LMFDB - Embedded newform 338.3.f.d.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,3,Mod(19,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	338.f (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2,0,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.20983293538$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.19
Dual form			338.3.f.d.89.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.03590 - 7.59808i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(4.96410 - 1.33013i) q^{11} +3.46410i q^{12} +11.1244 q^{14} +(1.09808 + 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(24.6962 - 14.2583i) q^{17} +(-6.00000 + 6.00000i) q^{18} +(24.8923 + 6.66987i) q^{19} +(1.26795 - 4.73205i) q^{20} +(-9.63397 - 9.63397i) q^{21} +(3.63397 + 6.29423i) q^{22} +(-15.1865 - 8.76795i) q^{23} +(-4.73205 + 1.26795i) q^{24} +19.0000i q^{25} +25.9808 q^{27} +(4.07180 + 15.1962i) q^{28} +(0.356406 - 0.617314i) q^{29} +(-5.19615 + 3.00000i) q^{30} +(23.3397 - 23.3397i) q^{31} +(5.46410 + 1.46410i) q^{32} +(2.30385 - 8.59808i) q^{33} +(28.5167 + 28.5167i) q^{34} +(9.63397 + 16.6865i) q^{35} +(-10.3923 - 6.00000i) q^{36} +(-21.2583 + 5.69615i) q^{37} +36.4449i q^{38} +6.92820 q^{40} +(11.2583 + 42.0167i) q^{41} +(9.63397 - 16.6865i) q^{42} +(63.7750 - 36.8205i) q^{43} +(-7.26795 + 7.26795i) q^{44} +(-14.1962 - 3.80385i) q^{45} +(6.41858 - 23.9545i) q^{46} +(-33.0000 - 33.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-11.1506 - 6.43782i) q^{49} +(-25.9545 + 6.95448i) q^{50} -49.3923i q^{51} -80.1051 q^{53} +(9.50962 + 35.4904i) q^{54} +(-6.29423 + 10.9019i) q^{55} +(-19.2679 + 11.1244i) q^{56} +(31.5622 - 31.5622i) q^{57} +(0.973721 + 0.260908i) q^{58} +(-10.1603 + 37.9186i) q^{59} +(-6.00000 - 6.00000i) q^{60} +(14.3038 + 24.7750i) q^{61} +(40.4256 + 23.3397i) q^{62} +(45.5885 - 12.2154i) q^{63} +8.00000i q^{64} +12.5885 q^{66} +(-12.8397 - 47.9186i) q^{67} +(-28.5167 + 49.3923i) q^{68} +(-26.3038 + 15.1865i) q^{69} +(-19.2679 + 19.2679i) q^{70} +(-7.03590 - 1.88526i) q^{71} +(4.39230 - 16.3923i) q^{72} +(-12.7654 - 12.7654i) q^{73} +(-15.5622 - 26.9545i) q^{74} +(28.5000 + 16.4545i) q^{75} +(-49.7846 + 13.3397i) q^{76} -40.4256i q^{77} -14.3538 q^{79} +(2.53590 + 9.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-53.2750 + 30.7583i) q^{82} +(-87.8372 + 87.8372i) q^{83} +(26.3205 + 7.05256i) q^{84} +(-18.0788 + 67.4711i) q^{85} +(73.6410 + 73.6410i) q^{86} +(-0.617314 - 1.06922i) q^{87} +(-12.5885 - 7.26795i) q^{88} +(52.2391 - 13.9974i) q^{89} -20.7846i q^{90} +35.0718 q^{92} +(-14.7968 - 55.2224i) q^{93} +(33.0000 - 57.1577i) q^{94} +(-54.6673 + 31.5622i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-131.488 - 35.2321i) q^{97} +(4.71281 - 17.5885i) q^{98} +(21.8038 + 21.8038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} + 22 q^{7} - 8 q^{8} + 12 q^{9} - 12 q^{10} + 6 q^{11} - 4 q^{14} - 6 q^{15} + 8 q^{16} + 78 q^{17} - 24 q^{18} + 58 q^{19} + 12 q^{20} - 42 q^{21} + 18 q^{22} + 12 q^{23} - 12 q^{24}+ \cdots + 108 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 + 22 * q^7 - 8 * q^8 + 12 * q^9 - 12 * q^10 + 6 * q^11 - 4 * q^14 - 6 * q^15 + 8 * q^16 + 78 * q^17 - 24 * q^18 + 58 * q^19 + 12 * q^20 - 42 * q^21 + 18 * q^22 + 12 * q^23 - 12 * q^24 + 44 * q^28 - 54 * q^29 + 128 * q^31 + 8 * q^32 + 30 * q^33 + 24 * q^34 + 42 * q^35 - 40 * q^37 + 42 * q^42 + 120 * q^43 - 36 * q^44 - 36 * q^45 - 54 * q^46 - 132 * q^47 + 42 * q^49 - 38 * q^50 - 168 * q^53 + 90 * q^54 + 6 * q^55 - 84 * q^56 + 102 * q^57 + 42 * q^58 - 6 * q^59 - 24 * q^60 + 78 * q^61 - 60 * q^62 + 120 * q^63 - 12 * q^66 - 86 * q^67 - 24 * q^68 - 126 * q^69 - 84 * q^70 - 42 * q^71 - 24 * q^72 + 136 * q^73 - 38 * q^74 + 114 * q^75 - 116 * q^76 + 192 * q^79 + 24 * q^80 - 18 * q^81 - 78 * q^82 - 192 * q^83 + 36 * q^84 + 42 * q^85 + 156 * q^86 - 96 * q^87 + 12 * q^88 + 60 * q^89 + 168 * q^92 - 222 * q^93 + 132 * q^94 - 42 * q^95 - 280 * q^97 - 92 * q^98 + 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$2$	0.366025	+	1.36603i	0.183013	+	0.683013i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−1.73205	+	1.00000i	−0.433013	+	0.250000i
$5$	−1.73205	+	1.73205i	−0.346410	+	0.346410i	−0.858771	−	0.512360i	$-0.828771\pi$
$5$	−1.73205	+	1.73205i	−0.346410	+	0.346410i	0.512360	+	0.858771i	$0.328771\pi$
$6$	2.36603	+	0.633975i	0.394338	+	0.105662i
$7$	2.03590	−	7.59808i	0.290843	−	1.08544i	−0.653621	−	0.756822i	$-0.726751\pi$
$7$	2.03590	−	7.59808i	0.290843	−	1.08544i	0.944463	−	0.328617i	$-0.106583\pi$
$8$	−2.00000	−	2.00000i	−0.250000	−	0.250000i
$9$	3.00000	+	5.19615i	0.333333	+	0.577350i
$10$	−3.00000	−	1.73205i	−0.300000	−	0.173205i
$11$	4.96410	−	1.33013i	0.451282	−	0.120921i	−0.0260172	−	0.999661i	$-0.508282\pi$
$11$	4.96410	−	1.33013i	0.451282	−	0.120921i	0.477299	+	0.878741i	$0.341616\pi$
$12$			3.46410i			0.288675i
$13$		0			0
$13$		0			0
$14$	11.1244			0.794597
$15$	1.09808	+	4.09808i	0.0732051	+	0.273205i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	24.6962	−	14.2583i	1.45271	−	0.838725i	0.454080	−	0.890961i	$-0.349968\pi$
$17$	24.6962	−	14.2583i	1.45271	−	0.838725i	0.998635	+	0.0522356i	$0.0166347\pi$
$18$	−6.00000	+	6.00000i	−0.333333	+	0.333333i
$19$	24.8923	+	6.66987i	1.31012	+	0.351046i	0.845268	−	0.534342i	$-0.179441\pi$
$19$	24.8923	+	6.66987i	1.31012	+	0.351046i	0.464853	+	0.885388i	$0.346107\pi$
$20$	1.26795	−	4.73205i	0.0633975	−	0.236603i
$21$	−9.63397	−	9.63397i	−0.458761	−	0.458761i
$22$	3.63397	+	6.29423i	0.165181	+	0.286101i
$23$	−15.1865	−	8.76795i	−0.660284	−	0.381215i	0.132101	−	0.991236i	$-0.457828\pi$
$23$	−15.1865	−	8.76795i	−0.660284	−	0.381215i	−0.792385	+	0.610021i	$0.791161\pi$
$24$	−4.73205	+	1.26795i	−0.197169	+	0.0528312i
$25$			19.0000i			0.760000i
$26$		0			0
$27$	25.9808			0.962250
$28$	4.07180	+	15.1962i	0.145421	+	0.542720i
$29$	0.356406	−	0.617314i	0.0122899	−	0.0212867i	−0.859815	−	0.510606i	$-0.829421\pi$
$29$	0.356406	−	0.617314i	0.0122899	−	0.0212867i	0.872105	+	0.489319i	$0.162755\pi$
$30$	−5.19615	+	3.00000i	−0.173205	+	0.100000i
$31$	23.3397	−	23.3397i	0.752895	−	0.752895i	−0.222124	−	0.975019i	$-0.571299\pi$
$31$	23.3397	−	23.3397i	0.752895	−	0.752895i	0.975019	+	0.222124i	$0.0712988\pi$
$32$	5.46410	+	1.46410i	0.170753	+	0.0457532i
$33$	2.30385	−	8.59808i	0.0698136	−	0.260548i
$34$	28.5167	+	28.5167i	0.838725	+	0.838725i
$35$	9.63397	+	16.6865i	0.275256	+	0.476758i
$36$	−10.3923	−	6.00000i	−0.288675	−	0.166667i
$37$	−21.2583	+	5.69615i	−0.574549	+	0.153950i	−0.534382	−	0.845243i	$-0.679456\pi$
$37$	−21.2583	+	5.69615i	−0.574549	+	0.153950i	−0.0401672	+	0.999193i	$0.512789\pi$
$38$			36.4449i			0.959075i
$39$		0			0
$40$	6.92820			0.173205
$41$	11.2583	+	42.0167i	0.274593	+	1.02480i	0.956113	+	0.292997i	$0.0946526\pi$
$41$	11.2583	+	42.0167i	0.274593	+	1.02480i	−0.681520	+	0.731800i	$0.738681\pi$
$42$	9.63397	−	16.6865i	0.229380	−	0.397298i
$43$	63.7750	−	36.8205i	1.48314	−	0.856291i	0.483323	−	0.875442i	$-0.339430\pi$
$43$	63.7750	−	36.8205i	1.48314	−	0.856291i	0.999817	+	0.0191514i	$0.00609644\pi$
$44$	−7.26795	+	7.26795i	−0.165181	+	0.165181i
$45$	−14.1962	−	3.80385i	−0.315470	−	0.0845299i
$46$	6.41858	−	23.9545i	0.139534	−	0.520750i
$47$	−33.0000	−	33.0000i	−0.702128	−	0.702128i	0.262739	−	0.964867i	$-0.415374\pi$
$47$	−33.0000	−	33.0000i	−0.702128	−	0.702128i	−0.964867	+	0.262739i	$0.915374\pi$
$48$	−3.46410	−	6.00000i	−0.0721688	−	0.125000i
$49$	−11.1506	−	6.43782i	−0.227564	−	0.131384i
$50$	−25.9545	+	6.95448i	−0.519090	+	0.139090i
$51$		−	49.3923i		−	0.968477i
$52$		0			0
$53$	−80.1051			−1.51142			−0.755709	−	0.654908i	$-0.772707\pi$
$53$	−80.1051			−1.51142			−0.755709	+	0.654908i	$0.772707\pi$
$54$	9.50962	+	35.4904i	0.176104	+	0.657229i
$55$	−6.29423	+	10.9019i	−0.114441	+	0.198217i
$56$	−19.2679	+	11.1244i	−0.344071	+	0.198649i
$57$	31.5622	−	31.5622i	0.553722	−	0.553722i
$58$	0.973721	+	0.260908i	0.0167883	+	0.00449841i
$59$	−10.1603	+	37.9186i	−0.172208	+	0.642688i	0.824803	+	0.565421i	$0.191286\pi$
$59$	−10.1603	+	37.9186i	−0.172208	+	0.642688i	−0.997010	+	0.0772673i	$0.975381\pi$
$60$	−6.00000	−	6.00000i	−0.100000	−	0.100000i
$61$	14.3038	+	24.7750i	0.234489	+	0.406147i	0.959124	−	0.282986i	$-0.0913249\pi$
$61$	14.3038	+	24.7750i	0.234489	+	0.406147i	−0.724635	+	0.689133i	$0.757992\pi$
$62$	40.4256	+	23.3397i	0.652026	+	0.376448i
$63$	45.5885	−	12.2154i	0.723626	−	0.193895i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	12.5885			0.190734
$67$	−12.8397	−	47.9186i	−0.191638	−	0.715203i	−0.993112	−	0.117173i	$-0.962617\pi$
$67$	−12.8397	−	47.9186i	−0.191638	−	0.715203i	0.801474	−	0.598030i	$-0.204050\pi$
$68$	−28.5167	+	49.3923i	−0.419363	+	0.726357i
$69$	−26.3038	+	15.1865i	−0.381215	+	0.220095i
$70$	−19.2679	+	19.2679i	−0.275256	+	0.275256i
$71$	−7.03590	−	1.88526i	−0.0990972	−	0.0265530i	0.208930	−	0.977931i	$-0.433002\pi$
$71$	−7.03590	−	1.88526i	−0.0990972	−	0.0265530i	−0.308027	+	0.951378i	$0.599669\pi$
$72$	4.39230	−	16.3923i	0.0610042	−	0.227671i
$73$	−12.7654	−	12.7654i	−0.174868	−	0.174868i	0.614246	−	0.789114i	$-0.289460\pi$
$73$	−12.7654	−	12.7654i	−0.174868	−	0.174868i	−0.789114	+	0.614246i	$0.789460\pi$
$74$	−15.5622	−	26.9545i	−0.210300	−	0.364250i
$75$	28.5000	+	16.4545i	0.380000	+	0.219393i
$76$	−49.7846	+	13.3397i	−0.655061	+	0.175523i
$77$		−	40.4256i		−	0.525008i
$78$		0			0
$79$	−14.3538			−0.181694			−0.0908470	−	0.995865i	$-0.528957\pi$
$79$	−14.3538			−0.181694			−0.0908470	+	0.995865i	$0.528957\pi$
$80$	2.53590	+	9.46410i	0.0316987	+	0.118301i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−53.2750	+	30.7583i	−0.649695	+	0.375102i
$83$	−87.8372	+	87.8372i	−1.05828	+	1.05828i	−0.0600859	+	0.998193i	$0.519137\pi$
$83$	−87.8372	+	87.8372i	−1.05828	+	1.05828i	−0.998193	+	0.0600859i	$0.980863\pi$
$84$	26.3205	+	7.05256i	0.313339	+	0.0839590i
$85$	−18.0788	+	67.4711i	−0.212692	+	0.793778i
$86$	73.6410	+	73.6410i	0.856291	+	0.856291i
$87$	−0.617314	−	1.06922i	−0.00709556	−	0.0122899i
$88$	−12.5885	−	7.26795i	−0.143051	−	0.0825903i
$89$	52.2391	−	13.9974i	0.586956	−	0.157274i	0.0468944	−	0.998900i	$-0.485068\pi$
$89$	52.2391	−	13.9974i	0.586956	−	0.157274i	0.540062	+	0.841625i	$0.318401\pi$
$90$		−	20.7846i		−	0.230940i
$91$		0			0
$92$	35.0718			0.381215
$93$	−14.7968	−	55.2224i	−0.159105	−	0.593790i
$94$	33.0000	−	57.1577i	0.351064	−	0.608060i
$95$	−54.6673	+	31.5622i	−0.575445	+	0.332233i
$96$	6.92820	−	6.92820i	0.0721688	−	0.0721688i
$97$	−131.488	−	35.2321i	−1.35554	−	0.363217i	−0.493366	−	0.869822i	$-0.664234\pi$
$97$	−131.488	−	35.2321i	−1.35554	−	0.363217i	−0.862178	+	0.506605i	$0.830900\pi$
$98$	4.71281	−	17.5885i	0.0480899	−	0.179474i
$99$	21.8038	+	21.8038i	0.220241	+	0.220241i
$100$	−19.0000	−	32.9090i	−0.190000	−	0.329090i
$101$	53.2461	+	30.7417i	0.527189	+	0.304373i	0.739871	−	0.672749i	$-0.234886\pi$
$101$	53.2461	+	30.7417i	0.527189	+	0.304373i	−0.212682	+	0.977122i	$0.568220\pi$
$102$	67.4711	−	18.0788i	0.661482	−	0.177244i
$103$			23.3205i			0.226413i	0.993571	+	0.113206i	$0.0361121\pi$
$103$			23.3205i			0.226413i	−0.993571	+	0.113206i	$0.963888\pi$
$104$		0			0
$105$	33.3731			0.317839
$106$	−29.3205	−	109.426i	−0.276609	−	1.03232i
$107$	−39.8660	+	69.0500i	−0.372580	+	0.645327i	−0.989962	−	0.141337i	$-0.954860\pi$
$107$	−39.8660	+	69.0500i	−0.372580	+	0.645327i	0.617382	+	0.786664i	$0.288193\pi$
$108$	−45.0000	+	25.9808i	−0.416667	+	0.240563i
$109$	103.655	−	103.655i	0.950964	−	0.950964i	−0.0478885	−	0.998853i	$-0.515249\pi$
$109$	103.655	−	103.655i	0.950964	−	0.950964i	0.998853	+	0.0478885i	$0.0152492\pi$
$110$	−17.1962	−	4.60770i	−0.156329	−	0.0418881i
$111$	−9.86603	+	36.8205i	−0.0888831	+	0.331716i
$112$	−22.2487	−	22.2487i	−0.198649	−	0.198649i
$113$	−88.5000	−	153.286i	−0.783186	−	1.35652i	−0.930077	−	0.367365i	$-0.880260\pi$
$113$	−88.5000	−	153.286i	−0.783186	−	1.35652i	0.146891	−	0.989153i	$-0.453073\pi$
$114$	54.6673	+	31.5622i	0.479538	+	0.276861i
$115$	41.4904	−	11.1173i	0.360786	−	0.0966723i
$116$			1.42563i			0.0122899i
$117$		0			0
$118$	−55.5167			−0.470480
$119$	−58.0570	−	216.672i	−0.487874	−	1.82077i
$120$	6.00000	−	10.3923i	0.0500000	−	0.0866025i
$121$	−81.9160	+	47.2942i	−0.676992	+	0.390861i
$122$	−28.6077	+	28.6077i	−0.234489	+	0.234489i
$123$	72.7750	+	19.5000i	0.591667	+	0.158537i
$124$	−17.0859	+	63.7654i	−0.137789	+	0.514237i
$125$	−76.2102	−	76.2102i	−0.609682	−	0.609682i
$126$	33.3731	+	57.8038i	0.264866	+	0.458761i
$127$	−147.651	−	85.2461i	−1.16260	−	0.671229i	−0.210677	−	0.977556i	$-0.567567\pi$
$127$	−147.651	−	85.2461i	−1.16260	−	0.671229i	−0.951927	+	0.306326i	$0.900900\pi$
$128$	−10.9282	+	2.92820i	−0.0853766	+	0.0228766i
$129$		−	127.550i		−	0.988760i
$130$		0			0
$131$	−44.8513			−0.342376			−0.171188	−	0.985238i	$-0.554761\pi$
$131$	−44.8513			−0.342376			−0.171188	+	0.985238i	$0.554761\pi$
$132$	4.60770	+	17.1962i	0.0349068	+	0.130274i
$133$	101.356	−	175.554i	0.762078	−	1.31996i
$134$	60.7583	−	35.0788i	0.453420	−	0.261782i
$135$	−45.0000	+	45.0000i	−0.333333	+	0.333333i
$136$	−77.9090	−	20.8756i	−0.572860	−	0.153497i
$137$	24.3775	−	90.9782i	0.177938	−	0.664074i	−0.818094	−	0.575084i	$-0.804969\pi$
$137$	24.3775	−	90.9782i	0.177938	−	0.664074i	0.996032	−	0.0889903i	$-0.0283640\pi$
$138$	−30.3731	−	30.3731i	−0.220095	−	0.220095i
$139$	−9.59808	−	16.6244i	−0.0690509	−	0.119600i	0.829433	−	0.558606i	$-0.188664\pi$
$139$	−9.59808	−	16.6244i	−0.0690509	−	0.119600i	−0.898484	+	0.439007i	$0.855330\pi$
$140$	−33.3731	−	19.2679i	−0.238379	−	0.137628i
$141$	−78.0788	+	20.9212i	−0.553751	+	0.148377i
$142$		−	10.3013i		−	0.0725442i
$143$		0			0
$144$	24.0000			0.166667
$145$	0.451905	+	1.68653i	0.00311659	+	0.0116313i
$146$	12.7654	−	22.1103i	0.0874341	−	0.151440i
$147$	−19.3135	+	11.1506i	−0.131384	+	0.0758547i
$148$	31.1244	−	31.1244i	0.210300	−	0.210300i
$149$	−36.0622	−	9.66283i	−0.242028	−	0.0648512i	0.135766	−	0.990741i	$-0.456651\pi$
$149$	−36.0622	−	9.66283i	−0.242028	−	0.0648512i	−0.377794	+	0.925890i	$0.623317\pi$
$150$	−12.0455	+	44.9545i	−0.0803034	+	0.299697i
$151$	161.406	+	161.406i	1.06892	+	1.06892i	0.997442	+	0.0714740i	$0.0227703\pi$
$151$	161.406	+	161.406i	1.06892	+	1.06892i	0.0714740	+	0.997442i	$0.477230\pi$
$152$	−36.4449	−	63.1244i	−0.239769	−	0.415292i
$153$	148.177	+	85.5500i	0.968477	+	0.559150i
$154$	55.2224	−	14.7968i	0.358587	−	0.0960832i
$155$			80.8513i			0.521621i
$156$		0			0
$157$	−14.4308			−0.0919158			−0.0459579	−	0.998943i	$-0.514634\pi$
$157$	−14.4308			−0.0919158			−0.0459579	+	0.998943i	$0.514634\pi$
$158$	−5.25387	−	19.6077i	−0.0332523	−	0.124099i
$159$	−69.3731	+	120.158i	−0.436309	+	0.755709i
$160$	−12.0000	+	6.92820i	−0.0750000	+	0.0433013i
$161$	−97.5378	+	97.5378i	−0.605825	+	0.605825i
$162$	−12.2942	−	3.29423i	−0.0758903	−	0.0203347i
$163$	−6.40381	+	23.8993i	−0.0392872	+	0.146622i	−0.982783	−	0.184762i	$-0.940849\pi$
$163$	−6.40381	+	23.8993i	−0.0392872	+	0.146622i	0.943496	+	0.331383i	$0.107515\pi$
$164$	−61.5167	−	61.5167i	−0.375102	−	0.375102i
$165$	10.9019	+	18.8827i	0.0660723	+	0.114441i
$166$	−152.138	−	87.8372i	−0.916497	−	0.529140i
$167$	−56.6769	+	15.1865i	−0.339383	+	0.0909373i	−0.424485	−	0.905435i	$-0.639545\pi$
$167$	−56.6769	+	15.1865i	−0.339383	+	0.0909373i	0.0851025	+	0.996372i	$0.472878\pi$
$168$			38.5359i			0.229380i
$169$		0			0
$170$	−98.7846			−0.581086
$171$	40.0192	+	149.354i	0.234031	+	0.873414i
$172$	−73.6410	+	127.550i	−0.428145	+	0.741570i
$173$	−62.1462	+	35.8801i	−0.359226	+	0.207399i	−0.668741	−	0.743495i	$-0.733167\pi$
$173$	−62.1462	+	35.8801i	−0.359226	+	0.207399i	0.309515	+	0.950895i	$0.399833\pi$
$174$	1.23463	−	1.23463i	0.00709556	−	0.00709556i
$175$	144.363	+	38.6821i	0.824934	+	0.221040i
$176$	5.32051	−	19.8564i	0.0302302	−	0.112820i
$177$	48.0788	+	48.0788i	0.271632	+	0.271632i
$178$	38.2417	+	66.2365i	0.214841	+	0.372115i
$179$	139.148	+	80.3372i	0.777363	+	0.448811i	0.835495	−	0.549498i	$-0.185181\pi$
$179$	139.148	+	80.3372i	0.777363	+	0.448811i	−0.0581316	+	0.998309i	$0.518514\pi$
$180$	28.3923	−	7.60770i	0.157735	−	0.0422650i
$181$			143.072i			0.790452i	0.918584	+	0.395226i	$0.129334\pi$
$181$			143.072i			0.790452i	−0.918584	+	0.395226i	$0.870666\pi$
$182$		0			0
$183$	49.5500			0.270765
$184$	12.8372	+	47.9090i	0.0697672	+	0.260375i
$185$	26.9545	−	46.6865i	0.145700	−	0.252360i
$186$	70.0192	−	40.4256i	0.376448	−	0.217342i
$187$	103.629	−	103.629i	0.554165	−	0.554165i
$188$	90.1577	+	24.1577i	0.479562	+	0.128498i
$189$	52.8942	−	197.404i	0.279863	−	1.04446i
$190$	−63.1244	−	63.1244i	−0.332233	−	0.332233i
$191$	142.703	+	247.169i	0.747137	+	1.29408i	0.949190	+	0.314705i	$0.101906\pi$
$191$	142.703	+	247.169i	0.747137	+	1.29408i	−0.202052	+	0.979375i	$0.564761\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	−85.5070	+	22.9115i	−0.443042	+	0.118713i	−0.473442	−	0.880825i	$-0.656989\pi$
$193$	−85.5070	+	22.9115i	−0.443042	+	0.118713i	0.0304000	+	0.999538i	$0.490322\pi$
$194$		−	192.512i		−	0.992327i
$195$		0			0
$196$	25.7513			0.131384
$197$	97.1725	+	362.653i	0.493261	+	1.84088i	0.539559	+	0.841948i	$0.318591\pi$
$197$	97.1725	+	362.653i	0.493261	+	1.84088i	−0.0462974	+	0.998928i	$0.514742\pi$
$198$	−21.8038	+	37.7654i	−0.110120	+	0.190734i
$199$	257.789	−	148.835i	1.29542	−	0.747913i	0.315813	−	0.948822i	$-0.397723\pi$
$199$	257.789	−	148.835i	1.29542	−	0.747913i	0.979610	+	0.200909i	$0.0643896\pi$
$200$	38.0000	−	38.0000i	0.190000	−	0.190000i
$201$	−82.9974	−	22.2391i	−0.412923	−	0.110642i
$202$	−22.5045	+	83.9878i	−0.111408	+	0.415781i
$203$	−3.96479	−	3.96479i	−0.0195310	−	0.0195310i
$204$	49.3923	+	85.5500i	0.242119	+	0.419363i
$205$	−92.2750	−	53.2750i	−0.450122	−	0.259878i
$206$	−31.8564	+	8.53590i	−0.154643	+	0.0414364i
$207$		−	105.215i		−	0.508287i
$208$		0			0
$209$	132.440			0.633683
$210$	12.2154	+	45.5885i	0.0581685	+	0.217088i
$211$	−27.2532	+	47.2039i	−0.129162	+	0.223715i	−0.923352	−	0.383954i	$-0.874562\pi$
$211$	−27.2532	+	47.2039i	−0.129162	+	0.223715i	0.794190	+	0.607669i	$0.207895\pi$
$212$	138.746	−	80.1051i	0.654463	−	0.377854i
$213$	−8.92116	+	8.92116i	−0.0418834	+	0.0418834i
$214$	−108.916	−	29.1840i	−0.508953	−	0.136374i
$215$	−46.6865	+	174.237i	−0.217147	+	0.810402i
$216$	−51.9615	−	51.9615i	−0.240563	−	0.240563i
$217$	−129.820	−	224.855i	−0.598248	−	1.03620i
$218$	179.536	+	103.655i	0.823559	+	0.475482i
$219$	−30.2032	+	8.09292i	−0.137914	+	0.0369540i
$220$		−	25.1769i		−	0.114441i
$221$		0			0
$222$	−53.9090			−0.242833
$223$	39.3949	+	147.024i	0.176659	+	0.659299i	0.996263	+	0.0863694i	$0.0275265\pi$
$223$	39.3949	+	147.024i	0.176659	+	0.659299i	−0.819605	+	0.572930i	$0.805807\pi$
$224$	22.2487	−	38.5359i	0.0993246	−	0.172035i
$225$	−98.7269	+	57.0000i	−0.438786	+	0.253333i
$226$	177.000	−	177.000i	0.783186	−	0.783186i
$227$	207.978	+	55.7276i	0.916203	+	0.245496i	0.685962	−	0.727638i	$-0.259382\pi$
$227$	207.978	+	55.7276i	0.916203	+	0.245496i	0.230242	+	0.973133i	$0.426048\pi$
$228$	−23.1051	+	86.2295i	−0.101338	+	0.378199i
$229$	−9.23463	−	9.23463i	−0.0403259	−	0.0403259i	0.686656	−	0.726982i	$-0.259078\pi$
$229$	−9.23463	−	9.23463i	−0.0403259	−	0.0403259i	−0.726982	+	0.686656i	$0.759078\pi$
$230$	30.3731	+	52.6077i	0.132057	+	0.228729i
$231$	−60.6384	−	35.0096i	−0.262504	−	0.151557i
$232$	−1.94744	+	0.521815i	−0.00839414	+	0.00224920i
$233$			397.061i			1.70413i	0.523439	+	0.852063i	$0.324649\pi$
$233$			397.061i			1.70413i	−0.523439	+	0.852063i	$0.675351\pi$
$234$		0			0
$235$	114.315			0.486448
$236$	−20.3205	−	75.8372i	−0.0861038	−	0.321344i
$237$	−12.4308	+	21.5307i	−0.0524506	+	0.0908470i
$238$	274.729	−	158.615i	1.15432	−	0.666448i
$239$	−198.688	+	198.688i	−0.831332	+	0.831332i	−0.987699	−	0.156367i	$-0.950022\pi$
$239$	−198.688	+	198.688i	−0.831332	+	0.831332i	0.156367	+	0.987699i	$0.450022\pi$
$240$	16.3923	+	4.39230i	0.0683013	+	0.0183013i
$241$	84.6699	−	315.992i	0.351327	−	1.31117i	−0.533717	−	0.845663i	$-0.679205\pi$
$241$	84.6699	−	315.992i	0.351327	−	1.31117i	0.885044	−	0.465508i	$-0.154128\pi$
$242$	−94.5885	−	94.5885i	−0.390861	−	0.390861i
$243$	124.708	+	216.000i	0.513200	+	0.888889i
$244$	−49.5500	−	28.6077i	−0.203074	−	0.117245i
$245$	30.4641	−	8.16283i	0.124343	−	0.0333177i
$246$			106.550i			0.433130i
$247$		0			0
$248$	−93.3590			−0.376448
$249$	55.6865	+	207.825i	0.223641	+	0.834638i
$250$	76.2102	−	132.000i	0.304841	−	0.528000i
$251$	−134.267	+	77.5192i	−0.534929	+	0.308842i	−0.743021	−	0.669268i	$-0.766608\pi$
$251$	−134.267	+	77.5192i	−0.534929	+	0.308842i	0.208092	+	0.978109i	$0.433275\pi$
$252$	−66.7461	+	66.7461i	−0.264866	+	0.264866i
$253$	−87.0500	−	23.3250i	−0.344071	−	0.0921936i
$254$	62.4045	−	232.897i	0.245687	−	0.916916i
$255$	85.5500	+	85.5500i	0.335490	+	0.335490i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−262.012	−	151.272i	−1.01950	−	0.588609i	−0.105541	−	0.994415i	$-0.533657\pi$
$257$	−262.012	−	151.272i	−1.01950	−	0.588609i	−0.913959	+	0.405806i	$0.866991\pi$
$258$	174.237	−	46.6865i	0.675335	−	0.180956i
$259$			173.119i			0.668414i
$260$		0			0
$261$	4.27688			0.0163865
$262$	−16.4167	−	61.2679i	−0.0626592	−	0.233847i
$263$	−25.2968	+	43.8154i	−0.0961856	+	0.166598i	−0.910103	−	0.414383i	$-0.863998\pi$
$263$	−25.2968	+	43.8154i	−0.0961856	+	0.166598i	0.813917	+	0.580981i	$0.197331\pi$
$264$	−21.8038	+	12.5885i	−0.0825903	+	0.0476836i
$265$	138.746	−	138.746i	0.523570	−	0.523570i
$266$	276.911	+	74.1980i	1.04102	+	0.278940i
$267$	24.2442	−	90.4808i	0.0908024	−	0.338879i
$268$	70.1577	+	70.1577i	0.261782	+	0.261782i
$269$	21.4474	+	37.1481i	0.0797303	+	0.138097i	0.903134	−	0.429360i	$-0.141261\pi$
$269$	21.4474	+	37.1481i	0.0797303	+	0.138097i	−0.823403	+	0.567457i	$0.807927\pi$
$270$	−77.9423	−	45.0000i	−0.288675	−	0.166667i
$271$	−478.614	+	128.244i	−1.76610	+	0.473226i	−0.987940	−	0.154836i	$-0.950515\pi$
$271$	−478.614	+	128.244i	−1.76610	+	0.473226i	−0.778163	+	0.628062i	$0.783848\pi$
$272$		−	114.067i		−	0.419363i
$273$		0			0
$274$	133.201			0.486136
$275$	25.2724	+	94.3179i	0.0918997	+	0.342974i
$276$	30.3731	−	52.6077i	0.110047	−	0.190608i
$277$	184.227	−	106.363i	0.665079	−	0.383984i	−0.129130	−	0.991628i	$-0.541219\pi$
$277$	184.227	−	106.363i	0.665079	−	0.383984i	0.794209	+	0.607644i	$0.207885\pi$
$278$	19.1962	−	19.1962i	0.0690509	−	0.0690509i
$279$	191.296	+	51.2576i	0.685649	+	0.183719i
$280$	14.1051	−	52.6410i	0.0503754	−	0.188004i
$281$	−27.2243	−	27.2243i	−0.0968837	−	0.0968837i	0.657004	−	0.753887i	$-0.271824\pi$
$281$	−27.2243	−	27.2243i	−0.0968837	−	0.0968837i	−0.753887	+	0.657004i	$0.771824\pi$
$282$	−57.1577	−	99.0000i	−0.202687	−	0.351064i
$283$	−126.526	−	73.0500i	−0.447089	−	0.258127i	0.259511	−	0.965740i	$-0.416439\pi$
$283$	−126.526	−	73.0500i	−0.447089	−	0.258127i	−0.706600	+	0.707613i	$0.749772\pi$
$284$	14.0718	−	3.77053i	0.0495486	−	0.0132765i
$285$			109.335i			0.383630i
$286$		0			0
$287$	342.167			1.19222
$288$	8.78461	+	32.7846i	0.0305021	+	0.113835i
$289$	262.100	−	453.970i	0.906920	−	1.57083i
$290$	−2.13844	+	1.23463i	−0.00737393	+	0.00425734i
$291$	−166.720	+	166.720i	−0.572920	+	0.572920i
$292$	34.8756	+	9.34490i	0.119437	+	0.0320031i
$293$	−25.3212	+	94.5000i	−0.0864205	+	0.322526i	−0.995579	−	0.0939237i	$-0.970059\pi$
$293$	−25.3212	+	94.5000i	−0.0864205	+	0.322526i	0.909159	+	0.416449i	$0.136726\pi$
$294$	−22.3013	−	22.3013i	−0.0758547	−	0.0758547i
$295$	−48.0788	−	83.2750i	−0.162979	−	0.282288i
$296$	53.9090	+	31.1244i	0.182125	+	0.105150i
$297$	128.971	−	34.5577i	0.434246	−	0.116356i
$298$		−	52.7987i		−	0.177177i
$299$		0			0
$300$	−65.8179			−0.219393
$301$	−149.926	−	559.530i	−0.498092	−	1.85890i
$302$	−161.406	+	279.564i	−0.534458	+	0.925709i
$303$	92.2250	−	53.2461i	0.304373	−	0.175730i
$304$	72.8897	−	72.8897i	0.239769	−	0.239769i
$305$	−67.6865	−	18.1366i	−0.221923	−	0.0594641i
$306$	−62.6269	+	233.727i	−0.204663	+	0.763813i
$307$	2.62178	+	2.62178i	0.00853999	+	0.00853999i	0.711364	−	0.702824i	$-0.248078\pi$
$307$	2.62178	+	2.62178i	0.00853999	+	0.00853999i	−0.702824	+	0.711364i	$0.748078\pi$
$308$	40.4256	+	70.0192i	0.131252	+	0.227335i
$309$	34.9808	+	20.1962i	0.113206	+	0.0653597i
$310$	−110.445	+	29.5936i	−0.356274	+	0.0954633i
$311$		−	386.038i		−	1.24128i	−0.784095	−	0.620641i	$-0.786873\pi$
$311$		−	386.038i		−	1.24128i	0.784095	−	0.620641i	$-0.213127\pi$
$312$		0			0
$313$	−35.1384			−0.112263			−0.0561317	−	0.998423i	$-0.517877\pi$
$313$	−35.1384			−0.112263			−0.0561317	+	0.998423i	$0.517877\pi$
$314$	−5.28203	−	19.7128i	−0.0168218	−	0.0627797i
$315$	−57.8038	+	100.119i	−0.183504	+	0.317839i
$316$	24.8616	−	14.3538i	0.0786758	−	0.0454235i
$317$	12.5307	−	12.5307i	0.0395292	−	0.0395292i	−0.687066	−	0.726595i	$-0.741102\pi$
$317$	12.5307	−	12.5307i	0.0395292	−	0.0395292i	0.726595	+	0.687066i	$0.241102\pi$
$318$	−189.531	−	50.7846i	−0.596009	−	0.159700i
$319$	0.948132	−	3.53848i	0.00297220	−	0.0110924i
$320$	−13.8564	−	13.8564i	−0.0433013	−	0.0433013i
$321$	69.0500	+	119.598i	0.215109	+	0.372580i
$322$	−168.940	−	97.5378i	−0.524660	−	0.302912i
$323$	709.845	−	190.203i	2.19766	−	0.588862i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	−34.9911			−0.107335
$327$	−65.7147	−	245.251i	−0.200962	−	0.750002i
$328$	61.5167	−	106.550i	0.187551	−	0.324848i
$329$	−317.921	+	183.552i	−0.966326	+	0.557908i
$330$	−21.8038	+	21.8038i	−0.0660723	+	0.0660723i
$331$	249.959	+	66.9763i	0.755163	+	0.202345i	0.615807	−	0.787897i	$-0.288830\pi$
$331$	249.959	+	66.9763i	0.755163	+	0.202345i	0.139356	+	0.990242i	$0.455497\pi$
$332$	64.3013	−	239.976i	0.193679	−	0.722818i
$333$	−93.3731	−	93.3731i	−0.280400	−	0.280400i
$334$	−41.4904	−	71.8634i	−0.124223	−	0.215160i
$335$	105.237	+	60.7583i	0.314139	+	0.181368i
$336$	−52.6410	+	14.1051i	−0.156670	+	0.0419795i
$337$		−	94.9461i		−	0.281739i	−0.990028	−	0.140870i	$-0.955010\pi$
$337$		−	94.9461i		−	0.281739i	0.990028	−	0.140870i	$-0.0449898\pi$
$338$		0			0
$339$	−306.573			−0.904345
$340$	−36.1577	−	134.942i	−0.106346	−	0.396889i
$341$	84.8160	−	146.906i	0.248727	−	0.430808i
$342$	−189.373	+	109.335i	−0.553722	+	0.319692i
$343$	200.930	−	200.930i	0.585802	−	0.585802i
$344$	−201.191	−	53.9090i	−0.584858	−	0.156712i
$345$	19.2558	−	71.8634i	0.0558138	−	0.208300i
$346$	−71.7602	−	71.7602i	−0.207399	−	0.207399i
$347$	−52.2302	−	90.4653i	−0.150519	−	0.260707i	0.780899	−	0.624657i	$-0.214761\pi$
$347$	−52.2302	−	90.4653i	−0.150519	−	0.260707i	−0.931418	+	0.363950i	$0.881428\pi$
$348$	2.13844	+	1.23463i	0.00614494	+	0.00354778i
$349$	78.0763	−	20.9205i	0.223714	−	0.0599440i	−0.145221	−	0.989399i	$-0.546389\pi$
$349$	78.0763	−	20.9205i	0.223714	−	0.0599440i	0.368935	+	0.929455i	$0.379723\pi$
$350$			211.363i			0.603894i
$351$		0			0
$352$	29.0718			0.0825903
$353$	44.1429	+	164.744i	0.125051	+	0.466696i	0.999841	−	0.0178053i	$-0.00566790\pi$
$353$	44.1429	+	164.744i	0.125051	+	0.466696i	−0.874791	+	0.484501i	$0.839001\pi$
$354$	−48.0788	+	83.2750i	−0.135816	+	0.235240i
$355$	15.4519	−	8.92116i	0.0435265	−	0.0251300i
$356$	−76.4833	+	76.4833i	−0.214841	+	0.214841i
$357$	−375.286	−	100.558i	−1.05122	−	0.281674i
$358$	−58.8109	+	219.485i	−0.164276	+	0.613087i
$359$	102.058	+	102.058i	0.284283	+	0.284283i	0.834815	−	0.550531i	$-0.185575\pi$
$359$	102.058	+	102.058i	0.284283	+	0.284283i	−0.550531	+	0.834815i	$0.685575\pi$
$360$	20.7846	+	36.0000i	0.0577350	+	0.100000i
$361$	262.504	+	151.557i	0.727159	+	0.419826i
$362$	−195.440	+	52.3679i	−0.539889	+	0.144663i
$363$			163.832i			0.451328i
$364$		0			0
$365$	44.2205			0.121152
$366$	18.1366	+	67.6865i	0.0495534	+	0.184936i
$367$	−238.856	+	413.710i	−0.650833	+	1.12728i	0.332088	+	0.943248i	$0.392247\pi$
$367$	−238.856	+	413.710i	−0.650833	+	1.12728i	−0.982921	+	0.184027i	$0.941086\pi$
$368$	−60.7461	+	35.0718i	−0.165071	+	0.0953038i
$369$	−184.550	+	184.550i	−0.500135	+	0.500135i
$370$	73.6410	+	19.7321i	0.199030	+	0.0533299i
$371$	−163.086	+	608.645i	−0.439585	+	1.64055i
$372$	80.8513	+	80.8513i	0.217342	+	0.217342i
$373$	−257.744	−	446.425i	−0.691001	−	1.19685i	−0.971510	−	0.236998i	$-0.923836\pi$
$373$	−257.744	−	446.425i	−0.691001	−	1.19685i	0.280509	−	0.959852i	$-0.409497\pi$
$374$	179.490	+	103.629i	0.479921	+	0.277082i
$375$	−180.315	+	48.3154i	−0.480841	+	0.128841i
$376$			132.000i			0.351064i
$377$		0			0
$378$	289.019			0.764601
$379$	−70.8449	−	264.397i	−0.186926	−	0.697617i	−0.994210	−	0.107454i	$-0.965730\pi$
$379$	−70.8449	−	264.397i	−0.186926	−	0.697617i	0.807284	−	0.590163i	$-0.200936\pi$
$380$	63.1244	−	109.335i	0.166117	−	0.287723i
$381$	−255.738	+	147.651i	−0.671229	+	0.387534i
$382$	−285.406	+	285.406i	−0.747137	+	0.747137i
$383$	−451.791	−	121.057i	−1.17961	−	0.316076i	−0.384839	−	0.922984i	$-0.625743\pi$
$383$	−451.791	−	121.057i	−1.17961	−	0.316076i	−0.794772	+	0.606908i	$0.792410\pi$
$384$	−5.07180	+	18.9282i	−0.0132078	+	0.0492922i
$385$	70.0192	+	70.0192i	0.181868	+	0.181868i
$386$	−62.5955	−	108.419i	−0.162165	−	0.280877i
$387$	382.650	+	220.923i	0.988760	+	0.570861i
$388$	262.976	−	70.4641i	0.677772	−	0.181609i
$389$		−	572.687i		−	1.47220i	−0.676871	−	0.736102i	$-0.736665\pi$
$389$		−	572.687i		−	1.47220i	0.676871	−	0.736102i	$-0.263335\pi$
$390$		0			0
$391$	−500.065			−1.27894
$392$	9.42563	+	35.1769i	0.0240450	+	0.0897370i
$393$	−38.8423	+	67.2769i	−0.0988354	+	0.171188i
$394$	−459.825	+	265.480i	−1.16707	+	0.673807i
$395$	24.8616	−	24.8616i	0.0629407	−	0.0629407i
$396$	−59.5692	−	15.9615i	−0.150427	−	0.0403069i
$397$	−15.8275	+	59.0692i	−0.0398679	+	0.148789i	−0.982991	−	0.183656i	$-0.941207\pi$
$397$	−15.8275	+	59.0692i	−0.0398679	+	0.148789i	0.943123	+	0.332445i	$0.107873\pi$
$398$	297.669	+	297.669i	0.747913	+	0.747913i
$399$	−175.554	−	304.069i	−0.439986	−	0.762078i
$400$	65.8179	+	38.0000i	0.164545	+	0.0950000i
$401$	−521.798	+	139.815i	−1.30124	+	0.348667i	−0.841920	−	0.539603i	$-0.818574\pi$
$401$	−521.798	+	139.815i	−1.30124	+	0.348667i	−0.459322	+	0.888270i	$0.651908\pi$
$402$		−	121.517i		−	0.302280i
$403$		0			0
$404$	−122.967			−0.304373
$405$	−5.70577	−	21.2942i	−0.0140883	−	0.0525783i
$406$	3.96479	−	6.86722i	0.00976550	−	0.0169143i
$407$	−97.9519	+	56.5526i	−0.240668	+	0.138950i
$408$	−98.7846	+	98.7846i	−0.242119	+	0.242119i
$409$	20.0237	+	5.36533i	0.0489577	+	0.0131182i	0.283215	−	0.959057i	$-0.408599\pi$
$409$	20.0237	+	5.36533i	0.0489577	+	0.0131182i	−0.234257	+	0.972175i	$0.575266\pi$
$410$	39.0000	−	145.550i	0.0951220	−	0.355000i
$411$	−115.356	−	115.356i	−0.280671	−	0.280671i
$412$	−23.3205	−	40.3923i	−0.0566032	−	0.0980396i
$413$	267.423	+	154.397i	0.647513	+	0.373842i
$414$	143.727	−	38.5115i	0.347166	−	0.0930230i
$415$		−	304.277i		−	0.733197i
$416$		0			0
$417$	−33.2487			−0.0797331
$418$	48.4763	+	180.916i	0.115972	+	0.432813i
$419$	−173.598	+	300.681i	−0.414315	+	0.717615i	−0.995356	−	0.0962592i	$-0.969312\pi$
$419$	−173.598	+	300.681i	−0.414315	+	0.717615i	0.581041	+	0.813874i	$0.302646\pi$
$420$	−57.8038	+	33.3731i	−0.137628	+	0.0794597i
$421$	286.555	−	286.555i	0.680654	−	0.680654i	−0.279494	−	0.960147i	$-0.590167\pi$
$421$	286.555	−	286.555i	0.680654	−	0.680654i	0.960147	+	0.279494i	$0.0901667\pi$
$422$	−74.4571	−	19.9507i	−0.176439	−	0.0472766i
$423$	72.4730	−	270.473i	0.171331	−	0.639416i
$424$	160.210	+	160.210i	0.377854	+	0.377854i
$425$	270.908	+	469.227i	0.637431	+	1.10406i
$426$	−15.4519	−	8.92116i	−0.0362721	−	0.0209417i
$427$	217.363	−	58.2424i	0.509048	−	0.136399i
$428$		−	159.464i		−	0.372580i
$429$		0			0
$430$	−255.100			−0.593256
$431$	−79.3602	−	296.176i	−0.184130	−	0.687184i	−0.994815	−	0.101701i	$-0.967572\pi$
$431$	−79.3602	−	296.176i	−0.184130	−	0.687184i	0.810685	−	0.585483i	$-0.199095\pi$
$432$	51.9615	−	90.0000i	0.120281	−	0.208333i
$433$	−73.2757	+	42.3057i	−0.169228	+	0.0977038i	−0.582222	−	0.813030i	$-0.697816\pi$
$433$	−73.2757	+	42.3057i	−0.169228	+	0.0977038i	0.412994	+	0.910734i	$0.364483\pi$
$434$	259.640	−	259.640i	0.598248	−	0.598248i
$435$	2.92116	+	0.782723i	0.00671531	+	0.00179936i
$436$	−75.8808	+	283.191i	−0.174039	+	0.649521i
$437$	−319.547	−	319.547i	−0.731228	−	0.731228i
$438$	−22.1103	−	38.2961i	−0.0504801	−	0.0874341i
$439$	−379.794	−	219.274i	−0.865135	−	0.499486i	0.000593556	−	1.00000i	$-0.499811\pi$
$439$	−379.794	−	219.274i	−0.865135	−	0.499486i	−0.865728	+	0.500514i	$0.833144\pi$
$440$	34.3923	−	9.21539i	0.0781643	−	0.0209441i
$441$		−	77.2539i		−	0.175179i
$442$		0			0
$443$	−323.836			−0.731006			−0.365503	−	0.930810i	$-0.619103\pi$
$443$	−323.836			−0.731006			−0.365503	+	0.930810i	$0.619103\pi$
$444$	−19.7321	−	73.6410i	−0.0444416	−	0.165858i
$445$	−66.2365	+	114.725i	−0.148846	+	0.257809i
$446$	−186.419	+	107.629i	−0.417979	+	0.241320i
$447$	−45.7250	+	45.7250i	−0.102293	+	0.102293i
$448$	60.7846	+	16.2872i	0.135680	+	0.0363553i
$449$	−91.5122	+	341.528i	−0.203813	+	0.760642i	0.785995	+	0.618233i	$0.212151\pi$
$449$	−91.5122	+	341.528i	−0.203813	+	0.760642i	−0.989808	+	0.142408i	$0.954515\pi$
$450$	−114.000	−	114.000i	−0.253333	−	0.253333i
$451$	111.775	+	193.600i	0.247838	+	0.429268i
$452$	306.573	+	177.000i	0.678259	+	0.391593i
$453$	381.892	−	102.328i	0.843028	−	0.225889i
$454$			304.501i			0.670707i
$455$		0			0
$456$	−126.249			−0.276861
$457$	−68.8763	−	257.050i	−0.150714	−	0.562473i	−0.999434	−	0.0336305i	$-0.989293\pi$
$457$	−68.8763	−	257.050i	−0.150714	−	0.562473i	0.848720	−	0.528842i	$-0.177374\pi$
$458$	9.23463	−	15.9948i	0.0201629	−	0.0349232i
$459$	641.625	−	370.442i	1.39788	−	0.807064i
$460$	−60.7461	+	60.7461i	−0.132057	+	0.132057i
$461$	−145.521	−	38.9923i	−0.315664	−	0.0845819i	0.0975085	−	0.995235i	$-0.468913\pi$
$461$	−145.521	−	38.9923i	−0.315664	−	0.0845819i	−0.413173	+	0.910653i	$0.635579\pi$
$462$	25.6288	−	95.6481i	0.0554736	−	0.207030i
$463$	−48.4115	−	48.4115i	−0.104561	−	0.104561i	0.652891	−	0.757452i	$-0.273556\pi$
$463$	−48.4115	−	48.4115i	−0.104561	−	0.104561i	−0.757452	+	0.652891i	$0.773556\pi$
$464$	−1.42563	−	2.46926i	−0.00307247	−	0.00532167i
$465$	121.277	+	70.0192i	0.260810	+	0.150579i
$466$	−542.396	+	145.335i	−1.16394	+	0.311877i
$467$		−	138.764i		−	0.297139i	−0.988902	−	0.148570i	$-0.952533\pi$
$467$		−	138.764i		−	0.297139i	0.988902	−	0.148570i	$-0.0474669\pi$
$468$		0			0
$469$	−390.229			−0.832046
$470$	41.8423	+	156.158i	0.0890262	+	0.332250i
$471$	−12.4974	+	21.6462i	−0.0265338	+	0.0459579i
$472$	96.1577	−	55.5167i	0.203724	−	0.117620i
$473$	267.610	−	267.610i	0.565771	−	0.565771i
$474$	−33.9615	−	9.09996i	−0.0716488	−	0.0191982i
$475$	−126.728	+	472.954i	−0.266795	+	0.995692i
$476$	317.229	+	317.229i	0.666448	+	0.666448i
$477$	−240.315	−	416.238i	−0.503806	−	0.872617i
$478$	−344.138	−	198.688i	−0.719955	−	0.415666i
$479$	221.959	−	59.4737i	0.463380	−	0.124162i	−0.0195733	−	0.999808i	$-0.506231\pi$
$479$	221.959	−	59.4737i	0.463380	−	0.124162i	0.482953	+	0.875646i	$0.339564\pi$
$480$			24.0000i			0.0500000i
$481$		0			0
$482$	462.645			0.959844
$483$	61.8365	+	230.777i	0.128026	+	0.477799i
$484$	94.5885	−	163.832i	0.195431	−	0.338496i
$485$	288.767	−	166.720i	0.595396	−	0.343752i
$486$	−249.415	+	249.415i	−0.513200	+	0.513200i
$487$	−471.064	−	126.221i	−0.967277	−	0.259181i	−0.259599	−	0.965716i	$-0.583591\pi$
$487$	−471.064	−	126.221i	−0.967277	−	0.259181i	−0.707678	+	0.706535i	$0.750257\pi$
$488$	20.9423	−	78.1577i	0.0429145	−	0.160159i
$489$	30.3032	+	30.3032i	0.0619696	+	0.0619696i
$490$	22.3013	+	38.6269i	0.0455128	+	0.0788305i
$491$	−453.156	−	261.630i	−0.922924	−	0.532850i	−0.0383572	−	0.999264i	$-0.512212\pi$
$491$	−453.156	−	261.630i	−0.922924	−	0.532850i	−0.884567	+	0.466414i	$0.845546\pi$
$492$	−145.550	+	39.0000i	−0.295833	+	0.0792683i
$493$		−	20.3270i		−	0.0412313i
$494$		0			0
$495$	−75.5307			−0.152587
$496$	−34.1718	−	127.531i	−0.0688947	−	0.257118i
$497$	−28.6487	+	49.6211i	−0.0576434	+	0.0998412i
$498$	−263.512	+	152.138i	−0.529140	+	0.305499i
$499$	−108.412	+	108.412i	−0.217258	+	0.217258i	−0.807342	−	0.590084i	$-0.799095\pi$
$499$	−108.412	+	108.412i	−0.217258	+	0.217258i	0.590084	+	0.807342i	$0.299095\pi$
$500$	208.210	+	55.7898i	0.416420	+	0.111580i
$501$	−26.3038	+	98.1673i	−0.0525027	+	0.195943i
$502$	−155.038	−	155.038i	−0.308842	−	0.308842i
$503$	202.861	+	351.365i	0.403302	+	0.698539i	0.994122	−	0.108264i	$-0.0345291\pi$
$503$	202.861	+	351.365i	0.403302	+	0.698539i	−0.590820	+	0.806803i	$0.701196\pi$
$504$	−115.608	−	66.7461i	−0.229380	−	0.132433i
$505$	−145.471	+	38.9789i	−0.288062	+	0.0771859i
$506$		−	127.450i		−	0.251878i
$507$		0			0
$508$	340.985			0.671229
$509$	40.0814	+	149.586i	0.0787454	+	0.293882i	0.994056	−	0.108866i	$-0.0347219\pi$
$509$	40.0814	+	149.586i	0.0787454	+	0.293882i	−0.915311	+	0.402748i	$0.868055\pi$
$510$	−85.5500	+	148.177i	−0.167745	+	0.290543i
$511$	−122.981	+	71.0033i	−0.240668	+	0.138950i
$512$	16.0000	−	16.0000i	0.0312500	−	0.0312500i
$513$	646.721	+	173.288i	1.26066	+	0.337794i
$514$	110.739	−	413.284i	0.215446	−	0.804054i
$515$	−40.3923	−	40.3923i	−0.0784317	−	0.0784317i
$516$	127.550	+	220.923i	0.247190	+	0.428145i
$517$	−207.710	−	119.921i	−0.401759	−	0.231956i
$518$	−236.485	+	63.3660i	−0.456535	+	0.122328i
$519$			124.292i			0.239484i
$520$		0			0
$521$	−239.636			−0.459954			−0.229977	−	0.973196i	$-0.573865\pi$
$521$	−239.636			−0.459954			−0.229977	+	0.973196i	$0.573865\pi$
$522$	1.56545	+	5.84232i	0.00299894	+	0.0111922i
$523$	497.663	−	861.978i	0.951555	−	1.64814i	0.209494	−	0.977810i	$-0.432818\pi$
$523$	497.663	−	861.978i	0.951555	−	1.64814i	0.742061	−	0.670332i	$-0.233848\pi$
$524$	77.6846	−	44.8513i	0.148253	−	0.0855940i
$525$	183.046	−	183.046i	0.348658	−	0.348658i
$526$	−69.1122	−	18.5185i	−0.131392	−	0.0352064i
$527$	243.616	−	909.188i	0.462270	−	1.72521i
$528$	−25.1769	−	25.1769i	−0.0476836	−	0.0476836i
$529$	−110.746	−	191.818i	−0.209350	−	0.362605i
$530$	240.315	+	138.746i	0.453425	+	0.261785i
$531$	−227.512	+	60.9615i	−0.428459	+	0.114805i
$532$			405.426i			0.762078i
$533$		0			0
$534$	132.473			0.248077
$535$	−50.5481	−	188.648i	−0.0944824	−	0.352613i
$536$	−70.1577	+	121.517i	−0.130891	+	0.226710i
$537$	241.012	−	139.148i	0.448811	−	0.259121i
$538$	−42.8949	+	42.8949i	−0.0797303	+	0.0797303i
$539$	−63.9160	−	17.1262i	−0.118583	−	0.0317741i
$540$	32.9423	−	122.942i	0.0610042	−	0.227671i
$541$	−74.1000	−	74.1000i	−0.136969	−	0.136969i	0.635298	−	0.772267i	$-0.280877\pi$
$541$	−74.1000	−	74.1000i	−0.136969	−	0.136969i	−0.772267	+	0.635298i	$0.780877\pi$
$542$	−350.370	−	606.858i	−0.646439	−	1.11966i
$543$	214.608	+	123.904i	0.395226	+	0.228184i
$544$	155.818	−	41.7513i	0.286430	−	0.0767487i
$545$			359.072i			0.658847i
$546$		0			0
$547$	961.854			1.75842			0.879208	−	0.476438i	$-0.158072\pi$
$547$	961.854			1.75842			0.879208	+	0.476438i	$0.158072\pi$
$548$	48.7551	+	181.956i	0.0889691	+	0.332037i
$549$	−85.8231	+	148.650i	−0.156326	+	0.270765i
$550$	−119.590	+	69.0455i	−0.217437	+	0.125537i
$551$	12.9892	−	12.9892i	0.0235738	−	0.0235738i
$552$	82.9808	+	22.2346i	0.150327	+	0.0402801i
$553$	−29.2229	+	109.061i	−0.0528444	+	0.197218i
$554$	212.727	+	212.727i	0.383984	+	0.383984i
$555$	−46.6865	−	80.8634i	−0.0841199	−	0.145700i
$556$	33.2487	+	19.1962i	0.0597998	+	0.0345255i
$557$	729.917	−	195.581i	1.31044	−	0.351132i	0.465054	−	0.885282i	$-0.346035\pi$
$557$	729.917	−	195.581i	1.31044	−	0.351132i	0.845390	+	0.534150i	$0.179368\pi$
$558$			280.077i			0.501930i
$559$		0			0
$560$	77.0718			0.137628
$561$	−65.6980	−	245.188i	−0.117109	−	0.437056i
$562$	27.2243	−	47.1539i	0.0484418	−	0.0839037i
$563$	−26.1250	+	15.0833i	−0.0464033	+	0.0267909i	−0.523022	−	0.852319i	$-0.675196\pi$
$563$	−26.1250	+	15.0833i	−0.0464033	+	0.0267909i	0.476619	+	0.879110i	$0.341862\pi$
$564$	114.315	−	114.315i	0.202687	−	0.202687i
$565$	418.786	+	112.214i	0.741215	+	0.198608i
$566$	53.4763	−	199.576i	0.0944811	−	0.352608i
$567$	50.0596	+	50.0596i	0.0882885	+	0.0882885i
$568$	10.3013	+	17.8423i	0.0181360	+	0.0314125i
$569$	−447.092	−	258.129i	−0.785751	−	0.453653i	0.0527137	−	0.998610i	$-0.483213\pi$
$569$	−447.092	−	258.129i	−0.785751	−	0.453653i	−0.838465	+	0.544956i	$0.816546\pi$
$570$	−149.354	+	40.0192i	−0.262024	+	0.0702092i
$571$			813.423i			1.42456i	0.701896	+	0.712279i	$0.252337\pi$
$571$			813.423i			1.42456i	−0.701896	+	0.712279i	$0.747663\pi$
$572$		0			0
$573$	494.338			0.862720
$574$	125.242	+	467.408i	0.218191	+	0.814300i
$575$	166.591	−	288.544i	0.289724	−	0.501816i
$576$	−41.5692	+	24.0000i	−0.0721688	+	0.0416667i
$577$	−336.660	+	336.660i	−0.583467	+	0.583467i	−0.935854	−	0.352388i	$-0.885370\pi$
$577$	−336.660	+	336.660i	−0.583467	+	0.583467i	0.352388	+	0.935854i	$0.385370\pi$
$578$	716.070	+	191.870i	1.23888	+	0.331956i
$579$	−39.6840	+	148.103i	−0.0685388	+	0.255790i
$580$	−2.46926	−	2.46926i	−0.00425734	−	0.00425734i
$581$	488.566	+	846.221i	0.840905	+	1.45649i
$582$	−288.767	−	166.720i	−0.496164	−	0.286460i
$583$	−397.650	+	106.550i	−0.682075	+	0.182762i
$584$			51.0615i			0.0874341i
$585$		0			0
$586$	−138.358			−0.236105
$587$	154.442	+	576.386i	0.263104	+	0.981919i	0.963400	+	0.268066i	$0.0863847\pi$
$587$	154.442	+	576.386i	0.263104	+	0.981919i	−0.700296	+	0.713853i	$0.746949\pi$
$588$	22.3013	−	38.6269i	0.0379273	−	0.0656921i
$589$	736.653	−	425.307i	1.25068	−	0.722083i
$590$	96.1577	−	96.1577i	0.162979	−	0.162979i
$591$	628.133	+	168.308i	1.06283	+	0.284784i
$592$	−22.7846	+	85.0333i	−0.0384875	+	0.143637i
$593$	−297.953	−	297.953i	−0.502450	−	0.502450i	0.409749	−	0.912198i	$-0.365616\pi$
$593$	−297.953	−	297.953i	−0.502450	−	0.502450i	−0.912198	+	0.409749i	$0.865616\pi$
$594$	94.4134	+	163.529i	0.158945	+	0.275301i
$595$	475.844	+	274.729i	0.799738	+	0.461729i
$596$	72.1244	−	19.3257i	0.121014	−	0.0324256i
$597$		−	515.578i		−	0.863615i
$598$		0			0
$599$	996.169			1.66305			0.831527	−	0.555485i	$-0.187467\pi$
$599$	996.169			1.66305			0.831527	+	0.555485i	$0.187467\pi$
$600$	−24.0910	−	89.9090i	−0.0401517	−	0.149848i
$601$	−126.265	+	218.698i	−0.210092	+	0.363890i	−0.951743	−	0.306896i	$-0.900710\pi$
$601$	−126.265	+	218.698i	−0.210092	+	0.363890i	0.741651	+	0.670786i	$0.234043\pi$
$602$	709.456	−	409.604i	1.17850	−	0.680406i
$603$	210.473	−	210.473i	0.349043	−	0.349043i
$604$	−440.970	−	118.158i	−0.730084	−	0.195625i
$605$	59.9667	−	223.799i	0.0991185	−	0.369915i
$606$	106.492	+	106.492i	0.175730	+	0.175730i
$607$	245.321	+	424.909i	0.404154	+	0.700014i	0.994223	−	0.107338i	$-0.0342328\pi$
$607$	245.321	+	424.909i	0.404154	+	0.700014i	−0.590069	+	0.807353i	$0.700899\pi$
$608$	126.249	+	72.8897i	0.207646	+	0.119884i
$609$	−9.38080	+	2.51358i	−0.0154036	+	0.00412739i
$610$		−	99.1000i		−	0.162459i
$611$		0			0
$612$	−342.200			−0.559150
$613$	137.311	+	512.451i	0.223998	+	0.835973i	0.982803	+	0.184655i	$0.0591168\pi$
$613$	137.311	+	512.451i	0.223998	+	0.835973i	−0.758805	+	0.651318i	$0.774217\pi$
$614$	−2.62178	+	4.54105i	−0.00427000	+	0.00739585i
$615$	−159.825	+	92.2750i	−0.259878	+	0.150041i
$616$	−80.8513	+	80.8513i	−0.131252	+	0.131252i
$617$	−536.185	−	143.670i	−0.869020	−	0.232853i	−0.203356	−	0.979105i	$-0.565185\pi$
$617$	−536.185	−	143.670i	−0.869020	−	0.232853i	−0.665664	+	0.746252i	$0.731852\pi$
$618$	−14.7846	+	55.1769i	−0.0239233	+	0.0892830i
$619$	−501.483	−	501.483i	−0.810151	−	0.810151i	0.174505	−	0.984656i	$-0.444167\pi$
$619$	−501.483	−	501.483i	−0.810151	−	0.810151i	−0.984656	+	0.174505i	$0.944167\pi$
$620$	−80.8513	−	140.038i	−0.130405	−	0.225869i
$621$	−394.558	−	227.798i	−0.635359	−	0.366824i
$622$	527.338	−	141.300i	0.847811	−	0.227170i
$623$		−	425.414i		−	0.682847i
$624$		0			0
$625$	−211.000			−0.337600
$626$	−12.8616	−	48.0000i	−0.0205456	−	0.0766773i
$627$	114.696	−	198.660i	0.182928	−	0.316841i
$628$	24.9948	−	14.4308i	0.0398007	−	0.0229790i
$629$	−443.781	+	443.781i	−0.705535	+	0.705535i
$630$	−157.923	−	42.3154i	−0.250672	−	0.0671672i
$631$	54.9524	−	205.085i	0.0870878	−	0.325016i	−0.908614	−	0.417638i	$-0.862858\pi$
$631$	54.9524	−	205.085i	0.0870878	−	0.325016i	0.995701	+	0.0926217i	$0.0295247\pi$
$632$	28.7077	+	28.7077i	0.0454235	+	0.0454235i
$633$	47.2039	+	81.7595i	0.0745717	+	0.129162i
$634$	21.7039	+	12.5307i	0.0342333	+	0.0197646i
$635$	403.389	−	108.088i	0.635258	−	0.170217i
$636$		−	277.492i		−	0.436309i
$637$		0			0
$638$	5.18069			0.00812020
$639$	−11.3116	−	42.2154i	−0.0177020	−	0.0660648i
$640$	13.8564	−	24.0000i	0.0216506	−	0.0375000i
$641$	−69.3499	+	40.0392i	−0.108190	+	0.0624636i	−0.553119	−	0.833102i	$-0.686562\pi$
$641$	−69.3499	+	40.0392i	−0.108190	+	0.0624636i	0.444929	+	0.895566i	$0.353229\pi$
$642$	−138.100	+	138.100i	−0.215109	+	0.215109i
$643$	543.346	+	145.589i	0.845017	+	0.226422i	0.655254	−	0.755408i	$-0.272561\pi$
$643$	543.346	+	145.589i	0.845017	+	0.226422i	0.189763	+	0.981830i	$0.439228\pi$
$644$	71.4026	−	266.478i	0.110874	−	0.413786i
$645$	220.923	+	220.923i	0.342516	+	0.342516i
$646$	519.643	+	900.048i	0.804401	+	1.39326i
$647$	−1005.44	−	580.493i	−1.55401	−	0.897208i	−0.997809	−	0.0661597i	$-0.978925\pi$
$647$	−1005.44	−	580.493i	−1.55401	−	0.897208i	−0.556200	−	0.831048i	$-0.687741\pi$
$648$	24.5885	−	6.58846i	0.0379452	−	0.0101674i
$649$			201.746i			0.310857i
$650$		0			0
$651$	−449.709			−0.690797
$652$	−12.8076	−	47.7987i	−0.0196436	−	0.0733109i
$653$	−220.045	+	381.129i	−0.336975	+	0.583658i	−0.983862	−	0.178928i	$-0.942737\pi$
$653$	−220.045	+	381.129i	−0.336975	+	0.583658i	0.646887	+	0.762586i	$0.276071\pi$
$654$	310.965	−	179.536i	0.475482	−	0.274520i
$655$	77.6846	−	77.6846i	0.118603	−	0.118603i
$656$	168.067	+	45.0333i	0.256199	+	0.0686484i
$657$	28.0347	−	104.627i	0.0426708	−	0.159250i
$658$	−367.104	−	367.104i	−0.557908	−	0.557908i
$659$	−274.521	−	475.485i	−0.416572	−	0.721524i	0.579020	−	0.815313i	$-0.303435\pi$
$659$	−274.521	−	475.485i	−0.416572	−	0.721524i	−0.995592	+	0.0937891i	$0.970102\pi$
$660$	−37.7654	−	21.8038i	−0.0572203	−	0.0330361i
$661$	−784.429	+	210.187i	−1.18673	+	0.317983i	−0.797593	−	0.603196i	$-0.793894\pi$
$661$	−784.429	+	210.187i	−1.18673	+	0.317983i	−0.389137	+	0.921180i	$0.627227\pi$
$662$			365.965i			0.552818i
$663$		0			0
$664$	351.349			0.529140
$665$	128.515	+	479.624i	0.193255	+	0.721239i
$666$	93.3731	−	161.727i	0.140200	−	0.242833i
$667$	−10.8252	+	6.24991i	−0.0162296	+	0.00937018i
$668$	82.9808	−	82.9808i	0.124223	−	0.124223i
$669$	254.653	+	68.2339i	0.380647	+	0.101994i
$670$	−44.4782	+	165.995i	−0.0663854	+	0.247754i
$671$	103.960	+	103.960i	0.154932	+	0.154932i
$672$	−38.5359	−	66.7461i	−0.0573451	−	0.0993246i
$673$	367.385	+	212.110i	0.545891	+	0.315170i	0.747463	−	0.664303i	$-0.231272\pi$
$673$	367.385	+	212.110i	0.545891	+	0.315170i	−0.201572	+	0.979474i	$0.564605\pi$
$674$	129.699	−	34.7527i	0.192431	−	0.0515618i
$675$			493.634i			0.731310i
$676$		0			0
$677$	124.308			0.183616			0.0918078	−	0.995777i	$-0.470735\pi$
$677$	124.308			0.183616			0.0918078	+	0.995777i	$0.470735\pi$
$678$	−112.214	−	418.786i	−0.165507	−	0.617679i
$679$	−535.392	+	927.325i	−0.788500	+	1.36572i
$680$	171.100	−	98.7846i	0.251618	−	0.145271i
$681$	263.706	−	263.706i	0.387233	−	0.387233i
$682$	231.722	+	62.0897i	0.339768	+	0.0910405i
$683$	11.2551	−	42.0045i	0.0164789	−	0.0614999i	−0.957197	−	0.289438i	$-0.906532\pi$
$683$	11.2551	−	42.0045i	0.0164789	−	0.0614999i	0.973676	+	0.227938i	$0.0731983\pi$
$684$	−218.669	−	218.669i	−0.319692	−	0.319692i
$685$	115.356	+	199.802i	0.168403	+	0.291682i
$686$	348.021	+	200.930i	0.507319	+	0.292901i
$687$	−21.8494	+	5.85452i	−0.0318040	+	0.00852186i
$688$		−	294.564i		−	0.428145i
$689$		0			0
$690$	105.215			0.152486
$691$	195.327	+	728.970i	0.282673	+	1.05495i	0.950523	+	0.310654i	$0.100548\pi$
$691$	195.327	+	728.970i	0.282673	+	1.05495i	−0.667850	+	0.744295i	$0.732785\pi$
$692$	71.7602	−	124.292i	0.103700	−	0.179613i
$693$	210.058	−	121.277i	0.303114	−	0.175003i
$694$	104.460	−	104.460i	0.150519	−	0.150519i
$695$	45.4186	+	12.1699i	0.0653505	+	0.0175106i
$696$	−0.903811	+	3.37307i	−0.00129858	+	0.00484636i
$697$	877.125	+	877.125i	1.25843	+	1.25843i
$698$	57.1558	+	98.9967i	0.0818851	+	0.141829i
$699$	595.592	+	343.865i	0.852063	+	0.491939i
$700$	−288.727	+	77.3641i	−0.412467	+	0.110520i
$701$			847.213i			1.20858i	0.796766	+	0.604289i	$0.206543\pi$
$701$			847.213i			1.20858i	−0.796766	+	0.604289i	$0.793457\pi$
$702$		0			0
$703$	−567.161			−0.806773
$704$	10.6410	+	39.7128i	0.0151151	+	0.0564102i
$705$	99.0000	−	171.473i	0.140426	−	0.243224i
$706$	−208.886	+	120.601i	−0.295873	+	0.170822i
$707$	341.981	−	341.981i	0.483708	−	0.483708i
$708$	−131.354	−	35.1962i	−0.185528	−	0.0497121i
$709$	209.535	−	781.996i	0.295536	−	1.10296i	−0.645254	−	0.763968i	$-0.723249\pi$
$709$	209.535	−	781.996i	0.295536	−	1.10296i	0.940791	−	0.338988i	$-0.110085\pi$
$710$	17.8423	+	17.8423i	0.0251300	+	0.0251300i
$711$	−43.0615	−	74.5847i	−0.0605647	−	0.104901i
$712$	−132.473	−	76.4833i	−0.186058	−	0.107420i
$713$	−559.092	+	149.808i	−0.784140	+	0.210110i
$714$		−	549.458i		−	0.769548i
$715$		0			0
$716$	−321.349			−0.448811
$717$	125.963	+	470.102i	0.175681	+	0.655651i
$718$	−102.058	+	176.769i	−0.142142	+	0.246197i
$719$	−685.421	+	395.728i	−0.953298	+	0.550387i	−0.894104	−	0.447860i	$-0.852186\pi$
$719$	−685.421	+	395.728i	−0.953298	+	0.550387i	−0.0591940	+	0.998246i	$0.518853\pi$
$720$	−41.5692	+	41.5692i	−0.0577350	+	0.0577350i
$721$	177.191	+	47.4782i	0.245757	+	0.0658505i
$722$	−110.947	+	414.061i	−0.153667	+	0.573492i
$723$	−400.662	−	400.662i	−0.554166	−	0.554166i
$724$	−143.072	−	247.808i	−0.197613	−	0.342276i
$725$	11.7290	+	6.77172i	0.0161779	+	0.00934031i
$726$	−223.799	+	59.9667i	−0.308263	+	0.0825987i
$727$		−	1014.52i		−	1.39549i	−0.716345	−	0.697746i	$-0.754186\pi$
$727$		−	1014.52i		−	1.39549i	0.716345	−	0.697746i	$-0.245814\pi$
$728$		0			0
$729$	351.000			0.481481
$730$	16.1858	+	60.4064i	0.0221724	+	0.0827485i
$731$	1050.00	−	1818.65i	1.43639	−	2.48789i
$732$	−85.8231	+	49.5500i	−0.117245	+	0.0676912i
$733$	−769.697	+	769.697i	−1.05006	+	1.05006i	−0.0513857	+	0.998679i	$0.516364\pi$
$733$	−769.697	+	769.697i	−1.05006	+	1.05006i	−0.998679	+	0.0513857i	$0.983636\pi$
$734$	−652.566	−	174.855i	−0.889054	−	0.238221i
$735$	14.1384	−	52.7654i	0.0192360	−	0.0717896i
$736$	−70.1436	−	70.1436i	−0.0953038	−	0.0953038i
$737$	−127.476	−	220.794i	−0.172966	−	0.299585i
$738$	−319.650	−	184.550i	−0.433130	−	0.250068i
$739$	255.155	−	68.3686i	0.345271	−	0.0925150i	−0.0820164	−	0.996631i	$-0.526136\pi$
$739$	255.155	−	68.3686i	0.345271	−	0.0925150i	0.427287	+	0.904116i	$0.359469\pi$
$740$			107.818i			0.145700i
$741$		0			0
$742$	−891.118			−1.20097
$743$	−202.345	−	755.161i	−0.272335	−	1.01637i	−0.957606	−	0.288080i	$-0.906983\pi$
$743$	−202.345	−	755.161i	−0.272335	−	1.01637i	0.685272	−	0.728287i	$-0.259683\pi$
$744$	−80.8513	+	140.038i	−0.108671	+	0.188224i
$745$	79.1980	−	45.7250i	0.106306	−	0.0613759i
$746$	515.487	−	515.487i	0.691001	−	0.691001i
$747$	−719.927	−	192.904i	−0.963757	−	0.258238i
$748$	−75.8616	+	283.119i	−0.101419	+	0.378502i
$749$	443.484	+	443.484i	0.592101	+	0.592101i
$750$	−132.000	−	228.631i	−0.176000	−	0.304841i
$751$	640.663	+	369.887i	0.853080	+	0.492526i	0.861689	−	0.507437i	$-0.169407\pi$
$751$	640.663	+	369.887i	0.853080	+	0.492526i	−0.00860865	+	0.999963i	$0.502740\pi$
$752$	−180.315	+	48.3154i	−0.239781	+	0.0642491i
$753$			268.535i			0.356620i
$754$		0			0
$755$	−559.128			−0.740567
$756$	105.788	+	394.808i	0.139932	+	0.522232i
$757$	−368.437	+	638.152i	−0.486707	+	0.843001i	−0.999883	−	0.0152821i	$-0.995135\pi$
$757$	−368.437	+	638.152i	−0.486707	+	0.843001i	0.513176	+	0.858283i	$0.328469\pi$
$758$	335.242	−	193.552i	0.442271	−	0.255345i
$759$	−110.375	+	110.375i	−0.145422	+	0.145422i
$760$	172.459	+	46.2102i	0.226920	+	0.0608029i
$761$	−370.661	+	1383.33i	−0.487071	+	1.81777i	0.0834780	+	0.996510i	$0.473397\pi$
$761$	−370.661	+	1383.33i	−0.487071	+	1.81777i	−0.570549	+	0.821264i	$0.693269\pi$
$762$	−295.301	−	295.301i	−0.387534	−	0.387534i
$763$	−576.548	−	998.611i	−0.755633	−	1.30880i
$764$	−494.338	−	285.406i	−0.647040	−	0.373569i
$765$	−404.827	+	108.473i	−0.529185	+	0.141795i
$766$		−	661.468i		−	0.863535i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	−66.4517	−	248.001i	−0.0864132	−	0.322498i	0.909165	−	0.416436i	$-0.136721\pi$
$769$	−66.4517	−	248.001i	−0.0864132	−	0.322498i	−0.995578	+	0.0939380i	$0.970054\pi$
$770$	−70.0192	+	121.277i	−0.0909341	+	0.157502i
$771$	−453.817	+	262.012i	−0.588609	+	0.339833i
$772$	125.191	−	125.191i	0.162165	−	0.162165i
$773$	−451.066	−	120.863i	−0.583526	−	0.156355i	−0.0450335	−	0.998985i	$-0.514339\pi$
$773$	−451.066	−	120.863i	−0.583526	−	0.156355i	−0.538493	+	0.842630i	$0.681006\pi$
$774$	−161.727	+	603.573i	−0.208949	+	0.779810i
$775$	443.455	+	443.455i	0.572200	+	0.572200i
$776$	192.512	+	333.440i	0.248082	+	0.429690i
$777$	259.679	+	149.926i	0.334207	+	0.192954i
$778$	782.305	−	209.618i	1.00553	−	0.269432i
$779$			1120.98i			1.43900i
$780$		0			0
$781$	−37.4346			−0.0479316
$782$	−183.037	−	683.102i	−0.234062	−	0.873532i
$783$	9.25971	−	16.0383i	0.0118259	−	0.0204831i
$784$	−44.6025	+	25.7513i	−0.0568910	+	0.0328460i
$785$	24.9948	−	24.9948i	0.0318406	−	0.0318406i
$786$	−106.119	−	28.4346i	−0.135012	−	0.0361763i
$787$	307.828	−	1148.83i	0.391141	−	1.45976i	−0.437113	−	0.899406i	$-0.643999\pi$
$787$	307.828	−	1148.83i	0.391141	−	1.45976i	0.828255	−	0.560352i	$-0.189334\pi$
$788$	−530.960	−	530.960i	−0.673807	−	0.673807i
$789$	43.8154	+	75.8904i	0.0555328	+	0.0961856i
$790$	43.0615	+	24.8616i	0.0545082	+	0.0314703i
$791$	−1344.86	+	360.354i	−1.70020	+	0.455568i
$792$		−	87.2154i		−	0.110120i
$793$		0			0
$794$	−86.4833			−0.108921
$795$	−87.9615	−	328.277i	−0.110643	−	0.412927i
$796$	−297.669	+	515.578i	−0.373956	+	0.647711i
$797$	−70.6886	+	40.8121i	−0.0886934	+	0.0512071i	−0.543691	−	0.839286i	$-0.682974\pi$
$797$	−70.6886	+	40.8121i	−0.0886934	+	0.0512071i	0.454997	+	0.890493i	$0.349640\pi$
$798$	351.109	−	351.109i	0.439986	−	0.439986i
$799$	−1285.50	−	344.448i	−1.60888	−	0.431099i
$800$	−27.8179	+	103.818i	−0.0347724	+	0.129772i
$801$	229.450	+	229.450i	0.286454	+	0.286454i
$802$	−381.983	−	661.613i	−0.476288	−	0.824954i
$803$	−80.3482	−	46.3890i	−0.100060	−	0.0577697i
$804$	165.995	−	44.4782i	0.206461	−	0.0553211i
$805$		−	337.881i		−	0.419728i
$806$		0			0
$807$	74.2961			0.0920646
$808$	−45.0089	−	167.976i	−0.0557041	−	0.207891i
$809$	−637.684	+	1104.50i	−0.788238	+	1.36527i	0.138808	+	0.990319i	$0.455673\pi$
$809$	−637.684	+	1104.50i	−0.788238	+	1.36527i	−0.927046	+	0.374949i	$0.877660\pi$
$810$	27.0000	−	15.5885i	0.0333333	−	0.0192450i
$811$	553.018	−	553.018i	0.681896	−	0.681896i	−0.278531	−	0.960427i	$-0.589847\pi$
$811$	553.018	−	553.018i	0.681896	−	0.681896i	0.960427	+	0.278531i	$0.0898475\pi$
$812$	10.8320	+	2.90243i	0.0133399	+	0.00357442i
$813$	−222.126	+	828.984i	−0.273217	+	1.01966i
$814$	−113.105	−	113.105i	−0.138950	−	0.138950i
$815$	−30.3032	−	52.4866i	−0.0371818	−	0.0644007i
$816$	−171.100	−	98.7846i	−0.209681	−	0.121060i
$817$	1833.09	−	491.176i	2.24369	−	0.601195i
$818$			29.3167i			0.0358395i
$819$		0			0
$820$	213.100			0.259878
$821$	−318.975	−	1190.43i	−0.388520	−	1.44998i	−0.832543	−	0.553961i	$-0.813116\pi$
$821$	−318.975	−	1190.43i	−0.388520	−	1.44998i	0.444023	−	0.896016i	$-0.353551\pi$
$822$	115.356	−	199.802i	0.140335	−	0.243068i
$823$	−557.525	+	321.887i	−0.677430	+	0.391114i	−0.798886	−	0.601482i	$-0.794577\pi$
$823$	−557.525	+	321.887i	−0.677430	+	0.391114i	0.121456	+	0.992597i	$0.461244\pi$
$824$	46.6410	−	46.6410i	0.0566032	−	0.0566032i
$825$	163.363	+	43.7731i	0.198016	+	0.0530583i
$826$	−113.026	+	421.820i	−0.136836	+	0.510678i
$827$	349.617	+	349.617i	0.422753	+	0.422753i	0.886150	−	0.463398i	$-0.153370\pi$
$827$	349.617	+	349.617i	0.422753	+	0.422753i	−0.463398	+	0.886150i	$0.653370\pi$
$828$	105.215	+	182.238i	0.127072	+	0.220095i
$829$	385.172	+	222.379i	0.464622	+	0.268250i	0.713986	−	0.700160i	$-0.246888\pi$
$829$	385.172	+	222.379i	0.464622	+	0.268250i	−0.249364	+	0.968410i	$0.580221\pi$
$830$	415.650	−	111.373i	0.500783	−	0.134184i
$831$		−	368.454i		−	0.443386i
$832$		0			0
$833$	−367.170			−0.440781
$834$	−12.1699	−	45.4186i	−0.0145922	−	0.0544587i
$835$	71.8634	−	124.471i	0.0860640	−	0.149067i
$836$	−229.392	+	132.440i	−0.274393	+	0.158421i
$837$	606.384	−	606.384i	0.724474	−	0.724474i
$838$	−474.279	−	127.083i	−0.565965	−	0.151650i
$839$	−91.3911	+	341.076i	−0.108929	+	0.406527i	−0.998761	−	0.0497600i	$-0.984154\pi$
$839$	−91.3911	+	341.076i	−0.108929	+	0.406527i	0.889833	+	0.456287i	$0.150821\pi$
$840$	−66.7461	−	66.7461i	−0.0794597	−	0.0794597i
$841$	420.246	+	727.887i	0.499698	+	0.865502i
$842$	496.328	+	286.555i	0.589463	+	0.340327i
$843$	−64.4134	+	17.2595i	−0.0764098	+	0.0204739i
$844$		−	109.013i		−	0.129162i
$845$		0			0
$846$	396.000			0.468085
$847$	192.572	+	718.690i	0.227358	+	0.848513i
$848$	−160.210	+	277.492i	−0.188927	+	0.327231i
$849$	−219.150	+	126.526i	−0.258127	+	0.149030i
$850$	−541.817	+	541.817i	−0.637431	+	0.637431i
$851$	372.784	+	99.8872i	0.438054	+	0.117376i
$852$	6.53074	−	24.3731i	0.00766519	−	0.0286069i
$853$	260.191	+	260.191i	0.305030	+	0.305030i	0.842978	−	0.537948i	$-0.180800\pi$
$853$	260.191	+	260.191i	0.305030	+	0.305030i	−0.537948	+	0.842978i	$0.680800\pi$
$854$	159.121	+	275.606i	0.186324	+	0.322723i
$855$	−328.004	−	189.373i	−0.383630	−	0.221489i
$856$	217.832	−	58.3679i	0.254477	−	0.0681868i
$857$		−	1647.00i		−	1.92182i	−0.276856	−	0.960912i	$-0.589292\pi$
$857$		−	1647.00i		−	1.92182i	0.276856	−	0.960912i	$-0.410708\pi$
$858$		0			0
$859$	63.1487			0.0735143			0.0367571	−	0.999324i	$-0.488297\pi$
$859$	63.1487			0.0735143			0.0367571	+	0.999324i	$0.488297\pi$
$860$	−93.3731	−	348.473i	−0.108573	−	0.405201i
$861$	296.325	−	513.250i	0.344164	−	0.596109i
$862$	375.536	−	216.816i	0.435657	−	0.251527i
$863$	−970.965	+	970.965i	−1.12510	+	1.12510i	−0.134143	+	0.990962i	$0.542828\pi$
$863$	−970.965	+	970.965i	−1.12510	+	1.12510i	−0.990962	+	0.134143i	$0.957172\pi$
$864$	141.962	+	38.0385i	0.164307	+	0.0440260i
$865$	45.4942	−	169.786i	0.0525944	−	0.196285i
$866$	−84.6115	−	84.6115i	−0.0977038	−	0.0977038i
$867$	−453.970	−	786.300i	−0.523611	−	0.906920i
$868$	449.709	+	259.640i	0.518098	+	0.299124i
$869$	−71.2539	+	19.0924i	−0.0819952	+	0.0219706i
$870$			4.27688i			0.00491595i
$871$		0			0
$872$	−414.620			−0.475482
$873$	−211.392	−	788.927i	−0.242145	−	0.903696i
$874$	319.547	−	553.471i	0.365614	−	0.633262i
$875$	−734.207	+	423.895i	−0.839094	+	0.484451i
$876$	44.2205	−	44.2205i	0.0504801	−	0.0504801i
$877$	1108.51	+	297.024i	1.26398	+	0.338682i	0.827721	−	0.561140i	$-0.189637\pi$
$877$	1108.51	+	297.024i	1.26398	+	0.338682i	0.436258	+	0.899822i	$0.356304\pi$
$878$	160.520	−	599.069i	0.182825	−	0.682310i
$879$	119.821	+	119.821i	0.136315	+	0.136315i
$880$	25.1769	+	43.6077i	0.0286101	+	0.0495542i
$881$	−68.2039	−	39.3775i	−0.0774164	−	0.0446964i	0.460792	−	0.887508i	$-0.347565\pi$
$881$	−68.2039	−	39.3775i	−0.0774164	−	0.0446964i	−0.538209	+	0.842812i	$0.680899\pi$
$882$	105.531	−	28.2769i	0.119649	−	0.0320600i
$883$			196.777i			0.222851i	0.993773	+	0.111425i	$0.0355416\pi$
$883$			196.777i			0.222851i	−0.993773	+	0.111425i	$0.964458\pi$
$884$		0			0
$885$	−166.550			−0.188192
$886$	−118.532	−	442.368i	−0.133783	−	0.499287i
$887$	182.971	−	316.915i	0.206281	−	0.357289i	−0.744259	−	0.667891i	$-0.767197\pi$
$887$	182.971	−	316.915i	0.206281	−	0.357289i	0.950540	+	0.310602i	$0.100531\pi$
$888$	93.3731	−	53.9090i	0.105150	−	0.0607083i
$889$	−948.308	+	948.308i	−1.06671	+	1.06671i
$890$	−180.962	−	48.4885i	−0.203328	−	0.0544815i
$891$	−11.9711	+	44.6769i	−0.0134356	+	0.0501424i
$892$	−215.258	−	215.258i	−0.241320	−	0.241320i
$893$	−601.340	−	1041.55i	−0.673393	−	1.16635i
$894$	−79.1980	−	45.7250i	−0.0885884	−	0.0511465i
$895$	−380.160	+	101.863i	−0.424759	+	0.113814i
$896$			88.9948i			0.0993246i
$897$		0			0
$898$	−500.032			−0.556828
$899$	−6.08952	−	22.7264i	−0.00677366	−	0.0252796i
$900$	114.000	−	197.454i	0.126667	−	0.219393i
$901$	−1978.29	+	1142.17i	−2.19566	+	1.26766i
$902$	−223.550	+	223.550i	−0.247838	+	0.247838i
$903$	−969.134	−	259.679i	−1.07324	−	0.287573i
$904$	−129.573	+	483.573i	−0.143333	+	0.534926i
$905$	−247.808	−	247.808i	−0.273821	−	0.273821i
$906$	279.564	+	484.219i	0.308570	+	0.534458i
$907$	1422.08	+	821.038i	1.56789	+	0.905224i	0.996414	+	0.0846081i	$0.0269638\pi$
$907$	1422.08	+	821.038i	1.56789	+	0.905224i	0.571480	+	0.820616i	$0.306370\pi$
$908$	−415.956	+	111.455i	−0.458102	+	0.122748i
$909$			368.900i			0.405831i
$910$		0			0
$911$	1061.82			1.16555			0.582776	−	0.812633i	$-0.301966\pi$
$911$	1061.82			1.16555			0.582776	+	0.812633i	$0.301966\pi$
$912$	−46.2102	−	172.459i	−0.0506691	−	0.189100i
$913$	−319.198	+	552.867i	−0.349615	+	0.605550i
$914$	325.926	−	188.174i	0.356593	−	0.205879i
$915$	−85.8231	+	85.8231i	−0.0937957	+	0.0937957i
$916$	25.2295	+	6.76022i	0.0275431	+	0.00738015i
$917$	−91.3126	+	340.783i	−0.0995775	+	0.371628i
$918$	740.885	+	740.885i	0.807064	+	0.807064i
$919$	−222.386	−	385.185i	−0.241987	−	0.419135i	0.719293	−	0.694707i	$-0.244466\pi$
$919$	−222.386	−	385.185i	−0.241987	−	0.419135i	−0.961280	+	0.275572i	$0.911133\pi$
$920$	−105.215	−	60.7461i	−0.114365	−	0.0660284i
$921$	6.20319	−	1.66214i	0.00673528	−	0.00180471i
$922$		−	213.058i		−	0.231082i
$923$		0			0
$924$	140.038			0.151557
$925$	−108.227	−	403.908i	−0.117002	−	0.436658i
$926$	48.4115	−	83.8513i	0.0522803	−	0.0905521i
$927$	−121.177	+	69.9615i	−0.130719	+	0.0754709i
$928$	2.85125	−	2.85125i	0.00307247	−	0.00307247i
$929$	1034.43	+	277.176i	1.11349	+	0.298359i	0.768247	−	0.640153i	$-0.221129\pi$
$929$	1034.43	+	277.176i	1.11349	+	0.298359i	0.345245	+	0.938513i	$0.387796\pi$
$930$	−51.2576	+	191.296i	−0.0551157	+	0.205695i
$931$	−234.626	−	234.626i	−0.252015	−	0.252015i
$932$	−397.061	−	687.731i	−0.426032	−	0.737908i
$933$	−579.058	−	334.319i	−0.620641	−	0.358327i
$934$	189.555	−	50.7911i	0.202950	−	0.0543802i
$935$			358.981i			0.383937i
$936$		0			0
$937$	1502.97			1.60403			0.802013	−	0.597307i	$-0.203763\pi$
$937$	1502.97			1.60403			0.802013	+	0.597307i	$0.203763\pi$
$938$	−142.834	−	533.063i	−0.152275	−	0.568298i
$939$	−30.4308	+	52.7077i	−0.0324076	+	0.0561317i
$940$	−198.000	+	114.315i	−0.210638	+	0.121612i
$941$	−414.136	+	414.136i	−0.440102	+	0.440102i	−0.892046	−	0.451944i	$-0.850731\pi$
$941$	−414.136	+	414.136i	−0.440102	+	0.440102i	0.451944	+	0.892046i	$0.350731\pi$
$942$	−34.1436	−	9.14875i	−0.0362459	−	0.00971205i
$943$	197.425	−	736.800i	0.209358	−	0.781336i
$944$	111.033	+	111.033i	0.117620	+	0.117620i
$945$	250.298	+	433.529i	0.264866	+	0.458761i
$946$	463.513	+	267.610i	0.489972	+	0.282885i
$947$	1580.62	−	423.526i	1.66908	−	0.447229i	0.704220	−	0.709982i	$-0.251297\pi$
$947$	1580.62	−	423.526i	1.66908	−	0.447229i	0.964863	+	0.262753i	$0.0846303\pi$
$948$		−	49.7231i		−	0.0524506i
$949$		0			0
$950$	−692.452			−0.728897
$951$	−7.94417	−	29.6481i	−0.00835349	−	0.0311757i
$952$	−317.229	+	549.458i	−0.333224	+	0.577161i
$953$	374.404	−	216.162i	0.392869	−	0.226823i	−0.290534	−	0.956865i	$-0.593833\pi$
$953$	374.404	−	216.162i	0.392869	−	0.226823i	0.683402	+	0.730042i	$0.260500\pi$
$954$	480.631	−	480.631i	0.503806	−	0.503806i
$955$	−675.279	−	180.940i	−0.707098	−	0.189466i
$956$	145.450	−	542.827i	0.152144	−	0.567811i
$957$	−4.48661	−	4.48661i	−0.00468820	−	0.00468820i
$958$	162.485	+	281.433i	0.169609	+	0.293771i
$959$	−641.629	−	370.445i	−0.669060	−	0.386282i
$960$	−32.7846	+	8.78461i	−0.0341506	+	0.00915064i
$961$		−	128.487i		−	0.133702i
$962$		0			0
$963$	−478.392			−0.496773
$964$	169.340	+	631.985i	0.175664	+	0.655586i
$965$	108.419	−	187.786i	0.112351	−	0.194597i
$966$	−292.613	+	168.940i	−0.302912	+	0.174887i
$967$	−239.455	+	239.455i	−0.247627	+	0.247627i	−0.819996	−	0.572369i	$-0.806024\pi$
$967$	−239.455	+	239.455i	−0.247627	+	0.247627i	0.572369	+	0.819996i	$0.306024\pi$
$968$	258.420	+	69.2436i	0.266963	+	0.0715326i
$969$	329.440	−	1229.49i	0.339980	−	1.26882i
$970$	333.440	+	333.440i	0.343752	+	0.343752i
$971$	93.4864	+	161.923i	0.0962785	+	0.166759i	0.910141	−	0.414298i	$-0.135973\pi$
$971$	93.4864	+	161.923i	0.0962785	+	0.166759i	−0.813863	+	0.581057i	$0.802639\pi$
$972$	−432.000	−	249.415i	−0.444444	−	0.256600i
$973$	−145.854	+	39.0814i	−0.149901	+	0.0401659i
$974$		−	689.686i		−	0.708096i
$975$		0			0
$976$	114.431			0.117245
$977$	−92.0852	−	343.667i	−0.0942530	−	0.351757i	0.902652	−	0.430371i	$-0.141617\pi$
$977$	−92.0852	−	343.667i	−0.0942530	−	0.351757i	−0.996905	+	0.0786139i	$0.974951\pi$
$978$	−30.3032	+	52.4866i	−0.0309848	+	0.0536673i
$979$	240.702	−	138.969i	0.245865	−	0.141950i
$980$	−44.6025	+	44.6025i	−0.0455128	+	0.0455128i
$981$	849.573	+	227.642i	0.866028	+	0.232051i
$982$	191.526	−	714.785i	0.195037	−	0.727887i
$983$	−671.365	−	671.365i	−0.682976	−	0.682976i	0.277694	−	0.960670i	$-0.410430\pi$
$983$	−671.365	−	671.365i	−0.682976	−	0.682976i	−0.960670	+	0.277694i	$0.910430\pi$
$984$	−106.550	−	184.550i	−0.108283	−	0.187551i
$985$	−796.440	−	459.825i	−0.808569	−	0.466827i
$986$	27.7673	−	7.44021i	0.0281615	−	0.00754586i
$987$			635.842i			0.644217i
$988$		0			0
$989$	−1291.36			−1.30572
$990$	−27.6462	−	103.177i	−0.0279254	−	0.104219i
$991$	107.875	−	186.845i	0.108855	−	0.188542i	−0.806452	−	0.591300i	$-0.798615\pi$
$991$	107.875	−	186.845i	0.108855	−	0.188542i	0.915307	+	0.402758i	$0.131948\pi$
$992$	161.703	−	93.3590i	0.163007	−	0.0941119i
$993$	316.935	−	316.935i	0.319169	−	0.319169i
$994$	−78.2698	−	20.9723i	−0.0787423	−	0.0210989i
$995$	−188.715	+	704.293i	−0.189663	+	0.707832i
$996$	−304.277	−	304.277i	−0.305499	−	0.305499i
$997$	862.781	+	1494.38i	0.865377	+	1.49888i	0.866673	+	0.498877i	$0.166254\pi$
$997$	862.781	+	1494.38i	0.865377	+	1.49888i	−0.00129579	+	0.999999i	$0.500412\pi$
$998$	−187.774	−	108.412i	−0.188151	−	0.108629i
$999$	−552.308	+	147.990i	−0.552860	+	0.148139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.3.f.d.19.1		4
13.2	odd	12		26.3.f.a.11.1	✓	4
13.3	even	3		338.3.f.c.249.1		4
13.4	even	6		338.3.d.d.239.1		4
13.5	odd	4		338.3.f.f.319.1		4
13.6	odd	12		338.3.d.d.99.1		4
13.7	odd	12		338.3.d.e.99.1		4
13.8	odd	4		338.3.f.c.319.1		4
13.9	even	3		338.3.d.e.239.1		4
13.10	even	6		338.3.f.f.249.1		4
13.11	odd	12	inner	338.3.f.d.89.1		4
13.12	even	2		26.3.f.a.19.1	yes	4
39.2	even	12		234.3.bb.b.37.1		4
39.38	odd	2		234.3.bb.b.19.1		4
52.15	even	12		208.3.bd.c.193.1		4
52.51	odd	2		208.3.bd.c.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.a.11.1	✓	4	13.2	odd	12
26.3.f.a.19.1	yes	4	13.12	even	2
208.3.bd.c.97.1		4	52.51	odd	2
208.3.bd.c.193.1		4	52.15	even	12
234.3.bb.b.19.1		4	39.38	odd	2
234.3.bb.b.37.1		4	39.2	even	12
338.3.d.d.99.1		4	13.6	odd	12
338.3.d.d.239.1		4	13.4	even	6
338.3.d.e.99.1		4	13.7	odd	12
338.3.d.e.239.1		4	13.9	even	3
338.3.f.c.249.1		4	13.3	even	3
338.3.f.c.319.1		4	13.8	odd	4
338.3.f.d.19.1		4	1.1	even	1	trivial
338.3.f.d.89.1		4	13.11	odd	12	inner
338.3.f.f.249.1		4	13.10	even	6
338.3.f.f.319.1		4	13.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	338.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.03590 - 7.59808i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(3.00000 + 5.19615i) q^{9} +(-3.00000 - 1.73205i) q^{10} +(4.96410 - 1.33013i) q^{11} +3.46410i q^{12} +11.1244 q^{14} +(1.09808 + 4.09808i) q^{15} +(2.00000 - 3.46410i) q^{16} +(24.6962 - 14.2583i) q^{17} +(-6.00000 + 6.00000i) q^{18} +(24.8923 + 6.66987i) q^{19} +(1.26795 - 4.73205i) q^{20} +(-9.63397 - 9.63397i) q^{21} +(3.63397 + 6.29423i) q^{22} +(-15.1865 - 8.76795i) q^{23} +(-4.73205 + 1.26795i) q^{24} +19.0000i q^{25} +25.9808 q^{27} +(4.07180 + 15.1962i) q^{28} +(0.356406 - 0.617314i) q^{29} +(-5.19615 + 3.00000i) q^{30} +(23.3397 - 23.3397i) q^{31} +(5.46410 + 1.46410i) q^{32} +(2.30385 - 8.59808i) q^{33} +(28.5167 + 28.5167i) q^{34} +(9.63397 + 16.6865i) q^{35} +(-10.3923 - 6.00000i) q^{36} +(-21.2583 + 5.69615i) q^{37} +36.4449i q^{38} +6.92820 q^{40} +(11.2583 + 42.0167i) q^{41} +(9.63397 - 16.6865i) q^{42} +(63.7750 - 36.8205i) q^{43} +(-7.26795 + 7.26795i) q^{44} +(-14.1962 - 3.80385i) q^{45} +(6.41858 - 23.9545i) q^{46} +(-33.0000 - 33.0000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-11.1506 - 6.43782i) q^{49} +(-25.9545 + 6.95448i) q^{50} -49.3923i q^{51} -80.1051 q^{53} +(9.50962 + 35.4904i) q^{54} +(-6.29423 + 10.9019i) q^{55} +(-19.2679 + 11.1244i) q^{56} +(31.5622 - 31.5622i) q^{57} +(0.973721 + 0.260908i) q^{58} +(-10.1603 + 37.9186i) q^{59} +(-6.00000 - 6.00000i) q^{60} +(14.3038 + 24.7750i) q^{61} +(40.4256 + 23.3397i) q^{62} +(45.5885 - 12.2154i) q^{63} +8.00000i q^{64} +12.5885 q^{66} +(-12.8397 - 47.9186i) q^{67} +(-28.5167 + 49.3923i) q^{68} +(-26.3038 + 15.1865i) q^{69} +(-19.2679 + 19.2679i) q^{70} +(-7.03590 - 1.88526i) q^{71} +(4.39230 - 16.3923i) q^{72} +(-12.7654 - 12.7654i) q^{73} +(-15.5622 - 26.9545i) q^{74} +(28.5000 + 16.4545i) q^{75} +(-49.7846 + 13.3397i) q^{76} -40.4256i q^{77} -14.3538 q^{79} +(2.53590 + 9.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-53.2750 + 30.7583i) q^{82} +(-87.8372 + 87.8372i) q^{83} +(26.3205 + 7.05256i) q^{84} +(-18.0788 + 67.4711i) q^{85} +(73.6410 + 73.6410i) q^{86} +(-0.617314 - 1.06922i) q^{87} +(-12.5885 - 7.26795i) q^{88} +(52.2391 - 13.9974i) q^{89} -20.7846i q^{90} +35.0718 q^{92} +(-14.7968 - 55.2224i) q^{93} +(33.0000 - 57.1577i) q^{94} +(-54.6673 + 31.5622i) q^{95} +(6.92820 - 6.92820i) q^{96} +(-131.488 - 35.2321i) q^{97} +(4.71281 - 17.5885i) q^{98} +(21.8038 + 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} + 22 q^{7} - 8 q^{8} + 12 q^{9} - 12 q^{10} + 6 q^{11} - 4 q^{14} - 6 q^{15} + 8 q^{16} + 78 q^{17} - 24 q^{18} + 58 q^{19} + 12 q^{20} - 42 q^{21} + 18 q^{22} + 12 q^{23} - 12 q^{24}+ \cdots + 108 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 + 22 * q^7 - 8 * q^8 + 12 * q^9 - 12 * q^10 + 6 * q^11 - 4 * q^14 - 6 * q^15 + 8 * q^16 + 78 * q^17 - 24 * q^18 + 58 * q^19 + 12 * q^20 - 42 * q^21 + 18 * q^22 + 12 * q^23 - 12 * q^24 + 44 * q^28 - 54 * q^29 + 128 * q^31 + 8 * q^32 + 30 * q^33 + 24 * q^34 + 42 * q^35 - 40 * q^37 + 42 * q^42 + 120 * q^43 - 36 * q^44 - 36 * q^45 - 54 * q^46 - 132 * q^47 + 42 * q^49 - 38 * q^50 - 168 * q^53 + 90 * q^54 + 6 * q^55 - 84 * q^56 + 102 * q^57 + 42 * q^58 - 6 * q^59 - 24 * q^60 + 78 * q^61 - 60 * q^62 + 120 * q^63 - 12 * q^66 - 86 * q^67 - 24 * q^68 - 126 * q^69 - 84 * q^70 - 42 * q^71 - 24 * q^72 + 136 * q^73 - 38 * q^74 + 114 * q^75 - 116 * q^76 + 192 * q^79 + 24 * q^80 - 18 * q^81 - 78 * q^82 - 192 * q^83 + 36 * q^84 + 42 * q^85 + 156 * q^86 - 96 * q^87 + 12 * q^88 + 60 * q^89 + 168 * q^92 - 222 * q^93 + 132 * q^94 - 42 * q^95 - 280 * q^97 - 92 * q^98 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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