LMFDB - Embedded newform 338.3.f.c.249.1

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)

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")

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);

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			249.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.249
Dual form			338.3.f.c.319.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-7.59808 + 2.03590i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(3.00000 - 5.19615i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-1.33013 + 4.96410i) q^{11} +3.46410i q^{12} +11.1244 q^{14} +(-4.09808 - 1.09808i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-24.6962 - 14.2583i) q^{17} +(-6.00000 + 6.00000i) q^{18} +(-6.66987 - 24.8923i) q^{19} +(-4.73205 + 1.26795i) q^{20} +(-9.63397 - 9.63397i) q^{21} +(3.63397 - 6.29423i) q^{22} +(15.1865 - 8.76795i) q^{23} +(1.26795 - 4.73205i) q^{24} +19.0000i q^{25} +25.9808 q^{27} +(-15.1962 - 4.07180i) q^{28} +(0.356406 + 0.617314i) q^{29} +(5.19615 + 3.00000i) q^{30} +(23.3397 - 23.3397i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-8.59808 + 2.30385i) q^{33} +(28.5167 + 28.5167i) q^{34} +(9.63397 - 16.6865i) q^{35} +(10.3923 - 6.00000i) q^{36} +(5.69615 - 21.2583i) q^{37} +36.4449i q^{38} +6.92820 q^{40} +(-42.0167 - 11.2583i) q^{41} +(9.63397 + 16.6865i) q^{42} +(-63.7750 - 36.8205i) q^{43} +(-7.26795 + 7.26795i) q^{44} +(3.80385 + 14.1962i) q^{45} +(-23.9545 + 6.41858i) q^{46} +(-33.0000 - 33.0000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(11.1506 - 6.43782i) q^{49} +(6.95448 - 25.9545i) q^{50} -49.3923i q^{51} -80.1051 q^{53} +(-35.4904 - 9.50962i) q^{54} +(-6.29423 - 10.9019i) q^{55} +(19.2679 + 11.1244i) q^{56} +(31.5622 - 31.5622i) q^{57} +(-0.260908 - 0.973721i) q^{58} +(37.9186 - 10.1603i) q^{59} +(-6.00000 - 6.00000i) q^{60} +(14.3038 - 24.7750i) q^{61} +(-40.4256 + 23.3397i) q^{62} +(-12.2154 + 45.5885i) q^{63} +8.00000i q^{64} +12.5885 q^{66} +(47.9186 + 12.8397i) q^{67} +(-28.5167 - 49.3923i) q^{68} +(26.3038 + 15.1865i) q^{69} +(-19.2679 + 19.2679i) q^{70} +(1.88526 + 7.03590i) q^{71} +(-16.3923 + 4.39230i) q^{72} +(-12.7654 - 12.7654i) q^{73} +(-15.5622 + 26.9545i) q^{74} +(-28.5000 + 16.4545i) q^{75} +(13.3397 - 49.7846i) q^{76} -40.4256i q^{77} -14.3538 q^{79} +(-9.46410 - 2.53590i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(53.2750 + 30.7583i) q^{82} +(-87.8372 + 87.8372i) q^{83} +(-7.05256 - 26.3205i) q^{84} +(67.4711 - 18.0788i) q^{85} +(73.6410 + 73.6410i) q^{86} +(-0.617314 + 1.06922i) q^{87} +(12.5885 - 7.26795i) q^{88} +(-13.9974 + 52.2391i) q^{89} -20.7846i q^{90} +35.0718 q^{92} +(55.2224 + 14.7968i) q^{93} +(33.0000 + 57.1577i) q^{94} +(54.6673 + 31.5622i) q^{95} +(6.92820 - 6.92820i) q^{96} +(35.2321 + 131.488i) q^{97} +(-17.5885 + 4.71281i) q^{98} +(21.8038 + 21.8038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 6 q^{6} - 20 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{10} + 12 q^{11} - 4 q^{14} - 6 q^{15} + 8 q^{16} - 78 q^{17} - 24 q^{18} - 44 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 - 20 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^10 + 12 * q^11 - 4 * q^14 - 6 * q^15 + 8 * q^16 - 78 * q^17 - 24 * q^18 - 44 * q^19 - 12 * q^20 - 42 * q^21 + 18 * q^22 - 12 * q^23 + 12 * q^24 - 40 * q^28 - 54 * q^29 + 128 * q^31 + 8 * q^32 - 24 * q^33 + 24 * q^34 + 42 * q^35 + 2 * q^37 - 78 * q^41 + 42 * q^42 - 120 * q^43 - 36 * q^44 + 36 * q^45 - 30 * 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 - 150 * q^58 + 72 * q^59 - 24 * q^60 + 78 * q^61 + 60 * q^62 - 132 * q^63 - 12 * q^66 + 112 * q^67 - 24 * q^68 + 126 * q^69 - 84 * q^70 + 108 * q^71 - 24 * q^72 + 136 * q^73 - 38 * q^74 - 114 * q^75 + 88 * q^76 + 192 * q^79 - 24 * q^80 - 18 * q^81 + 78 * q^82 - 192 * q^83 + 48 * q^84 + 114 * q^85 + 156 * q^86 - 96 * q^87 - 12 * q^88 + 138 * q^89 + 168 * q^92 + 162 * q^93 + 132 * q^94 + 42 * q^95 + 134 * q^97 - 8 * q^98 + 108 * q^99

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$2$	−1.36603	−	0.366025i	−0.683013	−	0.183013i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i	0.973494	−	0.228714i	$-0.0734519\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	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	$0.328771\pi$
$6$	−0.633975	−	2.36603i	−0.105662	−	0.394338i
$7$	−7.59808	+	2.03590i	−1.08544	+	0.290843i	−0.756822	−	0.653621i	$-0.773249\pi$
$7$	−7.59808	+	2.03590i	−1.08544	+	0.290843i	−0.328617	+	0.944463i	$0.606583\pi$
$8$	−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
$11$	−1.33013	+	4.96410i	−0.120921	+	0.451282i	−0.999661	−	0.0260172i	$-0.991718\pi$
$11$	−1.33013	+	4.96410i	−0.120921	+	0.451282i	0.878741	+	0.477299i	$0.158384\pi$
$12$			3.46410i			0.288675i
$13$		0			0
$13$		0			0
$14$	11.1244			0.794597
$15$	−4.09808	−	1.09808i	−0.273205	−	0.0732051i
$16$	2.00000	+	3.46410i	0.125000	+	0.216506i
$17$	−24.6962	−	14.2583i	−1.45271	−	0.838725i	−0.454080	−	0.890961i	$-0.650032\pi$
$17$	−24.6962	−	14.2583i	−1.45271	−	0.838725i	−0.998635	+	0.0522356i	$0.983365\pi$
$18$	−6.00000	+	6.00000i	−0.333333	+	0.333333i
$19$	−6.66987	−	24.8923i	−0.351046	−	1.31012i	−0.885388	−	0.464853i	$-0.846107\pi$
$19$	−6.66987	−	24.8923i	−0.351046	−	1.31012i	0.534342	−	0.845268i	$-0.320559\pi$
$20$	−4.73205	+	1.26795i	−0.236603	+	0.0633975i
$21$	−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	$-0.542172\pi$
$23$	15.1865	−	8.76795i	0.660284	−	0.381215i	0.792385	+	0.610021i	$0.208839\pi$
$24$	1.26795	−	4.73205i	0.0528312	−	0.197169i
$25$			19.0000i			0.760000i
$26$		0			0
$27$	25.9808			0.962250
$28$	−15.1962	−	4.07180i	−0.542720	−	0.145421i
$29$	0.356406	+	0.617314i	0.0122899	+	0.0212867i	0.872105	−	0.489319i	$-0.162755\pi$
$29$	0.356406	+	0.617314i	0.0122899	+	0.0212867i	−0.859815	+	0.510606i	$0.829421\pi$
$30$	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	$0.0712988\pi$
$32$	−1.46410	−	5.46410i	−0.0457532	−	0.170753i
$33$	−8.59808	+	2.30385i	−0.260548	+	0.0698136i
$34$	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
$37$	5.69615	−	21.2583i	0.153950	−	0.574549i	−0.845243	−	0.534382i	$-0.820544\pi$
$37$	5.69615	−	21.2583i	0.153950	−	0.574549i	0.999193	−	0.0401672i	$-0.0127891\pi$
$38$			36.4449i			0.959075i
$39$		0			0
$40$	6.92820			0.173205
$41$	−42.0167	−	11.2583i	−1.02480	−	0.274593i	−0.292997	−	0.956113i	$-0.594653\pi$
$41$	−42.0167	−	11.2583i	−1.02480	−	0.274593i	−0.731800	+	0.681520i	$0.761319\pi$
$42$	9.63397	+	16.6865i	0.229380	+	0.397298i
$43$	−63.7750	−	36.8205i	−1.48314	−	0.856291i	−0.483323	−	0.875442i	$-0.660570\pi$
$43$	−63.7750	−	36.8205i	−1.48314	−	0.856291i	−0.999817	+	0.0191514i	$0.993904\pi$
$44$	−7.26795	+	7.26795i	−0.165181	+	0.165181i
$45$	3.80385	+	14.1962i	0.0845299	+	0.315470i
$46$	−23.9545	+	6.41858i	−0.520750	+	0.139534i
$47$	−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
$50$	6.95448	−	25.9545i	0.139090	−	0.519090i
$51$		−	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	$0.772707\pi$
$54$	−35.4904	−	9.50962i	−0.657229	−	0.176104i
$55$	−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
$58$	−0.260908	−	0.973721i	−0.00449841	−	0.0167883i
$59$	37.9186	−	10.1603i	0.642688	−	0.172208i	0.0772673	−	0.997010i	$-0.475381\pi$
$59$	37.9186	−	10.1603i	0.642688	−	0.172208i	0.565421	+	0.824803i	$0.308714\pi$
$60$	−6.00000	−	6.00000i	−0.100000	−	0.100000i
$61$	14.3038	−	24.7750i	0.234489	−	0.406147i	−0.724635	−	0.689133i	$-0.757992\pi$
$61$	14.3038	−	24.7750i	0.234489	−	0.406147i	0.959124	+	0.282986i	$0.0913249\pi$
$62$	−40.4256	+	23.3397i	−0.652026	+	0.376448i
$63$	−12.2154	+	45.5885i	−0.193895	+	0.723626i
$64$			8.00000i			0.125000i
$65$		0			0
$66$	12.5885			0.190734
$67$	47.9186	+	12.8397i	0.715203	+	0.191638i	0.598030	−	0.801474i	$-0.295950\pi$
$67$	47.9186	+	12.8397i	0.715203	+	0.191638i	0.117173	+	0.993112i	$0.462617\pi$
$68$	−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
$71$	1.88526	+	7.03590i	0.0265530	+	0.0990972i	0.977931	−	0.208930i	$-0.0669980\pi$
$71$	1.88526	+	7.03590i	0.0265530	+	0.0990972i	−0.951378	+	0.308027i	$0.900331\pi$
$72$	−16.3923	+	4.39230i	−0.227671	+	0.0610042i
$73$	−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
$76$	13.3397	−	49.7846i	0.175523	−	0.655061i
$77$		−	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	$0.528957\pi$
$80$	−9.46410	−	2.53590i	−0.118301	−	0.0316987i
$81$	−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	$0.980863\pi$
$84$	−7.05256	−	26.3205i	−0.0839590	−	0.313339i
$85$	67.4711	−	18.0788i	0.793778	−	0.212692i
$86$	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
$89$	−13.9974	+	52.2391i	−0.157274	+	0.586956i	0.841625	+	0.540062i	$0.181599\pi$
$89$	−13.9974	+	52.2391i	−0.157274	+	0.586956i	−0.998900	+	0.0468944i	$0.985068\pi$
$90$		−	20.7846i		−	0.230940i
$91$		0			0
$92$	35.0718			0.381215
$93$	55.2224	+	14.7968i	0.593790	+	0.159105i
$94$	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
$97$	35.2321	+	131.488i	0.363217	+	1.35554i	0.869822	+	0.493366i	$0.164234\pi$
$97$	35.2321	+	131.488i	0.363217	+	1.35554i	−0.506605	+	0.862178i	$0.669100\pi$
$98$	−17.5885	+	4.71281i	−0.179474	+	0.0480899i
$99$	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	$-0.765114\pi$
$101$	−53.2461	+	30.7417i	−0.527189	+	0.304373i	0.212682	+	0.977122i	$0.431780\pi$
$102$	−18.0788	+	67.4711i	−0.177244	+	0.661482i
$103$			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
$106$	109.426	+	29.3205i	1.03232	+	0.276609i
$107$	−39.8660	−	69.0500i	−0.372580	−	0.645327i	0.617382	−	0.786664i	$-0.288193\pi$
$107$	−39.8660	−	69.0500i	−0.372580	−	0.645327i	−0.989962	+	0.141337i	$0.954860\pi$
$108$	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	$0.0152492\pi$
$110$	4.60770	+	17.1962i	0.0418881	+	0.156329i
$111$	36.8205	−	9.86603i	0.331716	−	0.0888831i
$112$	−22.2487	−	22.2487i	−0.198649	−	0.198649i
$113$	−88.5000	+	153.286i	−0.783186	+	1.35652i	0.146891	+	0.989153i	$0.453073\pi$
$113$	−88.5000	+	153.286i	−0.783186	+	1.35652i	−0.930077	+	0.367365i	$0.880260\pi$
$114$	−54.6673	+	31.5622i	−0.479538	+	0.276861i
$115$	−11.1173	+	41.4904i	−0.0966723	+	0.360786i
$116$			1.42563i			0.0122899i
$117$		0			0
$118$	−55.5167			−0.470480
$119$	216.672	+	58.0570i	1.82077	+	0.487874i
$120$	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
$123$	−19.5000	−	72.7750i	−0.158537	−	0.591667i
$124$	63.7654	−	17.0859i	0.514237	−	0.137789i
$125$	−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	$-0.432433\pi$
$127$	147.651	−	85.2461i	1.16260	−	0.671229i	0.951927	+	0.306326i	$0.0990999\pi$
$128$	2.92820	−	10.9282i	0.0228766	−	0.0853766i
$129$		−	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	$0.554761\pi$
$132$	−17.1962	−	4.60770i	−0.130274	−	0.0349068i
$133$	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
$136$	20.8756	+	77.9090i	0.153497	+	0.572860i
$137$	−90.9782	+	24.3775i	−0.664074	+	0.177938i	−0.575084	−	0.818094i	$-0.695031\pi$
$137$	−90.9782	+	24.3775i	−0.664074	+	0.177938i	−0.0889903	+	0.996032i	$0.528364\pi$
$138$	−30.3731	−	30.3731i	−0.220095	−	0.220095i
$139$	−9.59808	+	16.6244i	−0.0690509	+	0.119600i	−0.898484	−	0.439007i	$-0.855330\pi$
$139$	−9.59808	+	16.6244i	−0.0690509	+	0.119600i	0.829433	+	0.558606i	$0.188664\pi$
$140$	33.3731	−	19.2679i	0.238379	−	0.137628i
$141$	20.9212	−	78.0788i	0.148377	−	0.553751i
$142$		−	10.3013i		−	0.0725442i
$143$		0			0
$144$	24.0000			0.166667
$145$	−1.68653	−	0.451905i	−0.0116313	−	0.00311659i
$146$	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
$149$	9.66283	+	36.0622i	0.0648512	+	0.242028i	0.990741	−	0.135766i	$-0.0433495\pi$
$149$	9.66283	+	36.0622i	0.0648512	+	0.242028i	−0.925890	+	0.377794i	$0.876683\pi$
$150$	44.9545	−	12.0455i	0.299697	−	0.0803034i
$151$	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
$154$	−14.7968	+	55.2224i	−0.0960832	+	0.358587i
$155$			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	$0.514634\pi$
$158$	19.6077	+	5.25387i	0.124099	+	0.0332523i
$159$	−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
$162$	3.29423	+	12.2942i	0.0203347	+	0.0758903i
$163$	23.8993	−	6.40381i	0.146622	−	0.0392872i	−0.184762	−	0.982783i	$-0.559151\pi$
$163$	23.8993	−	6.40381i	0.146622	−	0.0392872i	0.331383	+	0.943496i	$0.392485\pi$
$164$	−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
$167$	15.1865	−	56.6769i	0.0909373	−	0.339383i	−0.905435	−	0.424485i	$-0.860455\pi$
$167$	15.1865	−	56.6769i	0.0909373	−	0.339383i	0.996372	+	0.0851025i	$0.0271218\pi$
$168$			38.5359i			0.229380i
$169$		0			0
$170$	−98.7846			−0.581086
$171$	−149.354	−	40.0192i	−0.873414	−	0.234031i
$172$	−73.6410	−	127.550i	−0.428145	−	0.741570i
$173$	62.1462	+	35.8801i	0.359226	+	0.207399i	0.668741	−	0.743495i	$-0.266833\pi$
$173$	62.1462	+	35.8801i	0.359226	+	0.207399i	−0.309515	+	0.950895i	$0.600167\pi$
$174$	1.23463	−	1.23463i	0.00709556	−	0.00709556i
$175$	−38.6821	−	144.363i	−0.221040	−	0.824934i
$176$	−19.8564	+	5.32051i	−0.112820	+	0.0302302i
$177$	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	$-0.814819\pi$
$179$	−139.148	+	80.3372i	−0.777363	+	0.448811i	0.0581316	+	0.998309i	$0.481486\pi$
$180$	−7.60770	+	28.3923i	−0.0422650	+	0.157735i
$181$			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
$184$	−47.9090	−	12.8372i	−0.260375	−	0.0697672i
$185$	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
$188$	−24.1577	−	90.1577i	−0.128498	−	0.479562i
$189$	−197.404	+	52.8942i	−1.04446	+	0.279863i
$190$	−63.1244	−	63.1244i	−0.332233	−	0.332233i
$191$	142.703	−	247.169i	0.747137	−	1.29408i	−0.202052	−	0.979375i	$-0.564761\pi$
$191$	142.703	−	247.169i	0.747137	−	1.29408i	0.949190	−	0.314705i	$-0.101906\pi$
$192$	−12.0000	+	6.92820i	−0.0625000	+	0.0360844i
$193$	22.9115	−	85.5070i	0.118713	−	0.443042i	−0.880825	−	0.473442i	$-0.843011\pi$
$193$	22.9115	−	85.5070i	0.118713	−	0.443042i	0.999538	+	0.0304000i	$0.00967812\pi$
$194$		−	192.512i		−	0.992327i
$195$		0			0
$196$	25.7513			0.131384
$197$	−362.653	−	97.1725i	−1.84088	−	0.493261i	−0.841948	−	0.539559i	$-0.818591\pi$
$197$	−362.653	−	97.1725i	−1.84088	−	0.493261i	−0.998928	+	0.0462974i	$0.985258\pi$
$198$	−21.8038	−	37.7654i	−0.110120	−	0.190734i
$199$	−257.789	−	148.835i	−1.29542	−	0.747913i	−0.315813	−	0.948822i	$-0.602277\pi$
$199$	−257.789	−	148.835i	−1.29542	−	0.747913i	−0.979610	+	0.200909i	$0.935610\pi$
$200$	38.0000	−	38.0000i	0.190000	−	0.190000i
$201$	22.2391	+	82.9974i	0.110642	+	0.412923i
$202$	83.9878	−	22.5045i	0.415781	−	0.111408i
$203$	−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
$206$	8.53590	−	31.8564i	0.0414364	−	0.154643i
$207$		−	105.215i		−	0.508287i
$208$		0			0
$209$	132.440			0.633683
$210$	−45.5885	−	12.2154i	−0.217088	−	0.0581685i
$211$	−27.2532	−	47.2039i	−0.129162	−	0.223715i	0.794190	−	0.607669i	$-0.207895\pi$
$211$	−27.2532	−	47.2039i	−0.129162	−	0.223715i	−0.923352	+	0.383954i	$0.874562\pi$
$212$	−138.746	−	80.1051i	−0.654463	−	0.377854i
$213$	−8.92116	+	8.92116i	−0.0418834	+	0.0418834i
$214$	29.1840	+	108.916i	0.136374	+	0.508953i
$215$	174.237	−	46.6865i	0.810402	−	0.217147i
$216$	−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
$219$	8.09292	−	30.2032i	0.0369540	−	0.137914i
$220$		−	25.1769i		−	0.114441i
$221$		0			0
$222$	−53.9090			−0.242833
$223$	−147.024	−	39.3949i	−0.659299	−	0.176659i	−0.0863694	−	0.996263i	$-0.527527\pi$
$223$	−147.024	−	39.3949i	−0.659299	−	0.176659i	−0.572930	+	0.819605i	$0.694193\pi$
$224$	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
$227$	−55.7276	−	207.978i	−0.245496	−	0.916203i	−0.973133	−	0.230242i	$-0.926048\pi$
$227$	−55.7276	−	207.978i	−0.245496	−	0.916203i	0.727638	−	0.685962i	$-0.240618\pi$
$228$	86.2295	−	23.1051i	0.378199	−	0.101338i
$229$	−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
$232$	0.521815	−	1.94744i	0.00224920	−	0.00839414i
$233$			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
$236$	75.8372	+	20.3205i	0.321344	+	0.0861038i
$237$	−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	$0.450022\pi$
$240$	−4.39230	−	16.3923i	−0.0183013	−	0.0683013i
$241$	−315.992	+	84.6699i	−1.31117	+	0.351327i	−0.845663	−	0.533717i	$-0.820795\pi$
$241$	−315.992	+	84.6699i	−1.31117	+	0.351327i	−0.465508	+	0.885044i	$0.654128\pi$
$242$	−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
$245$	−8.16283	+	30.4641i	−0.0333177	+	0.124343i
$246$			106.550i			0.433130i
$247$		0			0
$248$	−93.3590			−0.376448
$249$	−207.825	−	55.6865i	−0.834638	−	0.223641i
$250$	76.2102	+	132.000i	0.304841	+	0.528000i
$251$	134.267	+	77.5192i	0.534929	+	0.308842i	0.743021	−	0.669268i	$-0.233392\pi$
$251$	134.267	+	77.5192i	0.534929	+	0.308842i	−0.208092	+	0.978109i	$0.566725\pi$
$252$	−66.7461	+	66.7461i	−0.264866	+	0.264866i
$253$	23.3250	+	87.0500i	0.0921936	+	0.344071i
$254$	−232.897	+	62.4045i	−0.916916	+	0.245687i
$255$	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	$-0.466343\pi$
$257$	262.012	−	151.272i	1.01950	−	0.588609i	0.913959	+	0.405806i	$0.133009\pi$
$258$	−46.6865	+	174.237i	−0.180956	+	0.675335i
$259$			173.119i			0.668414i
$260$		0			0
$261$	4.27688			0.0163865
$262$	61.2679	+	16.4167i	0.233847	+	0.0626592i
$263$	−25.2968	−	43.8154i	−0.0961856	−	0.166598i	0.813917	−	0.580981i	$-0.197331\pi$
$263$	−25.2968	−	43.8154i	−0.0961856	−	0.166598i	−0.910103	+	0.414383i	$0.863998\pi$
$264$	21.8038	+	12.5885i	0.0825903	+	0.0476836i
$265$	138.746	−	138.746i	0.523570	−	0.523570i
$266$	−74.1980	−	276.911i	−0.278940	−	1.04102i
$267$	−90.4808	+	24.2442i	−0.338879	+	0.0908024i
$268$	70.1577	+	70.1577i	0.261782	+	0.261782i
$269$	21.4474	−	37.1481i	0.0797303	−	0.138097i	−0.823403	−	0.567457i	$-0.807927\pi$
$269$	21.4474	−	37.1481i	0.0797303	−	0.138097i	0.903134	+	0.429360i	$0.141261\pi$
$270$	77.9423	−	45.0000i	0.288675	−	0.166667i
$271$	128.244	−	478.614i	0.473226	−	1.76610i	−0.154836	−	0.987940i	$-0.549485\pi$
$271$	128.244	−	478.614i	0.473226	−	1.76610i	0.628062	−	0.778163i	$-0.283848\pi$
$272$		−	114.067i		−	0.419363i
$273$		0			0
$274$	133.201			0.486136
$275$	−94.3179	−	25.2724i	−0.342974	−	0.0918997i
$276$	30.3731	+	52.6077i	0.110047	+	0.190608i
$277$	−184.227	−	106.363i	−0.665079	−	0.383984i	0.129130	−	0.991628i	$-0.458781\pi$
$277$	−184.227	−	106.363i	−0.665079	−	0.383984i	−0.794209	+	0.607644i	$0.792115\pi$
$278$	19.1962	−	19.1962i	0.0690509	−	0.0690509i
$279$	−51.2576	−	191.296i	−0.183719	−	0.685649i
$280$	−52.6410	+	14.1051i	−0.188004	+	0.0503754i
$281$	−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	$-0.583561\pi$
$283$	126.526	−	73.0500i	0.447089	−	0.258127i	0.706600	+	0.707613i	$0.250228\pi$
$284$	−3.77053	+	14.0718i	−0.0132765	+	0.0495486i
$285$			109.335i			0.383630i
$286$		0			0
$287$	342.167			1.19222
$288$	−32.7846	−	8.78461i	−0.113835	−	0.0305021i
$289$	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
$292$	−9.34490	−	34.8756i	−0.0320031	−	0.119437i
$293$	94.5000	−	25.3212i	0.322526	−	0.0864205i	−0.0939237	−	0.995579i	$-0.529941\pi$
$293$	94.5000	−	25.3212i	0.322526	−	0.0864205i	0.416449	+	0.909159i	$0.363274\pi$
$294$	−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
$297$	−34.5577	+	128.971i	−0.116356	+	0.434246i
$298$		−	52.7987i		−	0.177177i
$299$		0			0
$300$	−65.8179			−0.219393
$301$	559.530	+	149.926i	1.85890	+	0.498092i
$302$	−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
$305$	18.1366	+	67.6865i	0.0594641	+	0.221923i
$306$	233.727	−	62.6269i	0.763813	−	0.204663i
$307$	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
$310$	29.5936	−	110.445i	0.0954633	−	0.356274i
$311$		−	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	$0.517877\pi$
$314$	19.7128	+	5.28203i	0.0627797	+	0.0168218i
$315$	−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	$0.241102\pi$
$318$	50.7846	+	189.531i	0.159700	+	0.596009i
$319$	−3.53848	+	0.948132i	−0.0110924	+	0.00297220i
$320$	−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
$323$	−190.203	+	709.845i	−0.588862	+	2.19766i
$324$		−	18.0000i		−	0.0555556i
$325$		0			0
$326$	−34.9911			−0.107335
$327$	245.251	+	65.7147i	0.750002	+	0.200962i
$328$	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
$331$	−66.9763	−	249.959i	−0.202345	−	0.755163i	−0.990242	−	0.139356i	$-0.955497\pi$
$331$	−66.9763	−	249.959i	−0.202345	−	0.755163i	0.787897	−	0.615807i	$-0.211170\pi$
$332$	−239.976	+	64.3013i	−0.722818	+	0.193679i
$333$	−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
$336$	14.1051	−	52.6410i	0.0419795	−	0.156670i
$337$		−	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
$340$	134.942	+	36.1577i	0.396889	+	0.106346i
$341$	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
$344$	53.9090	+	201.191i	0.156712	+	0.584858i
$345$	−71.8634	+	19.2558i	−0.208300	+	0.0558138i
$346$	−71.7602	−	71.7602i	−0.207399	−	0.207399i
$347$	−52.2302	+	90.4653i	−0.150519	+	0.260707i	−0.931418	−	0.363950i	$-0.881428\pi$
$347$	−52.2302	+	90.4653i	−0.150519	+	0.260707i	0.780899	+	0.624657i	$0.214761\pi$
$348$	−2.13844	+	1.23463i	−0.00614494	+	0.00354778i
$349$	−20.9205	+	78.0763i	−0.0599440	+	0.223714i	−0.989399	−	0.145221i	$-0.953611\pi$
$349$	−20.9205	+	78.0763i	−0.0599440	+	0.223714i	0.929455	+	0.368935i	$0.120277\pi$
$350$			211.363i			0.603894i
$351$		0			0
$352$	29.0718			0.0825903
$353$	−164.744	−	44.1429i	−0.466696	−	0.125051i	0.0178053	−	0.999841i	$-0.494332\pi$
$353$	−164.744	−	44.1429i	−0.466696	−	0.125051i	−0.484501	+	0.874791i	$0.660999\pi$
$354$	−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
$357$	100.558	+	375.286i	0.281674	+	1.05122i
$358$	219.485	−	58.8109i	0.613087	−	0.164276i
$359$	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
$362$	52.3679	−	195.440i	0.144663	−	0.539889i
$363$			163.832i			0.451328i
$364$		0			0
$365$	44.2205			0.121152
$366$	−67.6865	−	18.1366i	−0.184936	−	0.0495534i
$367$	−238.856	−	413.710i	−0.650833	−	1.12728i	−0.982921	−	0.184027i	$-0.941086\pi$
$367$	−238.856	−	413.710i	−0.650833	−	1.12728i	0.332088	−	0.943248i	$-0.392247\pi$
$368$	60.7461	+	35.0718i	0.165071	+	0.0953038i
$369$	−184.550	+	184.550i	−0.500135	+	0.500135i
$370$	−19.7321	−	73.6410i	−0.0533299	−	0.199030i
$371$	608.645	−	163.086i	1.64055	−	0.439585i
$372$	80.8513	+	80.8513i	0.217342	+	0.217342i
$373$	−257.744	+	446.425i	−0.691001	+	1.19685i	0.280509	+	0.959852i	$0.409497\pi$
$373$	−257.744	+	446.425i	−0.691001	+	1.19685i	−0.971510	+	0.236998i	$0.923836\pi$
$374$	−179.490	+	103.629i	−0.479921	+	0.277082i
$375$	48.3154	−	180.315i	0.128841	−	0.480841i
$376$			132.000i			0.351064i
$377$		0			0
$378$	289.019			0.764601
$379$	264.397	+	70.8449i	0.697617	+	0.186926i	0.590163	−	0.807284i	$-0.299064\pi$
$379$	264.397	+	70.8449i	0.697617	+	0.186926i	0.107454	+	0.994210i	$0.465730\pi$
$380$	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
$383$	121.057	+	451.791i	0.316076	+	1.17961i	0.922984	+	0.384839i	$0.125743\pi$
$383$	121.057	+	451.791i	0.316076	+	1.17961i	−0.606908	+	0.794772i	$0.707590\pi$
$384$	18.9282	−	5.07180i	0.0492922	−	0.0132078i
$385$	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
$388$	−70.4641	+	262.976i	−0.181609	+	0.677772i
$389$		−	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
$392$	−35.1769	−	9.42563i	−0.0897370	−	0.0240450i
$393$	−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
$396$	15.9615	+	59.5692i	0.0403069	+	0.150427i
$397$	59.0692	−	15.8275i	0.148789	−	0.0398679i	−0.183656	−	0.982991i	$-0.558793\pi$
$397$	59.0692	−	15.8275i	0.148789	−	0.0398679i	0.332445	+	0.943123i	$0.392127\pi$
$398$	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
$401$	139.815	−	521.798i	0.348667	−	1.30124i	−0.539603	−	0.841920i	$-0.681426\pi$
$401$	139.815	−	521.798i	0.348667	−	1.30124i	0.888270	−	0.459322i	$-0.151908\pi$
$402$		−	121.517i		−	0.302280i
$403$		0			0
$404$	−122.967			−0.304373
$405$	21.2942	+	5.70577i	0.0525783	+	0.0140883i
$406$	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
$409$	−5.36533	−	20.0237i	−0.0131182	−	0.0489577i	0.959057	−	0.283215i	$-0.0914009\pi$
$409$	−5.36533	−	20.0237i	−0.0131182	−	0.0489577i	−0.972175	+	0.234257i	$0.924734\pi$
$410$	−145.550	+	39.0000i	−0.355000	+	0.0951220i
$411$	−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
$414$	−38.5115	+	143.727i	−0.0930230	+	0.347166i
$415$		−	304.277i		−	0.733197i
$416$		0			0
$417$	−33.2487			−0.0797331
$418$	−180.916	−	48.4763i	−0.432813	−	0.115972i
$419$	−173.598	−	300.681i	−0.414315	−	0.717615i	0.581041	−	0.813874i	$-0.302646\pi$
$419$	−173.598	−	300.681i	−0.414315	−	0.717615i	−0.995356	+	0.0962592i	$0.969312\pi$
$420$	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	$0.0901667\pi$
$422$	19.9507	+	74.4571i	0.0472766	+	0.176439i
$423$	−270.473	+	72.4730i	−0.639416	+	0.171331i
$424$	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
$427$	−58.2424	+	217.363i	−0.136399	+	0.509048i
$428$		−	159.464i		−	0.372580i
$429$		0			0
$430$	−255.100			−0.593256
$431$	296.176	+	79.3602i	0.687184	+	0.184130i	0.585483	−	0.810685i	$-0.300905\pi$
$431$	296.176	+	79.3602i	0.687184	+	0.184130i	0.101701	+	0.994815i	$0.467572\pi$
$432$	51.9615	+	90.0000i	0.120281	+	0.208333i
$433$	73.2757	+	42.3057i	0.169228	+	0.0977038i	0.582222	−	0.813030i	$-0.302184\pi$
$433$	73.2757	+	42.3057i	0.169228	+	0.0977038i	−0.412994	+	0.910734i	$0.635517\pi$
$434$	259.640	−	259.640i	0.598248	−	0.598248i
$435$	−0.782723	−	2.92116i	−0.00179936	−	0.00671531i
$436$	283.191	−	75.8808i	0.649521	−	0.174039i
$437$	−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	$-0.500189\pi$
$439$	379.794	−	219.274i	0.865135	−	0.499486i	0.865728	+	0.500514i	$0.166856\pi$
$440$	−9.21539	+	34.3923i	−0.0209441	+	0.0781643i
$441$		−	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	$0.619103\pi$
$444$	73.6410	+	19.7321i	0.165858	+	0.0444416i
$445$	−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
$448$	−16.2872	−	60.7846i	−0.0363553	−	0.135680i
$449$	341.528	−	91.5122i	0.760642	−	0.203813i	0.142408	−	0.989808i	$-0.454515\pi$
$449$	341.528	−	91.5122i	0.760642	−	0.203813i	0.618233	+	0.785995i	$0.287849\pi$
$450$	−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
$453$	−102.328	+	381.892i	−0.225889	+	0.843028i
$454$			304.501i			0.670707i
$455$		0			0
$456$	−126.249			−0.276861
$457$	257.050	+	68.8763i	0.562473	+	0.150714i	0.528842	−	0.848720i	$-0.322626\pi$
$457$	257.050	+	68.8763i	0.562473	+	0.150714i	0.0336305	+	0.999434i	$0.489293\pi$
$458$	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
$461$	38.9923	+	145.521i	0.0845819	+	0.315664i	0.995235	−	0.0975085i	$-0.0310873\pi$
$461$	38.9923	+	145.521i	0.0845819	+	0.315664i	−0.910653	+	0.413173i	$0.864421\pi$
$462$	−95.6481	+	25.6288i	−0.207030	+	0.0554736i
$463$	−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
$466$	145.335	−	542.396i	0.311877	−	1.16394i
$467$		−	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
$470$	−156.158	−	41.8423i	−0.332250	−	0.0890262i
$471$	−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
$474$	9.09996	+	33.9615i	0.0191982	+	0.0716488i
$475$	472.954	−	126.728i	0.995692	−	0.266795i
$476$	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
$479$	−59.4737	+	221.959i	−0.124162	+	0.463380i	−0.999808	−	0.0195733i	$-0.993769\pi$
$479$	−59.4737	+	221.959i	−0.124162	+	0.463380i	0.875646	+	0.482953i	$0.160436\pi$
$480$			24.0000i			0.0500000i
$481$		0			0
$482$	462.645			0.959844
$483$	−230.777	−	61.8365i	−0.477799	−	0.128026i
$484$	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
$487$	126.221	+	471.064i	0.259181	+	0.967277i	0.965716	+	0.259599i	$0.0835905\pi$
$487$	126.221	+	471.064i	0.259181	+	0.967277i	−0.706535	+	0.707678i	$0.749743\pi$
$488$	−78.1577	+	20.9423i	−0.160159	+	0.0429145i
$489$	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	$-0.487788\pi$
$491$	453.156	−	261.630i	0.922924	−	0.532850i	0.884567	+	0.466414i	$0.154454\pi$
$492$	39.0000	−	145.550i	0.0792683	−	0.295833i
$493$		−	20.3270i		−	0.0412313i
$494$		0			0
$495$	−75.5307			−0.152587
$496$	127.531	+	34.1718i	0.257118	+	0.0688947i
$497$	−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	$0.299095\pi$
$500$	−55.7898	−	208.210i	−0.111580	−	0.416420i
$501$	98.1673	−	26.3038i	0.195943	−	0.0525027i
$502$	−155.038	−	155.038i	−0.308842	−	0.308842i
$503$	202.861	−	351.365i	0.403302	−	0.698539i	−0.590820	−	0.806803i	$-0.701196\pi$
$503$	202.861	−	351.365i	0.403302	−	0.698539i	0.994122	+	0.108264i	$0.0345291\pi$
$504$	115.608	−	66.7461i	0.229380	−	0.132433i
$505$	38.9789	−	145.471i	0.0771859	−	0.288062i
$506$		−	127.450i		−	0.251878i
$507$		0			0
$508$	340.985			0.671229
$509$	−149.586	−	40.0814i	−0.293882	−	0.0787454i	0.108866	−	0.994056i	$-0.465278\pi$
$509$	−149.586	−	40.0814i	−0.293882	−	0.0787454i	−0.402748	+	0.915311i	$0.631945\pi$
$510$	−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
$513$	−173.288	−	646.721i	−0.337794	−	1.26066i
$514$	−413.284	+	110.739i	−0.804054	+	0.215446i
$515$	−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
$518$	63.3660	−	236.485i	0.122328	−	0.456535i
$519$			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	$0.573865\pi$
$522$	−5.84232	−	1.56545i	−0.0111922	−	0.00299894i
$523$	497.663	+	861.978i	0.951555	+	1.64814i	0.742061	+	0.670332i	$0.233848\pi$
$523$	497.663	+	861.978i	0.951555	+	1.64814i	0.209494	+	0.977810i	$0.432818\pi$
$524$	−77.6846	−	44.8513i	−0.148253	−	0.0855940i
$525$	183.046	−	183.046i	0.348658	−	0.348658i
$526$	18.5185	+	69.1122i	0.0352064	+	0.131392i
$527$	−909.188	+	243.616i	−1.72521	+	0.462270i
$528$	−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
$531$	60.9615	−	227.512i	0.114805	−	0.428459i
$532$			405.426i			0.762078i
$533$		0			0
$534$	132.473			0.248077
$535$	188.648	+	50.5481i	0.352613	+	0.0944824i
$536$	−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
$539$	17.1262	+	63.9160i	0.0317741	+	0.118583i
$540$	−122.942	+	32.9423i	−0.227671	+	0.0610042i
$541$	−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
$544$	−41.7513	+	155.818i	−0.0767487	+	0.286430i
$545$			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	$0.158072\pi$
$548$	−181.956	−	48.7551i	−0.332037	−	0.0889691i
$549$	−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
$552$	−22.2346	−	82.9808i	−0.0402801	−	0.150327i
$553$	109.061	−	29.2229i	0.197218	−	0.0528444i
$554$	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
$557$	−195.581	+	729.917i	−0.351132	+	1.31044i	0.534150	+	0.845390i	$0.320632\pi$
$557$	−195.581	+	729.917i	−0.351132	+	1.31044i	−0.885282	+	0.465054i	$0.846035\pi$
$558$			280.077i			0.501930i
$559$		0			0
$560$	77.0718			0.137628
$561$	245.188	+	65.6980i	0.437056	+	0.117109i
$562$	27.2243	+	47.1539i	0.0484418	+	0.0839037i
$563$	26.1250	+	15.0833i	0.0464033	+	0.0267909i	0.523022	−	0.852319i	$-0.324804\pi$
$563$	26.1250	+	15.0833i	0.0464033	+	0.0267909i	−0.476619	+	0.879110i	$0.658138\pi$
$564$	114.315	−	114.315i	0.202687	−	0.202687i
$565$	−112.214	−	418.786i	−0.198608	−	0.741215i
$566$	−199.576	+	53.4763i	−0.352608	+	0.0944811i
$567$	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	$-0.516787\pi$
$569$	447.092	−	258.129i	0.785751	−	0.453653i	0.838465	+	0.544956i	$0.183454\pi$
$570$	40.0192	−	149.354i	0.0702092	−	0.262024i
$571$			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
$574$	−467.408	−	125.242i	−0.814300	−	0.218191i
$575$	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	$0.385370\pi$
$578$	−191.870	−	716.070i	−0.331956	−	1.23888i
$579$	148.103	−	39.6840i	0.255790	−	0.0685388i
$580$	−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
$583$	106.550	−	397.650i	0.182762	−	0.682075i
$584$			51.0615i			0.0874341i
$585$		0			0
$586$	−138.358			−0.236105
$587$	−576.386	−	154.442i	−0.981919	−	0.263104i	−0.268066	−	0.963400i	$-0.586385\pi$
$587$	−576.386	−	154.442i	−0.981919	−	0.263104i	−0.713853	+	0.700296i	$0.753051\pi$
$588$	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
$591$	−168.308	−	628.133i	−0.284784	−	1.06283i
$592$	85.0333	−	22.7846i	0.143637	−	0.0384875i
$593$	−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
$596$	−19.3257	+	72.1244i	−0.0324256	+	0.121014i
$597$		−	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	$0.187467\pi$
$600$	89.9090	+	24.0910i	0.149848	+	0.0401517i
$601$	−126.265	−	218.698i	−0.210092	−	0.363890i	0.741651	−	0.670786i	$-0.234043\pi$
$601$	−126.265	−	218.698i	−0.210092	−	0.363890i	−0.951743	+	0.306896i	$0.900710\pi$
$602$	−709.456	−	409.604i	−1.17850	−	0.680406i
$603$	210.473	−	210.473i	0.349043	−	0.349043i
$604$	118.158	+	440.970i	0.195625	+	0.730084i
$605$	−223.799	+	59.9667i	−0.369915	+	0.0991185i
$606$	106.492	+	106.492i	0.175730	+	0.175730i
$607$	245.321	−	424.909i	0.404154	−	0.700014i	−0.590069	−	0.807353i	$-0.700899\pi$
$607$	245.321	−	424.909i	0.404154	−	0.700014i	0.994223	+	0.107338i	$0.0342328\pi$
$608$	−126.249	+	72.8897i	−0.207646	+	0.119884i
$609$	2.51358	−	9.38080i	0.00412739	−	0.0154036i
$610$		−	99.1000i		−	0.162459i
$611$		0			0
$612$	−342.200			−0.559150
$613$	−512.451	−	137.311i	−0.835973	−	0.223998i	−0.184655	−	0.982803i	$-0.559117\pi$
$613$	−512.451	−	137.311i	−0.835973	−	0.223998i	−0.651318	+	0.758805i	$0.725783\pi$
$614$	−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
$617$	143.670	+	536.185i	0.232853	+	0.869020i	0.979105	+	0.203356i	$0.0651848\pi$
$617$	143.670	+	536.185i	0.232853	+	0.869020i	−0.746252	+	0.665664i	$0.768148\pi$
$618$	55.1769	−	14.7846i	0.0892830	−	0.0239233i
$619$	−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
$622$	−141.300	+	527.338i	−0.227170	+	0.847811i
$623$		−	425.414i		−	0.682847i
$624$		0			0
$625$	−211.000			−0.337600
$626$	48.0000	+	12.8616i	0.0766773	+	0.0205456i
$627$	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
$630$	42.3154	+	157.923i	0.0671672	+	0.250672i
$631$	−205.085	+	54.9524i	−0.325016	+	0.0870878i	−0.417638	−	0.908614i	$-0.637142\pi$
$631$	−205.085	+	54.9524i	−0.325016	+	0.0870878i	0.0926217	+	0.995701i	$0.470475\pi$
$632$	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
$635$	−108.088	+	403.389i	−0.170217	+	0.635258i
$636$		−	277.492i		−	0.436309i
$637$		0			0
$638$	5.18069			0.00812020
$639$	42.2154	+	11.3116i	0.0660648	+	0.0177020i
$640$	13.8564	+	24.0000i	0.0216506	+	0.0375000i
$641$	69.3499	+	40.0392i	0.108190	+	0.0624636i	0.553119	−	0.833102i	$-0.313438\pi$
$641$	69.3499	+	40.0392i	0.108190	+	0.0624636i	−0.444929	+	0.895566i	$0.646771\pi$
$642$	−138.100	+	138.100i	−0.215109	+	0.215109i
$643$	−145.589	−	543.346i	−0.226422	−	0.845017i	−0.981830	−	0.189763i	$-0.939228\pi$
$643$	−145.589	−	543.346i	−0.226422	−	0.845017i	0.755408	−	0.655254i	$-0.227439\pi$
$644$	−266.478	+	71.4026i	−0.413786	+	0.110874i
$645$	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	0.556200	−	0.831048i	$-0.312259\pi$
$647$	1005.44	−	580.493i	1.55401	−	0.897208i	0.997809	−	0.0661597i	$-0.0210747\pi$
$648$	−6.58846	+	24.5885i	−0.0101674	+	0.0379452i
$649$			201.746i			0.310857i
$650$		0			0
$651$	−449.709			−0.690797
$652$	47.7987	+	12.8076i	0.0733109	+	0.0196436i
$653$	−220.045	−	381.129i	−0.336975	−	0.583658i	0.646887	−	0.762586i	$-0.276071\pi$
$653$	−220.045	−	381.129i	−0.336975	−	0.583658i	−0.983862	+	0.178928i	$0.942737\pi$
$654$	−310.965	−	179.536i	−0.475482	−	0.274520i
$655$	77.6846	−	77.6846i	0.118603	−	0.118603i
$656$	−45.0333	−	168.067i	−0.0686484	−	0.256199i
$657$	−104.627	+	28.0347i	−0.159250	+	0.0426708i
$658$	−367.104	−	367.104i	−0.557908	−	0.557908i
$659$	−274.521	+	475.485i	−0.416572	+	0.721524i	−0.995592	−	0.0937891i	$-0.970102\pi$
$659$	−274.521	+	475.485i	−0.416572	+	0.721524i	0.579020	+	0.815313i	$0.303435\pi$
$660$	37.7654	−	21.8038i	0.0572203	−	0.0330361i
$661$	210.187	−	784.429i	0.317983	−	1.18673i	−0.603196	−	0.797593i	$-0.706106\pi$
$661$	210.187	−	784.429i	0.317983	−	1.18673i	0.921180	−	0.389137i	$-0.127227\pi$
$662$			365.965i			0.552818i
$663$		0			0
$664$	351.349			0.529140
$665$	−479.624	−	128.515i	−0.721239	−	0.193255i
$666$	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
$669$	−68.2339	−	254.653i	−0.101994	−	0.380647i
$670$	165.995	−	44.4782i	0.247754	−	0.0663854i
$671$	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	$-0.768728\pi$
$673$	−367.385	+	212.110i	−0.545891	+	0.315170i	0.201572	+	0.979474i	$0.435395\pi$
$674$	−34.7527	+	129.699i	−0.0515618	+	0.192431i
$675$			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	$0.470735\pi$
$678$	418.786	+	112.214i	0.617679	+	0.165507i
$679$	−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
$682$	−62.0897	−	231.722i	−0.0910405	−	0.339768i
$683$	−42.0045	+	11.2551i	−0.0614999	+	0.0164789i	−0.289438	−	0.957197i	$-0.593468\pi$
$683$	−42.0045	+	11.2551i	−0.0614999	+	0.0164789i	0.227938	+	0.973676i	$0.426802\pi$
$684$	−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
$687$	5.85452	−	21.8494i	0.00852186	−	0.0318040i
$688$		−	294.564i		−	0.428145i
$689$		0			0
$690$	105.215			0.152486
$691$	−728.970	−	195.327i	−1.05495	−	0.282673i	−0.310654	−	0.950523i	$-0.600548\pi$
$691$	−728.970	−	195.327i	−1.05495	−	0.282673i	−0.744295	+	0.667850i	$0.767215\pi$
$692$	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
$695$	−12.1699	−	45.4186i	−0.0175106	−	0.0653505i
$696$	3.37307	−	0.903811i	0.00484636	−	0.00129858i
$697$	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
$700$	77.3641	−	288.727i	0.110520	−	0.412467i
$701$			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
$704$	−39.7128	−	10.6410i	−0.0564102	−	0.0151151i
$705$	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
$708$	35.1962	+	131.354i	0.0497121	+	0.185528i
$709$	−781.996	+	209.535i	−1.10296	+	0.295536i	−0.763968	−	0.645254i	$-0.776751\pi$
$709$	−781.996	+	209.535i	−1.10296	+	0.295536i	−0.338988	+	0.940791i	$0.610085\pi$
$710$	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
$713$	149.808	−	559.092i	0.210110	−	0.784140i
$714$		−	549.458i		−	0.769548i
$715$		0			0
$716$	−321.349			−0.448811
$717$	−470.102	−	125.963i	−0.655651	−	0.175681i
$718$	−102.058	−	176.769i	−0.142142	−	0.246197i
$719$	685.421	+	395.728i	0.953298	+	0.550387i	0.894104	−	0.447860i	$-0.147814\pi$
$719$	685.421	+	395.728i	0.953298	+	0.550387i	0.0591940	+	0.998246i	$0.481147\pi$
$720$	−41.5692	+	41.5692i	−0.0577350	+	0.0577350i
$721$	−47.4782	−	177.191i	−0.0658505	−	0.245757i
$722$	414.061	−	110.947i	0.573492	−	0.153667i
$723$	−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
$726$	59.9667	−	223.799i	0.0825987	−	0.308263i
$727$		−	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
$730$	−60.4064	−	16.1858i	−0.0827485	−	0.0221724i
$731$	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	$0.983636\pi$
$734$	174.855	+	652.566i	0.238221	+	0.889054i
$735$	−52.7654	+	14.1384i	−0.0717896	+	0.0192360i
$736$	−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
$739$	−68.3686	+	255.155i	−0.0925150	+	0.345271i	−0.996631	−	0.0820164i	$-0.973864\pi$
$739$	−68.3686	+	255.155i	−0.0925150	+	0.345271i	0.904116	+	0.427287i	$0.140531\pi$
$740$			107.818i			0.145700i
$741$		0			0
$742$	−891.118			−1.20097
$743$	755.161	+	202.345i	1.01637	+	0.272335i	0.728287	−	0.685272i	$-0.240317\pi$
$743$	755.161	+	202.345i	1.01637	+	0.272335i	0.288080	+	0.957606i	$0.406983\pi$
$744$	−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
$747$	192.904	+	719.927i	0.258238	+	0.963757i
$748$	283.119	−	75.8616i	0.378502	−	0.101419i
$749$	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	$-0.830593\pi$
$751$	−640.663	+	369.887i	−0.853080	+	0.492526i	0.00860865	+	0.999963i	$0.497260\pi$
$752$	48.3154	−	180.315i	0.0642491	−	0.239781i
$753$			268.535i			0.356620i
$754$		0			0
$755$	−559.128			−0.740567
$756$	−394.808	−	105.788i	−0.522232	−	0.139932i
$757$	−368.437	−	638.152i	−0.486707	−	0.843001i	0.513176	−	0.858283i	$-0.328469\pi$
$757$	−368.437	−	638.152i	−0.486707	−	0.843001i	−0.999883	+	0.0152821i	$0.995135\pi$
$758$	−335.242	−	193.552i	−0.442271	−	0.255345i
$759$	−110.375	+	110.375i	−0.145422	+	0.145422i
$760$	−46.2102	−	172.459i	−0.0608029	−	0.226920i
$761$	1383.33	−	370.661i	1.81777	−	0.487071i	0.821264	−	0.570549i	$-0.193269\pi$
$761$	1383.33	−	370.661i	1.81777	−	0.487071i	0.996510	+	0.0834780i	$0.0266028\pi$
$762$	−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
$765$	108.473	−	404.827i	0.141795	−	0.529185i
$766$		−	661.468i		−	0.863535i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	248.001	+	66.4517i	0.322498	+	0.0864132i	0.416436	−	0.909165i	$-0.363279\pi$
$769$	248.001	+	66.4517i	0.322498	+	0.0864132i	−0.0939380	+	0.995578i	$0.529946\pi$
$770$	−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
$773$	120.863	+	451.066i	0.156355	+	0.583526i	0.998985	+	0.0450335i	$0.0143395\pi$
$773$	120.863	+	451.066i	0.156355	+	0.583526i	−0.842630	+	0.538493i	$0.818994\pi$
$774$	603.573	−	161.727i	0.779810	−	0.208949i
$775$	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
$778$	−209.618	+	782.305i	−0.269432	+	1.00553i
$779$			1120.98i			1.43900i
$780$		0			0
$781$	−37.4346			−0.0479316
$782$	683.102	+	183.037i	0.873532	+	0.234062i
$783$	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
$786$	28.4346	+	106.119i	0.0361763	+	0.135012i
$787$	−1148.83	+	307.828i	−1.45976	+	0.391141i	−0.899406	−	0.437113i	$-0.856001\pi$
$787$	−1148.83	+	307.828i	−1.45976	+	0.391141i	−0.560352	+	0.828255i	$0.689334\pi$
$788$	−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
$791$	360.354	−	1344.86i	0.455568	−	1.70020i
$792$		−	87.2154i		−	0.110120i
$793$		0			0
$794$	−86.4833			−0.108921
$795$	328.277	+	87.9615i	0.412927	+	0.110643i
$796$	−297.669	−	515.578i	−0.373956	−	0.647711i
$797$	70.6886	+	40.8121i	0.0886934	+	0.0512071i	0.543691	−	0.839286i	$-0.317026\pi$
$797$	70.6886	+	40.8121i	0.0886934	+	0.0512071i	−0.454997	+	0.890493i	$0.650360\pi$
$798$	351.109	−	351.109i	0.439986	−	0.439986i
$799$	344.448	+	1285.50i	0.431099	+	1.60888i
$800$	103.818	−	27.8179i	0.129772	−	0.0347724i
$801$	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
$804$	−44.4782	+	165.995i	−0.0553211	+	0.206461i
$805$		−	337.881i		−	0.419728i
$806$		0			0
$807$	74.2961			0.0920646
$808$	167.976	+	45.0089i	0.207891	+	0.0557041i
$809$	−637.684	−	1104.50i	−0.788238	−	1.36527i	−0.927046	−	0.374949i	$-0.877660\pi$
$809$	−637.684	−	1104.50i	−0.788238	−	1.36527i	0.138808	−	0.990319i	$-0.455673\pi$
$810$	−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	$0.0898475\pi$
$812$	−2.90243	−	10.8320i	−0.00357442	−	0.0133399i
$813$	828.984	−	222.126i	1.01966	−	0.273217i
$814$	−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
$817$	−491.176	+	1833.09i	−0.601195	+	2.24369i
$818$			29.3167i			0.0358395i
$819$		0			0
$820$	213.100			0.259878
$821$	1190.43	+	318.975i	1.44998	+	0.388520i	0.896016	−	0.444023i	$-0.146449\pi$
$821$	1190.43	+	318.975i	1.44998	+	0.388520i	0.553961	+	0.832543i	$0.313116\pi$
$822$	115.356	+	199.802i	0.140335	+	0.243068i
$823$	557.525	+	321.887i	0.677430	+	0.391114i	0.798886	−	0.601482i	$-0.205423\pi$
$823$	557.525	+	321.887i	0.677430	+	0.391114i	−0.121456	+	0.992597i	$0.538756\pi$
$824$	46.6410	−	46.6410i	0.0566032	−	0.0566032i
$825$	−43.7731	−	163.363i	−0.0530583	−	0.198016i
$826$	421.820	−	113.026i	0.510678	−	0.136836i
$827$	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	$-0.753112\pi$
$829$	−385.172	+	222.379i	−0.464622	+	0.268250i	0.249364	+	0.968410i	$0.419779\pi$
$830$	−111.373	+	415.650i	−0.134184	+	0.500783i
$831$		−	368.454i		−	0.443386i
$832$		0			0
$833$	−367.170			−0.440781
$834$	45.4186	+	12.1699i	0.0544587	+	0.0145922i
$835$	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
$838$	127.083	+	474.279i	0.151650	+	0.565965i
$839$	341.076	−	91.3911i	0.406527	−	0.108929i	−0.0497600	−	0.998761i	$-0.515846\pi$
$839$	341.076	−	91.3911i	0.406527	−	0.108929i	0.456287	+	0.889833i	$0.349179\pi$
$840$	−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
$843$	17.2595	−	64.4134i	0.0204739	−	0.0764098i
$844$		−	109.013i		−	0.129162i
$845$		0			0
$846$	396.000			0.468085
$847$	−718.690	−	192.572i	−0.848513	−	0.227358i
$848$	−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
$851$	−99.8872	−	372.784i	−0.117376	−	0.438054i
$852$	−24.3731	+	6.53074i	−0.0286069	+	0.00766519i
$853$	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
$856$	−58.3679	+	217.832i	−0.0681868	+	0.254477i
$857$		−	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	$0.488297\pi$
$860$	348.473	+	93.3731i	0.405201	+	0.108573i
$861$	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	$0.957172\pi$
$864$	−38.0385	−	141.962i	−0.0440260	−	0.164307i
$865$	−169.786	+	45.4942i	−0.196285	+	0.0525944i
$866$	−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
$869$	19.0924	−	71.2539i	0.0219706	−	0.0819952i
$870$			4.27688i			0.00491595i
$871$		0			0
$872$	−414.620			−0.475482
$873$	788.927	+	211.392i	0.903696	+	0.242145i
$874$	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
$877$	−297.024	−	1108.51i	−0.338682	−	1.26398i	−0.899822	−	0.436258i	$-0.856304\pi$
$877$	−297.024	−	1108.51i	−0.338682	−	1.26398i	0.561140	−	0.827721i	$-0.310363\pi$
$878$	−599.069	+	160.520i	−0.682310	+	0.182825i
$879$	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	$-0.652435\pi$
$881$	68.2039	−	39.3775i	0.0774164	−	0.0446964i	0.538209	+	0.842812i	$0.319101\pi$
$882$	−28.2769	+	105.531i	−0.0320600	+	0.119649i
$883$			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
$886$	442.368	+	118.532i	0.499287	+	0.133783i
$887$	182.971	+	316.915i	0.206281	+	0.357289i	0.950540	−	0.310602i	$-0.100531\pi$
$887$	182.971	+	316.915i	0.206281	+	0.357289i	−0.744259	+	0.667891i	$0.767197\pi$
$888$	−93.3731	−	53.9090i	−0.105150	−	0.0607083i
$889$	−948.308	+	948.308i	−1.06671	+	1.06671i
$890$	48.4885	+	180.962i	0.0544815	+	0.203328i
$891$	44.6769	−	11.9711i	0.0501424	−	0.0134356i
$892$	−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
$895$	101.863	−	380.160i	0.113814	−	0.424759i
$896$			88.9948i			0.0993246i
$897$		0			0
$898$	−500.032			−0.556828
$899$	22.7264	+	6.08952i	0.0252796	+	0.00677366i
$900$	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
$903$	259.679	+	969.134i	0.287573	+	1.07324i
$904$	483.573	−	129.573i	0.534926	−	0.143333i
$905$	−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	−0.571480	+	0.820616i	$0.693630\pi$
$907$	−1422.08	+	821.038i	−1.56789	+	0.905224i	−0.996414	+	0.0846081i	$0.973036\pi$
$908$	111.455	−	415.956i	0.122748	−	0.458102i
$909$			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	$0.301966\pi$
$912$	172.459	+	46.2102i	0.189100	+	0.0506691i
$913$	−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
$916$	−6.76022	−	25.2295i	−0.00738015	−	0.0275431i
$917$	340.783	−	91.3126i	0.371628	−	0.0995775i
$918$	740.885	+	740.885i	0.807064	+	0.807064i
$919$	−222.386	+	385.185i	−0.241987	+	0.419135i	−0.961280	−	0.275572i	$-0.911133\pi$
$919$	−222.386	+	385.185i	−0.241987	+	0.419135i	0.719293	+	0.694707i	$0.244466\pi$
$920$	105.215	−	60.7461i	0.114365	−	0.0660284i
$921$	−1.66214	+	6.20319i	−0.00180471	+	0.00673528i
$922$		−	213.058i		−	0.231082i
$923$		0			0
$924$	140.038			0.151557
$925$	403.908	+	108.227i	0.436658	+	0.117002i
$926$	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
$929$	−277.176	−	1034.43i	−0.298359	−	1.11349i	−0.938513	−	0.345245i	$-0.887796\pi$
$929$	−277.176	−	1034.43i	−0.298359	−	1.11349i	0.640153	−	0.768247i	$-0.278871\pi$
$930$	191.296	−	51.2576i	0.205695	−	0.0551157i
$931$	−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
$934$	−50.7911	+	189.555i	−0.0543802	+	0.202950i
$935$			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	$0.203763\pi$
$938$	533.063	+	142.834i	0.568298	+	0.152275i
$939$	−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	$0.350731\pi$
$942$	9.14875	+	34.1436i	0.00971205	+	0.0362459i
$943$	−736.800	+	197.425i	−0.781336	+	0.209358i
$944$	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
$947$	−423.526	+	1580.62i	−0.447229	+	1.66908i	0.262753	+	0.964863i	$0.415370\pi$
$947$	−423.526	+	1580.62i	−0.447229	+	1.66908i	−0.709982	+	0.704220i	$0.751297\pi$
$948$		−	49.7231i		−	0.0524506i
$949$		0			0
$950$	−692.452			−0.728897
$951$	29.6481	+	7.94417i	0.0311757	+	0.00835349i
$952$	−317.229	−	549.458i	−0.333224	−	0.577161i
$953$	−374.404	−	216.162i	−0.392869	−	0.226823i	0.290534	−	0.956865i	$-0.406167\pi$
$953$	−374.404	−	216.162i	−0.392869	−	0.226823i	−0.683402	+	0.730042i	$0.739500\pi$
$954$	480.631	−	480.631i	0.503806	−	0.503806i
$955$	180.940	+	675.279i	0.189466	+	0.707098i
$956$	−542.827	+	145.450i	−0.567811	+	0.152144i
$957$	−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
$960$	8.78461	−	32.7846i	0.00915064	−	0.0341506i
$961$		−	128.487i		−	0.133702i
$962$		0			0
$963$	−478.392			−0.496773
$964$	−631.985	−	169.340i	−0.655586	−	0.175664i
$965$	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	$0.306024\pi$
$968$	−69.2436	−	258.420i	−0.0715326	−	0.266963i
$969$	−1229.49	+	329.440i	−1.26882	+	0.339980i
$970$	333.440	+	333.440i	0.343752	+	0.343752i
$971$	93.4864	−	161.923i	0.0962785	−	0.166759i	−0.813863	−	0.581057i	$-0.802639\pi$
$971$	93.4864	−	161.923i	0.0962785	−	0.166759i	0.910141	+	0.414298i	$0.135973\pi$
$972$	432.000	−	249.415i	0.444444	−	0.256600i
$973$	39.0814	−	145.854i	0.0401659	−	0.149901i
$974$		−	689.686i		−	0.708096i
$975$		0			0
$976$	114.431			0.117245
$977$	343.667	+	92.0852i	0.351757	+	0.0942530i	0.430371	−	0.902652i	$-0.358383\pi$
$977$	343.667	+	92.0852i	0.351757	+	0.0942530i	−0.0786139	+	0.996905i	$0.525049\pi$
$978$	−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
$981$	−227.642	−	849.573i	−0.232051	−	0.866028i
$982$	−714.785	+	191.526i	−0.727887	+	0.195037i
$983$	−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
$986$	−7.44021	+	27.7673i	−0.00754586	+	0.0281615i
$987$			635.842i			0.644217i
$988$		0			0
$989$	−1291.36			−1.30572
$990$	103.177	+	27.6462i	0.104219	+	0.0279254i
$991$	107.875	+	186.845i	0.108855	+	0.188542i	0.915307	−	0.402758i	$-0.131948\pi$
$991$	107.875	+	186.845i	0.108855	+	0.188542i	−0.806452	+	0.591300i	$0.798615\pi$
$992$	−161.703	−	93.3590i	−0.163007	−	0.0941119i
$993$	316.935	−	316.935i	0.319169	−	0.319169i
$994$	20.9723	+	78.2698i	0.0210989	+	0.0787423i
$995$	704.293	−	188.715i	0.707832	−	0.189663i
$996$	−304.277	−	304.277i	−0.305499	−	0.305499i
$997$	862.781	−	1494.38i	0.865377	−	1.49888i	−0.00129579	−	0.999999i	$-0.500412\pi$
$997$	862.781	−	1494.38i	0.865377	−	1.49888i	0.866673	−	0.498877i	$-0.166254\pi$
$998$	187.774	−	108.412i	0.188151	−	0.108629i
$999$	147.990	−	552.308i	0.148139	−	0.552860i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.a.11.1	✓	4	13.5	odd	4
26.3.f.a.19.1	yes	4	13.4	even	6
208.3.bd.c.97.1		4	52.43	odd	6
208.3.bd.c.193.1		4	52.31	even	4
234.3.bb.b.19.1		4	39.17	odd	6
234.3.bb.b.37.1		4	39.5	even	4
338.3.d.d.99.1		4	13.2	odd	12
338.3.d.d.239.1		4	13.10	even	6
338.3.d.e.99.1		4	13.11	odd	12
338.3.d.e.239.1		4	13.3	even	3
338.3.f.c.249.1		4	1.1	even	1	trivial
338.3.f.c.319.1		4	13.7	odd	12	inner
338.3.f.d.19.1		4	13.9	even	3
338.3.f.d.89.1		4	13.8	odd	4
338.3.f.f.249.1		4	13.12	even	2
338.3.f.f.319.1		4	13.6	odd	12

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+(-1.36603 - 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{5} +(-0.633975 - 2.36603i) q^{6} +(-7.59808 + 2.03590i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(3.00000 - 5.19615i) q^{9} +(3.00000 - 1.73205i) q^{10} +(-1.33013 + 4.96410i) q^{11} +3.46410i q^{12} +11.1244 q^{14} +(-4.09808 - 1.09808i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-24.6962 - 14.2583i) q^{17} +(-6.00000 + 6.00000i) q^{18} +(-6.66987 - 24.8923i) q^{19} +(-4.73205 + 1.26795i) q^{20} +(-9.63397 - 9.63397i) q^{21} +(3.63397 - 6.29423i) q^{22} +(15.1865 - 8.76795i) q^{23} +(1.26795 - 4.73205i) q^{24} +19.0000i q^{25} +25.9808 q^{27} +(-15.1962 - 4.07180i) q^{28} +(0.356406 + 0.617314i) q^{29} +(5.19615 + 3.00000i) q^{30} +(23.3397 - 23.3397i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-8.59808 + 2.30385i) q^{33} +(28.5167 + 28.5167i) q^{34} +(9.63397 - 16.6865i) q^{35} +(10.3923 - 6.00000i) q^{36} +(5.69615 - 21.2583i) q^{37} +36.4449i q^{38} +6.92820 q^{40} +(-42.0167 - 11.2583i) q^{41} +(9.63397 + 16.6865i) q^{42} +(-63.7750 - 36.8205i) q^{43} +(-7.26795 + 7.26795i) q^{44} +(3.80385 + 14.1962i) q^{45} +(-23.9545 + 6.41858i) q^{46} +(-33.0000 - 33.0000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(11.1506 - 6.43782i) q^{49} +(6.95448 - 25.9545i) q^{50} -49.3923i q^{51} -80.1051 q^{53} +(-35.4904 - 9.50962i) q^{54} +(-6.29423 - 10.9019i) q^{55} +(19.2679 + 11.1244i) q^{56} +(31.5622 - 31.5622i) q^{57} +(-0.260908 - 0.973721i) q^{58} +(37.9186 - 10.1603i) q^{59} +(-6.00000 - 6.00000i) q^{60} +(14.3038 - 24.7750i) q^{61} +(-40.4256 + 23.3397i) q^{62} +(-12.2154 + 45.5885i) q^{63} +8.00000i q^{64} +12.5885 q^{66} +(47.9186 + 12.8397i) q^{67} +(-28.5167 - 49.3923i) q^{68} +(26.3038 + 15.1865i) q^{69} +(-19.2679 + 19.2679i) q^{70} +(1.88526 + 7.03590i) q^{71} +(-16.3923 + 4.39230i) q^{72} +(-12.7654 - 12.7654i) q^{73} +(-15.5622 + 26.9545i) q^{74} +(-28.5000 + 16.4545i) q^{75} +(13.3397 - 49.7846i) q^{76} -40.4256i q^{77} -14.3538 q^{79} +(-9.46410 - 2.53590i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(53.2750 + 30.7583i) q^{82} +(-87.8372 + 87.8372i) q^{83} +(-7.05256 - 26.3205i) q^{84} +(67.4711 - 18.0788i) q^{85} +(73.6410 + 73.6410i) q^{86} +(-0.617314 + 1.06922i) q^{87} +(12.5885 - 7.26795i) q^{88} +(-13.9974 + 52.2391i) q^{89} -20.7846i q^{90} +35.0718 q^{92} +(55.2224 + 14.7968i) q^{93} +(33.0000 + 57.1577i) q^{94} +(54.6673 + 31.5622i) q^{95} +(6.92820 - 6.92820i) q^{96} +(35.2321 + 131.488i) q^{97} +(-17.5885 + 4.71281i) q^{98} +(21.8038 + 21.8038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{6} - 20 q^{7} - 8 q^{8} + 12 q^{9} + 12 q^{10} + 12 q^{11} - 4 q^{14} - 6 q^{15} + 8 q^{16} - 78 q^{17} - 24 q^{18} - 44 q^{19} - 12 q^{20} - 42 q^{21} + 18 q^{22} - 12 q^{23} + 12 q^{24}+ \cdots + 108 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 6 * q^6 - 20 * q^7 - 8 * q^8 + 12 * q^9 + 12 * q^10 + 12 * q^11 - 4 * q^14 - 6 * q^15 + 8 * q^16 - 78 * q^17 - 24 * q^18 - 44 * q^19 - 12 * q^20 - 42 * q^21 + 18 * q^22 - 12 * q^23 + 12 * q^24 - 40 * q^28 - 54 * q^29 + 128 * q^31 + 8 * q^32 - 24 * q^33 + 24 * q^34 + 42 * q^35 + 2 * q^37 - 78 * q^41 + 42 * q^42 - 120 * q^43 - 36 * q^44 + 36 * q^45 - 30 * 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 - 150 * q^58 + 72 * q^59 - 24 * q^60 + 78 * q^61 + 60 * q^62 - 132 * q^63 - 12 * q^66 + 112 * q^67 - 24 * q^68 + 126 * q^69 - 84 * q^70 + 108 * q^71 - 24 * q^72 + 136 * q^73 - 38 * q^74 - 114 * q^75 + 88 * q^76 + 192 * q^79 - 24 * q^80 - 18 * q^81 + 78 * q^82 - 192 * q^83 + 48 * q^84 + 114 * q^85 + 156 * q^86 - 96 * q^87 - 12 * q^88 + 138 * q^89 + 168 * q^92 + 162 * q^93 + 132 * q^94 + 42 * q^95 + 134 * q^97 - 8 * q^98 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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