LMFDB - Embedded newform 220.2.l.c.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(23,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("220.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.l (of order $4$, degree $2$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.12494 - 0.857036i) q^{2} +(0.635010 - 0.635010i) q^{3} +(0.530980 + 1.92823i) q^{4} +(-1.96236 + 1.07199i) q^{5} +(-1.25857 + 0.170122i) q^{6} +(2.25370 + 2.25370i) q^{7} +(1.05524 - 2.62421i) q^{8} +2.19352i q^{9} +(3.12626 + 0.475891i) q^{10} -1.00000i q^{11} +(1.56162 + 0.887266i) q^{12} +(3.81013 + 3.81013i) q^{13} +(-0.603777 - 4.46679i) q^{14} +(-0.565395 + 1.92684i) q^{15} +(-3.43612 + 2.04770i) q^{16} +(2.04277 - 2.04277i) q^{17} +(1.87993 - 2.46758i) q^{18} -3.69010 q^{19} +(-3.10900 - 3.21467i) q^{20} +2.86225 q^{21} +(-0.857036 + 1.12494i) q^{22} +(2.52037 - 2.52037i) q^{23} +(-0.996311 - 2.33649i) q^{24} +(2.70169 - 4.20724i) q^{25} +(-1.02075 - 7.55159i) q^{26} +(3.29794 + 3.29794i) q^{27} +(-3.14898 + 5.54233i) q^{28} +8.82637i q^{29} +(2.28740 - 1.68301i) q^{30} -6.21463i q^{31} +(5.62038 + 0.641340i) q^{32} +(-0.635010 - 0.635010i) q^{33} +(-4.04873 + 0.547268i) q^{34} +(-6.83851 - 2.00664i) q^{35} +(-4.22961 + 1.16472i) q^{36} +(1.82696 - 1.82696i) q^{37} +(4.15114 + 3.16255i) q^{38} +4.83895 q^{39} +(0.742356 + 6.28084i) q^{40} -0.00765020 q^{41} +(-3.21986 - 2.45305i) q^{42} +(-5.73579 + 5.73579i) q^{43} +(1.92823 - 0.530980i) q^{44} +(-2.35143 - 4.30448i) q^{45} +(-4.99531 + 0.675217i) q^{46} +(1.19912 + 1.19912i) q^{47} +(-0.881662 + 3.48228i) q^{48} +3.15837i q^{49} +(-6.64500 + 2.41744i) q^{50} -2.59436i q^{51} +(-5.32370 + 9.36991i) q^{52} +(-5.59540 - 5.59540i) q^{53} +(-0.883532 - 6.53644i) q^{54} +(1.07199 + 1.96236i) q^{55} +(8.29239 - 3.53599i) q^{56} +(-2.34325 + 2.34325i) q^{57} +(7.56451 - 9.92913i) q^{58} -14.2640 q^{59} +(-4.01559 - 0.0670988i) q^{60} +2.14646 q^{61} +(-5.32616 + 6.99108i) q^{62} +(-4.94356 + 4.94356i) q^{63} +(-5.77294 - 5.53834i) q^{64} +(-11.5613 - 3.39244i) q^{65} +(0.170122 + 1.25857i) q^{66} +(-3.37532 - 3.37532i) q^{67} +(5.02360 + 2.85426i) q^{68} -3.20092i q^{69} +(5.97316 + 8.11820i) q^{70} -0.207408i q^{71} +(5.75627 + 2.31469i) q^{72} +(-0.0410558 - 0.0410558i) q^{73} +(-3.62099 + 0.489450i) q^{74} +(-0.956034 - 4.38724i) q^{75} +(-1.95937 - 7.11535i) q^{76} +(2.25370 - 2.25370i) q^{77} +(-5.44352 - 4.14715i) q^{78} +11.2676 q^{79} +(4.54780 - 7.70179i) q^{80} -2.39212 q^{81} +(0.00860602 + 0.00655650i) q^{82} +(11.8534 - 11.8534i) q^{83} +(1.51980 + 5.51907i) q^{84} +(-1.81883 + 6.19847i) q^{85} +(11.3682 - 1.53664i) q^{86} +(5.60483 + 5.60483i) q^{87} +(-2.62421 - 1.05524i) q^{88} +5.49019i q^{89} +(-1.04388 + 6.85754i) q^{90} +17.1738i q^{91} +(6.19811 + 3.52158i) q^{92} +(-3.94635 - 3.94635i) q^{93} +(-0.321249 - 2.37662i) q^{94} +(7.24129 - 3.95573i) q^{95} +(3.97626 - 3.16174i) q^{96} +(8.27782 - 8.27782i) q^{97} +(2.70684 - 3.55298i) q^{98} +2.19352 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.12494	−	0.857036i	−0.795453	−	0.606016i
$2$	−1.12494	−	0.857036i	−0.795453	−	0.606016i
$3$	0.635010	−	0.635010i	0.366623	−	0.366623i	−0.499621	−	0.866244i	$-0.666527\pi$
$3$	0.635010	−	0.635010i	0.366623	−	0.366623i	0.866244	+	0.499621i	$0.166527\pi$
$4$	0.530980	+	1.92823i	0.265490	+	0.964114i
$5$	−1.96236	+	1.07199i	−0.877593	+	0.479406i
$5$	−1.96236	+	1.07199i	−0.877593	+	0.479406i
$6$	−1.25857	+	0.170122i	−0.513811	+	0.0694520i
$7$	2.25370	+	2.25370i	0.851820	+	0.851820i	0.990357	−	0.138537i	$-0.0442399\pi$
$7$	2.25370	+	2.25370i	0.851820	+	0.851820i	−0.138537	+	0.990357i	$0.544240\pi$
$8$	1.05524	−	2.62421i	0.373083	−	0.927798i
$9$			2.19352i			0.731175i
$10$	3.12626	+	0.475891i	0.988612	+	0.150490i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	1.56162	+	0.887266i	0.450801	+	0.256132i
$13$	3.81013	+	3.81013i	1.05674	+	1.05674i	0.998290	+	0.0584508i	$0.0186161\pi$
$13$	3.81013	+	3.81013i	1.05674	+	1.05674i	0.0584508	+	0.998290i	$0.481384\pi$
$14$	−0.603777	−	4.46679i	−0.161366	−	1.19380i
$15$	−0.565395	+	1.92684i	−0.145984	+	0.497507i
$16$	−3.43612	+	2.04770i	−0.859030	+	0.511925i
$17$	2.04277	−	2.04277i	0.495445	−	0.495445i	−0.414571	−	0.910017i	$-0.636069\pi$
$17$	2.04277	−	2.04277i	0.495445	−	0.495445i	0.910017	+	0.414571i	$0.136069\pi$
$18$	1.87993	−	2.46758i	0.443104	−	0.581615i
$19$	−3.69010			−0.846566			−0.423283	−	0.905997i	$-0.639122\pi$
$19$	−3.69010			−0.846566			−0.423283	+	0.905997i	$0.639122\pi$
$20$	−3.10900	−	3.21467i	−0.695194	−	0.718822i
$21$	2.86225			0.624594
$22$	−0.857036	+	1.12494i	−0.182721	+	0.239838i
$23$	2.52037	−	2.52037i	0.525533	−	0.525533i	−0.393704	−	0.919237i	$-0.628807\pi$
$23$	2.52037	−	2.52037i	0.525533	−	0.525533i	0.919237	+	0.393704i	$0.128807\pi$
$24$	−0.996311	−	2.33649i	−0.203371	−	0.476933i
$25$	2.70169	−	4.20724i	0.540339	−	0.841447i
$26$	−1.02075	−	7.55159i	−0.200186	−	1.48099i
$27$	3.29794	+	3.29794i	0.634689	+	0.634689i
$28$	−3.14898	+	5.54233i	−0.595102	+	1.04740i
$29$			8.82637i			1.63902i	0.573068	+	0.819508i	$0.305753\pi$
$29$			8.82637i			1.63902i	−0.573068	+	0.819508i	$0.694247\pi$
$30$	2.28740	−	1.68301i	0.417621	−	0.307275i
$31$		−	6.21463i		−	1.11618i	−0.829780	−	0.558090i	$-0.811534\pi$
$31$		−	6.21463i		−	1.11618i	0.829780	−	0.558090i	$-0.188466\pi$
$32$	5.62038	+	0.641340i	0.993552	+	0.113374i
$33$	−0.635010	−	0.635010i	−0.110541	−	0.110541i
$34$	−4.04873	+	0.547268i	−0.694351	+	0.0938556i
$35$	−6.83851	−	2.00664i	−1.15592	−	0.339183i
$36$	−4.22961	+	1.16472i	−0.704936	+	0.194119i
$37$	1.82696	−	1.82696i	0.300350	−	0.300350i	−0.540801	−	0.841151i	$-0.681879\pi$
$37$	1.82696	−	1.82696i	0.300350	−	0.300350i	0.841151	+	0.540801i	$0.181879\pi$
$38$	4.15114	+	3.16255i	0.673403	+	0.513033i
$39$	4.83895			0.774852
$40$	0.742356	+	6.28084i	0.117377	+	0.993087i
$41$	−0.00765020			−0.00119476			−0.000597380	−	1.00000i	$-0.500190\pi$
$41$	−0.00765020			−0.00119476			−0.000597380		1.00000i	$0.500190\pi$
$42$	−3.21986	−	2.45305i	−0.496835	−	0.378514i
$43$	−5.73579	+	5.73579i	−0.874699	+	0.874699i	−0.992980	−	0.118281i	$-0.962262\pi$
$43$	−5.73579	+	5.73579i	−0.874699	+	0.874699i	0.118281	+	0.992980i	$0.462262\pi$
$44$	1.92823	−	0.530980i	0.290691	−	0.0800482i
$45$	−2.35143	−	4.30448i	−0.350530	−	0.641674i
$46$	−4.99531	+	0.675217i	−0.736518	+	0.0995554i
$47$	1.19912	+	1.19912i	0.174909	+	0.174909i	0.789132	−	0.614223i	$-0.210530\pi$
$47$	1.19912	+	1.19912i	0.174909	+	0.174909i	−0.614223	+	0.789132i	$0.710530\pi$
$48$	−0.881662	+	3.48228i	−0.127257	+	0.502624i
$49$			3.15837i			0.451196i
$50$	−6.64500	+	2.41744i	−0.939744	+	0.341878i
$51$		−	2.59436i		−	0.363283i
$52$	−5.32370	+	9.36991i	−0.738265	+	1.29937i
$53$	−5.59540	−	5.59540i	−0.768588	−	0.768588i	0.209270	−	0.977858i	$-0.432891\pi$
$53$	−5.59540	−	5.59540i	−0.768588	−	0.768588i	−0.977858	+	0.209270i	$0.932891\pi$
$54$	−0.883532	−	6.53644i	−0.120233	−	0.889496i
$55$	1.07199	+	1.96236i	0.144546	+	0.264604i
$56$	8.29239	−	3.53599i	1.10812	−	0.472517i
$57$	−2.34325	+	2.34325i	−0.310371	+	0.310371i
$58$	7.56451	−	9.92913i	0.993269	−	1.30376i
$59$	−14.2640			−1.85701			−0.928507	−	0.371314i	$-0.878907\pi$
$59$	−14.2640			−1.85701			−0.928507	+	0.371314i	$0.878907\pi$
$60$	−4.01559	−	0.0670988i	−0.518411	−	0.00866242i
$61$	2.14646			0.274826			0.137413	−	0.990514i	$-0.456121\pi$
$61$	2.14646			0.274826			0.137413	+	0.990514i	$0.456121\pi$
$62$	−5.32616	+	6.99108i	−0.676423	+	0.887869i
$63$	−4.94356	+	4.94356i	−0.622830	+	0.622830i
$64$	−5.77294	−	5.53834i	−0.721617	−	0.692292i
$65$	−11.5613	−	3.39244i	−1.43400	−	0.420780i
$66$	0.170122	+	1.25857i	0.0209406	+	0.154920i
$67$	−3.37532	−	3.37532i	−0.412361	−	0.412361i	0.470199	−	0.882560i	$-0.344182\pi$
$67$	−3.37532	−	3.37532i	−0.412361	−	0.412361i	−0.882560	+	0.470199i	$0.844182\pi$
$68$	5.02360	+	2.85426i	0.609201	+	0.346130i
$69$		−	3.20092i		−	0.385345i
$70$	5.97316	+	8.11820i	0.713929	+	0.970310i
$71$		−	0.207408i		−	0.0246148i	−0.999924	−	0.0123074i	$-0.996082\pi$
$71$		−	0.207408i		−	0.0246148i	0.999924	−	0.0123074i	$-0.00391766\pi$
$72$	5.75627	+	2.31469i	0.678382	+	0.272789i
$73$	−0.0410558	−	0.0410558i	−0.00480522	−	0.00480522i	0.704700	−	0.709505i	$-0.251082\pi$
$73$	−0.0410558	−	0.0410558i	−0.00480522	−	0.00480522i	−0.709505	+	0.704700i	$0.751082\pi$
$74$	−3.62099	+	0.489450i	−0.420931	+	0.0568974i
$75$	−0.956034	−	4.38724i	−0.110393	−	0.506595i
$76$	−1.95937	−	7.11535i	−0.224755	−	0.816186i
$77$	2.25370	−	2.25370i	0.256834	−	0.256834i
$78$	−5.44352	−	4.14715i	−0.616358	−	0.469572i
$79$	11.2676			1.26770			0.633850	−	0.773456i	$-0.281473\pi$
$79$	11.2676			1.26770			0.633850	+	0.773456i	$0.281473\pi$
$80$	4.54780	−	7.70179i	0.508459	−	0.861086i
$81$	−2.39212			−0.265792
$82$	0.00860602	+	0.00655650i	0.000950376	+	0.000724044i
$83$	11.8534	−	11.8534i	1.30108	−	1.30108i	0.373414	−	0.927665i	$-0.378187\pi$
$83$	11.8534	−	11.8534i	1.30108	−	1.30108i	0.927665	−	0.373414i	$-0.121813\pi$
$84$	1.51980	+	5.51907i	0.165823	+	0.602180i
$85$	−1.81883	+	6.19847i	−0.197280	+	0.672319i
$86$	11.3682	−	1.53664i	1.22586	−	0.165700i
$87$	5.60483	+	5.60483i	0.600901	+	0.600901i
$88$	−2.62421	−	1.05524i	−0.279742	−	0.112489i
$89$			5.49019i			0.581959i	0.956729	+	0.290980i	$0.0939812\pi$
$89$			5.49019i			0.581959i	−0.956729	+	0.290980i	$0.906019\pi$
$90$	−1.04388	+	6.85754i	−0.110035	+	0.722848i
$91$			17.1738i			1.80031i
$92$	6.19811	+	3.52158i	0.646197	+	0.367150i
$93$	−3.94635	−	3.94635i	−0.409218	−	0.409218i
$94$	−0.321249	−	2.37662i	−0.0331343	−	0.245130i
$95$	7.24129	−	3.95573i	0.742941	−	0.405849i
$96$	3.97626	−	3.16174i	0.405825	−	0.322694i
$97$	8.27782	−	8.27782i	0.840486	−	0.840486i	−0.148436	−	0.988922i	$-0.547424\pi$
$97$	8.27782	−	8.27782i	0.840486	−	0.840486i	0.988922	+	0.148436i	$0.0474240\pi$
$98$	2.70684	−	3.55298i	0.273432	−	0.358905i
$99$	2.19352			0.220458
$100$	9.54705	+	2.97552i	0.954705	+	0.297552i
$101$	10.7384			1.06851			0.534254	−	0.845324i	$-0.320593\pi$
$101$	10.7384			1.06851			0.534254	+	0.845324i	$0.320593\pi$
$102$	−2.22346	+	2.91850i	−0.220155	+	0.288975i
$103$	2.00929	−	2.00929i	0.197981	−	0.197981i	−0.601153	−	0.799134i	$-0.705292\pi$
$103$	2.00929	−	2.00929i	0.197981	−	0.197981i	0.799134	+	0.601153i	$0.205292\pi$
$104$	14.0192	−	5.97798i	1.37469	−	0.586189i
$105$	−5.61676	+	3.06829i	−0.548139	+	0.299434i
$106$	1.49903	+	11.0899i	0.145599	+	1.07715i
$107$	−0.0993579	−	0.0993579i	−0.00960529	−	0.00960529i	0.702288	−	0.711893i	$-0.252162\pi$
$107$	−0.0993579	−	0.0993579i	−0.00960529	−	0.00960529i	−0.711893	+	0.702288i	$0.752162\pi$
$108$	−4.60804	+	8.11032i	−0.443409	+	0.780416i
$109$		−	18.9553i		−	1.81559i	−0.419414	−	0.907795i	$-0.637764\pi$
$109$		−	18.9553i		−	1.81559i	0.419414	−	0.907795i	$-0.362236\pi$
$110$	0.475891	−	3.12626i	0.0453745	−	0.298078i
$111$		−	2.32027i		−	0.220231i
$112$	−12.3589	−	3.12909i	−1.16781	−	0.295672i
$113$	−8.60045	−	8.60045i	−0.809062	−	0.809062i	0.175430	−	0.984492i	$-0.443869\pi$
$113$	−8.60045	−	8.60045i	−0.809062	−	0.809062i	−0.984492	+	0.175430i	$0.943869\pi$
$114$	4.64426	−	0.627766i	0.434975	−	0.0587957i
$115$	−2.24407	+	7.64766i	−0.209260	+	0.713148i
$116$	−17.0192	+	4.68662i	−1.58020	+	0.435142i
$117$	−8.35762	+	8.35762i	−0.772663	+	0.772663i
$118$	16.0461	+	12.2248i	1.47717	+	1.12538i
$119$	9.20762			0.844061
$120$	4.45980	+	3.51699i	0.407122	+	0.321056i
$121$	−1.00000			−0.0909091
$122$	−2.41463	−	1.83959i	−0.218611	−	0.166549i
$123$	−0.00485795	+	0.00485795i	−0.000438027	+	0.000438027i
$124$	11.9832	−	3.29984i	1.07612	−	0.296335i
$125$	−0.791595	+	11.1523i	−0.0708024	+	0.997490i
$126$	9.79801	−	1.32440i	0.872876	−	0.117987i
$127$	−2.73233	−	2.73233i	−0.242455	−	0.242455i	0.575410	−	0.817865i	$-0.304843\pi$
$127$	−2.73233	−	2.73233i	−0.242455	−	0.242455i	−0.817865	+	0.575410i	$0.804843\pi$
$128$	1.74766	+	11.1779i	0.154473	+	0.987997i
$129$			7.28456i			0.641370i
$130$	10.0983	+	13.7247i	0.885677	+	1.20374i
$131$		−	14.9795i		−	1.30876i	−0.756165	−	0.654381i	$-0.772929\pi$
$131$		−	14.9795i		−	1.30876i	0.756165	−	0.654381i	$-0.227071\pi$
$132$	0.887266	−	1.56162i	0.0772266	−	0.135922i
$133$	−8.31639	−	8.31639i	−0.721122	−	0.721122i
$134$	0.904263	+	6.68980i	0.0781164	+	0.577911i
$135$	−10.0071	−	2.93639i	−0.861272	−	0.252725i
$136$	−3.20505	−	7.51628i	−0.274831	−	0.644515i
$137$	2.65639	−	2.65639i	0.226951	−	0.226951i	−0.584467	−	0.811417i	$-0.698696\pi$
$137$	2.65639	−	2.65639i	0.226951	−	0.226951i	0.811417	+	0.584467i	$0.198696\pi$
$138$	−2.74330	+	3.60084i	−0.233525	+	0.306524i
$139$	−7.42370			−0.629670			−0.314835	−	0.949146i	$-0.601949\pi$
$139$	−7.42370			−0.629670			−0.314835	+	0.949146i	$0.601949\pi$
$140$	0.238140	−	14.2517i	0.0201265	−	1.20449i
$141$	1.52290			0.128252
$142$	−0.177756	+	0.233321i	−0.0149169	+	0.0195799i
$143$	3.81013	−	3.81013i	0.318619	−	0.318619i
$144$	−4.49168	−	7.53722i	−0.374307	−	0.628101i
$145$	−9.46174	−	17.3205i	−0.785755	−	1.43839i
$146$	0.0109990	+	0.0813716i	0.000910286	+	0.00673436i
$147$	2.00560	+	2.00560i	0.165419	+	0.165419i
$148$	4.49287	+	2.55271i	0.369312	+	0.209832i
$149$			6.26390i			0.513158i	0.966523	+	0.256579i	$0.0825955\pi$
$149$			6.26390i			0.513158i	−0.966523	+	0.256579i	$0.917405\pi$
$150$	−2.68454	+	5.75474i	−0.219192	+	0.469872i
$151$			9.33076i			0.759326i	0.925125	+	0.379663i	$0.123960\pi$
$151$			9.33076i			0.759326i	−0.925125	+	0.379663i	$0.876040\pi$
$152$	−3.89394	+	9.68358i	−0.315840	+	0.785442i
$153$	4.48087	+	4.48087i	0.362257	+	0.362257i
$154$	−4.46679	+	0.603777i	−0.359944	+	0.0486537i
$155$	6.66199	+	12.1953i	0.535104	+	0.979552i
$156$	2.56938	+	9.33059i	0.205715	+	0.747045i
$157$	10.9679	−	10.9679i	0.875330	−	0.875330i	−0.117717	−	0.993047i	$-0.537558\pi$
$157$	10.9679	−	10.9679i	0.875330	−	0.875330i	0.993047	+	0.117717i	$0.0375577\pi$
$158$	−12.6753	−	9.65671i	−1.00840	−	0.768247i
$159$	−7.10627			−0.563564
$160$	−11.7167	+	4.76643i	−0.926287	+	0.376819i
$161$	11.3603			0.895320
$162$	2.69100	+	2.05014i	0.211425	+	0.161074i
$163$	12.5061	−	12.5061i	0.979555	−	0.979555i	−0.0202404	−	0.999795i	$-0.506443\pi$
$163$	12.5061	−	12.5061i	0.979555	−	0.979555i	0.999795	+	0.0202404i	$0.00644316\pi$
$164$	−0.00406210	−	0.0147513i	−0.000317197	−	0.00115189i
$165$	1.92684	+	0.565395i	0.150004	+	0.0440160i
$166$	−23.4931	+	3.17557i	−1.82342	+	0.246472i
$167$	−11.0723	−	11.0723i	−0.856801	−	0.856801i	0.134159	−	0.990960i	$-0.457167\pi$
$167$	−11.0723	−	11.0723i	−0.856801	−	0.856801i	−0.990960	+	0.134159i	$0.957167\pi$
$168$	3.02036	−	7.51114i	0.233026	−	0.579497i
$169$			16.0342i			1.23340i
$170$	7.35839	−	5.41411i	0.564362	−	0.415243i
$171$		−	8.09432i		−	0.618988i
$172$	−14.1055	−	8.01431i	−1.07553	−	0.611086i
$173$	4.03741	+	4.03741i	0.306958	+	0.306958i	0.843729	−	0.536770i	$-0.180356\pi$
$173$	4.03741	+	4.03741i	0.306958	+	0.306958i	−0.536770	+	0.843729i	$0.680356\pi$
$174$	−1.50156	−	11.1086i	−0.113833	−	0.842144i
$175$	15.5707	−	3.39305i	1.17703	−	0.256490i
$176$	2.04770	+	3.43612i	0.154351	+	0.259007i
$177$	−9.05778	+	9.05778i	−0.680825	+	0.680825i
$178$	4.70529	−	6.17614i	0.352676	−	0.462921i
$179$	−16.7270			−1.25023			−0.625117	−	0.780531i	$-0.714949\pi$
$179$	−16.7270			−1.25023			−0.625117	+	0.780531i	$0.714949\pi$
$180$	7.05146	−	6.81968i	0.525585	−	0.508309i
$181$	−1.96915			−0.146366			−0.0731829	−	0.997319i	$-0.523316\pi$
$181$	−1.96915			−0.146366			−0.0731829	+	0.997319i	$0.523316\pi$
$182$	14.7186	−	19.3195i	1.09101	−	1.43206i
$183$	1.36302	−	1.36302i	0.100757	−	0.100757i
$184$	−3.95438	−	9.27356i	−0.291521	−	0.683656i
$185$	−1.62667	+	5.54362i	−0.119595	+	0.407575i
$186$	1.05724	+	7.82157i	0.0775209	+	0.573505i
$187$	−2.04277	−	2.04277i	−0.149382	−	0.149382i
$188$	−1.67547	+	2.94888i	−0.122196	+	0.215069i
$189$			14.8652i			1.08128i
$190$	−11.5362	−	1.75609i	−0.836925	−	0.127400i
$191$			17.9312i			1.29746i	0.761020	+	0.648729i	$0.224699\pi$
$191$			17.9312i			1.29746i	−0.761020	+	0.648729i	$0.775301\pi$
$192$	−7.18277	+	0.148975i	−0.518372	+	0.0107514i
$193$	7.76442	+	7.76442i	0.558895	+	0.558895i	0.928993	−	0.370098i	$-0.120676\pi$
$193$	7.76442	+	7.76442i	0.558895	+	0.558895i	−0.370098	+	0.928993i	$0.620676\pi$
$194$	−16.4064	+	2.21766i	−1.17791	+	0.159219i
$195$	−9.49574	+	5.18728i	−0.680004	+	0.371469i
$196$	−6.09006	+	1.67703i	−0.435004	+	0.119788i
$197$	−4.37147	+	4.37147i	−0.311454	+	0.311454i	−0.845473	−	0.534018i	$-0.820681\pi$
$197$	−4.37147	+	4.37147i	−0.311454	+	0.311454i	0.534018	+	0.845473i	$0.320681\pi$
$198$	−2.46758	−	1.87993i	−0.175364	−	0.133601i
$199$	−4.82184			−0.341811			−0.170906	−	0.985287i	$-0.554669\pi$
$199$	−4.82184			−0.341811			−0.170906	+	0.985287i	$0.554669\pi$
$200$	−8.18973	−	11.5295i	−0.579102	−	0.815255i
$201$	−4.28672			−0.302362
$202$	−12.0800	−	9.20316i	−0.849947	−	0.647532i
$203$	−19.8920	+	19.8920i	−1.39615	+	1.39615i
$204$	5.00252	−	1.37755i	0.350247	−	0.0964481i
$205$	0.0150124	−	0.00820090i	0.00104851	−	0.000572776i
$206$	−3.98236	+	0.538297i	−0.277465	+	0.0375050i
$207$	5.52849	+	5.52849i	0.384257	+	0.384257i
$208$	−20.8941	−	5.29008i	−1.44874	−	0.366801i
$209$			3.69010i			0.255249i
$210$	8.94815	+	1.36212i	0.617481	+	0.0939952i
$211$			14.9396i			1.02849i	0.857645	+	0.514243i	$0.171927\pi$
$211$			14.9396i			1.02849i	−0.857645	+	0.514243i	$0.828073\pi$
$212$	7.81816	−	13.7603i	0.536954	−	0.945058i
$213$	−0.131706	−	0.131706i	−0.00902435	−	0.00902435i
$214$	0.0266184	+	0.196925i	0.00181960	+	0.0134615i
$215$	5.10699	−	17.4043i	0.348294	−	1.18697i
$216$	12.1346	−	5.17437i	0.825655	−	0.352071i
$217$	14.0059	−	14.0059i	0.950785	−	0.950785i
$218$	−16.2454	+	21.3236i	−1.10028	+	1.44422i
$219$	−0.0521417			−0.00352341
$220$	−3.21467	+	3.10900i	−0.216733	+	0.209609i
$221$	15.5665			1.04711
$222$	−1.98856	+	2.61017i	−0.133463	+	0.175183i
$223$	−5.04452	+	5.04452i	−0.337806	+	0.337806i	−0.855541	−	0.517735i	$-0.826775\pi$
$223$	−5.04452	+	5.04452i	−0.337806	+	0.337806i	0.517735	+	0.855541i	$0.326775\pi$
$224$	11.2213	+	14.1121i	0.749754	+	0.942902i
$225$	9.22868	+	5.92623i	0.615245	+	0.395082i
$226$	2.30410	+	17.0459i	0.153266	+	1.13388i
$227$	−2.90717	−	2.90717i	−0.192956	−	0.192956i	0.604016	−	0.796972i	$-0.293566\pi$
$227$	−2.90717	−	2.90717i	−0.192956	−	0.192956i	−0.796972	+	0.604016i	$0.793566\pi$
$228$	−5.76253	−	3.27410i	−0.381633	−	0.216832i
$229$		−	5.26735i		−	0.348076i	−0.984739	−	0.174038i	$-0.944318\pi$
$229$		−	5.26735i		−	0.348076i	0.984739	−	0.174038i	$-0.0556816\pi$
$230$	9.07876	−	6.67991i	0.598636	−	0.440461i
$231$		−	2.86225i		−	0.188322i
$232$	23.1622	+	9.31393i	1.52067	+	0.611490i
$233$	5.08072	+	5.08072i	0.332849	+	0.332849i	0.853667	−	0.520819i	$-0.174373\pi$
$233$	5.08072	+	5.08072i	0.332849	+	0.332849i	−0.520819	+	0.853667i	$0.674373\pi$
$234$	16.5646	−	2.23904i	1.08286	−	0.146371i
$235$	−3.63854	−	1.06766i	−0.237352	−	0.0696466i
$236$	−7.57389	−	27.5042i	−0.493018	−	1.79037i
$237$	7.15502	−	7.15502i	0.464769	−	0.464769i
$238$	−10.3580	−	7.89126i	−0.671410	−	0.511514i
$239$	14.3054			0.925342			0.462671	−	0.886530i	$-0.346891\pi$
$239$	14.3054			0.925342			0.462671	+	0.886530i	$0.346891\pi$
$240$	−2.00282	−	7.77861i	−0.129281	−	0.502107i
$241$	11.0377			0.710999			0.355499	−	0.934677i	$-0.384311\pi$
$241$	11.0377			0.710999			0.355499	+	0.934677i	$0.384311\pi$
$242$	1.12494	+	0.857036i	0.0723139	+	0.0550923i
$243$	−11.4128	+	11.4128i	−0.732134	+	0.732134i
$244$	1.13972	+	4.13886i	0.0729634	+	0.264963i
$245$	−3.38573	−	6.19786i	−0.216306	−	0.395966i
$246$	0.00962835	−	0.00130147i	0.000613881	−	8.29785e-5i
$247$	−14.0598	−	14.0598i	−0.894601	−	0.894601i
$248$	−16.3085	−	6.55792i	−1.03559	−	0.416428i
$249$		−	15.0540i		−	0.954011i
$250$	10.4484	−	11.8672i	0.660815	−	0.750549i
$251$			0.576620i			0.0363960i	0.999834	+	0.0181980i	$0.00579292\pi$
$251$			0.576620i			0.0363960i	−0.999834	+	0.0181980i	$0.994207\pi$
$252$	−12.1572	−	6.90737i	−0.765834	−	0.435124i
$253$	−2.52037	−	2.52037i	−0.158454	−	0.158454i
$254$	0.732003	+	5.41541i	0.0459300	+	0.339793i
$255$	2.78112	+	5.09107i	0.174160	+	0.318815i
$256$	7.61386	−	14.0723i	0.475866	−	0.879518i
$257$	14.9668	−	14.9668i	0.933605	−	0.933605i	−0.0643243	−	0.997929i	$-0.520489\pi$
$257$	14.9668	−	14.9668i	0.933605	−	0.933605i	0.997929	+	0.0643243i	$0.0204892\pi$
$258$	6.24313	−	8.19470i	0.388680	−	0.510179i
$259$	8.23485			0.511689
$260$	0.402601	−	24.0940i	0.0249683	−	1.49425i
$261$	−19.3609			−1.19841
$262$	−12.8379	+	16.8510i	−0.793131	+	1.04106i
$263$	−4.22913	+	4.22913i	−0.260779	+	0.260779i	−0.825371	−	0.564591i	$-0.809034\pi$
$263$	−4.22913	+	4.22913i	−0.260779	+	0.260779i	0.564591	+	0.825371i	$0.309034\pi$
$264$	−2.33649	+	0.996311i	−0.143801	+	0.0613187i
$265$	16.9784	+	4.98199i	1.04297	+	0.306041i
$266$	2.22800	+	16.4829i	0.136607	+	1.01063i
$267$	3.48633	+	3.48633i	0.213360	+	0.213360i
$268$	4.71616	−	8.30061i	0.288085	−	0.507041i
$269$			5.88120i			0.358583i	0.983796	+	0.179292i	$0.0573805\pi$
$269$			5.88120i			0.358583i	−0.983796	+	0.179292i	$0.942619\pi$
$270$	8.74077	+	11.8797i	0.531946	+	0.722975i
$271$		−	6.57722i		−	0.399538i	−0.979843	−	0.199769i	$-0.935981\pi$
$271$		−	6.57722i		−	0.399538i	0.979843	−	0.199769i	$-0.0640191\pi$
$272$	−2.83623	+	11.2022i	−0.171972	+	0.679233i
$273$	10.9056	+	10.9056i	0.660034	+	0.660034i
$274$	−5.26490	+	0.711657i	−0.318064	+	0.0429928i
$275$	−4.20724	−	2.70169i	−0.253706	−	0.162918i
$276$	6.17210	−	1.69962i	0.371517	−	0.102305i
$277$	−17.9213	+	17.9213i	−1.07679	+	1.07679i	−0.0799931	+	0.996795i	$0.525490\pi$
$277$	−17.9213	+	17.9213i	−1.07679	+	1.07679i	−0.996795	+	0.0799931i	$0.974510\pi$
$278$	8.35121	+	6.36237i	0.500872	+	0.381590i
$279$	13.6319			0.816123
$280$	−12.4821	+	15.8282i	−0.745948	+	0.945916i
$281$	−16.1189			−0.961572			−0.480786	−	0.876838i	$-0.659649\pi$
$281$	−16.1189			−0.961572			−0.480786	+	0.876838i	$0.659649\pi$
$282$	−1.71318	−	1.30518i	−0.102018	−	0.0777226i
$283$	−8.21473	+	8.21473i	−0.488315	+	0.488315i	−0.907774	−	0.419459i	$-0.862220\pi$
$283$	−8.21473	+	8.21473i	−0.488315	+	0.488315i	0.419459	+	0.907774i	$0.362220\pi$
$284$	0.399929	−	0.110129i	0.0237314	−	0.00653497i
$285$	2.08636	−	7.11022i	0.123586	−	0.421173i
$286$	−7.55159	+	1.02075i	−0.446535	+	0.0603583i
$287$	−0.0172413	−	0.0172413i	−0.00101772	−	0.00101772i
$288$	−1.40680	+	12.3284i	−0.0828962	+	0.726461i
$289$			8.65416i			0.509068i
$290$	−4.20039	+	27.5936i	−0.246656	+	1.62035i
$291$		−	10.5130i		−	0.616283i
$292$	0.0573651	−	0.100965i	0.00335704	−	0.00590851i
$293$	10.8688	+	10.8688i	0.634960	+	0.634960i	0.949308	−	0.314348i	$-0.101786\pi$
$293$	10.8688	+	10.8688i	0.634960	+	0.634960i	−0.314348	+	0.949308i	$0.601786\pi$
$294$	−0.537308	−	3.97505i	−0.0313364	−	0.231829i
$295$	27.9911	−	15.2908i	1.62970	−	0.890265i
$296$	−2.86644	−	6.72220i	−0.166609	−	0.390720i
$297$	3.29794	−	3.29794i	0.191366	−	0.191366i
$298$	5.36838	−	7.04651i	0.310982	−	0.408193i
$299$	19.2059			1.11070
$300$	7.95196	−	4.17299i	0.459107	−	0.240928i
$301$	−25.8535			−1.49017
$302$	7.99679	−	10.4965i	0.460164	−	0.604008i
$303$	6.81897	−	6.81897i	0.391740	−	0.391740i
$304$	12.6796	−	7.55621i	0.727226	−	0.433378i
$305$	−4.21212	+	2.30097i	−0.241185	+	0.131753i
$306$	−1.20044	−	8.88098i	−0.0686249	−	0.507692i
$307$	−11.3032	−	11.3032i	−0.645106	−	0.645106i	0.306700	−	0.951806i	$-0.400775\pi$
$307$	−11.3032	−	11.3032i	−0.645106	−	0.645106i	−0.951806	+	0.306700i	$0.900775\pi$
$308$	5.54233	+	3.14898i	0.315803	+	0.179430i
$309$		−	2.55184i		−	0.145169i
$310$	2.95749	−	19.4286i	0.167974	−	1.10347i
$311$			29.7868i			1.68905i	0.535514	+	0.844526i	$0.320118\pi$
$311$			29.7868i			1.68905i	−0.535514	+	0.844526i	$0.679882\pi$
$312$	5.10625	−	12.6984i	0.289084	−	0.718906i
$313$	−9.34655	−	9.34655i	−0.528298	−	0.528298i	0.391766	−	0.920065i	$-0.371864\pi$
$313$	−9.34655	−	9.34655i	−0.528298	−	0.528298i	−0.920065	+	0.391766i	$0.871864\pi$
$314$	−21.7380	+	2.93833i	−1.22675	+	0.165820i
$315$	4.40161	−	15.0004i	0.248002	−	0.845180i
$316$	5.98285	+	21.7264i	0.336562	+	1.22221i
$317$	−18.7069	+	18.7069i	−1.05069	+	1.05069i	−0.0520406	+	0.998645i	$0.516573\pi$
$317$	−18.7069	+	18.7069i	−1.05069	+	1.05069i	−0.998645	+	0.0520406i	$0.983427\pi$
$318$	7.99413	+	6.09033i	0.448288	+	0.341529i
$319$	8.82637			0.494182
$320$	17.2656	+	4.67969i	0.965176	+	0.261603i
$321$	−0.126186			−0.00704304
$322$	−12.7797	−	9.73621i	−0.712184	−	0.542578i
$323$	−7.53803	+	7.53803i	−0.419427	+	0.419427i
$324$	−1.27017	−	4.61256i	−0.0705650	−	0.256253i
$325$	26.3240	−	5.73632i	1.46019	−	0.318194i
$326$	−24.7868	+	3.35044i	−1.37282	+	0.185564i
$327$	−12.0368	−	12.0368i	−0.665638	−	0.665638i
$328$	−0.00807279	+	0.0200757i	−0.000445745	+	0.00110850i
$329$			5.40492i			0.297983i
$330$	−1.68301	−	2.28740i	−0.0926468	−	0.125917i
$331$		−	26.4300i		−	1.45273i	−0.687312	−	0.726363i	$-0.741209\pi$
$331$		−	26.4300i		−	1.45273i	0.687312	−	0.726363i	$-0.258791\pi$
$332$	29.1499	+	16.5621i	1.59981	+	0.908965i
$333$	4.00748	+	4.00748i	0.219608	+	0.219608i
$334$	2.96632	+	21.9450i	0.162310	+	1.20078i
$335$	10.2419	+	3.00529i	0.559574	+	0.164197i
$336$	−9.83504	+	5.86103i	−0.536545	+	0.319745i
$337$	1.12153	−	1.12153i	0.0610934	−	0.0610934i	−0.675900	−	0.736993i	$-0.736245\pi$
$337$	1.12153	−	1.12153i	0.0610934	−	0.0610934i	0.736993	+	0.675900i	$0.236245\pi$
$338$	13.7419	−	18.0376i	0.747462	−	0.981114i
$339$	−10.9227			−0.593242
$340$	−12.9178	−	0.215851i	−0.700568	−	0.0117062i
$341$	−6.21463			−0.336541
$342$	−6.93712	+	9.10562i	−0.375117	+	0.492376i
$343$	8.65790	−	8.65790i	0.467482	−	0.467482i
$344$	8.99927	+	21.1045i	0.485208	+	1.13788i
$345$	3.43134	+	6.28135i	0.184737	+	0.338176i
$346$	−1.08164	−	8.00204i	−0.0581493	−	0.430193i
$347$	17.9185	+	17.9185i	0.961913	+	0.961913i	0.999301	−	0.0373878i	$-0.0119037\pi$
$347$	17.9185	+	17.9185i	0.961913	+	0.961913i	−0.0373878	+	0.999301i	$0.511904\pi$
$348$	−7.83134	+	13.7834i	−0.419804	+	0.738870i
$349$		−	7.24250i		−	0.387682i	−0.981033	−	0.193841i	$-0.937905\pi$
$349$		−	7.24250i		−	0.387682i	0.981033	−	0.193841i	$-0.0620946\pi$
$350$	−20.4241	−	9.52767i	−1.09171	−	0.509275i
$351$			25.1312i			1.34140i
$352$	0.641340	−	5.62038i	0.0341836	−	0.299567i
$353$	−10.8571	−	10.8571i	−0.577863	−	0.577863i	0.356451	−	0.934314i	$-0.383987\pi$
$353$	−10.8571	−	10.8571i	−0.577863	−	0.577863i	−0.934314	+	0.356451i	$0.883987\pi$
$354$	17.9523	−	2.42662i	0.954154	−	0.128973i
$355$	0.222338	+	0.407008i	0.0118005	+	0.0216018i
$356$	−10.5863	+	2.91518i	−0.561075	+	0.154504i
$357$	5.84693	−	5.84693i	0.309452	−	0.309452i
$358$	18.8169	+	14.3356i	0.994502	+	0.757661i
$359$	−11.1587			−0.588934			−0.294467	−	0.955662i	$-0.595142\pi$
$359$	−11.1587			−0.588934			−0.294467	+	0.955662i	$0.595142\pi$
$360$	−13.7772	+	1.62838i	−0.726121	+	0.0858229i
$361$	−5.38318			−0.283325
$362$	2.21517	+	1.68763i	0.116427	+	0.0886999i
$363$	−0.635010	+	0.635010i	−0.0333294	+	0.0333294i
$364$	−33.1151	+	9.11896i	−1.73570	+	0.477963i
$365$	0.124577	+	0.0365550i	0.00652068	+	0.00191337i
$366$	−2.70148	+	0.365159i	−0.141208	+	0.0190872i
$367$	16.6075	+	16.6075i	0.866902	+	0.866902i	0.992128	−	0.125226i	$-0.0399656\pi$
$367$	16.6075	+	16.6075i	0.866902	+	0.866902i	−0.125226	+	0.992128i	$0.539966\pi$
$368$	−3.49934	+	13.8212i	−0.182415	+	0.720482i
$369$		−	0.0167809i		−	0.000873579i
$370$	6.58099	−	4.84212i	0.342129	−	0.251730i
$371$		−	25.2208i		−	1.30940i
$372$	5.51403	−	9.70489i	0.285889	−	0.503175i
$373$	22.9203	+	22.9203i	1.18677	+	1.18677i	0.977956	+	0.208811i	$0.0669593\pi$
$373$	22.9203	+	22.9203i	1.18677	+	1.18677i	0.208811	+	0.977956i	$0.433041\pi$
$374$	0.547268	+	4.04873i	0.0282985	+	0.209355i
$375$	6.57914	+	7.58448i	0.339745	+	0.391661i
$376$	4.41210	−	1.88138i	0.227536	−	0.0970248i
$377$	−33.6296	+	33.6296i	−1.73201	+	1.73201i
$378$	12.7400	−	16.7224i	0.655274	−	0.860108i
$379$	−11.3573			−0.583383			−0.291692	−	0.956512i	$-0.594218\pi$
$379$	−11.3573			−0.583383			−0.291692	+	0.956512i	$0.594218\pi$
$380$	11.4725	+	11.8624i	0.588528	+	0.608530i
$381$	−3.47011			−0.177779
$382$	15.3677	−	20.1715i	0.786280	−	1.03207i
$383$	−5.64892	+	5.64892i	−0.288646	+	0.288646i	−0.836545	−	0.547898i	$-0.815428\pi$
$383$	−5.64892	+	5.64892i	−0.288646	+	0.288646i	0.547898	+	0.836545i	$0.315428\pi$
$384$	8.20786	+	5.98830i	0.418856	+	0.305589i
$385$	−2.00664	+	6.83851i	−0.102268	+	0.348523i
$386$	−2.08012	−	15.3889i	−0.105875	−	0.783274i
$387$	−12.5816	−	12.5816i	−0.639558	−	0.639558i
$388$	20.3569	+	11.5662i	1.03346	+	0.587183i
$389$		−	38.2285i		−	1.93826i	−0.246542	−	0.969132i	$-0.579294\pi$
$389$		−	38.2285i		−	1.93826i	0.246542	−	0.969132i	$-0.420706\pi$
$390$	15.1278	+	2.30281i	0.766027	+	0.116607i
$391$		−	10.2971i		−	0.520746i
$392$	8.28823	+	3.33284i	0.418619	+	0.168334i
$393$	−9.51212	−	9.51212i	−0.479823	−	0.479823i
$394$	8.66415	−	1.17114i	0.436494	−	0.0590010i
$395$	−22.1110	+	12.0787i	−1.11253	+	0.607744i
$396$	1.16472	+	4.22961i	0.0585292	+	0.212546i
$397$	14.2438	−	14.2438i	0.714874	−	0.714874i	−0.252677	−	0.967551i	$-0.581311\pi$
$397$	14.2438	−	14.2438i	0.714874	−	0.714874i	0.967551	+	0.252677i	$0.0813109\pi$
$398$	5.42428	+	4.13249i	0.271895	+	0.207143i
$399$	−10.5620			−0.528760
$400$	−0.668196	+	19.9888i	−0.0334098	+	0.999442i
$401$	8.51872			0.425405			0.212702	−	0.977117i	$-0.431774\pi$
$401$	8.51872			0.425405			0.212702	+	0.977117i	$0.431774\pi$
$402$	4.82231	+	3.67388i	0.240515	+	0.183236i
$403$	23.6786	−	23.6786i	1.17951	−	1.17951i
$404$	5.70185	+	20.7060i	0.283678	+	1.03016i
$405$	4.69420	−	2.56432i	0.233257	−	0.127422i
$406$	39.4255	−	5.32916i	1.95666	−	0.264482i
$407$	−1.82696	−	1.82696i	−0.0905590	−	0.0905590i
$408$	−6.80815	−	2.73767i	−0.337054	−	0.135535i
$409$		−	38.3696i		−	1.89725i	−0.316398	−	0.948627i	$-0.602474\pi$
$409$		−	38.3696i		−	1.89725i	0.316398	−	0.948627i	$-0.397526\pi$
$410$	−0.0239166	−	0.00364067i	−0.00118115	−	0.000179800i
$411$		−	3.37367i		−	0.166411i
$412$	4.94126	+	2.80748i	0.243438	+	0.138314i
$413$	−32.1468	−	32.1468i	−1.58184	−	1.58184i
$414$	−1.48111	−	10.9573i	−0.0727924	−	0.538523i
$415$	−10.5539	+	35.9673i	−0.518072	+	1.76556i
$416$	18.9708	+	23.8580i	0.930121	+	1.16973i
$417$	−4.71412	+	4.71412i	−0.230852	+	0.230852i
$418$	3.16255	−	4.15114i	0.154685	−	0.203039i
$419$	30.8528			1.50726			0.753628	−	0.657301i	$-0.228302\pi$
$419$	30.8528			1.50726			0.753628	+	0.657301i	$0.228302\pi$
$420$	−8.89875	−	9.20119i	−0.434214	−	0.448972i
$421$	−2.85188			−0.138992			−0.0694960	−	0.997582i	$-0.522139\pi$
$421$	−2.85188			−0.138992			−0.0694960	+	0.997582i	$0.522139\pi$
$422$	12.8038	−	16.8062i	0.623278	−	0.818112i
$423$	−2.63030	+	2.63030i	−0.127889	+	0.127889i
$424$	−20.5880	+	8.77901i	−0.999841	+	0.426346i
$425$	−3.07548	−	14.1134i	−0.149183	−	0.684600i
$426$	0.0352846	+	0.261038i	0.00170954	+	0.0126473i
$427$	4.83748	+	4.83748i	0.234102	+	0.234102i
$428$	0.138828	−	0.244342i	0.00671048	−	0.0118107i
$429$		−	4.83895i		−	0.233627i
$430$	−20.6612	+	15.2020i	−0.996371	+	0.733104i
$431$			1.76475i			0.0850049i	0.999096	+	0.0425024i	$0.0135330\pi$
$431$			1.76475i			0.0850049i	−0.999096	+	0.0425024i	$0.986467\pi$
$432$	−18.0853	−	4.57893i	−0.870130	−	0.220304i
$433$	−9.22802	−	9.22802i	−0.443470	−	0.443470i	0.449706	−	0.893176i	$-0.351529\pi$
$433$	−9.22802	−	9.22802i	−0.443470	−	0.443470i	−0.893176	+	0.449706i	$0.851529\pi$
$434$	−27.7594	+	3.75225i	−1.33250	+	0.180114i
$435$	−17.0070	−	4.99039i	−0.815422	−	0.239271i
$436$	36.5502	−	10.0649i	1.75044	−	0.482021i
$437$	−9.30040	+	9.30040i	−0.444899	+	0.444899i
$438$	0.0586563	+	0.0446873i	0.00280271	+	0.00213524i
$439$	−0.773339			−0.0369094			−0.0184547	−	0.999830i	$-0.505875\pi$
$439$	−0.773339			−0.0369094			−0.0184547	+	0.999830i	$0.505875\pi$
$440$	6.28084	−	0.742356i	0.299427	−	0.0353904i
$441$	−6.92797			−0.329903
$442$	−17.5114	−	13.3410i	−0.832930	−	0.634568i
$443$	2.84350	−	2.84350i	0.135099	−	0.135099i	−0.636324	−	0.771422i	$-0.719546\pi$
$443$	2.84350	−	2.84350i	0.135099	−	0.135099i	0.771422	+	0.636324i	$0.219546\pi$
$444$	4.47402	−	1.23202i	0.212327	−	0.0584690i
$445$	−5.88540	−	10.7737i	−0.278995	−	0.510723i
$446$	9.99811	−	1.35145i	0.473424	−	0.0639929i
$447$	3.97764	+	3.97764i	0.188136	+	0.188136i
$448$	−0.528726	−	25.4923i	−0.0249799	−	1.20440i
$449$		−	16.8661i		−	0.795960i	−0.917394	−	0.397980i	$-0.869711\pi$
$449$		−	16.8661i		−	0.795960i	0.917394	−	0.397980i	$-0.130289\pi$
$450$	−5.30271	−	14.5760i	−0.249972	−	0.687118i
$451$			0.00765020i			0.000360234i
$452$	12.0170	−	21.1503i	0.565230	−	0.994826i
$453$	5.92512	+	5.92512i	0.278387	+	0.278387i
$454$	0.778843	+	5.76194i	0.0365529	+	0.270421i
$455$	−18.4101	−	33.7012i	−0.863079	−	1.57994i
$456$	3.67648	+	8.62186i	0.172167	+	0.403756i
$457$	−7.20177	+	7.20177i	−0.336885	+	0.336885i	−0.855194	−	0.518309i	$-0.826562\pi$
$457$	−7.20177	+	7.20177i	−0.336885	+	0.336885i	0.518309	+	0.855194i	$0.326562\pi$
$458$	−4.51431	+	5.92545i	−0.210940	+	0.276878i
$459$	13.4739			0.628907
$460$	−15.9380	−	0.266317i	−0.743112	−	0.0124171i
$461$	−5.66827			−0.263998			−0.131999	−	0.991250i	$-0.542140\pi$
$461$	−5.66827			−0.263998			−0.131999	+	0.991250i	$0.542140\pi$
$462$	−2.45305	+	3.21986i	−0.114126	+	0.149801i
$463$	−9.06753	+	9.06753i	−0.421404	+	0.421404i	−0.885687	−	0.464283i	$-0.846312\pi$
$463$	−9.06753	+	9.06753i	−0.421404	+	0.421404i	0.464283	+	0.885687i	$0.346312\pi$
$464$	−18.0737	−	30.3285i	−0.839053	−	1.40796i
$465$	11.9746	+	3.51372i	0.555308	+	0.162945i
$466$	−1.36115	−	10.0699i	−0.0630539	−	0.466477i
$467$	24.2160	+	24.2160i	1.12058	+	1.12058i	0.991654	+	0.128929i	$0.0411541\pi$
$467$	24.2160	+	24.2160i	1.12058	+	1.12058i	0.128929	+	0.991654i	$0.458846\pi$
$468$	−20.5531	−	11.6777i	−0.950069	−	0.539800i
$469$		−	15.2140i		−	0.702515i
$470$	3.17811	+	4.31941i	0.146595	+	0.199240i
$471$		−	13.9294i		−	0.641832i
$472$	−15.0519	+	37.4317i	−0.692821	+	1.72293i
$473$	5.73579	+	5.73579i	0.263732	+	0.263732i
$474$	−14.1811	+	1.91686i	−0.651358	+	0.0880443i
$475$	−9.96952	+	15.5251i	−0.457433	+	0.712341i
$476$	4.88906	+	17.7544i	0.224090	+	0.813771i
$477$	12.2737	−	12.2737i	0.561972	−	0.561972i
$478$	−16.0928	−	12.2603i	−0.736066	−	0.560772i
$479$	−7.87655			−0.359889			−0.179944	−	0.983677i	$-0.557592\pi$
$479$	−7.87655			−0.359889			−0.179944	+	0.983677i	$0.557592\pi$
$480$	−4.41350	+	10.4670i	−0.201448	+	0.477749i
$481$	13.9219			0.634785
$482$	−12.4167	−	9.45968i	−0.565566	−	0.430876i
$483$	7.21392	−	7.21392i	0.328245	−	0.328245i
$484$	−0.530980	−	1.92823i	−0.0241354	−	0.0876467i
$485$	−7.37034	+	25.1178i	−0.334670	+	1.14054i
$486$	22.6200	−	3.05755i	1.02606	−	0.138693i
$487$	−9.62376	−	9.62376i	−0.436094	−	0.436094i	0.454601	−	0.890695i	$-0.349782\pi$
$487$	−9.62376	−	9.62376i	−0.436094	−	0.436094i	−0.890695	+	0.454601i	$0.849782\pi$
$488$	2.26503	−	5.63275i	0.102533	−	0.254983i
$489$		−	15.8830i		−	0.718255i
$490$	−1.50304	+	9.87390i	−0.0679005	+	0.446058i
$491$			33.4772i			1.51080i	0.655261	+	0.755402i	$0.272559\pi$
$491$			33.4772i			1.51080i	−0.655261	+	0.755402i	$0.727441\pi$
$492$	−0.0119467	−	0.00678776i	−0.000538599	−	0.000306016i
$493$	18.0303	+	18.0303i	0.812042	+	0.812042i
$494$	3.76667	+	27.8661i	0.169471	+	1.25376i
$495$	−4.30448	+	2.35143i	−0.193472	+	0.105689i
$496$	12.7257	+	21.3542i	0.571400	+	0.958833i
$497$	0.467436	−	0.467436i	0.0209674	−	0.0209674i
$498$	−12.9019	+	16.9349i	−0.578146	+	0.758871i
$499$	−40.7777			−1.82546			−0.912730	−	0.408563i	$-0.866030\pi$
$499$	−40.7777			−1.82546			−0.912730	+	0.408563i	$0.866030\pi$
$500$	−21.9245	+	4.39526i	−0.980491	+	0.196562i
$501$	−14.0620			−0.628246
$502$	0.494184	−	0.648663i	0.0220565	−	0.0289513i
$503$	−7.26532	+	7.26532i	−0.323945	+	0.323945i	−0.850278	−	0.526333i	$-0.823566\pi$
$503$	−7.26532	+	7.26532i	−0.323945	+	0.323945i	0.526333	+	0.850278i	$0.323566\pi$
$504$	7.75629	+	18.1896i	0.345493	+	0.810227i
$505$	−21.0725	+	11.5114i	−0.937715	+	0.512249i
$506$	0.675217	+	4.99531i	0.0300171	+	0.222069i
$507$	10.1819	+	10.1819i	0.452194	+	0.452194i
$508$	3.81774	−	6.71937i	0.169385	−	0.298124i
$509$		−	0.780766i		−	0.0346068i	−0.999850	−	0.0173034i	$-0.994492\pi$
$509$		−	0.780766i		−	0.0346068i	0.999850	−	0.0173034i	$-0.00550813\pi$
$510$	1.23463	−	8.11066i	0.0546706	−	0.359146i
$511$		−	0.185055i		−	0.00818637i
$512$	−20.6256	+	9.30512i	−0.911531	+	0.411232i
$513$	−12.1697	−	12.1697i	−0.537306	−	0.537306i
$514$	−29.6639	+	4.00968i	−1.30842	+	0.176859i
$515$	−1.78902	+	6.09688i	−0.0788335	+	0.268660i
$516$	−14.0463	+	3.86795i	−0.618354	+	0.170277i
$517$	1.19912	−	1.19912i	0.0527372	−	0.0527372i
$518$	−9.26371	−	7.05756i	−0.407024	−	0.310091i
$519$	5.12759			0.225076
$520$	−21.1024	+	26.7593i	−0.925399	+	1.17347i
$521$	−5.88442			−0.257801			−0.128901	−	0.991658i	$-0.541145\pi$
$521$	−5.88442			−0.257801			−0.128901	+	0.991658i	$0.541145\pi$
$522$	21.7798	+	16.5929i	0.953276	+	0.726253i
$523$	10.3239	−	10.3239i	0.451433	−	0.451433i	−0.444397	−	0.895830i	$-0.646582\pi$
$523$	10.3239	−	10.3239i	0.451433	−	0.451433i	0.895830	+	0.444397i	$0.146582\pi$
$524$	28.8838	−	7.95380i	1.26180	−	0.347463i
$525$	7.73293	−	12.0422i	0.337493	−	0.525563i
$526$	8.38203	−	1.13300i	0.365474	−	0.0494012i
$527$	−12.6951	−	12.6951i	−0.553006	−	0.553006i
$528$	3.48228	+	0.881662i	0.151547	+	0.0383694i
$529$			10.2955i			0.447630i
$530$	−14.8299	−	20.1555i	−0.644170	−	0.875499i
$531$		−	31.2884i		−	1.35780i
$532$	11.6201	−	20.4517i	0.503793	−	0.886695i
$533$	−0.0291483	−	0.0291483i	−0.00126255	−	0.00126255i
$534$	−0.934001	−	6.90981i	−0.0404182	−	0.299017i
$535$	0.301486	+	0.0884655i	0.0130344	+	0.00382470i
$536$	−12.4193	+	5.29577i	−0.536433	+	0.228743i
$537$	−10.6218	+	10.6218i	−0.458365	+	0.458365i
$538$	5.04040	−	6.61600i	0.217307	−	0.285236i
$539$	3.15837			0.136041
$540$	0.348480	−	20.8551i	0.0149962	−	0.897460i
$541$	−23.6078			−1.01498			−0.507489	−	0.861658i	$-0.669426\pi$
$541$	−23.6078			−1.01498			−0.507489	+	0.861658i	$0.669426\pi$
$542$	−5.63691	+	7.39898i	−0.242126	+	0.317813i
$543$	−1.25043	+	1.25043i	−0.0536611	+	0.0536611i
$544$	12.7913	−	10.1711i	0.548421	−	0.436080i
$545$	20.3198	+	37.1971i	0.870406	+	1.59335i
$546$	−2.92164	−	21.6145i	−0.125035	−	0.925017i
$547$	4.82727	+	4.82727i	0.206399	+	0.206399i	0.802735	−	0.596336i	$-0.203377\pi$
$547$	4.82727	+	4.82727i	0.206399	+	0.206399i	−0.596336	+	0.802735i	$0.703377\pi$
$548$	6.53261	+	3.71163i	0.279059	+	0.158553i
$549$			4.70831i			0.200946i
$550$	2.41744	+	6.64500i	0.103080	+	0.283344i
$551$		−	32.5702i		−	1.38754i
$552$	−8.39987	−	3.37773i	−0.357522	−	0.143766i
$553$	25.3938	+	25.3938i	1.07985	+	1.07985i
$554$	35.5196	−	4.80120i	1.50909	−	0.203983i
$555$	2.48730	+	4.55321i	0.105580	+	0.193273i
$556$	−3.94183	−	14.3146i	−0.167171	−	0.607073i
$557$	−11.8037	+	11.8037i	−0.500140	+	0.500140i	−0.911481	−	0.411341i	$-0.865060\pi$
$557$	−11.8037	+	11.8037i	−0.500140	+	0.500140i	0.411341	+	0.911481i	$0.365060\pi$
$558$	−15.3351	−	11.6831i	−0.649187	−	0.494583i
$559$	−43.7082			−1.84866
$560$	27.6069	−	7.10817i	1.16661	−	0.300375i
$561$	−2.59436			−0.109534
$562$	18.1328	+	13.8145i	0.764885	+	0.582728i
$563$	5.58808	−	5.58808i	0.235510	−	0.235510i	−0.579478	−	0.814988i	$-0.696744\pi$
$563$	5.58808	−	5.58808i	0.235510	−	0.235510i	0.814988	+	0.579478i	$0.196744\pi$
$564$	0.808631	+	2.93651i	0.0340495	+	0.123649i
$565$	26.0967	+	7.65760i	1.09790	+	0.322158i
$566$	16.2814	−	2.20076i	0.684358	−	0.0925049i
$567$	−5.39114	−	5.39114i	−0.226407	−	0.226407i
$568$	−0.544281	−	0.218865i	−0.0228375	−	0.00918337i
$569$		−	20.5758i		−	0.862581i	−0.902213	−	0.431290i	$-0.858058\pi$
$569$		−	20.5758i		−	0.862581i	0.902213	−	0.431290i	$-0.141942\pi$
$570$	−8.44075	+	6.21048i	−0.353544	+	0.260128i
$571$		−	1.00989i		−	0.0422625i	−0.999777	−	0.0211312i	$-0.993273\pi$
$571$		−	1.00989i		−	0.0422625i	0.999777	−	0.0211312i	$-0.00672678\pi$
$572$	9.36991	+	5.32370i	0.391776	+	0.222595i
$573$	11.3865	+	11.3865i	0.475678	+	0.475678i
$574$	0.00461902	+	0.0341718i	0.000192794	+	0.00142630i
$575$	−3.79452	−	17.4131i	−0.158242	−	0.726174i
$576$	12.1485	−	12.6631i	0.506187	−	0.527629i
$577$	−23.0605	+	23.0605i	−0.960021	+	0.960021i	−0.999231	−	0.0392095i	$-0.987516\pi$
$577$	−23.0605	+	23.0605i	−0.960021	+	0.960021i	0.0392095	+	0.999231i	$0.487516\pi$
$578$	7.41692	−	9.73540i	0.308503	−	0.404939i
$579$	9.86097			0.409808
$580$	28.3739	−	27.4412i	1.17816	−	1.13943i
$581$	53.4281			2.21657
$582$	−9.01002	+	11.8265i	−0.373477	+	0.490224i
$583$	−5.59540	+	5.59540i	−0.231738	+	0.231738i
$584$	−0.151063	+	0.0644153i	−0.00625102	+	0.00266552i
$585$	7.44140	−	25.3599i	0.307664	−	1.04850i
$586$	−2.91179	−	21.5416i	−0.120285	−	0.889876i
$587$	19.3752	+	19.3752i	0.799698	+	0.799698i	0.983048	−	0.183350i	$-0.0586940\pi$
$587$	19.3752	+	19.3752i	0.799698	+	0.799698i	−0.183350	+	0.983048i	$0.558694\pi$
$588$	−2.80232	+	4.93218i	−0.115566	+	0.203400i
$589$			22.9326i			0.944921i
$590$	−44.5930	−	6.78811i	−1.83587	−	0.279462i
$591$			5.55186i			0.228373i
$592$	−2.53659	+	10.0187i	−0.104253	+	0.411767i
$593$	−8.73308	−	8.73308i	−0.358625	−	0.358625i	0.504681	−	0.863306i	$-0.331610\pi$
$593$	−8.73308	−	8.73308i	−0.358625	−	0.358625i	−0.863306	+	0.504681i	$0.831610\pi$
$594$	−6.53644	+	0.883532i	−0.268193	+	0.0362518i
$595$	−18.0686	+	9.87043i	−0.740742	+	0.404648i
$596$	−12.0782	+	3.32600i	−0.494743	+	0.136238i
$597$	−3.06192	+	3.06192i	−0.125316	+	0.125316i
$598$	−21.6055	−	16.4601i	−0.883513	−	0.673105i
$599$	35.4261			1.44747			0.723736	−	0.690077i	$-0.242423\pi$
$599$	35.4261			1.44747			0.723736	+	0.690077i	$0.242423\pi$
$600$	−12.5219	−	2.12076i	−0.511204	−	0.0865795i
$601$	7.75572			0.316362			0.158181	−	0.987410i	$-0.449437\pi$
$601$	7.75572			0.316362			0.158181	+	0.987410i	$0.449437\pi$
$602$	29.0837	+	22.1574i	1.18536	+	0.903069i
$603$	7.40385	−	7.40385i	0.301508	−	0.301508i
$604$	−17.9918	+	4.95444i	−0.732077	+	0.201593i
$605$	1.96236	−	1.07199i	0.0797812	−	0.0435824i
$606$	−13.5150	+	1.82683i	−0.549011	+	0.0742099i
$607$	−4.73081	−	4.73081i	−0.192018	−	0.192018i	0.604550	−	0.796567i	$-0.293353\pi$
$607$	−4.73081	−	4.73081i	−0.192018	−	0.192018i	−0.796567	+	0.604550i	$0.793353\pi$
$608$	−20.7398	−	2.36661i	−0.841108	−	0.0959786i
$609$			25.2633i			1.02372i
$610$	6.71039	+	1.02148i	0.271696	+	0.0413585i
$611$			9.13761i			0.369668i
$612$	−6.26089	+	11.0194i	−0.253081	+	0.445433i
$613$	3.50203	+	3.50203i	0.141446	+	0.141446i	0.774284	−	0.632838i	$-0.218110\pi$
$613$	3.50203	+	3.50203i	0.141446	+	0.141446i	−0.632838	+	0.774284i	$0.718110\pi$
$614$	3.02817	+	22.4026i	0.122207	+	0.904096i
$615$	0.00432539	−	0.0147407i	0.000174416	−	0.000594402i
$616$	−3.53599	−	8.29239i	−0.142469	−	0.334110i
$617$	14.4416	−	14.4416i	0.581398	−	0.581398i	−0.353890	−	0.935287i	$-0.615141\pi$
$617$	14.4416	−	14.4416i	0.581398	−	0.581398i	0.935287	+	0.353890i	$0.115141\pi$
$618$	−2.18702	+	2.87067i	−0.0879747	+	0.115475i
$619$	9.65309			0.387990			0.193995	−	0.981002i	$-0.437855\pi$
$619$	9.65309			0.387990			0.193995	+	0.981002i	$0.437855\pi$
$620$	−19.9780	+	19.3213i	−0.802335	+	0.775962i
$621$	16.6240			0.667100
$622$	25.5283	−	33.5083i	1.02359	−	1.34356i
$623$	−12.3733	+	12.3733i	−0.495725	+	0.495725i
$624$	−16.6272	+	9.90870i	−0.665621	+	0.396666i
$625$	−10.4017	−	22.7333i	−0.416068	−	0.909334i
$626$	2.50398	+	18.5246i	0.100079	+	0.740393i
$627$	2.34325	+	2.34325i	0.0935803	+	0.0935803i
$628$	26.9722	+	15.3248i	1.07631	+	0.611526i
$629$		−	7.46412i		−	0.297614i
$630$	−17.8075	+	13.1023i	−0.709466	+	0.522007i
$631$			2.57640i			0.102565i	0.998684	+	0.0512823i	$0.0163308\pi$
$631$			2.57640i			0.102565i	−0.998684	+	0.0512823i	$0.983669\pi$
$632$	11.8900	−	29.5685i	0.472958	−	1.17617i
$633$	9.48680	+	9.48680i	0.377067	+	0.377067i
$634$	37.0767	−	5.01166i	1.47250	−	0.199039i
$635$	8.29083	+	2.43279i	0.329012	+	0.0965424i
$636$	−3.77329	−	13.7025i	−0.149620	−	0.543340i
$637$	−12.0338	+	12.0338i	−0.476797	+	0.476797i
$638$	−9.92913	−	7.56451i	−0.393098	−	0.299482i
$639$	0.454954			0.0179977
$640$	−15.4121	−	20.0616i	−0.609216	−	0.793004i
$641$	6.79165			0.268254			0.134127	−	0.990964i	$-0.457177\pi$
$641$	6.79165			0.268254			0.134127	+	0.990964i	$0.457177\pi$
$642$	0.141952	+	0.108146i	0.00560241	+	0.00426820i
$643$	31.9574	−	31.9574i	1.26028	−	1.26028i	0.309321	−	0.950958i	$-0.399898\pi$
$643$	31.9574	−	31.9574i	1.26028	−	1.26028i	0.950958	−	0.309321i	$-0.100102\pi$
$644$	6.03211	+	21.9053i	0.237698	+	0.863190i
$645$	−7.80895	−	14.2949i	−0.307477	−	0.562862i
$646$	14.9402	−	2.01947i	0.587814	−	0.0794550i
$647$	−10.5926	−	10.5926i	−0.416437	−	0.416437i	0.467537	−	0.883974i	$-0.345142\pi$
$647$	−10.5926	−	10.5926i	−0.416437	−	0.416437i	−0.883974	+	0.467537i	$0.845142\pi$
$648$	−2.52426	+	6.27743i	−0.0991625	+	0.246601i
$649$			14.2640i			0.559911i
$650$	−34.5291	−	16.1076i	−1.35434	−	0.631790i
$651$		−	17.7878i		−	0.697160i
$652$	30.7551	+	17.4741i	1.20446	+	0.684340i
$653$	−7.61756	−	7.61756i	−0.298098	−	0.298098i	0.542170	−	0.840269i	$-0.317603\pi$
$653$	−7.61756	−	7.61756i	−0.298098	−	0.298098i	−0.840269	+	0.542170i	$0.817603\pi$
$654$	3.22471	+	23.8567i	0.126096	+	0.932870i
$655$	16.0578	+	29.3951i	0.627429	+	1.14856i
$656$	0.0262870	−	0.0156653i	0.00102634	−	0.000611628i
$657$	0.0900569	−	0.0900569i	0.00351346	−	0.00351346i
$658$	4.63221	−	6.08021i	0.180582	−	0.237031i
$659$	−3.59173			−0.139914			−0.0699569	−	0.997550i	$-0.522286\pi$
$659$	−3.59173			−0.139914			−0.0699569	+	0.997550i	$0.522286\pi$
$660$	−0.0670988	+	4.01559i	−0.00261182	+	0.156307i
$661$	−35.6017			−1.38475			−0.692373	−	0.721540i	$-0.743435\pi$
$661$	−35.6017			−1.38475			−0.692373	+	0.721540i	$0.743435\pi$
$662$	−22.6515	+	29.7322i	−0.880374	+	1.15557i
$663$	9.88487	−	9.88487i	0.383897	−	0.383897i
$664$	−18.5976	−	43.6139i	−0.721727	−	1.69255i
$665$	25.2348	+	7.40468i	0.978563	+	0.287141i
$666$	−1.07362	−	7.94273i	−0.0416019	−	0.307774i
$667$	22.2457	+	22.2457i	0.861357	+	0.861357i
$668$	15.4708	−	27.2291i	0.598581	−	1.05353i
$669$			6.40664i			0.247695i
$670$	−8.94586	−	12.1584i	−0.345609	−	0.469721i
$671$		−	2.14646i		−	0.0828630i
$672$	16.0869	+	1.83568i	0.620567	+	0.0708128i
$673$	2.26129	+	2.26129i	0.0871664	+	0.0871664i	0.749346	−	0.662179i	$-0.230368\pi$
$673$	2.26129	+	2.26129i	0.0871664	+	0.0871664i	−0.662179	+	0.749346i	$0.730368\pi$
$674$	−2.22284	+	0.300462i	−0.0856205	+	0.0115733i
$675$	22.7852	−	4.96519i	0.877004	−	0.191110i
$676$	−30.9177	+	8.51386i	−1.18914	+	0.327456i
$677$	21.8771	−	21.8771i	0.840806	−	0.840806i	−0.148158	−	0.988964i	$-0.547334\pi$
$677$	21.8771	−	21.8771i	0.840806	−	0.840806i	0.988964	+	0.148158i	$0.0473343\pi$
$678$	12.2874	+	9.36118i	0.471896	+	0.359514i
$679$	37.3115			1.43189
$680$	14.3468	+	11.3139i	0.550174	+	0.433867i
$681$	−3.69217			−0.141484
$682$	6.99108	+	5.32616i	0.267702	+	0.203949i
$683$	−6.24977	+	6.24977i	−0.239141	+	0.239141i	−0.816494	−	0.577353i	$-0.804085\pi$
$683$	−6.24977	+	6.24977i	−0.239141	+	0.239141i	0.577353	+	0.816494i	$0.304085\pi$
$684$	15.6077	−	4.29792i	0.596775	−	0.164335i
$685$	−2.36517	+	8.06039i	−0.0903686	+	0.307972i
$686$	−17.1597	+	2.31949i	−0.655162	+	0.0885584i
$687$	−3.34482	−	3.34482i	−0.127613	−	0.127613i
$688$	7.96369	−	31.4540i	0.303613	−	1.19917i
$689$		−	42.6385i		−	1.62440i
$690$	1.52329	−	10.0069i	0.0579906	−	0.380957i
$691$			26.8666i			1.02205i	0.859564	+	0.511027i	$0.170735\pi$
$691$			26.8666i			1.02205i	−0.859564	+	0.511027i	$0.829265\pi$
$692$	−5.64126	+	9.92882i	−0.214449	+	0.377437i
$693$	4.94356	+	4.94356i	0.187790	+	0.187790i
$694$	−4.80043	−	35.5139i	−0.182222	−	1.34809i
$695$	14.5679	−	7.95809i	0.552594	−	0.301868i
$696$	20.6227	−	8.79381i	0.781701	−	0.333328i
$697$	−0.0156276	+	0.0156276i	−0.000591939	+	0.000591939i
$698$	−6.20708	+	8.14738i	−0.234942	+	0.308383i
$699$	6.45261			0.244060
$700$	14.8103	+	28.2222i	0.559776	+	1.06670i
$701$	24.9469			0.942233			0.471116	−	0.882071i	$-0.343851\pi$
$701$	24.9469			0.942233			0.471116	+	0.882071i	$0.343851\pi$
$702$	21.5383	−	28.2711i	0.812912	−	1.06702i
$703$	−6.74165	+	6.74165i	−0.254266	+	0.254266i
$704$	−5.53834	+	5.77294i	−0.208734	+	0.217576i
$705$	−2.98848	+	1.63253i	−0.112553	+	0.0614847i
$706$	2.90865	+	21.5184i	0.109469	+	0.809857i
$707$	24.2011	+	24.2011i	0.910177	+	0.910177i
$708$	−22.2750	−	12.6560i	−0.837144	−	0.475640i
$709$			30.4405i			1.14322i	0.820526	+	0.571609i	$0.193680\pi$
$709$			30.4405i			1.14322i	−0.820526	+	0.571609i	$0.806320\pi$
$710$	0.0987036	−	0.648412i	0.00370428	−	0.0243345i
$711$			24.7157i			0.926911i
$712$	14.4074	+	5.79347i	0.539940	+	0.217119i
$713$	−15.6632	−	15.6632i	−0.586590	−	0.586590i
$714$	−11.5885	+	1.56642i	−0.433688	+	0.0586217i
$715$	−3.39244	+	11.5613i	−0.126870	+	0.432366i
$716$	−8.88169	−	32.2534i	−0.331924	−	1.20537i
$717$	9.08409	−	9.08409i	0.339252	−	0.339252i
$718$	12.5529	+	9.56341i	0.468469	+	0.356903i
$719$	−38.9407			−1.45224			−0.726121	−	0.687567i	$-0.758679\pi$
$719$	−38.9407			−1.45224			−0.726121	+	0.687567i	$0.758679\pi$
$720$	16.8941	+	9.97570i	0.629605	+	0.371772i
$721$	9.05670			0.337289
$722$	6.05576	+	4.61358i	0.225372	+	0.171700i
$723$	7.00903	−	7.00903i	0.260669	−	0.260669i
$724$	−1.04558	−	3.79697i	−0.0388586	−	0.141113i
$725$	37.1346	+	23.8462i	1.37915	+	0.885624i
$726$	1.25857	−	0.170122i	0.0467101	−	0.00631381i
$727$	−28.1816	−	28.1816i	−1.04520	−	1.04520i	−0.998929	−	0.0462682i	$-0.985267\pi$
$727$	−28.1816	−	28.1816i	−1.04520	−	1.04520i	−0.0462682	−	0.998929i	$-0.514733\pi$
$728$	45.0677	+	18.1225i	1.67032	+	0.671665i
$729$			7.31816i			0.271043i
$730$	−0.108813	−	0.147889i	−0.00402736	−	0.00547363i
$731$			23.4338i			0.866731i
$732$	3.35195	+	1.90448i	0.123892	+	0.0703915i
$733$	36.5912	+	36.5912i	1.35153	+	1.35153i	0.883954	+	0.467573i	$0.154872\pi$
$733$	36.5912	+	36.5912i	1.35153	+	1.35153i	0.467573	+	0.883954i	$0.345128\pi$
$734$	−4.44921	−	32.9156i	−0.164223	−	1.21494i
$735$	−6.08567	−	1.78573i	−0.224473	−	0.0658676i
$736$	15.7818	−	12.5490i	0.581726	−	0.462563i
$737$	−3.37532	+	3.37532i	−0.124332	+	0.124332i
$738$	−0.0143818	+	0.0188775i	−0.000529403	+	0.000694891i
$739$	−18.8156			−0.692143			−0.346071	−	0.938208i	$-0.612485\pi$
$739$	−18.8156			−0.692143			−0.346071	+	0.938208i	$0.612485\pi$
$740$	−11.5531	−	0.193047i	−0.424700	−	0.00709655i
$741$	−17.8562			−0.655963
$742$	−21.6151	+	28.3718i	−0.793515	+	1.04156i
$743$	−26.3574	+	26.3574i	−0.966958	+	0.966958i	−0.999471	−	0.0325133i	$-0.989649\pi$
$743$	−26.3574	+	26.3574i	−0.966958	+	0.966958i	0.0325133	+	0.999471i	$0.489649\pi$
$744$	−14.5204	+	6.19170i	−0.532343	+	0.226999i
$745$	−6.71481	−	12.2920i	−0.246011	−	0.450344i
$746$	−6.14044	−	45.4274i	−0.224817	−	1.66322i
$747$	26.0007	+	26.0007i	0.951316	+	0.951316i
$748$	2.85426	−	5.02360i	0.104362	−	0.183681i
$749$		−	0.447847i		−	0.0163640i
$750$	−0.900966	−	14.1706i	−0.0328986	−	0.517439i
$751$			37.7311i			1.37683i	0.725319	+	0.688413i	$0.241692\pi$
$751$			37.7311i			1.37683i	−0.725319	+	0.688413i	$0.758308\pi$
$752$	−6.57575	−	1.66488i	−0.239793	−	0.0607121i
$753$	0.366160	+	0.366160i	0.0133436	+	0.0133436i
$754$	66.6531	−	9.00952i	2.42736	−	0.328108i
$755$	−10.0024	−	18.3103i	−0.364026	−	0.666379i
$756$	−28.6634	+	7.89310i	−1.04248	+	0.287069i
$757$	−30.1312	+	30.1312i	−1.09514	+	1.09514i	−0.100167	+	0.994971i	$0.531938\pi$
$757$	−30.1312	+	30.1312i	−1.09514	+	1.09514i	−0.994971	+	0.100167i	$0.968062\pi$
$758$	12.7762	+	9.73358i	0.464054	+	0.353539i
$759$	−3.20092			−0.116186
$760$	−2.73936	−	23.1769i	−0.0993672	−	0.840714i
$761$	48.9417			1.77413			0.887067	−	0.461640i	$-0.152739\pi$
$761$	48.9417			1.77413			0.887067	+	0.461640i	$0.152739\pi$
$762$	3.90367	+	2.97401i	0.141415	+	0.107737i
$763$	42.7197	−	42.7197i	1.54656	−	1.54656i
$764$	−34.5755	+	9.52111i	−1.25090	+	0.344462i
$765$	−13.5965	−	3.98965i	−0.491583	−	0.144246i
$766$	11.1960	−	1.51337i	0.404529	−	0.0546803i
$767$	−54.3477	−	54.3477i	−1.96238	−	1.96238i
$768$	−4.10116	−	13.7709i	−0.147988	−	0.496915i
$769$		−	6.87619i		−	0.247962i	−0.992285	−	0.123981i	$-0.960434\pi$
$769$		−	6.87619i		−	0.247962i	0.992285	−	0.123981i	$-0.0395662\pi$
$770$	8.11820	−	5.97316i	0.292559	−	0.215258i
$771$		−	19.0082i		−	0.684562i
$772$	−10.8488	+	19.0943i	−0.390458	+	0.687220i
$773$	−1.12999	−	1.12999i	−0.0406428	−	0.0406428i	0.686493	−	0.727136i	$-0.259149\pi$
$773$	−1.12999	−	1.12999i	−0.0406428	−	0.0406428i	−0.727136	+	0.686493i	$0.759149\pi$
$774$	3.37066	+	24.9364i	0.121156	+	0.896321i
$775$	−26.1464	−	16.7900i	−0.939207	−	0.603116i
$776$	−12.9876	−	30.4578i	−0.466229	−	1.09337i
$777$	5.22921	−	5.22921i	0.187597	−	0.187597i
$778$	−32.7632	+	43.0048i	−1.17462	+	1.54180i
$779$	0.0282300			0.00101144
$780$	−15.0443	−	15.5556i	−0.538672	−	0.556980i
$781$	−0.207408			−0.00742164
$782$	−8.82497	+	11.5836i	−0.315580	+	0.414229i
$783$	−29.1088	+	29.1088i	−1.04026	+	1.04026i
$784$	−6.46739	−	10.8525i	−0.230978	−	0.387591i
$785$	−9.76547	+	33.2802i	−0.348545	+	1.18782i
$786$	2.54834	+	18.8528i	0.0908961	+	0.672457i
$787$	−17.8389	−	17.8389i	−0.635889	−	0.635889i	0.313650	−	0.949539i	$-0.398448\pi$
$787$	−17.8389	−	17.8389i	−0.635889	−	0.635889i	−0.949539	+	0.313650i	$0.898448\pi$
$788$	−10.7504	−	6.10803i	−0.382966	−	0.217590i
$789$			5.37108i			0.191215i
$790$	35.2254	+	5.36214i	1.25326	+	0.190776i
$791$		−	38.7658i		−	1.37835i
$792$	2.31469	−	5.75627i	0.0822491	−	0.204540i
$793$	8.17829	+	8.17829i	0.290420	+	0.290420i
$794$	−28.2308	+	3.81596i	−1.00187	+	0.135424i
$795$	13.9450	−	7.61782i	0.494580	−	0.270176i
$796$	−2.56030	−	9.29761i	−0.0907474	−	0.329545i
$797$	−16.1948	+	16.1948i	−0.573649	+	0.573649i	−0.933146	−	0.359497i	$-0.882948\pi$
$797$	−16.1948	+	16.1948i	−0.573649	+	0.573649i	0.359497	+	0.933146i	$0.382948\pi$
$798$	11.8816	+	9.05199i	0.420604	+	0.320437i
$799$	4.89906			0.173316
$800$	17.8828	−	21.9136i	0.632253	−	0.774762i
$801$	−12.0429			−0.425514
$802$	−9.58305	−	7.30085i	−0.338389	−	0.257802i
$803$	−0.0410558	+	0.0410558i	−0.00144883	+	0.00144883i
$804$	−2.27616	−	8.26578i	−0.0802741	−	0.291512i
$805$	−22.2930	+	12.1781i	−0.785726	+	0.429222i
$806$	−46.9303	+	6.34359i	−1.65305	+	0.223443i
$807$	3.73462	+	3.73462i	0.131465	+	0.131465i
$808$	11.3315	−	28.1797i	0.398643	−	0.991359i
$809$			12.9518i			0.455361i	0.973736	+	0.227680i	$0.0731142\pi$
$809$			12.9518i			0.455361i	−0.973736	+	0.227680i	$0.926886\pi$
$810$	−7.47841	−	1.13839i	−0.262765	−	0.0399990i
$811$		−	47.9707i		−	1.68448i	−0.539102	−	0.842240i	$-0.681236\pi$
$811$		−	47.9707i		−	1.68448i	0.539102	−	0.842240i	$-0.318764\pi$
$812$	−48.9186	−	27.7941i	−1.71671	−	0.975381i
$813$	−4.17660	−	4.17660i	−0.146480	−	0.146480i
$814$	0.489450	+	3.62099i	0.0171552	+	0.126916i
$815$	−11.1351	+	37.9479i	−0.390046	+	1.32926i
$816$	5.31247	+	8.91454i	0.185974	+	0.312071i
$817$	21.1656	−	21.1656i	0.740491	−	0.740491i
$818$	−32.8841	+	43.1635i	−1.14977	+	1.50917i
$819$	−37.6712			−1.31634
$820$	0.0237845	+	0.0245929i	0.000830591	+	0.000858820i
$821$	−31.3862			−1.09539			−0.547693	−	0.836679i	$-0.684494\pi$
$821$	−31.3862			−1.09539			−0.547693	+	0.836679i	$0.684494\pi$
$822$	−2.89135	+	3.79517i	−0.100847	+	0.132372i
$823$	−24.7186	+	24.7186i	−0.861638	+	0.861638i	−0.991528	−	0.129891i	$-0.958537\pi$
$823$	−24.7186	+	24.7186i	−0.861638	+	0.861638i	0.129891	+	0.991528i	$0.458537\pi$
$824$	−3.15251	−	7.39308i	−0.109823	−	0.257550i
$825$	−4.38724	+	0.956034i	−0.152744	+	0.0332848i
$826$	8.61228	+	63.7143i	0.299659	+	2.21690i
$827$	20.3177	+	20.3177i	0.706516	+	0.706516i	0.965801	−	0.259285i	$-0.0834868\pi$
$827$	20.3177	+	20.3177i	0.706516	+	0.706516i	−0.259285	+	0.965801i	$0.583487\pi$
$828$	−7.72467	+	13.5957i	−0.268451	+	0.472483i
$829$		−	22.3090i		−	0.774824i	−0.921907	−	0.387412i	$-0.873369\pi$
$829$		−	22.3090i		−	0.774824i	0.921907	−	0.387412i	$-0.126631\pi$
$830$	42.6978	−	31.4159i	1.48206	−	1.09046i
$831$			22.7604i			0.789551i
$832$	−0.893869	−	43.0975i	−0.0309893	−	1.49414i
$833$	6.45184	+	6.45184i	0.223543	+	0.223543i
$834$	9.34327	−	1.26293i	0.323531	−	0.0437318i
$835$	33.5972	+	9.85847i	1.16268	+	0.341167i
$836$	−7.11535	+	1.95937i	−0.246089	+	0.0677661i
$837$	20.4955	−	20.4955i	0.708427	−	0.708427i
$838$	−34.7075	−	26.4419i	−1.19895	−	0.913421i
$839$	−17.4454			−0.602283			−0.301142	−	0.953579i	$-0.597368\pi$
$839$	−17.4454			−0.602283			−0.301142	+	0.953579i	$0.597368\pi$
$840$	2.12481	+	17.9773i	0.0733128	+	0.620277i
$841$	−48.9048			−1.68637
$842$	3.20819	+	2.44416i	0.110562	+	0.0842313i
$843$	−10.2357	+	10.2357i	−0.352535	+	0.352535i
$844$	−28.8070	+	7.93263i	−0.991577	+	0.273052i
$845$	−17.1885	−	31.4649i	−0.591302	−	1.08243i
$846$	5.21318	−	0.704668i	0.179233	−	0.0242270i
$847$	−2.25370	−	2.25370i	−0.0774382	−	0.0774382i
$848$	30.6842	+	7.76878i	1.05370	+	0.266781i
$849$			10.4329i			0.358055i
$850$	−8.63594	+	18.5125i	−0.296210	+	0.634974i
$851$		−	9.20922i		−	0.315688i
$852$	0.184026	−	0.323892i	0.00630463	−	0.0110964i
$853$	−35.8340	−	35.8340i	−1.22693	−	1.22693i	−0.965118	−	0.261814i	$-0.915679\pi$
$853$	−35.8340	−	35.8340i	−1.22693	−	1.22693i	−0.261814	−	0.965118i	$-0.584321\pi$
$854$	−1.29598	−	9.58777i	−0.0443476	−	0.328087i
$855$	8.67699	+	15.8839i	0.296747	+	0.543220i
$856$	−0.365582	+	0.155889i	−0.0124953	+	0.00532819i
$857$	18.8617	−	18.8617i	0.644303	−	0.644303i	−0.307307	−	0.951610i	$-0.599428\pi$
$857$	18.8617	−	18.8617i	0.644303	−	0.644303i	0.951610	+	0.307307i	$0.0994279\pi$
$858$	−4.14715	+	5.44352i	−0.141581	+	0.185839i
$859$	14.1323			0.482186			0.241093	−	0.970502i	$-0.422494\pi$
$859$	14.1323			0.482186			0.241093	+	0.970502i	$0.422494\pi$
$860$	36.2712	+	0.606077i	1.23684	+	0.0206670i
$861$	−0.0218968			−0.000746241
$862$	1.51245	−	1.98523i	0.0515143	−	0.0676174i
$863$	27.6591	−	27.6591i	0.941525	−	0.941525i	−0.0568570	−	0.998382i	$-0.518108\pi$
$863$	27.6591	−	27.6591i	0.941525	−	0.941525i	0.998382	+	0.0568570i	$0.0181079\pi$
$864$	16.4206	+	20.6508i	0.558639	+	0.702554i
$865$	−12.2509	−	3.59480i	−0.416542	−	0.122227i
$866$	2.47222	+	18.2897i	0.0840096	+	0.621509i
$867$	5.49547	+	5.49547i	0.186636	+	0.186636i
$868$	34.4435	+	19.5698i	1.16909	+	0.664241i
$869$		−	11.2676i		−	0.382226i
$870$	14.8549	+	20.1895i	0.503628	+	0.684487i
$871$		−	25.7208i		−	0.871518i
$872$	−49.7427	−	20.0024i	−1.68450	−	0.677367i
$873$	18.1576	+	18.1576i	0.614542	+	0.614542i
$874$	18.4332	−	2.49162i	0.623511	−	0.0842802i
$875$	−26.9180	+	23.3499i	−0.909994	+	0.789372i
$876$	−0.0276862	−	0.100541i	−0.000935429	−	0.00339697i
$877$	−8.59239	+	8.59239i	−0.290145	+	0.290145i	−0.837137	−	0.546993i	$-0.815773\pi$
$877$	−8.59239	+	8.59239i	−0.290145	+	0.290145i	0.546993	+	0.837137i	$0.315773\pi$
$878$	0.869959	+	0.662779i	0.0293597	+	0.0223677i
$879$	13.8035			0.465582
$880$	−7.70179	−	4.54780i	−0.259627	−	0.153306i
$881$	−23.3307			−0.786031			−0.393015	−	0.919532i	$-0.628568\pi$
$881$	−23.3307			−0.786031			−0.393015	+	0.919532i	$0.628568\pi$
$882$	7.79355	+	5.93751i	0.262422	+	0.199927i
$883$	11.3431	−	11.3431i	0.381725	−	0.381725i	−0.489998	−	0.871724i	$-0.663003\pi$
$883$	11.3431	−	11.3431i	0.381725	−	0.381725i	0.871724	+	0.489998i	$0.163003\pi$
$884$	8.26548	+	30.0157i	0.277998	+	1.00954i
$885$	8.06480	−	27.4844i	0.271095	−	0.923878i
$886$	−5.63575	+	0.761786i	−0.189337	+	0.0255927i
$887$	−9.49729	−	9.49729i	−0.318888	−	0.318888i	0.529452	−	0.848340i	$-0.322398\pi$
$887$	−9.49729	−	9.49729i	−0.318888	−	0.318888i	−0.848340	+	0.529452i	$0.822398\pi$
$888$	−6.08888	−	2.44844i	−0.204329	−	0.0821644i
$889$		−	12.3157i		−	0.413057i
$890$	−2.61273	+	17.1638i	−0.0875791	+	0.575331i
$891$			2.39212i			0.0801392i
$892$	−12.4055	−	7.04844i	−0.415367	−	0.235999i
$893$	−4.42487	−	4.42487i	−0.148072	−	0.148072i
$894$	−1.06563	−	7.88358i	−0.0356399	−	0.263666i
$895$	32.8243	−	17.9311i	1.09720	−	0.599370i
$896$	−21.2530	+	29.1304i	−0.710013	+	0.973179i
$897$	12.1959	−	12.1959i	0.407210	−	0.407210i
$898$	−14.4548	+	18.9733i	−0.482364	+	0.633149i
$899$	54.8526			1.82944
$900$	−6.52689	+	20.9417i	−0.217563	+	0.698057i
$901$	−22.8603			−0.761586
$902$	0.00655650	−	0.00860602i	0.000218307	−	0.000286549i
$903$	−16.4173	+	16.4173i	−0.546332	+	0.546332i
$904$	−31.6449	+	13.4938i	−1.05249	+	0.448798i
$905$	3.86418	−	2.11090i	0.128450	−	0.0701687i
$906$	−1.58737	−	11.7435i	−0.0527367	−	0.390150i
$907$	−23.1830	−	23.1830i	−0.769777	−	0.769777i	0.208290	−	0.978067i	$-0.433210\pi$
$907$	−23.1830	−	23.1830i	−0.769777	−	0.769777i	−0.978067	+	0.208290i	$0.933210\pi$
$908$	4.06204	−	7.14934i	0.134803	−	0.237259i
$909$			23.5549i			0.781266i
$910$	−8.17288	+	53.6899i	−0.270928	+	1.77980i
$911$			33.6694i			1.11552i	0.830003	+	0.557758i	$0.188338\pi$
$911$			33.6694i			1.11552i	−0.830003	+	0.557758i	$0.811662\pi$
$912$	3.25342	−	12.8500i	0.107731	−	0.425504i
$913$	−11.8534	−	11.8534i	−0.392290	−	0.392290i
$914$	14.2737	−	1.92938i	0.472133	−	0.0638184i
$915$	−1.21360	+	4.13587i	−0.0401203	+	0.136728i
$916$	10.1566	−	2.79685i	0.335585	−	0.0924107i
$917$	33.7593	−	33.7593i	1.11483	−	1.11483i
$918$	−15.1573	−	11.5476i	−0.500266	−	0.381128i
$919$	−59.4102			−1.95976			−0.979880	−	0.199586i	$-0.936040\pi$
$919$	−59.4102			−1.95976			−0.979880	+	0.199586i	$0.936040\pi$
$920$	17.7010	+	13.9590i	0.583586	+	0.460215i
$921$	−14.3553			−0.473022
$922$	6.37647	+	4.85791i	0.209998	+	0.159987i
$923$	0.790252	−	0.790252i	0.0260114	−	0.0260114i
$924$	5.51907	−	1.51980i	0.181564	−	0.0499976i
$925$	−2.75056	−	12.6223i	−0.0904380	−	0.415020i
$926$	17.9716	−	2.42923i	0.590585	−	0.0798295i
$927$	4.40743	+	4.40743i	0.144759	+	0.144759i
$928$	−5.66071	+	49.6076i	−0.185822	+	1.62845i
$929$		−	26.0692i		−	0.855304i	−0.903944	−	0.427652i	$-0.859341\pi$
$929$		−	26.0692i		−	0.855304i	0.903944	−	0.427652i	$-0.140659\pi$
$930$	−10.4593	−	14.2154i	−0.342974	−	0.466140i
$931$		−	11.6547i		−	0.381967i
$932$	−7.09902	+	12.4945i	−0.232536	+	0.409272i
$933$	18.9149	+	18.9149i	0.619246	+	0.619246i
$934$	−6.48757	−	47.9955i	−0.212280	−	1.57046i
$935$	6.19847	+	1.81883i	0.202712	+	0.0594821i
$936$	13.1129	+	30.7514i	0.428607	+	1.00514i
$937$	−4.08119	+	4.08119i	−0.133327	+	0.133327i	−0.770621	−	0.637294i	$-0.780054\pi$
$937$	−4.08119	+	4.08119i	−0.133327	+	0.133327i	0.637294	+	0.770621i	$0.280054\pi$
$938$	−13.0389	+	17.1148i	−0.425735	+	0.558817i
$939$	−11.8703			−0.387373
$940$	0.126706	−	7.58284i	0.00413269	−	0.247325i
$941$	0.218988			0.00713882			0.00356941	−	0.999994i	$-0.498864\pi$
$941$	0.218988			0.00713882			0.00356941	+	0.999994i	$0.498864\pi$
$942$	−11.9380	+	15.6697i	−0.388961	+	0.510547i
$943$	−0.0192813	+	0.0192813i	−0.000627886	+	0.000627886i
$944$	49.0128	−	29.2084i	1.59523	−	0.950652i
$945$	−15.9352	−	29.1708i	−0.518373	−	0.948925i
$946$	−1.53664	−	11.3682i	−0.0499605	−	0.369612i
$947$	−15.3142	−	15.3142i	−0.497646	−	0.497646i	0.413058	−	0.910705i	$-0.364461\pi$
$947$	−15.3142	−	15.3142i	−0.497646	−	0.497646i	−0.910705	+	0.413058i	$0.864461\pi$
$948$	17.5957	+	9.99734i	0.571481	+	0.324698i
$949$		−	0.312856i		−	0.0101557i
$950$	24.5207	−	8.92059i	0.795556	−	0.289422i
$951$			23.7582i			0.770411i
$952$	9.71624	−	24.1627i	0.314905	−	0.783118i
$953$	−14.6683	−	14.6683i	−0.475153	−	0.475153i	0.428424	−	0.903578i	$-0.359069\pi$
$953$	−14.6683	−	14.6683i	−0.475153	−	0.475153i	−0.903578	+	0.428424i	$0.859069\pi$
$954$	−24.3261	+	3.28816i	−0.787586	+	0.106458i
$955$	−19.2220	−	35.1875i	−0.622009	−	1.13864i
$956$	7.59590	+	27.5841i	0.245669	+	0.892135i
$957$	5.60483	−	5.60483i	0.181178	−	0.181178i
$958$	8.86065	+	6.75049i	0.286275	+	0.218098i
$959$	11.9734			0.386642
$960$	13.9355	−	7.99217i	0.449765	−	0.257946i
$961$	−7.62162			−0.245859
$962$	−15.6613	−	11.9316i	−0.504941	−	0.384689i
$963$	0.217944	−	0.217944i	0.00702315	−	0.00702315i
$964$	5.86078	+	21.2831i	0.188763	+	0.685484i
$965$	−23.5599	−	6.91323i	−0.758421	−	0.222545i
$966$	−14.2978	+	1.93264i	−0.460025	+	0.0621817i
$967$	−8.71199	−	8.71199i	−0.280159	−	0.280159i	0.553014	−	0.833172i	$-0.313478\pi$
$967$	−8.71199	−	8.71199i	−0.280159	−	0.280159i	−0.833172	+	0.553014i	$0.813478\pi$
$968$	−1.05524	+	2.62421i	−0.0339167	+	0.0843453i
$969$			9.57345i			0.307544i
$970$	29.8180	−	21.9393i	0.957398	−	0.704429i
$971$		−	38.9615i		−	1.25033i	−0.780491	−	0.625167i	$-0.785031\pi$
$971$		−	38.9615i		−	1.25033i	0.780491	−	0.625167i	$-0.214969\pi$
$972$	−28.0665	−	15.9466i	−0.900235	−	0.511486i
$973$	−16.7308	−	16.7308i	−0.536366	−	0.536366i
$974$	2.57825	+	19.0741i	0.0826123	+	0.611172i
$975$	13.0734	−	20.3586i	0.418682	−	0.651997i
$976$	−7.37549	+	4.39530i	−0.236084	+	0.140690i
$977$	−7.67444	+	7.67444i	−0.245527	+	0.245527i	−0.819132	−	0.573605i	$-0.805544\pi$
$977$	−7.67444	+	7.67444i	−0.245527	+	0.245527i	0.573605	+	0.819132i	$0.305544\pi$
$978$	−13.6123	+	17.8674i	−0.435274	+	0.571338i
$979$	5.49019			0.175467
$980$	10.1531	−	9.81939i	0.324330	−	0.313669i
$981$	41.5790			1.32751
$982$	28.6912	−	37.6598i	0.915572	−	1.20177i
$983$	25.2898	−	25.2898i	0.806619	−	0.806619i	−0.177502	−	0.984121i	$-0.556801\pi$
$983$	25.2898	−	25.2898i	0.806619	−	0.806619i	0.984121	+	0.177502i	$0.0568015\pi$
$984$	0.00762198	+	0.0178746i	0.000242980	+	0.000569821i
$985$	3.89224	−	13.2645i	0.124017	−	0.422644i
$986$	−4.83039	−	35.7356i	−0.153831	−	1.13805i
$987$	3.43218	+	3.43218i	0.109247	+	0.109247i
$988$	19.6450	−	34.5759i	0.624990	−	1.10001i
$989$			28.9126i			0.919367i
$990$	6.85754	+	1.04388i	0.217947	+	0.0331767i
$991$			60.9819i			1.93715i	0.248713	+	0.968577i	$0.419992\pi$
$991$			60.9819i			1.93715i	−0.248713	+	0.968577i	$0.580008\pi$
$992$	3.98569	−	34.9286i	0.126546	−	1.10898i
$993$	−16.7833	−	16.7833i	−0.532603	−	0.532603i
$994$	−0.926447	+	0.125228i	−0.0293851	+	0.00397199i
$995$	9.46218	−	5.16895i	0.299971	−	0.163867i
$996$	29.0276	−	7.99339i	0.919775	−	0.253280i
$997$	3.62985	−	3.62985i	0.114959	−	0.114959i	−0.647287	−	0.762246i	$-0.724097\pi$
$997$	3.62985	−	3.62985i	0.114959	−	0.114959i	0.762246	+	0.647287i	$0.224097\pi$
$998$	45.8724	+	34.9479i	1.45207	+	1.10626i
$999$	12.0504			0.381258

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.4	✓	28
4.3	odd	2		220.2.l.d.23.10	yes	28
5.2	odd	4		220.2.l.d.67.10	yes	28
20.7	even	4	inner	220.2.l.c.67.4	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.4	✓	28	1.1	even	1	trivial
220.2.l.c.67.4	yes	28	20.7	even	4	inner
220.2.l.d.23.10	yes	28	4.3	odd	2
220.2.l.d.67.10	yes	28	5.2	odd	4

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12494 - 0.857036i) q^{2} +(0.635010 - 0.635010i) q^{3} +(0.530980 + 1.92823i) q^{4} +(-1.96236 + 1.07199i) q^{5} +(-1.25857 + 0.170122i) q^{6} +(2.25370 + 2.25370i) q^{7} +(1.05524 - 2.62421i) q^{8} +2.19352i q^{9} +(3.12626 + 0.475891i) q^{10} -1.00000i q^{11} +(1.56162 + 0.887266i) q^{12} +(3.81013 + 3.81013i) q^{13} +(-0.603777 - 4.46679i) q^{14} +(-0.565395 + 1.92684i) q^{15} +(-3.43612 + 2.04770i) q^{16} +(2.04277 - 2.04277i) q^{17} +(1.87993 - 2.46758i) q^{18} -3.69010 q^{19} +(-3.10900 - 3.21467i) q^{20} +2.86225 q^{21} +(-0.857036 + 1.12494i) q^{22} +(2.52037 - 2.52037i) q^{23} +(-0.996311 - 2.33649i) q^{24} +(2.70169 - 4.20724i) q^{25} +(-1.02075 - 7.55159i) q^{26} +(3.29794 + 3.29794i) q^{27} +(-3.14898 + 5.54233i) q^{28} +8.82637i q^{29} +(2.28740 - 1.68301i) q^{30} -6.21463i q^{31} +(5.62038 + 0.641340i) q^{32} +(-0.635010 - 0.635010i) q^{33} +(-4.04873 + 0.547268i) q^{34} +(-6.83851 - 2.00664i) q^{35} +(-4.22961 + 1.16472i) q^{36} +(1.82696 - 1.82696i) q^{37} +(4.15114 + 3.16255i) q^{38} +4.83895 q^{39} +(0.742356 + 6.28084i) q^{40} -0.00765020 q^{41} +(-3.21986 - 2.45305i) q^{42} +(-5.73579 + 5.73579i) q^{43} +(1.92823 - 0.530980i) q^{44} +(-2.35143 - 4.30448i) q^{45} +(-4.99531 + 0.675217i) q^{46} +(1.19912 + 1.19912i) q^{47} +(-0.881662 + 3.48228i) q^{48} +3.15837i q^{49} +(-6.64500 + 2.41744i) q^{50} -2.59436i q^{51} +(-5.32370 + 9.36991i) q^{52} +(-5.59540 - 5.59540i) q^{53} +(-0.883532 - 6.53644i) q^{54} +(1.07199 + 1.96236i) q^{55} +(8.29239 - 3.53599i) q^{56} +(-2.34325 + 2.34325i) q^{57} +(7.56451 - 9.92913i) q^{58} -14.2640 q^{59} +(-4.01559 - 0.0670988i) q^{60} +2.14646 q^{61} +(-5.32616 + 6.99108i) q^{62} +(-4.94356 + 4.94356i) q^{63} +(-5.77294 - 5.53834i) q^{64} +(-11.5613 - 3.39244i) q^{65} +(0.170122 + 1.25857i) q^{66} +(-3.37532 - 3.37532i) q^{67} +(5.02360 + 2.85426i) q^{68} -3.20092i q^{69} +(5.97316 + 8.11820i) q^{70} -0.207408i q^{71} +(5.75627 + 2.31469i) q^{72} +(-0.0410558 - 0.0410558i) q^{73} +(-3.62099 + 0.489450i) q^{74} +(-0.956034 - 4.38724i) q^{75} +(-1.95937 - 7.11535i) q^{76} +(2.25370 - 2.25370i) q^{77} +(-5.44352 - 4.14715i) q^{78} +11.2676 q^{79} +(4.54780 - 7.70179i) q^{80} -2.39212 q^{81} +(0.00860602 + 0.00655650i) q^{82} +(11.8534 - 11.8534i) q^{83} +(1.51980 + 5.51907i) q^{84} +(-1.81883 + 6.19847i) q^{85} +(11.3682 - 1.53664i) q^{86} +(5.60483 + 5.60483i) q^{87} +(-2.62421 - 1.05524i) q^{88} +5.49019i q^{89} +(-1.04388 + 6.85754i) q^{90} +17.1738i q^{91} +(6.19811 + 3.52158i) q^{92} +(-3.94635 - 3.94635i) q^{93} +(-0.321249 - 2.37662i) q^{94} +(7.24129 - 3.95573i) q^{95} +(3.97626 - 3.16174i) q^{96} +(8.27782 - 8.27782i) q^{97} +(2.70684 - 3.55298i) q^{98} +2.19352 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

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