0.840580i	$0.317785\pi$
$3$	−0.676586	+	2.08232i	−0.390627	+	1.20223i	−0.932315	+	0.361647i	$0.882215\pi$
$4$	−4.28739	+	3.11497i	−2.14370	+	1.55749i
$5$	−3.73062			−1.66839			−0.834193	−	0.551472i	$-0.814066\pi$
$5$	−3.73062			−1.66839			−0.834193	+	0.551472i	$0.814066\pi$
$6$	5.91544			2.41497
$7$	−2.19901	+	1.59768i	−0.831148	+	0.603864i	−0.919884	−	0.392191i	$-0.871717\pi$
$7$	−2.19901	+	1.59768i	−0.831148	+	0.603864i	0.0887358	+	0.996055i	$0.471717\pi$
$8$	7.21196	+	5.23979i	2.54981	+	1.85255i
$9$	−1.45123	−	1.05438i	−0.483743	−	0.351460i
$10$	3.11466	+	9.58594i	0.984942	+	3.03134i
$11$	−3.72715	+	2.70793i	−1.12378	+	0.816472i	−0.984777	−	0.173821i	$-0.944389\pi$
$11$	−3.72715	+	2.70793i	−1.12378	+	0.816472i	−0.139000	+	0.990292i	$0.544389\pi$
$12$	−3.58557	−	11.0353i	−1.03507	−	3.18560i
$13$	1.63410	−	5.02926i	0.453219	−	1.39486i	−0.419994	−	0.907527i	$-0.637968\pi$
$13$	1.63410	−	5.02926i	0.453219	−	1.39486i	0.873213	−	0.487338i	$-0.162032\pi$
$14$	5.94120	+	4.31653i	1.58785	+	1.15364i
$15$	2.52409	−	7.76835i	0.651717	−	2.00578i
$16$	4.16733	−	12.8257i	1.04183	−	3.20643i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−1.49764	+	4.60926i	−0.352997	+	1.08641i
$19$	−1.13252	−	3.48555i	−0.259819	−	0.799640i	−0.992842	−	0.119436i	$-0.961891\pi$
$19$	−1.13252	−	3.48555i	−0.259819	−	0.799640i	0.733023	−	0.680204i	$-0.238109\pi$
$20$	15.9946	−	11.6208i	3.57651	−	2.59849i
$21$	−1.83905	−	5.66001i	−0.401313	−	1.23511i
$22$	10.0699	+	7.31618i	2.14690	+	1.55981i
$23$	4.02195	+	2.92212i	0.838635	+	0.609304i	0.921989	−	0.387216i	$-0.126563\pi$
$23$	4.02195	+	2.92212i	0.838635	+	0.609304i	−0.0833540	+	0.996520i	$0.526563\pi$
$24$	−15.7904	+	11.4724i	−3.22321	+	2.34180i
$25$	8.91756			1.78351
$26$	−14.2871			−2.80193
$27$	−2.13654	+	1.55229i	−0.411178	+	0.298738i
$28$	4.45131	−	13.6997i	0.841218	−	2.58900i
$29$	1.43386	+	4.41297i	0.266262	+	0.819469i	0.991400	+	0.130866i	$0.0417757\pi$
$29$	1.43386	+	4.41297i	0.266262	+	0.819469i	−0.725139	+	0.688603i	$0.758224\pi$
$30$	−22.0683			−4.02910
$31$	3.86152	−	4.01106i	0.693550	−	0.720408i
$31$	3.86152	−	4.01106i	0.693550	−	0.720408i
$32$	−18.6063			−3.28916
$33$	−3.11704	−	9.59325i	−0.542606	−	1.66997i
$34$	−0.834890	+	2.56953i	−0.143182	+	0.440670i
$35$	8.20369	−	5.96033i	1.38668	−	1.00748i
$36$	9.50634			1.58439
$37$	−0.0760375			−0.0125005			−0.00625025	−	0.999980i	$-0.501990\pi$
$37$	−0.0760375			−0.0125005			−0.00625025	+	0.999980i	$0.501990\pi$
$38$	−8.01068	+	5.82010i	−1.29950	+	0.944144i
$39$	9.36690	+	6.80545i	1.49990	+	1.08974i
$40$	−26.9051	−	19.5477i	−4.25407	−	3.09076i
$41$	−2.92076	−	8.98916i	−0.456145	−	1.40387i	−0.869785	−	0.493430i	$-0.835743\pi$
$41$	−2.92076	−	8.98916i	−0.456145	−	1.40387i	0.413640	−	0.910441i	$-0.364257\pi$
$42$	−13.0081	+	9.45096i	−2.00720	+	1.45831i
$43$	0.801685	+	2.46733i	0.122256	+	0.376265i	0.993391	−	0.114778i	$-0.0366157\pi$
$43$	0.801685	+	2.46733i	0.122256	+	0.376265i	−0.871135	+	0.491043i	$0.836616\pi$
$44$	7.54461	−	23.2199i	1.13739	−	3.50053i
$45$	5.41399	+	3.93349i	0.807070	+	0.586370i
$46$	4.15058	−	12.7742i	0.611969	−	1.88345i
$47$	−2.45107	+	7.54362i	−0.357526	+	1.10035i	0.597005	+	0.802238i	$0.296357\pi$
$47$	−2.45107	+	7.54362i	−0.357526	+	1.10035i	−0.954531	+	0.298113i	$0.903643\pi$
$48$	23.8876	+	17.3554i	3.44788	+	2.50504i
$49$	0.119966	−	0.369216i	0.0171379	−	0.0527451i
$50$	−7.44518	−	22.9139i	−1.05291	−	3.24052i
$51$	1.77133	−	1.28694i	0.248035	−	0.180208i
$52$	8.65995	+	26.6526i	1.20092	+	3.69605i
$53$	−4.93522	−	3.58565i	−0.677905	−	0.492527i	0.194757	−	0.980852i	$-0.437608\pi$
$53$	−4.93522	−	3.58565i	−0.677905	−	0.492527i	−0.872662	+	0.488325i	$0.837608\pi$
$54$	5.77243	+	4.19391i	0.785528	+	0.570719i
$55$	13.9046	−	10.1023i	1.87489	−	1.36219i
$56$	−24.2307			−3.23796
$57$	8.02427			1.06284
$58$	10.1421	−	7.36869i	1.33173	−	0.967557i
$59$	−0.794154	+	2.44416i	−0.103390	+	0.318202i	−0.989349	−	0.145561i	$-0.953501\pi$
$59$	−0.794154	+	2.44416i	−0.103390	+	0.318202i	0.885959	+	0.463763i	$0.153501\pi$
$60$	13.3764	+	41.1684i	1.72689	+	5.31482i
$61$	5.45626			0.698602			0.349301	−	0.937010i	$-0.386419\pi$
$61$	5.45626			0.698602			0.349301	+	0.937010i	$0.386419\pi$
$62$	−13.5305	−	6.57349i	−1.71837	−	0.834835i
$63$	4.87582			0.614296
$64$	7.19956	+	22.1580i	0.899946	+	2.76975i
$65$	−6.09623	+	18.7623i	−0.756144	+	2.32717i
$66$	−22.0477	+	16.0186i	−2.71389	+	1.97176i
$67$	−2.61859			−0.319912			−0.159956	−	0.987124i	$-0.551135\pi$
$67$	−2.61859			−0.319912			−0.159956	+	0.987124i	$0.551135\pi$
$68$	5.29951			0.642659
$69$	−8.80598	+	6.39792i	−1.06012	+	0.770219i
$70$	−22.1644	−	16.1034i	−2.64915	−	1.92472i
$71$	−0.504720	−	0.366701i	−0.0598993	−	0.0435194i	0.557433	−	0.830222i	$-0.311786\pi$
$71$	−0.504720	−	0.366701i	−0.0598993	−	0.0435194i	−0.617332	+	0.786703i	$0.711786\pi$
$72$	−4.94147	−	15.2083i	−0.582358	−	1.79231i
$73$	4.42412	−	3.21431i	0.517805	−	0.376207i	−0.297972	−	0.954575i	$-0.596310\pi$
$73$	4.42412	−	3.21431i	0.517805	−	0.376207i	0.815776	+	0.578368i	$0.196310\pi$
$74$	0.0634830	+	0.195380i	0.00737974	+	0.0227125i
$75$	−6.03350	+	18.5692i	−0.696688	+	2.14419i
$76$	15.7130	+	11.4161i	1.80240	+	1.30952i
$77$	3.86964	−	11.9095i	0.440987	−	1.35722i
$78$	9.66646	−	29.7503i	1.09451	−	3.36856i
$79$	3.16963	+	2.30287i	0.356612	+	0.259093i	0.751637	−	0.659577i	$-0.229264\pi$
$79$	3.16963	+	2.30287i	0.356612	+	0.259093i	−0.395026	+	0.918670i	$0.629264\pi$
$80$	−15.5467	+	47.8479i	−1.73818	+	5.34956i
$81$	−3.44976	−	10.6173i	−0.383307	−	1.17970i
$82$	−20.6594	+	15.0099i	−2.28145	+	1.65757i
$83$	1.13943	+	3.50681i	0.125069	+	0.384922i	0.993914	−	0.110162i	$-0.0351371\pi$
$83$	1.13943	+	3.50681i	0.125069	+	0.384922i	−0.868845	+	0.495085i	$0.835137\pi$
$84$	25.5155	+	18.5381i	2.78397	+	2.02267i
$85$	3.01814	+	2.19281i	0.327363	+	0.237843i
$86$	5.67056	−	4.11990i	0.611472	−	0.444261i
$87$	−10.1593			−1.08920
$88$	−41.0690			−4.37797
$89$	7.45329	−	5.41513i	0.790047	−	0.574003i	−0.117930	−	0.993022i	$-0.537626\pi$
$89$	7.45329	−	5.41513i	0.790047	−	0.574003i	0.907977	+	0.419019i	$0.137626\pi$
$90$	5.58713	−	17.1954i	0.588935	−	1.81256i
$91$	4.44170	+	13.6702i	0.465617	+	1.43302i
$92$	−26.3460			−2.74676
$93$	5.73965	+	10.7548i	0.595174	+	1.11522i
$94$	21.4299			2.21033
$95$	4.22502	+	13.0033i	0.433478	+	1.33411i
$96$	12.5888	−	38.7442i	1.28484	−	3.95432i
$97$	11.1718	−	8.11678i	1.13432	−	0.824134i	0.148005	−	0.988987i	$-0.452715\pi$
$97$	11.1718	−	8.11678i	1.13432	−	0.824134i	0.986318	+	0.164852i	$0.0527148\pi$
$98$	−1.04887			−0.105952
$99$	8.26412			0.830576
$100$	−38.2331	+	27.7779i	−3.82331	+	2.77779i
$101$	5.12756	+	3.72539i	0.510211	+	0.370690i	0.812904	−	0.582398i	$-0.197886\pi$
$101$	5.12756	+	3.72539i	0.510211	+	0.370690i	−0.302693	+	0.953088i	$0.597886\pi$
$102$	−4.78570	−	3.47701i	−0.473854	−	0.344275i
$103$	−1.26862	−	3.90440i	−0.125001	−	0.384712i	0.868901	−	0.494987i	$-0.164827\pi$
$103$	−1.26862	−	3.90440i	−0.125001	−	0.384712i	−0.993901	+	0.110274i	$0.964827\pi$
$104$	38.1374	−	27.7084i	3.73968	−	2.71703i
$105$	6.86080	+	21.1154i	0.669545	+	2.06065i
$106$	−5.09306	+	15.6748i	−0.494681	+	1.52247i
$107$	−12.1800	−	8.84925i	−1.17748	−	0.855489i	−0.185595	−	0.982626i	$-0.559421\pi$
$107$	−12.1800	−	8.84925i	−1.17748	−	0.855489i	−0.991885	+	0.127137i	$0.959421\pi$
$108$	4.32486	−	13.3105i	0.416160	−	1.28081i
$109$	4.64374	−	14.2920i	0.444789	−	1.36892i	−0.437925	−	0.899011i	$-0.644286\pi$
$109$	4.64374	−	14.2920i	0.444789	−	1.36892i	0.882715	−	0.469910i	$-0.155714\pi$
$110$	−37.5669	−	27.2939i	−3.58186	−	2.60237i
$111$	0.0514459	−	0.158334i	0.00488303	−	0.0150284i
$112$	11.3273	+	34.8619i	1.07033	+	3.29414i
$113$	−7.50339	+	5.45153i	−0.705859	+	0.512837i	−0.881835	−	0.471558i	$-0.843692\pi$
$113$	−7.50339	+	5.45153i	−0.705859	+	0.512837i	0.175976	+	0.984394i	$0.443692\pi$
$114$	−6.69938	−	20.6186i	−0.627454	−	1.93111i
$115$	−15.0044	−	10.9013i	−1.39917	−	1.01655i
$116$	−19.8938	−	14.4537i	−1.84709	−	1.34199i
$117$	−7.67420	+	5.57563i	−0.709480	+	0.515467i
$118$	6.94335			0.639187
$119$	2.71813			0.249170
$120$	58.9082	−	42.7993i	5.37756	−	3.90702i
$121$	3.15955	−	9.72409i	0.287232	−	0.884008i
$122$	−4.55537	−	14.0200i	−0.412424	−	1.26931i
$123$	20.6944			1.86595
$124$	−4.06152	+	29.2255i	−0.364735	+	2.62453i
$125$	−14.6150			−1.30720
$126$	−4.07077	−	12.5286i	−0.362653	−	1.11613i
$127$	1.14196	−	3.51460i	0.101333	−	0.311870i	−0.887519	−	0.460770i	$-0.847573\pi$
$127$	1.14196	−	3.51460i	0.101333	−	0.311870i	0.988852	+	0.148900i	$0.0475732\pi$
$128$	20.8190	−	15.1259i	1.84016	−	1.33695i
$129$	−5.68018			−0.500112
$130$	53.2998			4.67470
$131$	11.8418	−	8.60356i	1.03462	−	0.751697i	0.0653933	−	0.997860i	$-0.479170\pi$
$131$	11.8418	−	8.60356i	1.03462	−	0.751697i	0.969228	+	0.246163i	$0.0791698\pi$
$132$	43.2467	+	31.4205i	3.76414	+	2.73481i
$133$	8.05921	+	5.85536i	0.698822	+	0.507724i
$134$	2.18624	+	6.72854i	0.188862	+	0.581257i
$135$	7.97064	−	5.79101i	0.686004	−	0.498411i
$136$	−2.75472	−	8.47817i	−0.236216	−	0.726997i
$137$	6.23881	−	19.2011i	0.533017	−	1.64046i	−0.214878	−	0.976641i	$-0.568935\pi$
$137$	6.23881	−	19.2011i	0.533017	−	1.64046i	0.747895	−	0.663817i	$-0.231065\pi$
$138$	23.7916	+	17.2856i	2.02528	+	1.47145i
$139$	−0.429295	+	1.32123i	−0.0364123	+	0.112066i	−0.967611	−	0.252447i	$-0.918765\pi$
$139$	−0.429295	+	1.32123i	−0.0364123	+	0.112066i	0.931198	+	0.364513i	$0.118765\pi$
$140$	−16.6062	+	51.1085i	−1.40348	+	4.31946i
$141$	−14.0499	−	10.2078i	−1.18321	−	0.859654i
$142$	−0.520861	+	1.60305i	−0.0437097	+	0.134525i
$143$	7.52833	+	23.1698i	0.629551	+	1.93756i
$144$	−19.5709	+	14.2191i	−1.63091	+	1.18492i
$145$	−5.34920	−	16.4632i	−0.444227	−	1.36719i
$146$	−11.9529	−	8.68431i	−0.989231	−	0.718718i
$147$	0.687658	+	0.499613i	0.0567171	+	0.0412074i
$148$	0.326003	−	0.236855i	0.0267972	−	0.0194693i
$149$	−3.50834			−0.287415			−0.143707	−	0.989620i	$-0.545902\pi$
$149$	−3.50834			−0.287415			−0.143707	+	0.989620i	$0.545902\pi$
$150$	52.7513			4.30713
$151$	−11.6318	+	8.45102i	−0.946585	+	0.687734i	−0.949997	−	0.312260i	$-0.898914\pi$
$151$	−11.6318	+	8.45102i	−0.946585	+	0.687734i	0.00341180	+	0.999994i	$0.498914\pi$
$152$	10.0958	−	31.0718i	0.818881	−	2.52026i
$153$	0.554320	+	1.70602i	0.0448141	+	0.137924i
$154$	−33.8326			−2.72631
$155$	−14.4059	+	14.9638i	−1.15711	+	1.20192i
$156$	−61.3583			−4.91260
$157$	−2.58981	−	7.97061i	−0.206689	−	0.636124i	−0.999640	−	0.0268378i	$-0.991456\pi$
$157$	−2.58981	−	7.97061i	−0.206689	−	0.636124i	0.792951	−	0.609286i	$-0.208544\pi$
$158$	3.27100	−	10.0671i	0.260227	−	0.800895i
$159$	10.8056	−	7.85071i	0.856937	−	0.622601i
$160$	69.4132			5.48759
$161$	−13.5129			−1.06497
$162$	−24.4012	+	17.7285i	−1.91714	+	1.39288i
$163$	−10.9648	−	7.96641i	−0.858832	−	0.623978i	0.0687353	−	0.997635i	$-0.478104\pi$
$163$	−10.9648	−	7.96641i	−0.858832	−	0.623978i	−0.927567	+	0.373657i	$0.878104\pi$
$164$	40.5234	+	29.4420i	3.16435	+	2.29903i
$165$	11.6285	+	35.7888i	0.905277	+	2.78616i
$166$	8.05954	−	5.85560i	0.625542	−	0.454483i
$167$	1.79407	+	5.52158i	0.138829	+	0.427272i	0.996166	−	0.0874836i	$-0.0278825\pi$
$167$	1.79407	+	5.52158i	0.138829	+	0.427272i	−0.857337	+	0.514756i	$0.827883\pi$
$168$	16.3941	−	50.4560i	1.26483	−	3.89276i
$169$	−12.1059	−	8.79546i	−0.931224	−	0.676574i
$170$	3.11466	−	9.58594i	0.238884	−	0.735208i
$171$	−2.03154	+	6.25243i	−0.155356	+	0.478136i
$172$	−11.1228	−	8.08120i	−0.848107	−	0.616186i
$173$	−5.38587	+	16.5760i	−0.409480	+	1.26025i	0.507615	+	0.861584i	$0.330527\pi$
$173$	−5.38587	+	16.5760i	−0.409480	+	1.26025i	−0.917096	+	0.398667i	$0.869473\pi$
$174$	8.48193	+	26.1047i	0.643014	+	1.97899i
$175$	−19.6098	+	14.2474i	−1.48236	+	1.07700i
$176$	19.1989	+	59.0881i	1.44717	+	4.45394i
$177$	−4.55220	−	3.30736i	−0.342164	−	0.248597i
$178$	−20.1370	−	14.6304i	−1.50933	−	1.09659i
$179$	3.63234	−	2.63905i	0.271493	−	0.197252i	−0.443705	−	0.896173i	$-0.646336\pi$
$179$	3.63234	−	2.63905i	0.271493	−	0.197252i	0.715199	+	0.698921i	$0.246336\pi$
$180$	−35.4646			−2.64337
$181$	−10.0961			−0.750434			−0.375217	−	0.926937i	$-0.622432\pi$
$181$	−10.0961			−0.750434			−0.375217	+	0.926937i	$0.622432\pi$
$182$	31.4175	−	22.8262i	2.32882	−	1.69199i
$183$	−3.69163	+	11.3617i	−0.272893	+	0.839879i
$184$	13.6948	+	42.1484i	1.00960	+	3.10722i
$185$	0.283668			0.0208557
$186$	22.8426	−	23.7272i	1.67490	−	1.73976i
$187$	4.60701			0.336898
$188$	−12.9895	−	39.9775i	−0.947355	−	2.91566i
$189$	2.21823	−	6.82701i	0.161352	−	0.496592i
$190$	29.8848	−	21.7126i	2.16807	−	1.57520i
$191$	13.6055			0.984462			0.492231	−	0.870465i	$-0.336182\pi$
$191$	13.6055			0.984462			0.492231	+	0.870465i	$0.336182\pi$
$192$	−51.0111			−3.68141
$193$	−13.2305	+	9.61250i	−0.952350	+	0.691923i	−0.951361	−	0.308077i	$-0.900315\pi$
$193$	−13.2305	+	9.61250i	−0.952350	+	0.691923i	−0.000988447		1.00000i	$0.500315\pi$
$194$	−30.1835	−	21.9296i	−2.16705	−	1.57445i
$195$	−34.9444	−	25.3886i	−2.50242	−	1.81811i
$196$	0.635758	+	1.95666i	0.0454113	+	0.139762i
$197$	−6.35231	+	4.61522i	−0.452583	+	0.328821i	−0.790615	−	0.612314i	$-0.790239\pi$
$197$	−6.35231	+	4.61522i	−0.452583	+	0.328821i	0.338032	+	0.941135i	$0.390239\pi$
$198$	−6.89963	−	21.2349i	−0.490335	−	1.50910i
$199$	4.14242	−	12.7490i	0.293648	−	0.903756i	−0.690024	−	0.723786i	$-0.742400\pi$
$199$	4.14242	−	12.7490i	0.293648	−	0.903756i	0.983672	−	0.179969i	$-0.0575999\pi$
$200$	64.3131	+	46.7262i	4.54762	+	3.30404i
$201$	1.77170	−	5.45274i	0.124966	−	0.384607i
$202$	5.29154	−	16.2857i	0.372311	−	1.14586i
$203$	−10.2036	−	7.41333i	−0.716151	−	0.520314i
$204$	−3.58557	+	11.0353i	−0.251040	+	0.772622i
$205$	10.8962	+	33.5352i	0.761027	+	2.34220i
$206$	−8.97331	+	6.51949i	−0.625200	+	0.454234i
$207$	−2.75575	−	8.48132i	−0.191538	−	0.589493i
$208$	−57.6939	−	41.9171i	−4.00035	−	2.90643i
$209$	13.6597	+	9.92436i	0.944861	+	0.686482i
$210$	48.5285	−	35.2580i	3.34878	−	2.43303i
$211$	11.7839			0.811238			0.405619	−	0.914042i	$-0.367056\pi$
$211$	11.7839			0.811238			0.405619	+	0.914042i	$0.367056\pi$
$212$	32.3284			2.22033
$213$	1.10507	−	0.802883i	0.0757184	−	0.0550127i
$214$	−12.5695	+	38.6849i	−0.859231	+	2.64444i
$215$	−2.99079	−	9.20470i	−0.203970	−	0.627755i
$216$	−23.5423			−1.60185
$217$	−2.08316	+	14.9898i	−0.141414	+	1.01758i
$218$	−40.6006			−2.74982
$219$	3.69992	+	11.3872i	0.250018	+	0.769475i
$220$	−28.1461	+	86.6248i	−1.89761	+	5.84024i
$221$	−4.27814	+	3.10825i	−0.287779	+	0.209084i
$222$	−0.449796			−0.0301883
$223$	17.8911			1.19808			0.599040	−	0.800719i	$-0.295549\pi$
$223$	17.8911			1.19808			0.599040	+	0.800719i	$0.295549\pi$
$224$	40.9155	−	29.7268i	2.73378	−	1.98621i
$225$	−12.9414	−	9.40249i	−0.862761	−	0.626833i
$226$	20.2723	+	14.7287i	1.34850	+	0.979740i
$227$	−7.45613	−	22.9476i	−0.494881	−	1.52309i	−0.817143	−	0.576436i	$-0.804443\pi$
$227$	−7.45613	−	22.9476i	−0.494881	−	1.52309i	0.322262	−	0.946651i	$-0.395557\pi$
$228$	−34.4032	+	24.9954i	−2.27841	+	1.65536i
$229$	5.69500	+	17.5274i	0.376337	+	1.15824i	0.942573	+	0.334002i	$0.108399\pi$
$229$	5.69500	+	17.5274i	0.376337	+	1.15824i	−0.566236	+	0.824243i	$0.691601\pi$
$230$	−15.4842	+	47.6556i	−1.02100	+	3.14232i
$231$	22.1813	+	16.1157i	1.45942	+	1.06033i
$232$	−12.7821	+	39.3393i	−0.839187	+	2.58275i
$233$	0.620165	−	1.90867i	0.0406284	−	0.125041i	−0.928685	−	0.370869i	$-0.879060\pi$
$233$	0.620165	−	1.90867i	0.0406284	−	0.125041i	0.969313	+	0.245828i	$0.0790598\pi$
$234$	20.7338	+	15.0640i	1.35541	+	0.984766i
$235$	9.14403	−	28.1424i	0.596491	−	1.83581i
$236$	−4.20863	−	12.9528i	−0.273958	−	0.843157i
$237$	−6.93984	+	5.04209i	−0.450791	+	0.327519i
$238$	−2.26934	−	6.98430i	−0.147099	−	0.452725i
$239$	16.9788	+	12.3359i	1.09827	+	0.797940i	0.980777	−	0.195134i	$-0.0625141\pi$
$239$	16.9788	+	12.3359i	1.09827	+	0.797940i	0.117493	+	0.993074i	$0.462514\pi$
$240$	−89.1159	−	64.7465i	−5.75240	−	4.17937i
$241$	8.36461	−	6.07725i	0.538812	−	0.391470i	−0.284831	−	0.958578i	$-0.591938\pi$
$241$	8.36461	−	6.07725i	0.538812	−	0.391470i	0.823644	+	0.567108i	$0.191938\pi$
$242$	−27.6242			−1.77575
$243$	16.5199			1.05975
$244$	−23.3931	+	16.9961i	−1.49759	+	1.08806i
$245$	−0.447547	+	1.37741i	−0.0285927	+	0.0879993i
$246$	−17.2776	−	53.1749i	−1.10158	−	3.39031i
$247$	−19.3804			−1.23314
$248$	48.8663	−	8.69402i	3.10301	−	0.552071i
$249$	−8.07322			−0.511619
$250$	12.2019	+	37.5535i	0.771714	+	2.37509i
$251$	4.18417	−	12.8775i	0.264102	−	0.812823i	−0.727796	−	0.685793i	$-0.759455\pi$
$251$	4.18417	−	12.8775i	0.264102	−	0.812823i	0.991899	−	0.127030i	$-0.0405445\pi$
$252$	−20.9045	+	15.1880i	−1.31686	+	0.956757i
$253$	−22.9033			−1.43992
$254$	−9.98427			−0.626469
$255$	−6.60815	+	4.80110i	−0.413818	+	0.300657i
$256$	−18.5506	−	13.4778i	−1.15941	−	0.842363i
$257$	−3.50670	−	2.54777i	−0.218742	−	0.158925i	0.473018	−	0.881053i	$-0.343165\pi$
$257$	−3.50670	−	2.54777i	−0.218742	−	0.158925i	−0.691760	+	0.722127i	$0.743165\pi$
$258$	4.74233	+	14.5954i	0.295244	+	0.908669i
$259$	0.167207	−	0.121483i	0.0103898	−	0.00754860i
$260$	−32.3070	−	99.4308i	−2.00360	−	6.16643i
$261$	2.57209	−	7.91606i	0.159208	−	0.489992i
$262$	−31.9937	−	23.2448i	−1.97658	−	1.43607i
$263$	4.65285	−	14.3200i	0.286907	−	0.883010i	−0.698913	−	0.715206i	$-0.746333\pi$
$263$	4.65285	−	14.3200i	0.286907	−	0.883010i	0.985821	−	0.167803i	$-0.0536673\pi$
$264$	27.7867	−	85.5188i	1.71016	−	5.26332i
$265$	18.4115	+	13.3767i	1.13101	+	0.821725i
$266$	8.31694	−	25.5969i	0.509944	−	1.56945i
$267$	6.23323	+	19.1839i	0.381468	+	1.17404i
$268$	11.2269	−	8.15684i	0.685794	−	0.498258i
$269$	−8.81819	−	27.1396i	−0.537654	−	1.65473i	−0.737843	−	0.674972i	$-0.764155\pi$
$269$	−8.81819	−	27.1396i	−0.537654	−	1.65473i	0.200189	−	0.979757i	$-0.435845\pi$
$270$	−21.5348	−	15.6459i	−1.31056	−	0.952180i
$271$	4.85152	+	3.52484i	0.294709	+	0.214119i	0.725308	−	0.688425i	$-0.241698\pi$
$271$	4.85152	+	3.52484i	0.294709	+	0.214119i	−0.430599	+	0.902544i	$0.641698\pi$
$272$	−10.9102	+	7.92672i	−0.661528	+	0.480628i
$273$	−31.4708			−1.90470
$274$	−54.5464			−3.29527
$275$	−33.2371	+	24.1481i	−2.00427	+	1.45619i
$276$	17.8253	−	54.8607i	1.07296	−	3.30223i
$277$	4.55728	+	14.0259i	0.273821	+	0.842733i	0.989529	+	0.144334i	$0.0461040\pi$
$277$	4.55728	+	14.0259i	0.273821	+	0.842733i	−0.715708	+	0.698399i	$0.753896\pi$
$278$	3.75336			0.225111
$279$	−9.83313	+	1.74946i	−0.588694	+	0.104737i
$280$	90.3955			5.40217
$281$	−1.91978	−	5.90849i	−0.114525	−	0.352471i	0.877323	−	0.479901i	$-0.159327\pi$
$281$	−1.91978	−	5.90849i	−0.114525	−	0.352471i	−0.991848	+	0.127430i	$0.959327\pi$
$282$	−14.4992	+	44.6239i	−0.863414	+	2.65731i
$283$	−19.6556	+	14.2806i	−1.16841	+	0.848896i	−0.990817	−	0.135209i	$-0.956829\pi$
$283$	−19.6556	+	14.2806i	−1.16841	+	0.848896i	−0.177588	+	0.984105i	$0.556829\pi$
$284$	3.30620			0.196187
$285$	−29.9355			−1.77323
$286$	53.2501	−	38.6885i	3.14875	−	2.28770i
$287$	20.7845	+	15.1008i	1.22687	+	0.891375i
$288$	27.0020	+	19.6181i	1.59111	+	1.15601i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−37.8365	+	27.4898i	−2.22184	+	1.61426i
$291$	9.34304	+	28.7549i	0.547699	+	1.68564i
$292$	−8.95545	+	27.5620i	−0.524078	+	1.61295i
$293$	−3.93284	−	2.85738i	−0.229759	−	0.166930i	0.466950	−	0.884284i	$-0.345353\pi$
$293$	−3.93284	−	2.85738i	−0.229759	−	0.166930i	−0.696709	+	0.717354i	$0.745353\pi$
$294$	0.709650	−	2.18408i	0.0413876	−	0.127378i
$295$	2.96269	−	9.11823i	0.172495	−	0.530884i
$296$	−0.548380	−	0.398421i	−0.0318739	−	0.0231578i
$297$	3.75972	−	11.5712i	0.218161	−	0.671431i
$298$	2.92908	+	9.01478i	0.169677	+	0.522212i
$299$	21.2684	−	15.4524i	1.22998	−	0.893634i
$300$	−31.9746	−	98.4076i	−1.84605	−	5.68156i
$301$	−5.70491	−	4.14486i	−0.328826	−	0.238906i
$302$	31.4264	+	22.8326i	1.80839	+	1.31387i
$303$	−11.2267	+	8.15666i	−0.644956	+	0.468588i
$304$	−49.4242			−2.83467
$305$	−20.3553			−1.16554
$306$	3.92087	−	2.84868i	0.224141	−	0.162848i
$307$	3.53181	−	10.8698i	0.201571	−	0.620372i	−0.798266	−	0.602305i	$-0.794249\pi$
$307$	3.53181	−	10.8698i	0.201571	−	0.620372i	0.999837	−	0.0180664i	$-0.00575101\pi$
$308$	20.5072	+	63.1147i	1.16851	+	3.59629i
$309$	8.98854			0.511340
$310$	50.4771	+	24.5232i	2.86691	+	1.39283i
$311$	1.48656			0.0842950			0.0421475	−	0.999111i	$-0.486580\pi$
$311$	1.48656			0.0842950			0.0421475	+	0.999111i	$0.486580\pi$
$312$	31.8945	+	98.1613i	1.80567	+	5.55729i
$313$	−6.93351	+	21.3392i	−0.391905	+	1.20616i	0.539440	+	0.842024i	$0.318636\pi$
$313$	−6.93351	+	21.3392i	−0.391905	+	1.20616i	−0.931345	+	0.364137i	$0.881364\pi$
$314$	−18.3185	+	13.3092i	−1.03377	+	0.751079i
$315$	−18.1899			−1.02488
$316$	−20.7628			−1.16800
$317$	−10.4595	+	7.59928i	−0.587464	+	0.426818i	−0.841407	−	0.540401i	$-0.818272\pi$
$317$	−10.4595	+	7.59928i	−0.587464	+	0.426818i	0.253943	+	0.967219i	$0.418272\pi$
$318$	−29.1940	−	21.2107i	−1.63712	−	1.18944i
$319$	−17.2942	−	12.5650i	−0.968292	−	0.703505i
$320$	−26.8589	−	82.6631i	−1.50146	−	4.62101i
$321$	26.6677	−	19.3752i	1.48845	−	1.08142i
$322$	11.2818	+	34.7218i	0.628710	+	1.93497i
$323$	−1.13252	+	3.48555i	−0.0630153	+	0.193941i
$324$	47.8630	+	34.7745i	2.65906	+	1.93192i
$325$	14.5722	−	44.8487i	0.808322	−	2.48776i
$326$	−11.3155	+	34.8255i	−0.626707	+	1.92881i
$327$	26.6185	+	19.3395i	1.47201	+	1.06948i
$328$	26.0370	−	80.1336i	1.43765	−	4.42464i
$329$	−6.66233	−	20.5045i	−0.367306	−	1.13045i
$330$	82.2518	−	59.7594i	4.52781	−	3.28965i
$331$	−4.54502	−	13.9881i	−0.249817	−	0.768857i	−0.994807	−	0.101781i	$-0.967546\pi$
$331$	−4.54502	−	13.9881i	−0.249817	−	0.768857i	0.744990	−	0.667076i	$-0.232454\pi$
$332$	−15.8088	−	11.4858i	−0.867621	−	0.630363i
$333$	0.110348	+	0.0801724i	0.00604702	+	0.00439342i
$334$	12.6900	−	9.21981i	0.694365	−	0.504486i
$335$	9.76898			0.533737
$336$	−80.2575			−4.37840
$337$	−8.34422	+	6.06243i	−0.454538	+	0.330241i	−0.791385	−	0.611318i	$-0.790640\pi$
$337$	−8.34422	+	6.06243i	−0.454538	+	0.330241i	0.336847	+	0.941560i	$0.390640\pi$
$338$	−12.4931	+	38.4497i	−0.679533	+	2.09139i
$339$	−6.27513	−	19.3129i	−0.340818	−	1.04893i
$340$	−19.7705			−1.07220
$341$	−3.53079	+	25.4066i	−0.191203	+	1.37584i
$342$	17.7619			0.960454
$343$	−5.55355	−	17.0921i	−0.299864	−	0.922885i
$344$	−7.14660	+	21.9950i	−0.385319	+	1.18589i
$345$	32.8518	−	23.8682i	1.76868	−	1.28502i
$346$	47.0891			2.53153
$347$	15.5855			0.836676			0.418338	−	0.908291i	$-0.362613\pi$
$347$	15.5855			0.836676			0.418338	+	0.908291i	$0.362613\pi$
$348$	43.5571	−	31.6461i	2.33490	−	1.69641i
$349$	11.3015	+	8.21102i	0.604956	+	0.439526i	0.847634	−	0.530581i	$-0.178026\pi$
$349$	11.3015	+	8.21102i	0.604956	+	0.439526i	−0.242679	+	0.970107i	$0.578026\pi$
$350$	52.9810	+	38.4930i	2.83195	+	2.05754i
$351$	4.31553	+	13.2818i	0.230346	+	0.708932i
$352$	69.3484	−	50.3846i	3.69628	−	2.68551i
$353$	6.15198	+	18.9339i	0.327437	+	1.00775i	0.970328	+	0.241790i	$0.0777346\pi$
$353$	6.15198	+	18.9339i	0.327437	+	1.00775i	−0.642891	+	0.765957i	$0.722265\pi$
$354$	−4.69778	+	14.4583i	−0.249684	+	0.768448i
$355$	1.88292	+	1.36802i	0.0999351	+	0.0726071i
$356$	−15.0872	+	46.4336i	−0.799619	+	2.46097i
$357$	−1.83905	+	5.66001i	−0.0973327	+	0.299559i
$358$	−9.81370	−	7.13007i	−0.518670	−	0.376836i
$359$	−6.96259	+	21.4287i	−0.367472	+	1.13096i	0.580947	+	0.813941i	$0.302682\pi$
$359$	−6.96259	+	21.4287i	−0.367472	+	1.13096i	−0.948419	+	0.317020i	$0.897318\pi$
$360$	18.4348	+	56.7364i	0.971597	+	2.99027i
$361$	4.50489	−	3.27299i	0.237099	−	0.172263i
$362$	8.42910	+	25.9421i	0.443024	+	1.36349i
$363$	18.1109	+	13.1584i	0.950578	+	0.690635i
$364$	−61.6255	−	44.7735i	−3.23005	−	2.34677i
$365$	−16.5048	+	11.9914i	−0.863898	+	0.627659i
$366$	32.2762			1.68710
$367$	−15.8618			−0.827982			−0.413991	−	0.910281i	$-0.635865\pi$
$367$	−15.8618			−0.827982			−0.413991	+	0.910281i	$0.635865\pi$
$368$	54.2390	−	39.4070i	2.82741	−	2.05423i
$369$	−5.23930	+	16.1249i	−0.272747	+	0.839429i
$370$	−0.236831	−	0.728891i	−0.0123123	−	0.0378932i
$371$	16.5813			0.860859
$372$	−58.1089	−	28.2310i	−3.01280	−	1.46371i
$373$	−13.1122			−0.678926			−0.339463	−	0.940619i	$-0.610245\pi$
$373$	−13.1122			−0.678926			−0.339463	+	0.940619i	$0.610245\pi$
$374$	−3.84634	−	11.8378i	−0.198890	−	0.612119i
$375$	9.88827	−	30.4330i	0.510628	−	1.57155i
$376$	−57.2041	+	41.5612i	−2.95008	+	2.14336i
$377$	24.5371			1.26372
$378$	−19.3941			−0.997527
$379$	27.9630	−	20.3163i	1.43636	−	1.04358i	0.447574	−	0.894247i	$-0.352288\pi$
$379$	27.9630	−	20.3163i	1.43636	−	1.04358i	0.988787	−	0.149330i	$-0.0477118\pi$
$380$	−58.6191	−	42.5893i	−3.00710	−	2.18478i
$381$	6.54588	+	4.75586i	0.335356	+	0.243650i
$382$	−11.3591	−	34.9598i	−0.581183	−	1.78870i
$383$	21.4715	−	15.5999i	1.09714	−	0.797120i	0.116550	−	0.993185i	$-0.462816\pi$
$383$	21.4715	−	15.5999i	1.09714	−	0.797120i	0.980591	+	0.196065i	$0.0628165\pi$
$384$	17.4111	+	53.5858i	0.888506	+	2.73454i
$385$	−14.4362	+	44.4300i	−0.735736	+	2.26436i
$386$	35.7455	+	25.9707i	1.81940	+	1.32187i
$387$	1.43808	−	4.42594i	0.0731015	−	0.224983i
$388$	−22.6143	+	69.5996i	−1.14807	+	3.53338i
$389$	−7.92989	−	5.76140i	−0.402061	−	0.292115i	0.368319	−	0.929700i	$-0.379934\pi$
$389$	−7.92989	−	5.76140i	−0.402061	−	0.292115i	−0.770380	+	0.637585i	$0.779934\pi$
$390$	−36.0619	+	110.987i	−1.82607	+	5.62005i
$391$	−1.53625	−	4.72809i	−0.0776915	−	0.239110i
$392$	2.79980	−	2.03418i	0.141411	−	0.102741i
$393$	9.90336	+	30.4794i	0.499559	+	1.53748i
$394$	17.1624	+	12.4692i	0.864630	+	0.628190i
$395$	−11.8247	−	8.59116i	−0.594966	−	0.432268i
$396$	−35.4315	+	25.7425i	−1.78050	+	1.29361i
$397$	−26.4642			−1.32820			−0.664101	−	0.747643i	$-0.731185\pi$
$397$	−26.4642			−1.32820			−0.664101	+	0.747643i	$0.731185\pi$
$398$	−36.2175			−1.81542
$399$	−17.6455	+	12.8202i	−0.883378	+	0.641812i
$400$	37.1624	−	114.374i	1.85812	−	5.71870i
$401$	−9.16603	−	28.2101i	−0.457730	−	1.40875i	−0.867900	−	0.496739i	$-0.834531\pi$
$401$	−9.16603	−	28.2101i	−0.457730	−	1.40875i	0.410170	−	0.912009i	$-0.365469\pi$
$402$	−15.4901			−0.772578
$403$	−13.8625	−	25.9751i	−0.690542	−	1.29391i
$404$	−33.5883			−1.67108
$405$	12.8698	+	39.6091i	0.639504	+	1.96819i
$406$	−10.5299	+	32.4077i	−0.522590	+	1.60837i
$407$	0.283403	−	0.205904i	0.0140478	−	0.0102063i
$408$	19.5180			0.966287
$409$	37.2818			1.84347			0.921733	−	0.387825i	$-0.126773\pi$
$409$	37.2818			1.84347			0.921733	+	0.387825i	$0.126773\pi$
$410$	77.0724	−	55.9964i	3.80633	−	2.76546i
$411$	35.7616	+	25.9824i	1.76399	+	1.28162i
$412$	17.6012	+	12.7880i	0.867147	+	0.630019i
$413$	−2.15861	−	6.64353i	−0.106218	−	0.326907i
$414$	−19.4922	+	14.1619i	−0.957991	+	0.696021i
$415$	−4.25079	−	13.0826i	−0.208663	−	0.642199i
$416$	−30.4047	+	93.5759i	−1.49071	+	4.58794i
$417$	−2.46077	−	1.78786i	−0.120505	−	0.0875517i
$418$	14.0965	−	43.3847i	0.689485	−	2.12202i
$419$	5.47381	−	16.8466i	0.267413	−	0.823012i	−0.723715	−	0.690099i	$-0.757567\pi$
$419$	5.47381	−	16.8466i	0.267413	−	0.823012i	0.991128	−	0.132913i	$-0.0424331\pi$
$420$	−95.1886	−	69.1586i	−4.64473	−	3.37459i
$421$	5.20993	−	16.0345i	0.253917	−	0.781475i	−0.740125	−	0.672470i	$-0.765234\pi$
$421$	5.20993	−	16.0345i	0.253917	−	0.781475i	0.994041	−	0.109005i	$-0.0347665\pi$
$422$	−9.83827	−	30.2791i	−0.478919	−	1.47396i
$423$	11.5109	−	8.36316i	0.559679	−	0.406631i
$424$	−16.8046	−	51.7191i	−0.816102	−	2.51170i
$425$	−7.21446	−	5.24161i	−0.349953	−	0.254256i
$426$	−2.98565	−	2.16920i	−0.144655	−	0.105098i
$427$	−11.9984	+	8.71733i	−0.580642	+	0.421861i
$428$	79.7854			3.85657
$429$	−53.3405			−2.57530
$430$	−21.1547	+	15.3698i	−1.02017	+	0.741198i
$431$	−4.29806	+	13.2281i	−0.207030	+	0.637173i	0.792594	+	0.609750i	$0.208730\pi$
$431$	−4.29806	+	13.2281i	−0.207030	+	0.637173i	−0.999624	+	0.0274232i	$0.991270\pi$
$432$	11.0055	+	33.8716i	0.529505	+	1.62965i
$433$	8.16980			0.392616			0.196308	−	0.980542i	$-0.437105\pi$
$433$	8.16980			0.392616			0.196308	+	0.980542i	$0.437105\pi$
$434$	40.2560	−	7.16212i	1.93235	−	0.343793i
$435$	37.9007			1.81720
$436$	24.6095	+	75.7403i	1.17858	+	3.62730i
$437$	5.63023	−	17.3281i	0.269331	−	0.828914i
$438$	26.1707	−	19.0141i	1.25048	−	0.908529i
$439$	26.7333			1.27591			0.637954	−	0.770074i	$-0.279781\pi$
$439$	26.7333			1.27591			0.637954	+	0.770074i	$0.279781\pi$
$440$	153.213			7.30415
$441$	−0.563391	+	0.409327i	−0.0268281	+	0.0194918i
$442$	11.5585	+	8.39775i	0.549782	+	0.399440i
$443$	−2.37486	−	1.72544i	−0.112833	−	0.0819781i	0.529938	−	0.848037i	$-0.322215\pi$
$443$	−2.37486	−	1.72544i	−0.112833	−	0.0819781i	−0.642771	+	0.766058i	$0.722215\pi$
$444$	0.272638	+	0.839094i	0.0129388	+	0.0398216i
$445$	−27.8054	+	20.2018i	−1.31810	+	0.957658i
$446$	−14.9371	−	45.9718i	−0.707293	−	2.17683i
$447$	2.37370	−	7.30549i	0.112272	−	0.345538i
$448$	−51.2332	−	37.2231i	−2.42054	−	1.75863i
$449$	1.50849	−	4.64266i	0.0711902	−	0.219101i	−0.909131	−	0.416511i	$-0.863253\pi$
$449$	1.50849	−	4.64266i	0.0711902	−	0.219101i	0.980321	+	0.197410i	$0.0632529\pi$
$450$	−13.3553	+	41.1033i	−0.629574	+	1.93763i
$451$	35.2281	+	25.5947i	1.65883	+	1.20521i
$452$	15.1886	−	46.7457i	0.714411	−	2.19873i
$453$	−9.72777	−	29.9390i	−0.457051	−	1.40666i
$454$	−52.7394	+	38.3174i	−2.47518	+	1.79833i
$455$	−16.5703	−	50.9982i	−0.776829	−	2.39083i
$456$	57.8707	+	42.0455i	2.71004	+	1.96896i
$457$	−19.9726	−	14.5109i	−0.934279	−	0.678793i	0.0127580	−	0.999919i	$-0.495939\pi$
$457$	−19.9726	−	14.5109i	−0.934279	−	0.678793i	−0.947037	+	0.321125i	$0.895939\pi$
$458$	40.2825	−	29.2669i	1.88228	−	1.36755i
$459$	2.64091			0.123267
$460$	98.2870			4.58266
$461$	11.6422	−	8.45857i	0.542232	−	0.393955i	−0.282681	−	0.959214i	$-0.591224\pi$
$461$	11.6422	−	8.45857i	0.542232	−	0.393955i	0.824913	+	0.565259i	$0.191224\pi$
$462$	22.8907	−	70.4502i	1.06497	−	3.27764i
$463$	−3.73917	−	11.5080i	−0.173774	−	0.534822i	0.825801	−	0.563961i	$-0.190723\pi$
$463$	−3.73917	−	11.5080i	−0.173774	−	0.534822i	−0.999575	+	0.0291396i	$0.990723\pi$
$464$	62.5749			2.90497
$465$	−21.4125	−	40.1219i	−0.992981	−	1.86061i
$466$	−5.42215			−0.251176
$467$	10.1429	+	31.2168i	0.469359	+	1.44454i	0.853416	+	0.521230i	$0.174527\pi$
$467$	10.1429	+	31.2168i	0.469359	+	1.44454i	−0.384057	+	0.923309i	$0.625473\pi$
$468$	15.5344	−	47.8098i	0.718076	−	2.21001i
$469$	5.75831	−	4.18366i	0.265894	−	0.193183i
$470$	−79.9470			−3.68768
$471$	18.3496			0.845503
$472$	−18.5343	+	13.4659i	−0.853109	+	0.619820i
$473$	−9.66937	−	7.02521i	−0.444598	−	0.323019i
$474$	18.7498	+	13.6225i	0.861206	+	0.625703i
$475$	−10.0993	−	31.0826i	−0.463390	−	1.42617i
$476$	−11.6537	+	8.46689i	−0.534145	+	0.388079i
$477$	3.38150	+	10.4072i	0.154828	+	0.476513i
$478$	17.5218	−	53.9267i	0.801430	−	2.46655i
$479$	−13.5750	−	9.86280i	−0.620257	−	0.450643i	0.232754	−	0.972536i	$-0.425226\pi$
$479$	−13.5750	−	9.86280i	−0.620257	−	0.450643i	−0.853011	+	0.521893i	$0.825226\pi$
$480$	−46.9640	+	144.540i	−2.14360	+	6.59733i
$481$	−0.124253	+	0.382412i	−0.00566546	+	0.0174365i
$482$	−22.5992	−	16.4193i	−1.02936	−	0.747877i
$483$	9.14265	−	28.1382i	0.416005	−	1.28033i
$484$	16.7440	+	51.5329i	0.761093	+	2.34240i
$485$	−41.6778	+	30.2807i	−1.89249	+	1.37497i
$486$	−13.7923	−	42.4483i	−0.625630	−	1.92549i
$487$	−5.46207	−	3.96842i	−0.247510	−	0.179826i	0.457113	−	0.889409i	$-0.348884\pi$
$487$	−5.46207	−	3.96842i	−0.247510	−	0.179826i	−0.704623	+	0.709582i	$0.748884\pi$
$488$	39.3503	+	28.5897i	1.78131	+	1.29419i
$489$	24.0073	−	17.4423i	1.08565	−	0.788768i
$490$	3.91293			0.176768
$491$	−14.5229			−0.655407			−0.327704	−	0.944781i	$-0.606275\pi$
$491$	−14.5229			−0.655407			−0.327704	+	0.944781i	$0.606275\pi$
$492$	−88.7251	+	64.4626i	−4.00004	+	2.90620i
$493$	1.43386	−	4.41297i	0.0645779	−	0.198750i
$494$	16.1805	+	49.7984i	0.727994	+	2.24054i
$495$	−30.8303			−1.38572
$496$	−35.3525	−	66.2422i	−1.58737	−	2.97436i
$497$	1.69575			0.0760650
$498$	6.74024	+	20.7443i	0.302038	+	0.929576i
$499$	−0.543909	+	1.67398i	−0.0243487	+	0.0749376i	−0.962492	−	0.271308i	$-0.912544\pi$
$499$	−0.543909	+	1.67398i	−0.0243487	+	0.0749376i	0.938144	+	0.346246i	$0.112544\pi$
$500$	62.6600	−	45.5252i	2.80224	−	2.03595i
$501$	−12.7115			−0.567909
$502$	−36.5825			−1.63276
$503$	−35.6991	+	25.9369i	−1.59174	+	1.15647i	−0.690341	+	0.723484i	$0.742539\pi$
$503$	−35.6991	+	25.9369i	−1.59174	+	1.15647i	−0.901401	+	0.432984i	$0.857461\pi$
$504$	35.1642	+	25.5483i	1.56634	+	1.13801i
$505$	−19.1290	−	13.8980i	−0.851229	−	0.618454i
$506$	19.1217	+	58.8506i	0.850065	+	2.61623i
$507$	26.5056	−	19.2575i	1.17716	−	0.855254i
$508$	6.05184	+	18.6256i	0.268507	+	0.826379i
$509$	7.93857	−	24.4324i	0.351871	−	1.08295i	−0.605931	−	0.795517i	$-0.707199\pi$
$509$	7.93857	−	24.4324i	0.351871	−	1.08295i	0.957802	−	0.287430i	$-0.0928009\pi$
$510$	17.8536	+	12.9714i	0.790572	+	0.574384i
$511$	−4.59327	+	14.1366i	−0.203194	+	0.625368i
$512$	−3.23954	+	9.97027i	−0.143169	+	0.440628i
$513$	7.83027	+	5.68902i	0.345715	+	0.251176i
$514$	−3.61885	+	11.1377i	−0.159621	+	0.491262i
$515$	4.73274	+	14.5659i	0.208549	+	0.641849i
$516$	24.3532	−	17.6936i	1.07209	−	0.778918i
$517$	−11.2921	−	34.7535i	−0.496626	−	1.52846i
$518$	−0.451754	−	0.328219i	−0.0198489	−	0.0144211i
$519$	−30.8725	−	22.4302i	−1.35515	−	0.984576i
$520$	−142.276	+	103.370i	−6.23923	+	4.53306i
$521$	39.0959			1.71282			0.856411	−	0.516295i	$-0.172689\pi$
$521$	39.0959			1.71282			0.856411	+	0.516295i	$0.172689\pi$
$522$	−22.4879			−0.984271
$523$	−7.75828	+	5.63672i	−0.339246	+	0.246476i	−0.744344	−	0.667797i	$-0.767237\pi$
$523$	−7.75828	+	5.63672i	−0.339246	+	0.246476i	0.405098	+	0.914273i	$0.367237\pi$
$524$	−23.9705	+	73.7737i	−1.04716	+	3.22282i
$525$	−16.3998	−	50.4734i	−0.715747	−	2.20284i
$526$	−40.6803			−1.77374
$527$	−5.48168	+	0.975271i	−0.238786	+	0.0424835i
$528$	−136.030			−5.91994
$529$	0.529928	+	1.63095i	0.0230404	+	0.0709109i
$530$	19.0003	−	58.4768i	0.825319	−	2.54007i
$531$	3.72956	−	2.70969i	0.161849	−	0.117590i
$532$	−52.7922			−2.28883
$533$	−49.9816			−2.16494
$534$	44.0895	−	32.0329i	1.90794	−	1.38620i
$535$	45.4388	+	33.0132i	1.96449	+	1.42729i
$536$	−18.8852	−	13.7209i	−0.815715	−	0.592652i
$537$	3.03775	+	9.34922i	0.131088	+	0.403449i
$538$	−62.3737	+	45.3171i	−2.68912	+	1.95376i
$539$	0.552682	+	1.70098i	0.0238057	+	0.0732664i
$540$	−16.1344	+	49.6566i	−0.694315	+	2.13688i
$541$	−14.7589	−	10.7230i	−0.634536	−	0.461017i	0.223433	−	0.974719i	$-0.428274\pi$
$541$	−14.7589	−	10.7230i	−0.634536	−	0.461017i	−0.857969	+	0.513702i	$0.828274\pi$
$542$	5.00667	−	15.4090i	0.215055	−	0.661871i
$543$	6.83086	−	21.0232i	0.293140	−	0.902192i
$544$	15.0528	+	10.9365i	0.645384	+	0.468899i
$545$	−17.3240	+	53.3179i	−0.742081	+	2.28389i
$546$	26.2747	+	80.8651i	1.12445	+	3.46071i
$547$	19.4782	−	14.1517i	0.832828	−	0.605085i	−0.0875301	−	0.996162i	$-0.527897\pi$
$547$	19.4782	−	14.1517i	0.832828	−	0.605085i	0.920358	+	0.391077i	$0.127897\pi$
$548$	33.0626	+	101.756i	1.41236	+	4.34681i
$549$	−7.91828	−	5.75296i	−0.337944	−	0.245531i
$550$	89.7986	+	65.2425i	3.82902	+	2.78195i
$551$	13.7578	−	9.99559i	0.586100	−	0.425827i
$552$	−97.0321			−4.12996
$553$	−10.6493			−0.452854
$554$	32.2350	−	23.4201i	1.36953	−	0.995025i
$555$	−0.191926	+	0.590686i	−0.00814678	+	0.0250732i
$556$	−2.27505	−	7.00189i	−0.0964836	−	0.296946i
$557$	−16.5469			−0.701116			−0.350558	−	0.936541i	$-0.614008\pi$
$557$	−16.5469			−0.701116			−0.350558	+	0.936541i	$0.614008\pi$
$558$	12.7049	+	23.8059i	0.537839	+	1.00778i
$559$	13.7189			0.580247
$560$	−42.2580	−	130.057i	−1.78573	−	5.49590i
$561$	−3.11704	+	9.59325i	−0.131601	+	0.405027i
$562$	−13.5792	+	9.86587i	−0.572804	+	0.416167i
$563$	−14.0134			−0.590595			−0.295297	−	0.955405i	$-0.595419\pi$
$563$	−14.0134			−0.590595			−0.295297	+	0.955405i	$0.595419\pi$
$564$	92.0343			3.87534
$565$	27.9923	−	20.3376i	1.17765	−	0.855610i
$566$	53.1047	+	38.5829i	2.23216	+	1.62176i
$567$	24.5490	+	17.8359i	1.03096	+	0.749038i
$568$	−1.71859	−	5.28926i	−0.0721102	−	0.221932i
$569$	−21.8298	+	15.8603i	−0.915153	+	0.664897i	−0.942313	−	0.334734i	$-0.891354\pi$
$569$	−21.8298	+	15.8603i	−0.915153	+	0.664897i	0.0271599	+	0.999631i	$0.491354\pi$
$570$	24.9929	+	76.9201i	1.04684	+	3.22183i
$571$	−2.54382	+	7.82909i	−0.106456	+	0.327637i	−0.990069	−	0.140580i	$-0.955103\pi$
$571$	−2.54382	+	7.82909i	−0.106456	+	0.327637i	0.883614	+	0.468217i	$0.155103\pi$
$572$	−104.450	−	75.8875i	−4.36728	−	3.17302i
$573$	−9.20531	+	28.3310i	−0.384557	+	1.18355i
$574$	21.4492	−	66.0139i	0.895273	−	2.75537i
$575$	35.8660	+	26.0582i	1.49572	+	1.08670i
$576$	12.9147	−	39.7473i	0.538112	−	1.65614i
$577$	−3.30951	−	10.1856i	−0.137777	−	0.424033i	0.858235	−	0.513257i	$-0.171561\pi$
$577$	−3.30951	−	10.1856i	−0.137777	−	0.424033i	−0.996012	+	0.0892241i	$0.971561\pi$
$578$	2.18577	−	1.58805i	0.0909160	−	0.0660544i
$579$	−11.0647	−	34.0537i	−0.459834	−	1.41522i
$580$	74.2164	+	53.9213i	3.08167	+	2.23896i
$581$	−8.10837	−	5.89107i	−0.336392	−	0.244403i
$582$	66.0861	−	48.0144i	2.73936	−	1.99026i
$583$	28.1040			1.16395
$584$	48.7490			2.01725
$585$	28.6296	−	20.8006i	1.18369	−	0.859999i
$586$	−4.05862	+	12.4911i	−0.167660	+	0.516004i
$587$	−12.4960	−	38.4587i	−0.515765	−	1.58736i	−0.781886	−	0.623422i	$-0.785742\pi$
$587$	−12.4960	−	38.4587i	−0.515765	−	1.58736i	0.266121	−	0.963940i	$-0.414258\pi$
$588$	−4.50454			−0.185764
$589$	−18.3540	−	8.91691i	−0.756264	−	0.367415i
$590$	−25.9030			−1.06641
$591$	−5.31248	−	16.3501i	−0.218526	−	0.672554i
$592$	−0.316873	+	0.975235i	−0.0130234	+	0.0400819i
$593$	33.9221	−	24.6458i	1.39301	−	1.01208i	0.397485	−	0.917609i	$-0.369883\pi$
$593$	33.9221	−	24.6458i	1.39301	−	1.01208i	0.995527	−	0.0944740i	$-0.0301169\pi$
$594$	−32.8715			−1.34873
$595$	−10.1403			−0.415712
$596$	15.0416	−	10.9284i	0.616130	−	0.447644i
$597$	23.7449	+	17.2517i	0.971813	+	0.706063i
$598$	−57.4621	−	41.7486i	−2.34980	−	1.70723i
$599$	4.70517	+	14.4810i	0.192248	+	0.591678i	0.999998	+	0.00215267i	$0.000685218\pi$
$599$	4.70517	+	14.4810i	0.192248	+	0.591678i	−0.807750	+	0.589525i	$0.799315\pi$
$600$	−140.812	+	102.306i	−5.74863	+	4.17663i
$601$	7.02743	+	21.6282i	0.286655	+	0.882233i	0.985898	+	0.167349i	$0.0535207\pi$
$601$	7.02743	+	21.6282i	0.286655	+	0.882233i	−0.699243	+	0.714884i	$0.746479\pi$
$602$	−5.88736	+	18.1194i	−0.239951	+	0.738493i
$603$	3.80017	+	2.76099i	0.154755	+	0.112436i
$604$	23.5455	−	72.4656i	0.958053	−	2.94858i
$605$	−11.7871	+	36.2769i	−0.479213	+	1.47487i
$606$	30.3318	+	22.0373i	1.23214	+	0.895206i
$607$	13.1037	−	40.3289i	0.531861	−	1.63690i	−0.218475	−	0.975843i	$-0.570108\pi$
$607$	13.1037	−	40.3289i	0.531861	−	1.63690i	0.750336	−	0.661057i	$-0.229892\pi$
$608$	21.0721	+	64.8532i	0.854586	+	2.63014i
$609$	22.3405	−	16.2313i	0.905283	−	0.657727i
$610$	16.9944	+	52.3034i	0.688083	+	2.11770i
$611$	33.9335	+	24.6541i	1.37280	+	0.997400i
$612$	−7.69079	−	5.58769i	−0.310882	−	0.225869i
$613$	19.0259	−	13.8231i	0.768448	−	0.558310i	−0.133042	−	0.991110i	$-0.542474\pi$
$613$	19.0259	−	13.8231i	0.768448	−	0.558310i	0.901490	+	0.432800i	$0.142474\pi$
$614$	−30.8789			−1.24617
$615$	−77.2032			−3.11313
$616$	90.3113	−	65.6150i	3.63874	−	2.64370i
$617$	11.7338	−	36.1130i	0.472386	−	1.45385i	−0.377065	−	0.926187i	$-0.623067\pi$
$617$	11.7338	−	36.1130i	0.472386	−	1.45385i	0.849451	−	0.527668i	$-0.176933\pi$
$618$	−7.50444	−	23.0963i	−0.301873	−	0.929069i
$619$	−1.14569			−0.0460490			−0.0230245	−	0.999735i	$-0.507330\pi$
$619$	−1.14569			−0.0460490			−0.0230245	+	0.999735i	$0.507330\pi$
$620$	15.1520	−	109.029i	0.608519	−	4.37873i
$621$	−13.1291			−0.526851
$622$	−1.24111	−	3.81975i	−0.0497641	−	0.153158i
$623$	−7.73824	+	23.8159i	−0.310026	+	0.954163i
$624$	126.320	−	91.7766i	5.05683	−	3.67400i
$625$	9.93510			0.397404
$626$	60.6203			2.42287
$627$	−29.9076	+	21.7292i	−1.19440	+	0.867779i
$628$	35.9317	+	26.1059i	1.43383	+	1.04174i
$629$	0.0615157	+	0.0446937i	0.00245279	+	0.00178206i
$630$	15.1865	+	46.7393i	0.605046	+	1.86214i
$631$	23.7171	−	17.2315i	0.944161	−	0.685973i	−0.00525757	−	0.999986i	$-0.501674\pi$
$631$	23.7171	−	17.2315i	0.944161	−	0.685973i	0.949419	+	0.314013i	$0.101674\pi$
$632$	10.7927	+	33.2165i	0.429310	+	1.32128i
$633$	−7.97283	+	24.5378i	−0.316892	+	0.975292i
$634$	28.2591	+	20.5314i	1.12231	+	0.815407i
$635$	−4.26024	+	13.1117i	−0.169062	+	0.520320i
$636$	−21.8730	+	67.3181i	−0.867320	+	2.66934i
$637$	−1.66085	−	1.20668i	−0.0658051	−	0.0478102i
$638$	−17.8473	+	54.9284i	−0.706582	+	2.17464i
$639$	0.345823	+	1.06433i	0.0136805	+	0.0421044i
$640$	−77.6680	+	56.4291i	−3.07010	+	2.23056i
$641$	−7.46644	−	22.9793i	−0.294907	−	0.907629i	−0.983253	−	0.182247i	$-0.941663\pi$
$641$	−7.46644	−	22.9793i	−0.294907	−	0.907629i	0.688346	−	0.725382i	$-0.258337\pi$
$642$	−72.0498	−	52.3473i	−2.84358	−	2.06598i
$643$	−32.4336	−	23.5644i	−1.27905	−	0.929288i	−0.279531	−	0.960137i	$-0.590179\pi$
$643$	−32.4336	−	23.5644i	−1.27905	−	0.929288i	−0.999524	+	0.0308489i	$0.990179\pi$
$644$	57.9351	−	42.0923i	2.28296	−	1.65867i
$645$	21.1906			0.834380
$646$	9.90174			0.389579
$647$	7.40003	−	5.37644i	0.290925	−	0.211370i	−0.432743	−	0.901517i	$-0.642454\pi$
$647$	7.40003	−	5.37644i	0.290925	−	0.211370i	0.723669	+	0.690147i	$0.242454\pi$
$648$	30.7528	−	94.6475i	1.20809	−	3.71810i
$649$	−3.65867	−	11.2602i	−0.143616	−	0.442003i
$650$	−127.406			−4.99728
$651$	−29.8042	−	14.4797i	−1.16812	−	0.567505i
$652$	71.8256			2.81291
$653$	13.8525	+	42.6335i	0.542089	+	1.66838i	0.727812	+	0.685776i	$0.240537\pi$
$653$	13.8525	+	42.6335i	0.542089	+	1.66838i	−0.185723	+	0.982602i	$0.559463\pi$
$654$	27.4698	−	84.5433i	1.07415	−	3.30590i
$655$	−44.1773	+	32.0967i	−1.72615	+	1.25412i
$656$	−127.464			−4.97664
$657$	−9.80952			−0.382706
$658$	−47.1246	+	34.2380i	−1.83711	+	1.33474i
$659$	4.48452	+	3.25819i	0.174692	+	0.126921i	0.671695	−	0.740827i	$-0.265566\pi$
$659$	4.48452	+	3.25819i	0.174692	+	0.126921i	−0.497003	+	0.867749i	$0.665566\pi$
$660$	−161.337	−	117.218i	−6.28004	−	4.56271i
$661$	−1.37090	−	4.21918i	−0.0533217	−	0.164107i	0.920849	−	0.389918i	$-0.127497\pi$
$661$	−1.37090	−	4.21918i	−0.0533217	−	0.164107i	−0.974171	+	0.225811i	$0.927497\pi$
$662$	−32.1483	+	23.3571i	−1.24948	+	0.907799i
$663$	−3.57784	−	11.0115i	−0.138952	−	0.427649i
$664$	−10.1574	+	31.2614i	−0.394185	+	1.21318i
$665$	−30.0659	−	21.8441i	−1.16590	−	0.847079i
$666$	0.113877	−	0.350477i	0.00441264	−	0.0135807i
$667$	−7.12831	+	21.9387i	−0.276009	+	0.849469i
$668$	−24.8914	−	18.0847i	−0.963078	−	0.699717i
$669$	−12.1049	+	37.2550i	−0.468002	+	1.44036i
$670$	−8.15602	−	25.1017i	−0.315095	−	0.969762i
$671$	−20.3363	+	14.7752i	−0.785073	+	0.570389i
$672$	34.2179	+	105.312i	1.31998	+	4.06249i
$673$	34.0454	+	24.7354i	1.31235	+	0.953480i	0.999994	+	0.00351559i	$0.00111905\pi$
$673$	34.0454	+	24.7354i	1.31235	+	0.953480i	0.312359	+	0.949964i	$0.398881\pi$
$674$	22.5441	+	16.3792i	0.868365	+	0.630904i
$675$	−19.0528	+	13.8426i	−0.733341	+	0.532803i
$676$	79.3003			3.05001
$677$	27.7221			1.06545			0.532723	−	0.846290i	$-0.321169\pi$
$677$	27.7221			1.06545			0.532723	+	0.846290i	$0.321169\pi$
$678$	−44.3859	+	32.2482i	−1.70463	+	1.23849i
$679$	−11.5989	+	35.6978i	−0.445125	+	1.36996i
$680$	10.2768	+	31.6289i	0.394099	+	1.21291i
$681$	52.8289			2.02441
$682$	68.2306	−	12.1392i	2.61269	−	0.464835i
$683$	0.347837			0.0133096			0.00665480	−	0.999978i	$-0.497882\pi$
$683$	0.347837			0.0133096			0.00665480	+	0.999978i	$0.497882\pi$
$684$	−10.7662	−	33.1348i	−0.411654	−	1.26694i
$685$	−23.2746	+	71.6320i	−0.889278	+	2.73692i
$686$	−39.2819	+	28.5400i	−1.49979	+	1.08966i
$687$	−40.3508			−1.53948
$688$	34.9862			1.33384
$689$	−26.0978	+	18.9612i	−0.994248	+	0.722364i
$690$	−88.7577	−	64.4862i	−3.37895	−	2.45495i
$691$	19.4411	+	14.1248i	0.739576	+	0.537333i	0.892578	−	0.450893i	$-0.148894\pi$
$691$	19.4411	+	14.1248i	0.739576	+	0.537333i	−0.153003	+	0.988226i	$0.548894\pi$
$692$	−28.5425	−	87.8447i	−1.08502	−	3.33935i
$693$	−18.1729	+	13.2034i	−0.690331	+	0.501555i
$694$	−13.0122	−	40.0475i	−0.493937	−	1.52018i
$695$	1.60154	−	4.92903i	0.0607498	−	0.186969i
$696$	−73.2688	−	53.2329i	−2.77725	−	2.01779i
$697$	−2.92076	+	8.98916i	−0.110631	+	0.340489i
$698$	11.6629	−	35.8948i	0.441448	−	1.35864i
$699$	3.55487	+	2.58276i	0.134457	+	0.0976891i
$700$	39.6948	−	122.168i	1.50032	−	4.61752i
$701$	−2.07756	−	6.39407i	−0.0784683	−	0.241501i	0.904126	−	0.427267i	$-0.140523\pi$
$701$	−2.07756	−	6.39407i	−0.0784683	−	0.241501i	−0.982594	+	0.185766i	$0.940523\pi$
$702$	30.5250	−	22.1777i	1.15209	−	0.837044i
$703$	0.0861143	+	0.265033i	0.00324786	+	0.00999589i
$704$	−86.8361	−	63.0901i	−3.27276	−	2.37780i
$705$	52.4148	+	38.0816i	1.97405	+	1.43423i
$706$	43.5148	−	31.6154i	1.63770	−	1.18986i
$707$	−17.2275			−0.647908
$708$	29.8194			1.12068
$709$	−5.68591	+	4.13105i	−0.213539	+	0.155145i	−0.689413	−	0.724368i	$-0.742132\pi$
$709$	−5.68591	+	4.13105i	−0.213539	+	0.155145i	0.475875	+	0.879513i	$0.342132\pi$
$710$	1.94314	−	5.98037i	0.0729247	−	0.224439i
$711$	−2.17176	−	6.68399i	−0.0814473	−	0.250669i
$712$	82.1270			3.07784
$713$	27.2517	−	4.84847i	1.02058	−	0.181577i
$714$	16.0789			0.601739
$715$	−28.0854	−	86.4379i	−1.05033	−	3.23259i
$716$	−7.35269	+	22.6292i	−0.274783	+	0.845694i
$717$	−37.1748	+	27.0091i	−1.38832	+	1.00867i
$718$	60.8745			2.27182
$719$	−8.63112			−0.321887			−0.160943	−	0.986964i	$-0.551454\pi$
$719$	−8.63112			−0.321887			−0.160943	+	0.986964i	$0.551454\pi$
$720$	73.0117	−	53.0461i	2.72098	−	1.97691i
$721$	9.02767	+	6.55899i	0.336208	+	0.244269i
$722$	−12.1711	−	8.84283i	−0.452962	−	0.329096i
$723$	6.99538	+	21.5296i	0.260161	+	0.800693i
$724$	43.2858	−	31.4489i	1.60870	−	1.16879i
$725$	12.7866	+	39.3530i	0.474881	+	1.46153i
$726$	18.6901	−	57.5223i	0.693656	−	2.13485i
$727$	11.5625	+	8.40065i	0.428829	+	0.311563i	0.781181	−	0.624305i	$-0.214618\pi$
$727$	11.5625	+	8.40065i	0.428829	+	0.311563i	−0.352351	+	0.935868i	$0.614618\pi$
$728$	−39.5954	+	121.862i	−1.46750	+	4.51652i
$729$	−0.827828	+	2.54779i	−0.0306603	+	0.0943627i
$730$	44.5919	+	32.3979i	1.65042	+	1.19910i
$731$	0.801685	−	2.46733i	0.0296514	−	0.0912577i
$732$	−19.5638	−	60.2112i	−0.723099	−	2.22547i
$733$	9.86622	−	7.16823i	0.364417	−	0.264764i	−0.390475	−	0.920614i	$-0.627689\pi$
$733$	9.86622	−	7.16823i	0.364417	−	0.264764i	0.754892	+	0.655849i	$0.227689\pi$
$734$	13.2429	+	40.7574i	0.488804	+	1.50438i
$735$	−2.56539	−	1.86387i	−0.0946260	−	0.0687498i
$736$	−74.8337	−	54.3699i	−2.75841	−	2.00410i
$737$	9.75988	−	7.09096i	0.359510	−	0.261199i
$738$	45.8076			1.68620
$739$	−49.5694			−1.82344			−0.911720	−	0.410811i	$-0.865246\pi$
$739$	−49.5694			−1.82344			−0.911720	+	0.410811i	$0.865246\pi$
$740$	−1.21619	+	0.883616i	−0.0447082	+	0.0324824i
$741$	13.1125	−	40.3561i	0.481700	−	1.48252i
$742$	−13.8436	−	42.6061i	−0.508214	−	1.56412i
$743$	2.47096			0.0906509			0.0453254	−	0.998972i	$-0.485568\pi$
$743$	2.47096			0.0906509			0.0453254	+	0.998972i	$0.485568\pi$
$744$	−14.9585	+	107.637i	−0.548407	+	3.94618i
$745$	13.0883			0.479519
$746$	10.9473	+	33.6923i	0.400808	+	1.23356i
$747$	2.04393	−	6.29057i	0.0747835	−	0.230160i
$748$	−19.7520	+	14.3507i	−0.722206	+	0.524713i
$749$	40.9221			1.49526
$750$	−86.4540			−3.15685
$751$	−4.82083	+	3.50254i	−0.175915	+	0.127809i	−0.672258	−	0.740317i	$-0.734676\pi$
$751$	−4.82083	+	3.50254i	−0.175915	+	0.127809i	0.496344	+	0.868126i	$0.334676\pi$
$752$	86.5379	+	62.8735i	3.15571	+	2.29276i
$753$	23.9842	+	17.4255i	0.874033	+	0.635022i
$754$	−20.4857	−	63.0486i	−0.746047	−	2.29610i
$755$	43.3940	−	31.5276i	1.57927	−	1.14741i
$756$	11.7555	+	36.1798i	0.427544	+	1.31584i
$757$	−2.45223	+	7.54719i	−0.0891278	+	0.274307i	−0.985679	−	0.168633i	$-0.946065\pi$
$757$	−2.45223	+	7.54719i	−0.0891278	+	0.274307i	0.896551	+	0.442940i	$0.146065\pi$
$758$	−75.5492	−	54.8897i	−2.74407	−	1.99368i
$759$	15.4961	−	47.6920i	0.562471	−	1.73111i
$760$	−37.6638	+	115.917i	−1.36621	+	4.20476i
$761$	−33.7915	−	24.5510i	−1.22494	−	0.889972i	−0.228441	−	0.973558i	$-0.573363\pi$
$761$	−33.7915	−	24.5510i	−1.22494	−	0.889972i	−0.996501	+	0.0835859i	$0.973363\pi$
$762$	6.75522	−	20.7904i	0.244716	−	0.753158i
$763$	12.6223	+	38.8474i	0.456957	+	1.40637i
$764$	−58.3322	+	42.3808i	−2.11039	+	1.53328i
$765$	−2.06796	−	6.36452i	−0.0747672	−	0.230110i
$766$	−58.0108	−	42.1473i	−2.09601	−	1.52284i
$767$	10.9946	+	7.98801i	0.396990	+	0.288430i
$768$	40.6162	−	29.5094i	1.46561	−	1.06483i
$769$	25.2544			0.910696			0.455348	−	0.890314i	$-0.349515\pi$
$769$	25.2544			0.910696			0.455348	+	0.890314i	$0.349515\pi$
$770$	126.217			4.54854
$771$	7.67785	−	5.57829i	0.276511	−	0.200897i
$772$	26.7815	−	82.4251i	0.963888	−	2.96654i
$773$	3.77382	+	11.6146i	0.135735	+	0.417749i	0.995704	−	0.0925977i	$-0.0295170\pi$
$773$	3.77382	+	11.6146i	0.135735	+	0.417749i	−0.859969	+	0.510347i	$0.829517\pi$
$774$	−12.5732			−0.451935
$775$	34.4354	−	35.7689i	1.23696	−	1.28486i
$776$	123.101			4.41906
$777$	0.139837	+	0.430373i	0.00501661	+	0.0154395i
$778$	−8.18349	+	25.1862i	−0.293392	+	0.902969i
$779$	−28.0243	+	20.3609i	−1.00408	+	0.729504i
$780$	228.905			8.19611
$781$	2.87417			0.102846
$782$	−10.8663	+	7.89486i	−0.388580	+	0.282320i
$783$	−9.91372	−	7.20274i	−0.354288	−	0.257405i
$784$	−4.23552	−	3.07729i	−0.151269	−	0.109903i
$785$	9.66160	+	29.7353i	0.344837	+	1.06130i
$786$	70.0494	−	50.8939i	2.49858	−	1.81533i
$787$	−3.97602	−	12.2369i	−0.141730	−	0.436200i	0.854846	−	0.518882i	$-0.173651\pi$
$787$	−3.97602	−	12.2369i	−0.141730	−	0.436200i	−0.996576	+	0.0826820i	$0.973651\pi$
$788$	12.8585	−	39.5745i	0.458066	−	1.40978i
$789$	26.6708	+	19.3774i	0.949504	+	0.689855i
$790$	−12.2029	+	37.5566i	−0.434159	+	1.33620i
$791$	7.79026	−	23.9760i	0.276990	−	0.852487i
$792$	59.6005	+	43.3023i	2.11781	+	1.53868i
$793$	8.91610	−	27.4409i	0.316620	−	0.974456i
$794$	22.0947	+	68.0005i	0.784112	+	2.41325i
$795$	−40.3115	+	29.2880i	−1.42970	+	1.03874i
$796$	21.9528	+	67.5636i	0.778095	+	2.39473i
$797$	10.5375	+	7.65596i	0.373258	+	0.271188i	0.758561	−	0.651602i	$-0.225903\pi$
$797$	10.5375	+	7.65596i	0.373258	+	0.271188i	−0.385302	+	0.922790i	$0.625903\pi$
$798$	47.6738	+	34.6370i	1.68763	+	1.22614i
$799$	6.41699	−	4.66222i	0.227017	−	0.164937i
$800$	−165.923			−5.86626
$801$	−16.5260			−0.583918
$802$	−64.8341	+	47.1047i	−2.28937	+	1.66333i
$803$	−7.78522	+	23.9604i	−0.274734	+	0.845546i
$804$	9.38915	+	28.8968i	0.331130	+	1.01911i
$805$	50.4116			1.77678
$806$	−55.1700	+	57.3065i	−1.94328	+	2.01853i
$807$	62.4795			2.19938
$808$	17.4595	+	53.7347i	0.614222	+	1.89038i
$809$	4.96563	−	15.2826i	0.174582	−	0.537309i	−0.825032	−	0.565086i	$-0.808843\pi$
$809$	4.96563	−	15.2826i	0.174582	−	0.537309i	0.999614	+	0.0277772i	$0.00884288\pi$
$810$	91.0318	−	66.1385i	3.19853	−	2.32387i
$811$	−38.1163			−1.33845			−0.669223	−	0.743062i	$-0.733373\pi$
$811$	−38.1163			−1.33845			−0.669223	+	0.743062i	$0.733373\pi$
$812$	66.8390			2.34559
$813$	−10.6223	+	7.71755i	−0.372540	+	0.270666i
$814$	−0.765687	−	0.556304i	−0.0268373	−	0.0194985i
$815$	40.9057	+	29.7197i	1.43286	+	1.04104i
$816$	−9.12427	−	28.0816i	−0.319413	−	0.983053i
$817$	7.69208	−	5.58863i	0.269112	−	0.195521i
$818$	−31.1262	−	95.7966i	−1.08830	−	3.34945i
$819$	7.96760	−	24.5218i	0.278411	−	0.856860i
$820$	−151.178	−	109.837i	−5.27935	−	3.83567i
$821$	−8.77000	+	26.9913i	−0.306075	+	0.942002i	0.673199	+	0.739461i	$0.264920\pi$
$821$	−8.77000	+	26.9913i	−0.306075	+	0.942002i	−0.979274	+	0.202540i	$0.935080\pi$
$822$	36.9053	−	113.583i	1.28722	−	3.96166i
$823$	26.2109	+	19.0433i	0.913654	+	0.663809i	0.941936	−	0.335791i	$-0.109004\pi$
$823$	26.2109	+	19.0433i	0.913654	+	0.663809i	−0.0282820	+	0.999600i	$0.509004\pi$
$824$	11.3091	−	34.8057i	0.393970	−	1.21251i
$825$	−27.7964	−	85.5484i	−0.967745	−	2.97841i
$826$	−15.2685	+	11.0932i	−0.531259	+	0.385983i
$827$	13.0448	+	40.1479i	0.453613	+	1.39608i	0.872755	+	0.488158i	$0.162331\pi$
$827$	13.0448	+	40.1479i	0.453613	+	1.39608i	−0.419142	+	0.907921i	$0.637669\pi$
$828$	38.2340	+	27.7787i	1.32872	+	0.965375i
$829$	22.0598	+	16.0273i	0.766167	+	0.556653i	0.900796	−	0.434243i	$-0.142984\pi$
$829$	22.0598	+	16.0273i	0.766167	+	0.556653i	−0.134629	+	0.990896i	$0.542984\pi$
$830$	−30.0671	+	21.8450i	−1.04364	+	0.758252i
$831$	−32.2897			−1.12012
$832$	123.203			4.27130
$833$	−0.314074	+	0.228188i	−0.0108820	+	0.00790625i
$834$	−2.53947	+	7.81569i	−0.0879347	+	0.270635i
$835$	−6.69300	−	20.5989i	−0.231621	−	0.712855i
$836$	−89.4786			−3.09468
$837$	−2.02398	+	14.5640i	−0.0699591	+	0.503406i
$838$	−47.8579			−1.65322
$839$	−10.7651	−	33.1317i	−0.371654	−	1.14383i	−0.945708	−	0.325016i	$-0.894630\pi$
$839$	−10.7651	−	33.1317i	−0.371654	−	1.14383i	0.574054	−	0.818817i	$-0.305370\pi$
$840$	−61.1604	+	188.232i	−2.11023	+	6.49463i
$841$	6.04311	−	4.39058i	0.208383	−	0.151399i
$842$	−45.5508			−1.56979
$843$	13.6022			0.468486
$844$	−50.5222	+	36.7065i	−1.73905	+	1.26349i
$845$	45.1626	+	32.8125i	1.55364	+	1.12879i
$846$	−31.0997	−	22.5952i	−1.06923	−	0.776841i
$847$	8.58805	+	26.4313i	0.295089	+	0.908191i
$848$	−66.5552	+	48.3552i	−2.28551	+	1.66052i
$849$	−16.4381	−	50.5913i	−0.564155	−	1.73629i
$850$	−7.44518	+	22.9139i	−0.255368	+	0.785941i
$851$	−0.305819	−	0.222191i	−0.0104834	−	0.00761660i
$852$	−2.23693	+	6.88455i	−0.0766358	+	0.235861i
$853$	−9.87690	+	30.3980i	−0.338179	+	1.04081i	0.626957	+	0.779054i	$0.284300\pi$
$853$	−9.87690	+	30.3980i	−0.338179	+	1.04081i	−0.965135	+	0.261752i	$0.915700\pi$
$854$	32.4167	+	23.5521i	1.10928	+	0.805937i
$855$	7.57891	−	23.3255i	0.259193	−	0.797715i
$856$	−41.4730	−	127.641i	−1.41752	−	4.36268i
$857$	−16.7277	+	12.1534i	−0.571407	+	0.415151i	−0.835616	−	0.549314i	$-0.814889\pi$
$857$	−16.7277	+	12.1534i	−0.571407	+	0.415151i	0.264209	+	0.964465i	$0.414889\pi$
$858$	44.5334	+	137.060i	1.52035	+	4.67914i
$859$	−38.3469	−	27.8606i	−1.30838	−	0.950592i	−0.308378	−	0.951264i	$-0.599786\pi$
$859$	−38.3469	−	27.8606i	−1.30838	−	0.950592i	−1.00000		0.000671608i	$0.999786\pi$
$860$	41.4950	+	30.1479i	1.41497	+	1.02804i
$861$	−45.5073	+	33.0630i	−1.55088	+	1.12678i
$862$	37.5782			1.27992
$863$	7.63757			0.259986			0.129993	−	0.991515i	$-0.458505\pi$
$863$	7.63757			0.259986			0.129993	+	0.991515i	$0.458505\pi$
$864$	39.7532	−	28.8824i	1.35243	−	0.982599i
$865$	20.0927	−	61.8389i	0.683171	−	2.10259i
$866$	−6.82088	−	20.9925i	−0.231783	−	0.713355i
$867$	−2.18948			−0.0743586
$868$	−37.7616	−	70.7563i	−1.28171	−	2.40162i
$869$	−18.0497			−0.612294
$870$	−31.6429	−	97.3869i	−1.07280	−	3.30172i
$871$	−4.27905	+	13.1696i	−0.144990	+	0.446234i
$872$	108.377	−	78.7408i	3.67012	−	2.66650i
$873$	−24.7710			−0.838370
$874$	−49.2256			−1.66508
$875$	32.1384	−	23.3500i	1.08648	−	0.789372i
$876$	−51.3338	−	37.2962i	−1.73441	−	1.26012i
$877$	44.9355	+	32.6475i	1.51736	+	1.10243i	0.962775	+	0.270305i	$0.0871244\pi$
$877$	44.9355	+	32.6475i	1.51736	+	1.10243i	0.554589	+	0.832125i	$0.312876\pi$
$878$	−22.3193	−	68.6918i	−0.753240	−	2.31824i
$879$	8.61088	−	6.25617i	0.290438	−	0.211015i
$880$	−71.6239	−	220.436i	−2.41444	−	7.43088i
$881$	4.76035	−	14.6508i	0.160380	−	0.493599i	−0.838286	−	0.545231i	$-0.816442\pi$
$881$	4.76035	−	14.6508i	0.160380	−	0.493599i	0.998666	+	0.0516313i	$0.0164420\pi$
$882$	1.52215	+	1.10590i	0.0512534	+	0.0372377i
$883$	−3.00401	+	9.24540i	−0.101093	+	0.311133i	−0.988794	−	0.149289i	$-0.952302\pi$
$883$	−3.00401	+	9.24540i	−0.101093	+	0.311133i	0.887701	+	0.460421i	$0.152302\pi$
$884$	8.65995	−	26.6526i	0.291266	−	0.896423i
$885$	16.9825	+	12.3385i	0.570862	+	0.414755i
$886$	−2.45081	+	7.54283i	−0.0823367	+	0.253406i
$887$	−8.90054	−	27.3930i	−0.298851	−	0.919768i	−0.981901	−	0.189396i	$-0.939347\pi$
$887$	−8.90054	−	27.3930i	−0.298851	−	0.919768i	0.683050	−	0.730372i	$-0.260653\pi$
$888$	1.20067	−	0.872334i	0.0402917	−	0.0292736i
$889$	3.10400	+	9.55313i	0.104105	+	0.320402i
$890$	75.1236	+	54.5805i	2.51815	+	1.82954i
$891$	41.6086	+	30.2304i	1.39394	+	1.01276i
$892$	−76.7063	+	55.7304i	−2.56832	+	1.86599i
$893$	29.0696			0.972776
$894$	−20.7534			−0.694098
$895$	−13.5509	+	9.84529i	−0.452956	+	0.329092i
$896$	−21.6150	+	66.5241i	−0.722106	+	2.22241i
$897$	17.7869	+	54.7424i	0.593887	+	1.82780i
$898$	−13.1889			−0.440118
$899$	23.2376	+	11.2895i	0.775018	+	0.376526i
$900$	84.7734			2.82578
$901$	1.88509	+	5.80170i	0.0628014	+	0.193283i
$902$	36.3547	−	111.888i	1.21048	−	3.72547i
$903$	12.4908	−	9.07509i	0.415667	−	0.302000i
$904$	−82.6790			−2.74986
$905$	37.6646			1.25201
$906$	−68.8074	+	49.9915i	−2.28597	+	1.66086i
$907$	−17.9675	−	13.0542i	−0.596602	−	0.433457i	0.248069	−	0.968742i	$-0.420204\pi$
$907$	−17.9675	−	13.0542i	−0.596602	−	0.433457i	−0.844671	+	0.535286i	$0.820204\pi$
$908$	103.448	+	75.1597i	3.43306	+	2.49426i
$909$	−3.51328	−	10.8128i	−0.116528	−	0.358637i
$910$	−117.207	+	85.1558i	−3.88537	+	2.82289i
$911$	−2.08121	−	6.40530i	−0.0689535	−	0.212217i	0.910642	−	0.413196i	$-0.135588\pi$
$911$	−2.08121	−	6.40530i	−0.0689535	−	0.212217i	−0.979596	+	0.200979i	$0.935588\pi$
$912$	33.4397	−	102.917i	1.10730	−	3.40792i
$913$	−13.7430	−	9.98489i	−0.454828	−	0.330452i
$914$	−20.6113	+	63.4351i	−0.681762	+	2.09825i
$915$	13.7721	−	42.3861i	0.455291	−	1.40124i
$916$	−79.0141	−	57.4071i	−2.61070	−	1.89678i
$917$	−12.2945	+	37.8387i	−0.406001	+	1.24954i
$918$	−2.20487	−	6.78590i	−0.0727716	−	0.223968i
$919$	12.8375	−	9.32696i	0.423469	−	0.307668i	−0.355563	−	0.934652i	$-0.615711\pi$
$919$	12.8375	−	9.32696i	0.423469	−	0.307668i	0.779032	+	0.626984i	$0.215711\pi$
$920$	−51.0903	−	157.240i	−1.68440	−	5.18405i
$921$	20.2448	+	14.7087i	0.667088	+	0.484668i
$922$	−31.4545	−	22.8530i	−1.03590	−	0.752624i
$923$	−2.66900	+	1.93914i	−0.0878511	+	0.0638276i
$924$	−145.300			−4.78001
$925$	−0.678070			−0.0222948
$926$	−26.4483	+	19.2158i	−0.869145	+	0.631471i
$927$	−2.27567	+	7.00378i	−0.0747427	+	0.230034i
$928$	−26.6789	−	82.1092i	−0.875777	−	2.69537i
$929$	−42.2439			−1.38598			−0.692989	−	0.720948i	$-0.743707\pi$
$929$	−42.2439			−1.38598			−0.692989	+	0.720948i	$0.743707\pi$
$930$	−85.2173	+	88.5174i	−2.79439	+	2.90260i
$931$	−1.42278			−0.0466299
$932$	3.28657	+	10.1150i	0.107655	+	0.331329i
$933$	−1.00579	+	3.09549i	−0.0329279	+	0.101342i
$934$	71.7441	−	52.1251i	2.34754	−	1.70559i
$935$	−17.1870			−0.562075
$936$	−84.5612			−2.76397
$937$	−42.5063	+	30.8826i	−1.38862	+	1.00889i	−0.392605	+	0.919707i	$0.628426\pi$
$937$	−42.5063	+	30.8826i	−1.38862	+	1.00889i	−0.996015	+	0.0891845i	$0.971574\pi$
$938$	−15.5576	−	11.3032i	−0.507973	−	0.369064i
$939$	−39.7438	−	28.8756i	−1.29699	−	0.942318i
$940$	48.4588	+	149.141i	1.58055	+	4.86444i
$941$	−39.7635	+	28.8898i	−1.29625	+	0.941782i	−0.999912	−	0.0133006i	$-0.995766\pi$
$941$	−39.7635	+	28.8898i	−1.29625	+	0.941782i	−0.296340	+	0.955083i	$0.595766\pi$
$942$	−15.3199	−	47.1497i	−0.499148	−	1.53622i
$943$	14.5203	−	44.6888i	0.472845	−	1.45527i
$944$	28.0385	+	20.3712i	0.912576	+	0.663026i
$945$	−8.27538	+	25.4690i	−0.269198	+	0.828507i
$946$	−9.97860	+	30.7110i	−0.324432	+	0.998500i
$947$	−19.1449	−	13.9096i	−0.622127	−	0.452001i	0.231537	−	0.972826i	$-0.425625\pi$
$947$	−19.1449	−	13.9096i	−0.622127	−	0.452001i	−0.853664	+	0.520825i	$0.825625\pi$
$948$	14.0478	−	43.2348i	0.456253	−	1.40420i
$949$	−8.93613	−	27.5026i	−0.290079	−	0.892772i
$950$	−71.4357	+	51.9011i	−2.31768	+	1.68389i
$951$	−8.74735	−	26.9216i	−0.283652	−	0.872992i
$952$	19.6030	+	14.2424i	0.635338	+	0.461600i
$953$	−31.3077	−	22.7464i	−1.01416	−	0.736828i	−0.0490799	−	0.998795i	$-0.515629\pi$
$953$	−31.3077	−	22.7464i	−1.01416	−	0.736828i	−0.965077	+	0.261967i	$0.915629\pi$
$954$	23.9184	−	17.3777i	0.774386	−	0.562624i
$955$	−50.7571			−1.64246
$956$	−111.221			−3.59714
$957$	37.8654	−	27.5108i	1.22401	−	0.889298i
$958$	−14.0091	+	43.1156i	−0.452614	+	1.39300i
$959$	16.9579	+	52.1910i	0.547598	+	1.68533i
$960$	190.303			6.14201
$961$	−1.17725	−	30.9776i	−0.0379759	−	0.999279i
$962$	1.08636			0.0350255
$963$	8.34542	+	25.6846i	0.268927	+	0.827673i
$964$	−16.9319	+	52.1111i	−0.545340	+	1.67838i
$965$	49.3579	−	35.8606i	1.58889	−	1.15439i
$966$	−79.9349			−2.57186
$967$	−30.9253			−0.994489			−0.497245	−	0.867610i	$-0.665655\pi$
$967$	−30.9253			−0.994489			−0.497245	+	0.867610i	$0.665655\pi$
$968$	73.7388	−	53.5743i	2.37005	−	1.72194i
$969$	−6.49177	−	4.71655i	−0.208546	−	0.151517i
$970$	112.603	+	81.8111i	3.61547	+	2.62680i
$971$	−2.43930	−	7.50740i	−0.0782809	−	0.240924i	0.904256	−	0.426990i	$-0.140426\pi$
$971$	−2.43930	−	7.50740i	−0.0782809	−	0.240924i	−0.982537	+	0.186066i	$0.940426\pi$
$972$	−70.8272	+	51.4590i	−2.27178	+	1.65055i
$973$	−1.16688	−	3.59128i	−0.0374084	−	0.115131i
$974$	−5.63675	+	17.3481i	−0.180613	+	0.555870i
$975$	83.5299	+	60.6880i	2.67510	+	1.94357i
$976$	22.7380	−	69.9804i	0.727826	−	2.24002i
$977$	−10.3127	+	31.7393i	−0.329933	+	1.01543i	0.639232	+	0.769014i	$0.279252\pi$
$977$	−10.3127	+	31.7393i	−0.329933	+	1.01543i	−0.969165	+	0.246415i	$0.920748\pi$
$978$	−64.8618	−	47.1249i	−2.07405	−	1.50689i
$979$	−13.1157	+	40.3660i	−0.419180	+	1.29010i
$980$	−2.37178	−	7.29957i	−0.0757636	−	0.233176i
$981$	−21.8083	+	15.8446i	−0.696284	+	0.505880i
$982$	12.1250	+	37.3168i	0.386924	+	1.19083i
$983$	−17.7003	−	12.8600i	−0.564553	−	0.410171i	0.268570	−	0.963260i	$-0.413449\pi$
$983$	−17.7003	−	12.8600i	−0.564553	−	0.410171i	−0.833122	+	0.553089i	$0.813449\pi$
$984$	149.247	+	108.435i	4.75783	+	3.45677i
$985$	23.6981	−	17.2177i	0.755083	−	0.548600i
$986$	−12.5364			−0.399239
$987$	47.2046			1.50254
$988$	83.0912	−	60.3693i	2.64348	−	1.92060i
$989$	−3.98550	+	12.2661i	−0.126732	+	0.390040i
$990$	25.7399	+	79.2194i	0.818069	+	2.51776i
$991$	15.1989			0.482809			0.241405	−	0.970425i	$-0.422392\pi$
$991$	15.1989			0.482809			0.241405	+	0.970425i	$0.422392\pi$
$992$	−71.8487	+	74.6311i	−2.28120	+	2.36954i
$993$	32.2028			1.02193
$994$	−1.41577	−	4.35729i	−0.0449054	−	0.138205i
$995$	−15.4538	+	47.5619i	−0.489918	+	1.50781i
$996$	34.6130	−	25.1478i	1.09676	−	0.796840i
$997$	1.29779			0.0411015			0.0205508	−	0.999789i	$-0.493458\pi$
$997$	1.29779			0.0411015			0.0205508	+	0.999789i	$0.493458\pi$
$998$	4.75544			0.150531
$999$	0.162458	−	0.118032i	0.00513993	−	0.00373438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.1	✓	96
31.8	even	5	inner	527.2.h.c.256.1	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.1	✓	96	1.1	even	1	trivial
527.2.h.c.256.1	yes	96	31.8	even	5	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:	\( N \)	\(=\)	\( 527 = 17 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	527.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834890 - 2.56953i) q^{2} +(-0.676586 + 2.08232i) q^{3} +(-4.28739 + 3.11497i) q^{4} -3.73062 q^{5} +5.91544 q^{6} +(-2.19901 + 1.59768i) q^{7} +(7.21196 + 5.23979i) q^{8} +(-1.45123 - 1.05438i) q^{9} +O(q^{10})\)	\(q+(-0.834890 - 2.56953i) q^{2} +(-0.676586 + 2.08232i) q^{3} +(-4.28739 + 3.11497i) q^{4} -3.73062 q^{5} +5.91544 q^{6} +(-2.19901 + 1.59768i) q^{7} +(7.21196 + 5.23979i) q^{8} +(-1.45123 - 1.05438i) q^{9} +(3.11466 + 9.58594i) q^{10} +(-3.72715 + 2.70793i) q^{11} +(-3.58557 - 11.0353i) q^{12} +(1.63410 - 5.02926i) q^{13} +(5.94120 + 4.31653i) q^{14} +(2.52409 - 7.76835i) q^{15} +(4.16733 - 12.8257i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-1.49764 + 4.60926i) q^{18} +(-1.13252 - 3.48555i) q^{19} +(15.9946 - 11.6208i) q^{20} +(-1.83905 - 5.66001i) q^{21} +(10.0699 + 7.31618i) q^{22} +(4.02195 + 2.92212i) q^{23} +(-15.7904 + 11.4724i) q^{24} +8.91756 q^{25} -14.2871 q^{26} +(-2.13654 + 1.55229i) q^{27} +(4.45131 - 13.6997i) q^{28} +(1.43386 + 4.41297i) q^{29} -22.0683 q^{30} +(3.86152 - 4.01106i) q^{31} -18.6063 q^{32} +(-3.11704 - 9.59325i) q^{33} +(-0.834890 + 2.56953i) q^{34} +(8.20369 - 5.96033i) q^{35} +9.50634 q^{36} -0.0760375 q^{37} +(-8.01068 + 5.82010i) q^{38} +(9.36690 + 6.80545i) q^{39} +(-26.9051 - 19.5477i) q^{40} +(-2.92076 - 8.98916i) q^{41} +(-13.0081 + 9.45096i) q^{42} +(0.801685 + 2.46733i) q^{43} +(7.54461 - 23.2199i) q^{44} +(5.41399 + 3.93349i) q^{45} +(4.15058 - 12.7742i) q^{46} +(-2.45107 + 7.54362i) q^{47} +(23.8876 + 17.3554i) q^{48} +(0.119966 - 0.369216i) q^{49} +(-7.44518 - 22.9139i) q^{50} +(1.77133 - 1.28694i) q^{51} +(8.65995 + 26.6526i) q^{52} +(-4.93522 - 3.58565i) q^{53} +(5.77243 + 4.19391i) q^{54} +(13.9046 - 10.1023i) q^{55} -24.2307 q^{56} +8.02427 q^{57} +(10.1421 - 7.36869i) q^{58} +(-0.794154 + 2.44416i) q^{59} +(13.3764 + 41.1684i) q^{60} +5.45626 q^{61} +(-13.5305 - 6.57349i) q^{62} +4.87582 q^{63} +(7.19956 + 22.1580i) q^{64} +(-6.09623 + 18.7623i) q^{65} +(-22.0477 + 16.0186i) q^{66} -2.61859 q^{67} +5.29951 q^{68} +(-8.80598 + 6.39792i) q^{69} +(-22.1644 - 16.1034i) q^{70} +(-0.504720 - 0.366701i) q^{71} +(-4.94147 - 15.2083i) q^{72} +(4.42412 - 3.21431i) q^{73} +(0.0634830 + 0.195380i) q^{74} +(-6.03350 + 18.5692i) q^{75} +(15.7130 + 11.4161i) q^{76} +(3.86964 - 11.9095i) q^{77} +(9.66646 - 29.7503i) q^{78} +(3.16963 + 2.30287i) q^{79} +(-15.5467 + 47.8479i) q^{80} +(-3.44976 - 10.6173i) q^{81} +(-20.6594 + 15.0099i) q^{82} +(1.13943 + 3.50681i) q^{83} +(25.5155 + 18.5381i) q^{84} +(3.01814 + 2.19281i) q^{85} +(5.67056 - 4.11990i) q^{86} -10.1593 q^{87} -41.0690 q^{88} +(7.45329 - 5.41513i) q^{89} +(5.58713 - 17.1954i) q^{90} +(4.44170 + 13.6702i) q^{91} -26.3460 q^{92} +(5.73965 + 10.7548i) q^{93} +21.4299 q^{94} +(4.22502 + 13.0033i) q^{95} +(12.5888 - 38.7442i) q^{96} +(11.1718 - 8.11678i) q^{97} -1.04887 q^{98} +8.26412 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9}+O(q^{10}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9	\( 96 q - 2 q^{2} - 4 q^{3} - 30 q^{4} + 6 q^{5} - 8 q^{6} - 10 q^{7} - 36 q^{9} - 13 q^{10} - 4 q^{11} - 14 q^{12} - 14 q^{13} + 17 q^{14} - 9 q^{15} - 58 q^{16} - 24 q^{17} - 24 q^{18} - 6 q^{19} + 43 q^{20} + 26 q^{21} + 42 q^{22} - 11 q^{23} - 38 q^{24} + 126 q^{25} - 44 q^{26} - q^{27} + 31 q^{28} - 10 q^{29} - 70 q^{30} + 21 q^{31} + 28 q^{32} - 36 q^{33} - 2 q^{34} + 2 q^{35} + 160 q^{36} + 54 q^{37} + 15 q^{38} - 10 q^{39} - 29 q^{40} - 14 q^{41} - 3 q^{42} + 6 q^{43} - 5 q^{44} - q^{45} - 17 q^{46} - 14 q^{47} - 93 q^{48} - 72 q^{49} + 108 q^{50} + q^{51} + 13 q^{52} - 30 q^{53} - 63 q^{54} - 12 q^{55} + 66 q^{56} - 62 q^{57} + 29 q^{58} + 8 q^{59} - 86 q^{60} - 14 q^{61} - 34 q^{62} + 86 q^{63} - 122 q^{64} + 13 q^{65} - 40 q^{66} + 126 q^{67} + 120 q^{68} - 34 q^{69} - 38 q^{70} - 39 q^{71} - 51 q^{72} - 60 q^{73} - 111 q^{74} - 41 q^{75} + 64 q^{76} - 26 q^{77} - 99 q^{78} - 33 q^{79} - 91 q^{80} + 81 q^{81} - 88 q^{82} + 22 q^{83} + 160 q^{84} - 4 q^{85} + 35 q^{86} + 70 q^{87} - 120 q^{88} + 101 q^{89} + 125 q^{90} - 13 q^{91} - 98 q^{92} + 47 q^{93} - 8 q^{94} - 64 q^{95} + 208 q^{96} + 16 q^{97} + 8 q^{98} + 280 q^{99}+O(q^{100}) \) 96 * q - 2 * q^2 - 4 * q^3 - 30 * q^4 + 6 * q^5 - 8 * q^6 - 10 * q^7 - 36 * q^9 - 13 * q^10 - 4 * q^11 - 14 * q^12 - 14 * q^13 + 17 * q^14 - 9 * q^15 - 58 * q^16 - 24 * q^17 - 24 * q^18 - 6 * q^19 + 43 * q^20 + 26 * q^21 + 42 * q^22 - 11 * q^23 - 38 * q^24 + 126 * q^25 - 44 * q^26 - q^27 + 31 * q^28 - 10 * q^29 - 70 * q^30 + 21 * q^31 + 28 * q^32 - 36 * q^33 - 2 * q^34 + 2 * q^35 + 160 * q^36 + 54 * q^37 + 15 * q^38 - 10 * q^39 - 29 * q^40 - 14 * q^41 - 3 * q^42 + 6 * q^43 - 5 * q^44 - q^45 - 17 * q^46 - 14 * q^47 - 93 * q^48 - 72 * q^49 + 108 * q^50 + q^51 + 13 * q^52 - 30 * q^53 - 63 * q^54 - 12 * q^55 + 66 * q^56 - 62 * q^57 + 29 * q^58 + 8 * q^59 - 86 * q^60 - 14 * q^61 - 34 * q^62 + 86 * q^63 - 122 * q^64 + 13 * q^65 - 40 * q^66 + 126 * q^67 + 120 * q^68 - 34 * q^69 - 38 * q^70 - 39 * q^71 - 51 * q^72 - 60 * q^73 - 111 * q^74 - 41 * q^75 + 64 * q^76 - 26 * q^77 - 99 * q^78 - 33 * q^79 - 91 * q^80 + 81 * q^81 - 88 * q^82 + 22 * q^83 + 160 * q^84 - 4 * q^85 + 35 * q^86 + 70 * q^87 - 120 * q^88 + 101 * q^89 + 125 * q^90 - 13 * q^91 - 98 * q^92 + 47 * q^93 - 8 * q^94 - 64 * q^95 + 208 * q^96 + 16 * q^97 + 8 * q^98 + 280 * q^99

Introduction

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