LMFDB - Embedded newform 82.2.g.b.77.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [82,2,Mod(5,82)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(82, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("82.5"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 82 = 2 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	82.g (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.654773296574$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 13 x^{14} - 24 x^{13} + 58 x^{12} - 66 x^{11} + 75 x^{10} - 430 x^{9} + 1721 x^{8} + \cdots + 32761 $ x^16 - 6x^15 + 13x^14 - 24x^13 + 58x^12 - 66x^11 + 75x^10 - 430x^9 + 1721x^8 - 6000x^7 + 16245x^6 - 33054x^5 + 53998x^4 - 71746x^3 + 73383x^2 - 55024*x + 32761
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			77.2
Root			$-2.22705 - 0.970763i$ of defining polynomial
Character	$\chi$	$=$	82.77
Dual form			82.2.g.b.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.587785 + 0.809017i) q^{2} +(1.59439 - 1.59439i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25872 - 0.408982i) q^{5} +(2.22705 + 0.352729i) q^{6} +(-2.58221 + 0.408982i) q^{7} +(-0.951057 + 0.309017i) q^{8} -2.08415i q^{9} +(-0.408982 - 1.25872i) q^{10} +(0.928992 + 0.473345i) q^{11} +(1.02366 + 2.00905i) q^{12} +(-0.902832 + 5.70026i) q^{13} +(-1.84866 - 1.84866i) q^{14} +(-2.65896 + 1.35481i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.849136 - 1.66652i) q^{17} +(1.68611 - 1.22503i) q^{18} +(-0.931683 - 5.88242i) q^{19} +(0.777929 - 1.07073i) q^{20} +(-3.46497 + 4.76912i) q^{21} +(0.163104 + 1.02980i) q^{22} +(5.75652 - 4.18236i) q^{23} +(-1.02366 + 2.00905i) q^{24} +(-2.62798 - 1.90934i) q^{25} +(-5.14228 + 2.62012i) q^{26} +(1.46022 + 1.46022i) q^{27} +(0.408982 - 2.58221i) q^{28} +(-3.68263 - 7.22756i) q^{29} +(-2.65896 - 1.35481i) q^{30} +(1.72811 + 5.31857i) q^{31} -1.00000i q^{32} +(2.23587 - 0.726478i) q^{33} +(1.84736 - 0.292592i) q^{34} +(3.41753 + 0.541284i) q^{35} +(1.98214 + 0.644038i) q^{36} +(-1.41094 + 4.34242i) q^{37} +(4.21135 - 4.21135i) q^{38} +(7.64896 + 10.5279i) q^{39} +1.32349 q^{40} +(2.54812 + 5.87427i) q^{41} -5.89496 q^{42} +(-0.770167 - 1.06004i) q^{43} +(-0.737252 + 0.737252i) q^{44} +(-0.852379 + 2.62335i) q^{45} +(6.76719 + 2.19879i) q^{46} +(9.82331 + 1.55586i) q^{47} +(-2.22705 + 0.352729i) q^{48} +(-0.156858 + 0.0509663i) q^{49} -3.24837i q^{50} +(-1.30323 - 4.01094i) q^{51} +(-5.14228 - 2.62012i) q^{52} +(-1.91121 - 3.75096i) q^{53} +(-0.323047 + 2.03964i) q^{54} +(-0.975747 - 0.975747i) q^{55} +(2.32944 - 1.18691i) q^{56} +(-10.8643 - 7.89339i) q^{57} +(3.68263 - 7.22756i) q^{58} +(0.259923 - 0.188845i) q^{59} +(-0.466835 - 2.94748i) q^{60} +(-4.52000 + 6.22124i) q^{61} +(-3.28705 + 4.52424i) q^{62} +(0.852379 + 5.38171i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.46771 - 6.80577i) q^{65} +(1.90194 + 1.38184i) q^{66} +(9.47300 - 4.82673i) q^{67} +(1.32256 + 1.32256i) q^{68} +(2.50983 - 15.8464i) q^{69} +(1.57087 + 3.08300i) q^{70} +(-13.2974 - 6.77536i) q^{71} +(0.644038 + 1.98214i) q^{72} +15.9512i q^{73} +(-4.34242 + 1.41094i) q^{74} +(-7.23426 + 1.14579i) q^{75} +(5.88242 + 0.931683i) q^{76} +(-2.59244 - 0.842335i) q^{77} +(-4.02130 + 12.3763i) q^{78} +(-3.73082 + 3.73082i) q^{79} +(0.777929 + 1.07073i) q^{80} +10.9088 q^{81} +(-3.25464 + 5.51428i) q^{82} -7.50785 q^{83} +(-3.46497 - 4.76912i) q^{84} +(-1.75040 + 1.75040i) q^{85} +(0.404901 - 1.24616i) q^{86} +(-17.3951 - 5.65201i) q^{87} +(-1.02980 - 0.163104i) q^{88} +(-2.31831 + 0.367184i) q^{89} +(-2.62335 + 0.852379i) q^{90} -15.0885i q^{91} +(2.19879 + 6.76719i) q^{92} +(11.2351 + 5.72459i) q^{93} +(4.51528 + 8.86173i) q^{94} +(-1.23308 + 7.78534i) q^{95} +(-1.59439 - 1.59439i) q^{96} +(4.43678 - 2.26065i) q^{97} +(-0.133432 - 0.0969437i) q^{98} +(0.986521 - 1.93616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{3} + 4 q^{4} - 6 q^{6} + 12 q^{11} + 4 q^{12} - 18 q^{13} - 10 q^{14} - 18 q^{15} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 16 q^{19} + 10 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 4 q^{25} - 2 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) $ 16 * q - 4 * q^3 + 4 * q^4 - 6 * q^6 + 12 * q^11 + 4 * q^12 - 18 * q^13 - 10 * q^14 - 18 * q^15 - 4 * q^16 - 4 * q^17 + 4 * q^18 - 16 * q^19 + 10 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 - 10 * q^29 - 18 * q^30 + 40 * q^31 - 60 * q^33 + 26 * q^34 + 44 * q^35 + 10 * q^36 - 16 * q^37 + 14 * q^38 + 80 * q^39 - 4 * q^41 + 16 * q^42 - 40 * q^43 - 2 * q^44 + 58 * q^45 + 10 * q^46 + 6 * q^48 + 20 * q^49 - 6 * q^51 - 2 * q^52 + 46 * q^53 + 18 * q^54 - 18 * q^55 - 60 * q^57 + 10 * q^58 - 2 * q^59 - 42 * q^60 - 60 * q^61 - 58 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 + 50 * q^67 - 16 * q^68 + 48 * q^69 - 26 * q^70 - 38 * q^71 - 4 * q^72 - 10 * q^74 + 6 * q^75 - 4 * q^76 - 38 * q^78 - 20 * q^79 + 10 * q^80 + 40 * q^81 + 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^86 - 70 * q^87 - 18 * q^88 + 36 * q^89 - 6 * q^92 - 12 * q^93 + 20 * q^94 - 72 * q^95 + 4 * q^96 - 10 * q^97 - 36 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/82\mathbb{Z}\right)^\times$.

$n$	$47$
$\chi(n)$	$e\left(\frac{1}{20}\right)$

Coefficient data

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

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

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

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	1.59439	−	1.59439i	0.920521	−	0.920521i	−0.0765454	−	0.997066i	$-0.524389\pi$
$3$	1.59439	−	1.59439i	0.920521	−	0.920521i	0.997066	+	0.0765454i	$0.0243890\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.25872	−	0.408982i	−0.562915	−	0.182902i	0.0137173	−	0.999906i	$-0.495634\pi$
$5$	−1.25872	−	0.408982i	−0.562915	−	0.182902i	−0.576632	+	0.817004i	$0.695634\pi$
$6$	2.22705	+	0.352729i	0.909188	+	0.144001i
$7$	−2.58221	+	0.408982i	−0.975983	+	0.154581i	−0.623999	−	0.781425i	$-0.714493\pi$
$7$	−2.58221	+	0.408982i	−0.975983	+	0.154581i	−0.351984	+	0.936006i	$0.614493\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$		−	2.08415i		−	0.694717i
$10$	−0.408982	−	1.25872i	−0.129331	−	0.398041i
$11$	0.928992	+	0.473345i	0.280101	+	0.142719i	0.588398	−	0.808572i	$-0.299759\pi$
$11$	0.928992	+	0.473345i	0.280101	+	0.142719i	−0.308296	+	0.951290i	$0.599759\pi$
$12$	1.02366	+	2.00905i	0.295505	+	0.579962i
$13$	−0.902832	+	5.70026i	−0.250401	+	1.58097i	0.466969	+	0.884274i	$0.345346\pi$
$13$	−0.902832	+	5.70026i	−0.250401	+	1.58097i	−0.717369	+	0.696693i	$0.754654\pi$
$14$	−1.84866	−	1.84866i	−0.494075	−	0.494075i
$15$	−2.65896	+	1.35481i	−0.686540	+	0.349810i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.849136	−	1.66652i	0.205946	−	0.404191i	−0.764812	−	0.644254i	$-0.777168\pi$
$17$	0.849136	−	1.66652i	0.205946	−	0.404191i	0.970757	+	0.240063i	$0.0771680\pi$
$18$	1.68611	−	1.22503i	0.397421	−	0.288743i
$19$	−0.931683	−	5.88242i	−0.213743	−	1.34952i	−0.828140	−	0.560522i	$-0.810601\pi$
$19$	−0.931683	−	5.88242i	−0.213743	−	1.34952i	0.614397	−	0.788997i	$-0.289399\pi$
$20$	0.777929	−	1.07073i	0.173950	−	0.239422i
$21$	−3.46497	+	4.76912i	−0.756118	+	1.04071i
$22$	0.163104	+	1.02980i	0.0347738	+	0.219553i
$23$	5.75652	−	4.18236i	1.20032	−	0.872082i	0.206001	−	0.978552i	$-0.433955\pi$
$23$	5.75652	−	4.18236i	1.20032	−	0.872082i	0.994316	+	0.106470i	$0.0339548\pi$
$24$	−1.02366	+	2.00905i	−0.208954	+	0.410095i
$25$	−2.62798	−	1.90934i	−0.525597	−	0.381868i
$26$	−5.14228	+	2.62012i	−1.00848	+	0.513848i
$27$	1.46022	+	1.46022i	0.281020	+	0.281020i
$28$	0.408982	−	2.58221i	0.0772903	−	0.487992i
$29$	−3.68263	−	7.22756i	−0.683847	−	1.34212i	−0.928070	−	0.372406i	$-0.878533\pi$
$29$	−3.68263	−	7.22756i	−0.683847	−	1.34212i	0.244223	−	0.969719i	$-0.421467\pi$
$30$	−2.65896	−	1.35481i	−0.485457	−	0.247353i
$31$	1.72811	+	5.31857i	0.310377	+	0.955243i	0.977616	+	0.210399i	$0.0674762\pi$
$31$	1.72811	+	5.31857i	0.310377	+	0.955243i	−0.667238	+	0.744844i	$0.732524\pi$
$32$		−	1.00000i		−	0.176777i
$33$	2.23587	−	0.726478i	0.389215	−	0.126464i
$34$	1.84736	−	0.292592i	0.316819	−	0.0501792i
$35$	3.41753	+	0.541284i	0.577669	+	0.0914938i
$36$	1.98214	+	0.644038i	0.330357	+	0.107340i
$37$	−1.41094	+	4.34242i	−0.231957	+	0.713889i	0.765554	+	0.643372i	$0.222465\pi$
$37$	−1.41094	+	4.34242i	−0.231957	+	0.713889i	−0.997511	+	0.0705174i	$0.977535\pi$
$38$	4.21135	−	4.21135i	0.683170	−	0.683170i
$39$	7.64896	+	10.5279i	1.22481	+	1.68581i
$40$	1.32349			0.209263
$41$	2.54812	+	5.87427i	0.397949	+	0.917407i
$41$	2.54812	+	5.87427i	0.397949	+	0.917407i
$42$	−5.89496			−0.909612
$43$	−0.770167	−	1.06004i	−0.117449	−	0.161655i	0.746245	−	0.665672i	$-0.231855\pi$
$43$	−0.770167	−	1.06004i	−0.117449	−	0.161655i	−0.863694	+	0.504017i	$0.831855\pi$
$44$	−0.737252	+	0.737252i	−0.111145	+	0.111145i
$45$	−0.852379	+	2.62335i	−0.127065	+	0.391066i
$46$	6.76719	+	2.19879i	0.997768	+	0.324195i
$47$	9.82331	+	1.55586i	1.43288	+	0.226945i	0.824122	−	0.566413i	$-0.191669\pi$
$47$	9.82331	+	1.55586i	1.43288	+	0.226945i	0.608755	+	0.793358i	$0.291669\pi$
$48$	−2.22705	+	0.352729i	−0.321446	+	0.0509121i
$49$	−0.156858	+	0.0509663i	−0.0224083	+	0.00728090i
$50$		−	3.24837i		−	0.459388i
$51$	−1.30323	−	4.01094i	−0.182489	−	0.561644i
$52$	−5.14228	−	2.62012i	−0.713106	−	0.363345i
$53$	−1.91121	−	3.75096i	−0.262525	−	0.515234i	0.721689	−	0.692217i	$-0.243366\pi$
$53$	−1.91121	−	3.75096i	−0.262525	−	0.515234i	−0.984214	+	0.176984i	$0.943366\pi$
$54$	−0.323047	+	2.03964i	−0.0439612	+	0.277560i
$55$	−0.975747	−	0.975747i	−0.131570	−	0.131570i
$56$	2.32944	−	1.18691i	0.311285	−	0.158608i
$57$	−10.8643	−	7.89339i	−1.43901	−	1.04551i
$58$	3.68263	−	7.22756i	0.483553	−	0.949026i
$59$	0.259923	−	0.188845i	0.0338391	−	0.0245855i	−0.570737	−	0.821133i	$-0.693342\pi$
$59$	0.259923	−	0.188845i	0.0338391	−	0.0245855i	0.604576	+	0.796547i	$0.293342\pi$
$60$	−0.466835	−	2.94748i	−0.0602681	−	0.380518i
$61$	−4.52000	+	6.22124i	−0.578726	+	0.796548i	−0.993555	−	0.113351i	$-0.963841\pi$
$61$	−4.52000	+	6.22124i	−0.578726	+	0.796548i	0.414829	+	0.909899i	$0.363841\pi$
$62$	−3.28705	+	4.52424i	−0.417456	+	0.574579i
$63$	0.852379	+	5.38171i	0.107390	+	0.678032i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	3.46771	−	6.80577i	0.430117	−	0.844151i
$66$	1.90194	+	1.38184i	0.234113	+	0.170093i
$67$	9.47300	−	4.82673i	1.15731	−	0.589679i	0.233435	−	0.972372i	$-0.425003\pi$
$67$	9.47300	−	4.82673i	1.15731	−	0.589679i	0.923876	+	0.382693i	$0.125003\pi$
$68$	1.32256	+	1.32256i	0.160384	+	0.160384i
$69$	2.50983	−	15.8464i	0.302148	−	1.90769i
$70$	1.57087	+	3.08300i	0.187755	+	0.368489i
$71$	−13.2974	−	6.77536i	−1.57811	−	0.804087i	−0.578179	−	0.815910i	$-0.696237\pi$
$71$	−13.2974	−	6.77536i	−1.57811	−	0.804087i	−0.999930	+	0.0118229i	$0.996237\pi$
$72$	0.644038	+	1.98214i	0.0759006	+	0.233598i
$73$			15.9512i			1.86695i	0.358648	+	0.933473i	$0.383238\pi$
$73$			15.9512i			1.86695i	−0.358648	+	0.933473i	$0.616762\pi$
$74$	−4.34242	+	1.41094i	−0.504796	+	0.164018i
$75$	−7.23426	+	1.14579i	−0.835341	+	0.132305i
$76$	5.88242	+	0.931683i	0.674759	+	0.106871i
$77$	−2.59244	−	0.842335i	−0.295436	−	0.0959929i
$78$	−4.02130	+	12.3763i	−0.455322	+	1.40134i
$79$	−3.73082	+	3.73082i	−0.419750	+	0.419750i	−0.885118	−	0.465367i	$-0.845922\pi$
$79$	−3.73082	+	3.73082i	−0.419750	+	0.419750i	0.465367	+	0.885118i	$0.345922\pi$
$80$	0.777929	+	1.07073i	0.0869752	+	0.119711i
$81$	10.9088			1.21209
$82$	−3.25464	+	5.51428i	−0.359415	+	0.608951i
$83$	−7.50785			−0.824094			−0.412047	−	0.911163i	$-0.635186\pi$
$83$	−7.50785			−0.824094			−0.412047	+	0.911163i	$0.635186\pi$
$84$	−3.46497	−	4.76912i	−0.378059	−	0.520354i
$85$	−1.75040	+	1.75040i	−0.189857	+	0.189857i
$86$	0.404901	−	1.24616i	0.0436616	−	0.134376i
$87$	−17.3951	−	5.65201i	−1.86495	−	0.605959i
$88$	−1.02980	−	0.163104i	−0.109777	−	0.0173869i
$89$	−2.31831	+	0.367184i	−0.245741	+	0.0389215i	−0.278090	−	0.960555i	$-0.589701\pi$
$89$	−2.31831	+	0.367184i	−0.245741	+	0.0389215i	0.0323490	+	0.999477i	$0.489701\pi$
$90$	−2.62335	+	0.852379i	−0.276526	+	0.0898486i
$91$		−	15.0885i		−	1.58170i
$92$	2.19879	+	6.76719i	0.229240	+	0.705529i
$93$	11.2351	+	5.72459i	1.16503	+	0.593612i
$94$	4.51528	+	8.86173i	0.465715	+	0.914018i
$95$	−1.23308	+	7.78534i	−0.126511	+	0.798759i
$96$	−1.59439	−	1.59439i	−0.162727	−	0.162727i
$97$	4.43678	−	2.26065i	0.450487	−	0.229534i	−0.214001	−	0.976833i	$-0.568650\pi$
$97$	4.43678	−	2.26065i	0.450487	−	0.229534i	0.664488	+	0.747299i	$0.268650\pi$
$98$	−0.133432	−	0.0969437i	−0.0134786	−	0.00979279i
$99$	0.986521	−	1.93616i	0.0991491	−	0.194591i
$100$	2.62798	−	1.90934i	0.262798	−	0.190934i
$101$	−0.426188	−	2.69085i	−0.0424073	−	0.267749i	0.957370	−	0.288865i	$-0.0932780\pi$
$101$	−0.426188	−	2.69085i	−0.0424073	−	0.267749i	−0.999777	+	0.0211163i	$0.993278\pi$
$102$	2.47890	−	3.41191i	0.245447	−	0.337829i
$103$	2.51821	−	3.46602i	0.248127	−	0.341517i	−0.666727	−	0.745302i	$-0.732305\pi$
$103$	2.51821	−	3.46602i	0.248127	−	0.341517i	0.914854	+	0.403785i	$0.132305\pi$
$104$	−0.902832	−	5.70026i	−0.0885300	−	0.558956i
$105$	6.31190	−	4.58586i	0.615978	−	0.447534i
$106$	1.91121	−	3.75096i	0.185633	−	0.364325i
$107$	0.339210	+	0.246451i	0.0327927	+	0.0238253i	0.604061	−	0.796938i	$-0.293548\pi$
$107$	0.339210	+	0.246451i	0.0327927	+	0.0238253i	−0.571268	+	0.820763i	$0.693548\pi$
$108$	−1.83999	+	0.937520i	−0.177053	+	0.0902129i
$109$	−6.81118	−	6.81118i	−0.652393	−	0.652393i	0.301176	−	0.953569i	$-0.402621\pi$
$109$	−6.81118	−	6.81118i	−0.652393	−	0.652393i	−0.953569	+	0.301176i	$0.902621\pi$
$110$	0.215866	−	1.36293i	0.0205820	−	0.129950i
$111$	4.67392	+	9.17308i	0.443629	+	0.870671i
$112$	2.32944	+	1.18691i	0.220112	+	0.112153i
$113$	1.11809	+	3.44114i	0.105181	+	0.323715i	0.989773	−	0.142652i	$-0.0455628\pi$
$113$	1.11809	+	3.44114i	0.105181	+	0.323715i	−0.884592	+	0.466366i	$0.845563\pi$
$114$		−	13.4290i		−	1.25775i
$115$	−8.95633	+	2.91009i	−0.835182	+	0.271367i
$116$	8.01182	−	1.26895i	0.743878	−	0.117819i
$117$	11.8802	+	1.88164i	1.09832	+	0.173957i
$118$	0.305558	+	0.0992817i	0.0281288	+	0.00913962i
$119$	−1.51107	+	4.65059i	−0.138520	+	0.426319i
$120$	2.11016	−	2.11016i	0.192631	−	0.192631i
$121$	−5.82667	−	8.01972i	−0.529697	−	0.729065i
$122$	−7.68988			−0.696209
$123$	13.4286	+	5.30318i	1.21081	+	0.478172i
$124$	−5.59227			−0.502201
$125$	6.41665	+	8.83176i	0.573922	+	0.789936i
$126$	−3.85288	+	3.85288i	−0.343242	+	0.343242i
$127$	−0.600664	+	1.84865i	−0.0533003	+	0.164041i	−0.974163	−	0.225845i	$-0.927486\pi$
$127$	−0.600664	+	1.84865i	−0.0533003	+	0.164041i	0.920863	+	0.389886i	$0.127486\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−2.91807	−	0.462176i	−0.256921	−	0.0406924i
$130$	7.54425	−	1.19489i	0.661674	−	0.104799i
$131$	7.09554	−	2.30548i	0.619941	−	0.201431i	0.0178267	−	0.999841i	$-0.494325\pi$
$131$	7.09554	−	2.30548i	0.619941	−	0.201431i	0.602114	+	0.798410i	$0.294325\pi$
$132$			2.35093i			0.204622i
$133$	4.81160	+	14.8086i	0.417219	+	1.28407i
$134$	9.47300	+	4.82673i	0.818342	+	0.416966i
$135$	−1.24080	−	2.43521i	−0.106791	−	0.209589i
$136$	−0.292592	+	1.84736i	−0.0250896	+	0.158409i
$137$	8.25099	+	8.25099i	0.704930	+	0.704930i	0.965465	−	0.260535i	$-0.0838988\pi$
$137$	8.25099	+	8.25099i	0.704930	+	0.704930i	−0.260535	+	0.965465i	$0.583899\pi$
$138$	14.2953	−	7.28380i	1.21689	−	0.620039i
$139$	−3.57113	−	2.59458i	−0.302900	−	0.220069i	0.425944	−	0.904749i	$-0.359942\pi$
$139$	−3.57113	−	2.59458i	−0.302900	−	0.220069i	−0.728844	+	0.684680i	$0.759942\pi$
$140$	−1.57087	+	3.08300i	−0.132763	+	0.260561i
$141$	18.1428	−	13.1815i	1.52790	−	1.11008i
$142$	−2.33463	−	14.7403i	−0.195918	−	1.23698i
$143$	−3.53691	+	4.86814i	−0.295771	+	0.407094i
$144$	−1.22503	+	1.68611i	−0.102086	+	0.140509i
$145$	1.67944	+	10.6036i	0.139470	+	0.880579i
$146$	−12.9048	+	9.37587i	−1.06801	+	0.775953i
$147$	−0.168833	+	0.331353i	−0.0139251	+	0.0273295i
$148$	−3.69388	−	2.68376i	−0.303635	−	0.220604i
$149$	−6.81852	+	3.47421i	−0.558595	+	0.284618i	−0.710407	−	0.703791i	$-0.751489\pi$
$149$	−6.81852	+	3.47421i	−0.558595	+	0.284618i	0.151812	+	0.988409i	$0.451489\pi$
$150$	−5.17916	−	5.17916i	−0.422877	−	0.422877i
$151$	2.32524	−	14.6810i	0.189225	−	1.19472i	−0.691956	−	0.721940i	$-0.743251\pi$
$151$	2.32524	−	14.6810i	0.189225	−	1.19472i	0.881181	−	0.472780i	$-0.156749\pi$
$152$	2.70385	+	5.30660i	0.219311	+	0.430422i
$153$	−3.47328	−	1.76973i	−0.280798	−	0.143074i
$154$	−0.842335	−	2.59244i	−0.0678773	−	0.208905i
$155$		−	7.40133i		−	0.594489i
$156$	−12.3763	+	4.02130i	−0.990895	+	0.321961i
$157$	14.1205	−	2.23647i	1.12694	−	0.178490i	0.434991	−	0.900435i	$-0.356752\pi$
$157$	14.1205	−	2.23647i	1.12694	−	0.178490i	0.691950	+	0.721945i	$0.256752\pi$
$158$	−5.21122	−	0.825377i	−0.414583	−	0.0656634i
$159$	−9.02770	−	2.93328i	−0.715943	−	0.232624i
$160$	−0.408982	+	1.25872i	−0.0323328	+	0.0995103i
$161$	−13.1540	+	13.1540i	−1.03668	+	1.03668i
$162$	6.41201	+	8.82538i	0.503775	+	0.693387i
$163$	−12.5915			−0.986243			−0.493121	−	0.869961i	$-0.664144\pi$
$163$	−12.5915			−0.986243			−0.493121	+	0.869961i	$0.664144\pi$
$164$	−6.37418	+	0.608156i	−0.497740	+	0.0474890i
$165$	−3.11144			−0.242225
$166$	−4.41300	−	6.07398i	−0.342516	−	0.471432i
$167$	−10.1844	+	10.1844i	−0.788096	+	0.788096i	−0.981182	−	0.193086i	$-0.938151\pi$
$167$	−10.1844	+	10.1844i	−0.788096	+	0.788096i	0.193086	+	0.981182i	$0.438151\pi$
$168$	1.82164	−	5.60644i	0.140543	−	0.432546i
$169$	−19.3141	−	6.27553i	−1.48570	−	0.482733i
$170$	−2.44496	−	0.387244i	−0.187520	−	0.0297003i
$171$	−12.2598	+	1.94177i	−0.937533	+	0.148491i
$172$	1.24616	−	0.404901i	0.0950185	−	0.0308734i
$173$		−	7.22825i		−	0.549554i	−0.961508	−	0.274777i	$-0.911396\pi$
$173$		−	7.22825i		−	0.549554i	0.961508	−	0.274777i	$-0.0886040\pi$
$174$	−5.65201	−	17.3951i	−0.428477	−	1.31872i
$175$	7.56689	+	3.85552i	0.572003	+	0.291450i
$176$	−0.473345	−	0.928992i	−0.0356797	−	0.0700254i
$177$	0.113326	−	0.715510i	0.00851808	−	0.0537810i
$178$	−1.65973	−	1.65973i	−0.124402	−	0.124402i
$179$	−1.18920	+	0.605926i	−0.0888848	+	0.0452890i	−0.497868	−	0.867253i	$-0.665884\pi$
$179$	−1.18920	+	0.605926i	−0.0888848	+	0.0452890i	0.408983	+	0.912542i	$0.365884\pi$
$180$	−2.23156	−	1.62132i	−0.166330	−	0.120846i
$181$	8.60225	−	16.8829i	0.639400	−	1.25489i	−0.312916	−	0.949781i	$-0.601306\pi$
$181$	8.60225	−	16.8829i	0.639400	−	1.25489i	0.952316	−	0.305113i	$-0.0986942\pi$
$182$	12.2069	−	8.86880i	0.904832	−	0.657399i
$183$	2.71244	+	17.1257i	0.200510	+	1.26597i
$184$	−4.18236	+	5.75652i	−0.308327	+	0.424376i
$185$	3.55194	−	4.88883i	0.261144	−	0.359434i
$186$	1.97256	+	12.4542i	0.144635	+	0.913189i
$187$	1.57768	−	1.14625i	0.115371	−	0.0838223i
$188$	−4.51528	+	8.86173i	−0.329311	+	0.646308i
$189$	−4.36780	−	3.17339i	−0.317711	−	0.230830i
$190$	−7.02325	+	3.57853i	−0.509520	+	0.259614i
$191$	16.2633	+	16.2633i	1.17677	+	1.17677i	0.980562	+	0.196211i	$0.0628637\pi$
$191$	16.2633	+	16.2633i	1.17677	+	1.17677i	0.196211	+	0.980562i	$0.437136\pi$
$192$	0.352729	−	2.22705i	0.0254560	−	0.160723i
$193$	11.0091	+	21.6066i	0.792453	+	1.55528i	0.831165	+	0.556027i	$0.187675\pi$
$193$	11.0091	+	21.6066i	0.792453	+	1.55528i	−0.0387114	+	0.999250i	$0.512325\pi$
$194$	4.43678	+	2.26065i	0.318542	+	0.162305i
$195$	−5.32216	−	16.3799i	−0.381128	−	1.17299i
$196$		−	0.164930i		−	0.0117807i
$197$	1.49219	−	0.484841i	0.106314	−	0.0345435i	−0.255377	−	0.966842i	$-0.582200\pi$
$197$	1.49219	−	0.484841i	0.106314	−	0.0345435i	0.361691	+	0.932298i	$0.382200\pi$
$198$	2.14625	−	0.339932i	0.152527	−	0.0241579i
$199$	−10.9252	−	1.73038i	−0.774466	−	0.122663i	−0.243323	−	0.969945i	$-0.578237\pi$
$199$	−10.9252	−	1.73038i	−0.774466	−	0.122663i	−0.531143	+	0.847282i	$0.678237\pi$
$200$	3.08938	+	1.00380i	0.218452	+	0.0709794i
$201$	7.40795	−	22.7993i	0.522517	−	1.60814i
$202$	1.92643	−	1.92643i	0.135543	−	0.135543i
$203$	12.4653	+	17.1570i	0.874889	+	1.20418i
$204$	4.21735			0.295274
$205$	−0.804889	−	8.43618i	−0.0562159	−	0.589208i
$206$	4.28424			0.298497
$207$	−8.71666	−	11.9974i	−0.605849	−	0.833880i
$208$	4.08093	−	4.08093i	0.282962	−	0.282962i
$209$	1.91889	−	5.90572i	0.132732	−	0.408507i
$210$	7.42008	+	2.41093i	0.512034	+	0.166370i
$211$	−0.337401	−	0.0534390i	−0.0232276	−	0.00367889i	0.144810	−	0.989460i	$-0.453743\pi$
$211$	−0.337401	−	0.0534390i	−0.0232276	−	0.00367889i	−0.168037	+	0.985781i	$0.553743\pi$
$212$	4.15797	−	0.658558i	0.285571	−	0.0452299i
$213$	−32.0038	+	10.3986i	−2.19286	+	0.712504i
$214$			0.419287i			0.0286619i
$215$	0.535883	+	1.64928i	0.0365469	+	0.112480i
$216$	−1.83999	−	0.937520i	−0.125195	−	0.0637901i
$217$	−6.63753	−	13.0269i	−0.450585	−	0.884323i
$218$	1.50685	−	9.51387i	0.102057	−	0.644361i
$219$	25.4324	+	25.4324i	1.71856	+	1.71856i
$220$	1.22951	−	0.626468i	0.0828938	−	0.0422365i
$221$	8.73299	+	6.34489i	0.587444	+	0.426803i
$222$	−4.67392	+	9.17308i	−0.313693	+	0.615657i
$223$	−10.9881	+	7.98336i	−0.735821	+	0.534605i	−0.891400	−	0.453218i	$-0.850276\pi$
$223$	−10.9881	+	7.98336i	−0.735821	+	0.534605i	0.155579	+	0.987824i	$0.450276\pi$
$224$	0.408982	+	2.58221i	0.0273262	+	0.172531i
$225$	−3.97935	+	5.47711i	−0.265290	+	0.365141i
$226$	−2.12674	+	2.92720i	−0.141469	+	0.194715i
$227$	−3.36269	−	21.2312i	−0.223190	−	1.40916i	−0.803760	−	0.594954i	$-0.797170\pi$
$227$	−3.36269	−	21.2312i	−0.223190	−	1.40916i	0.580570	−	0.814210i	$-0.302830\pi$
$228$	10.8643	−	7.89339i	0.719507	−	0.522753i
$229$	8.10290	−	15.9028i	0.535455	−	1.05089i	−0.451856	−	0.892091i	$-0.649238\pi$
$229$	8.10290	−	15.9028i	0.535455	−	1.05089i	0.987311	−	0.158798i	$-0.0507619\pi$
$230$	−7.61871	−	5.53532i	−0.502363	−	0.364988i
$231$	−5.47636	+	2.79035i	−0.360318	+	0.183591i
$232$	5.73583	+	5.73583i	0.376575	+	0.376575i
$233$	0.313969	−	1.98232i	0.0205688	−	0.129866i	−0.975267	−	0.221029i	$-0.929058\pi$
$233$	0.313969	−	1.98232i	0.0205688	−	0.129866i	0.995836	+	0.0911628i	$0.0290584\pi$
$234$	5.46072	+	10.7173i	0.356979	+	0.700610i
$235$	−11.7284	−	5.97594i	−0.765079	−	0.389827i
$236$	0.0992817	+	0.305558i	0.00646269	+	0.0198901i
$237$			11.8968i			0.772778i
$238$	−4.65059	+	1.51107i	−0.301453	+	0.0979481i
$239$	10.6415	−	1.68544i	0.688339	−	0.109022i	0.197540	−	0.980295i	$-0.436705\pi$
$239$	10.6415	−	1.68544i	0.688339	−	0.109022i	0.490799	+	0.871273i	$0.336705\pi$
$240$	2.94748	+	0.466835i	0.190259	+	0.0301341i
$241$	13.1107	+	4.25993i	0.844535	+	0.274406i	0.699155	−	0.714970i	$-0.253560\pi$
$241$	13.1107	+	4.25993i	0.844535	+	0.274406i	0.145380	+	0.989376i	$0.453560\pi$
$242$	3.06326	−	9.42775i	0.196914	−	0.606039i
$243$	13.0122	−	13.0122i	0.834730	−	0.834730i
$244$	−4.52000	−	6.22124i	−0.289363	−	0.398274i
$245$	0.218284			0.0139457
$246$	3.60275	+	13.9811i	0.229703	+	0.891400i
$247$	34.3724			2.18707
$248$	−3.28705	−	4.52424i	−0.208728	−	0.287290i
$249$	−11.9704	+	11.9704i	−0.758595	+	0.758595i
$250$	−3.37343	+	10.3824i	−0.213355	+	0.656638i
$251$	−22.7126	−	7.37977i	−1.43361	−	0.465807i	−0.513709	−	0.857965i	$-0.671729\pi$
$251$	−22.7126	−	7.37977i	−1.43361	−	0.465807i	−0.919898	+	0.392157i	$0.871729\pi$
$252$	−5.38171	−	0.852379i	−0.339016	−	0.0536948i
$253$	7.32745	−	1.16055i	0.460673	−	0.0729635i
$254$	−1.84865	+	0.600664i	−0.115995	+	0.0376890i
$255$			5.58163i			0.349535i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	5.29890	+	2.69993i	0.330536	+	0.168417i	0.611381	−	0.791337i	$-0.290614\pi$
$257$	5.29890	+	2.69993i	0.330536	+	0.168417i	−0.280844	+	0.959753i	$0.590614\pi$
$258$	−1.34129	−	2.63243i	−0.0835049	−	0.163888i
$259$	1.86737	−	11.7901i	0.116032	−	0.732600i
$260$	5.40109	+	5.40109i	0.334961	+	0.334961i
$261$	−15.0633	+	7.67515i	−0.932396	+	0.475080i
$262$	6.03583	+	4.38529i	0.372895	+	0.270924i
$263$	7.57066	−	14.8582i	0.466827	−	0.916199i	−0.530810	−	0.847491i	$-0.678112\pi$
$263$	7.57066	−	14.8582i	0.466827	−	0.916199i	0.997637	−	0.0687081i	$-0.0218877\pi$
$264$	−1.90194	+	1.38184i	−0.117057	+	0.0850466i
$265$	0.871596	+	5.50304i	0.0535417	+	0.338049i
$266$	−9.15221	+	12.5969i	−0.561158	+	0.772368i
$267$	−3.11085	+	4.28172i	−0.190381	+	0.262037i
$268$	1.66318	+	10.5009i	0.101595	+	0.641445i
$269$	1.05538	−	0.766779i	0.0643477	−	0.0467514i	−0.555146	−	0.831753i	$-0.687338\pi$
$269$	1.05538	−	0.766779i	0.0643477	−	0.0467514i	0.619494	+	0.785001i	$0.287338\pi$
$270$	1.24080	−	2.43521i	0.0755127	−	0.148202i
$271$	9.04729	+	6.57324i	0.549584	+	0.399296i	0.827632	−	0.561271i	$-0.189687\pi$
$271$	9.04729	+	6.57324i	0.549584	+	0.399296i	−0.278048	+	0.960567i	$0.589687\pi$
$272$	−1.66652	+	0.849136i	−0.101048	+	0.0514864i
$273$	−24.0569	−	24.0569i	−1.45599	−	1.45599i
$274$	−1.82538	+	11.5250i	−0.110275	+	0.696251i
$275$	−1.53760	−	3.01771i	−0.0927206	−	0.181974i
$276$	14.2953	+	7.28380i	0.860474	+	0.438434i
$277$	−1.10219	−	3.39219i	−0.0662242	−	0.203817i	0.912469	−	0.409146i	$-0.134173\pi$
$277$	−1.10219	−	3.39219i	−0.0662242	−	0.203817i	−0.978693	+	0.205329i	$0.934173\pi$
$278$		−	4.41416i		−	0.264744i
$279$	11.0847	−	3.60163i	0.663623	−	0.215624i
$280$	−3.41753	+	0.541284i	−0.204237	+	0.0323479i
$281$	−16.7346	−	2.65049i	−0.998300	−	0.158115i	−0.364162	−	0.931336i	$-0.618645\pi$
$281$	−16.7346	−	2.65049i	−0.998300	−	0.158115i	−0.634137	+	0.773220i	$0.718645\pi$
$282$	21.3282	+	6.92994i	1.27007	+	0.412672i
$283$	3.80604	−	11.7138i	0.226246	−	0.696312i	−0.771917	−	0.635723i	$-0.780702\pi$
$283$	3.80604	−	11.7138i	0.226246	−	0.696312i	0.998163	−	0.0605891i	$-0.0192979\pi$
$284$	10.5529	−	10.5529i	0.626197	−	0.626197i
$285$	10.4468	+	14.3789i	0.618818	+	0.851730i
$286$	−6.01735			−0.355814
$287$	−8.98225	−	14.1265i	−0.530205	−	0.833859i
$288$	−2.08415			−0.122810
$289$	7.93608	+	10.9231i	0.466828	+	0.642534i
$290$	−7.59132	+	7.59132i	−0.445778	+	0.445778i
$291$	3.46959	−	10.6783i	0.203391	−	0.625974i
$292$	−15.1705	−	4.92919i	−0.887785	−	0.288459i
$293$	−12.9405	−	2.04957i	−0.755992	−	0.119737i	−0.233471	−	0.972364i	$-0.575008\pi$
$293$	−12.9405	−	2.04957i	−0.755992	−	0.119737i	−0.522521	+	0.852626i	$0.675008\pi$
$294$	−0.367308	+	0.0581758i	−0.0214218	+	0.00339288i
$295$	−0.404403	+	0.131399i	−0.0235453	+	0.00765032i
$296$		−	4.56589i		−	0.265387i
$297$	0.665345	+	2.04772i	0.0386072	+	0.118821i
$298$	−6.81852	−	3.47421i	−0.394986	−	0.201256i
$299$	18.6433	+	36.5896i	1.07817	+	2.11603i
$300$	1.14579	−	7.23426i	0.0661525	−	0.417670i
$301$	2.42227	+	2.42227i	0.139617	+	0.139617i
$302$	13.2439	−	6.74810i	0.762100	−	0.388309i
$303$	−4.96976	−	3.61074i	−0.285505	−	0.207432i
$304$	−2.70385	+	5.30660i	−0.155076	+	0.304355i
$305$	8.23377	−	5.98218i	0.471464	−	0.342539i
$306$	−0.609806	−	3.85017i	−0.0348603	−	0.220099i
$307$	−11.9683	+	16.4730i	−0.683067	+	0.940161i	−0.999966	−	0.00829834i	$-0.997359\pi$
$307$	−11.9683	+	16.4730i	−0.683067	+	0.940161i	0.316899	+	0.948459i	$0.397359\pi$
$308$	1.60222	−	2.20526i	0.0912947	−	0.125656i
$309$	−1.51118	−	9.54119i	−0.0859678	−	0.542779i
$310$	5.98780	−	4.35039i	0.340084	−	0.247086i
$311$	−5.51660	+	10.8269i	−0.312818	+	0.613939i	−0.992867	−	0.119227i	$-0.961958\pi$
$311$	−5.51660	+	10.8269i	−0.312818	+	0.613939i	0.680049	+	0.733166i	$0.261958\pi$
$312$	−10.5279	−	7.64896i	−0.596024	−	0.433037i
$313$	−2.21739	+	1.12982i	−0.125334	+	0.0638609i	−0.515533	−	0.856870i	$-0.672406\pi$
$313$	−2.21739	+	1.12982i	−0.125334	+	0.0638609i	0.390199	+	0.920730i	$0.372406\pi$
$314$	10.1092	+	10.1092i	0.570494	+	0.570494i
$315$	1.12812	−	7.12265i	0.0635622	−	0.401316i
$316$	−2.39534	−	4.70111i	−0.134748	−	0.264458i
$317$	−13.2391	−	6.74567i	−0.743583	−	0.378874i	0.0407870	−	0.999168i	$-0.487013\pi$
$317$	−13.2391	−	6.74567i	−0.743583	−	0.378874i	−0.784370	+	0.620293i	$0.787013\pi$
$318$	−2.93328	−	9.02770i	−0.164490	−	0.506248i
$319$		−	8.45750i		−	0.473529i
$320$	−1.25872	+	0.408982i	−0.0703644	+	0.0228628i
$321$	0.933771	−	0.147895i	0.0521180	−	0.00825468i
$322$	−18.3736	−	2.91009i	−1.02392	−	0.162173i
$323$	−10.5943	−	3.44230i	−0.589483	−	0.191535i
$324$	−3.37100	+	10.3749i	−0.187278	+	0.576381i
$325$	13.2564	−	13.2564i	0.735331	−	0.735331i
$326$	−7.40110	−	10.1867i	−0.409909	−	0.564191i
$327$	−21.7193			−1.20108
$328$	−4.23866	−	4.79935i	−0.234041	−	0.265000i
$329$	−26.0021			−1.43354
$330$	−1.82886	−	2.51721i	−0.100675	−	0.138568i
$331$	18.7644	−	18.7644i	1.03139	−	1.03139i	0.0318941	−	0.999491i	$-0.489846\pi$
$331$	18.7644	−	18.7644i	1.03139	−	1.03139i	0.999491	−	0.0318941i	$-0.0101539\pi$
$332$	2.32005	−	7.14039i	0.127329	−	0.391880i
$333$	9.05025	+	2.94060i	0.495951	+	0.161144i
$334$	−14.2257	−	2.25312i	−0.778394	−	0.123285i
$335$	−13.8979	+	2.20121i	−0.759321	+	0.120265i
$336$	5.60644	−	1.82164i	0.305856	−	0.0993787i
$337$			32.9779i			1.79642i	0.439564	+	0.898211i	$0.355133\pi$
$337$			32.9779i			1.79642i	−0.439564	+	0.898211i	$0.644867\pi$
$338$	−6.27553	−	19.3141i	−0.341344	−	1.05055i
$339$	7.26918	+	3.70383i	0.394808	+	0.201165i
$340$	−1.12383	−	2.20563i	−0.0609480	−	0.119617i
$341$	−0.912119	+	5.75889i	−0.0493940	+	0.311862i
$342$	−8.77707	−	8.77707i	−0.474610	−	0.474610i
$343$	16.6903	−	8.50414i	0.901192	−	0.459180i
$344$	1.06004	+	0.770167i	0.0571537	+	0.0415246i
$345$	−9.64006	+	18.9197i	−0.519003	+	1.01860i
$346$	5.84778	−	4.24866i	0.314379	−	0.228409i
$347$	0.723943	+	4.57080i	0.0388633	+	0.245373i	0.999471	−	0.0325363i	$-0.0103584\pi$
$347$	0.723943	+	4.57080i	0.0388633	+	0.245373i	−0.960607	+	0.277910i	$0.910358\pi$
$348$	10.7508	−	14.7971i	0.576301	−	0.793210i
$349$	−19.5016	+	26.8417i	−1.04390	+	1.43680i	−0.149919	+	0.988698i	$0.547901\pi$
$349$	−19.5016	+	26.8417i	−1.04390	+	1.43680i	−0.893981	+	0.448106i	$0.852099\pi$
$350$	1.32852	+	8.38796i	0.0710125	+	0.448355i
$351$	−9.64197	+	7.00530i	−0.514650	+	0.373915i
$352$	0.473345	−	0.928992i	0.0252294	−	0.0495154i
$353$	5.53764	+	4.02333i	0.294739	+	0.214140i	0.725320	−	0.688411i	$-0.241692\pi$
$353$	5.53764	+	4.02333i	0.294739	+	0.214140i	−0.430582	+	0.902552i	$0.641692\pi$
$354$	0.645471	−	0.328884i	0.0343064	−	0.0174800i
$355$	13.9666	+	13.9666i	0.741272	+	0.741272i
$356$	0.367184	−	2.31831i	0.0194607	−	0.122870i
$357$	5.00562	+	9.82409i	0.264926	+	0.519946i
$358$	−1.18920	−	0.605926i	−0.0628510	−	0.0320242i
$359$	−0.483216	−	1.48719i	−0.0255032	−	0.0784907i	0.937495	−	0.347999i	$-0.113139\pi$
$359$	−0.483216	−	1.48719i	−0.0255032	−	0.0784907i	−0.962998	+	0.269508i	$0.913139\pi$
$360$		−	2.75836i		−	0.145378i
$361$	−15.6647	+	5.08978i	−0.824459	+	0.267883i
$362$	18.7148	−	2.96413i	0.983628	−	0.155791i
$363$	−22.0765	−	3.49658i	−1.15872	−	0.183523i
$364$	14.3500	+	4.66260i	0.752145	+	0.244387i
$365$	6.52375	−	20.0780i	0.341468	−	1.05093i
$366$	−12.2606	+	12.2606i	−0.640874	+	0.640874i
$367$	−7.80776	−	10.7465i	−0.407562	−	0.560961i	0.555060	−	0.831810i	$-0.312695\pi$
$367$	−7.80776	−	10.7465i	−0.407562	−	0.560961i	−0.962622	+	0.270850i	$0.912695\pi$
$368$	−7.11545			−0.370918
$369$	12.2429	−	5.31066i	0.637338	−	0.276462i
$370$	6.04292			0.314156
$371$	6.46921	+	8.90411i	0.335865	+	0.462278i
$372$	−8.91625	+	8.91625i	−0.462286	+	0.462286i
$373$	−1.67554	+	5.15679i	−0.0867563	+	0.267008i	−0.985018	−	0.172453i	$-0.944831\pi$
$373$	−1.67554	+	5.15679i	−0.0867563	+	0.267008i	0.898261	+	0.439461i	$0.144831\pi$
$374$	1.85467	+	0.602620i	0.0959030	+	0.0311608i
$375$	24.3119	+	3.85062i	1.25546	+	0.198845i
$376$	−9.82331	+	1.55586i	−0.506598	+	0.0802373i
$377$	44.5238	−	14.4667i	2.29309	−	0.745070i
$378$		−	5.39890i		−	0.277689i
$379$	6.30104	+	19.3926i	0.323663	+	0.996131i	0.972041	+	0.234813i	$0.0754477\pi$
$379$	6.30104	+	19.3926i	0.323663	+	0.996131i	−0.648378	+	0.761319i	$0.724552\pi$
$380$	−7.02325	−	3.57853i	−0.360285	−	0.183575i
$381$	1.98978	+	3.90516i	0.101939	+	0.200067i
$382$	−3.59796	+	22.7166i	−0.184088	+	1.16228i
$383$	−12.0558	−	12.0558i	−0.616024	−	0.616024i	0.328485	−	0.944509i	$-0.393462\pi$
$383$	−12.0558	−	12.0558i	−0.616024	−	0.616024i	−0.944509	+	0.328485i	$0.893462\pi$
$384$	2.00905	−	1.02366i	0.102524	−	0.0522385i
$385$	2.91865	+	2.12052i	0.148748	+	0.108072i
$386$	−11.0091	+	21.6066i	−0.560349	+	1.09975i
$387$	−2.20929	+	1.60514i	−0.112305	+	0.0815940i
$388$	0.778968	+	4.91821i	0.0395461	+	0.249684i
$389$	14.9542	−	20.5827i	0.758208	−	1.04358i	−0.239153	−	0.970982i	$-0.576870\pi$
$389$	14.9542	−	20.5827i	0.758208	−	1.04358i	0.997361	−	0.0726020i	$-0.0231303\pi$
$390$	10.1233	−	13.9336i	0.512615	−	0.705555i
$391$	−2.08193	−	13.1448i	−0.105288	−	0.664759i
$392$	0.133432	−	0.0969437i	0.00673931	−	0.00489639i
$393$	7.63722	−	14.9889i	0.385247	−	0.756089i
$394$	1.26933	+	0.922222i	0.0639479	+	0.0464609i
$395$	6.22189	−	3.17021i	0.313057	−	0.159511i
$396$	1.53654	+	1.53654i	0.0772142	+	0.0772142i
$397$	−4.86495	+	30.7161i	−0.244165	+	1.54160i	0.495492	+	0.868613i	$0.334988\pi$
$397$	−4.86495	+	30.7161i	−0.244165	+	1.54160i	−0.739657	+	0.672984i	$0.765012\pi$
$398$	−5.02176	−	9.85576i	−0.251718	−	0.494025i
$399$	31.2822	+	15.9391i	1.56607	+	0.797952i
$400$	1.00380	+	3.08938i	0.0501900	+	0.154469i
$401$			0.789586i			0.0394301i	0.999806	+	0.0197150i	$0.00627590\pi$
$401$			0.789586i			0.0394301i	−0.999806	+	0.0197150i	$0.993724\pi$
$402$	22.7993	−	7.40795i	1.13713	−	0.369475i
$403$	−31.8774	+	5.04888i	−1.58793	+	0.251503i
$404$	2.69085	+	0.426188i	0.133875	+	0.0212036i
$405$	−13.7310	−	4.46149i	−0.682301	−	0.221693i
$406$	−6.55337	+	20.1692i	−0.325238	+	1.00098i
$407$	−3.36621	+	3.36621i	−0.166857	+	0.166857i
$408$	2.47890	+	3.41191i	0.122724	+	0.168915i
$409$	17.8143			0.880860			0.440430	−	0.897787i	$-0.354826\pi$
$409$	17.8143			0.880860			0.440430	+	0.897787i	$0.354826\pi$
$410$	6.35191	−	5.60983i	0.313698	−	0.277050i
$411$	26.3106			1.29781
$412$	2.51821	+	3.46602i	0.124063	+	0.170759i
$413$	−0.593941	+	0.593941i	−0.0292259	+	0.0292259i
$414$	4.58262	−	14.1038i	0.225223	−	0.693166i
$415$	9.45025	+	3.07057i	0.463895	+	0.150729i
$416$	5.70026	+	0.902832i	0.279478	+	0.0442650i
$417$	−9.83054	+	1.55700i	−0.481404	+	0.0762468i
$418$	5.90572	−	1.91889i	0.288858	−	0.0938558i
$419$		−	2.74105i		−	0.133909i	−0.997756	−	0.0669545i	$-0.978672\pi$
$419$		−	2.74105i		−	0.133909i	0.997756	−	0.0669545i	$-0.0213282\pi$
$420$	2.41093	+	7.42008i	0.117641	+	0.362063i
$421$	−18.5629	−	9.45825i	−0.904699	−	0.460967i	−0.0612166	−	0.998125i	$-0.519498\pi$
$421$	−18.5629	−	9.45825i	−0.904699	−	0.460967i	−0.843482	+	0.537158i	$0.819498\pi$
$422$	−0.155086	−	0.304373i	−0.00754947	−	0.0148167i
$423$	3.24264	−	20.4732i	0.157663	−	0.995443i
$424$	2.97678	+	2.97678i	0.144565	+	0.144565i
$425$	−5.41348	+	2.75831i	−0.262592	+	0.133798i
$426$	−27.2240	−	19.7794i	−1.31901	−	0.958315i
$427$	9.12720	−	17.9131i	0.441696	−	0.866878i
$428$	−0.339210	+	0.246451i	−0.0163963	+	0.0119126i
$429$	2.12250	+	13.4009i	0.102475	+	0.647002i
$430$	−1.01931	+	1.40296i	−0.0491555	+	0.0676567i
$431$	17.0478	−	23.4643i	0.821163	−	1.13023i	−0.168342	−	0.985729i	$-0.553841\pi$
$431$	17.0478	−	23.4643i	0.821163	−	1.13023i	0.989504	−	0.144505i	$-0.0461588\pi$
$432$	−0.323047	−	2.03964i	−0.0155426	−	0.0981323i
$433$	29.6789	−	21.5630i	1.42628	−	1.03625i	0.435583	−	0.900148i	$-0.356542\pi$
$433$	29.6789	−	21.5630i	1.42628	−	1.03625i	0.990695	−	0.136103i	$-0.0434579\pi$
$434$	6.63753	−	13.0269i	0.318612	−	0.625311i
$435$	19.5839	+	14.2285i	0.938977	+	0.682206i
$436$	8.58259	−	4.37305i	0.411031	−	0.209431i
$437$	−29.9656	−	29.9656i	−1.43345	−	1.43345i
$438$	−5.62645	+	35.5240i	−0.268842	+	1.69740i
$439$	3.72338	+	7.30755i	0.177707	+	0.348770i	0.962628	−	0.270825i	$-0.0872966\pi$
$439$	3.72338	+	7.30755i	0.177707	+	0.348770i	−0.784921	+	0.619596i	$0.787297\pi$
$440$	1.22951	+	0.626468i	0.0586148	+	0.0298657i
$441$	0.106221	+	0.326916i	0.00505816	+	0.0155674i
$442$			10.7946i			0.513445i
$443$	−16.1467	+	5.24639i	−0.767155	+	0.249264i	−0.666347	−	0.745642i	$-0.732143\pi$
$443$	−16.1467	+	5.24639i	−0.767155	+	0.249264i	−0.100808	+	0.994906i	$0.532143\pi$
$444$	−10.1684	+	1.61052i	−0.482573	+	0.0764320i
$445$	3.06827	+	0.485966i	0.145450	+	0.0230370i
$446$	−12.9173	−	4.19710i	−0.611654	−	0.198738i
$447$	−5.33213	+	16.4106i	−0.252201	+	0.776195i
$448$	−1.84866	+	1.84866i	−0.0873409	+	0.0873409i
$449$	−14.3081	−	19.6934i	−0.675241	−	0.929389i	0.324624	−	0.945843i	$-0.394762\pi$
$449$	−14.3081	−	19.6934i	−0.675241	−	0.929389i	−0.999865	+	0.0164540i	$0.994762\pi$
$450$	−6.77008			−0.319145
$451$	−0.413375	+	6.66329i	−0.0194651	+	0.313762i
$452$	−3.61822			−0.170187
$453$	−19.6998	−	27.1145i	−0.925578	−	1.27395i
$454$	15.1999	−	15.1999i	0.713365	−	0.713365i
$455$	−6.17092	+	18.9921i	−0.289297	+	0.890365i
$456$	12.7718	+	4.14980i	0.598093	+	0.194332i
$457$	2.80951	+	0.444983i	0.131423	+	0.0208154i	0.221800	−	0.975092i	$-0.428807\pi$
$457$	2.80951	+	0.444983i	0.131423	+	0.0208154i	−0.0903761	+	0.995908i	$0.528807\pi$
$458$	17.6284	−	2.79207i	0.823722	−	0.130465i
$459$	3.67342	−	1.19357i	0.171461	−	0.0557109i
$460$		−	9.41725i		−	0.439081i
$461$	8.87957	+	27.3285i	0.413563	+	1.27281i	0.913530	+	0.406771i	$0.133345\pi$
$461$	8.87957	+	27.3285i	0.413563	+	1.27281i	−0.499968	+	0.866044i	$0.666655\pi$
$462$	−5.47636	−	2.79035i	−0.254784	−	0.129819i
$463$	−5.71916	−	11.2245i	−0.265792	−	0.521646i	0.719080	−	0.694927i	$-0.244563\pi$
$463$	−5.71916	−	11.2245i	−0.265792	−	0.521646i	−0.984873	+	0.173280i	$0.944563\pi$
$464$	−1.26895	+	8.01182i	−0.0589094	+	0.371939i
$465$	−11.8006	−	11.8006i	−0.547240	−	0.547240i
$466$	1.78828	−	0.911175i	0.0828405	−	0.0422094i
$467$	−5.80187	−	4.21530i	−0.268478	−	0.195061i	0.445398	−	0.895333i	$-0.353062\pi$
$467$	−5.80187	−	4.21530i	−0.268478	−	0.195061i	−0.713876	+	0.700272i	$0.753062\pi$
$468$	−5.46072	+	10.7173i	−0.252422	+	0.495406i
$469$	−22.4872	+	16.3379i	−1.03836	+	0.754415i
$470$	−2.05917	−	13.0011i	−0.0949823	−	0.599695i
$471$	18.9478	−	26.0794i	0.873069	−	1.20168i
$472$	−0.188845	+	0.259923i	−0.00869229	+	0.0119639i
$473$	−0.213712	−	1.34933i	−0.00982650	−	0.0620421i
$474$	−9.62468	+	6.99274i	−0.442076	+	0.321187i
$475$	−8.78310	+	17.2378i	−0.402996	+	0.790925i
$476$	−3.95603	−	2.87423i	−0.181324	−	0.131740i
$477$	−7.81756	+	3.98325i	−0.357941	+	0.182380i
$478$	7.61845	+	7.61845i	0.348460	+	0.348460i
$479$	3.34120	−	21.0955i	0.152663	−	0.963878i	−0.785795	−	0.618486i	$-0.787746\pi$
$479$	3.34120	−	21.0955i	0.152663	−	0.963878i	0.938459	−	0.345391i	$-0.112254\pi$
$480$	1.35481	+	2.65896i	0.0618382	+	0.121364i
$481$	−23.4791	−	11.9632i	−1.07055	−	0.545474i
$482$	4.25993	+	13.1107i	0.194034	+	0.597176i
$483$			41.9453i			1.90858i
$484$	9.42775	−	3.06326i	0.428534	−	0.139239i
$485$	−6.50921	+	1.03096i	−0.295568	+	0.0468134i
$486$	18.1754	+	2.87870i	0.824453	+	0.130581i
$487$	−5.88849	−	1.91329i	−0.266833	−	0.0866993i	0.172545	−	0.985002i	$-0.444801\pi$
$487$	−5.88849	−	1.91329i	−0.266833	−	0.0866993i	−0.439378	+	0.898302i	$0.644801\pi$
$488$	2.37630	−	7.31351i	0.107570	−	0.331067i
$489$	−20.0757	+	20.0757i	−0.907857	+	0.907857i
$490$	0.128304	+	0.176596i	0.00579619	+	0.00797778i
$491$	13.8868			0.626705			0.313352	−	0.949637i	$-0.398548\pi$
$491$	13.8868			0.626705			0.313352	+	0.949637i	$0.398548\pi$
$492$	−9.19328	+	11.1326i	−0.414465	+	0.501894i
$493$	−15.1720			−0.683311
$494$	20.2036	+	27.8079i	0.909004	+	1.25114i
$495$	−2.03360	+	2.03360i	−0.0914037	+	0.0914037i
$496$	1.72811	−	5.31857i	0.0775943	−	0.238811i
$497$	37.1076	+	12.0570i	1.66450	+	0.540830i
$498$	−16.7203	−	2.64824i	−0.749256	−	0.118670i
$499$	−19.1674	+	3.03583i	−0.858053	+	0.135902i	−0.569932	−	0.821692i	$-0.693030\pi$
$499$	−19.1674	+	3.03583i	−0.858053	+	0.135902i	−0.288121	+	0.957594i	$0.593030\pi$
$500$	−10.3824	+	3.37343i	−0.464313	+	0.150864i
$501$			32.4759i			1.45092i
$502$	−7.37977	−	22.7126i	−0.329375	−	1.01371i
$503$	16.0540	+	8.17993i	0.715813	+	0.364725i	0.773661	−	0.633600i	$-0.218424\pi$
$503$	16.0540	+	8.17993i	0.715813	+	0.364725i	−0.0578471	+	0.998325i	$0.518424\pi$
$504$	−2.47370	−	4.85491i	−0.110187	−	0.216255i
$505$	−0.564057	+	3.56131i	−0.0251002	+	0.158476i
$506$	5.24588	+	5.24588i	0.233208	+	0.233208i
$507$	−40.7998	+	20.7885i	−1.81198	+	0.923252i
$508$	−1.57256	−	1.14253i	−0.0697710	−	0.0506916i
$509$	2.70733	−	5.31344i	0.120000	−	0.235514i	−0.823191	−	0.567765i	$-0.807808\pi$
$509$	2.70733	−	5.31344i	0.120000	−	0.235514i	0.943191	+	0.332251i	$0.107808\pi$
$510$	−4.51564	+	3.28080i	−0.199956	+	0.145276i
$511$	−6.52375	−	41.1893i	−0.288594	−	1.82211i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	7.22917	−	9.95009i	0.319176	−	0.439307i
$514$	0.930331	+	5.87388i	0.0410351	+	0.259086i
$515$	−4.58725	+	3.33283i	−0.202139	+	0.146862i
$516$	1.34129	−	2.63243i	0.0590469	−	0.115886i
$517$	8.38931	+	6.09519i	0.368961	+	0.268066i
$518$	10.6360	−	5.41930i	0.467318	−	0.238111i
$519$	−11.5246	−	11.5246i	−0.505876	−	0.505876i
$520$	−1.19489	+	7.54425i	−0.0523995	+	0.330837i
$521$	−19.8919	−	39.0401i	−0.871481	−	1.71038i	−0.685829	−	0.727763i	$-0.740560\pi$
$521$	−19.8919	−	39.0401i	−0.871481	−	1.71038i	−0.185652	−	0.982616i	$-0.559440\pi$
$522$	−15.0633	−	7.67515i	−0.659304	−	0.335932i
$523$	2.03207	+	6.25407i	0.0888562	+	0.273471i	0.985604	−	0.169071i	$-0.0540767\pi$
$523$	2.03207	+	6.25407i	0.0888562	+	0.273471i	−0.896748	+	0.442542i	$0.854077\pi$
$524$			7.46070i			0.325922i
$525$	18.2118	−	5.91736i	0.794827	−	0.258255i
$526$	16.4705	−	2.60867i	0.718148	−	0.113743i
$527$	10.3309	+	1.63626i	0.450022	+	0.0712764i
$528$	−2.23587	−	0.726478i	−0.0973037	−	0.0316159i
$529$	8.53802	−	26.2773i	0.371218	−	1.14249i
$530$	−3.93974	+	3.93974i	−0.171132	+	0.171132i
$531$	−0.393581	−	0.541718i	−0.0170800	−	0.0235086i
$532$	−15.5707			−0.675074
$533$	−35.7854	+	9.22146i	−1.55004	+	0.399426i
$534$	−5.29250			−0.229029
$535$	−0.326176	−	0.448942i	−0.0141018	−	0.0194095i
$536$	−7.51781	+	7.51781i	−0.324720	+	0.324720i
$537$	−0.929960	+	2.86212i	−0.0401308	+	0.123510i
$538$	1.24067	+	0.403120i	0.0534893	+	0.0173797i
$539$	−0.169845	−	0.0269007i	−0.00731572	−	0.00115870i
$540$	2.69945	−	0.427551i	0.116166	−	0.0183989i
$541$	−0.219845	+	0.0714318i	−0.00945185	+	0.00307109i	−0.313739	−	0.949509i	$-0.601582\pi$
$541$	−0.219845	+	0.0714318i	−0.00945185	+	0.00307109i	0.304287	+	0.952580i	$0.401582\pi$
$542$			11.1831i			0.480354i
$543$	−13.2025	−	40.6332i	−0.566574	−	1.74374i
$544$	−1.66652	−	0.849136i	−0.0714516	−	0.0364064i
$545$	5.78769	+	11.3590i	0.247918	+	0.486566i
$546$	5.32216	−	33.6028i	0.227767	−	1.43807i
$547$	−14.2850	−	14.2850i	−0.610781	−	0.610781i	0.332369	−	0.943150i	$-0.392152\pi$
$547$	−14.2850	−	14.2850i	−0.610781	−	0.610781i	−0.943150	+	0.332369i	$0.892152\pi$
$548$	−10.3969	+	5.29746i	−0.444132	+	0.226296i
$549$	12.9660	+	9.42035i	0.553375	+	0.402051i
$550$	1.53760	−	3.01771i	0.0655634	−	0.128675i
$551$	−39.0845	+	28.3966i	−1.66506	+	1.20973i
$552$	2.50983	+	15.8464i	0.106825	+	0.674469i
$553$	8.10793	−	11.1596i	0.344784	−	0.474555i
$554$	2.09649	−	2.88557i	0.0890714	−	0.122596i
$555$	−2.13152	−	13.4579i	−0.0904778	−	0.571254i
$556$	3.57113	−	2.59458i	0.151450	−	0.110035i
$557$	11.5126	−	22.5947i	0.487802	−	0.957366i	−0.507601	−	0.861592i	$-0.669467\pi$
$557$	11.5126	−	22.5947i	0.487802	−	0.957366i	0.995403	−	0.0957738i	$-0.0305325\pi$
$558$	9.42920	+	6.85071i	0.399170	+	0.290014i
$559$	6.73785	−	3.43311i	0.284981	−	0.145205i
$560$	−2.44668	−	2.44668i	−0.103391	−	0.103391i
$561$	0.687865	−	4.34301i	0.0290417	−	0.183362i
$562$	−7.69203	−	15.0965i	−0.324469	−	0.636806i
$563$	39.7194	+	20.2380i	1.67397	+	0.852931i	0.992660	+	0.120938i	$0.0385904\pi$
$563$	39.7194	+	20.2380i	1.67397	+	0.852931i	0.681312	+	0.731993i	$0.261410\pi$
$564$	6.92994	+	21.3282i	0.291803	+	0.898077i
$565$		−	4.78869i		−	0.201462i
$566$	11.7138	−	3.80604i	0.492367	−	0.159980i
$567$	−28.1687	+	4.46149i	−1.18298	+	0.187365i
$568$	14.7403	+	2.33463i	0.618488	+	0.0979588i
$569$	−3.92663	−	1.27584i	−0.164613	−	0.0534860i	0.225551	−	0.974231i	$-0.427582\pi$
$569$	−3.92663	−	1.27584i	−0.164613	−	0.0534860i	−0.390164	+	0.920745i	$0.627582\pi$
$570$	−5.49223	+	16.9034i	−0.230044	+	0.708004i
$571$	−3.27325	+	3.27325i	−0.136981	+	0.136981i	−0.772273	−	0.635291i	$-0.780880\pi$
$571$	−3.27325	+	3.27325i	−0.136981	+	0.136981i	0.635291	+	0.772273i	$0.280880\pi$
$572$	−3.53691	−	4.86814i	−0.147886	−	0.203547i
$573$	51.8601			2.16649
$574$	6.14892	−	15.5701i	0.256651	−	0.649884i
$575$	−23.1136			−0.963903
$576$	−1.22503	−	1.68611i	−0.0510430	−	0.0702547i
$577$	18.4805	−	18.4805i	0.769353	−	0.769353i	−0.208639	−	0.977993i	$-0.566903\pi$
$577$	18.4805	−	18.4805i	0.769353	−	0.769353i	0.977993	+	0.208639i	$0.0669034\pi$
$578$	−4.17224	+	12.8408i	−0.173542	+	0.534109i
$579$	52.0021	+	16.8965i	2.16113	+	0.702195i
$580$	−10.6036	−	1.67944i	−0.440290	−	0.0697350i
$581$	19.3868	−	3.07057i	0.804302	−	0.127389i
$582$	10.6783	−	3.46959i	0.442630	−	0.143819i
$583$		−	4.38927i		−	0.181785i
$584$	−4.92919	−	15.1705i	−0.203971	−	0.627759i
$585$	−14.1842	−	7.22723i	−0.586446	−	0.298809i
$586$	−5.94810	−	11.6738i	−0.245714	−	0.482240i
$587$	3.52202	−	22.2371i	0.145369	−	0.917825i	−0.801917	−	0.597436i	$-0.796186\pi$
$587$	3.52202	−	22.2371i	0.145369	−	0.917825i	0.947286	−	0.320389i	$-0.103814\pi$
$588$	−0.262963	−	0.262963i	−0.0108444	−	0.0108444i
$589$	29.6760	−	15.1207i	1.22278	−	0.623036i
$590$	−0.344006	−	0.249935i	−0.0141625	−	0.0102897i
$591$	1.60610	−	3.15215i	0.0660661	−	0.129662i
$592$	3.69388	−	2.68376i	0.151818	−	0.110302i
$593$	3.45652	+	21.8236i	0.141942	+	0.896188i	0.951164	+	0.308685i	$0.0998889\pi$
$593$	3.45652	+	21.8236i	0.141942	+	0.896188i	−0.809222	+	0.587503i	$0.800111\pi$
$594$	−1.26556	+	1.74190i	−0.0519266	+	0.0714709i
$595$	3.80402	−	5.23578i	0.155949	−	0.214646i
$596$	−1.19713	−	7.55839i	−0.0490364	−	0.309604i
$597$	−20.1779	+	14.6601i	−0.825826	+	0.599998i
$598$	−18.6433	+	36.5896i	−0.762383	+	1.49626i
$599$	12.6779	+	9.21100i	0.518003	+	0.376351i	0.815851	−	0.578262i	$-0.196269\pi$
$599$	12.6779	+	9.21100i	0.518003	+	0.376351i	−0.297848	+	0.954613i	$0.596269\pi$
$600$	6.52612	−	3.32522i	0.266428	−	0.135752i
$601$	17.7392	+	17.7392i	0.723597	+	0.723597i	0.969336	−	0.245739i	$-0.0790305\pi$
$601$	17.7392	+	17.7392i	0.723597	+	0.723597i	−0.245739	+	0.969336i	$0.579031\pi$
$602$	−0.535883	+	3.38343i	−0.0218410	+	0.137898i
$603$	−10.0596	−	19.7431i	−0.409660	−	0.804003i
$604$	13.2439	+	6.74810i	0.538886	+	0.274576i
$605$	4.05420	+	12.4776i	0.164827	+	0.507285i
$606$		−	6.14296i		−	0.249541i
$607$	10.1714	−	3.30488i	0.412843	−	0.134141i	−0.0952289	−	0.995455i	$-0.530358\pi$
$607$	10.1714	−	3.30488i	0.412843	−	0.134141i	0.508072	+	0.861314i	$0.330358\pi$
$608$	−5.88242	+	0.931683i	−0.238564	+	0.0377847i
$609$	47.2293	+	7.48039i	1.91383	+	0.303121i
$610$	9.67937	+	3.14502i	0.391906	+	0.127338i
$611$	−17.7376	+	54.5907i	−0.717586	+	2.20850i
$612$	2.75641	−	2.75641i	0.111421	−	0.111421i
$613$	−4.09920	−	5.64206i	−0.165565	−	0.227881i	0.718171	−	0.695867i	$-0.244980\pi$
$613$	−4.09920	−	5.64206i	−0.165565	−	0.227881i	−0.883736	+	0.467986i	$0.844980\pi$
$614$	−20.3617			−0.821731
$615$	−14.7339	−	12.1672i	−0.594126	−	0.490630i
$616$	2.72585			0.109828
$617$	25.8164	+	35.5333i	1.03933	+	1.43052i	0.897706	+	0.440595i	$0.145233\pi$
$617$	25.8164	+	35.5333i	1.03933	+	1.43052i	0.141625	+	0.989920i	$0.454767\pi$
$618$	6.83074	−	6.83074i	0.274773	−	0.274773i
$619$	−13.0022	+	40.0167i	−0.522603	+	1.60841i	0.246405	+	0.969167i	$0.420751\pi$
$619$	−13.0022	+	40.0167i	−0.522603	+	1.60841i	−0.769008	+	0.639239i	$0.779249\pi$
$620$	7.03908	+	2.28714i	0.282696	+	0.0918536i
$621$	14.5130	+	2.29863i	0.582385	+	0.0922407i
$622$	−12.0017	+	1.90089i	−0.481226	+	0.0762188i
$623$	5.83619	−	1.89629i	0.233822	−	0.0759734i
$624$		−	13.0132i		−	0.520944i
$625$	0.554291	+	1.70593i	0.0221717	+	0.0682373i
$626$	−2.21739	−	1.12982i	−0.0886246	−	0.0451565i
$627$	−6.35657	−	12.4755i	−0.253857	−	0.498222i
$628$	−2.23647	+	14.1205i	−0.0892450	+	0.563471i
$629$	6.03867	+	6.03867i	0.240777	+	0.240777i
$630$	6.42544	−	3.27392i	0.255996	−	0.130436i
$631$	13.6150	+	9.89190i	0.542006	+	0.393790i	0.824829	−	0.565382i	$-0.191271\pi$
$631$	13.6150	+	9.89190i	0.542006	+	0.393790i	−0.282824	+	0.959172i	$0.591271\pi$
$632$	2.39534	−	4.70111i	0.0952814	−	0.187000i
$633$	−0.623150	+	0.452745i	−0.0247680	+	0.0179950i
$634$	−2.32440	−	14.6757i	−0.0923136	−	0.582845i
$635$	1.51213	−	2.08127i	0.0600070	−	0.0825926i
$636$	5.57942	−	7.67942i	0.221239	−	0.304509i
$637$	−0.148904	−	0.940146i	−0.00589981	−	0.0372499i
$638$	6.84226	−	4.97119i	0.270888	−	0.196811i
$639$	−14.1209	+	27.7137i	−0.558612	+	1.09634i
$640$	−1.07073	−	0.777929i	−0.0423242	−	0.0307504i
$641$	−24.0626	+	12.2605i	−0.950417	+	0.484262i	−0.859240	−	0.511573i	$-0.829063\pi$
$641$	−24.0626	+	12.2605i	−0.950417	+	0.484262i	−0.0911771	+	0.995835i	$0.529063\pi$
$642$	0.668506	+	0.668506i	0.0263838	+	0.0263838i
$643$	−3.77085	+	23.8082i	−0.148708	+	0.938904i	0.794636	+	0.607087i	$0.207662\pi$
$643$	−3.77085	+	23.8082i	−0.148708	+	0.938904i	−0.943343	+	0.331818i	$0.892338\pi$
$644$	−8.44541	−	16.5750i	−0.332796	−	0.653148i
$645$	3.48400	+	1.77518i	0.137182	+	0.0698978i
$646$	−3.44230	−	10.5943i	−0.135436	−	0.416828i
$647$		−	12.8206i		−	0.504028i	−0.967724	−	0.252014i	$-0.918907\pi$
$647$		−	12.8206i		−	0.504028i	0.967724	−	0.252014i	$-0.0810929\pi$
$648$	−10.3749	+	3.37100i	−0.407563	+	0.132425i
$649$	0.330855	−	0.0524022i	0.0129872	−	0.00205697i
$650$	18.5165	+	2.93273i	0.726278	+	0.115031i
$651$	−31.3527	−	10.1871i	−1.22881	−	0.399265i
$652$	3.89099	−	11.9752i	0.152383	−	0.468986i
$653$	5.15294	−	5.15294i	0.201650	−	0.201650i	−0.599057	−	0.800707i	$-0.704458\pi$
$653$	5.15294	−	5.15294i	0.201650	−	0.201650i	0.800707	+	0.599057i	$0.204458\pi$
$654$	−12.7663	−	17.5713i	−0.499202	−	0.687092i
$655$	−9.87418			−0.385816
$656$	1.39134	−	6.25013i	0.0543227	−	0.244027i
$657$	33.2447			1.29700
$658$	−15.2837	−	21.0362i	−0.595820	−	0.820076i
$659$	−0.173151	+	0.173151i	−0.00674500	+	0.00674500i	−0.710471	−	0.703726i	$-0.751518\pi$
$659$	−0.173151	+	0.173151i	−0.00674500	+	0.00674500i	0.703726	+	0.710471i	$0.251518\pi$
$660$	0.961488	−	2.95916i	0.0374259	−	0.115185i
$661$	16.8008	+	5.45891i	0.653475	+	0.212327i	0.616946	−	0.787006i	$-0.288370\pi$
$661$	16.8008	+	5.45891i	0.653475	+	0.212327i	0.0365293	+	0.999333i	$0.488370\pi$
$662$	26.2102	+	4.15128i	1.01869	+	0.161344i
$663$	24.0400	−	3.80756i	0.933636	−	0.147873i
$664$	7.14039	−	2.32005i	0.277101	−	0.0900355i
$665$		−	20.6077i		−	0.799131i
$666$	2.94060	+	9.05025i	0.113946	+	0.350690i
$667$	−51.4274	−	26.2036i	−1.99128	−	1.01461i
$668$	−6.53882	−	12.8332i	−0.252995	−	0.496530i
$669$	−4.79080	+	30.2480i	−0.185223	+	1.16945i
$670$	−9.94977	−	9.94977i	−0.384393	−	0.384393i
$671$	−7.14383	+	3.63996i	−0.275784	+	0.140519i
$672$	4.76912	+	3.46497i	0.183973	+	0.133664i
$673$	−13.6208	+	26.7324i	−0.525045	+	1.03046i	0.464410	+	0.885620i	$0.346266\pi$
$673$	−13.6208	+	26.7324i	−0.525045	+	1.03046i	−0.989455	+	0.144839i	$0.953734\pi$
$674$	−26.6797	+	19.3839i	−1.02766	+	0.746642i
$675$	−1.04938	−	6.62550i	−0.0403905	−	0.255016i
$676$	11.9368	−	16.4296i	0.459107	−	0.631906i
$677$	−18.5570	+	25.5416i	−0.713205	+	0.981643i	0.286517	+	0.958075i	$0.407503\pi$
$677$	−18.5570	+	25.5416i	−0.713205	+	0.981643i	−0.999722	+	0.0235676i	$0.992497\pi$
$678$	1.27625	+	8.05795i	0.0490142	+	0.309464i
$679$	−10.5321	+	7.65204i	−0.404186	+	0.293658i
$680$	1.12383	−	2.20563i	0.0430967	−	0.0845821i
$681$	−39.2122	−	28.4893i	−1.50262	−	1.09171i
$682$	−5.19517	+	2.64707i	−0.198933	+	0.101362i
$683$	−7.77048	−	7.77048i	−0.297329	−	0.297329i	0.542638	−	0.839967i	$-0.317426\pi$
$683$	−7.77048	−	7.77048i	−0.297329	−	0.297329i	−0.839967	+	0.542638i	$0.817426\pi$
$684$	1.94177	−	12.2598i	0.0742453	−	0.468767i
$685$	−7.01115	−	13.7602i	−0.267882	−	0.525749i
$686$	16.6903	+	8.50414i	0.637239	+	0.324689i
$687$	−12.4361	−	38.2745i	−0.474468	−	1.46026i
$688$			1.31029i			0.0499542i
$689$	23.1069	−	7.50790i	0.880304	−	0.286028i
$690$	−20.9726	+	3.32174i	−0.798415	+	0.126456i
$691$	−21.9827	−	3.48172i	−0.836262	−	0.132451i	−0.276406	−	0.961041i	$-0.589143\pi$
$691$	−21.9827	−	3.48172i	−0.836262	−	0.132451i	−0.559856	+	0.828590i	$0.689143\pi$
$692$	6.87448	+	2.23365i	0.261328	+	0.0849107i
$693$	−1.75555	+	5.40303i	−0.0666879	+	0.205244i
$694$	−3.27233	+	3.27233i	−0.124216	+	0.124216i
$695$	3.43391	+	4.72637i	0.130256	+	0.179281i
$696$	18.2903			0.693291
$697$	11.9533	+	0.741556i	0.452764	+	0.0280885i
$698$	−33.1782			−1.25581
$699$	−2.66001	−	3.66118i	−0.100611	−	0.138479i
$700$	−6.00512	+	6.00512i	−0.226972	+	0.226972i
$701$	8.20644	−	25.2568i	0.309953	−	0.953938i	−0.667829	−	0.744315i	$-0.732776\pi$
$701$	8.20644	−	25.2568i	0.309953	−	0.953938i	0.977782	−	0.209623i	$-0.0672237\pi$
$702$	−11.3348	−	3.68291i	−0.427805	−	0.139002i
$703$	26.8585	+	4.25396i	1.01299	+	0.160441i
$704$	1.02980	−	0.163104i	0.0388119	−	0.00614719i
$705$	−28.2277	+	9.17172i	−1.06312	+	0.345427i
$706$			6.84489i			0.257611i
$707$	2.20101	+	6.77402i	0.0827776	+	0.254763i
$708$	0.645471	+	0.328884i	0.0242583	+	0.0123602i
$709$	−8.83932	−	17.3481i	−0.331968	−	0.651523i	0.663337	−	0.748321i	$-0.269140\pi$
$709$	−8.83932	−	17.3481i	−0.331968	−	0.651523i	−0.995304	+	0.0967983i	$0.969140\pi$
$710$	−3.08986	+	19.5086i	−0.115961	+	0.732146i
$711$	7.77559	+	7.77559i	0.291608	+	0.291608i
$712$	2.09138	−	1.06561i	0.0783777	−	0.0399355i
$713$	32.1920	+	23.3889i	1.20560	+	0.875920i
$714$	−5.00562	+	9.82409i	−0.187331	+	0.367657i
$715$	6.44295	−	4.68108i	0.240953	−	0.175062i
$716$	−0.208788	−	1.31824i	−0.00780277	−	0.0492648i
$717$	14.2794	−	19.6539i	0.533273	−	0.733987i
$718$	0.919132	−	1.26508i	0.0343017	−	0.0472122i
$719$	−2.18592	−	13.8014i	−0.0815212	−	0.514704i	−0.994332	−	0.106321i	$-0.966093\pi$
$719$	−2.18592	−	13.8014i	−0.0815212	−	0.514704i	0.912811	−	0.408383i	$-0.133907\pi$
$720$	2.23156	−	1.62132i	0.0831652	−	0.0604231i
$721$	−5.08501	+	9.97989i	−0.189376	+	0.371671i
$722$	−13.3252	−	9.68133i	−0.495913	−	0.360302i
$723$	27.6955	−	14.1116i	1.03001	−	0.524815i
$724$	13.3983	+	13.3983i	0.497945	+	0.497945i
$725$	−4.12201	+	26.0253i	−0.153087	+	0.966556i
$726$	−10.1475	−	19.9155i	−0.376608	−	0.739134i
$727$	13.9492	+	7.10747i	0.517347	+	0.263601i	0.693111	−	0.720831i	$-0.256240\pi$
$727$	13.9492	+	7.10747i	0.517347	+	0.263601i	−0.175764	+	0.984432i	$0.556240\pi$
$728$	4.66260	+	14.3500i	0.172808	+	0.531847i
$729$		−	8.76654i		−	0.324687i
$730$	20.0780	−	6.52375i	0.743121	−	0.241455i
$731$	−2.42056	+	0.383380i	−0.0895278	+	0.0141798i
$732$	−17.1257	−	2.71244i	−0.632984	−	0.100255i
$733$	−41.5206	−	13.4909i	−1.53360	−	0.498296i	−0.583996	−	0.811756i	$-0.698512\pi$
$733$	−41.5206	−	13.4909i	−1.53360	−	0.498296i	−0.949601	+	0.313460i	$0.898512\pi$
$734$	4.10478	−	12.6332i	0.151510	−	0.466301i
$735$	0.348030	−	0.348030i	0.0128373	−	0.0128373i
$736$	−4.18236	−	5.75652i	−0.154164	−	0.212188i
$737$	11.0850			0.408323
$738$	11.4926	+	6.78316i	0.423048	+	0.249691i
$739$	−21.2137			−0.780359			−0.390179	−	0.920739i	$-0.627587\pi$
$739$	−21.2137			−0.780359			−0.390179	+	0.920739i	$0.627587\pi$
$740$	3.55194	+	4.88883i	0.130572	+	0.179717i
$741$	54.8030	−	54.8030i	2.01324	−	2.01324i
$742$	−3.40107	+	10.4674i	−0.124857	+	0.384271i
$743$	−39.9132	−	12.9686i	−1.46427	−	0.475772i	−0.534902	−	0.844914i	$-0.679651\pi$
$743$	−39.9132	−	12.9686i	−1.46427	−	0.475772i	−0.929373	+	0.369143i	$0.879651\pi$
$744$	−12.4542	−	1.97256i	−0.456595	−	0.0723175i
$745$	10.0035	−	1.58439i	0.366499	−	0.0580477i
$746$	−5.15679	+	1.67554i	−0.188803	+	0.0613460i
$747$			15.6475i			0.572512i
$748$	0.602620	+	1.85467i	0.0220340	+	0.0678136i
$749$	−0.976706	−	0.497656i	−0.0356880	−	0.0181840i
$750$	11.1749	+	21.9321i	0.408051	+	0.800846i
$751$	−5.63001	+	35.5465i	−0.205442	+	1.29711i	0.642199	+	0.766538i	$0.278022\pi$
$751$	−5.63001	+	35.5465i	−0.205442	+	1.29711i	−0.847641	+	0.530571i	$0.821978\pi$
$752$	−7.03271	−	7.03271i	−0.256457	−	0.256457i
$753$	−47.9789	+	24.4465i	−1.74845	+	0.890880i
$754$	37.8742	+	27.5172i	1.37930	+	1.00212i
$755$	−8.93106	+	17.5282i	−0.325034	+	0.637916i
$756$	4.36780	−	3.17339i	0.158855	−	0.115415i
$757$	1.65601	+	10.4556i	0.0601886	+	0.380016i	0.999334	+	0.0364955i	$0.0116195\pi$
$757$	1.65601	+	10.4556i	0.0601886	+	0.380016i	−0.939145	+	0.343520i	$0.888381\pi$
$758$	−11.9853	+	16.4963i	−0.435325	+	0.599174i
$759$	9.83243	−	13.5332i	0.356895	−	0.491223i
$760$	−1.23308	−	7.78534i	−0.0447284	−	0.282404i
$761$	−25.0152	+	18.1746i	−0.906802	+	0.658830i	−0.940204	−	0.340612i	$-0.889366\pi$
$761$	−25.0152	+	18.1746i	−0.906802	+	0.658830i	0.0334020	+	0.999442i	$0.489366\pi$
$762$	−1.98978	+	3.90516i	−0.0720821	+	0.141469i
$763$	20.3735	+	14.8022i	0.737571	+	0.535877i
$764$	−20.4930	+	10.4417i	−0.741410	+	0.377767i
$765$	3.64809	+	3.64809i	0.131897	+	0.131897i
$766$	2.66713	−	16.8396i	0.0963673	−	0.608439i
$767$	0.841798	+	1.65212i	0.0303956	+	0.0596547i
$768$	2.00905	+	1.02366i	0.0724952	+	0.0369382i
$769$	4.82167	+	14.8396i	0.173874	+	0.535128i	0.999580	−	0.0289716i	$-0.00922323\pi$
$769$	4.82167	+	14.8396i	0.173874	+	0.535128i	−0.825706	+	0.564100i	$0.809223\pi$
$770$			3.60765i			0.130011i
$771$	12.7532	−	4.14378i	0.459297	−	0.149235i
$772$	−23.9511	+	3.79348i	−0.862019	+	0.136530i
$773$	−11.1171	−	1.76078i	−0.399855	−	0.0633308i	−0.0467313	−	0.998907i	$-0.514880\pi$
$773$	−11.1171	−	1.76078i	−0.399855	−	0.0633308i	−0.353124	+	0.935577i	$0.614880\pi$
$774$	−2.59718	−	0.843874i	−0.0933536	−	0.0303324i
$775$	5.61353	−	17.2767i	0.201644	−	0.620596i
$776$	−3.52105	+	3.52105i	−0.126398	+	0.126398i
$777$	−15.8207	−	21.7753i	−0.567563	−	0.781184i
$778$	25.4416			0.912126
$779$	32.1809	−	20.4621i	1.15300	−	0.733130i
$780$	17.2229			0.616677
$781$	−9.14608	−	12.5885i	−0.327272	−	0.450452i
$782$	9.41061	−	9.41061i	0.336523	−	0.336523i
$783$	5.17639	−	15.9313i	0.184989	−	0.569338i
$784$	0.156858	+	0.0509663i	0.00560208	+	0.00182022i
$785$	−18.6884	−	2.95995i	−0.667018	−	0.105645i
$786$	16.6153	−	2.63161i	0.592649	−	0.0938663i
$787$	−13.1030	+	4.25742i	−0.467072	+	0.151761i	−0.533092	−	0.846058i	$-0.678970\pi$
$787$	−13.1030	+	4.25742i	−0.467072	+	0.151761i	0.0660199	+	0.997818i	$0.478970\pi$
$788$			1.56898i			0.0558925i
$789$	−11.6193	−	35.7604i	−0.413656	−	1.27310i
$790$	6.22189	+	3.17021i	0.221365	+	0.112791i
$791$	−4.29451	−	8.42845i	−0.152695	−	0.299681i
$792$	−0.339932	+	2.14625i	−0.0120790	+	0.0762636i
$793$	−31.3819	−	31.3819i	−1.11440	−	1.11440i
$794$	−27.7094	+	14.1186i	−0.983370	+	0.501052i
$795$	10.1637	+	7.38433i	0.360468	+	0.261895i
$796$	5.02176	−	9.85576i	0.177992	−	0.349328i
$797$	5.03409	−	3.65748i	0.178317	−	0.129555i	−0.495047	−	0.868866i	$-0.664849\pi$
$797$	5.03409	−	3.65748i	0.178317	−	0.129555i	0.673363	+	0.739312i	$0.264849\pi$
$798$	5.49223	+	34.6766i	0.194423	+	1.22754i
$799$	10.9342	−	15.0496i	0.386824	−	0.532418i
$800$	−1.90934	+	2.62798i	−0.0675054	+	0.0929133i
$801$	0.765267	+	4.83171i	0.0270394	+	0.170720i
$802$	−0.638789	+	0.464107i	−0.0225564	+	0.0163882i
$803$	−7.55041	+	14.8185i	−0.266448	+	0.522934i
$804$	19.3943	+	14.0908i	0.683983	+	0.496943i
$805$	21.9370	−	11.1774i	0.773176	−	0.393953i
$806$	−22.8217	−	22.8217i	−0.803860	−	0.803860i
$807$	0.460143	−	2.90523i	0.0161978	−	0.102269i
$808$	1.23685	+	2.42745i	0.0435121	+	0.0853973i
$809$	−30.8353	−	15.7114i	−1.08411	−	0.552382i	−0.181741	−	0.983346i	$-0.558173\pi$
$809$	−30.8353	−	15.7114i	−1.08411	−	0.552382i	−0.902369	+	0.430965i	$0.858173\pi$
$810$	−4.46149	−	13.7310i	−0.156761	−	0.482460i
$811$		−	7.63635i		−	0.268148i	−0.990971	−	0.134074i	$-0.957194\pi$
$811$		−	7.63635i		−	0.268148i	0.990971	−	0.134074i	$-0.0428060\pi$
$812$	−20.1692	+	6.55337i	−0.707800	+	0.229978i
$813$	24.9052	−	3.94460i	0.873464	−	0.138343i
$814$	−4.70193	−	0.744712i	−0.164803	−	0.0261022i
$815$	15.8491	+	5.14969i	0.555171	+	0.180386i
$816$	−1.30323	+	4.01094i	−0.0456223	+	0.140411i
$817$	−5.51807	+	5.51807i	−0.193053	+	0.193053i
$818$	10.4710	+	14.4121i	0.366109	+	0.503906i
$819$	−31.4467			−1.09884
$820$	8.27201	+	1.84143i	0.288871	+	0.0643054i
$821$	32.1343			1.12149			0.560747	−	0.827987i	$-0.310514\pi$
$821$	32.1343			1.12149			0.560747	+	0.827987i	$0.310514\pi$
$822$	15.4650	+	21.2857i	0.539403	+	0.742424i
$823$	8.56207	−	8.56207i	0.298455	−	0.298455i	−0.541953	−	0.840409i	$-0.682315\pi$
$823$	8.56207	−	8.56207i	0.298455	−	0.298455i	0.840409	+	0.541953i	$0.182315\pi$
$824$	−1.32390	+	4.07455i	−0.0461203	+	0.141944i
$825$	−7.26292	−	2.35987i	−0.252863	−	0.0821600i
$826$	−0.829618	−	0.131399i	−0.0288661	−	0.00457194i
$827$	37.2717	−	5.90326i	1.29606	−	0.205276i	0.529977	−	0.848012i	$-0.322201\pi$
$827$	37.2717	−	5.90326i	1.29606	−	0.205276i	0.766088	+	0.642736i	$0.222201\pi$
$828$	14.1038	−	4.58262i	0.490143	−	0.159257i
$829$			10.1597i			0.352862i	0.984313	+	0.176431i	$0.0564553\pi$
$829$			10.1597i			0.352862i	−0.984313	+	0.176431i	$0.943545\pi$
$830$	3.07057	+	9.45025i	0.106581	+	0.328023i
$831$	−7.16580	−	3.65116i	−0.248579	−	0.126657i
$832$	2.62012	+	5.14228i	0.0908364	+	0.178276i
$833$	−0.0482574	+	0.304685i	−0.00167202	+	0.0105567i
$834$	−7.03789	−	7.03789i	−0.243702	−	0.243702i
$835$	16.9846	−	8.65408i	0.587776	−	0.299487i
$836$	5.02371	+	3.64994i	0.173749	+	0.126236i
$837$	−5.24287	+	10.2897i	−0.181220	+	0.355664i
$838$	2.21755	−	1.61115i	0.0766041	−	0.0556561i
$839$	1.47282	+	9.29902i	0.0508474	+	0.321038i	0.999981	+	0.00616413i	$0.00196212\pi$
$839$	1.47282	+	9.29902i	0.0508474	+	0.321038i	−0.949134	+	0.314874i	$0.898038\pi$
$840$	−4.58586	+	6.31190i	−0.158227	+	0.217781i
$841$	−21.6302	+	29.7714i	−0.745867	+	1.02660i
$842$	−3.25909	−	20.5771i	−0.112316	−	0.709133i
$843$	−30.9073	+	22.4555i	−1.06450	+	0.773407i
$844$	0.155086	−	0.304373i	0.00533828	−	0.0104770i
$845$	21.7444	+	15.7982i	0.748030	+	0.543476i
$846$	18.4692	−	9.41052i	0.634983	−	0.323540i
$847$	18.3256	+	18.3256i	0.629675	+	0.629675i
$848$	−0.658558	+	4.15797i	−0.0226150	+	0.142785i
$849$	−12.6080	−	24.7446i	−0.432706	−	0.849233i
$850$	−5.41348	−	2.75831i	−0.185681	−	0.0946091i
$851$	10.0395	+	30.8983i	0.344148	+	1.05918i
$852$		−	33.6507i		−	1.15286i
$853$	15.6316	−	5.07901i	0.535215	−	0.173902i	−0.0289243	−	0.999582i	$-0.509208\pi$
$853$	15.6316	−	5.07901i	0.535215	−	0.173902i	0.564139	+	0.825680i	$0.309208\pi$
$854$	19.8569	−	3.14502i	0.679488	−	0.107620i
$855$	16.2258	+	2.56991i	0.554911	+	0.0878892i
$856$	−0.398766	−	0.129567i	−0.0136295	−	0.00442850i
$857$	2.53817	−	7.81169i	0.0867023	−	0.266842i	−0.898300	−	0.439382i	$-0.855197\pi$
$857$	2.53817	−	7.81169i	0.0867023	−	0.266842i	0.985003	+	0.172540i	$0.0551974\pi$
$858$	−9.59400	+	9.59400i	−0.327534	+	0.327534i
$859$	−27.8024	−	38.2667i	−0.948606	−	1.30564i	−0.952144	−	0.305650i	$-0.901126\pi$
$859$	−27.8024	−	38.2667i	−0.948606	−	1.30564i	0.00353779	−	0.999994i	$-0.498874\pi$
$860$	−1.73415			−0.0591342
$861$	−36.8443	−	8.20188i	−1.25565	−	0.279519i
$862$	29.0034			0.987860
$863$	−6.78127	−	9.33362i	−0.230837	−	0.317720i	0.677848	−	0.735202i	$-0.262913\pi$
$863$	−6.78127	−	9.33362i	−0.230837	−	0.317720i	−0.908685	+	0.417482i	$0.862913\pi$
$864$	1.46022	−	1.46022i	0.0496777	−	0.0496777i
$865$	−2.95622	+	9.09832i	−0.100515	+	0.309352i
$866$	34.8897	+	11.3363i	1.18560	+	0.385225i
$867$	30.0688	+	4.76243i	1.02119	+	0.161741i
$868$	14.4404	−	2.28714i	0.490140	−	0.0776305i
$869$	−5.23187	+	1.69994i	−0.177479	+	0.0576664i
$870$			24.2070i			0.820696i
$871$	18.9611	+	58.3563i	0.642472	+	1.97733i
$872$	8.58259	+	4.37305i	0.290643	+	0.148090i
$873$	−4.71154	−	9.24691i	−0.159461	−	0.312961i
$874$	6.62935	−	41.8560i	0.224241	−	1.41580i
$875$	−20.1812	−	20.1812i	−0.682248	−	0.682248i
$876$	−32.0467	+	16.3286i	−1.08276	+	0.551692i
$877$	7.77543	+	5.64918i	0.262558	+	0.190759i	0.711274	−	0.702915i	$-0.248119\pi$
$877$	7.77543	+	5.64918i	0.262558	+	0.190759i	−0.448716	+	0.893674i	$0.648119\pi$
$878$	−3.72338	+	7.30755i	−0.125658	+	0.246618i
$879$	−23.9000	+	17.3644i	−0.806127	+	0.585686i
$880$	0.215866	+	1.36293i	0.00727685	+	0.0459442i
$881$	−31.0062	+	42.6763i	−1.04462	+	1.43780i	−0.151245	+	0.988496i	$0.548328\pi$
$881$	−31.0062	+	42.6763i	−1.04462	+	1.43780i	−0.893378	+	0.449305i	$0.851672\pi$
$882$	−0.202045	+	0.278091i	−0.00680321	+	0.00936382i
$883$	6.56367	+	41.4414i	0.220885	+	1.39461i	0.809936	+	0.586518i	$0.199502\pi$
$883$	6.56367	+	41.4414i	0.220885	+	1.39461i	−0.589051	+	0.808096i	$0.700498\pi$
$884$	−8.73299	+	6.34489i	−0.293722	+	0.213402i
$885$	−0.435275	+	0.854276i	−0.0146316	+	0.0287162i
$886$	−13.7352	−	9.97923i	−0.461444	−	0.335259i
$887$	24.2027	−	12.3319i	0.812647	−	0.414064i	0.00228739	−	0.999997i	$-0.499272\pi$
$887$	24.2027	−	12.3319i	0.812647	−	0.414064i	0.810359	+	0.585933i	$0.199272\pi$
$888$	−7.27980	−	7.27980i	−0.244294	−	0.244294i
$889$	0.794974	−	5.01927i	0.0266626	−	0.168341i
$890$	1.41033	+	2.76792i	0.0472743	+	0.0927810i
$891$	10.1342	+	5.16361i	0.339507	+	0.172987i
$892$	−4.19710	−	12.9173i	−0.140529	−	0.432505i
$893$		−	59.2344i		−	1.98220i
$894$	−16.4106	+	5.33213i	−0.548853	+	0.178333i
$895$	1.74467	−	0.276329i	0.0583180	−	0.00923667i
$896$	−2.58221	−	0.408982i	−0.0862655	−	0.0136631i
$897$	88.0628	+	28.6133i	2.94033	+	0.955371i
$898$	7.52221	−	23.1510i	0.251019	−	0.772558i
$899$	32.0763	−	32.0763i	1.06980	−	1.06980i
$900$	−3.97935	−	5.47711i	−0.132645	−	0.182570i
$901$	−7.87394			−0.262319
$902$	−5.63369	+	3.58216i	−0.187581	+	0.119273i
$903$	7.72408			0.257041
$904$	−2.12674	−	2.92720i	−0.0707343	−	0.0973574i
$905$	−17.7326	+	17.7326i	−0.589451	+	0.589451i
$906$	10.3568	−	31.8750i	0.344082	−	1.05898i
$907$	23.5299	+	7.64532i	0.781297	+	0.253859i	0.672394	−	0.740194i	$-0.265266\pi$
$907$	23.5299	+	7.64532i	0.781297	+	0.253859i	0.108903	+	0.994052i	$0.465266\pi$
$908$	21.2312	+	3.36269i	0.704582	+	0.111595i
$909$	−5.60812	+	0.888239i	−0.186010	+	0.0294610i
$910$	−18.9921	+	6.17092i	−0.629583	+	0.204564i
$911$			3.90997i			0.129543i	0.997900	+	0.0647716i	$0.0206319\pi$
$911$			3.90997i			0.129543i	−0.997900	+	0.0647716i	$0.979368\pi$
$912$	4.14980	+	12.7718i	0.137414	+	0.422916i
$913$	−6.97473	−	3.55380i	−0.230830	−	0.117614i
$914$	1.29139	+	2.53450i	0.0427154	+	0.0838338i
$915$	3.58990	−	22.6657i	0.118678	−	0.749306i
$916$	12.6206	+	12.6206i	0.416995	+	0.416995i
$917$	−17.3793	+	8.85518i	−0.573914	+	0.292424i
$918$	3.12480	+	2.27030i	0.103134	+	0.0749310i
$919$	3.85078	−	7.55757i	0.127025	−	0.249301i	−0.818732	−	0.574177i	$-0.805322\pi$
$919$	3.85078	−	7.55757i	0.127025	−	0.249301i	0.945757	+	0.324875i	$0.105322\pi$
$920$	7.61871	−	5.53532i	0.251181	−	0.182494i
$921$	7.18217	+	45.3464i	0.236660	+	1.49422i
$922$	−16.8899	+	23.2470i	−0.556240	+	0.765599i
$923$	50.6266	−	69.6815i	1.66639	−	2.29360i
$924$	−0.961488	−	6.07060i	−0.0316306	−	0.199708i
$925$	11.9991	−	8.71784i	0.394527	−	0.286641i
$926$	5.71916	−	11.2245i	0.187943	−	0.368860i
$927$	−7.22371	−	5.24833i	−0.237258	−	0.172378i
$928$	−7.22756	+	3.68263i	−0.237256	+	0.120888i
$929$	17.3120	+	17.3120i	0.567987	+	0.567987i	0.931564	−	0.363577i	$-0.118445\pi$
$929$	17.3120	+	17.3120i	0.567987	+	0.567987i	−0.363577	+	0.931564i	$0.618445\pi$
$930$	2.61067	−	16.4831i	0.0856071	−	0.540502i
$931$	0.445947	+	0.875220i	0.0146153	+	0.0286842i
$932$	1.78828	+	0.911175i	0.0585771	+	0.0298465i
$933$	8.46674	+	26.0579i	0.277189	+	0.853099i
$934$		−	7.17150i		−	0.234659i
$935$	−2.45465	+	0.797564i	−0.0802756	+	0.0260831i
$936$	−11.8802	+	1.88164i	−0.388316	+	0.0615032i
$937$	5.33097	+	0.844342i	0.174155	+	0.0275834i	0.242903	−	0.970051i	$-0.421900\pi$
$937$	5.33097	+	0.844342i	0.174155	+	0.0275834i	−0.0687478	+	0.997634i	$0.521900\pi$
$938$	−26.4353	−	8.58935i	−0.863143	−	0.280452i
$939$	−1.73401	+	5.33674i	−0.0565874	+	0.174158i
$940$	9.30774	−	9.30774i	0.303585	−	0.303585i
$941$	12.4802	+	17.1775i	0.406842	+	0.559970i	0.962445	−	0.271478i	$-0.0875124\pi$
$941$	12.4802	+	17.1775i	0.406842	+	0.559970i	−0.555603	+	0.831448i	$0.687512\pi$
$942$	32.2359			1.05030
$943$	39.2366	+	23.1582i	1.27772	+	0.754136i
$944$	−0.321282			−0.0104568
$945$	4.19996	+	5.78075i	0.136625	+	0.188048i
$946$	0.966011	−	0.966011i	0.0314077	−	0.0314077i
$947$	8.19765	−	25.2298i	0.266388	−	0.819857i	−0.724983	−	0.688767i	$-0.758152\pi$
$947$	8.19765	−	25.2298i	0.266388	−	0.819857i	0.991370	−	0.131090i	$-0.0418477\pi$
$948$	−11.3145	−	3.67630i	−0.367478	−	0.119401i
$949$	−90.9259	−	14.4012i	−2.95158	−	0.467484i
$950$	−19.1082	+	3.02645i	−0.619953	+	0.0981910i
$951$	−31.8635	+	10.3531i	−1.03325	+	0.335722i
$952$		−	4.88992i		−	0.158483i
$953$	−15.5004	−	47.7052i	−0.502106	−	1.54532i	−0.805582	−	0.592484i	$-0.798147\pi$
$953$	−15.5004	−	47.7052i	−0.502106	−	1.54532i	0.303477	−	0.952839i	$-0.401853\pi$
$954$	−7.81756	−	3.98325i	−0.253103	−	0.128962i
$955$	−13.8195	−	27.1223i	−0.447189	−	0.877657i
$956$	−1.68544	+	10.6415i	−0.0545111	+	0.344169i
$957$	−13.4845	−	13.4845i	−0.435893	−	0.435893i
$958$	19.0305	−	9.69654i	0.614848	−	0.313281i
$959$	−24.6803	−	17.9313i	−0.796968	−	0.579031i
$960$	−1.35481	+	2.65896i	−0.0437262	+	0.0858175i
$961$	−0.221271	+	0.160763i	−0.00713777	+	0.00518589i
$962$	−4.12223	−	26.0267i	−0.132906	−	0.839136i
$963$	0.513640	−	0.706965i	0.0165518	−	0.0227816i
$964$	−8.10286	+	11.1526i	−0.260976	+	0.359202i
$965$	−5.02064	−	31.6991i	−0.161620	−	1.02043i
$966$	−33.9344	+	24.6548i	−1.09182	+	0.793256i
$967$	−13.3481	+	26.1971i	−0.429246	+	0.842442i	0.570530	+	0.821276i	$0.306738\pi$
$967$	−13.3481	+	26.1971i	−0.429246	+	0.842442i	−0.999776	+	0.0211654i	$0.993262\pi$
$968$	8.01972	+	5.82667i	0.257764	+	0.187276i
$969$	−22.3798	+	11.4031i	−0.718943	+	0.366320i
$970$	−4.66008	−	4.66008i	−0.149626	−	0.149626i
$971$	−4.69552	+	29.6463i	−0.150686	+	0.951396i	0.790243	+	0.612793i	$0.209954\pi$
$971$	−4.69552	+	29.6463i	−0.150686	+	0.951396i	−0.940929	+	0.338603i	$0.890046\pi$
$972$	8.35432	+	16.3963i	0.267965	+	0.525911i
$973$	10.2825	+	5.23922i	0.329643	+	0.167962i
$974$	−1.91329	−	5.88849i	−0.0613057	−	0.188679i
$975$		−	42.2716i		−	1.35378i
$976$	7.31351	−	2.37630i	0.234100	−	0.0760636i
$977$	−57.4318	+	9.09630i	−1.83740	+	0.291016i	−0.976140	−	0.217141i	$-0.930327\pi$
$977$	−57.4318	+	9.09630i	−1.83740	+	0.291016i	−0.861264	+	0.508157i	$0.830327\pi$
$978$	−28.0418	−	4.44139i	−0.896679	−	0.142020i
$979$	−2.32750	−	0.756249i	−0.0743871	−	0.0241698i
$980$	−0.0674535	+	0.207601i	−0.00215472	+	0.00663156i
$981$	−14.1955	+	14.1955i	−0.453228	+	0.453228i
$982$	8.16248	+	11.2347i	0.260475	+	0.358514i
$983$	8.93048			0.284838			0.142419	−	0.989806i	$-0.454512\pi$
$983$	8.93048			0.284838			0.142419	+	0.989806i	$0.454512\pi$
$984$	−14.4101	−	0.893970i	−0.459377	−	0.0284987i
$985$	−2.07653			−0.0661637
$986$	−8.91785	−	12.2744i	−0.284002	−	0.390896i
$987$	−41.4575	+	41.4575i	−1.31961	+	1.31961i
$988$	−10.6217	+	32.6901i	−0.337920	+	1.04001i
$989$	−8.86696	−	2.88105i	−0.281953	−	0.0916121i
$990$	−2.84054	−	0.449898i	−0.0902784	−	0.0142987i
$991$	8.37623	−	1.32667i	0.266080	−	0.0421429i	−0.0219689	−	0.999759i	$-0.506993\pi$
$991$	8.37623	−	1.32667i	0.266080	−	0.0421429i	0.288049	+	0.957616i	$0.406993\pi$
$992$	5.31857	−	1.72811i	0.168865	−	0.0548675i
$993$		−	59.8355i		−	1.89882i
$994$	12.0570	+	37.1076i	0.382425	+	1.17698i
$995$	13.0440	+	6.64626i	0.413523	+	0.210701i
$996$	−7.68549	−	15.0836i	−0.243524	−	0.477943i
$997$	4.89436	−	30.9018i	0.155006	−	0.978669i	−0.780448	−	0.625220i	$-0.785009\pi$
$997$	4.89436	−	30.9018i	0.155006	−	0.978669i	0.935454	−	0.353448i	$-0.114991\pi$
$998$	−13.7224	−	13.7224i	−0.434374	−	0.434374i
$999$	−8.40117	+	4.28061i	−0.265801	+	0.135433i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	82.2.g.b.77.2	yes	16
3.2	odd	2		738.2.u.b.487.2		16
4.3	odd	2		656.2.bs.b.241.1		16
41.7	odd	40		3362.2.a.bd.1.4		16
41.8	even	20	inner	82.2.g.b.49.2	✓	16
41.34	odd	40		3362.2.a.bd.1.13		16
123.8	odd	20		738.2.u.b.541.2		16
164.131	odd	20		656.2.bs.b.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
82.2.g.b.49.2	✓	16	41.8	even	20	inner
82.2.g.b.77.2	yes	16	1.1	even	1	trivial
656.2.bs.b.49.1		16	164.131	odd	20
656.2.bs.b.241.1		16	4.3	odd	2
738.2.u.b.487.2		16	3.2	odd	2
738.2.u.b.541.2		16	123.8	odd	20
3362.2.a.bd.1.4		16	41.7	odd	40
3362.2.a.bd.1.13		16	41.34	odd	40

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 82 = 2 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	82.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(1.59439 - 1.59439i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.25872 - 0.408982i) q^{5} +(2.22705 + 0.352729i) q^{6} +(-2.58221 + 0.408982i) q^{7} +(-0.951057 + 0.309017i) q^{8} -2.08415i q^{9} +(-0.408982 - 1.25872i) q^{10} +(0.928992 + 0.473345i) q^{11} +(1.02366 + 2.00905i) q^{12} +(-0.902832 + 5.70026i) q^{13} +(-1.84866 - 1.84866i) q^{14} +(-2.65896 + 1.35481i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.849136 - 1.66652i) q^{17} +(1.68611 - 1.22503i) q^{18} +(-0.931683 - 5.88242i) q^{19} +(0.777929 - 1.07073i) q^{20} +(-3.46497 + 4.76912i) q^{21} +(0.163104 + 1.02980i) q^{22} +(5.75652 - 4.18236i) q^{23} +(-1.02366 + 2.00905i) q^{24} +(-2.62798 - 1.90934i) q^{25} +(-5.14228 + 2.62012i) q^{26} +(1.46022 + 1.46022i) q^{27} +(0.408982 - 2.58221i) q^{28} +(-3.68263 - 7.22756i) q^{29} +(-2.65896 - 1.35481i) q^{30} +(1.72811 + 5.31857i) q^{31} -1.00000i q^{32} +(2.23587 - 0.726478i) q^{33} +(1.84736 - 0.292592i) q^{34} +(3.41753 + 0.541284i) q^{35} +(1.98214 + 0.644038i) q^{36} +(-1.41094 + 4.34242i) q^{37} +(4.21135 - 4.21135i) q^{38} +(7.64896 + 10.5279i) q^{39} +1.32349 q^{40} +(2.54812 + 5.87427i) q^{41} -5.89496 q^{42} +(-0.770167 - 1.06004i) q^{43} +(-0.737252 + 0.737252i) q^{44} +(-0.852379 + 2.62335i) q^{45} +(6.76719 + 2.19879i) q^{46} +(9.82331 + 1.55586i) q^{47} +(-2.22705 + 0.352729i) q^{48} +(-0.156858 + 0.0509663i) q^{49} -3.24837i q^{50} +(-1.30323 - 4.01094i) q^{51} +(-5.14228 - 2.62012i) q^{52} +(-1.91121 - 3.75096i) q^{53} +(-0.323047 + 2.03964i) q^{54} +(-0.975747 - 0.975747i) q^{55} +(2.32944 - 1.18691i) q^{56} +(-10.8643 - 7.89339i) q^{57} +(3.68263 - 7.22756i) q^{58} +(0.259923 - 0.188845i) q^{59} +(-0.466835 - 2.94748i) q^{60} +(-4.52000 + 6.22124i) q^{61} +(-3.28705 + 4.52424i) q^{62} +(0.852379 + 5.38171i) q^{63} +(0.809017 - 0.587785i) q^{64} +(3.46771 - 6.80577i) q^{65} +(1.90194 + 1.38184i) q^{66} +(9.47300 - 4.82673i) q^{67} +(1.32256 + 1.32256i) q^{68} +(2.50983 - 15.8464i) q^{69} +(1.57087 + 3.08300i) q^{70} +(-13.2974 - 6.77536i) q^{71} +(0.644038 + 1.98214i) q^{72} +15.9512i q^{73} +(-4.34242 + 1.41094i) q^{74} +(-7.23426 + 1.14579i) q^{75} +(5.88242 + 0.931683i) q^{76} +(-2.59244 - 0.842335i) q^{77} +(-4.02130 + 12.3763i) q^{78} +(-3.73082 + 3.73082i) q^{79} +(0.777929 + 1.07073i) q^{80} +10.9088 q^{81} +(-3.25464 + 5.51428i) q^{82} -7.50785 q^{83} +(-3.46497 - 4.76912i) q^{84} +(-1.75040 + 1.75040i) q^{85} +(0.404901 - 1.24616i) q^{86} +(-17.3951 - 5.65201i) q^{87} +(-1.02980 - 0.163104i) q^{88} +(-2.31831 + 0.367184i) q^{89} +(-2.62335 + 0.852379i) q^{90} -15.0885i q^{91} +(2.19879 + 6.76719i) q^{92} +(11.2351 + 5.72459i) q^{93} +(4.51528 + 8.86173i) q^{94} +(-1.23308 + 7.78534i) q^{95} +(-1.59439 - 1.59439i) q^{96} +(4.43678 - 2.26065i) q^{97} +(-0.133432 - 0.0969437i) q^{98} +(0.986521 - 1.93616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{3} + 4 q^{4} - 6 q^{6} + 12 q^{11} + 4 q^{12} - 18 q^{13} - 10 q^{14} - 18 q^{15} - 4 q^{16} - 4 q^{17} + 4 q^{18} - 16 q^{19} + 10 q^{20} - 12 q^{22} - 4 q^{23} - 4 q^{24} - 4 q^{25} - 2 q^{26}+ \cdots + 24 q^{99}+O(q^{100}) \) 16 * q - 4 * q^3 + 4 * q^4 - 6 * q^6 + 12 * q^11 + 4 * q^12 - 18 * q^13 - 10 * q^14 - 18 * q^15 - 4 * q^16 - 4 * q^17 + 4 * q^18 - 16 * q^19 + 10 * q^20 - 12 * q^22 - 4 * q^23 - 4 * q^24 - 4 * q^25 - 2 * q^26 + 8 * q^27 - 10 * q^29 - 18 * q^30 + 40 * q^31 - 60 * q^33 + 26 * q^34 + 44 * q^35 + 10 * q^36 - 16 * q^37 + 14 * q^38 + 80 * q^39 - 4 * q^41 + 16 * q^42 - 40 * q^43 - 2 * q^44 + 58 * q^45 + 10 * q^46 + 6 * q^48 + 20 * q^49 - 6 * q^51 - 2 * q^52 + 46 * q^53 + 18 * q^54 - 18 * q^55 - 60 * q^57 + 10 * q^58 - 2 * q^59 - 42 * q^60 - 60 * q^61 - 58 * q^63 + 4 * q^64 - 16 * q^65 + 4 * q^66 + 50 * q^67 - 16 * q^68 + 48 * q^69 - 26 * q^70 - 38 * q^71 - 4 * q^72 - 10 * q^74 + 6 * q^75 - 4 * q^76 - 38 * q^78 - 20 * q^79 + 10 * q^80 + 40 * q^81 + 10 * q^82 + 24 * q^83 - 2 * q^85 - 10 * q^86 - 70 * q^87 - 18 * q^88 + 36 * q^89 - 6 * q^92 - 12 * q^93 + 20 * q^94 - 72 * q^95 + 4 * q^96 - 10 * q^97 - 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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