LMFDB - Embedded newform 527.2.h.c.35.13

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			35.13
Character	$\chi$	$=$	527.35
Dual form			527.2.h.c.256.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0573542 + 0.176518i) q^{2} +(-0.417065 + 1.28359i) q^{3} +(1.59016 - 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 - 1.75793i) q^{7} +(0.595448 + 0.432618i) q^{8} +(0.953382 + 0.692673i) q^{9} +O(q^{10})$	\(q+(0.0573542 + 0.176518i) q^{2} +(-0.417065 + 1.28359i) q^{3} +(1.59016 - 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 - 1.75793i) q^{7} +(0.595448 + 0.432618i) q^{8} +(0.953382 + 0.692673i) q^{9} +(0.128829 + 0.396494i) q^{10} +(-4.52207 + 3.28548i) q^{11} +(0.819762 + 2.52297i) q^{12} +(1.77340 - 5.45795i) q^{13} +(0.449081 + 0.326276i) q^{14} +(-0.936810 + 2.88320i) q^{15} +(1.17256 - 3.60878i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.0675888 + 0.208017i) q^{18} +(-0.737722 - 2.27048i) q^{19} +(3.57183 - 2.59508i) q^{20} +(1.24735 + 3.83894i) q^{21} +(-0.839305 - 0.609791i) q^{22} +(-1.65419 - 1.20184i) q^{23} +(-0.803646 + 0.583883i) q^{24} +0.0454058 q^{25} +1.06514 q^{26} +(-4.56240 + 3.31478i) q^{27} +(1.81657 - 5.59081i) q^{28} +(1.74045 + 5.35656i) q^{29} -0.562667 q^{30} +(-5.56417 - 0.200037i) q^{31} +2.17629 q^{32} +(-2.33122 - 7.17475i) q^{33} +(0.0573542 - 0.176518i) q^{34} +(5.43488 - 3.94867i) q^{35} +2.31630 q^{36} +4.55430 q^{37} +(0.358468 - 0.260443i) q^{38} +(6.26617 + 4.55264i) q^{39} +(1.33749 + 0.971747i) q^{40} +(1.55644 + 4.79022i) q^{41} +(-0.606102 + 0.440359i) q^{42} +(2.97801 + 9.16536i) q^{43} +(-3.39505 + 10.4489i) q^{44} +(2.14149 + 1.55588i) q^{45} +(0.117272 - 0.360925i) q^{46} +(-2.06225 + 6.34694i) q^{47} +(4.14317 + 3.01019i) q^{48} +(0.600961 - 1.84957i) q^{49} +(0.00260421 + 0.00801494i) q^{50} +(1.09189 - 0.793304i) q^{51} +(-3.48570 - 10.7279i) q^{52} +(-2.30288 - 1.67314i) q^{53} +(-0.846791 - 0.615229i) q^{54} +(-10.1575 + 7.37983i) q^{55} +2.20126 q^{56} +3.22205 q^{57} +(-0.845707 + 0.614442i) q^{58} +(0.552196 - 1.69948i) q^{59} +(1.84135 + 5.66709i) q^{60} +3.77827 q^{61} +(-0.283818 - 0.993649i) q^{62} +3.52447 q^{63} +(-2.22031 - 6.83341i) q^{64} +(3.98340 - 12.2596i) q^{65} +(1.13277 - 0.823004i) q^{66} +5.18873 q^{67} -1.96555 q^{68} +(2.23258 - 1.62206i) q^{69} +(1.00872 + 0.732881i) q^{70} +(-12.5288 - 9.10269i) q^{71} +(0.268027 + 0.824902i) q^{72} +(-10.5139 + 7.63877i) q^{73} +(0.261208 + 0.803916i) q^{74} +(-0.0189372 + 0.0582826i) q^{75} +(-3.79623 - 2.75812i) q^{76} +(-5.16590 + 15.8990i) q^{77} +(-0.444232 + 1.36720i) q^{78} +(-0.758945 - 0.551405i) q^{79} +(2.63381 - 8.10604i) q^{80} +(-1.25953 - 3.87644i) q^{81} +(-0.756292 + 0.549478i) q^{82} +(-1.29150 - 3.97482i) q^{83} +(6.41870 + 4.66346i) q^{84} +(-1.81721 - 1.32028i) q^{85} +(-1.44705 + 1.05134i) q^{86} -7.60152 q^{87} -4.11401 q^{88} +(11.6872 - 8.49124i) q^{89} +(-0.151818 + 0.467247i) q^{90} +(-5.30384 - 16.3235i) q^{91} -4.01895 q^{92} +(2.57739 - 7.05870i) q^{93} -1.23863 q^{94} +(-1.65707 - 5.09994i) q^{95} +(-0.907656 + 2.79348i) q^{96} +(-0.642163 + 0.466559i) q^{97} +0.360950 q^{98} -6.58702 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 $

$2$	0.0573542	+	0.176518i	0.0405555	+	0.124817i	0.969284	−	0.245942i	$-0.0790974\pi$
$2$	0.0573542	+	0.176518i	0.0405555	+	0.124817i	−0.928729	+	0.370759i	$0.879097\pi$
$3$	−0.417065	+	1.28359i	−0.240792	+	0.741083i	0.755508	+	0.655140i	$0.227390\pi$
$3$	−0.417065	+	1.28359i	−0.240792	+	0.741083i	−0.996300	+	0.0859430i	$0.972610\pi$
$4$	1.59016	−	1.15532i	0.795082	−	0.577661i
$5$	2.24620			1.00453			0.502265	−	0.864714i	$-0.332500\pi$
$5$	2.24620			1.00453			0.502265	+	0.864714i	$0.332500\pi$
$6$	−0.250498			−0.102265
$7$	2.41959	−	1.75793i	0.914519	−	0.664437i	−0.0276347	−	0.999618i	$-0.508798\pi$
$7$	2.41959	−	1.75793i	0.914519	−	0.664437i	0.942154	+	0.335181i	$0.108798\pi$
$8$	0.595448	+	0.432618i	0.210523	+	0.152954i
$9$	0.953382	+	0.692673i	0.317794	+	0.230891i
$10$	0.128829	+	0.396494i	0.0407393	+	0.125383i
$11$	−4.52207	+	3.28548i	−1.36346	+	0.990608i	−0.365238	+	0.930914i	$0.619013\pi$
$11$	−4.52207	+	3.28548i	−1.36346	+	0.990608i	−0.998217	+	0.0596941i	$0.980987\pi$
$12$	0.819762	+	2.52297i	0.236645	+	0.728318i
$13$	1.77340	−	5.45795i	0.491852	−	1.51376i	−0.329954	−	0.943997i	$-0.607033\pi$
$13$	1.77340	−	5.45795i	0.491852	−	1.51376i	0.821806	−	0.569767i	$-0.192967\pi$
$14$	0.449081	+	0.326276i	0.120022	+	0.0872010i
$15$	−0.936810	+	2.88320i	−0.241883	+	0.744440i
$16$	1.17256	−	3.60878i	0.293141	−	0.902196i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$17$	−0.809017	−	0.587785i	−0.196215	−	0.142559i
$18$	−0.0675888	+	0.208017i	−0.0159308	+	0.0490300i
$19$	−0.737722	−	2.27048i	−0.169245	−	0.520883i	0.830079	−	0.557646i	$-0.188295\pi$
$19$	−0.737722	−	2.27048i	−0.169245	−	0.520883i	−0.999324	+	0.0367630i	$0.988295\pi$
$20$	3.57183	−	2.59508i	0.798684	−	0.580278i
$21$	1.24735	+	3.83894i	0.272194	+	0.837726i
$22$	−0.839305	−	0.609791i	−0.178940	−	0.130008i
$23$	−1.65419	−	1.20184i	−0.344923	−	0.250601i	0.401813	−	0.915722i	$-0.368380\pi$
$23$	−1.65419	−	1.20184i	−0.344923	−	0.250601i	−0.746736	+	0.665121i	$0.768380\pi$
$24$	−0.803646	+	0.583883i	−0.164044	+	0.119185i
$25$	0.0454058			0.00908116
$26$	1.06514			0.208891
$27$	−4.56240	+	3.31478i	−0.878035	+	0.637929i
$28$	1.81657	−	5.59081i	0.343299	−	1.05656i
$29$	1.74045	+	5.35656i	0.323194	+	0.994688i	0.972249	+	0.233947i	$0.0751642\pi$
$29$	1.74045	+	5.35656i	0.323194	+	0.994688i	−0.649056	+	0.760741i	$0.724836\pi$
$30$	−0.562667			−0.102729
$31$	−5.56417	−	0.200037i	−0.999354	−	0.0359277i
$31$	−5.56417	−	0.200037i	−0.999354	−	0.0359277i
$32$	2.17629			0.384718
$33$	−2.33122	−	7.17475i	−0.405813	−	1.24896i
$34$	0.0573542	−	0.176518i	0.00983616	−	0.0302726i
$35$	5.43488	−	3.94867i	0.918662	−	0.667447i
$36$	2.31630			0.386049
$37$	4.55430			0.748722			0.374361	−	0.927283i	$-0.377862\pi$
$37$	4.55430			0.748722			0.374361	+	0.927283i	$0.377862\pi$
$38$	0.358468	−	0.260443i	0.0581513	−	0.0422494i
$39$	6.26617	+	4.55264i	1.00339	+	0.729006i
$40$	1.33749	+	0.971747i	0.211476	+	0.153647i
$41$	1.55644	+	4.79022i	0.243075	+	0.748107i	0.995947	+	0.0899405i	$0.0286677\pi$
$41$	1.55644	+	4.79022i	0.243075	+	0.748107i	−0.752872	+	0.658166i	$0.771332\pi$
$42$	−0.606102	+	0.440359i	−0.0935235	+	0.0679488i
$43$	2.97801	+	9.16536i	0.454142	+	1.39770i	0.872140	+	0.489256i	$0.162732\pi$
$43$	2.97801	+	9.16536i	0.454142	+	1.39770i	−0.417998	+	0.908448i	$0.637268\pi$
$44$	−3.39505	+	10.4489i	−0.511823	+	1.57523i
$45$	2.14149	+	1.55588i	0.319234	+	0.231937i
$46$	0.117272	−	0.360925i	0.0172908	−	0.0532155i
$47$	−2.06225	+	6.34694i	−0.300810	+	0.925797i	0.680398	+	0.732843i	$0.261807\pi$
$47$	−2.06225	+	6.34694i	−0.300810	+	0.925797i	−0.981208	+	0.192954i	$0.938193\pi$
$48$	4.14317	+	3.01019i	0.598016	+	0.434484i
$49$	0.600961	−	1.84957i	0.0858516	−	0.264224i
$50$	0.00260421	+	0.00801494i	0.000368291	+	0.00113348i
$51$	1.09189	−	0.793304i	0.152895	−	0.111085i
$52$	−3.48570	−	10.7279i	−0.483380	−	1.48769i
$53$	−2.30288	−	1.67314i	−0.316324	−	0.229823i	0.418281	−	0.908318i	$-0.362633\pi$
$53$	−2.30288	−	1.67314i	−0.316324	−	0.229823i	−0.734605	+	0.678495i	$0.762633\pi$
$54$	−0.846791	−	0.615229i	−0.115234	−	0.0837221i
$55$	−10.1575	+	7.37983i	−1.36963	+	0.995096i
$56$	2.20126			0.294155
$57$	3.22205			0.426770
$58$	−0.845707	+	0.614442i	−0.111047	+	0.0806802i
$59$	0.552196	−	1.69948i	0.0718897	−	0.221254i	−0.908656	−	0.417546i	$-0.862890\pi$
$59$	0.552196	−	1.69948i	0.0718897	−	0.221254i	0.980545	+	0.196292i	$0.0628902\pi$
$60$	1.84135	+	5.66709i	0.237717	+	0.731618i
$61$	3.77827			0.483759			0.241879	−	0.970306i	$-0.422236\pi$
$61$	3.77827			0.483759			0.241879	+	0.970306i	$0.422236\pi$
$62$	−0.283818	−	0.993649i	−0.0360449	−	0.126194i
$63$	3.52447			0.444041
$64$	−2.22031	−	6.83341i	−0.277539	−	0.854176i
$65$	3.98340	−	12.2596i	0.494080	−	1.52062i
$66$	1.13277	−	0.823004i	0.139434	−	0.101305i
$67$	5.18873			0.633904			0.316952	−	0.948442i	$-0.397341\pi$
$67$	5.18873			0.633904			0.316952	+	0.948442i	$0.397341\pi$
$68$	−1.96555			−0.238358
$69$	2.23258	−	1.62206i	0.268771	−	0.195273i
$70$	1.00872	+	0.732881i	0.120566	+	0.0875960i
$71$	−12.5288	−	9.10269i	−1.48689	−	1.08029i	−0.975253	−	0.221090i	$-0.929039\pi$
$71$	−12.5288	−	9.10269i	−1.48689	−	1.08029i	−0.511639	−	0.859201i	$-0.670961\pi$
$72$	0.268027	+	0.824902i	0.0315873	+	0.0972156i
$73$	−10.5139	+	7.63877i	−1.23055	+	0.894050i	−0.996932	−	0.0782771i	$-0.975058\pi$
$73$	−10.5139	+	7.63877i	−1.23055	+	0.894050i	−0.233623	+	0.972327i	$0.575058\pi$
$74$	0.261208	+	0.803916i	0.0303648	+	0.0934533i
$75$	−0.0189372	+	0.0582826i	−0.00218668	+	0.00672989i
$76$	−3.79623	−	2.75812i	−0.435458	−	0.316379i
$77$	−5.16590	+	15.8990i	−0.588709	+	1.81186i
$78$	−0.444232	+	1.36720i	−0.0502993	+	0.154805i
$79$	−0.758945	−	0.551405i	−0.0853879	−	0.0620380i	0.544272	−	0.838909i	$-0.316806\pi$
$79$	−0.758945	−	0.551405i	−0.0853879	−	0.0620380i	−0.629660	+	0.776871i	$0.716806\pi$
$80$	2.63381	−	8.10604i	0.294469	−	0.906283i
$81$	−1.25953	−	3.87644i	−0.139948	−	0.430715i
$82$	−0.756292	+	0.549478i	−0.0835185	+	0.0606797i
$83$	−1.29150	−	3.97482i	−0.141760	−	0.436294i	0.854820	−	0.518925i	$-0.173668\pi$
$83$	−1.29150	−	3.97482i	−0.141760	−	0.436294i	−0.996580	+	0.0826314i	$0.973668\pi$
$84$	6.41870	+	4.66346i	0.700338	+	0.508825i
$85$	−1.81721	−	1.32028i	−0.197104	−	0.143205i
$86$	−1.44705	+	1.05134i	−0.156039	+	0.113369i
$87$	−7.60152			−0.814969
$88$	−4.11401			−0.438555
$89$	11.6872	−	8.49124i	1.23884	−	0.900070i	0.241320	−	0.970446i	$-0.422420\pi$
$89$	11.6872	−	8.49124i	1.23884	−	0.900070i	0.997521	+	0.0703757i	$0.0224198\pi$
$90$	−0.151818	+	0.467247i	−0.0160030	+	0.0492522i
$91$	−5.30384	−	16.3235i	−0.555993	−	1.71117i
$92$	−4.01895			−0.419004
$93$	2.57739	−	7.05870i	0.267262	−	0.731953i
$94$	−1.23863			−0.127755
$95$	−1.65707	−	5.09994i	−0.170012	−	0.523243i
$96$	−0.907656	+	2.79348i	−0.0926372	+	0.285108i
$97$	−0.642163	+	0.466559i	−0.0652018	+	0.0473719i	−0.619909	−	0.784674i	$-0.712830\pi$
$97$	−0.642163	+	0.466559i	−0.0652018	+	0.0473719i	0.554707	+	0.832046i	$0.312830\pi$
$98$	0.360950			0.0364614
$99$	−6.58702			−0.662021
$100$	0.0722027	−	0.0524584i	0.00722027	−	0.00524584i
$101$	−12.3764	−	8.99195i	−1.23149	−	0.894732i	−0.234492	−	0.972118i	$-0.575343\pi$
$101$	−12.3764	−	8.99195i	−1.23149	−	0.894732i	−0.997001	+	0.0773856i	$0.975343\pi$
$102$	0.202657	+	0.147239i	0.0200660	+	0.0145788i
$103$	5.21834	+	16.0604i	0.514179	+	1.58248i	0.784771	+	0.619785i	$0.212780\pi$
$103$	5.21834	+	16.0604i	0.514179	+	1.58248i	−0.270593	+	0.962694i	$0.587220\pi$
$104$	3.41718	−	2.48272i	0.335082	−	0.243451i
$105$	2.80179	+	8.62302i	0.273427	+	0.841521i
$106$	0.163259	−	0.502460i	0.0158571	−	0.0488033i
$107$	−1.98946	−	1.44542i	−0.192328	−	0.139734i	0.487454	−	0.873149i	$-0.337926\pi$
$107$	−1.98946	−	1.44542i	−0.192328	−	0.139734i	−0.679782	+	0.733414i	$0.737926\pi$
$108$	−3.42533	+	10.5421i	−0.329603	+	1.01441i
$109$	−4.73624	+	14.5766i	−0.453649	+	1.39619i	0.419064	+	0.907957i	$0.362358\pi$
$109$	−4.73624	+	14.5766i	−0.453649	+	1.39619i	−0.872714	+	0.488233i	$0.837642\pi$
$110$	−1.88525	−	1.36971i	−0.179751	−	0.130597i
$111$	−1.89944	+	5.84587i	−0.180287	+	0.554865i
$112$	−3.50688	−	10.7931i	−0.331369	−	1.01985i
$113$	1.53953	−	1.11853i	0.144827	−	0.105223i	−0.513012	−	0.858381i	$-0.671471\pi$
$113$	1.53953	−	1.11853i	0.144827	−	0.105223i	0.657839	+	0.753158i	$0.271471\pi$
$114$	0.184798	+	0.568749i	0.0173079	+	0.0532682i
$115$	−3.71564	−	2.69957i	−0.346485	−	0.251736i
$116$	8.95615	+	6.50703i	0.831558	+	0.604162i
$117$	5.47130	−	3.97513i	0.505822	−	0.367501i
$118$	0.331660			0.0305318
$119$	−2.99078			−0.274164
$120$	−1.80515	+	1.31152i	−0.164787	+	0.119725i
$121$	6.25557	−	19.2527i	0.568688	−	1.75024i
$122$	0.216700	+	0.666933i	0.0196191	+	0.0603813i
$123$	−6.79783			−0.612940
$124$	−9.07905	+	6.11032i	−0.815323	+	0.548723i
$125$	−11.1290			−0.995408
$126$	0.202143	+	0.622132i	0.0180083	+	0.0554239i
$127$	2.43668	−	7.49933i	0.216220	−	0.665458i	−0.782844	−	0.622218i	$-0.786232\pi$
$127$	2.43668	−	7.49933i	0.216220	−	0.665458i	0.999065	−	0.0432405i	$-0.0137682\pi$
$128$	4.60019	−	3.34224i	0.406604	−	0.295415i
$129$	−13.0066			−1.14517
$130$	2.39251			0.209837
$131$	14.8158	−	10.7643i	1.29446	−	0.940482i	0.294577	−	0.955628i	$-0.404821\pi$
$131$	14.8158	−	10.7643i	1.29446	−	0.940482i	0.999885	+	0.0151461i	$0.00482135\pi$
$132$	−11.9962	−	8.71573i	−1.04413	−	0.758607i
$133$	−5.77634	−	4.19675i	−0.500872	−	0.363905i
$134$	0.297595	+	0.915904i	0.0257083	+	0.0791221i
$135$	−10.2481	+	7.44565i	−0.882012	+	0.640819i
$136$	−0.227441	−	0.699991i	−0.0195029	−	0.0600238i
$137$	−2.26053	+	6.95720i	−0.193130	+	0.594394i	0.806863	+	0.590739i	$0.201164\pi$
$137$	−2.26053	+	6.95720i	−0.193130	+	0.594394i	−0.999993	+	0.00365530i	$0.998836\pi$
$138$	0.414371	+	0.301058i	0.0352736	+	0.0256278i
$139$	1.67240	−	5.14712i	0.141851	−	0.436573i	−0.854741	−	0.519054i	$-0.826284\pi$
$139$	1.67240	−	5.14712i	0.141851	−	0.436573i	0.996593	+	0.0824810i	$0.0262844\pi$
$140$	4.08037	−	12.5581i	0.344854	−	1.06135i
$141$	−7.28680	−	5.29417i	−0.613659	−	0.445850i
$142$	0.888211	−	2.73363i	0.0745370	−	0.229401i
$143$	9.91255	+	30.5077i	0.828929	+	2.55118i
$144$	3.61761	−	2.62835i	0.301467	−	0.219029i
$145$	3.90940	+	12.0319i	0.324658	+	0.999194i
$146$	−1.95139	−	1.41777i	−0.161498	−	0.117336i
$147$	2.12345	+	1.54278i	0.175139	+	0.127246i
$148$	7.24209	−	5.26169i	0.595296	−	0.432508i
$149$	−2.06734			−0.169363			−0.0846814	−	0.996408i	$-0.526987\pi$
$149$	−2.06734			−0.169363			−0.0846814	+	0.996408i	$0.526987\pi$
$150$	−0.0113740			−0.000928687
$151$	−14.4759	+	10.5173i	−1.17803	+	0.855888i	−0.991948	−	0.126646i	$-0.959579\pi$
$151$	−14.4759	+	10.5173i	−1.17803	+	0.855888i	−0.186081	+	0.982534i	$0.559579\pi$
$152$	0.542974	−	1.67110i	0.0440410	−	0.135544i
$153$	−0.364160	−	1.12077i	−0.0294406	−	0.0906087i
$154$	−3.10275			−0.250026
$155$	−12.4982	−	0.449323i	−1.00388	−	0.0360905i
$156$	15.2240			1.21890
$157$	−5.38891	−	16.5854i	−0.430082	−	1.32366i	−0.898043	−	0.439907i	$-0.855011\pi$
$157$	−5.38891	−	16.5854i	−0.430082	−	1.32366i	0.467961	−	0.883749i	$-0.344989\pi$
$158$	0.0538043	−	0.165593i	0.00428044	−	0.0131739i
$159$	3.10807	−	2.25815i	0.246486	−	0.179083i
$160$	4.88839			0.386461
$161$	−6.11522			−0.481947
$162$	0.612022	−	0.444660i	0.0480850	−	0.0349358i
$163$	−1.28699	−	0.935056i	−0.100805	−	0.0732393i	0.536241	−	0.844065i	$-0.319844\pi$
$163$	−1.28699	−	0.935056i	−0.100805	−	0.0732393i	−0.637046	+	0.770826i	$0.719844\pi$
$164$	8.00924	+	5.81906i	0.625417	+	0.454392i
$165$	−5.23638	−	16.1159i	−0.407652	−	1.25462i
$166$	0.627555	−	0.455945i	0.0487077	−	0.0353882i
$167$	−0.598260	−	1.84126i	−0.0462948	−	0.142481i	0.925237	−	0.379389i	$-0.123866\pi$
$167$	−0.598260	−	1.84126i	−0.0462948	−	0.142481i	−0.971532	+	0.236909i	$0.923866\pi$
$168$	−0.918066	+	2.82552i	−0.0708303	+	0.217993i
$169$	−16.1271	−	11.7170i	−1.24055	−	0.901310i
$170$	0.128829	−	0.396494i	0.00988072	−	0.0304097i
$171$	0.869366	−	2.67563i	0.0664821	−	0.204611i
$172$	15.3245	+	11.1339i	1.16848	+	0.848950i
$173$	−4.95819	+	15.2597i	−0.376964	+	1.16018i	0.565180	+	0.824968i	$0.308807\pi$
$173$	−4.95819	+	15.2597i	−0.376964	+	1.16018i	−0.942144	+	0.335209i	$0.891193\pi$
$174$	−0.435979	−	1.34181i	−0.0330515	−	0.101722i
$175$	0.109863	−	0.0798205i	0.00830490	−	0.00603386i
$176$	6.55415	+	20.1716i	0.494037	+	1.52049i
$177$	1.95114	+	1.41759i	0.146657	+	0.106553i
$178$	2.16917	+	1.57599i	0.162586	+	0.118126i
$179$	−0.119949	+	0.0871481i	−0.00896542	+	0.00651376i	−0.592259	−	0.805748i	$-0.701764\pi$
$179$	−0.119949	+	0.0871481i	−0.00896542	+	0.00651376i	0.583294	+	0.812261i	$0.301764\pi$
$180$	5.20286			0.387798
$181$	1.59739			0.118733			0.0593666	−	0.998236i	$-0.481092\pi$
$181$	1.59739			0.118733			0.0593666	+	0.998236i	$0.481092\pi$
$182$	2.57720	−	1.87244i	0.191035	−	0.138795i
$183$	−1.57579	+	4.84977i	−0.116485	+	0.358505i
$184$	−0.465047	−	1.43127i	−0.0342837	−	0.105514i
$185$	10.2299			0.752114
$186$	1.39381	+	0.0501088i	0.102199	+	0.00367416i
$187$	5.58958			0.408751
$188$	4.05345	+	12.4752i	0.295628	+	0.909851i
$189$	−5.21197	+	16.0408i	−0.379115	+	1.16680i
$190$	0.805191	−	0.585006i	0.0584147	−	0.0424408i
$191$	−2.51252			−0.181799			−0.0908997	−	0.995860i	$-0.528974\pi$
$191$	−2.51252			−0.181799			−0.0908997	+	0.995860i	$0.528974\pi$
$192$	9.69733			0.699845
$193$	15.6726	−	11.3868i	1.12814	−	0.819641i	0.142716	−	0.989764i	$-0.454416\pi$
$193$	15.6726	−	11.3868i	1.12814	−	0.819641i	0.985423	+	0.170123i	$0.0544165\pi$
$194$	−0.119187	−	0.0865943i	−0.00855711	−	0.00621711i
$195$	14.0751	+	10.2261i	1.00794	+	0.732309i
$196$	−1.18122	−	3.63542i	−0.0843728	−	0.259673i
$197$	10.2526	−	7.44891i	0.730464	−	0.530713i	−0.159246	−	0.987239i	$-0.550906\pi$
$197$	10.2526	−	7.44891i	0.730464	−	0.530713i	0.889710	+	0.456526i	$0.150906\pi$
$198$	−0.377793	−	1.16273i	−0.0268486	−	0.0826315i
$199$	−3.36414	+	10.3537i	−0.238477	+	0.733958i	0.758164	+	0.652064i	$0.226097\pi$
$199$	−3.36414	+	10.3537i	−0.238477	+	0.733958i	−0.996641	+	0.0818934i	$0.973903\pi$
$200$	0.0270368	+	0.0196434i	0.00191179	+	0.00138900i
$201$	−2.16404	+	6.66022i	−0.152639	+	0.469776i
$202$	0.877405	−	2.70038i	0.0617340	−	0.189998i
$203$	13.6277	+	9.90107i	0.956474	+	0.694919i
$204$	0.819762	−	2.52297i	0.0573948	−	0.176643i
$205$	3.49607	+	10.7598i	0.244176	+	0.751496i
$206$	−2.53566	+	1.84226i	−0.176668	+	0.128357i
$207$	−0.744595	−	2.29163i	−0.0517529	−	0.159279i
$208$	−17.6171	−	12.7996i	−1.22153	−	0.887493i
$209$	10.7956	+	7.84348i	0.746749	+	0.542545i
$210$	−1.36142	+	0.989133i	−0.0939472	+	0.0682566i
$211$	−4.65283			−0.320314			−0.160157	−	0.987092i	$-0.551200\pi$
$211$	−4.65283			−0.320314			−0.160157	+	0.987092i	$0.551200\pi$
$212$	−5.59496			−0.384264
$213$	16.9095	−	12.2854i	1.15862	−	0.841785i
$214$	0.141040	−	0.434076i	0.00964128	−	0.0296728i
$215$	6.68919	+	20.5872i	0.456199	+	1.40404i
$216$	−4.15071			−0.282420
$217$	−13.8147	+	9.29744i	−0.937800	+	0.631151i
$218$	−2.84468			−0.192666
$219$	−5.42011	−	16.6814i	−0.366257	−	1.12722i
$220$	−7.62596	+	23.4703i	−0.514142	+	1.58237i
$221$	−4.64281	+	3.37320i	−0.312309	+	0.226906i
$222$	−1.14084			−0.0765683
$223$	5.98045			0.400480			0.200240	−	0.979747i	$-0.435828\pi$
$223$	5.98045			0.400480			0.200240	+	0.979747i	$0.435828\pi$
$224$	5.26574	−	3.82578i	0.351832	−	0.255621i
$225$	0.0432891	+	0.0314514i	0.00288594	+	0.00209676i
$226$	0.285740	+	0.207602i	0.0190071	+	0.0138095i
$227$	0.784955	+	2.41584i	0.0520993	+	0.160345i	0.973721	−	0.227745i	$-0.0731351\pi$
$227$	0.784955	+	2.41584i	0.0520993	+	0.160345i	−0.921622	+	0.388090i	$0.873135\pi$
$228$	5.12358	−	3.72250i	0.339318	−	0.246529i
$229$	−7.21892	−	22.2175i	−0.477040	−	1.46818i	−0.843187	−	0.537620i	$-0.819324\pi$
$229$	−7.21892	−	22.2175i	−0.477040	−	1.46818i	0.366148	−	0.930557i	$-0.380676\pi$
$230$	0.263415	−	0.810709i	0.0173691	−	0.0534566i
$231$	−18.2533	−	13.2618i	−1.20098	−	0.872564i
$232$	−1.28100	+	3.94250i	−0.0841016	+	0.258838i
$233$	−0.519099	+	1.59762i	−0.0340073	+	0.104664i	−0.966619	−	0.256217i	$-0.917524\pi$
$233$	−0.519099	+	1.59762i	−0.0340073	+	0.104664i	0.932612	+	0.360881i	$0.117524\pi$
$234$	1.01548	+	0.737793i	0.0663843	+	0.0482310i
$235$	−4.63221	+	14.2565i	−0.302172	+	0.929991i
$236$	−1.08537	−	3.34042i	−0.0706515	−	0.217443i
$237$	1.02431	−	0.744204i	0.0665360	−	0.0483413i
$238$	−0.171534	−	0.527926i	−0.0111189	−	0.0342204i
$239$	−16.4703	−	11.9664i	−1.06537	−	0.774040i	−0.0902993	−	0.995915i	$-0.528782\pi$
$239$	−16.4703	−	11.9664i	−1.06537	−	0.774040i	−0.975075	+	0.221875i	$0.928782\pi$
$240$	9.30639	+	6.76149i	0.600725	+	0.436452i
$241$	20.4991	−	14.8935i	1.32047	−	0.959374i	0.320539	−	0.947235i	$-0.396136\pi$
$241$	20.4991	−	14.8935i	1.32047	−	0.959374i	0.999926	−	0.0121393i	$-0.00386414\pi$
$242$	3.75723			0.241524
$243$	−11.4172			−0.732416
$244$	6.00808	−	4.36513i	0.384628	−	0.279449i
$245$	1.34988	−	4.15449i	0.0862405	−	0.265421i
$246$	−0.389884	−	1.19994i	−0.0248581	−	0.0765053i
$247$	−13.7004			−0.871738
$248$	−3.22663	−	2.52627i	−0.204891	−	0.160419i
$249$	5.64069			0.357464
$250$	−0.638295	−	1.96447i	−0.0403693	−	0.124244i
$251$	7.43040	−	22.8684i	0.469003	−	1.44344i	−0.384875	−	0.922969i	$-0.625755\pi$
$251$	7.43040	−	22.8684i	0.469003	−	1.44344i	0.853878	−	0.520474i	$-0.174245\pi$
$252$	5.60449	−	4.07190i	0.353049	−	0.256505i
$253$	11.4290			0.718534
$254$	1.46352			0.0918295
$255$	2.45260	−	1.78192i	0.153588	−	0.111588i
$256$	−10.7719	−	7.82623i	−0.673243	−	0.489140i
$257$	15.4720	+	11.2411i	0.965116	+	0.701198i	0.954333	−	0.298744i	$-0.0965677\pi$
$257$	15.4720	+	11.2411i	0.965116	+	0.701198i	0.0107828	+	0.999942i	$0.496568\pi$
$258$	−0.745983	−	2.29590i	−0.0464429	−	0.142937i
$259$	11.0195	−	8.00616i	0.684721	−	0.497479i
$260$	−7.82958	−	24.0970i	−0.485570	−	1.49443i
$261$	−2.05103	+	6.31241i	−0.126955	+	0.390728i
$262$	2.74984	+	1.99788i	0.169886	+	0.123429i
$263$	−9.68621	+	29.8111i	−0.597277	+	1.83823i	−0.0542290	+	0.998529i	$0.517270\pi$
$263$	−9.68621	+	29.8111i	−0.597277	+	1.83823i	−0.543048	+	0.839702i	$0.682730\pi$
$264$	1.71581	−	5.28072i	0.105601	−	0.325006i
$265$	−5.17271	−	3.75820i	−0.317757	−	0.230864i
$266$	0.409505	−	1.26033i	0.0251084	−	0.0772757i
$267$	6.02499	+	18.5430i	0.368723	+	1.13481i
$268$	8.25094	−	5.99466i	0.504006	−	0.366182i
$269$	−1.44675	−	4.45262i	−0.0882096	−	0.271481i	0.897215	−	0.441594i	$-0.145587\pi$
$269$	−1.44675	−	4.45262i	−0.0882096	−	0.271481i	−0.985425	+	0.170113i	$0.945587\pi$
$270$	−1.90206	−	1.38193i	−0.115756	−	0.0841014i
$271$	−15.3081	−	11.1220i	−0.929899	−	0.675611i	0.0160693	−	0.999871i	$-0.494885\pi$
$271$	−15.3081	−	11.1220i	−0.929899	−	0.675611i	−0.945968	+	0.324260i	$0.894885\pi$
$272$	−3.06981	+	2.23035i	−0.186135	+	0.135235i
$273$	23.1648			1.40200
$274$	−1.35772			−0.0820230
$275$	−0.205328	+	0.149180i	−0.0123818	+	0.00899587i
$276$	1.67616	−	5.15870i	0.100893	−	0.310517i
$277$	3.13013	+	9.63355i	0.188071	+	0.578824i	0.999988	−	0.00494965i	$-0.00157553\pi$
$277$	3.13013	+	9.63355i	0.188071	+	0.578824i	−0.811916	+	0.583774i	$0.801576\pi$
$278$	1.00448			0.0602446
$279$	−5.16622	−	4.04486i	−0.309294	−	0.242160i
$280$	4.94445			0.295488
$281$	3.05874	+	9.41384i	0.182469	+	0.561582i	0.999896	−	0.0144507i	$-0.00459995\pi$
$281$	3.05874	+	9.41384i	0.182469	+	0.561582i	−0.817426	+	0.576033i	$0.804600\pi$
$282$	0.516588	−	1.58989i	0.0307624	−	0.0946768i
$283$	17.8997	−	13.0049i	1.06403	−	0.773062i	0.0891995	−	0.996014i	$-0.471569\pi$
$283$	17.8997	−	13.0049i	1.06403	−	0.773062i	0.974830	+	0.222951i	$0.0715691\pi$
$284$	−30.4394			−1.80624
$285$	7.23735			0.428704
$286$	−4.81663	+	3.49949i	−0.284813	+	0.206929i
$287$	12.1868	+	8.85426i	0.719366	+	0.522650i
$288$	2.07484	+	1.50746i	0.122261	+	0.0888280i
$289$	0.309017	+	0.951057i	0.0181775	+	0.0559445i
$290$	−1.89962	+	1.38016i	−0.111550	+	0.0810457i
$291$	−0.331048	−	1.01886i	−0.0194064	−	0.0597267i
$292$	−7.89353	+	24.2938i	−0.461934	+	1.42169i
$293$	4.46676	+	3.24529i	0.260951	+	0.189592i	0.710566	−	0.703630i	$-0.248439\pi$
$293$	4.46676	+	3.24529i	0.260951	+	0.189592i	−0.449615	+	0.893222i	$0.648439\pi$
$294$	−0.150539	+	0.463312i	−0.00877963	+	0.0270209i
$295$	1.24034	−	3.81738i	0.0722154	−	0.222256i
$296$	2.71185	+	1.97027i	0.157623	+	0.114520i
$297$	9.74087	−	29.9793i	0.565223	−	1.73958i
$298$	−0.118570	−	0.364922i	−0.00686859	−	0.0211394i
$299$	−9.49313	+	6.89716i	−0.549002	+	0.398873i
$300$	0.0372220	+	0.114557i	0.00214901	+	0.00661398i
$301$	23.3177	+	16.9413i	1.34401	+	0.976478i
$302$	−2.68675	−	1.95204i	−0.154605	−	0.112327i
$303$	16.7037	−	12.1360i	0.959605	−	0.697194i
$304$	−9.05868			−0.519551
$305$	8.48675			0.485950
$306$	0.176950	−	0.128561i	0.0101155	−	0.00734937i
$307$	2.18357	−	6.72035i	0.124623	−	0.383551i	−0.869209	−	0.494445i	$-0.835371\pi$
$307$	2.18357	−	6.72035i	0.124623	−	0.383551i	0.993832	+	0.110894i	$0.0353715\pi$
$308$	10.1538	+	31.2503i	0.578569	+	1.78065i
$309$	−22.7914			−1.29656
$310$	−0.637512	−	2.23193i	−0.0362082	−	0.126765i
$311$	27.2628			1.54593			0.772966	−	0.634447i	$-0.218772\pi$
$311$	27.2628			1.54593			0.772966	+	0.634447i	$0.218772\pi$
$312$	1.76162	+	5.42172i	0.0997323	+	0.306945i
$313$	−1.03708	+	3.19180i	−0.0586192	+	0.180411i	−0.976079	−	0.217418i	$-0.930236\pi$
$313$	−1.03708	+	3.19180i	−0.0586192	+	0.180411i	0.917459	+	0.397830i	$0.130236\pi$
$314$	2.61854	−	1.90248i	0.147773	−	0.107363i
$315$	7.91665			0.446053
$316$	−1.84390			−0.103727
$317$	7.49484	−	5.44532i	0.420952	−	0.305840i	−0.357069	−	0.934078i	$-0.616224\pi$
$317$	7.49484	−	5.44532i	0.420952	−	0.305840i	0.778021	+	0.628239i	$0.216224\pi$
$318$	0.576865	+	0.419117i	0.0323490	+	0.0235029i
$319$	−25.4693	−	18.5045i	−1.42601	−	1.03605i
$320$	−4.98725	−	15.3492i	−0.278796	−	0.858046i
$321$	2.68507	−	1.95082i	0.149866	−	0.108884i
$322$	−0.350733	−	1.07945i	−0.0195456	−	0.0601552i
$323$	−0.737722	+	2.27048i	−0.0410480	+	0.126333i
$324$	−6.48140	−	4.70901i	−0.360078	−	0.261612i
$325$	0.0805225	−	0.247823i	0.00446659	−	0.0137467i
$326$	0.0912397	−	0.280807i	0.00505330	−	0.0155525i
$327$	−16.7352	−	12.1588i	−0.925457	−	0.672384i
$328$	−1.14556	+	3.52567i	−0.0632530	+	0.194673i
$329$	6.16772	+	18.9823i	0.340037	+	1.04653i
$330$	2.54442	−	1.84863i	0.140066	−	0.101764i
$331$	3.46959	+	10.6783i	0.190706	+	0.586933i	1.00000		0.000471352i	$-0.000150036\pi$
$331$	3.46959	+	10.6783i	0.190706	+	0.586933i	−0.809294	+	0.587404i	$0.800150\pi$
$332$	−6.64590	−	4.82853i	−0.364741	−	0.265000i
$333$	4.34199	+	3.15464i	0.237940	+	0.172873i
$334$	0.290702	−	0.211207i	0.0159065	−	0.0115568i
$335$	11.6549			0.636776
$336$	15.3165			0.835584
$337$	−15.9590	+	11.5949i	−0.869340	+	0.631613i	−0.930410	−	0.366521i	$-0.880549\pi$
$337$	−15.9590	+	11.5949i	−0.869340	+	0.631613i	0.0610696	+	0.998134i	$0.480549\pi$
$338$	1.14331	−	3.51875i	0.0621879	−	0.191395i
$339$	0.793660	+	2.44263i	0.0431057	+	0.132666i
$340$	−4.41502			−0.239438
$341$	25.8188	−	17.3764i	1.39817	−	0.940983i
$342$	0.522159			0.0282351
$343$	4.67207	+	14.3791i	0.252268	+	0.776401i
$344$	−2.19185	+	6.74583i	−0.118177	+	0.363711i
$345$	5.01481	−	3.64348i	0.269989	−	0.196158i
$346$	−2.97799			−0.160098
$347$	27.3170			1.46646			0.733228	−	0.679983i	$-0.238013\pi$
$347$	27.3170			1.46646			0.733228	+	0.679983i	$0.238013\pi$
$348$	−12.0877	+	8.78221i	−0.647967	+	0.470776i
$349$	18.1163	+	13.1623i	0.969744	+	0.704560i	0.955393	−	0.295337i	$-0.0954318\pi$
$349$	18.1163	+	13.1623i	0.969744	+	0.704560i	0.0143508	+	0.999897i	$0.495432\pi$
$350$	0.0203909	+	0.0148148i	0.00108994	+	0.000791886i
$351$	10.0010	+	30.7798i	0.533812	+	1.64290i
$352$	−9.84136	+	7.15016i	−0.524546	+	0.381105i
$353$	−6.97222	−	21.4583i	−0.371094	−	1.14211i	−0.946076	−	0.323944i	$-0.894991\pi$
$353$	−6.97222	−	21.4583i	−0.371094	−	1.14211i	0.574982	−	0.818166i	$-0.305009\pi$
$354$	−0.138324	+	0.425717i	−0.00735182	+	0.0226266i
$355$	−28.1421	−	20.4464i	−1.49363	−	1.08518i
$356$	8.77444	−	27.0050i	0.465044	−	1.43126i
$357$	1.24735	−	3.83894i	0.0660166	−	0.203178i
$358$	−0.0222628	−	0.0161749i	−0.00117663	−	0.000854868i
$359$	−2.31765	+	7.13300i	−0.122321	+	0.376465i	−0.993403	−	0.114672i	$-0.963418\pi$
$359$	−2.31765	+	7.13300i	−0.122321	+	0.376465i	0.871083	+	0.491137i	$0.163418\pi$
$360$	0.602041	+	1.85289i	0.0317304	+	0.0976560i
$361$	10.7605	−	7.81796i	0.566342	−	0.411471i
$362$	0.0916172	+	0.281969i	0.00481529	+	0.0148199i
$363$	22.1036	+	16.0592i	1.16014	+	0.842890i
$364$	−27.2929	−	19.8295i	−1.43054	−	1.03935i
$365$	−23.6162	+	17.1582i	−1.23613	+	0.898101i
$366$	−0.946449			−0.0494717
$367$	−11.3120			−0.590484			−0.295242	−	0.955423i	$-0.595400\pi$
$367$	−11.3120			−0.590484			−0.295242	+	0.955423i	$0.595400\pi$
$368$	−6.27683	+	4.56038i	−0.327202	+	0.237726i
$369$	−1.83418	+	5.64502i	−0.0954834	+	0.293868i
$370$	0.586725	+	1.80575i	0.0305024	+	0.0938767i
$371$	−8.51328			−0.441987
$372$	−4.05661	−	14.2022i	−0.210325	−	0.736350i
$373$	18.9749			0.982482			0.491241	−	0.871024i	$-0.336544\pi$
$373$	18.9749			0.982482			0.491241	+	0.871024i	$0.336544\pi$
$374$	0.320586	+	0.986662i	0.0165771	+	0.0510191i
$375$	4.64151	−	14.2851i	0.239687	−	0.737680i
$376$	−3.97376	+	2.88711i	−0.204931	+	0.148891i
$377$	32.3224			1.66469
$378$	−3.13042			−0.161011
$379$	−10.1649	+	7.38524i	−0.522136	+	0.379354i	−0.817408	−	0.576059i	$-0.804590\pi$
$379$	−10.1649	+	7.38524i	−0.522136	+	0.379354i	0.295272	+	0.955413i	$0.404590\pi$
$380$	−8.52709	−	6.19529i	−0.437430	−	0.317812i
$381$	8.60984	+	6.25541i	0.441095	+	0.320475i
$382$	−0.144103	−	0.443504i	−0.00737297	−	0.0226917i
$383$	8.99671	−	6.53649i	0.459710	−	0.333999i	−0.333707	−	0.942677i	$-0.608300\pi$
$383$	8.99671	−	6.53649i	0.459710	−	0.333999i	0.793418	+	0.608678i	$0.208300\pi$
$384$	2.37149	+	7.29871i	0.121020	+	0.372461i
$385$	−11.6036	+	35.7123i	−0.591376	+	1.82007i
$386$	2.90887	+	2.11342i	0.148057	+	0.107570i
$387$	−3.50942	+	10.8009i	−0.178394	+	0.549039i
$388$	−0.482120	+	1.48381i	−0.0244759	+	0.0753291i
$389$	−25.6734	−	18.6528i	−1.30169	−	0.945735i	−0.301722	−	0.953396i	$-0.597561\pi$
$389$	−25.6734	−	18.6528i	−1.30169	−	0.945735i	−0.999971	+	0.00766074i	$0.997561\pi$
$390$	−0.997833	+	3.07101i	−0.0505272	+	0.155507i
$391$	0.631845	+	1.94462i	0.0319538	+	0.0983436i
$392$	1.15800	−	0.841335i	0.0584877	−	0.0424938i
$393$	7.63784	+	23.5069i	0.385278	+	1.18576i
$394$	1.90289	+	1.38253i	0.0958664	+	0.0696510i
$395$	−1.70474	−	1.23857i	−0.0857748	−	0.0623190i
$396$	−10.4744	+	7.61013i	−0.526361	+	0.382424i
$397$	11.0618			0.555175			0.277588	−	0.960700i	$-0.410465\pi$
$397$	11.0618			0.555175			0.277588	+	0.960700i	$0.410465\pi$
$398$	−2.02057			−0.101282
$399$	7.79603	−	5.66415i	0.390290	−	0.283562i
$400$	0.0532412	−	0.163860i	0.00266206	−	0.00819298i
$401$	−3.60036	−	11.0808i	−0.179793	−	0.553347i	0.820026	−	0.572326i	$-0.193959\pi$
$401$	−3.60036	−	11.0808i	−0.179793	−	0.553347i	−0.999820	+	0.0189782i	$0.993959\pi$
$402$	−1.29976			−0.0648264
$403$	−10.9593	+	30.0142i	−0.545920	+	1.49512i
$404$	−30.0690			−1.49599
$405$	−2.82916	−	8.70725i	−0.140582	−	0.432667i
$406$	−0.966114	+	2.97339i	−0.0479474	+	0.147567i
$407$	−20.5949	+	14.9630i	−1.02085	+	0.741691i
$408$	0.993362			0.0491787
$409$	32.9083			1.62721			0.813604	−	0.581419i	$-0.197502\pi$
$409$	32.9083			1.62721			0.813604	+	0.581419i	$0.197502\pi$
$410$	−1.69878	+	1.23424i	−0.0838969	+	0.0609546i
$411$	−7.98743	−	5.80321i	−0.393991	−	0.286251i
$412$	26.8530	+	19.5098i	1.32295	+	0.961180i
$413$	−1.65149	−	5.08278i	−0.0812647	−	0.250107i
$414$	0.361808	−	0.262869i	0.0177819	−	0.0129193i
$415$	−2.90096	−	8.92824i	−0.142403	−	0.438270i
$416$	3.85943	−	11.8781i	0.189224	−	0.582373i
$417$	5.90931	+	4.29336i	0.289380	+	0.210247i
$418$	−0.765341	+	2.35548i	−0.0374341	+	0.115210i
$419$	2.45188	−	7.54611i	0.119782	−	0.368652i	−0.873132	−	0.487483i	$-0.837915\pi$
$419$	2.45188	−	7.54611i	0.119782	−	0.368652i	0.992914	+	0.118832i	$0.0379150\pi$
$420$	14.4177	+	10.4751i	0.703511	+	0.511131i
$421$	6.17746	−	19.0123i	0.301071	−	0.926601i	−0.680043	−	0.733172i	$-0.738039\pi$
$421$	6.17746	−	19.0123i	0.301071	−	0.926601i	0.981114	−	0.193429i	$-0.0619610\pi$
$422$	−0.266859	−	0.821308i	−0.0129905	−	0.0399806i
$423$	−6.36246	+	4.62260i	−0.309354	+	0.224759i
$424$	−0.647413	−	1.99253i	−0.0314412	−	0.0967659i
$425$	−0.0367341	−	0.0266889i	−0.00178186	−	0.00129460i
$426$	3.13843	+	2.28020i	0.152057	+	0.110476i
$427$	9.14188	−	6.64196i	0.442406	−	0.321427i
$428$	−4.83350			−0.233636
$429$	−43.2937			−2.09024
$430$	−3.25036	+	2.36152i	−0.156746	+	0.113883i
$431$	−8.76077	+	26.9629i	−0.421991	+	1.29876i	0.483854	+	0.875149i	$0.339236\pi$
$431$	−8.76077	+	26.9629i	−0.421991	+	1.29876i	−0.905846	+	0.423608i	$0.860764\pi$
$432$	6.61260	+	20.3515i	0.318149	+	0.979162i
$433$	0.860962			0.0413752			0.0206876	−	0.999786i	$-0.493414\pi$
$433$	0.860962			0.0413752			0.0206876	+	0.999786i	$0.493414\pi$
$434$	−2.43349	−	1.90529i	−0.116811	−	0.0914568i
$435$	−17.0745			−0.818661
$436$	9.30932	+	28.6511i	0.445836	+	1.37214i
$437$	−1.50842	+	4.64243i	−0.0721573	+	0.222077i
$438$	2.63370	−	1.91349i	0.125843	−	0.0914303i
$439$	−25.2605			−1.20562			−0.602808	−	0.797886i	$-0.705952\pi$
$439$	−25.2605			−1.20562			−0.602808	+	0.797886i	$0.705952\pi$
$440$	−9.24089			−0.440542
$441$	1.85409	−	1.34708i	0.0882900	−	0.0641465i
$442$	−0.861715	−	0.626073i	−0.0409876	−	0.0297793i
$443$	−6.62170	−	4.81095i	−0.314607	−	0.228575i	0.419264	−	0.907864i	$-0.362288\pi$
$443$	−6.62170	−	4.81095i	−0.314607	−	0.228575i	−0.733871	+	0.679289i	$0.762288\pi$
$444$	3.73344	+	11.4904i	0.177181	+	0.545308i
$445$	26.2518	−	19.0730i	1.24445	−	0.904148i
$446$	0.343004	+	1.05566i	0.0162417	+	0.0499868i
$447$	0.862213	−	2.65362i	0.0407813	−	0.125512i
$448$	−17.3849	−	12.6309i	−0.821361	−	0.596753i
$449$	−0.732660	+	2.25490i	−0.0345764	+	0.106415i	−0.966855	−	0.255325i	$-0.917817\pi$
$449$	−0.732660	+	2.25490i	−0.0345764	+	0.106415i	0.932279	+	0.361741i	$0.117817\pi$
$450$	−0.00306892	+	0.00944517i	−0.000144670	+	0.000445250i
$451$	−22.7765	−	16.5481i	−1.07250	−	0.779219i
$452$	1.15584	−	3.55731i	0.0543661	−	0.167322i
$453$	−7.46260	−	22.9675i	−0.350624	−	1.07911i
$454$	−0.381419	+	0.277117i	−0.0179009	+	0.0130058i
$455$	−11.9135	−	36.6659i	−0.558512	−	1.71892i
$456$	1.91856	+	1.39392i	0.0898448	+	0.0652761i
$457$	−17.7127	−	12.8690i	−0.828565	−	0.601988i	0.0905877	−	0.995888i	$-0.471125\pi$
$457$	−17.7127	−	12.8690i	−0.828565	−	0.601988i	−0.919153	+	0.393900i	$0.871125\pi$
$458$	3.50776	−	2.54854i	0.163907	−	0.119085i
$459$	5.63944			0.263226
$460$	−9.02736			−0.420903
$461$	−0.254950	+	0.185232i	−0.0118742	+	0.00862710i	−0.593707	−	0.804682i	$-0.702336\pi$
$461$	−0.254950	+	0.185232i	−0.0118742	+	0.00862710i	0.581832	+	0.813309i	$0.302336\pi$
$462$	1.29405	−	3.98266i	0.0602045	−	0.185290i
$463$	6.25538	+	19.2521i	0.290712	+	0.894720i	0.984628	+	0.174664i	$0.0558839\pi$
$463$	6.25538	+	19.2521i	0.290712	+	0.894720i	−0.693916	+	0.720056i	$0.744116\pi$
$464$	21.3714			0.992144
$465$	5.78932	−	15.8552i	0.268473	−	0.735269i
$466$	−0.311782			−0.0144430
$467$	6.49105	+	19.9774i	0.300370	+	0.924443i	0.981365	+	0.192155i	$0.0615477\pi$
$467$	6.49105	+	19.9774i	0.300370	+	0.924443i	−0.680995	+	0.732288i	$0.738452\pi$
$468$	4.10771	−	12.6422i	0.189879	−	0.584388i
$469$	12.5546	−	9.12145i	0.579717	−	0.421189i
$470$	−2.78220			−0.128333
$471$	23.5364			1.08450
$472$	1.06403	−	0.773064i	0.0489760	−	0.0355832i
$473$	−43.5793	−	31.6622i	−2.00378	−	1.45583i
$474$	0.190114	+	0.138126i	0.00873222	+	0.00634433i
$475$	−0.0334969	−	0.103093i	−0.00153694	−	0.00473022i
$476$	−4.75583	+	3.45531i	−0.217983	+	0.158374i
$477$	−1.03658	−	3.19028i	−0.0474619	−	0.146073i
$478$	1.16764	−	3.59362i	0.0534066	−	0.164368i
$479$	−8.56614	−	6.22367i	−0.391397	−	0.284367i	0.374631	−	0.927174i	$-0.377770\pi$
$479$	−8.56614	−	6.22367i	−0.391397	−	0.284367i	−0.766028	+	0.642808i	$0.777770\pi$
$480$	−2.03877	+	6.27470i	−0.0930569	+	0.286400i
$481$	8.07658	−	24.8572i	0.368260	−	1.13339i
$482$	3.80468	+	2.76426i	0.173298	+	0.125909i
$483$	2.55044	−	7.84946i	0.116049	−	0.357163i
$484$	−12.2957	−	37.8421i	−0.558893	−	1.72010i
$485$	−1.44243	+	1.04798i	−0.0654972	+	0.0475865i
$486$	−0.654826	−	2.01535i	−0.0297035	−	0.0914180i
$487$	7.12183	+	5.17432i	0.322721	+	0.234471i	0.737336	−	0.675526i	$-0.236084\pi$
$487$	7.12183	+	5.17432i	0.322721	+	0.234471i	−0.414615	+	0.909997i	$0.636084\pi$
$488$	2.24977	+	1.63455i	0.101842	+	0.0739927i
$489$	1.73699	−	1.26200i	0.0785495	−	0.0570695i
$490$	0.810764			0.0366266
$491$	−13.3373			−0.601902			−0.300951	−	0.953640i	$-0.597304\pi$
$491$	−13.3373			−0.601902			−0.300951	+	0.953640i	$0.597304\pi$
$492$	−10.8097	+	7.85369i	−0.487338	+	0.354072i
$493$	1.74045	−	5.35656i	0.0783860	−	0.241247i
$494$	−0.785777	−	2.41837i	−0.0353538	−	0.108808i
$495$	−14.7958			−0.665020
$496$	−7.24624	+	19.8453i	−0.325366	+	0.891081i
$497$	−46.3164			−2.07758
$498$	0.323517	+	0.995684i	0.0144972	+	0.0446177i
$499$	11.4675	−	35.2932i	0.513354	−	1.57994i	−0.272903	−	0.962042i	$-0.587984\pi$
$499$	11.4675	−	35.2932i	0.513354	−	1.57994i	0.786257	−	0.617900i	$-0.212016\pi$
$500$	−17.6969	+	12.8576i	−0.791431	+	0.575009i
$501$	2.61294			0.116737
$502$	4.46285			0.199187
$503$	11.1082	−	8.07056i	0.495289	−	0.359849i	−0.311926	−	0.950107i	$-0.600974\pi$
$503$	11.1082	−	8.07056i	0.495289	−	0.359849i	0.807215	+	0.590258i	$0.200974\pi$
$504$	2.09864	+	1.52475i	0.0934808	+	0.0679178i
$505$	−27.7997	−	20.1977i	−1.23707	−	0.898786i
$506$	0.655500	+	2.01742i	0.0291405	+	0.0896853i
$507$	21.7660	−	15.8139i	0.966660	−	0.702319i
$508$	−4.78942	−	14.7403i	−0.212496	−	0.653996i
$509$	−2.03593	+	6.26594i	−0.0902408	+	0.277733i	−0.985984	−	0.166839i	$-0.946644\pi$
$509$	−2.03593	+	6.26594i	−0.0902408	+	0.277733i	0.895743	+	0.444572i	$0.146644\pi$
$510$	0.455207	+	0.330728i	0.0201569	+	0.0146449i
$511$	−12.0108	+	36.9654i	−0.531326	+	1.63525i
$512$	4.27789	−	13.1660i	0.189058	−	0.581861i
$513$	10.8919	+	7.91344i	0.480890	+	0.349387i
$514$	−1.09687	+	3.37581i	−0.0483807	+	0.148900i
$515$	11.7214	+	36.0749i	0.516508	+	1.58965i
$516$	−20.6827	+	15.0268i	−0.910503	+	0.661519i
$517$	−11.5271	−	35.4768i	−0.506961	−	1.56027i
$518$	2.04525	+	1.48596i	0.0898631	+	0.0652893i
$519$	−17.5194	−	12.7286i	−0.769017	−	0.558723i
$520$	7.67566	−	5.57669i	0.336600	−	0.244554i
$521$	−22.9346			−1.00478			−0.502391	−	0.864641i	$-0.667546\pi$
$521$	−22.9346			−1.00478			−0.502391	+	0.864641i	$0.667546\pi$
$522$	−1.23189			−0.0539183
$523$	30.2470	−	21.9757i	1.32261	−	0.960931i	0.322712	−	0.946497i	$-0.395405\pi$
$523$	30.2470	−	21.9757i	1.32261	−	0.960931i	0.999896	−	0.0144336i	$-0.00459451\pi$
$524$	11.1233	−	34.2340i	0.485924	−	1.49552i
$525$	0.0566368	+	0.174310i	0.00247183	+	0.00760752i
$526$	−5.81774			−0.253665
$527$	4.38393	+	3.43237i	0.190967	+	0.149516i
$528$	−28.6256			−1.24577
$529$	−5.81546	−	17.8982i	−0.252846	−	0.778181i
$530$	0.366713	−	1.12863i	0.0159290	−	0.0490243i
$531$	1.70364	−	1.23777i	0.0739317	−	0.0537145i
$532$	−14.0339			−0.608448
$533$	28.9050			1.25201
$534$	−2.92762	+	2.12704i	−0.126690	+	0.0920459i
$535$	−4.46871	−	3.24671i	−0.193199	−	0.140368i
$536$	3.08962	+	2.24474i	0.133451	+	0.0969580i
$537$	−0.0618362	−	0.190312i	−0.00266843	−	0.00821258i
$538$	0.702991	−	0.510753i	0.0303081	−	0.0220201i
$539$	3.35912	+	10.3383i	0.144688	+	0.445303i
$540$	−7.69397	+	23.6796i	−0.331096	+	1.01901i
$541$	28.0355	+	20.3690i	1.20534	+	0.875732i	0.994800	−	0.101852i	$-0.0324769\pi$
$541$	28.0355	+	20.3690i	1.20534	+	0.875732i	0.210543	+	0.977585i	$0.432477\pi$
$542$	1.08524	−	3.34004i	0.0466152	−	0.143467i
$543$	−0.666216	+	2.05040i	−0.0285901	+	0.0879912i
$544$	−1.76066	−	1.27919i	−0.0754877	−	0.0548450i
$545$	−10.6385	+	32.7420i	−0.455705	+	1.40251i
$546$	1.32860	+	4.08901i	0.0568588	+	0.174993i
$547$	−37.6640	+	27.3645i	−1.61039	+	1.17002i	−0.748146	+	0.663534i	$0.769056\pi$
$547$	−37.6640	+	27.3645i	−1.61039	+	1.17002i	−0.862248	+	0.506486i	$0.830944\pi$
$548$	4.44319	+	13.6747i	0.189804	+	0.584156i
$549$	3.60214	+	2.61711i	0.153736	+	0.111695i
$550$	−0.0381093	−	0.0276880i	−0.00162499	−	0.00118062i
$551$	10.8780	−	7.90331i	0.463417	−	0.336692i
$552$	2.03112			0.0864502
$553$	−2.80567			−0.119309
$554$	−1.52097	+	1.10505i	−0.0646198	+	0.0469490i
$555$	−4.26651	+	13.1310i	−0.181103	+	0.557379i
$556$	−3.28719	−	10.1169i	−0.139408	−	0.429053i
$557$	−36.9039			−1.56367			−0.781835	−	0.623485i	$-0.785716\pi$
$557$	−36.9039			−1.56367			−0.781835	+	0.623485i	$0.785716\pi$
$558$	0.417686	−	1.14392i	0.0176821	−	0.0484260i
$559$	55.3053			2.33916
$560$	−7.87715	−	24.2434i	−0.332870	−	1.02447i
$561$	−2.33122	+	7.17475i	−0.0984241	+	0.302918i
$562$	−1.48628	+	1.07985i	−0.0626949	+	0.0455505i
$563$	43.6679			1.84038			0.920191	−	0.391470i	$-0.128033\pi$
$563$	43.6679			1.84038			0.920191	+	0.391470i	$0.128033\pi$
$564$	−17.7037			−0.745460
$565$	3.45809	−	2.51245i	0.145483	−	0.105700i
$566$	3.32223	+	2.41374i	0.139644	+	0.101457i
$567$	−9.86208	−	7.16522i	−0.414168	−	0.300911i
$568$	−3.52225	−	10.8404i	−0.147790	−	0.454851i
$569$	−18.1847	+	13.2120i	−0.762343	+	0.553875i	−0.899628	−	0.436657i	$-0.856162\pi$
$569$	−18.1847	+	13.2120i	−0.762343	+	0.553875i	0.137285	+	0.990532i	$0.456162\pi$
$570$	0.415092	+	1.27752i	0.0173863	+	0.0535095i
$571$	7.94905	−	24.4647i	0.332657	−	1.02381i	−0.635207	−	0.772342i	$-0.719085\pi$
$571$	7.94905	−	24.4647i	0.332657	−	1.02381i	0.967864	−	0.251472i	$-0.0809148\pi$
$572$	51.0088	+	37.0601i	2.13279	+	1.54956i
$573$	1.04788	−	3.22505i	0.0437759	−	0.134728i
$574$	−0.863969	+	2.65902i	−0.0360614	+	0.110986i
$575$	−0.0751099	−	0.0545705i	−0.00313230	−	0.00227575i
$576$	2.61651	−	8.05280i	0.109021	−	0.335533i
$577$	−2.22442	−	6.84605i	−0.0926037	−	0.285005i	0.894018	−	0.448031i	$-0.147875\pi$
$577$	−2.22442	−	6.84605i	−0.0926037	−	0.285005i	−0.986622	+	0.163026i	$0.947875\pi$
$578$	−0.150155	+	0.109094i	−0.00624563	+	0.00453772i
$579$	8.07955	+	24.8663i	0.335774	+	1.03341i
$580$	20.1173	+	14.6161i	0.835325	+	0.606899i
$581$	−10.1124	−	7.34707i	−0.419532	−	0.304808i
$582$	0.160860	−	0.116872i	0.00666788	−	0.00484450i
$583$	15.9108			0.658958
$584$	−9.56513			−0.395808
$585$	12.2896	−	8.92894i	0.508114	−	0.369166i
$586$	−0.316665	+	0.974595i	−0.0130813	+	0.0402601i
$587$	−2.47917	−	7.63010i	−0.102326	−	0.314928i	0.886767	−	0.462216i	$-0.152946\pi$
$587$	−2.47917	−	7.63010i	−0.102326	−	0.314928i	−0.989094	+	0.147288i	$0.952946\pi$
$588$	5.15905			0.212755
$589$	3.65063	+	12.7809i	0.150422	+	0.526627i
$590$	0.744974			0.0306701
$591$	5.28540	+	16.2668i	0.217412	+	0.669126i
$592$	5.34021	−	16.4355i	0.219481	−	0.675494i
$593$	−19.3058	+	14.0265i	−0.792794	+	0.575999i	−0.908791	−	0.417251i	$-0.862994\pi$
$593$	−19.3058	+	14.0265i	−0.792794	+	0.575999i	0.115997	+	0.993250i	$0.462994\pi$
$594$	5.85057			0.240052
$595$	−6.71788			−0.275406
$596$	−3.28740	+	2.38844i	−0.134657	+	0.0978343i
$597$	−11.8869	−	8.63636i	−0.486500	−	0.353463i
$598$	−1.76194	−	1.28013i	−0.0720512	−	0.0523483i
$599$	2.36927	+	7.29185i	0.0968056	+	0.297937i	0.987720	−	0.156234i	$-0.0499355\pi$
$599$	2.36927	+	7.29185i	0.0968056	+	0.297937i	−0.890914	+	0.454171i	$0.849935\pi$
$600$	−0.0364902	+	0.0265117i	−0.00148971	+	0.00108234i
$601$	9.93615	+	30.5803i	0.405304	+	1.24740i	0.920641	+	0.390410i	$0.127667\pi$
$601$	9.93615	+	30.5803i	0.405304	+	1.24740i	−0.515337	+	0.856988i	$0.672333\pi$
$602$	−1.65307	+	5.08764i	−0.0673743	+	0.207357i
$603$	4.94684	+	3.59409i	0.201451	+	0.146363i
$604$	−10.8681	+	33.4486i	−0.442217	+	1.36100i
$605$	14.0513	−	43.2453i	0.571265	−	1.75817i
$606$	3.10025	+	2.25246i	0.125939	+	0.0915000i
$607$	−6.55842	+	20.1847i	−0.266198	+	0.819274i	0.725217	+	0.688521i	$0.241740\pi$
$607$	−6.55842	+	20.1847i	−0.266198	+	0.819274i	−0.991415	+	0.130753i	$0.958260\pi$
$608$	−1.60550	−	4.94123i	−0.0651117	−	0.200393i
$609$	−18.3926	+	13.3630i	−0.745304	+	0.541495i
$610$	0.486751	+	1.49806i	0.0197080	+	0.0606549i
$611$	30.9841	+	22.5113i	1.25348	+	0.910709i
$612$	−1.87392	−	1.36148i	−0.0757488	−	0.0550348i
$613$	−12.7956	+	9.29658i	−0.516811	+	0.375485i	−0.815401	−	0.578896i	$-0.803484\pi$
$613$	−12.7956	+	9.29658i	−0.516811	+	0.375485i	0.298590	+	0.954381i	$0.403484\pi$
$614$	1.31150			0.0529278
$615$	−15.2693			−0.615717
$616$	−9.95423	+	7.23217i	−0.401067	+	0.291392i
$617$	−0.443810	+	1.36591i	−0.0178671	+	0.0549894i	−0.959593	−	0.281393i	$-0.909204\pi$
$617$	−0.443810	+	1.36591i	−0.0178671	+	0.0549894i	0.941725	+	0.336383i	$0.109204\pi$
$618$	−1.30718	−	4.02310i	−0.0525826	−	0.161833i
$619$	29.6858			1.19317			0.596586	−	0.802549i	$-0.296524\pi$
$619$	29.6858			1.19317			0.596586	+	0.802549i	$0.296524\pi$
$620$	−20.3934	+	13.7250i	−0.819017	+	0.551209i
$621$	11.5309			0.462720
$622$	1.56364	+	4.81238i	0.0626961	+	0.192959i
$623$	13.3512	−	41.0907i	0.534903	−	1.64626i
$624$	23.7770	−	17.2750i	0.951841	−	0.691553i
$625$	−25.2250			−1.00900
$626$	−0.622892			−0.0248958
$627$	−14.5703	+	10.5860i	−0.581882	+	0.422762i
$628$	−27.7307	−	20.1475i	−1.10658	−	0.803974i
$629$	−3.68451	−	2.67695i	−0.146911	−	0.106737i
$630$	0.454053	+	1.39743i	0.0180899	+	0.0556750i
$631$	−22.1890	+	16.1213i	−0.883331	+	0.641778i	−0.934131	−	0.356931i	$-0.883823\pi$
$631$	−22.1890	+	16.1213i	−0.883331	+	0.641778i	0.0507997	+	0.998709i	$0.483823\pi$
$632$	−0.213364	−	0.656667i	−0.00848716	−	0.0261208i
$633$	1.94053	−	5.97234i	0.0771292	−	0.237379i
$634$	1.39106	+	1.01066i	0.0552459	+	0.0401385i
$635$	5.47327	−	16.8450i	0.217200	−	0.668473i
$636$	2.33346	−	7.18166i	0.0925278	−	0.284771i
$637$	−9.02911	−	6.56003i	−0.357746	−	0.259918i
$638$	1.80561	−	5.55710i	0.0714848	−	0.220008i
$639$	−5.63953	−	17.3567i	−0.223096	−	0.686620i
$640$	10.3329	−	7.50733i	0.408446	−	0.296753i
$641$	−2.90757	−	8.94858i	−0.114842	−	0.353447i	0.877072	−	0.480359i	$-0.159494\pi$
$641$	−2.90757	−	8.94858i	−0.114842	−	0.353447i	−0.991914	+	0.126911i	$0.959494\pi$
$642$	0.498354	+	0.362076i	0.0196685	+	0.0142900i
$643$	−18.5880	−	13.5050i	−0.733040	−	0.532585i	0.157483	−	0.987522i	$-0.449662\pi$
$643$	−18.5880	−	13.5050i	−0.733040	−	0.532585i	−0.890524	+	0.454937i	$0.849662\pi$
$644$	−9.72421	+	7.06505i	−0.383188	+	0.278402i
$645$	−29.2154			−1.15036
$646$	−0.443091			−0.0174332
$647$	16.0027	−	11.6266i	0.629131	−	0.457090i	−0.226968	−	0.973902i	$-0.572881\pi$
$647$	16.0027	−	11.6266i	0.629131	−	0.457090i	0.856099	+	0.516812i	$0.172881\pi$
$648$	0.927033	−	2.85311i	0.0364173	−	0.112081i
$649$	3.08654	+	9.49941i	0.121157	+	0.372884i
$650$	0.0483635			0.00189697
$651$	−6.17252	−	21.6100i	−0.241920	−	0.846964i
$652$	−3.12683			−0.122456
$653$	−12.6408	−	38.9045i	−0.494675	−	1.52245i	−0.817463	−	0.575981i	$-0.804620\pi$
$653$	−12.6408	−	38.9045i	−0.494675	−	1.52245i	0.322789	−	0.946471i	$-0.395380\pi$
$654$	1.18642	−	3.65142i	0.0463926	−	0.142782i
$655$	33.2792	−	24.1788i	1.30033	−	0.944742i
$656$	19.1119			0.746194
$657$	−15.3149			−0.597491
$658$	−2.99697	+	2.17743i	−0.116834	+	0.0848849i
$659$	30.0815	+	21.8555i	1.17181	+	0.851369i	0.991224	−	0.132190i	$-0.0422009\pi$
$659$	30.0815	+	21.8555i	1.17181	+	0.851369i	0.180585	+	0.983559i	$0.442201\pi$
$660$	−26.9458	−	19.5773i	−1.04886	−	0.762044i
$661$	12.1017	+	37.2452i	0.470701	+	1.44867i	0.851669	+	0.524080i	$0.175591\pi$
$661$	12.1017	+	37.2452i	0.470701	+	1.44867i	−0.380968	+	0.924588i	$0.624409\pi$
$662$	−1.68592	+	1.22489i	−0.0655250	+	0.0476067i
$663$	−2.39346	−	7.36633i	−0.0929545	−	0.286084i
$664$	0.950561	−	2.92553i	0.0368889	−	0.113532i
$665$	−12.9748	−	9.42674i	−0.503141	−	0.365553i
$666$	−0.307820	+	0.947371i	−0.0119278	+	0.0367099i
$667$	3.55869	−	10.9525i	0.137793	−	0.424083i
$668$	−3.07858	−	2.23672i	−0.119114	−	0.0865412i
$669$	−2.49423	+	7.67646i	−0.0964327	+	0.296789i
$670$	0.668458	+	2.05730i	0.0258248	+	0.0794805i
$671$	−17.0856	+	12.4134i	−0.659583	+	0.479215i
$672$	2.71460	+	8.35467i	0.104718	+	0.322288i
$673$	−7.27359	−	5.28457i	−0.280376	−	0.203705i	0.438705	−	0.898631i	$-0.355437\pi$
$673$	−7.27359	−	5.28457i	−0.280376	−	0.203705i	−0.719081	+	0.694926i	$0.755437\pi$
$674$	−2.96202	−	2.15203i	−0.114093	−	0.0828931i
$675$	−0.207160	+	0.150510i	−0.00797357	+	0.00579314i
$676$	−39.1817			−1.50699
$677$	47.4214			1.82255			0.911277	−	0.411795i	$-0.135098\pi$
$677$	47.4214			1.82255			0.911277	+	0.411795i	$0.135098\pi$
$678$	−0.385649	+	0.280190i	−0.0148108	+	0.0107606i
$679$	−0.733592	+	2.25776i	−0.0281527	+	0.0866450i
$680$	−0.510877	−	1.57232i	−0.0195913	−	0.0602957i
$681$	−3.42834			−0.131374
$682$	4.54805	+	3.56087i	0.174154	+	0.136353i
$683$	0.811231			0.0310409			0.0155205	−	0.999880i	$-0.495059\pi$
$683$	0.811231			0.0310409			0.0155205	+	0.999880i	$0.495059\pi$
$684$	−1.70878	−	5.25909i	−0.0653370	−	0.201087i
$685$	−5.07760	+	15.6273i	−0.194005	+	0.597087i
$686$	−2.27022	+	1.64941i	−0.0866772	+	0.0629747i
$687$	31.5290			1.20291
$688$	36.5677			1.39413
$689$	−13.2158	+	9.60185i	−0.503482	+	0.365801i
$690$	0.930759	+	0.676236i	0.0354334	+	0.0257439i
$691$	30.9831	+	22.5105i	1.17865	+	0.856342i	0.992019	−	0.126088i	$-0.0402421\pi$
$691$	30.9831	+	22.5105i	1.17865	+	0.856342i	0.186634	+	0.982430i	$0.440242\pi$
$692$	9.74558	+	29.9938i	0.370471	+	1.14019i
$693$	−15.9379	+	11.5796i	−0.605430	+	0.439871i
$694$	1.56675	+	4.82195i	0.0594729	+	0.183039i
$695$	3.75654	−	11.5614i	0.142494	−	0.438551i
$696$	−4.52631	−	3.28856i	−0.171569	−	0.124652i
$697$	1.55644	−	4.79022i	0.0589543	−	0.181443i
$698$	−1.28433	+	3.95277i	−0.0486127	+	0.149614i
$699$	−1.83420	−	1.33262i	−0.0693759	−	0.0504045i
$700$	0.0824826	−	0.253855i	0.00311755	−	0.00959483i
$701$	8.56663	+	26.3654i	0.323557	+	0.995807i	0.972088	+	0.234618i	$0.0753839\pi$
$701$	8.56663	+	26.3654i	0.323557	+	0.995807i	−0.648530	+	0.761189i	$0.724616\pi$
$702$	−4.85959	+	3.53070i	−0.183413	+	0.133258i
$703$	−3.35981	−	10.3404i	−0.126718	−	0.389997i
$704$	32.4914	+	23.6064i	1.22457	+	0.889699i
$705$	−16.3676	−	11.8918i	−0.616439	−	0.447869i
$706$	3.38789	−	2.46145i	0.127505	−	0.0926377i
$707$	−45.7530			−1.72072
$708$	4.74041			0.178156
$709$	−10.2342	+	7.43558i	−0.384353	+	0.279249i	−0.763138	−	0.646236i	$-0.776342\pi$
$709$	−10.2342	+	7.43558i	−0.384353	+	0.279249i	0.378784	+	0.925485i	$0.376342\pi$
$710$	1.99510	−	6.14028i	0.0748747	−	0.230441i
$711$	−0.341621	−	1.05140i	−0.0128118	−	0.0394306i
$712$	10.6326			0.398473
$713$	8.96379	+	7.01814i	0.335697	+	0.262832i
$714$	0.749183			0.0280375
$715$	22.2656	+	68.5263i	0.832685	+	2.56274i
$716$	−0.0900547	+	0.277160i	−0.00336550	+	0.0103579i
$717$	22.2291	−	16.1504i	0.830162	−	0.603148i
$718$	−1.39203			−0.0519501
$719$	−17.6425			−0.657954			−0.328977	−	0.944338i	$-0.606704\pi$
$719$	−17.6425			−0.657954			−0.328977	+	0.944338i	$0.606704\pi$
$720$	8.12586	−	5.90379i	0.302833	−	0.220021i
$721$	40.8594	+	29.6861i	1.52168	+	1.10557i
$722$	1.99717	+	1.45103i	0.0743269	+	0.0540017i
$723$	10.5677	+	32.5241i	0.393018	+	1.20958i
$724$	2.54012	−	1.84550i	0.0944028	−	0.0685876i
$725$	0.0790266	+	0.243219i	0.00293497	+	0.00903292i
$726$	−1.56701	+	4.82275i	−0.0581571	+	0.178989i
$727$	14.6480	+	10.6424i	0.543264	+	0.394704i	0.825296	−	0.564701i	$-0.191008\pi$
$727$	14.6480	+	10.6424i	0.543264	+	0.394704i	−0.282032	+	0.959405i	$0.591008\pi$
$728$	3.90370	−	12.0144i	0.144681	−	0.445281i
$729$	8.54032	−	26.2844i	0.316308	−	0.973496i
$730$	−4.38322	−	3.18459i	−0.162230	−	0.117867i
$731$	2.97801	−	9.16536i	0.110146	−	0.338993i
$732$	3.09729	+	9.53247i	0.114479	+	0.352330i
$733$	−9.84881	+	7.15558i	−0.363774	+	0.264297i	−0.754625	−	0.656157i	$-0.772181\pi$
$733$	−9.84881	+	7.15558i	−0.363774	+	0.264297i	0.390850	+	0.920454i	$0.372181\pi$
$734$	−0.648793	−	1.99678i	−0.0239474	−	0.0737024i
$735$	4.76969	+	3.46539i	0.175933	+	0.127823i
$736$	−3.60001	−	2.61556i	−0.132698	−	0.0964108i
$737$	−23.4638	+	17.0474i	−0.864300	+	0.627951i
$738$	−1.10164			−0.0405521
$739$	5.03196			0.185104			0.0925518	−	0.995708i	$-0.470498\pi$
$739$	5.03196			0.185104			0.0925518	+	0.995708i	$0.470498\pi$
$740$	16.2672	−	11.8188i	0.597993	−	0.434467i
$741$	5.71397	−	17.5858i	0.209908	−	0.646030i
$742$	−0.488272	−	1.50275i	−0.0179250	−	0.0551676i
$743$	28.8768			1.05939			0.529693	−	0.848190i	$-0.322307\pi$
$743$	28.8768			1.05939			0.529693	+	0.848190i	$0.322307\pi$
$744$	4.58842	−	3.08807i	0.168220	−	0.113214i
$745$	−4.64364			−0.170130
$746$	1.08829	+	3.34941i	0.0398451	+	0.122630i
$747$	1.52196	−	4.68411i	0.0556856	−	0.171383i
$748$	8.88836	−	6.45777i	0.324991	−	0.236120i
$749$	−7.35463			−0.268732
$750$	2.78779			0.101796
$751$	1.56164	−	1.13460i	0.0569852	−	0.0414022i	−0.558928	−	0.829216i	$-0.688787\pi$
$751$	1.56164	−	1.13460i	0.0569852	−	0.0414022i	0.615913	+	0.787814i	$0.288787\pi$
$752$	20.4866	+	14.8844i	0.747070	+	0.542778i
$753$	26.2548	+	19.0752i	0.956778	+	0.695140i
$754$	1.85382	+	5.70548i	0.0675122	+	0.207781i
$755$	−32.5157	+	23.6240i	−1.18337	+	0.859766i
$756$	10.2444	+	31.5290i	0.372585	+	1.14670i
$757$	−0.321758	+	0.990270i	−0.0116945	+	0.0359920i	−0.956733	−	0.290966i	$-0.906023\pi$
$757$	−0.321758	+	0.990270i	−0.0116945	+	0.0359920i	0.945039	+	0.326958i	$0.106023\pi$
$758$	−1.88663	−	1.37072i	−0.0685254	−	0.0497866i
$759$	−4.76663	+	14.6702i	−0.173018	+	0.532493i
$760$	1.21963	−	3.75363i	0.0442405	−	0.136158i
$761$	−1.12002	−	0.813743i	−0.0406007	−	0.0294982i	0.567300	−	0.823511i	$-0.307988\pi$
$761$	−1.12002	−	0.813743i	−0.0406007	−	0.0294982i	−0.607901	+	0.794013i	$0.707988\pi$
$762$	−0.610383	+	1.87857i	−0.0221118	+	0.0680533i
$763$	14.1650	+	43.5955i	0.512809	+	1.57826i
$764$	−3.99532	+	2.90277i	−0.144545	+	0.105018i
$765$	−0.817975	−	2.51747i	−0.0295739	−	0.0910192i
$766$	1.66981	+	1.21319i	0.0603326	+	0.0438342i
$767$	−8.29644	−	6.02772i	−0.299567	−	0.217648i
$768$	14.5383	−	10.5627i	0.524605	−	0.381148i
$769$	−34.3668			−1.23930			−0.619649	−	0.784879i	$-0.712725\pi$
$769$	−34.3668			−1.23930			−0.619649	+	0.784879i	$0.712725\pi$
$770$	−6.96938			−0.251159
$771$	−20.8818	+	15.1715i	−0.752038	+	0.546388i
$772$	11.7666	−	36.2138i	0.423489	−	1.30336i
$773$	10.3628	+	31.8933i	0.372722	+	1.14712i	0.945002	+	0.327063i	$0.106059\pi$
$773$	10.3628	+	31.8933i	0.372722	+	1.14712i	−0.572280	+	0.820058i	$0.693941\pi$
$774$	−2.10783			−0.0757643
$775$	−0.252646	−	0.00908285i	−0.00907530	−	0.000326266i
$776$	−0.584217			−0.0209722
$777$	5.68080	+	17.4837i	0.203797	+	0.627224i
$778$	1.82008	−	5.60163i	0.0652531	−	0.200828i
$779$	9.72787	−	7.06771i	0.348537	−	0.253227i
$780$	34.1962			1.22442
$781$	86.5627			3.09746
$782$	−0.307021	+	0.223064i	−0.0109791	+	0.00797675i
$783$	−25.6964	−	18.6696i	−0.918316	−	0.667195i
$784$	−5.97002	−	4.33747i	−0.213215	−	0.154910i
$785$	−12.1046	−	37.2540i	−0.432030	−	1.32965i
$786$	−3.71132	+	2.69643i	−0.132378	+	0.0961786i
$787$	−13.3365	−	41.0455i	−0.475395	−	1.46311i	−0.845425	−	0.534095i	$-0.820653\pi$
$787$	−13.3365	−	41.0455i	−0.475395	−	1.46311i	0.370030	−	0.929020i	$-0.379347\pi$
$788$	7.69735	−	23.6900i	0.274207	−	0.843922i
$789$	−34.2255	−	24.8663i	−1.21846	−	0.885264i
$790$	0.120855	−	0.371954i	0.00429984	−	0.0132335i
$791$	1.75872	−	5.41279i	0.0625330	−	0.192457i
$792$	−3.92223	−	2.84967i	−0.139370	−	0.101258i
$793$	6.70038	−	20.6217i	0.237938	−	0.732296i
$794$	0.634439	+	1.95260i	0.0225154	+	0.0692953i
$795$	6.98135	−	5.07225i	0.247603	−	0.179894i
$796$	6.61238	+	20.3508i	0.234370	+	0.721316i
$797$	15.2395	+	11.0722i	0.539812	+	0.392196i	0.824015	−	0.566568i	$-0.191729\pi$
$797$	15.2395	+	11.0722i	0.539812	+	0.392196i	−0.284203	+	0.958764i	$0.591729\pi$
$798$	1.44696	+	1.05128i	0.0512218	+	0.0372148i
$799$	5.39903	−	3.92263i	0.191004	−	0.138773i
$800$	0.0988164			0.00349369
$801$	17.0240			0.601514
$802$	1.74946	−	1.27106i	0.0617756	−	0.0448826i
$803$	22.4474	−	69.0861i	0.792152	−	2.43799i
$804$	4.25353	+	13.0910i	0.150010	+	0.461684i
$805$	−13.7360			−0.484130
$806$	−5.92661	−	0.213067i	−0.208756	−	0.00750498i
$807$	6.31874			0.222430
$808$	−3.47940	−	10.7085i	−0.122405	−	0.376723i
$809$	3.15310	−	9.70426i	0.110857	−	0.341184i	−0.880203	−	0.474597i	$-0.842594\pi$
$809$	3.15310	−	9.70426i	0.110857	−	0.341184i	0.991060	+	0.133413i	$0.0425938\pi$
$810$	1.37472	−	0.998794i	0.0483028	−	0.0350941i
$811$	−4.91233			−0.172495			−0.0862476	−	0.996274i	$-0.527488\pi$
$811$	−4.91233			−0.172495			−0.0862476	+	0.996274i	$0.527488\pi$
$812$	33.1092			1.16190
$813$	20.6605	−	15.0108i	0.724596	−	0.526450i
$814$	−3.82245	−	2.77717i	−0.133977	−	0.0973398i
$815$	−2.89084	−	2.10032i	−0.101262	−	0.0735711i
$816$	−1.58255	−	4.87059i	−0.0554004	−	0.170505i
$817$	18.6128	−	13.5230i	0.651179	−	0.473109i
$818$	1.88743	+	5.80890i	0.0659923	+	0.203103i
$819$	6.25028	−	19.2364i	0.218403	−	0.672174i
$820$	17.9903	+	13.0708i	0.628250	+	0.456450i
$821$	16.4456	−	50.6144i	0.573956	−	1.76646i	−0.0657505	−	0.997836i	$-0.520944\pi$
$821$	16.4456	−	50.6144i	0.573956	−	1.76646i	0.639707	−	0.768619i	$-0.279056\pi$
$822$	0.566258	−	1.74276i	0.0197505	−	0.0607858i
$823$	29.8227	+	21.6674i	1.03955	+	0.755280i	0.970198	−	0.242313i	$-0.0779059\pi$
$823$	29.8227	+	21.6674i	1.03955	+	0.755280i	0.0693548	+	0.997592i	$0.477906\pi$
$824$	−3.84078	+	11.8207i	−0.133800	+	0.411793i
$825$	−0.105851	−	0.325775i	−0.00368525	−	0.0113420i
$826$	0.802481	−	0.583037i	0.0279219	−	0.0202864i
$827$	6.89861	+	21.2318i	0.239888	+	0.738300i	0.996435	+	0.0843610i	$0.0268849\pi$
$827$	6.89861	+	21.2318i	0.239888	+	0.738300i	−0.756547	+	0.653939i	$0.773115\pi$
$828$	−3.83160	−	2.78382i	−0.133157	−	0.0967444i
$829$	−40.0956	−	29.1312i	−1.39258	−	1.01177i	−0.995577	−	0.0939489i	$-0.970051\pi$
$829$	−40.0956	−	29.1312i	−1.39258	−	1.01177i	−0.397001	−	0.917818i	$-0.629949\pi$
$830$	1.40961	−	1.02414i	0.0489284	−	0.0355485i
$831$	−13.6710			−0.474243
$832$	−41.2339			−1.42953
$833$	−1.57334	+	1.14310i	−0.0545129	+	0.0396059i
$834$	−0.418932	+	1.28934i	−0.0145064	+	0.0446462i
$835$	−1.34381	−	4.13582i	−0.0465045	−	0.143126i
$836$	26.2286			0.907134
$837$	26.0491	−	17.5313i	0.900387	−	0.605972i
$838$	1.47265			0.0508718
$839$	−1.45200	−	4.46881i	−0.0501288	−	0.154281i	0.922859	−	0.385139i	$-0.125847\pi$
$839$	−1.45200	−	4.46881i	−0.0501288	−	0.154281i	−0.972987	+	0.230859i	$0.925847\pi$
$840$	−2.06216	+	6.34667i	−0.0711512	+	0.218981i
$841$	−2.20204	+	1.59988i	−0.0759326	+	0.0551682i
$842$	3.71031			0.127866
$843$	−13.3592			−0.460116
$844$	−7.39876	+	5.37552i	−0.254676	+	0.185033i
$845$	−36.2247	−	26.3188i	−1.24617	−	0.905393i
$846$	−1.18089	−	0.857964i	−0.0405997	−	0.0294974i
$847$	−18.7090	−	57.5805i	−0.642850	−	1.97849i
$848$	−8.73826	+	6.34871i	−0.300073	+	0.218016i
$849$	9.22768	+	28.3999i	0.316693	+	0.974681i
$850$	0.00260421	−	0.00801494i	8.93237e−5	−	0.000274910i
$851$	−7.53368	−	5.47354i	−0.258251	−	0.187631i
$852$	12.6952	−	39.0718i	0.434930	−	1.33858i
$853$	−3.38089	+	10.4053i	−0.115760	+	0.356271i	−0.992105	−	0.125413i	$-0.959975\pi$
$853$	−3.38089	+	10.4053i	−0.115760	+	0.356271i	0.876345	+	0.481684i	$0.159975\pi$
$854$	1.69675	+	1.23276i	0.0580616	+	0.0421842i
$855$	1.95277	−	6.01000i	0.0667832	−	0.205538i
$856$	−0.559301	−	1.72135i	−0.0191165	−	0.0588346i
$857$	−38.1993	+	27.7534i	−1.30486	+	0.948038i	−0.999991	−	0.00435571i	$-0.998614\pi$
$857$	−38.1993	+	27.7534i	−1.30486	+	0.948038i	−0.304872	+	0.952393i	$0.598614\pi$
$858$	−2.48307	−	7.64211i	−0.0847707	−	0.260897i
$859$	41.9697	+	30.4927i	1.43199	+	1.04040i	0.989643	+	0.143553i	$0.0458527\pi$
$859$	41.9697	+	30.4927i	1.43199	+	1.04040i	0.442343	+	0.896846i	$0.354147\pi$
$860$	34.4218	+	25.0089i	1.17377	+	0.852796i
$861$	−16.4480	+	11.9501i	−0.560545	+	0.407260i
$862$	−5.26190			−0.179221
$863$	−17.2524			−0.587278			−0.293639	−	0.955916i	$-0.594866\pi$
$863$	−17.2524			−0.587278			−0.293639	+	0.955916i	$0.594866\pi$
$864$	−9.92913	+	7.21394i	−0.337796	+	0.245423i
$865$	−11.1371	+	34.2764i	−0.378672	+	1.16543i
$866$	0.0493798	+	0.151975i	0.00167799	+	0.00516433i
$867$	−1.34965			−0.0458365
$868$	−11.2260	+	30.7449i	−0.381037	+	1.04355i
$869$	5.24363			0.177878
$870$	−0.979295	−	3.01396i	−0.0332012	−	0.102183i
$871$	9.20168	−	28.3199i	0.311787	−	0.959582i
$872$	−9.12631	+	6.63065i	−0.309056	+	0.224542i
$873$	−0.935400			−0.0316585
$874$	−0.905986			−0.0306454
$875$	−26.9276	+	19.5641i	−0.910320	+	0.661386i
$876$	−27.8912	−	20.2642i	−0.942358	−	0.684663i
$877$	4.29516	+	3.12062i	0.145037	+	0.105376i	0.657938	−	0.753072i	$-0.271429\pi$
$877$	4.29516	+	3.12062i	0.145037	+	0.105376i	−0.512900	+	0.858448i	$0.671429\pi$
$878$	−1.44879	−	4.45893i	−0.0488944	−	0.150482i
$879$	−6.02856	+	4.38001i	−0.203338	+	0.147734i
$880$	14.7219	+	45.3094i	0.496276	+	1.52738i
$881$	−14.6119	+	44.9707i	−0.492286	+	1.51510i	0.328858	+	0.944379i	$0.393336\pi$
$881$	−14.6119	+	44.9707i	−0.492286	+	1.51510i	−0.821144	+	0.570721i	$0.806664\pi$
$882$	0.344123	+	0.250020i	0.0115872	+	0.00841861i
$883$	7.46758	−	22.9829i	0.251304	−	0.773435i	−0.743231	−	0.669035i	$-0.766708\pi$
$883$	7.46758	−	22.9829i	0.251304	−	0.773435i	0.994535	−	0.104400i	$-0.0332922\pi$
$884$	−3.48570	+	10.7279i	−0.117237	+	0.360818i
$885$	4.38266	+	3.18419i	0.147321	+	0.107035i
$886$	0.469437	−	1.44478i	0.0157710	−	0.0485382i
$887$	3.30107	+	10.1597i	0.110839	+	0.341128i	0.991056	−	0.133443i	$-0.0426033\pi$
$887$	3.30107	+	10.1597i	0.110839	+	0.341128i	−0.880217	+	0.474571i	$0.842603\pi$
$888$	−3.66005	+	2.65918i	−0.122823	+	0.0892362i
$889$	−7.28757	−	22.4288i	−0.244417	−	0.752239i
$890$	4.87238	+	3.53999i	0.163322	+	0.118661i
$891$	18.4316	+	13.3914i	0.617483	+	0.448628i
$892$	9.50990	−	6.90935i	0.318415	−	0.231342i
$893$	15.9319			0.533142
$894$	0.517863			0.0173199
$895$	−0.269429	+	0.195752i	−0.00900603	+	0.00654327i
$896$	5.25515	−	16.1737i	0.175562	−	0.540325i
$897$	−4.89390	−	15.0619i	−0.163403	−	0.502901i
$898$	−0.440051			−0.0146847
$899$	−8.61265	−	30.1529i	−0.287248	−	1.00566i
$900$	0.105173			0.00350578
$901$	0.879620	+	2.70719i	0.0293044	+	0.0901896i
$902$	1.61471	−	4.96956i	0.0537639	−	0.165468i
$903$	−31.4707	+	22.8648i	−1.04728	+	0.760892i
$904$	1.40061			0.0465836
$905$	3.58806			0.119271
$906$	3.62617	−	2.63457i	0.120471	−	0.0875276i
$907$	−13.7618	−	9.99855i	−0.456954	−	0.331996i	0.335381	−	0.942082i	$-0.391135\pi$
$907$	−13.7618	−	9.99855i	−0.456954	−	0.331996i	−0.792335	+	0.610086i	$0.791135\pi$
$908$	4.03928	+	2.93471i	0.134048	+	0.0973918i
$909$	−5.57092	−	17.1455i	−0.184776	−	0.568681i
$910$	5.78890	−	4.20588i	0.191900	−	0.139424i
$911$	−9.18592	−	28.2713i	−0.304343	−	0.936672i	−0.979922	−	0.199383i	$-0.936106\pi$
$911$	−9.18592	−	28.2713i	−0.304343	−	0.936672i	0.675579	−	0.737288i	$-0.263894\pi$
$912$	3.77806	−	11.6277i	0.125104	−	0.385030i
$913$	18.8994	+	13.7312i	0.625480	+	0.454438i
$914$	1.25572	−	3.86470i	0.0415355	−	0.127833i
$915$	−3.53953	+	10.8935i	−0.117013	+	0.360129i
$916$	−37.1477	−	26.9894i	−1.22739	−	0.891754i
$917$	16.9252	−	52.0904i	0.558919	−	1.72018i
$918$	0.323445	+	0.995462i	0.0106753	+	0.0328551i
$919$	23.5129	−	17.0831i	0.775618	−	0.563519i	−0.128043	−	0.991769i	$-0.540869\pi$
$919$	23.5129	−	17.0831i	0.775618	−	0.563519i	0.903661	+	0.428249i	$0.140869\pi$
$920$	−1.04459	−	3.21491i	−0.0344390	−	0.105992i
$921$	7.71550	+	5.60564i	0.254234	+	0.184712i
$922$	−0.0473192	−	0.0343794i	−0.00155837	−	0.00113222i
$923$	−71.9006	+	52.2388i	−2.36664	+	1.71946i
$924$	−44.3475			−1.45893
$925$	0.206792			0.00679927
$926$	−3.03957	+	2.20837i	−0.0998863	+	0.0725717i
$927$	−6.14953	+	18.9263i	−0.201977	+	0.621622i
$928$	3.78773	+	11.6574i	0.124338	+	0.382675i
$929$	−0.898497			−0.0294787			−0.0147394	−	0.999891i	$-0.504692\pi$
$929$	−0.898497			−0.0294787			−0.0147394	+	0.999891i	$0.504692\pi$
$930$	3.13078	+	0.112554i	0.102662	+	0.00369080i
$931$	−4.64274			−0.152160
$932$	1.02032	+	3.14021i	0.0334216	+	0.102861i
$933$	−11.3704	+	34.9944i	−0.372249	+	1.14566i
$934$	−3.15408	+	2.29157i	−0.103205	+	0.0749826i
$935$	12.5553			0.410603
$936$	4.97759			0.162698
$937$	20.3164	−	14.7607i	0.663708	−	0.482212i	−0.204205	−	0.978928i	$-0.565461\pi$
$937$	20.3164	−	14.7607i	0.663708	−	0.482212i	0.867913	+	0.496716i	$0.165461\pi$
$938$	2.33016	+	1.69296i	0.0760824	+	0.0552771i
$939$	−3.66445	−	2.66238i	−0.119585	−	0.0868834i
$940$	9.10486	+	28.0219i	0.296968	+	0.913973i
$941$	44.4225	−	32.2749i	1.44813	−	1.05213i	0.461870	−	0.886948i	$-0.347179\pi$
$941$	44.4225	−	32.2749i	1.44813	−	1.05213i	0.986263	−	0.165183i	$-0.0528214\pi$
$942$	1.34991	+	4.15460i	0.0439824	+	0.135364i
$943$	3.18244	−	9.79453i	0.103634	−	0.318954i
$944$	−5.48558	−	3.98551i	−0.178540	−	0.129717i
$945$	−11.7071	+	36.0308i	−0.380833	+	1.17208i
$946$	3.08950	−	9.50849i	0.100448	−	0.309148i
$947$	−39.9197	−	29.0033i	−1.29721	−	0.942481i	−0.297290	−	0.954787i	$-0.596083\pi$
$947$	−39.9197	−	29.0033i	−1.29721	−	0.942481i	−0.999924	+	0.0123057i	$0.996083\pi$
$948$	0.769025	−	2.36682i	0.0249768	−	0.0768706i
$949$	23.0468	+	70.9308i	0.748131	+	2.30251i
$950$	0.0162765	−	0.0118256i	0.000528081	−	0.000383673i
$951$	3.86374	+	11.8914i	0.125290	+	0.385604i
$952$	−1.78085	−	1.29387i	−0.0577178	−	0.0419344i
$953$	36.6696	+	26.6420i	1.18785	+	0.863021i	0.993035	−	0.117820i	$-0.0375907\pi$
$953$	36.6696	+	26.6420i	1.18785	+	0.863021i	0.194811	+	0.980841i	$0.437591\pi$
$954$	0.503689	−	0.365952i	0.0163075	−	0.0118481i
$955$	−5.64361			−0.182623
$956$	−40.0155			−1.29419
$957$	34.3746	−	24.9746i	1.11117	−	0.807315i
$958$	0.607285	−	1.86903i	0.0196205	−	0.0603857i
$959$	6.76075	+	20.8074i	0.218316	+	0.671907i
$960$	21.7821			0.703015
$961$	30.9200	+	2.22608i	0.997418	+	0.0718091i
$962$	4.85096			0.156401
$963$	−0.895506	−	2.75609i	−0.0288573	−	0.0888136i
$964$	15.3902	−	47.3662i	0.495686	−	1.52556i
$965$	35.2038	−	25.5770i	1.13325	−	0.823354i
$966$	1.53185			0.0492864
$967$	−57.8870			−1.86152			−0.930759	−	0.365632i	$-0.880853\pi$
$967$	−57.8870			−1.86152			−0.930759	+	0.365632i	$0.880853\pi$
$968$	12.0539	−	8.75769i	0.387428	−	0.281483i
$969$	−2.60669	−	1.89387i	−0.0837389	−	0.0608399i
$970$	−0.267717	−	0.194508i	−0.00859588	−	0.00624527i
$971$	−7.53706	−	23.1967i	−0.241876	−	0.744417i	−0.996135	−	0.0878398i	$-0.972004\pi$
$971$	−7.53706	−	23.1967i	−0.241876	−	0.744417i	0.754259	−	0.656577i	$-0.227996\pi$
$972$	−18.1553	+	13.1906i	−0.582331	+	0.423088i
$973$	−5.00178	−	15.3939i	−0.160350	−	0.493505i
$974$	−0.504893	+	1.55390i	−0.0161778	+	0.0497902i
$975$	0.284521	+	0.206716i	0.00911195	+	0.00662022i
$976$	4.43027	−	13.6350i	0.141810	−	0.436445i
$977$	12.3971	−	38.1542i	0.396617	−	1.22066i	−0.531078	−	0.847323i	$-0.678213\pi$
$977$	12.3971	−	38.1542i	0.396617	−	1.22066i	0.927695	−	0.373339i	$-0.121787\pi$
$978$	0.322389	+	0.234229i	0.0103089	+	0.00748983i
$979$	−24.9525	+	76.7960i	−0.797486	+	2.45441i
$980$	−2.65325	−	8.16587i	−0.0847551	−	0.260849i
$981$	−14.6123	+	10.6165i	−0.466535	+	0.338957i
$982$	−0.764947	−	2.35427i	−0.0244104	−	0.0751276i
$983$	9.94738	+	7.22719i	0.317272	+	0.230512i	0.735011	−	0.678056i	$-0.237177\pi$
$983$	9.94738	+	7.22719i	0.317272	+	0.230512i	−0.417738	+	0.908567i	$0.637177\pi$
$984$	−4.04776	−	2.94087i	−0.129038	−	0.0937514i
$985$	23.0293	−	16.7317i	0.733773	−	0.533118i
$986$	1.04535			0.0332908
$987$	−26.9379			−0.857442
$988$	−21.7859	+	15.8284i	−0.693103	+	0.503569i
$989$	6.08911	−	18.7403i	0.193622	−	0.595908i
$990$	−0.848598	−	2.61172i	−0.0269702	−	0.0830058i
$991$	59.0907			1.87708			0.938538	−	0.345175i	$-0.112180\pi$
$991$	59.0907			1.87708			0.938538	+	0.345175i	$0.112180\pi$
$992$	−12.1093	−	0.435340i	−0.384470	−	0.0138221i
$993$	−15.1536			−0.480886
$994$	−2.65644	−	8.17568i	−0.0842572	−	0.259317i
$995$	−7.55652	+	23.2566i	−0.239558	+	0.737283i
$996$	8.96963	−	6.51682i	0.284214	−	0.206493i
$997$	−36.3574			−1.15145			−0.575726	−	0.817643i	$-0.695280\pi$
$997$	−36.3574			−1.15145			−0.575726	+	0.817643i	$0.695280\pi$
$998$	6.88759			0.218023
$999$	−20.7785	+	15.0965i	−0.657404	+	0.477632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	527.2.h.c.35.13	✓	96
31.8	even	5	inner	527.2.h.c.256.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
527.2.h.c.35.13	✓	96	1.1	even	1	trivial
527.2.h.c.256.13	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)

\(f(q)\)	\(=\)	\(q+(0.0573542 + 0.176518i) q^{2} +(-0.417065 + 1.28359i) q^{3} +(1.59016 - 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 - 1.75793i) q^{7} +(0.595448 + 0.432618i) q^{8} +(0.953382 + 0.692673i) q^{9} +O(q^{10})\)	\(q+(0.0573542 + 0.176518i) q^{2} +(-0.417065 + 1.28359i) q^{3} +(1.59016 - 1.15532i) q^{4} +2.24620 q^{5} -0.250498 q^{6} +(2.41959 - 1.75793i) q^{7} +(0.595448 + 0.432618i) q^{8} +(0.953382 + 0.692673i) q^{9} +(0.128829 + 0.396494i) q^{10} +(-4.52207 + 3.28548i) q^{11} +(0.819762 + 2.52297i) q^{12} +(1.77340 - 5.45795i) q^{13} +(0.449081 + 0.326276i) q^{14} +(-0.936810 + 2.88320i) q^{15} +(1.17256 - 3.60878i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(-0.0675888 + 0.208017i) q^{18} +(-0.737722 - 2.27048i) q^{19} +(3.57183 - 2.59508i) q^{20} +(1.24735 + 3.83894i) q^{21} +(-0.839305 - 0.609791i) q^{22} +(-1.65419 - 1.20184i) q^{23} +(-0.803646 + 0.583883i) q^{24} +0.0454058 q^{25} +1.06514 q^{26} +(-4.56240 + 3.31478i) q^{27} +(1.81657 - 5.59081i) q^{28} +(1.74045 + 5.35656i) q^{29} -0.562667 q^{30} +(-5.56417 - 0.200037i) q^{31} +2.17629 q^{32} +(-2.33122 - 7.17475i) q^{33} +(0.0573542 - 0.176518i) q^{34} +(5.43488 - 3.94867i) q^{35} +2.31630 q^{36} +4.55430 q^{37} +(0.358468 - 0.260443i) q^{38} +(6.26617 + 4.55264i) q^{39} +(1.33749 + 0.971747i) q^{40} +(1.55644 + 4.79022i) q^{41} +(-0.606102 + 0.440359i) q^{42} +(2.97801 + 9.16536i) q^{43} +(-3.39505 + 10.4489i) q^{44} +(2.14149 + 1.55588i) q^{45} +(0.117272 - 0.360925i) q^{46} +(-2.06225 + 6.34694i) q^{47} +(4.14317 + 3.01019i) q^{48} +(0.600961 - 1.84957i) q^{49} +(0.00260421 + 0.00801494i) q^{50} +(1.09189 - 0.793304i) q^{51} +(-3.48570 - 10.7279i) q^{52} +(-2.30288 - 1.67314i) q^{53} +(-0.846791 - 0.615229i) q^{54} +(-10.1575 + 7.37983i) q^{55} +2.20126 q^{56} +3.22205 q^{57} +(-0.845707 + 0.614442i) q^{58} +(0.552196 - 1.69948i) q^{59} +(1.84135 + 5.66709i) q^{60} +3.77827 q^{61} +(-0.283818 - 0.993649i) q^{62} +3.52447 q^{63} +(-2.22031 - 6.83341i) q^{64} +(3.98340 - 12.2596i) q^{65} +(1.13277 - 0.823004i) q^{66} +5.18873 q^{67} -1.96555 q^{68} +(2.23258 - 1.62206i) q^{69} +(1.00872 + 0.732881i) q^{70} +(-12.5288 - 9.10269i) q^{71} +(0.268027 + 0.824902i) q^{72} +(-10.5139 + 7.63877i) q^{73} +(0.261208 + 0.803916i) q^{74} +(-0.0189372 + 0.0582826i) q^{75} +(-3.79623 - 2.75812i) q^{76} +(-5.16590 + 15.8990i) q^{77} +(-0.444232 + 1.36720i) q^{78} +(-0.758945 - 0.551405i) q^{79} +(2.63381 - 8.10604i) q^{80} +(-1.25953 - 3.87644i) q^{81} +(-0.756292 + 0.549478i) q^{82} +(-1.29150 - 3.97482i) q^{83} +(6.41870 + 4.66346i) q^{84} +(-1.81721 - 1.32028i) q^{85} +(-1.44705 + 1.05134i) q^{86} -7.60152 q^{87} -4.11401 q^{88} +(11.6872 - 8.49124i) q^{89} +(-0.151818 + 0.467247i) q^{90} +(-5.30384 - 16.3235i) q^{91} -4.01895 q^{92} +(2.57739 - 7.05870i) q^{93} -1.23863 q^{94} +(-1.65707 - 5.09994i) q^{95} +(-0.907656 + 2.79348i) q^{96} +(-0.642163 + 0.466559i) q^{97} +0.360950 q^{98} -6.58702 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more