LMFDB - Embedded newform 85.2.l.a.26.1

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			26.1
Character	$\chi$	$=$	85.26
Dual form			85.2.l.a.36.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.93083 + 1.93083i) q^{2} +(-1.42916 - 0.591976i) q^{3} -5.45623i q^{4} +(0.382683 - 0.923880i) q^{5} +(3.90247 - 1.61646i) q^{6} +(-0.483886 - 1.16820i) q^{7} +(6.67340 + 6.67340i) q^{8} +(-0.429267 - 0.429267i) q^{9} +(1.04496 + 2.52275i) q^{10} +(0.386141 - 0.159945i) q^{11} +(-3.22996 + 7.79781i) q^{12} -5.66390i q^{13} +(3.18991 + 1.32130i) q^{14} +(-1.09383 + 1.09383i) q^{15} -14.8580 q^{16} +(1.27807 - 3.92002i) q^{17} +1.65769 q^{18} +(-0.0948539 + 0.0948539i) q^{19} +(-5.04090 - 2.08801i) q^{20} +1.95600i q^{21} +(-0.436747 + 1.05440i) q^{22} +(-6.30014 + 2.60960i) q^{23} +(-5.58684 - 13.4878i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(10.9361 + 10.9361i) q^{26} +(2.13530 + 5.15508i) q^{27} +(-6.37399 + 2.64019i) q^{28} +(-0.126098 + 0.304427i) q^{29} -4.22400i q^{30} +(-0.559556 - 0.231776i) q^{31} +(15.3415 - 15.3415i) q^{32} -0.646540 q^{33} +(5.10115 + 10.0366i) q^{34} -1.26445 q^{35} +(-2.34218 + 2.34218i) q^{36} +(8.16448 + 3.38184i) q^{37} -0.366294i q^{38} +(-3.35290 + 8.09461i) q^{39} +(8.71922 - 3.61162i) q^{40} +(0.625194 + 1.50935i) q^{41} +(-3.77670 - 3.77670i) q^{42} +(-1.41246 - 1.41246i) q^{43} +(-0.872696 - 2.10687i) q^{44} +(-0.560864 + 0.232318i) q^{45} +(7.12581 - 17.2032i) q^{46} -5.06253i q^{47} +(21.2344 + 8.79557i) q^{48} +(3.81919 - 3.81919i) q^{49} +2.73061 q^{50} +(-4.14712 + 4.84573i) q^{51} -30.9036 q^{52} +(-1.09104 + 1.09104i) q^{53} +(-14.0765 - 5.83068i) q^{54} -0.417956i q^{55} +(4.56673 - 11.0251i) q^{56} +(0.191712 - 0.0794098i) q^{57} +(-0.344324 - 0.831272i) q^{58} +(0.997758 + 0.997758i) q^{59} +(5.96818 + 5.96818i) q^{60} +(2.98684 + 7.21086i) q^{61} +(1.52793 - 0.632889i) q^{62} +(-0.293755 + 0.709187i) q^{63} +29.5276i q^{64} +(-5.23277 - 2.16748i) q^{65} +(1.24836 - 1.24836i) q^{66} +12.1014 q^{67} +(-21.3885 - 6.97346i) q^{68} +10.5487 q^{69} +(2.44145 - 2.44145i) q^{70} +(-4.45766 - 1.84642i) q^{71} -5.72934i q^{72} +(-1.10994 + 2.67964i) q^{73} +(-22.2940 + 9.23447i) q^{74} +(0.591976 + 1.42916i) q^{75} +(0.517545 + 0.517545i) q^{76} +(-0.373696 - 0.373696i) q^{77} +(-9.15545 - 22.1032i) q^{78} +(4.00751 - 1.65997i) q^{79} +(-5.68590 + 13.7270i) q^{80} -6.81023i q^{81} +(-4.12145 - 1.70716i) q^{82} +(3.10563 - 3.10563i) q^{83} +10.6724 q^{84} +(-3.13253 - 2.68091i) q^{85} +5.45443 q^{86} +(0.360427 - 0.360427i) q^{87} +(3.64425 + 1.50950i) q^{88} -4.98704i q^{89} +(0.634369 - 1.53150i) q^{90} +(-6.61659 + 2.74068i) q^{91} +(14.2386 + 34.3750i) q^{92} +(0.662488 + 0.662488i) q^{93} +(9.77489 + 9.77489i) q^{94} +(0.0513346 + 0.123933i) q^{95} +(-31.0071 + 12.8436i) q^{96} +(0.243150 - 0.587015i) q^{97} +14.7484i q^{98} +(-0.234417 - 0.0970985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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 $

$2$	−1.93083	+	1.93083i	−1.36530	+	1.36530i	−0.498300	+	0.867005i	$0.666042\pi$
$2$	−1.93083	+	1.93083i	−1.36530	+	1.36530i	−0.867005	+	0.498300i	$0.833958\pi$
$3$	−1.42916	−	0.591976i	−0.825124	−	0.341778i	−0.0701535	−	0.997536i	$-0.522349\pi$
$3$	−1.42916	−	0.591976i	−0.825124	−	0.341778i	−0.754971	+	0.655759i	$0.772349\pi$
$4$		−	5.45623i		−	2.72811i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$5$	0.382683	−	0.923880i	0.171141	−	0.413171i
$6$	3.90247	−	1.61646i	1.59318	−	0.659915i
$7$	−0.483886	−	1.16820i	−0.182892	−	0.441540i	0.805668	−	0.592367i	$-0.201806\pi$
$7$	−0.483886	−	1.16820i	−0.182892	−	0.441540i	−0.988560	+	0.150827i	$0.951806\pi$
$8$	6.67340	+	6.67340i	2.35940	+	2.35940i
$9$	−0.429267	−	0.429267i	−0.143089	−	0.143089i
$10$	1.04496	+	2.52275i	0.330445	+	0.797765i
$11$	0.386141	−	0.159945i	0.116426	−	0.0482252i	−0.323710	−	0.946156i	$-0.604930\pi$
$11$	0.386141	−	0.159945i	0.116426	−	0.0482252i	0.440136	+	0.897931i	$0.354930\pi$
$12$	−3.22996	+	7.79781i	−0.932408	+	2.25103i
$13$		−	5.66390i		−	1.57088i	−0.618935	−	0.785442i	$-0.712436\pi$
$13$		−	5.66390i		−	1.57088i	0.618935	−	0.785442i	$-0.287564\pi$
$14$	3.18991	+	1.32130i	0.852539	+	0.353133i
$15$	−1.09383	+	1.09383i	−0.282426	+	0.282426i
$16$	−14.8580			−3.71449
$17$	1.27807	−	3.92002i	0.309978	−	0.950744i
$17$	1.27807	−	3.92002i	0.309978	−	0.950744i
$18$	1.65769			0.390720
$19$	−0.0948539	+	0.0948539i	−0.0217610	+	0.0217610i	−0.717904	−	0.696143i	$-0.754898\pi$
$19$	−0.0948539	+	0.0948539i	−0.0217610	+	0.0217610i	0.696143	+	0.717904i	$0.254898\pi$
$20$	−5.04090	−	2.08801i	−1.12718	−	0.466893i
$21$			1.95600i			0.426833i
$22$	−0.436747	+	1.05440i	−0.0931148	+	0.224799i
$23$	−6.30014	+	2.60960i	−1.31367	+	0.544140i	−0.925953	−	0.377638i	$-0.876736\pi$
$23$	−6.30014	+	2.60960i	−1.31367	+	0.544140i	−0.387717	+	0.921778i	$0.626736\pi$
$24$	−5.58684	−	13.4878i	−1.14041	−	2.75319i
$25$	−0.707107	−	0.707107i	−0.141421	−	0.141421i
$26$	10.9361	+	10.9361i	2.14474	+	2.14474i
$27$	2.13530	+	5.15508i	0.410939	+	0.992095i
$28$	−6.37399	+	2.64019i	−1.20457	+	0.498949i
$29$	−0.126098	+	0.304427i	−0.0234158	+	0.0565307i	−0.935155	−	0.354239i	$-0.884740\pi$
$29$	−0.126098	+	0.304427i	−0.0234158	+	0.0565307i	0.911739	+	0.410770i	$0.134740\pi$
$30$		−	4.22400i		−	0.771194i
$31$	−0.559556	−	0.231776i	−0.100499	−	0.0416281i	0.331867	−	0.943326i	$-0.392321\pi$
$31$	−0.559556	−	0.231776i	−0.100499	−	0.0416281i	−0.432367	+	0.901698i	$0.642321\pi$
$32$	15.3415	−	15.3415i	2.71201	−	2.71201i
$33$	−0.646540			−0.112548
$34$	5.10115	+	10.0366i	0.874840	+	1.72127i
$35$	−1.26445			−0.213732
$36$	−2.34218	+	2.34218i	−0.390363	+	0.390363i
$37$	8.16448	+	3.38184i	1.34223	+	0.555970i	0.934119	−	0.356961i	$-0.116187\pi$
$37$	8.16448	+	3.38184i	1.34223	+	0.555970i	0.408112	+	0.912932i	$0.366187\pi$
$38$		−	0.366294i		−	0.0594207i
$39$	−3.35290	+	8.09461i	−0.536893	+	1.29617i
$40$	8.71922	−	3.61162i	1.37863	−	0.571047i
$41$	0.625194	+	1.50935i	0.0976389	+	0.235721i	0.965150	−	0.261696i	$-0.0842818\pi$
$41$	0.625194	+	1.50935i	0.0976389	+	0.235721i	−0.867511	+	0.497417i	$0.834282\pi$
$42$	−3.77670	−	3.77670i	−0.582757	−	0.582757i
$43$	−1.41246	−	1.41246i	−0.215398	−	0.215398i	0.591158	−	0.806556i	$-0.298671\pi$
$43$	−1.41246	−	1.41246i	−0.215398	−	0.215398i	−0.806556	+	0.591158i	$0.798671\pi$
$44$	−0.872696	−	2.10687i	−0.131564	−	0.317623i
$45$	−0.560864	+	0.232318i	−0.0836087	+	0.0346319i
$46$	7.12581	−	17.2032i	1.05064	−	2.53648i
$47$		−	5.06253i		−	0.738445i	−0.929341	−	0.369223i	$-0.879624\pi$
$47$		−	5.06253i		−	0.738445i	0.929341	−	0.369223i	$-0.120376\pi$
$48$	21.2344	+	8.79557i	3.06492	+	1.26953i
$49$	3.81919	−	3.81919i	0.545599	−	0.545599i
$50$	2.73061			0.386167
$51$	−4.14712	+	4.84573i	−0.580713	+	0.678538i
$52$	−30.9036			−4.28555
$53$	−1.09104	+	1.09104i	−0.149865	+	0.149865i	−0.778058	−	0.628193i	$-0.783795\pi$
$53$	−1.09104	+	1.09104i	−0.149865	+	0.149865i	0.628193	+	0.778058i	$0.283795\pi$
$54$	−14.0765	−	5.83068i	−1.91557	−	0.793455i
$55$		−	0.417956i		−	0.0563572i
$56$	4.56673	−	11.0251i	0.610254	−	1.47328i
$57$	0.191712	−	0.0794098i	0.0253929	−	0.0105181i
$58$	−0.344324	−	0.831272i	−0.0452119	−	0.109151i
$59$	0.997758	+	0.997758i	0.129897	+	0.129897i	0.769066	−	0.639169i	$-0.220722\pi$
$59$	0.997758	+	0.997758i	0.129897	+	0.129897i	−0.639169	+	0.769066i	$0.720722\pi$
$60$	5.96818	+	5.96818i	0.770489	+	0.770489i
$61$	2.98684	+	7.21086i	0.382425	+	0.923256i	0.991496	+	0.130140i	$0.0415427\pi$
$61$	2.98684	+	7.21086i	0.382425	+	0.923256i	−0.609070	+	0.793116i	$0.708457\pi$
$62$	1.52793	−	0.632889i	0.194047	−	0.0803770i
$63$	−0.293755	+	0.709187i	−0.0370097	+	0.0893492i
$64$			29.5276i			3.69095i
$65$	−5.23277	−	2.16748i	−0.649045	−	0.268843i
$66$	1.24836	−	1.24836i	0.153662	−	0.153662i
$67$	12.1014			1.47842			0.739209	−	0.673477i	$-0.235200\pi$
$67$	12.1014			1.47842			0.739209	+	0.673477i	$0.235200\pi$
$68$	−21.3885	−	6.97346i	−2.59374	−	0.845656i
$69$	10.5487			1.26992
$70$	2.44145	−	2.44145i	0.291809	−	0.291809i
$71$	−4.45766	−	1.84642i	−0.529027	−	0.219130i	0.102150	−	0.994769i	$-0.467428\pi$
$71$	−4.45766	−	1.84642i	−0.529027	−	0.219130i	−0.631177	+	0.775639i	$0.717428\pi$
$72$		−	5.72934i		−	0.675209i
$73$	−1.10994	+	2.67964i	−0.129909	+	0.313628i	−0.975428	−	0.220317i	$-0.929291\pi$
$73$	−1.10994	+	2.67964i	−0.129909	+	0.313628i	0.845520	+	0.533944i	$0.179291\pi$
$74$	−22.2940	+	9.23447i	−2.59162	+	1.07349i
$75$	0.591976	+	1.42916i	0.0683555	+	0.165025i
$76$	0.517545	+	0.517545i	0.0593664	+	0.0593664i
$77$	−0.373696	−	0.373696i	−0.0425867	−	0.0425867i
$78$	−9.15545	−	22.1032i	−1.03665	−	2.50270i
$79$	4.00751	−	1.65997i	0.450880	−	0.186761i	−0.145675	−	0.989332i	$-0.546535\pi$
$79$	4.00751	−	1.65997i	0.450880	−	0.186761i	0.596556	+	0.802572i	$0.296535\pi$
$80$	−5.68590	+	13.7270i	−0.635703	+	1.53472i
$81$		−	6.81023i		−	0.756693i
$82$	−4.12145	−	1.70716i	−0.455138	−	0.188524i
$83$	3.10563	−	3.10563i	0.340887	−	0.340887i	−0.515814	−	0.856701i	$-0.672510\pi$
$83$	3.10563	−	3.10563i	0.340887	−	0.340887i	0.856701	+	0.515814i	$0.172510\pi$
$84$	10.6724			1.16445
$85$	−3.13253	−	2.68091i	−0.339770	−	0.290786i
$86$	5.45443			0.588167
$87$	0.360427	−	0.360427i	0.0386418	−	0.0386418i
$88$	3.64425	+	1.50950i	0.388478	+	0.160913i
$89$		−	4.98704i		−	0.528625i	−0.964437	−	0.264313i	$-0.914855\pi$
$89$		−	4.98704i		−	0.528625i	0.964437	−	0.264313i	$-0.0851451\pi$
$90$	0.634369	−	1.53150i	0.0668683	−	0.161434i
$91$	−6.61659	+	2.74068i	−0.693608	+	0.287302i
$92$	14.2386	+	34.3750i	1.48448	+	3.58384i
$93$	0.662488	+	0.662488i	0.0686968	+	0.0686968i
$94$	9.77489	+	9.77489i	1.00820	+	1.00820i
$95$	0.0513346	+	0.123933i	0.00526681	+	0.0127152i
$96$	−31.0071	+	12.8436i	−3.16465	+	1.31084i
$97$	0.243150	−	0.587015i	0.0246881	−	0.0596024i	−0.911055	−	0.412285i	$-0.864731\pi$
$97$	0.243150	−	0.587015i	0.0246881	−	0.0596024i	0.935743	+	0.352683i	$0.114731\pi$
$98$			14.7484i			1.48982i
$99$	−0.234417	−	0.0970985i	−0.0235598	−	0.00975877i
$100$	−3.85814	+	3.85814i	−0.385814	+	0.385814i
$101$	7.45004			0.741307			0.370653	−	0.928771i	$-0.379134\pi$
$101$	7.45004			0.741307			0.370653	+	0.928771i	$0.379134\pi$
$102$	−1.34889	−	17.3637i	−0.133560	−	1.71926i
$103$	13.5860			1.33866			0.669332	−	0.742963i	$-0.266580\pi$
$103$	13.5860			1.33866			0.669332	+	0.742963i	$0.266580\pi$
$104$	37.7975	−	37.7975i	3.70635	−	3.70635i
$105$	1.80710	+	0.748527i	0.176355	+	0.0730488i
$106$		−	4.21322i		−	0.409224i
$107$	−3.54909	+	8.56826i	−0.343103	+	0.828325i	0.654295	+	0.756239i	$0.272965\pi$
$107$	−3.54909	+	8.56826i	−0.343103	+	0.828325i	−0.997398	+	0.0720853i	$0.977035\pi$
$108$	28.1273	−	11.6507i	2.70655	−	1.12109i
$109$	−6.01065	−	14.5110i	−0.575716	−	1.38990i	−0.896625	−	0.442791i	$-0.853988\pi$
$109$	−6.01065	−	14.5110i	−0.575716	−	1.38990i	0.320909	−	0.947110i	$-0.396012\pi$
$110$	0.807003	+	0.807003i	0.0769447	+	0.0769447i
$111$	−9.66635	−	9.66635i	−0.917489	−	0.917489i
$112$	7.18956	+	17.3571i	0.679350	+	1.64010i
$113$	−1.15190	+	0.477131i	−0.108361	+	0.0448847i	−0.436205	−	0.899847i	$-0.643678\pi$
$113$	−1.15190	+	0.477131i	−0.108361	+	0.0448847i	0.327844	+	0.944732i	$0.393678\pi$
$114$	−0.216837	+	0.523492i	−0.0203087	+	0.0490295i
$115$			6.81922i			0.635896i
$116$	1.66102	+	0.688019i	0.154222	+	0.0638809i
$117$	−2.43133	+	2.43133i	−0.224776	+	0.224776i
$118$	−3.85301			−0.354698
$119$	−5.19782	+	0.403791i	−0.476483	+	0.0370155i
$120$	−14.5991			−1.33271
$121$	−7.65465	+	7.65465i	−0.695877	+	0.695877i
$122$	−19.6900	−	8.15588i	−1.78265	−	0.738399i
$123$		−	2.52720i		−	0.227870i
$124$	−1.26462	+	3.05307i	−0.113566	+	0.274173i
$125$	−0.923880	+	0.382683i	−0.0826343	+	0.0342282i
$126$	−0.802130	−	1.93651i	−0.0714594	−	0.172518i
$127$	−12.5973	−	12.5973i	−1.11783	−	1.11783i	−0.992059	−	0.125773i	$-0.959859\pi$
$127$	−12.5973	−	12.5973i	−1.11783	−	1.11783i	−0.125773	−	0.992059i	$-0.540141\pi$
$128$	−26.3300	−	26.3300i	−2.32727	−	2.32727i
$129$	1.18248	+	2.85476i	0.104112	+	0.251348i
$130$	14.2886	−	5.91855i	1.25320	−	0.519091i
$131$	1.71149	−	4.13191i	0.149534	−	0.361007i	−0.831308	−	0.555812i	$-0.812407\pi$
$131$	1.71149	−	4.13191i	0.149534	−	0.361007i	0.980842	+	0.194805i	$0.0624075\pi$
$132$			3.52767i			0.307044i
$133$	0.156707	+	0.0649102i	0.0135882	+	0.00562843i
$134$	−23.3657	+	23.3657i	−2.01849	+	2.01849i
$135$	5.57981			0.480234
$136$	34.6889	−	17.6307i	2.97455	−	1.51182i
$137$	9.04916			0.773122			0.386561	−	0.922264i	$-0.373663\pi$
$137$	9.04916			0.773122			0.386561	+	0.922264i	$0.373663\pi$
$138$	−20.3678	+	20.3678i	−1.73382	+	1.73382i
$139$	4.34294	+	1.79890i	0.368363	+	0.152581i	0.559183	−	0.829044i	$-0.311115\pi$
$139$	4.34294	+	1.79890i	0.368363	+	0.152581i	−0.190820	+	0.981625i	$0.561115\pi$
$140$			6.89915i			0.583085i
$141$	−2.99689	+	7.23514i	−0.252384	+	0.609309i
$142$	12.1721	−	5.04186i	1.02146	−	0.423103i
$143$	−0.905912	−	2.18707i	−0.0757562	−	0.182892i
$144$	6.37804	+	6.37804i	0.531503	+	0.531503i
$145$	0.232998	+	0.232998i	0.0193495	+	0.0193495i
$146$	−3.03082	−	7.31704i	−0.250832	−	0.605562i
$147$	−7.71910	+	3.19735i	−0.636660	+	0.263713i
$148$	18.4521	−	44.5472i	1.51675	−	3.66176i
$149$		−	0.775949i		−	0.0635683i	−0.999495	−	0.0317841i	$-0.989881\pi$
$149$		−	0.775949i		−	0.0635683i	0.999495	−	0.0317841i	$-0.0101189\pi$
$150$	−3.90247	−	1.61646i	−0.318635	−	0.131983i
$151$	1.61724	−	1.61724i	0.131609	−	0.131609i	−0.638234	−	0.769843i	$-0.720335\pi$
$151$	1.61724	−	1.61724i	0.131609	−	0.131609i	0.769843	+	0.638234i	$0.220335\pi$
$152$	−1.26600			−0.102686
$153$	−2.23137	+	1.13410i	−0.180395	+	0.0916865i
$154$	1.44309			0.116288
$155$	−0.428266	+	0.428266i	−0.0343991	+	0.0343991i
$156$	44.1660	+	18.2942i	3.53611	+	1.46471i
$157$			19.1134i			1.52541i	0.646745	+	0.762707i	$0.276130\pi$
$157$			19.1134i			1.52541i	−0.646745	+	0.762707i	$0.723870\pi$
$158$	−4.53272	+	10.9430i	−0.360604	+	0.870575i
$159$	2.20513	−	0.913395i	0.174878	−	0.0724369i
$160$	−8.30274	−	20.0446i	−0.656389	−	1.58466i
$161$	6.09710	+	6.09710i	0.480519	+	0.480519i
$162$	13.1494	+	13.1494i	1.03312	+	1.03312i
$163$	7.01440	+	16.9343i	0.549410	+	1.32639i	0.917918	+	0.396769i	$0.129869\pi$
$163$	7.01440	+	16.9343i	0.549410	+	1.32639i	−0.368508	+	0.929625i	$0.620131\pi$
$164$	8.23536	−	3.41120i	0.643074	−	0.266370i
$165$	−0.247420	+	0.597325i	−0.0192616	+	0.0465017i
$166$			11.9929i			0.930829i
$167$	−18.6147	−	7.71045i	−1.44045	−	0.596653i	−0.480540	−	0.876973i	$-0.659559\pi$
$167$	−18.6147	−	7.71045i	−1.44045	−	0.596653i	−0.959907	+	0.280320i	$0.909559\pi$
$168$	−13.0531	+	13.0531i	−1.00707	+	1.00707i
$169$	−19.0798			−1.46768
$170$	11.2248	−	0.871993i	0.860901	−	0.0668788i
$171$	0.0814353			0.00622751
$172$	−7.70668	+	7.70668i	−0.587629	+	0.587629i
$173$	17.6594	+	7.31475i	1.34262	+	0.556130i	0.934227	−	0.356678i	$-0.116091\pi$
$173$	17.6594	+	7.31475i	1.34262	+	0.556130i	0.408389	+	0.912808i	$0.366091\pi$
$174$			1.39185i			0.105516i
$175$	−0.483886	+	1.16820i	−0.0365783	+	0.0883079i
$176$	−5.73727	+	2.37646i	−0.432463	+	0.179132i
$177$	−0.835303	−	2.01660i	−0.0627852	−	0.151577i
$178$	9.62914	+	9.62914i	0.721735	+	0.721735i
$179$	14.0116	+	14.0116i	1.04727	+	1.04727i	0.998826	+	0.0484485i	$0.0154277\pi$
$179$	14.0116	+	14.0116i	1.04727	+	1.04727i	0.0484485	+	0.998826i	$0.484572\pi$
$180$	1.26758	+	3.06020i	0.0944797	+	0.228094i
$181$	8.19070	−	3.39270i	0.608810	−	0.252177i	−0.0569098	−	0.998379i	$-0.518125\pi$
$181$	8.19070	−	3.39270i	0.608810	−	0.252177i	0.665719	+	0.746202i	$0.268125\pi$
$182$	7.48374	−	18.0673i	0.554731	−	1.33924i
$183$		−	12.0736i		−	0.892505i
$184$	−59.4583	−	24.6284i	−4.38332	−	1.81563i
$185$	6.24882	−	6.24882i	0.459422	−	0.459422i
$186$	−2.55831			−0.187584
$187$	−0.133470	−	1.71810i	−0.00976030	−	0.125640i
$188$	−27.6223			−2.01456
$189$	4.98894	−	4.98894i	0.362892	−	0.362892i
$190$	−0.338412	−	0.140175i	−0.0245510	−	0.0101693i
$191$		−	10.6081i		−	0.767576i	−0.923421	−	0.383788i	$-0.874619\pi$
$191$		−	10.6081i		−	0.767576i	0.923421	−	0.383788i	$-0.125381\pi$
$192$	17.4797	−	42.1996i	1.26149	−	3.04550i
$193$	−8.98505	+	3.72173i	−0.646758	+	0.267896i	−0.681854	−	0.731488i	$-0.738826\pi$
$193$	−8.98505	+	3.72173i	−0.646758	+	0.267896i	0.0350962	+	0.999384i	$0.488826\pi$
$194$	0.663947	+	1.60291i	0.0476686	+	0.115082i
$195$	6.19534	+	6.19534i	0.443658	+	0.443658i
$196$	−20.8384	−	20.8384i	−1.48846	−	1.48846i
$197$	−9.10606	−	21.9840i	−0.648780	−	1.56629i	−0.814528	−	0.580125i	$-0.803004\pi$
$197$	−9.10606	−	21.9840i	−0.648780	−	1.56629i	0.165748	−	0.986168i	$-0.446996\pi$
$198$	0.640100	−	0.265138i	0.0454899	−	0.0188426i
$199$	−5.05440	+	12.2024i	−0.358297	+	0.865006i	0.637243	+	0.770663i	$0.280075\pi$
$199$	−5.05440	+	12.2024i	−0.358297	+	0.865006i	−0.995540	+	0.0943427i	$0.969925\pi$
$200$		−	9.43761i		−	0.667340i
$201$	−17.2948	−	7.16372i	−1.21988	−	0.505290i
$202$	−14.3848	+	14.3848i	−1.01211	+	1.01211i
$203$	0.416650			0.0292431
$204$	26.4394	+	22.6276i	1.85113	+	1.58425i
$205$	1.63371			0.114103
$206$	−26.2322	+	26.2322i	−1.82768	+	1.82768i
$207$	3.82466	+	1.58423i	0.265832	+	0.110111i
$208$			84.1541i			5.83504i
$209$	−0.0214556	+	0.0517984i	−0.00148411	+	0.00358297i
$210$	−4.93450	+	2.04393i	−0.340513	+	0.141045i
$211$	−7.61020	−	18.3726i	−0.523907	−	1.26482i	−0.935458	−	0.353438i	$-0.885013\pi$
$211$	−7.61020	−	18.3726i	−0.523907	−	1.26482i	0.411551	−	0.911387i	$-0.364987\pi$
$212$	5.95294	+	5.95294i	0.408850	+	0.408850i
$213$	5.27765	+	5.27765i	0.361619	+	0.361619i
$214$	−9.69117	−	23.3966i	−0.662475	−	1.59936i
$215$	−1.84546	+	0.764416i	−0.125860	+	0.0521327i
$216$	−20.1522	+	48.6516i	−1.37118	+	3.31032i
$217$			0.765828i			0.0519878i
$218$	39.6238	+	16.4127i	2.68367	+	1.11161i
$219$	3.17256	−	3.17256i	0.214382	−	0.214382i
$220$	−2.28046			−0.153749
$221$	−22.2026	−	7.23888i	−1.49351	−	0.486940i
$222$	37.3282			2.50530
$223$	4.49940	−	4.49940i	0.301302	−	0.301302i	−0.540221	−	0.841523i	$-0.681659\pi$
$223$	4.49940	−	4.49940i	0.301302	−	0.301302i	0.841523	+	0.540221i	$0.181659\pi$
$224$	−25.3455	−	10.4984i	−1.69347	−	0.701456i
$225$			0.607075i			0.0404717i
$226$	1.30286	−	3.14538i	0.0866648	−	0.209227i
$227$	24.5160	−	10.1548i	1.62718	−	0.674001i	0.632270	−	0.774748i	$-0.282123\pi$
$227$	24.5160	−	10.1548i	1.62718	−	0.674001i	0.994912	+	0.100747i	$0.0321233\pi$
$228$	−0.433278	−	1.04603i	−0.0286946	−	0.0692748i
$229$	−10.9924	−	10.9924i	−0.726395	−	0.726395i	0.243504	−	0.969900i	$-0.421703\pi$
$229$	−10.9924	−	10.9924i	−0.726395	−	0.726395i	−0.969900	+	0.243504i	$0.921703\pi$
$230$	−13.1668	−	13.1668i	−0.868192	−	0.868192i
$231$	0.312851	+	0.755290i	0.0205841	+	0.0496944i
$232$	−2.87306	+	1.19006i	−0.188626	+	0.0781314i
$233$	−1.45524	+	3.51327i	−0.0953363	+	0.230162i	−0.964352	−	0.264622i	$-0.914753\pi$
$233$	−1.45524	+	3.51327i	−0.0953363	+	0.230162i	0.869016	+	0.494784i	$0.164753\pi$
$234$		−	9.38897i		−	0.613776i
$235$	−4.67716	−	1.93734i	−0.305105	−	0.126378i
$236$	5.44399	−	5.44399i	0.354374	−	0.354374i
$237$	−6.71002			−0.435863
$238$	9.25647	−	10.8158i	0.600008	−	0.701082i
$239$	−5.80679			−0.375610			−0.187805	−	0.982206i	$-0.560137\pi$
$239$	−5.80679			−0.375610			−0.187805	+	0.982206i	$0.560137\pi$
$240$	16.2521	−	16.2521i	1.04907	−	1.04907i
$241$	8.06359	+	3.34005i	0.519421	+	0.215151i	0.626963	−	0.779049i	$-0.284298\pi$
$241$	8.06359	+	3.34005i	0.519421	+	0.215151i	−0.107541	+	0.994201i	$0.534298\pi$
$242$		−	29.5597i		−	1.90017i
$243$	2.37441	−	5.73233i	0.152319	−	0.367729i
$244$	39.3441	−	16.2969i	2.51875	−	1.04330i
$245$	−2.06693	−	4.99002i	−0.132051	−	0.318800i
$246$	4.87960	+	4.87960i	0.311112	+	0.311112i
$247$	0.537243	+	0.537243i	0.0341840	+	0.0341840i
$248$	−2.18741	−	5.28087i	−0.138901	−	0.335336i
$249$	−6.27689	+	2.59997i	−0.397781	+	0.164766i
$250$	1.04496	−	2.52275i	0.0660890	−	0.159553i
$251$			15.2424i			0.962093i	0.876695	+	0.481047i	$0.159743\pi$
$251$			15.2424i			0.962093i	−0.876695	+	0.481047i	$0.840257\pi$
$252$	3.86949	+	1.60279i	0.243755	+	0.100967i
$253$	−2.01535	+	2.01535i	−0.126704	+	0.126704i
$254$	48.6467			3.05236
$255$	2.88984	+	5.68582i	0.180969	+	0.356060i
$256$	42.6224			2.66390
$257$	10.2772	−	10.2772i	0.641077	−	0.641077i	−0.309743	−	0.950820i	$-0.600243\pi$
$257$	10.2772	−	10.2772i	0.641077	−	0.641077i	0.950820	+	0.309743i	$0.100243\pi$
$258$	−7.79524	−	3.22889i	−0.485310	−	0.201022i
$259$		−	11.1742i		−	0.694331i
$260$	−11.8263	+	28.5512i	−0.733435	+	1.77067i
$261$	0.184810	−	0.0765508i	0.0114395	−	0.00473838i
$262$	4.67342	+	11.2826i	0.288725	+	0.697043i
$263$	−13.4550	−	13.4550i	−0.829671	−	0.829671i	0.157800	−	0.987471i	$-0.449560\pi$
$263$	−13.4550	−	13.4550i	−0.829671	−	0.829671i	−0.987471	+	0.157800i	$0.949560\pi$
$264$	−4.31462	−	4.31462i	−0.265546	−	0.265546i
$265$	0.590465	+	1.42551i	0.0362720	+	0.0875682i
$266$	−0.427906	+	0.177244i	−0.0262366	+	0.0108676i
$267$	−2.95221	+	7.12726i	−0.180672	+	0.436181i
$268$		−	66.0278i		−	4.03329i
$269$	20.9581	+	8.68112i	1.27784	+	0.529297i	0.915338	−	0.402687i	$-0.131924\pi$
$269$	20.9581	+	8.68112i	1.27784	+	0.529297i	0.362499	+	0.931984i	$0.381924\pi$
$270$	−10.7737	+	10.7737i	−0.655666	+	0.655666i
$271$	9.96764			0.605491			0.302745	−	0.953071i	$-0.402097\pi$
$271$	9.96764			0.605491			0.302745	+	0.953071i	$0.402097\pi$
$272$	−18.9896	+	58.2435i	−1.15141	+	3.53153i
$273$	11.0786			0.670506
$274$	−17.4724	+	17.4724i	−1.05555	+	1.05555i
$275$	−0.386141	−	0.159945i	−0.0232852	−	0.00964504i
$276$		−	57.5562i		−	3.46448i
$277$	−4.48012	+	10.8160i	−0.269184	+	0.649868i	−0.999445	−	0.0332998i	$-0.989398\pi$
$277$	−4.48012	+	10.8160i	−0.269184	+	0.649868i	0.730261	+	0.683168i	$0.239398\pi$
$278$	−11.8589	+	4.91210i	−0.711247	+	0.294608i
$279$	0.140705	+	0.339693i	0.00842380	+	0.0203369i
$280$	−8.43821	−	8.43821i	−0.504279	−	0.504279i
$281$	−0.838071	−	0.838071i	−0.0499951	−	0.0499951i	0.681667	−	0.731662i	$-0.261255\pi$
$281$	−0.838071	−	0.838071i	−0.0499951	−	0.0499951i	−0.731662	+	0.681667i	$0.761255\pi$
$282$	−8.18335	−	19.7564i	−0.487311	−	1.17647i
$283$	4.25986	−	1.76449i	0.253222	−	0.104888i	−0.252462	−	0.967607i	$-0.581240\pi$
$283$	4.25986	−	1.76449i	0.253222	−	0.104888i	0.505684	+	0.862719i	$0.331240\pi$
$284$	−10.0745	+	24.3220i	−0.597812	+	1.44324i
$285$		−	0.207508i		−	0.0122917i
$286$	5.97202	+	2.47369i	0.353133	+	0.146273i
$287$	1.46071	−	1.46071i	0.0862228	−	0.0862228i
$288$	−13.1712			−0.776118
$289$	−13.7331	−	10.0201i	−0.807827	−	0.589420i
$290$	−0.899762			−0.0528358
$291$	−0.694998	+	0.694998i	−0.0407415	+	0.0407415i
$292$	14.6207	+	6.05609i	0.855612	+	0.354406i
$293$			3.09527i			0.180828i	0.995904	+	0.0904138i	$0.0288190\pi$
$293$			3.09527i			0.180828i	−0.995904	+	0.0904138i	$0.971181\pi$
$294$	8.73073	−	21.0778i	0.509186	−	1.22928i
$295$	1.30363	−	0.539983i	0.0759005	−	0.0314390i
$296$	31.9165	+	77.0531i	1.85511	+	4.47862i
$297$	1.64906	+	1.64906i	0.0956879	+	0.0956879i
$298$	1.49823	+	1.49823i	0.0867900	+	0.0867900i
$299$	14.7805	+	35.6834i	0.854781	+	2.06362i
$300$	7.79781	−	3.22996i	0.450207	−	0.186482i
$301$	−0.966569	+	2.33350i	−0.0557121	+	0.134501i
$302$			6.24524i			0.359373i
$303$	−10.6473	−	4.41024i	−0.611670	−	0.253362i
$304$	1.40934	−	1.40934i	0.0808310	−	0.0808310i
$305$	7.80498			0.446912
$306$	2.11864	−	6.49815i	0.121115	−	0.371475i
$307$	11.8387			0.675668			0.337834	−	0.941206i	$-0.390306\pi$
$307$	11.8387			0.675668			0.337834	+	0.941206i	$0.390306\pi$
$308$	−2.03897	+	2.03897i	−0.116181	+	0.116181i
$309$	−19.4165	−	8.04256i	−1.10456	−	0.457525i
$310$		−	1.65382i		−	0.0939306i
$311$	8.97392	−	21.6650i	0.508864	−	1.22851i	−0.435674	−	0.900105i	$-0.643490\pi$
$311$	8.97392	−	21.6650i	0.508864	−	1.22851i	0.944538	−	0.328402i	$-0.106510\pi$
$312$	−76.3938	+	31.6433i	−4.32494	+	1.79145i
$313$	10.5652	+	25.5068i	0.597183	+	1.44173i	0.876440	+	0.481511i	$0.159912\pi$
$313$	10.5652	+	25.5068i	0.597183	+	1.44173i	−0.279257	+	0.960216i	$0.590088\pi$
$314$	−36.9047	−	36.9047i	−2.08265	−	2.08265i
$315$	0.542789	+	0.542789i	0.0305827	+	0.0305827i
$316$	−9.05715	−	21.8659i	−0.509505	−	1.23005i
$317$	−29.4357	+	12.1926i	−1.65327	+	0.684807i	−0.997534	−	0.0701822i	$-0.977642\pi$
$317$	−29.4357	+	12.1926i	−1.65327	+	0.684807i	−0.655737	+	0.754989i	$0.727642\pi$
$318$	−2.49412	+	6.02135i	−0.139864	+	0.337660i
$319$			0.137720i			0.00771087i
$320$	27.2800	+	11.2997i	1.52500	+	0.631675i
$321$	10.1444	−	10.1444i	0.566206	−	0.566206i
$322$	−23.5449			−1.31211
$323$	0.250599	+	0.493059i	0.0139437	+	0.0274345i
$324$	−37.1582			−2.06434
$325$	−4.00499	+	4.00499i	−0.222157	+	0.222157i
$326$	−46.2409	−	19.1536i	−2.56104	−	1.06082i
$327$			24.2966i			1.34361i
$328$	−5.90033	+	14.2447i	−0.325791	+	0.786530i
$329$	−5.91406	+	2.44968i	−0.326053	+	0.135055i
$330$	−0.675607	−	1.63106i	−0.0371910	−	0.0897869i
$331$	18.4377	+	18.4377i	1.01343	+	1.01343i	0.999909	+	0.0135172i	$0.00430279\pi$
$331$	18.4377	+	18.4377i	1.01343	+	1.01343i	0.0135172	+	0.999909i	$0.495697\pi$
$332$	−16.9450	−	16.9450i	−0.929978	−	0.929978i
$333$	−2.05303	−	4.95645i	−0.112505	−	0.271612i
$334$	50.8294	−	21.0542i	2.78126	−	1.15204i
$335$	4.63099	−	11.1802i	0.253018	−	0.610840i
$336$		−	29.0621i		−	1.58547i
$337$	15.2613	+	6.32145i	0.831338	+	0.344351i	0.757432	−	0.652914i	$-0.226454\pi$
$337$	15.2613	+	6.32145i	0.831338	+	0.344351i	0.0739055	+	0.997265i	$0.476454\pi$
$338$	36.8399	−	36.8399i	2.00383	−	2.00383i
$339$	1.92869			0.104752
$340$	−14.6277	+	17.0918i	−0.793296	+	0.926932i
$341$	−0.253139			−0.0137082
$342$	−0.157238	+	0.157238i	−0.00850245	+	0.00850245i
$343$	−14.4871	−	6.00074i	−0.782229	−	0.324010i
$344$		−	18.8518i		−	1.01642i
$345$	4.03682	−	9.74574i	0.217335	−	0.524693i
$346$	−48.2208	+	19.9737i	−2.59237	+	1.07379i
$347$	−7.77787	−	18.7774i	−0.417538	−	1.00803i	−0.983059	−	0.183292i	$-0.941325\pi$
$347$	−7.77787	−	18.7774i	−0.417538	−	1.00803i	0.565521	−	0.824734i	$-0.308675\pi$
$348$	−1.96657	−	1.96657i	−0.105419	−	0.105419i
$349$	3.45460	+	3.45460i	0.184921	+	0.184921i	0.793496	−	0.608575i	$-0.208259\pi$
$349$	3.45460	+	3.45460i	0.184921	+	0.184921i	−0.608575	+	0.793496i	$0.708259\pi$
$350$	−1.32130	−	3.18991i	−0.0706266	−	0.170508i
$351$	29.1979	−	12.0941i	1.55847	−	0.645538i
$352$	3.47018	−	8.37776i	0.184961	−	0.446536i
$353$			22.6733i			1.20678i	0.797447	+	0.603389i	$0.206183\pi$
$353$			22.6733i			1.20678i	−0.797447	+	0.603389i	$0.793817\pi$
$354$	5.50655	+	2.28089i	0.292670	+	0.121228i
$355$	−3.41174	+	3.41174i	−0.181077	+	0.181077i
$356$	−27.2104			−1.44215
$357$	7.66753	+	2.49990i	0.405809	+	0.132309i
$358$	−54.1080			−2.85970
$359$	9.53237	−	9.53237i	0.503099	−	0.503099i	−0.409300	−	0.912400i	$-0.634227\pi$
$359$	9.53237	−	9.53237i	0.503099	−	0.503099i	0.912400	+	0.409300i	$0.134227\pi$
$360$	−5.29322	−	2.19252i	−0.278977	−	0.115556i
$361$			18.9820i			0.999053i
$362$	−9.26413	+	22.3656i	−0.486912	+	1.17551i
$363$	15.4711	−	6.40833i	0.812021	−	0.336350i
$364$	14.9538	+	36.1017i	0.783792	+	1.89224i
$365$	2.05090	+	2.05090i	0.107349	+	0.107349i
$366$	23.3121	+	23.3121i	1.21854	+	1.21854i
$367$	−0.731262	−	1.76542i	−0.0381715	−	0.0921543i	0.903644	−	0.428284i	$-0.140882\pi$
$367$	−0.731262	−	1.76542i	−0.0381715	−	0.0921543i	−0.941816	+	0.336130i	$0.890882\pi$
$368$	93.6073	−	38.7734i	4.87962	−	2.02120i
$369$	0.379540	−	0.916289i	0.0197580	−	0.0477001i
$370$			24.1308i			1.25450i
$371$	1.80249	+	0.746616i	0.0935806	+	0.0387624i
$372$	3.61468	−	3.61468i	0.187413	−	0.187413i
$373$	−24.9357			−1.29112			−0.645562	−	0.763708i	$-0.723377\pi$
$373$	−24.9357			−1.29112			−0.645562	+	0.763708i	$0.723377\pi$
$374$	3.57507	+	3.05966i	0.184863	+	0.158211i
$375$	1.54691			0.0798820
$376$	33.7843	−	33.7843i	1.74229	−	1.74229i
$377$	1.72425	+	0.714206i	0.0888032	+	0.0367835i
$378$			19.2656i			0.990916i
$379$	−6.35332	+	15.3383i	−0.326348	+	0.787874i	0.672509	+	0.740089i	$0.265216\pi$
$379$	−6.35332	+	15.3383i	−0.326348	+	0.787874i	−0.998858	+	0.0477856i	$0.984784\pi$
$380$	0.676205	−	0.280093i	0.0346886	−	0.0143685i
$381$	10.5462	+	25.4609i	0.540300	+	1.30440i
$382$	20.4825	+	20.4825i	1.04797	+	1.04797i
$383$	−14.2058	−	14.2058i	−0.725883	−	0.725883i	0.243914	−	0.969797i	$-0.421568\pi$
$383$	−14.2058	−	14.2058i	−0.725883	−	0.725883i	−0.969797	+	0.243914i	$0.921568\pi$
$384$	22.0430	+	53.2164i	1.12488	+	2.71569i
$385$	−0.488258	+	0.202243i	−0.0248839	+	0.0103073i
$386$	10.1626	−	24.5347i	0.517262	−	1.24878i
$387$			1.21264i			0.0616420i
$388$	−3.20289	−	1.32668i	−0.162602	−	0.0673520i
$389$	15.7531	−	15.7531i	0.798715	−	0.798715i	−0.184178	−	0.982893i	$-0.558962\pi$
$389$	15.7531	−	15.7531i	0.798715	−	0.798715i	0.982893	+	0.184178i	$0.0589622\pi$
$390$	−23.9243			−1.21146
$391$	2.17765	+	28.0319i	0.110129	+	1.41764i
$392$	50.9740			2.57458
$393$	−4.89198	+	4.89198i	−0.246768	+	0.246768i
$394$	60.0296	+	24.8651i	3.02425	+	1.25268i
$395$		−	4.33770i		−	0.218253i
$396$	−0.529792	+	1.27903i	−0.0266230	+	0.0642737i
$397$	−24.2702	+	10.0530i	−1.21809	+	0.504548i	−0.896801	−	0.442435i	$-0.854115\pi$
$397$	−24.2702	+	10.0530i	−1.21809	+	0.504548i	−0.321285	+	0.946983i	$0.604115\pi$
$398$	−13.8016	−	33.3200i	−0.691812	−	1.67018i
$399$	−0.185534	−	0.185534i	−0.00928831	−	0.00928831i
$400$	10.5062	+	10.5062i	0.525309	+	0.525309i
$401$	14.6020	+	35.2524i	0.729191	+	1.76042i	0.645277	+	0.763949i	$0.276742\pi$
$401$	14.6020	+	35.2524i	0.729191	+	1.76042i	0.0839140	+	0.996473i	$0.473258\pi$
$402$	47.2252	−	19.5613i	2.35538	−	0.975630i
$403$	−1.31276	+	3.16927i	−0.0653930	+	0.157873i
$404$		−	40.6491i		−	2.02237i
$405$	−6.29184	−	2.60616i	−0.312644	−	0.129501i
$406$	−0.804481	+	0.804481i	−0.0399257	+	0.0399257i
$407$	3.69355			0.183082
$408$	−60.0129	+	4.66208i	−2.97108	+	0.230807i
$409$	−19.0995			−0.944411			−0.472206	−	0.881488i	$-0.656542\pi$
$409$	−19.0995			−0.944411			−0.472206	+	0.881488i	$0.656542\pi$
$410$	−3.15442	+	3.15442i	−0.155786	+	0.155786i
$411$	−12.9327	−	5.35689i	−0.637921	−	0.264236i
$412$		−	74.1281i		−	3.65203i
$413$	0.682783	−	1.64838i	0.0335976	−	0.0811117i
$414$	−10.4436	+	4.32590i	−0.513277	+	0.212606i
$415$	−1.68075	−	4.05770i	−0.0825049	−	0.199185i
$416$	−86.8926	−	86.8926i	−4.26026	−	4.26026i
$417$	−5.14183	−	5.14183i	−0.251796	−	0.251796i
$418$	−0.0585868	−	0.141441i	−0.00286558	−	0.00691811i
$419$	−30.9970	+	12.8394i	−1.51430	+	0.627244i	−0.976440	−	0.215790i	$-0.930767\pi$
$419$	−30.9970	+	12.8394i	−1.51430	+	0.627244i	−0.537860	+	0.843034i	$0.680767\pi$
$420$	4.08413	−	9.85997i	0.199285	−	0.481117i
$421$		−	18.9396i		−	0.923058i	−0.887125	−	0.461529i	$-0.847301\pi$
$421$		−	18.9396i		−	0.923058i	0.887125	−	0.461529i	$-0.152699\pi$
$422$	50.1685	+	20.7805i	2.44216	+	1.01158i
$423$	−2.17317	+	2.17317i	−0.105663	+	0.105663i
$424$	−14.5618			−0.707186
$425$	−3.67560	+	1.86814i	−0.178293	+	0.0906179i
$426$	−20.3805			−0.987440
$427$	6.97847	−	6.97847i	0.337712	−	0.337712i
$428$	46.7504	+	19.3646i	2.25976	+	0.936025i
$429$			3.66194i			0.176800i
$430$	2.08732	−	5.03924i	0.100660	−	0.243014i
$431$	22.5308	−	9.33254i	1.08527	−	0.449533i	0.232914	−	0.972497i	$-0.425174\pi$
$431$	22.5308	−	9.33254i	1.08527	−	0.449533i	0.852354	+	0.522965i	$0.175174\pi$
$432$	−31.7263	−	76.5940i	−1.52643	−	3.68513i
$433$	−6.85275	−	6.85275i	−0.329322	−	0.329322i	0.523007	−	0.852329i	$-0.324810\pi$
$433$	−6.85275	−	6.85275i	−0.329322	−	0.329322i	−0.852329	+	0.523007i	$0.824810\pi$
$434$	−1.47869	−	1.47869i	−0.0709792	−	0.0709792i
$435$	−0.195062	−	0.470921i	−0.00935250	−	0.0225789i
$436$	−79.1753	+	32.7955i	−3.79181	+	1.57062i
$437$	0.350062	−	0.845124i	0.0167457	−	0.0404278i
$438$			12.2514i			0.585393i
$439$	2.97814	+	1.23359i	0.142139	+	0.0588759i	0.452619	−	0.891704i	$-0.350490\pi$
$439$	2.97814	+	1.23359i	0.142139	+	0.0588759i	−0.310480	+	0.950580i	$0.600490\pi$
$440$	2.78919	−	2.78919i	0.132969	−	0.132969i
$441$	−3.27891			−0.156138
$442$	56.8466	−	28.8924i	2.70392	−	1.37427i
$443$	−17.5623			−0.834412			−0.417206	−	0.908812i	$-0.636991\pi$
$443$	−17.5623			−0.834412			−0.417206	+	0.908812i	$0.636991\pi$
$444$	−52.7418	+	52.7418i	−2.50302	+	2.50302i
$445$	−4.60742	−	1.90846i	−0.218413	−	0.0904696i
$446$			17.3752i			0.822739i
$447$	−0.459344	+	1.10895i	−0.0217262	+	0.0524517i
$448$	34.4943	−	14.2880i	1.62970	−	0.675045i
$449$	7.08856	+	17.1133i	0.334530	+	0.807626i	0.998221	+	0.0596199i	$0.0189889\pi$
$449$	7.08856	+	17.1133i	0.334530	+	0.807626i	−0.663691	+	0.748007i	$0.731011\pi$
$450$	−1.17216	−	1.17216i	−0.0552562	−	0.0552562i
$451$	0.482826	+	0.482826i	0.0227354	+	0.0227354i
$452$	2.60333	+	6.28500i	0.122451	+	0.295622i
$453$	−3.26866	+	1.35392i	−0.153575	+	0.0636128i
$454$	−27.7289	+	66.9435i	−1.30138	+	3.14182i
$455$			7.16175i			0.335748i
$456$	1.80931	+	0.749439i	0.0847285	+	0.0350957i
$457$	−10.3999	+	10.3999i	−0.486487	+	0.486487i	−0.907196	−	0.420709i	$-0.861781\pi$
$457$	−10.3999	+	10.3999i	−0.486487	+	0.486487i	0.420709	+	0.907196i	$0.361781\pi$
$458$	42.4488			1.98350
$459$	22.9371	−	1.78186i	1.07061	−	0.0831700i
$460$	37.2072			1.73480
$461$	12.6921	−	12.6921i	0.591131	−	0.591131i	−0.346806	−	0.937937i	$-0.612734\pi$
$461$	12.6921	−	12.6921i	0.591131	−	0.591131i	0.937937	+	0.346806i	$0.112734\pi$
$462$	−2.06240	−	0.854275i	−0.0959516	−	0.0397445i
$463$		−	35.5792i		−	1.65350i	−0.562567	−	0.826752i	$-0.690186\pi$
$463$		−	35.5792i		−	1.65350i	0.562567	−	0.826752i	$-0.309814\pi$
$464$	1.87356	−	4.52317i	0.0869778	−	0.209983i
$465$	0.865582	−	0.358536i	0.0401404	−	0.0166267i
$466$	−3.97371	−	9.59337i	−0.184078	−	0.444404i
$467$	−20.8180	−	20.8180i	−0.963342	−	0.963342i	0.0360098	−	0.999351i	$-0.488535\pi$
$467$	−20.8180	−	20.8180i	−0.963342	−	0.963342i	−0.999351	+	0.0360098i	$0.988535\pi$
$468$	13.2659	+	13.2659i	0.613215	+	0.613215i
$469$	−5.85568	−	14.1369i	−0.270390	−	0.652780i
$470$	12.7715	−	5.29013i	0.589106	−	0.244016i
$471$	11.3147	−	27.3160i	0.521352	−	1.25866i
$472$			13.3169i			0.612959i
$473$	−0.771322	−	0.319492i	−0.0354654	−	0.0146903i
$474$	12.9559	−	12.9559i	0.595086	−	0.595086i
$475$	0.134144			0.00615493
$476$	2.20318	+	28.3605i	0.100982	+	1.29990i
$477$	0.936692			0.0428882
$478$	11.2119	−	11.2119i	0.512822	−	0.512822i
$479$	−15.4620	−	6.40457i	−0.706477	−	0.292632i	0.000368864	−	1.00000i	$-0.499883\pi$
$479$	−15.4620	−	6.40457i	−0.706477	−	0.292632i	−0.706846	+	0.707368i	$0.749883\pi$
$480$			33.5619i			1.53188i
$481$	19.1544	−	46.2428i	0.873365	−	2.10849i
$482$	−22.0185	+	9.12036i	−1.00292	+	0.415421i
$483$	−5.10437	−	12.3230i	−0.232257	−	0.560718i
$484$	41.7655	+	41.7655i	1.89843	+	1.89843i
$485$	−0.449282	−	0.449282i	−0.0204008	−	0.0204008i
$486$	6.48359	+	15.6528i	0.294102	+	0.710024i
$487$	−21.6579	+	8.97101i	−0.981415	+	0.406515i	−0.814950	−	0.579532i	$-0.803235\pi$
$487$	−21.6579	+	8.97101i	−0.981415	+	0.406515i	−0.166466	+	0.986047i	$0.553235\pi$
$488$	−28.1886	+	68.0533i	−1.27604	+	3.08063i
$489$		−	28.3541i		−	1.28222i
$490$	13.6258	+	5.64399i	0.615550	+	0.254969i
$491$	−18.0226	+	18.0226i	−0.813347	+	0.813347i	−0.985134	−	0.171787i	$-0.945046\pi$
$491$	−18.0226	+	18.0226i	−0.813347	+	0.813347i	0.171787	+	0.985134i	$0.445046\pi$
$492$	−13.7890			−0.621655
$493$	1.03220	+	0.883386i	0.0464878	+	0.0397857i
$494$	−2.07465			−0.0933431
$495$	−0.179415	+	0.179415i	−0.00806409	+	0.00806409i
$496$	8.31387	+	3.44372i	0.373304	+	0.154627i
$497$			6.10091i			0.273663i
$498$	7.09951	−	17.1397i	0.318136	−	0.768049i
$499$	26.5542	−	10.9991i	1.18873	−	0.492388i	0.301388	−	0.953502i	$-0.402550\pi$
$499$	26.5542	−	10.9991i	1.18873	−	0.492388i	0.887341	+	0.461114i	$0.152550\pi$
$500$	2.08801	+	5.04090i	0.0933786	+	0.225436i
$501$	22.0389	+	22.0389i	0.984625	+	0.984625i
$502$	−29.4306	−	29.4306i	−1.31355	−	1.31355i
$503$	0.00393607	+	0.00950252i	0.000175501	+	0.000423697i	0.923967	−	0.382472i	$-0.124927\pi$
$503$	0.00393607	+	0.00950252i	0.000175501	+	0.000423697i	−0.923792	+	0.382895i	$0.874927\pi$
$504$	−6.69303	+	2.77235i	−0.298131	+	0.123490i
$505$	2.85101	−	6.88294i	0.126868	−	0.306287i
$506$		−	7.78261i		−	0.345979i
$507$	27.2680	+	11.2948i	1.21102	+	0.501619i
$508$	−68.7339	+	68.7339i	−3.04957	+	3.04957i
$509$	−26.8066			−1.18818			−0.594091	−	0.804398i	$-0.702488\pi$
$509$	−26.8066			−1.18818			−0.594091	+	0.804398i	$0.702488\pi$
$510$	−16.5582	−	5.39858i	−0.733208	−	0.239053i
$511$	3.66744			0.162238
$512$	−29.6367	+	29.6367i	−1.30977	+	1.30977i
$513$	−0.691521	−	0.286437i	−0.0305314	−	0.0126465i
$514$			39.6873i			1.75053i
$515$	5.19912	−	12.5518i	0.229101	−	0.553098i
$516$	15.5762	−	6.45189i	0.685705	−	0.284028i
$517$	−0.809725	−	1.95485i	−0.0356117	−	0.0859742i
$518$	21.5755	+	21.5755i	0.947973	+	0.947973i
$519$	−20.9078	−	20.9078i	−0.917752	−	0.917752i
$520$	−20.4559	−	49.3848i	−0.897049	−	2.16567i
$521$	9.37063	−	3.88144i	0.410535	−	0.170049i	−0.167851	−	0.985812i	$-0.553683\pi$
$521$	9.37063	−	3.88144i	0.410535	−	0.170049i	0.578386	+	0.815763i	$0.303683\pi$
$522$	−0.209030	+	0.504644i	−0.00914902	+	0.0220877i
$523$		−	16.7568i		−	0.732724i	−0.930472	−	0.366362i	$-0.880603\pi$
$523$		−	16.7568i		−	0.732724i	0.930472	−	0.366362i	$-0.119397\pi$
$524$	−22.5446	−	9.33830i	−0.984867	−	0.407945i
$525$	1.38310	−	1.38310i	0.0603633	−	0.0603633i
$526$	51.9587			2.26551
$527$	−1.62372	+	1.89724i	−0.0707303	+	0.0826452i
$528$	9.60627			0.418059
$529$	16.6183	−	16.6183i	0.722534	−	0.722534i
$530$	−3.89251	−	1.61233i	−0.169080	−	0.0700351i
$531$		−	0.856609i		−	0.0371736i
$532$	0.354165	−	0.855030i	0.0153550	−	0.0370702i
$533$	8.54882	−	3.54104i	0.370291	−	0.153379i
$534$	−8.06133	−	19.4618i	−0.348848	−	0.842193i
$535$	6.55786	+	6.55786i	0.283521	+	0.283521i
$536$	80.7572	+	80.7572i	3.48818	+	3.48818i
$537$	−11.7302	−	28.3193i	−0.506196	−	1.22207i
$538$	−57.2283	+	23.7048i	−2.46729	+	1.02198i
$539$	0.863887	−	2.08561i	0.0372102	−	0.0898335i
$540$		−	30.4447i		−	1.31013i
$541$	−16.7559	−	6.94050i	−0.720390	−	0.298395i	−0.00779397	−	0.999970i	$-0.502481\pi$
$541$	−16.7559	−	6.94050i	−0.720390	−	0.298395i	−0.712596	+	0.701574i	$0.752481\pi$
$542$	−19.2458	+	19.2458i	−0.826679	+	0.826679i
$543$	−13.7142			−0.588532
$544$	−40.5313	−	79.7463i	−1.73776	−	3.41909i
$545$	−15.7066			−0.672796
$546$	−21.3909	+	21.3909i	−0.915444	+	0.915444i
$547$	20.8574	+	8.63943i	0.891799	+	0.369395i	0.781061	−	0.624454i	$-0.214679\pi$
$547$	20.8574	+	8.63943i	0.891799	+	0.369395i	0.110738	+	0.993850i	$0.464679\pi$
$548$		−	49.3743i		−	2.10916i
$549$	1.81323	−	4.37753i	0.0773869	−	0.186829i
$550$	1.05440	−	0.436747i	0.0449598	−	0.0186230i
$551$	−0.0169152	−	0.0408370i	−0.000720613	−	0.00173971i
$552$	70.3958	+	70.3958i	2.99624	+	2.99624i
$553$	−3.87836	−	3.87836i	−0.164925	−	0.164925i
$554$	−12.2335	−	29.5342i	−0.519750	−	1.25479i
$555$	−12.6297	+	5.23139i	−0.536101	+	0.222060i
$556$	9.81523	−	23.6960i	0.416258	−	1.00494i
$557$			5.97545i			0.253188i	0.991955	+	0.126594i	$0.0404045\pi$
$557$			5.97545i			0.253188i	−0.991955	+	0.126594i	$0.959595\pi$
$558$	−0.927568	−	0.384211i	−0.0392671	−	0.0162650i
$559$	−8.00002	+	8.00002i	−0.338365	+	0.338365i
$560$	18.7872			0.793905
$561$	−0.826325	+	2.53445i	−0.0348875	+	0.107004i
$562$	3.23635			0.136517
$563$	−2.52298	+	2.52298i	−0.106331	+	0.106331i	−0.758271	−	0.651940i	$-0.773955\pi$
$563$	−2.52298	+	2.52298i	−0.106331	+	0.106331i	0.651940	+	0.758271i	$0.273955\pi$
$564$	39.4766	+	16.3517i	1.66226	+	0.688533i
$565$			1.24680i			0.0524534i
$566$	−4.81814	+	11.6320i	−0.202521	+	0.488930i
$567$	−7.95574	+	3.29538i	−0.334110	+	0.138393i
$568$	−17.4258	−	42.0696i	−0.731171	−	1.76520i
$569$	31.1965	+	31.1965i	1.30783	+	1.30783i	0.922981	+	0.384846i	$0.125746\pi$
$569$	31.1965	+	31.1965i	1.30783	+	1.30783i	0.384846	+	0.922981i	$0.374254\pi$
$570$	0.400663	+	0.400663i	0.0167819	+	0.0167819i
$571$	−4.81154	−	11.6161i	−0.201357	−	0.486118i	0.790655	−	0.612262i	$-0.209740\pi$
$571$	−4.81154	−	11.6161i	−0.201357	−	0.486118i	−0.992012	+	0.126143i	$0.959740\pi$
$572$	−11.9331	+	4.94287i	−0.498949	+	0.206672i
$573$	−6.27975	+	15.1606i	−0.262340	+	0.633345i
$574$			5.64076i			0.235441i
$575$	6.30014	+	2.60960i	0.262734	+	0.108828i
$576$	12.6752	−	12.6752i	0.528135	−	0.528135i
$577$	14.5344			0.605075			0.302538	−	0.953137i	$-0.402166\pi$
$577$	14.5344			0.605075			0.302538	+	0.953137i	$0.402166\pi$
$578$	45.8634	−	7.16904i	1.90767	−	0.298193i
$579$	15.0442			0.625217
$580$	1.27129	−	1.27129i	0.0527875	−	0.0527875i
$581$	−5.13077	−	2.12524i	−0.212860	−	0.0881697i
$582$		−	2.68385i		−	0.111249i
$583$	−0.246788	+	0.595800i	−0.0102209	+	0.0246755i
$584$	−25.2894	+	10.4752i	−1.04648	+	0.433467i
$585$	1.31582	+	3.17668i	0.0544026	+	0.131340i
$586$	−5.97645	−	5.97645i	−0.246885	−	0.246885i
$587$	8.63007	+	8.63007i	0.356201	+	0.356201i	0.862411	−	0.506209i	$-0.168954\pi$
$587$	8.63007	+	8.63007i	0.356201	+	0.356201i	−0.506209	+	0.862411i	$0.668954\pi$
$588$	17.4455	+	42.1172i	0.719440	+	1.73688i
$589$	0.0750609	−	0.0310912i	0.00309283	−	0.00128109i
$590$	−1.47448	+	3.55971i	−0.0607034	+	0.146551i
$591$			36.8091i			1.51412i
$592$	−121.308	−	50.2472i	−4.98571	−	2.06515i
$593$	8.08169	−	8.08169i	0.331875	−	0.331875i	−0.521423	−	0.853298i	$-0.674599\pi$
$593$	8.08169	−	8.08169i	0.331875	−	0.331875i	0.853298	+	0.521423i	$0.174599\pi$
$594$	−6.36810			−0.261286
$595$	−1.61607	+	4.95668i	−0.0662522	+	0.203204i
$596$	−4.23376			−0.173421
$597$	14.4471	−	14.4471i	0.591279	−	0.591279i
$598$	−97.4374	−	40.3599i	−3.98451	−	1.65044i
$599$			27.2578i			1.11372i	0.830606	+	0.556861i	$0.187994\pi$
$599$			27.2578i			1.11372i	−0.830606	+	0.556861i	$0.812006\pi$
$600$	−5.58684	+	13.4878i	−0.228082	+	0.550638i
$601$	−10.3510	+	4.28754i	−0.422228	+	0.174893i	−0.583672	−	0.811989i	$-0.698385\pi$
$601$	−10.3510	+	4.28754i	−0.422228	+	0.174893i	0.161444	+	0.986882i	$0.448385\pi$
$602$	−2.63932	−	6.37189i	−0.107571	−	0.259699i
$603$	−5.19472	−	5.19472i	−0.211545	−	0.211545i
$604$	−8.82403	−	8.82403i	−0.359045	−	0.359045i
$605$	4.14267	+	10.0013i	0.168423	+	0.406610i
$606$	29.0735	−	12.0427i	1.18103	−	0.489199i
$607$	−15.3256	+	36.9992i	−0.622046	+	1.50175i	0.227252	+	0.973836i	$0.427026\pi$
$607$	−15.3256	+	36.9992i	−0.622046	+	1.50175i	−0.849297	+	0.527915i	$0.822974\pi$
$608$			2.91039i			0.118032i
$609$	−0.595458	−	0.246647i	−0.0241292	−	0.00999463i
$610$	−15.0701	+	15.0701i	−0.610171	+	0.610171i
$611$	−28.6737			−1.16001
$612$	6.18790	+	12.1749i	0.250131	+	0.492139i
$613$	29.1043			1.17551			0.587755	−	0.809039i	$-0.300012\pi$
$613$	29.1043			1.17551			0.587755	+	0.809039i	$0.300012\pi$
$614$	−22.8585	+	22.8585i	−0.922493	+	0.922493i
$615$	−2.33483	−	0.967117i	−0.0941493	−	0.0389979i
$616$		−	4.98765i		−	0.200958i
$617$	6.30101	−	15.2120i	0.253669	−	0.612411i	−0.744826	−	0.667259i	$-0.767467\pi$
$617$	6.30101	−	15.2120i	0.253669	−	0.612411i	0.998495	+	0.0548478i	$0.0174674\pi$
$618$	53.0188	−	21.9611i	2.13273	−	0.883405i
$619$	2.91366	+	7.03419i	0.117110	+	0.282728i	0.971555	−	0.236813i	$-0.0761029\pi$
$619$	2.91366	+	7.03419i	0.117110	+	0.282728i	−0.854445	+	0.519541i	$0.826103\pi$
$620$	2.33672	+	2.33672i	0.0938447	+	0.0938447i
$621$	−26.9054	−	26.9054i	−1.07968	−	1.07968i
$622$	24.5043	+	59.1585i	0.982532	+	2.37204i
$623$	−5.82588	+	2.41316i	−0.233409	+	0.0966811i
$624$	49.8172	−	120.269i	1.99429	−	4.81463i
$625$			1.00000i			0.0400000i
$626$	−69.6490	−	28.8496i	−2.78373	−	1.15306i
$627$	0.0613268	−	0.0613268i	0.00244916	−	0.00244916i
$628$	104.287			4.16150
$629$	23.6916	−	27.6826i	0.944648	−	1.10378i
$630$	−2.09607			−0.0835093
$631$	−26.3010	+	26.3010i	−1.04703	+	1.04703i	−0.0481871	+	0.998838i	$0.515344\pi$
$631$	−26.3010	+	26.3010i	−1.04703	+	1.04703i	−0.998838	+	0.0481871i	$0.984656\pi$
$632$	37.8213	+	15.6661i	1.50445	+	0.623165i
$633$			30.7624i			1.22270i
$634$	33.2934	−	80.3773i	1.32225	−	3.19219i
$635$	−16.4592	+	6.81763i	−0.653164	+	0.270549i
$636$	−4.98369	−	12.0317i	−0.197616	−	0.477088i
$637$	−21.6315	−	21.6315i	−0.857073	−	0.857073i
$638$	−0.265915	−	0.265915i	−0.0105277	−	0.0105277i
$639$	1.12092	+	2.70613i	0.0443428	+	0.107053i
$640$	−34.4018	+	14.2497i	−1.35985	+	0.563269i
$641$	3.29555	−	7.95617i	0.130167	−	0.314250i	−0.845337	−	0.534233i	$-0.820600\pi$
$641$	3.29555	−	7.95617i	0.130167	−	0.314250i	0.975504	+	0.219983i	$0.0706003\pi$
$642$			39.1743i			1.54609i
$643$	17.6673	+	7.31804i	0.696731	+	0.288595i	0.702801	−	0.711386i	$-0.251932\pi$
$643$	17.6673	+	7.31804i	0.696731	+	0.288595i	−0.00607035	+	0.999982i	$0.501932\pi$
$644$	33.2672	−	33.2672i	1.31091	−	1.31091i
$645$	3.08997			0.121668
$646$	−1.43588	−	0.468150i	−0.0564939	−	0.0184191i
$647$	−25.5972			−1.00633			−0.503164	−	0.864191i	$-0.667831\pi$
$647$	−25.5972			−1.00633			−0.503164	+	0.864191i	$0.667831\pi$
$648$	45.4474	−	45.4474i	1.78534	−	1.78534i
$649$	0.544861	+	0.225689i	0.0213877	+	0.00885907i
$650$		−	15.4659i		−	0.606623i
$651$	0.453352	−	1.09449i	0.0177683	−	0.0428964i
$652$	92.3972	−	38.2722i	3.61855	−	1.49885i
$653$	3.31942	+	8.01379i	0.129899	+	0.313604i	0.975425	−	0.220330i	$-0.0707133\pi$
$653$	3.31942	+	8.01379i	0.129899	+	0.313604i	−0.845527	+	0.533933i	$0.820713\pi$
$654$	−46.9127	−	46.9127i	−1.83443	−	1.83443i
$655$	−3.16243	−	3.16243i	−0.123566	−	0.123566i
$656$	−9.28911	−	22.4259i	−0.362679	−	0.875584i
$657$	1.62674	−	0.673818i	0.0634652	−	0.0262881i
$658$	6.68913	−	16.1490i	0.260770	−	0.629553i
$659$			36.0328i			1.40364i	0.712355	+	0.701819i	$0.247628\pi$
$659$			36.0328i			1.40364i	−0.712355	+	0.701819i	$0.752372\pi$
$660$	3.25914	+	1.34998i	0.126862	+	0.0525479i
$661$	6.64994	−	6.64994i	0.258653	−	0.258653i	−0.565853	−	0.824506i	$-0.691453\pi$
$661$	6.64994	−	6.64994i	0.258653	−	0.258653i	0.824506	+	0.565853i	$0.191453\pi$
$662$	−71.2001			−2.76727
$663$	27.4458	+	23.4889i	1.06590	+	0.912234i
$664$	41.4502			1.60858
$665$	0.119938	−	0.119938i	0.00465101	−	0.00465101i
$666$	13.5341	+	5.60602i	0.524437	+	0.217229i
$667$		−	2.24700i		−	0.0870041i
$668$	−42.0700	+	101.566i	−1.62774	+	3.92970i
$669$	−9.09389	+	3.76681i	−0.351590	+	0.145633i
$670$	12.6454	+	30.5288i	0.488536	+	1.17943i
$671$	2.30668	+	2.30668i	0.0890484	+	0.0890484i
$672$	30.0078	+	30.0078i	1.15758	+	1.15758i
$673$	−1.74487	−	4.21250i	−0.0672599	−	0.162380i	0.886675	−	0.462393i	$-0.153009\pi$
$673$	−1.74487	−	4.21250i	−0.0672599	−	0.162380i	−0.953935	+	0.300013i	$0.903009\pi$
$674$	−41.6727	+	17.2614i	−1.60517	+	0.664885i
$675$	2.13530	−	5.15508i	0.0821878	−	0.198419i
$676$			104.104i			4.00399i
$677$	32.8914	+	13.6240i	1.26412	+	0.523615i	0.911171	−	0.412029i	$-0.135180\pi$
$677$	32.8914	+	13.6240i	1.26412	+	0.523615i	0.352947	+	0.935643i	$0.385180\pi$
$678$	−3.72398	+	3.72398i	−0.143018	+	0.143018i
$679$	−0.803410			−0.0308321
$680$	−3.01381	−	38.7954i	−0.115574	−	1.48773i
$681$	−41.0486			−1.57299
$682$	0.488769	−	0.488769i	0.0187159	−	0.0187159i
$683$	−11.0606	−	4.58144i	−0.423222	−	0.175304i	0.160899	−	0.986971i	$-0.448561\pi$
$683$	−11.0606	−	4.58144i	−0.423222	−	0.175304i	−0.584121	+	0.811667i	$0.698561\pi$
$684$		−	0.444329i		−	0.0169894i
$685$	3.46296	−	8.36033i	0.132313	−	0.319432i
$686$	39.5585	−	16.3857i	1.51035	−	0.625608i
$687$	9.20259	+	22.2170i	0.351101	+	0.847632i
$688$	20.9862	+	20.9862i	0.800093	+	0.800093i
$689$	6.17953	+	6.17953i	0.235421	+	0.235421i
$690$	11.0230	+	26.6118i	0.419637	+	1.01309i
$691$	19.2122	−	7.95793i	0.730865	−	0.302734i	0.0139574	−	0.999903i	$-0.495557\pi$
$691$	19.2122	−	7.95793i	0.730865	−	0.302734i	0.716907	+	0.697169i	$0.245557\pi$
$692$	39.9109	−	96.3535i	1.51719	−	3.66281i
$693$			0.320831i			0.0121874i
$694$	51.2739	+	21.2383i	1.94633	+	0.806196i
$695$	3.32394	−	3.32394i	0.126084	−	0.126084i
$696$	4.81055			0.182343
$697$	6.71572	−	0.521709i	0.254376	−	0.0197611i
$698$	−13.3405			−0.504946
$699$	4.15955	−	4.15955i	0.157328	−	0.157328i
$700$	6.37399	+	2.64019i	0.240914	+	0.0997899i
$701$			13.1645i			0.497215i	0.968604	+	0.248607i	$0.0799729\pi$
$701$			13.1645i			0.497215i	−0.968604	+	0.248607i	$0.920027\pi$
$702$	−33.0244	+	79.7279i	−1.24643	+	3.00914i
$703$	−1.09521	+	0.453652i	−0.0413067	+	0.0171098i
$704$	4.72279	+	11.4018i	0.177997	+	0.429723i
$705$	5.53754	+	5.53754i	0.208556	+	0.208556i
$706$	−43.7783	−	43.7783i	−1.64762	−	1.64762i
$707$	−3.60497	−	8.70316i	−0.135579	−	0.327316i
$708$	−11.0030	+	4.55761i	−0.413519	+	0.171285i
$709$	7.77328	−	18.7664i	0.291932	−	0.704785i	−0.708067	−	0.706145i	$-0.750433\pi$
$709$	7.77328	−	18.7664i	0.291932	−	0.704785i	0.999999	+	0.00135939i	$0.000432708\pi$
$710$		−	13.1750i		−	0.494449i
$711$	−2.43286	−	1.00772i	−0.0912394	−	0.0377926i
$712$	33.2805	−	33.2805i	1.24724	−	1.24724i
$713$	4.13012			0.154674
$714$	−19.6316	+	9.97783i	−0.734695	+	0.373411i
$715$	−2.36726			−0.0885306
$716$	76.4504	−	76.4504i	2.85708	−	2.85708i
$717$	8.29881	+	3.43748i	0.309925	+	0.128375i
$718$			36.8108i			1.37377i
$719$	−11.1535	+	26.9270i	−0.415957	+	1.00421i	0.567550	+	0.823339i	$0.307891\pi$
$719$	−11.1535	+	26.9270i	−0.415957	+	1.00421i	−0.983507	+	0.180870i	$0.942109\pi$
$720$	8.33331	−	3.45177i	0.310564	−	0.128640i
$721$	−6.57405	−	15.8712i	−0.244830	−	0.591073i
$722$	−36.6511	−	36.6511i	−1.36401	−	1.36401i
$723$	−9.54690	−	9.54690i	−0.355053	−	0.355053i
$724$	−18.5113	−	44.6903i	−0.687968	−	1.66090i
$725$	0.304427	−	0.126098i	0.0113061	−	0.00468316i
$726$	−17.4986	+	42.2454i	−0.649435	+	1.56788i
$727$		−	18.9928i		−	0.704402i	−0.935924	−	0.352201i	$-0.885433\pi$
$727$		−	18.9928i		−	0.704402i	0.935924	−	0.352201i	$-0.114567\pi$
$728$	−62.4448	−	25.8655i	−2.31436	−	0.958639i
$729$	−21.2335	+	21.2335i	−0.786426	+	0.786426i
$730$	−7.91990			−0.293129
$731$	−7.34207	+	3.73163i	−0.271556	+	0.138019i
$732$	−65.8762			−2.43486
$733$	23.0263	−	23.0263i	0.850494	−	0.850494i	−0.139700	−	0.990194i	$-0.544614\pi$
$733$	23.0263	−	23.0263i	0.850494	−	0.850494i	0.990194	+	0.139700i	$0.0446138\pi$
$734$	4.82068	+	1.99679i	0.177934	+	0.0737029i
$735$			8.35509i			0.308182i
$736$	−56.6182	+	136.688i	−2.08698	+	5.03840i
$737$	4.67283	−	1.93555i	0.172126	−	0.0712970i
$738$	1.03637	+	2.50203i	0.0381495	+	0.0921010i
$739$	−21.7401	−	21.7401i	−0.799723	−	0.799723i	0.183329	−	0.983052i	$-0.441313\pi$
$739$	−21.7401	−	21.7401i	−0.799723	−	0.799723i	−0.983052	+	0.183329i	$0.941313\pi$
$740$	−34.0950	−	34.0950i	−1.25336	−	1.25336i
$741$	−0.449770	−	1.08584i	−0.0165227	−	0.0398893i
$742$	−4.92190	+	2.03872i	−0.180688	+	0.0748436i
$743$	−3.74040	+	9.03012i	−0.137222	+	0.331283i	−0.977520	−	0.210841i	$-0.932380\pi$
$743$	−3.74040	+	9.03012i	−0.137222	+	0.331283i	0.840298	+	0.542124i	$0.182380\pi$
$744$			8.84209i			0.324167i
$745$	−0.716884	−	0.296943i	−0.0262646	−	0.0108792i
$746$	48.1467	−	48.1467i	1.76278	−	1.76278i
$747$	−2.66629			−0.0975543
$748$	−9.37435	+	0.728243i	−0.342760	+	0.0266272i
$749$	11.7268			0.428489
$750$	−2.98682	+	2.98682i	−0.109063	+	0.109063i
$751$	11.9895	+	4.96623i	0.437504	+	0.181220i	0.590554	−	0.806998i	$-0.298909\pi$
$751$	11.9895	+	4.96623i	0.437504	+	0.181220i	−0.153050	+	0.988219i	$0.548909\pi$
$752$			75.2189i			2.74295i
$753$	9.02315	−	21.7838i	0.328822	−	0.793846i
$754$	−4.70824	+	1.95022i	−0.171464	+	0.0710227i
$755$	−0.875243	−	2.11302i	−0.0318534	−	0.0769008i
$756$	−27.2208	−	27.2208i	−0.990010	−	0.990010i
$757$	25.1081	+	25.1081i	0.912568	+	0.912568i	0.996474	−	0.0839060i	$-0.0267396\pi$
$757$	25.1081	+	25.1081i	0.912568	+	0.912568i	−0.0839060	+	0.996474i	$0.526740\pi$
$758$	−17.3484	−	41.8828i	−0.630124	−	1.52125i
$759$	4.07329	−	1.68721i	0.147851	−	0.0612419i
$760$	−0.484476	+	1.16963i	−0.0175738	+	0.0424268i
$761$			23.6745i			0.858200i	0.903257	+	0.429100i	$0.141169\pi$
$761$			23.6745i			0.858200i	−0.903257	+	0.429100i	$0.858831\pi$
$762$	−69.5237	−	28.7977i	−2.51858	−	1.04323i
$763$	−14.0433	+	14.0433i	−0.508402	+	0.508402i
$764$	−57.8802			−2.09403
$765$	0.193863	+	2.49552i	0.00700915	+	0.0902256i
$766$	54.8581			1.98210
$767$	5.65120	−	5.65120i	0.204053	−	0.204053i
$768$	−60.9140	−	25.2314i	−2.19805	−	0.910461i
$769$		−	5.83645i		−	0.210468i	−0.994447	−	0.105234i	$-0.966441\pi$
$769$		−	5.83645i		−	0.210468i	0.994447	−	0.105234i	$-0.0335591\pi$
$770$	0.552247	−	1.33324i	0.0199016	−	0.0480467i
$771$	−20.7717	+	8.60391i	−0.748074	+	0.309862i
$772$	20.3066	+	49.0245i	0.730851	+	1.76443i
$773$	21.6507	+	21.6507i	0.778721	+	0.778721i	0.979613	−	0.200892i	$-0.0643840\pi$
$773$	21.6507	+	21.6507i	0.778721	+	0.778721i	−0.200892	+	0.979613i	$0.564384\pi$
$774$	−2.34141	−	2.34141i	−0.0841601	−	0.0841601i
$775$	0.231776	+	0.559556i	0.00832563	+	0.0200998i
$776$	5.54002	−	2.29475i	0.198875	−	0.0823768i
$777$	−6.61486	+	15.9697i	−0.237307	+	0.572909i
$778$			60.8333i			2.18098i
$779$	−0.202470	−	0.0838658i	−0.00725424	−	0.00300480i
$780$	33.8032	−	33.8032i	1.21035	−	1.21035i
$781$	−2.01661			−0.0721600
$782$	−58.3296	−	49.9203i	−2.08586	−	1.78514i
$783$	−1.83860			−0.0657063
$784$	−56.7455	+	56.7455i	−2.02662	+	2.02662i
$785$	17.6585	+	7.31437i	0.630257	+	0.261061i
$786$		−	18.8912i		−	0.673827i
$787$	14.4822	−	34.9631i	0.516234	−	1.24630i	−0.423967	−	0.905678i	$-0.639363\pi$
$787$	14.4822	−	34.9631i	0.516234	−	1.24630i	0.940201	−	0.340621i	$-0.110637\pi$
$788$	−119.950	+	49.6847i	−4.27303	+	1.76995i
$789$	11.2643	+	27.1944i	0.401019	+	0.968145i
$790$	8.37537	+	8.37537i	0.297982	+	0.297982i
$791$	1.11477	+	1.11477i	0.0396367	+	0.0396367i
$792$	−0.916378	−	2.21233i	−0.0325621	−	0.0786118i
$793$	40.8416	−	16.9172i	1.45033	−	0.600746i
$794$	27.4509	−	66.2724i	0.974197	−	2.35192i
$795$		−	2.38682i		−	0.0846516i
$796$	66.5791	+	27.5780i	2.35984	+	0.977476i
$797$	5.27565	−	5.27565i	0.186873	−	0.186873i	−0.607470	−	0.794343i	$-0.707815\pi$
$797$	5.27565	−	5.27565i	0.186873	−	0.186873i	0.794343	+	0.607470i	$0.207815\pi$
$798$	0.716469			0.0253627
$799$	−19.8452	−	6.47028i	−0.702072	−	0.228902i
$800$	−21.6961			−0.767073
$801$	−2.14077	+	2.14077i	−0.0756404	+	0.0756404i
$802$	−96.2606	−	39.8724i	−3.39908	−	1.40795i
$803$			1.21225i			0.0427793i
$804$	−39.0869	+	94.3641i	−1.37849	+	3.32797i
$805$	7.96624	−	3.29973i	0.280773	−	0.116300i
$806$	−3.58462	−	8.65404i	−0.126263	−	0.304826i
$807$	−24.8134	−	24.8134i	−0.873472	−	0.873472i
$808$	49.7171	+	49.7171i	1.74904	+	1.74904i
$809$	−14.4204	−	34.8140i	−0.506995	−	1.22399i	−0.945605	−	0.325317i	$-0.894529\pi$
$809$	−14.4204	−	34.8140i	−0.506995	−	1.22399i	0.438610	−	0.898678i	$-0.355471\pi$
$810$	17.1805	−	7.11642i	0.603663	−	0.250045i
$811$	−2.63137	+	6.35270i	−0.0924001	+	0.223073i	−0.963322	−	0.268348i	$-0.913522\pi$
$811$	−2.63137	+	6.35270i	−0.0924001	+	0.223073i	0.870922	+	0.491421i	$0.163522\pi$
$812$		−	2.27334i		−	0.0797785i
$813$	−14.2453	−	5.90060i	−0.499605	−	0.206943i
$814$	−7.13162	+	7.13162i	−0.249963	+	0.249963i
$815$	18.3295			0.642055
$816$	61.6178	−	71.9977i	2.15706	−	2.52042i
$817$	0.267954			0.00937452
$818$	36.8780	−	36.8780i	1.28941	−	1.28941i
$819$	4.01677	+	1.66380i	0.140357	+	0.0581379i
$820$		−	8.91389i		−	0.311287i
$821$	8.99652	−	21.7195i	0.313981	−	0.758017i	−0.685569	−	0.728008i	$-0.740446\pi$
$821$	8.99652	−	21.7195i	0.313981	−	0.758017i	0.999550	−	0.0300089i	$-0.00955356\pi$
$822$	35.3141	−	14.6276i	1.23172	−	0.510195i
$823$	20.9981	+	50.6939i	0.731948	+	1.76708i	0.635995	+	0.771693i	$0.280590\pi$
$823$	20.9981	+	50.6939i	0.731948	+	1.76708i	0.0959532	+	0.995386i	$0.469410\pi$
$824$	90.6645	+	90.6645i	3.15845	+	3.15845i
$825$	0.457173	+	0.457173i	0.0159167	+	0.0159167i
$826$	1.86441	+	4.50110i	0.0648713	+	0.156613i
$827$	−16.2768	+	6.74207i	−0.566000	+	0.234445i	−0.647288	−	0.762246i	$-0.724097\pi$
$827$	−16.2768	+	6.74207i	−0.566000	+	0.234445i	0.0812877	+	0.996691i	$0.474097\pi$
$828$	8.64390	−	20.8682i	0.300396	−	0.725220i
$829$			11.9207i			0.414022i	0.978339	+	0.207011i	$0.0663736\pi$
$829$			11.9207i			0.414022i	−0.978339	+	0.207011i	$0.933626\pi$
$830$	11.0800	+	4.58948i	0.384592	+	0.159303i
$831$	12.8056	−	12.8056i	0.444221	−	0.444221i
$832$	167.242			5.79806
$833$	−10.0901	−	19.8525i	−0.349601	−	0.687849i
$834$	19.8560			0.687558
$835$	−14.2471	+	14.2471i	−0.493040	+	0.493040i
$836$	0.282624	+	0.117067i	0.00977475	+	0.00404883i
$837$		−	3.37946i		−	0.116811i
$838$	35.0593	−	84.6406i	1.21110	−	2.92386i
$839$	39.1157	−	16.2022i	1.35042	−	0.559364i	0.414013	−	0.910271i	$-0.364127\pi$
$839$	39.1157	−	16.2022i	1.35042	−	0.559364i	0.936410	+	0.350907i	$0.114127\pi$
$840$	7.06431	+	17.0547i	0.243742	+	0.588445i
$841$	20.4293	+	20.4293i	0.704459	+	0.704459i
$842$	36.5691	+	36.5691i	1.26026	+	1.26026i
$843$	0.701617	+	1.69385i	0.0241650	+	0.0583394i
$844$	−100.245	+	41.5230i	−3.45059	+	1.42928i
$845$	−7.30153	+	17.6274i	−0.251180	+	0.606403i
$846$		−	8.39207i		−	0.288525i
$847$	12.6462	+	5.23822i	0.434528	+	0.179987i
$848$	16.2106	−	16.2106i	0.556674	−	0.556674i
$849$	−7.13254			−0.244788
$850$	3.48992	−	10.7040i	0.119703	−	0.367145i
$851$	−60.2626			−2.06578
$852$	28.7961	−	28.7961i	0.986538	−	0.986538i
$853$	30.6477	+	12.6947i	1.04936	+	0.434659i	0.839663	−	0.543108i	$-0.182753\pi$
$853$	30.6477	+	12.6947i	1.04936	+	0.434659i	0.209696	+	0.977767i	$0.432753\pi$
$854$			26.9485i			0.922159i
$855$	0.0311639	−	0.0752364i	0.00106578	−	0.00257303i
$856$	−80.8639	+	33.4949i	−2.76387	+	1.14483i
$857$	−5.88221	−	14.2009i	−0.200932	−	0.485094i	0.791007	−	0.611807i	$-0.209557\pi$
$857$	−5.88221	−	14.2009i	−0.200932	−	0.485094i	−0.991939	+	0.126713i	$0.959557\pi$
$858$	−7.07059	−	7.07059i	−0.241386	−	0.241386i
$859$	−30.2680	−	30.2680i	−1.03273	−	1.03273i	−0.999446	−	0.0332837i	$-0.989404\pi$
$859$	−30.2680	−	30.2680i	−1.03273	−	1.03273i	−0.0332837	−	0.999446i	$-0.510596\pi$
$860$	4.17083	+	10.0693i	0.142224	+	0.343359i
$861$	−2.95228	+	1.22288i	−0.100614	+	0.0416755i
$862$	−25.4835	+	61.5227i	−0.867972	+	2.09547i
$863$			31.3841i			1.06833i	0.845382	+	0.534163i	$0.179373\pi$
$863$			31.3841i			1.06833i	−0.845382	+	0.534163i	$0.820627\pi$
$864$	111.845	+	46.3277i	3.80505	+	1.57610i
$865$	13.5159	−	13.5159i	0.459554	−	0.459554i
$866$	26.4630			0.899250
$867$	13.6950	+	22.4500i	0.465107	+	0.762441i
$868$	4.17853			0.141829
$869$	1.28196	−	1.28196i	0.0434876	−	0.0434876i
$870$	1.28590	+	0.532638i	0.0435961	+	0.0180581i
$871$		−	68.5410i		−	2.32242i
$872$	56.7262	−	136.949i	1.92099	−	4.63768i
$873$	−0.356362	+	0.147610i	−0.0120610	+	0.00499585i
$874$	0.955882	+	2.30770i	0.0323332	+	0.0780592i
$875$	0.894104	+	0.894104i	0.0302262	+	0.0302262i
$876$	−17.3102	−	17.3102i	−0.584858	−	0.584858i
$877$	−11.1890	−	27.0128i	−0.377827	−	0.912156i	−0.992373	−	0.123274i	$-0.960661\pi$
$877$	−11.1890	−	27.0128i	−0.377827	−	0.912156i	0.614545	−	0.788882i	$-0.289339\pi$
$878$	−8.13214	+	3.36844i	−0.274447	+	0.113679i
$879$	1.83233	−	4.42363i	0.0618028	−	0.149205i
$880$			6.20998i			0.209338i
$881$	−21.1976	−	8.78032i	−0.714164	−	0.295816i	−0.00413755	−	0.999991i	$-0.501317\pi$
$881$	−21.1976	−	8.78032i	−0.714164	−	0.295816i	−0.710026	+	0.704175i	$0.751317\pi$
$882$	6.33102	−	6.33102i	0.213176	−	0.213176i
$883$	21.1206			0.710766			0.355383	−	0.934721i	$-0.384351\pi$
$883$	21.1206			0.710766			0.355383	+	0.934721i	$0.384351\pi$
$884$	−39.4970	+	121.142i	−1.32843	+	4.07446i
$885$	−2.18275			−0.0733724
$886$	33.9099	−	33.9099i	1.13923	−	1.13923i
$887$	−16.6051	−	6.87805i	−0.557544	−	0.230942i	0.0860744	−	0.996289i	$-0.472568\pi$
$887$	−16.6051	−	6.87805i	−0.557544	−	0.230942i	−0.643619	+	0.765346i	$0.722568\pi$
$888$		−	129.015i		−	4.32945i
$889$	−8.62058	+	20.8119i	−0.289125	+	0.698009i
$890$	12.5811	−	5.21125i	0.421719	−	0.174682i
$891$	−1.08926	−	2.62971i	−0.0364917	−	0.0880986i
$892$	−24.5498	−	24.5498i	−0.821987	−	0.821987i
$893$	0.480200	+	0.480200i	0.0160693	+	0.0160693i
$894$	−1.25429	−	3.02812i	−0.0419497	−	0.101275i
$895$	18.3070	−	7.58301i	0.611936	−	0.253472i
$896$	−18.0181	+	43.4995i	−0.601942	+	1.45322i
$897$		−	59.7469i		−	1.99489i
$898$	−46.7297	−	19.3561i	−1.55939	−	0.645921i
$899$	0.141118	−	0.141118i	0.00470654	−	0.00470654i
$900$	3.31234			0.110411
$901$	2.88246	+	5.67130i	0.0960286	+	0.188939i
$902$	−1.86451			−0.0620815
$903$	2.76276	−	2.76276i	0.0919388	−	0.0919388i
$904$	−10.8711	−	4.50297i	−0.361569	−	0.149767i
$905$		−	8.86555i		−	0.294701i
$906$	3.69703	−	8.92542i	0.122826	−	0.296527i
$907$	51.6439	−	21.3916i	1.71481	−	0.710297i	0.714870	−	0.699257i	$-0.246486\pi$
$907$	51.6439	−	21.3916i	1.71481	−	0.710297i	0.999939	−	0.0110397i	$-0.00351410\pi$
$908$	−55.4072	−	133.765i	−1.83875	−	4.43914i
$909$	−3.19805	−	3.19805i	−0.106073	−	0.106073i
$910$	−13.8281	−	13.8281i	−0.458398	−	0.458398i
$911$	0.214803	+	0.518579i	0.00711673	+	0.0171813i	0.927398	−	0.374076i	$-0.122040\pi$
$911$	0.214803	+	0.518579i	0.00711673	+	0.0171813i	−0.920281	+	0.391258i	$0.872040\pi$
$912$	−2.84846	+	1.17987i	−0.0943218	+	0.0390694i
$913$	0.702481	−	1.69594i	0.0232487	−	0.0561274i
$914$		−	40.1610i		−	1.32841i
$915$	−11.1545	−	4.62036i	−0.368758	−	0.152744i
$916$	−59.9768	+	59.9768i	−1.98169	+	1.98169i
$917$	−5.65508			−0.186747
$918$	−40.8471	+	47.7281i	−1.34816	+	1.57526i
$919$	4.29583			0.141706			0.0708531	−	0.997487i	$-0.477428\pi$
$919$	4.29583			0.141706			0.0708531	+	0.997487i	$0.477428\pi$
$920$	−45.5074	+	45.5074i	−1.50033	+	1.50033i
$921$	−16.9193	−	7.00821i	−0.557510	−	0.230928i
$922$			49.0127i			1.61415i
$923$	−10.4580	+	25.2477i	−0.344228	+	0.831040i
$924$	4.12104	−	1.70699i	0.135572	−	0.0561558i
$925$	−3.38184	−	8.16448i	−0.111194	−	0.268446i
$926$	68.6974	+	68.6974i	2.25754	+	2.25754i
$927$	−5.83200	−	5.83200i	−0.191548	−	0.191548i
$928$	2.73583	+	6.60488i	0.0898081	+	0.216816i
$929$	8.82633	−	3.65598i	0.289582	−	0.119949i	−0.233163	−	0.972438i	$-0.574908\pi$
$929$	8.82633	−	3.65598i	0.289582	−	0.119949i	0.522746	+	0.852489i	$0.324908\pi$
$930$	−0.979021	+	2.36357i	−0.0321034	+	0.0775044i
$931$			0.724531i			0.0237455i
$932$	19.1692	+	7.94015i	0.627908	+	0.260088i
$933$	−25.6503	+	25.6503i	−0.839752	+	0.839752i
$934$	80.3921			2.63051
$935$	−1.63839	−	0.534178i	−0.0535812	−	0.0174695i
$936$	−32.4504			−1.06068
$937$	−39.4176	+	39.4176i	−1.28772	+	1.28772i	−0.351546	+	0.936171i	$0.614344\pi$
$937$	−39.4176	+	39.4176i	−1.28772	+	1.28772i	−0.936171	+	0.351546i	$0.885656\pi$
$938$	38.6023	+	15.9896i	1.26041	+	0.522078i
$939$		−	42.7075i		−	1.39371i
$940$	−10.5706	+	25.5197i	−0.344775	+	0.832360i
$941$	−27.2017	+	11.2673i	−0.886751	+	0.367304i	−0.779111	−	0.626885i	$-0.784329\pi$
$941$	−27.2017	+	11.2673i	−0.886751	+	0.367304i	−0.107640	+	0.994190i	$0.534329\pi$
$942$	30.8959	+	74.5894i	1.00664	+	2.43025i
$943$	−7.87762	−	7.87762i	−0.256530	−	0.256530i
$944$	−14.8247	−	14.8247i	−0.482501	−	0.482501i
$945$	−2.69999	−	6.51836i	−0.0878308	−	0.212042i
$946$	2.10618	−	0.872408i	0.0684778	−	0.0283644i
$947$	−12.0899	+	29.1876i	−0.392869	+	0.948469i	0.596443	+	0.802655i	$0.296580\pi$
$947$	−12.0899	+	29.1876i	−0.392869	+	0.948469i	−0.989312	+	0.145814i	$0.953420\pi$
$948$			36.6114i			1.18908i
$949$	15.1772	+	6.28660i	0.492673	+	0.204072i
$950$	−0.259009	+	0.259009i	−0.00840336	+	0.00840336i
$951$	49.2859			1.59821
$952$	−37.3818	−	31.9925i	−1.21155	−	1.03688i
$953$	−18.4486			−0.597610			−0.298805	−	0.954314i	$-0.596588\pi$
$953$	−18.4486			−0.597610			−0.298805	+	0.954314i	$0.596588\pi$
$954$	−1.80859	+	1.80859i	−0.0585554	+	0.0585554i
$955$	−9.80061	−	4.05955i	−0.317140	−	0.131364i
$956$			31.6832i			1.02471i
$957$	0.0815272	−	0.196824i	0.00263540	−	0.00636242i
$958$	42.2207	−	17.4884i	1.36409	−	0.565024i
$959$	−4.37876	−	10.5713i	−0.141398	−	0.341364i
$960$	−32.2982	−	32.2982i	−1.04242	−	1.04242i
$961$	−21.6609	−	21.6609i	−0.698740	−	0.698740i
$962$	52.3032	+	126.271i	1.68632	+	4.07114i
$963$	5.20157	−	2.15456i	0.167618	−	0.0694298i
$964$	18.2241	−	43.9968i	0.586957	−	1.41704i
$965$			9.72535i			0.313070i
$966$	33.6494	+	13.9380i	1.08265	+	0.448449i
$967$	27.1273	−	27.1273i	0.872354	−	0.872354i	−0.120374	−	0.992729i	$-0.538409\pi$
$967$	27.1273	−	27.1273i	0.872354	−	0.872354i	0.992729	+	0.120374i	$0.0384095\pi$
$968$	−102.165			−3.28371
$969$	−0.0662656	−	0.853007i	−0.00212876	−	0.0274025i
$970$	1.73498			0.0557067
$971$	−37.1678	+	37.1678i	−1.19277	+	1.19277i	−0.216486	+	0.976286i	$0.569459\pi$
$971$	−37.1678	+	37.1678i	−1.19277	+	1.19277i	−0.976286	+	0.216486i	$0.930541\pi$
$972$	−31.2769	−	12.9553i	−1.00321	−	0.415542i
$973$		−	5.94390i		−	0.190553i
$974$	24.4963	−	59.1394i	0.784913	−	1.89495i
$975$	8.09461	−	3.35290i	0.259235	−	0.107379i
$976$	−44.3783	−	107.139i	−1.42052	−	3.42943i
$977$	24.3083	+	24.3083i	0.777691	+	0.777691i	0.979438	−	0.201747i	$-0.0646618\pi$
$977$	24.3083	+	24.3083i	0.777691	+	0.777691i	−0.201747	+	0.979438i	$0.564662\pi$
$978$	54.7470	+	54.7470i	1.75061	+	1.75061i
$979$	−0.797652	−	1.92570i	−0.0254931	−	0.0615457i
$980$	−27.2267	+	11.2777i	−0.869724	+	0.360251i
$981$	−3.64891	+	8.80926i	−0.116501	+	0.281258i
$982$		−	69.5971i		−	2.22093i
$983$	26.5414	+	10.9938i	0.846539	+	0.350648i	0.763429	−	0.645892i	$-0.223514\pi$
$983$	26.5414	+	10.9938i	0.846539	+	0.350648i	0.0831107	+	0.996540i	$0.473514\pi$
$984$	16.8650	−	16.8650i	0.537637	−	0.537637i
$985$	−23.7953			−0.758180
$986$	−3.69867	+	0.287330i	−0.117790	+	0.00915045i
$987$	9.90228			0.315193
$988$	2.93132	−	2.93132i	0.0932578	−	0.0932578i
$989$	12.5846	+	5.21272i	0.400168	+	0.165755i
$990$		−	0.692839i		−	0.0220199i
$991$	−18.3049	+	44.1919i	−0.581474	+	1.40380i	0.310003	+	0.950736i	$0.399670\pi$
$991$	−18.3049	+	44.1919i	−0.581474	+	1.40380i	−0.891477	+	0.453066i	$0.850330\pi$
$992$	−12.1402	+	5.02863i	−0.385451	+	0.159659i
$993$	−15.4357	−	37.2650i	−0.489836	−	1.18257i
$994$	−11.7798	−	11.7798i	−0.373634	−	0.373634i
$995$	9.33932	+	9.33932i	0.296076	+	0.296076i
$996$	14.1860	+	34.2481i	0.449502	+	1.08519i
$997$	7.21729	−	2.98950i	0.228574	−	0.0946783i	−0.265457	−	0.964123i	$-0.585523\pi$
$997$	7.21729	−	2.98950i	0.228574	−	0.0946783i	0.494031	+	0.869444i	$0.335523\pi$
$998$	−30.0343	+	72.5091i	−0.950718	+	2.29524i
$999$			49.3097i			1.56009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.26.1	✓	24
3.2	odd	2		765.2.be.b.451.6		24
5.2	odd	4		425.2.n.f.349.1		24
5.3	odd	4		425.2.n.c.349.6		24
5.4	even	2		425.2.m.b.26.6		24
17.2	even	8	inner	85.2.l.a.36.1	yes	24
17.6	odd	16		1445.2.a.q.1.1		12
17.7	odd	16		1445.2.d.j.866.23		24
17.10	odd	16		1445.2.d.j.866.24		24
17.11	odd	16		1445.2.a.p.1.1		12
51.2	odd	8		765.2.be.b.631.6		24
85.2	odd	8		425.2.n.c.274.6		24
85.19	even	8		425.2.m.b.376.6		24
85.53	odd	8		425.2.n.f.274.1		24
85.74	odd	16		7225.2.a.bq.1.12		12
85.79	odd	16		7225.2.a.bs.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	1.1	even	1	trivial
85.2.l.a.36.1	yes	24	17.2	even	8	inner
425.2.m.b.26.6		24	5.4	even	2
425.2.m.b.376.6		24	85.19	even	8
425.2.n.c.274.6		24	85.2	odd	8
425.2.n.c.349.6		24	5.3	odd	4
425.2.n.f.274.1		24	85.53	odd	8
425.2.n.f.349.1		24	5.2	odd	4
765.2.be.b.451.6		24	3.2	odd	2
765.2.be.b.631.6		24	51.2	odd	8
1445.2.a.p.1.1		12	17.11	odd	16
1445.2.a.q.1.1		12	17.6	odd	16
1445.2.d.j.866.23		24	17.7	odd	16
1445.2.d.j.866.24		24	17.10	odd	16
7225.2.a.bq.1.12		12	85.74	odd	16
7225.2.a.bs.1.12		12	85.79	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+(-1.93083 + 1.93083i) q^{2} +(-1.42916 - 0.591976i) q^{3} -5.45623i q^{4} +(0.382683 - 0.923880i) q^{5} +(3.90247 - 1.61646i) q^{6} +(-0.483886 - 1.16820i) q^{7} +(6.67340 + 6.67340i) q^{8} +(-0.429267 - 0.429267i) q^{9} +(1.04496 + 2.52275i) q^{10} +(0.386141 - 0.159945i) q^{11} +(-3.22996 + 7.79781i) q^{12} -5.66390i q^{13} +(3.18991 + 1.32130i) q^{14} +(-1.09383 + 1.09383i) q^{15} -14.8580 q^{16} +(1.27807 - 3.92002i) q^{17} +1.65769 q^{18} +(-0.0948539 + 0.0948539i) q^{19} +(-5.04090 - 2.08801i) q^{20} +1.95600i q^{21} +(-0.436747 + 1.05440i) q^{22} +(-6.30014 + 2.60960i) q^{23} +(-5.58684 - 13.4878i) q^{24} +(-0.707107 - 0.707107i) q^{25} +(10.9361 + 10.9361i) q^{26} +(2.13530 + 5.15508i) q^{27} +(-6.37399 + 2.64019i) q^{28} +(-0.126098 + 0.304427i) q^{29} -4.22400i q^{30} +(-0.559556 - 0.231776i) q^{31} +(15.3415 - 15.3415i) q^{32} -0.646540 q^{33} +(5.10115 + 10.0366i) q^{34} -1.26445 q^{35} +(-2.34218 + 2.34218i) q^{36} +(8.16448 + 3.38184i) q^{37} -0.366294i q^{38} +(-3.35290 + 8.09461i) q^{39} +(8.71922 - 3.61162i) q^{40} +(0.625194 + 1.50935i) q^{41} +(-3.77670 - 3.77670i) q^{42} +(-1.41246 - 1.41246i) q^{43} +(-0.872696 - 2.10687i) q^{44} +(-0.560864 + 0.232318i) q^{45} +(7.12581 - 17.2032i) q^{46} -5.06253i q^{47} +(21.2344 + 8.79557i) q^{48} +(3.81919 - 3.81919i) q^{49} +2.73061 q^{50} +(-4.14712 + 4.84573i) q^{51} -30.9036 q^{52} +(-1.09104 + 1.09104i) q^{53} +(-14.0765 - 5.83068i) q^{54} -0.417956i q^{55} +(4.56673 - 11.0251i) q^{56} +(0.191712 - 0.0794098i) q^{57} +(-0.344324 - 0.831272i) q^{58} +(0.997758 + 0.997758i) q^{59} +(5.96818 + 5.96818i) q^{60} +(2.98684 + 7.21086i) q^{61} +(1.52793 - 0.632889i) q^{62} +(-0.293755 + 0.709187i) q^{63} +29.5276i q^{64} +(-5.23277 - 2.16748i) q^{65} +(1.24836 - 1.24836i) q^{66} +12.1014 q^{67} +(-21.3885 - 6.97346i) q^{68} +10.5487 q^{69} +(2.44145 - 2.44145i) q^{70} +(-4.45766 - 1.84642i) q^{71} -5.72934i q^{72} +(-1.10994 + 2.67964i) q^{73} +(-22.2940 + 9.23447i) q^{74} +(0.591976 + 1.42916i) q^{75} +(0.517545 + 0.517545i) q^{76} +(-0.373696 - 0.373696i) q^{77} +(-9.15545 - 22.1032i) q^{78} +(4.00751 - 1.65997i) q^{79} +(-5.68590 + 13.7270i) q^{80} -6.81023i q^{81} +(-4.12145 - 1.70716i) q^{82} +(3.10563 - 3.10563i) q^{83} +10.6724 q^{84} +(-3.13253 - 2.68091i) q^{85} +5.45443 q^{86} +(0.360427 - 0.360427i) q^{87} +(3.64425 + 1.50950i) q^{88} -4.98704i q^{89} +(0.634369 - 1.53150i) q^{90} +(-6.61659 + 2.74068i) q^{91} +(14.2386 + 34.3750i) q^{92} +(0.662488 + 0.662488i) q^{93} +(9.77489 + 9.77489i) q^{94} +(0.0513346 + 0.123933i) q^{95} +(-31.0071 + 12.8436i) q^{96} +(0.243150 - 0.587015i) q^{97} +14.7484i q^{98} +(-0.234417 - 0.0970985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100}) \) 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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