LMFDB - Embedded newform 338.3.f.c.319.1

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			319.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.319
Dual form			338.3.f.c.249.1

$q$-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 $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{11}{12}\right)$

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	−0.684819	−	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	0.512360	−	0.858771i	$-0.328771\pi$
$5$	−1.73205	−	1.73205i	−0.346410	−	0.346410i	−0.858771	+	0.512360i	$0.828771\pi$
$6$	−0.633975	+	2.36603i	−0.105662	+	0.394338i
$7$	−7.59808	−	2.03590i	−1.08544	−	0.290843i	−0.328617	−	0.944463i	$-0.606583\pi$
$7$	−7.59808	−	2.03590i	−1.08544	−	0.290843i	−0.756822	+	0.653621i	$0.773249\pi$
$8$	−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	0.878741	−	0.477299i	$-0.158384\pi$
$11$	−1.33013	−	4.96410i	−0.120921	−	0.451282i	−0.999661	+	0.0260172i	$0.991718\pi$
$12$		−	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	−0.998635	−	0.0522356i	$-0.983365\pi$
$17$	−24.6962	+	14.2583i	−1.45271	+	0.838725i	−0.454080	+	0.890961i	$0.650032\pi$
$18$	−6.00000	−	6.00000i	−0.333333	−	0.333333i
$19$	−6.66987	+	24.8923i	−0.351046	+	1.31012i	0.534342	+	0.845268i	$0.320559\pi$
$19$	−6.66987	+	24.8923i	−0.351046	+	1.31012i	−0.885388	+	0.464853i	$0.846107\pi$
$20$	−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	0.792385	−	0.610021i	$-0.208839\pi$
$23$	15.1865	+	8.76795i	0.660284	+	0.381215i	−0.132101	+	0.991236i	$0.542172\pi$
$24$	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	−0.859815	−	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	0.975019	−	0.222124i	$-0.0712988\pi$
$31$	23.3397	+	23.3397i	0.752895	+	0.752895i	−0.222124	+	0.975019i	$0.571299\pi$
$32$	−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	0.999193	+	0.0401672i	$0.0127891\pi$
$37$	5.69615	+	21.2583i	0.153950	+	0.574549i	−0.845243	+	0.534382i	$0.820544\pi$
$38$		−	36.4449i		−	0.959075i
$39$		0			0
$40$	6.92820			0.173205
$41$	−42.0167	+	11.2583i	−1.02480	+	0.274593i	−0.731800	−	0.681520i	$-0.761319\pi$
$41$	−42.0167	+	11.2583i	−1.02480	+	0.274593i	−0.292997	+	0.956113i	$0.594653\pi$
$42$	9.63397	−	16.6865i	0.229380	−	0.397298i
$43$	−63.7750	+	36.8205i	−1.48314	+	0.856291i	−0.999817	−	0.0191514i	$-0.993904\pi$
$43$	−63.7750	+	36.8205i	−1.48314	+	0.856291i	−0.483323	+	0.875442i	$0.660570\pi$
$44$	−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	−0.964867	−	0.262739i	$-0.915374\pi$
$47$	−33.0000	+	33.0000i	−0.702128	+	0.702128i	0.262739	+	0.964867i	$0.415374\pi$
$48$	−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	0.565421	−	0.824803i	$-0.308714\pi$
$59$	37.9186	+	10.1603i	0.642688	+	0.172208i	0.0772673	+	0.997010i	$0.475381\pi$
$60$	−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
$63$	−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	0.117173	−	0.993112i	$-0.462617\pi$
$67$	47.9186	−	12.8397i	0.715203	−	0.191638i	0.598030	+	0.801474i	$0.295950\pi$
$68$	−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	−0.951378	−	0.308027i	$-0.900331\pi$
$71$	1.88526	−	7.03590i	0.0265530	−	0.0990972i	0.977931	+	0.208930i	$0.0669980\pi$
$72$	−16.3923	−	4.39230i	−0.227671	−	0.0610042i
$73$	−12.7654	+	12.7654i	−0.174868	+	0.174868i	−0.789114	−	0.614246i	$-0.789460\pi$
$73$	−12.7654	+	12.7654i	−0.174868	+	0.174868i	0.614246	+	0.789114i	$0.289460\pi$
$74$	−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	−0.998193	−	0.0600859i	$-0.980863\pi$
$83$	−87.8372	−	87.8372i	−1.05828	−	1.05828i	−0.0600859	−	0.998193i	$-0.519137\pi$
$84$	−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	−0.998900	−	0.0468944i	$-0.985068\pi$
$89$	−13.9974	−	52.2391i	−0.157274	−	0.586956i	0.841625	−	0.540062i	$-0.181599\pi$
$90$			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	−0.506605	−	0.862178i	$-0.669100\pi$
$97$	35.2321	−	131.488i	0.363217	−	1.35554i	0.869822	−	0.493366i	$-0.164234\pi$
$98$	−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	0.212682	−	0.977122i	$-0.431780\pi$
$101$	−53.2461	−	30.7417i	−0.527189	−	0.304373i	−0.739871	+	0.672749i	$0.765114\pi$
$102$	−18.0788	−	67.4711i	−0.177244	−	0.661482i
$103$		−	23.3205i		−	0.226413i	−0.993571	−	0.113206i	$-0.963888\pi$
$103$		−	23.3205i		−	0.226413i	0.993571	−	0.113206i	$-0.0361121\pi$
$104$		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	−0.989962	−	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	0.998853	−	0.0478885i	$-0.0152492\pi$
$109$	103.655	+	103.655i	0.950964	+	0.950964i	−0.0478885	+	0.998853i	$0.515249\pi$
$110$	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	−0.930077	−	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
$115$	−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	0.951927	−	0.306326i	$-0.0990999\pi$
$127$	147.651	+	85.2461i	1.16260	+	0.671229i	0.210677	+	0.977556i	$0.432433\pi$
$128$	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	−0.0889903	−	0.996032i	$-0.528364\pi$
$137$	−90.9782	−	24.3775i	−0.664074	−	0.177938i	−0.575084	+	0.818094i	$0.695031\pi$
$138$	−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
$141$	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	−0.925890	−	0.377794i	$-0.876683\pi$
$149$	9.66283	−	36.0622i	0.0648512	−	0.242028i	0.990741	+	0.135766i	$0.0433495\pi$
$150$	44.9545	+	12.0455i	0.299697	+	0.0803034i
$151$	161.406	−	161.406i	1.06892	−	1.06892i	0.0714740	−	0.997442i	$-0.477230\pi$
$151$	161.406	−	161.406i	1.06892	−	1.06892i	0.997442	−	0.0714740i	$-0.0227703\pi$
$152$	−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	0.331383	−	0.943496i	$-0.392485\pi$
$163$	23.8993	+	6.40381i	0.146622	+	0.0392872i	−0.184762	+	0.982783i	$0.559151\pi$
$164$	−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	0.996372	−	0.0851025i	$-0.0271218\pi$
$167$	15.1865	+	56.6769i	0.0909373	+	0.339383i	−0.905435	+	0.424485i	$0.860455\pi$
$168$		−	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	−0.309515	−	0.950895i	$-0.600167\pi$
$173$	62.1462	−	35.8801i	0.359226	−	0.207399i	0.668741	+	0.743495i	$0.266833\pi$
$174$	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	0.0581316	−	0.998309i	$-0.481486\pi$
$179$	−139.148	−	80.3372i	−0.777363	−	0.448811i	−0.835495	+	0.549498i	$0.814819\pi$
$180$	−7.60770	−	28.3923i	−0.0422650	−	0.157735i
$181$		−	143.072i		−	0.790452i	−0.918584	−	0.395226i	$-0.870666\pi$
$181$		−	143.072i		−	0.790452i	0.918584	−	0.395226i	$-0.129334\pi$
$182$		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	0.949190	+	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
$193$	22.9115	+	85.5070i	0.118713	+	0.443042i	0.999538	−	0.0304000i	$-0.00967812\pi$
$193$	22.9115	+	85.5070i	0.118713	+	0.443042i	−0.880825	+	0.473442i	$0.843011\pi$
$194$			192.512i			0.992327i
$195$		0			0
$196$	25.7513			0.131384
$197$	−362.653	+	97.1725i	−1.84088	+	0.493261i	−0.998928	−	0.0462974i	$-0.985258\pi$
$197$	−362.653	+	97.1725i	−1.84088	+	0.493261i	−0.841948	+	0.539559i	$0.818591\pi$
$198$	−21.8038	+	37.7654i	−0.110120	+	0.190734i
$199$	−257.789	+	148.835i	−1.29542	+	0.747913i	−0.979610	−	0.200909i	$-0.935610\pi$
$199$	−257.789	+	148.835i	−1.29542	+	0.747913i	−0.315813	+	0.948822i	$0.602277\pi$
$200$	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	−0.923352	−	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
$214$	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	−0.572930	−	0.819605i	$-0.694193\pi$
$223$	−147.024	+	39.3949i	−0.659299	+	0.176659i	−0.0863694	+	0.996263i	$0.527527\pi$
$224$	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	0.727638	+	0.685962i	$0.240618\pi$
$227$	−55.7276	+	207.978i	−0.245496	+	0.916203i	−0.973133	+	0.230242i	$0.926048\pi$
$228$	86.2295	+	23.1051i	0.378199	+	0.101338i
$229$	−9.23463	+	9.23463i	−0.0403259	+	0.0403259i	−0.726982	−	0.686656i	$-0.759078\pi$
$229$	−9.23463	+	9.23463i	−0.0403259	+	0.0403259i	0.686656	+	0.726982i	$0.259078\pi$
$230$	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	$-0.675351\pi$
$233$		−	397.061i		−	1.70413i	0.523439	−	0.852063i	$-0.324649\pi$
$234$		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	0.156367	−	0.987699i	$-0.450022\pi$
$239$	−198.688	−	198.688i	−0.831332	−	0.831332i	−0.987699	+	0.156367i	$0.950022\pi$
$240$	−4.39230	+	16.3923i	−0.0183013	+	0.0683013i
$241$	−315.992	−	84.6699i	−1.31117	−	0.351327i	−0.465508	−	0.885044i	$-0.654128\pi$
$241$	−315.992	−	84.6699i	−1.31117	−	0.351327i	−0.845663	+	0.533717i	$0.820795\pi$
$242$	−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	−0.208092	−	0.978109i	$-0.566725\pi$
$251$	134.267	−	77.5192i	0.534929	−	0.308842i	0.743021	+	0.669268i	$0.233392\pi$
$252$	−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	0.913959	−	0.405806i	$-0.133009\pi$
$257$	262.012	+	151.272i	1.01950	+	0.588609i	0.105541	+	0.994415i	$0.466343\pi$
$258$	−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	−0.910103	−	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
$266$	−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	0.903134	−	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
$271$	128.244	+	478.614i	0.473226	+	1.76610i	0.628062	+	0.778163i	$0.283848\pi$
$271$	128.244	+	478.614i	0.473226	+	1.76610i	−0.154836	+	0.987940i	$0.549485\pi$
$272$			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	−0.794209	−	0.607644i	$-0.792115\pi$
$277$	−184.227	+	106.363i	−0.665079	+	0.383984i	0.129130	+	0.991628i	$0.458781\pi$
$278$	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	−0.753887	−	0.657004i	$-0.771824\pi$
$281$	−27.2243	+	27.2243i	−0.0968837	+	0.0968837i	0.657004	+	0.753887i	$0.271824\pi$
$282$	−57.1577	−	99.0000i	−0.202687	−	0.351064i
$283$	126.526	+	73.0500i	0.447089	+	0.258127i	0.706600	−	0.707613i	$-0.250228\pi$
$283$	126.526	+	73.0500i	0.447089	+	0.258127i	−0.259511	+	0.965740i	$0.583561\pi$
$284$	−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	0.416449	−	0.909159i	$-0.363274\pi$
$293$	94.5000	+	25.3212i	0.322526	+	0.0864205i	−0.0939237	+	0.995579i	$0.529941\pi$
$294$	−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	−0.702824	−	0.711364i	$-0.748078\pi$
$307$	2.62178	−	2.62178i	0.00853999	−	0.00853999i	0.711364	+	0.702824i	$0.248078\pi$
$308$	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	$0.213127\pi$
$311$			386.038i			1.24128i	−0.784095	+	0.620641i	$0.786873\pi$
$312$		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	0.726595	−	0.687066i	$-0.241102\pi$
$317$	12.5307	+	12.5307i	0.0395292	+	0.0395292i	−0.687066	+	0.726595i	$0.741102\pi$
$318$	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	0.787897	+	0.615807i	$0.211170\pi$
$331$	−66.9763	+	249.959i	−0.202345	+	0.755163i	−0.990242	+	0.139356i	$0.955497\pi$
$332$	−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	$0.0449898\pi$
$337$			94.9461i			0.281739i	−0.990028	+	0.140870i	$0.955010\pi$
$338$		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	0.780899	−	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
$349$	−20.9205	−	78.0763i	−0.0599440	−	0.223714i	0.929455	−	0.368935i	$-0.120277\pi$
$349$	−20.9205	−	78.0763i	−0.0599440	−	0.223714i	−0.989399	+	0.145221i	$0.953611\pi$
$350$		−	211.363i		−	0.603894i
$351$		0			0
$352$	29.0718			0.0825903
$353$	−164.744	+	44.1429i	−0.466696	+	0.125051i	−0.484501	−	0.874791i	$-0.660999\pi$
$353$	−164.744	+	44.1429i	−0.466696	+	0.125051i	0.0178053	+	0.999841i	$0.494332\pi$
$354$	−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	−0.550531	−	0.834815i	$-0.685575\pi$
$359$	102.058	−	102.058i	0.284283	−	0.284283i	0.834815	+	0.550531i	$0.185575\pi$
$360$	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	0.332088	+	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
$370$	−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	−0.971510	−	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
$375$	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	0.107454	−	0.994210i	$-0.465730\pi$
$379$	264.397	−	70.8449i	0.697617	−	0.186926i	0.590163	+	0.807284i	$0.299064\pi$
$380$	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	−0.606908	−	0.794772i	$-0.707590\pi$
$383$	121.057	−	451.791i	0.316076	−	1.17961i	0.922984	−	0.384839i	$-0.125743\pi$
$384$	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	$0.263335\pi$
$389$			572.687i			1.47220i	−0.676871	+	0.736102i	$0.736665\pi$
$390$		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	0.332445	−	0.943123i	$-0.392127\pi$
$397$	59.0692	+	15.8275i	0.148789	+	0.0398679i	−0.183656	+	0.982991i	$0.558793\pi$
$398$	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	0.888270	+	0.459322i	$0.151908\pi$
$401$	139.815	+	521.798i	0.348667	+	1.30124i	−0.539603	+	0.841920i	$0.681426\pi$
$402$			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	−0.972175	−	0.234257i	$-0.924734\pi$
$409$	−5.36533	+	20.0237i	−0.0131182	+	0.0489577i	0.959057	+	0.283215i	$0.0914009\pi$
$410$	−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	−0.995356	−	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	0.960147	−	0.279494i	$-0.0901667\pi$
$421$	286.555	+	286.555i	0.680654	+	0.680654i	−0.279494	+	0.960147i	$0.590167\pi$
$422$	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	0.101701	−	0.994815i	$-0.467572\pi$
$431$	296.176	−	79.3602i	0.687184	−	0.184130i	0.585483	+	0.810685i	$0.300905\pi$
$432$	51.9615	−	90.0000i	0.120281	−	0.208333i
$433$	73.2757	−	42.3057i	0.169228	−	0.0977038i	−0.412994	−	0.910734i	$-0.635517\pi$
$433$	73.2757	−	42.3057i	0.169228	−	0.0977038i	0.582222	+	0.813030i	$0.302184\pi$
$434$	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	0.865728	−	0.500514i	$-0.166856\pi$
$439$	379.794	+	219.274i	0.865135	+	0.499486i	−0.000593556		1.00000i	$0.500189\pi$
$440$	−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	0.618233	−	0.785995i	$-0.287849\pi$
$449$	341.528	+	91.5122i	0.760642	+	0.203813i	0.142408	+	0.989808i	$0.454515\pi$
$450$	−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	0.0336305	−	0.999434i	$-0.489293\pi$
$457$	257.050	−	68.8763i	0.562473	−	0.150714i	0.528842	+	0.848720i	$0.322626\pi$
$458$	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	−0.910653	−	0.413173i	$-0.864421\pi$
$461$	38.9923	−	145.521i	0.0845819	−	0.315664i	0.995235	+	0.0975085i	$0.0310873\pi$
$462$	−95.6481	−	25.6288i	−0.207030	−	0.0554736i
$463$	−48.4115	+	48.4115i	−0.104561	+	0.104561i	−0.757452	−	0.652891i	$-0.773556\pi$
$463$	−48.4115	+	48.4115i	−0.104561	+	0.104561i	0.652891	+	0.757452i	$0.273556\pi$
$464$	−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	$0.0474669\pi$
$467$			138.764i			0.297139i	−0.988902	+	0.148570i	$0.952533\pi$
$468$		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	0.875646	−	0.482953i	$-0.160436\pi$
$479$	−59.4737	−	221.959i	−0.124162	−	0.463380i	−0.999808	+	0.0195733i	$0.993769\pi$
$480$		−	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	−0.706535	−	0.707678i	$-0.749743\pi$
$487$	126.221	−	471.064i	0.259181	−	0.967277i	0.965716	−	0.259599i	$-0.0835905\pi$
$488$	−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	0.884567	−	0.466414i	$-0.154454\pi$
$491$	453.156	+	261.630i	0.922924	+	0.532850i	0.0383572	+	0.999264i	$0.487788\pi$
$492$	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	0.590084	−	0.807342i	$-0.299095\pi$
$499$	−108.412	−	108.412i	−0.217258	−	0.217258i	−0.807342	+	0.590084i	$0.799095\pi$
$500$	−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	0.994122	−	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
$505$	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	−0.402748	−	0.915311i	$-0.631945\pi$
$509$	−149.586	+	40.0814i	−0.293882	+	0.0787454i	0.108866	+	0.994056i	$0.465278\pi$
$510$	−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	0.209494	−	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
$526$	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	−0.772267	−	0.635298i	$-0.780877\pi$
$541$	−74.1000	+	74.1000i	−0.136969	+	0.136969i	0.635298	+	0.772267i	$0.280877\pi$
$542$	−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	−0.885282	−	0.465054i	$-0.846035\pi$
$557$	−195.581	−	729.917i	−0.351132	−	1.31044i	0.534150	−	0.845390i	$-0.320632\pi$
$558$		−	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	−0.476619	−	0.879110i	$-0.658138\pi$
$563$	26.1250	−	15.0833i	0.0464033	−	0.0267909i	0.523022	+	0.852319i	$0.324804\pi$
$564$	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	0.838465	−	0.544956i	$-0.183454\pi$
$569$	447.092	+	258.129i	0.785751	+	0.453653i	−0.0527137	+	0.998610i	$0.516787\pi$
$570$	40.0192	+	149.354i	0.0702092	+	0.262024i
$571$		−	813.423i		−	1.42456i	−0.701896	−	0.712279i	$-0.747663\pi$
$571$		−	813.423i		−	1.42456i	0.701896	−	0.712279i	$-0.252337\pi$
$572$		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	0.352388	−	0.935854i	$-0.385370\pi$
$577$	−336.660	−	336.660i	−0.583467	−	0.583467i	−0.935854	+	0.352388i	$0.885370\pi$
$578$	−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	−0.713853	−	0.700296i	$-0.753051\pi$
$587$	−576.386	+	154.442i	−0.981919	+	0.263104i	−0.268066	+	0.963400i	$0.586385\pi$
$588$	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	−0.912198	−	0.409749i	$-0.865616\pi$
$593$	−297.953	+	297.953i	−0.502450	+	0.502450i	0.409749	+	0.912198i	$0.365616\pi$
$594$	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	−0.951743	−	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
$604$	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	0.994223	−	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
$609$	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	−0.651318	−	0.758805i	$-0.725783\pi$
$613$	−512.451	+	137.311i	−0.835973	+	0.223998i	−0.184655	+	0.982803i	$0.559117\pi$
$614$	−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	−0.746252	−	0.665664i	$-0.768148\pi$
$617$	143.670	−	536.185i	0.232853	−	0.869020i	0.979105	−	0.203356i	$-0.0651848\pi$
$618$	55.1769	+	14.7846i	0.0892830	+	0.0239233i
$619$	−501.483	+	501.483i	−0.810151	+	0.810151i	−0.984656	−	0.174505i	$-0.944167\pi$
$619$	−501.483	+	501.483i	−0.810151	+	0.810151i	0.174505	+	0.984656i	$0.444167\pi$
$620$	−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	0.0926217	−	0.995701i	$-0.470475\pi$
$631$	−205.085	−	54.9524i	−0.325016	−	0.0870878i	−0.417638	+	0.908614i	$0.637142\pi$
$632$	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	−0.444929	−	0.895566i	$-0.646771\pi$
$641$	69.3499	−	40.0392i	0.108190	−	0.0624636i	0.553119	+	0.833102i	$0.313438\pi$
$642$	−138.100	−	138.100i	−0.215109	−	0.215109i
$643$	−145.589	+	543.346i	−0.226422	+	0.845017i	0.755408	+	0.655254i	$0.227439\pi$
$643$	−145.589	+	543.346i	−0.226422	+	0.845017i	−0.981830	+	0.189763i	$0.939228\pi$
$644$	−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	0.997809	+	0.0661597i	$0.0210747\pi$
$647$	1005.44	+	580.493i	1.55401	+	0.897208i	0.556200	+	0.831048i	$0.312259\pi$
$648$	−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	−0.983862	−	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
$656$	−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	0.579020	−	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
$661$	210.187	+	784.429i	0.317983	+	1.18673i	0.921180	+	0.389137i	$0.127227\pi$
$661$	210.187	+	784.429i	0.317983	+	1.18673i	−0.603196	+	0.797593i	$0.706106\pi$
$662$		−	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	0.201572	−	0.979474i	$-0.435395\pi$
$673$	−367.385	−	212.110i	−0.545891	−	0.315170i	−0.747463	+	0.664303i	$0.768728\pi$
$674$	−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	0.227938	−	0.973676i	$-0.426802\pi$
$683$	−42.0045	−	11.2551i	−0.0614999	−	0.0164789i	−0.289438	+	0.957197i	$0.593468\pi$
$684$	−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	−0.744295	−	0.667850i	$-0.767215\pi$
$691$	−728.970	+	195.327i	−1.05495	+	0.282673i	−0.310654	+	0.950523i	$0.600548\pi$
$692$	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	$-0.793457\pi$
$701$		−	847.213i		−	1.20858i	0.796766	−	0.604289i	$-0.206543\pi$
$702$		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	−0.338988	−	0.940791i	$-0.610085\pi$
$709$	−781.996	−	209.535i	−1.10296	−	0.295536i	−0.763968	+	0.645254i	$0.776751\pi$
$710$	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	0.0591940	−	0.998246i	$-0.481147\pi$
$719$	685.421	−	395.728i	0.953298	−	0.550387i	0.894104	+	0.447860i	$0.147814\pi$
$720$	−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	$0.245814\pi$
$727$			1014.52i			1.39549i	−0.716345	+	0.697746i	$0.754186\pi$
$728$		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	−0.998679	−	0.0513857i	$-0.983636\pi$
$733$	−769.697	−	769.697i	−1.05006	−	1.05006i	−0.0513857	−	0.998679i	$-0.516364\pi$
$734$	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	0.904116	−	0.427287i	$-0.140531\pi$
$739$	−68.3686	−	255.155i	−0.0925150	−	0.345271i	−0.996631	+	0.0820164i	$0.973864\pi$
$740$		−	107.818i		−	0.145700i
$741$		0			0
$742$	−891.118			−1.20097
$743$	755.161	−	202.345i	1.01637	−	0.272335i	0.288080	−	0.957606i	$-0.406983\pi$
$743$	755.161	−	202.345i	1.01637	−	0.272335i	0.728287	+	0.685272i	$0.240317\pi$
$744$	−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	0.00860865	−	0.999963i	$-0.497260\pi$
$751$	−640.663	−	369.887i	−0.853080	−	0.492526i	−0.861689	+	0.507437i	$0.830593\pi$
$752$	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	−0.999883	−	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
$760$	−46.2102	+	172.459i	−0.0608029	+	0.226920i
$761$	1383.33	+	370.661i	1.81777	+	0.487071i	0.996510	−	0.0834780i	$-0.0266028\pi$
$761$	1383.33	+	370.661i	1.81777	+	0.487071i	0.821264	+	0.570549i	$0.193269\pi$
$762$	−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	−0.0939380	−	0.995578i	$-0.529946\pi$
$769$	248.001	−	66.4517i	0.322498	−	0.0864132i	0.416436	+	0.909165i	$0.363279\pi$
$770$	−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	−0.842630	−	0.538493i	$-0.818994\pi$
$773$	120.863	−	451.066i	0.156355	−	0.583526i	0.998985	−	0.0450335i	$-0.0143395\pi$
$774$	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	−0.560352	−	0.828255i	$-0.689334\pi$
$787$	−1148.83	−	307.828i	−1.45976	−	0.391141i	−0.899406	+	0.437113i	$0.856001\pi$
$788$	−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	−0.454997	−	0.890493i	$-0.650360\pi$
$797$	70.6886	−	40.8121i	0.0886934	−	0.0512071i	0.543691	+	0.839286i	$0.317026\pi$
$798$	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	0.138808	+	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	0.960427	−	0.278531i	$-0.0898475\pi$
$811$	553.018	+	553.018i	0.681896	+	0.681896i	−0.278531	+	0.960427i	$0.589847\pi$
$812$	−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	0.553961	−	0.832543i	$-0.313116\pi$
$821$	1190.43	−	318.975i	1.44998	−	0.388520i	0.896016	+	0.444023i	$0.146449\pi$
$822$	115.356	−	199.802i	0.140335	−	0.243068i
$823$	557.525	−	321.887i	0.677430	−	0.391114i	−0.121456	−	0.992597i	$-0.538756\pi$
$823$	557.525	−	321.887i	0.677430	−	0.391114i	0.798886	+	0.601482i	$0.205423\pi$
$824$	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	−0.463398	−	0.886150i	$-0.653370\pi$
$827$	349.617	−	349.617i	0.422753	−	0.422753i	0.886150	+	0.463398i	$0.153370\pi$
$828$	105.215	+	182.238i	0.127072	+	0.220095i
$829$	−385.172	−	222.379i	−0.464622	−	0.268250i	0.249364	−	0.968410i	$-0.419779\pi$
$829$	−385.172	−	222.379i	−0.464622	−	0.268250i	−0.713986	+	0.700160i	$0.753112\pi$
$830$	−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	0.456287	−	0.889833i	$-0.349179\pi$
$839$	341.076	+	91.3911i	0.406527	+	0.108929i	−0.0497600	+	0.998761i	$0.515846\pi$
$840$	−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	−0.537948	−	0.842978i	$-0.680800\pi$
$853$	260.191	−	260.191i	0.305030	−	0.305030i	0.842978	+	0.537948i	$0.180800\pi$
$854$	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	$0.410708\pi$
$857$			1647.00i			1.92182i	−0.276856	+	0.960912i	$0.589292\pi$
$858$		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	−0.990962	−	0.134143i	$-0.957172\pi$
$863$	−970.965	−	970.965i	−1.12510	−	1.12510i	−0.134143	−	0.990962i	$-0.542828\pi$
$864$	−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	0.561140	+	0.827721i	$0.310363\pi$
$877$	−297.024	+	1108.51i	−0.338682	+	1.26398i	−0.899822	+	0.436258i	$0.856304\pi$
$878$	−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	0.538209	−	0.842812i	$-0.319101\pi$
$881$	68.2039	+	39.3775i	0.0774164	+	0.0446964i	−0.460792	+	0.887508i	$0.652435\pi$
$882$	−28.2769	−	105.531i	−0.0320600	−	0.119649i
$883$		−	196.777i		−	0.222851i	−0.993773	−	0.111425i	$-0.964458\pi$
$883$		−	196.777i		−	0.222851i	0.993773	−	0.111425i	$-0.0355416\pi$
$884$		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	−0.744259	−	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
$890$	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	−0.996414	−	0.0846081i	$-0.973036\pi$
$907$	−1422.08	−	821.038i	−1.56789	−	0.905224i	−0.571480	−	0.820616i	$-0.693630\pi$
$908$	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	0.719293	−	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
$921$	−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	0.640153	+	0.768247i	$0.278871\pi$
$929$	−277.176	+	1034.43i	−0.298359	+	1.11349i	−0.938513	+	0.345245i	$0.887796\pi$
$930$	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	0.451944	−	0.892046i	$-0.350731\pi$
$941$	−414.136	−	414.136i	−0.440102	−	0.440102i	−0.892046	+	0.451944i	$0.850731\pi$
$942$	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	−0.709982	−	0.704220i	$-0.751297\pi$
$947$	−423.526	−	1580.62i	−0.447229	−	1.66908i	0.262753	−	0.964863i	$-0.415370\pi$
$948$			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	−0.683402	−	0.730042i	$-0.739500\pi$
$953$	−374.404	+	216.162i	−0.392869	+	0.226823i	0.290534	+	0.956865i	$0.406167\pi$
$954$	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	0.572369	−	0.819996i	$-0.306024\pi$
$967$	−239.455	−	239.455i	−0.247627	−	0.247627i	−0.819996	+	0.572369i	$0.806024\pi$
$968$	−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	0.910141	−	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
$973$	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	−0.0786139	−	0.996905i	$-0.525049\pi$
$977$	343.667	−	92.0852i	0.351757	−	0.0942530i	0.430371	+	0.902652i	$0.358383\pi$
$978$	−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	−0.960670	−	0.277694i	$-0.910430\pi$
$983$	−671.365	+	671.365i	−0.682976	+	0.682976i	0.277694	+	0.960670i	$0.410430\pi$
$984$	−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	−0.806452	−	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
$994$	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	0.866673	+	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
$999$	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.319.1		4
13.2	odd	12	inner	338.3.f.c.249.1		4
13.3	even	3		338.3.f.d.89.1		4
13.4	even	6		338.3.d.d.99.1		4
13.5	odd	4		338.3.f.d.19.1		4
13.6	odd	12		338.3.d.e.239.1		4
13.7	odd	12		338.3.d.d.239.1		4
13.8	odd	4		26.3.f.a.19.1	yes	4
13.9	even	3		338.3.d.e.99.1		4
13.10	even	6		26.3.f.a.11.1	✓	4
13.11	odd	12		338.3.f.f.249.1		4
13.12	even	2		338.3.f.f.319.1		4
39.8	even	4		234.3.bb.b.19.1		4
39.23	odd	6		234.3.bb.b.37.1		4
52.23	odd	6		208.3.bd.c.193.1		4
52.47	even	4		208.3.bd.c.97.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.3.f.a.11.1	✓	4	13.10	even	6
26.3.f.a.19.1	yes	4	13.8	odd	4
208.3.bd.c.97.1		4	52.47	even	4
208.3.bd.c.193.1		4	52.23	odd	6
234.3.bb.b.19.1		4	39.8	even	4
234.3.bb.b.37.1		4	39.23	odd	6
338.3.d.d.99.1		4	13.4	even	6
338.3.d.d.239.1		4	13.7	odd	12
338.3.d.e.99.1		4	13.9	even	3
338.3.d.e.239.1		4	13.6	odd	12
338.3.f.c.249.1		4	13.2	odd	12	inner
338.3.f.c.319.1		4	1.1	even	1	trivial
338.3.f.d.19.1		4	13.5	odd	4
338.3.f.d.89.1		4	13.3	even	3
338.3.f.f.249.1		4	13.11	odd	12
338.3.f.f.319.1		4	13.12	even	2

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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