LMFDB - Embedded newform 85.2.l.a.36.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	85.l (of order $8$, 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:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			36.3
Character	$\chi$	$=$	85.36
Dual form			85.2.l.a.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09994 - 1.09994i) q^{2} +(2.77900 - 1.15110i) q^{3} +0.419729i q^{4} +(0.382683 + 0.923880i) q^{5} +(-4.32287 - 1.79059i) q^{6} +(-1.32205 + 3.19170i) q^{7} +(-1.73820 + 1.73820i) q^{8} +(4.27649 - 4.27649i) q^{9} +O(q^{10})$	\(q+(-1.09994 - 1.09994i) q^{2} +(2.77900 - 1.15110i) q^{3} +0.419729i q^{4} +(0.382683 + 0.923880i) q^{5} +(-4.32287 - 1.79059i) q^{6} +(-1.32205 + 3.19170i) q^{7} +(-1.73820 + 1.73820i) q^{8} +(4.27649 - 4.27649i) q^{9} +(0.595282 - 1.43714i) q^{10} +(-3.92026 - 1.62382i) q^{11} +(0.483150 + 1.16643i) q^{12} +0.127392i q^{13} +(4.96485 - 2.05651i) q^{14} +(2.12695 + 2.12695i) q^{15} +4.66329 q^{16} +(-4.11857 - 0.193278i) q^{17} -9.40776 q^{18} +(1.81966 + 1.81966i) q^{19} +(-0.387779 + 0.160623i) q^{20} +10.3916i q^{21} +(2.52594 + 6.09815i) q^{22} +(3.00465 + 1.24457i) q^{23} +(-2.82962 + 6.83130i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.140123 - 0.140123i) q^{26} +(3.50841 - 8.47004i) q^{27} +(-1.33965 - 0.554901i) q^{28} +(-1.87644 - 4.53013i) q^{29} -4.67904i q^{30} +(4.95543 - 2.05261i) q^{31} +(-1.65293 - 1.65293i) q^{32} -12.7636 q^{33} +(4.31758 + 4.74277i) q^{34} -3.45467 q^{35} +(1.79497 + 1.79497i) q^{36} +(-1.63681 + 0.677990i) q^{37} -4.00302i q^{38} +(0.146641 + 0.354023i) q^{39} +(-2.27107 - 0.940707i) q^{40} +(3.85069 - 9.29639i) q^{41} +(11.4301 - 11.4301i) q^{42} +(1.79227 - 1.79227i) q^{43} +(0.681566 - 1.64545i) q^{44} +(5.58751 + 2.31442i) q^{45} +(-1.93598 - 4.67388i) q^{46} +4.59479i q^{47} +(12.9593 - 5.36791i) q^{48} +(-3.48941 - 3.48941i) q^{49} +1.55555 q^{50} +(-11.6680 + 4.20377i) q^{51} -0.0534701 q^{52} +(1.15866 + 1.15866i) q^{53} +(-13.1756 + 5.45749i) q^{54} -4.24326i q^{55} +(-3.24984 - 7.84580i) q^{56} +(7.15144 + 2.96222i) q^{57} +(-2.91889 + 7.04683i) q^{58} +(-4.34287 + 4.34287i) q^{59} +(-0.892745 + 0.892745i) q^{60} +(-1.54679 + 3.73428i) q^{61} +(-7.70840 - 3.19293i) q^{62} +(7.99557 + 19.3030i) q^{63} -5.69034i q^{64} +(-0.117695 + 0.0487508i) q^{65} +(14.0392 + 14.0392i) q^{66} -6.88856 q^{67} +(0.0811242 - 1.72868i) q^{68} +9.78255 q^{69} +(3.79993 + 3.79993i) q^{70} +(-6.66802 + 2.76198i) q^{71} +14.8668i q^{72} +(-5.59682 - 13.5119i) q^{73} +(2.54614 + 1.05465i) q^{74} +(-1.15110 + 2.77900i) q^{75} +(-0.763763 + 0.763763i) q^{76} +(10.3655 - 10.3655i) q^{77} +(0.228107 - 0.550699i) q^{78} +(-4.75854 - 1.97105i) q^{79} +(1.78456 + 4.30831i) q^{80} -9.43315i q^{81} +(-14.4610 + 5.98994i) q^{82} +(10.2150 + 10.2150i) q^{83} -4.36164 q^{84} +(-1.39754 - 3.87903i) q^{85} -3.94276 q^{86} +(-10.4293 - 10.4293i) q^{87} +(9.63673 - 3.99166i) q^{88} -0.600876i q^{89} +(-3.60019 - 8.69163i) q^{90} +(-0.406598 - 0.168418i) q^{91} +(-0.522381 + 1.26114i) q^{92} +(11.4084 - 11.4084i) q^{93} +(5.05398 - 5.05398i) q^{94} +(-0.984791 + 2.37750i) q^{95} +(-6.49616 - 2.69080i) q^{96} +(-2.93763 - 7.09206i) q^{97} +7.67628i q^{98} +(-23.7092 + 9.82068i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 - 24 * q^9	$ 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.09994	−	1.09994i	−0.777774	−	0.777774i	0.201678	−	0.979452i	$-0.435361\pi$
$2$	−1.09994	−	1.09994i	−0.777774	−	0.777774i	−0.979452	+	0.201678i	$0.935361\pi$
$3$	2.77900	−	1.15110i	1.60446	−	0.664588i	0.612419	−	0.790533i	$-0.290196\pi$
$3$	2.77900	−	1.15110i	1.60446	−	0.664588i	0.992037	+	0.125945i	$0.0401964\pi$
$4$			0.419729i			0.209865i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$5$	0.382683	+	0.923880i	0.171141	+	0.413171i
$6$	−4.32287	−	1.79059i	−1.76480	−	0.731006i
$7$	−1.32205	+	3.19170i	−0.499687	+	1.20635i	0.449966	+	0.893046i	$0.351436\pi$
$7$	−1.32205	+	3.19170i	−0.499687	+	1.20635i	−0.949653	+	0.313305i	$0.898564\pi$
$8$	−1.73820	+	1.73820i	−0.614547	+	0.614547i
$9$	4.27649	−	4.27649i	1.42550	−	1.42550i
$10$	0.595282	−	1.43714i	0.188245	−	0.454463i
$11$	−3.92026	−	1.62382i	−1.18200	−	0.489601i	−0.296860	−	0.954921i	$-0.595939\pi$
$11$	−3.92026	−	1.62382i	−1.18200	−	0.489601i	−0.885143	+	0.465320i	$0.845939\pi$
$12$	0.483150	+	1.16643i	0.139473	+	0.336719i
$13$			0.127392i			0.0353322i	0.999844	+	0.0176661i	$0.00562359\pi$
$13$			0.127392i			0.0353322i	−0.999844	+	0.0176661i	$0.994376\pi$
$14$	4.96485	−	2.05651i	1.32691	−	0.549625i
$15$	2.12695	+	2.12695i	0.549177	+	0.549177i
$16$	4.66329			1.16582
$17$	−4.11857	−	0.193278i	−0.998901	−	0.0468767i
$17$	−4.11857	−	0.193278i	−0.998901	−	0.0468767i
$18$	−9.40776			−2.21743
$19$	1.81966	+	1.81966i	0.417458	+	0.417458i	0.884327	−	0.466869i	$-0.154618\pi$
$19$	1.81966	+	1.81966i	0.417458	+	0.417458i	−0.466869	+	0.884327i	$0.654618\pi$
$20$	−0.387779	+	0.160623i	−0.0867100	+	0.0359165i
$21$			10.3916i			2.26762i
$22$	2.52594	+	6.09815i	0.538531	+	1.30013i
$23$	3.00465	+	1.24457i	0.626513	+	0.259510i	0.673271	−	0.739396i	$-0.264889\pi$
$23$	3.00465	+	1.24457i	0.626513	+	0.259510i	−0.0467576	+	0.998906i	$0.514889\pi$
$24$	−2.82962	+	6.83130i	−0.577593	+	1.39443i
$25$	−0.707107	+	0.707107i	−0.141421	+	0.141421i
$26$	0.140123	−	0.140123i	0.0274805	−	0.0274805i
$27$	3.50841	−	8.47004i	0.675193	−	1.63006i
$28$	−1.33965	−	0.554901i	−0.253170	−	0.104866i
$29$	−1.87644	−	4.53013i	−0.348446	−	0.841224i	−0.996804	−	0.0798877i	$-0.974544\pi$
$29$	−1.87644	−	4.53013i	−0.348446	−	0.841224i	0.648358	−	0.761336i	$-0.275456\pi$
$30$		−	4.67904i		−	0.854272i
$31$	4.95543	−	2.05261i	0.890021	−	0.368659i	0.109646	−	0.993971i	$-0.465028\pi$
$31$	4.95543	−	2.05261i	0.890021	−	0.368659i	0.780375	+	0.625312i	$0.215028\pi$
$32$	−1.65293	−	1.65293i	−0.292199	−	0.292199i
$33$	−12.7636			−2.22185
$34$	4.31758	+	4.74277i	0.740459	+	0.813378i
$35$	−3.45467			−0.583947
$36$	1.79497	+	1.79497i	0.299161	+	0.299161i
$37$	−1.63681	+	0.677990i	−0.269090	+	0.111461i	−0.513149	−	0.858300i	$-0.671521\pi$
$37$	−1.63681	+	0.677990i	−0.269090	+	0.111461i	0.244059	+	0.969761i	$0.421521\pi$
$38$		−	4.00302i		−	0.649376i
$39$	0.146641	+	0.354023i	0.0234813	+	0.0566890i
$40$	−2.27107	−	0.940707i	−0.359087	−	0.148739i
$41$	3.85069	−	9.29639i	0.601377	−	1.45185i	−0.270787	−	0.962639i	$-0.587284\pi$
$41$	3.85069	−	9.29639i	0.601377	−	1.45185i	0.872164	−	0.489214i	$-0.162716\pi$
$42$	11.4301	−	11.4301i	1.76370	−	1.76370i
$43$	1.79227	−	1.79227i	0.273318	−	0.273318i	−0.557116	−	0.830434i	$-0.688092\pi$
$43$	1.79227	−	1.79227i	0.273318	−	0.273318i	0.830434	+	0.557116i	$0.188092\pi$
$44$	0.681566	−	1.64545i	0.102750	−	0.248060i
$45$	5.58751	+	2.31442i	0.832936	+	0.345013i
$46$	−1.93598	−	4.67388i	−0.285445	−	0.689126i
$47$			4.59479i			0.670219i	0.942179	+	0.335109i	$0.108773\pi$
$47$			4.59479i			0.670219i	−0.942179	+	0.335109i	$0.891227\pi$
$48$	12.9593	−	5.36791i	1.87051	−	0.774791i
$49$	−3.48941	−	3.48941i	−0.498487	−	0.498487i
$50$	1.55555			0.219988
$51$	−11.6680	+	4.20377i	−1.63385	+	0.588645i
$52$	−0.0534701			−0.00741498
$53$	1.15866	+	1.15866i	0.159155	+	0.159155i	0.782192	−	0.623037i	$-0.214102\pi$
$53$	1.15866	+	1.15866i	0.159155	+	0.159155i	−0.623037	+	0.782192i	$0.714102\pi$
$54$	−13.1756	+	5.45749i	−1.79297	+	0.742671i
$55$		−	4.24326i		−	0.572161i
$56$	−3.24984	−	7.84580i	−0.434278	−	1.04844i
$57$	7.15144	+	2.96222i	0.947231	+	0.392356i
$58$	−2.91889	+	7.04683i	−0.383269	+	0.925294i
$59$	−4.34287	+	4.34287i	−0.565393	+	0.565393i	−0.930834	−	0.365441i	$-0.880918\pi$
$59$	−4.34287	+	4.34287i	−0.565393	+	0.565393i	0.365441	+	0.930834i	$0.380918\pi$
$60$	−0.892745	+	0.892745i	−0.115253	+	0.115253i
$61$	−1.54679	+	3.73428i	−0.198046	+	0.478125i	−0.991437	−	0.130587i	$-0.958314\pi$
$61$	−1.54679	+	3.73428i	−0.198046	+	0.478125i	0.793391	+	0.608713i	$0.208314\pi$
$62$	−7.70840	−	3.19293i	−0.978968	−	0.405502i
$63$	7.99557	+	19.3030i	1.00735	+	2.43195i
$64$		−	5.69034i		−	0.711292i
$65$	−0.117695	+	0.0487508i	−0.0145983	+	0.00604680i
$66$	14.0392	+	14.0392i	1.72810	+	1.72810i
$67$	−6.88856			−0.841571			−0.420786	−	0.907160i	$-0.638246\pi$
$67$	−6.88856			−0.841571			−0.420786	+	0.907160i	$0.638246\pi$
$68$	0.0811242	−	1.72868i	0.00983776	−	0.209634i
$69$	9.78255			1.17768
$70$	3.79993	+	3.79993i	0.454178	+	0.454178i
$71$	−6.66802	+	2.76198i	−0.791348	+	0.327787i	−0.741485	−	0.670969i	$-0.765878\pi$
$71$	−6.66802	+	2.76198i	−0.791348	+	0.327787i	−0.0498626	+	0.998756i	$0.515878\pi$
$72$			14.8668i			1.75207i
$73$	−5.59682	−	13.5119i	−0.655058	−	1.58145i	−0.805345	−	0.592807i	$-0.798020\pi$
$73$	−5.59682	−	13.5119i	−0.655058	−	1.58145i	0.150287	−	0.988642i	$-0.451980\pi$
$74$	2.54614	+	1.05465i	0.295983	+	0.122600i
$75$	−1.15110	+	2.77900i	−0.132918	+	0.320891i
$76$	−0.763763	+	0.763763i	−0.0876096	+	0.0876096i
$77$	10.3655	−	10.3655i	1.18126	−	1.18126i
$78$	0.228107	−	0.550699i	0.0258280	−	0.0623544i
$79$	−4.75854	−	1.97105i	−0.535378	−	0.221761i	0.0985790	−	0.995129i	$-0.468570\pi$
$79$	−4.75854	−	1.97105i	−0.535378	−	0.221761i	−0.633957	+	0.773369i	$0.718570\pi$
$80$	1.78456	+	4.30831i	0.199520	+	0.481684i
$81$		−	9.43315i		−	1.04813i
$82$	−14.4610	+	5.98994i	−1.59695	+	0.661478i
$83$	10.2150	+	10.2150i	1.12124	+	1.12124i	0.991555	+	0.129685i	$0.0413967\pi$
$83$	10.2150	+	10.2150i	1.12124	+	1.12124i	0.129685	+	0.991555i	$0.458603\pi$
$84$	−4.36164			−0.475893
$85$	−1.39754	−	3.87903i	−0.151585	−	0.420740i
$86$	−3.94276			−0.425159
$87$	−10.4293	−	10.4293i	−1.11813	−	1.11813i
$88$	9.63673	−	3.99166i	1.02728	−	0.425513i
$89$		−	0.600876i		−	0.0636927i	−0.999493	−	0.0318463i	$-0.989861\pi$
$89$		−	0.600876i		−	0.0636927i	0.999493	−	0.0318463i	$-0.0101387\pi$
$90$	−3.60019	−	8.69163i	−0.379494	−	0.916179i
$91$	−0.406598	−	0.168418i	−0.0426230	−	0.0176550i
$92$	−0.522381	+	1.26114i	−0.0544620	+	0.131483i
$93$	11.4084	−	11.4084i	1.18299	−	1.18299i
$94$	5.05398	−	5.05398i	0.521279	−	0.521279i
$95$	−0.984791	+	2.37750i	−0.101037	+	0.243926i
$96$	−6.49616	−	2.69080i	−0.663012	−	0.274628i
$97$	−2.93763	−	7.09206i	−0.298271	−	0.720090i	−0.999971	−	0.00761730i	$-0.997575\pi$
$97$	−2.93763	−	7.09206i	−0.298271	−	0.720090i	0.701700	−	0.712473i	$-0.252425\pi$
$98$			7.67628i			0.775421i
$99$	−23.7092	+	9.82068i	−2.38287	+	0.987016i
$100$	−0.296793	−	0.296793i	−0.0296793	−	0.0296793i
$101$	16.8485			1.67649			0.838243	−	0.545297i	$-0.183583\pi$
$101$	16.8485			1.67649			0.838243	+	0.545297i	$0.183583\pi$
$102$	17.4580	+	8.21019i	1.72860	+	0.812930i
$103$	4.32255			0.425914			0.212957	−	0.977062i	$-0.431691\pi$
$103$	4.32255			0.425914			0.212957	+	0.977062i	$0.431691\pi$
$104$	−0.221433	−	0.221433i	−0.0217133	−	0.0217133i
$105$	−9.60054	+	3.97667i	−0.936917	+	0.388084i
$106$		−	2.54891i		−	0.247572i
$107$	1.80647	+	4.36120i	0.174638	+	0.421613i	0.986827	−	0.161782i	$-0.0517240\pi$
$107$	1.80647	+	4.36120i	0.174638	+	0.421613i	−0.812189	+	0.583395i	$0.801724\pi$
$108$	3.55512	+	1.47258i	0.342092	+	0.141699i
$109$	−5.86580	+	14.1613i	−0.561842	+	1.35641i	0.346450	+	0.938068i	$0.387387\pi$
$109$	−5.86580	+	14.1613i	−0.561842	+	1.35641i	−0.908292	+	0.418338i	$0.862613\pi$
$110$	−4.66732	+	4.66732i	−0.445012	+	0.445012i
$111$	−3.76827	+	3.76827i	−0.357668	+	0.357668i
$112$	−6.16508	+	14.8838i	−0.582545	+	1.40639i
$113$	−6.81048	−	2.82099i	−0.640676	−	0.265377i	0.0386052	−	0.999255i	$-0.487709\pi$
$113$	−6.81048	−	2.82099i	−0.640676	−	0.265377i	−0.679282	+	0.733878i	$0.737709\pi$
$114$	−4.60788	−	11.1244i	−0.431567	−	1.04190i
$115$			3.25221i			0.303270i
$116$	1.90143	−	0.787596i	0.176543	−	0.0731265i
$117$	0.544791	+	0.544791i	0.0503660	+	0.0503660i
$118$	9.55378			0.879496
$119$	6.06183	−	12.8897i	0.555687	−	1.18160i
$120$	−7.39415			−0.674990
$121$	4.95345	+	4.95345i	0.450313	+	0.450313i
$122$	5.80885	−	2.40610i	0.525909	−	0.217838i
$123$		−	30.2672i		−	2.72910i
$124$	0.861538	+	2.07994i	0.0773684	+	0.186784i
$125$	−0.923880	−	0.382683i	−0.0826343	−	0.0342282i
$126$	12.4375	−	30.0268i	1.10802	−	2.67500i
$127$	−5.67103	+	5.67103i	−0.503223	+	0.503223i	−0.912438	−	0.409215i	$-0.865803\pi$
$127$	−5.67103	+	5.67103i	−0.503223	+	0.503223i	0.409215	+	0.912438i	$0.365803\pi$
$128$	−9.56487	+	9.56487i	−0.845423	+	0.845423i
$129$	2.91763	−	7.04378i	0.256883	−	0.620170i
$130$	0.183080	+	0.0758343i	0.0160572	+	0.00665110i
$131$	5.43762	+	13.1276i	0.475087	+	1.14696i	0.961887	+	0.273448i	$0.0881643\pi$
$131$	5.43762	+	13.1276i	0.475087	+	1.14696i	−0.486799	+	0.873514i	$0.661836\pi$
$132$		−	5.35725i		−	0.466288i
$133$	−8.21348	+	3.40213i	−0.712199	+	0.295002i
$134$	7.57699	+	7.57699i	0.654552	+	0.654552i
$135$	9.16791			0.789048
$136$	7.49486	−	6.82295i	0.642679	−	0.585063i
$137$	8.53083			0.728838			0.364419	−	0.931235i	$-0.381268\pi$
$137$	8.53083			0.728838			0.364419	+	0.931235i	$0.381268\pi$
$138$	−10.7602	−	10.7602i	−0.915969	−	0.915969i
$139$	6.31676	−	2.61649i	0.535781	−	0.221928i	−0.0983522	−	0.995152i	$-0.531357\pi$
$139$	6.31676	−	2.61649i	0.535781	−	0.221928i	0.634133	+	0.773224i	$0.281357\pi$
$140$		−	1.45003i		−	0.122550i
$141$	5.28906	+	12.7689i	0.445419	+	1.07534i
$142$	10.3724	+	4.29640i	0.870434	+	0.360546i
$143$	0.206862	−	0.499410i	0.0172987	−	0.0417627i
$144$	19.9425	−	19.9425i	1.66188	−	1.66188i
$145$	3.46721	−	3.46721i	0.287936	−	0.287936i
$146$	−8.70612	+	21.0184i	−0.720523	+	1.73950i
$147$	−13.7137	−	5.68042i	−1.13109	−	0.468513i
$148$	−0.284572	−	0.687018i	−0.0233917	−	0.0564725i
$149$		−	7.04072i		−	0.576798i	−0.957510	−	0.288399i	$-0.906877\pi$
$149$		−	7.04072i		−	0.576798i	0.957510	−	0.288399i	$-0.0931229\pi$
$150$	4.32287	−	1.79059i	0.352961	−	0.146201i
$151$	4.49500	+	4.49500i	0.365798	+	0.365798i	0.865942	−	0.500144i	$-0.166720\pi$
$151$	4.49500	+	4.49500i	0.365798	+	0.365798i	−0.500144	+	0.865942i	$0.666720\pi$
$152$	−6.32586			−0.513095
$153$	−18.4396	+	16.7865i	−1.49075	+	1.35711i
$154$	−22.8029			−1.83751
$155$	3.79272	+	3.79272i	0.304639	+	0.304639i
$156$	−0.148594	+	0.0615495i	−0.0118970	+	0.00492790i
$157$		−	16.7739i		−	1.33870i	−0.742947	−	0.669351i	$-0.766572\pi$
$157$		−	16.7739i		−	1.33870i	0.742947	−	0.669351i	$-0.233428\pi$
$158$	3.06607	+	7.40214i	0.243923	+	0.588882i
$159$	4.55366	+	1.88619i	0.361129	+	0.149584i
$160$	0.894557	−	2.15965i	0.0707209	−	0.170735i
$161$	−7.94458	+	7.94458i	−0.626121	+	0.626121i
$162$	−10.3759	+	10.3759i	−0.815206	+	0.815206i
$163$	−1.75820	+	4.24468i	−0.137713	+	0.332469i	−0.977658	−	0.210203i	$-0.932587\pi$
$163$	−1.75820	+	4.24468i	−0.137713	+	0.332469i	0.839945	+	0.542672i	$0.182587\pi$
$164$	3.90197	+	1.61625i	0.304692	+	0.126208i
$165$	−4.88441	−	11.7920i	−0.380251	−	0.918007i
$166$		−	22.4717i		−	1.74414i
$167$	19.4260	−	8.04650i	1.50323	−	0.622657i	0.529079	−	0.848572i	$-0.322537\pi$
$167$	19.4260	−	8.04650i	1.50323	−	0.622657i	0.974147	+	0.225916i	$0.0725375\pi$
$168$	−18.0626	−	18.0626i	−1.39356	−	1.39356i
$169$	12.9838			0.998752
$170$	−2.72948	+	5.80391i	−0.209342	+	0.445139i
$171$	15.5635			1.19017
$172$	0.752266	+	0.752266i	0.0573597	+	0.0573597i
$173$	−11.5969	+	4.80360i	−0.881698	+	0.365211i	−0.777155	−	0.629309i	$-0.783338\pi$
$173$	−11.5969	+	4.80360i	−0.881698	+	0.365211i	−0.104543	+	0.994520i	$0.533338\pi$
$174$			22.9431i			1.73931i
$175$	−1.32205	−	3.19170i	−0.0999373	−	0.241270i
$176$	−18.2813	−	7.57236i	−1.37800	−	0.570788i
$177$	−7.06976	+	17.0679i	−0.531396	+	1.28290i
$178$	−0.660926	+	0.660926i	−0.0495385	+	0.0495385i
$179$	−8.59390	+	8.59390i	−0.642338	+	0.642338i	−0.951130	−	0.308791i	$-0.900075\pi$
$179$	−8.59390	+	8.59390i	−0.642338	+	0.642338i	0.308791	+	0.951130i	$0.400075\pi$
$180$	−0.971430	+	2.34524i	−0.0724061	+	0.174804i
$181$	−14.1007	−	5.84068i	−1.04809	−	0.434135i	−0.208883	−	0.977941i	$-0.566983\pi$
$181$	−14.1007	−	5.84068i	−1.04809	−	0.434135i	−0.839211	+	0.543806i	$0.816983\pi$
$182$	0.261983	+	0.632482i	0.0194194	+	0.0468827i
$183$			12.1581i			0.898750i
$184$	−7.38600	+	3.05938i	−0.544503	+	0.225540i
$185$	−1.25276	−	1.25276i	−0.0921049	−	0.0921049i
$186$	−25.0970			−1.84020
$187$	15.8320	+	7.44554i	1.15775	+	0.544472i
$188$	−1.92857			−0.140655
$189$	22.3956	+	22.3956i	1.62904	+	1.62904i
$190$	3.69831	−	1.53189i	0.268304	−	0.111135i
$191$			8.89972i			0.643961i	0.946746	+	0.321981i	$0.104349\pi$
$191$			8.89972i			0.643961i	−0.946746	+	0.321981i	$0.895651\pi$
$192$	−6.55015	−	15.8135i	−0.472716	−	1.14124i
$193$	16.9844	+	7.03519i	1.22257	+	0.506404i	0.898225	−	0.439536i	$-0.144857\pi$
$193$	16.9844	+	7.03519i	1.22257	+	0.506404i	0.324342	+	0.945940i	$0.394857\pi$
$194$	−4.56962	+	11.0320i	−0.328080	+	0.792054i
$195$	−0.270957	+	0.270957i	−0.0194036	+	0.0194036i
$196$	1.46461	−	1.46461i	0.104615	−	0.104615i
$197$	4.09074	−	9.87591i	0.291453	−	0.703629i	−0.708545	−	0.705666i	$-0.750648\pi$
$197$	4.09074	−	9.87591i	0.291453	−	0.703629i	0.999998	+	0.00203619i	$0.000648139\pi$
$198$	36.8808	+	15.2765i	2.62101	+	1.08566i
$199$	5.93889	+	14.3377i	0.420996	+	1.01638i	0.982054	+	0.188599i	$0.0603945\pi$
$199$	5.93889	+	14.3377i	0.420996	+	1.01638i	−0.561058	+	0.827777i	$0.689605\pi$
$200$		−	2.45819i		−	0.173820i
$201$	−19.1433	+	7.92942i	−1.35026	+	0.559298i
$202$	−18.5323	−	18.5323i	−1.30393	−	1.30393i
$203$	16.9396			1.18892
$204$	−1.76444	−	4.89740i	−0.123536	−	0.342886i
$205$	10.0623			0.702785
$206$	−4.75454	−	4.75454i	−0.331264	−	0.331264i
$207$	18.1718	−	7.52699i	1.26302	−	0.523162i
$208$			0.594066i			0.0411910i
$209$	−4.17872	−	10.0883i	−0.289048	−	0.697824i
$210$	14.9341	+	6.18591i	1.03055	+	0.426868i
$211$	3.34996	−	8.08752i	0.230621	−	0.556768i	−0.765630	−	0.643281i	$-0.777573\pi$
$211$	3.34996	−	8.08752i	0.230621	−	0.556768i	0.996251	+	0.0865134i	$0.0275726\pi$
$212$	−0.486324	+	0.486324i	−0.0334009	+	0.0334009i
$213$	−15.3511	+	15.3511i	−1.05184	+	1.05184i
$214$	2.81005	−	6.78406i	0.192091	−	0.463748i
$215$	2.34171	+	0.969967i	0.159703	+	0.0661512i
$216$	8.62432	+	20.8209i	0.586810	+	1.41669i
$217$			18.5299i			1.25789i
$218$	22.0286	−	9.12453i	1.49196	−	0.617991i
$219$	−31.1071	−	31.1071i	−2.10202	−	2.10202i
$220$	1.78102			0.120076
$221$	0.0246220	−	0.524674i	0.00165626	−	0.0352934i
$222$	8.28973			0.556370
$223$	−14.9621	−	14.9621i	−1.00193	−	1.00193i	−0.999998	−	0.00193640i	$-0.999384\pi$
$223$	−14.9621	−	14.9621i	−1.00193	−	1.00193i	−0.00193640	−	0.999998i	$-0.500616\pi$
$224$	7.46089	−	3.09040i	0.498502	−	0.206486i
$225$			6.04787i			0.403192i
$226$	4.38819	+	10.5940i	0.291898	+	0.704705i
$227$	−23.6821	−	9.80944i	−1.57183	−	0.651075i	−0.584741	−	0.811220i	$-0.698804\pi$
$227$	−23.6821	−	9.80944i	−1.57183	−	0.651075i	−0.987094	+	0.160145i	$0.948804\pi$
$228$	−1.24333	+	3.00166i	−0.0823416	+	0.198790i
$229$	−5.02072	+	5.02072i	−0.331779	+	0.331779i	−0.853262	−	0.521483i	$-0.825379\pi$
$229$	−5.02072	+	5.02072i	−0.331779	+	0.331779i	0.521483	+	0.853262i	$0.325379\pi$
$230$	3.57723	−	3.57723i	0.235876	−	0.235876i
$231$	16.8741	−	40.7376i	1.11023	−	2.68033i
$232$	11.1359	+	4.61264i	0.731108	+	0.302835i
$233$	−9.07503	−	21.9091i	−0.594525	−	1.43531i	−0.879091	−	0.476654i	$-0.841849\pi$
$233$	−9.07503	−	21.9091i	−0.594525	−	1.43531i	0.284566	−	0.958657i	$-0.408151\pi$
$234$		−	1.19847i		−	0.0783467i
$235$	−4.24503	+	1.75835i	−0.276915	+	0.114702i
$236$	−1.82283	−	1.82283i	−0.118656	−	0.118656i
$237$	−15.4929			−1.00637
$238$	−20.8456	+	7.51028i	−1.35122	+	0.486819i
$239$	0.109315			0.00707103			0.00353551	−	0.999994i	$-0.498875\pi$
$239$	0.109315			0.00707103			0.00353551	+	0.999994i	$0.498875\pi$
$240$	9.91860	+	9.91860i	0.640243	+	0.640243i
$241$	16.1558	−	6.69194i	1.04069	−	0.431066i	0.204127	−	0.978944i	$-0.434564\pi$
$241$	16.1558	−	6.69194i	1.04069	−	0.431066i	0.836558	+	0.547878i	$0.184564\pi$
$242$		−	10.8970i		−	0.700484i
$243$	−0.333278	−	0.804604i	−0.0213798	−	0.0516154i
$244$	−1.56739	−	0.649232i	−0.100342	−	0.0415628i
$245$	1.88846	−	4.55914i	0.120649	−	0.291273i
$246$	−33.2921	+	33.2921i	−2.12262	+	2.12262i
$247$	−0.231810	+	0.231810i	−0.0147497	+	0.0147497i
$248$	−5.04569	+	12.1814i	−0.320401	+	0.773518i
$249$	40.1459	+	16.6290i	2.54414	+	1.05382i
$250$	0.595282	+	1.43714i	0.0376490	+	0.0908926i
$251$			3.28782i			0.207525i	0.994602	+	0.103763i	$0.0330882\pi$
$251$			3.28782i			0.207525i	−0.994602	+	0.103763i	$0.966912\pi$
$252$	−8.10204	+	3.35597i	−0.510380	+	0.211406i
$253$	−9.75805	−	9.75805i	−0.613484	−	0.613484i
$254$	12.4756			0.782787
$255$	−8.34893	−	9.17111i	−0.522830	−	0.574317i
$256$	9.66087			0.603804
$257$	15.1307	+	15.1307i	0.943829	+	0.943829i	0.998504	−	0.0546752i	$-0.0174123\pi$
$257$	15.1307	+	15.1307i	0.943829	+	0.943829i	−0.0546752	+	0.998504i	$0.517412\pi$
$258$	−10.9569	+	4.53851i	−0.682149	+	0.282555i
$259$		−	6.12055i		−	0.380313i
$260$	−0.0204621	−	0.0494000i	−0.00126901	−	0.00306366i
$261$	−27.3976	−	11.3485i	−1.69587	−	0.702453i
$262$	8.45848	−	20.4206i	0.522567	−	1.26159i
$263$	7.16800	−	7.16800i	0.441998	−	0.441998i	−0.450685	−	0.892683i	$-0.648820\pi$
$263$	7.16800	−	7.16800i	0.441998	−	0.441998i	0.892683	+	0.450685i	$0.148820\pi$
$264$	22.1857	−	22.1857i	1.36543	−	1.36543i
$265$	−0.627064	+	1.51387i	−0.0385202	+	0.0929960i
$266$	12.7765	+	5.29218i	0.783375	+	0.324484i
$267$	−0.691668	−	1.66983i	−0.0423294	−	0.102192i
$268$		−	2.89133i		−	0.176616i
$269$	−13.9299	+	5.76996i	−0.849321	+	0.351800i	−0.764522	−	0.644598i	$-0.777025\pi$
$269$	−13.9299	+	5.76996i	−0.849321	+	0.351800i	−0.0847993	+	0.996398i	$0.527025\pi$
$270$	−10.0841	−	10.0841i	−0.613701	−	0.613701i
$271$	−6.80304			−0.413255			−0.206628	−	0.978420i	$-0.566249\pi$
$271$	−6.80304			−0.413255			−0.206628	+	0.978420i	$0.566249\pi$
$272$	−19.2061	−	0.901309i	−1.16454	−	0.0546499i
$273$	−1.32380			−0.0801201
$274$	−9.38338	−	9.38338i	−0.566871	−	0.566871i
$275$	3.92026	−	1.62382i	0.236400	−	0.0979203i
$276$			4.10602i			0.247153i
$277$	6.62876	+	16.0032i	0.398284	+	0.961542i	0.988073	+	0.153985i	$0.0492107\pi$
$277$	6.62876	+	16.0032i	0.398284	+	0.961542i	−0.589790	+	0.807557i	$0.700789\pi$
$278$	−9.82602	−	4.07007i	−0.589326	−	0.244107i
$279$	12.4139	−	29.9698i	0.743200	−	1.79424i
$280$	6.00492	−	6.00492i	0.358862	−	0.358862i
$281$	12.7436	−	12.7436i	0.760218	−	0.760218i	−0.216143	−	0.976362i	$-0.569348\pi$
$281$	12.7436	−	12.7436i	0.760218	−	0.760218i	0.976362	+	0.216143i	$0.0693479\pi$
$282$	8.22738	−	19.8627i	0.489934	−	1.18280i
$283$	−17.4625	−	7.23322i	−1.03804	−	0.429970i	−0.202432	−	0.979296i	$-0.564885\pi$
$283$	−17.4625	−	7.23322i	−1.03804	−	0.429970i	−0.835608	+	0.549326i	$0.814885\pi$
$284$	−1.15928	−	2.79876i	−0.0687909	−	0.166076i
$285$			7.74066i			0.458517i
$286$	−0.776856	+	0.321784i	−0.0459365	+	0.0190275i
$287$	24.5805	+	24.5805i	1.45094	+	1.45094i
$288$	−14.1374			−0.833057
$289$	16.9253	+	1.59206i	0.995605	+	0.0936504i
$290$	−7.62743			−0.447898
$291$	−16.3273	−	16.3273i	−0.957126	−	0.957126i
$292$	5.67134	−	2.34915i	0.331890	−	0.137473i
$293$			7.53184i			0.440015i	0.975498	+	0.220007i	$0.0706081\pi$
$293$			7.53184i			0.440015i	−0.975498	+	0.220007i	$0.929392\pi$
$294$	8.83616	+	21.3324i	0.515335	+	1.24413i
$295$	−5.67423	−	2.35034i	−0.330367	−	0.136842i
$296$	1.66663	−	4.02359i	0.0968707	−	0.233866i
$297$	−27.5077	+	27.5077i	−1.59616	+	1.59616i
$298$	−7.74435	+	7.74435i	−0.448618	+	0.448618i
$299$	−0.158548	+	0.382769i	−0.00916907	+	0.0221361i
$300$	−1.16643	−	0.483150i	−0.0673437	−	0.0278947i
$301$	3.35092	+	8.08984i	0.193144	+	0.466290i
$302$		−	9.88844i		−	0.569016i
$303$	46.8219	−	19.3943i	2.68985	−	1.11417i
$304$	8.48558	+	8.48558i	0.486681	+	0.486681i
$305$	−4.04195			−0.231442
$306$	38.7465	+	1.81831i	2.21499	+	0.103946i
$307$	−7.77074			−0.443499			−0.221750	−	0.975104i	$-0.571177\pi$
$307$	−7.77074			−0.443499			−0.221750	+	0.975104i	$0.571177\pi$
$308$	4.35071	+	4.35071i	0.247905	+	0.247905i
$309$	12.0124	−	4.97569i	0.683360	−	0.283057i
$310$		−	8.34352i		−	0.473880i
$311$	3.30824	+	7.98679i	0.187593	+	0.452889i	0.989495	−	0.144566i	$-0.0461786\pi$
$311$	3.30824	+	7.98679i	0.187593	+	0.452889i	−0.801902	+	0.597455i	$0.796179\pi$
$312$	−0.870254	−	0.360471i	−0.0492684	−	0.0204076i
$313$	−4.72153	+	11.3988i	−0.266877	+	0.644298i	−0.999333	−	0.0365165i	$-0.988374\pi$
$313$	−4.72153	+	11.3988i	−0.266877	+	0.644298i	0.732456	+	0.680814i	$0.238374\pi$
$314$	−18.4502	+	18.4502i	−1.04121	+	1.04121i
$315$	−14.7739	+	14.7739i	−0.832414	+	0.832414i
$316$	0.827308	−	1.99730i	0.0465397	−	0.112357i
$317$	−7.55046	−	3.12750i	−0.424076	−	0.175658i	0.160430	−	0.987047i	$-0.448712\pi$
$317$	−7.55046	−	3.12750i	−0.424076	−	0.175658i	−0.584506	+	0.811389i	$0.698712\pi$
$318$	−2.93405	−	7.08343i	−0.164534	−	0.397219i
$319$			20.8063i			1.16493i
$320$	5.25719	−	2.17760i	0.293886	−	0.121731i
$321$	10.0404	+	10.0404i	0.560398	+	0.560398i
$322$	17.4771			0.973960
$323$	−7.14269	−	7.84609i	−0.397430	−	0.436568i
$324$	3.95937			0.219965
$325$	−0.0900798	−	0.0900798i	−0.00499673	−	0.00499673i
$326$	6.60280	−	2.73497i	0.365695	−	0.151476i
$327$			46.1064i			2.54969i
$328$	9.46572	+	22.8523i	0.522657	+	1.26181i
$329$	−14.6652	−	6.07452i	−0.808519	−	0.334899i
$330$	−7.59794	+	18.3430i	−0.418253	+	1.00975i
$331$	16.5933	−	16.5933i	0.912049	−	0.912049i	−0.0843846	−	0.996433i	$-0.526892\pi$
$331$	16.5933	−	16.5933i	0.912049	−	0.912049i	0.996433	+	0.0843846i	$0.0268924\pi$
$332$	−4.28753	+	4.28753i	−0.235309	+	0.235309i
$333$	−4.10040	+	9.89923i	−0.224700	+	0.542475i
$334$	−30.2180	−	12.5167i	−1.65346	−	0.684884i
$335$	−2.63614	−	6.36420i	−0.144028	−	0.347713i
$336$			48.4588i			2.64364i
$337$	−21.9127	+	9.07655i	−1.19366	+	0.494431i	−0.888946	−	0.458012i	$-0.848562\pi$
$337$	−21.9127	+	9.07655i	−1.19366	+	0.494431i	−0.304716	+	0.952443i	$0.598562\pi$
$338$	−14.2813	−	14.2813i	−0.776803	−	0.776803i
$339$	−22.1736			−1.20430
$340$	1.62814	−	0.586590i	0.0882984	−	0.0318123i
$341$	−22.7596			−1.23250
$342$	−17.1189	−	17.1189i	−0.925684	−	0.925684i
$343$	−6.59159	+	2.73032i	−0.355912	+	0.147424i
$344$			6.23063i			0.335933i
$345$	3.74362	+	9.03790i	0.201550	+	0.486584i
$346$	18.0396	+	7.47223i	0.969813	+	0.401710i
$347$	2.68599	−	6.48456i	0.144192	−	0.348109i	−0.835240	−	0.549885i	$-0.814671\pi$
$347$	2.68599	−	6.48456i	0.144192	−	0.348109i	0.979432	+	0.201776i	$0.0646713\pi$
$348$	4.37746	−	4.37746i	0.234657	−	0.234657i
$349$	−20.7773	+	20.7773i	−1.11219	+	1.11219i	−0.119331	+	0.992855i	$0.538075\pi$
$349$	−20.7773	+	20.7773i	−1.11219	+	1.11219i	−0.992855	+	0.119331i	$0.961925\pi$
$350$	−2.05651	+	4.96485i	−0.109925	+	0.265382i
$351$	1.07902	+	0.446943i	0.0575936	+	0.0238561i
$352$	3.79583	+	9.16396i	0.202319	+	0.488440i
$353$		−	9.09110i		−	0.483870i	−0.970292	−	0.241935i	$-0.922218\pi$
$353$		−	9.09110i		−	0.483870i	0.970292	−	0.241935i	$-0.0777821\pi$
$354$	26.5499	−	10.9973i	1.41111	−	0.584502i
$355$	−5.10348	−	5.10348i	−0.270865	−	0.270865i
$356$	0.252205			0.0133668
$357$	2.00845	−	42.7984i	0.106299	−	2.26513i
$358$	18.9055			0.999188
$359$	3.70529	+	3.70529i	0.195558	+	0.195558i	0.798093	−	0.602535i	$-0.205843\pi$
$359$	3.70529	+	3.70529i	0.195558	+	0.195558i	−0.602535	+	0.798093i	$0.705843\pi$
$360$	−13.7351	+	5.68928i	−0.723905	+	0.299851i
$361$		−	12.3777i		−	0.651458i
$362$	9.08546	+	21.9342i	0.477521	+	1.15284i
$363$	19.4675	+	8.06372i	1.02178	+	0.423235i
$364$	0.0706900	−	0.170661i	0.00370516	−	0.00894506i
$365$	10.3416	−	10.3416i	0.541302	−	0.541302i
$366$	13.3731	−	13.3731i	0.699025	−	0.699025i
$367$	−6.97736	+	16.8448i	−0.364215	+	0.879293i	0.630459	+	0.776223i	$0.282867\pi$
$367$	−6.97736	+	16.8448i	−0.364215	+	0.879293i	−0.994674	+	0.103071i	$0.967133\pi$
$368$	14.0115	+	5.80377i	0.730402	+	0.302543i
$369$	−23.2885	−	56.2234i	−1.21235	−	2.92687i
$370$			2.75592i			0.143274i
$371$	−5.22991	+	2.16630i	−0.271524	+	0.112469i
$372$	4.78843	+	4.78843i	0.248268	+	0.248268i
$373$	18.5489			0.960428			0.480214	−	0.877151i	$-0.340559\pi$
$373$	18.5489			0.960428			0.480214	+	0.877151i	$0.340559\pi$
$374$	−9.22462	−	25.6039i	−0.476994	−	1.32395i
$375$	−3.00797			−0.155331
$376$	−7.98666	−	7.98666i	−0.411881	−	0.411881i
$377$	0.577102	−	0.239044i	0.0297223	−	0.0123114i
$378$		−	49.2675i		−	2.53405i
$379$	−7.67735	−	18.5348i	−0.394359	−	0.952067i	−0.988978	−	0.148060i	$-0.952697\pi$
$379$	−7.67735	−	18.5348i	−0.394359	−	0.952067i	0.594619	−	0.804007i	$-0.297303\pi$
$380$	−0.997904	−	0.413346i	−0.0511914	−	0.0212042i
$381$	−9.23188	+	22.2877i	−0.472963	+	1.14183i
$382$	9.78914	−	9.78914i	0.500856	−	0.500856i
$383$	−7.72751	+	7.72751i	−0.394857	+	0.394857i	−0.876415	−	0.481557i	$-0.840071\pi$
$383$	−7.72751	+	7.72751i	−0.394857	+	0.394857i	0.481557	+	0.876415i	$0.340071\pi$
$384$	−15.5707	+	37.5909i	−0.794587	+	1.91830i
$385$	13.5432	+	5.60978i	0.690226	+	0.285901i
$386$	−10.9436	−	26.4201i	−0.557013	−	1.34475i
$387$		−	15.3292i		−	0.779228i
$388$	2.97674	−	1.23301i	0.151121	−	0.0625965i
$389$	16.7947	+	16.7947i	0.851526	+	0.851526i	0.990321	−	0.138795i	$-0.0443228\pi$
$389$	16.7947	+	16.7947i	0.851526	+	0.851526i	−0.138795	+	0.990321i	$0.544323\pi$
$390$	0.596072			0.0301833
$391$	−12.1343	−	5.70657i	−0.613659	−	0.288594i
$392$	12.1306			0.612688
$393$	30.2223	+	30.2223i	1.52451	+	1.52451i
$394$	−15.3624	+	6.36333i	−0.773949	+	0.320580i
$395$		−	5.15061i		−	0.259155i
$396$	−4.12203	−	9.95145i	−0.207140	−	0.500079i
$397$	−26.2259	−	10.8631i	−1.31624	−	0.545205i	−0.389542	−	0.921009i	$-0.627367\pi$
$397$	−26.2259	−	10.8631i	−1.31624	−	0.545205i	−0.926699	+	0.375804i	$0.877367\pi$
$398$	9.23822	−	22.3030i	0.463070	−	1.11795i
$399$	−18.9091	+	18.9091i	−0.946637	+	0.946637i
$400$	−3.29744	+	3.29744i	−0.164872	+	0.164872i
$401$	−3.33935	+	8.06191i	−0.166759	+	0.402592i	−0.985063	−	0.172193i	$-0.944915\pi$
$401$	−3.33935	+	8.06191i	−0.166759	+	0.402592i	0.818304	+	0.574786i	$0.194915\pi$
$402$	29.7783	+	12.3346i	1.48521	+	0.615193i
$403$	0.261486	+	0.631282i	0.0130255	+	0.0314464i
$404$			7.07179i			0.351835i
$405$	8.71509	−	3.60991i	0.433056	−	0.179378i
$406$	−18.6325	−	18.6325i	−0.924714	−	0.924714i
$407$	7.51766			0.372637
$408$	12.9743	−	27.5883i	0.642325	−	1.36583i
$409$	10.5572			0.522020			0.261010	−	0.965336i	$-0.415944\pi$
$409$	10.5572			0.522020			0.261010	+	0.965336i	$0.415944\pi$
$410$	−11.0680	−	11.0680i	−0.546608	−	0.546608i
$411$	23.7072	−	9.81983i	1.16939	−	0.484376i
$412$			1.81430i			0.0893841i
$413$	−8.11967	−	19.6026i	−0.399543	−	0.964582i
$414$	−28.2670	−	11.7086i	−1.38925	−	0.575446i
$415$	−5.52831	+	13.3465i	−0.271374	+	0.655155i
$416$	0.210570	−	0.210570i	0.0103240	−	0.0103240i
$417$	14.5424	−	14.5424i	0.712147	−	0.712147i
$418$	−6.50020	+	15.6929i	−0.317935	+	0.767564i
$419$	13.2011	+	5.46806i	0.644915	+	0.267132i	0.681075	−	0.732214i	$-0.261513\pi$
$419$	13.2011	+	5.46806i	0.644915	+	0.267132i	−0.0361604	+	0.999346i	$0.511513\pi$
$420$	−1.66913	−	4.02963i	−0.0814450	−	0.196626i
$421$		−	18.2694i		−	0.890398i	−0.895432	−	0.445199i	$-0.853133\pi$
$421$		−	18.2694i		−	0.890398i	0.895432	−	0.445199i	$-0.146867\pi$
$422$	−12.5805	+	5.21102i	−0.612410	+	0.253669i
$423$	19.6496	+	19.6496i	0.955395	+	0.955395i
$424$	−4.02798			−0.195616
$425$	3.04894	−	2.77560i	0.147895	−	0.134637i
$426$	33.7705			1.63619
$427$	−9.87378	−	9.87378i	−0.477826	−	0.477826i
$428$	−1.83052	+	0.758227i	−0.0884816	+	0.0366503i
$429$		−	1.62598i		−	0.0785030i
$430$	−1.50883	−	3.64264i	−0.0727622	−	0.175664i
$431$	19.4407	+	8.05261i	0.936427	+	0.387881i	0.798113	−	0.602508i	$-0.205832\pi$
$431$	19.4407	+	8.05261i	0.936427	+	0.387881i	0.138314	+	0.990388i	$0.455832\pi$
$432$	16.3607	−	39.4982i	0.787154	−	1.90036i
$433$	2.52902	−	2.52902i	0.121537	−	0.121537i	−0.643722	−	0.765259i	$-0.722611\pi$
$433$	2.52902	−	2.52902i	0.121537	−	0.121537i	0.765259	+	0.643722i	$0.222611\pi$
$434$	20.3817	−	20.3817i	0.978355	−	0.978355i
$435$	5.64427	−	13.6265i	0.270622	−	0.653340i
$436$	−5.94391	−	2.46205i	−0.284661	−	0.117911i
$437$	3.20275	+	7.73212i	0.153208	+	0.369878i
$438$			68.4318i			3.26980i
$439$	3.03763	−	1.25823i	0.144978	−	0.0600520i	−0.309014	−	0.951057i	$-0.599999\pi$
$439$	3.03763	−	1.25823i	0.144978	−	0.0600520i	0.453993	+	0.891005i	$0.349999\pi$
$440$	7.37563	+	7.37563i	0.351619	+	0.351619i
$441$	−29.8449			−1.42119
$442$	−0.604191	+	0.550026i	−0.0287384	+	0.0261621i
$443$	−24.9391			−1.18489			−0.592447	−	0.805609i	$-0.701838\pi$
$443$	−24.9391			−1.18489			−0.592447	+	0.805609i	$0.701838\pi$
$444$	−1.58165	−	1.58165i	−0.0750619	−	0.0750619i
$445$	0.555137	−	0.229945i	0.0263160	−	0.0109004i
$446$			32.9147i			1.55856i
$447$	−8.10457	−	19.5662i	−0.383333	−	0.925447i
$448$	18.1619	+	7.52289i	0.858068	+	0.355423i
$449$	3.69533	−	8.92132i	0.174394	−	0.421023i	−0.812380	−	0.583128i	$-0.801828\pi$
$449$	3.69533	−	8.92132i	0.174394	−	0.421023i	0.986773	+	0.162105i	$0.0518284\pi$
$450$	6.65229	−	6.65229i	0.313592	−	0.313592i
$451$	−30.1914	+	30.1914i	−1.42166	+	1.42166i
$452$	1.18405	−	2.85856i	0.0556932	−	0.134455i
$453$	17.6658	+	7.31741i	0.830011	+	0.343802i
$454$	15.2590	+	36.8386i	0.716143	+	1.72892i
$455$		−	0.440098i		−	0.0206321i
$456$	−17.5796	+	7.28169i	−0.823239	+	0.340997i
$457$	14.4798	+	14.4798i	0.677338	+	0.677338i	0.959397	−	0.282059i	$-0.0910175\pi$
$457$	14.4798	+	14.4798i	0.677338	+	0.677338i	−0.282059	+	0.959397i	$0.591018\pi$
$458$	11.0450			0.516098
$459$	−16.0867	+	34.2064i	−0.750863	+	1.59662i
$460$	−1.36505			−0.0636457
$461$	−13.3288	−	13.3288i	−0.620785	−	0.620785i	0.324947	−	0.945732i	$-0.394654\pi$
$461$	−13.3288	−	13.3288i	−0.620785	−	0.620785i	−0.945732	+	0.324947i	$0.894654\pi$
$462$	−63.3692	+	26.2484i	−2.94820	+	1.22119i
$463$			2.13430i			0.0991892i	0.998769	+	0.0495946i	$0.0157929\pi$
$463$			2.13430i			0.0991892i	−0.998769	+	0.0495946i	$0.984207\pi$
$464$	−8.75038	−	21.1253i	−0.406226	−	0.980716i
$465$	14.9058	+	6.17417i	0.691238	+	0.286320i
$466$	−14.1166	+	34.0806i	−0.653941	+	1.57875i
$467$	16.4498	−	16.4498i	0.761208	−	0.761208i	−0.215333	−	0.976541i	$-0.569084\pi$
$467$	16.4498	−	16.4498i	0.761208	−	0.761208i	0.976541	+	0.215333i	$0.0690837\pi$
$468$	−0.228665	+	0.228665i	−0.0105700	+	0.0105700i
$469$	9.10700	−	21.9862i	0.420522	−	1.01523i
$470$	6.60335	+	2.73520i	0.304590	+	0.126165i
$471$	−19.3084	−	46.6146i	−0.889684	−	2.14789i
$472$		−	15.0976i		−	0.694921i
$473$	−9.93647	+	4.11582i	−0.456879	+	0.189246i
$474$	17.0412	+	17.0412i	0.782728	+	0.782728i
$475$	−2.57338			−0.118075
$476$	5.41020	+	2.54433i	0.247976	+	0.116619i
$477$	9.91002			0.453749
$478$	−0.120240	−	0.120240i	−0.00549966	−	0.00549966i
$479$	−28.8369	+	11.9446i	−1.31759	+	0.545763i	−0.927090	−	0.374839i	$-0.877698\pi$
$479$	−28.8369	+	11.9446i	−1.31759	+	0.545763i	−0.390500	+	0.920603i	$0.627698\pi$
$480$		−	7.03140i		−	0.320938i
$481$	−0.0863705	−	0.208517i	−0.00393816	−	0.00950755i
$482$	−25.1311	−	10.4096i	−1.14469	−	0.474146i
$483$	−12.9330	+	31.2230i	−0.588471	+	1.42070i
$484$	−2.07911	+	2.07911i	−0.0945048	+	0.0945048i
$485$	5.42803	−	5.42803i	0.246474	−	0.246474i
$486$	−0.518430	+	1.25160i	−0.0235164	+	0.0567737i
$487$	13.5374	+	5.60737i	0.613438	+	0.254094i	0.667698	−	0.744433i	$-0.267280\pi$
$487$	13.5374	+	5.60737i	0.613438	+	0.254094i	−0.0542599	+	0.998527i	$0.517280\pi$
$488$	−3.80230	−	9.17956i	−0.172122	−	0.415539i
$489$			13.8198i			0.624954i
$490$	−7.09196	+	2.93758i	−0.320382	+	0.132707i
$491$	9.80148	+	9.80148i	0.442334	+	0.442334i	0.892796	−	0.450461i	$-0.148741\pi$
$491$	9.80148	+	9.80148i	0.442334	+	0.442334i	−0.450461	+	0.892796i	$0.648741\pi$
$492$	12.7040			0.572742
$493$	6.85268	+	19.0203i	0.308629	+	0.856633i
$494$	0.509953			0.0229439
$495$	−18.1463	−	18.1463i	−0.815614	−	0.815614i
$496$	23.1086	−	9.57188i	1.03761	−	0.429790i
$497$		−	24.9338i		−	1.11843i
$498$	−25.8672	−	62.4489i	−1.15914	−	2.79840i
$499$	36.9847	+	15.3196i	1.65566	+	0.685798i	0.997734	−	0.0672815i	$-0.0214326\pi$
$499$	36.9847	+	15.3196i	1.65566	+	0.685798i	0.657929	+	0.753080i	$0.271433\pi$
$500$	0.160623	−	0.387779i	0.00718329	−	0.0173420i
$501$	44.7224	−	44.7224i	1.99805	−	1.99805i
$502$	3.61639	−	3.61639i	0.161408	−	0.161408i
$503$	15.0174	−	36.2551i	0.669591	−	1.61654i	−0.112704	−	0.993629i	$-0.535951\pi$
$503$	15.0174	−	36.2551i	0.669591	−	1.61654i	0.782296	−	0.622907i	$-0.214049\pi$
$504$	−47.4504	−	19.6546i	−2.11361	−	0.875486i
$505$	6.44763	+	15.5660i	0.286916	+	0.692676i
$506$			21.4665i			0.954303i
$507$	36.0819	−	14.9456i	1.60245	−	0.663758i
$508$	−2.38030	−	2.38030i	−0.105609	−	0.105609i
$509$	−26.7005			−1.18348			−0.591740	−	0.806129i	$-0.701559\pi$
$509$	−26.7005			−1.18348			−0.591740	+	0.806129i	$0.701559\pi$
$510$	−0.904353	+	19.2710i	−0.0400454	+	0.853333i
$511$	50.5253			2.23511
$512$	8.50339	+	8.50339i	0.375800	+	0.375800i
$513$	21.7967	−	9.02847i	0.962346	−	0.398617i
$514$		−	33.2857i		−	1.46817i
$515$	1.65417	+	3.99352i	0.0728914	+	0.175975i
$516$	2.95648	+	1.22461i	0.130152	+	0.0539106i
$517$	7.46113	−	18.0128i	0.328140	−	0.792200i
$518$	−6.73223	+	6.73223i	−0.295797	+	0.295797i
$519$	−26.6984	+	26.6984i	−1.17193	+	1.17193i
$520$	0.119839	−	0.289316i	0.00525527	−	0.0126874i
$521$	4.28773	+	1.77604i	0.187849	+	0.0778096i	0.474625	−	0.880188i	$-0.342584\pi$
$521$	4.28773	+	1.77604i	0.187849	+	0.0778096i	−0.286776	+	0.957998i	$0.592584\pi$
$522$	17.6531	+	42.6183i	0.772655	+	1.86535i
$523$		−	9.21401i		−	0.402900i	−0.979499	−	0.201450i	$-0.935435\pi$
$523$		−	9.21401i		−	0.402900i	0.979499	−	0.201450i	$-0.0645654\pi$
$524$	−5.51003	+	2.28233i	−0.240707	+	0.0997040i
$525$	−7.34794	−	7.34794i	−0.320690	−	0.320690i
$526$	−15.7687			−0.687549
$527$	−20.8060	+	7.49603i	−0.906324	+	0.326532i
$528$	−59.5202			−2.59029
$529$	−8.78447	−	8.78447i	−0.381934	−	0.381934i
$530$	2.35489	−	0.975427i	0.102290	−	0.0423699i
$531$			37.1445i			1.61193i
$532$	−1.42797	−	3.44743i	−0.0619105	−	0.149465i
$533$	1.18429	+	0.490548i	0.0512972	+	0.0212480i
$534$	−1.07592	+	2.59751i	−0.0465597	+	0.112405i
$535$	−3.33792	+	3.33792i	−0.144311	+	0.144311i
$536$	11.9737	−	11.9737i	0.517185	−	0.517185i
$537$	−13.9900	+	33.7749i	−0.603714	+	1.45749i
$538$	21.6686	+	8.97544i	0.934201	+	0.386959i
$539$	8.01321	+	19.3456i	0.345153	+	0.833274i
$540$			3.84804i			0.165593i
$541$	−29.5380	+	12.2350i	−1.26994	+	0.526025i	−0.912945	−	0.408083i	$-0.866197\pi$
$541$	−29.5380	+	12.2350i	−1.26994	+	0.526025i	−0.356991	+	0.934108i	$0.616197\pi$
$542$	7.48292	+	7.48292i	0.321419	+	0.321419i
$543$	−45.9089			−1.97014
$544$	6.48822	+	7.12717i	0.278180	+	0.305575i
$545$	−15.3281			−0.656583
$546$	1.45610	+	1.45610i	0.0623153	+	0.0623153i
$547$	7.76844	−	3.21779i	0.332155	−	0.137583i	−0.210372	−	0.977621i	$-0.567468\pi$
$547$	7.76844	−	3.21779i	0.332155	−	0.137583i	0.542527	+	0.840038i	$0.317468\pi$
$548$			3.58064i			0.152957i
$549$	9.35478	+	22.5844i	0.399252	+	0.963881i
$550$	−6.09815	−	2.52594i	−0.260026	−	0.107706i
$551$	4.82880	−	11.6578i	0.205714	−	0.496637i
$552$	−17.0040	+	17.0040i	−0.723740	+	0.723740i
$553$	12.5820	−	12.5820i	0.535042	−	0.535042i
$554$	10.3114	−	24.8938i	0.438087	−	1.05764i
$555$	−4.92348	−	2.03937i	−0.208990	−	0.0865665i
$556$	1.09822	+	2.65133i	0.0465747	+	0.112441i
$557$		−	1.01642i		−	0.0430670i	−0.999768	−	0.0215335i	$-0.993145\pi$
$557$		−	1.01642i		−	0.0430670i	0.999768	−	0.0215335i	$-0.00685486\pi$
$558$	−46.6194	+	19.3104i	−1.97356	+	0.817475i
$559$	0.228320	+	0.228320i	0.00965692	+	0.00965692i
$560$	−16.1101			−0.680777
$561$	52.5677	+	2.46692i	2.21941	+	0.104153i
$562$	−28.0343			−1.18256
$563$	7.34466	+	7.34466i	0.309541	+	0.309541i	0.844731	−	0.535191i	$-0.179760\pi$
$563$	7.34466	+	7.34466i	0.309541	+	0.309541i	−0.535191	+	0.844731i	$0.679760\pi$
$564$	−5.35949	+	2.21997i	−0.225675	+	0.0934777i
$565$		−	7.37161i		−	0.310126i
$566$	11.2516	+	27.1638i	0.472941	+	1.14178i
$567$	30.1078	+	12.4711i	1.26441	+	0.523735i
$568$	6.78947	−	16.3912i	0.284880	−	0.687761i
$569$	−16.9517	+	16.9517i	−0.710651	+	0.710651i	−0.966671	−	0.256020i	$-0.917589\pi$
$569$	−16.9517	+	16.9517i	−0.710651	+	0.710651i	0.256020	+	0.966671i	$0.417589\pi$
$570$	8.51425	−	8.51425i	0.356623	−	0.356623i
$571$	−4.53513	+	10.9488i	−0.189789	+	0.458192i	−0.989919	−	0.141635i	$-0.954764\pi$
$571$	−4.53513	+	10.9488i	−0.189789	+	0.458192i	0.800129	+	0.599827i	$0.204764\pi$
$572$	0.209617	+	0.0868261i	0.00876452	+	0.00363038i
$573$	10.2445	+	24.7323i	0.427969	+	1.03321i
$574$		−	54.0741i		−	2.25701i
$575$	−3.00465	+	1.24457i	−0.125303	+	0.0519021i
$576$	−24.3347	−	24.3347i	−1.01395	−	1.01395i
$577$	22.5581			0.939107			0.469553	−	0.882904i	$-0.344415\pi$
$577$	22.5581			0.939107			0.469553	+	0.882904i	$0.344415\pi$
$578$	−16.8656	−	20.3679i	−0.701517	−	0.847195i
$579$	55.2980			2.29811
$580$	1.45529	+	1.45529i	0.0604276	+	0.0604276i
$581$	−46.1079	+	19.0985i	−1.91288	+	0.792340i
$582$			35.9181i			1.48885i
$583$	−2.66079	−	6.42372i	−0.110199	−	0.266043i
$584$	33.2148	+	13.7580i	1.37444	+	0.569311i
$585$	−0.294839	+	0.711804i	−0.0121901	+	0.0294295i
$586$	8.28456	−	8.28456i	0.342232	−	0.342232i
$587$	−29.8211	+	29.8211i	−1.23085	+	1.23085i	−0.267210	+	0.963638i	$0.586102\pi$
$587$	−29.8211	+	29.8211i	−1.23085	+	1.23085i	−0.963638	+	0.267210i	$0.913898\pi$
$588$	2.38424	−	5.75605i	0.0983242	−	0.237376i
$589$	12.7522	+	5.28214i	0.525446	+	0.217647i
$590$	3.65607	+	8.82654i	0.150518	+	0.363383i
$591$		−	32.1540i		−	1.32264i
$592$	−7.63292	+	3.16166i	−0.313711	+	0.129943i
$593$	−6.00168	−	6.00168i	−0.246460	−	0.246460i	0.573056	−	0.819516i	$-0.305758\pi$
$593$	−6.00168	−	6.00168i	−0.246460	−	0.246460i	−0.819516	+	0.573056i	$0.805758\pi$
$594$	60.5136			2.48290
$595$	14.2283	+	0.667711i	0.583305	+	0.0273735i
$596$	2.95519			0.121049
$597$	33.0083	+	33.0083i	1.35094	+	1.35094i
$598$	0.595415	−	0.246629i	0.0243483	−	0.0100854i
$599$		−	17.0226i		−	0.695523i	−0.937583	−	0.347762i	$-0.886942\pi$
$599$		−	17.0226i		−	0.695523i	0.937583	−	0.347762i	$-0.113058\pi$
$600$	−2.82962	−	6.83130i	−0.115519	−	0.278887i
$601$	−18.7530	−	7.76773i	−0.764949	−	0.316852i	−0.0341247	−	0.999418i	$-0.510864\pi$
$601$	−18.7530	−	7.76773i	−0.764949	−	0.316852i	−0.730825	+	0.682565i	$0.760864\pi$
$602$	5.21252	−	12.5841i	0.212446	−	0.512891i
$603$	−29.4589	+	29.4589i	−1.19966	+	1.19966i
$604$	−1.88668	+	1.88668i	−0.0767679	+	0.0767679i
$605$	−2.68079	+	6.47199i	−0.108989	+	0.263124i
$606$	−72.8337	−	30.1687i	−2.95867	−	1.22552i
$607$	−18.6877	−	45.1162i	−0.758512	−	1.83121i	−0.502633	−	0.864500i	$-0.667635\pi$
$607$	−18.6877	−	45.1162i	−0.758512	−	1.83121i	−0.255879	−	0.966709i	$-0.582365\pi$
$608$		−	6.01552i		−	0.243961i
$609$	47.0750	−	19.4991i	1.90758	−	0.790144i
$610$	4.44590	+	4.44590i	0.180009	+	0.180009i
$611$	−0.585340			−0.0236803
$612$	−7.04578	−	7.73963i	−0.284809	−	0.312856i
$613$	−21.5320			−0.869669			−0.434834	−	0.900510i	$-0.643193\pi$
$613$	−21.5320			−0.869669			−0.434834	+	0.900510i	$0.643193\pi$
$614$	8.54733	+	8.54733i	0.344942	+	0.344942i
$615$	27.9633	−	11.5828i	1.12759	−	0.467062i
$616$			36.0347i			1.45188i
$617$	−1.77029	−	4.27386i	−0.0712692	−	0.172059i	0.884231	−	0.467050i	$-0.154683\pi$
$617$	−1.77029	−	4.27386i	−0.0712692	−	0.172059i	−0.955500	+	0.294991i	$0.904683\pi$
$618$	−18.6858	−	7.73992i	−0.751654	−	0.311345i
$619$	17.8427	−	43.0760i	0.717158	−	1.73137i	0.0358698	−	0.999356i	$-0.488580\pi$
$619$	17.8427	−	43.0760i	0.717158	−	1.73137i	0.681288	−	0.732016i	$-0.261420\pi$
$620$	−1.59191	+	1.59191i	−0.0639328	+	0.0639328i
$621$	21.0831	−	21.0831i	0.846035	−	0.846035i
$622$	5.14612	−	12.4238i	0.206341	−	0.498150i
$623$	1.91782	+	0.794386i	0.0768357	+	0.0318264i
$624$	0.683829	+	1.65091i	0.0273751	+	0.0660892i
$625$		−	1.00000i		−	0.0400000i
$626$	17.7314	−	7.34457i	0.708688	−	0.293548i
$627$	−23.2253	−	23.2253i	−0.927531	−	0.927531i
$628$	7.04048			0.280946
$629$	6.87237	−	2.47599i	0.274019	−	0.0987243i
$630$	32.5007			1.29486
$631$	18.5948	+	18.5948i	0.740246	+	0.740246i	0.972625	−	0.232380i	$-0.0746511\pi$
$631$	18.5948	+	18.5948i	0.740246	+	0.740246i	−0.232380	+	0.972625i	$0.574651\pi$
$632$	11.6974	−	4.84522i	0.465297	−	0.192732i
$633$		−	26.3314i		−	1.04658i
$634$	4.86498	+	11.7451i	0.193213	+	0.466457i
$635$	−7.40956	−	3.06914i	−0.294039	−	0.121795i
$636$	−0.791688	+	1.91130i	−0.0313925	+	0.0757881i
$637$	0.444523	−	0.444523i	0.0176127	−	0.0176127i
$638$	22.8856	−	22.8856i	0.906051	−	0.906051i
$639$	−16.7041	+	40.3273i	−0.660805	+	1.59532i
$640$	−12.4971	−	5.17647i	−0.493992	−	0.204618i
$641$	2.51210	+	6.06476i	0.0992222	+	0.239544i	0.965694	−	0.259682i	$-0.0836178\pi$
$641$	2.51210	+	6.06476i	0.0992222	+	0.239544i	−0.866472	+	0.499226i	$0.833618\pi$
$642$		−	22.0875i		−	0.871726i
$643$	−5.91935	+	2.45187i	−0.233436	+	0.0966925i	−0.496335	−	0.868131i	$-0.665321\pi$
$643$	−5.91935	+	2.45187i	−0.233436	+	0.0966925i	0.262899	+	0.964823i	$0.415321\pi$
$644$	−3.33457	−	3.33457i	−0.131400	−	0.131400i
$645$	7.62413			0.300200
$646$	−0.773695	+	16.4867i	−0.0304406	+	0.648662i
$647$	−8.03230			−0.315782			−0.157891	−	0.987457i	$-0.550470\pi$
$647$	−8.03230			−0.315782			−0.157891	+	0.987457i	$0.550470\pi$
$648$	16.3967	+	16.3967i	0.644123	+	0.644123i
$649$	24.0772	−	9.97311i	0.945114	−	0.391479i
$650$			0.198164i			0.00777265i
$651$	21.3298	+	51.4946i	0.835979	+	2.01823i
$652$	−1.78161	−	0.737969i	−0.0697734	−	0.0289011i
$653$	−17.6821	+	42.6883i	−0.691953	+	1.67052i	0.0488551	+	0.998806i	$0.484443\pi$
$653$	−17.6821	+	42.6883i	−0.691953	+	1.67052i	−0.740808	+	0.671717i	$0.765557\pi$
$654$	50.7142	−	50.7142i	1.98308	−	1.98308i
$655$	−10.0474	+	10.0474i	−0.392585	+	0.392585i
$656$	17.9569	−	43.3517i	0.701098	−	1.69260i
$657$	−81.7183	−	33.8488i	−3.18814	−	1.32057i
$658$	9.44921	+	22.8124i	0.368369	+	0.889321i
$659$		−	47.9496i		−	1.86785i	−0.357465	−	0.933926i	$-0.616359\pi$
$659$		−	47.9496i		−	1.86785i	0.357465	−	0.933926i	$-0.383641\pi$
$660$	4.94945	−	2.05013i	0.192657	−	0.0798012i
$661$	−26.7821	−	26.7821i	−1.04170	−	1.04170i	−0.999092	−	0.0426129i	$-0.986432\pi$
$661$	−26.7821	−	26.7821i	−1.04170	−	1.04170i	−0.0426129	−	0.999092i	$-0.513568\pi$
$662$	−36.5032			−1.41874
$663$	−0.535527	−	1.48641i	−0.0207981	−	0.0577274i
$664$	−35.5114			−1.37811
$665$	−6.28632	−	6.28632i	−0.243773	−	0.243773i
$666$	15.3987	−	6.37836i	0.596689	−	0.247157i
$667$		−	15.9468i		−	0.617463i
$668$	3.37735	+	8.15364i	0.130674	+	0.315474i
$669$	−58.8024	−	24.3568i	−2.27343	−	0.941687i
$670$	−4.10064	+	9.89981i	−0.158421	+	0.382463i
$671$	12.1276	−	12.1276i	0.468182	−	0.468182i
$672$	17.1765	−	17.1765i	0.662596	−	0.662596i
$673$	1.55425	−	3.75229i	0.0599119	−	0.144640i	−0.891089	−	0.453829i	$-0.850058\pi$
$673$	1.55425	−	3.75229i	0.0599119	−	0.144640i	0.951001	+	0.309189i	$0.100058\pi$
$674$	34.0863	+	14.1190i	1.31295	+	0.543844i
$675$	3.50841	+	8.47004i	0.135039	+	0.326012i
$676$			5.44967i			0.209603i
$677$	3.22013	−	1.33382i	0.123760	−	0.0512629i	−0.319944	−	0.947436i	$-0.603664\pi$
$677$	3.22013	−	1.33382i	0.123760	−	0.0512629i	0.443704	+	0.896173i	$0.353664\pi$
$678$	24.3896	+	24.3896i	0.936676	+	0.936676i
$679$	26.5194			1.01772
$680$	9.17174	+	4.31332i	0.351720	+	0.165408i
$681$	−77.1041			−2.95464
$682$	25.0342	+	25.0342i	0.958609	+	0.958609i
$683$	−13.0097	+	5.38880i	−0.497803	+	0.206197i	−0.617436	−	0.786621i	$-0.711828\pi$
$683$	−13.0097	+	5.38880i	−0.497803	+	0.206197i	0.119632	+	0.992818i	$0.461828\pi$
$684$			6.53245i			0.249775i
$685$	3.26461	+	7.88145i	0.124734	+	0.301135i
$686$	10.2535	+	4.24715i	0.391482	+	0.162157i
$687$	−8.17324	+	19.7319i	−0.311829	+	0.752821i
$688$	8.35784	−	8.35784i	0.318640	−	0.318640i
$689$	−0.147604	+	0.147604i	−0.00562328	+	0.00562328i
$690$	5.82338	−	14.0589i	0.221692	−	0.535212i
$691$	−41.2601	−	17.0905i	−1.56961	−	0.650153i	−0.582883	−	0.812556i	$-0.698075\pi$
$691$	−41.2601	−	17.0905i	−1.56961	−	0.650153i	−0.986724	+	0.162403i	$0.948075\pi$
$692$	−2.01621	−	4.86756i	−0.0766448	−	0.185037i
$693$		−	88.6562i		−	3.36777i
$694$	−10.0870	+	4.17819i	−0.382899	+	0.158602i
$695$	4.83464	+	4.83464i	0.183388	+	0.183388i
$696$	36.2563			1.37429
$697$	−17.6561	+	37.5436i	−0.668774	+	1.42207i
$698$	45.7076			1.73006
$699$	−50.4390	−	50.4390i	−1.90778	−	1.90778i
$700$	1.33965	−	0.554901i	0.0506340	−	0.0209733i
$701$			1.84833i			0.0698103i	0.999391	+	0.0349052i	$0.0111129\pi$
$701$			1.84833i			0.0698103i	−0.999391	+	0.0349052i	$0.988887\pi$
$702$	−0.695241	−	1.67846i	−0.0262402	−	0.0633494i
$703$	−4.21215	−	1.74473i	−0.158864	−	0.0658037i
$704$	−9.24011	+	22.3076i	−0.348250	+	0.840749i
$705$	−9.77291	+	9.77291i	−0.368069	+	0.368069i
$706$	−9.99965	+	9.99965i	−0.376342	+	0.376342i
$707$	−22.2745	+	53.7753i	−0.837717	+	2.02243i
$708$	−7.16390	−	2.96738i	−0.269236	−	0.111521i
$709$	11.4834	+	27.7233i	0.431267	+	1.04117i	0.978879	+	0.204438i	$0.0655367\pi$
$709$	11.4834	+	27.7233i	0.431267	+	1.04117i	−0.547613	+	0.836732i	$0.684463\pi$
$710$			11.2270i			0.421343i
$711$	−28.7791	+	11.9207i	−1.07930	+	0.447060i
$712$	1.04444	+	1.04444i	0.0391421	+	0.0391421i
$713$	17.4439			0.653281
$714$	−49.2847	+	44.8664i	−1.84443	+	1.67908i
$715$	0.540557			0.0202157
$716$	−3.60711	−	3.60711i	−0.134804	−	0.134804i
$717$	0.303788	−	0.125833i	0.0113452	−	0.00469932i
$718$		−	8.15119i		−	0.304200i
$719$	14.6916	+	35.4687i	0.547904	+	1.32276i	0.919034	+	0.394177i	$0.128970\pi$
$719$	14.6916	+	35.4687i	0.547904	+	1.32276i	−0.371130	+	0.928581i	$0.621030\pi$
$720$	26.0561	+	10.7928i	0.971055	+	0.402224i
$721$	−5.71461	+	13.7963i	−0.212823	+	0.513801i
$722$	−13.6147	+	13.6147i	−0.506687	+	0.506687i
$723$	37.1938	−	37.1938i	1.38325	−	1.38325i
$724$	2.45150	−	5.91846i	0.0911094	−	0.219958i
$725$	4.53013	+	1.87644i	0.168245	+	0.0696892i
$726$	−12.5435	−	30.2827i	−0.465533	−	1.12390i
$727$		−	0.0992434i		−	0.00368073i	−0.999998	−	0.00184037i	$-0.999414\pi$
$727$		−	0.0992434i		−	0.00368073i	0.999998	−	0.00184037i	$-0.000585807\pi$
$728$	0.999493	−	0.414004i	0.0370437	−	0.0153440i
$729$	18.1584	+	18.1584i	0.672532	+	0.672532i
$730$	−22.7502			−0.842022
$731$	−7.72798	+	7.03517i	−0.285830	+	0.260205i
$732$	−5.10310			−0.188616
$733$	10.2168	+	10.2168i	0.377365	+	0.377365i	0.870151	−	0.492786i	$-0.164021\pi$
$733$	10.2168	+	10.2168i	0.377365	+	0.377365i	−0.492786	+	0.870151i	$0.664021\pi$
$734$	26.2030	−	10.8536i	0.967169	−	0.400614i
$735$		−	14.8436i		−	0.547516i
$736$	−2.90929	−	7.02364i	−0.107238	−	0.258895i
$737$	27.0049	+	11.1858i	0.994739	+	0.412035i
$738$	−36.2264	+	87.4582i	−1.33351	+	3.21938i
$739$	−3.22478	+	3.22478i	−0.118625	+	0.118625i	−0.763928	−	0.645302i	$-0.776732\pi$
$739$	−3.22478	+	3.22478i	−0.118625	+	0.118625i	0.645302	+	0.763928i	$0.276732\pi$
$740$	0.525821	−	0.525821i	0.0193295	−	0.0193295i
$741$	−0.377364	+	0.911036i	−0.0138628	+	0.0334677i
$742$	8.13538	+	3.36978i	0.298659	+	0.123709i
$743$	12.7331	+	30.7404i	0.467131	+	1.12776i	0.965410	+	0.260738i	$0.0839658\pi$
$743$	12.7331	+	30.7404i	0.467131	+	1.12776i	−0.498278	+	0.867017i	$0.666034\pi$
$744$			39.6601i			1.45401i
$745$	6.50477	−	2.69437i	0.238316	−	0.0987139i
$746$	−20.4027	−	20.4027i	−0.746996	−	0.746996i
$747$	87.3686			3.19665
$748$	−3.12511	+	6.64516i	−0.114265	+	0.242971i
$749$	−16.3079			−0.595877
$750$	3.30858	+	3.30858i	0.120812	+	0.120812i
$751$	−24.4052	+	10.1090i	−0.890558	+	0.368881i	−0.780582	−	0.625053i	$-0.785077\pi$
$751$	−24.4052	+	10.1090i	−0.890558	+	0.368881i	−0.109976	+	0.993934i	$0.535077\pi$
$752$			21.4268i			0.781355i
$753$	3.78460	+	9.13684i	0.137919	+	0.332965i
$754$	−0.897710	−	0.371844i	−0.0326927	−	0.0135418i
$755$	−2.43267	+	5.87300i	−0.0885341	+	0.213740i
$756$	−9.40007	+	9.40007i	−0.341877	+	0.341877i
$757$	15.6840	−	15.6840i	0.570043	−	0.570043i	−0.362097	−	0.932140i	$-0.617939\pi$
$757$	15.6840	−	15.6840i	0.570043	−	0.570043i	0.932140	+	0.362097i	$0.117939\pi$
$758$	−11.9425	+	28.8317i	−0.433771	+	1.04722i
$759$	−38.3501	−	15.8851i	−1.39202	−	0.576594i
$760$	−2.42080	−	5.84433i	−0.0878117	−	0.211996i
$761$			23.1817i			0.840337i	0.907446	+	0.420168i	$0.138029\pi$
$761$			23.1817i			0.840337i	−0.907446	+	0.420168i	$0.861971\pi$
$762$	34.6696	−	14.3606i	1.25595	−	0.520231i
$763$	−37.4438	−	37.4438i	−1.35556	−	1.35556i
$764$	−3.73547			−0.135145
$765$	−22.5652	−	10.6121i	−0.815847	−	0.383680i
$766$	16.9996			0.614219
$767$	−0.553247	−	0.553247i	−0.0199766	−	0.0199766i
$768$	26.8475	−	11.1206i	0.968777	−	0.401281i
$769$			16.7701i			0.604747i	0.953190	+	0.302373i	$0.0977789\pi$
$769$			16.7701i			0.604747i	−0.953190	+	0.302373i	$0.902221\pi$
$770$	−8.72629	−	21.0671i	−0.314474	−	0.759206i
$771$	59.4653	+	24.6313i	2.14159	+	0.887076i
$772$	−2.95287	+	7.12886i	−0.106276	+	0.256573i
$773$	9.68077	−	9.68077i	0.348193	−	0.348193i	−0.511243	−	0.859436i	$-0.670815\pi$
$773$	9.68077	−	9.68077i	0.348193	−	0.348193i	0.859436	+	0.511243i	$0.170815\pi$
$774$	−16.8612	+	16.8612i	−0.606063	+	0.606063i
$775$	−2.05261	+	4.95543i	−0.0737318	+	0.178004i
$776$	17.4336	+	7.22124i	0.625830	+	0.259227i
$777$	−7.04537	−	17.0090i	−0.252751	−	0.610195i
$778$		−	36.9463i		−	1.32459i
$779$	23.9232	−	9.90931i	0.857137	−	0.355038i
$780$	−0.113729	−	0.113729i	−0.00407214	−	0.00407214i
$781$	30.6253			1.09586
$782$	7.07014	+	19.6239i	0.252828	+	0.701749i
$783$	−44.9537			−1.60651
$784$	−16.2721	−	16.2721i	−0.581147	−	0.581147i
$785$	15.4970	−	6.41908i	0.553113	−	0.229107i
$786$		−	66.4854i		−	2.37145i
$787$	−11.1862	−	27.0058i	−0.398743	−	0.962651i	−0.987965	−	0.154680i	$-0.950565\pi$
$787$	−11.1862	−	27.0058i	−0.398743	−	0.962651i	0.589221	−	0.807972i	$-0.299435\pi$
$788$	4.14521	+	1.71700i	0.147667	+	0.0611656i
$789$	11.6688	−	28.1710i	0.415420	−	1.00291i
$790$	−5.66535	+	5.66535i	−0.201564	+	0.201564i
$791$	18.0076	−	18.0076i	0.640275	−	0.640275i
$792$	24.1411	−	58.2817i	0.857816	−	2.07095i
$793$	−0.475718	−	0.197049i	−0.0168932	−	0.00699740i
$794$	16.8981	+	40.7957i	0.599692	+	1.44778i
$795$			4.92885i			0.174808i
$796$	−6.01797	+	2.49272i	−0.213301	+	0.0883522i
$797$	10.0043	+	10.0043i	0.354369	+	0.354369i	0.861732	−	0.507363i	$-0.169380\pi$
$797$	10.0043	+	10.0043i	0.354369	+	0.354369i	−0.507363	+	0.861732i	$0.669380\pi$
$798$	41.5976			1.47254
$799$	0.888070	−	18.9240i	0.0314176	−	0.669482i
$800$	2.33759			0.0826463
$801$	−2.56964	−	2.56964i	−0.0907938	−	0.0907938i
$802$	12.5407	−	5.19452i	0.442827	−	0.183425i
$803$			62.0584i			2.18999i
$804$	−3.32821	−	8.03500i	−0.117377	−	0.283373i
$805$	−10.3801	−	4.29958i	−0.365850	−	0.151540i
$806$	0.406753	−	0.981990i	0.0143273	−	0.0345891i
$807$	−32.0694	+	32.0694i	−1.12890	+	1.12890i
$808$	−29.2860	+	29.2860i	−1.03028	+	1.03028i
$809$	6.56799	−	15.8565i	0.230918	−	0.557486i	−0.765368	−	0.643593i	$-0.777443\pi$
$809$	6.56799	−	15.8565i	0.230918	−	0.557486i	0.996286	+	0.0861076i	$0.0274429\pi$
$810$	−13.5567	−	5.61539i	−0.476335	−	0.197305i
$811$	17.3259	+	41.8285i	0.608396	+	1.46880i	0.864744	+	0.502214i	$0.167481\pi$
$811$	17.3259	+	41.8285i	0.608396	+	1.46880i	−0.256348	+	0.966585i	$0.582519\pi$
$812$			7.11003i			0.249513i
$813$	−18.9056	+	7.83097i	−0.663050	+	0.274644i
$814$	−8.26897	−	8.26897i	−0.289827	−	0.289827i
$815$	−4.59441			−0.160935
$816$	−54.4112	+	19.6034i	−1.90477	+	0.686255i
$817$	6.52262			0.228197
$818$	−11.6123	−	11.6123i	−0.406013	−	0.406013i
$819$	−2.45905	+	1.01857i	−0.0859262	+	0.0355918i
$820$			4.22346i			0.147490i
$821$	−9.18115	−	22.1652i	−0.320424	−	0.773572i	−0.999229	−	0.0392539i	$-0.987502\pi$
$821$	−9.18115	−	22.1652i	−0.320424	−	0.773572i	0.678805	−	0.734319i	$-0.262498\pi$
$822$	−36.8776	−	15.2752i	−1.28626	−	0.532784i
$823$	16.5962	−	40.0669i	0.578509	−	1.39664i	−0.315642	−	0.948878i	$-0.602220\pi$
$823$	16.5962	−	40.0669i	0.578509	−	1.39664i	0.894151	−	0.447766i	$-0.147780\pi$
$824$	−7.51346	+	7.51346i	−0.261744	+	0.261744i
$825$	9.02522	−	9.02522i	0.314218	−	0.314218i
$826$	−12.6305	+	30.4928i	−0.439473	+	1.06098i
$827$	−35.5628	−	14.7306i	−1.23664	−	0.512233i	−0.333978	−	0.942581i	$-0.608391\pi$
$827$	−35.5628	−	14.7306i	−1.23664	−	0.512233i	−0.902663	+	0.430347i	$0.858391\pi$
$828$	3.15929	+	7.62721i	0.109793	+	0.265064i
$829$			54.4489i			1.89109i	0.325492	+	0.945545i	$0.394470\pi$
$829$			54.4489i			1.89109i	−0.325492	+	0.945545i	$0.605530\pi$
$830$	20.7612	−	8.59955i	0.720630	−	0.298495i
$831$	36.8427	+	36.8427i	1.27806	+	1.27806i
$832$	0.724904			0.0251315
$833$	13.6970	+	15.0458i	0.474572	+	0.521307i
$834$	−31.9916			−1.10778
$835$	14.8680	+	14.8680i	0.514528	+	0.514528i
$836$	4.23437	−	1.75393i	0.146449	−	0.0606610i
$837$		−	49.1740i		−	1.69970i
$838$	−8.50583	−	20.5349i	−0.293829	−	0.709366i
$839$	−10.9808	−	4.54840i	−0.379100	−	0.157028i	0.184993	−	0.982740i	$-0.440774\pi$
$839$	−10.9808	−	4.54840i	−0.379100	−	0.157028i	−0.564093	+	0.825712i	$0.690774\pi$
$840$	9.77541	−	23.5999i	0.337284	−	0.814275i
$841$	3.50507	−	3.50507i	0.120864	−	0.120864i
$842$	−20.0953	+	20.0953i	−0.692529	+	0.692529i
$843$	20.7453	−	50.0835i	0.714505	−	1.72497i
$844$	3.39457	+	1.40608i	0.116846	+	0.0483991i
$845$	4.96867	+	11.9954i	0.170928	+	0.412656i
$846$		−	43.2266i		−	1.48616i
$847$	−22.3586	+	9.26124i	−0.768251	+	0.318220i
$848$	5.40317	+	5.40317i	0.185546	+	0.185546i
$849$	−56.8546			−1.95124
$850$	−6.40664	−	0.300653i	−0.219746	−	0.0103123i
$851$	−5.76186			−0.197514
$852$	−6.44330	−	6.44330i	−0.220744	−	0.220744i
$853$	−31.7617	+	13.1561i	−1.08750	+	0.450457i	−0.853134	−	0.521692i	$-0.825301\pi$
$853$	−31.7617	+	13.1561i	−1.08750	+	0.450457i	−0.234365	+	0.972149i	$0.575301\pi$
$854$			21.7211i			0.743281i
$855$	5.95589	+	14.3788i	0.203687	+	0.491745i
$856$	−10.7206	−	4.44064i	−0.366424	−	0.151778i
$857$	7.05760	−	17.0386i	0.241083	−	0.582026i	−0.756308	−	0.654216i	$-0.772999\pi$
$857$	7.05760	−	17.0386i	0.241083	−	0.582026i	0.997391	+	0.0721899i	$0.0229988\pi$
$858$	−1.78848	+	1.78848i	−0.0610576	+	0.0610576i
$859$	17.2644	−	17.2644i	0.589054	−	0.589054i	−0.348321	−	0.937375i	$-0.613248\pi$
$859$	17.2644	−	17.2644i	0.589054	−	0.589054i	0.937375	+	0.348321i	$0.113248\pi$
$860$	−0.407123	+	0.982883i	−0.0138828	+	0.0335160i
$861$	96.6040	+	40.0147i	3.29225	+	1.36370i
$862$	−12.5262	−	30.2410i	−0.426645	−	1.03001i
$863$			22.5253i			0.766770i	0.923589	+	0.383385i	$0.125242\pi$
$863$			22.5253i			0.766770i	−0.923589	+	0.383385i	$0.874758\pi$
$864$	−19.7995	+	8.20121i	−0.673592	+	0.279011i
$865$	−8.87590	−	8.87590i	−0.301790	−	0.301790i
$866$	−5.56353			−0.189056
$867$	48.8680	−	15.0584i	1.65964	−	0.511409i
$868$	−7.77753			−0.263987
$869$	15.4541	+	15.4541i	0.524243	+	0.524243i
$870$	−21.1966	+	8.77994i	−0.718633	+	0.297668i
$871$		−	0.877548i		−	0.0297346i
$872$	−14.4192	−	34.8111i	−0.488297	−	1.17885i
$873$	−42.8919	−	17.7664i	−1.45167	−	0.601302i
$874$	4.98203	−	12.0277i	0.168520	−	0.406843i
$875$	2.44282	−	2.44282i	0.0825825	−	0.0825825i
$876$	13.0566	−	13.0566i	0.441140	−	0.441140i
$877$	21.6461	−	52.2583i	0.730937	−	1.76464i	0.0914856	−	0.995806i	$-0.470838\pi$
$877$	21.6461	−	52.2583i	0.730937	−	1.76464i	0.639451	−	0.768832i	$-0.279162\pi$
$878$	−4.72519	−	1.95724i	−0.159467	−	0.0660535i
$879$	8.66990	+	20.9310i	0.292428	+	0.705984i
$880$		−	19.7875i		−	0.667037i
$881$	30.6744	−	12.7058i	1.03345	−	0.428068i	0.199492	−	0.979899i	$-0.436071\pi$
$881$	30.6744	−	12.7058i	1.03345	−	0.428068i	0.833956	+	0.551831i	$0.186071\pi$
$882$	32.8275	+	32.8275i	1.10536	+	1.10536i
$883$	−11.2453			−0.378433			−0.189217	−	0.981935i	$-0.560595\pi$
$883$	−11.2453			−0.378433			−0.189217	+	0.981935i	$0.560595\pi$
$884$	0.220221	+	0.0103346i	0.00740682	+	0.000347590i
$885$	−18.4742			−0.621002
$886$	27.4315	+	27.4315i	0.921580	+	0.921580i
$887$	−0.934751	+	0.387187i	−0.0313859	+	0.0130005i	−0.398321	−	0.917246i	$-0.630407\pi$
$887$	−0.934751	+	0.387187i	−0.0313859	+	0.0130005i	0.366935	+	0.930246i	$0.380407\pi$
$888$		−	13.1000i		−	0.439608i
$889$	−10.6029	−	25.5976i	−0.355609	−	0.858516i
$890$	−0.863542	−	0.357691i	−0.0289460	−	0.0119898i
$891$	−15.3178	+	36.9804i	−0.513165	+	1.23889i
$892$	6.28002	−	6.28002i	0.210271	−	0.210271i
$893$	−8.36094	+	8.36094i	−0.279788	+	0.279788i
$894$	−12.6070	+	30.4361i	−0.421642	+	1.01793i
$895$	−11.2285	−	4.65099i	−0.375326	−	0.155465i
$896$	−17.8830	−	43.1734i	−0.597430	−	1.44232i
$897$			1.24622i			0.0416100i
$898$	−13.8775	+	5.74827i	−0.463100	+	0.191822i
$899$	−18.5971	−	18.5971i	−0.620249	−	0.620249i
$900$	−2.53847			−0.0846156
$901$	−4.54809	−	4.99598i	−0.151519	−	0.166440i
$902$	66.4174			2.21146
$903$	18.6244	+	18.6244i	0.619782	+	0.619782i
$904$	16.7414	−	6.93453i	0.556812	−	0.230639i
$905$		−	15.2624i		−	0.507341i
$906$	−11.3826	−	27.4800i	−0.378161	−	0.912961i
$907$	16.9354	+	7.01488i	0.562331	+	0.232925i	0.645697	−	0.763594i	$-0.276567\pi$
$907$	16.9354	+	7.01488i	0.562331	+	0.232925i	−0.0833657	+	0.996519i	$0.526567\pi$
$908$	4.11731	−	9.94006i	0.136638	−	0.329872i
$909$	72.0523	−	72.0523i	2.38983	−	2.38983i
$910$	−0.484081	+	0.484081i	−0.0160471	+	0.0160471i
$911$	10.6365	−	25.6787i	0.352402	−	0.850772i	−0.643921	−	0.765092i	$-0.722694\pi$
$911$	10.6365	−	25.6787i	0.352402	−	0.850772i	0.996323	−	0.0856806i	$-0.0273065\pi$
$912$	33.3492	+	13.8137i	1.10430	+	0.457417i
$913$	−23.4580	−	56.6327i	−0.776348	−	1.87427i
$914$		−	31.8538i		−	1.05363i
$915$	−11.2326	+	4.65269i	−0.371338	+	0.153813i
$916$	−2.10734	−	2.10734i	−0.0696286	−	0.0696286i
$917$	−49.0881			−1.62103
$918$	55.3193	−	19.9305i	1.82581	−	0.657806i
$919$	−13.6372			−0.449850			−0.224925	−	0.974376i	$-0.572214\pi$
$919$	−13.6372			−0.449850			−0.224925	+	0.974376i	$0.572214\pi$
$920$	−5.65300	−	5.65300i	−0.186374	−	0.186374i
$921$	−21.5949	+	8.94489i	−0.711575	+	0.294744i
$922$			29.3218i			0.965661i
$923$	−0.351855	−	0.849453i	−0.0115814	−	0.0279601i
$924$	17.0987	+	7.08253i	0.562507	+	0.232998i
$925$	0.677990	−	1.63681i	0.0222922	−	0.0538181i
$926$	2.34760	−	2.34760i	0.0771468	−	0.0771468i
$927$	18.4854	−	18.4854i	0.607139	−	0.607139i
$928$	−4.38635	+	10.5896i	−0.143989	+	0.347620i
$929$	−48.4225	−	20.0573i	−1.58869	−	0.658057i	−0.598931	−	0.800800i	$-0.704408\pi$
$929$	−48.4225	−	20.0573i	−1.58869	−	0.658057i	−0.989760	+	0.142743i	$0.954408\pi$
$930$	−9.60422	−	23.1866i	−0.314935	−	0.760320i
$931$		−	12.6991i		−	0.416195i
$932$	9.19587	−	3.80905i	0.301221	−	0.124770i
$933$	18.3872	+	18.3872i	0.601969	+	0.601969i
$934$	−36.1876			−1.18409
$935$	−0.820127	+	17.4762i	−0.0268210	+	0.571532i
$936$	−1.89391			−0.0619045
$937$	22.9966	+	22.9966i	0.751266	+	0.751266i	0.974715	−	0.223450i	$-0.0717318\pi$
$937$	22.9966	+	22.9966i	0.751266	+	0.751266i	−0.223450	+	0.974715i	$0.571732\pi$
$938$	−34.2006	+	14.1664i	−1.11669	+	0.462548i
$939$			37.1122i			1.21111i
$940$	−0.738030	−	1.78176i	−0.0240719	−	0.0581147i
$941$	16.0374	+	6.64290i	0.522804	+	0.216552i	0.628448	−	0.777852i	$-0.283690\pi$
$941$	16.0374	+	6.64290i	0.522804	+	0.216552i	−0.105644	+	0.994404i	$0.533690\pi$
$942$	−30.0351	+	72.5113i	−0.978598	+	2.36254i
$943$	23.1400	−	23.1400i	0.753541	−	0.753541i
$944$	−20.2520	+	20.2520i	−0.659148	+	0.659148i
$945$	−12.1204	+	29.2612i	−0.394277	+	0.951868i
$946$	15.4566	+	6.40235i	0.502539	+	0.208158i
$947$	5.46073	+	13.1834i	0.177450	+	0.428402i	0.987430	−	0.158055i	$-0.0505224\pi$
$947$	5.46073	+	13.1834i	0.177450	+	0.428402i	−0.809980	+	0.586457i	$0.800522\pi$
$948$		−	6.50280i		−	0.211201i
$949$	1.72131	−	0.712990i	0.0558761	−	0.0231446i
$950$	2.83056	+	2.83056i	0.0918356	+	0.0918356i
$951$	−24.5828			−0.797152
$952$	11.8683	+	32.9416i	0.384653	+	1.06764i
$953$	30.1090			0.975326			0.487663	−	0.873032i	$-0.337850\pi$
$953$	30.1090			0.975326			0.487663	+	0.873032i	$0.337850\pi$
$954$	−10.9004	−	10.9004i	−0.352914	−	0.352914i
$955$	−8.22227	+	3.40577i	−0.266066	+	0.110208i
$956$			0.0458829i			0.00148396i
$957$	23.9501	+	57.8207i	0.774197	+	1.86908i
$958$	44.8571	+	18.5804i	1.44927	+	0.600306i
$959$	−11.2781	+	27.2279i	−0.364190	+	0.879233i
$960$	12.1031	−	12.1031i	0.390626	−	0.390626i
$961$	−1.57724	+	1.57724i	−0.0508787	+	0.0508787i
$962$	−0.134354	+	0.324358i	−0.00433173	+	0.0104577i
$963$	26.3760	+	10.9253i	0.849954	+	0.352063i
$964$	2.80880	+	6.78105i	0.0904654	+	0.218403i
$965$			18.3838i			0.591796i
$966$	48.5689	−	20.1179i	1.56268	−	0.647282i
$967$	−12.3882	−	12.3882i	−0.398378	−	0.398378i	0.479282	−	0.877661i	$-0.340897\pi$
$967$	−12.3882	−	12.3882i	−0.398378	−	0.398378i	−0.877661	+	0.479282i	$0.840897\pi$
$968$	−17.2202			−0.553477
$969$	−28.8812	−	13.5823i	−0.927797	−	0.436328i
$970$	−11.9410			−0.383402
$971$	−8.22783	−	8.22783i	−0.264044	−	0.264044i	0.562651	−	0.826695i	$-0.309782\pi$
$971$	−8.22783	−	8.22783i	−0.264044	−	0.264044i	−0.826695	+	0.562651i	$0.809782\pi$
$972$	0.337716	−	0.139886i	0.0108322	−	0.00448686i
$973$			23.6203i			0.757234i
$974$	−8.72253	−	21.0581i	−0.279488	−	0.674744i
$975$	−0.354023	−	0.146641i	−0.0113378	−	0.00469627i
$976$	−7.21312	+	17.4140i	−0.230886	+	0.557409i
$977$	30.6475	−	30.6475i	0.980501	−	0.980501i	−0.0193125	−	0.999813i	$-0.506148\pi$
$977$	30.6475	−	30.6475i	0.980501	−	0.980501i	0.999813	+	0.0193125i	$0.00614775\pi$
$978$	15.2010	−	15.2010i	0.486073	−	0.486073i
$979$	−0.975716	+	2.35559i	−0.0311840	+	0.0752849i
$980$	1.91360	+	0.792640i	0.0611278	+	0.0253200i
$981$	35.4756	+	85.6457i	1.13265	+	2.73446i
$982$		−	21.5620i		−	0.688072i
$983$	41.0128	−	16.9881i	1.30811	−	0.541835i	0.383774	−	0.923427i	$-0.374624\pi$
$983$	41.0128	−	16.9881i	1.30811	−	0.541835i	0.924331	+	0.381592i	$0.124624\pi$
$984$	52.6105	+	52.6105i	1.67716	+	1.67716i
$985$	10.6896			0.340599
$986$	13.3837	−	28.4587i	0.426223	−	0.906310i
$987$	−47.7470			−1.51980
$988$	−0.0972974	−	0.0972974i	−0.00309544	−	0.00309544i
$989$	7.61573	−	3.15454i	0.242166	−	0.100308i
$990$			39.9195i			1.26873i
$991$	−22.0859	−	53.3201i	−0.701583	−	1.69377i	−0.720033	−	0.693940i	$-0.755873\pi$
$991$	−22.0859	−	53.3201i	−0.701583	−	1.69377i	0.0184501	−	0.999830i	$-0.494127\pi$
$992$	−11.5838	−	4.79815i	−0.367785	−	0.152341i
$993$	27.0122	−	65.2132i	0.857206	−	2.06948i
$994$	−27.4256	+	27.4256i	−0.869889	+	0.869889i
$995$	−10.9736	+	10.9736i	−0.347887	+	0.347887i
$996$	−6.97967	+	16.8504i	−0.221159	+	0.533926i
$997$	10.7781	+	4.46444i	0.341346	+	0.141390i	0.546770	−	0.837283i	$-0.315857\pi$
$997$	10.7781	+	4.46444i	0.341346	+	0.141390i	−0.205424	+	0.978673i	$0.565857\pi$
$998$	−23.8303	−	57.5315i	−0.754336	−	1.82113i
$999$			16.2425i			0.513891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.36.3	yes	24
3.2	odd	2		765.2.be.b.631.4		24
5.2	odd	4		425.2.n.c.274.4		24
5.3	odd	4		425.2.n.f.274.3		24
5.4	even	2		425.2.m.b.376.4		24
17.3	odd	16		1445.2.a.q.1.4		12
17.5	odd	16		1445.2.d.j.866.18		24
17.9	even	8	inner	85.2.l.a.26.3	✓	24
17.12	odd	16		1445.2.d.j.866.17		24
17.14	odd	16		1445.2.a.p.1.4		12
51.26	odd	8		765.2.be.b.451.4		24
85.9	even	8		425.2.m.b.26.4		24
85.14	odd	16		7225.2.a.bs.1.9		12
85.43	odd	8		425.2.n.c.349.4		24
85.54	odd	16		7225.2.a.bq.1.9		12
85.77	odd	8		425.2.n.f.349.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.3	✓	24	17.9	even	8	inner
85.2.l.a.36.3	yes	24	1.1	even	1	trivial
425.2.m.b.26.4		24	85.9	even	8
425.2.m.b.376.4		24	5.4	even	2
425.2.n.c.274.4		24	5.2	odd	4
425.2.n.c.349.4		24	85.43	odd	8
425.2.n.f.274.3		24	5.3	odd	4
425.2.n.f.349.3		24	85.77	odd	8
765.2.be.b.451.4		24	51.26	odd	8
765.2.be.b.631.4		24	3.2	odd	2
1445.2.a.p.1.4		12	17.14	odd	16
1445.2.a.q.1.4		12	17.3	odd	16
1445.2.d.j.866.17		24	17.12	odd	16
1445.2.d.j.866.18		24	17.5	odd	16
7225.2.a.bq.1.9		12	85.54	odd	16
7225.2.a.bs.1.9		12	85.14	odd	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	85.l (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.09994 - 1.09994i) q^{2} +(2.77900 - 1.15110i) q^{3} +0.419729i q^{4} +(0.382683 + 0.923880i) q^{5} +(-4.32287 - 1.79059i) q^{6} +(-1.32205 + 3.19170i) q^{7} +(-1.73820 + 1.73820i) q^{8} +(4.27649 - 4.27649i) q^{9} +O(q^{10})\)	\(q+(-1.09994 - 1.09994i) q^{2} +(2.77900 - 1.15110i) q^{3} +0.419729i q^{4} +(0.382683 + 0.923880i) q^{5} +(-4.32287 - 1.79059i) q^{6} +(-1.32205 + 3.19170i) q^{7} +(-1.73820 + 1.73820i) q^{8} +(4.27649 - 4.27649i) q^{9} +(0.595282 - 1.43714i) q^{10} +(-3.92026 - 1.62382i) q^{11} +(0.483150 + 1.16643i) q^{12} +0.127392i q^{13} +(4.96485 - 2.05651i) q^{14} +(2.12695 + 2.12695i) q^{15} +4.66329 q^{16} +(-4.11857 - 0.193278i) q^{17} -9.40776 q^{18} +(1.81966 + 1.81966i) q^{19} +(-0.387779 + 0.160623i) q^{20} +10.3916i q^{21} +(2.52594 + 6.09815i) q^{22} +(3.00465 + 1.24457i) q^{23} +(-2.82962 + 6.83130i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.140123 - 0.140123i) q^{26} +(3.50841 - 8.47004i) q^{27} +(-1.33965 - 0.554901i) q^{28} +(-1.87644 - 4.53013i) q^{29} -4.67904i q^{30} +(4.95543 - 2.05261i) q^{31} +(-1.65293 - 1.65293i) q^{32} -12.7636 q^{33} +(4.31758 + 4.74277i) q^{34} -3.45467 q^{35} +(1.79497 + 1.79497i) q^{36} +(-1.63681 + 0.677990i) q^{37} -4.00302i q^{38} +(0.146641 + 0.354023i) q^{39} +(-2.27107 - 0.940707i) q^{40} +(3.85069 - 9.29639i) q^{41} +(11.4301 - 11.4301i) q^{42} +(1.79227 - 1.79227i) q^{43} +(0.681566 - 1.64545i) q^{44} +(5.58751 + 2.31442i) q^{45} +(-1.93598 - 4.67388i) q^{46} +4.59479i q^{47} +(12.9593 - 5.36791i) q^{48} +(-3.48941 - 3.48941i) q^{49} +1.55555 q^{50} +(-11.6680 + 4.20377i) q^{51} -0.0534701 q^{52} +(1.15866 + 1.15866i) q^{53} +(-13.1756 + 5.45749i) q^{54} -4.24326i q^{55} +(-3.24984 - 7.84580i) q^{56} +(7.15144 + 2.96222i) q^{57} +(-2.91889 + 7.04683i) q^{58} +(-4.34287 + 4.34287i) q^{59} +(-0.892745 + 0.892745i) q^{60} +(-1.54679 + 3.73428i) q^{61} +(-7.70840 - 3.19293i) q^{62} +(7.99557 + 19.3030i) q^{63} -5.69034i q^{64} +(-0.117695 + 0.0487508i) q^{65} +(14.0392 + 14.0392i) q^{66} -6.88856 q^{67} +(0.0811242 - 1.72868i) q^{68} +9.78255 q^{69} +(3.79993 + 3.79993i) q^{70} +(-6.66802 + 2.76198i) q^{71} +14.8668i q^{72} +(-5.59682 - 13.5119i) q^{73} +(2.54614 + 1.05465i) q^{74} +(-1.15110 + 2.77900i) q^{75} +(-0.763763 + 0.763763i) q^{76} +(10.3655 - 10.3655i) q^{77} +(0.228107 - 0.550699i) q^{78} +(-4.75854 - 1.97105i) q^{79} +(1.78456 + 4.30831i) q^{80} -9.43315i q^{81} +(-14.4610 + 5.98994i) q^{82} +(10.2150 + 10.2150i) q^{83} -4.36164 q^{84} +(-1.39754 - 3.87903i) q^{85} -3.94276 q^{86} +(-10.4293 - 10.4293i) q^{87} +(9.63673 - 3.99166i) q^{88} -0.600876i q^{89} +(-3.60019 - 8.69163i) q^{90} +(-0.406598 - 0.168418i) q^{91} +(-0.522381 + 1.26114i) q^{92} +(11.4084 - 11.4084i) q^{93} +(5.05398 - 5.05398i) q^{94} +(-0.984791 + 2.37750i) q^{95} +(-6.49616 - 2.69080i) q^{96} +(-2.93763 - 7.09206i) q^{97} +7.67628i q^{98} +(-23.7092 + 9.82068i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 - 24 * q^9	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35} - 24 q^{36} + 24 q^{37} + 8 q^{39} + 16 q^{40} + 16 q^{41} - 24 q^{42} + 8 q^{43} + 16 q^{44} + 16 q^{45} + 8 q^{46} + 80 q^{48} + 8 q^{50} - 56 q^{51} - 48 q^{52} + 24 q^{53} - 32 q^{54} + 64 q^{56} + 32 q^{57} - 64 q^{58} + 32 q^{59} + 24 q^{60} + 32 q^{61} - 32 q^{62} - 56 q^{63} + 8 q^{65} + 96 q^{66} + 16 q^{67} - 40 q^{68} + 96 q^{69} - 24 q^{71} - 64 q^{74} - 8 q^{75} - 8 q^{76} + 24 q^{77} - 112 q^{78} - 32 q^{80} - 80 q^{82} - 96 q^{83} - 64 q^{84} - 16 q^{86} - 48 q^{87} - 8 q^{88} - 24 q^{91} + 80 q^{92} + 64 q^{93} + 56 q^{94} - 16 q^{95} - 168 q^{96} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

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