LMFDB - Embedded newform 85.2.l.a.36.1

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			36.1
Character	$\chi$	$=$	85.36
Dual form			85.2.l.a.26.1

$q$ -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 $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$ .

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

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

)

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

$2$	−1.93083	−	1.93083i	−1.36530	−	1.36530i	−0.867005	−	0.498300i	$-0.833958\pi$
$2$	−1.93083	−	1.93083i	−1.36530	−	1.36530i	−0.498300	−	0.867005i	$-0.666042\pi$
$3$	−1.42916	+	0.591976i	−0.825124	+	0.341778i	−0.754971	−	0.655759i	$-0.772349\pi$
$3$	−1.42916	+	0.591976i	−0.825124	+	0.341778i	−0.0701535	+	0.997536i	$0.522349\pi$
$4$			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	−0.988560	−	0.150827i	$-0.951806\pi$
$7$	−0.483886	+	1.16820i	−0.182892	+	0.441540i	0.805668	+	0.592367i	$0.201806\pi$
$8$	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	0.440136	−	0.897931i	$-0.354930\pi$
$11$	0.386141	+	0.159945i	0.116426	+	0.0482252i	−0.323710	+	0.946156i	$0.604930\pi$
$12$	−3.22996	−	7.79781i	−0.932408	−	2.25103i
$13$			5.66390i			1.57088i	0.618935	+	0.785442i	$0.287564\pi$
$13$			5.66390i			1.57088i	−0.618935	+	0.785442i	$0.712436\pi$
$14$	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	0.696143	−	0.717904i	$-0.254898\pi$
$19$	−0.0948539	−	0.0948539i	−0.0217610	−	0.0217610i	−0.717904	+	0.696143i	$0.754898\pi$
$20$	−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	−0.387717	−	0.921778i	$-0.626736\pi$
$23$	−6.30014	−	2.60960i	−1.31367	−	0.544140i	−0.925953	+	0.377638i	$0.876736\pi$
$24$	−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	0.911739	−	0.410770i	$-0.134740\pi$
$29$	−0.126098	−	0.304427i	−0.0234158	−	0.0565307i	−0.935155	+	0.354239i	$0.884740\pi$
$30$			4.22400i			0.771194i
$31$	−0.559556	+	0.231776i	−0.100499	+	0.0416281i	−0.432367	−	0.901698i	$-0.642321\pi$
$31$	−0.559556	+	0.231776i	−0.100499	+	0.0416281i	0.331867	+	0.943326i	$0.392321\pi$
$32$	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	0.408112	−	0.912932i	$-0.366187\pi$
$37$	8.16448	−	3.38184i	1.34223	−	0.555970i	0.934119	+	0.356961i	$0.116187\pi$
$38$			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	−0.867511	−	0.497417i	$-0.834282\pi$
$41$	0.625194	−	1.50935i	0.0976389	−	0.235721i	0.965150	+	0.261696i	$0.0842818\pi$
$42$	−3.77670	+	3.77670i	−0.582757	+	0.582757i
$43$	−1.41246	+	1.41246i	−0.215398	+	0.215398i	−0.806556	−	0.591158i	$-0.798671\pi$
$43$	−1.41246	+	1.41246i	−0.215398	+	0.215398i	0.591158	+	0.806556i	$0.298671\pi$
$44$	−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	$0.120376\pi$
$47$			5.06253i			0.738445i	−0.929341	+	0.369223i	$0.879624\pi$
$48$	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	0.628193	−	0.778058i	$-0.283795\pi$
$53$	−1.09104	−	1.09104i	−0.149865	−	0.149865i	−0.778058	+	0.628193i	$0.783795\pi$
$54$	−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	−0.639169	−	0.769066i	$-0.720722\pi$
$59$	0.997758	−	0.997758i	0.129897	−	0.129897i	0.769066	+	0.639169i	$0.220722\pi$
$60$	5.96818	−	5.96818i	0.770489	−	0.770489i
$61$	2.98684	−	7.21086i	0.382425	−	0.923256i	−0.609070	−	0.793116i	$-0.708457\pi$
$61$	2.98684	−	7.21086i	0.382425	−	0.923256i	0.991496	−	0.130140i	$-0.0415427\pi$
$62$	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	−0.631177	−	0.775639i	$-0.717428\pi$
$71$	−4.45766	+	1.84642i	−0.529027	+	0.219130i	0.102150	+	0.994769i	$0.467428\pi$
$72$			5.72934i			0.675209i
$73$	−1.10994	−	2.67964i	−0.129909	−	0.313628i	0.845520	−	0.533944i	$-0.179291\pi$
$73$	−1.10994	−	2.67964i	−0.129909	−	0.313628i	−0.975428	+	0.220317i	$0.929291\pi$
$74$	−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	0.596556	−	0.802572i	$-0.296535\pi$
$79$	4.00751	+	1.65997i	0.450880	+	0.186761i	−0.145675	+	0.989332i	$0.546535\pi$
$80$	−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	0.856701	−	0.515814i	$-0.172510\pi$
$83$	3.10563	+	3.10563i	0.340887	+	0.340887i	−0.515814	+	0.856701i	$0.672510\pi$
$84$	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	$0.0851451\pi$
$89$			4.98704i			0.528625i	−0.964437	+	0.264313i	$0.914855\pi$
$90$	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	0.935743	−	0.352683i	$-0.114731\pi$
$97$	0.243150	+	0.587015i	0.0246881	+	0.0596024i	−0.911055	+	0.412285i	$0.864731\pi$
$98$		−	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	−0.997398	−	0.0720853i	$-0.977035\pi$
$107$	−3.54909	−	8.56826i	−0.343103	−	0.828325i	0.654295	−	0.756239i	$-0.272965\pi$
$108$	28.1273	+	11.6507i	2.70655	+	1.12109i
$109$	−6.01065	+	14.5110i	−0.575716	+	1.38990i	0.320909	+	0.947110i	$0.396012\pi$
$109$	−6.01065	+	14.5110i	−0.575716	+	1.38990i	−0.896625	+	0.442791i	$0.853988\pi$
$110$	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	0.327844	−	0.944732i	$-0.393678\pi$
$113$	−1.15190	−	0.477131i	−0.108361	−	0.0448847i	−0.436205	+	0.899847i	$0.643678\pi$
$114$	−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	−0.125773	+	0.992059i	$0.540141\pi$
$127$	−12.5973	+	12.5973i	−1.11783	+	1.11783i	−0.992059	+	0.125773i	$0.959859\pi$
$128$	−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	0.980842	−	0.194805i	$-0.0624075\pi$
$131$	1.71149	+	4.13191i	0.149534	+	0.361007i	−0.831308	+	0.555812i	$0.812407\pi$
$132$		−	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	−0.190820	−	0.981625i	$-0.561115\pi$
$139$	4.34294	−	1.79890i	0.368363	−	0.152581i	0.559183	+	0.829044i	$0.311115\pi$
$140$		−	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	$0.0101189\pi$
$149$			0.775949i			0.0635683i	−0.999495	+	0.0317841i	$0.989881\pi$
$150$	−3.90247	+	1.61646i	−0.318635	+	0.131983i
$151$	1.61724	+	1.61724i	0.131609	+	0.131609i	0.769843	−	0.638234i	$-0.220335\pi$
$151$	1.61724	+	1.61724i	0.131609	+	0.131609i	−0.638234	+	0.769843i	$0.720335\pi$
$152$	−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	$-0.723870\pi$
$157$		−	19.1134i		−	1.52541i	0.646745	−	0.762707i	$-0.276130\pi$
$158$	−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	−0.368508	−	0.929625i	$-0.620131\pi$
$163$	7.01440	−	16.9343i	0.549410	−	1.32639i	0.917918	−	0.396769i	$-0.129869\pi$
$164$	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	−0.959907	−	0.280320i	$-0.909559\pi$
$167$	−18.6147	+	7.71045i	−1.44045	+	0.596653i	−0.480540	+	0.876973i	$0.659559\pi$
$168$	−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	0.408389	−	0.912808i	$-0.366091\pi$
$173$	17.6594	−	7.31475i	1.34262	−	0.556130i	0.934227	+	0.356678i	$0.116091\pi$
$174$		−	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	0.0484485	−	0.998826i	$-0.484572\pi$
$179$	14.0116	−	14.0116i	1.04727	−	1.04727i	0.998826	−	0.0484485i	$-0.0154277\pi$
$180$	1.26758	−	3.06020i	0.0944797	−	0.228094i
$181$	8.19070	+	3.39270i	0.608810	+	0.252177i	0.665719	−	0.746202i	$-0.268125\pi$
$181$	8.19070	+	3.39270i	0.608810	+	0.252177i	−0.0569098	+	0.998379i	$0.518125\pi$
$182$	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	$0.125381\pi$
$191$			10.6081i			0.767576i	−0.923421	+	0.383788i	$0.874619\pi$
$192$	17.4797	+	42.1996i	1.26149	+	3.04550i
$193$	−8.98505	−	3.72173i	−0.646758	−	0.267896i	0.0350962	−	0.999384i	$-0.488826\pi$
$193$	−8.98505	−	3.72173i	−0.646758	−	0.267896i	−0.681854	+	0.731488i	$0.738826\pi$
$194$	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	0.165748	+	0.986168i	$0.446996\pi$
$197$	−9.10606	+	21.9840i	−0.648780	+	1.56629i	−0.814528	+	0.580125i	$0.803004\pi$
$198$	0.640100	+	0.265138i	0.0454899	+	0.0188426i
$199$	−5.05440	−	12.2024i	−0.358297	−	0.865006i	−0.995540	−	0.0943427i	$-0.969925\pi$
$199$	−5.05440	−	12.2024i	−0.358297	−	0.865006i	0.637243	−	0.770663i	$-0.280075\pi$
$200$			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	0.411551	+	0.911387i	$0.364987\pi$
$211$	−7.61020	+	18.3726i	−0.523907	+	1.26482i	−0.935458	+	0.353438i	$0.885013\pi$
$212$	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	0.841523	−	0.540221i	$-0.181659\pi$
$223$	4.49940	+	4.49940i	0.301302	+	0.301302i	−0.540221	+	0.841523i	$0.681659\pi$
$224$	−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	0.994912	−	0.100747i	$-0.0321233\pi$
$227$	24.5160	+	10.1548i	1.62718	+	0.674001i	0.632270	+	0.774748i	$0.282123\pi$
$228$	−0.433278	+	1.04603i	−0.0286946	+	0.0692748i
$229$	−10.9924	+	10.9924i	−0.726395	+	0.726395i	−0.969900	−	0.243504i	$-0.921703\pi$
$229$	−10.9924	+	10.9924i	−0.726395	+	0.726395i	0.243504	+	0.969900i	$0.421703\pi$
$230$	−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	0.869016	−	0.494784i	$-0.164753\pi$
$233$	−1.45524	−	3.51327i	−0.0953363	−	0.230162i	−0.964352	+	0.264622i	$0.914753\pi$
$234$			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	−0.107541	−	0.994201i	$-0.534298\pi$
$241$	8.06359	−	3.34005i	0.519421	−	0.215151i	0.626963	+	0.779049i	$0.284298\pi$
$242$			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	$-0.840257\pi$
$251$		−	15.2424i		−	0.962093i	0.876695	−	0.481047i	$-0.159743\pi$
$252$	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	0.950820	−	0.309743i	$-0.100243\pi$
$257$	10.2772	+	10.2772i	0.641077	+	0.641077i	−0.309743	+	0.950820i	$0.600243\pi$
$258$	−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	−0.987471	−	0.157800i	$-0.949560\pi$
$263$	−13.4550	+	13.4550i	−0.829671	+	0.829671i	0.157800	+	0.987471i	$0.449560\pi$
$264$	−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	0.362499	−	0.931984i	$-0.381924\pi$
$269$	20.9581	−	8.68112i	1.27784	−	0.529297i	0.915338	+	0.402687i	$0.131924\pi$
$270$	−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	0.730261	−	0.683168i	$-0.239398\pi$
$277$	−4.48012	−	10.8160i	−0.269184	−	0.649868i	−0.999445	+	0.0332998i	$0.989398\pi$
$278$	−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	−0.731662	−	0.681667i	$-0.761255\pi$
$281$	−0.838071	+	0.838071i	−0.0499951	+	0.0499951i	0.681667	+	0.731662i	$0.261255\pi$
$282$	−8.18335	+	19.7564i	−0.487311	+	1.17647i
$283$	4.25986	+	1.76449i	0.253222	+	0.104888i	0.505684	−	0.862719i	$-0.331240\pi$
$283$	4.25986	+	1.76449i	0.253222	+	0.104888i	−0.252462	+	0.967607i	$0.581240\pi$
$284$	−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	$-0.971181\pi$
$293$		−	3.09527i		−	0.180828i	0.995904	−	0.0904138i	$-0.0288190\pi$
$294$	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	0.944538	+	0.328402i	$0.106510\pi$
$311$	8.97392	+	21.6650i	0.508864	+	1.22851i	−0.435674	+	0.900105i	$0.643490\pi$
$312$	−76.3938	−	31.6433i	−4.32494	−	1.79145i
$313$	10.5652	−	25.5068i	0.597183	−	1.44173i	−0.279257	−	0.960216i	$-0.590088\pi$
$313$	10.5652	−	25.5068i	0.597183	−	1.44173i	0.876440	−	0.481511i	$-0.159912\pi$
$314$	−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	−0.655737	−	0.754989i	$-0.727642\pi$
$317$	−29.4357	−	12.1926i	−1.65327	−	0.684807i	−0.997534	+	0.0701822i	$0.977642\pi$
$318$	−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	0.0135172	−	0.999909i	$-0.495697\pi$
$331$	18.4377	−	18.4377i	1.01343	−	1.01343i	0.999909	−	0.0135172i	$-0.00430279\pi$
$332$	−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	0.0739055	−	0.997265i	$-0.476454\pi$
$337$	15.2613	−	6.32145i	0.831338	−	0.344351i	0.757432	+	0.652914i	$0.226454\pi$
$338$	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	0.565521	+	0.824734i	$0.308675\pi$
$347$	−7.77787	+	18.7774i	−0.417538	+	1.00803i	−0.983059	+	0.183292i	$0.941325\pi$
$348$	−1.96657	+	1.96657i	−0.105419	+	0.105419i
$349$	3.45460	−	3.45460i	0.184921	−	0.184921i	−0.608575	−	0.793496i	$-0.708259\pi$
$349$	3.45460	−	3.45460i	0.184921	−	0.184921i	0.793496	+	0.608575i	$0.208259\pi$
$350$	−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	$-0.793817\pi$
$353$		−	22.6733i		−	1.20678i	0.797447	−	0.603389i	$-0.206183\pi$
$354$	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	0.912400	−	0.409300i	$-0.134227\pi$
$359$	9.53237	+	9.53237i	0.503099	+	0.503099i	−0.409300	+	0.912400i	$0.634227\pi$
$360$	−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	−0.941816	−	0.336130i	$-0.890882\pi$
$367$	−0.731262	+	1.76542i	−0.0381715	+	0.0921543i	0.903644	+	0.428284i	$0.140882\pi$
$368$	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	−0.998858	−	0.0477856i	$-0.984784\pi$
$379$	−6.35332	−	15.3383i	−0.326348	−	0.787874i	0.672509	−	0.740089i	$-0.265216\pi$
$380$	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	−0.969797	−	0.243914i	$-0.921568\pi$
$383$	−14.2058	+	14.2058i	−0.725883	+	0.725883i	0.243914	+	0.969797i	$0.421568\pi$
$384$	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	0.982893	−	0.184178i	$-0.0589622\pi$
$389$	15.7531	+	15.7531i	0.798715	+	0.798715i	−0.184178	+	0.982893i	$0.558962\pi$
$390$	−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	−0.321285	−	0.946983i	$-0.604115\pi$
$397$	−24.2702	−	10.0530i	−1.21809	−	0.504548i	−0.896801	+	0.442435i	$0.854115\pi$
$398$	−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	0.0839140	−	0.996473i	$-0.473258\pi$
$401$	14.6020	−	35.2524i	0.729191	−	1.76042i	0.645277	−	0.763949i	$-0.276742\pi$
$402$	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	−0.537860	−	0.843034i	$-0.680767\pi$
$419$	−30.9970	−	12.8394i	−1.51430	−	0.627244i	−0.976440	+	0.215790i	$0.930767\pi$
$420$	4.08413	+	9.85997i	0.199285	+	0.481117i
$421$			18.9396i			0.923058i	0.887125	+	0.461529i	$0.152699\pi$
$421$			18.9396i			0.923058i	−0.887125	+	0.461529i	$0.847301\pi$
$422$	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	0.852354	−	0.522965i	$-0.175174\pi$
$431$	22.5308	+	9.33254i	1.08527	+	0.449533i	0.232914	+	0.972497i	$0.425174\pi$
$432$	−31.7263	+	76.5940i	−1.52643	+	3.68513i
$433$	−6.85275	+	6.85275i	−0.329322	+	0.329322i	−0.852329	−	0.523007i	$-0.824810\pi$
$433$	−6.85275	+	6.85275i	−0.329322	+	0.329322i	0.523007	+	0.852329i	$0.324810\pi$
$434$	−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	−0.310480	−	0.950580i	$-0.600490\pi$
$439$	2.97814	−	1.23359i	0.142139	−	0.0588759i	0.452619	+	0.891704i	$0.350490\pi$
$440$	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	−0.663691	−	0.748007i	$-0.731011\pi$
$449$	7.08856	−	17.1133i	0.334530	−	0.807626i	0.998221	−	0.0596199i	$-0.0189889\pi$
$450$	−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	0.420709	−	0.907196i	$-0.361781\pi$
$457$	−10.3999	−	10.3999i	−0.486487	−	0.486487i	−0.907196	+	0.420709i	$0.861781\pi$
$458$	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	0.937937	−	0.346806i	$-0.112734\pi$
$461$	12.6921	+	12.6921i	0.591131	+	0.591131i	−0.346806	+	0.937937i	$0.612734\pi$
$462$	−2.06240	+	0.854275i	−0.0959516	+	0.0397445i
$463$			35.5792i			1.65350i	0.562567	+	0.826752i	$0.309814\pi$
$463$			35.5792i			1.65350i	−0.562567	+	0.826752i	$0.690186\pi$
$464$	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	−0.999351	−	0.0360098i	$-0.988535\pi$
$467$	−20.8180	+	20.8180i	−0.963342	+	0.963342i	0.0360098	+	0.999351i	$0.488535\pi$
$468$	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	−0.706846	−	0.707368i	$-0.749883\pi$
$479$	−15.4620	+	6.40457i	−0.706477	+	0.292632i	0.000368864		1.00000i	$0.499883\pi$
$480$		−	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	−0.166466	−	0.986047i	$-0.553235\pi$
$487$	−21.6579	−	8.97101i	−0.981415	−	0.406515i	−0.814950	+	0.579532i	$0.803235\pi$
$488$	−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	0.171787	−	0.985134i	$-0.445046\pi$
$491$	−18.0226	−	18.0226i	−0.813347	−	0.813347i	−0.985134	+	0.171787i	$0.945046\pi$
$492$	−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	0.887341	−	0.461114i	$-0.152550\pi$
$499$	26.5542	+	10.9991i	1.18873	+	0.492388i	0.301388	+	0.953502i	$0.402550\pi$
$500$	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	−0.923792	−	0.382895i	$-0.874927\pi$
$503$	0.00393607	−	0.00950252i	0.000175501	−	0.000423697i	0.923967	+	0.382472i	$0.124927\pi$
$504$	−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	0.578386	−	0.815763i	$-0.303683\pi$
$521$	9.37063	+	3.88144i	0.410535	+	0.170049i	−0.167851	+	0.985812i	$0.553683\pi$
$522$	−0.209030	−	0.504644i	−0.00914902	−	0.0220877i
$523$			16.7568i			0.732724i	0.930472	+	0.366362i	$0.119397\pi$
$523$			16.7568i			0.732724i	−0.930472	+	0.366362i	$0.880603\pi$
$524$	−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	−0.712596	−	0.701574i	$-0.752481\pi$
$541$	−16.7559	+	6.94050i	−0.720390	+	0.298395i	−0.00779397	+	0.999970i	$0.502481\pi$
$542$	−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	0.110738	−	0.993850i	$-0.464679\pi$
$547$	20.8574	−	8.63943i	0.891799	−	0.369395i	0.781061	+	0.624454i	$0.214679\pi$
$548$			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	$-0.959595\pi$
$557$		−	5.97545i		−	0.253188i	0.991955	−	0.126594i	$-0.0404045\pi$
$558$	−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	0.651940	−	0.758271i	$-0.273955\pi$
$563$	−2.52298	−	2.52298i	−0.106331	−	0.106331i	−0.758271	+	0.651940i	$0.773955\pi$
$564$	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	0.384846	−	0.922981i	$-0.374254\pi$
$569$	31.1965	−	31.1965i	1.30783	−	1.30783i	0.922981	−	0.384846i	$-0.125746\pi$
$570$	0.400663	−	0.400663i	0.0167819	−	0.0167819i
$571$	−4.81154	+	11.6161i	−0.201357	+	0.486118i	−0.992012	−	0.126143i	$-0.959740\pi$
$571$	−4.81154	+	11.6161i	−0.201357	+	0.486118i	0.790655	+	0.612262i	$0.209740\pi$
$572$	−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	−0.506209	−	0.862411i	$-0.668954\pi$
$587$	8.63007	−	8.63007i	0.356201	−	0.356201i	0.862411	+	0.506209i	$0.168954\pi$
$588$	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	0.853298	−	0.521423i	$-0.174599\pi$
$593$	8.08169	+	8.08169i	0.331875	+	0.331875i	−0.521423	+	0.853298i	$0.674599\pi$
$594$	−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	$-0.812006\pi$
$599$		−	27.2578i		−	1.11372i	0.830606	−	0.556861i	$-0.187994\pi$
$600$	−5.58684	−	13.4878i	−0.228082	−	0.550638i
$601$	−10.3510	−	4.28754i	−0.422228	−	0.174893i	0.161444	−	0.986882i	$-0.448385\pi$
$601$	−10.3510	−	4.28754i	−0.422228	−	0.174893i	−0.583672	+	0.811989i	$0.698385\pi$
$602$	−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	−0.849297	−	0.527915i	$-0.822974\pi$
$607$	−15.3256	−	36.9992i	−0.622046	−	1.50175i	0.227252	−	0.973836i	$-0.427026\pi$
$608$		−	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	0.998495	−	0.0548478i	$-0.0174674\pi$
$617$	6.30101	+	15.2120i	0.253669	+	0.612411i	−0.744826	+	0.667259i	$0.767467\pi$
$618$	53.0188	+	21.9611i	2.13273	+	0.883405i
$619$	2.91366	−	7.03419i	0.117110	−	0.282728i	−0.854445	−	0.519541i	$-0.826103\pi$
$619$	2.91366	−	7.03419i	0.117110	−	0.282728i	0.971555	+	0.236813i	$0.0761029\pi$
$620$	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	−0.998838	−	0.0481871i	$-0.984656\pi$
$631$	−26.3010	−	26.3010i	−1.04703	−	1.04703i	−0.0481871	−	0.998838i	$-0.515344\pi$
$632$	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	0.975504	−	0.219983i	$-0.0706003\pi$
$641$	3.29555	+	7.95617i	0.130167	+	0.314250i	−0.845337	+	0.534233i	$0.820600\pi$
$642$		−	39.1743i		−	1.54609i
$643$	17.6673	−	7.31804i	0.696731	−	0.288595i	−0.00607035	−	0.999982i	$-0.501932\pi$
$643$	17.6673	−	7.31804i	0.696731	−	0.288595i	0.702801	+	0.711386i	$0.251932\pi$
$644$	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	−0.845527	−	0.533933i	$-0.820713\pi$
$653$	3.31942	−	8.01379i	0.129899	−	0.313604i	0.975425	+	0.220330i	$0.0707133\pi$
$654$	−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	$-0.752372\pi$
$659$		−	36.0328i		−	1.40364i	0.712355	−	0.701819i	$-0.247628\pi$
$660$	3.25914	−	1.34998i	0.126862	−	0.0525479i
$661$	6.64994	+	6.64994i	0.258653	+	0.258653i	0.824506	−	0.565853i	$-0.191453\pi$
$661$	6.64994	+	6.64994i	0.258653	+	0.258653i	−0.565853	+	0.824506i	$0.691453\pi$
$662$	−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	−0.953935	−	0.300013i	$-0.903009\pi$
$673$	−1.74487	+	4.21250i	−0.0672599	+	0.162380i	0.886675	+	0.462393i	$0.153009\pi$
$674$	−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	0.352947	−	0.935643i	$-0.385180\pi$
$677$	32.8914	−	13.6240i	1.26412	−	0.523615i	0.911171	+	0.412029i	$0.135180\pi$
$678$	−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	−0.584121	−	0.811667i	$-0.698561\pi$
$683$	−11.0606	+	4.58144i	−0.423222	+	0.175304i	0.160899	+	0.986971i	$0.448561\pi$
$684$			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	0.716907	−	0.697169i	$-0.245557\pi$
$691$	19.2122	+	7.95793i	0.730865	+	0.302734i	0.0139574	+	0.999903i	$0.495557\pi$
$692$	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	$-0.920027\pi$
$701$		−	13.1645i		−	0.497215i	0.968604	−	0.248607i	$-0.0799729\pi$
$702$	−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	0.999999	−	0.00135939i	$-0.000432708\pi$
$709$	7.77328	+	18.7664i	0.291932	+	0.704785i	−0.708067	+	0.706145i	$0.750433\pi$
$710$			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	−0.983507	−	0.180870i	$-0.942109\pi$
$719$	−11.1535	−	26.9270i	−0.415957	−	1.00421i	0.567550	−	0.823339i	$-0.307891\pi$
$720$	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	$0.114567\pi$
$727$			18.9928i			0.704402i	−0.935924	+	0.352201i	$0.885433\pi$
$728$	−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	0.990194	−	0.139700i	$-0.0446138\pi$
$733$	23.0263	+	23.0263i	0.850494	+	0.850494i	−0.139700	+	0.990194i	$0.544614\pi$
$734$	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	−0.983052	−	0.183329i	$-0.941313\pi$
$739$	−21.7401	+	21.7401i	−0.799723	+	0.799723i	0.183329	+	0.983052i	$0.441313\pi$
$740$	−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	0.840298	−	0.542124i	$-0.182380\pi$
$743$	−3.74040	−	9.03012i	−0.137222	−	0.331283i	−0.977520	+	0.210841i	$0.932380\pi$
$744$		−	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	−0.153050	−	0.988219i	$-0.548909\pi$
$751$	11.9895	−	4.96623i	0.437504	−	0.181220i	0.590554	+	0.806998i	$0.298909\pi$
$752$		−	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	−0.0839060	−	0.996474i	$-0.526740\pi$
$757$	25.1081	−	25.1081i	0.912568	−	0.912568i	0.996474	+	0.0839060i	$0.0267396\pi$
$758$	−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	$-0.858831\pi$
$761$		−	23.6745i		−	0.858200i	0.903257	−	0.429100i	$-0.141169\pi$
$762$	−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	$0.0335591\pi$
$769$			5.83645i			0.210468i	−0.994447	+	0.105234i	$0.966441\pi$
$770$	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	−0.200892	−	0.979613i	$-0.564384\pi$
$773$	21.6507	−	21.6507i	0.778721	−	0.778721i	0.979613	+	0.200892i	$0.0643840\pi$
$774$	−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	0.940201	+	0.340621i	$0.110637\pi$
$787$	14.4822	+	34.9631i	0.516234	+	1.24630i	−0.423967	+	0.905678i	$0.639363\pi$
$788$	−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	0.794343	−	0.607470i	$-0.207815\pi$
$797$	5.27565	+	5.27565i	0.186873	+	0.186873i	−0.607470	+	0.794343i	$0.707815\pi$
$798$	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	0.438610	+	0.898678i	$0.355471\pi$
$809$	−14.4204	+	34.8140i	−0.506995	+	1.22399i	−0.945605	+	0.325317i	$0.894529\pi$
$810$	17.1805	+	7.11642i	0.603663	+	0.250045i
$811$	−2.63137	−	6.35270i	−0.0924001	−	0.223073i	0.870922	−	0.491421i	$-0.163522\pi$
$811$	−2.63137	−	6.35270i	−0.0924001	−	0.223073i	−0.963322	+	0.268348i	$0.913522\pi$
$812$			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	0.999550	+	0.0300089i	$0.00955356\pi$
$821$	8.99652	+	21.7195i	0.313981	+	0.758017i	−0.685569	+	0.728008i	$0.740446\pi$
$822$	35.3141	+	14.6276i	1.23172	+	0.510195i
$823$	20.9981	−	50.6939i	0.731948	−	1.76708i	0.0959532	−	0.995386i	$-0.469410\pi$
$823$	20.9981	−	50.6939i	0.731948	−	1.76708i	0.635995	−	0.771693i	$-0.280590\pi$
$824$	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	0.0812877	−	0.996691i	$-0.474097\pi$
$827$	−16.2768	−	6.74207i	−0.566000	−	0.234445i	−0.647288	+	0.762246i	$0.724097\pi$
$828$	8.64390	+	20.8682i	0.300396	+	0.725220i
$829$		−	11.9207i		−	0.414022i	−0.978339	−	0.207011i	$-0.933626\pi$
$829$		−	11.9207i		−	0.414022i	0.978339	−	0.207011i	$-0.0663736\pi$
$830$	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	0.936410	−	0.350907i	$-0.114127\pi$
$839$	39.1157	+	16.2022i	1.35042	+	0.559364i	0.414013	+	0.910271i	$0.364127\pi$
$840$	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	0.209696	−	0.977767i	$-0.432753\pi$
$853$	30.6477	−	12.6947i	1.04936	−	0.434659i	0.839663	+	0.543108i	$0.182753\pi$
$854$		−	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	−0.991939	−	0.126713i	$-0.959557\pi$
$857$	−5.88221	+	14.2009i	−0.200932	+	0.485094i	0.791007	+	0.611807i	$0.209557\pi$
$858$	−7.07059	+	7.07059i	−0.241386	+	0.241386i
$859$	−30.2680	+	30.2680i	−1.03273	+	1.03273i	−0.0332837	+	0.999446i	$0.510596\pi$
$859$	−30.2680	+	30.2680i	−1.03273	+	1.03273i	−0.999446	+	0.0332837i	$0.989404\pi$
$860$	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	$-0.820627\pi$
$863$		−	31.3841i		−	1.06833i	0.845382	−	0.534163i	$-0.179373\pi$
$864$	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	0.614545	+	0.788882i	$0.289339\pi$
$877$	−11.1890	+	27.0128i	−0.377827	+	0.912156i	−0.992373	+	0.123274i	$0.960661\pi$
$878$	−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	−0.710026	−	0.704175i	$-0.751317\pi$
$881$	−21.1976	+	8.78032i	−0.714164	+	0.295816i	−0.00413755	+	0.999991i	$0.501317\pi$
$882$	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	−0.643619	−	0.765346i	$-0.722568\pi$
$887$	−16.6051	+	6.87805i	−0.557544	+	0.230942i	0.0860744	+	0.996289i	$0.472568\pi$
$888$			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	0.999939	+	0.0110397i	$0.00351410\pi$
$907$	51.6439	+	21.3916i	1.71481	+	0.710297i	0.714870	+	0.699257i	$0.246486\pi$
$908$	−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	−0.920281	−	0.391258i	$-0.872040\pi$
$911$	0.214803	−	0.518579i	0.00711673	−	0.0171813i	0.927398	+	0.374076i	$0.122040\pi$
$912$	−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	0.522746	−	0.852489i	$-0.324908\pi$
$929$	8.82633	+	3.65598i	0.289582	+	0.119949i	−0.233163	+	0.972438i	$0.574908\pi$
$930$	−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	−0.936171	−	0.351546i	$-0.885656\pi$
$937$	−39.4176	−	39.4176i	−1.28772	−	1.28772i	−0.351546	−	0.936171i	$-0.614344\pi$
$938$	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	−0.107640	−	0.994190i	$-0.534329\pi$
$941$	−27.2017	−	11.2673i	−0.886751	−	0.367304i	−0.779111	+	0.626885i	$0.784329\pi$
$942$	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	−0.989312	−	0.145814i	$-0.953420\pi$
$947$	−12.0899	−	29.1876i	−0.392869	−	0.948469i	0.596443	−	0.802655i	$-0.296580\pi$
$948$		−	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	0.992729	−	0.120374i	$-0.0384095\pi$
$967$	27.1273	+	27.1273i	0.872354	+	0.872354i	−0.120374	+	0.992729i	$0.538409\pi$
$968$	−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	−0.976286	−	0.216486i	$-0.930541\pi$
$971$	−37.1678	−	37.1678i	−1.19277	−	1.19277i	−0.216486	−	0.976286i	$-0.569459\pi$
$972$	−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	−0.201747	−	0.979438i	$-0.564662\pi$
$977$	24.3083	−	24.3083i	0.777691	−	0.777691i	0.979438	+	0.201747i	$0.0646618\pi$
$978$	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	0.0831107	−	0.996540i	$-0.473514\pi$
$983$	26.5414	−	10.9938i	0.846539	−	0.350648i	0.763429	+	0.645892i	$0.223514\pi$
$984$	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	−0.891477	−	0.453066i	$-0.850330\pi$
$991$	−18.3049	−	44.1919i	−0.581474	−	1.40380i	0.310003	−	0.950736i	$-0.399670\pi$
$992$	−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	0.494031	−	0.869444i	$-0.335523\pi$
$997$	7.21729	+	2.98950i	0.228574	+	0.0946783i	−0.265457	+	0.964123i	$0.585523\pi$
$998$	−30.0343	−	72.5091i	−0.950718	−	2.29524i
$999$		−	49.3097i		−	1.56009i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.36.1	yes	24
3.2	odd	2		765.2.be.b.631.6		24
5.2	odd	4		425.2.n.c.274.6		24
5.3	odd	4		425.2.n.f.274.1		24
5.4	even	2		425.2.m.b.376.6		24
17.3	odd	16		1445.2.a.q.1.1		12
17.5	odd	16		1445.2.d.j.866.24		24
17.9	even	8	inner	85.2.l.a.26.1	✓	24
17.12	odd	16		1445.2.d.j.866.23		24
17.14	odd	16		1445.2.a.p.1.1		12
51.26	odd	8		765.2.be.b.451.6		24
85.9	even	8		425.2.m.b.26.6		24
85.14	odd	16		7225.2.a.bs.1.12		12
85.43	odd	8		425.2.n.c.349.6		24
85.54	odd	16		7225.2.a.bq.1.12		12
85.77	odd	8		425.2.n.f.349.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.26.1	✓	24	17.9	even	8	inner
85.2.l.a.36.1	yes	24	1.1	even	1	trivial
425.2.m.b.26.6		24	85.9	even	8
425.2.m.b.376.6		24	5.4	even	2
425.2.n.c.274.6		24	5.2	odd	4
425.2.n.c.349.6		24	85.43	odd	8
425.2.n.f.274.1		24	5.3	odd	4
425.2.n.f.349.1		24	85.77	odd	8
765.2.be.b.451.6		24	51.26	odd	8
765.2.be.b.631.6		24	3.2	odd	2
1445.2.a.p.1.1		12	17.14	odd	16
1445.2.a.q.1.1		12	17.3	odd	16
1445.2.d.j.866.23		24	17.12	odd	16
1445.2.d.j.866.24		24	17.5	odd	16
7225.2.a.bq.1.12		12	85.54	odd	16
7225.2.a.bs.1.12		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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	85.2.l.a.36.1

Level	$85$
Weight	$2$
Character	85.36
Analytic conductor	$0.679$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$